{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Kalman Filters\n",
    "\n",
    "Filtering Multiple Random Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to study and implement the full, multivariate form of the Kalman filter. In the last chapter we learned how multivariate Gaussians express the correlation between multiple random variables, such as the position and velocity of an aircraft. We also learned how correlation between variables drastically improves the posterior. If we only roughly know position and velocity, but they are correlated, then our new estimate can be very accurate.\n",
    "\n",
    "I prefer that you develop an intuition for how these filters work through several worked examples. I'm going to gloss over many issues. 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. 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 for non-Newtonian systems. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton's Equations of Motion\n",
    "\n",
    "Newton's equations of motion tells us that 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, our velocity is 10 m/s, and we travel for 12 seconds our final position is 133 ($10\\times 12 + 13$).\n",
    "\n",
    "We can incorporate constant acceleration with this equation\n",
    "\n",
    "$$x = \\frac{1}{2}at^2 + v_0t + x_0$$\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",
    "These equations were generated by integrating a differential equation. Given a constant velocity v we can compute the distance traveled over time with the equation\n",
    "\n",
    "$$x = vt + x_0$$\n",
    "\n",
    "which we can derive with\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",
    "\n",
    "When you design a Kalman filter you start with a system of differential equations that describe the dynamics of the system. Most systems of differential equations do not easily integrate in this way. We start with Newton's equation because we can integrate and get a closed form solution, which makes the Kalman filter easier to design. An added benefit is that Newton's equations are the right equations to use to track moving objects, one of the main uses of Kalman filters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kalman Filter Algorithm\n",
    "\n",
    "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\n",
    "    \n",
    "**Predict**\n",
    "\n",
    "    1. Use process model to predict state at the next time step\n",
    "    2. Adjust belief to account for the uncertainty in prediction    \n",
    "**Update**\n",
    "\n",
    "    1. Get a measurement and associated belief about its accuracy\n",
    "    2. Compute residual between estimated state and measurement\n",
    "    3. Compute scaling factor based on whether the measurement\n",
    "    or prediction is more accurate\n",
    "    4. set state between the prediction and measurement based \n",
    "    on scaling factor\n",
    "    5. update belief in the state based on how certain we are \n",
    "    in the measurement\n",
    "    \n",
    "As a reminder, here is a graphical depiction of the algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1100x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as book_plots\n",
    "book_plots.show_residual_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The univariate Kalman filter represented the state with a univariate Gaussian. Naturally the multivariate Kalman filter will use a multivariate Gaussian for the state. We learned in the last chapter that multivariate Gaussians use a vector for the mean and a matrix for the covariances. That means that the Kalman filter needs to use linear algebra to perform the estimations.\n",
    "\n",
    "I don't want you to memorize these equations, but I have listed the univariate and multivariate equations below. They are quite similar.\n",
    "\n",
    "<u>**Predict**</u>\n",
    "\n",
    "$\\begin{array}{|l|l|l|}\n",
    "\\hline\n",
    "\\text{Univariate} & \\text{Univariate} & \\text{Multivariate}\\\\\n",
    "& \\text{(Kalman form)} & \\\\\n",
    "\\hline\n",
    "\\bar \\mu = \\mu + \\mu_{f_x} & \\bar x = x + dx & \\bar{\\mathbf x} = \\mathbf{Fx} + \\mathbf{Bu}\\\\\n",
    "\\bar\\sigma^2 = \\sigma_x^2 + \\sigma_{f_x}^2 & \\bar P = P + Q & \\bar{\\mathbf P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q \\\\\n",
    "\\hline\n",
    "\\end{array}$\n",
    "\n",
    "Without worrying about the specifics of the linear algebra, we can see that:\n",
    "\n",
    "$\\mathbf x,\\, \\mathbf P$ are the state mean and covariance. They correspond to $x$ and $\\sigma^2$.\n",
    "\n",
    "$\\mathbf F$ is the *state transition function*. When multiplied by $\\bf x$ it computes the prior. \n",
    "\n",
    "$\\mathbf Q$ is the process covariance. It corresponds to $\\sigma^2_{f_x}$.\n",
    "\n",
    "$\\mathbf B$ and $\\mathbf u$ are new to us. They let us model control inputs to the system.\n",
    "\n",
    "<u>**Update**</u>\n",
    "\n",
    "$\\begin{array}{|l|l|l|}\n",
    "\\hline\n",
    "\\text{Univariate} & \\text{Univariate} & \\text{Multivariate}\\\\\n",
    "& \\text{(Kalman form)} & \\\\\n",
    "\\hline\n",
    "& y = z - \\bar x & \\mathbf y = \\mathbf z - \\mathbf{H\\bar x} \\\\\n",
    "& K = \\frac{\\bar P}{\\bar P+R}&\n",
    "\\mathbf K = \\mathbf{\\bar{P}H}^\\mathsf T (\\mathbf{H\\bar{P}H}^\\mathsf T + \\mathbf R)^{-1} \\\\\n",
    "\\mu=\\frac{\\bar\\sigma^2\\, \\mu_z + \\sigma_z^2 \\, \\bar\\mu} {\\bar\\sigma^2 + \\sigma_z^2} & x = \\bar x + Ky & \\mathbf x = \\bar{\\mathbf x} + \\mathbf{Ky} \\\\\n",
    "\\sigma^2 = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} & P = (1-K)\\bar P &\n",
    "\\mathbf P = (\\mathbf I - \\mathbf{KH})\\mathbf{\\bar{P}} \\\\\n",
    "\\hline\n",
    "\\end{array}$\n",
    "\n",
    "$\\mathbf H$ is the measurement function. We haven't seen this yet in this book and I'll explain it later. If you mentally remove $\\mathbf H$ from the equations, you should be able to see these equations are similar as well.\n",
    "\n",
    "$\\mathbf z,\\, \\mathbf R$ are the measurement mean and noise covariance. They correspond to $z$ and $\\sigma_z^2$ in the univariate filter (I've substituted $\\mu$ with $x$ for the univariate equations to make the notation as similar as possible).\n",
    "\n",
    "$\\mathbf y$ and $\\mathbf K$ are the residual and Kalman gain. \n",
    "\n",
    "The details will be different than the univariate filter because these are vectors and matrices, but the concepts are exactly the same: \n",
    "\n",
    "-  Use a Gaussian to represent our estimate of the state and error\n",
    "-  Use a Gaussian to represent the measurement and its error\n",
    "-  Use a Gaussian to represent the process model\n",
    "-  Use the process model to predict the next state (the prior)\n",
    "-  Form an estimate part way between the measurement and the prior\n",
    "\n",
    "Your job as a designer will be to design the state $\\left(\\mathbf x, \\mathbf P\\right)$, the process $\\left(\\mathbf F, \\mathbf Q\\right)$, the measurement $\\left(\\mathbf z, \\mathbf R\\right)$, and the  measurement function $\\mathbf H$. If the system has control inputs, such as a robot, you will also design $\\mathbf B$ and $\\mathbf u$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have programmed the equations of the Kalman filter into the `predict` and `update` functions in FilterPy. You will import them with:\n",
    "\n",
    "```python\n",
    "from filterpy.kalman import predict, update\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tracking a Dog\n",
    "\n",
    "Let's go back to our tried and true problem of tracking a dog. This time we will include the fundamental insight of the previous chapter and use *hidden variables* to improve our estimates. I could start with the math, but instead 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 - we are just multiplying and adding Gaussians.\n",
    "\n",
    "We start by writing a simulation for the dog. The simulation will run for `count` steps, moving the dog forward approximately 1 meter for each step. At each step the velocity will vary according to the process variance `process_var`. After updating the position we compute a measurement with an assumed sensor variance of `z_var`. The function returns an NumPy array of the positions and another of the measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from numpy.random import randn\n",
    "\n",
    "def compute_dog_data(z_var, process_var, count=1, dt=1.):\n",
    "    \"returns track, measurements 1D ndarrays\"\n",
    "    x, vel = 0., 1.\n",
    "    z_std = math.sqrt(z_var) \n",
    "    p_std = math.sqrt(process_var)\n",
    "    xs, zs = [], []\n",
    "    for _ in range(count):\n",
    "        v = vel + (randn() * p_std)\n",
    "        x += v*dt        \n",
    "        xs.append(x)\n",
    "        zs.append(x + randn() * z_std)        \n",
    "    return np.array(xs), np.array(zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predict Step\n",
    "\n",
    "For the prediction we need to design the state and covariance, the process model and the process noise, and optionally the control input. We'll take them in order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design State Variable\n",
    "\n",
    "We previously 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. 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. This requires us to use a multivariate Gaussian represented with the state vector $\\mathbf x$ and its corresponding covariance matrix $\\mathbf P$. \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 only reads position, so position is observed and velocity is hidden. We will learn how to track hidden variables soon.\n",
    "\n",
    "It is important to understand that tracking position and velocity 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. For now, recall that in the last chapter we showed that including velocity in the covariance matrix resulted in much smaller variances in position. We will learn how the Kalman filter computes estimates for hidden variables later in this chapter. \n",
    "\n",
    "In the univariate chapter we represented the dog's position with a scalar value (e.g. $\\mu=3.27$). In the last chapter we learned to use a multivariate Gaussian for multiple variables. 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 (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. I use Newton's dot notation for derivatives; $\\dot x$ represents the first derivative of x with respect to t: $\\dot x = \\frac{dx}{dt}$. 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.\n",
    "\n",
    "Another way to write this is $\\mathbf x =\\begin{bmatrix}x & \\dot x\\end{bmatrix}^\\mathsf T$ because the transpose of a row vector is a column vector. This notation is easier to use in text because it takes less vertical space.\n",
    "\n",
    "$\\mathbf x$ and the position $x$ coincidentally have the same name. If we were tracking the dog in the y-axis we would write $\\mathbf x =\\begin{bmatrix}y & \\dot y\\end{bmatrix}^\\mathsf T$, not  $\\mathbf y =\\begin{bmatrix}y & \\dot y\\end{bmatrix}^\\mathsf T$. $\\mathbf x$ is the standard name for the state variable used in the Kalman filter literature and we will not vary it to give it a more meaningful name. This consistency in naming allows us to communicate with our peers.\n",
    "\n",
    "Let's code this. Initialization of `x` is as simple as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10. ],\n",
       "       [ 4.5]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[10.0],\n",
    "              [4.5]])\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I often use the transpose in my code to turn a row matrix into a column vector, as I find it easier to type and read:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10. ],\n",
       "       [ 4.5]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[10., 4.5]]).T\n",
    "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10. ,  4.5])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([10.0, 4.5])\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of the array elements have the same type, typically either `float` or `int`. If the list contains all `int`s then the created array will also have a data type of `int`, otherwise it will be `float`. I will often take advantage of this by only specifying one number as a floating point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1., 0, 0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[19.]\n",
      " [48.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2], [3, 4]])\n",
    "x = np.array([[10.0], [4.5]])\n",
    "\n",
    "# matrix multiply\n",
    "print(np.dot(A, x))\n",
    "print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python 3.5+ we have the matrix multiplier @, where `np.dot(A, B) == A @ B`. It is somewhat less useful then you might realize because it requires both `A` and `B` to be arrays. It is entirely valid in the math in this book for some of these variables to be scalars, therefore the utility of `@` is often lost. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true,
    "tags": [
     "raises-exception"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[19.]\n",
      " [48.]]\n",
      "\n",
      "[[19.]\n",
      " [48.]]\n",
      "\n",
      "[19. 48.]\n"
     ]
    }
   ],
   "source": [
    "# alternative matrix multiply)\n",
    "print(A @ x)\n",
    "print()\n",
    "\n",
    "x = np.array([[10.0, 4.5]]).T\n",
    "print(A @ x)\n",
    "print()\n",
    "\n",
    "x = np.array([10.0, 4.5])\n",
    "print(A @ x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last returns a 1D array, but I have written the Kalman filter class to be able to handle this. In retrospect that might lead to confusion, but it does work. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design State Covariance\n",
    "\n",
    "The other half of the state Gaussian is the covariance matrix $\\mathbf P$. In the univariate 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 epoch.\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 21 m/s, so in the absence of any other information about the velocity we can set $3\\sigma_\\mathtt{vel}=21$, or $\\sigma_\\mathtt{vel}^2=7^2=49$. \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 covariances 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. Thus we have:\n",
    "\n",
    "$$\n",
    "\\mathbf P = \\begin{bmatrix}500 & 0 \\\\ 0&49\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "We can use `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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[500.,   0.],\n",
       "       [  0.,  49.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.diag([500., 49.])\n",
    "P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I could have written:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[500.,   0.],\n",
       "       [  0.,  49.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.array([[500., 0.],\n",
    "              [0., 49.]])\n",
    "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": [
    "###  Design the Process Model\n",
    "\n",
    "The next step is designing the *process model*. It is a mathematical model which describes the behavior of the system. The filter uses it to predict the state after a discrete time step. We do this with a set of equations that describe the dynamics of the system.\n",
    "\n",
    "In the univariate chapter we modeled the dog's motion with\n",
    "\n",
    "$$ x = v \\Delta t + x_0$$\n",
    "\n",
    "We implemented this as follows:\n",
    "\n",
    "```python\n",
    "def predict(pos, movement):\n",
    "    return gaussian(pos.mean + movement.mean, \n",
    "                    pos.var + movement.var)\n",
    "```\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",
    "$$ \\mathbf x = \\begin{bmatrix}5.4\\\\4.2\\end{bmatrix}, \\, \\, \n",
    "\\dot{\\mathbf x} =  \\begin{bmatrix}1.1\\\\0.\\end{bmatrix} \\\\\n",
    "\\mathbf x = \\dot{\\mathbf x}t + \\mathbf x$$\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 flow in a given pipe is determined by a linear combination of the settings of different valves. \n",
    "\n",
    "$$\\mathtt{pipe_1} = 0.134(\\mathtt{valve}_1) + 0.41(\\mathtt{valve}_2 - \\mathtt{valve}_3) + 1.34$$\n",
    "$$\\mathtt{pipe_2} = 0.210(\\mathtt{valve}_2) - 0.62(\\mathtt{valve}_1 - \\mathtt{valve}_5) + 1.86$$\n",
    "\n",
    "Linear algebra has a powerful way to express systems of equations. Take this system\n",
    "\n",
    "$$\\begin{cases}\n",
    "2x+3y=8\\\\4x-y=2\n",
    "\\end{cases}$$\n",
    "\n",
    "We can put this in matrix form by writing:\n",
    "\n",
    "$$\\begin{bmatrix}2& 3 \\\\ 4&-1\\end{bmatrix} \\begin{bmatrix}x\\\\y\\end{bmatrix} = \\begin{bmatrix}8\\\\2\\end{bmatrix}$$\n",
    "\n",
    "If you perform the [matrix multiplication](https://en.wikipedia.org/wiki/Matrix_multiplication#General_definition_of_the_matrix_product) 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",
    "$$\\mathbf{A} = \\begin{bmatrix}2& 3 \\\\ 4&-1\\end{bmatrix},\\, \\mathbf x = \\begin{bmatrix}x\\\\y\\end{bmatrix}, \\mathbf B=\\begin{bmatrix}8\\\\2\\end{bmatrix}$$\n",
    "\n",
    "And then we can use the SciPy's `linalg` package to solve for $\\mathbf x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.],\n",
       "       [2.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.linalg import solve\n",
    "A = np.array([[2, 3],[4, -1]])\n",
    "b = np.array([[8], [2]])\n",
    "x = solve(A, b)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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 this linear equation, where $\\mathbf{\\bar x}$ is the *prior*, or predicted state:\n",
    "\n",
    "$$\\mathbf{\\bar x} = \\mathbf{Fx}$$\n",
    "\n",
    "which we can make explicit as\n",
    "\n",
    "$$\\begin{bmatrix} \\bar x \\\\ \\dot{\\bar x}\\end{bmatrix} = \\begin{bmatrix}? & ? \\\\? & ?\\end{bmatrix}\\begin{bmatrix}x\\\\\\dot x\\end{bmatrix}$$\n",
    "\n",
    "Our job as Kalman filters designers is to specify $\\mathbf F$ such that $\\bar{\\mathbf x}  = \\mathbf{Fx}$ 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 to compute the position $x$ and another to compute the velocity $\\dot x$ . We already know the equation for the position innovation:\n",
    "\n",
    "$$\\bar x = x + \\dot x \\Delta t$$\n",
    "\n",
    "What is our equation for velocity? 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",
    "$$\\bar{\\dot x} = \\dot x$$\n",
    "\n",
    "This gives us the process model for our system \n",
    "\n",
    "$$\\begin{cases}\n",
    "\\begin{aligned}\n",
    "\\bar x &= x + \\dot x \\Delta t \\\\\n",
    "\\bar{\\dot x} &= \\dot x\n",
    "\\end{aligned}\n",
    "\\end{cases}$$\n",
    "\n",
    "This correctly has one equation for each variable in the state, isolated on the left hand side. We need to express this set of equations in the form $\\bar{\\mathbf x}  = \\mathbf{Fx}$. Rearranging terms makes it easier to see what to do.\n",
    "\n",
    "$$\\begin{cases}\n",
    "\\begin{aligned}\n",
    "\\bar x &= 1x + &\\Delta t\\, \\dot x \\\\\n",
    "\\bar{\\dot x} &=0x + &1\\, \\dot x\n",
    "\\end{aligned}\n",
    "\\end{cases}$$\n",
    "\n",
    "We can rewrite this in matrix form as\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\begin{bmatrix}\\bar x \\\\ \\bar{\\dot x}\\end{bmatrix} &= \\begin{bmatrix}1&\\Delta t  \\\\ 0&1\\end{bmatrix}  \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}\\\\\n",
    "\\mathbf{\\bar x} &= \\mathbf{Fx}\n",
    "\\end{aligned}$$\n",
    "\n",
    "$\\mathbf F$ is called the *state transition function* or the *state transition matrix*. In later chapters it will be a true function, not a  matrix, so calling it a function is a bit more general."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 0.1],\n",
       "       [0. , 1. ]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dt = 0.1\n",
    "F = np.array([[1, dt],\n",
    "              [0, 1]])\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test this! FilterPy has a `predict` method that performs the prediction by computing $\\mathbf{\\bar x} = \\mathbf{Fx}$. Let's call it and see what happens. We've set the position to 10.0 and the velocity to  4.5 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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [10.45  4.5 ]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.kalman import predict\n",
    "\n",
    "x = np.array([10.0, 4.5])\n",
    "P = np.diag([500, 49])\n",
    "F = np.array([[1, dt], [0, 1]])\n",
    "\n",
    "# Q is the process noise\n",
    "x, P = predict(x=x, P=P, F=F, Q=0)\n",
    "print('x =', x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This worked. If we call `predict()` several times in a row the value will be updated each time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [10.9  4.5]\n",
      "x = [11.35  4.5 ]\n",
      "x = [11.8  4.5]\n",
      "x = [12.25  4.5 ]\n"
     ]
    }
   ],
   "source": [
    "for _ in range(4):\n",
    "    x, P = predict(x=x, P=P, F=F, Q=0)\n",
    "    print('x =', x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`predict()` computes both the mean and covariance of the innovation. This is the value of $\\mathbf P$ after five innovations (predictions), which we denote $\\mathbf{\\bar P}$ in the Kalman filter equations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[512.25  24.5 ]\n",
      " [ 24.5   49.  ]]\n"
     ]
    }
   ],
   "source": [
    "print(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspecting the diagonals shows us that the position variance got larger. We've performed five 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 prediction. The initial value is in solid red, and the prior (prediction) is in dashed black. I've altered the covariance and time step to better illustrate the change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.stats import plot_covariance_ellipse\n",
    "\n",
    "dt = 0.3\n",
    "F = np.array([[1, dt], [0, 1]])\n",
    "x = np.array([10.0, 4.5])\n",
    "P = np.diag([500, 500])\n",
    "plot_covariance_ellipse(x, P, edgecolor='r')\n",
    "x, P = predict(x, P, F, Q=0)\n",
    "plot_covariance_ellipse(x, P, edgecolor='k', ls='dashed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the center of the ellipse shifted by a small amount (from 10 to 11.35) because the position changed. The ellipse also elongated, showing the correlation between position and velocity. How does the filter compute new values for $\\mathbf{\\bar P}$, and what is it based on? Note that I set the process noise `Q` to zero each time, so it is not due to me adding noise. 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": [
    "### Design 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 $\\bar x_k=\\dot x_k\\Delta t + x_{k-1}$. However, it is affected by a number of unknown factors. The cruise control cannot perfectly 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",
    "$$\\dot{\\mathbf x} = f(\\mathbf x) + w$$\n",
    "\n",
    "where $f(\\mathbf x)$ models the state transition and $w$ is *white process noise*.\n",
    "\n",
    "We will learn how to go from a set of differential equations to the Kalman filter matrices in the **Kalman Filter Math** chapter. In this chapter we take advantage of the fact that Newton already derived the equations of motion for us. For now you just need to know that we account for the  noise in the system by adding 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.\n",
    "\n",
    "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 the same, 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",
    "Deriving the process noise matrix can be quite demanding, and we will put it off until the Kalman math chapter. For now know that $\\mathbf Q$ equals the expected value of the white noise $w$, computed as $\\mathbf Q = \\mathbb E[\\mathbf{ww}^\\mathsf T]$. In this chapter we will focus on building an intuitive understanding on how modifying this matrix alters the behavior of the filter.\n",
    "\n",
    "FilterPy provides functions which compute $\\mathbf Q$ for the kinematic problems of this chapter. `Q_discrete_white_noise` takes 3 parameters. `dim`, which specifies the dimension of the matrix, `dt`, which is the time step in seconds, and `var`, the variance in the noise. Briefly, it discretizes the noise over the given time period under assumptions that we will discuss later. This code computes $\\mathbf Q$ for white noise with a variance of 2.35 and a time step of 1 seconds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.588 1.175]\n",
      " [1.175 2.35 ]]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.common import Q_discrete_white_noise\n",
    "Q = Q_discrete_white_noise(dim=2, dt=1., var=2.35)\n",
    "print(Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Control Function\n",
    "\n",
    "The Kalman filter does not just filter data, it allows us to incorporate the control inputs of systems like robots and airplanes. Suppose we are controlling a robot. At each time step we would send steering and velocity 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",
    "$$\\Delta\\mathbf x = \\mathbf{Bu}$$\n",
    "\n",
    "Here $\\mathbf u$ is the *control input*, and $\\mathbf B$ is the *control input model* or *control function*. For example, $\\mathbf u$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf B$ yields $\\Delta[\\begin{smallmatrix}x\\\\\\dot x\\end{smallmatrix}]$. In other words, it must compute how much $\\mathbf x$ changes due to the control input.\n",
    "\n",
    "Therefore the complete Kalman filter equation for the prior mean is\n",
    "\n",
    "$$\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu}$$\n",
    "\n",
    "and this is the equation that is computed when you call `KalmanFilter.predict()`.\n",
    "\n",
    "Your dog may be trained to respond to voice commands. All available evidence suggests that my dog has no control inputs whatsoever, so I set $\\mathbf B$ to zero. In Python we write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = [12.7  4.5]\n",
      "P = [[680.587 301.175]\n",
      " [301.175 502.35 ]]\n"
     ]
    }
   ],
   "source": [
    "B = 0.  # my dog doesn't listen to me!\n",
    "u = 0\n",
    "x, P = predict(x, P, F, Q, B, u)\n",
    "print('x =', x)\n",
    "print('P =', P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting $\\mathbf B$ and $\\mathbf u$ to zero is not necessary since `predict` uses 0 for their default value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(x, P, F, Q)[0] == predict(x, P, F, Q, B, u)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True],\n",
       "       [ True,  True]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(x, P, F, Q)[1] == predict(x, P, F, Q, B, u)[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Prediction: Summary\n",
    "\n",
    "Your job as a designer is to specify the matrices for\n",
    "\n",
    "* $\\mathbf x$, $\\mathbf P$: the state and covariance\n",
    "* $\\mathbf F$,  $\\mathbf Q$: the process model and noise covariance\n",
    "* $\\mathbf{B,u}$: Optionally, the control input and function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Update Step\n",
    "\n",
    "Now we can implement the update step of the filter. You only have to supply two more matrices, and they are easy to understand. \n",
    "\n",
    "### 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. We 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",
    "$$ \\mathtt{residual} = \\mathtt{measured\\, \\, position} - \\mathtt{predicted\\, \\, position}$$\n",
    "\n",
    "We need to compute the residual because we scale it by the Kalman gain to get the new estimate.\n",
    "\n",
    "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 meaningless; you can't subtract a temperature from a voltage.\n",
    "\n",
    "$$ \\mathtt{residual} = \\mathtt{voltage} - \\mathtt{temperature}\\;\\;\\;(NONSENSE!)$$\n",
    "\n",
    "\n",
    "We need to convert the temperature into a voltage so we can perform the subtraction. For the thermometer we might write:\n",
    "\n",
    "```python\n",
    "CELSIUS_TO_VOLTS = 0.21475\n",
    "residual = voltage - (CELSIUS_TO_VOLTS * predicted_temperature)\n",
    "```\n",
    "    \n",
    "The Kalman filter generalizes this problem by having you supply a *measurement function* that converts a state into a measurement. \n",
    "\n",
    "Why are we working in measurement space? Why not work in state space by converting the voltage into a temperature, allowing the residual to be a difference in temperature?\n",
    "\n",
    "We cannot do that because most measurements are not *invertible*. The state for the tracking problem contains the hidden variable $\\dot x$. There is no way to convert a measurement of position into a state containing velocity. On the other hand, it is trivial to convert a state containing position and velocity into a equivalent \"measurement\" containing only position. 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",
    "$$\\mathbf y = \\mathbf z - \\mathbf{H \\bar x}$$\n",
    "\n",
    "where $\\mathbf y$ is the residual, $\\mathbf{\\bar x}$ is the prior, $\\mathbf z$ is the measurement, and $\\mathbf H$ is the measurement function. So we take the prior, convert it to a measurement by multiplying it with $\\mathbf H$, and subtract that from the measurement. This gives us the difference between our prediction and measurement in measurement space!\n",
    "<img src=\"./figs/residual_chart_with_h.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to design $\\mathbf H$ so that $\\mathbf{H\\bar x}$ 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 residual equation will have the form\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\textbf{y} &= \\mathbf z - \\mathbf{H\\bar x}  \\\\\n",
    "\\begin{bmatrix}y \\end{bmatrix} &= \\begin{bmatrix}z\\end{bmatrix} - \\begin{bmatrix}?&?\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$\\mathbf H$ has to be a 1x2 matrix for $\\mathbf{Hx}$ to be 1x1. Recall that multiplying matrices $m\\times n$ by $n\\times p$ yields a $m\\times p$ matrix.\n",
    "\n",
    "We will want to multiply the position $x$ by 1 to get the corresponding measurement of the position. We do not need to use velocity to find the corresponding measurement so we multiply  $\\dot x$ by 0.\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\textbf{y} &= \\mathbf z - \\begin{bmatrix}1&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix} \\\\\n",
    "&= [z] - [x]\n",
    "\\end{aligned}$$\n",
    "\n",
    "And so, for our Kalman filter we set\n",
    "\n",
    "$$\\mathbf H=\\begin{bmatrix}1&0\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = np.array([[1., 0.]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have designed the majority of our Kalman filter. All that is left is to model the noise in the sensors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Design the Measurement\n",
    "\n",
    "The measurement is implemented with $\\mathbf z$, the measurement mean, and $\\mathbf R$, the measurement covariance. \n",
    "\n",
    "$\\mathbf z$ is easy. it contains the measurement(s) as a vector. We have only one measurement, so we have:\n",
    "\n",
    "$$\\mathbf z = \\begin{bmatrix}z\\end{bmatrix}$$\n",
    "\n",
    "If we have two sensors or measurements we'd have:\n",
    "\n",
    "$$\\mathbf z = \\begin{bmatrix}z_1 \\\\ z_2\\end{bmatrix}$$\n",
    "\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. We will learn to deal with these problems later.\n",
    "\n",
    "The Kalman filter equations uses a covariance matrix $\\mathbf R$ for the measurement noise. The matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is a covariance matrix to account for correlations between the sensors. We have only 1 sensor so R is:\n",
    "\n",
    "$$R = \\begin{bmatrix}\\sigma^2_z\\end{bmatrix}$$\n",
    "\n",
    "If $\\sigma^2_z$ is 5 meters squared we'd have $R = \\begin{bmatrix}5\\end{bmatrix}$. \n",
    "\n",
    "If we had two position sensors, the first with a variance of 5 m$^2$, the second with a variance of 3 m$^2$, 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": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = np.array([[5.]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We perform the update by calling `update`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0.]] [[680.587 301.175]\n",
      " [301.175 502.35 ]] [[5.]]\n",
      "x = [ 1.085 -0.64 ]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.kalman import update\n",
    "z = 1.\n",
    "x, P = update(x, P, z, R, H)\n",
    "print('x =', x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keeping track of all of these variables is burdensome, so FilterPy also implements the filter with the class `KalmanFilter`. I will use the class in the rest of this book, but I wanted you to see the procedural form of these functions since I know some of you are not fans of object oriented programming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing the Kalman Filter\n",
    "\n",
    "I've given you all of the code for the filter, but now let's collect it in one place. First we construct a `KalmanFilter` object. We have to specify the number of variables in the state with the `dim_x` parameter, and the number of measurements with `dim_z`. We have two random variables in the state and one measurement, so we write:\n",
    "\n",
    "```python\n",
    "from filterpy.kalman import KalmanFilter\n",
    "dog_filter = KalmanFilter(dim_x=2, dim_z=1)\n",
    "```\n",
    "\n",
    "This creates an object with default values for all the Kalman filter matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =  [[0. 0.]]\n",
      "R =  [[1.]]\n",
      "Q = \n",
      " [[1. 0.]\n",
      " [0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.kalman import KalmanFilter\n",
    "dog_filter = KalmanFilter(dim_x=2, dim_z=1)\n",
    "print('x = ', dog_filter.x.T)\n",
    "print('R = ', dog_filter.R)\n",
    "print('Q = \\n', dog_filter.Q)\n",
    "# etc..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we initialize the filter's matrices and vectors with values valid for our problem. I've put this in a function 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": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.kalman import KalmanFilter\n",
    "from filterpy.common import Q_discrete_white_noise\n",
    "\n",
    "def pos_vel_filter(x, P, R, Q=0., dt=1.0):\n",
    "    \"\"\" Returns a KalmanFilter which implements a\n",
    "    constant velocity model for a state [x dx].T\n",
    "    \"\"\"\n",
    "    \n",
    "    kf = KalmanFilter(dim_x=2, dim_z=1)\n",
    "    kf.x = np.array([x[0], x[1]]) # location and velocity\n",
    "    kf.F = np.array([[1., dt],\n",
    "                     [0.,  1.]])  # state transition matrix\n",
    "    kf.H = np.array([[1., 0]])    # Measurement function\n",
    "    kf.R *= R                     # measurement uncertainty\n",
    "    if np.isscalar(P):\n",
    "        kf.P *= P                 # covariance matrix \n",
    "    else:\n",
    "        kf.P[:] = P               # [:] makes deep copy\n",
    "    if np.isscalar(Q):\n",
    "        kf.Q = Q_discrete_white_noise(dim=2, dt=dt, var=Q)\n",
    "    else:\n",
    "        kf.Q[:] = Q\n",
    "    return kf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`KalmanFilter` initializes `R`, `P`, and `Q` to the identity matrix, so `kf.P *= P` is one way to quickly assign all of the diagonal elements to the same scalar value. Now we create the filter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = .1\n",
    "x = np.array([0., 0.]) \n",
    "kf = pos_vel_filter(x, P=500, R=5, Q=0.1, dt=dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can inspect the current values of all attributes of the filter by entering the variable on the command line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KalmanFilter object\n",
       "dim_x = 2\n",
       "dim_z = 1\n",
       "dim_u = 0\n",
       "x = [0. 0.]\n",
       "P = [[500.   0.]\n",
       "     [  0. 500.]]\n",
       "x_prior = [[0. 0.]].T\n",
       "P_prior = [[1. 0.]\n",
       "           [0. 1.]]\n",
       "x_post = [[0. 0.]].T\n",
       "P_post = [[1. 0.]\n",
       "          [0. 1.]]\n",
       "F = [[1.  0.1]\n",
       "     [0.  1. ]]\n",
       "Q = [[0.    0.   ]\n",
       "     [0.    0.001]]\n",
       "R = [[5.]]\n",
       "H = [[1. 0.]]\n",
       "K = [[0. 0.]].T\n",
       "y = [[0.]]\n",
       "S = [[0.]]\n",
       "SI = [[0.]]\n",
       "M = [[0.]]\n",
       "B = None\n",
       "z = [[None]]\n",
       "log-likelihood = -708.3964185322641\n",
       "likelihood = 2.2250738585072014e-308\n",
       "mahalanobis = 0.0\n",
       "alpha = 1.0\n",
       "inv = <function inv at 0x00000296F726A948>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All that is left is to write the code to run the Kalman filter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from kf_book.mkf_internal import plot_track\n",
    "\n",
    "def run(x0=(0.,0.), P=500, R=0, Q=0, dt=1.0, \n",
    "        track=None, zs=None,\n",
    "        count=0, do_plot=True, **kwargs):\n",
    "    \"\"\"\n",
    "    track is the actual position of the dog, zs are the \n",
    "    corresponding measurements. \n",
    "    \"\"\"\n",
    "\n",
    "    # Simulate dog if no data provided. \n",
    "    if zs is None:\n",
    "        track, zs = compute_dog_data(R, Q, count)\n",
    "\n",
    "    # create the Kalman filter\n",
    "    kf = pos_vel_filter(x0, R=R, P=P, Q=Q, dt=dt)  \n",
    "\n",
    "    # run the kalman filter and store the results\n",
    "    xs, cov = [], []\n",
    "    for z in zs:\n",
    "        kf.predict()\n",
    "        kf.update(z)\n",
    "        xs.append(kf.x)\n",
    "        cov.append(kf.P)\n",
    "\n",
    "    xs, cov = np.array(xs), np.array(cov)\n",
    "    if do_plot:\n",
    "        plot_track(xs[:, 0], track, zs, cov, **kwargs)\n",
    "    return xs, cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the complete code for the filter, and most of it is boilerplate. I've made it flexible enough to support several uses in this chapter, so it is a bit verbose. Let's work through it line by line. \n",
    "\n",
    "The first lines checks to see if you provided it with measurement data in `data`. If not, it creates the data using the `compute_dog_data` function we wrote earlier.\n",
    "\n",
    "The next lines uses our helper function to create a Kalman filter.\n",
    "\n",
    "```python\n",
    "# create the Kalman filter\n",
    " kf = pos_vel_filter(x0, R=R, P=P, Q=Q, dt=dt)\n",
    "```\n",
    "\n",
    "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 methods `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 work of storing the results, the loop reads:\n",
    "\n",
    "```python\n",
    "    for z in zs:\n",
    "        kf.predict()\n",
    "        kf.update(z)\n",
    "```\n",
    "\n",
    "Each call to `predict` and `update` modifies the state variables `x` and `P`. Therefore, after the call to `predict`, `kf.x` contains the prior. After the call to update, `kf.x` contains the posterior. `data` contains the actual position and measurement of the dog, so we use `[:, 1]` to get an array of measurements.\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` matrices; executing the filter is trivial.\n",
    "\n",
    "The rest of the code optionally plots the results and then returns the saved states and covariances.\n",
    "\n",
    "Let's run it. We have 50 measurements with a noise variance of 10 and a process variance of 0.01."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1wyAianMnTpxo9QqH/oZtPhEFoua09z5XpJvNZgC1wYeFhbl1rNVqRUZGBlJSUqDX670Rns9grvIJlDwB5nq5srIyJCQkuNq/QNLSNp+vITkxVzkFSq6ebu99rkh3ftwZFhbWoiLdZDIhLCxM6hcBwFxlFCh5Asy1KYE43KOlbT5fQ3JirnIKlFw93d4H1uBHIiIiIiI/4HaRvmnTJkyYMAFxcXFQFAXr16+v97wQAmlpaYiLi0NwcDBGjx6N3bt3eypeIiIiIiLpuV2kV1RUYODAgViyZEmjzy9cuBCLFi3CkiVLkJ2djZiYGCQnJ6O8vLzVwRIRERERBQK3x6SPGzcO48aNa/Q5IQQWL16MefPmYdKkSQCAlStXIjo6GqtXr8bMmTNbFy0RERERUQDw6I2jR48eRUFBAVJSUlzbjEYjRo0ahS1btjRapFssFlgsFtfjsrIyALWD761Wq1vXd+7v7nH+iLnKJ1DyBJhrU/sQERE5ebRILygoAABER0fX2x4dHY28vLxGj0lPT8f8+fMbbM/IyIDJZGpRHJmZmS06zh8xV/kESp4Ac3WqrKxsw0iIiMgfeGUKxsunlRFCNDnVzNy5c5Gamup67Jw/MiUlpUVTMGZmZiI5OVnqKX4A5iqjQMkTYK6Xc36CSERE5OTRIj0mJgZAbY96bGysa3tRUVGD3nUno9EIo9HYYLter2/xm3drjvU3zFU+gZInwFwvfY6IiOhSHp0nPTExETExMfU+1q2pqUFWVhZGjBjhyUsREREREUnL7Z70Cxcu4NChQ67HR48exY4dOxAZGYnOnTtjzpw5WLBgAXr27ImePXtiwYIFMJlMmDJlikcDJyIiIiKSldtFek5ODsaMGeN67BxPPm3aNKxYsQJPP/00qqqqMGvWLBQXF2PYsGHIyMiA2Wz2XNSNOFR0AS98sgvF5zQYP96rlyIiIpW9+uUBfL1Li5AeZzC2X5za4RAReZzbRfro0aMhhGjyeUVRkJaWhrS0tNbE5TadRsH3h8/BoFGuGB8REfm/w2cu4Gi5gqJyy9V3JiLyQx4dk66m2IggAECNQ0FxJeccJiKSmUFb+/ZVY3OoHAkRkXdIU6QbdVp0DDUAAE6XVKscDREReZNRpwUAWFikE5GkpCnSASAuIhgAcLq0SuVIiIjIm4z62rcvFulEJCupivROdUNeTrEnnYhIahzuQkSyk6pId/Wkl7AnnYhIZkYde9KJSG5yFenh7EknIgoELNKJSHZyFel1w13yS1mkExHJTF9XpNfYWaQTkZykKtI71Q13OcXhLkREUmNPOhHJTqoi3TncpbjSisoam8rREBGRtziL9Bori3QikpNURXpYsB5B2trVRnnzKBGRvAwc7kJEkpOqSAeAdsba77x5lIhIXheHu9hVjoSIyDukK9IjjbU96aeK2ZNORCQr54qjnCediGQlXZHezlD7/VRJpbqBEBGR1zgXM+KNo0QkK+mKdPakExHJz6hnkU5EcpOuSHeOST/NMelERNJyze7CIp2IJCVdke7qSefsLkRE0uJwFyKSnXRFurMnvaCsGjZOzUVEJCUDe9KJSHLSFelmPaDXKrA7BArKOOSFiEhGRs6TTkSSk65I1yhAbN3KoxyXTkQkJ4OOw12ISG7SFekAEFdXpHMaRiIiORlZpBOR5OQs0iOCAXAaRiIiWTkXM7I7BO8/IiIpSVmkd4pw9qSzSCcikpFBp7h+5rh0IpKRlEW6qyedY9KJiKTknIIRACxWFulEJB85i3TnmPRijkknIpKRTquBRqldF4M96UQkIymL9E6unvQqCCFUjoaIiLzBOeKFPelEJCMpi/SYup70aqsDxZVWlaMhIvJ/6enpUBQFc+bMcW0TQiAtLQ1xcXEIDg7G6NGjsXv37jaLSV/3Dmax2dvsmkREbcUrRXp5eTnmzJmDLl26IDg4GCNGjEB2drY3LtUoo06DjubapUc5wwsRUetkZ2fj7bffxoABA+ptX7hwIRYtWoQlS5YgOzsbMTExSE5ORnl5eZvE5epJ5zSMRCQhrxTpv/3tb5GZmYn33nsPO3fuREpKCsaOHYtTp05543KNujjkhePSiYha6sKFC5g6dSreeecdtGvXzrVdCIHFixdj3rx5mDRpEvr374+VK1eisrISq1evbpPYdK6edBbpRCQfnadPWFVVhbVr1+KTTz7BzTffDABIS0vD+vXrsXTpUrz00kuevmSjOrULxo4TJTjJnnQiohabPXs2br/9dowdO7Ze+3306FEUFBQgJSXFtc1oNGLUqFHYsmULZs6c2ej5LBYLLBaL63FZWRkAwGq1wmpt/vBEq9XqGu5SWV3j1rH+xpmbzDk6MVc5BUquzcnTnd+Bx4t0m80Gu92OoKCgetuDg4Px3XffNdjfUw228xjn99iw2uEuJ89XSPmiCJQXPBA4uQZKngBzbWofX7NmzRrk5uYiJyenwXMFBQUAgOjo6Hrbo6OjkZeX1+Q509PTMX/+/AbbMzIyYDKZ3IpPp6ld0Oj7H7bh/D75JwnIzMxUO4Q2w1zlFCi5XinPysrmj/DweJFuNpsxfPhw/OlPf0KfPn0QHR2NDz74ANu2bUPPnj0b7O/JBtspMzMTxfkKAC1+2n8Mn+NIi87jDwLlBQ8ETq6BkifAXJ3cabTbyokTJ/DEE08gIyOjQafLpRRFqfdYCNFg26Xmzp2L1NRU1+OysjIkJCQgJSUFYWFhzY7ParXiLzu/AQAMGDQYyX2jmn2sv7FarcjMzERycjL0er3a4XgVc5VToOTanDydndHN4fEiHQDee+89zJgxA506dYJWq8V1112HKVOm4Keffmqwr6cabKD+L8d4uBhrj+2APSgc48cPb3VOviZQXvBA4OQaKHkCzPVy7jTabSU3NxdFRUUYPHiwa5vdbsemTZuwZMkS7N+/H0Btj3psbKxrn6Kioga965cyGo0wGo0Ntuv1erdfC3qNAKDABkX61xHQst+Rv2KucgqUXK+Upzv5e6VI7969O7KyslBRUYGysjLExsbi/vvvR2JiYoN9PdlgX3pslw5mAMDpkmqpXxCB8oIHAifXQMkTYK6XPudrbr31VuzcubPetunTp6N379545pln0K1bN8TExCAzMxODBg0CANTU1CArKwuvvvpqm8TovHG0hjeOEpGEvFKkO4WEhCAkJATFxcX48ssvsXDhQm9erp5O7WpndymutKKyxgaTwaupEhFJxWw2o3///vW2hYSEoH379q7tc+bMwYIFC9CzZ0/07NkTCxYsgMlkwpQpU9okxotTMHKedCKSj1cq1y+//BJCCPTq1QuHDh3Cf//3f6NXr16YPn26Ny7XqLAgPcxGHcotNpwuqUKPKHObXZuIKBA8/fTTqKqqwqxZs1BcXIxhw4YhIyMDZnPbtLeuxYy44igRScgrRXppaSnmzp2LkydPIjIyEnfffTdefvnlNv9It1O7YOwrKMfJYhbpRESttXHjxnqPFUVBWloa0tLSVInHNdzFziKdiOTjlSL9vvvuw3333eeNU7ulU0RtkX6qhHOlExHJRseedCKSmFdWHPUVcXWrjp5mkU5EJB09x6QTkcSkLtKdN4+e4qqjRETS4ewuRCQzuYv0up50DnchIpKPa7gLi3QikpDcRTp70omIpFW7mBGHuxCRnOQu0ut60gvKqmHj3f9ERFJxzpPO4S5EJCOpi/SOoUYYtBo4RG2hTkRE8uBwFyKSmdRFukajIDYiCACHvBARyUbPIp2IJCZ1kQ4AceG8eZSISEYc7kJEMpO+SHfePMq50omI5HJxuAtvHCUi+chfpHMaRiIiKXG4CxHJTP4iva4n/STHpBMRSYXDXYhIZtIX6V0iTQCAg4UXIIRQORoiIvIUnWuedBbpRCQf6Yv0a+LDodMoKCir5pAXIiKJuIa7WDkmnYjkI32RbjLo0C8uDACQc6xY5WiIiMhTXMNduFgdEUlI+iIdAIZ0jQQA5OSdVzkSIiLyFNfsLlYW6UQkn4Ao0od2bQeAPelERDLh7C5EJLOAKNIHd6ntSd9fWI7SSqvK0RARkSc4e9Jr7A5ODEBE0gmIIr2j2YjEDiEQAvjpOHvTiYhkoFcu/szedCKSTUAU6QAwuEvtkJfsYxyXTkQkA90l72As0olINgFTpLvGpeexJ52ISAbaS3rSuaAREckmYIp05wwvP58ogcXGOXWJiPydogDGuu50tutEJJuAKdK7dQhBZIgBFpsDu06VqR0OERF5wMUinT3pRCSXgCnSFUVxjUvP4bh0IiIpGOqKdA53ISLZBEyRDnBcOhGRbNiTTkSyCqgi3bXy6LHznFOXiEgCBi170olITh4v0m02G/7nf/4HiYmJCA4ORrdu3fDiiy/C4VC/Ae0fFw6jToPiSisOn6lQOxwiImol3jhKRLLSefqEr776Kt58802sXLkS/fr1Q05ODqZPn47w8HA88cQTnr6cWww6Da5NiMC2o+eRc+w8ekSFqhoPERG1jkFfV6Rb1e8IIiLyJI/3pP/www+YOHEibr/9dnTt2hX33HMPUlJSkJOT4+lLtcgQjksnIpKGa7iLnUU6EcnF4z3pI0eOxJtvvokDBw4gKSkJP//8M7777jssXry40f0tFgssFovrcVlZ7fSIVqsVVqvVrWs797/ScYPiwwAA2UfPu31+X9KcXGURKLkGSp4Ac21qH3KfUacFwOEuRCQfjxfpzzzzDEpLS9G7d29otVrY7Xa8/PLLmDx5cqP7p6enY/78+Q22Z2RkwGQytSiGzMzMJp+rtAEKtMg7X4k16z9HmKFFl/AZV8pVNoGSa6DkCTBXp8rKyjaMRC6uMekc7kJEkvF4kf7hhx9i1apVWL16Nfr164cdO3Zgzpw5iIuLw7Rp0xrsP3fuXKSmproel5WVISEhASkpKQgLC3Pr2larFZmZmUhOToZer29yv5XHt2Bf4QVE9ByM/9cv2q1r+Irm5iqDQMk1UPIEmOvlnJ8gkvtc86RzuAsRScbjRfp///d/49lnn8Wvf/1rAMA111yDvLw8pKenN1qkG41GGI3GBtv1en2L37yvduyQxEjsK7yA7SfKMOHa+BZdw1e05vfkbwIl10DJE2Culz5HLcOedCKSlcdvHK2srIRGU/+0Wq3WJ6ZgdBpaN196bh5XHiUi8mecgpGIZOXxnvQJEybg5ZdfRufOndGvXz9s374dixYtwowZMzx9qRZzLmq063QZKmtsMBk8/msgIqI24BruwsWMiEgyHq9O//a3v+GPf/wjZs2ahaKiIsTFxWHmzJl4/vnnPX2pFusUEYy48CCcLq3GjuMlGNGjg9ohERFRC1zsSWeRTkRy8XiRbjabsXjx4ianXPQVQ7pG4tOfTyP7WDGLdCIiP2VgkU5EkvL4mHR/MbhL7aJGO05wUSMiIn/lXMyIRToRySZgi/ReMWYAwOEzFSpHQkRELWXU88ZRIpJTwBbp3TqGAABOFlei2srGnYjIH11ccZQ96UQkl4At0juGGmEO0sEhgLxzXO2PiMgfOYe7cHYXIpJNwBbpiqKge8dQAMDhMxdUjoaIiFqCs7sQkawCtkgHcLFIL2KRTkTkjy6uOMphi0Qkl8Au0qNqx6WzJ52IyD+5FjOysyediOQS2EW6a7gLZ3ghIvJHF3vSWaQTkVwCvEiv7Uk/cuYChBAqR0NERO66uJgRh7sQkVwCukjvHBkCrUZBRY0dhWUWtcMhIiI3cbgLEckqoIt0g06DLpEmAByXTkTkjzjchYhkFdBFOgB04zSMRER+i4sZEZGsAr5Id83wwmkYiYj8jkGnAOBiRkQkHxbpnOGFiMhvXexJt3MCACKSCot0DnchIvJbzjHpDgHYHCzSiUgeLNLrpmHML61GhcWmcjRERL5j6dKlGDBgAMLCwhAWFobhw4fjiy++cD0vhEBaWhri4uIQHByM0aNHY/fu3W0ao0F78W2MQ16ISCYBX6RHmAxoH2IAABw9yyEvRERO8fHxeOWVV5CTk4OcnBzccsstmDhxoqsQX7hwIRYtWoQlS5YgOzsbMTExSE5ORnl5eZvF6JyCEeDNo0Qkl4Av0gEOeSEiasyECRMwfvx4JCUlISkpCS+//DJCQ0OxdetWCCGwePFizJs3D5MmTUL//v2xcuVKVFZWYvXq1W0Wo1ajQK+tvXmUCxoRkUx0agfgC7pHheDHY+c5wwsRURPsdjs++ugjVFRUYPjw4Th69CgKCgqQkpLi2sdoNGLUqFHYsmULZs6c2eh5LBYLLJaLi8eVlZUBAKxWK6xWa7Pjce5rtVph0GpgtdtRUV0Dq0m+t7VLc5Udc5VToOTanDzd+R3I15q1AGd4ISJq3M6dOzF8+HBUV1cjNDQU69atQ9++fbFlyxYAQHR0dL39o6OjkZeX1+T50tPTMX/+/AbbMzIyYDKZ3I4vMzMTcGgBKPjqm42Idf8UfiMzM1PtENoMc5VToOR6pTwrKyubfR4W6eBwFyKipvTq1Qs7duxASUkJ1q5di2nTpiErK8v1vKIo9fYXQjTYdqm5c+ciNTXV9bisrAwJCQlISUlBWFhYs+OyWq3IzMxEcnIy0ndvQUWZBcOGj0T/Ts0/h7+4NFe9Xq92OF7FXOUUKLk2J0/np4fNwSIdQLe6GV6Onq2A3SGg1TT9BkNEFEgMBgN69OgBABgyZAiys7Px+uuv45lnngEAFBQUIDY21rV/UVFRg971SxmNRhiNxgbb9Xp9i9689Xo9jPraudIdiiJ1AdDS35E/Yq5yCpRcr5SnO/nzxlEA8e1MMGg1sNgcOF1SpXY4REQ+SwgBi8WCxMRExMTE1PtYt6amBllZWRgxYkSbxuScK91i5ewuRCQP9qSjdnaAxA4h2F9YjkNnLiAhUuJBjUREzfTcc89h3LhxSEhIQHl5OdasWYONGzdiw4YNUBQFc+bMwYIFC9CzZ0/07NkTCxYsgMlkwpQpU9o0Tuc0jJyCkYhkwiK9Tveo2iL9cNEFjOkVpXY4RESqKywsxAMPPID8/HyEh4djwIAB2LBhA5KTkwEATz/9NKqqqjBr1iwUFxdj2LBhyMjIgNlsbtM4jbra4S4s0olIJizS63CGFyKi+pYtW3bF5xVFQVpaGtLS0tomoCa4hrtwnnQikojHx6R37doViqI0+Jo9e7anL+VRnOGFiMg/cbgLEcnI4z3p2dnZsNsv9mbs2rULycnJuPfeez19KY9yzvByhEU6EZFfcfak17BIJyKJeLxI79ixY73Hr7zyCrp3745Ro0Z5+lIe1a2uJ/3shRqUVloRbpJ/iiAiIhlwTDoRycirY9JramqwatUqpKamNrm4haeWiHYec+l3dxg1QHSYEYVlFuwvKMGghAi3z9GWAmWJXSBwcg2UPAHm2tQ+1DIGjkknIgl5tUhfv349SkpK8NBDDzW5j6eXiAZavuxsuKJBITRY//UPyI8SLTpHWwuUJXaBwMk1UPIEmKuTO8tEU0Mc7kJEMvJqkb5s2TKMGzcOcXFxTe7jqSWigdYvO5vt2IsD204gNK47xqckuX18WwqUJXaBwMk1UPIEmOvl3FkmmhricBcikpHXivS8vDx89dVX+Pjjj6+4n6eXiG7NsT2ja/9TcPRcld8UDoGyxC4QOLkGSp4Ac730OWo5A1ccJSIJeXwKRqfly5cjKioKt99+u7cu4XGchpGIyP+4hrvYOSadiOThlSLd4XBg+fLlmDZtGnQ6/1kvyTkN4/FzlbDa2SNDROQPjHr2pBORfLxSpH/11Vc4fvw4ZsyY4Y3Te01MWBBMBi1sDoHj53kjFxGRPzBouZgREcnHK0V6SkoKhBBISvLtmy8vp9Eort70w0Uc8kJE5A+M+tobRzm7CxHJxGtj0v3VxXHpFSpHQkREzWHkPOlEJCEW6ZfpUVekHywsVzkSIiJqjos3jrInnYjkwSL9Mr1izACAfQUs0omI/IGRUzASkYRYpF+mT2ztXOmHii5whhciIj/AxYyISEYs0i/TKSIYoUYdauwOHD3LcelERL7OuZgRbxwlIpmwSL+MRqO4hrzszedS3UREvo43jhKRjFikN6I3x6UTEfkNDnchIhmxSG9E77px6fvYk05E5PM43IWIZMQivRF92JNOROQ3Lg53YZFORPJgkd6IpLoiPb+0GiWVNSpHQ0REV2LUc0w6EcmHRXojwoL0iG8XDIC96UREvs6grX0rs9oFHA6hcjRERJ7BIr0JvWM4Lp2IyB8Y9VrXz1x1lIhkwSK9CX1iOS6diMgfOMekA1x1lIjkwSK9Cc6e9L0s0omIfJpOo0BRan+22DkunYjkwCK9Cb3retIPFJTDzjGOREQ+S1GUizO8sCediCTBIr0JXduHwKjToMpqx/HzlWqHQ0REV8AFjYhINizSm6DVKOjlnC+dN48SEfk0LmhERLJhkX4FfTgunYjIL1xc0Ihj0olIDizSr8A5Lp096UREvo2rjhKRbFikX8HFGV5YpBMR+TJD3Zh0DnchIlmwSL+C3nVj0k+cr0J5tVXlaIiIqCnsSSci2bBIv4J2IQbEhAUBAA4Uclw6EZGvMnBMOhFJhkX6VTjHpe/NZ5FOROSrjJzdhYgkwyL9Kpzj0vdxXDoRkc/iPOlEJBsW6VfRxzXDC3vSiYh81cUVRznchYjkwCL9Ki72pJdDCKFyNERE1BjXcBc7e9KJSA5eKdJPnTqF3/zmN2jfvj1MJhOuvfZa5ObmeuNSXtetYwj0WgUXLDacLK5SOxwiImqEUe/sSWeRTkRy8HiRXlxcjBtvvBF6vR5ffPEF9uzZgz//+c+IiIjw9KXahF6rQY+ouiEvXHmUiMgnGbScgpGI5KLz9AlfffVVJCQkYPny5a5tXbt29fRl2lSfGDP25pdhX34ZkvtGqx0OERFdxqivW8yIw12ISBIeL9I//fRT3Hbbbbj33nuRlZWFTp06YdasWfjd737X6P4WiwUWi8X1uKysdhYVq9UKq9W9BYSc+7t73NX0jAoBAOw5Xerxc7eUt3L1RYGSa6DkCTDXpvahluONo0QkG48X6UeOHMHSpUuRmpqK5557Dj/++CMef/xxGI1GPPjggw32T09Px/z58xtsz8jIgMlkalEMmZmZLTquKWUlCgAtcg8X4PPPT3n03K3l6Vx9WaDkGih5AszVqbKysg0jkROHuxCRbDxepDscDgwZMgQLFiwAAAwaNAi7d+/G0qVLGy3S586di9TUVNfjsrIyJCQkICUlBWFhYW5d22q1IjMzE8nJydDr9a1L5BJDyy1YujcLZy0Kxoy9DcEGrcfO3VLeytUXBUqugZInwFwv5/wEkVrOeeMoFzMiIll4vEiPjY1F3759623r06cP1q5d2+j+RqMRRqOxwXa9Xt/iN+/WHNuY2HY6tA8x4FxFDY4VV2NAfITHzt1ans7VlwVKroGSJ8BcL32OWoeLGRGRbDw+u8uNN96I/fv319t24MABdOnSxdOXajOKoqB33aJGe/PZ40VE5GsMzjHpNo5JJyI5eLxIf/LJJ7F161YsWLAAhw4dwurVq/H2229j9uzZnr5Um+oXFw4A+PlkqcqREBHR5Vw3jrInnYgk4fEifejQoVi3bh0++OAD9O/fH3/605+wePFiTJ061dOXalPXdW4HAPgpr1jlSIiI6HIc7kJEsvH4mHQAuOOOO3DHHXd449Squa5LBABgf2E5yqutMAdxDCkRka8wsCediCTj8Z50WUWZg5AQGQwhgB0nStQOh4iILuEc7sLZXYhIFizS3XBxyEuJuoEQEVE9Rt44SkSSYZHuhsFdaov03OMcl05E5Etcw12s7EknIjmwSHeDsyd9+/FiOBxC5WiIiLwnPT0dQ4cOhdlsRlRUFO68884G0+sKIZCWloa4uDgEBwdj9OjR2L17tyrxOm8crbGzSCciObBId0PvGDOC9VqUV9tw6MwFtcMhIvKarKwszJ49G1u3bkVmZiZsNhtSUlJQUVHh2mfhwoVYtGgRlixZguzsbMTExCA5ORnl5eVtHq9zxVGLlcNdiEgOLNLdoNNqMDChdr50TsVIRDLbsGEDHnroIfTr1w8DBw7E8uXLcfz4ceTm5gKo7UVfvHgx5s2bh0mTJqF///5YuXIlKisrsXr16jaP16Dl7C5EJBevTMEos8Fd2mHrkfPIzSvGr6/vrHY4RERtorS0diG3yMhIAMDRo0dRUFCAlJQU1z5GoxGjRo3Cli1bMHPmzEbPY7FYYLFYXI/LympXcbZarbBarc2Ox7mv87sWtcV5jd2BmpoaKIrS7HP5ustzlRlzlVOg5NqcPN35HbBId5NrhhfePEpEAUIIgdTUVIwcORL9+/cHABQUFAAAoqOj6+0bHR2NvLy8Js+Vnp6O+fPnN9iekZEBk8nkdmyZmZkAgEobAOggBPDZf76ATsLPiZ25BgLmKqdAyfVKeVZWVjb7PCzS3TSorkg/fKYCJZU1iDAZVI6IiMi7Hn30Ufzyyy/47rvvGjx3eY+1EOKKvdhz585Famqq63FZWRkSEhKQkpKCsLCwZsdktVqRmZmJ5ORk6PV6VFvtmJv9NQBgzNgUmIPkeXu7PFeZMVc5BUquzcnT+elhc8jTirWRyBADunUIwZGzFdh+vARjekepHRIRkdc89thj+PTTT7Fp0ybEx8e7tsfExACo7VGPjY11bS8qKmrQu34po9EIo9HYYLter2/Rm7fzOK324tuZUDRSFgIt/R35I+Yqp0DJ9Up5upO/hB8Iet91zvnSefMoEUlKCIFHH30UH3/8Mb755hskJibWez4xMRExMTH1PtatqalBVlYWRowY0dbhQqNRePMoEUmFRXoLcFw6Eclu9uzZWLVqFVavXg2z2YyCggIUFBSgqqoKQO0wlzlz5mDBggVYt24ddu3ahYceeggmkwlTpkxRJWbXgkYs0olIAhzu0gLOlUd3nCiBze6ATsv/6xCRXJYuXQoAGD16dL3ty5cvx0MPPQQAePrpp1FVVYVZs2ahuLgYw4YNQ0ZGBsxmcxtHW8uo0+CCBahhkU5EEmCR3gI9o0JhNupQbrFhf2E5+sWFqx0SEZFHCXH1VZUVRUFaWhrS0tK8H1AzGF096VzQiIj8H7uAW0CjUXBt5wgAXNSIiMhXOIe7sCediGTAIr2FLo5LL1E3ECIiAgAYdVoAHJNORHJgkd5CgznDCxGRTzHqOdyFiOTBIr2Fru0cAUUBjp+vxJlyy9UPICIir3JOwcjhLkQkAxbpLRQWpEdSVO0MBpyKkYhIfRd70lmkE5H/Y5HeCtd1iQDAIp2IyBe4FjOyskgnIv/HIr0VXDePclw6EZHqXDeO2lmkE5H/Y5HeCs6bR385WcoxkEREKnMNd7HyxlEi8n8s0lshsUMI2pn0sNgc2H26VO1wiIgCmmu4CztNiEgCLNJbQVEUDO4SCQD44cg5laMhIgpszp50frJJRDJgkd5Ko5I6AACy9p9RORIiosDGxYyISCYs0ltpVFIUgNpFjcqrrSpHQ0QUuAw6LmZERPLweJGelpYGRVHqfcXExHj6Mj6jc3sTEjuEwOYQ+P4Qh7wQEanFqONwFyKSh1d60vv164f8/HzX186dO71xGZ8xKqkjACDrAIe8EBGphcNdiEgmOq+cVKeTuvf8cqN6dcSKLcew6cAZCCGgKIraIRERBZyLw11YpBOR//NKkX7w4EHExcXBaDRi2LBhWLBgAbp169bovhaLBRaLxfW4rKwMAGC1WmG1ujfG27m/u8e11uD4MBh0GpwqqcK+0yXoERXq9WuqlasaAiXXQMkTYK5N7UOtc3G4C8ekE5H/83iRPmzYMPzzn/9EUlISCgsL8dJLL2HEiBHYvXs32rdv32D/9PR0zJ8/v8H2jIwMmEymFsWQmZnZouNao1uIBvtKNXjr080YEyfa7Lpq5KqWQMk1UPIEmKtTZWVlG0YiLyN70olIIh4v0seNG+f6+ZprrsHw4cPRvXt3rFy5EqmpqQ32nzt3br3tZWVlSEhIQEpKCsLCwty6ttVqRWZmJpKTk6HX61ueRAsURuRhwRf7cUYXhfHjB3v9emrm2tYCJddAyRNgrpdzfoJIreMa7mJlkU5E/s8rw10uFRISgmuuuQYHDx5s9Hmj0Qij0dhgu16vb/Gbd2uObalb+sRgwRf7kX2sGFahwGTw+q8WgDq5qiVQcg2UPAHmeulz1HrOG0dr7CzSicj/eX2edIvFgr179yI2Ntbbl1JV944h6BQRjBq7A9uOnFc7HCKigONccZTzpBORDDxepD/11FPIysrC0aNHsW3bNtxzzz0oKyvDtGnTPH0pn6IoCkb14lSMRERqMWo53IWI5OHxIv3kyZOYPHkyevXqhUmTJsFgMGDr1q3o0qWLpy/lc0bXzZe+cX+RypEQEQUeZ086h7sQkQw8PnB6zZo1nj6l3xjRowN0GgXHzlXi2NkKdO0QonZIREQBw7WYEXvSiUgCXh+THkhCjToM6doOALDpIIe8EBG1pYuLGXFMOhH5PxbpHjYqKQoAkLWfRToRUVu6uJgRe9KJyP+xSPew0XU3j245fI69OUREbcg13IVFOhFJgEW6h/WOMSPKbESV1Y7so8Vqh0NEFDCcw11sDgG7o+1WfiYi8gYW6R6mKApGJTmnYuQsL0REbcU53AXgkBci8n8s0r2A86UTEbW9S4t0DjckIn/HIt0LburRERoFOFB4AadKqtQOh4goIOi0GmiU2p85Lp2I/B2LdC8IN+kxpGskAODzX/JVjoaIKHA4bx7lcBci8ncs0r3kVwPjAACf/HxK5UiIiAKHc9VRDnchIn/HIt1Lxl8TC51Gwa5TZTh85oLa4RARBQSDtvZtrZqrjhKRn2OR7iWRIQbcXDfLy6c7TqscDRFRYHD2pNfYWaQTkX9jke5FE6+tHfLy6c+nIQTn7CUi8jbnmPRqK4e7EJF/Y5HuRWP7RCNIr8HRsxXYeapU7XCIiKQXHqwHAJRUWlWOhIiodVike1GIUYfkvjEAgE845IWIyOuiw4wAgILSapUjISJqHRbpXjaxbpaXz34+zWWqiYi8LDosCABQWM4inYj8G4t0L7s5qSPCg/UoKrdg25FzaodDRCS1GGeRzp50IvJzLNK9zKDTYPw1sQA45IWIyNtiwmuL9IIyFulE5N9YpLcB5ywvn+/K5wIbREReFGWu60kvs6gcCRFR67BIbwPXd41ETFgQyqtt2Lj/jNrhEBFJy9mTXlhWzalvicivsUhvAxqNgl8550znkBciIq9xjkmvrLGj3GJTORoiopZjkd5GflU3y8tXewtRXs35e4mIvCHYoEVYkA4Abx4lIv/GIr2N9IsLQ/eOIbDYHMjYXah2OERE0nJOw8ibR4nIn7FIbyOKomDitZ0AAJ/8zCEvRETecnFcOm8eJSL/xSK9DTmHvHx/6CxXwyMi8hLXgkbsSSciP8YivQ117RCC67tGwu4QWLU1T+1wiIik5Lx5lJ0hROTPWKS3sek3dgUArP7xOKqtnDOdiMjTosOMADgmnYj8m9eL9PT0dCiKgjlz5nj7Un4huW80OkUE43xFDT7l2HQiIo9zDncpYpFORH7Mq0V6dnY23n77bQwYMMCbl/ErOq0GDwzvAgBY/v0xLrZBRORhzhtH2ZNORP7Ma0X6hQsXMHXqVLzzzjto166dty7jl349NAFBeg325pdh29HzaodDRCQV55j0M+UW2OwOlaMhImoZnbdOPHv2bNx+++0YO3YsXnrppSb3s1gssFguTpNVVlYGALBarbBa3Vv0x7m/u8e1tRC9gjuvjcOa7JNYtvkIBieEuX0Of8nVEwIl10DJE2CuTe3jazZt2oTXXnsNubm5yM/Px7p163DnnXe6nhdCYP78+Xj77bdRXFyMYcOG4e9//zv69eunXtAA2ocaodUosDsEzl6ocfWsExH5E68U6WvWrEFubi5ycnKuum96ejrmz5/fYHtGRgZMJlOLrp+Zmdmi49pSYg0A6PDV3kK89/HnaN/C9xB/yNVTAiXXQMkTYK5OlZWVbRhJ81VUVGDgwIGYPn067r777gbPL1y4EIsWLcKKFSuQlJSEl156CcnJydi/fz/MZrMKEdfSahR0DDWioKwahWXVLNKJyC95vEg/ceIEnnjiCWRkZCAo6OoN49y5c5Gamup6XFZWhoSEBKSkpCAszL0eZqvViszMTCQnJ0Ov17sde1vbdCEX3x8+h1Om7njg//Vy61h/y7U1AiXXQMkTYK6Xc36C6GvGjRuHcePGNfqcEAKLFy/GvHnzMGnSJADAypUrER0djdWrV2PmzJltGWoD0eFBKCirRkFZNQaqGgkRUct4vEjPzc1FUVERBg8e7Npmt9uxadMmLFmyBBaLBVqt1vWc0WiE0WhscB69Xt/iN+/WHNuWZoxMxPeHz+Gj3FP4r9t6w2Rw/8/hL7l6QqDkGih5Asz10uf8zdGjR1FQUICUlBTXNqPRiFGjRmHLli1NFumeGuJ4tWFEUaEGAMDp4gqfHU7UXBweJifmKh9PD2/0eJF+6623YufOnfW2TZ8+Hb1798YzzzxTr0APdGN6RaFrexOOnavE2p9O4YEbuqgdEhFRsxQUFAAAoqOj622Pjo5GXl7Ti7V5eohjU8OIqs9rAGjw/fY9iDy3y+3z+iIOD5MTc5WPp4Y3erxIN5vN6N+/f71tISEhaN++fYPtgU6jUTBtRFfM/2wPVnx/FFOv7wyNRlE7LCKiZlOU+m2WEKLBtkt5aojj1YYRHc86gs2Fh2COisf48f793sPhYXJirvLx9PBGr83uQs1zz+B4/DnjAA6fqcDmQ2cxKqmj2iEREV1VTEwMgNoe9djYWNf2oqKiBr3rl/L0EMemjotrFwIAOFNeI01RwOFhcmKu8vHU8EavrzgKABs3bsTixYvb4lJ+xxykx71D4gEAy78/qnI0RETNk5iYiJiYmHof69bU1CArKwsjRoxQMbJaXNCIiPxdmxTpdGUPjegKRQE27j+Dn0+UqB0OERGA2kXpduzYgR07dgCovVl0x44dOH78OBRFwZw5c7BgwQKsW7cOu3btwkMPPQSTyYQpU6aoGziA6LDa3vrCUhbpROSfWKT7gC7tQ3DXoE4AgNe+3K9yNEREtXJycjBo0CAMGjQIAJCamopBgwbh+eefBwA8/fTTmDNnDmbNmoUhQ4bg1KlTyMjIUHWOdKfoulVHyy02VFhsKkdDROQ+Fuk+4smxSdBrFXx36Cy2HDqrdjhERBg9ejSEEA2+VqxYAaD2ptG0tDTk5+ejuroaWVlZPjNBgDlIjxBD7WxihRzyQkR+iEW6j0iINGHK9Z0BAK9+uR9CCJUjIiLyb9Ecl05EfoxFug959JaeMBm0+PlECb7cXah2OEREfi3aXFukF5VZrrInEZHvYZHuQzqajZhxYyIA4M8Z+2F3sDediKilOMMLEfkzFuk+5nc3d0N4sB4Hiy5g3fZTaodDROS3nDePFnCGFyLyQyzSfUx4sB6zRncHAPwl8wAsNrvKERER+SfXNIzsSSciP8Qi3QdNG9EV0WFGnCqpwuptx9UOh4jIL8XU9aSzSCcif8Qi3QcF6bV4/NaeAIAl3xzCBc7xS0TkNufsLoW8cZSI/BCLdB9135AEdG1vwrmKGvzju6Nqh0NE5Hcu7Ul38EZ8IvIzLNJ9lF6rQWpKLwDA0o2HceJ8pcoRERH5l45mIxQFsDkEzlXUqB0OEZFbWKT7sDuuicX1iZGostoxb/0uLnBEROQGvVaD9iG8eZSI/BOLdB+m0Sh4ZdI1MOg02HTgDNbv4JSMRETuiAlnkU5E/olFuo/r1jEUT9TdRPriZ3tw7gJvgCIiai7nuHQuaERE/oZFuh/4/c3d0DvGjOJKK/70f3vUDoeIyG9EOW8e5YJGRORnWKT7Ab1Wg1fvHgCNAqzfcRrf7i9SOyQiIr9wcYYXfgpJRP6FRbqfGJgQgRk3JgIA5n28k3OnExE1A4e7EJG/YpHuR1JTkpAQGYzTpdX4y1eH1A6HiMjnXVzQiEU6EfkXFul+xGTQYcFd1wAA3tt2HMfKVQ6IiMjHRYfVzu7CnnQi8jcs0v3MTT074u7r4iEE8N4hLcqrrWqHRETks5zDXUoqrai22lWOhoio+Vik+6E/3tEHceFBOFut4JmPd3ORIyKiJoQH62HU1b7VFfHmUSLyIyzS/VCEyYC//XogtIpA5t4ivJl1RO2QiIh8kqIoiAnnzaNE5H9YpPupAfHhuCfRAQB47ct92HLorMoRERH5pmgzi3Qi8j8s0v3Y8CiBuwbFwSGAxz7YjgIu1kFE1IBzhpciFulE5EdYpPsxRQHm39EHfWLDcK6iBrPez0WNzaF2WEREPiXGOcMLOzKIyI94vEhfunQpBgwYgLCwMISFhWH48OH44osvPH0ZqhNs0OLN31wHc5AOPx0vwYLP96odEhGRT4nmgkZE5Ic8XqTHx8fjlVdeQU5ODnJycnDLLbdg4sSJ2L17t6cvRXW6tA/BX+67FgCwYssxfPzTSXUDIiLyIc4inbO7EJE/8XiRPmHCBIwfPx5JSUlISkrCyy+/jNDQUGzdutXTl6JLjO0bjdljugMAnv73L/h6b6HKERER+QbO7kJE/kjnzZPb7XZ89NFHqKiowPDhwxvdx2KxwGK52LtRVlYGALBarbBa3Vuox7m/u8f5o8ZyfXx0N5w8X4lPfs7HH97/Cf948DoMS4xUK0SPCZS/a6DkCTDXpvYh74i5ZLiLEAKKoqgcERHR1XmlSN+5cyeGDx+O6upqhIaGYt26dejbt2+j+6anp2P+/PkNtmdkZMBkMrXo+pmZmS06zh9dnuuoYOBIOw12FgMPr8jG7H52dAlVKTgPC5S/a6DkCTBXp8rKyjaMJPBE1d04WmNzoKTSinYhBpUjIiK6Oq8U6b169cKOHTtQUlKCtWvXYtq0acjKymq0UJ87dy5SU1Ndj8vKypCQkICUlBSEhYW5dV2r1YrMzEwkJydDr9e3Og9fdqVcU1Ls+P2q7dhy5Dz+cSgY7z88BEnRZpUibb1A+bsGSp4Ac72c8xNE8g6jTou48CCcLq3Gj8fO47Z+MWqHRER0VV4p0g0GA3r06AEAGDJkCLKzs/H666/jrbfearCv0WiE0WhssF2v17f4zbs1x/qbxnLV6/V4Z9pQTH13G3acKMH0lT/ho0eGo0v7EJWi9IxA+bsGSp4Ac730OfKuCQPj8NamI/h37kkW6UTkF9pknnQhRL1x5+R9IUYdVkwfit4xZhSVWzD13W04XVKldlhERKq4e3A8AODbfUU4e4HvR0Tk+zxepD/33HPYvHkzjh07hp07d2LevHnYuHEjpk6d6ulL0VVEmAz458PXo2t7E04WV2HSG1uwr4AfqxNR4EmKNmNgfDhsDoH120+pHQ4R0VV5vEgvLCzEAw88gF69euHWW2/Ftm3bsGHDBiQnJ3v6UtQMUeYgvP+7G9AjKhQFZdW4d+kP+P7QWbXDIiJqc/fU9ab/O/ckhBAqR0NEdGUeL9KXLVuGY8eOwWKxoKioCF999RULdJV1igjG2kdG4PrESJRbbJj2jx+54BERBZwJA+Ng0Gqwr6Acu0/zU0Ui8m1tMiad1Bdu0uO9h6/HhIFxsDkEUv/1M5Z8c5C9SUQUMCJMBiT3iwZQ25tOROTLWKQHEKNOi9fvvxYzR3UDAPxvxgHM/XgnrHaHypEREbUN55CXT3acQo2NbR8R+S4W6QFGo1Ewd1wfvDixHzQKsCb7BO5ZugXHzlaoHRoRkdfd1KMDosxGFFda8c2+IrXDISJqEov0APXg8K5458EhCA/W4+eTpbj9r5t5MxURSU+n1eCu6zoB4JAXIvJtLNID2K19ovHFEzdhWGIkKmrseOqjn/H4mh0orbKqHRoRkdfcc13dnOn7i3CmnHOmE5FvYpEe4OIigrH6dzfgqZQkaDUKPvv5NMa/vhm5eefVDo2IyCt6RpsxMCECdofAJzs4ZzoR+SYW6QStRsGjt/TER48MR0JkME6VVOHeN3/AvHU7cb6iRu3wiIg8jnOmE5GvY5FOLtd1bofPH78Jk67rBIcA3t92HGP+dyNWbjkGG2eAISKJ/GoA50wnIt/GIp3qMQfpsei+a7Hm9zegT2wYSquseOHT3bj9r99hC1cqJSJJhJv0nDOdiHwai3Rq1A3d2uP/HhuJl+7sjwiTHvsLyzHl3W34/T9zsOtUqdrhERG1mnPIy8c/ncTBwnKVoyEiqo9FOjVJq1Hwmxu6YONTozFteBdoFCBjTyHu+Nt3eGDZNmw5fJZjOYnIb93UowP6dwpDWbUNv357K/bmc9gLEfkOFul0VREmA+ZP7I8Nc27GndfGQatRsPngWUx5ZxvufGMLNuwqgMPBYp2I/ItOq8F7M4ahf6cwnKuoweR3tvKTQiLyGSzSqdmSos1Y/OtB2PjUaDw4vAuMOg1+PlGCR1blYsyfN+KvXx/EifOVaodJRNRs7UIMeP+3N+DahAiUVFox+Z2t2H68WO2wiIhYpJP7EiJNeHFif3z/7C14dEwPhAXpkHeuEosyD+Cmhd/i/rd+wL9yTuCCxaZ2qEREVxUerMd7D1+PoV3bobzaht+8uw0/HuVaEUSkLhbp1GIdQo146rZe2PrcrVh030Dc2KM9FAXYdvQ8nv73LxjyUiZmv/8TPso5gaLyarXDJSJqkjlIj5UzrseI7u1RUWPHtH/8iMw9hbzvhohUo1M7APJ/JoMOk66Lx6Tr4nG6pArrtp/C2p9O4siZCvxnZz7+szMfAHBNp3CM6dURo3pFYWB8OHRa/h+RiHyHyaDDPx4aipnv5SLrwBn87p856B1jxvQbu2LitZ0QpNeqHSIRBRAW6eRRcRHBmD2mB2aN7o5fTpbi631F2Li/CL+cLMXOU7Vff/3mEEwGLQbEh2NQ53YYlBCBQZ3boaPZqHb4RBTggvRavP3gYKR/vg8fZp/AvoJyPLN2J9K/2IfJ13fGb27ogk4RwWqHSUQBgEU6eYWiKBiYEIGBCRFITU7CmXILsg6cwbf7i7D5wBmUVduw9ch5bD1ycdxnfLtg9IkNQ8+oUPSMDkXPKDO6dQyBXlExESIKOEadFmm/6ocnxybhXzknsPKHYzhZXIWlGw/jrazDuK5zOwzqHIFrE2q/x4YHQVHYUBGRZ7FIpzbR0WzEPYPjcc/geDgcAofOXMD248XYfrwE24+X4EBROU4WV+FkcRUy9xTWO7ZTRBCCHRpsrN6FhHYmxEUEo1O7YMSGB6NjqBFhwTq+QRKp6I033sBrr72G/Px89OvXD4sXL8ZNN92kdlitFm7S43c3d8OMkYn4em8hVmw5hi2HzyEnrxg5ecUAjgIAosxGXJsQgcSOIYiva5/iIoLRKSIY5iC9ukkQkd9ikU5tTqNRkBRtRlK0GfcP7QwAKK+2YufJUhwoLMehMxdwsPACDhVdwLmKGpwqqQagwaHtpxs9n06jIDLEgMgQAzqEGtEuxABzkA5mow7mIB1CjTqYg/QIMeoQpNcgWK9FsEGLIL0WwXotjDoN9FoNdFoFeq0GBq0GGg2LfqLm+PDDDzFnzhy88cYbuPHGG/HWW29h3Lhx2LNnDzp37qx2eB6h1ShI6ReDlH4xyDtXgexjxdhxoraTYV9BOYrKLci4rHPByRykQ/sQA8JNBkQE6xFh0iMiWI/wYD1MRh1Mhtp2yGSo+9mghUFX2w4F6TUwaLVQYMcFK1BWZUWwUKDVKNBr2E4RyY5FOvkEc5AeI3p0wIgeHeptP3fBggMFpfh841ZEde2FgvIanCqpwumSKuSXVKPcYoPNIVBUbkFRuQWAZ5b21mpq3wh1GgVaRYFWW/uzRqndrqnruddoAI1S+1gBgLr3TAW1Q35qv188r4KLDy7v/BdCoKxcizeObPHaJwNNnbepq9WLvYk8mty/qScACOFAaYkW/zixrdGYGguz6Rjd+115u6x5ffKggBqzvGjRIjz88MP47W9/CwBYvHgxvvzySyxduhTp6ekqR+d5XdqHoEv7ENwzOB4AUFVjx67Tpfj5RAlOFlfhVEkVThVX4XRpFUoqrSivtqG82gaca+0aEjrMy/m23haNAug0Gmg0gFZRoLmk3XK2Sxql9t+Is61SUPsdSv3H9f+tX2y7FFebVruPcnGni/vj0mMbj765/36FECgu1uKfp36U/hNSIQTOM1e/NrZvNB4Z1d1r52eRTj6tfagRQ7q0Q1FHgfGjukGvr//RscVmx/mKGpy7UINzFTU4X2HB+QorLlTbUF5d+wZ5wWJDWbUVFRYbqq0OVNvsqK6xo9rmQFWNHRabHZcvmGp3CNgdAjVtmGstBfmVF9r8qupQkHdBvtUdLVa72iG0mZqaGuTm5uLZZ5+ttz0lJQVbtmxp9BiLxQKLxeJ6XFZWBgCwWq2wWq3NvrZzX3eO8QadAlzbyYxrO5kbPHfBYkNBaTVKq6woqbKitMqK0iobSiprf6602lFVU/tVabWjssaGqhoHauwOWG0OWGy1P9fYHLA1sqqzQwA1dgcg3UtOwdHyErWDaCPM1Z9172iq1wY1p11yp81ikU5+zajTIja8dnx6a9gdAla7o+5L1L0pOuBwoPa7ELDX/SwE4BACDlHbO+Coe+ycTlkIAQFACKD2pzqN/+his9mwbduPuH7Y9dBpPf9PUzR6VaCpaaBFvX1Eo9ubOuDSazV2fpvdjpzsHAweMrhBro2dv6m5qpuKxXNTW7t/oqiwIE9d3OedPXsWdrsd0dHR9bZHR0ejoKCg0WPS09Mxf/78BtszMjJgMpncjiEzM9PtY9QSVPcVDQDauq9mvlxq2xnAXvfluOS76wuoa59qX7nissfO73A9V9uj6XBuQP3nL91Wrz1A4w+a/PfY1HZOQU9+LtKSh88/z2uw/UrtUmVl8z9VY5FOBOfwFq2q8yBbrVaU7Be4sXv7Bp8YyMZqtaL6sMCtvaOkzzUQNDZkoamPtOfOnYvU1FTX47KyMiQkJCAlJQVhYWHNvqbVakVmZiaSk5Olfw05c70tJXByDaS/K3OVR3PydH562Bws0omIqEU6dOgArVbboNe8qKioQe+6k9FohNHYcE0EvV7fojfvlh7nj5irnJirfK6Upzv5e3zJx/T0dAwdOhRmsxlRUVG48847sX//fk9fhoiIVGYwGDB48OAGH+1mZmZixIgRKkVFRCQHjxfpWVlZmD17NrZu3YrMzEzYbDakpKSgoqLC05ciIiKVpaam4t1338U//vEP7N27F08++SSOHz+ORx55RO3QiIj8mseHu2zYsKHe4+XLlyMqKgq5ubm4+eabPX05IiJS0f33349z587hxRdfRH5+Pvr374/PP/8cXbp0UTs0IiK/5vUx6aWltVOsRUZGNvq8p6bjch5z6XeZMVf5BEqeAHNtah9/NWvWLMyaNUvtMIiIpOLVIl0IgdTUVIwcORL9+/dvdB9PT8cF+NeUXK3FXOUTKHkCzNXJnSm5iIgoMHi1SH/00Ufxyy+/4LvvvmtyH09NxwUEzhQ/AHOVUaDkCTDXy7kzJRcREQUGrxXpjz32GD799FNs2rQJ8fHxTe7n6em4Wnusv2Gu8gmUPAHmeulzREREl/J4kS6EwGOPPYZ169Zh48aNSExM9PQliIiIiIik5vEiffbs2Vi9ejU++eQTmM1m1yIX4eHhCA5u3dLtRERERESBwONF+tKlSwEAo0ePrrd9+fLleOihh656vBACQMvGaFqtVlRWVqKsrEz6j4+Zq3wCJU+AuV7O2d45279A0tI2n68hOTFXOQVKrp5u770y3KU1ysvLAQAJCQmeCIeIyG+Ul5cjPDxc7TDaFNt8IgpEzWnvFeFjXTcOhwOnT5+G2WyGoihuHeucGebEiRNuzwzjb5irfAIlT4C5Xk4IgfLycsTFxUGj8fhC0D6tpW0+X0NyYq5yCpRcPd3ee30xI3dpNJorzgbTHGFhYVK/CC7FXOUTKHkCzPVSgdaD7tTaNp+vITkxVzkFSq6eau8Dq8uGiIiIiMgPsEgnIiIiIvIxUhXpRqMRL7zwQqOLI8mGuconUPIEmCu1XiD9XpmrnJirfDydp8/dOEpEREREFOik6kknIiIiIpIBi3QiIiIiIh/DIp2IiIiIyMewSCciIiIi8jEs0omIiIiIfIw0Rfobb7yBxMREBAUFYfDgwdi8ebPaIbXapk2bMGHCBMTFxUFRFKxfv77e80IIpKWlIS4uDsHBwRg9ejR2796tTrCtlJ6ejqFDh8JsNiMqKgp33nkn9u/fX28fWfJdunQpBgwY4FqRbPjw4fjiiy9cz8uS5+XS09OhKArmzJnj2iZLrmlpaVAUpd5XTEyM63lZ8vQlbPP993XE9p7tvb/n2lZtvhRF+ocffog5c+Zg3rx52L59O2666SaMGzcOx48fVzu0VqmoqMDAgQOxZMmSRp9fuHAhFi1ahCVLliA7OxsxMTFITk5GeXl5G0faellZWZg9eza2bt2KzMxM2Gw2pKSkoKKiwrWPLPnGx8fjlVdeQU5ODnJycnDLLbdg4sSJrn/AsuR5qezsbLz99tsYMGBAve0y5dqvXz/k5+e7vnbu3Ol6TqY8fQHbfP9+HbG9Z3svQ65t0uYLCVx//fXikUceqbetd+/e4tlnn1UpIs8DINatW+d67HA4RExMjHjllVdc26qrq0V4eLh48803VYjQs4qKigQAkZWVJYSQP9927dqJd999V8o8y8vLRc+ePUVmZqYYNWqUeOKJJ4QQcv1NX3jhBTFw4MBGn5MpT1/BNr+WLK8jtvfy5BkI7b0Qbdfm+31Pek1NDXJzc5GSklJve0pKCrZs2aJSVN539OhRFBQU1MvbaDRi1KhRUuRdWloKAIiMjAQgb752ux1r1qxBRUUFhg8fLmWes2fPxu23346xY8fW2y5brgcPHkRcXBwSExPx61//GkeOHAEgX55qY5sv3+uI7b08eQZKew+0TZuv82jEKjh79izsdjuio6PrbY+OjkZBQYFKUXmfM7fG8s7Ly1MjJI8RQiA1NRUjR45E//79AciX786dOzF8+HBUV1cjNDQU69atQ9++fV3/gGXJc82aNcjNzUVOTk6D52T6mw4bNgz//Oc/kZSUhMLCQrz00ksYMWIEdu/eLVWevoBtvlyvI7b38uQZKO090HZtvt8X6U6KotR7LIRosE1GMub96KOP4pdffsF3333X4DlZ8u3Vqxd27NiBkpISrF27FtOmTUNWVpbreRnyPHHiBJ544glkZGQgKCioyf1kyHXcuHGun6+55hoMHz4c3bt3x8qVK3HDDTcAkCNPXxKov0/Z8mZ7L0eegdTeA23X5vv9cJcOHTpAq9U26EEpKipq8L8YmTjvIpYt78ceewyffvopvv32W8THx7u2y5avwWBAjx49MGTIEKSnp2PgwIF4/fXXpcozNzcXRUVFGDx4MHQ6HXQ6HbKysvDXv/4VOp3OlY8MuV4uJCQE11xzDQ4ePCjV39QXsM2XJ2+29/LkGcjtPeC9Nt/vi3SDwYDBgwcjMzOz3vbMzEyMGDFCpai8LzExETExMfXyrqmpQVZWll/mLYTAo48+io8//hjffPMNEhMT6z0vW76XE0LAYrFIleett96KnTt3YseOHa6vIUOGYOrUqdixYwe6desmTa6Xs1gs2Lt3L2JjY6X6m/oCtvn+/zpie8/2HvDfXBvjtTbfrdtMfdSaNWuEXq8Xy5YtE3v27BFz5swRISEh4tixY2qH1irl5eVi+/btYvv27QKAWLRokdi+fbvIy8sTQgjxyiuviPDwcPHxxx+LnTt3ismTJ4vY2FhRVlamcuTu+8Mf/iDCw8PFxo0bRX5+vuursrLStY8s+c6dO1ds2rRJHD16VPzyyy/iueeeExqNRmRkZAgh5MmzMZfe7S+EPLn+13/9l9i4caM4cuSI2Lp1q7jjjjuE2Wx2tUGy5Okr2Ob79+uI7T3be3/Pta3afCmKdCGE+Pvf/y66dOkiDAaDuO6661xTOfmzb7/9VgBo8DVt2jQhRO00Py+88IKIiYkRRqNR3HzzzWLnzp3qBt1CjeUJQCxfvty1jyz5zpgxw/Va7dixo7j11ltdDbYQ8uTZmMsbbVlyvf/++0VsbKzQ6/UiLi5OTJo0Sezevdv1vCx5+hK2+f77OmJ7z/be33NtqzZfEUKIFvbuExERERGRF/j9mHQiIiIiItmwSCciIiIi8jEs0omIiIiIfAyLdCIiIiIiH8MinYiIiIjIx7BIJyIiIiLyMSzSiYiIiIh8DIt0IiIiIiIfwyKdiIiIiMjHsEgnIiIiIvIxLNKJiIiIiHzM/wcAzYEL3SSOfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = np.diag([500., 49.])\n",
    "Ms, Ps = run(count=50, R=10, Q=0.01, P=P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is still a lot to learn, but we have implemented a Kalman filter using the same theory and equations as published by Rudolf Kalman! Code very much like this runs inside of your GPS, airliners, 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 (labelled *Track*). 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 $\\dot x$. 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 we quickly converge to small variances for both. \n",
    "\n",
    "The covariance matrix $\\mathbf P$ tells us the *theoretical* performance of the filter *assuming* everything we tell it is true. Recall that the standard deviation is the square root of the variance, and that approximately 68% of a Gaussian distribution occurs within one standard deviation. If at least 68% of the filter output is within one standard deviation  the filter may be 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.\n",
    "\n",
    "In the univariate 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 filters with this code merely by altering our 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 acceleration in 3D space. We can do that with the code in this chapter.\n",
    "\n",
    "I want you to get a better feel for how the Gaussians change over time, so here is a 3D plot showing the Gaussians every 7th epoch (time step). Every 7th separates them enough so can see each one independently. The first Gaussian at $t=0$ is to the left."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.book_plots import set_figsize, figsize\n",
    "from kf_book.nonlinear_plots import plot_gaussians\n",
    "\n",
    "P = np.diag([3., 1.])\n",
    "np.random.seed(3)\n",
    "Ms, Ps = run(count=25, R=10, Q=0.01, P=P, do_plot=False)\n",
    "with figsize(x=9, y=5):\n",
    "    plot_gaussians(Ms[::7], Ps[::7], (-5,25), (-5, 5), 75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Saver Class\n",
    "\n",
    "In the `run()` method I wrote boilerplate code to save the results of the filter\n",
    "```python\n",
    "    xs, cov = [], []\n",
    "    for z in zs:\n",
    "        kf.predict()\n",
    "        kf.update(z)\n",
    "        xs.append(kf.x)\n",
    "        cov.append(kf.P)\n",
    "\n",
    "    xs, cov = np.array(xs), np.array(cov)\n",
    "```\n",
    "\n",
    "There's an easy way to avoid this. `filtery.common` provides the `Saver` class which will save all attributes in the Kalman filter class each time `Saver.save()` is called. Let's see it in action and then we will talk about it more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.common import Saver\n",
    "kf = pos_vel_filter([0, .1], R=R, P=P, Q=Q, dt=1.) \n",
    "s = Saver(kf)\n",
    "for i in range(1, 6):\n",
    "    kf.predict()\n",
    "    kf.update([i])\n",
    "    s.save()  # save the current state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Saver` object now contains lists of all the attributes of the KalmanFilter object. `kf.x` is the current state estimate of the filter. Therefore `s.x` contains the saved state estimate that was computed inside the loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0.531, 0.304]),\n",
       " array([1.555, 0.763]),\n",
       " array([2.784, 1.036]),\n",
       " array([3.944, 1.105]),\n",
       " array([5.015, 1.086])]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see all the available attributes with the `keys` attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['alpha',\n",
       " 'likelihood',\n",
       " 'log_likelihood',\n",
       " 'mahalanobis',\n",
       " 'dim_x',\n",
       " 'dim_z',\n",
       " 'dim_u',\n",
       " 'x',\n",
       " 'P',\n",
       " 'Q',\n",
       " 'B',\n",
       " 'F',\n",
       " 'H',\n",
       " 'R',\n",
       " '_alpha_sq',\n",
       " 'M',\n",
       " 'z',\n",
       " 'K',\n",
       " 'y',\n",
       " 'S',\n",
       " 'SI',\n",
       " '_I',\n",
       " 'x_prior',\n",
       " 'P_prior',\n",
       " 'x_post',\n",
       " 'P_post',\n",
       " '_log_likelihood',\n",
       " '_likelihood',\n",
       " '_mahalanobis',\n",
       " 'inv']"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.keys"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many attributes there that we haven't discussed yet, but many should be familar.\n",
    "\n",
    "At this point you could write code to plot any of these variables. However, it is often more useful to use `np.array` instead of lists. Calling `Saver.to_array()` will convert the lists into `np.array`. There is one caveat: if the shape of any of the attributes changes during the run, the `to_array` will raise an exception since `np.array` requires all of the elements to be of the same type and size. \n",
    "\n",
    "If you look at the keys again you'll see that `z` is one of the choices. This is promising; apparently the measurement `z` is saved for us. Let's plot it against the estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "s.to_array()\n",
    "book_plots.plot_measurements(s.z);\n",
    "plt.plot(s.x[:, 0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While I've demonstrated this with the `KalmanFilter` class, it will work with all filter classes implemented by `FilterPy`. It will probably work with any class you write as well, as it inspects the object to retrieve the attribute names. We will use this class throughout the book to keep the code readable and short. Using the `Saver` will slow down your code because a lot happens behind the scenes, but for learning and exploring the convience cannot be beat."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Kalman Filter Equations\n",
    "\n",
    "We are now ready to learn how `predict()` and `update()` perform their computations. \n",
    "\n",
    "A word about notation. I'm a programmer, and I am used to code that reads\n",
    "\n",
    "```python\n",
    "x = x + 1\n",
    "``` \n",
    "\n",
    "That is not an equation as the sides are not equal, but an *assignment*. If we wanted to write this in mathematical notation we'd write\n",
    "$$x_k = x_{k-1} + 1$$\n",
    "\n",
    "Kalman filter equations are littered with subscripts and superscripts to keep the equations mathematically consistent. I find this makes them extremely hard to read. In most of the book I opt for subscriptless assignments. As a programmer you should understand that I am showing you assignments which implement an algorithm that is to be executed step by step. I'll elaborate on this once we have a concrete example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction Equations\n",
    "\n",
    "The Kalman filter uses these equations to compute the *prior* - the predicted next state of the system. They compute the prior mean ($\\bar{\\mathbf x}$)  and covariance ($\\bar{\\mathbf P}$) of the system.\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{\\bar x} &= \\mathbf{Fx} + \\mathbf{Bu}\\\\\n",
    "\\mathbf{\\bar P} &= \\mathbf{FPF}^\\mathsf T + \\mathbf Q\n",
    "\\end{aligned}$$\n",
    "\n",
    "$\\underline{\\textbf{Mean}}$\n",
    "\n",
    "$\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu}$\n",
    "\n",
    "As a reminder, the linear equation $\\mathbf{Ax} = \\mathbf b$ represents a system of equations, where $\\mathbf A$ holds the coefficients set of equations, $\\mathbf x$ is the vector of variables. Performing the multiplication $\\mathbf{Ax}$ computes the right hand side values for that set of equations, represented by $\\mathbf b$.\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. Thus, the prior $\\mathbf{\\bar x}$ is computed as the sum of $\\mathbf{Fx}$ and $\\mathbf{Bu}$.\n",
    "\n",
    "The equivalent univariate equation is\n",
    "\n",
    "$$\\bar\\mu = \\mu + \\mu_{move}$$\n",
    "\n",
    "If you perform the matrix multiplication $\\mathbf{Fx}$ it generates this equation for $x$.\n",
    "\n",
    "Let's make this explicit. Recall the value for $\\mathbf F$ from the last chapter:\n",
    "\n",
    "$$\\mathbf F = \\begin{bmatrix}1&\\Delta t  \\\\ 0&1\\end{bmatrix}$$\n",
    "\n",
    "Thus $\\mathbf{\\bar x} = \\mathbf{Fx}$ corresponds to the set of linear equations:\n",
    "\n",
    "$$\\begin{cases}\n",
    "\\begin{aligned}\n",
    "\\bar x &= 1x + &\\Delta t\\, \\dot x \\\\\n",
    "\\bar{\\dot x} &=0x + &1\\, \\dot x\n",
    "\\end{aligned}\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\underline{\\textbf{Covariance}}$\n",
    "\n",
    "$\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q$\n",
    "\n",
    "This equation is not as easy to understand so we will spend more time on it. \n",
    "\n",
    "In univariate version of this equation is:\n",
    "\n",
    "$$\\bar\\sigma^2 = \\sigma^2 + \\sigma^2_{move}$$\n",
    "\n",
    "We add the variance of the movement 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",
    "We can't simply write $\\mathbf{\\bar P} = \\mathbf P + \\mathbf Q$. 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",
    "$$\\bar x = \\dot x\\Delta t + x$$\n",
    "\n",
    "Since we do not have perfect knowledge of the value of $\\dot x$ the sum $\\bar x = \\dot x\\Delta t + x$ gains uncertainty. Because the positions and velocities are correlated we cannot simply add the covariance matrices. For example, if $\\mathbf P$ and $\\mathbf Q$ are diagonal matrices the sum would also be diagonal. But we know position is correlated to velocity so the off-diagonal elements should be non-zero. \n",
    "\n",
    "The correct equation is\n",
    "\n",
    "$$\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q$$\n",
    "\n",
    "Expressions in the form $\\mathbf{ABA}^\\mathsf T$ are common 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 admit this may be a 'magical' equation to you. Let's explore it.\n",
    "\n",
    "When we initialize $\\mathbf P$ with\n",
    "\n",
    "$$\\mathbf P = \\begin{bmatrix}\\sigma^2_x & 0 \\\\ 0 & \\sigma^2_v\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "the value for $\\mathbf{FPF}^\\mathsf T$ is:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{FPF}^\\mathsf T &= \\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\n",
    "\\begin{bmatrix}\\sigma^2_x & 0 \\\\  0 & \\sigma^2_{v}\\end{bmatrix}\n",
    "\\begin{bmatrix}1&0\\\\\\Delta t&1\\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix}\\sigma^2_x&\\sigma_v^2\\Delta t\\\\  0 & \\sigma^2_{v}\\end{bmatrix}\n",
    "\\begin{bmatrix}1&0\\\\\\Delta t&1\\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix}\\sigma^2_x +  \\sigma_v^2\\Delta t^2  &  \\sigma_v^2\\Delta t \\\\\n",
    "\\sigma_v^2\\Delta t & \\sigma^2_{v}\\end{bmatrix}\n",
    "\\end{aligned}$$\n",
    "\n",
    "The initial value for $\\mathbf P$ had no covariance between the position and velocity.  Position is computed as $\\dot x\\Delta t + x$, so there is a correlation between the position and velocity. The multiplication $\\mathbf{FPF}^\\mathsf T$ computes a covariance of $\\sigma_v^2 \\Delta t$. The exact value is not important; you just need to recognize that $\\mathbf{FPF}^\\mathsf T$ uses the process model to automatically compute the covariance between the position and velocity!\n",
    "\n",
    "Another way to think of this is to reflect on the $\\mathbf{Fx}$ multiplication. That projected $\\mathbf x$ forward in time. $\\mathbf {FP}$ might seem to be the equivalent operation, but $\\mathbf P$ is a matrix while $\\mathbf x$ is a vector. The trailing $\\mathbf F^\\mathsf T$ term ensures that we multiply by both the rows and columns of $\\mathbf F$. In the second line of the computation of $\\mathbf{FPF}^\\mathsf T$ we have the value for $\\mathbf{FP}$. You can see that it is an upper triangular matrix because we haven't fully incorporated $\\mathbf F$ into the multiplication.\n",
    "\n",
    "If you have some experience with linear algebra and statistics, this may help. The covariance due to the prediction can be modeled as the expected value of the error in the prediction step, given by this equation. \n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx - \\bar \\mu})(\\mathbf{Fx - \\bar\\mu})^\\mathsf T]\\\\\n",
    " &= \\mathbf F\\, \\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n",
    "\\end{aligned}$$\n",
    "\n",
    "Of course, $\\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]$ is just $\\mathbf P$, giving us\n",
    "\n",
    "$$\\bar{\\mathbf P} = \\mathbf{FPF}^\\mathsf T$$\n",
    "\n",
    "Let's 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 $\\mathbf{\\bar P}$ continues to change. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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 = F @ x\n",
    "    P = F @ P @ 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 about the position due to adding $\\dot x\\Delta t$ to x at each step. The height has not changed - our system model says 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 $\\bar x = \\dot x \\Delta t + x$. 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": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a828518321f448be916ab551fe70519e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, continuous_update=False, description='F00', max=2), FloatSlider(value…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "from kf_book.book_plots import IntSlider, FloatSlider\n",
    "\n",
    "def plot_FPFT(F00, F01, F10, F11, covar):   \n",
    "    plt.figure()\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, F @ P @ F.T, ec='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=IntSlider(value=1, min=0, max=2), \n",
    "         F01=FloatSlider(value=1, min=0, max=2, description='F01(dt)'),\n",
    "         F10=FloatSlider(value=0, min=0, max=2),\n",
    "         F11=FloatSlider(value=1, min=0, max=2),\n",
    "         covar=FloatSlider(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: https://git.io/vza7b). Or, go to binder using the link below, and open this notebook from there.\n",
    "\n",
    "http://mybinder.org/repo/rlabbe/Kalman-and-Bayesian-Filters-in-Python"
   ]
  },
  {
   "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 measurements are not *invertible*. For example, consider a  sensor that gives 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:\n",
    "<img src=\"./figs/residual_chart.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equations will be complicated because the state has multiple dimensions, but this operations is what we are doing. Don't let the equations distract you from the simplicity of this idea.\n",
    "\n",
    "$\\underline{\\textbf{System Uncertainty}}$\n",
    "\n",
    "$\\textbf{S} = \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R$\n",
    "\n",
    "To work in measurement space the Kalman filter has to project the covariance matrix into measurement space. The math for this is $\\mathbf{H\\bar PH}^\\mathsf T$, where $\\mathbf{\\bar P}$ 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. The linear algebra is changing the coordinate system for us. \n",
    "\n",
    "Once the covariance 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 the *system uncertainty* or *innovation covariance*.\n",
    "\n",
    "If you ignore the $\\mathbf H$ term this equation is the equivalent to the denominator in the univariate equation for the Kalman gain:\n",
    "\n",
    "$$K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2}$$\n",
    "\n",
    "Compare the equations for the system uncertainty and the covariance\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{S} &= \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R\\\\\n",
    "\\mathbf{\\bar P} &= \\mathbf{FPF}^\\mathsf T + \\mathbf Q\n",
    "\\end{aligned}$$\n",
    "\n",
    "In each equation $\\mathbf P$ is put into a different space with either the function $\\mathbf H$ or $\\mathbf F$. Then we add the noise matrix associated with that space.\n",
    "\n",
    "$\\underline{\\textbf{Kalman Gain}}$\n",
    "\n",
    "$\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}$\n",
    "\n",
    "Look back at the residual diagram. 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",
    "$$\n",
    "\\mu =\\frac{\\bar\\sigma^2 \\mu_z + \\sigma_\\mathtt{z}^2 \\bar\\mu} {\\bar\\sigma^2 + \\sigma_\\mathtt{z}^2}$$\n",
    "\n",
    "which we simplified to\n",
    "\n",
    "$$\\mu = (1-K)\\bar\\mu + K\\mu_\\mathtt{z}$$\n",
    "\n",
    "which gave us\n",
    "\n",
    "$$K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2}$$\n",
    "\n",
    "$K$ is the *Kalman gain*, and it is a real number between 0 and 1. Ensure you understand how it selects a mean somewhere between the prediction and measurement. The Kalman gain is 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: $\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of finding the reciprocal. 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",
    "$$\\begin{aligned} \\mathbf K &\\approx \\frac{\\mathbf{\\bar P}\\mathbf H^\\mathsf T}{\\mathbf{S}} \\\\\n",
    "\\mathbf K &\\approx \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{prediction} + \\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\n",
    "\\end{aligned}$$\n",
    "\n",
    "The Kalman gain equation computes a ratio based on how much we trust the prediction vs the measurement. We did the same thing in every prior chapter. The equation is complicated because we are doing this in multiple dimensions via matrices, but the concept is simple. The $\\mathbf H^\\mathsf T$ term is less clear, I'll explain it soon. If you ignore that term the equation for the Kalman gain is the same as the univariate case: divide the uncertainty of the prior with the of the sum of the uncertainty of the prior and measurement.\n",
    "\n",
    "$\\underline{\\textbf{Residual}}$\n",
    "\n",
    "$\\mathbf y = \\mathbf z - \\mathbf{H\\bar{x}}$\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",
    "The univariate equation is\n",
    "\n",
    "$$y = z - \\bar x$$\n",
    "\n",
    "and clearly computes the same thing, but only in one dimension.\n",
    "\n",
    "$\\underline{\\textbf{State Update}}$\n",
    "\n",
    "$\\mathbf x = \\mathbf{\\bar x} + \\mathbf{Ky}$\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 both scales the residual and converts it back into state space with the $\\mathbf H^\\mathsf T$ term which is in $\\mathbf K$. This is added to the prior, yielding the equation: $\\mathbf x =\\mathbf{\\bar x} + \\mathbf{Ky}$. Let me write out $\\mathbf K$ so we can see the entire computation:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf x &= \\mathbf{\\bar x} + \\mathbf{Ky} \\\\\n",
    "&= \\mathbf{\\bar x} + \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}\\mathbf y \\\\\n",
    "&\\approx \\mathbf{\\bar x} + \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\\mathbf y\n",
    "\\end{aligned}$$\n",
    "\n",
    "Perhaps a better way to *see* the ratio is to rewrite the estimate equation:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf x &= \\mathbf{\\bar x} + \\mathbf{Ky} \\\\\n",
    "&= \\mathbf{\\bar x} +\\mathbf K(\\mathbf z - \\mathbf{H\\bar x}) \\\\\n",
    "&= (\\mathbf I - \\mathbf{KH})\\mathbf{\\bar x} + \\mathbf{Kz}\n",
    "\\end{aligned}$$\n",
    "\n",
    "The similarity between this and the univariate form should be obvious:\n",
    "$$\\mu = (1-K)\\bar\\mu + K\\mu_\\mathtt{z}$$\n",
    "\n",
    "$\\underline{\\textbf{Covariance Update}}$\n",
    "\n",
    "$\\mathbf P = (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar P}$\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.  We can think of the equation as $\\mathbf P = (1-c\\mathbf K)\\mathbf P$. $\\mathbf K$ is our ratio of how much prediction vs measurement we use. 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 relatively larger. This means that we adjust the size of our uncertainty by some factor of the Kalman gain.\n",
    "\n",
    "This equation can be numerically unstable and I don't use it in FilterPy. The subtraction can destroy symmetry and lead to floating point errors over time. Later I'll share more complicated but numerically stable forms of this equation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An Example not using FilterPy\n",
    "\n",
    "FilterPy hides the details of the implementation from us. Normally you will appreciate this, but let's implement the last filter without FilterPy. To do so we need to define our matrices as variables, and then implement the Kalman filter equations explicitly.\n",
    "\n",
    "Here we initialize our matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 1.\n",
    "R_var = 10\n",
    "Q_var = 0.01\n",
    "x = np.array([[10.0, 4.5]]).T\n",
    "P = np.diag([500, 49])\n",
    "F = np.array([[1, dt],\n",
    "              [0,  1]])\n",
    "H = np.array([[1., 0.]])\n",
    "R = np.array([[R_var]])\n",
    "Q = Q_discrete_white_noise(dim=2, dt=dt, var=Q_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.linalg import inv\n",
    "\n",
    "count = 50\n",
    "track, zs = compute_dog_data(R_var, Q_var, count)\n",
    "xs, cov = [], []\n",
    "for z in zs:\n",
    "    # predict\n",
    "    x = F @ x\n",
    "    P = F @ P @ F.T + Q\n",
    "    \n",
    "    #update\n",
    "    S = H @ P @ H.T + R\n",
    "    K = P @ H.T @ inv(S)\n",
    "    y = z - H @ x\n",
    "    x += K @ y\n",
    "    P = P - K @ H @ P\n",
    "    \n",
    "    xs.append(x)\n",
    "    cov.append(P)\n",
    "\n",
    "xs, cov = np.array(xs), np.array(cov)\n",
    "plot_track(xs[:, 0], track, zs, cov, plot_P=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are identical to the FilterPy version. Which you prefer is up to you. I prefer not polluting my namespace with variables such as `x`, `P`, and so on; `dog_filter.x` is, to me, more readable.\n",
    "\n",
    "More importantly, this example requires you to remember and program the equations for the Kalman filter. Sooner or later you will make a mistake. FilterPy's version ensures that your code will be correct. On the other hand, if you make a mistake in your definitions, such as making $\\mathbf H$ a column vector instead of a row vector, FilterPy's error message will be harder to debug than this explicit code. \n",
    "\n",
    "FilterPy's KalmanFilter class provides additional functionality such as smoothing, batch processing, faded memory filtering, computation of the maximum likelihood function, and more. You get all of this functionality without having to explicitly program it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 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 multidimensional implementation of it.\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\text{Predict Step}\\\\\n",
    "\\mathbf{\\bar x} &= \\mathbf{F x} + \\mathbf{B u} \\\\\n",
    "\\mathbf{\\bar P} &= \\mathbf{FP{F}}^\\mathsf T + \\mathbf Q \\\\\n",
    "\\\\\n",
    "\\text{Update Step}\\\\\n",
    "\\textbf{S} &= \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R \\\\\n",
    "\\mathbf K &= \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1} \\\\\n",
    "\\textbf{y} &= \\mathbf z - \\mathbf{H \\bar x} \\\\\n",
    "\\mathbf x &=\\mathbf{\\bar x} +\\mathbf{K\\textbf{y}} \\\\\n",
    "\\mathbf P &= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar P}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "I want to share a form of the equations that you will see in the literature. There are many different notation systems used, 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",
    "This notation uses the Bayesian $a\\mid b$ notation, which means $a$ given the evidence of $b$. The hat means estimate. Thus $\\hat{\\mathbf x}_{k\\mid k}$ means the estimate of the state $\\mathbf x$ at step $k$ (the first k) given the evidence from step $k$ (the second k). The posterior, in other words. $\\hat{\\mathbf x}_{k\\mid k-1}$ means the estimate for the state $\\mathbf x$ at step $k$ given the estimate from step $k - 1$. The prior, in other words. \n",
    "\n",
    "This notation, copied from [Wikipedia](https://en.wikipedia.org/wiki/Kalman_filter#Details) [[1]](#[wiki_article]), allows a mathematician to express himself exactly. In formal publications presenting new results this precision is necessary. As a programmer I find it 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 in the literature, so each author makes different choices. I find it challenging to switch quickly between books and papers, and so have adopted my admittedly less precise notation. Mathematicians may write scathing emails to me, but I hope programmers and students will rejoice at my simplified notation.\n",
    "\n",
    "The **Symbology** Appendix 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. For example, it is common to use $\\mathbf{A}$ for what I call $\\mathbf F$. You must 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 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 velocity is a 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 $\\mathbf x=\\begin{bmatrix}x\\end{bmatrix}$ and compare it against a filter that uses $\\mathbf x=\\begin{bmatrix}x & \\dot x\\end{bmatrix}^\\mathsf T$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "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": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import sqrt\n",
    "from numpy.random import randn\n",
    "\n",
    "def univariate_filter(x0, P, R, Q):\n",
    "    f = KalmanFilter(dim_x=1, dim_z=1, dim_u=1)\n",
    "    f.x = np.array([[x0]])\n",
    "    f.P *= P\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_1d_2d(xs, xs1d, xs2d):\n",
    "    plt.plot(xs1d, label='1D Filter')\n",
    "    plt.scatter(range(len(xs2d)), xs2d, c='r', alpha=0.7, label='2D Filter')\n",
    "    plt.plot(xs, ls='--', color='k', lw=1, label='track')\n",
    "    plt.title('State')\n",
    "    plt.legend(loc=4)\n",
    "    plt.show()\n",
    "    \n",
    "def compare_1D_2D(x0, P, R, Q, vel, u=None):\n",
    "    # storage for filter output\n",
    "    xs, xs1, xs2 = [], [], []\n",
    "\n",
    "    # 1d KalmanFilter\n",
    "    f1D = univariate_filter(x0, P, R, Q)\n",
    "\n",
    "    #2D Kalman filter\n",
    "    f2D = pos_vel_filter(x=(x0, vel), P=P, R=R, Q=0)\n",
    "    if np.isscalar(u):\n",
    "        u = [u]\n",
    "    pos = 0 # true position\n",
    "    for i in range(100):\n",
    "        pos += vel\n",
    "        xs.append(pos)\n",
    "\n",
    "        # control input u - discussed below\n",
    "        f1D.predict(u=u)\n",
    "        f2D.predict()\n",
    "        \n",
    "        z = pos + randn()*sqrt(R) # measurement\n",
    "        f1D.update(z)\n",
    "        f2D.update(z)\n",
    "        \n",
    "        xs1.append(f1D.x[0])\n",
    "        xs2.append(f2D.x[0])\n",
    "    plt.figure()\n",
    "    plot_1d_2d(xs, xs1, xs2)\n",
    "\n",
    "compare_1D_2D(x0=0, P=50., R=5., Q=.02, vel=1.) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "The filter that incorporates velocity into the state produces much better estimates than the filter that only tracks position. The univariate filter has no way to estimate the velocity or change in position, so it lags the tracked object. \n",
    "\n",
    "In the univarate Kalman filter chapter we had a control input `u` to the predict equation:\n",
    "\n",
    "```python\n",
    "    def predict(self, u=0.0):\n",
    "        self.x += u\n",
    "        self.P += self.Q\n",
    "```\n",
    "\n",
    "Let's try specifying the control input:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_1D_2D(x0=0, P=50., R=5., Q=.02, vel=1., u=1.) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the performance of the two filters are similar, and perhaps the univariate filter is tracking more cloesly. But let's see what happens when the actual velocity `vel` is different from the control input `u`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_1D_2D(x0=0, P=50., R=5., Q=.02, vel=-2., u=1.) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we are tracking a robot which we are also controlling the univariate filter can do a very good job because the control input allows the filter to make an accurate prediction. But if we are tracking passively the control input is not much help unless we can make an accurate *apriori* guess as to the velocity. This is rarely possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How Velocity is Calculated\n",
    "\n",
    "I haven't explained how the filter computes the velocity, or any hidden variable. If we plug in the values we calculated for each of the filter's matrices we can see what happens.\n",
    "\n",
    "First we need to compute the system uncertainty.\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\textbf{S} &= \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R \\\\\n",
    "&= \\begin{bmatrix} 1 & 0\\end{bmatrix}\n",
    "\\begin{bmatrix}\\sigma^2_x & \\sigma_{xv} \\\\ \\sigma_{xv} & \\sigma^2_v\\end{bmatrix}\n",
    "\\begin{bmatrix} 1 \\\\ 0\\end{bmatrix} + \\begin{bmatrix}\\sigma_z^2\\end{bmatrix}\\\\\n",
    "&= \\begin{bmatrix}\\sigma_x^2 & \\sigma_{xv}\\end{bmatrix}\\begin{bmatrix} 1 \\\\ 0\\end{bmatrix}+ \\begin{bmatrix}\\sigma_z^2\\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix}\\sigma_x^2 +\\sigma_z^2\\end{bmatrix}\n",
    "\\end{aligned}$$\n",
    "\n",
    "Now that we have $\\mathbf S$ we can find the value for the Kalman gain:\n",
    "$$\\begin{aligned}\n",
    "\\mathbf K &= \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1} \\\\\n",
    "&= \\begin{bmatrix}\\sigma^2_x & \\sigma_{xv} \\\\ \\sigma_{xv} & \\sigma^2_v\\end{bmatrix}\n",
    "\\begin{bmatrix} 1 \\\\ 0\\end{bmatrix}\n",
    "\\begin{bmatrix}\\frac{1}{\\sigma_x^2 +\\sigma_z^2}\\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix}\\sigma^2_x  \\\\ \\sigma_{xv}\\end{bmatrix}\n",
    "\\begin{bmatrix}\\frac{1}{\\sigma_x^2 +\\sigma_z^2}\\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix}\\sigma^2_x/(\\sigma_x^2 +\\sigma_z^2)  \\\\ \\sigma_{xv}/(\\sigma_x^2 +\\sigma_z^2)\\end{bmatrix}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In other words, the Kalman gain for $x$ is \n",
    "\n",
    "$$K_x = \\frac{VAR(x)}{VAR(x)+VAR(z)}$$\n",
    "\n",
    "This should be very familiar to you from the univariate case. \n",
    "\n",
    "The Kalman gain for the velocity $\\dot x$ is\n",
    "$$K_{\\dot x} = \\frac{COV(x, \\dot x)}{VAR(x)+VAR(z)}$$\n",
    "\n",
    "What is the effect of this? Recall that we compute the state as \n",
    "\n",
    "$$\\begin{aligned}\\mathbf x \n",
    "&=\\mathbf{\\bar x}+\\mathbf K(z-\\mathbf{Hx)} \\\\\n",
    "&= \\mathbf{\\bar x}+\\mathbf Ky\\end{aligned}$$\n",
    "\n",
    "Here the residual $y$ is a scalar. Therefore it is multiplied into each element of $\\mathbf K$. Therefore we have\n",
    "\n",
    "$$\\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}=\\begin{bmatrix}\\bar x \\\\ \\bar{\\dot x}\\end{bmatrix} + \\begin{bmatrix}K_x \\\\ K_{\\dot x}\\end{bmatrix}y$$\n",
    "\n",
    "Which gives this system of equations: \n",
    "\n",
    "$$\\begin{aligned}x& = \\bar x + yK_x\\\\\n",
    "\\dot x &= \\bar{\\dot x} + yK_{\\dot x}\\end{aligned}$$\n",
    "\n",
    "The prediction $\\bar x$ was computed as $x + \\bar x \\Delta t$. If the prediction was perfect then the residual will be $y=0$ (ignoring noise in the measurement) and the velocity estimate will be unchanged. On the other hand, if the velocity estimate was very bad then the prediction will be very bad, and the residual will be large: $y >> 0$. In this case we update the velocity estimate with $yK_{\\dot x}$. $K_{\\dot x}$ is proportional to $COV(x,\\dot x)$. Therefore the velocity is updated by the error in the position times the value proportional to the covariance between the position and velocity. The higher the correlation the larger the correction. \n",
    "\n",
    "To bring this full circle, $COV(x,\\dot x)$ are the off-diagonal elements of $\\mathbf P$. Recall that those values were computed with $\\mathbf{FPF}^\\mathsf T$. So the covariance of position and velocity is computed during the predict step. The Kalman gain for the velocity is proportional to this covariance, and we adjust the velocity estimate based on how inaccurate it was during the last epoch times a value proportional to this covariance. \n",
    "\n",
    "In summary, these linear algebra equations may be unfamiliar to you, but computation is actually very simple. It is essentially the same computation that we performed in the g-h filter. Our constants are different in this chapter because we take the noise in the process model and sensors into account, but the math is the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adjusting the Filter\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. Designing a Kalman filter is as much art as science. We are modeling a physical system using math, and models are imperfect.\n",
    "\n",
    "Let's look at the effects of the measurement noise $\\mathbf R$ and process noise $\\mathbf Q$. We will want to see the effect of different settings for $\\mathbf R$ and $\\mathbf Q$, so I have given the measurements a variance of 225 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. Our first experiment holds $\\mathbf R$ constant while varying $\\mathbf Q$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/j4uLS0megvCY0el0bNmyhZYtW2JlZVXW4QjlnLhehHslrpWK4+mnn2bTpk0ArFu3jsjISIv1ffr0YfPmzQCsX7/ePJpkSXqU18u8efN4/fXXAXBycuKNN96gYcOGHD16lC+//JKkpCQAxo4dy1tvvfXQx3vnnXfMTdXr1avHpEmTqF27Nrt372bs2LGcO3cOgPfee88cV0VUWFjIypUr2bp1K1qtlsqVK9OvXz+CgoIe6XHT09OpVq1ayQ02JFUQ/fr1k5o0aWKxbNSoUVLDhg0lSZIko9EoeXp6SpMnTzavLywslBwdHaUZM2bc83GysrIkQEpNTS2ZwIXHVlFRkbRs2TKpqKiorEMRKgBxvQj3SlwrFcfs2bMlQAKkunXrSgkJCZIkSZLBYJBmzpxpXhcQECDp9fpHEsOjvF4iIyPN57B161aLdWfOnJHkcrkESD4+PpLRaHzo412+fFlycXExH/NuP/7+/lJ6evpDH+tJlJqaKgFSVlZWiZRXYTpWv/766+zdu5cJEyYQGxvLggUL+OGHHxg+fDhgasY0atQoJkyYwNKlSzl58iSDBw/GxsaG/v37l3H0giAIgiA8bvr27Yu/vz8Ahw8fJjAwkCZNmhAYGGgxKuSbb76JQqEoqzAf2LFjxwAIDg6mefPmFutCQkJo2rQpYJrHKzU19aGP5+/vz8aNG/9xbpfg4GA2bdqEs7PzQx9LeHgVpjlT/fr1Wbp0Ke+88w4ff/wxVapU4euvv2bAgAHmbcaMGUNBQQGvvPKKebK5DRs2iDkiBEEQBEEocdbW1qxatYqYmBhSUlLQ6XTs2rXLYpvhw4fzyiuvlFGED+dW59uioqK79jEtKioqtu3Dqlu3LufPn+e3335jyZIlpKen4+7uTr9+/ejVqxdqtbpEjiM8vAqTRAB07tyZzp07/+N6mUzGuHHjGDduXOkFJQiCIAjCE6tWrVocPXqUb7/9lp9//pmUlBTkcjktW7bktddeo0uXLhV2tMcGDRqwY8cOLl++zMqVK+natat53YEDB9izZw8AVatWLdF+pLa2trzwwgu88MILJVamUPIqVBIhCIIgCIJQ3nh6ejJhwgQ+++wzCgoKUKlUKJUV/xZr2LBh5kl++/bty4gRI2jWrBkHDx7k66+/ttiuoiZKwoOr+Fe4IAiCIAhCOSCTybCxsSnrMEpMnz59WLBgAatWrUKr1TJlyhSmTJlisU10dHSFba4lPJwK07FaEARBEARBKD0KhYLFixfzyiuvoFKpLNbJ5XL69+/P+vXrsba2LqMIhbIkaiIEQRAEQRCEu1Kr1UybNo2PPvqIP//8k+vXr+Ps7Ey3bt3MI1MJTyaRRAiCIAiCIAj/yt3dnZdffrmswxDKEdGcSRAEQRAEQRCE+yKSCEEQBEEQBEEQ7otIIgRBEARBEARBuC8iiRAEQRAEQRAE4b6IjtWCIAiCIAjCE+3cuXOsXr2anJwcfH196dmzJ87OzmUdVrkmkghBEARBEAThiZSSksJzzz3HmjVrLJa/+uqrjBw5kk8//RSFQlFG0ZVvIokQBEEQBEEQnjjp6ek0b96cc+fOFVtXUFDApEmTSElJ4aeffkImk5VBhOWb6BMhCIIgCIIgPHEmTJhgTiA8PDyYPHkyK1asYPjw4ebah9mzZ7N169YyjPK2ixcvcuDAPiAX0Jd1OKImQhAEQRAEQXiyFBYW8vPPPwOmWbl3795NYGAgAF26dCE8PJyhQ4cCMGPGDFq2bFmix5ckie0XUtlzMQ2jJGE0SkiAJIHBaEAmk1OYn0vcsb341ayNxk5DyqVz5GbeICAhD29HT55vWg0bVdndyoskQhAEQRAEQXiiXLhwgYyMDAA6d+5sTiBuGTx4MG+88Qa5ubns27evxI4rSRK7L6bx5YZzHL6SCYCxMB+52gaAgvgjyBQKNP7hSEYD2oQ8VAUpKDR2gBvgxp79BUA8a06m8cPAevi52JRYfPdDJBGCIAiCIAjCE0WSJPNrKyurYusVCoW5SZPRaCyRY+6PT+fLDefYdfw8cisN1nYONPfScf3sUeo2i8FKIyejeiAKhQIXD1tkgEzWCBmADGSAXCbDKEn8uq+IM0nZdPnfTv7Xry5Ngt1KJMb7IZIIQRAEQRAE4YlStWpV7OzsyM3NZeXKlSQlJeHl5WVev2jRIrKysgCIiIh4qGOt3XeS71Yf4nSR6UZff/UkXZpV47MXq+KgKuLGjUZ4e9vcTFqq31OZfetX4eX5pzl+NYtBP+/jnQ41eKFplVLtAC46VguCIAiCIAhPFBsbGwYOHAhAXl4eTZs2Zfbs2ezbt4/x48fz/PPPm7e91TfivxQVFZnLW7ZsCduOHWfI7B08/8N2Dp66iFIO/aOs2TW9Cz+MjsDdQYZGo8bPz/O+h5H1dtKwaGhDnqrni1GCz9acYdTCoxQUGe6rnIchaiIEQRAEQRCEJ84HH3zAypUruXr1KhcvXuS5554rtk337t3p0KFDseXZ2dlcunSJ8PBwwMC6dStRKnW0aRPJpcw0Zu2L59iWIhTWDlh7VKZn+xBea22Ln0vJ3XprrBR88VQ4tXwc+XjVaZYfvcaFlFxmllI/CVETIQiCIAiCIDxxvLy82LZtG5GRkcXWyWQy+vfvz5QpU5DJZBiNBhYtms+FC4eBFDIyTnDo0Cq02gPAUWrVUmPjYcPwBXF0+i6Fk1INlDYO9IjQsGm0G1/0dizRBOLOOJ9tFMCvL0ThaqvidFI2Xf+3k92xqSV+rL8TNRGCIJS569evc/78eVQqFbVq1cLa2rqsQxIEQRCeAAEBAezatYsDBw6wcOFCYmPP07RpPQYM6MXly/EcO7aOqlVbIJcXUrUqODqmARL+/mqGDGkHQEK6nqk7VSw/qsUoaQHoFK7h9TZ2BLmXzq12dKArK19twtB5hziRmMUzP+3j3Y41eL7Jo+snIZIIQRDKzKlTp/jggw9YsWIFBoOpHaeTkxPPPfccH330EQ4ODmUcoSAIglCRxMbGsnLlSjIzM/H29qZnz55UqlTJvD4vL4+MjAx8fX0BA4sW/ULVqt40bhxMeHg/Dh06Tv36NbG1lfDw8Eap9ANMiUG9ejXM5chkMiRJ4o+DBYxfmUNekWm0p7ahal6PsaOGV/ERnx41bydr/ni5Ie8uPcGfhxP5dPUZTiZmMbFnONaq++tzcS9EEiEIQpnYvXs37dq1Izc312J5ZmYmU6dOZdOmTWzduhVnZ+cyilAQBEGoKNLS0njxxRdZunSpxfLXXnuNnj178u23X1Opki2xsfs5dOgAQ4Z0RCYrIjq6Eg4OKiATe3sVLVrcbtqkVqv+8XipuQbeXpLNpjOFAERWtuKjLg7U8i395OFOGisFX/auTS0fRz5dfYZlR69x4bqpn0RJ1/GLPhGCIJQ6rVZL7969zQmEp6cnw4YN4+mnn0alMn1pHz9+nFGjRpVhlIIgCEJFkJOTQ4sWLSwSCJUK3NzAw6OI7dt/58MPn0KSzhISYs2AAc2QyUwjKQUEeOPi4nhfx9twSku7r9LYdKYQKwW83cGOhUNdyjyBuEUmkzGkcRXmPx+Fi62KU9ey6fq/XRy4lFGixxE1EYIglLrFixdz7do1AJo2bcq6deuwsTGNJHHu3DkaNGhAdnY2v/32G1988QXu7u5lGa4gCIJQzly/fh21Wo2joyPjx79HXNxJvL3Bz8+Jzp074OfnT1paAosWLUKn07N//062b99O8+bNH/iYuYVGPl6Zw6KDBQCEeCqZ2seRUO/ykTz8XcOqt/pJHORkYjbDFhwt0fJFTYQgCKVu7dq15tcff/yxOYEAqF69Oi+88AIAOp2Ov/76q9TjEwShYjMajaxcuZKuXbsSHBxMzZo1efnllzl+/HhZhyY8oOTkZI4ePQrogSz++msxZ85swGA4zNGjCwgIAC8vGQsW/MD777/Bs8/2ZvTo0YwbN85cxpIlSx74+Pvji+jwTRqLDhYgk8HQZrYsH+FabhOIW3ycrFn8ciN6RPhgMEr/vcN9EDURgiCUury8PPPrqlWrFlsfFBRkfv33PhPCv7t06RKLFi0iJSUFFxcXevbsSY0aNf57R0F4TOTk5NCzZ082bdpksfz06dPMnDmT8ePH8+GHH5ZRdMK/MRqNFBYWYm1tTUFBAZs2radBg3A8PGxJTz9GbOwpatfWI5PJ6NSpJra21ly/fo2MjDQ0GoiKiiIwMNCizJiYGKZMmUJGRiYnT56875gK9RJTN+byw/Y8JAl8nORM7eNEVOA/95d4FIxGI6dOxWFvb0NAgPd97auxUjC1T20C7CVGfV1yMYmaCEEQSl3lypXNr1evXl1s/apVq8yvAwICSiOkCi8vL49nnnmGwMBAxo4dy9SpU3n//fcJDQ2lc+fOpKY++jHDH0dFRUUcPHiQ7du3k5CQUNbhCPdgwIABFgmEra0tSuXtZ6YfffQRP/zwQ1mEJvxNbm4uJ0+eRJIkQMf69X+yffsyIA61+gI2NknIZBeBq4SGuvHUU83Nw5U6ONihUChu7mty5//zLXK5HIXCtNxoNN5XfGeTdXT7Xxozt5kSiN71rFk3yq3UE4idO4/i4tKK8PCnmTnzzwcqQyaT8UyUf4nGJZIIQRBK3bPPPmt+/fbbb7No0SL0ej2ZmZm89957rFmzBgA/Pz9atmxZVmFWGHq9nq5du/Lrr79a/EG9ZfXq1bRp00bU6twHrVbLhx9+iK+vL/Xr16d58+b4+/sTExPD7t27yzo84R8cPHiQlStXAqbhov/880+ysrJIT0/no48+Mm/38ccfo9fryyrMJ86tIbwlSWLjxg3ExZ0B0snIOM2+fSvIz98HHKduXQfq1XMHMpDLdbRu3QB3d5d/Ldvd3R0nJ1PH6L1795r7292yc+dO80OUkJCQe4vXKDFzWx5dv0vjbLIeF1sZMwc68UVvR+w1j+bWOT09ixUrtjFmzDecPh1nsS4oyJesLNP3965dxx7J8R+ESCIEQSh1devWpXv37gBkZWXRt29f7O3tcXV1ZcKECebtPvroo7s+WRIs/frrr2zevBkAe3t7PvnkE7Zu3cqXX35pHh/92LFjfPfdd2UZZoWh1Wrp0KEDn3zyCTdu3LBYt2nTJlq0aMHy5cvLKDrh38ydO9f8etKkSfTo0QOFQoG9vT3jxo2jU6dOACQmJpp/Z4SSl5uba07SDh7cw9Kl84AryGTnUKmuIJfHAvH4+MgYMiQGW1tTvwIPD1fc3Jzu61hKpZJu3boBpgcqL774EkuXLuXEiZP8/PPPvPfee+Zte/bs+Z/lJaTr6fdjOhPX5lBkgDY11Kwf5Ua7mpr7iuvfGAyGYg98fvttPd26vcEXX8xj48Z9Fus8Pd1o1Cicnj1b0rdvTInF8bDEX2dBEMrEvHnz6N27N+vWrQNMN263yGQyPv30U55//vmyCq9CmTFjhvn1kiVLiIkx/ZFp3rw5MTEx1K5dG0mSmDFjBm+//fYjm730cTF+/Hi2bt0KgEKhoGvXrvj7+7Ny5Uri4uLQ6XQMGDCA+Ph4i0mshLJ35coV8+uOHTsWW9+5c2dzE8rLly+XWlyPu6ysLHQ6HW5ubmRnX+f33+fRoUM0fn4O+Pvn4uTkBJgS8ubNI8z7yeUl8yx70KBB/PXXZq5evUpycjKffvpZsW2io6No3br1P5aRmGlg8cECftyRR26hhK1Kxged7elb37rEvjPnzFnJL7+s4uDBM5w48btF34YmTeqYX+/ceZSRI/tZ7Ltr188lEkNJEjURgiCUCTs7O1avXs3atWvp2bMnISEhhIeHM2LECE6ePMm7775b1iFWGIcPHwYgMDCQNm3aWKyrVasWTZo0AUw3WGlpaaUeX0VSUFDAzJkzAdMTzl27dvHnn3/y9ddfc+7cOXr16gWY+qD89NNPZRmqcBd2dnbm17GxscXWnz9/3vza3t6+VGJ6HOXn59/sy2AE8tm7dy179y4FjuHgkEC7dtXx8FAARbi7uxAU5PdI43FycuKHH2ZSp06dYutkMujQoT1TpnyJQmE5a7NWJ7HiWAEDf0qnyeQbfLUpl9xCicjKVqwd6crTDWzuO4HIzMxh06Z9zJxZfCSoS5eusXXrIXJz89m3z7KTd1hYVcaMGcSff37BtGlj7+uYZUXURAiCUGbkcjnt27enffv2ZR3KY+Fu/SH+bblQ3IEDB8jIME3I1Lt3b6KioszrlEolkyZNMg8TuX79et5+++0yifNJIUkSO3bs4Mcff+TkyZMolUoaNmzIyy+/TGhoaLHtO3bsyK+//grA+++/z/r1682JxenTp5k1axYAKpXqX59KCyaSJJlvovft20elSi4EBnqSnR3Hvn2r8fNLx9HRlsaNfVCprDANvwqVK3uVeqweHh789NMsTp48ybZt28jJycHNzY127drj5+drcU4nE/X8caiAZUcKyNbe/n5sGKiiT31rutbWoJD/e/Kg0+nJyMgu1mejRYuhHDt2HrlczjPPdMTW9vY80Q0a1ATAz8+DgoJCi/0UCgWTJ7/2wOdfFkQSIQiCUMHVq1ePPXv2EB8fz4YNG2jXrp153bFjx9i1axdgGhXL1dW1rMKsEO7sfH634YfvHC1MdFR/tAoLC3n22WdZuHChxfKDBw/yv//9j48++ogPP/zQ4klxr169GDNmDImJiezevZvAwEC6d+9Oeno6K1asQKfTAaYRnERTNEsGg4Hr16/j4uKCWq3m+PFDnDlznL592wP55OQcx97eCQjE3d3I4MFtzE/27exs/q3oUhUWFkZYWFix5el5RpYdKWDRwQLOJt/uVO/tKOepSGueqmuNv6vlbbEkSej1Bqysbi8vLCyidu1+XLx4lejoWuzYMctinwYNanLs2HmMRiOHD5+ladPbzbdatozk2rV1eHm5ldTplimRRAiCIFRwL7/8Mnv27AFMN1FvvPEGzZs35+DBg3z++efmmoiXX35Z9If4D3cmCStXruTjjz+2+MzuHJL4zqGKhZL3yiuvWCQQcrncPESnJEmMGzcONzc3hg8fbt5GrVazePFi2rVrR3Z2Njdu3ODHH3+0KDciIoKvvvqqdE6inDtz5gwyGYSEVKGwMJWVK38lJqY+Vaq44umZjlJpB5hGO2rTpq55v5Lqy/Co6Q0SOy4U8cehfDaeLkRnGiQKlRLa19TQO9KaRlVVxWod9u49wWuvfcH581d4++3BvP32YPM6tVpFdnYeer2B8+ev8HedOzdBrbaiQYOahIQEWKyzttZgbf3gHbQlSeLQoUMcOHCQxER7AgJC6dOnDw4ODg9c5sOoGFeBIAiC8I/69+9v7guRl5fHxx9/TOvWrRk7dqy5D0RERASvvvpqWYZZIYSGhhIZGQmYanGGDh1KSkoKRqORNWvWMGzYMPO2gwcPLqMoH38XLlzg559NHUmtra2ZNWsW+fn5ZGRk8MEHH5i3Gz9+PIWFls1CoqOj2bdvH3369LEY3c3FxYWxY8eybds2HB0dS+dEygHT03TTk/dr167xxx8L0OtTgCukpR0mPX0fcAobmxR6925A5cr2gB53dxdCQwP/rehySZIkTl/T8fm6HBpPvsGQORmsOWFKIGr5KPmkmwMH3nVncPVkdi5eQO+nxpCQkGxRhlptxYEDp8nKyuX8+eId8CMiqlO7djVatKiHTmc5VHDXrs357rsxDBzYiUqVnEvsvM6fP8/TT/dj6NCXmTVrFlOnfsWLL76Ij48PX3zxRZk0WxU1EYIgCBWcUqlk+fLlvPLKK8ybN6/YhErdunXj559/xtbWtowirFg+/vhjOnXqhCRJ/Pjjj/z4449oNBqLEcQaNmxIhw4dyjDKx9udQ7V+8MEH5pHa1Go1H3/8MadPn2bJkiXcuHGDtWvXmoeMviUkJISFCxeSlpbGhQsXUKlU1KxZE7VaXZqnUSaKiorIzs7Gzc0NMLJgwWzCwgKoXTsAG5treHsXoNdfRKlU06SJ5bwJzs5l80T7YRXpJfbFF7HpdCGbzmhJzLz9HehkLaOJbwHDO/pQw8vKvHzp0i18+qlpcIQBA9rj5+dpXhcc7I9cLsfPzwMnp+Id8Fev/uYRnk1xcXFxvPjiS3dtQpmbm8uYMWPIzc1l/PjxpRqXSCIEQRAeAzY2NsyZM4dPPvmEP/74g5SUFFxcXOjRowfVqlUr6/AqlA4dOvDTTz8xdOhQcxv6OxOIqKgoli9fXmykF6HkXLp0yfz61hwAd+rWrZu5g3t8fPw/luPq6vrY9wPS6XQkJiaSn5+Po6M1x4/v5PTpYwwa1AHIp0EDF1xdZUAmTk42NG5cp4wjLhmZ+Ua2nitk45lCtp0rJLfw9pN4aysZTYNVXPzrD7YumMNJycDn2duA20lE/fq3O+YfPnyWXr1ud7S3s7MhL28HGk35SDqnTp1qTiCCgoJ45plnsLaO4Lfflptr7D755BOeffZZAgNLr/ZIJBGCIAiPET8/P0aPHl3WYVR4Q4YMoWXLlsycOZMNGzZQUFBAYGAgzz33HF27dhWTID5id9aaxcfHFxuJ6c7E4UmpYbtzpKTjx48jSXpq1w7GaLzOhQu7uX7dD0dHb2rUUBEUFAHkAaan6o+Ly2l6Np4uZNOZQg5cKsJwR6WrRiqgR5QLMaFqGlVVo7GS8dzWJIz6IgCOHTtPw4bh5u0bN67N3LnjiYwMpXr14v2byksCkZiYyJ49ewHw9PRg9uyfsbGxAWrQpk1XPDw8mDhxornmdOLEiaUWm/gWFARBEIS7CAgIYOLEiaX6R1kwadu2rXm+jo8//pgWLVqYk4WEhASmTZsGmCam/PvcKI+L1NRUNBoNdnZ2XLkSx6ZNa3nmmS6oVHqKis4gSYWAhFqtp1OncAIC3AEshhSt6CRJ4vAVHZvOFLLuRD7xaZbt/kM8lRxb8wfpJ7bjZExnwqR1FgMhNGwYzuHD56hfPxR7e8sRpFxdnRg4sFOpnMfDOHv2rPl1p06dbiYQt73yyivm76hDhw6VamwiiRAEQRAEoVzp2rUrlStX5vLly+zfv5+goCD69OlDbm4uCxcuJC/P9JS9S5cupdp841G6evUqaWlp1K4dCuSzZs0CatasTL16gbi4ZFK/vhumkZKsiIwMsthXqXz8mtZdzTAwdkkWu2KLzMtkkpFGwRra1FDTpoYaPxclHdafYV3yBa4DV6+mWPRtePHFHrz4Yo8yiP7JIJIIQRAEQRDKFaVSyaJFi4iJiSE7O5vk5GS+/fZbi22qVq3KjBkzyijCB2c0GpHL5eTm5rJlyyYaN47AxUVFevpRrlyJo3Zt02g/XbuGY2dnDRRhZ2dDrVpB/15wBXbiRCy//baeo0fPMXJkf1KdwpmwOoe8IgmNEtKObyM/dh9Btpn8Ovlni33Hjh3EyJFPU79+KK6uTmVzAo9QSMjtzu+rV69hyJAhWFvfrm2aPn26+XW9evVKNTaRRAiCIAiCUO40aNCAvXv38u6777JixQrzqGM2NjY888wzfPrpp+V+wjij0UhGRoa5c/eGDauwstLTsmUEGk0WGk0ikmQPOBEe7kV4+O2Znu82KlBFVlCg5eTJixw9ep6BAzta9Dk4f/4yEyfORmFficw6NlwzZgNQP8CKL55y5OnOa7FyVdKoUR2LviEALVpElvq5lCYfHx8aNoxmz569XLmSTOfOT/PaayOwtU1m4cJl5lnYZTIZL7zwQqnGJpIIQRAEQRDKpRo1arB06VKSkpI4c+YMSqWSOnXqlNnkWvciLi4OJycnXFwcuXTpJJs2bWDgwA5YW+upVk1CobACUlEqISYmuqzDvW9/v4m/Vy+/PJG5c02TNdarV4O6dW8/Ya9duzp2tdvh3PJ5rhlt0FjBW+3sGdzIBoVcxp49s5+oiTJvfcY6nZ716/fSt+8wNm06xdWrOZw6lcjmze8U2+f999+natWqpRqnmGxOeCQkSeLKlSucOnWK9PT0sg5HEARBqMC8vLxo1aoVzZo1K7ME4lZNSH5+PsePH785yZ3EoUN7WLFiIZAGXGPPnhXEx/8FHMXHJ59u3WqjVhcABgICvC3a7FckWp3EpLU51Pgwhf4/prPkUAH5RZZz0ixatJGhQz+jY8fXiu1fp87toaaPHLndWfhapoGPt9ng2v5V5Gob6lW2Ys1rbjzfxNY8k/TjnkDk5RWYr689e06zevVRwA8rq1rY2YUTFBTD779vJyCgJn+fU87W1pZJkyaV+hwRUIFrIiZOnMi7777LyJEj+frrrwHTjev48eP54YcfyMjIICoqimnTplGzZs2yDfYJIkkSc+bM4auvvuLEiROA6Ze/U6dOvPfee0RHV7ynLoIgCMKT5dq1a6SmphIeXgvQsWjRbwQG+hAZGYpWe52DB9fg45OFWm2Dh0cG1tZy4BIAffo0xMrKdHulVqvw8Kj481QcTSjizT+yiL1uAGD3xSJ2Xyzig+UyOtbS0KuuhqgqKr799nd27ToGQHJyKp6ebuYymjSpw+DBXahTpxpNm0YgSRKLDhbw6aoccgol1EpT7cOQxjbm5OFxdf16OnK5HDc3J27cyGfp0p306NGTSpUC8PPzwM2tADCNttWiRUvAlEifOHGCrVu3smXLFrRaLcHBwfTp06fMZmCvkEnEgQMH+OGHHwgPD7dY/vnnnzN16lTmzJlDtWrV+PTTT4mJieHcuXPY2z9ebQvLI0mSeOmll8zt8+5cvmrVKtatW8eCBQvo3bt3GUUoCIIgCCZpaWnIZDJcXFzIzs5i5co/iYlphLu7HampR4mLiyU8XA9I1K3riIODBCTh4gLPPdfOXI6vr4dFubcSiLsxGCUy8o2k5Zp+UvNuv87WSrQMUdOyevmYnwCgUC/x9aZcZm7LwyiBm50c+4urOXc1D5vQluTjyuJDBSw+VICvswLHJgNQnkqB3BucOBFrkUTUr1+T2bNND3WTsgwMnp3BtvOmkZci/K2Y0tuRqpUq5G3pf7pxI4OLF68SHV0XsGXPnuPY27vRqlULXF1lxMT44ujoA6jw9fX9x3JkMhktW7akZcuWpRb7v6lw/1u5ubkMGDCAH3/8kU8//dS8XJIkvv76a9577z169uwJwC+//IKHhwcLFixg6NChZRXyE+Pnn3+2SCDq169PjRo12Lx5M1evXkWv1zNw4EDq169PQEBA2QUqCIIgPBGMRiOSJKFQKEhMTOTcubO0atUYKGDXrpXY2ipo3bouNjZ5BAfL0WiSATvCwz0JD/cETG1HgoL87vF4EutOFRJ3Q09qrpG0O5KEtDwj6XlGjNI/7z93Tz5da2v4qIsDrnZl0+I8KyuXtWt38dfRGxxTN+Z6oWkkoK61NYzv6kCjyNUknb2EavuvbD6+iZUn9aw+ruVqhoGrhOIzdBZ1/RSkOdqSrTXioLl9HpIk8cehAj5Zaap9UCnhzbb2PN/k8ah9KCrSoVJZYTAYWLNmN7VqhRMQUJ28PCVXr6ai09XAysqKmBgvNBoNIEcuhypVqpR16A+kwiURw4cPp1OnTrRp08YiiYiPjyc5OZm2bdual6nVapo3b87u3btFEvGISZLE1KlTze/nzp3LwIEDAdDpdAwZMoRff/2VwsJCZsyYwaRJk8oqVEEQBOExlZaWRmFhId7e3uh0+cyd+xPNm0cSFOSJ0RhHYeFp9Ho7lEolrVpVRa1WAVqUSgUNGoQ91LEz8oyMWphpfrr+T2QycLaR4WqrwNVOjqudHDdbOVqd6QZ7xTEtO2ML+aiLA11rax5Zf4CCAi0nTsQSEOCNu7uLefnVpHSGTT+HQ1QvZIUK3OzkfNrdgfZhGsDUtyE5OY0mTeoQYJfHpF7ufNTFgQ2ntSw+VMDO2CIOJxg4nJDNRyuyaVdTw1P1rKnqruT9pdlsOVdoKsfPVPsQ5F7hbkUByM/XcvHiVapXr4xKpWbnzlPcuJFPjx49UShscXYuRKWqCngTEOBDQEBt875/nzCuoqpQ/3O///47hw4d4uDBg8XWJScnA+DhYVmt6OHhweXLl/+xzMLCwpudo0yys03Diul0OnQ6XUmE/USIi4vj9OnTAERHR/P0009bfH6TJk3it99+w2g0smzZMj755JOyCrXE3Do/cZ0I90JcL8K9EtfKf7s1ek16ejpHjhyhadMGqFR6jhzZTGbmDbp1awToadDAHWfnAnS663h62uHp2QBJAp1OfzOBML1+WCcSdbz6ew6JmUbUSuhUS427vRwXWzmutjJTsmArx81OjpO1DKXi7olB30gV7yzN5VyKgZG/Z7HsSD7ju9jh5fjPk8np9XqLf+/FrFnLePXVLzAYDPzww3sMHtzFfB5j11jj2LCPacPL+1g9vQMutnLz5/Ttt2/h4GCLXG6qYdDp9Chl0LGmFR1rWpGcbWD50UKWHi3k4g0DK45pWXFMaz62SgkjW9nwXCNrlIqS+fwflaysXDIzc6hc2TT07urVe/D29iMiIoKcnHz27DmIm1s0bm7eVKnijpeXFp3O1D8hKsrUB7Q8/R6XdCwVJolISEhg5MiRbNiw4WYV0N39PWP/r6HIJk6ceNce7Vu2bHlsMsXSEBcXZ35tZ2fHmjVrim3j6OhIRkYGN27cuOv6imrjxo1lHYJQgYjrRbhX4loxKSgoID8//+ZcCxJ7927H29uZatW8KCjI5NSpMxgMh7C11WA06nFxkbNr11bz/mlpVx9ZbJIE2646Mv+0B3pJjrtNESPqJOLvcPPhpATkmn7SMP38l7dqw5p4V1bEurLlnI49san0rX6D5n6Z/FuLn3379lq8j41N5ODB85w6dZmxY/venLjOJD8/A4PB1El67dqtBFR1YXmsK2viXTFKMtRoaWZzlLY9ZZw5uvu+PhOAMAXUrAvx2Rp2JjqyL8mBPJ2CKo4FvFArCR95EX8Lt8xIkoReb8DKSkl+vpbDh+MIDa2GnZ0z588nERd3jZYtW2M0WnH5soy0tEySkk4gSRLu7pXZv/8ocNRc3smTJ8vqVP5Tfn5+iZYnk6S/DxZVPi1btowePXqgUNzOxg0GAzKZDLlczrlz5wgKCuLw4cNERESYt+nWrRtOTk788ssvdy33bjURfn5+JCUlmSeHEf5bSkoKfn6mNqNVqlTh9OnTFv9Xx48fJzLSNCFMZGQku3ff/5dSeaPT6di4cSMxMTFYWVmVdThCOSeuF+FePanXyq2HfgUFBRw8eJBatWrg5KTiyJEDnDhxjEGD2gOFnD0bj7OzfZmPeqTVSXy0Mpc/j5juIVqHqPi8px0O1iXTl+HCdT3vLsvlaILpSX2DACWfdbcnwNWyVkKv17Nhw1+0bdsapfL2s+GRI6cwffpiAFav/oaYmCj0eh1bt25lxYrV/P77Edzd7WjYsQtXfXoTm2q6HewUpuLDzna42JZcn4xCvcSFFAMhnop/rIUpLQUFWpKT06lSxRuQs3r1fmxsnGjZMga9XsWOHfupXbs2Li4u6HQ6ZDKZxedakaWlpeHl5UVWVlaJDJVcYT6V1q1bm4cMvWXIkCGEhIQwduxYAgMD8fT0ZOPGjeYkoqioiG3btjF58uR/LFetVqNWFx8JwcrK6on68n5Yvr6+tG3blg0bNhAfH8+IESP4/PPPcXFx4dSpUxazKA4aNOix+mzFtVKx6PV6Nm/eTFxcHDY2NrRs2dKcAJcGcb0I9+pxvlYKCgpISUm5OciGxIYNq1CpJFq0qAtkk5l5FINBh5WVG+HhDoSHN8XKSg8oqFUrqGyDBy6n6Xl5fhZnkvTIZfBWOzuGNrNFXoKdg0N9lCwZpuaX3fl8sT6X/Zf0dP5fBm+0tee5xjYoFTKGD5/M8uVbycjIJi2tjcXIUI0b1zYnEYcPn6FOnSqMHDmSuLh4AKpUVVIQ2IGtVj0gVcJBbWDSU650rPXPrT0elJUVRASUzbUsSRIHDpzCz88LLy9/EhJ0bN0aj79/SzQaJ+rX9775u+aOlRUWfWsft9+/kj6fCpNE2NvbExZm2enJ1tYWV1dX8/JRo0YxYcIEgoODCQ4OZsKECdjY2NC/f/+yCPmJ895777Fp0yaMRiM//fQTc+fOxcPDg6tXb1cl+/n58eyzz5ZhlMKTbN68ebz33nskJCSYl8nlcnr06MG0adOK9akSBKFkGI1GDh48iL+/L56e9iQlnWHTpk0MGtQRjcZIcLCEUqkAUrCygp49m5v31WjKz5CnAJtOa3l9URY5WglXWznf9XOkUdCjidFoMOCYspe2hiscVNYnUe/GhDU5rDpewORejty4kUFi4g0ATp+Ot5gFulWr+vz44/s0ahSOn18l+g15hSsZ1hh82mKw8UHnFonBrjIAquQd2F2eQ+iQaUDAIzmXR62wsAgrKyVyuZzjx2NJSsqmXbu2yGS2XLt2EUdHf7y8QvD31zNoUKS5abyPj08ZR15xVZgk4l6MGTOGgoICXnnlFfNkcxs2bBBzRJSSZs2aMWfOHJ577jn0ej06na5YArFu3boym21UeLJ98803jBo1qthyo9HIkiVLOHbsGLt376ZSpUqlH5wgPCb0ej1yuRy5XM7JkydJTr5MmzZRyOV5JCbuxcnJF0/Pyvj5SQwc2ByNxtQuv0qV8n8jZzBKTN2Yy7QteQDU9bfi+wFOeP5Lp+d7ZTQaiY1NQKWyIiDA27xcLpcxcOCHFBQUEljVl89/W8Anq3M4flVPl+/SqF2jM/aO+wmu6kFRkY4ivcTlNAMXb+iJS9UQ59iS1Vv1nE3MpCDoi2LHddRIVElbTMKJXygEZs+ew/jx4x76fEpDamomAG5uTqSna1m8eBvdunXFwyMABwdn9PpMwJQkde/e17yfUql8bJonlbUK0yeitGRnZ+Po6EhqaqroE/GALly4wPfff8/KlSvJzs7G19eXQYMGMWTIkDKbVfFR0Ol0rFmzho4dOz52VZ6Pm0uXLhEUFGTuSNi+fXt69OjBlStXmDlzJqmpqQA899xz/PTTT48kBnG9CPeqIl0rWVlZGI1GnJ2dyci4wZIlv9O1azPc3a2JiztPWlo69evXLOsw71lRURFr165l+fLlXLlyBZVKRWRkJO269mX6US92xpqGbx3cyIZ3O9qjUj5886W9e0/QseNIMjKyef31/kydOtpifcOGQ9i719ScOyNjC4VyGz5Yls2G06a+GIFucuxl2WQaHEjI+Pd5KOQF16lT1ZnwANPEbh1raVCTT+fOncnJyUWlsmLz5s1YW1v/cyFlJC0tkwsXEoiOjgBsWbVqNxqNI23adMJolHPx4kX8/Pz+dfCdJ11aWhpubm5PXp8IoeIIDg7mq6++4quvvirrUAQBgB9++MGcQIwcOZKvv/7avG7o0KHUrFmTnJwcFixYwJQpU3B2di6jSAWhdEmSRFpaGkajETc3N/Ownf8kNTWV2NhYoqPrAwVs374Ca2to06YOjo5aGjXyxM4uF9ATGOhFYKBXqZxHSUhLS+PVV1/l3LnzFsuX7YhlfrYRo6YIaysZk3o50K3O/d1kX7mSzMaNe9mz5wTDh/cmIuJ2s6PAQB8yMkzDyx8+fLbYvu+99xx6vYG6dUNwdLRDJpMxc6ATa08W8uHybOJSjYAdYATAViUjsJKCwEpKqlZSElhJwWdjh1KYehFfL1f+/GbF345gR1RUNJs2baKoSEdqamqp9hO7k8FgoKCgEDs7G4xGI6tX76JmzTACA0PIy7PiypVkIiJCUKvVtGx5a8I2BXK56d5DKF0iiRAE4bG3fft28+uxY8darPPz86Nfv3788MMPaLVaDh06RJs2bUo7ROExc+rUKbZs2UJhYSHBwcF06NChXNUqFBQUMG3aNKZPn24eotvb25sXX3yRl156CZVKhZubGwaDnsWLf6Nu3RoEB3uTnx9LQsIB6tYFlcqKZs380WhUQBFyuZzQ0MCyPbEHZDQaeeONNywSCLdKbqTYNSY7cDDIrZDnXeW1hml0q9PuH8sxJWVZuLo6Wgwvv3btLl5+eSIAoaFVLJIIFxcHatYMwNpaSXCwB6mpqbi5uZnXd+7ctNhxZDIZHWtpaBio4o+DeVy9fJGYqGpU8zLNT/H3oe2/M14n1VhIRkYGWq222NP6W3NtAXcdbOZRyc/XEhubQEhIACqVDbt2nePGjTx69XoKudwGF5ci1OoAwAd/f1/8/cPN+9ra2pZanMLdlc2c6oIgCKXozkmY7tak7s6ah/I0MZBQ8cTFxdG6dWvCwsJ49dVXefPNN+nWrRuVK1f+x6HGS1t2djYtWrTgrbfespjjJynpGlOmjKdt2wasXPkzcBaF4gRBQTIcHTOAJPz9benduwUqlSkhcnS0M0/aVpHt27ePEydOIiHH0S+cZ96fT5UBv5EZ9CLIrVCl7MJx3+usXvAdqakZnD9ffBLbceNm4uTUgkqV2nD5cpLFuoYNb9/87t17ex6BZcuW0aVLF9TqSxiNsRw+vJZOnTrxwQcfmCe//TfOtnKGNLKmlX8m0YEqPBwUd50bKzo6CoD8/ALmzJljsW779u3muQ2qVg18JP3Ciopuf69u23aYEycSABeKiipx8GA6WVmVgXBq1epA06bdAGdATePGjUXH53JM1EQIgvDYCw0NZd++fQDMnz+fl156ybyusLCQhQsXmt+HhIQU218Q7sWlS5do3LixxVPdW5KSkhg8eDBZWVm89tprpRLPrS6PMpmMa9eukZqaSnh4LV599SVOnNiPkxPY2UH9+uFkZOSRmXkRuRwMhkS2b1/AkCGtAahXr0apxFvajEaJuFQDJxJ1zFyZRVbkJPT2gaQrbfhmH0AhCjm808Gew79vYZ+hgE2bCqhUKQZPT1eSktZblGdlpSQ729Tpes+e4xYdpGvWDGTKlFFERYWZR1CaPXs2//vftGJx6fUG1qxZy/nzF5g168cSGRymb9++rFq1GoAff5zF/v37qV+/PhcuXGDbtu0W2/3bBL33Kjvb1L9Co1Fz6lQCBw7E8uyzzyKT2WJra0CtdgKq4OQEQ4YEm48pmpJWLCKJEAThsffCCy8we/ZswDQUdHZ2Nj169CAhIYGPP/6YS5cuAdCmTRuqVKlShpEKFdno0aPNCYS/vz+vvvoqnp6eLFq0iJUrVwLwxhtv0KtXr0fydDU2Nha1Wo2fny8ZGSksWfIHXbu2wt3dgdTUo8TFxVGpUgKnTy8iMBAcHGz58cfvqVnT1PH50qVLDBs2jOvXb3D8+DFOnTplXlfR3UoYTibqOJGo48RVHaeu6ckrutULuY7p4Tcg6bQUpsQR4i7j69cbU8dPxbxLUezbuxelEgoLITk5jYICLdbWt5sFBQf7U7WqLwEB3sVqZxQKBW+88Yz5fXx8PNOm3U4gmjRpQtOmTUhMTOTPP5eSm5tLbGwsP/zwA2+88cZDn39oaCgjRgw3Jy3Hjh3n2LHjFtu0adOG7t27P1D5WVm55Obm4+Pjjl5vxaJFe2nUqCmhoeH4+gah0dRCklyRyeRERjaw2LckkhahbIgkQhCEx17Dhg3p27cvCxcupKCggLfeeou33nrLYhuNRsOkSZPKKEKhoktMTGT58uUAuLu7c/jwYfMIf8888wwjRoxg2rRp6PV6Zs2axUcfffRAxzEajUiShEKh4MqVK5w8eYyOHZsDeZw9uwU3Nxv8/Gpgb6+jYUMP7OwyAS3h4d6Eh3uzcOFCjEYJtRqefba/RZIQEBDAiy++yGefTQBg8+YtFT6JOHCpiGlbcjkQr7sjYbhNJTdSy09NZtw+ks9sRZZxkVN7EkAyUr1ZXer4tQQgNvYiALa2EBJSjTp1alBQUGiRRPTpE0OfPjH3FNfixYu5NTbmkCGDGTFihHld9+7defrppykq0rFixUpeeWW4xXEe1JAhQ/D29mbWrFnmCecA3NzcePrpvgwaNAiF4t6Gq9VqCzl37jLVqweg0Thz6lQCCQkZ9O0bg1KppHNnd1xcXAArHB0dH6uRGYXbRBIhCMJjTyaT8csvv6BWq5k7d26x9R4eHvz+++/Uq1evDKITHgf79+/HaDSNjjN48OBiQ4SPHj3a/OR5z54991xuZmYmWq0WT09PdLoC5s79iebN6xIU5IFSeQkbm2vo9WdQKpV06hRx86muhFKppGbNqsXKu7Od/d2a7tWoUeOObbPuOc7y5n8L9jLvqIoU+e0mRdZWMkK9lVjlJLJq3nyKki/yyVvdGTtsICtW6Bm/eTMAHu62NGhQl6ZNIwA4fPgw69atAyAkxJZ163566CFQDx8+DJjmgfj7BKyVK1emVatWrFu33lwjUatW2N2KuW/t2rWjbdu2nD9/ntTUVOzs7AgNrWkx0/WdDAaDObE4ePA0Go0NYWHh6PUyDh06irt7M7y8fKhbN4AGDZTcuq309PQskXiF8k0kEYIgPBHUajW//PILb7/9NnPmzOHixYtYW1vTtm1bevfuLcYWFx7KnZ33bWxsiq2/cySZO7f9u6ysLA4fPoxerwWyOXZsG2lpyfTs2RQrqyIaN/bC3V0HZOLt7YS3d6R533tpFmJ6Omxy+PARmjdvbrH+0KFD5tflfa6k3Nx8jh+/QHZ2Hu3bNwLgXLKOqRtzWX8qAOQgGfR0qgGvdvAg2F2JUiHjyJEbLBy7mSpVfFCrTDfIbdu2Zdq070lNTcXHJ4/s7CNkZFgzdOhQDh68/Zn07NmzROZQuDWAg0KhuGt5d/aD0OtLdrAHmUxG9erVqV69usVyo9HItWs3cHS0w97elgsXktm+/ThDhgxCLrfDYChAr7cDgrGzg8GDA81DAovvzyeTSCIEQXii1KhRg8mTJ5d1GMJjJjz89ug7v/76K++88w4q1e128bf65IDpGrxx44Z5FJwVK5bg6+tG3brBGI1JpKQcwM6uCAigQQMPrKx8ANMkZyEhAQ8VZ8uWLfniiy/Q6fQsWrSQOnXq0KJFc2QyGYcOHbKYbLFdu38eyrS06XR6i6flRqMRL6/25ObmExTkx8Y9f/DVplxWHNMiSSBDIufEZrJ2LaDVrNep4eVr3rdWrSByc3dga3v75l2j0TBlyhRGjBhBbm4uOTm5rF+/wSKG6Ogohg0bViLnExgYSHz8JXQ6PZs3b6Zt27bmdQUFWrZs2QKYair8/f1L5Jh3c/78ZXJyCqhXry4ymYYNG3ZRv35DatWqg4dHHk2aBGE0eiCXK4mKamKx73/NKSI8/sQVIAiCIAgPqXr16jRtahrP/8KFC8TExLBu3TqOHTvGmDFjeP/99wGwtobWreuxevU84BxwlMBAPe7ueUASzs7Qq1dz7Oysb26vQaksued9Li4u9OzZEzANu/nmm2/SuXMXunfvzksvDSU7OweAli1blPkgA7GxCcTEvIKHR1vGjPnGYp1cLqdmzUAU9pVID+pO6y9TWX7UlEB0rKVm1lMGFoysSuL5eTz1lOW8L0ql0iKBuKVWrTDmzZtLly6dLTpG+/h4M2rUKL7++muLxPBh9OjRw/z6s88+Y9GiRSQlJXPgwEFGjBhBamoaAM2aNX/oGiGj0UhhoSkJTU3N5Ndf/yI7Ww1UpqDAm9xcH6AGMlkV+vZ9kbCwBoACBwcHqlevXqLXn/B4EVeGIAiCIJSAzz77jLZt26LVatm+fTv792/H3t6UOLi7g4sLDBrUh7Ztg9Hp9EAuAGFhQaUa56hRo0hKSmL79h0AxYakrV07nHHjxv1rGYmJiZw9a5pdOSQk5IFHmzpzJp5Vq3Zw/PgFRozoS1TU7bb/jo52bNq0H4Bjxy5Y7Hc9x0CldsPwa+6LJFNgkKBViJrRMXaE+VhhGmrJl/vl7+/PuHHjGDNmDCkpKahUKry8vEr8qXt0dDRNmjRm585d5ObmMXny50ye/LnFNjY21gwb9vJ9l63VFpKamomvrwegYOnSPXh4+NKkSSvs7ZUEBdkhlwcAdtSu7Waxr5jATbgfIokQBEEQhAeQkJCAvb09Tk6OXLp0ljNn9rN27Q+MH/8mKSnXAVMCAaBQyOnXrz+vvfbqPY+A86ioVCq+/PJLNm7cyJIlSzh58iRGo5Fq1arRo0dPOnfu9I+za8fFxTF16lT27Nlrsbxhw2hGjx5NYODdZ6xOTc3k4MHTtGvX0KLvxp49xxkz5lsAIiKqWyQRlSo54+npisFgxM3NCYCMPCMztufxy+48tLrKIIOGgSrebGdHvcolN+mdjY3NI62JkclkTJo0iQ8//JDNm7cUW1+pkhuTJ08mKOi/E0yj0Uh8fBI1amTh4eHDpUuZ7NhxjsGDm2Bl5UBUlNvNfjoOqNUQFRX1CM5IeBKJJEIQBKGcSk9PJzk5GScnJ7y9vf97B+GRunLlCikpKdSvXwvIY/v2pVSv7k1kZFU8PQto27Yavr7ubNiwnC1btnDw4EEKC4vw9/ejc+fOeHh4lPUpmMnlctq1a3df/R7Onz/Piy++RG5ubrF1e/bsZciQ55g5c0axUZ+GDBnPnDmmeTLi4pZTpcrtWovw8GDz6+PHY4uVe+bMYhwd7cjWSny1MYefd+aTU2gaGzXC34q32trRKEh9z+dQnlhbW/PFF19w9uxZVq1aRVJSMjY21jRs2JA2bdoUazql1+tRKEwzUp86dZGMjHyaNGmCTKbk1Kl8IiPd8fCoSWBgMH5+0VhZmWoVfH3vv0ZGEO6FSCIEQRDKmV27djFhwgTWrl1rnnU4MjKSN954o8RmlBXuLicnB4PBgJOTEzk52axatZRWraLw8LAnN/ckN25c5FZ3wp49690cv9+IRqO2mKG4bdu2Fp1lKzpJkvjggw/MCYSnpwedOnVCJpOxatVqzpxJJiEhl/btXyY+fovFNVq58u3hPvftO2mRRISFVeWXX8YRHh5MjRrFn/zL1LZ8vSmXn3flk6M1/S6Eeil5s50dLaurH4vfhZCQkLsOt5ucnIpSqcTNzYnr13NYtmwXTz3VAxcXHxQKFUplHhCETKajSZO2hISY5vRQqVQl1ndDEP6NSCIEQRDKkXnz5jF48GDznAO3HDx4kH79+nHgwAGmTJnyWNw8lQepqalcuHCBhg0bAPls27YcjUZGmzZ1sbHJo0oVCbU6GcgjNNSD0NDbtQklMQFYRXHo0CHOX7hIgdwT58AoGg4cwZ7rErYqGS99PIBnYzqTlZEP5LJjx26aNWts3rdJkzo0ahROVFQY1apVtihXo1EzaFDnYsfLyjfy0848Zu+6XfNQzUPJyNZ2dAhTI5c/ftd/YuJ14uISadq0IWDDnj3HcXX1olmz2jg7SzRv7oWNTWVAQ0hILYt9xfeBUBZEEiEIglBOnDt3jueee86cQPj7+9O8eXOOHz/OsWPHAJg6dSpRUVH06dOnLEOtUHQ6Hfn5+Tg6OmI0GvnjjwXUrRtCcLA3+fmxXL16gKIiGSqVFU2a+KJSWQH5KBQyoqNr/Wf5d6M3SOyNKyK3UKJViBqVsmLd5On1Bq5kSJy8puNkoo7Ve6xIa/Y7co0dScCsXYXmbdedApfn5qA4vpnck5tZueoviySiTZso2rS5t3b4mTeThzl3JA/VPZSMbGNH+5qPR/JQWFiEWq2iqEjHypW7iYyMpHLlauh0arKyijAaayCXy2nf3vPm/AsyrKwoNq+DIJQ1kUQIgiCUE9999515IrLnn3+eGTNmoFQqkSSJ77//nhEjRgDw1VdfiSTiX2i1WuLj46latSoqFezZs5EbNxLp1as5cnk+QUHg6JgByPD3t8Xfv4V5Xycn+38s979IksSRBB0rjmpZdVxLaq4pGQxwVfBOR3vahpbP5jcGo0R8qoEVO+KZv+Y0qUZHNJ5BFEl33iJ4INeApNdhSL/CoM5h1PSxIiHdwNIjBaRk22BftzP2dTvzlzKL77fm0jPCGk/He+tEnpF3M3nYnU/uzeQhxNNU89CuAicPer2e5OQ0vL0rIZcr2Lr1JNnZOrp27YlKZYuXlxFr6yDAnYAATwICbncsL4lJ7QThURJJhCAIQjmxYsUKwDS79pQpU8zjs8tkMl555RWmT5/OqVOn2Lt3L9evX8fd3b0swy1Xjhw5gq2thmrVfNFqr7Fz55+4uDTCw8OB8HBbJCmYW0Oq1qtXo0SPfSFFz/KjBaw4puVKusG83MlGhlIu41KagaHzMmlQxYoPOjlQy/fuIx+VhtWrd/Lnn5u5cDGJF95/h1OZjmw6U0hanhGwh0pRyIEiCdRKqOFlRS0fK3TXT/DzlK/RpSVQLyKYj7vONl+fb7Wz45Xxc9hyyZoi94ak48jn63L5Yn0uTYJU9KprTbuaGqxVxROB9Dwjs3bk8cvufPKKbicPo9rY0Ta04iQPRqPRPAzshQtXsLZW4+vrR3q6gTVrTtO9ey/c3SsTGup780GBMwCNGjUqw6gF4eGIJEIQBKGcyMrKAsDPzw8nJyeLdTKZjFq1anHq1Cnztk9aEpGXl4dSqUStVhMXd5GDB3fTu3c7ZLJ8cnKOI5OZmiE5OkoMGdLGfJP7MLUL/+RqhoGVx0yJw5kkvXm5jUpG21A1XetoaBKkpsggMXNbHj9sz2N/vI4u/0ujZ4SGt9rb43WPT+nv1//+t5AjR86RlZXL4sW35x7IKzSyZH8WK29UwzriGT7cpAIKALC2klHdQ86O5ctQ5iTSpq4Hv3z3MkqF6SY+N7c2O+cmUWCvJyPjDDNmzKB3794ALF68mIOrZmMPqO2cGfrpIlafMrL/ko4dF4rYcaEIO3U2HWtp6FXXmgZVrMjIl/hxRx5z70geQr2UvNa6fCYPer0eg8GIWq2isLCIY8fOU716AI6OThw/Hs/Ro7EMGvQ0oOLs2QtUqlQJX99auLkZ6dOnGo6OjoDsifudFR5vIokQBEEoJ3x8fMjOzubixYvExcVZjLlfVFTEtm3bAFAoFOVquNBH5dq1a+Tn5xMUFIjBkMuCBT/RpEk4NWr44OBwjYAAIwZDPEqlkmbNbjcDkclkj2SW3fQ8I6tPaFlxtIADl3Tm5Uo5tKhuShza1FBjo7o9MZlKKeONtvb0a2DDlPU5/HlEy59HtKw5qeWlprYMbW6Lrfr+JjIzGAycO3eZgwdP4+rqRKdOTSzWz5u3hv37TclmUno+u+JlrDupZfuFQor09bANNW1nKy+kZwNn2oepaVBFhZVCRlKvHnh6uhZrdmVnZ8dLL73EN9+Y5nSYPXsOs2fPKRbbS0MG8GxTZ55tCpfT9Px5uIAlh7VczTCw6GABiw4W4OusID3PSP4dycOoNnbElHFzL0mSkCQJuVxOUlIqFy5coVmzBoCK1au34+joQosWLZDJ4OLF8/j6VsXR0RdfXz80mlBuTW7XpcvT5jLlcnmxBwKC8LgQSYQgCEI58cwzz/Dee+8hSRIDBgxg3rx5BAUFkZqayuuvv05SUhIAXbt2xcHBoYyjLRkGgwGDwYBKpSItLY2dO7cTE9MIGxuIj99FRsYNgoKiUSgkOnSojqurBsjDzc0RNzfHUolxd2whP+7IZ8eFQvQ3B82SyaBBgBXd6ljTIUyDs+2/JwLeTgqm9nVicGMdn67KZv8lHd9uzuO3AwW82daOp+pZo7jL03eDwYBOp0ejuT0XQmLiDWrWNPWJadeuYbEkwr96CKd1lbGp1ojGX2RhlG6X6+skI9KjgF5RzjQO8Sj2xN/Ly3IG4zsNHDiQ/Px8Zs2axc2Rh81kMnjhhRd49tlnzcsquyp5Pcaeka3t2H9Jx5JDBaw5YUooAGp6m5KHNjXKJnlITk5Frzfg6+tBURHMn7+BFi2aERgYQmGhhszMAozGWsjlcho0cLo5bKorKhX063f7PF1cXHBxcSn1+AWhrMkk6e9fBU+27OxsHB0dSU1NxdXVtazDEcoxnU7HmjVr6Nix4z/O7ioIt9zL9ZKamkrNmjW5fv26eVnlypVJTEw0d7hWKpXs2rWLBg0alErcJU2r1ZKenn5z8jw9v/8+lypVPIiKCiE3N5X9+49Qv34o9va2Fu3My0JeoZGJa3OYv7fAvCzMR0m32tZ0rq154OZIkiSx/lQhE9fmcDnNdEMd4qnk/U72NAlWo9PpmT59Lr//voNjxy7wxRcjeeWV3hb7u7vHkJqaSSW/AFZu/ZXL6QYupRrYG1fE4Ss6i+OFeCppH6ahfZia6h7Kh75hv3r1KkuXLuPs2TOm8kNq0KNH93ua1Cy/yMi2c0XYa2Q0DlI98uRBqzWNIqXRqElOTmXv3tN06tQWKyt7Nm8+SEGBkU6dugNKTp8+ja+vb4VL0MXfIuFepaWl4ebmRlZWVolc56ImQhAEoZxwc3Nj3bp1dOjQgZSUFAAuX75sXq9SqZg/f36FSiD0ej0XLlzA29sbR0cNsbEH2bdvN0OGdEAuL6JxYw/s7GyATOzslLRqVd+8b1kmEPvji3jzjyxzR+n+UdY819iWIPeH/7Mpk8loH6bBw3CVb9YkszPDj7PJ8MxPGbQKUfNWjDUKhZw9e04AMnYduUzExUIupxm4lGbgcpoevxen4Wi0RY+Svj9kFDtGXX8r2odpaFdTTWXXkv1T7+vry6uvjnigfW1UcjrUenTza6SkpJGZmUP16lUADb//voU6depSp04t1Gp/nJzU6PWBWFlZ06yZt0Wzt9DQ0EcWlyA8jkQSIQiCUI5ERERw6tQpZs2axfz580lKSsLR0ZHu3bszfPhwi34S5VVsbCy5uTnUqVMNuTybvXtX0LhxDRwdfQgKklOlSiPk8iIA/Pw8/6O00qXVSXy5IYdZO/ORJPB2lPNFb0caB6n/e+e7kCSJa9duEBubQPPm9SzWLV60nl8mzEauseeZidPYdd2FzWcL2Xa+kGqOjfF+LgQrZ292KVXs+vHviYKpKZdcBk4qLYbMy2hTY1HmXsKHODpUbcnTEU9jb//4/Zk3Go0UFenQaNRkZ+eydesRmjVrjJOTJ1evZhIfr6V69QhARtu2Tjc7Ndvi7GxPixYtzOU8in4zgvAkEb9BgiAI5Yyrqytjx45l7NixZR3KPyoqKsJgMGBtbU1mZiZbt/5F69ZR2NvLyMk5QWbmdcCIXA6DBrVEoTA1/bmzbX95cyxBx+hFmVy8Yap96BNpzfud7XHQPHiNSIsWQ9m+/TBKpYLc3B2o1Srzujp1TJOHGbU5BGbt5KPXn2PS2hw2nC7kTIY9VpVMo0op5ODnrKCyq4IqbkoquyoIcFXiZW/g24lvs2/PbpSA3c1y04AZM86xdu0aZsyYUeFHBMrKyuXatRvUqFEFsGLFil04O1eiefPWaDRKbG31SFIQ4ExEhA/16t3+/zI1mxME4VEQSYQgCMIjkpeXx7x585g3bx5Xr14FYOfOnQwfPpyAgICyDe4+paamcu3aNcLDawFali//HW9vZxo3DkOtzsDRMRWj8SJgR0SEP+Bv3vdWAlFeFeklvtucy/db8zAYoZK9nMm9HGgV8t/NbrTaQr78cj4HDpzGw8OFmTPfs1jv728aRUuvN3DqVBx164aY1zVpUocZM96hTp3q1KoVhI2Nkh8GObPvYgGrd52jRWQ1qnqo8HZSYKUo3nfg888/Z9+e3eb3wcFB2Nracvz4cYxGicuXrzBmzBhmz55dLie5u5PRaKSwsAhraw16vZ6NG/dTq1ZNfH0DuXFDx549KQQHd0ap1NCggRtqtRpwRqWC1q1bm8spyyZwgvCkEUlEGTEajRw8eJDk5GRcXV1p0KCB6BAlCI+R2NhY2rVrR1xcnMXyKVOm8O233zJ37lz69u1bRtHdXVFREVqtFgcHB7RaLWvWrCAqKhwfH2dSU09y8uQhwsKKkMtlNG3qjbW1BsjC2lpOy5aRZR3+AzmTpGP0oizzXA9da2sY39Wh2GhLeXkFHD58Fmdne8LCgszLVSorPv98LtnZeXh7VypWfvPm9bh+PYOIiOo4OdlZrPPycmPo0F7F9qnrb0VBQiaNg1VYWd39z3RmZibLli0DQK1WMXXqVKKjowG4dOkSI0aMICkpmRMnTnL06FEiIiLu/UMpBXl5BcTFJRIaWgWFQsPWrUfJyzPQpUs3lEprVKocZLLqgA+Bgf5UrRplToRE7YIglA8iZS9lkiQxa9YsqlWrRlRUFN26daNJkyYEBAQwZcoUjEZjWYf4xDh9+jQjRowgNDSUqlWr0r59exYtWmQeBUcQHlRubm6xBMLNzc38lLSoqIgBAwawa9eusgoRgIKCAs6dO4dpkL4iNm9ezs6dy4DzqNVnqVQpG5XqKnCV6tUd6d+/tXlIUE9PNxwd7f6l9PJNb5CYtiWXrv9L40ySHhdbGd8PcOKbpx1xtLbc9tChMzg4NKdZsxf5/vvFFuvkcjmRkaYOubm5+aSnZ1msf+GF7qxf/z8mTXqVwMD/Hr3oXu3atYvCQlO/kp49e5oTCICAgACGDRtmfr9p06YSO+79unMAyB07jnD+fBLgQl6eE/v33yAnJxAIp1atDjRo0BFwAaxp3boNPj4+gOkzLu81KYLwJBJJRCl75513ePHFF7l48aLF8mvXrvHWW28xePBgkUiUgi+//JKwsDCmTZvGmTNniIuLY/369fTt25dmzZqRlpZW1iEKFdi8efPMCURoaCgHDx7k2rVr/Pzzz/Tv3x8wjf//2WeflXpsR44c4cqVS0AuGRnn2bZtMdnZu4ETNGjgSuPGlYEcZDIDTZtGUKmSM8BjdRMXe11PrxnpfLE+F50B2oaqebPmRaaMHEWlSm1Ys8YyuQsO9jN/Lx84cLpYeVOmjOTs2cVkZGzBxaV05q7IzMw0v65ZM6zY+rCwsDu2zSq2/lHJycmjqMg0xOzp05dYuHAH4AUE3fypBlShUqWaPPfccJycTPNSVKpU6YmYQFEQHiciiShFW7ZsYfLkyeb3rVu3Zty4cXTt2tW8bN68eSxYsKAswntiLFiwgDfffNP8hEypVFqMl7xnzx569eqFmEJFeFBz5841v54/fz716plG5XFycmLWrFlUrlwZgHXr1lnMCVFSJEky3/TGxsaydu0KIB1IIClpP5mZ+4BzeHoWMXhwaxwdTW3/XVwcK3Ttwn/ZuesYAz7eStsvkzmWoMNeI2NqH0dmDnQCbTZbthwkLS2L48cvWOzn4GBHly5NefHFHgwf3rtYuRERIVSvHlCq7fHvnNzs2LGjxdYfPXp7mbOz0yOLIyUljYSEZECGVqvgt992k5CgBGpSqVIzwsJikCQvwJGmTVtQrVo1wJSUPk6JqSA8iUSfiFL07bffml9/+eWXjB492vz+999/p1+/fubtnnnmmVKP70lgNBoZN26c+f2YMWN49913cXBwYP369QwePJiUlBS2bdvGli1baNWqVdkFK1RYtzpRu7u7F2uLrlQqiYmJuTnrr8TVq1cfevQcSZLQarVYW1uj1RawaNF8mjWrQ0CACxpNPPb2N5CkOGQyGR073u67IJfLUanK5llSRkYme/fuITs7m0qVKtGoUSM0mpKZPyBfq+PA2VQKlM5cSNETe0PPhRQ9ZxJdkeQeIIO6XnqmDfYyTxhXu3YwAJ6ed59kdMWKr0oktpLSpEkTNBoNWq2WpUuXERUVTYsWzZHJZJw7d47p06ebt23Xrt1DHctoNGI0GlEqlaSmZnLw4BlatWqCSuXImTOXycnR4+dXB41GTseOblSqVAlQU6mS5uZrQRAeRyKJKEW32qVWqlSJV1991WJd3759+fTTTzl16hQHDhwgOzu7ws2aWRHs27ePCxdMTxmbN29uUTPUvn17vvrqK3Nzk19++UUkEcIDsbc3Dc2ZlpZGamoqbm5uFuvPnj1rfv0gv+eSJJGWloaLiwtyuYytW9eSk3ODrl0bodHkUru2HU5OeYAcX18XfH1d/rPM0lJQUMDUqVNZtWqVudkLgIODPQMHDmTw4MH3/ERfq5OIu2FKEmJT9Jy/rmfzgQQKVS7IFEog03IHuRKDNpfMrbPp/FoDvBy7mVeFhASQkrIBd/fy81n9G3t7e5566inmz5+PXq/nzTffxNfXFxsba86fv12TUrduhEXTpnuRnp5FZmbOzT4cSn77bRM1aoRSt24DFAotklRIUVEQKpUdjRr53BwUxFSrcC+zVguC8HgQSUQpys/PB8DT07PYSEwymQw/Pz9OnToFmP7QiiSi5F25csX8umPHjsXW37ksISGhVGISHj+dOnXizJkzGAwG3nrrLX788UfzusWLF7Nz504AqlevTtWqVe+pzBs3biCTyXBzc+XGjUssW7aY7t2b4O6uoWZNK4xGTyAbgNq1q5X4OZWEwsJCRox41dzUxqhywmDrj6TUcEOh4culF9h4eTnNWsZQoJMoKJLM/2p1kF8kkVdoICU1l/Q8A7mSDRJ/axJj7Y4MMBYVUMvfhgBXuHx8K5dPbEOflkBBagq+GiNz5+5GpcphwIAByGQyFApFhUkgbhkxYjhXr15l69atwO0asFuCgoKYNGnSXZsN5eUVIEkSdnY25OUVsH37EaKjI3F29uTSpXROn75OYGBHwIqGDe1xcnICXHB2hg4dfMzlqFSqYmULgvBkEElEKapatSoXLlzg5MmTnD9/3tw2FEw3CNu2bQNMTyZdXe9epS48nFtPiAHOnz9fbP2dy+7cVhDux7Bhw/jmm2/Q6XTMmTOHbdu20bp1a3bv3s3p07c75o4cObLYDZ7RaEQul5OamkpsbCzR0Q2APPbsWY2trYzWrcNxc9PTtWs4bm5KwFghbn61Ookvfl7LnnR/9LXaYnCqjkFTvCPtnkLYsy73P0q73ezJQSOjmoeSIHfTz5ZlK9i7YQONwn14e/BAxo17h6TLV1ABKsDm5keVk5PDV199TUZGJq++OqLEzrM0WVlZ8cUXn7N+/QYWL/7DPD9EQEAAPXp0p127Djg4mDp6X72awoULCbRs2QjQsHHjYZycXGnRojVWVjJkshwMhmDAjfBwP+rUkXOr22RFmCVdEITSJ5KIUjRkyBDeffddJEmiR48e/O9//6N58+YcPHiQkSNHUlBQAMCgQYNQKsV/zaPQtGlT7OzsyM3NZf78+QwdOpT69esDptqfd955x7zt3WoqBOFeBAYGMmfOHAYNGoTBYCA+Pp5Zs2ZZbDNw4EC6dOlCfHw8VapUwWDQMnfubBo3jqBaNV/y8i5y5coB6tY1zUXQunUQ1tZqTLNAy/H0dLv7wUuZwWDg7NmzZGVl4erqan44ciXdwNEEHUeumH5OJ+nQGaKh+u2hSGUyqOKqwMFaTm7mDS7HnUdm0GJnbUPi5VSKCvJo3bw2bVrWwdpKhrVKhrWVjFeHfUry1USUBalcuLbUomZ3SKM+KL409S+bPHkyly+bah9dXJzp06cvfn6+7Nixk3Xr1gEwZ84c2rVra/FQpyKRy+V06NCeDh3ac+LEBYxGidq1w9BqZcydu4o2bVoRGBiE0WiPVgtGY03kcjlNm7rcnLDNDpUK2rfvYC5T/P0RBOFeiG+KUjRs2DBmzpzJ5cuXOX369F3b27u6uvLWW2+VQXRPBnt7e55//nm++eYbCgsLiY6OpmPHjnh5ebFy5UqSk5MB0//DgAEDyjhaoSLr378/vr6+jBs3ji1btpiX+/q68957r/PSSwPZuXMnOTkZVKkSjUJhoEEDVypVKgBSqFzZjsqVW5r3s7W1vstRyo7RaGThwkX8+ut8Em/koHcIRu9YHZVXBAbH6uTqi0+eKSvKRJl1jgC7HDo3DOPIX+s4tOoI3/8xmapVg2jbdhjZ2TkolfZc358DgJVnW14e18SinPShDVGplDRoEFbshvfW7Nj5+fmsWrUKAI1GzS+//GKepKx9+/ZUrRrItGnfA6YmZu+++27JfkCPSE5OHgqFAhsbDQkJKWzdeoKnn34KKytH8vJyADVQC40GOnRwvNmxWYO/vyP+/rcTJVHbLQjCwxJJRClycnJi06ZNdOzY0dy59063bmT9/f3LILonx4QJEzh06BA7d+7EaDSabzRusbGxYfHixdjZPb5DXQqPTlJSEqmpqdSqVYNmzeowZEgP3nlnEO7uVhw7dpCqVcOoV68GcnkyTZoE3uxEbACgZs176x9RlrQ6iVOJRXzx82oOX5bQVxmHMex2Z9oCAD0oMFDLT0O4txw3WToNq2kYOvAZZEB4i+ZknM3jl1mmiduOHDlL9eqVsbGxITs7B5XKSPXqlQkNDaRFi3rFYnj22c7/GefFi3Hk55tqd1u1alVsluO+ffsyY8YMDAYjx44df+DP41FLSUkjIyOHkJAqgA1Llmyldu0IIiIicHQMIjTUA6PRF1ATHd3CYl8/P7+yCFkQhCeESCJKWVBQECdOnODPP//kt99+4/r16zg7O9OrVy/69euHra1tWYf42LOxsWHDhg18/vnnTJ8+nZSUFMD0BLNbt2589NFHhIeHl3GUQnlmNBopKipCo9GQm5vLpk3radKkLm5u1ty4cYSLF89Tq5ZpNuFOnWpiZ2eDTCYjIyOZBg3CsLIyffWW5rwCD0JvkLhwXc/xqzqOJug4flXHuWQ9eiNAI9McYjc5KvKwzr9IdvxelFlnUebEofeMZNKGgxiNEjdubMDezpbc3Dz27t3L66+bhh1VKhVcu5bKoUOHSE42/S4GB1dlx46fHyp2g+H2zPPW1sVrcVQqFXK5HIPBaLFtWTAajeh0etRqFTk5efz110FkMiPgRmJiLnFxhYSERAAyOnZ0uTnohgYHB8xzkAiCIJQ2kUSUAbVaTb9+/czzQgilz9ramo8++oh3332XM2fOoNVqqVKlihjTXLir/Px8kpKSbo6kpGfNmj+xtpbRunVdNJpsHB1TkcvjAUfCwz0ID7/dYfjWDMY6XdneqP6dJEkU6iFbayRHK5GrlcjRGknLM3Liqo5jV3WcTNRToCs+6aKVIQfSz6DMPk+LWv7428lQSYW88dkz/PJLEt9+uwKAhITL5vM+cuQ8nTt35vffF6LVFrJgwQ989dUwOnduyYkTx3n77bfN5ffo0eOhz69y5QCUSgV6vYG//trMa6+9ZlG7uG7denNsQUFBD328+5GTk8e1azeoXj0AULJy5W4cHd1o0aI1arUSlSqHtLR0wJ+IiEDq1r3d+f5h5xQRBEEoKSKJEJ5oVlZWotZBKEaSJA4cOICfnw9eXo6kpJzmr7824e3dFmtrGfXqOd6sTchEqYSWLSP/s8zSlJ5n5Lf9+VzPNpKjNZJTKJFzM0nI0UrkFpr+1Rn+uyw7tYyaXgq81LmEuEu0jnCjb5fOyICAgADW/LSVK1eScXZ24PXX+9O//wDmzp1HZmYmWm0q1ar507hxbZyd7Rk8eDCbNv1Famoqly9fYt686cybN93ieGFhYbRv3/6hPwNnZydatWrFhg0byczMZOjQobzwwovmjtV3dnTv2bPnQx/vbgwGAwqFAoPBwJYtB6lRozo+PlVISSlkx45rBAZ2wMrKhshIt5tDpbqgUkFMTFvWrFkDIGZ1FgSh3BJJhCAIT6yioiKUSiVyuZyTJ0+QmBhPu3aNkMnyuHZtH46OPnh5VcbPT2Lw4FaoVKYbOi+v8jEy0t1cvKFnyOwMrqTfQ4aAaYQkO7UMB40MO7UcB2sZNbysqO1rRW0/K3TpVwmr2Qej0Uj//u3pHf26eWYGLy9PwsOtuHIlmYyMbM6evURoaCDu7pXIzMzE3l7HgQNLLG6EZ86cwZtvvkl8/KVisURHRzFhwoRi8+g8qFdeeYW9e/eSnZ3D2bPnePPNN4tt07p1K/MIbQ9Dr9eTkpKOp6crCoWCnTtPk56upWvXbigUNhgMqTeHUPWnSpXKBAZGm5uz+fj4/HvhgiAI5ZBIIgRBeGJkZmZiNBpxcXEhMzOFRYsW0LVrczw9bbGzu4KraxZwGYDu3RuZ96soQ17ujSti6LwMsgok/FwUdKutwV4jx14jw04jw14jx0Ejw/7mazu1DFuVjK1bD/Lll/PZt+8kP/74Pj263R4VqsjJB7lchtEIx49fwNHREbubfRuOHDnKa6+9T/fuzQkPDyYoyI+EhKvmgSN8fHyLPUkPCAhg4cKF7N69h23btpKTk4ubmxsdOrSnZs2aJfrk3c/PjxkzZjB27FgSEq4WW9+5c2feffedBz7mmTPx2NlZ4+dXmfR0A6tXn6J79164u/tTtao3vr6FgKn5Ubt2t4eMvjWClCAIQkVWMf4yCoIgPIDs7Gzi4+OpXTscyGfXrlUolTratauHg0MhLVpUxslJC0gEBHgSEOBZ1iE/sD8PFzB2SRY6A9T1t+LHQc642t3uuG0wGDh1Ko69204waFAnNJrbT/uzs/NYs2YXAHv3nqBHj9tJhEplRc+erdBoVNStG4JSqaRjx44sWvQHWq2WDRsWM3bsGIKDgzl+/DgTJ05EutmNomvXLneNVaFQ0LRpE5o2bXLX9SWpevXqLFmyhF27drF7924KCgrw9PSiU6eO9zQSnl5v6jehVCqJj0/k9OkrdOrUAbAhLi4Od3cX/PzCcHMz0qdPNRwdHQEZXl5e/1quIAhCRSeSCEEQHiu7d+/G19cDf39XsrLOc+TIXwQH52Jjo6FpUz80GjWgQy6XU61a5bIO96FJksTXm3L55q88ADrV0vBlH0c0VpZP14cOncBPPy0HIDw8mOjoWuZ10dFhALi5Od11xKiFCydavB84cCDr1q0jOzuHo0eP0q9f/5u1Fbc7YXt4uNOrV6+SOcmHpFAoaNasGc2aNfvPbZOTUykq0uPv70lRkZxfftlEy5YtCQqqjlrthr29EwZDAAqFgk6depv3k8vlODk5PcKzEARBKF/K9/iCgiAId2E0GjEajQCcOXOaNWuWAjeAS2RnH0erPQZcxMdHxrPPxmBjowHAwcEOlapk2tuXB4V6idGLsswJRAv3FAo2f0uHti8X2zYysob59b59Jy3WeXq6ERe3nOvXNzJx4oj/PK63tzffffcdLi7O5mV3JhA+Pt5Mm/Z9ub2p1uv1FBXpALhxI4OVK3dQVGQFVOLs2QKOH88H6qBSRdCyZV88PcMBJ7y9K9OsWTPRHEkQ7pEkSWzfvp0RI0bQt29fRowYwfbt25Gk4qO+CRVPhamJmDhxIn/++Sdnz57F2tqaRo0aMXnyZKpXr27eRpIkxo8fzw8//EBGRgZRUVFMmzaNmjVrlmHkgiA8LK1Wi1arxcnJidzcLBYunEe7dg3x9XXAzu4Kbm7ZwBUA2re/3Um2vM/D8KAkSSI+MZO3VxvZH69DIYfPujvw4zvj2bz5AACXLydRufLtJjVNm0bQu3cboqPDaNeuYbEyq1S5v869YWFhLFu2jDVr1rJ5819kZ2fj7OxMu3btiYlpg0ajebiTLEGZmTlkZGTfPEc1v/22hZo1a1G3bhRWVoVYW4NOVxWVypYmTbwt+sCU9vCvgvC4uHbtGr169WLv3r0Wy6dNm0Z0dDSLFy8WgwpUcBUmidi2bRvDhw+nfv366PV63nvvPdq2bcvp06fNE7R9/vnnTJ06lTlz5lCtWjU+/fRTYmJiOHfuHPb29mV8BoIg3Kv8/HwuX75MSEgIMlkRW7euwGDIo1OnKOzsCoiKqoSTUz4Afn6V8PN7Mub30Ov19Ov3HtsPX8Wu49sYbCthr5bx/TNONA1Wc65ZBJs3H0ClsuLUqYsWSUTNmlVZtGhSicZja2tL795P0bv3UyVa7sMqKNBy+PBZwsKq4+joSXx8GidPJlGlSkdASfPmDjf7Ljji5ARt2tye16OidKIXhPIsOzub1q1bc/bs2buu37t3L61bt2b//v03J08UKqIK8225bt06i/ezZ8/G3d2dQ4cO0axZM1O74K+/5r333jOP+f3LL7/g4eHBggULGDp0aFmELQjCv9Dr9eabtiNHjuDq6oy/vxtZWRfZuXMV3t7NcXS0JjraHaVSARQAEBb2+D4dLiwsYu/eE5w/fwVXV0d69mxlXqdUKjmZDKpOH2KwccTLQcac51yo7mlqojVwYEdatKhHgwY1sbYuPzUBJeXSpUssWrSIHTt2kJ+fj4uLG127dqZ79+6cOHEJUNOoUROUShWJiZcIDKyKo6MXYWGVqV27Dbda8N5Lh2pBEB7c999/b04g/P39+eyzz2jYsCF79+7l3Xff5cqVK5w7d45p06bxzjvvlHG0woOqMEnE32VlZQHg4uICQHx8PMnJybRt29a8jVqtpnnz5uzevVskEYJQxrRaLWfPniU4OBhbWw2HDu3h3LlT9O/fBdCSnLwfhcIJf/8gPDyMDBnSxpxgODk9XjWJubn5nD4dx/nzV6hfP/TmzMW317VoYfq+at26gUUSsfJYAYWNXkMhU2Cdn8S0QZ7mBAIgMNCXwEDfUjuP0rRy5So++OBjJMmIUgnZ2XD0aBZbtnzD+PGLmDp1BtWqVQP8sLKCPn0GmPctqXknBEG4N7cmc5TJZKxdu5bQ0FAAqlatSkREBGFhYUiSxI8//iiSiAqsQiYRkiQxevRomjRpQliYaVSR5ORkADw8PCy29fDw4PLly/9YVmFhIYWFheb32dnZAOh0OnQ6XUmHLjxGbl0f4jq5LTc3l+Tk5JvtyCXWrVuJo6OGhg3DKSzM5NChVbi4RKJSOePjk4+dXSV0ugQA2rSpA4BOpzeXd+friig7O4/jxy/QuHFtDAbT5G96vZ5Fizbx/PMfAzBlyiiLG38HBztcXBxIT8/m/PnL6HR6JElixvYCpm7KB5mC1tWtmNonDBuVrMJ/Rn9nNBqRyWTIZDJiYxO4fj0DKysFr746nrQ0Cb0eJMkKd3dP0tNN105aWhLDhw/n6NGjj8Xvo/huEe5HebtetFotFy9eBKBevXoEBwdbxBYcHExkZCQHDhwgPj6e7OxsrK2tyyrcJ0pJXyMVMokYMWIEx48fZ+fOncXW/X3SIEmS/nUioYkTJzJ+/Phiy7ds2YKNjc3DBys89jZu3FjWIZQZg8HAxYsX8fBww9XVmmvX4jlz5jQdO9ZDqTSQmXmDggIrdu0yVWtXrWpNXNwp4uJul5GUFF9G0T9aX3yxiDVr9gOwYME7eHm5ArBv31602gzzdtu376NePcvag759m2NlpcTfvxLbduzkl1Oe7Eh0AqBd5XT6BlznyIHSOY9HLSMjB7lcjqOjLTk5RWzdeooGDSKxt3fj8uU00tKyWbx4CZcvm0ZziYmJ4dlnn8XOzo6rV68ydepU4uLiuHr1Km+//TadO3cu4zMqOU/yd4tw/8rL9XJrbhWApKQkVq9ebXEfJkkSSUlJ5vcbNmwQtYWlJD8/v0TLq3BJxKuvvsqKFSvYvn07vr63//B6epomiUpOTraY5Of69evFaifu9M477zB69Gjz++zsbPz8/GjZsiWurq6P4AyEx4VOp2Pjxo3ExMQ89l+AOp0OpVKJTCbjyJEjZGffoHnzukhSLkuWXKRuXUcCA33Q6/2AZqXWOdVoNJCVlYWVlQo7O7tSOeadPv30Jw4cOEVRkY61a7+zWLd+/UlzEqFQOBAVFc2+fXuJioomNDScI0cSCA72o2HDcIs5GwAaNzZNwpaSbWDMklx2J+qQy+CDTrY8E+UGVCuV83sU0tOziItLJDIyDLBj1ao9aDRONG7cHoNBjq/vGapUqWIeMCM5OZkPPvgQgMDAQFasWGExxGqjRo2oW7cuYOpX8/3335f6OZW0J+m7RXh45fF6adCgAfv37ycxMRGAjh1vz9i+Zs0arl41zSAfGRlJt27dyiTGJ1FaWlqJlldhkghJknj11VdZunQpW7dupUqVKhbrq1SpgqenJxs3biQiIgKAoqIitm3bxuTJk/+xXLVajVqtLrbcysqq3PwyCuXb43itpKamolAocHZ25vr1RJYv/4OnnmqDs7MVzs5JWFnlYmV1DYB+/W632beyKp2vlBs3bjBv3jxWrlxJdnYOACEh1enbty+dOnUqsXH8JUkiLi6RQ4fO4ORkT9u20Rbrly3byvHjF1AoFOj1eovOzI0ahRMVFUZERHWqVLk9bKhSqcTd3YUff3z/H4+bmW9k+rY8ftmdh1YHNioZ/+vvSKuQitdZ2mg0snXrIYKCgvD3D0arVXHpUhIREbXQaDS0a1cZjUaDXC7Hygrz9/ctqamp5tetWrUqNnRsREQEnp6eJCcnk5SU9Fj9Lj6O3y3Co1Oerpfhw4ezf7/pIUqfPn14/vnnzR2rf/rpJ/N2I0aMKDcxPwlK+rOuMEnE8OHDWbBgAcuXL8fe3t7cB8LR0RFra2tkMhmjRo1iwoQJBAcHExwczIQJE7CxsaF///5lHL0glG/Xrl3j0qVLNGpUDyhg+/ZluLnZ0qxZTZydC2ja1A9r62xATXBw2XbcjY2NZdiwYaSnZ1gsP3v2HOPHf8yuXbv47LPP7rs2RJIk9HqDRSJ06dI1goK6A9CxY+NiSURERHWOH7+Avb0Nly8nExISYF7XpUszunS5PUPyvfRdyCs0MntXPjO355GjNTXfqetvxafdHQj1fvR/aHNzc8nOzsbBweG+a3aKinQolQrkcjnHjsVy5UoGXbp0QS63w2hMx2CoClSmcuXKVK58O1H4r2ajpqFYTU6ePFlsfXJyMtevXy+2rSAIZWfAgAEsWbKEFStWoNPpmDFjBjNmzLDYpkuXLjzzzDNlFKFQEirMTEzTp08nKyuLFi1a4OXlZf5ZuHCheZsxY8YwatQoXnnlFSIjI0lMTGTDhg1ijghBwNRU79ZT3cJCLfPn/8SlS0eABLTa06Sm7sdoPA5cJCamGo0aBQI6rKyUhIQEoNEUr7ErbUVFRYwePdqcQKhUVkRHRxMcfHvI102b/uLnn3++5zJ37TpKTMwruLq25uefl1usCwjwxsXFdGN66NDZYrOsfvjhC8THryA9fbNFAnG/CvUSc3bl0fyLVKZsyCVHKxHiqeSnZ51YMszlkScQBw8eZOTIkbRo0YIuXbrSokULRo4cycGDB/9xnytXkrl6NQWQkZ2tZ86cv0hOVgM1cHVtROXKjQAfwJE2bdoVqz2+V1WqVDFPGLp3717mzJljXnfrerg1e7loFiEI5YNCoeCPP/5g9OjRxR4U2NjYMHr0aBYvXixmf6/gKkxNxL1MkS6TyRg3bhzjxo179AEJQjmXlZXF6dOniYqKRC7Xsn//egoKsujSpRFqtZbQUA2OjpmAkcBAZwIDm5r3tbe3LbO4/83mzZtJTDQ1owoJqc4333yDm5sbAFu3buWtt97CaJRYuHAhzz77rLmpYlZWLvv3n2TfvpMMG/YUrq5O5jIlCTZtMlW7HzpkOTGSTCZj+PDeKBRy6tWrUWyghocdTtVglFh6RMtXG3NIzDTdCFd2VTA6xo4u4Rrk8n8eFKKk/PHHH0yaZNnkU5Jg585dbNu2i7feGs2AAf25ciWZw4dj6datAzKZDSdPXsDGxglf3zrY2UGLFs44O/sB1vj62uDr61ci8clkMkaPHs3zzz8PwJAhQ/juu++oUaMGW7Zs4do10/WgVqt5+eWXS+SYgiA8PJVKxZdffsmHH37ImjVruHHjBpUqVaJjx46i1vAxUWGSCEEQ7u7OCds2bdqIr68rISF+FBZe5tKlndSsWYSDgx3R0Z4olT7cmrCtbt2QMoz6wWzevNn8etSo180JBECLFi2IiYlh3boNZGZmcfjwERo2NDU/Gj/+B776agEAEREhdOrUxLxfnTrVkMlkeHi4YGtbvM/Bxx+X/I2pJEmsP1XIlxtyuXDd1MzJ3V7Oa63t6FvfGivFo08eAE6cOGHRZ8zR0Y3AwCASEy9x8WIyqanw6qtTCQrqSJUqdXF1dUCvr4KVlRXt2vU2P0WUy7k5R8OjMWTIEPbv38/MmTMBOHz4MIcPHzavt7Ky4tdff6Vy5cqPLAZBEB6Mo6Mj/fr1K+swhEdAJBGCUIEYjUZSU1NxdHRErVZz9Oh+Tp06woABHYE87OyuoVLlAxLu7jKLTs92dhV/yOKsrGzz69DQGhbrPv/8FxYvPklcHISHQ3Z2lnldVFSY+fW+fSctkgg7OxuSktbh7u7yr8NBl5TdF4uY+lcBxxJM43U7Wst4pYUdgxraYK0qneTBaDQil8uZNWsO6emgUMAzz7xA69Y9yc830rp1e8aMGcPUqVMB+PLLmSxatAh399sj35VmMwSZTMb06dNp1KgRX331FUePHgVALpfTtWtX3nnnHRo0aFBq8QiCIAgiiRCEcu/q1avo9XoCAnwpKkpj2bJfaN26HlWruuHnl4OtrTuSlIJMJiM6Ouy/C6zAbGzsyc4GgwEOHz5C06a3k4EjR85x4YKpaUtBwe3Z7AEaN67NiBF9iIoKo1mzusXK9fB49MM5H7uq4/MDfpxOMyVCNioZzzex4cVmtjhoHl33NL1eT1ZWrrkJ1/Llu/H09KV+/Ub88stusrJMn9Xbb//PYqS6iRMnMnfuXFJTU1m+fLk58SgrMpmMQYMGMXDgQK5du0Z2djZeXl44OTmVWUyCIAhPMpFECEI5k5GRwZEjR2jWrAFKpZbY2J1otVkEBESi0UDPnvVwdrYH9Li6Olm073+cGY1GZs7cTUEBqFTw5ZdT8Pb2omrVquj1etRq04zQKhXY2TlQp87tEYB8fT347rsxpR6zJElsv1D0//buOzyqamvg8G8mbTLpvYckQAIhoUY60jsIovQqKhZQil7L/a5gBRuKWBALRVBABVGqIE2KIL2FFkoCJCEkkF5mMnO+P2KGjAFNGRIC632ePMzZ+5x91sAmyZqzC1/+nsOOOB3ggI0VDG+hZXxHB7ycLP9pvsFg4Pz5RLy93XB2duXkySvs2XOCRx55FLXaifr1nXB0dCQvz5GMjKKnIVFRUaWWura1taVBgwZs27YNnU5HXl6eae+G6qRSqQgICCAgIKC6QxFCiHuaJBFCVJOScxk2bFiPn58r0dG1gEQyMw+Tm2uFs7Mj7dqFmQ0d8fR0rZ6Aq0BSUipvvvk1e/Yco2PHGN57b6KpTq1Wc999Dfj99wPodHDu3CUGDRpMnTq1uX79OleuXCM6GmxsYMqUx6tsz4qb0RUq/HI4ny9/z+HUlaI5D1ZqaOWXzptDQgnxsuxKV/HxSWRn59KgQQNUKi2//76b1q3DcHZuSFhYXXx9m6NSuQAq09wFRVFwdnYmMzOT/fv3k5GRYTbZsbgcwMnJ6V+XYhVCCHFvkSRCiCqSm5uLtbU1tra2HDt2kAMH/mDUqL5ANh4eaTg66gAb3Nygf/8b+wvcbUvgHT0ax7JlGzh/PpHRo/uY7b1gZ2fDZ5/9ANx847rBg7tSt24Ahw7tpLDwGgBxcWcBKN4WYvDgQQwZMuQ2v4uby8gz8t2eXBbsyuVKZtFqSw62KoY0t2dkCzsuHD9JgGudf2nl32VmZrN79zFat26Bo6MvV69mkpqqokGDBqjVMGLEk9ja2gJFyyneLAFQqVQMHTqUuXPnkpOTw5gxY/jiiy/w8vIiNTWVcePGkZ2dDcDQoUOrZL6IEEKImkOSCCFuk5ycHHJycvD29kavz+bbb7+kXbuG1KvnTUBAOra2vhiNyajVapo1q3krJf2TZcs2sGXLPs6fT+T779/GxeXGxmVnziTw1ltF+zjUrx9ilkS4u7tQt24wcXEX0esLSy2p+vTTA4GiTdF++mklK1euJCEhHltbO+67L4bBgwfTsmXLKv+F9+K1QubtzOX7vXnk6IqWo/ZxVvNIGy1Dm2txsVej1xdyoRxtKopCXl4BWm3RilHbth3E3t6V5s1bY2trjU6XgU4XBrgTE2O+1GxxAvFvJk+ezDfffENeXh4rV65kzZo11K1blzNnzqDXFw110mg0TJ48uRyRCyGEuBdIEiGEheh0OuLj46lVqxa2tgoHDmwmKSmeQYPux8ZGT8+eEXh62gM63NyccXNzru6QK0xRFE6evMDBg6fIzy9g7FjzTb42btzD118Xbdx27twlmjS5kSSFhd0Yy37u3OVSbf/880wCArxwdr71jsmOjo6MHDmCkSNHlEo0qtKRS3q++D2HtUfzMf61lU09X2seb+dA30YabK3/OS5FUdDrC7G1tcFgMLB3byxhYQF4e/ty5kwSW7ceYOzYkVhbu+LhYYudnQbwR6OBPn0eqHT8ERERLF++nIceeoi8vDz0ej2xsbGment7e3788Ufq1bu7klwhhBCVJ0mEEJWQnJzMhQsXqFs3iPz8JLZs+YE+fZrj7+9GkyauxMS4A0Wf6AYG+lRvsBVUUKAjJyfPtHNzsVatHiEjI5uAAO9SSUTJROH8+USzJCIiohZr1swiLCyQWrV8S92vfv3y7WxckQTiapaBudtyyMhTcLZX4aRR46RR4aRR4Wx6rTY7Lk4IjEaFLacK+OL3HPac15vabFfXlsfbOdCurm2pmIo3y8zOzmPPnmO0ahWNlZU9mzcfIC/PSJ8+vbCy0nDpUhze3mF4e9cmICCMHj3qoVL5AlZERUWX+32WRc+ePYmNjeWTTz7h+++/N20INWjQIMaPH1/hnaaFEELcGRRFYc+ePaxdu9ai7UoSIUQ5pKSkcOjQQbp0aQ1kcv16LAkJKurWbYazM4wa1QGNpmjSbE3fl+H06XgGD36Z48fP8dhj/fnss5dMdSqVisaNw9m27QCXL6dw9ep1vLzcTPUjRvSiS5fmhIUF4uFhnnzY22vo1ast1WX7mQImL8sgNdtYruvsrMFJo0algqtZRddaq+GBRhoea+dApL8NANnZuWRl5eLn5wmoWLp0Mw0aRFGvXhTp6e6kp6tp3Lg+jo5OREV5YzAYgKIE8+GHh5nu5+DgUGWrIYWEhPD+++/z/vvvV8n9hBBCVI0jR47wyCOPmG3QaSmSRAjxN0Vj0fPQarUoisLKlT8SERFIZGQQkEBh4WkKChyxtramRYsg2rZtZLq2OIGoKbZu3cecOcs5ceI806ePp0+fdqY6Hx8PDh06DRTtwfB3jzzyAN26taRJkwgcHe3N6oKDfQkOLv2UoTrpDQofbMzm8205KAqE+1jTr7GGzHyFrHwjWSX+zMy78bp4jkNBIRT8lXg42akY2tyeR9o64GRVwIEDR8l2jsLR0YPY2ETi4hIZNux+QEN0tB1eXl6AG05OAfTq1Qsbm6KEw8enZj6dEkIIcec7duwY999/PxkZGf9+cgVIEiHueQaDgaSkJLy8vLCzs2Hv3t+JizvBsGHdUalyCAnR4eqaAdji7W1Hr16tAdDrC2vEijWrVv3O9u0HOXHiAj/88LZZonPlyjW+/34jAEeOnDFLIlxcHImIqIW1tRUNG5ZeUWj06D5mx0XzJE4SF3cWa+ui4TdBQYGlrqsOF68V8sySDA79tUv0sBb2vNLbuUw7RBuMCqnp+SQkpaN18yRPpxB/+CC+rp74udQnLw+uXk0kL68Ojo5eREcH0bChCiiaEN2gQQMA00RlIYQQoio888wzpgQiMjKSsWPH8vzzz1us/QolETk5Obz99tts2rSJlJQUjEbzYQHnzp2zSHBC3C4XLlzAaDQSFhZIQUEKa9cupmvXGEJD3albVyEgIAS4DmA2nv9OlZycyuHDZ8jOzuWhhzqb1S1Z8itLlvwKwOnTCTRsWNdUVzz/wNraivT0rFLtHju2zLSXxT85cOAAM2d+wMmTJ83KW7VqyYsvvkhQUFC535OlrDqcx39XZJJVoOCsUfHOQy70jNb84zWFhYUcOHCS0NBAvLz8uZ6SwaFdp3nkkXZYWzvhovfE3t4e8MXeHh56aLDp2qJyIYQQovqcOHGCrVu3AhAWFsaff/5Jfn5+9ScRjz32GNu2bWPkyJH4+fnViE9jxb0tNTWVAwf207lza6ys8jh3bgeQT1hYE7RaGDKk1V+rASl39MpJOp2e3Nx8XF2dTGWKohAe/hBZWTkEB/uWSiIaNaprSiJOnDhfKok4ceJHatcOvOm+DGVJIHbt2sXkyVMoLCwsVffHH7sZM+YR5s37mlq1apX5fVpCnk7htVWZLN2bB0CzWjZ8NMSVQLeifTeMRiPXrmXi7u6MWq1mz55YMjML6dq1C9bWWuLj4/D0DMHLqzahoWEEBrbA2rpoxai6deve8r5CCCFEddu7d6/p9aOPPoqDgwP5+fkWvUeFkoh169axZs0a2rRpY9FghKgsnU5nWiN/7dpVBAd7EhUVjEp1CZ3uJHl5WhwdtXTsWM8s+f2n5UTvBCdPXmDIkP8SG3uOceMe5JNPXjTVqVQqGjasw86dh0lISCY9PcssyRg4sAuNGoUTGRlGYKC3Wbs2NtbUqxdS4bgKCgqYOnWqKYEID69Lr169ycvLZeXKlVy5kkJ6ejrTp09n7ty5Fb5PeZ1M1jPhu3TiUgyoVDC+gwOTujhy7mwCSfkO+Pn5kpycxerV+xk4cCBubv54e7vj5JQHFD01GThwuKk9Ozs77Oxq1nwXIe40RqOR3377jUOHDqFWq2nRogVt27aVDyKFuA1KjhIq695B5VWhJMLNzQ13d3dLxyJEuZXcBfrw4b0cObKXkSN7A9n4+WXi7KwGbPHwsKZPnxsrAt2JP7RiY8+xcuVWDh48xeTJw2jd+saEbW9vNw4fLprkfPjwmVLXDhnSjRYtomjUqC7W1uY7XIeFBRIWdnvmJvz2229cv54OQMuWLfnoo1mmpxdDhw5l2LBhJCYmsW/ffuLi4qhTp/K7Nf8TRVH45o8c3lyTid6gxkWfwiPRWUzq3hPQcvz4SQIDffHza4S3dyH9+tXF2dkTsJKlTIW4jdatW8eECRNKDXdu0KABX3zxBa1bt66myIS4OzVqdON3iIULFzJx4kSL30NdkYveeOMNpk6dSm5urqXjEeIf5ebmkpqaCoBOl8XixZ9z4cJ24CjBwdm0aROAolwF8mnSpN4dt0KQoiicO3eJH3/87a+lPW/YuzeW//u/z/jxx03s2HHIrM7d3YWwsAAaNAijQYOwUu1OmDCYmTMnM2pUnypdWrbkknFjxow2G/7k5OTEwIEDTccHDx68LTFkZmaTmppOeq6Rx+Zd5bk3V5B3LZWOEa5881gLGtWKRlHqAAH07z+c++4r+mXF2toaHx8frKys/vkGQohK+eWXX+jTp89N50seP36czp07s3PnzmqITIi7V5MmTYiJiQGKVmnq3Lkz69evt+g9KvQkYubMmZw9exYfHx9CQkJMyxUWux1r0Yp7k06n4+LFiwQHB2NjY2Tfvk2kpFzk4YfbYWuro2fPCLy8qn4X6IsXL7F//z5OnDiJg4MjMTHNyvR0Y8SIV/juu6L/xCdO/Gg2lKhJkwjT6yNH4kpde+rU8jLNUahKJVcccnV1LVVfssxSqxOlp2cRG3uOFi0aYWXlxJ9/nubw+WyWp4aSmGFEGxDBf/o1ZUL3hkX/JvUjTdfeiU+ghLibFRQU8Pjjj5uGVrRr147HHnsMnU7HnDlzOHDgAPn5+Tz22GPExsbK/1EhLGj27Nl07NiRgoICtm/fzvbt2y3afoV+I+nfv79FgxCipISEBFQqFUFBPuTmXmLTpmX06dMCf39XmjZ1Ra12B3QABAVV7ZOGy5cv884777Bz5y5T2Y8//khISAiTJk2iXbu2fPjht+zYcYiMjBx+++0zs+vr1w8xvT548KRZElG/fiiLF79BkyYRhIcHl7r3nZZAQNEmZcXWr19vNuFYURSzTz1KnvtvjEYj2dm5prkqq1fvIjS0Ng0aNEKnc+LixUtER4eTUWjFnznZfHk6AcWqgBAPLR9PGE50oMu/3EEIURVWrFhBSkoKAD169GDNmjWo1UWDIEaNGkXr1q3Zv38/J0+eZOvWrXTs2LE6wxXirtKqVSvWr1/PyJEjuXTpksXbr9BvJdOmTbN0HOIelpmZyZkzZ2jatCEqVTYnTmzFzq6QoKBGuLrCiBHt0WqLluSszl2gL1++zNixY0lNTaOwEIoXOXB0LFoydvLkSbz11lt8992v7NtX9IlaZma22aTtdu2a0LNna2JiIomONp8fYGNjzfDhPS0as9FoNA3/8vDwsPjQnT59+vD5559jMBj55ptvsLa24YEH+pKbm8fixYvYs+dPAHx9fWnRooXZtYqiYDAYsLa2RqfTc/p0PGFhgWi1juzbF8eZM0kMHz4C0OLnB87O3ugNfpzLvs45p2YM+PIAZ1KyixqzsmFAkwBe7x+Fo92dl2wJca/avXu36fXEiRNNCQQUTfYcP348Y8eONZ0rSYQQltWhQwfOnTvHqlWr2LBhg0UXOanUT9v9+/dz4sQJVCoVkZGRNGnSxFJxibvcsWPHcHV1JjDQjZycOI4f30h4eA5OTg506VLP7Jfd4gSiOuh0evT6Qhwc7Hn33XdNCcSRI0X1YWFeNGzoy5EjR1EUePPNN2nUqCv79sXi4GBPXNwlmja9sc9E+/bNaN++2W2POzs7m8WLF/PTTytNSYSnpycPPtifESNG4OhomdWovL29GTlyJAsWLMRoVPjqq6/46quvAFAUMBhArYZJkyZy5co1zp27TNu2TQFbfvnld9zcPLj//rYYDAb27NmHi8t9aLVh1KsXSq1aeYArV7MKOI8P835P4fczsWTl31hK1kqtolmwG8NbBtOvcYBF3pMQwnJKzv3SaEp/Ly+5r8rf54kJISzDxsaGAQMG0L59++pPIlJSUhgyZAhbt27F1dUVRVHIyMigY8eOLF26FC8vL4sFKO4OKSkpnDt3jpYtGwJZXLiwC39/RwIDI/D1VRg5sotpLOydMNH1998PMH78O5w8eYEZMyYwZEhH08Q/Pz9PUlIUkpPTuHIli88/X8m0adPYuPE3cnPziIry4vjx74mIqFUt7+X69es88cQTnD1rPokxNTWVL7/8ik2bNjF37lyLrLCmKAqjRo3BaDSyaNEisrOhsLAoccjPh/x8a/7v/16ma9enOHfuMteu5aMojVGpVDRp4vTXsqk+2NvDo49OAMBoVDifYWTLqQy2/HCGw5cyzO7p7mBLh3AvOtbz5v66XrhobW4SmRDiTtCwYUPT63nz5tGhQwfTsaIozJs3z3RccjUZIcSdr0JJxDPPPENmZibHjx+nfv36AMTGxjJ69GieffZZlixZYtEgRc1jNBrZvXs3ISH++Ps7kZt7isTEvej1KmxsrOnT58an8dU1kW7Dht2sXLmVI0fOMH/+NOrWvTEPwdFRy7FjZwE4ejSOyEgPFKWo7sEHH6RBg1yys3PRalUUFhoZPXo0Gzf+BkBSUjyRkaVXUDp48CA//PADhw8fwWAopHbtOjz4YH86duxo0WRj2rRppgTCykptWp1h3759GAxGzp07z7Rp0/j444/L3bbBYODYsbMEBnrj4eHFqVOX+f33w4wf/y4PPPACb745k7Nnz+Pu7k6bNm3o3bs3YWFhgC1hYS6Ehd2Y5BwcbD7vY9vpq6w6nMjWU1dJzS4wq4sKcKZThDcd6nnTKNAVK7VMvhSiJhgyZAjPPfcc2dnZLFq0CLVazeOPP45Op+Pjjz9m48aNAAQEBNCzp2WHcwohbq8KJRHr16/nt99+MyUQAJGRkXz66ad069bNYsGJmuXMmTMkJV3k/vuboFZncu3aQby9U4AgQkK0hIS0r4aYEjh06DQJCck899wIs7rdu48yZ86PABw6dNosiahfPwSNxo66dYMIDvY1243ZycmJmTOfQK8vZOfOHdja2uDkdGNzt8JC81WIjEYj7733Ht9//4NZ+dWrqezevZv77oth5syZODg4VPr9njt3zjTp28PDnblzvyA0NASA8+cv8MQT40hLu8auXX9w9uxZateuXaqN/PwCkpPTCAoqWv70zz9PkJGho2vXLlhZ2XP06GHs7Rvh4RFJcHAdevWKRq32JjTUl6+/nl+huOdsPcs760+ajh1srWhX14uO9bzoEOGNj3P1DWkTQlScs7Mz7733Hk899RRQtF79woULzc5RqVR8/PHHd+TiEUKIW6vQ/1ij0VhqWVcoGnNVcoc8cXfLzc1lw4Z1tG7dEG9vDSpVHIpyEShaGadPn5ZVFktmZjbXr2dRq5afWfmwYf8zTXJ+8smHcHC4Mf625MTmCxcSza6zt9eQlbXN9EPt6NGjprr169czZMgQs/PXrVtnev33TcsWLlxolkBotfbY2tqSnl40TGfv3n1MmzaN999/v1zv+Wa2bt1qej1q1ChTAlEUVwijR4/mgw8+pLAQVqxYzX/+U7T5zJo1u6hdO4x69epz/Xo6GzacYdCgxri6+uLp6YajYz5QlGSNGPF4ifeiRaut3GT3kgnEoJhA+jUO4L4Qd2ytK7SNjRDiDvPkk0+iKAr/+c9/yMnJMatzc3Njzpw5PPjgg9UUXc2UmZnJ/PnzWbRoEZcuXUKtVjNw4EAmTJhgtkqeELdThZKITp06MXHiRJYsWYK/vz9QtHLN5MmT6dy5s0UDFNXPaDSaVtTYtWs7eXnX6dy5KRpNBi4uqajVCYArdep4U6eOd5XGdv16Ji1bjuH06QS6d2/F+vXmQ3QaNqzDvn2xKIpCbOw57ruvgamuQ4dmbN/+FVFRtXF1dfp702afikVFRVG7dhhnz57j+PFYXnjhBUaMGEFqaipfffUVCxbc+AS+X7/+ptd5efmmT91UKnj++ecZMGAA1tbW7Ny5k1deeYWsrGy2bNnKmTNx1K1buR2dMzMzTa89PPy4di0Dd3cXrl3L5Lff9uPrW4/UVMjOhj/+uALUB+zw8jKg1foCwXh7Gxg5sr5pwmPRcKTbo2QCMaVrOM92lh9+QtyNnnrqKYYNG8Z3333HoUOHUKvVNG/enMGDB1f6g4h7zcmTJ+nevTsJCQlm5bNnz+azzz5j3rx5jBw5spqiE/eSCiURn3zyCf369SMkJISgoCBUKhUJCQlER0ezePFiS8coqkFhYSHW1takpFxh9erlPPxwJ5ydwdf3+l+bhl1BrYaOHWNueyyXLl3h++83sn//SR544H4GD74xZM7V1Ylr14p+cd6//wSKopjNsXjooU6EhPgTHV3HbLgSgJubM23bNi5TDCqVismTJ/Pss89iNCps2bKVLVu2ljpvyJAhBAUFmo537NhBVlbRMqS9e/c2e4LRrl07nnjiSdMTiHXr1lK37rNligeKkrtr1zJxdnbA1taGM2cSuHw5j6wsKCiAxYt/x9m5EW3aRGFvbyAw0I5Vq1ZR/HOnZcvOQNEP7+bNm5vatbKyMlsx5Xb5fJskEELcS1xcXEzDmkTFZGVl0aNHD7MEIiAggCtXrlBYWEhhYSFjxowhODiY9u2rfgixuLdUKIkICgriwIEDbNy4kZMnT6IoCpGRkXTp0sXS8YkqUlBQ8NdKObB69XJcXKxp1y4SV9frNG3qio1NGqAhLOz2LaNZUKDj4MFTREaGmu2tcPHiFZ57bhYAGo2tWRKhUqlo06YRiYlXadasPvn5Bdjb3xg/36tXW3r1amuR+Fq1asU777zDa6+9Rna2+SN5laoogZg8ebJZeUrKFdPrli1LD+9q1epG2ZUrKaXqFUUhL6/AtMztgQMn0Wg0REbWJyenkBUr9tOzZ0+Cgmpja+tGq1YKH364EoPBwE8/bWbgwMdQFFs0mqLVmWbPng2AWq1m6NChFf/LqKTPt53l7XWSQAghRHksXLiQ+Ph4oGjlq2+//ZaIiAiWLVvGpk2bWLBgAUajkenTp0sSIW67Ss1i6tq1K127drVULKIKFRYWYjAYsLOz49y5U2zatJZRo3phZ1dAVJQtGo0tkImtrRWNG0fc9nhmzfqOF16YjV5fyKpVH9KnTztTXaNG4ajVaoxGI0eOxJW69qef3q+yFZ46depEixYtWLt2Hfv37yM5OZlmzWJ48MH+BAYGljq/5H4M586dK1VfXKYo4OjoQGFhIYcPnyE01B93d09OnLjErl1HGTt2NGq1lvz8bNRqFyASR0eF/v19/1qq1ZpatcKoVSuMMWPG8PXXX5OXl8eDDz6Iv78/KpWKy5cvm+47evRogoKCLP73UxaSQAghRMWUHO3xzTffEBUVhV6vx8nJiTlz5rBt2zbOnz/Phg0bSE5OxtfXtxqjFXe7MicRs2fPZty4cWg0GtOnmbfy7LNlH5IhqobBYCAzMxM3NzfAyLJlC4iI8CMmJhRf3+t06BCClVU6YE1IiP9tiWHHjkNs3ryX/ftP8OOP72Jjc6P7BQR4o9cXrYC0Z88xsyRCq9WwdOl06tYNokGD0qsJVfUSsQ4ODgwc+DD9+/dn584dtGnT1uy9lNSqVSusrNQYDEa+//4Hunfvjq+vPwkJyfj6uvL553NJTS0aftSiRX/U6tqcOhWLu3sw7u51CA4Ow8kpGvAG1LRufeOTJZVKhbd36Tkon3zyCYmJiabJ3omJ5pPGe/bsyaeffmqxv4/ymFsigZjcRRIIIYQoj0uXLgFFG33+fV8NKysrOnfubNrwMzExUZIIcVuVOYn48MMPGT58OBqNhg8//PCW56lUKkki7gAGg4H4+Hi8vb1xdNRw7Nhu9u//kzFjeqFW59KunR8uLo5AHlqtptR8gcrIy8vn4sUrhIfXMiv/7LMfWLLkV6Bo74WSOzm3aBFFvXohtGgRRYsWUaXaHDiwZg2VKyjQkZdXgLe3N926deO779aTnp5N9+7DaNiwNSkpOZw4cYrr13MBqF27Nh06DEOtVjNs2COmdhwdHcu9u7RGo2HVqlUsX76czz//nH379gEQExPDE088wcMPP1wtm+DN3XaWGSUSiIldak4CodPp+PHHH01DCRwcHOjRowdPPPFEqf0uhBDidnFxceHy5cukpqaSkpJS6oOk2NhYs3OFuJ3KnEScP3/+pq/FnePcuXPk5uYQFVUHRclg8+bvadcuiogIP+rUgYCARqhU2YCK4ODb8+lE+/bj2LnzML6+Hly6tNasrkWLKFMSsW9frFkSERzsy4kTP96WmG4n5a8d6LKzczly5AxNmtTH3t6VvXvPkZSUzsCBg3j++QV8/307zpw5Axg5d26HWRve3t6sWrXKtAKWJVhZWTFo0CAGDRpksTYroyYnEImJifTs2ZMjR46YlR84cICZM2cyf/78ap1fIoS4d/Tp04fY2FiMRiOTJ09mwYIFprpvv/2WXbuK9gmKjIy8rSvrCQFQod9aXn/9dXJzc0uV5+Xl8frrr1c6KFE2165d4+effyI3NxlIJDX1AFeu7AJisba+zMiR7YmIKNo3wcHBHk9P10oP/cnKymHu3OWMG/cW7767sFR90dAdA5cvp5CUlGpW17dvOxYvfoO4uJU8/njNWBPcaDSa9j65ciWNo0eL52RYs3LlHxw9mgb4YzTW4tIlO3Jz6wL1adiwO126PAy44Orqw4EDB3jllVfw8fExta3Vann88cfZt2+f2caNd5uSCcSkLnVrVAKh0+no1auXWQJRclPAgoICRowYwZYtW6ojPCHEPeapp54yLYLy3XffERYWxqOPPsp//vMfHnnkxlPsSZMmVflQX3HvqVASUbQ6TXap8tzcXF577bVKByXMldzAb/36NezZswGIR6M5h6NjMoWFp4AkmjcPpXPnG0uu2tnZVuqep05dKJUIKIrCk0/O4Msvf2L58s2lrmvRIoro6Do88khfdDrznZvDwgIZPrwntWsH3lHf3ErGeeLEec6fvwyoycws5OuvN3DligoI5OpVR06c0AONgUY0aNANJ6dwwBdn52AGDRqOh4cnULRLa9H8kyKOjo68/vrrXLx4kZMnT3Ls2DFSUlL44osvqm2Cc1X44nfzBGJSl/Bqjqh8VqxYweHDhwGoVasWmzdvJisri8TEREaNGgUU/V+RD0+EEFUhJCSERYsWmfYxunTpEosWLfrrSXeRRx99lMcee6y6QhT3kAolEX9fi7/Y4cOH/1opRlSGoigUFhZNMj53Lo5vvvmcwsILQCy1auXh56cHUtFqVXTu3NxsOVRL2LBhNx4enalX72EWLlxtVufs7Eh4eNEY8GPHzpriLDZ9+niOHFnKvHnTSu0eXV0MBgP5+QVAUcKwe/dRrl3LAGw4diyRxYt/B/yBEC5dsiUlxQNogoNDDG3aPIizc33Ah6io1gwaNAIomk9Qt27dcvd3GxsbIiIiaNCggdkn2nejL34/y/S1NTeBAEwbBQLMmzePjh07olKp8PPzY968eYSHF72nrVu3cuHChWqKUghxLxk4cCDbt2+nb9++Zr+LRUVF8fXXX/Pll1/eUR/UibtXuZZ4dXNzQ6VSoVKpCA8PN+ukBoOB7OxsnnzySYsHeS/Iy8vD3t4eRTHy3XcLiIoKplGjIDw9rxAT44GiXAGsqV8/1CL3O306ng0bdrNnzzFeffUJate+sTxpcLAv6elZAOzefbTUtR999DyOjloaNw4329UZqn6lpGL5+QVYWVlhY2PNlStpnDoVz/333wfYsW7dDjQaR7p06YJarSY+/gyBgXVwdw8mKKgWWm0DFMUXlUpF164PmNq0srIiMjKyWt5PTVcygZjYuWYmEIApMbC3t6djx45mdVZWVvTq1YvTp08DkJCQQEhISBVHKIS4F7Vs2ZJffvmFtLQ04uPj2b9/P6NHj8bWtuIjEIQor3IlEbNmzUJRFMaOHctrr71mNvPf1taWkJAQWrVqZfEg7zZGo5HU1FScnZ3RaDQcPLibo0f3MXJkd1SqHJo3d8PDQw1k4+zsQFRUnQrfKy0tnRMnLpTamXn58s38979Fy3x26dLCLIkIDw8mIqIW4eHBdO3aolSbPXq0rnA8lVG8izZAXNxFdDo9kZF1KSy05ptvfqVDh/sJDw9Hp3Pk+vVs9PoG2NjYEBPj9td1nlhbw+DBI01turi4yAoWFmI0KpxPy+Hng5eZvblo7sjEznWZ3LVmJhBwY5+PvLw8EhMTCQgw32wxLi6u1LlCCFFVPDw8cHZ25uLFi/L0QVS5ciURo0ePBiA0NJTWrVtjY2NzW4K6G509WzT0JyIilMLCdFauXEDHjk2pW9eb0NB8PDxCgQxAVaHlVvX6wlJ7FQwc+CI//rgJgCtXNuDtfWPoTcuW0abXf/55nNGj+5iO1Wo1J08uL3cMlnbsWBze3u54e3sSH5/Gr7/uYdSoIWg0rly9mk5BAURGNsbaGrp1c8TLywtwICjIjaCgGxvk3cvrZCuKwtWsAgyKgreTBiu15X7IJGfkc+hiOkcupXP4UjpHLmWQlX9jeFtNTyCgaE+N4iVyX3rpJRYsWGBaHnfLli2sWbMGAH9/f6Kjo2/ZjhBCCHG3KXMSkZmZibOzMwBNmjQhLy+PvLy8m55bfN69RqfTYTQa0Wg0JCcn8/vvm+jfvwu2toUkJ+9Fp8smIiIbW1t46KFmuLo6AXpcXZ3+el0+BoOBfv2e4+jROPz8PNm9e4FZfUDAjfWjjx8/Z5ZE3HdfJLNnP0/LltE0alQ9v+jpdHoSE68SGOiNtbU1+/ad5sqVLHr37gFoOHr0MNHR4Xh7N8HTM4f27YOwsgoGbGjVqrNZWzVpGEm+3kCezoCzvY1FfqlXFIWUrAIupOZwIS2HC2m5XEjN4XxqDvFpueTpDQBYq1X4OGsIcLMnwNUef1cNAa7av/60x9/VHge7m39LSM/VceRSBkcupXPoYtGfKVkFpc6zs1bTwN+ZAU0DGdGy1k1aqlnGjRvHu+++S0FBAYsXL2b37t306tWLs2fPsnbtWtMSv08//bR8qCKEEOKeUuYkws3NjaSkJLy9vXF1vflSocUTrg0Gg0WDvFNdvXqVa9euERERDhSwbNl8IiNr0axZHbTaFAIC8iksjMPWVkObNubLWnp4uJbpHllZOWzZso89e47RrFl9BgzoZKqzsrLixInzJCQkk5aWgdFoNNtroEWLBnTo0IyoqNp4eprfz9FRyzPPDKnoWy8zo9FITk4eTk5Fk4i3bz+Il5c39erVJzMzjw0bztC/fxTe3kH4+Hij1WYBRU9ihg4da2rHwcGBiIiIm93ijpNTUMjl9DwuXc/l8vU8LhV/pedx+Xouqdk607lOdtY429vgUuLLVVv059/LXextyNcbiE/L5Xxazl9JQy7xaTnk6m79f06tArVKRaFR4XJ6HpfTb578A7hqbfB3sTclGtdydBy5lM6FtNJLOlupVdT1dqRxkCsNA11pFORCuI8TNlaW2++iugUGBrJw4UKGDx+OwWAgLi6O2bNnm53Tq1cvXnjhhWqKUAghhKgeZU4iNm/ebFqJ5l5aE72wsBC9Xo+9vT3Z2dls3vwbbdo0wcPDnsuX93Hy5AkiIjoBRjp1CsHZ2QHIwtnZnjZtGpfrXnl5+ahUKjQaO1PZ2bOX6NfvOQAGD+5qlkQAREXVJjU1naio2qSnZ+HufmN8/9ChPRg6tEdF33qZFa0mZcDGxpr8/AIOHjxFZGQYLi6eHDoUx7FjFxg1agSgwcoqF5XKG6iLu7uRESPqoNVqAWrMUqcFhQYuXsvjXEomvyepOLzuFEmZBX8lC7lcz9X/eyN/ySooJOuvpKMy1CoIdNNSy0NLqKcDtTwcCPXUEuLhQKCbFiu1ipSsfBLT87icns/l63kkpuf9dVz0lZVfSHqunvRcPbFJmaXuUctDS6NAVxoGutA4yJUG/i7Y21b9ztdVbfDgwfj5+fHaa6+xefONZY39/f2ZMGECzz//vDyFEEIIcc8pcxLRvn37m76+uxWwdu1yHB2t6dSpGRpNJg4OSYAT4ErDhl40buwDFO3jUHL4UHmsWbODqVM/58iRMyxe/AaDB3cz1UVF1Uar1ZCbm8+ePcdLXfvtt2/i4GBfJROqip80paamk5CQ/NeO07asWrUDZ2d3OnToiFqtIiHhHCEhdXFx8adOnSD8/XMBDwBat25nak+tVpsSiDtNTkEh8Wm5JFwr/rS/6BP/+LRcEjPy+GsUC2AFF+JLXe+ssSbQTUugW9Gn+sWvA93sCXTV4mBnRWZ+Iem5OjLy9KavzLyiX+JLlpX8srZSEeLhUPTlWZQo1PJwIMhNi631Pz8B8HOxx8/Fnma3GGWUma8vkVgUJRxaGysaBRUlDq7ae3fVj/vvv59NmzaRkJBAfHw8jo6OREdHl1qdTAghhLhXVOgn4Pr163F0dKRt27YAfPrpp3z55ZdERkby6aefmm2yVVPpdPsBD1q08MTW1gZIx9oaOndubjqn5NChf7NixWbWrdvF6dMJLF06HT8/zxLtqDhwoGg5zN27j5olEdbW1rz33kR8fNxp0SKqVLuOjrfnl/Dk5FQKCw0EBvqg0xn57rvfuP/+NoSFhZOeDidPXqRhw2isrW1p2tTtr09ivbG1hcGDR5jacXZ2vqPnyOgNRv48f40D8ddNQ4Pir+Vy9Sbj/UtysLUiyF2LrS6DmHqhBP31iX9x0uCs+fdPpt0dbHF3uHN+MXfW2ODsa0M93zv336u6BQcHExxc/oUPhCiLHTt28Omnn7Jt2zays7Np2LAh48aNY8iQIbJ0pxDijlOhJOI///kP77zzDgBHjx5lypQpPPfcc2zevJkpU6Ywf/58iwZZHWxti/5qfHw8/vVcvV5PRkYGy5ZtJi7uIoWFBj7+2HyM9PbtB/nqq5UAnDx5wSyJaN68AWq1mvr1Q256v6efHliJd3Jr6elZ2NraoNVqSE5OZdeu4zzwQA+srR2JjY0nN7eQwMCu2Nra0LSpHe7uwYArder4UqdOM1M7gYGBt77JHShfb2DHmVTWH0/mtxNXSL/F8CM3rQ3BHg6EeGip5V70iX+Ip5Zgdwc8HW0pLCxk7dq19OoZIcNZhBAVpigKzz//PB988IFZ+c6dO9m5cyeffvopa9euxcPj338eCSFEValQEnH+/HnTJlzLly+nb9++TJ8+nQMHDtCrVy+LBngnSU1N5/vvNxIXd5HGjcNp1SqCb775ht9++w2dTs/x41BQABqNLbNn/8dsiFFExI0xJBcuJJq16+HhSkbGVos/VTAYDKSnZ+Hq6oSVlRVnz14iIyObpk0bAhpWrtxG48ZNaNy4EXZ2wXh62lNYGIa1tYZ27fz+GqpR9B4aNmxo0diqWla+ni2nrvLrsWS2nEoxm4js7mBL+3AvansVzSWo5aGllrsDLlpJDIQQt99HH31klkA4OTlhbW3N9evXAfjzzz8ZOHAgmzZtkr0AhBB3jAolEba2tuTmFq3W8ttvvzFq1CgA3N3dycwsPSGzqn322We89957JCUl0aBBA2bNmkW7du3+/cISXnppNhMnDjXb6C0jI5vx44uewLRv35DPPotFr7+xLr6dXVESkZ+v4733PuKFFyaZ6vr370BMTCR16wbj4lJ6U6qKJhDp6VlkZ+cSGOgDwKZNewkM9CciIoLU1Ex+/nk/Dz/8IO7uPuTmKn/9UCpaz75375E4OTkBGtzcHLn/fi9Tu5b4ZD0jT09cSjYu9ta4O9jhYqElTcvqWo6O32KvsP54MjvOpKIzGE11/i4aujXwpUeUL/eFuFdpXEIIUUyn0zFjxgzT8QcffMDjjz/Ob7/9hqOjI8OHDyclJYUtW7awa9cu2rRpU43RCiHEDRVKItq2bcuUKVNo06YNf/75J8uWLQPg9OnT1T60ZdmyZUyaNInPPvuMNm3aMHfuXHr27ElsbGy5xjJ/9dXPtGnT2CyJqFXLF2trKwoLDezde5R69Ypm17q4OBMd3RCNJparV69hZwdLly6mVatmpuTF19cTX1/Pm97r31y7loFarcbV1Ynr1zPZuHE/3bp1wtXVk9OnU4iLu8SwYfcDdtjb52Nj4weE4eFRSP/+tXB2dgesiY6OMWu3aHM2y1EUhbiUbDafTGHzyRT2xV/HYDTNQEatAletLW5aGzwc7HBzsMHdwQ4PB1vcHGzN/nTW2GBlpcJKpUKtBiuVCiu1CrVahVpVurz407mkjDx+PZbMr8evsOd8GiVuT5inAz2iihKH6AAX+URPCFHtNm3aREpKCgAPPfQQkydPRq/Xo1KpaN++Pe+++y5jxowBYPHixZJECCHuGBVKIj755BOefvppfvzxR+bMmUNAQAAA69ato0eP27+k6D/54IMPePTRR3nssccAmDVrFr/++itz5swx+7SnLOLiLpodW1tbs2jR62zfvpXff98IQNeuXZg27VXs7TUYjUa+/noen3/+OVD0Db84iTAaFTLyFNJyjKRlG4v+zDGSkWvESg3WGLC3VWNvZ01m2hWuJSfTvFVz7Kw1bN8Qi6+PH23aRqEYVDh7qCkoDEVRXGnc2JemTdUU/1O2bt3GLF5v74qtGFVW+XoDf5xNY/PJFLacSuHSdfOlSn2c7cjTGcjML8SoFD0duJaj4+zVHIvGofprL4SSSQtAA39nevz1xKGOt6MkDkKIO8rly5dNr7t06VKqvmRZyXOFEKK6VSiJCA4OZvXq1aXKP/zww0oHVBk6nY79+/fz0ksvmZV369aNXbt2lautNWtm3XQ1pCFDuvPtt59ga1v0S/qLL77E1VxrYs/mk5ZjJDd0MOoYBzIKrNhkdKHL+1dIz1dxLUuHPj8PK/uinan1aZdApcLGPQCjPp+c41uxD22KtYs3+vR0CtNS0Ry/gkqlwljgjSrOCtXuPTcC2bgLWys1Llob3LQ2uGptcbW3wU1ri+tfx0Xlxa+Ly22ws67c2v6Xruey5WQKW05dZdfZVPL1N4YJ2VqraRXmQad63nSM8CbYo2iYlt5g5HpuUQJxLVvHteLXf32l5ei4XuI4M1+P0QgGRSmVGNyMohSdi6LgoWTQPyaEMV2aEOR+Zy4hK4QQAC4uN/b2OXbsWKn6kmWurq5VEZIQQpRJhRc5NxgMrFy5khMnTqBSqahfvz79+vXDyqr6Np9KTU3FYDDg4+NjVu7j40NycvJNrykoKKCg4MZynsVzOpo1q4+zs6PZnIe/n+Pn54utrR2/7M7l/Y25FGZeBcDarSOKoZC8c/s4ee4q1s6e6K8lkX/xOAEteuLhaIexQIezgx31GvljVCDZT4WNsydGK1vy9W4UFEZQoDdQUGikoFBDfmHRa12hEb2h6JdqncHI1ayCf12O9O/srNU4a6xx0ljjpLHBWWONs8YGR431X6+tcbK3+Ws35aK6gkID28+ksfX0Vc6kmD9F8HW2o0OEFx3CPWkV5o7W9ka30utvrHzkprHCTWNPbQ/7csULRU9yDIqCUSnx2qjw+/btPPHU06Rdu4ZKZYVRn098QQ4HgNghQ/jiiy/QaDTlvl9ZFL+3ku9RiFuR/iJupn379tjb25OXl8e8efMYOnQoTZo0ASA5OZmXX37ZdG6vXr2k/4hS5HuLKCtL95EKJRFxcXH06tWLy5cvExERgaIonD59mqCgINasWUPt2rUtGmR5/X3ISvEmaTczY8YMXnvttVLl+/btxcFBw/XrWSiKgru7MwaDgYMHzwJ25OfncOTIJSZP/oBabfsT5uxMbtoF7NUKZ4/uJv1KIvrUBCaMf5rQgEJsFXesdDG4uelQqfQQXjw/I6Hoj7pWwPUyvT+DAnoj5BYWfeXoVUV//vWVW6gqeq0vep1rKgcFFQWFRq5m67iarSvj36g5FQqhThDpZqSBq4KfthCVKoeCcxfYeq5CTVZIXFwc//3vf9Hpbv4+li5dSnx8PC+88MJtHca0cePG29a2uPtIfxF/16FDB9atW0deXh7t2rUjOjoaR0dHDh48SF5e0RBRHx8fbGxsWLt2bTVHK+5U8r1F/JviRZEsRaUoyr+PFfmbXr16oSgK3377Le7u7gCkpaUxYsQI1Go1a9assWiQZaXT6dBqtfzwww88+OCDpvKJEydy6NAhtm3bVuqamz2JCAoKIjFxD56ePmzcuIvCQujZsyeKYs2vv25m48bf+PjjjwFo3bo1S5Yswc/Pj6ysLP73v/8xZ84coOian3/++Ta/67IzGhWyCgrJyi8kM19PVv6N15l/vb5ZXVZ+IYUGhZhabnSI8KRdHU9c74DlT3v27MmmTZsA6Ny5M//73/8IDAzk559/Ztq0aeTkFD0x2bJly22ZjKjX69m4cSNdu3aVfSLEv5L+Im4lNzeXvn37sn379pvWe3p6sn79+hq/1La4PeR7iyirtLQ0/Pz8yMjIsMxGwEoFaLVa5ciRI6XKDx06pDg4OFSkSYtp3ry58tRTT5mV1a9fX3nppZfKdH1GRoYCKFeuXFEURVEKCgoUg8Fgdk5iYqLi4uKiAAqg2NjYKE2aNFGcnJxMZSqVStm6datl3pQo5fz586a/69DQUKWgoMCs/quvvjLVjxo16rbEoNPplJUrVyo6ne62tC/uLtJfxD/Jy8tT3n77bSU4ONj0vUur1Srjxo1Tzp8/X93hiTuYfG8RZZWamqoASkZGhkXaU1ck8bCzsyMrK6tUeXZ2Nra2thVKZixlypQpfPXVV8ybN48TJ04wefJkEhISePLJJ8vVTvHcDltbW9Rq878mPz8/Vq1aZZoQp9frOXjwoOnvRK1W88UXX9C+fXsLvCNxMydOnDC9HjhwYKl+N3z48JueK4QQdyKNRsOLL77I+fPnOXXqFJ9++imJiYnMnTuXkJCQ6g5PCCFKqVAS0adPH8aNG8eePXtQFAVFUdi9ezdPPvkkDzzwgKVjLJfBgwcza9YsXn/9dRo3bszvv//O2rVrqVWr1r9fXA7t2rXj6NGjvPjiiwQEBKBSqXBzc+ORRx5h//79piVmxe1RMmko3tW1pPT09JueWxPt27ePRx99lKioKCIjIxk6dChbt25FKf9IRCHEHU6tVhMaGkpAQABarawuJ4S4c1VoYvXs2bMZPXo0rVq1Mo2/0+v19OvXj48++siiAVbE008/zdNPP33b7xMUFMTbb7/N22+//Y+Tt4XlxcTEmFY0WbJkCf/973/NPq0ruSfI/fffXw0RVp7RaGTKlCml/k+dOHGCpUuXMnToUBYsWFDjkyQhhBBC1DwVSiJcXV35+eefiYuLIzY2FoDIyEjq1KnzL1fevSSBqFouLi6MGDGCL7/8kuzsbJo1a8bjjz9OcHAwK1asME24trKyYty4cdUcbcVMnz7dLIGwsbFBpVKZVqNasmQJrq6ufPbZZ9UVohBCCCHuURUazgTw9ddf079/fwYOHMjAgQPp378/X331lSVjE+IfzZgxg/DwcACuXbvGO++8w/jx400JBBTtYF4TxxNnZWXxzjvvAEUJ6vvvv096ejpZWVl8/fXX2NnZATB37lwuXrz4T02VW3x8PK+88gp9+/alX79+TJ8+/Zb7rAghhBDi3lShJOKVV15h4sSJ9O3blx9++IEffviBvn37MnnyZP73v/9ZOkYhbsrDw4MdO3YwZMiQUpschoSE8O233/Lss89WU3SV89NPP5GdnQ3A2LFjee6559Bqtdja2jJ27FheeOEFoGjI0+LFiy1yT0VRmDp1KmFhYbz55pusXr2aX375hf/7v/8jODiY2bNnW+Q+QgghhKj5KjScac6cOXz55ZcMHTrUVPbAAw/QsGFDnnnmGd58802LBSjEP/Hy8mLJkiW8//77bN26lby8PMLCwmjfvn217p5eWfHx8abXffr0KVXfp08f3njjjVLnVsZbb71lavPv9Ho9EydORKvVyqIBQgghhKjYkwiDwUBMTEyp8mbNmlFYWFjpoIQor4CAAIYPH85jjz1Gp06danQCAeDo6Gh6HRcXV6q+ZFnJcysqLS3NlPyrVCpefvllzp07x8mTJ80WKXj55ZfNNmcUQgghxL2pQknEiBEjTLsyl/TFF1+Yrc8vhKiYHj16mF5/+OGHXLp0yXR87do13nrrLdNxz549K32/b7/91pQcPP3000yfPp3Q0FAiIiL49NNPGTBgAACpqan88ssvlb6fEEIIIWq2Cg1ngqKJ1Rs2bKBly5YA7N69m4sXLzJq1CimTJliOu+DDz6ofJRC3GPq169Pt27d2LBhA4mJidSrV48BAwZgZ2fH8uXLTXtjREdH06lTp0rf7+TJk6bXJYcplixbsWJFqXOFEEIIcW+qUBJx7NgxmjZtCsDZs2eBorHpXl5eHDt2zHSeLHsqRMXNmzePdu3acf78eXJycli0aJFZvZeXF8uWLbPI/7Pi1Z6g6GnD35UsK3muEEIIIe5NFUoitmzZYuk4hBB/ExAQwO7du5k2bRqLFi0iJycHKNqBe9CgQbzxxhsWW762ffv2zJo1C4D33nuPnj17mjaxy87ONtuvon379ha5pxBCCCFqrgoPZxJC3H7e3t7MmTOH9957j+PHj2M0GqlXrx5ubm4WvU+fPn2oVasW8fHx7Ny5k0aNGjF69Gh0Oh3z5s0zrQAVExND8+bNLXpvIYQQQtQ8kkQIUQM4OjrSokWL29a+tbU1ixYtolu3buTn53Py5Elefvlls3NcXV2ZP3++DFMUQgghRMV3rBZC3F3atWvHtm3baNWqVam6Ll26sGvXLqKioqohMiGEEELcaeRJhBDCpHnz5uzatYtjx45x6NAh1Go19913H3Xr1q3u0IQQQghxB5EkQghRSlRUlDx1EEIIIcQtSRIhbkmv17Ny5Up+/vln0tPT8ff3Z9iwYbRv317GxQshhBBC3MMkiRA3dezYMfr168e5c+fMyr/88kvatWvH8uXL8fLyqqbohBBCCCFEdZKJ1TVQWloap0+fJi0t7ba0f/HiRTp16lQqgSi2fft2evToQX5+/m25vxBCCCGEuLNJElGDbNy4kS5duuDp6UlERASenp506dKFDRs2WPQ+M2bM4OrVqwA0btyYX3/9laSkJBYvXoyfnx8ABw4c4Ntvv7XofdPT05k9ezY9e/bk/vvvZ+TIkfz2228YjUaL3kcIIYQQQlSOJBE1xKxZs+jWrRubNm0yK9+0aRPdu3fnww8/tMh9CgoKWLRoEQAODg5s2LCBbt264evry/Dhw/nhhx9M53711VcWuSfAr7/+SkhICBMnTmT9+vVs376dxYsX07VrVzp16sS1a9csdi8hhBBCCFE5kkTUALt27WLy5Mmm49q1azNs2DDCwsJMZVOmTGHHjh2Vvtfly5fJzs4GoGvXrqXmPbRp04bg4GAATpw4Uen7Aezbt49+/fqRkZFx0/pt27bRr18/DAaDRe4nhBBCCCEqR5KIGqDkU4YXX3yR06dP8+2333LmzBlefPFFU92sWbMqfS9bW1vT65t9+q/T6cjMzCx1bmVMnTqVgoICAHr37s2RI0fIyclh2bJleHt7A7Bjxw5WrVplkfsJIYQQQojKkSTiDmc0Gvnll18A8PLy4vXXX0etLvpnU6vVvPHGG6ZftH/55ZdKf1ofEBBgesLx+++/l3q6MXfuXNLT0wFo3759pe4FkJiYyPr16wEIDg5mxYoVREdHo9VqGTRokNmQqa+//rrS9xNCCCGEEJUnScQdLi8vD51OB0C9evVKffpvY2NDvXr1gKJ9HSq7YpJKpWL8+PGm4y5duvDkk0/y2Wef8dBDD/Hss8+a6kqeV1Fnz55FURQAHnjggVLvr3fv3tjb2wMQFxdX6fsJIYQQQojKk30i7nBarRYXFxcyMjLYv38/6enpuLq6murT09PZv38/AM7Ozmi12krfc8KECaxdu5ZNmzZRUFDA3LlzS53z7LPP0qFDh0rfqzhBAEhKSipVf+3aNVNipNFoKn0/IYQQQghRefIk4g6nUqkYPnw4ALm5uYwcOZLk5GQAkpOTGTlyJDk5OQAMHz7cIjtJ29rasnr1aiZOnIiDg4NZnY+PDx988IFF5l8AREdH4+npCcDPP/9sSogAFEXhtddeMz2p6Ny5s0XuKYQQQgghKkeeRNQAkydPZsGCBeTm5rJ69WoCAwMJDQ3l/PnzpjkQWq2WSZMmWeyeGo2GWbNm8dprr7Fp0ybS09Px8/Ojc+fOFptQDWBnZ8cTTzzBW2+9RWFhIW3atGHo0KHUrl2b1atXs2fPHgCsrKx46qmnLHZfIYQQQghRcZJE1AB16tRh5cqVDBgwgOzsbAwGg9n8AEdHR1asWEF4eLjF7+3i4sKAAQMs3m5J//d//8fWrVvZuXMnBQUFLFiwoNQ5H3/8MbVr176tcQghhBBCiLKR4Uw1RNeuXTlx4gQvv/wytWvXxtnZmdq1a/Pyyy8TGxtL165dqzvECrO3t+fXX39l0qRJODk5mdVFRUWxfPlyeQohhBBCCHEHkScRNUhgYCDTp09n+vTp1R2KxTk4OPDhhx/yxhtvsGvXLrKzs6lVqxZNmza1yDwPIYQQQghhOZJEiDuKo6Mj3bp1q+4whBBCCCHEP5Ak4h6hKArx8fGkpaXh4+NDYGBgdYckhBBCCCFqKJkTcZdTFIUlS5YQExNDaGgoMTExBAUF0a5dO9auXVvd4QkhhBBCiBpIkoi73Msvv8ywYcM4cOCAWfmOHTvo3bu3xfZ7EEIIIYQQ9w5JIu5iq1at4p133jEdN2vWjHHjxlG/fn1T2eTJk017MQghhBBCCFEWkkTcxT788EPT6w8++IB9+/Yxd+5cjh8/zosvvmiqmz17dnWEJ4QQQgghaihJIu5SOTk5bNmyBYDatWszceJEU51KpeLVV1/F1dUVgDVr1lRHiEIIIYQQooaSJOIulZ2dbXodHh6OWm3+T63RaAgNDQUgMzMTRVGqND4hhBBCCFFzSRJxl3J3d0er1QKwc+dOsrKyzOovXbrEkSNHgKJN7GRDNyGEEEIIUVaSRNylbGxsGDJkCFD0pGHIkCEkJCQAcPr0aYYMGYLBYABg1KhR1RanEEIIIYSoeSSJuIv95z//MT2NWLt2LbVq1cLX15eIiAh27twJgIeHB+PHj6/OMIUQQgghRA0jScRdrF69evz88884OTmZyq5cuWJ67eXlxfr16/Hz86uO8IQQQgghRA1lXd0BiNurS5cunD59mi+++ILly5dz7do1vL29GTp0KGPHjsXd3b26QxRCCCGEEDWMJBH3AF9fX6ZOncrUqVOrOxQhhBBCCHEXkOFMQgghhBBCiHKRJEIIIYQQQghRLjUiibhw4QKPPvoooaGh2NvbU7t2baZNm4ZOpzM7LyEhgb59++Lg4ICnpyfPPvtsqXOEEEIIIYQQlVMj5kScPHkSo9HI3LlzqVOnDseOHePxxx8nJyeH999/HwCDwUDv3r3x8vJix44dpKWlMXr0aBRF4eOPP67mdyCEEEIIIcTdo0YkET169KBHjx6m47CwME6dOsWcOXNMScSGDRuIjY3l4sWL+Pv7AzBz5kzGjBnDW2+9hbOzc7XELoQQQgghxN2mRgxnupmMjAyz5Un/+OMPoqKiTAkEQPfu3SkoKGD//v3VEaIQQgghhBB3pRrxJOLvzp49y8cff8zMmTNNZcnJyfj4+Jid5+bmhq2tLcnJybdsq6CggIKCAtNxZmYmAHq9Hr1eb+HIxd2kuH9IPxFlIf1FlJX0FVEe0l9EWVm6j1RrEvHqq6/y2muv/eM5e/fuJSYmxnScmJhIjx49GDhwII899pjZuSqVqtT1iqLctLzYjBkzbhrDli1b0Gq1//YWhGDjxo3VHYKoQaS/iLKSviLKQ/qL+De5ubkWbU+lKIpi0RbLITU1ldTU1H88JyQkBI1GAxQlEB07dqRFixYsWLAAtfrGaKypU6fy888/c/jwYVPZ9evXcXd3Z/PmzXTs2PGm7d/sSURQUBBJSUl4eHhU5u2Ju5xer2fjxo107doVGxub6g5H3OGkv4iykr4iykP6iyirtLQ0/Pz8yMjIsMhc4Wp9EuHp6Ymnp2eZzr18+TIdO3akWbNmzJ8/3yyBAGjVqhVvvfUWSUlJ+Pn5AUWTre3s7GjWrNkt27Wzs8POzq5UuY2NjfxnFGUifUWUh/QXUVbSV0R5SH8R/8bS/aNGzIlITEykQ4cOBAcH8/7773P16lVTna+vLwDdunUjMjKSkSNH8t5773Ht2jWef/55Hn/8cVmZSQghhBBCCAuqEUnEhg0biIuLIy4ujsDAQLO64tFYVlZWrFmzhqeffpo2bdpgb2/PsGHDTEvACiGEEEIIISyjRiQRY8aMYcyYMf96XnBwMKtXr779AQkhhBBCCHEPq7H7RAghhBBCCCGqhyQRQgghhBBCiHKRJEIIIYQQQghRLpJECCGEEEIIIcqlRkysFkIIIYS4m+Tn55stWV9RRqORoKAgEhMTS+2hJe49Xl5epk2abzdJIoQQQgghqlB+fj4pKSkEBARgZWVVqbaMRiMuLi44OztLEnGPMxgMXL58GW9v7ypJJKS3CSGEEEJUoatXr1okgRCiJCsrKwICAizyhKssJIkQQgghhKhikkCI26Eq+5UkEUIIIYQQQohykSRCCCGEEELcUS5cuIBKpeLQoUPVHYq4BUkihBBCCCHELalUqn/8GjNmTHWHKKqBrM4khBBCCCFuKSkpyfR62bJlTJ06lVOnTpnK7O3tzc7X6/XY2NhUWXyiesiTCCGEEEIIcUu+vr6mLxcXF1Qqlek4Pz8fV1dXvv/+ezp06IBGo2Hx4sWkpaUxdOhQAgMD0Wq1REdHs2TJErN2jUYj77zzDnXq1MHOzo7g4GDeeuutm8ZgNBp5/PHHCQ8PJz4+viretvgX8iRCCCGEEEJUyosvvsjMmTOZP38+dnZ25Ofn06xZM1588UWcnZ1Zs2YNI0eOJCwsjBYtWgDw8ssv8+WXX/Lhhx/Stm1bkpKSOHnyZKm2dTodw4YN4+zZs+zYsQNvb++qfnviJuRJhBBCCCFENfvggw8IDAwkMDCQrVu3mtWdP3/eVPfMM8+Uunbo0KEEBwcTGBhYqm7BggWma1esWHG7wmfSpEkMGDCA0NBQ/P39CQgI4Pnnn6dx48aEhYXxzDPP0L17d3744QcAsrKy+Oijj3j33XcZPXo0tWvXpm3btjz22GNm7WZnZ9O7d2+Sk5PZunWrJBB3EHkSIYQQQghRzTIzM7l8+TIABQUFZnXFOxEDXL9+vdS1aWlppvq/y8nJMdXl5uZaMmQzMTExZscGg4G3336bZcuWcfnyZQoKCigoKMDBwQGAEydOUFBQQOfOnf+x3eIhUZs2bUKr1d62+EX5SRIhhBBCCFHNnJ2dCQgIAMDOzs6srngnYgA3N7dS13p4eJjq/87BwcFUdzt/CS9ODorNnDmTDz/8kFmzZhEdHY2DgwOTJk1Cp9MBpSdj30qvXr1YvHgxu3fvplOnThaPW1ScJBFCCCGEENVsypQpTJky5aZ1oaGhXLp06ZbXLlmyBGdnZ9Tq0qPUx4wZUy1LsG7fvp1+/foxYsQIoGhi9JkzZ6hfvz4AdevWxd7enk2bNpUawlTSU089RVRUFA888ABr1qyhffv2VRK/+HeSRAghhBBCCIuqU6cOy5cvZ9euXbi5ufHBBx+QnJxsSiI0Gg0vvvgiL7zwAra2trRp04arV69y/PhxHn30UbO2nnnmGQwGA3369GHdunW0bdu2Ot6S+BtJIoQQQgghhEW98sornD9/nu7du6PVahk3bhz9+/cnIyPD7Bxra2umTp1KYmIifn5+PPnkkzdtb9KkSRiNRnr16sX69etp3bp1Vb0VcQsqRVGU6g7iTpKZmYmLiwupqal4eHhUdzjiDqbX61m7di29evWSTXXEv5L+IspK+srd7+LFiwQFBVmkLaPRSGZm5i2HM4l7z636V1paGp6enmRkZODs7Fzp+0hvE0IIIYQQQpSLJBFCCCGEEEKIcpEkQgghhBBCCFEukkQIIYQQQgghykWSCCGEEEIIIUS5SBIhhBBCCCGEKBdJIoQQQgghhBDlIkmEEEIIIYQQolwkiRBCCCGEEEKUiyQRQgghhBCiwjp06MCkSZNMxyEhIcyaNava4hFVQ5IIIYQQQgjxr8aMGYNKpSr19e677/LGG2/c8jqVSsXKlSurLlBRJayrOwAhhBBCCFEz9OjRg/nz55uVeXl5YWVlddvvrdfrsbGxue33EWUjTyKEEEIIIUSZ2NnZ4evra/bVuXNns+FMJYWEhADw4IMPolKpTMcAq1atolmzZmg0GsLCwnjttdcoLCw01atUKj7//HP69euHg4MDb7755m18Z6K85EmEEEIIIUQ1URSFPL2hwtcbjUbydAasdYWo1eX7bNjexgqVSlXhe5fF3r178fb2Zv78+fTo0cP0xOLXX39lxIgRzJ49m3bt2nH27FnGjRsHwLRp00zXT5s2jRkzZvDhhx9WydMOUXaSRAghhBBCVJM8vYHIqb9Wy71jX++O1rZ8vwquXr0aR0dH03HPnj3/8XwvLy8AXF1d8fX1NZW/9dZbvPTSS4wePRqAsLAw3njjDV544QWzJGLYsGGMHTu2XDGKqiFJhBBCCCGEKJOOHTsyZ84c07GDgwNDhw4tdzv79+9n7969vPXWW6Yyg8FAfn4+ubm5aLVaAGJiYioftLgtJIkQQgghhKgm9jZWxL7evcLXG41GsjKzcHJ2qtBwpvJycHCgTp065b7u74xGI6+99hoDBgwoVafRaMzuJ+5MkkQIIYQQQlQTlUpV7iFFJRmNRgptrdDaWpc7iagqNjY2GAzm8z6aNm3KqVOnLJKQiOohSYQQQgghhLhtQkJC2LRpE23atMHOzg43NzemTp1Knz59CAoKYuDAgajVao4cOcLRo0dlFaYa4s5MWYUQQgghxF1h5syZbNy4kaCgIJo0aQJA9+7dWb16NRs3buS+++6jZcuWfPDBB9SqVauaoxVlJU8ihBBCCCHEv1qwYMFNy7du3Wp2fOHCBbPjvn370rdv31LXde/ene7dbz0fRFGU8oYoqpA8iRBCCCGEEEKUiyQRQgghhBBCiHKRJEIIIYQQQghRLjUuiSgoKKBx48aoVCoOHTpkVpeQkEDfvn1xcHDA09OTZ599Fp1OVz2BCiGEEEIIcZeqcROrX3jhBfz9/Tl8+LBZucFgoHfv3nh5ebFjxw7S0tIYPXo0iqLw8ccfV1O0QgghhBBC3H1q1JOIdevWsWHDBt5///1SdRs2bCA2NpbFixfTpEkTunTpwsyZM/nyyy/JzMyshmiFEEIIIYS4O9WYJOLKlSs8/vjjLFq0CK1WW6r+jz/+ICoqCn9/f1NZ9+7dKSgoYP/+/VUZqhBCCCGEEHe1GjGcSVEUxowZw5NPPklMTEyp9YcBkpOT8fHxMStzc3PD1taW5OTkW7ZdUFBAQUGB6bj4qYVer0ev11vmDYi7UnH/kH4iykL6iygr6St3P6PRiNFotEhbxXspKIpisTZFzWY0Gm/6/cPS31OqNYl49dVXee211/7xnL1797Jr1y4yMzN5+eWX//FclUpVqkxRlJuWF5sxY8ZNY9iyZctNn3gI8XcbN26s7hBEDSL9RZSV9JW7V1BQEC4uLhZtMysry6LtiZorLS2t1OJDALm5uRa9j0qpxu0AU1NTSU1N/cdzQkJCGDJkCKtWrTJLBgwGA1ZWVgwfPpyFCxcydepUfv75Z7MJ19evX8fd3Z3NmzfTsWPHm7Z/sycRQUFBJCUl4eHhUcl3KO5mer2ejRs30rVrV2xsbKo7HHGHk/4iykr6yt0vMTGRoKAgi7SlKApZWVk4OTn944em4t5x8eJFs+H9xdLS0vDz8yMjIwNnZ+dK36dan0R4enri6en5r+fNnj2bN99803ScmJhI9+7dWbZsGS1atACgVatWvPXWWyQlJeHn5wcUTba2s7OjWbNmt2zbzs4OOzu7UuU2NjbyzVuUifQVUR7SX0RZSV+5e6nVatRqy0xLLR7CpFKpLNbmrYwZM4aFCxfyxBNP8Pnnn5vVPf3008yZM4fRo0ezYMGC2xrH3UylUvHTTz/Rv3//CrehVqtv+r3D0t9PasTE6uDgYKKiokxf4eHhANSuXZvAwEAAunXrRmRkJCNHjuTgwYNs2rSJ559/nscff9wi2ZYQQgghxJ1gz549DBs2DE9PTxwcHGjZsiXvvfce6enpt/3eQUFBLF26lLy8PFNZfn4+S5YsITg4+LbfvzJk7zDLqhFJRFlYWVmxZs0aNBoNbdq0YdCgQfTv3/+my8EKIYQQQtREM2bMoGXLlixZsoS0tDTy8/M5deoUL730Eo0aNeL06dO39f5NmzYlODiYFStWmMpWrFhBUFAQTZo0MZUpisK7775LWFgY9vb2NGrUiB9//NFUbzAYePTRRwkNDcXe3p6IiAg++ugjs3tt3bqV5s2b4+DggKurK23atCE+Ph4oeiry90/rJ02aRIcOHUzHHTp0YMKECUyZMgVPT0+6du0KQGxsLL169cLR0REfHx9GjhxpNry+Q4cOPPPMM0yaNAk3Nzd8fHz44osvyMnJ4ZFHHsHJyYnatWuzbt06s/uXpd1nn32WF154AXd3d3x9fXn11VdN9SEhIQA8+OCDqFQq0/Hhw4fp2LEjTk5OODs706xZM/bt2/cv/1K3X41MIkJCQlAUhcaNG5uVBwcHs3r1anJzc0lLS+Pjjz++6VAlIYQQQoiaZtmyZfz3v/81Hbu4uFC/fn3TcUJCAr169TJ7SnA7PPLII8yfP990PG/ePMaOHWt2zv/+9z/mz5/PnDlzOH78OJMnT2bEiBFs27YNKBqGFRgYyPfff09sbCxTp07lv//9L99//z0AhYWF9O/fn/bt23PkyBH++OMPxo0bV+55HwsXLsTa2pqdO3cyd+5ckpKSaN++PY0bN2bfvn2sX7+eK1euMGjQoFLXeXp68ueff/LMM8/w1FNPMXDgQFq3bs2BAwfo3r07I0eONE1WLk+7Dg4O7Nmzh3fffZfXX3/dtIjC3r17AZg/fz5JSUmm4+HDhxMYGMjevXvZv38/L7300p0x1FERZjIyMhRASU1Nre5QxB1Op9MpK1euVHQ6XXWHImoA6S+irKSv3P0SEhLKfY3RaFSio6MVQAGUadOmKXl5eYrBYFD+/PNPJSoqylS3YMGC2xC1oowePVrp16+fcvXqVcXOzk45f/68cuHCBUWj0ShXr15V+vXrp4wePVrJzs5WNBqNsmvXLrPrH330UWXo0KG3bP/pp59WHnroIUVRFCUtLU0BlK1bt/5jLCVNnDhRad++vem4ffv2SuPGjc3OeeWVV5Ru3bqZlV28eFEBlFOnTpmua9u2ram+sLBQcXBwUEaOHGkqS0pKUgDljz/+qHC7iqIo9913n/Liiy+ajgHlp59+MjvHycmpXP+mt+pfqampCqBkZGSUua1/UiP2iRBCCCGEuJfFxsZy9OhRAFq2bGkaBmM0Gqlbty5z5syhXbt2AHz33XeMHj36tsXi6elJ7969WbhwIYqi0Lt3b7OFcmJjY8nPzzcNHyqm0+nMhjx9/vnnfPXVV8THx5OXl4dOpzONMnF3d2fMmDF0796drl270qVLFwYNGmRaPKesYmJizI7379/Pli1bcHR0LHXu2bNnTfNuGzZsaCq3srLCw8OD6OhoU1nx3mQpKSkVbhfAz8/P1MatTJkyhccee4xFixbRpUsXBg4cSO3atf/xmqogSYQQQgghxB0uKSnJ9Lp9+/al6lu1aoWNjQ16vd7s3Ntl7NixTJgwAYBPP/3UrK54xag1a9YQEBBgVlc8zPz7779n8uTJzJw5k1atWuHk5MR7773Hnj17TOfOnz+fZ599lvXr17Ns2TL+97//sXHjRlq2bIlarTZttFfsZpupOTg4lIqtb9++vPPOO6XOLZmg/H24kEqlMisrHlZV/F4r0+6/bRL46quvMmzYMNasWcO6deuYNm0aS5cu5cEHH/zH6243SSKEEEIIIe5wbm5uptc320jsxIkTpl+iS557u/To0cO02lH37t3N6iIjI7GzsyMhIeGmCQ/A9u3bad26NU8//bSp7OzZs6XOa9KkCU2aNOHll1+mVatWfPfdd7Rs2RIvLy+OHTtmdu6hQ4f+da5A06ZNWb58OSEhIVhbW+7XYEu1a2Njg8FgKFUeHh5OeHg4kydPZujQocyfP7/ak4gaObFaCCGEEOJe0rhxY2rVqgXAr7/+ypIlS0yfxGdkZDBx4kTTuQMGDLjt8VhZWXHixAlOnDiBlZWVWZ2TkxPPP/88kydPZuHChZw9e5aDBw/y6aefsnDhQgDq1KnDvn37+PXXXzl9+jSvvPKKaSIxwPnz53n55Zf5448/iI+PZ8OGDZw+fdo0kbxTp07s27ePb775hjNnzjBt2rRSScXNjB8/nmvXrjF06FD+/PNPzp07x4YNGxg7duxNf3kvK0u1GxISwqZNm0hOTub69evk5eUxYcIEtm7dSnx8PDt37mTv3r1mE+qriyQRQgghhBB3OCsrKyZPnmw6HjZsGI0bN+bBBx8kOjqazZs3A0VzCW7nfIiSnJ2db7kX1xtvvMHUqVOZMWMG9evXp3v37qxatYrQ0FAAnnzySQYMGMDgwYNp0aIFaWlpZk8ltFotJ0+e5KGHHiI8PJxx48YxYcIEnnjiCaDo6ccrr7zCCy+8wH333UdWVhajRo3615j9/f3ZuXMnBoOB7t27ExUVxcSJE3FxcanUZn2WanfmzJls3LjRtGSulZUVaWlpjBo1ivDwcAYNGkTPnj157bXXKhyrpaiUvw8ou8dlZmbi4uJCamoqHh4e1R2OuIPp9XrWrl1Lr1697oyl1sQdTfqLKCvpK3e/ixcvEhQUVO7rjEYjjz766C13hHZycmLNmjWmCdbi3nSr/pWWloanpycZGRkW2YhZnkQIIYQQQtQAarWaefPm8c0339CsWTNTub29PWPHjmXfvn2SQIgqIxOrhRBCCCFqCJVKxciRIxk5ciRpaWlkZWVhb2+Pl5dXpYbjCFFekkQIIYQQQtRAHh4euLm5kZmZWd2hiHuQpKxCCCGEEEKIcpEkQgghhBBCCFEukkQIIYQQQgghykWSCCGEEEKIKlaZjc2EuJWq7FeSRAghhBBCVCEvLy8uX74siYSwKIPBwOXLl/Hy8qqS+8nqTEIIIYQQVUij0eDt7U1SUhKV3fPXaDSSlpaGh4eHLPEq8Pb2RqPRVMm9JIkQQgghhKhiGo2GwMDASrej1+s5dOgQ0dHRssO5qFKSsgohhBBCCCHKRZIIIYQQQgghRLlIEiGEEEIIIYQoF0kihBBCCCGEEOUiE6v/pniVhKysLJmgJP6RXq8nNzeXzMxM6SviX0l/EWUlfUWUh/QXUVZZWVkAlV4RrJgkEX+TlpYGQGhoaDVHIoQQQgghhGWlpaXh4uJS6XYkifgbd3d3ABISEizyFyzuXpmZmQQFBXHx4kWcnZ2rOxxxh5P+IspK+oooD+kvoqwyMjIIDg42/a5bWZJE/E3xRi0uLi7yn1GUibOzs/QVUWbSX0RZSV8R5SH9RZSVpTYllInVQgghhBBCiHKRJEIIIYQQQghRLpJE/I2dnR3Tpk3Dzs6uukMRdzjpK6I8pL+IspK+IspD+osoK0v3FZViqXWehBBCCCGEEPcEeRIhhBBCCCGEKBdJIoQQQgghhBDlIkmEEEIIIYQQolwkiRBCCCGEEEKUiyQRJXz22WeEhoai0Who1qwZ27dvr+6QxB3g999/p2/fvvj7+6NSqVi5cqVZvaIovPrqq/j7+2Nvb0+HDh04fvx49QQrqtWMGTO47777cHJywtvbm/79+3Pq1Cmzc6S/CIA5c+bQsGFD0wZhrVq1Yt26daZ66SfiVmbMmIFKpWLSpEmmMukvotirr76KSqUy+/L19TXVW7KvSBLxl2XLljFp0iT+7//+j4MHD9KuXTt69uxJQkJCdYcmqllOTg6NGjXik08+uWn9u+++ywcffMAnn3zC3r178fX1pWvXrmRlZVVxpKK6bdu2jfHjx7N79242btxIYWEh3bp1Iycnx3SO9BcBEBgYyNtvv82+ffvYt28fnTp1ol+/fqYf5tJPxM3s3buXL774goYNG5qVS38RJTVo0ICkpCTT19GjR011Fu0rilAURVGaN2+uPPnkk2Zl9erVU1566aVqikjciQDlp59+Mh0bjUbF19dXefvtt01l+fn5iouLi/L5559XQ4TiTpKSkqIAyrZt2xRFkf4i/pmbm5vy1VdfST8RN5WVlaXUrVtX2bhxo9K+fXtl4sSJiqLI9xVhbtq0aUqjRo1uWmfpviJPIgCdTsf+/fvp1q2bWXm3bt3YtWtXNUUlaoLz58+TnJxs1nfs7Oxo37699B1BRkYGAO7u7oD0F3FzBoOBpUuXkpOTQ6tWraSfiJsaP348vXv3pkuXLmbl0l/E3505cwZ/f39CQ0MZMmQI586dAyzfV6wtFnENlpqaisFgwMfHx6zcx8eH5OTkaopK1ATF/eNmfSc+Pr46QhJ3CEVRmDJlCm3btiUqKgqQ/iLMHT16lFatWpGfn4+joyM//fQTkZGRph/m0k9EsaVLl7J//3727dtXqk6+r4iSWrRowTfffEN4eDhXrlzhzTffpHXr1hw/ftzifUWSiBJUKpXZsaIopcqEuBnpO+LvJkyYwJEjR9ixY0epOukvAiAiIoJDhw6Rnp7O8uXLGT16NNu2bTPVSz8RABcvXmTixIls2LABjUZzy/OkvwiAnj17ml5HR0fTqlUrateuzcKFC2nZsiVgub4iw5kAT09PrKysSj11SElJKZWtCVFS8YoH0ndESc888wy//PILW7ZsITAw0FQu/UWUZGtrS506dYiJiWHGjBk0atSIjz76SPqJMLN//35SUlJo1qwZ1tbWWFtbs23bNmbPno21tbWpT0h/ETfj4OBAdHQ0Z86csfj3FkkiKPpG3qxZMzZu3GhWvnHjRlq3bl1NUYmaIDQ0FF9fX7O+o9Pp2LZtm/Sde5CiKEyYMIEVK1awefNmQkNDzeqlv4h/oigKBQUF0k+Emc6dO3P06FEOHTpk+oqJiWH48OEcOnSIsLAw6S/ilgoKCjhx4gR+fn4W/94iw5n+MmXKFEaOHElMTAytWrXiiy++ICEhgSeffLK6QxPVLDs7m7i4ONPx+fPnOXToEO7u7gQHBzNp0iSmT59O3bp1qVu3LtOnT0er1TJs2LBqjFpUh/Hjx/Pdd9/x888/4+TkZPq0x8XFBXt7e9Pa7tJfxH//+1969uxJUFAQWVlZLF26lK1bt7J+/XrpJ8KMk5OTaV5VMQcHBzw8PEzl0l9Eseeff56+ffsSHBxMSkoKb775JpmZmYwePdry31vKvZ7TXezTTz9VatWqpdja2ipNmzY1Lcso7m1btmxRgFJfo0ePVhSlaMm0adOmKb6+voqdnZ1y//33K0ePHq3eoEW1uFk/AZT58+ebzpH+IhRFUcaOHWv6eePl5aV07txZ2bBhg6le+on4JyWXeFUU6S/ihsGDByt+fn6KjY2N4u/vrwwYMEA5fvy4qd6SfUWlKIpioeRHCCGEEEIIcQ+QORFCCCGEEEKIcpEkQgghhBBCCFEukkQIIYQQQgghykWSCCGEEEIIIUS5SBIhhBBCCCGEKBdJIoQQQgghhBDlIkmEEEIIIYQQolwkiRBCCGFxW7duRaVSkZ6eXt2hCCGEuA1kszkhhBCV1qFDBxo3bsysWbMA0Ol0XLt2DR8fH1QqVfUGJ4QQwuKsqzsAIYQQdx9bW1t8fX2rOwwhhBC3iQxnEkIIUSljxoxh27ZtfPTRR6hUKlQqFQsWLDAbzrRgwQJcXV1ZvXo1ERERaLVaHn74YXJycli4cCEhISG4ubnxzDPPYDAYTG3rdDpeeOEFAgICcHBwoEWLFmzdurV63qgQQggTeRIhhBCiUj766CNOnz5NVFQUr7/+OgDHjx8vdV5ubi6zZ89m6dKlZGVlMWDAAAYMGICrqytr167l3LlzPPTQQ7Rt25bBgwcD8Mgjj3DhwgWWLl2Kv78/P/30Ez169ODo0aPUrVu3St+nEEKIGySJEEIIUSkuLi7Y2tqi1WpNQ5hOnjxZ6jy9Xs+cOXOoXbs2AA8//DCLFi3iypUrODo6EhkZSceOHdmyZQuDBw/m7NmzLFmyhEuXLuHv7w/A888/z/r165k/fz7Tp0+vujcphBDCjCQRQgghqoRWqzUlEAA+Pj6EhITg6OhoVpaSkgLAgQMHUBSF8PBws3YKCgrw8PComqCFEELclCQRQgghqoSNjY3ZsUqlummZ0WgEwGg0YmVlxf79+7GysjI7r2TiIYQQoupJEiGEEKLSbG1tzSZEW0KTJk0wGAykpKTQrl07i7YthBCicmR1JiGEEJUWEhLCnj17uHDhAqmpqaanCZURHh7O8OHDGTVqFCtWrOD8+fPs3buXd955h7Vr11ogaiGEEBUlSYQQQohKe/7557GysiIyMhIvLy8SEhIs0u78+fMZNWoUzz33HBERETzwwAPs2bOHoKAgi7QvhBCiYmTHaiGEEEIIIUS5yJMIIYQQQgghRLlIEiGEEEIIIYQoF0kihBBCCCGEEOUiSYQQQgghhBCiXCSJEEIIIYQQQpSLJBFCCCGEEEKIcpEkQgghhBBCCFEukkQIIYQQQgghykWSCCGEEEIIIUS5SBIhhBBCCCGEKBdJIoQQQgghhBDlIkmEEEIIIYQQolz+H4QfRi9DgmwwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import seed\n",
    "seed(2)\n",
    "trk, zs = compute_dog_data(z_var=225, process_var=.02, count=50)\n",
    "\n",
    "run(track=trk, zs=zs, R=225, Q=200, P=P, plot_P=False, \n",
    "    title='R_var = 225 $m^2$, Q_var = 20 $m^2$')\n",
    "run(track=trk, zs=zs, R=225, Q=.02, P=P, plot_P=False, \n",
    "    title='R_var = 225 $m^2$, Q_var = 0.02 $m^2$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The filter in the first plot should follow the noisy measurement closely. 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. 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 a vacuum with math, but with wind, varying air density, temperature, and a spinning ball with an imperfect surface 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 20. 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. 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 trust 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 prediction, it is really good!\". More strictly this actually says there is very small amounts of process noise (variance 0.02 $m^2$), so the process model is very 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.\n",
    "\n",
    "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": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "run(track=trk, zs=zs, R=10000, Q=.2, P=P, plot_P=False, \n",
    "    title='R=$10,000\\, m^2$, Q=$.2\\, m^2$');"
   ]
  },
  {
   "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 225 $m^2$, 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 see the result of a bad initial guess for the position by guessing the initial position to be 50 m and the initial velocity to be 1 m/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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