Kalman-Filter-CA.ipynb

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  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.stats import norm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Kalman Filter Implementation for Constant Acceleration Model (CA) in Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Situation covered: You have an acceleration sensor (in 2D: $\\ddot x$ and $\\ddot y$) and try to calculate velocity ($\\dot x$ and $\\dot y$) as well as position ($x$ and $y$) of a person holding a smartphone in his/her hand.\n",
      "\n",
      "![Smartphone](http://farm8.staticflickr.com/7324/12470549875_d562b39f52.jpg)\n",
      "\n",
      "unter CC BY-NC 2.0 von flickr.com von Canadian Pacific"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "State Vector - Constant Acceleration"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Constant Acceleration Model for Ego Motion in Plane\n",
      "\n",
      "$$x= \\left[ \\matrix{ x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y} \\right]$$\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Formal Definition:\n",
      "\n",
      "$$x_{k+1} = A \\cdot x_{k} + B \\cdot u$$\n",
      "\n",
      "Hence, we have no control input $u$:\n",
      "\n",
      "$$x_{k+1} = \\begin{bmatrix}1 & 0 & \\Delta t & 0 & \\frac{1}{2}\\Delta t^2 & 0 \\\\ 0 & 1 & 0 & \\Delta t & 0 & \\frac{1}{2}\\Delta t^2 \\\\ 0 & 0 & 1 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 1 & 0 & \\Delta t \\\\ 0 & 0 & 0 & 0 & 1 & 0  \\\\ 0 & 0 & 0 & 0 & 0 & 1\\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y\\end{bmatrix}_{k}$$\n",
      "\n",
      "$$y = H \\cdot x$$\n",
      "\n",
      "Just the acceleration ($\\ddot x$ & $\\ddot y$) is measured.\n",
      "\n",
      "$$y = \\begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1\\end{bmatrix} \\cdot x$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Initial State"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]).T\n",
      "print(x, x.shape)\n",
      "n=x.size # States\n",
      "plt.scatter(float(x[0]),float(x[1]), s=100)\n",
      "plt.title('Initial Location')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 0.],\n",
        "        [ 0.],\n",
        "        [ 0.],\n",
        "        [ 0.],\n",
        "        [ 0.],\n",
        "        [ 0.]]), (6, 1))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "<matplotlib.text.Text at 0x10a491f50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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hx3o8HlJSUoa8X0NDA6tXryYmJobk5GRcLhetra2RRBARkXEQUbEJBAIkJiYG2wkJCQQC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\nr8DdIwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1091ab810>"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Initial Uncertainty"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.matrix([[10.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
      "              [0.0, 10.0, 0.0, 0.0, 0.0, 0.0],\n",
      "              [0.0, 0.0, 10.0, 0.0, 0.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 10.0, 0.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 0.0, 10.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 0.0, 0.0, 10.0]])\n",
      "print(P, P.shape)\n",
      "\n",
      "\n",
      "fig = plt.figure(figsize=(6, 6))\n",
      "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
      "plt.title('Initial Covariance Matrix $P$')\n",
      "ylocs, ylabels = yticks()\n",
      "# set the locations of the yticks\n",
      "yticks(arange(7))\n",
      "# set the locations and labels of the yticks\n",
      "yticks(arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = xticks()\n",
      "# set the locations of the yticks\n",
      "xticks(arange(7))\n",
      "# set the locations and labels of the yticks\n",
      "xticks(arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
      "\n",
      "plt.xlim([-0.5,5.5])\n",
      "plt.ylim([5.5, -0.5])\n",
      "\n",
      "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
      "divider = make_axes_locatable(plt.gca())\n",
      "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
      "plt.colorbar(im, cax=cax)\n",
      "\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 10.,   0.,   0.,   0.,   0.,   0.],\n",
        "        [  0.,  10.,   0.,   0.,   0.,   0.],\n",
        "        [  0.,   0.,  10.,   0.,   0.,   0.],\n",
        "        [  0.,   0.,   0.,  10.,   0.,   0.],\n",
        "        [  0.,   0.,   0.,   0.,  10.,   0.],\n",
        "        [  0.,   0.,   0.,   0.,   0.,  10.]]), (6, 6))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IyQlwTUpFUrLaIadVf7/cavdNmzat0fauXbsQGBiIgQMHmjIoIiIioJnv7tu5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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b027390>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Dynamic Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is calculated from the dynamics of the Egomotion.\n",
      "\n",
      "$$x_{k+1} = x_{k} + \\dot x_{k} \\cdot \\Delta t +  \\ddot x_k \\cdot \\frac{1}{2}\\Delta t^2$$\n",
      "$$y_{k+1} = y_{k} + \\dot y_{k} \\cdot \\Delta t +  \\ddot y_k \\cdot \\frac{1}{2}\\Delta t^2$$\n",
      "$$\\dot x_{k+1} = \\dot x_{k} + \\ddot x \\cdot \\Delta t$$\n",
      "$$\\dot y_{k+1} = \\dot y_{k} + \\ddot y \\cdot \\Delta t$$\n",
      "$$\\ddot x_{k+1} = \\ddot x_{k}$$\n",
      "$$\\ddot y_{k+1} = \\ddot y_{k}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = 0.5 # Time Step between Filter Steps\n",
      "\n",
      "A = np.matrix([[1.0, 0.0, dt, 0.0, 1/2.0*dt**2, 0.0],\n",
      "              [0.0, 1.0, 0.0, dt, 0.0, 1/2.0*dt**2],\n",
      "              [0.0, 0.0, 1.0, 0.0, dt, 0.0],\n",
      "              [0.0, 0.0, 0.0, 1.0, 0.0, dt],\n",
      "              [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
      "print(A, A.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 1.   ,  0.   ,  0.5  ,  0.   ,  0.125,  0.   ],\n",
        "        [ 0.   ,  1.   ,  0.   ,  0.5  ,  0.   ,  0.125],\n",
        "        [ 0.   ,  0.   ,  1.   ,  0.   ,  0.5  ,  0.   ],\n",
        "        [ 0.   ,  0.   ,  0.   ,  1.   ,  0.   ,  0.5  ],\n",
        "        [ 0.   ,  0.   ,  0.   ,  0.   ,  1.   ,  0.   ],\n",
        "        [ 0.   ,  0.   ,  0.   ,  0.   ,  0.   ,  1.   ]]), (6, 6))\n"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Measurement Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here you can determine, which of the states is covered by a measurement. In this example, the position ($x$ and $y$) as well as the acceleration is measured ($\\ddot x$ and $\\ddot y$)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H = np.matrix([[0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
      "print(H, H.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 0.,  0.,  0.,  0.,  1.,  0.],\n",
        "        [ 0.,  0.,  0.,  0.,  0.,  1.]]), (2, 6))\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Measurement Noise Covariance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ra = 10.0**2\n",
      "R = np.matrix([[ra, 0.0],\n",
      "               [0.0, ra]])\n",
      "print(R, R.shape)\n",
      "\n",
      "# Plot between -10 and 10 with .001 steps.\n",
      "xpdf = np.arange(-10, 10, 0.001)\n",
      "plt.subplot(121)\n",
      "plt.plot(xpdf, norm.pdf(xpdf,0,R[0,0]))\n",
      "plt.title('$x$')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.plot(xpdf, norm.pdf(xpdf,0,R[1,1]))\n",
      "plt.title('$y$')\n",
      "\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 100.,    0.],\n",
        "        [   0.,  100.]]), (2, 2))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FxX7gryjnz5gdqUOkQAVBdPOkco66G2zRJqcJHY7R9wIX/iiJCOd2ErXPe7Di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\nHXdyBorHjVa9z5CnjOgC1fIHyYwCFcm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CQeaSEJ2gtyE/P18fMmSInpqaqj///PO6ruv6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\nDigiIjISBxQRERnpA2xJGQP++rgFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b008b90>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Process Noise Covariance Matrix Q for CA Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Position of an object can be influenced by a force (e.g. wind), which leads to an acceleration disturbance (noise). This process noise has to be modeled with the process noise covariance matrix Q.\n",
      "\n",
      "$$Q = \\begin{bmatrix}\\sigma_{x}^2 & \\sigma_{xy} & \\sigma_{x \\dot x} & \\sigma_{x \\dot y} & \\sigma_{x \\ddot x} & \\sigma_{x \\ddot y} \\\\ \\sigma_{yx} & \\sigma_{y}^2 & \\sigma_{y \\dot x} & \\sigma_{y \\dot y} & \\sigma_{y \\ddot x} & \\sigma_{y \\ddot y} \\\\ \\sigma_{\\dot x x} & \\sigma_{\\dot x y} & \\sigma_{\\dot x}^2 & \\sigma_{\\dot x \\dot y} & \\sigma_{\\dot x \\ddot x} & \\sigma_{\\dot x \\ddot y} \\\\ \\sigma_{\\dot y x} & \\sigma_{\\dot y y} & \\sigma_{\\dot y \\dot x} & \\sigma_{\\dot y}^2 & \\sigma_{\\dot y \\ddot x} & \\sigma_{\\dot y \\ddot y} \\\\ \\sigma_{\\ddot x x} & \\sigma_{\\ddot x y} & \\sigma_{\\ddot x \\dot x} & \\sigma_{\\ddot x \\dot y} & \\sigma_{\\ddot x}^2 & \\sigma_{\\ddot x \\ddot y} \\\\ \\sigma_{\\ddot y x} & \\sigma_{\\ddot y y} & \\sigma_{\\ddot y \\dot x} & \\sigma_{\\ddot y \\dot y} & \\sigma_{\\ddot y \\ddot x} & \\sigma_{\\ddot y}^2\\end{bmatrix}$$\n",
      "\n",
      "To easily calcualte Q, one can ask the question: How the noise effects my state vector? For example, how the acceleration change the position over one timestep dt.\n",
      "\n",
      "One can calculate Q as\n",
      "\n",
      "$$Q = G\\cdot G^T \\cdot \\sigma_a^2$$\n",
      "\n",
      "with $G = \\begin{bmatrix}0.5dt^2 & 0.5dt^2 & dt & dt & 1.0 & 1.0\\end{bmatrix}^T$ and $\\sigma_a$ as the acceleration process noise."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Symbolic Calculation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import Symbol, Matrix\n",
      "from sympy.interactive import printing\n",
      "printing.init_printing()\n",
      "dts = Symbol('\\Delta t')\n",
      "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[dts],[dts],[1.0],[1.0]])\n",
      "Qs*Qs.T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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lFtFDJDwWbOllPPAmqPAOH494pESw3ZugYpnw46GnXqQqNGw+neM0knXU/3AFHviHgB7x\nSDigbHX64WuaH6q9GqdO1dAEFWsC1T/Ik5d10C+5mQXoEw+EA9pkE1QsmQd5ISs0EIeIJ4COOuWs\nZAH6xAMlgraqyuplaTXLLBI1sZ1TCJjarlMyjLzJL1AmOQB1Krc/MfTt8+z/WYA+8U1QYTK+ZrIJ\nKtS00nYZxPi52lmmTbr2Gk1QsWUnU/+w7Rb/nwkYOOPj2O2T82SgEX8eLrMiacRnpes8nRvx5+Ey\nK5JGfFa6ztO5EX8eLrMiWYjXz2jgPUcWROv8YxlYf+dA/eqVXtTL+Lb8Axl4LXyL/wMhcICRfVU3\nAwAAAABJRU5ErkJggg==\n",
       "prompt_number": 54,
       "text": [
        "\u23a1             4               4              3              3              2  \n",
        "\u23a20.25\u22c5\\Delta t   0.25\u22c5\\Delta t   0.5\u22c5\\Delta t   0.5\u22c5\\Delta t   0.5\u22c5\\Delta t   \n",
        "\u23a2                                                                             \n",
        "\u23a2             4               4              3              3              2  \n",
        "\u23a20.25\u22c5\\Delta t   0.25\u22c5\\Delta t   0.5\u22c5\\Delta t   0.5\u22c5\\Delta t   0.5\u22c5\\Delta t   \n",
        "\u23a2                                                                             \n",
        "\u23a2            3               3             2              2                   \n",
        "\u23a20.5\u22c5\\Delta t    0.5\u22c5\\Delta t      \\Delta t       \\Delta t     1.0\u22c5\\Delta t   \n",
        "\u23a2                                                                             \n",
        "\u23a2            3               3             2              2                   \n",
        "\u23a20.5\u22c5\\Delta t    0.5\u22c5\\Delta t      \\Delta t       \\Delta t     1.0\u22c5\\Delta t   \n",
        "\u23a2                                                                             \n",
        "\u23a2            2               2                                                \n",
        "\u23a20.5\u22c5\\Delta t    0.5\u22c5\\Delta t    1.0\u22c5\\Delta t   1.0\u22c5\\Delta t        1.0       \n",
        "\u23a2                                                                             \n",
        "\u23a2            2               2                                                \n",
        "\u23a30.5\u22c5\\Delta t    0.5\u22c5\\Delta t    1.0\u22c5\\Delta t   1.0\u22c5\\Delta t        1.0       \n",
        "\n",
        "            2\u23a4\n",
        "0.5\u22c5\\Delta t \u23a5\n",
        "             \u23a5\n",
        "            2\u23a5\n",
        "0.5\u22c5\\Delta t \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "1.0\u22c5\\Delta t \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "1.0\u22c5\\Delta t \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "     1.0     \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "     1.0     \u23a6"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sa = 0.1\n",
      "G = np.matrix([[1/2.0*dt**2],\n",
      "               [1/2.0*dt**2],\n",
      "               [dt],\n",
      "               [dt],\n",
      "               [1.0],\n",
      "               [1.0]])\n",
      "Q = G*G.T*sa**2\n",
      "\n",
      "print(Q, Q.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 0.00015625,  0.00015625,  0.000625  ,  0.000625  ,  0.00125   ,\n",
        "          0.00125   ],\n",
        "        [ 0.00015625,  0.00015625,  0.000625  ,  0.000625  ,  0.00125   ,\n",
        "          0.00125   ],\n",
        "        [ 0.000625  ,  0.000625  ,  0.0025    ,  0.0025    ,  0.005     ,\n",
        "          0.005     ],\n",
        "        [ 0.000625  ,  0.000625  ,  0.0025    ,  0.0025    ,  0.005     ,\n",
        "          0.005     ],\n",
        "        [ 0.00125   ,  0.00125   ,  0.005     ,  0.005     ,  0.01      ,\n",
        "          0.01      ],\n",
        "        [ 0.00125   ,  0.00125   ,  0.005     ,  0.005     ,  0.01      ,\n",
        "          0.01      ]]), (6, 6))\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(6, 6))\n",
      "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
      "plt.title('Process Noise Covariance Matrix $Q$')\n",
      "ylocs, ylabels = yticks()\n",
      "# set the locations of the yticks\n",
      "yticks(arange(7))\n",
      "# set the locations and labels of the yticks\n",
      "yticks(arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = xticks()\n",
      "# set the locations of the yticks\n",
      "xticks(arange(7))\n",
      "# set the locations and labels of the yticks\n",
      "xticks(arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
      "\n",
      "plt.xlim([-0.5,5.5])\n",
      "plt.ylim([5.5, -0.5])\n",
      "\n",
      "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
      "divider = make_axes_locatable(plt.gca())\n",
      "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
      "plt.colorbar(im, cax=cax)\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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B5nxUi5RZPSl3d3ds2bJFv/3NN99g9erViIyMVHxgjDHGmFlFqrGxEe7u7vrt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\n5+OeFGOMMWnJXGgsQXImRbl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RkejRo4fo1auXjUf24Pi5s9/nzt7Y9dciXb9+\nHQsXLoSrqytu3LiBFStW4MKFC3jjjTfg4+MDIQRWrFgBX19fWw/1gUVFReGbb75BTU0NevbsiUuX\nLkGj0eDll1/WzyCZ3BobG/HCCy/g559/hp+fH1QqFdatW4cxY8Zgz549th4eM4KfO9uz6yLVFfTp\n0wcjR45Efn4+bty4gcmTJ8Pb29vu+2xd2TfffIOxY8di7dq1eOmll2w9HGYGfu46H393n+S2b9+O\nvXv3Yv78+aitrUVCQgJmzZpl62ExMzQ2NsLd3V2/nZOTA3d3d8TFxdlwVMwU/NzZHs+kGLMiXq61\nX/zcyYGLFGNWxMu19oufOzlwkWLMigoKCrB3715cv34dtbW1mDx5Mi/X2gl+7uTARYoxxpi07PrD\nvIwxxmjjIsUYY0xaXKQYY4xJi4sUY4wxaXGRYowxJi0uUowxxqTFRYoxxpi0uEgxxhiTFhcpxhhj\n0vr/ACq6pDU5dQtgAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1093c0050>"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Identity Matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I = np.eye(n)\n",
      "print(I, I.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([[ 1.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  1.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  1.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  1.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  1.]]), (6, 6))\n"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Measurement"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "They are generated synthetically"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = 100 # Measurements\n",
      "\n",
      "# Acceleration\n",
      "sa= 0.1 # Sigma for acceleration\n",
      "ax= 0.0 # in X\n",
      "ay= 0.0 # in Y\n",
      "\n",
      "mx = np.array(ax+sa*np.random.randn(m))\n",
      "my = np.array(ay+sa*np.random.randn(m))\n",
      "\n",
      "measurements = np.vstack((mx,my))\n",
      "\n",
      "print(measurements.shape)\n",
      "print('Standard Deviation of Acceleration Measurements=%.2f' % np.std(mx))\n",
      "print('You assumed %.2f in R.' % R[0,0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(2, 100)\n",
        "Standard Deviation of Acceleration Measurements=0.11\n",
        "You assumed 100.00 in R.\n"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "plt.step(range(m),mx, label='$a_x$')\n",
      "plt.step(range(m),my, label='$a_y$')\n",
      "plt.ylabel('Acceleration')\n",
      "plt.title('Measurements')\n",
      "plt.ylim([-1, 1])\n",
      "plt.legend(loc='best',prop={'size':18})\n",
      "plt.savefig('Kalman-Filter-CA-Measurements.png', dpi=72, transparent=True, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XZSqAhw4dGm+88UbdBgEp2doLNuviX7WcaajFeGB7mTUjBXJMKvQAN1+j15XJ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\neQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1071a4550>"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Preallocation for Plotting\n",
      "xt = []\n",
      "yt = []\n",
      "dxt= []\n",
      "dyt= []\n",
      "ddxt=[]\n",
      "ddyt=[]\n",
      "Zx = []\n",
      "Zy = []\n",
      "Px = []\n",
      "Py = []\n",
      "Pdx= []\n",
      "Pdy= []\n",
      "Pddx=[]\n",
      "Pddy=[]\n",
      "Kx = []\n",
      "Ky = []\n",
      "Kdx= []\n",
      "Kdy= []\n",
      "Kddx=[]\n",
      "Kddy=[]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 60
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Kalman Filter](https://raw.github.com/balzer82/Kalman/master/Kalman-Filter-Step.png)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for n in range(m):\n",
      "    \n",
      "    # Time Update (Prediction)\n",
      "    # ========================\n",
      "    # Project the state ahead\n",
      "    x = A*x\n",
      "    \n",
      "    # Project the error covariance ahead\n",
      "    P = A*P*A.T + Q    \n",
      "    \n",
      "    \n",
      "    # Measurement Update (Correction)\n",
      "    # ===============================\n",
      "    # Compute the Kalman Gain\n",
      "    S = H*P*H.T + R\n",
      "    K = (P*H.T) * np.linalg.pinv(S)\n",
      "\n",
      "    \n",
      "    # Update the estimate via z\n",
      "    Z = measurements[:,n].reshape(H.shape[0],1)\n",
      "    y = Z - (H*x)                            # Innovation or Residual\n",
      "    x = x + (K*y)\n",
      "    \n",
      "    # Update the error covariance\n",
      "    P = (I - (K*H))*P\n",
      "\n",
      "   \n",
      "    \n",
      "    # Save states for Plotting\n",
      "    xt.append(float(x[0]))\n",
      "    yt.append(float(x[1]))\n",
      "    dxt.append(float(x[2]))\n",
      "    dyt.append(float(x[3]))\n",
      "    ddxt.append(float(x[4]))\n",
      "    ddyt.append(float(x[5]))\n",
      "    Zx.append(float(Z[0]))\n",
      "    Zy.append(float(Z[1]))\n",
      "    Px.append(float(P[0,0]))\n",
      "    Py.append(float(P[1,1]))\n",
      "    Pdx.append(float(P[2,2]))\n",
      "    Pdy.append(float(P[3,3]))\n",
      "    Pddx.append(float(P[4,4]))\n",
      "    Pddy.append(float(P[5,5]))\n",
      "    Kx.append(float(K[0,0]))\n",
      "    Ky.append(float(K[1,0]))\n",
      "    Kdx.append(float(K[2,0]))\n",
      "    Kdy.append(float(K[3,0]))\n",
      "    Kddx.append(float(K[4,0]))\n",
      "    Kddy.append(float(K[5,0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Plots"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Uncertainty"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,4))\n",
      "#plt.plot(range(len(measurements[0])),Px, label='$x$')\n",
      "#plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
      "plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n",
      "plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n",
      "\n",
      "plt.xlabel('Filter Step')\n",
      "plt.ylabel('')\n",
      "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
      "plt.legend(loc='best',prop={'size':22})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "<matplotlib.legend.Legend at 0x10a823050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GDhxocHQNa1eFKEBi5o8YUjEKLLC05DYC1cVGhyQmpz4OMQPlsZiFclnMQHks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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b06a650>"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Kalman Gains"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
      "plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
      "plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
      "plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
      "plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
      "plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
      "\n",
      "plt.xlabel('Filter Step')\n",
      "plt.ylabel('')\n",
      "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
      "plt.legend(loc='best',prop={'size':18})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "<matplotlib.legend.Legend at 0x10a8406d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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F1atXUzJKCCHtQFhYGPT09CgZJUQKma6QAtXDvyZNmsRdIX1dZGQkfvrpJ4SE\nhLR6gIQQQgghpH3z9vbGvXv36iw4RwghjWmVVXYDAwMxc+bM1iiKEEIIIYR0MEFBQfIOgRDSQbV4\nUSM/Pz+oqqpi1qxZrREPIYQQQgghhJBOokVXSI8cOYJff/0VsbGx9e4TFhYmcQNsQgghhBBCCCGK\n48WLF3B1dW3Wsc1OSM+cOYOdO3ciPj4eampq9e4nFApha2vb3GoIaRcWL16MgwcPyjsMQlqM+jJR\nFNSXiSKgfkwURUpKSrOPlWnI7syZMzFq1CjcvHkTRkZGCAwMxNKlS/HixQu88847GDJkCBYvXtzs\nIAghhBBCCCGEdD4yXSENDw+vs83Hx6fVgyGkvaKbWBNFQX2ZKArqy0QRUD8mpBUWNSKkM3BwcJB3\nCIS0CurLRFFQXyaKgPoxIZSQEkIIIYQQQgiRE0pICSGEEEIIIYTIBY8xxtqygtjYWFpllxBCCCGE\nEEIUVEpKCsaPH9+sY+kKKSGEEEIIIYQQuWj2fUhbW3l5OR4/fizvMAiR6vnz5+jatau8w2hT3bt3\nh6qqqrzDIG0sISGBFtEgCoH6MlEE1I8JaScJaXl5OYqKitCzZ0/w+XTRlrQ/PXr0kHcIbUosFuPe\nvXsQCoWUlBJCCCGEkDemXWR/jx8/pmSUEDni8/no2bMnjVLoBOiXeKIoqC8TRUD9mJB2kpACoGSU\nEDmj9yAhhBBCCHnT6BsoIYR0IgkJCfIOgZBWQX2ZKALqx4RQQkoIIYQQQgghRE4oISWEkE6E5isR\nRUF9mSgC6seEUEKqMBISEqCnp4fw8HB5h9IhtGV73blzBx4eHjA3N4eenh58fX1bvQ5CCCGEEEIU\nASWkb1hNIrR///46zyUmJsLY2BgDBw5EZmZms8rn8XgtDbHdKCsrQ0BAAFxdXWFhYQGhUAhTU1M4\nOztj06ZNyM7OblH5PB6vTdrL19cXV65cwfLly/Hdd9/B29u71esgpLlovhJRFNSXiSKgfkxIO7kP\naWdUOxE6e/YsvL29YWBggMjISBgbG8spsvbh9u3bcHd3R3Z2NhwcHLB48WIIhUK8fPkSaWlpCA0N\nxf79+3H9+nUYGBg0uXx7e3sUFhZCWbl13wIikQjJycmYP38+XRklhBBCCCGkEZSQtgMRERFYvHgx\nLCws8NNPP0EoFMo7JLl69eoV3NzcUFBQgODgYHzwwQd19hGJRDh06FCz6+DxeFBVVW1JmFI9evQI\njDHo6Oj64aDFAAAgAElEQVS0arlVVVUoLy+Hurp6q5ZLOh+ar0QUBfVlogioHxNCQ3blLjAwEAsX\nLsTgwYNx6tQpiWT0xYsX8PPzg7OzM8zNzWFoaIihQ4di8+bNePXqVaNlh4WFQU9PD5cuXcKuXbtg\nY2ODnj17wtnZGcnJyQCqh4pMmDABRkZGGDhwIHbt2lWnnKbEUVPn5cuXsW/fPtja2sLQ0BDDhw/H\nDz/8IFObBAcHIycnB0uWLJGajAKAQCDAsmXLJK6ONiVOaXNIWxq7r68vbGxsAABfffUV9PT0oKen\nhytXrgAAiouLsXLlSgwaNAgGBgawsrLCqlWr8PTpU6ltGB8fj507d8LW1hY9evTAiRMnZGo/Qggh\nhBBCOgq6QionjDHs3r0bW7duhaOjI0JDQ6GhoSGxT2FhIUJCQjB58mTMmDEDysrKSEhIwN69e5GW\nloaIiAiZ6tq8eTPEYjEWLVqE8vJyHDhwADNmzMCePXvw+eefw9vbG25uboiMjMT27dthbGyM6dOn\ntyiOLVu2QCQSwdvbG6qqqggMDISvry9MTU1hZ2fXYLxRUVHg8XiYO3euTK+vJXFKm0Pa3Ni9vLxg\nZWWFdevWwcXFBZMmTQIAWFhYoKSkBO+//z7y8/Ph4eEBGxsbpKamIjAwEJcuXcL58+ehpaUlUd6G\nDRtQWVkJLy8vaGtrw9zcvEntQYg0CQkJ9Is8UQjUl4kioH5MSAdMSHXXdHuj9T3d/qRNyg0KCsLt\n27cxceJEBAQEQEVFpc4+pqamSE9Ph5KSErfNx8cH27Ztw9dff42UlBTY2to2WpdYLMa5c+e4+ZL9\n+vXD7NmzsXDhQsTExHBX9WbPng0bGxv4+/tLJKTNiaOiogKxsbFcnZMnT4atrS38/f0bTUizsrKg\nra0NIyOjOq+j9tVETU1NqKmptWp7NTf2YcOGQSgUYt26dbC0tMS0adO457Zu3Yq8vDzs2rVLYpGj\nmquke/fuxdq1ayXKKysrQ3x8PPf6ZHHkyBE8efIE2dnZcHNzw927d/H48WNkZmbiyy+/RM+ePWUu\nixBCCCGEkLZGQ3blpKioCABgYmIiNRkFABUVFS65qqysxLNnz1BcXIwxY8YAAFJSUmSqy9vbW2Lx\nnhEjRgCoTqBqktGa+oYMGYK8vLwWx+Hj4yNRp6GhIczMzJCfn99ovKWlpdDW1q6z/caNG7CwsJD4\nz9/fv0VxStOS2OsTHR2Nt956C56enhLbvby80L17d5w6dUpqHE1JRo8ePQpra2t89tlnmD9/Pry8\nvNCtWzcMHjwYP//8M27cuNHs+InioF/iiaKgvkwUAfVjQjrgFdK2umL5pi1fvhyJiYk4cOAAGGPY\nsmWL1P0CAgIQFBSEmzdvQiwWSzz37NkzmeoyMTGReFyz4I60lXx1dHTw5EndNm5qHLXrBABdXV3c\nu3ev0Xi1tbVRWloqtczIyEgAwPXr17Fhw4Y6Q27bor2aEnt9CgoKYGtrCz5f8jcgJSUl9OnTB+np\n6XWOMTMza1IdT58+5a4A3717F3w+HxMnTsSrV68QHR2NkSNHNjt+QgghhBBC2kKHS0gVhbq6OsLD\nwzFz5kwcPHgQYrEYfn5+EvscOHAAGzZswLhx47Bo0SIYGBhAVVUVhYWF8PX1rZNw1ef1Iayvq50c\n1ac5cdRXJ2Os0foGDBiApKQkFBQUoHfv3tx2DQ0NODo61ht7W7eXLLG3ptpzihuzfPly7t+JiYmw\nt7cHUN3XKBklNWi+ElEU1JeJIqB+TAglpHKlpqaG8PBwzJo1C4cOHQJjDNu2beOeP3bsGIyNjXH8\n+HGJ486fP/9G43zTcbi6uiIpKQnBwcFYt26dzMe1l/aSxtjYGNnZ2aiqqpJIeCsrK5Gbm9vq952N\nj4+XmKtKCCGEEEJIe0RzSOVMTU0NYWFhcHJywnfffYc1a9Zwz9XMY3z9yl5lZSX27NnTpjHVHgb7\npuOYM2cOzM3NsW/fPqlzKwHpVyvl1V6ycHFxwePHjxEcHCyx/fvvv0dxcTEmTpzYovKrqqoQFxcH\nsViM+/fvIycnh7tCCgB79+5tUflEcdAv8URRUF8mioD6MSF0hbRdqElKZ8+ejcOHD4Mxhh07dmDy\n5MnYvHkzpk+fDhcXF5SWliIiIgKqqqptGk/tZK8145Bl2Kuamhp+/PFHuLu7Y+7cuXBwcICTkxP0\n9fVRWlqK7OxsREZGQllZWWLV2LZur5YM2V26dClOnjyJlStXIjU1FVZWVkhLS0NoaCjMzc3xySef\ntCi2I0eOYNWqVUhOTkZMTAw0NDTQo0cPAMDZs2fRt2/fFpVPCCGEEEJIW6CEtJ0QCAQIDQ2Fh4cH\n/P39wRjD9u3bwRhDSEgI1q5dC6FQiClTpmDmzJlS5wRKu6emtG2NqX3M0qVLWxxHzXZZ4zE2NkZc\nXBxCQ0MRFRWFgwcPoqSkBBoaGjAzM4Onpyc8PDwkFv5pjThbI3ZpunTpgtOnT2PHjh04ffo0wsLC\noK+vDx8fH6xevRqampoyxVEfOzs7TJ8+HZGRkRg0aBB27dqFjRs3onfv3ujduzfc3d2bHTtRLDRf\niSgK6stEEVA/JgTgsTZeqSU2NrbRez8WFhZyV3MIIfJD70XFR19+iKKgvkwUAfVjoihSUlIwfvz4\nZh1Lc0gJIaQToS8+RFFQXyaKgPoxIZSQEkIIIYQQQgiRE0pICSGkE0lISJB3CIS0CurLRBFQPyaE\nElJCCCGEEEIIIXJCCSkhhHQiNF+JKArqy0QRUD8mhBJSQgghhBBCCCFyQgkpIYR0IjRfiSgK6stE\nEVA/JoQSUkIIIYQQQgghckIJKSGEdCI0X4koCurLRBFQPyaEElJCCCGEEEIIIXJCCSkhhHQiNF+J\nKArqy0QRUD8mhBJSQgghhBBCCCFyQgkpIYR0IjRfiSgK6stEEVA/JoQSUkIIIYQQQgghckIJqYJI\nSEiAnp4ewsPD5R1Kh9CW7XXnzh14eHjA3Nwcenp68PX1bfU6CGkumq9EFAX1ZaIIqB8TQgnpG1eT\nCO3fv7/Oc4mJiTA2NsbAgQORmZnZrPJ5PF5LQ2w3ysrKEBAQAFdXV1hYWEAoFMLU1BTOzs7YtGkT\nsrOzW1Q+j8drk/by9fXFlStXsHz5cnz33Xfw9vZu9ToIIYQQQghRBMryDqCzqp0InT17Ft7e3jAw\nMEBkZCSMjY3lFFn7cPv2bbi7uyM7OxsODg5YvHgxhEIhXr58ibS0NISGhmL//v24fv06DAwMmly+\nvb09CgsLoazcum8BkUiE5ORkzJ8/n66MknaJ5isRRUF9mSgC6sekQ2AMaMOLXpSQtgMRERFYvHgx\nLCws8NNPP0EoFMo7JLl69eoV3NzcUFBQgODgYHzwwQd19hGJRDh06FCz6+DxeFBVVW1JmFI9evQI\njDHo6Oi0arlVVVUoLy+Hurp6q5ZLCCGEEEJIHVWVULlxFoLfAlFhPhai0UvarCoasitngYGBWLhw\nIQYPHoxTp05JJKMvXryAn58fnJ2dYW5uDkNDQwwdOhSbN2/Gq1evGi07LCwMenp6uHTpEnbt2gUb\nGxv07NkTzs7OSE5OBlA9hHjChAkwMjLCwIEDsWvXrjrlNCWOmjovX76Mffv2wdbWFoaGhhg+fDh+\n+OEHmdokODgYOTk5WLJkidRkFAAEAgGWLVsmcXW0KXFKm0Pa0th9fX1hY2MDAPjqq6+gp6cHPT09\nXLlyBQBQXFyMlStXYtCgQTAwMICVlRVWrVqFp0+fSm3D+Ph47Ny5E7a2tujRowdOnDghU/sR0hCa\nr0QUBfVlogioH5P2hldaBLULu9B152BohcyBSnYcBNfCq6+SthG6QionjDHs3r0bW7duhaOjI0JD\nQ6GhoSGxT2FhIUJCQjB58mTMmDEDysrKSEhIwN69e5GWloaIiAiZ6tq8eTPEYjEWLVqE8vJyHDhw\nADNmzMCePXvw+eefw9vbG25uboiMjMT27dthbGyM6dOntyiOLVu2QCQSwdvbG6qqqggMDISvry9M\nTU1hZ2fXYLxRUVHg8XiYO3euTK+vJXFKm0Pa3Ni9vLxgZWWFdevWwcXFBZMmTQIAWFhYoKSkBO+/\n/z7y8/Ph4eEBGxsbpKamIjAwEJcuXcL58+ehpaUlUd6GDRtQWVkJLy8vaGtrw9zcvEntQQghhBBC\nSKMYg/LtJAiSA6CS/gt44koAQJWeGUQjvFH+9iwasvu6sBvd3mh9s/o/aZNyg4KCcPv2bUycOBEB\nAQFQUVGps4+pqSnS09OhpKTEbfPx8cG2bdvw9ddfIyUlBba2to3WJRaLce7cOW6+ZL9+/TB79mws\nXLgQMTEx3FW92bNnw8bGBv7+/hIJaXPiqKioQGxsLFfn5MmTYWtrC39//0YT0qysLGhra8PIyKjO\n66h9NVFTUxNqamqt2l7NjX3YsGEQCoVYt24dLC0tMW3aNO65rVu3Ii8vD7t27ZJY5KjmKunevXux\ndu1aifLKysoQHx/Pvb7GxMTE4M8//8Rvv/2Gw4cPo1u36vdKVFQUgoKCEBkZKVM5RLHRfCWiKKgv\nE0VA/ZjIVVkJBP89DsFvAVAqugEAYDw+ygdOhGiEDyrNxgD8th9QS0N25aSoqAgAYGJiIjUZBQAV\nFRUuuaqsrMSzZ89QXFyMMWPGAABSUlJkqsvb21ti8Z4RI0YAqE6gapLRmvqGDBmCvLy8Fsfh4+Mj\nUaehoSHMzMyQn5/faLylpaXQ1taus/3GjRuwsLCQ+M/f379FcUrTktjrEx0djbfeeguenp4S2728\nvNC9e3ecOnVKahyyJqNPnjxBamoqVq5cibt37yIpKYl77sSJE9DX12927IQQQgghRHHwH2RC/eRK\n6GwfBI2olVAqugGxlj5ejV2B56v+xMs5wag0H/tGklGgA14hbasrlm/a8uXLkZiYiAMHDoAxhi1b\ntkjdLyAgAEFBQbh58ybEYrHEc8+ePZOpLhMTE4nHNQvuSFvJV0dHB0+e1G3jpsZRu04A0NXVxb17\n9xqNV1tbG6WlpVLLrLnKd/36dWzYsKHOkNu2aK+mxF6fgoIC2Nragl/rja2kpIQ+ffogPT29zjFm\nZmYyl3/x4kW4ubkhIyMDeXl5EleCk5KS8M9//rPZsRPFkpCQQL/IE4VAfZkoAurH5I2pLIdKZjQE\nyYFQyb/Cba4wGQnRyI9RMdAFUG79BT9l0eESUkWhrq6O8PBwzJw5EwcPHoRYLIafn5/EPgcOHMCG\nDRswbtw4LFq0CAYGBlBVVUVhYSF8fX3rJFz1eX0I6+tqJ0f1aU4c9dXJZJgQPWDAACQlJaGgoAC9\ne/fmtmtoaMDR0bHe2Nu6vWSJvTXVnlPckKlTpwIA1qxZA0dHRxgaGgIAbt26hYcPH3JXxQkhhBBC\nSOfBe/YXBL8fheBqMPgvHgIAmKoWRLZuENl5Q2wwUM4RUkIqV2pqaggPD8esWbNw6NAhMMawbds2\n7vljx47B2NgYx48flzju/PnzbzTONx2Hq6srkpKSEBwcjHXr1sl8XHtpL2mMjY2RnZ2NqqoqiYS3\nsrISubm5rXbf2aioKKxatYp7fOXKFejq6qJ///6tUj7p+OiXeKIoqC8TRUD9mLQJsRjKeZeqr4Zm\n/goeq74oUyXsj7IR81A+ZDogqDs9Tl5oDqmcqampISwsDE5OTvjuu++wZs0a7rmaeYyvX9mrrKzE\nnj172jSm2sNg33Qcc+bMgbm5Ofbt2yd1biUg/WqlvNpLFi4uLnj8+DGCg4Mltn///fcoLi7GxIkT\nW1zH06dP8eDBA7z99tvctoSEBLo6SgghhBDSCfBePYcg4d/osnsEtAOmQjUjGuDxUW49BaULolGy\nLBHlI3zaVTIK0BXSdqEmKZ09ezYOHz4Mxhh27NiByZMnY/PmzZg+fTpcXFxQWlqKiIgIqKq27fju\n2slea8Yhy7BXNTU1/Pjjj3B3d8fcuXPh4OAAJycn6Ovro7S0FNnZ2YiMjISysjJ69uzZJnE2N/b6\nLF26FCdPnsTKlSuRmpoKKysrpKWlITQ0FObm5vjkk09aHJ+KiorEAlm5ubk4f/48Pv/88xaXTRQH\nzVciioL6MlEE1I9Ja1AqvA5BcgBU/4wAr+JvAIC4iyFEw70gGj4XTFso5wgbRglpOyEQCBAaGgoP\nDw/4+/uDMYbt27eDMYaQkBCsXbsWQqEQU6ZMwcyZMzFy5Mg6ZUi7p6a0bY2pfczSpUtbHEfNdlnj\nMTY2RlxcHEJDQxEVFYWDBw+ipKQEGhoaMDMzg6enJzw8PCQW/mmNOFsjdmm6dOmC06dPY8eOHTh9\n+jTCwsKgr68PHx8frF69GpqamjLF0RAtLS3s3r0b3377LaysrJCfn4/S0lKpr50QQgghhHRglSKo\npP8CtWR/KN/5ndtcYTYGohE+qBgwAVDqGKkej7XxSi2xsbGN3vuxsLAQPXr0aMswCOl0tm/fjiNH\njiArK0vmBazovUgIIYQQ0n7xnv0FwW9HIPgjGPwXjwAATKAN0dszIbLzgVjfQi5xpaSkYPz48c06\ntmOkzYSQRvn5+WHYsGF49913IRaLERkZiYULF8qcjBJCCCGEkHaIMSjnxkOQFACVrNPcIkWVBgMh\nGjEP5YOnAQItOQfZfPRNlRAF8PjxY+zdu5e7h+z+/fthZGSEZcuWyTky0t4kJCTIOwRCWgX1ZaII\nqB+TBpWVQJD43f8vUpR56n+LFE1FycJfUfrJZZTbeXXoZBSgK6SEKITu3btjy5YtePjwITZu3AhN\nTU38+OOP9d5TlRBCCCGEtE9K9zMgSPaH6n+Pd8hFipqKElJCFMSCBQvkHQLpAGg1R6IoqC8TRUD9\nmHAqy6GS8QsEyQFQuZ3Mba4wc4RoxMcdapGiplLMV0UIIYQQQggh7RzveSEEvx+F4Or34JcWAQCY\nQAsi25kQjfCBWL+fnCNse5SQEkJIJ0L3vCOKgvoyUQTUjzspxqCcfwWCpP9AJfMUeOIqAECVsD/K\nRsxD+ZDpgEBbzkG+OZSQEkIIIYQQQkhbE72A6n+PQS3ZH0pFNwAAjK+E8kGTIRo5D5Wm9kAL7nvf\nUcmUkPr4+ODUqVPQ19fH9evXAQBPnjyBm5sb7ty5AxMTExw7dgw6OjptGiwhhJCWoV/iiaKgvkwU\nAfXjzoH/8BYEyYEQpISDJyoFAIi1hRANmwvRcE+wrp37HvAy3fbF29sbZ86ckdi2Y8cOvPPOO7h1\n6xbGjx+PHTt2tEmAhBBCCCGEENKhiKugkvkrtAKmoOvuEVBLOgyeqBQVJiPwYqY/nq9KRdk7azp9\nMgrImJCOHj0aurq6EtuioqLg6ekJAPD09MSJEydaPzpCCCGtiu55RxQF9WWiCKgfKx7ei8cQXPwW\nXXYOgVawB1Ry4sFUNCAaNhcln1zCi4W/osJ6KqCsKu9Q241mzyEtKiqCUFh9DxyhUIiioqJWC4oQ\nQgghhBBCOgqluykQJPlDNe1n8KrKAQBVen0gGuGD8rdnganT1Mb6tMqiRjweD7wGJuAuXrwYvXv3\nBgB07doVVlZW3Jj5hIQE6OnpoUcPulxNiLw9f/4ceXl5Eu9PAPRYwR7XaC/x0GN63JzHNdvaSzz0\nmB7T40742G4oVK+fQHLYbig9yoZTD4DxeIhRHoaKgR9gpNtSgM9vP/G24uPr16/j+fPnAICCggLM\nmzcPzcVjjDFZdrx9+zYmTZrELWrUv39/XLx4EQYGBrh//z7Gjh2LGzdu1DkuNjYWtra2DZZdWFhI\nCSkh7QC9FwkhhBBCGsZ79hcEvwVV3zv0ZTEAQKyug/KhHtX3Du1mIt8A5SAlJQXjx49v1rEyzSGV\nZvLkyTh69CgA4OjRo/jwww+bWxQhhJA3pOZXTkI6OurLRBFQP+5AGINyTjw0Q+ai61eDoX5xN/gv\ni1FpaIWXH+3F89XpePXB5k6ZjLaUTAnpzJkzMWrUKNy8eRNGRkYICgrC6tWrERMTAwsLC1y4cAGr\nV69u61hJAxISqoc+h4eHyzuUDqEt2+vOnTvw8PCAubk59PT04Ovr2+p1EEIIIYSQN0BUCkGSP7p8\nOxLaAVOgmhEN8JVQbvMRShadRunSiygf6gGoasg70g5LWZad6vvSfv78+VYNpjNISEiAq6srNm3a\nhCVLlkg8l5iYiFmzZkFTUxMREREYOHBgk8tvaC5vR1NWVobQ0FBERUUhKysLz58/h4aGBszMzDB6\n9GjMmjUL5ubmzS6/sbnPzeXr64vMzEysWLECQqEQJiYmrV5HfWJiYrBgwQIEBARg3Lhxb6xe0nG8\nPv+OkI6M+jJRBNSP26/qe4cG/O/eoS8AAOIuhhAN94Jo+FwwbaGcI1QcMiWkpPXVToTOnj0Lb29v\nGBgYIDIyEsbGxnKKrH24ffs23N3dkZ2dDQcHByxevBhCoRAvX75EWloaQkNDsX//fly/fh0GBgZN\nLt/e3h6FhYVQVm7dt4BIJEJycjLmz58vlyujSkpKUFNTU6gfJgghhBBC3ghxFVRunIMg6T9QybnI\nba4wHQXRiI9RYekCKKnILz4FRQlpOxAREYHFixfDwsICP/30E3c7nc7q1atXcHNzQ0FBAYKDg/HB\nBx/U2UckEuHQoUPNroPH40FVtfXv//To0SMwxqCj07pLe1dVVaG8vBzq6uoN7jdu3DhkZWW1at1E\nsby+KikhHRn1ZaIIqB+3D7yXT6D6RwgEyQFQenYXAMBU1FE+ZAZEI+ahytBSzhEqtmYvakRaR2Bg\nIBYuXIjBgwfj1KlTEsnoixcv4OfnB2dnZ5ibm8PQ0BBDhw7F5s2b8erVq0bLDgsLg56eHi5duoRd\nu3bBxsYGPXv2hLOzM5KTkwFUfxBOmDABRkZGGDhwIHbt2lWnnKbEUVPn5cuXsW/fPtja2sLQ0BDD\nhw/HDz/8IFObBAcHIycnB0uWLJGajAKAQCDAsmXLJK6ONiVOaXNIWxq7r68vbGxsAABfffUV9PT0\noKenhytXrgAAiouLsXLlSgwaNAgGBgawsrLCqlWr8PTpU6ltGB8fj507d8LW1hY9evTAiRMnZGo/\nQgghhBDSOKXCNGj8tBRddwyCxpkvofTsLqq6meDvD7bg+ZoM/D1lNyWjbwBdIZUTxhh2796NrVu3\nwtHREaGhodDQkJwMXVhYiJCQEEyePBkzZsyAsrIyEhISsHfvXqSlpSEiIkKmujZv3gyxWIxFixah\nvLwcBw4cwIwZM7Bnzx58/vnn8Pb2hpubGyIjI7F9+3YYGxtj+vTpLYpjy5YtEIlE8Pb2hqqqKgID\nA+Hr6wtTU1PY2dk1GG9UVBR4PB7mzp0r0+trSZzShrY2N3YvLy9YWVlh3bp1cHFxwaRJkwAAFhYW\nKCkpwfvvv4/8/Hx4eHjAxsYGqampCAwMxKVLl3D+/HloaWlJlLdhwwZUVlbCy8sL2traLZovS0gN\n+iWeKArqy0QRUD+Wg8pyqGT8ArWk/0D5zu/c5goLZ5SNnI9Ki/EAn67ZvUkdLiH90HXMG63vxMn4\nNik3KCgIt2/fxsSJExEQEAAVlbrj0U1NTZGeng4lJSVum4+PD7Zt24avv/4aKSkpjd7jFQDEYjHO\nnTvHzZfs168fZs+ejYULFyImJoa7qjd79mzY2NjA399fIiFtThwVFRWIjY3l6pw8eTJsbW3h7+/f\naEKalZUFbW1tGBkZ1Xkdta8mampqQk1NrVXbq7mxDxs2DEKhEOvWrYOlpSWmTZvGPbd161bk5eVh\n165d8Pb25rbXXCXdu3cv1q5dK1FeWVkZ4uPjudcniyNHjuDJkyfIzs6Gm5sb7t69i8ePHyMzMxNf\nfvklevbsKXNZhBBCCCGKglfyAILfj0Lw+xHwS4sAAGK1Lih/exZEIz6GuLuZnCPsvCj9l5Oiouo3\ngomJidRkFABUVFS45KqyshLPnj1DcXExxoypTspTUlJkqsvb21ti8Z4RI0YAqE6gapLRmvqGDBmC\nvLy8Fsfh4+MjUaehoSHMzMyQn5/faLylpaXQ1taus/3GjRuwsLCQ+M/f379FcUrTktjrEx0djbfe\neguenp4S2728vNC9e3ecOnVKahxNSUaPHj0Ka2trfPbZZ5g/fz68vLzQrVs3DB48GD///DNu3LjR\n7PiJ4qB73hFFQX2ZKALqx22MMSjd+Q2a4fPQ9V/WUI/9F/ilRagS9sfLD7+uvneoyzZKRuWsw10h\nbasrlm/a8uXLkZiYiAMHDoAxhi1btkjdLyAgAEFBQbh58ybEYrHEc8+ePZOprtq3HalZcEfaSr46\nOjp48uRJi+OQdqsTXV1d3Lt3r9F4tbW1UVpaKrXMyMhIAMD169exYcOGOkNu26K9mhJ7fQoKCmBr\nawt+rSEgSkpK6NOnD9LT0+scY2bWtA/Hp0+fcleA7969Cz6fj4kTJ+LVq1eIjo7GyJEjmx0/IYQQ\nQkiHUfEKqqk/Q5DkD+XCVAAA4/FRbukC0agFqDS1B+iOBO1Gh0tIFYW6ujrCw8Mxc+ZMHDx4EGKx\nGH5+fhL7HDhwABs2bMC4ceOwaNEiGBgYQFVVFYWFhfD19a2TcNXn9SGsr6udHNWnOXHUVydjrNH6\nBgwYgKSkJBQUFKB3797cdg0NDTg6OtYbe1u3lyyxt6bac4obs3z5cu7fiYmJsLe3B1Dd1ygZJTVo\nvhJRFNSXiSKgfty6eM/+giA5EIKr34P/d/UFFrGmHkTD5kJk5w2m00vOERJpKCGVIzU1NYSHh2PW\nrFk4dOgQGGPYtm0b9/yxY8dgbGyM48ePSxx3/vz5Nxrnm47D1dUVSUlJCA4Oxrp162Q+rr20lzTG\nxsbIzs5GVVWVRMJbWVmJ3NzcVr/vbHx8vMRcVUIIIYQQhcQYlPMSqu8dmvkreKz6AkRlz8EQjZyP\ncuspgIrsU6DIm0dzSOVMTU0NYWFhcHJywnfffYc1a9Zwz9XMY3z9yl5lZSX27NnTpjHVHgb7puOY\nMxnmvPMAACAASURBVGcOzM3NsW/fPqlzKwHpVyvl1V6ycHFxwePHjxEcHCyx/fvvv0dxcTEmTpzY\novKrqqoQFxcHsViM+/fvIycnh7tCCgB79+5tUflEcdB8JaIoqC8TRUD9uAXKX0L1tyPosscB2v6u\nUM2IBvhKENlMQ8k/zqLUNxblb8+kZLQDoCuk7UBNUjp79mwcPnwYjDHs2LEDkydPxubNmzF9+nS4\nuLigtLQUERERUFVVbdN4aid7rRmHLMNe1dTU8OOPP8Ld3R1z586Fg4MDnJycoK+vj9LSUmRnZyMy\nMhLKysoSq8a2dXu1ZMju0qVLcfLkSaxcuRKpqamwsrJCWloaQkNDYW5ujk8++aRFsR05cgSrVq1C\ncnIyYmJioKGhgR49egAAzp49i759+7aofEIIIYSQ9oBfnA9Bkj9Ur4WCX1YCABBrCyEa7gXRcE+w\nLgaNlEDaG0pI2wmBQIDQ0FB4eHjA398fjDFs374djDGEhIRg7dq1EAqFmDJlCmbOnCl1TqC0e2pK\n29aY2scsXbq0xXHUbJc1HmNjY8TFxSE0NBRRUVE4ePAgSkpKoKGhATMzM3h6esLDw0Ni4Z/WiLM1\nYpemS5cuOH36NHbs2IHTp08jLCwM+vr68PHxwerVq6GpqSlTHPWxs7PD9OnTERkZiUGDBmHXrl3Y\nuHEjevfujd69e8Pd3b3ZsRPFQvOViKKgvkwUAfVjGYnFUM65WD0s9+Y58P53kaCy9zCUjVyAikGT\nAOW2vWBD2g6PtfFKLbGxsY3e+7GwsJC7mkMIkR96LxJCCCGk3RCVQnDtBwiS/aH0KBsAwJQFKLee\nCtGo+ajqOVjOAZIaKSkpGD9+fLOOpSukhBDSiSQkJNAv8kQhUF8mioD6sXT8RzkQJPlDkBIGnugF\nAEDctQdEdj4QDZsLptVdzhGS1kQJKSGEEEIIIUS+xGIo34qFWtJhqNyK5TZXmI6CaOR8VAycCChR\n6qKI6KwSQkgnQr/EE0VBfZkoAurHAMpKILgWBkGSP5SK8wAATFkN5YOnQTRqAaoMB8k5QNLWKCEl\nhBBCCCGEvFH8h7f+Nyz3B/DKq4flVun0gmjEPJQP9QDT7CbnCMmbQgkpIYR0IjRfiSgK6stEEXS6\nfiwWQ+VmDARJh6GSHcdtrugzGqJR81HR/30altsJ0RknhBBCCCGEtJ2yEgj+CK0elvskHwDAVNRR\nPmQGykbOh9hgoJwDJPJECSkhhHQineqXeKLQqC8TRaDo/bh6WO5//jcs9yUAoErHCKKRH6N86Bww\nDV05R0jaA0pICSGEEEIIIa1DLIbyrfNQu/Kd5LBcM0eIRi1ARf/3AL6SHAMk7Q0lpIQQ0ol0uvlK\nRGFRXyaKQKH6cc1quVf+Q8NySZNQQkoIIYQQQghpFv6j7OrVcq+Fv7ZarhFEI/+3Wi4NyyWNoISU\nEEI6EYX5JZ50etSXiSLosP1YLIbyrVioJR2Gyq1YbnOFmSNEI+ejYsD7NCyXyIwSUkIIIYQQQkjj\nykoguBZevVpucS4AGpZLWo4SUkII6UQUar4S6dSoLxNF0FH6Mf9xLgRX/gNBShh4opphub3+NyyX\nVsslLUMJKSGEEEIIIUSSWAzlnDioXTkMlZsx3OYK01EQjVqIigETACVKJcj/sXfn0VGV2d7Hv1WV\nGkgIU5AQEALSAQFjIIJMYXiVa6sgtK1MgkBoESQg9G1x4n2xG0RoxasMQUAGFQIO2LFpkVbgKpAB\nFaOAAoJMoY2KTEmAVFWq6rx/pEkbCBIyVVL5fdZyLc+pqnN2ztopss9z9vOUndnfAUj5SElJISws\njLVr1/o7lGqhIq/XsWPHGDFiBFFRUYSFhZGQkFDu5xAprepwJ16kJJTLEgiqZB67zmFPX06dl7sR\nunIQ1m83YQQ5cHUaQc6j2zj38Pvk33SPilEpNypIK9nFQmjhwoWXvZaamkpkZCTt2rVj7969pTq+\nyWQqa4hVhtPpZPny5QwcOJDWrVsTHh5Oy5Yt6du3L3/5y184ePBgmY5vMpkq5HolJCSQlpbGlClT\nWLJkCfHx8eV+jivZtGkTLVu25H//938r7ZwiIiJS/ZlPH6XW+9OoO+cmgtdPxfLzQXx1Isj77f8j\n+8k9XLhvPt6Im/wdpgQg3drwk0sLoQ8//JD4+HgaN25McnIykZGRfoqsajh69ChDhw7l4MGDxMXF\nMWHCBMLDwzl//jy7d+8mKSmJhQsXsmfPHho3bnzNx+/RowdZWVkEBZXvr4DL5WLHjh2MHTvWLyOj\nFosFh8MRUDcmpHxVl34lkatRLksg8HseGwZBh7djT12Cdf8/MRkGAJ7ILjh7jCO/XT+wWP0Xn9QI\nKkirgHXr1jFhwgRat27Nu+++S3h4uL9D8qu8vDyGDBlCZmYmq1at4u67777sPS6Xi8WLF5f6HCaT\nCZvNVpYwi/Xzzz9jGAb16tUr1+N6vV7cbje1atX61ffddttt7Nu3r1zPLSIiIgHGfQHbV+/gSFuK\n5aeCvxsMiw3Xzb/H1eNhvE07+DlAqUn0yK6frVixgnHjxtGhQwc2bNhQpBg9d+4cs2bNom/fvkRF\nRREREUGnTp2YMWMGeXl5Vz32mjVrCAsLY9u2bcydO5eYmBiaNm1K37592bFjB1BwZ+6uu+6iWbNm\ntGvXjrlz5152nGuJ4+I5t2/fzoIFC4iNjSUiIoJbb72VN998s0TXZNWqVXz33XdMnDix2GIUwG63\nM3ny5CKjo9cSZ3E9pGWNPSEhgZiYGACef/55wsLCCAsLIy0tDYBTp04xdepUbrrpJho3bkx0dDSP\nP/44Z86cKfYabt26lRdeeIHY2FiaNGnCe++9V6LrJ/JrNKIkgUK5LIGgsvPYdPZf1PrnX6g7J5qQ\n5D9i+WkfvtBw8vo+RfYTu7kweJGKUal0GiH1E8MweOmll3j22Wfp1asXSUlJBAcHF3lPVlYWq1ev\nZsCAAQwePJigoCBSUlKYP38+u3fvZt26dSU614wZM/D5fIwfPx63201iYiKDBw9m3rx5PPbYY8TH\nxzNkyBCSk5OZPXs2kZGRDBo0qExxzJw5E5fLRXx8PDabjRUrVpCQkEDLli3p0qXLr8a7fv16TCYT\nI0eOLNHPV5Y4i3u0tbSxjx49mujoaKZNm0b//v255557AGjdujU5OTnceeedHDlyhBEjRhATE8Ou\nXbtYsWIF27ZtY/PmzdSuXbvI8aZPn47H42H06NGEhoYSFRV1TddDREREBMPAcuxTHKmLse7dgMnn\nBcBzfSyu7uNwRw+EoPJ/akykpKpdQfpd0POVer7feB6vkOOuXLmSo0eP0q9fP5YvX47Vevnz+S1b\ntuTrr7/GYrEU7hszZgzPPfccL774IhkZGcTGxl71XD6fj48++qiwX7JNmzYMHz6ccePGsWnTpsJR\nveHDhxMTE8OyZcuKFKSliSM/P58tW7YUnnPAgAHExsaybNmyqxak+/btIzQ0lGbNml32c1w6mhgS\nEoLD4SjX61Xa2Dt37kx4eDjTpk2jffv23H///YWvPfvssxw+fJi5c+cWmeTo4ijp/Pnzefrpp4sc\nz+l0snXr1sKf72o2bdrEV199xaeffsrSpUtp0KABUFDgr1y5kuTk5BIdRwKb3/uVRMqJclkCQYXm\nsceFbdffsKctJShrFwCGOQh3zH04uz+Mt3nnijmvyDXSI7t+8tNPPwHQokWLYotRAKvVWlhceTwe\nzp49y6lTp+jduzcAGRkZJTpXfHx8kcl7unbtChQUUBeL0Yvn69ixI4cPHy5zHGPGjClyzoiICFq1\nasWRI0euGm9ubi6hoaGX7d+/fz+tW7cu8t+yZcvKFGdxyhL7lbz//vtcd911jBo1qsj+0aNH07Bh\nQzZs2FBsHCUtRk+fPs2uXbuYOnUqx48fJz09vfC19957j0aNGpU6dhEREak+TLk/4dg0m7p/vZmQ\ndQkEZe3CFxJG3v/5E9mPf8X5oa+qGJUqpdqNkFbUiGVlmzJlCqmpqSQmJmIYBjNnziz2fcuXL2fl\nypV8++23+Hy+Iq+dPXu2ROdq0aJFke2LE+4UN5NvvXr1OH36dJnjuPScAPXr1+f777+/aryhoaHk\n5uYWe8yLo3x79uxh+vTplz1yWxHX61piv5LMzExiY2Mxm4veA7JYLNxwww18/fXXl32mVatWJT7+\nJ598wpAhQ/jmm284fPhwkZHg9PR0nnjiiVLHLoFFI0oSKJTLEgjKM48t//oSe+oSbHuSMXnzAfA0\nbo+rxzjcMfeDtWQ3uUUqW7UrSANFrVq1WLt2LcOGDWPRokX4fD5mzZpV5D2JiYlMnz6d2267jfHj\nx9O4cWNsNhtZWVkkJCRcVnBdyS8fYf2lS4ujKylNHFc6p/Hv6cR/Tdu2bUlPTyczM5PmzZsX7g8O\nDqZXr15XjL2ir1dJYi9Pl/YU/5rf//73ADz11FP06tWLiIgIAA4cOMCJEycKR8VFREQkgHg9WPe+\njyN1MUHHPgPAMJlwt+uHq8c4PC17gJaCkypOBakfORwO1q5dywMPPMDixYsxDIPnnnuu8PW3336b\nyMhI3nnnnSKf27x5c6XGWdlxDBw4kPT0dFatWsW0adNK/Lmqcr2KExkZycGDB/F6vUUKXo/Hw6FD\nh8pt3dn169fz+OP/eYogLS2N+vXrc+ONN5bL8aX6U9+dBArlsgSC0uax6cIZbJ+/gSN9Gebsgie4\nfI46uDuNwNVtLL4GNXs9e6le1EPqZw6HgzVr1tCnTx+WLFnCU089VfjaxT7GX47seTwe5s2bV6Ex\nXfoYbGXH8eCDDxIVFcWCBQuK7a2E4kcr/XW9SqJ///6cPHmSVatWFdn/xhtvcOrUKfr161fmc5w5\nc4Yff/yRW265pXBfSkqKRkdFREQChPmn/QQn/5G6c24i+J9/wZz9Pd6Gv+HCgOfJfvJr8vo9q2JU\nqh2NkFYBF4vS4cOHs3TpUgzDYM6cOQwYMIAZM2YwaNAg+vfvT25uLuvWrcNmq9ipuS8t9sozjpI8\n9upwOHjrrbcYOnQoI0eOJC4ujj59+tCoUSNyc3M5ePAgycnJBAUF0bRp0wqJs7SxX8mkSZP4+9//\nztSpU9m1axfR0dHs3r2bpKQkoqKiePTRR8scn9VqLTJB1qFDh9i8eTOPPfZYmY8tgUMjShIolMsS\nCEqUxz4fQQc2Fyzb8t0nhbvzo27D2WMcnqjboYRtWCJVkQrSKsJut5OUlMSIESNYtmwZhmEwe/Zs\nDMNg9erVPP3004SHh3PvvfcybNgwunXrdtkxiltTs7h9V3PpZyZNmlTmOC7uL2k8kZGRfPzxxyQl\nJbF+/XoWLVpETk4OwcHBtGrVilGjRjFixIgiE/+UR5zlEXtx6tSpw8aNG5kzZw4bN25kzZo1NGrU\niDFjxvDkk08SEhJSojh+Te3atXnppZd4+eWXiY6O5siRI+Tm5hb7s4uIiEgV58rF/sWb2NOWYjl1\nCADDGowrdiiu7mPxNWrj5wBFyofJqOCZWrZs2XLVtR+zsrJo0qRJRYYhUuPMnj2b1157jX379pV4\nAiv9LgY+9d1JoFAuSyAoLo/Np49hT38V++erMLkKVh3w1muGq9tDuDs/iFGrnj9CFflVGRkZ3H77\n7aX6rEZIRQLErFmz6Ny5M3fccQc+n4/k5GTGjRtX4mJURERE/MQwCDqShj1tCda9H2AyCubDyG/R\nDVePceS3vRss+rNdApMyWyQAnDx5kvnz5xdO4LRw4UKaNWvG5MmT/RyZVDUaUZJAoVyWQBDXpRO2\nL9ZgT11C0A97ADAsVlw3D8bVYxzepjF+jlCk4qkgFQkADRs2ZObMmZw4cYJnnnmGkJAQ3nrrrSuu\nqSoiIiL+Y8r9CfunK7F/uhLzuZ8B8NW+DleXeFxd4jFCw/0coUjlUUEqEiAefvhhf4cg1YD67iRQ\nKJelOrJ8vwt76hJsu9/F5M3nkyyIuyUaV49xuG/+PVgd/g5RpNKpIBURERERqSg+L9a9HxT0hx5J\nA8AwmXC378+Fjt3JHTQOyjCTv0h1p4JURKQG0YiSBArlslR5zhzsn6/Cnv4qljOZABj22rg6PViw\nbEuDFmhhNhEVpCIiIiIi5cZ88hD2tFexf7EGk/scAN4GLXF1fxjXLcPAUcfPEYpULSpIRURqEPXd\nSaBQLkuVYhgEHd6OPXUx1v0fYjIMAPJb9cLVYzz5bf4LzJdPNKg8FlFBKiIiIiJSOvlObLvWYU9d\nTNCPewEwguy4OtyPq/t4vBHt/RygSNWnglREpAbRnXgJFMpl8SdT7k/Yd6woWLbl/EkAfLUb4er6\nB1xdRmPUvq5Ex1Eei6ggFREREREpEUvWbuwpiwuXbQHwNLkZV49HcN/8Owiy+zlCkerH7O8ARESk\n8qSkpPg7BJFyoVyWSuPzYv1mA7WX9qfOgj7Yv3wTfB7c7fuT+/AGcid+jDt2SKmKUeWxiEZIRURE\nREQu58zBvjMJe9pSLGeOAZcv2yIiZaeCVESkBlG/kgQK5bJUFPPpo9jTlmLfuRqT6+KyLS3+vWzL\nA+W6bIvyWESP7AaMlJQUwsLCWLt2rb9DqRYq8nodO3aMESNGEBUVRVhYGAkJCeV+DhERESlHhkHQ\nkTRCVo+kztxOOFIXY3KdI79lD86NWEXOnz7H1WO81hAVqQAqSCvZxUJo4cKFl72WmppKZGQk7dq1\nY+/evaU6vslkKmuIVYbT6WT58uUMHDiQ1q1bEx4eTsuWLenbty9/+ctfOHjwYJmObzKZKuR6JSQk\nkJaWxpQpU1iyZAnx8fHlfo7iXLhwgZiYGJ555hkAlixZQps2bcjKyqqU80v1oH4lCRTKZSkXHje2\nL98mdOFthC7tj+2b98FswdVxKDmTPuHcw/8gv32/YtcQLQ/KYxE9sus3lxZCH374IfHx8TRu3Jjk\n5GQiIyP9FFnVcPToUYYOHcrBgweJi4tjwoQJhIeHc/78eXbv3k1SUhILFy5kz549NG7c+JqP36NH\nD7KysggKKt9fAZfLxY4dOxg7dmylj4wGBQVxww03FF6Phg0b0rJlSxwOR6XGISIiUtWZzp/C/tlr\n2NOXY879EQBfSBiuLvG4uv4BIzTczxGK1BwqSKuAdevWMWHCBFq3bs27775LeHjN/hLMy8tjyJAh\nZGZmsmrVKu6+++7L3uNyuVi8eHGpz2EymbDZbGUJs1g///wzhmFQr169cj2u1+vF7XZTq1atK77H\nZrORnJxcuH3fffdx3333lWscUv2pX0kChXJZSsP8034cqYuxffk2Jo8TAG/4jTh7PIK7w/1gvfK/\nsxVBeSyiR3b9bsWKFYwbN44OHTqwYcOGIsXouXPnmDVrFn379iUqKoqIiAg6derEjBkzyMvLu+qx\n16xZQ1hYGNu2bWPu3LnExMTQtGlT+vbty44dO4CCR0XuuusumjVrRrt27Zg7d+5lx7mWOC6ec/v2\n7SxYsIDY2FgiIiK49dZbefPNN0t0TVatWsV3333HxIkTiy1GAex2O5MnTy4yOnotcRbXQ1rW2BMS\nEoiJiQHg+eefJywsjLCwMNLS0gA4deoUU6dO5aabbqJx48ZER0fz+OOPc+bMmWKv4datW3nhhReI\njY2lSZMmvPfeeyW6fiIiIvILhkHQgS3UXnE/dV/ujv3zNzB5nOS3+S9yx7xLzuRU3J0frPRiVEQK\naITUTwzD4KWXXuLZZ5+lV69eJCUlERwcXOQ9WVlZrF69mgEDBjB48GCCgoJISUlh/vz57N69m3Xr\n1pXoXDNmzMDn8zF+/HjcbjeJiYkMHjyYefPm8dhjjxEfH8+QIUNITk5m9uzZREZGMmjQoDLFMXPm\nTFwuF/Hx8dhsNlasWEFCQgItW7akS5cuvxrv+vXrMZlMjBw5skQ/X1niLK6HtLSxjx49mujoaKZN\nm0b//v255557AGjdujU5OTnceeedHDlyhBEjRhATE8OuXbtYsWIF27ZtY/PmzdSuXbvI8aZPn47H\n42H06NGEhoYSFRV1TddDpDgpKSm6Iy8BQbksV5Wfh+3Lt3CkLsZy4gAAhrUW7tihOLuPw9eotZ8D\nVB6LQDUsSO9Y9mWlnu+jhzpWyHFXrlzJ0aNH6devH8uXL8dqtV72npYtW/L1119jsfynkX7MmDE8\n99xzvPjii2RkZBAbG3vVc/l8Pj766KPCfsk2bdowfPhwxo0bx6ZNmwpH9YYPH05MTAzLli0rUpCW\nJo78/Hy2bNlSeM4BAwYQGxvLsmXLrlqQ7tu3j9DQUJo1a3bZz3HpaGJISEhhj2R5Xa/Sxt65c2fC\nw8OZNm0a7du35/777y987dlnn+Xw4cPMnTu3yCRHF0dJ58+fz9NPP13keE6nk61bt15TD+hrr73G\n6dOnOXjwIEOGDOH48eOcPHmSvXv38uc//5mmTZuW+FgiIiLVkSnnR+w7lmP/dCXmC6cB8NWJwNXt\nIVydR2GENPBzhCLyS2V+ZHf27Nm0b9+e6OhoHnjgAVwuV3nEFfB++uknAFq0aFFsMQpgtVoLiyuP\nx8PZs2c5deoUvXv3BiAjI6NE54qPjy8yeU/Xrl2BggLqYjF68XwdO3bk8OHDZY5jzJgxRc4ZERFB\nq1atOHLkyFXjzc3NJTQ09LL9+/fvp3Xr1kX+W7ZsWZniLE5ZYr+S999/n+uuu45Ro0YV2T969Gga\nNmzIhg0bio3jWorR119/nZtvvpn//u//ZuzYsYwePZoGDRrQoUMH/va3v7F///5Sxy+BQ3fiJVAo\nl+VSlqzdBL/9CHWfj6HWxy9ivnAaT9OOnBuylOzHv8LZ549VrhhVHouUcYT06NGjvPrqq+zbtw+7\n3c6QIUN48803L/ujuzxV1IhlZZsyZQqpqakkJiZiGAYzZ84s9n3Lly9n5cqVfPvtt/h8viKvnT17\ntkTnatGiRZHtixPuFDeTb7169Th9+nSZ47j0nAD169fn+++/v2q8oaGh5ObmFnvMi5P27Nmzh+nT\np1/2yG1FXK9rif1KMjMziY2NxWwueg/IYrFwww038PXXX1/2mVatWl3TOc6cOVM4Anz8+HHMZjP9\n+vUjLy+P999/n27dupU6fhERkSrJ58O6/0Psqa9gPVywhIphMuNu3x9n3AS8kV0ggJbEEwlEZSpI\n69Spg9Vq5cKFC1gsFi5cuKBHAkuoVq1arF27lmHDhrFo0SJ8Ph+zZs0q8p7ExESmT5/Obbfdxvjx\n42ncuDE2m42srCwSEhIuK7iu5JePsP7SpcXRlZQmjiud0zCMq56vbdu2pKenk5mZSfPmzQv3BwcH\n06tXryvGXtHXqySxl6dLe4qvZsqUKYX/n5qaSo8ePYCCXFMxKhepX0kChXK5hnOdw57xJvbUxVhO\nFTzZZdhr4+o0Alf3cfgaVI/l85THImUsSBs0aMCf/vQnmjdvTq1atfjtb39L3759yyu2gOdwOFi7\ndi0PPPAAixcvxjAMnnvuucLX3377bSIjI3nnnXeKfG7z5s2VGmdlxzFw4EDS09NZtWoV06ZNK/Hn\nqsr1Kk5kZCQHDx7E6/UWKXg9Hg+HDh0q93Vnt27dWqRXVUREJBCYsr/HkfYqts9ex+zMBsBbvzmu\n7g/j6jQCHHX8HKGIXKsy9ZAeOnSIl19+maNHj5KVlcW5c+dISkq67H0TJkxgzpw5zJkzh1deeYWU\nlJTC11JSUsjOzi5LGNWaw+FgzZo19OnThyVLlvDUU08Vvnaxj/GXI3sej4d58+ZVaEyXPgZb2XE8\n+OCDREVFsWDBgmJ7K6H40Up/Xa+S6N+/PydPnmTVqlVF9r/xxhucOnWKfv36len4Xq+Xjz/+GJ/P\nxw8//MB3331XOEIKMH/+/BIdJzs7+7LfT20H1vYvVYV4tK3t0m5f3FdV4tF2xW6n/W0FO2f8jrrP\nd8SxbT7bDmezxXsj5x5YSc6fdrKFm0nZubvKxFvS7Yujo1UlHm1ru6Tbr7zySmF9N2HCBMrCZJTh\nOcS33nqLTZs2FU4ss2rVKnbs2EFiYmLhe7Zs2XLVmU2zsrJo0qRJacOoVlJSUhg4cCAzZswgISGh\ncL/L5WL48OF8/PHHjB07ljlz5jBv3jxmzJhBnz596N+/P7m5uaxbtw6bzcaXX37JE088weOPP17k\nuImJiQwdOhQoWM9y0qRJ/OMf/6B79+5F4ggLC2PYsGEsXLiwyP6EhATefPNNTp06VbjvWuL4tXPe\nc889HD9+nK+++uqq1+nYsWMMHTqUAwcOEBcXR58+fWjUqBG5ubkcPHiQ5ORkzp8/z5IlS/jd7353\nzXFe6/UqaeyZmZl07NixyLkAcnJy6Nu3b+GyL9HR0ezevZukpCRatWrFli1bCAkJuWocV7J8+XIe\nf/xxduzYwaZNm5g9ezZfffUVYWFhfPjhh3i93iuu6fpLNel3UUREqjifF+veDwr6Q48WrJ9umC3k\n3zQQZ9wjeJvd4ucAReSijIwMbr/99lJ9NqgsJ77xxhuZOXMmeXl5OBwONm/ezK233lqWQ9ZYdrud\npKQkRowYwbJlyzAMg9mzZ2MYBqtXr+bpp58mPDyce++9l2HDhhXbE1jcmprF7buaSz8zadKkMsdx\ncX9J44mMjOTjjz8mKSmJ9evXs2jRInJycggODqZVq1aMGjWKESNGFJn4pzziLI/Yi1OnTh02btzI\nnDlz2LhxI2vWrKFRo0aMGTOGJ598srAYvVocV9KlSxcGDRpEcnIyN910E3PnzuWZZ56hefPmNG/e\nvLDoFvnlHXmR6ky5HMBcudh3JmFPXYLlzDEAfI46uG8dhbPbWIx61/s5wPKjPBYp4wgpwPPPP8/r\nr7+O2WwuXKvxl8uYaIRUpPrQ72Lg0x8/EiiUy4HHdPZfONKWYP/sDUyugtn2vQ1a4uoxDtctD4C9\ntp8jLH/KYwkUZRkhLXNBejUqSEWqD/0uiohIZbNk7sSR+grWr9dj8nkByG/RDVfcBPLb3gnmtoXz\nqwAAIABJREFU4me/F5Gqw2+P7IqIiIiIXDOfF+veDThSFhF07DMADHMQrpj7ccU9gvf6wFh3XkSu\nTgWpiEgNosfDJFAol6spZ05Bf2ja0l/0h9bF3WU0zm4PYdStWevZK49FVJCKiIiISAUznzmOPX1p\nMf2h43HdMiwg+0NFpGRUkIqI1CC6Ey+BQrlcPVgyd+JIWYT1m3/8pz+0ZfeC/tAbf1vj+0OVxyIq\nSEVERESkPKk/VESugQpSEZEaRP1KEiiUy1VQseuH1i1YP7T72BrXH1oSymMRFaQiIiIiUgYF64cu\nxf7Z6+oPFZFrpoJURKQG0Z14CRTKZf+zHM8o6A/9+u9aP7SUlMciKkhFREREpKR8Xqz7NmJPWYT1\n6A4ADLMFd8x9OHs8grdZrJ8DFJHqRgWpiEgNon4lCRTK5UrmOof9i7XYUxdjOX0EAJ+jDu7OI3F2\nfxij3vV+DrB6Uh6LqCAVERERkSswZWdhT1+G/bPXMOedBcBbv3lBf2in4WAP9XOEIlLdqSAVEalB\ndCdeAoVyuWJZsvZgT1mEbde7mHweADzNO+PsmUB+27vBoj8hy4PyWEQFqYiIiIgA+HwEHdiMY3si\n1sPbATBMZtzRAwv6QyNv9XOAIhKIzP4OQMpHSkoKYWFhrF271t+hVAsVeb2OHTvGiBEjiIqKIiws\njISEhHI/h0hppaSk+DsEkXKhXC5H+XnYPnuNOi93I/T1oVgPb8ew1cbZfRw5j33B+QdWqhitIMpj\nERWkle5iIbRw4cLLXktNTSUyMpJ27dqxd+/eUh3fZDKVNcQqw+l0snz5cgYOHEjr1q0JDw+nZcuW\n9O3bl7/85S8cPHiwTMc3mUwVcr0SEhJIS0tjypQpLFmyhPj4+HI/R3EuXLhATEwMzzzzDABLliyh\nTZs2ZGVlVcr5RUSkejGd+xnHptnU/evNhCT/N5afD+Kr24QLd/2Z7Cf3kHfPbHwNIv0dpogEOD2y\n6yeXFkIffvgh8fHxNG7cmOTkZCIja/Y/AEePHmXo0KEcPHiQuLg4JkyYQHh4OOfPn2f37t0kJSWx\ncOFC9uzZQ+PGja/5+D169CArK4ugoPL9FXC5XOzYsYOxY8dW+shoUFAQN9xwQ+H1aNiwIS1btsTh\ncFRqHFK1qV9JAoVyufTMP+3HkbII21fvYPK4APA0iSnoD40eCBarnyOsOZTHIipIq4R169YxYcIE\nWrduzbvvvkt4eLi/Q/KrvLw8hgwZQmZmJqtWreLuu+++7D0ul4vFixeX+hwmkwmbzVaWMIv1888/\nYxgG9erVK9fjer1e3G43tWrVuuJ7bDYbycnJhdv33Xcf9913X7nGISIi1ZRhEHRoW0F/6IHNBbtM\nJtxt78IVNwFPy+4QQE9ZiUj1oUd2/WzFihWMGzeODh06sGHDhiLF6Llz55g1axZ9+/YlKiqKiIgI\nOnXqxIwZM8jLy7vqsdesWUNYWBjbtm1j7ty5xMTE0LRpU/r27cuOHQWLWaekpHDXXXfRrFkz2rVr\nx9y5cy87zrXEcfGc27dvZ8GCBcTGxhIREcGtt97Km2++WaJrsmrVKr777jsmTpxYbDEKYLfbmTx5\ncpHR0WuJs7ge0rLGnpCQQExMDADPP/88YWFhhIWFkZaWBsCpU6eYOnUqN910E40bNyY6OprHH3+c\nM2fOFHsNt27dygsvvEBsbCxNmjThvffeK9H1E/k16leSQKFcLiGPG1vGm4Qu6E3o8nuxHtiMEeTA\n1SWenD9+yvmRSXhu6KFi1E+UxyIaIfUbwzB46aWXePbZZ+nVqxdJSUkEBwcXeU9WVharV69mwIAB\nDB48mKCgIFJSUpg/fz67d+9m3bp1JTrXjBkz8Pl8jB8/HrfbTWJiIoMHD2bevHk89thjxMfHM2TI\nEJKTk5k9ezaRkZEMGjSoTHHMnDkTl8tFfHw8NpuNFStWkJCQQMuWLenSpcuvxrt+/XpMJhMjR44s\n0c9XljiL6yEtbeyjR48mOjqaadOm0b9/f+655x4AWrduTU5ODnfeeSdHjhxhxIgRxMTEsGvXLlas\nWMG2bdvYvHkztWvXLnK86dOn4/F4GD16NKGhoURFRV3T9RARkZrLlHcW26ev4Uh/FXPODwD4al+H\nq+tDuLqOwQgJ83OEIiIFql1B+s/G3Sv1fHf+mFYhx125ciVHjx6lX79+LF++HKv18n6Nli1b8vXX\nX2OxWAr3jRkzhueee44XX3yRjIwMYmNjr3oun8/HRx99VNgv2aZNG4YPH864cePYtGlT4aje8OHD\niYmJYdmyZUUK0tLEkZ+fz5YtWwrPOWDAAGJjY1m2bNlVC9J9+/YRGhpKs2bNLvs5Lh1NDAkJKeyR\nLK/rVdrYO3fuTHh4ONOmTaN9+/bcf//9ha89++yzHD58mLlz5xaZ5OjiKOn8+fN5+umnixzP6XSy\ndevWEveAbtq0ia+++opPP/2UpUuX0qBBA6CgwF+5cmWRx3ml5lK/kgQK5XLxzKePYk9ZjP2LJEzu\n8wB4w2/EGTcBd8z9YNW8AlWJ8lhEj+z6zU8//QRAixYtii1GAaxWa2Fx5fF4OHv2LKdOnaJ3794A\nZGRklOhc8fHxRSbv6dq1K1BQQF0sRi+er2PHjhw+fLjMcYwZM6bIOSMiImjVqhVHjhy5ary5ubmE\nhoZetn///v20bt26yH/Lli0rU5zFKUvsV/L+++9z3XXXMWrUqCL7R48eTcOGDdmwYUOxcZS0GD19\n+jS7du1i6tSpHD9+nPT09MLX3nvvPRo1alTq2EVEpOqzHPuMkKRR1JnbCUf6Ukzu8+T/pje5o98m\nZ3Iq7k4jVIyKSJVU7UZIK2rEsrJNmTKF1NRUEhMTMQyDmTNnFvu+5cuXs3LlSr799lt8Pl+R186e\nPVuic7Vo0aLI9sUJd4qbybdevXqcPn26zHFcek6A+vXr8/3331813tDQUHJzc4s95sVRvj179jB9\n+vTLHrmtiOt1LbFfSWZmJrGxsZjNRe8BWSwWbrjhBr7++uvLPtOqVasSH/+TTz5hyJAhfPPNNxw+\nfLjISHB6ejpPPPFEqWOXwJKSkqI78hIQlMuAz4t17wc4ti8kKPNzAAyLFdfNg3H1nIA34iY/ByhX\nozwWqYYFaaCoVasWa9euZdiwYSxatAifz8esWbOKvCcxMZHp06dz2223MX78eBo3bozNZiMrK4uE\nhITLCq4r+eUjrL90aXF0JaWJ40rnNAzjqudr27Yt6enpZGZm0rx588L9wcHB9OrV64qxV/T1Kkns\n5enSnuJf8/vf/x6Ap556il69ehEREQHAgQMHOHHiROGouIiIBAD3eew712BPXYzldMHTOz5HXVxd\nx+Dq9hBGnQg/BygiUnIqSP3I4XCwdu1aHnjgARYvXoxhGDz33HOFr7/99ttERkbyzjvvFPnc5s2b\nKzXOyo5j4MCBpKens2rVKqZNm1biz1WV61WcyMhIDh48iNfrLVLwejweDh06VG7rzq5fv57HH3+8\ncDstLY369etz4403lsvxpfrTnXgJFDUxl005P2JPfxX7pysx5xU89eOtH4kr7hFctzwA9tpXOYJU\nNTUxj0UupR5SP3M4HKxZs4Y+ffqwZMkSnnrqqcLXLvYx/nJkz+PxMG/evAqN6dLHYCs7jgcffJCo\nqCgWLFhQbG8lFD9a6a/rVRL9+/fn5MmTrFq1qsj+N954g1OnTtGvX78yn+PMmTP8+OOP3HLLLYX7\nUlJSNDoqIlLNmX/cS/C6BOo+H0OtT17CnHcWT/POnBv+GjmP7cTV/WEVoyJSbWmEtAq4WJQOHz6c\npUuXYhgGc+bMYcCAAcyYMYNBgwbRv39/cnNzWbduHTabrULjubTYK884SvLYq8Ph4K233mLo0KGM\nHDmSuLg4+vTpQ6NGjcjNzeXgwYMkJycTFBRE06ZNKyTO0sZ+JZMmTeLvf/87U6dOZdeuXURHR7N7\n926SkpKIiori0UcfLXN8Vqu1yARZhw4dYvPmzTz22GNlPrYEDvUrSaAI+Fw2DIK++wTH9oVYD35c\nsMtkwt2+P86eE/FG3urnAKU8BHwei5SACtIqwm63k5SUxIgRI1i2bBmGYTB79mwMw2D16tU8/fTT\nhIeHc++99zJs2DC6det22TGKW1OzuH1Xc+lnJk2aVOY4Lu4vaTyRkZF8/PHHJCUlsX79ehYtWkRO\nTg7BwcG0atWKUaNGMWLEiCIT/5RHnOURe3Hq1KnDxo0bmTNnDhs3bmTNmjU0atSIMWPG8OSTTxIS\nElKiOH5N7dq1eemll3j55ZeJjo7myJEj5ObmFvuzi4hIFeVxY9v1LvaURQT9+A0AhjUYV6fhuHqM\nxxfW0s8BioiUL5NRwTO1bNmy5aprP2ZlZdGkSZOKDEOkxpk9ezavvfYa+/btK/EEVvpdFBHxD1Pe\nWWyfvoYj/VXMOT8A4AsNx9VtLK4u8RjB9f0coYjIlWVkZHD77beX6rMaIRUJELNmzaJz587ccccd\n+Hw+kpOTGTduXImLURERqXzmM5nYU17BvnM1Jvd5ALzhN+KMS8Dd4X4Isvs5QhGRiqW/VEUCwMmT\nJ5k/f37hGrILFy6kWbNmTJ482c+RSVWTkpLi7xBEykV1z2XL8S8IWTOGOi/E4khbgsl9nvzf9CY3\n/h1yJqfi7jRcxWgNUN3zWKQ8aIRUJAA0bNiQmTNncuLECZ555hlCQkJ46623rrimqoiI+IHPh3X/\nh9i3L8R6NB0AwxyEq8MgXD0T8Ebc5OcARUQqnwpSkQDx8MMP+zsEqQY0m6MEimqVy/l52L58C8f2\nRVhOfgeAYQ/F1SUeZ/exGHWbXuUAEqiqVR6LVBAVpCIiIiIVwHTuJPYdy7HvWI75/EkAvPWux9Vj\nPK5OI8BRx88Rioj4nwpSEZEaRGveSaCoyrls/vk7HKmvYPtiLSaPEwBP0w44eyaQf9NAsOjPLylQ\nlfNYpLLoG1FERESkrAwDy7FPcWxfiHXfRkz/XlXPfeNvcfWciKdldyjDetYiIoFKBamISA2iO/ES\nKKpMLvu8WL95H8f2hQQd/wIAw2LDFTsEZ9wEfI3a+DlAqcqqTB6L+JEKUhEREZFr5T6Pfeca7CmL\nsJw5BoCvVn1c3f6Aq+tDGKGN/BygiEj1oIJURKQGUb+SBAp/5bIp9yfs6csKJirKOwuAt0ELXHEJ\nuG4ZCraQSo9Jqi99J4tUkYLUarXidDpxOBz+DkWkxnI6nVitVn+HISJSJZlPfItjeyK2L9/G5HUD\n4GnWCWevSeS3uxvMWvdZRKQ0qkRBGhYWxvfff0+TJk2wWPSFLlLZvF4vP//8M02bai28QKc78RIo\nKiWXDYOgI2nYty/Etv/Dgl0mE+72/XH2TMAb2aXiY5CApu9kkSpSkJrNZho1asSJEycw/j0rnYhU\nHpPJRKNGjTCbzf4ORUTE/7werN+sx7EtkaDvvwTACHLgvmUYzh6P4LvuN34OUEQkcFSJghTAbrcT\nERHh7zBEiqUeDwkUymUJFBWSy65z2HcmYU99BcuZTAB8IWG4uj6Eq+sfMGo3LN/zSY2n72SRKlSQ\nioiIiPiDKefHgomKPl3xn4mKwlrh7JmAO3YIWGv5OUIRkcBlMir4GdktW7YQGxtbkacQERERuWbm\nn/bjSEnE9uU7/5moKPJWnD0nkd/2Tk1UJCJSQhkZGdx+++2l+qxGSEVERKTmuDhR0bYF2L79qGCX\nJioSEfEbzWAiUgIpKSn+DkGkXCiXJVBccy57PVh3JxOa2JfQV+/B9u1HGEEOnF3GkPPfn3F+xBsq\nRqXS6TtZRCOkIiIiEsjc5wsmKkp5BcuZY4AmKhIRqUrUQyoiIiIBx5R7Anv6q9h3LP/FREU3/Hui\noqGaqEhEpByph1REREQEMJ84gCNlEbYv38LkcQHgad4ZZ69J5Le9SxMViYhUMeohFSkB9XhIoFAu\nS6AoksuGgeXoDkLeGE7dl7pi//wN8Lpxt+tHzviN5D7yIfnt+6sYlSpH38kiGiEVERGR6srnxbp3\nA45tCwg6/gUARpAdd+wwnHET8F33Gz8HKCIiV6OCVKQE4uLi/B2CSLlQLktAcF/gdsu32F+cjOX0\nEQB8terj6vYHXN3GYtS+zs8BipSMvpNFVJCKiIhINWE6dxL7jmUFExWdPwWAt34krrgJuDo9ALYQ\nP0coIiLXSj2kIiWgHg8JFMplqY7MJw9T673HqPvXm6m15XnM50+xJT+Kcw+sIOexnbi6j1UxKtWS\nvpNFNEIqIiIiVZQlcyeO7QuwfvM+pn+vUuducweuXpO48L2P/Oiefo5QRETKSgWpSAmox0MChXJZ\nqjyfD+u3H2HftgDr0XQADIsVV4dBOHsm4AtvC0DcDf4MUqR86DtZRAWpiIiIVAUeF7Yv38aRkojl\nxAEAfI46uLvE4+z+MEadCD8HKCIiFUE9pCIloB4PCRTKZalqTHnZ2D95mbrPdyDkb5OxnDiAr24T\nLtw9k+wndpN35zPFFqPKZQkEymMRjZCKiIiIH5jO/gtHyivYP1+FyX0OAE/jdrh6TsId83uwWP0c\noYiIVAaTYfx7loAKsmXLFmJjYyvyFCIiIlJNWH74Bvu2Bdh2/w2TzwNAfqveOHtNxBN1G5hMfo5Q\nRESuVUZGBrfffnupPqsRUhEREalYhkHQoW04ti3AevB/C3aZLbhj7sPZcyLepjF+DlBERPxFPaQi\nJaAeDwkUymWpVF4P1l3vErrw/xC6/F6sB/8XwxqMs/vD5Dz2BeeHvlrqYlS5LIFAeSxSDiOkZ8+e\n5aGHHuKbb77BZDKxYsUKunbtWh6xiYiISHXkPo/989XYU1/BciYTAF/t63B1fxhXlzEYwfX9HKCI\niFQVZe4hHTVqFL1792bMmDF4PB7Onz9P3bp1C19XD6mIiEjNYDr3M/a0pdh3rMCcdwYAb1grnL0S\ncHccClaHnyMUEZGK4Lce0uzsbLZv387rr79ecLCgoCLFqIiIiAQ+88lDOLYnYst4E5PHCYCnWSec\nvR8lv+1dYLb4OUIREamqytRDeuTIEa677jri4+OJjY1l7NixXLhwobxiE6ky1OMhgUK5LOXJkrmT\nkNUjqfM/t2L/7DVMHifutneRM+4Dch/5kPz2/SusGFUuSyBQHouUsSD1eDxkZGQwYcIEMjIyCAkJ\nYc6cOeUVm4iIiFQ1Ph/WfR9Se2l/6rxyB7Zv3gezFVen4WT/MZ3zI5Pwtuiq5VtERKREyvTI7vXX\nX8/1119P586dAbj//vuLLUgnTJhA8+bNAahbty7R0dHExcUB/7kzpG1ta1vb2q6c7YuqSjzaribb\nWz8m6NBW7sj+EMuJb/kkC3y2YLrfNxZn94fZvvsQHPiZuEZtKiWei/uqzPXRtra1re0atL1nzx6y\ns7MByMzM5KGHHqK0yjypUa9evVi2bBmtW7fmz3/+M3l5efz1r38tfF2TGomIiFRjzhzsn72OI3Ux\n5pwfAPDVicAZ9wiuziPBUcfPAYqIiL/5bVIjgAULFjB8+HDcbjetWrVi5cqVZT2kSJXzy7vwItWZ\ncllKypTzA47UJdg/XYnJlQuAN/xGnL0exX3z7yHI5tf4lMsSCJTHIuVQkMbExPD555+XRywiIiLi\nZ+YT3+LYvhDbl29j8uYDkH9DHM6ek/C06aveUBERKVdlfmT3avTIroiISBVnGFiOfYpj23xs+/5Z\nsMtkIr/9PTh7TcLb7BY/BygiIlWZXx/ZFRERkWrK58O6byOObfMJyix42skIcuC+ZRjOuAR8DW/w\nc4AiIhLoyrTsi0hNcXF2MZHqTrksAOQ7sX3+BnVe6krt1Q8SlPk5vlr1yLvtMbKf2MWF371Y5YtR\n5bIEAuWxiEZIRUREagxTXja2T1fiSFuCOfcnALz1rscVNwFXpxFgr+3nCEVEpKZRD6mIiEiAM2V/\njyN1MfZPX8fkPgeAJ+ImnL0eJT96IFisfo5QRESqM/WQioiIyGXMP+7FsT0R21fvYPJ5AMj/Te+C\nGXOj/o9mzBUREb9TD6lICajHQwKFcrkGMAyCjqQR8tpQ6s6Lw56xFgwf7pt/T87Ejzn3h2Q8rW+r\n9sWoclkCgfJYRCOkIiIigcHnxbr3g4IZc49/AYBhrYXrluG4ek7A16CFf+MTEREphnpIRUREqrN8\nJ7Yv38KxPRHLye8A8AU3wNXtIVzdxmKEhPk5QBERCXTqIRUREalhip0xt35zXHEJuDo9ALYQP0co\nIiJydeohFSkB9XhIoFAuV3+m7O+p9cH/o+6caII/nIE59yc8EdGcG/oqOX/aiav72BpRjCqXJRAo\nj0U0QioiIlItmH/ah2PbwqIz5rbqjbP3o3h+06faT1IkIiI1k3pIRUREqirDIOjoDuzb5mPb/2HB\nLpOZ/OiBOHtNwtu0g58DFBERUQ+piIhIYPH5sO7bWDBjbubnABhBDlydRmjGXBERCSjqIRUpAfV4\nSKBQLldxHhe2z1dR5+Vu1F79IEGZn+OrVZ+826aS/cRu8gY+r2L035TLEgiUxyIaIRUREfE/Zw72\nT1/DkboYc+6PAHjrXf/vGXOHg722nwMUERGpGOohFRER8RNTzo84Uhdj/3QlJlcuAJ7G7XH1ehT3\nzb8Di9XPEYqIiFydekhFRESqEfPPB3FsX4gt4y1MXjcA+Tf0xNlrEp7Wt2vGXBERqTHUQypSAurx\nkEChXPYvS+ZOQlaPpM5LXbF/vgp8+bhvuoecCZs4N/bveNr0VTFaQsplCQTKYxGNkIqIiFQswyDo\n2804ts3DeiStYFeQHVfsUJw9J+Jr2MrPAYqIiPiPekhFREQqgjcf266/4dg2H8tP+wDwOerg6voH\nXN0fxggN93OAIiIi5UM9pCIiIlWF6xz2z1fhSFmEOft7AHx1InDGPYKr80hw1PFzgCIiIlWHekhF\nSkA9HhIolMsVx3TuZxwfzaLuX28meMM0zNnf470uivP3LSB76pe4ek5UMVqOlMsSCJTHIhohFRER\nKRPz6aPYtydi35mEyeMEwBN5K85ek8m/8bdg1r1fERGRK1EPqYiISClYsnbj2DoP656/YzJ8ALjb\n3omz16N4W3T1c3QiIiKVRz2kIiIilcEwCDq0raAQ/e6Tgl3mIFwdh+DsNRFfeFv/xiciIlLN6Dki\nkRJQj4cECuVyKfm8WPe8R2ji7YQuvxfrd59g2EJw9niE7KkZXBiUqGK0kimXJRAoj0U0QioiInJl\n+U5sGWtxbFuI5fQRAHwhDXH1GIeryxiM4Pp+DlBERKR6Uw+piIjIJUx52dh3LMeetgTzuZ8B8DZo\ngbPnRNy3DANrLT9HKCIiUnWoh1RERKQcmLKzcKS+gv3T1zG5zwHgaXIzzt6Pkt9+AFj0z6aIiEh5\nUg+pSAmox0MChXK5eOYTBwheN5G6L3TEsT0Rk/sc+b/pTe4f/kbuxI/Jv/n3KkarGOWyBALlsYhG\nSEVEpAazHPsMx7b52PZ+AIBhMuOO/h3O3o/ibdrBz9GJiIgEPvWQiohIzWIYBH27GcfWl7EeTS/Y\nFWTHfcsDOOMS8DW8wc8BioiIVC/qIRUREbkabz623cnYt80n6Me9APgcdXF1/QOu7g9jhDbyc4Ai\nIiI1j3pIRUpAPR4SKGpkLrvPY09dQp25txDy9niCftyLr04EF+6eQfaTu3H+9v+qGK2GamQuS8BR\nHotohFRERAKU6fwp7OmvYk9fhvnCaQC810Xh7DUJd4dBEGT3c4QiIiKiHlIREQko5jPHsW9PxL5z\nNab8CwB4mt2Cs/cU8tveBWY9HCQiIlKe1EMqIiI1nvnHvTi2zse2+11MPi8A+W3+C2fvyXhadAOT\nyc8RioiIyKV0m1ikBNTjIYEi4HLZMAg6kkbt14ZQd14c9q/eBsDVYRA5j27n3Oi38LTsrmI0AAVc\nLkuNpDwW0QipiIhURz4f1v3/xPHJywQd3wmAYa2Fq9MIXD0T8NVv7ucARUREpCTUQyoiItWHx41t\n1zoc2+ZjOXEAAF+teri6jcXVbSxG7YZ+DlBERKTmUQ+piIgENtc57J+/gSNlEebsLAB8dZvijJuA\nq/ODYK/t5wBFRESkNNRDKlIC6vGQQFHdctl07iSOTc9R9683E7zh/2LOzsLbqA3nBy0ie2oGrrhH\nVIzWUNUtl0WKozwW0QipiIhUQebTxwqWbvkiCVN+HgCeyC44e08mv80dWrpFREQkQKiHVEREqgzL\nD19j3zof257kwqVb3Df+FmfvyXhbdPVzdCIiIlIc9ZCKiEj1ZRgEHUnFsXUe1gNbCnaZg3B1HIqz\n10R8jdv5OUARERGpKHrmSaQE1OMhgaJK5bLPh/Wb9wl95Q5CXx2A9cAWDGswzu7jyJ6awYXBi1SM\nyhVVqVwWKSXlsYhGSEVEpLJ5XNi+egfHtgVYfj4IgC+4wX+Wbglp4OcARUREpLKoh1RERCqHKxf7\nZ6/jSHkFc84PAHjrNcPVMwFXp+FgC/FzgCIiIlIa6iEVEZEqy3TuZ+xpS7GnL8PszAbAG94WZ+/J\nuG++FyxWP0coIiIi/qIeUpESUI+HBIrKzGXz6aPU+vtU6v41hlofv4jZmU1+i27kjnqTnMkpuDsO\nVjEqpabvZQkEymMRjZCKiEg5s/zwdcGMubuTMRk+ANxt78LZ+1G8kV38HJ2IiIhUJeohFRGRsrvC\n0i3uDoMKlm4Jb+vnAEVERKSiqIdURET8w+fDuu8DHFvnEXT8CwAMazCuzg/i7JmAUe96PwcoIiIi\nVZl6SEVKQD0eEijKLZc9bmw7k6jzcjdqrx5J0PEv8AU3IK/vk2Q/sZu8e2arGJUKpe9lCQTKYxGN\nkIqIyLVw5WL/7A0cKYt+sXTL9bh6TtTSLSIiInLN1EMqIiJXZTp3EnvaEi3dIiIiIpdRD6mIiFQI\n8+lj2LcnYv8iCVN+HgD5Lbri6jWZ/BvvAJPJzxGKiIhIdaYeUpESUI+HBIqS5rLlh2+8wq+BAAAg\nAElEQVQIfvNh6rzYCceOZZjy83C3vZOccR9wbtwH5Lf9rYpR8St9L0sgUB6LaIRUREQuMgyCjqYX\nLN3y7aaCXWYLro5DcPaahK9xOz8HKCIiIoFGPaQiIjWdz4d1/z8Llm7J/BwAw1oLV+cHccUl4Kvf\nzM8BioiISFWmHlIREbl2Hje2XetwbJuP5cQBAHy16uPq9hCu7g9jhIT5OUAREREJdOohFSkB9XhI\noEhJSQHXOewpr1B3biwh6yZiOXEAX92mXOj/HNlP7ML5X0+pGJUqT9/LEgiUxyLlNELq9Xrp1KkT\n119/Pf/4xz/K45AiIlLOTOdPYduZRN3/HYU57wwA3kZtcPZ6FHfMfRBk83OEIiIiUtOUS0E6b948\n2rVrR25ubnkcTqTKiYuL83cIIqVmPnO8YOmWnav47b+XbvE074yz9xTyb/wtmPWwjFQ/+l6WQKA8\nFimHgvRf//oXH3zwAdOmTeN//ud/yiMmEREpB+Yf9+LYtgDbrnWYfF4A8tv8F87eU/C06KplW0RE\nRMTvynxb/I9//CMvvPACZt1hlwCmHg+pTixHdxDy+jDqzovD/uVbALg6DCLn0e388zeT8LTspmJU\nqj19L0sgUB6LlHGE9P3336dRo0Z07NiRTz75pJxCEhGRa+bzYf12E46tLxN07FMAjCBHwdItPRPw\n1W9e8L5D+uNHREREqo4yFaRpaWmsX7+eDz74AKfTSU5ODiNHjuSNN94o8r4JEybQvHnBH0N169Yl\nOjq68Jn5i3eGtK1tbWtb26XY9nm4rfZPOLbNY/uX+wHo1aoerq5/YIspBqNWPeL+XYxeeie+SsSv\nbW2XcvvivqoSj7a1rW1t16TtPXv2kJ2dDUBmZiYPPfQQpWUyDMMo9ad/YevWrcydO/eyWXa3bNlC\nbGxseZxCREQucp/H/vlq7CmJWM7+CwBfnQiccRNw3ToS7KF+DlBERERqioyMDG6//fZSfbZcGz9N\n6kmSAHXxzpCIv5nOn8ax+a/U/WsMwe8/heXsv/BeF8X5+xaQPfVLXD0TfrUYVS5LoFAuSyBQHouU\n07IvAL1796Z3797ldTgREfkF09l/4dieiP3zVZjyLwDgaXZLwdItbe/S0i0iIiJSLZXbI7tXokd2\nRURKz/zT/oKlW756B5PPA0B+69sLlm5p2V2z5YqIiIjfleWR3XIbIRURkfJjOfYZjq3zsO3bCIBh\nMuOOuQ9nr0fxNon2c3QiIiIi5UPPeImUgHo8pFIYBkH7N1F7ST/qLL4T276NGEEOnF3GkPPYTs4P\nfbXMxahyWQKFclkCgfJYRCOkIiL+5/Vg252Mfds8gn7cC4DPUQdX14dwdX8YI7SRnwMUERERqRjq\nIRUR8Rf3BexfrMG+fSGWM5kA+EIb44x7BNeto8BRx88BioiIiFydekhFRKoRU95Z7OnLsKctwXz+\nFADehr/B2WsS7o6DIcju5whFREREKod6SEVKQD0eUh5M2d9Ta8P/pe6cm6m16TnM50/hadqRcw+s\nJOeP6bg7P1jhxahyWQKFclkCgfJYRCOkIiIVznziAI5t8wuWbvHmA5D/mz44+0zBc0NPLd0iIiIi\nNZZ6SEVEKoglcyeObfOx7t2AyTAwTGbybxqAs/dkvE1j/B2eiIiISLlQD6mISFVhGAQd2IJj6zys\nR1ILdgXZccUOw9lzIr6GN/g5QBEREZGqQz2kIiWgHg+5Kq8H61fvErqgN6GvDcZ6JBXDHoqz92Sy\nH/+KC/f+T5UoRpXLEiiUyxIIlMciGiEVESmb/DzsOy8u3XKM/9/encfJUdf5H3/X0cfcuUhCDgh3\nEggkEQhHCCgGFuVQQOWQOyqCArv89qfu/tx1DwF13RUQVxZEoyiguAiyGFiikgRIIAZwCOEQCAk5\ngFxz91VVvz+qurp7ZjIzmSM9XfN6Ph69XfWt7/db3+58cPsz1Z9qSXLrJih14heVnnc5P90CAADQ\nA2pIAaAfjI5dSqz8kRJP3ymzbZskyRl7YPDTLZ+RYskyrxAAAGDvoIYUAPYSo2mzkk//pxKrFsvI\ntEqScpNnK3Xy9coefqZkWmVeIQAAQOWghhToA2o8YL7/uqp//WU1fGeOksvvkJFpVfbgk9Vy1UNq\nuXapsrPOqYhklFhGVBDLiALiGOAKKQD0qOtPtxjKzDon+OmW2eVeHgAAQEWjhhQAOvM82W/83v/p\nlrf8v157VlyZD+V/uuWgMi8QAABg+KCGFAAGg5NT7OWHlXzqNtlbGiVJXqJO6eOuVOqEL8irn1jm\nBQIAAEQLNaRAH1DjEXHZDiWe/ZHqv3uMau//nOwtjXJrx6v9r/5Ru77aqI6/+sfIJKPEMqKCWEYU\nEMcAV0gBjGC7/+mWLykz5wJ+ugUAAGCIUUMKYMTZ/U+3XKfs4WdVxN1yAQAAhgtqSAGgD8z3X1dy\n+e2Kv/BLGU5WkpQ9+GSlTr5BuYMWSIZR5hUCAACMLNSQAn1AjUdlszY8r5qfXaL67x2vxOqfS25O\nmVnnqPlLv1frVQ8pd/DJIyYZJZYRFcQyooA4BrhCCiCqPE/2a08quexWxd5+xm+yE0rPzf90y4Fl\nXiAAAACoIQUQLU5O8T8/pMSy22RvXSvJ/+mW1HFXKX3iF+TVTSjzAgEAAKKFGlIAyLQrsfpeJZbf\nIWvXRkmSWzdRqflXK33s5VKyvrzrAwAAQBfUkAJ9QI3H8GW07VDyyW+p4VtHqvq3X5W1a6OccQer\n7dzvqen/vqD0gutIRosQy4gKYhlRQBwDXCEFUKGMXe8qufwOJZ7/mYxsuyQpN2Wu/9MtMz/OT7cA\nAABUAGpIAVQUc+srSi67XfGXfi3DzUmSsoeeqtSC65Q7cP6IuVsuAADAcEENKYDIs9avVPKpWxV/\n9XFJkmeYyhx1nlILrpMzaVaZVwcAAID+oIYU6ANqPMrEdRV75THV/fCvVH/nxxR/9XF5dlKp4xap\n+f/8SW0X3EUyuoeIZUQFsYwoII4BrpACGI5yGcVf/JWSy2+X9f7rkiS3apTSxy9S+vjPyavdp8wL\nBAAAwGCghhTA8JFuUeK5xUqu+E+ZzVskSW7DZKXmX6P0MZdIidoyLxAAAACdUUMKoKIZLe8r8cx/\nKbHyRzJTTZIkZ8J0pRZcp8xR50lWrMwrBAAAwFCghhToA2o8hoa57S1V/+ZGNXz7KFX98d9lppqU\nnXacWi+9T83XrVBm7gUko4OMWEZUEMuIAuIY4AopgDKwNr2o5FO3Kvbyb2V4riQpM/NjSi34spz9\n55V5dQAAANhbqCEFsHd4nuw3/qDkstsUe3OZ32TFlJn9KaUWfFnu+MPKvEAAAAD0BzWkAIYvJ6dY\n48NKLrtN9pZGSZKXqFX62MuVOvFqeQ2TyrxAAAAAlAs1pEAfUOPRD5l2JZ65S/XfPVq1D3xO9pZG\nubXj1X76P6jpK43q+Ng/k4yWAbGMqCCWEQXEMcAVUgCDzGjbocSzdynx7F0y23dIkpyxBym14Fpl\n5lwgxZJlXiEAAACGC2pIAQwKc+cGJZb/QInV98rItkuSclPmKnXydcrO/LhkWmVeIQAAAIYCNaQA\nysba8rIST92meONDMlxHkpQ99FSlTr5euQNOlAyjzCsEAADAcEUNKdAH1Hh04nmy31ym2nvOV/1t\nC5R46UFJUnr2p9R83XK1XvEr5Q6cTzI6DBHLiApiGVFAHANcIQWwJ1xHsbW/VfKp22VvekGS5MWq\nlT7ms0rPv1bu6KllXiAAAAAqCTWkAHqX7VD8T/cpufwOWTveliS5NWOVPv7zSh93lbyaMWVeIAAA\nAMqFGlIAQ8Jo36nEs3f7d8xt2yZJcsZMU+qkLykz9wIpXl3mFQIAAKCSUUMK9MFIq/Ewd25U1W+/\npoZbZqnqyZtltm1TbvJstV50j5pvfF6Z464kGa1QIy2WEV3EMqKAOAa4QgqgiLXlZSWW3a74n/+7\ncMfcQz7s3zH3wJO4SREAAAAGFTWkwEgX3DE3uew2xd74g99kWsocea7SC74sZ98jyrxAAAAADGfU\nkALYc05OsbWP+HfM3fySpPwdcy9Rev413DEXAAAAQ44aUqAPIlXjkWlX4tm7Vf/dY1R73yLZm1+S\nWzNOHaf9vZq+2qiOs24mGY2wSMUyRjRiGVFAHANcIQVGDKN1mxIr71bi2btltu+QJDljDwzumPsZ\nKVZV5hUCAABgpKGGFIg4c/vbSqz4gRKrfy4jl5Ik5abMVerk65Sd+XHJtMq8QgAAAFQyakgBdGFt\nXKPk8tsVe/m3MjxXkpSZfrrSC76s3LTjuWMuAAAAyo4aUqAPKqbGw/Nkv/q/qr3rbNX/4KOKNz4s\nmZbSH7pITTc8o7bL7lPugBNIRkewiolloBfEMqKAOAa4QgpEQy6j+EsPKrn8+7Lee1WS5CXqlJ53\nhVInfF5ew6QyLxAAAADoihpSoJKlmpVY9RMln7lTZvMWSZJbv69SJ16t9LGXScn6Mi8QAAAAUUcN\nKTDCGE2blHz6h0o8t1hGulWS5EyYodSCLytz5LmSHS/zCgEAAIDeUUMK9MFwqfGwtqxV9S+/qIZv\nz1Fy+R0y0q3KHniSWi5/QM3Xr1Bm7gUko+jRcIllYKCIZUQBcQxwhRQY/jxP9ptPKbns+4q98Xu/\nyTCVOfKTSi34spzJs8u8QAAAAKB/qCEFhisnq/iff6PE8u/L3tIoSfJi1Uof/Vml539R7pj9y7xA\nAAAAgBpSIFrSLUo8/zMlnv6hrF3vSpLc2vFKn/A5peddKa96dJkXCAAAAAwOakiBPtgbNR5G02ZV\nLfknNdwyS9X/8/9k7XpXzj6HqO3c76np/76o1IdvJBnFgFGvhKgglhEFxDEwwCukGzdu1KWXXqr3\n339fhmHo85//vK677rrBWhswIphbX1Fy+R2Kv/SgDCcrScoecILSJ31J2cNOk0z+bgQAAIBoGlAN\n6datW7V161bNnj1bra2t+tCHPqTf/OY3mjFjRtiHGlKgG54n+81lSi67veRGRdkjzlJq/rVy9ju6\nzAsEAAAA+qZsNaQTJ07UxIkTJUm1tbWaMWOGNm/eXJKQAijS442KrpY7Zlp51wcAAADsRYP2XcD1\n69frhRde0Lx58wZrSmDYGHCNR6pZieXfV8N35qrml1+QvaVRbu14dZz292r6aqM6zr6FZBR7BfVK\niApiGVFAHAODdJfd1tZWnX/++br11ltVW1vb5fg111yj/fbbT5LU0NCgWbNmaf78+ZIK/yGyz/5w\n3s/b0/FPL3lI8Zd/q4WtS2WkW/THzZIzaoqO++zfKjP7U1qxarW0Zm3ZXx/7I2e/sbFxWK2Hffb7\nu9/Y2Dis1sM++/3Zzxsu62Gf/b7uNzY2qqmpSZK0YcMGLVq0SP014N8hzWazOvPMM3XGGWfohhtu\n6HKcGlKMRNaml5RYfofijQ/JcB1JUvbA+UrPv1bZwxZyoyIAAABERtlqSD3P01VXXaWZM2d2m4wC\nI4rryn59qZLLv6/YW8slSZ5pKXPUeUqddK2cybPLvEAAAABgeBnQZZqnn35a9957r/7whz9ozpw5\nmjNnjpYsWTJYawOGjc5frSmRTSn+/E9Vf+sJqlv8GcXeWi4vUavU/GvU9LcvqO2Cu0hGMWz0GMtA\nBSGWEQXEMTDAK6Tz58+X67qDtRagohit25RYdY8SK38ks/UDSZJbv69SJ16t9LGXScn6Mq8QAAAA\nGN4GXEPaG2pIETXmB28oueI/FV9zv4xcSpKUm3Sk0vOvUebIT0pWrMwrBAAAAPaestWQAiOG58l+\n+2n/RkWvPh42Zw47TemTrlXuwPmSYZRxgQAAAEDl4VafQE+crGIvPqg1Nx6rurvOVvzVx+XZSaWP\nvUxNf71SbZffr9xBJ5GMomJQr4SoIJYRBcQxwBVSoFtGxy7Fn/upks/cKbN5i6ztknvIOKWPu0rp\n466SVzuu3EsEAAAAKh4JKVDE3P62Ek/fqcSffi4j0yZJcsYfqmM++UU1zfm0FKsq8wqBgcn/qDVQ\n6YhlRAFxDJCQApLnyXpnlZIrfqDYK/8jI7jPV/bgU5Saf41yh3xEMvl2OwAAADDY+JSNkcvJKvbi\nr1X3g4Wqv/Njiq99VDJjSn/oIjVdv0KtV/23cod9VDJNajwQGcQyooJYRhQQxwBXSDEC+fWhi5V8\n9i6ZTZslSW71GKXnXaH08Yvk1U0o8woBAACAkYHfIcWIYW57M6gP/YWMbLskydnnEKVO/KIycz4t\nxavLvEIAAACg8vA7pMDueJ7st1Yo8fR/Kvbq453qQ7+o3CGnUh8KAAAAlAmfxBFNubTia+5X3e2n\nqO7ucxRft0Sy4koffXFRfejCPiej1HggKohlRAWxjCggjgGukCJijNYPlFj1YyVW3iOz9X1Jklu7\nj9LzrlT6uCvl1e5T5hUCAAAAyKOGFJFgbVmrxNP/qfhLv5aRS0uSchNnKn3i1cocdb4US5Z5hQAA\nAEA0UUOKkcl1FXvtCSWe/qFiby6TJHmGocyMv1L6xKuVO/AkyTDKvEgAAAAAu0MNKSpPukWJZ/5L\n9f9+rGp/epFiby6TF69R6vjPq/lvnlPbpb9Q7qAFg5qMUuOBqCCWERXEMqKAOAa4QooKYu5Yr8Qz\n/6XE6p/LSLdIkpxRU5U+4XPKHH2JvKqGMq8QAAAAwJ6ghhTDW/5nW565U7F1vyv8bMu045Q+4QvK\nzvy4ZPF3FQAAAKBcqCFF9GRTir/0oBJP3yl761pJkmfFlT7yXKVP/IKcyUeVeYEAAAAABooaUgwr\nRtNmJZ/4phq+NUs1v75O9ta1cmvHq+PUr6jpK39W+6d/UJZklBoPRAWxjKgglhEFxDHAFVIMB54n\n651VSj57l2IvPyLDdSRJuUlHKX3iF5Q58pOSnSjzIgEAAAAMNmpIUT7ZlOJ/fkiJZ/5L9uaXJEme\naSl7+FlKnfB5OfvP42dbAAAAgGGOGlJUFKNpsxKrfqzEc4tltm2TJLnVY5Q+9nKlj7tCXsPkMq8Q\nAAAAwN5ADSn2Ds+TtX6lan5xpRq+PVtVf/iuzLZtyu07S23n3a6mrzYqdfr/G7bJKDUeiApiGVFB\nLCMKiGOAK6QYapl2xV/6tRLP3i17S6Mk/2u5mSPOVvqELyg37Ti+lgsAAACMUNSQYkiYO95RYtU9\nij9/r8yOnZIkt2ac0sdepvS8y4ftlVAAAAAAe4YaUgwPnif7L39U4tm7FXt1iYzgbx25KXOVPv5z\nyhz5Ce6WCwAAACBEDSkGLtWsxNM/VP2/z1PdPecpvu53khlTevan1XzN/6rl2ieVmfuZik5GqfFA\nVBDLiApiGVFAHANcIcUAWFvWKrHybsVf+JWMbLskyW2Y5N8t95hL5dWNL/MKAQAAAAxn1JBiz+Qy\niq39rRIrf6TY+pVhc/agBUofd5WyM86QLP7OAQAAAIwU1JBiyBlNm5R47qdKPP9TmS3vSZK8RK3S\ncy9U+rgr5Y4/rMwrBAAAAFBpqCHF7rmu7Nd/r5qfXeL/dujvvyOz5T05E6ar7Zx/066vrVXH2d8a\nEckoNR6ICmIZUUEsIwqIY4ArpOiG0bZD8T/9XInnFsva/pYkyTNtZWZ9QunjrlTugBP57VAAAAAA\nA0YNKXyeJ2vjaiVW/ljxxodk5NKSJGfUFGWOvUzpoz8rr25CmRcJAAAAYLihhhT9l25R/MUHlVj1\nE9lbGiVJnmEoe+hHlT7uSmUPWyiZVpkXCQAAACCKqCEdoaxNL6r6v2/QqJtmquY3N8re0ii3ZqxS\nC65T8//5k1qv+KWyM/6KZDRAjQeiglhGVBDLiALiGOAK6ciSblX8z//tXw3d9GLYnD3gRKWPvVzZ\nI86U7EQZFwgAAABgJKGGdASwtrys+KqfKPHiL2WkWyVJbtUoZeZeoPSxl42Iu+QCAAAAGBrUkKKr\nVLN/NfS5n8ne9ELYnNt/ntLHXq7MrLOlWFUZFwgAAABgpKOGNEo8T9aG51X96y9r1M2Hq+ahv5G9\n6QW5yQaljv+cmq5foZarf6fM3M+QjO4hajwQFcQyooJYRhQQxwBXSCPBaN+p+AsPKPH8z2S9ty5s\nzx5wgjLHXKrMEWeRgAIAAAAYdqghrVSuK/utZUqs/rliax8NfzfUrRnn14Yec4ncfQ4p8yIBAAAA\nRB01pCOIuXOD4n/6heJ/uk/Wro2Sgt8NPeTDSh9zqbIzzpDseJlXCQAAAAC9IyGtBNkOxdb+j381\n9M2nwmZn1FRlPnSRMh+6UO7o/cq4wOhbsWKF5s+fX+5lAANGLCMqiGVEAXEMkJAOX54n690X/Kuh\nLz0oM9XsN9sJZQ4/S5mjL1buwJMkk/tSAQAAAKhM1JAOM0bTZsVf/JUSa+6T9f7rYXtu8hylj75Y\n2aPOlVc1qowrBAAAAIACakgrXaZd8bX/o/ia+2S/+ZSM4G8Ebs04ZY46T5mjL5az7xFlXiQAAAAA\nDC4S0nJxXdnvrFR8zX2KNz4sI90qSfKsuDIzTldm7oXKHnqqZMXKvFBI1HggOohlRAWxjCggjgES\n0r3OfG+d4i8+qPiLD4Z3yZWk3NQPKT33QmWP/KS86tFlXCEAAAAA7B3UkO4FRtMmxV/6teIvPih7\ny8thu9swSek5n1Fmzmfkjj+0jCsEAAAAgP6hhnQYMjp2KfbyI34S+vbThbrQZIOys85RZvanlJt2\nPHfJBQAAGID8tRXP84Lt/L467Xvyu3bu7zd53bV3mjfs3u28/km97trllayz69z5PkXzd5pL4VJ3\nP1dpW+f3ofP68v+ndM7i83T3fnR97/I9C+suHa9u2oqO7e796WYdhXnUqa/XZe5wfB9fY7evpWiR\nJa+nm/bCGruet9fXVTJfH87f3b+7un/dg7GGyZOnasGCj2qokJAOpnSLYuseV7zxN4q99qQMJyMp\n+KmW6acrM/tTyh72UclOlHmh2FPUeCAqiOWe5T9klT7c4AOdu5vjA+nbt/nkeXI9N/zQ7LpuYb2u\nK0+FD2tu0QfZ3c3bpZ8bHFPXfp4UnMML1xJ+sAs+6Bavrft1dHoNnedQ19fh5T8Ydl5/MO4vb7yl\ngw4+oKh/8OGqqF/xuYr77H6Meh/fzXyDMT7899zdHP6bGPRTuO91sw7le/YwT+Hz5x7Mkx+kvs1V\n2O46V6G/Os3tlby+wnF12i+spZLt2tWqUaNqy70MoEfHHHMCCemwlmlX7LUnFP/zQ4q9+r8ycilJ\nkmcYyh50sjKzz1fmiLOkZH2ZFwqgrzzP/8Dvuq48L3h2PTmuE7R5cl0naCvq47lyHVeu55bMkT/m\nuUFb/rjjyA2SDr+fV9SvcMxz/Q/y/jrcLu0lx4MExc0nKl7p2Fdfe0Mb3nktbA/n2M244nN4Xtfj\n8rxw3eExqcsc+eSqeHz+Ea47/7702Kcwj7rtW0gIXdf/QOt2M5ff7nV6dssad9gzu3a16uWX+SCP\nUoZhyDAMSUawr077hgxDnfaNkvHhs2HI6GbefPfu51XQxyiZr8u58nMbOzRh/FjlBxvdzF+Yazfr\nNvxxJecL5yuaq4dzdPcaur4f4avrZk51em3Fa+7c1vVYYV2F19TlXMXvW7ev1eh2zi7n3M2x4nP2\n+D52O78Kiv5tunsfejt3n87TOW7VaZ5O4/bsXF1f66RJUzSUSEj7I5tS7PUn/SR03eMysu3hodz+\n85Q58pPKHHGWvPp9y7hIDKZKvaLkuq4cx5HrOnKcwsN1HDlBm98nF/ZzHbfTsXx/10+gXH9s5375\nOd2wn1ty/sJ2Pvlyetl3w3GlY4PnICl0ne7755M8J3/McYqSxKI5nNIkM78dZS+sWVHuJQx7pmlK\nMmSaRslz/kOgYRgyTFNGN33zx82gJKO4r/9sBB+SzaL5zfBDZdjXMGQYZtg3/2Exv91T//yHP//c\nwbZZ1Jb/MGN0c6xoW4ZkGmb4IbBkTHAes7tzdp7fKLx2BQlCr+cIP7AbwfGu4wrbwTnUdWx+TLfj\nw2ODMb6HMWFi0fM5JZXOUZQMhOOCTj2uPfwM2sM8RqcPrSVjS8cVj81/XO3uteT7Fcb3Npe6eZ/y\nY9TpfIX5usxRNDeAykNC2lfpVj8JfflRxV57IvyZFsm/Q66fhJ4tb9TQ/gUBQyOfjORyuaJHNtx2\nnPy+429ns8o5wXbQ18k5yjm5sM1xHDm5XNDmbztO0KfztuuE4918e5AI5tv8/k7RdqHdCdYSJpxB\nchf1xGoo5RMK07SKtguPfDJhmlawn982wuOG6X+Q7m5MPkkxgw/ppmnKtMzgw33hmBkmGYU1GMXt\nwTmKz9Vde5c582vu1De/lt0eL1pLPpHpfKw4IcsnSMV9zKKEw1+PGSYlYZ+i5K5rn85JWmFMmFwV\nHcsnhvl/p+4TvU6JFAAA2CtISHtgtG1XbN0SxdY+qthf/igjlw6P5SbPVubITyg76xNyR+9XxlVW\nFs/zlM1mlMlklMtllc1mlclklM3mH9ngkQmfc7lcuJ8rOu63Z8N5Sp5zWeWyuZK20iQzWzTe3+9J\nJdd42LYt07RkWYVHPonq0mZZsoqOhc9hHzM4XjwuSHIsS1bwbHaaI9+/OKErXkdPbd3NlU+qTKv7\nvuHDCJK8onbDMDuN6Zww5rejmZRQQ4qoIJYRBcQxQELahbHrXcVfeUyxtf8T3B03uHGEYfhfxz38\n48oefqbcMdPKu9BB4Hmecrms0um00ulU+JzJpJVJp5XOP6dTymQy/n7Qlslk/O3wOR3u5xPO/HMm\nk1Emm1E2aBuuTNOSbVuy7Zgsy5Zt27JjMdmWpVhslyZP2Ve2ZfnHgnbLtmUHffPb/li/n2XbsizL\nb9/tdtA32Dcty5/PtMJ+pQ9bpmn6fSy7JKG0g/7FSRwAAAAwXJGQuo6sjX9S7LX/VezVJ2RvaQwP\neVZM2QNPUebwM5WdeYa8ugllWaLjOEqlOpRKdaijo12pjg51FO+nOpRKpZROpRUzSEAAAB+MSURB\nVMJ+qXRKqY4OpdN+W3HCmU6nlUp1KJNJl+UmHrZtKx5PKBaLybZjisfjisXyj1jRw2+zbTvct4uP\n2bFwDv/ZLmzHYorZMVnBWNsuHLdtWzE7JjtmK2bHSxJCIOr4SzyiglhGFBDHwAhNSI2OJtlvLFVs\n3ROKvbFUZtv28JgXq1b2sFOVnXmmstNPk1fV0O/zOE5ObW1tam9vU3t7a2G7rVVt7fn2NqU62tXe\n3q72jjZ1dHSoo71NHUFbR0e7Mpl07yfrJ9uOKZFIKJFIKpFIKB73t+PxePCcUDxR2E7EE34CGY+H\n+/nteHAs/4jF4kHiGS9KOmNhPRcAAACAkW1kJKSuK2vry7Lf+KNirz0h+51VMlwnPOyM3l/Z6acr\nO32hcgecKMWSRUNdtbe3qaWlSS3NzWpuaVZLS5PaWlvU2taq1tYWtbW2qC3Ybm1rUVtrq9raWpVK\ndQzK8g3DUDJZpaqqaiWTVUpW+dtVySp/P1mlZDKpRDJZ2E8E+wm/fyHpTPp9gwTTtkdGCAwUNR6I\nCmIZUUEsIwqIYyCqCannydyxXvZfnlLszadkv7lcZvsOSVLWM/SBm9C28cdq+/jZ2j7qUDV5VWra\ntUu7Hl+t5qYn1dLSHDya1Nra0u+vtZqmqaqqalXX1KqmukY1NbWqrq5RdU2NaqprVVVdrZrqWiWr\nqvz2qhpVVVWpqrpG1dXBdlW1EolkZG+wAgAAAGDkMrwh/l2IpUuXau7cuUN5Cnmep7atb6m5cama\nX3tWTe80amdTs7bnYtqRs7U9Z2uHV6UdTkytmT1PLqura1RXVx88GlRbV6e62nrV1NSqprZOtbW1\nqq2pC7b9R01NraqqqkkkAQAAAETamjVrdOqpp/Zr7LC/Qup5nlpamrVt2/vavv0D//mD97V901+0\nfcs72r5jh7a1pZV2ixO/muDRmSvTtNTQ0KD6+lFqaBithoYGNTSMVn3DKDU0jFJD/SjV1TeECWht\nbb1isdheerUAAAAAMHLslYR0w86UYrahuGkqZhmK26ZipiHL9JPIVKpD7723peTxftF277WYhmpM\nR2Or4xo1aoxGTZyqUfseqNFjxmnU6DEaM3qsRo8Zq1Gjxqi2to6b6mCPUeOBqCCWERXEMqKAOAYG\nISFdsmSJbrjhBjmOo0WLFukrX/lKlz6Lfr2u+8GeK8PJynOz/k2G3Jzk1klulYzEftKUnDTJkeVm\nlVRWCeVUpYyqjayqbcOvyWwYq5qxk5QYM9H/TUfTkB0ku4ZpqNWQUqah91KG7PcdWduaZJmGLMOQ\nZUqWUehf3G4au9svbJuGP94M2vl6LgAAAAD03YBqSB3H0WGHHaYnn3xSkydP1jHHHKP77rtPM2bM\nCPssXbpUX39mp3Ku5Jm2ZNqSZUtWfFBewHBiSDINBQlqkLCahsxgu/g5n+QaUklCW9zPkCEzSJqN\nYN8yg/bifuG4wrZhBHPKH1tyTPk+RWswJBmGTBW158eotG++PT/OKGo3g6TcP09wLNwurCc8Fp5b\nMuUfyK8xnCfI8/NzG/nt/Dydz1O0L+3u3PljRf06rSu/r6JxhXN2M06la1LRfPl1dD5P8frCOMqf\nv2iO4nbtZh4AAACgHMpWQ/rcc8/p4IMP1rRp0yRJF1xwgR5++OGShFSSYv/7z4pLGp+UpsY6tF+s\nTVPjaU1KOJqYlOpsyTFjyhgxZWonKjXuMKXHHaLUmIOUHn2g0rX7yjFsZV1XOcdTzu30cDxlXU9O\n8Mi5nnJe6X747Clsd8I+kuMV+rleoZ/rBceL2nPBtut6cj1/rOtJnuSPczxlNaT3igK61SW5VVEi\nW5ygBxv5FNcoSnxVNIdRtGOoNKnufI7uxhpFnYrPtbs1F/p3SuI7rb/kuehgl3l2s97dnaPL2rrM\n1/3rLJ2367mMTgd39z52t2N011z0B5Ue5+ntPLvt0/V1lvC8buOlpzlL2kv6dPfuFu10Ole3fTs1\n7G5tffnTzW7X08O5e3vPd3uuPo0xeunT9f0xSo52P29P71+3Tbv5d+h94r69X50bez2X1/WPcV3H\n9O3/D3f936S+vGGduX2Mi54n8vpyql51XYu/nt5iqX96n8fr/j0t7TJI5xqM909+vA/SuQb8Pvfx\nutFee2/6eK4+zdNrj76+9t7ia/A+k/ct3gdoEP/N+zRPH1a8T3215h18wOCcsBsDSkg3bdqkqVOn\nhvtTpkzRqlWruvT74svFd7ZNSEooI2l98CiVkdQYPALd/LtYwSPRj3UPWE+B4kn5/8QGGv7enkzS\nx3677bY38+cBnGtPhxrdDOjP6dc5bZphdXejrOJzdZ15qN7Wwfp/KoNiaG/UXWJvvu7u/j2j4BW3\nTTPNnmMZqATEMqKAOEYleH3ODM373Y+GbP4BJaR9/argD3Zt1D6Gf6faapmaZibD//hecdskif1u\n9o0hmH/dMHp9lbRvSrLkDJv1sM9+f/fXu6lhtZ6+7Of/GDRc1jPTqvX3nfx+zcjYd9uH1XrWexl5\nhjls1rPWGUbvj1H+96Pf+3bw31eudUTsy7Tk2naP/T3D0Lpgf0ZwfNjvO4M1X93weD17/f1rG1br\n2eTsLLkB14oVK9TY2KimpiZJ0oYNG7Ro0SL114BqSFeuXKlvfOMbWrJkiSTp5ptvlmmaJTc2Wrp0\nqQ47aFy/F1hYqdWHPr0nyKbRlzvsDs5deI0+zNOXy+SDdk2+h3N5/vefehnfly8TdXeVsFOb54X1\noMX9S3v1NI8XTON109fr2tfoPKbTPJ3PUjJv8Xxe6bxep3158oxgjFcYU7p+r+gcXklbfs7C6l1/\nq5u+Xv6Yivt7Ra/P71Noc4MZ3OB9cAvzywv2uxtTWIN/LL9fPNaRZ6horFt6Ps+TJyc85gXz5ucM\n5/WcYE5XbjiHWzSfv+0ZwbOcYFzxnH67F8wXri9s89foBm2l/YPtfP/8uYraym5YXRovMGTKMGIy\nZcswbJmGLdOIyZD/bBpBu2Kdjtn+uKCPqViwH4xTLJivqI8RD84TK2qPhe2mES+MN+IyDFuWEZep\nom3DP09+2zTiMmRTjw0AQD+VrYb06KOP1htvvKH169dr0qRJeuCBB3Tfffd16VfTsN9ATgMAw0LX\npNVPZt2SfafQr0tbrqivK8/LlfQrHPPbS/dz8jxXbn6Ml5Mbzp/z24P+JX2Csa7nyPOyRfPmx2SD\neQp9/bVkC3N5ObnKhX1cZYv65IKEPi1X6b379f9B5ifMhSS187OfwMZ30xYLj5X262k/UXLMMhLd\nHzcTQXJOwgwAiJ4BJaS2bev73/++Tj/9dDmOo6uuuqrLDY2AKOB3wiBJhmH633wIShAq0YoVK7Rg\nEGPZC66A+8lqtihxzRYlw91se1m5yoaJcn6sfzxTNEehPezXqW84n5cJ2v02/zlb6Kdu2oJ+nnLB\nerLDNqkuJLDFzwn/2Szs5xPb4n3LTBT1j8syksGYpKxg358nGYxJFvXz9/PnGi6JMf+7jCggjoFB\n+B3SM844Q2ecccZgrAUAUGH8uzjbkmHLUrLcy+k3/+pzPknOhImrU7TtdtnOyvHSJfuulylqS3fq\nk5YTtmeK5k4H28X9M3LcdDifn8yn5XppSS1lfa8KiW5VkKwmwoTWNquC48mi5LaqKKkN2syqoudk\np21/rG0kS9qMPpXcAAAqzYBqSPti6dKlmjt37lCeAgCASPM8t5ColjwXktf8vuOlOyW1xW3Bdkl7\nKugbPHupsL/flg7bXC9Ttvcgn+jaJYlrlWyjKkh+q4L9wrbfv7po3O7aq/3noI/Zl/tWAABCZash\nBQAAQ88wTNlGlaSqsq6jkBgHSapbSFYdt6Mo8U0p56b8Zy8l102FyW/O7QjGdyjnpoLxKTn5bbcj\nbCv0TYVXiLNu05C/zkLyWy3LqJJtVgXb1WFiW0hki9tqggS5eNs/bhs1QXu1bKOaK74AECAhBfqA\nGg9EBbGMgShXYpxPhIsT1qdXPKOjj58eJLIdyoWJbNG221GU+LbLcVPKeR1F7d09t++V5LeQ8OaT\nWj9RtYLtmFkjy6gpOWab+f2aorbaoj41ssxqrvBWEP43GSAhBQAAw1w+EbZVJVmjJUm18c0aV3X0\noJ/L8zy5XjpIXNuVc9uDq7XtYdKa89qDY/lEti1MdHNuu3JeMK6kb1G7FyTMTkrSjkF/DX6yWxNc\npc0nsLVhMhsza2QbNWGfmFlb6J9vM0rb/Dre4XFDKwDRQg0pAADAXuRf8Q2S15IENr/d1ulYW5DI\nthfa3dZOfYNnr21I1mzI6pTA1pYkszGzNkhya8Pjhefu2mv42jIQIdSQAgAAVAj/iq+f3A22fLKb\nddvkuO3Kum3KeW1BwtpWSGbdtm6OBW1ua/DwE9ys2yrXyyjrNivrNqtjkNbaffJa1+N2zKor2vcf\ntlnL15SBCkZCCvQBNR6ICmIZUUEsd2+okl3HywQJrp+sFhLXtqCtTVm3pWi/tWQ7Gzzy2/7VXn9/\nMFhGtZ+gWnWF5NWsk51PXK26kiQ2fFj1JfuWmRiU9fQVcQyQkAIAAKAXlhGXZcUVt0YNynyu5wRX\nZVu6JKt+YtupzWkJ+rZ06tMSJriO066U896A1mUaiaIEtV4xq05xs1626T8XEtj6IMmtVzxMbPOP\nWr6ODOwBakgBAABQsTzPVc5rD5LWfJJa9HBawgQ24zaHbfkEN+M2K+e2KOM0y1NuEFZkBFdo/QQ2\nnk9UrYai7XrFzYaS43GrIXy2jGpuIoWKQg0pAAAARiTDMBUz/DrUgcjfYbmQtAbPbnO4XZy85mtq\n833z44qTYuU29e81yVbcqlfMLCSp8TCpbShKaP19P5ltCPvZZh0JLSoGCSnQB9R4ICqIZUQFsYzB\nZhiGLCOpKjOpKo3v9zz+15FblXGawqS1OIEtbv/Tyr9o+ocSYVu+n+N1KO3sUNrp388CGTLDBNV/\nHqV4kMTGrVGFtnwfq0Fxc1SQ0I7a67W0GNlISAEAAIBBYhqWn9hZDb32zYxboflTu/5hxfEywVXX\nXcHVWT+RzbhNyjpN/tVYp1kZt0kZZ5d/PL/tNCvntSnj7lTG3dmv12AZVUUJ66hge5RiVr0S1ugg\neR3VbR/LTPbrnBi5qCEFAAAAIsT1ssqECW2TMu6u4Cpsk9/u7CpKZv3nfMKbcXYNqJY2TGaDBDVh\njQ6uvI4O2kd3OjZaCWu0YmY9N4OqYNSQAgAAAJAkmUZMSXuskhq7x2M9z/OvsAZXW/1kNniE203h\ndtrZWZTU7pLjdagj16GO3JY9PLMRXHn1E9aENUpxa4wSRYlsPoH1j48JktwGmQYpTSXjXw/oA2qV\nEBXEMqKCWEYUDMc4NgyjcJOo2J6NLU5mC0nsznA7HSa0O4JkNp/k7gy+dhx8zTi7Z+eNmQ1Bsjqm\nkMhaY4KrsGPCZDaRb7fGKMaNn4YNElIAAAAAA1aczNbEpuzRWNfLBVdedyrj7FTaySeyO5XOJ7DB\nMb8tSGxd/6vIWbdJyq7v+1pllSSqfhKbT1rHBsfGFCW0Y5WwRss09jBLR6+oIQUAAABQkVzPUdZt\nChLYHWGimnaKE9sdwV2Lg213p3Jua7/OFzPrw0TVT1zHlOwnrDFK2GOL9kdGEksNKQAAAIARxzSs\nMCGUDurzOMdNK+PuLE1Uu2zvCK7O7lTa2R7e0TjrNqt1D67G+klscZI6Vgl7jJLWuE6J7Dg/yTUb\nRtQNnkhIgT4YjjUeQH8Qy4gKYhlRQByXj2UmVGVOVJU9sc9jPM9Vxm1S2tnuJ6u5HUHyul3pIGkt\nPG8PktkdRUns2306jyGr6KrrOCXs4NnKJ7FjlbDHFiW04yr6t2NJSAEAAACgF4ZhBnWmo/s8piSJ\nzW0rSlh3KO1sU9rZrlRuR0lb1m1WyvlAKecDSa/16Ty2WVtIVq2xStpjlbDG+W32uHA7GVyFtc3q\nfr4Lg48aUgAAAAAYJlwvG1yB9a+0ppxthQQ2tyPY3660s02poM+e/nasZVQHyWk+UR2rhLVPmMAW\nkld/2zKTPc5HDSkAAAAARIBpxFRlT1CVPaFP/T3PU9Zt8hPV3DalgmQ1ndseJq+pYD/tbFPK2SbH\na1dbdoPasht6nX9C9ck6db+HBvqydouEFOgDajwQFcQyooJYRhQQxxgMhmEobo1S3BolxQ/utb/n\necq5LWHimsptCxPVVO6D4GvEH4SJbLW975Cun4QUAAAAAEYIwzAUs+oVs+pVpwPKvRxqSAEAAAAA\n/TeQGtKR8wM3AAAAAIBhhYQU6IMVK1aUewnAoCCWERXEMqKAOAZISAEAAAAAZUINKQAAAACg36gh\nBQAAAABUHBJSoA+o8UBUEMuICmIZUUAcAySkAAAAAIAyoYYUAAAAANBv1JACAAAAACoOCSnQB9R4\nICqIZUQFsYwoII4BElIAAAAAQJlQQwoAAAAA6DdqSAEAAAAAFYeEFOgDajwQFcQyooJYRhQQxwAJ\nKQAAAACgTKghBQAAAAD0GzWkAAAAAICKQ0IK9AE1HogKYhlRQSwjCohjgIQUAAAAAFAm1JACAAAA\nAPqNGlIAAAAAQMUhIQX6gBoPRAWxjKgglhEFxDFAQgoAAAAAKBNqSAEAAAAA/UYNKQAAAACg4pCQ\nAn1AjQeiglhGVBDLiALiGCAhBQAAAACUCTWkAAAAAIB+o4YUAAAAAFBxSEiBPqDGA1FBLCMqiGVE\nAXEMkJACAAAAAMqEGlIAAAAAQL9RQwoAAAAAqDgkpEAfUOOBqCCWERXEMqKAOAZISAEAAAAAZUIN\nKQAAAACg36ghBQAAAABUnH4npH/7t3+rGTNm6KijjtK5556rpqamwVwXMKxQ44GoIJYRFcQyooA4\nBgaQkJ522mlau3atXnrpJR166KG6+eabB3NdwLDS2NhY7iUAg4JYRlQQy4gC4hgYQEK6cOFCmaY/\nfN68eXr33XcHbVHAcMM3ABAVxDKiglhGFBDHwCDVkN5zzz362Mc+NhhTAQAAAABGCLungwsXLtTW\nrVu7tN90000666yzJEnf/OY3FY/HddFFFw3NCoFhYMOGDeVeAjAoiGVEBbGMKCCOgQH+7MtPfvIT\n3XXXXVq6dKmSyWS3fR5++GHV1tb2e4EAAAAAgOGrtbVV55xzTr/G9jshXbJkiW688UY99dRTGjdu\nXL9ODgAAAAAYufqdkB5yyCHKZDIaM2aMJOn444/XD37wg0FdHAAAAAAgugb0lV0AAAAAAPprUO6y\n250lS5Zo+vTpOuSQQ/Stb31rqE4DDLqNGzfqwx/+sA4//HAdccQRuu222yRJO3bs0MKFC3XooYfq\ntNNO065du8q8UqB3juNozpw54Y3oiGNUol27dun888/XjBkzNHPmTK1atYpYRsW5+eabdfjhh2vW\nrFm66KKLlE6niWNUhCuvvFITJkzQrFmzwraeYvfmm2/WIYccounTp+uJJ57odf4hSUgdx9GXvvQl\nLVmyRK+88oruu+8+rVu3bihOBQy6WCym//iP/9DatWu1cuVK3XHHHVq3bp1uueUWLVy4UK+//rpO\nPfVU3XLLLeVeKtCrW2+9VTNnzpRhGJJEHKMiXX/99frYxz6mdevW6c9//rOmT59OLKOirF+/Xnfd\ndZfWrFmjxsZGOY6j+++/nzhGRbjiiiu0ZMmSkrbdxe4rr7yiBx54QK+88oqWLFmia665Rq7r9jj/\nkCSkzz33nA4++GBNmzZNsVhMF1xwgR5++OGhOBUw6CZOnKjZs2dLkmprazVjxgxt2rRJjzzyiC67\n7DJJ0mWXXabf/OY35Vwm0Kt3331Xjz32mBYtWqR8dQZxjErT1NSk5cuX68orr5Qk2bathoYGYhkV\npb6+XrFYTO3t7crlcmpvb9ekSZOIY1SEk046SaNHjy5p213sPvzww7rwwgsVi8U0bdo0HXzwwXru\nued6nH9IEtJNmzZp6tSp4f6UKVO0adOmoTgVMKTWr1+vF154QfPmzdN7772nCRMmSJImTJig9957\nr8yrA3r213/91/rOd74j0yz8Tz1xjErz9ttva5999tEVV1yhuXPn6nOf+5za2tqIZVSUMWPG6MYb\nb9R+++2nSZMmadSoUVq4cCFxjIq1u9jdvHmzpkyZEvbrSx44JAlp/qthQCVrbW3Veeedp1tvvVV1\ndXUlxwzDIM4xrD366KMaP3685syZo93du444RiXI5XJas2aNrrnmGq1Zs0Y1NTVdvtZILGO4e/PN\nN/W9731P69ev1+bNm9Xa2qp77723pA9xjErVW+z2FtdDkpBOnjxZGzduDPc3btxYkikDw102m9V5\n552nSy65RJ/4xCck+X/92bp1qyRpy5YtGj9+fDmXCPTomWee0SOPPKIDDjhAF154oX7/+9/rkksu\nIY5RcaZMmaIpU6bomGOOkSSdf/75WrNmjSZOnEgso2KsXr1aJ5xwgsaOHSvbtnXuuefq2WefJY5R\nsXb3eaJzHvjuu+9q8uTJPc41JAnp0UcfrTfeeEPr169XJpPRAw88oLPPPnsoTgUMOs/zdNVVV2nm\nzJm64YYbwvazzz5bixcvliQtXrw4TFSB4eimm27Sxo0b9fbbb+v+++/XRz7yEf3sZz8jjlFxJk6c\nqKlTp+r111+XJD355JM6/PDDddZZZxHLqBjTp0/XypUr1dHRIc/z9OSTT2rmzJnEMSrW7j5PnH32\n2br//vuVyWT09ttv64033tCxxx7b41xD9jukv/vd73TDDTfIcRxdddVV+trXvjYUpwEG3YoVK7Rg\nwQIdeeSR4VcMbr75Zh177LH69Kc/rQ0bNmjatGn65S9/qVGjRpV5tUDvnnrqKX33u9/VI488oh07\ndhDHqDgvvfSSFi1apEwmo4MOOkg//vGP5TgOsYyK8u1vf1uLFy+WaZqaO3eu7r77brW0tBDHGPYu\nvPBCPfXUU9q2bZsmTJigf/7nf9Y555yz29i96aabdM8998i2bd166606/fTTe5x/yBJSAAAAAAB6\nMiRf2QUAAAAAoDckpAAAAACAsiAhBQAAAACUBQkpAAAAAKAsSEgBAAAAAGVBQgoAAAAAKAsSUgDA\niFNXV6f169dLki6//HJ9/etfL++CAAAYoUhIAQCRNW3aNFVXV6uurk51dXWqr6/X1q1b1dLSomnT\npkmSDMOQYRiSpD/+8Y+aOnXqoK/jpptu0oEHHqi6ujpNnTpVF1xwQXjslFNO0Y9+9KNBPycAAJWA\nhBQAEFmGYejRRx9VS0uLWlpa1NzcrIkTJ3bp53neoJwvl8t1aVu8eLHuvfdeLV26VC0tLVq9erU+\n+tGPlqwRAICRioQUADDimKapt956K9w3DEPt7e0644wztHnz5pKrqZ7n6ZZbbtHBBx+scePG6TOf\n+Yx27twpSVq/fr1M09Q999yj/fffvyTRzFu9erVOP/10HXDAAZKkCRMmaNGiRZKkv//7v9fy5cv1\npS99SXV1dbruuuskSa+++qoWLlyosWPHavr06frVr34Vznf55Zfr6quv1mmnnab6+nqdcsop2rBh\nw5C9VwAADCUSUgBApPXl6qfneaqurtaSJUs0adKkkqupt912mx555BEtW7ZMW7Zs0ejRo3XttdeW\njF+2bJleffVVPf74413mPu644/TTn/5U//Zv/6bVq1fLcZzw2De/+U2ddNJJuuOOO9TS0qLbbrtN\nbW1tWrhwoT772c/qgw8+0P33369rrrlG69atC8f94he/0D/8wz9o27Ztmj17ti6++OIBvEMAAJQP\nCSkAILI8z9MnPvEJjR49WqNHj9a5557ba//O7rzzTv3rv/6rJk2apFgspn/8x3/Ugw8+KNd1wz7f\n+MY3VFVVpUQi0WX8xRdfrNtvv12PP/64TjnlFE2YMEHf/va3d3veRx99VAcccIAuu+wymaap2bNn\n69xzzy25SnrmmWdq/vz5isfj+uY3v6lnn31WmzZt6vP7AgDAcGGXewEAAAwVwzD08MMP6yMf+Ui/\n51i/fr0++clPyjQLf8O1bVvvvfdeuN/bjZAuuugiXXTRRXIcRw899JAuvvhizZkzRwsXLgzXmffO\nO+9o1apVGj16dNiWy+V06aWXhn2nTJkSHqupqdGYMWO0efNmTZ48ud+vEwCAcuAKKQBgxMsnhN3d\nYGi//fbTkiVLtHPnzvDR3t6ufffdt8v43liWpfPPP19HHnmkXn755W7H7rfffjr55JNLztfS0qI7\n7rhDkn81dePGjWH/1tZW7dixQ5MmTdqzFw0AwDBAQgoAGNE8zwu/MjthwgRt375dzc3N4fGrr75a\nf/d3fxfeOOiDDz7QI4880uf5Fy9erMcee0wtLS1yXVe/+93vtHbtWs2bNy8855tvvhn2P/PMM/X6\n66/r3nvvVTabVTab1fPPP69XX3017PPYY4/p6aefViaT0de//nUdf/zxXB0FAFQkElIAwIhTfFWy\n+HdIp0+frgsvvFAHHnigxowZo61bt+r666/X2WefHd7V9vjjj9dzzz3X7Vzdqa+v10033aT9999f\no0eP1le/+lX98Ic/1AknnCBJuv766/Xggw9qzJgxuuGGG1RbW6snnnhC999/vyZPnqx9991XX/va\n15TJZMLzXXTRRfqnf/onjR07Vi+88ILuvffewX6LAADYKwxvsH58DQAADLkrrrhCU6ZM0b/8y7+U\neykAAAwYV0gBAKgg/B0ZABAlJKQAAFSQ4q8YAwBQ6fjKLgAAAACgLLhCCgAAAAAoCxJSAAAAAEBZ\nkJACAAAAAMqChBQAAAAAUBYkpAAAAACAsiAhBQAAAACUxf8HOoQCsUzDpI0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1093c46d0>"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Covariance Matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(6, 6))\n",
      "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
      "plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
      "ylocs, ylabels = yticks()\n",
      "# set the locations of the yticks\n",
      "yticks(arange(7))\n",
      "# set the locations and labels of the yticks\n",
      "yticks(arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = xticks()\n",
      "# set the locations of the yticks\n",
      "xticks(arange(7))\n",
      "# set the locations and labels of the yticks\n",
      "xticks(arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
      "\n",
      "plt.xlim([-0.5,5.5])\n",
      "plt.ylim([5.5, -0.5])\n",
      "\n",
      "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
      "divider = make_axes_locatable(plt.gca())\n",
      "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
      "plt.colorbar(im, cax=cax)\n",
      "\n",
      "\n",
      "plt.tight_layout()\n",
      "plt.savefig('Kalman-Filter-CA-CovarianceMatrix.png', dpi=72, transparent=True, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mISEBgN69e5OSkkJsbCyjR48mNjaWoKAgUlJSjLGkpKQwceJETp48yR133MGQ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\niIjIttikiIjItv4GPd1jT0VDyZUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1093b0bd0>"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "State Vector"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "\n",
      "plt.subplot(311)\n",
      "plt.step(range(len(measurements[0])),ddxt, label='$\\ddot x$')\n",
      "plt.step(range(len(measurements[0])),ddyt, label='$\\ddot y$')\n",
      "\n",
      "plt.title('Estimate (Elements from State Vector $x$)')\n",
      "plt.legend(loc='best',prop={'size':22})\n",
      "plt.ylabel('Acceleration')\n",
      "plt.ylim([-1,1])\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.step(range(len(measurements[0])),dxt, label='$\\dot x$')\n",
      "plt.step(range(len(measurements[0])),dyt, label='$\\dot y$')\n",
      "\n",
      "plt.ylabel('')\n",
      "plt.legend(loc='best',prop={'size':22})\n",
      "plt.ylabel('Velocity')\n",
      "           \n",
      "plt.subplot(313)\n",
      "plt.step(range(len(measurements[0])),xt, label='$x$')\n",
      "plt.step(range(len(measurements[0])),yt, label='$y$')\n",
      "\n",
      "plt.xlabel('Filter Step')\n",
      "plt.ylabel('')\n",
      "plt.legend(loc='best',prop={'size':22})\n",
      "plt.ylabel('Position')\n",
      "plt.savefig('Kalman-Filter-CA-StateEstimated.png', dpi=72, transparent=True, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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u77eF2e8RX/qN4vHvPrgfn8mmNQ+eoyj5R0HnDSkpKS4f7OrgmS+1dvsoSdLg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\ny6XOnTurZ8+e2rNnT7jDsQ3uzsIpyGU4AXkMpyCXAYsWwEOGDFGPHj2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XqmlrYZfLpV69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\njBIWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b023f50>"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Position x/y"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,16))\n",
      "plt.scatter(xt[0],yt[0], s=100, label='Start', c='g')\n",
      "plt.scatter(xt[-1],yt[-1], s=100, label='Goal', c='r')\n",
      "plt.plot(xt,yt, label='State',alpha=0.5)\n",
      "\n",
      "plt.xlabel('X')\n",
      "plt.ylabel('Y')\n",
      "plt.title('Position')\n",
      "plt.legend(loc='best')\n",
      "plt.xlim([-20, 20])\n",
      "plt.ylim([-20, 20])\n",
      "plt.savefig('Kalman-Filter-CA-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nLrIzG/mZjfzM1ZjHC3mm0b322ms1b9487d69W9nZ2frv//5vvf/++1qxYoUs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\n1kMeYmpdAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a8c0cd0>"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Conclusion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dist=np.cumsum(np.sqrt(np.diff(xt)**2 + np.diff(yt)**2))\n",
      "print('Your drifted %d units from origin.' % dist[-1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Your drifted 62 units from origin.\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As you can see, bad idea just to measure the acceleration and try to get the position. The errors integrating up, so your position estimation is drifting."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}