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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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     "source": [
      "One Dimensional Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
      "import book_format\n",
      "from book_format import *\n",
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    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "One Dimensional Kalman Filters"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking A Dog"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
      "\n",
      "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n",
      "\n",
      "Implementing and/or robustly modeling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. We will talk about this in great detail later, but we need to model two kinds of noise. The *process noise* is the noise in the physical process. Something moving at a notionally 'constant' velocity will never maintain a perfectly constant velocity. Undulations on the ground, wind, and a host of other factors mean that there will always be slight variations in the velocity. The second noise we want to model is the noise in the measurement as no measurement is perfect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function, division\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy.random as random\n",
      "import math\n",
      "\n",
      "class DogSensor(object):\n",
      "    \n",
      "    def __init__(self, x0=0, velocity=1, \n",
      "                 measurement_variance=0.0, process_variance=0.0):\n",
      "        \"\"\" x0 - initial position\n",
      "            velocity - (+=right, -=left)\n",
      "            measurement_variance - variance in measurement\n",
      "            process_variance - variance in process (m/s)^2\n",
      "        \"\"\"\n",
      "        self.x = x0\n",
      "        self.velocity = velocity\n",
      "        self.noise = math.sqrt(measurement_variance)\n",
      "        self.pnoise = math.sqrt(process_variance)\n",
      "        self.constant_vel = velocity\n",
      "\n",
      "    def sense_position(self):\n",
      "        pnoise = abs(random.rand() * self.pnoise)\n",
      "        if self.velocity > self.constant_vel:\n",
      "            pnoise = -pnoise\n",
      "        self.velocity += pnoise\n",
      "        self.x = self.x + self.velocity\n",
      "        return self.x + random.randn() * self.noise"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `sense_position()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense_position()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. and a standard deviation of 1.0. *Variance* is defined as the standard deviation squared, so in `__init()__` we take the square root of the variances to get the standard deviation. Therefore the expression `self.x + random.randn() * self.noise` computes a simulated measurement with the variance that we desire. \n",
      "\n",
      "Let's look at some example output for that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(20):\n",
      "    print('{: 5.4f}'.format(random.randn()), end='\\t')\n",
      "    if (i+1) % 5 == 0:\n",
      "        print ('')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1.4246\t-0.1778\t 0.6594\t-1.6780\t 0.2510\t\n",
        "-0.1169\t 1.3496\t-1.8051\t-0.9663\t-0.3046\t\n",
        " 0.0541\t 1.0872\t 0.6392\t-0.2048\t 0.2456\t\n",
        " 0.1668\t 0.5042\t-0.8189\t 0.3422\t-2.3804\t\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n",
      "\n",
      "Okay, so lets look at the output of the `DogSensor` class. We will start by setting the variance to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal, so the results should be a straight line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.pylab as pylab\n",
      "import book_plots as bp\n",
      "\n",
      "dog = DogSensor(measurement_variance=0.0)\n",
      "xs = []\n",
      "for i in range(10):\n",
      "    x = dog.sense_position()\n",
      "    xs.append(x)\n",
      "    print(\"%.4f\" % x, end=' '),\n",
      "bp.plot_track(xs, label='dog position')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
       ]
      },
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1WbZsGc8//3zWuEGDBrFo0SImTZrExYsXue++++jXrx+vvfbaDc/557IzZMgQtm/fzoIF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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc3e2eb8>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that `sense()` returns the dog's position *after* updating his position, so the first position is 0.0 + 1, or 1.0.\n",
      "\n",
      "Now let's inject some noise in the signal."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def test_sensor(measurement_var, process_var=0.0):\n",
      "    dog = DogSensor(measurement_variance=measurement_var, \n",
      "                    process_variance=process_var)\n",
      "\n",
      "    xs = []\n",
      "    for i in range(100):\n",
      "        x = dog.sense_position()\n",
      "        xs.append(x)\n",
      "\n",
      "    bp.plot_track([0, 99], [1, 100])\n",
      "    bp.plot_measurements(xs, label='Sensor')\n",
      "    plt.xlabel('time')\n",
      "    plt.ylabel('pos')\n",
      "    plt.ylim([0,100])\n",
      "    plt.title('variance = {}, process variance = {}'.format(\n",
      "               measurement_var, process_var))\n",
      "    plt.legend(loc='best')\n",
      "    plt.show()\n",
      "\n",
      "test_sensor(measurement_var=4.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JYPIBTdOwsbGRHjUhhBBCiIeJj4cGDeCFF+Dq1UdmT05O5ttvv6WWuzvdBwzg\n0KFDuLi4MHHiRC5fvkxISAglS5aE1q0hPFw/3uX//u/x65WFL6GlJ+YBEsDkD/I5CiGEEEI8wtKl\ncPKk/t8dO8KuXWYH2ickJDBv3jymTZvGlStXAHB1dcXf3x9vb29sbW1Ny27ZEq5cyXoPz2OSIEYI\nIYQQQoiCyMdH3+vh46MPZjw8YOtWsLMDICYmhi+//JJZs2YRExMDQK1atQgMDMTT0xNLS8uHl5+D\nXyrL42RCCCGEEEIURJoGAwfC5ctQvjzs2QMTJ3L16lVGjRpFhQoVCA4OJiYmhmbNmrFhwwaOHz9O\nv379Hh3A5DDpiRFCCCGEEKIgK18etmwh7uOPCbp6lQWVKxvGFnfo0IFZtWtT/cgRtOLFszRe5Vl4\nPmohCoSff/4ZnU7HypUrc7sqQgghhBDiX0eOHKH3uHEUX7eOOYsWkZKSQs+ePTl48CA/bd6M248/\nou3cqe+xeU5IEJPP6XS6LL0WL16c21UVQgghhBA57d+FJJVS7Nq1i06dOtGwYUNWrlyJhYUFAwYM\n4PTp06xatYpGjRrBDz/An3/qp0l+881crvx/5HGyfG7JkiVGv8+dO5d9+/axcOFCo/QWLVo8y2oJ\nIYQQQohnLT0d1aYNEeXLM+jcOX7evx8AOzs73n//fUaOHEm5cuWM95kyRf9zxAjI5XEw95MgJp/r\n06eP0e9btmzh999/N0l/UEJCAoULF87JqgkhhBBCiGckNTWV34cMocWuXdgB+4BixYoxbNgwhg4d\nipOTk+lOp07B7t36CQDee+9ZV/mh5HEygZeXF7a2tly6dIlu3bpRtGhRunbtCsCxY8fo378/VapU\nwdbWlhIlSvDWW2/x999/m5QTFxeHv78/lStXxsbGhnLlytG3b18iIyMzPXZKSgpvvvkmRYoUYfv2\n7Tl2jkIIIYQQBVFSUhJz5syhTtWqlJ87F4Bpjo58Pm0aly9fJjg42HwAA7Bvn/7n+PFQpMgzqnHW\nSE+MACA9PZ0OHTrQtGlTpk6dSqFC+qaxbds2/vzzT7y8vChTpgznzp3jm2++4ffff+fEiROGxY0S\nEhJo1aoVJ0+epH///jRu3Jhbt26xefNmzp8/T5kyZUyOee/ePXr27Mmvv/7KTz/9xEsvvfRMz1kI\nIYQQIr+6c+cOc+bMYcaMGURFRREIlAdulS/P5IgIrM0tUPkgb2/o3BlcXHK6uo9NgpgnlNMrwqt/\nB109KykxV8WGAAAgAElEQVQpKXh4eDB16lSj9EGDBjFy5EijtG7duvHSSy+xdu1a+vbtC8CUKVM4\nduwYq1at4o033jDkHTNmjNnj3b17l+7du3P48GG2bt1KkyZNsvmMhBBCCCEKnhs3bvDFF1/w9ddf\nExcXB0Cb2rUZf/48JCbivHAhZCWAyVCqVA7V9OnI42TCwNfX1yTN9r5GHh8fT3R0NNWqVcPR0ZHD\nhw8btq1evZratWsbBTCZuXPnDq+++irHjh1j586dEsAIIYQQQjylixcvMmTIEFxdXQkJCSEuLo5W\nrVoRHh7O9o0bsXR3h06doF273K5qtpCemCf0rHtKcppOp6NixYom6bGxsQQGBrJ69WpiY2ONtmVE\n9wDnz5+nR48eWTrWyJEjSUxM5PDhw9SpU+ep6i2EEEIIUZCdPHmSH/z8iNi+nXSleBMo9dJL9Jgy\nhebNm/+XMTwc7t7NtXpmNwliBABWVlbozKzA2qtXL/bs2cOHH35IgwYNsLe3B8DT05P09HRDvsd5\nvO61115j+fLlfP7554SFhZk9rhBCCCGEyNz+/fsJCQnBesMGVjy4sUYNuD+AyWBn9yyq9kxIECMA\n8z1LsbGxbN++nU8//ZSxY8ca0pOSkoiJiTHKW6VKFY4fP56lY3Xt2pXOnTvz9ttvU7hwYRYsWPB0\nlRdCCCGEKACUUmzbto2QkBB27txJCSDi321327bFrmxZ/S/NmuVWFZ8ZCWIKIHO9JubSLCwsAIx6\nXABmzJhhEvT07NmTTz/9lNWrV9OzZ89H1sHT05OEhAQGDhxIkSJFmDlz5uOcghBCCCFEgZGWlsa6\ndesIDQ3l0KFDADg4ODBg0CB0JUvC779jFxamX8+lgJAgpgAy1+tiLs3BwYHWrVszefJkkpOTqVCh\nAr/99hu7du3CycnJaB9/f3/WrFnDW2+9xZYtW2jYsCG3b98mPDyc8ePH4+7ublL+gAEDiI+PZ8SI\nERQpUoTPP/88e09UCCGEECIPS05OZsmSJUyePJmICH2fi4uLC35+fvj6+lK0aNFcrmHukSCmgNE0\nzaTXxVxahrCwMIYPH87cuXNJSUmhVatW7Nixg1deecVoHzs7O3bt2kVwcDBr165l8eLFlCxZklat\nWlG9enWjY91v+PDh/PPPP3zyySfY29sTGBiYjWcrhBBCCJH3JCQkMG/ePKZNm8aVK1cAcHV1xd/f\nH29vb6PZYwsqTeW3abbMuH8WrYdFrElJSdjY2DyLKoln4Fl9ngcPHgSgcePGOX4sUfBI+xI5SdqX\nyEnSvh5fTEwMs2fPZtasWURHRwNQq1YtAgMD8fT0xNLSMpdr+Ow86v5demKEEEIIIYTIRZGRkUyf\nPp25c+cSHx8PQLNmzQgKCqJr167GM7nGxkKxYrlU0+eHzG0rhBBCCCFELjh79iwDBw6kUqVKTJs2\njfj4eDp06MDOnTvZs2cP3bp1Mw5gtm8HV1dYuDD3Kv2ckJ4YIYQQQgghnqEjR44QGhrK6tWrSU9P\npzywqkwZSvfpQ4UpU8zvFBsL774L//wD/46TKcikJ0YIIYQQQojff4cxY+DevRwpXinFrl276NSp\nEw0bNmTlypVYWFjg7e3NiU6daBoZSYWEhMx2hkGD4OpV/RowQUE5Use8RHpihBBCCCFEwZaYqO/l\nOHMGHB1h9OhsK1opxY8//khoaCh79uwB9LO6+vj4MGrUKMrdugUNGugze3qaL2TAAFixAgoXhiVL\noJDcwss7IIQQQgghCraPP9YHMDVrwrBh2VJkamoqK1asIDQ0lBMnTgBQrFgxhg0bxpAhQ3B2dtZn\nHDRI/9PPD8ysqwfAgQP6nzNnQpUq2VK/vE6CGCGEEEIIUXDt2gUzZoCFBSxeDPcvz6CUvlemUaPM\ne0kekJSUxMKFC5kyZQoXLlwAoEyZMowaNQofHx+KFCnyX+Z9++DHH/U9LJk9IqYUTJkCSUnQvfuT\nnmW+I0GMEEIIIYQomOLjwctLHyiMGQNNmhhv374dpk4FTYOYGPD1zbSof86fZ8O0aXy4Zg1RN24A\nUK1aNUaPHk2/fv2wtrY23Sk5Wd/706MHuLiYL1jT4NVXn/AE8y8JYoQQQgghRMF07x7UqQNFi+of\nKXtQu3YQGgqBgTB4MNy6BWPH6gOLf924cYOZM2dybcYMvk1M5BqwrEEDgoKCeP3117GwsMj8+O7u\ncPy4PpgRj0WCGCGEEEIIUTA5OcH69XD7NlhZmW7XNAgIgOLF4YMPYNw42LQJ9u/n0qVLTJ06lfnz\n55OUlET9f3fxBz4cOhTtzTezVgcLC7C1za4zKjBkimUhhBBCCFFwaRoUK/bwPAMHwqpVYGtL2pkz\nvNOvH1WqVGH27NkkJSXh4eHB13v2wP/+py/y/ffht9+eQeULLglihBBCCCGEeIT9ZcvSq21bnO/c\n4fslSwDo27cvx44dY+PGjTRv3lwf7AwfDikp+nEuFy/mbqXzMQlihBBCCCGEMEMpxdatW2nbti3N\nmjVj1aZNJFpbM2jQIM6ePcuSJUuoU6eO8U5Tp0LHjqDTwc2bpoWeOqWfUEA8FQliCoBTp07h6elJ\npUqVsLW1pWzZsrRu3ZpPP/00t6smhBBCCPHs3Lyp7yE5d+6h2dLS0li9ejVNmjShQ4cO7Ny5E3t7\newICArh48SJff/01lSpVMr9zoUKwfDn8/rvpbGepqfD66/q1Xv5dO0Y8GRnYn8/t3buXNm3aUK5c\nOby9vSlbtiyRkZEcPHiQSZMmMW7cuNyuohBCCCHEszF8uH4gf0qKfn2WByQnJ7NkyRImT55MREQE\nACVKlGDEiBEMGjQIR0fHrB3H0VH/etCSJRARAZUrg5vb05xJgSdBTD43YcIE7O3tOXDgAMUeGLR2\n01wXZx6RnJyMhYXFw6ctFEIIIYTIsGkTLFsGdnYwa5bRpoSEBObNm8e0adO4cuUKAK6urvj7++Pt\n7Y1tdswelpwMGU/BBAeDpeXTl1mAyeNk+dz58+epVauWSQAD+m8W7rdlyxZatWqFvb099vb2dOrU\niT/++MMoj5eXF7a2tkRGRvLaa69hb2+Pi4sL/v7+pKenG+VduXIlTZo0oWjRojg4OFCrVi0mTJhg\nlOfixYv07t0bJycn7OzsePHFF9mwYYNRnp9//hmdTkdYWBjBwcFUqFABOzs7rl69+jRvjRBCCCGe\nR59/rl+Zfvfu7Cvzn39g0CD9vz/7TN8TAsTExDB+/HhcXV0ZMWIEV65coVatWnz33XecPXuWwYMH\nZ08AAzB/vn6gf61a0KdP9pRZgElPTD5XqVIlfvvtN44dO0bdunUzzRcWFka/fv3o0KEDoaGhJCUl\n8b///Y+WLVty4MAB3O7r8kxPT+fVV1+ladOmTJs2ja1btzJt2jSqVKnCBx98AMC2bdvw9PTklVde\nITQ0FAsLC86cOcPu+/4g3bhxgxYtWpCQkMCwYcMoUaIE33//Pa+//jpLly7F09PTqI4TJ07EwsKC\nESNGoJSicOHC2fxuCSGEECLXrVkDR47oF5fMLmPGwN9/Q+PGMGwYkZGRTJ8+nblz5xL/7yD7Zs2a\nERQURNeuXdHpsvl7/vR0WLFC/+/x4/Vrw4inIkHMk7pvpVYjSmVP/mwyevRotm7dSsOGDWnUqBEt\nW7akbdu2tGvXDmtra0DfhTpkyBD69+/P/PnzDfsOGDAANzc3xo8fz9KlSw3pKSkp9OrVi4//XdnW\nx8eHRo0asWDBAkMQs2nTJooWLcpPP/2Elsm5h4aGcv36dX7++Wfc3d2Nyho5ciQ9e/akUKH/mmh8\nfDynT5/Ovm9EhBBCCPF8iYrSBzC2tvrV7EF/r/Tjj9Cli37GrydRqRI4OHBp7Fg+9/Vl8eLFJCcn\nA9ChQweCgoJo1apVpvcsTy09HapWhWrV9AP7xVOTx8nyuTZt2vDrr7/StWtXTp48yfTp0+natSsl\nS5Zk0aJFAGzdupXbt2/z1ltvcevWLcMrNTWVl19+mZ07d5qUO3DgQKPfX375Zf766y/D746OjsTH\nx/PTTz9lWrdNmzbRqFEjQwADYGNjg6+vL9evX+fIkSNG+d955x0JYIQQQoj8bMsW/c9WrcDGRv/v\n4cOhWzcICXniYo+2bYtXu3ZU7tGDefPmkZKSQs+ePTl48CA//fQTrVu3zrkABvQzli1YoH+kLCeP\nU4BIEPOklDL/yq782ah58+asX7+euLg4jh49yoQJE9A0DW9vb3bu3Mmff/4JQPv27XFxcTF6rVu3\nzmQCACsrK0qWLGmUVqxYMWJjYw2/+/r64ubmRufOnSlXrhxeXl788MMPRvtcunTJ6DG1DDVq1AD0\n42XuV6VKlSd+D4QQQgiRB4SH63+++up/aa++qr/xHzsWHvLl6IOUUuzatYtOnTrRoEEDFq9bh4WF\nBd7e3pw+fZpVq1bRqFGjbD4B8azI42QFiIWFBXXr1qVu3bo0b96cdu3asWTJEqpXrw7A4sWLKVu2\n7CPLyco3FSVKlODIkSNs27aNzZs3Ex4eznfffUfXrl3ZuHFjlsu5n/TCCCGEEPmYUrBnj/7f9wcx\nnTvDuHH6Gb369IFDh6BixYcUo9i0aRMhISHs+bc8Ozs7fHx8GDVqFOXKlcu5cxDPjAQxBVSTfxdf\nunbtGp06dQLA2dmZtm3bZtsxLC0t6dSpk6H8oKAgJk2axN69e2nevDmurq6cOXPGZL+MtIoP+QMl\nhBBCiHxG0+DMGdi3D/79gtVg7Fg4cEA/TfLrr+tnLnvgy83U1FRWrlxJaGgox48fB/RPigwbNowh\nQ4bg7Oz8rM5EPAPyOFk+t2PHDpSZx9b+7//+D9A/utWxY0ccHR2ZOHEiKSkpJnkffJwsKz0oMTEx\nJmn169cH4Pbt2wB07dqVw4cP89tvvxnyJCUlMWfOHEqXLi1dvEIIIURBY22tHw/z4L2GTgfff6+f\nGjktDe67z8i4d6hevTp9+/bl+PHjjCxalB/79uXypUsEBwdLAJMPSU9MPjds2DASEhLo0aMHNWrU\nID09ncOHD/P999/j7OyMn58f9vb2fPPNN/Tt25cGDRrw1ltv4eLiwuXLlwkPD6d27dosXLjQUKa5\noOhBAwYMIDo6mnbt2lGuXDmuXr3K7NmzKVOmjGEgf0BAAMuWLaNLly4MGzYMZ2dnlixZwpkzZ1i6\ndGn2T28ohBBCiLyrWDH9wP/SpcHOjjt37jBnzhxmzJhBVFQULwNlXV0Z/MEH9J4wAW3pUvD1hRYt\ncrvmIgdIEJPPTZs2jTVr1vDTTz+xYMEC7t27R9myZenXrx8fffQRFSpUAKBXr16UKVOGiRMnMm3a\nNJKSkihbtiwvvfSSYdpk0PfCmOuJeTC9X79+zJ8/n2+++YbY2FhKlSpF165dGTdunGF9lxIlSrB7\n924CAgL4+uuvuXv3LnXq1GHNmjV0797dpHwhhBBCFHBVqnDjxg1mfv45X331FXFxcQA0rluXX06e\nRHfpEnz0kX5K4169JIDJxzSVla/V87iMBg5QtGjRTPMlJSVhkzGdn8jzntXnefDgQQAaN26c48cS\nBY+0L5GTpH2JnJTd7evSpUtMnTqV+fPnk5SUBIC7uztBQUF0rF8f7a234NQpuHEDSpaEP/7Q/xR5\n0qPu36UnRgghhBBC5K7ff9cvSFmihMmmU6dOERoaSlhYGGlpaQB4eHgQGBhIi/t7WjLWtbt1Sz+2\nxt7+WdRc5BIJYoQQQgghRO5RCt58E/7+G06cgFq1ANi/fz8hISFs2LAB0C8V0bdvXwICAqhTp07m\n5ckg/gJBghghhBBCCJF7IiLg8mUoUQLl5sa2rVsJCQlh5789K9bW1nh7e+Pv70+lSpVyubLieSFB\njBBCCCGEeHxRUXD3rv4xsKcRHg7A5Ro1eL1pUw4dOgSAvb09vr6++Pn5UapUqaetrchnJIgRQggh\nhBCPJzERXnwRbt7UD6CvVu2JiklOTubGggWUAz769VcOoZ+9dMSIEQwaNAhHR8dsrbbIP2QhDiGE\nEEII8XjmzNE/ApaYCKNHP/buCQkJzJw5kxcqV8bpxAkATpcrx+zZs7l06RJBQUESwIiHkp6YByil\nZE2SfKAAzBwuhBBC5I74eAgJ0f/bwgKOH4fbtyELQUdMTAyzZ89m1qxZREdH4wz86OhIs0qV2Lt/\nP5aWljlbd5FvSBBzHysrK8PaIhLI5F1KKZKSkrC2ts7tqgghhBD5T3Q01KunHw8zfTo0bAhWVg/d\nJTIykunTpzN37lzi4+MBaNq0KUFBQXh4eKDTycNB4vFIEHMfnU6HtbU19+7dy+2qiKdkbW0tfxCF\nEEKInODqCtu2wZ074ODw0KyXL1/mf//7H4sXLyY5ORmA9u3bExQUROvWreVLY/HEnusgJjU1lU8+\n+YTly5dz7do1SpcuTd++fQkODsbCwsKQLzg4mHnz5hEbG0vTpk356quvqPXvHOOPS6fTPZNV3oUQ\nQggh8rSHBDBHjx4lKCiIHTt2kJ6ejqZp9OzZk8DAQBo1avQMKynyq+f6q+qJEycyd+5cvvzySyIi\nIpg5cyZff/01IRnPYQKTJk1i+vTpzJ49mwMHDuDi4kL79u0NXZVCCCGEECLnKaXYtWsXnTp1okGD\nBmzbtg2dToe3tzenT59m1apVEsCIbPNc98QcOHCAbt260aVLFwAqVKhA165d2b9/P6C/WL744guC\ngoLo0aMHAIsXL8bFxYWwsDB8fHxyre5CCCGEEAWBUopNmzYREhLCkT17sAXs7Ozo3r07ffv2NdzH\nCZGdnuuemE6dOrFjxw4iIiIAOHXqFDt37jRcDBcuXCAqKooOHToY9rGxscHd3Z09e/bkSp2FEEII\nIfKdmzfh2jWjpNTUVMLCwqhXrx4eHh5Y7NnDWU1jZ506XLp0iZEjR1KyZEnz5aWmQvfuMHUqpKU9\ngxMQ+c1z3RPj6+vLlStXqFmzJoUKFSI1NZWPP/6YDz74AIDr168DmFwgLi4uREZGmi3z4MGDOVtp\nUWBJ2xI5SdqXyEnSvsSjVJg8GeeNG7k4ZgzX2rXjxx9/5Pvvv+fq1auAfoHK9l27UnrJEsoeP87p\nTZvghRcA8+2ryB9/UGPjRpKOHuVE69bP8lREHlHtEQuoPtdBzKxZs1i4cCHLly/nhRde4MiRIwwf\nPpyKFSvi7e390H1ltgshhBBCiKdnde0azuvWoaWlsfzMGabNnElMTAwA5cuX55133qFz585YWVkR\nlZZG6e++o/z06ZyZPx/M3I/pEhJw+uEHAOKaN3+m5yLyj+c6iPn888/5+OOP6dWrFwAvvPACly5d\nIiQkBG9vb0qVKgVAVFQU5cqVM+wXFRVl2Pagxo0b53zFRYGS8Q2TtC2RE6R9iZwk7UtkRWLfvuhS\nU1lpaclHy5YBUL9+fYKCgnjjjTeMZozlyy8hPJwix45RbOtWYjt0MG5fn34KkyZBYiIAJb28KCnt\nT5gRFxf30O3P9ZgYpZTJWh86nc6wGnulSpUoVaoUW7ZsMWxPSkrit99+o0WLFs+0rkIIIYQQ+cml\nS5cY368flmFhpAIfp6Tg7u7O5s2bOXz4ML169TIOYEA/7fJnnwFQbvZstJQU4+3FiukDmJdfhgUL\noGPHZ3MyIt95rntiXnvtNUJDQ6lUqRK1atXiyJEjzJgxg3fffRfQPzLm5+fHxIkTqVGjBtWqVWPC\nhAnY29vTp0+fXK69EEIIIUTec+rUKSZNmkRYWBjfpqZSCNhavjyLli/P2pfE3t6wYweXWrZEWVoa\nb3vnHejWDSpWzImqiwLkuQ5iZsyYgYODA4MHDyYqKorSpUvj4+PDJ598YsgzevRoEhMTGTx4MLGx\nsTRr1owtW7ZQuHDhXKy5EEIIIUTesn//fkJCQtiwYQMAFhYWHO/aldupqbSfMyfrgUehQrB8OXfM\nTRjh6Kh/CfGUNJXxbFY+dv8zdUWLFs3Fmoj8SJ4pFzlJ2pfISdK+hFKKbdu2ERISws6dOwGwtrbG\n29ubDz/8kMqVKz9x2dK+xNN41P37c90TI4QQQgghsl96ejrr1q0jJCSEQ4cOAWBvb4+vry9+fn6Z\nTpAkxPNCghghhBBCiAIiOTmZpUuXMmnSJMNi4iVKlGDEiBEMGjQIR3nUS+QREsQIIYQQQuRzCQkJ\nzJ8/n6lTp3LlyhUAXF1d8ff3x9vbG1tbW0hNhZkzwdcXHhyQL8RzRoIYIYQQQoh8KiYmhtmzZzNr\n1iyio6MBqFWrFoGBgXh6emKZEawoBQMHwqJFcOAALFmSe5UWIgskiBFCCCGEyKvu3IEZM6BNG3B3\nNyRHRkYyffp05s6dS3x8PABNmzYlKCgIDw8P43X4lAJ/f30AY2cHgwc/45MQ4vFJECOEEEIIkRfd\nugWdOsHBgzBvHpw9y7mrV5k8eTKLFy8mOTkZgPbt2xMUFETr1q3RNM20nMmTYdo0/SNka9dC8+bP\n+ESEeHwSxAghhBBC5DVXr0L79nD6NADnAwP5qH9/Vq1aRXp6Opqm0bNnTwIDA2nUqFHm5axbB4GB\noGnw3XfQseMzOgEhno4EMUIIIYQQecm5c/oA5uJFEipVwqdiRcKGDgXA0tISLy8vRo8ejZub26PL\nat8eOnSA7t3B0zOHKy5E9pEgRgghhBAiD1H//EPqzZv8WaQILS9cIPbCBezs7PDx8WHkyJGUL18+\n64UVKQL/939gYZFzFRYiB+genUUIIYQQQuS21NRUwsLCqPfuu7yYkEDT+HgoVoxPPvmES5cuMWPG\nDOMAZvZsOHNG/+979/RjZ8yRAEbkQdITI4QQQgjxPLhwAebOhTp1oG5dcHMDKyuSkpJYtGgRU6ZM\n4a+//gKgTJkyjB81ioEDB2Jvb29a1g8/wNCh4OgIQUHwzTcQE6N/FM3Z+RmfmBDZT4IYIYQQQojn\nwb59MGmS4VdVqBC3nJyYHx/PmIQEAKpWrUpAQAD9+vXD2to687LattWPc9mwAQIC9Gm1asG1axLE\niHxBHicTQgghhHge1K4Nn3xCUufO3CpWDJWaSomoKAonJFC/fn1WrFjBmTNneO+99x4ewAAULgxr\n1uhnHnNzgzlz4I8/9L08QuQD0hMjhBBCCPEcuOTgwNSYGBbs3EliYiJ2wNv16/P24MEMHTDA/Bov\nD2NhASEh+pcQ+YwEMUIIIYQQuSElBSwtOXXqFJMmTSIsLIzU1FQAPDw8CAwMpEWLFrlcSSGeTxLE\nCCGEEEI8a1FRJNepw/ISJfA6dQoFWFhY0LdvXwICAqgjj30J8VASxAghhBBCPCNKKbZv385dLy+6\n3bxJsZs3sbK2xtvbmw8//JDKlSvndhWFyBMkiBFCCCGEyGHp6emsW7eO0NBQEg4e5BiQCvw5YAAX\nJ0ygVKlSuV1FIfIUCWKEEEIIIXJIcnIyS5cuZdKkSURERAAQbmVFoeRk7vXvz6j583O5hkLkTTLF\nshBCCCFENktISGDmzJlUqVIFb29vIiIiqFChAmuHDKFjcjIUKYK1zBomxBOTnhghhBBCiGwSExPD\n7NmzmTVrFtHR0QDUqlWLwMBAPD09sYyIgNOnoU0bKFkyl2srRN4lQYwQQggh8r/t26FsWahRwzj9\n32mOn1ZkZCTTp09n7ty5xMfHA9C0aVOCgoLw8PBAp/v34ZfatWHrVkhPf+pjClGQyeNkQgghhMjf\nbt+Gvn2hbl04dOi/9Lg4fdqsWU8cVJw7dw4fHx8qVarEtGnTiI+Pp3379uzYsYO9e/fSvXv3/wKY\nDJqmX4hSCPHEJIgRQgghRP4WFARRUfDii9CgwX/pa9bAmTMwfDh07gyRkVku8ujRo3h6euLm5sa8\nefNISUmhZ8+eHDx4kC1bttCmTRs0TcuBkxFCgAQxQgghhMjP9u2DuXOhUCH9z/t7Rby9Ye1acHKC\nn37S98qsXfvQ4n799Vc6d+5MgwYNWLFiBRYWFnh7e3P69GlWrVpFo0aNjHdQCv7+OwdOTIiCTYIY\nIYQQQuRPKSnw/vv6QMLfH154wTRPjx5w7Bh06ADR0fDGG/DHH0ZZlFL8+OOPvPzyy7i7u7N582bs\n7Ozw8/Pj/PnzLFiwADc3N9Oyr18HDw9o2lRfthAi28jAfiGEEELkT3/8AefOQeXK8PHHmecrUwY2\nb4avvtLnr1cPgNTUVFauXEloaCjHjx8HoFixYgwdOpShQ4fi7OyceZlr14KPjz54cXSEU6egZcvs\nPDshCjQJYoQQQgiRPzVurJ/OOCoK7Owenleng6FDAUhKSmLRokVMmTKFv/76C4AyZcowcuRIfHx8\nsLe3z7ycO3f0Y2wWLdL/3r49fPstlCuXDSckhMggQYwQQggh8q8KFfSvLLhz5w7ffPMNM2bM4Pr1\n6wBUrVqV0aNH887LL2Nds+ajCzl8WB/A2NjA5MkweLDxOBwhRLaQIEYIIYQQBdqNGzeYNWsWX331\nFbdv3wagfv36BAUF8cYbb2Bx5Ih+0H///voxLlFR+lfnzsaznQG0bq2fsrl9e9M1aYQQ2UaCGCGE\nEEIUSJcuXWLq1KksWLCAxMREANzd3QkKCqJjx47/TZF84oS+N2XePP0rg4ODaRADhsfShBA5R4IY\nIYQQQuQfhw5Bw4b6BSUzcerUKSZNmkRYWBipqakAeHh4EBgYSIsWLUx38PKCJk1g3Di4exdKltS/\nGjbMoZMQQjyKBDFCCCGEyPuUgtBQGDMGXn0VfvwRLCyMsvz++++EhISwfv16ACwsLOjbty8BAQHU\nqVPn4eW/8AKsXp1TtRdCPCYJYoQQQgiRt2WsAzNtmr4HpkcPQwCjlGL79u2EhISwY8cOAKytrfH2\n9ubDDz+kcuXKuVlzIcQTkiBGCCGEEHlXaioMHKifEczSEr7/Hnr3Jj09nXXr1hEaGsrBgwcBsLe3\nx9fXFz8/P0qVKpW79RZCPBUJYoQQQgiRd02cqA9g7Oxg7VqS27Rh6cKFTJo0iYiICABKlCiBn58f\nvnvLnG4AACAASURBVL6+ODo65m59hRDZQoIYIYQQQuRdfn7w668kBgXxv+PHmTZwIH///TcAFSpU\nwN/fH29vb+wetdilECJPkSBGCCGEEHlWbFoas93dmdmrF9HR0QDUqlWLwMBAPD09sbS0zOUaCiFy\nggQxQgghhMhzIiMjmTFjBt988w3x8fEANG3alKCgIDw8PNDpdLlcQyFETpIgRgghhBB5Q3Iy5y5d\nYvKUKSxevJjk5GQA2rdvT1BQEK1bt/5vgUohRL4mQYwQQgghnntHjxwh7vXXuXHxIsuAFE2jZ8+e\nBAQE0Lhx49yunhDiGZMgRgghhBDPrV9//ZWQkBAqbN7MN0AC4NejB2+HhODm5pbb1RNC5BIJYoQQ\nQgjxXFFKsWnTJkJDQ9m9ezdNgHX/bkuaNYvPhg7NzeoJIZ4DEsQI8f/s3Xt8zvX/x/HHtYPNNKzm\nMDIxQspUDn1zqERy+PrmFNu3MEIOY4zZVUrlsI0hmhyL5Ri+ocykpl8ZFUqbYpU5TMxh2hwydriu\n3x8fTcuhYdu1w/N+u7ld1z6f9+dzvT637xXf594nEREpErKysli9ejWhoaHs3bsXAK8KFdhiteJ0\n7hwMH849CjAiAmjpDhEREbGpS5cuMW/ePOrVq8d///tf9u7dS7Vq1QgPD2fff/9LxXPn4LHHYPp0\nW5cqIkWEemJERETEJs6dO8e8efOYOXMmJ06cAKBOnToEBQXRp08fnJyc4NIlcHaGUaOgTBkbVywi\nRYVCjIiIiBSq06dPM2vWLObMmUNaWhoAjRs3xmw20717d+zt7a82dnZWD4yIXEMhRkRERArFkSNH\nmD59OosWLSI9PR2A1q1bYzabad++vfZ4EZE8U4gRERGRArVv3z7CwsJYsWIFWVlZAHTu3Bmz2czj\njz9u4+pEpDjSxH4REREpEDt37qRr1640bNiQDz74AIvFgq+vL/Hx8XzyySfXBpijR+H55yE11TYF\ni0ixoZ4YERERuXX/+x+kp8MLL+Q6bLVaiYmJISQkhK1btwLg5ORE//79GTNmDLVr177+/eLioGNH\nOH4cypeHRYsK+glEpBhTiBEREZFbc+YM9OoF2dnw88/w1ltYrFbWrVtHaGgou3fvBsDV1ZWhQ4cS\nEBBA1apVb3y/LVugRw84fx5at4Zp0wrpQUSkuFKIERERkVuzcaMRYAAmTSL+u+94PjGRn3/5BYBK\nlSoREBDA0KFDqVix4s3vtXgxDBoEWVnQuzcsWQJOTgVbv4gUewoxIiIicmt69+ZSxYrEz5nDw599\nRqPoaJoB6Z6ejB07lv79++Pi4pK3e+3ZYwSYceNgyhSw03RdEflnCjEiIiKSZ6mpqURERDBr1izO\nnDnDf4Ahrq60nzWL9154AUdHx1u74cyZ0L49dOpUIPWKSMmkECMiIiL/6Pjx48ycOZN58+Zx4cIF\nAJo3b46f2Uy7f/8bu9vtQbG3V4ARkVumECMiIiI3dODAAaZOnUpkZCQZGRkAtGvXDrPZzJNPPvnP\nG1RmZUF0NLz/PjRuDBMmFELVIlLSKcSIiIjINX744QdCQ0NZs2YNFosFk8lE9+7dCQ4OpkmTJv98\ng7g4WLbM+HPihHFszx54/XX4p+AjIvIPFGJEREQkx7Zt2wgJCSE6OhoABwcH+vbtS1BQEPUrVIC8\nzHm5cAEGDoRdu4yf69WD/v2hTx8FGBHJF1oCREREpJSzWq1ERUXRsmVLWrduTXR0NC4uLowcOZKD\nBw/y/vvvU79+fWP/lipVYO7cm9/w55+NYWQDBsD27bB/PwQFwc32ihERuQXqiRERESmlsrKyiImJ\nYcCAAcTHxwPg5uaGv78//v7+uLu7X21stcL69WCxgLf3zW/86KPw/fcFWLmIlHZFvicmOTmZvn37\nUrlyZcqWLUvDhg356quvcrV54403qF69Oi4uLjz11FPs27fPRtWKiIgUfZcuXWLevHn06NGD8ePH\nEx8fT7Vq1QgPD+fIkSO8+eabuQMMwN69cOiQ0RPTvLltChcRuaJIh5i0tDRatGiByWRi06ZNJCQk\nEBERQeXKlXPahIWFMWPGDCIiIti1axeVK1emXbt2Ocs/ioiIFGu//moEiHxw7tw5pk6dSq1atRgy\nZAjHjh2jRo0aLFiwgIMHDxIYGIirq+v1L16/3njt0sVYFllExIaK9HCyqVOnUr16dZYsWZJzrGbN\nmjnvrVYrb7/9Nmazma5duwIQGRlJ5cqVWbFiBYMGDSrskkVERPLPyZPQtClcvAi7d0OjRrd1m9On\nTzNr1izmzJlDWloaAI0bN+b555+nTZs2NM9Lz8qfIea5526rBhGR/FSke2LWr19Ps2bN6NWrF1Wq\nVOHhhx9mzpw5OecPHTrEyZMneeaZZ3KOOTs707p1a3bs2GGLkkVERPLPPfdApUqQmQl+fsbrLThy\n5AgjRoygZs2aTJ48mfS0NNq2bEl0dDTff/897dq1w97e3ph4fzNZWUaYqlMH2rS5gwcSEckfJqvV\narV1ETfi7OyMyWRi9OjRPP/88+zZswd/f39CQ0MZNmwYO3bsoGXLliQlJXHvvffmXNe/f3+OHz/O\n5s2bATh79mzOuV9//bXQn0NEROR22V28SMPevXFKTubYkCEk9+//j9ccPHiQDz74gM2bN5OdnQ2A\nX+PGTD91istPPslvo0bltL131iyqLF9O4rRppD3xxM1vbLVqiWQRKRR169bNeV+hQoVrzhfpnhiL\nxcKjjz7K5MmT8fb2pl+/fowYMSJXb8yN/OMOwiIiIsWAxcWFw+PHA+CxcCHOBw7csO1PP/3E2LFj\n6dWrF1FRUVitVjo88ww/9OrFoh9/xO34cSrs2IHdpUs512RUqYLJaqVGeDh26ek3L0b/topIEVGk\n58RUq1aNBx54INex+vXrk5SUBEDVK+vNnzx5MldPzMmTJ3PO/V2edhkWuQW7d+8G9N2SgqHvlwDQ\npAnEx2O3fDkPOjkZP19htVqJiYkhJCSErVu3AuDk5ISfnx/mXr3wfPVV2LLFaDx8OGXDwnjExQUw\nvl+nevTAc+tWnPbs4ZGoKAgNLfTHk5JJf3/JnfjrSKrrKdI9MS1atCAhISHXsV9++YX77rsPgFq1\nalG1alW2/PmXM8aykbGxsTz++OOFWaqIiEjBmjoVfvwRrixkY7FY+Oijj2jWrBnt2rVj69atuLq6\nMm7cOA4fPszcuXPxfPdd2LEDqlWDTz+Fd96BKwEmh4MDzJtn9LJMnw4//WSDhxMRuTVFOsSMGjWK\nb775hilTpnDgwAHWrFnDO++8w7BhwwBjyFhAQABhYWGsW7eOH3/8kX79+uHq6oqvr6+NqxcREbkN\n48fD4sXGppJ/Vb481KxJRkYGS5YsoWHDhnTv3p3du3dTqVIlJk+eTFJSEqGhoVdHI8yfD8OHG0s0\n/2URnGs0awaDBxsT+K8MXRMRKcqK9HCyJk2asH79el555RUmTpxIzZo1mTRpEkOGDMlpExQURHp6\nOsOGDSM1NZXHHnuMLVu2UK5cORtWLiIichu+/x6mTDH2YWnZEv4ysfWPP/5g0aJFTJ8+naNHjwLg\n6enJ2LFj6d+/Py5/72EBcHMzel/yYsoUcHbOHWLS06FbN+jY0QhDmhMjIkVEkQ4xAB07dqRjx443\nbTNhwgQmTJhQSBWJiIgUAIvFCApWK4wcmRNgUlNTiYiIYPbs2aSkpADwwAMPMG7cOHx8fHB0dMyf\nz3dzg5kzcx/77DPYvBlSUsDfP38+R0QkHxTp4WQiIiKlxtKl8PXXULUqvP46x48fZ+zYsXh6evL6\n66+TkpJC8+bNWb9+PXv37qXPiy/i+MEHkJBgbIoZEAAZGflbkza4FJEiqsj3xIiIiJR4Z89CUBAA\nJwMDeW3MGCIjI8m4EkratWuH2WzmySefvLqFwMyZMHo0PPwwpKbC4cPg6AjTpuVPTdnZ8MknxnuF\nGBEpYhRiREREbO3kSS66uZFksdAwKAiL1YrJZKJ79+4EBwdff4laPz8ID4c9e4yfmzWDwMD8q2nH\nDmMYWa1a8LftDkREbE3DyURERGxo27ZtdAwIwPXnn3kiJQU7e3v8/PzYt28fa9euvfEeGxUrGquY\nlSsHPj7wf/9nDEXLL39ucdCunSb0i0iRo54YEREpXbKzjdW/bMhqtbJp0yZCQkLYvn07AC4uLvgM\nHEhgYCA1atTI242eecYYSpZfk/v/qlEj6NkTXn89/+8tInKHFGJERKR0OH7cmENy4oTRa2EDWVlZ\nrFmzhtDQUOLj4wFwc3PD398ff39/3N3db/2mBRFgAJo3h9WrC+beIiJ3SCFGRERKhwoVjOWCz541\n5pE8/HChffSlS5eIjIxk6tSpHDx4EAAPDw8CAwMZNGgQrq6uhVaLiEhJoDkxIiJSOpQrB/36Ge/f\nfbdQPvLcuXNMnTqVWrVq8fLLL3Pw4EHq1KnDggULOPTDDwQOHqwAIyJyGxRiRESk9Bg61HhdvtyY\nS1JATp8+zfjx46lZsybjxo3jxIkTeHt7s2rVKhISEhg4cCBOb78Nnp6wcmWB1SEiUlIpxIiISOlx\n//3Galvp6bBkSb7fPikpiREjRlCzZk0mT55MWloarVu3Jjo6mj179tCrVy/s7e3h/HmjNyg11VjC\nWEREbonmxIiISMk3eTLcdx907Wr0xmzfDhcu5Nvt9+/fT1hYGMuXLycrKwuAzp07Yzabefzxx6+9\nYOFCY25Oq1bw2GP5VoeISGmhECMiIiXb+fPGMsEmk7HzfOfOcOyYsc/K7bBaITMTypRh586dhIaG\nsn79eqxWK3Z2dvj6+hIcHMxDDz10/eszMmDmTON9UNDt1SAiUsopxIiISMn27bdgsUDTpsbkfrj9\nAANYp0whbdUq+lesyPrYWACcnJzw8/Nj7Nix1K5d++Y3WLUKfvsNHngAOna87TpEREozhRgRESnZ\nrmwmSYsWt37t2bPg5ATOzlgsFjauXEmzt96iakYG4UCSiwvt/P0JCAigatWqebtn/fpGeHn+ebDT\n1FQRkduhECMiIiXbnyGmZctbv3bkSKw7drDRx4eg1atJSEjAA9jk4EDjrCx2OTpi164d5DXAADRr\nBlFRxrA0ERG5LfoVkIiIlFxZWfD118b7m/XEXCdQpEdFQWQkl3/9ldFvvUVCQgKenp688s473H/8\nODz3HHZnz8Kzz8JHH916bSbTrV8jIiKAQoyIiJRkFgssWgSvvXb93pKtW+Hpp419Y65ITU1lyuuv\nc7xLFwAmAY4NGhAZGcmBAwcYPnw4LpUqwf/+Z0zMr1wZmjcvpAcSERHQcDIRESnJypSBXr1ufP7g\nQSPI/PEHyU8/zYwZM5g3bx5jL1zACzhYtixNIyN5q3t37P4+f8XODsLCYNw4uPvuAn0MERHJLc8h\n5sSJEyQnJ/Pwww/nHNu/fz8zZ87k7Nmz9OrVi27duhVIkSIiIgXC15fswEDsv/2Wrp6efJuVhSdg\nNpnAaqXWp59Su1Wrm9/jRgHms8/AxQUefxySk43hYx4e+f4IIiKlUZ5DzPDhwzl16hRfffUVAL//\n/jtPPPEEaWlpODs7s3btWtavX8+///3vAitWREQkv8TFxREaGkqzc+cYBQzKyuLe7t0JHjcOx6Qk\n2LMH0z8FmBuxWGDECEhIgCZNoHx5iI01Nrns0ydfn0NEpDTK85yYr7/+mvbt2+f8vGzZMlJTU/nu\nu+84c+YMLVq0IDw8vECKFBERyS+xsbF06tSJxo0bs2rVKhbY2wPQz8mJtQsW0KRpU+jeHSZNuv0P\nycgw7nHPPbB7tzFkLTNTc2dERPJJnkPMmTNnqFatWs7Pn3zyCa1ateKhhx7C0dGRXr168eOPPxZI\nkSIiInfCarUSFRVFy5YtadWqFZs2bcLFxYWRI0ey5dAheOYZ7CpUgP378+cDnZ2NEHT0qNH70qIF\nmM1Qr17+3F9EpJTL83Cyu+++m+TkZAAuXrzI9u3bef3113POm0wmLl26lP8VioiI3I7gYCy7drG1\nZUsC168nPj4eADc3N/z9/fH398fd3d1o+/77UKmSsRBAfipbFl56yfgjIiL5Js8hpmXLlrz77rvU\nr1+fzZs3c+nSJbpcWX4S4JdffqF69eoFUqSIiJRyly/Dnj3w2GN5an7p0iUurFiB+9GjvLV1K/GA\nh4cHgYGBDBo0CFdX19wX6N8vEZFiJc/DyaZMmYKTkxM9evRg0aJFjB49mgceeACArKws1qxZwxNP\nPFFghYqISCk2ZQr8618QGnr12Llz1zQ7d+4cU6dO5aGaNXE7epQM4PfatVmwYAGHDh0iMDDw2gAj\nIiLFTp57YurUqUNCQgL79u2jfPny1KpVK+dceno6c+bMoXHjxgVSpIiIlGLx8UaIAWO5YosFhg41\nNqjcvx/uvZfTp08za9Ys5syZQ1paGu0AeyCtTh3iEhKwvzJ5X0RESoZb2uzS0dERb2/va467urry\n3HPP5VtRIiIiAGRlQf/+xuvQodC6tXH899/hwgXOvfEG411cWLRoEenp6QC0atWKOTVqwIoV3NOl\nCyjAiIiUOHkeTgaQkZHBnDlz6NixIw0bNqRhw4Z06tSJuXPnkpmZWVA1iohIaTV9Onz3HXh65hpK\ndrB3bwAc3nuPle+8Q3p6Op07dyY2NpavvvqKuqmpRsMWLWxRtYiIFLA898SkpqbSpk0b4uLiqFKl\nCnXq1AHgu+++Izo6moULFxITE4Obm1uBFSsiIqXI5cswd67xfsECcHVl165dhISEsH79ej4GOgML\nGzak9ooVNGrU6Oq1H39sDEO78m+ViIiULHnuiTGbzfz0008sXryYY8eOsW3bNrZt28bx48eJjIzk\np59+wmw2F2StIiJS0nz+uTE07HqcnOC777AuWMDn9va0bduWZs2asW7dOsqUKcO+K8OYnzt6lEae\nnrmvdXCARx6B8uUL+AFERMQW8hxiNmzYwLBhw+jbty92dlcvs7Oz48UXX2TYsGFs2LChQIoUEZES\nKDkZunaF+++H+fMhOzvXaYvFwkdffknzhQtp164dMTExuLq6Mm7cOA4fPkzQunXQvj307Gn02oiI\nSKmR5+FkaWlpOUPIrqd27dqk/jkGWURE5K+OHoXUVPjrkK9Ll6BZM9i6FV5+2Rgy9s47ZDZtyvLl\nywkLCyMhIQGASpUqERAQwNChQ6lYseLVe2zaBHa3NL1TRERKgDz/ze/l5cX69euxWq3XnLNarWzY\nsOGmIUdEREqp9HTo1s3Y52Xr1qvHa9UyhpOtXg01asD330OLFoRVqoSfnx8JCQl4enryzjvvcPjw\nYV555ZXcAQYUYERESqk8/+0/fPhwYmJiaN++PVFRURw4cIADBw6wceNG2rdvT0xMDP7+/gVZq4iI\nFDdWKwwZArt3Q5Uq8Pdl+k0mUtu2JbRvX6aXLcsFYNXZszRo0IDIyEgOHDjA8OHDcXFxydvnnTsH\nv/2W748hIiJFS56Hk7388sukpKQwceJEPv/881znypQpw8SJExk8eHC+FygiIsVYRARERkLZsrBu\nHdxzT86p5ORkZsyYwbx587hw4QIA0Y88wqTXXqNLly655l/m2SefwAsvQN++sGRJPj2EiIgUNbe0\n2eX48eMZPHgwn3/+OUlJSQDUrFmTdu3acc9f/mESERHhyy9h1Cjj/fvv5/TCJCYmMnXqVJYsWUJG\nRgYAbdu2xWw289RTT2EymW7/M+fPN17r17+TykVEpIi7pRADEB8fz86dOzl8+DAmk4mTJ09SqVIl\nnn766YKoT0REiqtTp8DR0QgyvXsTFxdHaGgoq1evxmKxYDKZ6N69O8HBwTRp0uTOP2/kSNi2zXiv\nTS5FREq0PIeYP/74g+eff57o6GgA3NzcsFqtpKWl8fbbb9O+fXvWrFnDXXfdVWDFiohIMdKzJzz4\nILEnTxLSqRObNm0CwMHBgb59+xIUFET9/Owxadjw6vv8CEUiIlJk5XnAcWBgINHR0bz22mucPn2a\nM2fO8Pvvv3Pq1CnGjx/Pp59+SmBgYEHWKiIixYTVaiUqKoqWAwfS6qmn2LRpEy4uLowcOZKDBw/y\n/vvv52+AAejXD3x84M03jTk4IiJSYuW5J2b16tW89NJLvPnmm7mOu7u789Zbb3HixAnWrFnD/D/H\nI4uISOmQkQFLl4KvL1mOjqxZs4bQ0FDi4+MBo+fe398ff39/3N3dC66OMmVgxYqCu7+IiBQZeQ4x\nFouFhx9++Ibnvb29Wb16db4UJSIixUBmphFeJk6Ew4fZ8emnvPjddxw8eBAADw8PAgMDGTRoEK6u\nrjYuVkRESpI8Dyfr2LEjGzduvOH5qKgoOnXqlC9FiYhIEXbmDMyYAQ0awIABcPgwv9jbM2XNGg4e\nPEidOnVYsGABhw4dIjAwUAFGRETyXZ5DzGuvvcZvv/1Gp06diI6OztnsctOmTXTs2JHjx48zfvx4\nTp06leuPiIgUQzt3wujR1z+XmgqBgZCYyAE7O/4LNMjO5jdvb1atWkVCQgIDBw7EycmpUEsWEZHS\nI8/DyRpeWfVl7969OSuU3ajNn0wmE9nZ2XdQnoiIFDqrFQYNgkOHYMoUcHbOOZWUlMSsGTNoYG/P\nl9nZrLRYeLxVKzaazTz77LN3tseLiIhIHuU5xLz++uu3fHP9YyYiUgxt2wZxcbkO7d+/n7CwMJYv\nX05WVhYAnTt35svgYFpoTxYRESlkeQ4xb7zxRgGWISIiRcbs2cbra6+xa+9eQkJCWL9+PVarFTs7\nO3x9fRk3bhyNGjWybZ0iIlJq5TnEiIhIKZCUhHX9eqz29vh88QWrJ04EwMnJCT8/P8aOHUvt2rVt\nXKSIiJR2CjEiIgIYS+n/OmoU9bKzWQmsjo3F1dWVIUOGEBAQgIeHh61LFBERARRiRERKvczMTJYv\nX05YWBinEhIYAHxfoQKTxo5l2LBhVKxY0dYlioiI5KIQIyJSSl28eJFFixYRHh7O0aNHAfD09MRz\n7Fje6N8fFxcXG1coIiJyfQoxIiKlTGpqKnPmzGHWrFmkpKQA0KBBA4KDg/Hx8cHR0dHGFYqIiNyc\nQoyISHF26hS4u4PdP+9dnJyczMyZM5k7dy4XLlwAoFmzZpjNZrp06YJdHu4hIiJSFOhfLBGR4ioi\nAqpUgWeeuWmzxMREBg8ezH333ce0adO4cOECbdu2JSYmhm+++YbnnntOAUZERIoV9cSIiBRHO3fC\n6NHG+4cfvm6TuLg4QkNDWb16NRaLBZPJRPfu3QkODqZJkyZXG/72G/zwA3TsmKceHREREVvTv1Yi\nIsVNair06gWZmTB4MLz1Vq7TsbGxdOrUicaNG7Nq1Srs7Ozw8/Nj3759rF27NneAAaNH59//hlGj\nCvEhREREbp96YkREihOrFfr3h8OHoUkTmDULnJywWq1s2rSJkJAQtm/fjglYbW/PhfbtaTt3LjU8\nPa9/v4sXYeFC472PT2E9hYiIyB1RT4yISHFy+TI4OUH58vDhh2TZ27Ny5UoaN25M586d2b59OxUr\nVmRZz570zM7Gb9MmarzwgjFc7HpWrIDff4emTaF588J9FhERkdukECMiUpw4O8PKlVz+9lvmf/YZ\n9erVw9fXl/j4eDw8PJg2bRpJSUn4Ll0K774LlSrBtm3w6KMwZAhcWVIZMHp13nnHeD9iBJhMtnkm\nERGRW6QQIyJSjJw/f55p4eHc99RTvPzyyxw8eBAvLy/mz5/PoUOHGDNmDK6urkZvzZAh8MsvEBBg\nBJR582Dt2qs3++oriI83Vjjr2dN2DyUiInKLNCdGRKQYOH36NLNnzyYiIoK0tDQAvL29MZvN9OjR\nA3t7++tfWLEizJwJAwcaE/hfeunquebNYfFiyM42Qo+IiEgxUWx6YkJCQrCzs8Pf3z/X8TfeeIPq\n1avj4uLCU089xb59+2xUoYhI/jtx4gTh06ZRs2ZNJk2aRFpaGq1atWLTpk3s2bOHXr163TjA/NUD\nDxjDyxz+8rsrZ2fo1w8GDCiw+kVERApCsQgx33zzDQsXLqRRo0aY/jJmOywsjBkzZhAREcGuXbuo\nXLky7dq1y9mJWkSkuNq/fz/9+vXjrf/8h9GrV1MjPZ3OnTsTGxvLV199RYcOHXL9fSgiIlKaFPkQ\nc/bsWV544QUWL16Mm5tbznGr1crbb7+N2Wyma9euNGzYkMjISM6fP8+KFStsWLGIyO3btWsX3bp1\no2HDhsRHRrLWYqEZEPvCC3zyySe0aNHC1iWKiIjYXJEPMYMGDaJnz5488cQTWK3WnOOHDh3i5MmT\nPPPMMznHnJ2dad26NTt27LBFqSIit8VqtRITE0Pbtm1p1qwZ69atY7i9Pd/a2eEJXHjoISr9uZeL\niIiIFO2J/QsXLuTgwYM5PSt/HTpx4sQJAKpUqZLrmsqVK3P8+PEb3nP37t0FUKmIvlty6ywWC19+\n+SVLlizJmc9Xrlw5Pq1ShRYHDwJwqnt3jo4ahfXHH21ZqpRw+vtLCpK+X3I76tate9PzRTbE/Pzz\nz7z66qvExsbmTFq1Wq25emNuROPERaQoy8rKIjo6mg8++IDDhw8DULFiRXx8fOjZsyf3bt5M9pw5\nHH7lFVL/0tssIiIihiIbYr7++mtSUlJo2LBhzrHs7Gy2bdvG/Pnz+fHKbyVPnjzJvffem9Pm5MmT\nVK1a9Yb3bdKkScEVLaXSn79h0nermLtwwdj80dW1wD7i4sWLLFq0iPDwcI4ePQqAp6cnY8aMYcCA\nAbi4uBgNn3wSRozAq3p1fb+kQOn7JQVJ3y+5E2fPnr3p+SIbYrp27UqzZs1yfrZarfj5+XH//ffz\nyiuvULduXapWrcqWLVt49NFHAbh06RKxsbGEh4fbqmwRKY4uXoSHHoLMTPj+e6hcOV9vn5qaypw5\nc5g1axYpKSkANGjQgODgYHx698axTJncF5hMUL16vtYgIiJSkhTZEFOhQgUqVKiQ65iLiwtueuCg\nMQAAIABJREFUbm488MADAAQEBDBlyhTq169P3bp1mTRpEq6urvj6+tqiZBEprt5/H64M62LQIFi3\nzggSdyg5OZmZM2cyd+7cnKXfmzVrxpsDB/LMH39gt2gRxMXB9Ol3/FkiIiKlSZENMddjMplyzXcJ\nCgoiPT2dYcOGkZqaymOPPcaWLVsoV66cDasUkWLHx8fogVm8GDZsgMhIYxPI25SYmMjUqVNZsmQJ\nGRkZAHR94gnC6tenTlwcpoEDrzZOTobw8HwJTSIiIqVFsQoxX3zxxTXHJkyYwIQJE2xQjYiUGPfc\nY/TGPPkk9O0LI0dCly5w9923dJu4uDhCQ0NZvXo1FosFk8lE9+7dCQ4OpomHB/w5f69sWejQAXr0\ngE6dFGBERERuUbEKMSIiBerFF2HHDujc+ZYCTGxsLCEhIWzatAkABwcH+vbtS1BQEPXr17/acPx4\n8PY2Aox6jEVERG6bQoyIyJ9MJpg3L09NrVYr0dHRhISEEBsbCxjz9gYOHEhgYCA1atS49qKJE/Oz\nWhERkVJLIUZE5BZkZWWxdu1aQkNDiYuLA4w9Xvz9/RkxYgTu7u42rlBERKTkU4gRkdJpxw44exae\nfTZPc1IuXbpEZGQk06ZNIzExEQAPDw9Gjx7N4MGDcf3r/jKffAJJSTBsWEFVLyIiUqopxIhI6WO1\nwtixRpB57z3o3/+GTc+fP88H4eFMXriQ5ORkALy8vAgKCqJv3744OTnlvmDvXvD1NTbPrF3bmP8i\nIiIi+UohRkRKn23bjADj5gbPP3/dJqdPn2b27Nk4hYcTeOkSkUBlb2/MZjM9evTA3t7+ehcZq5pd\nuAC9exu9PCIiIpLvFGJEpPSZPNl4HTkS7ror16mkpCSmT5/OwoULSU9PZxpQFthavTrlYmMx/a19\njowM6N7d2DSzaVNjyWYtnSwiIlIg7GxdgIhIvsrIgFdfhdTU65/fvRu2bDGWOPb3zzm8f/9++vXr\nh5eXF7NnzyY9PZ1OnTrxeEwMPPAAdx07humee+CRR+CDD669b1CQ0cNTvTqsX2/sBSMiIiIFQiFG\nREqWiRNhyhRo1Ai2br32/LvvGq9DhsDdd7Nr1y66detGw4YNiYyMxGKx4OvrS1xcHBs3buTxNm3g\nww+N/V0yMmDPHvjjj2vvO3y4EXA2bIBq1Qr2GUVEREo5DScTkZKlb1/47DP49lt4+mkIDDSGj/05\nAf/dd7E++iixlSrxZtu2xMTEAODk5ISfnx9jx46ldu3aue/54IPwww9w7hzExYGX17WfW6eO0cuj\nIWQiIiIFTiFGREqWOnUgNtYILhMnwvTpRqjZuhWLmxsboqMJiYxk165dALi6ujJkyBACAgLw8PC4\n+b3Ll4dWrW58XgFGRESkUCjEiEjx9vnncOyYsayxo6NxzMEBJkwwVgd74QUsNWqw9JNPCJs6lf37\n9wPg7u5OQEAAw4YNo2LFijZ8ABEREblVCjEiUnxZrcaE+j17IDMTXnop1+mLDz1E5KBBzH37bfZG\nRQHg6enJmDFjGDBgAC4uLraoWkRERO6QQoyIFF+bNhkBpmpV+O9/cw6npqYyZ84cZs2aRUpKCgAN\nGjQgODgYHx8fHP/ssREREZFiSSFGRIqOtDSoUCFvc0usVnjrLeN9UBCULUtycjIzZ85k3rx5nD9/\nHoBmzZphNpvp0qULdnZakFFERKQkUIgRkaKjRw9jfsvKldC48c3bbtkCO3dC5cocbNeOqS+/zJIl\nS7h8+TIAbdu2xWw289RTT2HShHsREZESRSFGRIqGI0eMfV3KlIH77vvn9suXA7DCw4MXvb2xWCyY\nTCa6detGcHAwTZs2Ldh6RURExGYUYkSkaFi61Bgi1rUr/MNqYbGxsYSmpOAMfBoXh52DA3369GHc\nuHHUr1+/cOoVERERm1GIERHbs1phyRLjfb9+uc8tWwZ792INCSF682ZCQkKIjY0FoGzZsgwaNIjR\no0fj6elZqCWLiIiI7SjEiIjtxcZCYiJUrw5t2149/ttvWAcMwJSRQcQHHzDixAkAKlasiL+/PyNG\njMDd3d1GRYuIiIitKMSIiO2lp8NDD0HnzmBvD8ClS5eIjIriJzc33j55Ev8TJzhWvjzur73G4MGD\ncXV1tXHRIiIiYisKMSJie888A3FxkJnJ+fPnmTdvHjNnziQ5ORkA10qVmHz6NCHnz2OqVg0UYERE\nREo1bZogIkXC6ZQUXps4EU9PT4KCgkhOTsbb25tVq1bxVnIyhIVhslph3Tr44w9blysiIiI2pJ4Y\nEbGppKQkpk+fzsKFC0lPTwegVatWmM1mnn322at7vAQFGa8xMZCRAeXK2ahiERERsTWFGBGxiYSE\nBMLCwli2bBlZWVkAdOrUCbPZTIsWLa5/UVDQ1TAjIiIipZZCjIgUqt27dxMSEsK6deuwWq3Y2dnh\n4+NDcHAwjRo1snV5IiIiUgwoxIhIgbNarWzdupWQkBBiYmIAcHJ0ZO899+D+3HO4hYdreJiIiIjk\nmSb2i0iBsVgsrFu3jubNm9O2bVtiYmJwdXUlKCiIY6tWUffECdyiosDZ2dalioiISDGinhgRyXeZ\nmZmsWLGCsLAw9u/fD4C7uzsBAQEMHToUNzc36NfPaNynT87eMCIiIiJ5oRAjIvnm4sWLLFq0iPDw\ncI4ePQqAp6cnY8aMYcCAAbi4uBgNL1yAtWuN93372qhaERERKa4UYkTkjqWmpjJnzhxmzZpFSkoK\nAA0aNCA4OBgfHx8cHR1zX7B2rbHXS8uWULeuDSoWERGR4kwhRqS0Sk835qL8uQ/LbUhOTmbmzJnM\nmzeP8+fPA9CsWTPMZjNdunTBzu4G0+5++MF4/XNImYiIiMgt0MR+kdLom2/AzQ2aNIHY2Fu+PDEx\nkZdffplatWoxbdo0zp8/nzNx/5tvvuG55567cYABePtt+PVX6NXrDh5CRERESiuFGJHSKCYGLl+G\n77+HVq3AxweuzGG5mfj4eHx9fbn//vuZP38+GRkZdOvWjZ07d/LZZ5/Rpk0bTHnt2alTB+666w4f\nREREREojDScTKY1efRU6d4aFC+G992DVKtiwAX75Be6995rmsbGxhIaGEhUVBYCDgwN9+vRh3Lhx\n1K9fP3fjQ4fg8GFISjKC0Z+vK1YYvT8iIiIid0ghRqS08vaGiAgYOxaCgoxjfwkwVquV6OhoQkJC\n2B4bSwXgQScnBvznP/y3fXsq9ewJrq7X3rddO0hMvPb4kSMKMSIiIpIvFGJESruaNeHDDyEzE4Cs\nrCzWrl1LaGgocXFxfAo8DdiDMQRt9WrjT4MG8K9/XXu/xx6DatWgRg3jj6en8XrffYX3TCIiIlKi\nKcSICACXsrOJfP99pk2bRuKVnhQPDw/qli+P/c8/Q4UK4O5u/LnnnhtvULlsWSFWLSIiIqWRQoxI\nKXf+/HnmzZvHzJkzSU5OBsDLy4ugoCD69OmDc0YGlC0Lf9/rRURERMRGFGJESouYGFi6FEaNAm9v\nTp8+zezZs4mIiCAtLQ0Ab29vgoOD6dGjBw4OV/56cHa2YdEiIiIi11KIESktZs6EqCjSKldmwvvv\ns3DhQtLT0wFo1aoVZrOZZ599Nu9LJIuIiIjYiEKMSGnw668QFUWmnR0NZszgRHY2AJ06dcJsNtOi\nRQsbFygiIiKSd9rsUqSE2717Nxs7dABgqcXCKasVHx8f4uLi2LhxowKMiIiIFDvqiREpgaxWK1u3\nbiUkJISdMTH8duX48e7d+SUsDC8vL5vWJyIiInInFGJEiqMdO6BOHahcOddhi8XChg0bCA0NZefO\nnQD8u2xZymZkcLlpU8avXWuLakVERETylUKMSHFz5gx07QrZ2UaYuf9+MjMzWbFiBYsmTyb2118B\ncHd3JyAggKFDh+KYlQUpKTYuXERERCR/aE6MiK2cOQO9e8OhQ7d2XUAAnDoFDz7IxWrVeOedd6hT\npw67+/Vj46+/0qNyZWbPns2RI0d49dVXcXNzg0qVoEGDgnkOERERkUKmnhgRWxk5Ej78EM6dg02b\n8nbNxo2wbBnWsmWZ+8gjvFG7NqdPnwago6srFc6fZ/XZs5g8PcHFpQCLFxEREbEd9cSI2MKGDbB8\nOZQtC7Nn5+2atDSyBw4E4BWLhWEzZ3L69GmaNm3KRx99RPszZ2DwYEyXL0O3bvD++wX4ACIiIiK2\noxAjUtiuhA0AQkONCfr/IDExkQXPPw8nTvA1MPXyZdq2bUtMTAzffvstXbt2xc7REebOhddfB4sF\nBgyA+fML9llEREREbEAhRqSwjRwJJ09Cq1YwfHjuc2fPQpcuEBsLQHx8PL6+vtx///0M/uwzHgdW\ntmvHNzt38tlnn9GmTRtMJtPV600mePNNeOcdqFoV2rQpvOcSERERKSSaEyNSmKxWePBBcHMzhnvZ\n/e33CBER8MknZH75JcMeeYSF//d/ADg4ONCnTx/GjRtH/fr1//lzhg+HPn2gfPn8fwYRERERG1NP\njEhhMpkgOBiOHLlmGJnVaiW6USN2uLnheO4cQf/3f9RwdmbkyJEkJiayePHivAWYPynAiIiISAml\nnhiRO7FxIy6//87FBx64tetcXXPeZmdns2bNGkJDQ4mLi6McEGtvT+PsbBIfegjHkBBjAQARERER\nAdQTI3L7Ll+GwYN5oG9f7oqLu3rcaoW334bff/+Hyy+zYMEC6tWrh4+PD3FxcXh4ePDGtGnU2b8f\natTA0WqFH34o4AcRERERKV4UYkRu1/LlcPw4F728uPDQQ1ePL1sGo0YZc182b77msvPnzxMeHk6t\nWrUYPHgwiYmJeHl5MX/+fA4ePMiYMWO4q25diI6GY8dgz55CfCgRERGRok/DyURuR3Y2TJ0KwIk+\nfXJP0H/8cWjRArZvhw4djGNLl5Ly7LPMnj2biIgIUlNTAfD29iY4OJgePXrg4PC3/xwbNoTDh8He\nvhAeSERERKT4UIgRuR0bNsDPP0PNmqQ+80zuc15e8OWXMG0avPoqWCxk+PnR1MGBw5cuAdCyZUvM\nZjMdOnTIvUTy35UpU4APISIiIlI8KcSI3I533jFeAwOx/r0HBcDenoTnnmPFjh14b9zIsqwsDmdl\n0alTJ4KDg2nZsmXh1isiIiJSgijEiNyO//0P5s+HAQNg375cp3bv3k1ISAjr1q3DarViZ2dHr969\niQsOplGjRjYqWERERKTkUIgRuR133w1mc86PVquVmJgYQkJCiImJAaBMmTL4+fkxduxYvLy8bFWp\niIiISIlTpFcnCwkJoWnTplSoUIHKlSvTpUsXfvrpp2vavfHGG1SvXh0XFxeeeuop9v3tN+MiBcVi\nsfDFF1/g5+dH27ZtiYmJwdXVlaCgIA4fPsy8efMUYERERETyWZEOMV9++SXDhw/n66+/ZuvWrTg4\nONC2bduclZ0AwsLCmDFjBhEREezatYvKlSvTrl07Lly4YMPKpaTLzMwkMjKSBx98kKCgIH766Sfc\n3d2ZNGkSR44cISwsDA8PD1uXKSIiIlIiFenhZJv/tsfG0qVLqVChAjt27KBTp05YrVbefvttzGYz\nXbt2BSAyMpLKlSuzYsUKBg0aZIuypQS7ePEi7733HuHh4SQlJQFQtWpVXnjhBd58801cXFxsXKGI\niIhIyVekQ8zfnTt3DovFgpubGwCHDh3i5MmTPPOXJW6dnZ1p3bo1O3bsUIiRfJOWlsYuX18Wb9/O\nynPnAGjQoAHjxo2jXr16ODg4KMCIiIiIFJJiFWJGjhzJww8/zL/+9S8ATpw4AUCVKlVytatcuTLH\njx+/7j12795dsEVKiZKSksLKlSuJXbOGfenpPA2k1qlDm0GDeOKJJ7D7yyaX+m5JQdL3SwqSvl9S\nkPT9kttRt27dm54vNiFm9OjR7Nixg9jY2JtvDnhFXtqI3Mhvv/3G0qVL2bhxIxkZGYQCTkBi48a8\ntWCBvl8iIiIiNlQsQsyoUaNYvXo1X3zxBffdd1/O8apVqwJw8uRJ7r333pzjJ0+ezDn3d02aNCnQ\nWqV4i4+PJzQ0lA8//BCLxYLJZOKFzp0Z88UX8McfeM2fj1fTprmu+fM3TPpuSUHQ90sKkr5fUpD0\n/ZI7cfbs2ZueL9Krk4ExhOzDDz9k69at3H///bnO1apVi6pVq7Jly5acY5cuXSI2NpbHH3+8sEuV\nYmz79u107twZb29vVq5ciZ2dHf369SMhNpalZ89i/8cf0KYNNGtm61JFRERESr0i3RMzbNgwli1b\nxvr166lQoULOHBhXV1fKlSuHyWQiICCAKVOmUL9+ferWrcukSZNwdXXF19fXxtVLUWe1Wtm8eTMh\nISFs27YNgLJlyzJw4EACAwPx9PSErCzIyICqVWH6dBtXLCIiIiJQxEPM3LlzMZlMPP3007mOv/HG\nG7z++usABAUFkZ6ezrBhw0hNTeWxxx5jy5YtlCtXzhYlSzGQnZ3NmjVrCA0NJS4uDoCKFSvi7+/P\niBEjcHd3v9rYwQFWrwYXF/jrcRERERGxmSIdYiwWS57aTZgwgQkTJhRwNVKkHDwIr74KXbvC88/n\nPrdpE/zvfzB/vhFCrrh8+TKRkZFMnTqVxMREADw8PBg9ejSDBw/G1dX1+p/l6VlQTyEiIiIit6FI\nhxiRa6SkwKRJ8O67kJkJe/dCz57w52phf/wB/frB6dNG2w8/5HxmJvPnz2fGjBkkJycD4OXlRVBQ\nEH369MHZ2RkuXYLx42HkSKhUyXbPJyIiIiL/SCFGioeMDHj7bZg8Gc6dM0JL377w1ltXAwxAuXLw\nySfQoQN8/DEHGzTgybQ0jqalAeDt7U1wcDA9evTAwcHBuNfChTB7Nhw4AAkJsHatjR5SRERERPKi\nyK9OJpLjvfeM0NG+PezZA0uWXHeo19Fq1Qjt2JFkoPbhw/wvLY1OzZsTFRXFnj176N27Nw6nTsHQ\noVCtGowYYQSYevUgOLjQH0tEREREbo16YqR4KFMG5s0zemTat79uk4SEBMLCwli2bBlZWVksAHaU\nLcuj2dlsnD4dWrS42tjeHhYtMoakPfkkDBsG//kPODoWyuOIiIiIyO1TiJGix2IBu+t0Ej711HWb\n7969m5CQENatW4fVasXOzg4fHx+Cg4Op6u4O+/blDjAAVaoYE/+bNYOGDQvgIURERESkoCjESNFh\nscCsWcawsW+/Nea33IDVauWLL74gJCSEzz//HIAyZcrg5+fH2LFj8fLyutq4WrXr38TPLz+rFxER\nEZFCohAjRce8eTB6tPF+zRpjlbG/sVgsfPzxx4SEhLBz504A7rrrLoYMGcKoUaPw8PAoxIJFRERE\nxBYUYqToWLTIeI2IMFYe+4vMzExWrFhBWFgY+/fvB8Dd3Z2AgACGDh2Km5tbYVcrIiIiIjaiECNF\nw08/GSuOVawIAwbkLJt88eJF3nvvPcLDw0lKSgLA09OTMWPGMGDAAFxcXGxZtYiIiIjYgEKMFA3L\nlhmvPXuCszNpaWnMmTOHWbNmcfr0aQAaNGjAuHHj8PX1xVGriImIiIiUWgoxUjQ8+CA0a0ZKx45M\nGzeOuXPncv78eQCaNm2K2WzmP//5D3bXW7VMREREREoVhRgpEg7+619M3baNJb17c/nyZQDatm1L\ncHAwbdq0wXRleJmIiIiIiH6tLfnrq6/A1xeSk/PUPD4+Hl9fX+rWrcv8+fPJyMigW7du7Ny5k88+\n+4ynn35aAUZEREREclFPjOSf33+HJ54w3mdlwerVN2y6fft2QkJCiIqKAsDBwYE+ffoQFBREgwYN\nCqNaERERESmm1BMj+efSJahXz3i/Zg38+GOu01arlejoaFq3bk3Lli2JioqibNmyjBgxgsTERBYv\nXqwAIyIiIiL/SCFG8k+1arB/P7z4ovHzq68CkJ2dzYcffsgjjzxCx44d2bZtGxUrVmT8+PEcOXSI\nWbNm4enpacPCRURERKQ4UYiR/GUywbRp4OKC9auvWBoeTr169ejduzc//PADVatWZerUqRw5coSJ\n/v5UevRRGDsWrFZbVy4iIiIixYTmxEi+O+/iwmZfX17/5BMSxo4FwMvLi6CgIPr06YOzs7PRcMkS\nOHYMEhJyNrcUEREREfknCjGSb1JSUpg9ezYRERGkpqYC4O3tTXBwMD169MDB4W9ft6VLjdc/h5+J\niIiIiOSBQozcvsxMGD2a4z4+hH34IQsXLiQ9PR2Ali1bYjab6dChw/WXSE5IgN27oXx5+Pe/C7lw\nERERESnOFGLktp0KDqZyRARnIiKYfeVYp06dCA4OpmXLlje/eNky47VHDyhbtkDrFBEREZGSRRP7\n5VqnT0NcHFgs1z29e/duhj/zDOVnzAAg0GTCx8eHuLg4Nm7ceP0AY7FAdvbVn48dM+bBaCiZiIiI\niNwihRi56vvvoW9fqF4dGjcGDw9YuBAw9njZunUr7dq1o1nTpvT47DOcgR3338/cX39lxYoVNGrU\n6Pr3/eoraNoUFi++emzxYkhKgtatC/65RERERKRE0XAyMcydC0OHGu9NJmPPl+PHsZQrx8fr1xMS\nEsLOnTsB8Hdy4snLl8l2d+fxr7+Gu++++b2PHzcC0htvwH//e3X42L33FtzziIiIiEiJpZ4YMXTu\nDPfcA6NGwYEDZB46xMeTJtF84kS6du3Kzp07cXd3Z+LEiYS+9hqUKYP9nDn/HGAAnn/e6Nk5dgze\nfbfgn0VERERESjT1xIihRg04fpyLWVm89957hIeHk5SUdOVUDcaMGcNLL72Ei4uL0f7FF41r8sLO\nDiZPhk6dICQEXnoJKlQooAcRERERkZJOPTGljdUKGRnXHE5LS2PytGncd999jBgxgqSkJOrXr8+S\nJUtITExkxIgRVwMMgKfnrW1Q2aEDtGoFZ87A9On58CAiIiIiUlopxJQ2X3wBXl4QGQnAiRMnGDdu\nHJ6enowfP57Tp0/TtGlTPvroI3766Sf69u2Lo6PjnX+uyWT0wtSpYwQgEREREZHbpOFkpYnVakyu\n/+03fo+P59UhQ1i8eDGXL18GoG3btgQHB9OmTZvrb1B5p1q0ALMZypXL/3uLiIiISKmhEFOafPEF\nbNvG+TJlqD1zJmetVkwmE926dSM4OJimTZsWfA39+xf8Z4iIiIhIiaYQU0psj42lQs+ePAiEZGTw\nh4MD/V54gaCgIBo0aGDr8kRERERE8kwhpgSzWq1s3ryZkJAQHLZtYytwBsgaPJjEV17BU3NTRERE\nRKQYUogpgbKzs1m7di2hoaH88MMPALS/6y6OubpS0c+PqZMn27hCEREREZHbpxBTgly+fJnIyEim\nTp1KYmIiAFWrVmX06NEMHjyY8q6ukJVl4ypFRERERO6MQkwJcP78eebPn8+MGTNITk4GwMvLi6Cg\nIPr06YOzs/PVxvmxXLKIiIiIiA0pxBRjKSkpzJ49m4iICFJTUwFo1KgRZrOZHj164OCg/3lFRERE\npOTR/8stho4ePcr06dNZuHAhFy9eBKBly5aYzWY6dOhQMHu8iIiIiIgUEQoxxcjPP/9MWFgYy5Yt\nIzMzE4COHTtiNptp2bLltRf8+itUqgQVKxZypSIiIiIiBcfO1gXIP/vuu+/o0aMHDRo0YPHixWRn\nZ+Pj48MPP/xAVFTU9QOM1Qr9+sF990FsbGGXLCIiIiJSYNQTU0RZrVa++OILQkJC+PzzzwEoU6YM\nfn5+jB07Fi8vr5vf4PPPYccOuOceaNy4ECoWERERESkcCjFFjMVi4eOPPyYkJISdO3cCcNdddzFk\nyBBGjRqFh4fHzW/w5Zewfr3xB2DsWLjrrgKuWkRERESk8CjEFBGZmZmsXLmSsLAw9u3bB4C7uzsj\nR45k2LBhuLn9f3v3HxRVvf9x/LkLrIDhjzu4gooCZmCUXkZgvqklpjJhTuWYFpY/UjMNEyUjUZqL\npaw65uSvzR+V6YyK13KqKW+jBakMWU2Kc5URddCwUhIVi/zJ7vn+wW1rQ8sRl3Xh9ZjZGfjs5+y+\nj/Me3Nee8zmnbd0pYmfOQHk5BAdDXFz9F9qzB954o+7nqChIT2/EvRARERER8TyFGE86cgQ6d4YW\nLa475cKFC7z99tssWrSIiooKACIiIpgxYwYTJkwgeO9eGDcOjh2rCy+//FK34ejRsG5d/RdMSQGn\nE3r0gPvv11EYEREREWlyFGI8xemExx6D8+dh+3a4+263p6urq1mxYgVLlizh9OnTAMTGxjJz5kxG\njhxJwG83payu/v3UMICQEIiOhoiIa79vfHzdQ0RERESkiVKI8ZT334fS0rojMXfe6Ro+deoUSxYt\n4rDdztaLFwH4v4QEbMOG8UBWFmbzny4Yl5QEmzfXnRoWHQ3/+AfoPjAiIiIi0ozpEsue4HTCa6/V\n/ZydDRYL5eXlTJ48mcjISE6//jrvX7xIaatWlI8cSXFlJck5OZh//LH+a1mtMGIEJCbWXWlMAUZE\nREREmjkdifGEDz+E//4XOnXiQGIitqeeIj8/H6fTCUCPXr24euwY3c+ehY0b67bp1g0qKqBTJy8W\nLiIiIiJy+1OIudUMA159FYA327Th+YQEAPz9/Rk1ahQvv/wy3bt3h5oasNvrFv8PHw4DB8KfTyUT\nEREREZF6FGJuIcMw+PQ//6Hw6lX6AtMPHCAoKIhnn32WF198kc6dO/8++Y47ICvLa7WKiIiIiPgq\nhZhbwOFw8N577zF//nxKSkoAWNOmDS9NmcLUqVNp166dlysUEREREWk6ml+I+fe/4dCh3x/btkFY\nWP15mzZBYCDExNRdXcxiqTfl8uXLrF+/noULF3L06FEAwsLCyMzM5LnnnqNVq1ae3hsRERERkWan\n+YWYJ55w//3QoWuHmKws+P77up+DgsBmg6lTwWTil19+YdWqVSxevJiTJ08C0LVrV7Kyshg9ejSB\ngYEe3gkRERERkear+YWYRx6B7t0hNrbu0aNH/TmGUbfY/tAhKCuD8nKYNo1Le/Ywv2v+acb1AAAM\nqElEQVRXltrtnDt3DoAePXqQnZ3N448/jr9/8/vnFBERERFpbM3vU/eHH/79HJMJFi92/Vplt9Mq\nI4MtW7Ywx+EAoG/fvmRnZ5OamooJ4K234PHHoW1bz9QtIiIiIiKAbnb5l8rKyhg3bhwdpk0jvraW\nZx0OBg8ezO7du9m9ezeDBw/GZDJBQQFMnAgJCXU3uhQREREREY9pfkdibsC3336LzWZj69atGIaB\n2Wymx5NPsnHmTHr27Fl/g//dF4bx43WvFxERERERD1OI+R/DMCgsLMRms/HZZ58BYLFYGDt2LC+9\n9BJ33nnntTfMz4ddu6BNG5gypRErFhERERFpnpp9iHE6nXz00UfYbDa+/vprAO644w4mT57M9OnT\nCQ8Pv/7G589DWlrdz9Ongy6pLCIiIiLicc02xFy9epVNmzaxYMECSktLAQgNDSUjI4P09HTa3sgC\n/WPHwGqFFi3qLr8sIiIiIiIe1+xCzIULF3jnnXdYtGgR3333HQARERHMmDGDCRMmEBwcfOMv9s9/\nwokTcPkyhIR4qGIREREREfmjZhdiIiMjOX36NACxsbHMnDmTkSNHEhAQcHMvaLHUPUREREREpFE0\niUtp2e12oqKiCAoKIiEhgaKiouvOPX36NImJiWzdupWDBw8yZsyYmw8wIiIiIiLS6Hw+xGzevJlp\n06aRk5NDSUkJvXv3JjU1lRMnTlxz/meffcZXX33F0KFDMetyyCIiIiIiPsfnP8UvXryYZ555hvHj\nxxMTE8PSpUsJDw/nzTffvOb8AQMG1N2gUkREREREfJJPh5grV66wd+9eUlJS3MZTUlIoLi72UlUi\nIiIiIuJJPr2wv6qqCofDQfv27d3GrVYrp06duuY258+fb4zSpBnp1q0boN4Sz1B/iSepv8ST1F/i\nST59JEZERERERJofnw4xoaGh+Pn5UVlZ6TZeWVlJeHi4l6oSERERERFP8unTySwWC7169WL79u0M\nGzbMNb5jxw6GDx/u+r1169beKE9ERERERDzAp0MMQGZmJqNGjSIpKYnevXuzcuVKTp06xaRJk7xd\nmoiIiIiIeIDPh5gRI0Zw5swZ5s6dy8mTJ7n33nvZtm0bERER3i5NREREREQ8wGQYhuHtIkRERERE\nRG6UTy/sv1F2u52oqCiCgoJISEigqKjI2yWJj7HZbCQmJtK6dWusViuPPPIIBw8erDcvNzeXjh07\nEhwcTP/+/SktLfVCteLrbDYbZrOZF154wW1c/SU36+TJk4wZMwar1UpQUBBxcXHs2rXLbY76S25G\nbW0ts2bNIjo6mqCgIKKjo3nllVdwOBxu89Rfcqs1+RCzefNmpk2bRk5ODiUlJfTu3ZvU1FROnDjh\n7dLEh+zcuZMpU6bw5ZdfUlBQgL+/PwMHDuTcuXOuOQsWLGDx4sUsX76cb775BqvVyqBBg6ipqfFi\n5eJr9uzZw5o1a+jRowcmk8k1rv6Sm1VdXU2fPn0wmUxs27aNQ4cOsXz5cqxWq2uO+ktuVl5eHqtW\nrWLZsmWUlZWxZMkS7HY7NpvNNUf9JR5hNHFJSUnGxIkT3ca6detmZGdne6kiaQpqamoMPz8/4+OP\nPzYMwzCcTqcRFhZm5OXlueZcvHjRCAkJMVatWuWtMsXHVFdXG127djW++OILIzk52XjhhRcMw1B/\nScNkZ2cbffv2ve7z6i9piCFDhhhjx451Gxs9erQxZMgQwzDUX+I5TfpIzJUrV9i7dy8pKSlu4ykp\nKRQXF3upKmkKfv75Z5xOJ23btgXg2LFjVFZWuvVaYGAgDzzwgHpNbtjEiRMZPnw4/fr1w/jDckX1\nlzTEBx98QFJSEk888QTt27cnPj6eFStWuJ5Xf0lDpKamUlBQQFlZGQClpaUUFhby8MMPA+ov8Ryf\nvzrZX6mqqsLhcNC+fXu3cavVyqlTp7xUlTQFGRkZxMfHc9999wG4+ulavfbjjz82en3ie9asWUN5\neTkbN24EcDuVTP0lDVFeXo7dbiczM5NZs2axb98+13qr9PR09Zc0yPPPP8/3339P9+7d8ff3p7a2\nlpycHNetLtRf4ilNOsSIeEJmZibFxcUUFRW5fdC8nhuZI81bWVkZs2fPpqioCD8/PwAMw3A7GnM9\n6i/5O06nk6SkJObNmwdAz549OXLkCCtWrCA9Pf0vt1V/yd9ZunQpa9euJT8/n7i4OPbt20dGRgaR\nkZGMGzfuL7dVf0lDNOnTyUJDQ/Hz86OystJtvLKykvDwcC9VJb5s+vTpbN68mYKCAiIjI13jYWFh\nANfstd+eE7meL7/8kqqqKuLi4ggICCAgIIBdu3Zht9uxWCyEhoYC6i+5OR06dODuu+92G4uNjaWi\nogLQ3y9pmHnz5jFr1ixGjBhBXFwcTz/9NJmZma6F/eov8ZQmHWIsFgu9evVi+/btbuM7duygd+/e\nXqpKfFVGRoYrwNx1111uz0VFRREWFubWa5cuXaKoqEi9Jn9r6NChHDhwgP3797N//35KSkpISEgg\nLS2NkpISunXrpv6Sm9anTx8OHTrkNnb48GHXFzH6+yUNYRgGZrP7x0mz2ew6kqz+Ek/xy83NzfV2\nEZ7UqlUr/vWvf9GhQweCgoKYO3cuRUVFrF27ltatW3u7PPER6enprF+/ni1bttCpUydqamqoqanB\nZDJhsVgwmUw4HA7mz59PTEwMDoeDzMxMKisrWb16NRaLxdu7ILexwMBA2rVr53pYrVY2bNhAly5d\nGDNmjPpLGqRLly7MmTMHPz8/wsPD+fzzz8nJySE7O5vExET1lzTIkSNHePfdd4mNjSUgIIDCwkJm\nz57Nk08+SUpKivpLPMer10ZrJHa73YiMjDRatGhhJCQkGLt37/Z2SeJjTCaTYTabDZPJ5PaYM2eO\n27zc3FwjPDzcCAwMNJKTk42DBw96qWLxdX+8xPJv1F9ysz755BOjZ8+eRmBgoBETE2MsW7as3hz1\nl9yMmpoa48UXXzQiIyONoKAgIzo62pg9e7Zx+fJlt3nqL7nVTIZxAytHRUREREREbhNNek2MiIiI\niIg0PQoxIiIiIiLiUxRiRERERETEpyjEiIiIiIiIT1GIERERERERn6IQIyIiIiIiPkUhRkRERERE\nfIpCjIiI3HaSk5Pp37+/t8sQEZHblEKMiIh4TXFxMXPmzOH8+fNu4yaTCZPJ5KWqRETkdmcyDMPw\ndhEiItI8LVq0iKysLI4fP07nzp1d47W1tQD4+/t7qzQREbmN6X8HERHxuj9/n6bwIiIif0Wnk4mI\niFfk5uaSlZUFQFRUFGazGbPZzM6dO+utiTl+/Dhms5kFCxZgt9uJjo6mZcuWDBw4kIqKCpxOJ6+9\n9hqdOnUiODiYRx99lDNnztR7z+3bt9OvXz9CQkIICQkhNTWV/fv3N9o+i4jIraGvukRExCuGDRvG\nkSNH2LRpE2+88QahoaEAdO/e/bprYvLz87l8+TJTp07l7NmzLFy4kOHDh5OcnMzu3bvJzs7m6NGj\nLF26lMzMTNatW+faduPGjYwaNYqUlBTmz5/PpUuXWL16Nffffz/ffPMNMTExjbbvIiLSMAoxIiLi\nFffeey/x8fFs2rSJxx57zG1NjGEY1wwxP/zwA0ePHqVVq1YAOBwObDYbFy9eZN++ffj5+QHw008/\nkZ+fz+rVq2nRogW//vorU6ZM4ZlnnuGtt95yvd748eOJiYnh1VdfZcOGDR7eYxERuVV0OpmIiPiM\nYcOGuQIMQFJSEgBPP/20K8D8Nn716lVOnDgBwI4dO6iuriYtLY2qqirXo7a2lr59+1JYWNi4OyIi\nIg2iIzEiIuIz/ni0BqB169YAREREXHP83LlzABw+fBiAQYMGXfN1/xiARETk9qcQIyIiPuN6YeN6\n479d9czpdAKwbt06Onbs6JniRESk0SjEiIiI1zTWDS27du0KQGhoKA8++GCjvKeIiHiO1sSIiIjX\ntGzZEoCzZ8969H0eeugh2rRpQ15eHlevXq33fFVVlUffX0REbi0diREREa9JTEwEIDs7m7S0NCwW\nCwMGDADq3wCzIUJCQli5ciVPPfUU8fHxpKWlYbVaqaio4NNPP+Wee+5h7dq1t+z9RETEsxRiRETE\na3r16oXNZsNutzNu3DgMw6CgoOC694m5luvN+/P4iBEj6NChA3l5ebz++utcunSJjh070qdPHyZN\nmtTgfRERkcZjMm7lV10iIiIiIiIepjUxIiIiIiLiUxRiRERERETEpyjEiIiIiIiIT1GIERERERER\nn6IQIyIiIiIiPkUhRkREREREfIpCjIiIiIiI+BSFGBERERER8SkKMSIiIiIi4lP+H2MJDA2BjPWA\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc106320>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n",
      "\n",
      "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n",
      "\n",
      "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n",
      "\n",
      "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(measurement_var=100.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9+vUxadIkeHt7w9DQULrEcvv27dG3b9+aelmEEEIIIbXH8uX884oVQHBwzbal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\njIiIiIiIFCv/H3ixldyLqJhRAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc3e2518>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(measurement_var=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8vQl3c6PAK6/QLDDwnsWiJOYflMDkDPocRURERO6OqKgo3n//faZOncqZM2cA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\nFBEDAAAU5RsbfhirTVm5qgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc070898>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n",
      "\n",
      "So let's first look at the plot with some process noise but no measurement noise to obscure the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "np.random.seed(1234)\n",
      "test_sensor(measurement_var=0, process_var=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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spk2bZhwyUqtWLcLDw+nbty82NjaPFE6RWCcmv92bycnjZOJJk9vlIj/J8SXy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\n4gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fbfe9588>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will stay there until the random changes in velocity happen to result in the track going back to the original track. \n",
      "\n",
      "Finally, let's look at the combination of measurement noise and process noise."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(measurement_var=1, process_var=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hyJBX18+fnytXrhAWFsaCBQuIi4sDoFmzZuh0Otq0afOPe05JEiOEEEIIIURe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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fbfaa0b8>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Math with Gaussians"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "stats.plot_gaussian(mean=23, variance=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0+Ni1axdWrFiB1atXIyUlBSEhIZg4cSLu379f5/YajQZKpRLLli1D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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fbecd860>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n",
      "\n",
      "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n",
      "\n",
      "Let's look at 100 sensor readings in a plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(x0=23, velocity=0, \n",
      "                measurement_variance=5, process_variance=0.0)\n",
      "xs = range(100)\n",
      "ys = []\n",
      "for i in xs:\n",
      "    ys.append(dog.sense_position())\n",
      "               \n",
      "bp.plot_track(xs,ys, label='Dog position')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9C0DnjXH//v1obGxEr169UFpaqvlzNzU1oaCgAOPHj8dnn32m+fPJha3u6Pnv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\nERGR6f4/3fs/Qljg5S0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc0132e8>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n",
      "\n",
      "\n",
      "Recall the histogram code for adding a measurement to a preexisting belief:\n",
      "\n",
      "    def update(pos, measure, p_hit, p_miss):\n",
      "        q = array(pos, dtype=float)\n",
      "        for i in range(len(hallway)):\n",
      "            if hallway[i] == measure:\n",
      "                q[i] = pos[i] * p_hit\n",
      "            else:\n",
      "                q[i] = pos[i] * p_miss\n",
      "         normalize(q)\n",
      "         return q\n",
      "         \n",
      "Note that the algorithm is essentially computing:\n",
      "\n",
      "    new_belief = old_belief * measurement * sensor_error\n",
      "    \n",
      "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. \n",
      "    \n",
      "If we are implementing this with gaussians, we might expect it to be implemented as:\n",
      "\n",
      "    new_gaussian = measurement * old_gaussian\n",
      "    \n",
      "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n",
      "$$\n",
      "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n",
      "\n",
      "In other words the result is a Gaussian with \n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
      "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
      "\\end{aligned}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n",
      "\n",
      "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "\n",
      "def multiply(mu1, var1, mu2, var2):\n",
      "    if var1 == 0.0:\n",
      "        var1=1.e-80\n",
      "        \n",
      "    if var2 == 0:\n",
      "        var2 = 1e-80\n",
      "        \n",
      "    mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
      "    variance = 1 / (1/var1 + 1/var2)\n",
      "    return (mean, variance)\n",
      "\n",
      "xs = np.arange(16, 30, 0.1)\n",
      "\n",
      "mean1, var1 = 23, 5\n",
      "mean, var = multiply(mean1, var1, mean1, var1)\n",
      "\n",
      "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
      "plt.plot (xs, ys, label='original')\n",
      "\n",
      "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
      "plt.plot (xs, ys, label='multiply')\n",
      "\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Uq3hpW46Gda1YsQLz589HZGQkqlSpgiVLlsDLyyvTc4ODg7F48WKcO3cOsbGxKF++PEaP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\niIhkgZMTIiIiIiKSBU5OiIiIiIhIFv4Flm9O6+r0HZYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f26f1160>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n",
      "\n",
      "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
      "\n",
      "\"Measure twice, cut once\" is a useful saying and practice due to this fact!  The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n",
      "\n",
      "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.arange(16, 30, 0.1)\n",
      "\n",
      "mean1, var1 = 23, 5\n",
      "mean2, var2 = 25, 5\n",
      "mean, var = multiply(mean1, var1, mean2, var2)\n",
      "\n",
      "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
      "plt.plot(xs, ys, label='measure 1')\n",
      "\n",
      "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
      "plt.plot(xs, ys, label='measure 2')\n",
      "\n",
      "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
      "plt.plot(xs, ys, label='multiply')\n",
      "plt.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QEBAAHx8fHD58GIaGhtiyZUuxzzd8+HDo6uqiXr16GDZsGIYNG4Zu3boV+pqc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\n46IAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f014fac8>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n",
      "\n",
      "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24?  Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n",
      "\n",
      "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n",
      "\n",
      "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n",
      "\n",
      "One final test of your intuition. What if the two measurements are widely separated? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.arange(0, 60, 0.1)\n",
      "\n",
      "mean1, var1 = 10, 5\n",
      "mean2, var2 = 50, 5\n",
      "mean, var = multiply(mean1, var1, mean2, var2)\n",
      "\n",
      "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
      "plt.plot (xs, ys, label='measure 1')\n",
      "\n",
      "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
      "plt.plot (xs, ys, label='measure 2')\n",
      "\n",
      "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
      "plt.plot(xs, ys, label='multiply')\n",
      "plt.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Tk22+V6lUonv37oK6U6dOOWRcRORbWgoeTP/WZGdnm+sMBgM+/PBDm9oLDAwU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\nGzACfp5BtrbF0mi3wxohvaW4uBhZWVm2tkajwfjx40WMSL6ES7v27t0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       "text": [
        "<matplotlib.figure.Figure at 0x7f85f268c748>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n",
      "\n",
      "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
      "\n",
      "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
      "\n",
      "$$\n",
      "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
      "$$\n",
      "\n",
      "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n",
      "\n",
      "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n",
      "\n",
      "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n",
      "$\\sigma_1^2=0$, yielding\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n",
      "\\text{or just}\\\\\n",
      "\\mu&=\\mu_1\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n",
      "\\text{or just}\\\\\n",
      "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing the Update Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n",
      "\n",
      "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def update(mean, variance, measurement, measurement_variance):\n",
      "    return multiply(mean, variance, measurement, measurement_variance)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:\n",
      "\n",
      "    def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n",
      "        return multiply(dog_pos, dog_sigma, measurement, measurement_variance)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n",
      "\n",
      "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSensor` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(velocity=0., measurement_variance=5, process_variance=0.0)\n",
      "\n",
      "pos,s = 2, 5\n",
      "for i in range(20):\n",
      "    pos,s = update(pos, s, dog.sense_position(), 5)\n",
      "    print('time:', i, \n",
      "          '\\tposition =', \"%.3f\" % pos, \n",
      "          '\\tvariance =', \"%.3f\" % s)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "time: 0 \tposition = 3.566 \tvariance = 2.500\n",
        "time: 1 \tposition = 2.147 \tvariance = 1.667\n",
        "time: 2 \tposition = 2.152 \tvariance = 1.250\n",
        "time: 3 \tposition = 1.261 \tvariance = 1.000\n",
        "time: 4 \tposition = 0.745 \tvariance = 0.833\n",
        "time: 5 \tposition = 0.796 \tvariance = 0.714\n",
        "time: 6 \tposition = 0.638 \tvariance = 0.625\n",
        "time: 7 \tposition = 0.722 \tvariance = 0.556\n",
        "time: 8 \tposition = 0.871 \tvariance = 0.500\n",
        "time: 9 \tposition = 0.973 \tvariance = 0.455\n",
        "time: 10 \tposition = 0.898 \tvariance = 0.417\n",
        "time: 11 \tposition = 0.817 \tvariance = 0.385\n",
        "time: 12 \tposition = 0.965 \tvariance = 0.357\n",
        "time: 13 \tposition = 0.445 \tvariance = 0.333\n",
        "time: 14 \tposition = 0.360 \tvariance = 0.312\n",
        "time: 15 \tposition = 0.384 \tvariance = 0.294\n",
        "time: 16 \tposition = 0.470 \tvariance = 0.278\n",
        "time: 17 \tposition = 0.445 \tvariance = 0.263\n",
        "time: 18 \tposition = 0.292 \tvariance = 0.250\n",
        "time: 19 \tposition = 0.457 \tvariance = 0.238\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n",
      "\n",
      "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n",
      "\n",
      "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n",
      "\n",
      "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing Predictions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track non-moving objects? The histogram used a loop of sense and update functions, and we must do the same to accommodate movement.\n",
      "\n",
      "How how do we perform the predict function with gaussians? Recall the histogram method:\n",
      "\n",
      "    def predict(pos, move, p_correct, p_under, p_over):\n",
      "        n = len(pos)\n",
      "        result = array(pos, dtype=float)\n",
      "        for i in range(n):\n",
      "                result[i] =  \\\n",
      "                pos[(i-move) % n]   * p_correct + \\\n",
      "                pos[(i-move-1) % n] * p_over + \\\n",
      "                pos[(i-move+1) % n] * p_under          \n",
      "        return result\n",
      "        \n",
      "                \n",
      "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n",
      "\n",
      "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n",
      "\n",
      "How is addition for gaussians performed? It turns out to be very simple:\n",
      "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n",
      "\n",
      "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n",
      "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n",
      "\n",
      "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n",
      "\n",
      "So, here is our implementation of the predict function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def predict(pos, variance, movement, movement_variance):\n",
      "   return (pos + movement, variance + movement_variance)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What is left? Just calling these functions. The histogram did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# assume dog is always moving 1m to the right\n",
      "movement = 1\n",
      "movement_variance = 2\n",
      "sensor_variance = 10\n",
      "pos = (0, 500)   # gaussian N(0,500)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, \n",
      "                measurement_variance=sensor_variance, \n",
      "                process_variance=sensor_variance)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(10):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "    print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n",
      "    \n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "    \n",
      "    print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n",
      "\n",
      "    \n",
      "bp.plot_filter(ps)\n",
      "bp.plot_measurements(zs)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "PREDICT:     1.0000   502.0000\tUPDATE:     4.0880     9.8047\n",
        "PREDICT:     5.0880    11.8047\tUPDATE:     4.1639     5.4138\n",
        "PREDICT:     5.1639     7.4138\tUPDATE:     6.8504     4.2574\n",
        "PREDICT:     7.8504     6.2574\tUPDATE:    10.4530     3.8490\n",
        "PREDICT:    11.4530     5.8490\tUPDATE:     9.5694     3.6904\n",
        "PREDICT:    10.5694     5.6904\tUPDATE:     9.2446     3.6267\n",
        "PREDICT:    10.2446     5.6267\tUPDATE:    10.7525     3.6007\n",
        "PREDICT:    11.7525     5.6007\tUPDATE:     8.3439     3.5900\n",
        "PREDICT:     9.3439     5.5900\tUPDATE:     8.8032     3.5856\n",
        "PREDICT:     9.8032     5.5856\tUPDATE:     7.2800     3.5838\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xjh07FJ1Op8y+52/NnXPda9KkSYper1cuX76sKIqixMfHKzqdTpk2bVqBsep0OmXixIm5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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f26e4940>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n",
      "\n",
      "    movement = 1 \n",
      "    movement_variance = 2\n",
      "    \n",
      "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the `predict()` step.\n",
      "\n",
      "For now let's walk through the code and output bit by bit.\n",
      "\n",
      "    movement = 1\n",
      "    movement_variance = 2\n",
      "    sensor_variance = 10\n",
      "    pos = (0, 500)   # gaussian N(0,500)\n",
      "    \n",
      "  \n",
      "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we initialize the RFID simulator with\n",
      "\n",
      "    dog = DogSensor(pos[0], velocity=movement, \n",
      "                    measurement_variance=sensor_variance, \n",
      "                    process_variance=sensor_variance)\n",
      "\n",
      "It may seem very 'convenient' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n",
      "\n",
      "The next code allocates an array to store the output of the measurements and filtered positions. \n",
      "\n",
      "    zs = []\n",
      "    ps = []\n",
      "    \n",
      "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we just enter our `update() ... predict()` loop.\n",
      "\n",
      "    for i in range(10):\n",
      "        pos = predict(pos[0], pos[1], movement, sensor_variance)\n",
      "        print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
      "\n",
      "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `,DogSensor.sense()` assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the `sense()` first.\n",
      "\n",
      "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n",
      "\n",
      "    PREDICT: 1.000 502.000\n",
      "\n",
      "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the prediction step.\n",
      "\n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    \n",
      "Here we sense the dog's position, and store it in our array so we can plot the results later.\n",
      "\n",
      "Finally we call the update function of our filter, save the result in our *ps* array, and print the updated position belief:\n",
      "\n",
      "    pos = update(pos[0], pos[1], Z, movement_variance)\n",
      "    ps.append(pos[0])\n",
      "    print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
      "    \n",
      "Your result will be different, but I get\n",
      "\n",
      "    UPDATE: 1.6279 , 9.8047\n",
      "    \n",
      "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n",
      "\n",
      "Now the software just loops, calling `predict()` and `update()` in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n",
      "\n",
      "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%precision 2\n",
      "# assume dog is always moving 1m to the right\n",
      "movement = 1\n",
      "movement_variance = 2\n",
      "sensor_variance = 4.5\n",
      "pos = (0, 100)   # gaussian N(0,100)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, \n",
      "                measurement_variance=sensor_variance, \n",
      "                process_variance=0.5)\n",
      "\n",
      "zs, ps, vs = [], [], []\n",
      "for i in range(50):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)    \n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    vs.append(pos[1])\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "       \n",
      "bp.plot_measurements(zs)\n",
      "bp.plot_filter(ps)\n",
      "plt.legend(loc=2)\n",
      "plt.show()\n",
      "\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()\n",
      "\n",
      "for i in range(0,len(vs), 5):\n",
      "   print('{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(*[v for v in vs[i:i+5]]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KIJxcCa/VkRZ1uuHpducvhOX+okRCREREJIeWb1uYlkQAXIg9x+R5L/NYy2E0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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f2739160>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LlZWVuvXWW8PxeAAAAAAOEpYQcs011+jIkSNasGCBDh06pCFDhujV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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc020d68>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "102.0000 6.3099 4.6267 4.2812 4.1939\n",
        "4.1708 4.1646 4.1629 4.1624 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\""
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Animating the Tracking"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n",
      "<img src='animations/05_dog_track.gif'>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
      "\n",
      "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementation in a Class"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n",
      "\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance) \n",
      "    \n",
      "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n",
      "\n",
      "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n",
      "\n",
      "    class KalmanFilter1D:\n",
      "        def __init__(self, initial_state, measurement_variance, movement_variance):\n",
      "            self.state = initial_state\n",
      "            self.measurement_variance = measurement_variance\n",
      "            self.movement_variance = movement_variance\n",
      "\n",
      "That works, but I am going to use different naming. The Kalman filter literature has settled on one letter notations for each of these concepts, and so you might as well start getting exposed to it now. At first it seems impossiblely terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondance with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them. If you do not make this effort you will never be able to read the Kalman filter literature.\n",
      "\n",
      "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the movement error. This gives us:\n",
      "\n",
      "    class KalmanFilter1D:\n",
      "        def __init__(self, x0, R, Q):\n",
      "            self.x = x0\n",
      "            self.R = R\n",
      "            self.Q = Q\n",
      "            \n",
      "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n",
      "\n",
      "    def update(z):\n",
      "        self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
      "        self.P = 1 / (1/self.P + 1/self.R)\n",
      "\n",
      "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n",
      "\n",
      "    def predict(self, u):\n",
      "        self.x += u\n",
      "        self.P += self.Q\n",
      "       \n",
      "That give us the following code. Production code would require signficant comments. However, in the next chapter we will develop Kalman filter code that works for any dimension, including 1, so this class will never be more than a stepping stone for us, since we can, and will use the class developed in the next chapter in the rest of the book."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class KalmanFilter1D:\n",
      "    def __init__(self, x0, P, R, Q):\n",
      "        self.x = x0\n",
      "        self.P = P\n",
      "        self.R = R\n",
      "        self.Q = Q\n",
      "\n",
      "\n",
      "    def update(self, z):\n",
      "        self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
      "        self.P = 1. / (1./self.P + 1./self.R)\n",
      "\n",
      "\n",
      "    def predict(self, u=0.0):\n",
      "        self.x += u\n",
      "        self.P += self.Q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Relationship to the g-h Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* and *h* to the variances.\n",
      "\n",
      "The equation for our estimate is:\n",
      "\n",
      "$$\n",
      "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
      "$$\n",
      "\n",
      "which I will make more friendly for our eyes as:\n",
      "\n",
      "$$\n",
      "\\mu_{x'}=\\frac{ya + xb} {a+b}\n",
      "$$\n",
      "\n",
      "We can easily put this into the g-h form with the following algebra\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n",
      "\\mu_{x'}&=x-\\frac{a+b}{a+b}x  + \\frac{ya + xb} {a+b} \\\\ \n",
      "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n",
      "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b}  \\\\\n",
      "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "We are almost done, but recall that the variance of estimate is given by \n",
      "\n",
      "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} +  \\frac{1}{\\sigma_2^2}}\\\\\n",
      "= \\frac{1}{ \\frac{1}{a} +  \\frac{1}{b}}\n",
      "$$\n",
      "\n",
      "We can incorporate that term into our equation above by observing that\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n",
      " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n",
      " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
      " &= \\frac{\\sigma^2_{x'}}{b}\n",
      " \\end{aligned}\n",
      "$$\n",
      "\n",
      "We can tie all of this together with\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
      "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
      "&= x + g_n(y-x)\\\\\n",
      "\\blacksquare\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "where\n",
      "\n",
      "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
      "\n",
      "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n",
      "\n",
      "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n",
      "\n",
      "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#####Exercise:\n",
      "Modify the values of `movement_variance` and `sensor_variance` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n",
      "\n",
      "    movement_variance = 40\n",
      "    sensor_variance = 2\n",
      "    \n",
      "or:\n",
      "\n",
      "    movement_variance = 2\n",
      "    sensor_variance = 40"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction to Designing a Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n",
      "\n",
      "We do not have a real sensor to read, so we will simulate the sensor with the following function. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def volt(voltage, temp_variance):\n",
      "    return random.randn()*temp_variance + voltage"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n",
      "\n",
      "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
      "\n",
      "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly  +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
      "\n",
      "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
      "\n",
      "As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change over time. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `movement_variance = .2`. This is just the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n",
      "\n",
      "Let's see what happens. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variance = 2.13**2\n",
      "movement_variance = .2\n",
      "actual_voltage = 16.3\n",
      "\n",
      "N=50\n",
      "zs = [volt(actual_voltage, variance) for i in range(N)]\n",
      "ps = []\n",
      "estimates = []\n",
      "\n",
      "kf = KalmanFilter1D(x0=25,            # initial state\n",
      "                    P = 1000,         # initial variance \n",
      "                                      # large says 'who knows?'\n",
      "                    R=variance,       # sensor noise\n",
      "                    Q=movement_variance) # movement noise\n",
      "\n",
      "for i in range(N):\n",
      "    kf.predict(movement)\n",
      "    kf.update(zs[i])\n",
      "\n",
      "    # save for latter plotting\n",
      "    estimates.append(kf.x)\n",
      "    ps.append(kf.P)\n",
      "\n",
      "# plot the filter output and the variance\n",
      "bp.plot_measurements(zs)\n",
      "bp.plot_filter(estimates)\n",
      "plt.legend(loc='best')\n",
      "plt.xlim((0,N));plt.ylim((0,30))\n",
      "plt.show()\n",
      "plt.plot(ps)\n",
      "plt.title('Variance')\n",
      "plt.show()\n",
      "print('Variance converges to {:.3f}'.format(ps[-1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uuWYWLCtB5KOrOHPjMHLz5WeMamJqiwEdx6Olk0+lA4HSAUdKxhvpCEdcwgOZ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bAAAg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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc3e2c88>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VPMGDvTwAAACAoBU0wYPdywEAAIDgFTTBgxUPAAAAIHgFTfBgxQMAAAAIXkET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\nVVFRkZYsWaJjx45p0KBBeuedd9S9e3d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       "text": [
        "<matplotlib.figure.Figure at 0x7f85f8033e48>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Variance converges to 0.858\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
      "\n",
      "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The section **Explaining the Results - Multi-Sensor Fusion** explains why this happens."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Animation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
      "\n",
      "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our inital uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src='animations/05_volt_animate.gif'>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement, and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. \n",
      "\n",
      "> If this is not clear, I urge you to go back and review the g-h chapter. This is the crux of the algorithms in this book. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise(optional):"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n",
      "\n",
      "> use plt.hist(data,bins=100) to plot the histogram. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variance = 2.13**2\n",
      "actual_voltage = 16.3\n",
      "\n",
      "\n",
      "def VKF():\n",
      "    voltage=(14,1000)\n",
      "    for i in range(N):\n",
      "        Z = volt(actual_voltage, variance)\n",
      "        voltage = update(voltage[0], voltage[1], Z, variance)\n",
      "    return voltage[0]\n",
      "\n",
      "vs = []\n",
      "for i in range (10000):\n",
      "    vs.append (VKF())\n",
      "plt.hist(vs, bins=100, color='#e24a33')   \n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AAACAq0Z0RcThcEiS3G63nE5noN3tdge2ORwOeb1enT9/PuiqiMvlUmlpadhj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\n43uHYu7cufrd736nzz//XM8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       "text": [
        "<matplotlib.figure.Figure at 0x7f85f0149a58>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Discussion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Explaining the Results - Multi-Sensor Fusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**author's note:** I am not overly keen about this explanation. It is true that multiple sensors improve results, but we get good results merely by having an accurate model of the process. I explain this much better in the next chapter. I'll leave this section here while I mull how best to explain this at this stage of learning. For now don't worry if this section is not entirely convincing; it does need work.\n",
      "\n",
      "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30\n",
      "movement_sensor = 30\n",
      "pos = (0,500)\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, \n",
      "                measurement_variance=sensor_variance,\n",
      "                process_variance=0.5)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "vs = []\n",
      "\n",
      "for i in range(100):\n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "    vs.append(pos[1])\n",
      "\n",
      "    pos = predict(pos[0], pos[1], movement+ random.randn(), movement_variance)\n",
      "\n",
      "bp.plot_filter(ps)\n",
      "bp.plot_measurements(zs)\n",
      "plt.legend()\n",
      "plt.show()\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Intx3332kpKQwd+5cEhISmDt3bpbDpmbNmkWxYsXo3LkzFy5cyPipXr06ISEhrFixIqOu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\nUzQAAIDsFA0AACA7RQMAAMjuAwDePrgD1wmsAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f26ee278>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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//nydPn1aCxYsaHHjaq7r4LW5AAAAQORp0ZqO/Px8FRUVadSoUYGy+Ph4jRgx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\nrXpc0k89LukXKPObfhWfPqq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       "text": [
        "<matplotlib.figure.Figure at 0x7f85f003b0f0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distinctly jagged. But, it still mostly tracks the dog. What is happening here?\n",
      "\n",
      "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43.  From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n",
      "\n",
      "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n",
      "\n",
      "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagrees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematical model this sort of reasoning."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More examples"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Extreme Amounts of Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30000\n",
      "movement_variance = 2\n",
      "pos = (0,500)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, measurement_variance=sensor_variance)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(1000):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "    \n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "\n",
      "bp.plot_measurements(zs, lw=1)\n",
      "bp.plot_filter(ps)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+3H3tsRhhGIZhGIZhGMZh3OlW5ekJREW5rz2wGGEYhmEYhmGYkoskua+t1auB3bvd1x5Y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\nAAAA4ARhBAAAAIAThBEAAAAATvwLBH4fJ/Bx5kQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f268c7f0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Bad Initial Estimate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30\n",
      "movement_variance = 2\n",
      "pos = (1000,500)\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(100):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "    \n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "bp.plot_filter(ps)\n",
      "bp.plot_measurements(zs)\n",
      "plt.legend(loc='best')\n",
      "plt.gca().set_xlim(0,100)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xp8qKxQKhoeYnN/bvJ7VzJ5wTEljTJJjf2jsuxmNYLYx6sT0prjd+FbZgoatR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2PHXn9FyYYN5uT+9evNnxnGBQAAgA6iXQqTTZs2afbs2Zo/f76KioqUnZ2t8ePH69ixY03f4HZL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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85eabceef0>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Large Noise and Bad Initial Estimate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What about the worst of both worlds, large noise and a bad initial estimate?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30000\n",
      "movement_variance = 2\n",
      "pos = (1000,500)\n",
      "\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance) \n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(1000):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "    \n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "bp.plot_measurements(zs, lw=1)\n",
      "bp.plot_filter(ps)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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unToB995Lv//8MxAbq95vMMj1REQMiBBLL79M4kPLhUtsE69iPenjQ69uPABn\nS4mCqR8PK9H+F0/b4LyRG6SkpOC2gy9nYVaQN998EzNmzEBCQgIWLVpkt/+5557Dl19+ifHjx2Pq\n1KmIj4/HkiVLsH//fsTExMCY/wdFp9Ph3LlzeOSRR/D0009j4sSJqF27tmcujmEYhmHKO336FO7n\nXxqkp9PiVJIQdOCA+kl/cbBa5YVqUdm+nRa//fsX7fj0dPV7WwHSpQvFaxw7RsHtn38O1KhBn1NA\nALXJzVUfoxQU4eGyq5Krbmre3kCVKuptWVkU1F6/PtCyJW1LS5MX/rbB9ADwzDNA+/baiRPuu49c\n1MR5vvkGGDgQaN5cbvP441SfRJklTYiSvXuBJ5/U/vxE4gGlKFm2TB7Hli1Ahw6Fz0E+LEruYgYM\nGKB6r9PpcOzYMafH9enTB9WrV0dKSgpGjx6t2rdv3z4sX74cq1atwmOPPaY6V9euXfH1119jYv6N\nJkkSzp8/j02bNmHw4MEeuCKGYRiG+ReRmAiEhpb2KNSkpZEFx2qFpNfDY47eb73lmX6UqXndxfaB\nrW0q3kqV6Of114EvviBR0ro1/cyZQ21ycuj11i1y6xIZsZo2BX78kdylANnCkp5Or47iObQKVGZk\nkAjy8pIFQuPGNCbRt9a1CRc5W65eVWcPy83VtljVqUPWKGUKYvH6zDPax/j7Aw0byuc2GOh6hCtY\nxYouW0vYfesuZsmSJdi5c2fBz44dO+CrlS7ODdasWYOAgAD069cPt2/fLviJjIxEeHg4du3apWpf\nq1YtFiQMwzAMUxT+8x+5WndZIS0NMBigs1gglUDsabEpTkxKxYpqAZCVpV2p/N57KXZFifBMEaJk\nyhSqXi7Gs3gxWVXEnFks1PdLLwGrVjkek1a1dKUoEYt9vV5dYd0W2+KJ58/L1dV9fOheu3aN3u/c\nqXZbEwQFkVCztZQ4q+g+eLAsurp0oZoojsZVCGwpuYvp0KGDXaD7pUuXitVnXFwcMjIyUMXWlJjP\nLZusFBElmS+cYRiGKX1+/ZUyARW2KGGKhtZT8tImPR04fBjGK1fK3tiA4okSg4HiKUQ/Xl7AiRPy\n/oQEcl3LzbV3Vbp9m0SHKEYoMpOJhXvFiur2wn1LWdH9l18oE5bSBcxqtbckBAaSK1ZqKokSi4Xa\nRUYCY8aoRUlqKnDnjv3if8MG4H//o37OnqWfKVPIkpOaSi5ZtoiYmqeeAm7ckK/VmShZuJBejxwB\nhg8nC5K34cIYAAAgAElEQVTAy8t+bhzAokSBp2M+7kasVivCwsLw/fffa+6vaHNjcaYthmGYck6f\nPpQJqG3b0h5J+UNrQVra3H8/0KAB9Hl5nhclsbG0sC5qbZYXXgAOH6aF89Wr5DLlDjqdHI9iMlFl\n9EaN5P2vvEIZtiTJ3lUpOBj4+muKw7h8meJbBg2iz9DX1/774etL1deVFd1nzVJXdxcCy/YeCA8n\nUXDqFImSVauA69dlcaAUJXv2UGHKBg3UoqRmTYpHUQa0f/st8N579LtW6YiQELKUTJ2q3u5MlAge\nfRT46Sf1nAYEAC4+MC+DEpj5J3AUCF+/fn0kJyejY8eO6NWrl91PmzZt/uGRMgzDlHHeeMNxtePy\nQLVq9oG4jGcoi5YSoCBOIq19ewpU9hR9+lDqXFdZu5YCsAXdu9PC+dVXqTBfcTAa7QPGRa2ORo3U\nKX8Bqr3Rqxf9fvQoXYcQB8qAcUH16iRilIUHtdZe8+dr1zbx9iah8+mnajeq55+neRCIVL62lhLx\nXhlnIlwFw8KAWrXU58vOps/dNvgfINe0evXst9uSk0N95OQ4jm8phDL4TWD+Cfz9/ZGsUcxm5MiR\nsFqteOedd+z2WSwWpNgGhTEMw/zbmTMHeP/90h5FyeGsYjRTdKxWYPTowgvulQbe3oBOh7R77vFc\nzIuyeKKrfPIJLewFXbrQk/5ixs86xGwGHnsMqF2bPheAYjP++EPdTogESSJXpZgYed/lyzRugdJ9\nyxadjmp6XLhgv8/Hh641Kkp9vg4dtCu6z5snpykG1KKkVSvaZjKRNej55ymoXcmcORSob5uhDAC6\ndaMHL/Hx9vt27ADefJN+F6LEz09+kNGjB4k4F2BR8i+lQ4cOSE1NxQsvvICoqCh89913AICuXbti\n8uTJmD9/PgYOHIiPPvoIy5Ytw/Tp0xEREYFNmzaV8sgZhmGYfxRlpWfGs4in/WWtVomXF3Rms2eL\nJz7zDFWvd6c/W/FRqRJZJSIigMmT3R+D2Vx4nRMRv3HrlhzQvncvxWYoEW5XIrjbaqUYjowMEgyT\nJsltg4MLr9nhqHiijw/VKvHxof0TJ5KLltaYhaVEWN3OnaPrED9CxFy4QAUODQb7c5rN9HDlmWe0\n52b9enIps+XmTdk9KydHdnsTc5Sc7HIcEP+VuUtxtxq7bftJkybh+PHjWL16NZYsWQKArCQAZfVq\n27YtPv30U7z55pvw8vJCnTp1MGLECPQSpssijIFhGKZc0r+//VPH8gSLkpLj7bcpXiAtjeIbygr5\nKYELgrk9gbCUuCNKJk7UTkOblaUOpnaVs2eBBx+kyuiFjfHQIWp37pyc2leJ1Qo89BDwyCP0PieH\nqpYLi1dIiNz2//5P/t0dUeLtTSJHWFr0eur/zh2KF1GO2XZ8999PVpZ+/eTv7+DBwP79ZMHo1Mne\neuPMIuooi5bJRGmEr12jeTh+XH2tWvPnAP4rcxcyfvx4jB8/XnNf3bp1YbW5ubXa+/n5YcWKFQ7P\n8cQTT+CJJ54odBwXL150ZbgMwzDlm3XrymZcgKd45ZWSc5dhaNGpDH4ubaxWYOdOZB44gAqnT3vO\nUmLrvmU2k+ApbCHcrBm5U9nSp49jl6jCsFiozolIuStJFCtx4QJ9h2vUIBFkMqnHK77fx4/TftsE\nBceO0YJcp6MA/OXLtc/ftSvw0UfqbVqiZM8eEiAVK9L9IQTDX3+R2PjtN7ltcLB9vIeXF1V+Dwsj\nAdO9O9CmDTBgAMWI9eljPzblw4fFi8lK88QTslh2JJ5MJpq/AweAdu3kNMRizqxWir+RJKdJHViU\nMAzDMExx8Pcv7RGULI0by24kjOfRcqUpTR55RI6r0Ok8bykRC9/PP6cUsp9+6viYRo3UmZymTqUM\nXO3aFW8MJhOJjaQkEhFmM93fy5dTlqu8PLVlRzzpX7WKFvq9ewN9+8r9rl0r/169OmXZSk0li0zH\njvK+efPsx6S12N+xg2qlBASQGBEuVTt22D8AGTqUfpQYDGQVun0bePZZ6uv6dUr1q4x/USIC5sU4\nTSaq+i5ESWGWEoD2RUdT4g9AbSnp2ZNiVbKytC1fYioc7mEYhmEYhpk5kxZuTMmg17sX/F3SpKUB\ngYHQZ2Yi8PBh+yKC7nLpEi2EzWbghx9I7ABqC4Sr/P47WTmKiphni4ViIVq3VmfHAsgtbOdO+Z5X\njlNklmrfXhYKZjNZJWw5fZrqghRGVhZZGGyrvQtLTkICuYUJrFaqGyRqrTjCYCCxoHSbqlaNaojU\nqEGWEGWFd4BEmRiHxUICRYilCROAxERt8SzmTryKubIt9GixAF99VeiwWZQwDMMwDOMYTwY72/LR\nR8CaNSXT993CypVAw4alPQqZtDQgKAiGzEwEHD5MT8uLw5w5FJ8BqF21RHFBRwwfTgHnSo4fl4PI\nL12ip//uoLR+iJgZW1Eye7Y6A1WjRhSDAZAoURY+BMja8tNP9udydn0AnTcw0D69sRAlH38sW4XS\n0+Vznz1r39eCBcCMGfR7aiqJJ3H+t98GVq8m97G1a8maYev+tnAh8OSTdA6LheZFfO9//ZUsLlqB\n9qNHA507q0XJm2/Kmbr+/puu0YX5YFHCMAzDMIxjPBnsbMv58/TE+t/K0aP05DogoLRHIpOerg50\nLy733EPJINatA4YMkbdnZBT+2a9bR4t9kQVLcPgwvS5aBDgo9OwQsSgWWam0REmTJpTlS9C7t1wr\nxWiUx5OURALOkWAXi/DsbMfZ1RzVqcnIILdQLy9ZSPXuTVYVQPucOp3c9uJFtaUkJUWuD3P+PPWv\n5UZ18iTVRrFa1aJEBPYrA+wF1aqRWBHnNhhoLEKAhoSQFUZYXwqBRQnDMAzDFIdPPgG2bSvtUZQc\njgJcPYEbmXnuCnbtcrl6NQDg9dcpeLkskZYGeHtDbzJB8kSWTUexCL//ro7FsKVfP3pyf/CgersQ\nyMoFu6u0b08i0GKR7z1bUQKQC9fnn9sfL9y3AHJrXLlSHs/DD6vbClGyejUwfbr2eBwJv9xcEg3K\na9TrZSGh9X1UzrOXF8W2iKDz9HSyAAEkLgBg9277PoKDScDYum85E6idOslueW3a0I8SLy8WJQzD\nMAxT4kyaVLSaCXcD2dkUjFxSouSTT4D//Kdk+i4NevUi/3tXKYsV3TMzgenTEbp9u/3Ytm1zP8hc\nLEhtcZY4oXJlerWNQ5Akcms6c6ZIVcPxzTdkCREL7ZgYIDyc9p0/T6LDZNK2JDRqBLRoQb8LC6L4\nbnToQK9mM9U1EaJHmcjgzz/pOJE21zaLl+CRR2jezp2j/kSmsh49gJdfVn8fExMpHa8QJZJE7bt2\npbiYkycpW5comC2EwY8/ktVJGXwfEkKuX9OnU0KBGjXkcdreC4mJwNat9Puzz5LgO3qUYpCEu54g\nPJz60BJ6CsrYN8HzSCVlcmaYUoDvZ4Ypo9i6mJQXMjPpNSys5M5RljJPeQJ3LD+OFqWlyZ07QGgo\ndHl59mOLj6caHu5gMMji4cwZuZbHK68A993n+DghFJQuWh9/TNt//JHckYqSIKB7d7KE6HTUV82a\n8kJ96FASArm52qKpb1/guefoOvbskWNTatWi6wFoTJMm0QK/fXt1IoOpU0k0tGxJQsKRKB01itIM\nf/89zd38+VRjRLicKb8zK1ZQbJYQJaJN48ZUZPLnn+X4jhkz1C5sx45RMUWBvz/9LXvtNbrOWrVo\nu5YoOX+esowJTp4Enn5ae86PHaN5PXNGe38+LouSPXv2YMiQIahZsyb0ej1Wrlxp12bWrFmoUaMG\nKlSogJ49e+LkyZOq/bm5uZgyZQoqV66MgIAADB06FFdtMnokJydj7NixCAkJQUhICMaNG4fU1FRX\nh6nCx8cHOTk5sJSlrBYMU0QkSUJOTg58OC0nwzD/FGYzFVsTFaFLgrK2KC8ODRu6Z0koi5aS/HgA\nq58f0tu2VbtYFeXBWIsW8pPzxx6jxSug7TalRARV+/lRMcDbtyk2xdeXLHiBgUWzlAgiIiiFrRJR\nq2PQIFrUO2LfPrIKWK3UvkkTeZ+3N/XTpo1cPV2sQ20FeHAw8M475DJli7c3CbjYWLUb1Zgx6hTA\nwk1MnEfUNFG+F8yfr07V26yZ/N3OyKC2QUH2MTBff001U2zHp/z8cnLkekZZWeprNZlIDPbvb3+d\nClyuU5KZmYmWLVvi8ccfx7hx4+yqec+bNw8LFy7EypUr0ahRI7zzzjvo27cvzpw5g4D8AK4XXngB\nmzZtwnfffYfQ0FBMnz4dgwcPxsGDB6HP/1KOHj0aCQkJ2LZtGyRJwoQJEzB27Fhs2rTJ1aEWoNfr\n4evrC5PJhLyiFNlh/pWk52fdCAwMLOWR2GM0Ggu+KwzDMCVOSVdzHzu2aJW5yyrvvCO7vLiC1Upu\nMitXUkB4WcHbGxZ/f6R16IBKmzbJlcuLQmoqWQ1MJloQiwW6M1Ei3CJ9felp/61bQJ06VCtkwgSq\nvVG9etHHpYXZDGzZIlszAHrKbzZTALhALLglicagjCnT6+nHVhwojwNou48PsH49CTBl3ROA9m3a\nBFy+LB+n08nuYwIhSiZOpJ/sbLIACbcxsxlo3pysP2fPksVlwAA6LixMDoAfMYLmvEoVEiVK62jf\nvlTDpUMHOV7k77/Javb++zQmo1EWJf7+5Op25gyJO2HtUmY108DlvzQDBw7EwPy0cLbVwSVJwqJF\ni/Daa6/hwXw1vHLlSoSHhyMqKgpPP/00UlNT8eWXX2LFihXo3bs3AGDVqlWoU6cOdu7ciX79+uHU\nqVPYtm0b/vzzT3TMLzbz2WefoWvXroiLi0MjZQEdF9HpdDAWUqiFYWyJjY0FALRv376UR8IwzF1D\neXrar6SkRUmjRuXL9W3kSPfat25Nfv137pTMeIqKlxd0ZrN9Omjx1N2d+2LvXopnePVV4MQJuT9/\nf7kwny2ZmXQcILtRXb9OFol77qEn8ZMnqwsranHiBJ1HWANycmjRbvvUX3l9qanAlSvU1mgENm6k\nBb1SlAiLkaOHl0JweXtT7Q+RXU1c+6xZwIYNZP1xlEhCZK/y8aH9b79N1gaAKqgnJADdusmxK+KB\npb8/xa5cuSK7cwUGktg4e5bGU6ECHacUJeIzPXVK+5q2baP2QpQIL6a4OHKBCwmRRYnoD8AdcyZO\nnd2Ns+Pa4ULjCnhJu3cAHoopuXjxIm7evIl+/foVbPP19UW3bt2wb98+AMDBgweRl5enalOzZk00\nadIE0fnms+joaAQEBKCTyAcNoHPnzvD39y9owzAMwzBlimHDqGJxeaSkRUlJ1kC5G5g/nxbZZW0O\nAgJokWv7+QgB6Y6QFPEIomq66K9xY8dFAK9cofiL8+fl9spYnexs+4KDWjRvTql0BT//TBm9HGGx\n0LVnZ1MwfGamdoY4q5WsNY5iKJRWoGHDKPBdHAdQYHhKCi3sHYkSIcbEnOn11P7GDbJSLFsmj9nW\ng+L558m9bPhwmvfGjemcANUzee01spYEBsqB/c6+67ZFPsWcmEwFFpjEYB/8snkxFj9/H94b2whT\nPx6GWVPa4furv+FQ25pIqVB4vJVH/tLcuHEDAFClShXV9vDwcFy7dq2gjcFgQJhNsFyVKlUKjr9x\n4wYqi2wL+eh0OoSHhxe00eKAyNvMMB6E7yumJOD7qvyhf4me/VlL+bMtiXvLKyUFocOGIbGErk3X\nuzckQK6/8C+kQXo6bp0+jVQR2O2A4D17UHX1apxZvtxj527foQMOREfLi1Gx6MxPG1tx+3bcSUrC\nhfzPR9+2LRo3bIgzBw7A4mJtlWpXrkCfm4uQjAx4Gww4d+IEMoxG6Mxm+uw1FsJ+Z86gHoAz8fEI\nfeQR1PngA5yOi0OGvz8AIGziRCRfugRrIWtDAGgPICc3F7H5468YF4f6Gzbg+IYNyM2vuRHxyiu4\nOXYsMps3R2TlykhKTUXw9esI1OlwPCYGVRISIOn1uH7gAAwpKahw/jyMly/DPykJlx3ctzWHDMG1\nY8dgtXFNrBMZiRvvvovc+HhUjY+HISMDfunpuHXmDFIV69/Ka9bAEhSECABHTp5E5Rs3AIMBpoUL\nEXjwIFK6dUNYYiLOHziAytnZkLy8cFsxlvrp6TB8+SVujhxJqZ2bNUNK3bpoD+BSQgJud+hA8U8H\nDyLk/feRevAgGiUn4+q5c8gIDETVlSuRFx6OjObNkVunDs1TaiqSz51Dcv55Kicnow6A5Js3YThy\nCMcbhuCHntVgufAb0EBR58UNSvDxB2Ebe2ILZxNiGIZh7masSpeFcoY5JAS5NWvC+/Zt5FUq2kKj\nMKSStMLcJUh6PXQuWEqMV68iUBQOdJFKP/4Iq58f7gwYoHFiWn/pLJaCzyFk926Ebd2K8yIjk06n\nCm63BgTgZFSUW2OA1QpJp4POYkF2vXoF35fqn3wCS2AgbtiEBACAIScHVqMRloAA3Bo+HHU++ADQ\n61HvrbcQP2MGkgYPdunUmZGRyKlXTzUWADBkZECXlwdDZia8UlOhz84GAJxZvhxB0dHQ5+ZCMhig\nU9YzAeAbH48a//0vEp5/vtDvfcKLL8Lr9m0YExKQ3bBhwfbLr79e8HvYli3wu3wZKV262FlKqnz/\nPc4uXAizvz8kLy9cnzgRAFBp40ZAr4fk5UXZ0QDcevRRu/NLBgMqnD0Ln8RE3LKJB1KKySpRUciO\niIDk7U3uel5e0FmtqLr8M1zv3gmWED/k1aiKk9f+xs77fOHnEwfjRT0MegNqhJqROLIfjlbT4+T9\nkTB7Fd/5yiN/Darm+wTevHkTNRXVHm/evFmwr2rVqrBYLEhKSlJZS27evInu+T5yVatWxa1bt1R9\nS5KExMTEgn60YN9/xpOIp418XzGehO8rpqQo8Xvr5ZfJB57vXee88gowbZp7AdhhYahYr57z+U1M\nBE6edO9z/v57ICQEEVrH5KcjbqdMy3v8OFCnDtq3b4+jW7ci4OhRhD77LEKL89kvWUKF+gwG+K5b\nh6YREbQ9PByoXBk1tfpOTgbCw+laJQkwGNA4MhKIiUFYixbqiuuFMXs2/P39ESbOcfo0AKBpZCRd\n/xtvAKGhCIqIkOc/K4tcx3x80Lp5c4rFCAhAjfbt6Rg/PzR+5hkAQARA7k/x8fbxLd99R3EjTqrO\nh+zdi5A5c9Sfv06HFu3aAQ0aoE2vXrIwPHwYWLoUlUJCgAoVHN8LlSoBFgvqRESgjrLNyJGoX7s2\nBaA/9hjw4Yd03vbtgcqV0bhVK5wLNeDdN3ojuaIfgH3A3/vyB6oHkAJco2Kfx40A7nUtSYVfrgU9\n6vdApBRSaDuPxJTUq1cPVatWxfbt2wu25eTkYO/evejcuTMAoF27dvD29la1SUhIwOnTpwvadOrU\nCRkZGar4kejoaGRmZha00SIp9aYnLoNhGIZhGFtKMu7jtdeoCnp54YMPqFK5O8ydS0XxCmPTJvLd\nd7fEQV6evXvUb79Ralat2hNpaQXB2963biHgyBH7SuXuUrcuZZDS6dRjEVmjtFDGjOh0VOBPZIUa\nNIi237xJtS8KY8QIQGlVUWbBErEYtlnAWrWiVxFn0aaNumCi7Xfh3Dm5SrqSwq5PSUQEFTpUYjLR\nuGJi5DnLzCQBlJxMGcgU62kAJIAeeojGnJ5Owfm25//2WxLMIsYlM5MC4wHErfgIS69sxuLNs/MF\nSdFpluaNCQP+D48PmI7RnZ7AzM23MbBaJ0T4Fy7W3UoJfPbsWQCA1WrF5cuXceTIEYSFhaFWrVp4\n4YUXMGfOHDRu3BgNGzbEe++9h8DAQIwePRoAEBwcjKeeegozZsxAeHh4QUrgVq1aoU+fPgCAJk2a\nYMCAAXjmmWewfPlySJKEZ555Bg888AAaKsxftpy4dADdWt3v6qUwDMMwDOMqonJ1SXDqVNlKhesJ\nfvsNyF/7FKDTUaFAkVFKcOAApYMNKfwJMoYOBcaPd18cirS0SvLy5ErktsHiikWqpmgpCr1705z8\n8Yf9OERRP0lSZ7CrVAno0kV+nx+3BYuFFuoA8NNPVC/kiy9cH4sIHle6ZdmKkuBgygqWkUHtlO5P\nymBvUSHdUQFM0b/JRPMqMn6dP0+f+aRJwM6d2p9pXh6NVRSelCRg3DjteibKseXlkRVkyxa6Dg1R\nZL1xA/FIQ9alQ7he1YTYxG1I/vIn3Em/pdGp6/ibdWjctAt6XgFqHzsJRCoscNJ8YMcOSulcCC7f\nbTExMWjbti3atm2LnJwczJw5E23btsXMmTMBADNmzMCLL76IyZMno0OHDrh58ya2b98Of3FzA1i0\naBEefPBBjBgxAl26dEFQUBA2b96sijuJiopCq1at0L9/fwwYMABt2rTBqlWrCh1b7MV/b4AcwzAM\nU8osWGC/2CxPOMoO5Am0Mhvd7Ti6ntxc+21TpsjFBJ3RuDGlXnUHLUuJxULbfHzsi+SJDEwmEww5\nOZ5Jde3lpW3hycoCFi+m3999V041CwCdO1P1cVuU4/Hycr944qhRJA6Vlc+16qXk5gKXLtkvokXt\nD4Cqyy9a5LgApuh/7161JSUhgV5DQuQsZ7aYTPT5iJonQiAGBMhC8u237cdmsdC1tGxJYlAR/5Nn\nzsO+2O1YcP57LHywNj7d+A42NvPF+axrLgmS8JDq6N1uGLq1uh+1wxtAp9OjcnA1tG7YGWNr9sX7\nAQPw+MCXULtpR7WgBChF8axZlBGsEFy2lPTo0QNWJ3+UZs6cWSBStPDx8cHixYuxWNyEGoSEhDgV\nIbacvXIcWbkZqGB0LRMEwzAMw3iM//s/uVBYeePCBXqa+/LLJdP/5s3k5z9kiGf6+/VXck0qTqXv\n4uJIlGhZm1yt6N6hA7l4vfKKe2P59luqLyHSwQI0N47GmF/NHcuXo+bSpfaJCCZNoqf8Tz7p3Loj\nEE/7bVHWkDt0CDhyxL6N2QzMnEkF+sT4AGD2bBpHUT7nhQvp2KNHaWzLlsnWoRMngKZNZVFgS0gI\n0KsX/S7SHGtZlH74gVL3ikrrYv38229yimJJouO1hN+MGSTajh0j8ZWdTe1HjSJXr//7P1lsXrlC\nBUiVFdy9vOgz79cP2bt/wx855/Drhd+RbcoCXKgLXS2sNnpZauCeDg8gK6IWLFXCEXQnQ3XfWKwW\nGL6JAgY8Rtd/7BhZj7p0sRclzz9PlpJFi0icOKBclIa2WM2IvRBT2sNgGIZh/q1kZZX2CFzHatVO\nwStJ9sJK+Oy7U6XcXdyNkyiMAwc8219RcEeUOHL9ERw6RItygwGIjqZYAneYOBFo1ky9LS2N6koA\n5FaknK+33qIn8F5e0IsK7EquXiVXqvwadC6hrGh+8aLsgrR0Kb1Kkr2LmUCnA/7zH/n9+vX0umWL\nbClJTHR87iVL7ONO7rkHCA2l4ytVAipXlosJtmhB58zNVYsmQZ06wEcf0QL877/pGC1R8sEHFP/R\nvLna5WvsWLnN0KEU26HXA9euqS1mb7xBc/XKKzR/L7wArFunPpcQJe+9RyIof56zczJwsEEgVmcf\nwrIp3fD2wcX46fTPJEicUL9GM7z46Dy8NmYxOj7+CnRNm8LfNxBBaTl212jQG6hWi8lEGyZPdmwJ\nWbKEhLUTyoUoAYC4K8dKewgMwzDMv5W7qaL7Tz9pLxD27CEXISVmMzBwIC2uSgpnc3ftGlXzdgV3\n3Zs8TatWtNBXuiIJimIp+d//gHfeoWDtW7fIEuQOWpmqYmNl8dmhQ0FGKhXe3sgLC0N6mzbAypXy\n9txcqtrtTvHEGjVo8QoAL74oJwIQge9aLmYC4bo0dCi9F0HrAQG0CE9KAlq3dnzuN94AfvlFe1/X\nrsDatfR7mzYkAL286DOZOtWxUALoqf/PP9PYjEaq+aHE2xvo0weYPl0typQeR15eZJV59VWgY0d7\n8QhQtq3MTLKEiOMHDwb69lXVljmPVHx1dTvmdPfDKwcXYWXnEOy/GI3T9SsitxDvyMharfBgTk28\nlByB90cuwbSH3kW9apH2DTdv1v6eKl3frl6l75/VSvE4triQOr3ciJKEWxdLewgMwzAMU/ZxZEnI\nr9WgwtWK7qdOacdMOOP5550/Qf30U8DVgoFVq8ruNaXBhx8C3btTMLMrWK30VP3HH7X3i5iGN96g\nLE3uBp57e9u7OD3yiCwytfbnbzdVroz0tm0pta0gJ4dcmNwRJUePkljLzbWvCi4WtYVZSgDKPnbh\nAr1/4QUgKIgsHJGRVOXcEenplJWqMCSJXMfOnqV7Xaejz1GcOzra3oIoxIUk0Vwq50h5XYBjUWK1\nkrjasUOOM1Fy6xbNszL7ncFArqKbNpFwAvBHSBY+zo3G4dSzuBFUeHxWBWMAerR+AG81HIvFm9Ix\n+aHZ6KmvgzqZBgS2vocymmkxeDAJuN9+o7TRcXEkVDIzgZ49yW3r6lUSoLdvUwa3iAgatygDomV5\nsqHcVC26kRSPPLMJ3l4aPoAMwzAMwxDNmpFPvSu4KkoeeADYupX6zcighVzfvs6Pa96cnlAXhtIn\n3xlVq5Jlp7To3Zvco2wLAqalaccodOhA7kWOLEGVKwNPPEG/FyUblrBE2G4TGdVEYLTGcTqz2T7J\ngRAl7gjQrVtJXN13H6UXVvbXqJEceK/k0CE6j6hpApC4iYggy0hSEom/zp2Bzz4r/PzKvjMy6LoD\nFYEVly7RYvr++9Vtc3Pp/VdfAe3akQASiD6Cg7XPqRQlRqPcTlz7e+/Rov7ECZrjPn0o5bESZd9W\nK7BsGa726YQDe1ci4cY53L5xEUmWDKBW4ZcPAF7Qo1eHh9C99QMIrBBMabjFWHx86Fqdfdf37QNq\n1ybrT0iI7FZ38CBw5w7Nh58f/Q7QvWK1yu56nTrJLnsOx1lOsEpWXLt9GXWqOk4dzDAMwzAeZ9Qo\n7YVdWcVRit/77gO++Ua9zVVRolwwx8dTAUFXskq5UgNFpDp1hWbNtN1g/kmEO5QyzW2gg+jiTz8l\nawCqN5EAACAASURBVJGYg9WrKXZAWE5MJrJCzZ1LcQ+XL7s3Fq3MUsJakZhIi2KtufXzoyB3288n\nJ4cWy+5YSqzWggKIKqsBIAe3z5mjFlzLllHsx9NPy9vEcenp8nx6eck1RxzF8ii3L15Mx8+dqx5D\n69b293rv3rTw1soQZ7VS0P+rr2qfUznvrVuTNUQc16AB9f311yRE9PqCjGcquncH4uORY8pGTHAG\n9uf9hctR27TPZ4PRqkcDSyAqZprRICEDjQaOQEDnEXKD2rXlVMdGo1yTpbDvurhvxo2T510QG0tC\nEZBjeJRplwHg0UftxboN5UaUAMCF66dYlDAMwzD/LF98UXIpc0uC8HD1okwQGGhfX6NpU1pMOEMp\nSrKy7OtfOOLJJ2VLgCNsF7JlHSH4tGqEaCEWe5JEgdDKuZs4kUTAunUUG7Jzp3tj6dXLPr5FWJ7E\nPasUJXl5NJ4HH8SlWrUQ+PffagH7yy9kORA1N1xBnMvLS231MplkoVK1KvD55+pxCMvS6NGU2lYc\n16MHWS4AEk1GIz3pd3TP2RZs/M9/yLIninIvXSpbfpo2VR+nTB0M0L39++/OExQMHqwd39SrFwnR\nihWBFSvklL89ewIPPkht0tNh+XQZjgzpjO0xa3E9KR6oBsBJqSBvgw+GdBmHto26wP/9D6CfM5cS\nP+zeDdSzqTZfvz6JKgDo148sdt98o56rH38k8SLmWnx2jRuT5U/5N69xYzmF8/799CpEiZg7nc7+\noYcN5SamBADOXNZIJ8cwDMMwJYmfn5xS9G4gKEhdEK4wmjenBdRFJ3Gbly+TrzmgLsDnDC8v5wt3\nd9y3ygJCQNk++XaEEF2ivdJiINLBBgcD3bq5P5Z335XdaQR+frSIVMZFCKZMUcfv2LpvVasGvP46\nMHKk62NQipK6dWW3pLFjKWuUFkqXrilT6DUvjwLemzcnVyCBECVaNG+uDvQXn82NGzSvycnAxo1U\nHT00VF1vSGT3Uj7tv3OHhGLr1oUX/Zw0ib5ncXHq7WvXUoyFXk/nnDQJFr0OuSGBuBnmhztpidh/\ndBvmZuzCyq0fkiBxgRqV6uL5h99B99aDEVghBHqDlzze6dO1Ey/cuUNW3ogIEh62CQe2bKFAe4EQ\nzz4+dK9arfRAoUIFcm2bN4/aifvFVpR4eckJCxxQriwlZ6/GwmTOhY+X82AahmEYhmFc4JNPaBFa\nr55r7ZOTKZOXwGIhd5+iCrf33yfrjlj0FEZiImWL+r//K9q5isPNmzTGYcOAWrXkjEnOEKIkM5ME\nmq0AS0mhKuYjRgBNmrg3poMHySqgpF49Sq175Qo9ze/eXd6ncIMyXr6MgGPHyJpVHFJSKHDcy4vc\ntJTnchQjo6yl0qwZFQPMy6OMV0pOnaKn/o7urQULKGBc2a8495YtFKDuSBgJUaIcpxDIgwbJ7TIy\n6LOvX199/Pff03dBcd/m5uXg6LloHD77JxKebIzUwJYAbgPZ24BVCtesUMeZqnSShIa6UAz87xaE\nH42DweBlX6dPzF1hhUkzM9UiLCBALUqEIM3KAh5/nOJ/rFa6t4Vbn8lkn1VLWJBsRQlAmfRCQx0O\nqVyJkjyzCScuHkCbhvc5b8wwDMMw/0YyMmihER7uWntX4j4A2eJhWyX8t99oYablevTUU1T3Quk2\nY8uYMa6nJE5JoTS6pSFKkpOphoXRSAtUV4PSp0yhucvKooWhbRa0NWvIZz821n03Nq10u0uWUCar\nF16wH6NClPheuQL/48dJlBaH7t2piGPVqg7PZYfSUhIYSKmERfaxBx+kz9hopBTJ/v7aSQQAKqRp\n2y8g38/i+pWuZAIhSrp0kQWHreUIIHeld9+l4HGbc2V4Sdgd/Q3Ss1JxO/UGLl0/A5M536oT6Hpi\nJoPOgFqVI9DnRDoar90Jn7j87G6+QfI1nDhBDw9iYuR7qDBRYhtDcvu2er+41rw8suq8/DL11749\n7U9IINev6dPVxzVvDgwYQBYob291HFRh40E5c98CgINn9jhvxDAMwzD/VrZskV1ilEiStvhwFBiv\npG1b2U3GdvEZGEjBxVocOeK88KQ7WacuX5YLA/7TCPerb7+1z6Sk02m70ERH07xVry6LEtvPoHZt\n+XerlebS1bo4WnEtIoZEkuytOUqh4CxuwlWGDaMsYrYZxqxWenKek2N/f3XoQE/kBePH02JYr6c4\niexsspJMmeJYkGgh4k60grA3bVK39fOjcT37rBx/okxpnJZGC3kHtWYSkIH5YRexbf9a7Ivdjrgr\nx2RB4iJtG3XFq+uu4KMeMzH97zy0XLACPrp8IWF7r4iEEN9/L1tnChMBhaViFv0pi0N27CgLEoCs\nbE2a0Hff9jhJos9Fp5NTAl+6BPz5Z6HXW+5EybmrJyE5++PJMAzDMJ5i9mznaW1LA51OTsepxGTS\nXozs2aO9iNF6OqzVRvzv7dFD3X9hokQrs5Ethbn52HLwoGvtSgIRi9G5s33dCkA7y9X48eRGBdCT\n/4cesl8cr11Lvvje3uR65U46Xi1LibBC1K1rXzhRiBKLBYaMDEjupiDWwlGiAouFREVsLFUu796d\nBMr69RQ0fe+96vZicSz6E9flSjIBwVtvAY89Zh/ArjXGtWvlYo3KaxHfha+/BmbOVIlmq2TFobi9\nWPHLAsz3P4Vkg+tZ+YySAT56b4TfTEef2DS8MvojjB/4EqqnW0lc6vWUileI/5Ur1Z+tuIa8PHK5\n69iR2mjVobl1ixILOMu2pVWx/vXX5QKYWtSqZW+hAkhMLltW6ByUC1Fi9Jb92bJy0pGcfruQ1gzD\nMAzjQWbNooVOWUSrsNzt29pZcLSKJ/75J7ldORMlShcvWxETEFC4peTxxwvv2xXhUtpkZck1GBy5\nWDmr6F6nDrBokXpBN20auSrp9VRLY/t2eSHpiktdbCy5vylRxmvYotfTIj82FhEzZ9qLwTp1KEjc\nWeIDJY5EibiOvDzav2cPsG0b1TJRsnAhxQqJ+0BYw8Tx7lhKABJAvXur7yuDgWIsRDpbRxiNVM8E\nkIV4vkXpVsp1LP7hDaz4ZQEOxe2FVIiRqcbVVLTNCsR9f17EE9Hp+OBPPT54cT0WdHsTb356GEM6\njkaNyvXkeRLWxJdeIsuN2A5Qoc70dHmehXXso49IeKxfL6frFdy4AcyfT+3i4oDXXrMf5ODBFMxv\nK0piY+W/Kzt2UNFEJc2akbudLdevq2NYNCgXoqRGJXXwXcItFyupMgzDMIwncOaCVBpUqCC7Tiix\njfkojD/+oEWJsoidFn/+KVdmtxUlVqt2xWqB1pNcJe64b3nC3agoKC007ogSZy5SmZmydWDrViq4\nFxhImZ1cqd2ybJm9ZSU7W64hk5OjzhL29dcUlyDcnJRjs1rJqrNpk3ZKaUeI2AyA7gMReL5hA8Vr\nCFECaH/OX3xBosTPj1yTALUFyJEosVjs4x0AoEULcpczGsnyAND8xsY6z0rn7w+sWkVxG0ePFtRg\nOVzdC/OiXsSFa6c0D6uYmou2jbqi49/xmPbxH3hl/u8Y33AoRox9D22um+GbnQedGHPdusCECfLB\nXl6UJWv9evV3QQiqZ54B/vpLbSnx8qIMZQEBVEtFWOMEej25X33yCf09EHVUlAwYoC1KlG5fH34I\nHDtW+JwJXPi7Uy5ESc1w9R/LSzdKyZ+UYRiGYcoKjgKJnYkA27bPPadOwaqFt7e6HsH8+fK+1avp\n1ZFrtTMhMX8+1XFwBUdFCksasbCPiKB5HzZMnU4VcG4p0SI3lxbdvXrRwlwsPlNTaVHtjPvus1+0\n37hB4gYg96kVK+yPy481yWjVSg50F4tdpchwBaNRLjI4b57atU0UGRQitlo1eyF98iS5DHl7AwMH\nUizJwIE0Dn9/mgst90mTiawFjp7OjxhBxRQBmlNRwd0Fbm76Dr/ePoQfwlMx9cyn+KqND0x59gUl\njd6+GNlhDGb/9yDGD3wJj317GPVHPE2iSK8nUTZ1Kn0mgHYBw337yJVNFCzs2pXSKot24nseGkpz\noRQNjq7LYKC569yZ7o+sLMeiIThY/g4DZGkVqY61inM6QhmP4oByIUpqV2mgev/3iZ1uBxMxDMMw\nTLnCkSgJCLDf5ghXK7ofPy4/7dbpyM1EYLUCb7+tLT7eeEMdyK3Fpk0Ut+MKFSo4dwfzFJJEwbuA\nLEoeeYTSxd6+TVYOV/pYvRr473+195tMtGh87jmqJeFujIe3t72AmDlTjktwtKisUAHmoCBktG5N\nxRIB+V5wV5Rs3EhpiUVhRqUlSZxfbBPuR7Zs3kyWCYBqrOh0tKgeMIDGIxb1SsR1KYsyOsJodHyv\n79wJJCTgVsp1fPfrUry09FG8X+k8NnargT1hGi6PACJNAXg6sz7eeeoLdG7UQy6OCZCVqVMn+l5U\nrEjJDg4coH1aYxCukQEBNF+1alGCgN69ab/4ngcFkRXKaKTfAVmU2P4dUH4ORiMJPWHptMXXF+jb\nlzKd/fADjXX6dLKq/fQT8Pzz2scFBND3o1kzet+/v9OEGeVClLSIuAdGHzmDRHp2KmIvxJTiiBiG\nYZh/FaXlNlQYUVHai6wJE7Qrcmtdg6uipFMnOSYlJgaIVxR9EwtrLdq1s69zYIs7xRMbNChakcGi\nsHevXLtFiJLq1akCeUaG2i0qJUXbzaVTJ3pCLcSNLbm5skXEHTc2gZeXvejw9pYXulYrpQgWFgNB\nhQrQ5+RAUsYKiVgFd0XJDz/QvXjPPfafZe3adG+IbT4+JGJ27bKPg7BNuVujBvXtqHiimH/l+VJS\ntGOnvviCXKSUi3eTieZuwQIc3bcR8755AftidyDP7Lgopl6nxyM9n8Gk7IZonl0BfkZ/mq+wMPXn\nFxVFC/qdO2nba6+RkKhYkaxitlitJCZffpneV6hAxycnq2NjvL2ByZMppuPqVdqek2P//VN+DmKf\nMyvjsWNy9iylILd1DROYzfS5uOEuWi5EiZ/RH/c27a3aduryYQetGYZhGMaDPPmk63U0/kkeeUR7\nEesoxW+PHvJTcYGrokQZG7FgAbmcCIQLkhau1ECxfbpeGF26FL/Yn6so44hEnYvISMradPSoWpQE\nB2tnifrmG1pcW63AmTN03JAh8rFKQZeX5366Yy1LiIj5OXIE+OwzOu/u3eo2RiOsRqM6TbS4FwwG\n10XJpElkNRIV3W3jjf73P1qEf/IJBfUHBVEWrldftb9WR/eAO6JkyhT6fLSwvddffBHSZ59hW4Qe\nX1zf4dQDJyy4Cp4bNhNdWw6EzttHnveQEHJ3UooSHx+yauTmyskFTCZKsTtmjL3lRxx786YcZP72\n2yT+tbLT/fgjWSEff5y+Y7aufiEhVCMIkPc5EyXie/i//9F97ux7azDQHLiRpKLcFE9sEdERu4/8\nVPD+1OVDkCQJurL49IphGOZuRBTXEq4fDLF0qXtPjv8pLl6kBa+tIPD3p6fjthiNlKJWSe/ectBz\nYSgXXFlZ6mNMJsfxDw88oK6OrYWj7E2lTfPmFAMBUAzG1KnkoiLchVxN3SsWexs2AHfuUNCxuN4N\nG+R5TUmhGihRUa6PMTzcPohZmeoVICHQIN8N3mQqEA9HfvsNfmfOyAI2JIREU1ycbCFyxqZNZD1S\nihJxbeIJvri+RYvk45Qpfzt2BP7+2/Ei2JEoEaJAeZxYVAcEUPplJX5+QEQEsnIzsPXvNYitdxO3\nLVeBSMfZvfz9gtCkdhuEBoWjd7thZBkByAKYkWF/wIAB6rHo9bIo+eMP2j5mDNV1+eUXua0Qg2+8\nQfElEybQ3OXlUWFHW5dMg4HSAV+7RpYhW8ERFkZxOgDFojz1FMUsKYmNJevI6NFyn1YrxYYYjfK8\nNlCHUKjGIFz2XKRcWEoAIKJ6Y/goUgOnZSbjZnIh2T4YhmEY9+jZ0z5dJ0PuR+7EafxT9O+vnbrV\nx8c+Tawj+valRaltPQtbcnMppStAsRT+/vK+wEBtdzGAFi7OUrq64771T6J0Yxo8mFLXAvKi2+TY\nzUeFEF1CzCmtCT4+8uJ8yBB6vX5dLrbojGHDKI2vEm9vykAlxikCqAFaNCvdpJSWLIOBMjb16iUX\n53Pl2kQgu5cXHV+5Mu3r1k2OpRDcvEkWHKXVYsQIed8TT9ifw5EoCQmhiuPKe8dsphS6ly6RaFC6\nFt177/+zd93hUZTr9+xueg8ltECASC+hhCZFmogUxYLlUlRULIii/ix4EbCgyMUCChcuXhFEhIsF\nBUVQQFR6h9BrSEihpJG69ffHyceUndndhABR5jxPnmR3p3zzzTeb97zlvNj16ii8t2gcftv9Ay74\nazsaGh09j0FhrfFk3YF4d/RCjOz/PAbdPEwiJADP27SpMrXJ318SGABo9A8YIBntohA8JYVKawIu\nF9PUBg1SRkUCArjGFi0CWrdWDlLMXUkJ65UiI90vZONG1moFBTE6pSYuJ0+SBAsIQinO63KxSWi/\nfprzdEOTEj+LPxrWbqZ472Saly9RAwYMGDDgO5KS3BWFDFReVFSE4Ysv3NN7PKGwEHjrLclQnDKF\nXumyNP2T49FHfW9OabXSm1yRmDBBkrGVIzycTf7UsNuBe+/1HgESkJOS0FDtZpUbNzJCGRJCQy89\nnca7N/z2m3utUHg476fTSa/7a68pC81L021CDh9GaFKSfiGzQESEflM8YZh+9BHP9+yzTK97+WWS\nDLXB+scfwNtvK3upPPAAvfWXLgHr1im3X7yY83L77e7njowE3nyTalUCDgdJjMPBZpeTJyMz+yw2\n7l+NOcvfxOerpiM7X7vXXUhQOMbe8xbGzt2Kfg9NRPO7H+cHOTnsnaLGjBnAjz9qzwsgEdp58xjR\nFFCTg6FDSUoAKe1uyhSSnK5dOY8CLhejbfL+K3pIT6dABcD5iIlRfh4eTuJ29iwwerTkHIiIYJTQ\n6eTzplcTdiOTEgCIdyMlB6/TSAwYMGDgbwov6ikGKhH0Igznz5etV4kvdR9iO4DG9YYNykjBww+z\ngFmNwYO1DX45evdmPwRf4HT6vq2vWLqUBcVqhIRIhccCaWmUvK1VSxkt8oS77wZeeonzFhSkTUoW\nLqTB7nBIn/lC8rQ6uj/9NA1ydYd0wJ2UHDgAPP6453PceqsU/VDj1CkSNEBpnH73HdNB1UazqD+S\np2/VqsVoSUKC8hgOB2uggoKoSKWFTp1Y+C3fx98fcDpxyVmMz6ufwzsLn8HSdf/GwWR94lsnvDZe\nvH8aGsW2cr8/q1fz/qmhp36nRseOXAPFpZLCixZJJASQInLFxXxuL14kUT5U2hNF/vw4HEzNEspv\nns4vXxsPP0z5ZDlE09P8fD7P3bpRDCA2lnU5jz3GiM64cdrHT0uTUu98xN+KlKgjJcdSk+Ay/oEa\nMGDAQMXB+E79ayA/HzhwQDtSMmGCMi1DQF7ULIdeYbwcffpIpKRnT/6WHys8XLur+7Zt3qM53lSn\nLl2SIngHDpQ/IqN37sxM31OxTp+mKleVKsr3TSYWB6vxxx9MbWvYkEaiqLFQ3wdhXJY26wPg23UK\nxSw5rFZpPoOCgGHDpIiP3JD21thRwM/P8z0cMoTedXnqUkAAjezsbP6Ia7JauTa7dFGmHN1xB9MR\n5evAaqV6lQ8d3Z1OBxxOB3bFBeOzgfXxof9+/NN/G3aF5MMF97VtsfihZ0kMJhW0xluPfoaXHvkE\n1aNK64dEGlN+Pusw9HrNyFWxMjOVz9CYMVLak9nM6NHKlVK6lzxNVqSnzZrFGiNRxySkduXHFSRD\npBJ6IiVaa0OOsDBeo3j+WrSQnm2AdUUdO+oTQpF6qJe6qYG/TaE7AMTVbAx/SwBsDn55ZF86j4ys\nFNSq6kUD3YABAwYM/P1gMjEv2tei3PLi5ZeZYqRldF4vCK+rlrFotWobI2vXSjUkcmgZyWrIicvM\nmUz5ku8TGqpd+Cs33PSgpS4kx/HjNOp276aRWpHIySHp0erl4XRKnncBi4X9HiZPdt9e6xj33MMU\nmho1gLZtWbS8bJl7lMVs5npu3Nj3SIlel3SRGtW1K+/5s89KKVoyUmIpKIDJl/Q/b2mCsbHuxEXI\nAL/7LtPcNm8mMRNjff99d2NWRU6tcGBv+1gcCDwO64p3EOAXgFpV41CnWn2YTCaknDuBTUlrkF+U\nB6fLCafTATQEgBAAGmuxFFXCq+PRQa+ibky8/vU6nSQR330H3Hmn9vqUr9vatZVNDB0OSTBEkByL\nhWl6y5crG0wGB7NYXRxL1Ai98QZrQbTU8Ro3ZnrWt98yyqQmycXFJC5t2ujOgxspERg8mA031U0u\nKwB/q0hJgF8gGtVtpXgv6dQOna0NGDBgwECZ4Of311Pe0tPQr0j861+VTwBAGIBa5KOoiCk8evvI\nsWwZow/eSIk6xUtNZOTF1HJcuOC99sIbcYmIkGRSrwTC8y6HMPy1IiVbttAoBOgxF+lIega6t47u\nTz3FiFPfvpL3Pz4eSE2VtklK8p2UCE94u3ZKQiRPjQJITMT1WSyXP6s7cybC5bU8Bw6wEF5E4QQ8\nXbPJRHKhlhEW6zIoSGqe+J//UK1LjF1g8WKqfpUax06XE2u2LcM/5z+OL0a0xy7zBSSd3IZdR//E\nj5u/xH9WTMHcH97GT1u+Qk7+RdgdNhISD4hw+KF9YTjubXMfxg+fqU9IAEZ+hGqWiC6qI0rFxUy5\nk9d2FBVJ60u+nk0mXv/QoUx3U5OM4GBpfY8dS9lggD1eXC7+yNdC//50LixdSkECETVRj2/PHuk+\nPPKI+zNUtSqboKpJyaZNVy1i/rciJQDQon57xeuDBikxYMCAgYrBmjXKFAyXSzIiKiNq1tSXq6xo\naEUBriccDnrfW7Vy/8xq9W7QVqvGXglLl9KobN7c8/YrVypVeOSkJD2d59QjNloRBDm8pW9FRkoG\nlTCWymM0LVtGY04OEXHSIiVyT/iMGcCcOWUnJd5SpC5dIkGxWOg9//13esrvv9+7VLOfH5/ZQ4eU\nc2yzSd3RbTaSKRGZ2byZcralMMmvu6iI2yYlST0uABrN6muw2bi9IF1iXjIzGdnavp2pa61aSaRE\nrtImJyUrVpAE1amDtI/exr+Xv4GVm79EiU27m3pZ0bVVf7yR1QQP/Xczesxfo2jGrYkvvwR27qQi\nnUinU69PsdZr1+Zvi4UF6A8+yNdmM0nFvHlSpMThYGROi5SMH897I38WBLEZNIjEVWDVKhLcvn15\nD6ZMcb8GcYznnuPv1avdv8NCQtiEUf382Wye076uAH+r9C0AaNEgEct++8/l1yfTD6Og+BJCg7w0\nhTFgwIABA57Rq5fytd3O1IXKWmeil+t9NVDZemLpFdm2bi0p7njCxYs0Hm02elH79vW8vdpIefNN\nyWgeOpR58U2bau/rbe6++ca9mZwcIlLicknX7XKV/Z7U00j1FqQkXsNz7nQy3cZq5U9kpGR8C7Wp\nF16QtvcWKdGCKPzu1IkOgKQkSunK03sAzlFAAFNrBCwWRnLUDRTtdqZHTZ9OA/vcOU1J6+LYWJTU\nrYuA6dNZ0C8Ko9Ud3efMcb+GkSNpHJtM/HnxRZ7j3/9ms0aAcyrG5nSSlPTvz7oc2fFLvl2G44H5\n2BR+Gkknt2vWgJQFDWs3Q7O4tvCzBCC2egM0rtsapg2TlelV3rBoEaWFw8N539VrJziYx+rWja/V\nSlRijQ4ezPQ2QQ4KC92f2ylTSEZFtFE0apWngulFEvX6J1ksfD5FXUpBgVQcr0b9+sq+RjYbSWXv\n3hX+/fq3IyVVImJQq2o9pF88AwBwuZw4eHoXOjS95TqPzIABAwb+ZrBYKp8xLoevhbp/R+gZKr4Q\nEoGaNb0XwwKc56QkZa+Ep56S/i4pobJPhw7u+06bxhx6T9ixgxLD8v4ZcgQEcIyFhRzL+PFlM5Y2\nbKCCUVyc1CtCoLiYqk/C4y2HiIgUFUmd16tXpze8sNC36JnTyevauRN45x33z0XjyQce4HZ617V7\nN1Oh5KREwN9faZwuXUqD1uWS7q2GUtil9u1hj4pC5OzZJCWid4ialHTuTKO1Uyfpvb17SRT79qVC\n1pAhNNTNZs5X7dos2Pb352sRKSksvHx8m92GTUmrsWZCX1yKsAAnt7mN0eRyoZW5Buqk5cE+eCDy\nCnOQev4kLGY/VMktQa2V69Egoi6qPPgwImd9Cnz/vXYkRMgEa5GS778nEZTXuIiUQpeLRfiih8zl\ngZmkCF5MjDYpcToZzUxKYkNKgMRA/byJ1MiQEI4zJoYRNEH6PZESvaidvIklQFWvDRtYi6JGZCSv\nf9curlObjaID77zDSLRe6mpCAuvt5s/3udbrb0dKAKBFgw6XSQkA7DuxxSAlBgwYMFDRMJmknObK\naPwfPUov+o2I6tW1e0eYzZQvfe899/sm/7taNc6dlqSsGkVFVEsSntbly4GBAyXjShjsWujSRVsq\nWA5vzRMXLOB4S0poCJW10eLIkcCZM0yP0TL6tSIogHQeu126xlq1WK/z4YfKlK+cHG2J4B49OG9a\nzSlFrYCYO09pbJ7ECPz8lJESi4Xb22zS+2+9xaJz+eUFBcFstbLOYeFCqiz5+7uTErkxn5zMtTdi\nBL37q1YxWrN+Pfdt0UKSPga4bW6uFCkpKAAWL8bFTWsx33QIZ86fACK0+2DE126Okf1fQPSKNcDm\nFUDXEcoNFi0Cti4BEmoCwVWBEjuQVwBEaDTsfO01Gt8HZa0kHA5e5/jxTO2TkxKXi8+HVlNCATkp\nqVlTme43dSp7q4jmic8/TyW62rW115vTSQnezp35Wh7Z0iIlhYWMLnqKlKjXS8OG+tcCUDTk5595\nvrAwptR5kr12OPjdoKW6p4O/XU0JACTEd1K8PnR6F6z2CpQINGDAgAEDUmpGZU3fioq6Nulbzzzj\nrvC1cqV2Pce1Qmgoc83VuO02GsJa961fP2DuXGUdgC/54+qI1PDhypoVT6TEUw+UH3+kQaP2Z5F+\npwAAIABJREFU6qrx7bf01FepQo/1kCGex6vGLbeQHAUGunc/b9vWe92Uzaa8xrffpndYPgeRkdrk\n7ocfaNyKiElmJknSuXOSESuX6D12THsuPJESdfqW2H7lSqlD+unTbrs5wsPhEvf1oYekSIm6aF3e\n6LB+fWDSJEYAatZkGp8ozvfz43kLCznXAPDEE/Smr1oFPP88zjaujZWuk5iW8h0JiQaCAkLwyICX\n8Oy9UxAdXk3qMK5GURGfA3Fuu51EQK/ppLyLPEAi8tBD2kILTiefpXnztI8F8J6LfkBHjvC1+D7y\n92etlbjHTifnpFcvNipUQ4+QJidzzajHt2cPpZ4HDNB2zFgsJEICRUUUWfAE8Rz++SfHWlzs+fu1\nHM0T/5aRkro1bkJUWFXk5F8EAFjtJTicvAetVWTFgAEDBgyUAbm5/OdVs6b0njAqr1XtRlkg8rOF\nAXS1MH26u1H08880xq4nUlJoqMu9mYMG0XD873+19xEGkegS/dBD3j2o6vuvNu5ECpIWunRh13Et\nDBrEue3SxTMpyc4uUy8ENzRpwihA27bA//7n+359+7ITt81Gj79QprPbmVrja28TYexNnkyZ199/\n59qtXl2ZAuZwcD4mTHD30NtsfBaLilhALhcd+OUXkgT1Oe12ySCWK3oFBAAmE9KeeAL+GRmouXgx\nP+venZGo4mKpFkFcr5pwtW1Lp8DHH7PAW05Kioq4HoqKkGsvRFb+eew+uhH7MrYiy3YO2A4g2J0I\nV7FZ0LhNL/Rqe4ey1YOeuEBxMe+DOLcoJv/hB6YhyVMMAY5X3lldkB21JPVPP/G+eIsOjxzJYwoI\n0iEgnhtxD2bPlnqQqOHvr52i9dZbdCKoSb/ZTHW4RYuU90rAYmG0VECvK/u8eexN0qiRlK7WtavU\nZ8bTHNzoHd0FzCYzWsd3Vry378SW6zQaAwYMGPiLQxQRDxpE76AcI0Zo71MZ8OSTzJ+/2ggMZOpJ\nZcNjj9FAlePpp6mk9cgjvhkLDz/Megs97zLAtXHpEns2AO5GakyMvtFjNntufhcf7z19KydHafyV\nFXJPf1kh6jWmTpUiNIKU+NrEURjVIioljFSTSTlvw4bxd1ISiVp6uvTZO++wjiM/H/jHP/heSgqf\nz2bN3Oe4XTueUxBWYdQLCWIB+RoJCuK9rFePhfUCRUXK+zN8OEnJ3Xcrozx+fkBMDJzdumL/2+Pw\nwcRBeP2zR/Hh/17Fb3tWICvvnOb0tGzYEa/7dcPkVTn4x08n3XvP6TVv7NaNtTglJUyNGjaM9yY9\nnYpkubnK4u6HHpKaSAKcM1GEL18fTz7JZ8hbX6Jx45QCCTExTIMTuHCBhEHc7yZNtKMaLheJavv2\n7p8FBpL46ZHy+HhGrrTw3/96/35cuVKSf5ZHLEVDxwqOlPwtSQkAN1KSdHI7HA6d3DoDBgwYMKCP\nqCgaIX/+KSnnADSAqlXzXbHmWiMoiAbT9UDHjlI/gesFb8a8r1i+nKlUehDncDgkBaz33qPRBbBW\nIzqa3v+yoEcPrr1evTz3IVFHSt54Q19JSAv33EOFMIdDUkuSY9Eid3In8H//5x61cDhoDL//vm/n\n1yMlcuzZw74RVavy2rZsYX8cOUaO5L26eFEiijt3ap9z82aeq18/pr8JY1NVn+AIDXVvvKfGqVNs\nmFlSwmPK0xbFsZYuxYniDCyMTsc/G6Rh3vHvcDrWM5G3mP0wpPsjeHzQeFT3C+d62rRJudHLL9Mh\n8OabyvenTuW13HcfPftvvEFCbrdLRe2TJ7M3ih70IiUWC+e6a1e+vnABOHvW8xxpQdzjL79k9FIP\na9Yw7UzgxAnWhcnHWB4cPsxaKk+oWpUF8C+/rPw+6dSJpNkbKcnPL1OkusJIid1ux2uvvYaGDRsi\nODgYDRs2xOuvvw6Hir1OnjwZderUQUhICHr16oWD8qIiACUlJRg7diyqV6+OsLAw3HnnnThbjpsd\nX6e5Qga4sCQfx88e8LCHAQMGDBjQhdwrK1BUpPT8VTYEB0uSrtcaI0cqi2avB/RqMc6c8W7IvPqq\nREA91X2I8wBKSd7PPmMEQ2D6dLdCal0SICCMoKZN2UBPD+pIySeflI0AtWxJQ9psptGrnrONG/VV\ny8aMURrthYWUyI2O9r3jdefOlBD2REpWrCB5EGlXgGQwjxnDc/XsKd2z/Hx9kYKePelgkKcP6ZAS\nZ2goj+8J48ezpioggGtLrAerlfM5ZAg2dG+AGc1LsOPwBhQU6xc+m11AnCUat/98BK+N+Bi9290J\nk8nEiEL37u5G8Ecfcd21bQs8/jiQliaNacMGRh9eeUWaB0FKnE4l2RBiBXIIg//uu5WRUPn9Wb+e\nERYt5TRf0awZMGqUflF6UJDyeywri88TIEUsygNfRCyqVeOa2rqVz4lourpkCXvzaNWtCfz+OwUE\n5FE1L6gwUvLOO+9g7ty5+Pjjj3HkyBHMmDEDs2fPxruyL6H33nsPH3zwAT755BNs374dMTExuPXW\nW5Evy5kcN24cvv32WyxZsgR//PEH8vLyMGjQIDjL6O2xmC1o1bCj4r0tB9de2UUaMGDAwI0Krdxh\ntQexsmHmTMlbf6Pg229pwBw/zuiG2sAuLGQxd3Ky9N7hw/TGiu7UAA0KMXeic7UeoqIYaRCN5O69\n130fLUPb4aCxo4c+fZjy4q1m6d13WRh+6hQjCBcueK5B0YPJJKXsCOTm0sD31Rst7Bl1Go7JxH4U\naqxbx22bNZPS3rTmShA0eZF5SQl/Zs9mdCQ8XCqszs7Wl3MWaTcmE43anj1pYALaSk5duni+5tL0\nKYfLiVRLIc5kHkfazHex//3x+ObW+pjQJwjf3NNad/ewwDDEVm+IgV2G4b1NFrz49ircftKJ6lGy\n+opu3dgwUr0ObDbeewD49FOSLQERLZOnE0ZH01nhcCjTsubNk3qFCAQG8nwffCDVCwESiSsqYn3K\nunXevwcvXFCSjvfek3r/mM28BwcOMDXv0CHlvsHByoivfG3rkRJfohO+yH1Xrcr0TZOJaXtyEtKk\niX4NDCBJdXtSKFOhwmLu27dvxx133IGBAwcCAOrVq4dBgwZha+kXjsvlwkcffYTx48fjrrvuAgAs\nWLAAMTExWLx4MUaPHo3c3Fx89tln+Pzzz9GnVAXgiy++QFxcHH799Vf0kxdu+YA2jW5WEJFdR//E\ngM4PKhe6AQMGDBjwjFdfZVMzQGloaqnSVDaU14tYFjzzDL2xdete/XN5w5NP0qsvCIXauBXkUm6M\nbNxIj3ZhIXDXXZwz4UkGPCs7CQgS4u9PL2qTJsp9tI7hbf3885/87Y38PvMM8+ZNJhrj4ti+4tQp\njnnsWF671SrVcnz2GdO3WmsY1SJdTe5ttlho+N5/v/b2avTrR4PTbGY3+ehoGshqAiOvOxAoKWHt\nSmws60ACA5WkRM8TLiR8hw7lDyAZjlqkpF8/pgwB2HNsE9bt/h7nstMQHBCCkKAwFESnwAYnSuYM\ng9Um8+iHALglHnC4p1AGO82odzQDNycORtsftwOpfwJTBwHLV3DcX37pPm699SJ3mIjrByQiKa8Z\n2rqV5CUzU7mutKKKXboAazWc2YIgbtzISI23NCYAuPlmRrvE/RM9SuTntlgYEQwNldY+4E5K5Gu7\nXj3taHBcHJ0Fq1aR8Gqlh82aJZFRPVSrRlIiIkWpqVTtWrbM837lRIW5uG6//XasW7cOR0pDhwcP\nHsT69esvk5RTp04hMzNTQSyCgoLQo0cPbCrNEdy5cydsNptim9jYWDRr1uzyNmVB07i2qFlF+ifh\ncjmx++ifHvYwYMCAAQNuePddNsny81N6xip7pAS4NuObNctzGsO1gs1GA0KoDAFSgzWBb7/l79Gj\nJUNHSMYKwmmz0XhzOOglzsvzbuSrU7zUJESPlJSUaBfwqreTG6NOJyV35RAeY3l9i6/IyqKRtWED\nX8ujIoLUakVKli1jUTdAYlNUpK8EBXjv6P7hhyQY3buzD8Tu3VJDQmG4/vYbVbnkYxOpayYT71XL\nlpwP4Ql/5BFlbYmnwn4h+VsKp9OBExlHsLnoJBbOfQ6f/TQNp9OPoLD4Ei7mZSLl3Alkma24ZLYr\nCYkOzGYL7rnlMbyT1Rxj5mxG2/B4rjeHQyJSYoxqaEXMvvxS+ezJ15i4Z+qmiP3707CWryuLhQa3\nL5HV224jcZCnLXpT4rJYmGYoapPk828ycYwzZ7LnjppIBgdzX3Ft8mt89FHWtqjXVlgY1+fzzzOd\nUA/enpObb6aAg7jW/Hxg3z7P+1wBKixS8vTTTyM1NRXNmjWDn58f7HY7JkyYgCeffBIAkJGRAQCo\noZKli4mJQVppDmBGRgYsFguqqvIwa9SogUwhT6iBHTt26H4WF9USGVkpl19v3r8eVcwNdLc3YEDA\n07oyYKC8+Cuvq8hp01DUoAGspdcQkJ6O1qmp2Ll5M1ze0gCuA9r5+2P34MFwXeU5TwRQcuEC9l/n\ne7v7zz/RFsDe3bsRePYs6iQk4Ei1auyIXooWEybA2awZgtetw96tW+EIC0OVlBREZmYi+9gx3ARg\n9/btaAvgyMGDaPDuu0h7/HHYIyKQ4+n6nnuOhkvpNi1KSnBi3z4UX7qEgMxMRKelwT8rC6myY5gL\nCtAOQFFODg5oHLvu9OnIGDECjQsLceLgQRSXkiiTzYa2jz+OXbKC6hqZmfC/eBHm4mLEANi3Zw+s\nHuwGOYKOH0d8Tg5SDx9GIwB7d+yArTRdp/bJk6gNIO30aaSpxljl2DFE5uTg1I4daDZiBJLHj0dx\nXBwSbDbsVm2bCMBms2Gv+n2nEzt27tQkz6H796NuYSEO79iBGmlpqP3ppzjcti2K4+JQZeJEhBw9\nipQdO9CwVi3k3H8/snbsQJP0dJx99lnk5+fDYrMh8MknUeeTT5C5eTPySg3X5vn5yPjxR2TbbHCp\nDeCff77cXXx/6kbsT/kTdqdNPbRyobopAolNBqPh/F/gXLAAmaNGIT89HTUuXID/pUtITU9HYwDW\natWQfOgQclW2oJ/DgcDhw1Egn8PGjS/XbiUCSD51Cud37EAiAMesWTickABbtWqIbdkSBa+8gvMi\nMgQgtqAAhZmZyNqxA1XPnEGDVauQMmUKMoXKmR5GjED4Dz8gMCMD9Uvfyjh/XrG21WhhtSL9l19Q\n8/PPcXDJEtQ4exb+Fy/C/vTTCMjMRERhIYqOHUN0WhpS0tORKTuW/7lzSDh7Fvu/+w4lcXEIO3gQ\nTVH6v8TlQmLHjtixbZs7MYqKQuKRI7DNm4e9997rNqZEAEm1aqHYy/dWxE03ocaWLTi2YweCjx9H\nQ7td83n1FY0aNdL9rMJcSDNnzsT8+fOxZMkS7N69GwsXLsSsWbPw2Wefed3XdBU7Adet2ljx+mJ+\nGgpL8nS2NmDAgAEDesjt3h1WWVqJvTSkb75eClfeIPdCX2MEHz+O+npSnFcJplLPsMnphEmnDsNk\nt+Pk22/DGRx82ePqslhgstthEt7WUi+1yemEyW5HTs+eyOnZ0/PJRS1EKTJGjIC9alVYCgrQ/MEH\n4QwMhFMlS3v5fDr1KpGbN8NcVISDixYpPboaKUbiGuByobBRIzjkHa+9oOqqVQg+dQomlwvWmBjY\nZfUgppISZPXpg9zSgvw6s2bBJCIULheqrl6NwNRUmGw2EnOLBSanE5acHDQX0ryXB+nSfq1jA5ms\n1stkvyg+HpaCAgSmp8MVGIiLgwcj5cUXAQDWmjURvW4dqv74I1JeeAFFpUafIzwchU2bsjO7LMXH\nZLej4aRJsOgomtnsJdh0bCV2J68vMyHxdwDhNjMCrLxfkXlW1K3SGEPy6uPOuHtQpzgQdWfORHH9\n+si55Ra4/Pwu3zdHSAgcQUEoaN4cJg0Pvj0qCgUJCW7vB50+jbpCiUwWRXD5+yPkyBGEJiUh7amn\nUHPBAsV+qePGIWvAAL4oXU8uH9NRq3/3HYJLyZvTz+8yidXD5fUpnpHSdXJxwABk9euHoJQUOEvr\nQFyq59ZWvTqKY2Mv76s4l8PB7T3Y0erjCdgjI72OGwAKmzRBWmmAwWS3w+Xnh6Djx2HJ88GW1ive\n10GFRUqmTJmCCRMm4L777gMAtGjRAsnJyXj33XcxatQo1CxttpWZmYlY2T+1zMzMy5/VrFkTDocD\nFy9eVERLMjIy0KNHD91zJyYmehzb9pRVSM44evm1KbwEia0972PgxoXwZHtbVwYMlAV/23VVpQra\nJiT4rjR0LeFyoX1ioudiTpOJhd7eeg54QWBgoPLe/ve/wE8/oZonKd0KglhbbZo3BwC0btGCKR9R\nUe7rzWJBq3btAH9/tG3ThspRqanA5s2oUtoksW3LlgCAxkOHAhMnok2HDp6bE5aUsOag9PwAAHHe\nc+eAkBDETZsGAKgtPp82japFn3+O4Hff1X4uAgLQKiGBBuPw4UyRAphC4uen3GfbNqZP2e3A//0f\n2sqb1HlDaUTlpoYNga5d0f7mm6XPoqOBtm1R5aGH+Przz1HrueeANm0uN8dsFRoKWCxo0bYt+0I8\n9RTadu4MpKUpxujv54fE+HggI4N5/qUGdGJYGAufP/9cOa7sbKBqVR4jMRFYvRo3NW4sza3AggXA\nnDmI3rdPuydFnTqIrlVL2u/oUSA2Fm1at3YrVL6Ym4lPvp2Ii3n6UaYqETEY8O+fYVr4BQAXQh8Y\niagVa+BaugQxb/wL/uNeYBPKo0fZGyQyFnhsKEULSg3Z8N690XzkSKbMBQcDhYVo1qEDUFKC6CpV\nEF2/vvI6T5zg8eTSuAIuFz+PjkZcs2aIS0wETpyA3+jRaBAaSoXAVasAs1n/+/f4cQBAvYYNUU+9\nzeLFFG+Qk+rIyMupZuYffkDd22+Hx4qysDA0iI0FQkI4hk2bALsdNQYOZM0SgKr16umPwd+fz0LD\nhuwxc+kS101JCWCxePy/EhAcrP25vz/atm7N++ILTp1iL6LISLScP5/3csoUoHdv7e3Xr+dne/cq\narJyPch7V5gLyeVywaxiY2azGa5ST0CDBg1Qs2ZNrFmz5vLnxcXF+PPPP3Fz6RdA+/bt4e/vr9gm\nNTUVhw8fvrxNedC6obKT+/4THtQ+DBgwYMCA7/ClCPp64dw533qoeNPq9wVXMeLvM0QOfUgIJW4n\nTnTfRigRyWtALBYlcbPbmTNfs6ZvsqFnz0p5/fn57HgtH5NWc8RXXmHhb5cu+uvn+HESJnW/FXkU\nKC0NePttFvzedBPz65s29TxeNcT1adVIhYe7E251br/NJl2nvz/laE0mCgeIaEhWFmW1R49Wkrc+\nfUim9u51H5forq513QJ5eaz/8fQchoQoJZJF3UhpUb9j1044Ro7AqfTDmPn1PzUJSfWgKmjvrI57\nsqpi/PCZ6LgjFR0ad0eHpj3R/FAmasc0QJ1cB/wdLq6fCRO4BhctokTzyJHAv/8tqZKJ9RYeznUm\nmisGBTEVUN7JHuD8zJunfX2ijmfHDmDwYL7XsCHvS2ioFFkTjRO1InMPPEBJYXmkxOXivD3xhHsx\nuctFg3vKFG2i5DaB1SU5YoDSuqtXs5eM2Qw8+CAJbVQUu6erIb/3ZjNrRgBtYQI19J7fsvYxOn+e\nNWmiu/zevVR900NpwOG6qG8NGTIEU6dORYMGDdC8eXPs3r0bH374IR4q9S6YTCaMGzcO77zzDpo2\nbYpGjRrh7bffRnh4OP5RGuKMjIzEo48+ipdffhkxMTGoUqUKXnjhBSQkJKCvkE4rB1rHd8KKTV9c\nfn0sNQlFJQUIDgy9sos2YMCAgRsBJhMNSK1ibm89LK4nvDV9EyhDcy9NvPSSfnO9a4mSEhrkwhgQ\nNZzi/ogeFyLVShhnhw7RiBs6lN76gABpTkTvDE8Q3ccBRgGefRYQaTFqw1qOunW9r5/t20k21Olb\n+fk0kjIzga+/phFcXrGB0FA2aAwNBerUUX721lvu28fFKV+/9hrlZ0U0acQI4IUXOIdFRSQF4jN5\n7xazGfj1Vxp3Tiev4667uO9TT5HoyNem0wmcPk0DWaiDHT3KPiJPPumZlKibSZrNyPt0Nn43ncXv\nNWwobm8F/veq267+5gCMnPcnEvancy6KLwH+QZKRHxAgrSmrleey2UgSo6LYnPDYMd5reRG9KGhv\n145RFYDrcehQksCHH2YkTT5XekXZgpSURvouo6iI91QQHoeD9y4/X3tNyqWDARLJRo20Vb+cTq6V\nZ57RHpMaq1dTpEDcNz8/knmh3OV08l4/9BAL6dXQk8XOzvbci6l2bf0mrk8/zSiVrzCb+SzOmUN1\nMG/d2sWzVIYoeoWRkg8//BAREREYM2YMMjMzUatWLYwePRoTZZ6al19+GUVFRRgzZgyys7PRuXNn\nrFmzBqGhEjn46KOP4Ofnh/vvvx9FRUXo27cvFi1adEV1JzWqxCImqjbO5bCg3uG04+DpXWjfpHv5\nL9iAAQMGbiScPEnDJitLKX1bmSMldjs9neqeEXI0aSKpGZUXb7+t7Um91ggPp1ErkJFBI2jsWMrN\njhxJJabQUEqByr2twrgQhqDwgE6Y4BspkTehkxtwasNaoHlzKk3Fx7M/gyeoFa3EeESfjisllRYL\n8NhjJFKCTOnhjTcktatRo4CVK2lYP/64RDzEHISG8pmRK6DddhsbDcohDO4HH+T2W7fy7yFDlETL\n4aAR3L27lA5js9HAlhvtx45x3SckoLAkH4ce7IPk3BQUrZmJ6IjqOJaahFPPt4PTUprWrmPr16/W\nHDfH9kHC/lL519GjJWNeRLjEj9nMsQQH8/rr1+d6E31oBDEQKCrij9woNpmYinb8uLt335NXX0/x\nrLiYcy/ObbfzZ+tWSv1OnqzcvlYtpQGt19F9/XoS4rLWq0VESF3gAem44jv0wQf1JczFPVbDmzLt\njBn6z4dWJNUTLBZ+Z7RqJZFST7Z5RATV0UJ9DwBUGCkJDQ3F9OnTMV10mdTBpEmTMMlD8V9AQABm\nzpyJmTNnVtTQAACt4jth7c7vLr/ef3KbQUoMGDBgoCx44AHKQcob7w0dKnn/Khs2baJR/fvv+tss\nXuzu+S4rAgL0owHXEnXrKjtLT5rETtfyhoCiobG8CNtTv5DXX2ffk4ICdh7XgstFQ/KzzyhhqzYo\nteZXbpDpGU3h4Yx2qQ3SsDAe026vGFLiSSJXDbUh5+9Pb7pcWVRI0IoIhZz0Ohzu9TnCqBYSvsJI\nNZuV62rMGGDXLq7n6dO5ti9ckNJpnE64XC6c++lr5KSdwrGkulh/fjdsJg1j3uLZ0dsjYSDqhSbA\nYpUVugcHS/0qxDMl1lVJCf9+4AESvLg4/hYqTXJS0ro1ZXmrVXOP4ADuEQuAc7FxIx0AEyZoz58a\nr7zCcZw7x6aKzz7LdKusLM5jdja/uwQxmjJFub94blwu5fqYMIGRoLJ+b7Rrxx8Bp5PEfMYMZd8S\nLZTWvLihalU2XtSDhurWZbz0Emt+2rTxOOzLkBNfcX+8ETO12IO3U5Rp678wWqnqSg6e3gm7o2Jk\n7gwYMGDghsDKlUCKJLGOlBT+I/VUBH09ERTkObUBoJGg7uVREWjYUL8A9FpBGPP+/p47knvrN/Pr\nr8DSpfqfy3uDCINy5kymGjVrRpnZkhJlncDMmdodzuUYPJj3MC7OPQXEz48GoxYp+egjpsb4iuee\nk7qWP/usQkIZAF//5z/a+z7wANCihfI9MQdbt7pf46hRwLhxyvdEfYfFokznkePYMc5B/fqsQ8jI\nAJ57Dq7f1uNUTCCWRZ3DB10CMfm9IZiCrZhV+xzWXNipTUh0YDH7oe7ZPIy47Xnc2/NxmE1mpRqV\nluEv1JVEull8vFI0Quz/++8UlACYrhYRoaxzUR9TTRItFpKIXbvct69Xj8ISciQlAUeOMCrVtCnJ\n+uuvSylkDgejW56EKMRzo34+LBZerzDmMzL4U1aI3ixff01p4/JAr6O7L9iyRdls0hvkzoHmzUnm\nKljd8IYhJfVrNkJ4SNTl18XWQhxLTbqOIzJgwICBvxC0wvSi8LGyIjjYOym5Wnj5Ze1u0NcSwrM5\nd+5lpShNaEVKZs5kmgrgve5DePNdLskgX7JESQwWLmQjN4F+/UhS5OlmaggjKCKC+fhy+PvrR0oW\nLrysqOUTunalYQvQkFUX7yYnk1hp4a672KxQjo0bOe5atdw9/tWruyleoV49FoSLtDQtUrJxI/Dp\np3BazHDYrDhQww9LE8MxteopfNg9FH8kb8Lp4kxkB5ct1d3iAvrH9cTbXyZj+rC5eGnuTnRoeou0\ngZ8fU/8AbXnX4GDWITkcwPvvK+tA8vJIIurXZ7G4OA7gWVxC3ewQ4Bz16KFtBIeGklSKIneHgylG\nv/5Kp8m770rpW35+UrNQOdlwONyNe7OZ2z/wgPL5kN+fY8cYjZw7V/969CCOUacOiWp5Uj6vhJSI\nyJyvqF1b6jT/xhtUvLsCESot3DCkxGy2oFXDDor3DBUuAwYMGLgCVOaO7lYr00Qqaw+Vq4XVq2lU\nb9zITvPCu+3JcLFYaEC6XJJhtGsXIx2AsiheC/HxrDdwOqm0c+ut7vtoGdpFRcCePfx740b3VI+b\nb6ZBq1XkKyIlLVqwYDcri13L166lwVuWju5yiDoCgYwMGm+eIk1akF97YSGjHGryZLeTbAUHk9jI\nU2Jkc1VUUoAfSw5jatNLGDesDp6P3I25iQHYWM2K9FDvhmyAfxBiYxoiPCQK1SJrovXB87in03CM\nQ1tMymyIAbc9gYgvlsDignYamyAaej0nROQhLExKhXrxRRLbLVtY0zRnDpXGBMS12u2U85XP1xdf\nKAUBAHrmx4zR/75xOBjJnTdPuvciEiMiLw4HCUBQEJ8HORlfu1YiNXKIYn25U0aexpSSwjXire45\nO1v5DH71FXCLjPzVq0cHysaNVJTzFVdCSnxR1pOjShXWvQi0bMkUvApEJf1vcnWgTuF6IbKvAAAg\nAElEQVTaf3IbnM5yfnEZMGDAwI2Cl16SCm7lxoOnWoTrDWHUeTMmd+688qL0UaM8S2NeS7z+OvPP\nRU8PMQ+ejI+hQ5nGsnAhDa6cHM6JMLx8UVgTJOSmm4CpU/l62jRg/nzpc/kxvviCaTxi/SxdSkNN\njiefpHdci/z+/DPTcho2ZHH63r00hGfN4r0oq/jC+PGct+xs5Zp5+GFg82apduKNN6SojSicViMq\nip56AYeDBrJ628JCyRA2m3kfAM5b6f4n0w5jyhfPYHXxYaSF+HZNZpgQlwc0RCR65IRi/PAZePnW\n1zAl5i5MfHgOHlu0B7e0uh0Nn5uEqHc/IJFo0oQ1WFrP87BhFLpQG6BnzrC2Raum49QpIDeXJE9L\nPECcJyuLtUoxMaz9ALjetFSt9BSoAOn8qanupEREXsLDGdkIDCQBkK8rPXWv8+fdC7XlaUxlqa2Q\nR05dLkklTzxrFgufnbJ0S4+IKH/q186dvEdlwbx57qlyFYgbipQ0rtsaAf5SQWZuQRZ2Hq0EMo4G\nDBgwUJkxbRpzswMCpDQXwLORcL0hjAZPyi8uFxu0XSkpmT8fuALZ+grDqVOU0HU4JAMrMpLGz8SJ\nfG/WLL7/8ss0uAApnUXMw759JCjZ2TQ6vUVKAHfiYjazCFt4fdWkZMUKqm6dP8815Yncqslvbi6J\ngrwIXFyDvL6lLPj6a2D2bHqq5aTE6aRn3WrlfEyeLKWlffAB5YD79VNG5NRGuqjrcTppcAoPucsl\nPT9hYcBnn8Fmt+F847rIDTJh3dQxmPm/V5FXkO1x6CaYULNKXbSs3QpD1ibjzcRn8aJ/Z4xztsG9\nOTGomnSCaWNDhnAHvcL+O+7QJ/ENGvDaRYPHPXsYSfvf/7RJSUYG+5IkJmr3jRHGvDyVSoxJpFqp\n4UleWpzfZpP2FfdEfb3NmknF5eJ9i4WkVN0fRQvdu0viBb6SEouFNTWlXeDdxBscDkYnV64sW/Qi\nLq78KbQBAe6phN5w5AiJ5FVCJf1vcnXg7xeAtjcp899+3LwYNrtR8G7AgAEDXrFokSTxCfAfaVmL\nJa8VXC4WsB88qL+NMAqEoXAlqAxzsHEjfzudvDcPPQQ8+qhUd2GzMZoA0Ai/dIl/q0mJMOouXAA+\n/pipM6IQXA8zZzKyISBUtS5coAdcTUr8/KTi7uJi5uXLuj4D4PgLCtzJb0aGlNsuIDduxRyUBYGB\nkmfdJrMJHA6JlFy4wPdEuozDQTL2669KY1mLlIgidpdLmnd5fxcAJ84ewFsLnsRbC57C65+OwvLg\ns3B6yArqGBiHR1zNMemR/+C1ER9jdJcn0HvnOUR07QW8+iqVl8aMcTfwHQ5JNlg+RoBKa3q4cEGq\n0br3XtbaWCycO2FIb9zIaN3587x3esZ63bpAhw5lIyW9erGHixbkpEQeNQFIynv2JMG2WknUO3dm\nREsoB1osjPxs9SGtf+JEEtPUVN9JSXAw606WLJG2dzhYS1K1KteFIIRlISVXgpISd5EGb8jPlxTY\nrgJuKFICALd1ug8Ws3TDs/LOYVPS6us4IgMGDBj4i2DoUCnlAGAtAVA+5ZmrDV+iOMLw8cU7Wlak\npWmnrVitTIW5GpAby3IjT05KhMEjj2yoowxiXoqL+VmvXsDw4Z7PLW+MB1CdqGVLGmHPP6+UXgWY\nqpWZyf2cTkrELlqkPOZ33/E6cnNpRAtopXPJr+Ef//As1/rCC0qjd9IkRpkKC9lHpH9/5bmaNmUK\nozAaxTw7nfRsqyVjBSl55RWmqYm1aLEwLWn3bm5XGinJyErBT5u/wsffTkROvn4aYK30PAxvdAee\nvPN1THx4DoY/OQNtx72DKhHV6WX/6iuSTYG6dZlOJ6KFdetKBvvw4UoyLuYjWyMq8/rr3E++fuSk\ncvBgKfUuO5vXJwiuXgQsPl7qgSPum7ineqSkXj1t+dq8PCkKJEhJdDQJRlER184rrwBvvqkUvli8\nWFLIkxMiXzBtmrKfSkyM5+0jIkjO5STI4WC9jUjhEzVHlTUlFiChDg/nd1hZFO58xA1HSqpF1kTX\nVv0U763etgwl1husGNKAAQMGrhS1ajGfuTI2T1R5oTUhDJ+r0ehw4kRg1Sr392fPlshcRUMYzWpS\nsm0bo0ZytR15SpY6UiIiBX37+qbOU1CgJA0ACWyTJiQUgYF8rZbVrVmThqHLRaNOXocBKA3V9u2l\n9+XXJiBvdDd8uLLBpxoffqhMQfnlFxKSoiKOWW5gChWtIUPcSYnDoR2Je+wxznd+Pq9fTkpk/Sas\n1mLMv7cZ3vliLH7etlS3xjUwIBiPDnwV41dno2PNNmhevz2qRdZUbpSaCvzxh3ZES0he33cfx1BY\n6J4+FBBAYqO1NqdO5bby/iEWC+/7xo0kPgDnSNTfiLXUvj3leNWCE9WqMV3M10jJuXNS53c1HA4S\nkEGDeKyoKKbJdexII3rsWP3jCoh1riYlu3ax9kKN4mKS7NhY9ucZNUr7uAIREazVEsRczH/DhlIE\nTkTbrlWkpKzIzeXzGh7OCGpsrESwKwg3HCkBgH4d7lPUluQX5WLLwess3WjAgAEDf0X4Um+wdu21\nrz2JiFA2edRCRZAS4XlVEyBh8KkJWxm6G5cZwliOiSGhGD2ar1u04PzLjUp5pMRmU3a9t9uZShUX\n55uBtG8fu3cD9J6KLtPffktjVK8OICiIRqseqS0ooDdfrB1xn+QG7I8/MloREcF0oH79PBMScQz5\n/bLbeV8KC93XaY0aklEvbxQI6I/7zTfpqRfN96pWBY4fh6ugAMn1orCjXR2s3fkd/m/p09jdorr2\nMQDULLaghyUO44fNRMJNnbWjf6dPM89fr1Ab4LXVrcv0JUDqDi4aHp47R2Wstm1Z26KG3c5ohJzU\n+vlJJE3ci4sXJanmTz/lHLz/PkmNTSdN3mwmEbTZpOP06aPsdQJQ5eq997SPYbHwOP/9LyMiFguN\nfXF8cZ9cLiA9XfsYHTvyR012Fy4EfvrJffviYq7fmBjgkUe0jymHaIwoIiXdu/O+ASQqvXpJz4m3\nqMv1giCW4eHSPFVw2molpWNXFxGhUejZZjDWbF92+b2N+1ejR8JAmLx51gwYMGDgRoPJxFQakSIh\nh5bUqxrbt+sb/r//Tm/mwIFXPk45TCbfmzqWN9Jz/jwNiIkTge+/V34mDER1qlGNGtrSoxUBq5Vp\nRuq+GU6nu6dbTianTGGtyWOP0YCVG9S+RErkUaktW+hNvflmGi716+uTki5dvCt7rVnDBpfC6Pbz\n4+99+1jLsWULxzhokFSE7W2sgNKAF6lWLpf7WJdJdgKsVkZ3HniArz3YCw6nAymhDpTYz8F0Ngmb\nD/yK46lJyH24NBr05wLN/UICw/DgxWpI6H0/axB6tgUiqktjP3uW0QyR179sGdPg+vTRn0fRWV4O\ns5lpaz168L4fOKB7LQCY0lZYyOgGwPsgIiQCVivPZbOxy31wMPDDD3y+PTklRFNFsR7Pn2dURBBd\nMV490iVSobSMefn3U04O0K2bdooaoN1JfsYMidzLIUiJr3j1VdbriEiJ0ykJTYgxBgby3jZr5vtx\nryXkUcvVq5XvVRBuSFICAN1b345fd3wDp4uLNSMrBSfTDiK+ThmLfgwYMPD3QnZ25e1Qfj1x5gw9\nq2lpVOIR8EUutnt3d8+nwF13MZXmaqRQATx2dLS2ARkZCXTqVP5zC+/vhAnKxoCAFIVRNyjTMnwq\nCs2aKXPmL16U+jf88QfTlh57jJ9NmSLVB8mJk+hDsH07DeCnnvJ+XrkHX650FB5OEqbuzwHQI5+Y\nyN++NDoUhqefH/slADR2S0q0vftyJCXRcx4SwuNs2yYdQ4z5jjuAhATPx4mNZSM+Ua8yaRLHJCJD\nAFwuFzYf+AWrtixBbvXSFLFvJ3q9vIASO/qvPoJOK3Yg/B8PAS0y3aVXRQ3CjBkSsbVapciHeA4L\nC9n4UhD96GhJBEFARM7MZsngF8RVi0Tm51NtTCiHtW4tSdGKtW6z0ei22/lsPfecRDh8MV7FM6rV\nPFGdbqb+TI+waDlNXC5G1NasUX4vNGigHcmMilK+3rqVETx5jZQvaNlSWjvyZ0aMsW5dOn8qKywW\nPjcREdIzXsGO/BsyfQsAIsOqoFXDjor3/txvFLwbMHBDw+FQGisGlBg1il5rOe64gwaIJwQG6qct\naf1Tc7kqru9HzZqee5X85z9lV6ARcLlYb+Dv7264CENNbSyFhSlJXXnwySdsOKfG4MFSrwuA1/bB\nB1LUIyoKeOstfnbPPdKY9frN1KkDPP4460U2bNAfj8tFo3f6dKVB6XDQgNHyYAsiZDLR45yXx87q\ncjRoIK0PuVHaoAHVn/Q6uqvRqhXw5ZfS6w4dlIa3nkSuGvXrs2+JHFFRl1XDMrJSMOu7SViydjZy\nC3yXTY0MrYJ/frQJfdcdR3hIpGSkWizKcb32Gu/J8uVUbcrPZ06/v78ykpCdzfv28ccsfLdY3GV5\nmzblvIlaFxF96qBsMg2A9zcqij8ilW3+fOm5sVqZ2mOzMQVsxgwS0pdflsZfFo+6FnE3mxlp0FIH\n80ZKcnNJRO+7j9dgMjFCm56u/G74+mv3KMU990iRMYEPP+R98Pa9p8b48XTQAFIKYvv2TDMVkRJ1\nXVVlgnyN+ao6VtZTVOjR/mLo2qq/4vWe45twqbCMjWQMGDDw94GWh86AhK++UnZa3reP/5zlvUu0\n4MnLOWSIe1rYjz9WXKdgT8WtAA1KeT1FWSC81FqIiaEcr9pg7tePefZXgrFj2QPCG4Sx5u/vmZhp\nqVnJsXmz54Zp8pQoYVB+9hl7WTz7rKRcJaRwAaZ4ydNffvpJEXEAQCPSauX427VTRrTEfdUiJZ9/\nrkxHGjKEdR16mD5dqkP54gupl4uAw6GUO5ajWzegf38cOLUD05e8hKMp+/TPA8BsMqNBzSa4ueWt\n6Jt4DwZ2GYaXHvwA0Q5ZNE3Lu3/2LJ+J6tX5DJ4/zyL7b77hGmzRgtcp1pzVypoFtTJecTHn8fPP\n6bkXxEctjqCGp+coLY01TFYrxygnNuUlJepxiNfqgnkxNiEqkZfHOhsB8XzOm8cURdFfJDCQqWue\nJJABEpW2bd3H8t57Eik5e1YqVvcVYq5FbxJ1ymVlhPx7vH59/jZIScWhcb3WCgULh8OObYfWXccR\nGTBg4LrC0z/lGx0mk3tU4/RpKbfYE9q00VdpGTnSvXtzWRvfeYJQ97ka8FRz8fHHLPb1pSajPPCl\nV4BQe3rgAc9zoBUp+fprKbrgLUVPeM9dLomUrFjBlD9x3NWrKdUrMGQI06qEsS+6eQM0LLdupcFj\ns/H3xo3SeQCew2bTJiXLlyvVwAIDpeJ0Ldx+u2RgnjvnLtlsNtOo1TDKre0S8Ev0JfxnxTuw2ooV\nn/n7BaBW1Xrws/gjNDgCA7sMw/QxS/H8/e/hgT5jcEfXEbit41BEhEaxOF7I3WqRkkOHgH/9S0q7\nMpmk9CF/f6B2bdbx7N4tXa9cwjcvj9GBAQOY2gVIKURmMz9PTNR/Ti0WbVIyezYJgVDAkteZnDsn\nqZOV5XtVyzkkItha695kYoTjiScY0evfX5J1DgriGAWpEscNCiKxEw4Jp1OZ+ugJ6lS52Fh9ZTA9\nyNO3QkOBt98u2/7XA8HBkkPlkUeoSta8eYWe4oZ2CZpNZnRtdRu+lxWcbTu0Hr3bDTEK3g0YuBGh\nl8ZiQBvePOwCnr5Pe/Rwf69ZM/ciWgFfa34yMqhoczVJSfXqwBtvlH2/33+nUdSxo/dttdCvHyNU\nWvjzT3r9d+xgEbQw5D1FSkJCWHsjrzE4doxpL4B3hbWOHVnI63IxatahA4vQ77tPShvSMrRzciSj\nVawjh4MG+vvv09ATpEQNofI0fDjnwumksZ2fz9Q/+bm8kRI5hLSwQGoqo14hIUBREewhQcgryMbF\nvExs2r8Gh1P2oqDIXYGodrX6eGTAS6gRXYck5557gIu/ARs7S1GZoiIadt26sdZApLlpzZXwUlss\n3M9sliJNQsZXPI/ieuX1TMnJbKQYFSW9Z7Hw79BQEtBhw/TnRQgMqPHUU6w/cjiUKYz33ssIw7x5\nJJ6evlfPnGEkS6R4iiaTctSoQeKlF9XMy2O64rp1LOoXjRMBKfJiNktzrCYlp04Bt97qWw8heRqT\n+G7xRX78/Hmpg/qpU9KzefYs5yolhRHDHj2810ldD/j7My1QQJ3KWwG4oUkJAHRs1gsrNn5xueA9\n/eIZnM44gga1mnrZ04ABA387+Gpk/xXx3nusCamukiDNzaUx4cnofOEFerbVxdxXi8TpEYlffqFB\n7kthumi65yntpLCQxkF5a0qio+n9v/9+YMECyUh87DEayz17au/3yy8clydSsmkT50AUFstx3336\nvU5mzqQBfOgQ03eEwICnSMcnnzDtJjeXHlth0AnDyxeFNRFN6duXP+vWMV9+zBgaWupjrFsH/Pyz\ntH7EuaxWiUAMHUqSofVMTpvG+RbGm8NBo7JdO6bSyA1oOSnJyGC6jCj4F1i4kEbxpUtKUtK3L85/\nOQ8nOsXh4C8fISl1D+wu/UieyWTGnd0eQq+2d0jOTbudhrLJpBxXZiaJQHIyjeVevfj++PHudTjy\nYujkZImU1KnD+y3mQBANu53XIc/9FypsYj6nTZOO36QJj/XPf2pf2IIF7s6AXbuYwtm6tfszdugQ\nnQvt2nnv4XHvvUqFvn/8QxlVE8jL048Qink9cYJRL3mkRUReOndmFA2QomuClHiqS1FDnsbka21F\naiq/D0RqmZ8fn7mjR5Xpak8/TXJdGUnJNcDf9L+v7wgPiULTOGW+4Pyf/oVz2WnXaUQGDBi4bhCF\ny39HzJmj3bncl27s779PY8jPT9kDwpeu6QBTeeTynt4QGKhdvJxWhu/l0m7ZqFZN39g4dkzb+AE4\nL75EzB98kB59UaR98CC93/LaGzVKve4e0bu3Pql59FHtzzZsoNdZ1AfExNCI69aNKTbp6cDSpdz2\nzTdJyATkdSfLlrGoeu9eXpsvCmtq77YwguWREPkxtm8nMXG5mBYiJyVyw1OL+KamMhIkN9zENiKl\nTn6uLl0kcYGUFHp796lqPzZtQt7zY7Bpy7f4OToXmw/8ih2HN2Dm4Lp468/3sXjwTdiTstMjIQkM\nCMbowa+hd7s7ldkW8uaJ8p4wYo0CNN5ffZV/JyTwe6hjRxr+Yv4cDta/3H67lL4lTzkSpMRkIlEu\nLlY2y1STEjlsNpISPbW1OnXoEBBr5sgREufVq7UNequVCm+NG2sXz8uhFonQgtNJJ4KesS4/f1GR\ncs1o1ah8+il/yzusnznjuf5MIDFRqqPzlZSIvkniuZdHW+TjS06+epHdvwBueFICALe0GaR4nZN/\nEf/9cSocOt1VDRgwUA5MnOheMFjZEBlJ470ydii/UuipFJXlWufOVRaGOhyU1RR6+3ooLqZB4Stq\n15Yai8nRubN+WpcaondGUhJzvrVgt9M43b7d/TNfC1e//pq/RarTrFks8NbLTz9/nilo3kjJ3XdL\nnnNfMXs2CZHTyXszYgQVkMR9P3WKykgAiaL8GuWkRBhme/ZQojQ+3vtY3niDHn4BkUaUnCxFO+Rr\nzc+Pa9LPj3PlcLAOIDQU+L//Y4rbsGHaRnRSEvDRR+5j8PeHs6QE56oGI89eut5++40e+379+FpE\nTEp7VRQUX8KqLUvwdvwFTHixM5b0icVPtYrx1a+fYOHqD3E81nuzy0D/IPRpPwSvj5yNFg0S3TcQ\n1xAfz5qNS5ckguCJ+GZmSrUuFgvranJyGFmYOpXktlT5C4CyJu6rr3hP+vThazUpkafnAb71pDl1\nSjLCX32VpFJEZkRB+cWLjHDZ7SRdvkRSfSElLpcUcdOCMPBNJt5j+XmbNCHpW7CAqVIAiV+zZkp1\nN0C/h4kcI0ZIMtZy0ucJgmgLZ4WItowcyboM+XgrsqbuL4YbPn0LAJrFtUXHZr2w7dD6y++lXzyD\nTftXo3vCgOs4MgMG/kZISqKRU9nRvz+NBm8yo9cLxcVMBfGkJqS3n1azL3m3Y2+RgYceUr5OTGRK\nxbFj7mlhcjgc+sdes4ZKSerUMC14UvFSQ+6F1oMwvrWiGiEhksKMtzGJwmNAMnqPHWPTtTfflPqB\nAEwTmj1bP0Ij0LGjMpLhC6xW3mO5kpKcjOp1dAeUHbrFvAhPe4cO3r3d6sLk4cOlNbpiBYmmqBmw\n2Ug8GjWS9hs6lCmCog9Ju3ZMtfnySxqK+/fTuAwI0EyzLCzJx66u9fFb9/o4VyUIpgs/oMUPabhp\n9ykcibCj8PQ3qF2tPsLPZSP90Y7IO7IY5w9/isLiUkUwHRE1LQTaXAirWhPhGVmID4/FbY+9g6AA\njZ4VP/xAJbmxYzneO+5gBEPUZ3hao5cukTSKNSg6ghcVMYoioi3rSsV5Tp0igfz4Y+kY8iJktczw\n2LGUFRYF4ep+OlooKpKK6/38pMhF06aMXAG8rt9+k+61L5FUX0iJxQLcdpv+56Jvi1jTciM/K4vG\nf9euXHN16vCcIoon394X9cXMTGDyZJJmcX3erkHMrTyy4nCQyB86RGeYQEUpD15NZGRwjTZqVKGH\nNSIlpbi/99NoWq+N4r0127+Gze6hONCAAQO+49ZbqY5S2eGtqNcXmEz6udlXijfeKF/EqbhYm2gJ\nA7Q80aGbbqLij7d9z5yRIgpqfPGF0pACmKalbvYG0BC7807fxubNCw1I1651v202fblfOdSe4JIS\nGm4TJ7LIN1clMy/Sd7xFSspToF9URCNRTkpuuUWSD9br6K4+n83GOpuRI32bg9xcdwI1cKC0TgMC\nOA6Rzy/Ok5jIPipmM9MC5QaOPEJiMvF46el8LYsIWO0l+P7PzzFh3iP4353NcK4KibcLLiSd2o7l\nURdwyJyD5Mxj2HzgF6w5vwP7W9VCclGmREh8QGz1hrjNHosnfsvCe99nYdIjc/HCiUjcGdhcm5AA\nUnGzuJbRoxnBEMphntbowYM09sX6io8n8dcz8rOyGF1q00b787AwFlBv2sR5V0euevUC1q71PAlq\nUlJSwudX3Ldq1SR1MHHsRo2k3jh68IWUeENmJptZAiRncjWsUaM4Hk/1ZeK58IWUFBUpHTzTp7vL\nmmvhyBHJeSMcLE2bUg5YpBe6XJ4dPJUFK1YwNU8uv1wBMEhJKfz9/DHs1mfhb5G+gHMLsrB+9w/X\ncVQGDPyN4IvnujLAl/x5X6BVv1ERaNpUv9ZADy6XfvrWlZAS4MpJ3Lp17gbt9u0szFcjJoZGrC+o\nV897ZM4TKRH9MTxh3z73tLSSEmVTNXUqht3OKIAnry9AsqdFwObMAV5/XXufwkKm6zRowEjFHXcw\nbUTkv+tFSvLyJE+82K5RI0YmfOlavX69FOk6cEDqESLIkNrQE+cNDaU3X6uQ3unkMyRqKmRRMpfd\njouhFuzY9wumfTgMa3cuh91RMXn4wS4/dG7eB03j2qJW1XqolWPHXW3uxYv3T8PA4lpocSkA5pIS\nkov9+z2nJwklrxYtqIoWGEh5ZlGIHhzM+6yFAwfcBRi0Utl27SLxkdcoaKFWLWWvGbOZjgrxDLRv\n73l/l4vbq0kJQMUqh4MRrcBAEi4hFT52LPDuu/rHBZR1auVF1apsbBkWxsik/JhifVmt+mmZVauS\naPiSbqaOOr/4om/7NW4s/Z2QQAllgM+aL6pflQnien2VUfYRRvqWDJFhVXBzq37YsGfl5fdWb/sf\nurS4lV1WDRgwUH744rmuDKiISIk4ztVAWVRiBFwuzv++fe4yjoGBLNbW8xDabDREvvySqSdq+KLM\nVFZURBNLi8W7B1akmGiNPz6eDf484fhx/n7lFXpnARpqb73FnP8TJ7RJSWIiSYMn6EXDUlNZp7Fx\no3sH9MJCpuQkquoaRP8QvUjJiBE0rO68k2Tp4kXg8GH9lD815Mby0qU8R4sW7PoNuJNhMSd3383f\nWo6A0m0ci77AzuBcHLmtHpLXvoNi2FFQkAtHFwDrZ5Up7UoLJpgQmVOIto26ofn6vajXtT+Cb31M\ne2Orlcbkgw9K6WxjxugfPCCAz4/FopSyFR77unVZ56DGjBl8/8EHle87nez9YbFIfTsmTOAY6tYt\n23NoNlOB7P332XPiwAHPKVxjx0r7ARxDhw4kW4BE4kXErVkzXv/Gjd6jgmPHuvcqKissFp5Pq9O6\n+I7aupXRerHu1NDqJK8FOTkrL8xm36KQlRVXqaO7QUpUuK3jfdhxeAMKSsO6NrsVm5LW4LaOQ6/z\nyAwY+Itj4EBtedPKBLudhl1FGNlXi4CVh5SYzZx7dSoRwNQBT8a3zcbzJSfz98mTyjQbXyJLw4bp\ne/e15kncB3WdiyC2ZZnbvDwaEFrGVmIic+q1SKi6iFgLojndxIkkJgD3ad1aIjxapMQXQ18P58+z\nXmXePHdS0r+/MuKRl8e8byEt/OOPUvTltdck0QB5jYaQlx09mganL/095KREfn12u+SBVm8fFUUV\nqdJxFrpsSDlzGHaHDSXZF7Dr8O/Ifb4HkuNOAWtmAM2igQLPggrBASFoXr896tVohHPZZ3EhNwOu\ngwfQyBSNam264ESwFUUlBajlCkG9ei0QU68ZosKqwBwQCBT/CPzDi0nUsyefv8REoHt3KlWpiYMc\ncvEAOc6ckdaHFg4d4vyru8g7HIw6dOokkQSrlcat2jnw6690QAjyooaohZKTDE/fK/n5rI8SaNSI\n3x1z5pB0iEJ5EQUCmMLqq2LelX5fivHn5OiTEjmmTuX8CAEEwL3gXA/btvH78EaGmKcK/j9nkBIV\nwoIjcGuHe7D8j88vv/fnvlXo2/4uWCzGdBkwUG6InNnKjDNn+LsivD9Xk5SUhzSVh8wAksHudALP\nPssibbkRf9ttSkNYCyEh+p5FrXlyOJj+kZ+vlIedO5cytfKiUG8YNIiRCz1C/OaKF94AACAASURB\nVP77+jLQO3YwrUXvXtpsjB6FhEiN0ET+vN0uFWXLUb26Z4NUYOlSGu7qNK/z55mOpZU2oe4K/dNP\njOB88AHH2rIlfwA6CQT0+s1068bfZ87QUNZLOXM6gW++odde7m12OJhKo5ZxLSVBh5P3YPkf85GR\nnQqnltplnA9NMktxc8t+uLPbwwgODFF+YP8fpZKP/4H2InIjh8ulVK3yBLkCWUiI90icuhGjgLce\nFHpEf9o0qnfNn88akkmTmOooGkzK19qECTz3ggVAq1bux4qPZ+RAfNd5i3j6+yufc1EzJ+51To5E\njtas4bxOnKgdCboaENGn3Fx3UlJczBqd7t0lwrRjB69JTkr27vXtXL/+WjFjBoABAziXagdDZcdV\nipT8BRK8rz06t+iLAH/Js5NbkIVdx/68jiMyYOBvgMxMSaGlssLh4D9rX4xGb7hapCQ6umw52AsW\n8B9eeUmJMFScTknbX2DDBhrIcpUfLVgs+ilxXbu6pzIJw0Fd6K1XF+MJ3grGmzfX7xDfqZPnOfNU\nd1K3LtNw1GT8uefcG/dpYcsWpTqQwPnzPLa3lBhAIrAijUgP3pqGJiVJUsJaEGtEniK2bBkLe7/7\nDhcaxeLrdXOxbPXH2Jz0C74/8AM+fW84Zi+fjLSLydqExAfUS85GH1stvPTgB3igz9MSIVm+XBJK\nuO8+1m14ivgsWSI9r0eOaPfUWbxYWQguIhSekJgIfP+99mctW2pHLgHtFNKcHBLa4GCm12Vl8f28\nPHrta9dmpGzCBL4fFkYCo655slp57OnTpcgP4P37Qa+ju1j/cXH822RiXZOYz2uVsrtoEUnTc89p\n12esWcPvGUHKBYkuDxISlP1ckpM99yXyhFWrWDT+V4No7mmQkquPkMAwdGym1GRf/vv8yyldBgwY\nKAe2bqVyVGVGRXUoP3lSUoIBgMxMxGr1VSgPbrrJe4dkOQ4fpuJORZAStYFx4IC2SpYaERH6BtjD\nD7OLsRyCdKm9zJcuSbUbvsKT4s6V7uupt8PPPzP9Ri99xhv0mtydO8f58aXA1Gym6tmiRdoee/m5\n1Ot+0ybgX//i395S9IRnWtSu+Pld9iafyEnGv756Eb/vX4U/Dq/FV2tnYe2eH7CvoGzpL/XC6+DJ\nn9PxzN1v4ZEBL2ECOuP/Pvwdd4YloG5MQ+XGa9dKBfKAsqO7wEMPsSZCNBoUsFppzKuxY4dSOKFj\nR+8RwsBAfXnXo0f10/i0ohYZGZSPFQ0Yxdq4+26gb19Gbbp25fMOSBFG4dEuKaFh3qKFVAslX2O5\nuXwW9aD3LHzzDdMCIyIYTZMjOVlSTLvaCAjgep08memT8tS3Z54hSVPXjJS3pkN9f+rXJ7EtL67V\nHFUkevWi46SCmw0bpEQHPdsMhtkkTc+lolz8sfen6zgiAwb+4iivUXwt4c1j7CsaNFCmHf38M2p+\n+eWVHxeg53XePN+379ePqUsVQUrUqIj56t+fHbfl6NmTDQ/V3v3cXHbk9gWHDvG45ZHWFfA2Z127\nsl6mrMjPZ5NFTzhyxD0yBTCfvVUrfVKyezcjLJ98AvzxB9+z2z3PQVgYPe4FBdJ9Tk8HNm/m32Yz\nawNEpHPtWmWN0O23Uy3N6QQSElAQXw/booqxaExvfLLl3ygqKfB8raUIv1SM+MAaqFNoQe20XDQP\ni8PteVXx4v9O4P+q3Ybm5mpoXLcV2jbqipiASHqs+/aVDrB9O9MLRTNGAS1Ssn69duRWXQdy+jSv\nKyREGXWYOlXyunvDpk1S/QzAe2G3szeLUGCSQ4uUiKiXkBMWz90330g1XvLnURTWC9Kcl+fejNLP\nTzLSx4zx3B9Dj5T07MnnwOVSRhwTE0mGFy+WGjheTaSns3GouN5z56TPBBkJCpKcBL/9BvzyS/nO\npaV05kvTRT1UhLDK9UCnTldWH6cBg5ToICa6Nvp1UBa3/773JyNaYsBAefFXICUVFSlR46abYKsI\nLX5A34Ouh7AwGqlxccypViMri95i0aFYjeBgGqBaalFXa74A7SLhskQ87HZGVjyRkgsX9KU4161j\nipSnNduyJQ0yURwu8MMPTCPRQ0mJfuG/QHIy06bUiIzkvZQb43J89RXTQbZskbpXe4vWfPcdmzr2\n6EED/uhRvi+u3Wym/K1QnNq5k+eRozTl6Gi/jngr5Wssqp2LbY3C4fCSmuXvMuP2Tg9gfEotvDlp\nDZ6L7o1XjoTj1Wm/4clHZ+D2oS8h7oKV8xEXJ+04bBjJkSjWB6g8NmaMklwBSlKyYQP7eagjXOvW\nsb5IFG0LNG0q9Z4pKuK6EnNvtfpW32W1KtPtCguZIrpiBQva1XjySToT5GtPEJWaNbkG9GqxxPOo\njpSI/eXEZdEidocHKFfrSVHqn/+kSpccq1cDK1dqf7fv3UtjOyGBogpXG+Latb6P7Ha+P2qUVHd1\nyy2MdpUHWnV9V/K/7a9KSq4CDFLiAb3a3aGoLckvysWXv3zsYQ8DBgzoYvlypg9UZpjNUq5sRcLf\nH9batd3fnzKl7P/MyhqdCAtjHcLu3dqFuSJPXm8cQUFU3WnYkIZQbKz0ma8EafZs3/K3t2+XxhMd\n7T6mssyV6IsTHe0+xpQU5nL/9BPTPbQgPK3eiNAzzwDffis1rVu7lmQoNVV/H2HgeoKneb3pJjdS\nYyopoVdaGIgOh+S5jo6mIbxvn9QB/P33STQEBAm022m4PfssydWRI24GcHa9Gkjp1gYlVl7D3uOb\nMddyELOqncXs5ZNRWKLfo6dlgw6Ir9MCrcIb4OHPt2OK3y24/e4XUOtsDixOF8cgbx4niK+clBw6\nxLGLjvHyaxC/5WslNlYSOvjlF/YKiY1V3vvDh9llftUqJRkWa9xup/KV1cp7PGcOyc6PP+peq9sx\nBBISpD5GWuurWTP2fZF/Xwrv/LhxJDJa60NOSjp3Vs6JICV6jgRPqYgA51ueZpmSwijN1q3apMTh\nYB1SaCjQu7f+cSsKarEC+XgqQmJcjubNSVblqGhZ9BsUhpyUBwQHhqJ76/5Yu3P55feSTm7DwdO7\n0Lx+Ow97GjBgwA1/heZQzZvTUClPQbUnOJ1wqT2bLhcNy7J6EcsanahRgykWegWnZWme+MEHwOOP\nS68dDnqeU1I8F98XFPhWA/H992yk2KcPvfFa5xcN+bxB1MB89pn7Zxs30qC6/XZ2pH7kEaWyEiB5\ny70V6gqjVBQe338/c9v1rjc5mUSxpMRd8liOUaOUEqxe4JebC7z0Eq9FeMR79+Z8CrWnP/5g1Kx3\nbxrnLVpIykz+/lI0QSiHAThzaBu2u9KRPK47LlQNRcms+2CzW4G2gOnf/4ALpV5eM4BgABrLKDKs\nKu6tfysSnn8H2Ff6//S334A9HwEh4Zxrmw149VWqpQ0dSrnWZ55h1ECkj7VvL+27b5+7YpEg3f7+\n0npevJjbCVJcUkKS/swzymdPPFNBQUpSIozdnj3Z4yI4mHMjSIUvpFxNSuT1VXpRPDVJMJu5dlwu\nPoNaBF1umA8fzrQu4USQkxKzmWlpYWFSypY3UpKby+dY4NNPmUY6aZKUGiXw6KMc54ULTBu7FvBE\nSjp0oIDJTz9REECv672v0OrXVF5SMmCAUgHsBocRKfGCAZ2HIa5mY8V7KzcvgssItxkwUDaovZqV\nFUOHXll+sBZq1cLFAQOU7xUXk/iUVZ0mL69sBK9KFRqrerm/gpT4EoV46imlx7FvX0YE5EXFWhAE\nQet7c/duyTisVs1zXntZUgBFpEQLKSlMgzl9mq+1ujxbrTTw9ZS5BMT9E9cmOronJQHvvOM+N6+9\nxiL4gADPRK1nTxpSPsJcXMy6B+FRF0Zafr5ESkRfFTFuuSEl+lYAl0lJcr0ofHRmOTac2YTT9asg\nPzyQhKQUlwmJDmKCq+CRAS9j8sNzkVA7QUopSkuT0tuCgzmWZ59l6lV0NNdqYiLTg1q2pJf+yy+p\nOjVvnn60UBDjwYOlyMicOcqeEiUl9N4LMpCdTbIh5qVaNRqvgNR01GLh8ebM4VjlDgtPDoKsLDo6\n1KQkPp4CBIBnUiIvxBaKgCYT50j9nOTkMMozfrz0XqdOUkqWICUWC/9+4w2l6pOnxokAI3vy9C4x\nXxYL95OrT/kqrVuReOopqYAfUM53tWpcT8uXsybraiAkxPs2Wpg6Fbj11oody7VAXt5Vuc8GKfEC\nfz9/3NfrCcV7qedO/j971x0eRbW+3+2ppJAGAUKooYYSehPpRbqgKEoRBLkoKIIoCihdLkVRUJQi\nTQWkXERBwCtFEUJvIfROgCSkZ3ezu78/vhzmzOzM7ibZQPzdfZ+Hh+zu1DNnZr73K++Hs1dLuLSp\nBx6UNNSqJWjbl2S4o6O7SkU9BRiiovCgf3/xMrm59C9TOdUF69fbq1ulpAgGjSvYuZNScJQiP8wo\nmj+f0pAKgnr1SG7VmZfQYiEJUjkFqFWrhKJvlqudkECecIDOd+VK+lutJg+wK9dHTi2M4cYNofM6\nIL89qVGoBCVScuMGjb00jYsRA29ve7lWHgUs0Ffn5JBhxKdvaTSkCsS6w/OGp1pNvUrmzKHPGg1s\neXmwAUiHCbu718VXw5siz1bwXHm9zgsvtv8XJo9YjvpVm1OPrxo1hLmckUHXNziYvMRqNdU0KKUG\nsoaZ2dk0l5X6ijBS0ratkL7EEzGA5qCfnzC2WVkU7WLLGAxkwALCNZXOI4OBiCXgOFKi0dD1l5IS\nb28hTVTpGkvlpgMCHBMgo5EiSNK0IgbWk4PJB0uL6SdPtu9zw8MRKQEoOsgie/xyAQHAggXK23UX\n/PwoQgNQVIcXAxk3jsgnT7zdiTVrCid4AVCkMiLCvcfzJHDmDD3/CyuFrAC3kpK7d+/i1VdfRVhY\nGLy9vVGrVi3s27dPtMzUqVMRGRkJHx8ftG3bFuckOuxGoxFjxoxBaGgo/Pz80LNnT9xmxXpPCeXD\nKiO2ilgd5te/f/BESzzwoCBwZCRKwaRFnwZc6VDuChwZnIBQU8CMbzns3m3/+4svyhesK2HhQvLW\nO4uUnDunXOzuCK6QOBbdkIty/PyzkOLBDKXNm4Uu88nJVHvDsHq1a/MoNpYUluRw44bYeJO73o56\nkDBs2CA03GRedbNZiAgYDPId3XU64O23HW+/bFmqH+CxZw/Qq5fs4o8jJXXrUnTh3XfJUx4VJRiJ\nvCQqG8O9e3E54W+srGbGW+80wFsLe2JyC2BbBTMy/eWJrFqlgUFj/1vNig3xatgzmDZgEZrVak9R\nITkiysakYkWKoMqpTVmtFNE6wPUIK12a5oPFQka4tPCakS+eTEojANJICSuClhrZ7BgqSeSGAbqu\nrPbJEVFgxLJdO7EjgSlZzZypnLojTadyVr/lrPmhlxelLPLL80IOPXoIkUM5OCMlt28LEbngYEqD\nrV6d0pMWL1berrtQoQLNfYCUx3i5ZjY2WVluN6IBECGJjHT/dksy2HV3cy2N20jJo0eP0KJFC6hU\nKuzYsQMJCQlYvHgxwrii0Tlz5mD+/PlYvHgxjhw5grCwMHTo0AGZnKdw7Nix+Omnn/D9999j//79\nSE9PR/fu3WF9ykVEnRuLvZw37l/CuWsyOc8eeOCBPByl00jBGoU9DSilGRVmOxxq9e8PFW+gsdQd\nR03dli8ndRsecnKUjpCZSZ25r1+nwmUpgoPJwxkVRS+aRYvEOe/JyZRuotRF3ZkxBAi/OztuPvWI\nGT1yKlyuQKu17+zMcPMmee4Z5K53//7AO+/Q3599Zt+DASAVJ4BSR2w2oaFebCx9z0jJ3r0UKQIE\nYvDhh4JsqxxCQgTPLwNThrJahehRPh6Tkt696dhbtBAbSiYTYDbDqtXg73N7sa6mBktHNMXYLt5Y\ntHMWjvk5JtFlSlfAlMFf4dNR6zE/qBfmRjyP6a+twPTXVuBTXTssSojAyJ4fouG42fA15V/vf/9b\nfmytVjq/MWPos5wjwGql8/3sM+E7npRs2WI3BujQgfbHE3BppKRbN6ox4NMWtVqKrNSsKb4mWi1w\n+bL98fMEwxEpYR3ddTpxF3dGSiZNkq95+u47ciTw0U2WepWSIt/XwpX7ULr8mDGC8MHFi47TCY8e\nFafraDQUUWJKZPfuCR5/phCn0dD4PYl6QkepnWxsVq8WzycPCo+S3tF97ty5iIyMxMqVKxEXF4eo\nqCi0bdsWMfneKJvNhoULF2LSpEno3bs3atWqhVWrViEjIwPr8j1iaWlpWL58OebNm4d27dqhfv36\nWL16NU6dOoXd+Y2YnhYiQ6NRt3IT0XeeaIkHHhQAL7wADBzo2rLsZf6kYTRSmN8d97XkYa1PShKT\nEmb8OCIlgH1UoKDSypmZJH1Zs6Z8JKRfPzKQWQ+EvXvF5CUjg4yKixfp88WL4v27ElmaMMFeEYlf\nnyE6mrz8eXk0LiyFinm1LZaCX5vsbPuoVY8etB8vL4o8yR1/RAR58gFKw5IzrMxmilx88gmlM1it\nVKhtMND1NxjoXK5cIVJz/z6NZ2GVgBjpUamoEJ4bz7zgYNo3j5wcwftdtSosoSFYHZ2Ltb99hkOR\nKpyrGQ6rk6CTWqVGx0bPY+JLC1E6IBwGvTfUp05BdfUqSvkGoZRvEAw2NVTqfOOcr2FRSrOyWqnp\nGmvWd+WKmEDduSPUdfHXplQpGr/atWmuuIK8PNrGjz/S5379KLXS2xvo2ZP2o9US8T571rWi4yb5\ntkByMtX+KIGlI0rn/bZtjhWpLl+mSAMTIQCEOpp168SRQwaps+LRI8fKYOz5xP/v6LmybBmlhzFE\nRtK9w8QHkpIEUuLvT9fpjTecRxvdBVdIyZdfAp97FFTdAnZfF7Qm0gncRkq2bNmCxo0bY8CAAQgP\nD0f9+vXxBdcc6urVq0hKSkJH7ob38vJC69at8eeffwIAjh49CrPZLFqmXLlyqFGjxuNlniY6NRYr\nLlxPuojz12U6v3rggQf2qF6d/rmCp0VK/vqLDLnCdvrlIXlYW3U6qPn88ZAQMo5dUaXiIaeR7wiZ\nmVQr8vChY6NjyxYyYnr3FkdnGAnIyyPPaqNGZHAwtGlDqROO4O1Nhirb/+zZVLgMiMdp3z4yVlkN\nys8/kzHPPMPt2pHaV0EwbZq9d3TqVKpfMBqBjz5SNkTPnKH5sGOHvIqQyUREoHRpijj5+FCKDEvl\n0uvpXC5cII/4K68QSXClZ81XX9k31mMkjRVbc3Mnp2pVyp3ncfIkMGAA0rJScDwmGJ/5XMDRTBnP\nvwz0Oi+0ju2GjwZ/he5VOkC9ZatAahk5YrBagW+/pYhRTg6lR9lsyqREWqjOBB9WrqTahPHjKUXx\n9dfFRJRFGLp0IVLmCoYOJc89H3UqW5bm+LZtpMRV0F47LPrirP+LSiUm1Qze3o73KRf10Osp8qTR\nUA2W1LiWPhfu36e5qVSzwuSVWVTJmbODFbQzDBhAKYgMly8LKVNjx9JzZPToJyMHzI5P6fivXqX0\nslGjSMjEg6KjmCIlbpMEvnLlCr788ku8/fbbeP/993H8+HGMyQ/Njh49Gvfu3QMAhPN5fgDCwsJw\n584dAMC9e/eg0WhQWqLSEx4ejiQHuc7xcl1ZiwnlgqvhVkri488//LYU3eq9Jur+7sH/DzzJefW/\nAHVWFnwSEpDJPGsOYLh5E3Xy8hB/+LDbH3qO4H/uHMrExSHx5k3XO4fLIA7A7Tt3cDd/Dulv30bd\ntDSoTCbRvKqUnY3Uc+eQyhf4SrbzKC0Nl7h1vK5dQ5ngYFx1cX7WTU2F7dtvYfH3x4Nq1fBAYb24\n1FQYDx3CjdatEXbrFi7mL2e4dQt1ANy/fRshW7bA6uuL0/HxsAQGIvCPP2DTapGm1cp3x+YQCyCn\nc2fcHTYMoXv24NEzzyAlPh5VwsNhql0bN+LjEX3iBNK8vOB98ybKALickICAAwcQArofY1JScPPK\nFWTxqTBOEPngAazp6Y+vBY9aFSvi/IMHsGZmihWa2O/9++PK9OmoBeBqQgKSJduIvncPabdvI0W6\nbYsFtaKicK1DB5j9/VHuxAkEA0g1GpE8ahQe6fVOx6vSxo1ITU5GKme8Bl+4gID0dFyNj0c9rRan\nDx2ChUtRkz6zNOdP43ysN/7+ZhhsXaOA1GsO9xleKgoBPiGIKh2D0n5loNd64UridSSdOYMa+fUb\n8UeOoMLt28jx9n48l8KuXUM5mw2pV68i0GDA8WPHEHDgAKoCiGfSzhYLNFlZsJQqBU1GBnxGjEAG\nd7xlli2DT2IiTOHh0CUnIxjApSpVUHH9euQ0aIALy5ZBDUA3bhyM8fFAbCy0v/6KPJlx9I+Ph9po\nRFqLFkDr1lDdv4/6ubk4xi1bOzUVeo0GibdvQz1yJNK536r+61+4MmsWLKw2SAJ1djZitVocd+Ee\n1G3dCvPp0yLyXXrbNhhu38adUaNk1ylz9y5UZjPuSLcfF4eQzZtREcDtc+dEc1qVl4fKsbFImzgR\nD55/HrqHDxELIP74cdEzVGUywabTAe3bo9ZXX+Hy7dvIjY9HzdxcXD1zBjkyJMaVd2HczZs4cesW\n8litXFoapXQB1H+omN+nPoMHw6hSwRIfD8PNmzCXLg1rviJWHICre/ci2VFzSA8KBP2dO6gL4NiJ\nE7AWcFyrVq2q+Jvb3vZWqxUNGzbEjBkzEBsbi8GDB+PNN98URUuUoHJz+Kc4EVteXGCamn0fl5I8\n0RIPPHAG/f37iJo926VlDfmKRaonXOyuslphc0OH8lNbtiDphRcef/bKJzhqyQs/t2JFWJjUpwLS\nmzZFqYMHEcqKVFUq3Bk5UnF5lWQfqe3bwxwaCpXRCJUDT2hyly5Ij4uj8+eXy/e+qvILbW1qNVT5\nnmvfM2fgnZgotzk7nNy1CzadDiqjEfqkJJjyHVQPu3fHg/yO6CqzGTatFjmVKsFiMEBlNkNtMsGc\n75FWmUwI3LePGgW6CJtWqziPzv74o8MXqk2rhSbfyFLL7JMdrx00GpzduBFZderAVLbs4/1bvbyo\n9sOlA7evwVKbzWRQArDp9XbXGgDyLGYYzTn4+/KvWJW2A4dqBSpK99Yo2wRd6gzG2NUJGFZ2IDrV\nGYSmlbugTGA0/O6noPz8+fknKn5Hq7jjAIC8gACYwsOhycp6PJ5+J06I1tE/eICa+embFn9/ZDRu\njKpjxkCTH4HyvnQJmqws0TnZVCqas/n7t/r4wMiichoN8hRkxn3PnoUfJ8Vs0+mgZmlcbCxzcx+v\nn968uWh9n4sXnc6xR61bO/ydwRwSYjd+2rQ0qB1Fgrl7TAqbQtqMTatFZv36MORHFS28FHA+Ag4c\nQP1nn308l7Xp6bDkp5H6XLyI0M2bXTonOcQfOWJ3PQzXr0PPiEkxQ3/vHoLyhS3q9OmDSlwPmvS4\nOJiKoynu/zBMZcsiYdkyWN2RVcDBbZGSsmXLombNmqLvYmJicCNfmSQiP9cwKSkJ5TivYFJS0uPf\nIiIiYLFYkJycLIqW3Lt3D60dPADimHzfE0JS7iXEXxBSCE7fOYheHV6Cj8F1750HJRfMK/Sk59VT\nRWIidYkuzqhEqVKAVuvauOZHTxvWru24GNjdePgQCAws+rWXrp/fB0NlMom37Ww/TZuiQv/+JD96\n8iSiZs2i3PiQEEUVJqhU5JVkEanvv6dUimPHUCEyEhWU9tmmDZCcjNCaNQEfH+E4873FoUFBgEYD\ntV6PenXrUqpGWBgQFIRyro5XUBACqlQBUlMR06EDpZDw6/r5IbhGDTreK1dQqXx5Si9ZvpyOR62G\n76pVKPPpp86FEP76i2o9WrQAsrJQtjDX1M8PMfnvq6jQUERJt/HuuwiuXNl5P5F84lm6fHmUDg9H\npbg4Sk0rX15QDJLCxwfBy5dTQ0GG2FggLw8h3t6w+vmibkx1qCtGIz4+HrnmbFx+dATHLx6E1ZZv\nfCv4+yJDozGq5xSU8s1PI1PPBCpVpmdAqVI0h06fBk6dQrjknOPi4oCUFIROn46KTFI5Lg4oWxZe\n27YBAwfSMuXKAX5+wjy6dcv+/j9zBvUbNaI5VqoU4OODUlzkp2qbNkCrVvDPzS3YPfn778D9+yjD\nr6PXI65uXSFdyWIBKlVCTFiY/X3o64t6FSpQyk/16vLpia1bw+XOS5s20fVmRe0//wwEBSFiwwba\nvjQV7bffgPR08fEz5CuWRpYvj0jp77/9Bvj4IIJ9/+uv4nFr0gRQq9EgLo7GwWZD7DPP0N9NmiCs\nQweEccsX+l149y6lKtaoQfeGtNapOPDf/wK5uaiYf6yB/LPW2xulatZ0/rz1oGAo5Him8UIqErjN\nAmnRogUSEhJE3yUmJqJifqFgdHQ0IiIisGvXrse/5+bm4sCBA2ie76Vo2LAhdDqdaJlbt24hISHh\n8TIlAc+1GAS9VlDFyMpJx69///gUj8gDD4qI2FjnBddFRUEKtHNzqSD1SRISQDkHvqiwWpETHQ2j\nXJpWerqyFO9ff1ENx44d1Bgtf1tOyePdu0ReWC+FXbtIAldOaODWLZI9PXqUcq+HDqVu1wzh4VTf\nMXo07ZcviC1od3m1muZZUhLl9UvB1yow1a3UVKEGg81RV+aRyUT1NKwOQQ43bwopJlLMnUuNHVn9\njLTjO0C1KCEhZIDZbEDfvuKu1wyvvUbHsWyZoOa0dStdXyVYrSQq0KTJ45oKm1aL03dPY+GPk/D2\nuAYYu3Ucxn7WB9uOf4Wf4hfjaOJ+gZBI4G2yonZwNfRuNRTj+s8mQnL7NtVVHD5MBdSBgVTcf+IE\nERM2zvx8s1iogFna90alorFgtQ56vbjGRVonkZVF14d59C0W+ttoFK5X3bqkgFbQe1JOfIHVdqxY\nQdc9O5uK1FmN0oULVDOVlUXLXr9O17NRI/vtf/ABSRUbja7VdxmN4tqxrCyqP/r8c3uFNYDqNfr1\nkxd1YHUscs8A6fOrUyfx72o1jS1bNyVFIGkVKxb8ebt2rX3dE0DneulSMTSQ9gAAIABJREFUwZ8P\nRYGjju68mp8HJRpuu0rjxo1D8+bNMXPmTPTv3x/Hjx/H559/jlmzZgGgFK2xY8di5syZiImJQdWq\nVTF9+nT4+/tjYP6LMiAgAMOGDcOECRMQFhaG4OBgvP3224iNjUV7JjtXAhDkH4L2cX2w49D6x9/t\nO/kzWtTuiPBg+dxwDzwo0XBkuLkLq1eT0esKjEblZn/FCZ2ueDrPW60wRkbCxoe6jx+nHhebN5OH\n09V+TK6QEpuNipy9vYHOnYl0Nmwo36Rr8WK6LnFxVKSs1QJ9+gi/BwaSYZiRQfutWlXYvyvHApC3\nPzpaaCZnNgN//il03Wa4epWOu1s3MpDUalIRYl3VeRUuZ2DpT0wJiCEriwzw4cOph0vZsoL0Lw9G\nHjIz6ZwbNJDfzwcf0Nw+eJD2uXSp/fZq16ao0OXLghHLHZfVakFWbga89D7Iys2ACirk+KpwsUVF\n3C2fh9xdCwEA95Jv4taDfBWw/CiI1WbFo+wHisOg1ejQuckAtIntBsP+PwFdGKA1UCF9RgbNvx49\nhOt44wY1qKxVi5pYAuJUIaOR5HOlc0kqpS0lIdLPrBWAVkvkIzubolrZ2SR2ANB1Zn1EeBw5Qs8H\npSiTXO+cgQPpGJcupeL2nBwqfGYqX/fv073Qp49Q0M2K9qW4cIEIWKtWROCYBLQSpPfJp5/S/ajT\nCf2KeFSqRGQhNVXcGwSgqMP48fKqR86cKlLFLR7SvijOkJxMpGrUKEGNjIFds+XLxQ6O4oQjUiI3\nhzwokXAbKYmLi8OWLVvw/vvv45NPPkFUVBSmT5+OUVwh14QJE5CTk4PRo0cjNTUVTZs2xa5du+DL\n3fQLFy6EVqvFgAEDkJOTg/bt22PNmjUlru7k2Ya98NfZ3UjNoJeB1WrBziMb8EqncU7W9MCDEgit\ntmAys4WBJJLqELm5ys3+ioI7d8h4VFJg6diRVKKysuSNkcJCrnEkK/5s27ZgalrOiMDAgZQ2cfq0\nYIw7Ui9kZPTZZ8lDzHei52EwUMTk9deF7ywW8pReukSpP0rIyCCj5+ZN8vS+/z4Z8lJSMnw4ETSA\nlIYAIilMIOXGDUp54ufqDz+QESf1aLMxf+MN8ffJydSXZfhwOvd584h09OghXo4RoMqVxd2hpWAN\nGpOTKaVs/Hh7UhIaSuc8ZQrQqRNSHtzCmdK5uGI7g0vLhiAjJw02aYSjuQYkDwAgoYCKY/moHVwN\nA/q8hwDffO/6unVAs2YkNbtvH31m3nHeaGOSzAwhIcLfrO+G1Inx6qsUMWJwRkr8/QXp4Lw82m6X\nLkDz5pQuVbMmpd81bWrvoNiwgY7JESlh+5o3D3jrLSJhbF/Z2UR8o6MFaWFeTYg5D5SMWaaqxpZ3\nBul2duyg9Da56BuDI5IwcaKyqpmrpOT2bfqfEcCCkpL//pfufTnScfq0QOodNWR0J6Tnzs+19u2f\nXt8rDwoEtyaQd+3aFSdOnEBOTg4SEhLwL5nJOmXKFNy5cwc5OTn4/fff7epQ9Ho9PvvsMzx8+BBZ\nWVnYunUrIktgp0y91oCeLV8VfXcs8QDSslKe0hF54DbYbNCmlMDraDIVXzRDoyn+SElBSEajRsUj\n3bh4MTWWc4QhQ4qkvCWLKlWQKpXGzMmhMfH1dd79XbqeXCM/hrVriSC4ul123WvWpH4mSkaNXi8m\nJABdo6tXncv0MoJw4wZ5lStXFoy6mzeJIAAUTZAaoJ9/Lu7OLE0D3LVL3NSNQalZJ094b9+m9C25\nFC6TiZrYtWplT554sH3YbEC9euLfvvsO+M9/SJJ26FBk6oANKyZh2rox2Oh7G8f0j5CenWpPSAoJ\nH5sW3QwxmHmqFGatuY4RtV8UCAkg39GdSR3zY5WXB7RuLXRTL1+ejMvcXIqcyUVW+a7oAMk3d+ki\n/p3Vi5w6BcyZI5BmtZq6m3foINRv1KtH++/Rg+SqAXIqdOliLyksRcuWwHPP0d8ffCA2UPPyKPog\nFQngO5SvWUP3g3RcGPg56swD37Ejpcfx63TpQsRQiQQwGWSlbYeECNFDHvv3i4mhFOyaq1QkK7xi\nhfBbXl7BSIm0ozsPdzp0XMUnn4ifQ3zj1BkznNd9eVAwmM2O008LCY+ObRFQr2pzBPkL7NtqteDb\nn+fAai1mj7MHxQrfc+dQT5qL+7Qwaxa9IAF6SfbuXTz7eRLpW0FBAFPzcYZ69ezzod2BLl0oRcQR\n5FI/CgKzWXjpM9SsiWRpsWduLqUmPXggX4cAkDf7xx/purOXamAg8PXXzo/j2jXyWMp1cZceL0De\n5CNHCpbm0KIFkQxnkR6LhTyqDx+Sd5wnFitXAt98Q3+zXguHD4s9rCzVCKD0mnypTwDyfSAA+egU\nQOPOUmKYopnc9WY9QZyB7cNmo+NkXd4BpJ89jmMX9mPVr/Px8cqReP+thtjfpJyiGparqBUdhwkD\n5+PNfjMwstaL6FmhD1477YUZ1qbo5FMTfiYbfHPM9teSNzylxja/LOvDwd8rPGHUaoUxX7+e0nek\nXcabNCFCx1C6NNXI/Pe/dB8ePCj8plZT1INPneQjgny64OnTziMCcXFEivhz4cdAjpSw7anVRBhY\nMa7cfjIzBcLmLFKSkUFpWHLpqEokgEUtCpohsn8/EUgldO1KzxqVyj5y9fPPYhLpDI5ISceOQp2c\nXMpocaBePSHy9PCh8+eeB0VDRgZFNd0MT+VPEaBWqdG0Zjv88vf3j7+7dvcCjiUeQFyMA8+aByUa\nVp0O2VWrwsf5osWP998nz+HLL9ODvjhC0BkZ9AIp7hRJJSNRCUwK1J2KYN7e8jncPFzpUO4IzNhm\nOfNKyMkhD/CZM48Vruxw4gSp7bzwgmD0jR5NhqAzLKQ6BOj1QmqS2Uyecd74Y2T0xAkyngqae+0K\nieMjGzqdmJRs2CDelsVC0ZEOHYSO6jNmUG2Mv789sVVqtPnMM5T6IwWLUAFUZLx+vfzxszQlR5g+\nXagFstkoNa1VKySl3MIPvy/FpbL5NVQXXJNNVkEFH29/ZOdmwmazolwGEHMzEwGjxgIAtD/vQBXf\nSIT3+EBYafx0eNWqBb90KzQ6A6WyNW1KzwzWII9BLlICUOoZ71l2loMfGCiIKFgsRCKXLKEO7ffv\n0/4fPSJi/sEH4nUvX6aIR+3awndyzQKtVjquXbuE5pbMeeKqIAXbpjQ1zVmkBBCikXLKW4mJFO2R\nblsOBgONC0/QGCZOFHdJZyhoKhUDu3+Uiro3bhT+NhrF876gz39HpESlImW+rl2VG5O6GzVq0NwH\niqcu0AMxisle8ERKioh2DXujbGnxg3/HofUwmgvYpdmDkoOieMndjT59gBEj6O/AwOIp/k5JIe+a\npLGp26GUTqOEli3llV2KAldJSVHmADO2Jdsot2ABAnkDJDeXDMGQEOX0oLfeovSmZ54BFiyg73j1\nK2fo21fI21+5kryWfH0AQNd+wwbyesXGUsrR1KnC79eu0f6VeszIGZRS8L9LSQkP9r3UsFIiHgB1\naz9zxv57nU6e7PHpW998Q+kucsc/d67geU1IEMafx+ef05gOGgRkZsIUUxXbDnyHWWvfwqVbMsfE\noXRAOHq0eAVjNY0xLzECi97cjIVv/oRZI77Dp6PW4+Nh32LCm9+hxw/xaFOqJtrU644WDw0It+W7\nS/bsoWvj5QWVyUS9UHQ6um9Gj6ZIo5RoGI32nZg7dwaqVSPD2WYDdu4E6td3bBRPmCCoQDEVNbWa\nDGwWxXv0SL4Wx8dHEDFgkHMEWCzAlStUh8NQUFIijZIAwMiRVEchJSVMGY9F0VQqUsCSS018/XUh\nvcuZcWYw0Lj6yLi5Ro8Wk3KGLVuUo6dZWcp1GtKu7o7w9deUMldYsPF3VORfEMXFouJJ7ssDDykp\nqdDrDBjabQJUXEf3h2n38OXmqXiY9mSaBnngXqhsNtieYBdxhwgKIo8TUHx1H66mqRQVw4cLed6u\nwJEhWlh4eYmlOaXIzqZIgjtIicQ40GZkQMvrs7dtS9GA5GTg3XeVtyd9+Lv68vXyouJ1RkqSkshA\neukl8XKTJ5PxZbWS4eTrS8SE4f59MszOnqXPV6+Ki6BdiSwtXkyeTICMxKpVhfQa/vwiIqiuJS+P\nrgGLNul0NE/Z91I4uy9u3BAiGhERJLnKH7/cNqtWFfL2HzwQUr1UKooqZWUB6enIWbwQvw5qhW+/\nm4AZL1fF7qM/OUzhDXmQic61umHSS5+hvW8NVNq8B3pjHlQq1WNBF73OgEC/0mS8R0QI481LJi9Z\n8liFSm0yIbNOHcFQlsOAAbQd1k2Z9cZYtkycKtWxI7B9u+AMkcNvvwn1Soz4MblZRgKUoi0mE33P\n/3bokLge5+pV2r5OJ55bLG2sWTPH58rAp6vt2EFpPePGkRNASpiCg2kesOJ5R8/F8uXJK3/vnvNa\nBWfPHDlkZhJ5ksPhw1T3JgdXHAQMb75JogyFRVAQHaMjgYsXXyTC+yTgISVPFgEBlFrsZpQQy+uf\njbCgSLSoI85/v3o3AZ9v+hDZRicpHB6UPLgqc/okwL9Ui+uh60qaijtQp46gdOMKioOUREeTnKcS\nNmwgyVo5r6arYEaBxNC16vVQ8efTqRORhmPHSL3KVTjzhqpUFDkwmWi+MFKi0VCUSMnQOnSIJDyl\n9UXsPFJSKBWnRw9KX2Fo2tS54eHrK4zpoUPAl18Kxe08KRkzhmpPLBaqpXrhBWD3bmEueHnJ3wPO\ncuGXLKFIEUDN6kaPFn4bP14sgczj0iUSDvjmGyA7m6R7fXSwnjsLXLuG021qYeKpL7Dj3M84mXIB\nqf72YxuaZsKzRx/g5bNWTK4xGB/O2IOuDftBrzMQ2du/X36ez5lDc5URMkCc1mMwEMnYtw/6e/eQ\n/NxzVJyuBK2WoiHM6G7VinqllC7tvJ9EejqpnKWkkIHNkyNGSjZtoggCIyVK0Qxzfq0L/4w1GOjz\ntWuU8tOzJxm8r78uJqJM9WvQIMfKVQwajWB4f/yxcJ/5+9PzyBEcPReZZHl4uGuRkoL2gHJELjQa\nikixWkPpeq6+Iz75hKSJC4uGDem+coQXXxScEcUNDyl5slCpikWMxlNT4iY813wQEm+cxP1Hdx5/\nl5rxADv//hG9Ww91sKYHJQ4qFSxFMUrdiVGjhEhJvXrF89AtbP5yQWG1Uh56167Ol924kfp4uJuU\nZGWRB1YpVc1iIcOtKEotcpGSs2dR6tAhGKX56SwdryBNy/R6517i/fuJCGRmuk5KADKSp00TkxJ2\nHmlpwKpVghELkKFfvTp5rp1Bq6UUsTVrBMUngDzUb79NfyckCB73iAjqRm80Coa5nOpSSIhzAzUg\ngAxqObA8dBnkvD8Bieo0HKnojZtVyyBt8fOwzuwK7cOfgD0/Ia+Lcl+qUj5BaB/7HNo89ILqy6FA\n0p/A8A+pCJtFYC5cIGIqN9+2b6fx4uV3eTLAjN3z5+HtSg49X5zOwGqNnKlZXbtGBLFTJ2DsWHlS\nwoxzRkr++IMK2xlsNqpZMpmogH7iRPE+Ro4EevWiWg4vL4pCNGpEaXTTplFKobe3a4o/hw9T88Pn\nn6d1AaEZpyv46COqGWHPXin483eGr76y7zXiDI5ICRtfuZq16tXpGaukMGiz0bE/jR5QxY233hKe\ndR78Y+EhJW6Ct8EHbz0/C19snoI7D689/v7349sQ4Fcazzbo+fQOzoMCIbdiRdzv3x9PuJe4PPim\nVL16Fc8+nlT6lsVCRpArKWjbt1Nak7u7zG/ZQoWzq1fL/+6ODsRBQZR+whuKx4/D6/ZtcaQEEMiR\nUqE7QGk269bRcQ0YQAainJeUR24uzZ26dQUvs1YrGPizZ1O0gN/vhAlkiEkjJcw4YoYr88Y+eEAp\nMK+/7hopOXSIUoLu3BEbwEOHCvPcaKS52Lw5GaYrVxJh695dqIX59VdK8WKfXelpExAg27jz6t0L\nOJa4HzabDQG+wUhOT4JOq0dwqTAcTzyIay2sALgxypfuzbMpOwc0ai1a1u2Mbs1egpc+3xhl193H\nRyzTnJBA10EurZFFbPlICe+95zzwRldk8+V6i/D7cjTvWfqRzUapa7xRHhFBzTFPnCBpZmY0Hz0q\n3obZTMteuUKpe9Wri38/fJh6h/B1L2zuMiOaqXQ5w+nT1JuH9+Ty4+gMN29SDd8zz8j/XqYMzUFX\nICfd6wzOIiVsGSni4pTJN0DOnldecV5X90/Ek4rIeFCsKCE5Kv8/4O8TgLHPz4Kvl9jA2LJ/BXYe\nlilm86BEQpOejgrz5j3tw7DHu++Sp9rdCA+n5lI5OWR8FFehv7PwelaW8CJmZMTdNTTOUvOceYxd\ngVpNqlG8wZ9/XiqpUdS6NRlcSpESHx8y1P7+myQ7AWoqyBr2KSE4mPL+u3Ujgx6g8S9XjtIu5syx\nH9vGjcmjq0RK8vLo3Fj62Pvvk+FXkPFSq4X0HYaXXxbqHJixO3EiFWADNDZvvUV5/Go1eb5ZYzZA\nmZTs2CHUzwQECBKvADJz0rH1wEos/PE9/HFiO/ad/Bn/+XM1/jyzC3+c2I7N+5bj2j0HaX4K6HU4\nBdNfW46+bV4TCAk7L4COk5ESk4kIVkwM1e2wgnEGq5UK6e/doxSyFSsovY55wVlKW+PGSGFjBRDp\n+/134LXXqNicwZHsd1AQ3X/JyfL3P/vu77+BSZNovx070jNj4ECqSXrtNTqmhg1p2bJlxdeFN7TH\njrXfh8VC84/1Y9LphEL9gnr25Yx6JeloORgMRJT9/eVTK9u2lT8HJYwYIa+Yt3YtzW0pXImUyN13\nzp5fgwYVvL7FAw+eIDykxM3w0ntjcJfx0GnEnuef/1qL345sekpH5UGBUBAFk+LGmjVC+kFaWvG8\nUMqXB/buJe+it7drPTAKA77XgByqVxeKkXNzKUe9f3/gp5/cd97OXtruiJQobPdRy5a4L02rMJlo\nn1u3yhtMWVlkIB05IkR3XKl5stlozPhiWaYk1L69uGN9QgKl1P30Eyk6jRxJpIWhShWaE5MnC5ES\nq1UgSfx4bdvmOMdejpTwx8xH7VgkhJE7dm3UapJJZn1Lzp2Tl0A1Gh8TAEspf9yzpOP89ePYemAl\npq4YgT1HtxS5XwgABHgHotMDX8x4bSWeXbUXvt4yBJMVyQ8eLJASNgbR0XSt7t4Ve7ktFqrj6NoV\nWLqUIkpeXkKkpHlzIjQWC2z8mJ88SddvyxbxnDIY5O+9LVsoSrF2LY1506ZENvllGzcmQpKeTsb6\nypVEDM1mSrfSaum6dO0qEMGICPkO7zabvFqaxUIk3GgkUmIwAJGRlMJaUFIiJ77A0rdmzlS+17p3\nF2qXcnMpsuuOXgyPHsnfs6tWkXqcFM8+q1zozu5bufvMVVUyd2HhQrGDwAMPiggPKSkGVK8Qi9d7\nToZeK36Qbv9rLc5dO6qwlgclBTaVCqqSIguckSH0pyiopG5BwLyo7do5zLEvEtjLVylawl6ov/1G\nxd/MEBk2jHLTf/ml6MfgjHR4eVHaBkCGhLvSx6xW5AUFwcJLtK5dS8ZZ+/ZkePF1Fk62JTsPbDZx\nPYtWS+lVbC6HhZFHvHp1MsoSEuj7MWME6eWMDMpVZ0XoAKWqDB8O1KolRIH0eiFPnj+W1FT5Yx44\nkK6fRkP7vnuXOp3zYNGE/fvpf5b2wowwdk4aDRnozMNctaq8gWa14moAsOqXf2PC1VWY2VKPJVum\nYc/RLTAVQLLdP9OEZiiDdwbMxbw3fsCCMZsw/Ln3MeDZUZj8yhf45HwQus1YB//oasr9IVgj0AMH\nxGp6NpuQVsePATtfgH5//XUh4sUwYABFk/Lvm4ADByhKwssq83P9iy+I4LGmdmvXkojA4sVE7Nh1\nPHyYaj62bhXWVamImFy9SpLB3boRgTCbyVkSEGBPBKTefqZyptfb31fDh5O6G4uUVKxI27dYhKJy\nHnv2yKbjifYtfYa3a0fRG15imEdeHhHtGzfExenuiNbKnQOgPF/u3iV1LDnExBC5VYqUPClSkpND\n0dJ7HpVRD9wHDykpJlQrXxejek2BgQvh22xWLPvPLCRcP/EUj+wfjFu3BE+6O7Fzp7gbcUEUTIob\nfB54QZsPFgSO9P/nzLFvgFYYHD9O/zsjJR07kmHAUj9ycwXFJoAMqMLCagW+/VZ5Hg0ZQt3T09Ko\n8ZxcD4FC7tdOZnrNGjIQd+ywrzWQgjewlEjJunWUnjFhAhFLrVZs8AJk9LH9MIlf5pWuXZu8s0qG\nUkgIGXQ//kiiC4yUnDgheL4DA+XrI9LSyNi8fp0M6TFjKA2Nh05HY/LOO/RZraZIAWuAyFKf2PyM\niwMAWOKPIOmz2dg3/kXsPbYFF2+dQUr6fWxMPYwF9W04mrgfZqtzw7Lx5Sz0imqHDnF90bB6azx7\n5B7GXQnCDFVLvNjrPURFVINeZ4BGrUGdSo3Rok4nhAVFkhEPkNysI0ybRoW4p0/b/8YigbwB/OGH\n9H9oKBmiSp26u3RBXkAAIlatolQjFumVu5c//VSY+4cOkSQ1690jXVZuHkRFCSlV7NmUlkbXvUcP\nISIEyJMSlUq+4Jzt29ubHBL795Nq1k8/yRdmL1liX7PCg+37/n1STgMo3aphQ2WpYr5Wg5fxdUfU\nXCnFsFUrwQnCw1md35w51INIiidJSm7dkp83HnhQBHgK3YsRlSNrYmjXCViyZdrj7yzWPHy7Yw7e\n7DsD5cOKySP9/xU1a9KD2tnLv6Do3Jk8TytW0GerFRqlxlVPGtOnC13cL1ygF+Zrr7l/P6wHitxL\nzV11Ha50/eb3Xa0arWM0kiGk15MUba1aha97Yeosjgo9x4wBFi2iyAWLJhQVdesiTVqAyqeS+fo6\nJiXS9U6eFPfaAATvMJ965etLaSnMIOKNO94Q1uspVaZ6dWURgMBAIj0MbJuXL5MwQe3ayh5hq5Ui\nTzt3kqJWfLxATnNzSdlpyxYyvnkjkEt3s9lsuHT7DM7X8cHNWs2RpT4G65q38DD5FkywAOUB7F+p\nOGxS+PsEol3D3mj5w37og0OB9fOA91dT2hEAvDIbOL3VXqlt8mSSl2XXjjkKnM3J11+naIUUmZnA\nwYP0N59W1LMnzfcKFahvjFI9xMyZMMXHC80TWZRE6V6WFpEzUiIlukrGJkvd0mqJMGRkUASGpfYx\nNGkiNCRkKF2a1ktLo3qZMWPoey8vutYVKgjS0RUqECn54Qfx2LZpYy8pLEWDBjRf79yhSBB7ZjJC\nL7cu36GcRQqnTSu6g2rxYhLXeO89+98mTaJ/UjiTaVdSBUtJeUzWix2OOrp74EEh4YmUFDNqRNVH\nv2eGi74zmnLw2aYPcP3eRYW1PJBFv34Fa75XEHBeQd9z56AujiaFhcH160K6xcGDAnFyN7RaevnK\npTe5q2+L1Uo51EpKSSkplJLRpw8tV7680JFZr6fjc7VQVQkDBxKpcURK+NSPwpCfixfJUJ0xQ/iu\ncWM8evZZ8XL8WPv4yHdwvnyZOokPGyZ00K5fH5g1y/7YeM/0w4c0lqmpFHVi4CNtjJSYzXRNXn2V\nPMuuGhnMw1u5sligQI6UMKllk4nOlRc9WL5cSBViUcrdu4GUFKRlpWDXkY2YvWQo3vqsNz7f9CF2\nVzXgQvVQ3DI+xJ3k60RIXIC/TyCqlKuNhhneeEEVgymDv8KzDXpCD43QNJM39uS821YrXVd+HF2N\nXvKEgMfVq5S+B9jP76pVaTzbtydSI4d79+B79qxASpTSt6THwK5ZQSIlAC139Sr9nppKxLdlS2Dz\nZvFytWsLaWsMDx7Q9QaEyClA41y/vrg/EP/c4cf4/HlxxEwONWtSupu0o7vSNeDPV60mMsW6phf1\nXcCuqTOFOOk6hVFEPHvWcY+lQYMowuEOeEiJB8UAT6TkCaB1bDfkWfKwZb9gUBpNOVi3+3NMGLgA\nGrXnpnYJ0dHu71sBkPe8du3HH60GA9Lj4kqGJDCPBQso5cLdOH2aPO8GA3nKpfK058+L09sKC1fS\nz3JyyBALD6flWaE3i+QU5MWuBGaEKYHPjS9M6gabo85qRPhIiVz6ls1GBsSGDVQbwvq7fPABpfbY\nbOLx5EnJtm1CbQbvcY2Pp/8HDhRHShiRYN22XcHgweRJ3rFDIEgVK8rLqEq9zTwp4RXl8lOPzi/8\nCPsHtMS51Euw2oqWPmPQe+PlDm+hTuXGUKvyI41NKgM6Tmb2xg0yRHmiJ0ewmIF54wadd+3a4msg\nvSY8lAxivZ7mvM2mbABHR9O/li0pwlC/vvDbkSMo8803AikJD6f6ibFj7Q1b/hjY+BsMNM9YrxRW\n+6E0D0JCiPRu2UIiCKdO0bEtXUrRDV9finglJlKTP2ln+MRE2gfv6JDrem610n26ZYtYDp1FaFyZ\np2+/LdQkSc9fCqnU7g8/0P9FlZo1GIgMNGrk+jqFbWjrLPVY2sW+KPCQEg+KAZ5IyRNC2/o97HqV\n3E2+gfW7F8NWUoqqSzocySQWBYsWiTohq4qroDwrq+BeqmrVhJSP4ODiaXJ49Ch1xG7dmvYlfQnv\n30/GRVHhbFwbNCADYvZs8rDOmEFG74svCkZs+fJCoz1HWLFCuT+AM1LiLFJy757jFz/7TbKu78mT\niJ48WfiCj5R0725/vA8ekIGfl0fRHT6tSs74OH+e1LUAQVLVZhMI9549gmGk0QhGYEwMyZUGBlI9\nzRdfAOPGCbUop0+TipK02d3LL1NBNH9ftmpln15oNDokJblaFW6UD8Txiwex8Ni3eO+lKCzpEIYz\nKYkuExK9MQ/hmTaULR2FYP9Q6LR6qNUahAWWxaieUxBbpSkREoCuPd/MTqUir/iVKxSRYjh4UExK\nZs4UOtkfOUK/X7tGRIwZzY46y4eEUCM9u4PPl6o9fNi+dwdAHe6//57+TksTjMFLl+h6e3lBbTIJ\npKR6dWo02Lev2GC0WOjcpZGS5s2J5L74Is2XvXuJoDmKKOzcKURqdr80AAAgAElEQVQ2Klak77Oy\niGDu2kWfr1wR15gwmM20Ln9scqTEYqGUP5bixe/faHTtGf3XX5QCxqDRyKdLAQKZZM9Ys5lqV44d\nc74fRzAYhPouV/HggXLtnNlMqbxyeJLKkez6udIjxwMPXIQnUvKEoFKp0LPlYKRmPMTxiwcff3/4\n/O8IDSyDjo2eh6q4ipj/v6C4SMnQoeLPckXJ7sCECVSsXRAS6uUlFLiyFCt3g08VGDmScraHDBF+\nd9dYvPOOci402w9/fno9vdAXLiTD+Nln6TtpgbQc/vxT3KOBh5eXMilh6lNsnsmlIpUpQ0RWSR1H\nrqM7ABUAw507wheDBwsGHW8oHT1KNTTMwyt3zZlRz5PU/fvJmAHs01YAoU/Hd9/Rftl1ZY0YrVaK\nkgUGkhjAtGl0/tevk1HMIiC3b1PvEL6TN5++9cYbtD6Dlxfw2WcwJ93DFWsKEg+uxo0bZ5D6UhXc\nX9QL6B8BIALY8Wn+8o49r6EBZdC0dgcE+4ci99wphE6ciiqXHkI9fATwwSLlFY8cIXLXsSP9z6BS\nUbS0TRtxtEqam//zzwLB49Ojxo6lsejdWyAPcvD1FXqv8GD9RpRIdE4OEfEKFcQedNa7ZuRIqEwm\nPGrbFt4sxU8Oc+eSU4Sl3fXpQ0XgffsS8WF45hlqHqgEVuPG45lnqGj+1i1xJEbOEGdRDp6UjB8v\nrs1JSKA5pdPZP/O1WuoTolT4z6NaNeF8jx6l+cw7BqTgn82FjVZIIUe4nGHIEHH9Fo+UFHIgsbRe\nHsX1jpSDwUD3EpPu9sADN8ATKXmCUKlU6NvmNQT6lRZ9//Nf67Dj0DpPxMQZJk4U5+kXF4pL5aow\nLwvm/QSEFCZ3g3/5yhGfGTPEnZELiwYN7AtfeUi9fMxYA4A6dah5pKtgik1y2LHDPtedYcECSmUL\nCCCCJiWsDHwa4dWr5JlmUIiUWLy8oOaVsIYMITUjKeLiyHPNrrXcNZfziPboQcalSkUefalBxYxA\nvZ4iGi1aiH9PTxeK5PlGe0yK99o1imKNGUOyzQz16tH1AWjf330n2mxysDd+zD6ByUOr4Ys3muO3\n+E24cP8C7qtdM9TKlK6Abo+C8VJyGN5ZdQaTX/0SHR6VQsPdp9DCvzqqqYKhXrdePgrBY8gQ8t6/\n+qo4/WnECHIWjB9vn0J3+zYVnF+5QlEBRux4UYgGDSj9KjDQcSrL9OlUsyMFP895TJpEhqdOR+mT\njx6JHQhMtnbHDmjT0nD7jTeEIn05aLV0joy4tG1LdSAF7c1Tr569Qfz77yQZvGSJQESUVK5Ynxre\n2cGkngEibjVrUmPJli3t579OR3OQzTlHOHdO2O6GDfYy1I5Q2LoOKXh5YVehVivvW6OhebRjh/x6\nT0o5MiCAImYeeOBGeEjJE0Yp3yD8q88n8NaLi9F2Ht6AJVs/RlZuxlM6shKC1FRxASQPJdUUd0Oj\ngcVRsWBh0ayZsvdLCf/+t+ARjI4mY9LdMJvFpERqBLjjxcywZ4+yypRcpKSwNUQxMTTeUqSmkmGp\nRDotFpK9jY0lA0uONFSpQoYqv81t28TbAMSk4cgR+J08CbWrHtNHjxyTknr17CNufGHwpk32Xmqe\nlCiBnYeUlGg0lLa2caOIHKctnIPjQXlIaFgJWbkZOH/nDH5pXxnf/Tof83+ciA++fhXTPuqIA17J\nyNEX7N4t6x+BMX2n472XFqFTThiapOgRlZRDEeU7d6i+KjeXCMELLwjpTEooVUrU1f0xoqLoHpOr\n6/nySxoTVqDPIFdI7kyOdfVqcXNEBm9vIa3u+nUypK1Wkl7OzBTuTYNB6HjPPhuNwJw50CUnK++X\nQasVF9J7eVHambOGonJwFPFk8+7YMXsSkJpKx9yzp7gXDkDfpacLPXOSk6nO5f59Qb4aIFEEufuS\nx9mzpBLGQ6dzXSjj4EGKILojUtK9u1Dc7w6w8ZWL9ubliYUtpLBai6cu0wMP3ARP+tZTQFhQWQzr\nPgnLts+E0SQ8WBKuH8e89eMxuMs7iIqo9hSP8CnixAlKG5GrYViwgIyHfv2K9RDSmzSBNiUFDhIh\nCofCqFjx6R6NG9M/d4P3CMpFY9wZoRk6lAxHlrbE4+uvKUWFQa7JmqsoW1Y+v3/JEjL0Zs6UX89q\ndU7C0tPJwGWQErmGDSmNhckPA8D+/fA/ehQqV8/HaqVtBgeTx/yLL8j47tiRjPGtW8UFvGwdNr+C\ng+0NN2bMxMfTcj3FNW5YuFAwnuQiJSYTzFo1HviroTGm4vr537HBuB/GU38Bp7jtdI4BLuxz7Tw5\nlPMKRdnE24ge/BaiV/yEMhOmQsU8/23aULRg2zZg3z7y1OfkiBWy/v6bvMdt2gDz51Ntw6+/CjsI\nCJAnJQxyCmhszLy9BdWwwYPl5bOdkRKl9Es/P8HrPXcuEaGLF4XryY5h+nRxVJPzwGfwkR8l8D2P\neBQ0UqIERvTZ8VaoYF8jU7myIP0sJTZ//EHHkpZGzRnz8gTizadRxsQ4P5ZLlygKNHiw8F1BSAkz\n+Ku54T3s5eUegQ4Gdq3kHCuVKjmO8n/9Nc0jdylweeCBm+GJlDwlVCtfByN72Hd9T05PwmebJuPW\ngytP6cieMrKyKFVCDpcvF0/32IkT7dIRKk2ZUvheGEqoX1++4RWPc+eUG/a99prYI+8uNGlCufKP\nHpGHMTNT/HulSqTm4w7wqks8bDYiKqVKURFnRgYZItIUpexsoVGfI0RHC83neDjzCrviNe7dW2gg\nB9iTEq2Wij/5ZaxWWL29XY+UsOZ3ZcpQQfmffwoG9uTJlGImtw4zSAYNsq95YcbMzZvypP+ZZ4Q5\nL0NKzlcKxNRe4Zgda8SMlF+wZtciGL0K7tdSWW2Iy/DFsG4TMbTrBLza+W3MGbkOE8r2wMsJKrSo\n0wll538lEBKACGbbtnRtliyh+pmsLDIemcHHR9p+/51SS/haCVdIiZQ08k39WCSlVSsyrseNE9ed\nuEJKlMj9okVUN8L2n5gokBJGQvbvp1RBVtPBIolhYbjO98DIyKDalldecW3/NhvVBWRn03PQ1efe\nyJF0LV54gT6z+6ZSfv+tYcPs+/yo1ZSa9frrRLx4sHvv4EGKEmk0YgJWEMjVVhQk8mowUHpjdjbV\nIhUVQUFFlzNn4KWLpXD2/HrzzeJpQOyBB26Ch5Q8RVSOrIV3X/w3osuIPT/mPBN+3PsVLNYS0lX8\nSeKPP5SLLAuTZuAK5s4VK6yoVLAxWUx3IjbWeZ+VM2fEpOTkSYHIpKYWT+i9dWsyeDZupPHni7EB\nIlOjR7tnX0qkJCdHMLaGD6cUvldeoXqWvXuF5RITKZe8oIWjDM68wq54jZcuFXs+XREgsFqRFxCA\n85J6CxFWrBAIoc1GHmFGwK5do0ghO0a5+6BOHaGWRu54GjcmIzE4WDy3jx0jEQImKPDRR+RNzS8Q\nPhxqxaypXbHktUbI8C64R12t1iA0sCw6xPXFnOyGWPTer3glJRyxVZqhXtXmaFi9NbwNPjQHHKVN\nsmujVlNa0P37lH7EhA/4ucWaLvIpLs5ISZ06FKkFyAEyYICYlAweTIbq0KEUjWnThiK3ly8ToXj+\neWDdOuXtJyaS2IUccnPp+m7fTud3967wvPvoIzaQFB1j175cOYqkSudscjIZ/az3C4NSBDAtjfb9\n669Uk9K7N0WZnD3/EhMpVYg1s1Wp6FnSsqXyOowsXLtm7/xgpK55cyEq5e1NDRcLSkp48QUGnY6e\nbUuWOF+fFad36VL06HReHkVXC6K+5QjOSImj55e732kffOD4nvLAgwLCQ0qeMsKDy2FM30/QtFZ7\n0ffX7l3A6p0L/veK3x2RDnc18ZODVPbxSaqY8LBaiZQsXUqf8/LIOwo4l9QtCliKVnQ08NZbxbOP\n6dMprULOYOZfpnyB7IkTwLx5lIu/bZtwTaQGjatwRmx9fQVVqcxM+YaGPMxmSqlylt5mtcKm1cJU\ntqzw3RdfiAufP/yQiCcg6pvj8jl06CCkZMkdT0AApdMsWkT/WKpW+/ZkNNlssKqA43l3sSnKhC92\n/xtvLuqFNSfW4W6ec8NDrdYg2KRGk1t56N9iCN7oNRVTBn+Ff4/+ER9+fRLPBTaAtzpf/jY7W1D9\nYmBdxZWKZ1kaGZsbFgtdq/BwMoyzs4W5xTzs/DjVrUuE7Msv7fPxz58XahkAMrQuXhSTklat5HtW\nfPUVGfVRUY6dBrm5lHqm9BtA0cqKFcl4Zs87Pz96HkhFIqpUodQ+iwU2lQohrGhdp6PtSY3ToUMp\nSsHuoa1bKZXq9GlK62Fj9eefJAQhjWRIodXSmDOy44ojhz1XpcXf+/bZN3BkJFOuX8z69Y7vTRY1\n46Vza9emtM4vv3R8jIBwfO4gEuz43SWeotNRepvc9pyREndj5kznz0gPPCgAPKSkBECr0WFg+3+h\nSmQt0ffHEg/g0/Xv4MTFP4vcQOwfA2f5sEoyrEWF5OVjU6mKR8UkLY3SK5TAXuqscJXPAy8uVTBA\n8Pazl9rt20KYf8wY17yLzsCMPmekhJcSzc2lF/rNm5S2xNZ1lgqxcyelgEhhtZJSllJNyYcfkqf2\n4UPyhH/6qf0yqakCKcrLo+JkplqlBDlCvXix4GUGyDtrNFI0Q6oyxxt7StGc3bvJWPnsM8eFwMHB\nZMyz5nB5ecj01uL3aB2mf9wNK8If4I8T23HhpkyKGAdDng21faMwqv5gfNbyQyz410ZMPe2Hl2o/\nj5ZxPRETVQ+lA8KpOSwbs6QkMo5HjgT4lCOAPPSTJtmnHTFUrUpGJjv3efPo//R0irKtXy/MDzZ/\n+Ptl9GiKoEycKCZtq1ZRndratcJ3bN5FRpK33JFxyoqwU1IcOzJee41IvxyYgW40Eim5e5ciQEwm\nuHVr5UhHv36w6XSoOHMmnS9LU5LOEZtN7HDYsoXGXNrRnf3vzCDX6cSkpFUrcVRTDoyUSFOp+Jo2\nhrg4isbwzT0Z3nrLOSnJzKT6LoZOnSjVzBWiwSIl7jDw5UhVUbFsGUmkS/GkSQlQPIqQHvzPwkNK\nShAGdhiDAIlc8K0HV7B8x1ws3foJso2F9A7/kyDtJi5FcUWOuAe5ymyGOi+veCIl48c7TvFg+2TG\n1ZAhAom5d891CUal5lpKYPnmzOBdtoxIIEAEwBEZciXVA6BloqLsC7QB5UgJK2RmXlM2Ls5ehCdO\nCN3LeQQGklEuXf/iRSqOBsgwPnKEomc8aWCYOFG4hhYLnY8z8YWmTe2LkaVEhXlnq1eXHyN+vfPn\n7b3yrOnjmDGOVd5u3gQ2bYLJlIvUjAdY0zsG71e+i82BD/DQ37HBptXo0L35y1j05mZ8ujMHIyp0\nQ43Dl4D160kVy2i0N54PHKDj3buX0hEXLKAiZ56csnSryEjn9x2ba+3zo8vMoK9RQzDUGjWibUqJ\noM1GhjTfPPH2bYpG8sYcMyQHDRJLr167Zt8Vm90bziIF/fop99b4/Xf6v0wZoU7lxReFdDbWYFEO\nX38Nm04Hq1ZLx8BLiPNgETY2JkwJjJES9r2UnChBGinhi/KVwOSI9+8nMsjA0iH59X18iMRmZ4uN\n+tdfp348jlL9qlendDvp9XfU0Z1HhQqkYOcOAz8xUblnUmFRpoz8M+KLLxxHWYvDqfW/ls3hQbHC\nQ0pKEEICIjCmz8cw6L3tfku4fhzzv5+AOw+vP4Uje4KoUkUwUKQYP95xx+SigHtRBTIDoTge4Hq9\nY4OaPeCZwXbsmLB8YqLzXgwAvcRjYgpGqlj6FjNc+P4ozlKeOnUiz64zWK300pTzFlss5E0/cEAc\nKWHGIYvksHNyRkpyc8Web4bx48lol0Zr7t0TOj876+jOFwzL9WLYtYvmDt9X5dlnkd68uf058+sa\nDPa1Mjk5dMz8tpo1I8NMWvvDpxxeuybbEyM14yF2nNyKKZdWY3yvIExZPhyHG5S1W04Kf59A9Gk9\nDHNHrUPHRv2IgLB5wefvm0z2XmEm8f3++0RM/P3F9R+LF1PKIuvSbbGQQchf41OnBELOe78BwShu\n1kyIBERFUaRLeg+zCAJvmKrVZPDzc9xolFdMunrV3qngKilxZBAfOkT/z55NUTdpilFEBPD554qb\nDvzvf4Xjl4s6sP3zErfsmkkjJWw7zox3rZaiFQWRDD9zRmheeIqTbPPyomcWf70YaVepxN9fu0b/\nOyIl0dFEAgtLSry8iEi7g0zUr0/RyyeB+vXFAhtSjB3rmlCIq5g8mVLiPPDATfBIApcwhAVFYtzz\ns7F533K79In7j+5gztqxqBFVH23qP4caUS7IQP7TUKqUWBaWR/XqQs69O+HlZfdiTenQAcHulHEE\nyPD4+WfHMpN16lBBvByhWLuWDDsl5OWRIco6GOfkOPa4M2zfTh7JWrVo315eZKQxSdt792iZESPk\n1/f3d20/jmpi+LQ1PlLw6BEZuYw0MUPEGSkxm+2NdgaNxl5lKTNTIFa8kS29DteukXIVkyWVS5fg\n6wMcQY6U8MfFegosWUIF0qzh47x5RKCkx8Yf96xZZKCMHAkAuHInAXuPbcaZy4dhhXPPZs2oBoiL\niEX5TTsRNGsBdBo9EREezz1Hnv/Tp4Xr16aNoL4EUMRp+nT7HfCk5IsvhPNlHbwHDqRUR17G+MAB\nGoNBg0icgoHdu7yReuMGFYG/+qp4v9nZ9sasSiWQS/Y/S9+SwmSi8z15kmoy+vd3DympWJHGUmle\n+/qSBzwmxl7RCkDlDz4QPuj1JI7By+HK7Z+vv7lzRxgXVyMls2bRGPHPyd276RkWHq683l9/EbF8\n5hnhOzlCrlRDyMbIWX2dnDPFVVICAB9/TO+iwsqSMxgM5AgpCeDvG3fgk0/cuz0P/ufhiZSUQJQN\nicLoPtPw3kuL7PqV2GDDuevHsGTLNOw6svH/XyF8ly7yefxA8RWfr1hBRbD5UFmtsBVHQXl8PNUf\nODKoY2NJxYePCrDi2JAQxy/U69dJ+cbHh5Z1tQBx40ZKhRk2TOh/8Z//0LgApC7kqBOyq30OHNXE\nhIeTkpLVSrUOVavS9+PG0ZgwI7ZePTJyS5Ui4+fyZfntSSNOPNi2vvyS8uoBqj9hUtS8cSm9v/7+\nmzyoLJWGj+owKHR0B4Cqb75J67Px4OfZgAHi3g179lDjtbw8+p7vuSHXuTk+XkhZy/eKW21W7Dm6\nGYs2vo9Tl/92SkjiKjXHO90+wsjLvoi7loPw3w9D/3c8VB9+aE9Kx44lAsnfl2PH0jViuHFDvos5\nT0r4lEV2XnxDT7Y8u28CAwWFvsWLhQgCn5K1ZAnJ4krJspzCF7sGajVFWO7cIYOZqXoxHD1KAgHJ\nySS6sHMnpffVrEkKTRkZjkUiGjWyr6NhMBgoffCll+x/W7WK1L2ys8VzKjOTzhGAOZjrqqTV0j3d\nvbt4OyaT+PnJ/o6IIMLTujVtn0WCnN3T1arRePEE5OOPnaeOms1EXJnzBBBqOHgokRJXFQjl1i9X\nzp6sKcFkIieSo2aETwsJCU+uc7sHHjxBeEhJCUbZkCi82Xc6GtdoK/v79j/XYNMf3zzho3qKKC5S\n8sILYhnL4iool9aLKGHkSDLGmWHG0p2cNTEsVYqKfgEyxlwlJXzzxEWLKCR/8SKliwHOx8JVqeZp\n04AGDZR/lzO0y5QhslKqFBXlAiRDGR5OaQhydSOAME5yBgwziHfutC+cf/SIjCNm/EmNWja+GRnU\nTyEw0L53jFxHd7br9HRhG2PHCoXM7HOVKmRw//knnYOXl2NixeM//xE6kpvNeKDKxeebPsTWA6tg\nkxHKUENFiln+oehcsyv+Pe8IXnluAqKqNCByevIkkduEBKqrOHyYVnzwQFxrI5VfnT+fDHg2Tn5+\nVOshNUKZcchHpfR6UhFTqcRGMUuZk55zcrIwz/l6NGmqEkDLHT8OvPGG+HuVishVXJzQQDEwkK4F\nj6Qk4Jdf6G9eFGLwYEqrnDzZcepM2bKUYiYHvZ7+KUVnFiwgQsUTr9TUx2l9xshI5Djrcr5/v1h1\nrFMnuq/KlBET3mbNaP4zie6CwJVIBEuh469vRIS98a9ESgwG5x3dAVqXj0rfukWOh2HDnK8LiJ+L\nJQ0tW7q/TsUDD0oAPKSkhEOn1eOlDm9iSNcJiAy1z8Xfd/Jn7Di0HuY8NzVmKsl45RVBxrQYobLZ\niidSwudwO0Lp0mQQSF/wSj0+GP7+m4w0m42IjMlEBqW0QPbjj8VpYHyXaFa7UaGCYER+951ziVpm\nYNy/L+/tBaiHhrSLMw+Nxt6QDwykl29IiFCIzkNJGIH1dvn2W4og8Xj3XcrdP3+evNyAMEbjx1MD\ny9KlKSddmp7Aiw506UJGS1wcKUoxOIiU2AwGgTiMGydvxFaoIChEGQyAxQJLnhnmPDNsNhsSb57G\nr41CsefKH9h38mecu3YUyWlJyG3eGGnvv4PbZQOwwecWZmTsxuXbZ+02H+ofhj6th2H2qHVYOGYT\npg5dhq7VO0OXlUPECKB5cO8ejbvNRp9PniTj+/PPxTUPNWpQFIDh4EFBxjo9na65wUDXUqWiSOjK\nlUJfFDZO77xD5GftWntCodEQUePrcgYMoGiBRkNGO9/IUM44TkoiQsJqGhhefJHIxvPP03xipBGg\nVD0ms8xfK76je0wMRYcCAhwb5N9+K9/0EpBv7DdqFKUOsXtCSkqYk2LNGuRUroykgQOV982Ov00b\n4fPAgfa9TIqCo0cpNcsZKTGbhX4zDHyBPsPNm/L3R2gopY45Q+nSNGcYzpxRjsLLgX8uljQkJ1M6\nowce/D+Dp6bkHwCVSoX6VZujXpVmOHx+Lzb8dxlMZiHU/evfPyDhxgmM7j0NBp2b6yCeNHJzyZsp\n51Esrh4dEtg0GljdXU8CkPE1dqzr+cV6vbhYu3Rp+5QMHsywzs0V1Hzq16fC2Y4dheXmziVvMJPF\n5VNlmKHz3nuCZ9xgcJwr/9JLgiFiNgv7lsNff1FqVkiI/W9ykZKAAGWPYOPGNCZKv4WGkoJYTIzg\nWb1/n87H15eiQUx6OSyMvKoWC6WHtWhB/6TIyCDZ4ClT6No8ekSG7KpVAmGWi5T88Qd8L1+meSXt\nkSEHoxGpuWn4o7oWxxt2QOoXz0MFFWws/apRCHDxF4BvJcEaoE9kkVXxNfPWeqPnmj/RdNcZqKVk\njqULMrLASElCAo0LI52//UZpc3zErkMH8bb4VJyMDKBJE6BHD5LO3bSJ6mNmz6bf69ala/jNN2Qg\nm0z2qVsAHY+0GP2334hIBAbSfZWURDUs3btTlG/1aiJ+DOXK0TJSidbISOHvwEBxM7gVK4RIWKlS\n9H+jRuJICT+GjlKefvmFthEba/9bo0ZEOE6epKjNnTs0JvPnK5MSrZbG65VXYBo+HPqkJOV9s+X5\n6xYe7rj2o7BwREoePaLzGDZMPO5KkHM6zJ4tXAslXL1KBJdv+qrTFaz57N27xdOs1l1gzo2CgM3b\nkhoB8uB/Hp5IyT8IKpUKTWq2w5t9p0OrEb+0r929gG+3z0ZyupMXU0lHUhJ5QOXwwQeODV6Vyi0v\nkZTOnZHepEnhHvqOUNDmjzqdkLIEkFGl1F+DbR8Qe3ojIuxTvgYPFqs58WkKLFLCEwRnaWO1awvy\nokePOlbi+vBDoWu2FJ98Ym/gSo1EHo0bOy6wHzSIUof4QtWPPqJ+Fuw7Ng5+flQU7cywzM6mfWo0\nZFCfOCGkFbLx79uXDPqFC4X1fvkF/seOwarXy5KSu8k3sPPwBqz8ZR6mTW6PcS+UwZQ7G7G3ApAa\nTDUQNhcK1JUQE1Ufk9q8i+aHbkAtR7gjIqgOge/zcfcuFfafPSsYmj4+zjvY8wX7Dx9SBOOFF+j6\nsvFm94GfH9Vh9OkjbF+ttpdYrl4d6NqVfjt+nCIsej2RH3ZsV64I/V0ePBAIJ4NeT1EoVjskBykJ\n5qOMAQFkSPfrJ46UMDibO47GbckSEpro2ZPmTrNmtA8+ZbVHD7ExqdXSOGs0yKpdG6YyZZT3DdDz\nxFl/n6LAFdWu5s3JKdKypWPBD0A5MhwVJU57lMOdO/YqaQU9/wMHSICgpKIwNSWzZhW9Q70HHhQj\nPKTkH4gK4VUw/Ln34W0QG2QJN05g+nejcSzxHxzWTUsTililOHfOufpWQaMpjx7JFqdWYF3E3YkW\nLZxLGh89SkpXcujbl/LClcCMl1276B8gyH3yYIXwDP370+ekJNo/S69g2wsOdtyHY9kyocbAWc2P\nEsGxWMjgCwkhbzEzHkJDxbUxqalCrcvnnztOK5s7lyIzfAGtlHCx4w0IIK+xs6L9Bg2EupgGDchA\nZvUPbJsGA22LN5zyCalVorB1P/UOVv3yb8xa8yZ+/mstjiUeQHKILywa99Q0BZcKw6BOYzGq50cI\n9MsvhpYzGr29yRDmSUm/fhTVSk8X1vH2FjzuP/xg38flhx/oN3aOr78unjvSXhhaLfCvf9FYsUiA\nn58gssBQpw6RTI2GirvXraN1+QZ3/HVl9SAffijeTvXqjguxg4LE861xY8ErHxBAY1GnDqlHzZwp\nrm1whZQ4U40zmYh48B3p2Rw1m4lQM2g0j+sz0ps1w8NevYTf5s+3r51xtn+jkYx5V8VTVq2iNFGm\nnsZqzxwRBrWaiIkraVHO0lUdQa7+UC5FzhFatCi+ZrXuQGHqK6dMUU4h9MCDEoBiIyWzZs2CWq3G\nGEmqytSpUxEZGQkfHx+0bdsW586dE/1uNBoxZswYhIaGws/PDz179sRt1lnag8eoEVUfEwcuRJC/\nuBjRYsnDql/n40jCH0/pyIoIpoYkB0cGI3tAuyr3yJCRQRryrJdCPmyFKao3mx2v07Sp0PCNoXdv\noXM6QOknPCmx2cgwtNmIJDny9FmtRDAuXRJyqb297SM+0iLgV18lueKZMykFSaMB2rYlYxEgA1tO\n1pWBNx6cvcSVDI0zZ2h8AKBdOyE68t13YqP2jz/IsJTWiQOhzqoAACAASURBVMiBGZdSmV2NhojZ\nwoXCsbz3HqWUOCvaHzBAiOZERhKRA5xHD6xW2FQq3HznHaBnT+RZzNj0xzeYufpfOJrogGgqINAQ\ngMY12qJJzXaoGFEdeknaZniuGj1bDsaklz9Do5hnSM63TBmK7PDXyGik75YsoVSnnBwiBCNHUs1B\nw4ZEviZNolQpHx+BWE6fbh8VGzuWtsmIYEyMWOKbV7oCxCRV2tRQZgyhVlNa4ezZNOYTJlCndLYt\ndg0YGZEqOlWr5piUfPst1a59+SWR7bFjhbno709CEF26UOSnWzcywE+dov198AGJOShh504aZyXM\nm0fjKSUlbdsSOffysm+2OXCg/Hx95x0xgQFom47uz1OnaE6/8Ybj5zBDSgpF0th9plYTYVNqEMmW\ncfW5WhRSIhVfAChN8PBhYPPmwm2zpKGk1rt44EERUCw1JYcOHcKyZctQt25dkbb9nDlzMH/+fKxa\ntQrVqlXDxx9/jA4dOuDChQvwy++JMHbsWGzbtg3ff/89goOD8fbbb6N79+44evQo1E+opuCfguBS\noXij91Qs3foxktOEtC2bzYrVOxfgjxPb0aZeNzSKeebpHWRB4eil6Sj9Sc5L+fAhGTwREfLrAIKR\n//vvVH/BUBhSEhBAxpxcQbYStmyhCMjLL9Nnq5XkacPCqCBdpaJ0E4vFcZ8Ptq5aTUYU8+D6+NhH\nSsaPV87ZB8hwUqlcU7hh6zLD0tH1mzCBDEI5Q0OpoztDXh55yJmc6/nzzo8vM5P+50kJIx1aLdCq\nlbirNEBecZYSlpNDnlUlRaXQULo2gwc79kIPGIC0hJP4vW9jJF5Zj3WXViDX5FpqoLfBF/WqNEfF\nlT8hevdhqM4nwNqlM8JX/gh1TI3Hy5nyjHiU8RCmu7fg3aotSnftC0zsJd6YwSCuZ/j4Y0oX6tWL\nCuv52oWuXelvf38iFR07EmHOyqLzNpnkCZzRSCRBWi9QvjxFOvkeGF9/TfOFzQcWKdm+XUjV4sEK\n7pm3W6ula8MEGXgjljknpNuoWVPctI8hPp7Gp04d+nz9utB9nEGtBoYMsV/3++8pLWbTJnqOKNVp\nPHzouJ6I3X9SUhIdTc+JHj3ETgkvL3KobNokvz3pfVa3rlitbvduShVjzx42VocOAUuXOo+YsPuE\npZTJEQEp/Pzs0+qUoERKLlygiE5beVVKAHQuRiNJhleuTN9FRtL82rJFnBb7T0STJiU7tcwDDwoJ\nt5OStLQ0vPzyy1ixYgWmTp36+HubzYaFCxdi0qRJ6J3/QFi1ahXCwsKwbt06jBgxAmlpaVi+fDlW\nrlyJdu3aAQBWr16NqKgo7N69Gx35Yl0PAADhQZGY9NJn+PXvH7Dn2BaR9OeNpItYvXMhVFAhLqaN\ng62UIDgyardvp7QkuWZWcv0i2rShl5LUW8qDveTlGtEV1EuXk6NcL8GQmUn75FMcmPEMkCHAN/ID\nyEDJy3MuVfzccxRlmDiRlktLk0/fkuvAy4w91j05MZGIUWAgGa4jRpBnWA688aBWK3vwDhygyJQz\nUqLU+2PoUKHwPy+PPPqvvipP1JYuFZo/8ileVitFXw4ckO/s/tVXVK9w9y5FDrRaYM0a8TKZmeRt\nvXuXFJKGDEHeV0ug0emgAnVNP3RuD9KzUuGl98LJ+kY8bB4DIB1wMBXL5hnQwBKC4NgmiG7cATa1\nCkF+IdBotMCUdUBSJhAUCTzMAbTiMdZrDQi7/gB4ZTiwfD0RAGdYvpyiUzqd0DkbEI+9n58wPzt2\npPFr0oQ+r1pF1+zyZTJuW7Sge7NZM2HsGZKTaR9qNc3RQYPIWTB1qmDcbttGhKdZM5onUnnctm3p\nHxMgWLpU7HDg5yGbg9L7ZcgQe/L400/kGJg7VyAlSs0T5cCUxlJTHT8zOnd2bLSzcWfywGPH0vH7\n+gopT9L0I62WojZycEYQli4lQsNICbv/XE3fkpKS2rXtIs52aNuWBAocEQqGYcPknyX79pHSoDNS\ncvUqjfnFfDUIHx9K+eQVuf6p2LhRXizEAw/+4XB76GHEiBF4/vnn0aZNG1Fjv6tXryIpKUlELLy8\nvNC6dWv8mf+QOHr0KMxms2iZcuXKoUaNGo+X8cAeep0BPVq+glc7vw2Vyv6Srtu9GH+c2I6b96+U\n/GaLhQ1Jq1T2TbH69iUvsCMwUsKNi8pkgoqRgIKgb1/KoXeEVavsJUl5I9BqFVKBbt4UDGOzmcjF\njz8qb9vPj4hEWhoZHIsXk+FcpYp9Z2spuPx0AFRnw+45s1mZDJnNZIjwNRqdO8sv+3/sXXd4FNX6\nfrcm2SSEJKQASQjpEKoJioqIioCCiAoo4rWDqFdFVPzptcBVURQVvIgIdqUKKEVEVCyUUEIn9JYQ\nQirp2Wyd3x/fHubM7GxJCBDivs+TJ8nulDNnzu5871feTxDIoFWSBfYUKWEGJ99X5OGHXY/rt9+o\nQPuKK6RytRERRLSsVvKys5Sx8nJRJvmtt6hxIauPkOO772B9+EEcLj2KFcd+xZQ72mNC6VK88Nn9\neHfBBLz+xaP4efMCbNy7Br9v/xGlHhSgw4Ij8MCgCZhY2xkDqsOQOfB+hIe2RZuQaCIkctjtRASY\nPDEDI2e3307pVp5gMNAxtFqaX0Ego52f++uvF2WTe/USCQkbh0ZDBG/OHDIW6+rISLXbKX/dZqN1\nZTTStsOGkSHM7sHgwRSNefJJURXLU9oOe69/fyn5CQ8X5XvbtCGZXjlhVaudlYdYCh5/3XKFLoZ1\n68iolh8T8NzRvV8/aWNJOdh3n15PzQVZWhqDXu+cvmkwUJqZEjw5VeQF/+w6GktKlGR95bjlFtc1\ng3KkptI8yDFlCn023SEmhtbU+XR0b86IiaFIWUPhyzbxoZmjST+dc+fOxfHjxzHfoXrBp24VFhYC\nAKJkoe3IyEgUFBSc20aj0SBcJvMZFRWFIjdyh9muGqg1An75+bAFBsLqSd2jWcIf/VKHY/Pxn2E0\niwYLy18HgKTIHrg6aTBUKhWiv/wSRaNHQ2hG8oARZWUIGDECeQr3NPrJJxGyYQMOubrfjz4qSU9o\nY7Ui0GxGrpv1EXDoENIB5OflodCxXcSPP0JfXIzdx47B4kr5SQGJZWUoy81FhZvzReTnw3DmjDgm\npuvv+D8yNxft1WqUFxejaMMGdFy5Enq1Gnu3bUNaSQkCZs1CtlIKCYe0w4dhDw5G7dGjCFu/Hqe7\ndkXE3r3n5k1lsaDLXXdhL9f0L/zUKYQUFqK1SoUd2dlIOXsWhSdOoCo7G8nl5Sg6ehRVCtelqalB\nTwC7S0thyc6GKjISqueeg11h27Tqapx67DHU+vk5NT0MyslB2tatODZ1Kjpardi5ezcE3sARBGTa\n7Th+5AgSABzfvx8JAHatXQurgixwYmkp/HfsgNpkwl7+XKNGIWz1aoRkZeFEWRkwZgyQnQ1dcTE6\nzZ2LPXfeiY4VFag6cgQdAZwtKcFxx/5WmwXHivfgTPV6lPx3IIyGCuD0JqA1jdNsNSG/2I2ykwwq\nu4D4iHT0ShwEodqAgpJSaCsrkS+bm3affoq6229H0qZNyM7ORnyXLgh87DHkvfQSqjMyzm3nf/Qo\nEmtrkZOdDf9jx2Bu1w52NzUanQQBxbt3I8piQdUffyB6/nyUDh6M6rw8lLExsDQshfvZta4Oh3Ny\nEHTyJFqVlOBMURG6AMjevRuGAwfQ+b//xf6EBNSlpiITwPadOyX3NNNmg2nAAJSMGIE2q1bh+NVX\no668HJn19Tj68ceo4DzhuuJiBO/YgbODBiG+TRu0gYvv/WHDkKlSYffKlWjTuzfUhYU47eH5EJGX\nhw4A8vLzUezYNv70aVRHRorzwO7FggWASoUC7vnQ8exZhAMwW604sGsXLC7U59rm5kJdX+9yPBEF\nBQgYPhx5O3aQSpzRKJn3VhMmoCY3F/aSEpfXwuYkE4DdZsMON9eeolajFbeP/7Fj6AKgrq4OBnh+\nrrY6fRopAE6cPu00Ty7h708Oj/N4ZmeePAl4MT7/nj2RuGABcrjtIo4dQ8DZs4rPl38CoseORU3P\nnqhp4PU3pY3lgw/Jycku32sy2nzo0CH85z//wbx586BxeJwEQfDKM69yl5JykdH1jjuQyMulXmaI\nDU/BXZlPoVtMH8X3jxbvwomSfQCAmFmzoHeQxeYCW6tWMLvoJGxMSoJNnhbCIf6//4WGIxGCXg+V\nB7UVS1QUjB07SiMlgoCiu++GpYHhcVNsLKx812oZgrduRfD27dIIjMxrV5uejoprr4XKbofKaoWg\n1ULQaKCyWnFk+nTYvEgpKRk+HDU9e0JtNEJls0Hw86PIjwOCTgddaSlUjjS48BUroDaZYAkLQ60j\n1UlltUJwfI7VJhPCV69WPpnNBmtwMCyO6Ieg1cLuQqZX5Sn9DICutBTG5GTn5pUqFQSVCjZH3wI2\n9lYuHpYqqxUBJ07ArFRPpFAvpCspgcZoRHltETZ11OCQtgx/9+mIn7rosXLXXCze+gEWbnkPW47/\njDx9LYyGhhN5FVTIiO+PkVdOwIhez+LNV9fgupRh8NdRnYxdp5OuV6sVsFoRtmYNjElJqE1NBQCc\nfO01WCIinCN5avW5dZzw6qvwk3fIlsHu7w9NbS0ErRYaR7GyymaDoNHALzcXsR5qo8oGDYItKAiC\nI0JQ37EjsrdtA1QqaB2fw86Oepv6uLhz64mHoNEg6ttv6bq564mZOVOynb6wEJEO73hlnz4oGTrU\n7dhabd2K0ttvxxm+qaULCGxNOqJFqvp6qMxmRWeNymqFrqgIQTt2IPa996CprBTXqqdIiWNuXY5D\nq4XKTXQjeOdORHhTgA6geMQI5D3/vNttjr3zDvZwzRPPXa+XkZKa9HQcnDsX5f36nXst9LffoLqQ\nssMACu+9F4Us5cwdFL5vVB7uQUtH4UMPocZdtM4HHy4xmixSkpWVhdLSUqSnp597zWazYf369fj0\n00+xbx8ZwkVFRYiJiTm3TVFREaIdhkN0dDRsNhvKysok0ZLCwkL07dvX5bkz+U6+TYDgxMQmP+bF\nxpW9rsTv25OwYuM3kjoTANhwZDnyKnOw86l+sJuyYcvfi47RqejT7RYEG1wU9V4sOOY9Rum9khIg\nOBiZPXpQGoPcC7x9O9qkplJoGyAVqgMH0MbTvZwxAzH+/ohxbJfn8IY2eA188w3clNRTTczhw0C/\nfohwdezMTEqH+OknhKekUOH16tXoERdHnlOt1vO4MjOp8VpWFgAgMT0d8PeX7hcSgoykJCrKffxx\nUhvq1QuwWpFpNgN79yJ15Uoq3NdqgV9+QfiaNc7nKi0F9Hrv5spgQKf0dGnnbX7Me/YgLiYG2L8f\nikfTaJD8xBNAWBg6xsQAb7yBhLg4JCgdLzAQCAxE8EsvOY/t2DHYV/+Eos/fQ/kTDyPALxAH1n+B\nH56+CkW75gJpOgD5wPButH1t43v/3LjlDAxllQi8ZShMGTchYe0GxGv/IE94rRmZvXqJhlNdHVBY\niCg23mnTqFYjMBBdO3cGDh4U5yUkBK2SkqRzuW0bcOIEXa9ej/Tu3d1LJkdEIDgmBujdG4H33w+U\nlSF83jyE+/nRff/xR0TNnw+sWQPk5VHa0vffi/t//jnaAdSQ8uBBhPNjycykFKp776Xx5OYq3lP/\nwEBa1wYDOqemnrsef4NBet8EQVzDjtcjAEpv7NdPTNsCgORkdPzyS+qF0UfZOSOBow4iLj4ecSoV\n8PTTwNKlCA8JQYK82H3pUqC6GhGBgcDffyPqww+BgQOBPXugz89H9w0bxMaQcjjIertOnZTf79IF\nsNno2EoICgI6dkQsPy9ffw2MGoVsR/H+uTlzpHnGe7x4DpmZgCDAsHo1MHiwd59pjpAAAG68kdS7\nPDU3PB846srcftcC55qkSq7DbAYqK8XPmA9ucS7y5psvH5oQlW4yUJqMlNxxxx24kmvKIwgCHnro\nIaSkpODll19GcnIyoqOjsXbtWmQ4Ug7q6+uxYcMGTJs2DQCQkZEBnU6HtWvXYtSoUQCA/Px8HDx4\nENdcc01TDdU97rvPuYHbZYqbMoYhLa47lm/4GgfzpAXYecVHgcQQoJgKYg/m7sS6HT9i4JUjcWPG\nMKgValMuOZiH+88/Se3m99+l78tz0QcOVO4ML8dtt0n+VQnChdGnt9vFonVP47nhBsr51unEvGpP\nsrM8AgNJKclqJfLGn3PCBCITlZVibw7m7f3lF+o7YLGQkQu4nwtPEro8PvhA7B+hBE+KZ6wu5v77\nxf4YrubSYkF1RAj2VR6EcceP0Gp0iI1MwpFTe7Cr7Bfk3x0FwASsc0i0dm14umaATYWYNh3RIbgd\n+tx0P1QqNQrPnoJ10QJ0mL8KrY7miWpVsx9HdlkZRXjKysjInjRJOrfM8VJfT0SA5b8r3Xeluotv\nvpFcv8f8/nHjqMbh2WepBkevFxWnFi8Wi6p37qTO7hsc/Y+qqqgWhaV2uVJdGjWKflzhiivonhcX\n0zWyY7Rr5+xwYDVPcpW9M2echRwCAmh9eFufplLR+Tt1Ept1duyovC2r4+E7ut9xBxn0M2a4l8N1\nRUYYPNUIyDu6A5QKxROypsCtt3pfVyJHc6rZ4L87GS6WHeGDDz40Ck327RESEoIQmXSmwWBAaGgo\nOjsKJcePH48pU6YgLS0NycnJePPNNxEcHIx777333DEeeeQRTJw4EZGRkeckgbt3747+8v4OFwrN\n6Uu1CdA+oiOeuGMSNu79BYvWudHIB2Cy1GPFxm/w85aFGNBrOHqn90dIYJjbfS4qBgwgwvj778qG\nsNxQCw313PlXCY6eEk0OQSAPoiuJWYZWrejn8GHpWvTUWX3ePCrunjKFin4DA2l7Pz/pfqzAlXkr\neEOPGcChoWIR8Z9/UjGyEpSkmEeNIgNNXtDuJtoJQNr8TgmffQZBEFBWWYgzhQdxYkhn1NTuQMn3\nRyBAQIA+ECFBodBr/XHmnk44WhsMW002sL7p8qFDKk3IiO6K7n/uR0xmP+hWbAaWfEB9Tp56CqEd\negL1KwG7VuwPIwh0L8rKIPj5kcGsVlMhuByVleTdP32ayCMjJfL7zje3ZEhKokLi9u1JMtXT9xjr\nog6I93H8eCr01+lEA5tJ8RYWkpLRzp2k/sNEFzp2JHllbzF+PHnU33hDVHSrqKCxV1SQqtp77zlf\n75491CdmyRJ67T//IbW7u+6SbhsYSHPv7ff4bbeRxz8piYre5QICPA4cIAXAv/4S5yw2ln6+/LLp\nekfU1QEvvCA2JgSUSYnRSPPRHFJyjh8/F81tFkhLA7j0NB988KH544J+e6hUKkm9yMSJE2E0GvHk\nk0+ivLwcvXv3xtq1axHIhaunT58OrVaLu+++G0ajEf3798d333138epObr1VVJtpQbi260D46fyx\nZssiFFcUuN3WYjXjp6z5WLN1Mbp07IX+GXeiQ7TrwqTzxpkz9EBjUp9//EFGgvyeM7namhpn5Zia\nGmrkxRu1771HxrkXeeU8BK0W9sYom7zyCnk75epaDHY7eVX59997j1RiWP8NHp07S5uxabXA6NGu\nz19ZKXa8HzCAfoKDSUGJV/JhBi4zvvhICSM+8+ZRDwSASI2rCIa/PzVs5JGVJe2KzWPPHiJlSj1G\nlAxtAGerSvDHzuU4XnAAp4qPiW/0TwZspwBXy1l9ft8ZrQJD0S2xN9LjMxATkQB/fQD8gkKAmuXA\nWD31O/jbET1YtYqirO3bk0efqUhZrRT5WLcOAXY77DqdsqQ1g8lEaYdsX1ekJCnJWXbXbicC4RAO\naZCBzGSYv/2W1ufBg3QN1dUkHXzjjbRdaakzOe7dm37ef5+iWC5qwgAQwZ0xg7bnt3vuOfrcA8pR\nHqW+I5s307UyUlxXR/dk0yZSCXv0UfeNEhmiosTeIkoS2jzS0mhu+EgJg6eO7p5gNJIjont3+i77\n9FPPpMRspmjJX82oWW5zICXFxZTadhnXh14Q2GxixN4HH5ohLui3xx/sIcPh9ddfx+tKHkIH9Ho9\nPvroI3zEDKKLjX/969Kc9yIgM+16ZKT2RV7RERw9vR/YugWtuvVCuc6GdTtXoK5e6iG02azYfTQL\nu49moVtib/RIuhqd4zNg8HddbN4obNtGspYrV9L/N91Ehon8Af/YY9RbYtcuZ1LCFGl4UlJY2CgJ\nxOJ77kHIxo1kgDWk2N2Tp1+p+eHEidQn4Z57qLkZr70fGSmNNqjVwFdfuT6+Usf7AQPICORlcRnp\nYCSQ349FSvhUKlZArdS8MiyMmk4eOEDpKV98QY3nXBW7zpxJXcKHDydywhswTz4peVgKgoCsnN/w\nw/ovYDK7MRTPA34mG6Lj0hD+91YEDhyC+O/XIu2BZxF8s6N54JYtwK87gLGZdE2CIEqg8g0neeLw\n8ssU5fj5ZyIqNTXAypUwJCaSCIC7vjk2GxG9ujo6nr8/9Z358EMiqImJlGI3bZqztK3NJiXy7rqj\ny3HVVdQk8cYb6TisLqusjOSHmUy7weA6jXD2bGrw546UsDli/UquvJJ6jXTqJPbmiYpyrlVgEr/8\n+tZqicSxNVRdTVGYe++l8R0+3HCi4ImUACIpa2pScuIERRn37yeiIZ/jP/+kz40czU3mvTnIzpaX\nU12dj5RI8dxz1IdJnvrsgw/NBM3ApeHDxYRKpUKH6BR0iE4B3voGeOwtQK1GZtr1mLvqbZwuOaG4\n355jm7Hn2GYAQETrdkhqn45uiVehc3xG46NYo0aRURIfLz7Mi4vpIav0gN+1y7UHnj3A+U7S3tQ7\nbN1KpOjJJyUvt5szh7y5DSElOTnuu4zffLOzIQmQ0bp5MxlzGzaQoeVoHirBjTdS9MJV8bISaWCG\nKZ9+ZbEQ2WFKXmPHUsrLkSP0wLJanQnW2LGujZ+lS4mcdOokpiy5IiUsxe6uu6jYm3ng2Zi0WmDX\nLhyL0OP7Pz5FQVmu8nG8RKjagMAqI4ztIlFvMcJaXYm01gno3/F6tH3kaejrLcCZlcCsvsBr/wKm\nrQD8ONJ94AB53seOpXGPGye+x9cH8dEDg4F++DQ9rRZQqWDX691HSlgNEEut0+mAESMoJe/vv+mz\ncs89RMrla4lXG7r2WvfkQI7wcPpRSoEExHsfECASsM8+IycOW0fepL7yETmAtp84kT6HbLxcMfs5\nREWRQfXzz+JrrOEn3yWejT09Hdi+nRoietOzhUGno3vnriaHkbd//UtK/M6XlJjN4j1VOs7Jk8pp\nlEqfy/ffJzI5a5b357fZKG0wNtb7mjqViog7V0/aLOCpPu2fihkzLvUIfPDBLXykRI6DB+nLrAWm\ncEkgCNSV2vHwCWsViefvfg8Hcncit+gwNu37FdV1FYq7llQUoKSiAFk5v6J355tw901PQKNuxMN4\n4UJgxw7KYWcP4c+on4riA4WRDKUHts0GJCdLH9pKkQM5jh4lL/QVV0iK4gUXqURusWwZ5cW7gqsO\nxDU1YrO2v/8mjy9PSu67j0hTaan7SIwSKWFpYfy8WK1Sg+vpp6kp3JgxZOzeeCOlkPARzU8/dX1e\n3hhkhrmclKhUZPCwef3rL2q4x0jJ8uXAggWwzvwfVk95FL9fGwsBrj3AbQMi0DY2FTERCWgbHod6\ncx1KKwuhVmlQXH4aOq0ePZKvQcr245Trv9wx/ptvBibeCmReBcyeS+lGAM074NxNvq6O0kAefZRq\nPf73P/E9eaREfm9sNkoHTUggkqFWo7pXL9cpeGfOUATLz4/ma9IkcSx2O6Uh3nWX8n0GqJkgS4X1\nVhDh7FlaVykp9H9hIaVRsTGy8wwaRJEQg0EkYOPHU40HT0o8fd7Y8eTpgsXFyk01ecg/z1ot8Mkn\nYlRFoyGnhcFA9+2bb1w7MdyhqoqKx2fMIBIoR/fu9CMHLzTQGKxZA+zeTX8rzaNSLdqQIUQK5Hjt\nNZqDhpCS0lJyqkyaROvBnUgBD5YGqtOJEbZLDVfiCz744EOzho+UyLFkCYXv33rrUo/kwoIZ+JxH\nTKPRoktCL3RJ6IVbrroHB/N2YXXWAlLqcoHN+39HRU0Zbu/zINq16dDwqAkz5thDmHn9lIwqZowN\nHiwWMAoCheqVvJS5uWREPv206/NbLORR/OknqVJXYx9qjYkaVVfT9dTVUcHwxo3AI48An39O71dW\nUnqaUvoXD28jJZ9/TikzPFgqTHy8GNr3ZCTy+zIy4oqUANTNu317UdmopgaCIKCg9CQ2l2/FkQw7\nSpc+C/O1MYCMkOi1frjePwlxRXVo9+FcRDz7MjDWfR8GAEBOgTQywdZ9q1aURia/x61bi3NmsZAU\nLkDN3uTyssHBFEl57TXluo/rrqOu1AsWADNnQpg8mWqVIiPJWJ45k1KzGPLzSVUuMpIMQn5s7G+7\n3TUpGTMGcEive1R4Aygd6IsvaCxLl4qvy9PL0tOJWIWG0ty0akX3UT4OOaFTAh/VWLiQCIDNRqSE\nKSX99htFKeU1M4LgTEoiIkQiptHQveb385ac/fknGeRsbe7a5XZzRVx9NZFKdwpz7sBHPLyNuLz1\nljLJbUzEht3L774jZ423pIR91psTEVCraV3n5rqPXvvggw/NCs0g+bOZQUlqsyWCGRC//67o4VOr\nNegcn4Hn7nkPTwybhF5p/Vwe6mDeLkydPx7vzHvGZfqXS2i15EFn/Q/YQ03pHuzcSYYh//D7+mtK\nO1EiJd48INkDVbat4Kk+xBU8kRKTSax/YUYIaxy3dy/9rq8HTp0S92nViow3lp5TVAQoNTN85BFS\nJALIKM3PVyYlSkXSWi2dl83hjh3i3FxxhejBVYI8UtKvn+h5d8CmVuGvgDJM727Dq9iE/3vrFjx3\nowbPfTwSU+c/i7/qDqMgUIDZ5pza1CPpGrw4ejpue2Meup82I6K0lgqcuY70Tvi//yNDNzmZvPkM\ndjuRvhtuUK4BWr2a6jiOHKFUualTaTu+i7bJRPVN3vpH3gAAIABJREFUFRUkc3z4MPDqq87GaFgY\nFUbztTkMtbWUYsPDz4/SlFasIMOQT89i43RHSgoKKBK0Y4e0hsgV9uyhdCh5mpI87Ssigq7/3Xdp\nHV1zDZEZ9pnLz6fvEW/Ttzp2pEjgm29SBCY+nuaCGcGPPy4W6/N44AGKejG8+CKRFwa2dlUqkZR5\n8xn+9VdaD0wCGxAjlw1BRYV3ZNAVnnmGUgUBmnNv5MxDQpwkzQE0rq5D7hjyBk8+SfVIABFVR7f1\nSw61mr4nW3CNqA8+tET4IiVyLFpEnsGWDpZqsXcvFViyNBYZVCoV0jr0QFqHHuifeSdyC4+gzlSD\nX7OXotZYJdn2TFkePlr6CsaPeAdtw93o9fNwdFE+ByUDjocgUHoGMwCZV7d1a2dp0ClTKALiDszw\n5ju6m0zUAb2hXr/4eGD6dPfbbNlC6kYsXeiFF8SUIKaexKJHGzaQhz4khEiJIJAM6+nTZBTKjQc+\nvSM/n8hE374kDjBvnnvZUFbrwAyTm28GDh2C7asvsa+tFvkn/0CE/iwyUvtCo9ZAEARU11WiqjAX\nxbnb4GfshVSbBSabCXn9uqG+eB+Mp2pxsvAwyiqLcOQDvgO3DdA6DG6b6+7PIUHhuO/mp5Ea50iV\nYb0qAEqz3L6dCqsZSkuJIFxzDUUnxo2jwvDERHGbtm3Js26xkNHJp9Q9/TSRjBkzaD1NnUqvh4dL\ni59376bUs/79RXI/aJDrudVqgaQkGPneF0r1TgEB9LpSPwuerNvtRFojImhsDCzy2bOnd2k7AQEU\npeOJRJ8+dO08Ro+mc7FUO/4aNBqaj1mziBDLya4cvXrRmnZIJKN/f+deEt6mTsrrGPR6Urf74QcS\nzoiJcS1lzaOsTDwvQ2NIiaeO7p5gMIhEJClJFKJwhw4d6HsuWyZ7fT6RkoZcw8yZ4t8qVfNRdQoN\nJWdEYeGlHknzgiw7wgcfmht8pESO3bs9P1hbAmw2MrQ2bpQabW7QNjwObcPjAABXpPTB/5a8gpLK\nM5JtjKZavP3dU+iedDVuueputGsTLz0IkztlBppWS8YOM5gFgWoZlO7Bp59S/UdamhhZycwk4zs2\nViqfC9A5lKR2eShEStp++SUMhw97n77E4I3UIp/mo1KR4Tt1KpGTrCwpKTl5kry3sbGUwmW3U2+H\nWbOoFsAd9HoiMhs3knc5IUHa+2HMGMpHZ43X9HrY6404EhuEo1nzsf3JDJTOexTQARjQDjj5J3Dy\nTyz8fRb0On8YTbUQBMecjeoGVG0AZm4A2G1bLesz0QCo7AIyOvfD8OvHSJXeWGEzQGv3zBlaT4yg\nTpxI1yoIznUzDAsWkDd6yRIyjPm0pTlzxMgI7/EePlxKSpgRr9NRxENuAD7wAEU8TpygdarRACNH\nwpiaKm6jVO8UFKRcAzFnDt2vV1+l/QYOpHVw001SuWtW3CsIZKR6ipYYDFL1KkA54sjLSfNg27LI\n5TPPuD8fIG3QWFhIa3nDBkqBY0bx0aNEONPSxP3q62ke3KVi6nQkofvDD3RdI0Z4/vwDopHGk8T6\nes/NDJWO01RKWA0pzlfCxYqUNFeEhJA4xZtvXuqRNC98/LFUDMYHH5oZfOlbSmgOkoYXGgEB5DVe\nv75h0qEOtA4Kx/Oj3sctV92D8JAop/d3H83CtIUvYMfhDdI3vvgCmD+f/p4yhbywvHJRRITYM0CO\nzEznsep0IrF4+WWS02Tw83OvdASQp/auu6QPYkHAmYcearjYQffu7udy1SpSGeINXtZ7ZcAA2rdv\nXzI27XbR6GORko0byTNuNnsmP3o97a/TiUSod29g40aYrSYcUlXgTBURyoLpb2LRwRWYMHUwPr4t\nFr9sXYzScGVjzmqzoK6+WiQkTYAAv0CkaiPR9+/jeOyAFm9sVuP+gc86S09rNKSGFh9PJCE3l4qv\nmeLXwIFkiAK0Jnhje8QIKsxmx+HTeurrqcCfvc6n/yQmknFvNFL64KZN4nHZHMuN+PJyukelpdRo\nr7hYuQhe/j0jJyUWC62DX36ha+7Th87144+U0idf24yUmM3eedlZLQa/lrxVkBIEikSp1eendKTV\nkjOB997abM7S1yYTkTJPYPdtwwYq2Jap6ilCrghmNNKacBUpKSsjUYsHHpC+3pSk5HwxcaKYyukt\nWhIpAVynOf6TMW6ccrqfDz40E/giJUpoDt1xLzR0Ouro/PnnDfcIOhDgZ8Atve/BoKvuxqJ1s7Bp\n36+S9602C75Z8wFsdqtYk6LXiySCeQNzckSjzZ0RwYwfi0Xs52AwELkCyBAZOFDcXquVGvdK6NyZ\ncti5Ls4qQaCakobCXY0DQMZldbVynrvBQMbQDTfQvVm7VvSmjxtHhkJYGF1zfb3n3H2ul0ZhVSHy\n0yNQGlKOs/uXYV/OHNSkW4Cza4AZawAVgDMANBc+rK9WqXF9jyFIC09BdL0amrTOCA5oBZVaDRin\nkfd89jTlnTUaMgQHD6Y0y507KbrUty9FBvhCa3mkZMkSmr/p0+k427ZR3ck771Aq2IMPiqSERUoY\nmevfn74Tli+n+8BqVBgpkd8Ls5nukyCQcbh7N8nZAtCWl1Nkb9ky5zUZGCiNSjz0EKWFsXGsXSu+\nx9YBj9WriQi5k7PlwSIWfKR0xQrn9C0lqFSkfAWIfWwaA74OROl1/n+leo2hQ6nYu2tX+j82lozx\nt96iyEqrVp7HII+U3Hor9YFx9Z2Rl0cOkJMnqaaNgXV7v5jpvytWKMvxNqY/h8FA9/F//2s4oWmO\n8JESH3y47OAjJXKkppKR+k+AXk+GTSMiJTxUKhVG3DAOdkHA1v3rYOe86HbBjm9/mY7y6lIM6DVc\nTHnh4aoZmxyMlCxZQgbiwoVUyPzLL/S+3AOuUpGKjqccWnlPELsdwoXIu7Xbac6VjKv0dCokBkgV\nasECMnDUarFXBCDW4HhIMSwzVWDP9QnY0TsBuUteoBQrAKg75na/hkCn1cNus8EmSO9dUEAI4tum\nwk/rh4jQdghvFQWdVo/Wh04irt9QaINlhuKwYWSoBwW5XwfDhlHUqFs3klGeM4eiallZ9D4vSSuP\nlACi4cy2Yd2+KyrIENdoqMCapX8FBNDcx8bSz6xZFK3jDf4uXZylnllHd77L9ttvA7t3k9T0iRN0\nHc8+K91Prab0RIAK0MvKXHd09/d3VhdiDWddpa7JkZpKtUb33iu+5ipKycNkoromVgvSWFEIgFJJ\nlD5rjDAxMPlluaGZl+d8bvZ95m19Azt/bKy4P586JgerbZKTlp49L3494nvvUcT5PL/DJXjqKfq5\n3BEQQD1lfPDBh8sGLYuUHD5MahtKuu3ewtsHekuAXk+GRVaW+1xtL6BRa3Bv/39jRL+x2LJ/Hb7/\n41NJn4lVm77D8dP7kWo9hTCLBe0qzqCipgxmSz20FiPsj9yB6OpSBPoHo7quAiaLESGBYQgM4AzY\nrl3JO75okbIHTEk5jXlQGwJBuDDFgHY7PSj54mSG0FAx5YY9TJUiPBoNpSIp1QF9+CHOoBY/p+qx\n68gm4I6GX7sKKiTkVaLL3gLEmP3QZu9RBP76J/yH3426n5ajJjoM/vpAGPwDodXoaO08+yxKf/kR\ntcZqBBtCEPq/OVAl9aZaIUEQpYxT+iif9JdfiGROn+4+DeiNN8S/Y2KoIDw8nIx3Fj1j8zVzJs0j\n36uBkZIePYjQsrqkykoiCWo1rZeXXyajePRoMRoAEGFp354IR0gIGfBDhhAxmDWLiFXv3mIRPQ/H\nd4qdOQJCQ5VrMLZto5S07GyKnLkjJcXFlDJY4egnFBJCxDYjQ2y+6A5RUVJC4i2OH6eUR5Yq2a4d\nRZO8xciR5Mm//36SMJZHWV55xfk7WKOheX3+eRIjAKin0e7dzp8RZqB7iiYy9OtHUQ5GRPz93Xd1\nlzdtZAgOVm6O2hicOUNr2JM0fWkpEdg772ya87YkXHcd/fjggw+XDVoWKbFaKff+fPDww1LPdEuG\nXk+56qdPN9khdVo9+nQbBIN/EL5dOx02m2hM7c/dgf2tAbQG8LUsGuUH4AtpQa0KKnRsl4bb+zwA\nQRCw7wQpzCRVn0LEmWOIAMgwKy4mI/L338loYZgwgVSk3DU0VICg05Hx2FDMm0cpNPPmuTiwQIY0\n66pbW0sG6PjxRILkRKt/f0lna0EQUDNyGEqMhSjedxxmmxm1xmqo1WqUV5dgFzagTm0DjjR86Hqt\nHrf0vhcZrVPR+tobKEozfDhwtg7Q6AGdDga1HoZQWZFkmzbA4MFoExKNNiGO3icHDgJxDu/9e+9R\n0fL+/WRwnzpF5EFexMyu31uP+xVXUKSBdQIvLCQSMXIkvc/y/evqgP/+l00gedajokRBgTVrxEjJ\ne+8B//43EfQ2bZzPefo0GeBxcbTP6dPSGobWrYmUsEgJj6VL4adSwRQTQ5EGV8S3spLSgnQ695GS\n2Fg6Byv8B0S54KIi7+awsZCnUnXuTPfz5ZfJa+8Ohw4RGRw/noQkli1z3sZicS5QV0rzOnBA+h5A\n6VRPPUVywW+8QQIBvOqZElg3e4aAAOfUOPlYzGbnz+v5dnTnceIECXt4IiUHD1IUzkdKpKitJYIu\nFz/5p4N9br0l7D74cJHRslZmcTF9SZ8PXn65acZyOeDGG+kBzBoRegOrlYwqViTrAlek9EGrwFDM\nXv4GzBY3D3g3ECDgeMEBfLj4/ySv/wYAw9oi8usnEG/yR9jBEyjpmoTyp/sg5PRaBP+ZB5O5HmUh\nJ1B/YjFCV+5Er7R+SOvQE346f9SbjTCaahHgZ0CAXyBMZiN0Oj+oVWRkHLh/BGr3bURd9lrEdb0G\nJrMRwYbWFBlwB09GtTz1pLqaHpzz5xOZ3r1baowlJsJoqsWe/b/jt+wfUFSeD7QF8LsLZSs36dMR\nIW2RkH0Y7W4bhdZvvY/U2YtgDA/BzlPbIbz+Oq78bBVC2nagfhSsrkKnI6+7xeI6pz85mdJWNmyg\nQuznnydSxuRj27QhA2HfPmDzZioULy0lo5FPFQoOpgiQOw+1HDExRHZ0OiIIsbHOhiJv0AsC1Qss\nXCimet1yC6VMhYSQQ+LZZ6Ve+ldeoZqemBgxUsIfm+/ozs7z66907Opq0Sj66iv433ADTHFx4n5K\nxJfVqOj1YqRk9Giqf7njDiI+a9bQWHNypCpNrEi/SxeKJl4oKJEkq5XqMDyREhYVUauJBBYXi/LY\nDF26ONeCyDvBs3HwvwGqSbvzThrPr7+SupwnUiJHQID7degqfaspScmCBaJUsTucj8hAS4bJRLUx\nPlIixUMP0dwsXnypR+KDD4poWaTkn9D0sKlQUEBfTI88QjUa3uLFFyl9wovC1qT26Xjqzv9iwW8f\no6As9zwGq4ziigIUA0AHAFVHgIRwoOY4sPs4bdAagKUc+ce3Yu/xrR6P529Xo14tPuB/27gH2Eip\nPyqVGmHBEUiO6YKbMu5AVFiMdGdBcFbWkmPYMLEoHxCNGH9/aninVsO+9hccspagPrkjjpzaiy0H\n1sFiNbs+phtEtG6HrglX4tquAxHRui3woOONe14AomNgCAtD/6gOQO8cICya0h4tFtFgt9vJA67X\nUwSC74PCY906Mtb79BEFA5ix7ucn1hCx42ZlURRm/Xqp5y40lMjuwYOuc/pzc+mY0dFEKNavp9fK\nykgmOTlZaswxA3ruXDLYp00TyaNWS+NhaYxsjLyRu2gRRV0EgVJD+QiKTicdP/ubGdQs4hoeLiWk\nTDlLiZSwOWLHZpLZeXmUupiRQUZ3fT1wzFEfxNYRa66pUl3YLtZaLdX0fP45fX+wcXvjfZUrXfn5\nOcvf3nef8r5Tpkgj4ex8PBFgIgVXX03rbO5csbmftwgJcf8sCQmhtXD99dLXm5KUeHucpk4zPXmS\n1s7l3svCR9aU8d13l/+99aFFo2WRkqb4sOXnk8GupGhyOePPP8l4Y2ktlZVkTI4bJ00B8YTWrRtk\n8HSITsHE0R9i3/Gt+HPnSlQe2w+bIQAVQj209Wb4QwuNTg8jrDCpBUkdysUGT0jkEAQ7yqqKULa/\nCNsPrceNGcPQt/utCDY4lIpsNlR9/glqhg5ClM0KjUbho3XrrdL/bTbYtRqcigrAtju7Ys+8J1FR\n4zCoG5GCxRAdFovBV49Gt8SroOI/E8uW0b2W100xqdXevalQ12CgyMBHH1H6G0DF5a4g7+jOF/Pr\n9aJkLzO4zWb6nN13HxFclYoIxaRJpJ42aRKtVyV8+CHtP3gw/RiN1A188GA6j9zDzcbGVK3efZde\nGzSIrnfBAjKsWbqVvEC+tpaI1qOPkhHOw1WkhMFmo0aOY8YAixaJ4glff+1aqGDJEiIgbdvS32z+\n7XaKJP32m2jYs2s1meie3X47RZ8aojh06hRt35DeBRoNpa+9+KKUlHhjSLNt+N/edkGXRxq1WooY\n8cXM1dVEjnNyaF2xtdcQjBlDvZLGjVN+PyJCbHjKIyur6dSevCUlN98M7NnTNOcEKKr00Ue0Ph96\nqOmOe7HBeuf44IMPlxVaFilpigfCpk2U88yKYFsKdu2iPGVGSphXj5fo9QaxsVQY2gCoVWp0S+yN\nbom9qbB2yBDYht4GdXArqIYOBa7sDtTWovTFp3Fq6qtI/N+30Pz1F1aV70B+6QlU11XAYjWjprb8\nwqhiNRAWmxm/bF2M37KXIbF9ZwT4BaKwNA9Fb1BXb8NnDyE5pgtsdhvqTbVoH9ERPZP7oKr2LNbt\nXI6yyiJEh8WilaDD0bFdURmsBxAE1HiRrgHA4BeE+J3HEHrnvQgIDIFdsKGi5iy0u3YjWReJzNFT\noVErGDVHj1J6VlaW66ZyBgOlWgGiQewJvEHOVKvYmuLV1u65h4q7WTRmxw6qKygvF9Wv3Bm3a9eS\nEV1dTYXlgwdLm9z5+dH/fL0GiyCw11hqWlQU/ci7h0dGiqREEKjg2M+Pionl0OspYvDZZ8qkZNQo\nimps3kwpV4yUDh5Mjo+VK4HHHpPuw/pzsC7qDHa7eA45KWHnfeEFUvxqyGckPZ0ieN984/0+fn5E\nBPiohZI0shLkaVhKynubNlHEi79+Bn5taLVU4+NOmMTb6PmqVeSIiowkwnXypHf7uRrb+cLbYz3x\nBKnQNSVee43m4HImJWo1fU+cPu1rFsjj1Vebdp364EMTo2WRksYoLcmhpODUEmA2S9NFmBExaxYV\nhPNo1YpSaNq1cz7O+Wq/h4cDwcHQWDgj1mgEPv4YbaZMQZuaAKDGBGj8cfdNsmJ4lQpCQADqdmfj\n1MMjcHDK88jftQHBW3fBv99N8M85jFb/ehgQgLKqIlT9shKG43kQhgzBflMBKmupC7pWo4PV5h0R\nU0EFvc4PJoW6GJvdisOnnL2UdfXV2H0069z/R0/n4K9dqyTbVNc5FJOCvSuob1tYjbZnzej777eR\n8OMfwJx5wNs/SaVTrzpL65cRkvx8MryZ0cZ6oXTp4vpENhsZ9ocOkbITQMbhoUPOMq0M8kjJ009T\n/QMgjZSwrvRsLbJ9QkLIMy0I7o3bDz4Ajhyh1Jxly8jY50mJRkP7lpfT8f73PzLQX31VJCV2OxGN\nm26iiIS8Dig/n8hbVRURDoDWLB+BEQSaQ9aJPD+fyL48vY2l6jHJYv5zk59PZEZOSoYMIXEDeUqT\nzSZGoHhS8thjYrqYxUKpXmzc3qC6mq63IWjThupAMjLo/5oaSnPzhpQwg6hTJ/o9ZIizsMirr9L1\nyxW95L0zRo507Q1n0V9vvss3b6aGcllZREpMJteNEy8WkpO9I5ft2ztLUp8vvI1cNWewz8iECRe2\nvupyAxP98MGHZoqWRUr0eo8F2B4xfbp3zcOaO+rrqdCTdW+VP2iZR/qXX8jbxqO6mhR8LgQpYWkP\nhYX022ajfH7mdWVGhgtPvspuR2BwGNL82yHtuoeAmmjg6S+A8XOA+s1Az6HixgkDyTsfeR0sN92A\n4wUH4K83ICYyATabFb9lL8OZDWsQtW0/2gZFQXsiF9q0Tihp2w6Jm/ch9t4HIYweDZVKBbPFhJ1H\nNuCHv79EnakBRt95IFjtj0RdGwweNgFRHTrRurz2OEULAKlC0Pz5JCnMp9bFxpIX/IcfKO1JpfJc\nSG61ksF8552kmrV4sXJRL8OpU5RqxQxIm43UmDp0IKP9xAlKL+nfn2pWEhOBlBQivbzxw7rPu4uU\nsNSv6Gi6ju+/l/bZ+eADMszLyqiYna01/kEcG0skhkVyBgwQjb/Jk8nI//xzGnNFBaXyhIRI581m\nowJ7Fnnx93dft+C4HhNfT+TqcxQToxwhsNtpfiwW0Qu8e7e0PwXrru4qCuYKjVEs5OsnKiqIRHhj\n8LRvT9E69l3ENztlkEevXCE11fm1Tp3o3gwcSPfaXdohA5NUZtfTHEhJUpK0kaYrXHEF/WRnN+25\nd+1quuNdCuj1RO59zRN98OGyQsv6xAYG0oO6sRAEMqQa2524OeHnn6nbMYNcptRmI+/34cPOHd1T\nUlw34+rf35nENASlpWTsMoPaaqWULjY2QSB9/uRk532XLiWVpuhoIlwAFTtrtRQlk3eDj4sjQ95q\nhU6rR2pcd3T4eyc0dgF6nR9uvXoUHqnugCGbziBjWy66/7kP6dV6XPfOHIQfyQXi48/VZOh1friq\n802Y9PBcDLvuQfjpm65ZmUatRZohBqm51biiUMD9xW0w48NdeKsiHQ/nt0ZUeCzdL7ud6id27SK5\nU540fvaZssd72zb6/f77ZHyxqMUbbyjnxVutYkfwkhKqwWApT3IYjZQulJNDkYelS8mbzeRJDx2i\nex0URN7o1q2p7uGZZ2jsvBfbZiNJ5//8x7XHnfWHYKpd1dWk3sSMeHZtNTWuU3r++osIEzv3Dz+I\njoxFi4jQsGJpjYZSY/z96bzy5ouuSFSHDpSCxNLftFrgjjtIeYvN8dVXK5OvoCDnSMdPP1E6V3Aw\nEaGBA6no/euviXQyNKa4d/ly4IsvGrYPICUlOh39eNNwT6ORigUYjcA770i3ycqi+jc5Zs3yHAV6\n912KvJhMFDViDRHdQZ5SZjI5fydebNxwQ9OnZXmL2bPPX1r/UkOnI9lpHynxwYfLCi3rE6tWKzeV\n8xbMc9sS0rdSUshjzSBX+0lKIi8w4ExAmEdWCfHx5JlrLLZvJ69qdDQZQ337Sotd27ZVbi4IUNGw\nkiHHjMMZM6h4n4fc63r33WLna4DSjO64Q/SWarVQWa0oGT6cCmZl8NcH4MYrhmHSQ3Mw+uancXuu\nFncG9sCj1/8br26wYtqTi/DEsEm4b8AzePCW59G3+2CJlHCkfxjuWboPw/uNwfU9huD2Pg9g0kNz\n8MSYmXjy5wI8GH4dMrsPgMpuFw0/lh61fz/NT12ds3LTH3+I18CDXbtWS5EApo5VV0d/CwLw5pv0\nmsFAnmZWCG+zUU52bS3VROTnS499222iCtF115Gi1qRJ4tj4KAYbi0pFBObbb6WfM52OxlRYSGtX\nCRoNedoZYd2xg3737UvXYrNR6k9YmDOxGTGCjBR2HP7cR46QccxeV6mkaVIqFc0Tk85mkRU2R/I1\nWVxM2xQXi+fjo0JseyXnR1CQWINjNtOcbd9Ohnz37kTAFi0io7lrV6kCFBtnQ5wqQ4c2TtQjKIia\nHwLuvy88wWgkIsGjpoaU7OR46y3PTSGZClhWFvDxx941h+Trj9j5PT0D3nmH5KNbIvR6IsCXO843\nqu+DDz5cdLSs9K3zBTMceve+tONoCsi9pm3bSlPbwsIodWXGjIaRkspK6pnAd7puCFhhvb+/WEjJ\nDHCA+kK4Arsm5rVm0ZXkZNp/1y7nh6lS75BJk8Q6mp49yXAxmShq5CAl5wrqzWaKygweLDlEoH8w\nrup8I5A/G4hpBQy671xKWlqHHue2uyKlD+66/lFY/LQou6IzosYNg3rzd0B36fEA0LwPGED3hkVG\ntFq6hhMnyDD19yfjXSmaoJQLztYAu54XX6TfjKzZbDQfr7wiGsMrV4p1EiyiNXMm1S7EcFLIbI3w\nRjmvdmQ0Sj3OrLM7QLn7P/wg1oRMnkxF10uWkGyvEjQaWnssOsAKvxcvpshgYqL4mjxSsmQJrb3p\n0+k4Z8/SGn78cSJTX38tJSXy6NDgwXQOdm5m+CvVwJjNdE18ZIVfg+xeKH3G+vQR5zwjg9LytFp6\nbd488mBXVdHx5Q3+WO8BV40ZmxJt2lC0DTg/UqJkOE6eTBE1OZSUujp3ptQllrI2bBhd+7Bh3qfy\nyiMlvXq5jhQzvPQSfad++KF357hQ2LDBtROnMWgJWQIMPlLigw+XHXyfWB4WC3kAX3/9Uo/k/CEn\nJa1bU0oJD+bRlj+Au3Vzn1PtqmO5N9DpnCWI1WrvJBzZNc2eLe3cvns3kRElkYKPPhIb+THIDair\nr6baE7UaeOcdlPfvLxp1q1ZRMa4r2GxEGNx00VapVNCPvh9tA9pAzcvlyjFrFkWioqOpkJg3jOPj\naUw6HRkOSnUDSn0vmJHBfnfvTrUnjKwpPbjnz6eoC++t5gvTGdLTyVPP9k9NFft9AM6RkkWLxHH7\n+VHOd3o6pZ3t20ckxp2H+oYbRPnXF18kw9hqpWPW1YmpVHJZX/lcMBKVl0e/eRJTUCBN32Lo3Vu5\ny/ugQcBdd4n/22xit/i9e4ns3HILETA5lLz4N91EBGj7dkqL4zu62+2UjvT55yIpKSgQ610mTaLf\nF0MK9fBhqcLa+ZASOYF67TVRZIGHSuV8nmPHnCNV3bq57qmjBHZ+JuSQlCRNi3OFhjT6vFCYN8+1\nfPY/HcHBynWRPvjgQ7NFyyIl27aRp7mxUPKwXq6QkxK12tkLxq511Cjpe19/TcaiEjx1O/aEsjLl\nfOXnn/fspQsPJ+Of97jzUCIlHTqI6kTs+EoGFDPOV66EpqZGPL6rfhIMNpt3hcVffkmpN1otpSAp\nGY59+tBYtVry+iulBun1lG7F91BgJOfVV51ZlHi8AAAgAElEQVQJI4tUsGs3m6nWg82VUr3IvHmU\nKsYwezYdR06mystpvGyMn30GPPgg8OOPRAaNRikpYfU/POrqaP4eeYTO6c6gfuIJMYqZkUGkhkkQ\nM0Kj0RCpe/ttcb/335fOQXAwOR7YWBiJKS4mApqYSMfmI6aVlcqG7ujRdP6VK0VRAL1enNPCQlF6\nm0e7dpRK6ArffiuSG0ZKjEb67BQUiKTk7rvFIme7nVKWhg93fdymws030zgAurZRo7zft08fcd8/\n/6Q6M2+QlyfeS4BqkJREGDp2VE5ldIWMDCKQfBTQG8gjVZcCubnkwPDBGXfeKf0e8MEHH5o9WhYp\nsVjEnPnGQK/3rljzckBMDHm8GZQiEX5+lE++fLnU4Jw8mdKZlKDT0XEa6xkdM0bsg8Gwcycwdqxo\nXOzaRWkZcgUYlUpUYDpwgF7LyyNP+4EDlEfOk5JRo6THYAY4ny7GwEjJzJnQVFXBzghb587uvW02\nm5g+sWOH+3ob5hVmDetOnSKyYrcrR09GjxaldRn69SOiJQji/WTGUUiImIIFkOG3yiFFzJR8WM49\nS9+y252NOtbHg4GRQPn6qaqi9DdW19CnD6W+lJSQetWIEUCPHnTN998v9g1gtSAArSO9ngx7k8n7\neq4RI6imhSclkydT3Ujr1mKxPQC89554HcePi31LNBoyiquraV0/9xwZ+/ffT2leLD0JcE1KWD3T\nwYMUWWLXI69T+OYb6FiNCaCcfiU/LiAlJSw1rqCAUpNSU+kzXF5O52Xr2tVntykREiIa/mo1GX/T\np3ver6YG2LhRJIjy6K0n8I6L06fpN79+ly2j1LyGICTEvUy2KzQHUrJxIynN+eCMiRNbVjqaDz78\nA9CySIkgkMpPYx/KQUFk2LQEVFdLvfxKkZK4OPJQy1Oqpk51bRwuX07GT2OjJa1aUSoSj7lzSZqY\n4fnniWTI0xL69iXjrKJCVN9auBD49FPadu9e6biPH3deC6NGkSEnfz0xkWoorFbkvvwyTB06kKHp\nqbkk89QyI9edxr88wpObK/aqUIrQde0KpKVJXxszhoz/4cPFlCCjkYhRp07S47dtK/buGTeOyAwj\nJePHU32Gq7xrtZqMtSefpOuXCwZkZ5Pa1qRJRDx+/JFeHzSI7l15Ob3ew1Ff8+23RMD++ov2KSsT\n50+no2hJZqZz0bM7hITQvlotGez+/mLxOQ++sLxHDyJuLKrywAMUzdBqqejblbe8okJZKpx1dWcp\nZMHBRJSTkyk9i53744+h50lJVpZUvlkOFlnRaomIfvedSErmz6f7fc89lEY1bhwJHbDrvhgNRkNC\npEXnhYUUYfUENja25hqSZgVIU+h4IQKGSZOcBRkuBJRSJX1oXpg2zUdKfPDhMkPLIiXMaLoYOdXu\nsHcvkaMLhRdf9Oyl++03qadXHinZsoW6R48d62x4u5KABUipCGg8KYmLo5z4v/8mg3f1ammaEuvY\nDTgb6hs2OI+L7WuzkbHOF6TLr0OrJePuuedEQ2bBAlKWSkykOTObIWg0CFu9mjqIt25NBrUr9Ool\nKlnl5Lj39N97rzQtjo2d9+yuWCGNJPCIjxcNU97THhRE8qHuCjsjIqhLNUtVCgqiH52OPIoAnZdF\nlljNSVwcSawOGCA1oh98kAxilYr2WbOGXq+spO3Ly+l/3nhjdRorV4o1QXxkQaMho555wJVw5Ig4\nX0lJVM/DhBMAiqAwlSwGrZbUkj74QFwTrEBdo6HrYulpruSIb71VuTkri5QEBhLZUalozeh0VKPA\n1rXdLoonANLO8UrgIyVdu9J8yuXOv/+eUs7OnKEIBIvEXYziXrOZCDWDu7njwcbG5iU0lCSivcG4\ncZ5rBJSELS4EJkyQppJdKvgKuV2jMRLZPvjgwyVFy/pG4xVxGouKCspVPh+88goVT18ozJ7tmZQw\nDzTDvn1Sj+Lp02IPC3mkRCmlh38vObnxkpHMKCwpoejGs89KSclLL4kF1j17ivsxqVOVSmro2u10\nLXV1tD0vCa1UkwFQTcZ999F93rqVvPw//0y1FPX1EDQa8YGm1ys3eGNgRb7795PR5CpSMmMGjY+P\nfCiNb/lySmeTo0cPae8Gf38ihtu3U/rSnXd6VpupryfvOr8u/P2pFgWg3HqWimUw0HxMnEhzNW6c\n2MEboLz9P/6gdBl5R/eICNekhI1PEIhEajQ0ntWrqRB+zhyKnLnCCy9QtIXBaKSUufXrpfPCQ6Oh\nyNIzz4hre+xYui61mqJukZGuC+QBImG8xDYDi5QEBkqVxwDp/W2oEpBeLyo8sX0feIDeO3xYvHYW\naQgJIdIbGHhxDNXycilZd9f0koeclHiKLvKQfy8ZDM4F8bt3A//+t3fHOx+8/bao4HcpkZnpXS+W\nfyK8EU/xwQcfmhVaFilhX0DnQ0pyc89ff97bws3GQqmgWw5WcMuQlSXtEMwbTPJIidUqGpVy2O2k\nNtTQrtH8/swQ8fMTi63lvRuWL6e+JPx+KhX9TJggyn3abBT9yMlxNorsdkrHW7rUeRzLltHrdjt5\n+r/+mgzMkycR+f33ELz1srF8f6uVDGJX92X8ePLq82DX/dpr1Mjw+eepFsNsds5xZ9EDtZo88hoN\nkYwrrxSNOk+Gr0ZDJGzlStfbsPGzdCZXSEggY37mTHEOpk+n1K02bZRJyYsvSnt8bNpEHn6tliIg\nX37pXBzPY/duShvj7zOTFGZQqtXgPy+MFHfsSMYcn5amUhEJaAgOH6beOCxSwuOFF+izsnMnsGMH\nrSmGnBwiYa7QpYsYVWP3NTSUUhhZn5b6eooWAZQWOWUK/b4Y6VvsvAxK0shKYPeOzYVW27Dva/7e\n63TKBnljrn/RImdSeTlg6FD3n9N/MqzWczLtPvjgw+WBltWnhEmdno93xBuD3xMu9MPNmzGytBgG\npY7uzIiYM4cMHkAkBb//rqyo4y61yxtERZHRabPReKxW+nvuXEq9cZWCx4qT/fwofUceFTManY0i\nm43UulwVvrZqRfeKGaa8wcN6VRQUUPRMyUsOiJESnmS5AlMdKyggzzwjJd2708/11xOh1WhEbzgD\nG5tKRQXwe/eScervT/UxWi2lk/AGfVkZvc686Tod3WcmfaoE+firq8nwk6sZJSRQpIupb9lsREpq\naykdiqmAyXPv2T1i0sbM4GZGbl2da8/vzz8TOWPrz2ajeefPERBAxKWigtL0APKcs/XN7nNAAG3D\np/t07UopeydPknMiKEgaHVLCyJE0nz16OHvOO3ak38ww4o3lnBzqneJKgYs3NNlnLilJKoVtNBIh\nHzFCVJh74AHntXMh8J//SNfEwoXeFX6ze8fGe9VV7mtreHz6qfT/Xr0oKidHQ0lJTg5FEAsKGu9s\nuVRISWl4Xc4/CW+95bxufPDBh2aLlhUp0ekon7uxpKKwkIyp8yUlco9pU6KsjAxXT8SrsJD6XjCY\nTFJSwqdbDB7s/DB2lVLhLrXLGyxZIkq5MiM+M5NqcCoq6PgpKdKGYDYb1b+wCItGI5IEVjSflkYG\nDo/ly+l1pft5333kiWbXw+RXWb0JM5hXr3afO67T0T15/XUiJ8ePu96WEamrrqI6gIQEIhgMrD8G\n8x7Pni0W9LM537eP6oFCQ8UoQX091XScPi0VN0hLE9OxvvuOejp06iQqlymBv+/Hj5PMrVKxaIcO\nFPnZs4dIgM0mkj+DgRwEkydTBKSggOqHAIpEhIdLO9XzcBcpYdfG5sJkoutnRujjj1P069AhaQrm\nM8+IxmtCgpTU9O0rrv2PPyayt2gRKXB5U3TPyH27dkD//srbOIiYlSeDDUnnYmtUXi+xdy9de1WV\naOTr9dLI0YWC/Hvgk0+86+2hUokyyQCl3t16a+PGEB3t3Og2MLDh0a6aGvp9Pt9rlwoDB9Ja9cEZ\n7dv7BAl88OEyQ8siJQAZSMwrymA2A99847xtSYn0/7w8erg2Z1LCCs2VxsiTFbkH0WSSfkG7qrdQ\nqajTuivFqZEjG9aTQA6bjQrK+UjJ00+LylCCQAX6110n7lNfT9v8+Sddn7+/WA/z0ENUm9C/v3N/\nhsREMjj5aApTrBo8mIx2ppq1e/c5z2/UokXQFxUR8ZGTOTnKy2l8f/1FURneS7tlizQqwYx7lu6U\nkiI1KHhSYrfTNbI6EmbA/vwzGXVvvEG1IIyU/PCDs7hCaSkZ6AClp+3ZI5KSr74SC9x58KRk/34S\nJeCN559+onz6lBSKolRV0XZ33y0a96xu5qefqPC9bVuqqVGpiJBNnSoSE34d79oFfPGFa2+1nJRY\nLNJ7U11Na9xkct1v6PBhuh527k8/FYntmjVEtJSaJ7qCfLstW0gUID+fyDYbb2oqLLxy1GOPiYpl\nnnDgADVVlCugvfIKRWPWraNUsd9/v3jFvfKIaVKSd/1RVCqp3HRZGfW08QaLFknrqpTwwgu0xhsC\neUd3H1oGxo93/93tgw8+NDu0vG/hjh2djYmNG8UiUR6RkdKu1d6k4HiDG264cN5KRniYZ5QHr840\nerTUIJYb1zfc4Fr1xl2H5rS0hj/0eVgsRAhuuYUKzm+7jV5n0YGYGGfpVdYZvE8f+l+pCaTFQkYL\n35sFkBpy5eXUgG/hQhIi6NUL+Ne/qBEcI3uOc58dMIDGZjYTUVVq+AiQ4c1kZOVkePFiaW3OF1+Q\nUeyquFejobSd7t3F7tV8QfDmzeK60uuJpBUUkJLZnDnK65Zde3Y2FcMzUmIyEQmrrBSNQpZGxmCz\nEbGpqCDSdfAgEZCyMiJsTA2qa1caNyMTbMx81IOXQ37kEZJuldcTsLUdHe18HYBIStj6CAkRlcpK\nS2lO33mHasLkqXwjRkjXOyMlgkARB/41lUpalO8OcnKfn0/eerudSCqgXDdRUyMVl5BDEETZ6vx8\nGotcYOKNN2hOOnWi41VVXbzi3nbtpD10GtvVvayM6pK8wdy5nlPTvFUB4yHvKeMN5s8Hbr+9Yefx\n4eKioeISPvjgwyVHy/jE2u3kNVyxQvl9dw8p/gFusZBhefPN5zeezz93n8ZzPqitpa7TSupX/ANZ\n7jHt1UuqShQX5zpf3pOB8dFH9CBn6TomE6UveQN27KgoGtOcOfQ6M9Q/+IC8wrNni4pKLE2HXZfR\nKDXo4uLISD9yRNqJnG3PFzlrNHR/WAShd28iSf36kXoRm1dmqDDD0FWdkM0mzrO8x41c8GDXLqpX\ncFXcq1aTode9O/3Nk5INGyjVhRFLrVaM9J08KY6Fx99/i71eGJEbOVJsVGm3E2n64ANxfHyzyWHD\nRLL27bd0P2prRXIQGSlGPADntCu+CJ0JFfCQq9xpNBRJufFG57kB6N4MHEjF/QysbiM1leRxWRRK\nHin54QepR76qigr+zWbxc8CTEm9rp+QF3gUFZLDzfYGUSKintBK7XZxPXkigb1/l7f38iDxbLBen\nN0NKCnmiGRpLShpiOMo/NwUFlCbI47//pWdBQ9CYSMmCBa6fNz40D/hIiQ8+XHZosk/s22+/jV69\neiEkJASRkZEYOnQocnJynLabNGkS2rdvD4PBgBtuuAH7ZUakyWTCU089hYiICAQFBeH222/HaXd9\nCwAyyrKyXDfNSkqSpgwwZGRIvWNWKxkU51sY5+fX8LxmJSQmOhsztbWi8pQc7kjJ3XeL0q+ekJAg\nbVImx4cf0m/mCd63j4wBb6DRiEYfD97gOHqU6gPY2qivF41xtZrO9c474r5ffUXpXko1Ci++SPUj\ngEhK5M0Tu3enNDC1GnjoIVT36CE+zNh2rgwuq1WcZ5abzsBIgyAQ2UhMpOMyI1OON98UDeT9+6U9\nJ2JiyPBjxrafH53vgQfEtSa/9uuuE6WpmaEaG0u1NIysefvgZiSmtlaMiERHUwoY258RU9ZZvKZG\naliz1DmGiAigWzfxf0+pR/HxFOFTgsFA6VsajbK0r1Lxc1GRlMCYzXTPGpK+9e670roGRkpUKqrx\n+e03Gre8jueqq1wTDIC+0+Tpfrt3i2mLDBUVRH79/Kj+yG6/NDKo50NKGlKYzp/DZKL55sEU+hoC\ntn1DUn1c1T350HwQGkqOEx988OGyQZORkr/++gv//ve/kZWVhXXr1kGr1aJ///4o59JXpk6dig8+\n+AAzZ87Etm3bEBkZiZtvvhk1nDE3fvx4LFu2DAsXLsT69etRVVWFIUOGwO7uQSsIlFc9eTKlacjh\nSq1KbpwqeVgvFQSBoi1PPy193RUpEQRpKoncwFPq6M4weTLVGzBMmEBqNK7w88/0hc+O3xBjJD+f\nxiHf5+GHxXQzFpVghjsfKamvF4t+5VC6z+3aiQSLzY9GI40IAGLh7qxZsBsMYqM7pgzkKtWGpQAB\nZITzc8xUl6xWkiDWaskAYkarHJmZYi1QSoqyqIBeTwSqd286X1CQGAGbMEEsjJdDfu/ZXHkTEXjw\nQXE9ydcfv+ZGjiRxBbudusWHhYnOALWaInw85ApxnhrfpaYSyVRCQADNh0ZDRGzsWPG9r75yJoF3\n302kiicwv/5K6X1xcUR+WDd6d+jSRVy3//oXNf9kkRJAVPiSp3NefTUwaJDr4/JppYyUrFzpXIcy\nZw7V6DCDesYMUsa62LjtNveqbq6wfz+lBXqDX36hhpEMhw+LUcLzQUoKfR80JOV24EAxbdOH5onH\nHmsevWR88MEHr9FkpGTNmjV44IEH0LlzZ3Tp0gXffvstSkpKsGnTJgCAIAiYPn06XnrpJdxxxx1I\nT0/H119/jerqasx31AFUVlbiiy++wLRp03DTTTehZ8+e+Pbbb7Fnzx789ttvrk/Oy8gqFZm3aaP8\n4JOTkg4dlEnNpQAzImfPlpKL+HhlDyvz7DJj12AgeVMGd7nmmzaRGhRAhOCtt9yPLS1NbNQmR0WF\ne4/jgAHOpGT9eqqBYR5/1jyQbRMURPfv5ElRKWvfPvp96BARnS1byMDhjdrrrxejOYBoQJeWUm8Q\nHixi8PLLsPn7Q2Dk9MEHyRh2R0pCQ8ngvu46aZE2Oze7DlZXsXYtRSv27HHuPs5j/HixjoYhNZUM\nWkGg1KugICJqKSmU3uRKlnXoULGgGxAjH57U1K65Rhy3zeZMSrp0kaYBPv642EF93z6xW/u4cZTu\nd/Ys1XgBzg0+5YXcDUFAAHUYv/VWiozyn5EvvxT/ZkYsU1vbuJEiLABFnbp1o94iP/zgfadxhmXL\nSOGMJ51sbmfPhoadBxClnF2BJ62MlNTVOYsA+PnRPDKD2mp1X6tyoTBkCDXybChYeqA3GDuWCDlD\nZaXzNr/+6rkYXo7AQOcmjJ7wyCNEQH1ovpg82Tl67YMPPjRrXLCEy6qqKtjtdoQ6in9PnDiBoqIi\nDBgw4Nw2/v7+6Nu37znisn37dlgsFsk2MTEx6NSp07ltFMEMGY2GvPjyeg61WioxyzBnjjQ/PS1N\n2mCwIWCGdVOBGdAGg5Ro9e+vXLTPvN4sMnX0qJhvD7iPlPAd3WtrKXfdFb78kry1M2eKRm7PnqRc\nBpDB784ostnEpnAMb7whFk0DlMYEiN7t2FjySjJD026nonZBoLGuWEH/r1tHx58zB1i1iggLf81B\nQeTRZSTh77/F93r2PFe4enzqVJgjIsQianlzSR6dO9PcrlxJtRC8R37oUDoHI2nyVKkdO8iQdYXe\nvZ17dlx7LTBmDM3366+TQWU0UhH7dde5jnoMHy5tRnnXXSSB6y59y2AgdTBW22K3kxeel3C97Taa\nu88+k+7LE2SAUiInTqQ0pjFjyKCUN/hMSSGVsMZAr6d1zDqsy8fC0K8f/Wafr/HjxTXSr5/rfjTe\nIDCQxA1uvJEiXr16ieeeOhUaXizhueekPUfk4O9JmzZE1JXkkjdtoloZvp7pYjRPlGPfPhJ9aCga\nkub66afS9L3rrnN2In38sejU8OGfjY8/vjwbYvrgwz8YF4yUPPPMM+jZsyeuduS0FzpSWaJktR2R\nkZHn3issLIRGo0G4jEBERUWhiPd4y8FICXuQe9PECyCPqlLBuBJuv919TcaCBaTIwhoBNgSrVzsb\nEsxoCg529va8+65z/Yy/P3nR2Ty9/TZJnDLIIyVLl4oGoF4vEglP6Tx79zqTPj8/0XiOiXFfxGu3\nkxf6xx/JyFi0SJq/f+KEWCAuNy6ZZ5JdB5+yZrPRPXr4YQrbM4LCX0u7dlTUzcjNqlV0r9avJ8M6\nK+ucgdp640ZS6QLo4eaqwdujj9J+gHOtyCefiLUubFueKCrJMi9e7FysD9CajosT/2fqa088QeTn\nnnvcE4xhw8SGhgAZtyEhRNYff1x5H7WaUnLatycylJ5OxEGep52bS+vfE9h9PnCASK3FIo2UBAbS\nOnTVIweg9acUDY2Konu3YAFFt3hotcBTT5HTgBn1rEBdoxHTtxqj3MQjMFC8Jo2GyAS7v/J7ExQk\n7SkjB79taChtm5MjFasAxAaGYWFieuClKO71tgZHjvbtXfd38YS2benzwsNTCqAP/xxcLHlsH3zw\noclwQTq6T5gwAZs2bcKGDRug8sJr58027rBv716kBQej7PrrEbVwIXL27IGR85Co6+qgqa6GhSNE\nhoMHEbhnD0pGjpQezGpF640bUcGazjmQuWIFTNnZ2OtCBrKd2Yx2AHZs3Igrxo5F1Zw5OPzJJ16N\nv+2qVWgPIDs7WxxzfT16qFQw63Q4smkTTJxR3Pnzz3GyXTvUsX4QDqSbzTi2axfqa2rQsbAQlfn5\nOJudDVitaL9wIXRaLU46zhG9bh00tbU4nZ6OhJoalB86hPLsbOhKStDJbscebiw8Ys+cgQlAsYv3\nYbcj02xG9rZtih7brnV1OJyTg7BNm6CyWND2q69Q060bCo4eRXXr1kh+6imEONJccuLioJk7F/rC\nQrS32+HnmKP2paVoC2D7tm2IKyqCac8eBJw4gdr0dBSbzcgEUHr4MFpbLNi7Zw9sMonhVh07IgVA\n0alT0OTkwBQbC+OWLWi/eDGYH1pQq1FYUID87GwyZF2kmbQ6cQJRZWU44piPTADZW7c6GYZhq1ej\nPj4edcXFpBIFoM2xYwg8exa53FwmfvIJym65BRUyD1/KE0+g1alT4hqxWpGhVmPv+vWwBwbCGhqK\n5IoKFB09iipX98YVrrmGJINlCJk8GVWxsRB4IsVvZ7MhcvFiGFNS0K6iAodcnNfRrQNlRUUoOnQI\nnQHknzmDqCFDYG3VCjncfj379sXun3+G3YWYQ+d778WJ11+HMTVV+sakSQCA0FOnEFpUhOPcMZNr\nalCcmAhLZiY6bN+OA9nZ8B81CtbgYCQEB+PMjBmozs5G+JEjCK6oOPcZaSjS1Woc37oVRocqXXJ5\nOYqOHUNVdja61defq1PK9uL4gVVViO3aFQezs6ErKkInmw36X39FSWCgZL3onnoKfiNHoiY7G3G3\n3466kycRdPZso6+hsWhz7BgCKyokY/MGwUePom15OQ430Xgzf/gBFSUlOOptl/gWBm/W1j8F3axW\nHNi5ExZ5zy4fGgzfuvKhKZGcnOzyvSZ3qT377LNYtGgR1q1bh3guhz3a0XtAHvEoKio69150dDRs\nNhvKysok2xQWFp7bRgn1CQmo7dIFZubBlXlHgnfsQPyUKZLX/E+cQBBf3O2AympFwssvK5/Ijdel\npmdPVPXqBZXDS6eTN2Z0A0HBO2vX67Fv8WLYDAZoZN5RwUXhvqDVQuUYo8piOXdcjdGIiKVLcdJh\nuAGAymaj4wCw63RQc5ESbXk59HJVm3MnEdx7YtVq2LVaqFylOwkCBLWazq/VQtBooDabIbBjCgKM\nHTogb8IEGFNTEbVgAdrPni2Zo9NPPAG7o8GgymZDu7lzEbZmjXgMx/XBZkPEjz8ictEi6RAdnnaV\n1QqVIMA/Lw8RS5acez/unXfcp7vxl6PRnLvnAGCX/U8v2hE3bRr8ZUW5Krv93D0AgOgvv0Rwdjag\nUiHt4Yeh5UQidNxnQlNTQ/Ps54eYjz9Ga0camqqJJTAr+/ZVXJs8Yj/8kObdZkPbuXOhlX12eYSv\nWXNufIJGA5vBgKPvvy9uIAhQm0ywu6lJMhw5ArWbSIqg0zmtPfZ54Y9dn5AAa+vWgFoNleM+Czod\nvdZI2AICoOY+q6cmTEBt165Q1ddDX1zcoHtjDQtDtaP5okoQIKhU2LluHfJkDS8t0dGocdRD5P3f\n/10yz7DKWwllGQSN5tx3VlPBGhLSsB3sdoSvXNmkY/Dh0kNbUQEtiyT64IMPlwWaNFLyzDPP4Pvv\nv8cff/yBlJQUyXsdO3ZEdHQ01q5diwxHYWx9fT02bNiAadOmAQAyMjKg0+mwdu1ajHJ0Dc/Pz8fB\ngwdxDZ8PL0NmZiawaRNCzGZg9Wqkp6VRTweG/HygTRvajmHLFiAxEeH8awClj9jt0m3x/+ydd3gU\nVdvG7y3ZVJIQQggldFB6Cx0BG0VAxIYiYAcFEUFfK34WRCxYXlFsKPraQAFRwQLSA5EioHQRkNBC\nT0gvu/P98XByZmZntiQbkqzP77pybXZ29syZEnju8zQA996L0Bo13LcLHA4gPR0d2rQBAIQ7HOb7\n6klPBw4cMN5fUdCye3dtyEy1amh5ySWyY7Rqe6tLLqHE46goxLVoQfucOAFERGjHX7wYAFAnORl4\n9lnE16yJRg0bUiiO04m2y5YBM2e6z6dGDaBhQ9T3dG6ff45OXboYh8I0boy2nTrR9Q8PB+x2RIaE\n4NKdOykJPioKqFYN9evWpWPs3UtlPy/koSRfcw2FN9ls6NSxI4WthIUBWVlo0LgxGlyYV43YWMBi\nQb3ISMBu1873xAkgLg4JsbEyF6GwsCSELeTMGeTXr4/EmjWRaLNRSJrZaltuLhAWJq+t3Y5O7dtr\nY/+LioCsLDRu0ACNk5MpPC0ykpohZmUhQXz39deB7Gw0bd4cOH0a7Vu1opAzoCS5PDk5mebz229A\nbCzioqIQl5iIhsnJwHffITomJrDlSuf7b2gAACAASURBVHftoqpaO3aY7nLppZcC4eGotmIF6j7y\nCDX5M6Hlhb+PpAYNgMhItGnZUnaALygAbDYkq0vsGtCidm33Z19w+jTwyCNITkujPBsAuO8+xHbq\nRHk4NWvSNWzdmkJ/YmMR3aQJjXdhzMQjR6gaU6NG7vlPnnj9dbRo317+rYo5CsF/wWj36d+F5GTg\nuutQG6CQxrAwdDArh6zmxhuB779HvLrU8sVgxgwgJwc1ff03T1CrFhAa6vu/ld44dAjxNWog3qxs\nuhF//w08/zwa6fsMVSHESnbArmMw4HSiVUoKcMGWYPyHnyumPMg0KlJygYAtq44fPx6ffPIJvvji\nC8TExCA9PR3p6enIEavSFgseeughvPzyy/j222+xY8cO3HHHHahWrRpGjBgBAIiJicHdd9+NRx99\nFMuXL8fWrVsxatQotGvXDlf5EnfscFCcvH6lurDQvdFVRgbtq2b7dqqMZBST/MEHlKdhRtu2lLAt\nvuty0Uq7vjeDEf36aeP91QwdqhUkP/9MIsZodVHdpK2wkPIIXC73bu6ANga8c2eZtB4TQ8m+Zp4O\nUa1p3Tptc8C5c+W5Dx9uHpufkkJx5CKm326nfIVFi6jEp8tFRqootykM7GuvlXkULhd1EVcU2jcp\niarntGghvRtFRdTTITra/X4OGkRGVFGRPB9FofydyZNhy86m1XOnkxqxbdhgfC4ACZrDh+W1yM11\nFwXiXol5jB4NrFxJhufAgXI/sdIs8gKeeUaWahahcKdOUf8Lu50EotNJ+Sai+piZIFm6lJKi/WHz\nZuqz4QlFoTl66nmyfz8gPCLCEyFKM6u9Hnl57tWljDDb58orZcEEdeGE226j58Rmc8/p6dJFFsH4\n+mu6L0uWUAL/xx97n4uafv2M+yJc+FtwllYsequQpiY01L9+G4Fi507jYiLeSEoyLtxRWurXN+/j\nZAYnQwcn1apRPhbDMFWGgImSd999F9nZ2bjyyitRp06dkp/XVOEZjz76KCZNmoTx48ejc+fOOHHi\nBJYuXYpI1X8ib775JoYNG4bhw4ejV69eiI6Oxg8//OB73smiRWSwqhGGj9qQz8yk/gXqcqEbN1I1\nJEUpfVdk9bHOnqXVWm9jCTHljcOHycAKCXE3tIuLqRO9MIpatKBXRXGvcgQYJ1kDZDROmmQuSsaO\npf4KTz1FIg6gbt+33krHcTqpW7YnfvsNOHNGJhpPnUpCSPT8GDeOVucBWer0yBEykEXy4qZNZIA/\n+SRVgxoxghLYRZGDxx6jxH/1tTp1SvbxaNtWlie22SjZ/UIYVPTmzbBnZpJYMxJ0alauJGP6k0/o\nvTDKt2yh5+nWW2U+ipiHSIjv1k3bu0PdWdpmo2R9EQYonn8RAma30/Vv04bOOSWlxPtlyOLFNJ5g\n+XLvK4hr1lDJYrXQ6N/f/f7+8QfdMzNR0rgxNbCsWZPE75Qp9LzrwxAPHDAu86rm1Cn3MsmCzEx5\nr4z6DV15JS0uAPLYU6fSfQZIaP/xhzyH0iRuC3JyqFkmUDKeq7SipFYtKg3uia+/pp4MFZXc262b\nrGxW1eBk6OBkzBi5CMIwTJUgYKLE5XLB6XTC5XJpfv5P1w/imWeewbFjx5CXl4eVK1eipa4Ep8Ph\nwFtvvYXTp08jJycH3333HerWrev7ROrVc2+CJQxstQEkSpKqu8ULQ70sFVzCw2UlJLECp6+YU1rm\nzaMSmNOna1d8AQrx+Ppruf3118lwNfOUjBxJoR5GeOrO3L49HUNtUF5I3IbTSfNQh84Z8dBDVDb1\nlluoNK0QJ8XFZLSqqxKJexkTQ8ajkdEl5rt6NZVH/fpraWiqe1/s3VuSEI1OnUjI3H8/9f0oKiID\nv3VrAEBmt27k0SgooA72q1cbn8uLL5LnRW8Ef/stebV27ZJG/Ftv0fOm9xAIbDa6Ls2b0++FhdIw\nrl6dqrsJcSmOFxZGRv65c56f2ZkztdXjiotJGB4+rBXmapxOeob37yevye+/03XQn2tCAlW88pTT\nou7cPXUq7W+3a+fcti1VhfOEaISpJyuLfnr3ptLDek/d0KEkpEVvEPH85uRQ+I56m5hnWfNzRO8f\nAFDle/lNVBQtOHiiqIg8qBUlSkrb0b0yUNoFKKZyU8o8J4ZhKo5yqb510XG5yAivVYu6KusRnhin\nUxpUo0aRQaJuYCZEiS/eDT0nTpCR17IleQ5OnKAwpRo16Di+hKV44/x5KoNp1ODRqJypMFAiIqg0\n7dGjNCfAc6y8MDAGDiRj7r773PdRixIhujyF8OjHr1ePfkR/CzGeMJDXriWB06gRGcNCnFitZCir\ny8kmJND3jx6lXAB112+1wDTyDvXpQ9ekbl3yAImyu+IcCgrIuDRrlCbOWW+onz5NAickRD5ju3fT\nc6E3xtVzHTGCRInVKvuDABQeFxND1wSQ91rM18h75glxvQ8dAj76SNuUTqBOqv7hBzpPdaM+gbrM\nrtm9NyqQMHu2Vlzb7TIPxF+eeILC/4QXSn8/fviBPG2PPkoCfetWCjvLzSVv29q18pqoPValRV8o\nQQjRspQc9na8r76iZ64iRIm6rHhVg0VJcBLgwh8Mw5Q/wfEXu3EjreBe6Hfixo03kuGkNtp69aKV\nWbUoEbHb33xjHP7hieXLZdM/u10a/5GR3rvKKorsNyA4doxW8NUYNU8TeBIljRqRZ2T4cN/OJSGB\nvvPzz8DnnxvvoxYlImSquNh3UaI3YPSG+l9/AatWUW+PYcOkp8dqBR58UNus76GHqA+FUVWyUaOk\nSDELWWvaFBg/nsbu0QMFdeqUlG9FQQHFJputApuJkqwsymcJCaHPb7yRDEaLxb2fiWDSJAqPAijM\nrF49eS1r1SIxII4j7vWoUXROcXGe+3t8+KG2f464Vt7u1403UliTzUbnFBGhLfU8bpwMPXzhBfMY\n7urV3Rsjbt6sFT5lQTwfNhvdK/XfggjHdDjk8zFtGolQtbjNyaG/Q3039tJgsdDfxZ499P7cOSjl\nmeshDGvhHb3YVGVPiae+SkzVpWbN0uU5MQxTYQSHKFEUipn/6ivzjuxGBmtoqLunxMxA+89/ZDM9\nI86eNQ7x+fVXKVA8Ub261pgoLCRh8vPPFLYFeBYlekMM0IZyqFduFyzQ5hf8+KPWyL/qKgpLUjNn\nDq30Czx5SvbuJVFhxMGDxl23r7uOxIEgJISM7P79yfskVucPHtQa62qM7nF8vOwabSZKAJr3mTPA\nZ5+hKC5Ojt+5M4m0jAzjpn16USIM4Px8uleiy/g330hvQc2axoZQ69YywV+EyOnn63BQcrAwcIVQ\nCA2lZpRm3azvuUf7tyHC2ryFOISGUh8Tq5XEtT6JWH1N77jDvCFgWBjl8KgpKgqcQagWJSNGaMOd\nvvuOXsUzBZB3pHZtrZhft47yaOrWpTBFfS8Uf9A3cg0PL99O6+Icxo4lT+3FpksX+jutijRtatin\nh6niTJliHDnBMEylJThEiTBEi4vNK6kcPOhuMOlFSceO5t2FZ8wwDnER7N9PIkJPs2beDa+PPqJX\ntfdArGDv3SurJl13nexGrsfIU7JsmTTm1R3dly7VioZDh+R/ykePUgdzgRAyX31FScDCqOvWTSbV\nC1HicMhjqOPp1bRtS+epFiU//0zndqHfAgCtcGnXjkK4PvpIVsras4fm8scfJCaWLaNkeHWo1oX8\nkBK8iZITJ4C334YrLEz2D5k9m+7hM89QbokaRaHviTA9gJKbDx6kayI8G+riBxYL5ZbccAN5gi4k\n1xvy4ovu5XWjo7UhThkZlMzZoQO99+QtUSPC2rxVdhKluK1WEkB6UdK1qyzp64nCQrq+eXmy2EBh\nof8eSTMcDvI0NWtGz6baQBYV8M6ckYUDBJs3y20bN5JY79ePxN3IkaWfTyC8Lf4grmNBQcV4LG66\nSVu0oSoRFkY5ZkxwMWMG/ZvDMEyVIThEiRAWLhcZz0Yei/h49xXhG2+k5FdBr16UQ6FGUWRZVE8x\n+2VZBRXhXUb5LWFhcrX1qqu0hrv++Js3kzgCgNRU+o9WGEVqT8m5c2SICQGhPsbx49rEZ/GdvDyq\n1jRmDF3fKVPIIAUocVkYx+qwJyOcTvpeXJzcNn68+38eamP+ppsohEqs9LtcwJtvkpAZMICMyZkz\nqZeGuEdDhlCZUjWJiYDo9XDsmHZFuU8f+gkJwV/vvoui+Hh53x0OMshVzQxLrs2IEXRthwyhbUJM\n9e9PVafeflv2q9DnVfz6q3kCPUDVovThB7GxdO6Cc+fIy9a5M4lqX2Oou3SReSJm32nWjOYA0HNU\nqxZVp1Nz553kVXjpJc/H++MPMlrPnqXCADk5gfeUOBx0LmbPnsvlXuZ32jTKQ1KPEQjsdrpXFyum\nXRR2UBcUYJh/Mx9/TAsRDMNUGYJLlAiD1CjMxoj4eAqF8cS+fTIUxJdY7fR0abilpZEx6w1hfAth\nAEhREh7uXr1r9mzZv0LQuTOtvovwneuvJwNQoPaUZGQA//d/MhxN7THSh/OoRQlA5Xz1HqEaNWRe\nQatWZHR6Mgyfe44M8qVLgZ9+onkK8bRvHx1LH+Kl9yIB1E8iPV2GbXXrRsn5L71k3F+jfXvg8cfp\n96NHgf/+l7wfW7eSB2r3birlCyD84EFpaAsPmf65slppDFFmFpCx9Q8+SKv1LVrIa/Pgg2TYC4w8\nN59+KpPZ1aSnk5dJT/360oPjT2Knw0HCUOQbGaGuXNa+PV2j9u3d98vKAmbN8nw8kUcjcj4WLw6s\npyQ2lp7jzEztNQbob0j0g0lM1H4WHV0+cecWiyzAcDFwOCgs0KigAMP8G6moSnQMw5Sa4PjfSxiv\nd91Fr3qPxqlT7ismM2eax9//9JM0wtXhMJ48JaLz9v79VHq1TRvggQe0uRve5q9PurdatV4MwY8/\nyt4XavTNE4XBl5ZGpWnFHMWK/6ZN9KoWJepwnhdfpLK4AF0PYXB7M3r0YXFqhOjZvZvEyGOPkUgS\nxxw+nObasSOV6wUokV0tSvSr2TYbjRcfT0bnb7+5V4jSI6oF/forCZG5c6kC0wUUtSgSRq6R2FV7\ndNTj6lmyhModqzvDG4mSOXMonE7P2LGyL4yauDgqIwyUrtpM06bmzetmzpT5UP37G5eQnjePBJO3\nyl/i2RTna7PR34nZ36C/3H8/iV2j6x8aSiFZt90m84sE/ftTmEd54ClcMNCEhdF95IpDDEOoF+IY\nhqkSBMf/Xr17UziKMPj0BtLrr1MSsJqlS83LvI4ZI+PMfa2YM3gwJcaK3I7Dh0kIqcOUBHXranMJ\nhFGrNm6bNqXY+/Bwd1FilNANaCtYqcuirlhB+QuLFtF7IUpEyJTeU5KXR6FQTzwhhUFeHuXkFBaW\nTZQI0SMMVLWRCsiV3gYNyGD86ivyRqhzhd5/X7vibbORd+Gvv2RXcHHffvhBekfUCIGlKOQ1URmm\nze+7Dy67XRq3QtAaNYXUe3SMqhDl5wPPP09hZmr0RusHH1A4l8UC3H23NrTLlzCEQBukV11FngRP\nvPMONXQsLqacDrP7fvIkPVPqcruDBsnnK1A4HO5zEH8vubnuhSLKczX1m2+8e2IDRXQ08OqrvucU\nMUywk57uXtWSYZhKTXCIkurVgQ0bKOfh6qvdjQx12U+Bp1VMm41yMqZPJ+N28GBaNR40yHwO1apR\nvkJxsUz4LiwkQaQvhXrsGCVuC4qLqalf48Zym8NBlZg6dCCPi35+ZqJELXBE4ru+eeLTT1M+xdSp\n9D45mQQIQPPet8999fw//yEh4IunZMIEmSCtp0EDmWRtt0uvx6pV5LHQG9bff0+v6qT37dult6VL\nF7oeEybQfRIVysT5nj9vLD7FiroQSS4XeTKqVYPjxAnylBQWkngVgsAo1EjvKTESJWfOkCAR9ywj\ng+alfwZF8QGrlfqcqP9D9UVs/Pxz2SpGlQZR8tjpJLFo5jER4lwtQs36tZQFURJXeAEB8pJ07Wpc\nvc6oUeqJE1Q+uaxJsh06ePfYBZr584Frrrm4x2SYysjp0+45cAzDVGqCQ5QIQkNpxVBvZBQVUT+E\nf/6R24xESUoKlQW122nl/bffSBj88AMJg8WLzY9dty7w7rtaUeJyURK7PgejRQttxaLHHgMeeYTK\nlA4Zol3prVdPllJ98UUylNSx/uvXS0+AOnyruJhyTE6fdhclt99OeQRNmtD7xERK8gdINNx/v7th\nff/9JJoUhY6zdSuFhQl+/FF6YLp3d+84LzhwgDwBwlMSG0vHX7aMwqf0ibriPJs1k2FULhfla8TG\nkiiJjaWKVi1bSsOzVi3gf/8zNjoBKR6EKFEUalp4zz2wZ2XRtpwcEjpnztDr/Pnu4whPifDkpKTI\na6k/B/H60kuUg3H11ZQHIxDCw2Kh+3XvvbKKmbfk5X37SEgHsufCsmXew6vWr6d76q3nSceO2sR2\n4SUL5Mp+UhLllADav/UBA+ieJCS4ey7btnUv2b16NXlLRQJ8VSIsjPtuMIzAl3L8DMNUGoJLlABU\n7UgktQqEga02tJ1OKit7661y2y+/UKiTzVb6CjZqUeJ0kkjS5yLUrasVRBERVGr1nXdI+JgZah9+\nSGOpDe2jR4G//6YQoS5dpNjp2ZMMyoICWvH31VBp0IByc4zKii5eTCFgXbuSCBDJ5AMGUGL9oUM0\nd2/J/Xv3khFtt5OR+Npr9Op0uifqCkM+Lo68FiLcZtkyEjMzZ1L+juDMGTLoZ84kIWGzkVfiu+9I\naIryyrGxZPQLkbVtG3nbANgzM2HPyKDKU6GhdBxRXUtNbq6s4CUMWPHczJ5N1/3FF6kvDCDvmTDG\nBw3SNshUhzaFhVEIoRA73p7HPXuATz7xvI+affvoGfHEggUkzAUbNlCyvpr8fKqs9X//5z18zG6n\nZ33UKHrezTx+peXcOXl8oy7dn36qFYEAnY/esyDGiIgo23waNLj4Xc45uZdhiBEjZB4lwzBVguAT\nJYmJ7v1IhIGtNoBcLjJcdu2S20QStjokxV+SksgYFp3Ua9aUomTHDukh0BsOwqsSHm5uVAgvwMiR\nsszszp1kPH73HbBypTQ0V6yQ4kjvKfGGp+7MXbtSsrDaoPznH/l+wwYSKZ74+GMSUN26UchbYqI0\n1Js21Ya8uFyUX/H447Sq7c3ouvFGSmju0YPC+qxWKlxw3XXkiXn3XdovJobC2P7zHylqmjUrMVAL\na9WixOnQUDrnMWPcj5WRQfPq2NFd9E2YQNfj8GHpKXv5ZTKczcKWbDYyZJOS5DUQ4rVRI/eGlvrv\n+vO8KgrleezcaewBArTexN27SZDqm2J++il1cp80yfeclv/9j+57IMO3Cgvp78xup7HVFbVOnaLG\njkacPOnuyRQC0KxRqa+kp198gcCihGEIb41hGYapdNi971IFcDrJ0M3PJ2NQT3y83E/wyCNkdBj1\nBhkwgDwc/oSWHDlCoqFtWzJyb7qJyrV+8AHFt2dm0vaTJ8kI1IuEnByaj5FgEeTm0upt//5ym0i+\nNmqeKAyUpk3p2qSl0Zy8ERoqPS+TJwO33OK+j9oILi6m73gL4RGEhJAAiIuTxv6GDVSNSyTjHz5M\nlaicTvIoiIRrq5WuldH5Au4NE9UeKaOQvX79pFHatWtJ2V3FYvEu5sR4+pwl0dE9NJS2i2esuJju\nlzqJXo3VSgJM3bFdzHfGDM9z8VeUiOds+3a65kaVtWbPJo8SQGFpc+ZIMSwQ1dkA/42A556T45eV\nlBR6FeJWfT9yckiwG/G//1GI3GuvyW1ClJTVU6LuDXSxYFHCMARXomOYKkdw/MUuWECNA826iE+f\nTsaq2mi75hpKbFZXthL5BTNmUH6BECXDh5tXFRIsXEghTQAZNcL4j4wko0jEuufnkydHnzSdnk5G\npzAqNm1yNxSNEnXF/D2JkuHDyZj05sEQREdTv5FNm8zLpaqNYKeTPAXFxb6LEr0npm5dEnaCjAzg\n66/J6G3VSntOI0aQIT19uvdk5CuvlH08zIob1KlDDRytVqBGDbjUTfhKI0oKCmQjP7udPrv7bsoP\nslrNcylGj5bhhE8/TUaxmG+NGu4eQDX+ihJ1R3dP90s8tzYbCSlPJW7ffts/I6BZM22J5LIg7pPI\n8VH/LXgqaqEXMEDgwrfy840rtpUndvvFF0IMUxmpXVv2iGIYpkoQHKJkyxbySMyeDTz8sPE+Rkab\nvtyueqVXJJifP0/G8T33UK8JM/LzqfqRnsGDybA36kWiRjQ7FEIiN5e8Kjk5wLhxMilbb0CJ8fSG\nGKBdNbVYyFg5fJjCbdRkZMgGgQCtXv/0k7wmGRnu3zESJcLIXbOGVqD1OJ0U6uVwuIuSzp1lk0pA\nCpfrryeBKEhNpX2tVioMYOQZUxMdTXkDJ096Nk5dLgplWrwYhTVr0vgOB9C3r9znxAntM2QkShRF\nKx5DQshTN3u2TOKPjaVqbXqaNSOvFkBJ2VFRvve5sNkoZE8t7Lzt73R6924Ir4HVSufpaT7jx/t2\n7PJAhM9ZrcBTT9G1FKxda9yQEjD+u0lIoFdv5ZB9IVDNIX2lb9+S3CiG+Vfz3//6vhDHMEylIDhE\niTDMc3Pdu58LVq7UJkQDtBKq7n/Rty8ZvAAZkQ6HLC06fz4JDDMyMynhXE9MDK3Ei3Cd1FT3xNrx\n4ynfZMgQ4KOPyBgVK9gWi0xgfust94RnISaMPCXz5slEPxFKcvIk8O232v1cLhk2tXMn8MUXUjQU\nFlIFrzlz6ByFiGvbljxNABm2AweS8S1EkLokq+D8eSqTGhKiDV+aP58S9NVliPWldgXiPETzyF9/\nNW5qePiwFDlWK63IexMlW7cC334LV0QEFKuVhOnHH8t92rWj6ycQZY2bNJEi5K67gPfekzkhaq+Q\nSOIfN44aQk6bZjwXwezZvq/0NWggj+ELInxL3SzTCFE4wWqle2YUMucvixcHfjU/NJTuF0B/p2oP\njKopphs7d7qXjO7Rg+Zn1GPIHzIzyz6Gv+Tnm+eDMcy/iVmzqDIgwzBVhuASJU4nJTJ/+aX7PtWr\nuxtUUVFUAlhw7bXUiBEgcSNCkgDvRpS36kjCCD92TOudyc+nRNzQUDr+ddfJ/AybTXZ0t9uNV6Ib\nNSI3tcNBFZg2bqRjrV9PIVvCWBbdbdVdtQXqZod79lAomphvYaFc+b/zThIV27dT5aprr6V9fvuN\nKoe1aCHHNvIICaHVpIlcyXa5KP9Gj74poX4cUQb53Dlj78AHH8jqYIKmTSlPRvDGG/IYQ4bQudnt\n2PXll5ToLiprCcLDtSI2OprCrX75RRrEdjtd67vuovf33Sd/V4dKHT1KQs8TQ4b43ueicWMSoL6G\nTyUmUsUwT+Fbl19OQgyg+3r55e4eM8GTT/oePjZkiPY6BoLQ0NIlpov+OOVBIDwt/qKvXscw/1bm\nzvXdc8wwTKUgOP73UosSwPcurlaru/dEkJdHBqG/q447d8pu7Xv3aj0OYly1sXLbbZQTExXlHkpm\ns8lqYGrPwqJFFKoDUKjJqlVk+PbtS2FXZ85Q2JMaEb5l5C0QokR8LlbFAdouRInNRqLl7Fnt95OS\npODr25c8O0aiRIw9bBgJmb/+kr1NhKjbvZuO7akCmD6R12il32iFrF8/bZjaM8+QMb1vHyXTHz9O\noXoCfQPJiAitJy4xkZK11YSEUGiWqJRVr56slf/44zIv5Ngx43KV779P+UV6du0C+vRx367Gn8RO\nm428CW3bSnGpR116ulkz6nujDqVT89pr/v2tBLoHSESEuQho3LikgIEbu3fLJPlgQN/nh2H+rXDR\nB4apcgSHKCkuphXwSZPovX7F9tAh95XZp582X0X580/qvRAW5runRITPrFpFYVNNm1IYyKlTtD0p\niQzehg2pfO+8ebRdlACOitIa8moDMyxMawynpMiO8CEh0lAUCdT6UK4NGygEKynJWJSI1X2RqG6z\n0XwWLKCkciFKxJjeDF+150WNOlTo999pH9EtXdCvHxnl1asDr7xiPr4ao/n44mGw2ahj/P79JKT+\n/lv2WBHzVD9L4eHm4YEC0Slez/r15NESoiQ9XTaDVDNrlnHy/rRpUuyaUZpqM506kUg04rnnpDHf\npQt5x8wIdM8Rf0lKomIXRsTGmvdkqV49uJJh2VPCMASLEoapcgTH/14jR5JxVbs2vdcbRyNHuhss\nCxbIykJ6vviC8gvCw2n1NyLCe2z4iBG0nxAER45oE4MTEylMSVTjEV4R4fGoUUNrTPTtSz0gAPeE\nfJFcrc+5EH0f9KJk+nTKhVixwjyvQggJ4c3Ys4cEwksvSa+R+F5ZRIn4rggjE+WaBcKoCg+nJnvv\nv++eq7NgAVVTS0qS18NoDgDd92HD3MWP+F5xMXl+nn+eChXs3Ik2Q4fKqkzq1X9fRImRhyczk8IK\n1eFkOTnu1bQWLCBBbLGQWBIiW4zhjUCXwOzZ01g4GVFURHkyvnIxV/MD2Q+lsuNPGXOGCWaOHPHe\nyJdhmEpFcIiSq6+mFeb77qO+F/rVEX3JVsBz0rOITV+yRFZvmjePyvyaeUzsdgoBEoJAXa3o7bcp\nTAiQokQYSaKMsWhABwDffEMJ78IgfOstbbUmm40qDLVv7z4HI0+JKFELUBiOUYWyuXNls0WbjaqN\n7dkjvzN2rO+ipHNn6m+ix2KRHiWRJB4XJ6/JF19QroV6/K++0nq0hg0jg91iodyXmBjPoiQ/n8Ld\n4uPdw3SsVm0zy3r1gJYtEXL6NCxOJ3k8Nm6U+9ep491jZiRKDhwAPv9c3vOcHDonfQ7EoUNyXoWF\n2gRsX8TG779f/MRqQXExJeZXRjp1ci8u4Yl//gFefbXcplOubN9OOVsM829n3z7OKWGYKkZwiBJB\nWBgZ7/pV0aIiagCobqBmJEqWLKEqWOHhJDDWrKFGhdOnUwL8oUPmK7yhoRSeZSRKFEUa3g89RB6T\ntWupozlAPSyuvJJ+f+ABCh1TsiuKsAAAIABJREFUd86++WaqZiXyHcS8Q0JIiO3YIberRcmdd1Je\ni7rfRt26xjkEQ4aQKGnXjvqjqCuTNWlC+QSi0Z3VSuMK0QKQwS+M6nr1gMsucz9G7dpUfQzQJtwL\nwSXOT32N9av/Qkg0b06ehquuMg7Vat+eEv3V39XnGonrJe6ROERhISxCWEydKvefN897Xse0aSQY\n1QiRLF4XLSKRog+bEnO1WOh+LVggn2VvnoXTp8nT42sJ4YrmYpbKTU4Ghg71ff8FC4BHHy2/+ZQn\n4eEXvwwxw1RGsrKA+++v6FkwDOMHwSVKAEom1se+FxXRyrNR9/bbb5f5GXPnUtiWCMMqTTyqWpTo\nK2gBZEhXr04JtqKfQFyc9GT89BN5VkQZYMHq1bQKCpQ0+UPPnjRGYSGQnU3lW3v2pON17UqhQNnZ\n9LmnJoBq2rYlA05fLhmguu+rVpEgmDePPBsA5c+8/joJjsJC4xK9ak6dor4R+mpownOgFhJ6USKq\ncokywvPnu4eAASQmP/hAa6SnptI1EYwfLxP409Lk9QUQcvYsiaXISPPzOHZMllIWWCy0QvfLL/T+\nhx+AZ5+l34XAsNup0pe6L4v6vK1WKbSEGPFFlKi7knsjP1+Gv/nKvHnmx3j6ad8rhfXubXzPKgvq\nUMmqBsfRMwwRFcX5VQxTxQi+v9j4eLmiLygqIoNJ7UERYUrHj8t8A5FPER5OxnVp4tA7dCAPiCh9\na7fTsQsKKDTp5En6LCGBDOfwcKoCJbBaKX9AHwt75Ig0Iq+5RoaKZWRQQv0LL5DH5IYbqEzwp59K\nA0UdvuUrERHG4qJPHxJV6sTmAwdk88QffqBcEE9s2kT3KTFRu13dcFBgJEp8iZtPTKR7oRYln35K\nq+CCKVOoLHDjxvRe5flxRkVR00tPHcf/+kt2i1ezaZNsHnnuHHmVAPKO5Oebd3QXc42P1zYDBICO\nHQObaG61UrJ9aiqwdKn3/dPSKKRQ39ND8MADxg0hjVi9mp7Ri8Wff8oS0r5QUSFwgUCU/mYYhmGY\nKkZwiJLiYsrDUIfaqKlfn1ZN1EbbK6+Qt0HtERCejWbNKA7dn6TRf/6hn2uuoVCo7dvJGI2IIC/F\n6tWUnP3FF7TafPvtdCy9F8NsZefwYdkLo2tXoFcvmm9uLokOo+aJQpT07k1C4p9/fD+fAwfI9f3R\nR8Yrx8IIdrko9CkkhN77Uv0nJITCxPTem/Bw8hIJo3DsWDovvSg5f953A1z93cxM9/CmIUNknsuF\nfTdv2oTiuDht2JsRZnlJOTlSYNntdI+FUBb3yWj+ViuF49Ws6R6CM3GieTUywH9RIvZft843UbJz\nJ7BsmXnzRG+d4SuSU6e0uUHeGDtWVs2raojmogzDMAxTxaikVoSfvP46rXKbreL+8gt5LdRG2/Dh\nJFQiI6VHQHhP+vShpHMhSiZNonAjPUePyvCdOXNktSyAvBrCYA0Lo7llZJCBHxEhQ7yGDdMatmrD\nTl3N6MgRKUoAyqUYO1YKBk+i5LXX6Dy7dze+PuLcGzeWBk1CAhlmjz9uXMFEGLXCMBceDF8qQJn1\nINFXt/r4YzrH+vXlNrudOqKnpFDCvjdDvEULMvSrVaNQNiMRERtLIWv6eZdWlGRnS6+B3U6/33MP\nnZ/Vau7tGTSIPA4ACVg1MTHuHkA1vnqQBMJ49VVMiPM0y1mJjqZKbZURT0UtjLBaK3d4mSfsdhYl\nDMMwTJUkOETJJ59QMvqHH1JpVyPMVpL1nhJhoEVGknA5fpy8G1dfLXtrCP7v/2SysstFoUtGoRMD\nB5JwAuT3w8KomtM332jzBaxWyutwOGSTwtxcWqlWi5JGjSiBV92c0UyUiN8VhUrkfvCB+xytVhJO\nYrzJk+mcHQ5apc/O1u6vFyVqz8mxY8YVvgoKSFyZ9fIYOFAm/4tjjBihbTL44YeUN2O10jUVneHN\nCA+ncrzHj1MVNTPjVN1DRZCUBLRsKd9nZ2tL85oZu1lZstyv8Ly9+qpsbBcZSZ4rPfXrA61a0e8i\n7M9XbDa6tkbX1QiLhY6Rl+ebKBH7mF2/yEjgjjt8O/bFZtcubTnmYKZ2bd+bxzIMwzBMJSI4RIm6\n5K9ZkuqcORSqo0ftKRk6FLjkEvq9fn1qHvfJJ+Qx2L+f+naIClOAVoAoCokWI6MwJETO77nnyPjv\n3596cADkwRD5DK+9RrkQLVpIQzAigvJF1LHuopfKsmX03kiUvPuu7FgvYs337dNWIVMTFgYsX05V\nyIqKSDzUrUtlecPDySgX16ppUzLYhWHevTt5WlwuMnR/+MF9/L17KbzNzFNy1VUUliYwEpJCXO3f\nT+8PHvQthj4yko7rSZTojfPhw6kymmDmTBK/AlHWWM0nn1COkBAl6lAtEdp2+eUk+ETVNCMcDuDL\nL72fl0B0M/cnhKp+feoB44sXQYxrFr5VmfEnbLGqk5fHvUoYhmGYKknwiBJhLH3wgXHsfXS0cSjO\nY4/JxOzbb5dhM6KLufo/eJEAL1AbaPqyr3rU34uMpHEnTyaDNS1NGn0DBlBJ2euu0xqLYgVdsGgR\nCYyePeWq+rFjVL3r7FkqK9y2rdZYVRRtKV49YWGU+7J8Oc3X4aD+L5060XemTSNj+8gRKit87710\nTXbvlmWN7XbyAhiJDmH4x8VRXow3zLxbLheVOxb4aoS1b6/1fMyZQ4UHAOC226QgFfz0k7a7uj68\nLCnJvf+FEKBdutD73r1lzwu18Jk7Vytw9djt5p3WjahWjYSnP6JE5Fn40tdCFG4YM8b489dfN+5E\nXxmYOpUE/L8B7ujOMAzDVFGC438vtackK4vKo/pK7dqU8K5GdEU36uitDt/68ENpNAsxsmIFhVq5\nXBQ2IigslLkR0dFkOLz5Jnktjh3TCpxmzWheZuJh7VoqhStE1p9/UoPF1q0pD2PjRvc+C8JT4im+\nPiyMPCGieZ/DQSFimzfT5+J76lLBVqtMFAeop8onnxh7jER4XJMm5CUwEi7bt8tr6UmUqPE1X2Dk\nSMrbEPz3v7Tt+HHg1lvdQ8GmT9f2YtGLknbtKL9FTUgIedwuv5zeV69OJZQBCi0UcxWiV8+bbxqH\n36xfT0LVDEWhH386pdeoQSK4b1/v+9apQ/k96hBCNR9/LAVeZaNaNfdGo8GKCBFkGIZhmCpGcIgS\nl4tWle+6y72ykcslS7KqGTtWKzDUnD0rDTz1KnxkpNYoBeSqpChx+tlnVNGoY0etd+Pqq6njdUQE\neXJefVUbTqSvtuQpYVz00xBlY0Wol755omDRItlN3Zsoyc2lz3v3Bp54Qvu5GLO0iezqvI2UFONx\nOneW9+W//6XrZTRPYXitXVv6hoE2G4W/nToFvPee++cOh/Y8IiLc778es3PfvZsS1cU5m4mS114z\nLizw6afAd9+ZH1c8r/4apCNHypLInmjeHPjPf8w/97f6F1M+sKeEYRiGqaIEx/9eU6ZQI7169WRp\nWkFeHuVo6Pn0U/NQK5FgDpCBOXgw/R4VZZ6zMnYsGZ0FBWS86yuBdepEIiU6mrwIubn0Kprs6WP1\nR46kcCkjhBEuwoIEQpDpRclNN9Fq8ZYtnkXJihXkzbFaaWW8XTvj43ozevTGPEChXbt3y+R7M9Gl\nNqpGj6YSwfoV+NWrKYfl+uu1OShGHD9OYWxGPVfEcQoKjPtYhIRoPT56T4kRRqLk5EnybC1cKLfl\n5roLrlWrKDTOSFh4a0jpS9Wz8uTUKW2/HaZiKC7m6lsMwzBMlaQKZq0aMH48veblkaF39Kj8zKys\nqyfj/JJLKCfj448pjKpdO6rcNH++u0dDzeDBtMqtFxgnT5IRvXgxlXa12WQfhJdfplf1uNu308r9\nO+8YH0cYn6IjvECUhVWLEpFHIsbv1YsEnBGijLHZdfFVlERFkVdIjRBp9erJa683vv/6i0SAevwP\nP6QCBQkJ9H7qVJmEL+67J5xOup6vvkoCMDXV/XxsNmOBumuXNu8jNtZzh3fAWJRs2UKhW7170/vC\nQkrQ13tKRE6G0fX15gGx2ShpvaLIzAS+/77ijs8Qd91F/2YxDMMwTBWj0npKZs2ahUaNGiE8PBzJ\nyclISUnx/qXwcDIa1Z4SIUoefpgSmwVGouSrr6Tx3LYtJXJPnEhei6uvpmpZffqYH/+zz2QPEvVq\nZUgIdY1v3pxyA6xW2fEbICNeVNaaMoWM2N9/Nz+OmHdMjDbRWh++9cgjMrxJGLUtW0rj2Ii+felc\njRC9N0T54C1b5Gd//CHDykJCqLO8GquVQrMWLDCuWgVIAaA2wPUeAHGOTZp4FwjiuAB5qNLTtZ+p\nRYnR6nJamlaUXHWVtheNEf36uTcjdLm0YYV791Ils1q1jOdqJEC8iRKLBWjY0PM+5QnnMVQOevb0\nLRyPYRiGYSoZlVKUzJs3Dw899BCmTJmCbdu2oUePHhg4cCAOmzVHVDNqFPDss/T70qWUiBwaSl4U\nkaAtkoJFRarWralL+KxZ2vKhwgA2Q1TOUosgIQjURm5YGIV92WwkPmw2mTdRqxZ18BYG6cqVVBFM\n7wVRY7NRfkh0tBQv585RyNW111Ljt9atKVzq5EnP3h09vXqZC68JE4Cff6bxV62iikuHD9N3Fiyg\n8KSCAm0ivP66ALSPUT6P8ByoRYhelNjt5ImYPdv3Cl6A7Gh/4ID8bORIuU92tns1rPPngRdeMB97\n9266DmosFuCjj2ReyM6dFIamDiu02SgPKCZG+11xnqXxlFwMXn6Z7rMR48YZ915hGIZhGIbxgUop\nSl5//XXceeeduPvuu3HJJZfgrbfeQu3atfHuu+96/3JMDBn5ABm+O3eSKFEn4gpDVyQGx8SQca/v\nbq1Pmtdz5ZUkDs6ckduuuop6eNhsch6hoRSyI4SKzUbv27ShPBO1oWy1ei+t2qULlS/Oy6M59u4N\nXHEF5U888ADN4emnaSyR4xIo+vcnb5C4ngUFdFzx/qOPjBsnqr0j0dHGoT5ClHjylPjbuVyIEuGJ\nWrtWfnb//dS8UoSGqcP+APIMebp2K1cC8+a5b3/8cZl7lJ9Pz4fFQsn9ns5BzNXIA3TVVfRTUZw5\nQ6LErLLdiBGyuhzDMAzDMIyfVDpRUlhYiC1btqBfv36a7f369cP69euNv1RcTFWU9MZweDgZhZdc\nohUlYjVb0KoVhdToQ7q8GcCiy3lODvUMOXqU+jh07EhleoWRKzwya9bQ+wkTKCnY5XLPd/ElWblF\nC+p+np9Pc9y/n7wTRh3dASol63JpxU9Z0Xd0FwLOrPqP2lNisRg3sgwPp3wXIUqefpquoXq8kBDK\nX/ClYSKgDd8C3MO0brxRrvD7mig+diyJm/x84wpaWVky1E2cs9pgNxO7VitdF9F4Uc311/vXTDHQ\nHD1K3jgzkaYX9AzDMAzDMH5Q6RLdT58+DafTiVq6ePuEhASk63MCLnBi5EjkNWmCmK1bsV/01AAQ\neegQkmJjseeZZ1DvjTdQpCg4IT5v3bqk/0ZSdjYK9+5FXFYWDu3di9wLhld7ANs3bUL8998jp00b\nZOt6HbQ6fRrhAHZs3IiE+fOR16gRTt18s9zh2LGSX5MBHPrxR5y6sAqeeOIEoiMjcb5pU6Sr5tw8\nJwcXzGccnjgRJ0RjRx22nBxUv/tuJH72GazFxVCysnDw77+RLYxvAE3On8eZY8eQMXEiLKmp6HD5\n5dhiJuwA1HvjDeS0aYNzPqzIV//nH8SdPo2jf/yBJkVFOHP8OGxZWSgqLETo6dM4rDonAIh8/nlY\nFy9GUVwc8k2a9TmOHsUlmZnYfuG7rT7/HOevvx7HDh6E80JhgJpHj6LBnDnY3bMnojduxPF77/U8\nUacTrRo3xsHDh9ESwKE9e3BKNzcAaNGiBdL27kWOyujebLAfAHScMwfn0tKQ36gRrHl5OKraz1Jc\njI7Fxfh9+3bAYkHY33+jNYDjyclI2LcPWzdvhuP4cVySm1tyngJ7WBgcN92EXJPjAvDccLEcCdu/\nH60BHExLwxmD+dnPnkW1m2/GOU9zZwCYP1cMU1b42WLKA36umEDSTN8TTkVQLG3WmjcPcb/8guor\nVyJh7lwAQPWlS1Hryy9hFWE0NhssJqvrrtBQ2k8XKnTmmmvgSE9H7Nq1uPTee2E/dw52VfiKLS8P\nRXFx9F1FQfSmTbAa5VMAyOzeHcWqHAJnZCQyu3VD+ujR2h0tFrgueE9sHsrAOmNikN2hAxSbDYrN\nBkthIRR94r7FIj0DF7w1MSkpiF292nBMW24ubOfPmx5TjXKhtK/lwjVTbDZYnM6S5m0NXngBNlW/\njZw2bVB9+XLEe6jQVBwbi5O33CI3WK04fd11cKo8B6euvx759evDlpPjcSx5UjbsnDcPuS1bIrNb\nNxSrRJv2hBQ6J084nQg5dQrWoiJU27wZloKCkntVMuW8PLjUfVTsduQ1aIDjd95Zss0VEoJig/yL\n4rg45LZo4f2cKoIL18btGbtAcVycT2KWYRiGYRjGiErnKYmPj4fNZsMJXV7FiRMnUNtDqcvoCzkD\n9WvVQv3kZOq5ccGYTU5OBt59F7BaUc8o3KZJE8rPuO8+tLziCqBuXdo+dy5qDRsGbN0KAGi/ZQvF\n1r/yCn1eWAgkJaFlgwaU/L1gAarXru3eGRwAEhIQ07IldUinSQEAkvT7zZhBFbjOnkWdevVQR+yv\n58knqZndggXURT0/Hy3atJHjA8A776B6zZo0t6IiQFHQTIQ+GY2blISamzej4aBBVMVHT34+nXN0\ndEk+SfVLLwWiopDUvz/1dzl1isafNw81mzeX1xKgz9asQeIXXxifEwD06SOvSVQUWl16qXs37tBQ\nNL9QejfZ7PoYUbs2Yi65xPjcw8LQsnVroEOHklUht7HPnqVnBYCjqAh1YmOB2rVRV73fli1ATo78\nbmwsYLejY4cOgN0utw8YAD9mXvFcCEdr3KwZGvtzzZkSTJ8rhikj/Gwx5QE/V0x5kJmZafpZpfOU\nOBwOdOrUCUt1ZVWXLVuGHj16mH9RhN38+ivF/GdkkDG7eDFtj4w0jv8HgIceIiP/oYe0RjSgzSkR\nVbQEeXmya7vwwpjlOhQWulfB+uwzYONG7bY+fUhA9erluVP5jBmUcN6pE61iR0WR8JgzhyqC7d9P\nuSfx8bS/yGspLvbc0X3ZspKwNjfmzqWiADk5VPlqyhQqMfzTT1SaeORI6h8SEWHcQLFGDfPzMcKs\nS7jLRX1j1AUGfKFXL21ux7ffUm8UgKpHeevvEBoqq4bl5tI16NhRu0/Hjtp+IfXqkXCs6OaGZUU8\nM2bloj/9lIpKMAzDMAzDlIJK5ykBgMmTJ2PUqFHo0qULevTogffeew/p6em47777zL8kDP7CQkrK\ntdkob6R5c+8HNEosFhQVyYR3fUfvvDwZpvP55/T6zTfAPffQCvnhw9JrUlhIhrqalStpe5cu2u2t\nW8vSwUbs2CEbCAIkCpKSSIgNG0YJ/2fPysaMAM3T5SIjPyzMeFyx3cx4FvNRCy+Hg0oRC0RDw6+/\n1nZDB8iz408PBU+ipDRMnqx9/9ln1Ezxr7+oJ403hCixWun6q/OH1KhzZsLCqPlmfj7wf//n/RjT\np9M8jRp+ViQxMcATT0iRq2fRIvKmCJHOMAzDMAzjB5Vy6fbmm2/Gm2++iRdeeAEdOnTA+vXr8eOP\nPyIpyS3YSXLFFdSjIzSUDMaMDDKkMjLcS71mZpJXxBfU3dD1okRdulaIn2nTyFPRqpVWEE2YQJ4L\nAPjiC1qZ13te1HhaWRcr8eL4TZvSeVerRpWf1JWuzp0Dli+nfRs18tzJXogSs8/FmL6s+Bt1Nu/e\nnTw8vjJlinFDwPDwwHgdrFZqqFhYCLz1lnEDRTXi/Fet8ixkjcjMNL/Xal54wf26VQZq1gRefNH8\nczMByTAMwzAM4wOVUpQAwP3334+DBw8iPz8fmzZtQq9evcx3fvRR6hfSsKE0hjMyyFvx/ffUN0JN\ndjat5PtCURH1/gBkiWGzObRpQ587HJrKWwCAoUMplAcg0ZCdDRw86B6+JXj8ceqjYYQw/vSr++Hh\nNF/RvwSgUsWPP06i5MABz6Jk3Dha/ffmKfFFEOjDt/r29d/DMXQo8PbbWiEIkKeoWzcSob4QHW1s\n6IvzsVhIpHoTJQCdV9u2wDvv+HZsADhyhLxi3rrBb99OYWFVMczr77+pmSbDMAzDMEwpqILWjwEv\nv0y9OKZPJwFRXEx5Gb17G4dNeTLM1SxcSHkQ119PRmV8PJCYaL7/lVfSsbyF3ths1CDx558phEhP\nURFwww3uHb8FIs9F5MsILBYywNX9JIqKtLksN9wA6HrAlBAbS983uzb+iJJXXpH5Gy4XsHp16bqS\nv/mmVlD8+CMwaBA1PBQd2b2RlWXc9E99PiK8zRsi/ExfNc0TK1aQJ8bb+BkZ9FoZurf7y7FjwG+/\nVfQsGIZhGIapogSHKBFERFAIU1EReU6qVaMcgNBQWtkWMf1mouS99yjMRvDss/TTrRut9PftSyv3\nZrzxBiXKOxyeV91tNmDpUuCOO9w9JTNmAJs2kRFvhuj4nZ4OTJqk/axaNconsdsp3GbRIq0o6d6d\nchzMuO464+pUAF1fMf+zZ2WHcoC8PuvWyff9+sku6qKbe2mMbbOO7g0bygaFvmB0v8W4FossBOCN\nnTvNxaIZLpd5w0Sz+VQ1quKcGYZhGIapNASXKAGo+tE338j3DzxABnRBAa2YG4UwbdxIq+/TpgHq\nPh02m3FH92HDyDvjdNL+6lV44ZnxJkoAEjt6AZCaCowYQYas2cp6dLRMKN67l15FKd6xYyl3pWFD\nqsB15Ih71S9PDBoEdOhg/NnAgSRybDZg924KWVuzhjwWqaky1EofbuWp4pc3jERJURHw6qvAgAG+\njyOEnBrRVd5qpTmePevf3L75Bjh50vM+eXnAnXfSPfBVlFTW8K1x48wrs914o3vlOoZhGIZhGB+p\nlNW3ykRYmMzdEBQVyUTcJk2AefO0RrLNRl4Hp9PdADYyJBctop9t24AePah608yZ9Nltt5FoiIgw\nL4ErjmG2ei+6dhcXu4eeAZTYPmkSVfmy24Fbb6VyvadOUWljwYoVJMbsAbzNQ4fKuTudVB749Gn5\n/qWX6ByeeUZ+R3hKSoOZp8QfzATi8OE0lkjwz8wEatXyfdypU6mYQUKC+T7Cg5CfT9XYPCGeh9IK\nuPIkP59CItXNLdVccw3wzz8XdUoMwzAMwwQPlXRJ1k+Kisjbcc89xp/HxpKhJzqM169P+ScCUVXL\n5dIahN4MYCE+cnKAXbsoT+Tllym8Z/du8soYce21tLJsZKirDXCzKkx16pAQEXNMS5O/68eKjwcu\nu4zeHzhQ+nK6emw2WWLYbpeJ7UZVw9TVwPzhrbdkCV5BSAjlXvgSauULt90mPUm+zNHlopLNAD0z\nZr1vBOJ5uvRSKt3sCauV+s5URlGSm0uvZnPTC3qGYRiGYRg/CA4r4pZbKIxG3bRO0LUriRWbjRLA\nAQrlueEGuY8QJXrDSoRvffkleVfU2wEpSnJzgeefp2R4QWKieT8QkQzvKc8BkL1PjAgNpZX+kBD5\nHSNR0rEj8NRT9L51a/fQqtJitdL1EqFZDgeFrhmJkshIYMkS/4/x668kqPRCcccOSqr2pwKWN2rX\nNr9fagoLKSzuo4/oefNVlLRv7z3crFkzEmKVEXEeZsKtTRvzanEMwzAMwzBeCA5RsnAhJV2vXg18\n8glta9WKjOaICDLErVYKs5kwQSZsC8LDSVjoPSVDhpAX4uefSfgUF1Ois1hZj44mg1t8d906CqHy\nhfh444RpX1ebbTZg8GAyEs0MRqtV6xmxWsmYTk317Rjeju90yvwch4O8GkKUvPmmTHwPCQF69izd\nMR56SHtPkpOB6tUpFGrBgrKfh8DXjuuHD9O+f/5J772JElHZa9w472PHxFA4YGXEU8ghQD1wrrn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jaioqKwe/du/PLLL1i3bh26du0KAHj//fdx2WWXYd++fWjWrBmWLl2KXbt2IS0tDXXr1gUA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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85eabce550>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
      "\n",
      "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30000\n",
      "movement_variance = 2\n",
      "pos = None\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(1000):\n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    if pos == None:\n",
      "        pos = (Z, 500)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "\n",
      "bp.plot_measurements(zs, lw=1)\n",
      "bp.plot_filter(ps)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eoohONlmzZg18fHwQERGBuLi4rL/q1asjMDAQu3btUm1fvnx5FiQMwzBM/sI4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Nv5s7ph3xdfsIzzp5/y988/57EuW6btKanIQk9xsbHy3SdOMEzw7Fn9sEKAovCWW5TqbzIxMZyX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f26fc978>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n",
      "\n",
      "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers,  laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Interactive Plots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.html.widgets import interact, interactive, fixed\n",
      "import IPython.html.widgets as widgets\n",
      "\n",
      "\n",
      "def plot_kalman_filter(start_pos, \n",
      "                       sensor_noise, \n",
      "                       movement, \n",
      "                       movement_noise,\n",
      "                       noise_scale):\n",
      "    # your code goes here\n",
      "    pass\n",
      "\n",
      "interact(plot_kalman_filter,\n",
      "         start_pos=(-10,10), \n",
      "         sensor_noise=widgets.IntSliderWidget(value=5, min=0, max=100), \n",
      "         movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
      "         movement_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.),\n",
      "         noise_scale=widgets.FloatSliderWidget(value=1, min=0, max=2.))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<function __main__.plot_kalman_filter>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_kalman_filter(start_pos, \n",
      "                       sensor_noise, \n",
      "                       movement,\n",
      "                       movement_noise):\n",
      "    n = 20\n",
      "    zs = []\n",
      "    ps = []\n",
      "    \n",
      "    dog = DogSensor(start_pos, velocity=movement, measurement_variance=sensor_noise)\n",
      "    random.seed(303)\n",
      "    pos = (0., 1000.) # mean and variance\n",
      "\n",
      "    for _ in range(n):       \n",
      "        move_error = random.randn()*movement_noise\n",
      "        dog.x += move_error\n",
      "        \n",
      "        z = dog.sense_position()\n",
      "        zs.append(z)\n",
      "\n",
      "        pos = update(pos[0], pos[1], z, sensor_noise)\n",
      "        ps.append(pos[0])\n",
      "\n",
      "        pos = predict(pos[0], pos[1], movement, movement_noise)\n",
      "\n",
      "    plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
      "    plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n",
      "    plt.legend(loc='best')\n",
      "    plt.show()\n",
      "\n",
      "interact(plot_kalman_filter,\n",
      "         start_pos=(-10, 10), \n",
      "         sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n",
      "         movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
      "         movement_noise=widgets.FloatSliderWidget(value=.1, min=0, max=.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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990JsLISHg831H+DtdoMfVu5k6q+b8x29aFGvGo/f3oawUG21UNIUMkRERETE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\nA+vZ6UvbdC8UAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85fc020780>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "<function __main__.plot_kalman_filter>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise - Nonlinear Systems"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our equations are linear: \n",
      "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n",
      "new\\_position &= old\\_position*measurement\\end{aligned}$$\n",
      "\n",
      "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
      "\n",
      "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n",
      "\n",
      "    Z = math.sin(i/3.) * 2\n",
      "    \n",
      "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#enter your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30\n",
      "movement_variance = 2\n",
      "pos = (100,500)\n",
      "\n",
      "zs, ps = [], []\n",
      "\n",
      "for i in range(100):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "\n",
      "    Z = math.sin(i/3.)*2\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "plt.plot(zs, c='r', linestyle='dashed', label='input')\n",
      "plt.plot(ps, c='#004080', label='filter')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lGKFwKyCnAsIwnlfoyc3JBsfmDoC9jYWaqwrGztocJ+cPVFlBOX7zKfrN3ktF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\n3JSsQ1Hstxxq3jz1c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0eW+7PsW3SnrNGH7LYEq27dujAYDBYRUWZmJurVq2evZpCLmDhx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\nRERkNwxAiIiIiIjIbhiAEBERERGR3fwfR2OFTstoLecAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f26fb8d0>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Discussion\n",
      "\n",
      "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n",
      "\n",
      "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n",
      "\n",
      "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise - Noisy Nonlinear Systems"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement the same system, but add noise to the measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#enter your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30\n",
      "movement_variance = 2\n",
      "pos = (100,500)\n",
      "\n",
      "zs, ps = [], []\n",
      "\n",
      "for i in range(100):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
      "\n",
      "    Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
      "p2, = plt.plot(ps, c='#004080', label='filter')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Lly+HjY1Njvu++BQh8wuTEEIIIYT8PV9fX7i7uwMAevXqBYFAgPr162Pq1KlSa0Aye/fu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5uyYMO+fYa/niPAAhDVcAqMHI4qUc0wGSZL5xUVFeHixYv4WNDT1rVrV5w6dcpUb+P4VK1KhlYF\nBbSfkUGbn591z0sbwgDk8GEqF96+TfMNK1bQMLQmuEDFnrPMtoJiidbbm3wNfH2pGlK/vnP15y5d\nSiaCYWG09e1r3KKM4ThwMtpFRSTBW6eOYa/j4QEMGkSeKxxr1pCilpcXJUMskRBp2VJZSdBYunXj\nK2v98w9JOzsrGzZQdf3xY9pYlp8QBiBJSUzogqERk630UlNTUVpaimBBCTgoKAjJyckqn3Ne0SuC\nUUbgRx+hxMcHhdWro7BaNUh1KdFZmVp370IxRCq6fRtux46V7ScdOoSnWgacXJOT0bBXL5R4eaHU\nxwcFNWrg7sKFep8L+1yp4Pvv+ftONAdS/fhxBMfHl7UzPnZzQ3JAgN6v44ifK1FxMWRisXFDynZM\n1P798FbYT6heHRkG/p49Y2JQVyEAKTx/HtdPnYJMh4FzW/5suVepAsXGD+nx47h8/DikzrywdHWV\nJzSePuUb0toQlv5c1ejRA4XVqiHzpZeQHxnJ2n0VKS2FSCaDzI4TrBEmbuO13/8JBybVHDr0ZsYl\nI4O3/6JRIwT880/ZfrnERO2vkZ1Nf+bkwCUnB6XOdIOTyeCSloYSbbLCDL1xT0ri7RfqaorpoFRd\nsgReV6/CPSkJrikpuLlpE/KdsL1MVFyM8rdv847lGNFjnVe3LnLr1EFB9epI69UL2c2bO0RgV1it\nGvIiI1FYqRKyY2KQ3aqVcwcfDLU8+OILa5+CzeKRkIB6Q4agpEIFFPv5IbdePZ3+v0RFRTolMewR\nkwUggYGBkEgkeCaQAn327Bkqq1GOaWapIWWG+Zkxg2YLUlKAlBQEdOpEpfr/CHj+HAHaft8vXvB2\nPatW1f0zcvgw7h8+jNx69VC/f3/7uPEXFZFc4ZEjtOXlAamp9nHu9sLChcDJk7xDtTp10ksggcsi\nOsz16skT4NKlst16Hh6WE4ywJc6f589CVamChj16GCdcce0ayksk0LW+Zjefrdu34SkSwcYbgRn/\nYTefK2fivyStS1YWXLKy4FGjBgKbNSPjxqtXqUKfkAAkJ5NUOkdQEK0Jatakitvy5dRWbQWysrJM\n+nomC0Dc3NzQtGlT/PPPP+jXr1/Z8f379+N1RQMshmPSvz9/X+hJcecOfdE0yTcKpXS1uaBzZGQA\nb7+NMEWzr82btc+cWBsXF+qlVqweXb1KPgH6kp5OfclBQTSE76AZE72RSPjzLm5uhvf5OwpCWVah\nyZWzIJMBr74KnDlD38FWrYxXzVNMHpSUUFLBUK8gW8JW1QQZDHtBOCfLqVRKpWSYXFIi/9lXX1GQ\n8eKF/HnJyeQptG6dZc7XAphUBWvSpElYu3YtVq1ahVu3bmH8+PFITk7GBx98YMq3YdgDQUF8NZbS\nUu0mbkKXUF0DkGPH+E7DgHYHdVtALFYeTD161LDXOnQIaNKEFFnc3YEhQ4w/P0dg7FhgzBj6u0QC\n/O9/Vsse2QwsACGaNwf+/puuO3fuAF9+adrXv3iRhB/q1gXeeQfYtMm0r89gMOwH4fqHUwp1cVH2\nK+PmfoXXZmNNRW0Mk86ADBgwAGlpaZg1axaePn2K6Oho/P3338wDxFhyckjVyJ6yUCIRsGwZqXdF\nRen2xRG0YEHXQWFV+v2GVBGsQfv2wI4d8v0jR4AJE/R/HeHFzctL+TEXL1LbyfXrtP34IxlGOjoL\nFtD/z/DhTP0KYAGIEJGI/C5MzblzVGW5dYu23Fxg8GDTvw/DcsydS+pm1arR9uabQNeu1j4r2+Xu\nXeDgQWDkSPtav5gDdUbBAEm8K3q+JSSQ1869e/znGOPpY4OYfAh91KhRGDVqlKlf1vkYOxa4coU+\nlMnJNBtggHKPVdH3ZvvRR8D48SQjmZ6uehGtCqHTd/369uMU2r49f//YMe2taqrQdHHj+OorfrBz\n+bLtBCA3b1KVrE4dw2WYs7NVt7u4uABbthh3fo6EMAAxcV8v4z8saUBoaUpLqWok9BhydOLjaVHN\n+XO1amXd87FVpk8Htm4F4uJo/6WXlO/TzkZODn9f8R4tVAjlghEHD0BM2oLFMCFHj5JDLydhbC+G\nhMbi4gIEBlJGUle1oipVKGADUOrpSYZf9kKDBnKPF7GYLkTaWtVUoUsAIrwB2JIU75w59H/h4wO0\naUOVIH1Ys4Yuzkz2UTt165JJ2PXrdFM0tO2PoZ7r18kvQhF7D0BKS2lR+dZb5LjerBnf/V0bP/9M\nC/aJE8kfwh5hJoS6cfGiPPgA+A7pzsqiRSQ88/QpJZf79pX/TKhCyAUgaWn8ypEweWTnMBleWyUi\ngr9AvHsXiImx3vlo4tQpYP166mmsWJFmEdq2tew5LF6MK926QerhgcacA7g9IBYDP/xAAUPbtvy5\nGX0QDv2rCkDq1+fv29JindOrz8+nz5M+fa6nTlF7lUwG9OoFnD0r769lKOPlpWwaxjAtws+vWAw0\nbWqdczEVYjFVqR8+lB87eJC+c9o4c4bacGQy+nuNGlTttjdYAKIbvXoBe/fK93ftcm7zSg5XV6BS\nJdoUadgQ6NyZEpC1asnXerNnA599RgIz9+4pByp2DgtAbBWh4YstV0AuXaLhXo6RIy0fgAAoFn6p\n7YV33zX+NapVo8z28+eUNbGnCkhWFrVzcIjFus/wyGTA5Mlypav794F+/aiCom8bG8N5WLCARC5i\nYuhaa+r+9Dp1qAWVGzwfNkz3llJbRSSiheXSpfJjf/2lWwCSn0/JFc6l/eefWQDiyPToIRf/AChJ\nlJZmf23klqJDB9pU4e5OHSHmmFOzMiwAsVWEka4tZauFCOXlVGWfZTIgKYkWxkwi1vQoOsYryvkp\nEhVFmdnSUtp/9Ej93IQluXiRv1+njnyxVlAAlCun/rk7dgCnT/OPjRjBgg+GekpLgZkz5T3Z/v50\nfTV1AmPlSlqcy2T8dgt7RhiA7Nql28yap6c8+ADoXmBvZGfTxuHmRu3CDGVCQ6ml9upV2pdKgT17\naGjfkhQWUvKWc6t3d7d9eX4nggUgtopiBtjHx/qLRE1oCkA+/pjK9HFxdMO/cIFatFSRm0s3KmdX\nyzAWdUPc7u5UnfL1pXasevVsY1ifa7/iaNaMhtLnzwd27qQbiKrWtJISYNo0/rFevYChQ813rgz7\n58YN/kCoWEwzDabGwwN44w3Tv641ad+ekgPc/9/Tp3RNb95c8/NCQsx+ambH25vEYB4/pi0jg92r\nNNGzJwUg0dF0XbZGC+I33wCffy7fr12bBSA2BAtAbJXGjenL0749LdgNVQayBOr0rQGSn1TMcN++\nrT4AqViRFpX+/rSdP69aYpdhOIrZS1uhShUqP58/T1LM69bxzZZWrqTecyFZWVTVuX2b9sVikslk\n6EdODv2/V65s7TOxDGfO8PdjYthCUlfc3UnK+o8/6J7Uvr28oqqJ4GCqGBQV0X5mpm1UX/VBJKIW\nooAA21EPtGXGjAHef5+qIdZCKEjD3SssTUkJtSF6ebFrjQKsT8FWkUioetCihW0HH4DmCkjt2vyf\nKfb6K5KfT1txMQ1U371LGURnIycH+OcfZQUdR2bIEDJSzMykG8R/imZlLFhAnwshAQHA9u2kFte6\nNZm9ObvUo66cPw+0bEktkd7epGzkLKgKQBi6M3488NtvVA3Yv1+3/z+xGBD6gSkOszMcjypVrBt8\nAKpbA7kg2JJcvkzBtocHVQN1sSjIyOC3LTogNr6yZdgFU6dSj3NKCm2KmtbCAERdBiIjg7/v7+9c\nmYJnz4A+fYB//5VXgYYMca5ZBrGYKhqffw6sWiWX6nz8mHw81Lm7t2lDQUhBgeXO1d5xc+P7VDiT\nGaFwZogFIPrx0ku6P/b5c2qfdHcHBg2iqmVoKC3CqlY13zkyGCUlyubGAFkbWLolkOsSKSyk2cvU\nVOXHJCWRJHpCAsnw7txJAYifH0nMT5hg+RkaM8MCEIbxvPoqbaqIiuLvq6uACI/7+xt/XvZEYCC1\nq3ED5OnppFLVoIH253IVo6Ag2ipUsO/gLTCQlMGWLZMf++EHyhqp+3eJRM5ZMTMUoZ78w4fUSqOP\n/LG98tVXFIScOUOZSXv357BlJk+mhVSfPsCAASQ16upq7bNiOAPp6aqPP31q+QBE2CWiSqXyzBnV\nSbaMDJqzEhoZOgBOlF5lWAXFCoinJw09c5KpiijK+ALKzqCOjkQCtGvHP6arGd8//1BWMiqKsiX6\nDGGnpqq/UFuTiRPlwYarK9CokX6mZwzNeHvzJTGLi+1TmcgQXn+dBA5OnaKMvLe3tc/IMSkooBbJ\nrCxg7Vqge3eqVNorqu5bDP2RSi3zPqqqDOPHWye5qWlOlkPbmsfBXNABFoDYD48e0WDujh3WPhP9\nCAykPuHERCqHnjypOos9fTopxnA/GzHCsudpC7Rvz9/XNQARXty0SUMmJNCwdps2lIlZtUrXM7Qc\n4eFUBZk2DXjwAFi9moLXpCQ6f4bxCKsgztSGxcGy8eZj3z5+C0xwsHKSxZ5o3pzmWGJigP796Z7M\n0E5pKVUcp0+niv78+ZZ5X3d3qih07UrCN3360Dyh0GPNEgjv0aoqINoCEAdzQQdYAGL7nDxJX5iQ\nEBqyXbDA2mekP5070/lrmmeIjgZ+/ZVmRKZP183cytEQBiBHj+qWLdLl4qbInj3Ap59SBlgmIzMx\na/HllzTfce+ecoZx1SpgzhwaZuSYNo2qauPGKf+7GfrB3dDEYvp+sgoTQ1/y8qjFasQIvvM1QIPq\nivTvb98tfg8e0Dza2bNyFTCGdn7+mURC5swBrl0j7xhLUKsWsHEjBcIXLgDbtlnmfVVRXEwBEYeq\ne7S3t/p7t0hk/YF+M8ACEFunShUaSOI4dcr8C4UffiBJzvbtLZ/liYwEZs1yruFrjgYNyKMjKIj6\npWfNUq3+JETfAKRnT/7+yZPWacN6+hT44gvSZa9Vi4ZSNUl6XrlCN5SSEmDJEnrOlSsWO12HY84c\nurbk51OFUt0cF4OhipUrqY0vNpb+vnmz/Gf5+RSYKGLP/gv5+eTkzeHiov06yyC6dePvnzhhm22/\n5mTBAvoMZWXRvKY6Y1KhATVH9eoOaeDMQnhbJyyMNq49oqiIgpDOnc3zfjdvAlOmUDY6ORmYPRv4\n6Sf1jz95kn5esSJtzZoBXbqY59wcHYmEMkRVq+o3RK5vAFKjBhkRXr9O+5xLrTqVKXNx4QJ/v1o1\nzRnSadP4VRLu38EwDHU3OwZDF2rV4ivP7d4tFzJITSVvn337KIlSpQq1fK5aRcFuYiIlt/bts482\nOOF8VOXK9l3NsSRhYSSPfuMG7ZeWAv36UTu5PfnAGItIpN1Uul8/MmwMD6eteXNKODtowMYCEHug\nY0d+n/7Bg+YLQP74gxZ5AQE0+NumjebHX7tGWWmOYcNYAGIM1arp/5zISFLZePaMghFdMnO9eskD\nEIDK4pYOQFQ5oKvj8GEKkhSZN48tAhi6s3kzsGIF0KoV9fG3aqV9XoqhnrZtqWLLeRWkppKST5s2\nlLH96y9S8Nmxg4IQsZjaa589k79GUhIlEmydx4/5+4Zcp52Zvn3lAQhAcvP37tEagyFn0iTVxx2w\n/QpgLVj2QadO/P1Dh8z3Xteu0Z9paRToqFKSUESTCaEQqZQyX9z5b9kCxMUZfq4M4scfydMhMZGy\nJS1ban+OYhtW1arKJmGWQJ8ApHJlqsxxtGtHqjoMhq4cOUKB7Jw5wGuvAYsXW/uM7BtXV+W2PWHb\nlZ8fzS5yoiLChZS9mBEmJ/P3WQCiH1OmAHXq0N9dXYE//7Rc8FFSQnM727cDy5cD33xjmfdlaIVV\nQOyBDh3oz3r1KBgxV4VBJqOWKkW0VUB00beWyUhr/8YNublcQgKpHBUU0LzDp5/SIDrDOHRt3WrZ\nkhZir7xCNwJL+4bIZJQFU6R5c/WPnziRP+T6zTf27XXCsDxCB/RWraxzHo7Ea6+ReAjH7t2aF3gh\nIXwDzMRE852bKXnjDaoaJyVRNYRJN+uHtzdw/Dj9H44fb5kuib/+ooSctzfQoxd+P8wAACAASURB\nVIf8uFhM/jSsem51WABiD1SqRK01mqoLpiAxEXjyRL7v4QE0bqz5ObpUQEQikmPkgg8AGD1aPky/\neTNw7Bi9P1MWsQwSCc1UWAuplFqozp+nQOTuXXmGTBXDh1PlrKiIglXmXm06ZDLqMb5/n9r5HLEv\nOydHXt3lYAaExvPKK+Sr0KkTBSPahAzstQICkAx4ZCRtDP0JCKAgxFIL/6++Uq6yA3Tvef6cquqW\noLCQWhEDA9n6RgD737AXzB18AMrVj+bNtQ8I6mKwA5B0qqLb+b59/J9/9BH7cnLIZNSaduQIbRUq\naBYCsEckEqqAvfsu7Wtz4e7fn7JmBQXkJ8AwDcOGAVu3yv0a9uyhRaWjcf48X9I6Kso6hmSOhq8v\n3QN0XVQKHajtpQLCMA2aPidr11LyQ51ClL5oah9/+tRyAciFC/JOkoAAmundskX942UyahkLC6OO\nEgeu9LMVH0NO27bA0qUUiJw8SV8amYyyzooa1orMnAkMHkyVkJQU9dmhqCj17xsQAIwcafz5OwqX\nLpESBkdAALBsmWNLE+uygKlQgTaG6Sgt5ZvFOaoZ4dmz/H1WQTMdit/dbdsooB04kORXy5XjP7ZV\nK+Djj6kSEhIC1K1r2XNl2CY7d1KVGyDfkGHDjH9NbQGIpVDsEklLA3JzNT9+/Xqam1JE6JHlILAA\nhCEnNJRao2Ji5NKsy5eTk6jQVIqjfXtlAz1V1K6t/mcTJ1J5m0E0bEiZoOxs2k9Lo/kZVTMyjx4B\nt25RpiQoiCpQ9iBrybANnMUN/aOPqLJz5gxtzPPEPKxbR4vJX//f3p2HN1WmbQC/ky60CFRoaUtp\noYCoUGhZSlWKgAoIyuIyiriAzigiy4AIo0BRUBZFcQSkn8goiBvogNsAigy77CAoMCAICAXa0kqh\nrUCXnO+PxzQ5SdomzclJk96/68plz0l68govyXne5Xk+lc+wd99V1//o1KnivV5U82zeLH3EPEP5\nt7/JxvGhQ6t+zStXZNlleayXmnuaq2nyp0zxWFOqGwYgvkxRPDM9V1ioLiplXQixqswzINdcI4/s\nbBkdCw4GRoxw//r+JCBAsjxZV4zdsMFxALJ6tXr26IkngPffd/09jx6V9ztzBnjjDdd/n3xTTQlA\nAgMlsE9K4myrp+TlqRNFXLoEtGzpvfZoxWSSG9ratb3dEv908qSssrD29NMyO/vMM1W7pnXRSLNe\nvWTZVaNG8jmgF2eXqZvVoAQHDEB8SVGRZBBZt05S5LZpI0umtGZboOzYMfeDnY4dJXtITIzlOllZ\nwL59so6Y1Lp1UwcgGzcCo0bZv872w83V/REXL0pGLPP+nMBAIC2Nfyc1RfPm6mN/DUDI877+Wn0j\ned11lScx8QWnTkmgXr++pN9t315mekgbjz0mN90PPij1YszGjwfuvVeS8LgqIEBSP+fkyOPaa+1T\nROvF1RmQyZPlz8IsLU37NlUTDEB8yaZN6vR1p0975n2io2W0x5yl6tIl+Ufszkb4WrWk3oS1qChZ\nJ0z2bJe1/fCD4yDQ1Q83W2Fh6r0lJSWSIMB62YTWVq6UpX2dOkntj5QUfZIskD3zDEhwsCzBbNHC\nu+0h31RUBMycqT73wAP+sYHWXITwwgV52O5rIffdc4/sH7r/fulLoaEyAFeV4AOQ33v3XW3bWFWB\ngZLwwlzNvLLv6HvukULTa9fKHqlhwzzfRi/x412tfqhzZ7lRMDtxwjMjlgaD41kQ0k+7dlL/5fnn\ngVWrZIbC0Ze5uwEIoC5KCKhnXjxh40YJQqZMkfeeNcuz70fli4mRgYzLlyXzWnl7vYgqEhBgv+zl\noYe805aKfPON632cVdD10bevFAusX1++g5zZW+oLZs+WfxtFRbL35N57K359UBCwZo1sXt+3z37g\n1o9wBsSX1K4tWUQ2brScW7fOkj2iqkpKZH9BYqIEOampMhL600/yfFCQfSVYQEbl33xTRq8bNpSR\n7H793GsLicBA5yreZ2Wpj6sSgPTrB7z+uuV41SrpE55Ki+xKAULyLKPR/2+ozp6Vdd/+MBpfXQUE\nSGFTc8Xzxx4rv7Ds+vUyAHHqlKThffppbbIeVWbuXGDMGPk+i42tvMiuGQMQ/fTpI4Oq/pjtMCjI\n+dS/BoPUDfFzDEB8zR13aB+A/PwzcPiwPD77TIKJr76SjFjXXQfExTlOk/q//8m0qdmQIQxA9GZO\n15udLY+qBCC33CKjThcuyPHvv0umoC5dtGunmckkedGtJSdr/z5EgCRpuOsumem5+WZ5PPecf6e0\n9pYnn5TkGb//LoNR5QV8W7fKqLCZJz5nbI0bZ3nPoiJgwAD5jLOd6XeEAYi+Kgo+Dh+uOKMm+RQG\nIL7m9tuBF1+0HJtnKdxhW4AwNVVuSivjTBV08iwtMlYFBspN2k8/yTR4v36eqxJ99Ki67kT9+vaZ\nmIi0sGuXFLAEZBZkxQoZNBk/3rvt8mfOVAm3rYauRzHCdu3Ux7m5wN13A9u2VV6QsrBQAlZzmlgG\nIN7x+efAI49InayEBNd/f8sWmXU7d04+DyZPZrIVL2MA4mtSUmST0q23SjCSmOj+NR0FIM5gAOI/\n3n9fvb/IU3bvVh8nJ3NpDGnv2DG5wTQn0gCkn3G/kffZVkM/dcoz77NqlSx76doVePRR6RNTp1qe\n/+UXuaFdvbri6yxcKEkzMjNlNoSJGvRVWCiJUQYNktS8K1ZUHoB8840kzomIkEfr1jJDZ872CMiK\nDQYgXsUAxNcEBQFffKHtNW0DkM6dnfs9BiD6ys+XtLmeGIHTI/gAgPvuk1HH3btlhJrLr6oHk0lG\nBk+ckFSYt93m7RZVnaJIPRzbz6e5c+0TLpD+9JoBSUuT0fLatWWwbvZsCUI+/lieb9hQvZqgIoGB\n8rnL2Q/9LV0qmaBKS+XYdkmcI3PmSKkCs2+/lf0X1gHIuXPaDOBW5I8/5H0iI4E6dTjYZoMBSE2X\nlSXF58xq1bLsK6gMAxDPO3ZM0glu3Ch7J+6/37czFYWGWtbiU/Xw88+SCODqVTlOSAAOHPBum9xh\nMABLlkiK76NH5dwLLwAjR3q3XSRiYtRLmrKzJQtbaKh275GZKcEHIDeBK1cCixYB770nAU9Ojpyz\nrYND1U+DBpIUxcyZACQnR30cEWG/AfzcOffbVplduyzZvEJCgN69tR9A9mEMQGq6qCjZfLxzp8yE\nXLwoQYg1RZEP9Dp11FU6X35ZpjHPn5dH69b6tr0myM1VZ6jauNH9opBE1ho1sgQfgMyClNfH9uwB\n/vlP2cibkiKzpR06VL/aCM2ayWbnvn1lX8KMGd5uEZkFBQGvvSY3lk2bypIs2+8cd1lXZAckwDZn\nFfrySwmA6tfX9j3JM2xnnXwpALEepL1yRT5XqQwDEH/hzghSvXpS+KZHD/X5V18FPv1URuH/+AP4\n5BNZh2mWkuK5zcokOnQArrlG1sECMmN15IhkAjl2TEavIyMlkIyOliBRK6dPA+HhsoSB/Fd4uPSb\nggI5/uMP+eK0zaiWnQ306mUpqPX55/Lfdu0so83WrlyRUe6gIFnConfQHBEhyzCCghiwVzfjxnn2\n+rb7Ovr0sfwcHu7Z9yZtuRqAKIr2AUhxsdz/DB7s2meJFnW6/BhzEfo6k0k2yDVtql7fqIXz5yUz\nknkjJ4sR6i8oyD5NpTkN88qVsqeiSxegZUspWuiufftk7XS7djIyOXIkR238ncFgn4ns+HH71739\ntiX4sFbePp6xYyV4Dg6WEefAQMsSPC0+q0wm2cD8/fcye+uon5rfn2qOkhIp5GbNOgCpyPLl6r5/\n8aLMQvMz0HsiI+Wz49prpbbMTTepl2TZKixUz+iGhMggWmKiFAEcPhx45RVJ5uOssWOBxx8HHnjA\nMlDjDAYgFWIA4suOHpXNosOHS7Dwt79Z1tVqgdXQq4du3dTHGzbIf20/3KKi3H+vJUuA6dOB/fvl\neNEiWWZXVOT+ta2/FKh6sQ1ATpywf82lS46LU5aXsru4WH1cWiqzIjt2APPnV62dgCxJTEqSWZum\nTWVW5rvvqn498i8lJbLEa8AACUDDwytPdqEowLRpkra5Xz8JPAD5/IuIkBvYli1l+SHpKyBA/j4u\nXJAB0VWrKi6SazJJwclHH5U9F7ffLoMsvXpJBq3582WQ7fbbnXv/996TwRdAAtTOnR1/PjrCAKRC\nDEB82c6dwKZNluMffnDvi90WA5DqwbyJDZBlVubN/p74cPv73+VL29qHH8qGXnOhwqo4c0ZGolq0\nAAYOlPolttPk5D3NmskNfdu2QP/+jqvwvvWWfPE++KAc9+0rAUB5AYijUcobbpCZu7lzq95W88zs\n5cuWc6+8IhW1KxoZpZohJAQYOlT2euTmyoyxo0K6ZkVFsrRm8mQ5PnRI+nhJiWW5z5Ur8v1n3edI\nP64sA65XTwLFDz+UpXgrV1b9fS9fts+UZk7asW5d5b9fp44sITPPwjIAUWEA4sseflhy3VubMAE4\nedK53z95Ul0UzhYDkOohORlYsECWrZw9a7l580QAEh8vo8m266T377d/P2ft3y/T5oAsb/jsMykG\nx5vF6mPWLJnh+Okn4KuvgJ49Hb8uNlaysJWUSK79kyeBVq0cvzYwUG4GrW/+li6VopfuKK/Y3cKF\nciNJZFarVuU1IwID7Wd416wBRo+WfXDWmIa3ZgkNlYFd23S9ubnOzYbNmiV96MoVmcUZMMAz7fRR\nDEB8mcEAvPOORPxmhYXAiBHO/f4zz8i6yvbt5Xd+/VX9fFyc7EEA5B9iZKRlGc2WLTK9+dhjsj7S\nl1PDVndBQTKid/316g1wnpreTU0Ftm+XJQeAjN58+aWMXrvq229lj4p1qmdApsejo91vK2kjONi1\nzZUVjSibLVwoI4glJbIsoqio/GDFFdb9sH592VMyeLBkunrlFfevT56Xmyv7y/r1k+V03qwHZDQC\nixdbBknM0tNlsMQaA5CaJz5eMur95S+Wcy1bygyLswwGuU/TMtW0H2AWLF8XGytrop9+Wo5TUpyr\n9msySUE4k0k2Hu/bZ58nPzAQ2LxZApFGjdQ3KEePqtddP/KILK0h/XTrJqkss7PlocUeELPrrpP+\nce+90re6dq3addautd+017+/BM5UcxgMlsEMd7VvL6OS11/veKkYVX9BQerlwsHB8l1k9NKYaGio\nDLLcdJOlMnvjxvYDJwxAaoYtW2SJVZs2MoPWooUEozNmyPLhr79mFXUNMADxB089Jf8gbrtNNl85\nMzp58KBlox0gN7KORrhtR4XMWITQ+1591bPXDw+XDe/l3RRMnixLHHr0kBFMRxsDX3tNll2Ziy+N\nHi0ViZ3po+R9JSUVb/jUwtmz9gMcgGz+PH0amDhRncmqTh3ZCEq+q149uYHLy5PjoiJJMW6bKtVV\n7tRIio6WZYWpqRLcfv21bFw+ccKy96NxY/faR1V3+bIEhOZlcbfd5vo1tm2Te59z5+QxbJjjaugr\nV6q/X59/Xo4nTZIBOQ58aEKzb5YLFy7gxRdfxNq1a/Hbb78hIiICffv2xbRp09CgQQOt3oYcMRjk\ng9OVD94fflAf33KLa6NPDEBqhvL6REmJ7EW5dEkCkXr15AuhRw/giScsG9kDAoCPPgLuuENqyPz9\n7/q1ndw3cKBkrxo3Tm7MtKynkZ8PzJwJvPmmjC7272957vRp4Nln5TXLlwPvvy8bP8l/NG1qCUAA\nqVDuKAB56y1ZAtOvn6TTLe/mr6RE6iOlpMjr7rzT9WWpiYlSOyYhQT7DDh6UoObCBbn5tU3QQfrY\nsUOWWpp16CBFUR355hvpSxER8khKstyf/POflvpFgAxkOApADh5UH1vvI2LwoRnNApCzZ8/i7Nmz\neP3119G6dWtkZGRg+PDhGDRoEL5jikTPc/XGwDYASU117fcZgHiHogD/+5/MTNx4o/OpBLW2e7cE\nH2aXLsnm5TVrZEbOWu3aspTP0yPp5J7iYrnxP3FCHrGxMnOlKPJ3e/PNMjKoxYDSmjWSV99cDOy5\n5+SGsVYteb9hwywJMg4ckMD29Gn1fjfybU2aWNJ9A7L0yfom0+zTTyXj4+efy4DIihWON/Nu2yb7\nGH/9VX4nMlL6l6vLumyL6xoM0uc5kOo9MTHq44qKES5eLH3EbNkyS+Y+Z4sRHjigPm7TpvI27t0r\n7TTvbczPl8/RyEgJWvj9Z0ezBZcJCQlYvnw5+vbti+bNm6Nr1654/fXXsXbtWhS4UriFtJWZKSOI\n5mKCZhER6ulkBiDV37//Lfs8EhIkacCiRd5ry9q1js937So3kbb44Vv9DR4sa5179JAgcsAAdQG2\noiLZ9K2F6GhZcmN27Bgwb578/PHHkuvf2vTpDD78TdOm6uPffrN/TWamBB9mJpN9gGBmW/28Z0/v\n7SkhbUVHq/8us7PLryvlqAq6mW0g4ygAKSxU1/kwGmWwzxGTSZbqde8OdOwIzJljeW7HDpl9adRI\n9jz16+f4GjWYR/91Xrx4EbVq1UJtV3I4k3bOn5dlDH/5i0ThDz8sI5lXr8pU5OnTkkbzk08qX95Q\nWipfEOa6I6++Ktf6179kGUVSksf/d2q8qCh14Ldhg/cq9A4ZIlmOBg5Uf8D36OGd9pD74uPVx7ap\nSceN024JVmKiZHaz9sorkmN/9Gj1+S5dpNgq+ZdHH5Xvnh9+kO+isWPtX2NbwyE5WT2Kbd4wDtgH\nIM5WP6fqLyjIPmvi2bOOX1tRAOLMDMihQ+rjFi3Kz1710UcyULNxoxy/844l6YrtIC0zYNnx2LBk\nXl4eJk+ejKFDh8JYzijE7t27PfX2NZuioMGaNYh74w0EmdfYFhbKtPSnnyK3d2+csE5X2bKl/ZpH\nM5MJrR9+GCGnTsH4Z2XjvZs2wRQaKqMJ5hGF3Fx5VAP+2q8MAQFoX6sWjOaRn4wM/DZxIgratEFR\ndDRKw8L0bVC7dvIYOxahR4+i3s6dyGvWDFf99M/fX/uVWYTBgPhynrsaHY2fmzWTpXcaCbzvPrT5\n6CMEmr+wL13ChZEjYWjVCtf+uUTUVKsWDo4Zg6t792r2vtWRv/cthwICLKm+MzPlYaPFhx/Ces7t\nTIcOOLd7NwxXriBu7lxEfPUV/rd4MUrq10fSvn1lr1MMBuyPikJJTfxzteJP/erGBg1QxyroOLx2\nLQrat7d7XdK5c7DOt7f/7FkU/zmYUi8/H9ZVhPKPHMERmz+joJwc1B83DqG//oqQ48dxNTYWJ8v5\nczQ2b47EsDAEmhP65OXht5dfxvkHH0Tk7t1oYvXabACnfPzvo6X536tGKg1A0tLSMGPGjApfs2HD\nBnS1StNZUFCAfv36IS4uDrOcSQlL2iotRb1t2yzBh40868ralTEaYbxypSz4AIBaZ87gsm2RQvI4\nJTgYBW3bop7Vh1jTPzN1ZD7yCDLGjPFOw4xGXL7hBlyuSp0QqjaKKsjwkzVokObL6Erq18fZp55C\nkz8Lel3o3h2nR49GUePGaLB6NZq8+SYyBw/GVdulOlQzlJSgjlVQAQB5Xbsi9NgxNJ80CaHHjwMA\nmk+ahDPDhsEUGAjjn8VNC1u3RgnTpPqVouhoFGVloSgyEsWRkTCFhNi/yGSyBAN/KrEamLsSG4vc\n3r1RHBGB4oYNccXBZ0txw4bIdrKkgCkkBNn334+Y998vOxf16ac4f//9CLpwQX1drZav+hGDolS8\nhiM3Nxe5lYxsx8XFIfTP6aWCggLcddddMBgMWL16td3yq4tWnSNM7xHbmkRRgF27ZAPWsmWWfOZ1\n6sjaa1eWxd15p2waNVuxQupDVDPm0Z5kbxa18rSXXwZeesn+/KxZUl2cNFcj+hUg+zCsR7iuuQaY\nOlU2dW7dCtStq/17FhdLdrQRI+zTamZny8ZfP94/VGP6VlX98YdkpfrmG6lVtWOHZEx76CH160aM\nkKXA69bJUqw2bezrWtUgftmvnEmxXFQkn1k5OfIoLJRiuJ507pwsX7VesvrFF7J88F//spxLT5fi\nzz5M6/v3Sj/Zw8PDER4e7tTF8vPz0adPn3KDD9KRwSCb9VJSpFDh1q3A0qXyZe7q30uLFupj24rp\npJ9u3eTv8M+RvjJaVUGnmqtJE9ln1KQJ0KwZ0Ly5rMsfO1bb9LvWgoIkuYIj7NNUu7Zs3rXewDtw\noAQZH3xgOTd/PtC7t6zHd5Qhi3yfM59BwcGSsEJPjRrJ/trFi+Xzc+RI2be2c6fUVsvOljTO/Dyz\no9nQUn5+Pnr16oX8/Hx8+eWXyM/PR/6faRTDw8MRpFUVXHKd0Sj/ILp0qdrv2y63OnbM/TZR1aSm\nSu78e+8Fvv/ecp4fbuSu4GCH6/CJdKEoklXImSKl8+ZJtWrrwbApU4C77/ZcsExUnvHjZXBw0CBL\nFsgZM+QByEwv2dEsANmzZw927NgBg8GA66+3bPMxGAxYv369ao8I+RhzAFKvnvx88iRw662Serdh\nQyli+Pjj3mxhzREYKI/sbPV5BiBE5GveeEOWyJw6JY8VK4C77qr89+rWlXTNqamSofHBByUDEYMP\n8obWreVRHg7AO6RZANK9e3eYTCatLkfVSY8eklIuPFw+4JcskTSsZpcuMQDRW9++sl4/O1seUVHe\nbhERkWsOHJA9HmbWaXUrc9NNsvetQQP5PmLwQe764gvZM5uQII+UFCnISh7hv7v7SDu1a6v3jdjm\n2WYRQv1Nm+btFhARucc2C5E5AFmzRgKMyja6OqodQv7r99+lCrr58cQTrs8u7N0LbN4sm8fPnQPu\nuceSVGfjRglAzKZOBV58Ubv2kwoDEHIdq6ATEZG7mjRRH//2m+xDuvNOWWrarRvQvz8wahRnOEiW\nOWVlWY5791b3oZUrZVYtIkIeHToAcXHqa6xaBUyebDmOjrYEIAcOqF+bkFD1tppMwHffyd5bT2QQ\n9AMerYROfooBCBERucvRDIi5+nlJiSzP+vBDBh8kbJdDZWSoj5cvB154AXjySZnZcJSC17YaunVF\ndS0CkMuXJfNoQIDsZ5ozRxIskB0GIOQ6BiBEROQu2xmQ8+el5oc16xS8VLNVFoDY3ptERNhfwzYA\nOXdO/puTo55dCQ62zwDqjDffBP7xD8vx5MkyU0N2uASLnFdcLBmwevQAkpJkOvT8eaBjR2+3jIiI\nfE3TprLxt0kT+bl2bfubRgYgZFZZAGK7P9WVAOTgQfX5G2+sWhHUJ58E0tLU56wDGyrDAIScs3q1\nfBGUlsrxnXdKVW4iIqKqqFVLlsqYrVol1c/NGjcG2rXTv11UPXkyAOnQAVi7VgKRgwel71VFVJTM\neFgv/7rzzqpdy88xACHnNG5sCT4AFiMkIiJtRUUBgwfLPpDcXEk3zv0fZNasmSyLio2VR3Ky+nln\nApCGDYGnnpJApFEjICZG9mjUrQvccYc83PV//ydZ3LKzZSnX4MHuX9MPMQAh57RooT4+eVKWZLHA\nDhERaaFjR+CDD2Swa/t2oH59b7eIqpOBA+XhiKLI3ovz5yUQyclx3H8CAoB33/VsO+PjgV27JN1v\nly72yRYIAAMQctY118hogXm6srRUUiZWZZMWERFReQICpMo5kbMMBmDCBG+3wqJJE+CRR7zdimqN\nWbDIebbBBpdhERGRVoqLgQsXvN0KItIBAxBynm0AMnq0rHUkIiKqit27ZZlKXBwQEgI8/LC3W0RE\nOmAAQs57913g448tx7/8Aqxf7732EBGRbzMagR9+kIxGJpMUIyTSU3o60KYN8NBDwLRpwJ493m5R\njcA9IOS8wEAWISQiIu3YFiM8dEg2FDP7FTmSnQ0cPy4Ba0YGcPvtQGKia9c4cgRYsUL2tJ49KxXU\nAUm/u2yZpIdmfTOPYwBCrnGm0igREZEzwsPtz82cCUycqH9bqPp78UVgwQLL8Zw5EoB8+y2wbZvc\nk0RESABx/fWOr3H4cMX9KyFB2zaTQwxAyDWcASEiIq0YDFIEbu9ey7nevb3XHqreyitG+N13wFtv\nWc6//jowbpzja8TEVPwebdpUvX3kNO4BIdcwACEiIi298IIs8QWAIUMkICFypLwAxJXVGbbV0K3V\nrSsJEcjjOANCrpk7Fxg/Xv6xnz8v1T6JiIiq6oEHgJtvBvLyOPpMFSsvAHGmCrpZVJTMvCmK/XMJ\nCdx/pBMGIOSa2Fj7DwAiIiJ3xMVx5Jkq52wAUtHqjKAgeT4723Ju8WIJgB1VTyePYABCRERERNVf\nbKxsOm/cWH5u1kzOuzIDAsj+EEWR5ViNGgGpqUBoqGfaTA4xACEiIiKi6q9OHWD/fvvzzz8PnDkj\ngUhODhAZWfF1xo/3TPvIaQxAiIiIiMh3PfOMt1tALmIWLCIiIiIi0g0DECIiIiKqWQoLgeJib7ei\nxmIAQkREREQ1y7x5wDXXAG3bAg89BKxe7e0W1SjcA0JEREREviEvD/jxR0nBm5Ehlc2HDHHtGllZ\nwIQJ8vOBA/K49Vbt20rlYgBCRERERL5h+3agTx/1uZ9/ltS7ERFAcjLQrl3F17h82f5cQoJ2baRK\nMQAhIiIiIt/gqBjy7NmWnydPrjwAiY62P8cARFfcA0JEREREvsFRAGKtsiKEABASol5ydfPNFVdP\nJ81xBoSIiIiIfENYmGweLyx0/LwzAQgAfPopMGUKYDLJrAnpigEIEREREfkGg0FmQY4ccfy8swFI\n48bAwoXatYtcwgCEiIiIiHxHz55AmzYSiMyZo37O2QCEvIoBCBERERH5jnnzLD/fdBNw8iSQkyOP\nxo291ixyHgMQIiIiIvJNgwZ5uwVUBcyCRUREREREumEAQkREREREumEAQkREREREuuEeECIiIiLy\nHaWlwLffAhkZ8sjOBhYs8HaryAUMQIiIiIjIdxiNwP33A1evWs7FxQG33QakpnqvXeQ0LsEiIiIi\nIt9hLkZobfJkYNky77SHXMYAhIiIiIh8i20AAgANG+rfDqoSBiBEREREDgPSwgAADBtJREFU5Fsc\nBSCsgu4zNA9AFEVBnz59YDQasXz5cq0vT0REREQ1HQMQn6Z5ADJ79mwEBAQAAAwGg9aXJyIiIqKa\n7uab7c8xAPEZmmbB2rVrF+bOnYs9e/YgKipKy0sTEREREYl77gH+8x/g11+BnBx5NG/u7VaRkzQL\nQPLz8/Hwww9j4cKFaMhNQERERETkSXff7e0WUBUZFEVRtLjQI488goiICMyZMwcAYDQa8e9//xv3\n3Xef6nUXL14s+/no0aNavDUREREREXlIy5Yty34OCwtz+3oVzoCkpaVhxowZFV5g/fr1OHXqFH76\n6Sfs3r0bgGxEt/4vERERERERUMkMSG5uLnJzcyu8QFxcHIYPH44lS5bAaLTsaS8tLYXRaETnzp2x\nadOmsvPWMyBaRFBEZuYAODk52cstIX/CfkWewr5FnsB+RZ6g9f17hTMg4eHhCA8Pr/Qi06dPx/jx\n48uOFUVB27ZtMXv2bAwYMMDtRhIRERERkX/QZBN6TEwMYmJi7M7HxcUhPj5ei7cgIiIiIiI/wEro\nRERERESkG03rgFgzmUyeujQREREREfkozoAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQERER\nEZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFu\nGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQ\nEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQERER\nEZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFu\nGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQ\nEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuGIAQEREREZFuNA1Adu7ciZ49e6Ju3bqo\nV68eUlNTkZubq+VbEBERERGRDwvU6kI7duxA79698Y9//ANz5sxBcHAwDhw4gKCgIK3egoiIiIiI\nfJxmAcizzz6LkSNHYsKECWXnrrvuOq0uT0REREREfkCTJVjZ2dnYvn07oqOj0aVLF0RFRaFr165Y\nt26dFpcnIiIiIiI/YVAURXH3Itu3b0fnzp3RoEEDvPHGG2jfvj0+++wzzJo1C3v27EFiYmLZay9e\nvOju2xERERERkReEhYW5fY0KZ0DS0tJgNBorfGzatAkmkwkAMGzYMDz++ONISkrC9OnT0alTJ7zz\nzjtuN5KIiIiIiPxDhXtAnn32WQwePLjCC8TFxSEzMxMA0Lp1a9VzrVq1wqlTp9xsIhERERER+YsK\nA5Dw8HCEh4dXepH4+HjExMTg8OHDqvO//PILkpKSVOe0mLYhIiIiIiLfpEkWLIPBgPHjx+Oll15C\nYmIi2rVrh88++ww7d+5Eenq6Fm9BRERERER+QLM0vKNHj8bVq1fx3HPPITc3F23atMHq1avRtm1b\nrd6CiIiIiIh8nCZZsIiIiIiIiJyhSR0QV6Snp6NZs2YIDQ1FcnIytmzZoncTyIfNnDkTnTp1QlhY\nGCIjI9G/f38cPHjQ7nVTpkxB48aNUbt2bdx22204dOiQF1pLvmrmzJkwGo0YNWqU6jz7FVXFuXPn\nMGTIEERGRiI0NBQJCQnYtGmT6jXsW+SKkpISTJw4Ec2bN0doaCiaN2+OyZMno7S0VPU69iuqyKZN\nm9C/f3/ExsbCaDTigw8+sHtNZX3o6tWrGDVqFBo2bIg6depgwIABOHPmTKXvrWsAsmzZMowZMwZp\naWnYt28fOnfujD59+uD06dN6NoN82MaNGzFy5Ehs27YN69atQ2BgIHr06IELFy6Uvea1117Dm2++\nibfffhu7du1CZGQkevbsiYKCAi+2nHzF9u3bsXDhQiQmJsJgMJSdZ7+iqsjLy0NqaioMBgNWrVqF\nw4cP4+2330ZkZGTZa9i3yFUzZszAggULMG/ePBw5cgRz5sxBeno6Zs6cWfYa9iuqTGFhIRITEzFn\nzhyEhoaqvvMA5/rQmDFjsGLFCixduhSbN2/GpUuX0Ldv37ISHeVSdJSSkqIMHTpUda5ly5bKhAkT\n9GwG+ZGCggIlICBA+c9//qMoiqKYTCYlOjpamTFjRtlrLl++rNStW1dZsGCBt5pJPiIvL09p0aKF\nsmHDBqV79+7KqFGjFEVhv6KqmzBhgtKlS5dyn2ffoqro27ev8vjjj6vODR48WOnbt6+iKOxX5Lo6\ndeooH3zwQdmxM30oLy9PCQ4OVj755JOy15w+fVoxGo3Kd999V+H76TYDUlRUhL1796JXr16q8716\n9cLWrVv1agb5mUuXLsFkMqF+/foAgBMnTiArK0vVz0JCQtC1a1f2M6rU0KFD8cADD6Bbt25QrLbH\nsV9RVX355ZdISUnBwIEDERUVhfbt22P+/Pllz7NvUVX06dMH69atw5EjRwAAhw4dwvr163H33XcD\nYL8i9znTh/bs2YPi4mLVa2JjY9GqVatK+5lmWbAqk5OTg9LSUkRFRanOR0ZGlhUyJHLV6NGj0b59\ne9xyyy0AUNaXHPWzs2fP6t4+8h0LFy7E8ePH8cknnwCAaiqa/Yqq6vjx40hPT8fYsWMxceJE/Pjj\nj2V7i0aMGMG+RVUyfPhwZGRkoFWrVggMDERJSQnS0tIwbNgwAPzMIvc504cyMzMREBBgVzMwKioK\nWVlZFV5ftwCESGtjx47F1q1bsWXLFrt1i4448xqqmY4cOYJJkyZhy5YtCAgIAAAoiqKaBSkP+xVV\nxGQyISUlBdOnTwcAJCUl4ejRo5g/fz5GjBhR4e+yb1F55s6di0WLFmHp0qVISEjAjz/+iNGjRyM+\nPh5//etfK/xd9itylxZ9SLclWBEREQgICLCLiLKystCoUSO9mkF+4tlnn8WyZcuwbt06xMfHl52P\njo4GAIf9zPwcka1t27YhJycHCQkJCAoKQlBQEDZt2oT09HQEBwcjIiICAPsVuS4mJgatW7dWnbvx\nxhtx6tQpAPzMoqqZPn06Jk6ciAcffBAJCQl49NFHMXbs2LJN6OxX5C5n+lB0dDRKS0uRm5urek1m\nZmal/Uy3ACQ4OBgdO3bEmjVrVOe///57dO7cWa9mkB8YPXp0WfBx/fXXq55r1qwZoqOjVf3sypUr\n2LJlC/sZlevee+/FgQMHsH//fuzfvx/79u1DcnIyBg0ahH379qFly5bsV1QlqampOHz4sOrcL7/8\nUjZwws8sqgpFUWA0qm/hjEZj2awt+xW5y5k+1LFjRwQFBalek5GRgcOHD1fazwKmTJkyxSMtd6Be\nvXp46aWXEBMTg9DQUEybNg1btmzBokWLEBYWplczyIeNGDECS5Ysweeff47Y2FgUFBSgoKAABoMB\nwcHBMBgMKC0txauvvoobbrgBpaWlGDt2LLKysvDuu+8iODjY2/8LVA2FhISgYcOGZY/IyEh8/PHH\naNq0KYYMGcJ+RVXWtGlTTJ06FQEBAWjUqBH++9//Ii0tDRMmTECnTp3Yt6hKjh49isWLF+PGG29E\nUFAQ1q9fj0mTJuGhhx5Cr1692K/IKYWFhTh06BAyMzPx3nvvoW3btggLC0NxcTHCwsIq7UMhISE4\nd+4c5s+fj6SkJFy8eBHDhg3Dtddei9dee63ipVraJfByTnp6uhIfH6/UqlVLSU5OVjZv3qx3E8iH\nGQwGxWg0KgaDQfWYOnWq6nVTpkxRGjVqpISEhCjdu3dXDh486KUWk6+yTsNrxn5FVbFy5UolKSlJ\nCQkJUW644QZl3rx5dq9h3yJXFBQUKM8995wSHx+vhIaGKs2bN1cmTZqkXL16VfU69iuqyPr168vu\no6zvrZ544omy11TWh65evaqMGjVKCQ8PV2rXrq30799fycjIqPS9DYrixC5LIiIiIiIiDehaCZ2I\niIiIiGo2BiBERERERKQbBiBERERERKQbBiBERERERKQbBiBERERERKQbBiBERERERKQbBiBERERE\nRKQbBiBERERERKSb/wcdETsoVFQ9TwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f85f2702a90>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Discussion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
      "\n",
      "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This information in this chapter takes some time to assimilate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n",
      "\n",
      "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}