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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": [
      "The g-h Filter"
     ]
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      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import book_format\n",
      "book_format.load_style()"
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     "source": [
      "Building Intuition via Thought Experiments"
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     "metadata": {},
     "source": [
      "Imagine that we live in a world without scales - the devices you stand on to weigh yourself. One day at work a coworker comes running up to you and announces her invention of a 'scale' to you. After she explains, you eagerly stand on it and announce the results: \"172 lbs\". You are ecstatic - for the first time in your life you know what you weigh. More importantly, dollar signs dance in your eyes as you imagine selling this device to weight loss clinics across the world! This is fantastic!\n",
      "\n",
      "Another coworker hears the commotion and comes over to find out what has you so excited. You explain the invention and once again step onto the scale, and proudly proclaim the result: \"161 lbs.\" And then you hesitate, confused.\n",
      "\n",
      "\"It read 172 lbs just a few seconds ago\" you complain to your coworker. \n",
      "\n",
      "\"I never said it was accurate,\" she replies.\n",
      "\n",
      "Sensors are inaccurate. This is the motivation behind a huge body of work in filtering, and solving this problem is the topic of this book. I could just provide the solutions that have been developed over the last half century, but these solutions developed by asking very basic, fundamental questions into the nature of what we know and how we know it. Before we attempt the math, let's follow that journey of discovery, and see if it does not inform our intuition about filtering. "
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     "source": [
      "#### Try Another Scale\n",
      "\n",
      "Is there any way we can improve upon this result? The obvious, first thing to try is get a better sensor. Unfortunately, your co-worker informs you that she has built 10 scales, and they all operate with about the same accuracy. You have her bring out another scale, and you weigh yourself on one, and then on the other. The first scale (A) reads \"160 lbs\", and the second (B) reads \"170 lbs\". What can we conclude about your weight?\n",
      "\n",
      "Well, what are our choices?\n",
      "\n",
      "* We could choose to only believe A, and assign 160lbs to our weight estimate. \n",
      "* we could choose to only believe B, and assign 170lbs to our weight.\n",
      "* We could choose a number less than either A or B\n",
      "* We could choose a number greater than either A or B\n",
      "* We could choose a number between A and B\n",
      "\n",
      "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A instead of B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they both measured. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not probably the answer is somewhere between A and B. \n",
      "\n",
      "In mathematics this concept is formalized as *expected value*, and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we made one million separate readings. Some of the times both scales will read too low, sometimes both will read too high, and the rest of the time they will straddle the actual weight. If they straddle the actual weight then certainly we should choose a number between A and B. If they don't straddle then we don't know if they are both too high or low, but by choosing a number between A and B we at least mitigate the effect of the worst measurement. For example, suppose our actual weight is 180 lbs. 160 lbs is a big error. But if we choose a weight between 160 lbs and 170 lbs our estimate will be better than 160 lbs. The same argument holds if both scales returned a value greater than the actual weight.\n",
      "\n",
      "We will deal with this more formally later, but for now I hope it is clear that our best estimate is just the average of A and B. $\\frac{160+170}{2} = 165$.\n",
      "\n",
      "We can look at this graphically. I have plotted the measurements of A and B with an assumed error of $\\pm$ 8 lbs. The overlap falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 pounds."
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      "plt.errorbar([160], [1], xerr=8, fmt='o',label='A', capthick=2, capsize=10)\n",
      "plt.errorbar([170], [1.05], xerr=8, fmt='o', label='B', capthick=2, capsize=10)\n",
      "plt.ylim(0, 2)\n",
      "plt.xlim(145, 185)\n",
      "plt.legend()\n",
      "plt.gca().axes.yaxis.set_ticks([])\n",
      "plt.show()"
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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c17c66a0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So 165 lbs looks like a reasonable estimate, but there is more information here that we might be able to take advantage of. The only weights that are possible lie in the intersection between the error bars of A and B. For example, a weight of 161 lbs is impossible because scale B could not give a reading of 170 lbs with a maximum error of 8 pounds. Likewise a weight of 171 lbs is impossible because scale A could not give a reading of 160 lbs with a maximum error of 8 lbs. In this example the only possible weights lie in the range of 162 to 168 lbs.\n",
      "\n",
      "That doesn't yet allow us to find a better weight estimate, but let's play 'what if' some more. What if we are now told that A is three times more accurate than B? Consider the 5 options we listed above. It still makes no sense to choose a number outside the range of A and B, so we will not consider those. It perhaps seems more compelling to choose A as our estimate - after all, we know it is more accurate, why not just use it instead of B? Can B possibly improve our knowledge over A alone?\n",
      "\n",
      "The answer, perhaps counter intuitively, is yes, it can. First, let's look at the same measurements of A=160 and B=170, but with the error of A $\\pm$ 3 lbs and the error of B is 3 times as much, $\\pm$ 9 lbs."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.errorbar([160], [1], xerr=3, fmt='o',label='A', capthick=2, capsize=10)\n",
      "plt.errorbar([170], [1.05], xerr=3*3, fmt='o', label='B', capthick=2, capsize=10)\n",
      "plt.ylim(0, 2)\n",
      "plt.xlim(145, 185)\n",
      "plt.legend()\n",
      "plt.gca().axes.yaxis.set_ticks([])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c14799b0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The overlap of the error bars of A and B are the only possible true weight. This overlap is smaller than the error in A alone. More importantly, in this case we can see that the overlap doesn't include 160 lbs or 165 lbs. If we only used the measurement from A because it is more accurate than B we would give an estimate of 160 lbs. If we just averaged A and B together we would get 165 lbs. Neither of those weights are possible given our knowledge of the accuracy of the scales. By including the measurement of B we would give an estimate somewhere between 161 lbs and 163 lbs, the limits of the intersections of the two error bars.\n",
      "\n",
      "Let's take this to the extreme limits.  Assume we know scale A is accurate to 1 lb. In other words, if we truly weigh 170 lbs, it could report 169, 170, or 171 lbs. We also know that scale B is accurate to 9 lbs. We do a weighing on each scale, and get A=160, and B=170. What should we estimate our weight to be? Let's look at that graphically."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.errorbar([160], [1], xerr=1, fmt='o',label='A', capthick=2, capsize=10)\n",
      "plt.errorbar([170], [1.05], xerr=9, fmt='o', label='B', capthick=2, capsize=10)\n",
      "plt.ylim(0,2)\n",
      "plt.legend()\n",
      "plt.gca().axes.yaxis.set_ticks([])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c17c6588>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see that the only possible weight is 161 lbs. This is an important result. With two relatively inaccurate sensors we are able to deduce an extremely accurate result.\n",
      "\n",
      "> So two sensors, even if one is less accurate than the other, is better than one.\n",
      "\n",
      "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight will play a large role later, so don't forget it.\n",
      "\n",
      "So, what if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's just write a simulation for now."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10000\n",
      "import random\n",
      "weight_sum = 0\n",
      "for i in range(N):\n",
      "    # choose a random number between 160 and 170, assuming true\n",
      "    # weight of 165\n",
      "    measurement = random.uniform(160, 170) \n",
      "    weight_sum += measurement\n",
      "    \n",
      "average = weight_sum / N\n",
      "print('Average of measurements is {:.4f}'.format(average))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Average of measurements is 165.0186\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The exact number printed depends on your random number generator, but it should be very close to 165.\n",
      "\n",
      "This code makes one assumption that probably isn't true - that the scale is just as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `random.gauss()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy meaurements very similar to how a real scale would."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10000\n",
      "weight_sum = 0\n",
      "for i in range(N):\n",
      "    # choose a random number centered around 165 lbs, with a 5 lb error.\n",
      "    measurement = random.gauss(165, 5.) \n",
      "    weight_sum += measurement\n",
      "    \n",
      "average = weight_sum / N\n",
      "print('Average of measurements is {:.4f}'.format(average))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Average of measurements is 164.9325\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The answer again is very close to 165. \n",
      "\n",
      "Okay, great, we have an answer to our sensor problem! But it is not a very practical answer. No one has the patience to weigh themselves ten thousand, or even a dozen times. \n",
      "\n",
      "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n",
      "\n",
      "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the weighings along with the error bars, and then some possible weight gain/lossses that could be explained by those measurements in dotted green lines."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.errorbar([1,2,3], [170, 161, 169], \n",
      "             xerr=0, yerr=10, fmt='o', capthick=2, capsize=10)\n",
      "\n",
      "plt.plot([1,3], [180, 160], c='g', ls='--')\n",
      "plt.plot([1,3], [170, 170], c='g', ls='--')\n",
      "plt.plot([1,3], [160, 175], c='g', ls='--')\n",
      "plt.plot([1,2,3], [180, 152, 179], c='g', ls='--')\n",
      "plt.xlim(0,4); plt.ylim(150, 185)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('lbs')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SygUAULFERczxmQNTE1MM8lCd6FwqkaJDlQ5oX6W9GFGJ6D1Y7BCRVjX/ojn8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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c140d208>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a human's weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n",
      " \n",
      "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based soley on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, just one that is reasonable and could be explained by the measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.errorbar(range(1,11), [169, 170, 169,171, 170, 171, 169, 170, 169, 170], \n",
      "             xerr=0, yerr=6, fmt='o', capthick=2, capsize=10)\n",
      "plt.plot([1,10], [169, 170.5], c='g', ls='--')\n",
      "plt.xlim(0,11); plt.ylim(150, 185)\n",
      "\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('lbs')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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63f+b+99U9ifZhtOTRrQf4XZxtD9s/4Oe3PCk4U3kEz2e0HOpxguSV+1Zpenv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\nI1VWVqazZ8+6zMbk5+erV69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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c13ff080>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another what if: what if the readings were 158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0? Let's look at a chart of that and then answer some questions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,\n",
      "           169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n",
      "plt.errorbar(range(1,13), weights,\n",
      "             xerr=0, yerr=6, fmt='o', capthick=2, capsize=10)\n",
      "\n",
      "plt.xlim(0,13); plt.ylim(145, 185)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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o3T0A9+kfE6tmbUP09ZcH9M3fcvX1lwc05ekXmSUFAFSbcpeTffzxxw7vW7Zs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\nKkWIAQAAKkWIAQAAKkWIAQAAKuUbU3JPsd6o/FEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c13a4a58>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. We can't be sure, but that surely looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n",
      "\n",
      "So let's look at two hypotheses. First, let's assume our weight did not change. To get that number we agreed that we should just average all the measurements. Let's look at that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "ave = np.sum(weights) / len(weights)\n",
      "plt.errorbar(range(1,13), weights, label='weights',\n",
      "             yerr=6, fmt='o', capthick=2, capsize=10)\n",
      "plt.plot([1,12], [ave,ave], c='r', label='hypothesis')\n",
      "plt.xlim(0,13); plt.ylim(145, 185)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IBgDKj0oMAAAAAIdCJQYAABdTVuXkxkoNlRYA1Q2VGAAAAAAOhSQGAAAAgENh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1451358>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That doesn't look very convincing. In fact, we can see that there is no horizontal line that we could draw that is inside all of the error bars.\n",
      "\n",
      "Now, let's assume we we gained weight. How much? I don't know, but numpy does! We just want to draw a line through the measurements that looks 'about' right. numpy has functions that will do this according to a rule called \"least squares fit\". Let's not worry about the details of that computation, or why we are writing our own filter if numpy provides one, and just plot the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = range(1, len(weights)+1)\n",
      "line = np.poly1d(np.polyfit(xs, weights, 1))\n",
      "plt.errorbar(range(1,13), weights, label='weights',\n",
      "             yerr=5, fmt='o', capthick=2, capsize=10)\n",
      "plt.plot (xs, line(xs), c='r', label='hypothesis')\n",
      "plt.xlim(0,13); plt.ylim(145, 185)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RERERGRSGGCIiIiIiMigMMUREREREZFAYYoiIiIiIyKCY6roAIiIiIiKqX/b1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\nNKQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c129ae48>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This looks much better, at least to my eyes. Notice now the hypothesis lies very close to each measurement, whereas in the previous plot the hypothesis was often quite far from the measurement. It seems far more likely to be true that I gained weight than I didn't gain any weight. Did I actually gain 13 lbs? Who can say? That seems impossible to answer.\n",
      "\n",
      "\"But is it impossible?\" pipes up a coworker.\n",
      "\n",
      "Let's try something crazy. Let's just assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, just assume I know it is approximately correct. Maybe I am eating a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. Let's just see if we can make use of such information if it was available without worrying about the source of that information just yet.\n",
      "\n",
      "The first measurement was 158. We have no way of knowing any different, so let's just accept that as our estimate. If our weight today is 158, what will it be tomorrow? Well, we think we are gaining weight at 1 lb/day, so our prediction is 159, like so:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a lot of the plotting code is not particularly useful to read, \n",
      "# so for each chapter I have placed the uninteresting code in a \n",
      "# file named xxx_internal. I import this  file and call whatever \n",
      "# function I need.\n",
      "\n",
      "import gh_internal\n",
      "gh_internal.plot_estimate_chart_1()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kiYiUALe0KEGpUqVodINxxuXKleOxxx4rsKZERESkkB06BJMmwfvvw6VL1rWq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\nZGQoLi5OmZmZ1w1JAAAAAFCaKhuQrhYSEqLQ0FA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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c14249b0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Okay, but what good is this? Sure, we could just assume the 1 lb/day is accurate, and just predict our weight for 10 days, but then why use a scale at all if we don't incorporate its readings? So let's look at the next measurement. We step on the scale again and it displays 164.2 lbs."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gh_internal.plot_estimate_chart_2()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KVBl0JCk8PFzPPPOMZs+erc8++0yff/65du3apcOHD0uSgoOD1alTJ11zzTXq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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11a4dd8>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the measurement is in blue, the previous estimate (output of the filter) is black, and the estimate is red. So we have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right?. If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n",
      "\n",
      "> The key insight to this entire book is in the next paragraph. Read it carefully!\n",
      "\n",
      "So what do we do? If we only take data from the measurement than the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italized the key point)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should like between 159 (the prediction) and 164.2 (the measurement).\n",
      "\n",
      "Should it be half way? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when A was much more accurate than B - we scaled the answer to be closer to A than B. Let's look at that in a chart."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gh_internal.plot_estimate_chart_3()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7fWE1OtofN+rUqZO8vb21ffv2XMuvXbumzz//XFarVf/73/908OBB24iOJM2Z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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c12b6f98>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try a randomly chosen number to scale our estimate: $\\frac{4}{10}$. Our estimate will be four tenths the measurement and the rest will be from the prediction. In other words, we are expressing a belief here, a belief that the prediction is somewhat more likely to be correct than the measurement. We compute that as\n",
      "\n",
      "$$ new estimate = prediction + \\frac{4}{10}(measurement - prediction)\n",
      "$$\n",
      "\n",
      "The difference between the measurement and prediction is called the *residual*, which is depicted by the black vertical line in the plot above. This will become an important value to use later on, as it is an exact computation of the difference between measurements and the filter's output. Smaller residuals imply better performance.\n",
      "\n",
      "Let's just code that up and see the result when we test it against the series of weights from above.. We have to take into account one other factor. Weight gain has units of lbs/time, so to be general we will need to add a time step $t$, which we will set to 1 (day)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import book_plots as bp\n",
      "\n",
      "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, \n",
      "           169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n",
      "\n",
      "time_step = 1 # day\n",
      "scale_factor = 4/10\n",
      "\n",
      "def predict_using_gain_guess(weight, gain_rate): \n",
      "    # store the filtered results\n",
      "    estimates = []\n",
      "\n",
      "    # most filter literature uses 'z' for measurements\n",
      "    for z in weights: \n",
      "        # predict new position\n",
      "        prediction = weight + gain_rate * time_step\n",
      "\n",
      "        # update filter \n",
      "        weight = prediction + scale_factor * (z - prediction)\n",
      "\n",
      "        # save for plotting\n",
      "        estimates.append(weight)\n",
      "\n",
      "\n",
      "    # plot results\n",
      "    n = len(weights)\n",
      "    plt.xlim([1, n])\n",
      "\n",
      "    bp.plot_filter(range(1, n+1), estimates)\n",
      "    bp.plot_measurements(range(1, n+1), weights, label='Scale')\n",
      "    bp.plot_track([1, n],[160, 160+n], label='Actual Weight')\n",
      "    plt.legend(loc=2)\n",
      "    plt.xlabel('day')\n",
      "    plt.ylabel('weight (lbs)')\n",
      "    plt.show()\n",
      "\n",
      "predict_using_gain_guess (weight=160, gain_rate=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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atHGlrGM66UoKGaTnur+ZcVlcKjahTsUmlDEpy43ou9yIvvvccYqi5+zs/ML7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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c14e90b8>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is pretty good! The dotted blue lines, showing our estimates, are not a straight line, but they are straighter than the measurements and somewhat close to the trend line we created. Also, it seems to get better over time. \n",
      "\n",
      "This may strike you as quite silly; of course the data will look good if we assume the conclusion, that our weight gain is around 1 lb/day! Let's see what the filter does if our initial guess is bad. Let's see what happens if I predict that there is no weight gain."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predict_using_gain_guess (weight=160, gain_rate=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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e9Ho9Z65FERq5gYs3c5/KXqFcRbq81Ycuzh5UKFexECPMf0YtE33hwgUAdDod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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c13ae0b8>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is not so impressive. Clearly a filter that requires us to correctly guess a rate of change is not very useful. Even if our initial guess was useful, the filter will fail as soon as that rate of change changes. If I stop overeating the filter will have extremely difficulty in adjusting to that change. \n",
      "\n",
      "But, 'what if'? What if instead of just leaving the weight gain at the initial guess of 1 lb (or whatever), we compute it from the existing measurements and estimates. On day one our estimate for the weight is:\n",
      "\n",
      "$$\n",
      "(160 + 1) + \\frac{4}{10}(158-161) = 159.8\n",
      "$$\n",
      "\n",
      "On the next day we measure 164.2, which implies a weight gain of 4.4 lbs (since 164.2 - 159.8 = 4.4), not 1. Can we use this information somehow? It seems plausible. After all, the weight measurement itself is based on a real world measurement of our weight, so there is useful information. Our estimate of our weight gain may not be perfect, but it is surely better than just guessing our gain is 1 lb. Data is better than a guess, even if it is noisy.\n",
      "\n",
      "So, should we just set the new gain/day to 4.4 lbs?  Hmm, sounds like our same problem again. Yesterday we though the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n",
      "\n",
      "$$new gain = old gain + \\frac{1}{3}\\frac{measurement - predicted~weight}{1~ day}\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weight = 160  # initial guess\n",
      "gain_rate = 1.0 # initial guess\n",
      "\n",
      "time_step = 1\n",
      "weight_scale = 4/10\n",
      "gain_scale = 1/3\n",
      "estimates = []\n",
      "\n",
      "for z in weights:\n",
      "    # prediction step\n",
      "    weight = weight + gain_rate*time_step\n",
      "    gain_rate = gain_rate\n",
      "    \n",
      "    # update step    \n",
      "    residual = z - weight\n",
      "    \n",
      "    gain_rate = gain_rate + gain_scale   * (residual/time_step)\n",
      "    weight    = weight    + weight_scale * residual\n",
      "  \n",
      "    estimates.append(weight)\n",
      "\n",
      "# plot results\n",
      "n = len(weights)\n",
      "plt.xlim([1, n])\n",
      "   \n",
      "days = np.linspace(1, n, n)\n",
      "bp.plot_filter(days, estimates)\n",
      "bp.plot_measurements(days, weights, label='Scale')\n",
      "bp.plot_track([1, n], [160, 160+n], label='Actual weight')\n",
      "plt.legend(loc=2)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FA5AyxaJKMsR9GxsbC+iWFgpRGLlHxJPIPVLz5ORlEx2/i92xm0lOu1tkP68W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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1514828>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I think this is starting to look really good. We used no methodology for choosing our scaling factors of $\\frac{4}{10}$ and $\\frac{1}{3}$ (actually, they are poor choices for this problem), and we 'luckily' choose 1 lb/day as our initial guess for the weight gain, but otherwise all of the reasoning followed from very reasonable assumptions.\n",
      "\n",
      "One final point before we go on. In the prediction step I wrote the line\n",
      "\n",
      "    gain_rate = gain_rate\n",
      "    \n",
      "This obviously has no effect, and can be removed. I wrote this to emphasize that in the prediction step you need to predict next value for **all** variables, both *weight* and *gain_rate*. In this case we are assuming that the the gain does not vary, but when we generalize this algorithm we will remove that assumption. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The g-h Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This algorithm is known as the g-h filter. *g* and *h* refer to the two scaling factors that we used in our example. *g* is the scaling we used for the measurement (weight in our example), and *h* is the scaling for the change in measurement over time (lbs/day in our example)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This filter is the basis for a huge number of filters, including the Kalman filter. In other words, the Kalman filter is a form of the g-h filter, which I will prove later in the book. So is the Least Squares filter, which you may have heard of, and so is the Benedict-Bordner filter, which you probably have not. Each filter has a different way of assigning values to *g* and *h*, but otherwise the algorithms are identical. For example, the $\\alpha$-$\\beta$ filter just assigns a constant to *g* and *h*, constrained to a certain range of values. Other filters such as the Kalman will vary *g* and *h* dynamically at each time step.\n",
      "\n",
      "**Let me repeat the key points as they are so important**. If you do not understand these you will not understand the rest of the book. If you do understand them, then the rest of the book will unfold naturally for you as mathematically elaborations to various 'what if' questions we will ask about *g* and *h*.\n",
      "\n",
      "* Multiple data points are more accurate than one data point, so throw nothing away no matter how inaccurate it is\n",
      "* Always choose a number part way between two data points to create a more accurate estimate\n",
      "* Predict the next measurement and rate of change based on the current estimate and how much we think it will change\n",
      "* The new estimate is then chosen as part way between the prediction and next measurement\n",
      "\n",
      "Let's look at a visual depiction of the algorithm."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gh_internal.create_predict_update_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Hjh0oLi5WKCIiIiIiZTFBVZggCBgzZgyGDBkiK8/Pz0dZWZkyQREREREpiAmqExAEAePH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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c13cb710>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's explore a few different problem domains to better understand this. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23km at time t and moving at 60 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of 500 meters. So at t+1 sec the measurement could be anywhere from 22.5 km to 23 km. But the train is moving at 60 kph, which is 16.6 meters/second. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.0166 km because a train cannot slow down very much at all in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n",
      "\n",
      "Now consider the problem of tracking a thrown ball. We know that a ballistic object moves in a parabola in a vacuum when in a gravitational field. But a ball thrown on the surface of the Earth is influenced by air drag, so it does not travel in a perfect parabola. Baseball pitchers take advantage of this fact when they throw curve balls. Let's say that we are tracking the ball inside a stadium using computer vision. The accuracy of the computer vision tracking might be modest, but predicting the ball's future positions by assuming that it is moving on a parabola is not extremely accurate either. In this case we'd probably design a filter that gave roughly equal weight to the measurement and the prediction.\n",
      "\n",
      "Now consider trying to track a child's balloon in a hurricane. We have no legitimate model that would allow us to predict the balloon's behavior except over very brief time scales (we know the balloon cannot go 10 miles in 1 second, for example). In this case we would design a filter that emphasized the measurements over the predictions.\n",
      "\n",
      "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution (in a least squares sense). In this chapter we will merely be assigning different values to *g* and *h* in a more intuitive, and thus less optimal way. But the fundamental idea is just to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Notation and Nomenclature"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I'll begin to introduce the nomenclature and variable names used in the literature. Some of this was already used in the above charts. Measurement is typically denoted $z$ and that is what we will use in this book (some literature uses $y$). Subscript $k$ indicates the time step, so $z_k$ is the data for this time step. A bold font denotes a vector or matrix. So far we have only considered having one sensor, and hence one sensor measurement, but in general we may have *n* sensors and *n* measurements. $\\mathbf{x}$ denotes our data, and is bold to denote that it is a vector. For example, for our scale example, it represents both the initial weight and initial weight gain rate, like so:\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "So if the weight is 62 kg and the weight gain is 0.3 kg/day, the vector would be\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}62 \\\\ 0.3\\end{bmatrix}$$\n",
      "\n",
      "Finally, a hat '$\\hat{}$' indicates an *estimate*. So the output of the predict step time $k$ at is the *estimate* of our state, which we denote as $\\mathbf{\\hat{x}_k}$. \n",
      "\n",
      "So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$. We then enter a loop, predicting the state for time $k$ from the values from time $k-1$. We then get the measurement $z_k$ and choose some intermediate point between the measurements and prediction, creating the estimate $\\mathbf{\\hat{x}_k}$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Write Generic Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the example above, I explicitly coded this to solve the weighing problem that we've been discussing throughout the chapter. For example, the variables are named \"weight_scale\", \"gain\", and so on. I did this to make the algorithm easy to follow - you can easily see that we correctly implemented each step. But, that is code written for exactly one problem, and the algorithm is the same for any problem. So let's rewrite the code to be generic - to work with any problem. Use this function signature:\n",
      "\n",
      "    def g_h_filter(data, x0, dx, g, h):\n",
      "        \"\"\"\n",
      "        Performs g-h filter on 1 state variable with a fixed g and h.\n",
      "\n",
      "        'data' contains the data to be filtered.\n",
      "        'x0' is the initial value for our state variable\n",
      "        'dx' is the initial change rate for our state variable\n",
      "        'g' is the g-h's g scale factor\n",
      "        'h' is the g-h's h scale factor\n",
      "        'dt' is the length of the time step \n",
      "        \"\"\"\n",
      "\n",
      "Test it by passing in the same weight data as before, plot the results, and visually determine that it works."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def g_h_filter(data, x0, dx, g, h, dt=1., pred=None):\n",
      "    \"\"\"\n",
      "    Performs g-h filter on 1 state variable with a fixed g and h.\n",
      "    \n",
      "    'data' contains the data to be filtered.\n",
      "    'x0' is the initial value for our state variable\n",
      "    'dx' is the initial change rate for our state variable\n",
      "    'g' is the g-h's g scale factor\n",
      "    'h' is the g-h's h scale factor\n",
      "    'dt' is the length of the time step \n",
      "    'pred' is an optional list. If provided, each prediction will\n",
      "    be stored in it\n",
      "    \"\"\"\n",
      "    \n",
      "    x = x0\n",
      "    results = []\n",
      "    for z in data:\n",
      "        #prediction step\n",
      "        x_est = x + (dx*dt)\n",
      "        dx = dx\n",
      "        \n",
      "        if pred is not None:\n",
      "            pred.append(x_est)\n",
      "        \n",
      "        # update step\n",
      "        residual = z - x_est\n",
      "        dx = dx    + h * (residual) / dt\n",
      "        x  = x_est + g * residual\n",
      "        \n",
      "        results.append(x)\n",
      "        \n",
      "    return np.asarray(results)\n",
      "\n",
      "def plot_g_h_results(measurements, filtered_data, \n",
      "                     title='', z_label='Scale', ):    \n",
      "    bp.plot_measurements(measurements, label=z_label)\n",
      "    bp.plot_filter(filtered_data)\n",
      "    plt.legend(loc=4)\n",
      "    plt.title(title)\n",
      "    plt.gca().set_xlim(left=0,right=len(measurements))\n",
      "    plt.show()\n",
      "\n",
      "\n",
      "plt.xlim([0,10])\n",
      "bp.plot_track([0,11],[160,172],label='Actual weight')\n",
      "data = g_h_filter(data=weights, x0=160, dx=1, g=6./10, h=2./3, dt=1.)\n",
      "plot_g_h_results(weights, data)\n",
      "print(len(weights))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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H/hPbadndk7LVnYz2KedclUn9/46Ls1S8Eq+mNncAQgghhBCFno8PbNhQ5KZh6fV6Nm/e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\n58fWrVszk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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1398898>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "12\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Choice of g and h"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The g-h filter is not one filter - it is a classification for a family of filters. Eli Brookner in *Tracking and Kalman Filtering Made Easy* lists 11, and I am sure there are more. Not only that, but each type of filter has numerous subtypes. Each filter is differentiated by how *g* and *h* are chosen. So there is no 'one fits all' advice that I can give here. Some filters set *g* and *h* as constants, others vary them dynamically. The Kalman filter varies them dynamically at each step. Some filters allow *g* and *h* to take any value within a range, others constrain one to be dependent on the other by some function $f(\\dot{}), \\mbox{where }g = f(h)$.\n",
      "\n",
      "The topic of this book is not the entire family of g-h filters; more importantly, we are interested in the *Bayesian* aspect of these filters, which I have not addressed yet. Therefore I will not cover selection of *g* and *h* in depth. Eli Brookner's book *Tracking and Kalman Filtering Made Easy* is an excellent resource for that topic, if it interests you. If this strikes you as an odd position for me to take, recognize that the typical formulation of the Kalman filter does not use *g* and *h* at all; the Kalman filter is a g-h filter because it mathematically reduces to this algorithm. When we design the Kalman filter we will be making a number of carefully considered choices to optimize it's performance, and those choices indirectly affect *g* and *h*. Don't worry if this is not too clear right now, it will be much clearer later after we develop the Kalman filter theory.\n",
      "\n",
      "However, it is worth seeing how varying *g* and *h* affects the results, so we will work through some examples. This will give us strong insight into the fundamental strengths and limitations of this type of filter, and help us understand the behavior of the rather more sophisticated Kalman filter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: create measurement function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's write a function that generates noisy data for us. Recall from chapter 0 (**author's note**: I have not yet written chapter 0!) that we model a noisy signal as the signal plus white noise generated by `numpy.random.randn()`.  We want a function that we call with the starting value, the amount of change per step, the number of steps, and the amount of noise we want to add. It should return a list of the data. Test it by creating 30 points, filtering it with `g_h_filter()`, and plot the results with `plot_g_h_results()`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "def gen_data(x0, dx, count, noise_factor):\n",
      "    return [x0 + dx*i + random.randn()*noise_factor for i in range (count)]\n",
      "\n",
      "measurements = gen_data(0, 1, 30, 1)\n",
      "data = g_h_filter(data=measurements, x0=0, dx=1, dt=1, g=.2, h=0.02)\n",
      "plot_g_h_results(measurements, data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KcsgpSsqK2Zj2BRtSV1JqZ7VugI6BPZk37TGC/O2sEi4izV6N5mTk5eVhNptp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\nREREpFb/H7npPILRAnkeAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c120db00>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Bad Initial Conditions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now write code that uses `gen_data` and `g_h_filter` to filter 100 data points that starts at 5, has a derivative of 2, a noise scaling factor of 10, and uses g=0.2 and h=0.02. Set you initial guess for x to be 100."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_data (x0=5, dx=2, count=100, noise_factor=10)\n",
      "data = g_h_filter(data=zs, x0=100., dx=2., dt=1.,g=0.2, h=0.01)\n",
      "plot_g_h_results(measurements=zs, filtered_data=data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vo2OjeP/75/KMD/HzCuDua58mNLCQL+HNm8OsWfke8vTwZli36xnU+Ro2Ra7g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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1414ba8>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The filter starts out with estimates that are far from the measured data due to the bad initial guess of 100. You can see that it 'rings' before settling in on the measured data. 'Ringing' means that the signal overshoots and undershoots the data in a sinusodial type pattern. This is a very common phenomena in filters, and a lot of work in filter design is devoted to minimizing ringing. That is a topic that we are not yet prepared to address, but I wanted to show you the phenomenon."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Extreme Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rerun the same test, but this time use a noise factor of 100. Remove the initial condition ringing by changing the initial condition from 100 down to 5."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_data (x0=5, dx=2, count=100, noise_factor=100)\n",
      "data = g_h_filter(data=zs, x0=5., dx=2., g=0.2, h=0.02)\n",
      "plot_g_h_results(measurements=zs, filtered_data=data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zgawsUfxEyYaYtpACCKUyMlIAZSqQmTEDmDoV6NYNNbVVyArRAlA13N0pPtmx\nYzSCgQwRkbt68klxI+erqBAL/Vu3FsFkY2+/rcyYiFqyH38U/WCeekrpkVjvtttE5ck2bZQ5/6ef\nivetiAjjx4wZ0/DHC5cOQ+OlC2JiIuIRGmTisQ7EQIaIiMhaFy4Ad9whMmEnT5o9nIgcrLBQbBuX\nQ1dCcTHg5SWmmFqalZ0+3bZzlZeLAgWJibY9XhISIm4WalZ2OUGZaWUAq5YRERFZz1AzTCJSjhTI\nKLnWBRC9bMLDgQ0bHHueDRvEVLBOnfR6uzhD00Cms0IL/QEGMkRERNZjIEPkOmprRXbCx8e6/i2N\njRgBtGsH5OSYP9YUqSFmUJDZQ4vK8vHb0Q24lHfW+vOsWKH7c0GB9Y+3kVqjxvncU3r7lFroDzCQ\nIWrZMjOBe+4B9u83fyy5Pq0WWLMGePNN8WdyHCmQsWI6BpFizp0D/u//gPXrPbPHUeNpZSqV6WON\nuXJFFAuwNyiQmkoGBpo8rLi8AG+vmImvty7C21/PxIkL6dadR/qdAdHM0kmy88+jtq664efQoAhE\nhStUthpcI0PUsj3xBLB5M/DTT6LKErmXnTuBgAAgNVV0XlapgEcfBa5eFdMbOnRQeoSeq7xcbA1l\nZH79FTh8GPjDH1gOm1zDunXAvHni5usLDBoEDB8OPPgg0Lmz0qOzX2gosHIloFbb/hxNygvbzMKM\nzPrfv0ZppTiXVqvBDzs+R3KHNHipLMwxNA5krlyR7b2mqCwfyze9h4LSPHSITUK3xL5I6dAHIVl5\nwJw5ONfFH2h0/aZTfApUtgaPMmAgQ9SSSSn0+nplx0G2GT1alOssKtJVm+nVSwSnR44wkHGkqCgx\nFSU1tfl9y5cDH30EvP8+AxlyDUOGALNmAVu2AOnpItj+9Vfgiy+AszZMa3I1wcHAfffZ9xxSINM4\nQLCFBRmZ/OIr2HNii96+3MLLOLZyEXpNmGbZeRoHXFeuWDtKndpaIDZW/P7nzmHV9k9x6vJhAMC1\nklykn94BFVToEJaA7tm7cCq2IxCi+92UaoQpYSBD1JKFhys9ArKVRmO4iVnjQOauu5QZW0swYoS4\nGSJlaTxxCg+5p969xQ0QX4C3bBHTqPgeoRMZKbb2ZmSCgsSUUxMZmQ17V0KjaZ492pixAT21T1mW\n4WgccNkzlbisTFRaU6lQWVOOY+ebTzXXQosLpVm4cGfzoKWzgutjAAYyRC3bc8+JK8qTJik9ErKW\nFMSEhOgeC8t3AAAgAElEQVSX+OzVS2yPHHH+mEhgIEOuYNYskXV/9VX98ryRkcC99yo3LlclV0bm\n6FGTd+cVZmFfxnaD912K8MKpS4eR3KG3+fNMmSLWxixaZFFhAaMaNcM8em4v1BrLZ2j4+QYgIdrO\n0s92YiBD1JJNmCBu5H6kD5+wMP39DGSUx0CGXMHatcDx48DMmUqPxD3MnAk884yYZuVA635fAa3W\neLnkjfu/tSyQmTtXngE1yuwfOrNL765ObVJQU1eF7GsXDD60U1RneHtZ2CvHQRjIEBG5IymQaTo9\nMCUFePhhIC3N+WMiQapkxkCGlCQVpGBlPcvEOb7yVnb+BRw4vVNv3/C+92BL+g8NP5/NOobMnAx0\nik92+HgANAQyla3DkXHpkN5d9w57DG2jO6Go7BpOXEjH8UWv43THcNT6+8C/uh63ff4LcL9zhmkM\nAxkiInfk7Q3cckvzBf0BAcDixcqMiYTUVOCpp4ChQ5UeCbVkLSmQmT8f2LMHmDYNuPlmpUdj1Lrf\nv9L7OSE6EXfd9BCysk/jVO6Jhv2b9n+LJ+7+h8nnqqmtwqnLhxHbqh1iIxNsH9T1i2LHOofrTSuL\nDm+DhCgxbSwyNAo39bwNNw0tQp23Cle9axD+0GMI6TfI9vPKhIEMEZE7Sk4GfvlF6VG0XPv3iwWy\nqalAdLT+fUOGiBuRkhqvo/N0O3cC330HjB+v9EiMupR3FkfO/a63b/TAifBSeWHkjffh1OpXG/Yf\nP78f2fnnja4/uVqUjfdXzUZR+TV4e/lgym3T0aerje85I0cC+fk4uG0BkKObktw7aXDzogMPPABf\nAAlr1gAVtS7REJgNMYlauuJiYN8+4PRppUdC5D5ee018Adi50/yxRM5WWytu3t6Av7/hY377DejR\nQ/SScXdSE8vWrZUdR3296ONlYFrpz7uX6/3cITYJPRL7AwCSOvRGx7gb9O7ftP87g6fIL76Chav+\niaLyawAAtaYeyzbMx6XsDNvG7OODqtBAZOSd0NvdO+km449xoYbADGSIWqr6euCtt8SV4wEDgIUL\nlR4RkfuQPshd4IokUTNeXsA33wCff268072vrygGcOKE4fvdiVRpTKo8ppTTp0WxgL599XZn5pzE\niYsH9PaNHjSpIeOhUqkwsv8f9e4/ePo3XC3K1ttXUJKH9757GSXlBXr76zT1+GTtGyipsK3i2tHM\nvVCrddPKosLj0NZUNTIXev9jIEPUUpWUAH/7m/ggA0RPASKyjAtdkSRqxsdHlFiePNn4Me3aia0n\nvPfLEciUlgJJSUDnzrY/h9QMs0k55J+aZGM6x3dDcnv9ymQ9EvsjPqpjw89aaLE5/fuGnwtL87Fw\n1csNmZimSqpL8Onauairr7V62E2rlfVOusl0Lxt/f7E+0wkFEsxhIEPUUhUX6//sCR9mpPPee6I/\nUG6u0iPxTC50RZLIJrGxIuC5dk33BdxdyTG1LDgYOHsWOH8eUDdvVmmRykqxDQxs2HX68hGcydLv\nLXPn4AebBQoqlQoj++lnZfad/AVFZfkoKruGhav+gcLSq3r3R6n99H6+kHsKK7d+CK0VDTKraipw\n8tJBvX1pSYNNP2jyZODCBWDOHIvP4ygMZIhaKimQkRYqM5BxL8ePA7/+KuZjG/LNN8BXXwGHDhm+\nn+xjKpCpqADef180qiNyVV5eQML1alfu/P6v1QLffgt88YV9Fxa8vUU5e61WzFiwRZOMjFarbZaN\nuaFdKrokdDf48LSkwYgOb9Pws1pTjx9/W4r3Vv0TBSV5esf23X8Zf/e5CckV+mugfj+5Fb8cXGPx\nkI+d32dgWlknwwdv3Sp6z33wgcXP72iyBTJvvPEG+vfvj/DwcMTExODuu+/GcWnKSiOvvPIKEhIS\nEBQUhGHDhuFEk7mZNTU1eOaZZxAdHY2QkBCMHTsW2dnZzZ6HiOwkBTLJyeIDLS9PLA4l9zBvnii/\nvHat4fvZGNOxhgwBhg0DIiKa31ddDTz9NPDSS84flzX27gUefRT46COlR0JK8YTpZSoVMHq06HRv\najqUJSIjxbaoyLbHN8nInLx4AOev6C/CHz1okuHHbt0Krw8WYXg7/WxI+qlfkV+co7cvrcAbk5cf\nhE+r1viTJgUxV8v17v9h5+c4eVE/y2LMwZXv6/1sclrZ5cvAypXA7t0WPbczyBbIbN++HU8//TR2\n796NrVu3wsfHByNGjEBRoxfD3Llz8c477+C9997Dvn37EBMTg5EjR6K8XPcPMH36dKxatQorVqzA\njh07UFpaijFjxkCjMd4FlYhsIAUyUVHiC/HIkbq+A+T6pCuGTRtiShjIONaSJeLqZFRU8/ukq8Ku\n3hDz0iXg00/F1WxqmT7/HMjOZs8jibTGptC2RfNQqcT0tusBUeM1LgDQvWM/JLa5wdAjxf/FZ55B\n/xwNwkOMT5FL7TwQD+2vhLdGC0RGIigxCY9tzkOg1rvhGK1Wg89//k+zYgFNVdVUIiNE/wKmyWll\n9v79OIBsgcz69esxdepUdOvWDT169MDSpUuRn5+PXbvEAiKtVov58+fjxRdfxLhx49C9e3csWbIE\nZWVlWL5cpN1KSkqwePFizJs3D8OHD0daWhqWLl2KI0eOYPPmzXINlYgAoFMn4PnngTFjxBeyDRuU\nr/hClrvexAxhYYbvlwKZo0cN30+O4+8vspy1taI6oKuSGgfu2gXU1Sk7FpLX9u3A/fcDH35o+rjO\nnYH4eDGtiuzPyIwdK9YcLVmC2roaZOac1Lt79KCJxh8bGgoA8C2vxK19xho8pEdif0y946/wvnss\n8OSTQJcuwIMPIvb3o5h6z9+hgi6TUlVbiY/XzEFVjfELKsfO70O9t+4xrcNjjU8rA3TfEWz9+3EA\nh62RKS0thUajQeT1F8X58+eRl5eHUaNGNRwTEBCAoUOHNgQ76enpqKur0zumbdu2SElJaTiGiGSS\nlga8/Tbw5z8rPRKyhbmMTPfu4urgyZOcMuhsKpXrZ2UqKoCcHFF1rbISOHDA/GPIfZw+LdbJpacr\nPRL3smSJKJBy6612P9XFvDPQaHRFA6LC49AuxkRFNOmiVGkpBvcYheBA/YtU3Tr2xcOjZ8LH21cE\nMYsWATfcoHf/3UOm6j3malE2Fv/0Fmrragye8tCZ3/R+TutiplqZFOgdPiwW+9cYfl5n8nHUEz/3\n3HNIS0vDoEGDAAC51yvnxMbG6h0XExODnJychmO8vb3RuknVidjYWOTl6S9yamz//v1yDp2Iryly\nGLleWz2uXkUAgGOXLqHay/A1qahZs1CbkICyAweg9XHY2z0Z0MvPD34ADu/ahTqpoIYDWfu6Cj5y\nBCmPPNLw8+Xly5HHq/IeI/bkSbQDkFdRgct2vOe02M/Cy5ftfoojl/Wb5Yb5RZv8+2xTWooEAFdO\nnUL24WPo32EUtmd8By20aN86GWltRuLwocMmzxmmTUCn6J7IzNdl4k9dPoy5S/+KW7tNgL+Prppa\nbX0Njp/XD3T96yNNjtHn2jX0BsTFj8REnHrvPZTdeKPJMTWVlJRk1fHmOOST7fnnn8euXbuwc+dO\n05HddZYcQ0REOhUpKaiPiEC9sallAK6NH+/EEVFj18aOhVd1NTS+vkoPxSCfsjK9n0MPHkTelCkK\njYbk5nV90bm6URlgT9Vq3Tq02rQJBbffjqJGM3qUll+mHwzFhLUzebz6ehbX63oWt33rZNzb/znU\n1FchIsiyiyEqlQqDutyJ0qoCXCvXFQjIL8vChqNfYES3SQjyF1PYsorOQKPVZYxCfUPRKth0Xxh1\nRAQyX3sNnV5+GQCgcYHXl+yBzIwZM7By5Ups27YNHTt2bNgfd71pTl5eHtq2bduwPy8vr+G+uLg4\nqNVqFBQU6GVlcnNzMdTEQrR+/frJ/FtQSyVdieBriuQm+2tr/XoAQG8zh5EDlJSI0tcxMYCxq5Gf\nfgoAcHS7OJtfV6dPi+2ttwJPPYWIm29Gv5gYmUdHivnmGwBAfNeuiLfktaHV6lX8cqvPwm++AXbs\nQMQddwAuMl6NVoNv9r+rt2/YoDvQprWJYKaiAqisROywYYi18/dI6Z6MRT+8guxrFxr2FVfmY+vp\nrzBt3KuIjmiDQ2s36T1mQM/h6N+/v/knHzgQ+Ppr4NgxpPTrp1uPaaESW0tbGyHrGpnnnnsOX3/9\nNbZu3YquXbvq3ZeYmIi4uDhs3LixYV91dTV27tyJwYNFhYS+ffvC19dX75isrCxkZGQ0HENEDlBV\nJb6Ybdig9EiIXN+pU8Ddd4sSy+5KWqzbtSvwxz+KoIw8h1SBMiTE9HFarVhPFxjouuu5zJEqaLlC\nsZriYqCgALl55/UW2Qf5hyC2VYLpx95yi1j3cv/91p83K0sU7bj+dxEWHIFn7n0dneO76R1WWHoV\n81fOwrns4zhxQX9dXFrXIZafz4UaAssWyEybNg2ff/45li1bhvDwcOTm5iI3NxcV139ZlUqF6dOn\nY+7cufj+++9x7Ngx/OlPf0JoaCgmTRI1tcPDw/HII49g5syZ2LJlCw4ePIgpU6YgNTUVI0aMkGuo\nRAQAixcD8+eLhY25ueJN9LHHlB4VkeuTPsTNfUl0ZVIgIy3eJc/y2GPAihWAualWKpVYsF1TI8u6\nEEUUFIhta+Mli53mhReAqCicX/WZ3u7ENsnwUsn0lTs7G5g7F1i1SrfvsceAm24Swcx1Qf4h+Mu4\n2eiRqJ9lKasqwYJv/4F6ta5SYauwGNOFCJqSAmVPCmQWLVqE8vJyDB8+HPHx8Q23t99+u+GYmTNn\nYsaMGZg2bRr69++PvLw8bNy4EcGN/iLmz5+PcePGYcKECRgyZAjCwsKwZs0arqMhktv8+cCMGSKI\niY8X+3JyALXa9OOIWjoXuhpps4gIoEcPoEMHpUdCjtC7t+jAbsnCamm6v7s2xZQyMnIEMvv2AQkJ\n5gNAY6qqAADnvEr1difGJ9s7Mp2MDGDWLGDhQt2+Nm3E9soVvUP9fPzxyJhZGJAyTG+/Flq9n9OS\nBlv3PbttW3FzgYs5sq2RsbRh5ezZszF79myj9/v5+WHBggVYsGCBXEMjIkMal+/19xdTS65eBfLy\ndIENub85c8R85nfflaWkKMGlrkba7Omn3XtqHMmn3fV1G+6akZFzapm/v7igZ2um8nqRhfP1+g0j\nO8Wn2DsyHUO/r5FABgC8vbwxaeQzCAkMw9YDqw0+Ze8uN1k3Bhcq1+6wPjJE5OKKi8U2IkJsE67P\n33XXq3ItydWrYrH/sWPmj83OBo4ccakPHrdnSUbm119FnyZ36uNRU9PwRYxaEHcPZD76CPjuO9Hk\n2V72NsSsqkJJmD8K1OUNu7y9fNA+tov9Y5MYmhZ6vWgWrrc6acpL5YWxQ/6Eu256qNl9rcJirBvf\n//4H3HUXsGaN5Y9xIAYyRC2RWt28M7w0vSA7W5kxkeX27AHuuAN48UXzx6amiu1h0/0HyArx8cDo\n0WL6jjHffy/my//yi9OGZZdXXhEXNZYtU3ok5GzSe7+RL8Eub9AgYPx4IDTU/ueSshyFhaaPM6ay\nEpmJ+pmhdjGd4efjb/6x9fUiKJs/3/RxhgIZExkZiUqlwsh+4zFx+DSoGq3XGfrVDqisKTCQkQGs\nXSuaLbsAdkgjaomkHhJhYYDUBG/IEPFnV6j8QqY1DUJNkb5sHzrkuPG0NHfcIW6mSNkad6kE1bo1\nUF0tMkks+tGyTJkCTJokphm3UFqtFtW1VfAL8Ie3r6/4v1BVJaq5WSMkBJkJ+lOzO1m6PkalAp58\nUmyffRYw0ujY4NSyjh2BtDSLslKDeoxEm6gO+P34FrTJKsKQzauBsVas4bE3ayUzBjJELZGXF/Dy\ny6L0pmTmTOXGQ9ZpvL7JnB49xL93RoaYOuRvwZVBsp+7BTJSr7YdO5QdB8lj8mSRef/oI/MXPOTI\nZLixmrpq/G/tGzh16TDaxXTGIx3j0OrMZfFF3dpA5uefcf6rF4CrZxt2JbaxcH2Mt7d436ioEDdj\n/y633CKyNwMH6vb162fV9OGOcV3RMa4rsGQJoIV1rwF7s1Yy49QyopYoLAz417+A115TeiRkC2sy\nMkFBonJRfb3LTAVoEaRqPq4ayOzZA5w4AUiFenr0EFPLLl4UN3Jvq1aJ8stSxp2M2vD7Spy6JKbe\nXr56Dp+9PB71RYW66VpWqKmrRlZ+pt6+xDZWZDuk93Rp1oQho0eL9XfDhhk/xlLSeawJZPz8xDYj\nw/7zy4CBDBGRu7EmIwOILzTZ2br1MuR4rpyRUavFuoIePXT7vL3F9FKAWRl3p1aLaVEqlfUZhRam\nsDQfvxzSX7R+sfAC1h79Qfz9Weli7hlotLoqvtER8QgLjrD8CaSAorTU9HFyseaimET6e/n1V/nH\nYwMGMkRE7qZTJ2D4cMt6RABinUx8vE0fzGSjnj2B554DbrtN6ZE0JwXCYWH68/CHDhXBsYvMfScb\nNa6qZ2ydhafYskW8F86bZ9PDf96zXK8xpGTrgdU4fn6/1c93/op+1ruTNdkYQBdQOCuQsSUjM3Uq\n8NZbwMGDjhmTlbhGhojI3Tz+uLiRMn77TQQDAwYAUVGGj+nfX9xckaGqR4DoK/P885yO5O6kPkfW\nrn2pqxPZnIAA+cfkKOfOAVu3AomJVj80Kz8T+07+YvT+Lzf+FzMnvYvIUCP/xw0NJ0c/kEm0tn/M\nAw+ICwrG3lfk9u9/i+qX1vyf9/YG/u//HDcmK3l4qE5EVtm6VdSId9bVIFczZ47IXpian0w0ezZw\n550uc0XSasYCmcBABjGeQApkrOm6/uyzohDIl186ZkyOIi04b93aqodptVqs3rFEr8N9ZGg0vBqV\nJa6oLsMX69+BWqO26Dk16npcyG6SkbG0Ypnkr38V619s6Ylz6RKweTOQmWn+WImXl8gCuXFzXwYy\nRC3Rpk3iSszvv+vvnz5dlF49d06ZcSntpZdEv5Vvv1V6JOTKpKk71nxRdCVSM1xbu5eTa2vTBvjh\nB/P9SBoLDxdVLN2tKWZBgdha2Tbg5MWDOHVZv7fWhFufxOhBk/T2ncs5gfW/f23Rc165nIHq+uqG\nn4MDQhEb2daqcZlVXy8upCxc2Py+d98FRo4UzUFbEM8MZKqrgU8+MdkYiKhF+/ln4B//AHbu1N8v\nNUbLynL+mFzB6NFiGx2t7Dgcpb7eNRefuxvpire7XsX09xfT4rp3V3ok5AihocDYsbr3M0u0aye2\n7vbeb0NGRqNR48edS/T2dW3XCykd+mBEv/G4wSdG776Ne79pqGpmSmbWCb2fE9skQyX3usSiIlFx\n9JVXmt8nVVlz18amNvLMQObdd8X8cakuPhHpk67IRjSpptLSAxmpCpi0GNqTvPOOyCC8847SI3F/\njRdTu6ObbxbZ2AULlB4JuQopkGkBGZm9J39BToF+ifGxQ6ZCpVLBS+WFKWE3IqxEl1nRQoulG+aj\ntKLY5PNm5uqXI7Z6fYwlpGmhhn5fKZBpYRfxPTOQOXZMbM+eNX0cUUslfVFvGsgkJIgtAxllx2HO\n2rViPVN9veWPiY4WDTEPm7+ySGZYEshUV4upPW+/7ZwxyenCBeCLL1z//wHJR7qI5W6BzBtvAOvW\nATfdZNHhtXU1+Gn3Mr19/ZJvQbuYzg0/h0XFY8qX6VA1ahhdWlmEpRvf1Sut3NT5Av21KVZXLLOE\nlIEyNC3UlkCmcVNsN+WZgcx//yu2wcEe8Y9EJDtzGZnsbOeOx1VIpS9d+QucVgvcc48oOaq2bBEq\nAF0PmUOHHDOulmTkSGDUKNNVoTQaYMYMse7K3UyZIkqssp9MyyFlZGpqlB2HtVJSgNtvB2JjLTp8\n28EfUVKh60jv4+2LMYMe1D8oMhI3nLmGUcfK9XafunQYm/cZXn9SXF6Awmpdxsbb2wftY7tY+Es0\ncuKEmFX088+G7zeVkYmLE1trppZ16CC+B+TkWDdOF+KZgUxUFBATI66aXbqk9GiIXI8UyDRtqNiz\nJzBpksVXtzzOE08Au3cDf/6z0iMxrqpKBDD+/uJmqeRkwNdXFHJgVTb7fPklsGGD6YxMYKDo21NT\nY13A6Qqkadku0vCOnCA8XLy3WFPxys2UVRZjc/oqvX239B6DVmH6a2KkIOH27RfROb6b3l0/7V6O\nw2d3N3vuzCZll9vHdIGvj5/1g0xPFyXQv/rK8P3GKg4CYkbFTTeJZreWKi4WF+6Cgqwfq4vwzEAG\nEIsYAwMZyBAZ8vjjwMyZuqtwkgEDgGXLROWylubiRfFB3qOHxVf39Gg0zsnkSOdoGoSa4+cHdLv+\noXz0qLxjouZUKt2XA3crsMBAxr0tXy6ytitXWv4Ylcq9+sfYYP3vK1FTW9Xwc1BAKEb2/2PzA68H\nCd6FRXjo9ucRHKDLvGqhxRfr38WF3NN6Dzl/RX99jNVllyVSltdYC4Ru3UShnnvuMTzunTuBxYst\nO5dWa1upbhfjuYHMt9+Kq44336z0SIhcz5NPAnPn2vaF3VPNny+CmEWLbHv83/8uUvuOLl0tfcBJ\n0+Cs0bu3mEaQlyfvmMgwKWPjaoHMgQPA/v3GxzV4sOgvkZ6u+6JD7uPoUWD1aq4TbuRqUTZ+O7ZB\nb99tA+5DkL+BL/CtWwP5+UBeHiJDozD19r/q9ZepU9fi4x//jWsluilc53KaViyzcaG/9L5uLJDp\n3Rt47TVgwgTbnr+xigoRzAQFAT4+9j+fQjw3kGnVio29iMhy0hzh+HjbHp+RIRZ4O7pJoq0ZGQB4\n/32xWHTcOHnHRIa5aiDzxBNA//66wjhNhYYCffqIYhJ79jh3bGQ/D7jKLre1u5dB06ixZevwWNzc\n6w7DB3t5iSUK17/cJ3fojftv/YveIeVVJfhw9WuoqC5DTW0VcvIv6N2faOtCfymQccb0X+kcptb6\nuQH3DcFMKSkRQUxQkHhBEhGZY28g07692Dp6OmtQEHDXXUDnzuaPbcpdywW7q8ceE59HrvZFwdQ8\ne8nkyWK+vVQJidxHSwlkTp4U6xn79gXee8/oYTW1VTh6bq/evrsGT4GPt6/FpxrcYyQKS/OwcZ+u\nWfLVomz8b+2bGNF3nF41s5iIeIQG2XChCTA/tUxODGRc2H33ic7lGzaIyjJEROZIgYxUgtpazgpk\nevQAfvzRsecg465dE2tH4uOBgQNNH/vii84Zk7WMVS1s7LnnnDMWkp89gUxZmftMJ8zJERlDM2t7\nzmQdg1qjK1UfFR6HtCTrC9rcOehBFJReRfop3dqxc9nHcaVA/z2/kz39Y2JigGeesf1zyBpduwK1\ntUBlpePP5UCema6Q0vhuXIWBSDH794tGeXv3mj/WU2i1ukDm3ntFeV1rOSuQIWUdOQL88Y+uG6SY\no9XqAhlTGRlyX7YGMps3i6lNkyfLPyZHkHqqmGmGmXFJf7pvSoc+UKlUVp9OpVJh0ohnmlUyq6zW\nnwaWGGVDtlwSGSk+f//2N9sen5Ul1kft22fZ8b6+tk1TdiGeH8hcuiQWbRGRcPasqHpirLzjDz+I\nq7Hr1jl3XEqqqgL69RNXwY4etfxDoDEGMi2D9CXRXafplZWJctDBweJLDHmeV18FvvtOrHOyhjSt\n1l2aYhYUiG3r1iYPO3lRv3dWcofelj2/VtusdLqvjy8evetFxEQaz5h0WuPAan/z5gFz5uiCuKZ+\n/llUNPvwQ8eNwcV4ZiAjpclmzxbNfj77TNnxELmSjAzg3/8WvTAMkZpiZmU5b0xKCwoSzf8uXBA/\nl5aKcsqWqq0VC6MTE4FevRwyRNmo1cCpUyzBbCvpQpm7BjK1tcAf/mBbryg2mHYPAwYA48frGiRa\nSirHf/mye/xbW5CRKSjJQ36xrtmjt5cPurbtaf65X3hB9On65JNmdwUHhOLJsS8jJLB5JiO4vAYx\n/iambNrrnXdEk92qKsP3S//mV644bgwuxjMDGemDpvf1qPv4ceXGQuRqzM2Pb4mBjMTHR3xBbVxf\n3xJnzohS7wEBltfwV8qqVaI55qxZSo/EPbl7IBMVBWzbJtaQWmPjRuDGG41fCSb3FxoqphlVV8Pb\nnp5YWq3Ian/8sXxjM8SCjEzGJf1sTGKbG+DvF2j+uX19gbo6o6/3qPA4PH73S/D11m96mXi+EKog\nB743SOMxNi1UKs6Rm2v4fg/kmYFMYKC49e8vfmYgQ6QjBTLG5sW25EAG0P29WPNBbsniabn8/juw\ndq3NV9zqenRHbmwIjpZfwNYDP2BL+g+4WpRj/oEkWBPI7NgBvPkmsGuXY8fkaFot8Mor4svpE0+4\nx9V6ss31rIyfPb2mSkpEL6KnnhLFMRxlxgxReOP++40ecvKi/vqY5A5plj23FCiYCNw7xnXFQ7c/\nDxV06236788S3z8doaoKqKkRmSJj55ACGUs+H6yZdeDCPLNqmdQESioxefKk+AdjKWYi3Rd0ZmQM\nCw8XC/+tKX/pzEDmnXdEx+6vvgIeeMDkoZU15ThwaidyCi4ivzgH+cVXUFR2DdoXh4sDdnwOANiS\n/j1eeGAeWoVFO3jwHqBjR2DsWCA11fyx69eL+eyvvSa+2LkrlQpYulTMcvj2W+Dzz4GHH1Z6VOQI\niYlAaSm8jU1dskREBDB8uMj6rVnjuNdK27a6zysD1Op6nL58RG9fcnsL18dI09Wk75FGpHYZiGfv\nfR0Hz/yGjt9uQu/DOfYXmvr2W+D0aeDBB8XyCEnjbIyxYgUxMWJ79aqYRmyqn+I//wn85z/A668D\n//d/9o1ZQZ4ZyEgiI0V0euWKmPveqZPSIyJSnrkv3a1bA48/Lv7vtMQLAMuXiw8Ja/q0ODOQsbAh\nZk1dNRZ88xJyCi6afcryqhJs3PcNHhj+lBwj9Gxjx4qbJVy1IaYtOncWDVWnThXlYYcMAZKSlB4V\nyW31akClQvn+/fY9z7hxIpD5/nvFgt6LeWdQXasrLRwSGI62MRZ+D7QgIyPpnNAdnRO6A8v3i0BC\naiJprxEAACAASURBVGppq48/Fi1E+vY1HMiYqtLm5yeqKgYHiwbNpjLHZWVizZybF/3w7EAGENPL\nLl+2bpoIkSe77TZRlvPmmw3fr1IBH33k3DEpbe9e8Xt366ZbW2cNZwYyUqbIzIfl6p1LLApiJL+f\n2IpR/e9jVkZOnhTIAMCUKaKa4YoV4s+7dxu/MtzS1NaKL5FKq6wUC/2joowXdDHF3n/PigpRwr9P\nH/FcGzeKL8wKNF1sOq3shvap8FJZeGFOChasycx//LE864KMNcWMihIZXnOB0rffmr5fIj2/mzfE\n9PxLratXAwcOAGkWzosk8nQjRoiKfoMGKT0S1/Hss6LSz+HDtj3ez09MOfL3F1chf3Vg+U0LMjIn\nLqRj5xHj5bMjVIFIyqtFmMq/YZ9aU4/N6atkGybBNQOZjAzx+rRlMbBKBSxaJKbJzZnDIAYQV70H\nDRJrFlxhul1pqXgP2rRJmfMfOyaq4v3lL6IyXk2NYqX8M5quj7F0WhkgMo4VFaK3jrNJgUqZfn8a\ntGkj+ldNmybPeaTnd/NAxvMzMkRE5kjNMKU+CtZ67DFxW7cOuP12ESw66ouEmYxMeVUplm96T29f\ndHgb3D1kKqIj2iAqPA5+viKA2X18M77arDt29/FNGNX/XkSEmO7LQBZyxUDm/feB994D5s8X/aKs\nFREB7NzZ8oIYqcBB0987IEB8IdRoxDSqxYuV/buxtRmmXC5ezwK3bw9MnCh6miiwPqyiugyX8s7q\n7bO4fwwgplspNeVKem+3JhtkCw8JZDwvI1NbK0ryVVcrPRIicgcaja7Ci1TxxVbOaIo5cqQIlgyU\n39RqtVix5QOUVuoWqHqpvDDl9hlI7TIQ8VEdGoIYABiQ/Ae0CtVNJVOr67El/XvHjb2l6d5dLKK1\ndE2NM0iLl42Vb7WEqwYxVVXAG2/Y1tDWnFmzjFef++YbIDpaZEsvWj6d0yGUDmSk97727YH77gP+\n+leTC/JtVl4uenbdeafBu09dOgwtdNX14qM6IjzYxNoSVyIFFk0zMnKTLrDYu6ZHYZ4XyOzfL+YR\nDhum9EiIyB3k54tmlq1bi6lh9nBGQ7nFi0Xmx8BVtL0nt+LIuT16+0b1vw8d47oafCpvbx+M7H+v\n3r5dRzeipIK9QozaskVMWbakn0qvXsBbb4kr065CjkDGVaWnA3//u2hmKCe1Wvy/+/BDw+WEU1J0\nVeyOHGl+vzPJEcjk5SFIqvZqLSmQa7xI3RGuXRNNfY8dM3i3XdPKlDZ0KDBzpuOnf+/YIdZU3Xij\nY8/jYJ4XyEgRpr3l74hassuXRf+LlrDov+m0su++E2vqXn3V+ucKCxNrV6qqdM3anKSgJA/fbv+f\n3r72sUm4bcB9Jh83IOVWRIZENfxcp67F1vQfHDJGj/D3v4vpMqdOKT0S20iFKTwxkImNFVu516jt\n3i2+OO/aZbz5ohTInDwp77mtJUcgk5KCbg89BB8zpYcNapyRcSQTFby0Wm2zRpgplvaPscfly6Ls\nsb39WUaNAubOFVOUbXH1qijPv2aN6eNUKrG2y8e9V5l4XiBTeb3UXuOSc7m54grm2bOGH0PUUmi1\n4mrlq6+afrPNzRWLCltCIOPtLT44brpJ/FxeDhw6BJw7Z9vzOWN6WRMajRpLN8xHTa2u94Ovjx8e\num06vL1Nf0j5+vhiRL/xevt2Hl2Psspih4zV7VnTENMVSV9O5aqwl58vroy7AmlqqL+/vBnR1avF\nduxY49Pqnn9e9N6aOVO+89qib1/g559FQRdbSU0xr161/rFJSaJimTXl620hXSgyEMjkFmahuFx3\nIcnXxw+d4lNsO09dncjIWaJbNxFMS8Gk3BYvBl56yXywnJEBTJokLka2AJ4XyBj6kHnzTWD0aMtL\n0hF5qqoq4O23xTxyU/1hWlJTzF69RJWfRYvEz1I1MGtKtp86JQIXtRq44w7xIRIQIP9Yjdic/j0y\nr+h/uN1z88OIiUww/qDycmDVKuDzzzGw+wi9+eN19bXYemC1o4br3owEMhqNGhqNhV94lNSvn5iy\nEhVl/lhztm4F4uKAJ56w/7nkEBIisqI1NWYbGVpMq9UPZIyJjwcSEpRfPxQdLd6D7FlgLwUyeXnW\nP3bePDHFr2kZe41G3qIXUiBjIEPWdFpZl4Qe8PWxoTT28OGiIuXu3eaP1WrF5ysgshyOsHKlqBZ4\n/rzp46SA3pbKhG7I8wIZKSPTeGpZ9+5ie/y488fj6g4fFm86lZXmjyX3J305N3c1NiZGpJvz81te\n4Qxp4aM1gczNN4s54deuiSkBy5aJq3NOcPlqJn7e85Xevm4d+2JIz9tNP7CoSDROe+EF+Ho3z8rs\nOLIO5VUOrprjjgwEMicuHMDsxY/h5f/9GRv3fuPaAc0XX4gpUnFx9j/XgAG6L3rZ2fY/nzXq6w1P\nnZGmiEpTRu2VkQGcOSOu/EtZW09nTyBjyJo14v3xxRfleT7A5NSyptPKrKpW1pgUkFgSFEuZGx8f\nx1U7k8ZhqiEmoPu/feWK49ZquhDPC2RUKjH3t/EXNQYyxr32mrhC9z0rFbUIljZu9PbWXdWR6wuB\nu7A2I6PV6v5eTfR2kcXly6JCUno6AKC2vgZfbHhH74tzcEAoJo14GipzV4bbthXvlQUFQE4OBvUY\nibAg3bqJ2rpq/HLwR4f8Gm6tSSCj1Wrx9dZFKKkoRFlVCdbuXoYPfngVpRVF4sv2f/4DvP66ggN2\noJAQUUEPcO5niFoNTJ0K3H038O67+vcNHSoyEnJlRnx8gEcfFT1i3HwtgcXkDmTi4kR2//vv5fti\nPXGiKO7UpLBDXX0tzmbrFwBIbm/j+hhpHZklhT0cnY1pPA5z69tCQ8X7U1WV8RLOGo3lU+ZcnOcF\nMo88Iv6x335bt0+6MnrypMf8w8kmI0Nst21rEZF7i2dNB3ppepmzr7QqzdpAprpaXI3z93f8dLJd\nu4D77xdZHwBb039AXqH+9L8Hhk9DWLAFC7lVKt30j8OH4efjj+F9x+kdsv3wT6iobl4CtLD0KrYf\nWotV2z/Fscx90GjtXNzqLrRaMb1ozJiGrP/V4hwUleXrHXb68hHMXT4Dp7KPiTUTL79s/wJgV/XH\nP4rtd98553xqNfDnPwPLl4tAqmllp48+EmtEpAuY9kpKAj75REyZaim6dEFVhw6ol6u/SL9+4vMk\nK0sEH3KIjBTrgbp00dt9LvsE6uprG36OCGmNuFY2ln+WMh+WBDKGZgPZqrRUXAB55x39/SayUM00\nzsoYcv68CMzl+n+ioJZxeSEiQsxdzc4W/3hNXvgtllotUuYA8OmnwH//674LWFuy334DpkwRpUFH\njTJ9rAVd4Rs89pioziSVFG4p2rUTfSgs+bAArAsO7dXo30+r1WLPiS16d9/YbThSuwy0/Pm6dBEX\nMa6XTL2p523YvP87lFWJ89TUVuGXg2sweuBEZOVn4ui5vTia+Tuyr11oeIpfDq1BdHgb3JI2Bjem\n3Ap/PwdekVSaSiW+QDdyPifD4KFllcX44IdXMequHrj9p+PwrqxUrreHI40ZI6bS/PqrqJYUE+PY\n882aJabHBQeLIj4DrXi9O0N9vfjC6ei/B0e6/34c79QJACBLBxiVChg3Dli4UKzL699fjmc1qPm0\nsjTz2WljpM8AS6aW1deLz47oaPPHmlNdLS6AREWJIhKAuBBizWfNhAli3MYyRFKmxgOyjO7/G1hq\n3DjxImDWQefCBdFAVFJaykDGHU2eLP4tb7vN/Os7KUn0tbAkOHn4YVmG5/K+/VZ8YAwZIt7U/f3F\nFURLKRHIhIXhYt4ZFJbqqgr5evth3FAr/82kq3bXF4X6+frj1r73YPXOJQ2HbDv4I/ae2IqicgP9\nM67LL7mCb3/5BD/tWoZBPUbi5tTRaB0Wa91Y3NT5K4YDGQDQQosNwzvjbIdwTM3PQkRIshNH5iQR\nEcCDD4r/NzU1jj1XXh6wYIH4Yrxmjfg/60p27QJuvVV8Ud+xQ5kxvPUWsH27+AI8fLhzz71vnwji\n0tKaB3Ljx+sCmTlzHFYUQdb+MZGRYpyWrCFu106+SpXSOs3GDTE1GjGNsqzMsjU4//636ful55Yr\n66aglhPILFyo9AhcT0aTD+CSEvs7m5PzDRwoAhlLdO4sOo2TUFcnpmqpVLZ/CVOrRUO861cwAQA/\n/ij+TZ58UiyGlot0FS08HAdO6X9R6pbYF0H+Vl7xHzwYeOopsWj7uiE9b8fm/asappTV1lWjts6y\ngg9VtZXYemA1th1cg16db0SfrjfDz8cPXl7e8FJ56W39fQMQ16otvLy8rRuzi2laLa5X5xtx9Nxe\nva7i57pEYe761zDljr+iW8c+zh6iTk6OaNjYsSOQLGNQ9dln8j2XKdnZwA03iP9rrtj0ulMn8T5y\n5Ii4qKREBbP0dDG1bsoU55/7v/8VhU4WL25+IWzIEJGtiIoS72MOWE9YUl6InIKLDT+rVF64oX2q\n7U/4l78ATz9tusKnI/j7i4tqNTXiJv387LPyPL9WK/rMAJbPPHBhLSeQoeaCgsRV/A0bxM/GFoWR\na3vpJWDFCqCr4e7tZEJennhTj4uzPcXeowdw4oT+vmnTxHzwu+4CEhPtH6fkekZGExaKA2d26t3V\np+vN1j/f7bfrFmtf5+8XiGF9xmLtri+NPkylUiHx7DWEl1bjSGo81F76X9i0Wg0On92Nw2dNly1t\nG9MJT93zCkICw6wfuwuoqC7TW6OkUnnhwZHP4VKvM/hiw7t6vXgqaivw0Y+v48mxLzunOZ8hW7eK\nL7gTJzabImeNc9nHse3gGlwtykZYcCRahUajVViM7hYajfCQ1vCWO0jt00dU2nTVz6q4OJGJuHpV\nTNfs2NH5Y5CjIaatpIxEhw7N7/PxATIzHTquptPK2sd2QXCAHRkHR1UfM0elElmZwkKROfH3l/f5\nP/xQ3Pz8gBkz5H1uBXheIFNYKF4EoaEeMffPoYYNE7cRI4AtW6wrN0uuQ/qwvHhRpJ+dffXInUkV\n2aSSrXJp314EMpcuyRvI9OoFjB+Pcx0iUHpJN2/b3zcA3Tv2le00N/cajV8P/YTSSt05fH38kNIh\nDT0SB6C7TyxCn+sJACgJ88fOW5Ox8/aeBgsDmJJ1NROLf5qLp8a9Ah9vhb402OHClVN6P8e3bo9A\n/yDc0D4Vf5s0H0s3vItTlw833K/VarBs0wK8+OB/EaxE8CZNgzRX9ciIgpI8rP5tCQ6d2dWwL7fw\nssFjvVRe6NFpAMYPfQStwmRYNyBRqUxfza+vF+t1CguBe++1/Txr1gDz54uMpVTQwBK9egGbN+sy\nX87mCoGM1BS4KTnHJGWRN25smNYr67QypTUOZOTo+dTYQw+J3khPP+2amU0red43/YkTxQt73bpm\nVxrJiNGjxZSj2JYxp93jhISIlH6bNgxkrOXIQGbXrv9n77zDoji3MP7uLr0qHUQpgigiRcXea+ya\n2KKJMcaY3JjkmqIpJjHJTS+mmcQ0Y4ndGHusWAEVRECaqBQRlC69LLt7/zgMu7N1toLI73l4Vqfs\nDOzszHe+c877Gq5mmmHpUmDpUiRErWct7uM/EBbmhpu1s7a0wQuz3sfpqwdgLjBHL9++COoWBguz\n5mNcvEiv/fvDsaYGU/YlYcJLXyHeHTh79SCrvEMTN/NTsfv0r5g/9gXdm3JNRUEBDZJ9fIDBg5Et\nF8j4eUrLtRxsO+E/s9bgZNzfOHxxOyTNym6VNeXYdfoXLJ70uul/X6ZpWct+rrqGWpyI/xtnrh5A\nk0jIaR+xRIzkWxeRV3gTLzz6AdzVmbMaADGTBcyMhuuPf2LCqVswnzWLpOR14e+/KYM1bpx2+4WF\nUSCTlETy0KbGQIGMWUkJrPLyaFzApadSJJIaKBtbIEYsphI6sbhFJUwsESNDZtIAQOtlPg3BCy9Q\nb44xAlJGKKOt32850v4CGRWuyx2ogVHF6ODBxVC1s/J88AFlen7+2fDp7baAqkDmxReBEydIynXU\nKO3fl5mRNHQgA0AkakLizRjWsr49DN/07OXig4XjX1K+srGR+gH8/Oh3TU+H+dHjGPzFFxgUPBY3\n7lzDlevnUVV7H2KxCCKJCBKxGCKJGGKxCPerS1mSxbGpJ+Dh3BWjI1ph4KcN8fE0WTZ1KnDwoEKj\nv58Xu++Ez+NjwoA5EIoacezy7pblV29Eo4//APTvOdIkp90CE8hwzMiIxSJcSovCoditrDI5rQ5Z\nXYJvd7+FF2auQVe37jq9hzokEgmuZV3GkYvbUcCo6U0MQpmTDZ4sKtKt71MkAg4don/PmKHdvqGh\nlDEScgv4DI6BAhnPP/+E+65dJAMs59WilIIC+rt5eBj/WVFVRUGMvX1LD+KdoizUyBj4WlnYwMc9\n0LjnIUtlJWU8O3WSNuvrg769rFVVwK5ddB0+/7zi+nYSxADtMZBRp+UdF0dqHmPGUK1tBx20FdLT\ngffeI+O8oCDjHeeHH6hh9tlnKQuniZ076dxCQ4EVK4x3Xq1F166kaCjT7A6AtPczM6nWXReMGMhk\n3rnGemBbW9rq7lytKyNGALdu0b9PnybfriNHgC++AI/HQ4+uoejRNVTl7tV1lfh650qUVkgN9/ad\n3wi3Tl7o7aeFYpypkZkoE4makHsvk7Xa37OX0t0mDpiL1JwruFOU1bJs95lf0b1Lb3S2N3DZiDq0\nCGSyCjKw+8wvyC/OVrq+m1sAJg2aD4lEgrKqYpRVFqEsIxFld26i1NkWNRKpeEZNXSW+//sdPDf9\nHQR00cG3gml4lkEikSA99yqOxG7D7aKbCrvERXZF+LXT6OO5QPvjxcSQUWxAAAl5qEEikSD51iVc\nSjsFB9tOGPXIFHiUl7feQPHPP+nc9cyK1DMlsSkp6jdkkEiABQtMM4lcWkqvMo3qybcusjbp0TUU\nAoEBhrgSCQUpDg7qP9OdO4Fly8jL8Pff9T+uPIcPU6ZvyhRuWcK6OsrgOznRaztutWh/NSjqMjLb\nt1OUe/Soac+pgw408eijJAOsTS02QAPl9eup3IUL27aRmSJXx+Zm40W8845RBuWtzrRpJAe6ZAl7\nOVODz6WpOCeHFACZew9AEyXPPAOMNPyM+5Xr7M86LGCwfv0le/YA//ufNDulLUOH0sxoTo50gKEB\nO2sHLJv2DqwspBNOEokYG49+jbulbfg6k3m+5JfkoLFJOlh3sOkMJwfl3iFmAnM8OeEV1udU11CD\nbSd/MK2ZaHAwDYI09G0l3ojB93+vVhrEONo64YkJ/8Wr879Ab7/+CPGPxIiwyZg5fDGW1Pnj9Q8P\n4+MzjRjcezxrv4bGOvz8zwdIyYrT7pzj42lQLmNynZl3Dd/tfhvr93+oNIhh2Jl5UOu+LQDUPwBQ\nNkbN4LW0shC/HPgIfxz+DCnZcYhJOYHPdryKnad/QWWNbhksvRkyhO5regYUtYHN2YzkZG47dOtG\nimW//qp5223bgE8/1T1rJWcMKWrOHMpisAkRJyfKsmh6FtTV0ashDDGVce4c9WxxNRR1caHgpawM\nmDSJvGnaKe0vkGEyMsq+xIyDaWqq6c6nrXLlCpmKMYaYHbQuixfTq7ZSiHFxJBEp85BXC9Psy1X6\ncto0Cq5qaqjcylQ+TKdPk5u2iSkqL0Bm3jU0OTaXBnARwHjzTZq1PXBAumzwYJqVW6DDbLAahE2N\nSL51ibWsny5qZbKsW0fZQHk5dq5YWJBnRmkp4OzMbZ/CQnj+tReLx74MHk/6GGporMOvBz5GdV0b\nVaWSCWQUyso8g9T2vHg6d8W0IWxJ3Ou3k3Ah2YQTaytXUsnkmDEqN4nPOIuN/34FsVjEWm4usMDE\nAXPxzqIfMaDXaPB5SoYPjz4KAOAfPYb5g57C2H6zWKuFokb8fuhTxGWc5X7Oa9cCxcWou5ePS2mn\n8N2e1Vi3910F2WsA4IHHup4qRXX459wG7sdiiI6mVxVlZSJRE07G78UnW15CWs4V1jqxRIzoa0fx\nv03P49jl3WgUGtlbx0jUMRn71FQSUDAkK1cCb7+t++QJM2HSfL9Jz0lARU1Zy2oLcytEBA7V9ywJ\npkysrEz9dszYU5UBpb4wx+cq1MHnSz+3kycpy9hOaX+BjL09XXjKouKOQEbKrl3AU09ROrSD1qdf\ns+KUto2pd+/SK9dmdWZgrk2z7/ff03fq4EHKXhibigoaaC1bBly7ZvzjNROXcRYfb16OdXvfxc9d\nSkhSmEsgY0JDzPRNa1HfKDVns7fphEDvEP3eVM4UUyfCwrSriw8PB1asQPDhWMwazvabKK0sxB+H\nPuPcVG5SmEDGzk6x0d9LhS/LhQuU8Tp9GiMjpiJA7vPaf2EjCsvzjXG2WnMx9RS2HPtWIUvUr8dw\nrF70I6YMXgBLCzUDNW9v8rWqqwPv6FHMGPYUpg1dxNpELBFjy7FvcC7piMbzEWbfQnLaWWx4OhKr\nu93G1hM/4Fa+8ud3WMBgvLHwW0yIZCuVXU4/jWtZlzUei8WFCzQDPniwwqrsuxn4cvtrOBC9GcKm\nRiU7Ew3CehyO3Yr/bX4Bl9JOKQSGbR2xnR0avLyoHy4zU/MO2sCUveUpV7zTyIgRVPK8bh0A4GLa\nSdbqvj2GwUrddaoNzOSipkDG2BkZpixUm8nOKVPodeNGtZMXDzrtr2hO3s9BluBges3IoKY0XdVM\n2gPM7GvPnlQydOwYDWimTWvd83pY8fam1zt31G8nDzOjZWVFBmQNDer9IXQZdHt5URnAunWmMUyV\n/V4mJAB9+hj9kBU1Zdh9+pcWE8Mb5tW40rcLBpgqkKmro3I/dXKtjY1IOLcH6OvdsigicIj+hpJM\nIMMExcbm3Dlp0BQdjZErVuBeWR5iUo63bHKrIA07o9ZjwbgX25aSWVAQSfqGhiL77inWKlnFMhZn\nzlDG6+23wR89Gk+MfxmfbV3REpAKmxrx17FvsWLuZ4b3XdGC6GvHsDPqZ9YyHo+PBeNexMBgLQZB\njz1GqnZ//w3Mno3x/R+FjaUtdkWtZ5mE7jnzK84lHoKjnTMcbDvD0daJfuycYG5mgZSsOCReO4W6\npyNpB7HyrEBv3/6YPPjxFiEBt85euHbrEks5b2fUz+juFQwbK44N8AIBMJyd6aytr8aB6M2s61QW\nP8+eqK6tQHEF+3tUUV2KrSd+wOmrBzF39PPwVxXwtkHuDxsGd7HY4Jl4cVdv8C9d0j2QsbZuMXSt\nrClXKFcc3FtLpTl1MIFDebn67dT1Z+tCbCwp8A4aRH5/2mZkAJqwNkC/VFvHoBmZc+fOYfr06fD2\n9gafz8emTZsUtnn//ffRpUsX2NjYYPTo0UiTCzwaGhrw0ksvwdXVFXZ2dpgxYwby8w00W+XgQB9o\nQ4O0UfVhRTaQSUmh2e+ffmrdc3qY6dIsTXrnjnYPDWbw2b07zbrs3k1BujIaG2nAbGam/c32+eeB\nq1ep/trY2NkBH39M/05MVL+tgdh3fiMr0wEAx5dNhPiddzTvbIhA5r//pb6Fq1dVbtJQVoyU3h6s\nZTqZYMqjS0YmKYkGIWId+jvef1/674IC8Hg8zBm1TCFTcSmNsgNllcVoMzz2GLB7N8qnjGOprpkJ\nzOHtqkI8gylzbs7mODm44bGRS1mb5BbewIm4PUY5ZS6cuXpQIYjh8/hYNPEV7YIYQNrnx8jjAhja\nZyKemvQaBHz23GnR/YJmhbtziErYh3/Ob8DGf7/Cbwc/QWzqCdTxVV9fPbqG4pW5n+G5Ge+w1NDM\nBOZYMP4lVulbZU059p77Q7vfoxmJRIKEzAv4ePNypUGMjZU9Hh+7HP+d8wneevJ7PDZyqdKAqaAk\nB+v2vouySh0FRFqBvJUr6ZnSWweBBjkKy/MRlbAP3//9Dl4d2oSVn01Gcr7+9/fL6adZGUQPp67w\n9TCgYA4TOGjKyNjZ0XNcR48mBWJj6V7J9HTL9QVxwsam3QcxgIEzMjU1NQgNDcVTTz2FRYsWKcyk\nff7551i7di02bdqEHj164MMPP8T48eNx/fp12DVLBa5YsQIHDhzAjh074OTkhFdffRVTp07FlStX\nwDeEP8bLL9NAz14Pt9cHncZGCuR4PFJlYWadOwwxWw97e7phaetnwgQy/v6ULbl7l1TJlBmSSSSU\nVamv115Rh883rfxyeLMKl5qBvd6UlQF79yLT3RJXshTFEopqS3ClNA2Rrhoa9pnvDde+I2UwWai9\ne4EI5d4HKZmxaLSU3rI727nA19MAD2wmy8Y1kJFIaJawvp6kXrVtKv75Z2DNGmDhwpbAWCAwwzOT\nV+HrnatQUiE9j/jrZ5F4MwYjwqZgfORj+rl0GxD5/phubgEwN1MhuCAXyADAgF6jcS3rEqvf6ejl\nXQj27Ydu7gEGP191nIjfi4PRm1nLBHwzLJ70OsICBmn/hn5+1JAcHs7ytKJyHxv8cfgztSVZ6nBy\ncEP/oBHoFzQCns4qTBdBju7jIx9jSV5fTj+NiMChWjWBl1cVY/fpX5GSrVygYECv0ZgxbDHsbei7\nzxfwMTJ8KiKdgnHixWk4O8IfTebSLFuTSIj46+cUyt8Mxo0bwHPPUeDxww/GOYYqfvyRBvLTpgEC\nAUSiJtwqSENKdjxSs+NRfF+mH4YHNFiZY5M4E2+U58NNR48hiUSCi6nssrJBvccZNovr5EQBgaZm\n+TVr6MdQML05jMjAW2+RFYKPj+GO0U4waCAzadIkTJo0CQCwmGlebkYikeDbb7/FW2+9hVmzqAFw\n06ZNcHNzw7Zt27Bs2TJUVFRgw4YN2LhxI8aOHQsA2LJlC3x8fHDy5ElMmDBB/5Pkoofe3rl1i4I5\nf38qSZL/wnTQOkycqP0+U6bQjHqPHlSWdPcukJ2tPJCxtASWL9f7NE0CM5hPS6OBszHKi9LT0fT8\nMuxaMxlwUH4rPHZ5F/r1GKa+fKt7d9Q4OeDvq1tRfL4Yof4DMSz0EVgnppBowZAhVNOtjn79vwQM\negAAIABJREFUIAHAu6lagSnhNnswFdFjmPKGa22JiKDmW3kJalVUVNBD3d5eMYgpKaHSseamb6UE\nBQE7digstrV2wHPT38HanatQJ5MdaxIJEZWwD7GpJzC+/2MYET5FaszZSij6x6gJKJUEMjweD/PG\nvIDsggxU1VEgLBaL8OuBj7F02lvw9ehh8HNGXR2Z4Lm5AcOGQSKR4Oilnfj3EvuzMBOY45kpb+in\n+sT0/MkR7NsXLz76IXaf+ZUlRa0OWyt79O0xHP2CRmgUVJBlQuRcJN+6xFLB23HqJ7z1xPcaS8zE\nEjEuJB/FwejNaBAqDmDdOnlh7pj/oEdX5WWvNt38MeNSCYZfyMbfP7+Ka/ekEsbJNy8aL5ApLqZ7\nDtOvYSoqKkgMxsYGTRXlOHzhL0RfO6aQ5ZZHyJdg24l1eHn2RzqVyGYVpKFIJkAS8M0Q2XOU1u+j\nlvXruSmxGRpmsr2qWXVv3jzTn8MDgsl6ZLKzs1FYWMgKRqysrDBixAjExMRg2bJluHLlCoRCIWsb\nb29v9OrVCzExMYYJZDqg+tJXX5V+UbSRmu3A8Fy8SKplEyZQY702vCRjWOjnR+no7GyjyP6aFA8P\nysb06mU8P4b8fESNDkCRXBDD4/FbXNiLyvNx9UY0+gWpDkTE589hw941uHGTlI5y72XiZPzfGF7l\niJEfbYD9i6+oDGSKygsQl3EGCeIYVHw+BZE38jG9oRbWluzSv9qGaqSVsYMcg5lghoYCX3zBfXsm\nc+PBLnODWEyfV0kJNQcHam9G5+7kjeWPfoi/jn+He2Xs+vm6hhociN6M80lHMHnw44jsOUr//iAd\nUWj0V9UfAygNZADA3sYR88ctx28HP2lZVllbju/3rMbj45YbfkCWn09lX35+QFYWziYeUghizM0s\nsGzaagR1CzPssWXw8+yJlfO/Rm19FSpqylBRU46K6rLmf5ehsqYM1XWVcHH0QETgUPTsFq6TH4i5\nmTkWjn8Za3euaik9qqgpwz/nNmDhBBUGwocP466/O3Zc26MQrAKUORzf/zGM7z9bdQaOISwMTidO\nYK5Zb6QgtaU/6HbRTZRVFsPJwVXr30kjBjLD1Jpc6kcS+XTDpqNrkSTn6aKOrLvpOJd0BKMitO/P\njZXLxvTxH9CSHTMYhqgE0oWOCWbOmCyQudf88HN3d2ctd3NzQ0Fzw/K9e/cgEAjgLCfh6e7ujkI1\nvhfxzbraPKEQgooKiG1sIDaWckR74fHH6TU+HoKqKkQAaCorQyJXjfJ2TrwJ/w6do6LQ/fp1lHXp\ngiw9jtvF0hKeAApiYlAQoqeSlQb41dWw37geyWP7wdEnBJ1s9H8o2yUkoFquHMWYqmWWcedxbAJ7\n5jvQPQJiiQi3iqTeCfvOboa40lrlTHBq/kXcuMM+z7rGWhy3rMXpNePRtyAF3tFRsLWkB1N07Hnk\nlKQhq/gaiqtkxB0szRAd4oSkP57DkKCZ8HCUlhDcLEyCSCLtfbK36ozC2+UoyjP999X+yhUEAaiy\ns8N1uevVr29fOB8/jtvr16OIucfowLieT+JWURISb59DXSPbB6S8ugRbT/yAo7F7MLLnbNhZGnjg\nooEmkRB5Rewey4rCesSXK/8sLJua4PL006jr3h1lCt9vPnp49EPmPamEb5NIiC3HvkVCyiVE+KiQ\nOVaCpnuWTWoqggHUWFoiMfY8Dl7ZwlpvxrfAmJ7zUFUkRHyRaa8rMzjCme8IZ3s/QKZ6sK4UuFqq\nWx+F/eXLsLxzByEhfZFcLP19LqVHob66CTaW9uDz+OCBDx6PDzNhE8x/+wanRvlDZKb4N3e198bg\ngKnoZOaCpMQkjcf3dnODB4Dq42fgMrAL67t++Mxu9PLimAHVgk6JiQgAUN7UhFt6PsNqGypxv7YY\nsZcaYS6wULut4/nz6M4DNk7opjKI4fP4cHf0gXfnQOSX30LBfel3aP+FTZBUW8Lemlv/R8Crr0Jc\nfBdXnmeb7jpb+Jj02W1M7PLz0RNAdUEBMtrJ78QQqMMklzrahGqZoeoZbTIy0GvJElSHhCDjzz8N\n8p4PAyIbG5RMm4amh7lvqBUxLykBAAhd9QsGSidORHVICOp6GKEsRQaRuAnZh9YhNqQBTWXR4JfH\nYmTQbHR11v24NhkZ6Pncc6jp1QspG/5AblkG6ptq0bVzIOeHm7acsbsLoYX0FmhpZo0In9FobKpH\nVtG1lhnUiroS5Jamw9clWOE9ymoKcTX3tMpjCC3McMkXiLuyDn6ufSAUNeBO2Q2IJaqlWKuFVTie\nsgXBXgMR4TMaAr4ZckrYkrO+Lr1bTc3LrNnDQajEM6Zi6FA4Hz8Ox5gYvQIZPo+PQPcI+LmEIP3u\nZaTciYFQxPbjKK2+iyNJf2Bkz9lwd1DdL2FIHC9cwN3GIkgspc3F9ladYW2hega8wdcX+S+8oHL9\nAP+JMBdYIDU/lrU8NT8W92uLMbzHLIOU0pk1l6iI7O2RXnAJQpG0T8VcYIFxwQvg6uCtavcHDu8f\nf4RtWhoG/f4rcq1dUFFX0rIuKU+FgfA4xf4kc4EF+vqMRQ+Pvlp952qb78PWN2/CZ/IsViBzuzTD\nKIGMoLmkTKyHl0lJVQFS8y/idmk6JJDAkm+BiSUu6OoZiqr+yssNze8WYPfsUCT5sY9rYWaNrk6B\n8O4cCM9O/i3XsY9zT+y/+kvLd1okbkLMzUOYEPIkp7+xVW4u4r35EEF6H7W1dIBnJ/VGrw8SDV5e\nKFiyBA1ddOsfepgwWSDj0VyGUFhYCG9v6c2ysLCwZZ2HhwdEIhFKS0tZWZl79+5hhJoa8/7Ml6u5\n6dbO1VW6rANuNJv5eWjYrL3DzOaY9PrZtQsA4B4eDnd9jmuCc87MS8auqA0o6toEgMp6xBIxYrIO\n4rXIL+DhpKNCytq1AID6qWNxIWcvcgvJqPVK9kn09o/EqPBpCPQOMdjg/VrWZdzoxJZzfXTUMxjc\nm+4zd6qvIT7zfMu6GyXxeHTiE6zZcWFTI77a8TorKLG2sAGfL1BwExdLxLhVpHkWV5a0gksoqy/A\nrBFLcK8ih7Vu6qi5apudjcrt20CfPnAaOBBO8tecjw/w/vtwTEhA/169qKxKLAZWrQKeeYZKz+QR\nCgFz1WU6gzAYNXVP43jcHpxLPgKRSPq51QtrcTJ1G+aOfg6DQ8arfA+DsXgxsj0bganSoLanb5je\n94sBkQMQl3EG20/+yPLPyS+/iTM3duDZaW/DtZNy6XPO96ws6kkx8++GzKIE1qpHBs3H+P4z9fgN\nlCCRUJlrfr6ClLFJCAwE0tIQ0skJ9kPfwDe73lDwx9FEiF8k5ox+Dp3tXbQ/vrU1cOwYnEaOxJRR\ncxC/UVoGVVSZhx69AuBga2Dvqcvkl+Ps4wNnLa5JsUSM1Ox4RCXsV/DpaRA34oBTAYbcLcOssMWw\nNLdirZdIJNh/7EdED2UHEU72rvjvnE/Q2V75BJ1FJwm2nZQKEhRW3ka9RTGGh03WfMLV1bg4iF11\nMDx8EgZEGj445ExeHlUTuLuTMqghmEx/i/YTnhEVBhaWMlnxn5+fHzw8PHD8uFS+sL6+HhcuXMCQ\nZuWafv36wdzcnLXNnTt3kJGR0bKNWmRcl9Vy9CiZQco6cXfQQWvBeMEUFgKRkcZr6jtyhFT7jmrv\nJF5Zcx+bj32DdXvfYzVXMjQ01uH3g5+irqFGyd4ayM0Fdu1CYngXfOFb0hLEAIAEEqRkXca6ve/i\n822vIDb1pErFo9r6amQVZCA29SRiUk6g+L5yX5RGYQP+PvMba5mfZ0+WzOzEgfPAE0tlsO+W3kbS\nTXbJxMHoLaxGYgCYP2453l/yG2aNWAJHW26ZpO43SzA/3w6jIqYrrLtXloef933AGoB5OndrvSAG\noEb+5GTgo48U17m6kmhAYyMQFUXLdu8Gvv4amDSJLQ1eX0/y787OqiXDm7G1dsCsEUvwzqIfEeIX\nyVonEjdh+6kf8ffZ3yEytulgTQ2yfdmfq7+XkuBMByJ7jsLLsz+Ggy1bvvVeWR6+3rkKCZkXUFlz\nX/cDNPtgnO1uyWrCtrWyx4jQSbq/ryqSk0kWftEizdvKMn06Kdrpa7vAzGTn58PHIxATIudw3tXe\n2hFPT16JZ6e9rVsQA5ByWHQ08N57cHZ0h7erf8sqCSRIydbSpJMLM2YAJ05wFnURNjUiJuU4Ptny\nEn47+IlKs1EAiHGqx5fbX1Moqzx6eRei7NgeKw62nbH80Q9VBjEAMDB4DHr6sBUa90dvRmml6jYC\nAIBYjHxrEW53k35PeOBhUPBY9fvpQ309CSmoY8IE8oO7cUP9drpw9Sqp0XVUGinF4PLLN5o/RLFY\njNzcXCQmJsLZ2Rldu3bFihUr8Mknn6Bnz54IDAzERx99BHt7eyxYsAAA4OjoiGeeeQarVq2Cm5tb\ni/xyWFgYxo3jYHDEBDKa+mOSkoDNm6khbrri4KGDDkwKI6Hs4wN8+y335r6YGBIKGD6cAiAu2//w\nAw02H3mE0yHEEjFiU07gQPRmjUFK0f0CbD72DZ6d9rZWalrC79Zi38xgnB/uDwhVq+0UlORg+8l1\nOBi9BUP7TIC9TSfcK7uDwuafylpFw7IuLr4IDxyC8IAhcHeiTPDxuN0ok/EA4fP4mDv6edY5uzt5\no29aCa6ESB/Exy7vQljAIPB5fGTkJuJM4kHWsQb0Go2IwKEAgNER0zGszyTEffISTjrcRwmPrXzk\n6uiJyF6jELluD5z/igZ+WQSMWIIQv0hsPfE9y6NEHoN4x8izfz8JRcyfL5W+1pUnnyQBAW9vClAY\n35i33mKbnVpZUXNyVRXN3Adolh12dnDH0mlv4ejFnTh6eSdr3dnEQ7hXmofFk183mkyzpKYG2X7s\nQMbPEBLYzfh69MDr87/C7wc/xe0iqbhDbX0VNv77FQDAztoRXi4+8HLxRRcXH9yvruXWo+btjbqZ\n03DGjV2iN7rvDFgaygVdlpAQEpLJyaEsnjIlRXnKyoDDh+k6+eUX/Y7PSNk3TxRNGjQfrp29kH03\nA2JxE0RiMcRiEcRiEUQSEcTnz0NSXIRuwyZj2PxXDX4NhQUMwp1iqVJb0s2LGBJiYAGjLl2kAZwG\nUrLisP3kuhbVPC4Uledj7c43MHXIQozuOwNnrh7Evxe3s7axtbLH8lkfqswgMvBOn8bjV2vxiYsF\nGsQ0OdUorMeOkz/hhVnvq86+37+P2IHsaymoWxicHNw4/x5akZtLiqDe3uoNPBmlOD3K+lSSlkbK\naVVVZHzdAQuDBjJxcXEYM4ZmNXk8HtasWYM1a9Zg8eLF2LBhA1atWoW6ujosX74c5eXlGDRoEI4f\nPw5bmQzKt99+CzMzM8ybNw91dXUYN24c/vrrL24lJYyzqqaMDDPoi1OuDd+uuXYN2LqVVJQmc0jh\ndmB8du4kI0wXF+CVV6SmmJqu+SNHyDjygw+4BTJaGjeWVhRi07G1yJFTaGIY2nUQGv7Zjfj+0nKy\n1Ox4HL24E5MHc+uPKMpNx0bza7gz3F9hnYNtZ1TWKAYn1XUVLH8IdeSX5CC/JAeHY7fBw6krevv1\nw5mrh1jbjAifii6uvgr7Tky8j4RgF0j49DkUlOTg2q3LCOgSjK0n2OpyTo18PDbyWdYyczNzDHlv\nPQaKRUi8EY0zcf/CysIWk4bNJhlZADjerJ7UrDLXo2sfvLnwW+w9+wcupUcp/Z0MplYmy/79NNsX\nEKB/ICM7G7xlC5nv+voqfwCHhNDMe2oqp0AGoMBz8uDH4enSDX8d/46Vobuel4Svd6zEs9NWw9PZ\n8EZwRdYS1NpKG5+tLGx0L6dUQSc7Z7w852NsO7EOCTLljQzVdRXIzEtGZp5UkELAN0O9xWKMDJ+q\n+o2nTME51xrUxW5rWWRjaYfhoUZ6DggENMly6BBw9iwFuJo4dYpKEUeM0F95Sy6Q4fF4iOw5EpE9\nVSg6xlQCmeeANxYARgiEQ7sPxmGZv31mXjJqG6phY2lihTGQAuCmY2vR0Kh84iioaxi87YNhZW6D\nuNx/WVl4kbgJ+y9sQlzGWRSU5LD2s7KwwQuz3uf23Tt2DJ2/+AIzP3sZO61yWxZfz0tCbOoJlUGe\nsLgQ8f3YvVxGLStlDCjLFZ9FLJjxpzGEpphjG8pss51h0EBm1KhREGtwemaCG1VYWFjg+++/x/fa\nytACdON0c9PsfMpo3CclAQ0NpjX6a22io4HPPweKijoCmbaCiwv9ACSJXVVFQYemmxZTkuapfuar\nBS0CmYqaMvzw9zuszAWDl4sv5o15Hn7O/hAKglBUehK3q6RlIEcv74S3mx9Cu6s307ty/Rx2nPoJ\nDV4OrOUCvhlmDHsKI8OnImvlszhTmozkMC9I9GyPuVeWpyDp62jrhEkD5yvd3kNshYjEfCT0lT40\nj17eCRdHD1TUSF2eeWIJniz3VJBMlv4+AvQLGgFJFa3392qW6k1Pp++huzv5ADVjbWmLhRNeRoj/\nAOyI+gk1ddIMnY+ZE1yrRYCBS+tbrqG7ysvxdEIopCAbAN57D7BQonwUEgIcOwakpFBZjBZEBA6F\ni6Mnfj/4CcqrpY3cJRX3sHbXKgwOHofwwKHw9exhGL8dsRjZHuzP2Nejh2YJaIkE+PRTqhj46CNO\ncuIWZpZ46pFX4eXcDYdit2rcXiRuwt9nf4edtSP6BSnP2NU11OJ0ArucenTf6SqvW4MwahQFMmfO\ncAtkmLJyQ1gthITQMTV5ODEoK5U0IB5O3nDr3AVF5XSvFImbkJodb3iZbQ7EXz+nEMTw+QL07TEM\nY/rOgLerf0vv1coFa/HP23MR483+DskHMRZmlnh+xnvo6tad20k0O84Pya7H1QmhrMD8n/N/opdP\nhNLStGRRIWsywdbKHiF+RuyNsbOjsWVNDZXMKruPAcbNyJQ1P280jW0fUlpJINtILF5MfQZffaV+\nO0dHMmVrbKQ63oeJjGZt/CC5cogzZ4DvvqMUZgetByOEceeO+u0A6aBTNpD5+Wdg8GBg+3bF7Tk6\n0Nc11GD9vg8VghgLcyvMHL4YKx//mnwzLCxgPmMWnpnzPuyt2e+55di3CkEDQKVq6blX8fuhz7Dp\n6FoFszlnR3e8MvczjIqYBh6Ph+5BA/HMxji8l2SNMX1nwNpC9aBLwDeDp3M3hAcOQaB3H/A4DF5n\njViieiDn6IiJxzMhO+zML85G0k22utT4k5nobsMxmJTl7Fl6HTlScXArkSAsYBDeWvg9wgOGgMfj\nw65Rgrmf7QUSEhTfS18YTxjGI8YQXL1K2ZbAQNWD2N696TUlRfl6DXR188dr87+Cvye7T6WhsQ5n\nEg/i291vYs2GZ/H32d+RVZCudbM3i6YmZI9nD5jU+scw8HjAhx8Cn3yilVEhj8fDhAFz8MrczzGo\n9zh0cwvQKIO79cT3yLmXqXTd+eQjqG2obvm/taUtRoRN4Xw+OsH4WTHXujokEmkgo4s5sDyRkVRC\nvnSp/u9lAHg8HsLkJnfk++5MgUQiQUzKcday8IAhWLN4PRZNfIXVywMAluZWmB82F89U+cDGTPkg\n3UxgjmenvS2dpOFCcyDDy7uDx8cth4WMiEBDYx02HV2L1Ox41jULALHpp1j/j+w1WrOnjz7weJqz\nMhKJNCNjyEBm/XrgzTel47aOjIxS2oT8cqswYABw/TqVl3Epy2kvMF+InnI3nC1bgA0bgN9+A4IV\nZWY7MBHe3jRTf+cO0Ee5a3QLTEaGKaEAKJC/eBEYM0Zxew4ZGWGTEH8c+gz5crNtwb79MHf080pN\n3Drbu+LpKauwbu97EDc3WzcI6/H7wU/x2vwvYW1pi7LKIlxMO4VLaVEq+z/CA4fg8bHLYW0pUxoa\nQc2gzpeTMfPP7Zg0cD4up5/GrYI0CPhmcHfyhoeTNzycusLZ0QMCmdnxqtoKXMu6hMQbMcjMS1YY\nxAZ1C2vpaVHKhg3wBBB2bQcSs5QPOLrVm2PS0evAJB1SJE5OwNChgGz/X3Q0lWb17g1s3QoH205Y\nMmUVahuqYTlhMgR3KqRGaYaEayAjEgEXLlDwrEnme8AAUsq6c0e1ig/jd6RHJsjBthOWP/ohdp/5\nBRflDPIAoKK6FGcTD+Fs4iE42johLGAwBgaPRVc3xXJGtVhYICvIHSiTTjJwCmQAmtVtaKBZXS1L\nT/w8g1r6cMRiEYor7qGgJBcFJTkoKMlBanZ8y7XdJBLit4Of4LV5X7K+qw2NdTidsJ/1vqPCp7G/\na8YgPJzKy/r316hOh7w8uqe5uOhf3thWkEiAffuodHL1aoQFDMaJ+L9bVqfnJqBBWK+gBGZM8opu\nIb84u+X/PB4fs0Y8rbYxH088gTA8gW5VJfjr+Hcs3yw+X4CnJ6/U3kS1OZDBnTtwdnDH9KGLsOfM\nry2rswrS8cuBj8ADD54uPujuFQwvFx9kynl2De7NoX9aX5ycqNm/rIwy6PI0NZHRrFBoOMUygPrE\nEhOl98mOQEYpD28gs3w5MHcuzV4/TKgKZDpcZNsG69bRjdCbg5+DsoyMX7NQY06O4vavvUaKUyrM\nqMQSMbae+F7hQdHbtz+WTnuLFSTIE9ClNx4dsQR7ZNTAiu4X4LdDn0LAFyDzdnKLL4s8ZgJzPDri\nGQztM1GxFy4khNL6GRlAbS0sbWwwPGwyJ4lOextHDAmZgCEhE1BTV4lrWXFIuhmL/JJseJh3wpO3\n7cG7fBkYOFD5G/j6AgAesZuvNJAxN7PAk5kCCMQSzn1HLObOpR/WSdtTyWsVW77ZxtIOqGj+bmrI\nqOkE10CmuJjKhVxcNKv4AHRtqit9DA+n93HRURmqGXMzczw+djm8Xf1xMGaLytr/ipoynEs6jHNJ\nhxHiF4lHBs5DN3duvTk19VUolAlieDw+fDw4eifZ2gKlpRTI6OEXxecL4N65C9w7d0FEICl57jyy\nAdE3pCVjVbX38evBj7Fizqewam7iP5/8L0sS3NrCBiMj1PTTGAozM+CcCs8Webp1o7/RjRut56Zu\naHg84D//oQmmhQvR1bc7Otu5tJRCCpsakZF7FWEBBhqHvPQSTdB+/bXKibCYlGOs/wf79FUfxMjQ\n2d4Fy2e9j9NXD+BE/F6Y8c0w13sM+uyKAkY0AVzUZRmYQKa5gX5Y6CO4eiNaQTlNAklL0C6Pr0eQ\naRQcXV3p2lSVUTU3B27eVL5OH5hx2ezZwPPPa/f3fYh4eAMZVYOX9kxtLanHmJkB/nKzkR2BTNuA\nq5mlRAKsWEGlO24yai3Ng29kZyvuM1O9T8T+8xsVmot93AOxePLraoMYhuGhk5FXeIvVpH7zjvqS\nIS9nHzw5cQW6uKpQyreyomCmsZECt+4c66/lsLV2wKDeYzGod7NE55dfAqtWAq++qvFe4OXii7CA\nwQolZbOGL4F7bhQNGFQN1ktLSSlOLOamkBgcTL9zVhbN/snWRDOlgcbIyAQGkrqYfMmpPIXN0qge\nBnKcMjfXO4hh4PF4GBE2GQODxyAtJwGJN6KRmh2PxqYGpdunZMchJTuOc0AjL3rh5dyNe38JI0BT\no175Txf63qiC+J4lYj2kv2dBSQ42H12LpVPfhFAkRJRcNmZk+LRWaTLXiIODtIe1vRAaSpLIycng\n+fkhNGAQziZKBUeSbl40XCBz6RJVmagYcNc31iH+OvseP6SPdv1IfL4AY/vNwpi+M2ni6eOPgXfe\nIa8obQbaLi6kZOjtDUgk4PP4WDj+JXy76y2lCpTKGGSKbAxAwXhrGBAz9/qIiA6FXTU8vIHMg8Zn\nnwF79pCqiz4zsr//TjOg8il+5j0NbFTUgQbWrQO++AL4738pY8IVHg94+23F5UxGRlkgo4aohP04\nfZXdCOzWyQvPzXiXc9kDj8fD3DHP425ZHm4XqtbSNzezQLhPJAaFjEeAT5hmRcL4eO3S9d99Rw+e\nzZtVKxgqK8tTwyMD5uHarUstJTy9fftjaJ+JwBeP0OenCpGIGt47d+b2IDIzo4dWbCz1wsiWnVUa\nOSOjRoSlBSZjY6hAxghYmlshInAIIgKHoFHYgPTcBFy9EYOU7Dg0yvVkAdwDmmy5QIZzWRlg1EDG\nZd8+zDt7BjU/voDkRqnoRkp2HA5Eb4GDbSdUy0jsWppZmSYb8yCxcSNlQydO1F8tTZ6wMApkkpKA\nGTMQFjCYFcikZMehSSSEmcAAfR7Vzf0kKn6HhMzzrO+Ao60Tgn11Cxxb7tu3m720fHy0fQPqG5PB\nxdEDqxf9iLScK7hVkIas/DQUlOYq3d3S3Mo4Co7KaI0gBqBrElDI0HfApn0FMkVF9Nq5s/pa3AeR\nt96i1z17yCFbF2xsgCVLlK/ryMjoj0RCGRIuZWEMubmUWhcKNW/LhS5daDB87x7NynFoPLxy/Rz2\nnWcbbTnYdMZ/Zq6BnbWG2f+YGArAwsOBn3+GuZkFnpnyBr7a/pqCP0E3twAM6j0O/YKGw/q/rwEz\n3qSeLFXXJIM2QUxNDWWqAJodVBUcahnIdHH1xVOTXse5pMNw7+yFmcOXcJOEd3UlVcTycvBraiDW\nJA0P0Ix0bCwFcLKBzLx5lKUxRkaGKw9AICOLhbklwgIGIyxgMBqbGpCWfQWnEvYhV0lDPBPQ9PLp\ni2DfvvD36gUvF9+WbGT23QzW9n7aNDY/+yypsnFVGNSC2qAgdD5zBk9mWeK7vv64UyT1KolK2Adz\nM7ZAwMiwyUbz2WlzxMZSlmLkyJZ+OwUkEsrMlpfTfcHQgUxoKL0mJQEA/D17wt7aseX+WN9Yi8y8\nawj27av/sZgBr4rfIeYau8l/UO9xnLLtasltDjS4+ARxwNrSBv2Chreo79XUVyGrIB1ZBWm4lZ+O\n23evw1wowjz3wS2lk+2WjnEZJ9pXILNoEUl5HjlCLtLtiWXLyBCptlbztrrQpw/wwgvUfNzWiYmh\nWuDRozUr1JmSr78GVq4k0QSuplXaSihrQiCgrJ2nJydZ8eu3k/DXcbbUuaWFNZ6b8S4/dHjIAAAg\nAElEQVScHZU0NSrj4kUqnWqms70LXpj1AXae/hl19TXo6ROOQcHj2F4t2dm0j5uBTcwOyphU/uc/\nqrdjXMM5BjIAWmb5tYLHowf8jRuwKCxEvXxJpzL696fXTLnB9k8/aXdsY/CABTKyWJhZIjxwCMIC\nBiPjdiL+vbgDOfcUPZLScxOQnkvKcBbmVvB1D4SfV0/k6pORWbZMr3NXR21zOaDllUQsW7MbX+14\nneW/JOuzY9nQhNH91JeYtit27SKT4S+/VB3IlJRQEGNvb5zrOqy5Cb5ZIZXPF6BP94Es5bDkW7GG\nCWTUZGTyim6xTFZ54GnXKJ+cTM3n3btT4Mega0aGI7ZW9ujjPwB9/EkxUDR5EnDsGAQHnjfK8doU\n06dTL9EAI8pLtwPaSUddM1wNMeXR4H3TJlDXxG0IBg4EfvwRWLDAOO9vSAoKqOxGy/Ipo7NyJb2+\n9BL3fbTMDHBixAjqedDQMFtRU4Y/Dn8OkbipZZmAb4alU97krugk17DJ0MXVF6/O/RyrF63DYyOX\nKhpOMp+dn4reGF3ZsYNev/tOvToUl7/78ePUS6ZrBpSheabSggkC8vIoU3TihPLtZ84kpa8//tDv\nuMbAxYXuFfJiIfrS0EBqfSaAx+Ohl08EXpn7Gf4zcw18PVT3BTUK65F55xqOXd6NRpE0ILC36QRn\nB46BvpGpZT6Lq1fRydYJy6atVsjCMAxPLIGtpiyrMcjKoj6KtWuVrz9zRjoINyRypphKud4coAYF\nGaeEqGdPysi98gplfwCFnpjkW5dbFB91RiJRG8jEpLDvNz19IuDkoMVEUnExTab8LVVdg0Ri8IyM\nJgQlpSSw4uxskuNxoqaGmv1LSjRvqw2TJwOrV7e/vjED074CGab+mKu85b179FBmvAzaMjr2PrRL\nGC33vXu5+a2YGi28IlqUx2QH1AMHkgqWIfuVbt2iAbnMQCI25QTqG9kZvoXjX9JORtPTkwKme/eo\nIZ8LIpE0IGfECQzB/fvAv//SYGTOHPXbPvss/agLZCQS+r7lKfrhaEVzsGfBNMqfOkWfw48/Kt/e\n0ZFKBFurLlsdzzxDGTh9gztZhEL6nUNCtPvu6IlCQOOpQehABj/PntxKC42FWEzB8LlzELq4QOjk\nRNd/Tg66uQfgiQkrFHaxaGjCmJvKhQ+MTmEhNYX/9pviuqIiyq536WK4ElsGbQMZY2BhQdUUL7zQ\n8p0O9A5heWJV11UgS650USdOn6Z7oJxpY4OwHvHX2V4+Q0K0NB1lSuSuXZNO/opE1Fu3YoVxeveU\n0RrmkGIxHZdpX5Dn7Fn1fln6UFxM7/vee4Z/73ZC+wxkuGZkXFzIiC0jg5uUaGvCDPiMlZF5kGD8\nUACpilJbgLmx7t7NfR9lpWX371MQoy5I++sv4H//k8ppayI3l0reDkgb+lOz41mbPDJwHvr3HMn1\nzAkzMxqAMP1BXCgooAGLuzv372pFBc3aqvt9GxpIonL+fM2lem+9RYMLdcdn6pNVBZQNDeSpoimT\n8PjjwA8/oJrxxpA1wmxLHD8OvPwyleaaEnNzmqgRi7lfz7py+DAda8+elkUtAc2cz/D6/K8wc/hi\nhHYfpGDyKkvPbq3sc3L2LAXDixYBEgkKli6lDF6zDHhE4BBMGbyQtcvIEivYjTSRypM8/fvTBGNG\nhuI9+2Sz98+gQYbvbeUSyDAlnMYKZJRgJjBHb3+2f528KqLW8HjAsGHAI48orErIvMCSJHew6YwQ\nv/7avb+rK5XeVVVJszBmZqRW9s03up1zTg7w+usKTf9qKS2lV1NmZI4coeMtXqx8vTHMMBnu3aPn\nvWwmrAMW7SuQYS4mrhkZMzOgb3Ndany8+m1bm9BQahY8c0a3/fPzgWnTaFbsQUc2kJH9d2tz7BgN\nkJQ8SFSSn08zgrJGV4xYgLpAZts2mqG5oVodjAUzGG8e6FTW3EeunLLYsD5anLcsKsrLVML4hmhT\nVvbttzRrq67cyt2dSsq2beP+vurQpOSXl0dmf1M1KEBNmAC8+CLqmd+3rQYycXEkFX3+vOZtDQ1j\n+Jaaqn47fRAKSR0wJ4eCy7Q01moej4du7gEY03cmlk59Ex89uxHvPvUznpjwXwwNHgevSjGs64QI\nb3DEwOCxxjtPLmzZQq9PPgnw+SieM4dEM2TuIxMiZ2POqGXwcQ/EyPCpmPzZTuoVaQ3MzaX9l2fZ\nmQEca/Y1maBlhoALTCCjbpJl2DDguefou2xCwrrLlZfdvAiJRLnXlr7I9uMAwMDgMRAIdGiRZrIy\nzf0+elNZSb2lf/3FbfvaWtrH3Fw37y5dYSYpmWyQPExJn5Zmt5xojQzUA0b7avZ3cqILXZsemchI\nmlW9fLltCgTk5ZHqyuDB0puILqSmAocO0U1g9WrDnV9r0FYDmf79pY3aXLG3l0osMsg4HqtEmRmm\nOpi/U/PNPy3nCmt1N7cAONjq6Br8yy/SWXUu9O1LwQzXUjRA2qibmKjduQmFwM6dVGPcq5d2+2oK\nZJi/qRYlFeb37lG5mqOjtAmYCzdu0AAwONh4pmhMozNzbZmSkBCaBEhR7zukF5s2UYmllRVJl2u4\nHng8Hlw7ecK1kycGZNwH3jtIz5iLFwEzLTMHMTFU8jNkiP7Pmdpaadb3ySdVKhrxeDzO5rEmYeRI\n6gs7e1ZqBCuRUCYQME4g4+1NQYq6e9O0afRjYnr5RMDczKJFjKG8ugR5Rbc4G7RyJb84R0Glb3DI\neN3eLDSUPq/kZFLh0xfZSTCJRHM5rY0NXe+3bpGwjalgJgjKlfjbvPkmTbQBximvY47ZWcfn80NA\n+8rIJCZSs5U2BmuMGkRcnHHOSV+OHKF6/1Wr9HsfpmRDrkk3LuMMPv3rZfxy4CNUrf8e+Pxzqntt\ny6xeLe1rUnZjedDhkpFR16x+/z4N/GXNNeUCmdRs9vXeW9syA1lCQqgsw0J5g7FKtNmeKcu6erWl\nYZYTa9bQYO/zz7U7N0BzICOX5eKCfQKpYWHYMM0P4qYmadbgwgXq6fn1V87H0homkGFECUwJk5Ex\nViDT0AB8+CH9e8MG4N13tetBmjWLslWnTlEtvLYkJQEffWSYbOH+/TQDPHAgdwPdtgCTgZTNyKSk\n0PXm6Sm9BgyJrS2wfj3wxhuGf289sTC3RLAPW6lM7/IyJcSmsrMxQd3C4OKoozrbggU0MaSqxEpb\nOnWiz6i6mntPqK2tfpO6uqAuIyMQ0P1l2jQqkzMkBQXA8uX0745ARiXtK5DRhcjmOtVbt1r3PFRx\n6RK96iu/xzQ0ygQy2Xcz8Nex73C39DZSs+OxPWkXzS60dfMlLy8yLgPaVkbGUGgKZIRCajrk8ZTL\nFzs4UN/GjRvSlLdM9qBJJETGbXZmQ69AxhR07UoPk9JS7r04ALB0KYkRbNum3X4APTAzM1ULbMgF\nh1yoiowkU9oXXlC/oURC13nv3vQ7Mw95YzbUagpkKitpYsUYwUbv3lQaqG35RFOT5m0A+uydnGiw\nPG+e9ucHAC++KA2otYUpW4qK0i4QV8bWrfS6aJF+72NqIiMpGGSUBQG6h82fTz9tUdzCUGRkUBZQ\nbiIiVE697GLqSdQ3Gk7wolHYgLj0M6xlQ0Im6v6GERGUTWMyKfrC42lfmtwayGZk5L+/K1bQ8/bA\nAcOrcN6/L5207CgtU0lHIOPvT7J5cvXSbYbLl+l14ED93kcuIyMSNWHHqZ8ggfRLmdLTBQUe9g+G\n+dKiRcC+fcCjj7b2mRie+fPp5rV+vfL1TLOsu7tys0g+X6rpz4hDzJxJJWBTp+JWfhoaZNydHWw6\nw5ur3HJrweOxszKyqBsY+vsDjz1Gwd9339GyXbuATz/V3KTP49Hsu7sKmV0dAhmhqyspfk3WUO7D\n40ln269ckX4njWmGqSmQSUsDpkzh7pGkDUFBdNzNm9Vv98EHpHxVXQ388w99Plyy6f7+JNl+/LhG\nWXKj0Ls3NUsXFCj6A2nLxo3AunW6B2SthaUlBYOymZeQEGD7dtWyzO2FvDy65+zcyVoc4tcfFmZS\nv6+qugpEXdmn2zHOnKGA+YMPWhZdvRGNOhllSjtrR/SRExnQi//9D3j/fdVqXlx4EAIZCwu6P3p7\nK3r5uboaXo6eQbbs/EH7vpuQjkCGxyODp7Y4G1RZSYMHc3P2TKAuvjdygczpqwdwt/S2wmZRYwIM\nK/trLMLCqEaXi8GgKYmLo6ZWLoM9VZ9jp05UaqGq9MjGhhok1ZUbyqvcRUSQKV9kJFLkysqC/fqB\nz3sAbgWPPALMnq0YOPzwA/WQHTqkfD/G3+eXX+g7tX07zY7q21jeqRP38p4ffoDf6tWw0ibzy/Rb\nxcebJiPj5gZ88QVdW8owphkml/tvWRmpGz33HAWRsbF0fb/8Mrd7Ip+vuqfs5k0qH7t/n8pEsrK0\nOn2N8HjAmDH076go/d7LxYXKTeRVm/79l4QnlBmnRkVRAK9OvasD48GUu8v5jFhb2mJ03+msZVEJ\n+1BRraKpXB35+VSCKhMox8p5xwwMHgMzgQGV4X76iQKnBj1kvV96ico9TV0upi1379L9RlufQn1g\nJq7s7UnVrwOlPACjl4eY+HiabQ4PpwbVs2fpQaxLk93evcCffwLduqG0ohD/XtqhdLP4ft4oL9Gy\nBKcDmpUaNYp0/GNipJk0dTz5JA1G9u/X7lhOTuSs/MorqrdR4TskkUgUZJe1luHUB6GQgnNd/EJW\nrqQmZ3l1oe3bqQGbkV+XJzKSTEIrK6ksx1AmpI89Rsd9803N2546Befjx2GtjXw6Y4JmqoyMuTn9\njRcuVL7emIEMF7ZtI4GIiRNpZvSdd+hcLl7krnqkimeeoQzv9OkULA8ebPgsPRPInDpl2PdlKC4m\neWllgdJXX9GMLtOj1QHxxx/UO8VV/VFXmKCTkQ6WYWy/R1lS341NDThycbv2x5Azw7xbehtZd9lZ\n58G9dWzyV0Z9Pd0TBALuojPKmDaNJv6YkmpV1NU9GJOshoQxNq2qejCM21uJ9hPINDSQtnl7av52\ndqZZdMbcz9GRbhy6zBYOHAgsXgwJn4/dZ35tUUqRRyzg42xejB4n/ZBy5Yo00ASo50rTjaeggGaZ\njSHZyAQycgPnovsFKKmQlg4JBGYI6qqFepYqhgyh61WTO3dWFpXZGMqENjubBrI2NuplkD/+mFSx\nli2T9sp06WKYc+BCs+u1hTaN9EwgEx9PWb7Fi1vXvLe1A5kNG+iVyXY6OEhFHN54Q7/evs2b6Xo4\nf54ye01N2qnqcWHSJCoJ08YzQxsYKwH50kvg4VY+Skuj7/+uXYrrNm8mQRBjG00zGZnSUoVSWCsL\nazwyaD5r2cW0U0orJtQiF8hcTD3JWt3Duw/cOus5eSML08Pp7a28xNnQHD9OWfAnnjD+sdoKAoE0\nA6Rqoq6DdhTIXL1K5TQT9WhkMzbFxeSKy5WwMCqHYUpjZAenOjaMJt6MUZDe7dGVndKNrsxAbYOG\nAWlr0dhIsqkm1vzXCHNT79mTeioaGjQ3lxsqM6CMJUuA27epVEgGebWywC4hsLQwgIlXSQkFZZrq\nnJkg3FBNkczgZPp09Sn/YcMogwK0zoBcl0AmKIgG1927U9/Un39KvThaA6Y3qzUCmatX6cfJiZ2R\nfuIJKrm4d49UwWSprOTe7+fjQwMlV1cadEZF6d7Yr4quXakkzFhKYz17UuY+K0tRBIX5f1sJZCQS\nmtE3BWlplL3boaQKgRHBMbYZpo0NfTb19Yo9FgCG9B4Pt07S54BEIsb+C5u0O4ZMICMWi5CQeYG1\nWmfJZXnS06n6gJloab63GZ2kJHrVJ/vzIPL++9RDZkq56QeM9hPIMDcHXesXxWK6qRkroyORUINv\nRITuZlKOjvQgqq3VqbmurqEGf5/9nbWsu1cwlk1fzUptN4gaEZ18TLdzNDYVFdTvo6lR29QwQYu3\nNxDQ7ANw86b6fRi/DlWBjFjMXZVJHldXGjjJ3fxS5MrKDKZWxjRs3tYwi8jMfBoqkGGaZ+fPV78d\nQ3ExyYu7uFDzsSZWrqQHp76yuVZWAAB3ZYMpVQgEFBhGRbXs36r06EHlUcYaiIvFdG/cs0dxHbNs\n4UL258bnA99/T4P40aPZ+3z+OV1njOeKJoKDKZOak6Odx48pEImoB0YoVL2NmZm0z0Deb4l5rpnS\nRFAVf/9Nn5u1tWZxB0OgyhSzooKCc2trw6lwqeOjj6ifT0k/mEBghunD2Cp0aTlXkJmnxVhBJpC5\nVZCGihppn42luRX6+OspGMTg4EDVB8wkASMsY2yYcVNb76UxNK+/TmXkxqjcaCe0n0CGSbvpGsg8\n8QQ9DFU1DOtLTAyViIhENLOqJY1NDaiqrVDZ+8CFQzFbUVkjDdQEfDPMHfMfWJhZYmQ4uyznbOIh\nCJvUPDRbC2ZmUSIhxTLGWK01aWigAbJAQA3TXAKZ6moqhbG0VD64ePVVesDqW/vPsHQpapc/h6x8\ndgBosECGmZXjGsgYQqShvJxKNRwdSQiAC5aWlKXiqvdfW0uz/Upq27WiOVNc1bevhg3laEsiJK+8\nQv0d4w1YZy/P4MFUSivv1/Dhh5QxeeklxX0iI0m4QfYaKCoilbqyMu0Gqfb2pm3m5cqpUzQRNmqU\n+u0Y41jZ8jKJpG2VlsmKFHANMvWBCWTkhQ6YbExgoGmU7F57jVTbVAxI+/gPhL8X26R13/mNEEs4\n9ka8+CIpl82diyvXz7Pfu/tAWJhzmLjhgpeX9DNctYq8ZUzBwxrIdKCR9hPIMBkZXaPWPn3olUuT\nti78/LP031u3ajXTnnQzFmv+WIrVvz2FjY90Q72lmdbqM7n3MnEh+V/WsrH9ZsHTmR7yw0InwcJc\nOutbWVuO+IwzWh3DJDCBjIsLya8eOdK65wOwS8QEAipjuH4deOop1fsUFtIg1ctL+WDV0pLK6JSV\nar33HjWYc83KicXAhg3IiDkEsURqdurh1FV3YzR5uEpo6puRuXuXlHL+/JMGZdnZ1J/EJbsC0D4r\nV3I3yFNnihkbSyp1XBR7AgORfPAgbjAO0G2V6Gjy3vnlF9Mfm8+X9gDJK8oJBBRAqTKjlB+Ifv45\nTW5Nndo+1H6YzIWm0umXX6aeseeeky4TiWiibs4cmhxpbWStBPS1FeACU4p09y67b9FUZWUc4fF4\nmDmcrXZ5pzgLV66f4/YGPj7AyJFo8vZC4g12n2u/HgYsxebxpMHEyJHU+6Uvb7xBTf/KDCcB+i7f\nvElZx169lG/TwUNL+wlk9M3IMMaYXDwJdGHQILphvvMOzZpwaI6TSCQ4dWUfNhz+AjX11Mia4CbB\nN789j9KxHGvl6+og6u6PHb+vYnnGuDh6YMKA2S3/t7Gyw5CQCaxdTyXs4z4bZCqYmUVvbxq81NSo\nL7cwBV26UP0uUzYUEEDlN+qc67t3pwEwY3gqjzpTzF9/pYEa19+7qgqQSJAazlaF6e3Xj9v+XOBa\nWtapE/29dM3I5OZSnwETEPD59Lc0FuoCmXnzyKiWY99Lo4cHxG1hIKmO27dJyclYylqaYAIZfUw3\n8/OlEsQffqj/ORkDiYS7ZG1VFU3aAJobnYODKTiQndAzM6PPVFmze2tgbU1BlZ0dKTcaG0tLyiCI\nRJQ5Zxg0iMoS25CxqK9HD0QEsp/th2K2qhTnUUZGbiKrx9XWyh49uxm434sJZJi+FX05coSqYXJz\nla8vKKDJr+Bg9c/VDh5K2k8gY2FBAyRlTudcYDwbEhMNr1YDUNo3PZ0MpIKDNW4ueutN7PpqGfZf\n2MgKQADgblkevtrxOm7c4SAckJaGs934yLdnL547+nmWERcAjAqfBj5f2lNRVJ6PlCwjBXa6wmRk\nnJykJVmtLcloYUE39iFDtNvP3Jx6WZTBBAbygUxTE2VieDzVRo2ySCRAcTHEPCCthwtrVW8/Axqj\nzZlDg+Dff1e/3e+/0++k60xsnz70u6el6eddwBV1gYwOhpg6IRJRbf2WLcY9DqDZFNPYMGaJ+gQy\nn3xCTdWzZ0tLrdoSGzZQluDLL7ltv2cPVRwMG9b2fLN0ZcsWul+Yqr9i1SqSoJYdBAcGUqmiOrXD\nVmDa0Cch4EsnOsurinE2kXvJ+5VMdllZeOBQCAQGVhVjAhltxIvUoWkiLDCQ+teMNdHcwQNN+wlk\nnniCBkiMHKe2dOpEs+gNDfo9RNXBsd69rrYSv1ZcQLRFscptauqr8OM/7yP6muqm/CaREEkJx3Bk\nEtt1tl/QCPT0UZyhcSqtRr8mtsnaqSv/cDpnkzFpEt08P/lEOoCUV+hpD6jKyBQWUnDi6qo5q/e/\n/9HM7EcfIdenM2pspEZo1pa28PM0oBtxp070MDK2DKetLWU2m5r0N7TkgqpApqmJZsp5PLb7sjFI\nS6OSIVPMHLeVQEafz3bhQmDsWJbDeZvCwYG+x1yMMSUSCmIB8rppL1hamrZfZ9Uq6lFpCz1CGnBx\n9MDwUHa51om4Paip06zA1yCsx7Usdnl8vyAjKHzOmEHjpE1aKqupgmtpckc2pgMltJ9AxhCMHEmz\n6rqY9RmI8qpifLdtJdKD2LPnVhY26OXDbhQWi0XYGfUzdp/+FSKRtOfmbult/HNuA977Yyn+qL2M\nRkvp4NLa0hazhi9RfvCbNzH2S7aqUvbdDGQVtCGFMHt7GuwEBj4cgYy8ip42ks02NjQznZiI1GB2\nL0wvn74Q8B9QOUdGFleZX4ahmTaNHq6MhwkDo9jj6Gj8RmFTDshVBTJ37lBmQFfFRa706UPKaMOH\n0yD+p5+0D6qGDAFOnuSU+W4VGHW1mBjNzxqJhPoHpkzhrszXQdvk8mVgxQpOSm0TB8yBtYW0PLCu\nsRbHLmsWRkjJikOjUCpr3cnOWUFAwCA4O1MZqLm55m25wDWQ6aADJZjAxegB4tdfjfr2EokEtfVV\nsDC3gpnAHDy5DE1e0S38cuAjlrIYAHS2d8XzM96Fh1NXHLu8S8H193zyERSW5SE8cCgupZ1CbqFq\nl+LpQxfBwVZFKYyjI7zuVqFXfj3Su0gb/09e+QfLjHEz1Je1a6kMUFUDcGsjkdCPLgNdV1cK0OSd\n3BnJZi5a+kxDvYUFUiaFASJpVsFgamWtAWNkGR9v/FlqOzupu7IsTPDs6Ki4ztAYS+5YGZ060Wx5\nVRX1nzE9h9HRNJCePdu4SlNeXtL+nHPnqB/qiy9I1KEtKbjpg7MzBeOJiSQYMWaM6m35fOrFmjdP\n++M0NHAXwejA+Ny4QUp68+drzK7aWjtgfORsHIiWBj3nk//FsNBH4NZZhZHv9Om4EiwCPKXBRd8e\nw8DnPQDz1R2BTAd60BHIGJPaWsDSEiJIcD75X5y8srclSBHwzWAlsICVhTWsrO1hZWGDvOIs1mwK\nAHRzC8Cy6avhYEsp8UcGzoOnczdsOfYNGmUaADPvXEOmhp6ZoX0eUW+K1TxoHhtXiPQu0trllKzL\nKCy7A3cnb1V7tg4jR7b2GajmnXeAH38EvvmGHNnlqamhjImqwRmPp3yQHBoKrF/PzZSwOZAp5zei\nQCaI4fH4CPZpg70DXHn2WWDjRtMO8OXh8WhmXdeePG34z38oaH/8ceMfi8cjxTJ7e3aZYGuYiDJZ\nsIUL208QwzBmDAUyp06pD2R0IT2dMjjOztRTkJhIPxERbc8f52GCkSzmKOU+Mnwqzif/i/IqKjEX\niZuw6/QvWD7rA4VJUACoTbiE9JHs3sN+QSP0O2dTMWoUsH27VOyjgw60oCOQkaGipgyJN2KQfTcD\nXs4+GB42GdaWengKfPYZ0s/sxd75/VAoZNfYi8RNqBE3oUZYC9Qov7GFdg7EotkfKei/h72wBi6p\nl/DbOzNQ1qi+btbawgb9Ogdh4Mj58PHUIDPZHMgEZtxDN7exuF0k9UE5lbAPC8a9qH7/h5WBAynz\ncuiQdGArENCsvSovmb59qbExKUm7AbmvL1taVdO2AFJt2OUrfp5BsLV2ULKDAZBIqDldWa9MYiKt\nDwrSz9wrKAgoKdF9f0Pg58etx8EQdO1KsqSmUjxTJhtu6kCmqkqa+Xn6afXbPoiMHUuz88Wq+yB1\npksXymDl55Oy4YEDwJo1NLnSEcgQO3cCe/dSkDx9ummO6dJcLs7x3mVuZoHpQ5/EpqNrW5Zl5iUj\n/vpZRPYcpbB9op89RGbS7ItbJy94uz4g4hA+PqqFH3JyqBKhTx/l2fEOHnraTyDDaMRzdexuprqu\nEkk3Y5GQeQE376S0KIQl4AKiEvZjXP9HMSJsitZmUsUlefin7CxSHgsAhNqrao2ReGP67A/AV3Zc\nFxd0KajEa1bDsMElB7cK0hQ26dE1FIOCxyI0YJCCOplKmjMAvIoKjO0/C38ekarqXE6LgqdzN4wK\nn6Z0NuihRSQCEhKo+Vu2DEyTKebdu9S/okq1zBB07gw4OiJVrt+qt6+Rysree4+UgT7/XLlx4Vtv\nAUePAvv3m27w0F5obVdnpqTRVIHMrl2U0R4xQvpdak+MHUv9b8YQinBwoL/ZzZuUnWH67IytrteW\nKS4myXaBgCS5z5+na2zAANOdg5YZGQDo22M4LqaewvU8qczxP+f+RLBvP9hayVw7QiESQtkqln2D\nhrePZ/XWrRSEv/IKZaY76ECO9hPILFlCg6RDhyitroa6hhok37qEhMwLuH47UaVXSm1DNQ5Eb8aZ\nxIOYOGAuBvceBzOB+ua2+sY6HI/bg9Px/0AUqKiQwsgbi8UihXXM+sdGPIPhYZNVH6S5ZMg+twDL\n3/0AB6O3IDrlOBxtOqNfzxEY2GsMnB05SPPKY2NDzYgODgjzHwhnR3eUVhTS+UrE+OfcBty8k4IF\n419i30RNyWOP0QP6r7+kJqatSVERBTGuroCVtK9IbSBTVUU/VlZGH1w03shA5s6XAZG0DNFo/TFW\nVtS8rEpCkzHDbC8Ssg8Tps7IMGVl7TEbA9Bkm7oJt/R0EvzQNdCJiKB7z9Wr0l7XLWAAACAASURB\nVEDmAVDsMhpCISldurlRINMaZphaZmQAMsmcM/o5fLb1v2gSkW9YdV0FDlzYjMfHLW/ZrqI4HzcC\n2BNWD0xZmSYYgRFG8rmDDuRoP4FMbS29ajDEvH47CX/++xVqmw0muVBZU47dp39BVMI+TB70OPr1\nGA4ej4+a+iqUVhSitLKw+fUeUrLjFZr1GQYGj8W0IU/A3qYTmkRC1K95B/W//oT6+bNR/8ZraBQ2\nwNO5G5wcNNTdM03c2dkwE5hj1oglmDn8af1nX3g86ukAydnNHPY0/jj8GWuTa1mX8cW2V7F40uvw\n01SqZgzS0+nH2EpRXGHkkbvINWDKBjISCbvGX7ZhX9Nn1thI/TQ6DkJuVN+BUCaIcbJ3hadzN53e\nSyPdmt9XWcOmWEwlAkBLydsDQ58+FJzl5Dy8g8GhQ0n61FRB6LffkrrT7Nmat21vSCTAggVAVhap\nr0Xq4PcUEUGleQkJHYEMQAEMn08TT0Jh6wQydnbkHeTsrPhMUINbZy9MHDAHh2O3tSyLTT2BAb1G\noXsX6ilJuH4eEr70/bzd/OGuShTgQYMx3ewoi+xABe0nkKmpoVc1gUxFdRk2HPkCdQ01KrfxdugC\n38MXEB/ZFfVW7D9PaUUhthz7FvsvbEKDsB4Njdxkmn09g/DYiKXw8ZCqa5mbWcD8iadh/8mXwOZ/\ngC9+5l4DLxPIMBgjhRwWMAjPTHkD2078gLrG2pbl5VXF+G7P25g25EmM7jvdtKoosiaE587RLNug\nQcD775vuHGTJz6dXbzkhBBcXKvGoraVzlh1EMIGMJgnlw4fJrG3qVODgQU6n0yQSorAsHwWlOSgo\nyUFq9hXW+t5+kcYrN1CnPHPvHqkoubo+eHXOFRUkt1xR8fAOBt9917THi4zUbQDfHrhwgfrJ3Nx0\nn4Xu2yzVX1RkOuPWtoyZGRkI371Lxop5eSQdzDxLTQGPB7z+uk67juk7C/EZ51BYLvUV2xH1M95Y\n8A3MBOZIuJfE2r5fj3aSjamtJbU3gQDo1QaVUztoE7SfQIbJyKioJZdIJNgR9f/27jwuqur9A/hn\nZtgFQdk32UREcmVRFBQ3BNfMTLM0NTO/mUv2y0r9ftMyzUorTVstt0wtW9Tcc8VdcQUFQhNQFkGQ\nRVmcub8/DhdmYJh9mMXn/XrxGrj3zL0HuAzz3HPO86yRG8R4tPZFeEgsugbHwM3JE5jvjSF7ruPg\n5o9wLPu0zB1tAE2OuDTkWCPE8KEzERHSR/6bx9BQlonoqafY9CRV+fuzF2aOa7qNRMKCOy3nYHdu\nGw0f10D8uOdTZEmldZZIxPgzaR3+ybmGF+Nn6m/xeEPS/5RLSoB9+/RfhFERfkSmYSAjELCRI3d3\n9iIsraSETcNSlkKZTxzAn+PxY3an1suLjZzVXlPp2Vdx9voh5Ny7hfz7ORBLmr6WwgLCVf3O1Keo\nOvPNm+yxOd846IqjI3vjI10U8+pVtgA/NLR5Mpc1p2vXgA8/ZL+rJUsM3Zsnz8qV7PHVVzVPnxwX\nx15nHB2Bjz5if5tt9DQSayq8vVkgc/Qo+zooyLD/O9RgaWGJMf3/g5W/zq/bln8/B4cu/IGu7WJw\nu0B2CnO3dr2au4va27SJZaOcMKE+PXVKCnsvExYmO3WbECmm8VesCiUjMufTjiLl1nmZbT3CBiCu\nyzB4uTTIltG3L1ps3owRd2wQN/Fr7Du7DSdTDjS5rqUhC5El+nUbgYGdhsHaXkmdic31w8UqDzcH\nBrK1CIpehG/eZPVVoqNZ4TUtODu6Y/boJdhxYiOOXNwhsy/l3/NYtvkNTH/mff0PZVdV1X/fdnbG\nURBzyhQgIUF+xeGmRlxGjGCBd1WV4mPzgQEfyBQUsOkirq5s6g2AzDupWP37e+CaWOclzVZkg7Y+\nTyltpzFvb3b9lpSwJAjSAZyFBTBggHGsa1IXnwa7VCpD4PLlrKr12rVsfZ45qagAtmwBwsMpkNG3\nsjK28NzLi9WWycoCfv+d/b1Mm6b5caXX4Lzzjm76aur412NbW5b2Wtnrr5Fp6x2GHh3643Tq33Xb\n9p39BfceyBaMDfLqgFYOekwioy937rDfi/QUMqGQFSUOCjJcv4jRM59Axt2drSeQM23lQcV9bD/y\nvcy2AM/2GNvvP3WL72XExbEA48gROL72Gp7rNw19u43AnjNbcOHGsbrMZlYW1nB2dIdzS3c4O7qj\ndUs3OLd0R6BXKOw1GaHYvp1ldpo6FXjrrabbCQTK7yRdra0po6OsOBYiSzzTezKCfZ7CT/tX4mFV\ned2+kvIirN+zHP/3/Kf6nWbG3xF3cmI/A2MIZGxsNMuqJBAov8Pk5sZ+z4WFLMNZgylpHMdh58mN\nKgUx9mVVGNNnguoZ7DRhbc2yA7Vu3Tgg79EDOHBAf+fWJz6QkR6RMefpOvxIYV6e4nZEe19+Ccyb\nx4KWr75iH2IxG6lXNvWUqOfll9lNp5gYk004MiLmJVy9dQ4Vj9hNlRpxNc5IBTaACS/ylzc1OTyc\npQ8nRAHzCWTOnpW7meM4bD30tcwbb0uRFcYNnCE/iAFYIAMAR47UjZK4OnliwqA3MKrPFNwvLYBj\nC2c42Dnqdr3B6dNscXh5ufK2yvCBjLp3wPftY0XUhgxhC0Yb6BgYhbnjVmDdnuX4Ny+tbnvOvZu4\nkHZMbn57nWndms1v5qcRGkMgo09CIRvluH2b3a26e5dtr32Dk559BTfvXm/0NEd7Z3i7+MPLxR/e\nDp7win8GbvfKIbq7Tv995lOMmpMnLZBxr814mJ/PpnUYS2INc8QXw+RrEg0Zwhaiz5xpuD6ZKzNI\n+d7CtiVGxk7Cpv1fyN0vFIrQJbhnM/dKRxStsSREAfMJZJpwIe0Yrt2UDXKG9ByneBpU27bA9Ols\nweTjx2xRYK0WNg76Sz3MB2Pduytupwo+kFF3sejvv7PK3i4ucgMZAGjd0g2znv0Qa/9ahmu3ztVt\n33XyJ3Rp2xOWFnKmWemChYXsnTT+TeQD9ev0mAxfXxa4FRfLZDvjOA57zmyRaRri2xkTE99svF7J\npjXgbGOeQUZzWLWK3Tl3lJomKj06aG6srVlSg+Jitg4oN5dlv+ralVKg6lp4OBs1T09nU0hjYtgH\nMU/797PpwfHxwOjRGh0isn0czqQeQkbO1Ub72vt21mw2iDGgQIZoyKxvtZVWFOPXo7JTyvw9QhDX\nZZjiJwoE7I3L5MkyQYxePX4MnK9dw6OLbD2ajsjwRR2VBAcikQVG9p4MkbA+Fi4uu4ejl3apdz5t\nODiwukH79jXfOdXFcdpN0TlyhK2NiYiQmVombzRmcPQ4+UkX0tNZ6mATWdhqdJyd2Wig9Jofcx6R\nAerrxeTlAbt3AxMnAhs3GrRLZsnCAujTh33Oj8roUkUFG+lXlBiGNJ9r14Dvv2eZ6TQkEAgwpt80\niESNX8/Ds6vlPMNEeHmx9165ueolPyJPPLMNZDiOw7bDX8vUi7EQWeIFRVPKtDsh0LcvG8nRZKrT\nypVsITugWrV3jmNTP+QVXBSL2QuBhYX6KQv5QEZ6YXMTXJ08EdMpQWbbgXO/1s3f1TuBgE3F6Gmk\nQ+kcx9YbeHrW13IA2BQxVV+opd88P/ccsGEDuKefbjQaE+rXrem6PlZWhq8Mb2569GC1VVq3NnRP\n9GPFCmDPHpbpqrmLYT5p+vdnj7oOZDiOrRmNjgZ+/FG3xyaa4YtiFhVpdRi3Vt6Ij5CtsWRZLUbH\nAtUSEhklKytWcuDcOZVr7BACmHEgk5x+HFcyz8hsGxI9Du6tfZp4hpZSU9nd823bNKuTER/PMq69\n+65q7ZOS2BuLF19svE8kYgEOn+ZXHfLWAyiQEPUcbK3q3yQ/qn6IvWe3qXdOU3XtGpuCM2KE/P0C\nQf16g8xM9lhWxta9ODmpf5c0NBQYPx4ZbpaNRmMSuo9Rs/N69Pix7D/qwkKWPOPiRcP1Sdd+/pn9\nDZrriExCAvto2ZICGX2LjwfGjgUGD9btcaXfDL78sm6PbaqSktgshfnzlbfVB356b2Gh1ocaEDEK\nPq71U61jk27BpoWSLKnGLjGRTekXiVgx2LVr6wspE9IE8whkKivZG/d79wAApRUl+OXIdzJN/Dza\noW9XPS72++039jhihGZTeJ56igUeqqY7lVMUsxEFxUGbpMaIDMAWH8ZHyc71TbqyF/dKctU/t6nJ\nyWG/s4cPm27DZzTjR8746WFubhrddeI4DntOqzEa09ySk9kai4ED67dduAC88ALw5puG6xfRHAUy\n+tWhAwuMn3tO98fm1x0QZtgwdgNK3kyG5qCjERmA1ZaZMeoDjI6bivG5rTBsV6rpFRtWZO1aVt7g\n8GFD94QYOfMIZK5cYTVTBg9u/illPD6QeeYZzY+hTgDk5cWGYgsK6mvo6EKXLmxU6OmnVX5K785D\n0Foqb71Y8hg7T+phPv2SJez3vHat7o+tiTt32KO3ksQRQP0/zgaZx9SVkXMVmXdTZbYZ1WiMpyfL\ndCW9YJMPtk2xGCahQMaUffYZe1ywwLD9MBb8tG8dlSVQGx/I6GBEBgBsrVsgtvNgROZKIJJw5hXI\nXLnCHinBCFHCPAIZqWKY/9y5hiuZp2V2J/Z4Hh6tNbgzlZICjBzJ7goocvMmcOkSe3Hk5zvrm1AI\n+NUW8rx9W3fH7dyZBQxqBGSWFlYY0lN2ituljJO4lZvWxDM0lJ3NAoLKSt0eV1N8oUofBdMV+UJe\nDUdk1AlkysqAtDTjH40B2FQ6S0v2j5pf82XqgczZs+wNCJ8q90nzzDPAmDGKA3ZinEaNYkU2Fy0y\ndE+Mi6EKLHp6AqtXszVousSXbDCXQKaykqUhFwrZiCUhCphHIMNP7bGzw4W0YzK72rgHo1+3JtYw\nKGNjA/zxB/uQKCg6ePo0myY0dGh9NeXmoMr0smYSHhILHzfZImN/Hl8HTpfZcuRlilq5EoiNrR8R\na06qjsjY2NRfP/yIDF90UBmxmK3Dad8eGbcuGvdoDFBf+waoH5W5eZM9mmogY2XFpoLo6C6qyfnw\nQ2DLFvNdD2TufH2pFhDvt99Y2mND1emxswNee43dINWlTz4BTpyor4Fn6lJT2f++kBDA1tbQvSFG\nzjxe3WpHZMQt7HAlU7ZmTGL3MRBpOqUsMJDdbS8qYqMzTRk3jt1pX7xYs/NoKiyM3a2QDrIqKoAz\nZ3RTVFMNQoEQT8dMktl2M/d6o4QLWuEDmVat6rfdvs0WcPJvlpuTKoFMnz7sd7JhA/taImGZrlQd\nkRGJWN0YAHu+lU0EYXSjMbw2bdgjH8jwgbaJVtNulAAjJ4dl9LreuBip2bh7l633G2NkgTIh2hg5\nkiXk0WT9qDELDGTZO/mpa6YqI4NlgwwPZ1/TtDKiArMKZDLdrFH+qD7blq2VHULadNb8uAJB/R2O\nI0cUt3V3b/43aitWsABrmFRdnLNnWWrYAQOaty8A2vl2RJh/hMy2HSc2QCzWUU54eSMy/OeapLzW\n1o4dLJhRNJ1QJJK9G/rWWywwnjtX9fP4+iIj2AWZnrJ3poxuNIbn68uCzbLadWoJCWy00lDTObTV\nMJA5dIhlmFI1MYcpsrJi1/eBA4buCSHkSWFrC5w8yT5/5x3t1hyTJ4Z5BDLW1oC/Py57yxavfCow\nChYiLQta8oGMqWTO4AthGuhOxvCYlyAQ1F9W90ru4sS1/bo5uLEFMiIRG1nR5O6eGhnLOB9v7EmQ\nHXlp79fVOEdjAGD9elYRnk8YsXgxsHMny9RmiqQz+Ukk5l8ME2CjhhYWrP5RVZWhe0MIeRJ4etbX\nTlu4UD+Z/IjZMY9S3+PGQfL8WFz+/mVAKhNul2AdFErs25c9njnD6n4Ye6EmPpDp2FHzYyxfzkYN\nFi5kd2bV4Onsi+iw/jh5rf5O7p7TP6Otdxi8XPw07xPARsXu35cd+dJxICN8+BAO58+zXPbNOK/8\ndl46rt48h5rH7E2j9Mqiyk42yHSQnTKQaKyjMYBsEU9zYGHBgtWKCjZlk7/WHE28ZoMiQiEbZb5z\nhxXe5acLEkKIvvA3B7Oz2WuPqU5HJs3KPAIZALfu3kDpw/rq6daWNmjfpov2Bw4IAI4dAyIijD+I\nAXQTyCxdygKZN94AXF2Vt28gscfzOJ92HNU1LLtYRWUZPv/lXUwePBft/bT4nbi71xeY5Ok4kPFd\nvhyuO3awu+8LF+rkmMrcvHsDq7YvgFjSxBS8BplC2WhMe/13jNS7eZNlJbSxqZ9iZs4jMgC7O3rn\nDvC//7GpkJQ9iBDtbdnCRqhfeEH3RVDNga8vC2SysymQISox2qlla9asQUBAAGxtbREREYGkpCSF\n7S//c0rm67CASFhaqDeaIJdAwLJiycucceoUqz5bU6P9eXRBImHFvgDtAhk1i2I25NiiNQZGjJLZ\nVln9EF/v+EBmpEYnoqPZtD8dpbO04VMqf/yxTo4HgP1esrKAGzfk7t55cmPTQYwcRj0aY67c3Nhr\ngEDwZEwtA+rrxqxfbzpTawkxdpcvA5s3s5INuiAWs7IJsbFs1oip44u4StciI0QBowxktm7ditmz\nZ2PBggW4dOkSevbsicTERGQ3cWFzHNcokOnSNlr/HV26lFUw//FH/Z+rKXfuAEePstSwpaVsTU9U\nFODsrPkx+SkzGgYyADAw4hnEdEyQ2SaRiLHl79XYcWIjJJyCdNbqcHFh33O7djo5XObSpewTjquv\ngyJPTY3q/zQOHmQ1f156iWVlkcoo98+dFGTeUZARr4Eov+40GmNoHToA8fHmf7fwvffYWhmAimES\noiv8/2ZdpXOvqGDFIy9dMo1ZI8p88AHLCDlqlPK2hMBIp5atWLECkyZNwssvvwwAWLlyJfbu3Yuv\nvvoKS+RkCsrKz0Bxef2LgqWFFUL9u+m3k2VlwP797IVj+HD9nkuRadOAXbuA7dtZho9du7Q/Jj8i\n8+CB4nYKCIUijO77KlycPFk9GalVHwfPb0fhg1y8GD8LVhbNWHdHBY9bt0ZFSAhapKWxtM4DB8pv\n+NlnbMrNggXKq2a3bcsez55lAVevXuzYAPad3SbTtI17MLq16yW1pf4fk6uTJzr46fm61pWHD9kd\ntaQktt5i6FCNpikapTffZB/mLiKCXa+nT1MgQ4iu8CmSdRXImFsxzOBgQ/eAmBijC2Sqq6uRnJyM\nuQ3S08bHx+Mkn5avgUvJ+2S+7uAfDmtLG731EQCrI1FVBcTEGPafvD6KYmo5tYwnEAjQr9sIOLd0\nx4Z9K1DzuLpu36WMkygpK8Irw96Fg51xTdEp7d6dBTL79jUdyOTksN+/KhnL2rRhC8Yf104fq60h\n829eOtKyLss0HRk7CUHeZrAWISJCts7KpUvmE8g8SfLy2CMFMoToBj8iU1Skm+OZWyBDiJqMLpAp\nLCyEWCyGe4NF3W5ubsjj/6k2kHxxP2BfnymppdAD58+f13nfRCUlEJWXo9rHB4Hff4/WALIjI5Gv\nh3Opyt3CAr4ACs6cQZaO+tG6e3dYe3ujuLoalTo5pgUGdngRh65vRWVNRd3Wf/PSsHTDbAx86gU4\n2LRS8HzA4exZBCxahAc9e+L2/Pk66FPT7icmosrHBw969kRNE99/0NWraAUgs7ISxSr8jJ7y8oJN\nVhYAIF8kQvb58ziUulWmjXvLNijOfYjzuYa7nnQl2NER0jm9kouLITHg34nO6CBzoT5em/SC49At\nNxdCAMl37kBSXKz0KcRwTOa6esK1KChAKIDy27dxQwe/M7sbN9ABwEOhEKl6uAbouiK6FqzjUTej\nXCOjrmKpIEYoEMGnVVudn8Pp0CF0HTgQvp9/DkFVFRxPnGDn5uvMGEhV7d19q7t3dXbM+wkJyJ0y\nBZX+/jo7pouDFwZ3mgQnO9m78uVVJTiRsQOckvUmFiUlsCoogEhqfYm+PGrbFoUjR6KmYYY0KZb3\n7gEAqlWsjVLl41P3eY2LC4rK85BTnCHTpqNvjAa9NU7VUj+7x46OkJj43ULP775D15gYeGzcaOiu\nNBuBWIz8559HwTPPQGJnZ+juEGIWKv38cOt//8Od11/XyfGED1nNCTH9jZInlNGNyLi4uEAkEiE/\nP19me35+Pjw9PZU+v0NAOKJ79FLaTm3OzsDbb6PVlSsI79IF+Pxz4PJldDLk+hiATVkC4FRcjIiI\nCMP2RQXdI6Pxw+6PZaZUFZRmw8HNUnFq5tq7Qq0DA9G64fc5YQKQksLWCWkTfH36Kf598AD3BwxA\ntz59FLetvTsdOnCgajU2+vSpq1jsExWFfRWyC/z9PUIwrP9oCMxhsSbA6vD8+ScAwCI42CSuTYVq\np5L6ODjAR8Pvhb+zaVI/ix49AAAmWsr0iWCS19WTbsAA3R2rfXsgMhIOlpaIeOopnR2WriuiLw+0\nWH8tj9GNyFhZWSE8PBz798tWgz9w4AB69lRe4FJv2coCAljmqeJilnnqlVeAL7/Uz7nU7Ve3bmz9\nwQ8/1KdfNlK21i0wbfh/0c63k8z23Wd+VjwqoyjlbUoKkJys3eJJsRj473/hv3gxBGKx8rZlZWyK\nkQrBNQBgyRKWmMHHB7kuto2y7A2KMqMgBqhPoQnUr+MyZXwmv3v3gF9/ZcVZCSHE0Oztga5dAR0G\nMYSYEqMLZABgzpw5WLduHdauXYvr169j1qxZyMvLw7Rp0xQ+TyQQ4amASP11jJ9GZkw1FRwdgQsX\ngEmTgJdfBt5/39A9UkokssCwnuNltv2bm4YbWQry6ksFMrfz0rH69/ewbs+nKHv4QDdFMTMzgcpK\nVLu5QcwnO2j6G2AZ3YqLAUtL1c/x1VdAdjb2C7JkNvu4BqKDf7gGnTZi0iNjhh611AX+msjIAEaP\nZsXsCCGEEGJQRje1DACee+45FBUVYfHixcjNzUXHjh2xe/du+Erf5ZWjnUd72NnocS5+XBwrDnfk\nCKt6b0yuXmWP2hTCbEZ+HsEIC4hAyq36hYR7Tm9B+zZd5I9M1AYp+Y6WWLl9QV0GtKLSAsxxbMmS\nFGszXFn783vUtsH6KrEYqKxsnJ1MIKi/S6+GguK7SE6XLe5qdqMxANC3r3kUZ+Pxv+vbt9mjuRfD\nJIQQQkyAUY7IAMB//vMf3Lp1C5WVlTh37hxiYpQvhO7SIU6/nYqLY3eajbEQ3pUr7FEXgUxmJiuG\n99132h9LgcTuY2W+/jcvDddvX5Tf+NNPIb6ZiU2Od2XSON/OS8dlv9ogQ5sRmdopeQ+lA5nvv2dT\n9pYv1/y4DRw4vx2cVDFQT+c26BjUXWfHJ3rCBzK1mecokCGEEEIMz2gDGXUJBUL9vyH092f1Wj77\nTL/n0QQ/ItOpk+J2qsjOZlPUNm3S/lgKtHFv22gq4J7TTayVsbfHwXvncbvwZqNdu7yrIBYKtAtk\n+BGZoKD6bS4ubPrYvn1NPEk9RaX5OHfjiMy2+MhnIRSYzZ+h+YqJYSN+v/3GvqZAhhCiqS+/BJ5+\nGjh2zNA9IcTkmc07qLY+T8HeVsnaBnNVWMgK17VooV3WLp6OCmKqIrGH7KjM7fwMXL+d3KhddkEm\n9pzZ2mg7ABRY1uDsn9+w7GWamjgRePttVEiPaPXrx7LCnTmjXZBU6+D53yGR1CcScHXyQtdgPWTY\nI7pnZcX+Lvi/CQpkCCGaSk5mWR3T07U/1uLFLOHPr79qfyxCTJDZBDJd2irPaGa2JBJg7lyWSU2o\ng18pP41G2ZqT48fZi2dursan8nULwlOBUTLbdp/eIjMqU/O4Ghv3fS4TBDS0J/80alqpv2alztCh\nwEcfoUp6HVbLlkB0NFsn8/ff9duLioCaGrUOX1xWiNOpB2W2xUeOglAoauIZxCh5erI7qZF6TCpC\nCDFvLi7sUZtMm7zMTODixWa58UiIMTLKxf7qEkCATk/yOgM3N2DZMt0dT9URma++An7+GVi7Fpg8\nWePTJXYfi2s3z9Z9nZWfgdR/LyAsgOWv/+vUT8i7ny3znFF9puCPpHUQix8DAErKi5B0ZS/6dtNx\nhqxBg1jAtn8/MGoU2/bMM2zbkSNA7951TS+kHceVzNN4WFmOyuqHqKx+hEfVFaisfoTqmkqZw7Zu\n6YaIECW1aojx6d+ffRBCiKacndljUZH2x+KLRJt40WFCNGUWIzKBrfzR8sEjQ3fDfEgHMooyT6XU\nFnX09dVyVCawUSC6p3ZUJiPnGg4n75DZ1z20H/p0GYrYjoky2/ef+wWPqh5q3A+5Bg1i04qqquq3\n5eSwn4tU9fpzN45g/d7luJhxAmnZl3E7PwP5xTkorShuFMQAwMCIURCJzOI+AiGEEHXockSGAhny\nhDOLd1Jdvv8TWHm8rvo70ZK1Ncta5uDA3rDLSw38+DFw4wb7PD4eGD8e2LBB41MmdB+DK5ln6r7O\nKvgHyenHsfPkJnCoD6ZaObjimT4vAwAGRj6LUykHUFUbKFRUluHwxT8xuMfzGvejkW7dgPv369Mv\ncxxw5w773NsbAPCwshy/H/tR5UO2sndBVGg/3fWRNB+JhP09mFu6bEJI86ERGZ2QSCSorq5W3pA0\nGysrKwh1scRBDWYRyHS6kgt08jF0N8zLwoWK92dmAtIvILXpizXl4xqITkE9cCXzdN22Dfs+l0lV\nDAAvDJwJW2sWVDjYOaJvtxHYK5UE4HDyn4jtNBgOdlqsl5EmFMrWkCkqYqMzjo51/zh2ndyE8keK\n1xMJIIC1lS08nH3xbJ9XYGmhRiFNYhwiItgi3ZQUIDTU0L0hhJiqqChg2zbdlHJ4QgMZiUSCqqoq\n2NjYmF8dNhPFcRwqKythbW3drMGMWQQyrR7IKVhI9IufVtarF3DiBJCaykZpLDS/pBK7j5EJZBoG\nMXGXi9BulmydnL5dR+D4pb9QUcVezKtqKnHg3K91ozYqGTsW8PICPvhAeVt+NMaHBc5Z+f/gxFXZ\n9Mx9ugxFt3axsLGyg42VLWytW8DK0prSLJs6oZCNyGlTeJUQQry8gNGjEnvKmgAAIABJREFUdXOs\nX35hZQLat9fN8UxEdXU1BTFGRiAQwMbGpi7AbC7m886KApnm5esLTJsGvPgi0KYNG6XIzNTqkN6u\nAegc1EPuPvf8Mgy90XgI2dbaDvGdZRf4H7+6B/dLC1Q76f37wNatwDffALa2yts/eMDmN/v4QCIR\nY9vhb2Smvrk6eWF4r5cQ4BkCT2dftHJwgY2VLQUx5oDP5rdpE1BWZti+EEIIALRty7Io2tkZuifN\njoIY42OI34n5vLt6Av+IDSoykmUtmzYN4Guv8EU5tZDQfWyjbUIIMH5TMqwc5NfuiAkfjlbF9cke\nxOLHTdacaYSfEhcWplrq6t69gXv3gL/+wqmUg8jKz5DZ/WwcTRszW3wgs3o1cPeuYftCCCGEEDMJ\nZNq1q5vqQwygUycgIEB2zYyGvF39G9UEGtQiDG2yS5osQmhpZYOEY1ky285eP4zcomy57WXwwVfH\njorblZWxqu7bt7Mvq8qx88RGmSZd2vZEqF9X5eckpslRat0VFcQkhBBCDM4s1sggLc3QPTA/f/4J\nJCWxminR0YrbfvghsGSJzk79bNwrKHyQhzuF/yIipDfi46YBI2YpTAUddbsKh/LLkO/uAICtr9l9\n6ie8PPQdxSfjR2Seekpxu7NnWR2Zjh2BUaOw88QGPKxdlwMAVpY2GNlb81o6xATwackB2aCGEEL0\nrawMmDCBTSVr2xYIDmaPPj66KYRNiImiq5/Id+AA8OmnqqW01vGcyJYtWmHuuBVYPn0rxg+aDZG1\nDeDqygp/NkHk6IQhf12X2XY58zT+TFoPiUTc9MlUHZGJiWHTF69exc0rx3E69W+Z3Yndx6CVg4vi\nYxDT9t//skdra6AZFzISQszQe+8BAwcCly+r1j4zE/jjD/Z/edo0VpjXz48yKBKtrVu3DkKhEFlZ\nWcobGyEKZIh8/B1nA2ZoshCpsdZk/Xp03rQPbVxl01n+feF3fPXn+6h4VCr/eV99xerfhIcDAKof\nV+JeaY7MaAsA9uY1Lg5ioQC/HP1OZpdHa1/EdRmmel+JaeKLotK0MkKIti5cAA4eBG7fVq19mzYs\nMc3ixcDEiezmmrs7207MSmpqKsaOHYuAgADY2trC29sbcXFxWLRokaG7ZpTMY2oZ0T1+Gk2pnABg\n+3Y2JWvkSLY+xhh07AgBgGddp+GLX+dBLH5ctyst6zI+2fJ/mDL0Hfg0CHTQsSPQsSOKywpx6Oj3\nSLqyF2LJY+y9tgFt3NsixLczQtp0hr9HCCwHDcLx8hu4I5H9mYzuOxUiEf0pmT2BAHj+ecqQSAjR\nnkvtCL6qRTFbtwaee67x9poa3fWJGNypU6fQt29f+Pj4YPLkyfD29sbdu3dx/vx5LFu2DO+9956h\nu2h06N0XkU9RILNtG/vw9zeeQKaWv0c7zBy1GGv/WobSiuK67fdLC/DZtncwtv90RLbvU7e9oPgu\n/r7wO85ePwyxpD744TgJbuel43ZeOvaf+wVWFtYIau2HW4myufojQvog2EfJtDRiHjw8gM2bDd0L\nQog5cHZmj4WF2h3HkrJkmpPFixfDwcEB586dQ6tWrWT23bt3z0C9Mm7mMbUsPR2oqDB0L8yLoqll\nfDHMsLD6bQ8fAqdPA2fO6L9vSgR4tsdbzy9HoKfs3OGax9XYuO8z/HZ0LbILMrFuz3J8uPF1nEo5\nIBPEyFP9uArXi9JRaVv/T8PGyg5Px07Ux7dACCHEnKkyIrNkCfDGG+w9DnkiZGZmokOHDo2CGABw\ndXWV+frAgQPo168fHB0d0bJlS0RERGDt2rV1+48fP44xY8bAz88PNjY28PLywtSpU1FcXNzw0HKd\nO3cOgwcPhpOTE+zs7BAbG4sjR45o9f3pg3kEMiEhwKFDhu6FeenaFVi6lBW8lFZTU/+iKr3IcP9+\nlt3sf//TfV9692Z3wy9dUvkpji1a4/VR7yO20+BG+45c2olPfn4TyenHwXGSRvstRVYqnWNI9Di0\nbNH4xYYQQghRiA9kFI3IbNwIfP45UFLSPH0iBhcQEIDk5GRcuXJFYbuNGzdi0KBBuHfvHt5++218\n8skniIqKwu7du+va/PrrrygrK8O0adOwevVqPPvss9i0aROGDBmitB9Hjx5FbGwsSkpK8N5772HZ\nsmWoqqpCfHw8jh49qvX3qUvmM7WMCmLqVmio/Gwo//zDgpmAANm1AnzWLz6dsTJLlrARncREwEpJ\n4JCfzz7UzBRlIbLE6L5T0cY9CFsPfY3HYsVziV0cPRDsEo5At45oH9YOaVmXkZ59BTeyLslMUwMA\nX7cgxHRKVKs/hBBCCABg0CBg1y6WQlmekhLgxg32/7Fz5+btmzlqKrtqU2Ud1G2vI3PnzsWBAwfQ\nrVs3hIeHIzY2Fv369UP//v1hbW0NACgtLcXrr7+OiIgIHD9+vG57Qx999BFsbW1ltkVHR+OFF17A\niRMn0KtXL7nP4zgOr776Knr37o39+/fXbZ82bRq6du2KefPm4cSJEzr6jrVnPoEMLcBtHvy0sg4d\nZLcHBLBg8u5d4P59tjCxKffuAfPns8937ACCghofTxp/N0pRtqh9+4C5c4F+/YDPPpPZ1b1Df3g6\n+2Htro9QXN747pdn6zaIj3oWXYJ74WLyRQBsRCcqtC+iQvuC4zjk3c9BevZl/JuXjhY29hjcYxxE\nQlHT/SGEEEKa0qaN4oxj586xx65dWdZM8kTo27cvjh8/jmXLluHgwYM4d+4cVqxYgZYtW+Lzzz/H\nxIkTsX//fpSVleGdd95pMogBUBfEcByHsrIyVFdXI7q2LmBycnKTgczly5eRnp6Ot99+G4UNRgwH\nDBiAL7/8EpWVlbAxkjIEFMgQ9XTrBqxaBXh7y24XCtkIy7lzbFSmd++mj3HwYP3nw4ezAGTZMvlt\nOU61QKaqCrhyBfD1lbu7jXtb/N/zn2L9nuVIz2G1Y/z+vY/4yw8Q9vdvEAqanmUpEAjg6ewLT2df\n9GmyFSGEEKIj/HrT7t0N2w9zoe5Iip5HXhSJjo7GH3/8AbFYjJSUFOzatQuffPIJJk+eDD8/P2Rm\nZgIAnlJSyDs7OxtvvfUW9uzZg7KyMpl9DxSU1kivXT7w8ssvy90vEAhQVFQE74bvAw3EfAIZmlrW\nPAIDgddfl7+vY0cWyFy9qjiQOXCAPUZFAWfPAqmpTbetrASqq5UXIeSDHAV/nA52Tpj+zPvIyv8H\nVn8fhsfsVyEYNgxQEMQQQgghzY4CmSeeSCRCp06d0KlTJ0RHR6N///7YtGkTQkJClD5XLBYjPj4e\nRUVFmDdvHkJDQ9GiRQuIxWIkJCRAImm8PpjH71u2bBnCa2vsNeTiYjwFwM0jkAkKAhwcDN0LEhsL\nFBQ0Hq2RxnEsMQAAzJzJkglcv950e1VGY6T3K1kUKRAI4OcRDNzYwDZ0pNTJhBBCjMxnnwGjR7Pp\n0uSJFxkZCQDIzc3F4MEsidHVq1fRrl07ue2vXr2KtLQ0rF+/HuPHj6/bnpGRofRcQUFBAAB7e3v0\nM4HrzzxuRf/zD+DmZuhemJ9Fi9joy6NHqrWfOBHYuRN4+umm29y4Ady5w35fo0axKWm3brGRF3k8\nPIDycuDyZcXnVjGQqcMnJVAyNEsIIYQ0u7ZtgQkT2P9A8sQ4dOgQODnT2vhsZO3bt0d8fDxatmyJ\njz76CJVNvHcSidga3oYjL59++qnSPkRERKBt27ZYsWIFysvLG+03tno25jEiQ/Tj66+BvDxg3jyg\nQeYLjXl6AuvXs7o/NjZsNC0jg6V0lldcUyBg65+UrYFSN5Dhp7PRiAwhhBBDePVVNhV782ZWYJo8\n8WbOnImKigqMHDkS7du3h0QiQXJyMjZu3AgXFxfMnj0bDg4O+OKLLzB58mRERERg3LhxaN26NVJS\nUnD37l1s374doaGhCA4OxptvvomcnBy0atUKe/bswZ07d5T2QSAQYO3atUhISECHDh0wefJkeHt7\n4+7du3Wplw8ZUckTCmRI01q2ZIFMaSng5aWbYzo5sbtMvGHDgNxcwELLS9HBAbhwQfkUNN6lS2xK\nmwpzTQkhhBCdu3iRrSvNy6NAhgAAli9fju3bt2Pfvn1Yu3Ytqqqq4O3tjfHjx2P+/PloU5vp7qWX\nXoKbmxuWLl2KJUuWQCQSISQkBNOnTwcAWFhYYOfOnZg1axY++eQTiEQiJCYmYu3atfCQM8onaJBu\nOjY2FqdPn8YHH3yANWvWoLS0FJ6enoiMjMSUKVP0/4NQg4CTN4ZlAqQzLjjyVeiJbkVGAufPs0WH\nUVFshObQIXYXqX9/Q/dOL86fPw+ADa0Sokt0bRF9oOvKhA0eDOzZw6ZkDx1q6N7IMPbrypjS/xJZ\nyn43un7/bh5rZIh+8BcYf9EdPAj88gurFUMIIYQQzTk7s8eiovptEolBU/8SYmrMI5DJyjJ0D8xT\ny5bssbSUPfLrSsLCmn5Ofj6wdi2waZNu+kAv6IQQQswRn8JWOpC5cIEFOK++apg+EWJizCOQGTnS\n0D0wTxMnAl98wRbhV1ezRfkCAdC+fdPPuXkTmDIFkJcZQyxWvw/vvMMCqtWr1X8uIYQQYqz4ERnp\n6ulnzgDFxapnCyXkCWcei/2pGKZ+DB9e//m1a8DjxyzLmKKfNz9ac/06a88v4i8uZsU0BwwAtm1j\nAZEqiouBsjLtkwFIKylRPSkAIYQQog/jxgExMSzVMo8KYRKiFvMYkVGWmpdoLyWFPSqaVgaw0RM/\nv/oRHN6hQyyAuHevcRBz/jzw+efya8WoWhATAN5/HwgOZqksm5KXB7RqBYSG0rQ1QgghhhMYCMTF\nAT4+9dsokCFELeYRyNCIjP4lJLBg5J13lLfla7PwRScBYP9+9jhwYOP2mzYBb7wB7N3beJ86gUxJ\nCSuOmpvbdJuTJ9mjt7fqo0KEEEKIvt2/z24A2tjIr6tGCGnEPAIZGpHRP0dHoG9fIDpaeVs+kLl6\ntX7bgQPsUV4gExrKHq9fb7xPnUBGlaKYSUnsMSZG+fEIIYSQ5pKWBlhZAd26sUdCiFLmsUbGz8/Q\nPSDSBg1iKST5WjOZmcCtW2xKV3h44/aKAhk+9TMFMoQQQsxZdDTLEnrvnqF7QojJMI9AZvFiQ/fA\nPGVksGxhbdoAc+ao/rw+fdgH7/p1wNaWBTYiUeP20oEMx8lO+UpNZS/sDg7Kz6sskKmoAJKTWR96\n9FDteyGEEEKai7W17JoZQohC5jG1jOhHQQFLv/zrr9odZ+hQNvd35Ur5+11dWRrKsrLGxTZFIjaS\no0rWMmWBTE4OEBLChu3t7VXvPyGEEKIPw4cDXbrU12sjhKjFPEZkiH40LIipDRsbwNOz6f0zZ7Kg\nRZt5wXFxbFSHLzLWUEgIy75WVaX5OQghhBBduXIFuH2b1ZLh/+cSQlRGgQxpmqMje0xJYWmXFywA\nnn9eP+f63/+0P0bLlqr9I7C21v5chBBCiLacnVkgU1TE0jETQtRCU8tI06SDgtRUtoCfEEIIIbrB\nzyA4epRN5yakCf/++y+EQiHWr19ft23dunUQCoXIysoyYM8MyzwCmfJyQ/fAPDVcYK+sGKa07GyW\nIODddzU/v0RCRSsJIYSYL2dn9vjWW4C7OwtoyBOLD0zkfcyYMQMCgQACJTXwNm/ejC+++KKZemx4\n5jG17NAhtmCO6JZIBHz0UX0RzPbtVX9uTQ3w2Wfs8zffbHrdiiJ797Lf6zPPANu2qf98QgghxJhJ\n/28UCNjCf/LEW7RoEYKCgmS2hYSEYPv27bBQkvxo8+bNSElJwaxZs/TZRaNhHoGMnZ2he2C+EhNZ\nIBMczBbsq8rfv/7zmBjgxg31z11SAojF8lM2q+u339g/jO7daY0MIYQQ4zBzJtCuHTBjBitFwK9N\nJU+0QYMGISoqSuPnKxu10cSjR49ga2ur8+NqyzymlrVoYegemK+0NPaozrQyABBKXVpt26r2nM2b\ngVdeYVlcgPo0yqoUw+QlJLAc/Ddv1m/jOOC111htm9u3VT8WIYQQok9t29avP+3e3bB9IUZN3hqZ\nhuLi4rB79+66tvwHj+M4rFq1Ch07doStrS3c3d0xZcoUFBUVyRzH398fiYmJ+Pvvv9G9e3fY2tri\n448/1tv3pg0akSGKPfsskJcHPHyo/nNXrmRT01asUK397t3ATz+xF/NOnTQLZAoKgDt3gOLi+m2Z\nmUB+PqtXExys+rEIIYQQfTtzhj1SIKM3M794Wm/HXjnrD50fs6SkBIWFhXL3KRptWbBgAebOnYuc\nnBx8/vnnjfb/5z//wQ8//ICJEydi5syZyMrKwqpVq3D27FmcO3cO1rUzVgQCAf755x+MHj0aU6dO\nxSuvvII2bdro5pvTMfMIZGhERn8EArYAURMzZrAPVYWGssfr19mjJoGMvKKYSUnsMSaGfT+EEEKI\nsfDzY///evQwdE+IkUhISJD5WiAQ4Ao/W0WBAQMGwMvLCyUlJRg3bpzMvpMnT+Lbb7/Fxo0b8cIL\nL8icKzY2Fhs2bMArr7wCgI3cZGZmYseOHRg6dKgOviP9MY9ApmF2LWKaGgYyZWXsUZeBDCGEEGJM\nlixhH4TUWrVqFUL590S1bNRZpyzHtm3bYG9vj/j4eJnRnpCQELi5ueHw4cN1gQwA+Pr6Gn0QA5hL\nIKPpiAExLh06sEc+kPnqK5b5TJ1RFHmBzPHj7DE2Vvs+EkIIIYToUWRkZKPF/v/++69Wx0xPT0d5\neTncm3jPfO/ePZmvA02kQKt5BDLEPAQFARYWbEH+w4ds7ZO6dyAaBjIcxxIInDpFaS0JIYSQJ5A+\n1rGYGolEAmdnZ2zdulXu/latWsl8bYwZyuShQIYYD0tLYNUqwMNDNuuZOt5+G5g1iy3sB9hozv/9\nn+76SAghhBBipJpKBhAUFISDBw+ie/fuaGFGa8t1ln7522+/Rd++feHk5AShUIisrKxGbYqLizF+\n/Hg4OTnByckJEyZMwIMHD2TaZGVlYdiwYbC3t4erqytmzZqFmpoaXXWTGLtp04Cnn1Z/JIbn7s4W\nTlImO0IIIYQ8YVq0aIFi6cyttcaOHQuJRIL333+/0T6xWIwS6Sn5JkRngcyjR4+QkJCARYsWNdlm\n3LhxuHTpEvbt24e9e/ciOTkZ48ePr9svFosxZMgQVFRUICkpCT///DN+/fVXvPnmm7rqJiGEEEII\nIWYpMjISDx48wOzZs7F582Zs2bIFABAbG4vp06fjk08+QWJiIj777DOsWbMGc+bMQWBgIHbs2GHg\nnmtGZ1PLZs2aBQA4f/683P3Xr1/Hvn37cOLECXSvzZX+zTffIDY2FhkZGQgODsb+/fuRmpqKrKws\neHt7AwA+/vhjTJkyBUuWLIG9vb2uukuMHccB1dVAbU5zQgghhBBzp6hOjCrtX3vtNVy9ehWbNm3C\nqlWrALDRGIBlQ+vWrRu+/vprLFiwABYWFvDz88OYMWPQr18/jftgSM22RubUqVOwt7dHdHR03bae\nPXuiRYsWOHnyJIKDg3Hq1Cl06NChLogBgPj4eFRVVeHChQvo06dPc3WXGNrDh4C9PdC6NdCg4iwh\nhBBCiLmZOHEiJk6cKHefv78/JBKJ0va2trZYt25dk+eYNGkSJk2apLAft27dUqW7RqHZApm8vDy4\n8guwawkEAri5uSEvL6+uTcO0cC4uLhCJRHVt5GlqFIiYLsuCAnQGUC0U4oqGv1/X7dvRIiUF90aO\nREXHjmo9l64poi90bRF9oOuK6IOxXld+fn5a11Uh+lFWVoZr1641uT84OFin51O4RmbBggUQCoUK\nP44dO6bTDnEcp9PjEdPjvXo1wp57DgAgVrPYqUVhITqOGIEOY8fC6fBhuOzcCauCAn10kxBCCCGE\nGJDCEZk33ngDEyZMUHgAX19flU7k4eHRqNgOx3EoKCiAh4dHXZuTJ0/KtCksLIRYLK5rI09ERIRK\nfSAmIi8PqKgAANh6eKj3+y0tBe7eZVnP8vMBAEETJgCenio9nb/7RNcU0TW6tog+0HVF9MHYr6vK\nykpDd4E0wcHBQeF10zBbsbYUBjLOzs5wdnbWyYmio6NRXl6OU6dO1a2TOXXqFCoqKtCzZ08AbM3M\nhx9+iDt37tStkzlw4ACsra0RHh6uk34QExAaCuzdyz7nC1yqyt6e1aDhX+SCglQOYgghhBBCiOnQ\n2RqZvLw85OXlIT09HQCQkpKC+/fvw8/PD61atUJoaCgSEhLw6quv4ttvvwXHcXj11VcxbNiwuvly\n8fHxCAsLw4QJE7B8+XIUFhZi7ty5mDp1KmUse5KEhtZ/3qDSrFJCIeDoCPA51GNjddcvQgghhBBi\nNHRWR+brr79Gt27d8OKLL0IgEGDIkCEIDw/Hzp0769ps3rwZnTt3xqBBg5CQkICuXbti48aN9Z0R\nCvHXX3/Bzs4OvXr1wtixY/Hss8/i008/1VU3iSngA5lu3YAfflD/+dKjODExuukTIYQQQggxKjob\nkVm4cCEWLlyosI2Tk5NM4CKPr6+vTPBDnkB8IJOWBlhaqv98PpBZsAAYPFh3/SKEEEKIUeA4zqTq\nnTwJDJGwq9nSLxOiMmdnYNcuoF07QJMXqZ07ASsrVoNGJNJ9/wghhBBiMFZWVqisrISNjQ0FM0aC\n4zhUVlbCupkLmVMgQ4zTkCGaP1eqoCohhBBCzItQKIS1tTWqqqoM3RUixdraGkKhzlatqIQCGUII\nIYQQYlKEQiEVxSS6W+xPCCGEEEIIIc2FAhlCCCGEEEKIyaFAhhBCCCGEEGJyKJAhhBBCCCGEmBwK\nZAghhBBCCCEmhwIZQgghhBBCiMkRcIYow6kDDx48MHQXCCGEEEIIIRpwdHTU+hg0IkMIIYQQQggx\nORTIEEIIIYQQQkyOyU4tI4QQQgghhDy5aESGEEIIIYQQYnIokCGEEEIIIYSYHApkCCGEEEIIISbH\nZAOZNWvWICAgALa2toiIiEBSUpKhu0RMyNKlSxEZGQlHR0e4ublh+PDhSElJadRu4cKF8Pb2hp2d\nHfr27YvU1FQD9JaYqqVLl0IoFGLGjBky2+m6IurKzc3FSy+9BDc3N9ja2iIsLAzHjh2TaUPXFVHX\n48ePMW/ePAQGBsLW1haBgYH473//C7FYLNOOri2iyLFjxzB8+HD4+PhAKBRi/fr1jdoou4aqqqow\nY8YMuLq6wt7eHiNGjMCdO3eUntskA5mtW7di9uzZWLBgAS5duoSePXsiMTER2dnZhu4aMRFHjx7F\n66+/jlOnTuHQoUOwsLDAgAEDUFxcXNdm2bJlWLFiBb788kucO3cObm5uGDhwIMrLyw3Yc2IqTp8+\nje+++w6dOnWCQCCo207XFVFXSUkJevXqBYFAgN27d+PGjRv48ssv4ebmVteGriuiiSVLluCbb77B\nqlWrkJaWhi+++AJr1qzB0qVL69rQtUWUqaioQKdOnfDFF1/A1tZW5n8eoNo1NHv2bPz222/YsmUL\njh8/jtLSUgwdOhQSiUTxyTkTFBUVxU2dOlVmW3BwMPfuu+8aqEfE1JWXl3MikYjbtWsXx3EcJ5FI\nOA8PD27JkiV1bR49esQ5ODhw33zzjaG6SUxESUkJFxQUxB05coSLi4vjZsyYwXEcXVdEM++++y4X\nExPT5H66roimhg4dyk2cOFFm24QJE7ihQ4dyHEfXFlGfvb09t379+rqvVbmGSkpKOCsrK27z5s11\nbbKzszmhUMjt27dP4flMbkSmuroaycnJiI+Pl9keHx+PkydPGqhXxNSVlpZCIpGgVatWAIBbt24h\nPz9f5jqzsbFB79696TojSk2dOhWjR49Gnz59wElluKfrimjijz/+QFRUFMaMGQN3d3d07doVq1ev\nrttP1xXRVGJiIg4dOoS0tDQAQGpqKg4fPowhQ4YAoGuLaE+Va+jChQuoqamRaePj44PQ0FCl15mF\nfrqtP4WFhRCLxXB3d5fZ7ubmhry8PAP1ipi6WbNmoWvXroiOjgaAumtJ3nV29+7dZu8fMR3fffcd\nbt68ic2bNwOAzBA7XVdEEzdv3sSaNWswZ84czJs3DxcvXqxbdzV9+nS6rojGXnvtNeTk5CA0NBQW\nFhZ4/PgxFixYgGnTpgGg1yyiPVWuoby8PIhEIjg7O8u0cXd3R35+vsLjm1wgQ4iuzZkzBydPnkRS\nUlKjeZ3yqNKGPJnS0tIwf/58JCUlQSQSAQA4jpMZlWkKXVekKRKJBFFRUfjwww8BAJ07d0ZGRgZW\nr16N6dOnK3wuXVdEkZUrV+LHH3/Eli1bEBYWhosXL2LWrFnw9/fH5MmTFT6Xri2iLV1cQyY3tczF\nxQUikahRhJafnw9PT08D9YqYqjfeeANbt27FoUOH4O/vX7fdw8MDAOReZ/w+Qho6deoUCgsLERYW\nBktLS1haWuLYsWNYs2YNrKys4OLiAoCuK6IeLy8vdOjQQWZb+/btkZWVBYBer4jmPvzwQ8ybNw/P\nPfccwsLC8OKLL2LOnDl1i/3p2iLaUuUa8vDwgFgsRlFRkUybvLw8pdeZyQUyVlZWCA8Px/79+2W2\nHzhwAD179jRQr4gpmjVrVl0Q065dO5l9AQEB8PDwkLnOKisrkZSURNcZadLIkSNx7do1XL58GZcv\nX8alS5cQERGB559/HpcuXUJwcDBdV0RtvXr1wo0bN2S2paen1918odcroimO4yAUyr4VFAqFdaPI\ndG0RbalyDYWHh8PS0lKmTU5ODm7cuKH0OhMtXLhwoV56rkctW7bEe++9By8vL9ja2mLx4sVISkrC\njz/+CEdHR0N3j5iA6dOnY8OGDfjll1/g4+OD8vJylJeXQyAQwMrKCgKBAGKxGB999BFCQkIgFosx\nZ84c5Ofn49tvv4WVlZWhvwVihGxsbODq6lr34ebmhp9++gl+fn546aWX6LoiGvHz88OiRYsgEong\n6emJv//+GwsWLMC7776LyMhIuq6IxjIyMrBu3Tq0b98elpaWOHwFjSkfAAABbUlEQVT4MObPn4+x\nY8ciPj6eri2ikoqKCqSmpiIvLw9r165Fx44d4ejoiJqaGjg6Oiq9hmxsbJCbm4vVq1ejc+fOePDg\nAaZNmwYnJycsW7ZM8RQ03SVca15r1qzh/P39OWtray4iIoI7fvy4obtETIhAIOCEQiEnEAhkPhYt\nWiTTbuHChZynpydnY2PDxcXFcSkpKQbqMTFV0umXeXRdEXX99ddfXOfOnTkbGxsuJCSEW7VqVaM2\ndF0RdZWXl3Nvvvkm5+/vz9na2nKBgYHc/PnzuaqqKpl2dG0RRQ4fPlz3Pkr6vdWkSZPq2ii7hqqq\nqrgZM2Zwzs7OnJ2dHTd8+HAuJydH6bkFHKfCKlRCCCGEEEIIMSImt0aGEEIIIYQQQiiQIYQQQggh\nhJgcCmQIIYQQQgghJocCGUIIIYQQQojJoUCGEEIIIYQQYnIokCGEEEIIIYSYHApkCCGEEEIIISaH\nAhlCCCGEEEKIyfl/FDrRIKqSSIQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11e2978>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This doesn't look so wonderful to me. We can see that perhaps the filtered signal varies less than the noisy signal, but it is far from the straight line. If we were to plot just the filtered result no one would guess that the signal with no noise starts at 5 and increments by 2 at each time step. And while in locations the filter does seem to reduce the noise, in other places it seems to overshoot and undershoot.\n",
      "\n",
      "At this point we don't know enough to really judge this. We added **a lot** of noise; maybe this is as good as filtering can get. However, the existence of the multitude of chapters beyond this one should suggest that we can do much better than this suggests."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: The Effect of Acceleration"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a new data generation function that adds in a constant acceleration factor to each data point. In other words, increment dx as you compute each data point so that the velocity (dx) is ever increasing. Set the noise to 0, $g=0.2$ and $h=0.02$ and plot the results. Explain what you see."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gen_data(x0, dx, count, noise_factor, accel=0):\n",
      "    zs = []\n",
      "    for i in range(count):\n",
      "        zs.append(x0 + dx*i + random.randn()*noise_factor)\n",
      "        dx += accel\n",
      "    return zs\n",
      "   \n",
      "predictions = []\n",
      "zs = gen_data(x0=10, dx=0, count=20, noise_factor=0, accel = 2)\n",
      "data = g_h_filter(data=zs, x0=10, dx=0, g=0.2, h=0.02, pred=predictions)\n",
      "plt.xlim([0,20])\n",
      "plot_g_h_results(measurements=zs, filtered_data=data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1eOwfr9K2SReDkkl5oFuzRERERApz9iw88gj89XDCBx+EiRONzeQhbHYbC5Kn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\njbsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1442a90>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Each prediction lags behind the signal. If you think about what is happening this makes sense. Our model assumes that velocity is constant. The g-h filter computes the first derivative of $x$ (we use $\\dot{x}$ to denote the derivative) but not the second derivative $\\ddot{x}$. So we are assuming that $\\ddot{x}=0$. At each prediction step we predict the new value of x as $x + \\dot{x}*t$. But because of the acceleration the prediction must necessarily fall behind the actual value. We then try to compute a new value for $\\dot{x}$, but because of the $h$ factor we only partially adjust $\\dot{x}$ to the new velocity. On the next iteration we will again fall short.\n",
      "\n",
      "Note that there is no adjustment to $g$ or $h$ that we can make to correct this problem. This is called the *lag error* or *systemic error* of the system. It is a fundamental property of g-h filters. Perhaps your mind is already suggesting solutions or workarounds to this problem. As you might expect, a lot of research has been devoted to this problem, and we will be presenting various solutions to this problem in this book.\n",
      "> The 'take home' point is that the filter is only as good as the mathematical model used to express the system. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Varying g"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's look at the effect of varying g. Before you perform this exercise, recall that g is the scale factor for choosing between the measurement and prediction. What do you think of a large value of g will be? A small value? \n",
      "\n",
      "Now, let the `noise_factor=50` and `dx=5`. Plot the results of $g = 0.1\\mbox{, } 0.5,\\mbox{ and } 0.9$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_data(x0=5, dx=5, count=100, noise_factor=50)\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0., dx=5., dt=1.,g=0.1, h=0.01)\n",
      "plot_g_h_results (zs, data, 'g = 0.1')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0., dx=5., dt=1.,g=0.5, h=0.01)\n",
      "plot_g_h_results (zs, data, 'g = 0.5')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0., dx=5., dt=1.,g=0.9, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.9')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oypF46QTW7v4WOYXKGucd7Z0xuv8k9IkaWnMb4G+/1f5zz5669Nq8VCqREd7H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\n/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cXq3bs3eQWvDRkyRAcOHPBoO3TokPsfVPh7hcYyDENWq+fXO6vV6h7tJbfQVA3JoYED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\nAAAAADAFihMAAAAApvD/mDKfFfir7qEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1220a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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J1sesRDHUX+ItzGXo4R6of1/0oVQ2HjS99JLw+8jPb1v7c+YIn6NPPlGXVVQA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zp6RB2u3veVEK0k7yvRVuS9JdpCXp5p3bjWaNXMSVhYGH5+fmzcuNHQVlpays6dOxk1SkkFGxMT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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c15262b0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ceGvL80K55nBtBG5b+l+9boEaqFh9PMKd7qCjvaMNDc1WRb7JQLZ0KSxfDtx8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NXBSX2bMDjhwKG2pXxc961qvIx2DDrGUqkMKwpu8vp6sdWTVe0h2Lz09nE9V1KmeNDD74FCCCGE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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11b2160>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is clear that as $g$ is larger we more closely follow the measurement instead of the prediction. When $g=0.9$ we follow the signal almost exactly, and reject almost none of the noise. One might naively conclude that $g$ should always be very small to maximize noise rejection. However, that means that we are mostly ignoring the measurements in favor of our prediction. What happens when the signal changes not due to noise, but an actual state change? Let's look. I will create data that has $\\dot{x}=1$ for 9 steps before changing to $\\dot{x}=0$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = [5,6,7,8,9,10,11,12,13,14]\n",
      "\n",
      "for i in range(100):\n",
      "    zs.append(14)\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=0.1, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.1')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=0.5, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.5')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=0.9, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.9')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V+uvrD2lfwU6TOgMAAJ2NENEDMJUJgcJuC9JtM3+mc0ZeYqjXN9bqqTd/ox0H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\nVQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c118ed30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DMe3C3FKLKgEAAABSw7CEiFAopIsuukg7duzQiy++2OelTFVVVcPxsUkXiYT1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\n4WQzDMMYiQ9qaGgw39+4bqkkaezoMt2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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11c8710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oNze3xdfu2rWro2/bYQXl3o8yxTp7a8+evT1eB1pmRd9AYKGPoDX0EbSE/oHW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c118e9b0>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see the effects of ignoring the signal. We not only filter out noise, but legitimate changes in the signal as well. \n",
      "\n",
      "Maybe we need a 'Godilocks' filter, where is not too large, not too small, but just right? Well, not exactly. As alluded to earlier, different filters choose g and h in different ways depending on the mathematical properties of the problem. For example, the Benedict-Bordner filter was invented to minimize the transient error in this example, where $\\dot{x}$ makes a step jump. We will not discuss this filter in this book, but here are two plots chosen with different allowable pairs of g and h. This filter design minimizes transient errors for step jumps in $\\dot{x}$ at the cost of not being optimal for other types of changes in $\\dot{x}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = [5,6,7,8,9,9,9,9,9,10,11,12,13,14,15,16,16,16,16,16,16,16,16,16,16,16]\n",
      "    \n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=.302, h=0.054)\n",
      "plot_g_h_results(zs, data, 'g = 0.302, h = 0.054')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=.546, h=0.205)\n",
      "plot_g_h_results(zs, data, 'g = 0.546, h = 0.205')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IsLKDrZU9bK2VbzZW9rD713vlcTuYScy0+zykyh8Cu/r20lvdDSGKIsory1D6j2AhKy+u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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1233828>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bB3XAkwNegSAIViqQiKh+4kwEERHZp7w8YMgQ4PRp7HmsLXY8ECACvJvihWFv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\nt26tgIAAtW7dWk8//bRcLldF5EMZJX31odbvXG6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IOrfublEqAAAAoPrz+HSmtWvXqnv3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\nAIByoYkAAAAAUC40EQAAAADK5f8AAzTy+bIR4RcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11a4fd0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Varying h"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's leave g unchanged and investigate the effect of modifying h. We know that h affects how much of we favor the measurement of $\\dot{x}$ vs our prediction. But what does this *mean*? If our signal is changing a lot (quickly relative to the time step of our filter), then a large $h$ will cause us to react to those transient changes rapidly. A smaller $h$ will cause us to react more slowly.\n",
      "\n",
      "We will look at three examples. We have a noiseless measurement that slowly goes from 0 to 1 in 50 steps. Our first filter uses a nearly correct initial value for $\\dot{x}$ and a small $h$. You can see from the output that the filter output is very close to the signal. The second filter uses the very incorrect guess of $\\dot{x}=2$. Here we see the filter 'ringing' until it settles down and finds the signal. The third filter uses the same conditions but it now sets $h=0.5$. If you look at the amplitude of the ringing you can see that it is much smaller than in the second chart, but the frequency is greater. It also settles down a bit quicker than the second filter, though not by much."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = np.linspace(0,1,50)\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0, dx=0., dt=1.,g=.2, h=0.05)\n",
      "plot_g_h_results(zs, data, 'dx=0, h = 0.05')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0, dx=2., dt=1.,g=.2, h=0.05)\n",
      "plt.ylim([-1,5])\n",
      "plot_g_h_results(zs, data, 'dx=2, h = 0.05')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0, dx=2., dt=1.,g=.2, h=0.5)\n",
      "plt.ylim([-1,5])\n",
      "plot_g_h_results(zs, data, 'dx=2, h = 0.5')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A/6LKXqnU/euVsPkLFVQWOZ2xyKJhfcYoJny2OrXtZm5AoBGieAAAAPxdZVWF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c00beb00>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1trZqwYIF139CP3VdZC6PsxABZUT6aA1LGe4bewyPdhxmzQgAAIBwYzP6cMP/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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c00c3d30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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igxMlfZzyRURERETkWMZFkmI51WtyP1O9eliuSymsyLFJTERERERENDJOn6QYDN3IKZZu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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1262eb8>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking a Train"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try a practical example. Earlier in the chapter we talked about tracking a train. Trains are heavy and slow, thus they cannot change speed quickly. They are on a track, so they cannot change direction except by slowing to a stop and then reversing course. Hence, we can conclude that if we already know the train's approximate position and velocity then we can predict its position in the near future with a great deal of accuracy. The train just cannot change its velocity much in a second or two. \n",
      "\n",
      "So let's write a filter for a train. Its position is expressed as its position on the track in relation to some fixed point which we say is 0 km. I.e., a position of 1 means that the train is 1 km away from the fixed point. Velocity is expresses as meters per second. We perform measurement of position once per second, and the error is $\\pm$ 500 meters. How should we implement our filter?\n",
      "\n",
      "First, let's just simulate the situation without a filter. We will assume that the train is currently at kilometer 23, and moving at 15 m/s. We can code this as \n",
      "\n",
      "    pos = 23*1000\n",
      "    vel = 15\n",
      "    \n",
      "Now we can compute the position of the train at some future time, *assuming* no change in velocity, with\n",
      "\n",
      "    def compute_new_position(pos, vel, dt=1):\n",
      "        return pos + (vel * dt)\n",
      "        \n",
      "We can simulate the measurement by adding in some random noise to the position. Here our error is 500m, so the code might look like:\n",
      "\n",
      "    def measure_position(pos):\n",
      "        return pos + random.randn()*500\n",
      "        \n",
      "Let's put that in a cell and plot the results of 100 seconds of simulation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "\n",
      "def compute_new_position(pos, vel, dt=1):\n",
      "    \"\"\" dt is the time delta in seconds.\"\"\"\n",
      "    return pos + (vel * dt)\n",
      "\n",
      "\n",
      "def measure_position(pos):\n",
      "    return pos + randn()*500\n",
      "\n",
      "\n",
      "def gen_train_data(pos, vel, count):\n",
      "    zs = []\n",
      "    for t in range(count):\n",
      "        pos = compute_new_position(pos, vel)\n",
      "        zs.append(measure_position(pos))\n",
      "    return np.asarray(zs)\n",
      "\n",
      "    \n",
      "pos = 23*1000\n",
      "vel = 15\n",
      "zs = gen_train_data(pos, vel, 100)\n",
      "\n",
      "plt.plot(zs/1000)# convert to km\n",
      "plt.xlabel('time(sec)'); plt.ylabel('km')\n",
      "plt.title('Train Position')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q6QQFQgRBEARBGEZj0x5me9wzRnVCRMoZ94wx21QjRAAUCBEEQRAEYRDDo4No6TrO7JMh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\nz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f4d2jJa6qpQPDGupN5XnjSLE5MxUDUd9Im4N5guLIGaI6TwOVNSuStUYmz1wAuoSB1k\ny0Znq6ezKS1G5fo1UVOpxDBV47BZ7ETARiqiR2hmwC2ExG+iIEtEIWQQdHx2KtUKipCR1jivf4yw\nlTjsLu6gRK0wA1V1WON6hthCqCwlrjgWi6JroJW4Tu8w1R+kYosDWGvcdFWE2BlC6qEcMxn6hDdh\njUs3QygVvQEmhaAI0TY2NWucLMtsfLbCMEolhcUoRQjg2eMm+oSYxDineiGkpGLl+jVxqSpCwhpn\nFJIkKT6fQhGaGfCscaIQEmSLKIQMwma1K65KTUaPkJHR2QAnNU6XNY7s9amraGRmyND2uB46OjtN\n3DJtjRvxDCAWi2o+xqkCo/IJG4AiSrOE6M9GmZsNSkhA92CpfSYj0QjxnjObLHmJSqaVEl/AoxhR\nH41FIKcsmJjNFkW7mVuh8KgoMUYRAtjAhAudpxCJhgGwBV06RQjgW0d56XpGoqb6CGucsSjNEhI9\nQjMDXny2KIQE2SIKIQNRsscpFUJ0sZJNapyRiXEAYKNWibXGZ/MS4+or52BO7UJiHx2Y0EdFZ9el\nKYRsVjtRFMTlOIa9A5qOcSrh8ZOpWSUu0SOkBBOWEFFQhFQWCegJ5WqFEG+GUC57UZSwUbNqIrGw\n4ueV3q+kBgEqipBBYQkAUF3WQJzcRGJhXOg6BYAzTDXN4FKAb+fLtTXOaXcxfZDJy4QiZCgOhVlC\nQhGaGdhtDmZxIdtFX4FAFEIGwrPHOYuKFX8M6bCEUf+w4kpuOoxMjAN4c4S0KUIj3kHiBNFuc6C8\nuEqDIqQ9OjtBRSl5QjYdk+PoAA0RlqAMvfKf6N8Z9dIhIsqKEBNgoqsQmnxbHDBuGdLaJ0SnP6r1\nVvAKIbejVLV3Ty+SJDE9hGc6xucJMdY4DYUQbzEq16+LyWSGQ+E7XvQIGYuyIiR6hGYKdI+iSI0T\nZIsohAyE9yNcraAGAeMnbqlf4LFYVDV2Wo1CscbRFre6ikZIkoSmmvmQUgaB9g13JqNx4/EYowil\n6xECgKoS8rkdHOtTuObURcwR0g59MhRWsMapfTbcjhLifeoPeZNWLZpCCEpIQBcJ9CDSBHR/kFqs\nNK8fzcj+oAR0IXS2fbxPSM8MoQS8hQJ60G4ucCsUPC6hCBmKUiEkFKGZw6oFH8bIMb4AACAASURB\nVEr+v8RVziyyCgR6Uc4iFeiGZ8tQssUlKHFVoH+kK7k96hvWtPJJQ69cZ2+NoxUhbda47sE2Yru+\nsgnAeNFXX9GIrpTL23vfx+I5qzHk6Uc0NpEi53KUaLLBVDKKUI+mY5wqhMIB4nk3my2KkcYCNUUo\n/QyhBCaTGcXOUuLz5PGPcAuAQlGEALZ/RilCm/4cq6k7vM+gUYlxqbQ0riS2O/rOwxcYY4o5t8ps\nowRca5w996+L01EMjHD2C0XIUJwK1jjRIzRzuGbdn8HtKMXQWB82r9iRl75MwfRCKEIGwltBVZoh\nlMCowAQjZwgB7EpxOBLSZNujgxLqK5qS/2+qo/qEesf7hHozsMUBQOU0V4QYNchRlpcelKkCvfKf\nUD9GmM+GsjUOYFU3peS4QiqE6MUTWk1JENYwQygBT4ExMighQbGzDLOq5ia3Zcg4e+l4RooQ3xo3\nGYoQf+FG9AgZi9POLyytFtskH4kgX5hMZmxesQM7N9+eE4VaMPMQhZCB8H6o0ylCRg1VHaP7ILK0\nxplNZiJNSoZMqDZK9FBBCXWVExa3uXSfUM94nxDdH5QuKCFBPhShzv6L+PvH/goP/Ovn8cSen2Fo\nrD9nj8VEZwsvtCrMQNVwAPF4jEneS/fZ0Lo4UUjWOFq9UbTGhamwBN2FUG5OPJg+ofYjTJ+TFqWc\nTv0D2DTBXKDUC6R04i7IDF5YgtVsg8lkzsPRCASC6YAohAyE509XmiGUQOvqczpG/cZa4wD99ri4\nHEc31SPUUDkn+X9ecpwsy+ilo7PL0/cHAUAlNUtoMhSh37/+K3QNtGLUO4g3jv0Rf/vrr+C3L/0Y\nAzkowsQMIX0wA1UjAXgCo8R8LWdRcdrVY7YQ4qc5FrIiRA8jTUD3+qla4zjx2byBhkawqGk1sX2m\n4yh8fqoQ0mAz4xVvk/G68Io0m7UIVouw7RgJr0fIyPAOgUAw8xA9QgbCtcal7RHSdtKlBm/V25BC\nyFqEQMiX3A5FQnCpLK4Oe/qJYslhdxHHUVfZBJvFnjwZ8wRGMezpRy8TlKDNGlfmroTJZEY8HgMw\nbgcKhQM5mxsSi8eS0b4T+6LYf2I33j75MtYuuhLXrv+EYY/H9H2JoARVaEUmHA4yiXFlGpRSrSot\nowjZ86gIUUWCUo+Q1mGq4/fJntzT87uMYn7DUpjNluRcpsHRXiaSOuOwhElQ6nhFmkuhsV+QOTyr\nYTaDwwUCgUAoQgZC/1DbrEVp446N6BHyBT3EqrfD7jLkx8FO3UckTXJcD6c/KLWnxWwyo7FmPnGd\n1p6zbI+QRmucyWRmmrcHx3IXod0/0qVoD4zLcRw8/Sr+36NfxWtnnsaIP3vLHD1DSERnq2OjLFDB\nSICdIZSmPwjQrtKGClkR0hiWYLcpF0Jms4WY8WM2WxgV1ihsVjua65cQ+2RM9CSaTRZNBQ1vMSpf\nipDoDzIeJycsRq3PTSAQCNIhCiEDqS6rJ1K9mhuWpG1uZ4eq6i+EmBNmDSunWrBSlgN6NZmmixmk\n2sRch466PH7xIPwhb3LbZrHrst9Ulk6ePa5roC3tdWTIaB04iWeP/AJnO97L6vFoJUIMU1WHPlEO\nRQJMYpyWEBF6qKrHx4kDQ2FZ45g5QhoVIXpwMs32dTcnlZmr13wsZ2orACyi0uNSGY81Tx8UUmRz\nEr2NANs7lgt4ipBIjDMe3nNqtYqgBIFAkDnCGmcgVosNn7n2Xjy77z/gtLtx85V3pb2NEYoQM4Hd\noF4S2jaTbpaQWlBCgjlUctyx998itmvKZ8Ekaa/P6RXqXPTqJKALoatW34DGmvl48eDvmDlIcTmO\nFw88gZbGFRk/Hp0aVyyscarQPUKhcJBJUyxzaVCEqIJz1K/UI0Ra4yajKV8JrQNV6cHI6forrlh1\nPRbPWYNYPIo6DbO9smFR0yo8u/8x7mVaRwpIkoQSRxmGvQPJfZOjCHGscaIQMhxej5CavVMgEAjS\nIQohg1nRvAErmjdovj5dCNGhB1rIJGZWC8xQ1Yh6IdQ9pEERqiUVIbq40hqdnaCS6sEayqki1Eps\nz65uxoYlV2Pdoitx5P39ePHAk8ScpHOXjmNorD/jyGE6LKFEhCWowkuNo3uEtClCWlPjaEWo8Aeq\nsnOE0p9Epgt8MYrGmvlw2F1EX2ICLXPFEsypa8Hw++OFkM1ahJpJOH4Xp59KWOOMh5saJ8ISBAJB\nFghrXJ5x2t3EQLBwJMisNKeDLoSMssaxhZCyNS4ej6F3kOz14RVC5cVVqr0uWvuDEtDN27lVhFqJ\n7YYPZp+YTGZc1nI5/ten/wlNNQuSl8uQcfD0qxk/Hh2AIRQhdWwWO9FgH4mFMewhe7W0xMrTPUIe\n/2gykCMVNj47jz1ClPpA9w0mYMISCqi/wmQyo2U2X0HVUwjt3Hw7WmavQF1FIz5zzV8Ka9w0wmax\nMwM06V5WgUAg0IMohPKMJEnM7Au9yXF0j5BR1ji6f0DNGjc41odILJzcdjlKuAWPJElMn1AqtTrt\nN7Q1LleKUCDkw1DKSbVJMjHzjkySCRuWXk3sO3hqj6ZBtDSyLIuwBJ1IkgQb1fzfO9JFbGsJS7Ba\nbIQFR5bj3J4bNjUuf4WQxWwlCjFZjiMQ9DLXy0QRmkzoGO0Eegqh6rJ63PNnf4tv3f5DrF74YaMO\nTRUXR/3h7RNkD22PE4qQQCDIBlEIFQB0c7beWUJMj5COkwY19FjjuumgBJWChp4nlIpea1wVHZYw\n2ptR4ZEO+u+rLm/gzqNZ23IF0ePUN9KF1p6zuh8vGPYThaXVYsur9WqqUET16dBhCWUarHEAx7LK\n+UwWkjUO4PUJsfa4ELWYYS+wk0h6sGoCnvWskDCbLXBQiiCvn0WQPbTlUPQICQSCbBCFUAGQbWCC\nl2mqN0Y5YAaqRpWtcUwhlDJIlWaugiIkSSZUlzXoOMJx+0mq9SUcDTFKihF0Ura4WR/Y4mhcjhLM\nLicLvQOn9uh+PDYooUxTatZMR83qZTZZNDfd059JD6d3r5BS4wBtEdrhAgp44FFVWsdE4gPGLe7k\nEvr55wUoCLJHKEICgcBIRCFUAGQboe1hwhKMUoSoFC4VRUhLYlyCxtr53P1VpXW6J7FLkoSqEjpC\n2/hZQt1UYlyDSqHXXEPGAL9z9nVEomGFa/NhgxJEf5AW1PpBSlzlmhMJtcwSKqQeIYAdgMqz89GK\nULrUuMlGkiSuPU5rAZtPaEtyoatYUxU6MKHQVE2BQDC1EIVQAcAoQgpxvUqw1rjchCVE1KxxQ9Qw\nVU5QQgKn3Y3acjYUQa8tLgEzSygHgQl0dHZ9lXIhNKt8AeyWiZPiQMiH4xcP6no8uhgWM4S0oVYI\naUmMS5BOpY3HY0S/jQQp70UFrUDwCiGmR6gAbUU8e5xR32m5ZGXzxuT/S5zlzKgAgTEwipAISxAI\nBFkg4rMLAC39CGp46bAEowohjda4WDyG3mEqMS5N6MGcuoXMbfQmxiWoYBQhYwMTZFkmYrEBZWsc\nAJhNZsyrXobT3RPFz4GTe7Bm4WbNj0krQsUOUQhpQc0ap2WGUIJ0hVAwQlnMbA5d869yAf2551rj\ndM4RygctnMGq7ilgM9u69uModpZiYLQXm5Zdw6SbCYyhjAo8ESEyAoEgG4QiVACUZtEjFItF4Q9N\npENJkAzzptPWOKWwhIGRbsRi0eR2ibM8rZWFF5hAp7BphQ1MMFYRGvb0E/0gRTYnyjl9DKnMp+xx\np9rewZhvROHaLEwhJBQhTdBhCanoUYTYzySp0gZDtC0u/702TI8QZ6gqG5+d/+OmcTtK0NywJLlt\ntxYx88IKEZNkwsal2/DRTbdlPDtMkJ4NS65OqkLlxdVYqWNun0AgENAIRagAyCYsgZ4g73QUw2wy\nG3JctPdaKT6bDkpQ6w9KwIvQ1hudnYCO0DZaEaKDEhoq56QNLqhw1aG+sin53MTlOA6d2Yutl31M\n02PS7wGx6qkNu01ZEdIyQyhBukHHhRaUAADuIv3WuELtr7hly5fw2O5/gS/owY2bby+oeUeC/FJb\nMRvfuv2H6B5sR2PtfJHOJxAIskIUQgVAiZOOz9beI+T15yY6G2C91/RqcgI2MU65PyhBQ9UcWM22\nZES0BMm4HiGDwxLo/qAGlf6gBJIkYcOSq/HMG79O7jt4ao/mQohOvhNhCdpQUzi0zBBKwAxVpdS8\nQgtKAFhFiC6E4nKcWcwo1MStWdVz8b9u+8d8H4agQClxlTOLFQKBQJAJwhpXALidJUR/QSDkUx1e\nmoqXSowrNrCpmF6FVQpL6B7SXwhZzFZcseojye11i6+Cw+5SuYUyFSU1xPawZ4Cw6mVL96D2oIRU\n1i2+ClLK69o50IrO/ouabjvmF2EJmaAWlqB1hhDAV2lT51MV2gwhgF0EoXuE6M+vzWLPe1+TQCAQ\nCAT5RChCBYBJMqHYWUYoQR7fCKN08KB7SYxMV2IUIYXirGeQTIyrq0hfCAHAxy7/LBY1rUY0FsGy\neesyO0iMn9CVuMqTdjJZjmPYO4Aqg/oKtM4Qoil1VWBx02qcansnue/tU3twc/W8tLdleoSENU4T\nqoqQjrCEIpsTVostGXseiYURCPuSNpyCtMYxA1XJQoiOv6d7AAUCgUAgmGmI5cACIdPkOCY622mk\nIkT1CHGscdFYBH0jXcS+eg09QsC4fWzJnDVY0bwh65Vppk9o1Bh7XCQaRv8w/fdpK/SA8cbeVA6f\n3ptWrYrLccYaJwohbagpM3rCEiRJUu3dY61x+VeE2IGqHmKbTn0sxMQ4gUAgEAgmE1EIFQjsSZe2\nPiHaGmdkjxCTGsdRhPqGuxCPx5LbZe7KjC1u2cAGJhhTCPUMXUJcjie3K4qrdf19K+ZvgCNFLfAE\nRnGq7V3V2wSCXsTiE8WS3VokmsU1oqRyOGxO3c9hqVN50HEhKkIOu4uwYgbDfkSikeQ2G5Qg3lMC\ngUAgmNmIQqhAYOJ6/VoVodz1CDFzhDg9Qj3UINU6HWqJkdA2wgGDFKEuOjFOoy0ugc1ix5oWcn7Q\ngVN7VG8zJoISMkZJmdETlJBATaUtxELIJJngopLj/MEJVYgOOxHWOIFAIBDMdEQhVCDQyXFaI7Rp\nC5XbQAsVbZ3hWePoIIGGfBVClCI0ZJAilG0hBAAblmwltt+7eAC+oEfh2oCHKoLFDCHtKPUI6bHF\nJaADKlJfF8YaZ8+/NQ7g9AmlWGfphQy7RVjjBAKBQDCzEYVQgZBpj5Anl9Y4WhGKhonkLADozjAo\nwWiYCG2jFCG60NOYGJfKvPrFRHBDLBbFO2ffULy+CErIHCW7V5mOoIQEtBJX6NY4QH2oqlCEBAKB\nQCAgyVsh9N3vfhfr169HaWkpampqcOONN+LEiRPEdR544AEsWbIEbrcbFRUV2L59O/bv35/2vvfu\n3Yu1a9fC4XBg/vz5+NnPfparP8MwMh2q6qPmCBUbGJZgNltgNk0EC8pyHNHYRM9BXI6jc4CMg9Ya\nlGA0tCI0YJgilH0hJEkS1lOhCWr2uDFqZo2wxmlH2RqXiSJEz/ea+EyGKEVILa1uMlEbqkoXQqJH\nSCAQCAQznbwVQnv37sU999yD/fv345VXXoHFYsH27dsxPDxxsrF48WL85Cc/wfHjx/HGG29g3rx5\n2LFjB3p7lU9yL168iOuvvx6XX345jhw5gm9+85v46le/iqeffnoy/qyMYXqENIYlsIqQcYUQoG6P\ne/nwfxHKiwQJdRX5KYTK3BVE0eYLjDH2Jb14/COEOmMxW1Fd1pDRfW1YsoXYbus5qxjoQPeHGVnc\nTneUVI5SVyaF0NRKjQPUh6rS1lahCAkEAoFgppO3OUIvvPACsf3oo4+itLQU+/btw0c/+lEAwKc/\n/WniOg8//DD+9V//FceOHcM111zDvd+f/vSnmD17Nn7wgx8AABYtWoS3334b3//+93HzzTfn4C8x\nBrXVZyUi0Qhh0ZEkE5xFbkOPy2YtQiDkS26HoyG4AFzoOo3n9v0Hcd1l89apDrTMJSaTGRXF1egf\n7U7uGxztxazquRnfJ60G1VU0wmwyZ3RflSW1aG5Yggtdp5L7zna8h03L2FlRtDVOTFDXjpFhCezi\nROFb4+iFEJ9Kj5CIzxYIBALBTKdgeoTGxsYQj8dRXs4/6QuHw/j5z3+OyspKrF27VvF+9u/fj2uv\nvZbYd+211+LQoUOIxWIKt8o/Ja5yIvrWGxhNDnNUgonOLio2fFI8LznOF/Tg1y88TMRKu4qKccvV\nXzL0sfVSUVpDbGcboW2ELS6VRU2rie33Lx3nXm9M9AhljGKPkAGpcakqbaEWQi4HaY1L7RGi5wgJ\na5xAIBAIZjp5U4Ro7r33XqxZswabNm0i9j/77LP41Kc+Bb/fj+rqajz33HOoqFC2ufT29qK2llxl\nr62tRTQaxcDAAHMZABw6dMiYPyJLHFYX/OGJNLHX97+KEofy3zro7SG2zZLN8L8lGiGLx3ePvoP3\nLr2BYU8/sX/jvOtx/kwrgFZDH18PcohUa44cP4TwcGYKDgAcO3eY2I4HzLqeX/q6cS/5cTtx4TAO\nHjwISZKI/b0D5ADXzrZuhIYK4z06FTCbLMQcJgBoPd+Bvo4RhVvwkWUZEiTIGA8ICYT9eOvt/bCY\nrRjzkvd17sz76G4byO7ANaL2HuzvGyS22ztbk9dvbW9lrlso332C/CPeC4JcId5bAiNZuHChofdX\nEIrQ1772Nezbtw9PPfUUc1K4detWHD16FPv378cNN9yAnTt3oq2tTeGepjYuO2lr8YfGFK45TjDi\nI7aLrMYPMrWYrMT2ic796Bg6S+xb2rARsyuMfWNmgruIVE68IX0nvjQjvj5iu8xVo3BNbVQVzyL6\nmPxhDzxB1gIZDFOvq81Yu+N0x2omVUwJUkafDUmSmOc+EPECAKPW0o+ZL+xWUpkKRiaUq2icPGb6\nsy0QCAQCwUwj74rQfffdhyeeeAJ79uzB3LlzmcudTieam5vR3NyMDRs2oKWlBbt27cJDDz3Evb+6\nujr09JBKSW9vLywWC6qqqri3WbduXdZ/hxG817cH/Z5Lye2aWZVYt0T52OKnPMDJie2G2tmG/y1v\nd/yBOKa2wVPE5U21C/E/bv46LOb8n1SZS0N4p+2Vie0iOePnIx6P4bdvkavrWzZdy8yW4ZFY/eI9\n9sFLS3G241hyu6hcwrrlE9eLx2N4dB9pu9q88QpYLTZdxz+Tef54MYKjE8VkibsCG9ZvyOi+9pyr\nQUffhEo7p7kR8+oX4dF9ZFHxoQ2bYDbn9utU7X2VoKa3DC+f/G1y22yduP6Z4f3ARAsdFjQvJN57\ngpmJlveVQJAJ4r0lyAWjo6Ppr6SDvCpC9957Lx5//HG88soraGlp0XSbWCyGeDyuePmmTZuwe/du\nYt/u3buxfv16mM2Z26Qmg/JislAb9qhbbVIToQDjE+MA9T4Ch82Jz32kMIoggI3QzmaWUP9oDyKx\niZNdt6NUUxGUjoWzlxPb5y69R2z7gh7IKb1XDrtLFEE6od+zZRkkxiXg9QmFoyHiNbJabDkvgrTC\nDFRNGdwbilCR3wWSdCcQCAQCQb7IWyF09913Y9euXXjsscdQWlqKnp4e9PT0wOcbX8n1eDz49re/\njQMHDqC9vR2HDx/GXXfdha6uLtx6663J+7njjjtw5513Jre//OUvo7OzE/fddx9OnTqFX/7yl/j1\nr3+Nr3/965P+N+qlzE0XQv0K1xzH68/dMNUENotyIfTJ7fcwg0zzSWUJG5ZAD4DVStdAK7GdbVBC\ngoWzVxDb5/7/9u49Oqoqzfv471QqSVUuVCIkQIIQCPegyEAYuchN5MWGidC2CIp0t93SjpGhoV9b\nQRqD0y3aPbq8EUFXjzJeGi8LsbV5FUaSAAPtKwq+bTJcVGiCLVEgJIRLSFLn/SNDkVNVqYSQpE66\nvp+1spZnn506u2AT68ne+3mO/MUyRmoIXT7/D/gtyRjn+17/QOhMuW0TJUjB0mdX+OZXQNY4pz22\n8wEAEC5hC4See+45VVVV6frrr1daWprv6/HHH5ckOZ1OlZSUaObMmerfv79ycnJUXl6ubdu2KSsr\ny/c6paWlKi0t9V1nZGRo48aN2rp1q4YNG6aVK1fqmWee0cyZM9v9PV6q5MQUy/XJJleErIFQW2QX\ni4kOvhox9uobNazf6FZ/3uWIcyVaPpTW1J4PSEXdXIGBUMZljOyinl37Wj6AVp4u13cnLyZH8B8v\nNYQunX9x06QWFFO9IDEuMIV2YA0h+wRCMc5YRUdd/DdbV1frK6RKHSEAAKzCtp8j1PY2SXK73c0q\nglpQUBDQNm7cOH3yySdBettbwNa4qtCBUFsXU5WCrwild8nQzOt+3OrPulyGYahzp1R93SCIOV5Z\n1qI6PAGpszu3zoqQMypavdMGat/hz3xtB458rtTkdEmBxVSpIXTpYmOsc9a/RtelCFZU9Vy1/4qQ\nfbaYGYaheHeiTlZdPN92+mylXDHugBWhWOoIAQAinC2yxqGe/9a4pleE/M8Itf7WOP9tRjHRLv34\ne/fZ9txKZ083y/WxFp4Tau0aQg0Fbo+7WE8ocEWIGkKXyv/fUUpSWotfK1hRVTtvjZMCfyFy4edE\ndcCKkH0COAAAwoFAyEYS4jpZDl2fPX9GZ/1++9yQ/xmhtthGNajXP1iub530z77VCzvyPyd0ogVF\nVc+dP2spxmoYDnXrfOVlj+2CYAkTLpzjIBC6fNcOvt53ViatS4aG9G55xiL/1aSKM8G2xtkroPAv\nqnphC63/1jhWhAAAkc4eqY4gSXIYDiUldLZkOztZdUzu2J5B+7fH1rg+aQP1s5xl2nt4jwb1GqbB\nGcNb/RmtyT95Q0syx31z3LoalJLUvVUPlvdM7auYaJfvg+mpMydVVn5E3a64MiBZAoHQpUvr0kvL\n7nhWxyrKlJ6ScVlZDf2TVXSIFSGXdWX49P9kjquu9UuWwBkhAECEY0XIZvwTJjSWQvt8TbXlN7wO\nR5Tcsa1fUFWSsnqP0M3jf2r7IEgKTKF9rAUrQm25LU6SoqKcykwbbGm7sD3Of0WoE4FQi8S7O6lX\nt36XndrdPxCtOlOhM+eqLG12C4QCM8dd2Brnlz6bQAgAEOEIhGwm2f+cUCMJE/wzxiW4O8kwjDYb\nV0fhvyJ0ogUrQl/7ZYxLb6WMcQ31baSeEMkS7CXaGa0418WtZqZMfVfxjaWP3bbG+Z8VPH22UnXe\nOtXV1fraDMNhm/pfAACEC4GQzTS3qKp/ooTENtgW1xFd4XdGqLzquOUDYHN847ci1L2VMsY11N8v\nEPriSLFM01QlZ4Rsxz9hwnflf7Nc231F6PS5yiCps2P5xQkAIOIRCNlMczPH+W+hSqDejKT6OioN\nV1FM06sTTRSmbcg0zYAaQm2xItQjNdOSka/qbIW+PnZQZ86esvQjwA0//3NC3570D4TsvSJUdbYy\nMHV2iELJAABECgIhm2luLaHA1Nl8YL6gSydrCu1LSZhQfuqYzjY4DB8b41Zyp5QQ39EyUY6ogHNC\new7skCnTdx3vSrRkEUR4+G9PLPcLrP1TzIdbvCswEOJ8EAAAgQiEbKb5W+P8UmcTCPlc4bFujzt+\nCQkTvvj6c8t198495TDa5p+Jfz2hT/Zvs1xzPsgemvp7sNvWuAS/9Nmnz55SdY1/xjhSZwMAQCBk\nM0mJgVvjLtSYaejUmcBkCajnnznu4Dd7m/V9586f1bs7XrG09Uzt22rj8udfT8h/5YrzQfbQ8QIh\nv4KqQc8IsSIEAACBkM24Y+It21Zq6s776oA0FJA1jg/NPml+Z3r+738X+LKyhfL+R6+rouq479rh\niNLYq6e29vB8eqT0ljvEh2gCIXvwPyPkz25nhOJd1hWhM2dPBdQ+YmscAAAEQrZjGEbAqlCw7XFV\nrAg1akjvEUpJSrO0vfafz6ra77fiDX1z/LAK97xraZs4LEfdrriyTcYo1QdamelZjd6nhpA9dLQV\noagopyXANmXqZIMAX2JFCAAAiUDIlppTSyggfTZZ43yinTG6bfK9MnQxPfDxijL9acerQfubpqk3\nCtbI663ztSUldNbUkbPafKz+9YQaYkXIHvzTZ/uzWyAkBabQPlH5reWaM0IAABAI2VJyojVLmX+W\nKkk6FVBQlUCoocz0wbpu6PcsbUV73tNXfws8L7RrX5G+/LrY0vb9cT9pl2xg/gkTGiJZgj10ir8i\n5H1XrL22xkmBPw/8U8iTPhsAAAIhW2pqa5xpmkG2xhEI+fun0XMtBVZNmXrtP5/R+dqLGbTOVFdp\nw7aXLN83sNcwDe07ql3GmJ6SobjYhKD3WBGyB1eMu9GtZA5HlKKjYtp5RE2L98sc578iFBtDIAQA\nAIGQDQVsjfMLhM7XnFNN3XnftTMq2nYHtu0gNsatOdfnWtq+Lf9a7//5dd/1xp1/sBSnjYpy6gfj\n75JhGGoPDsOhzPTBQe9xRsg+Gvu7cMXEtdtcuRQJria2xrEiBAAAgZAdNVVUNXBbXCdbfhizgwE9\nh2r0kBssbR9+ukF/PXpApd9+pW3/7/9Y7k0e/n2lJlsTLbS1xrbHJTaRrQztp7Ftinb9BYT/GaHK\n0+WWa84IAQAgUbbehoLVEmrIP1FCAokSQrpp7I9UfOhTX2ps0/Tqtf98RrHRbpmm19evc6euuiH7\n5nYfX7BAyDAcAYUxET6NB0L2S5QgBWaRNGWtRUb6bAAAWBGypcCsccctGc0abuWSOB/UFHdsvGZP\n+mdL2zfHD+vQ0X2Wth9MuEsxzvb/TXn3Lj0Dar8kuDvJ4Yhq97EgOE8jCRM6yoqQP9JnAwBAIGRL\nMdGxlg/GXtOrygbBT0DqbAKhJmX1HqGRgyY2ev+qPiOV1XtEO47oIofhUF+/ekKcD7KXxoqqdpQV\nIX8EQgAAEAjZVqjMcf4Z46gh1Dwzx90ZNBNbtDNGN4//aRhGdJF/PSEy/ls2wwAAGthJREFUxtlL\nR9saF+8KHQjFckYIAAACIbsKVVTVP1lCPCtCzRLvStSsiXcHtP+v7FssabbDYWjfUZZteQN7DQvj\naOCvoyVLaOp8GWeEAAAgWYJthVwR8guE2BrXfEP7Xqt/HDRJH/33FklSz9S+mvgPM8I8KikpobP+\necZD+nPJh+reuacmXDM93ENCAx1va1zonwlsjQMAgEDItkLVEgosphp6Gwysbrthgfr3HKpz1ac1\ncvAkRTujwz0kSVJm+uBGawohvDraipArNk4OwyFvg6yIDREIAQBAIGRbAbWETn3n+++AZAmcEbok\nhmEoe+D4cA8DHUi8O1EOR5Qle6Nk3xUhh+FQvCsxYBvtBWyNAwCAM0K2FVhU9bjvvwMKqhIIAW3K\nYTiCZvKLtemKkBQ6hTYFVQEAIBCyrcaKqpqmGXBGiDpCQNsLdk7IritCUugts7FOVoQAAGBrnE0l\nxXeWIcNXEf7UmZOqratRTe151dXV+vrFOGPZ5gK0g2DnhOx6RkhqfEUoyuFUVBQ/+gEAYEXIpqKi\nnEqMv7gVx5SpiqoTOkWiBCAsggdCNl4RaqSWEL84AQCgHoGQjSUnpliuT5z6LiBRQgKFN4F20dEC\nocZWhDgfBABAPQIhGwtWVLXq7ElLGytCQPvwxF8R0GbvrXHBi6qSOhsAgHoEQjYWrKhqQOpsEiUA\n7aKjrQg1lkSFrXEAANTjxKyNBSuqapqmpY3U2UD7CJ4+275BRWOrxawIAQBQj0DIxgJWhKqOBWR7\nInU20D78V4RiY9xyGPZdVI93Bd8aF+vkjBAAABJb42ztimBb4/yyxiWyIgS0i6SELkpNTvdd903L\nCuNomsaKEAAAobEiZGPBiqr6f7ghWQLQPgzD0E+nP6D3P3pdMc5YTR89N9xDCokzQgAAhEYgZGOJ\ncUmKcjhV560voHqmukonKr+19GFrHNB+ul1xpX504/8O9zCaJSY6VtHOGNXUnvdrJxACAEBia5yt\nOQyHPAnWlL3HKo5argmEADQmWFFV6ggBAFCPQMjm/DPH+UuIY2scgOCCFVVlaxwAAPUIhGzO/5xQ\nQ7ExbsWQAQpAI4KdIWRrHAAA9QiEbC45MaXReyRKABAKK0IAADQubIHQypUrlZ2dLY/Ho9TUVOXk\n5Ki4uNh3v7a2Vvfff7+GDh2qhIQEpaWl6fbbb1dpaWnI1y0sLJTD4Qj42r9/f1u/pTaRnNC50XuJ\n7sACjwBwQfAVIVaRAQCQwhgIFRUV6d5779XOnTu1ZcsWOZ1OTZ48WeXl5ZKk06dPa/fu3Vq2bJl2\n796td955R6WlpZo6darq6uqafP2SkhIdPXrU99W3b9+2fkttItTWOFaEAIQSrKgqK0IAANQLW/rs\n999/33L98ssvy+PxaMeOHZo2bZo8Ho82bdpk6bNmzRplZWVp7969ysoKXcwwJSVFnTs3vprSUSSH\nCoQopgoghGBb42KcBEIAAEg2OiNUWVkpr9er5OTkRvtUVFRIUsg+F4wYMUJpaWmaPHmyCgsLW2uY\n7S5U1jhSZwMIJdjPCJIlAABQzzBN0wz3ICRp1qxZ+vLLL7Vr1y4ZhhFw//z585o4caJSUlK0YcOG\nRl9n//79KiwsVHZ2tqqrq/Xyyy9r9erVKioq0tixY339LgRVknTgwIHWfTOtyDRN/eHPv1Wttybg\n3oiMGzQ4/R/DMCoAHcHRikPa9PkrlrZ/uuYuJcd3DdOIAABouX79+vn+2+O5/AWBsG2Na2jx4sXa\nsWOHtm/fHjQIqq2t1dy5c1VZWan33nsv5Gv1799f/fv3911fe+21OnTokH73u99ZAqGOwjAMxcV2\nUuXZ4wH3XNFxYRgRgI4i1hn4M8LpiA7DSAAAsJ+wB0KLFi3SG2+8oYKCAmVkZATcr62t1Zw5c1Rc\nXKzCwsJmbYvzN3LkSL3++uuN3h8xYsQlv2Z7+uhwD1WWBgZCV2Vdo0G9hoVhRAhl165dkuw/r9Cx\ntGReVZ4u17t7nre0Df+HbHWKv/Sfo/j7xM8rtBXmFtpCwx1drSGsgdDChQv15ptvqqCgwLKKc0FN\nTY1mz56tkpISFRYWKjU1tUXP2bNnj9LS0i53uGHTWOa4RJIlAAghWNY4zggBAFAvbIFQbm6uXnnl\nFW3YsEEej0dHjx6VJCUmJio+Pl51dXW65ZZbtGvXLr377rsyTdPXJykpSS5X/f/M582bJ8MwtHbt\nWknSk08+qd69e2vw4ME6f/68XnnlFb3zzjtav359eN5oK2gsYQLJEgCEEhXl1JWpmSr99ktJUkpS\nGumzAQD4H2ELhJ577jkZhqHrr7/e0p6Xl6fly5ertLRUf/zjH2UYhoYPH27p89JLL2nevHmSpNLS\nUsu5opqaGt133306cuSI3G63hgwZoo0bN2rq1Klt/6baSGMptKkjBKAps6+/R28VviCvt04zx/0k\n6DlMAAAiUdgCIa/XG/J+RkZGk30kqaCgwHJ933336b777russdlNsK1x7th4OaM49AwgtCtTM7Vo\n1qPhHgYAALZjmzpCaFywFSG2xQEAAAAtRyDUAQQ7I5RIIAQAAAC0GIFQBxAb45Y7Nt7SlhDH+SAA\nAACgpQiEOojkxBTLNVvjAAAAgJYjEOog/LfHEQgBAAAALUcg1EF09liLyXqoDA8AAAC0GIFQBzFi\n4AQ5jPq/rtgYt67ue22YRwQAAAB0XGGrI4RLk9Gtv+6b87gOHd2vgb2ukSf+inAPCQAAAOiwCIQ6\nkPSU3kpP6R3uYQAAAAAdHlvjAAAAAEQcAiEAAAAAEYdACAAAAEDEIRACAAAAEHEIhAAAAABEHAIh\nAAAAABGHQAgAAABAxCEQAgAAABBxCIQAAAAARBwCIQAAAAARh0AIAAAAQMQhEAIAAAAQcQiEAAAA\nAEQcAiEAAAAAEYdACAAAAEDEIRACAAAAEHEIhAAAAABEHAIhAAAAABGHQAgAAABAxCEQAgAAABBx\nCIQAAAAARBwCIQAAAAARh0AIAAAAQMQhEAIAAAAQcQiEAAAAAEQcAiEAAAAAEYdACAAAAEDEIRAC\nAAAAEHEIhAAAAABEHAIhAAAAABGHQAgAAABAxAlbILRy5UplZ2fL4/EoNTVVOTk5Ki4u9t2vra3V\n/fffr6FDhyohIUFpaWm6/fbbVVpa2uRrFxUVafjw4XK73crMzNSaNWva8q0AAAAA6GDCFggVFRXp\n3nvv1c6dO7VlyxY5nU5NnjxZ5eXlkqTTp09r9+7dWrZsmXbv3q133nlHpaWlmjp1qurq6hp93YMH\nD+p73/uexo4dqz179mjJkiVasGCB1q9f315vDQAAAIDNOcP14Pfff99y/fLLL8vj8WjHjh2aNm2a\nPB6PNm3aZOmzZs0aZWVlae/evcrKygr6uqtXr1aPHj301FNPSZIGDBigjz76SP/2b/+m73//+23z\nZgAAAAB0KLY5I1RZWSmv16vk5ORG+1RUVEhSyD47d+7UlClTLG1TpkzRrl27Qq4kAQAAAIgcYVsR\n8rdw4UINGzZMo0aNCnr//Pnz+sUvfqGcnBylpaU1+jplZWXq2rWrpa1r166qra3VsWPHAu5JFwMs\noDX069dPEvMKrYt5hbbAvEJbYW6hI7BFILR48WLt2LFD27dvl2EYAfdra2s1d+5cVVZW6r333gvD\nCAEAAAD8PQl7ILRo0SK98cYbKigoUEZGRsD92tpazZkzR8XFxSosLAy5LU6SunXrpqNHj1raysrK\n5HQ61aVLl9YcOgAAAIAOKqyB0MKFC/Xmm2+qoKBA/fv3D7hfU1Oj2bNnq6SkRIWFhUpNTW3yNUeN\nGqW3337b0rZ582ZlZ2crKirK1+bxeC7/DQAAAADokAzTNM1wPDg3N1evvPKKNmzYoEGDBvnaExMT\nFR8fr7q6Ot18883atWuX3n33XXXv3t3XJykpSS6XS5I0b948GYahtWvXSpIOHTqkIUOG6K677tL8\n+fP1X//1X8rNzdW6des0c+bM9n2TAAAAAGwpbIGQw+GQYRjyf3xeXp6WL1+uQ4cOqU+fPkH7vPTS\nS5o3b54kaeLEiTIMQ1u2bPHd37p1qxYtWqTi4mKlp6fr/vvv1/z589v+TQEAAADoEMIWCAEAAABA\nuNimjlB7y8/PV+/eveV2uzVixAht37493ENCB7Jy5UplZ2fL4/EoNTVVOTk5Ki4uDuiXl5en9PR0\nxcXFaeLEiSopKQnDaNFRrVy5Ug6HQwsWLLC0M69wqb755hv98Ic/VGpqqtxut7KysrR161ZLH+YV\nLlVtba2WLl2qPn36yO12q0+fPvrVr34VULeRuYVQtm7dqpycHPXo0UMOh8N33KWhpuZQdXW1FixY\noJSUFCUkJOimm27S119/3eSzIzIQev311/Xzn/9cy5Yt0549ezR69GjdeOONKi0tDffQ0EEUFRXp\n3nvv1c6dO7VlyxY5nU5NnjxZ5eXlvj6PPfaYnnjiCT377LP6+OOPlZqaqhtuuEFVVVVhHDk6ij//\n+c964YUXdPXVV1vKCjCvcKlOnjypMWPGyDAMbdy4UXv37tWzzz5rSUDEvEJLPPLII1qzZo2eeeYZ\n7du3T0899ZTy8/O1cuVKXx/mFppy+vRpXX311XrqqafkdrsDSuk0Zw79/Oc/1/r167Vu3Tpt27ZN\nlZWVmj59urxeb+iHmxFo5MiR5vz58y1t/fr1M5csWRKmEaGjq6qqMqOiosz33nvPNE3T9Hq9Zrdu\n3cxHHnnE1+fs2bNmYmKiuWbNmnANEx3EyZMnzczMTLOwsNCcMGGCuWDBAtM0mVdomSVLlphjx45t\n9D7zCi01ffp080c/+pGlbd68eeb06dNN02Ru4dIlJCSYa9eu9V03Zw6dPHnSjImJMV977TVfn9LS\nUtPhcJgffPBByOdF3IrQ+fPn9emnn2rKlCmW9ilTpmjHjh1hGhU6usrKSnm9Xl+dq4MHD6qsrMwy\nz1wul8aNG8c8Q5Pmz5+vW265RePHj7cki2FeoSU2bNigkSNH6tZbb1XXrl01bNgwrVq1ynefeYWW\nuvHGG7Vlyxbt27dPklRSUqKCggJNmzZNEnMLl685c+iTTz5RTU2NpU+PHj00aNCgJudZ2Auqtrdj\nx46prq5OXbt2tbSnpqYGFGIFmmvhwoUaNmyYRo0aJUm+uRRsnv3tb39r9/Gh43jhhRf01Vdf6bXX\nXpMkyxYB5hVa4quvvlJ+fr4WL16spUuXavfu3b5zZ7m5ucwrtNg999yjI0eOaNCgQXI6naqtrdWy\nZct09913S+JnFi5fc+bQ0aNHFRUVpc6dO1v6dO3aVWVlZSFfP+ICIaC1LV68WDt27ND27dsD9rUG\n05w+iEz79u3Tgw8+qO3bt/sKQJumGVBCIBjmFRrj9Xo1cuRI/eY3v5EkDR06VAcOHNCqVauUm5sb\n8nuZVwjl6aef1osvvqh169YpKytLu3fv1sKFC5WRkaE777wz5Pcyt3C5WmMORdzWuC5duigqKiog\nQiwrK7MUbQWaY9GiRXr99de1ZcsWZWRk+Nq7desmSUHn2YV7gL+dO3fq2LFjysrKUnR0tKKjo7V1\n61bl5+crJiZGXbp0kcS8wqVJS0vT4MGDLW0DBw7U4cOHJfHzCi33m9/8RkuXLtWsWbOUlZWluXPn\navHixb5kCcwtXK7mzKFu3bqprq5Ox48ft/Q5evRok/Ms4gKhmJgYDR8+XJs2bbK0b968WaNHjw7T\nqNARLVy40BcE9e/f33Kvd+/e6tatm2WenTt3Ttu3b2eeoVEzZ87U559/rs8++0yfffaZ9uzZoxEj\nRmjOnDnas2eP+vXrx7zCJRszZoz27t1radu/f7/vlzf8vEJLmaYph8P6UdLhcPhWsZlbuFzNmUPD\nhw9XdHS0pc+RI0e0d+/eJudZVF5eXl6bjNzGOnXqpIceekhpaWlyu9369a9/re3bt+vFF1+Ux+MJ\n9/DQAeTm5uo//uM/9Oabb6pHjx6qqqpSVVWVDMNQTEyMDMNQXV2dHn30UQ0YMEB1dXVavHixysrK\n9PzzzysmJibcbwE25HK5lJKS4vtKTU3Vq6++ql69eumHP/wh8wot0qtXL61YsUJRUVHq3r27Pvzw\nQy1btkxLlixRdnY28wotduDAAb300ksaOHCgoqOjVVBQoAcffFCzZ8/WlClTmFtoltOnT6ukpERH\njx7V73//e1111VXyeDyqqamRx+Npcg65XC598803WrVqlYYOHaqKigrdfffdSkpK0mOPPRZ6C13r\nJbzrWPLz882MjAwzNjbWHDFihLlt27ZwDwkdiGEYpsPhMA3DsHytWLHC0i8vL8/s3r276XK5zAkT\nJpjFxcVhGjE6qobpsy9gXuFS/elPfzKHDh1qulwuc8CAAeYzzzwT0Id5hUtVVVVl/uIXvzAzMjJM\nt9tt9unTx3zwwQfN6upqSz/mFkIpKCjwfY5q+Nnqxz/+sa9PU3OourraXLBggdm5c2czLi7OzMnJ\nMY8cOdLksw3TbMYpXAAAAAD4OxJxZ4QAAAAAgEAIAAAAQMQhEAIAAAAQcQiEAAAAAEQcAiEAAAAA\nEYdACAAAAEDEIRACAAAAEHEIhAAAbWLChAmaOHFiWMfw+OOPKzMzU16vN2xjyM7O1v333x+25wMA\ngiMQAgBclh07dmjFihWqqKiwtBuGIcMwwjQq6dSpU1q5cqV++ctfyuEI3//uli5dqlWrVqmsrCxs\nYwAABCIQAgBclsYCoc2bN2vTpk1hGpX07//+7zp37pzmzZsXtjFI0owZM9SpUyetWrUqrOMAAFgR\nCAEAWoVpmpZrp9Mpp9MZptHUB0LTpk2T2+0O2xik+pWxH/zgB1q7dm3AnxEAIHwIhAAALZaXl6df\n/vKXkqTevXvL4XDI4XCoqKgo4IzQoUOH5HA49Nhjjyk/P199+vRRfHy8Jk+erMOHD8vr9epf//Vf\n1aNHD8XFxemmm27S8ePHA565adMmjR8/XomJiUpMTNSNN96ozz77zNLn4MGD+stf/qIbbrgh4Ps/\n/PBDjRs3TldccYXi4+PVt29fLViwwNKnurpaK1asUL9+/eRyudSjRw8tXrxYZ8+eDXi9devW6dpr\nr1VCQoKSk5N13XXX6Y9//KOlz+TJk1VaWqpPPvmk+X+4AIA2Fb5f1QEAOrybb75ZBw4c0B/+8Ac9\n+eST6tKliyRp0KBBjZ4RWrdunaqrq/Uv//IvOnHihH7729/qlltu0YQJE7Rt2zYtWbJEX3zxhZ5+\n+mktXrxYa9eu9X3va6+9pjvuuENTpkzRo48+qnPnzun555/Xddddp48//lgDBgyQVL9dT5JGjBhh\neXZJSYmmTZumoUOHasWKFYqLi9MXX3xh2cJnmqZmz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       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11a4048>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see from the chart how poor the measurements are. No real train could ever move like that. \n",
      "\n",
      "So what should we set *g* and *h* to if we want to filter this data? We have not developed the theory for this, but let's try to get a reasonable answer by the seat of our pants. We know that the measurements are very inaccurate, so we don't want to give them much weight at all. To do this we need to choose a very small *g*. We also know that trains can not accelerate or deaccelerate quickly, so we also want a very small *h*. For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_train_data(23000, 15, 100)\n",
      "data = g_h_filter(data=zs, x0=23000, dx=15., dt=1.,g=.01, h=0.0001)\n",
      "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.0001', z_label='Measurements')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nwQp7VoiIiMi3vP66XFl/6y1vt8Q+2jAabVgNOa6wUJZasPLqq8CKFcCAAe47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\nIYQQQohJomSFEEIIIYQQYpL+H5IY3GkaJJUyAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11ddb70>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is pretty good for an initial guess. Lets make *g* larger to see the effect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_train_data(23000, 15, 100)\n",
      "data = g_h_filter(data=zs, x0=23000, dx=15., dt=1.,g=.2, h=0.0001)\n",
      "plot_g_h_results(zs/1000, data/1000, 'g=0.2, h=0.0001', z_label='Measurements')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wpKezcEMbROer+vTTT9G9e3f4+PjA398fTz/9NK4LsZsamD17NmQyGf773//q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\n/PYb3SfnzNH3xysvB+68kzL7ts7qC4yYWRExjyUzRI5k926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SMFMD6qYmurk6g0R0RgYp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\nR42ulhntY9n5BAVR/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SWGdzIBgzUrM2bMwLp167B7925eNEQfMpkMcn3tRbVw+vRphFlC\nbWdn0xdERAR11unTh+orjh0z3JrV1nDRFC7X1J5cvUriSSVPOz1Le5hWJq/DDw+G4+ylfxuESmlF\nMX7Y9gnPe8TN1QOebso2ijXyWtwqMFDMaoKD/Um1jk1dEu7TOkFOuMtvAateiKyX5cuBtDRclebx\nNqu3RQYAoa8EE9eeRrR7CG/7wfS/sef0n8af05ZIJOQorkLBvVyknd6s8ym1dTX45o/3kVt0AwBw\n9ALfmLBbuwHWEWYffUQ1UjNnWvzQbq4eSIrW/LLu7BEBkVxh286CW7cC8+bp9hqqR70rGId7jQyt\n953S3+LZEVi8GHjoIWru4EhwnYo8LJC+KRQqW8lq+/559VXKzWcwGAyGTvSKlalTp2LlypX4+eef\nIZFIGloMV9RfdMvKyjB37lwcPXoUN27cwIkTJ/D0008jJycHjz76aMNxJk+ejCeeeKLh/pIlS/DH\nH3/gypUrOH/+PN5880388ccfmKbFZdpkrl6lW64Nsq8vFdzW1QEHD5p//KIiKtLljOfMwc+PvszK\nysw/lrmotT2srC5HVs4FnbvL5DJ8v2MRzl47ApmsDj9s/wwlFXzH+scHv6RR4H4tJ0P/OIwUK1XS\nCmTk8Y+VHK99hSmhjB/JuWxEoXwD7dujKLkd7lYoW/WKRS7ai5efew4uS77AlAHTNDqBbdr3A9Iz\njxl/Xjuycd/3DZ2mAGpaMLrPE7x9KqXl+GrTAlzIPoXsPH76VLd2A6wzMFdXw7VdTz0FdO9ucKKv\nja4JmqaPXeLuA155BRg1yuTjNZotW4D336cFFj1EhSYgyE9zgSfuVgUJLEtMtq3Jyy8Dv/2mbJzg\nKJiwYGIUnFhRv877+wOffqo0xGQwGDRXGzeOrrvGGhYzmjx6xcry5ctRXl6OQYMGISwsrOFn0aJF\nAACxWIyMjAyMHTsWCQkJGDVqFIqLi7F//34kqaQf3Lx5Ezdv3my4X1tbi9mzZ6NTp07o168fDh48\niG3btmGMlo5EJqMuVgDyyQCAvXs19zeVtDSgXz+aFBlDeTlNGrQZG23bRh/MAQPMH5e5cN459WLl\n4o3TkCuUK7OhAa0xMXUaBFCumMvlMny/7ROs+PNDXLvN7+qT2vUhdIrrhdhW/BqSq7eNEyslniKs\n/vtzLN/0Lv44sBKnrhxEcVkBFPUXr3OZRyGTKyfULSShaB2sPZUutsoNQpnyb8kvvo1KqXaHcG2o\ni5uolm3gItaSzz52LDB1KnzadMBzo+bCzVU5WVRAgR//WoTbBdeNPq89uJB9CulZ/EnyqD5PYFDX\nsXiwx3je9pLyInz9x3u8bXE5lQj05UeWbMqZMwYn+cjP57c2rqddVBd4ufs03A/wDUZs3xHAZ5+R\n67KtMOBizyEQCLSabiZk1S88WGqy3dxISaH23JYyi+TEijGmuAxGc+f2bWU7b0dLnWbYDb3LlIZS\nuTw8PPD777/r3QcA0tL4aSKzZ8/G7NmzjRheI9AlVhYtsoxYuXSJbtsY2Ra0tJQm4NqKgh1pMsFF\nVurbUqtPWJOiU9AriZzA1+5aBkV9tblcLuN5VABAgncEhrd5EAA0xEpmzgXIFXKeaziP+v/TGv98\nZFyg11L1+L6e/oioEqOoJA/wVeZ/d0noozP1yH3lKkRuehtZeZcatuWWXDe6CFy9ZbG2FDB1WgZG\n4Kmhs/HN5vehqBd90tpqrNj8Pl6Z8Cl8vbS3/7YnMlkdft/7HW9bdMu2SGlD+fRDe0xAeVUpr05C\noeBfI7rf1OG9Yyu0mUKqMnkytRLfsYNMJlVwFbth8oOz8Nve/0EscsH4gc/bpzGCkWIFALq17Y/t\nh9fwtiVcyqdfHD2y4qi4uADBFvRIateO0gjZKjHDWlRXU5aGBZpC2J3r1+lWS300o/liks+KUzBw\nIDB1KtC7t3Jb377Ao48CTzyh+3nG0hixAji+e71KZEUul+HCdb4A4fL5eyWlYkLqVF6ERRV/KfDE\njG8g2rkLABAWGAkPV2W+f2V1Ge7c1W2uiDlzUJJzHRdctKfGlVYWI11RgFxf/iRSVwoYAMDNDQkR\nnXib8kqu695fBYVCgSu3+K0g48Pb69ibT2JUF4zrz1+RLy4vxLd/foiikjs6nmUDjh6lVWM1v5J9\nZ7bhTrHytRFAgHH9pzSIQIFAgIeTxqLLeb7HCoertA6dS9y0PmYTFAqKmgC6xQpXn7Nde2F6u8hk\nzJ28DG9MWtLQQMDmmCBWWkhC0SlO2eUwKrQNWt6sT8d0pMUQR6WuDlizhtKxrMXmzRTxa2un9xOj\nafPii7Qw4eYGvPWWvUejn4oKYMoU4LnndO/DxApDC01PrIweDXz5JV+suit0bwAAIABJREFU+PkB\n69bRh8RcOLFi7BePs4gVmQzw8QH8/XE97woqqpViwcPNizdx65WUqpESBgAikRhP/1sCn4qaBpMz\noVCE6EB+CtzV23qM4FxccDb/fEPkxhhC/MMR1kK/70ZCa340JPdeVkNKmT4K7uWipFxZr+IickVk\niHGNJgCgX6fh6NtxGG9b9p0reHfl8/hm8/u4kH2Kl25nE5YsIRPI5csbNpVV3sP2I2t5u/VIGoSI\nkDjeNqG/Px7//hDaXNIULB0zS+Ee2so6Y+ZQKGiCqY2yMkrv8vLSXRDPudlv22ad8VkCE8QKADyW\nOg0jek3C4JRxeHr4axCcOQOcPcsiK8YgElGK32uvOUajEwbDVP75R/m7j4/u/RwBhQL47jtg9Wrd\n+2TVm0czscJQoemJFWuiUCjFytSpwK+/Gn6Os4iV6dNprB9+iIzr/OLkdpFdIFJLh+mZdgET152G\nQGW+/8iA5xB54TbdCVX6UsSW8EVNpoG6lTNXD/Hux7VKQkxYO+11IgB6Jg0y2H0qKrQt7/mVNWUo\nqy7W8wwAUimuTJvE2xQd1hYuYhf9z1Pjof7PoG1kMm+bAgqczzqO5ZsW4IMfpyLt1GZUSm2Q015T\nQ92mAF4Xpi0Hf0Z1jTLS4u7qiZG9H9d8vosLxD4SPPP9UUQERvEeum/ecvoisha7d1OKDic41DGU\nAgZQC3OJBLh8Gbh2zfJjtATJycD8+dQpywg83LwwpPsjGHnf/8HPOxCIj6cufUJ2eTeIQKCsJ+Qm\nSbbi22+BL75QRgMZjMaguijhyO71gDLaW1WlOy2Si6xEO7ZXFMO2OJ5tuiNTXU1pZhs3AufOARd0\nd8tqwJBYkcsBqdRxVkEFApxXa1msraUr3NzQ89B1tOzaD+cmDkZsqyS0i0wGcnPp8frICgDEercC\nKpV1H1dzMqBQKLQKjLLKElxRi7xMGDQVwf5hkMllyC3KRvbWtcj+awMKW3giStIa/UsNX6BdxC6I\nCWvHc/rOvWdgclJRgauiMgDK4+utVzl/Hvj6a5osvvRSw2aRUISnhr6KZRvfwY07VzSeVlCSi437\nvsfWgz8jpW0/3J88GiEB4Rr7WYS9e+k9mZTUUNd1485VHD6/i7fbgz3Gw8dTh1FpUBDcr9zDCx0e\nx+aCI7hx5wp6tR+C2FZW9vRwc6MIoK4W5BER5JFRpd0oEQB1ExsyBNiwAdi1y7C/0V9/0es6ZEhD\nm26r07Ej/TBsQ0wMvcaZmSQUbcWiRbT4NWiQZWtkGM0L1bmDA5pL8xCL6aeujtrQa6uxmTmT5ln3\n3Wf78TEcFrb0ZgoeHtSlYskSun/HiLqDsWOpC8wPP2g+tnUrpSGotHm2N8VlBbhdeL3hvkAgRGKk\nli/wevEVmV+NEb0fJ6FSXk4/7u68FZ4Iv9ZwqVH6r5SUF+FuqfbVxHOZR3lF22GBkQj2p/asIqEI\n4UExuK91Dzy27jReWnYQoz5cB3GmcSuiCWpCw1DdiqKiAlfi+M7SesVKTg6lIGrpIuTh5oUZD3+I\nianTEB6spTMcgJo6KQ6m78SHq6bjx+2LkHf3ptb9zGLTJrqt77ynUCjw+97veGl3wf6t0K/TMG3P\nJuojF14llZiYOhWvT1qif39LwbW4Vau1acDFhWrJOnfWf5zu3YGEBOMiDxs2kBfG0aOmjZXhPHCR\nlcx6D6gvvwRCQoD33tP9HEugZWGHwTAZZxIrgDK6oq3pEAB06kSNUOxtlM1wKJhYaQwh9a1ZjREr\nAgFNsrSFZ7mWlhZ2+jSHDLXC+qjQBHh5aIkKcbmxqnn1VVXkR/HAA7yWg2IvH0Rm8z1YdPmtqKeA\nqRYPN5CcTEKPu5j5G+istWwZIBYjYf1O3ua8kut660XyC7JRKlEWKbuK3RCpVsPBg3uNddQauIhd\n0CspFbMnLMLMRz9GSpv+EAk1g5sKKHDi8n4sXPUSVm7/rMF80WwUCqWQGjMGCoUCfx/7FZm5/Ajh\nQ/2egVikJ9WtRb2Au3tX9z7WgKtD0SVWjOXVV2lF2xgzPu5ctjSFZNgWdbFy7x6lZumaTJlKURHV\nEN1SaSxSUUHXCTc3w9cvBkMfziZWuPHqi4AzGGo0LbGyZg3wzjuUoqWNAweACROApUvNO48pYkUf\njuRgX4+2lsVa0VYEHBREk2Fu9Z7D0xOxmfyJrbYi+0ppOS5nneBt0ypWAgKAYcOA1q3pvqELtFgM\nyGRoXSLndSaT1lUhRyWKpM7lPP4kPiasHUQiPZmT3P/EgPgUCASIbtkGkx+ciQVP/w/De02iWgM1\nFFDg5OUD+Gj1DPyw7VPkFGbrPa5BZDLg44+BKVMg69wJ63Z/ha2HfubtkhSdgsSoLvqP89NPlLpo\nCV8kU+AEg640MGvAxErTp2dPYNo0YPBgum9pU8hvv6XV4i++UG7joiqhocxLgmEec+bQ925ODr2X\nHZ0lS+g7xNGbATAciqZVs7J+PU2U27XTnl9+5w51BSsooILyxsIVjzclsZKXhxoPN1y+eZa3OSnK\ngFgxZnUkMBBxPuHYobJJW5F9euYxyITKL+5g/1ZoGRih+7hcu2VDK5P1kw5htRRx4e1xLlOZ0nMx\n+zTCg7SnZV0pvMq7b9BfxUBkRRu+Xn54oPsjSE15CGeuHsLfRzcgp4gvShRQ4NSVf3Hqyr/oktAH\n4/pP0V1Pog+xGJg0CVUPj8H3f77Pq98BKHI0tu/Tho+jLUp4oz76ExJCq8XWgEsD02LoaDWcTayk\np1PqaXIyXQ8ZhunenX44rOVgr2oKyVLAGJZCtfOpM/DYY/YeAcMJaVqRFW2GkKr0I3M7HDpk3oQn\nKorSkMydDDiSWElKwtVebVFbp/y/+Hu30N0SOCmJvtRPntT+uCrR0YhatZlnBJl/LwelFfxuXKfV\nUsA6x/XS3+WL+78ZiqxwYefqaiS05hcu/3NyE8qrNMWFQqHA1aoc3rb41gbEioktZ1URCUXoktAH\nr01ajGeGv46wFlFa9zt5+QA+WfMKsnIvaX3cEEWld7Bkw5saQsXD1RPPjprTUB9kMs88A0RGAvv2\nNe75xuDnR5/bAu0+L1bBXmLlgw8oXa3WRJPN0lK6Dt60Qr1Tc4FbgLFU0xNuBVlVrISFAfPmAf/3\nf5Y5B4PBYDRhmo5YUSiUrUh1FWYFBQGJifRldOyY9n10UVNDnZ727aMvsWHDKLRvzLh04eOjLPKV\nyXTvZ23kcuDePaQnhvI2J0an6BYLIpFJK+hurh4ID+a/LtdylGlW1TVVuJh9ive41hQwVRYvpteE\nS8vThUpBX8fYnrxUroqqUvy+T7Pdbt7dmyhX8Zpxc/VA62ADBX+ensB//0sFuo10qxYKhOgU1wuv\nPfZfPDP8DbTSIlpKyovwxa9zsP/MNqO8Yjiy8y7jv+te16iBCfANxsuPfqwh5EyCS32zZotugYCK\n6HUxaRLQvj0tRliKxx6j7jRcyqGt+Owz6hZVpt0cVSdcVMBRugs6I9aKrKi+lrGxwLvvkqEfg8Eg\nli+nuZWWJjWM5k3TESu5uSRCWrTQv9Levz/d7t1r2vGvXQNeeAF46inTnjdyJE3gdu7UfEwopNz/\n0lKa/NuL8nIo5HJktOeLlaSorhY9TVyrRN79TJUi+4zrJ1AnU64iB3j460zPamDsWHLCNbTqrSJW\n/H1a4MHu43kPH7+4V6OxwJVb/Lqn2LBEDa8ZDQQCmtg+/bTZeegkWnpi9mP/xZQRmqJFJq/Dhj0r\n8PPOL1BTKzV4vNNXDuKL3+airJIfxYsMTcCsRz9By0AzJ+OO4Cd08SK1oDXms5SVBRw+bHiRYOpU\nEqARetIRrUFjo3RcVIC51zeezz+n75MJEyxzPG1pYAwGQ5MjR4Dt25n3EEODpiNWDKWAcTRWrFy8\nSLdt2pj2vJISWlHTFYUQO0DZUHExckN9cNdfuRrrInI1faX977/pQqOjwDwmjC9WVIvsT189yHus\nc1hn/Slg8+ZRru7Bg7r34Rg0iNJp/v4bAJDadSz8Pfm+But2L0d1jbL+5spNvlgxWK9iJYQCITrG\n9sSrExdhYBfNgvajF9Lw3/Wvo+BersZjd0vzcSh9J37Y9il+2PYpL8UPADrH98b0ce/B16uRHWRU\nuyVxr7k9TcmMMYXk6NmTDCId9UuxsWKFRVbMx9ub6hI5kWEuLVpQ2mykjpRaBsMcamspJVquu7Ol\n08AZQjL3eoYaDjBTthAxMZR+Y2iyNHgwGb2ZWpTGOdebKlYcYcXZEPfu4XwSP5UqvnUHuLqYWCg9\neza16Dx5Uqu5WmxYO979nILrqJJWQCQUI0O9C1jyEP3nunSJ0n1u3DD8WqqttItEYvSKG4HtZ39o\n8BcpLivAloOr8fCA/0CukGsYU8aHt9d/DisjEoowpu+TiAxNwC87v4C0VikUcgqv47M1r2BC6jQI\nBQJcunEGl26eRcG9HJ3HS00ZhxG9J/HqiIzm1i3yKQkIULZjtff7XKEwTawEBZFQKShwzCJnc8UK\ni6yYxunT5KHVvr3lfa+6dqXGBwyGNXjvPaUnUCPTj23K8uW0yDhtGtCjB/8xJlYYOmg6YiU8nFI2\nDBEQQD4gpsKJlbZtTXueyiROJpfhxp0rEAnFiNDn12FrpFJkdOKnAelsWaxObS2ls4lE/Hac6uzf\nD6+SErT0D0duMU1wFVAgM+cC6mR1qKlTpjJJvAMRGWZAFAbWt/otLDRunGq08AlDu7AeyMg5rBzi\nmW3o2qYvXMVuqFSpV/Fw9UR4UHSjzmNpkuN7IywwAv/b8hHuFCt9G6pqKvHDtk8MPl8oFGH8/c+j\nV/vBjR+Evz+lGxUW0pejQkGrxuXlyo5d1qSujt5zqqaOFRU0UffwMG4MnKCxZbG+KTRWrIwaRdcq\nFlkxjfR0mvCNH+9QJr0MhkFOn7b3CExj3z5g7Vpg6FC+WKmro8UvgcD2abcMh6fppIFZG/XIyk8/\nURrJ11/rf55K4fFve/+HxevfwGdrX8Xaf77Sa0hoSyo6tkNmJD8VSGfLYlV69wZcXeliWVtLEz+h\nEAgO1tx3wgRg5EjE+EXxNl/LuaBpBBnb0/CKPydWiooMj1MHnSP6I1CijCgpoMAvu77EBbVC/1i5\nL4SG6lVsSEhAOF6Z8Ck6x5kWHfSXueCF0W+bJ1QAEgMeHlRvVV5Or3lGBkW5rO0Z0acPFdmrO8qr\nRlWMGQMnVhw1DeyJJ8gTJyHBtOf5+NBzbN0QwNnhjCG5Ji3W5s03gY8+os8Qg2EOtmzlbgl0mULe\nukU1hGFh1mt/z3BamFgxltGjgYcfJg8XgFaVDx8GLlzQ/RyFoqEDTF5dCQ6c3d7w0MH0v7H5wE+0\nT0WFXd1cL2afgkJFOIUFRiLA14hUGldXui0tVXrOBAVpL3CuL4KPk/BXTC7fOKNhRGmwCxigrCH6\n6CPD++pALHLBhIH8bjx37t7C9sNredviK024cBYWAs8+Czz0UKPHZQzurh54athsjOn7pE5hJxKK\nEdsqCcPTKzBz8T683fZJtIkwooOdMdgrMsG959SNISMiSCzt2KH5HG1wglrf+GtqqIXwl1+aPk5z\nmTABeO01wzV4DMvAdZDkXOytSU0NXbfmzHGMmkWGczN3Lt2+9ZZ9x2EsKg1veLRsSQX2P/5o+zEx\nHB52pTSW11/n3zfGxV4goA9kWRmOpGu24tt9chN8/tmHQQt+oDals2ZZcMDGk551nHc/0dgUMNVU\nlbw8+l1X/n/9akqMOz9F7EY+33jRx0OiUduilZEjgd9+A4YPN26sAK3aqAmpNhGd0DNxEA5n/NOw\nrVbGX6mKdzVCuHH4+NDFtqaGih4NecCYgUAgwMAuY9A6OA5rdy1DQUkuwgIjkRDRCW0jOiE2LBFu\nEAGP+9IKbi8Lmoe1aEHioKBAuSptC7jOb5z/CYdIZFo0IT4e6NxZf41NWRlNBPz9Kb+a0XQJDqb3\n1t27lOpbUkLpKvHxlj8X950REmLfLpCMpkGfPrZLwbUEusSKmxvfnJXBUKF5i5XSUuqg0ZgJpTFi\nBQBEIsh8fXDs4h6tD//hfxfe3Vqjh52MIeVymUbak9Etizmzs9JS+lKfOFF3rmn9JNNf7oJA3xAU\nlWr/v3WM7WlcytXkyVQMm5RkeN/ycppwurpqrsgDGNP3KWRcP4nSymKNxzwrahDWQktamy7c3ICU\nFCogPHwYePBB45/bSOLD22POE8ugkMt5HjIAqJUvQBFBf3/LnTQoiFaFdXR+sxrcF7K6WDGVGTPo\nRx/O5l7PaDwCAYnu9HRlyq8lox4XL9JnJTmZudczLI+zCBVAdxoYg6GHppEGdvYsFUV+9ZXxz/nw\nQyq2/+abxp3TWLECSrNSd2tXZc2Ezkiv0Ww9a01Kyu8i7eRmfLZuNq+Y3NPdB1Etjex4phpZSUwE\nfvlFd1qWyop4rJrfiiqdXv7AuI5rAgF12TGm65G7OxXvVVdr7Zbi6e6Nhwf8R+tT464VQWjqFwHX\nncyYtsoWQigQagoVgMRcaSmwbZtlT7hxI0WPhhjo2mZpuPeRFtFpcZhYaV7MnAksW6a8b8mOaqmp\n1C47L4+JFUbzZtw4yj4YPdreI2E4EU0jsnLmDLBhAxX6GusIHB1NaUF79mimeBmDCWLlSMZu3v2o\n0Da4WXANMlkdAEAuEuKHkAJMzbmAGD0pUDK5DJXV5aiuqWz4qZIqf6+plcLL3Qe+Xv6QeAfA1zMA\n3p6+DTUNVdIKnLl6GMcv7cWVm+ca2vaq0i4y2bD5IYevrzLVzRA9etCXv0SCWPdEHL2QprGLp4sn\n4jNygNYW7gQiFlO6hUxGokWLC3rn+N7oGNsTZ68d5m2Pv1oIjDBxsmoHsaIXV1fLt4JU7TZVVETp\nYMHBtABgTby86D1ni6JSZxQrc+fStfC991hXK1N5+mm6festioJYsqMaF4UuL2dihdG86dKFfhgM\nE2gaYoUzhOSKJI1hwAC63b+fOllpmcDqpUULIC1NKVp0UFFVinNZ/M5Fo/s8gdLKe1i57dMGwVAr\nBL7Z/D5mPPwhwlqQeVidrBbZeVdw9XY6rtw8h6zcSxr1FIYQCkXw8fSDj4cEeXdv8lzitdErKdX4\ng7//PkVSjOm+tHBhw6+xxbe17tIhqB1EcoV1PCI8PGiiUF2t87V+ZMCzuHLzLKpqlClGCfP+C3S+\nz7Rz9apvEHDkiNY6mSbHhg3ACy9QY4HGRiqNZckSYOlS63cdA+wrVi5coI6DMTHAf7RH/bRy+zZw\n+bJtIk9NFS49xZLXIVUX+5496brZ0UTTXQaDwWimNA2xwrWbNKVzTsuWlG506RJw4gR9gejivfdo\nxfjJJ5W5oUKhUvDoQi7HiUv7GyIoABAkaYmYsHYQCASouP85rE9Ttj6uklZg+aYF6NPxQVy9fR5Z\nORd5/iONQS6XoaS8CCXlulv8ChRAXOsOGNhltGmu9aYKvHqC/MLg4yFBWRW/3qFzQH36lzXEirs7\nTRSqqpSrnGpIvAPw+AMvY+W2z1Arq0Hv9kPQclAjQtWhocCff9LqUVMXKoBtDSF11RE88gh9jn/8\nEejb1zLnatkSeOMN8nCyNdnZNKEdPNg0scJNtJnPSuOQy5VRO0u2T+XESlkZMGgQNXdgMBhEXR3V\nVUZEADt38j20GAw0FbHCRVZMbfM5YACJlbQ03WKlthZ4911aIefSBIxl9WocPvs90FpZwN89cSAE\n9avCfTo+iLLKe9h+RNkqt6TiLrYe+sW08zSS8FslSDlxC8mfr4F/ByM7gFkAgUCA2FZJOH1VmSbl\n7uqJBI+w+jtWEitGpKx1iOmOd6d8h8rqcgT5mZGmMWJE45/rbNjbvR4g5+OsLNME9PnzlMbZr592\nERQTw4sI2hTmYG8fBALqCFZVZdnonWoaGIPB4HPrFs3jqqqYUGFohYmVzZv1fzgyM0n1R0aavFp5\nu+Q2bqkIFQEE6N5uAG+fB3uMR3lVKfafNa4A2sPVEx7u3vBw9YS72B3uHt7wcPWCu6sHxGJXlFeV\noLSiGCUVd1FaUYwqKT8dJNA3BClt+6HrlmMI/exzWpG2hFBZuZK+kEeMMGpFMi6cL1aSolPgUlMf\ngbLGROvaNZrIGjEB8XL3gZe79uiLU5GeTl27DKQqNhqZjFaKuY5gEol1zmMMqqaQxnL//fS8nBzH\nqx/gxEpZmf791LFGClNzQiCgrnmW7JwHUBQ/N9e56p8YDFtx/TrdWrq2ktFkcH6xolBQzvy1a5R+\nYwqPPAKMH69/AqvmXH+rIBN/HVkHVxd3jLpvMvy8A3U+9Yj0OqCy0NsmohP8ffiTKYFAgHH9n0F5\nVQlOXflX4xi+Xv6ID++AeLkE8dXuaNF7EAShoTRB7NaNnK7feElnulFNnRSlFcUorSiGu6snWgZG\nQCCXA/83n3aYPVv3324sCgXw3HOUPmFkS9ke7QYi7dRmFJXcgZuLO4b2mABIQinXXiYzf0zqcGaC\nzYlnniGn9717KXpgSa5eJaf0mBjgvvqaHntGVjixEmxCm+mgIHpeQYHjihVTIyssDcw8Pv4YOH4c\nWLzYsul/n35quWMxGM5Mejp9Htq2Bd58k7YxscIwgPOLFYGAVkjvv9/05xpTT6AiVvLu3sTnv86B\ntIYmBNm5l/HKhE/h6e6t8TSZrA7HhYW8bT0SB2o9hVAowuNDXkagbwgu3zqHFpIQxId3QFx4ewT7\nhVHa2LRp1Fbz00+BV1+lVrRXrlD3n3/+AVavBsLCNI7tKnZDC0koWkhUhJxIRO2et28nwWMOcjmt\nTNfU0Mq6rknSjRuUdtO6NdC+PdxcPfDW418iK/ciwoOilf/D5rzyuGYN8Ouv5Jretq15x6quBk6d\nos+HNfLjAwJIpBYUULOJuDjThII5cF3duAheRQWJZDc3ZW2AMQQHAxkZ+l3s7UVjxcratbSQocvv\niKGfrVup6crzz9unVonBaOoUFFDzkAEDmFhhGA1LDjREvVipTIjBt38ubBAqAFBQkosf5z4E+bsL\nNJ52/voJlIuUEQIPV090iO2h8zQuYheM6jMZr074FE8OfRX3dXgAIf6tGupbcPYs3XboQLcTJwJ/\n/UUTrrQ06iyzZYvxf5enJ/U7N4dLl/jO4foiWxs3AsOGAStWNGxyEbsgoXUHrWLPIejdm9yBzTGv\nqq01zjhRKqWaqN9/p1Vdczlxgs7dvr11Ih5+fvTal5aSZ9GVK/T6Wptt26i+5KGHlNtUU8BMqTPg\nUsby8y03Pkvh40Oi9cMPTXteWBgVqjqTSZwjERNDt5mZ1jn+3bvAlCnAJ59Y5/gMhqOjzcGeEyvR\n0TYfDsM5YGLFEBMnQj7/bfwkuY2CezkaD19o7Yktleka249k/MO736VNP7iKddRy1NYChYV0qw2F\nAjh3jn7nxAoAPPAAecwMHkxeFyNHKvezBeqr2PpSaVRMIZ0ChQI4dAj499/Gp5B99x1Fm957z/C+\nf/6pvHgvXdq486nCebxwbZQtjVBIERWA3ru2govcqbbmjYyk9//+/aYdixMruiIraWlUYH/4sPbH\nrYlIRH4fU6fa/tzNGWuLlRs36LqwapV1js9gODqcWFFdBFy6lBZkR42yz5gYDg8TK4YYNAhbB8ch\n4+4VnbvsalmLk5cPNNwvq7yH89dP8PbRlQIGAEhJoYnT+fPaH799G7h3DwgM1BQEoaEUYfn4Y+Cl\nl/hixtqor9jri6xwYsWcKIW5yOXG18NI61tGu7k1vv1weDj9vcaYQ/7wA90uWWKZ+ppDh+iWM6i0\nBtxk35ZiRZvoFQgoLc3UFILERKq34USXOjt2kGDYs6cxI2U4I1yU7aOPrHN8ZgjJaO5wC06qkRUf\nH5q7mNIghdGsYGIFIBO1Zcsof12Nk5cPYOfx33jbIoLj4OvF7xbz884vcLsgCwBw/OI+yOXKSXFI\nQDgiQ+J1n9+vvmPYvXvaH1dNAdOW5iIUAq+9Bnz+ue5zWAPOTRwAnnqK/AN0Ye/IyqRJJDo2bDBu\nf0sYAvboQf+fEyf0t0zOySHB6eJC49SGQmHauePjKR3IWpEVgFIQJRLTO1aZgyXfR1OnAgcOAI89\npv1xZ3SwZ5jHlCl0O3KkZY9bUkLXgbQ0us/ECqO5oi2ywmAYwPnFyoABwJgxxtUF6GLJEipg37iR\nt/l2QRZ+2clPyfH19Md/Rr6FZ4a/AZFQ2Z+gtq4G325ZiPKqUo0UsJ6Jg5S1J9owJFaCgsiQsrFf\noHX1LYH/8x9KP9CVbmYqQqEyFey//1V+0WvDmEnmJ5/Qfu+8Y5nxqcL5bxjwWWnAEhNVPz8gKYma\nD5w8qXs/mYxem8cf177Kf/cuRQD27TP+3B9/TOI7IcH0cRvLzp30nu3Tx3rnUIerxbCFQzsTK82P\nzp0pkv3bb4b3NYW0NIqgc13BmFhhNFeCgoDvv7f94irDqXFusVJeTm1Zt283rQuQOlwnMZV0j/Kq\nUny7ZSHPQV4kEuOZEa9D4h2A6JZt8Eg//uT8bmk+lv42FzlF2Q3bhAIhUtr2139+TqwUF2t/vFs3\nShOaNcvoP6mB48dphX3JEuB//6NUManU8POMxdeXJnOGzM5CQ6nGJkWPp0tlpfVWW7QV9enDUhNV\nLg1LXypY69bA11/TBVwbS5ZQWtegQcDPP5s3HksiFJLQOnXKejn+6nCvh6mRpsbAvQecpQ2wQgHE\nxtLn3Rrtv5sLYWGmmYsag4+abxMTK4zmipcXZWKMGWPvkTCcCOduXXztGt3GxJhcV1AlrUBtXS28\nPHwg6l8vJv79F6ipgUwswsptn+JuKb9L0CMDnkN0S2VL2d6dHsStS8dxIPd4w7bcohu857SL7AKJ\nV4D+wXAGZLoiK+awaBF5YsycSfdffNE8YadOdrZx//tOnSjVSR/WdN82VaxERJDQM5fevamdrDmR\ngLffJhH32WeUujR0KNVoOALFxUCXLjSeoiLrny8khCbiqkauCoVtxA1BAAAgAElEQVRl3cY57B1Z\nWbOGivv/7//0i3yO2loSjSJR4+usGNZB9Zr7xRdAfwMLWAxGc8Fa129Gk8K5xUojnOvlchk2HfgR\ne0/9CQUUEEAATw8f+Mx/EN6FpfBZOw+VPu64fIvfVatPx6Ho3X6wxvHGjXsDuRvn49pt7cXxegvr\nOQICKLpijdXiH3+kiTeXYjV9umWPb8lJkTXFCrc6bmzkxt0d6NrV/PNOnEjpXeb8n8RiSh85fRrY\ntYt+X7jQ/LFZAs4HxFaGkAKB5hfb2LEUuVqzRn/dlKk8/DCZwdYbwtqcv/8GVq6k1CRjxAr3+XGW\nSFBzghMr7dpZ/hrMYDgzCxaQpcH8+WQuzWBowbnTwLjISmysUbvX1Erx3daPsefUZihAwkABBSqq\nSpHn74ar8UE4VXwJl26c4T0vVhKJcf2e0XpMkUiMp4fNhr+3Zq2BZ0UNkro9aFiEvP02rVA3Js3L\nEK6uVL9w9ixw7Jj+jl32xhaRlZoayx9bH66ulhN0H3xAt198AeTlWeaY5sLVikkk9htDbi61H25M\nBOToUWobzdV1qfL44/TZSUw0f4yNwVRjSE6IW+PzwzAPLg3MULosg9HcyMqia7jYudfOGdbFucWK\nCZGV8qpSfPn72ziXedSkU/gVV+HpEa9DJNL9QfLx9MMzI96Ai4jfcjblxC24iF0dI8TZoYN1Jl3V\n1TShW7PGMscCrDPZmjuX0ofmz7f8sRuLqcKpe3fghRfINDIwUPs+587R66GvoN9SKBTKVqy2iqxo\nQ9UU0lRGjKDe/k3BxZ5FVhwXX1+KkNmytTyD4Qww93qGETi3WPngAzKCM1CoVVRyB0vWv4HreZd4\n21W7eWnDVVqHKVuuw6dFmMGhRITEYWLqVAhAwsRV5Ir++zLNn8StX089/y9dMryvPcjJAd54g37M\n5X//oza4Eyeafyx1RCJ+nYMjMGIEdbMz5bX96ivg2Wd1FwBv2UKvxXffWWSIejl/Hhg+nH53VrFi\nyBjSnrDIStPBz48aUWzdau+RMBj2Z9YsYMIE8uhiYoVhBM4ddwsKMjhBuZl/DV//8R7KKvnF62GB\nkXh+zNvw8ZCgvLoU5ZUlKK8qRVnlPZRVlUB+/jw6zPwAwZ16Gj2clLb9ESgJQVbuRSRVeSGocAPQ\nysxJ3KpVNAGNjbVf7rw+uJV1rqOZPv7+m4qWR4/WHm0Siy1b/O/I3LhB9SeuruRXYim4rmPWNIPk\nUG2zbELdmNkoFDQxd3Oj6FR5OYm3xgimpiRWYmOpwF4ut96YGAwGw1z++IOuVfPnA7du0XygdWt7\nj4rhwDjYUrNluZB9Cl/8OkdDqMSHd8CMRz6En3cgRCIxJF4BaBUUjTYRnZDStj/uTx6FQfluCC6s\nANq21XH0ev78kyZqL74IAIhu2RYDu4xBSF19Spi5K86qhpCOCFcQx41TH6NGUTG0JVsnW4s1a6hl\n9OLFljne9evAL78oDRR/+okm3WPGKLvBmYtCQd2jAOuaQXJwqWhCIfns2IqUFGp/eeYMrcwBJPga\nk27JCUVHFCu9e1M3v/HjjdvfxQWIjja6ho9hY06eJAPS5cvtPRIGw75w0d+sLFpcadWKFu4YDB04\nd2RFD0cydmPNP8t4TvIA0DWhLx4b/BJcxAb66D/8MBAebjg0KRBQoX9WFn97ZSVN4owRKwoFTWLL\nyuhDy1FSQivwbm62Xbk2hVatKB3Izc3wvp6eJFQqKx0/VeXWLWpdPGCAZY43fjwVc+/cSR2rVq6k\n7U89ZZnjA1TDVVhI7X2joy13XF24uFBE7d49ahChq47G0nA1GZWVtBpXVdV4U1guspKfr/nYBx/Q\n3zhzpuV9N4yhQwfHXaRgmE5GBi2CKBRUe8ZgNFe4a3hQEF2/HXGxiOFQNEmxkp55DD/v/EJj+6Cu\nYzDyvskQCowIKEVE0I8hQkLo9s4d/vahQ6nDkDFF1PfuUftiiYTvtZKeTreJiY7bKeObb4DZs4G3\n3jK8r6cnTWqtZfxoCIWCXhNjJp7cGC3lsdG7N4mVgwdpBenaNRJ6qamNP2ZtLRlJ9uxJPjZcCliv\nXrZr6hAURO/ZggLbiRXuNeG8a9zdGy9+O3UChgwhI0BVFApg3jy6feWVxo+VweDgUmaZISSjuaPq\ne+buzlLAGAZx3jQwHe2A5Qo5/jy4irdNAAHG9Z+C0X2eNCxUliwhf439+40bhy6xAtCE0ZiIg2pu\numq++bl6r5eOHY0biz2IigI2bACSkw3vq7oibmt27aJI17Bhxu1vafdyVSf7/HxqIT15snltjT/6\nCHj+eaVQ7NmTtk2ebP54jaVVK5p82fI15cSKJc757LPAjh0USVVFKqVrjCVbTzOaN/v20S3r1sZo\n7pjqe8Zo9jivWBk/ngrO9+7lbT6fdZznIi8QCPHksNno33mEccfNyqLc4t27jdufy3nPz298YatI\nRH34uXQwjr59yQBwwoTGHdfRMDTJbN+eCuwvX7b8uTnRaKyDvaXdy7kakkOHgIceAm7eNC4apY/n\nn6f/17ZtwIED9Hl4/XWqC7IVaWnUEa5LF9ud08uLbrnIijWwt3s9o+mxZQvd3rpl33EwGPbmtdeA\nn39maa4Mo3FesXLmDE1qVbpQKRQK7Dz2G2+3LvH3ITnehM5IXI3Cnj3G7e/uTulbdXWU4tRYuL9D\nNQ0sKQl49VXgwQcbf1xHYsAAKrLXtbJYXk4TUGsU2qmGnY3B0pPV8HBKKywtpdx1S3Q+CwpSGonO\nmWPYfLSp4OlJ4rO21nrncEaxsmYNEBNDnkIMx+O992hRat48e4+EwbAvgwdTswmWEskwEucUK9XV\nVEwsEvHa+V69fV7DSyU1ZZxpx+7Xj24PHTJ+YnvsGOXsBwSYdi5VtImVpsbnn1PLwoQE7Y/bwsHe\n2Nf07beBI0eAkSMtN4b/+z9g2jTL/n2zZtH7bt8+Kt5vDqxYQa/jU09pd563BJauWWoMCgUtVjz3\nnHFC9O5digybs2jCsB5z59Jr46jNUhgMW6OaScJg6ME5xcrFi5RyFRfHm/jtOv47b7fEqK5oFRRl\n2rG5ImGplCasxhAfT54TqkXN1dWmpYW1bElFvs7Q1tdaWFOsmJojGxFBjvFcTZIleP99YOlSy05W\nJBJK/QKAtWstd1xHRvVzNm4cRaj++suy55BI6PP//POWPa4pCATAsmVKcWYIZgrp+LD6JwaDqK2l\nRdoWLay36MRoMjinWOG6ZLVv37DpZn4mLmSf5O022NSoCsd779HtCCPrXLQxcSJ9Mf3xh3H779gB\n3L5NE+Tmii0iKzKZ/v2ckWnTgI0bbeNa72jk51PqoDkpdXv2AOvW8b8wg4OBBQvs3wnMx4dujTGG\n5D4/rICbwWA4Ordu0YKuh4fjdjtlOAzOKVY4TxMVsbLrOL9WJSasHWJbJTbu+G+9RWldXEpYY+Am\nF83Fkd1cFAplVMmYDmqm0qoVTUbV/XCaAp6eZC5pq3bFjgTXn59rdNEYHn2UmlhwBpOOhCku9tYU\n+wwGg2FJrl+nW0NedgwGnFWszJsHFBUB06cDAPKLc3D66iHeLo2OqgDU4rZFC3NGqJxcNNbBfu5c\nakHLtS9uDtTU0P/NGpNugYClYDRFOLHCmTs2Bu65jmhMZopY4dLAWGSFwWA4Mn/8AQwcSL8zscIw\nAucUKwAVFdfXl+w+uREKhbI+JCwwEolRXW0/JtUiWHPFyh9/AKtWNa0+5Jcv09914YLmYwIBmTVy\naS8Mhi64KFxxMX3OxGJeV0CTaSpiZd48ajzy1FPWHRODwWCYg+ocgIkVhhE4r1ipp6T8Lo5cSONt\nS015CAJbpsSkpVGBvKq/RUkJ3TZGrNTUUBMBgYDaFzcVVq+mdKX16+09EsMMGQL06KHd7JNhXzZt\nolSnoUMpWqbe3MJUVL2SHI3p04Hly6mJhyH8/IDYWPO6EjIYDIa1UU1VZWKFYQROX9WUdmozZDJl\nYWygJATJCX1sOwh3dyAvj8zxOLhOYMaKldpaSm1TKCh3vq6OJh6cAV5TwJLO49bm5El6PYROr+eb\nHtz7SCIhYV9ebt7xtEVWDh+mVtC9egGpqeYd3xzGmZHOymAwGI4Il6r6zDPU0p/BMIBTz8Qqq8vx\n7zl+y9JBXcZCJLRxbQLX3lZ1FT4/nwSIsT4Nf/5J0ZkXX1TWqXTsaNlx2ht7ixUufciYltLOaArY\nXOBek4oKEpONTbXkSEmhqGhEhHLbgQPUunj7dvOOzWAwGAw+XGSlttY6JtCMJofzRVZycwF/f8Dd\nHfvObIW0Vuk/4OPphx6JA20/JlWxolAoU1JMacenagrJiZUOHSw3RkfAVK8TSxMdDWRn048+FApW\nrOzIWFr0PvWUZp2HI5hCMhgMRlPE3nMBhtPhfJGVJ54AvLwg/Xs79p7ewntoQPIouIjtoNK9vOhH\nKjWuEFYbqmLl5ZeBbdvIq6UpoW+SeeQIFdjff7/1zs+t4Bgy2OMed3NjaWCOCJcaWVFhvXNw71Em\nVhkMBsOy9OhBNawvv2zvkTCcBOeLrKSnA3I5DgvvoKK6rGGzu6sn+nR4wH7jCgkBMjMp/UsiMf35\nqmIlJISKh5sakZHAyJFAly6aj1VXU52Oakc1S8OFng2JFZYC5th4elLU0pqtqJ3xPTBqFJCRAfz2\nG9Cpk71Hw2AwGNqJjKQfBsNI9C4bL1y4EN26dYNEIkFwcDBGjRqF8+fP8/aZN28e2rVrB29vbwQE\nBCA1NRWHDh3ScUQle/fuRdeuXeHh4YHY2Fh88803hkdbVATk5uJ2TDD+zuR3AOvbcSg83OxYjP7v\nvzTBMaZrjzY4gXPvnuXG5Gj06QNs3gy8+qrmY7YwtOOObSj0LJEAZ85QgTXD8WjdmnKdjx83rv6o\nMTiKWDl5kurYli83vG92NnDtmnUFP4PBYDAYNkavWNm7dy+mTZuGQ4cOYffu3RCLxUhNTUVxcXHD\nPm3btsVXX32F9PR0HDhwANHR0XjggQdwR0/L16ysLAwbNgx9+vTB6dOn8eabb2L69On4/fff9Y/2\n/HlcaBuEJS/0QFlVScNmF5Er+nceaeSfbCVCQ5UpIzU1NNkxZdIgkVAL1uDg5jnZUE29shbc62Mo\nsiIWU3ODrnbw6mEYhqsJe+wxSh3cvNny5xgxApgzx/7vgRs3SKj89Zfhfbn3NUtdYzAYDEYTQm8a\n2F9qX5CrVq2CRCLBwYMHMXz4cADApEmTePssWrQI3333Hc6ePYvBgwdrPe7XX3+N8PBwfP755wCA\nNm3a4MiRI/jss8/w0EMP6RzPv2f/wob/9IRcxNdYA5JHwtfLDFM4S/P771RvMn48sHatcc8Rix3T\nlM5W2CqyIhbTqjzD+SkooMiKOYaQHFu3UoOMyZPpPTJ6NP3Ym8Y42FvzM8RgMBgMho0xqXq4tLQU\ncrkc/v7+Wh+vqanBihUrEBgYiK56ViQPHTqEIUOG8LYNGTIEx48fh0wm0/qczQd+wjpZhoZQ6ddp\nOIb3esyUP8P6cBOLxrixN8eoCmAbsbJ9OwkVe/pmMCwHJ+45U0dzePJJ6vlfWGj+sSyJKWLFFp8h\nBoPBYDBsjEkF9jNmzEBycjJ69erF275lyxZMnDgRlZWVCAoKwtatWxGgx0X5zp07COHa/dYTEhKC\nuro6FBYWajwGALtOaKaIdYsegijvZJw8ecqUP8PqhJw/j9YA8iorcev4cZOemzB1KkSlpch65x1U\nx8ZaZ4COSGIiBP/+C8jlUJj4PzOH4zY8F8OydM7NhRjAqVu3IDPTGDLJxwcehYU4v2cPquLizB6b\npd5XbtnZ6ACguqAA6QaOmVxRARGAkxcuQH7zpkXOz3As2PWKYS3Ye4thSeIbW7+tA6PFyqxZs3Dw\n4EEcOHAAAi5nvJ6BAwfizJkzKCwsxIoVKzBy5EgcPXoUkVbq9iASitE3YSwiAttY5fhmUVcHUX1L\nVZm3t2nPVSjgef48xBUVqLNEaouDIairg++hQxDIZLg3YIDagwIomDkUw0iE1dUQ1wsUmbmmkADq\n/P2BrCyIVerxHAFZfZtmkRFtmtPXr4dQKoXc3k0BGAwGg8GwIEaJlZkzZ2L9+vVIS0tDVFSUxuOe\nnp6IiYlBTEwMunfvjoSEBKxcuRLz58/XerzQ0FDk5eXxtt25cwdisRgtWrTQOxYfDwmeHTUXkaGW\nVW1mc/w4MHAgkJQEdO8OAGjVti1apaQYf4zsbPKOCApC5wfs2IbZWpSXA716UYcla3pkGAG3ipSi\n7fXZuhV46y1qs/z++zYeGcMogoIafk2p/7yZRWwscPIk2vj7k6N9I9H7vmoMUinwxRdwCQiw3DEZ\nTofF31cMRj3svcWwBiUlJYZ3MgGDYmXGjBnYsGED0tLSkJCQYNRBZTIZ5Hpaivbq1QsbN27kbdu5\ncye6desGkR7vhJCAcDw/eh4CfTXTxOyOry9QVkZFunI5GRCauuJ78CDdtmpl+fE5AlyXIq5TmlqE\nzmG4cwc4e1a7HwzDMYiKovqS/fstczxO/HB1MJ9+SkJh+vTG+SZZCjc3GgODwWAwGM0UvWJl6tSp\nWL16NTZt2gSJRNIQDfHx8YGXlxfKysrw8ccfY9SoUQgNDUVBQQGWLVuGnJwcPProow3HmTx5MgQC\nAX788UcAwPPPP48vv/wSM2fOxLPPPot///0XP/74I9bq6ZyVEN4BT494HZ5uJqZW2QquziY/H1i6\nlH5MLZZ/9lm6vXrVsmNzFEQimnxJpVQMbOsWqwqFccaTjuKxwdAN52JfV2eZ4/XqBZSUAFy9ymef\n0Wf5P/+xr1hhMBgMBqOZo7cb2PLly1FeXo5BgwYhLCys4WfRokUAALFYjIyMDIwdOxYJCQkYNWoU\niouLsX//fiQlJTUc5+bNm7ipUvAZFRWFbdu2Yd++fUhOTsbChQuxdOlSjB07VudYnm/5IDwvXiMP\nE0fE15cm4hUVyhQnUyMHa9dSVGX7dsuPz1HgBIC6MaMtuqC9+y5FvD74QP9+3NiYWHFcuNfGUumE\njz8OrF4NDB1K95lgZTAYDAbDIdAbWdGXygUAHh4eho0cAaSlpWls69evH06cOGHwuRziWa8AR44A\naWmAenG2IyAQUHTlxg1KI4qJMf0Yw4cDt25ZfmyOhKcnUFxMk0HVjnEvvAD88AOwbBkwZYp1zs21\ndDVkCskmqo4PF1nhXitLolAoBSszWGQwGAwGw66Y5LNiV86fp1uViI3DERICCIVAUZG9R+K4DB0K\nPPwwGe+pUl1NUTM9NUtmw8RK08HHB/D2BnT4MplFbS0d18VF833qqGRkAK1bAyNG2HskDAaDwWBY\nFCf5JgZ1kgoJ4XUBcjh27aIVX2tOuJ2db7/Vvt1WDvaAZgqaOrNmARMnKuuQGI7H99/TjzVwNLH6\nzTfA4cPAtGmALrPdsjKKyrZsaduxMRgMBoNhZZxHrACOHVUBlN2/iorodxcX+47HmbCFWOFSegxF\nVkJCmFBpzri4AO+9R1FSRyAtDVi3DhgyRLdYYe71DAaDwWiiOJdYad/e3iMwjEwGcF4xMpnjTHgc\nHVtFVoRCai3NYKizYQOQl0f1U3Pn2ns0SrhFkNJS3fuwGhsGg8FgNFGcZyadmgr07GnvURim3lUb\nPj5MqJiCLcTKI4+QgFy92nrnYDgvL74IvPSS49WcGSNWWGSFwWAwGE0U54ms7Nxp7xEYBzehMNUQ\nsrmzezcV2FuzoNlRTSgZjkFQEBlN5uc7Vhogi6wwGAwGoxnjPGLFWbh3j26ZWNHO2bPA5ctA585K\nAz6AolBsVZhhT4KDgQsXlC72joIxYmXMGCA7m3yEGAwGg8FoQrA8JUty5QrQsSP9zsSKdr75htKx\nduyw90h0M3YskJwMXLpk75EwbAnXaTA/377jUCc1Ffjf/4BJk3Tv4+EBREQAoaG2GxeDwWAwGDaA\nRVYsSWCg8nd/f/uNw5Hh2sFaw8zPUhw+TIXWLNLTvODEyq5d5OuUnAw89JB9xwRQYxFnaC7CYDAY\nDIYVYJEVS+Lnp6y52LjRvmNxVOwtVmQy/eeurCSh4uIChIfbblwM+9O/P/Dss4BUCrz/PrBpk71H\nxGAwGAxGs8d5xIqjdejRhlBIee+A46WSOAq6xIpCYf1z37pFYjIhQfc+16/TbWQkM/dsbowfT2mK\nvXvTfUcxhWQwGAwGoxnjPGKFm0Q6OlwXoTt37DsOR4XrVqQuVjw9Ke3KkLu8ORjjYJ+VRbfR0dYb\nB8OxcTQHewaDwWAwmjHOI1batbP3CIwjJATw8tLfuac5k5BABexcIwKAoirV1ZR+4+ZmvXNzYkWf\ng31mJt0ysdJ8ccY2wG++SQX2q1bZeyQMBoPBYFgU5ymwd5ZVzs2bqd6BoZ0HH6QfVaRSunV1ta6R\npqpYUSi0+648/zwwbBhLAWvOOFpkRSoFpk+n2x9/1L5PQQFw86bys8RgMBgMRhPBecSKs8CEiunY\nyn1bLKafujoI6uqg0PZaubgAsbHWHQfDsUlNpfdiv372Hgnh4gJ8+y39/v332oU0Fw1iHewYDAaD\n0cRgYoVhf2wlVgBaLa+thUAq1S5WGM2blSupG9xbbyk7+9kboRDw8QHKyoDyckAi0dyH+ww5U+oa\ng8FgMBhG4Dw1K4ymiy3Fyr17QGUl5N7e1j8Xw/mYPZvqPxyt+6AhF3tbfoYYDAaDwbAhTKww7E9U\nFFBXB1y8aP1zaatTYTA4HNXF3pBYccamAAwGg8FgGIGD5Dkwmg0VFcCOHZRiM2qUcrtIZP+JllxO\nYoYJmuZLUBBw4QIVrDsShsTKhg2UIsb5PDEYDAaD0URgkRWGbSksBMaNA6ZNs/dINFm/nuoBZs2y\n90gY9oKb7DuaWJkzB/j5Z93NHwIDycjU3oKfwWAwGAwLwyIrDNuiy8HeEcjKoiJma7ZPZjg2XBrY\niy9SN7CWLe07Ho6RI+09AgaDwWAw7AKblTFsi73FilxO566r03yMM4SMibHtmBiOQ2oq3d6963hF\n9gwGg8FgNEOYWGHYFi5NpaqKjBkBuuV+tzZDhwJeXvA9dkzzsawsumVipfny0ENAdDT97sgpVQoF\nkJsLHDhARpGc0GYwGAwGo4nBxArDtgiFfCd5AFi3jgrsH3/c+uevP7dQm9M3N+HjJquM5omjOdir\n8vHHQIcOgLc3EBYG9O0LPPkkkJZm75ExGAwGg2EVWM0Kw/aMG0fpWDIZ3ZdKaaVYmzO3pakXK4Ka\nGv52mYza1QoEVKjMaL5wbYAdUawUFQHp6fR7QAAV3MfEAK1b23dcDAZDLwqFAjU1NVDYKovASCLr\nv++qucVDBsMAAoEArq6uENiwcyoTKwzbs3o1/74tDe10RVZEImoLm5fHjPWaO1xkxRHTwJ5/Hhg/\nnkSKn5+9R8NgMIxALpdDKpXC1dUVIlssypmAO/u+Y5iITCZDdXU13NzcILRRQyImVhj2x5ZipX4C\nqjUNTCik1BpG80WhAN5/nwSLi4u9R6MJq6diMJyOmpoauLu723QlmsGwFiKRCO7u7pBKpTYTu0ys\nMOyPrcWKuzuloTEY6ggEwOuv23sUDAajicGECqMpYev3MyuwZ9gfLsphC7GyeDFQVYWCRx+1/rkY\nDAaDwWAwGGbBIisM+/P228Bbb9mufTGDwWAwGAwGwylgkRWG7TlyBFizBsjOVm4Ti+1bI1BYyFLD\nGAwGg8FgMBwMJlYYtmfxYuCxx4BDh+w9EiWJidSq9s4de4+EwWAwGAwGg1EPEysM28P5V3AtYu1N\nWRlQUEC/BwXZdywMBoPBYDgBK1euhFAohFAoxIEDB7TuExcXB6FQiPvvv9/Go2OocvDgQSxYsAAl\nJSX2HkqjYGKFYXvsKVYUCqC6GkJVA6ysLLqNiqL2xQwGg8FgMIzCw8MDv/zyi8b2w4cPIzMzk7Vt\ndgCYWGEwTEVdrMhktiuu37AB8PBA1IIFym2cWGEeFgwGg8FgmMTQoUOxYcMG1NXV8bb/8ssvaNu2\nLWJjY+00MstQUVFh7yFYDIWTNjJiYoVhe9TFyogRVGC/Y4f1z8052KtGVjIz6ZaJFQaDwWAwTGLi\nxIm4e/cudqh8h8tkMqxfvx6TJk3S2F+hUGDp0qXo0KEDPDw8EBISgilTpqCoqIi33+bNmzFy5Ei0\nbt0a7u7uiIqKwmuvvQapmqnznTt3MGXKlIb9QkNDMWzYMGRkZDTsIxQKsUB1kbKeqKgoPPXUUw33\nudS2tLQ0vPTSSwgJCYGPj0/D48eOHcOwYcPg5+cHT09P9O3bF3v27OEd85133oFQKMTFixfx+OOP\nw8/PD0FBQZgzZw4A4ObNmxg9ejQkEglCQ0Px2WefaYxLKpViwYIFiI+Ph7u7O8LDwzFr1ixUVVXx\n9hMKhXjhhRewadMmtG/fHu7u7mjfvj3vtXjnnXfw2muvAQCio6MbUvf27dsHADh58iSGDRuG4OBg\neHh4ICoqCpMnT0a16jzJzrDWxQzb07EjMH48kJRE96urqROXq6v1z82JlZoa5bbqasDbG4iOtv75\nGQwGg8FoQoSHh6Nv37745ZdfMHz4cADArl27kJ+fj4kTJ2LNmjW8/V944QV8//33ePLJJ/HSSy/h\nxo0bWLp0KY4ePYpjx47Bzc0NAAkHDw8PzJgxAxKJBIcOHcLixYtx8+ZN3jEffvhhpKenY/r06YiO\njkZ+fj727duHK1euIDExsWE/baloAoFA6/bp06cjICAA8+bNa0id2rt3Lx544AF06dIF8+fPh1gs\nxqpV/9/enQdFeaR/AP++AwIj4Miig+KFoBJg1SCH941Eo4WbqPEIHnGVMhIXo1FLZaPEFWKsWBoE\nr7hqRDfiURqPciU6YgiaqIu6wgqaxAUScdWIBOWc6d8fI/Nj5EaYdyDfT9XUMP32vN0vPo7z2G93\n70VgYCASEhIwdOhQo3NMnToVHh4eWLduHU6ePImoqCioVDDc3zQAABm3SURBVCp8/vnnCAgIwCef\nfIK4uDgsXboUPj4+hnk9Qgi88cYbuHDhAkJCQuDp6Ym0tDTExsYiNTXVKBEBgIsXL+L48eOYP38+\n7Ozs8Nlnn2HChAnIzMzEH/7wB0yYMAG3b9/GP/7xD2zcuBFt2rQBAHh4eODBgwcYNWoU1Go1li1b\nBgcHB2RmZuL48eN49uyZyXaor5EwY7m5uYYHNWP9+gkBCJGc3PhtXbggBCDyXn1VXL58+f/LdToh\niosbv31q1i5fvmwcV0QNgHHVtBUUFNTtDfoboys+Gqp+A9m1a5eQJEl89913Ytu2bcLW1lY8e/ZM\nCCHE9OnTRf/+/YUQQnh5eYnhw4cLIYT49ttvhSRJIi4uzuhcSUlJQpIksX37dkNZ2bnKi4yMFAqF\nQmRlZQkhhHj8+LGQJEl8+umn1fZVkiQRERFRodzFxUW88847Fa6pX79+QqvVGsp1Op1wd3cXo0aN\nMnp/cXGx8PLyEgMGDDCUrVq1SkiSJObMmWMo02q1olOnTkKSJBEZGWkoz83NFS1bthTBwcGGsn37\n9gmFQiEuXLhg1Na+ffuEJEnizJkzRtdlbW0tfvjhB0PZjRs3hCRJYvPmzYay9evXC0mSxH//+1+j\ncx49elRIkiSuXr1ayW+tetXFdUN/f+dtYCS/sqFGU2TwZSMrLwwjQ5Lk3eeFiIioiZo0aRJKSkpw\n9OhRFBQU4OjRo5XeAhYfHw87OzsEBgbi4cOHhoe7uzvUajU0Go2hrlKpBADodDo8efIEDx8+xMCB\nAyGEQEpKiqGOlZUVNBoNHj9+3GDXM3fuXCjKLbhz/fp1ZGRkYOrUqUb9fvLkCQICAvDdd99VuG1q\nzpw5hp8VCgV8fHwgSRL+/Oc/G8pVKhXc3d3xU9nc2ee/ox49esDT09OorSFDhkCSJKPfEQAMHz4c\nruVuY+/ZsydatWpldM6qtG7dGgBw/PjxCnOOzAlvAyP5lf0Ffz7026hsbAArKwiu+kVEROaorpOg\nzWDStIODA1577TXExcVBoVCgoKAAkydPrlAvIyMD+fn5cHJyqvQ8D8q2EQBw8+ZNLF26FImJiRXm\napTdmmVtbY1169bhgw8+gJOTE/r27YvXX38d06dPR8eOHet9PS8uCpCRkQEARolGeZIk4dGjR+jQ\noYOhrHPnzkZ1VCoVWrRoAbVabVTeqlUro+vOyMhAeno62laylYIkSUZ1K2sH0P951CZ5Gzp0KCZO\nnIiIiAhs2LABQ4cORVBQEKZNm4aWZfOLzQCTFZJf2fwRU4ys9OwJFBXh1pUrjd8WERHR78S0adMw\nY8YM5OXlYdSoUYa5EeXpdDo4OjriwIEDlZ7DwcEBgD4ZGT58OOzt7REZGYlu3bpBqVQiOzsbs2bN\ngk6nM7wnLCwM48ePx7Fjx5CQkIA1a9YgMjISJ06cqDCP5EVVjSaUjeqU7zcArFu3Dj4+PpW+58Xr\ntbCwqFCnqiWcRbmEU6fTwcvLC5s2baq0rrOzc43tvHjO6sTHx+Py5cs4ceIEEhISEBISgqioKFy6\ndKnShEkOTFZIfnfuAKWlQBV/4YiIiMi8jR8/HtbW1khOTsaePXsqrePm5oavv/4affv2ha2tbZXn\n0mg0ePToEY4cOYLBgwcbyhMSEiqt7+LigrCwMISFheHnn3/Gq6++irVr1xqSFQcHB+Tm5hq9p7i4\nGPfu3avVtZWNtNjZ2WHEiBG1ek99devWDVevXm3Qdmra58bPzw9+fn6IiIjA6dOn8frrr2PHjh1Y\nsWJFg/XhZfBeGDK9X38FDhwATp7Uvy6bLyLHrVn37+uXLi4pMX3bREREzYRSqcSWLVuwatUq/OlP\nf6q0zpQpU6DT6fDRRx9VOKbVag0JRdloQfkRFJ1Ohw0bNhi9p6CgoMItYh06dEDbtm2NNkB0c3ND\nYmKiUb3t27cbnb86vr6+6NatGzZs2ID8/PwKx1+8Nasqtdkcc/Lkybh//z62bNlS4VhRUVGl7dek\nLDH89ddfjcpzc3MrjMB4e3sDgFltIMmRFTK9u3eBKVMAb2/g+TKHstm+HfjwQ2DZMuDjj+XtCxER\nURMWHBxcaXnZF+LBgwcjNDQU69evx40bNxAYGAhra2vcuXMHhw8fxpo1azBjxgwMGjQIjo6OmDlz\nJhYsWABLS0scOnSowgaN6enpGDFiBN566y14enrC2toap06dwq1bt/Dpp58a6s2ZMwfz5s3DxIkT\nERAQgOvXr+PMmTNo06ZNrW6XkiQJO3fuxOjRo+Hp6YnZs2ejQ4cO+OWXXwxJ0Llz52o8T1VtlS8P\nDg7GoUOHEBoaisTERMOiAunp6Th48CAOHTqEIUOG1KkdPz8/AMDy5csxdepUWFlZYeTIkdi3bx9i\nYmLw5ptvwtXVFQUFBdi1axcsLS0xceLEGq/HVJiskOm9uCmknLh7PRERUb3UZqTgxb1MoqOj0adP\nH2zduhXh4eGwtLREly5dMHnyZMOtTw4ODjh58iQWL16MVatWwd7eHhMmTMC8efPQq1cvw7k6d+6M\n4OBgnD17Fvv374ckSXB3dzfs41Jm7ty5+Omnn7Bz506cPn0aQ4YMQUJCAkaOHFnhGqq6psGDB+PS\npUtYs2YNYmNjkZeXh/bt28PPz89o5a+q9m6pbbkkSThy5Ag2btyIPXv24NixY1AqlXBzc0NoaCh6\n9uxZw2+84jX4+PggKioKsbGxmD17NoQQ0Gg0GDZsGK5cuYL4+Hjk5OSgVatW6NOnD2JiYgwJjjmQ\nRG1n4Mig/BCUSqWSsSfUoDIzgS5dgE6d9D+bWlERUi5ehNbWFr5LlgCJiUBCAhAQYPq+ULNy5fnC\nDb6+vjL3hJoTxlXTVlhYaD6b6xE1kOriuqG/v3POCple+ZEVIQCt1rTtt2kD7+HDoXj2TD9fBeDu\n9URERERmiMkKmV75ZOV//wMsLYEXluJrVM//J8AiPx/IztZP7K9knXIiIiIikhfnrJDp2dgAEycC\ntrZA2SoeliYMxefJSouHDwFfX/3IDnevJyIiIjI7TFbI9BQK4OBB/c/p6fpnU97P+3yzJ62dHfD9\n96Zrl4iIiIjqhLeBkbwKC/XPpkxWnrelKCoyXZtEREREVGdMVkheciQr9vbQ2tpCMvXEfiIiIiKq\nE94GRvIqLtbvYG/KZOXbb5HyfClQIiIiIjJfTFZIXoMH6ye4c5SDiIiIiF7A28BIHhoN8MUXwL17\n+pEVU64G9lyr5GTgP//R7/VCRERERGaHIyskj7VrgbNngTNngPbtTd68RV4eeoSF6fd8yc83eftE\nREREVDOOrJA8ym8MKQPrX37R/+Dqqh/ZISIiIiKzU22yEhUVBT8/P6hUKqjVagQFBSE1NdVwvLS0\nFMuWLUPv3r1hZ2cHZ2dnvP3228jKyqq20fPnz0OhUFR4ZGRkNMxVkfmTM1kpLYXy9m39z127mr59\nIiIiIqqVapOVxMREvPfee7h48SLOnTsHS0tLBAQE4PHjxwCAp0+fIiUlBeHh4UhJScGxY8eQlZWF\n0aNHQ1uLCdNpaWnIyckxPLp169YwV0XmryxZycsz/eT6Dz5A148+0v/s6mratomIiJq5u3fvQqFQ\nYM+ePYay3bt3Q6FQIDMzU8aeUVNU7ZyV06dPG73eu3cvVCoVkpOTMXbsWKhUKpw5c8aozrZt2+Dl\n5YVbt27By8ur2sbbtm0LR0fHenadmrSyZGXNGmDePGDZMuDjj03TdvllkjmyQkREVGe7d+/G7Nmz\nKz02duxYSJIEqYbbrPfv348HDx4gLCysMbpIzUSdJtjn5eVBp9PBwcGhyjpPnjwBgGrrlPH19UVR\nURE8PT0RHh6OYcOG1aU71JT17Qs8eQLcuQP8/DNgZWW6tssnKzUk1ERERFS1iIgIuLm5GZW5u7vj\n8OHDsKxhpc/9+/cjNTWVyQpVq07JSlhYGLy9vdG/f/9KjxcXF2Px4sUICgqCs7NzledxdnbG1q1b\n4efnh6KiIuzduxcjR45EYmIiBg0aVOl7rnATv+bFwwPw8ECHzZvR/tIlZD96hBwT/Rm3e/QIHQHk\nTJ+O7NatAcYWNTB+XlFjYFw1TV26dIGNKTc+NrHXXnsN/v7+9X5/TaMv9VFQUAClUtng56X/99tv\nv+HmzZuVHuvevXuDtlXr1cAWLVqE5ORkHD58uNLAKi0tRXBwMPLy8rBr165qz9WjRw+EhITA29sb\n/fr1Q0xMDEaPHo3169fX/QqoSVMUFwMAhAlHVnTP25Ket01EREQNp7I5Ky8aNmwYTp06Zahb9igj\nhEB0dDR69uwJpVIJJycnzJkzB48ePTI6j4uLC8aMGYOzZ8+ib9++UCqV+OSTTxrt2sj0ajWy8v77\n7yM+Ph4ajQYuLi4VjpeWlmLq1KlITU3F+fPna3UL2Iv8/f1x4MCBKo/7+vrW+ZzUBKhUAIBO3buj\nk6n+jK9dg7ZlS0ChYFxRgyr7n2/GFTUkxlXTVlhYWKf6f9n0p0bqCfBZ2NEGP2dubi4ePnxY6bHq\nRk3Cw8OxdOlSZGdnY+PGjRWOv/vuu/j73/+OWbNm4S9/+QsyMzMRHR2N77//HpcvX4a1tbWhjTt3\n7mDSpEkICQnB3Llz0blz54a5OKqSvb19lZ9JZVNCGkqNyUpYWBgOHjwIjUaDHj16VDheUlKCKVOm\nIC0tDefPn4dara5XR65du1btrWPUTJWW6p9NOUQ+Zw5SXn0VAOBkulaJiIiandGjRxu9liQJN27c\nqPF9AQEBcHZ2Rm5uLqZNm2Z0LDk5Gdu3b8fevXvx9ttvG7U1ePBgfPHFF5g7dy4A/QjMDz/8gK++\n+grjxo1rgCsic1NtshIaGoq4uDgcPXoUKpUKOTk5APTZlK2tLbRaLSZNmoQrV67g+PHjEEIY6rRu\n3dpwj+aMGTMgSZJhOHDjxo3o2rUrPD09UVxcjLi4OBw7dgxHjhxpzGslc7RjB7BtGyCE3D0hIiKi\nOoqOjoaHh4dR2cvO0YmPj4ednR0CAwONRm3c3d2hVquh0WgMyQoAdOrUiYlKM1ZtsrJlyxZIkoSR\nI0cala9evRoffvghsrKy8NVXX0GSJPj4+BjV2b17N2bMmAEAyMrKMhoKLCkpwZIlS5CdnQ2lUok/\n/vGPOHXqVIXsnJqxe/eAs2eBtm2B116TuzdERERUD35+fhUm2N+9e/elzpmRkYH8/Hw4OVV+/8OD\nBw+MXrtyz7RmrdpkRafTVftmFxeXGusAgEajMXq9ZMkSLFmypBbdo2YrNRWYPh0ICGCyQkRE9Fxj\nzCtpanQ6HRwdHaucy/zi3Giu/NW81WnpYqIGU/bB8uyZvP0gIiIiWVQ1Ad/NzQ1ff/01+vbtC1tb\nWxP3isxNrZcuJmpQZTvYM1khIiL6XbK1tcXjx48rlE+ZMgU6nQ4fffRRhWNarRa5ubmm6B6ZCY6s\nkDzKkpXcXP3k+kbYFIqIiIjMl5+fH+Lj47Fw4UL4+/tDoVBgypQpGDx4MEJDQ7F+/XrcuHEDgYGB\nsLa2xp07d3D48GGsWbPGMC+amj8mKySPsmTl7l1AodDPYfH0lLVLREREVHt13X3+xfrz58/Hv//9\nb8TFxSE6OhqAflQF0K8y1qdPH2zduhXh4eGwtLREly5dMHnyZIwYMaLefaCmRxLCfNeMLb+pjOr5\n5oHUTOTlAe++C+zfr3/9ww+ACVfz4CZr1BgYV9QYGFdNW2Fh4Usv5UtkbqqL64b+/s45KySPVq2A\nffuAdu30r/lBTkREREQvYLJC8ios1D8zWSEiIiKiFzBZIXkxWSEiIiKiKjBZIfkIoX8AgLW1vH0h\nIiIiIrPD1cBIPpKkH1nR6fQrghERERERlcNviCSfEyeAzz8HKtkQioiIiIiIIysknw8/BFJSAG9v\nwNFR7t4QERE1CiEE9wOhZsPUu55wZIXko1TqnwsK5O0HERFRI7GyskJhYSG0Wq3cXSF6aVqtFoWF\nhbCysjJZmxxZIfmU7WL/7Jm8/SAiImokCoUCNjY2KC4uRklJidzdMfLbb78BAOzt7WXuCTUVkiTB\nxsbGpCOFTFZIPmUrgD19Km8/iIiIGpEkSbA2w1Uvb968CQDw9fWVuSdEVeNtYCSf//xH//zmm/L2\ng4iIiIjMEpMVkk+/fvpnCwt5+0FEREREZonJCsln5kz984gR8vaDiIiIiMwSkxWST2Gh/tnGRt5+\nEBEREZFZYrJC8mGyQkRERETVYLJC8iktBSwtmawQERERUaUkYeptKOvgyZMncneBiIiIiIjqQaVS\nvfQ5OLJCRERERERmickKERERERGZJbO+DYyIiIiIiH6/OLJCRERERERmickKERERERGZJSYrRERE\nRERklsw6WYmNjUXXrl2hVCrh6+uLpKQkubtETUhUVBT8/PygUqmgVqsRFBSE1NTUCvVWr16NDh06\noGXLlhg+fDjS0tJk6C01VVFRUVAoFFiwYIFROeOK6urevXuYOXMm1Go1lEolvLy8cOHCBaM6jCuq\nq9LSUqxYsQKurq5QKpVwdXXFX//6V2i1WqN6jC2qzoULFxAUFISOHTtCoVBgz549FerUFENFRUVY\nsGAB2rZtCzs7O4wfPx4///xzjW2bbbJy4MABLFy4EOHh4bh27RoGDBiAMWPGICsrS+6uURORmJiI\n9957DxcvXsS5c+dgaWmJgIAAPH782FBn3bp12LBhAzZv3ozLly9DrVZj1KhRyM/Pl7Hn1FRcunQJ\nO3bsQK9evSBJkqGccUV1lZubi4EDB0KSJJw6dQq3bt3C5s2boVarDXUYV1QfkZGR2LZtG6Kjo5Ge\nno5NmzYhNjYWUVFRhjqMLarJ06dP0atXL2zatAlKpdLo3zygdjG0cOFCHDlyBF9++SW++eYb5OXl\nYdy4cdDpdNU3LsyUv7+/CAkJMSrr3r27WL58uUw9oqYuPz9fWFhYiBMnTgghhNDpdKJdu3YiMjLS\nUKegoEDY29uLbdu2ydVNaiJyc3OFm5ubOH/+vBg2bJhYsGCBEIJxRfWzfPlyMWjQoCqPM66ovsaN\nGydmzZplVDZjxgwxbtw4IQRji+rOzs5O7Nmzx/C6NjGUm5srrKysxP79+w11srKyhEKhEP/85z+r\nbc8sR1aKi4vxr3/9C4GBgUblgYGBSE5OlqlX1NTl5eVBp9PBwcEBAPDTTz/h/v37RnFmY2ODIUOG\nMM6oRiEhIZg0aRKGDh0KUW4FeMYV1cfRo0fh7++PyZMnw8nJCd7e3oiJiTEcZ1xRfY0ZMwbnzp1D\neno6ACAtLQ0ajQZjx44FwNiil1ebGLp69SpKSkqM6nTs2BEeHh41xpll43T75Tx8+BBarRZOTk5G\n5Wq1Gjk5OTL1ipq6sLAweHt7o3///gBgiKXK4uyXX34xef+o6dixYwd+/PFH7N+/HwCMhsMZV1Qf\nP/74I2JjY7Fo0SKsWLECKSkphnlQoaGhjCuqt/nz5yM7OxseHh6wtLREaWkpwsPDMW/ePAD8zKKX\nV5sYysnJgYWFBRwdHY3qODk54f79+9We3yyTFaKGtmjRIiQnJyMpKanCfZaVqU0d+n1KT0/HypUr\nkZSUBAsLCwCAEMJodKUqjCuqik6ng7+/P9auXQsA6N27N27fvo2YmBiEhoZW+17GFVXns88+w65d\nu/Dll1/Cy8sLKSkpCAsLg4uLC2bPnl3texlb9LIaIobM8jawNm3awMLCokKmdf/+fbRv316mXlFT\n9f777+PAgQM4d+4cXFxcDOXt2rUDgErjrOwY0YsuXryIhw8fwsvLCy1atECLFi1w4cIFxMbGwsrK\nCm3atAHAuKK6cXZ2hqenp1HZK6+8gszMTAD8vKL6W7t2LVasWIG33noLXl5eCA4OxqJFiwwT7Blb\n9LJqE0Pt2rWDVqvFo0ePjOrk5OTUGGdmmaxYWVnBx8cHZ86cMSpPSEjAgAEDZOoVNUVhYWGGRKVH\njx5Gx7p27Yp27doZxVlhYSGSkpIYZ1SlN954Azdv3sT169dx/fp1XLt2Db6+vpg6dSquXbuG7t27\nM66ozgYOHIhbt24ZlWVkZBj+g4WfV1RfQggoFMZf9xQKhWE0mLFFL6s2MeTj44MWLVoY1cnOzsat\nW7dqjDOL1atXr26Unr+kVq1aYdWqVXB2doZSqcTf/vY3JCUlYdeuXVCpVHJ3j5qA0NBQfPHFFzh4\n8CA6duyI/Px85OfnQ5IkWFlZQZIkaLVafPzxx3B3d4dWq8WiRYtw//59bN++HVZWVnJfApkhGxsb\ntG3b1vBQq9XYt28funTpgpkzZzKuqF66dOmCiIgIWFhYoH379jh79izCw8OxfPly+Pn5Ma6o3m7f\nvo3du3fjlVdeQYsWLaDRaLBy5UpMmTIFgYGBjC2qladPnyItLQ05OTnYuXMnevbsCZVKhZKSEqhU\nqhpjyMbGBvfu3UNMTAx69+6NJ0+eYN68eWjdujXWrVtX/e1iDbeQWcOLjY0VLi4uwtraWvj6+opv\nvvlG7i5REyJJklAoFEKSJKNHRESEUb3Vq1eL9u3bCxsbGzFs2DCRmpoqU4+pqSq/dHEZxhXV1cmT\nJ0Xv3r2FjY2NcHd3F9HR0RXqMK6orvLz88XixYuFi4uLUCqVwtXVVaxcuVIUFRUZ1WNsUXU0Go3h\ne1T571bvvPOOoU5NMVRUVCQWLFggHB0dRcuWLUVQUJDIzs6usW1JiFrMCiUiIiIiIjIxs5yzQkRE\nRERExGSFiIiIiIjMEpMVIiIiIiIyS0xWiIiIiIjILDFZISIiIiIis8RkhYiIiIiIzBKTFSIiIiIi\nMktMVoiIiIiIyCz9HyorOii2B0LpAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c145f9e8>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We made `g=0.2` and we can see that while the train's position is smoothed, the estimated position (and hence velocity) fluctuates a lot in a very tiny frame, far more than a real train can do. So emperically we know that we want `g<<0.2`.\n",
      "\n",
      "Now let's see the effect of a poor choice for *h*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_train_data(23000, 15, 100)\n",
      "data = g_h_filter(data=zs, x0=23000, dx=15., dt=1., g=0.01, h=0.1)\n",
      "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.1', z_label='Measurements')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Wegjff0cRERGRy07km3at92zJYlNRYXFIjhlo2NbrdThdcLhbx0CekWOar+Lj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\nERGRJLFYISIiIiIiSfp/kZWuvv93auwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c11f92e8>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the position changes smoothly thanks to the small *g*, but the large *h* makes the filter very reactive to the measurements. This happens because in the course of a few seconds the rapidly changing measurement implies a very large velocity change, and a large *h* tells the filter to react to those changes quickly. Trains cannot change velocity quickly, so the filter is not doing a good job of filtering the data - the filter is changing velocity faster than a train can.\n",
      "\n",
      "Finally, let's add some acceleration to the train. I don't know how fast a train can actually accelerate, but let's say it is accelerating at 0.2 m/sec^2. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gen_train_data_with_acc(pos, vel, count):\n",
      "    zs = []\n",
      "    for t in range(count):\n",
      "        pos = compute_new_position(pos, vel)\n",
      "        vel += 0.2\n",
      "        zs.append(measure_position(pos))\n",
      "    return np.asarray(zs) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_train_data_with_acc(23000, 15, 100)\n",
      "data = g_h_filter(data=zs, x0=23000, dx=15., dt=1.,g=.01, h=0.0001)\n",
      "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.0001', z_label='Measurements')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CRERERKZTXCwCFXd3wMZG6d4Y1xdfAHFxwMKFvSNYmTNHPMyI08CIiIiIyHQK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\nrQ2EyxrVAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c1372048>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we see that the filter is not quite tracking the train anymore due to the acceleration. We can fiddle with *h* to let it track better, at the expense of a less smooth filtered estimate."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_train_data_with_acc(23000, 15, 100)\n",
      "data = g_h_filter(data=zs, x0=23000, dx=15., dt=1.,g=.01, h=0.001)\n",
      "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.001', z_label='Measurements')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PAUBWVpY5XSVShJ8rsgV+rsgW+LkiW2kNn63o/HyEADh75Qque3gg4J13cCs6GpWt4LW5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1VFwufFF0n4mFvE/PrrwJtv0ur544+PeIhaCVcjv+II8isOo6yuACq1UtDpg/xDkZU0CVlJk5CR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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f25c008e828>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are two lessons to be learned here. First, use the *h* term to respond to changes in velocity that you are not modelling. But, far more importantly, there is a tradeoff here between responding quickly and accurately to changes in behavior and producing ideal output for when the system is in a steady state that you have. If the train never changes velocity we would make *h* extremely small to avoid having the filtered estimate unduly affected by the noise in the measurement. But in an interesting problem there is almost always changes in state, and we want to react to them quickly. The more quickly we react to it, the more we are affected by the noise in the sensors. \n",
      "\n",
      "I could go on, but my aim is not to develop g-h filter theory here so much as to build insight into how combining measurements and predictions lead to a filtered solution, so I will stop here. Do understand that there is extensive literature on choosing *g* and *h* for problems such as this, and that there are optimal ways of choosing them to achieve various goals. In the subsequent chapters we will learn how the Kalman filter solves this problem in the same basic manner, but with far more sophisticated mathematics. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "g-h Filters with FilterPy"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Final Thoughts"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*author's note*: the following few paragraphs really belong in the not yet written least squares chapter.\n",
      "\n",
      "Near the beginning of the chapter I used `numpy.polyfit()` to fit a straight line to the weight measurements. It fits a n-th degree polynomial to the data using a 'least squared fit'. How does this differ from the g-h filter?\n",
      "\n",
      "Well, it depends. We will eventually learn that the Kalman filter is optimal from a least squared fit perspective under certain conditions. However, `polyfit()` fits a polynomial to the data, not an arbitrary curve, by minimizing the value of this formula:\n",
      "$$E = \\sum_{j=0}^k |p(x_j) - y_j|^2$$\n",
      "\n",
      "I assumed that my weight gain was constant at 1 lb/day, and so when I tried to fit a polynomial of $n=1$, which is a line, the result very closely matched the actual weight gain. But, of course, no one consistently only gains or loses weight. We fluctuate. Using 'polyfit()' for a longer series of data would yield poor results. In contrast, the g-h filter reacts to changes in the rate - the $h$ term controls how quickly  the filter reacts to these changes. If we gain weight, hold steady for awhile, then lose weight, the filter will track that change automatically. 'polyfit()' would not be able to do that unless the gain and loss could be well represented by a polynomial.\n",
      "\n",
      "Another advantage of this form of filter, even if the data fits a *n*-degree polynomial, is that it is *recursive*. That is, we can compute the estimate for this time period knowing nothing more than the estimate and rate from the last time period. In contrast, if you dig into the implementation for `polyfit()` you will see that it needs all of the data before it can produce an answer. Therefore algorithms like `polyfit()` are not well suited for real-time data filtering. In the 60's when the Kalman filter was developed computers were very slow and had extremely limited memory. They were utterly unable to store, for example, thousands of readings from an aircraft's inertial navigation system, nor could they process all of that data in the short period of time needed to provide accurate and up-to-date navigation information. \n",
      "\n",
      "\n",
      "Up until the mid 20th century various forms of Least Squares Estimation was used for this type of filtering. For example, for NASA's Apollo program had a ground network for tracking the Command and Service Model (CSM) and the Lunar Module (LM). They took measurements over many minutes, batched the data together, and slowly computed an answer. In 1960 Stanley Schmidt at NASA Ames recognized the utility of Rudolf Kalman's seminal paper and invited him to Ames. Schmidt applied Kalman's work to the onboard navigation systems on the CSM and LM, and called it the \"Kalman filter\".[1] Soon after, the world moved to this faster, recursive filter.\n",
      "\n",
      "The Kalman filter only needs to store the last estimate and a few related parameters, and requires only a relatively small number of computations to generate the next estimate. Today we have so much memory and processing power that this advantage is somewhat less important, but at the time the Kalman filter was a major breakthrough not just because of the mathematical properties, but because it could (barely) run on the hardware of the day. \n",
      "\n",
      "This subject is much deeper than this short discussion suggests. We will consider these topics many more times throughout the book."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I encourage you to experiment with this filter to develop your understanding of how it reacts. It shouldn't take too many attempts to come to the realization that ad-hoc choices for $g$ and $h$ do not perform very well. A particular choice might perform well in one situation, but very poorly in another. Even when you understand the effect of $g$ and $h$ it can be difficult to choose proper values. In fact, it is extremely unlikely that you will choose values for $g$ and $h$ that is optimal for any given problem. Filters are *designed*, not selected *ad hoc*. \n",
      "\n",
      "In some ways I do not want to end the chapter here, as there is a significant amount that we can say about selecting $g$ and $h$. But the g-h filter in this form is not the purpose of this book. Designing the Kalman filter requires you to specify a number of parameters - indirectly they do relate to choosing $g$ and $h$, but you will never refer to them directly when designing Kalman filters. Furthermore, $g$ and $h$ will vary at every time step in a very non-obvious manner. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is another feature of these filters we have barely touched upon - Bayesian statistics. You will note that the term 'Bayesian' is in the title of this book; this is not a coincidence! For the time being we will leave $g$ and $h$ behind, largely unexplored, and develop a very powerful form of probabilistic reasoning about filtering. Yet suddenly this same g-h filter algorithm will appear, this time with a formal mathematical edifice that allows us to create filters from multiple sensors, to accurately estimate the amount of error in our solution, and to control robots."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*  [1] NASA Kalman Filtering Presentation<p> http://nescacademy.nasa.gov/review/downloadfile.php?file=FundamentalsofKalmanFiltering_Presentation.pdf&amp;id=199&amp;distr=Public\n",
      "\n",
      "\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}