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      "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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     "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 to you. After she explains, you eagerly stand on it and announce the results: \"172 lbs\". You are estatic - 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",
      "\"What? 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 more than 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 measure. 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 youself 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 that will both 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",
      "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 counterintuitively, is yes, it can. Consider this case. We know scale A is accurate to 1 lb. In other words, if we weight 170 lbs, it could report 169, 170, or 171 lbs. We know that scale B is accurate to 9 lbs. We do a reading, and A=160, and B=170. What should we estimate our weight to be?\n",
      "\n",
      "Well, if we say 160 lbs we would be wrong, because B can only be 9 pounds off, and 170 lbs - 160 lbs is 10 lbs. 160 is not a possible measurement for B. In fact, the only number that satifies all of the constraints is 161 lbs. That is 1 lb within the reading of A, and 9 lbs within the reading of B. \n",
      "\n",
      "This is an important result. With two relatively inaccurate sensors we were able to deduce an extremely accurate result. Now sure, that was a specially constructed case, but it generalizes. What if A is accurate to 3 lbs, B is accurate to 11 lbs, and we get the measurements of A=160 lbs and B=170 lbs? The result can only be from 159 lbs to 163 lbs, which is better than the range of 157 lbs to 163 lbs that is the range of values that A alone allows.\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. \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 1,000,000 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. I will not prove it, but it can be proved that the average of a large number of weighings will be extremely close to my actual weight. Consider a simple case - the scale is accurate to within 1 lb. If I weigh 170, it will return one of either 169, 170, or 171. The average of a bunch of 170 is 170, so we can exclude those. What is left is measurements of 169 and 171. But we know there will be as many 169s as there are 171s. The average of those will also be 170, and so the average of all must be 170, my true weight. It's not that hard to extend this to any arbitrary accuracy.\n",
      "\n",
      "Okay, great, we have an answer! But it is not a very good answer. No one has the patience to weigh themselves a million, or even a hundred 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 - bad measurements. 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! \n",
      "\n",
      "Shall we give up? No, let's play 'what if'. 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, but it seems pretty likely that my weight held steady.\n",
      "\n",
      "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."
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      "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.plot(weights)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.show()"
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bT1zEY8Otc8OZPWQ3OSkIL90Tize+K8YXJy9CkhxnDrsn+X1w9ALu6OeLuKA+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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16faf62ad0>"
       ]
      }
     ],
     "prompt_number": 117
    },
    {
     "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. Lets look at that in a chart. 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.plot([0,12], [ave,ave], c='r')\n",
      "plt.plot(weights, c='b')\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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3qzwe4Mknw9GmjRPJyXapyyESWllnrr06ct2qVSvce++9UCgUqFKlCgAgOjoa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\nswAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb0bbdd0>"
       ]
      }
     ],
     "prompt_number": 119
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That doesn't look very convincing. \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(len(weights))\n",
      "line = np.poly1d(np.polyfit(xs, weights, 1))\n",
      "plt.plot (xs, line(xs), c='r')\n",
      "plt.plot(weights, c='b')\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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LwNSpesh5HyAip2DPNRGRQEyapMT162LMnav3dChldvSoBP37B2HIECPi4kxe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\n3q8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fade6b90>"
       ]
      }
     ],
     "prompt_number": 120
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This looks much better, at least to my eyes. 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 assume that somehow 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 somehow. 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.\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": [
      "import gh_internal\n",
      "gh_internal.plot_estimate_chart_1()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GG27ocbd8xYoVGjlypCRp4MCBSk9Pb/+nnqs3MMfWHFdVVdlqPeF2TP5BOp4y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\nb0Jwkb85ZG8W+ZtF/uaQvXM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       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb15c190>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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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ksMYeHD16tMaPH6977rlHkuRwOLRs2TI98MADGjx4sE6dOiVJstvtevjhh/XX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\nKru7uzQaDdLpNJOTk0Oo+vdRz/1/tNt3ux6QLy8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       "text": [
        "<matplotlib.figure.Figure at 0x7f170541c910>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "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 follows. 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. \n",
      "\n",
      "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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LFi1CUlISDh48iMTExAr7f/jhh4iMjIREwjX+GiP2oYnF/MVh9mIxf7GYf8MZMECHo0fv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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2efd50>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try a randomly chosen number: $\\frac{4}{10}$. 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",
      "$$ \\verb,new estimate, = \\verb,prediction, + \\frac{4}{10}(\\verb,measurement, - \\verb,prediction,)\n",
      "$$\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": [
      "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",
      "    p1, = plt.plot (range(1, n+1), estimates, 'b--')\n",
      "    p2, = plt.plot(range(1, n+1), weights, c='r')\n",
      "    p3, = plt.plot([1, n],[160, 160+n],c='g')\n",
      "    plt.legend([p1, p2, p3], ['filter', 'measurements', 'actual'], 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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bc/nyZYuPbd++nf79+wPw008/0axZM4KDgwGoV68ep06dIjQ01BZhCiGEEMJN\nef74I8oNG8jav79Kr2Npto/4gfG0rd0WrVbBxo1KPvvMh+xsBS+/rGHBgjyqV3e6uSfcmt17rpOS\nkhg4cCAAN27coHbt2qxfv55vvvmG2rVr88cff9g5QscgvXvuQfLsHiTP7kHy7ET0evwmTSJv9mxM\ntWqV+bCy5thoMpJ6OZWYlBjCVoWRfDaZ0eGjOTHyBHGRcYTXCUehUGA0wg8/eDNzZh7//ncWY8dq\npLB2QnadLeTcuXPk5+fTokWLIvufe+45AFJSUlBIh74QQgghqpDPihWYgoLQ/ll/WEtps31YolLB\n55/nWDUGYXt2La6Tk5PNo9YAtWvXJj093bydnp5O7dq1LR47duxYQkJCAKhWrRpt2rSha9euwP8+\nSbradiFHiUe2rb/dtWtXh4pHtuX9LNvyfnb1bdX16/RauJDsHTtI/bMlpKzHF+678/E8Qx7ptdNZ\n98s6jl8/Tvca3c1tH/v37+fo3v/j7Nn7eeABI9Wr/2D31y/bln8/p6amcvHiRQBGjRpFedhsEZnL\nly8zZsyYIjc09uvXj+XLl9OoUSOAYjc0vvDCC+zcubPYueSGRiGEEEJUmslEwF/+gv6RR8ifPLnC\npylpkZe+jfqalyA/frzgBsXERG/69tUxbpyGNm0M1nologo55A2Nc+bMISUlhYyMDCIjI5k9ezbB\nwcH4+/ubC2sApVLJlClTiI6OBuCtt96yRXhO4c5PxsJ1SZ7dg+TZPUieHZ/31q14XLlC/rhxFTp+\n0/ebOON/ptS2j+vXFbz4YgCXLnnw0ksaDh3Kok4d6aN2ZTYprmNjY4mNjS22f8uWLcX2DRw4sEir\niBBCCCGEtSkyMvCbORP1F1+AUlnm4+6c7eP49eM81/o5c9uHpfvEatUyMWFCPn366PCySdUl7M1m\nbSHWJG0hQgghhKgMvwkTMPn4kLdgwT2fW5a2D5MJ9Hrw9q7qyIWtOWRbiBBCCCGEo/Davx/v778n\nMy2t1OeVZbYPtRo2bFDy2We+jBqVz8iR2qoOXzg4u89zLcrm7hkGhGuSPLsHybN7kDw7KI0Gv8mT\nyZ0/3+L64WqtmoSTCURtjqLPl33I0GQQPzCe1GGpxETEmAvr69cVjBhxm7Ztq7F7tzdxcbm89JIU\n1kJGroUQQlQxr+++Q9+xo8VCRghb8/3HPzC0aIHu8cfN+yy1fYwOH12k7eNOf/yhoHv3IDp3vsne\nvVk0bOgp16nwAAAgAElEQVR0HbaiCknPtRBCiCrjeewYgU88gbFePXK++AJDWJi9QxJuzOP0aQKf\neIKsPXsw1a9vse1jaOjQEhd5udPlywopqt2E9FwLIYRwDCYTftOnk/u3v2Hy8yPg6afJmzkT7YgR\nIKvvClszGvGbNIkbUyeyMWM36w6s49TNUwxpMaTU2T5KIoW1KIn0XDsJ6d1zD5Jn9+AueVZu2gRa\nLdrhw9ENGUL29u34rliB35gxBXeBuTh3ybMzMJqMHFz1Di+3/o1mhr+TfDaZ0eGjOTHyBHGRcYTX\nCS+xsM7KKvm8kmNhiRTXQgghrE+tRjV7Nrl/+xt4FPyvxti8OVkpKeDlRVDv3nj88oudgxSu7kLm\nBeIOxhGxKpypF5fTolc0h0ccJiEqgaimURb7qQsZDPDRRz507FiNjAz5pkWUnfRcCyGEsDrf997D\n49Ilcpcvt/i4MiEBVWwsee++i/bPVXmFsIY7F3kpbPsY+eVp2tSPQDNzVpnOcfKkB6+/7o+/v4lF\ni3Jp3NhYxVELRyY910IIIezK4/x5fL74gqy9e0t8jnbYMPTt2hHw0kt4paUVTIvm52fDKIUrKW22\nj4DvfkB1+Duy9iXc8zxaLSxa5MvKlT68/XYeI0ZoC794EaLM5EfGSUhfl3uQPLsHV8+zatYsNGPH\nYqpfv9TnGVu1Iuv770GjIbBvXzx++81GEdqGq+fZEZjbPuIjmLZnGq1qtira9pGnxe/NN8lduBBU\nqnue79YtBadPe/LDD1m8+OK9C2vJsbBERq6FEEJYjdfu3Xj+/DM5K1eW7YCAAHKXL0cZH0/gwIHk\nxsWhGzKkaoMUTs1S20dJs32o5s1D1707+u7dy3TuevVMfP55TlWELdyI9FwLIYSwDp2OoO7dyZs5\ns8gCHWXlefw4/i+9hD4yktz33wdf3yoIUjgjS20f0S2jS1zkBcDz6FEChg0jKy0NU3CwjSMWrqS8\nPdfSFiKEEMIqfFatwlivHrqBAyt0vKFNG7J27UJx8yaB/fvj8X//Z+UIhbO5Z9tHSbN96HT4TZxI\n3ty5FgtrtRo+/dQHo9ynKKqAFNdOQvq63IPk2T24Yp4VN27g+8EH5M6bV7kFYoKCyFm9Gu3w4QT2\n64d3UpL1grQxV8yzLai1ahJOJhC1OYo+X/YhQ5NB/MB4UoelEhMRU6bVE30+/RRT7dpon3mm2GO7\nd3vRtWsQx497kp9fuVglx8IS6bkWQghRaap589AOGYKxZcvKn0yhQPPKK+gfegj/l1/GKy2NvDlz\nQKms/LmFQyptto/S5qK2xOP8eXyXLCH7u++KfNDLzFQwa5aKH37wZuHCHB57TG/tlyEEID3XQggh\nKsnz+HECnnmGrEOHMFWvbtVzKzIy8IuJweP6dXJWr8ZYjr5H4fguZF5g3S/rWH9qPf7e/gxrOYyh\noUPLNDptkclEwDPPoIuMRPP66+bd5855EBUVSP/+OmJjcwkKstILEG5B5rkWQghhOyYTqhkzyJs+\n3eqFNYCpenVy/vUvfJYuJbBPH3IXL0bXv7/VryNspzyzfZSXctMmFOnpaMaMKbL/gQeMfPGFmg4d\nDJU6vxBlIT3XTkL6utyD5Nk9uFKevbdtQ5GVhXbEiKq7iEKBZtw41GvW4Pfmm6hiY0Gnq7rrWYkr\n5bmyjCYjqZdTiUmJIWxVGMlnkxkdPpoTI08QFxlHeJ3wShfWilu3UM2aRe6iReDtXeQxT0+qpLCW\nHAtLZORaCCFExeTmooqNJXfZsoLqpYoZOnUia/du/MeMITAqCvXnn2Nq0KDKrysqzlLbR2yX2Iq3\nfZRCNWsW2qefRhseQdX/NApRMum5FkIIUSG+cXF4/vorOatW2fbCRiO+ixfjs3w5OR9/jL5PH9te\nX5TKUttHdMtoq7R9lMRr7178xo3jswn/5h+f1Wb37ix8yncfpBAlkp5rIYQQVc7j0iV8Vq4ka88e\nO1zcg/xJk9B37Ij/6NFohg0jf9o08JL/pdmLNWf7KLe8PJSvT+adGktI/mctVqzIkcJa2JX0XDsJ\n6etyD5Jn9+AKeVa98w6a0aMxNWxotxj0XbqQ9cMPeP3nPwQMHozi2jW7xWKJK+T5Xiq8yIuVGI1w\n6q+L+OZaBJ5P9SclJZs2bWx306I75FiUn3zMF0IIUS5eqal4Hj1KztKl9g4FU506qDdtwveDDwjq\n1YucZcvQd+9u77BcWlXO9lFe55NOEbp3NcqtqUR2qeSKMEJYifRcCyGEKDu9nsCePcmfMgXdU0/Z\nO5oivP682VEzciT5kyfb5CZLd2Gp7SO6ZbRt2j5KDMpIYP/+aKKHoX3pRfvEINyC9FwLIYSoMso1\nazBVr47uySftHUox+h49yNq1C/9XXiHgwAFyli/HVLu2vcNyarac7aO8fFavBk9PtC9U4TSQQlSA\n9Fw7Cenrcg+SZ/fgrHlW3L6Nav588uLiiiwr7UhM992Hets29O3bE9SzJ14HDtgtFmfNs1qrJuFk\nAlGbo+jzZR8yNBnED4wndVgqMRExdimstVpISfnfeKDi6lV84+LI+cc/wMN+pYyz5lhULRm5FkII\nUSa+cXFoo6IwtG5t71BK5+VF/qxZ6B95BP+XXiJ/zBg048fbtQhzdHad7eMe/vtfT8aP9+P++430\n7KnHywv8pk9HM3IkxtBQu8YmhCXScy2EEOKePE6eJPCpp8g6eBBTcLC9wykzxeXLBLz8MsYaNcj9\n5BOnit0WLLV9DA0d6hBtH3l5MH++inXrlLz3Xh7PPKNFoQDv5GRUc+cWTAPp62vvMIUbkJ5rIYQQ\n1mUy4ffWW+S/+abTFaemhg3JTk5G9e67BPboQc7nn2Po0MHeYdmVI832UZJTpzwYMSKA1q0N7NuX\nRZ06f44DZmXhN306OcuXS2EtHJZ8R+YkpK/LPUie3YOz5dk7ORmP9HQ0L71k71AqxtubvLlzyYuL\nI2D4cHw++QRMVf+lrSPl2Wgykno5lZiUGMJWhZF8NpnR4aM5MfIEcZFxhNcJd5jCGqBuXROxsXms\nXp3zv8IaUL33HrrevdF36WLH6P7HkXIsHIeMXAshhChZXh6qWbPIXbLE6VdA1A0cSHbr1viPHInX\nwYPkfvQRpmrV7B1WlXLk2T5KU6OGiccf1xXZ53n4MMrkZLLS0uwUlRBlIz3XQgghSuT7wQd4/vQT\nOWvW2DsU69FoUMXG4r1zJzmrVmFo187eEVmVpbaP6JbRDtX2UW5aLUE9e5I3ZQq6wYPtHY1wMw7Z\ncz1//nwSExMJDg4mKSkJgB9//JGZM2diMBho3rw5ixYtAuDjjz/mm2++AWDAgAGMGzfOFiEKIYS4\ni+LKFXw+/ZTsXbvsHYp1+fiQFxeH/pFHCBg6lPw/Z55w1OkFy8KRZ/sozTffeLNmjZK1a3NKnczF\n9+OPMTZogO7pp20XnBAVZJOe6759+7J8+XLzttFoZOrUqcyZM4evv/6a2NhYoGBE+quvviIpKYlt\n27axbds2rly5YosQHZ70dbkHybN7cJY8q+bMKZju7IEH7B1KldA99RTZ336LMj4e/1GjICvLque3\nRZ4vZF4g7mAcEfERTNszjVY1W3F4xGESohKIahrlsIX1jRsKXnnFn1mzVIwbpym1sPY4exafTz4h\n94MPHO4DkLO8l4Vt2aS4bt++PdWrVzdvnzhxguDgYHNrR40aNQAICAjAy8uL/Px8NBoN3t7eBAYG\n2iJEIYQQd/A8eBDvtDTyJ060dyhVytikCdk7dmAKCiKod288T5ywd0j35IiLvJSVyQSbN3vTtWsQ\n9eoZ2bs3iy5d9KUe4DdlCvmTJmEMCbFdoEJUgl3uTvn9998JDAxk1KhR3Lx5k6FDhzJs2DBq1KjB\niBEj6NGjB0ajkWnTphEUFGSPEB1O165d7R2CsAHJs3tw+DwbDPjNmEHu7Nng72/vaKqeSkXuP/6B\ncuNGAp5+mrxZs9D+9a+VHiW1Zp6dte3jbj/84MUHH6j417/UPPyw4Z7PV65fjyIzE82rr9oguvJz\n+PeysAu7FNcajYajR4+SnJxMQEAAQ4YMoVu3bigUCtavX8+uXbvQ6XRER0fTo0cPateubY8whRDC\nLSnXrgVfX3RDhtg7FJvSDh2Kvm1bAl56Ca8DBwraEOz84cJZZ/soSc+eevbsyUKpvPdzFTduoJo9\nG/WGDU4/U41wL/f8aTUYDFy8eJFr166Rn5+PSqWibt26hISE4OnpWaGL1q5dm6ZNm1KvXj0AwsLC\nOHfuHDk5ObRp04aAgAAAWrVqxcmTJ4mMjCx2jrFjxxLy51dE1apVo02bNuZPkIU9UK60ffz4ccaM\nGeMw8ch21Wzf2b/nCPHItvu9nw9++y09Z88md+tWUCjsHo+tt/emp+P57rv03rqVoN692fv666hD\nQmz6fs4z5JFeO511v6zj+PXjdK/R3bzIy/79+/n16K/U6VrHIf57lXd7//6yP181cyb/16ULJ7Oz\nKRwftnf8d29/+umnLl9/uON24b8vXrwIwKhRoyiPEqfiy8nJYc+ePRw7dgyVSkXt2rXx8fFBo9GQ\nnp5Obm4uERERdO/eHf8yfLK/fPkyY8aMISkpiezsbB5//HGSkpJQqVQMGTKEJUuWoFarmTlzJhs3\nbsRoNPLkk0/y6aef8uCDDxY5lztOxZeammpOvnBdkmf34Mh5Vr39Ngq1mtzFi+0dit0p165FNXs2\neXPnon3uuXIfX548W2r7iG4Z7XRtH4WMRjh92oOWLY0VOt5r1y78Jk8ma/9+u397UBpHfi8L6ynv\nVHwlFteLFy/moYceok2bNlSzMMl+RkYGx48f5+jRo0yYMKHUi8yZM4eUlBQyMjKoWbMmsbGxaLVa\nli1bhl6vJyoqilf/7Ke6cyq+wYMH8/LLLxc7nzsW10IIUdU8Tp8m8IknyEpLwyTteAB4nDxJwEsv\noe/Uidz580Glsur5LbV9DA0d6rRtHwBnzngwYYIfKhVs3Kguf+t6bi5BXbqQu2AB+sceq5IYhSgP\nqxXXer0erzL0OJX1edYkxbUQQliZyUTA0KHoevVCM3asvaNxLNnZ+E+ejMepU+SsXo2xadNKnc4l\nF3kB9Hr45BMfPvrIlzfeyGfUKA0V6R5VzZ6Nx5Ur5Kxcaf0ghagAqy0iU9aC2daFtbuSr57cg+TZ\nPThinr137MDj0iU0r7xi71AcT2AgOStWoIyPJ3DAAHLnzy/TKoF35tnZZvu4eVPB+fMe5OcryMuD\n/HwF+flw//1GOnUqPstHaqoXM2eqqF7dREpKNo0aVawdxPP4cZQJCWTd0fvqyBzxvSzsTypjIYRw\ndxoNqrffJnfBAvD2tnc0jkmhQPviixjat8d/5Ei80tLIe+898PUt9bCKzPZhMGAuaL28oHr14l8w\nnz/vwaFDXkUK37w8Ba1bGxg0SFfs+Tt2ePP3v/uan1dYNA8erOWDD/KKPT8tzYtFi3zx9TXh6wsq\nVcHfPXroLBbXdeoYmT49n379dBWfwdBgwG/iRPJmzcJUx3nbYoQosS3kTllZWXh5eeHn54dGo+HI\nkSP4+vrSrl07PEpbVqmKSFuIEEJYj8/ixXgdOkROQoK9Q3EOWVn4jx+Px8WLBW0ijRoVeVitVfPp\nnmT+eXwdNzx+4cGcodx/cwSqzPZ06mjg1Vc1xU65ZYs3kyf7kZ+vQKfDXNAOHarlb38rXvympnrx\nz38qixS+vr4m2rc30K9f8eL6jz8UXLzogUrFnwWzCZUK/PxM9/p8YDM+y5fjnZyMOjHR4VZiFO7N\naj3Xd/r0008ZNGgQDRo0YP369dy4cQOTyURISAhPPvlkpQKuCCmuhRDCOhTXrhHUtSvZO3divGtm\nJlEKkwmfFSvw/fBDchcuRPP4wCJtH2FBXaj3+19p7d2fQD+fP4tZE40bG4mIKD7ym5cHGo0CX18T\nPj7uV1sqLl8mqEcPsr/5BmOzZvYOR4girNZzfacbN27QoEEDDAYDv/32G5MnT0ahULBo0SK7FNfu\nSPq63IPk2T04Up5V776L9q9/lcK6HEwmOHHCi5ScCdx+5EGCN73Cml9N+NVpwLBWw81tHwV5Big+\nUn03lapgBNotmUz4vfkmmldfdbrC2pHey8JxlKm4ViqV3L59m/T0dOrWrYu/vz96vR6D4d5Llwoh\nhHBMnv/5D9579pB58KC9Q3F4JhMkJXmTkuJNyh4Nppab8Hr4C9SdThLd9Cm+3PgbEd9oyF01CKMT\nT6NnD96JiXieP09OfLy9QxHCKspUXHfq1IklS5ZgMpkYNGgQABcuXJBlyW1IPhm7B8mze3CIPBuN\n+E2fTt6sWRAYaO9oHJ4JI//an8atFmvIbZlE1/s7E91y1P9m++hrQvfxxwT26UPukiXo+vVzjDw7\nOEVmJn5vvYX6888p05roDkZyLCwpU3Hdo0cPWrdujUKhoFatWgDUqFGDIUOGVGlwQgghqoZy/fqC\nGTCefdbeoTgMtRr27vWmVSuDeSq5IrN9tC1c5GVW8dk+FAo048ej79CBgFGj0Kamkh8Tg6lePTu8\nEuehmjMHXf/+GB55xN6hCGE1ZZ7qo3bt2ubCGiA4OFhGrm0o1Unm/BSVI3l2D3bPc1YWqvfeIzcu\nDuww45OjMJng1189WLrUh6efDqBVq+qsXOnDxWs5JJxMIGpzFH2+7EOGJoP4gfGkDkslJiKm9Gn0\nHnmErN27UWRk4NehAwFPPonyiy9Q3Lxpw1fmHDwPHsR7xw7y3nnH3qFUmN3fy8IhlWnk2mg0cvz4\ncU6fPk1OTg4BAQGEhoYSFhbm1KtJCSGEO1ItXIiuZ08MDz1k71DsauXKgtUE+/TR8fKoPMbM38NX\nF9Yx4ljlFnkx1apF7kcfkfb000Tm5qLcsgW/2Fj0nTqhHTwY7cCBEBRURa/KSWg0+E+cSO68eZiq\nVbN3NEJYVZmm4vv666/57bffCA8Px9/fH7VazU8//UTz5s0ZMGCALeIsQqbiE0KIivE4e5bAfv3I\n2r8fU9269g7HJjIyFBYXYtFq4WruBdafKrrIy9DQoaWOTleIWo33jh0ot2zBOzUVXWQk2qefRtev\nH/j5WfdaTsB3wQI8jx0jZ+1a95t3UDidKpmK79ixY0yYMAF/f3/zvg4dOrBkyRK7FNdCCCEqRjVz\nJvmvv+7ShXV+fsEKgykp3nz3nTfBwSZ27Mg2P67Wqkk8k8i6X9Zx6uYphrQYQvzAeNrWblt138YG\nBKAbMgTdkCEoMjLw3r4dn3/9C79Jk9A/9hjawYPR9eoFPo63FLq1efz6Kz4rVpC1e7cU1sIllanZ\nLigoiPz8/CL78vPzCXL3r7VsSPq63IPk2T3YK89e332H52+/oXn1Vbtcv6rpdDBsmD/Nm1fn739X\nUauWic8/z+Gbb7IxmoykXk4lJiWGsFVhJJ9NZnT4aE6MPEFcZBzhdcKtXliXlGdT9epohw9HvXkz\nWf/+N7pHH8Vn6VKqtWyJ37hxeO3aBXq9VWNxGEYjfpMnk//mm5gaNrR3NJUmv7OFJSWOXH/33Xfm\nf993330sX76c0NBQc1vI6dOnadGihU2CFEIIUUlaLX5vv03e+++77Oiotze8+KKGpUtzqVGjoA3k\nQuYFFhwu2vZRuMiLIzDVro125Ei0I0eiuHIF5VdfoZo3D4/XXkM7aBC6wYPRP/KIy9x4qly7FkV+\nPppRo+wdihBVpsSe682bN5fpBPaYjk96roUQonx8li7Fe/du1Bs2OO1X8VeuKPjuu4JWj/Hj8+nY\n0fJCZpbaPqJbRldt24eVeZw/j3LrVry3bMHj1i20Tz2FdvBgDBERTps/xR9/ENS1K+otWzCEhdk7\nHCHKrLw912W6odHRSHEthBBlp/jjD4K6dCF7+3aMzZvbO5xy+flnTzZtUpKS4sW1ax707Knnscd0\n9O2rK3KTotFkJO1KGut+Wcf2swWzfUS3jK7QbB+OxuPUKZRbt6LcsgX0+oL+7MGDMbRq5VSFtv+o\nURjvv5+82Fh7hyJEuZS3uK7U90x5eXmVOVyUg/R1uQfJs3uwdZ5V772H9i9/cbrCGuC33zzw8jKx\ncGEup09nsnJlDs8+qzUX1hcyLxB3MI6I+Aim7ZlGq5qtODziMAlRCUQ1jbJrYW2tPBtDQ8mfMYOs\nw4fJiY9HYTDgHx1N0KOP4rtgAR5nzljlOlXJKyUFz6NHyXvzTXuHYlXyO1tYUqbZQkrywQcfMGvW\nLGvFIoQQwso8jx3DOyWFzEOH7B2KRQYDHDniyR9/ePDEE7pijz/1lI6nniq63y6zfTgChQJD27bk\ntW1LXmwsnv/+N8otWwiMisJYt27BiPbTT2MsxwibTajV+L3xBrmLFrnltIPC/VS4uM7JyXHtX2IO\npmvXrvYOQdiA5Nk92CzPJhN+06eT99ZbDrVoyY0bCnbt8iYlxZtdu7y47z4jzz6rLfUYS20fFV3k\nxVaqNM8KBYaOHcnr2JG899/HKy0N5ZYt+PbsibFJk4LFap580iGWX1fFxaHv3Bl9z572DsXq5He2\nsKTE4nrlypUlHmQ0GklPT6d9+/ZVEpQQQojKU27aBFot2uHD7R2KWXY2dOoUROfOevr00TF7di4N\nGpR868+FzAus+8VxZ/twCJ6e6Lt1Q9+tGyxYgNfu3Si3biUoLg5D27YFi9UMGoQpONj2oR07hnLj\nRrL277f5tYWwlxKL6ytXrjBo0CCLj3l6elKrVi0aNGhQZYGJolJTU+UTshuQPLsHm+RZrUY1ezbq\nVascahq3wEA4fToTr1K+N3WVtg+7vJ+9vdE/9hj6xx6D/Hy8v/vOfsuv6/X4TZxI3uzZmGrVqvrr\n2YH8zhaWlPjrzcPDQ2bkEEIIJ+W7aBG6rl0xdOpktxhMJsuTWVgqrJ2x7cPh+fqie+IJdE88UWT5\ndb9p02yy/LrPsmUFC+Y891yVnF8IR1XiVHxZWVkOuwKjTMUnhBAl8zh/nsA+fcjauxdT/fp2ieG3\n3zwYP96fLVuyS63dLLV9DA0dKm0fVahw+XXlli14HjlSJcuve1y8SGCvXmTv3InxwQetck4h7KW8\nU/GVOHLtqIW1EEKI0qlmzUIzdqzdCutTpzwYMiSQt97Ks1hYu0rbh7MqXH5dO3w4ivR0vJOS8Fm6\nFL+YGHQDB6IdPBh99+6Wv2Io0wVM+E2ZgiYmRgpr4ZYcpxFPlErm0nQPkmf3UJV59tq9G8+ffyZ/\n7Ngqu0ZpTp70YPDgQN55J4/hw/83A4jRZCT1cioxKTGErQoj+Wwyo8NHc2LkCeIi4wivE+5yhbUz\nvJ8Ll19XJyeTtW8fhlatUM2bR7VWrVC98QZeaWlgNJbrnN5btuBx9Sr548ZVUdSOwxlyLGyvxI+l\na9euJTIykoYNG5Z48KVLl9i7dy/DHehOdCGEcFs6HX4zZpA3dy74+tr88j//7MkzzwQwd24uzzxT\nMDe1zPbhPEwNGqAZOxbN2LHm5ddV06aVa/l1xe3b+M2ciXrNGvD2tmH0QjiOEnuuz5w5Q0pKCvn5\n+TRu3JhatWrh4+ODRqMhPT2d8+fPo1Kp6NOnD02bNrVp0NJzLYQQxfmsWIH3N9+g3rLFLstif/KJ\nD/fdZ+Sxx28Xa/uIbhktbR9Oqsjy6waDebEaS8uv+73+OiaVirz58+0UrRDWV96e6xKL60JXr17l\n9OnTXL9+nby8PFQqFfXq1aN58+bUt1M/nxTXQghRlOLmTYIefZTsxESMoaE2v76l2T6iW0bLbB+u\nxGTC8/hxlFu24L1lC/j5FUztN3gwxqZN8UpNxf+118hMS3OoRYuEqCyrF9eOyB2La5lL0z1Int1D\nVeTZb8oUTN7e5MXFWfW89yKzfZTMpd/PJpN5+XXlV19hrFsXxe3b5M2bh+7xx+0dnc24dI6FmdVm\nCxFCCOEcPE+cwHv7drIOHrTJ9WS2D2Fp+XWPs2fdqrAWoiQyci2EEM7MZCIgKgrtM8+gffHFKrvM\n3W0fLf27MLhxNCMeeUzaPoQQLk1GroUQwo14b9uGIisL7V//WiXnt9T28bjPXCaOakyzFTn4eOmr\n5LpCCOGsZJ5rJyFzaboHybN7sFqec3NRxcYW9Fl7elrnnBS0fSScTCBqcxR9vuxDhiaD+IHxpA5L\nJTx3AhNHNWbFihx69JDCujTyfnZ9kmNhiU1GrufPn09iYiLBwcEkJSUB8OOPPzJz5kwMBgPNmzdn\n0aJFpe4XQghRlO+SJRgefhh9586VPpel2T5Gh48uMtvHnj1ejBrlz6pVOXTrJoW1EEJYYpOe6//+\n9794e3szY8YMkpKSMBqNDBgwgL/97W9ERERw69YtgoODi+2/ffs2NWrUKHY+6bkWQrg7j0uXCOzR\ng6w9ezCVstjXvZR1to/LlxX06hXEF1/k0LmzFNZCCPfhkD3X7du35/Lly+btEydOEBwcbC6Qg4OD\nLe63VFgLIYQA1TvvoBk9ukKFdUVm+2jY0MSePVncd5/T3QMvhBA2ZZee699//53AwEBGjRrF008/\nTUJCQqn7hfR1uQvJs3uobJ69UlPxPHqU/PHjy3yM0WQk9XIqMSkxhK0KI/lsMqPDR3Ni5AniIuMI\nrxN+z2n0pLAuH3k/uz7JsbDELrOFaDQajh49SnJyMgEBAQwZMoRu3bqVuN/SUPzYsWMJCQkBoFq1\narRp08Y8kXvhD7srbR8/ftyh4pFt2ZZt+7yf9+/ZQ7dJk8ibMwf8/O75/E3fb2LXzV2k5abh7+3P\no76P8lGLj4jqGeUw/z1kW7addfv48eMOFY9sW2e78N8XL14EYNSoUZRHmXquT548SatWrYrtP3Xq\nFKFlXGb38uXLjBkzhqSkJA4cOMDixYtZv349AFOmTGHQoEEolUqL+yMjI4ucS3quhRDuSrlqFcqt\nW1EnJkIJI82W2j6iW0aXa5GXvDxQqawZuRBCOKfy9lyXqS1k06ZNFvcnJiaW+UJ3CgsL4+rVq2Rm\nZo156YMAACAASURBVKLVavn1118JCQkpcb8QQghQ3L6Nav78gqn37iqSrdH2UWjbNm/69QvEaKyK\nVyGEEK7Nq6IHqtVqjGX8zTtnzhxSUlLIyMggMjKS2NhY3nrrLV544QX0ej1RUVE0btwYoMT97i41\nNdX8tYVwXZJn91DRPPvGxaGNisLQurV5n6XZPmK7xBab7aOsNm/2ZuZMPzZuVOMhKyFUiryfXZ/k\nWFhSanG9YMECAHQ6nfnfhXJzc3nooYfKdJHY2FhiY2OL7e/fv7/FfZb2CyGEO/M4eRLl1q1kHTxY\nodk+ymLDBiWzZ6vYvDmbVq1k2FoIISqi1J7rc+fOAfDPf/6TESNGYDIVPFWhUBAYGEitWrVsE+Vd\npOdaCOFWTCb8nn6KH/q3ZE2TbPMiL9Eto4ss8lIZ69Ypee+9gsI6NFQKayGEKGTVea4ffPBBoKCY\nlvYMIYSwvQuZF9jw1RzWdTyIKuAGw2pWru2jJDodbNuWTbNmUlgLIURllKmj7p133qnqOMQ93Dk9\njHBdkmf3cK88q7VqEk4mELU5ij5f9iZ7/3esiYgjdXgqMRExVi+sAUaM0EphbWXyfnZ9kmNhSZlv\naDQajajVavR6fZH9hasrCiGEqDijyUjalTTW/bLO3PYxOnw0g746iV/ez+T0f8neIQohhCiDMs1z\nffjwYXbs2IFWqy322Ny5c6sksNJIz7UQwlVYmu1jaOhQ6vjVQXHlCkGRkWR//z3GBx6wd6hCCOGW\nrNpzXSglJYUhQ4bQvHlzvLwqPHufEEIILC/yYmm2D9WcOWheesnqhfXnn/vw6KM6mRFECCGqQJl6\nrv38/GjWrJkU1nYkfV3uQfLsuu5c5KXlypb3XOTF8+BBvA8cIH/iRKvGsWSJD5984kNQ0D2/tBSV\nJO9n1yc5FpaUWC2fPXvW/O+2bduybt06IiIiUN21Hm6TJk2qLjohhHBylto++rfqT1TPqJIPMhjw\nmzGD3Nmzwd/farEsXOjLunVKkpKyqV9fimshhKgKJfZcf/DBB2U6wRtvvGHVgMpCeq6FEI7MUttH\ndMvoMi/yolyzBp9168j++utiy5xX1IIFvmzerOSrr7KpV08KayGEKCur9Vzbo2gWQghnVdJsH+Vd\n5EWRmYlq3jzUX35ptcL62DFPtm1TkpiYTd26UlgLIURVKlPPtbA/6etyD5Jn53Mh8wJxB+OIiI9g\n2p5ptKrZisMjDpMQlUBU0yiLhXVpefZdsABdv34YwsOtFmO7dgZ++CFLCmsbk/ez65McC0vKdIfi\nggULUCgU5uXPAfNXm4GBgTRp0oTIyEiUSmXVRCmEEA6krLN9lJfH6dMoN2wgKy3NitEW8Kn8CulC\nCCHKoEzzXH/99ddcuXKFDh064O/vj1qt5siRIzRs2JCGDRty5MgR/P39eeaZZ2wRs/RcCyFszlLb\nR3TL6HK3fZTIZCJg6FB0vXqhGTu28ucTQghhFVUyz/Xx48eZNGlSkZHpVq1asWjRIvr370/z5s3L\nfAOkEEI4E0uzfcR2ibX6EuTeO3bgcekSmldeqdR5TCa4fNmD+++XOayFEMIeytRz7eHhwdWrV4vs\n+/333/HwKDhcr9cXaRkR1id9Xe5B8uwY1Fo1CScTiNocRZ8v+5ChySB+YDypw1KJiYipdGFdLM8a\nDaq33yZ33jzw9q7weY1GmDpVxeTJfpWKT1iHvJ9dn+RYWFKmket+/foRHx9Pw4YNCQgIIDs7m6tX\nr/L0008DcP78edq1a1elgQohRFWy1mwfFeGzbBmGFi3Q9+5d4XMYjTBlih8nT3qycWO2FaMTQghR\nHmXquQbIysrit99+Q61WExAQQLNmzQgKCqrq+CySnmshhLVYavsYGjrU6m0fJVFcu0ZQ165k79yJ\n8cEHK3QOoxEmTPDj7FkPvvxSTWCglYMU4v/bu/OwqOr2DeD3bMzAzKCCmHtmmEsoQZaZ+MMKlyRM\nJVO0Vw2XVDRteV3SMivfUCtFzSULpZJs0UosF8xcRlPztUX0tcUdl1QQmRmY/fz+IEllVJaZObPc\nn+vqygNnDg8+jj7z5Z7vIQpgbslcA0BoaCjuvffeahVFRORN3LXbR3UEv/YaLP/6V7UHa6BssD52\nTIrPPjNAo3FhcUREVGU12ud67ty5rqqDboG5rsDAPruPQ3BAl69DWm4aojKjsO7IOoyMHom81Dyk\nx6cjul60xwbrK32W7dsHxbZtKH3++Rpdr1cvCz79lIO1t+Hz2f+xx+RMpVeundHrmesjIu/mqd0+\nqszhQMjkySh9+WXUNMfRtavNRUUREVFN3XC4XrFiBYYOHQoAWLZsmdNzbDb+he4pcXFxYpdAHsA+\nu4Y3xT6ciYuLQ9AnnwASCSxPPil2OeQmfD77P/aYnLnhcH317h+nT59Gr169Kpxz+vRp91RFRFRF\nYu72UWV6PYLfeAOGDz8EpDVK5xERkZe54d/qVw/XUqkUsbGxFf6T8h8Fj2GuKzCwz1V34vIJpO9O\nR2xWLCZtm4Q24W2wd/BeZCdlIykyyfsGawAFzz0Ha5cusFfxTeIWCzB6dAgOH+bfvb6Az2f/xx6T\nM5XKXE+cONHpxzt37uzSYoiIKsPbYx83Iz1yBE1zc1Gyd2+VHmc2A0OHqqFQAM2b8+6LRETeqtL7\nXHsT7nNNFHicxT5SWqd4Z+zjRoqLoRkwANYePWB+9tlKP8xkAv71Lw3UagHLlhlrchNHIiKqIrfs\nc22327F7924cPHgQJSUlmDBhAv78808YjUZER0dXu1giolvx2t0+qkiSnw9t//6wduwI85gxlX5c\naSkwaJAGYWECliwxQl6jPZ6IiMjdKhXc27BhA37//XfExcWVb79Xu3ZtbN++3a3F0T+Y6woM7HMZ\ng8WA7EPZSFqdhIRPE1BkLkJWzyzoBuqQFpvmc4O17KefENq9O8yDBqF0zhzodu+u9GP37JGjfn0H\nB2sfxOez/2OPyZlK/VV94MABPPfcc1AqlVizZg0AIDw8HEVFRW4tjogCh0/t9lEFim++QciECSiZ\nNw/WxMQqP75LFxu6dOG2p0REvqJSw7VcLofFYoFS+c8/cAaDASEhIW4rjK7FvTQDQyD22V9iHxUI\nApSLF0P17rswfPYZ7DEx5Z8KxD4HIvbZ/7HH5EylhuvY2Fh89NFHeOihhyAIAk6dOoXNmzfzTYVE\nVC2+vNtHpdhsCJ4yBYpdu6DfsAGOKrwRhoiIfFulMtddunRB27ZtsXHjRjgcDqxevRqRkZGIj493\nd330N+a6AoM/99khOKDL1yEtNw1RmVFYd2QdRkaPRF5qHtLj0xFdL9o/Bmu9HppBgyA7ehTF69c7\nHaxv1OfLlyXYv1/m7grJQ/z5+Uxl2GNyplIr1waDAZ07d+a+1kRUZX4b+3BCcvo0NCkpsN97L0pm\nz0ZV9swrKpIgOVmDzp1tiI0tdWOVRETkTpUarufPn4+goCA0bdoUTZo0QZMmTdCwYUPIK/nW9Vmz\nZmHt2rUICwtDTk4OAOCXX37BtGnTYLfbcdddd2HevHnl5xsMBvTo0QOpqalITU2txrflZ4xGdBEE\n8C1N/s9f8nt+H/twQvbrr9AMHAjTM8/APHYscJPv8/o+FxZK0LevBp062TB9Ogdrf+Evz2e6MfaY\nnKnUdDx16lQUFBTg9OnTOHPmDDZt2oTz58+jTp06GD169C0f361bNyQmJmLKlCkAAIfDgYkTJ+LN\nN99EbGwsLl26dM35S5YsQVRUlN/+I1xVqiVLoHrzTRhycmDr2FHscoic8tfdPipDsXEjQsaORcnb\nb8Paq1eVHltQIEGfPho89JANr75aerOZnIiIfEClMtcSiQR169ZF/fr1ERoaiuDgYDRu3BitW7eu\n1BeJiYlB7dq1y4/z8vIQFhZW/obIOnXqlH/u6NGjKCwsRFRUFATB524e6XolJVC+9x4ODR0K9YgR\nkBQUiF0RuZEv5vdOXD6B9N3piM2KxaRtk9AmvA32Dt6L7KRsJEUm+f1grXzvPYQ89xwMn3xS6cH6\nSp/tduCJJzTo2tXKwdoP+eLzmaqGPSZnqnRLgszMTISGhiIhIQGRkZGQyar3xpuzZ89Cq9Vi+PDh\nKCgoQL9+/TBw4EAAwDvvvIOpU6di9erV1bq2v1GuXAnb/ffjaO/euFOjgXr0aBhWrQKklXpdROQW\ngRj7qMBuR/DUqVBs3Qr9+vVw3H57lS8hkwGLFhnRqpWDgzURkZ+o0nA9ceJEnDp1CkeOHMH69etR\nt25dPPXUU1X+omazGfv378e6deug0WiQnJyMzp07448//kCzZs3QoEEDrloDgNUK5cKFML7/PuLu\nuw+lHTpAm5QE5cKFMD/7rNjVkRt4c34vkGMfFRgMUI8cCUlJCfQbN0KoVatKD7+6z61bO1xdHXkJ\nb34+k2uwx+RMpYbrCxculOetT58+XZ63vjrqURURERGIjIxE/fr1AQBRUVE4evQofv31V2zatAnf\nffcdLl26BKlUinr16uGxxx6rcI0xY8agadOmAIBatWqhbdu25X/Ir/yYxtePHz5zBo7bb8c2sxnQ\n6RAXFwfD++8juHNnHAwOxt0jRnhVvTz2z+MvvvsCWwq2YFfJLqgVanRUdcSClguQ9FCSV9Tn6eMf\nv/4aHV5/HULHjjCuWAHd3r1eVR+PecxjHvO4ZsdXfn3y5EkAwPDhw1EVkt9+++2WS8SzZ88u3yXk\nyk4hiipsMQUA+fn5GD16NHJycqDX65GYmIicnBwEBwcjOTkZ8+fPxx133FF+/sKFC6FWq/H0009X\nuNapU6f8/wY2DgdC4+JQ8vrrsD3yCHQ6XXnzFRs2IHjiROi3boUQFiZyoeRKV/dZTM5iHymtUwIr\n9uGELC8PmpQUmFNTYZow4aY7glzPaAR++UWOBx+0eU2fyb3YZ//HHgeG/fv3o0kVbgYmr8xJEydO\nrHZBADBjxgzk5uaiqKgI8fHxmD59Ol566SUMGTIENpsNSUlJ1wzWBChycyEoFLA9/HCFz1l79IBc\np0PI2LEwrlxZpX/giW6EsY+bk+fmQj1mDEpmzYK1b99KP85gADIzlVi0SIWEBCsefNDmxiqJiEhs\nlVq59jaBsHKtffRRmEaMuPE/4hYLtD17wtKnD8xpaZ4tjvyKs5u89GvVzy9v8lJdQZmZCJ4zB4YV\nK2Dv0KFSj9HrgfffV2HxYiU6d7bhxRdLma8mIvJBblm5Js+S7d4NyfnzsD7++I1PCgqCMTMT2oQE\n2Dp0gL19e88VSD6Pu31Ukt2O4OnTocjNhf7bb+Gowk/YJk8OgcUiwdq1erRqxaGaiChQcD83LxQ8\ndy5M48aV7dP1t6tD9lc4mjZFydy5UA8fDklRkSdLJDdx1mdXcQgO6PJ1SMtNQ1RmFNYdWYeR0SOR\nl5qH9Ph0RNeL5mB9NaMR6qFDIfvlF+g3bKjSYA0A8+eXYNkyo9PB2p19Ju/BPvs/9pic4cq1l5Ed\nPAjZgQOwZGVV6nxrYiLkO3YgZNw4GD/8kPlrqsBZ7GN6p+mMfdyE5K+/oBk4EPaWLWH84AMgKOiG\n55pMgEpV8ePVvA0AERH5OGauvUzIyJGwR0VVbR9rsxnaRx+FpX9/mJ95xn3Fkc/gbh/VJz10CJqU\nFFieegqmF1+84QvWwkIJFi9W4qOPlNi1qxhhYT73VykREVUCM9c+THr8OBRbtqDkrbeq9kClsix/\n3a0bbPffD3tMjHsKJK/G3T5qTr5lC9SjRqF05kxY+vVzek5BgQTvvqtEVpYSSUlWbNyo52BNRETl\nmLn2Isp334V5yBAgNLTC526V63I0a4aSOXOgHjYMKC52V4nkZtXJ7524fALpu9MRmxWLSdsmoU14\nG+wdvBfZSdlIikziYF1JQVlZUI8ZA2NW1g0H62++UeC++0JRVCTF1q16zJtXgttvr/qbFZnTDAzs\ns/9jj8kZrlx7Ccn58whavRrFu3dX+xrWxx+HXKeD+tlnYVy+nPlrP8bdPlzI4UDwa69BsW4d9N98\nA8edd97w1Pbtbdi+vRiNG3OlmoiInGPm2kuo3ngDkqIilFY1EnI9kwna7t1hGTwY5mHDXFMceQVn\nsY+U1imMfdREaSnUo0ZBcuECjB9/zDueEhFRBcxc+6LiYihXrIB+8+aaX0ulKstf9+gB2333wd6u\nXc2vSaLibh/uITl/HppBg2Bv3hzGL78ElGUvUM6elSAjQ4X+/S2IibGLXCUREfkaZq69gHLFClgf\nfhiOZs1ueE5Vcl2OO+9ESXo61KmpzF/7mCt9NlgMyD6UjaTVSUj4NAFF5iJk9cyCbqAOabFpHKxr\nSHr4MLTdu8P6yCMoWbIEUCpx+rQEEycGo1OnUMjlQKNG7rvxC3OagYF99n/sMTnDlWuxmUxQLVkC\nw+efu/Sy1uRkKHQ6qJ9/HsZly5i/9gEOwYED+gP4JJe7fbiTfNs2qEeMQOlrr8EyYAAuXpQgPV2F\nNWuC8NRTFuzeXYx69XwuLUdERF6Cw7XIglatgr1tW9jvvvum58XFxVX52iX/+Q+0Xbsi6MMPYRky\npLolkpsx9uE5QR9/jODXX4cxMxO2v59TMhlQu7aAvXuLUbeuZ4bq6jyfyfewz/6PPSZnOFyLyW6H\nasEClCxc6J7rBweX5a8TE2Fv3/6WAzx5Dnf78DCHA6qZMxH05ZfQ5+TAcddd5Z+qU0fAtGkmEYsj\nIiJ/wsy1iBRr10KIiIDtgQdueW51c12Ou+5C6RtvlOWvDYZqXYNcwyE4oMvXIS03DVGZUVh3ZB1G\nRo9EXmoe0uPTEV0vGjt37hS7TP9jMkE9YgTs3+3EnnnfXTNYi4U5zcDAPvs/9pic4cq1WAQBqowM\nmCZPdnse2tK/P+Q7diDk3/9GyaJFzF97GGMf4pFcvAjZE//CvqKm6Gf4Hi/lC2gNi9hlERGRH+M+\n1yKRb9mCkGnTUKzTAVIP/ADBaERoQgJMY8fCMmiQ+79egHMW+0hpncLYhwedzD2C21L7I9vRH4UT\npmLEMxZnNz8lIiK6Ke5z7SNUGRkwjR/vmcEaANRqGDIzoe3VC7bYWDhat/bM1w0gzm7ywt0+xCHd\nrkPjQcOxvccMJC/sj9BQrlYTEZFnMHMtAtm+fZAePw5L376Vfowrcl2O1q1R+uqr0KSmAkZjja9H\nZU5cPoH03emIzYrFpG2T0Ca8DfYO3ovspGwkRSZVabBmfq/mglatgnbEMCg+W4ouH/b3ytVq9jkw\nsM/+jz0mZ7hyLQJVRgbMY8cCCoXHv7Zl4EDIdTqETJrkvl1KAgB3+/AeBgOg0aDsfQzp6Qj67DPo\nv/4ajlatxC6NiIgCEDPXHib97Tdoe/XC5Z9+AkJCxCnCYEDoI4/A9PzzsPTvL04NPshZ7COldQpj\nHyL59VcZ5sxRobBQgm/WFCBk3DjIjh2DYeVKCPX4ZlEiInINZq69nGr+fJhHjBBvsAYAjQaG5cuh\nffxx2GJivGJrMm/G3T68y88/yzB7tgo//yzHuHEmPJ10Bpo+/4IQEQH92rVAcLDYJRIRUQBj5tqD\nJPn5UKxfD/Pw4VV+rKtzXY42bVA6bVrZ/telpS69tj8wWAzIPpSNpNVJSPg0AUXmImT1zIJuoA5p\nsWluG6yZ37u5l14KxqBBGnTpYsN//3sZad0OoV7v7rDffz+My5f7zGDNPgcG9tn/scfkDFeuPUi1\naBEsgwZBqF1b7FIAAJbBg6HQ6RAyZQpK5s0TuxzRcbcP7zdsmBmvvFIKlQqQ//AD1EOHonTKFFiG\nDhW7NCIiIgDMXHuMpLAQoe3bo1ing9Cwodjl/EOvR+jDD6N08mRYk5PFrkYUzmIf/Vr1Y+zDiwV9\n/jmCp06FcckS2B5+WOxyiIjIjzFz7aWUy5bB+thj3jVYA4BWC2NmJjR9+0IfHQ1HZKTYFXkEd/vw\nXrt2ybF0qRKLFhmhVl/3SUGAas4cBK1cCf1XX8HRpo0oNRIREd0IM9eeYDRC+cEHMI0bV+1LuDPX\nZW/bFqVTppTlr00mt30dsTkEB3T5OqTlpiEqMwrrjqzDyOiRyEvNQ3p8OqLrRYs+WAdyfk+nk6NX\nLw3Gjg1B165WBAVdd4LFgpC0NCg2boR+40afHqwDuc+BhH32f+wxOcOVaw9QfvghbA8+CEeLFmKX\nckOWp5+GYscOBE+bhtK33hK7HJfibh/ebf9+GV55JRjnzknxwgsmPPGEpcIW8JJLl6AeMgRCrVpl\nO4JUWNImIiLyDsxcu5vFglqxsTB89BHsMTFiV3NzxcUI7dIFpS+/DGufPmJXUyPOYh8prVMY+/BC\ne/bIcPy4DMnJFsidvNyXHjsGzYABsHbrhtJXXwVkMo/XSEREgYuZay8T9MUXsLdo4f2DNQCEhsL4\nwQfQPPkk9PfcA8cdd4hdUZVwtw/vVFQkwa5dcpw4IcXo0eYKn+/QwY4OHexOHyvbsweaoUNR+u9/\nw5Ka6u5SiYiIaoyZa3dyOKDKyIBpwoQaX8pTuS57TAxML75Ylr82VxyEvNGJyyeQvjsdsVmxmLRt\nEtqEt8HewXuRnZSNpMgknxqs/SG/Z7cDGzYoMHVqMLp00aJdu1r44AMlbLaqXUexZg00Tz0F4/z5\nfjdY+0Of6dbYZ//HHpMzXLl2I8X69RA0Gtj+7//ELqVKzCNHQr5zJ4KnT0dperrY5TjF3T68l0QC\nZGcH4Z577Jg1qwQxMfaKb068GUGAau5cKJcvh+HLL2GPinJbrURERK7GzLW7CAK0XbvC9OyzsPbq\nJXY1VSYpKoK2SxeUvv46rElJYpcDwHnsI6V1CmMfHqbXA7t3y6HTKZCaasbttztcd3GLBSHPPw9Z\nXh4M2dnet3UlEREFHGauvYR8505IiothTUwUu5RqEWrXhvH996EZOBD6du3guP120Wrhbh/i27tX\nhvXrg7Bjhxy//SZDbKwNnTrZEBTkutfmksuXy3YECQ6Gft06QKNx2bWJiIg8xSOZ61mzZqFTp05I\numoF9JdffkFSUhJ69uyJCX9nkv/66y+kpKTgscceQ9++fbFr1y5PlOcWqnnzyva1dtHOBmLkuuzt\n28M0fjzUw4YBFotHv7bBYkD2oWwkrU5CwqcJKDIXIatnFnQDdUiLTfPbwdpb83uHDsmgVAqYMaMU\nf/xRhK+/NmDiRBMaNHDNcC09cQLa7t1hb9UKxo8/9vvB2lv7TK7FPvs/9pic8cjKdbdu3ZCYmIgp\nU6YAABwOByZOnIg333wTsbGxuHTpUlkxcjleffVVtGzZEmfOnMGAAQOwfft2T5ToUrJff4Xsf/+D\nZeVKl1zvt9+cvwbS64GPPlJCrRag0QjQagWo1UCdOg60aeOaH9Wbx4wpy1/PmIHSmTNdcs0b4W4f\n4igpAfbulUOnk6NxYweGDq34QsrZx1xF9uOP0AweDNOECTA/84zbvg4REZEneGS4jomJQX5+fvlx\nXl4ewsLCynPTderUAQCEh4cjPDwcANCwYUNYrVZYrVYorr+jhJdTzZsH05gxgLJmA6EgAAsWKLFk\niQpbt3YGcO0qoc0mQX6+FAaDBEajBAaDBAYDoNUKWLXKWOF6+fkS9O2rhUYjlA/kGg3QpIkdr7xS\n8c6MJSXAvn0K1B65GA+M6Yzi1nFAr0ehVrt2q2HGPv4RFxfnka+Tny9BVpYSOp0CeXkyREXZERdn\nRbt2zrfEcxfFmjUImTQJJQsXwtq9u0e/tpg81WcSF/vs/9hjckaUzPXZs2eh1WoxfPhwFBQUoF+/\nfhg4cOA15+zYsQN33323zw3W0iNHIN+xA8aMjBpdp7QUGD8+BH/8IcOmTcWoV6/ij9/r1BHwn/+U\nVvqat90mYOVKw99D+JWB/MaDcmGhBG+9pYLB0BgtZNl4d8IT+L/JnWBv1Bh79hRXOP/0aQmmTQv5\ne2j/57+GDQX063ftyqfBYsBXv6/FyoOf4M/L3O3D06xWCQQBmDixFPffb/P8DQ/NZgS/8goUmzbB\nsHo17O3aebgAIiIi9xBluDabzdi/fz/WrVsHjUaD5ORkdO7cufydmBcuXMDs2bOxaNEiMcqrEdXC\nhTA//TSg1Vb7Gvn5EgwerEFkpB3ffKNHSEhZrqumr5AVCqBFi8rHRRo3FrB2reHvoygo54/BgW/6\noThnHYCKL3q0WgGPPWa5ahVdgsJCKazWshcG18c+2tV6EL9+MAHmvMeQJVHii79X09u1s+PDDyuu\nvBcXA3v2yFG3roCICAfq1hWgUlXnd8J7uaLPJhOwb19ZzCMvT4aPPjLi+tcrd9zhwLRpFX9a4QnS\nEyegTk2Fo0ED6L//HkLt2qLUISZX9Jm8H/vs/9hjckaU4ToiIgKRkZGoX78+ACAqKgpHjx5FkyZN\nYDabMX78eEyaNOmm256MGTMGTZs2BQDUqlULbdu2Lf8DfuUNBp4+7hwZCcXXXyN3wQJYrnrCVfV6\ngwbZcO+9v+PttxtAIin7/IEDB0T//uLGjoVCp0PhmNH439ChTs9PTrZWePwX332BMZ9twa6SXVAr\n1Oio6ogFLRcg6aEkIAXYsSMXFosU7dp1gtEowd69/4VOZ6xw/QYN/g9Ll6pw/HgJiouVKC5WISgI\niIo6h5de2lfh/Lvv7oyff5bh1Kn9qFXLjJ4974NCIeLvn5uP9+5NwNatcuzbJ0HTpnr06KHA0KFm\n7Nihg1Qqfn1xcXFQfPstFGlp+O2JJ9Bw9mxAIvGa3z9PHnvF85nHPOZxjY8PHDjgVfXw2DXHV359\n8uRJAMDw4cNRFR7b5zo/Px+jR49GTk4O9Ho9EhMTkZOTg+DgYCQnJ2P+/Plo1qwZXnjhBbRv375C\nTORq3rrPdfCrrwImU41vvGI21ziu7TaSggKExsfDOHcubF273vA8Zzd5SWmd4tLYhyCUvanTaJQ4\n3bXi4EEZpk4NxsWLEly8KEVhoQQajYBu3axYsqSkwvkFBRIcOiRD3boOREQIqFNHcGm23N2WhCxc\nSwAAHhxJREFULlWieXM7OnSwITRU7GquY7Ui+LXXoPj6axjffx/2++8XuyIiIqJKqeo+1x4ZrmfM\nmIHc3FwUFRUhPDwc06dPh8ViwZIlS2Cz2ZCUlIRnnnkG+/btw9ChQxEZGVn+2GXLliEiIuKa63nj\ncC25fBmhsbHQb90KRxUa4IvkP/wA9dNPo/i77yA0alT+cW+/yYvDARQVSWAyAQ0bVvxj/9//yjB9\nejAuXpTi4kUJioslqF1bQFKSFW+/XXEYP39egiNH/hnGa9USKsQvXMFiAfbvl2HnTgV0OjnGjzeh\nSxeb67+Qm0jy86EZNqxs7/TFiyGEhYldEhERUaV55XDtat44XKvmzoX0999RsnixW66v03lXrkv1\nzjuQb94Mw9q1OGE8XWG3j36t+vn8bh82W9mbOm0258P4zp1yvP56MAoKJLhwQYLSUgnCwwUkJ1vw\n+usV32h67pwEJ09KEREhoG5dBzQaVBjGr+7z+vUKLFumxL59cjRvbkenTjZ07mzDgw9avW9l+gbk\nublQjxsH06hRMD/7LCD1yNb6Xs/bns/kHuyz/2OPAwPv0CiG0lIoly6Ffs2aKj3s119lWLtWIdob\ny2ri4pjh2PTnF8iaH4tDmlK/3O1DLofTXVqu6NTJhg0b9OXHZjNw8eKNv/e8PBnS08uG8YsXpbDb\ngfBwAYMGmTF5csU/A2FhDgwfbkZmphG1a/vYa2CbDao334Ry1SoYMzNhe/BBsSsiIiLyCK5cu4Dy\ngw8g/+47GLOzK/2Y1asVmDw5BG+9VYLHH7e6sTrXqRD7iLgXw5b/hC4TFkOWEDh7FLtKSQlQUCCF\nVCqgUSOfexrekOTsWahHjAAUChjfew/CdbEuIiIiX8KVa0+z2aBcsADG996r1Ol2O/DGG8H46isF\nvvzSgKgoz960ozpudpMX+W06qEeMQPGWLRAaNBC7VJ8SEgKEhLjmTpreQr5tG9SjR8M8dChML7zg\n2rsNERER+QAGIGtI8dVXcDRuXKndD4qLgZQUDfbvl2HzZn2VBuurt4fxBIPFgOxD2UhanYSETxNQ\nZC5CVs8s6AbqkBabVp6ntsXFwTx0KNTPPFP2yoFqxNN9dhm7HapZs6AePRrGxYthmjiRg/VN+Gyf\nqUrYZ//HHpMzXLmuCUGAat48lE6fXqnTpVKgY0cbxo41wRtvPOlst4+R0SNvuduH6cUXofnhB6hm\nz4ZpyhQPVkzeQHL+fNmLK5ut7CcYf+9fT0REFIiYua4BeW4ugl97Dfrt2ytu++BDnMU+qrrbh+Sv\nvxD60EMwLl4MW3y8G6slbyLftQvqESNgTkmBafLksneBEhER+RFmrj1INW8eTBMm+ORg7ewmLzXZ\n7UO47TYYFy2CesyYstXL225zQ9XkNRwOqDIyoFy6FMYFC256QyEiIqJAwsx1Ncl274b0zBlYH3/c\n6eeNxrLdIFzFFbkuh+CALl+HtNw0RGVGYd2RdRgZPRJ5qXlIj09HdL3oGm2jZ+vSBeaBA6EeNYr5\n62ryhfyepLAQmgEDoNi4EcWbN3OwrgZf6DPVHPvs/9hjcobDdTWp5s+Hadw4pz8GP3lSikcf1eKz\nz4JEqKyiE5dPIH13OmKzYjFp2yS0CW+DvYP3IjspG0mRSS69e6Jp0iTAaoXqnXdcdk3yHrI9exAa\nHw97q1bQ5+RAaNxY7JKIiIi8CjPX1SA9dAjavn1x+aefgODgaz6n08kxYoQazz5rwqhRZtESI85i\nHymtUzxykxfJmTMIfeQRGN9/H7ZOndz6tchDBAHKRYugyshASUYGrI8+KnZFREREHsHMtQeo5s+H\n+ZlnrhmsBQH44AMl5sxRYelSI7p0sXm8ruru9uFqQsOGMC5YAPXIkSjeupU3EfFxkqIihIwdC+m5\nc9Bv3gxH06Zil0REROS1GAupIunJk1Dk5sI0bNg1H1+5MgjLlyuxYYPeLYP1zXJdnox9VJYtIQHm\n/v3L8tcO/7pRijt5W35P9tNP0D70EByNG0P/zTccrF3E2/pM7sE++z/2mJzhynUVKd99F5bBg4HQ\n0Gs+npxsweOPW6DVeqYOV+/24Q6ml16CNikJqowMmJ57TuxyqCoEAcr334dq9myUvPXWDd+4S0RE\nRNdi5roKJBcuILRDBxTv2iXKjTKcxT5SWqd4PPZRFZL8fIQmJMCwYgXsDzwgdjlUGcXFUI8fD+nR\nozAuXw5H8+ZiV0RERCQaZq7dSPnee7D27u3xwdrZTV6md5pepZu8iEVo3BjG+fOhGTGiLH8dHi52\nSXQTsgMHoH76adj+7/+g37gRUKnELomIiMinMHNdWXo9lMuXwzBqLDIylNDr3fvlDBYDsg9lI2l1\nEhI+TcChY4eQ1TMLuoE6pMWm+cRgfYWtWzdY+vSBeswY5q9vQbT8niAgKCsLmr59UTp5MkreeYeD\ntRsxpxkY2Gf/xx6TMxyuK0mZlYWSjvFIntQO27YpYLe7Ptd8s5u8jGwyssY3eRFT6csvQ3LpEpQL\nF4pdCl3PYEDIqFFQLV0K/TffwPrEE2JXRERE5LOYua4MsxkhbWORHLQWt/eOwquvljq7d0y1OYt9\n9GvVz6dWpytDeuoUtAkJMHz0Eez33y92OQRA+r//QTN0KGz33YeS2bOBkBCxSyIiIvIqzFy7wW/T\nvoDxcls8Nr81+vcvdck1fWG3D1dzNGmCkrlzoR4xAvqtWyHUqSN2SQEt6JNPEPzyyyidMQOWQYPE\nLoeIiMgvMBZyK3Y77lyTgdrp49G/v6VGl7pZ7CM9Pv2msQ9/yXVZe/aEtWdPhIwdW3bnHbqGR/pc\nUoKQceOgmjcP+rVrOViLwF+ez3Rz7LP/Y4/JGa5c34Ji3Tpo76wN+dDqbyPny7t9uEPpjBnQPvoo\nlEuWwDx6tNjlBBTpH3+UxUDuvhvF330HaDRil0RERORXmLm+GUGA9pFHYHrxRVh79qzSQ53FPlJa\np/h17KMqpMePQ9utGwyrVsEuwp7lgUixejVCJk9G6dSpsAwZAvDPIRER0S0xc11DZjOg/Pt+LPJt\n2yApKYG1R49KPdbZTV5GRo/06pu8iMXRrBlK3noL6mHDyvLXtWqJXZL/MpkQMnUq5Fu3wrB6Nezt\n2oldERERkd9i5vpvggAsXqxE376a8iiwKiMDpvHjAenNf5tOXD6B9N3piM2KxaRtk9AmvA32Dt6L\n7KRsJEUmuWSw9sdcl7VXL1i7dkXIuHHMX//N1X2WHjsGbY8ekBQUoPj77zlYewl/fD5TReyz/2OP\nyRmuXAMwmYAXXgjBgQMyfPyxERIJINu/H7I//4QlOdnpYwJxtw93KH3tNWh79IDy/fdhHjFC7HL8\nimLtWoS88AJM//532e8t/1wSERG5XcBnrs+ckWDwYA2aNnVgwQIj1Oqyj6uHDIGtY0eYR40qP9dZ\n7COldQpjHzUkPXoU2u7dYfjiC9ijo8Uux/dZLAiePh2K9eth/OAD2O+9V+yKiIiIfBYz11VQUCBB\n166hGD7cjAkTTOULe9Lff4f8hx9gXLQIAHf7cDdH8+YomTUL6tRUFH//PRAaKnZJPkt68iTUqalw\n1KtXlmWvXVvskoiIiAJKQGeuw8MFfPGFHs89Z7rmJ+aqBQtQMOxfyD7xNZJWJyHh0wQUmYuQ1TML\nuoE6pMWmeXyw9vdcl7VvX9ji46GeMCGg89c16bNiwwZou3aFpXdvGFeu5GDtxfz9+Uxl2Gf/xx6T\nMwG9cg0ArVs7yn/tEBz44Ze1+Nz6Gb4KVeHBI52424cHlcycCW23bghasQKWp58WuxzfYbUi+I03\nELRmDQwffgh7hw5iV0RERBSwAj5zDVwb+9AWGvCv0lbo/VwmYx8ikP7xB7Q9e8KwZg3sbduKXY7X\nk5w+Dc2wYRC0WhiXLIEQHi52SURERH6lqpnrgImF5OXJcPCgrPzYYDEg+1D2NbGPD+MW4JeFdjwz\ndCkHa5E4WrRA6X/+A3VqKqDXi12OV5Nv3ozQRx6BtXt3GD79lIM1ERGRFwiI4fqrrxTo00eDo8cA\nXb4OablpiMqMwroj6zAyeiTyUvOQHp+O+7/cDVvPRAiNGoldcgWBlOuy9OsHW8eOCE1IgHrECKhm\nzkRQdjZku3dDcu6cX2eyK9Vnmw2qmTOhHj8exvffh+m55265Fzt5l0B6Pgcy9tn/scfkjF9nrh0O\n4M03VVj5zWk89tYHePliNtTbbrDbh9EI5bJl0OfkiFcwlSt55x3I/vtfyI4fh/TYMci3b4dyxQpI\njx+HpKQEjttvh/2OO+C4446y/zdrBscdd8DRpAkg998/1pJz56AeORKQyVD8/fcQ6vEnLERERN7E\nI5nrWbNmYe3atQgLC0PO38PrL7/8gmnTpsFut+Ouu+7CvHnzAADffvstMjIyAACTJ0/GQw89VOF6\nlclcny0woP9rG3GyzkeQNTiIfq2SkdI65YY3eVG+9x7kOh2MH35Y02+X3K24GLITJyA9dgzSY8cg\nO3YM0r+HcOlff8HRqBEczZpdM3Rf+TVCQsSuvtrk27dDPWoUzIMHw/TvfwMy2a0fRERERDXilftc\nd+vWDYmJiZgyZQoAwOFwYOLEiXjzzTcRGxuLwsJCAIDFYsHbb7+Nzz//HGazGYMHD3Y6XN/I1Td5\n+fq3bxHeIA5zew9Dz8hb7PZhtUK5cCGMmZk1+j7JQ0JDYW/b1vkbHs1mSE+ehPT48bKh+9gxyHfu\nhOzoUUhPnYJQuzbsV1a5mzWDvXnz8gFcqFPHO+9iaLdD9c47UGZmwrhoEWxVeE4QERGRZ3lkuI6J\niUF+fn75cV5eHsLCwspXn8PCwgAAv/76K1q0aFF+XL9+fRw+fBitWrW66fWd3uQltfI3eQlavbps\ndbN9++p8ex6h0+kQFxcndhneT6mEo0ULOFq0gO36zzkckJw5Ux41kR47hqB168pXvQGUDd3XRU3s\nzZpBaNjQI7nm6/ssuXAB6meeASwWFG/ZAqFBA7fXQO7H53NgYJ/9H3tMzogSTj179iy0Wi2GDx+O\ngoIC9OvXDwMHDsSFCxcQERGBVatWoVatWoiIiMD58+edDtcGiwFr/1yLT/73CQ4XHEZyy2Rk9cy6\nYezjhhwOqDIyUDJzpgu/Q/JKUimExo1ha9wYuP4vQ0GA5NIlSI8eLV/1lu/eDVl2dlnO+/JlOJo2\n/Wfobt78nxXwpk2BoCCXlyv/4QeoR4yAuX9/mKZM8essORERkb8Q5V9rs9mM/fv3Y926ddBoNEhO\nTkbnzp3Lh+IBAwYAAHJzc284KEdlRuHBRg9iZPRIdG3WDapq3uRFsXEjBJXK63/UzlfGbiaRQAgL\ngz0sDPb27WG9/vNGI6QnTpRFTY4ehezwYSjWry9b9T5zBo7bboPj74jJ9ave0GorXUZcXBzgcEC5\nYAFUixbBuHAhbF27uvI7JS/A53NgYJ/9H3tMzogyXEdERCAyMhL169cHAERFReHo0aOIiIjAhQsX\nys+7spLtzMMHH8ZdRXfhhx9O4+VvbXjppUN48skYAP9sjXPlD/0Njzt1gmruXPzcvTvO7tx56/N5\nHPDHjjZtyo5jYso/v3PrVgSfP4/7w8MhO34cZ3U6qNevR8Tly5CeOAFLUBCMDRpA3a4dHM2a4X9W\nK0oaNEDU449DqFsXup07y68vKSyEecAACAYDLN99B6FxY6/6/nnMYx7zmMc89vfjK78+efIkAGD4\n8OGoCo/doTE/Px+jR49GTk4O9Ho9EhMTkZOTg+DgYCQnJ2P+/Plo1KgRHn300fI3NA4ZMgSbNm2q\ncK0ru4X88IMcqalqjBljwtix5iq/F02+axdCnn0WxXv2eP3OCzodc10+SRAgOXfumpz31bubSKzW\nsnjJlf8++wzSfv1Q+sorgEIhdvXkJnw+Bwb22f+xx4HBK3cLmTFjBnJzc1FUVIT4+HhMnz4dL730\nEoYMGQKbzYakpCTccccdAIAXXngBKSkpAICXXnrphtdcsSIIb74ZjEWLjHjkEVu16lLNmwfTuHFe\nP1iTD5NIIDRoAFuDBkDHjhU/XVT0z9B9/DgOjB6Nu8aPF6FQIiIicgWPrVy70qlTpzBmTBesXGnA\nnXc6qnUNWV4eNE8+ics//QQoq5fXJiIiIiL/5pUr1+6waVMxQkOr/3hVRgZMo0ZxsCYiIiIil3H/\nxr1uUpPBWnrsGOTffw/z0KEuq8fdrg7Zk/9inwMD+xwY2Gf/xx6TMz47XNeEauHCssG6JhM6ERER\nEdF1fDZzfeXujlUl+esvhHbsiOI9eyDcYJs/IiIiIiKg6pnrgFu5Vi5dCssTT3CwJiIiIiKXC6zh\nurgYyqwsmNPSxK6kypjrCgzsc2BgnwMD++z/2GNyJqCGa+Xy5bAmJMBx++1il0JEREREfihwMtcm\nE2rFxEC/ejUcbdq4pzAiIiIi8ivMXN9A0KpVsEVHc7AmIiIiIrcJjOHaZoNq/nyYJkwQu5JqY64r\nMLDPgYF9Dgzss/9jj8mZgBiuFV9/DeG222B/4AGxSyEiIiIiP+b/mWtBgDY+HqapU2Ht3t29hRER\nERGRX2Hm+jry776DxG6HtVs3sUshIiIiIj/n98O1KiOjLGstkYhdSo0w1xUY2OfAwD4HBvbZ/7HH\n5IxfD9eyvXshPXUKlj59xC6FiIiIiAKAX2eu1U89BVuXLjAPH+6BqoiIiIjI3zBz/Tfp4cOQ//gj\nzAMHil0KEREREQUIvx2uVfPnwzxyJBASInYpLsFcV2BgnwMD+xwY2Gf/xx6TM3KxC3AH6alTUGzY\ngOL9+8UuhYiIiIgCiF9mroMnTwaCglD62mserIqIiIiI/E1VM9d+t3ItKShA0GefoXjnTrFLISIi\nIqIA43eZa+V778HaqxeEBg3ELsWlmOsKDOxzYGCfAwP77P/YY3LGv1auDQYoMzOh37BB7EqIiIiI\nKAD5VeZauWgR5D/+COPy5SJURURERET+JnAz1xYLVIsWwfDxx2JXQkREREQBym8y10Gffw77XXfB\nfs89YpfiFsx1BQb2OTCwz4GBffZ/7DE54x/Dtd0O1fz5ME2YIHYlRERERBTA/CJzrcjJgSojA/rc\nXEAiEbEyIiIiIvInVc1c+/7KtSBAlZEB0/jxHKyJiIiISFQ+P1zLd+yARK+HNTFR7FLcirmuwMA+\nBwb2OTCwz/6PPSZnfH64Vs2bB9OzzwJSn/9WiIiIiMjH+XTmWvbzz9A89RQu798PBAWJXRYRERER\n+ZmAylyrMjJgGjOGgzUREREReQWPDNezZs1Cp06dkJSUVP6x1q1bo3fv3ujduzdmzpxZ/vGFCxci\nMTERiYmJWLhw4Q2vKT1yBHKdDubBg91au7dgriswsM+BgX0ODOyz/2OPyRmP3KGxW7duSExMxJQp\nU8o/plKp8NVXX11z3qlTp/D1119j48aNsNvtePTRR9GnTx80atSowjVV8+fDnJoKaDRur98bnDt3\nTuwSyAPY58DAPgcG9tn/scfkjEeG65iYGOTn59/yPI1GA7lcDpPJBIfDAYVCAa1W6/Rcxdq1KN63\nz9Wlei2lUil2CeQB7HNgYJ8DA/vs/9hjcsYjw7UzFosFffv2hVKpxAsvvID27dujTp06GDx4MLp0\n6QKHw4FJkyYhNDTU+eP794cQHu7hqomIiIiIbky04Xr79u0IDw/HgQMHMHbsWOTm5uL8+fNYtWoV\ntmzZAqvVipSUFHTp0gUREREVHm9OSxOhavGcPHlS7BLIA9jnwMA+Bwb22f+xx+SMaMN1+N+rzm3b\ntkW9evVw6tQp/Pbbb2jbti00f+eo27Rpg0OHDiE+Pv6ax5rNZuy7cAG4cMHjdYulY8eO2L9/v9hl\nkJuxz4GBfQ4M7LP/Y48Dg16vr9L5ogzXRUVFUKlUUKlUyM/Px19//YVGjRqhpKQEBw4cgMVigcPh\nwMGDBzF27NgKj4+MjBShaiIiIiKim/PIcD1jxgzk5uaiqKgI8fHxePLJJ5GTk4OgoCDIZDLMnDkT\nKpUKbdu2RdeuXdGnTx8AwJNPPonmzZt7okQiIiIiohrzyTs0EhERERF5I5++QyMRERERkTfhcE1E\nRERE5CKi7RZClVNcXIxVq1bBZDJBLpejW7dufEOnHzObzZg3bx46deqEuLg4scshFzt16hS++uor\nOBwO3HbbbRgwYIDYJZEbbNmyBXl5eQCAqKgoPPzwwyJXRK6wfv16/PLLL1Cr1Rg3bhwA4MCBA9i8\neTMkEgl69OiBVq1aiVwl1dT1fa7OHMbh2stJpVL06tUL9evXR1FREd577z1MnDhR7LLITbZu3YpG\njRpBIpGIXQq5mMPhwOrVq9G3b180bdoUJSUlYpdEblBYWIiff/4ZEyZMgCAImDdvHmJiYlCnTh2x\nS6Mauvvuu9GuXTusWbMGAGCz2bBp0yaMGjUKVqsVmZmZHK79wPV9rs4cxliIl9NoNKhfvz4AoHbt\n2rDb7bDb7SJXRe5w4cIFGI1GNGzYEILA9xn7mzNnziAkJARNmzYFAISEhIhcEbmDSqWCTCaDzWaD\n1WqFXC6HSqUSuyxygaZNm17zvM3Pz0e9evWgVqtRu3Zt1KpVC2fPnhWxQnKF6/tcnTmMK9c+5I8/\n/kDDhg0hk8nELoXcIDc3Fz179uQNCfzU5cuXoVKpkJWVBYPBgPbt26NDhw5il0UuFhISgo4dO2LO\nnDkQBAE9evRAcHCw2GWRGxgMBmi1WuzduxchISHQaDTQ6/Vo0KCB2KWRm1R2DuPKtY/Q6/XYsGED\nkpKSxC6F3ODw4cMIDw9H7dq1uWrtp6xWK06ePInevXtj+PDh+OGHH1BYWCh2WeRily5dwt69e/Hi\niy/i+eefh06nq/Ld3ci33H///YiKigIARvr8WFXmMK5c+wCr1YpVq1ahR48eCAsLE7sccoP8/Hwc\nOnQIhw8fhtFohEQigVarRXR0tNilkYtotVpERESgVq1aAICGDRvi4sWLfE77mfz8fDRq1AhKpRIA\n0KBBA5w9exZarVbkysjVtFrtNS+crqxkk/+p6hzG4drLCYKANWvWoF27dmjRooXY5ZCbJCQkICEh\nAUDZTgNKpZKDtZ9p1KgRLl++jNLSUigUCvz1118crP1QWFgYTp8+DZvNBkEQcPbsWe4W4qcaNWqE\n8+fPw2g0wmq1ori4uDybS/6jOnMY79Do5Y4fP47ly5ejXr165R8bPHgwXx37sSvDdadOncQuhVws\nLy8P27Ztg91uR3R0NOLj48Uuidzg6q34YmNjua2mn8jJycGhQ4dQUlICtVqNXr16wWq1YvPmzQCA\nnj17omXLliJXSTV1fZ/vu+8+bN26tUpzGIdrIiIiIiIX4RsaiYiIiIhchMM1EREREZGLcLgmIiIi\nInIRDtdERERERC7C4ZqIiIiIyEU4XBMRERERuQiHayIiP/Tyyy/z9upERCLgcE1ERERE5CIcromI\niIiIXEQudgFERFRzZ8+exZo1a3Dp0qVrbrf9+++/Y9OmTbh06RIUCgXuvfdedO3aFQCQlZWFVq1a\noUOHDgCAkpISzJkzBy+++CLUarUo3wcRka/jcE1E5OMEQcBnn32G++67Dx06dMDGjRvLPy4IApKS\nktCkSRMUFRVh6dKlaNy4MVq3bo3o6Gj8+OOP5cP1wYMH0axZMw7WREQ1wFgIEZGPKywsxKVLl/DA\nAw9AJpOhU6dOAACJRIKWLVvi9ttvh1QqRVhYGJo3b45z584BAFq3bo2zZ8+iuLgYAJCXl4d27dqJ\n9n0QEfkDrlwTEfm4kpISqFQqSKVl6yVXrzzn5+dj48aNOH/+POx2O6xWK+rWrQsAUCqVaNmyJQ4c\nOIB77rkH+fn5GDhwoCjfAxGRv+BwTUTk49RqNUwmE+x2O2QyGQwGA4CyWMinn36KBx98EE8//TSk\nUimys7MhCEL5Y6Ojo7F161YolUpERkZCqVSK9W0QEfkFxkKIiHxcnTp1EBYWhj179sBut2PXrl3l\nn7NYLAgODoZEIsHRo0fx559/XvPYFi1aoLCwELt27WIkhIjIBbhyTUTk4yQSCZ588kmsXr0aW7Zs\nQefOncs/3qtXL6xfvx45OTmIjIzEXXfddc1jZTIZ7r77bvz6669o2bKlGOUTEfkVyW+//Sbc+jQi\nIvJX33//PQoKCvDEE0+IXQoRkc9jLISIKICZzWbs378fMTExYpdCROQXGAshIgpQP/74I9avX492\n7drhzjvvFLscIiK/wFgIEREREZGLMBZCREREROQiHK6JiIiIiFyEwzURERERkYtwuCYiIiIichEO\n10RERERELsLhmoiIiIjIRf4fasw9nhXV66cAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2715d0>"
       ]
      }
     ],
     "prompt_number": 116
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is pretty good! The blue dots, 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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NQmZmJnJzcxEdHY3ExEQEBQXB19e3vLAGAJVKhTfffBNxcXEAgHfeeccZ4bmF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\nJiIiIiJyExbXRERERERu8v9czlUFX0OyUAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fadb2890>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[159.2, 161.2, 160.84, 160.464, 161.1184, 162.51104, 165.346624, 166.1679744, 166.26078464, 168.156470784, 169.3738824704, 170.66432948224]\n"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly a filter that requires us to correctly guess a rate of change is not very useful. \n",
      "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",
      "$$\\verb,new gain, = \\verb,old gain, + \\frac{1}{3}\\frac{measurement - predicted~weight}{1~ day}\n",
      "$$"
     ]
    },
    {
     "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",
      "p1, = plt.plot (range(1, n+1), estimates, 'b--')\n",
      "p2, = plt.plot(range(1, n+1), weights, c='r')\n",
      "p3, = plt.plot([1 ,n], [160,160+n], c='g')\n",
      "plt.legend([p1, p2, p3], ['filter', 'measurements', 'actual'], 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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atQqdTsfQoUPJyMi45nzScy2EEEIIe/OfNg1VdjaFS5Y45XrW2j5iI2JlddrN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\nLsLhmoiIiIjIRThcExERERG5yP8DUjYYfdSlkyUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb0f9990>"
       ]
      }
     ],
     "prompt_number": 115
    },
    {
     "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. 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*, constained to a certain range of values. Other filters will vary *g* and *h* dynamically, and filters like the Kalman filter will vary them based on the number of dimensions in the problem.\n",
      "\n",
      "\n",
      "**Let me repeat the key insights 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 measurements are more accurate than one measurement\n",
      "* Always choose a number part way between two measurements to create a more accurate estimate\n",
      "* Predict the next measurement 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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Ro0c3+JjVpk2bhi1btuDo0aNmpa8KCgowb948AMDHH3+MoKAgrFixAqWlpfD3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\nuXOxYMECi1gmT56M33//HU8++STKy8sxa9Ysea7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Y+RcIUQ6HQ3l5eT2ub2xs1LFjxxQf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\n2t38ut1JSEhQQUGBCgoKOFcViHCEVgARKyoqSiNGjNCIESPU1tamQ4c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       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb151290>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I'll begin to introduce the nomenclature and variable names used in the literature. 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 $\\mathbf{z_k}$ is the data for this time step. A bold font denotes a vector. So far we have only consided 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 inital weight gain rate, like so:\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\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 $\\mathbf{\\hat{x}_k}$, and again this is a vector of all the state variables. So for our scale example it containes the estimate of both the weight and the gain rate.\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, this is specialized code. Rewrite it to work with any data. 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 results\n",
      "\n",
      "def plot_g_h_results (measurements, filtered_data, title=''):    \n",
      "    p1, = plt.plot (filtered_data, 'b--')\n",
      "    p2, = plt.plot(measurements,c='r')\n",
      "    plt.legend((p1,p2), ('filter', 'measurement'), 4)\n",
      "    plt.title(title)\n",
      "    plt.show()\n",
      "\n",
      "\n",
      "plt.xlim([0,10])\n",
      "plt.plot([0,9],[160,170],c='g')\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)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5WN51OQ4OO4jRzUf7bEHszvtF4OLFcLRowW29K4EyrT5hsViQlZWFLVu2ICQk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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb12d450>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "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 $k$. 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 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": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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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vFTGbEza/gUCAgQMHMnToUP74xz+ye/du9uzZc/j5PXv2UK1ataO+tm/fvtSs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2d9cd0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "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": 14
    },
    {
     "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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XWg4XmkEWERERKSf2xYuJfPJJvF274mvfPjRj+PprAuecg3HmmQD07OmlZ0+vaVvjrLPA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\nREREROQs/x+6JEJgKVXCiAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2c1590>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "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": 16
    },
    {
     "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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OI6y9HfnLloEdPKi+jXzhpRWHGYVYUQGxJTPNgQ0NHH71Kx3WC6tV8sB3dWHq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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb0f6710>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "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 noisey 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 existance 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": [
      "Excercise: 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": 18
    },
    {
     "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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v4Ovc2eiITGf7dgtDhyZxyilBVqwopWnToNEhickdt5ViypQp3HbbbZXjvXv3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\nEAKQYCyEEEIIIQQgwVgIIYQQQggA/g9DBFAXk14UvQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb293790>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "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": 20
    },
    {
     "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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TT3o+AEWBaft2KAb9m1vraE9psagI2tChAU8o1czMtjPOmobwJ59E+LPPomb1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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb0b4dd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3wHr+JYh5edCqW+55So+MhFBVBZSWAgAsFgHffWdCZqaIvLyLY+SMMxEREZET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BAP6pEV56NHjyI1NRV9+/ZFTEwMdDod8vLy1AdUWgpotVffRja0VdboJM9Z++mnEDMyIA8Zovq+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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2d9b10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cItqSBt6K7hw9Npamjz4a+MHAz9hTU5lqzePoEecppFpejuO8Lfdcnk94OI62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\n7s9CFnV6CE0Tf0FwcN8JVMZ7TpVQJCICw088gfAf/Qg9XRK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YEdMzPRdeGRUx\nz4hZKhNstvHt9X/Jh2XOKkDl4sVBPxPT08dyvNnm5qsqcKacRSKH1gWRQ+uC+JPfcpwtFgsSEhKw\nY8cO7N69GwkJCWhvb0dHR4ds+6SQJPAnivFS4TJELslGRP3kBei+GK0aOKpFSMBgbeDynNmmJnDF\nxYr724srYJ2RA5UKmHbLCoSeLnDkJ3igee892K+9FlKs+11dUadzlN12Uz2w80Q9DjfPAADsrcxE\nb3GD4vnLYc1mNKnSkZEhKL5Hmp6BLTkmaDQX2iwWBqnlH2Pa7WsmNB9vXM2pGoQQQkgg+P3lwLvu\nugtbtmxx284oqNDmC6apCTY7i6FpyUi7NgXhQ53AwMCkPMtrggC2thZC5oUd54ouPTpKA3TyhySB\nbWmB6vRpxbdE1JcjYkkOAGDLXWEoZeeAO37C432aN9+E7Z57PD8gMhJQq8elr1yamxbVVoPYRemO\n7jOTEDPUCtjtiv8Ml2LNZiy4NRlLligPnMWMjLGAdVRxEYut6v1gN631eS7eEpOTwVgsyD8oAA1N\nEJOvnuInlLNI5NC6IHJoXRB/8tvvlBMTE2G5KO3AYrEgMTERg4ODTu0JCQmyYzz88MMwnC9EERMT\ng9zc3LFfsYwufHef9UePYkS9EIuXCGhvP4FKZMFYaYK4cIGi+336vGgRoFIh//hxt/0L33kH10RH\nAxERY9dtIVGINHf5dz4KPx/buxcb7XZwZWWA3e5x/sd378aq4UGkr9ID4GGzfYpP2LXQvvMZItes\ndvm81UlJ4KqrcSg8HFJ+vsf5bdXrwbS04PDZs7hYfn4+IIq4fqgOqWsMyM/PR2+vBq1IQlRjEw43\nNfr087jebIaYlobPP1f+8xOTkyF1dODIwYNYsd5xgobW8jeERAqwTp8+Jf/9Rj+v16bgJ7c3YjM3\ngMPl5Vh1vgDKVK+nqf585vyLqcEyH/ocHJ9HBct86HNwfKbvC/o8Kj8/H+bzKZ4PPfQQfMFUVFQo\nT+68RGNjI77xjW/ggw8+gM1mw5YtW/D222/DarXiS1/6Evbt2+ey/VINDQ1YuHChr1MBAHBP/QzP\nvxCOL5u/g9BQoHXdV5H80HqI9945oXHdCX/8cYhJSRj53vfc9lPv3YuQl1/GwL/+Ndb22bpfIUHH\nYNYO9/dOBrasDJEPPAAwDAZfeQXC3Llu+3NHj6Fy+9MIPb0HKSmOJVPy+2NY+taPMXL4oMv7Rh7/\nGaJUQ7D/4meK5hW5fTtGvv1t2cp7gxVNUF1zPVSWUnCcI6OjVHcLjK98F5E3Xato/EtF3HcfbLfd\nBvv27V7dF71sGQZeew3iLMf5zyEvvgiurAxDv/udT/PwVehNX8B/5t+MnyX+Fnz5qSl9NiGEEHK5\nKiwsRFqasuJnF/M5VePpp5/GXXfdhdraWqxZswb5+fl4/PHHcffdd+OBBx7Aj370IwCARqORbZ8M\n1vwitBsWIjTU8Tl9ywxoaib3LGeusBDqPXs89jPvq8Kp4UuKbCRoIbUFJseZbW6GmJwMfsECcArS\nNWxFFTBHzkJy8oV/Z8376gKE1pvAdHfL3iPxApi//xOHM+9XPK+esCSc+lD+Z9L8WT1aIjLHiuMx\nDNATY0B3oe95zqzZDNFo9Pq+i/OLAUeZbfvatT7Pw1fsDCNW47OrqvgJIYQQEig+B85PPvkk8vPz\ncfbsWXz66ae47rrrsHXrVuzduxd79+7F2ouCCFftfiVJiCgrguaaeWNNQnb25BZBsdnAVVaCraoC\n4+GFx6FTJpjDZo5rUyVroe4OUODc0gIxORnC/PlQFRV57B9ZX4bN352OcenpISHgly1zFEORcea3\n+ejkErD0oRzF8+oJT0LFJxdSey7+FUu0pRbqWenj+luTDBip8P1kDdZshmhQfobzKCEjA3UH6x0n\na9hsUB89Cn7N1L0YODaP9HRsn/YpIrKvruInl/5qnhCA1gWRR+uC+NMVUzmQbWhASLQaX3s6bqxt\nsgNnrrwczaEZKE1ZD/WBA277RjRUInzRjHFthsVxSAsLTNntsR3nvDxwCgJnrqICQo5zAGxfs8Zl\n+W3rn3ag95Z7wXqxykIydAjpkq8eaOSrkblx/O7w+oeSMT+6TvkDLsL09kKyC7BGTPP6XjE9HUXv\nNKKqioXq5EkImZmQ4uI83+hnotEIdXcHxFTacSaEEEIm2xUTOHNFRRAW5CEu7kIqgZiZ6Tjn99ID\nd/31zJISnBIW4C9tN0Alk7c9RpKQ1FsB/dpLA+d4JEoBCpxbWsAnJmH511eCLSv3+DPiKiogzJrl\n1M6vXStbCKVg/wCWd+9B9pM3ezWvyGwdogdaxgoqjib3AwBXWwvhfPGTsbZMAzizfPlrT9iGBtRK\nRpwqVHt9r5iRgVmaKvz4x+HofzcwaRqAI4AHAOkqO4ru4nVByChaF0QOrQviT1dW4JyXN74xJARi\nairYmppJeaZQUIIjIwtRkrwJ3Mefugw+B2stEEQGxsXjdyQlrRZMR2BSNYT6ZpT2pUFrDEOfNt1x\nuoYLTE8PmIEB2eBMmD0bTF8fbJXj0yXOPfEBWnPXgUv0bhdWbdAjlW2BxeJ8ZCFbWzsWKI6aSBEU\n1mxGNe/dGc6jhPR0GPgaHDmiQlzhp+ADHDjTGc6EEELI5LtiAmfV6dPgLw2cAZhUM1H9YdWkPJMt\nLkHStlzs+CQcyM6E6tgx2X5NB6vREJEDlXp8MChNmwamrw/g+UmZnzu2ula8vCsd69bZURq+yO0L\ngmxFBYTsbEDu/G2WhcmwFu8/dnRc85fEV5Hwvbu8npeo1yOFbUZDg2NpjuWmSRK42lqI5497G+uf\nlASmsxOwWr1+lq3SjFopHTqd9wfLiEYj4vrNuG9rC0KqysAvW+b1GP4gxcRAjI296gJnylkkcmhd\nEDm0Log/XRmBsySBKy6GMH++06WGiJno+nwSAmdBQET1Odz/m2xwHGDfuBFqF+kaM+zlSFo3w/kC\nxzmC586pL4ISYmmCOiMJ69bxONC9BCo3FQT7jlagJ3mmy+uR21cjvvDQWOzKVlQgtq8B2HSd1/MS\ndTroxWYkJojj2pmuLkgsC2naJfnIKhXEpCSwjY1eP2uwtBH9WqPsvwc8Cg0Fk6jF75e8Cn7pUiAk\nxIdB/GPw5Zdl02gIIYQQ4l9XRODM1tdDDAuHpNM5XdPMz4LK5P8XBNmqKoiJiUB0NIDzgfP+/bJ9\nIxoqEbVEJnDG+XSNqQ6cR0agHhnAtKw45OYKOGpbBOGE6xcE63ZX4fOeOS6vR968BtfhYxzY5zgn\nLuTNN2G74w5ApfJ+buHhYCLCYIxy/ExGc9MK36pHX+J02VuENCPsJu/TNcRqM/gU70/UGHtuRgZC\nXnstYPnNo/j16337WV/GKGeRyKF1QeTQuiD+dEUEzlLBaexuX4LBQedr2muzoO2o8PszuTNnIOTm\njn0W5s0D09cHtrbWuW9lpeyJFADQJiag/sTUBs5sSwu6QpKQZgRYFtBtnA1NdaXLdIfw2jKEL3Z9\npJyYlgbEROPUa5UAz0Pz1luw3n23z/OTdDowreNP1jjzfgMsUfKB88nODBx9o9nr54RbzJi2MNWn\nOQLnz3KuqpIt1kIIIYSQK88VETj3HCxBbfzC0WrW4ySty0SGrQI9XT4XSJSlujQ1hGVh37BBNl2D\nNZkgZmXJjmO26tBwauoD5xY2BWlpjnSIX78IIGs6uNJS2f5JXeVIWi8//7ExN65G2JFD4Hd9AjE5\nGeJM16kdnohJSWDPB86juWlcbS00szPkbzCmQazxfsc5vq8Od/2X7+cfixkZEBMTIcye7fMYxDeU\ns0jk0LogcmhdEH+6IgJnnCqCfd4C2UtMTDQGNHEwHfR+R9IdrqQE/Lx549rq525Cx+uXpGsMDIDt\n6HBZZEOI04JvntrAmWluBp+UjMxMx2kSDAMILs5z7qrpQ5TYg+Tl7l8+4zauwR3T9kN69U1Y7713\nQvMT9fqxwBlwHFYyrbMW0QvlK/yFzTYgtNW76oFMby8YUYQUG+vzPPklS2C95x75lyYJIYQQcsW5\n/ANnSUKCuQgx1+W67BKSl4X5GvndVF+fKZ46g+ro8ad4DK1ch7iKE7B3D4y1cdXVEKZPx1id6Evp\ntGAsFvlrk4Rtbsac6xOh11/YhRfy8qCSOVmjfo8JDZEzwXDulwq/ejXm9R+B9vTHsN9yy4TmJ10U\nOK9atQpVVSxmaUxQZcvvOMctTEVcb51Xz2DNZggGw4SCXv7aazHyxBM+3098RzmLRA6tCyKH1gXx\np8s+cGZra9EtxmDuOtfV30LzshDV4L88Z9ZsRrc1AgPhiePajXMjUBazDGd/e+HXQnt+U4tqteu0\nBXWyFqruKU7VOF818GJ8Xh44mZM14lorIM30XDJbio2FmJMNfsOGCe3iAo4d5xPvWTA05PhcWsph\nulTjVPxkVPS8NKSJdejqUh4E+1pqmxBCCCFXr8s+cOaPnUZF5CJkZYku+wg5OX4tvT2UX4LTWICZ\nM50LZ9g2bMTIuxfKb/NnTRjJyHY5VpghHqH9U7zj3NICMWl8bq8wZw64qipgeHhc+0zhHNJvcD3/\niw3/8IcY/v73Jzw/UafDcE07GhtZ5OfnIze9B1FSPyS9Xv6G5CTEMd1orx9R/AwKnC9vlLNI5NC6\nIHJoXRB/uuwD54iyIqz41hywbv4kYna2XwPnroNn0ZY6Xzb7IvPR65DXvAfNTY7PMc0ViF7m+sU6\n7ex4zIpr89vclJDbcUZoKHp0WRg5cW5cM1dRAdHFiSCX4tevV9zXHVGvRxrXjMZGx3/U2SE1QGa6\n67QKlgWXnoLZEcpLbw+VNaAjggJnQgghhCh32QfOXHGxbMXAiwnZ2WArKwHJPydrsEV8f555AAAg\nAElEQVTFwIJ5stdC5maCjQrHZ/9Xhu5uBhm2CkxbLn+GMwCEp2uRyLT7ZV5KsS0tkC4NnAF8bl2M\nhn+fGdfGlZdDmMAJGb6QkpKgExyB86pVq8DW1rpM0xglpqV5VXrbUtCI3WWZE50qCRDKWSRyaF0Q\nObQuiD9d3oGzKDqOhfMQOEtaLcAwfnsJL7GpGNrr57q8HnLL9bgn+kOcK5YwXaqGlOU6QBMTEsBO\n5cuBggCpzYI6q/MxbMziPFiPXpTn3NcHpqfHcU7zFBJ1OsSOtKLp/EEZbG0tRE+Bs9HoVeAc3m5G\n+Oyp/XMRQggh5PJ2WQfObHU1xLg4SHFx7jsyDCzxOfjTt5X/Kt/lUK2tiAixI3eri3xbAKrt1yPi\n0D60HGlAf4QOCA93PWBUlOO8tRHl+bkTwbS3o4eNQ31LqNO11O25SKi7cLIGV1EBITsbbvNgJkNo\nKPjQSPTWdCM/Px+ckh1ngwGcF4FzXF89YhdQ4Hy5opxFIofWBZFD64L402UdOHOXFiFxg8/Khr1k\n4nnOXEkJuEW5iI5xfYIDv2IFWJMJ96QdQtRS94VDwDCQ4uPBdHRMeG5KsM3NaEIqDAbnlynTts6E\n0V6F2lJHEH/qb9XoS514zrIvpCQ97l7r2HJma2shpqe77S8YDIp3nJneXkiihLTc6IlOkxBCCCFX\nkcs6cO49UIy2tIWK+kYuyUJcW4WrqtJguroQuW2bx3QOVUmJ52BdowG/ejXCXnwRyPEQOON8usYU\nBc5iYwvq+RQkJzsHzkxoCFriZqHszXIAQNVOEwbSpja/eZQqTYdFSY0oLl4Pe3kdxOny5bZHiQYD\n7JVm9Pd7HttWUY86pCM5xb/VJMnUoZxFIofWBZFD64L402UdOPd/UoRj/CJFfdk52cgLLUNZmfNR\nGDYbcG77M2DPlSLkpZfcjiNXMVCOfeNGcGVljlQHDzrYBJz4sNtjP38YKGtBV3gK1Gr566pl85Fr\nPYneXgbGwTLErgzMjvNo2e0970sI6W6DmJrqvr/BAJupAUePqjyObatsgC3Z4LImDSGEEEKInMs3\ncO7rQ1pHMVJudF0x8GJiTg5yxHKUlIyPlkZGgGe3n0VO1R50vf0+Ql59FejrczkOV1wMQUngfP31\njucqCJy7uQRUH5uawHm4qhUj8c4vBo6K3zgPOQOFKCnhkMuVQpoVoMBZrwfT0oqBMzUQU1IBlfuA\nWNLpECH2o+6c51zxuL56zN3mfKoIuXxQziKRQ+uCyKF1QfzpsgycucJChCxfi9c1DyJrqbI8VTE1\nFVF8N+pKBsfaBgeBL94VikfLvwX1b5+Gask88GvXIuT112XHYLq7wXZ3e0wbAByB3PD/+3/gcz0H\n9oxOC7Zjak7WiOlvQuYa1y82CgsWQFVUhNLjQ4gTOwJWJETS6TBU3Y5ZGpPjDGdPGAb9cQb0Fjd6\n7ErFTwghhBDii8srcJYkhPzhDwi97S48MvRL6N/4H08bkRewLJhZWXjqrhIAjk3l22+PxP0Df0Rq\nbjTEO24FAIw8+ihCX3wRcsnQRa+eQ03MfMWnTIx897tAZKTHfqpkLVTdU5PjPG24GctuTXB5XZg5\nE6zZjOHPitCXlIVA5TOIej2Ga1qxSl8HQcE/VACAT0mD3eT5BUG2oYEC58sc5SwSObQuiBxaF8Sf\nLpvAmensRMTdd0Pz3nu4P/tzrPrNFqxbx3s1hpiTDZXJcbLG3/8eghUZjbiv/hkM/+qXY1XphHnz\nMDR9Nop/8K7T/T2fnEFbkrJTPLwRlq5F+BSV3ZatGngxjQbCzJm4j3sD6nnKSm1PBlGvx3B1G5KG\najyeqDFKlWWAqrHBYz/acSaEEEKILy6LwFl15Aii166FmJOD/l278LudCbjlFrvX41xcevsb37Di\nGdv3Yb3/fqcy0V1f/TZS/vE71FWPP3UhvLwEIdcoy6n2RmSGFtFWC3jv/h3gPUkC29ICMcl1jjMA\n8Hl5yDz1LkIWBuZEDcBRPTAjpAnLtcc9Fj8ZFTrLgLyYGths7gaWwJnNEI1G/0yUBATlLBI5tC6I\nHFoXxJ+CPnAOeeUVRDz4IAZ//WsMP/00oFZDo/FtrLHS2wDUn30K1YkTGHn8cad+UTesQIg+Bgce\n2T/WZrMB6V1FSN7mumKgr5jEeCwytEF0PiHOv8/p6YGkVntMHxHy8sAMDEDICcyLgQAgJiZC1WlB\ndHuTx+InoyRDGm5ZUOV2fdjae2HjWUgxMX6aKSGEEEKuFsEfOD//PAbeegv8+VMqJkIY3XG2WhH+\ngx9g+Oc/l6/qxzAIf+pb2FD4HApPOX5EpSeGkQYzQhf4P31BSkhAvNDu8z8IlGJaWiB52G0GMFbC\nXJgZuB1nhIRAiopCRFub4t1hJWW32443oEZI98MESSBRziKRQ+uCyKF1QfwpqANnprMTTHc3+Nlz\n/DKeOH062MZGhP761xAyM2HfssVlX+7WrTBO68H73z4OSQIaPipDS/wcuDwAeSLzio93FECRJrcg\nR39pM8xiisd+Qk4ObDfeGPB0BlGvh6TXA2FhyvorqB7YW9yI7hjKbyaEEEKI94I6cOaKilAVvQAv\nvaIscPJIrYZoMCD0hRcw/Oyz7vuyLFQ/fhR31/8KJhOLWwwnkXC9fwJ4JxERjtMrBgYmZ/zzOkva\ncK4nzXNHtRqDr78esBM1Rkl6Pbri4pT312rBWK1uz+EeKTdjWEeB8+WOchaJHFoXRA6tC+JPwR04\nny7C3q6l2LrV+xcBXeEXLsTw976naDdVuPN2LI0uxayhQmjOlYBd4v8TNUaN7TpPIltNM6xaz6ka\nwULU6zGkd33mtBOGgZiWBq7B9ckaTL0ZSKfAmRBCCCHeC+rA2fp5EUrDFiEtzX9vzQ09/zysjz2m\nrLNGA+s3voHQ//s/cCUlEBQUM/GVpNWCmUjgPDjosYvU2AIp5fKpmMcvWoT4m2/26h7RYEBXoRm3\n3hqJtjbG6XpYmxkhMxXsupOgRjmLRA6tCyKH1gXxp6AOnFXFRWCX+nmX18v0A+v990N1+DA4kwnC\n7Nn+nctF+kITsPOVXp/u5QoKEDNvHtyfwwZoLM3QZFw+O862L38Ztnvu8eoewWhEwqAZ11zDY+PG\nKJSWjl/i09l66Jam+nOahBBCCLlKBG3gzLS1gRkaQuaGAO8ORkXB+uUvO8psK3xJzRcj0QmoPtrl\n073iT38DsbsPzIlTbvtF9TYjcublEzgD3uemiWlp4Mz1+P73R/DEE8O4+eYo7N9/vrykJEE/XIeE\nJbTjfLmjnEUih9YFkUPrgvhT0AbOXHExyiIWYdlyIdBTwchjj2HwpZcm9RnqFC3UPd6narClpZAK\nivCS+mEwBw+57ZvCNMNwjc7HGV4eRIMB7Pkc5y98wY6//W0Ajz4agT//OcRxjjXH0RnOhBBCCPFJ\n0AbOqtOnMfeBXMyePclVQZSIiIAwZ5JO1DgvzBCPyMF2r6sH2n/6f/g9+yi+8Oo6RBz91HXH4WGE\n8IOIz1F+SkUw8DY3TTQawZ05A9VnnwF9fVi2TMCePf1ISBCp1PYVhHIWiRxaF0QOrQviT6pAT8AV\nrqjI6/zWyxmjS0CKphQWC4OkJGXnObP19eA+PgjmW7+DZp0I7uuljqPYoqOd+7a0QNTrAcb5hbkr\niTBnDmy33oqwZ58Fd/YsxORkzFq0CNkLFoAx9VHgTAghhBCfBeeOsyRBVVQEfsGCQM9kyohaLZLV\n7WhrU/6fxPaz5/EX7j/wpUdDgLAw8IsWQX3kiGxftrkZYvLlc6LGKK9z09RqjDzxBPp370ZPbS0G\n//xn8MuWgTt3Dur33we/ZMnkTJRMKcpZJHJoXRA5tC6IPwXljjPT0gIIAqQUz1XurhRSQgJma9tg\nUXj0HtPWhvgD72DjrhOIinK02deuherQIdg3b3bqzyost31FUakgzJ0LYe5c2L70pUDPhhBCCCGX\nuaDccVYVFUHIy7vi0wouJsbHI2rYgvh4ZWkaoS++CNtttyFpvnasjV+zBupP5fOcmct0x5ly04gc\nWhdEDq0LIofWBfGnoAycBw4VoTX16knTAM4XQOnsBETPO85Mby80f/0rrI88Mq5dyM3FQLUFrYWt\nTvdUfNwGs3D17OATQgghhPjblAXOu3btwqZNm7Bp0yb8//buPTjq8t7j+Htz2aThEgzZJLBkCZdw\nJwQqIKhEkKYGJ+gwp1VGDmhhKmNkREAK2GOpIiOO9KDVUcQWhcphQKGAVIg3qCkIR9JwPWEAhdzD\nRgK5QXY32fMHshLzS0xgk2zYz2uGgd/z++0vz24+s/Odh+f3PF988UWj1176NItPSv1sLqrZjLtD\nB0yXfnoTlJC//AVncnL9B90CA8nudg9nVtefz1X+f4VcCGt/hbPmpokR5UKMKBdiRLkQb2qVOc4O\nh4OVK1eyefNmqqurmT59OuPHjze+2O0mOu/fRP7OyzsGtgNuiwWT3Y77ttsavqiqipC336Z861bj\n8xOTCN65F/iPOs2dywswD4zxXmdFRERE/EyrjDgfOXKE+Ph4IiIi6NatGzExMWRnZxte6zqTS1VN\nCMNSLK3RNZ9SGxlJQEnjm6Ccf+l/OBUxitqBAw3P95x5Fwn2zym9bhPCmhqwVOfTdVj7K5w1N02M\nKBdiRLkQI8qFeFOrFM4lJSVYLBY2btzIxx9/jMVi4fz584bXFmw/zMmOPzdaiviW5wiP5K3nyxu+\nwOkk/J3XOZQ8v8FLQgbGYQo1c/C9M562orwaLNgx227tXQNFREREWlKrPhz48MMPk5KSAoCpgRUz\nKvYc5lI//3ow8JqA6EjOfX2BmgZ2Gc99eStn3L24d0kj01hMJi6MGE9t+j89Tfajdi4FR0JwsJd7\n3PI0N02MKBdiRLkQI8qFeFOrzHG2WCzY7XbPsd1ux2KpPxXjiSeeYFH2Ub4cdA8n3nyToUOHev6L\n5Vrwb+Xj/tWXsYWex243cfr0l3XOb3r/aya+tpIzs1YyyNz4/WIfvYuIt98mIyOeu+66i7jgfJyW\ncL7KyPCp99uU42t8pT869o3jo0eP+lR/dOwbx9f4Sn907BvHjX1fOBwOsrOzCQoKokuXLgBc+v4h\n/fDwcB2302O3202XLl2IjIzk4MGDXJORkUFOTg4As2bN4kaYTp482bSFg2+Cw+EgJSXF83DgjBkz\nSE9Pr3NNbm4uI4YPJ7x3b8oOHsRtUFjf6kLWrGH7im+J/mAFiYk/DDvv2RPEvv9cxxMxH9D5qw8J\nCGx8fWtTSQmdb7+dS6dOQXAwwdu3Y968mcr161v6LYiIiLQLDoeD4uJirFYrAQE+uTqv3ITa2lry\n8/OJjo7GbDbXO5+ZmUlsbGyz7xvkjc79FLPZzPz585k6dSoAS5YsMbwu4NtvcXfq5JdFM1zdBKV7\n0AEKigOAHwrnOwZeIDX0earWfkDNTxTNcHVN6Nq4OAIzM6kZPZqAwkJq/W3XQBERkUaUlJSoaL6F\nBQQEYLVaKSoqorsXN4BrtbRMmjSJ3bt3s3v3bu655x7DawL//e+rOwb6KbfFQhTnKSysWxzf9tZ/\nU/PLidQMGdLke7mSkgjesweAgHa6ayDU/y9YEVAuxJhyIUYay4WK5ltbS/x+fSoxQVlZ1Az3zwcD\n4epydD3D7PziF05PW0BODuZ167jcwCh9Q5xJSQR9v/22qbAQt0acRURERG6KTxXOgVlZuPx8xDmk\nzI7V+sO089Bly6ieNQt3M0eMXXfcQeDho+z96HK7HnG+9jCHyPWUCzGiXIiR9pyLd955h/j4eGw2\nG//85w+rZc2fP59XXnmlzrULFy7EZrMRGRnJ3u8HzsT7fKpwrvnfI/49VeO2265uue1yARB46BDB\nGRlcmTOn+TcLC6Ns4Ag2PnGIC0eLNMdZRESkHXE6nfzhD39g27Zt5OTkMG7cOM+5lStXsmDBgjrX\nv/zyy+Tk5NCjR48Gl/xNTU1lvRYKuCk+VTiXBkU2vt30rS4w8Grx/N134Hbzs//6Ly4vWgQdO97Q\n7cwpSfwy4FPCKwrabeGsOYtiRLkQI8qFGGmvuSguLubKlSv079/fa/dsqKCWpvOpwvlCrxFt3YU2\n5/5+2+3gnTsxlZXheOSRG76X654kHqz5AFdQKHTo4MVeioiISEsZM2YMY8aMAaBXr16eqRrp6enY\nbDaio6N58cUXm3y/P/3pT9hsNvbv38/vfvc7bDYb9957r+d8aWkpjz/+OAMGDGD48OGsW7euzuvT\n0tJYvHgx06dPx2azMWzYMCoqKrzzZtuZVlmOrqmCxvjvNI1rai0WTAUF/GzpUqpefhkCA2/4XjWJ\niXQOqKA6tocXe9i62vPcNGk5yoUYUS7ESHvMxf79+8nNzSUxMZGzZ8/WWR0iJyeHtLS0Zo0ez5s3\nj3nz5jF58mR+/etfM23atDrnZ8+eTVRUFIcPH6awsJD777+fhIQEEq+bPrtp0ybefPNN3nvvPY4f\nP05QkE+VkK3Gp961JaWRraT9hDsykp+98gq1cXG4Jky4uZsFBlKTNI7gqiqqvdM9ERERaQVud+P7\n0/3U+aa+rqioiM8++4wzZ84QEhJCXFwcqamp7Ny5s07hfPfdd5OcnAzAkGYsj3ur8ampGqafJ7R1\nF9pcbWQkgYcOUfX88165nzMlhZrBg71yr7bQXuemSctSLsSIciFGbiYXL70USkTEbfX+vPRSaJOv\nb+jatvLjker8/HwAEhMT6dWrF7169WLDhg3Y7fY61/Xp06fV+ujLfGrEmc6d27oHba6mf3+qf/tb\nagcN8sr9HN/v1igiIiLNs2jRFRYtutJi19+MhqZqmM1mampqDM8ZbQhitVoJDQ3lm2++aXT6hzaL\nuUqfgo9xPPYYl5cvb+tu+Iz2ODdNWp5yIUaUCzFyq+aioakaffv2Zd++fYbnoqKiOHHiRJ22mJgY\nxo4dy9KlS6msrMTpdHLgwAGOHz/u9T7fClQ4+xotFSMiIiLUH1WeMmUKNpuNDz74gD//+c/YbDae\nfPLJOtc8++yz7Nixg9jYWJ577rk659LS0tizZw+DBw/mgQce8LSvXr2akpISRo4cSb9+/XjhhRfq\njVprKburTCdPnryx2eVelpuby4gRWo5O6srIyLhlRwvkxikXYkS5ECMN5aKgoIDu7XRXXWm6hn7P\nmZmZxMbGNvt+GnEWEREREWkCFc7i0zR6JEaUCzGiXIgR5UK8SYWziIiIiEgTqHAWn6Z1WcWIciFG\nlAsxolyIN6lwFhERERFpAhXO4tM0N02MKBdiRLkQI8qFeJMKZxERERGRJlDhLD5Nc9PEiHIhRpQL\nMaJciDepcBYRERERaQIVzuLTNDdNjCgXYkS5ECPKxa2ra9eunD17tlV/pgpnEREREWlX3G53nb9b\niwpn8WmamyZGlAsxolyIkfaYiw0bNjBhwgQGDx7Mb37zG6ZOncrAgQM5ceIEtbW1rFixgsTERAYM\nGMCiRYtwuVwAnDt3jgceeIDevXvTs2dPHnvsMcrKyjz33b17N6NGjcJmszFy5Eg+//xzz7lhw4ax\nd+9ez/GPR3PT0tJYvHgx06dPx2azMWzYMCoqKgDYsWMHY8eOpXfv3jz00EMUFxd7XpOamkq/fv14\n7rnnGD16NBMmTODy5csAlJaW8vjjjzNgwACGDx/OunXr6vy8OXPmMGnSJGw2G3PmzPGc+9WvfkXP\nnj0BGDduHDabjWeffdZbH3+jVDiLiIiI+JiQkBD279/Prl27mDlzJtOmTWPr1q28/vrr7N69m127\ndvH1119z8uRJVq9eDYDD4WDGjBkcO3aMY8eOUVpayooVKzz3nDt3LkuWLCEnJ4ctW7bQrVs3zzmT\nyYTJZGq0T5s2bWLatGmcO3eO999/n6CgIA4dOsRTTz3FG2+8wenTp0lISODpp5/2vGb06NG89dZb\nrFmzhvT0dEJDQzl48CAAs2fPxmw2c/jwYbZu3cqKFSvIysryvHbPnj2sWbOGffv2sW3bNjIzMwHY\nvHkzOTk5AHz55Zfk5OTw4osv3uQn3jQqnMWnaW6aGFEuxIhyIUbaay569epF586diYiIoG/fvths\nNux2O++//z7PPPMMMTExdOzYkZkzZ/LRRx8BEB8fz5QpUwgLC6NTp05MnjyZ48ePe+4ZEBDAt99+\nS1lZGbGxsQwcOLBZfbr77rtJTk7GZDIxZMgQQkND+dvf/sbUqVMZPnw4AQEBpKWlkZ6ejsPh8LyP\nuLg4IiMjCQ8Px2azUVJSQlFREZ999hnLli0jJCSEuLg4UlNT2blzp+fnpaSkYLVa6dGjB4MGDeLM\nmTNe+GRvTlBbd0BERETEF90WEeGV+5ReuNDs11wb/Q0KCiIwMJCgoCBcLhf5+fnMnj2bgICrY5+1\ntbXExMQAYLfbWbRoEV999RVVVVU4nU4SExM991y7di2rVq3itddeIz4+nldffbVZxXOfPn3qteXn\n57Nv3z42bNjgaQsJCfFM17jW98DAQM+x0+mkoKAAoE7/ampqmDJliuc4PDzc82+z2Ux1dXWT+9pS\nVDiLT8vIyGi3owXScpQLMaJciJGbycWNFLwtye12Y7VaeeONN7j99tvrnX/++ecJDAzkwIEDdOzY\nkdWrV7Nt2zbP+VGjRrFhwwYcDgdPP/00y5cvZ/369cDVYvfaXOnr50Vf71qxfr0ePXqwYMEC5s6d\n26z3YrVaCQ0N5ZtvvvnJKSINudHX3QxN1RARERHxcddWj3jkkUdYvnw5RUVFuN1uTp8+zRdffAFA\nZWUlHTt2JCwsjHPnzvHuu+/Wef2mTZuoqKjwFJydO3f2nO/Tpw+HDh0CYPv27U3u19SpU1m7di1H\njhzB7XZjt9vZunVrvX7/WHR0NGPHjmXp0qVUVlbidDo5cOBAnaklDX0G19/jxIkTTe6rN6hwFp+m\n0SMxolyIEeVCjLTHXPz4Qb1rxyaTibS0NMaMGcOkSZOIi4tjxowZfPfddwAsXLiQrKws4uLimDlz\nJikpKZ77uN1uNm/ezNChQ4mPj6e4uLjOShTPPPMMmzZtYuLEiRQXFxuO5hq1jRw5kmXLlvHkk08S\nFxfHvffey5EjRwz7/mOrV6+mpKSEkSNH0q9fP1544QVqamoa/Hk/Pv7973/PwoULGTx4MMuWLWv0\nM/UW08mTJ1t3AbwG5ObmMmLEiLbuhoiIiPiBgoICunfv3tbdkBbW0O85MzOT2NjYZt9PI87i09rj\n+pvS8pQLMaJciBHlQrxJhbOIiIiISBOocBaf1h7npknLUy7EiHIhRpQL8SYVziIiIiIiTaDCWXya\n5qaJEeVCjCgXYkS5EG9S4SwiIiJ+qba2tq27IC2oJX6/Wo5ORERE/I7D4aC4uBir1Wq4I560b7W1\nteTn5xMdHY3ZbK53/kaXo9OW2yIiIuJ3zGYz0dHRFBUVtXVXpIU0VDTfjBsqnFesWMH27duJiIhg\nx44dnvZ//OMfvPrqqwAsWrSI8ePHN9ou8lMyMjL0RLTUo1yIEeVCjDSWC7PZrE1QpFluqHBOTk7m\n/vvvZ/HixZ42h8PBypUr2bx5M9XV1UyfPp3x48c32C7SFBoJECPKhRhRLsSIciHedEOF8/Dhw8nL\ny6vTduTIEeLj44mIiAAgJiaG7OxsKioqDNsHDBhwk10XfxASEtLWXRAfpFyIEeVCjCgX4k1em+Nc\nUlKCxWJh48aNhIeHY7FYOH/+PFVVVYbtKpxFREREpD1ptHB+9913+fDDD+u0TZw4kaeeeqrB1zz8\n8MMAfPLJJw22m0ymG+qs+J+cnJy27oL4IOVCjCgXYkS5EG9qtHB+9NFHefTRR5t0I4vFgt1u9xzb\n7XaioqKorKys126xWOq9vry8nMzMzCZ2W/zFmDFjlAupR7kQI8qFGFEuxEh5efkNvc5rUzWGDh3K\nqVOnuHDhAtXV1RQXFzNgwAAcDodh+48NGjTIW10REREREfG6Gyqc//jHP/LJJ59w8eJFkpKSWLp0\nKePHj2f+/PlMnToVgCVLlgBXl3oxahcRERERaU98ZudAERERERFfpj0mRURERESaQIWziIiIiEgT\neO3hwJtx9OhRPv30U0wmE/fdd5/WePZTZWVlbNy4kStXrhAUFERycjJ9+/ZVPoTq6mpWrVrFnXfe\nyV133aVMCLm5ufz973+ntraWmJgYHnroIeVC+Pzzzzl27BgAQ4YMYcKECcqFn/r44485fPgwHTp0\nYM6cOUDD9WZzMtLmhbPL5SI9PZ3Zs2fjdDr561//qlD7qYCAACZPnkxMTAwXL17k7bffZv78+cqH\nsGfPHqxWKyaTSd8ZQm1tLR9++CFTpkzBZrNRVVWlXAgXLlwgKyuLuXPn4na7WbVqFQkJCcqFnxo8\neDAJCQls2bIFaLjebO53R5tP1cjLyyMqKooOHTrQpUsXwsPDKSwsbOtuSRvo2LEjMTExAHTp0oWa\nmhpycnKUDz9nt9uprKyke/fuuN1ufWcIBQUFhIWFYbPZAAgLC1MuhNDQUAIDA3G5XDidToKCgigv\nL1cu/JTNZiMsLMxz3NB3RHO/OwLnzJmztBX636C8vDwqKyspKyujtLSUS5cuERERQdeuXduyW9LG\nTp06xcWLF4mMjFQ+/Ny2bdtITk6msLCQwMBAAgIClAk/l5ubi91uJysri3/961+43VcXh1Iu/Ftw\ncDABAQGsX7+effv2MWHCBNxut3Lhx65cucKRI0cYPXp0g/Xm5cuXm5WRNh9xvmbUqFEMGTIEQFty\n+7ny8nJ27dpFamqqp0358E/Z2dl07dqVLl26eIqja5QJ/+V0OsnJyeHBBx9k1qxZ7N+/n9LSUkC5\n8GelpaUcPHiQBQsWMG/ePDIyMnC5XIByIT+4PgsNtTeWkTaf49ypU6c62x5WVFTQqVOnNuyRtCWn\n08nGjRu57777iIiIoLy8XPnwY3l5eZw4cYLs7GwqKysxmUyMHj1amfBznTp1wmHkDwwAAAFwSURB\nVGKxEB4eDkD37t1xuVzKhZ/Ly8vDarUSEhICQLdu3SgtLVUuBDCuNzt37kx1dXWzMtLmhbPVauX8\n+fNUVlbidDopKyvzzHMV/+J2u9myZQsJCQnEx8cDyoe/mzhxIhMnTgSuPi0fEhLCHXfcwapVq5QJ\nP2a1Wrl06RKXL18mODiY4uJixo0bR2ZmpnLhxyIiIsjPz8flcuF2uyksLCQpKUm5EKDhesLlcjWr\nzvCJnQOvLQMCMGnSJPr379/GPZK2cPbsWdauXUtUVJSnbfr06Zw9e1b5EE/hfOedd+o7Qzh27Bh7\n9+6lpqaGYcOGkZSUpFxIneXoRowYUWf5SlAu/MmOHTs4ceIEVVVVdOjQgcmTJ+N0Og2z0JyM+ETh\nLCIiIiLi63zm4UAREREREV+mwllEREREpAlUOIuIiIiINIEKZxERERGRJlDhLCIiIiLSBCqcRURE\nRESaQIWziIiIiEgTqHAWEREREWmC/wd/bGA3WZePOAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16faffe490>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "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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TWr06R7t2HdfSpbmWN8F2zi4ckJ89VfjNcnbg2LtXjiNHVJyaanUpgJGqVZNG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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2aca50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AAKA7ys/PV0ZGRlDXdtsZ4bJ12/RFwliKYAAAALSo2xbC7CgXPHqlzEZ+5iI7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\nCQk8MZwtLQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb0f9590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PcOSGDQovK1PjQw/1yfMBAAAgdPTZfYQzMzP10Ucfqba2Vk1NTTp48KBXE9zX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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb01fa50>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "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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sztmf3DjmmGOOz94WKPWUleP2UVGKvOsu/dy9u/Z26KA2/1uudfV6ZvOnmjo1\nSI0bXx9QXx/HHBsdn70tUOrh2D/HZ/+8b98+SdKQIUPkigu+yUVaWpqGDx+u5OTkc26fNWuWIiIi\ndO+99xZ5DG9yAQDeY9mwQRFDhyrr//5P+QaLDwBQkbj6JhfFjj1MmTJFffv21Z49e9S+fXtt2LCh\n1AWi4vrrT2zAWeTCNcFLlypi+HBlLFxYrhtfcgEj5AKeYCnuzsTERCUmJhreN2rUKK8UBAAw4HQq\n5MUXFbJggWyrV8vRuLGrD9ecOSGKj89X3boOLxUJAIHvgmMP7mDsAQA8yG5X2IQJsnz5pTKWLZOz\nVi2XHp6dLY0ZE65ffw3SwoUZql2bFywDKD9cHXsoduUXAOBnOTmKGDpUppMnZfvgAyk62qWHHzxo\n0t13R6pePYfWrLEpPNxLdQJAGeHyPr+Au5jVghFycX6mU6cU2bu3ZLEoY/lylxvfzZuD1KnTmTeu\nmDcvs0w1vuQCRsgFPIHmFwACkCktTVHx8bI3b67MefOkENffcvinn4I0Y0bgvHEFAAQCZn4BIMCY\nt29XVJ8+yhk6VLm8uBgAisXMLwCUYZbUVEUMGqSsadOU37u3v8sBgHKHsQf4DLNaMEIu/mRduVIR\ngwYpc/58lxvfvDwvFeUn5AJGyAU8geYXAAJAyJw5Cn/0UWWsWKGCdu1ceuy6dRbdcEO0MjO9VBwA\nlCPM/AKAPzkcCpsyRda1a5WxfLkcsbElfqjTKb30UojmzAnVggUZuu46uxcLBYDAxMwvAJQVeXkK\nv/9+Bf3+u2wpKXLGxJT4oSdPmjRqVLiOHDHro4/SeeMKACghxh7gM8xqwUiFzUV6uiL79JEpM1O2\nlStdanzz8qSbb47SpZc69MEHtnLZ+FbYXKBY5AKewMovAPiY6fBhRfbpI/vVVyvrmWekoCCXHh8c\nLL37bobq1HF4qUIAKL+Y+QUAHzLv2qXI229XXv/+ynnwQfHuEwBQOsz8AkCACvr2W0UOGKDsSZOU\n16+fv8sBgAqJmV/4DLNaMFJRcmFNSVFkv37KfOmlEje+Doc0c2aIVq+2erm6wFNRcgHXkAt4Aiu/\nAOBlwW+8obDp05Xx9tuyl3Ak7I8/TBo+PEKnT5v02msZXq4QACoOVn7hM23atPF3CQhA5ToXTqdC\np01T6EsvybZmTYkb32++CVKHDtFq0sSu998vn7s5XEi5zgXcRi7gCaz8AoA3FBQofOxYBf3885k9\nfGvUKNEsKwB0AAAgAElEQVTDkpKCNW1amGbOzFTnzgVeLhIAKh5WfuEzzGrBSLnMRWamIvr3l/ng\nQdlWry5x4ytJrVoVaP369Arf+JbLXKDUyAU8geYXADzIdPy4onr0kLNqVWUsWSJFRrr0+CZNHBVy\nzAEAfIV9fgHAQ8x7957Zw7dHD+VMnMgevgDgA67u88vKLwB4QND33yuqSxflDhumnEcfvWDje+yY\nSa+/Huyj6gAAZ9H8wmeY1YKR8pALy4YNirz9dmU984xyBw++4PmpqRZ16BCttDSznEw4GCoPuYDn\nkQt4Ars9AEApBC9dqrDERGUsXCj7ddcVe67dLs2YEarXXw/RrFmZuummiv2iNgDwB2Z+AcAdTqdC\nXnxRIQsWKGPZMjkaNy729OPHTbrvvggVFEivvpqpiy9myRcAPMHVmV9WfgHAVXa7wsaPl+Xrr2Vb\nu1bOWrUu+JDgYKc6dszX8OG5svDMCwB+w8wvfIZZLRgpc7nIyVHEoEEK2rFDtjVrStT4SlJ0tHT/\n/TS+JVXmcgGfIBfwBJpfACgh06lTiuzdW7JYlLF8+ZmOFgBQptD8wmd4T3YYKSu5MKWlKSo+Xvbm\nzZU5b54UEnLec7/6yqKcHB8WVw6VlVzAt8gFPIHmFwAuwLx9u6Lj45Xbv7+yn3pKMhs/daanS2PG\nhGvo0Ajt2cPTKwAEIp6d4TPMasFIoOfCkpqqqJ49lTV5snJHjjzveevWWdS6dSWZTNKXX57WP/7h\n8GGV5U+g5wL+QS7gCbz0AgDOw7pqlcLHjVPm/PkqaNfO8Jy8vDOrvV9/bdGsWZlq3569ewEgkLHP\nLwAYCJk7V6EzZyrj7bdlb9r0vOc5ndLChcG69dY8RUb6sEAAgCT2+QWA0nE4FDZliqxr18q2dq0c\nF3hCNZmkAQPyfFQcAKC0mPmFzzCrBSMBlYu8PIUPHy7Lxo2ypaRcsPGF9wRULhAwyAU8geYXACQp\nPV2RffrIlJkp28qVcsbEnHP34cMmDR4cod27edoEgLKMZ3H4DPszwkgg5MJ0+LCiEhLkqF9fmUlJ\nUlhY4X1Op7RkSbDatYtW/fp2XXIJuzj4QiDkAoGHXMATmPkFUKGZd+1S5O23K+/uu5UzduyZId7/\nSUsz6d//jtDRoya9806GmjWz+7FSAIAnsPILn2FWC0b8mYugb79VVEKCcv7zH+U8+OA5jW92ttSl\nS5SuvbZA69fbaHx9jOcLGCEX8IRiV36nT5+u9957TzExMUpOTtaRI0c0ZswY2Ww2BQcH66GHHtIN\nN9zgq1oBwGOsKSkKHz1ambNnq6BTpyL3h4VJqanpio72Q3EAAK8pdp/frVu3ymq1avz48UpOTtYf\nf/yh48ePq1GjRjp48KD69u2rzz//vMjj2OcXQCALfuMNhU2froxFi2TnuQoAyjSP7vPbokULpaWl\nFR5XrVpVVatWlSTVqlVL+fn5ys/Pl9VqdbNcAPAhp1OhTz+t4HfekW3NGjnq15ckHThgUq1azr9O\nPQAAyim3Z36/+OILXXHFFTS+KDFmtWDEZ7koKFD46NGyrl9/Zg/f+vVVUCDNnBmi9u2j2cIswPB8\nASPkAp7g1m4Px44d0zPPPKOXX375vOeMGDFCsbGxkqRKlSopLi6ucIuSs+HluGIdnxUo9XAcGMfb\ntm3z+ucLysnRP+fPl8lu10ePPCL7r78q5nhNPfBAhAoKTurpp7/SZZddFRDfD455vuDYv88XHAf+\n8dk/79u3T5I0ZMgQuaLYmV9JSktL0/Dhw5WcnCxJys3N1b333qsRI0YUFvN3zPwCCBSm48cV2bev\n7I0aKeuFF5Qvq158MVRz54bo0UezNWBAHuMOAFCGeXTm9++cTqfGjx+vbt26nbfxBYBAYd6798we\nvj17KmfCBMlkkiNXOnLEpE8+SVft2sX+7A8AKIeKHXKbMmWK+vbtqz179qh9+/Z6+eWX9dFHH2nZ\nsmXq2bOnevbsqWPHjvmqVpRxf/91JiB5LxdBP/ygqK5dlTtsmHImTizcwzckRHr22Wwa3wDH8wWM\nkAt4QrErv4mJiUpMTDzntpEjR3q1IAAoLcuGDYoYNkxZzz+v/G7d/F0OACCA8PJm+AyjMjDi6VwE\nv/22IoYP13v3LFGHF+9Ubq5HLw8f4fkCRsgFPMGlmV8ACFhOp0JmzpTz5dfVq9J6Hfy0iZ54Iksh\nIf4uDAAQSFj5hc8wqwUjHsmF3a7sfz2iQ8+tUOfwL3Tro/X14Yc2XXedvfTXhl/wfAEj5AKewMov\ngLItJ0cRQ4fK/vtpvfPwh1o5NFRWa76/qwIABKgL7vPrDvb5BeALplOnFNGvn5w1ayrz5ZfFjAMA\nVDyu7vPL2AOAMiUnR8rIkExpaYqKj5e9eXNlzptH4wsAKBGaX/gMs1owUtJcOBzSsmXBuvbaaKW+\n8qui4+OV27+/sp96SjLzVFbe8HwBI+QCnsDML4CA98knFk2eHKaQEGn5yLVqNeNeZU2dqvzevf1d\nGgCgjGHmF0DAysuT7rwzUvv2mTVpUrZudSxXxLhxypw/XwXt2vm7PABAAHB15peVXwABKzhYGjEi\nR+3aFShywVyFzpypjBUrZG/a1N+lAQDKKAbl4DPMasHIhXJx0415in4yUSELFsi2di2NbwXB8wWM\nkAt4As0vAL/LyZE+/tjgF1F5eQofPlyWjRtlW7tWDhd+rQUAgBGaX/gM78mOv7PbpYMHO+raa6OV\nlBQi+1/fkC09XZF9+siUlSXbypVyVqnitzrhezxfwAi5gCcw8wvA544dM+mtt0L0xhvBuvhip+bM\nydL11xcU3m86fFiRffrIfvXVynrmGSkoyI/VAgDKE1Z+4TPMauGsl18O1e7dZr3xRqYefTTlnMbX\nvGuXom65RfnduyvruedofCsoni9ghFzAE1j5BeBziYnZhX/+679lQd9+q8gBA5T92GPKu+suP1QG\nACjv2OcXgFds327Whg1WjRqVW6LzrSkpCh89WpmzZ6ugUycvVwcAKC9c3eeXsQcAHpOXJ737rlVd\nu0bqttuiZLOZzn0R23kEv/GGwseOVcbSpTS+AACvovmFzzCrVb698kqImjWrpDffDNG//pWrH344\nrfHjc4of2XU6dXTECIW+9JJsa9bIzm+M8D88X8AIuYAnMPMLwCMuv9yu1attatTIUbIHFBQofOxY\nXbR5s2xr18pZvbp3CwQAQMz8AnCR3e6BDRgyMxUxeLBMdrsyXn9dioz0SG0AgIqHmV8AHud0St99\nF6SRI8MVHx9VqmuZjh9XVI8eclatqozFi2l8AQA+RfMLn2FWq+zJypIWLgxWx45Ruu++CDVqZNeS\nJRluX8+8d6+i4uOVf+ONypo1S7JayQUMkQsYIRfwBGZ+AZxXnz6RiopyauLEbHXsWCBzKX5cDvr+\ne0XedZeyH3pIeYMGea5IAABcwMwvADkcMmxsc3OlkJDSX9+yYYMihg1T1vPPK79bt9JfEACA/3F1\n5peVX6ACSk+XvvrKqs8+s+iLLyzq3Dlfjz2WU+Q8TzS+wUuXKiwxURlvvin7ddeV/oIAAJQCM7/w\nGWa1/G/LliB16hSlpk0ra+7cEFWv7tQLL2RpwoSijW+pOZ0KeeEFhU6bJtt775238SUXMEIuYIRc\nwBNY+QXKIadTMpmK3l67tkOPPZatVq0KFBrqxQLsdoWNHy/L11/LlpIiZ61aXvxkAACUHDO/QDng\ncEjbtwcVjjHs2hWkzZvTDRtgr8vJUcTQoTKdOqWMhQul6Gg/FAEAqCiY+QUqEKdTGj48XB9/bFXl\nyk61a1egvn3z1LZtgV8aX9OpU4ro10/OmjWVsWyZZ4aGAQDwIGZ+4TPMarkvJ0fKyyt6u8kk9e6d\np08+SdemTemaMSNLPXvmq2pVj/9C54JMaWmKio+XvXlzZc6bV+LGl1zACLmAEXIBT2DlF/CT883l\nzpsXotRUi44dM+nYMbOOHjUrN1dasiRDN95YUOT8Tp2K3uZr5u3bFdWnj3KGDVPuyJH+LgcAgPNi\n5hfwsnfesSo11VrYzJ7976xZmerZM7/I+Rs2WHT6tEk1ajhVvbpDNWo4VamS0z/zuyVgSU1VxKBB\nypo2Tfm9e/u7HABABcPML+BleXnSjz8GadMmizZtsmjv3jOrs489lq077ig6mxAVJV15ZYGqVz/T\nzJ79b2Sk8fU7dvT/Sm5JWVeuVPjDDytz/nwVtGvn73IAALggml/4TGpqqtq0aePvMkrt2WdD9eGH\nVrVqZVfnzvlq0MCuiy5yqkYNh+H5N99cdHW3PAiZM0ehL72kjBUrZG/a1O3rlJdcwLPIBYyQC3gC\nzS/wFwUFZ7YM27TJosqVHerdu2jjOmFCjiZO9MKbQpQVDofCpkyRde1a2daulcOFXzUBAOBvNL/w\nmUD9aT0tzaSkpBB9+61FW7daVKuWQ61aFahbN+OV3ECdvfWJvDyF33+/gn7//cybV8TElPqSgZoL\n+Be5gBFyAU+g+UWFcb7dFez2MzeOGpWjq6+2q0oV328TViakpyty4EA5IyJkW7lSCgvzd0UAALiM\nfX7hM77enzE9XfrkE4ueeSZUt90WqWuuiZbToK+99FKHJk7MUadOBTS+52E6fFhRCQly1K+vzKQk\njza+7NsJI+QCRsgFPKHY5nf69Olq3bq1EhISCm/74IMPdPPNN+vmm2/WJ5984vUCAVfl5UkdO0bp\niisq69lnQ5WVZdK99+ZqzRpbxR5ZcJN51y5F3XKL8rt3V9Zzz0lBQf4uCQAAtxW7z+/WrVtltVo1\nfvx4JScnKy8vT/Hx8Vq+fLlyc3M1YMAArVu3rsjj2OcX/rZrl1mXXupQcLC/Kynbgr79VpEDBih7\n0iTl9evn73IAACjC1X1+i135bdGihSpXrlx4/OOPP+ryyy9XTEyMLr74YtWsWVM7duxwv1qgFNLS\nTNq1yzjCl19O41ta1pQURfbrp8yXXqLxBQCUGy7N/B47dkzVq1fX0qVLlZKSourVq+vo0aPeqg3l\njCdmtQoKpLVrrerbN0Lt2kXrm294zaY3BL/xhsLHjlXG22+roFMnr34uZvhghFzACLmAJ7jVOfTt\n21eStG7dOpnOM0Q5YsQIxcbGSpIqVaqkuLi4wi1KzoaX44p1fJY7j8/MtGjr1g56660QRUae1i23\n/FevvXapIiIC5+srF8dOp46OHKnan34q25o1ctSv7/XPv23btsD5+jkOmOOzAqUejgPjmOcLjs9K\nTU3Vvn37JElDhgyRK4qd+ZWktLQ0DR8+XMnJyfruu+80b948zZkzR5J09913a+LEiWrcuPE5j2Hm\nF56WmSk98USY+vfPU9Omdn+XUz4VFCh87FgF/fyzMpYskbNGDX9XBADABbk682tx5eJxcXHatWuX\nTpw4odzcXB05cqRI4wt4Q0SE9PTT2f4uo/zKzFTE4MEy2e2yrV4tRUb6uyIAALyi2JnfKVOmqG/f\nvtqzZ4/at2+v1NRUPfjgg7rzzjt1zz33aMKECb6qE+XA33+d+Vd2u7RunUX9+kXo3XetPqwKpuPH\nFdWjh5xVqypj8WKfN77F5QIVF7mAEXIBTyh25TcxMVGJiYlFbu/SpYvXCkLFcuiQSW+9FaKFC4NV\nvbpTAwfm6uab8/1dVoVh3rtXkbffrrwePZQzcWIFf+9mAEBFcMGZX3cw84uS2Lw5SLffHqlevfI1\ncGCurrySWV5fCvr+e0XedZdyHnxQuYMH+7scAADc4tWZX8CTmje368cfTysqyt+VVDyWDRsUMWyY\nsp5/Xvnduvm7HAAAfMalfX4Bd2RmStnZRWe1LBbR+PpB8NKlihg+XBlvvhkQjS8zfDBCLmCEXMAT\naH7hVR9+aNUNN0QrJYUXsfmd06mQF15Q6NSpsq1eLft11/m7IgAAfI6xB3jFwYMmjR8frp9/DtLM\nmVlq375AUht/l1Vx2e0KmzBBlq++km3tWjlr1fJ3RYXObl4O/BW5gBFyAU9g5Rce5XRKr74aovbt\no9W4sV2pqen/a3zhNzk5ihg0SEG//CLbmjUB1fgCAOBrNL/wKJNJOnXKpDVrbBo/PkehoX/ex6yW\n75lOnVJk796SxaKM5cul6Gh/l1QEuYARcgEj5AKeQPMLjxs3LkcNGzr8XUaFZ0pLU1R8vOzNmytz\n3jwpJMTfJQEA4Hfs8wuUQ+bt2xXVp49yhg1T7siR/i4HAACvcXWfX1Z+4Za0NJPuuSdCu3YRoUBj\nSU1VVM+eypo8mcYXAIC/oXOBSwoKpNmzQ9ShQ7SaNLErNrbk4w3ManmfddUqRQwapMz585Xfu7e/\nyykRcgEj5AJGyAU8ga3OUGJbtgTp3/8OV5UqTq1da1ODBsz1BpKQuXMVOnOmMlaskL1pU3+XAwBA\nQGLmFyWSni7deGO0xo3L0R135Mlk8ndFKORwKGzKFFnXrlXGO+/I4cLcEwAAZZ2rM7+s/KJEoqOl\njRvTZSExgSUvT+H336+g33+XLSVFzpgYf1cEAEBAY+YXJVbaxpdZLQ9LT1dknz4yZWbKtnJlmW18\nyQWMkAsYIRfwBJpfnCM/X3r3XaucHh+GgSeZDh9WVEKCHPXrKzMpSQoL83dJAACUCTS/KLRpU5A6\ndozSokUhysjw/PV5T3bPMO/apahbblF+9+7Keu45KSjI3yWVCrmAEXIBI+QCnsAEJ3T6tElPPBGq\nDz4I1hNPZOnWW/N5QVuACtq0SZF3363sSZOU16+fv8sBAKDMofmt4Pav+F5Tx+XpqqsL9OT0PEVG\nOqVPvfO5fvrpJzVlCy63mffvV9iTTypz9mwVdOrk73I8JjU1ldUcFEEuYIRcwBNofisqp1OhTz2l\nK5Yu1ey6DRWd65QWePdTNjh1SqEbNnj3k5RnVqsyli6VnW0EAQBwG81vRZSfr/AxYxS0c6dsn34q\nc7Vq8sKIbxEWySefB2ULqzgwQi5ghFzAE2h+K5qMDEXee69kNsu2erUUEeHvigAAAHyG3R4qkD9+\nOa6wrj3kqFlTGYsW+bzxZX9GGCEXMEIuYIRcwBNofiuIA5/tlaV9vH685GZlzZxZ+nesAAAAKINM\nO3fu9PjbGezfv18teVFOwNi1+Htd+sBd2nbreF316t3+LgcAAMBjtmzZojp16pT4fFZ+y7ltz2xQ\n/fvv0I7R/0fjCwAAKjya33Ls4FNL1PiZkfrvjCVqNulmf5fDrBYMkQsYIRcwQi7gCQx+lkdOp0Jn\nzFDj5W/pvyuT1ahtA39XBAAAEBCY+S1v7HaFjxunoE2blLFsmZw1a/q7IgAAAK9xdeaXld/yJDtb\nEf/6l0wZGbK9/74UHe3vigAAAAIKM7/lxKnfTiqkWy85w8KU8fbbAdn4MqsFI+QCRsgFjJALeALN\nbzlweGOaHDd01baoG5Q1Z44UHOzvkgAAAAISM79l3O6V23XxfX20vctoXfXmEH+XAwAA4FPs81uB\nbJ/1pWKH9NLOf02l8QUAACgBmt8y6uiLK9QwcZB2PfmGmk9N8Hc5JcKsFoyQCxghFzBCLuAJ7PZQ\nBoXMmqUG8+bot+Ur9Y+OTfxdDgAAQJnBzG9Z4nAobNIkWTdskG35cjlr1/Z3RQAAAH7FPr/lVW6u\nIkaMkOnQIdk++EDOKlX8XREAAECZ4/bM76xZs9S1a1d17dpVs2bN8mRN+BtbWrqs3W+X8vOVsWJF\nmW18mdWCEXIBI+QCRsgFPMGt5nf//v1avXq1kpOTtWrVKq1atUoHDhzwdG2QdHTrIWW36qafnFco\n8/XXpdBQf5cEAABQZrnV/EZGRspisSgnJ0e5ubmyWq2KiorydG0V3u8f7lJ45y7a3+Z2NVw7VQoK\n8ndJpdKmTRt/l4AARC5ghFzACLmAJ7g181ulShUNGDBAHTp0kMPh0MMPP6zoAHw73bJs52vf6rJx\nA7RtwJO66v9u83c5AAAA5YJbK79paWlaunSpNmzYoHXr1um1117TsWPHPF1bhXXitTVqMK6/dk6c\noxblqPFlVgtGyAWMkAsYIRfwBLdWfn/88UfFxcUpMjJSktSkSRNt375d7du3LzxnxIgRio2NlSRV\nqlRJcXFxhb+uOBtejoseh7z2mi6ZNk0fTXpcbcd08Hs9njw+K1Dq4Tgwjrdt2xZQ9XAcGMdnBUo9\nHAfGMc8XHJ+Vmpqqffv2SZKGDBkiV7i1z++2bdv06KOPavny5XI4HOrRo4deeeUV1a9fXxL7/LrF\n6VToU08pePVqZSxfLkfduv6uCAAAIOD5ZJ/fuLg4derUSb169ZIk3XHHHYWNL9yQn6/wMWMUtHOn\nbCkpclar5u+KAAAAyiW39/kdNWqU1qxZozVr1mjw4MGerKlCyTySIXPPu2T64w/ZVq8u143v33+d\nCUjkAsbIBYyQC3iC280vSu/EL8eU3rKndqRfosy33pIiIvxdEgAAQLnm1szvhTDze2EHPturyNtv\n13+vuUMt33tIJrPJ3yUBAACUOa7O/LLy6we7Fn2v6r276L+9Ruuq9/9D4wsAAOAjNL8+lv72etV/\n4A7tGPOCrprb39/l+BSzWjBCLmCEXMAIuYAnuLXbA9wTvGiR6jzxhPYuXKRmXVr5uxwAAIAKh5lf\nX3A6FTpjhoLfeuvMHr6XX+7vigAAAMoFn+zzCxfY7QofN05BmzfLtnatnDVr+rsiAACACouZXy/K\nPpEt9R4o8+7dsiUnV/jGl1ktGCEXMEIuYIRcwBNY+fWSU7+dVPqN/ZVTM1YNUxdIwcH+LgkAAKDC\nY+bXCw5vTFNw9zu0Jy5eLdZOlNnCAjsAAIA3sM+vn+1Z+bMqdY3X7s6DdNX6STS+AAAAAYTOzIOy\n13yh2CG3aue/purqhUP8XU7AYVYLRsgFjJALGCEX8ARmfj3E+u67qjR+vPYteF3Ne7T2dzkAAAAw\nwMyvB4TMmqXQOXNkW7ZMjiZN/F0OAABAhcE+v77kcChs0iRZN2xQ+tq1ctau7e+KAAAAUAxmft2U\nm54re59/Kej772VLSaHxLQFmtWCEXMAIuYARcgFPYOXXDba0dB1vO1D26CpqsPFdKTTU3yUBAACg\nBJj5ddHRrYekLn108LLWitvwpIKCg/xdEgAAQIXFPr9e9PuHuxTeuYv2tblDV34+lcYXAACgjKH5\nLaG8Dd/okn4J+vXuR3X18lEymU3+LqnMYVYLRsgFjJALGCEX8ARmfkvA+v77qvTvf+vA3Llq2buj\nv8sBAACAm5j5vYCQ115T6IwZyli8WPbmzf1dDgAAAP6CfX49xelU6FNPKXj1atk++ECOunX9XREA\nAABKiZlfA/lZ+crrd7+sn34qW0oKja+HMKsFI+QCRsgFjJALeAIrv3+TeSRDB1sPkdkapODNq6WI\nCH+XBAAAAA9h5vcv/th+THmd7tTRWs10xRfPyBLKzwYAAACBjH1+3XTgs72ydOiigy1uVrONM2h8\nAQAAyiGaX0n2r79Tjd5d9N9eo3XV+/9hD18vYVYLRsgFjJALGCEX8IQK3/xa1q1TzIC+yps1Q1fN\n7e/vcgAAAOBFFXrmN3jRIoU98YQy3nxT9muu8Xc5AAAAcBH7/JaE06nQGTMU/NZbsiUny3H55f6u\nCAAAAD5Q4cYe7Hl2Zd3zH1mTk2Vbu5bG14eY1YIRcgEj5AJGyAU8oUKt/GafyNbvrYcppCBTYZuT\nZaoU7e+SAAAA4EMVZub31G8nlX5jf6XHXKqGqS8oODLY3yUBAACglNjn18DhjWly3NBVxxpepyab\nZ9H4AgAAVFDlvvl1fv+TqiTEa3fnQbpq/SSZLeX+Sw5YzGrBCLmAEXIBI+QCnlCuO0HL55+r8h23\nyvHsE7p64RB/lwMAAAA/K7czv9Z331X4hAnKXLBABa1b+7UWAAAAeAf7/EoKmTVLoXPmyLZypRxN\nmvi7HAAAAAQIt8cefvjhByUkJKhLly4aM2aMJ2tym6PAofT7Jilk0SKlr11L4xtgmNWCEXIBI+QC\nRsgFPMGtlV+Hw6Fx48Zp2rRpatmypU6ePOnpulyWm56r/7Z+QFG2Q4rakiJTTGV/lwQAAIAA49bK\n708//aSYmJjCud4qVap4tChX2dLSdeDKO2VyFKjG98tofANUmzZt/F0CAhC5gBFyASPkAp7gVvN7\n6NAhRUVFaciQIerVq5cWL17s6bpK7Oj3h5XdKkGnL2mkRltfVWjlUL/VAgAAgMDmVvObm5urLVu2\n6Mknn9TChQuVlJSk/fv3e7q2CzLt2KnIm+O1r83tav75VAUFB/m8BpQcs1owQi5ghFzACLmAJ7g1\n81u9enU1aNBANWvWlCQ1bdpUu3fvPmebiREjRig2NlaSVKlSJcXFxRX+uuJseEtzHLN9u66fMUM5\nTz6unH9coi+/+tKj1+fY88dnBUo9HAfG8bZt2wKqHo4D4/isQKmH48A4vtDzxXfffaewsDBVrnxm\n/PH06dOSzvQhHJft45CQEP3yyy86KzU1Vfv27ZMkDRkyRK5wa59fm82mrl27Kjk5WWFhYerdu7dm\nzpypevXqSfL+Pr/W999X+L//rcy5c1XQsaPXPg8AACgbMjIylJubq6pVq/q7FHjBH3/8oZCQEEVG\nRha5zyf7/EZFRWnChAkaOHCgCgoKlJCQUNj4elvwggUKmzFDGcuXy968uU8+JwAACGynT59WrVq1\n/F0GvCQmJkYHDx40bH5d5fY+v7fccotWrVql999/X0OHDi11IRfidDh1csRTCn3lFdnWrKHxLYP+\n/utMQCIXMEYuYKS4XJhMJplMJh9WA1/y5N+vWyu/vpafla9f2j6oqkd36uSmFAXVrObvkgAAAFAG\nub3y6yuZRzK098oBCs34Q1W2rKDxLcPOviAB+CtyASPkAkbKci7mz5+vyy+/XLGxsfr8888Lb3/w\nwQf13HPPnXPuuHHjFBsbq2rVqumzzz7zdanlXkA3vyd2HNfpq3opq/LFqv9DksKrR/i7JAAAAJfk\n58w4YvIAAA8eSURBVOcrMTFRq1ev1r59+9SuXbvC+2bMmKGHHnronPOfeeYZ7du3T7Vr1z7vr/oT\nEhK0cOFCr9ZdXgVs82v6bbeCb4zXweY3q9nGGbKElokJDRSDGT4YIRcwQi5gpKzm4siRI8rJyVGj\nRo08dk3mm90XkM1v0HffKbpbV4U8OkpXv/+QTGb+ggEAQNlz/fXX6/rrr5ck1atXr3Ds4aOPPlJs\nbKwuuugiPfXUUyW+3vPPP6/Y2Fh9/fXXevjhhxUbG6ubbrqp8P6TJ09q6NChaty4sVq0aKE333zz\nnMePHDlS48eP14ABAxQbG6srr7xSGRkZnvliy4iAW061rFuniBEjlDVzpqzx8f4uBx5Ulme14D3k\nAkbIBYyUxVx8/fXX2r9/v5o3b669e/fKbP5z3XHfvn0aOXKkS6u4Y8eO1dixY9W9e3fdcccd6t+/\n/zn3Dxs2TDVq1NAPP/ygQ4cOqWvXrmrWrJma/2WXrGXLlumVV15RUlKSfv75Z1ksAdcOelVAfbXB\nixYp7IknlLFokezXXOPvcgAAAErN6Sz+/cQudH9JH3f48GF9/PHH+u233xQSEqK6desqISFBa9as\nOaf5bdu2rTp37izpzLv0VjQBMfbgdDh1bPTzCn3uOdmSk2l8y6myOqsF7yIXMEIuYKQ0uXj66VDF\nxFQp8vH006ElPv985/rL31eMDxw4IElq3ry56tWrp3r16mnx4sU6duzYOedddtllPqsxEPl95dee\nZ9e29hN08e/f6o9vUmSNrenvkgAAQDnzyCM5euSRHK+dXxrnG3sIDg6W3W43vO+v4xNnXXLJJQoN\nDdXu3buLHaUwemxF4tevPuuPbP165WBFHdmt8E2raXzLubI4qwXvIxcwQi5gpLzm4nxjDw0aNNBX\nX31leF+NGjW0ffv2c26rWbOmbrjhBk2ePFmZmZnKz8/Xxo0b9fPPP3u85rLMb83vqd9O6niL22QP\nCVedHxcp6pJof5UCAADgVX9fib311lsVGxurd955Ry+99JJiY2M1atSoc86ZOHGikpOTVadOHT32\n2GPn3Ddy5Eh9+umnuuKKK9SjR4/C2+fOnavjx4+rVatWatiwoZ544okiq8cVfZs0086dO92bsi7G\n/v371bJly/Peb96/X6eu///27jUmyjPv4/hvYBAWhsNiYznIOFWxKBS1T8HUpn1hG4K00KxJt0s0\nGmGTklCealuJpYftttSEN41ttCs1KU1biMEUYu0BSWtPxlZTecQqeUythWmhUFSa4WBhBmdfNMwq\n3riCMwPT+X7emHtu5r4vhl/++XN5cV9/1Xdp92t5U4VCzME9/R4sDh069If9rR1TRy5ghFzAyLVy\n0dXVpaSkJD+PCP400c+4paVFKSkp130dv3edoSdPKjo3V1FPbNT/fPwMjS8AAAD8xq9/8Gb+4gtF\n/f3vGqqqUuhf/uLPW2MGYBYHRsgFjJALGCEX8Aa/Nb9h776ryIoKDdbUyHXXXf66LQAAAODhlzUH\n3Vv+pch//EP9jY00vkGM53bCCLmAEXIBI+QC3uDTmd9Lrks6ft8/Zf3/T9T9RZP+tGiuL28HAAAA\nXJPPmt9hx7DO3PW/mu34WbOOfKA/zYv11a0QIFirBSPkAkbIBYyQC3iDz5rfrqV/kykyXje31isi\nbmZtBwgAAIDg5LM1v78mL9at//c6jS88WKsFI+QCRsgFjJALeIPPZn6XffGSTCHBvYMIAAAAZhaf\nzfzS+GI81mrBCLmAEXIBI+Tij2v27Nlqb2/3y73YXg0AAADTxu12X/Gvr9H8wm9YqwUj5AJGyAWM\nBGIu6urqtGrVKqWnp6uoqEiFhYVavHix2tradOnSJVVVVWnZsmVKS0vT1q1b5XK5JEkdHR168MEH\nNX/+fM2bN08bN26Uw+HwXPfAgQPKzs6W1WpVVlaWDh486Dm3dOlSff75557j8bOqpaWleuqpp7R+\n/XpZrVYtXbpUAwMDkqT9+/dr5cqVmj9/vh5++GH19PR43pOfn69Fixbpueee04oVK7Rq1SpdvHhR\nktTX16dHHnlEaWlpWr58ud56660r7ldWVqa8vDxZrVaVlZV5zj300EOaN2+eJOmee+6R1WrV008/\n7a2P3xDNLwAAgA+Fh4frq6++UlNTk4qLi7Vu3To1NjZqx44dOnDggJqamvTNN9/o9OnTqq6uliSN\njIxow4YNOnnypE6ePKm+vj5VVVV5rrlp0yZVVFTIbreroaFBiYmJnnMmk0km07WXn9bX12vdunXq\n6OhQbW2tzGazjh07pscee0w7d+7UmTNnlJmZqc2bN3ves2LFCu3atUu7d+9Wc3OzIiIidPToUUlS\nSUmJZs2apdbWVjU2NqqqqkrHjx/3vPezzz7T7t27dfjwYe3bt08tLS2SpL1798put0uSvvzyS9nt\ndr300ks3+IlfG80v/Ia1WjBCLmCEXMBIoObilltuUUxMjOLj47Vw4UJZrVb19vaqtrZWW7ZsUUJC\ngiwWi4qLi/X+++9LklJTU7VmzRpFRkYqOjpaBQUFOnXqlOeaISEh+uGHH+RwOJSSkqLFixdPakx3\n3323cnJyZDKZlJGRoYiICL3zzjsqLCzU8uXLFRISotLSUjU3N2tkZMTzfdhsNt10002KjY2V1WrV\nuXPn1N3drU8++USVlZUKDw+XzWZTfn6+PvjgA8/9Vq9ereTkZM2dO1dLlizR999/74VPdmp8usMb\nAADATPDn+HivXKfvwoVJv2dsFtZsNis0NFRms1kul0udnZ0qKSlRSMjvc5GXLl1SQkKCJKm3t1db\nt27V119/raGhITmdTi1btsxzzZqaGm3fvl2vvvqqUlNT9corr0yqAV6wYMFVr3V2durw4cOqq6vz\nvBYeHu5Z+jA29tDQUM+x0+lUV1eXJF0xvtHRUa1Zs8ZzHBv7n83OZs2apeHh4eseq7fR/MJvDh06\nFLC/tcN3yAWMkAsYuZFcTKVp9SW3263k5GTt3LlTd9xxx1XnX3jhBYWGhurIkSOyWCyqrq7Wvn37\nPOezs7NVV1enkZERbd68Wdu2bdPbb78t6feGdWzt8OXrhC831nBfbu7cuXryySe1adOmSX0vycnJ\nioiI0NmzZ//rcouJTPV9U8GyBwAAAD8ae6rB2rVrtW3bNnV3d8vtduvMmTP69NNPJUmDg4OyWCyK\njIxUR0eH3nzzzSveX19fr4GBAU/TGBMT4zm/YMECHTt2TJL03nvvXfe4CgsLVVNToxMnTsjtdqu3\nt1eNjY1XjXu8m2++WStXrtTzzz+vwcFBOZ1OHTly5IplGhN9Bpdfo62t7brHeiNofuE3zOLACLmA\nEXIBI4GYi/F/fDZ2bDKZVFpaqjvvvFN5eXmy2WzasGGDzp8/L0kqLy/X8ePHZbPZVFxcrNWrV3uu\n43a7tXfvXt12221KTU1VT0/PFU9I2LJli+rr63Xfffepp6fHcFbV6LWsrCxVVlbq0Ucflc1m0733\n3qsTJ04Yjn286upqnTt3TllZWVq0aJFefPFFjY6OTni/8cfPPPOMysvLlZ6ersrKymt+pjfKdPr0\naa8/VO3HH3/U7bff7u3LAgAAGOrq6lJSUtJ0DwM+NNHPuKWlRSkpKdd9HWZ+4TeB+HxG+B65gBFy\nASPkAt5A8wsAAICgQfMLvwnEtVrwPXIBI+QCRsgFvIHmFwAAAEGD5hd+w1otGCEXMEIuYIRcwBto\nfgEAQMBzu90TPocWgc+bP18edQYAAALewMCAhoeHNXv27OkeCnzg/PnzCg8Pl8ViuercZB91xvbG\nAAAg4FksFg0PD6urq2u6hwIfmKjxnYopN78DAwPKzc1VUVGRioqKvDIY/LHdyJ7s+OMiFzBCLmDk\nv+WCWV9cjymv+d21a5cyMjIMt7gDjHR3d0/3EDADkQsYIRcwQi7gDVNqfs+ePasLFy4oIyODxeW4\nbuHh4dM9BMxA5AJGyAWMkAt4w5Sa35dfflllZWXeHgsAAADgU5Nufg8ePCibzabExERmfTEpdrt9\nuoeAGYhcwAi5gBFyAW+Y9KPOtm/frg8//FChoaHq6+tTSEiIKioq9MADD3i+pq2tTdHR0V4fLAAA\nAHC5/v5+LVmy5Lq//oae87tjxw5FRUVp48aNU70EAAAA4Dfs8AYAAICg4ZMd3gAAAICZiJlfAAAA\nBA2aXwAAAASNKW9vPJFvv/1WH3/8sUwmk3Jzc5WWlubtWyAAPfvss0pISJAk2Ww23X///dM8IkyH\njz76SK2trYqKivI8K5yaAaNcUDPgcDi0Z88e/fbbbzKbzcrJydHChQupGUFuolxMpmZ4tfl1uVxq\nbm5WSUmJnE6n3njjDUIJSVJYWJhKS0unexiYZunp6crMzFRDQ4MkagZ+Nz4XEjUDUkhIiAoKCpSQ\nkKBff/1Vr7/+up544glqRpAzykV5efmkaoZXlz389NNPmjNnjqKiohQXF6fY2Fj9/PPP3rwFgABm\ntVoVGRnpOaZmQLo6F4AkWSwWz0xeXFycRkdHZbfbqRlBzigXLpdrUtfw6szvwMCAoqOjdfToUUVG\nRspisai/v1+JiYnevA0CkMvl0muvveb5LwqbzTbdQ8IMQM3ARKgZuNx3332npKQkDQ4OUjPgMZYL\ns9k8qZrh9TW/kpSdnS1JOnXqlEwmky9ugQBTXl4ui8Wizs5O1dbW6vHHH5fZ7JP4IQBRMzAeNQNj\n+vv71dTUpLVr16qrq0sSNQNX5kKaXM3w6rKH6Oho9ff3e47HZnUAi8UiSUpOTlZMTIz6+vqmeUSY\nCagZmAg1A5LkdDq1Z88e5ebmKj4+npoBSVfnQppczfDqr9HJycn65ZdfNDg4KKfTKYfD4VmXgeB1\n8eJFmc1mhYWFqa+vTw6HQ3FxcdM9LMwA1AwYGRoaUlhYGDUjyLndbjU0NCgzM1OpqamSqBkwzsVk\n+wyv7/A29ggSScrLy9Ott97qzcsjANntdjU0NMhsNstkMiknJ8cTWASX/fv3q62tTUNDQ4qKilJB\nQYGcTic1I8iNz0VWVpZaW1upGUGuvb1dNTU1mjNnjue19evXq729nZoRxIxykZ+fP6k+g+2NAQAA\nEDTY4Q0AAABBg+YXAAAAQYPmFwAAAEGD5hcAAABBg+YXAAAAQYPmFwAAAEGD5hcAAABBg+YXAAAA\nQePf33zTqby1620AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2c1a10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+X4mnooy7WK2y3Huv9vbpoyNdu6rTfyvcrVu3avr069S9e5CmTMnUF1/4RryM\nGbtjfPE+X4mHsXfGF/+elJQkSRo5cqRKw3TgwIFil3CTk5M1ZswYJSQkFLg/Pj5eYWFheuCBBwqd\nc/ToUXXo0KFUgQAASsZ/yxaFjRql9JdfVo7B4kNKiknVq7tY8QVQJezcuVONGzcu8fxi2x6mTZum\nwYMH6/Dhw+rSpYu2bNly2QGi6vr9b2zAReRF6QSuWKGwMWNkX7rUsPCVpBo1Kn7hS17ACHkBd/Av\n7mBcXJzi4uIMjz388MPlEhAAwIDLpaBXX1XQokWyrV8vZ8uW3o4IACqkS7Y9lAVtDwDgRg6HQiZP\nlv8XX8i+apVcDRrkH7pwwaRq1Sr+Si8AlJVb2x4AAF6Wmamw4cPl9+OPsn34YYHCNznZpFtvtWrb\nNj8vBggAFQvFLzyGXi0YIS+KZkpJkaV/f8nfX/bVq6Vq1fKPHT1qVmysVQ8+mKUbbnB4McryQV7A\nCHkBd6D4BQAfZEpOljUmRo527ZT25ptSUFD+saNHzerTx6JRo7I0ZkyWF6MEgIqHnl8A8DHmfftk\nHTRImaNGKesPHy6+WPiOHp2lUaMofAGgtD2/xe72AADwLP+tWxU2fLjSZ85UTv/+hY6bTC498USm\n7r032wvRAUDFR9sDPIZeLRghL/4nYO1ahQ0frrSFCw0LX0lq1MhVJQpf8gJGyAu4Ayu/AOADgubP\nV/Brr8m+Zo0crVt7OxwAqLTo+QUAb3I6FTJtmgI2bZJ99Wo5IyO9HREAVCjs8wsAFUV2tkLHjJH/\ntm2yJSYWKnyPHDHr5ZeDvRQcAFROFL/wGHq1YKTK5kVqqiyDBsmUlibb2rVyhYcXOHz4cN6uDjVr\nOr0UoHdV2bxAscgLuAPFLwB4mOnkSVljY+WMilLakiVSSEiB44cOmdWnj1Xjx2fqL3+p/B9uAwBP\noucXADzIfPCgLAMGKHvoUGVOmCCZTAWOHzpkVt++Vk2YkEHhCwAlwD6/AOCj/L75RpZhw5Qxdaqy\nhwwxnDNhQiiFLwCUI9oe4DH0asFIVcmLgMREWYYMUdprrxVZ+ErSihV2Cl9VnbxA6ZAXcAdWfgGg\nnAUuXqyQWbNkX7lSjku0hAUFeSgoAKii6PkFgPLicin4hRcU+N57eXv4RkV5OyIAqHTo+QUAX5Cb\nq9Dx4+W3d69siYly1a1baMrJkybVq+f642feAADliJ5feAy9WjBSKfMiLU1hQ4fKfPy4bOvXGxa+\nP/1k1u0ax1oaAAAgAElEQVS3V9OOHX5eCND3Vcq8wGUjL+AOFL8A4EamM2dk7dtXrlq1ZH/3Xcli\nKTTnwAGz+vWz6umnM3TddQ4vRAkAVRc9vwDgJuYjR/L28O3bV5lTphTaw1eS9u83q39/q555JkOD\nBrGrAwBcrtL2/LLyCwBu4Pf997L27Kms0aOV+fTThoXvTz+ZddddVsXFUfgCgLdQ/MJj6NWCkcqQ\nF/5btsgyYIDSX3xRWSNGFDmvZk2XXnopXQMHUvheSmXIC7gfeQF3oPgFgMsQuGKFwsaMkX3pUuX0\n7l3s3Dp1XOrVK8dDkQEAjNDzCwBl4XIp6NVXFbRokeyrVsnZsqW3IwKAKol9fgGgvDkcCpk0Sf5f\nfSXbpk1yNWjg7YgAACVE2wM8hl4tGKlweZGZqbDhw+W3f79sGzcWWfju3eunZ58N9nBwlUeFywt4\nBHkBd6D4BYASMqWkyNK/v+TvL/vq1VK1aobz9u710913WxQdzR6+AOBr6PkFgBIwJSfLOmCAcm67\nTRnTp0tm47WDXbv8NGiQRTNnpqtfPz7cBgDljX1+AcDNzPv2qVpMjLKGDlXG888XWfju2OGngQMt\nmj2bwhcAfBXFLzyGXi0Y8fW88N+6VdY771T63/+urIceKnKeyyXNnBmiefPS1bs3he/l8vW8gHeQ\nF3AHdnsAgCIErFun0IkTlbZwoXI7dy52rskkrV5tL2pRGADgI+j5BQADQQsWKHjePNlXrpSjdWtv\nhwMAKAL7/ALA5XA6FTJtmgI2bZJt0yY5S3FBBQD4Pt6gg8fQqwUjPpUX2dkKHTNG/tu2yZaYWGzh\nu2OHnxzsZFZufCov4DPIC7gDxS8ASFJqqiyDBsmUlibb2rVyhYcXOXXNmgANHWrR0aNcQgGgoqHn\nF0CVZzp5UpZBg+S49lqlv/ii5OdX5NyVKwM1bVqI3nvPplatnB6MEgBghH1+AaAUzAcPytqjh3L6\n9FH67NnFFr5Llwbq2WdDtHYthS8AVFQUv/AYerVgxJt54ffNN7LGxirziSeUOWFC3n5lRVi3LkAv\nvRSsDRtsatGCwre8cb2AEfIC7lBs8Ttr1izdfPPNio2NlST99ttvuueee9S7d2/ddddd+vLLLz0S\nJAC4W0BioixDhyrttdeUPWTIJeffemuuPvjAriuvpPAFgIqs2J7f7777TgEBAZo0aZISEhJ09uxZ\nnTlzRi1atNDx48c1ePBgffbZZ4XOo+cXgC8LXLxYIbNmyb58uRxcqwCgQnPrPr/t27dXcnJy/rhW\nrVqqVauWJKlBgwbKyclRTk6OAgICyhguAHiQy6XgF15Q4HvvybZxo5xRUd6OCADgYWXu+f388891\n9dVXU/iixOjVghGP5UVurkLHjVPAxx/n7eFbTOHrcok9fL2M6wWMkBdwhzJ9w9vp06f14osv6p//\n/GeRc8aOHavIyEhJUvXq1RUdHa1OnTpJ+l/yMq5a44t8JR7GvjHes2dPuT+fX2am/rxwoUwOhz56\n6ik5fvpJnerWNZz/+edbtWhRKzVr1kBTpmR6/edTVccX+Uo8jH1j7InrBWPfH1/8e1JSkiRp5MiR\nKo1L7vObnJysMWPGKCEhQZKUlZWlBx54QGPHjs0P5o/o+QXgK0xnzsgyeLAcLVoo/ZVXpGLerXI6\npSefDNF33/lr9Wq7atZ0+zboAAA3K9d9fl0ulyZNmqTevXsXWfgCgK8wHzkia0yMcm69Venx8cUW\nvg6H9Nhjodqzx19r1tgofAGgkiq2+J02bZoGDx6sw4cPq0uXLvrnP/+pjz76SKtWrdKdd96pO++8\nU6dPn/ZUrKjg/vh2JiCVX1747dola69eyho9WplTphS7h29urvTww6E6dMis996zqVq1cgkJpcD1\nAkbIC7iDf3EH4+LiFBcXV+C+hx56qFwDAoDL5b9li8JGj1b63LnK6d37kvOzsqQ6dVyaM8eu0FAP\nBAgA8JpL9vyWBT2/ALwlcOVKhTzzjOxLlshxww3eDgcAUM7cus8vAFQYLpeC5s1T0KJFsq1fL2fL\nlt6OCADgg8q8zy9QWvRqwYhb8sLhUMhTT+V9eUViIoVvJcD1AkbIC7gDxS+Aii0zU2HDh8tv/37Z\nNm6Uq0GDYqfb7dKLLwYrJ8dD8QEAfArFLzyG7fFg5HLywpSSIkv//pK/v+yrVulS2zSkpkoDBliV\nnGyWmaufT+N6ASPkBdyByz+ACsmUnCxrTIwc7dop7c03paCgYudfuGBS//5WXX11rl55JV1+fh4K\nFADgUyh+4TH0asFIWfLCvG+fqsXEKGvoUGU8/7wutYybnGxSz55WdeyYq5deymDVtwLgegEj5AXc\ngd0eAFQo/lu3KmzECKXPmKGc/v1LdM6MGSEaPDhLDz+cVdx3XQAAqgD2+QVQYQSsW6fQiROVtnCh\ncjt3LvF5DodocwCASop9fgFUSkELFih43jzZ16yRo3XrUp1L4QsAuIjON3gMvVowcsm8cDoVEheX\n9+UVmzaVuvBFxcT1AkbIC7gDxS8A35WdrdAxY+S/bZtsmzbJeYm3tRwOaf78IGVleSg+AECFQ/EL\nj2F/RhgpMi9SU2UZNEim9HTZ1q6Vq2bNYh8nPV26//4w/d//BVD8VgJcL2CEvIA7UPwC8Dmmkydl\njY2VMypKaYsXSyEhxc4/c8akvn2tslhcWrnSfqnvugAAVGEUv/AYerVg5I95YT54UNYePZTTp4/S\nZ8++5KfVDh82q0cPqzp3ztHrr6crMLA8o4WncL2AEfIC7sBuDwB8ht8338gybJgynnlG2ffeW6Jz\nXn01WGPHZmr48Oxyjg4AUBmwzy8AnxCQmKjQceOU9o9/KLdbtxKf53KJL64AgCqMfX4BVDiBixcr\nZNYs2VeskKOUvzhT+AIASoOeX3gMvVooxOXSqbFjFfzaa7Jt3FjqwheVF9cLGCEv4A4UvwC8IzdX\noePGqd6OHXl7+EZFFTs9J0eaMydYaWkeig8AUCnR9gCPYX9G5EtLU9iIETI5HHJt2SJZLMVOT02V\n/vIXi4KC3P4RBfgorhcwQl7AHVj5BeBRpjNnZO3bV65atWR/551LFr4nTpgUG2tVkyZOLV2aprAw\nDwUKAKiUKH7hMfRqwXzkiKwxMcq59Valx8dLAQHF5sX+/Xl7+Pbtm6M5c9Llz3tVVQbXCxghL+AO\n/KcEgEf4ff+9LPfeq4zHH1f28OElOmfx4iBNmpSpwYPZwxcA4B7s8wug3Plv2aKw0aOVPneucnr3\n9nY4AIBKpLT7/NL2AKBcBa5YobAxY2R/+20KXwCA11H8wmPo1apiXC4FvfKKgmfOlG3DBjluuMFw\nGnkBI+QFjJAXcAeKXwDu53Ao5MknFfj++7IlJsrZokWx0zMzpb//PUSpqR6KDwBQZfGBN3gM+zNW\nEZmZChs1SqaUFNk2bpSqVSt2+tVX36K77gpTRIRLQUEeihE+j+sFjJAXcAdWfgG4jSklRZb+/SV/\nf9lXrbpk4fvzz3lbmV1zjUMLF6ZR/AIAyh3FLzyGXq3KzZScLGtMjBzt2intzTd1qUp20aJA9ehh\nVbduezV9eobMXI3wO1wvYIS8gDvQ9gDgspn37ZN10CBljh6trIceKtE5drtJH35o06lTv0oq+RY1\nAABcDvb5BXBZ/LduVdjw4UqfOVM5/ft7OxwAQBVT2n1+WfkFUGYBa9cq9MknlbZwoXI7d/Z2OAAA\nXBJddvAYerUql6D58xX69NOyr1lTbOG7dau/du3yK+Y4eYHCyAsYIS/gDhS/AErH6VRIXJyC/vUv\n2TZtkqN1a8NpmZnS00+HaNSoMNlsJg8HCQCAMdoe4DHsz1gJZGcr9JFH5Pfrr7IlJsoVHm44bfdu\nP40eHaarrnLo889TFR5e9EcLyAsYIS9ghLyAO7DyC6BkUlNlGTRIprQ02dauLbLwfeONIPXvb9Gj\nj2bqX/9KK7bwBQDA0yh+4TH0alVcppMnZY2NlTMqSmlLlkghIUXOveoqhz75JFUDB2bLVIJuB/IC\nRsgLGCEv4A7FFr+zZs3SzTffrNjY2Pz7PvzwQ91xxx2644479Mknn5R7gAC8y3zwoKw9eiinTx+l\nz54t+RX94TVJ6to1V40asdoLAPBNxe7z+9133ykgIECTJk1SQkKCsrOzFRMTo9WrVysrK0vDhg3T\n5s2bC53HPr9A5eD3zTeyDBumjKlTlT1kiLfDAQCgkNLu81vsym/79u1Vo0aN/PHu3bvVvHlzhYeH\nq379+oqIiND+/fvLHi0AnxWQmCjLkCFKe+01w8L3ww8D9PbbgV6IDACAsitVz+/p06dVp04drVix\nQomJiapTp45OnTpVXrGhkqFXq+IIXLxYoePHy75ypXK7dStwzGaTHnkkVE8/HaKrrnJc9nORFzBC\nXsAIeQF3KNNWZ4MHD5Ykbd68WaYiPtEyduxYRUZGSpKqV6+u6Ojo/C1KLiYv46o1vshX4mFsMHa5\ndOqhh9To009l27hRzqioAse//tpPDzzgp7ZtT+o//6kmq/Xyn3/Pnj2+8/oZ+8z4Il+Jh7FvjLle\nML5o69atSkpKkiSNHDlSpVFsz68kJScna8yYMUpISNC3336rN998U/Pnz5ck3XfffZoyZYpatmxZ\n4Bx6foEKKDdXoePHy2/vXtnffVeuunULHF6yJFAvvBCiuXPTFROT46UgAQAoqLQ9v/6lefDo6Ggd\nPHhQ586dU1ZWln777bdChS+ACigtTWEjRsjkcMi2fr1ksRSactttuerZM1V16rCTAwCg4iq253fa\ntGkaPHiwDh8+rC5dumjr1q2aMGGC7rnnHv3lL3/R5MmTPRUnKoE/vp0J32A6c0bWvn3lqlVL9nfe\nMSx8JalxY2e5FL7kBYyQFzBCXsAdil35jYuLU1xcXKH7e/bsWW4BAfAc85EjsgwYoOy+fZU5ZYpK\n9K0UAABUYJfs+S0Len4B3+f3/fey3HuvMidMUNaIEXI6pW3b/LViRaCcTum119K9HSIAAJdUrj2/\nACoH/y1bFDZ6tNLnztX+P/XRyhmBWr06UMHB0uDBWbr77mxvhwgAQLko1T6/wOWgV8s3BK5YobAx\nY2R/+23Zu/XWoEEW2WwmLV6cpi+/TNW4cVlq2NBzH2ojL2CEvIAR8gLuwMovUFW4XAp69VUFLVok\n2/r1crZsqSBJ27en0uoLAKgy6PkFKjGXS9q500+r3vXT+KQJanZiq+wrV8rVoIG3QwMAwC3o+UWV\nkJ4uHTli1m+/mXXy5MWbSVFRTo0alVVo/u7dflq/PkDVqrkK3CIjnWrRwumFV1C+jh41a9WqQK1a\nFSi/nEytChqqRtXOyLZxo1StmrfDAwDAayh+4TFbt27N/4pCIy6XZLNJJ078r6ANC3Opd+/C3ya2\nbZu/Jk0KVf36TtWr51REhEtNmzrVurXD8LGDglwKDZXOnTPryBGTUlNNstlM6tgxVy1aZBaa/8EH\nAZoxI0RWa8Fi+eabc3T33YXjycmR/Pwksw900X/9tZ+GDrWob98cvT4jWZ3n3iNXRITS/rlaCgry\ndniFXCovUDWRFzBCXsAdKH7hES6XdPx4mPbu9dPVVxcuULdt81P//laZzVL9+k5FROQVtdddZ1zM\n3nprrr7+OrXEz9+ihdOwyC1K5845iopyKDXVVOBWs6Zxl9DKlYF64olQNWjgVOPGTjVs6FSjRk51\n7pyrm2/OLfHzusO11zq0d+8FBZ9OlnXAAOXcdpsypk/3jcocAAAvo+cX5SolxaQVKwL1r38FKS3N\npK5dcxQfX3j/2OxsKStLslq9EKSbZGRIx46ZlZxs1tGjeX9efbVDffoUXinetClAn33mr0aN8orl\nRo3ybrVru0r04bMffvDTihWBGj8+U+Hhhf8vbN63T9ZBg5Q5erSyHnrIHS8PAACfRM8vfILTKT36\naKg2bAhQt265evnldN14Y26RhV1gYN6tIgsJkZo1c6pZs0v3EDdo4FSDBk4lJZn11Vf++cXy2LFZ\nGj++8Ar10aNm2WzSli0BWrkyUBcumDRwYLacBk/lv3WrwoYPV/rMmcrp398dLw0AgEqD4hflwmyW\nbrstR1OnZqhOnbyVSXq1/qdNG4fatCnc0mFUzErS+vUBWrIkSDfckKuZMzN00025hl0MAevWKXTi\nRKUtXKjczp3dHHX5IC9ghLyAEfIC7kDxi8uWlWX8Oao77yz8dj+KV1Rb7sMPZ+nhhwvvYvF7QQsW\nKHjePNnXrJGjdetyiA4AgIqPnl+USXq6tHZtXi/vNdfkatasDG+HVHU5nQqZNk0BmzbJ/t57cpai\n7wkAgIqOnl+Uq/37zVq8OEirVweqY8dcTZyYodtv9+xuBvid7GyFPvKI/H79VbbERLnCw70dEQAA\nPo29j1Bidrt0770WWa0uffqpTe++m6bu3XPl51ey8/lOdjdLTZVl0CCZ0tJkW7u2wha+5AWMkBcw\nQl7AHVj5RYlZLNK336aWaCsulC/TyZOyDBokx7XXKv3FF1Xi30AAAKji6PlFATk5UmJigOrWdeqG\nG4y/YALeZT54UJYBA5R9333KHD9e/DYCAKjKStvzS9sDJOXtI/v888Fq27a63ngjSDk5FFS+yG/7\ndlljY5X5xBPKnDCBwhcAgFKi7aGKO/d/32nh7EwdOOCnzp1z9e+nctS4sVPKlfSJe5/rhx9+UGu2\n4Coz89GjCnnuOaX94x/K7dbN2+G4Dft2wgh5ASPkBdyB4reqcrkU/PzzavLuCo2t3kJ12jvllyZp\nbfk9ZbOUFAVv2VJ+T1DZBQTIvmKFHLQUAQBQZhS/VVFOjkIffVR+Bw7I9p9PZaldW57Ypddfkt0D\nz4OKhVUcGCEvYIS8gDtQ/FY1drssDzwgmc2yrV8vhYV5OyIAAACP4QNvVcjZH88opFdfOSMiZF++\n3OOFL/szwgh5ASPkBYyQF3AHit8q4th/jsi/S4x2N7xD6fPmSf4s+gMAgKqHfX6rgIPvfK8r/nav\n9tw1Sde8cZ+3wwEAAHAb9vlFAXte3KKoRwZq/7iXKXwBAECVR/FbiR1//l21fPEh/TznXbWZeoe3\nw6FXC4bICxghL2CEvIA70PhZGblcCp4zRy1XL9PPaxPU4pZm3o4IAADAJ9DzW9k4HAqdOFF+27fL\nvmqVXBER3o4IAACg3JS255eV38okI0Nhf/2rTHa7bB98IFWr5u2IAAAAfAo9v5VEyi/nFdS7n1wh\nIbKvXOmThS+9WjBCXsAIeQEj5AXcgeK3Eji5LVnOm3ppj/Umpc+fLwUGejskAAAAn0TPbwV3aO0+\n1X9wkPb1HKdr3h7p7XAAAAA8in1+q5B98V8ocmQ/HfjrDApfAACAEqD4raBOvbpGV8UN18HnFqvd\njFhvh1Mi9GrBCHkBI+QFjJAXcAd2e6iAguLj1ezN+fpl9Vr96bZW3g4HAACgwqDntyJxOhUydaoC\ntmyRbfVquRo18nZEAAAAXsU+v5VVVpbCxo6V6cQJ2T78UK6aNb0dEQAAQIVT5p7f+Ph49erVS716\n9VJ8fLw7Y8If2JJTFdBngJSTI/uaNRW28KVXC0bICxghL2CEvIA7lKn4PXr0qNavX6+EhAStW7dO\n69at07Fjx9wdGySd+u6EMq7rrR9cVyvtX/+SgoO9HRIAAECFVabi12KxyN/fX5mZmcrKylJAQICs\nVqu7Y6vyfv2/gwrt3lNHOw3QVZtmSH5+3g7psnTq1MnbIcAHkRcwQl7ACHkBdyhTz2/NmjU1bNgw\nde3aVU6nU08++aSq+eDX6VZkB976RldOHKY9w57TNS/f7e1wAAAAKoUyrfwmJydrxYoV2rJlizZv\n3qy33npLp0+fdndsVda5tzaq2cShOjBlvtpXosKXXi0YIS9ghLyAEfIC7lCmld/du3crOjpaFotF\nktSqVSvt27dPXbp0yZ8zduxYRUZGSpKqV6+u6Ojo/LcrLiYv48LjoLfeUsOZM/XR1Gd1y6NdvR6P\nO8cX+Uo8jH1jvGfPHp+Kh7FvjC/ylXgY+8aY6wXji7Zu3aqkpCRJ0siRI1UaZdrnd8+ePXr66ae1\nevVqOZ1O9e3bV6+//rqioqIksc9vmbhcCn7+eQWuXy/76tVyNmni7YgAAAB8nkf2+Y2Ojla3bt3U\nr18/SdLAgQPzC1+UQU6OQh99VH4HDsiWmChX7drejggAAKBSKvM+vw8//LA2btyojRs3asSIEe6M\nqUpJ+80u8533ynT2rGzr11fqwvePb2cCEnkBY+QFjJAXcIcyF7+4fOd+PK3UDndqf2pDpS1bJoWF\neTskAACASq1MPb+XQs/vpR37zxFZBgzQzx0HqsOGx2Uym7wdEgAAQIVT2p5fVn694ODy71Wnf0/9\n3G+crvngCQpfAAAAD6H49bDUlR8r6m8Dtf/RV3TNgqHeDsej6NWCEfICRsgLGCEv4A5l2u0BZRO4\nfLkaT5+uI0uXq03P67wdDgAAQJVDz68nuFwKnjNHgcuW5e3h27y5tyMCAACoFDyyzy9KweFQ6MSJ\n8tuxQ7ZNm+SKiPB2RAAAAFUWPb/lKONchtT/fpkPHZItIaHKF770asEIeQEj5AWMkBdwB1Z+y0nK\nL+eVeutQZUZE6qqti6TAQG+HBAAAUOXR81sOTm5LVmCfgTocHaP2m6bI7M8COwAAQHlgn18vO7x2\nr6r3itGh7sN1zcdTKXwBAAB8CJWZG2Vs/FyRI+/Sgb/O0LVLR3o7HJ9DrxaMkBcwQl7ACHkBd6Dn\n100C3n9f1SdNUtKif6ld35u9HQ4AAAAM0PPrBkHx8QqeP1+2VavkbNXK2+EAAABUGezz60lOp0Km\nTlXAli1K3bRJrkaNvB0RAAAAikHPbxllpWbJMeiv8vv+e9kSEyl8S4BeLRghL2CEvIAR8gLuwMpv\nGdiSU3XmlvvlqFZTzba9LwUHezskAAAAlAA9v6V06rsTUs9BOn7lzYre8pz8Av28HRIAAECVxT6/\n5ejX/zuo0O49ldRpoNp+NoPCFwAAoIKh+C2h7C1fq+GQWP1039O6dvXDMplN3g6pwqFXC0bICxgh\nL2CEvIA70PNbAgEffKDqjz2mYwsWqEP/27wdDgAAAMqInt9LCHrrLQXPmSP7O+/I0a6dt8MBAADA\n77DPr7u4XAp+/nkFrl8v24cfytmkibcjAgAAwGWi59dATnqOsoc8ooBPP5UtMZHC103o1YIR8gJG\nyAsYIS/gDqz8/kHab3Ydv3mkzAF+CtyxXgoL83ZIAAAAcBN6fn/n7L7Tyu52j041aKOrP39R/sH8\nbgAAAODL2Oe3jI7954j8u/bU8fZ3qM22ORS+AAAAlRDFryTHV9+qbv+e+rnfOF3zwRPs4VtO6NWC\nEfICRsgLGCEv4A5Vvvj137xZ4cMGKzt+jq5ZMNTb4QAAAKAcVeme38DlyxUyfbrsb78tR8eO3g4H\nAAAApcQ+vyXhcil4zhwFLlsmW0KCnM2bezsiAAAAeECVa3twZDuU/pcnFJCQINumTRS+HkSvFoyQ\nFzBCXsAIeQF3qFIrvxnnMvTrzaMVlJumkB0JMlWv5u2QAAAA4EFVpuc35ZfzSr11qFLDr9BVW19R\noCXQ2yEBAADgMrHPr4GT25LlvKmXTl91g1rtiKfwBQAAqKIqffHr+v4H1YyN0aHuw3XNx1Nl9q/0\nL9ln0asFI+QFjJAXMEJewB0qdSXo/9lnqjHwLjlfmq5rl470djgAAADwskrb8xvw/vsKnTxZaYsW\nKffmm70aCwAAAMoH+/xKCoqPV/D8+bKtXStnq1beDgcAAAA+osxtD7t27VJsbKx69uypRx991J0x\nlZkz16nUB6cqaPlypW7aROHrY+jVghHyAkbICxghL+AOZVr5dTqdmjhxombOnKkOHTro/Pnz7o6r\n1LJSs/TzzX+T1XZC1p2JMoXX8HZIAAAA8DFlWvn94YcfFB4ent/XW7NmTbcGVVq25FQda3uPTM5c\n1f1+FYWvj+rUqZO3Q4APIi9ghLyAEfIC7lCm4vfEiROyWq0aOXKk+vXrp3feecfdcZXYqe9PKuO6\nWF1o2EItvntDwTWCvRYLAAAAfFuZit+srCzt3LlTzz33nJYuXaolS5bo6NGj7o7tkkz7D8hyR4yS\nOg1Qu89myC/Qz+MxoOTo1YIR8gJGyAsYIS/gDmXq+a1Tp46aNWumiIgISVLr1q116NChAttMjB07\nVpGRkZKk6tWrKzo6Ov/tiovJeznj8H37dOOcOcp87lll/qmhvvjyC7c+PmP3jy/ylXgY+8Z4z549\nPhUPY98YX+Qr8TD2jfGlrhfffvutQkJCVKNGXvvjhQsXJOXVIYwr9jgoKEg//vijLtq6dauSkpIk\nSSNHjlRplGmfX5vNpl69eikhIUEhISHq37+/5s2bp6ZNm0oq/31+Az74QKGPPaa0BQuUe9tt5fY8\nAACgYrDb7crKylKtWrW8HQrKwdmzZxUUFCSLxVLomEf2+bVarZo8ebLuv/9+5ebmKjY2Nr/wLW+B\nixYpZM4c2VevlqNdO488JwAA8G0XLlxQgwYNvB0Gykl4eLiOHz9uWPyWVpn3+e3Ro4fWrVunDz74\nQKNGjbrsQC7F5XTp/NjnFfz667Jt3EjhWwH98e1MQCIvYIy8gJHi8sJkMslkMnkwGniSO/99y7Ty\n62k56Tn68ZYJqnXqgM5vT5RfRG1vhwQAAIAKqMwrv56S9ptdR9oOU7D9rGruXEPhW4Fd/EAC8Hvk\nBYyQFzBSkfNi4cKFat68uSIjI/XZZ5/l3z9hwgTNnj27wNyJEycqMjJStWvX1n/+8x9Ph1rp+XTx\ne27/GV24pp/Sa9RX1K4lCq0T5u2QAAAASiUnJ0dxcXFav369kpKS1Llz5/xjc+bM0eOPP15g/osv\nvqikpCQ1atSoyLf6Y2NjtXTp0nKNu7Ly2eLX9MshBd4ao+Pt7lCbbXPkH1whOjRQDHr4YIS8gBHy\nAkEj0AwAAA7BSURBVEYqal789ttvyszMVIsWLdz2mPQ3l51PFr9+336rar17Kejph3XtB4/LZOYf\nGAAAVDw33nijbrzxRklS06ZN89sePvroI0VGRqpevXp6/vnnS/x4c+fOVWRkpL766is9+eSTioyM\n1O23355//Pz58xo1apRatmyp9u3b6+233y5w/kMPPaRJkyZp2LBhioyMVNu2bWW3293zYisIn1tO\n9d+8WWFjxyp93jwFxMR4Oxy4UUXu1UL5IS9ghLyAkYqYF1999ZWOHj2qdu3a6ciRIzKb/7fumJSU\npIceeqhUq7jjx4/X+PHj1adPHw0cOFBDhw4tcHz06NGqW7eudu3apRMnTqhXr15q06aN2v1ul6xV\nq1bp9ddf15IlS7R37175+/tcOViufOrVBi5frpDp02VfvlyOjh29HQ4AAMBlc7mK/z6xSx0v6Xkn\nT57Uv//9b/3yyy8KCgpSkyZNFBsbq40bNxYofm+55RZ1795dUt639FY1PtH24HK6dHrcXAXPni1b\nQgKFbyVVUXu1UL7ICxghL2DkcvLihReCFR5es9DthReCSzy/qLne8scV42PHjkmS2rVrp6ZNm6pp\n06Z65513dPr06QLzrrzySo/F6Iu8vvLryHZoT5fJqv/rNzr7daICIiO8HRIAAKhknnoqU089lVlu\n8y9HUW0PgYGBcjgchsd+3z5xUcOGDRUcHKxDhw4V20phdG5V4tVXn342Qz+1HSHrb4cUun09hW8l\nVxF7tVD+yAsYIS9gpLLmRVFtD82aNdOXX35peKxu3brat29fgfsiIiJ000036e9//7vS0tKUk5Oj\nbdu2ae/evW6P+f/bu/+gKMu9j+PvhUU4sPx4sDEEWTcVQiH8cQInm/rDGgYpcA7z9PQwOjrKmYkZ\n5KSVjGF5OknO8E9jpR3JmWgqGAc7MEY/kCmzciyd5BFT5mEyEwyCRHH4ZbDgPn807KN44xHcXdj2\n8/rHufdm7/ti+cx3vlxe3Jc3m7Tm98qPXXQu/k+GA4OJPVVOaEzYZA1FRERExK1Gz8RmZ2djtVr5\n4IMPeOONN7BarWzYsOGGr9m6dSs1NTXExsaybdu2G87l5+dz+PBhEhMTWblypfP10tJSOjs7SUlJ\nIT4+nu3bt980e+zrj0kzNTU1TWyV9S1cuHCBJUuWjHne78IFrjzwX/yQ8BiLa4vwM/v29LuvOHLk\nyB/2t3aZOOVCjCgXYuRWuWhrayM6OtrDIxJPGutnXF9fT2xs7G1fx+Ndp//p04SmpxPy7Dr+/NkL\nanxFRERExGM8+gdv5q++IuSvf6W/pAT/v/zFk7eWKUCzOGJEuRAjyoUYUS7EFTzW/Ab8618EFxXR\nV1bG0IMPeuq2IiIiIiJOHllz0L75nwT//e/0VFer8fVhem6nGFEuxIhyIUaUC3EFt878Xhu6xslH\n/4H1fz+n/ata/hQ/y523ExERERG5Jbc1vwPdA5x98G9M7/6Facc+5k+zw911K/ESWqslRpQLMaJc\niBHlQlzBbc1v28L/xhQcyd0NlQRFTK3tAEVERETEN7ltze+VmPnc+z9vqfEVJ63VEiPKhRhRLsSI\nciGu4LaZ30VfvYLJz7d3EBERERGRqcVtM79qfGU0rdUSI8qFGFEuxIhy8cc1ffp0zp8/75F7aXs1\nEREREZk0Dofjhn/dTc2veIzWaokR5UKMKBdixBtzUVFRwfLly0lMTGT9+vXk5OQwf/58GhsbuXbt\nGiUlJSxatIiEhAS2bNnC0NAQAM3NzaxcuZI5c+Ywe/Zs1q1bR3d3t/O6Bw8eJDU1FavVSkpKCocO\nHXKeW7hwIV9++aXzePSsan5+Ps8//zxr1qzBarWycOFCent7AaipqWHZsmXMmTOHJ598ko6ODud7\nMjMziY+PZ9u2bSxdupTly5dz9epVALq6unjqqadISEhg8eLFvPvuuzfcr6CggIyMDKxWKwUFBc5z\nTzzxBLNnzwbg4Ycfxmq1snXrVld9/IbU/IqIiIi4UWBgIN988w21tbXk5uayevVqqqur2bVrFwcP\nHqS2tpbvvvuOpqYmSktLARgcHGTt2rWcPn2a06dP09XVRUlJifOaGzdupKioiJaWFqqqqpg5c6bz\nnMlkwmS69fLTyspKVq9eTXNzM+Xl5ZjNZk6cOMHTTz/N7t27OXv2LMnJyWzatMn5nqVLl7Jnzx72\n7t1LXV0dQUFBHD9+HIC8vDymTZtGQ0MD1dXVlJSUcPLkSed7Dx8+zN69ezl69CgHDhygvr4egP37\n99PS0gLA119/TUtLC6+88sodfuK3puZXPEZrtcSIciFGlAsx4q25uOeeewgLCyMyMpJ58+ZhtVq5\nePEi5eXlbN68maioKCwWC7m5uXz00UcAxMXFkZ2dTXBwMKGhoWRlZXHmzBnnNf38/Pjpp5/o7u4m\nNjaW+fPnj2tMDz30EGlpaZhMJpKSkggKCuL9998nJyeHxYsX4+fnR35+PnV1dQwODjq/D5vNxl13\n3UV4eDhWq5XOzk7a29v5/PPPKS4uJjAwEJvNRmZmJh9//LHzfitWrCAmJoZZs2axYMECfvzxRxd8\nshPj1h3eRERERKaC/4iMdMl1ui5fHvd7RmZhzWYz/v7+mM1mhoaGaG1tJS8vDz+/3+cir127RlRU\nFAAXL15ky5YtfPvtt/T392O321m0aJHzmmVlZezcuZPXX3+duLg4XnvttXE1wHPnzr3ptdbWVo4e\nPUpFRYXztcDAQOfSh5Gx+/v7O4/tdjttbW0AN4xveHiY7Oxs53F4+P9vdjZt2jQGBgZue6yupuZX\nPObIkSNe+1u7uI9yIUaUCzFyJ7mYSNPqTg6Hg5iYGHbv3s39999/0/mXX34Zf39/jh07hsViobS0\nlAMHDjjPp6amUlFRweDgIJs2bWLHjh289957wO8N68ja4evXCV9vpOG+3qxZs3juuefYuHHjuL6X\nmJgYgoKCOHfu3L9dbjGWib5vIrTsQURERMSDRp5qsGrVKnbs2EF7ezsOh4OzZ8/yxRdfANDX14fF\nYiE4OJjm5mbeeeedG95fWVlJb2+vs2kMCwtznp87dy4nTpwA4MMPP7ztceXk5FBWVsapU6dwOBxc\nvHiR6urqm8Y92t13382yZct46aWX6Ovrw263c+zYsRuWaYz1GVx/jcbGxtse651Q8yseo1kcMaJc\niBHlQox4Yy5G//HZyLHJZCI/P58HHniAjIwMbDYba9eu5dKlSwAUFhZy8uRJbDYbubm5rFixwnkd\nh8PB/v37ue+++4iLi6Ojo+OGJyRs3ryZyspKHn30UTo6OgxnVY1eS0lJobi4mA0bNmCz2XjkkUc4\ndeqU4dhHKy0tpbOzk5SUFOLj49m+fTvDw8Nj3m/08QsvvEBhYSGJiYkUFxff8jO9U6ampiaXP1Tt\nwoULLFmyxNWXFRERETHU1tZGdHT0ZA9D3Gisn3F9fT2xsbG3fR3N/IrHeOPzGcX9lAsxolyIEeVC\nXEHNr4iIiIj4DDW/4jHeuFZL3E+5ECPKhRhRLsQV1PyKiIiIiM9Q8yseo7VaYkS5ECPKhRhRLsQV\n1PyKiIiI13M4HGM+h1a8nyt/vnrUmYiIiHi93t5eBgYGmD59+mQPRdzg0qVLBAYGYrFYbjo33ked\naXtjERER8XoWi4WBgQHa2tomeyjiBmM1vhMx4ea3t7eX9PR01q9fz/r1610yGPlju5M92eWPS7kQ\nI8qFGPl3udCsr9yOCa/53bNnD0lJSYZb3IkYaW9vn+whyBSkXIgR5UKMKBfiChNqfs+dO8fly5dJ\nSkrS4nK5bYGBgZM9BJmClAsxolyIEeVCXGFCze+rr75KQUGBq8ciIiIiIuJW425+Dx06hM1mY+bM\nmZr1lXFpaWmZ7CHIFKRciBHlQowoF+IK437U2c6dO/nkk0/w9/enq6sLPz8/ioqKePzxx51f09jY\nSGhoqMsHKyIiIiJyvZ6eHhYsWHDbX39Hz/ndtWsXISEhrFu3bqKXEBERERHxGO3wJiIiIiI+wy07\nvImIiIiITEWa+RURERERn6HmV0RERER8xoS3Nx7L999/z2effYbJZCI9PZ2EhARX30K80IsvvkhU\nVBQANpuNxx57bJJHJJPh008/paGhgZCQEOezwlUzxCgXqhnS3d3Nvn37+O233zCbzaSlpTFv3jzV\nDB83Vi7GUzNc2vwODQ1RV1dHXl4edrudt99+W6EUAAICAsjPz5/sYcgkS0xMJDk5maqqKkA1Q343\nOhegmiHg5+dHVlYWUVFRXLlyhbfeeotnn31WNcPHGeWisLBwXDXDpcsefv75Z2bMmEFISAgRERGE\nh4fzyy+/uPIWIuLFrFYrwcHBzmPVDIGbcyECYLFYnDN5ERERDA8P09LSoprh44xyMTQ0NK5ruHTm\nt7e3l9DQUI4fP05wcDAWi4Wenh5mzpzpytuIFxoaGuLNN990/heFzWab7CHJFKCaIWNRzZDr/fDD\nD0RHR9PX16eaIU4juTCbzeOqGS5f8wuQmpoKwJkzZzCZTO64hXiZwsJCLBYLra2tlJeX88wzz2A2\nuyV+4oVUM2Q01QwZ0dPTQ21tLatWraKtrQ1QzZAbcwHjqxkuXfYQGhpKT0+P83hkVkfEYrEAEBMT\nQ1hYGF1dXZM8IpkKVDNkLKoZAmC329m3bx/p6elERkaqZghwcy5gfDXDpb9Gx8TE8Ouvv9LX14fd\nbqe7u9u5LkN819WrVzGbzQQEBNDV1UV3dzcRERGTPSyZAlQzxEh/fz8BAQGqGT7O4XBQVVVFcnIy\ncXFxgGqGGOdivH2Gy3d4G3kECUBGRgb33nuvKy8vXqilpYWqqirMZjMmk4m0tDRnYMW31NTU0NjY\nSH9/PyEhIWRlZWG321UzfNzoXKSkpNDQ0KCa4ePOnz9PWVkZM2bMcL62Zs0azp8/r5rhw4xykZmZ\nOa4+Q9sbi4iIiIjP0A5vIiIiIuIz1PyKiIiIiM9Q8ysiIiIiPkPNr4iIiIj4DDW/IiIiIuIz1PyK\niIiIiM9Q8ysiIiIiPkPNr4iIiIj4jP8DvyvDcKuDmFoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb2e40d0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "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 predictiton. 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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FjNAXpSvzj1xtfHiujtfpoAYThsnU/kad3L5Dua++WmaHYokVYwAAABRRwO+/K2Nciiql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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb113c90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A7WexcDwyAAAIvIAOwLfeyvYP8PZb2a1p01zaudOq//3PFqSKEA7I9MEMfQEz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\nlaX6vn1ldOumhD3DbFk7crR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j0eB6vX4y8N234p9sgnuPogCYz+cMBoPf/oT+\nA9vtlqIoeDwetNttFosFdV2bjcCVZcl6vabf73/ulsslZVmajYAdj0c2m83nPJ1Ov4xBA3MRsncB\nnkwmZiJwh8OBPM+J45goipjNZqRp+u1cuApZkiRJQXETnCRJkoJiAZYkSVJQLMCSJEkKigVYkiRJ\nQbEAS5IkKSgWYEmSJAXFAixJkqSgWIAlSZIUlD+f3vbBd+PUZQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb05a310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZZ1e9NuSK8TZNb2nIUd6tFGnduv2Ki+vk0x8Dmh4ywKhk5067li1zas6cQn8P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\ngQa4BomJhhITDW3fzo8JAACgqaCzO4m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       "text": [
        "<matplotlib.figure.Figure at 0x7f16fb088e90>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Final Thoughts"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "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. 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 consistantly only gains or loses weight. We flucuate. 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 sytems 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 direcly 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] http://nescacademy.nasa.gov/review/downloadfile.php?file=FundamentalsofKalmanFiltering_Presentation.pdf&amp;id=199&amp;distr=Public"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}