diff --git a/01-g-h-filter.ipynb b/01-g-h-filter.ipynb index 5c97cf8..b3b119d 100644 --- a/01-g-h-filter.ipynb +++ b/01-g-h-filter.ipynb @@ -1,2580 +1,2585 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# The g-h Filter" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#format the book\n", - "%matplotlib inline\n", - "%load_ext autoreload\n", - "%autoreload 2 \n", - "from __future__ import division, print_function\n", - "import sys\n", - "sys.path.insert(0,'./code')\n", - "from book_format import load_style\n", - "load_style()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Building Intuition via Thought Experiments" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Imagine that we live in a world without scales - the devices you stand on to weigh yourself. One day at work a coworker comes running up to you and announces her invention of a 'scale' to you. After she explains, you eagerly stand on it and announce the results: \"172 lbs\". You are ecstatic - for the first time in your life you know what you weigh. More importantly, dollar signs dance in your eyes as you imagine selling this device to weight loss clinics across the world! This is fantastic!\n", - "\n", - "Another coworker hears the commotion and comes over to find out what has you so excited. You explain the invention and once again step onto the scale, and proudly proclaim the result: \"161 lbs.\" And then you hesitate, confused.\n", - "\n", - "\"It read 172 lbs 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. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "** Try Another Scale**\n", - "\n", - "Is there any way we can improve upon this result? The obvious, first thing to try is get a better sensor. Unfortunately, your co-worker informs you that she has built 10 scales, and they all operate with about the same accuracy. You have her bring out another scale, and you weigh yourself on one, and then on the other. The first scale (A) reads \"160 lbs\", and the second (B) reads \"170 lbs\". What can we conclude about your weight?\n", - "\n", - "Well, what are our choices?\n", - "\n", - "* We could choose to only believe A, and assign 160lbs to our weight estimate.\n", - "* We could choose to only believe B, and assign 170lbs to our weight.\n", - "* We could choose a number less than either A or B.\n", - "* We could choose a number greater than either A or B.\n", - "* We could choose a number between A and B.\n", - "\n", - "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A instead of B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they both measured. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not probably the answer is somewhere between A and B. \n", - "\n", - "In mathematics this concept is formalized as *expected value*, and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we made one million separate readings. Some of the times both scales will read too low, sometimes both will read too high, and the rest of the time they will straddle the actual weight. If they straddle the actual weight then certainly we should choose a number between A and B. If they don't straddle then we don't know if they are both too high or low, but by choosing a number between A and B we at least mitigate the effect of the worst measurement. For example, suppose our actual weight is 180 lbs. 160 lbs is a big error. But if we choose a weight between 160 lbs and 170 lbs our estimate will be better than 160 lbs. The same argument holds if both scales returned a value greater than the actual weight.\n", - "\n", - "We will deal with this more formally later, but for now I hope it is clear that our best estimate is the average of A and B. $\\frac{160+170}{2} = 165$.\n", - "\n", - "We can look at this graphically. I have plotted the measurements of A and B with an assumed error of $\\pm$ 8 lbs. The overlap falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 pounds. a lot of the plotting code is not particularly useful to read, so for each chapter I have placed the uninteresting code in a file named xxx_internal. I import this file and call whatever function I need. If you want to read the code, the file exists in the code subdirectory." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import gh_internal as gh\n", - "gh.plot_errorbar1()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So 165 lbs looks like a reasonable estimate, but there is more information here that we might be able to take advantage of. The only weights that are possible lie in the intersection between the error bars of A and B. For example, a weight of 161 lbs is impossible because scale B could not give a reading of 170 lbs with a maximum error of 8 pounds. Likewise a weight of 171 lbs is impossible because scale A could not give a reading of 160 lbs with a maximum error of 8 lbs. In this example the only possible weights lie in the range of 162 to 168 lbs.\n", - "\n", - "That doesn't yet allow us to find a better weight estimate, but let's play 'what if' some more. What if we are now told that A is three times more accurate than B? Consider the 5 options we listed above. It still makes no sense to choose a number outside the range of A and B, so we will not consider those. It perhaps seems more compelling to choose A as our estimate - after all, we know it is more accurate, why not use it instead of B? Can B possibly improve our knowledge over A alone?\n", - "\n", - "The answer, perhaps counter intuitively, is yes, it can. First, let's look at the same measurements of A=160 and B=170, but with the error of A $\\pm$ 3 lbs and the error of B is 3 times as much, $\\pm$ 9 lbs." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_errorbar2()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The overlap of the error bars of A and B are the only possible true weight. This overlap is smaller than the error in A alone. More importantly, in this case we can see that the overlap doesn't include 160 lbs or 165 lbs. If we only used the measurement from A because it is more accurate than B we would give an estimate of 160 lbs. If we average A and B we would get 165 lbs. Neither of those weights are possible given our knowledge of the accuracy of the scales. By including the measurement of B we would give an estimate somewhere between 161 lbs and 163 lbs, the limits of the intersections of the two error bars.\n", - "\n", - "Let's take this to the extreme limits. Assume we know scale A is accurate to 1 lb. In other words, if we truly weigh 170 lbs, it could report 169, 170, or 171 lbs. We also know that scale B is accurate to 9 lbs. We do a weighing on each scale, and get A=160, and B=170. What should we estimate our weight to be? Let's look at that graphically." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_errorbar3()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we can see that the only possible weight is 161 lbs. This is an important result. With two relatively inaccurate sensors we are able to deduce an extremely accurate result.\n", - "\n", - "> So two sensors, even if one is less accurate than the other, is better than one.\n", - "\n", - "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight of using all measurements regardless of accuracy will play a large role later, so don't forget it.\n", - "\n", - "What if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's write a simulation for now." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Average of measurements is 164.9700\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "measurements = np.random.uniform(160, 170, size=10000)\n", - "print('Average of measurements is {:.4f}'.format(\n", - " measurements.mean()))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The exact number printed depends on your random number generator, but it should be very close to 165.\n", - "\n", - "This code makes one assumption that probably isn't true - that the scale is as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `numpy.random.normal()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements very similar to how a real scale would." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Average of measurements is 165.0224\n" - ] - } - ], - "source": [ - "measurements = np.random.normal(165, 5, size=10000)\n", - "print('Average of measurements is {:.4f}'.format(\n", - " measurements.mean()))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The answer again is very close to 165. \n", - "\n", - "Okay, great, we have an answer to our sensor problem! But it is not a very practical answer. No one has the patience to weigh themselves ten thousand, or even a dozen times. \n", - "\n", - "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n", - "\n", - "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the weighings along with the error bars, and then some possible weight gain/losses that could be explained by those measurements in dotted green lines." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Gh7OHdD2ygPZB7Tn9+mmWpC0h8WgiadfTAIiqGYW7k7tBfJGmCIVCYXTRN2F+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\n/REREYFr16412b66uhqhoaFwdnZGfn4+NmzYgLVr12L9+vU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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_hypothesis()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a humans' weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n", - " \n", - "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based solely on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, merely one that is reasonable and could be explained by the measurement." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_hypothesis2()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Another what if: what if the readings were 158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0? Let's look at a chart of that and then answer some questions." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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aP23a2usJB4AHqvWJTb6+vurTp4/69OlTH/EAgFPFDo7T+v2d7V4DAGAE1Sby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\nXLa0Jjc3V5GRkYqMjNSFCxe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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_hypothesis3()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. We can't be sure, but that surely looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n", - "\n", - "So let's look at two hypotheses. First, let's assume our weight did not change. To get that number we agreed that we should average the measurements. Let's look at that." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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jjz9055136tFHH1Xz5s1VqVIlbdy4UatWrdKIESNu9CO2IHkEbtKNfgtqC9+C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\nkr+/v44dO6a3335btWvXtmp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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_hypothesis4()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That doesn't look very convincing. In fact, we can see that there is no horizontal line that we could draw that is inside all of the error bars.\n", - "\n", - "Now, let's assume we we gained weight. How much? I don't know, but numpy does! We 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 plot the results." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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W3m7ZsmWP/dnt27cP06ZNw+rVq+v+Qaup1vD4ySefICoqCuvWrcPmzZvl06zW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\nvv/+e2VnZ+v666/XF198oYCAADU0NMjPz0/BwcF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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_hypothesis5()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This looks much better, at least to my eyes. Notice now the hypothesis lies very close to each measurement, whereas in the previous plot the hypothesis was often quite far from the measurement. It seems far more likely to be true that I gained weight than I didn't gain any weight. Did I actually gain 13 lbs? Who can say? That seems impossible to answer.\n", - "\n", - "\"But is it impossible?\" pipes up a coworker.\n", - "\n", - "Let's try something crazy. Let's assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, assume I know it is approximately correct. Maybe I am eating a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. Let's see if we can make use of such information if it was available without worrying about the source of that information yet.\n", - "\n", - "The first measurement was 158. We have no way of knowing any different, so let's 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", - "execution_count": 12, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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URz0JIiIiIj9Ufj58+KE1Y7B0KXznA1YhXbtaMwYjRkCTJu4do4ibqUgQERGRysduh02b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\noKAAHR0dWLRoEVJSUtDT0zNh/6GhITzzzDMIDg5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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_estimate_chart_1()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Okay, but what good is this? Sure, we could assume the 1 lb/day is accurate, and predict our weight for the next 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", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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rKwfGQR6MhRwYB3kwFnJgHOTQoAl/Y8eEn4iIiIgaG0PlsBylh4iIiIjIjDHh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\ne/xPPvkEzz33HM6ePYvdu3ejZcuWcHFxAQDExMT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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_estimate_chart_2()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right? If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n", - "\n", - "> The key insight to this entire book is in the next paragraph. Read it carefully!\n", - "\n", - "So what do we do? If we only take data from the measurement then the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italicized the key point)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should lie 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 scale A was much more accurate than scale B - we scaled the answer to be closer to A than B. Let's look at that in a chart." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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bt89ofV5eHn744Qfk5+fj0qVLOHnypGGEHwBmzJhh1P727dvIzMxEw4YNjdbv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\nm/Hmm2/iwoULSE1NhZmZGZydnQEABw8eVJgi85tvvsHevXt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JiOj/lJaWoqamBu7u7q22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\ngg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.plot_estimate_chart_3()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's try a randomly chosen number to scale our estimate: $\\frac{4}{10}$. Our estimate will be four tenths the measurement and the rest will be from the prediction. In other words, we are expressing a belief here, a belief that the prediction is somewhat more likely to be correct than the measurement. We compute that as\n", - "\n", - "$$\\mathtt{new\\_estimate} = \\mathtt{prediction} + \\frac{4}{10}(\\mathtt{measurement} - \\mathtt{prediction})$$\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 code that and see the results 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). \n", - "\n", - "I hand generated the weight data to correspond to a true starting weight of 160 lbs, and a weight gain of 1 lb per day. In other words on the first day (day zero) the true weight is 160lbs, on the second day (day one, the first day of weighing) the true weight is 161 lbs, and so on. \n", - "\n", - "We need to make a guess for the initial weight. It is too early to talk about initialization strategies, so for now I will assume 159 lbs." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "previous: 160.00, prediction: 161.00 estimate 159.80\n", - "previous: 159.80, prediction: 160.80 estimate 162.16\n", - "previous: 162.16, prediction: 163.16 estimate 162.02\n", - "previous: 162.02, prediction: 163.02 estimate 161.77\n", - "previous: 161.77, prediction: 162.77 estimate 162.50\n", - "previous: 162.50, prediction: 163.50 estimate 163.94\n", - "previous: 163.94, prediction: 164.94 estimate 166.80\n", - "previous: 166.80, prediction: 167.80 estimate 167.64\n", - "previous: 167.64, prediction: 168.64 estimate 167.75\n", - "previous: 167.75, prediction: 168.75 estimate 169.65\n", - "previous: 169.65, prediction: 170.65 estimate 170.87\n", - "previous: 170.87, prediction: 171.87 estimate 172.16\n" - ] - }, 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CCCFyjP/9738sXLhQn37vvffYu3evPj1p0iQ++eQTfbpYsWJYWVmlVKDVQlJS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\nwoIrV66wefNmJk+eTPfu3Y3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p09SzZ8+qly9fVrds2aJGREQY1PXkyRP9S+RugYGBamBg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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import book_plots\n", - "import matplotlib.pyplot as plt\n", - "\n", - "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, \n", - " 169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n", - "\n", - "time_step = 1 # day\n", - "scale_factor = 4/10\n", - "\n", - "def predict_using_gain_guess(weight, gain_rate, do_print=True): \n", - " # store the filtered results\n", - " estimates, predictions = [weight], []\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\n", - " estimates.append(weight)\n", - " predictions.append(prediction)\n", - " if do_print:\n", - " gh.print_results(estimates, prediction, weight)\n", - "\n", - " # plot results\n", - " gh.plot_gh_results(weights, estimates, predictions)\n", - "\n", - "initial_guess = 160.\n", - "predict_using_gain_guess (weight=initial_guess, gain_rate=1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is pretty good! There is a lot of data here, so let's talk about how to interpret it. The thick green line shows the estimate from the filter. It starts at day 0 with the initial guess of 160 lbs. The red line shows the prediction that is made from the previous day's weight. So, on day one the previous weight was 160 lbs, the weight gain is 1 lb, and so the first prediction is 161 lbs. The estimate on day one is then part way between the prediction and measurement at 159.8 lbs. Above the chart is a print out of the previous weight, predicted weight, and new estimate for each day. Finally, the thin black line shows the actual weight gain of the person being weighed. \n", - "\n", - "The 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", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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8hQKek6xevXoVy+TNjzPIwcGBMWPGMGzYsP/s6+3tre2J5uPj88z5KVOm0KpV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TAAAg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\nd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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "predict_using_gain_guess(initial_guess, 0, do_print=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is not so impressive. Clearly a filter that requires us to correctly guess a rate of change is not very useful. Even if our initial guess was correct, 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 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 set the new gain/day to 4.4 lbs? 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. Hmm, sounds like our same problem again. 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", - "$$\\text{new gain} = \\text{old gain} + \\frac{1}{3}\\frac{\\text{measurement - predicted weight}}{1 \\text{ day}}\n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Wzdib+qTHObe4EKayIhBW7oTj559dJ6+diuONd/i/qT/TpmFe9Hobysw7ypkz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\nZ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "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 = [weight]\n", - "predictions = []\n", - "\n", - "for z in weights:\n", - " # prediction step\n", - " weight = weight + gain_rate*time_step\n", - " gain_rate = gain_rate\n", - " predictions.append(weight)\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", - "gh.plot_gh_results(weights, estimates, predictions);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "> **note**: the semi-colon on the last line suppresses a string similar to `` being printed in the output. The notebook prints the value of the last line in the input cell unless you use a semi-colon as a terminator.\n", - "\n", - "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", - "```python\n", - "gain_rate = gain_rate\n", - "```\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 gain does not vary, but when we generalize this algorithm we will remove that assumption. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The g-h Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This algorithm is known as the g-h filter. $g$ and $h$ refer to the two scaling factors that we used in our example. $g$ is the scaling we used for the measurement (weight in our example), and $h$ is the scaling for the change in measurement over time (lbs/day in our example)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This filter is the basis for a huge number of filters, including the Kalman filter. In other words, the Kalman filter is a form of the g-h filter, which I will prove later in the book. So is the Least Squares filter, which you may have heard of, and so is the Benedict-Bordner filter, which you probably have not. Each filter has a different way of assigning values to $g$ and $h$, but otherwise the algorithms are identical. For example, the $\\alpha$-$\\beta$ filter assigns a constant to $g$ and $h$, constrained to a certain range of values. Other filters such as the Kalman will vary $g$ and $h$ dynamically at each time step.\n", - "\n", - "**Let me repeat the key points as they are so important**. If you do not understand these you will not understand the rest of the book. If you do understand them, then the rest of the book will unfold naturally for you as mathematically elaborations to various 'what if' questions we will ask about $g$ and $h$. The math may look profoundly different, but the algorithm will be exactly the same.\n", - "\n", - "* Multiple data points are more accurate than one data point, so throw nothing away no matter how inaccurate it is.\n", - "* Always choose a number part way between two data points to create a more accurate estimate.\n", - "* Predict the next measurement and rate of change based on the current estimate and how much we think it will change.\n", - "* The new estimate is then chosen as part way between the prediction and next measurement.\n", - "\n", - "Let's look at a visual depiction of the algorithm." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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EAmzfvh01NTVYunQpsrOz25w3orMoAbBROTk5OHr0KLfs7OyMxMREm3vamC1g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\n0wdz5syBQqEwKNdoNNi3bx+ysrKg1+t5io5YG5Z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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh.create_predict_update_chart()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let me introduce some more formal terminology. The predict step is known as **system propagation**. The *system* is whatever we are estimating - in this case my weight. We *propogate* it into the future. Some texts call this the **evolution**. It means the same thing. The update step is usually known as the **measurement update**. One iteration of the system propagation and measurement update is known as an **epoch**. \n", - "\n", - "Now let's explore a few different problem domains to better understand this algorithm. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23 km at time t and moving at 18 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of $\\pm$ 250 meters. The train is moving at 18 kph, which is 5 meters per second. So at t+1 second the train will be at 23.005 km yet the measurement could be anywhere from 22.755 km to 23.255 km. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.005 km because a train cannot slow down very much in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n", - "\n", - "Now consider the problem of tracking a thrown ball. We know that a ballistic object moves in a parabola in a vacuum when in a gravitational field. But a ball thrown on the surface of the Earth is influenced by air drag, so it does not travel in a perfect parabola. Baseball pitchers take advantage of this fact when they throw curve balls. Let's say that we are tracking the ball inside a stadium using computer vision. The accuracy of the computer vision tracking might be modest, but predicting the ball's future positions by assuming that it is moving on a parabola is not extremely accurate either. In this case we'd probably design a filter that gave roughly equal weight to the measurement and the prediction.\n", - "\n", - "Now consider trying to track a child's balloon in a hurricane. We have no legitimate model that would allow us to predict the balloon's behavior except over very brief time scales (we know the balloon cannot go 10 miles in 1 second, for example). In this case we would design a filter that emphasized the measurements over the predictions.\n", - "\n", - "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to $g$ and $h$ in a more intuitive, and thus less optimal way. But the fundamental idea is to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself.\n", - "\n", - "We can express this as an algorithm:\n", - "\n", - "**Initialization**\n", - "\n", - " 1. Initialize the state of the filter\n", - " 2. Initialize our belief in the state\n", - "\n", - "**Predict**\n", - "\n", - " 1.Use system behavior to predict state at the next time step\n", - " 2. Adjust belief to account for the uncertainty in prediction\n", - " \n", - "**Update**\n", - "\n", - " 1. Get a measurement and associated belief about its accuracy\n", - " 2. Compute residual between estimated state and measurement\n", - " 3. New estimate is somewhere on the residual line\n", - " \n", - "We will use this same algorithm throughout the book, albeit with some modifications. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Notation and Nomenclature" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I'll begin to introduce the nomenclature and variable names used in the literature. Some of this was already used in the above charts. Measurement is typically denoted $z$ and that is what we will use in this book (some literature uses $y$). Subscript $k$ indicates the time step, so $z_k$ is the data for this time step. A bold font denotes a vector or matrix. So far we have only considered having one sensor, and hence one sensor measurement, but in general we may have *n* sensors and *n* measurements. $\\mathbf{x}$ denotes our data, and is bold to denote that it is a vector. For example, for our scale example, it represents both the initial weight and initial weight gain rate, like so:\n", - "\n", - "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n", - "\n", - "So if the weight is 62 kg and the weight gain is 0.3 kg/day, the vector would be\n", - "\n", - "$$\\mathbf{x} = \\begin{bmatrix}62 \\\\ 0.3\\end{bmatrix}$$\n", - "\n", - "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 $\\mathbf{x}_k$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## NumPy arrays\n", - "\n", - "We will find NumPy's array data structure to be indispensible through the rest of the book, so let's take the time to learn about them now. I will teach you enough to get started; refer to NumPy's documentation if you want to become an expert with them.\n", - "\n", - "`numpy.array` implements a one or more dimensional array. Its type is `numpy.ndarray`, and we will refer to this as an ndarray for short. You can construct it with any list like object. The following constructs a 1-D array from a list:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1 2 3]\n", - "\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "x = np.array([1, 2, 3])\n", - "print(x)\n", - "print(type(x))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can create a 2D array with nested lists:" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[1 2 3]\n", - " [4 5 6]]\n" - ] - } - ], - "source": [ - "x = np.array([[1, 2, 3],\n", - " [4, 5, 6]])\n", - "print(x)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can create arrays of 3 or more dimensions, but we have no need for that here, and so I will not elaborate.\n", - "\n", - "By default the arrays use the data type of the values in the list; if there are multiple types than it will choose the type that most accurately represents all the values. So, for example, if your list contains a mix of `int` and `float` the data type of the array would be of type `float`. You can override this with the `dtype` parameter." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 1. 2. 3.]\n" - ] - } - ], - "source": [ - "x = np.array([1, 2, 3], dtype=float)\n", - "print(x)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can perform matrix addition with the `+` operator, but matrix multiplication requires the `dot` method or function. The `*` operator performs element-wise multiplication, which is **not** what you want for linear algebra." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "addition:\n", - " [[ 2. 4.]\n", - " [ 6. 8.]]\n", - "\n", - "element-wise multiplication\n", - " [[ 1. 4.]\n", - " [ 9. 16.]]\n", - "\n", - "multiplication\n", - " [[ 7. 10.]\n", - " [ 15. 22.]]\n", - "\n", - "dot is also a member of np.array\n", - " [[ 7. 10.]\n", - " [ 15. 22.]]\n" - ] - } - ], - "source": [ - "x = np.array([[1., 2.],\n", - " [3., 4.]])\n", - "print('addition:\\n', x+x)\n", - "print('\\nelement-wise multiplication\\n', x*x)\n", - "print('\\nmultiplication\\n', np.dot(x,x))\n", - "print('\\ndot is also a member of np.array\\n', x.dot(x))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can get the transpose with `.T`, and the inverse with `numpy.linalg.inv`." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "transpose\n", - " [[ 1. 3.]\n", - " [ 2. 4.]]\n", - "\n", - "inverse\n", - " [[-2. 1. ]\n", - " [ 1.5 -0.5]]\n" - ] - } - ], - "source": [ - "print('transpose\\n', x.T)\n", - "print('\\ninverse\\n', np.linalg.inv(x))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, there are helper functions like `zeros` to create a matrix of all zeros, `ones` to get all ones, and `eye` to get the identity matrix. If you want a multidimensional array, use a tuple to specify the shape." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "zeros\n", - " [ 0. 0. 0. 0. 0. 0. 0.]\n", - "\n", - "zeros(3x2)\n", - " [[ 0. 0.]\n", - " [ 0. 0.]\n", - " [ 0. 0.]]\n", - "\n", - "eye\n", - " [[ 1. 0. 0.]\n", - " [ 0. 1. 0.]\n", - " [ 0. 0. 1.]]\n" - ] - } - ], - "source": [ - "print('zeros\\n', np.zeros(7))\n", - "print('\\nzeros(3x2)\\n', np.zeros((3, 2)))\n", - "print('\\neye\\n', np.eye(3))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exercise - Create arrays\n", - "\n", - "I want you to create a NumPy array of 10 elements with each element containing 1/10. There are several ways to do this; try to implement as many as you can think of. " - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# your solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution\n", - "\n", - "Here are three ways to do this. The first one is the one I want you to know. I used the '/' operator to divide all of the elements of the array with 10. We will shortly use this to convert the units of an array from meters to km." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n", - "[ 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n", - "[ 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n" - ] - } - ], - "source": [ - "print(np.ones(10) / 10.)\n", - "print(np.array([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]))\n", - "print(np.array([.1]*10))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here is one I haven't covered yet. The function `numpy.asarray()` will convert its argument to an ndarray if it isn't already one. If it is, the data is unchanged. This is a handy way to write a function that can accept either Python lists or ndarrays, and it is very efficient if the type is already ndarray as nothing new is created." - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 0.1 0.2 0.3]\n", - "[ 0.4 0.5 0.6]\n" - ] - } - ], - "source": [ - "def one_tenth(x):\n", - " x = np.asarray(x)\n", - " return x / 10\n", - "\n", - "print(one_tenth([1, 2, 3])) # I work!\n", - "print(one_tenth(np.array([4, 5, 6]))) # so do I!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise: Write Generic Algorithm" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the example above, I explicitly coded this to solve the weighing problem that we've been discussing throughout the chapter. For example, the variables are named \"weight_scale\", \"gain\", and so on. I did this to make the algorithm easy to follow - you can easily see that we correctly implemented each step. But, that is code written for exactly one problem, and the algorithm is the same for any problem. So let's rewrite the code to be generic - to work with any problem. Use this function signature:\n", - "\n", - "```python\n", - "def g_h_filter(data, x0, dx, g, h, dt):\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", - "\n", - "Return the data as a NumPy array, not a list. Test it by passing in the same weight data as before, plot the results, and visually determine that it works." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution and Discussion" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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XrlyhTJkyDBkyhKCgoNS7KxERSZZh2Pc4/O8y+HYTxCckbdOgGvRrC60DwEU9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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from gh_internal import plot_g_h_results\n", - "\n", - "def g_h_filter(data, x0, dx, g, h, dt=1., pred=None): \n", - " x = x0\n", - " results = []\n", - " for z in data:\n", - " #prediction step\n", - " x_est = x + (dx*dt)\n", - " dx = dx \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", - " results.append(x) \n", - " return np.array(results)\n", - "\n", - "book_plots.plot_track([0, 11], [160, 172], label='Actual weight')\n", - "data = g_h_filter(data=weights, x0=160, dx=1, g=6./10, h=2./3, dt=1.)\n", - "plot_g_h_results(weights, data);" - ] - }, - { - "cell_type": "markdown", - "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 size fits all' advice that I can give here. Some filters set $g$ and $h$ as constants, others vary them dynamically. The Kalman filter varies them dynamically at each step. Some filters allow $g$ and $h$ to take any value within a range, others constrain one to be dependent on the other by some function $f(\\dot{}), \\mbox{where }g = f(h)$.\n", - "\n", - "The topic of this book is not the entire family of g-h filters; more importantly, we are interested in the *Bayesian* aspect of these filters, which I have not addressed yet. Therefore I will not cover selection of $g$ and $h$ in depth. *Tracking and Kalman Filtering Made Easy* is an excellent resource for that topic. 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 use design criteria that can be mathematically reduced to $g$ and $h$, but the Kalman filter form is usually a much more powerful way to think about the problem. 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", - "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": "markdown", - "metadata": {}, - "source": [ - "## Exercise: create measurement function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's write a function that generates noisy data for us. In this book I model a noisy signal as the signal plus [white noise](https://en.wikipedia.org/wiki/White_noise). We've not yet covered the statistics to fully understand the definition of white noise. In essence, think of it as data that randomly varies higher and lower than the signal with no pattern. We say that it is a serially uncorrelated random variable with zero mean and finite variance. If you don't follow that, you will by the end of the *Gaussians* chapter. You may not be successful at this exercise if you have no knowledge of statistics. If so, just read the solution and discussion.\n", - "\n", - "White noise can be 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", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# your code here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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sjLe3NwMGDODixYupjuPn50fHjh1ZsWIFTZs2xdnZmU8++STXrk2ypp5IERHJ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\nggiOAAAAAPwDIdKLvqk1lL9LytsifbhFOvyVJIV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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from numpy.random import randn\n", - "def gen_data(x0, dx, count, noise_factor):\n", - " return [x0 + dx*i + 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)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Discussion\n", - "\n", - "`randn()` returns random numbers centered around 0 - it is just as likely to be greater than zero as under zero. It varies by *one standard deviation* - don't worry if you don't know what that means. I've plotted 3000 calls to `randn()` - you can see that the values are centered around zero and mostly range from a bit under -1 to a bit more than +1, though occasionally that get much larger." - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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X/SGRh63nGo3rlHBsbUCx/+TF/8Sau3XzF0VRUFF/QiiNUX3S4fxtWh+QgOJK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Zc6vZDlY9qn+CyCfYXJZEZRJDTmYQhbPp+PaqpaPicNXQDlhTW6qYjVEkdCMI+CcJSSlAYZadnW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\nMHPmTPD5fPDrX//a6+gRBEEQB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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot([randn() for _ in range(3000)], lw=1);" - ] - }, - { - "cell_type": "markdown", - "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", - "execution_count": 32, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# your code here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution and Discussion" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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FTnltU+v5W5W8Lm7dugVApUqVyJs3Lx9++CGff/65pVxE5G3yys9kmkwmtm/f\njoeHB2nSpKFSpUoMHz6cDBkyAHDgwAGioqLiJJNeXl7kz5+fnTt3KskUERF5zRmGwfnz54mJiSFH\njhxYW1s/s/4fBwyaDoKQ+4/L7O1in4d8vzxUKhKG39T5HDhwADc3N3r2rEn58m4AxMQYXL0FV27G\nTSzt7UxcunSJESNGcO7YOfaF56BG0S/w8vJKyktPNCVKlADgl19+wc7Oju3bt8cpFxF5m5gM459r\nsj2bi4sLEydOpE2bNpay3377DScnJ7Jnz8758+cZPHgwMTExHDhwADs7O+bPn0/btm2JioqK01a1\natXIkycPkydPtpSFhoZavj5z5syrXJeIiMhLWbduHStWrCAyMpJSpUrh4+ODnZ1dSoeVYoKDg+nf\nvz8nTpwAIHv27IwaNYps2bJhGAarV69m586dWFtb895773GdBoxekpUYc+wIo72tmb6NL1KzRAiO\n9i//mExwcDBt27blzp07ljI3Nzdmz54d72yq14lhGIwYMYKlS5daytzc3Jg6dSre3t4pGJkkhty5\nc1u+dnV1TcFIRF4PrzyS2bx5c8vXBQsWpGTJknh7e7N69WoaNmz4qs2LiIgkm19//ZWxY8davj98\n+DCnT59mzJgxWFk9dxmDt45hGJYE08nJCWtra86fP0/v3r357bffmDhxIvPmzfv/2tasO1UHU8bH\nCVMG14f80OEsBbL+/cqx+Pn5cefOHQoXLkzr1q2ZO3cuR44cYdasWfTr1++V209qJpOJgQMH8r//\n/Y8TJ06QOnVq3nvvPdKlS5fSoYmIJLpE38IkY8aMeHl5ERgYCICnpycxMTHcvn0bNzc3S73g4GAq\nVqwYbzvaj0ris3//fkD3iMRP94gkxL/vk5iYGKpUqQLELsaSJ08e2rZty/bt24mMjKRChQrJGl9M\nTAyLFi3ixIkTeHl58eGHH+Ls7JysMZw/f54TJ07g4uJCUFAQ9vb25M2bl0uXLnHlyhXmzZuHtbU1\nXw8bx4ztNTgf8ng0p1Q+WPq9HZkzFEiUWMLCwgAYOnQojRo1Inv27DRr1owHDx4k6f/rif37pHTp\n0onSjrxe/jkbT0SSIMm8efMmV65cIWPGjACULFkSW1tbNmzYwIcffgjA5cuXOXny5AttuiwiIpKU\nQkNDefDgAfb29vTt2xeTyUSlSpVYsWIFly7Fs3pNEomOjqZevXqsXbvWUubr68u2bdvifGCb1GJi\nYlfgsbF9i6OjAAAgAElEQVSxwd7eHjs7O8vU4YsXL4FjXrKW6M6sQ104H/L4vNpl7rNohMsT+12+\nihw5cgCxHwDExMQwevToOOXPcu3aNebMmcOdO3coVaoUjRs3TtGVZkVE3nbPTTLDwsIsz0eazWYu\nXLjAn3/+iZubG+nSpWPIkCE0adIET09PgoKCGDhwIB4eHpapsq6urvj4+NC/f3/c3d1Jly4dvXv3\npmjRolSvXj1pr05ERCSB0qZNS4YMGbh58yYdO3Ykd+7crFu3DoB8+fIlayxTp05l7dq1uLm54ePj\nw9KlSzl+/DhffPEFU6dO5ebNm/j6+nL+/Hly5cpFr169kmTaZfbs2cmfPz8nTpwgb9682No5E3Qn\nF06FvuDHra0xFe9FkAFcfnyO1ZVvWPBNn0RNMAG++OIL/P392bNnD82aNQNiZ08NHDjwmeedOHGC\nSpUqcfPmTUtZu3btmDFjhhJNEZEk8twkc9++fVStWhWIfZ5gyJAhDBkyhHbt2jFp0iSOHj3KnDlz\nuHv3LhkzZqRq1aosXrwYJycnSxu+vr7Y2NjQvHlzwsPDqV69OnPnztUvdxEReW2YTCamTJlCs2bN\n+OWXXyzlXbt2TfYVQA8cOADA4MGD6dWrF++99x7VqlXjwIEDBAcHU7ZsWS5evGipP3/+fPbs2ZPo\no5zW1tYsWryUGk1HcyW6BqStjSmjM38Df/9r5w0jJgwCfRjerwQuLq82rffmzZsEBgaSKVMmy6I4\nmTNnZv/+/Xz//fecO3eOnDlz8vnnn5MpU6ZnttWlSxdu3rxJuXLlqFSpEuPHj8fPz4/GjRtTt27d\nV4pTRESe7rlJZuXKlTGb418N7tGnvM9iZ2fH+PHjGT9+/ItFJyIikowaNWrEjh07mD17NuHh4VSp\nUoXWrVsnexzp06cHYv/GNmjQAH9/f0v5sGHDuHjxIsWLF6dLly74+vpy7NgxRo4cyahRo16p35CQ\nEMLDw/H09OTMJRMz18CctXkITvMzT/tY2NnRIIfbWWJurcTTfj/tx9enZcuWrxTD+PHj6dOnD9HR\n0QB06NCBKVOmYG1tTebMmZkwYcILtffXX38BsGDBArJkyUJYWBjjx4/nzz//VJIpIpJEEv2ZTBER\nkTdZ2bJlKVu27FOPhYeHc+DAAcxmMyVLlowzaycxderUialTp7J+/XqyZ88OxI609u7dmx9++AGA\nIUOGUL9+fZycnGjZsiWnTp166f7u379P+/btWbJsI7g1wdH7UyJsSz61bo5MsXtd1i0HFYuZsLfL\nDfR+6b7/aePGjfTs2ROAwoULc+LECaZPn0727Nn54osvXqpNd3d3QkJCmDlzJg0aNGDTpk2WchER\nSRr/vfXYRUREXsKxY8coUKAAFSpUoFKlSuTOnduy8mhiy5kzJ1u2bKFChQpkyJCBYsWKsXz5cmrW\nrEmWLFkAmDhxIr///jtTpkwBIGvWrC/Uh9lscPKCgd9qg+JN9rAk8EtMZe5gyjX9iQTTIx30bQmH\n58CZhTCul4kaZUzY2yXuYy8rVqwAoE+fPhw+fJi5c+cCsHz58pdu89Ezm0OGDKFo0aIcP36cHDly\nxNmCTUREEpdGMkVERJ4jOjqahg0bEhQUhLe3N7a2tgQGBtKgQQPOnDmDo6NjovdZvHhxtm3b9kT5\nwIED8ff3Z+PGjWzcuBEANzc3evTsw+FAgz1Ho1i68QKXbliTOrUL7hnSY2MNNtZgbQXW1nDrLuw+\nBiH3H7VaDdO/BmUNcxRl89xkUMdM1HoHbG2Sfh2FR2s1PFrV9tG/r7KGQ9u2bbGxsWHMmDGW1WV9\nfX1xdXV99YBFROSplGSKiIg8R2BgIGfOnCF9+vScOHECGxsb8uTJQ1BQEIcPH453em1SyJ07N3v2\n7GHAl+M5fCkLNq6lcUxfniId7Yl8CGAL5IqtfBU4mfC2rawMiuc2EXJmEmf3fc1nvSbwwf+Sb8Sv\nQYMGTJgwAV9fX9asWWPZc7tRo0av1G6rVq1o1apVYoQoIiIJoCRTRETkOWxsYv9cRkVF8ffff2Nn\nZ0dERAQQuwJrcjEMg4C/YOKSPKwO/okYK+D+/79eQvo08G5B+GvHz1w4ugDPNNcwRabm7L59pEqV\nivLlyydm+M9VtWpVJk+eTM+ePTl9+jQQuzpsnz59kjUOERF5NUoyRUREniNHjhyUKlWK/fv34+3t\njbW1Nffu3SNfvnwULVo0yfsPCzeYvxEmLoHDgfHXszVf5WHIHj5uXoI6lb1ZvHgBCxYsonadurRp\n257oGIiJAQc7KJkPcmaOnYp64UItatcex4kTp7hyEZycnJg3bx5eXl5Jfm3/1rlzZ1q0aMG5c+fI\nmDEjGTNmTPYYRETk1SjJFBGRZBEdHc2kSZPYsWMHqVOnpmPHjpQpUyalw0oQKysrli5dSpMmTdiz\nZw8ARYoUwd/fH1tb2yTr98pNgx9/gxmr4O5TRisrFYc670LxPLGvD2o3ZdepXeS0H06tMj2ZOWYe\n3FlNCe8CtKge/3ON3t7eHDp0iF27dvH3339TqlSpFF19NU2aNMm+N6mIiCQeJZkiIpLkDMOgRYsW\nLFmyxFLm5+fHihUrqF27dorEFBYWRlhYGGazGSur5y+27uXlxa5duzhy4gr3/4Z3imfC2jppFmmP\niDQYswBGzIa/I+IeS+UArd+Dro2hcM64iWO3bt3YtWsXgwYNYtCgQUDsqGTbtm2f26e9vT2VK1dO\nrEsQEZH/MG1hIiIiSW7Tpk0sWbKE1KlTM2nSJNq1a0d0dDTdunVL9lgePnxIx44dqVKlCu+//z7e\n3t5s3779uecdPWfQ+mso0SkzFXpmJltjE+2+NZi91uDyDSNRYjMMA/8tBgVawZc/x00wc2aGMd3h\n8jKY0t/0RIIJ0LJlS6ZOnUqmTJmwsrKicOHCbNy4kdy5cwOwefNmGjZsSOXKlenXrx8PHjxIlLhF\nRET+yWQYRuL8ZUwEoaGhlq+1tLjE59G+dKVKlUrhSOR1pXvk9TNp0iS6du1K27Zt8fPz4+HDh9jb\n2wOx02iTc/Gc3r178+OPPwKxo3xhYWGkTp2ao0ePWvag/KeDpwy+mwX+W5/dbp4sULUUVC4O7xYC\nL/cX23rjcKDBZ+Ng88G45YVzwvBOsdNirawS3t6/R2hXrVpF/fr1MZvNlrIyZcqwbds2y38LeZJ+\nn0hC6D2sSFyaLisiIknO29sbgNWrV7N48WJ27doFxE5BTc4EE2Du3LkATJ48mWLFijFw4EC2bNnC\nypUr6dKli6Xe7qMGw2fB6p1PtuHkCGHhcctOX4p9TVka+32m9PBuIYN3CsE7BaFkXrC3iz3v5t3H\nr1t3YedR+GUl/CP/w80Vvu0IHT4Am5fYo/LfU4AHDBiA2Wymc+fO1K5dm65du7J3716WLFlCy5Yt\nX7h9EXlxhmEQFRUV58MekTeRlZUVtra28X6YqiRTRESS3HvvvUe1atX4/fffadq0qaV81KhRyR7L\nw4cPAUifPj02NjZ4eHjEKb8RYtB+GKzd/eS59SvAoLZQLDccPA2/74c/DsCOwxDxMG7dq7dgyZbY\nF4CtDVhbPVnv36yt4dOGMNQH0qV+8eQyPhcvXgTg66+/xt3dnd9//53x48dz4cKFROtDROJnGAYR\nERHY2dk98825yOvOMAzMZjMRERE4ODg89V5WkikiIknOxsaGVatWMXz4cMvqsp07d6ZWrVrJHkuN\nGjVYvHgxnTp1ImvWrPz5559YW1tTpUoVjp83qNsPgq49rm8yQbOqMLANFMn1+A9pmQKxr4FtYhfq\n2XUUfj8Au4/C3uPw4F8jnVHREPWc2KqXgh97QsEcif/mM3fu3Bw6dIiuXbtSvXp15s2bZykXkaQX\nFRWFnZ1dss/eEElsJpMJa2tr7OzsLPf1E3X0TKa8afR8jDyP7hF5llu3bvH++++zd+9eAGxtbZky\nZQpZCrWn6WC4FxZbz2SCj96Dz9tAPu8XS/piYgyOnYddR2HPsdh/T8UOJOJgBxnSQoY04JbaIOxu\nEOH3L1I4SzDD+1Ukc+ZMiXm5FgEBAdSoUYPIyEhLWa1atVi1apXe9D6Dfp9IQiTkPWxERAT29vYa\nwZS3hmEYREZG4uDg8MQxjWSKiMhrLTQ0lDFjxnDy5Em8vLz47LPPnrpAT0KlT5+eHTt24Ofnx/37\n92nSpAlrDnhRpy/ExMTWcXKE+UPhg/+93JtBa2sTRXJBkVzQqUFs2f0wA5Mptm2TyYTZbKZFixZs\nWLQIgIPAmvkZ2LZtG/ny5Xvp64tPhQoV2LNnD1OnTuXOnTuULl2aHj16KMEUSUZKMOVt8qz7WUmm\niIi8tkJDQylXrhzHjx+3lM2dO5c9e/aQPXv2l27XxsaGYsWKEWMG32Ve/Ljg8TEvd1gxEorlSdw3\ngy5Ocdvz9/dn0aJFuLq60qtXLzZt2sSOHTvo3r07GzduTNS+HylatCiTJk1KkrZFREQe0T6ZIiLy\nVFFRUezatYvNmzdz9+7dFIlh/PjxHD9+nDx58jBz5kzKly/PzZs3GTx48Cu3/XekFQN+yRknwSyZ\nF3b/nPgJ5tMcPnwYgE8++YShQ4cya9asOOUiIiJvKiWZIiLyhAsXLlC8eHHKlStH1apVyZ49O5s2\nbUr2OM6cOQPAZ599Rrt27fj222/jlL8MwzBYud2g/dh8bDuaxlLeoCJsmQiZMiTPdLZHq9quXbuW\ngwcPMm3aNAA8PT2TpX8REZGkoiRTRESe8OGHH3Ls2DEyZsxIwYIFuXv3Lo0bN+bGjRvJGkfWrFkB\nmDZtGmvWrGXMmDHA4303X4RhGGzaZ1DuE6g/AM4HO1qO9W0Ji4eDk2PyPS/VqlUrsmfPztGjRylZ\nsiQjR44EYNCgQckWg4hIUgoKCsLKysoyUwPAz88PKysry7ZK8nZSkikiInHcvXuXXbt2YWNjw7Fj\nxzhy5AilS5fm3r177Nq1K1ljaevTkzT5BnIweip1h9di9dXR2HkPoEfvr1+onR2HDap2h5q9YM/j\nxztxsIvh5wEwqqsJK6vkXZAjTZo0BAQE0LRpU3LlykXZsmVZvHgxzZo1S9Y4RERexaOk8Wmv7t27\nYzKZnrvg0fz58xk3blwyRSzJQQv/iIhIHDY2sX8aYmJiuH//PqlSpSIsLHZfj+RYidRsNth6CGas\ngiVb0hORbjiP3p6YHPMSlXkENb+AZlUNOjWAdws9ucJdVLRB4GU4dh5mroK1u+P2YWcLjcpdp031\nYGpVLZbk1xSfzJkzs3DhwhTrX0QksXz99dfkzJkzTlnevHlZsmSJ5e9KfObPn8+xY8fo2bNnUoYo\nyUhJpoiIxOHs7Mz777/P6tWryZMnD6lSpSIkJIRMmTJRsWLFRO8vPNIg6BqcvQIHT8HstXDu6rPP\niXwIc9bFvgrnhI9qGTwIhxNBcOwcnL4E0TFPnmdjDe3rwuC2cP3S5US/FhGR/6r33nuPMmXKvPT5\nSbG9S3h4OI6Ojs+vKIlO02VFROQJs2fPpmbNmkRGRhISEkLOnDlZs2YNqVOnBmDHjh3069ePvn37\nsm3btgS3ey/MYNxCg4+HG1TqYpClgYFTVSjYCur1h6G/PJlgFs8DE3rDxaUw7XMo9a8tJI+chf4T\n4ZsZsOgPOB70ZIJpGGZcH65k//S/mdrfRBYP7VUnIpLUnvZM5r9VrlyZNWvWWOo+ej1iGAYTJkyg\ncOHCODo64uHhQYcOHbh9+3acdrJly0bt2rX5/fffKVu2LI6OjowaNSrJrk2eTSOZIiLyhHTp0rF+\n/XquXr1KZGQkWbNmtUyVnTlzJj4+PhiGAcCYMWOYPHkynTt3fmabx88bNBoYO8r4PGlcoGUN8PkA\niv9jOxGfD2Jf+08YTF0Ov26EvyOe3oYReQEPl1u8U8SZQ+t7cfHUev5Y8yNF8vRK2A/hBS1fvpx1\n69Zha2tL8+bNKV++PBC7Um+HDh0ICAjAxcWFzp07M3To0GSZeiwiklzu3r3LrVu3nnrsWaOUgwcP\npn///ly+fBlfX98njn/66afMmDGDdu3a0aNHDy5evMiECRPYu3cv+/btw97e3tJHYGAgTZs25ZNP\nPqFjx46WxeMk+SnJFBGReGXKlCnO96GhoXTp0gXDMOjcuTM2Njb89NNP9OjRgyZNmpA+ffqntrN4\ns0H74RAW/uQxa2vI7BZNZOhJIkKP4+l4kmGdStO4YZ144yqV30Sp/DC6m8Hc9bDnGHi6QYFsUDAH\nfNigBGdP/8n6P/+kaNF8fP99ZQYOXM+5c+de5ccRr6FDh/L1148XI5o4cSJz5syhXr16VKtWjbNn\nzwIQGRnJsGHDiImJ4bvvvkuSWETk7TD0F4NvZiRd+199DEN9Em9WR61ateJ8bzKZErTvb/Xq1cmU\nKRN3796lZcuWcY7t3LmTn3/+mTlz5tCqVas4fVWoUIHZs2fTsWNHIHbE8+zZs6xYsYK6desmwhXJ\nq1CSKSIiCXbu3DkiIiLInTs3kydPBmDr1q0cOXKEM2fOPJFkRkcbDPoZfpj3uCyVA3zZHornhpyZ\nwcX+Lu+ULUnw+fMA3AWa7IClS5fSoEGDZ8bj6myia2Po2jhuea7sHpw9HfsJeatWrZg+fToAOXLk\neLUfwFOcO3eOr7/+GisrKwYNGsSNGzeYOnWqZWT37Nmz5MmThy1btrB3714aNGjAhAkTGD58eJI8\ngyQikhImTJhA/vz545Q5ODi8UpsLFy7E2dmZmjVrxhklzZs3L+7u7mzevNmSZAJkyZJFCeZrQkmm\niIgkmIeHBxCbWC1ZsgRbW1tOnjwJgKenZ5y6t+4afDgEft//uCxnZljyHRTJ9Ti5mjBhLufPn6dQ\noUL88ssv/Prrr/j6+vLtt98+N8mMz4gRI9i+fTurVq1i1apVABQuXJgOHTq8VHvPcuLECQAqVKjA\nN998g2EYLF26lBs3blj2gStcuDAZM2akatWqAISFhREdHY2trW2ixyMikhJKly79xMI/QUFBr9Tm\n6dOnefDggeVvz7/dvHkzzvdJ8UGivBwlmSIikmCZMmWiY8eOTJs2jSZNmljKP/roI7Jly8bDKIOH\nUXD0HLT4Ci5ef3xunXdhzleQNnXc0bvg4GAAPvjgA8qUKUOaNGnw9fW1lL+M4sWLs3fvXsaOHUtw\ncDCFCxdm4MCBODs7v3Sb8fHy8gJg3759LFu2jBs3bnDjxg1sbGyoXLkyJpMJf39/WrdubUnIS5Ys\nqQRTRJ5pqI+JoT4pHUXKMpvNuLm58dtvvz31eNq0aeN8r5VkXx9KMkVE5IV8/8MkrhkN+eNIVh5a\neWFl48BvF2yZ+7/4z/nqY/iqPVhZPTk9tFChQgBMmTIFZ2dn1q5dG6f8ZRUoUMAyTTYpFSlShCZN\nmrB48WIaNmxoKR84cCDvvPMOo0aNol+/fsybFztn2NPTEz8/vySPS0TkTRHfowM5c+Zk06ZNlC1b\nFicnp2SOSl6FkkwREUmQw4EGk5fC3PXWhIXXgv9fHDXmKftRPuLqHDt6Wbd8/M8eNmvWjAULFrBi\nxQoGDRoEQPr06Rk3blxihp9kTCYT8+bNo0CBApbVZVu2bMmnn34KQN++falcuTI7d+7E2dmZ+vXr\n4+bmlsJRi4i8PpycnAgJCXmivEWLFkyePJlvvvmGkSNHxjkWExPD/fv3SZMmTXKFKS9ASaaIiMQr\n8qGB/1aY7A/bn79IIDbWYGcLtjbwTkEY/xnkzvLsxW2sra3x9/dn1qxZHDp0iAwZMuDj40PmzJkT\n6SqSnp2dHV9//XWcFWb/qVSpUpQqVSqZoxIReTOULl2ahQsX0qtXL8qUKYOVlRUtWrSgQoUKdO3a\nlR9++IHDhw9Ts2ZN7O3tCQwMZMmSJXz77be0adMmpcOXp1CSKSLyFlizZg0DBgzg4sWL5M6dm3Hj\nxln2aVy/fj0jRozg+vXrFC5cmDFjxpAlS5bntrlxr4HPCLh848ljBbND54bQuDI4Oz5OLF92tVRr\na2s+/vjjlzpXRERS1ov+7v93/S5dunDkyBHmzp3LhAkTgNhRTIhdtbZEiRJMmTKFwYMHY2Njg7e3\nN82bN7cspvYyMUjSMhmPdtN+DYSGhlq+dnV1TcFI5HW2f3/sUpUaFZD4vK33SFhYGJMmTeL06dNk\nyZKFLl26kD59erZu3UrVqlUxm82Wug4ODuzZs4erV69Sp04d/vmr3svLi0OHDsW7p2V4pMHAyTB+\nUdxyG+vYpPLTRlCh6Jv/B/1tvU8kcek+kYRIyHvYiIiIV97SQ+R1E999bZUCsYiIyAt68OABFSpU\noH///kyfPp0hQ4ZQsmRJrl27xrhx4zCbzXTq1Ilr167RpEkTIiIimDJlCt9++y2GYdClSxf27t1L\n8eLFuXz5MjNnznxqP3+dMSjjEzfBTJ8GvukIF5fCr9+YqFjMFG+CGRMTw9ixY6lduzb16tVj0aJF\nT60nIiIiby8lmSIibwBfX18OHTpE9uzZ8fX1pVixYly8eJEvv/ySO3fuAFCnTh08PT2pWbMmALdv\n37ZsA9KpUydKly5t2Xfy39uDxMQY/DDPoEwHOHb+cXnd8nBkDgxuZ8LT7dkjl4Zh4OPjQ58+fVi3\nbh0rV66kWbNm+Pr6JtaPQURERN4ASjJFRN4Ax48fB2K3xejZsyejRo2ylD+axtetWzd69+5tWaG1\ndOnSlm1AOnXqxIgRIyzPujwqN5sNjp0zqN4TBkyCqOjY/lI5wOR+sHwkeKRL2LTYw4cPM2vWLBwc\nHJgxYwbDhw+3xBwREZEIPwURERF5E2jhHxGRN8CjlVbnzJlDoUKFmDp1qqV8yJAhbN26lf379/Pj\njz8CUKNGDXr06EHDhg3Zs2cPu3fvZveBc5CqKPmqNCHgahumdjQ4fCaaiKi4fwpK54/ddiRP1hd7\n5vLChQsAlC9fnvbt2wMwduxYbt++zY0bN8iaNesr/QxERETkzfDckcxt27ZRr149vLy8sLKyYtas\nWU/UGTp0KJkzZyZVqlRUqVLF8on7I5GRkXTv3p0MGTJY9gi7cuVK4l2FiEgK2bFjB/369aNfv35s\n3749yfrp0aMH6dOnJyAggHLlyrFkyRIcHBwYOHAgLi4uBAQEMGfOHIYNG8Zvv/3G2rVrsbOzI22G\nHHQffgrP965hKh2MqeBGTkV2wm+NFXuPEyfBNIwYMsZM5/dxD184wYTYTbMh9u/GuHHjGDBgALdv\n38bJyQlPT89E+1mIiIjI6+25SWZYWBhFihRh3LhxODo6PrHYw8iRIxk7diw//fQT+/btw93dnRo1\navDgwQNLnV69euHv78+CBQsICAjg3r171K1bN85KiCIib5rp06dToUIFRo8ezejRo6lYsSLTp09P\nkr6yZMnCrl27aNq0KUWKFKFu3boEBARQokQJIHY12datWzNo0CCaNm1KwF9WfPS1Qeb68OWM1Fy/\n7xFv26lsH1A61y0yBDfi6p5PWLN6+UvFWLBgQbp27UpUVBS9evWyTOn19fXFzs7updoUERGRN89z\np8vWrl2b2rVrA9CuXbs4xwzDwNfXl4EDB9KwYUMAZs2ahbu7O/Pnz+eTTz4hNDSUGTNm4OfnR7Vq\n1YDY6V7e3t5s2rTJskCFiMib5O7du3Tr1g3DMPj0008BmDx5Mt26daNx48akTZs20fvMlSsXCxcu\njPf4zRCDGavhl5UQePnJ4w52UDQXFMwBhXNCn09rEXP/EFdunsHVNQOdOmXk5595pZkmEyZMoHjx\n4mzYsAE7OztatWpFrVq1Xrq959mxYwdffPEFFy5cIFeuXIwaNcqSeIuIiEjKeKVnMs+fP8/169fj\nJIoODg5UrFiRnTt38sknn3DgwAGioqLi1PHy8iJ//vzs3LlTSaaIvJECAwOJjIwkX758TJo0CYAt\nW7Zw4sQJzpw5Q5kyZTAMg+vXr2Nvb58kSecjV24ajJ4P01bA309ZX6dkXvD5AD6sAa7Oj2ej/DLs\nGkeO3KR9+/b873//Y8GCBQDkzZv3pWMxmUz4+Pjg4+Pz0m0k1P79+6latSoPHz4EYp8JrVixIvv2\n7SN//vxJ3r+IiIg83SutLvtoCXwPj7jTsNzd3S3HgoODsba2xs3NLU4dDw8Prl+//irdi4ikmEe/\n9wIDA1m2bBnLly/nzJkzAHh6enLy5EmKFi1KxowZSZcuHR988AEhISGJGsP5qwadRxnkbArjFsZN\nMFP/H3v3HRbV0QVw+HeXDgIigtixN6xorBix1yBWUKPYQ+wajcYYSwxqYonR2GvsvYEFuzH23lHU\n2FAUC0gve78/9nN1IyiKCup5n4cHdnbuvXNhgD07M2es4BtPOD4fjs5T+MZTMQgwAaZNm4aFhQXr\n1q1jwIABRERE0KpVK/3slYxuwoQJxMfH07p1a86fP0+jRo2Iiorijz/+SO+mCSGEEJ+195ZdNqWN\nulPr2LFj76gl4lMlfUS8zvvuI40bN8bf31+/XACgUaNG3Lx5k9atWxMSEoK5uTkJCQn4+/vTtGlT\nJkyYkObr/htqxoLt2dl2PAtJWsO/tYVyRuNdI5TaZR5jbqqSFAEpfRvMzc2ZP38+GzduJDIykhIl\nSuDh4cHx48fT3MYPITg4GNBt1RIdHY2rqysBAQEEBQW90c9e/paI1JB+Il6lUKFC6d0EITKUNAWZ\nz7IFhoaGkitXLn15aGio/jknJyeSkpJ4+PChwWjmvXv3qF69elouL4QQ6Wro0KHkyJGD3bt3A1Cj\nRg06derEsWPHCAkJIXfu3CxZsoRHjx7RrFkz9u3bx9OnT7G2tubUqVOcPXsWKysratasSebMmV97\nvTsPTZkZkINtJ7KgqobBpYtzJJ3q3qVq8Qje5D2+AgUK0K9fvze674yiUKFCHDt2jMmTJ3P58mU2\nbNigLxdCCCFE+klTkJkvXz6cnJwIDAzE1dUVgNjYWPbv38/48eMBcHV1xcTEhMDAQLy9vQG4ffs2\nlxZ7iGwAACAASURBVC5dokqVKime+9nm4kL817N3k6WPiJS86z6yZcsW/vrrL+Li4qhTpw7du3dH\no9GtNqhUqdJL9cPCwgDdlNpq1aoRFRWFqakpsbGxuLi48OeffzJy5Eh9/fnz57Nr164U1xE+eKwy\neiHMWAcJiYbPuZeDoT7gXi4TilL4ndzvx2LatGmcPXuWc+fOMWvWLAC++OILJk2ahKWl5WuPl78l\nIjWkn4jUCA8PT+8mCJGhvDbIjIqK0q8z0mq13Lhxg1OnTmFvb0/u3Lnp27cvfn5+FC1alEKFCjF6\n9Gisra1p06YNALa2tnTu3JlBgwbh6OhIlixZ6N+/P6VLl6Z27drv9+6EECKN5syZQ9euXfWP161b\nx/Hjx1+5VUnFihWxtrbm2LFjVKhQgUePHhEbG0uZMmW4du0aI0eOxNjYmA4dOnD69GmOHTtGp06d\nOHjwoMF5IqNVJq2A8UvhabThNRpW1gWXlV3StjThY5Y5c2YOHjzIggUL+PfffylYsCA+Pj6Ym5un\nd9OEEOKzsWDBAjp16gTo9kmuVq3aS3UKFizItWvX+PLLL/Wzf8SHd+DAAbZv307fvn2xtbV9r9d6\nbZB59OhRatasCejWWQ4fPpzhw4fj4+PDvHnzGDRoEDExMfTo0YPHjx9TqVIlAgMDsbKy0p/j999/\nx9jYmNatWxMTE0Pt2rVZvHhxmtdtCiHE+5SYmKifSjp48GDy5MlDv379mDt3Lj179qRMmTLJHufg\n4MDKlStp3bq1fn1jgQIFWLFiBYGBgQB4eXkxdvxsrt+O4IuKVTlyPpF/zmhJTFKIi4dLN2HMXxD6\nyPDcVUvBWF+oWkr+fgJkypSJnj17pnczhBDis2dhYcHSpUtfCjIPHTrEtWvXMDc3l9f+6ezAgQOM\nHDmSjh07pn+QWaNGDbRa7SvrPAs8U2Jqasoff/whGf+EEB+VBw8eEBkZiY2NDWPGjAFg48aNbN26\nlatXr6YYZALUr1+f4OBgjhw5gpmZGVWrVkVjZE5I1C3I+yurr3zFkkYANihlzqICbr4pt6W4M/h9\nA02qpT2xmhBCCPGuNWjQgFWrVvHHH39gbPw8xFi6dClFixbFyMgoHVuXdlFRUQaDaB8zVVXf+zXS\ntIWJEEJkNLdv32bSpEkMHjyYoUOHpmnbkKxZs2JlZUVERATDhw9n3rx57NmzB9CtSX8dBwcHipdt\nSFB4LVoPN8e+AYzdWBMl53fEGaVu/WQuR5gzBE4thK/cFAkwhRBCZEje3t48evSIbdu26cuSkpJY\nuXIlbdu2fam+qqpMmTKFkiVLYmFhQbZs2ejSpQsPHz40qLdx40aaNGlC7ty5MTc3x9nZmUGDBhEX\nF2dQLzQ0lC5duujrOTk50bBhQy5cuKCvo9FoDHIiPOPs7EzHjh31jxcsWIBGo2H37t307t2bbNmy\nYW1trX/+6NGjNGzYkMyZM2NpaYmbm5v+9cEzI0aMQKPRcOnSJdq1a0fmzJlxcHBg6NChANy6dQsP\nDw9sbW1xcnLS57N5UVxcHCNHjqRQoUKYm5uTK1cu+vfvT0xMjEE9jUaDr68v69evx8XFBXNzc1xc\nXAx+FiNGjGDQoEGA7jWMRqNBo9Gwb98+AE6cOEHDhg1xdHTEwsICZ2dn2rdvT2xsMhtwp8J728JE\nCCHSIiEhgVmzZnHmzBmyZctGt27dDLJYJ+fGjRtUrFhRvwfvzp07Wb16NYcOHcLOzu6N22BiYsJv\nv/3Gt99+y6hRo/Tl7du3p2zZsikep6oqgUd0e1duPfSKC2jjMEoKwT5LJnI6ZcXMVMHUBMxMwNwU\napTT7XVpYSaBpRBCiOQlJiZy69YtrK2tyZo1a7q1I1euXLi5ubF06VIaNWoEwI4dO7h//z7e3t4s\nW7bMoL6vry/z5s3Dx8eH3r17c/PmTaZMmcKRI0c4evQoZmZmgC7gs7CwoE+fPtja2nLw4EEmTZrE\nrVu3DM7ZokULzp07R69evciXLx/3799n3759XLlyheLFi+vrJfdmraIk/yZur169yJIlC8OGDdMn\nd9q7dy/16tWjXLlyDB8+HGNjYxYtWkTdunXZvn07X375pcE5vL29KVasGOPGjSMgIIAxY8Zga2vL\nnDlzqF27Nr/++iuLFy9m0KBBuLq64u7uDuheS3h6erJv3z66detG8eLFuXDhAtOmTeP8+fMGASTA\nwYMH2bRpE99++y2ZMmXijz/+oHnz5ty8eZMsWbLQvHlzrly5wrJly/j999/1faVYsWI8ePCAOnXq\n4OjoyPfff4+dnR03b95k06ZNREdHv12uAzUDefLkif5DiJQcPXpUPXr0aHo3Q7xH8fHxau3atVVA\n/5E1a1Y1KCjolcd16NBBBdSSJUuqw4cPV4sVK6YC6rBhw9LUnvXr16vNmjVTGzVqpE6aNElNTExM\ntl5UjFadsU6rFm+jVZUqyX8UaqVVe03UqgH/aNXIaO1L59BqteqWLVvUMWPGqHPnzlXDw8PT1HaR\nMvlbIlJD+olIjdS8ho2JiXnn192/f7+aM2dO/f/K1q1bq1FRUe/8Oq8yf/58VVEU9fDhw+rMmTNV\nKysrNTo6WlVVVf3666/VypUrq6qqqiVKlFDd3d1VVVXVf/75R1UURV28ePFL96Moijpr1ix92bNz\nvcjPz0/VaDTqrVu3VFVV1cePH6uKoqgTJkx4ZVsVRVFHjhz5Urmzs7PasWPHl+6pUqVKalJSkr5c\nq9WqRYoUUevUqWNwfHx8vFqiRAm1SpUq+rLhw4eriqKoXbp00ZclJSWpuXPnVhVFUf38/PTlT548\nUS0tLdV27drpy5YsWaJqNBp13759BtdasmSJqiiKGhgYaHBfZmZm6tWrV/VlZ86cURVFUadOnaov\n++2331RFUdQbN24YnHP9+vWqoijq8ePHk/muvVpK/Vqmywoh3qvExER+++036tWrh4eHB+vWrXvt\nMYsWLWLHjh04Ojoyfvx43NzcCAsLo3///q887lkm7O7du9O4cWMGDBhgUP62PDw8WLNmDf7+/vTt\n2/eldSW376sMma6Suyn4/gYX/33+nKJA/UowpT9cXgGXVyj80U+hYRUFKwvDd01VVaVr1640aNCA\nIUOG0LlzZ1xdXQkJCUlT+4UQQnx6QkJCaNSoEXfu3MHe3h4jIyNWrFhBnz590q1NLVu2JCEhgfXr\n1xMTE8P69euTnSq7cuVKMmXKRN26dQkLC9N/FClSBEdHR4MMtBYWFoBul4vw8HDCwsKoWrUqqqpy\n8uRJfR1TU1N2796dpmUy/9W1a1f9lmUAp0+f5vLly3h7exu0Ozw8nNq1a3P48OGXppd26dJF/7VG\no8HV1RVFUejcubO+3NbWliJFinD9+nWD71HhwoUpXry4wbWqV6+OoigvZel1d3cnf/78+sclS5bE\nxsbG4JwpebZX96ZNm0hMTHxN7dSR6bJCiPdGVVW+/vprli9fri/buHEj06ZNw9c35Sw358+fB6BH\njx4MGDCAevXqUbJkSYN1FcnJmzcvBw4cYPHixSQmJrJ48WJ9+fsQn6Dy6xIYvQDiEwyfs7aETo2h\nVwvInzN1013XrVvH3LlzsbS0pGPHjuzatYuLFy/Sp08fVq1a9e5vQAghxEdr69athIeHU61aNXbv\n3s3p06cpX748y5YtY9asWemyht/Ozo569eqxePFiNBoNMTExtG7d+qV6ly9fJjIykmzZsiV7ngcP\nHui/PnfuHIMGDWLv3r0vrUV8NoXVzMyMcePG8d1335EtWzYqVqxIw4YN+frrr1+71OZVChQo8FK7\nAYMA8UWKovDw4UNy5sypL8uTJ49BHVtbW0xMTHB0dDQot7GxMbjvy5cvExQUhIODQ7LXebFuctcB\n3c8jNUH3l19+SYsWLRg5ciQTJ07kyy+/5KuvvqJNmzap2nc6ORJkCiHem6NHj7J8+XIsLS2ZPn06\n169fZ8SIEQwcOJCuXbsaZJ97UY4cOQBYs2YNtWrVYtGiRQblKRk2bBj+/v4cOnSIQ4cO6Y/p27fv\nO7wrnWMXVbqMhTPBhuX5c0CvltCxEdhYvdk/+CNHjgDQu3dvxowZw5kzZyhdurS+XAghhHgmIUH3\n7mbmzJkxNjbG3t4e4J2NRL2tNm3a0L59eyIiIqhTp06y60S1Wi329vasWLEi2XM8y6MQHh6Ou7s7\n1tbW+Pn5UbBgQSwsLLh9+zY+Pj4GO2D06dMHDw8PNmzYwPbt2/n555/x8/PD39//pXWS/5XS9+zZ\nKOqL7QYYN24crq6uyR7z3/tNLqtuSm8AqC9kfdVqtZQoUYLJkycnW/e/r4lSyt6rpjKT7MqVKzl6\n9Cj+/v5s376dbt26MWbMGA4dOpRsoPs6EmQKId6bGzduALqtkNq3bw/A+PHjiYyM5OHDhym+g9mx\nY0emTp3KmTNn9PttaTQafvrpp1der1ixYhw+fJgBAwZw7949XF1dGTFiBE5OTu/snqJjVUbMhYnL\n4cXdncoXhaE+0LgKGBm93bvHz/6p7t+/n7t37+Lv7w9AlixZ0tpsIYQQnxh3d3dMTU3x9/enfPny\n+v+59evXT9dM5B4eHpiZmXHgwAEWLlyYbJ0CBQqwY8cOKlas+MptQXbv3s3Dhw9Zu3Ytbm5u+vLt\n27cnW9/Z2Zk+ffrQp08f7ty5Q5kyZfjll1/0QaadnR1PnjwxOCY+Pp67d++m6t6ejWxmypSJmjVr\npuqYt1WwYEGOHz/+Tq/zun5RoUIFKlSowMiRI9m6dSsNGzZk9uzZ/PDDD298LVmTKcRnSFVVzp49\ny86dO7l37957u07BggUBXZbXqVOnMmDAAP2+k1mzZiU+Pp5x48bh6emJj48Phw8fBnRB1T///EO7\ndu0oWbIkderUITAwkLp16772msWKFWPUqFHMmjWL2bNnG0xZSas9J1TKdIDxS58HmJbmMLE3HJwF\nHm7KWweYAF9//TX29vbs37+fHDly6NOc9+vX7100XwghxCekcOHCLFq0CAsLC44fP05YWBhffPEF\ns2fPTtd2WVhYMH36dIYPH07Tpk2TrePl5YVWqzXI3P5MUlKSPhB8Njr34oilVqtl4sSJBsfExMS8\nNJU2Z86cODg46KfUgi5I3Lt3r0G9WbNmGZz/VcqXL0/BggWZOHEikZGRLz3/3ymsKUnNmwCtW7cm\nNDSU6dOnv/RcXFxcstd/nWcB/aNHjwzKnzx58tKI57Ms+i9+/96EjGQK8ZmJjo6mZcuWbN68GQBj\nY2OmTp1K9+7d3/m1ypQpQ5cuXZgzZw69evXSl0+ZMgWApk2bsmXLFn35kiVL2LRpE/Xr1ydHjhz6\nabJplZioEvoY7obB3YegqlDTFTJZpi4gvP9Y5cdZMGejYXmt8jBzUOrXXL5Ojhw52Lt3L76+vpw6\ndQpHR0eGDBmiHwUWQgghXtSqVStq1KjB6dOnsbGxoXz58ilOm/yQ2rVrl2z5s0DGzc2NHj168Ntv\nv3HmzBnq1q2LmZkZwcHBrFmzhp9//pn27dtTrVo17O3t6dChA7169cLY2JjVq1cTFRVlcN6goCBq\n1qxJq1atKF68OGZmZmzevJlLly4xYcIEfb0uXbrwzTff0KJFC2rXrs3p06cJDAwka9asqZpWqigK\nc+fOpX79+hQvXpxOnTqRM2dOQkJC9MHrrl27XnuelK71Ynm7du1YvXo1PXr0YO/evfpkR0FBQaxa\ntYrVq1dTvXr1N7pOhQoVABgyZAje3t6YmppSq1YtlixZwp9//kmzZs3Inz8/MTExzJ8/H2NjY1q0\naPHa+0mOBJlCfGa+//57Nm/ejJWVFcWLF+fo0aP4+vpSunRpKlWq9E6vpSgKM2fOpEKFCuzYsQNz\nc3Pat29P7dq12bhxI1u2bCFLliyMHz+evXv3snDhQvr27culS5fe+ppRMSor9zlw4IItkQkqd8Mg\nLFwXWL7I3hb6e6n0bA7WKaydjIxWmbhcN3IZ+cIbpLaZYHxPXWKfdz0lqUSJEvqNkYUQQojXcXR0\npE6dOunahtT8L/zvXpRTpkyhXLlyzJgxgx9//BFjY2Py5s1L69at9VNE7ezsCAgIYMCAAQwfPhxr\na2uaN2/ON998Q6lSpfTnypMnD+3atWPnzp0sXboURVEoUqSIfh/OZ7p27cr169eZO3cuW7dupXr1\n6mzfvp1atWq9dA8p3ZObmxuHDh3i559/Ztq0aURERJA9e3YqVKhgkEk2pb03U1uuKApr167l999/\nZ+HChWzYsAELCwsKFChAjx49KFmy5Gu+4y/fg6urK2PGjGHatGl06tQJVVXZvXs3NWrU4NixY6xc\nuZJ79+5hY2NDuXLl+PPPP/WB6ZtS1NSuBv0AXhyOtbW1TceWiIzs2LFjgG7Kgnhz+fLl499//2Xf\nvn24ubnRtWtX5syZw08//cTIkSM/WDsmTZpE//796datGzNnzuTp06fY2NhgbGysT2bwJh48Vpm6\nBv5cA48iUn9cFhvo56XLAvssUU9CosrcTTByHoQazijBww3+HAA5HNJvvYt4N+RviUgN6SciNVLz\nGjY2NvbtNrUXIgNLqV/LSKYQn5lnGV0jIiJQVZWIiAiD8g/F2dkZ0G3b4e7uzp49ewBdEPwmrt1R\nmbAc5vtDbHzydRQFrM1jCA8Lgvh7YFEExVx3nUcRMGwWTFgGfVupFM0Lw+dA0E3Dc5TIB2N8oVGV\ndz96KYQQQgjxKcmwQWZUjPrSRuVCiLTz8vJi9OjRNGnShOzZsxMSEoKpqSmenp4ftB1NmjShZs2a\n7Nq1C29vb0CXQXb8+PEG9WLiVMKe6ILBRxHw+On/v34Kxy/Bmj2GWV4BsmeJo02NUFo3zEP2rOBo\nBxW/qMbJ0ycZNWoU7b4uSd22YwiObYVirssU9+QpjJj7cjtzOsDILtChwdtnjRVCCCGE+Jxk2CBz\n2loY2Da9WyHEp+enn34iNDSU2bNnExISQubMmZk/fz4uLi4ftB3GxsYEBAQwduxYDh06hK2tLd9+\n+60+zfjNeyo/zYal2yExKXXnLFtY93fD2focxkZQvlhe/XPPNiP+6quvyOeci1Y1ovAbU4wG7Zdw\nObolV+8YnsvGCgZ/Db1bgqW5BJdCCCGEEKmVYYPMX5fAN03VFBNyCCHejomJCbNmzcLPz4+wsDCc\nnZ3TbY2Iubk5I0aMMCh7HKHi9xdMXQNxKUx//a9arkkMbm9ETVfdVNb/L6EyUL58ef7991+8vb2p\nXbs28+bNAzURn0YKnp6wbAeMWwT/3oNuHjC0A9jbyt8fIYQQQog3lWGDzIfhMGU1/NAhvVsixKcp\na9asZM2aNb2boRcbpzJlNYxZpJu6+qLs9rpssHbWYGuVxJGD2wi9fRESw+DxVu5FJFFu5D4UxS7F\n80+ePJmTJ09y8eJFLl68CICPjw8tWrRAURS+rg9f1wetVkWjkeBSCCGEEOJtadK7Aa8yYRmER2aY\n5LdCiPcgMVFl4WaVIt7w/TTDAPOL4rB7KtzZqHBmkcLeaQpV7McT+k9jssdP5MeOJhTIHsm5c+cY\nPnz4K6+TI0cOjh8/zuzZsxk9ejT+/v7MmzfvpSQ+EmAKIYQQQqRNhh3JBF2Cj8kr4adO6d0SIcS7\nFhmtMi8Afl8B/941fK5gLvilO7RwfzmT66lTpwAYOXIkXbt2pVKlSjRu3Fhf/iq2trYGe1gJIYQQ\nQoh3L0MHmQCTVkCvFip2NjK6IER6W7duHYsXLyY+Pp46derQs2dPNJo3mxBx54FuWuysDS9Pi3XI\nrHtTqZsHmBgn/zvv4OAAwIYNG6hRowYrV64EdJtRCyGEEBmZqqqyDZb4ZKhqyjNOM2yQWSSPbp+6\n8EiYuBx+7pbeLRLi8zZ16lR69eqlf+zv78+pU6eYO3cuiqIQGBjIhg0bUBQFT09PatWqZXD8mWCV\nict0CXYSEg3PncUGerWE/q15bbKvHj16sGDBAgICAggICAB0mWr79+//bm5UCCGEeA9MTU2JjY3F\n1NQUIyOj9G6OEGmSlJREfHw8ZmZmyT6vqK8KQT+w8PBw/debj9jQdoTu60wWcG01ZM0s7/wIOPb/\n1KHly5dP55a8W48ePeL8+fNkzpwZFxeXDPVOZ1xcHHZ2dsTExDBixAhy5sxJz549iYuL4/Tp0+ze\nvZu+ffsaHDNt2jR8fX2JilH5fppuW6L/KpgL+nnp9qB8k21CTpw4wYABA7h8+TJ58uTBz88Pd3d3\n/fOfah8R75b0E5Ea0k9Earz4GtbW1jbFeqqqEh8f/8oRICE+BoqiYGpqmuLr1Qw7ktmqJvgthPPX\nITIGxi+Dsb7p3Soh3o9Vq1bh4+NDdHQ0AO7u7qxbt+6V/6g+pPv37xMTE0OWLFn0CXZWrFjBjh07\nOHXqFN999x0AAwcOJDExkUmTJtG3b18KlG5Lz8nWBN82PF/VUtDfC76qBkZGbx5MlytXjt27d6f5\nvoQQQogPSVGUFEd+hPiUZNjsskZGCsM7P388dTXcfyzv+ohPz6VLl2jXrh3R0dGULFkSGxsbdu/e\nTc+ePdO7aXqOjo5YWlry6NEjhg4dyrRp09i3bx8AGo2GxMRESpYsya+//srEiRMpVMSFeKcRNByU\nySDArF8JDsyEv6creH6pvFWAKYQQQgghMrYMO5IJ0OxLKFUQzgRDdCyMWwwTer3+OCHS05MnTzhw\n4AAajYYqVapgY2Pzyvrbt28nPj6epk2bsnbtWi5cuICLiwubNm36QC1+PTMzMyZOnMg333yDn5+f\nvrx79+5Ur14dgAsXLrB8+XKu3ctEsPkiFPvSaP//vpC1JfzeF3wavpwtVgghhBBCfFoydJCp0SiM\n7KLiOVj3ePpaGNhGxcleXqSKjOnAgQN4eHgQFhYGQPbs2fH396dcuXIpHvMsO2tMTAyqqhIVFQU8\nD8YePXrEqFGjOHv2LNmyZWPgwIGULVv2Pd/Jy7p3706uXLkMsst269YNjUZDly5dmbN4D96DLkHO\nIShWpvrj3MvBvKGQ10l+b4UQQgghPgcZOsgE3Zot1yJwPAhi43Vbmoz7Nr1bJcTLoqOj8fT0JCws\njJIlS5KYmMjFixdp1qwZV65cwcTEJNnjGjZsiKWlJdu2bSNPnjzcv38fgNatWxMREUHVqlW5dOmS\nvv7atWvZu3cvFStW/CD39aJGjRrRqFEjAO6GqSzdDruOqex4MAOlnGEQaW6qMvZbhZ7NdW8YCSGE\nEEKIz0OGXZP5jKIoDPV5/nj6WngcIWszRcZz9uxZ7t+/T758+Th58iSnTp3CycmJGzducOXKlRSP\ny5cvH2vXrsXe3p47d+6QkJBAixYtmDhxInPnzuXSpUsUKVKEDRs20KJFC+Li4hg6dOgHvDMdVVU5\nEaTy3VQVl7YqOT2g/ShYsBluPzAMIisWh5MLFHq3VCTAFEIIIYT4zGT4kUzQjWYWd4YL/+oyzU5Z\nrduwXYj0cvDgQZYvX05CQgL16tXDw8NDny3u6dOnPHnyhISEBP3UV1NT01edjnr16nH79m2uXbuG\nra0tOXPmBODff/8FoEOHDnz11Vc4OzuzevVqffmHcD1EN2K5NBAuvuKy1pa6qbGNq+rWXhobS3Ap\nhBBCCPE5+iiCTI1GYXB7lfajdI//WAX9vVQyWcqLWPHhLVu2jHbt2qHVagGYPn06w4cPZ9iwYZQu\nXZrTp0+TI0cOVFUlISGBKlWqUKBAgdee19zcnOLFixuUFSpUCIBZs2aRM2dOli1bBkDBggXTfB+x\ncSpHL0KSFjQa0CjPPysKnLysCyz3n0n+eFMTqOICtSpALVcoX1QCSyGEEEIIAYqagXaDfdVGtomJ\nKkW84XqI7vH4XtDfS17Qfo7Sc2Ps+Ph4HBwciIiIoFu3bjg6OuLn54dWq+XKlSuYmZnh5eXFgQMH\nAN1+l0uXLsXJyemtrhcTE4ObmxvHjx/Xl1lbW7N//35KlSr11vex54SK109w//GbHWdlocv63LoW\n1CgHluYZ83fwbfpITEwMO3fuJCIigvLly1O4cOH31TyRQaTn3xLx8ZB+IlLjVa9hhfgcfRQjmaAb\nIRnUVsX3N93jCUuhRzMVM9OM+SJXfJpCQkKIiIgga9aszJgxA0VR2L9/P3v27CEoKIhGjRqxf/9+\nHj58iEajIUuWLGm6noWFBXv27GH8+PGcPXsWJycn+vTp89YBkKqqTFkNA6ZAUlLqjjEygnpfQJu6\n4OEGVhaf3u/c7du3qVOnjj7BkpGREVOmTMHX1zedWyaEEEII8fH5aIJMgA4NYNQ8uPtQ97FwC3Tz\nSO9Wic+Jg4MDxsbGhIWFMXv2bLJly8aRI0cAyJEjB6BLVpU1a9Z3ds1MmTIxYsSINJ8nJk7F91f4\na+vzMntbcMkPWi1oVdBqVW7evM290Pto48MpkOU8SyZ/RYWyzmm+fkbWuXNnLl26RL58+ShatChb\ntmyhZ8+eVK1aNU0jxkIIIYQQn6MMn132ReZmCv29nz/+dbFuGq0QH4qVlRVDhgwBdPtGNm3alOjo\naJo1a0aZMmVee/zdu3dZv34927ZtIzo6+r22NSkpid27d/PXX3+xcetJqvsaBpgVisHJBbB7qsLe\naQp/T1eo6Tic21vzkniyAtrztbnydx9aetYwmAb0qVFVlT179gCwf/9+Nm/eTMuWLdFqtfz999/p\n2zghhBBCiI/QRxVkAnT3gCw2uq+vhcCKnenbHvH5GTlyJNOmTaNKlSpUqFCBH3/8kWXLlqEor55G\nun79egoWLIinpyf169enZMmSBAcHv5c2xsbG0qhRI2rWrEmHXnPx+CkHx4OeP+/TCPb+Cbkcn7dZ\nVVWmTJkC6PbiDA0NpXjx4ty4cYPNmze/l3ZmFJaWlgBcvHiRmJgYrl+/blAuhBBCCCFS76OaLguQ\nyVKhd0uVEXN1j8cuAu86quzFJz4YRVHw9fV9o/V6d+7coU2bNsTExFClShVCQ0O5evUq3t7eC2mf\nBgAAIABJREFUHD169JXHJiSq+P8Dmw+CkQYcMoOjHTjY/f9zZrCzhofhumnk9x7CwmV72XO5IaYu\n35Jo0xAVIwCMFC2T+2vw9eSloFir1RIZGQlAjRo1sLOzo2TJkly4cOGTHslUFIXOnTszYcIEateu\njZGREUlJSTg6OtK4ceP0bp4QQgghxEfnowsyAXq2gPFLdXtmnr8Om/7RJSQRIqM6ePAgMTExVKtW\njX379hEZGUmWLFk4duwY4eHhyWaiu3ZHZc4mWLBZFzi+mboo2euS8EKJGh9Knfzz+LbZD8keYWRk\nRMWKFTlw4ADu7u6UKFGCVatWAVCxYsU3bcBHZcyYMSQkJDB9+nQSEhJwcXFhyZIlODg4pHfThBBC\nCCE+Oh/ddFmALDYK33g+fzzmL91UPyEyKnNzcwAePHhAdHQ0d+7cITExEQBTU1N9vYRElTW7Ver1\nVSnYSjdS/+YB5suyml+DM+XJl/XOK+vNmzePnDlzcvr0aZYuXYpWq2XcuHGULVs27Y3IwExMTJg8\neTLR0dE8ffqUs2fPSsIfIYQQQoi39FGOZAL0aw1TVkNcPBy5ALuOQy3ZwkpkUDVq1CBPnjwEBQVh\nb29PXFwcAF5eXlhYWJCUpDJzA/w8H0IfvXx8dnvo0BByOuj2tnzwBB78//P9x/D4qW6tcnZ73Ud4\n2CU2rZkNCXfRJNzmQfg/GBlp6NChwyvbWaRIEc6ePcvGjRt5+vQplStXxtXV9X18SzIkY2NjMmXK\nlN7NEEIIIYT4qKU5yBwxYgSjRo0yKHNyciIkJMSgzuzZs3n8+DEVK1bkzz//pHjx4mm6bvasCp0a\nq0xfq3s8ci5UL6NiYixrM0XGkylTJrZt20br1q05c+YMAK1atWLWrFkcPKfSayKcCDI8RlGgQSXo\n8hU0qkKyfVur1RIQEMCVK1dwdnamSZMmmJiYAMWYVqwgP/wwj/DwcJycnJg5cyZffPHFa9tqZ2f3\n2mBUCCGEEEKIlLyTkcyiRYvqtwAA3dquZ8aNG8fEiRNZuHAhhQsXZtSoUdSpU4egoKA0jxgMbAOz\nNug2ld9/Bpp+Dyt+VslkKYHm5yopKcmg/2UkRYsW5dSpUzx69AgzMzOiE6zoMwUWBBjWy5EVOjeB\nTo0hr1PKfTkhIYFmzZrh7++vL6tevTpbtmzB0tKSb7/9Fl9fX54+fYq1tfVrs98KIYQQQgjxLryT\nNZlGRkY4OjrqP+zt7QHdOsnff/+dIUOG4OnpSYkSJVi4cCFPnz5l6dKlab6uc3aF/l7PH285BDV6\nwr2Hsj7zU5WYmMj9+/eJjY01KN+0aRP58+fH2NiYPHny6BPWZDSKopA5cxYWbrOiqLdhgGluCiO7\nQPBKGNlFeWWACTBlyhT8/f2xs7Oje/fuZMuWjX379uHn52dwPRsbGwkwhRBCCCHEB/NOgsxr166R\nM2dO8ufPj7e3t36PuevXrxMaGkrdunX1dc3NzalevToHDhx4F5dmrC/86PP88YkgqNIdgm5IoPmp\n2bBhA05OTjRq1IgaNWrw448/oqoqBw4cwNPTU9/vbt26RevWrdmxY0c6t9hQ8G2VSctVXDtBr4nw\n5Onz55pWhwtLYVhHBXOz1AWEBw8eBGDs2LHMmDGDP//806BcCCGEEEKI9JDm6bKVKlVi4cKFFC1a\nlNDQUEaPHk2VKlU4f/489+7dAyBbtmwGxzg6Ohqs2UzOsWPHUt2Gr8pCUkxWxq3Mg1ZV+PcuVOyS\nyISuwZTOH/XmNyUynKCgIHx8fEhMTMTa2pqnT5/yyy+/EBMTQ1BQEElJSXh4eDB48GB+//13VqxY\nwdixY8mcOXO6tTlJC+dvWLHvbGb+PmfL9VCLl+rkzhrLgOa3qFI8grA7EPbq5K8GEhJ0G5SsX7+e\nIkWKsGLFCkA3g+BNfn8+ZfJ9EKkh/USkhvQT8SqFChVK7yYIkaGkOcisX7++/msXFxcqV65Mvnz5\nWLhw4Sv31nvX0/c8q4SR1SaBoQvzERtvRES0MT2nFWbU19dxL/3knV5LfHiBgYEkJiZSv359Ro0a\nxaZNm/j555/ZsmULTk5OgK7/GRsbU7JkSVasWEFUVNreYLh8+TKbNm0iOjqa0qVL07hxYzSa1w/+\nh0UYM3tLDvacyczjSJNk65iZaOlY9y5t3UMxM3m7UfdmzZoREBDAli1b2LJlC6D7vWrRosVbnU8I\nIYQQQoh34Z1vYWJpaUmJEiUIDg6madOmAISGhpIrVy59ndDQUH1gkJLy5d98P5Ly5aFaRZXG3+m2\ndohL0DB4fgHG+sIAb9BoZF3axypLliwAlCpVCkVR9KPjxsbGNG7cmN27dzN16lRu377Npk2bAGjQ\noMFb9SOAHTt20LFjR+Lj4wHYuHEjN2/eZP78+Sm+QaKqKit2Qs8J8Cji5ectzKB2eWhSDb5y0+Bo\nlwvI9XLFVCpfvjw5cuSgd+/e+uyyv/76K56enq8/+BP3bMThbX/+4vMg/USkhvQTkRrh4eHp3QQh\nMpR3sibzRbGxsVy8eJHs2bOTL18+nJycCAwMNHh+//79VKlS5V1fGoAKxRQOzIRCuXWPVRW+nwYN\nB8DdMFmn+bGqU6cOAOPHj+fbb7/l+++/15f37t0bDw8PwsPDWbhwIY8ePaJu3br6Om/jm2++IT4+\nntatW/Prr79iaWnJwoUL2bt3b7L1HzxWaT0M2gw3DDCzZdFlit0wDh5shg2/KnT5SsHR7t284VG7\ndm0uXLhAQkICV65ckQBTCCGEEEKkuzQHmd999x379u3j+vXrHD58mBYtWhATE6PfZ69v376MGzeO\ndevWce7cOXx8fLC2tqZNmzZpbnxKCuRS+GcGVHZ5XhZ4BEp3gE37JdD8GKiq4c+pYcOGjBo1Cq1W\ny9GjR4mKiqJBgwaMHj0aY2Nj1q5dy9atW5k6dSoBAQFs3rwZMzOzt7p2QkICV69eBWDRokUMHDiQ\nZs2aAbq1of+1ZreKSztYvft5WZ5sEDAe7myA2YMVmlRTsDSXkXQhhBBCCPHpS/N02Tt37uDt7U1Y\nWBgODg5UrlyZQ4cOkTu3bihx0KBBxMTE0KNHDx4/fkylSpUIDAzEysoqzY1/layZFXZPVRk2G8Yv\n1Y1ohj0Bj+/hG0+V8T2RF/0Z0KVLl+jcuTNHjhzBzs6Ofv36MXjwYBRFYdiwYXh5ebFx40bs7e1p\n3769fo2kRqOhXr161KtX742ud/HiRaZNm8aDBw8oV64cffr0wczMjGzZshEaGsovv/xCxYoV9aPx\nOXPm1B/7MFyl9yRYtt3wnJ2bwIReYGMl/UsIIYQQQnx+FPW/Q0bp6MX57La2tu/svLuOq7QfBSFh\nz8uKOcOS4VCmsAQCGcWDBw8oVaqUPivxM2PHjjWY+vqu1sccO3aMGjVqGCQIqlGjBoGBgfz11190\n6dLFoL6bmxs7d+7ExMSEjX+rfPMb3Hv4/PmcDjB7MNSvJH0qvckaKpEa0k9Eakg/Eanxvl7DCvGx\neudrMjOimq4Kp/8Cz+rPyy7+C5W6wbjFKomJGSbO/qytXbuWe/fuUb58ecLCwpg/fz6Afv/Hd61/\n//5ERUXRpEkTZs2ahZOTE3v27GHZsmV07tyZVatWUatWLb744gv69+/Pli1biIwxxudnlaaDDQNM\nn4ZwdpEEmEIIIYQQQrzz7LIZlb2twmo/lbmboO9kiI6F+AQYMh1W7oQ5Q1TKyqhmuoqI0GXMKVOm\nDPb29ri7uwPvL2Pb5cuXAfj999/Jnz8/165dY+zYsfryFi1aGGwHsvmASrdxhiPiTvYwcxA0qSZ9\nRwghhBBCCPhMRjKfURRdZs/j88C1yPPyk5fhiy4weLpKTJyMan4It27dYvXq1WzevFk/XbVSpUoA\nLFiwgPbt29OgQQMAKleunObrPXr0iAsXLhAZGakvy5MnDwCjR48mICCAlStXGpQ/Ex6p0nmMSuOB\nhgFm27pwbrEEmEIIIYQQQrzoswoynymSV+HALBjjC+amurKkJPh1MZTpAHtPZuxAU6vVsmHDBvz8\n/FiwYIHBmsKPwapVqyhUqBAtW7akUaNGlCpViuDgYNzc3Pjpp59ITExk0aJFXLx4kXz58jFz5sy3\nvpaqqgwePBgHBwdKlCiBo6Mjc+bMAcDPzw8jIyPmz59P48aNuXbtGqVKlaJt27YAPHmqsnKnSqn2\nMN//+Tkd7WCNHywarpDFRgJMIYQQQgghXvRZJP55lSu3dFMg9540LO/mAb/2yHgZQrVaLV5eXqxa\ntUpfVrx4cfbu3UvWrFk/eFumTJnCsmXLSEhIoEGDBvz000+YmpqmeMzNmzcpXLgwcXFxVK9enZCQ\nEIKDg/niiy84fPgwAIcOHeLo0aPY2dnx1VdfYWNjY3CON0nCMHXqVHr16gXoRihv3rwJwK5du3B3\nd2f//v1MnDiRsLAwipWsSvXGQzl22Yp9p+DUFV1W4he1rgVT+uuyF4uMSxJ1iNSQfiJSQ/qJSA1J\n/COEoc9mTWZKCuVW2PmHypxNMOhPiPj/oOCsDbDzGKz4WaVckYwTUCxcuJBVq1ZhY2ODj48PAQEB\nXLhwgUGDBjFv3rwP2pahQ4cyduxY/eMTJ05w6dIlVq1aRWJiIqNHj2bTpk0YGRnRqlUrBgwYwMGD\nB4mLi8Pd3Z1du3YRERGBnZ0dR44cISoqCisrKypVqqSfOptWz6bAzpkzh86dO9O3b18mT57K7MV7\neWpcg0s3q2JXoSrXLsGc0zD7VPLnyZoZ/hwALWtmnL4ghBBCCCFERvTZB5kAGo1CNw9oVEWl5wTY\n8Leu/OodqNIdxvdU6dFct6YzvR09ehSAwYMHM2TIEFq2bImbm5u+/EOJiIjgt99+A2D+/PnY29vj\n5eXFmjVrOHfuHGPHjmXp0qX6+seOHeP27dvUrFkTgLt37xIVFcWNGzfQarVoNBpMTEzS1KbLN1W2\nHoan0RAbB3EJEJzUE/K3ZdFBd/yvqPxzfghUGsfyS6YsH/zq82k0ULYQ1KoA/b3A0S79f/5CCCGE\nEEJkdBJkviCng8LaMSrLtoPvb7pgJT4Bek/STaedPVgls3X6BhpZsmQBYM+ePfj4+ODv729Q/rbi\n4uLYuXMnYWFhlCtXDhcXl1fWv3//PklJSTg5OdGhQwcURaFcuXLs37+fI0eOsHTpUszMzFixYgXR\n0dG0bduWKVOm0K9fP/LkycOlS5ews7MjISEBgLZt275ymm1KVFVl5zGYvBICDiRXoyWKE+y7+Oyx\nI0oKK5GNjHQJob4sC1+WgaqlwDaTBJZCCCGEEEK8CQky/0NRFNrUhQrFVLx+0mWeBVizB05chuWj\nVCoUS7/Ao1OnTkyZMoXAwEBy5MihL+/Xr99bn/PBgwfUrVuXU6eezxX18/NjyJAhAOzbt485c+YQ\nGRlJ9erV6dmzJ7ly5cLa2pp79+7RvXt37O3t+eeff1AUBSsrKwBKliyJh4cHAEOGDOHGjRtERUWx\nbds2vL29OXXqFIqi0LZtW2bMmPFGbY5LUJjnrzJ5JZy9+ub3nNMBiuaFInl0n4s5wxfFwDqDrcEV\nQgghhBDiY/PZJ/55ldg4le+mwrS1z8tMjGHct9CnVfpNnz1x4gQ9evTgwoULZM+enREjRuDl5fXW\n5/Py8mLFihXkypULV1dXNm3ahFarZe/evTx48IBWrVqh1Wr19Vu0aMHKlStZvnw57dq1M3jul19+\noWPHjuTOnZukpCQGDBhAVFQUM2bMwNLSktDQUDJlygTAkydPMDc3x9zcPNVtffBYZeiUENb848Dj\nSMPptYoCDStDqYJgZgJmprrswWYm8PhRKNGRYVQu64Cbq6MEk584SdQhUkP6iUgN6SciNTLaa1gh\n0psEmamwerdKlzHPkwIBVC+jSwRTIv/HH6w4OTkRGhrK2bNncXFxwdfXlxkzZvDzzz8zffp0QkJC\n8PX1pWzZsgwYMICnT5/qs7MePHhQn+infv36NGzYEIBJkybRv39//TUURWH+/Pl06NDhrdp4N0zl\nt6Uwcz3ExBk+Z2kOPg11gX+h3B//z0OknbwoFKkh/USkhvQTkRoZ9TWsEOlFpsu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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "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)" - ] - }, - { - "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 sinusoidal 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": "markdown", - "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", - "execution_count": 34, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# your code here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution and Discussion" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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JiRMnVIsWLZS7u7saMGCACg0NTe7Qk805X0051o5L2OzdNXXyYsIJW+nSpRWg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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "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)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This doesn't look so wonderful to me. We can see that perhaps the filtered signal varies less than the noisy signal, but it is far from the straight line. If we were to plot just the filtered result no one would guess that the signal with no noise starts at 5 and increments by 2 at each time step. And while in locations the filter does seem to reduce the noise, in other places it seems to overshoot and undershoot.\n", - "\n", - "At this point we don't know enough to really judge this. We added **a lot** of noise; maybe this is as good as filtering can get. However, the existence of the multitude of chapters beyond this one should suggest that we can do much better than this suggests." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise: The Effect of Acceleration" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Write a new data generation function that adds in a constant acceleration factor to each data point. In other words, increment dx as you compute each data point so that the velocity (dx) is ever increasing. Set the noise to 0, $g=0.2$ and $h=0.02$ and plot the results. Explain what you see." - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# your code here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution and Discussion" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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PsXPnToKCgmjSpImzy3KKbb8Y/GMGzEyBc4WOfe2aw5hYiAhVwBQRKU2Z76N5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\nXIqIiFwvpQbN9957D5PJZL8tyXkjR47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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def gen_data(x0, dx, count, noise_factor, accel=0):\n", - " zs = []\n", - " for i in range(count):\n", - " zs.append(x0 + dx*i + 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)\n", - "plt.xlim([0, 20])\n", - "plot_g_h_results(measurements=zs, filtered_data=data)" - ] - }, - { - "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": "markdown", - "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", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# your code here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution and Discussion" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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EKSujUBTOFczsGeMSvL1TVoNxvRQffKlzM1vXVrg4pVxQd8FX8fMKmL1W52DG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\no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zIyUj/99JPb66dPn1a/fv1UrFgx5cuXT23bttW+ffvs+xTXmE2bNqlXr146e/asGjZs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\naNSoUXrwwQd12223q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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import book_format\n", - "np.random.seed(100)\n", - "zs = gen_data(x0=5, dx=5, count=50, noise_factor=50)\n", - "data1 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.1, h=0.01)\n", - "data2 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.4, h=0.01)\n", - "data3 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.8, h=0.01)\n", - "\n", - "with book_format.figsize(y=6):\n", - " book_plots.plot_measurements(zs, lw=1, color='k')\n", - " book_plots.plot_filter(data1, label='g=0.1', marker='s')\n", - " book_plots.plot_filter(data2, label='g=0.4', marker='v')\n", - " book_plots.plot_filter(data3, label='g=0.8', lw=2)\n", - " book_plots.show_legend()\n", - " book_plots.set_limits([20,40], [0, 250])" - ] - }, - { - "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 have a look. I will create data that has $\\dot{x}=1$ for 9 steps before changing to $\\dot{x}=0$. " - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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wQTp16lRp6mhOTg6lpXWfE8nPz4/w8HAAfv75Z+x2O8OGDatWM2TIENavX/+H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\n5Npt2bdC2K1po6rLxhqkZXj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k57fffgfA3z/A9cHTMOjZoycRkZGuurI+7NqVTm5eHhbD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\n2Lt3r1ZcXl6eaNq0qQAgvLy8hIeHhwAgPD09RX5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q4cZCRER1Q4kVS3/g67USUu8LnPgb\niIkD/r0cuF9KX9eSCx9aFctiVcsrtyKwcadAy6ZAiyaAgx0wblIEriUXXnEZAGxsdsjjYsJJj6uo\nGvnqv97Bhsh+GPSi/qv3VmAN2PpzYf8VrUICgJOTE8zNzZGQkKDz2qVLl7T6f+mllx77nEh/f38Y\nGxsjJiZG68I6+fn5OH36NAYPHvxE475ypbCqUdoVv6limERSpfjrssCZS5rlGSNYhSQiooorK1Fz\naiChfwjQPwQ4sA2I1lO1tDQHCowApar0dd24Dby6ULPcwAYouApkOUZoGuX+i7X9o7Sr0zLhpCKD\nXuyH3Xv24qUX+pYdbOD+jYyM0KtXL2zfvh03b96Ub0Vz6dIl7N69Wyv2Sc6JtLOzQ69evbB582ZE\nRETIt+P69ttvkZ2djSFDhsixSqUSly5dgr29vXyLrfv378PW1lbrtjMFBQX45JNPYGpqKt+mkCof\nk0iqFMXPhTQ1Aea/ZrixEBERFdehNRD1HyAuETh3GZj9AZBUjvfdfwCIHO2L9BT54wzQeoSAR2Og\nqQvg4QL87wIQp47QE63dxmSzfpMkCV+tXVFlV66v7P4jIiIQFRWFZ555BpMnT5Zv8eHv74+zZ8/K\ncU9yTiQALFiwACEhIejWrRsmTpyImzdvYtmyZejZsyf69+8vxyUlJcHX1xdjxoyR7x3566+/4uOP\nP8aQIUPg4eGBtLQ0bN68GefPn8dHH32k96qvVDmYRFKF/XVZ4HSxoxzeGc4qJBERVb/SLtZjaiIh\nwAcI8AG+jASS9FQsm7oAIT2B+BuFj+xSLgypVgMXrxc+ihQeJqsbe+4KMHGxQGMHoLEDcCIOuKDU\nHSerm/VHVd/6rDL7DwwMxO7du/Huu+/iww8/RJMmTRAeHo74+HhcvHixwv23b98e+/fvx6xZs/DO\nO+/AxsYG48ePxyeffKI3vvhnCwgIgJ+fH7777jvcuXMHpqamaNeuHX788UetKiZVPiaRVGFjHqlC\nfjzRcGMhIqL6q6JJlWdj4If5hTuoQgjcugs8OxQ4W/a1QkqVlgF8tV2zXFKyeeoi0H+GgINt4fmY\nDnbAkXPAZSlCJ1aljoAQQmuHurwJ5+Mkpobs83FjqeqEhobi5MmTWm0vvPACmjRpUin9d+7cGX/8\n8UepMR4eHlCr1VptgYGBOrf4oOrBJJIq5PxVgdhiVci3h7EKSURENVtpFcsikiTBrRFgb4Ni50Fq\ndA4AVq8svFBPYgpwLQX4Zp3e0HJ7kAPsOa7dJm7oTzgPnwFMuwE2lgK2loCNJXD9BPDAQfdzXbkV\ngYj1AuamhVejPXoOuKQnMb3/IAIHTwkYGwFGRoCxEfDXFeBUjm5sdl4Ezl8REACEAM5fAU7qicvI\nisCBkwIFysJzUgtUQMzfwN8q3djElAh8+KVAXj7wsKDw9i17jgOp1rqx+uaPqk5ubq58Ow4ASEhI\nwK5duzBuHO/lVl8xiaQKGTNf89zEGFjwuuHGQkREVB6PU8EqSjg1V2e1kdsDfAoPkS1ycp/+C/v4\neQJvvAUk3wWS7wG/fFf6VWTLS6UC0h8UPgBAZAOSg27cjdvA/A2a5ZIS07OXgB5TtdtKqpqe+Bto\nM6rsuNMJQM9p5evzWjLw8dePxKYBkrVuLFUvLy8vjBs3Dp6enkhMTMSaNWtgbm6OmTNnGnpoZCBM\nIumJ/X1N4FS8ZnnaEFYhiYiobilKOE+cOAEACA4OLjG2tArnGy9p/j5eOqY/2WzfApg/H7iXAdzL\nLPx34xeAvlthVvEpdURawsLC8MMPPyAlJQVmZmYICQnBwoUL4e3tbeihkYEwiaQnVvxcSBNjYNEk\nw42FiIjI0Mpb4Swt2Xyus3Z2eGQnkKIn4ezaDtj3c+EhsJnZhY8xrwNn8nRjPV2BUeMKDw/NfQj8\ntAm4rWdc9jZA23aASg0o/zn89O87QI6eWEtzwNOj8LkkAVdSAX3XIbK1AoLaFx4aa2Jc+O/RTP2H\n/TZxBl59FTA31TxWLAXihZ5gqlYbNmwoO4jqFSaR9Fia+/fFrYyGyHuohrrRq5Dse0PkJcLi3kwY\nG28x9PCIiIhqvCc5nFZfu4mxhIa2QEPbwjY7KwB6ksimzsC8CZrk9OwB4LaeLK6tD3AwUjuJ7T5A\nf9W0Q2vg4PdSmXHtWwC/r3qkzzj9sV6uQPh47dgfNgDxFTnRlIiqBJNIeizZ+RbIsRkDqWlfzX2z\nClLR2NHKkMMiIiKqkyor4XySOEP3+bixRFR9mETSY7mTlg2Y7oGw7wNJkiCEAO5uhqKZRdlvJiIi\noipT3oTzcRJTQ/b5uLFEVH0Uhh4A1R4qlQrKggLAvj8gCgobs04A9v2QX1Bg2MEREREREVG1YBJJ\n5WZkZAQza1fAvhckhalchYR9H1hZWhp6eEREREREVA2YRNJjMWo8EVLRdcVvrwXs+0GSJNjb2xt2\nYEREREREVC14TiSV2+WbArkmnQEAQggoMrbDx7MpGjsc4wnuRERERET1BJNIKrdR8wEoCjcZE2MJ\nD27uhJkZi9lERERERPUJMwAql8s3BY7/pVl+/QUwgSQiIiIiqoeYBVC5jP5I89xYASx703BjISIi\nIqK64+jRo+jSpQusrKzg4uKCN998E9nZ2eV6b3Z2NmbMmIGmTZvC3NwczZs3x5IlS6BWq6t41PUb\nD2elMl29KXDsnGb5tYGAqalkuAERERERUZ1w+vRp9OzZE76+vli+fDmSkpKwbNkyxMfHIyoqqtT3\nqlQqhIWF4fjx45g8eTL8/Pzwxx9/YNasWbh+/TpWrVpVTZ+i/mESSWUa9bHmubECWDHNcGMhIiIi\norrj/fffR4MGDXDw4EHY2NgAADw8PPDaa69h9+7dCAsLK/G9v/zyCw4fPow1a9bg9ddfBwBMnDgR\njRo1wsqVKzFp0iT4+/tXy+eob3g4K5UqMVng6FnN8qsDWIUkIiIiqk8OHjyI4OBgWFhYwMfHB+vW\nrUNERAQUioqlEpmZmdi/fz9efvllOYEEgNGjR8Pa2hpbtmwp9f1//PEHAODll1/Wan/llVcghMCP\nP/5YofFRyViJpFKNKnYupJECWDndcGMhIiIiouoVGxuLfv36wdXVFfPmzYNKpcL8+fPh6OiouXc4\ngIyMDBQUFJTZn4mJCezs7AAA586dg1KpRHBwsE5Mu3btEBsbW2pfDx8+hCRJMDc312q3sLAAAJw8\nebJcn5EeH5NIKlFissDhM5rlV59nFZKIiIioPgkPD4eRkREOHz4MV1dXAMDQoUPRqlUrrbiBAwci\nOjq6zP66d++O33//HQCQnJwMAGjcWPeG4y4uLoiLiyu1r1atWkEIgcOHDyM0NFRuP3ToEADg5s2b\nZY6HngyTSCrR6GLnQhopgM94LiQRERFRhSk6iyrtX32kcr70V6lU2L9/PwYOHCgnkADg7e2NsLAw\n7Ny5U25bvnw50tPTy+yzQYMG8vPc3FwAgJmZmU6cubm5/HpJXnnlFcyfPx8TJkxAZGQkWrdujSNH\njmDu3LkwNjYu8/305JhEkl7Xbwv8cVqzPP45wNycVUgiIiKi+iI1NRV5eXnw8fHRec3HxwdCaJLh\nwMDAx+6/6LDThw8f6ryWl5cHS0vLUt/fqFEj/Pbbbxg1ahT69+8v97lkyRLMnz9f6zxLqlxMwfAp\nzwAAIABJREFUIkmv0TwXkoiIiKhKVFalsCZJS0tDfn5+mXGmpqZo2LAhAM1hrEWHtRaXnJysVf0s\nSUhICC5duoTz588jMzMT/v7+MDExwbRp09CjR4/H/BRUXkwiSUdSqkB0sfOYx/RnFZKIiIiovnFy\ncoK5uTkSEhJ0Xrt06ZLWhXVeeumlxz4n0t/fH8bGxoiJicHw4cPlmPz8fJw+fRqDBw8u1zglSdK6\nlceOHTsghEDv3r3L9X56fGUmkdHR0Vi6dClOnTqFW7duYePGjRgzZgwAQKlU4oMPPsCePXtw+fJl\n2NraIjQ0FJ988gmaNGlS5YOnqlG8CqlQAKveNtxYiIiIiMgwjIyM0KtXL2zfvh03b96Em5sbgMIE\ncvfu3VqxT3JOpJ2dHXr16oXNmzcjIiJCPvz022+/RXZ2NoYMGSLHKpVKXLp0Cfb29nBxcSmx/+zs\nbMydOxfu7u4YMWLEY31eKr8yk8js7GwEBARgzJgxGD16tNY3DtnZ2YiNjcWcOXPQrl07pKenY8aM\nGejXrx/Onj0LIyOjKh08Vb6kVIGDpzTLY8JYhSQiIiKqryIiIhAVFYVnnnkGkydPhkqlQmRkJPz9\n/XH2rOZm4k9yTiQALFiwACEhIejWrRsmTpyImzdvYtmyZejZs6d8niMAJCUlwdfXF2PGjMHGjRvl\n9m7duuHpp5+Gj48P0tLSsH79ety6dQu7d++Wz7mkyldmEhkWFoawsDAAwNixY7Ves7OzQ1RUlFbb\n2rVr4efnh7i4OPj5+VXeSKlKqdVq7NixA++ubwPAE0BhFTLyHcOOi4iIiIgMJzAwELt378a7776L\nDz/8EE2aNEF4eDji4+Nx8eLFCvffvn177N+/H7NmzcI777wDGxsbjB8/Hp988one+OIFLQDo0KED\nfv75ZyQlJcHa2hqhoaHYtm0bfH19Kzw2KlmlnxOZkZEBQLtUTTWbSqWCrVN75MAHaDQWkoMnRP5t\nSCkfoU3wJST8tdfQQyQiIiIiAwkNDcXJkye12l544YVKO32tc+fO+OOPP0qN8fDwgFqt1mlfunQp\nli5dWinjoPJTVGZn+fn5mDFjBgYMGFCuqylRzfDVV18h56E54Pw6JIfnAQCSqTOUNs/B1IrzSERE\nRFSfPXq/xYSEBOzatQvdu3c3zIDI4CqtEqlUKjFy5EhkZmbit99+KzX2xIkTlbXax2Ko9dZ0u3bt\nAowdAFWG3CaEANL3wszJvtp/bpyn2oNzVTtwnmoHzlPtwHmqHSpznpo3b15pfdVWXl5eGDduHDw9\nPZGYmIg1a9bA3NwcM2fONPTQyEAqJYlUKpUYMWIEzp8/j4MHD/JQ1lrGxsYGcBoANHxO05i+F7Dv\nB0mKKvmNRERERFTnhYWF4YcffkBKSgrMzMwQEhKChQsXwtvb29BDIwOpcBJZUFCA4cOH48KFCzh4\n8CCcnJzKfE9wcHBFV/tYir6Nqu711haTpobj+7eaQFKYQeQnAyYuhUmkx3LY2Byrtp8b56n24FzV\nDpyn2oHzVDtwnmqHqpinout91GcbNmww9BCohinXLT6KbjCqVquRmJiI06dPw8HBAa6urhgyZAhO\nnDgh39QzJSUFAGBvbw9zc/OqHT1VigU/+kAqOjs2/zZwc8k/VUje2oOIiIiIiLSVeWGdmJgYBAYG\nIjAwEHl5eQgPD0dgYCDCw8ORlJSE7du3Izk5GUFBQXB1dZUfW7ZsqY7xUwWlpgns/VOz3MgqES5m\nsejqfRRdHSLg0dhwYyMiIiIiopqnzEpk9+7d9V5Ot0hpr1HNN/ZjzXNJAq7sGwgri4GsQhIRERER\nkV6Vfp9Iqj1S0wT2FKtCDusJWFsyeSQiIiIiopJV6n0iqXYZv1DzXJKAdf8y3FiIiIiIiKh2YBJZ\nT91NF9h1TLM8pAerkEREREREVDYmkfXUuAWa55IErOO9YomIiIiIqByYRNZDd9MFdh3VLA/uAdha\nswpJRERERERlYxJZD726EBD/PJck4EtWIYmIiIjoEV9//TUUCgUUCgUOHz6sN8bHxwcKhQKhoaHV\nPDoq7ujRo5g3bx4yMjKqZX1MIuuZtEyB345oll/qxiokEREREZXMwsICmzdv1mk/fvw4rly5AnNz\nc94ezsCYRFKVGv9oFXKWQYdDRERERDVcWFgYfvrpJyiVSq32zZs3o1WrVvD29jbQyCpHdna2oYdQ\naYQQZQdVAiaR9UhapsCOPzTLL3YF7G34rRERERERlWzEiBFIS0vD3r175TaVSoUtW7bglVde0YkX\nQuDzzz9HmzZtYGFhAWdnZ0yYMAH37t3Titu+fTuef/55NGnSBObm5vDw8MDMmTPx8OFDrbjbt29j\nwoQJcpyLiwv69++PCxcuyDEKhQLz5s3TGYuHhwfGjRsnLxcdonvgwAFMmzYNzs7OsLGxkV+PiYlB\n//79YW9vD0tLS3Tp0gUHDx7U6jMiIgIKhQJxcXEYOXIk7O3t0ahRI3zwwQcAgBs3bmDgwIGws7OD\ni4sLli5dqjOuhw8fYt68eWjevDnMzc3h7u6Od955B7m5uVpxCoUCkydPxrZt2+Dv7w9zc3P4+/tr\nzUVERARmziw8P83T01M+BDk6OhoAcOrUKfTv3x9OTk6wsLCAh4cHRo8ejby8PJ1xlZfxE7+Tap1X\nF2lXIb+abdDhEBEREVEt4O7uji5dumDz5s149tlnAQD79+9HamoqRowYgR9++EErfvLkydiwYQPG\njh2LadOm4fr16/j888/xv//9DzExMTAzMwNQmNBZWFhg+vTpsLOzw7Fjx7BixQrcuHFDq8/Bgwfj\nr7/+wtSpU+Hp6YnU1FRER0cjISEBvr6+cpy+Q2olSdLbPnXqVDRs2BBz586VDwE9dOgQ+vbti8DA\nQISHh8PY2Bjffvst+vTpg3379qFbt25afYwYMQKtW7fG4sWLsXPnTixatAh2dnb46quv0KtXLyxZ\nsgTfffcdZs6ciaCgIPm8USEEXnzxRURHR2PixInw9fXFhQsXsHr1apw/f14rQQSAY8eOYceOHXjj\njTdgbW2Nf//73xg0aBCuX7+Ohg0bYtCgQUhISMAPP/yAzz77DI6OjgCA1q1b486dO+jduzecnJzw\nr3/9Cw0aNMD169exY8cO5OTkwNzcvHwbwaNENUlPT5cf1S0mJkbExMRU+3prkvuZaqHorBZSSOHj\npVlqQw9JB+ep9uBc1Q6cp9qB81Q7cJ5qh6qYp/Lsw+bm5lbqOots3bpVTJw4UUyZMkUcPny4StZR\nmo0bNwpJksSff/4p1q5dK6ysrEROTo4QQohRo0aJTp06CSGE8PPzE6GhoUIIIY4cOSIkSRLfffed\nVl+HDx8WkiSJdevWyW1FfRW3cOFCoVAoxI0bN4QQQty/f19IkiSWLVtW6lglSRLz5s3Taffw8BDj\nxo3T+UxPP/20UKlUcrtarRYtW7YUvXv31np/fn6+8PPzEyEhIXJbeHi4kCRJTJgwQW5TqVSiSZMm\nQpIksXDhQrk9PT1dWFpaipEjR8pt33//vVAoFCI6OlprXd9//72QJElERUVpfS4zMzNx+fJlue3s\n2bNCkiSxatUque3TTz8VkiSJxMRErT63bdsmJEkSJ0+e1PNTK11p2zUPZ60nJiwCig6RlgCsf9+g\nwyEiIiKiUsyZMweDBw/GunXrEBkZia5du+pU/KrTkCFDUFBQgG3btiE3Nxfbtm3Teyjrli1bYG1t\njT59+uDu3bvyo2XLlnBycsKBAwfkWAsLCwCAWq1GRkYG7t69i86dO0MIgdjYWDnG1NQUBw4cwP37\n9yvt87z22mtQKDSp0JkzZxAfH48RI0ZojTsjIwO9evXCn3/+qXP454QJE+TnCoUCQUFBkCQJr776\nqtxuZ2eHli1b4urVq1o/oxYtWsDX11drXV27doUkSVo/IwAIDQ2Fl5eXvNymTRvY2tpq9VkSe3t7\nAMCOHTt0zmmtCB7OWscJIXDxUgp+OeSMwvQReL4Lz4UkIiIiqqkSEhKwYMECGBkZYe7cuUhOTsba\ntWsxadIkDBo0CKamptU+pgYNGqBv37747rvvoFAokJubi2HDhunExcfHIysrC87Oznr7uXPnjvz8\nr7/+wsyZM3Ho0CGdcwGLDjE1MzPD4sWL8e6778LZ2RlPPfUU+vfvj1GjRsHd3f2JP8+jFwOKj48H\nAK0EsDhJknDv3j24ubnJbU2bNtWKsbOzg4mJCZycnLTabW1ttT53fHw8Ll68iEaNGuldT/FYfesB\nCuejPEl1t27dMHjwYMybNw/Lly9Ht27dMGDAALz88suwtLQs8/0lYRJZh3m07IEbafZQK5yBZvMh\nmThC3P0ZZ7Z/CXyyx9DDIyIiIiI94uLiABQmAOHh4RBCYOvWrbh37x5SUlL0JhXV4eWXX8bo0aOR\nmZmJ3r17y+feFadWq+Hg4IAff/xRbx8NGjQAUJgkhoaGwsbGBgsXLoSPjw8sLCyQlJSEsWPHQq1W\ny++ZPn06Bg4ciF9//RX79u3DRx99hIULF+K3337TOU/xUSVV34qqoMXHDQCLFy9GUFCQ3vc8+nmN\njIx0Ykq61YkodtVUtVoNPz8/rFy5Um+sq6trmet5tM/SbNmyBTExMfjtt9+wb98+TJw4EYsWLcLx\n48f1JrLlwSSyjlIqlUi+p4TaaSKkBn01LxhZwdKmseEGRkRERESlKqqwHT9+HL/88guSk5Nx7949\nmJiY6E3cqsvAgQNhZmaGo0ePYtOmTXpjvL29sX//fjz11FOwsrIqsa8DBw7g3r17+Pnnn9GlSxe5\nfd++fXrjPTw8MH36dEyfPh03b95Eu3btsGDBAjmJbNCgAdLT07Xek5+fj+Tk5HJ9tqLKpLW1NXr0\n6FGu9zwpHx8fnDx5slLXU9Z9Ojt06IAOHTpg3rx52LNnD/r3748vv/wS77//ZOe48ZzIOurs2bPI\nz5eA9L3ytxRCCCB9D6xsDPfLh4iIiIhK165dOwwaNAg5OTl46aWXMGXKFACF50lW5BDEirKwsMCa\nNWsQHh6OF154QW/M8OHDoVarMX/+fJ3XVCqVnOgVVdeKVxzVajWWL1+u9Z7c3FydQ13d3NzQqFEj\n+ZBXoDAJPHTokFbcunXrtPovTXBwMHx8fLB8+XJkZWXpvP7oIaYlKSuZA4Bhw4bh9u3bWLNmjc5r\nDx8+1Lv+shQl7GlpaVrt6enpOhXL9u3bA4DWz+9xsRJZRxUUFAAKM6DRGM3GnB4F2PeDwH8NOzgi\nIiIiKpEkSdi8eTMWLFiAqKgomJiYYNSoUVoXcjGUkSNH6m0vSlS6dOmCKVOm4NNPP8XZs2fRp08f\nmJmZ4dKlS/jPf/6Djz76CKNHj8YzzzwDBwcHjBkzBlOnToWxsTG2bt2K7OxsrX4vXryIHj16YOjQ\nofD19YWZmRl27dqFuLg4LFu2TI6bMGECJk2ahMGDB6NXr144c+YMoqKi4OjoWK7DPiVJwvr169Gv\nXz/4+vpi/PjxcHNzw61bt+Tk9Pfffy+zn5LWVbx95MiR2Lp1K6ZMmYJDhw7JFxO6ePEifvrpJ2zd\nuhVdu3Z9rPV06NABADB79myMGDECpqam6NmzJ77//ntERkbipZdegpeXF3Jzc7Fx40YYGxtj8ODB\nZX6ekjCJrKPatGkDyWkEhFUAAE0VEh7LYWlx1MCjIyIiIqLSmJqaYt68eZg3b55Bx1Geytqj92L8\n/PPPERgYiC+++AJz5syBsbExmjVrhmHDhsmHcDZo0AA7d+7EjBkzEB4eDhsbGwwaNAiTJk1CQECA\n3FfTpk0xcuRI/Pe//8XmzZshSRJatmwp34eyyGuvvYarV69i/fr12LNnD7p27Yp9+/ahZ8+eOp+h\npM/UpUsXHD9+HB999BFWr16NzMxMNG7cGB06dNBK4Eu692R52yVJws8//4zPPvsMmzZtwq+//goL\nCwt4e3tjypQpaNOmTRk/cd3PEBQUhEWLFmH16tUYP348hBA4cOAAunfvjhMnTmDLli1ISUmBra0t\nAgMDERkZKSeeT0IS5T0js4KKl0vt7OyqY5WyEydOACgsU9cXWTkCtj2yASMrCFUOcH0uYN8HUoO+\n6OoQgYPbDfsLSZ/6OE+1FeeqduA81Q6cp9qB81Q7VMU8lWcfNi8v78lv2k5UQ5W2XbMSWUdNXAzA\nqOhkZgXs8Cf8PSxhbHwMHryuDhERERERPSEmkXVQVo7Aj8VOe+zf2Ry/HTtcrsMRiIiIiIiISsOr\ns9ZBkz8Fih+kvPGD8h3PTkREREREVBYmkXVMVo7A5mK31+n3FODUkAkkERERERFVDiaRdcwbS7Wr\nkF/PMdxYiIiIiIio7mESWYfk5GlXIfuyCklERERERJWMSWQdMvlTQK3WLG/8wHBjISIiIiKiuolJ\nZB2RkyfwfZRmuXcHwMWBVUgiIiKi6lBNt14nqhZlbc9MIuuIN5exCklERERkCAqFAuriO2JEtZxa\nrYZCUXKqyCSyDsjJE/hmj2a5VzDg2ohVSCIiIqLqYGJigvz8fKhUKlYkqVYTQkClUiE/Px8mJiYl\nxhlX45ioikxdrl2F5BVZiYiIiKqPJEkwNzdHQUEBCgoKDD0cogpRKBQwNzcv9T7zTCJrubw8gU27\nNcuhQaxCEhEREVU3SZJgampq6GEQVQsezlrLvblCuwq5iVVIIiIiIiKqQmUmkdHR0RgwYADc3d2h\nUCiwadMmnZiIiAi4ubnB0tISoaGhuHDhQpUMlrTl5Qls2qVZ7tYecHdiFZKIiIiIiKpOmUlkdnY2\nAgICsHLlSlhYWOgcG7t48WIsX74cq1atQkxMDJycnNC7d29kZWVV2aCp0PSVgKp4FXKu4cZCRERE\nRET1Q5nnRIaFhSEsLAwAMHbsWK3XhBD47LPPMHv2bLz44osAgE2bNsHJyQmbN2/GxIkTK3/E9Vxz\n/75IznRE3sN8qGyfh+Q0CkL1AOa33kZT5/WGHh4REREREdVxFTon8urVq7h9+zb69Okjt5mbm6Nr\n1644evRohQdHupSwQ7b1KKh9tkByGlXY+DAJjR0NOy4iIiIiIqofKnR11pSUFACAs7OzVruTkxNu\n3bpV4vtOnDhRkdU+MUOttzLduZ8DiD0Q9n0gSVLhvYhSN+KhbW6d+HxA3Zin+oJzVTtwnmoHzlPt\nwHmqHSpznpo3b15pfRHVFVV2ddbS7itCT66goACw7wuoMgsbcuMAu568JxEREREREVWLClUiXVxc\nAAC3b9+Gu7u73H779m35NX2Cg4MrstrHVvRtVHWvtypYWdki376vVhUSzRbDLv8/tf7z1aV5qus4\nV7UD56l24DzVDpyn2qEq5ikjI6PS+iKqKypUifT09ISLiwuioqLktry8PBw+fBghISEVHhzpMnYa\npKnypv0K2PWEJElo7NLYsAMjIiIiIqJ6ocxKZHZ2NhISEgAAarUaiYmJOH36NBwcHNCkSRO89dZb\nWLhwIVq1aoXmzZvj448/ho2NDV5++eUqH3x9k58vcE/qB6DwyrhS2k9o5mqGJg2OwMutyo5MJiIi\nIiIikpWZRMbExKBHjx4ACs9zDA8PR3h4OMaOHYsNGzZg5syZyM3NxZQpU3D//n08/fTTiIqKgpWV\nVZUPvr6ZsQoQRnYACufi0qnv4OXO5JGIiIiIiKpPmUlk9+7doVarS40pSiyp6uTnC6zdplnu5A8m\nkEREREREVO2YhdQS70UCSpVm+ZsPDTcWIiIiIiKqv5hE1gJKpcAXv2iWn/IDvN14CxUiIiIiIqp+\nTCJrgXdXAQXFq5BzDTcWIiIiIiKq35hE1nBKpcCanzXLT/kCzZuwCklERERERIbBJLKGey/ykSok\nz4UkIiIiIiIDYhJZgymVAqv/o1nu2JpVSCIiIiIiMiwmkTXYrDXaVchNPBeSiIiIiIgMjElkDaVU\nCny+VbPcoRXQshmrkEREREREZFhMImuo2V8ABUrNMs+FJCIiIiKimoBJZA2kVAr8+yfNclBLViGJ\niIiIiKhmYBJZA32wllVIIiIiIiKqmZhE1jBqtcDKYlXIwBZAaw9WIYmIiIiIqGZgElmDHD16FH1f\ni0F+gaZtE6uQRERERERUgxgbegBUqGHjYNx/6AY06A/JpQOEOhdS0jy88PxpJPy119DDIyIiIiIi\nAsAkskaIjo7G/QcKoOlkSA36AgAkhQWETXeYWqUaeHREREREREQaPJy1Bjh+/DigsADyEuQ2IQSQ\nvheOTk0MODIiIiIiIiJtTCJrADs7O6BBX8BxhKYxfS9g3w+SxIvqEBERERFRzcEksgZ48cVBgNOr\nkEwcIFS5chUS9n0MPTQiIiIiIiItPCeyBoj81QGS6T8L+TeBlEhWIYmIiIiIqEZiEmlgarXAks2a\nZUvje7A1i0ULb1tI0jF4NDbc2IiIiIiIiB7FJNLAPtoIPMzXLB/57im0bX6QVUgiIiIiIqqRmEQa\nkFotsPg7zbKfJ9CuBZNHIiIiIiKquXhhHQNa8DWQV6wKuWmuoUZCRERERERUPkwiDUStFlj0rWbZ\n1xMIbMkqJBERERER1WxMIg1k4TfaVciv5xhuLEREREREROXFJNIA1GqBRZs0y609gOBWrEISERER\nEVHNxyTSABZ/B+QWr0J+YLixEBERERERPQ4mkdVMrRb4+GvNcqtmQAdfViGJiIiIiKh2YBJZzZZ8\nD+Q+1Cxv4rmQRERERERUizCJrEZqtcDHGzXLLZqyCklERERERLULk8hqtHQzkMMqJBERERER1WIV\nTiKVSiXef/99eHl5wcLCAl5eXpg7dy5UKlVljK/OUKsFPtqgWW7RBHjKj1VIIiIiIiKqXYwr2sHC\nhQuxdu1afPPNN2jTpg3OnDmDsWPHwszMDHPmsNRWZMWPQHaxKuRGXpGViIiIiIhqoQonkTExMRgw\nYACeffZZAEDTpk3x3HPP4X//+1+FB1dXZGQ8QPiXligq/DZvAnRqwyokERERERHVPhU+nDUsLAy/\n//47Ll68CAC4cOECDhw4gP79+1d4cLWdl29vmDgPhr3PFGSnJwAAROZhZMc+b+CRERERERERPZkK\nVyLfeOMNJCUloXXr1jA2NoZSqcScOXMwadKkyhhfrXYnXUDpMAFSg76aRnU+bGwcDTcoIiIiIiKi\nCpCEEKIiHfz73//GokWLsHLlSvj5+SE2NhbTp0/Hp59+ivHjx8txGRkZ8vOEhISKrLJWyM3NRddn\n5wDW7QGP5ZAkCUII4No78HJ+gB+/nGzoIRIRERFRGZo3by4/t7OzM+BIiGqOClciFyxYgDlz5mDo\n0KEAAD8/PyQmJmLRokVaSWR9k5+fD0gS4DAEkvTP+Y8ZBwD7fgC2GHRsRERERERET6rCSaQQAgqF\n9qmVCoUCpRU4g4ODK7rax3LixIlqX68QAqYOh5Fv00lexv0dgMdyONseqvafQW1giHmiJ8O5qh04\nT7UD56l24DzVDlUxT8WPpiOiQhVOIl944QV88skn8PT0hK+vL2JjY7FixQqMGTOmMsZXa0mSBJXj\n+H8OY1UBN+YB9v0gSRJMTU0NPTwiIiIiIqInUuEkcsWKFbC1tcWUKVNw+/ZtNG7cGBMnTsSHH35Y\nGeOrtT7/SUBt4v7PkgTrgmj4NymAmdkxeDQ26NCIiIiIiIieWIWTSCsrKyxduhRLly6tjPHUGXPW\naZ57uSlw6chBzbmRREREREREtVSF7xNJulb/R+BBjmZ5/WwwgSQiIiIiojqBSWQVeP8LzXMPF6B7\nIBNIIiIiIiKqG5hEVrI1vwhkFqtCfjnbcGMhIiIiIiKqbEwiK9nsNZrnzVyAnsGsQhIRERERUd3B\nJLISrd0mkJmtWV73L8ONhYiIiIiIqCowiaxEs1Zrnjd1Bnp3ZBWSiIiIiIjqFiaRleSr7QIZxaqQ\na1mFJCIiIiKiOohJZCWZGal53sQJ6PsUq5BERERERFT3MImsBBt2CKRnaZbXzjTcWIiIiIiIiKoS\nk8hK8F6xKqS7E9CvE6uQRERERERUNzGJrKCNOwXuP9Asf/Ge4cZCRERERERU1ZhEVtC7n2ueuzUC\n+oewCklERERERHUXk8gK2LRLuwq5hlVIIiIiIiKq45hEPoFmLXvA1GUIxk5eAiHUEEIFJH2Mt1/v\nZ+ihERERERERVSljQw+gtklMTETS7VyoXV+F1KCv3C6sgmFqdcWAIyMiIiIiIqp6rEQ+piVLlkCt\nNgWyTkIIAQCF/6bvhaNTEwOPjoiIiIiIqGoxiXxMiYmJgFU7wGkMJOmfi+ik7wXs+2mWiYiIiIiI\n6igmkY+pefPmgMskwNQVQqjkKiTs+xh6aERERERERFWOSeRjatU5ApJlq8KqY/4t4No7rEISERER\nEVG9wQvrPKYPN9rKzyVVJizyoxHQ1AJmpsfg0diAAyMiIiIiIqoGTCIfw4/7Be6ka5a3rvDDi91O\nsgpJRERERET1BpPIxzBthea5UwPgpe5MHomIiIiIqH7hOZHltOW/2lXIf79tuLEQEREREREZCpPI\ncipehWxkDwztySokERERERHVP0wiy2Hr7wKp9zXLrEISEREREVF9xSSyHKY+UoUc1otVSCIiIiIi\nqp+YRJbh54MCt9M0y5+9ZbixEBERERERGRqTyDK8uVzz3NEeGNGbVUgiIiIiIqq/mESW4pdDAin3\nNMufTTfcWIiIiIiIiGoCJpGleHOZ5rmDLfByH1YhiYiIiIiofmMSWYJfowWSi1UhV7AKSURERERE\nxCSyJG8s1TxvaAuM7McqJBERERERUaUkkcnJyRgzZgycnJxgYWEBPz8/REdHV0bXBrHjsHYVcvk0\nw42FiIiIiIioJjGuaAfp6eno3Lkzunbtil27dqFRo0a4cuUKnJycKmN8BvFoFXJ0GKuQRERERERE\nQCUkkUuWLIGbmxu+/vprua1Zs2YV7dYg4uPjseq7K7h5pw+AwsRx2VTDjomIiIiIiKhZI6eBAAAI\nWUlEQVQmqfDhrNu2bUPHjh0xbNgwODs7o3379oiMjKyMsVUr52YhaPn0e/h84/8ghBpCCIibn+Lj\nmf0MPTQiIiIiIqIao8JJ5JUrV7B69Wr4+PggKioK06dPx6xZs2pVIpmUlITUNCXgMhlS07mQJCNI\nkgRYtoGplauhh0dERERERFRjSEIIUZEOTE1N0bFjRxw+fFhu++CDD/DLL7/gwoULcltGRkZFVkNE\nREREZFB2dnaGHgJRjVDhSqSrqyt8fX212lq1aoXr169XtGsiIiIiIiKqYSqcRHbu3BlxcXFabfHx\n8fDw8Kho10RERERERFTDVPjqrG+//TZCQkKwcOFCDB06FLGxsfj888+xaNEirTiW/4mIiIiIiGq/\nCp8TCQC7du3C+++/j4sXL6JZs2Z488038eabb1bG+IiIiIiIiKgGqZQkkoiIiIiIiOqHCp8TWRus\nXr0anp6esLCwQHBwsNaVZKn6RUdHY8CAAXB3d4dCocCmTZt0YiIiIuDm5gZLS0uEhoZqXemXqsei\nRYvQoUMH2NnZwcnJCQMGDMD58+d14jhXhhUZGYm2bdvCzs4OdnZ2CAkJwa5du7RiOEc1z6JFi6BQ\nKDB16lStds6VYUVEREChUGg9XF1ddWI4R4aXnJyMMWPGwMnJCRYWFvDz80N0dLRWDOeKqOrU+STy\nxx9/xFtvvYU5c+bg9OnTCAkJQVhYGG7cuGHoodVb2dnZCAgIwMqVK2FhYVF4T85iFi9ejOXLl2PV\nqlWIiYmBk5MTevfujaysLAONuH46dOgQ3nzzTRw7dgy///47jI2N0atXL9y/f1+O4VwZXpMmTbBk\nyRLExsbi5MmT6NGjB1544QWcOXMGAOeoJjp+/Di+/PJLBAQEaP3+41zVDK1atUJKSor8OHfunPwa\n56hmSE9PR+fOnSFJEnbt2oW4uDisWrUKTk5OcgzniqiKiTquY8eOYuLEiVptzZs3F7NnzzbQiKg4\na2trsWnTJnlZrVYLFxcXsXDhQrktNzdX2NjYiLVr1xpiiPSPrKwsYWRkJH777TchBOeqJmvYsKFY\nt24d56gGSk9PF97e3uLgwYOie/fuYurUqUII/n+qKcLDw4W/v7/e1zhHNcfs2bPFM888U+LrnCui\nqlenK5H5+fk4deoU+vTpo9Xep08fHD161ECjotJcvXoVt2/f1pozc3NzdO3alXNmYJmZmVCr1WjQ\noAEAzlVNpFKp8H//93/Iy8tD165dOUc10MSJEzFkyBB069YNotglCThXNceVK1fg5uYGLy8vjBgx\nAlevXgXAOapJtm3bho4dO2LYsGFwdnZG+/btERkZKb/OuSKqenU6ibx79y5UKhWcnZ212p2cnJCS\nkmKgUVFpiuaFc1bzTJ8+He3bt0enTp0AcK5qknPnzsHa2hrm/9/e3YSkssZhAH8mcZpa5KZCLbBv\nIwuJ7HvTJmgbtLBVtWljEEWLoiCFimgVhEJJREFBtW6RUUJJbS36LlzUJiGCoCAIfc8quZ57Twj3\npEM9PxgY3nkH/vDwOvwdx1EU9Pb2YmNjA2azmRmpjNfrRSgUwsTEBADE/ZSVWalDQ0MDlpeXsb29\nDa/Xi4eHBzQ1NeHp6YkZqUgoFILH40FJSQl8Ph/6+/sxPDwcaySZFdHX+9/viSRKlt+fnaTkGRwc\nxOHhIQKBQEI5MKvkKi8vx8nJCZ6fn7G5uQm73Q6/3//pOcwoua6urjA6OopAIACNRgMAEELE3Y38\nE2aVPG1tbbH9yspKNDY2orCwEMvLy6ivr//jecwouaLRKOrq6jA5OQkAsFqtuLm5gdvthsPh+PRc\nZkX0d3zrO5HZ2dnQaDQIh8Nx4+FwGAaDIUVV0Wf0ej0A/GdmH8couQYGBrC+vo69vT0UFBTExpmV\nemi1WhQVFaG6uhpTU1NoaGiA2+2Ofc4xo9Q7OjrC4+MjLBYLtFottFot9vf34fF4IMsysrOzATAr\ntcnMzITFYsHt7S3Xk4oYjUZUVFTEjZWXl+Pu7g4Ar09EyfCtm0hZllFTUwOfzxc3vrOzg6amphRV\nRZ8pLCyEXq+Py+zt7Q2BQICZpUB/f3+sgSwrK4s7xqzUKxKJIBqNMiMVaW9vx+npKY6Pj3F8fIxg\nMAibzYbOzk4Eg0GUlpYyKxV6e3vDxcUFDAYD15OKNDc34/LyMm7s+vo69kUnsyL6ehqn0+lMdRFf\nKSsrC+Pj4zAajcjIyMDExAQCgQCWlpag0+lSXd6P9Pr6ivPzczw8PGBxcRFVVVXQ6XR4f3+HTqdD\nJBLB9PQ0zGYzIpEIBgcHEQ6HsbCwAFmWU13+j+FwOLCysoLNzU3k5+fj5eUFLy8vkCQJsixDkiRm\npQLDw8NQFAXRaBT39/eYnZ3F2toaZmZmUFxczIxUQlEU5OTkxLbc3Fysrq7CZDKhq6uL60klhoaG\nYuvp+voafX19CIVCmJ+f5/VJRUwmE1wuFzQaDQwGA3Z3dzE2NoaRkRHU1tZyPRElQ4r/HTYpPB6P\nKCgoEOnp6cJms4mDg4NUl/Sj+f1+IUmSkCRJpKWlxfZ7enpic5xOpzAYDEJRFNHS0iLOzs5SWPHP\n9Hs+H5vL5Yqbx6xSq7u7W5hMJpGeni5yc3NFa2ur8Pl8cXOYkTr98xUfH5hVatntdmE0GoUsyyIv\nL090dHSIi4uLuDnMSB22traE1WoViqIIs9ks5ubm/jWHWRF9HUmIBJ7qJyIiIiIiIsI3fyaSiIiI\niIiI/i42kURERERERJQwNpFERERERESUMDaRRERERERElDA2kURERERERJQwNpFERERERESUMDaR\nRERERERElDA2kURERERERJQwNpFERERERESUsF/ZdnFPR2HW5QAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", - "for i in range(50):\n", - " zs.append(14)\n", - "\n", - "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.1, h=0.01)\n", - "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.5, h=0.01)\n", - "data3 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.9, h=0.01)\n", - "\n", - "with book_format.figsize(y=5):\n", - " book_plots.plot_measurements(zs)\n", - " book_plots.plot_filter(data1, label='g=0.1', marker='s')\n", - " book_plots.plot_filter(data2, label='g=0.5', marker='v')\n", - " book_plots.plot_filter(data3, label='g=0.9', lw=2)\n", - " book_plots.show_legend()\n", - " plt.ylim([6, 20])" - ] - }, - { - "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 'Goldilocks' 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", - "execution_count": 41, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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hTHuy8GGnCUmGe8bAdz/nloVdDwteAL8iZmgVERGRC0MBUkRESs0DDzzAi6//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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = [5,6,7,8,9,9,9,9,9,10,11,12,13,14,\n", - " 15,16,16,16,16,16,16,16,16,16,16,16]\n", - "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.302, h=.054)\n", - "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.546, h=.205)\n", - "\n", - "with book_format.figsize(y=5):\n", - " book_plots.plot_measurements(zs)\n", - " book_plots.plot_filter(data2, label='g=0.546\\nh=0.205', marker='s')\n", - " book_plots.plot_filter(data1, label='g=0.302\\nh=0.054', marker='v')\n", - " book_plots.show_legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Varying h" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's leave g unchanged and investigate the effect of modifying h. We know that h affects how much of we favor the measurement of $\\dot{x}$ vs our prediction. But what does this *mean*? If our signal is changing a lot (quickly relative to the time step of our filter), then a large $h$ will cause us to react to those transient changes rapidly. A smaller $h$ will cause us to react more slowly.\n", - "\n", - "We will look at three examples. We have a noiseless measurement that slowly goes from 0 to 1 in 50 steps. Our first filter uses a nearly correct initial value for $\\dot{x}$ and a small $h$. You can see from the output that the filter output is very close to the signal. The second filter uses the very incorrect guess of $\\dot{x}=2$. Here we see the filter 'ringing' until it settles down and finds the signal. The third filter uses the same conditions but it now sets $h=0.5$. If you look at the amplitude of the ringing you can see that it is much smaller than in the second chart, but the frequency is greater. It also settles down a bit quicker than the second filter, though not by much." - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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q4eHhNG/e3GZOYWxsLM888wzt2rVj/PjxALz22mts3LiRIUOGsGPHDutCNAWZ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Sy+KgMOZEF09XcZL9U4ChKvzmDvukcoMOl0jF7GR6tm1Gh9r4rpiIiIiFRPYdLLNYu1aN/SsPcg\nnD0Hm3KhT5dv/r7atnUPfPal3W4QARk9PNsf8R5XCmAh9Sxu6Aw3dIZJP4WC04bVWzJ4eFQWXxp7\namyf22Zw6ox9B7Og7M/TZXc0L7/LeFVCJh06WCTGQ2Iz7D8T7K/W8RB1lQVYPPNsR558cQxT/m8Q\nEWFBLv33iIiIiMjlFCZ9QEoX2HtxbeKaHO8Ik5WnuN7WB8I0xVUqqWkAi7rKYnAfi3OTKqbG3jG0\n6qBXWmo4cxYKTmdw8x1ZbLtgF8bZtKJmdw77pfXk/Q0bNWVVRERExE1q/r/nxWNSu1a0vWHd5KVV\nXIf181xfxD/cMTSTO/tyxaAXFGQRGWHRLDaIiWMziPo6iwmjal4Yx7Isfv34I7rTKCIiIuImCpM+\noPK6yfd3wLnzxnOdAT76BPYfstvRkZCuKa7yHbm6NrEm4bO684iIiIiIeyhM+oCWTS3aNrPbRcWw\n+RPP9qfyFNchffCKgkDi+1wJeiqMIyIiIuJ5CpM+IqXSVNc1Hpzqqimu4i0UJEVEREQ8S2HSR1Se\n6ro2x3P92JQLn+fZ7YYN7Ae8i4iIiIhI4FGY9BGVi/Bkb7ef1+cJTlNcUyA0RHeHREREREQCkcKk\nj0hMsGgdb7dPF8GW3XXfh9JSw99XVby+S1NcRUREREQClsKkD6k81XWNB6a6bsyFg/l2u1ED6J9U\n930QERERERHvoDDpQ5yK8Gyp+/MvfK+iPTQVQuppiquIiIiISKBSmPQhle9MZm+HC3W4bvLSKa4/\n7F9npxYRERERES+kMOlD2jaHFnF2+9QZyNlbd+devwO+/Npux0RD3251d24REREREfE+CpM+xLIs\nj62brFzF9fY0qKcpriIiIiIiAU1h0sc4rZvcWjfnLCkx/ENVXEVEREREpBKFSR9T+c7kum120Ktt\n7++Aw0ftdmxD5z6IiIiIiEhgUpj0Me1bQkKM3T5ZCNs/q/1zVq7iqimuIiIiIiICUM/THRDXWJZF\naN4kzGH79bD7KoryJCbAX2ZPduv5SkoM/1hd8VpTXEVEREREBBQmfVJIPbBaOQDYB+w7WvaOw+3n\nWpsD+cfsdtPGkKIpriIiIiIigsKkT2oYCZyu3XM88NAkDhyGPQfBHLG3BZ2Bnz3s/rufIiIiIiLi\nexQmfVBEGLUeJg8chrVHHRABVit722HgwGFH7Z5YRERERER8ggrwiIiIiIiIiMsUJv3IhRL3Hevs\nOfcdS0RERERE/I/bprnOmTOHv/3tb2zdupWCggIOHDhAq1at3HV4qSQxAcDBufPw4ccVIfIrNz1y\n8vwFQ+4BIMY9xxMREREREf/jtjBZVFREZmYmQ4YMYdy4ce46rFShcgGc11cYfjTJbn8KLN9oSO/5\n3Z4D+cRsOHUaLIVJERERERGphtvC5JgxYwDYvHmzuw4pNfDD/vD3lfDPNfbrB5+GHa8aoiO/XaD8\nz3rD7xbYbfOFgzbNoFXTivftu6IiIiIiIhLoVM3Vx1mWxazHDGu3wZET8N+v4JfPw58ed/1YB/MN\n9z958bitHAzsBW8/C0FB3+1Op4iIiIiI+B8V4PEDcY0sZv6y4vWfF8M7G1xbQHn+gmH4JDhWYL9u\nHgvzfq0gKSIiIiIiVbOMMdWmjokTJzJ16tQrHmD16tWkpKSUv968eTM9evSotgDPyZMny9t79+79\nNn2Wajw+tw3v5TQGIDb6HK9PyKVBRM1KvL7w7+bMfy8egOAgw4ujdtOlXS0/zFJERETER7Rv3768\nHR0d7cGeiHiPK05zHTduHPfdd98VD9CyZUu3dki+vfHDDrLl0wYcLwzh65Oh/P5fLfjNPZ9/4/et\nz40qD5IAD918SEFSRERERESu6IphMiYmhpiY2ivpmZSUVGvHrkpZcaC6Pm9dmmMMwyba7cWbmvDQ\nsCYMSq5+qup/vzI8+ZuK1xk94Y+/ak5QUIta7mndC4Txl+pp/AObxj+wafwDm7vGv/LsOhGxuW3N\nZF5eHjk5OezZsweAXbt2kZOTw/Hjx911CqmBO/pa3H1TxesRT8PxgqpnMl+4YD9W5OjFvxubNYH5\nWicpIiIiIiI14LYw+dJLL9GtWzfuvfdeLMti0KBBXH/99bz99tvuOoXU0PNZ0NReOsnhozD2uar3\nm/QKZG+320FBsGAyxDZSkBQRERERkW/mtjDpcDgoLS2ltLSUkpKS8j+/ac2luF9MtMWLj1W8fnUp\n/Hud893JZRsN0+ZXvJ78IKR0UZAUEREREZGa0aNB/NSQFIt70ite//xZOHrSDpRffm348W8r3hvQ\nHR7/cR13UEREREREfJrCpB97bhzEX6yflHcUxvzeXid5jwOOnLC3J8TAq5O0TlJERERERFxzxWqu\n4tsaR1nMHm8YPNwBwGuvwJKFcPzUxR0seO15B3FaJykiIiIiIi5SmPRzt95o0bQxfBXpAOAEYDWy\n32t13kFaNwVJERERERFxnaa5BoDvVfPIyNZN67YfIiIiIiLiPxQmA0C94Kq3W7opKSIiIiIi35LC\npIiIiIiIiLhMYVJERERERERcpgI8ASAxAcBRzXYRERERERHXKUwGgL/MnuzpLoiIiIiIiJ/RNFcR\nERERERFxmcKkiIiIiIiIuExhUkRERERERFymMCkiIiIiIiIuU5gUERERERERlylMioiIiIiIiMsU\nJkVERERERMRlCpMiIiIiIiLiMssYY+ryhCdPnqzL04mIiIiIuFV0dLSnuyDiFXRnUkRERERERFym\nMCkiIiIiIiIuq/NpriIiIiIiIuL7dGdSREREREREXKYwKSIiIiIiIi4LqDA5a9Ys2rRpQ3h4OElJ\nSWRnZ3u6S1IL1q5dy+DBg2nRogVBQUHMmzfvsn0cDgfNmzcnIiKCvn37kpub64GeirtNmzaN7t27\nEx0dTVxcHIMHD2bXrl2X7afx908zZ87kuuuuIzo6mujoaJKTk1myZInTPhr7wDFt2jSCgoIYPXq0\n03ZdA/7J4XAQFBTk9NWsWbPL9tHYi7hXwITJN954g7FjxzJx4kRycnJITk5m4MCBHDx40NNdEzc7\nffo0nTt35rnnniM8PBzLspzef+aZZ5gxYwYvvPACH374IXFxcQwYMIDCwkIP9VjcZc2aNYwaNYoN\nGzawcuVK6tWrx0033cTx48fL99H4+6+WLVsyffp0tm7dykcffUS/fv0YMmQI27ZtAzT2geSDDz7g\n5ZdfpnPnzk7/Buga8G8dO3YkLy+v/GvHjh3l72nsRWqJCRA9evQwI0aMcNrWvn178/jjj3uoR1IX\nIiMjzbx588pfl5aWmvj4eDN16tTybUVFRaZBgwZm9uzZnuii1KLCwkITHBxsFi9ebIzR+Aeixo0b\nmzlz5mjsA8iJEydMu3btzOrVq01aWpoZPXq0MUaff383adIkc+2111b5nsZepPYExJ3Jc+fOsWXL\nFtLT0522p6ens379eg/1Sjxh//795OfnO10LYWFhpKSk6FrwQwUFBZSWltKoUSNA4x9ISkpKeP31\n1zl79iwpKSka+wAyYsQIhg0bRmpqKqZSwXpdA/5v3759NG/enLZt2zJ8+HD2798PaOxFalM9T3eg\nLhw5coSSkhKaNm3qtD0uLo68vDwP9Uo8oWy8q7oWDh065IkuSS0aM2YMXbt2pXfv3oDGPxDs2LGD\n3r17U1xcTHh4OAsXLqRDhw7lvzBq7P3byy+/zL59+1iwYAGA0xRXff79W69evZg3bx4dO3YkPz+f\nKVOmkJyczK5duzT2IrUoIMKkSE1curZSfFtWVhbr168nOzu7RmOr8fcPHTt2ZPv27Zw8eZJFixZx\n9913s2rVqit+j8beP+zevZsnnniC7OxsgoODATDGON2drI6uAd+XmZlZ3r722mvp3bs3bdq0Yd68\nefTs2bPa79PYi3w3ATHNtUmTJgQHB5Ofn++0PT8/n4SEBA/1SjwhPj4eoMproew98X3jxo3jjTfe\nYOXKlSQmJpZv1/j7v5CQENq2bUvXrl2ZOnUqvXr1YubMmeV/12vs/deGDRs4cuQI11xzDSEhIYSE\nhLB27VpmzZpFaGgoTZo0AXQNBIqIiAiuueYaPv30U33+RWpRQITJ0NBQrr/+epYvX+60/d133yU5\nOdlDvRJPaNOmDfHx8U7XwtmzZ8nOzta14CfGjBlTHiSvvvpqp/c0/oGnpKSE0tJSjX0AGDp0KDt3\n7mTbtm1s27aNnJwckpKSGD58ODk5ObRv317XQAA5e/YsH3/8MQkJCfr8i9SiYIfD4fB0J+pCVFQU\nkyZNolmzZoSHhzNlyhSys7OZO3cu0dHRnu6euNHp06fJzc0lLy+PV155hU6dOhEdHc358+eJjo6m\npKSEp59+mg4dOlBSUkJWVhb5+fnMmTOH0NBQT3dfvoNf/OIXzJ8/n0WLFtGiRQsKCwspLCzEsixC\nQ0OxLEvj78cmTJhAWFgYpaWlHDx4kD/84Q8sWLCA6dOn065dO429nwsLCyM2Nrb8Ky4ujtdee43W\nrVtz//336/Pv5x599NHyz/+ePXsYNWoU+/btY/bs2fq3X6Q2ebiabJ2aNWuWSUxMNPXr1zdJSUlm\n3bp1nu6S1IJVq1YZy7KMZVkmKCiovP2Tn/ykfB+Hw2ESEhJMWFiYSUtLM7t27fJgj8VdLh3zsq/J\nkyc77afx908PPPCAad26talfv76Ji4szAwYMMMuXL3faR2MfWCo/GqSMrgH/dPfdd5tmzZqZ0NBQ\n07x5c3PnnXeajz/+2Gkfjb2I+1nG1GBluoiIiIiIiEglAbFmUkRERERERNxLYVJERERERERcpjAp\nIiIiIiIiLlOYFBEREREREZcpTIqIiIiIiIjLFCZFRERERETEZQqTIiIiIiIi4jKFSREREREREXGZ\nwqSIiIiIiIi47P8BEUq0DCZAghwAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = np.linspace(0, 1, 50)\n", - "\n", - "data1 = g_h_filter(data=zs, x0=0, dx=0., dt=1., g=.2, h=0.05)\n", - "data2 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.05)\n", - "data3 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.5)\n", - "\n", - "with book_format.figsize(y=5):\n", - " book_plots.plot_measurements(zs)\n", - " book_plots.plot_filter(data1, label='dx=0, h=0.05')\n", - " book_plots.plot_filter(data2, label='dx=2, h=0.05', marker='v')\n", - " book_plots.plot_filter(data3, label='dx=2, h=0.5', marker='s')\n", - " book_plots.show_legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Interactive Example\n", - "\n", - "For those of you running this in IPython Notebook I've written an interactive version of the filter so you can see the effect of changing $\\dot{x}$, $g$ and $h$ in real time. As you adjust the sliders for $\\dot{x}$, $g$ and $h$ the date will be refiltered and the results plotted for you.\n", - "\n", - "If you really want to test yourself, read the next paragraph and try to predict the results before you move the sliders. \n", - "\n", - "Some things to try include setting $g$ and $h$ to their minimum values. See how perfectly the filter tracks the data! This is only because we are perfectly predicting the weight gain. Adjust $\\dot{x}$ to larger or smaller than 5. The filter should diverge from the data and never reacquire it. Start adding back either $g$ or $h$ and see how the filter snaps back to the data. See what the difference in the line is when you add only $g$ vs only $h$. Can you explain the reason for the difference? Then try setting $g$ greater than 1. Can you explain the results? Put $g$ back to a reasonable value (such as 0.1), and then make $h$ very large. Can you explain these results? Finally, set both $g$ and $h$ to their largest values. \n", - " \n", - "If you want to explore with this more, change the value of the array `zs` to the values used in any of the charts above and rerun the cell to see the result." - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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77+sm8jVrQni4ZgGnZ81Uat68OR4eHly5cgUnJyftzacDBgzQLtRUGIyMjFix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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from IPython.html.widgets import interact, interactive, fixed\n", - "from IPython.html.widgets import FloatSlider\n", - "\n", - "zs = gen_data(x0=5, dx=5, count=100, noise_factor=50)\n", - "\n", - "def interactive_gh(x, dx, g, h):\n", - " data = g_h_filter(data=zs, x0=x, dx=dx, dt=1., g=g, h=h)\n", - " plt.scatter(range(len(zs)), zs, edgecolor='k', facecolor='none',\n", - " marker='o', lw=2)\n", - " plt.plot(data, color='b')\n", - " plt.show()\n", - "\n", - "interact (interactive_gh, \n", - " x=FloatSlider(value=0., min=-50, max=50.), \n", - " dx=FloatSlider(value=5., min=-50., max=50.), \n", - " g=FloatSlider(value=0.1, min=0.01, max=2, step=.02), \n", - " h=FloatSlider(value=0.02, min=0.0, max=0.5, step=0.01));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Don't Lie to the Filter\n", - "\n", - "You are free to set $g$ and $h$ to any value. Here is a filter that performs perfectly despite extreme noise." - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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w9fWVK2dFV7t2bejr6yMsLAxDhw6FtrY2bt26BQ0NDTRo0EDZ4SlEXFwcvv/+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\nAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_data(x0=5, dx=.2, count=100, noise_factor=100)\n", - "data = g_h_filter(data=zs, x0=5, dx=.2, dt=1., g=0, h=0)\n", - "with book_format.figsize(y=2.):\n", - " book_plots.plot_measurements(zs)\n", - " book_plots.plot_filter(data, label='filter', lw=2)\n", - " book_plots.show_legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I brilliantly extracted a straight line out of very noisy data! Maybe I shouldn't try to collect my Fields Medal in mathematics just yet. I did this by setting both $g$ and $h$ to 0. What does this do? It makes the filter ignore the measurements, and so for each update it computes the new position as $x + \\Delta x \\Delta t$. Of course the result is a straight line if we ignore the measurements. \n", - "\n", - "A filter that ignores measurements is useless. I know you would never set both $g$ and $h$ to zero as that takes a special kind of genius that only I possess, but I promise that if you are not careful you will set them lower than they should be. You can always make great looking results from test data. When you try your filter on different data you will be disappointed in the results because you finely tuned the constants for a specific data set. $g$ and $h$ must reflect the real world behavior of the system you are filtering, not the behavior of one specific data set. In later chapters we will learn a lot about how to do that. For now I can only say be careful, or you will be getting perfect results with your test data, but results like this once you switch to real data:" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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ZTBw5cgSAEiVK4OjoSI8ePfIdp169egD873//IyEhwdxfNSAggJMnT1KpUiXC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\nUylXrhy5cuVi6tSp3Lp1i+7du9OmTRtmzJhhcL5/jpS+7W+Z0qd0VKp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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_data(x0=5, dx=-2, count=100, noise_factor=5)\n", - "data = g_h_filter(data=zs, x0=5, dx=2., dt=1., g=.005, h=0.001)\n", - "with book_format.figsize(y=2.):\n", - " book_plots.plot_measurements(zs)\n", - " book_plots.plot_filter(data, label='filter', lw=2)\n", - " book_plots.show_legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Tracking a Train" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We are ready for a practical example. Earlier in the chapter we talked about tracking a train. Trains are heavy and slow, thus they cannot change speed quickly. They are on a track, so they cannot change direction except by slowing to a stop and then reversing course. Hence, we can conclude that if we already know the train's approximate position and velocity then we can predict its position in the near future with a great deal of accuracy. A train cannot change its velocity much in a second or two. \n", - "\n", - "So let's write a filter for a train. Its position is expressed as its position on the track in relation to some fixed point which we say is 0 km. I.e., a position of 1 means that the train is 1 km away from the fixed point. Velocity is expressed as meters per second. We perform measurement of position once per second, and the error is $\\pm$ 500 meters. How should we implement our filter?\n", - "\n", - "First, let's simulate the situation without a filter. We will assume that the train is currently at kilometer 23, and moving at 15 m/s. We can code this as \n", - "\n", - "```python\n", - "pos = 23*1000\n", - "vel = 15\n", - "```\n", - "\n", - "Now we can compute the position of the train at some future time, *assuming* no change in velocity, with\n", - "\n", - "```python\n", - "def compute_new_position(pos, vel, dt=1):\n", - " return pos + (vel * dt)\n", - "```\n", - "\n", - "We can simulate the measurement by adding in some random noise to the position. Here our error is 500m, so the code might look like:\n", - "\n", - "```python\n", - "def measure_position(pos):\n", - " return pos + random.randn()*500\n", - "```\n", - " \n", - "Let's put that in a cell and plot the results of 100 seconds of simulation. I will use NumPy's `asarray` function to convert the data into an NumPy array. This will allow me to divide all of the elements of the array at once by using the '/' operator." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Ozl7UGDvNgFyZ0HCtRY2DPVKPBq1GhwmGAu5+fUq6dHtA4e8DW7qUqktHacF0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\n6KGHcPr0adTX1yses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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from numpy.random import randn\n", - "\n", - "def compute_new_position(pos, vel, dt=1):\n", - " \"\"\" dt is the time delta in seconds.\"\"\"\n", - " return pos + (vel * dt)\n", - "\n", - "def measure_position(pos):\n", - " return pos + randn()*500\n", - "\n", - "def gen_train_data(pos, vel, count):\n", - " zs = []\n", - " for t in range(count):\n", - " pos = compute_new_position(pos, vel)\n", - " zs.append(measure_position(pos))\n", - " return np.asarray(zs)\n", - " \n", - "pos, vel = 23*1000, 15\n", - "zs = gen_train_data(pos, vel, 100)\n", - "\n", - "plt.plot(zs / 1000.) # convert to km\n", - "book_plots.set_labels('Train Position', 'time(sec)', 'km')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see from the chart how poor the measurements are. No real train could ever move like that. \n", - "\n", - "So what should we set $g$ and $h$ to if we want to filter this data? We have not developed the theory for this, but let's try to get a reasonable answer by the seat of our pants. We know that the measurements are very inaccurate, so we don't want to give them much weight at all. To do this we need to choose a very small $g$. We also know that trains can not accelerate or decelerate quickly, so we also want a very small $h$. For example:" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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jWbFiBRs2bAAgICBALZQi/zH9jxMREQA8PDxYvnw5I0eOZNOmTfj5+TF48GBa\ntmzp6NBE5Cbt3LmTAQMGYLFYaNeuHTExMezfv5+nnnqKyMhIR4dXYNq0aUODBg3YuHEjzZo1s5WP\nGTPGgVGJ3J6UeIqIiI2Pjw+TJk1ydBgiks/Wrl2LxWKhS5cuzJ07l9OnTxMYGMjq1auxWCxFZq3V\nf3N1dWXp0qW8+uqrtlltn3322SK95I9IYaXEU0RERKSI8/T0BODgwYMkJyeza9cuwNrTISdrV97K\nihcvzqeffuroMERue0o8RURERIq4du3aERQUxJ9//om3tzcWiwWA//3vfzedeF68eJG4uDjKlClT\n5CcrEpG8K5r9KkRERETExt/fn2XLlnH33XdjsVhwdXVl0KBBjBs3Ls91GobBO++8g7+/P1WrVqVk\nyZJ89tln+Ri1iBQlavEUERERuQ3UqFGDP//8k+TkZNzc3HBycrqp+iIiIhgxYgQAZcqUITY2lv79\n+xMaGmqbGVtE5Cq1eIqIiIjcRjw9PW866QSYPXs2AP/3f//H8ePHefXVV+3KRUT+SYmniIgUqBUr\nVvDAAw9QsWJF2rdvT0xMjKNDEpF8kJGRAUCJEiUA8PX1BbCtEyoi8k/qaisiIgVm1apVtGzZ0vZF\n9NChQ2zYsIGtW7dSrlw5B0cnIjejbdu2LFu2jH79+vH111+zfv16W7mIyL+pxVNERArMuHHjyMzM\npE+fPmzfvp0HHniAc+fOMXnyZEeHJiI3adCgQfTt25f09HTbOqEvv/wyTzzxhKNDE5FCSImniIgU\nmFOnTgHQu3dv7rzzTjp37mxXLiK3LrPZzJdffklMTAxLly7l0KFDjBs3rsivCyoieaOutiIiUmBq\n1qzJ1q1bGTBgAF27drUt4l6zZk0HRyYi+aVKlSpUqVLF0WHw888/s3TpUlxcXOjWrRv169d3dEgi\n8g9KPEVEpMCMHTuWVatWsXPnTnbu3AlA48aNee655xwcmYgUJW+++SajRo2yPZ40aRLfffcdjz76\nqAOjEpF/UuIpIiIFJjg4mM2bNzN16lROnDhB1apV6d27N66uro4OTUSKiIMHDzJq1ChMJhMvv/wy\np06dYurUqfTt25eHH35YnzcihYQSTxERKVB+fn688MILjg5DRIqoPXv2ANbeFGPHjsUwDBYtWsS5\nc+eIi4ujfPnyDo5QROAGkwuNHTuWevXq4ePjQ0BAAB06dGD37t1Zbt+vXz/MZjMffPBBtgdduXIl\nZrP5mttut3bjAAAgAElEQVS+ffvydhYiIiIiclsKCQkBYNOmTSxevJipU6dy7tw5nJ2dKVmyZL4c\nwzAMYk8b/LreYPxMg15vGdTubbB0o5Ev9YvcDrJt8YyKimLAgAHUq1cPi8XCyJEjadGiBdHR0bZF\ngq+aN28emzZtIiQkJMezmUVHR+Pn52d7nF8fDiIiIoVZamoqv//+O2fOnKFWrVrcddddjg7plrV+\n/XoWLlyIyWTi4YcfpmHDho4OSf5jtWrVokOHDixatIj27dvbyl966SW8vLxyVdf5iwYHT2B3O3Ac\ndh2GhEvXbv/nfmjV4GbPQOT2kG3iuWTJErvHERER+Pj4sG7dOtq1a2crP3r0KEOGDCEyMpI2bdrk\n+OClSpXC398/lyGLiIjcus6dO0erVq3YunWrrWzUqFGMHj3acUHdor7++mv69u2LYVhbnd577z2+\n/vpr+vTp4+DI5L9kMpn4/vvvGT16NL/99hsuLi50796dAQMGZLnPhYsG2w/AjoOw/QDsOgj7Y6+f\nXGZn96GbDB6wWCykpaXdfEUiDubq6orZnHWH2lyN8bx48SIWi8WutTMjI4PHH3+cN954g/Dw8FwF\nV7duXVJTU6lWrRojRoygSZMmudpfRETkVjN48GC2bt1KmTJlqF+/PgsXLmTMmDHcf//9NG/e3NHh\n3TIuXLhA//79MQyDZ555BsMwmDJlCs8//zwdO3akRIkSjg5R/kNubm6MHTuWsWPH2pWnpRvsOw47\nD8KuQ7Djr2TzeB6WEnbmMvWqe3BnZSdqVoQaFaBmhZuL2zAMUlNTcXd31/qnckszDIOUlJRsr+Vc\nJZ6DBw+mVq1aNGrUyFY2atQoAgIC6NevX47rCQkJYfLkydSrV4/U1FQiIiJo3rw5UVFR3Hfffdfd\nZ/PmzbkJVW5DukYkJ3SdSE4U5HWybNkyAMaNG0d4eDguLi7MmTOH7777Dh8fnwI7blGze/duUlNT\nCQsLo2/fvgAsXbqUo0ePsmjRIqpVq1bgMejzpPBIyzARe9aNo6fcORTvzqE4Dw7GeXD0tDuZlpwn\ndG4uFkr7p+KSeZS923/BOeMod1b2Yv+ORVw6F03Fij14uukg68YZcDCL6UkqV66cs7jT0nB1dVXS\nKbc8k8mEq6sraWlpuLm5XXebHCeew4YNY926daxZs8b2n2PlypVMnz6dbdu22W17tctLVv690HDD\nhg05cuQI48ePzzLxFBERKQo8PDwAOHDgABUqVODIkSN25ZIzV+eIOH78OKtXr7ZO/hIba/ecFC1J\nKWZOJbhy6oIrJ866ceyMG0dPu3PstDtx512xGDlP3lycLFQITqFySDKVQq5QufQVQgNTKFk8HZMJ\n3nrrLfYeWcRzAwfSs2dn1qwJZOjQofz555/5ek6GYeDk5JSvdYo4ipOTE+np6Vk+n6PEc+jQoXz/\n/fesWLGC0NBQW3lUVBRxcXEEBwfbyjIzM3n55ZeZNGkSx44dy3Gg9evXZ86cOVk+X7du3RzXJbeX\nq7846xqR7Og6uXnR0dEMGjSIXbt2ERISwsiRI3nkkUccHVa++i+uk4EDB/Liiy8yevRo3nzzTSwW\nC97e3rzwwgt2f2Plxrp3786MGTMYNmyYraxnz552E8wUBH2eFIwL/5jY59BJOBIPsafg+GnrLfFy\n3uotH2TtFlv9r66xd1WG8HJmXJy9gOtPPnR1CZYLFy5Qu3Ztli5dCkBAQECO3vfExMS8BStShN0w\n8Rw8eDBz585lxYoVdq2UAM8//zyPPvqo7bFhGLRu3ZonnnjC1u0lp7Zt22abDltERAqXY8eOcf/9\n93P+/HkATp06RceOHfn555/tJpuTGxs6dChJSUm8//77JCUlUaVKFaZNm6akMw+++eYbypcvz48/\n/ojJZKJTp0688cYbjg4r31gsFvbv309KSgpVq1bNsvvarcAwDM4m/J1EHv8roTwW//fssRdyObHP\nP5lM1gSzSlkIL29NMGtUgGphUNwr991Ye/fuzeTJk5kxYwYzZ8609eZ75pln8h6kyG0u28Szf//+\nzJgxgwULFuDj40N8fDwA3t7eeHl5UapUKUqVKmW3j4uLC0FBQXZ923v27InJZGL69OkATJw4kbCw\nMKpVq0ZaWhozZsxg4cKF/PDDD/l9fiIikg++/vprzp8/T+PGjfn666/55JNPmDhxIuPHj1fimUtm\ns5mRI0cyYsQIrly5kuvlHvJbWloahw8fxsfHh6CgIIfGklsuLi68/fbbvP32244OJd/Fx8fTsWNH\nNmzYAFjnx/jhhx9o0KDwrt1xJdXg0Ak48FciGXMkg43bz3LyvDsXU7xJy7i5LqVurlCmFJQJgNAg\nqFLu70SzYmnwcMu/cZK1a9dm4cKF9OvXj+PHj+Pr68s777xDt27d8u0YIrebbBPPzz//HJPJdM0s\ne6NHj2bkyJE5Psjx48ftBk2np6czfPhwYmNj8fDwoEaNGvzyyy+5WopFRET+O2fPngWgTZs2VKxY\nka5duzJx4kRbueSe2Wx2eNIZGRnJE088wenTpwHo2rUr06ZN03jTQuDJJ59kw4YN+Pj4UKxYMU6c\nOMFDDz3Evn37HD5jb+Jlg+gj1llidx+C6MOw5yicOPPvLZ2BnP+Y4eEGvh4XOHFoFaQcgpTDkHac\nB5vVYOoXbxHgy386Cc+DDz7IsWPHSEpKwtPTUxMAidykbBNPi8WS6woPHz58TdmKFSvsHg8fPpzh\nw4fnum4REXGMWrVqATB+/HgSExNZtGiRXbnceo4ePcojjzzC5cuXCQoK4uzZs3z//ff4+voyefJk\nR4d3W0tISGD58uU4OzsTExODv78/tWvXZufOnaxZsybPY1gzM61jKHcdgoTLcCX171tK2t/36RmQ\nkQEZmX/f0jMgOQX2HoPY03k7LyMjkXKBUL2yD2UCoGwAlAu0tlZWCIEAXwv+/mFw8SKvvvoqlSrV\nYuDAb/h13kKODu9AYP36eTvwTXL0D0RFzZEjR6hQoQJTp06lV69eAEybNo2nnnqKI0eOUK5cOQdH\nKAUlV8upiIjI7alPnz789NNPLFq0iHHjxgFQsWJFxo8f7+DIJK9++eUXLl++TIsWLfjtt9/YvHkz\nDRo0YM6cOUo8C5GrrWy5aW3LzDQ4mwh7jljXrNxx4O91LK+kFlCggJOTtQtsxdKwMWoWCfFbeP+t\nfjzYtArfTnmH8ePeoMuwYXzwwQfX3f/s2QtcvHgRT09P3n33XQAWLFjATz/9xKFDh6jvoMRTcu9q\nInk97dq1w2Qy3fCanjVrFmfOnGHw4MEFEaI4gBJPERG5IScnJ3744Qfmzp1rm9X2ySef1LqTt7DM\nzEzA2ppjNpspXry4Xbk4TokSJWjcuDFRUVFUrVqV4sWLc/ToUUqWLMm9996LYRhEH4ZV2+HQCTh1\n/q/bBev9mQTIQ6e1HHN1gfByUD3MOlNs9TCoFgphIeDibE0m6tWbyOa4zVjOBlKu5HNs27IKINvP\nDF9fX3x8fEhMTOTll1+mUqVK/P777wBUqFCh4E5ICsyYMWOoWLGiXVl4eDjz58/H2Tn7NGTWrFns\n3r1biWcRosRTRERyxMnJiccee8zRYdxSLBYLly9fxtvbu9CND2vRogUuLi4sXLiQWrVq2dYT1WRR\nhcOsWbN45JFH2LRpExcuJFCybGN6DvyGfh+UIOpPa3KZF8H+ULMihJQEdzdwd7WOrbx6c3e1JpbO\nTtabi/Pf9y5OUKE0VCoNzs7ZX88DBgygd+/evPLKK7zyyisAFC9enO7du2e5j5OTExMnTqRPnz68\n//77tvLu3btTr169vJ2wOFTr1q1vqqW6ID43r1y5onHsDqLEU0REipz09HRMJtMNf1EvSJ9++imv\nv/46iYmJBAcH88UXX/DQQw85LJ5/q1q1KjNmzKB3795s27YNgPvvv5/PPvvMwZHdvgzD4MQZ2Hcc\nYo4Fc88TG3CvdZldh905l+TChwtyXpevN4QGw12VrInmnZXgzopQyve/+QGkV69eXLlyhbfeeotT\np05Rs2ZNvvzyyxu2XPbu3Zvg4GCmTp1KSkoKzZo1o3///oXuhxvJu+uN8fy3Jk2asGqVtZXcbDbb\nyq/OP2MYBp988glffvklBw4coHjx4jz00EO89957+Pv727YPDQ3ljjvu4MUXX+S1115jx44dvPLK\nK4waNaoAz1CyosRTRESKjDNnztCnTx9+/fVXTCYTHTt2ZMqUKTc9C2haWhonTpygZMmSeHt733D7\n2bNnM2DAAMDaihMXF0enTp1Yv359jhaf/6907dqVZs2asWvXLnx8fLjrrrvsvuQVVQkJCbzyyius\nX78eHx8fBgwYQNeuXQv8uGnpBifPWtewjD1jXccy9q/bkThrwpmc8s89TMD1rzd/H3jgLqhTFYJL\nQqAvBPpZbwG+4Ori+ETt2Wef5dlnn8UwjFwljq1bt6Z169YFGJn8VxISErKc/Ty7a2LEiBG89NJL\nxMbGMnHixGuef+655/jmm2/o3bs3gwYN4tixY3z88cf88ccfbNq0ybbmrclk4sCBAzz66KM888wz\n9O3bV5MXOZASTxERKRIsFgsdOnSwrXsIMG/ePC5dumRLRPPihx9+4OmnnyYhIQEnJyeGDh3Ke++9\nl22CNmXKFADGjh3Lyy+/TJ8+fZg+fTrTpk0rVIknQMmSJWnSpImjw/jPpKSk0KJFC7Zs2WIrW716\nNUlJSfTp0yffjnMxyWBrDGyJgS17rfcHYsEw8lZfyRLQ+G5oXMt6qx4GZrPjk8ucUGtl/hn9tcGb\n3xRM3SOfgtFP5+979e+lEk0mEzt27Ljhfi1atCAkJISEhASeeOIJu+fWrVvHl19+SUREBE8++aTd\nse6//36+/fZb+vbtC1hbRg8ePMiiRYvyPBu05B8lniIiUiTs3LmTDRs24Ovry44dO0hJSeHOO+/k\nt99+49ixY5QvXz7XdW7dupVu3bqRkZFBqVKlOHPmDBMmTCAoKIgXXnghy/2Sk5MBqF69OiaTiWrV\nqtmVi+P89NNPbNmyhbJly/Ltt9+ycuVKxowZw6hRo3KdeBqGwanzcOik9XbwBMQctSaZ+4/nLT5f\nb+vEPeHloHJZqPLXJD5VyyuBk1vPxx9/zB133GFX5u7uflN1fv/99xQrVoxWrVrZtaaGh4cTEBDA\nihUrbIknQNmyZZV0FhJKPEVEpEi4fPkyAIGBgZQuXRqLxUKJEiW4cuUKSUlJeapz7ty5ZGRk0KNH\nD6ZPn86sWbPo3r07M2bMyDbxbNKkCRs2bKB37940bdqUxYsX28rFsU6ePAlAq1ataNKkCXXq1GHM\nmDGcPHky2y6hpy8YbNoDm/bAyk0ViT3jRnzCv7vGZs9ksk7uc3UNy9KloGwglCkF5YKgSlnw91Fy\nKUVHvXr1rplc6OpEZnm1b98+Ll++TGBg4HWfP3PmjN1jzYhceCjxFBGRIqFmzZr4+Piwd+9emjZt\nSmpqKnFxcQQFBV0znX9OpaenA1CqVClMJhMBAQF25VkZOXIkW7ZsYdmyZcyfPx+Afv360aNHjzzF\nIfmnevXqYHJl1o9/kub1PdF7D4HfI5QpV4Zf1oOT2cDJDJkW6xqYm/9KNo/G/7OWG48ZdnKCGmFQ\nuyrUCbfe7qwEHm5KLCXvRj9tYvTTjo7CsSwWC/7+/syZM+e6z/v6+to91gy2hYcSTxERKRKKFy/O\nnDlz6NKlC1FRUYD1C8jcuXNtE03kVuvWrfnggw/48MMP2bRpE3/++Sdw7bilf/Pw8ODXX39l1apV\nHD9+nKpVq97UkgKSM6lpBheT4FIyXEyCi8mQeNk6cc/+WGv3133HmmNulEwKZmZstu5nqgrHgIeG\n5/6YPsWgYmmoEGJdx7JiaetMskoyRW5OVr0PKlasyO+//06DBg3w8vL6j6OSm6HEU0TkNpOUlMQb\nb7xBVFQUnp6e/O9//6Nnz55FYvxY69at2bNnDytXrsRsNtO8efMsu2PlRMuWLXnvvfd45ZVXWL16\nNQDt27fnrbfeuuG+Tk5ONG3aNM/HlutLTjHYcwR2HYLdh2H3X/fx5yEt+4bof8j9zL1urlCrMtS9\nA0q6HyY0MIX2Le7Ar7j1/41hGGzdupVjx47hZVTGw61Gro8hIn/z8vLiwoUL15Q/9thjfP7557z5\n5pu89957ds9lZmZy6dKlm57JXAqGEk8RkdtIZmYmHTp0YPny5bayNWvWcP78eYYOHerAyPJPmTJl\nsl2kPrdeeuklunbtSnR0NEFBQdSqVatIJOmFkWEYnEuEE2f+up21LjVy4gycPGttsTx0Mu8zw15l\nMkH5IKhcBrw9rd1qMy2Qmfn3vy0Wawtm/WpQ7w6oUQFcnK3v++bN5wFsSWd6ejo9evSw6/o3aNAg\nJk6cqGtFJI/q1avH999/z5AhQ6hfvz5ms5nHHnuM+++/n/79+zN+/Hh27NhBq1atcHNz48CBA8yf\nP5+33nqLnj17Ojp8uQ4lniIiWTh69Cjbt2/Hz8+Phg0b4ux8639krly5kuXLl+Pv78/MmTOJjo5m\n2LBhjBo1isGDB98WazjmRWhoKKGhoY4O45ZlGAaJl63jJI+dsq5fGX/O2kp56q/7+PPWsvSMvB/H\n2cna9bW4lzWhLO5pvQ8uaZ0dtkpZ661CCLjnYzfYCRMmMGfOHDw9PbnvvvtYsWIFH330EXXq1NEX\n4Hx24MABfvnlFwzDoHXr1lStWtXRIUkWcvujy7+3f/7559m5cyczZszg448/BqytnWCdLbd27dpM\nnjyZESNG4OzsTPny5enWrRvNmjXLcwxSsEyGcbO/GxacxMRE2799fHwcGIkUZps3WwfpFLa18aRw\nye118vnnnzNw4EAyMzMBaNSoEYsXL75m0oJbzbfffkuvXr3o1KkT8+fPx2Kx4OrqSmZmJhcvXsTb\n+/qL1d8u9HlyczIzDXYfhg27Ydt+OPZXonk03jruMj+YzdaWyhoVoFqY9b56mLV10t31v/mi+e/r\npGnTpqxcuZJZs2bx+OOPM2HCBIYPH0737t2JiIgo8HhuVcePHychIYFKlSrlaAKYxYsX06VLF1JS\nrFMJu7q6MnPmTLp06VLQoeZaTr/DpqSk3PTyIiKFSXbX9K3/872I3DYyMjLYvHkzycnJ3H333fj5\n+RXIcTZt2kT//v0xDIPGjRuze/du1q9fz8CBA5kxY0aBHLOgXLp0CbPZbJuA4ep6kj///DNvvfUW\ne/bsITMzk9KlS1OsWDFHhioF5Ny5cwwcOJDly5fj7u5O7969eeONN3BycspznWfPnrV2c9t7CpcS\n91K+Rjeij3nzxx5IunJz8Rb3si4zUrrkX/cBfz8uH2Rd3zI/Wyvzw9XJq2JjY+3uXV1dHRZTYZaU\nlESPHj348ccfAfDz82PmzJnZTtqVnJxM9+7dSUlJoV27dri4uLBgwQJ69+5NixYtNKZP5BagxFNE\nbgknT56kbdu2bN++HQBvb29mz55N27Ztb7jvxo0b+eabb3BycsLDw8O6nEI2IiMjMQyDXr16MW3a\nNHbs2MFdd93FsmXLbvo8Ll++zJkzZyhdunSBfimNjY3lySefZNWqVYB1Qpxp06ZRt25dBg0axEcf\nfcTIkSMB65fjKVOmqEtSHuzZs4fXX3+d/fv3ExoayptvvkmtWrUcHZZNeno6Dz74IJs2bbKVjRkz\nhkuXLvHBBx/ceP8Mg4RLcDjOOr7ywAnYfSCVn5YdJ8U0HJOLP5wFDtw4Fg83a+JYLtC6jmVISQjy\nhyA/+3tP91vvOuzZsye//fYbL730Eu+++y4JCQmYTCYtn5OFIUOG8OOPP+Lq6kpgYCDHjx+nc+fO\n7Ny5M8s1Fw8cOEBCQgLly5fnp59+AqBGjRpER0ezZ88eGjVq9F+egojkgRJPEbkl9OjRg+3btxMY\nGEhAQAA7d+6ka9euxMTEULp06Sz3+/LLL3n22We5Oqrg66+/Zt68eTz00ENZ7nO19SIuLo7MzMx8\nab0wDIORI0cybtw4MjIyKF68OF988YVtvEp+ysjIoH379mzfvh0nJycsFgs///wz3bp1Y9myZUyc\nOJF77rmHlStX4unpSY8ePbj77rvzPY6i7uDBgzRq1MjWpW7Xrl0sX76cDRs2ULNmTQdHZ7Vq1So2\nbdpEUFAQS5cu5eDBg3Ts2JFJn3xFl97jiDnmzO7DEHMMziVau8NevmK9v5Sc1SyxbuB6N1mlhyEl\noVENqFfN2iX2arLp71N0x1s98cQTxMfH8/rrr5OQkEDx4sX55JNPaNKkiaNDK5TmzZsHwLp166hd\nuzYPPvggv/32G7/++iv9+/e/7j5XhznExcWxadMmXF1dOXbsGIBaO0VuEUo8RaTQS0lJsc3CumPH\nDkqVKkXjxo1ZvXo1q1evzjJ5i4uLs3WZ7dChA5cvX2b58uX06tWLuLi4LNd2fOSRRxg5ciRLly7F\nz8+PixcvAtxU68Vnn33G22+/DUCpUqU4c+YMTz75JKGhoTRs2DDP9V7Pn3/+yfbt2wkICCA6Opqk\npCSqVq1KZGQksbGxlC1blm7dutGtW7d8Pe7t5sMPPyQxMZEWLVrw9ttv8+6777Jo0SLef//9QjGu\nzzAMDh2/DN73UrJaJ2auqcHuQ9Ux1TlIpmt57n325ieS8nSH0JIX2L3xG+4oe5Gl88dQJqBoJpc3\nMmzYMAYMGMCZM2cIDAwsEpORFRSLxQL8/SPf1R/1spt2pGzZsnTs2JEff/yRBg0a2MpbtWqlCYZE\nbhGavlBECj2z2WybbTUxMZH09HQuX74MkO04td27d5ORkUH9+vV54403GDduHEFBQVy4cMH2S7lh\nGJw7d47k5L9nPgkLC+Onn34iJCSEixcvYjabef755xkzZkyez2HmzJkAfPXVV5w6dYq+fftisViY\nPXt2nuvMytWJN/z8/PD19SUoKMg2fvPKlZscgCc2J06cAKBXr140aNCAp59+GrB2Cy8op06dYtq0\naUyZMoV9+/ZhGAbx5wzW7jCIWGIw5huDHmMMGvzPwK8N9JvSAVPN1exOGcr7M2DxOhO4hWEy5ezP\nv9lsnSW2ZkXo1Bhe6g4tK8zF2NWEO9PbM2vwzwSd6wpHh1OvwtHbNum8ytXVldKlSyvpvIEOHToA\n1knbatSowU8//YSrqystW7bMdr8ZM2bQr18/22dbr169mDt3bpFtSRcpavTJKCKFyq5du/j888+5\ncOECdevWZeDAgbi6utK5c2fmzp1LjRo1KFasGOfPnycgIMBu2vR/K1WqFGAdh7d9+3YuXbrEqVOn\nAGtStmvXLh577DF2794NQPfu3fniiy/w9PSkSZMmHD9+nPj4eHx8fGyT8+RVWloaAAEBAZhMJgIC\nAgDrGLz8dtddd+Hr68vevXtp2LAhKSkpnDlzhvLly2c5fkpyr3r16ixYsIAxY8Zw9uxZvvrqK+Dv\nCZzyS2amwfHT8NOyvbwy5muSLaXBvQKmz9Nw9c4gLSP3f8qdzAaVy5qoHmadGbZ6mLWLrPdfy48U\n++v+erPExj1yP3WXD2X7ppM8/PAvgLWr44gRI/LlfKXo++STT4iLiyMyMpLo6Gi8vLz49ttvCQ8P\nz3Y/T09PJk+ezOTJk/+jSEUkP2k5FbnlafmDomPt2rW0bNnSrlWudevWLF68mMuXL9O9e3d+/vln\nAMqXL8+8efOyfd8Nw6Bt27YsWbLErrxv3768//77VK9enZMnT+Lm5kZqaioAvXv3ZurUqfl+biNG\njOCdd97By8uLunXrsnr1aiwWC4sWLcp2vGleRUZG0rlzZ9vnaGBgIIsXL6ZOnTr5fqyiJDefJxcv\nXuTee+9l165dtrKKFSuyYcMGSpYsmeNjZmYaxJ+H43+tb3nslPXfR+JgfywcPJHVWMsbK+ZhXb/S\nz+MsmUl7CS5xkSc73U2zhiG4uea9lejEiRO8+eab7N+/n/Lly/P6669TqVKlPNd3q9HfnZtnGAbR\n0dEkJiZSrVq1IjdOU8upyO0qu2s628Rz7Nix/PDDD+zbtw83NzcaNmzI2LFjs5wRsl+/fkyZMoXx\n48fzwgsvZBtUVFQUw4YNIzo6mpCQEF566SX69etnt40ST8kJfQEoOurVq8fmzZvp1KkTLVu2ZMSI\nEZw7d47vv/+eRx99FID4+HiSk5MpV65cjrqzJSUlMXz4cBYsWIDZbKZXr16MHj2ahQsX8uijj1Kz\nZk02btzIvn37uPvuu3F2dubKlSv53lUuNTWVxx9/3LZ8AMDo0aMZNWpUvh7nn06fPs3atWtxcnLi\ngQceKHJf7ApCbj9PLl++zGeffcaBAwcIDQ3lueeey3Kt18xMgwOx1vUtt+2H7QdgzxE4cQYyMvMe\ns5d7OlXLu1ChNFQIgQqlrUuOVCkLgX5Fd0IfR9LfHbkRJZ5yu8rzOp5RUVEMGDCAevXqYbFYGDly\nJC1atCA6OvqaP6zz5s1j06ZNhISE3PCP3OHDh2nbti3/+9//mDVrFqtXr+b555+nVKlSdOrUKZen\nJ3J9iYmJrF27FovFwj333FNgaz7eSHJyMtOnT+fIkSNUqlSJHj166I9MFvbt2wfAp59+SlBQEDEx\nMUycONFWDhAUFJSrOr28vPjss8946qmngL+/KF4dBxkUFISHhwflypUDrDPCZmRk5Hvi6ebmxvz5\n89m+fTsnTpzgjjvuKPBurwEBAXTs2LFAj3G7K1asGC+99NI15ecSDXYfhl2HYOdB2L4fdhyE5JS8\nHadUCQunj63DlHKA559qSfVKHrzx4uOcO7GJX1Ys4v7777/JMxERESlY2X6z+nf3tIiICHx8fFi3\nbh3t2rWzlR89epQhQ4YQGRmZ7eK/V02ePJkyZcowadIkAMLDw9m4cSMTJkxQ4in5YvPmzbRv3942\nns/f35+FCxdy7733/qdxJCYm0rhxY9vak2BdzmP58uV4enr+p7HcCsqVK8euXbsYM2YMbdu2Zf78\n+QrWCxcAACAASURBVLby/Hbvvffi5ubGsmXLaNy4sW2yofvuu6/AfhgwmUzcfffdWrqkCDmXaLD3\nKOw9ak0ydx+C3Ych7lzu6ilZwrrkSNkA6xqX5QKtt8ploVIZKO7lRPfuXzBz5kw+fe3v/WrVqpXv\nsyKLiIgUhFz9pH/x4kUsFotda2dGRgaPP/44b7zxxg0HhV+1fv16WrVqZVfWqlUrpk+fTmZmZraz\nVIrcSFpaGp06deLUqVNUr14dZ2dntm/fTqdOnTh06NBNTxKTG2+//Tbbt2+nQoUKdO/enW+++YaN\nGzcyfvz4Au1ieasaO3YsDz/8sN3kEXXr1rV1s81PYWFhTJ8+nV69erFq1SrA+iPY/7N332FRXF8D\nx79LFRFQaSqgVBGxl1hijS1iYu9GjdEYozFEE/XVn91EjESjKZpgi8aSINEYG1bs2LCDAoICUqSo\ngNLZef8Y2YhKM8BS7ud59hm47M6cgQHm7L333LKwDIZQ+qKiovj88885c+YMhoaG/N///Z+ql1yp\nlAiLkRPKnCQzMFx+xD8p2nFqG0MzB2jqIG8b28nrXFatUvBwWA8PD6pWrcq2bdvIzMykR48ebNiw\nAW1tbUAuzOXt7Y1CoaBPnz5iiYlyIiAggA0bNpCYmEi7du0YN26cqoq3IAhCRVKk4kJDhw4lJCSE\ny5cvq4bT/u9//8Pf35+///4bkG/mpk6dyvTp0/Pcj6OjI6NHj85VAe/UqVN06dKF6OhozM3Ngdzj\n44ODg4t2ZkKlFRISwvDhwzE2Nmbfvn0oFAoGDRpEZGQkmzZtolGjRqUWy5QpU7h48SLLly+na9eu\n7N+/n4ULF9KlSxfc3d1LLY7y5PLly/zxxx8kJSXh5OTExIkTS/TNgocPH+Lv70/VqlVp1qyZGAZd\nCT179ozRo0cTEREBOnVAzxmqNqJJu5EodRsQGl2F1IyivSGqq63ExjwV29pp2NZOpb5FCg51UjE2\nzPrP8UqShCRJuZKTI0eOMH/+fLKy5P3r6OiwdOlSOnfu/J+PJ5Sca9eu8dlnn6mKm4FcUG3JkiVi\nbm455+DgoPpYzPEUKpM3nuP5ounTp3Pu3DnOnDmj+mN44sQJNm/ezLVr13I9twwXyhUqgZyFqNPS\n0njy5AlaWlo8e/YMQNUzUFpyRgccO3YMW1tbfHx8crULr2rVqlWpFuwwNzdXvdklVHxZ2fD4qTaR\n8TpExFUhIk6XCzceEVFzDxoWDkga/77JcTOm4P3paiupZ5ZGPTM5wbStlYZd7VQsTNLRLKFOK4VC\nkSspSU5OZvHixWRlZdG9e3eysrI4ceIECxYs4ODBg+jp6ZVMIMJ/tmzZMtLT0+nSpQtNmjRhw4YN\nHDp0iD59+tCuXTt1hycIb+y3335TjRo5deoUHTp0eOU59vb2hIaG0rlzZ9X9kVD6zp07x5EjR/ji\niy9KvJhroRLPadOm4enpiY+PD9bW1qr2kydPEh0dTe3atVVt2dnZzJo1i9WrV6vmTL2sVq1axMTk\n/o/+8OFDtLS08ixBLyrHCXl5ubpgy5Ytad++PefOneP9999HoVCQmZlJ8+bNGT58eKkO5f7666/x\n8fHh0KFDHDp0CJDXIVuyZEme1aGFkiGqUFYOT1MkboXK8y3DYuS5ljEJ8jY6AWIfg1L58qtqo9CH\n/N4yNakOjWzAyQYa1JWrxjaoB5ZmGmho6AOlN4T/Zb6+vqSlpdGwYUMOHz4MgK2tLffv38fQ0JCm\nTZuqLbaKqrj+nty/fx+Af/75BwMDA1JTU1m3bh3Z2dnib1U59+KovcpMT0+P7du3v5J4nj9/ntDQ\nUKpUqSJ699Xs3LlzLFq0iHHjxqk/8XR1dWXnzp34+PhQv379XF+bPHlyrrlXkiTRq1cvRo4cyccf\nf5znPtu1a5drSQGQhwm1bt1azO8s59LT09m4cSOBgYFYWVkxfvz4Ul/CQaFQsGvXLkaNGsWxY8cA\nuWDMjh07Sv36atWqFceOHWP27Nncu3cPe3t73N3dRdIpCMXgXpTEpdty1dic6rGhUf9tnzoaT9HK\nvMuzuIvY1HrG+h+m0cgWzGqU3RujnIrd9+/f59KlS2RkZBAVFZXra2WFJEncvn2buLg4nJycMDMz\nU3dIamVhYUF4eDjLli2jS5cuHDhwQNUuCBVB79692blzJz/88EOuavHbt2+nQYMG5f6+/9mzZ6Va\nO6QklcqIVSkfkydPlgwNDaXjx49L0dHRqsfTp0/zfI21tbW0YsWKXG2jR4+WxowZo/r83r17kr6+\nvvTFF19IAQEB0rp16yQdHR1p165duV735MkT1UMo+1JTU6X27dtLyB0HEiDZ2dlJDx8+LNHjXrp0\nSbp06dJrv/b48WPp0aNHJXp8oXzI7zoRyodnqUpp/1mlNHWlUnIcppQU7d/sYeailFqNU0oj5iul\neR5KafMBpdR/9DIJrZqqv13GxsbSzZs31X3KhaJUKqU+ffrk+tsLSIMHD1Z3aLmkpKRI/fr1U8Wn\nra0teXh4qDusN1Jcf09+//33V35urVu3ltLS0oohSkGdCnsPm5qaWkoRla5NmzZJCoVC8vLykjQ0\nNKR9+/apvpaVlSWZm5tLX3/9tdSoUSOpa9euqq8plUrphx9+kBo1aiRVqVJFMjMzk8aPHy/Fx8fn\n2v+ePXuk9957T7K0tJR0dXWlevXqSTNmzHjldycmJkYaP3686nnm5uZS7969JX9/f9VzFAqFtHDh\nwlfOoV69etKHH374yjkdP35cmjp1qmRmZiYpFArV1y9evCj17t1bMjIykvT09KQOHTpIPj4+ufa5\nYMECSaFQSLdv35ZGjRolGRkZSSYmJtKcOXMkSZKk8PBwqW/fvpKhoaFkbm4uubu7vxJXWlqatHDh\nQsne3l7S1dWVLCwspGnTpkkpKSm5nqdQKKRJkyZJu3fvlpydnSVdXV3J2dlZ8vb2fiWelx8nT56U\nJEmS/Pz8pN69e0umpqZSlSpVpHr16kmjR4/O97rN72v59niuXbsWhUJBt27dcrUvXLiQ+fPnFzq5\njYiIyNWNbm1tzYEDB5g2bRpr167FwsKCH3/8Uaw3V8798MMPnDt3DgsLCyZPnsz27dvx9/dn7ty5\neHh4qCWm0u5tFQSheAWGSez3hUPn4dR1SM/I//mamvJQ2MZ28lIktY2htsnzrTGY1wQd7Vd7L0e/\nO5M9Ax1VQx5nzpxZbnqdFAoFf/75J9OnT2fPnj2qgmplrYDZnDlz2LNnD3p6ejRo0ICrV6/yySef\n0Lhx40q7JMwHH3yAvr4+P//8M4mJibRt25ZvvvkGXV1ddYcmlHOPHz/m0aNHWFlZqWpfqIOlpSUd\nO3Zk+/btqqUYjx49SmxsLCNGjGDHjh25nv/pp5+yceNGPvzwQz7//HPCw8P58ccfuXjxIpcuXVL9\nbvz222/o6enh6uqKkZERvr6+fP/990REROTa5+DBg7l16xZTp07FxsaG2NhYTp06RXBwMA0bNlQ9\n73XDfV+eT59j6tSp1KxZk3nz5qmGVJ88eZJevXrRokULFixYgJaWFr///js9e/ZULdv2ohEjRuDk\n5MS3337L/v37cXNzw8jIiPXr19O9e3eWL1/O1q1bmTlzJi1btqRr166A3Cs5YMAATp06xcSJE2nY\nsCEBAQGsWbMGf39/1bSuHL6+vuzdu5fJkydTrVo1fvjhBwYNGkR4eDg1a9Zk0KBBBAcHs2PHDlat\nWqWa8ujk5ERcXBw9evTAzMyMWbNmUaNGDcLDw9m7dy8pKSlvVhQrz5S0DBA9nurl5+cn/fzzz9KW\nLVukx48fF/j8Dz74QAKktWvXSpIkSUeOHJEAqW3btiUap+jJEgqjPF8nV69elb744gtpwoQJ0u+/\n/y4plUp1h1RilEqldClAKc1eq5ScRuTfc6n/jlLq9YVSmvmzUvrdWyldC1JKaen/7XtTnq+Tss7O\nzk4CpOPHj0uSJEkTJkyQAGn+/PlqjqzoxHUiFERdPZ7p6emq3y1AMjExydXDVVpyegcvXLgg/frr\nr5K+vr6qR2706NFSu3btJEmSJGdnZ1WP59mzZyWFQiFt3bo1177OnDkjKRSKXCMkXu7dkyRJWrp0\nqaShoSFFRERIkiSPelMoFK+MxHyZQqGQFi1a9Eq7tbW1NG7cuFfOqW3btlJ2draqXalUSo6OjlKP\nHj1yvT4jI0NydnaW2rdvr2rL6WGcMGGCqi07O1uysrKSFAqFtHTpUlX7kydPpKpVq0offPCBqm3b\ntm2ShoaGdOrUqVzH2rZtm6RQKKTDhw/nOi9dXV0pJCRE1Xbjxg1JoVBIP/30k6rN3d1dUigUUlhY\nWK59/v3335JCoZD8/Pxe813L2xv3eAqV13fffceMGTNUn1tZWXHs2LFc5cFfllMZdOfOnbRr147N\nmzfnahcEoegOHTpE3759yciQu/rWr1/P6dOn+fXXX9UcWfGQJImkZ3AlEHafgj2nIeJh3s93toFe\nbeHdNtChCVTRLbtzL4XccpZ/SUlJQZIkUlJSgNf3NAiC8GbmzZvH+vXrUSgUmJiYEBcXx4ABA7h+\n/Xq+93AlaciQIUydOpW///6b/v378/fff+Pm5vbK8zw9PalWrRo9e/YkPj5e1e7o6IiZmRk+Pj6q\nGjI51bqVSiXJyclkZmby9ttvI0kSV69exdLSEj09PXR0dPDx8WHcuHHFtqLAxx9/nGs5q+vXrxMU\nFMSsWbNyxQ3QvXt3fvrpp1eWGJkwYYLqYw0NDVq2bElkZCTjx49XtRsZGeHo6Mi9e/dyfY/q169P\nw4YNcx2rU6dOKBQKfHx86NGjh6q9a9eu2Nraqj5v3LgxhoaGufaZl5xRg3v37qVJkya55ui+KZF4\nCq+4evUqM2bMQKFQMGzYMPz9/bl58ybjxo3jzJkzeb7us88+Y+PGjRw/fpxmzZoB8vIls2bNKq3Q\nBaHCmThxIhkZGYwYMYLGjRuzePFiPDw8+PDDD8vFcgtp6RJXguCCP/jfg4TE548kefsoSV7iJC9V\nq0Cvt6B3O+jVBqzMRZJSXg0dOpRvvvmGvn37YmlpSXh4OFpaWvTv31/doQlChZEzzNTb25vu3bvT\nr18/9u3bx549e/jqq6/UElONGjXo1asXW7duRUNDg9TUVIYNG/bK84KCgnj69GmeHRZxcXGqj2/d\nusXMmTM5efIkqampuZ6XM/xVV1eXb7/9lq+++gpzc3PatGmDi4sLo0ePxtLS8o3Px87O7pW4gVxJ\n44sUCgUJCQm5pm/UrVs313OMjIzQ1tZ+peCaoaFhrvMOCgoiMDAQU1PT1x7nxee+7jgg/zweP378\n2lhf1LlzZwYPHsyiRYtYuXIlnTt3pm/fvowcOZKqVasW+PrXEYmn8Irz588D8k3Cjh07ePToEcbG\nxpw/fx6lUpnrXZ4XWVtbc+bMGWbMmKGqarto0aJycXMs5C0uLo5Zs2bh5+eHiYkJX375JS4uLuoO\nq1JISUkhPDwchULB77//jqamJtevX+fPP//k9u3bZe53KytLIjQKLgTIiebFALgWnH9i+To1DOD9\nt2FAF+jRGqpWEclmRbBgwQKio6PZuHEj4eHhGBgYsHHjRtUblYIg/HeZmZkAGBsbo6GhoapsnZWV\npc6wGDlyJGPGjCEpKYkePXq8dvlEpVKJsbExf/7552v3kdNjmZiYSNeuXTEwMGDp0qXY29ujp6fH\ngwcP+PDDD1G+sGaWq6sr/fr1Y8+ePRw5coQlS5awdOlS9u3b98q8y5fl9T17eW3knON9++23tGzZ\n8rWvefl8X1fNN6/RH9IL1WaVSiXOzs6sXr36tc+tU6dOgcd5eZ/58fT05NKlS+zbt48jR44wceJE\n3NzcOH/+/GuT34KIxFN4hYGBAQD+/v7Ex8erejkNDAwKHBLVsGFD9u/fX+IxCqUjOTmZjh07EhgY\nqGo7fvw4u3fvrtS9FA8ePGD27Nn4+/tTp04d5s6dWyLFUfT09FTvTLq7u9O0aVPVEkHqKnyTli4R\ncB9CIuWlS0Kj4F4k3IuW180sapIJUE1PLgDUozUM6AydmoG2lkg2KxptbW02bNjA0qVLiY+Px8bG\nptDvmqelpXHx4kXS09Np1apVsQ2Zq8hSU1PR0tJCW1tb3aEIpah3795s2rSJbt260aBBAy5cuICG\nhkau4Zfq0K9fP3R1dTl37pxqKtbL7OzsOHr0KG3atMl3iRIfHx8SEhLYtWsXHTt2VLUfOXLktc+3\ntrbG1dUVV1dXIiMjadasGd98840q8axRowZPnjzJ9ZqMjAyio6MLdW45PaDVqlXjnXfeKdRr3pS9\nvT1+fn7FepyC7u1bt25N69atWbRoEd7e3ri4uLBu3TrmzJlT5GOJxFN4xfvvv0/dunW5detWrncz\npkyZIubiVDLbt28nMDCQ+vXrs379ev766y9Wr17NwoULK23iGRsbS9u2bYmMjATkoemHDx/mxIkT\ntG/fvliPpVAo+Prrr5kyZQqzZ89WtXfp0uWVauMlITVd4now+AXClSC4ckceLlvU5LK+FbRxhpYN\nwMIEjI2ePwzlra6O+LtSmZibmxdp7n9ISAi9e/cmODgYkOcdeXl5lcrvQHkUFhbG6NGjOX36NJqa\nmgwfPpxffvmFatWqqTs0oRSsWrWK+/fv4+Pjw4ULF9DW1mbt2rV59sSVFj09PdauXUtoaGie9w/D\nhw9n7dq1LF68mG+//TbX17Kzs0lOTqZ69eqqXrwXezaVSiUrV67M9ZqcIbgv9lBaWFhgamqqGo4L\ncuJ48uTJXK/18PDItf/8tGrVCnt7e1auXMno0aNf+V2Li4srVO9gYe6xhw0bxoEDB1i7di2ffvpp\nrq+lp6eTmZlZ5N/1nCT/0aNHuYbmPnnyBCMjo1xxNW/eHCDX968oROIpvMLIyIhjx47x0Ucf4evr\ni4GBAZMnT2bRokXqDk0oZTmL0Pfr14+OHTtiZWXF6tWrVe2V0S+//EJkZCQtW7bk+++/55dffmH7\n9u0sWbKEgwcPFvvxJk+eTI0aNfDw8ODZs2d07NiRxYsXF8sk/5dFPJQ4cwNOX4dzN+UkM7uISWYt\nY2juAG85Q1tnaO0ENQ1FYim8GUmSGDp0KMHBwVhZWVG9enVu3rzJoEGDuHv37muH61VmaWlpvPvu\nu9y5cweFQkF2djbbtm0jMzMzz+GLQsViaGjI0aNHuXr1KgkJCTRq1OiV4Zfq8sEHH7y2PWfYZ8eO\nHZkyZQru7u7cuHGDnj17oqury927d/nrr79YsmQJY8aMoUOHDhgbGzN27FimTp2KlpYWXl5ePHv2\nLNd+AwMDeeeddxg6dCgNGzZEV1eXAwcOcOfOHVasWKF63oQJE5g0aRKDBw+me/fuXL9+ncOHD2Ni\nYlKoIakKhYINGzbw7rvv0rBhQz766CMsLCyIiopSJbTHjx8vcD95HevF9g8++AAvLy+mTJnCyZMn\nVQWVAgMD2blzJ15eXnTq1KlIx2ndujUAs2fPZsSIEejo6NCtWze2bdvGzz//zMCBA7G1tSU1NZVN\nmzahpaXF4MGDCzyf1xGJZxmV31zK0mBvb8+pU6fUHkdJuX//PqdPn0ZbW5vu3bsX+uYlMzOTBw8e\nULNmTYyMjEo4SvVzdnYG5EqqpqamqvWhXlz7qrLJ6ekcNWoUHTt2RFtbm+3bt6vaS8KIESMYMWJE\nse4zK0siMBzO3oQz1+VkMyymcK91sAKnemBdG2wtwLaO/LCuLeZjCsUrPj6eK1euUKVKFW7dukW1\natVo1aoVV69e5cKFC6p1AQXZuXPnuHPnDlZWVly7do2YmBgaNWqEp6cnHh4eleL/lvBvlVR1K0wP\n3strZf7444+0aNGCX375hblz56KlpUW9evUYNmyYanhpjRo12L9/P19++SULFizAwMCAQYMGMWnS\nJJo0aaLaV926dfnggw84duwY27dvR6FQ4OjoqFonNMfHH3/MvXv32LBhA97e3nTq1IkjR47QrVu3\nV84hr3Pq2LEj58+fZ8mSJaxZs4akpCRq165N69atc1WwzWtt0MK2KxQKdu3axapVq9i8ebNqbWQ7\nOzumTJlC48aNC/iOv3oOLVu2xM3NjTVr1vDRRx8hSRI+Pj506dKFy5cv4+npSUxMDIaGhrRo0YKf\nf/5ZlawWlUIq7OxSNXixG7cy/LGUJImff/6Zr7/+mri4OBo3bsy6deve+IdbWVy+fBmQhzoUxq5d\nuxg1ahRpaWkAmJqacvDgwQL/SHt7ezNmzBji4uJQKBR8+umnrF69ukR6nsoKpVJJ//792bt3r6rN\nyMiIkydP0rRpUzVGVnRFvU7ysmrVKqZNm4aVlRUzZsxgx44d+Pr6MmTIEDw9PYsj1GIX+1jiZgjc\nuIu8DZF7M9Mz8n+dQgGOdaFFfWjRAFo6QvP6YKj/+n+8iYmJREREYGlpqSrDXt4U13XyXyQmJnLw\n4EGSk5Np27ZtoW4kKqonT55Qo0YNNDU1CQ0NxcTEhKZNm3L37l0OHTpEz5491RJXWbhOXmffvn28\n//77tGnTBl9fX9LT0zExMeHZs2dER0dTq1YtdYdYaRT2HvblZTYEobzL75oWiWcZsmHDhlzvioA8\nZOL69etYW1urJ6hyoCg3ALGxsdjY2JCSkkK3bt14/PgxV65cwdbWluDg4Dx7d+/cuUPz5s1JS0vD\n2NiYhIQEQF4va/HixcV3MmVQVlYWGzdu5MqVKxgbGzNhwgRsbGwKfF1GRgY7d+7k3r172NnZMXjw\nYLUWuSiuG8W0tDS6dOnChQsXVG1mZmacP3++UN+XkvQ0RS78czMEboX++3j4qHCv19OFdo2gQ1Po\n2BTecgKDPJLMl3333XfMnj2brKwsNDU1WbRoEXPmzCl388LVnVDcvXuX7t27ExYWBsjvTK9evZqp\nU6eqJZ6ywMXFhYMHD6Kjo4Ouri7JycnUrVuXgICAfAuQlCR1Xyd5iYmJUQ2J69q1K/Hx8dy8eRNH\nR0du375d7n4fyzOReAqVlUg8y4nmzZtz7do1VqxYwcSJExkwYABHjx5lyZIlzJ07V93hlTmSJOHh\n4cFPP/1Eeno6ffr04Ztvvsm3SuLBgwdxcXGhdevWXLhwgczMTExNTUlKSlL11LyOm5sbc+bMoV+/\nfuzatYv9+/fTt29fbG1tCQkJKalTLLdSUlLo0aMH586dU7V17twZb29vtf2DLc4bxdTUVNasWaOq\najt58uQSmUOTlSVxLxoCw+VHdAKkpkNaBqSly4/UDLkt4qFcYbYoLEzl3swOTeVKsi0c36yarJeX\nF0OGDAHAxsZGtTD11q1bGTVqVJH3p07qTig6dOjA2bNncXZ2pkGDBvz1118oFAquX79eaXs+Hz16\nxMiRI1VD/Z2cnPDy8lLrkH91Xyf52b17NyNHjlSN6qlduzbe3t65hiAKJU8knkJlld81XXHHCJZD\nycnJAHTq1Ek1j+Xo0aMkJSWpObKyyc3Njf/973+qz1etWsWtW7fw9vbOc92inEpfkZGRxMXFERsb\ny9OnTwHyfec8Z10sU1NTNDQ0VAv85rQLubm5uXHu3Dnq1KnDsGHD2LFjBydPnsTd3Z158+apO7z/\nTE9Pjy+//LJY9pWeIRERC/ei4H6MvExJYJicaIZEQmYxLL2mpwuNbKGxHTSxhyZ28sfGRsXT++Hl\n5QWgepPM3d2dmTNnsnPnznKXeKpTdnY2vr6+AJw+fZoaNWowZMgQvLy88PX1rbSJZ82aNfH29iY2\nNpb09HQsLCwqZO2B4jJgwAACAwM5e/asqkhIeR36LghCxSISzzKkXbt2hISEMGTIEDp37swff/wB\nUOxLNFQEWVlZLFmyBIBZs2ZhZWXFvHnzOHr0KGfPns2zolebNm1o3LgxN2/ezFXOf8iQIfmuC9ej\nRw8WLlzI+vXruX37Nrdu3QLg3XffLcazqjhyegNWrlzJsGHDaN68OWPGjFG1VzaSJBH+8N85lnfC\n5HUv70dDVDwU17gTTU156ZJGtv8+GtuBTW3Q1Cy5IXbZz0vf5ow2yHkTp7Cl6AWZhoYGVatW5enT\np1y8eJE2bdpw584d4N/1lSuznDf8hILVrVs317IIgiAIZYFIPMuQlStXcv36dW7evMn9+/cB+Oyz\nz+jXr596AyuDnjx5QlpaGnp6egwaNAiFQkH79u3Zv39/vgv+6ujocPDgQcaOHcvx48fR1NRkxIgR\nrFmzJt/jtWvXjp9++onPP/+cs2fPAvDOO+/kKsct/CsniT9w4ACdOnVSLTNSs2ZNdYZVYrKzJR4n\nQ3wixD+Rt5Fx/86xvBkCSc8K3s/r1DGRC/zUr/u8aqyu3INZRRf0dJ5vdcHESH6eOtbEfO+99/Dy\n8mLGjBn88ccf+Pn5qdqFwsspWubu7p7rTS0rKytcXFzUGFnpyczMJC0tTSTagiAIFZCY41nGpKam\nsm/fPh4+fEiTJk0KXIunspIkidq1a/Pw4UN69eqFhYUFW7ZsISsrixs3bhRqSFpGRgYaGhpFqkob\nERHBrVu3MDExoWXLlmK4Vx7Onz9Px44dycr6d5yojo4OZ8+eVducqP8yJ0uSJOKfyD2VOfMtg8Lh\nbiTEPoZHSW/ea6mhAZamclJpXQus68i9lo515W1hi/uokyRJzJ49O9eC31988QUrV64sd8VM1D13\nLysrizlz5rB27VpSUlJo06YNmzdvxsHBQS3xlJaMjAymT5/Or7/+SlZWFs7Ozmzfvr3MzktU93Ui\nlH1ijqdQWYniQkKFtH//fgYOHEhGxr9rQvzf//0fbm5uaoxKyHH06FFmzJhBaGgo9vb2rFixgi5d\nuqgtnsLeKD5LlZceuRYM1+/Kw2PvhMHj5P92/JqG8tzKRnbyEFh7SznRtDQDHe3ylZzlJTw8nNDQ\nUKytrcttJe6yklBIkkR2dnaFXq7pRdOnT+f7778HQEtLi6ysLMzNzVVv9JU1ZeU6EcoukXgKAXrQ\nzgAAIABJREFUlZUoLlQGJSUlERMTg6WlZb5VWIW89enThwsXLrBy5UoyMjIYPnw4/fv3V3dYwnPd\nu3fn6tWr6g4jT5Ik8SBWXtPyxvME81owBEW8We9ldQN5uKtpdXlrXB0a1Pu3kE8dk8Itpl2eiXll\nxUehUFSapFOSJDZs2ACAj48Pbdq0oWPHjvj5+bF//37Gjh2r5ggFoWRJklTh/z8IlUNB/ZmV479a\nGSJJEl9//TWLFy8mKyuLKlWqsGrVKj755BN1h1YuNWvWjM8//xwQ7zwLeXuWKnHzvj53o/TYfEru\n0bwRAk+K0IuprycPf82Zb5kzFNbCVO7NfJNlSARBkKWmpgLQoEED9PT0sLa2xs/Pj5SUFDVHJggl\nS0dHR9VDJJJPoTyTJIm0tDR0dXXzfI5IPEvZb7/9xvz58wGwsLAgMjKSSZMmYW1tTa9evdQcnSCU\nb5IkERUP14Pl3sucXszgByBJDQq1Dw0NOals5gBNHaCpvTw0tjL0WAqCOigUCjp37szRo0dp164d\njo6OHDp0CE1NTTp27Kju8AShRGloaKCrq0t6erq6QxGE/0xXVzff+ici8SxlOUukrFq1CldXV2bO\nnIm7uzt//PGHSDwFIR/pGRL+9+RE8l4UJCTBo0R5m/DCNiWt8Ps0qvbvUNgm9tC8PjjbQNUqpZ9g\nJicn888//5CQkECrVq3EMkpCpbJx40Z69uzJnTt3uH//PpqamqxZs4ZGjRqpOzRBKHEaGhpinqdQ\nKYjEs5TlVPnMWW4iZ3mJnHXwBEGAJ8kS1+/C1SC59/JqMATcg6w3/DXR0IC6pqk41Emly1s15UTT\nDqzMy0Yv5oMHD+jatSt3795VtYlCWUJlYmVlxZUrVzh+/DhJSUm0bt0ae3t7dYclCIIgFCOReJYy\nFxcXjh8/zscff4yHhwe+vr4A9O7dW82RCULpUyolQqPk5DKnguz1uxAW8+b7NKgq9142tZeHyjZz\nkHsxA24FANCqlXExRV98Jk+ezN27d3F0dKRt27Zs376dZcuW0b17d7p166bu8AShVOjp6dGnTx91\nhyEIgiCUkHwTTzc3N3bt2kVQUBC6urq0bdsWNzc3nJ2dVc+ZN28eXl5eREREoKOjQ4sWLViyZAnt\n2rXLc78nTpzgnXfeeaX9zp071K9f/z+cTtn3xRdfEBAQwMaNGzl79iwAs2fPZvjw4WqOTBDeTHZ2\nNnFxcdSsWRMdHZ1Xvv4sVeJ+NNyL5t9tlLy9+wCephb+WLZ15OGwTtZy9Vhjo+cPw38/NqhaNnox\niyLnDai9e/fi4OCAvr4+a9aswdfXVySegiAIgiBUCPkmnidPnuSzzz6jdevWKJVK5s+fT/fu3QkI\nCFANFW3QoAFr1qzBxsaGlJQUvv/+e3r16kVwcDDm5ub5HjwgIEA11BQok2t1FTdNTU02bNjAjBkz\nCA8Px8HBARsbG3WHJQhvZNeuXUycOJGEhAR0DWz54OOvad5uOHfCITAM7oTDg9ii71dbS+6lbOYA\nzeo/L/RjD0bVyldCWVhGRkbEx8fj4+ODsbExV65cUbULgiAIgiBUBAqpoAVXXvDs2TOMjIzYs2dP\nnsNhkpKSqF69OocOHaJHjx6vfU5Oj2dcXBzGxnkPeyvs4rtC5SYW8i4d2dkSEbEQEik/zlyOZquX\nL5KuLYoqdqBp8Eb7Na0uJ5VNnieXzRzk9S+Le3mSsnydrFq1imnTpuVqMzU15caNG9SqVUtNUVVO\nZfk6EcoOcZ0IBRH3sILwqiLN8UxKSkKpVKp6O1+WkZGBh4cHxsbGtGzZssD9tWrVivT0dBo2bMjc\nuXPp0qVLUcIRBKEEZGfL8y797z1/hMrbwHDIyHzxmbWh5kAKSg+1NKFeLbCpDdZ1wLoW2NSRP7ep\nA2Y1yt/Q2OLm6upKZmYmK1asICEhgZYtW7J+/XqRdAqCIAiCUGEUqcdz6NChhISEcPny5Vw3ivv2\n7WPEiBGkpKRgamrKP//8w1tvvZXnfoKCgjhx4gStW7cmPT2d33//nV9++YWTJ0/SoUMH1fNefLco\nODi4qOcmCEIeMrIURD/SISpBl8h4XSITdIhM0CUyQZfw2CqkZ+a9BlNe9LTTSEnwo7ruQ8YMeQtr\n8zTqmaVRxzgdLc0SOIkKSpKkSp+Il6S7d+9y9epVdHV16dixY55vpAqCIPwXDg4Oqo9Fj6cgyAqd\neE6fPh1PT0/OnDmDtbV1rq+lpKQQExNDfHw8Hh4e7N27l4sXL1KvXr1CB9KnTx+0tLTYs2ePqk0k\nnoJQNCnpGsQ81uHhYx3iE7V59FSLx8naPH6qxaOnWjxK1uZxshYJydpIUtGTm5rVMrE0TcfCJJ2M\npACO7v0VjYx7tGxUHf/rp0h59owPP/yQKVOmlMDZCcJ/s3v3bpYtW4ZSqQTkZa1+/PFHHB0d1RyZ\nIAgVjUg8BeFVhUo8p02bhqenJz4+PoWqOlu/fn1GjRrFggULCh3IokWL+PPPPwkICFC1ifHxQmFU\n5Lk2SqXEoyR4lASPk+XHix8/fAQRD+XlR8Ifym3FobaxhLONgoY24GwrF/ppaA3VDf5NViVJYtas\nWbi7u6va+vTpg5eXV4ELYe/fv5/FixcTFRWFs7Mzq1atokGDBsUTfB4q8nUiFCwkJARHR0eys7MZ\nPHgwYWFhXLp0CScnp1z/d8R1IhSGuE6Egoh7WEF4VYFzPF1dXdm5c2ehk06Ql1fIeUe5sK5du0ad\nOnWK9BpBKK8ysySSUyDpmfx4lCQnj2ExcD8Gwp9/HBH78rzK4qFQgJWZvDyJjQVkJN7Ba9ty0p4E\nQFowtZvassVjX75zDBUKBcuXL2fs2LHcvn0bCwsL2rRpg4ZG/sN0vb29ef/998l5z+vBgwd07NiR\nq1evYmlpWaznKQg5Ll++THZ2Nj179mTnzp2kpaVhaGjI7du3SUxMFDeGgiAIglDC8k08p0yZwtat\nW/n7778xMjIiJkZe1d3AwAB9fX2Sk5P59ttv6du3L7Vq1SIuLo6ff/6ZqKgohg4dqtrPmDFjUCgU\nbN68GZArONrY2NCwYUMyMjLYunUre/bsYdeuXSV4qoJQeiRJIioergTClSC4Ggi3wyDxqZxopmWU\nzHF1tKGuufyoYwJmNeXiPWbVn2+fP2oZg4623HsZFhaGk1NL0lJTadq0KVFRWvj5+TFu3DgOHjxY\n4DGdnZ1zre1bkG+//RZJkvjss8+YMmUKEydO5PTp06xfv56FCxe+6akLQr4MDQ0BCAwMJCoqiqCg\nIDIzM9HU1ERPT0/N0QmCIAhCxZdv4rl27VoUCsUrC5gvXLiQ+fPno6WlRUBAAJs2bSIhIQFjY2Pe\neustTp8+netGNCIiIlexjMzMTGbMmMGDBw/Q09OjUaNGHDhwgHfffbeYT099JEni0qVLBAUFUbdu\nXTp06FBgT5BQviiVEvGJEBn37+N+NFy/KyecsY+L5zhG1cDYEGoYQM3n2+rPPzap/m+iWddcTio1\nNIo2d/PEiROkpqbSrVs3jhw5QnR0NBYWFhw+fJjMzEy0tbWL50Sei4uLA2DUqFE0aNCAPn36cPr0\naWJj32DBT0EopC5dutCwYUMCAgKwsLBQtX/yySfo6OioMTJBEARBqBzyTTwLGi6rp6dXqF5KHx+f\nXJ/PmDGDGTNmFCK88kmSJD755BPWrVunanvvvff466+/Sv0GR5Iktm7dyq5du5Akif79+zN27FhR\nNbMIHiVJ3AyBW6FwMwRu35eHwEbGQWbWm+1TQwMM9cGgKhhWlZNLKzOoV1teeqSe+fNtLahWtWR/\nVlpa8p+B5ORksrOzVfNSNDU1S+TNkmbNmuHv78/HH39M//79Wbt2rapdEEqKnp4ehw8fZvz48fj4\n+KCnp8dHH33EsmXL1B2aIAiCIFQKRVrHUyicjRs3sm7dOqpUqULv3r05fvw4+/btY+nSpaU+lHDh\nwoUsXrxY9fmePXsICgpi6dKlpRpHWfc0ReJetNxjeS8a7kVBwD052YxOeLN9GlSF5vXlRwtHaGov\n90gaVIWqVcrO2pU9evTA2NiYixcvUrt2bVXiOXToUDQ1i38dlOXLl3Pu3Dlu3brFrVu3AHBxceGj\njz4q9mMJwossLCzw9vZWzS8uK7+DgiAIglAZlJvEMyYmptwspn7ixAkAli5dyrRp0/Dy8mLIkCH4\n+PiUauIZFxfH119/DcCKFSvQ0NBg+vTpLFu2jM8++6zSFXOSJImwGLhxF26Gwq0QCImUE82ExIJf\n/zrVDcDCBCxMwcJM/tjZRk407SyKPuxVHczMzNi3bx9Dhw4lIiICIFdPZHGrU6cOfn5+bNmyhejo\naJydnRk5cmSJJLmC8Doi4RQEQRCE0lduEs8OHTpw+fJlqlevru5QClS1alUAbt++jSRJ3LlzJ1d7\naQkLC0OpVOLk5MT06dMB2LRpEzdu3CAsLKxCJ55p6RI3QsAvEK4H/ztMNjml6PuqogMNbaCRDTSy\ng0a2cjVYC1PQ16sYN7Bt27YlNDSUsLAwqlWrhrm5eYker0aNGri6upboMQRBEARBEISyo9wkniEh\nIWzZsoXPP/+cI0eOsGbNGpKTk2nfvj1z5swpcN3A0jR27FjWr1/PunXr+O2338jMlNfDGD9+fKnG\nUa9ePTQ0NLh9+zbLly9HU1OTGzduoFAosLa2LtVYSlJGloK7UXr4PZC4fAf87siJZlZ24fehoy3P\np7SuBdZ15G19K2hsJ/dcampWjAQzP1paWtjZ2ak7DEEQBEEQBKECKjeJJ0BUVBQ7d+5k2LBhqjk6\nx44d4+zZsxw6dEhVJEXd2rdvz86dO/n000+JjY3F0NCQZcuWMXjw4FKNw9TUlAULFrBgwQJmzZql\nap87dy61a9cu1ViKg1IpD5W9GSIPlb35fMhsUHhzspWFSwyNjaCxLTS2l7cN6oFNHahtXD6GxQqC\nIAiCIAhCeVQ2MrVCcnJyYsaMGUiSxOeff06HDh2YMmUKx48f5+DBg7z//vvqDlFl4MCBDBgwgMTE\nRAwNDdW2lMq8efNwcHDIVdV21KhRaoklL0nPJMIfQngMRMbL8y0TEuFRMjzK+ThJriT7+qGyr08Y\nHaygVQNo5iAX9mlsJ69fKeZ3CYIgVA6HDh3i6NGj6OrqMmzYMBo3bqzukARBECqtcpN49uzZkxEj\nRjBu3DhAXoS+SpUqeHt7s3HjRu7fv6/eAF9DoVCofU6qQqFgxIgRjBgxQi3HlySJ+CeoKsbej5G3\nEQ+Rk82HkPj0vx/H0iSNt5tWoYWjnGy2cASjauU/wZQkiczMTLHOoCAIQhEtWbKE+fPnqz53d3dn\n9+7duLi4qDEqQRCEyqvcJJ779u1DW1sbOzs77t69y6RJk2jXrh1//fUXAPb29mqOsHKTJImIh3Ix\nH79AuXJsaKScaKakFd9xXh4q29gO0p9cpaquklatWhXfgdRMqVSyYMECVq1axdOnT2nWrBmbN2+m\nSZMmBb42NTWVy5cvo1QqadmyJdWqVSuFiAVBEMqOwMBA5s+fj4aGBtOmTSMiIgJPT0/GjRtHdHS0\n2kYhCYIgVGblJvHU1tYG4IcffqBv375s3ryZzZs3A9CvXz969eqlzvDKpdjYWD755BMOHz6Mjo4O\no0ePxt3dHV1d3Xxfl/hU4n403H0AV4PlYj5+gRD/5M3i0NOFuubyw8IMTIygpqGcZNY0eL41BPOa\n8jqYLw+VvXxZ+WYHfo309HSWL1/O2bNnMTAwYOLEifTo0aPY9l9Y33zzjWopHIBr167RvXt3bt68\nmW/FWX9/f9577z3VCIBatWqxZ88e3nrrrZIOWRAEoczw9/cHoHv37nz33XcolUoOHDhAbGwssbGx\n5WZ5ttJ29+5dbty4gampKe3btxfLXAmCUKzKTeKZo3fv3pw5c4Z169aRlJREu3btmDp1qnj3sogy\nMzNxcXHBz88PgJSUFH788UeePXvGhg0bSEmTuBYM14LltS7vR8m9l/ei4Uly0Y5lqA82tcG69vPK\nsc+3OcmmSfWyMe8yOzubAQMGcPDgQVWbl5cXf/75J0OHDi3VWH755RcAPD09cXFxoVu3bly4cIHd\nu3czadKk174mKyuLgQMHcv/+faytrdHR0SEoKIj+/ftz9+7dUl/ORxAEQV1y3qC7ePEiJ06cICws\njKdPn6KtrU2NGjXUHF3Z5O7uzqxZs1TFGzt16sTevXsxNDRUc2SCIFQU5S7xBGjTpg1t2rRRdxjl\nmq+vL35+ftSqVYsjx3057ZfI5Bkb2HSqJedHZhEYoYmyiB2JhvrQ0lGeX9myATjWlZclqW5QNhLL\nghw5coSDBw9So0YNfvrpJy5evMjq1auZPn16qSeeyclydt+6dWv09fVp2LAhFy5c4OnTvCfEhoSE\nEBQUhImJCQEBAWhra+Po6EhoaCjXr1+nXbt2pRW+IAiCWrVt25Zu3bpx7NgxunbtqmqfOXNmgaN6\nKqMTJ04wc+ZMFAoF3bt35+rVq5w6dYqvvvoKDw8PdYcnCEIFUS4TT6Hokp9J3I2Uh8cGR4CPbz1w\nPsEjo4Y0mWACgMJ2NQC3w/LfVxUdudfSujY428hJZktHeb3L8rwkSc7w1Pfff5+RI0cydOhQVq9e\nTWRkJFlZWaW6XE/Hjh05cOAA3bt3p3nz5uzatQuAt99+O8/X5MSXnp7Os2fP0NXVJTU1NdfXBEEQ\nKgNNTU327NnD//3f/6mq2o4dOxZXV1d1h1YmHTt2DIDJkyfz008/cf78edq1a8eRI0fUHJkgCBWJ\nuButQJRKicg4uBP2/BEOgWEQGA6RcS8/uy4Ko7pk5rEvhUJe47JFfXCylte6zBkua16zfPRgFpWd\nnR0Ae/bsYf369Vy8eBGAunXrlnri9uuvv9KtWzeCgoIICQkBwM3NLd9eS1tbW9566y0uXrxIvXr1\n0NTUJDk5GUdHR5o1a1ZaoQuCIJQJ+vr6/Pjjj+oOo1zI6QV+8OABSqWS8PDwXO2CIAjFQSSe5cyz\nVImIWHneZWjk822U/HFolERaRtETQkmZCWmB6GTcZPLYdgzqZU0zB6hWteIll/np1q0bAwYMYPfu\n3Xz88ccAaGho8MMPP5R6LJaWlly5cgVvb28eP35Mq1atCkweFQoFu3btYsiQIfj6+gLQtGlT/vrr\nL1VxLkEoayIiIti4cSPx8fG0aNGCMWPGiIImglDKhgwZwjfffMOePXuoXr26arrH2LFj1RyZIAgV\niUg8yxBJkqvFXgmUeytjEuDhI3kb83z7NDW/PeSdKGprgW0dcLACe8vnDwuQ0oK5c/0IelW0ee+9\n96hTp06xn1eO8PBwli9fzv3793FwcGD27NmYmZmV2PGKSkNDA09PT3744QfOnDmjqmqb3/DWkqSv\nr8+gQYOK9BoLCwvOnj3LgwcPkCQJS0tLUXhLKLP8/f3p1KkTjx49UrXt27ePnTt3iutWEEqRo6Mj\n//zzD2PHjiU6OhotLS2mTZvGzJkz1R2aIAgViELKKV9WBiUmJqo+NjIyKtRrsrOzuXnzJunp6TRu\n3LjMVvLMzpYIfiAnmVeC4GqgvDRJUSvGviIrHinlDtU0o/g/1/40cdChQT15mKyWlvp6MO/fv89b\nb71FXNy/Y37r1q3L5cuXMTU1/U/7vnz5MkCFWsdTKH7iOil73nnnHXx8fOjUqRO9evXC3d2dJ0+e\n4OnpyZAhQ9QSk7hOclMqlSQkJGBkZISOjo66wykzKup1olQqiY2NpXr16lSpUkXd4ZRrb3IPKwgV\nXYV6SzkiIoJWrVrRvHlz2rZti62tLefOnVN3WCQ+lTh9TeInL4mPl0m0mSBh2AMajoQPFsHKHeBz\npXBJp+7zwj7vtIQJfWHRRxlIgUPhRisu/RxK8vGq2Kd9xNPrw2lR6zjvd1DgYKUo1qQzLi6Ojz/+\nmNatW+Pi4sKJEycKfM3ixYuJi4ujQ4cO/PnnnzRr1ozw8HC+++67YotLEITyJWetxU2bNjFnzhzV\nEPdbt26pMyzhuUOHDmFhYYGZmRkGBgbMnz+fMvxetVAMNDQ0qFWrlkg6BUEoERVmqK0kSQwfPpxr\n165hYmKCgYEB9+7do1+/fgQHB1O9evUSjyH5mcTtMAi4BwH35QI//vfgXlTh91HDQF6OpIk9WJpC\nLWOobSxva9UEo2q5C/skJDxl/gQvdHR1cbQ3p2rVqpiYmHD37l3S09OL/RyTkpLo0KEDQUFBqrZD\nhw5x4MABevXqlefrQkNDAZg9ezYuLi6kpaUxduxYVeEcQRAqn1q1ahEbG8uaNWsYMmQI+/btU7UL\n6uXv70+/fv1IT0+natWqpKSksGTJEmrWrMkXX3yh7vAEQRCEcqjCJJ4JCQmcO3cOHR0d7ty5Q/Xq\n1WnevDk3b97E19eX3r17F8txkp5J3It6oahPFIQ8kJcgeRBbtH3VMparxjavLyebzetDvVpFqxhb\ns2ZNmjdvztWrV2natCmmpqZcuHABfX192rZtW8SzK9iWLVsICgqiQYMGrFmzhh07drBu3ToWLFiQ\nb+JpY2PDyZMnWb58Oenp6aqCPTY2NsUeoyAI5cP8+fMZPHgwK1asYMWKFQDY29szcuRINUcm/Pnn\nn6SnpzNo0CA8PT3ZsmUL48aN47fffhOJpyAIgvBGKkzimVOIQpIksrKyyM7OJisrCyh8IidJEk+S\nISwGwh5C+PNtxEO5LTQK4p8UPTZtLXlJkqb2ck9mztasxn8f/qpQKPjjjz/o3bs3oaGhhIaGoq+v\nzx9//FEivQYPHjwAYPDgwXTt2pU6deqwbt06IiMj833dvHnz+Oeffzh58iQnT54E5MqtX331leo5\nYWFhPHz4EAcHB2rUqFHssQuCULYMGjSIPXv24O7uTkJCAs2bN2fFihViPlQZkJaWBoC1tTUaGhrY\n2trmahcql8TERL7//nsCAwOxsrLC1dUVCwsLdYclCEI5U2ESz5o1a9K1a1d8fHxwcHBAX1+fmJgY\nateuTfOW7QkMk7gfA/ej5QqxCYnyI/4JJCTJ2/hESPkP/1MVZNLAWpNGtho4WYNTPWhoA451QUe7\n5Ar71K9fn5s3b3LmzBnS0tJo06YN5ubmJXIsJycnADw8PDA1NeWff/4B5Ip4+bG1teXy5cssW7ZM\nVdX2f//7H+bm5mRmZjJ+/Hh+//13QF437Oeff2b8+PElcg4lQZIkfHx8uH37NpaWlri4uIglTASh\nEPr27Uvfvn3VHYbwknfeeQd3d3e+//57/P39Vesad+vWTc2RCaUtMTGR9u3bExAQoGrbsmULFy5c\noF69emqMTBCE8ibfqrZubm7s2rWLoKAgdHV1adu2LW5ubjg7O6ueM2/ePLy8vIiIiEBHR4cWLVqw\nZMmSfBe6Bzh58iTTp08nICCAOnXqMHPmTD755JNczylsRTBJknj4CC5cf8SXc38hJFIDqlija+BI\nNZNGPEouvgRAR1uuEFtd7xHnT2yHtFDq19UmIvgoqY9v4vr5FFatWlVsxytrMjMz6d27N8eOHVO1\nGRkZcfr0aRo3bvxG+5w7dy7ffPMN2traODg4EBAQgEKh4MyZM7Rv377A16u7uqBSqWTs2LFs3bpV\n1fb222/j7e1NtWrV1BKT8KrSuk7i4uJYuXIloaGh2NjYMH369DK1bJCQP3X/PSlLFi9ezIIFC1Sf\nd+nShb1794q/a1Su6yTnOqhfvz4zZ85k/fr1nD9/ntGjR7NlyxZ1h1dmiaq2gvCqfHs8T548yWef\nfUbr1q1RKpXMnz+f7t27ExAQoBoKmTPXz8bGhpSUFL7//nt69epFcHBwnr1u9+7dw8XFhQkTJrB9\n+3ZOnz7N5MmTMTU1ZeDAgXnGk54hL0GSU7wnMAyCH0BwBCSnANQExRwUlvLzM4BHRVyeRE9XnmdZ\nrxbUrQV1zZ9/bg42daCOCWhoKPjf/1Zy/t5SJk2axNq13+Pj48M777zDgQMHKnTiqa2tzYEDB1i7\ndi3Xrl3DzMyMTz75RDUM6038/fffAOzatYv33nuPSZMm8euvv/LPP/8UKvFUt02bNrF161b09fUZ\nPHgwhw4d4uzZs8yfP5+VK1eqOzyhFD18+JA2bdoQFhamatuxYwcXL14ssVEIglBS5s+fz5AhQ7h1\n6xbm5ua8/fbbaGpqqjssoZTlFBP88ssvGT9+PDY2NnTr1i1XkUFBEITCyDfx9Pb2zvX577//jpGR\nEefOnaNPnz4AjBo1KtdzVqxYwYYNG7hx4wY9evR47X5/+eUXLC0tWb16NSAP07xw4QLfffddnomn\n0wiJu5GQnV24E3uRpiZYmckJpHUtqG0CptXBpDqYGIGxkbw1qQ4GVQs3J1RLS/7WJSYmynNDnzx5\nfqyK/09ZR0cHV1fXYt+vUqnMtS1KkSV1ylmyZ+HChXz11VccPHgQFxcXzp49q+bIhNLm5uZGWFgY\nzZo1w9XVldWrV3Pt2jWWLl2q+nsnCOWJk5OTaoqFUDlZWVkBsH79eqytrVXFAevWravOsARBKIeK\nNMczKSkJpVKZZ+GXjIwMPDw8MDY2pmXLlnnux9fXl549e+Zq69mzJ5s3byY7O/u1yVtgeP6xGeqD\ngyU4WIG9JdhZyD2U1rXkXsriXMcSYODAgbi5ubFjxw5OnDhBdHQ0AMOHDy/W41QGAwcOxN/fn0GD\nBmFnZ0dgYCAKhaLczPsyMDAA4NKlS6Snp+Pr6wuAoaGhOsMS1CA4OBiAOXPmMGTIEAwMDBg8eLDo\nGRAEodxydXVly5YtXLp0SVW9Xl9fn3nz5qk5MkEQypsiJZ6urq40b978lfmb+/btY8SIEaSkpGBq\nasr+/fupWbNmnvt5+PDhK8POzM3NycrKIj4+Pt8habVrpmNbKw2bWqlYm6dR1zSNumbp1KiWxSsd\nZFkQ+0B+lISvv/6aJUuWEB0djUKhYODAgfTq1Us190MoHBcXF65evcq+ffsIDAxEV1de52PUAAAX\nuElEQVSXmTNnoq2tXaTvpbq+723atEFHRwdPT088PT1V7T169BDXQhlUkj8TPT09QO75jImJ4bff\nfgOgatWq4looZ8TPSyiMynKdeHh48OuvvxIWFoa5uTkfffQR6enpleb834SDg4O6QxCEMiff4kIv\nmj59Op6enpw5cwZra+tcX0tJSSEmJob4+Hg8PDzYu3cvFy9ezLPamaOjI6NHj2bu3LmqtlOnTtGl\nSxeio6NVieeLE7P/OR6JtVkaerrKop5jiUpPTyc6OpoaNWqIyeP/UUxMDI8ePcLKykrVi1heXLp0\niWXLlhEeHo6pqSmffvop77//vrrDEkpZVFQUY8aMeaWoxObNm8XSA4IgCJXIi4mnuD8UBFmhEs9p\n06bh6emJj48P9evXL3Cn9evXZ9SoUbmq4b2oc+fONG7cmJ9++knVtnPnTkaNGkVqaqpqqK2oCCYU\nRlmqLpjXUHFB/UrrOgkNDWXRokWEhoZia2vL/PnzsbOzK9FjCsWnLP09EcoucZ0IBRH3sILwqgKH\n2rq6urJz585CJ50g33znFIh5nXbt2rF79+5cbUeOHKF169bipl0o18r69RsbG8u5c+fQ1tamY8eO\nFWoeqiRJREVFkZ2djaWlJRoaGmqJw9bWls2bN6vl2IIgCIIgCGVVvndmU6ZM4bfffmPbtm0YGRkR\nExNDTEwMz549AyA5OZm5c+dy8eJFwsPD8fPz46OPPiIqKoqhQ4eq9jNmzBjGjh2r+nzSpElERkYy\nbdo0bt++zfr169m8eTNfffVVCZ3mv1JSUkhJSSnx4whCWXP48GHs7e0ZMGAA7733Hg0bNuTGjRvq\nDqtYREdH06lTJywtLalXrx7NmjVTFfoRBEEQBEEQ1C/fxHPt2rU8ffqUbt26UadOHdVjxYoVgLyk\nSEBAAAMGDKB+/fr07duXx48fc/r0aZydnVX7iYiIICIiQvW5tbU1Bw4c4NSpUzRv3hw3Nzd+/PFH\nBgwYUEKnKff09OrVC319ffT19enduzdxcXEFvk6pVLJx40YmTpzIV199RUBAQInFKAgl5dGjRwwd\nOpTk5GTeeustnJyciIyMZPDgwfmOTigPJEli8ODBnDlzBj09PQwMDLh58ybvvfceGRkZ6g5PEARB\nEARBoIChtgXdkOrp6bFr164CD+Lj4/NKW6dOnfDz8yvwtcVBqVTSv39/fH19USgUSJKEt7c3AwYM\n4PTp03muFylJEmPGjGHbtm2qtjVr1nD48GE6dOhQKrELQnG4cuUKiYmJNGnShPPnz5Oenk6tWrUI\nDg7mwYMH5Xo9toiICM6dO4e+vj6hoaHo6enh5OREUFAQV65coW3btuoOURAEQRAEodJTzySoUnbn\nzh18fX0xMjIiMjKSyMhIDA0NOXv2bL7r6x05coRt27ZRrVo1vv32W/r3709qaiqTJk0qxegF4b+r\nUqUKAAkJCSQmJhITE0NqaioAurq66gztP8vMzARAR0eHatWqoaenR9WqVQHIyspSZ2iCIAiCIAjC\nc0Vax7O8yrnBrl69OmZmZoBcYSwpKUn1tde5ffs2AMOGDWPmzJk8ffoUAwMD7ty5gyRJefaUCkJZ\nkzO89vbt25iZmZH1/+3de1BU5/3H8feyyAIiqMCClzZo4gWIGkcgJkZjrLFYCSZpNdqkmqRtJilS\nEjpOq5IW2iTU6UwnCZHUOG3UJE40VbFeanUKiFtxjA04KuEyBi2oGJOJMICsXM7vD+uO+xMVrcsB\n9vOa2Rl4znPwc2a+wn73POectjYMw2D27Nk3fG5ubxAVFcXYsWMpLy8nNjYWm81GVVUVERER3Hff\nfWbHExERERG8pPGMiYnBbrdz6tQpJk+ejGEY1NTUEBERwZgxY66735Xn7u3evZu9e/eyb98+17ia\nTulN/Pz82LVrFwsXLuTgwYMAJCcns3btWnOD3QFWq5UtW7YwZ84cqqurAbDb7eTl5REUFGRyOhER\nEREBL2k8AwIC+Otf/8rcuXNdz94aPHgwmzdvJiAg4Lr7PfbYYyQkJHDo0CFmzZrlGv/d737n8cwi\nd1pUVBTFxcVcuHABX1/fPtWURUdHU1ZWxqFDh2hvbycuLo4BAwaYHUtERERE/ssrGk+AqVOnUlFR\nQVFRERaLhWnTphEWFnbDfWw2G3v37mXFihWua0SXLFni0bvvinjawIEDzY7gEf7+/kybNs3sGCIi\nIiLSCa9pPAHCw8P5/ve/f0v7BAcHk5OT46FEIiIiIiIifZ9X3NVWREREREREzKPGU0RERERERDxK\njaeIiIiIiIh4lBpPERERERER8Sg1niIiIiIiIuJRXnVX296uubmZvXv3Ul9fT3x8PNHR0WZHEpO0\ntLTgcDhobm4mISGByMhIsyOJiIiIiFyXGs9eoqamhkcffZSKigoAfHx8ePPNN0lNTTU5mXS36upq\nEhMTqaysBCAwMJCPPvqIxx9/3ORkIiIiIiKd01LbXuInP/kJFRUVjBw5kqSkJDo6OkhLS6OkpMTs\naNLNnn76aSorK4mKimLy5Mk0Nzfzwx/+kNraWrOjiYiIiIh0So1nL7Fv3z4A9u/fz/bt21mwYAGG\nYeBwOExOJt2psbGR4uJirFYrpaWlHDhwgIcffpiLFy/yr3/9y+x4IiIiIiKdUuPZS/Tv3x+Ao0eP\n0tzczIkTJ9zGxTv069cPi8VCe3s7Z8+epaWlhfPnzwNgs9lMTiciIiIi0jk1nr3ET3/6UwASExMJ\nCgri008/JSIigscee8zkZNKdbDYbCxYsACAmJoawsDDKysoYPnw4M2bMMDmdmOHcuXOsX7+ev/zl\nL1RXV5sdR6RPcDqdVFVV8c0335gdRUSkz1Dj2Uu89tprpKenY7PZMAyD8ePHs2fPHsLDw82O5nFH\njx4lNTWVH/3oR6xatYq2tjazI5lq9erVzJs3D8MwaG5uJiYmhr///e8EBwebHU262YEDB4iOjmbx\n4sX8+Mc/JiYmhq1bt5odS6RX27p1K5GRkYwePZrQ0FBSUlK8/u+OiMidYDEMwzA7xPXU19e7vg4J\nCTExSc/R3t6O0+kkMDDQ7CjdoqioiO9+97u0tLS4xh5//HE2b96Mj8/lz00OHz4MQFxcnCkZzdLQ\n0MDFixex2+1YLBaz4/R4fa1O2traGDFiBLW1tUyePJng4GD27NlD//79OXXqFKGhoWZH7JX6Wp3I\nrTly5Ajx8fG0trYSGRlJXV0dAL/97W959dVXXfNUJ3Izeg8rci2d8exlrFar1zSdAKmpqbS0tPCD\nH/yAt99+m4EDB5KXl8fOnTvNjma64OBgIiIi1HR6qVOnTlFbW0tYWBj79+9n9+7dTJw4kaamJkpL\nS82OJ9IrbdmyhdbWVhYsWMCZM2fYvHkzABs2bDA5mYhI76fGU3q0K88tXbNmDampqa7rG6+Mi3ir\nAQMGAJc/VS8vL+fMmTOuR+pc2SYit+bKktpBgwZhsVgYPHgwcHm1kYiI/G9u2HhmZ2cTHx9PSEgI\ndrud5ORkjh8/7tre1tbGL3/5SyZMmEBQUBBDhw7l6aefpqam5ob/aGFhIT4+Pte8Kisr78xRSZ/x\nrW99C4CsrCx27tzJ9u3bAfj2t79tZiwR09ntdp588klaW1sZN24cw4cP5/z588TFxTFp0iSz44n0\nSomJiQC8++67PPDAAyQlJQHwve99z8xYIiJ9wg0bz3379rFkyRKKi4vJz8/H19eXmTNnuu7y1tTU\nRElJCRkZGZSUlLBt2zZqampITEzs0qeDZWVl1NXVuV733HPPnTkq6TOys7MBePPNN0lKSuL06dPc\nf//9zJ071+Rkd5ZuXCG3Y926dSxatAibzYavry9z5sxhx44dWK1Ws6OJ9EpTp04lJycHq9XKwYMH\naWpqYs6cOa6/RSIicvtu6eZCTU1NhISEsG3bNubMmdPpnM8//5zY2FiOHj1KbGxsp3MKCwuZMWMG\n58+fv+ENMHRhtgDs3r2bnJwc6uvrSUhIICsry20pYW++yUNubi5ZWVl8+eWXREdH89577/HQQw+Z\nHatP6s11cjMdHR0YhqGG8w7oy3UiXXf69GnKysqw2+2MHz/+mmvpVSdyM3oPK3It31uZ3NDQQEdH\nB4MGDbrunCv/0W4054q4uDicTicxMTFkZGQwffr0W4kjXiIxMdG1/KkvWb9+PSkpKa7vP//8cxIT\nE/nss88YPXq0icmkt7lyh2cRuTOGDRvGsGHDzI4hItKn3NIZz/nz53PixAkOHz7c6Z00L126xCOP\nPEJ4eDh5eXnX/TmVlZUUFhYSHx+P0+nkgw8+4E9/+hP79u1zO9tz9adFVVVVXY0p0is899xzHDt2\njJ///OfMnz+fX/3qVzgcDp5//nleeukls+OJiIjIbRo1apTra53xFLmsy2c809PTOXDgAA6Ho9Om\ns62tjWeeeYaGhgZ27Nhxw581evRotzM6kydP5uTJk/zhD3/QMkPxGk1NTQCMGzcOm83G2LFjcTgc\nrnERERERkb6iS43nK6+8wqZNmygoKCAqKuqa7W1tbSxcuJDjx49TWFjYpWW2/19CQgIbN2687nZd\nRyHX01uvtZk5cyZr1qwhMzOTGTNm8MknnwDw5JNP9rpj6Q16a51I91KdSFeoTuRmrl61JyKX3fTC\noLS0NDZu3Eh+fn6n1521trby1FNPcezYMQoKCrDb7bcVpLS0lKFDh97WvneCYRh8+eWX+kUh3Wbl\nypXExcVx+vRpPvjgA1paWnjppZeYN2+e2dFERERERO6oG57xTElJ4cMPPyQvL4+QkBDq6uqAyw8n\n79+/P+3t7cybN4/Dhw+zfft2DMNwzRk4cCD+/v4ALFq0CIvFwrp164DLj8YYMWIEMTExXLp0iQ8/\n/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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_train_data(pos, 15, 100)\n", - "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.0001)\n", - "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.0001')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is pretty good for an initial guess. Lets make $g$ larger to see the effect." - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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YyPIeeUDSDJSBgYEULVqUPXv2AFC5cmVThiVymb3HFcOnw97jhu15/we/T1K8\nWfvl/h03MzNj5cqVbNq0ibNnz1K8eHHefvttLC0tM1T/6tWr3Lx5k7Jly+Lg4PCCo83dxi6EPf8Y\nHv+8Bro2Bc9Kpo1JiLxAWiKFEK8ETdOwtbWVBDKPaNasGe+++y73798nICCAzZs3kz9/fmbOnGnq\n0EQG7flbseuYQqnsb9kJvaLo8JWiQf/kBBIgMRE6joQzl17+1iRN02jWrBmDBw+mffv2GUogHz9+\nTK9evShevDi1atXCxcWFBQsWvPhgc6ldxxRjFyRvf90LPCvJ/wghMkJaIoUQ4jlcuXKF1atXc//+\nfRo2bIi3t7epQ3qpaJrGwoULadq0KQcPHqRAgQL06NGD0qVLmzo0kQGjflWMmWd47FMdZgxTVCyZ\n9ZvzW1GKMfNh9npISEwutzAHe1u4cxdi7kOr4bB/rqJQfkkInvTNN98wf/58zM3NKVOmDGfPnqV3\n795UqFDBOM7yVXHnrqEbq15v2PapDl+8Z9qYhMhLpCVS5CilFJcvXyY8PBx90l9uIfKYgwcP4uHh\nwZAhQwgICMDHx4dvvvnG1GG9dHQ6He+99x5Tp05lzJgxkkDmET+vTk4gAXYchWrdIWCu4mHc87cQ\n/rJBUbYjTF+TMoHs3AROL4XNU8DGylB2/ip0+AoeJ7z8LZKZsW7dOsAwcdWZM2fo06cPer2eDRs2\nmDiynKWUos8EuBph2C6UHwK/BjMz+dBBiIySJFLkmCtXrlCnTh1KliyJu7s7NWrU4OLFi6YOS4hM\n69GjB9HR0fj4+PDhhx9iZmZGQECAcfkQIV5Vy7YoBk1JXf44AcYuAI/3YHNI5hK7R3GKDyYo+k6E\ne7HJ5d7VIeQXWDpao7SbRo0KGotGJj+//QgM+JEX0p02r0q6Fjqd4fbPzMwsRfmrYtZ6WPfEUsHz\nvgQ3R0kghcgMSSJFjtDr9bRp04aDBw+SL18+7O3t+fvvv2nZsiWPHz82dXhCZNjDhw85deoUmqax\nadMmZsyYQevWrQE4evSoiaMTwnT+DFG8/w0k5SN1K8OeWVDnteR9LlwDvyHQ9WvF9dvpJy6Xbyga\nfmSYMCdJhRIQNBG2TUs9fq19I41v+iZvzw2Cqauy8qpeLm3atAGgXbt2VKlShVmzZqFpGq1atTJx\nZDnn+AXFkKnJ2x+3h1ZvSAIpRGZJEilyxPnz5zly5AgODg5cunSJq1ev4uzszOnTpzl+/Hj6BxAi\nl7CyssJJf15cAAAgAElEQVTOzg6lFKtXr+bkyZMcOnQIgMKFC5s4OiFMI+Skov2Xyd1MXysF/zcJ\nvKpqBM+GGUPBIV/y/sv/gjId4P1vnj35zrbDilq94dCZ5LJ334LD8+HtBtozJ8n6sjt0a5q8/ek0\n+GPfq9XS9iwBAQG8++67PH78mJMnT2JpacmcOXPw8vIydWg5IvaRouvXEBdv2K5aBr7/2LQxCZFX\nSRIpckRCQgIAlpaW2NraYm1tjZWVYfBKYmJiWlWFyFV0Oh1Dhw4F4N1336VKlSpcvnwZDw8PmjZt\nmk5tIV6cO3fuMGLECDp16sTw4cNzbE3NU2GKFkMh9pFhu4QzbJqMcVIbnU6jf1uNM8tSJneP4iFw\nE/h8DBW7wMTFihuRhoRy0lJF08FwO9qwr7kZ/DQYFo4EW+u0W400TWPu54aWUDBMnNI5AE5elETS\n0tKSwMBAwsLC2LdvH9evX+eDDz4wdVg5QinF4J/gZJhh28YKlo8BaytphRTiecjsrCJHlC9fnjJl\nynDhwgUqVaqEmZkZly9fplixYlStWtXU4QmRKQEBAdja2jJ79mwePHjAG2+8wfTp07G2tjZ1aOIV\ndefOHerWrUtoaKixbPHixRw4cIBixYq9sPNevqHwG2KYFRWgSAH4czIUc0p9Y+5cSCPwa+jRwrC2\n49Fzyc+FXoEvZsKIOYZWzOMXkp9zKQwrv4EG1TJ+s29tpbHuW0XtD+DKTcNYys4BcGyheqUnT0lM\nVAQfh5VbS3LmUklKOEOFkopKJaFiSSjtCubmqa9PYqLidnQie0JOYaZi8X3jNfLnz2+CV/B8lDK8\n5355Yv6gnwZDpVKv7ntBiKySJFLkCHNzc9avX0/Lli0JDw8HwNXVlaCgILnxFnmOTqdj+PDhDB8+\n3NShCAHApEmTCA0N5bXXXmPo0KHMmjWLAwcOMHr0aObOnftCznn3gSGBTJrhMp8N/D4JKqSzlEfj\nWhqH5imOnIVffoNlW+DuA8NziYkpE0ivqoYE0vU5Jj1xLqSxYaKifn9DK+nJMFi7Ezr4ZvpQuZZS\niis3DS21zoWePruoXq/YexxWboM12+F65LOPZ2EOZYspXIsYlkq5cxfu3IPoewBmQFWUSsT25pf8\nNtcPX9/cfzGTWiCnPTE2tnMT6P226WIS4mUgSaTIMVWqVOH06dMcPnwYpRQ1atTAzs7O1GEJIUSe\nl9QCOXz4cN5//31cXFxo3rw5586dS6fm85uyAs5cMjy2tIC1E6BWBhdq1zSNmhWhZkX4YaBi9XbD\n5Dm7npjg+MN2MPkTsLR4/taiauU0BnVUTFhk2B6/EN5ppJ45njKjVm9XHD4DdjaG5Dnpe9JX2WJQ\n3PnFtnKdvGiYsXbfCcO2mRm4FFK4OYJbEXB1NExyFLQbrt3K2DEfJ8DpcMPXs2iaGQ9dJtKy10DC\nD1TByckpqy/lhdHrFR9NgjlByWVtG8KCEWT5PSDEq06SSJGjbGxsaNCgganDEEKIl0qJEiUAmDVr\nFi4uLkyZYlhno2TJki/kfI/iFDPWJm9PGwJNPJ/vptzWWqN7M+jeDM5dVmzYA5XdoVm97LnJH9wR\nflppaI38+zxs3Ast6z//8Zb/ZZicJS3mZrBklKKDb/YnKnHxivGL4NtAQ9KXJDHRkCymlzA6FoD2\njaBJLUOr5JlLcPYSnLmc3Kr8VAlRFCjgQPR9w3QaD11/4ttfDvPjl7kziUxMVPSZCAs2Jpd1agyL\nAsDiKV12hRCZI0mkEEIIkccNGTKEJUuWsH//fvz8/ADInz8/X3311Qs535LNEBFleFzMCXo0z57j\nli+hMbRr9hwriWNBjX5tFJOXG7bHLYAWXs/XGvngoWFsXXoSEqH7N+BaRFHfI/sSluB/FH2+TW4B\nBkMXVId8yZMQPU2RAtDOGzo2hobVnj7uEeDeA8W5K3ArGgraQ6H8YGUeS0nX/GiaYtepS7z/rRtH\nQzU0TcfU32vSsIGiTcPclZQlJCh6jYfFfyaXvecHv37x7NcuhMgcSSKFEEKIPM7Nzc04BjI0NJQS\nJUowcuRIKlSokO3nUio5IQP4pEPub9n5tDPMWGtY2iHkFGw9BE08M3+cScuSW+ucChrG1d1/CA+S\nvh7B4TN6rkfqiIuH1p/BvjmKcsWzdn3uPlB8PhNmrUtZXq8KzP0cXnPXiItX/Hvb0BKZ9P1uLNSv\nCj7VM5Y82dsZuhmnZEeLFs3YuHEjntXLY5u/BMp1NZptFfRKR+cACJqoeKtO7ngPPE5QvDfaMAY0\nSc+WMGf408eMCiGejySRQgghxEugRIkS/Prrr5muFxUVxfLly7l16xbVqlWjVatWabbS/RkCp8IN\nj/PZwAd5YIISV0eNXi0VM//rgjtuYeaTyCs3Fd8tTt4e2xc+aJV8nW7cuEGXLl34d184VN2HZunM\nnbvQ/FPYO1vhWPD5EphdxxTdRqXspprPBiZ8CB+2NSyhAmBlqeHuCu6uz3WaNC1cuJBOnTqxdetW\nHj06R7F8vdGV3MmVW9bEP4a2n8MfPyq8q5s2SdPrFe+OhlVPJJD92sD0T5OvkxAie0gSKYQQQryi\nrly5QsOGDY2zZgN0796dBQsWPDORfLIVsldLKGCfN27Oh3eDuUGGrqY7j8LuYwqbTNT/chY8jDM8\nfr0c9GyR/Jxer6dNmzaEhIRgbm4O59uRUGELmpktF64ZWiS3TlPYZHJNwu2HFS2HJZ8XDOM5p3+a\n9sQ94eHhTJw4kfDwcMqVK8eXX36Ji4tLuue7fv06S5cuJTo6mrp169K8eXM0TaNw4cJs2bKFq1ev\n8ujRI9zd3fn3thkNP4LLNw1rfr49DLb8pKhT2XTvh69mp0wgB3aAKYNkEh0hXgSdqQMQQgghhGl8\n8sknhIeHU7VqVfz9/cmXLx+LFi1izZo1T93/+AXFloOGxzodDOqYg8FmUUkXjfeaJW+PX5TxuvtP\nKJZsTt6ePChl18hz584REhKCg4MDV69e5d9zQeS73g+l9Ib6J6H7GENLWUbtPKp4e3hyAulYAJaN\nhqCJaSeQYWFh1KpVi1mzZrFp0yamTZtG7dq1iYhIa9YcOHHiBB4eHgwdOpSxY8fSsmVLBg0aZHxe\n0zSKFy9OuXLlMDc3p4SLxl9ToWhhw/P3H0KzT+HPkIy/xuy0YKNi4hMtxZJACvFiSRIphBBCvKIO\nHz4MwNKlS/nxxx8ZOHBgivL/9WQrZDtvcHfNWzfon79rSH7hv265l2zTraPXK/x/St5u70Oqbptx\ncYZML1++fBQqVIiCBQtSWNsDYf7GfdbsgGEZmJQHDK2kLYcZZpQFcC0CwbOhUxMt3aTom2++ITIy\nkoYNG7J69Wpq1KjBlStXmDRpUpr1+vbty+3bt6lfvz5DhgzB2tqaadOmsW3btmfWKVtMY8tPhol7\nwLCeZLMhMGiK4mFcziWTu48p+n2XvN2yPvw4UBJIIV4kSSKFECIPCAkJYfr06SxdupR79+6ZOhzx\nkihc2NCMtGbNGsLCwti+fXuK8iddv52yNW5I5xwJMVuVK67RqXHy9rwtRdOts3SLYTIeMKyHOfGj\n1PtUrFgRNzc3rl27Ro0aNahZsyaXLl3ChVV83C55HY7Jy2HqKoVSz06wgv9RtBhqmKgHDC1926YZ\nEraMuHjxIgCfffYZ7du3N7YmJpU/y9GjRwFYt24dP/zwA++++y4Ax44dS6sar7lr/DnZMNFQkmmr\nwLMXHD2XtUTy0aNHaV4rgIvXFO2+TF7upGoZWPK1TKIjxIsmSaQQQuRyX3/9NXXr1mXAgAF069aN\nGjVqcPnyZVOHJV4CQ4cOBWDUqFGULl2a/fv34+TkZEwgnjR9bfKNer0qULdK3rxJ/6J78uNdxwsQ\neu3ZIyMfPFR8MTN5278TlHZL/bqtrKxYu3YtTk5OnDhxgn/++YciRYqwdu1apgw2p23D5H0HTwGP\n92DiYsXViJQJ0v4TiuafGrqGAjgXgq3TDEufZFTp0qUB+Pbbb1m9erVxzdCk8mdxdHQEYPHixZw8\neZLdu3cDUKRIkXTPWb28xj+B8PYT62+eCoe6fQyvMzExc8nkgQMHeO2117CxscHBwYGxY8c+NZmM\nuW/o8hsZY9h2KggbvjPMMiuEeLE0ld5HPNkkJibG+NjBwSEnTinyoEOHDgFQq1YtE0cicrNX6X2y\na9cuvL29MTc3p3Pnzhw8eJCzZ8/SvHlzNm7cmP4BXmGv0vskKwIDA5kwYQIRERG8/vrrTJ8+PdXS\nILGPFCXawp27hu2VY+GdRnn3Rr39F4p1uwyP36x+hz9/Tt3yCjDqV8WYeYbHzoXg7HLIn0aCEh0d\nzd69e1FK4eXlRcGChua52EeKxgOTWzSTaBo0qgHvvgUlXKDdF3D3geE5p4Kw/WeoVCpz1zksLIza\ntWtz+/ZtY1nx4sU5dOgQTk5Oz6w3ffp0BgwYkKKsXLlyHD58GHt7+wydWynF3A0wZGpyV1yAhq8b\nxicWsAedZuhSrNPAzMxwDW5HG5ZOuXoLToZG8/OcIOI1J7BwhkcXIPoPvv6kLqO+6mc8ZkKCIYH8\nM8SwbWVpaLGt9wI+3JB7WCFSkyRS5Cp5+abvr7/+Yv78+cTGxtKoUSM+/vhjzMzMTB3WSykvv09C\nQ0PZunUrZmZm+Pn5Ubx48TT3nzhxIp9//jl9+vRhzpw5hIWFUbp0aRwcHIiOTmN1cZGn3ye5zax1\nio/+G1Ln7grnlmd/d8Fbt27h7+/P/v37yZ8/PwMGDKBXr17Zeo4kh88oPHsbHmuaYt8cjRrlU66l\neOWmomKX5Ilt5n4Ovd9+/tccGaMYNh1Wbk2ZYD2NYwFDAvma+/Od79KlS6lmZ3V2dk6zjlKKuXPn\n8tNPPxEdHU2dOnWYNm0abm5umT7/ucuK7t/AgVPp75sZNSpAs7rQ3AuWbobpT8z/FBgA3d56MR9s\nyD2sEKnJEh9CZIMlS5ak6P61fv16Dhw4QGBgoAzsF0Zr166la9euxkk47O3tCQoKolGjRs+sk9QC\n8PfffxMdHc2uXYbmE7mRETlFr1dMWZG8/UmH7E8gY2Nj8fX15cSJE8ay3r178+jRIz766CmDELOo\nZkWNZnUVf+wHpTTq9jG0jjkXVLg5GiayuXYrOYGsXh56NM/aOQs7aMz7EqYOVqzdCYs3wdbD8L8f\n5RcpYOjC+rwJJEDJkiWZMWNGpupomkbfvn3p27fvc583SfkSGrtnKsYuMKzJqddn+ZAAHDlr+Bq3\nMGX5V++/uARSCPF00hIpcpVntRwopYiIiMDOzo58+fKZIrRnUkpRpEgR7ty5g7+/PxUrVsTf35/Y\n2Fj27t1LvXr1TB3iSycvtjDduXOHEiVK8ODBA1q0aEFsbCzbt2/HycmJK1euYGlp+dR6EREReHh4\ncPPmzRTlEydOZPjw4TkRep6VF98nudFvexStPzM8dsgHl9dm/5iz5cuX06VLF9zd3Vm5ciU7duxg\n2LBhuLq6cu3atWw9V5K9xxUN+mds3x3ToeHr2Z+kXLulWLoZFv8Jxy8YJtH540fwKPvyJET7TigC\n5sLFfw3JpF4ZvsfHJxAVfZfHCYnoEmNwc1J41y1D4sPLLFv4PWYJ13mjXmWOXbAhWquHzuEN1FPa\nPt5pBMvHgE734q6Z3MMKkZpMrCNyvSNHjlC+fHlcXFywt7fn/fff5+HDh6YOyyg6Opo7d+5gYWHB\nDz/8QN++fXnrrbcAuHDhgomjE7nF8ePHefDgAR4eHvz222/89ddfFC1alIiIiDRnTXRycmLr1q3U\nqVMHMzMzihQpwrhx4xg2bFgORi9eZU8u69GnVdYTyPj4eE6cOEFoaKhxspSkNQx9fHyoVasWffr0\nAeDmzZvpzs75vLyqavi3vUKFYrE4Fnj2fp0av5gEEsDNUWNYN42/F2lcWQ/nVrxcCSQYxihu+Unj\nwiqNsDUal9ZqHF8Qg9WJMjzeVwQOOqM/Up4rmyrgdHc4S791Z2SfIiTeXs+O38YRfWoE1cyHcG5J\nDKvGQs+W4PLfEFbv6rBgxItNIIUQT5dmd9YJEyawdu1azp07h5WVFXXr1mXChAlUrlz5qfv369eP\nuXPn8v333/Ppp5++kIDFq+XWrVv4+flx69YtbG1tiY2NZdGiRVhbWzN79mxThwcYPpUsWLAgUVFR\nfPnll1SsWJEtW7YA4O7ubuLoRG6RP39+AC5fvsz58+e5f/++ceKL9D7Zrly5Mvv370ev16PTyWd/\nIueEnFTsMKz8gJkZDHwna8c7dOgQ7dq148qVKwB4eXmxdu1aPDw8AFi2bBkuLi4cOHAAAA8Pjxc6\nJKCLTwRdfCKoVasW8Y8V1yPh39uGrqzXbhmW9MhqN9aMcnN8dRKhP/74gytXrlClShX27NnDoUOH\naNKkCbNnz2bSpEmMGTOGNm3acOzYMYoUKULTpk2xtramTClo38jQxToiyjB2VJbyEMI00kwid+7c\nyYABA/D09ESv1xMQEECTJk04deqUccaxJKtXr+bgwYO4urrKGDCRbf78809u3bpFrVq12LNnD8eP\nH8fT05NFixYxc+bMXHFDrdPp+OGHH+jVqxfffvutsbxDhw54eXmZMDKRm1SrVo0GDRqwZ88eypcv\nbyxv164dRYumv1YdkCve7zktMkYxfQ28Xg5avSH/W3KSUorPnhhW18kXijs//88gJiaGli1bcvPm\nTYoWLcr9+/fZu3cv3bp1Y8uWLXz00UfMmDGDCRMmAIYPV+bOnZvVl5FhlhYaJV2gpEuOnfKVdf/+\nfcAw+6uDgwPVq1cH4OHDhyQmJmJubk6NGjWoUaPGU+vrdJqxNVIIYRppJpGbNm1KsR0YGIiDgwN7\n9+6lRYsWxvJLly4xePBgtm7dip+f34uJVLySkiYgcXZ2xsrKimLFigHw+PHjF9bF6Xn07NkTZ2fn\nFLOzDh48WD5QEUY6nY6goCD69+/Pxo0b0el0dOzYkalTp5o6tFzr7gOF70DDWDGASQMVQzrL71RO\n2bgXdv23zry5GYz6IGvHCw4O5ubNm1SuXJmjR48SGRlJ8eLF2bp1KzExMfz88880adKEffv24eDg\nQLdu3ShVqlSWX8fzWLduHdOmTSMmJoZ69eoxbtw4GQuXjby8vNDpdKxbt442bdpw7tw5AOrVq4e5\nucz5KERekKnf1Lt376LX61O0QiYkJNClSxdGjhyZal0pIbKqYcOGWFhYsHHjRt544w3CwsIA8PX1\nzXXLZzRv3pzmzXOo35PIkwoVKsTKlSuNH4DIhwwGCQkJhIWFYWNjg5ubG5qmkZCg6ByQnEACDJ0G\nGgp/EyWSkTGKm3egQomXvwtdQoLi8ydaIfu2hrLFsvaa9f9N0Wlubo5Op8Pc3Nz4O6CUQtM02rZt\nS9u2bbN0nqwKDAyke/fuxu0jR44QEhLCnj17sLKyMmFkL4/KlSvz888/M2DAAIKCggAoVaoUCxcu\nTKemECK3yNTsrB07duTChQscOnTI+If/q6++4uTJk6xfvx4wjAEbOHAgQ4YMSVH3yZmtQkNDsyN2\n8YrYtGkT33zzDfHx8QCUKVOGqVOnprloshAibzh9+jSfffYZ169fB6BOnTqMGzeemX9WYW2w41Pr\nDG5zha6NInIyTP6NtKT3lIpE3rWgUL7H+FSLxrdaFDXK3sM8d32elS2C9hVm3PJSANhaJbJ25AkK\n2Sdk6ZgxMTG0b9+emJgY3NzcuH//PjExMbz++us52m01Pa1ateL69ev06tWLmjVrMnr0aCIiIpgw\nYQJNmjQxdXgvlYsXL3LixAlsbW2pW7durpt9PUm5cuWMj6VFWgiDDLdEDhkyhL1797Jnzx5jArlj\nxw4WLlzIsWPHUuybm7oZirzPz8+P6tWrc+bMGWxtbalWrdozl0PIDqdPn2bRokVERkZSunRp+vXr\nl2oMsBAi6+7evcvgwYO5c+cOBQoU4OHDh4SEhNB31CnC9MlrZ77re4MTl+w4dsGwZuaU9cXRNMOk\nKDll9h+uRN61AODOfQvWBjuyNtgRB7sEvKtG0/j1KGqVu4eFed7///coXmPOH67G7fca38hyAgmG\nm+8ffviB4cOHG5ftqFChAmPHjs3ysbNT0kyx3bt3x87ODi8vL9avX28sF9mndOnSlC5d2tRhCCGe\nQ4ZaIv39/Vm5ciXbt29PMSHE6NGjGTNmTIrJHhITE9HpdLi6unL58mVjuayxIzLC1Ou67d+/Hx8f\nH+NYTICyZcty8OBBChRIYw54kaNM/T4RmRcVFcX+/fvR6XR4eXlhb2/P+vXradu2LR4eHhw8eJB/\n//0X95qDocIaNM3wf6XLm7D4a3jwEFoMhd1/Jx9zymD4pMOzu1hm1/vk5EWFR/fUi8L/L6eCsHAk\nvFUnb3d1nbBI8dV/k1+7FIbQFWBnk32vKTY2lhMnTmBlZUWVKlVMOjThae8RDw8Pjh8/TuvWrfHy\n8uKbb77h/v37bNq0ybh8kzAtpRTR0dE4ODjkyIRjmbmH1ev1xp5TQuRllpaWaf5+pdsSOWjQIFat\nWpUqgQT46KOP6NChg3FbKcVbb71F165djWs8CZGXBAQEEBcXR4cOHejZsydDhw7l1KlTzJ07N1et\ny3f16lX8/f05fPgwRYoUYejQoXTs2NHUYQnxVMHBwbRu3ZrIyEgAXF1d2bhxI4mJiQDY2NhgYWHB\n+esOaOWWwH8JZH0P+PULw9jRfLawcZKi+aew5x/DcQdPMYyRHJhGIpkdAuYmJ5B+deGL92D1Dli7\nw7AMRJKIKGg1HBaOVHRukjcTydvRiomLk7dH9c7eBBLA1taW2rVrZ+sxs9OMGTNo2rQpQUFBxvF6\nXbt2pWnTpiaOTAAEBQXRr18/bt68Sb58+Rg7diyDBg0ydViA4T44Li4Oa2trGfMu8jSlFI8ePUrz\nvZxmEvnxxx+zePFi1q9fj4ODAzdu3ADA3t4eOzs7HB0dcXRMOWbFwsICFxeXFP3HhcgrklrPP//8\nc2rUqME///zD559/zqVLl0wcWbLo6GgaNmxonGQoLCyMTp06kZiYSJcuXUwcnRApPXjwgHbt2hEZ\nGUnVqlWJj4/n7NmztG3bll27dpE/f35CQkKoULUJF+2WgLmhxb+MG6wdD9ZWyf+88tlqhkRyKAT/\nl0gOmgIPHimGdgFz8+y/aTt4WrFuV/L2uH5QvbzGG6/D5E8UIadgzQ5YvMmQRD5OgG6j4M5dxUft\n8t5N5NgFcPeB4XHFktCrRZq7v5QaNGjA4cOHmTdvHjExMdStW5cePXq8sKTgypUrfPjhhwQHB5M/\nf34+/vhjhg0bJknIUxw8eJD27duTmJiIpaUl9+/fZ/DgwRQpUoRu3bqZOjzi4+OxtLSUn53I8zRN\nw9LSkvj4+GdOKJZmH4CZM2dy//59GjdujKurq/Hrhx9+eCEBC2FqSR9+DB8+nHnz5jFz5kyAVK3w\nprRs2TLCwsKoUqUKx44d46uvvgJg/PjxJo5MiNT++ecfIiIiKFOmDEePHuWff/7BycmJ8PBwHjx4\nwIqVa8nn6keo+WT05s4AONjp+b/vwbFg6hsxezuN3yeBV9Xksi9ngUd3WL9LZfuY/JFzkh938DUk\nkEl0Oo16VTQmDdA4NA8qlTKUKwUDfoAx87I/nvQcOKXo/51i++HMn/fiNcXMdcnb4/u/mMQ8L6hU\nqRLff/89c+bMoVevXi+sy2TSPdbGjRuJjo7m8uXLfPbZZ/L3/BkWLVpEYmIiPXr04NGjR3z33XcA\n/PrrryaOzEApletmjhfieZmZmaX5PyzNv4p6vZ7ExET0en2Kr4CAgGfWCQsLSzUzqxB5xcSJE3Fw\ncGDr1q307t2bS5cuUatWrVzVPfvmzZsAvPXWW1SrVo3evXsDGHsKCJGbJH2Cee/ePe7evUtk5B3u\nJ7qBywAG/FyMjt/78qDU72h2hqzQwlyxfqKOCiWfnbzY22n8/kPKRPLMJWj3BTT8CPYez57EbccR\nxeYDhsc6HYxOY53EYk4au2ZA7deSy0b9amgp1eufHs/u3bsZM2YM3333HRcvXsxyvDuPKnw+hjlB\n0OxTOHQ6c9dh5FxDSyoYuhK3fiPLIYl0/Pbbb4SGhlK+fHkuXrxoXOJi8uTJJo4sd3r48CFg+GBX\n0zQqVqyYolwIkXNkRVchnvDaa69x5MgRpk6dyvXr16latSr+/v7Y2NiYOjQjDw8PAObMmYOtrS1b\nt24FoFq1aqYMK8dcv36d/fv3kz9/fmrUqJEjkyqI51e1qgflPVpw7oYjjnWD0Ns3ggqH0YBtR1Pv\nP/dzDe/q6bd+5bfT+OsnxeQVMHFxchfM4H+gQX9o21DRtYEVJZ3j0j7QMyilGPFEK2T3ZlAxjcQW\noLCDIab2X8KWg4ayn1fDnRiYP0Jh8V+r3r0HitET5/HD1GVg6QoJ0YyeMJff1/+Ct7f3c8W7/4Ti\n7WHw6L/5POIfQ4cRcHi+olD+9K/nodOKZVuStyd+JOuY5oSoqCgAPD09cXd3p1ChQoBh2IJer5e/\nb/+jUaNG/Prrr4waNYqQkBB27txpLBdC5KxMrROZFTI7q8gImXUzfUopunXrxrJly4xljo6O7Nq1\ny/ip7Mtq3rx59O/fn8ePHwPg4+NjHLMtcoeEBMWxUMPkN3v+NnyPiEq7TkkXeLM2dPeDBtUyn7jc\njlaMXQAz1yW3pAGY6RTeVaPp905BmtfL3AQxG/cakjIAC3M4twJKumSsfly8ovs3sGpbclnFkqBp\ncDUC7sU+vZ5Z4g1a+LjgWQlqVTR8FXZI/5zHzil8P4Hoe6mfa+EFQRMNXW+fJTFR8eYg2PFfUt/O\nG1aPfzUSSFP/zzlw4AB16tTB3NycXr168ffffxMSEkLt2rUJCQkxSUy5mVKKTz75hJ9//tlY5ufn\nx7p167C2tn5h583oPWzSRCRCvCzSek9LEilylez8h37o0CE++eQTTp8+TbFixRg7diytW7fO8nFz\nA9FJk8EAACAASURBVL1ez4oVKzhy5AiFCxeme/fuuLq6pl8xDzty5Aienp7o9XqqVKnCpUuXuHfv\nHu+//z4LFiwwdXgCuHJT0fAjuJROz+r8dtCohiFxfNMTyhbLnlavi9cUI+eSokUtia01vF3fMK6x\nWT2wsXr2+fR6Rc2e8Pd5w/aAd2Cqf+biS0xUfPyDoWtpVtSrAgG9oGntp1+jU2EKnwFwO9qw7VgA\nhnWD4dOT9xnbF758/+nxxz5SdBsFQbsN22Zm/8/eeYdFcbxx/LNIlypNxa4RG0bB3jWKvXcl9t4w\nGkk0GkR/gl0j9ti7xt5i12gsiKKxSzTYGxbAglJ2fn+s3HmCgAgc6n6e5x5vZ2dn3j2Xu/nOvPO+\ncGE5SboTf0noW0QC+Pj4MGbMGM2xo6Mj+/fvp0SJEnqzKbNz+vRprl69irOzM1WrVk33FVtVRKp8\nragi8gsjNjaWLFmyfJGuRmn1gx4SEoK7uzsvXrzQlEmSxJ9//qnm+fpMmTBhAj///DOenp54eXlx\n9epVPD09cXJyUveDZhL6TxHM2Ziw3MYSKrsq++yqlYJyRdM3YMvpK4Kf58D+U4mfz2oGTapAu9pK\nyg6j92xZu0/Q3kd5b24K19ZBdruPt1cIRdT6LdUtNzaM483zUIx5RK0qRbn1IJZLt8yQslh8sK3K\nJWFMD6jprrXj2h1B9X5wX8mcgo0lHJgBpQpLDJspmPLWWcHAAPZMh1ruuvfwOFzQxBtOXNSWDW0P\nkwZ8eb8tHyIziEiAw4cPc+zYMaysrGjVqhWOjo56tUdFF1VEJs6NGzcoUKAAixcvpnPnzgAsWbKE\nbt26cePGDfLkyaNnC1U+laSeaXVP5GdESEgIXbp0ITAwkKxZs9KvXz/+97//YWio/je+z/z583nx\n4gUNGjRg/vz5TJgwgYCAAKZNm6aKyM8UIyMjAJ4+fYosy4SHK0svX8vzH/lSsGI3ZDFQ3D/zOCn/\npnUOv9QS8UKw7E/tccsaUKsMVCkJxfMn7U6Z1rgXkdj7G6zbfoH9Z2z5+0pOLt/Qnn8ZpaxWrt4L\n9jbQ9jvB9/WgbFGIi4NfF2jrDmqdOgEJysTV/3op+zMfPoVcjuDsAFbmUK1aJ06cOMEuzb5QAzr3\nm0i1BkMIugynLsPZfyFWSaXJ0XPw3SCo6SYY0xNyO0LtQVoBaWEGf05RBCSAfx84eQmO/AOyDB18\nIHixIKeDcj70nqD+EAi5rbX3xw4wvm+qblXlE6lWrRrVqlXTtxkqKgmIF4WJ0bBhQyRJSnZRY9Wq\nVYSFhWWafJ4qacPXMfr6AggPD6d27drcvq384j9//pwJEyYgSRL+/v56ti7z8fTpUwA8PDxwdnam\nSZMmBAQEaMpVPj+aNGnCqFGj2LlzJ8eOHdPMDH8NuTFD7wkaDUNHCMVjZy3I4wT5skMHD2hZUz+i\ncslORZyBIhrX/U//gVkKZH9Ngfr3mTsyJxdDYd1+5fWucHocDrM2KK/CuaHUN/Dv2/PWFjCsQ/L9\nCCF4+PAhMTExODs7J3Ctcy/y/udgyM6dO/Hy8uLAgQOYmprStWtXfv55MFmySHR9m5vxbpjAbxks\n2Krd63kwGKr2VVyC44MJmRrDtklQvri2H0NDiTVjBG5d4eFTZV9qu19hf4Dg/HVo+KNSDspezamD\nwKtN5piQUFFRyXz4+vpSsGBBnTIXFxc2bNiQ7GTuqlWruHjxoioivzDUsF+fCTt27OD27du4urry\n7Nkztm/fDii5PDM6D9nngLu7OwBjxoxh6NCh9O7dG9C/y5JK6ilUqBCbNm3CwcGB8PBwhBB069aN\ncePG6du0dOXkJUHFXokLSIAnEXAmBDYdVqJx9p4oeP0mY78TZFkwa4P2eEAr/QvId5EkiRIFJMb0\nlLi8Gs4sAW9PZWXwXUJuw7p3guEM6wC2yUQ2ffz4MXXq1CFHjhzkyZMHV1dXLl++nKxNtra2LFu2\njDt37nDt2jV++eWXBPnlnB0kZg2VCFkL3Rop+xXjiReQRoaw0Z9EI9rmsJdY7au4s4IS5KjtKKjR\nXysgTYxh7dgvV0CGhYXh4+NDly5d8PPz4/nzRKIPqaQbz549w9PTEwcHB3LmzMmwYcOIjo7Wt1kq\nqaBu3bp06NBB5+Xu7o6xsXGK9qSmx2+CmtpFv6gi8jMhMjISUBIg29jYUKFCBUBJVKyKyIT07t2b\nhg0b8vTpU6ZOncp///2Hq6vrFy84vnQ8PDy4e/cumzZtYv/+/SxcuBBjY+NPavPo0aPUq1cPV1dX\n2rZty40bNz7q+vT8+9v0l6DmAG10U2MjaF9HCUpTIKciIN7n9y28DW6Tcd8Lu07AtTvKextL8MzE\nHuOSJPHtNxLj+0qErod9M6BLA8Ud9F0cbRVX1uTo0KED+/fvx8TEBEtLSy5dukSDBg149eoDIVhT\nQd7sEguGS1xeBd/X04rCLFlgzRioV+HDg7MabopLbTybD8OLt+MuG0vYPQ1a6Wn1Or25d+8e7u7u\njBkzhqVLl/LLL79QqVIlze+pSvoSFxdH48aNWblyJY8fP+b+/ftMnjyZAQMG6Ns0lTTixo0bGBgY\naPKbJkaNGjXYuXOnpm78Kx4hBAEBAbi6umJmZoaTkxM9evTgyZMnOu3ky5eP+vXrs3//fsqXL4+Z\nmRkTJ05Mt3tTSR7VnfUzoVKlSkiSxB9//IEsy1y6dElTruaRSoihoSFbtmxh48aNXLlyBWdnZ9q1\na4e5ubm+TVP5RIyMjMiVK1ei565du8bly5fJmTMnbm5uCWY+n0QIbj2Eu2HKK/DMbZauvoJsOAgk\nYy7sHs/hwxU5c+YM2bNnT9KOx+HKnrLr9yDgB0HHuikbiEe+FExaCTFxUL+CEnDm/SAzQij5D4fN\nhHiNms0KNo/XTYEhy4IHT+DWQwhYr41KeuoKuHeFVaMFHuXTXyDMfGcVslujzLNPMzmyZJGo5Q61\n3GHmUMHWv2HVHrj3GCb1Bwvz5Fch9+7di5GREdeuXSNbtmy4urry33//cfz4cb777rs0tbdQLoml\no2B4J8GWI8pkQrliyX/W3h3h2HnYflRbltsJdk6G4gU+j/+r1ODj48Pt27dxc3Oje/fuTJs2jQsX\nLjB16lRGjx6tb/O+eE6ePMnRo0exs7Pj4MGDPHjwAA8PDxYsWMDkyZOxsrLSt4kqH0F4eDiPHz9O\n9FxSq4wjR47E29ubO3fuMH369ATn+/bty6JFi+jSpQuDBg3i1q1bBAQEcPLkSYKCgjAxMdH0ce3a\nNVq3bk2vXr3o2bOnGrhHz6gi8jPh22+/ZerUqQwZMoT169cDyqzM4sWL9WxZ5iVLliy0bp2CpQSV\nLwJfX1+dgWGTJk1Yt26d5geo32TB3E3vX5UbHLoR//NnYF2BB6eLMHfu3GQHmUNmwOmryvvvx0Dk\nK0Hf5kkPyO8/FjQYqk0dMXEF2FlDw4qCxlWgbnllf5vXb+hEOS2UC3ZMhm9y67ZvYCCR0wFyOkD5\n4oLyxeHHACUYy9NIqD8UfHsIRnRKv8A2IbcEu04o7yUJ+jVPl27SHXNTiXa1lYitKSU+X6mRkRHW\n1taYmppiYaFEWI2NjU3q0mQ5duwYgYGB2NjY0KxZM2xtbTXniuSVKJI35W0ZGEgsHam4RYfchpKF\nlOfJ2eHLFZCAxq3Yz8+PunXrYmpqSvfu3bly5YqeLfs6ePZMcaEoUqQIrq6uFCtWDBsbG8LDwwkP\nD//qReTohYIxi9Kv/V+7wejuafc3Xq9ePZ1jSZI4d+5cstfVrl2bnDlzEh4eTocOupvMjx07xvz5\n81m+fDkdO3bU6atq1aosW7aMnj17Asrk6vXr19m6dSuNGjVKgztS+VRUEfkZMXjwYGrVqsWJEyew\nsrKiQYMGX/2XsIoKwLZt2xg9ejQGBgZUr16dkydPsnXrVkaPHo2/vz9HzyUmIBMiS1mhwBzu3t2W\nZL3dgUqk1HfpPxlevBIM65j4j/bVm4J6QxLmUHwSAct2KS8TY8jrpBv4pXJJ2OQP9jaJtyvLMhs3\nbuTChQvkyJGD7RM86TbenHuPlVXMX39XonQuHSmS3d+XGma9I3YbVYICzl+2MHmX7NmzU6pUKc6e\nPUuJEiWwsrLiwoUL2NraUrZs2VS3O3r0aHx9fTXHPj4+HDhwgEKFCqW6TVsricAFgjMhUMkVjI2+\n/P+neI+F2bNnY2Zmppl0dXZ21qdZXyQvX74kMDAQWZYpV64cVlZWlCxZEkNDQ44ePYqnpydhYWGE\nh4eTI0eOLz6v8ZdIQEAARYsW1Sn71HQm69atw8LCAg8PD51VThcXFxwdHTl48KBGRALkzp1bFZCZ\nCFVEfmaULFmSkiVL6tsMlc8UIQQXL14kNDSUAgUKULx4cX2blCbs2bMHgJ9//plx48axY8cOGjVq\nxJ49e/Dz82PkfG3dXI5QLJ+yenfy701cDN5D3nz5uZXFGwApWyNeW3z4q/FllKDvJO2xqTG8fhsn\n4qfZ8CJKMLq7rnvP8QuCxsOU1UFQ9rK1qQWHzyputfG8idYVkO1qw6IRYGqS+IA/Li6O1q1bs2mT\nViEXLjyVP7f8zaCZ9vz1Nn3E9qNQpD2M7CLo3SztBMTzl4IlO7THA1qlSbOfDfFbDBo0aMC///4L\nQLZs2diwYQPZsmVLVZvHjh3D19cXQ0NDPD09CQ4O5ty5c/Ts2ZODBw9+kr3WFhI13D6pic+KESNG\nsG3bNrZu3crWrVsBsLe3Z/DgwXq27Mvin3/+oWHDhty9excAJycntm7dSrly5ZgzZw69e/dm5cqV\nAFhYWLBy5cqvJjXTl0TZsmUpV66cTtnHxhB4n5CQEF68eIGTk1Oi58PCwnSOCxQo8En9qaQt6l+x\nispXgizL9OrVi4ULF2rK+vTpw6xZsz77fbXxOSQfPHiAEIL79+9ryvefQiOmDLPAwQAomEsRUTdv\nulOx4gBuBt6H/FmRcvQHYNeVujx6JnC0TSi2fBbCDaV5sllB4O/QY7y2j7GL4fkrmDJQIEkSW48o\nieuj3ijnzU3hj/9B/YoSQghOX4EtR2Dr33D+uraf4Z1gbM+k3VCXLl3Kpk2bsLGxoXv37mzfvp2r\nV68yyW8oexctZfhcNAnnw8LBazr8tg7+11vQptanu7gu/VO5V4Ci+aB26hffPlsKFSrE+fPnCQwM\nJCYmBnd3d2xsbFLdXmBgIACenp4sXryYBw8ekCNHDk25SsopWbKkRpTfvHmTwoULM27cOHLnzq1v\n074YYmJiaN68OXfv3qVQoUIYGhpy5coVmjVrxvXr1+nRowdubm7s378fIyMjmjZtSv78+fVtdqZg\ndHeJ0d31bYV+kWUZOzs71q5dm+j5d934AczMzBKtp6IfVBGpovKVMHv2bBYuXIiJiQlVqlTh8OHD\nzJ07l1KlSmlSoHyI8PBwNm7cyLNnzyhTpgzVq1fPIKtTRrt27ZgxYwaLFi1iy5YtmqhuHTt66qxC\ndm2kFZAAefPm5cyZM8ybN4/QWyFsvRnJs1dWPImUGDQV1ozV7ef0FcH0d37rJg9Q2tsxWdDqFzR7\nA6evhZevwa2woP8UJdk7gIMNbJ8MZYsqNkiSRJmiUKYojO0F/90VHDgNBZyhlnvyAu/06dMAeHt7\nM3z4cFq2bEmlSpUIDg7G0FBi0gCoXFIweLoSfAfgv3tK4vnJq2B8X0HtsqkTku+n9ejfMnOl9chI\nTExM0ixRfLwADQ4O5sGDB5pVdmtr6zRp/2vj22+/ZePGjclXVEkV//77L6GhoTg5OXHhwgWyZMnC\nN998w40bNzh//jzlypXDzc0NN7evaAlcJQEf+m0oWLAg+/bto3z58mTNmjWDrVL5VD7v5QcVFZUU\ns3u3sokvICCAffv2MW3aNEDrCvohbty4QalSpejevTs//vgjNWrUwNvbO93t/RjKlSvHmjVrsLGx\n4cmTJxgaGjJq1CjylOrPSSWQMSbGMKpLwmudnJz49ddfWbxgBqv/p91jvO4AbD6sTZMRGyvoNUEr\nCL8rA50bKO/NTSU2+UOLd7T171ug7yRt/YLOcHSeVkAmRgFniR5NpBQJSFBc8wD27t3LjRs32LBB\nUXV2dnaaOs2qSVxZDZMHKiun8QRfBY/BUO8HweGz4qNTlewLgqu3lPdWWaFTvaTrZxZev37N6tWr\nmTRpEtu2bUOO/w/KJDRr1ozcuXNz7tw5cuTIQefOnQEYNGiQni1TUUlIvBdIVFQUkZGRvHjxgpcv\nX+qcU1HJmjWrJtDSu7Rr1w5ZlhkzZkyCc3FxcYSHh2eEeSqpRBWReuD58+d07twZS0tLLCws6Nix\nIxEREfo2S+ULJ/4HPd7V812Xz6To06cPN2/epESJEvTo0QNjY2MmTZrEgQMHkrwuo2nVqhWPHj3i\n5s2bREREMHq0Lz4LtOf7NINcjkmLM4/yEl0aaI/7TYZnkYq4mrYWzoQo5abGMGeY7uyqibHEmjFK\nHr/3KVNEEZCFcqXtSl337t2xtbXl4MGD5M+fnylTpgAwdOhQnXqmJhJD2klcWwc/fw9mJtpze04q\nyedLfg+zNggiX6ZMTAas177v2jD5dBiZgYiICKpWrUqHDh3w9vamSZMmtG7dmri4OH2bpiH+/7NG\njRqYmZmRPXt2/Pz8+Pnnn/VtmopKAgoWLEi5cuWIjIwkT548ODs7ExYWhqurK66urvo2TyWTULZs\nWSIiIhg8eDCrVq1izZo1AFStWpX+/fszadIk6tevz7Rp05g9ezZDhgyhQIECmr3MKpkUkUGEh4dr\nXl8zsiyLBg0aCEDnVadOHSHLspBlWSxfvlx06tRJ9OjRQxw4cEDfJmcoQUFBIigoSN9mfJFs2LBB\n87zZ29tr3m/bti3J62xsbAQgQkNDhRBC9OnTRwDC398/A6xOnJQ8J2v2ykKqpLyy1pLFw6dyitp+\nGiGLHI2113bzk8X1O7Iwr6ktG7/8w23Fxcmiz0Rt3fpDZPH8Zcr6Tg3nz58X1atXF/b29sLV1VWs\nX78+2WvuPJJFD39ZZKmitTP+ZfGdLHpPkMXZkA/bfO22LAwqK/UNKsvi39vpd3+fwvvPyaBBgwQg\ncuXKJfr16yesra0FIGbPnq1HK1X0SUb95kRHR4sxY8aIqlWritq1a4ulS5cKWc6cfzcfy927d0Xl\nypU1vyllypQRN27c0LdZaUpKx7BRUVEZZFHGsXjxYmFgYCACAwMTnAsNDRWSJImlS5cmqH/z5k1N\n2atXr0Tnzp2FnZ2dMDAwEAYGBjrtLFq0SJQrV06Ym5sLKysr4erqKoYNGyZu376tqZMvXz5Rv379\ndLhDlaRI6plWRWQGc/36dQEIMzMzce7cOXHx4kVhYWEhAHHlyhXxww8/6IhLSZLEsmXL9G12hqGK\nyPTlt99+E6ampppnMCWD53z58mkG2vfu3RPu7u4CEHPmzBFxcXHCz89P5M+fXzg5OYk2bdqIR48e\npft9JPecxMTIwqWtVhgNn/Nxg7UNB3WFVdH22velOskiOibp9mRZFjuPyWLtvuTr6pPLNxTBa/ld\nQjEpVZJF+R6y6DVBFv9bIotlf8rirzOyCL0ni0HTtHUaDs2c9yfLsjh48KA4efKkpqx8+fICELt2\n7RJCCDFt2jQBiC5dumiuOXfunNi/f7948OCBXuxWyVgy4jdHlmXRunXrBJPH48ePT9d+MxJZlsX9\n+/fFvXv3vhhx/C5fs4hU+bpRRWQmIjg4WAAif/78mpXHb775RgBizZo1AhCGhoZiwoQJmllzS0tL\nER0drW/TMwRVRKY/UVFR4saNG+L169cpqj99+vQEg58cOXKIsLAw8csvvyQ4V6pUqRS3nVqSe04W\nbdeKHBsPWTyN+PhBTetfEoqqLFVkEXTpyxsgRbyQxawNsijRMXExmdTrz+OZ7/NYs2aNZrXd0tJS\nLFy4UAghRN26dQUghgwZIp48eSKaNWsmADF48GDx4sULHS8RIyMjMX/+fD3fiUp6kxG/OadOnRKA\nMDc3F2vXrhVTp04VgDAxMUn370qVtEEVkSpfK0k90+qeyBQSExPDkydPPjr4xPu4uLhga2tLaGgo\n9erV0+QXs7Ky0gR4qFmzJt7e3vz222/Y2try/PlzHjx4kEzLKiopw9TUlLx582JiYpJ8ZZSAHlOn\nTiVXrlyYm5tTvXp1Dh06hK2tLVOnTgVgzZo1nD9/nly5cnH27Fn279+fnreQJNExgjGLtMdD2yuJ\n1j+WgCG6gWgABrWGMkkExvlcscoq0a+FxLnlcGiWkp/SKAWxuwvnBo9yydfLSA4dOkT79u15/Pgx\nWbJk4fnz53Tv3p1t27ZpgtNMnToVOzs7Nm/ejJmZGT179sTb25udO3diYWFBmTJliImJoXfv3mpq\nDZVP5vZtJflr5cqVadOmDYMHD8bW1pY3b94kyIOnoqKi8rmgishkEELg4+ODpaUl9vb25M6dm337\n9qW6PXNzc1atWoW5uTl79uxh165dmJmZsXLlSlxcXAA4evQoa9asYcqUKTx79gwTExMcHBzS6pZU\n0gkhBPM2CwZMEUxdI9h+VBBySxAT+2kTD/pGkiR++OEHbt++zcuXLzl06BCFCxcmKiqKqKgosmTJ\nQvPmzSlRogTu7u4AmhQb+mDBNrj5ds7F3ga8WqeuHadsEtO8tMd5s8OYHp9uX1K8efOGixcvEhoa\n+skTVqlBkiSqlZJY5StxezNsGg+/DVaEeJtaUKE45LQHSVKC80zz+vRck2nNkiVLEEIwYMAAjh8/\nTrdu3QBYuHAhDRo0YN26dXzzzTeYmZlRqlQp9u7dS7FixdixYwcAf/75J0FBQXTr1g0hBLt27dLn\n7ah8ARQuXBiAgwcPMn78eAYOHMizZ8+wsrL6YJJ1FRUVlcyOmicyGaZPn64JPWxqasrdu3dp0qQJ\nwcHBFClSJFVt1qtXjwsXLrBnzx6EEHh4eFCgQAGEELRt25a1a9fSvn17Tf2xY8diamqa6nsIDQ1l\nxIgRXL16ldy5c/Prr79qBvtfOkGXBWv2QdOqUK1Uyge7L14JrtwEN5eUD5KnrAbvWQnLs2SBAjkF\nhXND2aLKapaNZeYaeKcGCwsLChcuTEjINarW7U+uPAXZum0nAKVLl9aLTa9eC8Yt0R7/5AmWWVP/\nWXvWhbBwOH4eRndP3wikx48fp1WrVty7dw+A7777jnXr1pEtW7Z06zMpHG0lmlZN/Fx0jMBAAkPD\nzPccv3r1CoCiRYsiSRL58uXTKW/dujWtWyecWciSJQsAkZGRCCF4/vy5TnlmQZZlNm3axPnz53Fy\ncqJ9+/aa3JIqmZNixYoxZMgQpk6dyvDhwwFlwmbWrFlqGgwVFZXPl/T3plX4XPdEurq6CkAsWbJE\nxMXFafbQ+Pj4pEt/MTExYty4caJGjRrCw8NDLF++/JPau3PnjnB0dNTZs2ZqaipOnz6dRhanDeHh\n4ZrIXU5OTuLnn3/+pH2gsiyLKatlYVhV2bdlWFUW2/5O2d6t0HuyyNdCua6ptyxiUhAY5fh5WRhV\nTdkesuyNZLFyt/zZBh949VoWh4KVYCsVuj4VUvlwzb1R5r6o0D5IHDkri7i49Lu/xPYxxcbKwnuW\n9nPO2VgWr15/Hp9xWFiYyJYtm2a/qbm5uQBE06ZN9W3aZ8esWbM0+89q1qwpsmbNKgAxbty4JK8b\nMWKEAISBgYHImTOnAISxsbG4cOFCBlmePHFxcaJt27Y63+f58+cXd+7c0bdpny0ZtQ9flmWxcuVK\n0aVLF9GrVy/x119/pXufKmmHuidS5WtFDazzCcQHvfn777+FEEIMGTJEAOKnn37Ss2Up46effhKA\nqFSpkjhy5Iho2bKlAETLli31bZqG2NhYUa1atQQBWvr06aOps/uELPI2l0WFHrLYcjhpARb+XBYt\nhycUb+Y1ZXH8fNKi4l6YLAq11r2u5/ik+3sSodgWX790Z1n0nSSL2oNkkaf5h8Vk7UGyuHoz9SLn\naYQsflsni4On018oPXiiiMaKPWVhXC1lYjlPc1n8GCCL01fSXjC/P/DbdUIWrp66/c/a8HkISCGE\nWLdunSY0fkxMjLhx44YmOnNmGpTIsiwWLlwoypYtK4oWLSp69eolnj17pm+zdIiLixPff/+9zndJ\ns2bNkp2Uio6OFt27d9dcY2NjIzZt2pRBVqeMFStWCEBYWVmJH3/8URQvXlwAok2bNvo27bNFDeam\nkhJUEanytZLUM626syZDzZo1+ffff2nWrBnly5fX7I+pWbOmni1LGXfu3AGgU6dOVKlShejoaDZs\n2KApzwwEBQVx+PBhsmXLxowZM3jy5AleXl7MmzePCRMm8Pi5JW1GQeRLuPUQmv0MFUvAuN6CGm66\n7nTnrgla/QLX3rk9AwOQZYh6A4294e85Ape8Cd3wnkYK6v4A1+/qli/YCvlzwPBOCW0XQtBtnGIX\ngI0lbPSHfDm07b96Lbh2B4Iug88CuPdYKd9/Ckp2gp88BcO/VxLCp5SwZ4Lq/eHKTeW4o4fgtx8g\nWwoCyBy/IDjyD+R1gpruittiYgghCLwIszbAugMQE/vhNnPYKSPvB+9shbz9UHHxnbIaiuaDsT0F\nzasrblxpxYX/BMNmwu73Yp+UKQI9GqdZN+lOfFAtIyMjDAwMNEGPhDLRp0/TdJgxYwaDBw/WHF++\nfJmzZ89y5MgRjI2N9WiZFgMDA5YuXUrfvn3Zu3cvOXLkoHv37hgYJB0CwMjIiAULFjB+/HgeP35M\nvnz5PmkbQXpw+vRpAH744QdGjx5N+/btcXd3Jzg4WM+WqaioqKh8bagiMhkmTZrE5cuXOXLkiCbw\nwujRo6lbt66eLUsZRYsWBWDChAlER0ezdOlSnfLMQHwQlmLFiuHi4oIsy9ja2vLs2TMehoXT0c+S\nyJe61xy/ALUGQt3ygnG9wc1FYulOQb/JiliMZ0Ar6N0Uag6Ex+HwJALqD4Vj8wTZ7bRi5vlL9kmk\n3AAAIABJREFUQYOhcOE/5ThLFqjsCofPKse/zIM8ToKOdXUF0G/rYOvf2uNFI3QFJIC5qUTJQlCy\nELSpJfh1AQSsV4RtdAyMXQyr9sCsoQKP8skLrPDngnpDtAISYOUe2H8a5v8kaFQ58TbOXROMnA/b\nj+qWlyggqOkOtdyheikwMYa1+xTxePpq4jYUzQeVS0KVt6/8OZX7OfIPrN4HGw7C00ht/cs3oNUv\nUKM0TPMSfPvNpwnJxxGGzPszJ9sClX7jyWoGwzoogWCMjTLffr0PUb16daysrDh+/DhFihTR/E14\neHhgZmamZ+sUhBCa/eFTp06lTJkytG3blpMnT7J7924aN848ql2SJCpWrKjZb5acgHwXe3t77O3t\n08u0TyLern379tGpUyf++OMPAOzs7PRploqKiorKV4gkMmiaOyIiQvPe2to6I7pMM2JjYzly5AgP\nHz7E1dWV4sWL69ukFPPixQuqVq3K2bNnNWW5cuXixIkTODs769EyLbdv36ZAgQLExsbSsGFDwsPD\nOXr0KE5OTrT96S4B65UBoJEhdKyrCK7oGN023F10BU9WM/j9Z2hXWxESJy8Jag2EV6+V86ULw8GZ\nSmqD128EjYbBgdPa65f9qkSjrD8EDr6d5DcyhF1Toaa70mbQZUGVPtoVukGtYfrglAmXMyGCfpMg\n8JJu+aDWMKEfmBgn3s7LKGW19Nj5D7fdub4SNTM+eM9/dwU+C2DVXkjur93AALKawvNXCc9VLAF9\nmkO98uDwgdXLeKJjBPuCYO1+2PQXvIjSnpMk6N4Y/tfrw6ugSbFqj6CnfxxR0dqAJwYG0LWhEj01\nh/3nIx7fZf/+/bRp04anT58CUK5cObZs2UL27Nn1bJlCdHS0ZoX0zZs3GBsb06FDB1avXs38+fPp\n2bNnhtsUFxfHo0ePsLW1TXTV8NSpUwCUKVMmo01LF+7du8e3337L48ePdcr/+OMPWrVqpSerPm++\ntGdEJX1I6Rj29evXmc6DQUXlU0jqmVZF5FfAy5cvmTlzpiY6a//+/XF0dNS3WTrMmzePvn37alz3\nzM3N8R5/FN8132rqTB0Eg9tK3Hwg8F0Iy3bprkLFUywf/DEOiubTFRM7jgma/Qxxccpx7TKweQJ0\n8NFdTZw5FPq1UK4Nf64IxUs3lHPWFvD3HHB2ALeucOO+Ul6mCPw998OrX7t372b9+vXExcXRqFEj\nWrRogSwLft8Kw+dC+HNtXXcXWDMGCubSbev1G0ETb9h3Slu2YDjYW0PvifDwqbbc2QGmDFRWUudv\ngdg47TlJUqLVPomAExeTdlM1MYb2daB/C3Avkjpx9jRSMHohzNmk/ewBrLLCyC4wsNWHRfP7LN4h\n6OGvK4brloeJ/cG14OcpHt/l+fPnXLhwAXNzc1xdXT9qBS0jcHFxISQkhMaNG/Ptt98yadIk3rx5\nw7Fjx6hYsWKG2rJ9+3a6du3K48ePMTIywtvbm7Fjx+q4S3+JAuHKlSsMGDCAc+fO4eTkxMiRI2nb\ntq2+zfps+RKfEZW0RxWRKl8rqohU+SwICgpiyZIlGBoa0rzdD7TwzasRV02rKnsN3x0gXgoV/Po7\nbPxL20aHOjDX+8OpGBZtV0RIPDnttXsUAcb1huGddK+99UBQsRfcf7vfL48TlCgAO48rx1ZZIXgx\nFHBOvM9Zs2YxYMAAnbKxY8cycuRIAB4+FfSZCFuOaM9bmisrqW2+U9qMjRW0GQWbD2vrTPMCrzbK\n+ScRAq9pympjUjSuDP/rrRVcL6MER8/BgWA4eFpZzZVlyJdDWXXs3gjsrNNGnF2+IRgaALtO6JYX\nygWLf4HKJZPu5/etgt4TtMd5HF8z72dT6qbABVglbThy5Aj16tXTpMsAGDhwIDNmzMhQO/755x/K\nli1LTEwMVlZWREYqvtPTp0/Hy0ub3DMzCITQ0FD27duHJEl4eHiQJ08evdmikpDM8IyoZH5UEany\ntZLpRGTWrFkxNFS3Y6ok5NSpU8TESgxZ6KZx9czjBMFLPhw0JuiyYNUeKF8c2n6XfOCWsYsV9873\n8faE8X0Tv/ZMiKBaP3gZlfDcH/+DljUTvy4yMhJHR0fevHmDt7c35ubmjB49GkmSuHXrFrly5QKU\n/WYB62HYTN2VwV5NlRXFvpNgxW5tuW8PGNU1YZ8bDwn6TlJyG75L1W/Br0/yQi38uSAsHArkhCxZ\n0kec7TymiMmrt7RlBgZKTkefbomv5s7dpOx3jaew8ytm9g+hdnX95KP8mrl69SorVqzgxYsXVKlS\nhRYtWqRpsKSUMGLECPz9/WnXrh2rVq1i6dKldO3aldKlS+sEmdG3QNi+fTtt2rQhKkr54rCwsGDj\nxo3UqVNHL/aoJETfz4jK54EqIlW+VpJ6pvXiK+Xp6ZmpIg6qZC5mb8+pEZCGWRTXzqSijpYtKjHN\nS6JdbSlFg9mRXaBnU92y3s3Av8+HryldWGLdWCXgzrv0a/FhAQlw8+ZN3rx5Q4ECBZgwYQI+Pj6U\nKVMGIQTXrl3T1JMkiUGtJY7OVQRcPPO3QN4WugJyaHvlHhKjRQ2JCyvixbSy93PHZDg0K3kBCco+\nym9yS+kmIAEaVJI4t1xZSbXKqpTJMvgvg0q9lRXLd5m1QVdAurvArP4h2GSNQyV9ePz4MTNmzODX\nX39ly5YtOt/XLi4ujB07lmnTptGyZcsMF5Cg7MkEyJ07N5IkaVb34sszA5GRkXTs2JGoqCg8PDyo\nVasWL168oH379hpRqaKiopLZWbJkCQYGBhgYGPD3338nWqdQoUIYGBh8NpkLvlSOHTuGr6+vzqRH\neqIXEbl27VrOnDmjj65VMjlHLliz8qA2kMi43lChRNoOUiVJYtYQJQANKAJy1tDkVzDrV5SY/aP2\nuHRhmDzgw/UBnJ2dMTAw4L///mPevHksX75cE+QoMbe2MkUlTi+G1rW0Ze9GOe3ZVNn/l5StDrYS\nq8dIvNgPpxdL1K+YMnGdkRgZSni1kTi3DGq6acuDr4J7V5i5Xklt8ds6wcCp2vPlisHe38BaFZCf\nzJEjR6hTpw7FihWjZcuWmkmN//77j1KlSuHl5cXYsWNp1qwZ3bt3z1QTf7Vr1wZgypQp1KlThxYt\nWgBkqhW+S5cuERkZiYuLC7t27WLv3r3kyZOHJ0+eEBISom/zVFRUVD4KMzMzVq1alaD8xIkT/Pff\nf5iamma6scbXxlchIkFZoVFRiUeWBX8eF/iuzKcpa1BRWXVLDwwNJRaPlIg9AnOGSRgYpOyLr2cT\niY3+MKor7J6WfG7HbNmy4e3tDUCfPn3o1KkTsbGx9OzZkwIFCiR6jbWFxJoxMGeYEtgmng51YHYK\nxG48Zh+Rd1Jf5Mkusfc3mDwQjJVsDLyOhkHTwK0L/PCbtm6F4spnHh91ViX1HD16lO+++459+/Zx\n+fJlNm7cSKVKlbh79y79+/fn7t27uLm5MXToULJmzcrixYvZunWrvs3WUL9+fcaMGYMsy+zbt4+I\niAg8PDzw8/PTt2kaLC0tASWi6rVr17hy5QphYWGAGhdARUXl86N+/fr88ccfxMbqRuNbtWoVRYoU\noWDBgnqyLG14+fJl8pU+EzJq0ldvIvKbb77RV9cqmYiXUYI5mwTFO0LDHyHylbJX1tkBlowkxeIu\ntaSm/WbVJHx7SNjbpOxaPz8/5syZQ61atahRowaTJ09mzpw5SV4jSRK9m0mcmK+smI7pCYtHpt8+\nRX1iYCAxpJ1E0EIll2Y8/2i9falcEnZNUwS2yqfj5+dHTEwMnp6eBAUFUalSJcLCwpgzZ45mT+Ha\ntWuZPHkyvXv3Bsh03iOjRo3i6tWrbNy4kWPHjvHnn39ibm6ub7M0FCtWjJo1a/L8+XMKFy5M8eLF\niYqKon79+uTNm1ff5qmoqKh8FO3bt+fp06fs3q3dXxMXF8e6devo2LFjgvpCCAICAnB1dcXMzAwn\nJyd69OihyYMcz9atW2ncuDG5c+fG1NSUfPny4e3tnWB7wsOHD+nRo4emXvbs2WnQoAGXLmlzpRkY\nGODr65vAlnz58tG1a1fNcbyL7sGDBxk0aBBOTk6aiT9QAj02aNAAGxsbzM3NqVq1KocOHdJpc/To\n0RgYGHDlyhU8PT2xsbHBwcGBX375BVDS1zVt2hRra2uyZ8/O5MmTeZ83b97g6+vLN998g6mpKbly\n5WLIkCEJtjwYGBjQt29fNm/eTIkSJTA1NaVEiRI6/xejR4/WLFrkz59f44J8+LASkTE4OJgGDRrg\n6OiImZkZ+fLlo1OnTrx+/TqBXSlFL9FtBg0aRIkSJfTR9WfPxf8EI+aCS17F1dPI8PMcVN96IJi5\nARZs001vAWBmHMeaMVlSLNIyO5Ik0adPH/r0SWLT5Qf49huJxSPTwahMiGtBicDfBaN+hymrtWk8\nqpWC7ZM+HHFX5cPs2bOHH374gevXr5M/f34mT55Mw4YNuX9fyU3Ts2dPypQpQ9u2bTl27Bj379/H\n3t6eR48esXr1atq2bcvBgweBzJnQvnDhwhQuXFjfZiSKJEls2LCBvn37smXLFiRJomXLlsyaNUt1\n+VJRUUkxQgju379PbGwsuXLl0lvqp1y5clG1alVWrVpFw4YNAdi3bx+PHj2iffv2rF69Wqd+3759\nWbRoEV26dGHQoEHcunWLgIAATp48SVBQkCbv8JIlSzAzM8PLywtra2uOHz/OtGnTuH37tk6brVq1\n4sKFCwwcOJD8+fPz6NEjDh8+zL///kuxYsU09RL7fpWkxLf1DBw4kGzZsjFq1CiNC+hff/1F3bp1\ncXNzw8fHB0NDQ5YvX46Hhwd79+6levXqOm20b9+eokWLMmHCBHbs2IG/vz/W1tYsWLCA2rVrM3Hi\nRFasWIG3tzfu7u6afaNCCJo3b87hw4fp1asXxYoV49KlS8yePZuLFy/qCESA48ePs23bNvr164eF\nhQUzZsygZcuW3Lp1i2zZstGyZUv+/fdfVq9ezfTp07G3twegaNGihIWFUadOHRwdHfnpp5+wtbXl\n1q1bbNu2jVevXqU+GJTIIMLDwzUvWZYzqtsvipv3ZZGjsSykSsqrg48sYmM/r88yOkYW3fxkYVhV\nex/xL+s6sugw4r7YsusffZv5VXL8+HHRuHFj4e7uLjp16iTu3LnzyW2ePXtW+Pj4iJEjR4qjR4+m\n+LpDwbJoOFQW/SfL4sWrhM94UFCQCAoK+mT7vmROnDghDA0NBaB5GRgYiMOHD4vvv/9eAKJ06dJi\n4sSJwtnZWQBiypQpYsmSJTrXACJXrlwiLCxM37f00WSW50SWZfV3L5OSWZ4RlczNu2PYpIiKikrT\nfh88eCCqVaum+S4uUaKEuHr1apr2kRyLFy8WkiSJwMBAMW/ePJE1a1bx6tUrIYQQ33//vahYsaIQ\nQojixYuLmjVrCiGEOHr0qJAkSaxYsUKnrb///ltIkiTmz5+vKYtv6138/PyEgYGBuH37thBCiGfP\nnglJksSUKVOStFWSJOHr65ugPF++fKJr164J7qlChQoiLi5OUy7LsnBxcRF16tTRuT46OloUL15c\nVKpUSVPm4+MjJEkSPXr00JTFxcWJ3LlzC0mShJ+fn6Y8PDxcmJubC09PT03ZypUrNb/J77Jy5Uoh\nSZLYs2ePzn2ZmJiI69eva8rOnTsnJEkSM2fO1JRNmjRJSJIkbt68qdPm5s2bhSRJ4vTp04l8akmT\n1DOtl+kMdRb244l8KWg0DB684wWwei8MmJpxvs9pwfjlsHi7btL5gs7w22C4vQl+aH6HnHbR+jPw\nK+XYsWNUq1aNbdu2cfr0aZYtW0bFihU1e7hSw4YNGyhbtiy+vr7873//o0qVKsydOzdF11YvLbF9\nssTMoRJZzdTvi9QwZ84cYmNj6dSpE+Hh4fTs2RNZlpk1axb+/v7kzp2bM2fO4O3tzd27d6lUqRL9\n+vWjc+fOLFmyhOLFi5M9e3bq16/PX3/9pZnVVPl4PjQLrqKiovIhhBC0adOGw4cPY2pqiqWlJRcu\nXKBBgwZ6i0TdunVrYmJi2Lx5M1FRUWzevDlRV9Z169ZhYWGBh4cHjx8/1rxcXFxwdHTUeLiAErAH\nQJZlIiIiePz4MZUrV0YIodlGYWZmhrGxMQcPHuTZs2dpdj89e/bUWdn9559/CAkJoX379jp2R0RE\nULt2bQIDAxO4f/bo0UPz3sDAAHd3dyRJonv37ppya2trXFxcCA0N1fmMChcuTLFixXT6qlatGpIk\n6XxGADVr1tSJpeHq6oqVlZVOmx/CxsYGgG3btiXY0/op6G1PJCi+wD/++CMFCxakUKFCifpAqyiJ\n5tuOggv/JTw3bzMMT2Zc/iZaMHaxwNVTMHi6IPKlfkRnXJzg93dic1QrBVsmwJXVMLC1hGVWdZCl\nL3x9fYmJiaFDhw4cOnSI0qVLc/v2bebPn5+q9qKioujWrRsxMTG0b9+eXr16IYRg4MCBPHjwII2t\nV0mM8HAlWWjNmjWxtramVi0l5G9ERATOzs6cPn2acePG0a9fP2bMmMGBAwc0Li2dO3fmwoUL3L9/\nn507d34wCJSKioqKSvpw//59Dh8+jJmZGaGhody7d488efJw/fp1goKC9GKTra0tdevWZcWKFWzd\nupWoqCjatm2boF5ISAgvXrzAyckJR0dHndejR490JqjjhbGlpSW2trY4OjpSo0YNQJuf08TEhAkT\nJrBr1y6cnJyoWrUq/v7+3Llz55Pu5/1gQPGRs7t3757A7hkzZiCESLCn8/1I+9bW1hgZGeHo6KhT\nbmVlpSOAQ0JCuHr1Kg4ODjr9xLf3/iR+YhH9bW1tUySqq1evTqtWrfD19cXOzo4mTZqwYMECXr16\nley1SaGXPZHxdO7cmbVr12qOJ02axJ07dxINIfy1IoRgwFTYHagtWzQCDpzW5g6cuAKsswqGd0oo\nwk5cEPTwh0s3lOOLobDpMMz5UdCgUsaKtl2BcOeR8t7BBvZMTzyxvErGE/9F7OXlRbly5ejQoQNn\nzpzh7t27qWrv5s2bREZG4uzszMqVK5EkieDgYE6dOsWlS5fInj178o2ofBLly5dny5YtDBs2jJMn\nT7JhwwYAypUrB4CDgwMjRozQp4kqKioqKh8gJiYGACMjIywtLTE1NdUED0vL1aSPpUOHDnTq1InI\nyEjq1KmTqJeKLMvY2dnpjPHfxdbWFlBEYs2aNbG0tMTPz49ChQphZmbGnTt36NKlC7Isa67x8vKi\nadOmbNmyhb179zJ27Fj8/PzYvn17gn2K7/Ohzyt+FfRduwEmTJiAu7t7ote8f79Z3k8gzoc9Lt/1\nHJRlmeLFi/Pbb78lWjdnzpw6x4n1836bSbFu3TqCgoLYvn07e/fupVevXvj7+3PixAkcHBxS1Mb7\n6E1EhoaGsnbtWoyNjdmxYwdCCBo2bMjq1avx9/dXo9e9ZeoaJeF8PKO6QpeGEh3rCp6/gi1HlPJf\n5oG1haBfC+XBffFK8Mt8mLleG6AkntsPodEw8KwrmOYFdtYZI+R+f+c+OjdQBWRmokiRIly6dIkh\nQ4bQrl07zZeai4tLqtqL/5K9d+8eW7duxcrKShNB7f3ZOZX0YciQIRw6dIg9e/ZoogHXqFGDn3/+\nWc+WqaioqKgkR+7cuTXBVooXL465uTlXrlzB3t4eNze35BtIJ5o2bYqJiQnHjh1j6dKlidYpWLAg\n+/bto3z58mTNmvWDbR08eJAnT56wceNGqlatqinfu3dvovXz5cuHl5cXXl5e3L17l1KlSjFu3DiN\niLS1tdV44cQTHR2tCSaXHPErkxYWFhrvnfSiUKFCnD59Ok37SW7bRNmyZTXbjHbt2kWDBg34/fff\nUz2hrDd31vhl2gIFClC7dm3q1KlD/vz5dc597Ww8JPCepT3uUAdGv3WxNjKUWO0L35XRnh8wBVbs\nFuwOFLh+DwF/aAVkVjP4oR3Y22jrr9gNxTrAuv0i3fdV3g0TbD+mPe7ROF27U/lIJkyYgIODA0eP\nHmXgwIHcuXOHChUqaNI7fCz29vb07t0bIQTNmjWjVq1avHr1isaNG1O8ePE0tl4lMUxMTNi5cycb\nN25k0qRJrF+/nj179iSYeVVRUVFRyXwYGBiwceNGChQowM2bN7l8+TL29vZs3rwZKysrvdllZmbG\nnDlz8PHxoVmzZonWadeuHbIsM2bMmATn4uLiNEIvfnXt3RVHWZaZOnWqzjVRUVEJ0l44Ozvj4OCg\ncXkFRQT+9ddfOvXmz5+v035SlClThkKFCjF16lRevHiR4HxK9UlK9sC3bduWhw8fJpry7c2bN4n2\nnxzxgv3p06c65eHh4QnG+aVLlwbQ+fw+Fr2tRBYuXBhTU1OuXLlC586dEUIQEhKCmZmZmkMSOHlJ\n8P0YrQisUhIWDNd9ME1NJDb5C+p4QeDbNDmdxyZceaxbHuZ6Q97sEsO/FwyeDqveTvKEhUO7X2HN\nPpgzTOCULX1WBxdth/i/4ZpuUDiPugqZmShUqBDBwcHMnj2b+/fvU6xYMQYMGJD6sM/AzJkzcXJy\nYu3atcTFxdGwYUP8/f3VACMZSJYsWWjevLm+zVBRUVFRSQUuLi5cvHiRkydPEhcXh7u7u14FZDye\nnp6JlscLlapVq9K/f38mTZrEuXPn8PDwwMTEhGvXrrFhwwbGjh1Lp06dqFKlCnZ2dnTu3JmBAwdi\naGjI+vXrefnypU67V69epVatWrRp04ZixYppJkmvXLnClClTNPV69OhBnz59aNWqFbVr1+aff/5h\nz5492Nvbp2ixRJIkFi5cSL169ShWrBjdunXD2dmZe/fuacTpgQMHkm3nQ329W+7p6cn69evp378/\nf/31lyaY0NWrV/njjz9Yv3491apV+6h+ypYtC8Dw4cNp3749xsbGfPfdd6xcuZJZs2bRokULChQo\nQFRUFIsXL8bQ0JBWrVolez8fQm8i0sbGht9//50uXbqwbNkyQBnwLFiwAGtra32Z9dGsW7eOgIAA\nIiIiqFixIuPHj9f4eqeW0HuCpj9B1NsYQ4VywUZ/RTS+j4W5xI4pgpoD4Px1XQFpZw3TvKCjh1Z8\n2ttIrBgN7eoI+k6Cu28nVTYfVtxcAxcIDAzSdpAfFydYtF173LNpmjavkkbkypULPz+/NGvP0NAQ\nX1/fRBP/fumEhYWxd+9eYmNjqV69uuqer6KioqKSKkxNTZMVE+lNSiZ/349CHRAQgJubG3PnzmXk\nyJEYGhqSN29e2rZtq3HhtLW1ZceOHQwdOhQfHx8sLS1p2bIlffr0oWTJkpq28uTJg6enJ/v372fV\nqlVIkoSLi4smD2U8PXv2JDQ0lIULF7Jr1y6qVavG3r17+e677xLcw4fuqWrVqpw4cYKxY8cye/Zs\nIiMjyZEjB2XLltWJxPqhqNspLZckiY0bNzJ9+nSWLl3Kli1bMDMzo2DBgvTv3x9XV9dkPvGE9+Du\n7o6/vz+zZ8+mW7duCCE4ePAgNWrU4NSpU6xbt44HDx5gZWWFm5sbs2bN0gjP1CCJDMoP8e5y6bsi\n8fTp02zbtg1JkmjcuLFe/bw/lsWLF9OtWzedstKlS3Ps2LFUr+DcuK8IwptvA1hms4Lj8+Gb3En/\nAT94IqjWD669DVTVvo4iIB1tP3xdxAvBT7N191xun8QnBdwRQrBo0SIWL15MVFQUtWrVokqj/9F8\nhDGgCNs7m8HEOPE+Tp06BSguBSkhJCSEfv36ERwcjIODAz/99FOC/xOVL4+PfU4ykhMnTtCoUSNN\nBDczMzNWr15N06bq7ElGk5mfE5XMgfqMqKSED41h3+f169ef5MGjopLZSOqZ1mt0VlBUs5ub22fp\n4jZ69GgAfHx8qFWrFt9//z1nzpxhy5YtiYY8To6bDwS1BmoFpImxsgKZnIAEyG4ncXy+YPkuKF1Y\nybOXHNYWEnO9wdxUMP1tAK3pa6FBpY82XcPEiRN1AncEBwezPLApUBlQAup8SEB+LI8ePaJ69eqa\nlBHPnj2je/fuGBgY6MxMZXYCAwPZvXs3RkZGNG/enCJFiujbJJVUEhsbS9u2bXny5AnlypXD0tKS\n/fv34+npyY0bN7Czs9O3iSoqKm+Jjo7myJEjmhD5qpBUUVFRSTl6C6zz+o1g4yFBm5GCrLXAxkMw\nNEBwN0w/OQxTw7179wAlCmK1atXw8PAASHEUqHe59VZA3nh7qYkxbPKHaqVSLrjsrCUGt5VSJCDf\nxasNxOda3XcKzl1L3f9BbGysxnUxICCAP//8Eyt7Fx7GltfU6ZmGAXVWrVrFgwcPKFeuHDdu3NC4\nYr7rH5/ZmTt3LhUrVsTHx4cRI0ZQunRpdu7cqW+zMoQHDx6wfv16Nm/enKbJg/XJrVu3uHXrFnZ2\ndvz999/s3buXUqVK8eLFC86ePatv81S+YrZv3863336Lra0tFSpUIDAwMPmLvmCePXtG5cqVGTJk\nCGPHjqVs2bL89NNP+jZLRUVF5bNBLyKym58ge2No9QusPwivoyHyJUxbAwVbQ8/xgn9vZ34xGR9l\nskOHDowbN47Vq1cDUKxYsY9q5/ZDQc2BEKpoUoyNYKMf1KuQMauzebNLtKqhPZ6eeFqfZAkPDycq\nKgozMzP69+9PvXr1yPntCCRJWfCuVgpc8qbdPcVHn6pWrRp58+bVBBB5PxFsZuXu3bsMHDgQIQTd\nu3enWbNmvH79mk6dOhEdHa1v89KVPXv2ULhwYVq3bk3z5s0pWrQowcHB+jbrk4mPjBYZGcm1a9d4\n8OCBZrLJwsJCn6apfMXs37+fJk2acO7cOcLDwwkMDKRWrVpcvnxZ36bpjaFDh3Lq1CkcHByoXbs2\nRkZGTJw4kR07dujbNBUVFZXPAr2IyCU7FNGYGNExsHAbFO0A7X8VnA3JvGJyzpw5ZM2alR07djBy\n5EhevnxJp06dqFOnTorbuP1Q2QP5voCsXzFj3Xt/aKd9v3IP3H/88Z+7nZ0djo6OREWkhTcqAAAg\nAElEQVRF0blzZ0aP9uVqeBXN+Z5N0sJSLfGJYGfPno2Xl5fGhfhDCWIzG+fPnyc2NpZKlSqxYMEC\nNm7ciIODA0+ePOHOnTv6Ni/dCA8Pp02bNjx//pwKFSpQsmRJHj58SKtWrfSaQDktcHJyolmzZsTE\nxFCsWDFy5szJo0ePcHNz+2yeS5Uvj+nTpyOEoG/fvty5c4cmTZrw6tUr5s6dq2/T9Mbhw4cBZQuG\nv78/gwcP1ilXUVFRUUmaZEWkv78/ZcuWxdraGkdHR5o0acLFixd16owaNYqiRYtiYWFBtmzZqF27\nNsePH0+284LOMLILXFgB2yZBpXcCEckyrN0Pbl2h42hBdEzmE5MVK1YkODiY4cOH069fP5YtW8aS\nJUtSvL/zziPFhfW/twLSyBA2+H1aYJvUUr64RMUSyvuYWJi98ePbkCSJBQsWYGRkxPLly/GdfhRM\nlNyftpbQskba2QvQpEkTevTowatXr5gxYwbnzp0jb968zJw5M207SiccHBwAuHjxIoGBgezcuZOw\nsDAkSfqkCL9xcXGsWrWKkSNHMnfuXJ4/f55WJqcJZ86cISIighIlSnDs2DGCgoLIli0boaGh3Lp1\nS9/mfTLLli2jY8eOGBoaYmBgQL169dixYweGhnrfgq7ylRLvtdG4cWOcnZ01Wy/ezyX2NRHvNRAS\nEkJMTIxmXJNUYnQVFRUVFS3JRmetV68e7du3p2zZssiyzK+//srx48e5dOmSZqC7cuVKcubMSf78\n+Xn16hXTpk1j7dq1/Pvvvzg5OQG6ka1GL7GigweUKaIbnlYIwZF/wH8Z7H5vu8bE/vBjh88v+M6H\neD+aaryAbFRZf/e4/qCgzUjlvZ013NoEZomkFUmO4OBgVqxYwdYrnvwXoSQz9WoD07ySb+tjI+UJ\nIdi5cydnzpzB3t6etm3bfnKKlYxClmU8PDzYv3+/Tnnv3r1TvUIQGxtLkyZN+PPPPzVlLi4uHDly\nRCNa9c2JEyeoWLEi2bNn58KFC0RGRlK0aFHevHnDvXv3yJEjR7JtfA4RFePi4pBlGSMjI32b8tXy\nOTwnGcGgQYMICAggX758tGjRgmXLlvH48WOmT5+Ol5eXvs3TC7Nnz6Z///46ZRYWFpw5c4ZChQrp\nySqVzIoanVXlayXJZ1p8JC9evBBZsmQR27dv/2CdiIgIIUmS2LNnj6YsPDxc80oJpy7LovEwWUiV\nlFe+FrKIiZE/1txMSUyMLGr0196bcTVZbD2i/3uLiZFF/pZau+Zt/rBNe/fuFU3/396dx1VZ5v8f\nfx02WUQs4YA7brhQKqmMpWmM5mi5kJrLtFg6ORUaaX0rFU1zn2pmtLSflqktlmaFuYyTk4gyMFlq\nNq6ZS6iJqamEiMDh+v1xxqMnSY4lnAO8n4+Hj8e57/u6z/258SOez7mu+7r69DGdO3c2zzzzjMnJ\nyXE6fuxkkfG9/dJ77Tzg2v198cUX5osvvvhN91GeZGdnm+HDh5u6deuaBg0amKSkJJOfn/+r32/O\nnDkGMKGhoea5554zTZs2NYAZNmzYdYz6t8nPzzc333yzAYyXl5cBDGC6d+/u8ntUtjyRX0d5Ynf6\n9GnTunVrx7+1i//efsvvmvKuqKjIzJw50wQFBRnANGnSxGzatMndYYmHcvUz7Pnz58soIpGycbWc\nvubxVdnZ2RQVFf1ib09+fj7z58+nRo0av+kZoDbNLCydbKjfF06esS97sWIT9Isr+dzz589z6NAh\nQkNDPab35XLjX4fUbfbXFgssnQy9Orq/l9XHx8IT9xpGz7Zv/30p/KmXwcvLObaPP/6Yfv36Yf7X\niZ2amkpaWhopKSn4+dnXg1y0Bgpt9vYdW0KLBu6/P08UHBzMvHnzrtv7XZycZuzYsYwaNYo//OEP\nxMXFedSkNb6+vqxZs4b77rvP8fxRnz59WLhwoZsjE6mYqlevTnp6OkuXLiUzM5OmTZvSv39/vL29\n3R2a21gsFp555hni4uLIz8+nQ4cO7g5JKghjTLlctk7k58zVB6te+8Q6iYmJxMTEcOuttzrtX7Vq\nFcHBwQQEBPDSSy+xevVqbrzxxmt9eycBVSz8+bL1uWctK/mc5cuXEx4eTosWLbBarfz5z392TNax\nf/9+Bg4cSExMDL17975uH6yP/GD4crcp8YcNsDLNMPOdS9uT/gTxnTznl83QnhAcaH+95ztY+58r\n2zz77LMYYxgxYgQff/wxNWvWJD09nRUrVgBQWGh445NL7R/RGutlJjQ0FIA1a9Zw4MABli9f7rTf\nU9SpU4fU1FR++ukncnNzSU5OLjfDkEXKo4CAAB566CEmTJjAwIEDK3UBeTmLxUKVKlXcHYZUEH5+\nfuTl5bn0eVDEkxljyMvLc3QOFafEZyIvN3r0aJYtW0ZaWhqRkZFOx3Jzc8nKyuLkyZPMnz+flStX\nsnnzZurXrw84jyfft2+fyzdx4qwvfSbdRKHNXu8uemo3LerlFtt27969DBkyBJvNhtVq5cSJExhj\neOSRR+jduzcPPPAAZ86ccbSvUqUKCxYsoGnTpi7Hc7mvDwaxJCWcDV9Xp8hY6NDiDC88cIjgQFux\n7Y+e9OPBl5rz03l7B/Btzc/y1+HfOtZo9BR//7gOSzbYn2VtF5XNnATnv68OHTqQn5/P+vXrCQ4O\nZsaMGXz44YcMfXQ83rX+zIqMUE6ctSddcEAhq1/4Gn8//UK9VqdPn+all15i27ZtBAQE0K9fPwYP\nHnzVbziPHj3K/fffT05OjmOfxWJh9uzZtG/fvizCvi6MMfz000/4+fnp+RIREXGrJk2aOF5f7ZlI\nsM93UNGX6ZLKwc/PD6+rFCkuD2cdNWoUy5YtIyUl5YoCEiAwMJCGDRvSsGFDYmNjiYqKYtGiRTz/\n/PO/KvCLwkIK6Nr6NGu31ABgaaqVSQ8cKrbthg0bsNlsdO/enRdeeIGNGzfy9NNPs27dOnJzczlz\n5gytW7dmxIgRvPPOO2zYsIFFixYxffp0l+OxFUHq19V5NyWc/x5yXvft37uqM+TlZrw4bD+NauU5\nHbtQYGHMwoaOAjLihgtMfOCgxxWQAAM7/8D7qVaKjIUvvqnGN0cDiKp93nG8bt267N+/n+nTpxNz\nS1v+kWGg2ccs+roX5mvnG+r1u1MqIH+FCxcukJCQ4PSFy9/+9jfy8vIYOnToL55Xu3Zt5s+fz8sv\nv8zBgwexWq0MHz68XBWQ+/fvZ9y4cezfvx+LxcJdd93Fc889p2JSREQ8npeXl/6/kkrBpSIyMTGR\nDz74gJSUFKKiolx644szExbnWmfKeyHIsPZP9tf/+qoGb4yvQc3QK3tjkpOTAahfvz7t2rVzLG3g\n6+uLzWbvHUxISGDYsGHUrVuXDRs2cP78eZfiOXfe8OYq+5Dai0tyFOfISX+GzYpmwRgY2PVSjI/+\nxbDnsplYk/9ShdgWMa7cvlv032RYtt7+et1/W/DHPpfu5ZU5C+h93wzW7e3IulODsUQ2wIJ9toaL\nwm+EP/WCMQ+GE+gf4fJ1NZuiXXJyMvv27aNevXqsXLmSrVu38vDDD/Puu+8yZ86cq/ZGtm3blsGD\nB5dhtNfPmTNniI+P5+jRo/j5+ZGfn8/q1asJDw9nwYIFjnbKE3GF8kRKohwRV1w+mk5E7ErsB0tI\nSGDRokW8++67hISEkJWVRVZWFufOnQPgp59+Iikpic2bN5OZmcmWLVsYOnQo33//PQMGDLguQbZt\nbqFDS/vrgkJ47ePi2/Xo0QOLxcK8efNo27YtPXv2BODuu++mefPmgH3dy1deeYXnnnsOgGbNmpV4\n/dPZhtg/QeLfnQtIXx946C7Y/pZ9cpygAPv+3DwY/Dw8/aqhsNDw9lrD/BWXzvvrExDbwnOegyzO\nqEGXXi9ZB8kbDePnGzo9Zoif1glb0zVY6ozF4t/A6bzft7H/LL77CCYPtxDo79n36alOnjwJQPv2\n7WnZsiWDBtn/QrKzsyv0MJl//etfHD16lJtuuonTp0+zbZt9Bqq33nrL8WyziIiIiLhXiT2Rr732\nGhaLhS5dujjtnzhxIhMmTMDHx4ddu3axcOFCTp06RY0aNYiNjWXTpk1ER0dft0ATB8C/v7a//n/J\nMPZBg//P1jDs0KEDc+fOZeTIkWzZsgWwz/o4bdo0bDYbH330Edu3b+eJJ54AoF69ekyePPmq1zXG\nMHwm7D50ad+N1eDReyChL44e0ZsbQYtIQ9+xsO+wvd1f34PNO2HrN5fOHdQVHu/7638OZeV30RZu\nvcmQscNeuPcd88ttb6wGQ+6CP/eBqHoqGq+HmBh7L/VHH31EYmIiO3bsAKBFixYVehKIvDz7MPBa\ntWoRGBjoeKa6sLCQwsJCfHyueUJpEREREbnOrmlind/C1YVaf0lhoaHxAMg8bt9+YwwM7Vl8wZKV\nlcXu3buxWq20aNHCMfQvJyeHOXPm8M0331CvXj0ef/zxEpcAmZdseOzFS9vTH4MR/SAooPhrn/nJ\nMGQyrPz3lcea1YfNb0DVwPJRaC1PMQxIKv5YdAPoHANxt8Bdt9ln0r0eNLTokvHjxzNlyhTHdkhI\nCJ9++imxsbFujKp0HThwgObNm5Ofn0/nzp3JzMzk4MGDdOjQgbS0NEc75Ym4QnkiJVGOiCt+62dY\nkYqo3Hyt7+NjYUR/wzNz7NuzlsHDdxe/Fk9ERAQREc7P4R04alixKYh/ZD7Dl4dgQEMIrnb1a+44\nYBg169L2o/fAs/dfvViqHmzh4xmGqYth4gK4WKIH+sPyqeWngASIvx3iO9nX52xW/1LR2DkGrDeU\nn/soryZPnkznzp3ZtGkTVatWZeDAgdSrV8/dYZWqhg0bsnjxYh566CFSU1MB+6x4b7/9tpsjExER\nEZGLyk1PJNifTazXF879b6LQf82G37cpvpgxxvDVPkjeaC+Cvv72yjadYyB5BoRUvfI9cvMMscNg\n1yH79s2N4D+vX1uP25p0w0NTIfscvPM89I8rn4WXzWbw9i6b2PWtsAAcPnyYzZs3ExQURKdOnQgM\nDHQ6rjwRVyhPpCTKEXGFeiJFrlRueiIBbqhmYUgPw9yP7NuzltoncrlcZpbhjZXw9lr4Luvq75e6\nDTonwJqXDLXCnIukUbMvFZABVeD9F659yOZdt1n47iNDQSFUC/LMAvLEiRO8+uqrfPfddzRu3Jgn\nnniCatWcu2jLqoAsa1lZWWRmZhIZGYnVanV3OHKZunXrUrduXXeHISIiIiLFKFdFJMDI/jiKyFXp\n8O0RQ4OasPZzmJcMazKguJVFqvhB17bQ53Y4fhrGz7fv//pb6PAo/PNvxjEpzAfrDa9fNpvqrCeh\neeSvK6QCqlgI8NB5ULKysvjd735HZmamY9+SJUvIyMio0N+0GWMYO3YsM2fOxBiDl5cXEydOZPz4\n8S6fn5+fX6EnuJFLCgoKyMnJoXr16lddWkVERESksvDApe7tzp49y9ChQ6lXrx5NmjRhypQp2Gw2\nmta3cNet9jbGwJDJ0Ohe6PV/sOrfzgVkSFW4rxssmwI/rIKVL1r4U28L44ZYWJQE3t72dt9lQcfH\nYPMuw6Fj9tlYLxrwexjWq+zuuyxNmjSJzMxMWrduzZw5c4iKimL37t28+OKLJZ9cjr355pvMmDED\ngOjoaIqKipgwYQJLly696nlFRUUkJSURHByMv78/rVu3Zvv27WURsriBzWbjmWeeISgoiBtvvJHG\njRuTnp7u7rBERERE3M4ji8jCwkJ69uzJwoULOXz4MN9++y3jx4/n2WefBezLfVyUsePSjK0XdWlr\nLxyPr4K3n7fQP85C8M+Gkz7Yw8KKGfYJbwBOnoHfj4SeT8PZHPu+yJow71kqbO/D7t27AZgyZQqP\nP/44Y8eOBWDv3r3uDKvUffyxfaHRWbNmsWPHDqZNmwZAcnLyVc+bMmUKU6dOdayRun37du68806O\nHz9+1fOkfJo6dSovvvgiBQUF+Pn5ceDAAXr06OHUcy8iIiJSGXlkEZmRkUFaWhqhoaFs3ryZ5cuX\nA/YP/Xl5eXRtBy0inc+pEQJP/xH2vg/rZtkLRz/fqxd/d91m4bPZ9nMBcvMuPQfp4w1LJhY/6U5F\nUadOHcC+FujGjRt58803Aahdu7Y7w/JY8+bNA2D58uWcO3eO9u3bc+LECUdRKhXLxX8PH374ITk5\nOXTp0oXs7Gw+/PBDN0cmIiIi4l4eWUSeOHECgNatW9OuXTvi4+OpWrUqhYWFnD17FovFwlsT4Jam\n9l7Hd56HI8nwlwQLTepeW9H3u2gLaa9BvXDn/ZOHQ/ubKm4BCTBmzBiCgoJYvXo1nTt3ZuPGjdSo\nUYNRo0a5O7RSdc899wCQmJjITTfd5OiBjY+Pv+p5OTn2LupbbrmFwMBAmjdv7rRfKpbz5+3TQEdF\nReHr60uDBg2c9ouIiIhUVh5ZRLZs2RKLxcJnn33GY489Rnx8PDk5OdSqVYuwsDAAbmlq4cs3Layb\nZeGP3SxU8fv1BV/T+hb+PQ9aN7Fvx3eC//vj9bgTzxYdHU1GRgZ9+/alTZs2DBo0iM8//5z69eu7\nO7RSNXToUJ577jkAdu7ciZeXF5MnT2bgwIFXPe/2228HoGvXrvTv35/FixcD0LFjx9INWNwiLi4O\ngG7dunHXXXexYMECAO644w43RiUiIiLifh67TuTLL7/M008/7dgODAzkk08+oUuXLqUSH9jXQ/z2\nCDSuU3GXtfB0Zblm17Uu8XH06FG6du3Knj17HPtmzJjheFZXyk5Z5MnJkyfp3r07W7ZsAezPRr/4\n4os89dRTpXZNub60BqCURDkirtA6kSJX8tglPp566iliY2P57LPPqFKlCv3796dJkyalek1vbwtN\nK3YnnFwmIiKCiIgIl9vXrl2bLVu2sHbtWk6fPk3btm1p1apVKUYo7hQaGkp6ejqpqamcOnWK1q1b\n06xZM3eHJSIiIuJ2HltEgn344MUhhCKeIDAwkL59+7o7DCkjfn5+3Hnnne4OQ0RERMSjeOQzkSIi\nIiIiIuKZPLonUq7NDz/8wO7duwkLC6N58+YVdn1LERERERFxH/VEVhBvvPEGderU4Y477iA6Opr4\n+HgtRSAiIiIiItedisgK4PPPP2f48OEUFBQQExPjmMn24jIWIiIiIiIi14uKyApgzZo1GGMYNmwY\nW7duZc2aNQCsWrXKzZGJiIiIiEhFoyKyAvD29gYgNzcXYwznzp0DwMtLf70iIiIiInJ9qcqoAPr0\n6YOvry/vvfcekZGR9OrVC4ABAwa4OTIREREREaloVERWAK1ateK9996jWrVqZGZmUlRUxNChQ5k4\ncaK7QxMRERERkQpGS3xUEP369aNHjx4cPHiQsLAwrFaru0MSEREREZEKSEVkBRIYGEh0dLS7wxAR\nERERkQpMRWQpstls/Pe//yUvL4+bb76ZoKAgd4ckIiIiIiLym+iZyFJy9OhR2rVrR0xMDLfeeisN\nGjRg06ZN7g5LRERERETkN1ERWUoGDx7Mtm3bCA0NpVGjRpw4cYL4+HhOnTrl7tBERERERER+NRWR\npeDMmTNs2rQJHx8fdu/ezd69e4mJieHHH38kPT3d3eGJiIiIiIj8aioiS4GXl/3HaowhPz+foqIi\nCgoKALBYLO4MTURERERE5DdREVkKqlWrxp133onNZqNp06bUq1ePHTt2EB4eTseOHd0dnoiIiIiI\nyK+mIrKUvPPOO9x+++3k5OSQlZVF3bp1WbVqFdWrV3d3aCIiIiIiIr+alvgoJVarldTUVA4cOMCF\nCxdo3Lgxfn5+7g5LRERERETkN1ERWYosFguNGjVydxgiIiIiIiLXjYazioiIiIiIiMtURF7GGENu\nbq67wxAREREREfFYKiL/58033yQsLIygoCBq167NihUr3B2SiIiIiIiIx1ERCaxYsYJhw4Zx6tQp\nAL7//nv69etHRkaGmyMTERERERHxLCoigddffx2ApKQkioqKGDZsGDabjYULF7o5MhEREREREc+i\nIhI4d+4cAK1atcJisdCyZUun/SIiIiIiImKnIhK4/fbbARg+fDgDBw5kzJgxAHTq1MmdYYmIiIiI\niHgcFZHAuHHj6N69O6dPn2bZsmXk5ubywAMP8Mgjj7g7NBEREREREY/i4+4APEGVKlVYtWoVKSkp\nZGZmEhUVRYcOHbBYLO4OTURERERExKOoiPwfb29vunbt6u4wREREREREPJqGs4qIiIiIiIjLVESK\niIiIiIiIy1REioiIiIiIiMtURIqIiIiIiIjLVESKiIiIiIiIy1REioiIiIiIiMtURIqIiIiIiIjL\nVESKiIiIiIiIy0osIqdPn067du0ICQnBarXSu3dvdu7c6TheWFjIs88+S6tWrahatSq1atXivvvu\n4/Dhw6UauIiIiIiIiJS9EovI1NRURowYQUZGBuvXr8fHx4euXbty+vRpAM6dO8e2bdtISkpi27Zt\nrFixgsOHD9O9e3dsNlup34CIiIiIiIiUHZ+SGqxdu9Zp++233yYkJIT09HTuvvtuQkJC+PTTT53a\nzJs3j+joaPbs2UN0dPT1jVhERERERETc5pqficzOzqaoqIgbbrjhF9ucPXsW4KptREREREREpPyx\nGGPMtZwwYMAA9u/fz5dffonFYrnieH5+PnFxcYSFhZGcnOzYf7GwBNi3b99vCFlEREREpGw0adLE\n8TokJMSNkYh4jhKHs15u9OjRpKenk5aWVmwBWVhYyP333092djarVq26bkGKiIiIiIiIZ3C5iBw1\nahTLli0jJSWFyMjIK44XFhYyePBgdu7cyYYNG646lLVt27a/Klip+L788ktAOSJXpzwRVyhPpCTK\nEXHF5aPpRMTOpSIyMTGRDz74gJSUFKKioq44XlBQwKBBg9i1axcbNmzAarVe90BFRERERETE/Uos\nIhMSEnjnnXdITk4mJCSErKwsAIKDgwkKCsJms3Hvvffy5ZdfsnLlSowxjjbVq1fH39+/dO9ARERE\nREREykyJs7O+9tpr5OTk0KVLF2rVquX48/LLLwNw+PBhPvnkE44dO0abNm2c2ixbtqzUb0BERERE\nRETKTok9kUVFRVc9HhkZWWIbERERERERqRiueZ1IERERERERqbxURMpV5efn88MPP6i3WURERERE\nABWR8guMMUyYMIHg4GDCw8OpVasWa9eudXdYIiIiIiLiZioipVizZ89m8uTJ5OfnExQUxPHjx4mP\nj2fHjh3uDk1ERERERNxIRaQUa9GiRQAsXLiQ7Oxs+vfvz4ULF1i6dKl7AxMREREREbdSESnFysvL\nA6BBgwZ4eXkRGRnptF9ERERERCqnEpf4kMqpS5cu7Nmzh759+xIbG8unn37q2C8iIiIiIpWXeiKl\nWDNmzCAuLo4ff/yRtWvXUlRUxKRJk+jevbu7QxMRERERETdST6QUq2rVqqxbt46MjAyysrK46aab\naNasmbvDEhERERERNyu3RWRBQQGZmZlUq1aNsLAwd4dTIXl7e9OxY0d3hyEiIiIiIh6kXA5n3bhx\nI/Xr16dx48ZYrVYGDRpEbm6uu8MSERERERGp8MpdEXnkyBF69erFsWPHCAsLw8fHh6VLl/Lkk0+6\nOzQREREREZEKr9wVkf/4xz/Izs6mc+fOHDt2jIyMDADee+89jDFujk5ERERERKRiK3dFZGFhIQDV\nqlXD29ubG264AQCbzebOsERERERERCqFcjexTpcuXfDz82PlypW0adOGQ4cOAdCjRw8sFot7gxMR\nEREREangyl1PZFRUFG+//TYBAQFs3bqVH3/8kfbt2zN//nx3hyYiIiIiIlLhlbueSIABAwYQFxfH\n119/TUhICDExMXh7e7s7LBERERERkQqvXBaRAGFhYXTp0sXdYYiIiIiIiFQq5W44q4iIiIiIiLiP\nikgRERERERFxmYpIERERERERcZmKSBEREREREXGZikgRERERERFxmYpIERERERERcZnFGGPK4kJn\nz54ti8uIiIiIiJSKkJAQd4cg4hHUEykiIiIiIiIuUxEpIiIiIiIiLiuz4awiIiIiIiJS/qknUkRE\nRERERFymIlJERERERERcVmZF5Ny5c2nQoAEBAQG0bduWtLS0srq0eJjp06fTrl07QkJCsFqt9O7d\nm507d17RbuLEidSuXZvAwEDi4uLYtWuXG6IVTzF9+nS8vLwYOXKk037liRw7dowhQ4ZgtVoJCAgg\nOjqajRs3OrVRnlRehYWFjB07loYNGxIQEEDDhg0ZP348NpvNqZ1ypHLZuHEjvXv3pk6dOnh5ebF4\n8eIr2pSUExcuXGDkyJGEhYVRtWpV+vTpw9GjR8vqFkTcqkyKyKVLl/Lkk0+SlJTEV199xW233UaP\nHj04fPhwWVxePExqaiojRowgIyOD9evX4+PjQ9euXTl9+rSjzcyZM/nrX//Kq6++yhdffIHVauXO\nO+8kJyfHjZGLu/znP//h9ddfp2XLllgsFsd+5YmcOXOGDh06YLFYWLNmDXv27OHVV1/FarU62ihP\nKrdp06Yxb948XnnlFfbu3cusWbOYO3cu06dPd7RRjlQ+586do2XLlsyaNYuAgACn/1vAtZx48skn\n+eijj3j//ffZtGkT2dnZ9OzZk6KiorK+HZGyZ8pAbGysGT58uNO+Jk2amDFjxpTF5cXD5eTkGG9v\nb7Nq1SpjjDFFRUUmIiLCTJs2zdHm/PnzJjg42MybN89dYYqbnDlzxjRq1Mhs2LDB3HHHHWbkyJHG\nGOWJ2I0ZM8Z07NjxF48rT6Rnz57moYcectr34IMPmp49expjlCNiTNWqVc3ixYsd267kxJkzZ4yf\nn59ZsmSJo83hw4eNl5eX+ec//1l2wYu4San3RObn57N161a6devmtL9bt26kp6eX9uWlHMjOzqao\nqIgbbrgBgIMHD3L8+HGnnPH396dTp07KmUpo+PDh3HvvvXTu3Blz2WTSyhMBSBptsckAAASzSURB\nVE5OJjY2loEDBxIeHk5MTAxz5sxxHFeeSI8ePVi/fj179+4FYNeuXaSkpHD33XcDyhG5kis5sWXL\nFgoKCpza1KlTh+bNmytvpFLwKe0LnDx5EpvNRnh4uNN+q9VKVlZWaV9eyoHExERiYmK49dZbARx5\nUVzOfP/992Uen7jP66+/zoEDB1iyZAmA03Aj5YkAHDhwgLlz5zJ69GjGjh3Ltm3bHM/NJiQkKE+E\nxx9/nCNHjtC8eXN8fHwoLCwkKSmJRx99FNDvErmSKzmRlZWFt7c3NWrUcGoTHh7O8ePHyyZQETcq\n9SJS5GpGjx5Neno6aWlpVzyPUBxX2kjFsHfvXsaNG0daWhre3t4AGGOceiN/ifKk8igqKiI2Npap\nU6cC0KpVK/bt28ecOXNISEi46rnKk8ph9uzZLFy4kPfff5/o6Gi2bdtGYmIikZGRDB069KrnKkfk\n55QTInalPpw1NDQUb2/vK76VOX78ODVr1izty4sHGzVqFEuXLmX9+vVERkY69kdERAAUmzMXj0nF\nl5GRwcmTJ4mOjsbX1xdfX182btzI3Llz8fPzIzQ0FFCeVHa1atWiRYsWTvuaNWtGZmYmoN8nAlOn\nTmXs2LEMGDCA6Oho7r//fkaPHu2YWEc5Ij/nSk5ERERgs9k4deqUU5usrCzljVQKpV5E+vn50aZN\nGz799FOn/evWreO2224r7cuLh0pMTHQUkFFRUU7HGjRoQEREhFPO5OXlkZaWppypRO655x527NjB\n9u3b2b59O1999RVt27Zl8ODBfPXVVzRp0kR5InTo0IE9e/Y47fvmm28cX0zp94kYY/Dycv644+Xl\n5RjVoByRn3MlJ9q0aYOvr69TmyNHjrBnzx7ljVQK3hMnTpxY2hepVq0azz//PLVq1SIgIIApU6aQ\nlpbGwoULCQkJKe3Li4dJSEjgrbfe4oMPPqBOnTrk5OSQk5ODxWLBz88Pi8WCzWZjxowZNG3aFJvN\nxujRozl+/Djz58/Hz8/P3bcgZcDf35+wsDDHH6vVyrvvvkv9+vUZMmSI8kQAqF+/PpMmTcLb25ua\nNWvy2WefkZSUxJgxY2jXrp3yRNi3bx+LFi2iWbNm+Pr6kpKSwrhx4xg0aBDdunVTjlRS586dY9eu\nXWRlZbFgwQJuvvlmQkJCKCgoICQkpMSc8Pf359ixY8yZM4dWrVpx9uxZHn30UapXr87MmTM17FUq\nvrKaBnbu3LkmMjLSVKlSxbRt29Zs2rSprC4tHsZisRgvLy9jsVic/kyaNMmp3cSJE03NmjWNv7+/\nueOOO8zOnTvdFLF4isuX+LhIeSKrV682rVq1Mv7+/qZp06bmlVdeuaKN8qTyysnJMU899ZSJjIw0\nAQEBpmHDhmbcuHHmwoULTu2UI5VLSkqK4/PH5Z9JHn74YUebknLiwoULZuTIkaZGjRomMDDQ9O7d\n2xw5cqSsb0XELSzGuDBLhYiIiIiIiAhl8EykiIiIiIiIVBwqIkVERERERMRlKiJFRERERETEZSoi\nRURERERExGUqIkVERERERMRlKiJFRERERETEZSoiRURERERExGUqIkVERERERMRlKiJFRERERETE\nZf8faM0psw+kwFIAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_train_data(pos, 15, 100)\n", - "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.2, h=0.0001)\n", - "plot_g_h_results(zs/1000, data/1000, 'g=0.2, h=0.0001')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We made `g=0.2` and we can see that while the train's position is smoothed, the estimated position (and hence velocity) fluctuates a lot in a very tiny frame, far more than a real train can do. So empirically we know that we want `g<<0.2`.\n", - "\n", - "Now let's see the effect of a poor choice for $h$." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Nk3V7OwGKFy+Ov78/xXOHoaq6NTE1jnXo1G2ImSMTQmQnMrmQEEJkM1qtljZt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\nXw65XI7ffvsN165dQ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_train_data(pos, 15, 100)\n", - "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=0.01, h=0.1)\n", - "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.1')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here the position changes smoothly thanks to the small $g$, but the large $h$ makes the filter very reactive to the measurements. This happens because in the course of a few seconds the rapidly changing measurement implies a very large velocity change, and a large $h$ tells the filter to react to those changes quickly. Trains cannot change velocity quickly, so the filter is not doing a good job of filtering the data - the filter is changing velocity faster than a train can.\n", - "\n", - "Finally, let's add some acceleration to the train. I don't know how fast a train can actually accelerate, but let's say it is accelerating at 0.2 m/sec^2. " - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "def gen_train_data_with_acc(pos, vel, count):\n", - " zs = []\n", - " for t in range(count):\n", - " pos = compute_new_position(pos, vel)\n", - " vel += 0.2\n", - " zs.append(measure_position(pos))\n", - " return np.asarray(zs) " - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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XOKZNm8bXX3+tbTcuLo7evXsTFRWFvb19ucQghBDlRXo8hRBCCPHUyM3Nxd/f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\nUFFRERkZG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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_train_data_with_acc(pos, 15, 100)\n", - "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.0001)\n", - "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.0001')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we see that the filter is not quite tracking the train anymore due to the acceleration. We can fiddle with $h$ to let it track better, at the expense of a less smooth filtered estimate." - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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8tGvRogVOTk7Ex8fj4eHB3bt3yczMpGXLlgZp7RRCPJ60eAohhBBCVGD9+/fH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\noQl0bgYOlSXRFEIUH0k8hRD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K/2Lfvn0A7N69m/r16zNixAhWrFhBREREmUg8MzIyAHjm\nmWdQqVTaZU3u3r1ryLB0NGvWDGNjY3bv3s2gQYM4f/48OTk5eHt7F7qURLt27UhISCA7OxtTU1NZ\n97AUyMpWOHVWM/nPnwlwNBFO/gX3svK2qIHK/vETANWoAs+1hMAW4O8LDpWf/PPs2bMnP/zwA5Mm\nTSI1NRU3Nze+/PLLJ5rNsyDe3t6cOnWK2NhYFEWhQYMGhSadeaytrWnWrFmJxPUge3t7IiMj2b17\nN6mpqTRq1IiWLVuW+HHLu5mvq5hZ/PczyhS1Wk2VKlVYv379Y19/+Ca8zGBbehQp8Rw3bhxNmjSh\nVatW2rIZM2ZQrVo1RowYoXc9zs7OLF++HF9fX7KysggODqZLly5l5kvWk6hevTrR0dEsW7ZMO6vt\nW2+9hbX149f4EuJBubm5gGaGNxsbG0xNTbXXTt5rouyxsrICNMMP6tatS1JSkk55ade+fXt++ukn\nJkyYQFhYmLa3TPv27Q0c2f94enqyePFixowZw7p16wCoUqUKa9as0bsOWYfQMO7fVzh5Fg6ehuh4\nOJqgmQDovp5/8ozJoLJxIs+1gCkjGvOMR8ks0TB48GAGDx5MTk6O3klgnnPnzpGeno6Xl5feX5JN\nTU31nkjIUMzNzenVq5ehwxBlVH6/px4eHvz222+0aNFCvj+XMXonnhMmTCAqKorIyEjthbBv3z5W\nr17NsWPHdLYtbKY0Ly8vnUmEWrZsyblz51iwYEG+iWd0dLS+oZYJD3Y/i4uLM2Ak5Ud5u0by06xZ\nM2JiYvD29sbOzo6zZ89ibW2NjY1NhXkPnkRpfI+6devG8uXL6devH8bGxuTm5lKpUiU8PT1LZbwP\na9WqFV27diUsLIwNGzYAmqnwO3bsWKri9/PzIzg4mKNHj2Jubk67du1QFOWxMZamuCuaa+mmnDpn\nzanz1pw6Z03cRSsyswsflwlQzTYbT5cMvFzv4eWSgZfLPVyqZJG3GkP2zRj+HX5ZLJ70OsnIyGDa\ntGns378fAFtbWz766COdG/yibJIlY56ctbU1aWlpj5QPHDiQZcuW8eGHH/LJJ5/ovJabm8vt27dl\nneVSSq/EMygoiNDQUMLDw3WW/IiIiODKlSs662zl5uYyefJkFi1axIULF/QOxM/PL98mcyHE/3z4\n4YeMHz+epKQkbty4QaVKlZg7d26FmJyrvBo2bBiZmZn8+OOPZGVlUatWLWbNmkX16tUNHZpejI2N\nmT17Nv369SMlJQVnZ2eaNGmis/ZaaeHt7V3kYSGiZCgKXL1pSnyKFQkXrUi4pPl5NV2/lmXXqpl4\nu2bg45qBT01Nsmlf6X4JR128FixYwP79+zE3N8fe3p7U1FQmT57MunXrcHZ2NnR4QhiUr68voaGh\njB8/Hj8/P4yMjBg4cCDt2rVj9OjRLFiwgBMnThAQEIC5uTlnzpxh06ZNfPTRRwwZMsTQ4YvHKDTx\nHDduHBs2bCA8PPyRpU5GjRpFv379tM8VReG5557j5Zdf1plNSh/Hjh0r8I+szNgp8pN3x7kiXSMB\nAQH8+eefZGRk0LhxY7mzp4fSfp34+fnx7bffcu/evTK7VIevr6+hQ3hipf06KYsyMhWSL8PZBx7x\n5+BoEvxzU786ajlBywbgW18zw2xjT7CzsQQsgac/SWFxXSd547sPHz5Mw4YNCQwMJCwsjMuXL0sX\n1TIuPT3d0CEYXFG7tD+8/ahRozh58iQhISEsWbIE0LR2gma23KZNm7J8+XKmTZuGiYkJtWvXZsCA\nATpLNsqY/NKlwMRz9OjRhISEsGXLFmxtbUlNTQU004ZbW1vj6OiIo6Ojzj6mpqZUr15dp4vBkCFD\nUKlUrF69GoCFCxfi7u5O/fr1yc7OJiQkhK1bt7J58+biPj8hyiUTE5MSm7SiuERGRjJlyhSSk5Op\nU6cOCxYsKFcTS/z555/Exsbi7OxMhw4d9FrsvjDGxsZlNukUAiDnvkLUSdh5AKJOwl+XIPV60eqw\nNAffetCigSbZbFEfnB3L55dH9b+LiOZNWpU3NrSwIUtClHZDhw5l6NChj33Nzc1Ne+0XtL2lpSWr\nVq3K9xjDhg0rdIbx5ORkfcIVT0mBieeyZctQqVR06dJFp3zmzJlMnz5d74NcvHhR545DTk4OEydO\nJCUlBUtLSxo2bMjOnTtLzbT7QognExMTQ5cuXcjOzgY069d26tSJQ4cO0ahRIwNH92QUReGdd97h\niy++0JZ17tyZbdu2ySQHokK68o/CrkPwywH49TDcKsJkxpWtoYmX5tHUG5p6gVdNMDEpn4nmw158\n8UXWrl1LixYtcHFxIT4+HgsLCwICAgwdmhBCFLsCE8+H70bo43F3FsLDw3WeT5w4kYkTJxa5biFE\n2bBw4UKys7MZMGAAH3/8MZMnT2bz5s0sXryYb7/91tDhPZGNGzfyxRdfYGpqSo8ePdi/fz979+7l\ng4TdUZ4AACAASURBVA8+4PPPPzd0eEKUGLVa4eJViDv37+M8xMRrljIpiLEx1HaCOs7g7qL56eGi\n6S5bxxmMjCpGkvk4X331Fampqezdu5f4+HhsbGwIDg7Gw8PD0KEJIUSxK9JyKkIIoY+8xZtfeukl\n6tatS58+fdi8eTNXr141cGRPLm9M1vvvv8+MGTP49ddfee655x65wSYEQFZWFtevX6datWqYmJT+\n/3IzMhUu/A3nU9H+PH8F4s9rEs2MzMLrqOUE3Vtr1sl8xgNqVqs4LZhFZWtry2+//UZcXBzp6ek0\naNCAypUrGzosIYQoEaX/f0EhRJnTuHFjdu/ezcSJEzlx4oR2fHfjxo0NHNmTy1tbMyEhAbVaTXx8\nvE65EKDpkj1//nxmzJhBVlYWdnZ2LF++nAEDBhg6NG7fVUhKgYQLkHgRkv79eS5V/8l+HmRiDO2e\nhW6toHsrqOcmE3oUhUqlon79+oYOQwghSpxKKcUj2B+cEczW1taAkfw/e/cdX9P5B3D8c292Iktk\nkE2EJChipRWKoHbtn1G7OqigqlpK0VJVNVLU3qOR2tSOPWMkCDKMJLZEEpkk9/z+OHIrDVkiN+F5\nv173dZIn957zPXHknu99nuf7CCWZqEJZ8jx58oQPP/yQc+fOqdvq1avHgQMHNDYPsqiukwsXLlC/\nfn2ePn2Kjo4Oz549A2Dp0qV5FjkQSr6iuk6WL1+uvh5MTU1JSEhAqVRy5MgR3n///deOMy+p6RKR\ntyE8GsJj5G1EDIRFwd0CFvt5kYUpuDtBVSdwc5STzAYeYFrm7Uk0ExIS+OmnnwgODsba2pqRI0dS\nq1atbM8prvedmzdvsmnTJtLS0mjatCn169d/o8cTik5+72HT0tLQ19cvjpAEoVjkdk2LHk9BEIqc\nsbExR48eZdWqVdy4cYNKlSrRu3fvt+LNtWbNmmzevJlBgwZx584djIyM+PHHH19ZvU94N61cuRKQ\n5zsPGzaML774ggULFrB69eoiTTyfPpO4chNCIiEkAi5GysNiox/I62QWlLYW2FmBo408L9PeWv7a\n1UFONC3N354E82WSk5Np1KgRISEh6rasJeW8vLyKNZYjR47Qpk0bnjx5Asg9o7Nnz+arr74q1jgE\nQRCKikg8BUF4IwwMDBg8eLCmw3gjWrVqRUxMDImJiRgbG6NUKjUdklDCpKXJkyEdHBxQKBTY29sD\n8pzPwpAkiXuxcoIZHAEXI+Svr9yEjMyC7UtHG1zs5Oqxle3/3VayhfIWoKX1dieXuVm+fDkhISHq\nJaD++usv/P39+e6779Tzu4uDJEn07t2bJ0+e0Lx5c+zs7Fi2bBnDhw+nTZs2VKxYsdhiEQRBKCoi\n8RQEQSgEhUIhpgAIr9S8eXNOnDhBnz59eP/99zlw4IC6PTeSJPHgMdx8XtAn+HkvZnBEAedfSpnY\nlntGNRd9KttDZTvUW0eb1y/2c/z4cUaMGEF4eDiOjo788ssvtGzZ8rX2WRJkVebv27cvnTp1ws3N\nDX9//2JfC/Dhw4dERUVhaGjIzp070dbWJioqiv3793P+/HmReAqCUCqJxFMQBEEQitjYsWMJCQlh\n8+bN7NmzB4BRo0apiwulpEmcugznw+HGHTnRvHFHLvCTn8qxL3KyUXEnYjfpj89Q0ToJnYxwrgXv\nRKpgxeYNkejp6RXpuV28eJFmzZqpe3UfP35MmzZtCAwMxNvbu0iPVdxcXFwAWLJkCRUrVmTDhg0A\nxb68ibGxMVpaWqSkpLBr1y6cnJy4ePEiABYWFsUay5ty+PBh5s6dS3x8PPXr1+e7777DwMBA02EJ\ngvAGicRTEARBEIqYrq4uGzduJCgoiJiYGCrYuxH7tArf/QlHLkgEXYVnGQXbp45WOk8fn4WUEEi5\nCMnB+LxvzU+jv6VBA3n4ZdjJMCRJwtHRkdu3bxMeHk61atWK9NzmzZtHWloanTp1Ys6cOUyYMIEl\nS5Ywe/bsUp949u3blyVLlhAUFMQnn3wCyBWrf/3112KNw8DAgKFDhzJ79mzatWunbq9Xrx4NGzbM\n8/Xx8fGcPXsWPT096tatW+QfPryu7du306FDB/V68Xv27OHw4cPs3bsXHR0dDUcnCMKbIhJPQRAE\nQShCaekSl67DuTA4d60OZ67U4UJ4/ov9mBiBc3l5zmV1F6hRCSrbpvJeVVPIzGD16tXY2HSmU6c1\n7Nt9nP59ugByshEbG0tGRgaJiYkAb6SgV1xcHAAfffQRtra2tGvXjiVLlhAb+xrlcksIAwMDDh48\nyLRp0wgODsbKyorhw4fj4eFR7LH89ttvmJiYsHz5ctLT0/Hx8cHPzy/P9WAPHDhAly5dePz4MQCu\nrq7s3Lmz2HttczNq1ChUKhWDBw+madOm+Pr6cujQIbZs2UKXLl00HZ4gCG+ISDwFQRAEoRCy5mOG\n3oCL1+FCmJxsht7IX8Efdyfwqi4X93GuICebzhXA3DjnOphRUY9QZWZQtmxZevbsiUKhoHbt2hw8\neBBDQ0Pq1KlDUFAQFSpUQJIkVCoVDRs2fCPJhqenJ/7+/owbN45r166ph6N6enoW+bE0wcjIiEmT\nJmk6DLS1tZk0aVKBYomNjaVz587Ex8dTrVo14uPjCQsLo1u3bgQFBZWY9VVv3rwJwLRp0zAzM+PQ\noUPMnz9f3S4IwttJJJ6CIOQpMzOTe/fuYWZmprF1OAVBkx4nysNjL9+A0JtyNdkrNyEuMX+vVyqh\nVmXwrgne70HDGgVbmqR8+fKULVuWuLg4evfujY2NDYcOHUKhUFCjRg22bt1Kr169CAwMBKBly5as\nXLnyjSQavr6+7Nmzh/379zNjxgxAXs9ywoQJRX4soWBOnTpFfHw8NWvW5OzZsyQlJWFtbc25c+d4\n9OgRlpaWmg4RkOfMhoaGMmzYMJo0aYK/v7+6XXg7LF++nAEDBgDyfN6XDRF3cXHh+vXrNG7cWP23\nSyh+x48fZ+/evQwfPvyNF00UiacgCLnav38/n3zyCXfv3kWpVPLll18yc+bMPId7CUJplamC4HCJ\nk5fh1GU4eVmuMFsQle2htivUqiInnPU9wMSo8Emgjo4OS5cupWvXrqxdu1bdPnXqVHWF0wMHDvDk\nyRMUCgVlypQp9LHyoqenx65du9iwYYO6qm337t3finV6S7us+ZFJSUmkp6eTkJBARoY8mbgk/c2e\nOXMmbdq0YdWqVaxatQqQPyxp3769hiMTipqBgQFr167NkXiePHmS69evo6+vX2J64t9Vx48fZ+LE\nifTv318knoIgaE5ERATt27cnJSUFU1NTEhIS+OOPPzA3Ny8RQ9EE4XUlp0pcviEvWRISCcfPuxIa\nZUjq0/y9vowBuDvLw2bfqywnm+9Vfr0k81U6dOjA6dOn8ff359mzZ7Ro0SLH8izGxsZFftyX0dbW\npkePHsVyLCH/3n//fRwcHIiIiKB8+fKkpaWRkZFBy5YtMTc313R4ai1atODYsWPMnz+fhIQE6tWr\nx8iRI9HS0tJ0aEIRa9WqFRs2bGDOnDnZPvxYu3YtVatWLfX/5snJyW/NSDApv4UIXoNY9VwQhFfa\ntGkTKSkptG7dmri4OLZu3Qqg/oRaKLmSkpL4/PPPsbe3x8nJidGjR/P0aT6zqbdUXKLErpMSE5dK\ndP5OwrW7hElzaPApfPoL+G2AsxHGpD7NeSOkrQWeVWBgO5jxFfzzO9zaCAl74eQiBUvHKvDtpsC7\npuKNJJ1ZatasyZQpU5g+fXqea4IK7x4jIyN27txJ1apVSUhIID09nebNm7N69WpNh5ZDvXr1WLZs\nGRs3bmTMmDHo6upqOiThDejRowdxcXHs3r1b3ZaZmYm/vz+9evXK8XxJkvDz86N69eoYGBhgbW3N\noEGDchQv27p1K+3atcPe3h59fX31+1x6enq2592/f59Bgwapn2djY0Pr1q0JDQ1VP0epVDJx4sQc\nsTg5OdG/f3/198uXL0epVBIYGMiwYcOwtrbO9mHfmTNnaN26NWZmZhgaGuLt7c3Bgwez7fPHH39E\nqVRy9epVevfujZmZGZaWlowdOxaA6OhoOnTogKmpKTY2Nvz222854kpPT2fixIlUrlwZfX197Ozs\nGDlyJKmpqdmep1Qq+eKLL9i8eTPVqlVDX1+fatWqZfu3+PHHHxk9ejQAzs7OKJVKlEolhw8fBuDc\nuXO0bt0aKysrDAwMcHJyok+fPurltApK9HgKgvBKWX/Ay5cvj1KpxNbWFqDUJTC3bt1i+/btaGlp\n4eDggJWVlaZDeqMkSaJbt278888/6rbp06fz4MEDli9frrnAitGzDImLkaiHy566DGHR+X+9rSV4\nVZOHyDbwgNpVwEBPDAcTSj4PDw8uX75MTEwMurq62NjYaDokQQMeP35MXFwc9vb2Gk3q7ezs8Pb2\nZu3atbRp0waAffv28eDBA3r06MG6deuyPf+LL75g6dKl9OvXj2HDhhEVFYWfnx+nT5/mzJkz6qWB\nli9fjoGBAb6+vpiamnLixAlmzpxJdHR0tn126dKFS5cu8dVXX+Hs7MyDBw84fPgw4eHhuLu7q5/3\nsuG+CoXipe1fffUVZcuW5YcffiAhIQGAQ4cO0bJlS2rXrs2ECRPQ1tZm1apVtGjRgr1799K4ceNs\n++jRowdubm5MmzaNHTt2MHXqVExNTVm8eDE+Pj78+uuvrF69mtGjR+Pp6UmTJk0A+f29Y8eOHD58\nmMGDB+Pu7k5oaCjz5s3j8uXL2ZJKgBMnTrBt2za+/PJLypQpw5w5c+jcuTNRUVGULVuWzp07Ex4e\nzrp165g1axblypUDwM3NjYcPH9K8eXOsrKz49ttvMTc3Jyoqim3btpGSklK46RVSCRYfH69+CMKr\nnDlzRjpz5oymw3grnThxQlIoFBIgffjhh5KFhYUESH379tV0aPm2ZcsWycDAQAIkQCpbtqx0/Phx\nTYf1RoWEhEiAVKZMGen48ePSnj17JC0tLQmQ7t+/X+zxqFQq6fTp09KmTZukK1euFPm+b95VSduP\nqaSpK1VS7x9VUs0+KkmvsUpSvJ/3Q6uhSnLvqZK6j1NJk5eppBlLw6Ttey4UaYzC20e87wh5ye89\nbGpqapEeNz09XRo0aJD6Pa9cuXLSrl27ivQY+bFs2TJJoVBIp06dkhYsWCAZGRlJKSkpkiRJ0ief\nfCJ5eXlJkiRJHh4eUpMmTSRJkqRjx45JCoVCWr16dbZ9HT16VFIoFNLChQvVbVn7etGUKVMkpVIp\nRUdHS5IkSY8fP5YUCoU0Y8aMXGNVKBTSxIkTc7Q7OTlJ/fv3z3FODRo0kDIzM9XtKpVKqlKlitS8\nefNsr3/69Knk4eEhvf/+++q2CRMmSAqFQho0aJC6LTMzU7K3t5cUCoU0ZcoUdXt8fLxkaGgo9e7d\nW922Zs0aSalUSocPH852rDVr1kgKhULas2dPtvPS09OTIiMj1W0hISGSQqGQ/vjjD3Xb9OnTJYVC\nId26dSvbPjdv3iwpFArp7NmzL/mtvVpu17QYaisIwis1aNCAOXPmoKWlxcGDB4mNjaVhw4bMmjVL\n06HlS1xcHL169SI1NZW6detSrVo14uLi6Natm7rgxtvo0aNHgLx+n5eXFz4+Pupej+JeazE9PZ1O\nnTpRr149OnbsiJubG99//32h9/coXmLrEYkx8yUafylh1gKcO0O7b+D7P2HNHgiOgKfPcr5WRxvq\nusGQzrBsLJxdBkn74PIaBesmgbvJJoIP/sQ/WxYRExPzGmctCIKgGT/88AOLFy9GoVBgaWnJo0eP\n6NixI+Hh4RqLqWvXrjx79ozNmzeTmprK5s2bXzrM1t/fnzJlytCiRQsePXqkflSpUgUrK6tslW8N\nDAwAUKlUJCQk8OjRIz744AMkSeL8+fPq5+jq6hIYGKhe17YofPrppyiV/6ZQwcHBhIWF0aNHj2xx\nJyQk4OPjw6lTp3IMTR00aJD6a6VSiaenJwqFgoEDB6rbTU1NqVKlCjdu3Mj2O3J1dcXd3T3bsRo1\naoRCochRHbhJkybqAnQA1atXx8TEJNs+X8XMzAyAbdu2Fdk9U65DbadOncrGjRsJCwtDT0+PBg0a\nMHXq1FcupPzZZ5+xaNEipk+fztdff53rgQ8dOsTIkSMJDQ2lQoUKjB49ms8++6zwZyIIwhsxdOhQ\n2rZtS0hICBYWFjRo0KDUFAO4cOECSUlJvPfee8ydO5fMzEzatWtHTEwMt27demtL93t4eKCrq8u5\nc+fo27cvSUlJ3L59GzMzM5ydnYs1lp9++onNmzdTpkwZvLy8OHDgAFOnTsXT05POnTvn+lpJkrh6\nC46GwImLcPxiwYbLOtrIw2TruUODanJ1Wf2XDJeVJEn9/pVl3bp1HDx4kOrVq+f/gIIgCBqWNcx0\n165d+Pj40KFDB7Zv386WLVsYNWqURmIyNzenZcuWrF69GqVSSWpqKt27d8/xvLCwMPUSQC/z8OFD\n9deXLl1i9OjRHDp0KMfcxqzhr3p6ekybNo1Ro0ZhbW1N/fr1ad26NZ988gl2dnaFPp//3juEhYUB\nZEsaX6RQKIiNjVVPVwJwcHDI9hxTU1N0dHRyTAUyMTHJdt5hYWFcu3btpUsjKRSKbM992XFA/vfI\nTyLeuHFjunTpwsSJE/n9999p3Lgx7du3p2fPnhgaGub5+pfJNfE8dOgQQ4cOpW7duqhUKsaPH4+P\njw+hoaE5qqMFBARw5swZKlSokGdZ5Bs3btC6dWsGDRrE2rVrOXLkCF9++SWWlpZ06tSpUCciCMKb\n4+TkhJOTk6bDKLCsJSXu3LnDo0ePSEpKUr8hvS1V6F7GysqKP//8k0GDBrFy5UpAfgNesWLFay95\nIUkSSUlJGBkZZfvE91X27NkDwOrVq+nQoQMTJ07kxx9/ZO/evTkST5VKnpd56AIcuQCHL8DD+Lxj\nKmsC1SuBhzNUq/jv12bG+ZuTuXfvXhYtWoShoSHdunUjODiY8+fP89lnn3H8+PF87UMQBKEkePZM\nHu5hYWGBUqmkbNmyABof5dOzZ0/69OlDYmIizZs3V88lfJFKpcLCwoK//vrrpfvIyj0SEhJo0qQJ\nxsbGTJkyBRcXFwwMDIiJiaFfv36oVCr1a3x9fenQoQNbtmxh7969TJ48mSlTprB9+/Yc8y7/61W/\ns6ze1hfjBpg2bRqenp4vfc1/z/dlH+C/Kn+SXqg2q1Kp8PDwYPbs2S99boUKFfI8zn/3mRt/f3/O\nnDnD9u3b2bt3L4MHD2bq1KmcPHmyUOsC55p47tq1K9v3q1atwtTUlOPHj6snCINcuGP48OHs37+f\njz76KM+D/vnnn9jZ2al/aVWqVOHUqVP89ttvIvEUBKHIeHp6UqdOHYKCgmjdurW6vUOHDm99wY3+\n/ftTo0YNdu3ahZaWFh06dMDNzS3bc549e4aWlla+EkiQC0IMHDiQqKgojI2NmTBhAiNHjsz1w8as\nQhC3b99GkiT1EFaFthEXwiSuRsG1KDh3FY6EQPyT3GPQ1ZGry75fXX7Uc4cK5V79hp0fwcHBAPTp\n04eBAwcSGxvLRx99pG4XBEEoLVq1asWyZcto1qwZVatW5dSpUyiVSo1Xwe7QoQN6enocP36cFStW\nvPQ5lSpVYt++fdSvXz/XD4cDAwOJjY1l48aNeHt7q9v37t370uc7OTnh6+uLr68vt2/fpmbNmvz8\n88/qxNPc3Jz4+Oyfcj59+pS7d+/m69yyekDLlClD06ZN8/WawnJxceHs2bNFepy83j/r1q1L3bp1\nmThxIrt27aJ169YsWrSoUNNmCjTHMzExEZVKla23MyMjgx49evDDDz9QpUqVfO3nxIkTtGjRIltb\nixYtCAoKIjMzsyAhCYIgvJKWlhbbt2+nVatWaGlpoa2tTa9evd6Z5WA8PT0ZO3YsY8aMyZZ0Xr9+\nHW9vb/T09DAyMmLIkCE5StD/16VLl2jbti1RUVEolUqePHnCqFGjWLp0aa6v69J9ABi/z5BJIRi4\nL2Tx8S4oPG+y4Pxv1O4PPSfAxCWw7djLk86yJtDBG34dAkf/hPjdcGyBgulDFXRsrMDWMmfVwV27\ndjFkyBC++uqrHKXsXyZraNOBAwe4du0a27Zty9YuCIJQWsyaNYsmTZqQkJDAqVOn0NHRYeHCha/s\niSsuBgYGzJ8/nwkTJvDxxx+/9Dn/+9//UKlUL10nPDMzU50cZvXivdizqVKp+P3337O9JjU1Nccw\nXFtbWywtLdWjn0BOHA8dOpTteQsXLsy2/9zUqVMHFxcXfv/9d5KSknL8/L/DX18lPx+gdu/enfv3\n7zN//vwcP0tPT3/p8fOSleTHxcVla4+Pj8/RM1qrVi2AbL+/gijQciq+vr7UqlULLy8vdduECROw\nsrIq0PzM+/fv5xi/bW1tTUZGBo8ePXrl2G5BEISCsra2ZufOnZw8eRKFQkH9+vU1HZJGJScn06JF\nCyIjIwFIS0tj3rx5qFSql76RZVm9ejXp6el06dKF9evXM3fuXHx9fVm0aBEDBw5EkiQib0PQVQiJ\ngEvX4WIk3LrXF0X1vgA8BfJ6W7UuC41rgndNaFwL3J1Aqcx/b+aMGTOyzWP6448/WLRoUbZCDv/V\nqVMnpkyZQlhYGL1791a3v04RpNJCpVKxYsUKTp48iZmZGQMGDMj3h8iCIJQ8JiYm7Nu3j/PnzxMb\nG0u1atVyDL/UlBf/vr4oK7nx9vZmyJAhTJ8+nZCQEFq0aIGenh4RERH8/fffTJ48mT59+tCwYUMs\nLCzo27cvX331Fdra2gQEBJCcnJxtv9euXaNp06Z069YNd3d39PT02LlzJ1evXmXGjBnq5w0aNIjP\nP/+cLl264OPjQ3BwMHv27KFcuXL5GpKqUChYsmQJH330Ee7u7gwYMABbW1vu3LmjTmgPHDiQ535e\ndawX23v37k1AQABDhgzh0KFD6oJK165dY8OGDQQEBNCoUaMCHadu3boAfPfdd/To0QNdXV2aNWvG\nmjVrmDt3Lp06daJixYqkpqaybNkytLW16dKlS57n8zL5TjxHjhzJ8ePHOXr0qDojP3jwICtWrODC\nhQu5nlBRCAoKKvJ9Cm8XcY0IudHWlv/cvevXyaFDh4iMjMTBwYFly5Zx8+ZNBg4cyKJFi+jbt6/6\n9/RfN2/eBOQqd+fPnyddVQbMPiI8rRUfDIrn8i0jElPy/1mmllLCtlw6jlZpOFql4WSdxnvOSThY\npZP1oW9aHJyLy30/L3r06JF6Iew+ffqQnp7OX3/9xdChQ6lcuXKuQ7dmz57NjBkzCA0NpUyZMvTo\n0YNatWq91deLJEn88MMP2dZ98/PzY+7cuaKoUj69zdeH8HoqV66ssWNnVUnVtPz04P13rUw/Pz9q\n167Nn3/+ybhx49DW1sbR0ZHu3burh5eam5uzY8cOvv76ayZMmICxsTGdO3fm888/p0aNGup9OTg4\n0Lt3b/bv38/atWtRKBRUqVJFvU5olk8//ZQbN26wZMkSdu3aRaNGjdi7dy/NmjXLcQ6vOidvb29O\nnjzJ5MmTmTdvHomJiZQvX566detm++DzVWuD5rddoVCwceNGZs2axYoVK9iyZQsGBgZUqlSJIUOG\n5Otv93+P4+npydSpU5k3bx4DBgxAkiQCAwP58MMPCQoKwt/fn3v37mFiYkLt2rWZO3euOlktKIWU\njyxxxIgR+Pv7ExgYiKurq7p94sSJTJo0Kdv8oMzMTJRKJRUqVCAqKuql+2vcuDHVq1fnjz/+ULdt\n2LBBvexBVhf6i924miwDLQiC8Lb4559/GD9+PA0aNMDPz4+UlBSaNGmCSqXi8OHDOYomZGRC1EN9\ntu6NZM2mYJRlqqNfti6pku0rjpCdtpYKJ6s0XCqkUql8Kk42aThZpWFbLh3tIi6OfO7cOT777DOq\nVq2qHk798ccfc/v2bdatW4eLi0vRHrCUO3bsGMOHD8fIyIj+/ftz4cIFjh49iqurK2vWrNF0eIJQ\nqr2YeJqamr7yeWlpaa9d9E0QSpLcruk8P5729fVlw4YNOZJOgC+//JKuXbuqv5ckiZYtW9KzZ08+\n/fTTV+7Ty8uLTZs2ZWvbu3cvdevWfWX1pTp16uQVqvCOyvrEWVwjQm7EdSIzNzdn0qRJnDx5kokT\nJ3Lr1i1UKhXVa32IjnlDrsRAeDRExMDlG3D1FjzLAPBAYd8eCUh9xceV5sZysZ+aleXKsjVcwNVe\nia6OEfDmqwhn1R+IjIzkxo0bpKamcvv2bRQKBc2aNctXBb6CXidpaWmsXLmSiIgIHB0d6devX6mp\nmJw1BKx37974+fnx+PFjypYty61bt975/yd5EX9PhLwUdg6cILzNck08hwwZwurVq9m8eTOmpqbc\nu3cPAGNjY4yMjLC0tMzxRq6jo4ONjU22T3r69OmDQqFQV7H6/PPP+eOPPxgxYgSDBw/m2LFjrFix\ngvXr1xf1+QmCIJQo9+/f5+7du1SsWBETE5NiPbYkSegYVWTIuB34LQlk+1U3MKiCsr4rl7TMeL8A\nSynraKmo6aqgvoeC+u5ywuli93rVZV9XpUqV6Nu3LytWrKBbt27q9mHDhhWq7HteUlJSaNq0KadO\nnVK3LViwgCNHjuTaw1FSZM37+ueffwgMDGT//v3Z2gVBEAShKOWaeM6fP1/9SfGLfvzxR8aPH5/v\ng0RHR2e7GXFycmLnzp2MGDGC+fPnY2tri5+fHx07dixg+IIgCKVDZmYmI0aMwM/PD5CXGfHz88t1\ndMjreJIscfE6XAiXi/xcui4/EpIAmoN9c3Whn7zmWzhYy+tjelR8vnUGD2clerqaSzJfZfHixVSu\nXJlt27ahUCjo2rUrw4cPfyPH+u233zh16hR2dnYMHDiQ1atXc/HiRSZNmpStcEVJ1bFjR2rXrs25\nc+eyleZ/WUVJQRAEQXhduSae+S0j/KIbN27kaAsMDMzR1qhRI86ePVvg/QuCIJRGM2fOxM/PoD/Q\nrAAAIABJREFUD4VCQaVKlYiIiGDw4MG4urrmuYh1Xu4+kgi6CsEREBwubyNiCrYPQ32obCf3WrrY\nQWV7cHOSq8qalil5CearaGtrM3bsWMaOHfvGj5VVWO/nn3+mT58+1KxZk44dO+YouFcSXLx4kcOH\nD6Ovr0/btm2xtrZGX1+fffv28f3336ur2n711VdiPW1BEAThjSjQciqCIJRsaWlpfPvtt/j7+6NS\nqWjXrh0zZ87E2NhY06G98zZs2ADIy5L07NmTYcOG4efnx99//13gxPN+nMTBcxB4Dg6eg7Do/L/W\nzBiqV4RqleStm5OccJYvp9lhsqVR1jqfAQEB1KtXj7/++itbe0mxePFiPv/8c/U62eXKlWPXrl14\nenpibm6e6zI6b0JkZCQPHz6kSpUq2dYFFwRBEN5uIvEUhLfIgAEDWLdunfr7JUuWEB0dza5du0RS\noWFZBcR1dXUBeajti+2vEpcoERYlJ5enQuVE88rNvI+npQVVHZ4X+nGRk8zqlcDWUiSYRWXYsGGs\nWrWKbdu2sW3bNkD+9/366681HNm/bty4wRdffEFmZiZdunQhJiaGkydP0qNHD65du1as10J6ejp9\n+vTB398fkP8PLFiwgL59+xZbDIIgCILmiMRTEN4Sd+7cYd26dWhra7N//34MDQ1p0qQJe/bsITQ0\nFA8PD02H+E5r3749Z86coWfPnvz888/q4Zjt2rUD4OFjidNXICRCrip77XmyGZuPwoh6ulC3KtR0\nlRPN91zkeZj6eiLBfJPc3d05fPgw33zzDRERETg5OTFlypQSVek0KCiIjIwMmjVrxoYNG0hPT8fU\n1JTw8HB1FdviMnbsWPz9/dHT08PFxYXLly8zYMAA3N3dC70mnCAIglB6iMRTEN4Sjx8/BsDGxgZv\nb28UCgUVK1YkJCSE2NhYDUdXMA8fPiQ+Ph5HR0d1D2FpN2bMGK5fv86yZcu4EHINpWkj2vWcxLKj\njfhikcSNO/nfl64ONPCAxrWgSW3569KaZEZERLBw4UIePXpE7dq1+eyzz9DR0dF0WPnm6enJgQMH\nNB3GK2VV1w0LCyMmJobIyEjS09NRKpXFvuzLli1bANi+fTs+Pj4MGDCAZcuWsX37dpF4Cu80SZLE\nSBThrZDXKC6ReArCW6JixYqYm5sTExNDhw4dMDQ0JCQkBH19/VLT25mens7gwYNZuXIlIM9FW7Nm\nDS1atNBwZIWTnCpx9RZcuQVXbmoRb72ESp3/5NZ9bTJVCrYG570PAz1wtQdXB6jqCI1qglc1MNQv\n/TcpFy5coHHjxiQmJgKwbNkydu7cybZt2165prNQMI0bN6Z69epcvHgRe3t7dfvgwYPVw72LS9aN\nddZc04yMjGztgvAu0tXVJS0tDX19ffF/QSjVJEkiLS0t1/eWdyrxvHbtGrt27QKgVatWuLq6ajgi\noaRKSkpCT0+vVPW8GBgYsHLlSrp27aqeb6atrc2SJUuwsLDQcHT5M2bMGFauXIlSqcTS0pL79+/z\n8ccfExISgouLi6bDU5MkiZgHcvXY+3HwMB4eJUBs/L9f342F6Psve/XLryk9XajtCp5V5YI/rvby\nw9YSlMq382bE19eXxMREWrRoQatWrfjpp5/4559/8Pf3p0ePHpoO762gp6fH7t27GTRoEAcOHEBf\nX5/+/fvzyy+/FHssnTp1Ytq0abRt2xYnJyciIiLQ0tJSDzcXhHeRUqlET0+P9PR0TYciCK9NT08P\npVL5yp+/M4nn5s2b+d///qf+j51V+bN9+/YajkwoSS5fvkyvXr0IDg5GW1ubTz/9lFmzZpWa4Z5t\n27YlODiYbdu2IUkSLVq0oEaNGpoOK9/Wr18PwP79+2nUqBHt2rVT94CNGDFCY3E9ipc4cwXOXIGg\nq/L2flzh96dQgJsj1HOHuu5Qz00u/KOr83YmmK9y5coVABYsWICTkxN3797l119/5erVqxqO7O1S\nvnx5duzYoR4CpalelUmTJnH79m1Wr15NREQEhoaGLFq0CE9PT43EIwglhVKpRF9fX9NhCMIb904k\nnomJifTp04f09HTat2+PJEls27aNTz75hNu3b1OmTBlNhyiUAHFxcTRv3py7d++ipaVFRkYG8+fP\nR1tbmzlz5mg6vHxzdXUtUVU1CyJr6J2ZmRlKpRITExNAHpqXmZnJTz/9xOLFi0lJSaFx48bMnz8f\na2trAPbt28eGDRvIzMykTZs2dOzYsZAxSFy8DscvwomLcOIyBZp/+SJtLXlNTDdHqOok92S6OUIV\nByhjmL+bf5VKxS+//MLChQtJTk6mUaNGzJ07Fxsbm8IFVYLY2dnx8OFDpk+fTufOndm0aRMAtra2\nGo7s7aTpYXy6urqsWrWKKVOm8PDhQ1xcXNT/xwVBEIS3n0LKaxaoBiUk/FvOMatAQmGcOXOGevXq\nUblyZa5duwZA5cqViYyMJCgoSHzaWsoFBQUBvHYlybVr19KrVy/ee+89jh8/zrlz5/D29sbQ0JCk\npCSN37S9C/r168eKFSswNTXFxcWFs2fPoqWlxdmzZ1m/fn2O4YHVq1fn9OnTrFq1isGDB2f72cSJ\nExk/frz6+1ddJ0kpEkdD4FgInLgkL1mSnJp3rMaG4FkFnMqDhSlYmkM50+cPM7A0A0eb1+/FHD9+\nPJMnT87WVq1aNc6cOVPqPyHfvn27+sPALO7u7pw6dUpjHwgW1d8T4e0mrhMhL0V1DysIb5N3oscz\na4HqmJgYzp07hyRJ3L59O9vPhLdPSEgI27ZtQ6VS0bp16zw/YEhJSQHAyckJQ0NDqlatCsgFbzIz\nM9HWfif+u2jU7NmziYqKIjAwkLNnz6Krq8uiRYuoVq0as2bNAuDvv/+mWrVq+Pj4cPHiRXbs2MGw\nYcMAGDlyJMbGxkyaNIkJEybQr18/HBwcsh0j/anEycuwPwgCz8Gpy5CRmXtcerpQqzLUcYO6zx+u\n9m9+7qVKpWLGjBmAPAy5Zs2atGzZkkuXLrFnz55SP1Wgbdu27N69mxkzZhAbG0utWrWYOnWqGIUi\nCIIgCG+hd+JOulKlSrRp04YdO3Zk+3SyXbt2ODs7azAyIUt6ejr//PMP9+/fp3r16rz//vuvtb+A\ngAB69uzJs2fPALn3a9myZXzyySevfM0HH3yAlpYWW7ZsoVWrVkRERADQsGFDkXQWE1NTU/bt20dw\ncDBxcXFUq1YNa2trkpOTSUtLQ6lU0qZNG/T09KhZsybR0dGEh4eTlpaGg4ODOknbtWsXp06d4uq1\ncNIV9ly+AbuP2HAh0piQm5CaRw0He2t4vxp4VZe3NVw0M/8yPT2dlJQUFAoFHTp0QF9fH09PT27d\nulXqlsh5lebNm9O8eXNNhyG8xOXLlxkyZAgXL17E2tqacePG0bNnT02HJQiCIJRS78RQW5CrlA4f\nPpxNmzahUCjo2LEjs2bNKvZ1zIScHj9+TPPmzTl79qy6bdiwYcyaNStfw1v/O+QpKSmJ8uXLk5SU\nRPfu3dXzivT09Lhz506uC6YvWbKEzz//XD3X0MXFhX379uHo6Pg6pygUATc3N65evYq3tzeVK1dm\n2bJlABw7dowPGrdC0nVm8LBpxKdZEbDzKir9KuiZ1uBpxqurq2Wp4SKviflBdXmpEnvrkjOsulq1\naly+fJlGjRpRtWpVFi9ejEqlIjg4uFQVjiotxBBKWUxMDDVr1szxAcdff/1Ft27dNBRVySGuEyEv\nYqitIOT0ziSeQsk1cOBAli5dip2dHY0bNyYgIID09HQ2btyYrwIx/70BCA4OpmbNmjg7OxMZGYlC\noaB69epcunSJY8eO5dmbGhERwenTpzE2NqZZs2YYGhq+/kkKr0WSJPYEBtP1kzE8eWYF+pVAvyKO\nrk1JlSrwML5g+3Oxgyae0MwTmtQGS/OSk2j+19mzZ2nevDmPHz9Wt/388898//33Gozq7SUSCtnP\nP//MuHHj8Pb2Zs2aNSxYsICff/6Z+vXrc/LkSU2Hp3HiOhHyIu5hBSEnMX5Q0LijR48C4O/vj5eX\nF46OjkyZMoVjx44VqjJpuXLlAIiOjmb//v3o6uoSGRmZ7We5cXFxKVFrRr4rVCqJ2w8hPAYinj8i\nYyDyDkTehuTU98DpH15MEaMev3J3auUtwMMZLAzvU8Uulf6dnXC0KbmJ5n95enpy8eJFAgICSE5O\nxtvbG29v7zd2vJiYGHx9fTl9+jRly5ZlxIgR9OvX740dTyiZ4uLk9YKaNGmCvb09HTt25Oeff35r\nhngLgiAIxU8knoLGGRsbA3D69Glq1arFhQsXAApdYMTW1pZevXqxZs2abHPHOnToQOXKlV8/YKFQ\nnmVI3H0Ed154RN2XE8zwaDm5THtauH3r6YJzeahkK/dmujvLyaabI5ibyElmUFAMAI42pW9et62t\nLb6+vm/8OAkJCTRu3Jjr168DchLav39/MjMzGThw4Bs/vlByZBVjmzlzJomJiezevTtbuyAIgiAU\nlEg8BY37/PPP+fTTTxk+fDjDhw8HwMjIiN69e+fr9XFxcerKs1paWoA8V7N8+fIEBAQgSRLt27dn\n2rRpb2xJlOTkZObMmcPVq1exs7Nj6NChlC9f/o0cq6SLfyJxIRzOhcGFMLh8A24/hAf56J3MjYmR\nnFS62EJFWznJzHrYWr75CrPvgg0bNnD9+nXc3d3x9/dny5YtjB07ll9++UUknu+Y//3vf+zYsYO1\na9eqK0q7uLgwc+ZMDUcmCIIglFYi8RSKVEJCAr///jtXr17FwcGB4cOH57kY/MCBA0lOTmby5MnE\nxsbi5ubG4sWL8xzuGh8fT69evdi5cycg3xQFBATw3nvvoaenx/Tp05k+fXqRndurJCcn07BhQ3VP\nLcDSpUs5depUjqU8Sru0dIm4RIhNhNgE1F/fi4WQCDgfBtfvFH7/FqZQ2U5OMCs9TzJd7OTk0sIU\nsZbqG/bw4UNAHl7p4eGBmZkZY8eO5cGDBxqOTChuSqWS1atX07VrV3VV2+7du4u5aoIgCEKh5Zp4\nTp06lY0bNxIWFoaenh4NGjRg6tSpeHh4qJ/zww8/EBAQQHR0NLq6utSuXZvJkyfj5eX1yv0ePHiQ\npk2b5mi/evUqrq6ur3E6giYlJCTg5eXFlStX1G0rV67k1KlTODk5vfJ1CoUCX19fhg0bRkZGBjo6\nOvk6Xr9+/di5cyfa2tro6+sTERFB69atCQ0NLdabIz8/Py5cuICzszPffPMNK1as4NSpU3z//fes\nXr2aZ8+esXHjRm7evImLiwsdOnQo8cuzxCVKXIyUk8mL1+FSJITehMTkwu9TqQRrc6hQTn6ULyf3\nVFayhcr2cpKZNSxW0IyaNWsCsGzZMoyMjNTzr7PahXeLQqHg448/5uOPP9Z0KIIgCMJbINe730OH\nDjF06FDq1q2LSqVi/Pjx+Pj4EBoairm5OQBVq1Zl3rx5ODs7k5KSwsyZM2nZsiXh4eFYW1vnevDQ\n0NBsS1vkp/CLUDgqlQpJktRDUd+E2bNnc+XKFVxdXRkzZgyLFi3ixIkTjB8/npUrV+b5eoVCke+k\nMyUlhS1btgDymp3lypVj8ODBhIaGcvjwYdq1a/da51IQV69eBWDUqFF88cUXuLu78+GHH3Lt2jVS\nUlJo2bKl+gYe5HULt2/fjq6ubrHFmCUzUyI2Ee7Hyb2U9x8/38bJj7uxcOWmPP+ysHS0oVpFqOkK\ntV2hZmVwKi8nndraIrEsyT766CMGDRrE4sWL+fXXXwGwtLRk/vz5Go5MEARBEITSLtfEc9euXdm+\nX7VqFaamphw/fpw2bdoA0KtXr2zPmTFjBkuWLCEkJCTPRcEtLS2xsLAoTNxCPsXHx/P555+zadMm\nJEmiQ4cOLFiwINe1LAsrLCwMgK+//pr+/fvj6OhIs2bN1O1FKWudTW1tbYyNjdHV1cXExCTbz4qL\nnZ0dAMuXL8fd3R0/Pz91+5QpUzh69Cjly5enc+fOrF+/nr179zJz5ky+/fbbIo1DpZK4dU/umbxy\nE6IfwMPH8tzK+3Hy9lECvM4CStpa8pDXsiZgYSJvyz7/3s0RalcBdyfQ0xUJZmmkUChYuHAhrVu3\n5syZM5QtW5ZevXq9s/OVNeX48eMsWrSIJ0+e8MEHH/DVV1+V+FESgiAIgpCXAr2TJSYmolKp1L2d\n//X06VMWLlyIhYVFvirf1alTh/T0dNzd3Rk3bhwffvhhQcIp8dLT07lz5w7W1tYaWQtSkiS6devG\n3r171W0BAQE8evSIAwcOFPl8uaz5jIsWLcLR0VGdgL3uPMcTJ04wb9484uPjqV+/Pt988w0mJiZ4\neXlx4sQJ/ve//2FmZkZ4eDjGxsa5DvN+E4YOHcrSpUs5c+YMTZo0AUBfX59x48bx3XffAXJvcNeu\nXalVqxYDBw7k9OnTr3XM+3ESZ65AcARcvSknm1dvQWr6a57Mc/q6cmXY6hWhusvzbSWwLivmWb7t\nFAoFHTt2LNRSRsLr27ZtGx07diQzMxOAv//+myNHjhAQEIBSqdRwdIIgCIJQeApJyn//R7du3YiM\njCQoKCjbzef27dvp0aMHKSkpWFpasnXrVurVq/fK/YSFhXHw4EHq1q1Leno6q1at4s8//+TQoUM0\nbNhQ/bwXF98NDw8v6Llp1NatW/ntt99ITU1FR0eHTz/9lH79+hXrTXtMTAwdO3bEwMCA1atXo1Qq\n6d27N8nJyWzYsCHXeZeFERsbS58+fbIVIjEwMGDp0qWFXhfz+PHjjBw5Un0TBlC3bl3mzJnDw4cP\n8fX15caNG4BcCXfq1KnFnngC3Lt3j3nz5nHr1i2srKwYMGAAbm5ufPfdd+zbt4+PP/6YIUOG8Ntv\nv7F7927at2/PDz/8kK99p6YruRJtSGiUEZdvydu7cXqFjtXUKIOyZZ5R1uQZFsYZlDV+hoXxM8o+\n/9q2XDp25dLRfnOjsgVBeIUOHTpw584dOnTooB5BkZSUxB9//EH9+vU1HZ4gCPn04vJtoiiXIMjy\n3eM5cuRIjh8/ztGjR3MkT02bNiU4OJhHjx6xcOFC2rVrx+nTp3F0dHzpvlxdXbMVEWrQoAE3b95k\n+vTp2RLP0ur06dNMnjwZgLJlyxIXF8e8efOwsrJSD1EuDsnJciUYMzMz7OzsUCgUlC1bluTkZPXP\nipKFhQXLli1jwYIF3Lp1CxsbG/r370+lSpUKvc9Zs2aRmZlJu3btqFOnDrNmzeLMmTMcPnyYpk2b\nsmbNGi5fvkx6ejpVq1bV2B93GxsbJk2alKO9W7duHDhwgM2bN7N582ZAHh7cpUsX9XOeZSiITdTm\nTpwed+N0ufdYlzux8td3n7eppPx9YGFe5hnONmk4WadhVy4dC+NnmGcllWWeYVYmQySUglBCZWRk\ncOeOXBZ6zJgxaGtrExISwo4dO4iKihKJpyAIglCq5SvxHDFiBP7+/gQGBr60l8zQ0JCKFStSsWJF\n6tWrh6urK8uXL2fChAn5DqRevXr89ddfr/x5nTp18r0vTfvzzz8B+ff2+++/M2vWLEaMGMGxY8cK\n9Dt5XR4eHlhYWHD37l1Gjx6NUqkkOjoac3NzOnfuTJkyZd7IcVu3bl1k+8q6CVu5ciVmZmbcu3eP\n+fPno1Qq1ddEVkGikniNVHX3JF27KtNmB3A/3gAzy6q8V7clq4JsuLsb7sXJy5IUlL6uPJ/Ssyp4\nOMvzK92coJyZLqALmBTxmZR+QUFBQMm8ToSSQ9PXiZ2dHTExMfz111/Ur1+fEydOAPDhhx+Ka7cE\n0fR1IpR8L47aEwRBlmfi6evry4YNGwgMDMz3UieZmZmoVKoCBXLhwgUqVKhQoNeUVM+ePQPAysoq\n2zarvbgYGBiwfv16OnXqxKFDhwAoU6YM69ate2NJZ1Fzdnbm6tWrfP311zRt2pSAgAAAKlasqOHI\n/hWXKBERg/px/TZE3IbI23JRH2gIRg3BCB4B+4MLtn9JUkFqKHamt/l+WHMaVFNSrSLoiAqxgvDW\nmTFjBt27d2fWrFnqthYtWtCiRQsNRiUIgiAIry/XxHPIkCGsXr2azZs3Y2pqyr179wAwNjbGyMiI\nJ0+eMG3aNNq3b4+NjQ0PHz5k7ty53Llzh27duqn306dPHxQKBStWrADk4ZPOzs64u7vz9OlTVq9e\nzZYtW9i4ceMbPNXi07JlS1auXMm4cePYvXs3J0+eVLcXt6zlb/bt24ckSfj4+GBvb1/scRTW77//\nTrt27Vi6dClLly4F5KHd7du3f+PHliSJJyn/LjVyP05efuTuI7hxR04uI2IgLvH1jqNUgpU5OFrL\ny444loc1S6cQE3GUj5pUpXUzDyZOGEPMhVish/1NLddORXOCgiCUON26dcPc3JwFCxaQmJjIBx98\nwJgxY97oUliCIAiCUBxyTTznz5+PQqGgWbNm2dp//PFHxo8fj7a2NqGhoSxbtozY2FgsLCyoV68e\nR44cwcPDQ/386OjobPNCnz17xjfffENMTAwGBgZUq1aNnTt38tFHHxXx6WlGjx49uHDhAtOnT+fg\nwYOAvOzMqFGjXnvfycnJPHnyBCsrq3xXOLSzs6Nfv36vfWxNaNWqFYcOHWLevHkkJCRQr149Ro8e\n/VpLCzx58oSRI0eye/dudHR06Nx9EO26fUNYtBZXbsG1W3KF2DuPXr9KrI42OJcHFztwrgC2lmBT\nFmws5G35clDOFLS0svde+o2aAikprFq4inLlyhF+LQQ/P783sjSNIAglS/PmzfNcjkwQBEEQSpsC\nVbUtbi+Ojy+NFcHCwsIICwvDwcGB6tWrv1ZF2/T0dIYOHcqSJUuQJAlnZ2fWrVtH/fr1UalUTJ8+\nneXLl5OWloaPjw+//fZbqfydFUZec20kSeJeLNy4C5ExEhOmruDGXQn0KoJBVRS61q91fAM9ObGs\nbAcVbeWvKz3f2lnmTCrzw93dnStXrvDFF1/QsmVLhgwZwu3bt1m7di09evR4rXjfVWJOlpAf4joR\n8kNcJ0JeSvs9rCC8CSLxLCV8fX2ZM2cOIC8bkpycjLm5OZcvX2b27NlMmzYt2/O9vb0JDAx8J4Zn\nZd0AuLp5ci1K7q28FiX3XF6LkudaFrbnUl9X7p20NpfXsLQqK3/tVB4q24OLrdxrWdTL5GzdupWP\nP/6YF/97NmjQgIMHD6KnV/ilVN5l4kZRyA9xnQj5Ia4TIS/iHlYQcir8eMV3RFRUFJ999hknT57E\nxMSEoUOHMmrUqGJdjxPkqq4AR44coX79+jRp0oRjx46xadMmfv/9dwDWr1+Pk5MTbdu25ciRIxw7\ndoxGjRoVa5xvWmq6RORtCI+G8Bh5e/6KK1EP9HhU2LmWqlSk1Gu083HF090QN0eo6ignl8aGRZ9U\n5kf79u3Zt28ffn5+PH78mHr16jF+/HiRdAqCIAiCIAilkkg8c5GYmEiTJk24fv06APHx8YwePZrM\nzEzGjBlTrLGkpaUBYG9vj46ODjY2NuqYnj17hpGREV27dkWpVFK7dm327NnDgwcPijXGopKUIieX\nkS9Uh418XjE2+gHk7KM3znOf5sZQsQJYm6Wwc9NcpNRIWjWtyrMnV9m3fTGWlhZs/OUO2iWoUmzT\npk1p2rSppsMQBEEQBEEQhNcmEs9cbN26levXr+Pm5saOHTsIDAxk4MCBzJw5s9gTz+bNm7Nt2za8\nvLyoXLkyhw8fRktLi7Zt26orCXfs2BFHR0f27t2LQqGgRo0axRpjQTzLkLh++/mQ2CgIi4aw51t5\nCZKC09WR51lWdQRXB3lbxUFuMzfJSiiN+KOiIV99tZB/1skt+vr6rFq16rUKFgmCIAiCIAiC8Gri\nTjsXjx8/BqBu3bo4OztjamrKwIEDiYuLQ5KkYh2CuWjRIlq1asX58+e5e/cuOjo6LFy4kBo1arBi\nxQrat2/P1q1b1c//5Zdf8r3ualGRJImH8fLcyut3IDYR4p/A4yeQkCRvHz+BB4/lQj+ZmQU/hlIJ\nTjbP51fayVtSw3GwSqNd8+r5KuQzdOhQPD092bNnD7q6unTq1IkqVaoUPBhBEARBEARBEPJFJJ65\nyCoasHbtWvT09Lhw4QIgJ6LFPe/P2tqaU6dOcezYMRISEqhVqxYODg6AvFbn+fPn2bBhA2lpaTRr\n1owmTZoUeQySJBH/RF7L8l4s3I2Vh7+GR//ba5mQ9PrHeXEJkmxVYm3lJUl0dbL/7oOC5MmdBake\n6+XlhZeX1+sHKwiCIAiCIAhCnkTimQsvLy/GjRvHTz/9xKJFiwA5AVyyZIlG4tHR0eHDDz986c+q\nVKnCuHHjCrQ/SZL4c/FfbNtziQyFBXUatMDG3p3HTyAuER4nytsHj+Vk834cPH1WBCfynJ2VPBTW\n1UHeVnEAV3twsC7cEiRC6REXF8fKlSu5c+cOHh4e9OrVSwx1FgRBEARBeIuJO708TJ48GR8fH06e\nPImpqSmdO3fG0tJS02EVSFyixJWbcs9kVtGeyNtwMSyZtMzuQHcA9v39+scqY/B8XqU9WJmDmbFc\n2MeszPOt8b+FfowMRHL5Lrpz5w4ffPABN2/eVLetX7+ebdu2ieRTEARBEAThLSXu8vKhcePGNG7c\nWNNh5Eqlkoh5IK9heeUWXLkpf331ltxj+XJGBT5OGQN5PUvr5+tZOtvKvZRZvZU2FppZfkQoPb75\n5htu3rxJ9erV6dixI/PmzWPXrl0sWbKEzz77TNPhCYIgCIIgCG+ASDxLEUmSiE3IXgE2PPrfbdrT\ngu9TSRruFfWxtYQDe/7macp9fIf0xtHWBHNjMDeRey6tzeVkU/RSCq8rODgYgIULF9KgQQMMDQ0Z\nM2aMul0QBEEQBEF4+4jEswRKSJK4eVdOKK9FPU8unyeaj58UfH/6uv/OoaxkJxfryUwO49PeTdDR\njmfMkMXcvn2bXZdHo6+vz7Shg9DTEwmm8GZYWVlx+fJlVq1ahYmJCdu3b1e3C4IgCIJr6/NeAAAc\nm0lEQVQgCG8nkXhqgEolcTESzoVB1H2Ivg8xDyD6gbx9klK4/ZYzk4e7VnUENydwe751tAGlMnsi\nKUmuHNj8IevWraNXr17q9p9++gk9Pb3Cn5wg5OHbb7/l4MGDzJs3j3nz5gFQrlw5Bg0apOHIBEEQ\nBEEQhDelVCaekiRx69Ytnjx5gouLCwYGBpoOKVfPMiTOXYPDF+BIMBwNkde3LAxDfahs928BH9fn\ncysr20NZk/z3UioUClauXMl7772nXs+yT58+9OjRo3CBCUI+tWzZku3btzNp0iTu3r2Lh4cHM2fO\nxM7OTtOhCYIgCIIgCG9IqUs8nzx5Qo8ePdixYwcAFhYWrF+/Hh8fHw1HJifEtx/+O0Q2LAouXYcT\nlyAlLf/7MdCTlxSp/DyhdM16OECFckVXvEdbW5tvv/2Wb7/9tkj2Jwj51bp1a1q3bq3pMARBEARB\nEIRiUuoSzyFDhrBjxw709fWxtLQkOjqajh07cvnyZRwcHAq1T0mSWLVqFfv27UNPT4/evXu/tIpt\nRobEvTh5OGzMQ3l7+6E8VDY8Rk44k1Pzd0zrsuD9njzf0t4a7K3kh50VlDURlWEFQRAEQRAEQXh7\nlKrEU5IkAgICAAgKCsLNzQ0fHx8CAwPZs2dPoeeI+fr64ufnJ3+jNGLJujMM+3YO5Z29iYiByBiI\nuA13HoFKVbjYncpDo/fAuyY0qiknnCK5FARBEARBEAThXZBr4jl16lQ2btxIWFgYenp6NGjQgKlT\np+Lh4aF+zg8//EBAQADR0dHo6upSu3ZtJk+ejJeXV64HPnToECNHjiQ0NJQKFSowevTofK3hJ0kS\nADo6OigUCnR0dLK15yU1XeLGHbh1D27egzMhD1m22wtFjZ6UsahGUrq8tuWcXfnaXQ7mxv9WkK38\nfH3Lum7gYCOSTEEQBEEQBEEQ3k25Jp6HDh1i6NCh1K1bF5VKxfjx4/Hx8SE0NBRzc3MAqlatyrx5\n83B2diYlJYWZM2fSsmVLwsPDsba2ful+b9y4QevWrRk0aBBr167lyJEjfPnll1haWtKpU6eXvkaS\nJBQKBe3bt8ff35+6detSvnx5rl27hoGBQY45nhkZEuEx8hzLi5Fw+TpcugERMZA9R7VEUe5/ACSl\n5/0LszKXh8PaWYJt1tYSKtn+v717j6qqzvs4/j6Hu4BH5Sr6KNLjDR41E1xZYzcv6Yg0NJnXxGpV\npjkk1vTgpXSmVGrZlNc0ZxQzM2S8dHHKUhSQWo4KXiDRyZpBA9RISUwEzn7+8PGMZ1TEC2yEz2st\nVpzf/vE73x1fcH/5/fZvny8y/WyayZRbU3p6OpmZmfj4+PDII48QEhJidkgiIiIi0kBYjJpOFQJl\nZWXYbDY2bNjAoEGDLtuntLSUZs2a8fnnn9OvX7/L9nnppZdYv349+fn5jrannnqK3NxcsrKyHG2n\nTp1yfJ6QkMDSpUv56aeTxDw8hu07j4JHazx92/LbYc9iC+jIsRIoLoHin87PaJ6rqOmZ/ZvVUkXV\nmX/gcu47nn2iPx3+y8p///+zL9sEgYe7isr6ZufOnQBERkaaHMn1q6qqwsXFxbT3f/XVV5k2bZrj\ndYsWLfjyyy/p3r27aTHdbA0hT6T2KU+kJpQncjUXX8PabDYTIxGpP67pHs/S0lLsdrtjtvM/nTt3\njiVLluDn50ePHj2uOM5XX31F//79ndr69+9PcnLyFS/A/5IVw+bfnKKkrBmnK9Zj6Xa+vRxYlVHz\nc7BaITQY2oVAm+Dzn3+cOp+/Z6ZC+fdUlR8Fqnh9zhwSEgbWfGCR67Bo0SKmT5/OsWPHCA8PZ8mS\nJdx99911GkN2djbTpk3DxcWFJ598kry8PDIzM4mLi2Pv3r11GouIiIiINEzXVHjGx8fTvXv3S+7f\n/OSTTxg+fDhnzpwhICCATz/9lBYtWlxxnOLi4kuW4QYFBVFZWcmJEycuu0TX0iKGf524lmjP7xb7\nP+0gIgy63Ab/Ewad24Knh/Os5f+OGktS0qn/39W2E3FxcYwYMeLa3kzkGq1YsYJx48Y5Xufl5fHg\ngw+ye/duOnToUGdx7N69G4DY2FgWL17MmTNn8Pb2Zt++fZSXl+Ph4VFnsYiIiIhIw1TjwjMhIYGs\nrCwyMzMvuYfxgQceYM+ePZw4cYIlS5YwePBgduzYQdu2bW96wABNPKoIaVFOUPNz+DWtpIVvBS18\nKmnRtOL8576VBNrO4ePlvAVtVSns33f5MQcMGMCAAQMcry8so5Fbx632PXvjjTcAmDBhAo8++iiJ\niYlkZmaSlJTEs88+W2dxlJSUAJCVlUVqaioHDhwAwNvbm7179za4e5ZvtTwRcyhPpCaUJ3Il7du3\nNzsEkXqnRoXnxIkTSUlJIS0tjdDQ0EuON2nShLCwMMLCwujZsycdOnRg+fLlvPLKK5cdLzg4mKKi\nIqe24uJiXF1d8ff3v+zXNCmIY9aMsXQO88LWpIoGdi0sjVBZWRkAXbt2xdPTk06dOpGZmeloryu9\nevUiLCyMw4cPM2TIEEf7iBEjGlzRKSIiIiLmuGrhGR8fz5o1a0hLS6vx8r+qqirs1TzwslevXqxb\nt86p7YsvviAqKuqKG6zs+Ox/CQ8Pr9H71yW73c7x48dp1qyZliSa5Fbd5KFPnz4sXbqUGTNm8MAD\nD5CSkgLAww8/XOfnsn37dp599lnHrrbPPPMMv//977FarXUaR226VfNE6pbyRGpCeSJXc/HmQiJy\nXrWF5/jx41m5ciXr16/HZrM5Zil9fX3x9vbm559/JikpiZiYGIKDgzl+/DgLFizghx9+4NFHH3WM\nM3r0aCwWC8nJyQCMHTuW+fPnM3HiRJ5++mm2b99OcnIyq1evvmIs9bHo3LRpE3FxcRQVFeHq6soL\nL7zAa6+91qAu1qX2vP7662RnZ7Nr1y5WrFgBnP/ZuHjW8WbLycnhyy+/xM3NjcGDBxMWFgacX4Xw\nn38MEhERERG5WaotPBctWoTFYqFPnz5O7dOnT+fll1/G1dWVvLw8li1bxo8//oifnx89e/YkIyOD\niIgIR/+CggKnJXuhoaFs3LiRiRMnsmjRIlq1asW8efOIjY29yadXe7755hseeughzp49i7e3N2Vl\nZcyePZsWLVrw4osvmh2e1JIzZ85w+PBh/P39CQ4OvqGxmjdvzvbt29m4cSOFhYV06dKF3r1736RI\nL7Vs2TKeeuopqqqqAJgyZQobNmy45OdbRERERORmq7bwrG65LICXlxdr16696pukpaVd0nbPPfew\na9euq35tfZWSksLZs2eJjY0lNTWV1atXM3LkSJYvX35DhefmzZuZPXs2xcXFdOvWjaSkJEJCQm5i\n5HK91q1bx5gxYygtLQUgLi6OJUuW4O7uft1jenh41MkfXAoLCxk7dixVVVUMHz6ckpISPv/8c0aO\nHElBQQFubm61HoOIiIiINF7X9DgV+bfy8nIA2rRpg9Vqdezge6H9emzatImBAwc6Cv59+/aRmZnJ\nrl27qn08jdS+/fv3M3ToUCoqKmjTpg1Hjx4lOTmZoKAgkpKSzA7vqvbu3cu5c+e48847WbVqFXa7\nnaCgIIqLiykoKHAsuRURERERqQ26GfE6XVieOHfuXPr3709MTAwAffv2ve4xZ8yYgd1u55lnnmH7\n9u107dqV77//nuXLl9+MkOUGbNiwgYqKCoYMGcL333/Pxo0bARwbAtV3zZs3ByA/P599+/axbds2\nfvzxR6dj1+uXX37h4MGD2khBRERERK5Ihed16tOnDzNnzsQwDL744gtKSkq49957Hc9mvB4//PAD\nAM899xx33XUXDz/8sFO7mOfCLHSTJk2wWCw0adIEAMMwzAyrxiIjI+nduzc//fQTXbt25YEHHsAw\nDB5//PEbKjxXrFhBQEAAHTt2xM/Pj8TExFvm/4mIiIiI1B0VnjcgMTGR/Px8UlNTSU9PZ/Pmzfj6\n+l73eBc2ZBo3bhxz5sxh4cKFQP3c0bexGThwIFarleTkZLp3786DDz4IQHR0tMmR1YzVauWjjz5i\n1KhRjo2REhISWLRo0XWPmZGRwZgxYygrKyMkJISqqipmz57NggULbmLkIiIiItIQqPC8QR06dOC3\nv/0tvXv3vuIzSGtqzpw5+Pv7k5GRwQsvvMCxY8fo27cvo0ePvknRyvWKjIxk6dKluLu7k5OTw5kz\nZ4iOjub11183O7Qaa9asGe+99x7Hjx+nsLCQOXPm3NCzZ1NSUjAMg3HjxnH06FGWLl0KwAcffHCz\nQr4lGYZBRkYGycnJpKenawZYREREBG0uVK907NiR7OxslixZ4tjV9qmnnsLVtX59m+x2O6tXryYn\nJ4eAgADi4uIIDAw0O6xa9/jjjxMdHc0333yDv78/nTt3dnpMUGNTWVkJ/Pse0Qv/vfC4lsaosrKS\nESNGsGbNGkfbI488wgcffFDvfo5FRERE6pKuhOqZ1q1b84c//MHsMK7IbrczdOhQUlNTHW1/+tOf\nyMjI4LbbbjMxsroREBBAQECA2WHUC7/+9a955513mDlzJmlpaezevRs4vyy5sZo7dy5r1qzBx8eH\ngQMH8re//Y3U1FTuvPNOJk2aZHZ4IiIiIqbRUlu5JikpKaSmpmKz2Zg6dSpRUVEUFhYSHx9vdmhS\nxwYPHsyrr74KQFZWFmfPnmXYsGFMnjzZ5MjMs23bNgDeeustUlJSmDt3LgBbt241MSoRERER82nG\nU67Jnj17ABg/fjx//OMfGTFiBOHh4Y52aVymTJnCqFGjOHjwIK1atWr0y48v7Hacm5uLYRjs378f\nAG9vbzPDEhERETGdZjzlmly4l/Ozzz5j//79jmeMNoZ7POXy2rZtS79+/QgPD2/URSfAE088AZxf\nfu7q6sqbb74JwJNPPmlmWCIiIiKma5CF55kzZzh58qTZYTRIjz32GK1bt2b37t106dLFsatrYmKi\nyZGJmK9fv368//77+Pv7Y7fb8ff3Z+XKlfTr18/s0ERERERM1aAKz9LSUoYMGYK3tzfNmzcnKiqK\nb7/91uywGpQLj3t56KGHaNu2LZGRkaSmpvLII4+YHZpIvTBixAiOHTtGaWkpx44dY+TIkWaHJCIi\nImK6BnWP55gxY1i3bh0Abm5u7Ny5kwEDBrB37168vLxMjq7hCA0NZf369WaHIVJvWSwWfH19zQ5D\nREREpN5oMDOep06dYt26dVitVg4ePMiJEycIDQ3lH//4B9u3bzc7PBERERERkUarwRSe5eXlAHh4\neNCqVSt8fX0dG96cPXvWzNBEREREREQatQaz1DYgIICIiAhyc3O544478PPzY8eOHXh7exMVFWV2\neCIiIiIiIo1Wgyk8LRYLKSkpDBgwgPz8fOD8s/M++OADgoKCTI5ORERERESk8ap2qe2sWbOIiorC\nZrMRGBhITEwMubm5juOVlZW89NJLdOvWDR8fH0JCQhg5ciQFBQXVvunWrVuxWq2XfBw8ePCGTiY8\nPJzc3Fw+/vhj/vrXv3Lo0CEGDx58Q2OKiIiIiIjIjal2xnPbtm0899xzREVFYbfbefnll+nbty95\neXk0b96csrIysrOzmTp1KrfffjsnT55k0qRJjp1kXVxcqn3zvLw8WrRo4Xjt7+9/wyfk6+tLdHT0\nDY8jIiIiIiIiN0e1hednn33m9Pq9997DZrORlZXFoEGDsNlsbNq0yanP4sWLiYiI4MCBA0RERFT7\n5gEBAfj5+V1n6CIiIiIiInIruKZdbUtLS7Hb7TRv3vyKfU6dOgVQbZ8LIiMjCQkJoW/fvmzduvVa\nQpFbkGEYZGdns379evbv3292OCIiIiIiUkeuqfCMj4+ne/fu9OrV67LHz507x6RJk4iJiSEkJOSK\n44SEhPDOO++wdu1a1q5dS8eOHenTpw+ZmZnXFr3cMiorK3nssce44447iI2NpUuXLvzud7/DMAyz\nQxMRERERkVpmMWp45Z+QkEBKSgqZmZmEhoZecryyspIRI0bwzTffkJ6eXqMZz4sNGjQIV1dXNmzY\n4Gi7MHsKcOjQoWsaT+qX9957j7lz5+Lh4cHtt9/Orl27qKysZNq0acTExJgdnoiIiMhN0759e8fn\nNpvNxEhE6o8azXhOnDiRDz/8kC1btlyx6Bw+fDj79+9n8+bN11x0AvTs2VPFZQP29ddfAzB58mTm\nz5/PhAkTANixY4eZYYmIiIiISB246nM84+PjWbNmDWlpaXTo0OGS4xUVFQwbNoy8vDy2bt1KYGDg\ndQWSk5NT7fLcyMjI6xpX6oeAgAAA3N3diYyMZPXq1QAEBwff8Pd2586dgHJEqqc8kZpQnkhNKE/k\nai5etSci51VbeI4fP56VK1eyfv16bDYbRUVFwPlHlnh7e1NVVcWQIUPYuXMnH3/8MYZhOPo0a9YM\nT09PAEaPHo3FYiE5ORmAt956i3bt2hEeHs65c+dYuXIlGzZsYO3atbV5rnKNSkpK2Lt3L02bNuX2\n22/Har2mW4KdPPbYY3z66ackJibyxhtvUFJSAsCoUaNuVrgiIiIiIlJPVVtJLFq0iNOnT9OnTx9C\nQkIcH3PmzAGgoKCAjz76iMLCQnr06OHUJyUlxTFOQUEBBQUFjtcVFRW8+OKLdOvWjXvuuYesrCw2\nbtzIb37zm1o6TblW69ato02bNtx///306NGD3r17c+LEieseb+jQobz55pt4enpSUlKCj48Pf/nL\nX+jbt+9NjFpEREREROqjGm8uZIaLlynoxuy68+233xIREUF5eTldu3blyJEjlJSUEBsbe8Oz0uXl\n5Rw/fpygoCDc3NxuSrxa8iQ1oTyRmlCeSE0oT+RqdA0rcqnrXzspDdaWLVsoLy9nwIAB5OTksGvX\nLgA2btyI3W6/obE9PDxo3br1TSs6RURERESk/lPhKZdwcXEB4MyZM9jtdn7++WcArFYrFovFzNBE\nREREROQWdNVdbaXxefDBB2natCnp6em0atXKsRHQ0KFDVXiKiIiIiMg104ynXKJVq1Z89NFHBAcH\nU1xcTEVFBbGxscybN8/s0ERERERE5BakGU+5rHvvvZd//vOffPfddzRt2pSWLVuaHZKIiIiIiNyi\nVHjKFbm7u9OxY0ezwxARERERkVucltqKiIiIiIhIrVLhKSIiIiIiIrVKhaeIiIiIiIjUKhWeIiIi\nIiIiUqtUeIqIiIiIiEitUuEpIiIiIiIitcpiGIZhdhBXcurUKbNDEBERERG5bjabzewQROoFzXiK\niIiIiIhIrVLhKSIiIiIiIrWqXi+1FRERERERkVufZjxFRERERESkVqnwFBERERERkVpVrwvPhQsX\n0q5dO7y8vIiMjCQzM9PskMQks2bNIioqCpvNRmBgIDExMeTm5l7Sb/r06bRq1YomTZpw//33k5eX\nZ0K0Ul/MmjULq9XKhAkTnNqVJ1JYWEhcXByBgYF4eXkRERFBenq6Ux/lSeNWWVnJ5MmTCQsLw8vL\ni7CwMKZNm0ZVVZVTP+VJ45Genk5MTAytW7fGarWSnJx8SZ+r5UN5eTkTJkwgICAAHx8fHnroIY4e\nPVpXpyBiqnpbeH744Yc8//zzTJ06lZycHO666y4GDhxIQUGB2aGJCbZt28Zzzz3HV199xZYtW3B1\ndaVv37789NNPjj5JSUm8+eabzJ8/n7///e8EBgbSr18/Tp8+bWLkYpavv/6ad999l65du2KxWBzt\nyhM5efIkd999NxaLhY0bN3LgwAHmz59PYGCgo4/yRGbOnMnixYuZN28e+fn5vP322yxcuJBZs2Y5\n+ihPGpeysjK6du3K22+/jZeXl9O/LVCzfHj++edZu3Ytq1evJiMjg9LSUqKjo7Hb7XV9OiJ1z6in\nevbsaTz99NNObe3btzcSExNNikjqk9OnTxsuLi7GJ598YhiGYdjtdiM4ONiYOXOmo88vv/xi+Pr6\nGosXLzYrTDHJyZMnjdtuu83YunWrcd999xkTJkwwDEN5IuclJiYav/rVr654XHkihmEY0dHRxpgx\nY5zaRo8ebURHRxuGoTxp7Hx8fIzk5GTH65rkw8mTJw13d3dj1apVjj4FBQWG1Wo1Pv/887oLXsQk\n9XLG89y5c+zevZv+/fs7tffv35+srCyTopL6pLS0FLvdTvPmzQH47rvvKC4udsoZT09P7rnnHuVM\nI/T0008zZMgQ7r33XoyLNu5WngjA+vXr6dmzJ0OHDiUoKIju3buzYMECx3HliQAMHDiQLVu2kJ+f\nD0BeXh5paWkMGjQIUJ6Is5rkw65du6ioqHDq07p1azp37qyckUbB1ewALufEiRNUVVURFBTk1B4Y\nGEhRUZFJUUl9Eh8fT/fu3enVqxeAIy8ulzM//PBDnccn5nn33Xc5fPgwq1atAnBaCqU8EYDDhw+z\ncOFCEhISmDx5MtnZ2Y77gMePH688EQDGjRvHkSNH6Ny5M66urlRWVjJ16lTGjh0L6PeJOKtJPhQV\nFeHi4oKfn59Tn6CgIIqLi+smUBET1cvCU6Q6CQkJZGVlkZmZecn9FZdTkz7SMOTn5zNlyhQyMzNx\ncXEBwDAMp1nPK1GeNB52u52ePXvy2muvAdCtWzcOHTrEggULGD9+fLVfqzxpPObOncuyZctYvXo1\nERERZGdnEx8fT2hoKE888US1X6s8kYspH0TOq5dLbf39/XFxcbnkrz/FxcW0bNnSpKikPpg4cSIf\nfvghW7ZsITQ01NEeHBwMcNmcuXBMGr6vvvqKEydOEBERgZubG25ubqSnp7Nw4ULc3d3x9/cHlCeN\nXUhICOHh4U5tnTp14l//+heg3ydy3muvvcbkyZN59NFHiYiIYNSoUSQkJDg2F1KeyMVqkg/BwcFU\nVVXx448/OvUpKipSzkijUC8LT3d3d3r06MGmTZuc2r/44gvuuusuk6ISs8XHxzuKzg4dOjgda9eu\nHcHBwU45c/bsWTIzM5UzjUhsbCz79+9nz5497Nmzh5ycHCIjIxk+fDg5OTm0b99eeSLcfffdHDhw\nwKnt4MGDjj9m6feJwPnVElar82WS1Wp1rKBQnsjFapIPPXr0wM3NzanPkSNHOHDggHJGGgWX6dOn\nTzc7iMtp2rQpr7zyCiEhIXh5efHqq6+SmZnJsmXLsNlsZocndWz8+PGsWLGCNWvW0Lp1a06fPs3p\n06exWCy4u7tjsVioqqpi9uzZdOzYkaqqKhISEiguLmbJkiW4u7ubfQpSBzw9PQkICHB8BAYG8v77\n79O2bVvi4uKUJwJA27ZtmTFjBi4uLrRs2ZLNmzczdepUEhMTiYqKUp4IAIcOHWL58uV06tQJNzc3\n0tLSmDJlCsOGDaN///7Kk0aorKyMvLw8ioqK+POf/0yXLl2w2WxUVFRgs9mumg+enp4UFhayYMEC\nunXrxqlTpxg7dizNmjUjKSlJS3Kl4TN1T92rWLhwoREaGmp4eHgYkZGRRkZGhtkhiUksFothtVoN\ni8Xi9DFjxgynftOnTzdatmxpeHp6Gvfdd5+Rm5trUsRSX1z8OJULlCfy6aefGt26dTM8PT2Njh07\nGvPmzbukj/KkcTt9+rQxadIkIzQ01PDy8jLCwsKMKVOmGOXl5U79lCeNR1pamuP64+Jrkscff9zR\n52r5UF5ebkyYMMHw8/MzmjRpYsTExBhHjhyp61MRMYXFMGqw64aIiIiIiIjIdaqX93iKiIiIiIhI\nw6HCU0RERERERGqVCk8RERERERGpVSo8RUREREREpFap8BQREREREZFapcJTREREREREapUKTxER\nEREREalVKjxFRERERESkVqnwFBERERERkVr1f0LLvLarhRdUAAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "zs = gen_train_data_with_acc(pos, 15, 100)\n", - "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.001)\n", - "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.001')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There are two lessons to be learned here. First, use the $h$ term to respond to changes in velocity that you are not modeling. But, far more importantly, there is a trade off here between responding quickly and accurately to changes in behavior and producing ideal output for when the system is in a steady state that you have. If the train never changes velocity we would make $h$ extremely small to avoid having the filtered estimate unduly affected by the noise in the measurement. But in an interesting problem there are almost always changes in state, and we want to react to them quickly. The more quickly we react to them, the more we are affected by the noise in the sensors. \n", - "\n", - "I could go on, but my aim is not to develop g-h filter theory here so much as to build insight into how combining measurements and predictions leads to a filtered solution. There is extensive literature on choosing $g$ and $h$ for problems such as this, and there are optimal ways of choosing them to achieve various goals. As I explained earlier it is easy to 'lie' to the filter when experimenting with test data like this. In the subsequent chapters we will learn how the Kalman filter solves this problem in the same basic manner, but with far more sophisticated mathematics. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## g-h Filters with FilterPy" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "FilterPy is an open source filtering library that I wrote. It has all of the filters in this book, along with others. It is rather easy to program your own g-h filter, but as we progress we will rely on FilterPy more. As a quick introduction, let's look at the g-h filter in FilterPy.\n", - "\n", - "If you do not have FilterPy installed just issue the following command from the command line.\n", - "\n", - " pip install filterpy\n", - " \n", - "Read Appendix A for more information on installing or downloading FilterPy from GitHub.\n", - "\n", - "To use the g-h filter import it and create an object from the class `GHFilter`. " - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from filterpy.gh import GHFilter\n", - "f = GHFilter (x=0., dx=0., dt=1., g=.8, h=.2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "When you construct the object you specify the initial value and rate of change for the signal (`x` and 'dx'), the time step between updates(`dt`) and the two filter parameter (`g` and `h`). `dx` must have the same units of `x`/`dt` - if `x` is in meters and `dt` is in seconds then `dx` must be in meters per second.\n", - "\n", - "To run the filter call update, passing the measurement in the parameter `z`." - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "(0.96, 0.24)" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "f.update(z=1.2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`update()` returns the new value of `x` and `dx` in a tuple, but you can also access them from the object." - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.96 0.24\n" - ] - } - ], - "source": [ - "print(f.x, f.dx)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can dynamically alter `g` and `h`." - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1.965, 0.375)\n" - ] - } - ], - "source": [ - "print(f.update(z=2.1, g=.85, h=.15))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can filter a sequence of measurements in a batch." - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ 1.965 0.375 ]\n", - " [ 2.868 0.507 ]\n", - " [ 3.875 0.632 ]\n", - " [ 4.9014 0.7306]]\n" - ] - } - ], - "source": [ - "print(f.batch_filter([3., 4., 5.]))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can filter multiple independent variables. If you are tracking an aircraft you'll need to track it in 3D space. Use NumPy arrays for `x`, `dx`, and the measurements." - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " x = [[ 1. 2.]\n", - " [ 3. 4.]]\n", - "dx = [ 10. 12. 0.2]\n" - ] - } - ], - "source": [ - "x_0 = np.array([1., 10., 100.])\n", - "dx_0 = np.array([10., 12., .2])\n", - " \n", - "f_air = GHFilter (x=x_0, dx=dx_0, dt=1., g=.8, h=.2)\n", - "f_air.update(z=np.array((2., 11., 102.)))\n", - "print(' x =', x)\n", - "print('dx =', dx_0)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The class `GHFilterOrder` allows you to create a filter of order 0, 1, or 2. A g-h filter is order 1. The g-h-k filter, which we haven't talked about, also tracks accelerations. Both classes have functionality required by real applications, such as computing the Variance Reduction Factor (VRF), which we haven't discussed in this chapter. I could fill a book just on the theory and applications of g-h filters, but we have other goals in this book. If you are interested, explore the FilterPy code and do some further reading.\n", - "\n", - "The documentation for FilterPy is at https://filterpy.readthedocs.org/." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Summary" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I encourage you to experiment with this filter to develop your understanding of how it reacts. It shouldn't take too many attempts to come to the realization that ad-hoc choices for $g$ and $h$ do not perform very well. A particular choice might perform well in one situation, but very poorly in another. Even when you understand the effect of $g$ and $h$ it can be difficult to choose proper values. In fact, it is extremely unlikely that you will choose values for $g$ and $h$ that is optimal for any given problem. Filters are *designed*, not selected *ad hoc*. \n", - "\n", - "In some ways I do not want to end the chapter here, as there is a significant amount that we can say about selecting $g$ and $h$. But the g-h filter in this form is not the purpose of this book. Designing the Kalman filter requires you to specify a number of parameters - indirectly they do relate to choosing $g$ and $h$, but you will never refer to them directly when designing Kalman filters. Furthermore, $g$ and $h$ will vary at every time step in a very non-obvious manner. \n", - "\n", - "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": "markdown", - "metadata": {}, - "source": [ - "## References" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "* [1] NASA Kalman Filtering Presentation

http://nescacademy.nasa.gov/review/downloadfile.php?file=FundamentalsofKalmanFiltering_Presentation.pdf&id=199&distr=Public\n", - "\n", - "\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.4.1" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The g-h Filter" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#format the book\n", + "%matplotlib inline\n", + "%load_ext autoreload\n", + "%autoreload 2 \n", + "from __future__ import division, print_function\n", + "import sys\n", + "sys.path.insert(0,'./code')\n", + "from book_format import load_style\n", + "load_style()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Building Intuition via Thought Experiments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Imagine that we live in a world without scales - the devices you stand on to weigh yourself. One day at work a coworker comes running up to you and announces her invention of a 'scale' to you. After she explains, you eagerly stand on it and announce the results: \"172 lbs\". You are ecstatic - for the first time in your life you know what you weigh. More importantly, dollar signs dance in your eyes as you imagine selling this device to weight loss clinics across the world! This is fantastic!\n", + "\n", + "Another coworker hears the commotion and comes over to find out what has you so excited. You explain the invention and once again step onto the scale, and proudly proclaim the result: \"161 lbs.\" And then you hesitate, confused.\n", + "\n", + "\"It read 172 lbs 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. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** Try Another Scale**\n", + "\n", + "Is there any way we can improve upon this result? The obvious, first thing to try is get a better sensor. Unfortunately, your co-worker informs you that she has built 10 scales, and they all operate with about the same accuracy. You have her bring out another scale, and you weigh yourself on one, and then on the other. The first scale (A) reads \"160 lbs\", and the second (B) reads \"170 lbs\". What can we conclude about your weight?\n", + "\n", + "Well, what are our choices?\n", + "\n", + "* We could choose to only believe A, and assign 160lbs to our weight estimate.\n", + "* We could choose to only believe B, and assign 170lbs to our weight.\n", + "* We could choose a number less than either A or B.\n", + "* We could choose a number greater than either A or B.\n", + "* We could choose a number between A and B.\n", + "\n", + "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A instead of B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they both measured. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not probably the answer is somewhere between A and B. \n", + "\n", + "In mathematics this concept is formalized as *expected value*, and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we made one million separate readings. Some of the times both scales will read too low, sometimes both will read too high, and the rest of the time they will straddle the actual weight. If they straddle the actual weight then certainly we should choose a number between A and B. If they don't straddle then we don't know if they are both too high or low, but by choosing a number between A and B we at least mitigate the effect of the worst measurement. For example, suppose our actual weight is 180 lbs. 160 lbs is a big error. But if we choose a weight between 160 lbs and 170 lbs our estimate will be better than 160 lbs. The same argument holds if both scales returned a value greater than the actual weight.\n", + "\n", + "We will deal with this more formally later, but for now I hope it is clear that our best estimate is the average of A and B. $\\frac{160+170}{2} = 165$.\n", + "\n", + "We can look at this graphically. I have plotted the measurements of A and B with an assumed error of $\\pm$ 8 lbs. The overlap falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 pounds. a lot of the plotting code is not particularly useful to read, so for each chapter I have placed the uninteresting code in a file named xxx_internal. I import this file and call whatever function I need. If you want to read the code, the file exists in the code subdirectory." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import gh_internal as gh\n", + "gh.plot_errorbar1()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So 165 lbs looks like a reasonable estimate, but there is more information here that we might be able to take advantage of. The only weights that are possible lie in the intersection between the error bars of A and B. For example, a weight of 161 lbs is impossible because scale B could not give a reading of 170 lbs with a maximum error of 8 pounds. Likewise a weight of 171 lbs is impossible because scale A could not give a reading of 160 lbs with a maximum error of 8 lbs. In this example the only possible weights lie in the range of 162 to 168 lbs.\n", + "\n", + "That doesn't yet allow us to find a better weight estimate, but let's play 'what if' some more. What if we are now told that A is three times more accurate than B? Consider the 5 options we listed above. It still makes no sense to choose a number outside the range of A and B, so we will not consider those. It perhaps seems more compelling to choose A as our estimate - after all, we know it is more accurate, why not use it instead of B? Can B possibly improve our knowledge over A alone?\n", + "\n", + "The answer, perhaps counter intuitively, is yes, it can. First, let's look at the same measurements of A=160 and B=170, but with the error of A $\\pm$ 3 lbs and the error of B is 3 times as much, $\\pm$ 9 lbs." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_errorbar2()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The overlap of the error bars of A and B are the only possible true weight. This overlap is smaller than the error in A alone. More importantly, in this case we can see that the overlap doesn't include 160 lbs or 165 lbs. If we only used the measurement from A because it is more accurate than B we would give an estimate of 160 lbs. If we average A and B we would get 165 lbs. Neither of those weights are possible given our knowledge of the accuracy of the scales. By including the measurement of B we would give an estimate somewhere between 161 lbs and 163 lbs, the limits of the intersections of the two error bars.\n", + "\n", + "Let's take this to the extreme limits. Assume we know scale A is accurate to 1 lb. In other words, if we truly weigh 170 lbs, it could report 169, 170, or 171 lbs. We also know that scale B is accurate to 9 lbs. We do a weighing on each scale, and get A=160, and B=170. What should we estimate our weight to be? Let's look at that graphically." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_errorbar3()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see that the only possible weight is 161 lbs. This is an important result. With two relatively inaccurate sensors we are able to deduce an extremely accurate result.\n", + "\n", + "> So two sensors, even if one is less accurate than the other, is better than one.\n", + "\n", + "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight of using all measurements regardless of accuracy will play a large role later, so don't forget it.\n", + "\n", + "What if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's write a simulation for now." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average of measurements is 165.0140\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "measurements = np.random.uniform(160, 170, size=10000)\n", + "print('Average of measurements is {:.4f}'.format(\n", + " measurements.mean()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The exact number printed depends on your random number generator, but it should be very close to 165.\n", + "\n", + "This code makes one assumption that probably isn't true - that the scale is as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `numpy.random.normal()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements very similar to how a real scale would." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average of measurements is 164.8406\n" + ] + } + ], + "source": [ + "measurements = np.random.normal(165, 5, size=10000)\n", + "print('Average of measurements is {:.4f}'.format(\n", + " measurements.mean()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The answer again is very close to 165. \n", + "\n", + "Okay, great, we have an answer to our sensor problem! But it is not a very practical answer. No one has the patience to weigh themselves ten thousand, or even a dozen times. \n", + "\n", + "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n", + "\n", + "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the weighings along with the error bars, and then some possible weight gain/losses that could be explained by those measurements in dotted green lines." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Gh7OHdD2ygPZB7Tn9+mmWpC0h8WgiadfTAIiqGYW7k7tBfJGmCIVCYXTRN2F+\nD4oe6LoOqdPVHLh6AC1avCt4G73wr+1RmwFhA2hUtRGqIBUNqzbERmljkVxnH5zNS6teYkKrCXwU\n+ZFFnlMIYV5SJAghLMrR1pGf+//MwGUDWXZ8GcGVgx/ZPUaYXk33mkxqO4lJbSeRdj2NJWlLeM73\nOaOxa0+v5ZU1r9A/tD+xYbE082mm6xr2eD3Emj52XvIFtKH8wny6LupKkbZIr/1azjWO3ThmEK9Q\nKFjUe5Gl0tOZunMqYzeMBYrvDga6BTKiyQiL5yGEMC0pEoQQFmdvY09in0TGbxzP6BajzTJgUvy1\nMK8wwlRhj9yeeDSRK/euMHXXVKbumkqQWxCxYbEMbTgUMJwiUzyZQk0h+6/sR52u5rXmr+Hi4KK3\n3cXBhebVm+sWIVMqlDT1aYoqUEVF+4rkkmuNtHW0Wi0JWxP4MOVDXVsD7wZ0r9PdilkJIUzFakVC\nSkoKU6ZM4cCBA1y5coXZs2czZMjD26dKpfHb2yNHjuTLL78EID8/n3HjxpGYmEhubi6RkZF8/fXX\nVK8u87MLUdLZKm35IuoLa6chHkGj1bDz0k69tvQ76Xyy/RPqedZDq/3rIuGPdxvkTkGxYzeOseHs\nBt0ieFn5WQA0qNqAzrU6G8QPDh9M8+rNiQyKpG1AW1wdXXXbbnDDYnkb8/mOz/UKhFZ+rVg9cDVu\njm5WzEoIYSpW62iak5NDeHg406dPx8nJyWB2k8zMTL2fVatWAdC/f39dzJgxY/j5559JTExk27Zt\nZGVl0bVrVzQajUVfixDCtLRaLfmF+dZOo1xTKpScev0USYOSGNpwKK4OxRenjraO9KjTw+g+fxwU\nLYz7MOVD/p70d1adWqUrEKB45WxjXm32KtOip9GtTje9AqEkGBw+mODKwQDE1Ixhw+ANUiAIUYZY\n7U5CTEwMMTExAMTHxxts9/Ly0nu8YsUK6tSpQ5s2xdO13b17l1mzZjFnzhwiI4tndJg/fz4BAQFs\n2rSJTp06mfcFCGEBa9akABso/lUtZM2aTnTp0tbKWZmXVqtlzPoxHL1xlJWxK6lgX8HaKZVbtkpb\nOgV3olNwJ77p8g1JZ5NIv51u0C0G4H7Bffyn+lPfuz6xobH0De0LVLV80lZ26e4l1Olq/Fz9UAWp\nDLarAlUkpiXqHvtW8i1epyCwvSXTNIlqLtXYOHgj/975b76I+gJ7G3trpySEMKFSMSYhOzubxMRE\n/vGPf+iV6M1gAAAgAElEQVTa9u/fT0FBgV4x4OvrS926ddmxY4cUCaLUW7MmhdGjk4CHM4WMHj0J\noEwXCu9sfocZe2YAEL0wmjUD11DJoZKVsxIOtg5/2td87em13Htwjx2XdrDj0g7GJI2BuPZwKK74\np4y6nXtb131IfV7Nmd/OANCnXh+jRUKHGh3oF9oPVaAKVZCKmu41S/U6IUGVg/hP5/9YOw0hhBmU\niiJh0aJFFBQU6I1ZyMzMxMbGBg8PD71Yb29vrl279shj7du3z2x5lndybk1r8uQfOXv2///4RnwA\nEf/gLNB138fw/6d6RK0RvFz7ZYN9vz/1PTNPzzRoLw3xWTcfdsHYfnE7rv9y/dN4k+SzxszHL4fx\nGq0GamyGPDc4FKf3+VAa8n+a+D/aeHoje/buQalQGo1fenSpyfJ5edHLpeL8lKZ4PpgJWxNg6wfy\nt82M5NyaR61applYolRMfj1z5kx69uxpUBAIUZY9eFA+b90PrTmUFlVaWDsNYSppsdbO4JnkFeWx\n+8ZuEtMT/zoYcFA68FyV5xhUYxAPNA/MnJ1lZBdkWzsFIYQVlPg7Campqezfv59//etfeu1Vq1al\nqKiIW7du6RUPmZmZtG376K4YTZs+/rzd4vH8/k2AnFvTqlJlxV/G+Pj4GD3vq7NXw+nSGx+VHcWu\n5F0lJh+Jf7p4zkTB6eIZe/64X2nJf8P1Dcw5O4cCTQFKhZJJXSdR2anyI+OHNBjCd12/w8HWwSL5\n//7Z6+PjY7bzc/LmSdZsWmMYbKLjl4Z4+dtmenLdYF537941yXEU2hKwhrqLiwtfffUVcXGG/VZH\njhzJhg0bOHPmjF773bt38fLyYs6cOQwYMACAjIwMAgICWL9+PR07dtSL/Z2ra8maHaIskF928/h9\nTMLZsw/HJAQHv8P06dFlekzCH80+OJtPf/2ULUO2UM2lmsmPL+9d83rUFKhZ+Vl4T/EmrzBP1+bu\n5E7vur2ZrJqMVwX9iSssSavV4j/Nn4ysDINtK/qvoEeI8ZmdrMHc798DVw8QtSCKm/dvAsXrmyzq\ntYje9Xqb5flKEpm+17zks9e8THXda7U7CTk5OZw+XVyqazQaLly4QGpqKh4eHvj5+QFw//59Fi5c\nyIQJEwz2d3V1Zfjw4bz99tt4eXnh7u7O2LFjadCgAR06dLDoaxHCHH4vBLp2fQ+wAYrKVYEAMLTR\nUAbWH2jwzawo3c7fOY9vJV/dIF+A33J/Y3HaYqZFTzPrc2u1Wo7dOIY6XU2X2l2oUbmG3naFQoEq\nSMW8Q/N0baGeoaiCVAS6BZo1t5Jkd8ZuOs7vyL0H9wCoYFeB5f2X0zG441/sWfqVx1nlhDDGakXC\n3r17UamKZ35QKBQkJCSQkJBAfHw8s2bNAmDJkiXk5uYydOhQo8eYNm0atra29O/fn9zcXDp06MCC\nBQtK9UwRQvxR8R+mtn94bL1crEUKhLIn3DucU6+d4mDmQRLTEklMS+RS1iV61OmBs52zQXz2g2xO\n3zpNw6oNn+rz/cKdC8UzEJ1Xo05Xcz3nOlA8uHp0i9EG8b1CeuFg44AqSEVEYARVK5a/qVxrutfE\nz9WPYzeOUdmxMmtfXEsL37I/Vqi8zionhDEloruRuUl3I/OS24bmJbe9DWm0GiZumkhcgzhCvUKf\n+jjy3jWvx33varQadmXsoqJ9RcK9ww22Lzy8kEHLB1HHow6xYbHEhsUSUiXksfN4f8v7eisD/657\nne6sjF352Mcpacz9/r2cdZl+P/Xj2y7fUt+7vlmeo6SJinqXDRsmG2l/j/XrDd9D4unIZ695meq6\n95lnN9qxYwfr1q0jJyfnWQ8lhBB/SavVMnrdaD7b8RkRcyNIzUy1dkriGSkVSlr6tTRaIAAkHi2e\nWejkrZP8I/kf1P2qLg2/bciqk6sAuHn/Jj8d+4mfjv1kdP//Xa/g9/EPvUJ6mfBVlD3VK1Vn+9Dt\n5aZAAMjPN97BIi/PxsKZCGF9j93daPLkyfz666+sW7dO19a9e3dWr14NFM8S8OuvvxIQEGD6LIUQ\n4v+l30ln7qG5QPHFYfu57UkalETz6s2tnJkwB61Wi6ezJxXsKpBT8PDLqEPXDvHfg//lvS3vceja\nIQAaeDegT70+Bsd43vd5etTpQduAtqiCVIR7h6NUlIoZwC1Cq9Wi0WqwURpeCJe37rsODoVG2x0d\niyyciRDW99ifkosWLaJu3bq6x6tWrWL16tWMHz+exYsX8+DBA70VkYUQwhxqVK7BprhNuDm6AXAn\n7w4d5nVg+8XtVs5MmINCoWBWj1lcf+s6S/sspVfdXtgri9cQWXlypa5AgOLC4eb9m6w7vY5b92/p\n2h1sHVgRu4Kxz4+lYdWGUiD8gUarYWzSWF5a9VLxAnjl3BtvdCI4eJJeW3DwO7z+etkfsC3E/3rs\nOwkZGRmEhDzsA7ps2TJq1qzJJ598AsDJkyd1A46FEMKcmldvjjpOTcf5HbmVe4t7D+4xcfNEUuJT\nyt03n2VRQVEBe6/sJeVCCm+3ehulQomznTN9Q/vSN7QvWflZ1P2yLleyrwBgo7DhOd/nUAWquHX/\nFj0Se6BFS8caHYkNi6VnSE8qOVSy8qsqeQo1hYxYNYI5qXMAcHNw499R/y7Xv0Myq5wQDz12kaBQ\nKCgqeni7bdOmTfTq9bA/Z/Xq1cnMzDRtdkII8QiNqjUiOT6ZyHmRVHGuwvL+y8v1xU1pl5qZyqZz\nm1Cnq0m5kKLrWtQpuBONqzXWi63kUImRzUZyO+82kUGRtPZvjYuDCwD/PfBfCjQFAKw7s451Z9bh\nYOPAi/Vf5L89/mvZF1WC5RXmMWDZAFaceLho46WsSxRpi7BVlPh1Vs1KZpUTothjfxLUrl2b5cuX\n88orr5CUlMSVK1eIiYnRbc/IyKBy5cpmSVIIIYwJ9QolZWgKlRwqUcW5irXTEc/g70l/Z+v5rQbt\n6nS1QZEAMKntJIM2gCrOVXje93l2ZuzUteUX5Zssz7LgXv49ei7piTpdrWsb3mg433X9zui4BCFE\n+fTYRcJbb71FbGws7u7uZGdnU69ePb1FyzZv3kyjRo3MkqQQQjxKbY/a1k5BPIbzd86jTldT36s+\nzao3M9geGRSpVyQEuAYQGRRJk2pNnuh5eoT0oEdID87fOc+StCUkHk0kNTOV2LBYo/HbL24nrzCP\niMAIbJXl4xt0LVru5N3RPR73/Dg+6/iZ3IkTQuh57E/Efv364e7uzpo1a3Bzc2PkyJHY2dkB8Ntv\nv+Hh4cHgwYPNlqgQQjyJIk0R2y5uIyIwwtqplEs3cm5A/Y0QpIYgNUHT0wF4rdlrRouE6JrRHLtx\nDFWQClWQiiC3oGe6aA10C2R86/GMbz2eEzdPUNO9ptG4fyb/k43nNuJVwYt+9foRGxbL837Pl+nB\nzZUcKrH+xfW0ndOWuPA4JrSeIAWCEMKALKYmnpksimJespjak9NoNbz0y0vMTp3NN12+4ZWmrxiN\nk/eu+cw7NI8hK4YYtNetUpdjo45ZISND17Kv4fNvH4NZffwq+bE5bjO1PGpZKbPH86zv3/sF942u\ncC3kc9fc5LPXvEx13fvE91bv3bvHli1bOH/+PACBgYG0b98eFxeXp05CCCFMacqOKcxOnQ3Aq2te\nJa8wjzEtxlg5q7Il+0E22y5s42r2VYY1Gmaw/X8XMKtgV4E2AW1QBarQaDUl4pv6Im0RrzV7jaXH\nlpKZ/XDijdzCXIIqB1kxM8uQAkEI8WeeqEj47LPP+Oc//8n9+/f12p2dnXnvvfcYP368SZMTQoin\nMaLxCJYdX8aey3uA4kGxuQW5TGwz0cqZlV6FmkK2X9zO5nObUZ9Xs+fyHgo1hVRyqERcgziD/vy+\nlXzh0CC4VRvSVfyW3gx7G3srZW+cj4sP02Om8++of5NyIYXEtER+Ov4Tfev1NTo+4XrOdX448AP9\nQ/sT7B5shYyf3I5LO5h1cJYMShZCPLHHLhK++OILJkyYQEREBKNGjaJWreLbsKdOneKrr75i4sSJ\n2NjYMG7cOLMlK4QQj6OyU2U2Dt5Il0VddIusvaN+B88KnrzU+CUrZ1c6FWmK6LywM7mFuXrtWflZ\nHLh6wPiK18vn6/5pX4KvT22UNrQPak/7oPZ82flL7j24ZzTup2M/MUk9iUnqSTSv3pzY0Fj6hfaj\neqXqFs748SSdSeKFJS/o/s9mdpspYw+EEI/tse/3zpgxgw4dOrBp0yZ69+5NeHg44eHh9OnTh82b\nNxMZGcl//vMfc+YqhBCP7ffBmb93e2lcrTF96vWxclYll0ar4VDmIabunMrN+zcNtjvYOtDav7Ve\nW7h3OGOeG6Nb/bossLOxw93J3ei2xLRE3b/3XN7D2A1j8Zvqxxc7vrBUeo9t6dGldFvcTVcg/HLy\nFzKyMqyclRCiNHnsOwk3b95k/PjxKJWGdYVSqaRnz5689dZbJk1OCCGeRQX7CqwesJoJmybwfrv3\ny9TFrCmc/e0sG89tRJ2uZsv5LbrioHql6vQL7WcQHxsWS3DlYFRBKiICI/Cs4GnplK3qlaav4Oro\nStKZJN2CbVq0RmdrsqaZ+2fyt9V/Q0vxiFt/V382Dt6In6uflTMTQpQmj10kNG7cmKNHjz5y+9Gj\nR2WUuhCixHGyc2J6zHRrp1Eiffrrp8w8MNOgXZ2uNlokDGs0zOgg5fJiYP2BDKw/kN9yf+Pn4z+T\nmJbI6d9OG9xh+d2kzZOo712fbrW7UcG+gkVyLNIUMf/wfF2BEFIlhI2DNxaPERFCiCfw2EXCl19+\nSXR0NP7+/owaNYqKFSsCxbMdffXVVyxfvpwNGzaYLVEhhDC1Qk2htVMwq+s519mSvgU3RzeiakYZ\nbFcFqfSKBE9nT1RBKiKDIi2ZZqnj7uTOS41f4qXGL5FbkGt0pqaMrAw+2f4JWrQ42znTvU53YkNj\nia4ZjYOtg9lys1Ha8MuAX2g/tz02ChvWD1ovq5ELIZ7KI4uEunXrGgxwUigUTJw4kXfffRdvb28A\nMjMz0Wg0VK1alf79+3PsWMmY/1oIIf5MkaaIhEMJFGoKWddkXYmbeedp3Mu/hzpdXfxzXk3a9TQA\nooKjjBYJ7QPb071OdyKDIlEFqQj1DJWBrU/Iyc7JaPvSo0t13+bfL7hPYloiiWmJ1POsR9qraWY9\nz26ObiQNSsLR1pFKDpXM9jxCiLLtkUXC70XAH3l5eVG7dm29tpo1H65iKX9chBClgUar4aVVL7Hh\nSvHdz95Le/Nj3x9xtHW0cmbP5uiNo/Rc0tOgfdvFbTwoemBQCHlX9GZl7EpLpVeu9AzpSc6DHBan\nLeb4zeO69k41Olnkb6VXBS+zP4cQomx7ZJGwdetWC6YhhBCWo0BBZcfKuserT62m++LurIhdUaIX\nmHpQ9IDdGbs5cPUAo1uMNtje1KcpLvYuuik87ZR2tPBtgSpIRV5hXpm4W1Ja1Khcg/favce7bd/l\nyPUjujsJsWGxRuPnpM7hyLUjxIbF0tSn6WMVErmFuSw4t4DwRuHyfyuEMDmFVmt8wfGLFy8+1QH9\n/f0fKy4lJYUpU6Zw4MABrly5wuzZsxkyZIhezKlTp5gwYQJbtmzhwYMHhISEsHDhQkJCQgCIiIgg\nJSVFb5/Y2FgWLVqk12aq5amFcbK8unn98VrB+G+reBparZbhC4cz++xsXVvbgLasHrAaF4eSs4L8\n3st7dd2Htl3YppvS8vLYy/i4+BjEv5n0JrZKW1RBKlr7t7bYgFlj5L2r7/c/t8YKgOd+eE63+F9w\n5WBiw2KJDYslzCvM6LFu596m3fftOHKnuLBY8MICWSzNhOS9a15y3WBeprrufeSdhMDAwCc+mEKh\noKio6LFic3JyCA8PZ8iQIcTFxRl8aKanp9OqVSvi4+N5//33cXNz48SJE7oB078/37Bhw/j44491\nbU5OxvuHCiHEHykUCkaGjMTBxoFvT30LFA9kLmndJuNWxHHi5gmD9i3pW3gx/EWD9i+iSt6c/aLY\no95b526f0xUIAGdvn+WjbR/x0baP2P/yfhpXa6wXn5mdSaf5nThy5whQvH7DoPqD6FK7i/mSF0KU\nO48sEmbNmmXWJ46JiSEmJgaA+Ph4g+2TJk0iOjqazz//XNdmrHBxcnLCy0v6Xgohns7wWsOpGVCT\nxKOJrB24lor2Ff96JxPRarWcvX0WdbqatgFtCakSYhCjClTpFQnBlYOJDIqkpntNg1hROvlV8mP9\ni+tJPJrIz8d/Jis/C4BAt0AaVW2kF5t+O52O8zty9vZZXdv06OlSIAghTO6RRYKxC3dL0Wg0rF69\nmgkTJhAdHc2BAwcIDAxk3Lhx9OunP3d3YmIiiYmJeHt7ExMTQ0JCgt7dBiGE+CtvtnyT15973SL9\nuq/eu6pbwEydruZS1iUAJrefzKS2kwziu9XpRtaDLCKDImkf2J4AtwCz5ygsy87GjqiaxTNQfdPl\nG9afWU9iWqLR2ab+kfwPXYGgQMGboW/yxnNvWCNtIUQZ98gxCZbk4uLCV199RVxcHFA8raqPjw/O\nzs5MnjwZlUrF5s2befvtt1m5ciWdO3cGYObMmQQGBuLj40NaWhoTJ06kVq1aJCUl6R3/j32zTp8+\nbbkXJoQJNGv2sM/m3r37rJiJMIX5Z+cz48QMg/amHk35psU3VsjIfOS9a3q5hbn0Te7LtbxrAChR\n0qxKMzr5dCKiagSV7GTKU1OQ964ozWrVqqX7t1nGJFiTRqMBoGfPnowZMwaA8PBw9u3bx5dffqkr\nEkaMGKHbJzQ0lODgYJo3b87Bgwdp1KiR4YGFEOIJFGoKmXpsKoNqDKKac7XH2ie7IJuDvx0kryiP\njj4dDbY3raI/UK+CbQUauTeipWdLk+QsyjYnWydc7Fx0RYIGDbtv7mb3zd1cyLnA6yGvWzlDIURZ\nUSKLhCpVqmBra0u9evX02kNCQliyZMkj92vcuDE2NjacOXPmkUWCjKQ3PZmlwHLkHJvWn713izRF\nDPx5IEsvLGXn7Z2oh6iNjgN4UPSAbRe2sTl9M+p0Nfuu7KNIW0SNyjWY2H2iQXwjTSN+vP6jbmrS\npj5NsVWWyI9ik5L3rulsD9nOsuPL+GHXDxz87aCu/e8d/k7Dqg0N4rVabYkbkF+ayHvX9OS6wbz+\n2IPmWZTIv0z29vY0a9aMEyf0Z/Q4derUn866dOTIEYqKiqhW7fG+8RNCiEc5dO0QK06sAOBS1iXa\nzm7LprhN1PPU//LiTt4dOszvYLD/udvnOH/nPIFugXrtNkobfhnwi9nyFmXH6lOriQyKNFjV2bui\nNyObjaS5ojmZuZmcsj3FroxdNPBuYPQ4EXMjCHQLZEDYACKDIrGzsbNE+kKIUs5qRUJOTo5ufIBG\no+HChQukpqbi4eGBn58fb7/9Nv369aNNmza0b9+eLVu2sGTJElauLF4d9Ny5cyxYsIAuXbrg4eHB\nsWPHePPNN2ncuDGtWrWy1ssSQpQRjas1ZvWA1fRI7EFuYS5Xs68SMSeCjYM30qDqw4sxrwpe1Peq\nz5HrxdNRKlDQqFojVIEqbBQyb714OlN3TmXshrF0rd2Vn/v9/MgL+6pOVenatOsjj3P8xnFSLqSQ\nciGFeYfm4eHkQZ96fYgNi6VdQDu5wyCEeCSrFQl79+5FpVIBxXNHJyQkkJCQQHx8PLNmzaJHjx58\n//33fPzxx4wePZratWszf/583bSp9vb2qNVqZsyYQXZ2Nn5+fnTt2pWEhAT50BNCPJOTN0/qZiD6\n4wJVN+7f4MOUD/mp30968XEN4jh/5zyqIBURgRG4O7lbOmVRRmi1Wt7f8j6Tt00Giu8mTE6ZzD/a\n/+Opjrf29Fq9x7dyb/Hd/u/Yen4rx0cdf+Z8hRBll9WKhIiICN0A5UcZMmSIwSrMv/P19WXr1q1m\nyEwIUd6N2ziO1adWG7T7VfJjbs+5hvEtx1kiLVHGabQaXl/7Ol/v+1rX1tq/NWOfH/vUxxz7/Fja\nBbYjMS2RJUeXkJGVAUBsWKzRL9QKigqwVdrKl21CCJTWTkAIISztyr0rLDy8kEO/HTK6XRWo0ntc\ntWJVYmrG8EWnL6hgX8ESKYpy6Ks9X+kVCDE1Y0galISr49NPYahQKGjq05QpnaZwYcwFtg3dxqhm\noxgQNsBo/EfbPiL061D+mfxPTt069dTPK4Qo/UrkwGUhhDClO3l3dIuXqdPVHL9Z3M2iq29XGrgb\nDvbsFNyJXnV7oQpUoQpSEVIlRL5ZFWY3oskIVp5cyeb0zcSGxTK351yTLvCnVChp7d+a1v6tjW7X\narUkpiVy8tZJErYmkLA1gUZVGxEbFsvQhkPxrOBpslyEECWfFAlCiDJvS/oWei/tbdC+9+ZejK0n\nGeoVyrJ+yx7r2HmFeey9vJc2AW2eOU9RvjnaOrK8/3K+3fctY58fqzcexhIuZV3SrQD+u4OZBzmY\neZCutbtKkSBEOSPdjYQQpV5eYR5b0rfww4EfjG5vF9gOBQ/vBNjb2NM+sD0v+L9AkbboqZ/3QdED\n+v3YD9U8FUuPLn3q4wjxOxcHF95q9ZbFCwQAf1d/ro+7zpI+S+gZ0lN3FyPcO9xg6l8ovvNwO/e2\npdMUQliI3EkQQpQ6Gq2GPZf3oE5Xszl9M79e/JX8onzsbex5sf6LBvPKuzu5M6ThEHwq+qAKUtHS\nryVOdk66BX2e1oRNE1h1ahUAA5YNIK8wj7gGcc90TFE+XLp7CTdHN1wcXKydip4K9hXoF9qPfqH9\nuJt3lxUnVuBs52w09vC1wzSd2ZSo4Chiw2LpUadHiXs9QoinJ0WCEKJU6rywM7fz9L/FfFD0gB2X\ndhBZI9IgfnaP2SbPYVzLcaw7s44TN0+g0WqIXxFPXmEeLzd52eTPJcqOkzdP0nF+R2p51GLNwDU4\n2jpaOyWjXB1dGdLQ+AyDAIlpiRRqCllzeg1rThe/jq61u/JKk1eM/g4KIUoX6W4khChxtFotJ2+e\n5Ju933Dl3hWD7UqFkvZB7fXa6njU4dWmr+JVwctSaeLj4kNyfDLh3uEAaNHyt9V/Y+WJlRbLQZQu\nB64eoPXs1lzKuoQ6Xc2QFY++CC/pzt05p/c4rzCPn479xJ7Le6yUkRDClOROghCiRLh09xKbzm1C\nfb54BqLfiwN7G3uGNx5uEN8rpBeVHCrpZiCqXqm6pVMGildc3jJkC1ELoth3ZR+RQZFE1YyySi6i\nZEu5kELXRV259+AeABXsKvBSo5esnNXTW9JnCf+K/BdLji5hcdpiDl87DED/sP5G49Nvp+Pv6m+V\n8RZCiCcnRYIQokSYumsqU3dNNWhXn1cbLRJeDH+RF8NftERqf8ndyZ1NgzeRsDWBj1QfldjuI8J6\n9l/ZT9SCKPIK8wCo7FiZtS+upYVvCytn9myCKgcxofUEJrSewLEbx0g+n0yNyjUM4rRaLap5KvIK\n8+hbry8DwgbQwreFTC0sRAkm3Y2EEBZxO/c2K06sYO3ptUa3q4L0FzBzdXClR50edKrRyRLpPTNX\nR1emRU+TxdaEUeHe4XSs0REoXpwvOT651BcI/6ueZz1ebfaq0W17Lu/h/J3zZGZn8p89/6HlrJYE\nTQ9i/MbxFGmefoYxIYT5yJ0EIYRZ5BbkknIhRTcD0YGrB9CipZVfKzrX6mwQ3zagLVHBUbQPbE9k\njUgaVW1UZrol5BXm4WDjIN+almN2NnYs6bOEV9e8yvvt3jf6bXtZdvneZbwreHMt55qu7cLdC2w5\nv6XM/J4LUdZIkSCEMIuzt88SvTDaoH335d1kP8imon1FvfZKDpVYP2i9pdKzmLzCPLot7kaQWxDf\ndv0WpUJu4JZXTnZOzOk5x9ppWEWvur3oXqc7yeeTSUxLZNnxZdzOu82AsAFG4zOyMijUFBLoFmjZ\nRIUQOlIkCCGeSqGmkANXD7Dj0g5GPzfa4FvyUM9QPJ09uXH/BlA8I1GTak1QBanIL8w3KBLKogdF\nD+iztA+bzm0CiguGWT1mYauUj96yTKPVcL/gfrl4jz8JW6UtkTUiiawRyVddvmLj2Y008WliNPbf\nO//N1F1TaeHbgtjQWPqG9sXHxcfCGQtRvslfKiHEY0u7nsbmc5vZnL6Z5AvJZOVnAdC5Vmdqe9TW\ni1UoFAxvNJzcwlxUQSraBrTFzdHNGmlbjVKhxN3JXfd4/uH55BXmsbDXQuxs7KyYmTCXQk0hI1aN\n4MTNE2wavEnGqDyCvY09XWp3MbpNo9Ww5OgSAHZl7GJXxi7+nvR32gW2Y3r0dN2Uw0II85IiQQjx\n2IatHMbeK3sN2tXpaoMiAeCTDp9YIq0Sy1Zpy5yec3C0dWTmgZkA/HjsR/KL8lnaZykOtg5WzlCY\nUl5hHgOWDWDFiRUAvLDkBVYNWCX/z0/ot9zfaFi1IddzrlOoKQSK1yDZen6rXtEthDAv6RwrhNDJ\nyMpg3qF5HLl2xOj2/52ByMfFh8HhgwmpEmKJ9EolpULJd12/443mb+jaNFpNmR/EvGZNCvAu8AHw\n7v8/Lrvu5d+jy6IuugIBwN/VX7qWPYUqzlVYM3ANmW9m8n3X71EFqVCgoI1/G3wr+RrEa7Qafj7+\nM/cL7lshWyHKLvn0EqIcu3X/Fup0tW4GotO/nQZgfKvx/Mv7XwbxMTVjOHf7HKqg4gXMarnXKvMX\nu6agUCiYFj0NJzsnDlw9wI99f8Text7aaZnNmjUpjB6dBHykaxs9ehIAXbq0tVJW5pOVn0XH+R31\nVhoe9/w4Puv4mfx+PAMPZw9GNBnBiCYjuHrvqm580//afnE7vZf2poJdBXqE9CA2NJaomlFl+ndM\nCEuQIkGIcmzJ0SWMWjvKoF2drjYa3y6wHe0C25k7rTJJoVDwSeQnFGgKyvzFy4wZGzh79iO9trNn\nP+I//3mvTBYJFe0rElw5WFckfKz6mAmtJ0iBYELVXKpRzaWa0W2JaYkA5BTksOjIIhYdWYSboxuT\n2njobVMAAB8rSURBVExiXMtxlkxTiDJFigQhyrD7BffZcWkHN+/fJDYs1mB7ZFCk3mNHW0da+7em\nY42OaLVaucgxMYVCUeYLBID8fON/WvLyyuZ8+EqFkrk955L9IJvOtTrzStNXrJ1SuVLHow51POpw\n8tZJXdudvDs42zlbMSshSj+rjUlISUmhe/fu+Pr6olQqmTt3rkHMqVOn6NWrF5UrV6ZChQo0adKE\nEydO6Lbn5+fz+uuv4+npScWKFenRoweXL1+25MsQokQp1BSy/eJ2/pn8TyLmRFD508p0nN+RMevH\noNVqDeJre9SmR50evNf2PbYO2cqd8XfYOHgjb7d6WwoEC8p5kMPfVv2N6znXrZ2KSTg4FBptd3Qs\nuyvr2tnYsTJ2pRQIVjC6xWiOjzpO6t9SGd9qPAGuASgVSvrU62M0fvnx5ey/st/oZ6IQ4iGr3UnI\nyckhPDycIUOGEBcXZ3BBkp6eTqtWrYiPj+f999/Hzc2NEydOULHiw3mnx4wZwy+//EJiYiLu7u6M\nHTuWrl27sn//fpRKGZMtyp/cglwi5kRQpNW/GLuWc41jN44R6hWq165QKFgRuwJhPbkFuXRP7I46\nXc22i9vYFLep1M8H/8YbnTh7dpJel6Pg4Hd4/XXDxfVKo0fdZZPC2noUCgUNqjagQdUGfBL5Ccdv\nHsergpdBXKGmkL+t/hs37t+gpntNYkNjiQ2LNfhsFEJYsUiIiYkhJiYGgPj4eIPtkyZNIjo6ms8/\n/1zXFhgYqPv33bt3mTVrFnPmzCEysrjLxPz58wkICGDTpk106tTJrPkLYQ1arZbjN4+jTlczpMEQ\nXBxc9La7OLjQvHpzdmbs1LXV86yHKlAl0zCWUNsvbmfr+a0AHL95nLaz26Ieosbf1d+6iT2D38cd\ndO36HmADFDF9enSZGI+w/sx6Pkz5kDUD15S7dT9KC4VCQb3/a+/eo5q68j2Af5NAeKhQBcJDLOIU\n8YmKQCsjKAgIjkWptqJdCh3n4thVq3Jbq1fn0qqjrVYHrWhHekcpSsVWWx+jhbE+gMFaoKCoY6Wi\n1hcOUAVBUUzO/YMhyyiPJBBOAt/PWlkrOdnn8Dub3yL8svfZx2FQk+8dvXxUfQH0z7/+jJXZK7Ey\neyWGOw3HqT+c6hLTAYm0ZZRft6tUKhw8eBADBw5EeHg4FAoF/Pz8sHv3bnWbgoIC1NfXaxQDrq6u\nGDhwIHJzc8UIm8gwnrsCeH8GTJkB53XOGLx5MOYdnofsX7KbbB49JBqzR8xG2itpuBl/E+fePIdP\nJnyCF3q90LFxk1ZCfxOKL6Z8oV4q89KdSwjcFohLv14SObK2aSgIVqBhCdQVnaJASD+bjsgvIpF7\nLRcT0yZyyU0TpOimwKxhs9BDrvkFi721PQsEoqdIBCOYlNejRw8kJSVh1qxZAICysjK4uLjA2toa\nK1euRHBwML777jssWrQI+/btw4QJE5CWloaYmBjU19drHGvcuHHo378/tmzZot5WVVWlfl5SUtIx\nJ0WkBV9fn9YbTZkBDP3i2e258UDmOo1NeXn57RQZdbQTZSewpHAJ6lUNf9NedXsVi4YsEjmqtnky\nv009N/f+shcfFn8IAQ0fmc5Wzvj0pU/hYm3aU8O6qofKh8gtz0XmzUxk387Gu4PfxaTnJ6nf70y5\nS12Ph4eH+rmtra3exzHK1Y1UKhUAYPLkyViwYAEAwMvLC/n5+di0aRMmTJggZnhEHetysGaRcL8X\ncCUIuD5KvJio3Y1xGoN1Puvwbv678LP3Q/ygeLFDov9IuZSCTRc2qV+7d3fHJ36fwNHKUcSoqC0s\nZBYIcgpCkFMQ7j++D6nEKCdWEInKKIsEe3t7mJmZYdAgzTmFAwYMQHp6OgDAyckJSqUSlZWVsLOz\nU7cpKytDYGDzw9o+Plp8c0s6yc9v+JaFfas7bcbx9mU5YO3Z3yJqeBSC3YMxzGlYCx9o/B3owthy\n1wc+8B/mj8GKwbA0sxQ7nHZlLH2sK0EQsPXWVvVrHxcfHH79MOyt7UWMqoGx5W9nxf5tf8xdw3py\nBk1bGGWRIJfL4evrq7HcKdCwJGrjxcsjR46Eubk5MjMzMX36dADA9evXceHCBfj7+3d0yEQG09u6\nNxL9EvnHtIsY6TJS7BDoCRKJBFt+twV36+6i/H459kXvg42FjdhhEREZnKhLoDZeH6BSqXD16lUU\nFRXBzs4Offr0waJFi/Daa68hICAAQUFBOHbsGNLT07Fv3z4ADXOsZs+ejUWLFkGhUKiXQB02bBhC\nQkLEOi0iIoOoqqvChYoLeNH1RbFD6XJkUhlSo1IhQOh0IzxERM0RbRJeXl4evL294e3tjbq6OiQk\nJMDb2xsJCQkAgEmTJmHr1q34+OOP4eXlhaSkJKSmpqqXTQWAxMREREVFYdq0aRg9ejRsbGxw4MAB\nrlVNRJ1KzaMaTEibgKCUIGReyhQ7nC7JwsyCBQIRdSmijSSMHTtWfYFyc2JiYhATE9Ps+3K5HBs3\nbsTGjRvbOzwiIqMRdyAOudcalnZ++YuXsee1PZjYf6LIUXU+dx7cwfxv5+PjsI+bvBEXdQ66fo/Y\nWnvx14gkMgxezk9EZOSWBy1X31ztkfIRotKj8NX5r0SOqnMpqynDmO1jkHomFRE7I1D9sFrskIiI\nRMUigYjIyL3Q6wVkxWahX89+AIDHqseY9tU05PySI3JkncPlO5cx+m+jUfzvYgDAj7d+5LSuTkwQ\nWn/k5eUjLy9fq7ZEnRWLBCIiE+D2nBuyYrPgaecJAHh10Kt4yfUlkaMyfef+fQ6jt43GpTsNd7iW\nSWT4fPLnmDpoqsiRERGJi0UCEZGJ6G3TGydiT+CdUe8gNSoVZlKjXMXapOw6uws3790E0HCDrb3T\n9mLmsJkiR0VEJD5+whARmRDH7o5YG7ZW7DA6jQ+CPsD1e9ex5/we7J++H2P7jhU7JCIio8CRBCKi\nTuJB/QMInCStE6lEiuSXk5H3X3ksEIiInsAigYioE7hbdxcB2wKw9OhSFgo6MpOawdPeU+wwiIiM\nCosEIiITV/OoBhN2TkDBrQKszlmN+Ix4FgpNSC5Ixo3qG2KHQURkElgkEBGZODOpGeys7dSvE08l\n4s2/vwmV0PINK7sKQRDwp6N/QtzBOITtCEPl/UqxQyIiMnosEoiITJylmSX2vLYHUwZOUW/7tOBT\nzN4/G0qVUsTIxKcSVJh3eB5WZq8EAJwvP4//Pfa/IkdFRGT8WCQQEXUCcpkcu6buwutDX9fYLpFI\nRIpIfPXKesz8eiaS8pLU2yJeiODqUEREWuASqEREnYSZ1Awpk1NgZWaF2vpafPbyZ5BKuu53QV+e\n/xJpxWnq19FDopEyOQVymVzEqIiITAOLBCKiTkQmleGvL/8VKkEFmVQmdjiimj5kOk5dP4WNP2zE\nH0f+EZsmbOryfUJEpC0WCUREnYxUIu3SIwiNJBIJ/hL+FwS4BWDKwCldeuoVEZGu+ClCRNRFVNyv\nwB/2/wHVD6vFDqXDSCVSTB00lQUCEZGOWCQQEXUBd+vuIiw1DP9X+H8ITQ3FnQd3xA6pXV2ouIDS\nO6Vih0FE1GmwSCAi6gIOlxxGYVkhAOCHGz8g+PNglNeWixxV+yi4WYCAbQEITQ3FrXu3xA6HiKhT\nYJFARNQFTB86HVt+t0X9uqisCGNTxpr8P9UnrpxAUEoQKu5XoPROKV7Z/QrvNk1E1A5YJBARdRF/\n9Pkjtk3apr6o+Xz5eXz242ciR6W/gxcPInxnOO49ugcA6GnZE4njE3n9ARFROxCtSMjKykJkZCRc\nXV0hlUqRkpKi8X5sbCykUqnGw9/fX6PN2LFjn2kzY8aMjjwNIiKTEjs8Fjtf2QmZRIbZI2ZjaeBS\nsUPSy4WKC5i8azLqHtcBAJy7OyPrjSy86PqiyJEREXUOoi2BWltbCy8vL8TExGDWrFnPfPMjkUgQ\nGhqK1NRU9Ta5XP5Mm9///vdYtWqVepuVlZVhAyciMnHRQ6LRr2c/jHQeabJLpQ6wH4DFoxfjz9l/\nhvtz7jgy6wj69ewndlhERJ2GaEVCREQEIiIiADSMGjxNEATI5XIoFIoWj2NlZdVqGyIi0uTX20/s\nENpsRdAKdJd3x6xhs+DSw0XscIiIOhWj/QpJIpEgJycHjo6O8PT0RFxcHMrLn12JY9euXXBwcMCQ\nIUPw7rvvoqamRoRoiYg6h1v3buF02Wmxw9CKRCLB4tGLWSAQERmA0d5xOTw8HFOmTIG7uzsuX76M\nZcuWITg4GAUFBeppRzNmzEDfvn3h4uKCs2fPYsmSJThz5gwyMjJEjp6IyPSU15YjJDUEN+/dxLev\nf2s08/sfqx7j5r2beN72ebFDISLqMiSCEawV16NHDyQlJWHWrFnNtrl16xbc3NyQnp6OqKioJtvk\n5+fDz88PBQUFGDFihHp7VVWV+nlJSUn7BU5E1InM/X4u8ivzAQDdzLrhL75/wYheI1rZq3m+vj7q\n53l5+Xod46HyIZYVLsP5qvNIHpUMF2uOGhARtcTDw0P93NbWVu/jGO10o6c5OzvD1dUVP//8c7Nt\nvL29IZPJWmxDRERNWzBwAZ6TPwcAqH1ci7d/eBs/VPwgWjy1j2uxIG8Bjt8+jn/X/RtvnXoL1fXV\nosVDRNSVGO10o6eVl5fjxo0bcHZ2brZNcXExlEpli218fHyafY/0k5/f8A0h+9Yw2L+Gw77V5AMf\nDB86HCGpISirKUOdsg7x+fEonFOIgQ4D23ZsHfu48n4lInZGqEc2AGDasGkIeimI90H4D+av4bBv\nDYv9a1hPzqBpC9FGEmpra1FUVISioiKoVCpcvXoVRUVFuHbtGmpra/HOO+/g+++/x5UrV3D8+HFE\nRkbC0dFRPdWotLQUy5cvR0FBAa5cuYJDhw4hOjoa3t7e+O1vfyvWaRERmbTBisE4EXsCrjauAIC4\nkXEYYD+gQ2N4UP8AgdsDkXczT71tVfAqrAldwwKBiKiDiFYk5OXlwdvbG97e3qirq0NCQgK8vb2R\nkJAAmUyGs2fPYtKkSfD09ERsbCwGDhyIkydPolu3bgAa7plw9OhRjB8/HgMGDMD8+fMRHh6OI0eO\n8EOEiKgN+tv1R1ZsFpYFLENieMffwdjK3AqzvBquUZNAgi2/24IlAUv4t52IqAOJNt1o7NixUKlU\nzb7/7bfftri/q6srjh8/3s5RERERALj3dMeK4BWi/fz3Rr+H6ofVGOo4FNFDokWLg4ioqzKZaxKI\niMg43K+/D2tza4P/nD+P+7PBfwYRETXNZFY3IiIi8d28dxPDPx2OxO8T2+2YD+oftNuxiIiofbBI\nICIirZTXliPk8xCU/FqChRkLsSp7VZuPufvcbnh84oGfKn5qhwiJiKi9sEggIiKtWJhZwM7aTv16\n6dGl+NPRP0Hfe3ImFyQj+qto3Lh3A6Gpofil6pf2CpWIiNqIRQIREWnFxsIG377+Lca5j1NvW5m9\nEu/+412dC4WPcj5C3ME4CGjYr5u8G6QSfiQRERkL/kUmIiKtdZN3w8EZBzHBY4J6m5lUtzUwlhxZ\ngsXfLVa/9nHxQfYb2ep7MxARkfi4uhEREenE0swSX0/7GtFfRaOPTR+sHrdap3sYPG/7vPr52L5j\nsS96H2wsbAwRKhER6YlFAhER6Uwuk2P3q7shk8h0vsnZXN+5+PXBr/jh5g9In5oOSzNLA0VJRET6\nYpFARER60XWa0ZP+J+B/oBJUkEll7RgRERG1F16TQERE7erq3auIOxAHmNUBaPqCZolEwgKBiMiI\ncSSBiIjazY3qGwj+PBild0qBGaWAtB44vBHAMLFDIyIiHXAkgYiI2s2ef+1pKBAAoN93QN8sYOZ4\nlFSWiBsYERHphEUCERG1m7dffBsrglZobrSuwOnbp8UJiIiI9MIigYiI2tWywGVYF7YOUJoDdTZA\n+l5MHTRV7LCIiEgHvCaBiIjaXfyoePx3yEyg3hqo7yZ2OEREpCMWCUREZBj3HcSOgIiI9MTpRkRE\nREREpIFFAhERERERaeB0IyIi0plE0r7thabvuUZERCLhSAIREREREWkQrUjIyspCZGQkXF1dIZVK\nkZKSovF+bGwspFKpxsPf31+jzcOHDzFv3jw4ODige/fumDRpEm7cuNGRp0FE1CUJQuuPvLx85OXl\na9WWiIiMi2hFQm1tLby8vLBhwwZYWVlB8tRYtEQiQWhoKMrKytSPQ4cOabRZsGAB9u7di127diE7\nOxvV1dWYOHEiVCpVR54KEREREVGnIto1CREREYiIiADQMGrwNEEQIJfLoVAomty/qqoKf/vb37B9\n+3aMGzcOAJCamgo3NzccOXIEYWFhBoudiIiIiKgzM9prEiQSCXJycuDo6AhPT0/ExcWhvLxc/X5B\nQQHq6+s1igFXV1cMHDgQubm5YoRMRERERNQpGO3qRuHh4ZgyZQrc3d1x+fJlLFu2DMHBwSgoKIBc\nLkdZWRlkMhns7Ow09nN0dMTt27ebPW5VVZWhQ+9yPDw8ALBvDYX9azjsW8Ni/xoW+9dw2LeGxf41\nDUZbJEybNk39fPDgwRg5ciTc3Nzw97//HVFRUSJGRkRERETUuRntdKOnOTs7w9XVFT///DMAwMnJ\nCUqlEpWVlRrtysrK4OTkJEaIRERERESdgtGOJDytvLwcN27cgLOzMwBg5MiRMDc3R2ZmJqZPnw4A\nuH79Oi5cuPDMUqm2trYdHi8RERERkakSrUiora1FSUkJAEClUuHq1asoKiqCnZ0devXqhYSEBEyd\nOhVOTk64cuUKlixZAkdHR/VUI1tbW8yePRuLFi2CQqFAr169EB8fj2HDhiEkJESs0yIiIiIiMnkS\nQRDnNjbHjx9HcHBwQxASCRrDiI2NxebNmzF58mQUFhbi7t27cHZ2RnBwMFasWIHevXurj/Ho0SO8\n8847SEtLw4MHDxASEoLNmzdrtCEiIiIiIt2IViQQEREREZFxMpkLl1uzefNmuLu7w8rKCj4+PsjJ\nyWmxfXFxMcaMGQNra2u4urpixYoVHRSpadKlf69cuQKpVPrMIzMzswMjNg1ZWVmIjIyEq6srpFIp\nUlJSWt2Huas9XfuXuau91atXw9fXF7a2tlAoFIiMjMS5c+da3Y/5qx19+pf5q52kpCQMGzYMtra2\nsLW1hb+/Pw4dOtTiPsxb7enav8xb/a1evRpSqRTz5s1rsZ2++dspioT09HQsWLAAy5YtQ1FREfz9\n/REREYFr16412b66uhqhoaFwdnZGfn4+NmzYgLVr12L9+vU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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_hypothesis()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a humans' weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n", + " \n", + "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based solely on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, merely one that is reasonable and could be explained by the measurement." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_hypothesis2()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another what if: what if the readings were 158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0? Let's look at a chart of that and then answer some questions." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Qt99+63AMAAAA1bmc9FZm5KR3bMI4FW0/bdd2aNuPenh0smsCwnVxuCJ/6623qrCwUAcO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\nXLa0Jjc3V5GRkYqMjNSFCxe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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_hypothesis3()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. We can't be sure, but that surely looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n", + "\n", + "So let's look at two hypotheses. First, let's assume our weight did not change. To get that number we agreed that we should average the measurements. Let's look at that." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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jjz9055136tFHH1Xz5s1VqVIlbdy4UatWrdKIESNu9CO2IHkEbtKNfgtqC9+C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\nkr+/v44dO6a3335btWvXtmp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_hypothesis4()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That doesn't look very convincing. In fact, we can see that there is no horizontal line that we could draw that is inside all of the error bars.\n", + "\n", + "Now, let's assume we we gained weight. How much? I don't know, but numpy does! We 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 plot the results." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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JycHAgQPx4MEDmJmZ4auvvsK3336LkSNHam2wRERERNQ46uyJKAgCsrJVzx5evQXk/tOw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\nz89PwcHBXq8LDQ1VY2OjSakBAAAAoGfy2fI4bdo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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_hypothesis5()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks much better, at least to my eyes. Notice now the hypothesis lies very close to each measurement, whereas in the previous plot the hypothesis was often quite far from the measurement. It seems far more likely to be true that I gained weight than I didn't gain any weight. Did I actually gain 13 lbs? Who can say? That seems impossible to answer.\n", + "\n", + "\"But is it impossible?\" pipes up a coworker.\n", + "\n", + "Let's try something crazy. Let's assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, assume I know it is approximately correct. Maybe I am eating a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. Let's see if we can make use of such information if it was available without worrying about the source of that information yet.\n", + "\n", + "The first measurement was 158. We have no way of knowing any different, so let's 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", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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URz0JIiIiIj9Ufj58+KE1Y7B0KXznA1YhXbtaMwYjRkCTJu4do4ibqUgQERGRysduh02b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\nIon/AQI5mbqSKgLDAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_estimate_chart_1()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Okay, but what good is this? Sure, we could assume the 1 lb/day is accurate, and predict our weight for the next 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", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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YMWMwevRoE7aWiIiIqPFSKBTw8WmBvXsLMXp0CXTLe9QICCjBnj1FHIO/EZMy4VepVACA\noKAghIWFwcvLC3PnzsWkSZOwevVqAMCWLVtw6tQprFixAoB4cLfs95qUH/KL05zmNKc5zWlOc7qp\nTisUCgwY0ALLl59HQkIhtm4VX7t3Z2LrVrU22ZelvU1l2lCkTPjbtGkDS0tL9OrVS2d+jx49cPny\nZQDAwYMHcebMGdja2sLKygrNmjUDAAQHB2PIkCEN3mbST2Iix1eWBeMgB8ZBDvzbJBfGwjQUCgXU\n6nwMGmSNbt1S0K1bCtq2zUCrVlbs2W/kFGp9u8SNyM7ODmvWrEFISIh2nmaEns8//1w7b/r06bh1\n6xZiYmJw9epVZGdna5ep1Wp4enrigw8+wGOPPabzgK+hXktMRERERNRQDJXDmuyh3fz8fJw/fx6A\nKOFJT09HcnIynJyc4OrqioULF2LSpEnw8/ODv78/YmNjER0djZ07dwIAOnbsiI4dO1bYr6ura6Wj\n+RARERERNUUm6+GPi4vD8OHDRSMUCm3tfWhoKDZu3AgAiIqKQmRkJDIyMuDu7o7w8HAEBwdXuU+l\nUolvvvkGEyZM0JnPHn4iIiIiamwMlcNKUdJjbEz45aGpy+Swa6bFOMiDsZAD4yAPxkIOjIMcmPDX\nAhN+IiIiImpsDJXDSjlKDxERERERGQYTfiIiIiIiM8aEnxoUx7qWA+MgD8ZCDoyDPBgLOTAO5oU1\n/EREREREEmINPxERERER1YgJPxERERGRGWPCTw2KNYFyYBzkwVjIgXGQB2MhB8bBvLCGn4iIiIhI\nQqzhJyIiIiKiGjHhJyIiIiIyY0z4qUGxJlAOjIM8GAs5MA7yYCzkwDiYF9bwExERERFJiDX8RERE\nRERUIyb8RERERERmjAk/NSjWBMqBcZAHYyEHxkEejIUcGAfzwhp+IiIiIiIJsYafiIiIiIhqxISf\niIiIiMiMmTThj4+Px/jx4+Hi4gKlUomoqKgK66SlpWHChAlwdHSEjY0N+vXrh9TUVO3yp59+Gvff\nfz9atmwJZ2dnBAUF4ezZsw15GlQLrAmUA+MgD8ZCDoyDPBgLOTAO5sWkNfx79uxBQkICHnroIYSE\nhGDdunUICQnRLr948SJ8fHwQGhqKqVOnwsHBAampqejduzdcXFwAAJ9++ik8PDzg6uqKmzdvIiIi\nAomJiUhPT4elpSUA1vATERERUeNjqBxWmod27ezssGbNGp2Ef8qUKbCwsMCWLVv03s+pU6fQp08f\nnDt3Dt27dwfAhJ+IiIiIGh+zf2hXpVIhJiYGPXv2REBAAJydneHj44Ovv/66ym3y8/OxadMmdO/e\nHV26dGnA1hIRERERyUnahD8zMxN5eXmIjIxEQEAADhw4gMmTJ2Pq1KnYvXu3zrpr166FnZ0d7Ozs\nEBMTg++//15bzkNyYU2gHBgHeTAWcmAc5MFYyIFxMC/SJvwqlQoAEBQUhLCwMHh5eWHu3LmYNGkS\nVq9erbPutGnTkJycjMOHD6NXr14IDAzE7du3q91/+X/EnG6YaW9vb3h7e0vTnqY6DYhYyNKepjxd\nNg4ytKepTmv+NsnSnqY8DfDvkwzT/P9ajmlDkTbhb9OmDSwtLdGrVy+d+T169MDly5d15tnb26Nb\nt27w8/PDN998g7/++gvbt29vyOYSEREREUlJ6od2fX190a1bN3z++efaedOnT8etW7cQExNT6X6K\niorQunVrrF69Gk888QQAPrRLRERERI2PoXJYkxa65+fn4/z58wBECU96ejqSk5Ph5OQEV1dXLFy4\nEJMmTYKfnx/8/f0RGxuL6Oho7Ny5EwBw4cIFfPPNNxg5ciTatGmDK1eu4O2330aLFi0wduxYU54a\nVaHsrUIyHcZBHoyFHBgHeTAWcmAczItJe/jj4uIwfPhw0RCFApqmhIaGYuPGjQCAqKgoREZGIiMj\nA+7u7ggPD0dwcDAA4MqVK5g5cyaSkpKQnZ2Ndu3aYejQoViyZAnc3d21x2EPPxERERE1NmY3Dr8x\nMeEnIiIiosbG7MfhJyIiIiKi+mPCTw0qMZHj+sqAcZAHYyEHxkEejIUcGAfzwpIeIiIiIiIJsaSH\niIiIiIhqxISfiIiIiMiMMeGnBsWaQDkwDvJgLOTAOMiDsZAD42BeWMNPRERERCShBn/T7o0bN5CQ\nkICzZ8/ixo0bUCgUaNOmDXr27IlBgwahTZs2dW4EEREREREZR7UJf1FREb788kts2rQJCQkJ1e5o\n0KBBeOKJJzBt2jQ0b97coI0kIiIiIqK6qbKGf926dejWrRvmzJkDR0dHfPjhhzhy5Aj+/PNP3Llz\nB/n5+bhy5QqOHDmCDz/8EI6Ojnj22WfRrVs3fPzxxw15DtSIsCZQDoyDPBgLOTAO8mAs5MA4mJcq\na/hdXFzw0ksv4cknn9S7Zig7OxsbN27EBx98gIyMDIM2tD5Yw09EREREjY2hctgqE/7i4mI0a9as\nTjutz7bGwISfiIiIiBobo794qz4Ju0zJPhERERFRU6b3OPzXrl3DyZMndeadPXsWM2fORHBwMLZv\n327wxpH5YU2gHBgHeTAWcmAc5MFYyIFxMC96j8M/ceJEZGZmIj4+HgCQlZWFHj16IDs7Gy1atEB+\nfj527NiBcePGGbXBdcGSHiIiIiJqbIxe0lPesWPHMHr0aO30F198gVu3biEpKQk3b96Er68v3nvv\nvTo3hIiIiIiIDE/vhP/mzZvo2LGjdnrXrl3w8/ODp6cnrKysEBwcjJSUFKM0koiIiIiI6kbvhL91\n69b466+/AAB37txBQkICRo0apV2uUChQWFho+BaSWWFNoBwYB3kwFnJgHOTBWMiBcTAv1b5pt6zB\ngwdj7dq16NGjB/bu3YvCwkKMHz9euzwtLQ2dOnUySiPJfHh7e5u6CQTGQSaMhRwYB3kwFnJgHMyL\n3j38kZGRaN68OSZOnIjPPvsM8+bNQ69evQAAJSUl2LZtG4YOHVqrg8fHx2P8+PFwcXGBUqlEVFRU\nhXXS0tIwYcIEODo6wsbGBv369UNqaioA4NatW3j++efRs2dPtGzZEp07d8acOXOQlZVVq3YQERER\nEZkrvXv477//fqSmpuLMmTOwt7dHly5dtMsKCgqwZs0a9OnTp1YHz8/Ph5eXF2bMmIGQkBAoFAqd\n5RcvXoSvry9CQ0OxdOlSODg4IDU1Fba2tgCAq1ev4urVq3j33XfRq1cvXLlyBXPmzMHkyZOxb9++\nWrWFiIiIiMgc6T0sp7HZ2dlhzZo1CAkJ0c6bMmUKLCwssGXLFr33s2fPHowdOxY5OTnaCwMOyykP\nTT0gbxWaFuMgD8ZCDoyDPBgLOTAOcjBUDqt3Dz8A3L17F59//jliYmKQnp4OAHBzc8Ojjz6KGTNm\nwNKyVrurlkqlQkxMDBYtWoSAgACcOHECbm5umD9/PiZNmlTldjk5OWjevDlatmxpsLaQ4fAPhxwY\nB3kwFnJgHOTBWMiBcTAvetfwZ2Zmon///nj66adx+PBh7fzY2Fg8/fTT6NevH/7++2+DNSwzMxN5\neXmIjIxEQEAADhw4gMmTJ2Pq1KnYvXt3pdtkZ2djyZIlmDlzJpTK6k+t/JPnnOY0pznNaU5zmtOc\n5rRM04aid8L//PPP4+zZs9iwYQOuX7+OEydO4MSJE7h+/To+++wznD17Fs8//7zBGqZSqQAAQUFB\nCAsLg5eXF+bOnYtJkyZh9erVFdbPy8vDuHHj4OrqihUrVhisHUREREREjZneNfz29vaYOXNmlW/T\nfemll7B+/Xrk5ubWqSHla/iLi4tha2uLiIgILF68WLveG2+8gejoaJ2XfOXl5WHMmDFQKBTYs2dP\nhXIe1vDLQ3PlyluFpsU4yIOxkAPjIA/GQg6MgxwavIa/WbNmcHNzq3K5m5sbmjdvXueGVHa8/v37\na4fg1EhLS9Npx+3btxEYGFhlsk9y4R8OOTAO8mAs5MA4yIOxkAPjYF70Tvj/9a9/4T//+Q+eeeYZ\nWFlZ6SwrLi7G1q1bERwcXKuD5+fn4/z58wBECU96ejqSk5Ph5OQEV1dXLFy4EJMmTYKfnx/8/f0R\nGxuL6Oho7Ny5E4BI9keNGoXbt29jx44duH37Nm7fvg0AcHJyqtBOIiIiIqKmpsqSnuPHj+tM37lz\nBy+++CIUCgWeeeYZdO/eHYDocf/kk0+gUCiwatWqWr18Ky4uDsOHDxcNUSigaUpoaCg2btwIAIiK\nikJkZCQyMjLg7u6O8PBw7YWFZvuy22r2FRsbiyFDhgBgSQ8RERERNT6GymGrTPhrGuWm0p0pFCgt\nLa1zY4yFCb88WBMoB8ZBHoyFHBgHeTAWcmAc5GD0hH/z5s112mFoaGidG2MsTPiJiIiIqLExesJv\nTpjwExEREVFjY6gctvZ1O0RERERE1GhUOUrPa6+9BoVCUesdLl26tF4NIvPGmkA5MA7yYCzkwDjI\ng7GQA+NgXgz60C5w7w25MmFJDxERERE1NkZ/8ZaMiTsREREREdUOa/iJiIiIiMwYE35qUImJidq6\nQDIdxkEejIUcGAd5MBZyYBzMS5U1/EOGDMErr7yC0aNH12qHe/fuxVtvvYXDhw8bpIGGwBp+IiIi\nImpsjF7D/+CDD+Kxxx5Dx44d8c9//hMjR46Et7c3HBwcdNa7desWEhMT8cMPP2Dbtm3466+/MHPm\nzDo3iIiIiIiIDKfaF29dunQJq1atwhdffIGbN28CABwcHODo6Ai1Wo2srCzk5uYCANq2bYvp06fj\nhRdeQOfOnRum9XpiDz8RERERNTYN+qbdu3fv4ujRo/jxxx+RmpqqTf7btGmDnj17YvDgwRg4cCCs\nrKzq3BBjYsIvD47rKwfGQR6MhRwYB3kwFnJgHOTQoAl/Y8eEn4iIiIgaG0PlsBylh4iIiIjIjDHh\nJyIiIiIyY0z4qUFxXF85MA7yYCzkwDjIg7GQA+NgXljDT0REREQkIdbwExERERFRjZjwExERERGZ\nMb0TfqVSia+++qrK5Vu3boWFhUWtDh4fH4/x48fDxcUFSqUSUVFRFdZJS0vDhAkT4OjoCBsbG/Tr\n1w+pqana5Z9++in8/f3h4OAApVKJy5cv16oN1LBYEygHxkEejIUcGAd5MBZyYBzMi6WhdqRSqWq9\nTX5+Pry8vDBjxgyEhIRAoVDoLL948SJ8fX0RGhqKpUuXwsHBAampqbC1tdWuU1BQgICAAAQFBWHu\n3Ln1Pg8yLr7AQw6MgzwYCzkwDvJgLOTAOJgXgyX8x48fh6OjY622CQwMRGBgIAAgNDS0wvJXXnkF\nAQEBePfdd7Xz3NzcdNZ58cUXAYBXoURERERElai2pGfVqlXo0qULunbtCgAICwtD165dK3w5Ojri\no48+wtixYw3WMJVKhZiYGPTs2RMBAQFwdnaGj48Pvv76a4Mdg4iIiIjI3FWb8Ldt2xYeHh7o1asX\nAMDFxQW9evXS+fLw8MDo0aPx7rvvYt26dQZrWGZmJvLy8hAZGYmAgAAcOHAAkydPxtSpU7F79+56\n77/8HQFON8y0piZQlvY05emy82RoT1Od5u+DHNNl4yBDe5r6NP8+mX66/O+FqdvTVKcNpdqSnilT\npmDKlCkAgGHDhuHVV1/FiBEjjNKQ8jTPBAQFBSEsLAwA4OXlhcTERKxevRpjxoxpkHaQYWlqAo31\nD5r0x/pMOXh7e/P3QQL8fZAL42F6/P/avEjz4i07OzusWbMGISEhAIDi4mLY2toiIiICixcv1q73\nxhtvIDo6GikpKTrbJyYmwsfHB5cuXULnzp11lvHFW0RERETU2Bgqh631Q7unT5/GxYsXcevWLVR2\nraBJ2OurWbNm6N+/v84QnIAYprP8g7tERERERFQ5vRP+CxcuYOrUqTh+/Hi169Um4c/Pz8f58+cB\niBKe9PR0JCcnw8nJCa6urli4cCEmTZoEPz8/+Pv7IzY2FtHR0di5c6d2H9euXcO1a9eQlpYGQFyQ\nZGVl4b777qv1qEFkfJpbg7xda1qMgzwYCzkwDvJgLOTAOJgXvUt6RowYgZ9++glvvfUWBg8eXGUy\nXZve97i4OAwfPlw0RKHQ3jEIDQ3Fxo0bAQBRUVGIjIxERkYG3N3dER4ejuDgYO0+IiIi8Prrr+vs\nQ6FQYNPCC44pAAAgAElEQVSmTdqLD5b0EBEREVFjY6gcVu+E39raGuHh4Vi6dGmdD2YqTPiJiIiI\nqLExVA5b7bCcZTk5OcHBwaHOByIiIiIiooand8I/Z84cfPHFFygpKTFme8jMVTamLzU8xkEejIUc\nGAd5MBZyYBzMS5UlPeXfaKtSqbBixQoUFRUhJCQEnTt3hoWFRYXtJk2aZJyW1gNLeoiIiIiosTF6\nDb9SqXfn/72dKRQoLS2tc2OMhQk/ERERETU2Rh+H/9ChQ3XeKRERERERyUGaN+0aE3v45cFxfeXA\nOMiDsZAD4yAPxkIOjIMcGnxYzsaMCT8RERERNTZGL+kpz9/fHwqFosrlCoUCLVq0gIuLC4YNG4Z/\n/vOfsLTUe/dERERERGQEevfwDxs2DH/++ScuXLgAR0dHuLm5Qa1W49KlS8jOzka3bt3QqlUrXLx4\nEbdu3YKnpycOHjyINm3aGPscasQefiIiIiJqbBr8xVuvv/46srKysHnzZmRmZiIpKQknTpxAZmYm\nNm3ahFu3bmHVqlW4fv06Nm7ciDNnzmDRokV1bhiZJ47rKwfGQR6MhRwYB3kwFnJgHMyL3j38AwYM\nwJAhQ/Duu+9Wunz+/Pk4cuQIfv75ZwDAM888g127duHq1auGa20dsYefiIiIiBqbBu/h/+233+Dm\n5lbl8vvuuw+nTp3STvft2xc3b96sc8OIiIiIiKj+9E7427dvj6+//rrSF2uVlJRg27ZtaN++vXZe\nVlYWWrdubZhWEhERERFRneg9jM5LL72E559/HgMGDMDTTz+N+++/HwBw/vx5rF+/HidPnsRHH30E\nAFCr1fj666/h4+NjnFZTo8VxfeXAOMiDsZAD4yAPxkIOjIN5qdU4/OvWrcOSJUuQlZWlM9/JyQkR\nERF49tlnAQBFRUU4duwYunTpgvvuu8+wLa4D1vATERERUWNjshdvFRcXIzExEenp6QBE7X7//v1h\nZWVV50YYGxN+IiIiImps+KbdWmDCT0RERESNjdHftHv58mUAQOfOnXWma6JZn6gyrAmUA+MgD8ZC\nDoyDPBgLOTAO5qXKHn6lUgmFQoGCggI0a9YMSmXNA/ooFIpKR/ExNfbwExEREVFjY/Qe/o0bN4oV\nLC11pg0lPj4e7733Hk6cOIGrV69i06ZNmDFjhs46aWlpWLRoEWJjY1FcXIwePXrgyy+/RI8ePQCI\nh4Pnz5+PrVu3oqCgAI888gjWrl2LTp06GbStRERERESNVZUJf2hoaLXT9ZWfnw8vLy/MmDEDISEh\nUCgUOssvXrwIX19fhIaGYunSpXBwcEBqaipsbW2164SFheG7777D1q1b0bp1a8ybNw9jx45FUlKS\nXnckiIiIiIjMXZ0e2i0sLMTNmzfRpk0bNG/evN6NsLOzw5o1axASEqKdN2XKFFhYWGDLli2VbpOT\nkwNnZ2ds3rwZkydPBgBcuXIF9913H/bs2YNRo0bprKvBkh7TYk2gHBgHeTAWcmAc5MFYyIFxkIOh\ncthadYMfPnwYvr6+sLW1RefOnZGQkAAAuH79OoYPH479+/fXuSFlqVQqxMTEoGfPnggICICzszN8\nfHzw9ddfa9dJSkrC3bt3dRJ7FxcX9OzZEz/++KNB2kGG5+3tzT8eEmAc5MFYyIFxkAdjIQfGwbzo\nnfDHxcVh5MiRyMnJwXPPPYeyNwbatm0LAPjss88M0qjMzEzk5eUhMjISAQEBOHDgACZPnoypU6di\n9+7dAIBr167BwsICTk5OOtu2a9cOf//9d43H0Fy5cprTnOY0pznNaU5zmtMyThtKlTX85S1ZsgR9\n+vRBQkICcnJy8NFHH+ksHzp0KDZv3myQRqlUKgBAUFAQwsLCAABeXl5ITEzE6tWrMWbMGIMch4iI\niIjI3Oldw9+yZUu88847eP7553Hjxg04OzvjwIEDGD58OABg/fr1eP7551FYWFjrRpSv4S8uLoat\nrS0iIiKwePFi7XpvvPEGoqOjkZKSgkOHDmHEiBG4fv26Ti+/h4cHJk2ahGXLlmnnsYZfHporV94m\nNC3GQR6MhRwYB3kwFnJgHORg9GE5y2vWrBlKSkqqXP7nn3/C3t6+zg0pf6z+/fsjNTVVZ35aWhrc\n3NwAAP369YOVlRX279+v89BuamoqBg0aZJB2kOHxD4ccGAd5MBZyYBzkwVjIgXEwL3on/IMGDcK2\nbdswd+7cCsvy8vKwceNGDBs2TO8D5+fn4/z58wBECU96ejqSk5Ph5OQEV1dXLFy4EJMmTYKfnx/8\n/f0RGxuL6Oho7Ny5E4C4ynnqqaewcOFCODs7a4flfPDBBzFixAi920FEREREZM70Lun55Zdf4Ofn\nhyFDhmDy5Ml46qmn8M4778DW1hYrV67E1atX8dNPP8HT01OvA8fFxWnLgRQKhfYh4NDQUO1LvqKi\nohAZGYmMjAy4u7sjPDwcwcHB2n0UFxdj/vz5+Oqrr1BQUIARI0ZU+uItlvQQERERUWNjqBy2VuPw\nHz58GM888wzS0tJ05t9///3YsGED/Pz86twQY2LCLw/WBMqBcZAHYyEHxkEejIUcGAc5mCThBwC1\nWo1ff/0VaWlpUKlU6NatG7y9vSu8KVcmTPiJiIiIqLExWcLfGDHhJyIiIqLGpsFH6XFzc8PQoUMx\nZMgQ+Pn5wd3dvc4HJSIiIiKihqF3wu/n54fDhw9jy5YtAMQbbQcPHowhQ4ZgyJAhePDBB43WSDIf\nrAmUA+MgD8ZCDoyDPBgLOTAO5qXWJT0ZGRk4cuSI9uvs2bNQq9Vo1aoVfH19ERMTY6y21hlLeoiI\niIiosZGihv/WrVvYuXMn3nnnHZw7dw6AGFNfNkz4iYiIiKixafAafgC4du0a4uPjtV+nT5+GpaUl\nvL298fLLL0s7LCcRERERUVOldw+/u7s7Lly4gJYtW2LgwIEYMmQIBg8ejIEDB8La2trY7awX9vDL\ngzWBcmAc5MFYyIFxkAdjIQfGQQ4NXtKjVCqhVCoRGBiI4cOHY+jQoXjooYekHn9fgwk/ERERETU2\nDZ7wnzt3DvHx8dqHddPT02FnZwdfX1/tSD0+Pj6wtKxVlVCDYMJPRERERI2NyR/azcjIQHx8PI4e\nPYoffvgBf/zxB6ytrZGfn1/nxhgLE34iIiIiamwMlcMq67LR7du3kZKSgt9++w2//vorMjIyAAB3\n796tc0OoaUhMTNTWBZLpMA7yYCzkwDjIg7GQA+NgXvTu4d++fbt2dJ5Tp05BpVLB2toaAwcOhJ+f\nH/z8/PDwww+jZcuWxm5zrbGHn4iIiIgaG5M8tOvo6AhfX18MHjwYfn5+8Pb2hpWVVZ0P3lCY8BMR\nERFRY9Pg4/D/+uuv6N27d6MYlYeIiIiIiAS9E35PT09jtoOaCI7rKwfGQR6MhRwYB3kwFnJgHMxL\nnUfpaUxY0kNEREREjY1JR+khIiIiIqLGwWQJf3x8PMaPHw8XFxcolUpERUXpLA8NDdW+3VfzNWjQ\nIJ11Lly4gMcffxzOzs5o1aoVgoODkZmZ2ZCnQURERGQW1Go17ubkoCAhAYXR0SiMjkZBQgLu5uSg\nCRSEmDWTJfz5+fnw8vLCqlWrYG1tXeFhYIVCgZEjR+LatWvar927d+tsP2rUKCgUCsTGxiIhIQHF\nxcUYN24c/1FKjOP6yoFxkAdjIQfGQR6MhWmo1WoU/vwzFJMmocXgwWjxr3+Jr8GDoQgORuHx48yv\nGjEpavjt7OywZs0ahISEaOeFhobi5s2b2LVrV6Xb7N+/H4GBgcjKytLWNOXm5sLR0RH79+/HI488\nol2XNfxERETUJB05AqjVgK8vYGFR6SqaZL9FQAAUZXImnXVatULh3r1oMWAAR2xsQGZfw69QKHD0\n6FG0a9cODzzwAGbOnInr169rlxcVFUGhUKB58+baec2bN4dSqURCQoIpmkxEREQkj23bgCFDgKFD\nAXd3YOVKIDu7wmolubmwWrasymQfABQ5ObCKiEBJbq4xW0xGIm3CHxAQgC1btuDQoUN4//33cfz4\ncQwfPhzFxcUAgIcffhi2trZYsGAB7ty5g/z8fMyfPx+lpaX466+/TNx6IiIiIhO7efPez3/8Abz0\nEtCpEzBrFnD6tHZRSUoKLPbvr3F3Fvv2oaTMdtR4SJvwBwcHY+zYsfDw8MDYsWOxZ88enDt3Dt9/\n/z0AoE2bNti2bRv27NkDOzs7ODg4IDc3F3379oVSWfNpla8P5HTDTGtqM2VpT1OeLjtPhvY01Wn+\nPsgxXTYOMrSnqU/z75Me02o1UFCAX/fuBVJTgZ9+Avbtw4XISODTT4EVK4DLl5HfsyfQrNm9Hdy5\nA3zyCdC7N+DpicTjx6G4cgX6FOkoABScO2ea822i04ai94u3TK1Dhw5wcXHB77//rp03cuRI/P77\n78jKyoKlpSXs7e3Rvn17TJ482YQtpepoXuBhrH/QpD++TEUO3t7e/H2QAH8f5NIk4lFaCuTmotnV\nq0ByMpCTA2Rnwyk5GfjxR+30fRcuAJaW2unemZlAQYEozbl7Fw+W2223ctM21bUhJQUtLl0y6GmR\nnKR9aLe869evw8XFBRs2bMC0adMqXefgwYMYNWoUUlNT0b17d+18PrRLREREBlVYKJLu/yXi2u+V\nzavsuwy18J06AenpKPjpJzEaTw2rqwEUJiTAutww6WQ8hsphTdbDn5+fj/PnzwMAVCoV0tPTkZyc\nDCcnJ7Ru3RrLli3DxIkT0b59e1y6dAnh4eFo164dHn/8ce0+Nm3ahB49esDZ2RnHjh1DWFgY5s2b\np5PsExEREelQqUTCXVNiXt2y/z1TaFLNmgEODuKrVauKP7dqBRw9CuzfL0qANNq0ASIigNmzAaUS\nlr17o3TUKFjWUMdfOno0LD08jHtOZBQm6+GPi4vD8OHDRSMUCu3YrqGhoVi7di2CgoJw8uRJZGdn\no0OHDhg+fDjeeOMNdOrUSbuP8PBwbN68GVlZWejSpQtmzZqFsLCwCsdiD788NKULTeJ2rcQYB3kw\nFnJgHOShVywKC/XrRa8qib99WzcBNhV7+4oJenXJe/nvLVpUv//Ll4H77rs3bWUFvPgisGSJOPb/\nqNVqFB4/jhajR1c5Uo/KwQFFe/ZwWM4GZqgcVoqSHmNjwk9ERCQJlUok3HUthcnOBoqKTH0W93rX\nq0vIq0ve7eyqHBffYIqKgIEDxTMCjz4qhuV0d690Vc1Y/FYREbDYt09b3qMGUBoQgLvLljHZNwEm\n/LXAhJ+IiMhAiopq15tefl5urhy963Z2tetNL79uTb3rsigqEuVHdnY1rqpWq1GSm4uS06ehyMgQ\n81xdYenhAUt7eyb7JsCEvxaY8BMREUH0rufl1b0UJidHlNOYmpVV/Uph7O2N37tOZACN/qFdappY\nJysHxkEejIUcGk0ciovr9oBp2d51lcrUZyF6m6tIyP+6cweldnZw8fCoOnlv0QJgb7NRNZrfCdIL\ne/iJiIgaglqtf+96VcsKCkx9FmJM+LqWwmh61y3Z31gvbm5Aly5AbOy9eXFxwPDhwKZNwIwZhjuW\nsfZbFykpQJ8+wL59wCOPGG6/b7wBzJ8PWFsbbp8Gwh5+IiKihnT3bt0eMC37XYbedVvbupfCODiI\npIi966alUFQeg6rm1yQ5GdixA3jiCd1Rfeq7X0ObNw/w8zNssg8A06YBTz4JfPWVHOdpBEz4iYjI\n/KnVQH5+/V6UdOeOqc9C9IzXpje9fBLP3nXzUFlxxtCh4g5QXeKbnAy8/rroyS+f8Ndnv4Z07Bhw\n4ACwc6fh992lCzBiBPDee8CCBYbfvwT4W08NijWBcmAc5MFY6EnTu17X0WFycoDSUlOfBWBjU7de\ndc33li3NtgdSwyx/J0pLxfMXxiwZUSjEUKH1UeZCQicO9d2vIaxdC7RtC4wZY5z9h4QAffsCTz8t\nftfMDGv4iYjIuNRq0Tte1zHXs7Pl6F23sKj9WOvle9etrEx9FlQXmzeLko8ffgCOHBH17H//DTzw\nALB4MRAcXPm6P/4opjMygPXrRQ18URHw/vvAl18Cf/whHkD28xM97H366B43IwN46SVRsw6I3vYP\nPhAlLV27AocO3Vu3qlr74mLgww9Fucr58+LfYPfuQGgo8Oyz4o27r79e8ZxnzBD7qmq/N24Ay5YB\n330HZGYC7doB48eLfbVuXfHzOHgQSEoC1q0D/vxT3El45RWRaNekpARwdBT7//LLmtevq/BwcR6V\nvMTVVFjDT0REDaOkpPredX2Sdhl611u2rN+LkmxszL53nWrw8svi4vO558SF7KZNwOTJYqjS8g+0\nzp8vfneeeUZc7PXoIe5UBQSI8pSQEOCFF8Tvx/r1gK8vEB8P9Osnts/OBoYMAa5cAWbPBnr1upd8\nV/fwdtl/o8XFwOjRwOHD4ntIiLjAOHUK+PZbkfD/4x/AtWvAp5+KBLxnT7Ftt25V7zcnBxg0CLhw\nAXjqKdEzfuKESOYPHQKOHxfPipS1eLH4nGbPFncM1q0TFx333y/2VZ2kJFGS5+NT/Xr1NXQoEBkp\nVcJvKEz4iYjMmaZ3vT4vSsrPN/VZAEpl/UphWrVi7zrV382bIlnWvMRq1izAy0s8TBocrPsyrsJC\n4ORJ3XkffCCS7337gJEj782fMwfo3VtcJGhG3lmxAkhP1+1ZnzULmDsXWLVKv/Z++KE43uLFwJtv\n6i7TFHh4eoq38X76qWjTkCE173fFCuD330WZzaxZ9+b36SMuhlasqHjXoLgY+OWXe88CTJwo7lKs\nXl1zwn/mjPhe/iJE49NPxR2H1FRxUZOeLu46/PabaIuLS83nBIgLil9+EQ/XK5X6bdNIMOGnBmWW\ntZmNEOMgjxpjUVIixk6vz4uSSkoa8IyqYG1dt151zXdbW6P2rvN3Qh5Sx2L2bN031trbi4R38WLR\n+x4QoLtu+bfxfvGF6EHv21ckqGWNGAF8/rko+WneXIya0759xZKXl1/WP+H/8ktRXrN0acVlNfw+\naeNQ2cJvvwWcnYGZM3XnP/MM8NprYnn5hH/OHN0Hfzt2BNzdxYVDTa5fF9/LlgpprF8PPPQQ0L+/\nSNZHjhRlRJ07izsWM2bon/A7Ooq/lxcvVn1x0Ugx4acGJeUf8CaIcWggarW49V5NQu6t+fmDDypf\nJy/P1Gdxr3e9rqPDtGolx0N/1eDvhDykjoWm3KWyeRcv6s53d6+47tmzoue/bdvK969QiAuBTp1E\nff+AARUT8/btxe+UPs6fFxcXdfj908YhLq7iwosXRW94+V5wCwvxfEBycsVtunatOK91a/GcQk00\nn0Flj53evCmSfUD07CuVQFCQ+Nt7+LB4PkJfCoVI+rOymPATETUZpaX6965XtezuXVOfhehlrOuY\n65redTO7vU1kdC1bVpynVosSoJUrq96uTRvjtcmULCwqn6/P2DGaC6SsrIrLFi2693NcnKjDB8Rd\nxfLJfmysKJ2q6oJL004zfFaHCT8RmSe1WvSk1edFSbdvm/osxH88teldLz+vVStRHkBE9XfmDDBu\nXMV5QOU92OW5u4vacn//mpPKrl2BtLSK9eR//SX+RunjgQfEXYXi4up7+Wub4HbtKurlS0t1E/mS\nEtFmfT6L2vD0FN/Pn69+vYMHdZ8pKG/hQiAmpvp9ZGWJkXrMDBN+alBS12Y2IY0iDipV1b3r+ibt\nxcWmPguRbFeTmP+Zn48SW1vc5+VVeRJvZ8fe9QbQKH4nmgipY7FunajNt7cX0zk5wMcfizIQTc9y\ndUJCxIudVq4Uw22W9/ff95LNoCDg7bdFXX9o6L113nlH//ZOnSqS3DffrFhTr1bfS/Q1I+rcvKld\nXG0N/+OPi9FsPvtM1O1rrF8vSpJmz9a/jfro00d85seO6c4vLRWjAj3yiBhp6Nw53TisWCHOHxAd\nOPn51Sfzmvd1MOEnqh8p/4A3QQ0Sh8LCuj1gqvmem2v8Nuqjvr3r5R/aK6dTA50GVY9/m+QhdSza\nthV19U88cW9YzitXROJbw+86AODFF8X4/AsWiETV318kspcvi95pa+t7Y+svXCjGzn/6aTEspWZY\nzp9+EmU/+pTCvPgisGuXSPg1D7S2aAGcPi164n/4Qaynqcdfvlz0cNvYwLtrVzG/shr+hQuBbdvE\nsJ4nToiE/ORJYONGMfyoJsnWhz7nYWEBTJggHmQue7fik0/EqEBnzwK7d4syKs0DujEx4g4HAHzz\nDbB9u7gwW75cDLtpY1PxOElJouRK8meO6oIJPxFVpFKJ3pC6lsJkZ8vRu96sWf1q1+3sqq47JaKm\n5513xFj5a9bce/HWl18C//qX7npVlchYWgLffy+Gs9yyRbz0ChAP6fr46I7l7+AgXvI1b57o5QeA\nYcNEHfojj1R+jPLzrKyA/fvFi76++kqMWtOihSgteuKJe+u5uopk/Z13xGg6d++Kuwqace/L79fe\nHkhIuPfirU2bxMPEs2eLUXrKJ9NVfR4Khf7lRLNni9F3YmJE8g+IdxdMnQpERwMPPijuwCxcCLi5\niS/NCEcTJ4rhVEeO1D3v8g4fFndWzBDftEtkjoqK6lcKk5urX6+Lsdnb1+/Npvr0uBER1UTztti4\nOP3GqSfjCAwUZTnx8bXfdtgwUXLUvXvly1UqMbzn7t3iAkwSfNMuNUpS12bKQtO7Xp8XJRUVmfos\nRM9SXXvXHRyaTO86fyfkwDjIg7GQg5RxeP990ZN/4IB4b4G+iorEMKfdu4tnDCobCembb8Q+JUr2\nDclkCX98fDzee+89nDhxAlevXsWmTZswo8ytrNDQUHyuuYX1PwMHDsSPP/6onb569SoWLFiAQ4cO\nITc3F927d8fChQsxZcqUBjsPqplarUZubi5SUlJw5coVAEBRURF69+4Ne3t7KMxt+KuiotqXwJRN\n3mXpXbezq3vtuqZ33dxiawRS/WfahDEO8mAs5CBlHHr1qttQx7/9JmrzAfHys7Aw3eXXr4vSrK1b\n699GSZks4c/Pz4eXlxdmzJiBkJCQCkmfQqHAyJEjsWXLFu28ZuUeopg2bRry8vLw3XffoW3btti+\nfTumT58OV1dX+NXmRQtkNGq1Gj///DOWLVuG/fv36ywbPXo0XnvtNfj4+MiT9KtU4kVHtR1rvez3\nwkJTn4WoE61P7bq9ve4bEYmImjpZ/p+i2rv/fvFA7/r19+r/y1q+XIy2ZG3d8G1rIFLU8NvZ2WHN\nmjUIKfP66NDQUNy8eRO7du2qdrvVq1fr3Blwc3PDCy+8gHnz5mnnsYbfNDTJfkBAgE4MymrVqhX2\n7t2LAQMGGCbpLy6uXylMbq5I+k3N1rZ+vevW1vzPiYiIqJEz+xp+hUKBo0ePol27dnBwcMDQoUOx\nfPlytC3zdrTAwEBER0dj3LhxcHBwwK5du3Djxg2MqE1dFxlNbm4uli1bVmWyD4h/yBEREYiOjkYr\ne3vd3vW6DOlYUNCAZ1gFC4u69apr1m2A3nUpazObKMZCDoyDPBgLOTAO5kXaHv7o6GjY2NigS5cu\nuHjxIl599VWUlpYiKSlJW9pTUFCA8ePH4+DBg7C0tETz5s3x1VdfYVy5t+Cxh980EhISMHjw4BrX\n8wTwY/fusL1wQY7edRub+o0M07Ile9eJiIio3gyVw0r7+sbg4GCMHTsWHh4eGDt2LPbs2YNz587h\n+++/164zbdo03L59GwcPHkRSUhIWLFiA6dOn49SpUzXuX3PlymnjTWse0K1JKADb8+cNk+wrlUDr\n1ijq2FEMr+XvDwQF4cbYseIFJMuWAStX4uKSJcB//ytedJKYiN++/VY8uV9cDOTlIXHnTvFikh9/\nBHbvRuJLL4nxfd9+G1i0CIne3sDkyWKIsEGDkHjnjniy38YGUCik+Pw5zWlOc5rTnOZ04542FGlL\nesrr0KEDXFxc8PvvvwMAzp49i2+//Ra//vorPD09AQCenp44cuQI/v3vf2P9+vWmbC7VwjYAs1q1\nQsucHNE73qoVClq0gHW7dtqe88y7d+F8//3a3vU/bt5E1759tb3qv166hAeHDtUm3L8lJurchryU\nmIg2ZaZvJiaiS5npIrUacHJqyNMmIiIiahDSlvSUd/36dbi4uGDDhg2YNm0aTp8+DU9PT/z222/w\n8PDQrjd69Gi4urris88+085jSY9p6FvSAwAJR45g0IABYux2MjpNDwJrM02PsZAD4yAPxkIOjIMc\nGv1Du/n5+Th//jwAQKVSIT09HcnJyXByckLr1q2xbNkyTJw4Ee3bt8elS5cQHh6Odu3a4fHHHwcA\n9OjRAz169MCcOXPw3nvvoXXr1tixYwcOHDiA7777zlSnRWX07t0bo0aNqjAcZ3mjR4+Gh6cnk/0G\nxD/g8mAs5MA4yIOxkAPjYF5M1sMfFxeH4cOHi0YoFNA0IzQ0FGvXrkVQUBBOnjyJ7OxsdOjQAcOH\nD8cbb7yBTmXegPbHH3/g5ZdfxtGjR3H79m10794d8+bNw/Tp03WOxR5+01Cr1Th+/DhGjx5d5Ug9\nDg4O2LNnj+GG5SQiIiIyE4bKYaUo6TE2JvymoxmLPyIiAvv27dNZFhAQgGXLljHZJyIiIqoEE/5a\nYMJvWmq1Grm5uTh9+jTOnTsHAHjggQfg4eEBe3t7JvsmwNpMeTAWcmAc5MFYyIFxkAMT/lpgwk9E\nREREjY3Zj8NPRERERET1x4S/CYiLi4NSqURUVJSpm2J0KSkpsLS0xMGDB6tcR1NW1BB27tyJ5s2b\na98fQURERNTQmPCbieTkZERERCA9Pb3S5QqFwuS18snJyZg5cyZ27dpltGPMmzcPfn5+eOSRRypd\n/sknn2Dy5Mk672kwpsceewyenp54+eWXG+R4+kpMTDTa2/yodhgLOTAO8mAs5MA4mBfW8JuJzZs3\n48knn0RcXByGDBmis0ytVuPu3buwtLSEUmm6a7zq2mgIx44dg6+vL3bu3Ilx48ZVWL5+/Xrk5ORg\n/sWn1h8AABfxSURBVPz5eOutt+Ds7IynnnrK4O0ob8uWLZgxYwZSUlLQq1cvox+PiIiIzANr+KlS\nlV2/KRQKNGvWzKTJflnGusZcu3Yt2rZtizFjxlS6fMiQIZg/fz4AIDw8HL6+vkZpR3kTJkxAy5Yt\n8fHHHzfI8YiIiIjKkiMDbKKKiooQGRkJDw8PWFtbw9HREePHj0dycrLOeoWFhYiIiMADDzwAGxsb\nODo6wsvLCwsXLgQARERE4MknnwQA+Pv7Q6lUQqlU4oknngBQeQ3/5s2boVQqcejQIbz55ptwc3ND\ny5YtMWDAACQkJGi3Gzx4MGxtbdGxY0e8+eabFc4hLy8Pr776KgYMGIC2bduiRYsW6N69O8LDw1FQ\nUKBdr6Y21ubzqExJSQl27NiBESNGwMLCotJ1HnjgAZ3pHj161LhfQ7CxsYGfnx+++eabBjkeERER\nUVmWpm5AU3X37l0EBATg2LFjCAkJwQsvvIDs7GysX78evr6+iI+PR79+/QAAzz77LDZt2oQZM2Zg\n0KBBKCkpQVpaGmJjYwEA//jHP3Dt2jV8+umneOWVV9CzZ08AQLdu3XSOWVkN/6JFi6BSqRAWFoai\noiK8//77CAgIwIYNGzB79mzMmjUL06dPR3R0NJYuXYouXbpg6tSp2u2vXLmCDRs2YOLEiZg2bRos\nLS0RFxeHFStW4OTJk9i7d2+FNj7xxBPaGntNG2vzeVQmKSkJ+fn58PHxqWtIjGrgwIHYt28fzp07\nV+HCwxQ4vrI8GAs5MA7yYCzkwDiYGXUTkJ2drf2SxcqVK9UKhUK9f/9+nfm5ubnqzp07q4cNG6ad\n5+joqH700Uer3d+mTZvUCoVCffjw4QrLYmNj1QqFQh0VFVVh/X79+qnv3r2rnf/dd9+pFQqF2tLS\nUp2UlKSdX1xcrO7QoYP64Ycf1tl3cXGxuqSkpMIxlyxZolYoFOrjx4/r1cbafB6V2bhxo1qhUKh3\n7dpV6fJPPvlEvXz5cvX06dPVP/zwg/qzzz5TR0ZGqidPnqzOyMiodt+GsGXLFrVCoVBv377d6Mci\nIiIi82CoHJYlPSbyxRdfoGfPnujbty9u3Lih/SoqKsKIESNw9OhRFBUVAQAcHByQkpKC06dPG7wd\ns2fPhqXlvRs9gwcPBgA8/PDD6Nu3r3a+lZUV+vfvj/Pnz+tsb2VlpS2hKSkpwa1bt3Djxg1tD/7x\n48f1akdtPo/KXL9+HQDQunXrCsvWr1+Phx56CIsXL8bzzz+PiRMnwsnJCd7e3ti6datRPtfynJyc\nAACZmZlGPxYRERFRWSzpMZGzZ8+isLAQbdu2rXS5QqHAjRs30KlTJ3z44YeYPn06PD090bVrV/j7\n+2PcuHEYN25cvYfa7Nq1q860o6MjAKBLly4V1nV0dMTNmzcrzF+7di0+/vhjnDlzBiqVSmfZrVu3\n9GpHbT6PqpYDlT8QfPPmTfTv3x8AkJ6eDqVSiaCgIBQUFODw4cPw8/PTq431oWmXqYdGJSIioqaH\nCb+JqNVqeHl5YeXKlVWu06ZNGwDA+PHjcenSJezevRuHDx/GgQMHsGHDBvj5+eHAgQOwsrKqczuq\nesC1qvnlrVy5EvPnz8fo0aMRFhaGjh07olmzZrhy5QpCQ0MrXAAAQGpqaqVDh+r7eVRGc6GQlZVV\nYdmiRYu0P8fFxWHo0KEAAGtr60qT/djYWPTu3bvKi4+qXLhwAcuXL8fGjRsrLNO0q7b7NBbWZsqD\nsZAD4yAPxkIOjIN5YcJvIu7u7sjMzIS/v79evb6Ojo6YOnWq9oHZRYsWYcWKFdi5cycmTpxosp7j\nLVu2oEuXLtizZ4/OfM3DumVp2ljZ6Di1/TzK8/T0BIAKJUflHTx4ELNmzap2nYULFyImJqZWx1+9\nejWSkpJw6dKlSpdr3rTbu3fvWu3XWPgHXB6MhRwYB3kwFnJgHMwLa/hNJCQkBNeuXauyR/vvv/8G\nAKhUKmRnZ1dY3qdPHwD3SmZsbW0BoNKSG0Mqn4xr6v/L9uSXlJTg7bffrrBtdW3U9/OoSp8+fWBv\nb49jx47pzC8tLcUPP/wAlUqFq1ev4ty5c9oefgBYsWKFzvq3b99Gfn4+2rVrV+3xynvuuecQGhpa\n5fKffvoJ7du3R/fu3Wu1XyIiIqL6Yg+/ibz44ov44YcfsGDBAhw6dAj+/v6wt7fH5cuXcfDgQVhb\nW+PQoUPIzc1Fhw4d8Nhjj6FPnz5wdnbGxYsXsW7dOrRu3Vr7RlkfHx8olUosX74cWVlZsLGxQdeu\nXQ0+TGX5GvmJEyciPDwcgYGBePzxx5Gbm4uvvvoKzZo1q7BtdW3U9/OoioWFBSZMmIAdO3aguLhY\ne/xPPvkEzz33HM6ePYvdu3ejZcuWcHFxAQDExMT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_estimate_chart_2()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right? If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n", + "\n", + "> The key insight to this entire book is in the next paragraph. Read it carefully!\n", + "\n", + "So what do we do? If we only take data from the measurement then the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italicized the key point)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should lie 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 scale A was much more accurate than scale B - we scaled the answer to be closer to A than B. Let's look at that in a chart." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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bt89ofV5eHn744Qfk5+fj0qVLOHnypGGEHwBmzJhh1P727dvIzMxEw4YNjdbv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\ngg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_estimate_chart_3()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's try a randomly chosen number to scale our estimate: $\\frac{4}{10}$. Our estimate will be four tenths the measurement and the rest will be from the prediction. In other words, we are expressing a belief here, a belief that the prediction is somewhat more likely to be correct than the measurement. We compute that as\n", + "\n", + "$$\\mathtt{new\\_estimate} = \\mathtt{prediction} + \\frac{4}{10}(\\mathtt{measurement} - \\mathtt{prediction})$$\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 code that and see the results 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). \n", + "\n", + "I hand generated the weight data to correspond to a true starting weight of 160 lbs, and a weight gain of 1 lb per day. In other words on the first day (day zero) the true weight is 160lbs, on the second day (day one, the first day of weighing) the true weight is 161 lbs, and so on. \n", + "\n", + "We need to make a guess for the initial weight. It is too early to talk about initialization strategies, so for now I will assume 159 lbs." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "previous: 160.00, prediction: 161.00 estimate 159.80\n", + "previous: 159.80, prediction: 160.80 estimate 162.16\n", + "previous: 162.16, prediction: 163.16 estimate 162.02\n", + "previous: 162.02, prediction: 163.02 estimate 161.77\n", + "previous: 161.77, prediction: 162.77 estimate 162.50\n", + "previous: 162.50, prediction: 163.50 estimate 163.94\n", + "previous: 163.94, prediction: 164.94 estimate 166.80\n", + "previous: 166.80, prediction: 167.80 estimate 167.64\n", + "previous: 167.64, prediction: 168.64 estimate 167.75\n", + "previous: 167.75, prediction: 168.75 estimate 169.65\n", + "previous: 169.65, prediction: 170.65 estimate 170.87\n", + "previous: 170.87, prediction: 171.87 estimate 172.16\n" + ] + }, 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CCCFyjP/9738sXLhQn37vvffYu3evPj1p0iQ++eQTfbpYsWJYWVmlVKDVQlJS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\nwoIrV66wefNmJk+eTPfu3Y3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p09SzZ8+qly9fVrds2aJGREQY1PXkyRP9S+RugYGBamBg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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import book_plots\n", + "import matplotlib.pyplot as plt\n", + "\n", + "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, \n", + " 169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n", + "\n", + "time_step = 1 # day\n", + "scale_factor = 4/10\n", + "\n", + "def predict_using_gain_guess(weight, gain_rate, do_print=True): \n", + " # store the filtered results\n", + " estimates, predictions = [weight], []\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\n", + " estimates.append(weight)\n", + " predictions.append(prediction)\n", + " if do_print:\n", + " gh.print_results(estimates, prediction, weight)\n", + "\n", + " # plot results\n", + " gh.plot_gh_results(weights, estimates, predictions)\n", + "\n", + "initial_guess = 160.\n", + "predict_using_gain_guess (weight=initial_guess, gain_rate=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is pretty good! There is a lot of data here, so let's talk about how to interpret it. The thick blue line shows the estimate from the filter. It starts at day 0 with the initial guess of 160 lbs. The red line shows the prediction that is made from the previous day's weight. So, on day one the previous weight was 160 lbs, the weight gain is 1 lb, and so the first prediction is 161 lbs. The estimate on day one is then part way between the prediction and measurement at 159.8 lbs. Above the chart is a print out of the previous weight, predicted weight, and new estimate for each day. Finally, the thin black line shows the actual weight gain of the person being weighed. \n", + "\n", + "The 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", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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8hQKek6xevXoVy+TNjzPIwcGBMWPGMGzYsP/s6+3tre2J5uPj88z5KVOm0KpV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TAAAg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\nd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "predict_using_gain_guess(initial_guess, 0, do_print=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is not so impressive. Clearly a filter that requires us to correctly guess a rate of change is not very useful. Even if our initial guess was correct, 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 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 set the new gain/day to 4.4 lbs? 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. Hmm, sounds like our same problem again. 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", + "$$\\text{new gain} = \\text{old gain} + \\frac{1}{3}\\frac{\\text{measurement - predicted weight}}{1 \\text{ day}}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Wzdib+qTHObe4EKayIhBW7oTj559dJ6+diuONd/i/qT/TpmFe9Hobysw7ypkz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\nZ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "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 = [weight]\n", + "predictions = []\n", + "\n", + "for z in weights:\n", + " # prediction step\n", + " weight = weight + gain_rate*time_step\n", + " gain_rate = gain_rate\n", + " predictions.append(weight)\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", + "gh.plot_gh_results(weights, estimates, predictions);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> **note**: the semi-colon on the last line suppresses a string similar to `` being printed in the output. The notebook prints the value of the last line in the input cell unless you use a semi-colon as a terminator.\n", + "\n", + "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", + "```python\n", + "gain_rate = gain_rate\n", + "```\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 gain does not vary, but when we generalize this algorithm we will remove that assumption. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The g-h Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This algorithm is known as the g-h filter. $g$ and $h$ refer to the two scaling factors that we used in our example. $g$ is the scaling we used for the measurement (weight in our example), and $h$ is the scaling for the change in measurement over time (lbs/day in our example)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This filter is the basis for a huge number of filters, including the Kalman filter. In other words, the Kalman filter is a form of the g-h filter, which I will prove later in the book. So is the Least Squares filter, which you may have heard of, and so is the Benedict-Bordner filter, which you probably have not. Each filter has a different way of assigning values to $g$ and $h$, but otherwise the algorithms are identical. For example, the $\\alpha$-$\\beta$ filter assigns a constant to $g$ and $h$, constrained to a certain range of values. Other filters such as the Kalman will vary $g$ and $h$ dynamically at each time step.\n", + "\n", + "**Let me repeat the key points as they are so important**. If you do not understand these you will not understand the rest of the book. If you do understand them, then the rest of the book will unfold naturally for you as mathematical elaborations to various 'what if' questions we will ask about $g$ and $h$. The math may look profoundly different, but the algorithm will be exactly the same.\n", + "\n", + "* Multiple data points are more accurate than one data point, so throw nothing away no matter how inaccurate it is.\n", + "* Always choose a number part way between two data points to create a more accurate estimate.\n", + "* Predict the next measurement and rate of change based on the current estimate and how much we think it will change.\n", + "* The new estimate is then chosen as part way between the prediction and next measurement.\n", + "\n", + "Let's look at a visual depiction of the algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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EAmzfvh01NTVYunQpsrOz25w3orMoAbBROTk5OHr0KLfs7OyMxMREm3vamC1g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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.create_predict_update_chart()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let me introduce some more formal terminology. The predict step is known as **system propagation**. The *system* is whatever we are estimating - in this case my weight. We *propogate* it into the future. Some texts call this the **evolution**. It means the same thing. The update step is usually known as the **measurement update**. One iteration of the system propagation and measurement update is known as an **epoch**. \n", + "\n", + "Now let's explore a few different problem domains to better understand this algorithm. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23 km at time t and moving at 18 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of $\\pm$ 250 meters. The train is moving at 18 kph, which is 5 meters per second. So at t+1 second the train will be at 23.005 km yet the measurement could be anywhere from 22.755 km to 23.255 km. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.005 km because a train cannot slow down very much in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n", + "\n", + "Now consider the problem of tracking a thrown ball. We know that a ballistic object moves in a parabola in a vacuum when in a gravitational field. But a ball thrown on the surface of the Earth is influenced by air drag, so it does not travel in a perfect parabola. Baseball pitchers take advantage of this fact when they throw curve balls. Let's say that we are tracking the ball inside a stadium using computer vision. The accuracy of the computer vision tracking might be modest, but predicting the ball's future positions by assuming that it is moving on a parabola is not extremely accurate either. In this case we'd probably design a filter that gave roughly equal weight to the measurement and the prediction.\n", + "\n", + "Now consider trying to track a child's balloon in a hurricane. We have no legitimate model that would allow us to predict the balloon's behavior except over very brief time scales (we know the balloon cannot go 10 miles in 1 second, for example). In this case we would design a filter that emphasized the measurements over the predictions.\n", + "\n", + "Most of this book is devoted to expressing the concerns in the last three paragraphs mathematically, which then allows us to find an optimal solution. In this chapter we will merely be assigning different values to $g$ and $h$ in a more intuitive, and thus less optimal way. But the fundamental idea is to blend somewhat inaccurate measurements with somewhat inaccurate models of how the systems behaves to get a filtered estimate that is better than either information source by itself.\n", + "\n", + "We can express this as an algorithm:\n", + "\n", + "**Initialization**\n", + "\n", + " 1. Initialize the state of the filter\n", + " 2. Initialize our belief in the state\n", + "\n", + "**Predict**\n", + "\n", + " 1.Use system behavior to predict state at the next time step\n", + " 2. Adjust belief to account for the uncertainty in prediction\n", + " \n", + "**Update**\n", + "\n", + " 1. Get a measurement and associated belief about its accuracy\n", + " 2. Compute residual between estimated state and measurement\n", + " 3. New estimate is somewhere on the residual line\n", + " \n", + "We will use this same algorithm throughout the book, albeit with some modifications. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notation and Nomenclature" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I'll begin to introduce the nomenclature and variable names used in the literature. Some of this was already used in the above charts. Measurement is typically denoted $z$ and that is what we will use in this book (some literature uses $y$). Subscript $k$ indicates the time step, so $z_k$ is the data for this time step. A bold font denotes a vector or matrix. So far we have only considered having one sensor, and hence one sensor measurement, but in general we may have *n* sensors and *n* measurements. $\\mathbf{x}$ denotes our data, and is bold to denote that it is a vector. For example, for our scale example, it represents both the initial weight and initial weight gain rate, like so:\n", + "\n", + "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n", + "\n", + "So if the weight is 62 kg and the weight gain is 0.3 kg/day, the vector would be\n", + "\n", + "$$\\mathbf{x} = \\begin{bmatrix}62 \\\\ 0.3\\end{bmatrix}$$\n", + "\n", + "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 $\\mathbf{x}_k$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## NumPy arrays\n", + "\n", + "We will find NumPy's array data structure to be indispensible through the rest of the book, so let's take the time to learn about them now. I will teach you enough to get started; refer to NumPy's documentation if you want to become an expert with them.\n", + "\n", + "`numpy.array` implements a one or more dimensional array. Its type is `numpy.ndarray`, and we will refer to this as an ndarray for short. You can construct it with any list like object. The following constructs a 1-D array from a list:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 2 3]\n", + "\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "x = np.array([1, 2, 3])\n", + "print(x)\n", + "print(type(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can create a 2D array with nested lists:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1 2 3]\n", + " [4 5 6]]\n" + ] + } + ], + "source": [ + "x = np.array([[1, 2, 3],\n", + " [4, 5, 6]])\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can create arrays of 3 or more dimensions, but we have no need for that here, and so I will not elaborate.\n", + "\n", + "By default the arrays use the data type of the values in the list; if there are multiple types then it will choose the type that most accurately represents all the values. So, for example, if your list contains a mix of `int` and `float` the data type of the array would be of type `float`. You can override this with the `dtype` parameter." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 2. 3.]\n" + ] + } + ], + "source": [ + "x = np.array([1, 2, 3], dtype=float)\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can perform matrix addition with the `+` operator, but matrix multiplication requires the `dot` method or function. The `*` operator performs element-wise multiplication, which is **not** what you want for linear algebra." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "addition:\n", + " [[ 2. 4.]\n", + " [ 6. 8.]]\n", + "\n", + "element-wise multiplication\n", + " [[ 1. 4.]\n", + " [ 9. 16.]]\n", + "\n", + "multiplication\n", + " [[ 7. 10.]\n", + " [ 15. 22.]]\n", + "\n", + "dot is also a member of np.array\n", + " [[ 7. 10.]\n", + " [ 15. 22.]]\n" + ] + } + ], + "source": [ + "x = np.array([[1., 2.],\n", + " [3., 4.]])\n", + "print('addition:\\n', x+x)\n", + "print('\\nelement-wise multiplication\\n', x*x)\n", + "print('\\nmultiplication\\n', np.dot(x,x))\n", + "print('\\ndot is also a member of np.array\\n', x.dot(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can get the transpose with `.T`, and the inverse with `numpy.linalg.inv`." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "transpose\n", + " [[ 1. 3.]\n", + " [ 2. 4.]]\n", + "\n", + "inverse\n", + " [[-2. 1. ]\n", + " [ 1.5 -0.5]]\n" + ] + } + ], + "source": [ + "print('transpose\\n', x.T)\n", + "print('\\ninverse\\n', np.linalg.inv(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, there are helper functions like `zeros` to create a matrix of all zeros, `ones` to get all ones, and `eye` to get the identity matrix. If you want a multidimensional array, use a tuple to specify the shape." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "zeros\n", + " [ 0. 0. 0. 0. 0. 0. 0.]\n", + "\n", + "zeros(3x2)\n", + " [[ 0. 0.]\n", + " [ 0. 0.]\n", + " [ 0. 0.]]\n", + "\n", + "eye\n", + " [[ 1. 0. 0.]\n", + " [ 0. 1. 0.]\n", + " [ 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "print('zeros\\n', np.zeros(7))\n", + "print('\\nzeros(3x2)\\n', np.zeros((3, 2)))\n", + "print('\\neye\\n', np.eye(3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise - Create arrays\n", + "\n", + "I want you to create a NumPy array of 10 elements with each element containing 1/10. There are several ways to do this; try to implement as many as you can think of. " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# your solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution\n", + "\n", + "Here are three ways to do this. The first one is the one I want you to know. I used the '/' operator to divide all of the elements of the array with 10. We will shortly use this to convert the units of an array from meters to km." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n", + "[ 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n", + "[ 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n" + ] + } + ], + "source": [ + "print(np.ones(10) / 10.)\n", + "print(np.array([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]))\n", + "print(np.array([.1]*10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is one I haven't covered yet. The function `numpy.asarray()` will convert its argument to an ndarray if it isn't already one. If it is, the data is unchanged. This is a handy way to write a function that can accept either Python lists or ndarrays, and it is very efficient if the type is already ndarray as nothing new is created." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.1 0.2 0.3]\n", + "[ 0.4 0.5 0.6]\n" + ] + } + ], + "source": [ + "def one_tenth(x):\n", + " x = np.asarray(x)\n", + " return x / 10\n", + "\n", + "print(one_tenth([1, 2, 3])) # I work!\n", + "print(one_tenth(np.array([4, 5, 6]))) # so do I!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise: Write Generic Algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the example above, I explicitly coded this to solve the weighing problem that we've been discussing throughout the chapter. For example, the variables are named \"weight_scale\", \"gain\", and so on. I did this to make the algorithm easy to follow - you can easily see that we correctly implemented each step. But, that is code written for exactly one problem, and the algorithm is the same for any problem. So let's rewrite the code to be generic - to work with any problem. Use this function signature:\n", + "\n", + "```python\n", + "def g_h_filter(data, x0, dx, g, h, dt):\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", + "\n", + "Return the data as a NumPy array, not a list. Test it by passing in the same weight data as before, plot the results, and visually determine that it works." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution and Discussion" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XrlyhTJkyDBkyhKCgoNS7KxERSZZh2Pc4/O8y+HYTxCckbdOgGvRrC60DwEU9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\nlGSKiIiIiIhImlGSKSIiIiIiImnm/wF63RCkNFQEowAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from gh_internal import plot_g_h_results\n", + "\n", + "def g_h_filter(data, x0, dx, g, h, dt=1.):\n", + " x = x0\n", + " results = []\n", + " for z in data:\n", + " #prediction step\n", + " x_est = x + (dx*dt)\n", + " dx = dx\n", + "\n", + " # update step\n", + " residual = z - x_est\n", + " dx = dx + h * (residual) / dt\n", + " x = x_est + g * residual \n", + " results.append(x) \n", + " return np.array(results)\n", + "\n", + "book_plots.plot_track([0, 11], [160, 172], label='Actual weight')\n", + "data = g_h_filter(data=weights, x0=160, dx=1, g=6./10, h=2./3, dt=1.)\n", + "plot_g_h_results(weights, data);" + ] + }, + { + "cell_type": "markdown", + "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 size fits all' advice that I can give here. Some filters set $g$ and $h$ as constants, others vary them dynamically. The Kalman filter varies them dynamically at each step. Some filters allow $g$ and $h$ to take any value within a range, others constrain one to be dependent on the other by some function $f(\\dot{}), \\mbox{where }g = f(h)$.\n", + "\n", + "The topic of this book is not the entire family of g-h filters; more importantly, we are interested in the *Bayesian* aspect of these filters, which I have not addressed yet. Therefore I will not cover selection of $g$ and $h$ in depth. *Tracking and Kalman Filtering Made Easy* is an excellent resource for that topic. 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 use design criteria that can be mathematically reduced to $g$ and $h$, but the Kalman filter form is usually a much more powerful way to think about the problem. 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", + "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": "markdown", + "metadata": {}, + "source": [ + "## Exercise: create measurement function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's write a function that generates noisy data for us. In this book I model a noisy signal as the signal plus [white noise](https://en.wikipedia.org/wiki/White_noise). We've not yet covered the statistics to fully understand the definition of white noise. In essence, think of it as data that randomly varies higher and lower than the signal with no pattern. We say that it is a serially uncorrelated random variable with zero mean and finite variance. If you don't follow that, you will by the end of the *Gaussians* chapter. You may not be successful at this exercise if you have no knowledge of statistics. If so, just read the solution and discussion.\n", + "\n", + "White noise can be 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", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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TVd3yQbemUDzuv7CpKF8N/Yu3njMT4J8fgBs3UnkUq4iIpOpOKEzpY8iQIZhM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\nyWIhOAIAAACoHyHSy5SXG9p7SNr+vbRtv/Ttfse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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy.random import randn\n", + "def gen_data(x0, dx, count, noise_factor):\n", + " return [x0 + dx*i + 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)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Discussion\n", + "\n", + "`randn()` returns random numbers centered around 0 - it is just as likely to be greater than zero as under zero. It varies by *one standard deviation* - don't worry if you don't know what that means. I've plotted 3000 calls to `randn()` - you can see that the values are centered around zero and mostly range from a bit under -1 to a bit more than +1, though occasionally that get much larger." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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47uDJbXDo5A5v6UmC3uetbS/An9/+b35AjkASAXadlhFgUqkvP3J2L3MgW775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fgh46hdEA4E3d9lbniZ163PIVe3VecU21zvzTucE17fJURkbY6SrLXfWOLeVeqDMx4kVDDXd287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\n/aEoO7bRGp3paTILu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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot([randn() for _ in range(3000)], lw=1);" + ] + }, + { + "cell_type": "markdown", + "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", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution and Discussion" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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BxYsXU6xYsQzrNG7cGFNTUw4fPkyDBg0IDQ0FwNvbGxMTkwzrNW/enOXLlzN9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "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)" + ] + }, + { + "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 sinusoidal 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": "markdown", + "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", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution and Discussion" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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cSVI3j3ftCvK0u4wQLyPXiEgKuU4+TCNX5EIpFwDKFggjOMyaa/fSER0LDX+I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i988TrUClahKCKO4dixY+zatQs/Pz+aNm2KzebwE2dERESknHKauxDDMJg7AYZ0B9dLZtiu2QZt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\nmaNHj9rXl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "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)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This doesn't look so wonderful to me. We can see that perhaps the filtered signal varies less than the noisy signal, but it is far from the straight line. If we were to plot just the filtered result no one would guess that the signal with no noise starts at 5 and increments by 2 at each time step. And while in locations the filter does seem to reduce the noise, in other places it seems to overshoot and undershoot.\n", + "\n", + "At this point we don't know enough to really judge this. We added **a lot** of noise; maybe this is as good as filtering can get. However, the existence of the multitude of chapters beyond this one should suggest that we can do much better than this suggests." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise: The Effect of Acceleration" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Write a new data generation function that adds in a constant acceleration factor to each data point. In other words, increment dx as you compute each data point so that the velocity (dx) is ever increasing. Set the noise to 0, $g=0.2$ and $h=0.02$ and plot the results. Explain what you see." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution and Discussion" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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PsXPnToKCgmjSpImzy3KKbb8Y/GMGzEyBc4WOfe2aw5hYiAhVwBQRKU2Z76N5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\nOVFRUSGtZ/LkyaxevRqAnJyckH53h6bTBkdr/Pd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def gen_data(x0, dx, count, noise_factor, accel=0):\n", + " zs = []\n", + " for i in range(count):\n", + " zs.append(x0 + dx*i + 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)\n", + "plt.xlim([0, 20])\n", + "plot_g_h_results(measurements=zs, filtered_data=data)" + ] + }, + { + "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": "markdown", + "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 $g = 0.1\\mbox{, } 0.4,\\mbox{ and } 0.8$." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution and Discussion" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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EKSujUBTOFczsGeMSvL1TVoNxvRQffKlzM1vXVrg4pVxQd8FX8fMKmL1W52DG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\no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zIyUj/99JPb66dPn1a/fv1UrFgx5cuXT23bttW+ffvs+xTXmE2bNqlXr146e/asGjZs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\naNSoUXrwwQd12223q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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import book_format\n", + "np.random.seed(100)\n", + "zs = gen_data(x0=5, dx=5, count=50, noise_factor=50)\n", + "data1 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.1, h=0.01)\n", + "data2 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.4, h=0.01)\n", + "data3 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.8, h=0.01)\n", + "\n", + "with book_format.figsize(y=6):\n", + " book_plots.plot_measurements(zs, lw=1, color='k')\n", + " book_plots.plot_filter(data1, label='g=0.1', marker='s')\n", + " book_plots.plot_filter(data2, label='g=0.4', marker='v')\n", + " book_plots.plot_filter(data3, label='g=0.8', lw=2)\n", + " book_plots.show_legend()\n", + " book_plots.set_limits([20,40], [0, 250])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is clear that as $g$ is larger we more closely follow the measurement instead of the prediction. When $g=0.8$ 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 have a look. I will create data that has $\\dot{x}=1$ for 9 steps before changing to $\\dot{x}=0$. " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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wQTp16lRp6mhOTg6lpXWfE8nPz4/w8HAAfv75Z+x2O8OGDatWM2TIENavX/+H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\n5Npt2bdC2K1po6rLxhqkZXj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k57fffgfA3z/A9cHTMOjZoycRkZGuurI+7NqVTm5eHhbD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\n2Lt3r1ZcXl6eaNq0qQAgvLy8hIeHhwAgPD09RX5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q4cZCRER1Q4kVS3/g67USUu8LnPgb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", + "for i in range(50):\n", + " zs.append(14)\n", + "\n", + "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.1, h=0.01)\n", + "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.5, h=0.01)\n", + "data3 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.9, h=0.01)\n", + "\n", + "with book_format.figsize(y=5):\n", + " book_plots.plot_measurements(zs)\n", + " book_plots.plot_filter(data1, label='g=0.1', marker='s')\n", + " book_plots.plot_filter(data2, label='g=0.5', marker='v')\n", + " book_plots.plot_filter(data3, label='g=0.9', lw=2)\n", + " book_plots.show_legend()\n", + " plt.ylim([6, 20])" + ] + }, + { + "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 'Goldilocks' 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", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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hTHuy8GGnCUmGe8bAdz/nloVdDwteAL8iZmgVERGRC0MBUkRESs0DDzzAi6//\nyLHan/BjPFAbcmJf/bSiw+P+Q/Yaj3lnWh10B7w5ouj7JEVEROTC0RBWEREpNc2aNaNZs6sK3Neo\nTuHhsaBlOiYOhrefVngUEREpT9QDKSIipSY+0bDvaCBUL/k5RS3TISIiIuWLAqSIiJSK4ycMocMg\n8WTusNXizFlseOzlopfpEBERkfJDAVJERM5Z3AlDl6Gw5c+SHW8v0wEvzsstq18LvpmmmVZFRETK\nMwVIERE5J8cSDLf9B7btzi1rYsKpe9ow1uA69s+0dMMjk+GDZbn7WjeFxVOhbg2FRxERkfJMAVJE\nRM7akeOG24bCr3vsbcuCd94MZ9AdBQfB+ETDvc9qmQ4REZGLlQKkiIiclcPHDZ2fyp051bJgzjPQ\nv3vBQXBfrL1Mx/a/c8sG3QEzR4CbZloVERG5KChAiojIGTsUZ7j13/DHP/a2ZcHcZ6Fv14KD4NZd\nhttHQMyx3LKJg+GZvoUv7SEiIiLljwKkiIickdhjhlufgh3/2NsuLjDvOXiwkGU3lq033Pec8zId\n744p/HgREREpvxQgRUSkxA4escPjn/vsbVdX+GAs9O6cGwYHDH6avbGeWFjEHINd+wFjwKQS2Hyy\nlukQERG5iClAiohIiRw4Yuj0b9i93952dYX54dCrk3MY7B4WQv8XLU56hQJg1QdzfBnVAy1Wz9Qy\nHSIiIhczl7JugIiIlH/7DxlCnsgNj26u8PH4/OERoFu3ULxOLsMYA9hrPvqkRPLLl10UHkVERC5y\nCpAiIlKkfbGGjk/CXwfsbTdXWDAB7umYPwweOGK45XGLY1YoxC8HwPVEJG+9FEbdGvovR0RE5GKn\n/81FRKRQ/8QYQp6EvQftbXc3WPQi3H1L/vC4Ybvh2kHw859AYCjE272QbWtH8uB9oRe24SIiInJe\nFBkg16xZw5133km9evVwcXFh3rx5hR776KOP4uLiwvTp00u9kSIicuH9fdAetvpPjL3t4Q6fToI7\nb84fHt9fagfN2OxlOtzcLAY9HIr/keGMfCJMS3WIiIhUEEUGyOTkZFq2bMmMGTPw9vYu9APAokWL\n2LRpE3Xr1tWHBBGRCuCvaDsQ7jtkb3t6wGeT4PYbnf+Nz8w0jHzd0H8ipKbZZVX9IfIVeGdyGPd2\nhJ53qfdRRESkoihyFtauXbvStWtXAPr371/gMVFRUQwdOpSVK1cSFhZW6g0UEZELa0+0Pdtq9GF7\n29MDvpiEvfDgAAAgAElEQVQMoe2cw2N8oqFPOCxbn1vWvBF8OQUuvcQ+dvasV/TFooiISAVyTvdA\nZmRk8MADD/D8889z+eWXl1abRETkPNm6dSsdOnSgRo0atG7dmsWLFzvt37XPHraaEx69POCrKfnD\n4659hvaDncPjnTfBulm54RFQeBQREalgzmkdyHHjxlGzZk0effTR0mqPiIicJ3v27OGWW24hMTER\ngKNHj9KjRw+WLVtGly5d2BlluPXfEJN9H6O3Jyx+GTpd4xwCIzcYeo+FhKTcsjH94IV/gYuLAqOI\niEhFdtYBcvXq1cybN49t27Y5lees+1WUzZs3n22156Ss6pWyo/e88tF7XrjXXnuNxMRErr/+esaM\nGcOHH37IwoULGTduHAlpdRnyelPiEt0B8PLIJOKRPfibJHJ+pcbA/1bX5LUv65Fl7KDo6Z7F833+\noUub42zZUlavTO97ZaT3vPIpq/f8sssuK5N6Rcqrsx7C+v333xMTE0OdOnVwd3fH3d2dqKgonn76\naRo0aFCabRQRkVIQHx8PQPv27alTpw4dO3YE4HBidYb8X2549PbI5NVH93DNZbldjGkZFhPmN+TV\nL+o7wmPNgDTe/s+fdGlz/AK/EhERESkrZ90D+fjjj9OrVy/HtjGG0NBQ+vTpwyOPPFLkuW3btj3b\nas9KzjdWF7peKTt6zysfvefFCw0NZfHixbz//vu4ubnxxRdfQJUWxFT9iJQkOzz6esM301256eor\nHOfFHjPcMwZ++j33Wtc3h89e8qB2tWYX+mU40fte+eg9r3zK+j1PSEgok3pFyqsiA2RycjK7d+8G\nICsri6ioKLZt20a1atWoX78+NWrUcDre3d2d2rVrq6tfRKQcevTRR/n6669ZunQpL7/8MlRpiVvL\nVaRk+gHgVwWWRsANV+Xex7jlT8Ndo3Mn1QHo1xVmjgQvT93vKCIiUtkUGSA3bdpEp06dAHsmvXHj\nxjFu3Dj69+/Pu+++e0EaKCIipcPNzY0a9dpyZbuGxCdmcCipNhnRMwBwd4PIxeFc3yI3FC5YYRg4\nCU6l2tsuLjD1CRh2v2ZXFRE5XVZWFmlpaWXdDJFz5uHhgYtL4Xc6FhkgQ0JCyMrKKnFlf//9d8lb\nJiIiF1xUrMVO1zchEAiEnBjYwjs3PGZlGcbOhknzcs8L8IX/jYew6xUcRUROZ4whNTUVLy8vfcEm\nFzVjDCkpKUX+WT6nZTxEROTikniy4HL/Ktn7kw19J8CXP+Tua1ofvpwClzfUhyIRkYKkpaXh4eGh\n8CgXPcuy8PDwIC0tDU9PzwKPOetZWEVE5OLy807DL3sK37/3gOGGR53DY2g7WP+OwqOISFGMMbi6\nupZ1M0RKhaura5FLM6oHUkSkEti8w9BlGGRm5g5bzSs+PZh2j8CxPJMNDn8ApgwBV1eFRxEREbEp\nQIqIVHA54TE+sfBjfjvxMDnfNXq4w6xR0K+bgqOIiIg4U4AUEanATg+PHu5wVZVwfL0hy7jwV3JX\nYlKvxWAPvapVFT57Cdq3UHgUERGR/BQgRUQqqM07DLcNhYQke7uqP9xYP4X4k56kZ1hs/zuLhKSv\ngSVgUmnbZTKfT4Z6NRUeRUREpGCaREdEpALaVEB4XDEDHr4vhE3RN/BTQjgnqoZjNQgHv/bceFNH\nvn9T4VFERC68devWcfPNN+Pj40Pt2rV58sknSU5OLtG5wcHBuLi45HsMGTKkyPM++ugjXFxc8Pb2\nLnC/MYZZs2bRunVrfHx8qF69Oh07dmTTpk1n/PoqGvVAiohUMJt2GLqcFh5XvgYtm8CmHaGkHBqO\nadgFy7IwxlDfM5I18yNwcVF4FBGRC2vbtm3ceuutNGvWjIiICKKjo5k+fTq7du1i+fLlxZ5vWRZX\nX301I0eOdCpv2rRpoeckJSUxatQofHx8yMzMLPCYgQMH8tFHH9G3b1/+/e9/k5SUxK+//sqhQ4fO\n7AVWQAqQIiIVyMY/DKHDcsNjtQC757HxJdD3BfhouYUJCIX45RAUiufJSF4ZF4aLiwakiIjIhTdm\nzBiCgoJYvXo1fn5+gN2r+Mgjj7B06VK6du1a5PnGGOrUqUOfPn1KXOfEiRPx9/enU6dOLFq0KN/+\nhQsXMm/ePD7//HN69OhxZi+oEtAnBhGRCqKw8GhZcO0g+Cjni9zAULxPLcMYQ6sakfS8K7TM2iwi\nIuXf6tWradu2Ld7e3jRp0oS3336b8PDwc/7y8cSJE6xYsYI+ffo4wiNA37598fX1ZeHChSW6jjGG\n9PT0Eg173b17N6+++iqvvPJKoWt3RkRE0K5dO3r06EFWVhZJSUkle0GVhAKkiEgFUFB4/PZV2LQD\nrn8E/tyXe+zAOyzemRyK/5HhjHw8DMvS0FURESnY1q1bCQsLIy4ujvHjxzNo0CBeeOEFvvjiC6f/\nPxISEjh69Gixj4SE3AWHf/vtNzIyMmjbtq1Tne7u7rRq1YqtW7eWqI3ff/89VapUwc/Pj+DgYF59\n9dVCjx06dCidOnUiLCyswP0nTpxg06ZNtG3bljFjxhAQEIC/vz+NGjVi/vz5JWpPRachrCIiF7mN\nf9j3PJ7I/uK1WgB8NQWm/y9PryNQxQveHAF9u1oYE8Z3K9X7KCIiRRs3bhyurq6sXbuWunXrAnDf\nffdxxRVXOB3Xo0cP1qxZU+z1QkJC+O677wCIiYkBoE6dOvmOq127Njt37iz2eldffTU333wzl19+\nOUePHuW9995j+PDhREdHM23aNKdjv/76a7799lt+/fXXQq/3119/YYzh448/xt3dnWnTphEYGMj/\n/d//8dBDD1GlShXuuuuuYttVkSlAiohcxAoKjzNHwMBJzr2OzRvBwolwZbD9bbFlWcye9Yp6H0VE\npFCZmZmsWLGCHj16OMIjQOPGjenatStff/21oywiIoL4+PhirxkUFOR4furUKQA8PT3zHefl5eXY\nX5Qvv/zSaXvAgAF07dqVGTNm8NRTT9GgQQMA0tLSGDZsGEOGDMkXfvPKGa4aFxfH+vXrufbaawE7\nIDdp0oQXXnhBAbKsGyAiImdnw3Z72Gre8PhET+g7AVLSco8beDu8NgyqeDmHRYVHEREpyuHDh0lJ\nSaFJkyb59jVp0gRjjGO7TZs2Z3z9nCU0UlNT8+1LSUmhSpUqZ3xNgGHDhhEZGcnq1avp27cvAK+8\n8opjGG5J2tSoUSNHeAQ70N599928+eabnDx58qzbVhEoQIqIlBMZGRl8+umn7N69m+DgYHr16lXg\nt7KQPzxWDYDrmsELc3OPqeIFM0fCw2EKiiIicn7FxcWRlpZW7HEeHh5UrVoVyB26mjOUNa+YmBin\nXs8zUa9ePUebwL4/c+LEiTzxxBPEx8c7ekqTkpIwxhAVFYW3tzc1a9Z01FmrVq18161VqxbGGBIS\nEhQgRUSkbKWmptK9e3dWrlzpKHv99ddZsWIFvr6+Tseu/90QNjw3PAb6gZ83LP0p95gWl8KCCblD\nVkVERM5UzZo18fLyYvfu3fn27dmzx2kkS8+ePc/4HsgWLVrg5ubGpk2b6N27t+OYtLQ0tm3bxr33\n3ntW7d67dy8ANWrUAOD48eMkJyczdepUpk6dmu/4Ro0acfvtt/PVV19Rt25dateuzYEDB/IdFx0d\njZubmyMAV1YKkCIi5cCrr77KypUrqVmzJg8++CCffPIJGzZsYMKECUyZMsVx3Onh0dcbTqVAfGLu\ntQobsioiInImXF1d6dy5M1999RUHDhzgkksuAezwuHTpUqdjz+YeyICAADp37sz8+fMJDw93LOXx\nwQcfkJycTK9evRzHZmRksGfPHgIDA6lduzZgB0N/f3+n5TjS09OZPHkyHh4edOrUCbB7Dj///PN8\nt27MmDGDtWvX8sknnziuCXD//fczY8YMVqxYQefOnQGIj49n0aJF3HjjjYWODqosFCBFRMqBzZs3\nAzBp0iQGDRrEzTffTM+ePR3lkD88erpDUp75BTRkVURESlt4eDjLly/npptuYsiQIWRmZvLGG2/Q\nokULp9lMz+YeSIAXX3yRG264gVtuuYXBgwdz4MABpk+fzq233kq3bt0cx0VHR9OsWTP69evH3Ln2\n/RpffvklEydOpFevXgQHBxMXF8f8+fPZvn07EyZMcAyR9fb2pkePHvnq/uyzz3BxceHOO+90Kn/m\nmWdYuHAh99xzD8OHDycgIIB33nmH5ORkpy91KysFSBGRciDnG9nIyEi6devGN998A+AYJrP+d/ue\nx8ST9vGuLpCannu+hqyKiMj50KZNG5YuXcqIESMYO3Ys9evXZ9y4cezatYs///zznK/funVrVqxY\nwejRoxk+fDh+fn4MHDiQyZMnF3h83l7Eli1b0rx5cz788EOOHDmCh4cHrVq1YsGCBU69l4WxLKvA\nCeVq1qzJ2rVrGTFiBK+++ippaWlcd911zJ49m+uuu+7sX2wFYZm80yedR3kXDQ0ICLgQVTrkfIN/\n+iKlUnHpPa98Lvb3/JdffqFdu3ZOM9G5urqyatUq3INucgqPp6vMQ1Yv9vddzpze88qnrN/zknyG\nTUlJwcvL60I1qVy466672LFjR6mESCl/ivoz7XKB2yIiIgW4+uqr+fbbb7nmmmvw9/enZcuWLFmy\nBLciwqOPN7w/FmY/Y1XK8CgiIhfG6esx7t69m2+++YaQkJCyaZCUKQ1hFREpJ26++Wanex5/+t0Q\nVkh4bHEpLJwIVzRUcBQRkfPr0ksvZcCAATRq1IioqChmzpyJl5cXo0aNKuumSRlQgBQRKYfW/WaH\nx6RT+fcNugNmDK2cQ1ZFROTC69q1K//73/+IjY3F09OTG264gUmTJtG4ceOybpqUAQVIEZFyov+j\n4/gnBhKS4de/PMgKvAPL5yrHfh9ve5bVh0IVHEVELjY5/8afLrgOvDdrfLm9NsC77757zteQikMB\nUkSknFi2Yj2H0toBFpAGxz7FHFsEJpWrOk7WkFURkYvYPzGw5lh4AXsKKis/1xY5nQKkiEg54elT\nFzxvwAoKdZSZ48sIdN/L+nc0ZFVEpCL6fiu43HhuiyKYfWA1KKUGiRRDs7CKiJQDHywz7HN/HuKX\nkbO6kjEG4iNp2eCQwqOIiFxw4eHhuLi4cPjw4bJuipQjCpAiImUoM9Pw2FRDvwlgeTWCwFCIX27v\njI+EwLACFzkWERGpCNatW8fNN9+Mj48PtWvX5sknnyQ5ObnY8+Li4nj55Zfp0KEDNWvWJCgoiPbt\n27Nw4cICj09NTWX06NFccsklVKlShXbt2rF8+fJ8x/Xv3x8XF5d8jyuvvPKcX2tFoSGsIiJl5M8o\nw93PwM6oPIWBofDPcExgFztABkcAP5VVE0VE5Dy7pTWs/urcvigMuRPWHCulBl1A27Zt49Zbb6VZ\ns2ZEREQQHR3N9OnT2bVrV4HhLq9169bx3HPP0b17d55//nnc3NxYtGgRvXv3Zvv27Ywf7zx5UP/+\n/fn0008ZOnQoTZs25b333qN79+6sXLmSDh06OB3r7u7O3LlzncoCAgJK50VXAAqQIiIXWEaGIWIB\nPP82pGfkllsZh2jm9wWmXgJ/Rj3B5fVTqFF9PMF1yq6tIiJSOux/y8MLKS+/1z6fxowZQ1BQEKtX\nr8bPzw+A4OBgHnnkEZYuXUrXrl0LPbdFixbs2bOH+vXrO8qGDBlC586dmTJlCiNGjHBcc+PGjSxY\nsIApU6YwcuRIAB5++GFatGjByJEj2bBhg9O1XV1d6dOnT2m/3ApDAVJE5AL6fa9h0CTYtMO5PNAX\nNsyuxWX1H8OYR/nXo8OYPetNDV8VEakgSmM5jbK4NkB8fDyjRo3iyy+/xBhDz549eeONN/D29j7r\na544cYIVK1bw1FNPOYIeQN++fRk2bBgLFy4sMkAGBwcXWN6jRw++++479u7dy9VXXw3AokWLcHFx\nYfDgwY7jPD09GTRoEGPGjCEqKoqGDRs69hljMMaQlJTk1DaxKUCKiFwA6RmGKR/ChLnOvY4ADWvB\nD29BvZp2WLQsi9mzXlF4FBGRcqF37940btyYyZMn8/PPPzN79mxq1qzJ5MmTAUhISCA9Pb3Y67i7\nuzuGgv72229kZGTQtm3bfMe0atWKrVu3nlVbY2NjAahevbqjbOvWrTRp0iTfMNRrr70WsIfS5g2Q\naWlp+Pv7k5ycTGBgIL1792bq1Kn4+vqeVZsqGgVIEZHzbNsuw6CXYOuu/PuubAgrXoM61Z3DosKj\niIiUF23atGH27NmO7WPHjjFnzhxHgOzRowdr1qwp9johISF89913AMTExABQp07+cba1a9dm586d\nZ9zOuLg4Zs+ezY033sgll1ziKI+JiSmwnpyygwcPOsrq1q3L008/TZs2bcjKymLp0qW89dZbbNu2\njTVr1uDmpvik34CIyHmSlm6Y+B5M/gAyMvPvv6oxfDsDagYpLIqISPn1yCOPOG3fdNNNfP755yQl\nJeHr60tERATx8fHFXicoKMjx/NSpU4A9lPR0Xl5ejv0llZWVxYMPPsiJEyd44403nPadOnWq0Hry\ntgVg0qRJTsfcd999NG3alGeffZYFCxbw4IMPnlG7KqJiA+SaNWuYNm0aW7Zs4eDBg8ydO5d+/foB\nkJGRwbPPPsuyZcv466+/8Pf3p2PHjkyePNnphlYRkcpm8w7DwEnw+96C97duCstfhWoBCo8iIlK+\nNWjQwGk7JwgeP34cX19f2rRpc8bXzLl/MjU1Nd++lJQUqlSpckbX+/e//01kZCQffPABLVu2zFdX\nYfXkbUthhg0bxvPPP8/KlSsVIClBgExOTqZly5b069ePvn37Og2rSk5OZuvWrTz33HO0atWK+Ph4\n/vvf/xIWFsavv/6Kq6vreW28iEh5k5JqCH8Xps2HrKyCj7muGSydDkH+Co8iIlL+FfaZ3hgD2ENH\n09LSir2Oh4cHVatWBXKHj+YMZc0rJiaGunXrlrh948ePZ+bMmUyZMqXAgFenTh327dtXYD1AsXV5\neXlRtWpV4uLiStymiqzYANm1a1fHDEj9+/d32hcQEJBvjZZZs2bRvHlzdu7cSfPmzUuvpSIiZcwY\nQ3JyMj4+PgXeo/jT7/YMq3nXdXR3c54054ar4Jvp4O+j8CgiIhVDz549z/geyBYtWuDm5samTZvo\n3bu345i0tDS2bdvGvffeW6K633jjDcaPH8+wYcMcS3ScrnXr1qxatYr4+HgCAwMd5TnLd7Rq1arI\nOhITEzl69Cg1atQoUZsqulK/BzIhIQFwHuMsInKxe//99xk+fDjHjh2jZs2avPbaa9x///0AnEwx\nPP8OvLoAsr+MBaBhbYiKzd3u0AqWvAy+VRQeRUSk4jibeyADAgLo3Lkz8+fPJzw83LFcxgcffEBy\ncjK9evVyHJuRkcGePXsIDAykdu3ajvIFCxbwn//8h4ceeojp06cXWu+9997LtGnTePvttxk1ahRg\nD52dO3cubdu2dczAmpqaSlpaWr6lOyZMmABAWFhYsa+xMijVAJmWlsZ///tf7rzzzjPqdhYRKc+W\nLl3quPfbsiwOHz7MAw88QK1atXAJvIV/vQR7onOP9/WG9lfBtxtzy25tC19MBh9vhUcREalYzuYe\nSIAXX3yRG264gVtuuYXBgwdz4MABpk+fzq233kq3bt0cx0VHR9OsWTP69evH3LlzAdi4cSN9+/al\nWrVqdOrUiQ8//NDp2jfeeCONGjUC4LrrrqNXr14899xzHD16lCZNmvD+++8TFRXlNLtsTEwMrVu3\npk+fPlx++eUAREZGsnTpUrp06cI999xzVq+zoim1AJmRkcFDDz3EiRMnWLJkSZHHbt68ubSqPSNl\nVa+UHb3nlc/5eM9ffvllwF7c+Mknn2TatGksXPQ1A8afIOq0Wz7aXZ5AraA0vlqfO8yl/ZUJjLv/\nL3ZsN8j5ob/rlY/e88qnrN7zyy67rEzqLQ8syyp0WanSWG6qdevWrFixgtGjRzN8+HD8/PwYOHCg\nY3mQourcsWMH6enpHD16lIEDB+Y7bu7cuY4ACfZIorFjx/Lhhx8SFxfHVVddxeLFi7nlllscxwQF\nBXHHHXfw7bffMm/ePDIzM7nsssuYNGkSI0aMOOfXW1FYxpgSf6Lx8/PjjTfeoG/fvk7lGRkZPPDA\nA2zfvp3Vq1dTs2bNfOfmDG0F2L179zk0WUTkwurWoz9HkqrRMLgR1apWZX9MEkcSA8GysBra/8n5\nemfwnx7R/BldhUVrc/8N7NAinkkD9uLhpvAoInIxyhsgT1+IPkdKSopjSQiRiqCoP9Pn3AOZnp5O\n7969+eOPPwoNj6dr27btuVZ7RnK+sbrQ9UrZ0Xte+ZzP9/y2W29g/oYu7PO9h31pQDXAZRlgfxPa\n/QZ4c4QbL8wNZtHa3PPuCYGPwgPxcL+m1NskNv1dr3z0nlc+Zf2e5+0EERFwKe6A5ORktm3bxrZt\n28jKyiIqKopt27axf/9+MjMz6dWrFxs2bGD+/PkYY4iNjSU2NtaxroqIyMXu7bdep0ryZ47pyo0x\nEB9JUP3beH8sfP4SjH0H5izOPad3Z/jfePBw1z2PIiIiUnEUGyA3bdpEmzZtaNOmDSkpKYwbN442\nbdowbtw4oqOj+eqrr4iJieGaa66hbt26jsfChQsvRPtFRM4bYwyff2+4ZqA7J/0fhvjsZYviI7nu\nhjD+mO9C71uh30SYtzT3vL5h8MFYcHNTeBQREZGKpdghrCEhIWQVtho2FLlPRORite43w6g3YN1v\n2QWBofDPcExgF5r4RvLTwggys6BPOCxalXveoDtg1ihwcVF4FBERkYqn1NeBFBG5mO3aZxjzFnz2\nvXN5oJ/F7feH8uXi4Ux+OYz0DIv7n4ev8tzz+Njd8PpwhUcRERGpuBQgRUSAQ3GGF+bC219CZmZu\nuYc7PHEPjOkLVf3D+FdyJN26dqHnM7B0fe5x/7kPIp4qnWnNRURERMorBUgRqdSSTxkiPoaXP4Kk\nU877+twGEwbD+PHh3POwXZaR6U/dNuOJT7S3rQbhjHwQJg9ReBQREZGKTwFSRCqljAzD3G9g3GyI\nPea8L6Q1TH0C2l5pB8J/YmDNsfDcA4LACgKzL5zn+sP4fyk8ioiISOWgACkilYoxhiU/wuiZsOMf\n533NG8GUx6Fr+5IFwuA68MIjCo4iIiJSeShAikilsfEPw9NvwvdbncvrVocXHoF+XcHVNX8gPJVa\n8PUa1j4PjRQREREpxxQgRaTC+yva8NzbsGClc7lfFXj6IRh6P1TxKrgn8eedhq27gLrnv50iIiIi\n5Z0CpIhUWEfjDRPfg5mfQ3pGbrmbKzx6F4wdADWCCh+CuvQnw33P2+dqoKqIiIiIAqSIVECnUg0z\nFsLkD+BEsvO+ezvCi4/CZfWLjoRzvzYMnpK7pIfrgXBaXAoBvrnHBNcp5YaLiIiIlHMKkCJyURsw\n+Gn2xnqSlJiEAU6mLebvGENaWipWw8mO425qac+sen2LooOjMYYJcyF8Tm5Zw2vDWRoBVwarH1JE\nRKS0rVu3jqeffpotW7bg5+fHvffey5QpU/Dx8Sn23Mcee4z169ezb98+UlNTqV+/Pj169GDUqFFU\nq1bN6djU1FTGjRvHBx98wPHjx7nqqquYMGECXbp0cRxjjGHevHl89tlnbNu2jbi4OBo1akTv3r0Z\nMWIEnp6epf76LzYKkCJyUeseFkL/Fy1OeoU6yozXMsi+p/HyBjD5cbjzpuJnVs3IMDw+HWZ/lVt2\ndRP4ehrUraHwKCIiUtq2bdvGrbfeSrNmzYiIiCA6Oprp06eza9culi9fXuz5P//8M507d6ZRo0Z4\neXmxZcsWXnvtNZYsWcLWrVvx8PBwHNu/f38+/fRThg4dStOmTXnvvffo3r07K1eupEOHDgAkJycz\ncOBA2rdvz5AhQ6hZsybr1q1j3LhxrFixglWrVp2338XFQgFSRC5aMUcNf8SHkn5kOKZeFyzLwhgD\n8ZHUahPB+H/BoNvBza348Jd8ytB7LHy9LrfstmvhkxfB30fhUURE5HwYM2YMQUFBrF69Gj8/PwCC\ng4N55JFHWLp0KV27di3y/E2bNjltDxo0iMaNGzNixAjWrFlD586dAdi4cSMLFixgypQpjBw5EoCH\nH36YFi1aMHLkSDZs2ACAp6cn69at4/rrr3e6ZnBwMOPGjWP58uVOPZaVkUtZN0BE5EwYY/h+q+H+\n5w0Ne0L4HIs031CIz/6WMj6SXj3D2LPQ4tG7rBKFx8PHDR2fdA6PfcNg8csKjyIiIqtXr6Zt27Z4\ne3vTpEkT3n77bcLDw3FxObcoceLECVasWEGfPn0c4RGgb9+++Pr6snDhwrO6boMGDQBwd3d3lC1a\ntAgXFxcGDx7sKPP09GTQoEFs2rSJqKgoxzl5w2OOu+66C4AdO3acVZsqEvVAishFISHJ8MEyeOtz\n+OOf03YGhuK6fxiZgV1oUyuSBf/3SrHDVXPs3m/oOhz2Hswte6YvTBxc/JBXERGRim7r1q2EhYVR\nt25dxo8fT2ZmJi+88ALVq1d3+n8yISGB9PT0Yq/n7u5OQEAAAL/99hsZGRm0bds23zGtWrVi69at\nBV0in4yMDOLj40lNTeX333/n2Wef5aabbnIMS815HU2aNHHUnePaa68F7KG0DRs2LLSO2NhYAKpX\nr16iNlVkCpAiUq79usfw5mfw0XJIPpV/f4dW0OfWRD6euZ8f/hhCs9ssTp48WaIb7zdsN9wxCo7G\n29suLvB/w2HI3QqOIiIiAOPGjcPV1ZW1a9dSt669KPJ9993HFVdc4XRcjx49WLNmTbHXCwkJ4bvv\nvgMgJiYGgDp18k9rXrt2bXbu3FmiNq5evdppWGlYWBiffPKJU8CNiYkpsJ6csoMHD+bbl9fUqVPx\n9/enW7duJWpTRaYAKSLlTmqa4dPV9vqNP/6af7+vNzzcFYbcDYEeB2jfvj3R0dHg6seH8xL547dN\nrPk9hkYAACAASURBVFmzpsgQ+dUPhgfGwalUe9vbE+aPhx43KzyKiIgAZGZmsmLFCnr06OEIjwCN\nGzema9eufP31146yiIgI4uPji71mUFCQ4/mpU/Y3wwXNbOrl5eXYX5xrrrmGFStWkJiYyNq1a3nj\njTfo2bMn33zzDa6uro66Cqsnb1sKMmnSJFauXMmbb77p1P7KSgFSRMqNqFjDrC9gzmI4UsD/Qc0b\nweP3wENdwC/73sT+/Z8jOjqaK6+8km7duvHpp5+yZcsWZsyYwZgxYwqs563PDU9GQFaWvV0tABb/\nf3t3Hmdj2fhx/HPPjNmYzTJ2ZiwpS4+17DtjKcIUSrZQUmT0U3mKkayhUoiUSHpQslS2EAnZ0iZb\nQvZ1LNOMMTPX74/TnJljhhlmxpnl+369zmvOuc69XOfcbud8z7XcE1K/xIeIiEhucubMGaKjoylX\nrlyy58qVK2ebuO5f1atXv+3te3l5AbbLa9woOjoab2/vNG0nICCApk2bAraW0KpVq/Lkk0+yYMEC\nHn/8cfu+brafpHW50YIFC3jttdfo06cPzzzzTJrqk9MpQIqIU8XHG1Zvg+mL4estiaEugZsrhDax\ntTbW/0/ycYkJg9mff/55atWqRbly5ejfv3+K3V6MMbw6E8bOTSwLLgYrJsE9pRQeRURE7tSFCxeI\niYlJdTl3d3fy588PJHYfTejKmtTJkycdWj1vR8eOHenRowfbtm2zB8iiRYty9OjRFPcDpLivNWvW\n0L17dx566CHef//9O6pLTqQAKSJOcf6SYfbXtklxDqUw7KBEIDz9iO0yHEUK3DzcFS9eHLDNrpYn\nTx4++eQTh/IEMdcN/cbB3JWJZTXvtc20Wji/wqOIiMiNAgMD8fT05MCBA8meO3jwoMOPuh07drzt\nMZCVK1fGzc2N7du306VLF/syMTEx7N69m9DQ0Duqd0xMDPHx8Q6zxFarVo3169cTERGBv7+/vTzh\n8h1Vq1Z12MaPP/5Ihw4deOCBB1i4cGG6Z5zNSRQgRSTT9Or3EodOeWCR+AFzOdJw5eo1jnmP41oK\nP1S2qGXrptq2Ttqu3/jf//6XFStWsG7dOvsHUmBgIM8995x9mSuRhtD/wpokl4pqUwf+9zrk81Z4\nFBERSYmrqyvNmzdn2bJlHD9+3P7j7MGDB1mxYoXDsncyBtLPz4/mzZszf/58wsPD7Zfy+OSTT4iM\njOTRRx+1LxsbG8vBgwfx9/enSJEiAFy8eBFfX1/7OMcEM2fOBKBBgwb2stDQUCZOnMjMmTMZOnQo\nYOs6O3v2bGrWrOkwA+sff/xB27ZtKVOmDF999VWKYydzMwVIEck0bVs1pudoi388Q+xl5uJKwMJK\n8r+Pvw/0bAPPPHL7XUlr1KjB999/T1hYGKdPn6Z69eqMGTPG/iF38pyh7YuwO8mPp70fgvf/L20B\nVUREJDcLDw9n9erV1K9fn/79+xMXF8fUqVOpXLkyv/ySONPdnYyBBBg9ejR169alUaNG9OvXj+PH\njzNp0iSaNWvmMOPpsWPHqFixIj169GD27NkALF26lFGjRtGpUyfKlClDVFQUGzduZNmyZTRr1owO\nHTrY13/ggQd49NFHefXVVzl37hzlypVj7ty5HDlyhFmzZtmXu3LlCiEhIURERDB06FCWL1/uUN9y\n5cqleJ3I3EQBUkQy3LUYw5bf4OdzIViXwjAeLbEsyzbYPmIVBE0GoEYF6N8RujQHb887D3M1a9Zk\n8uTJ9vsJ/jhsaDMEjpxKXHbEUzC8l67xKCIikhbVq1dnxYoVvPjiiwwfPpySJUsyYsQI9u/fz759\n+9K9/WrVqvHtt9/y8ssvExYWho+PD71792bcuHEpLp/087tWrVrUqVOHzz//nFOnTmFZFhUqVGDs\n2LGEhYUlW3fu3LkMHz6cefPmceHCBapUqcLy5ctp1KiRfZnz589z7NgxLMvi5ZdfTraNnj17KkA6\nuwIikv3FxRl27Ye1O2D9Ttj0S8LlMSyMewhErIaAEIhYRZ6CrejW1qJ/R6h1X+aFuE0/G9q/BBev\n2B67utpaHZ96WMFRRETkdjRp0oSdO3c6lD3yyCOULFkyQ7Zfr149vv/++1suExQURPwNM+1VqlSJ\nefPmpXk/Hh4ejB8/nvHjx9/WfsSRAqSI3DZjDH8ctgXGdTvhu5/g0tWbLOwfAofDMP4tKeWxip3r\nJ1PQP3ND3BfrDd1exz7G0tsTFo6CNnUVHkVERG5XVFSUw2UuDhw4wDfffEOvXr2cWCtxFgVIEUmT\nI6eMLTDugHW74NT5Wy9frgQ0rQFNa1hcPRHC4NfDmDyhFQX9M3cWsymLDIPfgYRLUwUGwFdvQs1M\nbO0UERHJycqUKUOvXr0IDg7myJEjTJ8+HU9PT/tkNJK7KECKSIrOXDSs3wlrd9q6pf55/NbLFy0A\nzWomhEYoVSQxsBnTih++X0XHR0JusYU70/PpERw+CZevXOH4OQ/ORCQOdr+nXjgrJkGZ4gqPIiLi\nXCnNTG4wlClyjdkzb96l0tnbBmjdujWfffYZp06dwsPDg7p16zJmzBjKli2b7m1L9qMAKZJL3fhh\nExsHl64a4uOu4VZmHL/+eev1/X2gSTVoWtMWHCuUuvnENJZlMWvGW5kycc3hk7DxfLjtgS9Yvra7\n+c6H88P7ZHp3WRERkbRIaWZy7+iVDOyV/s+pzNw2wEcffZQh25GcQQFSJBcwxnDhMpy+AGcu2v7i\n15gtWy1ifVK4xIZJvg1vT2jwH2hSA5rVgKrlwdU17R9MmTXracIkOTf6TzmFRxERyTo6dWjFxOmD\n+TEycWbyyJOrCH1zMtbEFD54b4MxIXAyDIISt105/yo6PvJWBtVeJJECpEgWlJauKHFxhvP/hkL7\n7d9weCbJ/YTQGBvnuA9jQuBcGORL+RIbbq5Qu9K/gbEmPFgRPNyzTiCLumZ4eTr8chCsUsmfd83c\noZYiIiK3xbIsXuwfQs/Rq20thRGrwL9VhvzAalkWxj9x1vO811bxf/+X/m2Hh4fz+uuvc+rUKQID\nA9NdT8kZFCBFsqC2rRrT4w2LKK/E1kHXyyuJwKJqD8PpC3A2AtIzy/SNHzZErCK4Yis6PWLRtIat\ntTGfd9YJjEnt2mfoNhL2HnF2TURERNIuaStk0h9tM0SSWc+zU+vj5s2beemll9i1axc+Pj6EhoYy\nfvx48ubNm6b1ly1bxsiRI/njjz8oWLAgPXv2ZPjw4bi5Jcac7777jqZNm6a4/tatW3nggQduuv0W\nLVqwdu1ann76aaZPn357Ly6HUoAUyQLi422Xxdj8G2z5FX74JYR/Tjl2RYk9v4pffCZjpTL76c34\n5rXNSFo4PxQOgMD8EBgQwtxpYfxlWlKjyCq2r8mccYoZJTbWMOFTCP8weYuqiIhIVpfQCvnUS2F8\nNLUVnTpkZHcZi88X27adEa2Pd8Pu3btp1qwZFStWZPLkyRw7doxJkyaxf/9+Vq9ener6K1as4JFH\nHqFJkya8++67/Prrr4wZM4ZTp04xc+bMZMs/99xz1K5d26HsVhMBLV68mK1btwKZNxQnO1KAFHGC\ny5GGH3+HLb/Zblt/v/E6ipbtl8QkrYMpdXMJ8Pk3ECYJhQn37eX5bcHRyyOl//gsKgfYPmxemZC1\nP2z+PGbo8QZs/jWxLK8XVKkC7m7hXLliGwzp4+MDQFBRJ1RSREQkFZ06tGLFysyZmTwzt50Zhg0b\nRkBAAN99913i53dQEH379mXFihW0bt36luu/+OKLVKlShTVr1uDiYgvjPj4+jBkzhhdeeIGKFSs6\nLF+/fn0ee+yxNNUtOjqaIUOG8PLLL/Paa6/dwavLuRQgRTKZMYY/j9uCT0Jg/PXPxOsU3kyegiF4\nHA/jqmlJSY9VhI+aTJEbQqF7nvQHvqz+YWOM4cPlMHgKREYllteuBHOHQ7kSIwHYsWMHADVr1nRG\nNUVERNIkM2cmz6xtR0REMHToUJYuXYoxho4dOzJ16lS8vLzueJuXL1/m22+/ZeDAgfbwCNC9e3cG\nDx7MwoULbxkg9+zZwx9//MGUKVPs4RHg2WefZfTo0SxatIgRI0Y4rGOM4erVq3h6ejp0cU3JhAkT\nABgyZIgC5A0UIEUyWNQ1w44/ErujbvnNNl4xNYEBULcK1Kls+1ujgsVXX9taB9+a0IpOD2XOrDCZ\n+UGWXqcvGPqNg+U/JJa5ucKIp+ClJ8DNLevVWUREJDWZ+ZmbGdvu0qULZcuWZdy4cezcuZNZs2YR\nGBjIuHHjALh06RLXr19PdTt58uTBz88PgF9//ZXY2NhkP/zmyZOHqlWr8tNPP91yWwnP37h+0aJF\nKVGiBLt37062Tt++fbl69Squrq7Ur1+fCRMmUKtWrWTLHT16lPHjxzN79mw8PT1TfV25zS0D5MaN\nG5k4cSK7du3ixIkTzJ49mx49ejgsEx4ezgcffMDFixd58MEHmTp1arLmYpGc5MYZUq/FwKVIg2Wu\nke/ecfy0P/XxeS4ucH9ZqP1vWKxbGYKLJf9P/261DmbF8Ljse0PfcY7h+97S8MlwqHFv1quviIhI\nTlW9enVmzZplf3z+/Hk+/PBDe4Bs3749GzduTHU7jRs3Zt26dQCcPHkSsAW+GxUpUoS9e/feclup\nrX/ixAn7Yw8PD0JDQ2nTpg0FCxbk999/Z+LEiTRs2JDvv/8+WQgdMmQI1atXT3N319zmlgEyMjKS\n+++/nx49etC9e/dkXzLHjx/P5MmTmTNnDvfccw+vv/46LVq0YN++feTLly9TKy7iLG1aNabHKIto\n7xSun/hHyuv4+0CdSomB8YH7wCdv6iEoK7cOZpYrkYbBU+CjrxzLnwuFcf3B2zP3vBciIiJZQd++\nfR0e169fny+//JKrV6+SL18+Jk+eTERE6t2tAgIC7PejomzjUjw8PJIt5+npaX/+ZlJbP2l96tSp\nQ506deyPH3roIUJDQ7n//vt55ZVXWLNmjf259evXs3jxYrZt25bq68mtbhkgW7dube973LNnT4fn\njDG8/fbbvPLKK3To0AGAOXPmEBgYyPz58+nXr1/m1FjESS5HGuavhhlLQ4g67ThD6o1Tcd9bGupU\nsYXGulVsj11c7iz45ITweObMGU6fPk1wcPAtf1za/Kuh++twKPFHQ4oVhI+GQcsHs//7ICIikh2V\nKuV4weWEIHjx4kXy5ctH9erVb3ubCeMnr127luy56OhovL2907V+auMzy5YtS/v27fniiy+Ii4vD\n1dWV2NhYBg4cSPfu3alRo0ZaX0quc8djIP/66y9Onz5Ny5Yt7WWenp40bNiQzZs3K0BKjrFzr2HG\nUvhsTcIkLslnSK1cvRXt21nUrWxrZczvq7ADEBcXx8CBA5k2bRpg+89++vTpybrCx1w3jPwIxs9z\nvLblo01h+v/p/RQREXEmV1fXFMvNvzMCXrhwgZiYmFS34+7uTv78+YHErqcJXVGTOnnyJMWKFbvl\ntpKuX7p06WTrp2VSvRIlSnD9+nWuXLmCv78/c+fOZf/+/cycOZPDhw87LHv58mWOHDlCYGBguiYP\nygnueFaOU6dOAVC4cGGH8sDAQPtzItnV1X8MHywz1OptqPUUzFrmOAOoV+EQCrESYwwPFlvFL8tD\neKOfRZu6lsJOEhMmTGDatGlYlkVwcDBRUVH07t2bLVu22JfZ85ehTj8YOzcxPPrls411/N/rCo8i\nIiJZXceOHSlWrFiqt9DQUPs6lStXxs3Nje3btztsKyYmht27d1O1atVb7jPh+RvXP3HiBMePH091\nfYBDhw7h4eGBr68vAH///TfXr1+nXr16lClTxn4DmD9/PsHBwaxYsSL1NySHy5RZWFPrcpcw3f7d\n5qz9ivPc7jHff8yLxZsLsWpHfiKvJf+1LbhIFB3rnaV1zQts/7Eco6YPouOz97Jz586MqnKOMmfO\nHABGjx5NixYtGDNmDF9++SVTp07F1TUPi74vxHvLS3DteuJvWTXKX2bE44cpkv86d/K26jzPnXTc\ncx8d89zHWce8fPnyTtlvdnInYyD9/Pxo3rw58+fPJzw83H4pj08++YTIyEgeffRR+7KxsbEcPHgQ\nf39/ihQpAkClSpW49957mTVrFs8++6y9lXT69OkADmH17NmzFCpUyKEuP//8M8uWLSMkJMR+GZAu\nXbpQrVo1h+WMMXTo0IFWrVrxzDPPpDhra25zxwEy4eCdPn2aEiVK2MtPnz5tf04kO4i65sKanwL4\ncnMhfj+SN9nz7m7xNKt6kQ51z/KfMpEk/D7StPGD/LDlR5o0euAu1zj7iP+3SdHd3R1IHOgeeT2A\ngdPLs22/r31Zd7d4nn3oOF0ancElc65YIiIiIpngTsZAgu0H5rp169KoUSP69evH8ePHmTRpEs2a\nNaNNmzb25Y4dO0bFihXp0aMHs2fPtpe/+eabtGvXjpYtW9KlSxd+//133nvvPXr37k2lSpXsy3Xu\n3Blvb2/q1KlDYGAge/bsYebMmeTNm9d+vUeAChUqUKFChRTrGhQURLt27e7odeY0dxwgg4ODKVKk\nCKtXr7YPMo2OjmbTpk1MnDjxluve7Qt96wLjuU9ajvmvfxpmLIF5q+ByZPLnK5SCfu2he2sXCvgV\nBAomW2bpF3NzxCQ3maVz58688cYbDBs2jEqVKtmu2VSgM2vPTeJqdB77cv8pB5+McKFymVJAqZtv\n8BZ0nudOOu65j4557uPsY37p0iWn7DcrsCzrpt9zMuL7T7Vq1fj22295+eWXCQsLw8fHh969e9sv\nD5LaPtu2bcuXX37JyJEjGThwIAULFuSVV15hxIgRDst16NCBTz/9lLfeeovLly9TqFAhOnXqxIgR\nIyhbtmy6X0duY5mE0a8piIyM5MCBAwDUq1ePl19+mYcffpgCBQpQsmRJJkyYwJgxY5g9ezbly5fn\njTfeYNOmTezbt4+8eR1bcpKefAkXEL1bnP0fj9x9NzvmUdcMC9fCzKWw5bfk67nngU6NbcGxYdWc\nMQOqMz3Z9zVWf7ePM2fOAG7gVR7yBAJglQrHsuD/noCRT4GHe/rea53nuZOOe+6jY577OPuYp+U7\nbHR0tC44LznKrf5N37IFcvv27TRt2hSwfZEeMWIEI0aMoGfPnnz00UcMHTqUqKgoBgwYwMWLF6ld\nuzarV69OFh5FnG3PX7aZVD9ZCRFXkj9fviT0bQc920BBf4XGjPL3aRfOBi7ACnQsN0fDCSoKc16F\nBlX1fouIiIhkF7cMkI0bN7aPYbqZhFApkhX06vcSh055cPXKVeKNRXTsck6cM1y+eg2rtGN3iDxu\n0KEh9HsEmlRXa2NGMsawYy8cOAakMNN14QKwew745tV7LiIiIpKdZMosrCLO0rZVY3q+YfGPV4i9\nzLishCSXgihTDPq2h15tITBAASYjHT1l+HS1raV37xEwZ8FKYUjjvaUUHkVERESyIwVIyVHcCoZw\n/VwYpkRLLMuyXeA2YhVuZSfzSEPb2MZmNcHFReElo1yJNCzeYAuN63fBzUdVi4iIiEh2pwApOcLf\npw2D3oYlGy1MvhCIWA0BIViXVtHl0VZMHm5RpEDGhMaeT4/g8Mnk5UFF4eMZIzNkH1ldXJxh7Q7b\nDLaLN8A/0cmXyecF3vnhzN2vnoiIiIhkEgVIydZiYw3vfQHDP4CrUf8W+ofgenQwcf4tebDYKj59\n+607Ht8YH284dwlOnIUT52y3DT/BkTzhyZY9cCyc12Ya/PKBXz7w9cZ+3y9v4t+8XqmPt8yqIfW3\nQ4a5K2D+att7cSMXF2heE55sBY80hAEvwOGT4cmWCyqa+XUVERERkYynACnZ1s69hqcnwK59juVF\nPXeRJ+Aixw8/y5WS12jSPjxZ8DLGcOFyYig8cQ5O3vD3xHnb/dg4x+2bkymP6ztxFkbPSb3erq7g\n623sgdI3Sbj0/ffvxt1w2C08hbVTKstcZy4aPltj66J643udoFIwdG8Nj7eE4oUSw3FuaZEVERER\nyS0UICXbuRJpeO0DeO8LSDpJcMUgyHPhI36+3Bvj8zGcD2OP6zSs8xYHj4Xz2KvGITDGXHdO/ePi\n4OIV2+1mzImUQ+oPv0D1noZShaFUEShVGEr/+7dUYSicP2PGd0ZfMyz/wRYaV2y11flGgQHQtYUt\nOFYtr1lsRURERHIDBUjJVpZ+b3h+MhxLMrDOwx1e6wlhXeDBVkcBW5gxQZPtoeb4Wfh8/Z3tM8AH\nihVMvK1dAsdSWK5scXjyKbh0FS5FwuWrifcvXYXL/9j+Rl27s3qArTV09wHbLSXueaBkoLEHy5KF\nHUNmycLg5WF7T1LqJnspEiKj4Wy+cC5dTb59D3doXx+ebA0tH4A8bgqNIiIiIrmJAqRkC4mT5DiW\nt6gFo/rZunze3x0OHExsuUutRcw3r2MwLJr0foHEsoTAlaDxNjh2Pvn2SgTCiN6pB6qY64bLkSmH\ny4SyGe/C8VS3lNK24c/jttvNBAbYAuZf2+C8b3iy583R8GStn/Xvt4XGR5uAv49Co4iIiEhupQAp\nWVpcnG2SnNdmJpkkB1v3yacfgT+PQcNnU++OWqY4jB7pGBDzet1ZELJNABN+k/LUueexKOgPBf1v\nvsy3i+F4CiG1TmV4exIcOQVHT/97S3L//KXU93/mou1mIsDyvflyZYrZQmO3llC2hEKjiIiIiChA\nSha2c6/hmQmw84aJW+pWgQuXYdTs5Ou4ukJ88mJKBkKX5hkTgu7GxDC3CqkPVLR4oGLK6139x/D3\nmZsHzGNnkk8KdKOiBWHRdNv7rHGNIiIiIpKUAqRkOTebJMc/H0TFwOZfk6/zQEVbi+TaL+HYmXCu\nXLHNUOPj4wNkv8tG3GlIzedtcV8Q3BeU8vNxcYaT521hss+zsDeFtH1PSah3v4KjiIiIiCSnAClZ\nSkqT5FgWGAMRN0zqktfLdtmIp9tD9Qq2wNOrrS147dixA4CaNWvelXpnF66uFiUCbeM1AwNgbwrd\nZEVEREQAPv74Y3r37g3Axo0bqV+/frJlypUrx6FDh2jUqBHr19/hjIWSbps3b2bNmjW88MIL+Pn5\nZeq+FCAlS7jZJDlgC49JVSkLz3SAJ1qCb161lN2p9I7lFBERkdzBy8uL+fPnJwuQW7du5dChQ3h6\nemrYi5Nt3ryZkSNH0qtXLwVIydluNknOjTzc4bGmtm6qdSprbF5GuBtjOUVERCT7a926NYsWLWLK\nlCm4uSXGh/nz53Pvvffi6urqxNqlX2RkJHnz5nV2NTKEubHlJRO4ZPoeRP5VvnII3iW6kqdwKG6B\noXgU74l70Cu8EPbyTcNj+ZIw8Xk4tgTmvGZRt4qVanhcunQpQ4YMYcCAAYwePZrr11OZovUOrFq1\nig4dOtC8eXNGjBhBdHR0hu9jw4YNhIaG0qxZM15++WUiIyMzfB8//vgjnTt3pmnTpoSFhXHpUhqm\ncRUREZFcpWvXrly4cIFVq1bZy+Li4li4cCFPPPFEsuWNMbz77rtUqVIFLy8vChcuTJ8+fTh/3nHs\nzLJly3j44YcpWbIknp6eBAUFMXToUK5dc7xo9unTp+nTp499uSJFitCmTRv27NljX8bFxYWRI5P/\nOB4UFESvXr3sjz/++GNcXFxYv349AwcOpHDhwvY5MwC2b99OmzZt8Pf3x9vbmwYNGvDdd985bDM8\nPBwXFxf27t1Lt27d8Pf3p1ChQvz3v/8F4O+//6Z9+/b4+flRpEgRJk6cmKxe165dY+TIkZQvXx5P\nT09KlChBWFgYUVGOX4pdXFzo378/S5YsoXLlynh6elK5cmWHYxEeHs7QoUMBCA4OxsXFBRcXFzZu\ntHXt27VrF23atCEwMBAvLy+CgoLo3r37HX9/VQuk3DWXo92J8u2BFRAC2GZLNRdXAo6B0M0VOjSy\ntTY2qX57rY2zZs2ib9++9sfbtm1jx44dLF68OMNaLRcsWECXLl3sj9euXcvmzZtZuXJlhv0C9/XX\nX9OuXTvi/51FaN26dWzcuJHvvvsOd3f3DNnHhg0baNGihT1gr1+/nnXr1rF582a8vb0zZB8iIiKS\nPjExMRn22X+nSpQoQYMGDZg/fz5t27YF4Ntvv+XMmTN07dqVzz77zGH5/v3789FHH9GzZ08GDhzI\n0aNHeffdd9m2bRvbt2/Hw8MDsIU5Ly8vBg0ahJ+fH1u2bOGtt97i77//dthmaGgov/32G88//zzB\nwcGcOXOGjRs3cuDAASpWTJyaPqXvepaVcuPD888/T/78+XnttdfsP6Bv2LCBkJAQqlevzogRI3Bz\nc+OTTz6hZcuWrFmzhkaNGjlso2vXrtx3332MHz+er7/+mrFjx+Ln58esWbNo3rw5EyZMYN68eQwd\nOpQaNWrQpEkTwBawO3TowMaNG+nXrx8VK1Zkz549TJs2jd9//90hHAJs2bKF5cuX8+yzz5IvXz6m\nTJlCp06dOHr0KPnz56dTp04cOHCAzz77jLfffpuCBQsCcN9993H27FlatGhBYGAgL730EgEBARw9\nepTly5fzzz//4OnpmbZ/BEmZuyQiIsJ+u9u2b99utm/fftf3K4mioqIMvo0MRQcZ6sQZq268oU6c\n7fGD0caqG29Kd4g3oz+ONyfPxd/RPuLi4oyfn58BzFNPPWVGjRplfHx8DGC+//77DHstJUqUMIAZ\nPHiwWbBggSlQoIABzNdff51h+6hYsaIBTL9+/cwXX3xhihUrZgDz2WefZdg+ateubQDTrVs3s2TJ\nElOmTBkDmPfffz/D9nE36TzPnXTccx8d89zH2cc8Ld9ho6KiMny/ixYtsn/nKF68uFm4cGGG7yM1\ns2fPNpZlmR9//NHMmDHD5M2b1/zzzz/GGGOefPJJU6dOHWOMMZUqVTJNmjQxxhjzww8/GMuyzLx5\n8xy2tWnTJmNZlpk5c6a9LGFbSY0ZM8a4uLiYv//+2xhjzMWLF41lWWbSpEm3rKtlWWbkyJHJNvQk\nyQAAHcxJREFUyoOCgkyvXr2SvabatWubuLg4e3l8fLypUKGCadGihcP6MTExplKlSqZu3br2shEj\nRhjLskyfPn3sZXFxcaZkyZLGsiwzZswYe3lERITx9vY23bp1s5d9+umnxsXFxWzcuNFhX59++qmx\nLMusXr3a4XV5eHiYP//80172yy+/GMuyzHvvvWcve/PNN41lWebIkSMO21yyZImxLMvs3LkzhXft\n5m71b1pdWOWuOHPmDPg0AP8QiFhtK4xYBf6t8I6Ywldvwp+LYFgPiyIF7qyl8PLly1y6dAl3d3ee\nfvppWrVqRfPmzQE4fPhwhryOuLg4jh07BsD48eN57LHHeOihhzJ0HwBHjhwB4I033qBjx4506tQp\n0/YxYsQI2rdvz+OPP+5QLiIiIs7x3Xff8dhjj9m/cxw/fpzOnTs7dZbTRx99lOvXr7NkyRKioqJY\nsmRJit1XFy5cSL58+WjZsiXnzp2z3ypUqEBgYKDDa/Dy8gIgPj6eS5cuce7cOerVq4cxhp9++sm+\njLu7O+vXr+fixYsZ9nr69u2Li0tiFPr555/Zv38/Xbt2daj3pUuXaN68OT/++GOyLp99+vSx33dx\ncaFGjRpYlsVTTz1lL/fz86NChQr89ddfDu/RPffcQ8WKFR321bBhQyzLSnacmzRpQpkyZeyPq1Sp\ngq+vr8M2b8bf3x+A5cuXExsbm8Z359YUIOWuGL+wGJQa/m+AXGkb4BuxCvxbUrHEGdrUtXB1TV8X\nUz8/PwoWLEhMTAxvvvkmCxcuZOXKlYBtiumM4OrqSnBwMABPP/0077//Pl9++WWG7iPptp5//nlm\nzZpl78aRGfsYMmQIs2fP5qOPPsrwfYiIiMjt++CDDzDGMGDAAGJjY3nuuecwxjBz5kyn1SkgIICQ\nkBDmzZvHsmXLiIqKonPnzsmW279/P1evXqVw4cIEBgY63M6cOcPZs2fty/7222+0adMGHx8fAgIC\nCAwMpHHjxgD2bqUeHh6MHz+elStXUrhwYRo0aMDYsWPt4fpOlS1bNlm9AZ566qlk9Z4yZQrGmGRj\nOEuVKuXw2M/Pjzx58hAYGOhQ7uvr6xB+9+/fz759+yhUqJDDfhK2l/Q9Smk/YDseaQnUjRo1IjQ0\nlJEjR1KgQAHatWvHrFmz+Oeff1Jd92Y0BlIy3SMvGZZtciWh+7nxD4HDYeDfCsuyyJtB4+0sy+K9\n996ja9euLFq0yF7eo0cPHnzwwQzZB8C7775L+/btmT17NrNnzwagY8eO9tbOjPD2228TEhLCggUL\nWLBgAQAtW7akQ4cOGbaPSZMm0bhxY5YtW8ayZcsAqFu3Lt26dcuwfYiIiMjtu3LlCmC7nrWrq6v9\nutZXr1691WqZ7vHHH6d79+5cvnyZFi1a2MfaJRUfH0+BAgXs319uFBAQANgCYpMmTfDx8WHMmDGU\nK1cOLy8vjh07Rs+ePe3zQAAMGjSI9u3bs3TpUtasWcOoUaMYM2YMX331VbJxiTe6WatbQutn0nqD\nrYdZjRo1Ulznxteb0twXN5tzwySZHTU+Pp5KlSrxzjvvpLhssWLFUt3Pjdu8lYULF7J9+3a++uor\n1qxZQ79+/Rg7dixbt26lUKFCadpGUgqQkmliYw11noade5MUXj+Df+wKoqI2ULr4PxQtsCVDrzvY\nuXNn+2xX0dHRdOzYkaeffjpDL/vRtm1bNm3axKxZs7h8+TL16tVjwIABDt0g0qtx48Zs3bqV999/\nnwsXLvDAAw8waNCgDJ0mu1atWmzbto2pU6dy5swZqlWrRlhYmNMH6ouIiOR29evXZ/ny5bzwwgus\nXbuW5cuXA1CvXj2n1qt9+/Z4eHiwefNm5syZk+IyZcuW5dtvv+XBBx+85aUx1q9fz/nz51m8eDEN\nGjSwl69ZsybF5YOCghg0aBCDBg3i+PHjVK1aldGjR9sDZEBAABEREQ7rxMTEcPLkyTS9toQWyXz5\n8tG0adM0rXOnypUrx86dOzN0P6l9161Vqxa1atVi5MiRrFy5kjZt2vDBBx8wbNiw296XAqRkiqv/\nGKo8CUdOJZb5eMOujwMpW9zWDSCzruXYqFEj+39YCb/YZbTatWtTu3btTNl2gmrVqjFjxoxM3Uel\nSpWYNm1apu5DREREbs/gwYPZvHkzS5cuZd68eQA8/PDDDBkyxKn18vLyYvr06Rw6dIhHHnkkxWW6\ndOnC9OnTef311xk/frzDc3FxcVy5cgV/f3/7j+JJWxrj4+OZPHmywzoJl7VI2mJYvHhxChUq5HD5\nsbJly7JhwwaHdWfOnOmw/VupWbMm5cqVY/LkyTz55JPky5fP4fmzZ8+mqbUuLd9vO3fuzDfffMP0\n6dPp37+/w3PXrl3j+vXryfafmoTvvhcuXHDo8hoREYGfn59DvapVqwZwx5dvU4CUDHfsjKFqd7hw\nJbGsaAH4dR7k97X9482s8CgiIiKS3eXJk4fFixezdu1aDh06RJkyZWjWrFmG9na6Uzcb6pLQnbJB\ngwYMGDCAN998k19++YWWLVvi4eHBwYMH+eKLLxg1ahTdu3enfv36FChQgB49evD888/j5ubG559/\nnuy61/v27aNp06Y89thjVKxYEQ8PD7755hv27t3LpEmT7Mv16dOHZ555htDQUJo3b87PP//M6tWr\nKViwYJq6elqWxYcffkirVq2oWLEivXv3pnjx4pw4ccIeTNetW5fqdm62r6Tl3bp14/PPP2fAgAFs\n2LDBPnHQvn37WLRoEZ9//jkNGza8rf3UqlULgFdeeYWuXbvi7u5Os2bN+PTTT5k6dSodO3akTJky\nREVFMXv2bNzc3AgNDU319aREAVIy1C8HDXX6QVSS679WDIZdH4G7u0KjiIiISFq4uLjQokULZ1cj\nTT/633itxXfffZfq1avz/vvv8+qrr+Lm5kbp0qXp3LmzvdtmQEAAX3/9NUOGDGHEiBH4+PjQqVMn\nnnnmGe6//377tkqVKkW3bt1Yu3Yt8+fPx7IsKlSoYL/OZIK+ffvy119/8eGHH7Jy5UoaNmzImjVr\naNasWbLXcLPX1KBBA7Zu3cqoUaOYNm0aly9fpmjRotSqVcthxtWbXVsyreWWZbF48WLefvtt5syZ\nw9KlS/Hy8qJs2bIMGDCAKlWqpPKOJ38NNWrUYOzYsUybNo3evXtjjGH9+vU0btyYHTt2sHDhQk6d\nOoWvry/Vq1dn6tSp9tB5uyyT1tGX6ZS0idTPz+9u7NJux44dQOZ1ZxSbVT8aHv4/iI1LLGtWE1a9\nBS4udzc86pjnPjrmuZOOe+6jY577OPuYp+U7bHR09J1dkF0ki7rVv2nnt4NLjvDRckObIY7hsXtr\nWPOOddfDo4iIiIiIZA4FSEm3ER8Y+oyDpG3Zw3vDx68qOIqIiIiI5CQaAynp0vMNw9wViY8tCz54\nCXo/rPAoIiIiIpLTKEDKHYmPN7R4AdbvTCxzc4Xlb0LIgwqPIiIiIiI5kQKk3LaYGEP1XrDncGKZ\nlwdsngH/Ka/wKCIiIiKSUylAym25cNlQpRucPJ9Ylt8Hds+FEoEKjyIiIiIiOZkm0ZE0+/O4IbiT\nY3gsXQQOL1Z4FBERERHJDRQgJU22/Gqo9ARc+SexrMa9cGAB5PNWeBQREZHc7S5dWl0k06X2b1kB\nUlK1+DtDg2ch5npiWbv6sP1DCzc3hUcRERHJ3dzd3YmOjlaIlGzPGEN0dDTu7u43XSbdYyBjY2MZ\nPnw4//vf/zh58iRFixbliSeeIDw8HFdX1/RuXpzs7QWGsCmOZc+FwpTBCo4iIiIiAC4uLnh4eHDt\n2jVnV0Uk3Tw8PHBxuXk7Y7oD5JgxY5gxYwZz586lSpUq/Pzzz/Ts2RMPDw9effXV9G5enChsiuHt\nBY5lbz4HQ7oqPIqIiIgk5eLigqenp7OrIZLp0h0gt2/fTrt27Wjbti0ApUqV4qGHHmLbtm3prpzc\nXVeuXGHz5s3Ex8czfV1Tvtqc2HTtYsH8cHisucKjiIiIiEhule4A2bp1a8aPH8++ffuoUKECe/bs\nYf369QwbNiwj6id3SanyjTl20R8TD3iUBLetgAFzDY+y4/h2CtT/j8KjiIiIiEhulu4A+eyzz3Ls\n2DHuu+8+3NzciI2N5dVXX+WZZ57JiPrJXRAbG8vJ89cxRZ7BCgixl5uLK7HizvPzXKhQWuFRRERE\nRCS3s0w6p4uaMmUKY8eO5Z133qFSpUr89NNPDBo0iDfffJPevXvbl7t06ZL9/oEDB9KzS8lghw8f\n5tE+s8G7PARNxrIs2yxih8MILnqdhTN6ObuKIiIiIk5Rvnx5+30/Pz8n1kQka0h3C+To0aN59dVX\neeyxxwCoVKkSR44cYezYsQ4BUrKuExH5odx0+Od3iFgNASEQsQr8W+HutsTZ1RMRERERkSwi3QHS\nGJNsmlcXF5dbXgenZs2a6d3tbdmxY4dT9psdrNlmeHEuWB5g3EvA4TCMf0tbgAyaTOECm7Pl+6Zj\nnvvomOdOOu65j4557uPsY560F52IZECAfOSRRxg3bhzBwcFUrFiRn376ibfeeosePXpkRP0kE835\nxtB7DCRkfcuyMP4hcDgM/FthWRaWpbGPIiIiIiJik+4A+dZbb+Hr68uAAQM4ffo0RYsWpV+/fgwf\nPjwj6ieZZNRHhhEfJikw1ynp+jnFS/3Gn5E7ubesL5a1haCiTquiiIiIiIhkMekOkHnz5mXixIlM\nnDgxI+ojd0GfsYaPvkp8bFkw7f/y8PQjjwO2bslqeRQRERERkRulO0BK9hEfb2gVBt9uTyxzdYGl\n46FN3cTAqPAoIiIiIiIpUYDMJWJiDDWegt8PJZZ5usOm96F6BQVGERERERFJnQJkLhBxxVC5G5w4\nl1jmnw92z4VShRUeRUREREQkbVxSX0Sys7+OG4I6OYbHkoFw+AuFRxERERERuT0KkDnYj78bKj4B\nlyMTy6qWhz8XgW8+hUcREREREbk9CpA51NKNhvrPwLXriWVt68KOj8DNTeFRRERERERunwJkDvTe\n54aOr0BcfGLZMx1g+ZsWLi4KjyIiIiIicmc0iU4OM3SqYeJ8x7Ixz8DLTyo4ioiIiIhI+ihA5iCd\nXzMsWpf42MWCucPh8ZYKjyIiIiIikn4KkDlAfLyh4bOw+dfEsjxusOotaFxd4VFERERERDKGAmQ2\n90+0oWp3OHg8sSyvJ2z7EO4LUngUEREREZGMowCZjZ06b/hPdzgbkVhWyB9+/QQC8ys8ioiIiIhI\nxtIsrNnUH4cN5R9zDI/lSsBfXyg8ioiIiIhI5lCAzIa+22Wo2gMioxPL6laBvZ+Bt6fCo4iIiIiI\nZA51Yc0GylZqybEL/ly/HotxyQvupcFyAXMNq/Q4OjeHz0YqOIqIiIiISOZSgMwGzl6MJyagN1ZA\nCAkx0VxcCcQz9AkY96zCo4iIiIiIZD51Yc3iDh48yJWr1yFiJcYYANvfiFUEBfyt8CgiIiIiIneN\nAmQWd+rUGSjyDPiHQMRqW2HEKvBvRQGPA86tnIiIiIiI5CoKkFlYbKyh//u1sAp1+TdArrS3PuLf\nEi8vL2dXUUREREREchGNgcyiIq4Y7u8Ox87YDpFlWRj/EDgcBv6tsCwLV1dXJ9dSRERERERyEwXI\nLOjISUPVnnDpamKZ27VfCbQ+JyJmN/cEuuDru4Wgok6rooiIiIiI5EIKkFnMjr2Ghv0hOiax7P5y\nsO2DKri7f4gxBsvSxDkiIiIiInL3aQxkFvLVD4Y6fR3DY6vasGs2uLvbQqPCo4iIiIiIOIsCZBYx\nY4mh/VCIi08s69cevplk4eKi0CgiIiIiIs6nLqxZwLD3DeM+cSx7ox8M66HgKCIiIiIiWYcCpJN1\nCzfMX5P42LJg9n+he2uFRxERERERyVoUIJ0kPt7Q+DnY9HNimZsrrJwMTWsqPIqIiIiISNajAOkE\n0dG2y3Ts/zuxzNsTfpwFlYIVHkVEREREJGtSgLzLzlww3N8dzlxMLCvoB798AkUKKDyKiIiIiEjW\npVlY76J9RwxlH3MMj2WLw+HFCo8iIiIiIpL1KUDeJRt/srU8RkYlltWtAvv+B96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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = [5,6,7,8,9,9,9,9,9,10,11,12,13,14,\n", + " 15,16,16,16,16,16,16,16,16,16,16,16]\n", + "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.302, h=.054)\n", + "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.546, h=.205)\n", + "\n", + "with book_format.figsize(y=5):\n", + " book_plots.plot_measurements(zs)\n", + " book_plots.plot_filter(data2, label='g=0.546\\nh=0.205', marker='s')\n", + " book_plots.plot_filter(data1, label='g=0.302\\nh=0.054', marker='v')\n", + " book_plots.show_legend()" + ] + }, + { + "cell_type": "markdown", + "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 we favor the measurement of $\\dot{x}$ vs our prediction. But what does this *mean*? If our signal is changing a lot (quickly relative to the time step of our filter), then a large $h$ will cause us to react to those transient changes rapidly. A smaller $h$ will cause us to react more slowly.\n", + "\n", + "We will look at three examples. We have a noiseless measurement that slowly goes from 0 to 1 in 50 steps. Our first filter uses a nearly correct initial value for $\\dot{x}$ and a small $h$. You can see from the output that the filter output is very close to the signal. The second filter uses the very incorrect guess of $\\dot{x}=2$. Here we see the filter 'ringing' until it settles down and finds the signal. The third filter uses the same conditions but it now sets $h=0.5$. If you look at the amplitude of the ringing you can see that it is much smaller than in the second chart, but the frequency is greater. It also settles down a bit quicker than the second filter, though not by much." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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q4eHhNG/e3GZOYWxsLM888wzt2rVj/PjxALz22mts3LiRIUOGsGPHDutCNAWZ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Sy+KgMOZEF09XcZL9U4ChKvzmDvukcoMOl0jF7GR6tm1Gh9r4rpiIiIiFRPYdLLNYu1aN/SsPcg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\nwqSIiIiIiIi47P8BEUq0DCZAghwAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = np.linspace(0, 1, 50)\n", + "\n", + "data1 = g_h_filter(data=zs, x0=0, dx=0., dt=1., g=.2, h=0.05)\n", + "data2 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.05)\n", + "data3 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.5)\n", + "\n", + "with book_format.figsize(y=5):\n", + " book_plots.plot_measurements(zs)\n", + " book_plots.plot_filter(data1, label='dx=0, h=0.05')\n", + " book_plots.plot_filter(data2, label='dx=2, h=0.05', marker='v')\n", + " book_plots.plot_filter(data3, label='dx=2, h=0.5', marker='s')\n", + " book_plots.show_legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interactive Example\n", + "\n", + "For those of you running this in IPython Notebook I've written an interactive version of the filter so you can see the effect of changing $\\dot{x}$, $g$ and $h$ in real time. As you adjust the sliders for $\\dot{x}$, $g$ and $h$ the date will be refiltered and the results plotted for you.\n", + "\n", + "If you really want to test yourself, read the next paragraph and try to predict the results before you move the sliders. \n", + "\n", + "Some things to try include setting $g$ and $h$ to their minimum values. See how perfectly the filter tracks the data! This is only because we are perfectly predicting the weight gain. Adjust $\\dot{x}$ to larger or smaller than 5. The filter should diverge from the data and never reacquire it. Start adding back either $g$ or $h$ and see how the filter snaps back to the data. See what the difference in the line is when you add only $g$ vs only $h$. Can you explain the reason for the difference? Then try setting $g$ greater than 1. Can you explain the results? Put $g$ back to a reasonable value (such as 0.1), and then make $h$ very large. Can you explain these results? Finally, set both $g$ and $h$ to their largest values. \n", + " \n", + "If you want to explore with this more, change the value of the array `zs` to the values used in any of the charts above and rerun the cell to see the result." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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cHK655hp2795NTEyMp/0DDzzA/v37+fjjj8nMzOTee++l+LRL+wcMGMDFF1/M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\nvDyjkkyPHmBMfod57mvRwgj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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "None" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from IPython.html.widgets import interact, FloatSlider\n", + "\n", + "zs = gen_data(x0=5, dx=5, count=100, noise_factor=50)\n", + "\n", + "def interactive_gh(x, dx, g, h):\n", + " data = g_h_filter(data=zs, x0=x, dx=dx, g=g, h=h)\n", + " plt.scatter(range(len(zs)), zs, edgecolor='k', facecolor='none',\n", + " marker='+', lw=1)\n", + " plt.plot(data, color='b')\n", + " plt.show()\n", + "\n", + "interact (interactive_gh, \n", + " x=FloatSlider(value=0., min=-50, max=50.), \n", + " dx=FloatSlider(value=5., min=-50., max=50.), \n", + " g=FloatSlider(value=0.1, min=0.01, max=2, step=.02), \n", + " h=FloatSlider(value=0.02, min=0.0, max=0.5, step=0.01));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Don't Lie to the Filter\n", + "\n", + "You are free to set $g$ and $h$ to any value. Here is a filter that performs perfectly despite extreme noise." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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w9fWVK2dFV7t2bejr6yMsLAxDhw6FtrY2bt26BQ0NDTRo0EDZ4SlEXFwcvv/+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\nAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_data(x0=5, dx=.2, count=100, noise_factor=100)\n", + "data = g_h_filter(data=zs, x0=5, dx=.2, dt=1., g=0, h=0)\n", + "with book_format.figsize(y=2.):\n", + " book_plots.plot_measurements(zs)\n", + " book_plots.plot_filter(data, label='filter', lw=2)\n", + " book_plots.show_legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I brilliantly extracted a straight line out of very noisy data! Maybe I shouldn't try to collect my Fields Medal in mathematics just yet. I did this by setting both $g$ and $h$ to 0. What does this do? It makes the filter ignore the measurements, and so for each update it computes the new position as $x + \\Delta x \\Delta t$. Of course the result is a straight line if we ignore the measurements. \n", + "\n", + "A filter that ignores measurements is useless. I know you would never set both $g$ and $h$ to zero as that takes a special kind of genius that only I possess, but I promise that if you are not careful you will set them lower than they should be. You can always make great looking results from test data. When you try your filter on different data you will be disappointed in the results because you finely tuned the constants for a specific data set. $g$ and $h$ must reflect the real world behavior of the system you are filtering, not the behavior of one specific data set. In later chapters we will learn a lot about how to do that. For now I can only say be careful, or you will be getting perfect results with your test data, but results like this once you switch to real data:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ZTBw5cgSAEiVK4OjoSI8ePfIdp169egD873//IyEhwdxfNSAggJMnT1KpUiXC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\nUylXrhy5cuVi6tSp3Lp1i+7du9OmTRtmzJhhcL5/jpS+7W+Z0qd0VKp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_data(x0=5, dx=-2, count=100, noise_factor=5)\n", + "data = g_h_filter(data=zs, x0=5, dx=2., dt=1., g=.005, h=0.001)\n", + "with book_format.figsize(y=2.):\n", + " book_plots.plot_measurements(zs)\n", + " book_plots.plot_filter(data, label='filter', lw=2)\n", + " book_plots.show_legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Tracking a Train" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are ready for a practical example. Earlier in the chapter we talked about tracking a train. Trains are heavy and slow, thus they cannot change speed quickly. They are on a track, so they cannot change direction except by slowing to a stop and then reversing course. Hence, we can conclude that if we already know the train's approximate position and velocity then we can predict its position in the near future with a great deal of accuracy. A train cannot change its velocity much in a second or two. \n", + "\n", + "So let's write a filter for a train. Its position is expressed as its position on the track in relation to some fixed point which we say is 0 km. I.e., a position of 1 means that the train is 1 km away from the fixed point. Velocity is expressed as meters per second. We perform measurement of position once per second, and the error is $\\pm$ 500 meters. How should we implement our filter?\n", + "\n", + "First, let's simulate the situation without a filter. We will assume that the train is currently at kilometer 23, and moving at 15 m/s. We can code this as \n", + "\n", + "```python\n", + "pos = 23*1000\n", + "vel = 15\n", + "```\n", + "\n", + "Now we can compute the position of the train at some future time, *assuming* no change in velocity, with\n", + "\n", + "```python\n", + "def compute_new_position(pos, vel, dt=1):\n", + " return pos + (vel * dt)\n", + "```\n", + "\n", + "We can simulate the measurement by adding in some random noise to the position. Here our error is 500m, so the code might look like:\n", + "\n", + "```python\n", + "def measure_position(pos):\n", + " return pos + random.randn()*500\n", + "```\n", + " \n", + "Let's put that in a cell and plot the results of 100 seconds of simulation. I will use NumPy's `asarray` function to convert the data into an NumPy array. This will allow me to divide all of the elements of the array at once by using the '/' operator." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Ozl7UGDvNgFyZ0HCtRY2DPVKPBq1GhwmGAu5+fUq6dHtA4e8DW7qUqktHacF0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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy.random import randn\n", + "\n", + "def compute_new_position(pos, vel, dt=1):\n", + " \"\"\" dt is the time delta in seconds.\"\"\"\n", + " return pos + (vel * dt)\n", + "\n", + "def measure_position(pos):\n", + " return pos + randn()*500\n", + "\n", + "def gen_train_data(pos, vel, count):\n", + " zs = []\n", + " for t in range(count):\n", + " pos = compute_new_position(pos, vel)\n", + " zs.append(measure_position(pos))\n", + " return np.asarray(zs)\n", + " \n", + "pos, vel = 23*1000, 15\n", + "zs = gen_train_data(pos, vel, 100)\n", + "\n", + "plt.plot(zs / 1000.) # convert to km\n", + "book_plots.set_labels('Train Position', 'time(sec)', 'km')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see from the chart how poor the measurements are. No real train could ever move like that. \n", + "\n", + "So what should we set $g$ and $h$ to if we want to filter this data? We have not developed the theory for this, but let's try to get a reasonable answer by the seat of our pants. We know that the measurements are very inaccurate, so we don't want to give them much weight at all. To do this we need to choose a very small $g$. We also know that trains can not accelerate or decelerate quickly, so we also want a very small $h$. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ERCQP1OIpIiKFTvv27VmzZg1ff/01ly9f5v7776dfv36YTCZHhyYiIiJ5oMRTREQKpYYN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\n/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data(pos, 15, 100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.0001)\n", + "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.0001')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is pretty good for an initial guess. Lets make $g$ larger to see the effect." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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YyPIeeUDSDJSBgYEULVqUPXv2AFC5cmVThiVymb3HFcOnw97jhu15/we/T1K8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\nZf8faM0psw+kwFIAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data(pos, 15, 100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.2, h=0.0001)\n", + "plot_g_h_results(zs/1000, data/1000, 'g=0.2, h=0.0001')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We made `g=0.2` and we can see that while the train's position is smoothed, the estimated position (and hence velocity) fluctuates a lot in a very tiny frame, far more than a real train can do. So empirically we know that we want `g<<0.2`.\n", + "\n", + "Now let's see the effect of a poor choice for $h$." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Nk3V7OwGKFy+Ov78/xXOHoaq6NTE1jnXo1G2ImSMTQmQnMrmQEEJkM1qtljZt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\nRKRX/wczC32YVeCI3QAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data(pos, 15, 100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=0.01, h=0.1)\n", + "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the position changes smoothly thanks to the small $g$, but the large $h$ makes the filter very reactive to the measurements. This happens because in the course of a few seconds the rapidly changing measurement implies a very large velocity change, and a large $h$ tells the filter to react to those changes quickly. Trains cannot change velocity quickly, so the filter is not doing a good job of filtering the data - the filter is changing velocity faster than a train can.\n", + "\n", + "Finally, let's add some acceleration to the train. I don't know how fast a train can actually accelerate, but let's say it is accelerating at 0.2 m/sec^2. " + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def gen_train_data_with_acc(pos, vel, count):\n", + " zs = []\n", + " for t in range(count):\n", + " pos = compute_new_position(pos, vel)\n", + " vel += 0.2\n", + " zs.append(measure_position(pos))\n", + " return np.asarray(zs) " + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XOKZNm8bXX3+tbTcuLo7evXsTFRWFvb19ucQghBDlRXo8hRBCCPHUyM3Nxd/f\nn1mzZvHHH3+wfv16fH192bRpU7nHsmLFCgD27NnDzZs3ad++PVevXmXLli3lHosQQpQ1STyFEEII\n8dTYunUru3fvxsbGhp9//pk33niD/Px8Jk+eXO6xZGZmAtC4cWNMTEyoX78+AHfv3i33WIQQoqxJ\n4imEEEKIp0ZycjIAAwcOZPjw4cyfP19bXt6T+3Tv3h2ATp060bNnT9atW4dGo6FLly7lGocQQpQH\nGeMphBBCiKdGo0aNAPjll1/o0KEDe/fu1ZYrilKusfz3v/+lV69eREVFce7cOQwNDVmyZAmenp7l\nGocQQpQHSTyFEEII8dTo06cPffv2Zdu2bYwePRoAQ0NDFi5cWO6xODo6EhERQUhICOnp6bRu3Vqb\nGD/NVFUlOTmZzMxMGjVqhLGxsb5DEkKUArnUVgghhBBPDQMDAzZt2sS8efMYNGgQI0eOZO/evfTp\n00cv8ZiYmNCrVy+GDh361CSdqqqyfPlyPD09qVevHgEBAVy4cAGAq1ev0q1bNxo2bIiHhweNGzfm\n8OHDeo5YCFEapMdTCCGEEE8VIyMjpkyZou8wnlpLly4lMDBQez8lJYUTJ04QERHBiBEjCA0Nxdzc\nHAsLC86dO4e/vz+xsbFYW1vrMWohxJOSHk8hhBBCiKecqqps376dTz75hOXLl5Oenl5mbc2dOxeA\nzz77jOPHj+Pq6kp8fDxr165l+/btKIpCbGws586do3nz5ly5coW//vqrzOIRQpSPIhPPOXPm0LZt\nW6ysrLCzs2PAgAFER0frbDNy5Eg0Go3OrWPHjo9sODQ0lNatW2NmZkajRo349ttvn+xIhBBCCPHU\nuXbtGps2bWLTpk1cu3ZN3+FUSqqqMmbMGPr27cu///1vxowZQ6tWrUhJSSmT9lJTUwEYMWIEnp6e\n2ll8L1++DIBGo8HExAQDAwPt+M7ynnFYCFH6ikw8Q0NDGTduHPv372fPnj0YGhri5+fHjRs3tNso\nikKPHj24dOmS9rZt27YiG01KSqJv3774+Phw7Ngxpk2bxvjx49m4cWPpHJUQQgghqrx9+/bh6urK\noEGDGDRoEG5ubuzfv1/fYVU6v/76K9999x3VqlVj3LhxeHh4cPr0aSZMmPBE9SYnJzNlyhRGjBjB\n/PnzteuWtmjRAoDnnnuOKVOmEBQUBED79u3p2rUreXl5NGnSBHd3dyIiIqhRowadOnV6soMEsrOz\nyc/Pf+KEUKodAAAgAElEQVR6hBCPp8gxnjt27NC5HxQUhJWVFeHh4fTr1w8o+AbK2NgYOzu7Yjf6\nzTffULduXb788ksA3NzcOHjwIJ999hnPPfdcSY9BCCGEEE+Zu3fvMnjwYK5fv07Lli0BOHr0KM89\n9xxJSUmYmprqOcLKIyIiAoDx48czd+5coqKi8PT0fKJJfWJiYujUqZNOZ8Vvv/3G7t27WbZsGd26\ndSMsLIywsDAAAgMD8fX1pUmTJvTv35+///6ba9euUatWLX755RdsbW0fO5a4uDhefvllDh8+jKmp\nKWPHjmXevHkYGRk9dp1CiJIr0eRCN2/eJD8/X2dwt6IohIWFYW9vT40aNejSpQuzZ88u8g1i//79\n9OzZU6esZ8+erFy5kry8PAwMDEp4GEIIIYQoL6qqEhISQkJCAg0aNMDPz6/c/3fHxMRw+fJlGjRo\nwOHDh1FVlYYNG3Lu3DliY2O1vWri0Qo/1+3du5eUlBQ2b94MQM2aNR+7zsmTJ3Pjxg26detGQEAA\nn3zyCfv27eP7779n7NixREZGsnr1atLT0/H29qZ///5AwRIzhw4d4vjx42RmZuLp6YmFhcVjx5GW\nloafn5/2suHMzEwWLlyIRqPh888/f+x6hRAlV6LEc8KECbRs2ZIOHTpoy3r37s3gwYNxdnYmKSmJ\nDz74gO7du3PkyJGHrrt0+fJl7O3tdcrs7e3Jzc3l6tWr9z0G//s2ToiHkXNEFIecJ6I45Dx5uLy8\nPD788EN27typLWvfvj2fffYZJiYm5RbH6dOnAbh+/bo2luvXrwOQmJhIbm5umcdQVc4TT09PrK2t\nCQ8Pp169etrygQMHPvYxHj9+HIAxY8bg4uLCgAEDWLp0KaGhobRp0waAbt26abc/cuTIfXUYGRkR\nGxv7WO0X+uOPP0hJSaFRo0YsX76cmJgY3nzzTZYuXcrw4cNRFOWJ6n8YFxeXMqlXiMqs2LPavv32\n24SHh/PLL7/o/JEOGzYMf39/mjZtir+/P9u3bycuLo6tW7eWScBCCCGE0J9ffvmFnTt3Uq1aNXr3\n7o2VlRUHDhzghx9+KNc4nJycaNasGbdu3aJfv3707duX27dv4+npSYMGDco1lsrOxsaGb7/9lpYt\nW2Jubk69evX48MMP8ff3f+w6CzsRVq1axcGDB/njjz90ysvLnTt3AKhXrx4WFha4uroCkJWVRV5e\nXrnGIsTTrlg9npMmTWLdunUEBwfj5ORU5LYODg7UrVuXxMTEh25Tu3ZtLl26pFN2+fJlDA0NsbGx\neeA+hd+OCfFPhd/GyjkiiiLniSgOOU8e7bPPPgNg3rx5BAYGsn79eoYOHcrp06fL/XnbtWsXL730\nErt27QKgR48eBAUFlXlyUxXPkzZt2jBkyJBSq++LL77A19eXbdu2aSedbNSoETNnzqRGjRql1s6j\nmJmZMXfuXEJCQvjoo4+Ij48HoGPHjrRv377M2i3L5WiEqKwemXhOmDCB9evXExwcrP2WqCipqamc\nP38eBweHh27ToUMHfv31V52ynTt30rZtWxnfKYQQQlRghePt/v77b/Ly8rRJ2JOMw3tc9vb27Ny5\nk4yMDL3FIB6sc+fOhIaG8umnn3L58mU8PT2ZPXt2uSadAE2bNmXx4sWMGzdOO3bV2dm53HvohRCg\nqEUsjBQYGMiqVavYtGkTTZo00ZZbWlpibm7O7du3mTFjBgEBAdSuXZvk5GSmTZvG+fPniYmJwdzc\nHChYp0lRFFauXAkUTK/drFkzxowZw2uvvca+ffsIDAxkzZo1DBo0SNvOvd8WWVlZlfrBi6qhKn7z\nLEqfnCeiOOQ8ebQDBw7g4+Nz32WKW7Zs0c54X9XJeVL5xMTEcODAASwtLenVqxeWlpZl2p58hhXi\nfkX2eC5duhRFUfD19dUpnzlzJtOnT8fAwICoqCiCgoJIS0vDwcGB7t27s2HDBm3SCXDu3DmdcaFO\nTk5s27aNSZMmsXTpUurUqcOiRYt0kk4hhBBCVDzt27fn119/Zdy4cZw9e5batWszf/78pybpFJVT\nkyZNdDpRhBDlr8jE81GL7Jqamt631ueDBAcH31fWuXPnB85gJoQQQjwJVVW5fv06Go1GZ/kvUXr6\n9+9P//79yc7OfugM9kIIIcS9ij2rrRBCCFHRnTt3Dh8fH2xsbKhZsyZ+fn5cuXJF32FVWZJ0isjI\nSAYOHEjLli0ZMmQICQkJ+g5JCFFBlWgdTyGEEKKiys3Nxd/fn+PHj2NsbEx+fj67d+9m8ODB/PXX\nX2W2Xp8QT6sTJ07QsWNH7ZIlx44dY8+ePRw5cuSRqyBUdvn5+fz1118kJSXRuHFjfHx85D1GiEeQ\nHk8hhBBVwvHjxzl+/Di2trZcvHiRs2fPYmFhQVhYGElJSWXSZkxMDIMGDcLT0xN/f3+OHj1aJu0U\nR15eHgkJCSQmJj5yqIwQpWHu3LncuXOH/v37ExYWRteuXbl+/ToLFy7Ud2hlKicnh0GDBtGtWzdG\njRpF586defHFF2VdUCEeQRJPIYQQVUJWVhYA1atXx8rKilq1alGtWjWdx0rTqVOn6NChA5s2bSIq\nKoqtW7fi4+PDiRMnSr2tR0lISKB58+a4urri4uJC69atSU5OLvc4KpL09HRGjx5NgwYNcHV1Zfbs\n2ZIYlLLz588D8Prrr9OpUydGjhypU15VzZ8/n82bN2NlZcXQoUMxNzfn559/5uuvv9Z3aEJUaJJ4\nCiGEqBKaN2+Ora0tp06donXr1rRo0YIrV67QoEEDGjduXOrtLViwgPT0dPz8/Dh48CADBgzgzp07\nzJs3r9TbKkpOTg79+/fn5MmTWFtbU6NGDY4dO8bAgQOf2p7PvLw8/P39WbFiBWfPniUhIYEPPviA\nqVOn6ju0KqVwltj333+fRYsW8fHHHwPg7u6uz7DKXGhoKABff/01a9eu5bPPPtMpF0I8mCSeQggh\nKiVVVbl3KWpzc3M2btxIrVq1iIyMJCYmBgcHBzZu3IiRkVGpt1/Yq/PKK6/g7e3N6NGjAbhw4UKp\nt1WUEydOEBcXR+3atTl79ixJSUlYW1sTGRlJfHx8ucZSUYSHhxMWFkatWrU4ePAg69evB2DhwoVk\nZmbqObqqY+bMmTg5OXH8+HHeeustEhMTadasGVOmTNF3aGWqcMnAv4/FcidT1V7lYGFhoc+whKjw\nZHIhIYQQlcrdu3eZNGkSq1evJicnh969e7Ns2TJsbW3x8fEhPj6eAwcOoCgKnTp1onr16mUSR9Om\nTdm0aROzZs0iNTWV7777DgAPD48yae9hCns1DQ0NMTIyQqPRYGhY8O/93sT8aZKamgpAy5Yt8fb2\npnXr1lhYWJCRkUF6ejqmpqZ6jrBqsLe3JyIigiVLlnDmzBlcXFwIDAzE0tJS36GVqus3VWKSKbid\ngXPm30Crz/linxNf1Hse9epaFEVh1KhR+g5ViApNUSvwf6X09HTt71ZWVnqMRFRkERERALRp00bP\nkYiKTM6TquPFF19k9erVOmXe3t7s27dPm3A9rpKcJzdv3rxvTGfjxo3Zv38/NjY2TxRHSWRlZeHm\n5saZM2eoX78+eXl5nD9/HldXV6Kjo5/4OamMEhMTcXV1BWDs2LGcO3eOLVu24ODgQEpKChrNk13w\nJe8nVVvqDZWQoxD8N4T8DbFnHr6tem4W9tnfsGjRIoYMGaItl8+wQtzv6ftvJIQQotK6fv06q1ev\nRqPRsH//fmxtbWnXrh2HDh0iIiKC9u3bl1ss1atXJzw8nKVLl5KYmIiTkxNjx47F2tq63GIAMDEx\nYfPmzfTv35+zZ88C0KhRIzZt2vRUJp1Q8AXAvHnzmDJlCkuXLgWgWrVqBAUFPXHSKaqe6zdVQu9J\nNKNOF28/AwMYM/59lkyeIUupCFEMT+d/JCGEEJXSrVu3gIIehFatWmFoaIiTkxOpqak6PQzlxcLC\nokKMZ2vevDlxcXFERkaiKApeXl6YmJjoOyy9mjx5Mt7e3uzevRsTExMCAgK0vaDi6ZaeofLXsf8l\nmpGJUNT1f8ZG4OEETZzAvUHBzyYNwKUeGBsZl1PUQlR+kngKIYSoNOrUqUPdunVJSUmhe/fu1KxZ\nk8OHD2NqaoqXl5e+w9MrU1NT2rVrp+8wKpTOnTvTuXNnfYfxWPLz81m4cCErV64kMzMTPz8/Pv30\nU5nApoSyc1TizsLxRDiaAH8dhb/joagJn40MwdsDuraEbq2hQzMwM5EeTSGelCSeQgghKg1DQ0PW\nrFlDv3792Lt3LwBGRkasWLGC2rVr6zk6IUrP9OnTmT17tvZ+fHw8J0+eZNeuXRgYGOgxsoor7ZbK\n4ZiCHswTpwp+xiRDTm7R+xkYQBs36NoKurWCTs3B3EwSTSFKmySeQgghKpVOnTpx8uRJtm3bRk5O\nDt26davy6waKp0tWVpZ2Pdgff/yRBg0aMHDgQEJCQti/fz8+Pj56jlD/snNUIhPh0Mn/3eLOFm9f\njQZauvwv0XzGCyzNJdEUoqxJ4imEEKLCysnJITs7W7tuXiFHR0f+9a9/6Skq/Tlx4gTr168nJyeH\nnj170q1bN32HJMpAWloaOTk5WFhY8OKLL6LRaGjbti1//vknly5d0nd45erGTZWEFIg/Bwn/f4s/\nVzABUHZO8epoUBuaN4LmjaFtE+jcAmpYSqIpRHmTxFMIIUSFk5WVxcSJE1m+fDm5ubm0bNmSn376\niSZNmug7NL3ZsmULgwcPJjs7G4C5c+cyf/58Jk+erOfIRGmztbXF3t6ey5cvM3ToUBo0aMCuXbsA\n8PT01HN0ZSMnVyX2DPwdB0fj4VgCnEyGq2nFr8PQoCC5bOUGXo0Lbs0aSpIpREUhiacQQogK5513\n3uGbb74BQKPRcPToUXr06EFUVBQ1atTQc3TlLzc3l5EjR5Kdnc3QoUOpXbs2ixYt4t1332Xw4ME4\nOzvrO0RRijQaDT/88AMDBw7kl19+0ZZ/9NFHuLm56TGy0nE3Sy2Y7Ce+YKKfY/Fw4jRkZZesHmdH\naOdR0IvZrim0dJVJgISoyCTxFEIIUaHk5+fz3XffAbBv3z68vLzo0KEDJ06cYMeOHQwfPlzPEZa/\nCxcucO3aNWrWrMmaNWtQFIXjx48TEhJCVFSUJJ5VUO/evTly5Ajr1q0jMzMTX19fevbsqe+wSiw9\nQ+VYQkFPZuHP2LOQl1e8/U2NoXFdcK0HjeuBo/Vtbl89ioP1Tfx7tcPGxqZsD0AIUWok8RRCCFGh\n5OXlkZWVBYC7uzvm5uY4OTlx4sQJ7ty5o+fo9KNmzZoYGBhw/fp11q5di4ODA0ePHgWQ2XyrsKZN\nmzJr1ix9h1EsqqpyPvV/l8lGJhQsX5J0ofh11Lcv6LVs4QqtXAsum61nBxpNQS/moUOH8Pf3JzU1\nFQBra2s2bdpUaZfMEeJpI4mnEEKICsXIyIhOnToRFhZGu3btaNSoEX/88QeGhoZ06tRJ3+HphYWF\nBRMnTuTzzz/n+eef15b37NmT1q1b6zGykjl16hRLly4lNTUVLy8vAgMDMTEx0XdYooQy7qhEJxUs\nWXLiNET9/8/ijsdUlIIezHuTzJauUMvq4ZfJZmdn89xzz2nPHUNDQ44cOcLgwYNJTk6+bwIyIUTF\nI4mnEEKICufHH3+kR48eJCYmkpiYiKGhId9++22VGN9W6Pr161y7do369esXK/n69NNPsbGxYdWq\nVdpZbefOnYtGoymHaJ/ciRMneOaZZ0hPT9eWbdmyhT/++AMjIyM9RiaKoqoqUadh12EIi4Tjp+D0\nBVDV4u1vZAgeTtDS7X8JpldjsKhWsrGYCQkJnD9/HgcHBw4fPoyBgQGurq6cOnWKqKgo2rVrV/KD\nE0KUqyITzzlz5rBx40bi4+MxMTGhffv2zJkzh6ZNmz5w+9dff53//ve/zJ8/n3feeeeh9YaEhNC9\ne/f7ymNjY3F1dS3hIQghRPnLyMggOTmZ2rVryxijMuDs7ExkZCS7d+8mIyMDb29vGjdurO+wSkVO\nTg7jxo1j2bJlQMHlgitXrqR///5F7mdgYMDUqVOZOnVqeYRZ6t5++23S09Px8/Pj2Wef5eOPPyY4\nOJhVq1bx6quv6js8cY+zl1R2RcDu/79duVG8/aqbQwsX8HIpWCezhQt4OIOx0ZNP+GNqagrArVu3\nuHLlCkZGRty4cUPnscoqPz9fO1u1EJWZsbFxkV+GFpl4hoaGMm7cONq2bUt+fj7Tp0/Hz8+PkydP\nYm1trbPthg0bOHz4MI6OjihK8d5gTp48Sc2aNbX35cObEKIy+P777wkMDOTu3bsoisJbb73FF198\nUWl6nioLc3NzBgwYoO8wSt2sWbNYtmwZiqJgb2/PpUuXCAgI4OjRo3h4eOg7vFKTn5+v8zcRGxsL\nwOLFi3Fzc+PKlSt89NFHxMXF6StEAaTdUrWzyx6Ng0MxkJhS9D4GBgWXyno2hGaNwLNRwe/OjhT7\nM2BJNWzYkGeeeYa9e/dSr149FEUhPz+fNm3a0KxZszJpszyoqkpWVhampqZl9twJUR5UVSUzM7PI\nc7nIxHPHjh0694OCgrCysiI8PJx+/fppy8+cOcPEiRPZvXs3vXv3LnaAtra21KpVq9jbCyGEvu3d\nu5fRo0ejqipOTk4kJyfz5ZdfUq9evSKv9BAPlpuby/79+7l69SpeXl40bNhQ3yGVuTVr1gDw+++/\n07dvX4YMGcIvv/zCxo0bq0Ti+dNPPzFt2jRSUlJwcXFhyZIl+Pn5UbduXVJSUpg/fz7Dhw9n3bp1\nANStW1fPET897mapRMRAeFTB7LJ/x8Gp84/er2Z18G0D3VsXLF/i3gBMy3nZEkVR+OWXXxgxYgQ7\nduxAVVW6devGqlWrMDAwKNdYSlN2djbGxsaSdIpKT1EUjI2Nyc7OfujwkRKN8bx58yb5+fk6vZ25\nubk8//zzfPjhhyUee9OmTRuysrLw8PDggw8+oGvXriXaXwghytvGjRtRVZU333yTJUuWsGrVKl5+\n+WXWrVsniWcJpaWl4e/vz759+4CCtQu/+OILJkyYoOfIylZubi4ANWrUQFEU7f/UvOKuL1GBbdmy\nhZdeekl7Pz4+nn79+nHgwAE++ugjevfuzXfffaddLsfNzY0RI0boK9wq78oNlX3HYd8JCD8OR+Ig\nJ/fR+5mZwDNeBcmmX9uCMZmFM8vqk62tLdu3bycjIwNVVbG0tNR3SE9MVdVKnTgLcS8DAwNycnIe\n+niJEs8JEybQsmVLOnTooC2bMWMGdnZ2vP7668Wux9HRkW+++Ya2bduSlZVFUFAQvr6+hIaG4uPj\n88B9IiIiShKqeArJOSKK40nPk4sXLwIFX8RFRERo79+6davKnIOZmZmkpKRgaWmJvb19mbUzc+ZM\n9u3bR40aNWjcuDERERFMnDgRCwsLvLy8yqzd4ijL17JNmzacOXOGXr164eTkRHR0NIqiUL9+/Up/\nDn3yyScAjBgxgjFjxvDRRx/x559/MmfOHN59913tlzU3btzA1dWVN998k/j4eD1H/fgqwut1644B\n568Zk3LVhPPXTLhwzYTzV004d9WEi9cfPWmVoUE+jRwycat7B/e6d3CvdxuXOncxMSqYPSjvJvz9\nd1kfRdXj4uKi7xCEqHCKnXi+/fbbhIeHExYWpr0cICQkhJUrV3Ls2DGdbdVHTHXm6uqqM4lQ+/bt\nSU5OZv78+Q9NPIUQoiLw8fFh7dq1rFq1iiNHjpCYmAjAM888o+fISsfevXuZMWMGt27dAsDPz48Z\nM2aUyeQdhw4dAmDRokW4u7sze/ZsNm3axOHDh/WSeN65c4czZ85gaWlJnTp1yuzStwkTJnD+/HkO\nHDhAdHQ0BgYGvPvuu3h6epZJe+WpcJ1VLy8vTE1NadasGX/++Se3b98GoHXr1pVq+ZeSiIqK4ttv\nv+XSpUvUr1+fcePG4ezsXKpt5OVD4gUzjp2y4OhpSyJPW3DtZslmBG5gl0lz5ww8nW7jXu82DR0y\nMTYs5hS1QgjxBIqVeE6aNIl169YRHByMk5OTtjw0NJSLFy/i4OCgLcvLy+O9997jyy+/5OzZs8UO\nxNvbm7Vr1z708TZt2hS7LvF0KfzGWc4RUZTSOk/atGlDdnY27777LjExMQC89NJLLF68uNIvCREf\nH8/7779PZmYm9evX5+LFi+zatQs3NzcWL15c6u1ZWFiQmpqKpaUlLVu2JCsrCyiYRKS8/543b97M\nyy+/zM2bNwHw9/fn559/xsLCokzaCw8PJzIykqtXr9K0aVOd/6OVWY8ePYiMjGTevHlERUWxYcMG\nAPr371+l3qP/+X5y5MgRxo4dqz2Hk5OTOX78OH///fdjJ5+qqnLlBkSdhoPREHYcwk/AzdvFr8PY\nCNo2gY6e0Mmz4KdNDTPADLB9rLhE8dy7bJAQooCiPqJ7csKECaxfv57g4OD7xnCmpqaSmpqqva+q\nKr169eKFF15gzJgxJbrMYNCgQdy6dYtdu3Zpy+79o7Wysip2XeLpIomnKI7SPk8uXrxIfHw8jo6O\nVeaSqgULFvD222/Tv39/fvvtN/bv30+nTp2ws7Pj8uXLpd7ezJkzmTVrFlCQhGZkZGBubk5kZCSN\nGjUq9fYeJiEhAU9PT7Kysqhbty6pqalkZWUxevRoli9fXm5xVERXr14lPj4ee3v7Yr0mt2/fpnfv\n3oSFhWnLhg4dyurVq6vUOLZ/vp8MHTqU9evXM3ToUN59913effdd9uzZw8SJE1mwYMEj67t5WyUy\nAaKSIPo0RCcVJJzXipG7mBpDQ0doWKdgVtlGdf7//v//bmKs/7GZT6PifoYtnAVUiKqiqHO6yB7P\nwMBAVq1axaZNm7CysuLSpUsAWFpaYm5ujq2tLba2ut+YGRkZUbt2bZ0PYiNGjEBRFFauXAnAwoUL\ncXZ2xsPDg+zsbFatWsVvv/3Gxo0bn+hAhRCivDg4OFTqXqqQkBBCQ0OpVq0aQ4YMwcnJifz8fABM\nTExQFEU7K92jhk88rg8//JC0tDQWL15MRkYGjo6OBAUFlWvSCbB9+3aysrLw9/dn+vTpxMbGMmLE\nCH799denOvFctmwZ48aN004UMXz4cFauXImxsfFD9zE3N2fPnj1s27aNs2fP4ubmRo8ePar8jJ2F\nY71fffVVWrduzQsvvMCePXu05ffKy1M5mQwHogtuh6LhZDIU98/M0aZg4h8fr4KfzRpWjIl/hCiu\n5ORkGjZsyPfff88rr7wCwA8//MCoUaNITk6mfv36eo5QlJUiE8+lS5eiKAq+vr465TNnzmT69OnF\nbuTcuXM6/3RycnKYMmUKKSkpmJmZ0axZM7Zt21aipViEEEI8ntmzZ/PBBx9o73/00Ufs2LGD3r17\nM23aNDZs2ICnpydJSUlAwWWSZcHAwICFCxcyZ84c0tPTsbOz0+taqIX/pwp/llXCXRns27ePsWPH\noqoqzZs3JzY2ljVr1uDk5MScOXOK3NfIyIhnn322nCKtGJo1a0ZYWBiTJ0/mxIkTLFmyRFt+J1Nl\nfxSEHi24VPbQSci4W7x6LcygqTN4Ngaf5gWJppND2a2VKURpKUwkH6Rfv34oivLI83j16tWkpqZW\n+ZnOnyaPvNRWn+RSW1EccqmtKA45TwpERUXh6emJRqNh7NixxMfHs2vXLho3bkxCQgJr167l1Vdf\n5e7dgk/GvXr1Yv369cVatkBVVe7evYuZmVml+mAcHx9P8+bNycrKon79+ly+fJmsrCxGjRqlXfbj\naTN16lQ+/fRTxo4dy9KlS9m+fTt9+/bFw8OD6OhofYend/98P7ly5QodO3bk1KlToKkGlh2p7TYc\nZ69XOBJn8MglTAwMoJkzeDaCpg0LejGbNYR6dtKbWVk97ZfaFiaes2bNuu8qFjc3Nzw9PTE0NNR+\n2figHk9/f3+io6O1X4KKyuGxL7UVQghRtRw9ehQo+Ie+ZMkScnJyMDMzIzExkYyMDIYNG0bPnj2J\njo6mZs2aNGnSpFhJ5Pr163nrrbe4dOkSdnZ2LFiwgBdeeKGsD6dUuLq6snbtWl5++WXtpHh9+/bl\nyy+/1HNk+lP4YTA7O1vnZ2X6QqGspd82YH+UStwZiD1ri/uz0WRE3eRqhjX5GHAZuPyQHN2hFnRo\nBt5NoX1TaO0G5mby3Iqqp1evXnh7ez/2/mXxnlP4Bakof5J4VgGqqvLll1+ycuVKMjMz8fX1Ze7c\nuWU2G6MQovKysbEBCnpsIiMjiY6OJi8vDzMzM+0/Ymtr6xItbRUSEsKwYcO0l6ZeuXKFF198kVq1\natGrV6/SP4gy8Oyzz3L+/Hl+/fVXLC0tGThw4FOdZA0cOJBPP/2UFStWEBoaSnJyMgABAQH6DUxP\n8vJUIhMLLpcNPQp7jzXnRsY/Z7E2BmweuL+HE3RpBZ29CmaWrWsnSbx4ej1ojOc/de3alb/++gtA\nZwhG4VwEqqqyePFili1bRmJiItWrV6d///58+umn1KpVS7u9k5MTTZo0YfLkybz//vscP36cqVOn\nMmPGjDI8QvEwknhWATNmzOCjjz7S3o+NjSUmJoY///yzSs0iKIR4cr6+vrRu3ZojR47QokULbfk7\n77zz2O8X3333HaqqEhgYyKJFi5gyZQqff/45y5cvrzSJJxRMnOfh4QFIUuDt7c3KlSt5/fXXCy4f\nBUaPHq0zNrgqy81VOZYAocf+P9GMhPSMe7coeumkZg2hS8uCW+cWYGddvufTsWPH2LNnD8bGxgwY\nMEAmaxF6k5aWxtWrVx/4WFHvsx988AHvvvsuKSkpLFy48L7H33jjDVasWMHIkSN56623OHv2LIsW\nLeLQoUMcPnxYOzmeoigkJiYyZMgQXnvtNcaMGSN/D3okiWcll5WVxaeffgoUXB/v5OTEoEGD2LNn\nD/v37y9Rr4UQouozNjbmjz/+4K233iIkJIRq1arxr3/9iylTpjx2nRkZBZ/Ivby8UBQFLy8voGBp\nDdCnqMMAACAASURBVFF5vfTSSzz77LOcOnUKOzs7HB0d9R1Smbl1W+XAPWtlHoiG24+YAMjEKB/3\nBhrc6oNrfXBvQMHv9cDSXH9fXPz3v/9l7Nix2p6hf//732zdulU+D1QRM79T+c+Ksql7+iiYObp0\nz91/ThyqKArHjx9/5H5+fn44OjqSlpZ237CN8PBwli1bRlBQEC+++KJOW8888ww//vgjY8aMAQp6\nRk+dOsXmzZvx9/cvhSMST0ISz0ouLS2N7OxsLCwsePnll9FoNHh7e/PHH39ol78RQoh71apVi59+\n+qnU6uvcuTObNm3inXfeYc+ePWzfvl1bLio3S0tLnZ7xqkBVVZIvwv6oglv4/7F33/E1nX8Axz/3\nZlzZkS2bLMQmVhEjdlvVojVKrVolrbZara2olpaiVFujRu1S6menMYNYQSSxIoOEJDKIzHt+fxy5\npEGGyE143q/XfZ2bJ/ec870c1/2e53m+z3k4dwUe5mlPVcUSWjeQezAt9S7gbJ1J48blq1hZVFQU\nI0eORK1W07t3b+Li4ggICKBPnz5ERkZqtWq08GpasGABNWrUyNf2vMWUNmzYgLGxMR06dMjXm+rl\n5YWNjQ0BAQGaxBPAyclJJJ3lhEg8Kzhra2tsbW2Jj4+nd+/euLi4sHfvXkAu4y4IgvCijR49mmPH\njrFx40bWrVsHyHMmP/30Uy1HJhRGkiR27NhBUFAQ5ubm9OnTBwcHB22HVaoeZEqcCnuUaB67APFJ\nhe/naCPPyfRtAK3rg7vjo6GBwcGZLzjqkjl79iw5OTm0atWKtWvXkpOTg4WFBdHR0cTFxb3UvdZC\n+eTj41OguFDenPGSioiI4N69e9ja2j7x93fu3Mn3c7Vq1Z7rfELpEYlnBadUKlm+fDlvvfUWGzZs\n0LRPnTqV6tWrazEyQRBeNsHBwYwYMYILFy5QpUoVpkyZQv/+/dHV1WX9+vWMGjWKK1euUK1aNXx9\nfUXvSgUwZswYFi5cqPl59uzZBAQEULt2bS1GVXLJafLczDMRaLaXbkBu7rP3Uyigjhu8VufhozY4\n21W8eb6VK1cG5FoPYWFhxMbGkpaWhkKhEMvSvSSmDFYwZbC2o9AutVqNpaUl69evf+Lv8/4d5BEV\nbMsPkXi+BDp37sypU6dYt24dmZmZtGvXrsCYekEQhOdx9epV2rZtS1paGgDXr19nwIABGBgY0LNn\nTxQKBb6+vvj6+mo5UqGoDhw4wMKFC6lUqRIfffQRx48f59ChQwwdOpSgoCBth1eoe+kSp8LheCic\nDIXTEXD9ZtH2NTWCJjWhaS25ymxTbzAzrniJ5n81a9aMxo0bc+LEiXzDG4cOHYqRkZEWIxOE4nta\n8SE3Nzf27dtHkyZNxHVdwYjE8yVRq1YtvvnmG22HIQjCS2r58uWkpaXRsWNH1qxZw/z585k+fTrz\n58+nZ8+e2g5PKIGzZ88CchGh77//noSEBKytrTXt5UFmlkRiCiSlQWIKhN2AE5fkRDM0svB5mXmq\nu8hJZrOHjxouoKNT8RPN/9LV1WXnzp2MGDGCvXv3oq+vT//+/ZkxY4a2QxOEYjMyMuLu3bsF2t97\n7z0WL17MtGnTNAU28+Tm5pKWloa5uXlZhSkUg0g8BUEQhEIlJycD0KJFCywtLenQoQPTp08nJSVF\ny5EJJWVtbQ3AwYMHOX/+PHv27AHAxsamzGNJSJbYfRx2BcGFa48SzfSM4h1HTxe8q0I9T6jvAfU9\noa67dqvMljVLS8t8U28EoaLy8fFhw4YNfPzxxzRu3BilUsl7771Hy5YtGTVqFN9//z0hISF06NAB\nlUrFlStX2Lx5M9OnT6d///7aDl94ApF4CoIgCIVq0qQJixYtYvbs2cTGxrJ7926AAkUjhOeXkpLC\nzp07SUtLo1mzZi9svmX37t3x8vIiPDycOnXqaNq//PLLF3K+x6nV8jDZncdg1zG5F1OSincMpVJO\nMn1qQOOa8ta7KujrvTpJpiCUZ8VdD/m/rx85ciTnz59n9erVLFiwAJB7O0GultugQQOWLFnChAkT\n0NXVxcXFhXfffZe2bduWOAbhxVJIUnE/6svO43fSxaR44WmCg4MBaNSofJW1F8oXcZ08H7VazYAB\nA1i9erWmrXbt2gQEBGBpaanFyEqXtq+Ty5cv4+fnR1RUFCB/aZo3bx5jxox5Iee7desWY8aM4fjx\n45iZmTFmzBiGDBlSql/WsnMkLkfD+atyb+aFa/ISJneSC99XVwcsTB89HKyhUXU50WzoBcaG2vlS\nqe3rRCj/ivodNiMj47mXFxGE8uRZ17To8RQEQRAKpVQq+eOPP+jTpw8XL16kSpUqdO/eHUNDQ22H\n9lIZOHAgUVFReHt7U716dbZs2cLHH39MmzZtXkjPZ5UqVdi4cWOpHEutloiKf5RcXrwG56/J8zKz\nsp+9r1Ipz73s3BTaNJTXzLQwBRND0WMhCILwshCJpyAIglAkCoWCzp0707lzZ22H8lLKycnh2LFj\nABw6dIjKlSvTs2dPNm3axLFjx8rVEifpGfLamMFhcOG6nGRevA73HxT9GDaV5USzU1No3xgsTEWC\nKQiC8DITiacgCIIglAM6OjoYGhpy7949jh8/TpMmTQgLCwPAxMREa3Gp1RLhUXD8IgRdhBOhck9m\nYWtjPs7JFmpVhVpuUNtNXjOzVjVQKkWyKQiC8KoQiacgCIIglAMKhYKRI0fy3Xff5etVdnZ2pkuX\nLi/8/JIkEXtH7rkMvS4vVxJ6Xf459X7RjmFpJieU3lXBuxrUrib/bG4iEkxBEIRXnUg8BUEQBKGc\nmDFjBpIksWTJEu7fv0/Tpk1ZsWJFqRbYy8qWuBID4VHy/MuIh9vQSEhLL/pxarhCk5pQ10NOLmtV\nk4fPijmZgiAIwpOIxFMQBEEQygldXV2+++47Zs+ejVqtRkdHp9jHkCSJ5DS4fguu34TIuIfbWxAR\nLbcXZ5gsyAllk5rQ2Fve+tQAM2ORYAqCIAhFJxJPQRAEQShnFApFkZLOnByJSzfg5CX5cSpMTi6L\nOjT2v8xN5GGyNatCTVf5eQ1XsLcSPZmCIAjC8xGJpyAIgiC8ANnZ2ezatYuYmBiqV69O69atnyt5\ny82Vi/yciZCryQaHyc/TM4p3HIUCXOzAy/nhw0Xe1nABO0uRYAqCIAgvxjMTz1mzZrFlyxYiIiJQ\nqVQ0bdqUWbNm4e3t/cTXDxs2jF9//ZXvv/+eTz/99JknDgwMZOzYsYSGhmJvb8+4ceMYNmxYyd+J\nIAiCIJQT9+/fp3Pnzhw6dEjT9v7777NixQqUSmWh+z/IlLh4Dc5chtPhcDYCQq7Cg8yind+wElSt\nAq4PH1XtwdUO3BzA0xkMVCK5FARBEMrWMxPPwMBAPvroI3x8fFCr1UyaNAk/Pz9CQ0OpXLlyvtdu\n2rSJkydPYm9vX+jd0uvXr9OlSxeGDBnC2rVrOXToECNHjsTa2pq33377+d+VIAjCK2LXrl2sW7eO\nnJwcunTpQu/evUWPVTkwefJkDh06hK2tLR07dmTz5s2sWrUKX19fBg8eDMhzMaPj5SI/eY+Ih9uo\n+KKfy9EGGlWXHz41oI67KPIjCIIglD/PTDx37dqV7+dVq1ZhZmbG0aNH6dq1q6b9xo0bfPzxx+zf\nv59OnToVetIlS5bg6OjI/PnzAfDy8uL48ePMmTNHJJ6CIAhFtGTJEkaMGKH5ec2aNZw/f55Zs2Zp\nMSoB4PDhwwAsW7aMLl26UMO7AeOnrWLZPwrOpkicuyz3YBZ3Lqa9FTTwgnoecpLZqDpUsRIJpiAI\nglD+FWuOZ2pqKmq1Ol9vZ05ODr1792bixIl4eXkV6TjHjh2jQ4cO+do6dOjAypUryc3NLVEVP+HV\nlJ6eTlBQEJmZmTg6OmJnZ6ftkEpNTk4OR48e5e7du9SrVw8XFxdthySUI+np6XzyyScAfPHFF1Su\nXJmvvvqKb7/9lqFDh1KtWjUtR/jqUaslbiXC5WhIM+gFLt35bKkLn69WE3bjIxR1x3AsHo5tLvxY\nSqU8LLaeB9T3fPSwqSySTEEQBKFiKlbi6e/vT/369WnWrJmmbfLkydjY2BRrfmZ8fDy2trb52mxt\nbcnJySEhIaHA7wCCg4OLE6rwCoiOjmbMmDHExMQAMGHCBL755ht8fX21HNnzS05Oxt/fn9DQUAB0\ndHQYN26cGBFQCl6Wz5IbN26QkZGBjY0NPXr0AKBOnTqcPXuWnTt30rRpUy1HWLEVdp3k5MKVmwZc\nuGHExRtGhEcbEp1QiczsvPmbn6BwgLA7eXs8OWE0NczB1TYDF5sMnG3krYtNJo5WmejpSvleG3UV\nokr4ftLT07l8+TIqlQoPDw9xg7eUvCyfJ0Lp8/Dw0HYIWrVixQoGDRoEwMGDB2nRokWB17i7u3Pt\n2jV8fX0JCAgo6xCFh44ePcrevXv5+OOPS3XN6CcpcuI5duxYjh49yuHDhzXzRv79919WrlzJ2bNn\n871WkqQnHUIQStXXX39NTEwMDg4OWFhYcP78eSZMmMCWLVuwtrbWdnjPZfbs2YSGhmJhYYGrqyun\nT59m9uzZeHt7F3lkgfBys7KyQkdHh9u3b7N27VpMTU25ePEiwEvV868NkgSZ2QruPdDhXoaOZpt8\nT49L0YZyohlj+FiSWZSDqrE2TaWOmxoPhwd4OqTj4fAAG7NsXvRUzFOnTvHFF1+QkpICyNNbfvjh\nB2xsbF7siQVBeOUZGBiwdu3aAolnUFAQ165do1KlSmI+upYdPXqUqVOnMnDgwPKReH7yySds2LCB\ngIAAXF1dNe2BgYHcunWLKlWqaNpyc3P54osvmD9/PlFRT743a2dnR1xcXL62+Ph4dHV1sbKyeuI+\njRo1KkqowisiJSWFS5cuoaury+rVqzEyMuKTTz7hyJEjpKenV/jr5eTJk4D8YeDl5UXfvn1Zu3Yt\n8fHx9O3bV8vRVUx5PRMV/dp43JQpU5g4cSI//vijpm3QoEGaHlDh2bKyJcJuwLkrEPLwcSY8i7v3\n9MhVl+yLkIUpeDiCuyO4O4G7A1Stkksddx2MDSsXfoBSlpCQQPv27UlJScHDw4Pk5GTCw8OZPXs2\ngYGBZR7Py+Jl/DwRSlfejZ5XXefOndm4cSM//fQTurqP0o61a9dSvXr1Cj/64v79+xgZGWk7jFJR\nFh2Hhd6u9ff3Z/369Rw4cABPT898vxs5ciTnz5/n3LlznDt3jrNnz2Jvb8/YsWPZv3//U4/ZrFkz\n9u7dm69t7969+Pj4VPgLUCgb+vr6AJrh2RkZGSQkJACgUqm0GVqpyHsPMTEx5OTkcOvWLeDR+xYE\nkHv9V6xYQceOHfHz82Pu3LksXbpU22GVG+kZEldjJA6dlVi/T+LHdRKfL5ToO0Wi3gAJEz+oNwAG\nTIe5f8Lek5CQql/kpNO1CvRqC3NGw8GfIeF/kPA/Bcd+VbBqsoLJgxT07aigeR1djA21c0f/8OHD\nJCcn07BhQ8LCwggNDUVHR4eDBw+SmpqqlZgEQXh19O7dm6SkJHbv3q1py83NZcOGDU+8kS5JEgsW\nLKB27doYGBhga2vLkCFDSExMzPe6v//+mzfeeAMnJycqVaqEq6sr48aNIzMz/5pT8fHxDBkyRPM6\nOzs7unTpopnKBKBUKpk6dWqBWFxdXRk4cKDm57zlsAICAhgzZgy2traYmJhofn/y5Em6dOmCubk5\nhoaGtGzZkn///TffMadMmYJSqSQsLIx+/fphbm6OtbU1X3/9NSBPI+vWrRtmZmbY2dkxZ86cAnFl\nZmYydepUPDw8qFSpEo6OjowdO5YHDx7ke51SqWTEiBFs3bqVWrVqUalSJWrVqpXv72LKlCmMGzcO\ngKpVq6JUKlEqlRw8eBCA06dP06VLF2xsbDAwMMDV1ZX+/fuTkVHMBaQfemaP56hRo1i9ejVbt27F\nzMxM00tpYmKCkZER1tbWBYY06unpYWdnl29se//+/VEoFKxcuRKA4cOHs3DhQj755BM+/PBDjhw5\nwsqVK1m3bl2J3oTw6jEwMKBXr15s2LCBXr16oa+vT2ZmJs7OzrRu3Vrb4T23/v37M2fOHPz8/DA2\nNubevXuYmprSrVs3bYcmlCMKhYIBAwYwYMAAbYfyTGq1mqCgIGJjY6levTq1a9cu9XOkZ0gEh8Gx\nCxB0AY6HQlxi4fs9jb4emBmBmfGjrbkxVHeFJjWhcU2wtSj/w8Py1gzNysoiNzeXjIwM1Gp1vt8J\ngvDyuXv3LklJSTg5OWn1prWjoyMtW7Zk7dq1mhUx9u3bx+3bt+nduzd//vlnvtePGDGCZcuW8cEH\nHzBmzBiioqJYsGABJ06c4OTJk5ob8ytWrMDAwAB/f3/MzMw4duwYP/74I9HR0fmO2aNHDy5cuMDo\n0aOpWrUqt2/f5uDBg1y+fJmaNWtqXvek4b4KheKJ7aNHj8bCwoKJEydqerYDAwPp2LEjDRo0YPLk\nyejq6rJq1So6dOjA3r17C9Qf6d27NzVq1GD27Nn8888/zJo1CzMzM3777Tf8/Pz47rvvWL16NePG\njaNhw4a0adMGkBPz7t27c/DgQT788ENq1qxJaGgoP//8MxcvXsyXVIJc0HX79u2MHDkSY2Njfvrp\nJ9555x2ioqKwsLDgnXfe4fLly/z555/MmzdPM/K0Ro0a3Llzh/bt22NjY6MpYhgVFcX27dtJT0+n\nUqVKRbsIHic9g0KhkJRKpaRQKPI9pk6d+tR9XF1dpblz5+Zra926tdSmTZt8bYGBgVKDBg0klUol\nVatWTfrll18KHCs5OVnzEIT/Sk1NlXr06CEBEiDVrl1bunTpkrbDKhWZmZnSsGHDJIVCIQGSk5OT\ndOjQIW2HVaGdPHlSOnnypLbDeOU8ePBA6tq1q+bfKSB99tlnklqtLvEx1Wq1dCVaLa3ZrZZG/6CW\nGg1US3ot1ZKiefEfVd9RS93GqaWJS9XSpgNqafM/IdLho8Gl+CegXXfv3pVsbW0lQLK1tZWMjIwk\nQOrUqZO2Q6vQxOeJUJiifod98OBBqZ43MzNTGjJkiObz1srKStq1a1epnqMoli9fLikUCun48ePS\nL7/8IhkZGUnp6emSJEnS+++/LzVr1kySJEny9vbW5AhHjhyRFAqFtHr16nzHOnz4sKRQKKSlS5dq\n2vKO9biZM2dKSqVSio6OliRJ/vxTKBQF8pL/elpu4+rqKg0cOLDAe2ratKmUm5uraVer1ZKXl5fU\nvn37fPtnZWVJ3t7eUvPmzTVtkydPlhQKhTRkyBBNW25uruTk5CQpFApp5syZmvbk5GTJ0NBQ6tev\nn6ZtzZo1klKplA4ePJjvXGvWrJEUCoW0Z8+efO9LpVJJV69e1bSFhIRICoVCWrhwoabt+++/lxQK\nhXTjxo18x9y6daukUCikU6dOPeFP7emedU0/s8cz765ocVy/fr1A25MqVbVq1YpTp04V+/iCkMfE\nxISNGzcSGBhIdnY27dq1e2kmqOvr67NkyRLmzp1Lamoqtra2onfiJfDgwQO2bNlCbGws3t7edOnS\n5aW5Zp9m2rRp/PPPP5iamvLaa6+xd+9e5syZg4+PD7169SrSMZLTJE6EQtBFOBEKJy5BQnLh++np\nQhVLee1LeyuoYvXoeTV7qOMOZsb5//yDgzOfcrSKydzcnB07dmjucAO0bt2aP/74Q8uRCYLwIkyc\nOJHffvsNhUKBlZUVd+7coXv37pw7d05rlXZ79uzJ6NGj2bp1K2+99RZbt2594nrTGzZswNjYmA4d\nOmimT4FcEM3GxoaAgACGDh0KyCPfQM5V0tLSyM7O5rXXXkOSJM6cOYOjoyMGBgbo6+sTEBDAwIED\n8y0H+TyGDh2a7zvZuXPniIiI4IsvvsgXN4Cfnx8LFy4kIyMjXw/hkCFDNM+VSiUNGzYkNjaWwYMH\na9rNzMzw8vLKl1tt2LABT09Patasme9crVq1QqFQEBAQQPv27TXtbdq0ybe8Wu3atTE1NX1ivvZf\n5ubmAGzfvp06derkm6NbUs9/BOGVlJWVRXR0NJaWlpoLU1vyJnW/jF/gjYyMXppJ66+6u3fv0qZN\nG86dO6dpe/fdd1m7du1LfVMhb77/6tWreeONN5g+fTqTJk1i//79T0w87z+QOHsZTl6CU2HyNiK6\naOeq4QpNa0Ezb2hWS/5ZqXz5PheKq1GjRly5coUrV65gYGCAi4vLS/l5KQgCmmGmu3btws/Pj27d\nurFjxw62bdvGZ599ppWYKleuTMeOHVm9ejVKpZIHDx7w7rvvFnhdREQE9+7de+KyigB37mjWp+LC\nhQuMGzeOwMDAAnMb84a/qlQqZs+ezWeffYatrS1NmjShS5cuvP/++zg6Opb4/bi5uRWIG8iXND5O\noVCQmJiIg4ODps3Z2Tnfa8zMzNDT0ytQbdzU1DTf+46IiCA8PPyJqzcoFIp8r33SeUD++7h79+4T\nY32cr68vPXr0YOrUqfzwww/4+vry5ptv0qdPHwwNDQvd/0lE4ikU2/bt2/nggw9ISkpCoVAwYsQI\n5s+fXyp3QgShJDIzMxk/fjzr168nNzeXLl26MG/ePExNTbUdmsb48eM5d+4crq6udOnShdWrV7N+\n/Xo6dOigWevsZZR3h/f69etIkqS5y1qpUiXuP5AIuQqnw+FUuJxoXrwORRlsY27yaK5ls1ry88qm\nIpl6Gj09PWrUqKHtMARBeMGys7MBsLS0RKlUYmFhAcjFGLWpT58+9O/fn9TUVNq3b//EVSzUajWW\nlpasX7/+icfI67FMSUmhTZs2mJiYMHPmTNzd3TEwMCAmJoYPPvgg34hNf39/unXrxrZt29i7dy/T\np09n5syZ7Nixo9B135/2Z5bX2/p43CAvhdewYcMn7vPf9/ukYqpPuyEoPVZtVq1W4+3tzfz585/4\nWnt7+0LP899jPsuGDRs4efIkO3bsYO/evXz44YfMmjWLoKCgEi1dKDIFoVguXrxIjx49yMrKwsbG\nhtu3b/Pzzz9jbW3NlClTtB2e8IoaOnQoq1at0vy8fPlyoqOj2bNnT7np2QkKCgLk2Fq3bo2zszNf\nfvklJ06ceKkTzwEDBnDw4EH8P5vJlzN38UBZHYXnarZHd2dRh6Ilmbo6UNcdGnvLCWaTmuDhJHoz\nBUEQ/qtz584sX76cdu3aUb16dY4fP45Sqcw3/FIbunXrhkql4ujRo5pio//l5ubGvn37aNKkyTNH\newUEBJCYmMiWLVto2bKlpv2/K2bkcXV1xd/fH39/f2JjY6lXrx4zZszQJJ6VK1cmOTn//I2srCzN\nigKFyesBNTY2pm3btkXap6Tc3d05depUqZ6nsO9JPj4++Pj4MHXqVHbt2kWXLl349ddf+eqrr4p9\nrpd3fJfwQmzZsoWsrCx69OhBXFwcW7duBShQlUwQysrt27dZtWoVOjo6HDhwgODgYExNTdm3bx8h\nISHaDk8j707tnj17SExM5NChQwBaH6pemhJTJALPSPy+XWL8YoleEyQWHhyIqmUGCp9bZLj9g6Lq\nXLDqQ2S8wROTToUCarpC/07w0ydw9BdI2QsnlylY9KmC/p0VeLkoRNIpCILwBPPmzaNNmzakpKRw\n/Phx9PT0WLp06VN74sqKgYEBixcvZvLkybz11ltPfM17772HWq1m2rRpBX6Xm5urSQ7zevEe79lU\nq9X88MMP+fZ58OBBgWG4Dg4OWFtb51tn1c3NrcC6xkuXLi1yrZtGjRrh7u7ODz/8wL179wr8/r/D\nX5+mKDfK3333XeLj41m8eHGB32VmZj7x/IXJS/KTkpLytScnJxfoGa1fvz5Q8nVqRY+nUCyPD+FQ\nKBRYWloC2h/CIby68uYp2NjY0Lp1axQKBe7u7pw+fbrAh6g2+fv78++//zJr1ixNUQUjI6Onzgkp\nz9RqiSsxcO7Kw8dleRtz+2l7PLmUv1IJ1Z2hvifU8wSfGlDfA0yMRFIpCIJQEnk3Xs+cOUNiYiK1\natUqMPxSW/r16/fE9rzkpmXLlowaNYrvv/+ekJAQOnTogEql4sqVK2zevJnp06fTv39/WrRogaWl\nJQMGDGD06NHo6uqyadMm7t+/n++44eHhtG3bll69elGzZk1UKhU7d+4kLCyMuXPnal43ZMgQhg8f\nTo8ePfDz8+PcuXPs2bMHKyurIg1JVSgU/P7773Tq1ImaNWsyaNAgHBwcuHnzpiahPXDgQKHHedq5\nHm/v168fmzZtYtSoUQQGBmoKKoWHh7Nx40Y2bdpEq1atinUeHx8fQJ4S1Lt3b/T19WnXrh1r1qxh\n0aJFvP3221SrVo0HDx6wfPlydHV16dGjR6Hv50lE4ikUS6dOnZg+fTq//PILISEhXLhwQdMuCNrg\n6uqKhYUFt27d4s0338TExITTp0+jUqmoVatWofvfunWL4OBgjIyMaN68ecnWpSqCt956izVr1jBp\n0iRu3rxJzZo1WbRokdaqDBZVQrLE+asQchXOX4UL1+R5mPcfFL7v48yMwcNRriTbwAsaeMrPDSuJ\nJFMQBKE05VVJ1bai9OD9d63MBQsW0KBBA5YsWcKECRPQ1dXFxcWFd999VzO8tHLlyvzzzz98+umn\nTJ48GRMTE9555x2GDx9OnTp1NMdydnamX79+7N+/n7Vr16JQKPDy8tKsE5pn6NChXL9+nd9//51d\nu3bRqlUr9u7d+8TVEp72nlq2bElQUBDTp0/n559/JjU1lSpVquDj45Ovgu3T1gYtartCoWDLli3M\nmzePlStXsm3bNgwMDHBzc2PUqFFFWif7v+dp2LAhs2bN4ueff2bQoEFIkkRAQACtW7cmODiYDRs2\nEBcXh6mpKQ0aNGDRokWaZLW4FFJRZ5dqwePduGZmZlqMRHjcokWL8Pf3Jzc3F4COHTuyefNmrVVf\nDQ4OBuShDsKr6X//+x9vv/02GRkZgDwMZ9myZfTv31/zmiddJ5s2baJ///6aoTg1atRg165dc/6I\nLQAAIABJREFUT6wC97KTJIlrsXA6Qi72cyZCTjbjEot+DJU+eFeVezHdncDdEdwd5K2lWcWoPC0+\nT4SiENeJUJiifof97zIbglDRPeuaFj2eQrGNGjWKt956iwsXLmBjY0O9evUqxBdKoWSSkpKYMGEC\np06dwsrKirFjx9KuXTtth5VP586dCQkJ4e+//yY3N5eOHTtSt27dZ+4TGRlJv379yMzMpFmzZsTE\nxHDp0iXef//9AnM9Xja5uRIR0XJyeToCzoTL25RiTA2xs5QL/tRxl7f1PMDTCXR1xWeBIAiCIAgF\nicRTKBEHB4d86xEJL6f79+/j6+urGVIN8tpgf//9N127dtViZAV5eHjw6aefFvn1hw8fJjMzk3bt\n2rFv3z4SExOxsrLi4MGDZGZmolKpXmC0ZedBpkTo9UdJ5tmHPZnpGUXb30Al92LWcoM6blD74cOm\nskgwBUEQBEEoOpF4vuJOnz7N/v37UalUdOvWDRcXF22HJJQja9eu5cKFC7i5ubF48WL++usvFi9e\nzMSJEwtNPA8cOMC4ceO4fv06bm5uzJkzp9AJ7y9CVlYWM2bMYOPGjejq6jJ48GBGjx6tSSwTEhLI\nyMjg5s2bAOjq6j513avyJitbLvJzKRJuxMOtBHlo7K3HHslpRT+ehSk09IL6XvK2rju4OYCOjkgy\nBUEQBEF4PiLxfIX98ssvjBw5UlMuesKECezYsUMryYFQPsXExADwzjvv0L59ezw9PVm8eLGm/WmO\nHz9Op06dNFWQk5KSaN++PceOHaNBgwYvPO48kiQxYMAA1q1bp2n7+OOPuXnzJl9++SV2dnacO3cO\nS0tLzTzPPn36oKur/Y9GtVoi9T4k35OTx+R7EH1bTjLDbsjbq7GQk1uy41exfFRNtqGXXPDH2bZi\nzMMUBEEQBKHi0f63K0EroqKi+Oijj1Cr1fTr14+4uDj27dtH3759uXHjBkqlWOJVgOrVqwOwbNky\nHB0d+d///geAl5fXM/f76aefyM7Opl+/fsyaNYvPPvuM9evXs3DhQpYtW/bC484TGhrKunXrqFSp\nEtOmTePevXtMmzaNOXPmMH78eHbv3k2vXr0IDw8H5DXEfv755xcel1otcSsRrsXCtZt5D4nz4feI\nu6tDRnYl0h4oKY3Sbzo64Gr3MMn0kLf1PcHOUiSYgiAIgiCUHZF4vqLOnj1LTk4Ovr6+rFq1itzc\nXCwsLIiJieHWrVti/qYAQK9evVi5ciW7d+9mzJgxABgbGzNv3rxn7peYKJdCfeONN3B0dOT1119n\n/fr1mvaykjd8tn79+rRp0waA33//ndjYWG7fvk2dOnW4dOkSt2/fxtDQEBMTk1I9f2KKRHgURESh\n2UZEw5VYyMz676sVQPHP72wLNVzlIbH2VlDFSu7NrGIpP7cyA6VSJJmCIAiCIGiXSDxfUZUrVwbk\nHqGLFy8SGxtLamoqCoVCLF0jaOjo6LB9+3YWL17M6dOnsbS0ZNiwYXh6ej5zv4YNG7J7924+/fRT\ngoODWb16taa9LFWvXh2FQkFQUBALFy7k3r17xMbGYmRkhJOTEyAPLbW1tX3qMXJzc5845zM7RyLs\nBkTHw80EiE2A2DvyPMvYOxAVD0mpzxe/oSoXS3MdzI3B3BhsKoOXC9RwkZNNTycwNhRJpSAIgiAI\n5Z9Yx/MVlZOTo1ns9nHDhw9n8eLFWoqqZMR6auXP/fv3adeuHcePH9e0tWjRgj179mBgYFCmscya\nNYuvvvpK87NSqWTFihW8//77z9zv/PnzDBw4kDNnzmBmbs7A4dNp6DuCk5fgRKhcJTajQK9l0Vma\nQTV7qFoFdmxewP3E8yyZ/wVtX3Nj0lcfsW71L8ycOZ3x48eX/CRCsYnPE6EoxHUiFKY463iqVCox\nv154KUiSRGZmpljHU8hPV1eXHTt28NFHH7F371709fV5//33+eabb7QdmvCC5FV3/d///oeenh59\n+vRh5MiRL+Q/OyMjIwIDA1m/fj3Xrl3D3d2dXr16oa+vr3lN3rBud3d3TQ/8izB+/Hjq1q3LihUr\nUCqVjB49mtdee+2Jr03PkLh2E05dTGbU2HXczx0AXtO5a9yIH/+1gn+Ld24Dldwr6eUMHk5yb6WX\nM3g4grnJoz9355VzuH87GtfKPXBzqEZqUiSQi56eXonftyAIglD+6evrk5GRQaVKlUTyKVRokiRp\nbqQ8jUg8X2GWlpb8+eef2g4DkIczHj16lPj4eLy9valRo4a2Q3qpSJJEv3792Lhxo6bt6NGj3Lx5\nkxkzZryQc6pUKvr371+gPScnhxEjRvDbb78B8n+6P/30E8OGDXshcQB06dIFGxsbALxrN+T8VUkz\n3/JyDFyOlivExmmmoJqDzTcU9hXAxU5OLO2twN5a3jpYyw/7h3MtizK/sm/fvnz77bd06tSJypUr\nc/fuXQwNDenevftzvW9BEAShfFMqlahUKjIzM7UdiiA8N5VK9cwCpSLxFLTu3r17vPnmmwQEBGja\npk6dyqRJk7QY1cvl/PnzbNy4EQMDA9auXUtiYiJDhgxh9uzZfPnll6VeVOdZZs+ezW+//YaOjg6e\nnp5cunSJ4cOHU716dXx9fUvlHJlZcs/l5ccSy9OhHkTfqUR8csmOKeXcRS/zLF+OakPjmtC4JthU\nLp2709OmTePu3bssXbqUu3fvYmtry+rVq3FzcyuV4wuCIAjll1KpfOrQREF4mbyUiWd6ejrZ2dli\nXmgF8eWXXxIQEICFhQWNGzdmz549TJ48mcaNG9OpUydth/dSiI2NBeT5SG+99RaSJDFhwgTi4uK4\nfft2mSaeW7ZsAeDPP/+kZ8+ejB49moULF7Jt27ZiJZ6SJBGXKK9pGRYlb8NvyNVjo+J5wlIkpoUe\nU1dH7sU0N0gi+PBGlFnXad6wClFh/xAVvp9Ob7zOtKFti/Fui0ZPT48lS5bw3XffkZycjL29fblY\nS1QQBEEQBKG0vFTfbFJTUxk8eDCbNm0CwMfHhz///FP0GpRz+/fvB+SExNfXl88//5w5c+awf/9+\nkXiWkrz1OA8fPsyECRNISEggLi4OExMTHB0diY2N5cMPP+TQoUMYGxszfPhwJkyY8ELXc82by5K3\nzatzlpUtcTMBbiVCYsrDR+qj50mpciXZsChIuVf88+royAV9PBzleZceTvJwWXdHcLIBXV0FYMmk\nSTeZPv07DsfI+3l6er7wwlumpqaYmhaeIAuCIAiCIFQ0z0w8Z82axZYtW4iIiEClUtG0aVNmzZqF\nt7e35jUTJ05k06ZNREdHo6+vT4MGDZg+fTrNmjV76nH//fdf2rYt2GsQFhZW6DINzzJw4EBNb4qu\nri4nT56kc+fOnDt3rswraZYnqampBAUFIUkSTZs2LXc9wXnDS65fv07Lli2JjIzM1y48v6pVqzJ1\n6lQmT56smdOpVCpZvHgxubm5tGvXjvDwcADS0tKYPHkyWVlZL6TYVIcu73E6Qsm7o7ZiNTOG2ynV\nofpf7Ixpy5+vS9y++/znUCjk9S09HMHdSd6ScQVn6wze6FALfb3Ch8hOmzaN119/nVOnTmFhYUHX\nrl0xNjZ+/uAErYqIiODIkSMYGBjQsWPHF1rYShAEQRCER565nEqnTp3o3bs3Pj4+qNVqJk2axLFj\nxwgNDdX8Z71mzRrs7e2pWrUq6enp/Pjjj6xfv57Lly8/dW28vMQzNDQUCwsLTbuVlVW+HpbiLKeS\nkpKCubk5SqWSS5cuYWdnR926dYmMjGTv3r34+fkV7U/kJRMcHMwbb7xBXFwcALa2tmzbto0mTZpo\nObJH5s2bxyeffALI1VDv37+PSqUiODiYWrVqFbq/KGtfdH///Te7d+9GV1eXXr168dprr7Flyxbe\neecd3Nzc2LdvH6dOnaJHjx4YGRmRlpZWoip7yWkSEdHysNeIKLh2E67EyI+7aaX3fkyNoLoLVHd+\nuL6lq9x7Wc0eKqnyxy2uE+GPP/5g8ODB5OTkAGBvb8+ePXvy3UwV14lQFOI6EQojlgQUhIKe2eO5\na9eufD+vWrUKMzMzjh49SteuXQG5GuPj5s6dy++//05ISAjt27d/5smtra2xtLQsSdwF5FUDU6lU\nODo6YmBggI2NDZGRkWRkZJTKOSqarKws3n77beLi4qhRowYKhYLQ0FDefvttrl69Wm56FP39/UlK\nSmL27Nncv38fW1tbVqxYUaSkUyieN998kzfffDNf2927chdjvXr1cHV1xdraGpDX4szKyipQFjs7\nR+LOXbh9F+LvQnySPCz2cjSaSrHP02upVIKdhVwV1socLE3BwkzeWprJDzsLeVkSO0tE+XmhSK5f\nv86QIUPIycmha9euREdHExISQu/evQkJCdF2eIIgCILw0ivWHM/U1FTUavVThyZlZWWxdOlSLC0t\nadiwYaHHa9SoEZmZmdSsWZMJEybQunXr4oSTj7W1Nd7e3ly8eJEGDRpgaWnJiRMnMDIywsfHp8TH\nrcjCwsKIjo7G3t6ec+fOoVAocHNzIyoqiosXLxbp76gsKBQKpk2bxoQJE0hOTi7Q811eJCcnM2XK\nFM6cOYOVlRVjx4596nqQFUneHfu//vqLgQMHcunSJdAxwbPuG2wI0Cfshrz0SHjUo3mXz8NAJc+n\ndHOAag7yvEpHa3C0kZchsbPIm2cpCKXnxIkTZGdn065dO3bs2EF6ejpmZmacP3+e1NRUMbdWEARB\nEF6wZw61/a9evXpx9epVgoOD8/Uy7Nixg969e5Oeno61tTV///03jRs3fupxIiIi+Pfff/Hx8SEz\nM5NVq1axZMkSAgMDadGiheZ1jw9TuHz5cqHxXbt2jTFjxhAfHw+AgYEB33zzDa1atSrqW3ypREZG\n0rNnT0xMTNi8eTMKhYIePXqQkpLCn3/+ibu7u7ZDrDAyMjIYNGhQvutQR0eHn3766ZnXenn2IFNJ\nTIKKmAQVW3ef5+ip22DgDpW8UKgcnuvY+rpqnKwzcbHJwNk6AyfrTBytM3G0ysTKNBvRSSmUtcOH\nD/PJJ5/g4ODAihUriI2N5YMPPkCpVHL48GH09PS0HaIgCC8RDw8PzXMx1FYQZEVOPMeOHcuGDRs4\nfPgwrq6u+X6Xnp5OXFwcCQkJLF26lO3bt3PixAlcXFyKHEjXrl3R1dVl27ZtmrbiJp4gDw88ffo0\n2dnZ1K5dWzNs8FWkVqsZOHAgoaGh6OvrA3KvtJeXFytXrkRHR0fLEVYcW7ZsYdasWdjb2/PZZ59x\n4MABduzYgbe3NytWrNB2eE+Vma0gJkFF1O1KRD/cRt1REXNHRUKqfomOqVBImBvlUNk4BwuTbCxM\n5K2DVV6imYld5SzKYae18ArLyMigb9++REVF5Wvv1q0bEyZM0FJUQlElJydz9OhRsrOzadCgAU5O\nTtoOSRCeSSSeglBQkRLPTz75hA0bNhAQEFCkqrOenp707duXyZMnFzmQqVOnsn79ekJDQzVtYmL2\n87t58ybvvfcehw4dAqB58+asX78eR0dHLUdWesqiyMOECROYMWMG48ePZ+bMmVy7dg03NzdsbW01\nhZue5tKlS0yZMoXIyEjc3d2ZNm1aqS3xk5srcSsRIm9BZNzD7S24EScX8nnyepaF09OVi/R4PSza\nU91Ffu5sC1ZmFXMorCgGIkRGRjJgwAAOHTqEvr4+AwcO5Mcff8w3311cJ+XP6dOn6dSpE3fu3AFA\nX1+fFStW0Lt3b63FJK4ToTDiO6wgFFToHE9/f382btxY5KQTIDc3F7VaXaxAzp49i729fbH2EQpn\nb29PYGAgCQkJgFw5uCIWY0lPTyctLQ0bGxutxJ9353L58uVUrVqV7du352t/mvDwcJo2bUpqaiog\nzzPbvXs3p06dKtKIgMwsieu3ICpOTiKj4uU1LKPi5eQy+jZk55TsPenqQFV7cHcAN0d53qW7g7yu\nZdUqFTO5FIRncXV1JTAwkOzsbHR0dMrlXHIhP0mSePfdd7lz5w6NGjXCxsaGnTt3MnDgQFq1aoWD\nw/NNCxAEQRDKzjMTz1GjRrF69Wq2bt2KmZmZpmfHxMREs9TC7NmzefPNN7Gzs+POnTssWrSImzdv\n0qtXL81x+vfvj0KhYOXKlYC8fEbVqlWpWbMmWVlZrF69mm3btmnW4BRKl0KhqLBDjrOyshgzZgy/\n/vorarUaV1dX/vzzT5o2bVqmcfTp04fly5cTGBjIhx9+CIChoSE//PDDM/f79ttvSU1NpWPHjnzx\nxRdMmTKFgwcPMnfuXH766ad8r719V+LcZTh3BUKuyNtLkZCTW/K4lUpwtZOTSQ8nuRfTw0lOMF3s\nRHIpvJrEfM6KIz4+nitXrmBkZMSRI0fQ19enRYsWHDlyhNOnT4vEUxAEoQJ5ZuK5ePFiFAoF7dq1\ny9c+ZcoUJk2ahK6uLqGhoSxfvpzExEQsLS1p3Lgxhw4dyrcuWnR0dL5equzsbD7//HNiYmIwMDCg\nVq1a7Ny5k06dOpXy2xMquvHjx/PLL78AcqIXGRlJ586duXDhQpl+4dDT02PXrl3Mnz9fU9V21KhR\n1KhR45n7RUdHAzBy5EhatWrN270/5uBZicMRbkz5XeLGLbh+S16CJC6xZLFZm4NrFfnhYvfwuZ3c\nm1nNHlT6IrkUBKFiMjIyAuT6DXmf+5GRkQAYGxtrMTJBEAShuIpV1basifHxgpWVFYmJiRw4cIAW\nLVrQrl07Dh06xOLFixk+fDhQvubaZGRKXLsJV2Plx7K1gZy/nI7KrCa5uo7kqotf0MnFTh766mwL\nTrbgbCc/d7GTlyIxMhCJZVGUp+tEKL/EdVL+vP/++6xevTpfW61atTh16pSmcF5ZE9eJUBjxHVYQ\nCirWOp6CUNYyMzMBcHZ2Rk9PTzMPOK+9rKVnSFyNfVTA50be3Ms4uBH/pF5LXxSVIQugkGnPhpWg\ndjWo4wF13eVHbTcwNSpeYvnPP/+wceNG1Go1b7zxBj179izW/oIgCOXJ0qVLMTAw4I8//iAnJ4e2\nbduyfPlyrSWdgiAIQsmIxFMo1/z8/Ni6dSstW7bEy8uLf//9F6VSSevWrV/YOdPuS9yIl6vCXo6G\nyzFw5eE29s7zHdtQ7z7Vq6rwcNLFtQqYqpI4c2wL2ffCaVLPFv8xH2FgYFDi4//000/4+/trfl61\nahWTJ09mypQpzxe4UGSSJBEYGMi1a9eoWrUqrVu31lpBr/T0dM6ePYuOjg7169cXX9SFCsnAwICl\nS5eyZMkS1Go1urriq4sgCEJFJD69hXLtl19+ISoqitOnT3Pr1i10dXVZvHgxdevWLdHxMjIlbibI\nCeTNhEeVYvOqxt6Ih+S0kserVMpDYN3soZoDuDnI1WLdHOT5lsaGj+YkhYeH07x5c5KSkgDYug62\nbd1CQEBAvuUdiiolJYXPP/8cgK+++gpDQ0MmTpzItGnTGDJkyEu1hE55lZOTw3vvvcfmzZs1bd27\nd2fDhg1l/mU5ODiYbt26cfPmTQDc3d35559/ilydXBDKG6VSKSoRC4IgVGAi8RTKNRsbG4KCgjh8\n+DApKSnUr1+/wDIk2TkKbqfooQ6VuJMMd+5CQgry82SIT4TYh8lmYspTTlREOjryfMtq9vnnWuY9\nHKyKXil23LhxJCUl4evry7vvvsvMmTMJCgrit99+46OPPip2bFFRUWRlZVGtWjVmzJgBwNatWwkO\nDubq1asi8SwD8+bNY/PmzZiYmNC1a1d27tzJX3/9xY8//qi5KVAW0tPTNUlntWrVyMzM5MqVK3Tv\n3p2QkBB0dIo/11gQBEEQBOF5iMRTKPf09PRo06YNIM+xDLogcToCTofD2csQcqUeObmldxdcX09O\nKKvZy72VHk7g8XDrWgX0SmkJkrCwMAB++OEHGjRoQGpqKl9++aWmvbgcHBxQKpVcu3aNRYsWYWho\nyNmzZwF5jqzw4h06dAiQE9BBgwaxYsUKBg4cyMGDB8s08Txz5owm6QwLCyMrKwsnJydCQ0OJjIzE\nzc2tzGIRBEEQBEEAkXgK5ZAkSSQky3MqH59jefE6XLoB6gJFeoqedOrogJ0FOFjLvZMONnJPZV7P\npbMt2FQGpfLFz8lzcnIiIiKCuXPnMmjQINasWaNpLwkLCwvGjx/PjBkz8vWYDh8+nKpVq5ZKzGUh\nIyODvXv3cvfuXRo0aECtWrW0HVKR5S39cO7cOSRJ0iT+ee1lJa9HMysri6ysLDIyMsjJyQEQQxUF\nQRAEQdAKsZyKoDU5OfLSI5duQOh1uBQJYTfkRDPlXvGOZW2WhaOtPtbm8rqWVg8f1uZga/EwybSW\nk0odnfKx/MiRI0do06YN2dnZmraqVasSHByMhYXFM/c9ePAgK1asID09nTZt2jB06FCUSiWSJPH7\n77+zYcMGJEni9ddfZ/To0RUm2YiLi6N9+/ZcuHABAIVCwbfffsu4ceOe+9hlsfzB/v37ad++PY9/\nrCoUCvbs2YOfn98LO+9/ZWZm4u3tzdWrV6lcuTI5OTmkpaXRuHFjgoKCtFbsqCIQy2QIRSGuE6Ew\n4jusIBQkEk/hhZEkicQUuWhP9G2Ifri9cUtONsOjICu78OM8TqEAL2do4An1veStdP8spoa5FfIL\nQFBQEN9++y1xcXHUqlWLb775Bjs7u2fus379enr37p0vufnggw9YtmxZhU8ounfvztatW3F2dqZ+\n/fps374dtVrNkSNHaN68+XMdu6y+KK5fvx5/f3/i4+OxtbVl3rx5vPfeey/0nE8SHh5O9+7duXTp\nEgA+Pj5s2bJFzPUthEgohKIQ14lQGPEdVhAKEonnQ5IkERcXh0qlKrS3SZDl5soVYm/EQeTDNS0j\nb8mJ5Y14OdHMyCrZsY0MHs2rdHeUn3u5yOtcGhvmT67KwxeAmJgYJk6cSFhYGI6Ojnz99dfUq1ev\n1M8jSRI2NjYkJCQwatQovLy8+OKLL3jw4AFBQUE0adKk1M9ZliwtLUlKSiI8PBxPT08GDx7MsmXL\n+Pbbb/niiy+e69hleZ1IksSDBw8wMDDQ6s2A3Nxcrl+/jo6ODq6urhX+xkRZKA+fJ0L5J64ToTAi\n8RSEgsQcT+DSpUv07NmTixcvAvD666+zatUqzM3NtRxZ+ZF2X+LcFTgTAWevwNkIec5lcXss/8ve\nCmq4PvZwAU8nqGJFhfmSHB8fT9OmTYmNjdW0/fPPPxw5coT69euX6rmSk5NJSEhAX1+fBQsWoFAo\nCAgI4K+//uLy5csVPvE0NDQkKSmJ8+fP4+zszOXLl4GynyP5vBQKBYaGhtoOAx0dHdzd3bUdhiAI\ngiAIgkg87927R6dOnYiKisLIyIjMzEx27NjBgAED2LZtm7bDKxOSJJGUKq9reSvh4TZRfsTehvPX\n4EpMyY5tagRONuBkC442D5/bQHUX+WFuUj6Ty7S0NCpVqoSenl6hr124cCGxsbE0atSIWbNmsWjR\nIrZu3cr06dPZsmVLqcZlZmaGmZkZKSkpTJ06FS8vL/bt2weAq6trqZ5LG4YOHcrkyZPp0aMHSqUS\ntVqNhYUFb7/9trZDEwRBEARBEJ5DhUk884atlbbDhw8TFRWFh4cHZ8+eJT4+Hnd3d/7++29SU1Mx\nNTUt9XNqU3KaxPmrEJL3uAwXrsP9ByU7nrW5vMSIaxW5Imze87wKsaZG5TOxfJoLFy7Qt29fQkJC\n0NXVZciQIcybNw+VSvXUfaKjowEYOHAgfn5+6OnpsXXrVqKioko9PqVSyXfffcewYcOYOnWqpv2t\nt97itddeK/XzlbWvv/6ajIwM5s2bx4MHD6hRowarVq3C3t5e26EJgiAIgiAIz6HCJJ7t27fnwIED\n6Ovrl+px8yqKmpubY2BggJWVFXp6emRmZuarNlqaIiIimDlzJlFRUXh6ejJp0qRS/2Kddl/SVIsN\njZQrxp6/Khf6KQkdHXkYbH1PqOsB9T3krYVpxUosnyUpKYkOHTpw69YtdHR0yMnJYcmSJejq6rJg\nwYKn7ufp6QnI63Hq6uqyYsUKALy8vF5InB9++CE2NjYsW7ZMU9V23LhxFWZo8rPo6Ogwc+ZMvvnm\nGzIyMsrFcFVBEARBEATh+VWY4kLm5ub8+uuvDB48mN9++42FCxeSlpZGs2bNmDdvHtbW1iU6x+3b\nt3F3dyctLY369euTlJTEjRs3aNCgAcHBwaX+ZT48PJwmTZrke28ODg4EBwcXWs30aVLuSRwJgUPn\n4NwVOdksboJpbCAvN1LFUp53aWclb6tYyoV9alWDSqrymdiUVpGHtWvX0rdvX+rVq8eRI0c4c+YM\nLVq0wNDQkHv37j31Wrh37x6vvfYaISEhmjYbGxuOHz/+Ugx/fVmIYiBCUYjrRCgKcZ0IhRHFhQSh\noArT4wlw+fJlFixYgL+/v6bt+vXrhISEcPz48RL1jtjY2LBx40Z69erFmTNnAHB3d2f9+vUvpAdp\n+vTppKSk4Ofnh7+/P1OnTiU4OJgff/yR2bNnF+kY8UkSh87BwbNw+GGyWdTbB/p6UNMV6rhBbXd5\nW8cdbC1K573ev3+fxYsXEx4ejpOTEyNGjCjxTYGylp6eDoCLiwuGhoaaHsvMzExyc3PR1X3yPxdj\nY2MOHz7MvHnzCA8Px8HBgTFjxuDg4FBmsQuCIAiCIAhCeVahEk8XFxemTZsGwI8//kirVq145513\nuHDhAjt27KBXr14lOm7Hjh25evUqJ0+eRKVS0bx5cypVqlSaoWvcuHEDgM8//5wOHTpw584dBg0a\nxNXrscTekYv8JKVCQrJc3OdmAsQlPir2czNB/l1h9HTl6rA1q8rVYmu6gndV8HQGPd0X03N5//59\nWrVqxenTpzVtv/32G0FBQRVijl6LFi3Q0dFh27ZtdOrUiStXrgDQsmXLpyadeUxMTJg4cWJZhCkI\ngiAIgiAIFU6FSTy9vb3p168fo0ePBmDw4MGYmJjg6+tLZGQkt2/ffq7jW1lZ0blz59KB9nFRAAAd\n40lEQVQItYDMLInIW3A1FrIth4HrO/SeaojxgiRuJXSGJvfYEmvIlrdKdnylEup5QMu60Ly2PCzW\n3fHFJZhPM3/+fE6fPo2rqysff/wxK1eu5MyZM0yYMIFly5aVaSwlUb16dZYuXcqwYcPYvXs3AB4e\nHpo5m4IgvLrCwsK4ePEidnZ2NGvWDKVSqe2QBEEQBKFCqTCJ56FDhzA1NaVOnTqcPXuW7t2707Bh\nQ9atWwdA3bp1yzQeSZK4fRcib8nzKe8kQ2IKJKRA0sNtYgrE34WY248Phe2Lwh7uAneTACUUNz3U\n14MmNaFFXWhVD5rVKh/VY0NDQwH48ssvGTZsGLVq1cLPz49Lly5pObKiGzRoEL6+vpw4cQITExPa\ntm0rCtwIwituypQp+apI+/n5sXXr1gq3vqwgCIIgaFOFSTwrV64MwK+//oqfnx/79+9n//79AIwZ\nM4aWLVuW2rmysuWkMj4J4pLk7a1EOcGMipOTzRtxkJFVaqdETxcszcDCBCxM5Yfdw0I/VaweFf2p\nYgk2lUFHR/uJ5n/lzWlctWoVtWvXZsmSJQAVYpjt49zc3HBzc9N2GIIglAM7d+5k6tSpKJVK2rdv\nz/Hjx9m3bx9fffUV8+fP13Z4giAIglBhVJjEM0+jRo04d+4ca9asITU1lebNm/PGG28U6xiSJJGQ\nDJdjICIKIqLhcrT8c+wduaeyNCkU4GQDbg5QzUHeujlANXs5ibQwBcNKVPjlMEaPHs3y5cs5cuSI\nZk1JlUrFV199peXIBEEQSibvBudnn33G7NmzOXDgAO3atWPfvn1ajkwQBEEQKpZnJp6zZs1iy5Yt\nREREoFKpaNq0KbNmzcLb21vzmokTJ7Jp0yaio6PR19enQYMGTJ8+nWbNmj3zxIGBgYwdO5bQ0FDs\n7e0ZN24cw4YNK1LQLi4uT01mklIlzl+VeyQTUyAxVd4mPdwmpsCNeEhOK9KpnsncBFztwMUObCzA\nykzutfzv1skGVPoVO6ksCkdHR44dO8b48eMJDw/H2dmZyZMn07BhQwBiY2OZM2cON27cwN3dnXHj\nxmFlZaXlqAVBEJ5OpVIBEBUVhSRJmgJxee2CIAiCIBTNMxPPwMBAPvroI3x8fFCr1UyaNAk/Pz/+\n3969R1VV5/8ffx4QBG9HRC6SF1QgFfEyCj/z0k1jUoyWNhWNDmrLcZrIQW1aLvOStkqtJstJKUvH\nLMdLlnlBJ8sEkbCLJt6Qi5cSU1BL5Qsqt7N/f/D1fD2j4rGADfJ6rHUWns/+nL3fe/leh/1mf/bn\nk5GRYR/62qlTJxISEmjfvj0XL17kjTfe4Pe//z05OTn4+fldd7/Hjh1jyJAhjB07lhUrVrBjxw6e\nfvppfHx8GD58uFOBl5YZ5OTCviOw7zDsP1KxrMiJ3zbHEFBxh9LXC/xagH+Lip++XtDGr6LQDGxV\nUWxam9z+xeSt6tixIx999NE17cePHyciIoL8/P9bYPSTTz7h22+/xdvbuyZDBCruev/yyy+4ubnR\nrFmzGj/+7cIwDFJTUzl06BB33HEHkZGRuLm5mR2WSJWJiYnh9ddfZ9WqVSQmJlJYWAjA6NGjzQ1M\nRESkjrEYhrMrQFYsl2G1Wlm/fj1RUVHX7VNQUEDz5s3ZsmULDzzwwHX7TJ48mXXr1pGVlWVv+/Of\n/8zBgwdJS0uzt129+O7yrc0qhsP+75DYY6egvNzZyK/V2LNiuZGQNhUzwIa0rfh3O3/waV47n6Gs\ny8aOHcuSJUvo06cPcXFxvPrqq+zfv5/Jkyczd+7c37TvW13I+8iRIzz++OPs3r0bgIceeohly5bZ\n/5gizjEMg3HjxrF48WJ724ABA9i8eTNNmjQxMbLr04Lv4ozr5cmmTZt48sknOX36NO7u7kyePJlZ\ns2bV+ccj5NfT94nczNXXsFar1cRIRGqPW3rGs6CgAJvNdsML9JKSEt599128vb3twyuvZ+fOnURG\nRjq0RUZGsmzZMsrLy3F1db3mM+PnORdjQ/eK9SrvbFsxzNXbCt7NHH+28q6YsOe3XjQYhsHWrVvZ\nu3cvvr6+DB8+vFZecNcGV9bEnD59OkOGDMFmszFq1Ch7e025fPkygwcPJicnh4YNG1JaWsrGjRv5\n05/+RGJiYo3GUtctX76cxYsX4+npybBhw9i6dSs7duxg+vTpvPHGG2aHJ1JloqKiOHXqFKdPn6ZF\nixa4u7ubHZKIiEidc0uFZ3x8PD179rzm+c3ExESeeOIJLl68iI+PD5s2baJFixY33E9+fv41w3D9\n/PwoKyvj7NmzNxyi+9/8mpcQFHCR4IBLBN1xiaCAS7T1uUyDa+tWO6MQThbCyR+dOsSN92MYzJkz\nh08//dTeNmPGDN555x09t3gdVwryF154gaysLJYsWQKAh4eH/S/Hv5Uz+9m9ezc5OTn4+/uzcuVK\nLly4wCOPPMKmTZvYunUrzZs3r5JY6oO1a9cCMGbMGMaMGUOfPn3429/+xpYtW6rs/7Q61ObYpPa4\nUZ6cOHGihiOR2kzfJ3IjwcHBZocgUus4XXhOmjSJtLQ0UlNTr7lTeP/997N3717Onj3Lu+++y0MP\nPcS3335Lu3btqizQh/7fWdr6XKaNT/H/vi7j4e70KOEql5SUxKeffkrDhg2Jiopi165d/Pjjj8yb\nN4/Zs2ebFldt9eSTT5KSksKuXbvsv6hbtmzJyJEjazSOkpKKNXCaNWtG48aNadCgAQ0bNuTixYv2\nbeKcK+ubZmdnU1ZWZl+vVeueioiIiMh/c+oZz4kTJ/LRRx+RlJRESEjITXcaEhLCiBEjeOGFF667\n/Z577iEsLIwFCxbY29asWcOIESO4dOmSfahtbR4fP3nyZF599VWmTJnC7Nmz2bNnD7/73e9o3749\nR48eNTu8Wunw4cO8/PLL/PjjjwQHBzNjxgz72p+/xa08a/Pzzz/ToUMHCgoKCA8P5/z58+Tk5NC5\nc2cOHDiAi4vLb46nvti3bx8REREUFxc7tK9cuZKYmBiToroxPZMlzlCeiDOUJ3IztfkaVsQsN73K\njo+PZ/Xq1Wzbts2pohOgvLwcm812w+133XUXX3zxhUPbF198QXh4+HWf76yNrgzJTEtL48yZM2zZ\nsgXQl0tlgoKCWLp0Kdu2bWPRokVVUnTeKm9vb9asWUOzZs347rvvyMnJoW3btnz88ccqOm9Rt27d\n2LRpEx07dgQq7mC/88471Vp0GoZBdnY26enpXLp0qdqOU9usWLGCe++9l969e/Pss89SVFRkdkgi\nIiIit6TSobZxcXEsX76cdevWYbVaycvLA6Bp06Y0btyY//mf/+GVV14hOjoaf39/zpw5w8KFCzl5\n8iSPPfaYfT+xsbFYLBaWLVsGwFNPPcWCBQuYOHEi48aN46uvvmLZsmWsWrWqGk+1ao0cOZJ//OMf\nbN++HV9fX3v7hAkTTIxKnBEZGcnhw4fZuXMn7u7u9O/fX5NC/UoDBw7k8OHDlJSUVPuEK2fPnuWR\nRx4hJSUFAF9fXz7++GMGDBhQrcc1W0JCAnFxcfb3u3fvZvfu3WzdupUGDW7pMX0RERER01R6i+ft\nt9+msLCQgQMHEhAQYH+9/vrrADRo0ICMjAyGDRtGSEgI0dHRnDt3jh07dhAaGmrfT25uLrm5ufb3\ngYGBbN68mZSUFHr27MmcOXN46623GDZsWDWdZtVr06YN27Zto0+fPnh4eNCuXTsWLVrEqFGjzA5N\nnODj40N0dDQPPvigis4qUBOzfI4ZM4aUlBSaNm1KmzZtOH36NNHR0Zw+XQWL99ZShmEwbdo0AObO\nnct//vMffHx82L59O19++aXJ0YmIiIg4r9I/l1c2XBbA09PTPrNlZZKSkq5pu/vuu+3rKNZV3bt3\nZ+fOnWaHIXLbKy4uZtOmTQAcPHiQgIAA+vbty7fffktycrLDCIvbyaVLlzh37hwAf//733F1deX+\n++9n9erV/PTTTyZHJyIiIuI8jdMSkTrFYrFgsVjsz+Q6MT9andWoUSPatm3L8ePHGTlyJGFhYaxf\nvx6Azp07mxydiIiIiPM0m4rcUH5+Plu2bCEtLY2ysjKzw5F6rGHDhgwePBiArl27EhQUxNdff43V\nauWee+4xObrq9d577+Hu7s6qVauYOnUqly9f5i9/+cs16ymLiIiI1Ga64ynXtXr1akaPHs3ly5eB\niinjN23a5DCRkkhNev/99xk2bBhfffUVFy5coGXLlqxZswZ/f3+zQ6tWkZGRfPPNN3zwwQcUFRUx\nYMAARowYYXZYIiIiIrdEhadcIycnh9jYWEpKSggPD+fHH39k165djB07lg0bNpgdntRTPj4+7Nix\ng0OHDnHx4kW6dOlCo0aNzA6rRvTo0YMePXqYHYaIiIjIr6bCU66RlJRESUkJUVFRJCYmkpubS9u2\nbdmyZQs2m03rXYppLBYLXbp0MTsMEREREblFqiDqGMMwKC8vr9ZjuLm5AXDu3DnKyso4c+YMULF8\njsViqdZji4iIiIjI7UeFZx1RXl7O9OnT8fLywt3dnT59+pCZmVktxxo8eDBeXl6kpaXh6+tLeHg4\nAH/84x9VeIqIiIiIyC1T4VlHvPjii7z00ktcuHABm83GN998w8CBA/nll1+q/Fj+/v4kJibSpk0b\nzp07h81mIyYmhvnz51f5sapTaWkp6enpfP/995SUlJgdjoiIiIhIvaXCs45ISEgAYO3atZw7d44e\nPXpw8uTJapvsp2/fvhw7dowffviBn3/+mZUrV9apiVxycnIICwujZ8+e9OrVi06dOnHgwAGzwxIR\nERERqZdUeNYRBQUFANx11100b96c0NBQh/bq4OrqSrt27WjRokW1HaM6lJeX8/DDD5OVlYWfnx8B\nAQEcO3aM6OhoiouLzQ5PRERERKTeUeFZR/Tr1w+A+++/n8cff5yVK1cCFXcmxVFOTg6HDh3C29ub\nw4cPc+TIEVq3bs2xY8fYv3+/2eGJiIiIiNQ7Wk6ljliyZAkDBw7k0KFDHDp0CIBXX32V3r17mxxZ\n7XNlAiTDMLDZbPbX1dtERERERKTmqPCsI9q3b096ejqbN2/mwoULRERE0LNnT7PDqpWCgoLo2rUr\nBw4coEOHDri6unL69GmCgoIICwszOzwRERERkXpHhWcd0qxZM2JiYswOo9ZzdXVl3bp1PPzwwxw8\neBCA4OBg1q9fj7u7u8nRiYiIiIjUPyo85bbUsWNH9u7dS1ZWFoZhcOedd9KggdJdRERERMQMmlzo\nJvLy8nj00Udp06YNoaGhvP322xiGYXZY4gRXV1e6dOlCaGioik4RERERERPparwSRUVF3HfffWRm\nZtrbnn76aUpKSoiPjzcxMhERERERkbpDdzwrsWHDBjIzMwkKCmLfvn3Mnz8fgLlz55ocmYiIiIiI\nSN2hwrMSZ86cAaB///6EhYURGxsLwNmzZzXcVkRERERExEkaaluJK8uVrFy5Ei8vL3bv3g1Ajx49\ntB6kiIiIiIiIkyq94zlnzhzCw8OxWq34+voSHR1tX54CoKysjMmTJ9O9e3eaNGlCQEAAI0aMIDc3\nt9KDJicn4+Lics0rOzu7as6qigwYMICJEydSXFzMG2+8QUpKCi1atGDx4sVmhyYiIiIiIlJnVHrH\nc/v27TzzzDOEh4djs9mYMWMGgwYNIiMjAy8vL4qKitizZw/Tpk2jR48enD9/nmeffZYHH3yQffv2\n4erqWunBMzIyaNGihf19y5Ytq+asqtC8efMYNGgQO3fuxGq1EhMTQ+vWrc0OS0REREREpM6otPD8\n7LPPHN5/+OGHWK1W0tLSiIqKwmq18vnnnzv0WbRoEaGhoWRmZhIaGlrpwX18fPD29v6VodecIUOG\nMGTIELPDEBERERERqZNuaXKhgoICbDYbXl5eN+xz4cIFgEr7XNG7d28CAgIYNGgQycnJtxKKiIiI\niIiI1BEW4xamZ33sscc4cuQIu3btuu7kOiUlJdx33334+Piwbt26G+4nOzub5ORkwsPDKS4u5sMP\nP+Sdd95h+/bt9O/f397vShELkJOT42yYtYJhGOzbt4/jx4/j7+9Pr169cHHRJMIiIiIit7vg4GD7\nv61Wq4mRiNQeTs9qO2nSJNLS0khNTb1u0VlWVsbIkSMpKCggMTGx0n2FhIQQEhJif9+nTx9++OEH\nXnvtNYfCs66y2Wy89NJLbNy40d7Wt29fXnvtNdzd3U2MTEREREREpOY5VXhOnDiRjz76iKSkJAID\nA6/ZXlZWxhNPPMHBgwdJTk52apjtf4uIiGD16tU33N67d+9b3qdZFi9ezMaNG/H09GTo0KFs3bqV\ntLQ0PvvsM1588cVKP5ufn8+//vUvTp8+Tbdu3YiNjb3pJE313a5du4C6lSNS85Qn4gzliThDeSI3\nc/WoPRGpcNPCMz4+njVr1pCUlORwl/KK0tJSYmJiyMjIIDk5GV9f318VSHp6OgEBAb/qs7XN9u3b\nAZg9ezYTJkzgk08+4Q9/+IO9/UaOHDnCgAEDOHXqlL1t7dq1rFu3TsWniIiIiIjUWZUWnnFxcSxf\nvpx169ZhtVrJy8sDoGnTpjRu3Jjy8nIeffRRdu3axcaNGzEMw96nefPmeHh4ABAbG4vFYmHZsmUA\nvPnmm7Rv354uXbpQUlLC8uXLWb9+PWvXrq3Oc60xjRo1AuDAgQMYhsGBAwcAaNy4caWfmzRpEqdO\nnSIiIoKhQ4fy5ptvkpiYyPLlyxk1alS1xy0iIiIiIlIdKi083377bSwWCwMHDnRonzlzJjNmzCA3\nN5cNGzZgsVjo1auXQ5/333+f2NhYAHJzcx2eCy0tLeW5557jxIkTeHp60rVrVzZv3syDDz5YVed1\nXWVlZWRmZgLQqVMnGjRw+hHXWzJmzBiWLFnCkiVLWLp0KTabDYCxY8dW+rn9+/cDFUN1w8LCKC8v\nZ9asWfZ2ERERERGRuqjSyutKwXQjgYGBN+0DkJSU5PD+ueee47nnnnMivKqTnZ1NdHQ0WVlZQEXh\nuWHDBodZx6pKnz59+OSTT/jrX//KqVOn8PLyYu7cuQwfPrzSz/n5+XHs2DEWL17M6NGj7ZMT+fv7\nV3mMIiIiIiIiNeWWllOpaVc/mP1bpqIuLS2la9euZGdn4+PjA8CZM2fo1KkT+/fvr7Y7n4ZhUFRU\nROPGja87E/B/S0xMJDo6mqv/S1q3bs2ePXto2bJltcR4O9AkD+IM5Yk4Q3kizlCeyM1U1TWsyO2k\nXiwsmZGRQXZ2tv2O4tGjR/Hx8SEzM9M+9LY6WCwWmjRp4lTRCTB06FA2btxIv379CAoKYvjw4aSm\npqroFBERERGROq16bvXVYleKwCs/a9sN36ioKKKioswOQ0REREREpMrUi8KzS5cuBAUFcfjwYTp2\n7IhhGJw+fZqQkBA6d+5sdngiIiIiIiK3tXox1NbNzY2NGzcSFBREXl4e+fn5BAcHs2HDhmp7vlNE\nREREREQq1Juqq1OnTmRkZHDw4EEsFgtdunTBzc3N7LBERERERERue/Wm8ISKO589evQwOwwRERER\nEZF6pV4MtRURERERERHzqPAUERERERGRaqXCU0RERERERKqVCk8RERERERGpVio8RUREREREpFqp\n8BQREREREZFqZTEMwzA7iBu5cOGC2SGIiIiIiPxqVqvV7BBEagXd8RQREREREZFqpcJTRERERERE\nqlWtHmorIiIiIiIidZ/ueIqIiIiIiEi1UuEpIiIiIiIi1apWF54JCQm0b98eT09PevfuTWpqqtkh\niUnmzJlDeHg4VqsVX19foqOjOXjw4DX9Zs6cyR133EGjRo247777yMjIMCFaqS3mzJmDi4sL48eP\nd2hXnsipU6cYNWoUvr6+eHp6EhoaSkpKikMf5Un9VlZWxvPPP0+HDh3w9PSkQ4cOTJ8+nfLycod+\nypP6IyUlhejoaFq3bo2LiwvLli27ps/N8qG4uJjx48fj4+NDkyZNePjhh/npp59q6hRETFVrC8/V\nq1czYcIEpk2bRnp6On379mXw4MHk5uaaHZqYYPv27TzzzDPs3LmTbdu20aBBAwYNGsS5c+fsfV55\n5RXmzZvHggUL+O677/D19eWBBx6gsLDQxMjFLF9//TXvvfce3bp1w2Kx2NuVJ3L+/Hn69euHxWJh\n8+bNZGZmsmDBAnx9fe19lCcye/ZsFi1axFtvvUVWVhbz588nISGBOXPm2PsoT+qXoqIiunXrxvz5\n8/H09HT43QLO5cOECRNYu3Ytq1atYseOHRQUFDB06FBsNltNn45IzTNqqYiICGPcuHEObcHBwcaU\nKVNMikhqk8LCQsPV1dVITEw0DMMwbDab4e/vb8yePdve59KlS0bTpk2NRYsWmRWmmOT8+fNGx44d\njeTkZOPee+81xo8fbxiG8kQqTJkyxejfv/8NtytPxDAMY+jQocbo0aMd2mJjY42hQ4cahqE8qe+a\nNGliLFu2zP7emXw4f/684e7ubqxYscLeJzc313BxcTG2bNlSc8GLmKRW3vEsKSnh+++/JzIy0qE9\nMjKStLQ0k6KS2qSgoACbzYaXlxcAx44dIz8/3yFnPDw8uPvuu5Uz9dC4ceN49NFHueeeezCumrhb\neSIA69atIyIigscffxw/Pz969uzJwoUL7duVJwIwePBgtm3bRlZWFgAZGRkkJSURFRUFKE/EkTP5\nsHv3bkpLSx36tG7dms6dOytnpF5oYHYA13P27FnKy8vx8/NzaPf19SUvL8+kqKQ2iY+Pp2fPntx1\n110A9ry4Xs6cPHmyxuMT87z33nscPXqUFStWADgMhVKeCMDRo0dJSEhg0qRJPP/88+zZs8f+HHBc\nXJzyRAB4+umnOXHiBJ07d6ZBgwaUlZUxbdo0nnrqKUDfJ+LImXzIy8vD1dUVb29vhz5+fn7k5+fX\nTKAiJqqVhadIZSZNmkRaWhqpqanXPF9xPc70kdtDVlYWU6dOJTU1FVdXVwAMw3C463kjypP6w2az\nERERwcsvvwxA9+7dycnJYeHChcTFxVX6WeVJ/fHPf/6TpUuXsmrVKkJDQ9mzZw/x8fEEBgby5JNP\nVvpZ5YlcTfkgUqFWDrVt2bIlrq6u1/z1Jz8/n1atWpkUldQGEydOZPXq1Wzbto3AwEB7u7+/P8B1\nc+bKNrn97dy5k7NnzxIaGoqbmxtubm6kpKSQkJCAu7s7LVu2BJQn9V1AQABdunRxaOvUqRPHjx8H\n9H0iFV5++WWef/55HnvsMUJDQxk5ciSTJk2yTy6kPJGrOZMP/v7+lJeX8/PPPzv0ycvLU85IvVAr\nC093d3d69erF559/7tD+xRdf0LdvX5OiErPFx8fbi86QkBCHbe3bt8ff398hZy5fvkxqaqpyph4Z\nNmwYBw4cYO/evezdu5f09HR69+7NE088QXp6OsHBwcoToV+/fmRmZjq0ZWdn2/+Ype8TgYrREi4u\njpdJLi4u9hEUyhO5mjP50KtXL9zc3Bz6nDhxgszMTOWM1AuuM2fOnGl2ENfTrFkzXnjhBQICAvD0\n9OSll14iNTWVpUuXYrVazQ5PalhcXBwffPABa9asoXXr1hQWFlJYWIjFYsHd3R2LxUJ5eTlz587l\nzjvvpLy8nEmTJpGfn8+7776Lu7u72acgNcDDwwMfHx/7y9fXl3//+9+0a9eOUaNGKU8EgHbt2jFr\n1ixcXV1p1aoVX375JdOmTWPKlCmEh4crTwSAnJwc3n//fTp16oSbmxtJSUlMnTqVmJgYIiMjlSf1\nUFFRERkZGeTl5bFkyRLCwsKwWq2UlpZitVpvmg8eHh6cOnWKhQsX0r17dy5cuMBTTz1F8+bNeeWV\nVzQkV25/ps6pexMJCQlGYGCg0bBhQ6N3797Gjh07zA5JTGKxWAwXFxfDYrE4vGbNmuXQb+bMmUar\nVq0MDw8P49577zUOHjxoUsRSW1y9nMoVyhPZtGmT0b17d8PDw8O48847jbfeeuuaPsqT+q2wsNB4\n9tlnjcDAQMPT09Po0KGDMXXqVKO4uNihn/Kk/khKSrJff1x9TTJmzBh7n5vlQ3FxsTF+/HjD29vb\naNSokREdHW2cOHGipk9FxBQWw3Bi1g0RERERERGRX6lWPuMpIiIiIiIitw8VniIiIiIiIlKtVHiK\niIiIiIhItVLhKSIiIiIiItVKhaeIiIiIiIhUKxWeIiIiIiIiUq1UeIqIiIiIiEi1UuEpIiIiIiIi\n1UqFp4iIiIiIiFSr/w9+L/Z2r7g1DAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data_with_acc(pos, 15, 100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.0001)\n", + "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.0001')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see that the filter is not quite tracking the train anymore due to the acceleration. We can fiddle with $h$ to let it track better, at the expense of a less smooth filtered estimate." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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8tGvRogVOTk7Ex8fj4eHB3bt3yczMpGXLlgZp7RRCPJ60eAohhBBCVGD9+/fH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\noQl0bgYOlSXRFEIUH0k8hRD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K/2Lfvn0A7N69m/r16zNixAhWrFhBREREmUg8MzIyAHjm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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data_with_acc(pos, 15, 100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.001)\n", + "plot_g_h_results(zs/1000, data/1000, 'g=0.01, h=0.001')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are two lessons to be learned here. First, use the $h$ term to respond to changes in velocity that you are not modeling. But, far more importantly, there is a trade off here between responding quickly and accurately to changes in behavior and producing ideal output for when the system is in a steady state that you have. If the train never changes velocity we would make $h$ extremely small to avoid having the filtered estimate unduly affected by the noise in the measurement. But in an interesting problem there are almost always changes in state, and we want to react to them quickly. The more quickly we react to them, the more we are affected by the noise in the sensors. \n", + "\n", + "I could go on, but my aim is not to develop g-h filter theory here so much as to build insight into how combining measurements and predictions leads to a filtered solution. There is extensive literature on choosing $g$ and $h$ for problems such as this, and there are optimal ways of choosing them to achieve various goals. As I explained earlier it is easy to 'lie' to the filter when experimenting with test data like this. In the subsequent chapters we will learn how the Kalman filter solves this problem in the same basic manner, but with far more sophisticated mathematics. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## g-h Filters with FilterPy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "FilterPy is an open source filtering library that I wrote. It has all of the filters in this book, along with others. It is rather easy to program your own g-h filter, but as we progress we will rely on FilterPy more. As a quick introduction, let's look at the g-h filter in FilterPy.\n", + "\n", + "If you do not have FilterPy installed just issue the following command from the command line.\n", + "\n", + " pip install filterpy\n", + " \n", + "Read Appendix A for more information on installing or downloading FilterPy from GitHub.\n", + "\n", + "To use the g-h filter import it and create an object from the class `GHFilter`. " + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from filterpy.gh import GHFilter\n", + "f = GHFilter (x=0., dx=0., dt=1., g=.8, h=.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When you construct the object you specify the initial value and rate of change for the signal (`x` and 'dx'), the time step between updates(`dt`) and the two filter parameter (`g` and `h`). `dx` must have the same units of `x`/`dt` - if `x` is in meters and `dt` is in seconds then `dx` must be in meters per second.\n", + "\n", + "To run the filter call update, passing the measurement in the parameter `z`." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.96, 0.24)" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f.update(z=1.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`update()` returns the new value of `x` and `dx` in a tuple, but you can also access them from the object." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.96 0.24\n" + ] + } + ], + "source": [ + "print(f.x, f.dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can dynamically alter `g` and `h`." + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1.965, 0.375)\n" + ] + } + ], + "source": [ + "print(f.update(z=2.1, g=.85, h=.15))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can filter a sequence of measurements in a batch." + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1.965 0.375 ]\n", + " [ 2.868 0.507 ]\n", + " [ 3.875 0.632 ]\n", + " [ 4.9014 0.7306]]\n" + ] + } + ], + "source": [ + "print(f.batch_filter([3., 4., 5.]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can filter multiple independent variables. If you are tracking an aircraft you'll need to track it in 3D space. Use NumPy arrays for `x`, `dx`, and the measurements." + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " x = [ 3.8 13.2 101.64]\n", + "dx = [ 8.2 9.8 0.56]\n" + ] + } + ], + "source": [ + "x_0 = np.array([1., 10., 100.])\n", + "dx_0 = np.array([10., 12., .2])\n", + " \n", + "f_air = GHFilter (x=x_0, dx=dx_0, dt=1., g=.8, h=.2)\n", + "f_air.update(z=np.array((2., 11., 102.)))\n", + "print(' x =', f_air.x)\n", + "print('dx =', f_air.dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The class `GHFilterOrder` allows you to create a filter of order 0, 1, or 2. A g-h filter is order 1. The g-h-k filter, which we haven't talked about, also tracks accelerations. Both classes have functionality required by real applications, such as computing the Variance Reduction Factor (VRF), which we haven't discussed in this chapter. I could fill a book just on the theory and applications of g-h filters, but we have other goals in this book. If you are interested, explore the FilterPy code and do some further reading.\n", + "\n", + "The documentation for FilterPy is at https://filterpy.readthedocs.org/." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I encourage you to experiment with this filter to develop your understanding of how it reacts. It shouldn't take too many attempts to come to the realization that ad-hoc choices for $g$ and $h$ do not perform very well. A particular choice might perform well in one situation, but very poorly in another. Even when you understand the effect of $g$ and $h$ it can be difficult to choose proper values. In fact, it is extremely unlikely that you will choose values for $g$ and $h$ that is optimal for any given problem. Filters are *designed*, not selected *ad hoc*. \n", + "\n", + "In some ways I do not want to end the chapter here, as there is a significant amount that we can say about selecting $g$ and $h$. But the g-h filter in this form is not the purpose of this book. Designing the Kalman filter requires you to specify a number of parameters - indirectly they do relate to choosing $g$ and $h$, but you will never refer to them directly when designing Kalman filters. Furthermore, $g$ and $h$ will vary at every time step in a very non-obvious manner. \n", + "\n", + "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": "markdown", + "metadata": {}, + "source": [ + "## References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* [1] NASA Kalman Filtering Presentation

http://nescacademy.nasa.gov/review/downloadfile.php?file=FundamentalsofKalmanFiltering_Presentation.pdf&id=199&distr=Public\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.4.3" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/08-Designing-Kalman-Filters.ipynb b/08-Designing-Kalman-Filters.ipynb index e2e9985..3cc7132 100644 --- a/08-Designing-Kalman-Filters.ipynb +++ b/08-Designing-Kalman-Filters.ipynb @@ -407,7 +407,7 @@ "$$\\mathbf{x} = \n", "\\begin{bmatrix}x & \\dot{x} & y & \\dot{y}\\end{bmatrix}^\\mathsf{T}$$\n", "\n", - "There is nothing special about this organization. I could have used $\\begin{bmatrix}x & y & \\dot{x} & \\dot{y}\\end{bmatrix}^\\mathsf{T}$ or something less logical. I just need to be consistent in the rest of the matrices. I like keeping positions and locations next to each other because it keeps the covariances between positions and velocities in the same sub block of the covariance matrix. In my formulation `P[1,0]` contains the covariance of of $x$ and $\\dot{x}$. In the alternative formulation that covariance is at `P[2, 0]`. This gets worse as the number of dimension increases (e.g. 3D space, accelerations).\n", + "There is nothing special about this organization. I could have used $\\begin{bmatrix}x & y & \\dot{x} & \\dot{y}\\end{bmatrix}^\\mathsf{T}$ or something less logical. I just need to be consistent in the rest of the matrices. I like keeping positions and velocities next to each other because it keeps the covariances between positions and velocities in the same sub block of the covariance matrix. In my formulation `P[1,0]` contains the covariance of of $x$ and $\\dot{x}$. In the alternative formulation that covariance is at `P[2, 0]`. This gets worse as the number of dimension increases (e.g. 3D space, accelerations).\n", "\n", "Let's pause and address how you identify the hidden variables. This example is somewhat obvious because we've already worked through the 1D case, but other problems won't be obvious There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n", "\n", diff --git a/13-Smoothing.ipynb b/13-Smoothing.ipynb index 22ccf45..d439102 100644 --- a/13-Smoothing.ipynb +++ b/13-Smoothing.ipynb @@ -415,7 +415,7 @@ "\n", "* Fixed Interval Smoothing\n", "\n", - "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed interval smoother will collect all the data than estimate the state at each measurement using all available previous and future measurements. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n", + "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed interval smoother will collect all the data, then estimate the state at each measurement using all available previous and future measurements. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n", "\n", "\n", "* Fixed Lag Smoothing\n", diff --git a/README.md b/README.md index 6ed3bc6..c48e016 100644 --- a/README.md +++ b/README.md @@ -14,7 +14,7 @@ The website http://nbviewer.org provides an IPython Notebook server that renders The Preface contains instructions on how to host the book online, for free, on a cloud server (cloud.sagemath.com) that allows you to run and alter the code insde the Notebooks. It takes 5 minutes to set up. -Issues or Questsions +Issues or Questions ------ If you have comments, you can write an issue at GitHub so that everyone can read it along with my response. Please don't view it as a way to report bugs only. Alternatively I've created a gitter room for more informal discussion. [![Join the chat at https://gitter.im/rlabbe/Kalman-and-Bayesian-Filters-in-Python](https://badges.gitter.im/Join%20Chat.svg)](https://gitter.im/rlabbe/Kalman-and-Bayesian-Filters-in-Python?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)