{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Table of Contents](./table_of_contents.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The g-h Filter"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#format the book\n",
"import book_format\n",
"book_format.set_style()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before we start, be sure you understand how to use [Jupyter Notebooks](http://jupyter.org/), and are familiar with the [SciPy](https://scipy.org), [NumPy](http://www.numpy.org/), and [Matplotlib](https://matplotlib.org/) packages, as they are used throughout this book. The Preface contains an introduction to these packages."
]
},
{
"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 co-worker 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 co-worker 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 co-worker. \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 were 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 informs 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 both A and B.\n",
"* We could choose a number greater than both A and 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 the answer is somewhere between A and B. \n",
"\n",
"In mathematics this concept is formalized as [*expected value*](https://en.wikipedia.org/wiki/Expected_value), and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we took one million 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. \n",
"\n",
"$$\\frac{160+170}{2} = 165$$\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 measurements falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 lbs. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import kf_book.book_plots as book_plots\n",
"from kf_book.book_plots import plot_errorbars\n",
"plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A word on how I generated this plot. I import code from the module book_plots in the `kf_book` subdirectory. Generating this plot takes a lot of boilerplate Python that isn't interesting to read. I take this tack often in the book. When the cell is run `plot_errorbars()` gets called and the plot is inserted into the book.\n",
"\n",
"If this is your first time using [Jupyter Notebook](http://jupyter.org/), the code above is in a *cell*. The text \"In [2]:\" labels this as a cell where you can enter input, and the number in the bracket denotes that this cell was run second. To run the cell, click on it with your mouse so that it has focus, then press CTRL+ENTER on the keyboard. As we continue you will be able to alter the code inside the cells and rerun them. Try changing the values \"160\", \"170\", and \"8\" to some other value and run the cell. The printed output should change depending on what you entered.\n",
"\n",
"If you want to view the code for plot_errorbars, either open it in an editor, or create a new cell and type the function name followed by two question marks. Press Ctrl+Enter, and your browser will open a window displaying the source code. This is a feature of Jupyter Notebooks. If you want to just view the documentation for the function, do the same but with one question mark.\n",
"\n",
"```Python\n",
"\n",
" plot_errorbars??\n",
"```\n",
"or\n",
"```Python\n",
" plot_errorbars?\n",
"```\n",
"\n",
"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 169 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": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180))"
]
},
{
"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": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_errorbars([(160, 1, 'A'), (170, 9, 'B')], xlims=(150, 180))"
]
},
{
"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.** I will harp on this for the remainder of the book. We never throw information away, no matter how poor it is. We will be developing math and algorithms that allow us to include all possible sources of information to form the best estimate possible.\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. I will use NumPy, part of the [SciPy](https://scipy.org/) ecosystem for numerical computation."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average of measurements is 164.9353\n"
]
}
],
"source": [
"import numpy as np\n",
"measurements = np.random.uniform(160, 170, size=10000)\n",
"mean = measurements.mean()\n",
"print(f'Average of measurements is {mean:.4f}')"
]
},
{
"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 similar to how a real scale works."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average of measurements is 164.9762\n"
]
}
],
"source": [
"mean = np.random.normal(165, 5, size=10000).mean()\n",
"print(f'Average of measurements is {mean:.4f}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again the answer 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'. 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 measurements 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": 8,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import kf_book.gh_internal as gh\n",
"gh.plot_hypothesis1()"
]
},
{
"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. In fact, there are an infinite number of choices. Shall we give up? Not me! Recall that we are talking about measuring a human's weight. There is no reasonable 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). \n",
"\n",
"The behavior of the physical system we are measuring should influence how we interpret the measurements. If we were weighing a rock each day we'd attribute all of the variance to noise. If we were weighing a cistern fed by rain and used for household chores we might believe such weight changes are real.\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": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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 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.\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"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 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 (I use [polyfit()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html) if you are interested), and just plot the results."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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 co-worker.\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 on 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. This is a thought experiment, the details are not important. Let's see if we can make use of such information if it was available.\n",
"\n",
"The first measurement was 158. We have no way of knowing any different, so let's 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": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\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": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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. And, of course, there would be no reason to ever measure since our predictions are perfect.\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 form estimates from the measurement then the prediction will not affect the result. If we only form estimates 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 bolded 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",
"One more time, this is so important. We agreed that when presented two values with errors, we should form an estimate part way between the two values. It does not matter how those values were generated. In the start of the chapter we had two measurements, but now we have one measurement and one prediction. The reasoning, and hence the math is the same in both cases. We *never* throw information away. I mean it. I see so much commercial software that throws away noisy data. Don't do it! Our prediction of a weight gain might not be very accurate, but so long as there is some information we should use it.\n",
"\n",
"I have to insist you stop and really think about this. All I have done is replaced an inaccurate scale with an inaccurate weight prediction based on human physiology. It is still data. Math doesn't know if the data came from a scale or a prediction. We have two pieces of data with a certain amount of noise, and we want to combine them. In the remainder of this book we are going to develop some fairly complicated math to perform this computation, but the math never cares where the data come from, it only makes computations based on the value and accuracy of those values. \n",
"\n",
"Should the estimate be half way between the measurement and prediction? 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": 15,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\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",
"$$\\mathtt{estimate} = \\mathtt{prediction} + \\frac{4}{10}(\\mathtt{measurement} - \\mathtt{prediction})$$\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 160 lbs."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"previous estimate: 160.00, prediction: 161.00, estimate 159.80\n",
"previous estimate: 159.80, prediction: 160.80, estimate 162.16\n",
"previous estimate: 162.16, prediction: 163.16, estimate 162.02\n",
"previous estimate: 162.02, prediction: 163.02, estimate 161.77\n",
"previous estimate: 161.77, prediction: 162.77, estimate 162.50\n",
"previous estimate: 162.50, prediction: 163.50, estimate 163.94\n",
"previous estimate: 163.94, prediction: 164.94, estimate 166.80\n",
"previous estimate: 166.80, prediction: 167.80, estimate 167.64\n",
"previous estimate: 167.64, prediction: 168.64, estimate 167.75\n",
"previous estimate: 167.75, prediction: 168.75, estimate 169.65\n",
"previous estimate: 169.65, prediction: 170.65, estimate 170.87\n",
"previous estimate: 170.87, prediction: 171.87, estimate 172.16\n"
]
}
],
"source": [
"from kf_book.book_plots import figsize\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 = 1.0 # day\n",
"scale_factor = 4.0/10\n",
"\n",
"def predict_using_gain_guess(estimated_weight, gain_rate, do_print=False): \n",
" # storage for the filtered results\n",
" estimates, predictions = [estimated_weight], []\n",
"\n",
" # most filter literature uses 'z' for measurements\n",
" for z in weights: \n",
" # predict new position\n",
" predicted_weight = estimated_weight + gain_rate * time_step\n",
"\n",
" # update filter \n",
" estimated_weight = predicted_weight + scale_factor * (z - predicted_weight)\n",
"\n",
" # save and log\n",
" estimates.append(estimated_weight)\n",
" predictions.append(predicted_weight)\n",
" if do_print:\n",
" gh.print_results(estimates, predicted_weight, estimated_weight)\n",
"\n",
" return estimates, predictions\n",
"\n",
"initial_estimate = 160.\n",
"estimates, predictions = predict_using_gain_guess(\n",
" estimated_weight=initial_estimate, gain_rate=1, do_print=True) "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[158.0,\n",
" 164.2,\n",
" 160.3,\n",
" 159.9,\n",
" 162.1,\n",
" 164.6,\n",
" 169.6,\n",
" 167.4,\n",
" 166.4,\n",
" 171.0,\n",
" 171.2,\n",
" 172.6]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot results\n",
"book_plots.set_figsize(10)\n",
"gh.plot_gh_results(weights, estimates, predictions, [160, 172])\n",
"weights"
]
},
{
"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. Below 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",
"Walk through this for each day, ensuring you understand how the prediction and estimates were formed at each step. Note how the estimate always falls between the measurement and prediction.\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",
"The results of the filter 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 predict that there is a weight loss of 1 lb a day:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"e, p = predict_using_gain_guess(initial_estimate, -1.)\n",
"gh.plot_gh_results(weights, e, p, [160, 172])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is not so impressive. The estimates quickly divert from the measurements. 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 extreme difficulty in adjusting to that change. Note that it is adjusting! The estimates are climbing even though we tell it we are losing 1 lb a day. It just can't adjust fast enough.\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",
"People really balk at this point, so make sure you are in agreement. Two noisy measurements of weight give us an implied weight gain/loss. That estimate is going to be very inaccurate if the measurements are inaccurate, but there is still information in this computation. Imagine weighing a cow with a scale accurate to 1 lb, and it shows that the cow gained 10 lbs. The cow might have gained 8 lbs up to 12 lbs, depending on the errors, but we know it gained weight, and roughly how much. This is information. What do we do with information? Never throw it away!\n",
"\n",
"Back to my diet. Should we set the new gain/day to 4.4 lbs? Yesterday we thought 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": 19,
"metadata": {},
"outputs": [
{
"data": {
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6YWf3eIkoRMmRQEoIIYQQoizp3h28vOD8+dzHzc2heXNDeVaWyU3tu3jxIlOnGhIwqFQqRo0axXPPPceaNWvYvHkzO3fuJDMzk7Fjx7J9+/ZSqWNsUga7IzdTbd4sWh3awoIR3xHjbMiA18jdgfZdQ0iYOoxhtauiui+Y9fDwACDz9E7cz62A5s8Rl3JvxM3BUsfppdO4fWYXCRV88fb25uTJk9jb29O/f3+mTJlCjx49qFChQsk2WDwRCaSEEEIIIcoSlQq6dYMff8x9XKs1jEadPm1YRxUcDCNHQtu2pVPPQvrpp5/Q3ZmuOH78eKZPn45GoyElJYWPP/6Yli1bcurUKXbs2MHRo0fx8fEpkXqdjb/F6qPXWHX0GseupjJq11+EHtgIwKeHwzn9xXx6+rhRs3LFh17jmWeeoXbt2sTExLBL+ZEP61Wm64uvc0tjxtZVan6Y9hG3MzIAwxqo0NBQZs2aRbdu3bA2sYBY3COBlBBCCCFEabp507Dmydb23rHZs+HnnyEnx/D8/tGoiRPh1i1YvBiaNjWZQOrgwYPGx6+++mquMmtra4YOHcpHH31kPLe4Aim9Xs+xq6msPnqN1ceucfb6LeNUSTMVnAh+idsHIrG0sSJgUE8COtd55DXNzMyYOHEir7zyCgAzpk9j5hcz0Ov16PX3Jvk1bdqUPXv2SPBUTkggJYQQQghRGhITYe5cmD8fJk2Cd965V2ZnB7//Ds8/b3h+dzRKpTJ8ODgYgqkXXsh9zaQk+O47ePFFqP3wzHCl4f6pcBqNJk/5/cfMzMyK9N46nZ4DscnG4Ck2KRPfq6f4aPsfbKzfltjnh9CzsRvdvKtS2c4a2q4BH5/cwe2/0Gq11K5dm3bt2rFz584798ydLKR9+/ZERUVJEFWOSCAlhBBCCFEa4uJg2jTD41mzYNQosLG5Vx4aapjC988/hs/duxuOT54MEybA7t1QrVrua/71F3zyieHjq6/g7bdLpCkF0aZNG6KiogD45ptv+Pbbb41laWlpLFiwwPi8KJJN5Gh17IlJYtXRa6w5do34W1nGsoapV4n89V0A/DXxmL04J3cmxNatH339nBy2bNmCoiiEhYVx/fp1qlevzuDBg0lPT+fEiRNkZ2dTv359/vOf/xAUFFS207uLQpPeFEIIIYQoCTqdIX35XT4+EBQEK1ZAnz6QkZE7kFKpDIHWmDGGz/dn6rOxgc6d897jt9/uPe7UKXdZTg5kZxd4lKWoDR8+nMmTJ6PRaPjuu++4fv06zz33HJs3b+bDDz/k4sWLAHTp0oV69eo91j2ycrRsP3uD1Uevse74dZIz7o1y2Vlb0KWRKz0bu9G5QQ+4FAnR0ZipMGyy26jRI6+v0WjYsGEDiqIQERHBjRs3qFmzJi+++CKhoaG0adOmyEfTRNklgZQQQgghRHE6eRKmTzdMu7szImM0ezZ8/bVhb6j8dO0Kx48X/F6//gp//AF79oCfX+6yVatg8GBDkopx48DXt1DNeFLu7u7MmjWLsWPHAhg3nb2fo6Mj33zzTaGum5Gdw+ZTCaw6eo0NJ+NJy8oxllWqYMHrxNLjxhmqTZ2GtYX5vRd+9hkMGAAvv/yv+3JlZWWxbt061Go1kZGRJCcnU6dOHUaMGEFoaCgtWrTINW1RPD0kkBJCCCGEKC46HfTtaxjxANi7F1q2vFfu5VW096tZEz78MP+y336DtDT45RfD2qsSDqQA3n77bWxtbZkwYQKJiYm5ypo3b86iRYvw9vZ+5HVSMjVsOHmd1Uevsfl0Arc199Yjudpb09PHjZ6N3Wj78RuYLVtmKHj1RUNyjns3NHzkIzMzkzVr1qAoClFRUaSmptKgQQPeeOMNQkNDadq0qQRPQgIpIYQQQohiY2YG779vSFNeqRLExOQOpEqSi4shSYWV1b31VncdOQKRkSWSpOLVV19lyJAhhEdEsvHoJS4lpBDcqyvD+3XCwvzh0+IS07JYd/w6q45eY8e5G2i097LheThXoJePOz0au9HMwwkzsztBTvv2cDeQ+r//g3nzHnr99PR0Vq5ciaIoREdHk56eTpMmTRg3bhyhoaF4e3tL8CRykUBKCCGEEOJJ6fWwaZMhwcMvv4Cj472yV16B27dh+HCwty+lCmIIImbNMkw1tLTMXbZggaHun3wCYWGGtVvFaNPZZL6JqUJcjh1Ugmm70ll4YiMT+3nT08fdeF5cSiZr7mTa2xOThO5e7ERdVzt6+bjR08cNbzd7VGvWQBVPQw7zu157DSIi4NVXYeDAPPVITU1lxYoVqNVqVq1aRWZmJs2aNeOjjz4iJCSEBg0aFONXQZg6CaSEEEIIIZ7UtGnw3/8aHn/3nSGr3l3W1mUne56NTd61UzodLF1qeGxlBf7+ucvT0gwja0WUpGL10ThGLdmP/oHj11JuM2rJfj4LbExGtpZVR69xMPZmrnN8qjvcGXmqSl3XO0HpP/9A/1Gwbx/MmWNY/3VXhQqwcWOuayQnJxMVFYWiKKxZs4bs7Gxat27N5MmTCQkJwauop1uKcksCKSGEEEKIJ/X88/Dpp4agJCrKsE7JVKaBmZnBzp2GJBU3bhimIN7vhx8MKddDQuDjj+ExM+oBaHV6JkcdzxNEAcZjn0QeMx5TqaCFZyV6+rjRo7EbHs75BHO2toYgCmDmTEMa+QoVcp1y48YNIiMjURSFv//+G41GwzPPPMOMGTMIDg6mZs2aj90m8fSSQEoIIYQQoqBycgwBR506hvU3d9WrZxiF8vY2BFWmEkTd9W9JKpYsMYxKLV5sCKSewJ6YJOJSbj/yPJ9qDgxs7UkP76q4OtyXEl6nM2Q/rFLl3rHGjQ17bp07Zwhm72x4e/36dSIiIlAUhY0bN6LT6ejUqRNz584lKCiI6tWrP1FbhJBASgghhBCiIGJiDOnIz583TH97YMoYU6eWSrWKVVYWtGhhaHvDhnlHo1atgv37DWnVC5Ck4kpyRoFu+2onLwL97gt0tFrDZsNTpoCnp+G+9/v5Z7C352pcHGHffYeiKGzduhWVSkVAQADffvstAwYMoGrVqgW6vxAFIYGUEEIIIURBeHreS9KwaRMcPJh3vVF5Y21tCFK+/RauXMlbPn8+rFxpWB+2b1++6cT1ej1Hr6SydO8l1PsuF+i2rvY2uQ/odIYRvwsXDPtq7dkDrVsDcOnSJdRqNYqisGPHDiwsLOjatSv/+9//CAwMpMr9o1dCFCEJpIQQQgghHpSaaggMAgLuHTM3N0x/++MPwxS38h5E3c/GxjCd8X43b8K6dYbHHh55vh6pF66wPOYWvx1O4ERcqvF4jVsJOKan5HsbFWDmVpXWtZ1zF1hawkcfGbLwtW/P+atXUc+ahaIo7NmzBysrK3r06MHixYvp168flR5c5yVEMZBASgghhBDiftOmGdKEazRw8SJUrnyvbOhQQzpzAU5OcOaMIbC0swMzM3Q6PbvOJ/LnP7F0/OJDAk9sxaZ+e+Y+O4wWbb0Z1NSVFp39sE688dDLauzsMV870zB18r408qfbtUMZMQJl/34OBAVhY2ND7969efvtt+nbty8ODg4l0Ggh7nn4rmclYMuWLfTr149q1aqhUqmIiIjIVa5SqfL9mDVrlvGcrKws3nrrLapUqULFihXp378/ly8XbNhYCCGEECKPK1cMoy3p6fDNN7nLTC2JRHG7k6QibsgI5v19hs6zNzL4p92s2XeBHie3Y5+dSeC5Xaz8pA/zBjWjvXc1rL1qo3/I11EPWKbdggMH0M+bx7Fjx5g8eTJNmzalQZMmTPvzT+rVq8eyZctISEhArVYzePBgCaJEqSjVQCo9PR1fX1/mz5+fb3lcXFyujwULFqBSqQgJCTGeM3bsWMLDw/nzzz/Ztm0baWlp9O3bF61WW1LNEEIIIYSpunzZsJnu/T74wJBSe/hweOml0qmXCcjO0bH6aBzDFu7hmRkbmLPuNLFJmdhbW/CyjzM5QcHoHRywDA3GqYqT4UUqFUyZgurBr/l9DqpUfAJ4z5yJj48Pc+bMoWnTpoSHh5OQkMDSpUt57rnnsLOzK5F2CvEwpTq1r1evXvTq1euh5W5ubrmeR0ZGEhAQYNwoLSUlhZ9//plff/2Vrl27ArBkyRI8PDxYv349PXr0KL7KCyGEEMJ0nT8Pn38Ov/wC4eHQt++9spo1DaNSTk6lVr2y7Gx8Gsv2xqLed5nE9Gzj8da1nRnY0oPeTdypYGUOr3SG27ch5YH1UN26GTb+zTa8Vg/sAxSVCsXKinNZWTjZ2zMgJIRZISF069YN6zspzYUoS0xmjdT169eJjo5m8eLFxmP79u1Do9HQvXt347Fq1arh4+PDjh07HhpIZWVlkZWVZXyemmpYAKnRaNBoNMXUgtJxtz3lrV1PA+k70yV9Z5qk30zX4/Sd6sABLBYsAEA3dSra7t1zT9urWNGwRkoAkJ6Vw6pj1/lr3xX2X7ppPO5iZ0VQs2qENq9O7SoV7xzVodHoDA/NzcHZOffX8uhRzLOz2Q0ogBq4CFTW6wns3Jmvx4zB398fKysr40vk57LsKc+/MwvaJpMJpBYvXoy9vT3BwcHGY9euXcPKyipPZpaqVaty7dq1h15r+vTpTJ48Oc/xtWvXYmubz47Z5cC6u1l1hMmRvjNd0nemSfrNdP1b36m0WvTm5vcOmJkR4OmJTWIiMTVrcioqCr2FyfxbVCL0eriYBrvizdh/Q0WWzhBomqHHu5Ketq56vJ0yMM85y4k9ZznxiOtptVpOnjzJzp072eXkxI2bN6kKBAPBKhW+Xl7sGDWKnJwc1q9fX9zNE0WkPP7OzMgo2H5nJvMbY8GCBbz44ovY2Ng88ly9Xo/qXxaDTpgwgXHjxhmfp6am4uHhQffu3cvdYkWNRsO6devo1q0blnf3vhAmQfrOdEnfmaby3G/Xr1/nwoULVKhQgUaNGpWP9sXGwg1D5rccjYbdu3fTpk0bLO62zcUFatRAtXUrZjNmoK9XD91XX+W+Ru3a4OGBl4MDXiVb+zItKT2byENx/LXvMmfi043Hazrb8lyL6gQ1q4arfcGm2uXk5LB161bCwsKIiIjg+vXrVK9enRdeeongGjXo9OGHmAPo9eR8/TW975tlJMq28vw78+5stUcxiUBq69atnDp1iqVLl+Y67ubmRnZ2NsnJyblGpeLj42nfvv1Dr2dtbZ3vXFtLS8ty941wV3luW3knfWe6pO9MU3nqt3379jFp0iSio6PR31nc7+7uzujRo3n//fdNd91JVha0bw/XrwNgCfg/eI6bm2HD3H79ICMDtm7F/NNPoWrVe+c8TftAPYJWp2fb2Rss+yeWtcevodEavl9sLM3o7ePO8608aFPb+V/fqL5Lo9GwYcMGFEUhIiKCGzduULNmTV588UVCQ0Np06YNZmZmoNej++sv2LcPXYsWWPTuLVkRTVB5+p15V0HbYxKB1M8//0yLFi3w9fXNdbxFixZYWlqybt06nn/+ecCQ6e/o0aPMnDmzNKoqhBBClAmrV69mwIABudYEg+Hv5CeffMLGjRuJjo4u0EyPMsfKCjw9ISEBdLq85WZmhg1iXV1h5EiYOxfc3SEmJncgJbicnMFfey/z195YrqbcNh5vUt2R51t50N+3Go4VHv1PZVZWFuvWrUOtVhMZGUlycjJ16tRhxIgRhIaG0qJFi7xBmEqFbupU0l59FdupUzGTIEqYmFINpNLS0jh79qzxeUxMDAcPHsTZ2RlPT0/AMLT2119/MWfOnDyvd3R0ZMSIEbz77rtUrlwZZ2dn3nvvPZo0aWLM4ieEEEI8bZKTk3nhhReMQVSNGjXo27cvsbGxrFq1Cp1Ox4YNG/jss8+YNm1aKdf2MdxJoU3PnvmX63SGcpUK3nvPMPI0aBDIGigAsnK0rD12nWV7Y9l29oYx+7tjBUuCmlXn+ZYeeFd79FKHzMxM1qxZg6IoREVFkZqaSoMGDRg9ejShoaH4+vo+cgRL36ULG+fPp3eXLkXRNCFKVKn+Rtm7dy8BAQHG53fXLQ0dOpRFixYB8Oeff6LX6xk0aFC+1/jyyy+xsLDg+eefJzMzky5durBo0SLM719QKoQQQjxFFi5cSMqdlNN9+/ZFURTjNL4dO3bQuXNncnJy+PHHH/nkk0+oUKFCaVb38XTvDq1awf79cP/ekWZm0KKFoRwMI1FDhpROHcuYk9dSWfpPLBEHrpCccS8r2TN1K/N8Sw96NHbDxvLf/39KT09n5cqVKIpCdHQ06enp+Pj4MG7cOEJDQ/H29i7Q9D8hyoNSDaT8/f2Nc7Yf5rXXXuO11157aLmNjQ3z5s1j3rx5RV09IYQQwiStXLnS+HjmzJm51kK1b9+e5557jj/++IOkpCR2796Nv79/KdTyCT1sVOr+0SjBrdsaog7FsXRvLIdibxqPuznY8FzLGjzXwgPPyv+esTg1NZXo6GgURWHVqlVkZmbSrFkzPvroI0JCQmjQoEExt0KIsknGuIUQQohy5tatW8bHdevWzVNev379fM81OXdGpfT79xvSm5uZoWre/N5o1FNKr9ez92IyS/+JJfpwHJkaw4idhZmKro2qMrCVB53qu2Bu9vBgMzk5maioKBRFYc2aNWRnZ9O6dWsmT55MSEgIXl6S51AICaSEEEKIcqZmzZrs2bMHMIxOBQYGGsv0ej3R0dHG53fXJJukO6NSqjujUiqdDqZOfWpHoxJuZaHef5lle2M5n3AvbXkdl4q80MqToObVqWL38EyNN27cIDIyEkVR+Pvvv9FoNLRv354ZM2YQHBxMzZo1S6IZQpgMCaSEEEKIcubll1/mr7/+AuCNN97A1taWrl27kpSUxOTJk9m7dy8Avr6+NG3atDSr+vj0ekPA1L07uhYtMLuTQtusHI1GaXV69sQkEX/rNq72NrSu7ZxnFClHq2Pz6QSW/hPLhpPx5OgMSyZsrczp29Sdga08aO5Z6aHrlq5fv05ERASKorBx40Z0Oh2dOnVi7ty5BAUFUb169WJvpxCmSgIpIYQQopzp1asXbdu2ZdeuXVy5coXu3btjb29Peno6uvvShU+ePNk0EwOkpYG/P7z5Jrz8crlMob36aByTo44Td19KcndHGyb286anjzsXE9NZtjcWZd9lrqfeS3HfzNOJgS096OtbDTvr/P/Nu3r1KmFhYSiKwtatW1GpVPj7+zN//nwGDBiAm5tbsbdPiPJAAikhhBCinDE3NycyMpI+ffoYR5/uXwtlbm7OvHnzck35MynTpsG+fTBsGBw7hn7atHKVQnv10ThGLdnPg+m4rqXcZuSS/dSvasfp62nG484VrQhqVp2BrTyoX9U+32teunQJtVqNWq1m+/btWFhY0LVrV/73v/8RGBhIlSpVirFFQpRPEkgJIYQQ5ZCrqys7duwgLCyMBQsWcO7cOSpUqEDXrl0ZPXo09erVK+0qPh69Hi5eNDy2soJ/yexrirQ6PZOjjucJogDjsbtBVKf6LrzQyoOujapiZWGW5/zz58+jVqtRFIU9e/ZgZWVFjx49WLx4Mf369aNSpUrF1xAhngISSAkhhBDllKWlJQMHDmTgwIGlXZWio1LBb78ZRqNOnoR69UCjefTryrjbGi0XEtNZdeRarul8DzNvUDP6+VbLc/z06dMoioKiKBw4cAAbGxt69+7N22+/Td++fXFwePRGu0KIgpFASgghhBCmp2tXw4eJScnQcDbhFufi0zmbkMa5+DTOJqQRm5SB7t+31sxFd2cfTr1ez/Hjx1EUBbVazZEjR6hYsSJ9+vRhwoQJ9OrVCzs7u2JqjRBPNwmkhBBCCCGKkF6v52rKbUOQFJ/GuYR7n2+kZT/0dfbWFrg6WHPuvtTlD7t+yuWzfKL+AUVROHnyJPb29vTv35/PPvuMHj16UKFChaJulhDiARJICSGEEKLsW7IEGjWCFi1KuyZG2Tk6LiSm5w6YEtI4n5BORrb2oa9zd7ShjosddV3tqONSkTqudtR1scPF3hqdHjp8sYFrKbdzrZPS6/VkXztLxqntZJ3ZwdCZV3FyciIwMJBZs2bRrVs3rK0fvkeUEKLoSSAlhBBCiLItNhZefx0yM2HUKJg/v0Q33U29rTEESnem4Z2LT+dcQhqXkjLQPmQ+noWZipqVbe8ES4agqa6rHV4udg9NSw5groKJ/bwZtWQ/6HVkXT1FxqkdpJ/ajjY1HrMKDnTv3Zexr75MQEAAVlZWxdVsIcQjSCAlhBBCiLLtyy8hI8Pw2Nw8VxCl1enZHZPEvhsqKsck0a6ua55NawtCr9dzLfW2Ye1S/C3OJaQbR5nib2U99HV21hbGUaV7o0x21Kxsi6V53kx6j6LVaqmYfBbfy+GsiookO/UGZhWdsK3fHo/mAcx6cyB9/DwKfV0hRNGTQEoIIYQQZduMGVC9Onz/PUyebDyce9Nac345szfXprX50Wh1XExM5+ydUaV7o0xppP/LdLyqDta5AqW7n6s6WD/xpsY5OTls2bIFRVEICwvj+vXrVK9enddefoFG7bvjVt8Xd6eKtK7t/FhBohCieEggJYQQQoiyzcoK3n0X3n4bLAz/uvzbprWjluxn7vO+1HaxyxUonU1I41JiBjkPmY5nbqaiprOtYc3SfQGTl0tFHGwsi7RJGo2GDRs2oFarCQ8P58aNG3h6evLiiy8SGhpKmzZtMDMr/IiWEKLkSCAlhBBCCNNwJ4gqyKa17yw79NDL2FqZ50r2cG86XsV8N7YtKllZWaxfvx5FUYiMjCQ5ORkvLy9GjBhBSEgILVu2fOLRLSFEyZFASgghhBBlT2Ki4XPlynmK9sQkFWjTWscKljRyt88zHc/d0abEApbMzEzWrFmDoihERUWRmppKgwYNGD16NKGhofj6+krwJISJkkBKCCGEEGXP+PEQHg5Tp8JrrxmSTNwRf+vRQRTAZ4GNCfSrXlw1fKj09HRWrlyJWq1mxYoVpKen4+Pjw7hx4wgNDcXb21uCJyHKAQmkhBBCCFG27NkDP/9sePzhhxASAq6uxuLEtIdn0bufq71NcdQuX6mpqURHR6MoCqtWrSIzM5NmzZrx0UcfERISQoMGDUqsLkKIkiGBlBBCCCHKFg8PeOklwya8kycbg6gcrY5vNpxl3t9n/vXlKsDN0YbWtZ2LtZo3b95k+fLlKIrCmjVryM7OplWrVkyaNImQkBDq1KlTrPcXQpQuCaSEEEIIUba4u8Ovv8Kbb0Lz5gBcuZnJ2D8P8M+FZADaeVVm13nDOqr7k07cnTA3sZ93saQKT0xMJDIyEkVRWL9+PRqNhvbt2zNjxgyCg4OpWbNmkd9TCFE2SSAlhBBCiLKpTRsAVh2JY7z6MKm3c7CztuDzIB8C/ao/sI+Ugdsj9pF6HNevXyciIgJFUdi4cSM6nY5OnToxZ84cgoODqV695NdhCSFKnwRSQgghhCgb9Hq4LwlDZraWKdHH+X33JQB8PZyY90IzPCvbAtDTx51u3m7sPBvP2q276d6xDe3quhbJSNTVq1cJCwtDrVazZcsWVCoV/v7+zJ8/nwEDBuDm5vbE9xBCmDYJpIQQQghR+o4cgREj4Msv4ZlnOHXtFm/9sZ/T19MAGNm5Du92r4+lee59nszNVLSp7UziCT1tajs/URB16dIlwsLCUBSFHTt2YG5uTteuXfnf//5HYGAgVapUeaImCiHKFwmkhBBCCFG69Hp46y345x/o0IGNX/yPkak1yMrR4WJvzdznfelYz6VYbn3+/HnUajWKorBnzx6srKzo0aMHCxcupH///lSqVKlY7iuEMH0SSAkhhBCidCUmws2bACS4VmdkfBWyLHT4N3Bh9nO+VLGzLtLbnT59GkVRUBSFAwcOYGNjQ69evfjtt9/o27cvDg4ORXo/IUT5ZPboU4rPli1b6NevH9WqVUOlUhEREZHnnBMnTtC/f38cHR2xt7enbdu2XLp0yVh+7do1hgwZgpubGxUrVqR58+YoilKCrRBCCCHEE6lShd3L1jCr/1u81/k1dNbW/LdPIxYMbVVkQdTx48f57LPPaNq0KQ0aNODzzz+nXr16LFu2jISEBMLCwhg8eLAEUUKIAivVEan09HR8fX0ZNmwYISEhecrPnTtHhw4dGDFiBJMnT8bR0ZETJ05gY3Nvg70hQ4aQkpLC8uXLqVKlCr///jsDBw5k7969NGvWrCSbI4QQQohCytHqmLfhLPM2nEHXqAe1q1QkfFAzfKo7PtF19Xo9hw8fNo48nTx5Ent7e/r378/kyZPp0aMHtra2RdQKIcTTqFQDqV69etGrV6+Hln/88cf07t2bmTNnGo95eXnlOmfnzp18//33tG7dGoD//ve/fPnll+zfv18CKSGEEKIMu3ozk7F/HmTPhSQAQprX4LPAxlS0frx/T/R6PXv37kVRFNRqNWfPnsXJyYnAwEBmzZpFt27dsLYu2mmCQoinV5ldI6XT6YiOjuaDDz6gR48eHDhwgNq1azNhwgQGDBhgPK9Dhw4sXbqUPn364OTkxLJly8jKysLf3/+h187KyiIrK8v4PDU1FQCNRoNGoymuJpWKu+0pb+16GkjfmS7pO9Mk/Vay1h6/zrHxU4mp24GKlaswuZ83gb7ugL5QfaDT6dixYwcLFy5kzJgxXLp0icqVKxMYGMhXX32Fv78/VlZWxvOlf8sW+bkzXeW57wraJpVer9c/+rTip1KpCA8PNwZJ165dw93dHVtbW6ZOnUpAQACrV6/mo48+YuPGjXTu3BmAlJQUBg4cyJo1a7CwsMDW1hZFUejWrdtD7zVp0iQmT56c5/jvv/8uw/xCCCFEMcrWQsRFM6x27GOhMpl06wrse2UEyb26FvgaWq2WkydPsnPnTnbu3EliYiJOTk60bduWdu3a4ePjg7m5eTG2QghRnmVkZDB48GBSUlL+dd1kmR6RAggMDOSdd94BwM/Pjx07dvDDDz8YA6n//ve/JCcns379eqpUqUJERATPPfccW7dupUmTJvlee8KECYwbN874PDU1FQ8PD7p3717uFplqNBrWrVtHt27dsLS0LO3qiEKQvjNd0nemSfqt+J2+fouxyw5z5noaEdv/AKBiVibtn2mNvnfvf31tTk4OW7duJSwsjMjISK5du0a1atV44YUX6N+/P2lpafTs2VP6zsTIz53pKs99d3e22qOU2UCqSpUqWFhY4O3tnet4o0aN2LZtG2BIRjF//nyOHj1K48aNAfD19WXr1q18++23/PDDD/le29raOt850paWluXuG+Gu8ty28k76znRJ35km6beip9fr+W33JaasOE5Wjo4q9jZkhkXAgi/h7FksXnoJVHk30tVoNGzcuBFFUQgPD+fGjRt4enoyePBgQkJCaNu2LWZmZmg0GlauXCl9Z8Kk70xXeey7granzAZSVlZWtGrVilOnTuU6fvr0aWrWrAkYht0AzMwe2OXc3Nw4oiWEEEKI0nMzI5sP1UdYfewaAJ3ruzDn+Tt7Q7X9H2g0uYKorKws1q9fj6IoREZGkpycjJeXFyNGjCAkJISWLVuiyifoEkKIklaqgVRaWhpnz541Po+JieHgwYM4Ozvj6enJ+++/z8CBA+nUqZNxjVRUVBSbNm0CoGHDhtStW5fXX3+d2bNnU7lyZSIiIli3bh0rVqwopVYJIYQQAmBPTBJj/zzA1ZTbWJqrGN+zIcOfqY2Z2X2BkKUlmZmZrFmzBkVRiIqKIjU1lQYNGjB69GhCQ0Px9fWV4EkIUeaUaiC1d+9eAgICjM/vrlsaOnQoixYtIigoiB9++IHp06czZswYGjRogFqtpkOHDoBh2G3lypV8+OGH9OvXj7S0NOrWrcvixYvp/Yi51kIIIYQoHlqdnvkbzvL136fR6aFWZVvmDWpOE10KaHPAzJL09HRWrVqFoiisWLGC9PR0fHx8GDduHKGhoXh7excoeLp06RLbtm1j7969VK9enZYtW5ZAC4UQopQDKX9/fx6VNHD48OEMHz78oeX16tVDrVYXddWEEEII8Riu3sxk7NKD7Im5tzfU5MDG2JlDatN2RKemotSuzap9+8jMzKRZs2ZMmDCBkJAQGjZsWOD7XLx4kbFjx7J8+XLjdP4vv/ySVq1aMWfOHDp27Fgs7RNCiLvK7BopIYQQQpiW1UevMV59mJRMDRWtzPk8qAn+tSsStvR31LNmsebECbKAVsnJTJo4kZDQUOrUqVPo+8TExPDMM88QFxeXp+yff/6hS5cuREZG0qtXryJolRBC5E8CKSGEEEI8kdsaLVOjj7Nk1yUAGlaCZ21i+N/H3/D8+vVoNBraN23KdE9Pgi9douaGDdCmzWPfb+TIkcYgqmrVqrzyyivExcWxf/9+jh49ikaj4eWXX+bSpUtUqFChSNoohBAPkkBKCCGEEI/t9PVbvPX7AY6fv0TGmV04X9/P+iN7WKvT0alTJ+bMmUNwcDDVq1cHnQ62b3+iIOr06dOsXbsWgBo1anDgwAEcHR1ZuXIlP/zwA0FBQaxZs4YbN26wdOlSXnnllSJqqRBC5CaBlBBCCCEKTa/X8130Xj6bv5CUE9vIij2GuZmKZv7+vDt/PgMGDMDNzS33i8zM4AnXLm3ZssX4eNSoUVSpUgWNRgOAhYUFEyZMYM2aNQBs2rRJAikhRLGRQEoIIYQQBXbp0iV++/Mvvvn5V66dPgxmZlTzbs37877lpYGhVKlS5d7Jen2+G+0+iaysLONjFxeXPOWurq75niuEEEXN7NGnCCGEEOJpdv78eWbNmkWbNm2oWbMmH380gRSdNa59x/Ll8n+IPbSdsW+MzB1EASxaBM8/D5cuFVldGjRoYHy8dOnSPNl///zzz3zPFUKIoiYjUkIIIYTI4/Tp06jVahRFYf/+/djY2FC/RUdc+r2HTZ3WeFWrwjeDmtG0hlP+F7h5E8aPh4QEiI6GkyfBw+OJ6xUQEEDNmjW5ePEif//9N8OHD2fs2LEkJiYyY8YMpk2bBoBKpZJpfUKIYiWBlBBCCCEAOH78OIqioCgKR44cwdbWlr59+/L6mHGsvunG/rjb2ALBzarz2QAf7Kz/5d+IkyfvPe7du0iCKABzc3NmzZrF888/D8CiRYtYtGhRnvPGjBlDrVq1iuSeQgiRH5naJ4QQQjyl9Ho9hw4d4pNPPqFRo0Y0btyY2bNn06RJE8LCwkhISGDEp1/z3UUX9sfdpqKVOXOf92XuQL9/D6IA2raF06fhnXdgzpwirfdzzz3Hzz//jI2NTb7lb775JnOK+J5CCPEgGZESQgghniJ6vZ59+/YZp+2dPXsWJycnAgMDmTVrFl27dsXGxobbGi3TVp7gl50XAWhaw5FvXmhGrSoVC34zJyeYO7dY2jF8+HD69evHwoUL2bJlC3FxcXTu3JnXXnuNhg0bFss9hRDifhJICSGEEOWcTqdjz549xml7Fy9epHLlygQFBTFv3jyeffZZrKysjOefuX6Lt/44wMlrtwB4rZMX73VvgJVF2ZrI4uLiwgcffMA777zDypUr6d27N5aWlqVdLSHEU0ICKSGEEKIc0mq17NixA0VRCAsL4/Lly1StWpWgoCBCQ0Pp3LkzFha5/w3Q6/X8sSeWz1Yc47ZGRxU7K+Y870fn+nnTjOcrPR1+/BFGj4aHTLsTQojyQgIpIYQQopzIyclhy5YtqNVqwsLCuHbtGtWqVSMkJITQ0FCeeeYZzM3N831tSoaGCeGHWXnkGgAd61VhzvO+uNoXIiCaPh0+/xy++w5+/RXatSuKZgkhRJkkgZQQQghhwjQaDRs3bkRRFMLDw7lx4waenp4MHjyYkJAQ2rZti5nZv0/J23cxiTF/HOTKzUwszFR80LMB/+nghZlZITbTTU6GL780PL50CSpXfoJWCSFE2SeBlBBCCGFisrKyWL9+PYqiEBkZSXJyMl5eXgwfPpzQ0FBatmyJSvXoIEir0/PdxrN89fcZtDo9NSvb8s0LzfD1cCp8pSpVgl274K23DBn76tcv/DWEEMKESCAlhBBCmIDMzEzWrl2LoigsX76c1NRU6tevz+jRowkNDcXX1/ehwZNWp2dPTBLxt27jam9D69rOxN+6zdg/D7I7JgmAoGbVmfKovaEepUkT2LgRcnIe/xpCCGEiJJASQgghyqj09HRWrVqFoiisWLGC9PR0fHx8GDduHCEhITRu3PiRI0+rj8YxOeo4cSm3jccq2VqSlaMjI1uLrZU5Uwf4ENy8RtFUWqUCyZxXJPR6PceOHSMxMRFXV1caNmxYoJFGIUTJkEBKCCGEKENSU1OJjo5GURRWrVpFZmYmzZo1Y8KECYSEhBRqj6TVR+MYtWQ/+geOJ2doAPBwrsAvw9tQuzB7Qz3owgWoVevxXy/y0Ov1LFq0iJkzZ3Ly5Enj8SZNmjBhwgQGDRpUirUTQtxVqEAqJSWF8PBwtm7dyoULF8jIyMDFxYVmzZrRo0cP2rdvX1z1FEIIIcqtmzdvsnz5ctRqNWvWrCErK4tWrVoxadIkQkJCqFOnTqGvqdXpmRx1PE8Qdb8crR5PZ9vHr/jly+DjA/7+8NVXULfu419LAIYg6t133+XLu4k77nPkyBEGDx7MqVOnmDRpUslXTgiRS4F21ouLi+PVV1/F3d2dzz77jPT0dPz8/OjSpQs1atRg48aNdOvWDW9vb5YuXVrcdRZCCCFMXmJiIgsWLKB37964uroydOhQbty4wbRp07hw4QJ79uzhgw8+eKwgCmBPTFKu6Xz5iUu5zZ47a6Qey/vvG/aOio6Gb755/OsIo6ioqFxBVMeOHRk3bhxt27Y1Hps8eTIbN24sjeoJIe5ToBEpX19fXn75Zfbs2YOPj0++52RmZhIREcHcuXOJjY3lvffeK9KKCiGEEKYuPj6e8PBwFEVh48aN6HQ6OnbsyJw5cwgODqZ69epFd69b/x5EFfa8fAUGwpYtkJUFMkJSJL7++mvj42+//ZbRo0cbn8+YMYMJEyYYzwsICCjx+gkh7ilQIHXs2DFcXP59V/MKFSowaNAgBg0aREJCQpFUTgghhDB1V69eNQZPW7ZsQaVS4e/vz/z58xkwYABubm7Fct+CbqRbqA13H/TCC9C3Lxw7Bs7Oj38dAcDt27eNI021a9dm5MiRucrvTvmLj49n9erV6PV6ST4hRCkqUCD1qCDqSc8XQgghypPY2FjUajWKorBjxw7Mzc3p2rUr//vf/wgMDKRKlSrFXgfvag5YmKnI0eW/SkoFuDkaUqE/ETs7aNPmya4hAMPsHr3e0F9eXl55NlK2tLSkZs2axMfHk5WVhVarxcJC8oYJUVoKtEbqfosXLyY6Otr4/IMPPsDJyYn27dtz8eLFIq2cEEIIYSrOnz/PrFmzaNu2LZ6enowfP55KlSqxcOFC4uPjWbVqFSNGjCiRIEqj1THmjwP/GkQBTOznjbmZjGiUFQ4ODjg6OgKwY8cOEhMTc5VfvnyZAwcOAFCtWjUJooQoZYUOpKZNm0aFChUA2LlzJ/Pnz2fmzJlUqVKFd955p8grKIQQQpRVp0+fZvr06bRo0YI6derw6aefUq1aNX777TcSEhKIiopi6NChVKpUqcTqpNfr+Tj8CJtPJ1DB0pwPezbE3TH39D03Rxu+f6k5PX3cC3+Dt96C//7XkGRCFClzc3OGDBkCGEanQkJCOHHiBACHDh0iNDSUnDubHb/yyiulVU0hxB2FfisjNjaWunfSm0ZERBAaGsprr73GM888g7+/f6GutWXLFmbNmsW+ffuIi4sjPDycAQMG5DrnxIkTjB8/ns2bN6PT6WjcuDHLli3D09PTeM7OnTv5+OOP2b17N5aWlvj5+bFq1SpjwCeEEEIUlePHj6MoCoqicOTIEWxtbenTpw/jx4+nd+/e2NnZlWr9vv77DMv2XsZMBfMHN6NLo6q82smLPTFJxN+6jau9YTrfY41E7d0L334Lej1ERMDhw2BW6Pdkxb949913+fXXX0lJSWHz5s14e3tTsWJF0u8LXF1dXXnrrbdKsZZCCHiMQMrOzo7ExEQ8PT1Zu3atcRTKxsaGzMzMQl0rPT0dX19fhg0bRkhISJ7yc+fO0aFDB0aMGMHkyZNxdHTkxIkT2Njce2dt586d9OzZkwkTJjBv3jysrKw4dOhQnnnFQgghxOPQ6/UcPnwYRVFQq9WcOHECe3t7+vXrx+TJk+nRowe2tk+wF1MRWrY3lq/WnwFgygAfujSqCoC5mYp2dSo/+Q327wcLC9BoYPhwCaKKQa1atVi9ejX9+/c3Ju+6P4iqVq0a0dHRxZakRAhRcIUOpLp168Z//vMfmjVrxunTp+nTpw9gyOxXq5A7m/fq1YtevXo9tPzjjz+md+/ezJw503jMy8sr1znvvPMOY8aM4cMPPzQeq1evXqHqIYQQQtxPr9ezf/9+48jT2bNncXJyIjAwkJkzZ9K1a9dcb+qVBZtPJzAh7AgAbwTU4cU2NYv+Jq+9Bp07GzbflRGRYtO2bVtOnz7NokWLUBSFxMREXFxceOGFFxgyZAj29valXUUhBI+xRurbb7+lXbt2JCQkoFarqVzZ8A7Xvn37GDRoUJFVTKfTER0dTf369enRoweurq60adOGiIgI4znx8fHs3r0bV1dX2rdvT9WqVencuTPbtm0rsnoIIYR4Ouh0Ok6dOsX48ePx8vKiZcuW/N///R/+/v6sWrWK69evs2jRIvr27VvmgqijV1IYvWQfWp2e4GbVea97g+K7WYMG8P33YGlZfPcQODk5MXbsWLZt28aJEyfYsmULo0ePliBKiDKk0CNSTk5OzJ8/P8/xyZMnF0mF7oqPjyctLY0ZM2YwdepUvvjiC1avXk1wcDAbN26kc+fOnD9/HoBJkyYxe/Zs/Pz8+OWXX+jSpQtHjx596MhUVlYWWVlZxuepqakAaDQaNBpNkbajtN1tT3lr19NA+s50Sd+ZDq1Wy86dOwkLCyM8PJwrV67g4uJCUFAQwcHBdOrUKVdmtLLYp5eTMxm2cA/p2VraezkzpX8jY0KCp4X8zJku6TvTVZ77rqBtUunvblhQCMnJyfz888+cOHEClUpFw4YNGT58OM5PsBmfSqXKlWzi6tWrVK9enUGDBvH7778bz+vfvz8VK1bkjz/+YMeOHTzzzDNMmDCBadOmGc9p2rQpffr0Yfr06fnea9KkSfkGfr///nuZmecuhBCieGi1Wo4fP86OHTvYtWsXycnJODs7065dO9q3b0/Dhg0xNzcv7WoWSLoGvj5mzvVMFe62et5urKVCEWfEto+NxS42lrh27UA2fxVCPAUyMjIYPHgwKSkpODg4PPS8Qv+63bx5M/3798fR0ZGWLVsCMG/ePKZMmcLy5cvp3Lnz49f6PlWqVMHCwgJvb+9cxxs1amScuufubkjbmt85ly5deui1J0yYwLhx44zPU1NT8fDwoHv37v/6xTJFGo2GdevW0a1bNyxlGoZJkb4zXdJ3ZY9Go2HTpk2EhYURGRnJjRs38PT05OWXXyY4OJg2bdqg1WpNqt+yNFpeWbyP65k3cXOwZulrbfKkOX9iej3mPXtitnEjuoAAtIsWgftjpEwvZvIzZ7qk70xXee67u7PVHqXQgdQbb7zBwIED+f77743v2Gm1WkaPHs0bb7zB0aNHC3vJfFlZWdGqVStOnTqV6/jp06epWdOwgLZWrVpUq1Yt33P+LYmFtbU11tbWeY5bWlqWu2+Eu8pz28o76TvTJX1XurKysli/fj1qtZqIiAiSk5Px8vJi+PDhhIaG0rJlS1T3jbDcncphCv2m0+kZ/9cR9l68ib2NBYuHt8GzSjGsndm40fABmF24gJmra5leG2UKfSfyJ31nuspj3xW0PYUOpM6dO4darc417cHc3Jxx48bxyy+/FOpaaWlpnD171vg8JiaGgwcP4uzsjKenJ++//z4DBw6kU6dOBAQEsHr1aqKioti0aRNgmA74/vvvM3HiRHx9ffHz82Px4sWcPHkSRVEK2zQhhBAmLjMzk7Vr16IoCsuXLyc1NZX69eszevRoQkND8fX1zRU8marpq04QfTgOS3MVPw5pQQO3YkpA4O8P4eHwzjvw5ZdQxpJsCCFEaSp0INW8eXNOnDhBgwa5MwKdOHECPz+/Ql1r7969BAQEGJ/fnW43dOhQFi1aRFBQED/88APTp09nzJgxNGjQALVaTYcOHYyvGTt2LLdv3+add94hKSkJX19f1q1bR506dQrbNCGEECYoPT2dVatWoSgKK1asID09HR8fH9555x1CQ0Np3LhxuQie7lqwLYb/2xoDwOznfGlfp0rx3UylggEDoFcvsLIqvvsIIYQJKlAgdfjwYePjMWPG8Pbbb3P27Fnatm0LwK5du/j222+ZMWNGoW7u7+/Po3JdDB8+nOHDh//rOR9++GGufaSEEEKUb7du3WLFihWo1WpWrlxJZmYmfn5+TJgwgZCQEBo2bFjaVSwWq47EMSX6OADjezYk0K96ydw4n+nwQgjxtCtQIOXn54dKpcoV9HzwwQd5zhs8eDADBw4sutoJIYQQd9y8eZOoqCgURWHNmjVkZWXRqlUrJk2aREhISLmfibD3QhJvLz2IXg9D2tZkZGevR7/ocV26BJ6exXd9IYQoBwoUSMXExBR3PYQQQog8EhMTiYyMRFEU1q9fj0ajoX379kybNo3g4GBq1apV2lUsEecS0vjPL3vJztHRtVFVJvUvxumKq1ZB//4wZgxMnAjlLJutEEIUlQIFUnez5AkhhBDFLT4+noiICBRFYcOGDeh0Ojp27MicOXMIDg6mevUSms5WRsTfus3QBXu4maHBz8OJeYOaYW5WTEFUVha8/Tbk5MDcudCyJQwaVDz3EkIIE1egQGr58uUFvmD//v0fuzJCCCGeTlevXiU8PBxFUdiyZQsAAQEBzJ8/nwEDBuDm5lbKNSwd6Vk5jFi0l8vJmdSqbMvPQ1tSwaoYNwvW6+HFF2HGDEMQ9cILxXcvIYQwcQUKpAYMGFCgi6lUKrRa7ZPURwghxFMiNjYWtVqNoijs2LEDc3NzunTpwo8//khgYCAuLi6lXcVSlaPV8ebv+zlyJQXnilYsGtaaynbFnPTBxsYwnW/oUMjONmTtE0IIka8CBVI6na646yGEEOIpEBMTYwyedu/ejZWVFd27d2fhwoX079+fSpUqlXYVywS9Xs8nkUfZeCoBG0szfh7aklpVKpZcBZ6StWdCCPEkCr2PlBBCCFEYp0+fNgZP+/fvx8bGhl69erFkyRL69u2Lo6NjaVexzJm/4Sx/7InFTAXzBjWnmacEmEIIUdaYFeSkP//8s8AXjI2NZfv27Y9dISGEEKbv+PHjfPbZZ/j6+tKgQQOmTp1KnTp1WLp0KQkJCYSFhfHiiy9KEJUPZd9l5qw7DcDkQB+6eVct3hvm5Bg23P31V8MaKSGEEAVSoEDq+++/p2HDhnzxxRecOHEiT3lKSgorV65k8ODBtGjRgqSkpCKvqBBCiLJLr9dz6NAhPv30U7y9vWncuDGzZ8/Gx8eHsLAwEhISWLZsGc8//zx2dnalXd0ya+uZBD5UHwZgZOc6DGlbAllzf/wRVq+Gl1+GUaOK/35CCFFOFGhq3+bNm1mxYgXz5s3jo48+omLFilStWhUbGxuSk5O5du0aLi4uDBs2jKNHj+Lq6lrc9RZCCFHK9Ho9+/fvR1EUFEXh7NmzODk5ERgYyBdffEG3bt2wsbEp7WqajGNXUxi1ZD85Oj2BftX4oEeDkrnxvn33Hg8dWjL3FEKIcqDAa6T69u1L3759SUxMZNu2bVy4cIHMzEyqVKlCs2bNaNasGWZmBRrgEkIIYaJ0Oh179uxBURTUajUXLlygcuXKDBgwgHnz5vHss89iZWVV2tU0OVduZjJs4T+kZeXQzqsyM0ObYlZce0U9aMECGDgQtm+Hdu1K5p5CCFEOFDrZROXKlQkMDCyOugghhCiDtFotO3bsQK1Wo1aruXz5Mq6urgQHBxMaGkrnzp2xsJDcRY8rJUPDKwv2EH8ri/pV7fhhSAusLYpxr6j89Ohh+BBCCFFg8pdPCCFEHjk5OWzduhVFUQgLC+PatWtUq1aNkJAQQkJC6NChA+bmJfzPfjmUlaPltV/3ciY+jaoO1iwa1hrHCpalXS0hhBAFIIGUEEIIADQaDRs3bkRRFCIiIkhISMDT05NBgwYRGhpK27Zty+UUbr1ez4YNGwgPD+fYsWNs27aNIUOG0LRp02K9r06n572/DrM7Jgk7awsWDWtNNacKxXpPo1WrwN0d/PxK5n5CCFEOSSAlhBBPsaysLNavX49arSYiIoLk5GS8vLwYNmwYoaGhtGzZEpWqhNbqlILz588TEhLCwYMHjcc2bdrE7Nmz6d+/P7/88kuxpWj/YvVJog5dxcJMxY9DWtDI3aFY7pNHSgq88grcuAGvvw7ffAMyNVMIIQpNfnMKIcRTJjMzk7Vr16IoCsuXLyc1NZX69eszatQoQkND8fPzK9fB013Xr1/H39+f2NjYfMuXL19Ov379+Pvvv7G0LNrpdot3XODHLecBmBnalGfqVinS6/+refMgPt7w+Pp1CaKEEOIxFfq352effcZ7772Hra1truOZmZnMmjWLTz/9tMgqJ4QQomikp6ezatUqFEUhOjqatLQ0GjduzDvvvENoaCiNGzd+KoKn+82YMcMYRNWrV49PP/2UmzdvotVqmTx5MsnJyWzdupU///yTIUOGFNl9Vx+9xqSoYwC836MBwc1rFNm184iNhYSE3Me6djUEUr/+Cu+/X3z3FkKIcq7QgdTkyZMZOXJknkAqIyODyZMnSyAlhBBlxK1bt4iOjkZRFFauXElmZiZ+fn58+OGHhISE0LBhw9KuYqnJzs5m0aJFANjY2LBx40ZcXV1ZuXIlvXv3xtvbm+7duwPwf//3f0UWSO27mMzbfx5Ar4fBbTwZ7V+nSK6br6wsaNXKMOr0MEFBcOECWFsXXz2EEKKcKnQgpdfr833X8tChQzg7OxdJpYQQQjyemzdvEhUVhaIorFmzhqysLFq1asWkSZMICQmhTp1i/MfdhFy5coWbN28C0K1bN6pXr45GozGWd+3alerVq3PlyhWOHDlSJPc8n5DGfxb/Q1aOji4NXfmsfzGPAlpZgaenYURKp8tbbmYGHh6G84QQQhRagQOpSpUqoVKpUKlU1K9fP9cvf61WS1paGiNHjiyWSgohhHi4xMREIiMjURSF9evXo9FoaNeuHdOmTSM4OJhatWqVdhXLnPv3vcrIyMhTrtVquX37NkCRpHm/kZbFKwv/ITlDQ9Majswb3AwL82LOgKhSwZQp0LNn/uU6naH8KZvSKYQQRaXAgdRXX32FXq9n+PDhTJ48OVcWIysrK2rVqkU72RFdiCJx5MgR9uzZw5EjR6hdu3axp2EWpic+Pp6IiAgURWHDhg3odDo6duzInDlzCAoKokaNYlx3Uw5Ur16dGjVqcPnyZTZs2MD+/ftp0qSJsfzXX38lMTERgPbt2z/RvTKycxix6B8uJWXg6WzLz0NbYWtVQgkeuneH5s1h//7cx83NDcfvTF8UQghReAX+TT506FAAateuTfv27Ys8g5EQAv755x/efvttdu7caTz29ddf07lzZ7755hsJqJ5yV69eJTw8HEVR2LJlCwABAQHMmzePoKAg3NzcSrmGpsPMzIyRI0fy3//+F71eT0BAAK+//jo6nY7ly5ezePFi47mjR49+7PvkaHW89fsBDl1OoZKtJYuGtcLFvgTXI6lU0LFj3kBKq5XRKCGEeEKFfkusc+fO6HQ6Tp8+TXx8PLoH5l136tSpyConxNNk+/btdOvWjczMzDxlmzdvpkOHDmzatInmzZuXQu1EaYmNjUWtVqNWq9m+fTvm5uZ06dKFH3/8kcDAQFxcXEq7iibrnXfeYfny5ezZs4fU1FRmzZqV55yhQ4fSo0ePx7q+Xq/n0+XH+PtkPNYWZvw0tBVeLnZPWu3CmzvXkKEvKcnwXEajhBCiSBQ6kNq1axeDBw/m4sWL6PX6XGUqlQqtVltklRPiaaHVann55ZeNQVTDhg15+eWXOXbsGLt27eLcuXPcunWLV155hUOHDj11aaqfNjExMajVahRFYffu3VhZWdG9e3cWLlxI//79qVSpUmlXsVywtbVl3bp1vPnmm/zxxx/k5OQYy+zs7Bg7diyTJk167J+37zad4/fdl1Cp4OsXmtGiZin1m5kZLFgAAwYYnstolBBCFIlCB1IjR46kZcuWREdH4+7uLv/QCVEEVq9ezfnzhs0527Zty6ZNmzAzM2PlypV8++23dOrUicOHD3PkyBG2bt0qI7/l0OnTp43B0/79+7GxsaFXr14sWbKEvn375lqXKoqOg4MDv/zyCzNmzCAqKopdu3YREBBAUFAQ9vb2j33d8AOXmbXmFACT+jWmp08JTbu8dQvefBP++1+oV+/e8f79DanQ//nH8FlGo4QQ4okVOpA6c+YMiqJQt27d4qiPEE+lzZs3Gx+/++67WFtbG1Mx29raMnbsWIYPHw7Ali1bJJAqJ44fP46iKKjVag4fPoytrS19+vRh/Pjx9O7dGzu7UpgG9pSqVq0aw4cPx83Njd69ez/ROuDtZ2/wgXIYgNc6eTG0fa0iquUjXLgAvXvDiROwdy/s2gV3g0GVCqZNgzFjDJ/lTVAhhHhihc692qZNG86ePVskN9+yZQv9+vWjWrVqqFQqIiIi8pxz4sQJ+vfvj6OjI/b29rRt25ZLly7lOU+v19OrV6+HXkeIsiw7O9v4uHLlynnK7z+WlZVVInUSRU+v13P48GE+/fRTvL29ady4MbNnz8bHx4ewsDASEhJYtmwZzz//vARRJupEXCojf92HRqunb1N3PuxZgpseV658L0C6ehVOnsxd3rUrHD9u+CyEEOKJFWhE6vDhw8bHb731Fu+++y7Xrl2jSZMmed61K0xWsfT0dHx9fRk2bBghISF5ys+dO0eHDh0YMWKEMeX6iRMnsLGxyXPuV199JdMMhclq2PDeP1u///47AQEBucp///134+NGjRqVWL3Ek9Pr9ezfvx9FUVAUhbNnz+Lk5ET//v354osv6NatW76/04TpuXozk2EL/+FWVg5tajsz53lfzMxK8O+SvT1ERMDw4bBwIcjMESGEKFYFCqT8/PxQqVS5kkvcnWYEGMsKm2yiV69e9OrV66HlH3/8Mb1792bmzJnGY15eXnnOO3ToEHPnzuWff/7B3d29wPcXoqx44YUXePfdd8nIyOCnn37CwcGB4cOHExsby5gxY1i6dCkAzs7OBAUFlXJtxaPodDpOnTrFli1bCAsL48KFC1SuXJkBAwYwb948nn32WaysrEq7mqIIpWRqGLbwH66l3qaeqx3/G9ISa4sn38j3X6WmGjLwVax471i9erBli0zdE0KIElCgQComJqa465GHTqcjOjqaDz74gB49enDgwAFq167NhAkTGHA38xCGHekHDRrE/PnzC7yHSlZWVq7pUampqQBoNBrjupTy4m57ylu7ypuKFSvy6aef8uGHHwIwd+5c5s6dm+e8KVOmYGFhIf1ZBul0Onbu3ElYWBhhYWFcuXIFFxcXgoKCCA4OplOnTlhY3PuVK31Y9jzu78vsHB2v/7KPU9dv4WpvzU9DmmFrWcx9fOoUFqGh6H190f7661MfOMnfOtMlfWe6ynPfFbRNKv2DOcxLiUqlIjw83BgkXbt2DXd3d2xtbZk6dSoBAQGsXr2ajz76iI0bN9K5c2cAXn/9dbRaLT/99FO+18nPpEmTmDx5cp7jv//+O7a2tkXeNiEKQq/XoygKf/zxR5792SwsLHj55Zfp379/KdVO5Eer1XL8+HF27NjBrl27SE5OxtnZmbZt29K+fXsaNWqEuXkxj0qIUqXTw5KzZuy7YYa1mZ4xPlpqVHz0656EmUZD15EjqZCYCMCR4cM5L78bhBCiyGRkZDB48GBSUlJwcHB46HmFDqSWL1+e/4VUKmxsbKhbty61a9cuXG3JGwBdvXqV6tWrM2jQoFzrQ/r370/FihX5448/WL58Oe+++y4HDhwwLswuSCCV34iUh4cHN27c+NcvlinSaDSsW7eObt26PVEWKlFyrly5wqJFi9i3bx8JCQn06tWLESNGULVq1dKumsDwM7Vp0ybCw8OJjIwkISEBDw8PgoODCQ4Opk2bNmi1Wvm5M0GP8/ty9toz/Lg1BgszFf8b0oyOdasUcy0NVJGRWDz3HPrGjcn566+nfj2U/K0zXdJ3pqs8911qaipVqlR5ZCBV6PTnAwYMyLNeCnKvk+rQoQMRERFPtGlklSpVsLCwwNvbO9fxRo0asW3bNgA2bNjAuXPncHJyynVOSEgIHTt2ZNOmTfle29raGmtr6zzHLS0ty903wl3luW3lTa1atZg0aRIajYaVK1c+cSpm8eSysrL4+++/URSFiIgIkpOT8fLyMibKadWqVa5kN3enBMjPnWkqaL/9uusiP241TH2fHtyEZxuV4Brd0FBYtgxVr15YSoZHI/mZM13Sd6arPPZdQdtT6PTn69ato1WrVqxbt46UlBRSUlJYt24drVu3ZsWKFWzZsoXExETee++9Qlf6flZWVrRq1YpTp07lOn769Glq1qwJwIcffsjhw4c5ePCg8QPgyy+/ZOHChU90fyHE0y0zM5PIyEiGDBlC1apV6dOnD9u3b2fUqFHs37+fs2fP8sUXX9C6dWvJGPoUWnf8OhMjjwIwrlt9nmvpUXw3O3UKlizJe/y550CCKCGEKDWFHpF6++23+d///kf79u2Nx7p06YKNjQ2vvfYax44d46uvvsqV1e9h0tLScu1JFRMTw8GDB3F2dsbT05P333+fgQMH0qlTJ+MaqaioKONIk5ubW74JJjw9PR9reqEQ4umWnp7OqlWrUKvVrFixgrS0NBo3bszYsWMJDQ2lcePGEjQJDlxK5q0/9qPTwwutPHjr2WKcVrd8Obz0EmRkgIcH3FkfLIQQovQVOpA6d+5cvnMFHRwcOH/+PAD16tXjxo0bj7zW3r17c+2XM27cOACGDh3KokWLCAoK4ocffmD69OmMGTOGBg0aoFar6dChQ2GrLYQQ+bp16xbR0dEoisLKlSvJzMzEz8+PDz/8kJCQkFx7fAlx4UY6Ixbv5bZGR0ADF6YO8Cne4HrHDrh1y/B4yhQJpIQQogwpdCDVokUL3n//fX755RdcXFwASEhI4IMPPqBVq1YAnDlzhho1ajzyWv7+/nnWWj1o+PDhBRrduquMJCEUQpRhN2/eJCoqCkVRWLNmDVlZWbRs2ZKJEycSEhJC3ad84b7IX2JaFq8s3ENSejZNqjsyf3BzLMwLPUO+cD7/HA4cACcnWLCgeO8lhBCiUAodSP38888EBgZSo0YNPDw8UKlUXLp0CS8vLyIjIwHDlL1PPvmkyCsrhBCPKzExkeXLl6MoCuvWrUOj0dCuXTumTZtGcHAwtWrVKu0qijIsM1vLiMV7uZCYQY1KFfj5lZZUtC70n9BH02oNm+zeZW4O4eFQocJTv1eUEEKUNYX+K9CgQQNOnDjBmjVrOH36NHq9noYNG9KtWzfMzAzvzP1b6nEhhCgp8fHxREREoCgKGzZsQKfT0bFjR2bPnk1wcHCBRs6F0Or0jPnzAAdjb+Jka8ni4a1xtbcp+hstXw4ffAAbNkC1aveOy/6GQghRJj3W22kqlYqePXvSs2fPoq6PEEI8kbi4OMLCwlCr1WzevBmAgIAA5s2bR1BQUL4JaoR4GL1ez6Tlx1h3/DpWFmb89HJL6rgUQ6a8X3+Fl182PA4JgU2bIJ9tOoQQQpQdBQqkvvnmG1577TVsbGz45ptv/vXcMWPGFEnFhBCioGJjYwkLC0NRFLZv3465uTldunThxx9/JDAw0LieU4jC+nHLeX7ddRGVCr4e6EfLWs7Fc6OePQ1Z+WJjwdPTMMVPCCFEmVagQOrLL7/kxRdfxMbGhi+//PKh56lUKgmkhBAlIiYmBrVajaIo7N69GysrK7p3786CBQvo378/zs7F9A+veGpEHrzCjFUnAfikjze9mhTjhrsuLoa1UBs3wrvvynooIYQwAQUKpGJiYvJ9LIQQJenMmTMoioKiKOzfvx8bGxt69uzJkiVL6Nu3L46OjqVdRWGitDo9u2OS2HdDReWYJFCZ8d5fhwAY0aE2wzsU8d6EGzdChw5gaXnvWIsWhg8hhBAm4bFTDmVnZxMTE0OdOnWwsCiGzEVCCAEcP37cOPJ0+PBhbG1t6dOnD+PHj6d3797Y2RXDehXxVFl9NI7JUceJS7kNmPPLmb2oAD3Qp4k7H/duVHQ30+lg0iTDnlBvvgnz5hXdtYUQQpSoQm+AkZGRwYgRI7C1taVx48ZcunQJMKyNmjFjRpFXUAjxdNHr9Rw+fJhPP/0Ub29vGjduzKxZs/Dx8SEsLIyEhASWLVvG888/L0GUeGKrj8Yxasn+O0HUPXd3JOzRuCpmZkU4ze7kSfjiC8Pj+fMNGfqEEEKYpEIHUhMmTODQoUNs2rQJG5t76V+7du3K0qVLi7RyQoing16vZ9++fUyYMIEGDRrg6+vLvHnzaNWqFcuXLyc+Pp7ffvuNoKAgbCUVtCgiWp2eyVHHedg27ipg+qqTaHVFuNG7tzd8+y2YmcHMmRAQUHTXFkIIUaIKPScvIiKCpUuX0rZtW1T3LYb19vbm3LlzRVo5IUT5pdPp2LNnj3Ha3oULF3B2diYoKIhvvvmGZ599Fisrq9KupijH9sQk5RmJup8eiEu5zZ6YJNrVqVx0N/7Pf+CZZ6BREU4ZFEIIUeIKHUglJCTg6uqa53h6enquwEoIIR6k0+nYsWMHiqKgVqu5fPkyrq6uBAcHExISQufOnbG8f/G9EMXoWkpmgc6Lv/XwYOtf3V0P1bAhDB6cu0yCKCGEMHmFDqRatWpFdHQ0b731FoAxePq///s/2rVrV7S1E0KYvJycHLZu3YqiKISHhxMXF4e7uzshISGEhobSoUMHzM3NS7ua4imi0+lZcSSOmatPFeh8V3ubR5/0oKwsw8a60dFQoYJhSp+fX+GvI4QQoswqdCA1ffp0evbsyfHjx8nJyeHrr7/m2LFj7Ny5k82bNxdHHYUQJkaj0bBp0yZj8JSQkICHhwcvvPACISEhtGvXDjOzQi/RFOKJ6PV6/j4Rz+y1pzh57RZg2K5J/5AlUCrAzdGG1rUfY08yKyu4O3sjKwv27pVASgghyplCB1Lt27dn+/btzJ49mzp16rB27VqaN2/Ozp07adKkSXHUUQhhArKysvj7779RFIXIyEiSkpLw8vJi2LBhhISE0KpVK5n+K0rN9rM3mLXmFAdjbwJgb23Bq5288HC2ZdzSgwC5kk7c/U6d2M8b88fJ2qdSwXffwbVrMG4cdO36JNUXQghRBj3WBlBNmjRh8eLFRV0XIYSJyczMZO3atSiKQlRUFCkpKdSvX5+RI0cSGhqKn5+fBE+iVO27mMzsNafYeT4RgAqW5rzyTC1e7+SFk63VnWNm9+0jZeDmaMPEft709HEv2I10Orh+HdzvO9/GBlauLLK2CCGEKFsKHUi9+OKL+Pv74+/vT7169YqjTkKIMiw9PZ3Vq1ejKAorVqwgLS2Nxo0bM3bsWEJDQ2ncuLEET6LUHbuawpy1p9lwMh4AK3MzBrfxZHRAnTxrnnr6uNPN242dZ+NZu3U33Tu2oV1d14KPRN28CS+9BKdOwZ49UKlSEbdGCCFEWVToQMrOzo45c+bw+uuv4+bmRufOnencuTP+/v40bNiwOOoohChlt27dIjo6GkVRWLlyJZmZmfj5+TF+/HhCQkJoJBnIRBlxNj6NL9edJvpIHADmZiqea1GDt7rUo7pThYe+ztxMRZvaziSe0NOmtnPhpvO99pohqQTA0KGwfPmTNEEIIYSJKHQg9eOPPwJw7do1Nm3axKZNm/j666954403cHV1JS4ursgrKYQoeTdv3iQqKgq1Ws3q1avJysqiZcuWTJw4kZCQEOrWrVvaVRTCKDYpg6/WnyH8wGV0esMSpX5Nq/FOt/rUrlKxeG8+cyZs2GB4PGZM8d5LCCFEmfFYa6QA7O3tqVSpEpUqVcLJyQkLCwvc3NyKsm5CiBKWmJjI8uXLURSFdevWodFoaNeuHdOmTSM4OJhatWqVdhWFyOV66m3mbTjD0n9i0WgN6SK6eVfl3e71aejmUDKVqFXLMApVrZrhsRBCiKdCoQOp8ePHs3nzZg4dOoSPjw+dOnViwoQJdOrUCScnp2KoohCiOMXHxxMREYGiKGzYsAGdTkfHjh2ZPXs2wcHB1KhRo7SrKEQeSenZfL/pLL/svEhWjg6AjvWq8G73Bvh5OBXfjW/ehO+/h/Hj4f4U/u3bF989hRBClEmFDqRmzZqFi4sLEydOJDAwUNZGCGGC4uLiCAsLQ61WG/d/8/f3Z968eQQFBcnosiizUm9r+GnLeX7eFkN6thaAljUr8V6PBrT1qly8Nz92DAYMgLNnQaOBTz8t3vsJIYQo0wodSB04cIDNmzezadMm5syZg7m5uTHZhL+/vwRWQpRRsbGxhIWFoSgK27dvx9zcnC5duvDjjz8SGBiIi4tLaVdRlHGXLl1i37596HQ6fH19S3SdXEZ2Dot2XODHzedJydQA0LiaA+/1aIB/fZeSyRR5+TKcO2d4PG8evPWWZOgTQoinWKEDKV9fX3x9fRlzZ0HtoUOH+OqrrxgzZgw6nQ6tVlvklRRCPJ6YmBjUajWKorB7926srKzo3r07CxYsoH///jg7O5d2FYUJOHv2LOPGjWPFihXo9fe2re3SpQtz5szB19e32O6dlaPlj92XmL/xHDfSsgCo62rHuG716dnYDbPH2Sz3cfXoAdOmwdKlEB4uQZQQQjzlHivZxIEDB4wZ+7Zu3Upqaip+fn4EBAQUdf2EEIV05swZY/C0b98+bGxs6NmzJ0uWLKFv3744OjqWdhWFCTl58iQdO3bkxo0becr+/vtvOnTowPr162nTpk2R3jdHq0O9/zLf/H2WKzczAfBwrsDYLvUZ0Kx64dKT/5vYWEhIuHPTHBzPnYMDB8DCAnJyDAkk7l8nOH48vP02VHh4KnUhhBBPh0IHUpUqVSItLQ1fX1/8/f159dVX6dSpEw4OJZQdSQiRx/Hjx43B0+HDh7G1taVPnz588MEH9O7dGzs7u9KuojBRw4YNMwZR7u7uDB06FCsrK3799VdiYmJIS0vjxRdf5NSpU5ibmz/x/XQ6PVGHr/LV+jPE3EgHoKqDNW89W4/nW3pgZWH2iCsUQlYWtGoF168DYAn4P3hOpUoQFwfW1obnKpUEUUIIIYDHCKR+/fXXIguctmzZwqxZs9i3bx9xcXGEh4czYMCAXOecOHHCmClQp9PRuHFjli1bhqenJ0lJSUycOJG1a9cSGxtLlSpVGDBgAFOmTJF33UW5ptfrOXLkCIqioCgKJ06cwN7enr59+zJx4kR69uyJra1taVdTmLi9e/eya9cuAOrVq8c///xj/N364Ycf4u/vz549ezh37hyrV6+mT58+j30vvV7PuuPXmbvuNCev3QLAuaIVo/3r8FLbmthYPnmQloeVFXh6GkakdLr8z0lNNYxayb5pQgghHlDoQKpv375FdvP09HR8fX0ZNmwYISEhecrPnTtHhw4dGDFiBJMnT8bR0ZETJ05gY2MDwNWrV7l69SqzZ8/G29ubixcvMnLkSK5evYqiKEVWTyHKAr1ez/79+40jT2fOnMHR0ZHAwEC++OILunXrZvzZEKIo/P3338bHY8eOzfUGVYUKFfjggw8IDQ0FYMOGDY8VSOn1eradvcHstac5FHsTAHsbC17r6MWwDrWxs37s7Q4fTaWCKVOgZ8+Hn1OzJlhaFl8dhBBCmKxi/Av1aL169aJXr14PLf/444/p3bs3M2fONB7z8vIyPvbx8UGtVhuf16lTh88//5yXXnqJnJwcLCxKtXlCPDG9Xs+ePXuM+zxduHABZ2dngoKC+Prrr+nSpQtWVlalXU1RTt2+fdv42N3dPU/5/cfuP7eg9l5IYtaaU+yOSQKggqU5w56pxWudvHCyLaHv627doHFjOHkS7k+WZG4OLi5w+DBUrFgydRFCCGFSymykodPpiI6O5oMPPqBHjx4cOHCA2rVrM2HChDzT/+6XkpKCg4PDvwZRWVlZZGVlGZ+npqYCoNFo0Gg0RdaGsuBue8pbu8oznU7Hzp07+euvv1i2bBk3btzA1dWVwMBAgoOD6dSpE5b3vUMufVv2lJefu/vfuPrzzz/zzEj4888/c51b0PYeu5rKl+vPsvmMYe2VpbmKQa08GNW5NlXsDGuRSuJrp1qzBvMxY1DFxOQt1GrJ+ekn9FZWhj2jRJlWXn7mnkbSd6arPPddQduk0t+fy7YUqVSqXGukrl27hru7O7a2tkydOpWAgABWr17NRx99xMaNG+ncuXOeayQmJtK8eXOGDBnC1KlTH3qvSZMmMXny5DzHf//9d1lXIkqFVqvl+PHj7Ny5k507d5KcnEylSpVo164d7du3p1GjRkWykF+IwsjKymLEiBGkpaUBEBgYSN++fTE3N2fdunUsXboUnU6HhYUFP//88yPXpl7LgJWxZhxKMiSMMENPG1c93WvocLYu3raocnIA0N/3JpvD+fMEjBsHgKZCBcyzsjDT6dCZmZHi5cWWWbMM0/+EEEI8VTIyMhg8eLBxgOZhymwgdfXqVapXr86gQYP4/fffjef179+fihUr8scff+R6fWpqKt27d6dSpUosX7481zv2D8pvRMrDw4MbN26Uu+yDGo2GdevW0a1bt3/9moiSp9Fo2Lx5M2FhYURGRpKQkICHhwfBwcEEBQXRokUL/v77b+k7E1Sefu6+//573n777X8956OPPmLSpEkPLb+UlMH8jeeIPBSHTm+ITfo2cWPMs3WoVbmYp80dPIj5/PmoVqxA+/336IOC7pXp9Vj4+KCvWRN9o0aYz5tnLMpZsQJ99+7FWzdRZMrTz9zTRvrOdJXnvktNTaVKlSqPDKTK7NS+KlWqYGFhgbe3d67jjRo1Ytu2bbmO3bp1i549e2JnZ0d4ePgjO9Pa2hpr67xvf1paWpa7b4S7ynPbTEl2djbr169HURQiIyNJSkqidu3avPLKK4SGhtKqVStUd94BvzusLH1nuspD37311ltkZmby8ccf57vh+nvvvceUKVMwM8ublvxaym2+2XCGZf/EkqMzvGfX3bsq47rXp6FbCb1plZQEv/wCgMXy5fD887nLjx1DZWkJej26HTsw27cPXYsWWPTuLaNRJqg8/Mw9raTvTFd57LuCtqfMBlJWVla0atWKU6dO5Tp++vRpatasaXyemppKjx49sLa2Zvny5ZK1TJQ5t2/fZs2aNajVapYvX05KSgr16tVj5MiRhIaG4ufnZwyehChrVCoV48eP54UXXuCnn35i9+7d6HQ6mjVrxquvvkr9+vXzvCYxLYvvN53jl10Xyc4xpBXvWK8K73VvgK+HU9FXMikJIiMhLAw++gjatbtXFhAAjo6GRBL5JY24+8dSpUI3dSppr76K7dSpmMnPpBBCiEco1UAqLS2Ns2fPGp/HxMRw8OBBnJ2d8fT05P3332fgwIF06tTJuEYqKiqKTZs2AYaRqO7du5ORkcGSJUtITU01Jo5wcXGRNSWi1GRkZLBq1SoURWHFihWkpaXRuHFjxo4dS0hICD4+PhI8CZNSs2ZNpkyZ8q/npGRq+GnreRZsiyE92zB61bJmJd7r0YC2XpWLr3IrVsDw4YbH9evnDqSsrGDjRmjUCB7xRpu+Sxc2zp9P7y5diq+uQgghyo1SDaT27t1LQECA8fm4O4t+hw4dyqJFiwgKCuKHH35g+vTpjBkzhgYNGqBWq+nQoQMA+/btY/fu3QDUfWCzxJiYGGrVqlUyDRECQ2AfHR2NoiisWrWKjIwM/Pz8GD9+PCEhITRq1Ki0qyiKU2ysYWNXgJwcHM+dgwMH4G5yA1dXqFGj9OpXBLQ6PXtikoi/dRtXexta13bG3ExFRnYOC7df4MfN50i9bUjq4FPdgXe7N8C/vkvRvWlw/jyEh0NwMNSufe94v36Gr3NODuzcmfd1zZoVzf2FEEKI+5RqIOXv78+jcl0MHz6c4XffaXyM1wtRnG7evElUVBRqtZrVq1eTlZVFy5Yt+fTTTwkJCckT4ItyKisLWrWC69cBsAT8HzzHzQ0uXIB81meagtVH45gcdZy4lHv7Rbk5WNOxngsbT8VzIy0bgLqudrzbrT49fdyKdtR1wQIYMcLwWKuFDz64V1apEsyfD02bQps2RXdPIYQQ4l+U2TVSQpRVSUlJREZGoigK69atQ6PR0K5dOz7//HNCQkJkJPRpZGUFnp6GESmdLm+5mRl4eBjOM0Grj8Yxasl+Hnzb6lpqFn/tuwyAp7MtY7vWI9CvOuZmTxBA6fWwbx/Uq2dY23TX/VtehIXlDqQAXn/98e8phBBCPAYJpIQogPj4eCIiIlAUhY0bN6LVaunQoQOzZ88mODiYGiY+ZUs8IZUKpkyBnj3zL9fpDOUmuC5Oq9MzOep4niDqfo4VLFn7TidsLJ9wXery5fDmm4ZpkgsXwiuv3CurUweGDIHGjeH+FOZCCCFEKZFASoiHiIuLIzw8HEVR2Lx5M2CYTvrNN98QFBSEm5tbKddQlJpPPjGMmqSnw53vDbp3N0zv27vXMKpyl7k5NG9uKL99G/z8DOt7unaFd98tleo/ilan52x8Gocu32TtsWu5pvPlJyVTw4FLN2lXpxAJJbKzDSN1922Qi4uLIYgCw6jT/YEUGNOYCyGEEGWBBFJC3Cc2NpawsDAURWH79u2Ym5vTpUsXfvzxRwIDA3FxcSntKoqSkJAAc+fC6dPQsiVMmJC7fO1a2LPH8DgzEypUePiolFZ7bzTqwgU4dcrwUalS3vsOGgSXLoGXF/z0U4msp9Lr9VxKyuDQ5RQOx97k8OUUjl5NISM7755R/yb+1r8HW0b//ANff23ItPfHH9Cr172yNm2gVi1Dhr3Q0ELdXwghhChpEkiJp15MTAxqtRq1Ws2uXbuwsrKiW7duLFiwgP79++Ps7FzaVRTF4fBhiIgwBEujRsEzz9wrU6lgxgzD49TUvIFU/fqGQMrODi5fNqznAcOoU/Pm6A8dQqXVojc3R3V3NAogPt6wl1F6umGq2oN274aYGDh2LO96qh9+MCRU8PIyjIi1avVYzb6eeptDdwKmQ5dvcuRKCjczNHnOs7Uyx6e6Iy52VkQfufbI67raF3APvytX4LffDI/DwnIHUmZmhv4oZxs7CiGEKJ8kkBJPpTNnzqBWq1EUhX379mFtbU2vXr1YsmQJffv2xfH+Re7CdG3aZAh4zpyB777L/Q/6gQMwcaLhccuWuQOpypUNI0bJyYbA5kGffw4zZxoy8d2/7kmlgmnTUN0ZlVLdPxoF0KkT3LplGPEyM8t9TZ3OkL4bDMHSg+upjh279/FgooUzZ+DZZw3B2aBBxsQLNzOyOXw5hcOXbxpGnC7f5HpqVp7mWJmb0cjdnqY1nGhawxFfDyfquNhhbqZCq9Nz+fCfaK/H57tOSgWYuVWlde373nBISDAEqWFhMG1a7vTj3buDra2hL/5tg1whhBCijJNASjw1Tpw4gaIoKIrC4cOHsbW1pU+fPrz//vv07t0be3v70q5i+Xb/Pkv5eZx9lrRaWLfu3ijGqFG5y7/7Dv76y/D4gw/ujRyBYVTprlOncr9OpTJMPXNzM2Tje1B+x+7q3h1dixaY7dtn+Hx3NOr+a7u65n2dmZlhWl9GBiQl5S3PzjZM9cvKyjuade6cYWTs8mUOenizwOEAhy/f5EJiBgCRi9/BX6/jlEtN3u87jnqu9jSt4UhTDyd8azjSwM0ea4v8E0WYa7JZ9vMYrBNvPLTJWZVdMJ8cdG8qYlgYjBxpeNyiRe5AytYWtm8Hb2+TzWIohBBCgARSohzT6/UcOXIERVFQq9UcP34ce3t7+vbty8SJE+nZsye2tralXc2nwwP7LOXrYfss3bplGD06fdqQsa1du3tlZmYQEmIIPurVyxtI3R84nT6d+3mTJobNXevXN4wAPah9+wI3LxeVCt3UqaS9+iq2U6diVthMfba2ho8H/fgjfP89XL1KdhVXTt2Zmnf48k0cV+xmVAUHnDNT+eOGBcsPXTW+rHYlaxonxGChzcHLyZqek3pQ0fq+X/3vv28IfOrUgW+/zf010uvBygprr9rokxJR5bNvnx6wrlEtd1AUGGjoC73eMF3xQX5+hfuaCCGeavHx8WRl5R1NF6VLp9Ph4eHB1atXMXtwloUJcHFxwcamgNPSH0ICKVGu6PV6Dhw4YBx5OnPmDI6OjgQGBjJjxgy6dev2xD804jE8ap8llcowlW7ZMujTB+5fl7ZvHwQEGB6PHZs7kFKpDIHQwYNw/jxoNLmnhj33HPj4GM5p1Cj3Pe3sYMCAImpgbvouXdg4fz69u3R54mtpdXrOJ6QZp+YdupzCiatHyNbe93V0a8n/jfkdL6scvGtU4r267sZpek5pN+F/nnDxIraN6oP1A7/2T50yfO3Onzckzbjf338bpgpWrpxvEAWGqX20b597KqKbmyEoa9XKMCIlhBCPKTU1FZVKhYeHR2lXRTxAp9Ph6OiIg4ODyQVSWq2WK1eu4Orq+kT/F0ogJUyeXq9nz549xuDpwoULODs7ExQUxNdff02XLl2wkilEpetR+yzp9XDiBLz8MqxfD/cHIPdPwTt9Ou9r33vPMOJVv37edUV+fiU++qHV6dkdk8S+GyoqxyTRrq5rgTeo1ev1XE7OvDPSlMKh2JscvZJCej4Z9BwrWBqm59VwpGkNJ3xrOOHmmM8fA1tXw9Q/jQbS0vKWW1uDvb1h6mC1arnLzp2DGzcMHzVrGqYPavPJ5nfsWN5jD44OCiHEY0hJSZG9GkWRMzc3p3r16ly9evWJgnQJpIRJ0ul07NixA0VRCAsLIzY2FhcXF4KDgwkNDaVz585YyqL1suXuPkv79+f+Z9zc3LA26uJFw/PTp3MHUu7uMG6cYepZfkHRiy8Wa7ULY/XROCZHHb+z75I5v5zZi7ujDRP7edPTxz3P+fG3bnM49t5I05ErKSSlZ+c5r4KlOT7VHe4lg6jhRM3KtqgKM23Q0jL/lOt//WUIZG/ezD8BRvXqhkx7r78OH32U9/WvvgoffljwegghRCEV6nedEAVkbv6Em8gjgZQwIVqtlq1btxqDp7i4ONzd3QkJCSE0NJQOHToUyQ+FKCYqFbz1lmHU6X5arSERxKFDhvU5HTrkfd2cOSVXz8e0+mgco5bsz5PZ7lrKbUYt2c/s532pam9jXNd0+HJKvhvdWpqraOjmYAyYmno4UtfFDgvzYpw2cXdq5YNGjTJ83L5tOCc8/F4gfHej4R9/zDsSKIQQQjwFJJASZZpGo2HTpk0oikJ4eDgJCQl4eHgwcOBAQkNDadeuncnNy31qZWSQMu0LHDEkKFABOSozTlerx6WOA+g5enQpV/DxaXV6Jkcdzzc9+N1j7y47lKdMpYK6LnaGqXkehil6jdwfnkGv1NydP37/9MwHU7sLIYQQTxkJpESZk52dzfr161Gr1URERJCUlETt2rV55ZVXCA0NpVWrVjLMb4L+PnAB2wwz2nEnQQFgodfxRfvBbPntAN+/pMp3+ltRyNHqyNRoua3RcVujvfOh43aO4XFmtpbbOfeX3Tv37uuyNFpu59w5985rM7O1ZOXoSMnMJik976a2D3Kxt6J17cr43lnX5FPdEbsHkz+UZXenZ/7zj+Hzg6ndhRBCFLlFixYxduxYbt68WdpVEQ8wob/gojy7ffs2a9euRVEUli9fTkpKCvXq1WPkyJGEhobi5+cnwZMJ0+r0/HdLHAnPT2H8poV0unCABjcuccitHptrNwfgvxHHqGxnjUaryzeQua3RkvXAc2OQczcgyi9Y0mjJ0eWfca6k/bePN4F+1Uu7Go/vzobDjBlj+Cw/k0IIE6DV6dkTk0T8rdu42tvQurZzgZMAPY5XXnmFxYsX5zneo0cPVq9e/a+vrVWrFmPHjmXs2LHGYwMHDqR3795FXc08JGArPAmkRKnJyMhg1apVKIrCihUrSEtLo3Hjxrz99tuEhobi4+MjwVM5sfPcDcN6IHMLPu/yKpsuHGTS+h+Z2Xmo8Z/xG2lZPPfDzmKvi42lGTaW5lSwNMfG0hxri/uf33ts/cDzu49tLMyxsTLH5u7rrMw5c+0WH0UcfeS9Xe3LQer9rl3h+PHSroUQQhRI7iRABv+WBKio9OzZk4ULF+Y6Zv3gPokFVKFCBSo8uD2FKBMkkBIl6tatW0RHR6NWq1m5ciUZGRn4+voyfvx4QkJCaPTgXj/CJN3MyObApZuc3neCbanm7L6cmqt8ey0/uv3n+zyvc65oSeWK1vcFM/kEMsYPM2wsDIHM3ce5yu4Llu4+t7YwK5bgvLlnJeZtPMu1lNv5rpNSAW6OhndBhRBClIxHJQH6/qXmxRZMWVtb4+bmlm/ZpEmTWLBgAdevX6dy5cqEhobyzTff4O/vz8WLF3nnnXd45513AMO2GA+OFE2aNImIiAjGjBnDpEmTSEpKYsiQIcyfP585c+Ywd+5cdDodb7/9Nh9//LHxvnPnzmXhwoWcP38eZ2dn+vXrx8yZM7Gzs2PTpk0MGzYMuJclceLEiUyaNIns7Gz++9//8ttvv3Hz5k18fHz44osv6NSpEwAXL15kzJgxbNu2jezsbGrVqsWsWbNKZBSttEkgJYpdSkoKUVFRKIrC6tWrycrKomXLlnz66aeEhIRQt27d0q6ieAI6nZ7zN9LZfzGZfReT2XcpmbPxaTjcTiPil3H42TlzbMAEkmwdH3mtbwe3oF2dyiVQ66JlbqZiYj9vRi3Zjwpy/dG+G7ZN7OddrFNJhBCivNPr9WRq8tnLLh9anZ6Jy489NAmQCpi0/DjP1K1SoN/NFSzNi+SNOEVR+PLLL/nzzz9p3Lgx165d49AhQzKisLAwfH19ee2113j11Vf/9Trnzp1j1apVrF69mnPnzhEaGkpMTAz169dn8+bN7Nixg+HDh9OlSxfatm0LgJmZGd988w21atUiJiaG0aNH88EHH/Ddd9/Rvn17vvrqKz799FNOnToFgJ2dHQDDhg3jwoUL/Pnnn1SrVo3w8HB69uzJoUOHqFq1Km+++SYajYYtW7ZQsWJFjh8/bnxteSeBlCgWSUlJREZGoigK69atQ6PR0K5dOz7//HNCQkKoVatWaVdRPKaM7BwOxt40Bk4HYm9yMyNvooXv1s/HK/kqXslX2XziV7oFvMf11PI7YtPTx53vX2qeZwqJWwlMIRFCiKdBpkaL96driuRaeuBa6m2aTFpboPOPf9YDW6uC/9u8YsWKPMHE+PHjqVixIm5ubnTt2hVLS0s8PT1p3bo1AM7Ozpibm2Nvb//Q0ay7dDodCxYswN7eHm9vbwICAjh16hQrV67EzMyMBg0a8MUXX7Bp0yZjIHX/uqvatWszZcoURo0axXfffYeVlRWOjo6oVKpc9z537hx//PEHly9fptqdTdvfe+89Vq9ezaJFixg/fjyxsbGEhITQpEkTALy8vAr8dTJ1EkiJIhMfH09ERARqtZoNGzag1Wrp0KEDs2fPJjg4WHYmN0F6vZ4rNzPZdzHZEDhdSuZE3C20DyRvsLYww9fDiRY1K9HCsxLNPJ2oHFQFgoJAo8H+/75n4D8xfLVXD+hRqczuu4cOUPFuQE2TH7Hp6eNON283dp6NZ+3W3XTv2IZ2dV1Nvl1CCCEKJyAggO+/zz2F3dnZmfT0dL766iu8vLzo2bMnvXv3pl+/flhYFO5f8lq1amFvb298XrVqVczNzXNtCVO1alXi4+ONzzdu3Mi0adM4fvw4qamp5OTkcPv2bdLT06lYsWK+99m/fz96vZ769evnOp6VlYWzs+HNzzfffJM33niDtWvX0rVrV0JCQmjatGmh2mOqJJASTyQuLo7w8HAURWHz5s0A+Pv788033xAUFPTId1RE2ZKVo+XY1VTjaNP+S8lcT83Kc141Rxua16xEc89KtKhZiUbuDlhZPLCfV5s2sHcvxMZyLD2dT4f3R1utCc5dXsPCwcV4mvZWIkl//4+vtpsxYNOmQv8xKWvMzVS0qe1M4gk9bYo5M5QQQjxNKliac/yzHgU6d09MEq8s/OeR5y0a1qpAsyEqWBZuf7+KFSvmu3TB2dmZU6dOsW7dOtavX8/o0aOZNWsWmzdvxtLSssDXf/BclUqV7zGdTgcY1jH17t2bkSNHMmXKFJydndm2bRsjRoxAo3n49h06nQ5zc3P27duHuXnur4GtrS0A//nPf+jVqxfR0dGsXbuW6dOnM2fOHN56660Ct8dUmfZ/LKJUxMbGEhYWhqIobN++HXNzc5599ll++OEHBgwYgIuLy6MvIsqEhFtZ7L+UbAycDl9JITtHl+scCzMVjas50LymIWhq7lmJak4FzB5UrRpUq8ak554jLS0NTu+kjrs1L787GZtKVTl39ADzJ44nMz6e7achIiKC0NDQYmipEEIIU6dSqQo8va5jPRfcHW0emQSoYz2XEn/Dq0KFCvTv35/+/fvzxhtv0LBhQ44cOULz5s2xsrJCqy3YOrDC2Lt3Lzk5OcyZM8c4arVs2bJc5+R372bNmqHVaomPj6djx465ynQ6HamphmRSHh4ejBw5kpEjRzJhwgT+7//+TwIpIe6KiYlBrVajVqvZtWsXlpaWdO/enQULFtC/f3/j8K4ou7Q6Paeu3WLffYHTpaSMPOc5V7SiuWclmtd0ooVnJZrWcKKCVQHeiYuLg23b4Lnnch1OTEwkPDwcAFdXV1ZGr7g3haBDA1p6OtCnTx8AfvrpJwmkhBBCPLHSTgKUlZXFtWvXch2zsLBgxYoVaLVa2rRpg62tLb/++isVKlSgZs2agGHK3pYtW3jhhRewtramSpUqRVKfOnXqkJOTw7x58+jXrx/bt2/nhx9+yHVOrVq1SEtL4++//8bX1xdbW1vq16/Piy++yMsvv8ycOXNo1qwZN27cYMOGDTRu3JgOHTrwzjvv0Lt3b+rXr09ycjIbNmx4arIwSyAlHurMmTOo1WoURWHfvn1YW1vTq1cvfv31V/r164ej46OzsInSk5Kp4WDsTeP6pgOXkknPzv1Ok0oF9V3tjaNNLWpWolZl28JnJsrKgpAQ2LkTPvjAsFnrnSkA58+fN77D1a9fvzzzsHv27ImDgwOpqamcPn368RsshBBC3Kc0kwCtXr0ad/fc12/QoAEzZsxgxowZjBs3Dq1WS5MmTYiKiqJyZUPG2s8++4zXX3+dOnXqkJWVhV5fNBvK+/n5MXfuXL744gsmTJhAp06dmD59Oi+//LLxnPbt2zNy5EgGDhxIYmKiMf35woULmTp1Ku+++y5XrlyhcuXKtGvXjp49ewLw/+3dd1gU19fA8e+CFKkKSIuAWLCLPbGCDVuMRqMmGkvUGI3dxB5bYjca88bE8osFW9RYiIktVuwRUeyKIioqii00pe68f6xsXAEFBZbF83meeWRnZmfPcFfYw7333NTUVAYMGMCtW7ewsbGhRYsW/PDDDzkSd36nUnKqhQxYTEwMtra2REdHY2Njo+9wckyqWsn2pPeLFy+yYcMGNm7cyOnTp7GwsKB169Z06NCBVq1a6UxsFLknu22nKArhD+K185qCbzzmSlQcL/7vtjIrRDX3Is96nIpS1a0ItoWzPiY7UytWQI8emq/d3ODkSXj2V7QzZ87g7e0NwAcffMAff/yh89SYmBjs7e1JSUmhXLlyXLx48c3j0bPk5GS2bdtGq1atsjXmXeiXtJvhkrYzXK9qu4iICNzc3N7oNVLVCsfDHxEVm4CjtaZCrMxffXNpQ/tsbGx0ilwYkszeX1nNDfTaI3XgwAFmz55NcHCwtmhBu3btdM65ePEio0aNIjAwELVaTcWKFVm/fj3u7u6Apuv066+/5rfffuPp06c0adKEX3755a2vEKe7krcxK66cyHAlb0VROHv2rLbnKa32f5s2bZgwYQItWrTQTiYUeSMrbfc0KZXTt/7Vmd/0OIMS5B72FtR4ljTV8CiKl5N17vzy6NYNYmJg7FgICNAmUQDly5fHycmJe/fusXXrVoKDg6lRo4b2+KxZs0hJSQE0hUoMWVxcHAEBAYSHh3Pz5k1Kly5NxYoV9R2WEEK81YyNVAa5RqHI//SaSMXHx+Pt7c1nn31Ghw4d0h0PCwujfv369O7dm8mTJ2Nra8vFixcxNzfXnjN06FD+/PNP1q5di729PV999RXvv/9+htVF3havWsn7l67VcEq+y4YNG9iwYQNXrlzB1taWtm3bMn36dPz8/HS+xyLvZNZ2kdEJ9Ft1kkZli/EwPokLd2JIeaEEuWkhI7yL22qr6VV3L0oxa7O8CVylgoED4ZNPwF73l5WJiQlffPEF3377rbYkfvfu3Slbtizbt29n9+7dzy6h4ssvv8ybeHOYoihMnz6dGTNmEBsbq93/66+/0rJlS5YsWZJuiIcQQgghDJteE6mWLVvSsmXLTI+PGzeOVq1aMWvWLO2+5xf5io6OZsmSJaxcuZKmTZsCsGrVKtzc3Ni9ezfNm2etRGZBkqpWmPznhXQfxBVFITEylCeXD/Ph4iMkPr6LnZ0d7dq148cff6RJkyaYmprqJWahkVnbPW/f5fvar51szLRV9Gp4FKWiq236EuR5zT7jv/iNGjWK3bt3c+TIERISEli8eHG6c6ZNm6ZdzM/QDB8+nHnz5mV4bPv27TRo0IBjx47l2KRhIYQQQuhfvi02oVar2bp1KyNHjqR58+acOnUKT09PxowZox3+FxwcTHJyMn5+ftrnubq6UqlSJY4cOZJpIpWYmEhi4n9r46SVbkxOTn5pLX1D8E/4I50JlUn3rxN3ZhdPLh8hNfY+Rha2WHjVYcbcXvTt1FpnPLKh37uhe7HtMjPAx5OONYvjamuuWxRCSSU5OedLpmYoNhbjnj1J/fZbyMLQNRMTE7Zu3crYsWPx9/fnyZP/qgV6enoybtw4unfvbpDvwRMnTmiTKJVKRffu3fHz82Pnzp3s3LmTe/fuERYWxoQJE/jxxx/1G6x4qbT3nyG+D9920naG61Vtp1artWshifwlrcyCoigG20ZqtTrD915Wf5bk20QqKiqKuLg4ZsyYwZQpU5g5cyY7duygffv27Nu3Dx8fH+7evYupqSlFixbVea6Tk1O6kpPPmz59OpMnT063/++//zb4+UDBD1TAf0MaE+9c5smlg1h41cWibF3MildEZWTMo9RUdu3apb9AhY7YZFgbZgS8ukcp9s5VTh+5wuncDytjajW1Zs3C9dgx1Lt2cXzUKO5Xq5alpzZv3px69epx4cIFnj59ioODA+XLl8fIyIht27blcuC546efftJ+3aNHD+0fetq3b0+DBg0YMGAASUlJLFu2DB8fHxk2awDkZ6PhkrYzXJm1nZubm1QJzueeH9JuaB4+fEhISEi6/c//wfdl8m0ilZbZtm3blmHDhgGa0o1Hjhxh4cKF+Pj4ZPpcRVFeWr55zJgxDB8+XPs4JiYGNzc3/Pz8DL5qn334I1ZcOaF9bFWpMVZVmqFS6X5Aj7N04z0fL+wsZTifPt16/JSlh6+zPuQ2iSlZ+2uOX4N3eTcLq7DnmkePKJSg6TkzNjOjVseO4OWlv3j0bMyYMYCm123evHlYWFiQnJzMrl276NKlC3v37uW3334jISEBNzc3atWqpeeIRWbS2q1Zs2ZS+c3ASNsZrle13Z07dwz+s1lBpSgKsbGxWFtbZ3/ZlHzC3t4+w2kFaaPVXiXfJlIODg4UKlSIChUq6OwvX748hw4dAsDZ2ZmkpCQeP36s0ysVFRVF3bp1M722mZkZZmbpJ+GbmJgY/A/gOqUddVbyVhlnfD+bQu6w7fxdOtV0o0/9krjbG3ZPnKEJvRfLwv1h/HH6DqnPikZUeceGm4+fEv0k+aWrsGeljH2ucnKCw4fh889RdeuGyVtelS5taIOxsTEWFhY6P0NMTEx0ermNjIwM/mfM26Ag/C54W0nbGa7M2s7IyMhgS2sXdGmdHiqVymDbKLPfy1n9OZJv79rU1JRatWpx+fJlnf2hoaHa1Z9r1KiBiYmJTndwZGQk586de2kiVZClreQN/63cnUb1bOtd35NK79iQkKxmxdEb+H6/jwFrTnLm1r95HO3b5+TNx/TxP4HfDwfYdOo2qWqF+qUdWNPnXf4YWJ8Z7TV/Fcmo7SB3V2HPFgsLWL0ani3G9zarUqUKAAkJCaxZs0bn2OPHj9m4cSOg+ZlWtmzZPI9PCCGEELlDrz1ScXFxXL16Vfs4PDyckJAQ7OzscHd3Z8SIEXTu3JmGDRvSqFEjduzYwZ9//sn+/fsBsLW1pXfv3nz11VfY29tjZ2fH119/TeXKlbVV/N5GWVnJW1EUjoY9ZNGBawSG3mfrmUi2nonkvZJ2fNGwFL5lixlsN21+oygKB6484Jd9V/kn/BGgqRbeoqIz/XxK4e1WRHuuPldhf6nYWLC0BAP9i1Nu6tu3L+vXrwegf//+3Lhxg+bNm3Pw4EHGjRvHv//+C0CnTp3SzecUQgghhOFSKWnjUvRg//79NGrUKN3+Hj16sHz5cgCWLl3K9OnTuXXrFmXLlmXy5Mm0bdtWe25CQgIjRoxgzZo1OgvyZmcV7KyuXmxoUtUKR69G8ffBf/Br8G6mQ8IuRsbwvwPX2HL6jnZtorJO1nzesCQfeLvqv6S2gUpVK2w/F8mC/WGcv6MZa2tirOLDau/Qt2EpSjtavfS5WWm7PJGcDM2bg40NrFwJ1tb6iSOfUhSFzp078/vvv2d6joODA0FBQZQoUSLvAhPZlpyczLZt22jVqpUMDzMw0naG61VtFxERka3PdC88Ge7fz/y4oyMUL/56184HJk2aREBAgLZYQs+ePfn3338JCAh47Wtm5xpqtZqYmBhsbGwMdmhfZu+vrOYGeu2R8vX15VV5XK9evejVq1emx83Nzfnpp590KmcJDWMjFe962vHwosK7nnaZfhAv72LD3M5V+bp5WZYdDmfNPze5fC+Wr38/zfc7L9Orfgk+qe2Otbn8csqKxJRUNp+8zaID1wh/EA9AYRNjPqntTp8GnrgWKfzKa2S17fLE11/Dvn2ar9u3B6mKpUOlUrFy5UqKFCnCr7/+mu5nWoUKFfj9998liRJCiLyUmAi1asG9e5mf4+wM169DBvPm30TPnj3x9/cHoFChQri5udG+fXsmT56MpaVljr7W83788cdXfq5Oc/36dTw9PTl16hRVq1Z9rWuIfFxsQuQ91yKFGde6AgMbl2HNPzdZdjicuzEJTNt2iZ/2XKXLu+58Vs8TZ1sp35yRuMQUfvvnJr8eusa9GM06ZbaFTehZtwQ965agqKFWSGzVCvz94elT+PZbfUeTL5mZmbF48WLGjh3LqlWrCA8P5/79+/Tv35/mzZsb7F/qhBDCYJmagru7pkcqozWOjIzAzU1zXi5o0aIFy5YtIzk5mYMHD9KnTx/i4+NZsGCBznnJyck51ouaE2XipdR89shvd5GObWET+vuW4uCoRsz6qAqlHa2ITUxh0YFrNJi1l69/P03oPcNdMyCnPYpPYu7fl6k3Yy9Tt13kXkwizjbmfNO6PEdGN2ZYMy/DTaJAM6zv+HFNcYk6dfQdTb5WokQJvvnmGxYuXEjv3r1p2rSpJFFCCKEPKhV8913GSRRo9n/3nea8XGBmZoazszNubm506dKFrl27EhAQwKRJk6hatSpLly6lZMmSmJmZoSgK0dHR9O3bF0dHR2xsbGjcuDGnT+uuGDljxgycnJywtramd+/eJCQk6Bzv2bOndi1DzS2qmTlzJqVLl8bMzAx3d3emTp0KgKenJwDVqlVDpVLh6+ub4TUSExMZPHgwjo6OmJubU79+fYKCgrTHDx06hLGxMXv27KFmzZpYWFhQt25dnWJxp0+fplGjRlhbW2NjY0ONGjU4ceK/pXoMmfyGF5kyK2RMp5pu/D20IUt61KR2CTuSUxU2BN/C74cD9FoexLFrD9/aLuDb/z5l0pbz1J2xh//be5Xop8mUdLBkZofKBI70pU+DkliaFZBOXy8v+OgjfUchhBBCwNy5mrlNxYvDswJkWuHh/x3780/N8D5j4/TXMDEBPz/dfcuX//fcTZtyNOTChQuTnJwMwNWrV1m/fj0bN27Uzm9q3bo1d+/eZdu2bQQHB1O9enWaNGnCo0eaIlXr169n4sSJTJ06lRMnTuDi4sIvv/zy0tccM2YMM2fOZPz48Vy4cIE1a9bg5OQEwPHjxwHYvXs3kZGRbMrkfkeOHMnGjRvx9/fn5MmTlC5dmubNm2vjSjNu3DjmzJnDiRMnKFSokM60nK5du1K8eHGCgoIIDg5m9OjRBWYuYwH5lCdyk5GRiiblnWhS3olTNx+z+MA1dpy/y95LUey9FIV3cVv6NixFi0rO+aM0dy67GhXLwsBrBJy6rS3OUekdG770LU3zigXge/D0qaYH6iWLXgshhBB6ExMDt29rvk5M1D2WmvrfsX//1fQ6ZbRUR3Jy+t6o+Pj/nvvkSY6Fe/z4cdasWUOTJk0ASEpKYuXKlRQrVgyAvXv3cvbsWaKiorTrnH7//fcEBASwYcMG+vbty7x58+jVqxd9+vQBYMqUKezevTtdr1Sa2NhYfvzxR+bPn0+PHj0AKFWqFPXr1wfQvra9vT3Ozs4ZXiNtKOLy5ctp2bIlAP/73//YtWsXS5Ys4auvvtKeO3XqVHyefW4YPXo0rVu3JiEhAXNzc27evMmIESMoV64cAGXKlHnN72T+Iz1SIluquRdlwac12PuVL13fdceskBGnb0UzYM1JGs/Zz8qj13malKrvMHPF6Yh/+WLlCZr9cIANwbdIUSvUKWnPyt61+XNgfVpVdjH8JEpRoE8faNQIZs/WPBZCCCHyExsbeOcdzfZioQhj4/+OFS2q6XV6sVfKxARcXdNf19Lyv+c+t5j66/jrr7+wsrLC3NycOnXq0LBhQ21hNA8PD20iAxAcHExcXBz29vZYWVlpt/DwcMLCwgC4ePEidV4YXv/i4+ddvHiRxMREbfL2OsLCwkhOTqZevXrafSYmJtSuXZuLFy/qnJu2piKAi4tmqZaoqCgAhg8fTp8+fWjatCkzZszQ3lNBID1S4rV4Olgy9cPKDGvmxYqjN1hx9Do3Hj5h/B/n+WH3FbrX8aB7nRLYGfLcIDSlrQ9ffciCwKscvvpQu9+vghP9fUtRzb2ArQu0eTOkLSo7eTJ06gTPFsAWQggh8oXhwzVbRjw94dYt3X0v9kr9+adm/u+LevbUbDmgUaNGLFiwABMTE1xdXXWGsr1YuU+tVuPi4qJdJ/V5RYoUea3XL1z41RWCXyVt6saL64oqipJu3/P3l3ZM/Wx+2qRJk+jSpQtbt25l+/btTJw4kbVr1/Lhhx++cYz6JomUeCMOVmYMb+ZFP5+S/H7iFr8eukbEo6fM232FhYFhdKzhRp8GnnjY52C5zzxYF0KtVth5/i4LAsM4cysagEJGKj6o6kp/n1KUcSqgaym1awcTJ2qq861cKUmUEEIIw5fWKxUUpPn3xblRucDS0pLSpUtn6dzq1atz9+5dChUqlOlSGeXLl+fYsWN0795du+/YsWOZXrNMmTIULlyYPXv2aIcDPs/0WbXC1NTMRxGVLl0aU1NTDh06RJcuXQBNlcETJ04wdOjQLNzZf7y8vPDy8mLYsGF88sknLFu2TBIpIdJYmBaiR90SdH3XnR3n77Io8Bpnb0ez8tgNVv9zg5aVXOjbsCTebkXe7IVyeV2IpBQ1ASG3WRgYxrX7mjWgzE2M+LiWZg2o4kXfrKs/3zMygkmT4OOP4dlYZiGEEMKgqVQwbRoMHqz5N5cq9b2upk2bUqdOHdq1a8fMmTMpW7Ysd+7cYdu2bbRr146aNWsyZMgQevToQc2aNalfvz6rV6/m/PnzlCxZMsNrmpubM2rUKEaOHImpqSn16tXj/v37nD9/nt69e+Po6EjhwoXZsWMHxYsXx9zcPF3pc0tLS/r378+IESOws7PD3d2dWbNm8eTJE3r37p2le3v69CkjRozgo48+wtPTk1u3bhEUFESHDh3e+PuWH0giJXJUIWMj3q/iSuvKLhy99pDFB66x//J9tp6NZOvZSN4raccXDUvhW7ZYum7hLMmldSGeJKXw2/EIfj14jchozcRNG3NNctizbgnsrXJ2sb58T5IoIYQQBUnTpnDhgr6jyJBKpWLbtm2MGzeOXr16cf/+fZydnWnYsKG2yl7nzp0JCwtj1KhRJCQk0KFDB/r378/OnTszve748eMpVKgQEyZM4M6dO7i4uNCvXz9As1Dw//3f//Htt98yYcIEGjRokOHQwhkzZqBWq+nWrRuxsbHUrFmTnTt3UrRoUe3QvZcxNjbm4cOHdO/enXv37uHg4KBdnLggUClva+3q58TExGBra0t0dDQ2Njb6DidHJScns23bNlq1aqW3UpOX7saw+MA1toTc0Va583Ky4vMGJWlb9R1MC2Wz5snOnRlX4EmzY0fGY58z8O+TJJYfuc7yI9f594mmLKmjtRl9GnjySW13rM31V54zT9ouNRVGjIAhQ2QYXw7KD//vRPZJuxkuaTvD9aq2i4iIwM3NTQ+RiVdRq9XExMRgY2NjsGsmZvb+ympuID1SIteVc7ZhbqeqfO1XlmWHw/nteASh9+IYseEMc/4O5bN6JfjkXXdsspq0pI11PnlSkwikMTaG6tWzNPY5MvopSw6Gs+b4TZ48qzLoYW/BFw1L0b76O5ibZLDmREE0bhz88AOsWgUbN0KDBvqOSAghhBDCIEgiJfKMa5HCjGtdgUFNyrDmn5ssOxzO3ZgEpm+/xE97r9L1XXc+q+eJs635yy+Utlr5i71SqamvXKX82v04FgVeY9OpWySnanrHKrjY0N+3VMEoX54dcXGa5Ang0SPNmhpCCCGEECJLJJESec7G3IR+PqX4rF4J/gi5w/8OXONKVByLDlxj6eFwPvB+h74NS1LW+SWV8fz8oGZNOHHiv30VK2baG3X2VjQLAq+y/dxd7dJItT3t+NK3FD5erzlfy9BZWWkW3v34Y3j/fWjcWN8RCSGEEEIYDEmkhN6YFTKmU003PqpenP2hUSwKvMY/4Y/YePIWG0/eolHZYvRtWIr3StqlT3RUKpgyRbdXas4cnd4oJSaGo1GJLAi8xsErD7T7m5Z3pL9vKWp42OX2LeZ/RYvCtm2aIh1CCCGEECLLJJESemdkpKJxOScal3MiJOJfFh8IY8e5u+y7fJ99l+9TpbgtXzQsRYtKzjpD71KbNuNp5WpYnT1FXOVqFG7aDGM0a0DtungPu487YBwdw+PGfTB2LcMH3q584VOScs4Fq6BItqSmapKm5xNT47dkPpgQQgghRA6SRErkK1XdivBL1xpcfxDPr4eu8fuJW5y5Fc2ANSdxt7OgTwNPOtZwIzA0isl/XqBkhQ5MuvOASRU6EDZzH80rOnEk7CGOxw+x+twRAFZtnUHsuUu4Odm+4tULOEWBfv00ZeN/+eW11tkSQgghhBAakkiJfKmEgyVT2lVmWFMvVhy9wYqj17n56AkT/jjPzO2XiH9WaS+yRFWa9VmgeVJMAv5HbwDgZmrCo3c8sLt9gyJzZ1HkbU+iAH7+GX79VfP19euwe3e+W5RQCCGEEMJQyMQIka/ZW5kxrJkXR0Y34du2FXErWlibRGXG2rwQcxYOxe5aKPj7Q9euuifEx8O6dRkv6FuQOTiA+bOKiL16SRIlhBBCCPEGJJESBqGwqTHd65RgevvKrzw3NiGFS5GxYGoK3bunL6Qwa5amUl3dunD2bC5FnA99/DEcOgQzZ6ZPLoUQQgghRLZIIiUMysP4pCydFxWbkPGB+/dh9mzN18HBb988oRo1YORIfUchhBBCCD1QqVQEBAToO4wCQxIpYVAcrV+xWO+rzitWDAICNGtODRoEXl45F1x+o1bDxYv6jkIIIYR4Kx05cgRjY2NaPL9USxaUKFGCefPm5U5QIkdJIiUMSm1PO1xszclsdo8KcLE1p7bnS9aI8vODkBDNOlTPUxTNkLelSzVlwg3dlClQtSosW6bvSIQQQoi3ztKlSxk0aBCHDh3i5s2b+g5H5AJJpIRBMTZSMbFNBYB0yVTa44ltKuisN5WhQoXAwkJ335YtsGYN9O4NnTvnSLx6s28fTJwISUma+7lwQd8RCSGEEG+N+Ph41q9fT//+/Xn//fdZvny5zvEtW7ZQs2ZNzM3NcXBwoH379gD4+vpy48YNhg0bhkqlQvWsMNSkSZOoWrWqzjXmzZtHiRIltI+DgoJo1qwZDg4O2Nra4uPjw8mTJ3PzNt96Uv5cGJwWlVxY8Gl1Jm25wN2Y/+ZCOduaM7FNBVpUcnm9CwcG/ve1oRdjqF8fBg6E+fNh+nSoUEHfEQkhhBBv7MmTJ1y6dCnPX7dcuXJYvPgH2JdYt24dZcuWpWzZsnz66acMGjSI8ePHo1Kp2Lp1K+3bt2fcuHGsXLmSpKQktm7dCsCmTZvw9vamb9++fP7559mKMTY2lh49evB///d/AMyZM4dWrVpx5coVrK2ts3UtkTWSSAmDExoaSsD8uVz47TeSbD0wtXWgViUvxvXtTOPXTaIA5s6FDz6A33+Hdu10j8XEaOYcFSnyJqHnHRMT+OknzX00bqzvaIQQQogccenSJWrUqJHnrxscHEz16tWzfP6SJUv49NNPAWjRogVxcXHs2bOHpk2bMnXqVD7++GMmT56sPd/b2xsAOzs7jI2Nsba2xtnZOVsxNn7h9/2iRYsoWrQogYGBvP/++9m6lsgavSZSBw4cYPbs2QQHBxMZGcnmzZtp99wH2J49e+Lv76/znHfffZdjx45pH9+9e5cRI0awa9cuYmNjKVu2LGPHjuWjjz7Kq9sQeWjXrl20a9eOJ0+eaHbEnCUxAvae28fetYuYOXMmI9+kKp2vr2Z70bffatak+vZb+PxzzdBAQ9Ckib4jEEIIIXJMuXLlCA4O1svrZtXly5c5fvw4mzZtAqBQoUJ07tyZpUuX0rRpU0JCQrLd25QVUVFRTJgwgb1793Lv3j1SU1N58uSJzM/KRXr9NBgfH4+3tzefffYZHTp0yPCcFi1asOy5yfKmpqY6x7t160Z0dDRbtmzBwcGBNWvW0LlzZ06cOEG1atVyNX6Rt27dukX79u21SZSVlRW1a9fm4sWLREZGAjBq1CgqVqxI69atc+6Fr1yB//s/SE6G4cPh/ffBzS3nrp9TFiyAjz7SVCYUQgghCiALC4ts9Qzpw5IlS0hJSeGdd97R7lMUBRMTEx4/fkzhwoWzfU0jIyMURdHZl5ycrPO4Z8+e3L9/n3nz5uHh4YGZmRl16tQhKSlrS8eI7NNrsYmWLVsyZcoU7QS7jJiZmeHs7Kzd7Ox0q7EdPXqUQYMGUbt2bUqWLMk333xDkSJFZHJdAbRgwQLi4uIAeP/997l16xZ79uzh5s2bjB8/Xnve7LR1onKKhYUmQQH4+uv8mUQtXQpffgm1amkqEgohhBAiz6WkpLBixQrmzJlDSEiIdjt9+jQeHh6sXr2aKlWqsGfPnkyvYWpqSuoL1YOLFSvG3bt3dZKpkBd+3x88eJDBgwfTqlUrKlasiJmZGQ8ePMjR+xO68v34pP379+Po6EiRIkXw8fFh6tSpODo6ao/Xr1+fdevW0bp1a4oUKcL69etJTEzEN6PhWc8kJiaSmJiofRwTEwNoMvsXs3tDl3Y/BeG+fv/9dwCMjY35+eefsbCw0N7XN998w9q1a7ly5QqBgYHcvn1b533yRhwdwd8fVf/+KJUqaXqm0qjVGM2di7pnT3BwyJnXeybLbZeYSKHvvtNULbxxg5R//kGpWDFHYxHZU5D+371NpN0Ml7Sd4XpV26nVatRqdV6G9Ea2bNnC48eP+eyzz7C1tdU51qFDB5YsWcKcOXNo1qwZJUuWpHPnzqSkpLBjxw5GjBgBgIeHB4GBgXTq1AkzMzMcHBxo2LAh9+/fZ+bMmXTo0IGdO3eyfft2bGxstN+f0qVLs2LFCqpXr05MTAyjRo2icOHCKIqi8z3Mqe9pWlL34vUNiVqtzvC9l9WfJSrlxX5CPVGpVOnmSK1btw4rKys8PDwIDw9n/PjxpKSkEBwcjJmZGQDR0dF07tyZnTt3UqhQISwsLNiwYQPNmjXL9LUmTZqkM8EvzZo1a7JVkUXkrW7duhEbG4uTkxOLFi1Kd/yHH34g8Fnlvfnz51O8ePFcj6l4YCA1fviBJEtLzvTty20fn1x/zYyYP3pE7enTeVymDGf79tVLDEIIIUROc3Nzo2TJkvoOI8s+/vhj1Go169evT3fs9OnT+Pr6sn//fm7evMns2bO5fPky1tbW1K1blxUrVgCaMubDhg3j6tWrJCYm8vjxY0CzLtXcuXP5999/adOmDaVLl8bf358zZ84AcObMGYYOHcqFCxcoXrw448ePZ/z48fTv35/+/fsDULRoUVatWpWzUyAM2LVr14iIiEi3/8mTJ3Tp0oXo6GhsbGwyfX6+TqReFBkZiYeHB2vXrtUOBxw0aBDHjx9n2rRpODg4EBAQwA8//MDBgwepXLlyhtfJqEfKzc2NBw8evPSbZYiSk5PZtWsXzZo1w8TERN/hvJFKlSoRGhqKkZERYWFhOmOP1Wo1FStWJCwsDIA7d+7gkMM9ROkoCoWqVEF1+TIAKVu3orwkgc+ubLddQgIYG2sq9gm9Kkj/794m0m6GS9rOcL2q7e7cuYNbfhxSL1AUhdjYWKytrbXrXRmaiIgIXF1d0+2PiYnBwcHhlYlUvh/a9zwXFxc8PDy4cuUKAGFhYcyfP59z585R8dlQJm9vbw4ePMjPP//MwoULM7yOmZmZtkfreSYmJgX2B3BBuLfOnTvz3XffoVar6devH6tXr8be3p6kpCQmTJigTaIaN26Mi8sblEHPjr17Ydw4ePCAQq1a6R5TFMiBHyxZbjsDb9+CqCD8v3sbSbsZLmk7w5VZ2xkZGWFkpNcp/SITacP5VCqVwbaRkZFRhu+7rP4cMahE6uHDh0RERGg/JKdVb3ux8YyNjQ12rKbIXL9+/fjxxx+JiYlh586dFC9enOrVqxMaGqozmfKNyp9nl6srLFsGKSnpjw0cCElJMGUKODnl7OvOmQNRUTBtmqYXSgghhBBC5Cm9JlJxcXFcvXpV+zg8PJyQkBDs7Oyws7Nj0qRJdOjQARcXF65fv87YsWNxcHDgww8/BDQ1/UuXLs0XX3zB999/j729PQEBAezatYu//vpLX7clcomrqyt//PEHH3zwAbGxsSQkJHDkyBGdc+bNm0fz5s3zPrgX15U6exYWLtQs4rt9O1y7Bi+U7n9tO3bAyJGaa587B1u2SDIlhBBCCJHH9NoPl7bWU9p6T8OHD6datWpMmDABY2Njzp49S9u2bfHy8qJHjx54eXlx9OhRrK2tAU2327Zt2yhWrBht2rShSpUqrFixAn9/f1q9OMxKFAi+vr6cPn2awYMHa0vhm5mZ0bFjR44cOcKQIUP0HOEzly+DpaXm60GDci6JArh1678hgzVrShIlhBBCCKEHeu2R8vX1Tbe42PN27tz5ymuUKVOGjRs35mRYIp/z9PTkxx9/ZN68eSQlJWFqapr/Jjl+9BE0bAg//AAvJncpKZoeq9ddMLpPHyhVClavhokT3zxWIYQQQgiRbYY5M0wINJMbzczM8l8SlcbREaZPB3Nz3f1LlkD16tC9O9y+/XrXbtQIfv0VDHRypxBCCCGEoZNPYULkpehoGD9e8/XKlXD9etaed/9+roUkhBBCCCGyTxIpIfKShQV88w0ULQodO0K9errHIyLg5EnNduoUtmFhqGbOhBIlYO5czfwoIYQQQgihdwZV/lwIg2diAoMHw6efwnOLQgOax+XLQ3y85lTA9/njX32lKXd++zZksA6aEEIIIYTIO5JICaEPzyoO6ggJ0SZRmfL0zNkKgEIIIYQQ4rXI0D4h8otFi159zpQp/5U+F0IIIUSm1Go1v//+O40bN8ba2horKysaNGjA6tWrSUlJybXX7dmzJyqVin79+qU79uWXX6JSqejZs2euvf7bQKVSERAQoO8wJJESIt/43/80i/haW6dfG8rYGGrVAj8//cQmhBBCGJDExEQ+/PBDOnXqxL59+4iLiyM+Pp5Dhw7x6aef0qJFC+JfNQrkDbi5ubF27VqePn2q3ZeQkMBvv/2Gu7t7rr1uTkhKStJ3CAZDEikh8gtjY/jiC1i/HlJTdY+lpsJ330lvlBBCCJEFQ4cOZcuWLdrH77zzjk4Cs2fPHvr27Ztrr1+9enXc3d3ZtGmTdt+mTZtwc3Oj2nPrSCqKwqxZsyhZsiSFCxfG29ubDRs2aI+npqbSu3dvPD09KVy4MGXLluXHH3/Uea39+/dTu3ZtLC0tKVKkCPXq1ePGjRuApnesXbt2OucPHToUX19f7WNfX18GDhzI8OHDcXBwoFmzZgBcuHCBVq1aYWVlhZOTE926dePBgwfa5zVu3JiRI0cybNgwihYtipOTE4sXLyY+Pp7PPvsMa2trSpUqxfbt23Ve/1XX9fX1ZfDgwYwcORI7OzucnZ2ZNGmS9niJEiUA+PDDD1GpVNrHp0+fplGjRlhbW2NjY0ONGjU4ceLEK1rqzUgiJUR+07w51KqF8qxXSpHeKCGEECLL7t69y6+//gqAubk5mzZtIiIiguvXr7N9+3asra0B+O2337h27VquxfHZZ5+xbNky7eOlS5fSq1cvnXO++eYbli1bxoIFCzh//jzDhg3j008/JTAwENAMTyxevDjr16/nwoULTJgwgbFjx7J+/XoAUlJSaNeuHT4+Ppw5c4ajR4/St2/fbK+x6e/vT6FChTh8+DCLFi0iMjISHx8fqlatyokTJ9ixYwf37t2jU6dOOs9bu3YtDg4OHD9+nEGDBtG/f386duxI3bp1OXnyJM2bN6dbt248efIEIMvX9ff3x9LSkn/++YdZs2bx7bffsmvXLgCCgoIAWLZsGZGRkdrHXbt2pXjx4gQFBREcHMzo0aMxMTHJ1vch2xShREdHK4ASHR2t71ByXFJSkhIQEKAkJSXpOxSRHTt2KAr8t+3Yoe+IRDbI/zvDJO1muKTtDNer2u7mzZvZvub8+fMVQAGU0aNHpzs+depU7fFp06Zl+/qv0qNHD6Vt27bK/fv3FTMzMyU8PFy5fv26Ym5urty/f19p27at0qNHDyUuLk4xNzdXjhw5ovP83r17K5988kmm1//yyy+VDh06KIqiKA8fPlQAZf/+/S+N5XlDhgxRfHx8tI99fHyUqlWr6pwzfvx4xc/PT2dfRESEAiiXL1/WPu+9995TUlNTFUVRlJSUFMXS0lLp1q2b9jmRkZEKoBw9ejRb161fv77OObVq1VJGjRqlfQwomzdv1jnH2tpaWb58eYbfh8xk9v7Kam4gVfuEyI/8/FDXqIFRcLDmX+mNEkIIIbIkMjJS+7WPj0+6488Pa3v+3Jzm4OBA69at8ff3R1EUWrdujYODg/b4hQsXSEhI0A6lS5OUlKQz/G/hwoX8+uuv3Lhxg6dPn5KUlETVqlUBsLOzo2fPnjRv3pxmzZrRtGlTOnXqhIuLS7ZirVmzps7j4OBg9u3bh5WVVbpzw8LC8PLyAqBixYra/cbGxtjb21O5cmXtPicnJwCioqKydd0qVaroHHNxcdFeIzPDhw+nT58+rFy5kqZNm9KxY0dKlSr10ue8KRnaJ0R+pFKhnjKFmOLFUUulPiGEECLLihYtqv06JCQk3fFTp05leG5u6NWrF8uXL8ff3z/dsD61Wg3A1q1bCQkJ0W4XLlzQzpNav349w4YNo1evXvz999+EhITw2Wef6RSEWLZsGUePHqVu3bqsW7cOLy8vjh07BoCRkRGaDpz/JCcnp4vT0tIyXWxt2rTRiSskJIQrV67QsGFD7XkvDp1TqVQ6+9KGGKbd65tcN+0amZk0aRLnz5+ndevW7N27lwoVKrB58+aXPudNSY+UEPmU0qQJ++bPp1WTJvoORQghhDAYbdu25euvvwbg+++/p3Xr1tpektDQUKZNm6Y998MPP8zVWFq0aKFNepo3b65zrEKFCpiZmXHz5s0Me84ADh48SN26dfnyyy+1+8LCwtKdV61aNapVq8aYMWOoU6cOa9as4b333qNYsWKcO3dO59yQkJBXzh2qXr06GzdupESJEhQqlHPpQk5d18TEhNQXC3MBXl5eeHl5MWzYMD755BOWLVuWq20sPVJCCCGEEKLAKF26tLZS3cOHD/H29qZx48Y0a9aMChUqcOfOHUBTdS5tiFxuMTY25uLFi1y8eBHjF5Y2sba25uuvv2bYsGH4+/sTFhbGqVOn+Pnnn/H399fey4kTJ9i5cyehoaGMHz9eW1wBIDw8nDFjxnD06FFu3LjB33//TWhoKOXLl9fe44kTJ1ixYgVXrlxh4sSJ6RKrjAwYMIBHjx7xySefcPz4ca5du8bff/9Nr169MkxgsiqnrluiRAn27NnD3bt3efz4MU+fPmXgwIHs37+fGzducPjwYYKCgrTfh9wiiZQQQgghhChQlixZok2SFEVh37597N69W/thvVy5cqxevTpPYrGxscHGxibDY9999x0TJkxg+vTplC9fnubNm/Pnn3/i6ekJQL9+/Wjfvj2dO3fm3Xff5eHDhzq9UxYWFly6dIkOHTrg5eVF3759GThwIF988QWg6QUbP348I0eOpFatWsTGxtK9e/dXxuzq6srhw4dJTU2lefPmVKpUiSFDhmBra4uR0eunDzl13Tlz5rBr1y5tOXljY2MePnxI9+7d8fLyolOnTrRs2ZLJkye/dqxZoVJeHDj5FoqJicHW1pbo6OhM3+iGKjk5mW3bttGqVavcLwEpcpS0neGStjNM0m6GS9rOcL2q7SIiInBzc3uta8fFxTFv3jwWLVrErVu3AHB2dubzzz/nq6++wtbW9o1if9up1WpiYmKwsbF5o+RKnzJ7f2U1N5A5UkIIIYQQosCxsrLim2++YezYsdy9exdFUXBxcTHYD/0i/5FESgghhBBCFFhGRka4urrqOwxRAElKLoQQQgghhBDZJImUEEIIIYQQQmSTJFJCCCGEEEIIkU2SSAkhhBBCiHxLCkyL3PAm62GlkURKCCGEEELkS7a2tjx48EDfYYgCJjU1ldu3b1OsWLE3uo5U7RNCCCGEEPmSjY0NUVFRRERE6DsU8QK1Ws3Dhw+xt7c3yJLyjo6OmJubv9E1JJESQgghhBD5lqOjo75DEBlITk4mJCSEypUrv7ULYRte+iiEEEIIIYQQeqbXROrAgQO0adMGV1dXVCoVAQEBOsd79uyJSqXS2d5777101zl69CiNGzfG0tKSIkWK4Ovry9OnT/PoLoQQQgghhBBvG70mUvHx8Xh7ezN//vxMz2nRogWRkZHabdu2bTrHjx49SosWLfDz8+P48eMEBQUxcOBAgxyrKYQQQgghhDAMep0j1bJlS1q2bPnSc8zMzHB2ds70+LBhwxg8eDCjR4/W7itTpkyOxSiEEEIIIYQQL8r3xSb279+Po6MjRYoUwcfHh6lTp2onHUZFRfHPP//QtWtX6tatS1hYGOXKlWPq1KnUr18/02smJiaSmJiofRwdHQ3Ao0ePSE5Ozt0bymPJyck8efKEhw8fvrUTAQ2VtJ3hkrYzTNJuhkvaznBJ2xmugtx2sbGxQBbWMFPyCUDZvHmzzr61a9cqf/31l3L27Flly5Ytire3t1KxYkUlISFBURRFOXr0qAIodnZ2ytKlS5WTJ08qQ4cOVUxNTZXQ0NBMX2vixIkKIJtssskmm2yyySabbLLJluEWERHx0vxF9SyJ0TuVSsXmzZtp165dpudERkbi4eHB2rVrad++PUeOHKFevXqMGTOGadOmac+rUqUKrVu3Zvr06Rle58UeKbVazaNHj7C3t0elUuXYPeUHMTExuLm5ERERgY2Njb7DEdkgbWe4pO0Mk7Sb4ZK2M1zSdoarILedoijExsbi6ur60roL+X5o3/NcXFzw8PDgypUr2scAFSpU0DmvfPny3Lx5M9PrmJmZYWZmprOvSJEiORtsPmNjY1Pg3uRvC2k7wyVtZ5ik3QyXtJ3hkrYzXAW17WxtbV95jkGVtnv48CERERHaBKpEiRK4urpy+fJlnfNCQ0Px8PDQR4hCCCGEEEKIt4Bee6Ti4uK4evWq9nF4eDghISHY2dlhZ2fHpEmT6NChAy4uLly/fp2xY8fi4ODAhx9+CGiGA44YMYKJEyfi7e1N1apV8ff359KlS2zYsEFftyWEEEIIIYQo4PSaSJ04cYJGjRppHw8fPhyAHj16sGDBAs6ePcuKFSv4999/cXFxoVGjRqxbtw5ra2vtc4YOHUpCQgLDhg3j0aNHeHt7s2vXLkqVKpXn95MfmZmZMXHixHRDGUX+J21nuKTtDJO0m+GStjNc0naGS9oO8k2xCSGEEEIIIYQwFAY1R0oIIYQQQggh8gNJpIQQQgghhBAimySREkIIIYQQQohskkRKCCGEEEIIIbJJEqkC7pdffsHT0xNzc3Nq1KjBwYMH9R2SeIXp06dTq1YtrK2tcXR0pF27dunWShP53/Tp01GpVAwdOlTfoYgsuH37Np9++in29vZYWFhQtWpVgoOD9R2WeIWUlBS++eYbPD09KVy4MCVLluTbb79FrVbrOzTxggMHDtCmTRtcXV1RqVQEBAToHFcUhUmTJuHq6krhwoXx9fXl/Pnz+glWaL2s3ZKTkxk1ahSVK1fG0tISV1dXunfvzp07d/QXcB6TRKoAW7duHUOHDmXcuHGcOnWKBg0a0LJlS27evKnv0MRLBAYGMmDAAI4dO8auXbtISUnBz8+P+Ph4fYcmsigoKIjFixdTpUoVfYcisuDx48fUq1cPExMTtm/fzoULF5gzZw5FihTRd2jiFWbOnMnChQuZP38+Fy9eZNasWcyePZuffvpJ36GJF8THx+Pt7c38+fMzPD5r1izmzp3L/PnzCQoKwtnZmWbNmhEbG5vHkYrnvazdnjx5wsmTJxk/fjwnT55k06ZNhIaG8sEHH+ghUv2Q8ucF2Lvvvkv16tVZsGCBdl/58uVp164d06dP12NkIjvu37+Po6MjgYGBNGzYUN/hiFeIi4ujevXq/PLLL0yZMoWqVasyb948fYclXmL06NEcPnxYeuwN0Pvvv4+TkxNLlizR7uvQoQMWFhasXLlSj5GJl1GpVGzevJl27doBmt4oV1dXhg4dyqhRowBITEzEycmJmTNn8sUXX+gxWpHmxXbLSFBQELVr1+bGjRu4u7vnXXB6Ij1SBVRSUhLBwcH4+fnp7Pfz8+PIkSN6ikq8jujoaADs7Oz0HInIigEDBtC6dWuaNm2q71BEFm3ZsoWaNWvSsWNHHB0dqVatGv/73//0HZbIgvr167Nnzx5CQ0MBOH36NIcOHaJVq1Z6jkxkR3h4OHfv3tX5zGJmZoaPj498ZjEw0dHRqFSqt6ZHv5C+AxC548GDB6SmpuLk5KSz38nJibt37+opKpFdiqIwfPhw6tevT6VKlfQdjniFtWvXEhwczIkTJ/QdisiGa9eusWDBAoYPH87YsWM5fvw4gwcPxszMjO7du+s7PPESo0aNIjo6mnLlymFsbExqaipTp07lk08+0XdoIhvSPpdk9Jnlxo0b+ghJvIaEhARGjx5Nly5dsLGx0Xc4eUISqQJOpVLpPFYUJd0+kX8NHDiQM2fOcOjQIX2HIl4hIiKCIUOG8Pfff2Nubq7vcEQ2qNVqatasybRp0wCoVq0a58+fZ8GCBZJI5XPr1q1j1apVrFmzhooVKxISEsLQoUNxdXWlR48e+g5PZJN8ZjFcycnJfPzxx6jVan755Rd9h5NnJJEqoBwcHDA2Nk7X+xQVFZXuLz4ifxo0aBBbtmzhwIEDFC9eXN/hiFcIDg4mKiqKGjVqaPelpqZy4MAB5s+fT2JiIsbGxnqMUGTGxcWFChUq6OwrX748Gzdu1FNEIqtGjBjB6NGj+fjjjwGoXLkyN27cYPr06ZJIGRBnZ2dA0zPl4uKi3S+fWQxDcnIynTp1Ijw8nL179741vVEgc6QKLFNTU2rUqMGuXbt09u/atYu6devqKSqRFYqiMHDgQDZt2sTevXvx9PTUd0giC5o0acLZs2cJCQnRbjVr1qRr166EhIRIEpWP1atXL90SA6GhoXh4eOgpIpFVT548wchI96OMsbGxlD83MJ6enjg7O+t8ZklKSiIwMFA+s+RzaUnUlStX2L17N/b29voOKU9Jj1QBNnz4cLp160bNmjWpU6cOixcv5ubNm/Tr10/foYmXGDBgAGvWrOGPP/7A2tpa26toa2tL4cKF9RydyIy1tXW6eWyWlpbY29vL/LZ8btiwYdStW5dp06bRqVMnjh8/zuLFi1m8eLG+QxOv0KZNG6ZOnYq7uzsVK1bk1KlTzJ07l169euk7NPGCuLg4rl69qn0cHh5OSEgIdnZ2uLu7M3ToUKZNm0aZMmUoU6YM06ZNw8LCgi5duugxavGydnN1deWjjz7i5MmT/PXXX6Smpmo/s9jZ2WFqaqqvsPOOIgq0n3/+WfHw8FBMTU2V6tWrK4GBgfoOSbwCkOG2bNkyfYcmssnHx0cZMmSIvsMQWfDnn38qlSpVUszMzJRy5copixcv1ndIIgtiYmKUIUOGKO7u7oq5ublSsmRJZdy4cUpiYqK+QxMv2LdvX4a/23r06KEoiqKo1Wpl4sSJirOzs2JmZqY0bNhQOXv2rH6DFi9tt/Dw8Ew/s+zbt0/foecJWUdKCCGEEEIIIbJJ5kgJIYQQQgghRDZJIiWEEEIIIYQQ2SSJlBBCCCGEEEJkkyRSQgghhBBCCJFNkkgJIYQQQgghRDZJIiWEEEIIIYQQ2SSJlBBCCCGEEEJkkyRSQggh3jq+vr4MHTpU32EIIYQwYJJICSGEEEIIIUQ2SSIlhBBCCCGEENkkiZQQQogCLT4+nu7du2NlZYWLiwtz5szROb5q1Spq1qyJtbU1zs7OdOnShaioKAAURaF06dJ8//33Os85d+4cRkZGhIWF5dl9CCGEyF8kkRJCCFGgjRgxgn379rF582b+/vtv9u/fT3BwsPZ4UlIS3333HadPnyYgIIDw8HB69uwJgEqlolevXixbtkznmkuXLqVBgwaUKlUqL29FCCFEPqJSFEXRdxBCCCFEboiLi8Pe3p4VK1bQuXNnAB49ekTx4sXp27cv8+bNS/ecoKAgateuTWxsLFZWVkRGRuLm5saRI0eoXbs2ycnJvPPOO8yePZsePXrk8R0JIYTIL6RHSgghRIEVFhZGUlISderU0e6zs7OjbNmy2senTp2ibdu2eHh4YG1tja+vLwA3b94EwMXFhdatW7N06VIA/vrrLxISEujYsWPe3YgQQoh8RxIpIYQQBdarBl3Ex8fj5+eHlZUVq1atIigoiM2bNwOaIX9p+vTpw9q1a3n69CnLli2jc+fOWFhY5GrsQggh8jdJpIQQQhRYpUuXxsTEhGPHjmn3PX78mNDQUAAuXbrEgwcPmDFjBg0aNKBcuXLaQhPPa9WqFZaWlixYsIDt27fTq1evPLsHIYQQ+VMhfQcghBBC5BYrKyt69+7NiBEjsLe3x8nJiXHjxmFkpPk7oru7O6ampvz000/069ePc+fO8d1336W7jrGxMT179mTMmDGULl1aZ6igEEKIt5P0SAkhhCjQZs+eTcOGDfnggw9o2rQp9evXp0aNGgAUK1aM5cuX8/vvv1OhQgVmzJiRrtR5mt69e5OUlCS9UUIIIQCp2ieEEEJkyeHDh/H19eXWrVs4OTnpOxwhhBB6JomUEEII8RKJiYlERETQt29fXFxcWL16tb5DEkIIkQ/I0D4hhBDiJX777TfKli1LdHQ0s2bN0nc4Qggh8gnpkRJCCCGEEEKIbJIeKSGEEEIIIYTIJkmkhBBCCCGEECKbJJESQgghhBBCiGySREoIIYQQQgghskkSKSGEEEIIIYTIJkmkhBBCCCGEECKbJJESQgghhBBCiGySREoIIYQQQgghskkSKSGEEEIIIYTIpv8Hx4kPSoEYZ/AAAAAASUVORK5CYII=\n",
"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, [160, 172])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I think this is starting to look really good. Because of the poor initial guess of the weight gain being -1 it takes the filter several days to accurately predict the weight, but once it does that it starts to accurately track the weight. 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), but otherwise all of the math followed from very reasonable assumptions. Recall that you can change the value of the parameter `time_step` to a larger value and re-run the cell if you want to see the plot drawn step-by-step.\n",
"\n",
"One final point before we go on. In the prediction step I wrote the line\n",
"```python\n",
"gain_rate = gain_rate\n",
"``` \n",
"This obviously has no effect, and can be removed. I wrote this to emphasize that in the prediction step you need to predict the next value for all variables, both `weight` and `gain_rate`. This will become relevant shortly. 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](https://en.wikipedia.org/wiki/Alpha_beta_filter) or the $\\alpha$-$\\beta$ 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). $\\alpha$ and $\\beta$ are just different names used for this factors."
]
},
{
"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 Benedict-Bordner 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 scaled by how accurate each is.\n",
"\n",
"Let's look at a visual depiction of the algorithm."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"book_plots.predict_update_chart()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let me introduce some more formal terminology. The *system* is the object that we want to estimate. In this chapter the system is whatever we are trying to weigh. Some texts call this the *plant*. That terminology comes from control system theory. https://en.wikipedia.org/wiki/Plant_(control_theory)\n",
"\n",
"The *state* of the system is the current configuration or values of that system that is of interest to us. We are interested only in the weight reading. If I put a 100 kg weight on the scale, the state is 100kg. We define the state based on what is relevant to us. The color of the scale is irrelevant to us so we do not include those values in the state. A QA engineer for the manufacturer might include color in the state so that she can track and control the manufacturing process. \n",
"\n",
"The *measurement* is a measured value of the system. Measurements can be inaccurate, so it may not have the same value as the state.\n",
"\n",
"The *state estimate* is our filter's estimate of the state. For example, for the 100 kg weight our estimate might be 99.327 kg due to sensor errors. This is commonly abbreviated to *estimate*, and I have done that in this chapter.\n",
"\n",
"In other words, the state should be understood as the actual value of the system. This value is usually *hidden* to us. If I stepped on a scale you'd then have a *measurement*. We call this *observable* since you can directly observe this measurement. In contrast, you can never directly observe my weight, you can only measure it. \n",
"\n",
"This language of *hidden* and *observable* is important. Any estimation problem consists of forming an estimate of a hidden state via observable measurements. If you read the literature these terms are used when defining a problem, so you need to be comfortable with them.\n",
"\n",
"We use a *process model* to mathematically model the system. In this chapter our process model is the assumption that my weight today is yesterday's weight plus my weight gain for the last day. The process model does not model or otherwise account for the sensors. Another example would be a process model for an automobile. The process model might be \"distance equals velocity times time. This model is not perfect as the velocity of a car can vary over a non-zero amount of time, the tires can slip on the road, and so on. The *system error* or *process error* is the error in this model. We never know this value exactly; if we did we could refine our model to have zero error. Some texts use *plant model* and *plant error*. You may also see *system model*. They all mean the same thing.\n",
"\n",
"The predict step is known as *system propagation*. It uses the *process model* to form a new *state estimate*. Because of the *process error* this estimate is imperfect. Assuming we are tracking data over time, we say we *propagate* the state into the future. Some texts call this the *evolution*. \n",
"\n",
"The update step is 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 many minutes for them 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. 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. At t+1 seconds 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 inaccurate. Even if at time t the engineer slammed on the brakes the train will still be very near 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 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, something I do at work. 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 helium party 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 some mathematical sense). In this chapter we will merely be assigning different values to $g$ and $h$ in a more intuitive, and thus less optimal way. But the fundamental idea is 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\n",
"\n",
"I'll begin to introduce the notations 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 state, and is bold to denote that it is a vector. 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",
"Here I use Newton's notation of a dot over the x to denote velocity. More precisely, the dot implies the derivative of x with respect to time, which of course is the velocity. For a weight of 62 kg with a gain of 0.3 kg/day we have\n",
"\n",
"$$\\mathbf{x} = \\begin{bmatrix}62 \\\\ 0.3\\end{bmatrix}$$\n",
"\n",
"So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$, the initial estimate. We then enter a loop, predicting the state for time or step $k$ from the values from time (or step) $k-1$. 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": [
"## 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": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"from kf_book.gh_internal import plot_g_h_results\n",
"def g_h_filter(data, x0, dx, g, h, dt):\n",
" pass # your solution here\n",
"\n",
"# uncomment to run the filter and plot the results\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": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n",
"[159.2 161.8 162.1 160.78 160.985 163.311 168.1 169.696\n",
" 168.204 169.164 170.892 172.629]\n"
]
},
{
"data": {
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L2waaNm3Kli1b8PHxwcLCQpe3JCohaUESQgghhKgikpOTAXBxccHGxkarTKVSaQ1DfW/Y6+rm/fffx9fXV7O+f/9+Dh06TIGjB46TlmLbfzoqCzusjFWk/L6cm988R+KxQE1ydM/AgQMlORL3JQmSEEIIIUQVUa9ePQCioqKIi4vTKissLOTo0aNAcbJka2tb4fFVhFq1arFz504+/PBDateuTa0mnXGY8Dl2g2ZiaOOEpbE+s/s158isnkzo6sqOrZv58ccfdR22qELkETshhBBCiCpi5MiRzJ8/n6KiIsaPH89PP/1E3bp1ycrKYubMmdy4cQMAPz8/rQENqoPY2Fjq16+PSqXCyMiIjoPG0zK3OTez9QEwUOczpU9rJnR1wcLEEIDPPvtMlyGLKkpakIQQQgghqogXX3xRk/gEBQXh5ORE+/btcXBw4KuvvgKKW49mzpypyzDL1Lp16+jUqRNOTk6cPXuWw1du4//1USasDClOjgpzsb99mmUD6jKlRxNNciTEw5IWJCGEEEKIKsLR0ZGtW7cyYMAA0tPTKSgoIDQ0VFOup6fHN998Q7du3XQYZdlKSkoiJCQE4wateG7NRW4pxRPFmhjqMa6LCxM9nfnjgAHdu3TUcaSiupAWJCGEEEKIKsTb25vz58/z+uuv4+joiEqlok6dOowfP57Tp08zadIkXYdYaufOnePNN9+kRYsWxMfHa5U16dwb+xHvUe+pD7mlWGKkr8d4TxcOzvRltl8LrM2MdBS1qK6kBUkIIYQQoopxcnJi0aJFLFq0CEVRUKlUug7pkfz2228sXLgQgMDAQF566SXOxabxaVA4+8OTqOXSDkN9FcMfc2LyE41xsKql44hFdSYtSEIIIYQQVVhVSY4KCwv5/fffmTx5MllZWVplAQEBQPEjgqejEnhu1UkGfnmY/eFJ6OupGP5YA/bN8GHBUHdJjkS5kxYkIYQQQghR7mbMmMHnn38OgK+vryYpAmjTpg2ffPszl/Td+D0iBeXiLVQqGNK2PlN6NMHV1kxXYYsaSFqQhBBCCCFEmcnKymLTpk0UFRVpbe/fv79mOTAwULN8PTmLGevO8GVUbYLCU1AU6N/GgaBp3Vg8oq0kR6LCSQuSEEIIIYQoEx999BFz5swhJyeHQ4cO4eXlpSnz9fXl6aefxs/PDz8/P2JTs/libyTrT8dSpFYA6NWyLtN6NqWlo6WubkEISZCEEEIIIUTp3blzh9q1a2ttq1evHjk5OQBs2LBBK0EyNDTkxx9/JCEtl0V7I1kTEkNBUXFi5NPMjum9mtKmgfb5hNAFSZCEEEIIIcQD27x5M1988QXBwcFcunSJJk2aaMoGDhxI/fr16d+/P/7+/lrHJWXk8XVwFD8fv05+oRqAro1tmN6rKR0aWlfoPQjxbyRBEkIIIYQQD+zKlSvs3bsXKG4lmjVrlqasdu3a3LhxQ2tkvZSsfJYfjGLV0evkFBT3S+roUofpvZrRpZFNxQYvxAOQBEkIIYQQQmiJjIzkt99+Y/PmzWzfvh0bmz8TGX9/f15//XXc3NywtCzZV+hecpSWU8B3h67y/eFosvKLEyMPp9rM6NUU7ya2VWZ4clHzSIIkhBBCCCG0fPPNN3z00UcAbNmyhQkTJmjK3NzcuHjxIs2bN79vkpOZV8gPh6P55tBVMnILAWjlaMn0Xk15orm9JEai0iv1MN8HDx5k4MCBODo6olKp2LRpk1a5SqW67797v2QAeXl5vPLKK9ja2mJmZsagQYOIjY195JsRQgghhBAPRlEUTpw4wVtvvUVeXp5W2V/7D4WFhZU4tkWLFiUSnez8QpYdiML7w318EhRBRm4hzepasGxMe7a94kWPFnUlORJVQqlbkLKysvDw8GDChAlaE3zdEx8fr7W+c+dOJk2apLXv1KlT2bp1K2vWrMHGxoYZM2YwYMAATp06hb6+/kPchhBCCCGEKI2pU6dqJm7t2rUrfn5+mrJOnTrxxRdf0L9/f1xdXf/1PLkFRfxyPIavgyO5nZkPgJudGVN7NmWAuwN6epIUiaql1AlSv3796Nev3z+W16tXT2t98+bN+Pr64ubmBkBaWhorVqzgp59+omfPngD8/PPPODk58fvvv9OnT5/ShiSEEEIIIf5BQUEBhw8fxsfHR6sF54knntAkSBs2bNBKkPT09Jg8efK/njevsIh1ITf4cn8kt9KLW6CcrU15tUcTBrd1xEC/1A8qCVEplGsfpFu3brF9+3Z+/PFHzbZTp05RUFBA7969NdscHR1p3bo1R48evW+ClJeXp9X0m56eDhT/whcUFJTjHYjK7N5rL3Wg5pI6IKQOCKkD/+6zzz7j/fffJzU1lT/++IP27dtrynx9fRk4cCD9+/dn4MCBD/wzLChSExgax9Lgq8Sl5QLgYGXCyz5u+LdzxFBfD0VdRIG6qFzuqUQ8UgdqvLJ+7cs1Qfrxxx+xsLDQeo41ISEBIyMj6tSpo7Vv3bp1SUhIuO95Fi5cyLx580ps379/P6ampmUbtKhygoKCdB2C0DGpA0LqgJA6APn5+RgZGWltu3r1KqmpqQB89NFHjB07Vqt80qRJAISEhPzn+dUKnLytYvcNPW7nFbdEWRoq9G6gpot9JgaJZwnafbYsbuWhSB2oubKzs8v0fOWaIH3//fc89dRTmJiY/Oe+iqL8Y8e92bNnM336dM16eno6Tk5O+Pr6ag07KWqWgoICgoKC6NWrF4aGhroOR+iA1IGa7erVq1y4cIHz58/zzDPPYGdnp+uQhA7I+wDs2rWL7777jqCgIM6dO4ezs7OmrEOHDqxevZo+ffowbtw4evXqVerzq9UKOy/c4ot9kVy9XfxB1MbMiOe7uTKqYwNMDHXbf1zqgEhOTi7T85VbgnTo0CHCw8NZu3at1vZ69eqRn59PamqqVitSYmIinp6e9z2XsbExxsbGJbYbGhrKL4KQeiCkDtQwISEhzJo1i3379mm2ffDBB4wZM4aFCxfKF2c1VE1+HwgLC2PLli0AbNu2jVdffVVT1qBBA5KSkh7qZ6MoCrsv3GLJ7xFcTsgAoLapIc93a8Q4z4aYGlWu2WJqch2o6cr6dS+33nMrVqygQ4cOeHh4aG3v0KEDhoaGWs2g8fHxnD9//h8TJCGEEALg999/x9vbWys5AsjJyeHbb7+la9euJCUl6Sg6IcpPXFwcX375Jb1799b0xb7n3kjB9vb2qNXqEseW9sOjoijsu3yLgV8e5oWfT3E5IQMLEwOm92rKoZm+vOjTqNIlR0KUpVLX7szMTCIjIzXr0dHRhIWFYW1trWnSTU9P57fffuOTTz4pcbyVlRWTJk1ixowZ2NjYYG1tzWuvvYa7u7tmVDshhBDi77Kzsxk1apRm0B43NzcCAgI4c+YMR48eJTMzk/DwcKZMmcKvv/6q42jLn1qtsPdyIievp9C9iR1dGtnIHDPV2Pvvv8/SpUsB2LFjByNHjtSUtWjRgmPHjtGxY8dHmi5FURQOR97m06AIQmPuAGBmpM+Erq486+2Glam0zoiaodQJ0smTJ/H19dWs3+sbNG7cOFauXAnAmjVrUBSFUaNG3fccixcvxsDAgOHDh5OTk0OPHj1YuXKlzIEkhBDiH/3666/cvn0bgF69erFt2zZUKhU7duzgyy+/5PHHHyc1NZX169fzySef4OjoqOOIy0dhkZqtZ+P4OjiKiFuZACw/cJXm9SyY5OXKoLaOGBvI39Oq6vLly2zZsoXp06djYPDnx7SAgABNgnTo0CGtBEmlUtG5c+dHuu7xq8l8EhTBiegUAEwM9RjXxYXnuzfC2szoP44WonopdYLk4+ODoij/us9zzz3Hc88994/lJiYmfPHFF3zxxRelvbwQQoga6q+PZs+ZMwcjIyPN0K4uLi48++yzLFq0iMLCQg4cOPCPX9JVVbkFRfx28gbLD14lNjUHAAtjA7yb2rL/chKXEzJ4ff1ZPtwVztNdGvLU487YmJfsvysqr6lTp/LZZ58B0LFjR60vpL29vXnvvfcYNGgQ7u7uZXbN0zGpfLongsORxV8+GBno8dTjzrzo0wh7i/8eZEuI6kgeIBVCCFEl5OTkaJb/OkrXPU5OTvfdt6pLzy3g5z+u8/3haG5n5gPFI4hN9HJlbJeGWJoYcic7n19P3ODHo9dISM/l06AIlu6PZGi7+kz0cqVpXQsd34X4K7VaTVhYGO3atdN6LLJz586aBGnDhg1aCZKBgQFvv/12mcVwLjaNT4PC2R9e3GfPUF/FiI5OvOzbGAerWmV2HSGqIkmQhBBCVAmNGjXSLAcGBjJlyhTNuqIoBAYGatbd3NwqNLbycDszj+8PR/PTsetk5BUCUL92LZ7v7sbwx5y0hlaubWrEiz6NeMbblR3n4llxOJqzsWmsCbnBmpAbdGtqxyQvV7o1sZV+Sjq2dOlSPvjgA2JjYzl//jytWrXSlPXv3x8fHx8GDRqkNYdkWboUn87ioAj2XLwFgL6eioD29XnliSY4WcvckkKAJEhCCCGqiPHjx7N48WIA3nzzTUxNTRk+fDgpKSlMnTpVM7Kdm5sb3bp102Woj+RGSjbfHrrK2pAb5BUWj0jWxN6cF30aMdDDEUP9fx6A1lBfj8Ft6zPIw5GT11NZcSiaPRcTOBiRxMGIJJrYmzPRy5Wh7errfO6amqCoqKhE/+rCwkJiY2OB4laivyZIFhYW7N+/v1xiiUzMYPHvV9h+Nh4AlQqGtK3Pqz2a4GJrVi7XFKKqkgRJCCFEldCmTRtGjRrFr7/+SlZWFs8++yzPPvtsif0WLFiAnl65zWJRbq7cyuDr4Cg2n4mjSF3c19fDqTYv+zSiZ4u66Ok9eMuPSqWio4s1HV2siUnO5oej0awLucGVxExmbzzHR7vDGfO4M2O6NJR+JuVg//79rFy5ku3bt3PhwgXq1q2rKfP39+eNN96gZ8+etG3bttxjuXY7i8/3XmFT2E3uViv6t3FgWs8mNLaXRy+FuB9JkIQQQlQZK1asoKCggPXr15coMzAwYMmSJVqje1UFoTGpfBUcRdDdR54AvBrb8pJPozIZutvZxpQ5A1sxrVdT1oXc4Icj17h5J4fP90Wy7MBVBno4MsnLlZaOlo96K+KuoKAgVq1aBcCmTZt4/vnnNWVOTk4kJydjZla+rTaxqdl8sTeS9adjNQl375Z1mdarKS0c5LUW4t9IgiSEEKLKqFWrFuvWrePo0aN8++23XLx4kczMTAYNGsRLL71038EbKiNFUTgSmcxXwZEcjUoGih956tOyHi/6NMLDqXaZX9PSxJBnvN0Y7+nCnou3+O7QVU7H3GHD6Vg2nI7Fs5ENk7xc8W1mX6rWqpoqNTWVrVu3snXrVlatWkWtWn8ObBAQEMDChQuxsLAgLS2txLHlmRwlpOXy5f4rrA25QUFRcWLk08yO6b2a0qZB7XK7rhDViSRIQgghqhSVSkXXrl3p2rUrBQUF7NixAz8/PwwNK/8klmq1wp6LCXwVHMXZ2OIPzgZ6Koa0q88L3d0q5JEnA309/Nwd8HN3IDQmlRWHo9l5PoGjUckcjUrGzdaMCV1dCOjQAFMj+ZjwT15//XVWrFgBwJgxYxg8eLCmrH379uzatQsfHx+MjStmqPXEjFy+Do7il+Mx5N/tu9a1sQ3TezWjQ8M6FRKDENWFvPMJIYQQ5aygSM2m0JssOxBFVFIWUDwR58iOzjzbzY36tXUzrHI75zp8OboON+/k8OPRa/x6Ioart7N4Z/MFPt4TwejHnRnXxYV6VjW3n1JsbCzbt2/n2Wef1erb5u/vr0mQdu/erZUgqVQq+vTpU+6xKYrCxfh0NofFserYNXILihOjTi7WTO/dlM5uNuUegxDVkSRIQgghRDnJyS9iTUgM3x68SlxaLgAWJgaM93RhvKdLpZnItX7tWrzp14IpPZqw/uQNfjh6jevJ2XwdHMW3B68yoI0Dk7zccG9gpetQK9Rrr73GJ598AoCHhwedO3fWlPXo0YPXXnuNwYMH4+npWWExpeUUcPjKbYLDEzkQkURiRp6mrK1TbWb0bopXYxnOXYhHIQmSEEIIUcbSsgtYdewaPxy9RkpW8eSudhbGTPJy5anHnbEwqZyPA5obGzC+qytju7iw99ItvjsczYnoFDaFxbEpLI5OLtZM9HKlV8u66FezfkpRUVFac20BWkNwb9y4UStBMjY25qOPPir3uNTq4laiewnR6Zg7mkEXAGoZ6uPZyIbRjzvzRHN7SYyEKAOSIAkhhBBlJDE9lxWHo/nleAyZdyd3dbKuxfPdGvFkhwZVZu4hfT0VvVvVo3erepy/mcaKw9FsPRPHiWspnLiWgrO1KeM9XRje0Qlz46r9UeKbb75h8eLFXL58maioKK1JhgcNGkS7du0YPHgwI0aMqLCY7mTnc+jKbYLDkzgQkcTtzDyt8sb25vg0taN7Mzs6ulhXmXolRFVRtd/VhBBCiEogJjmb5Qej+O1UrKaDfPN6Frzo04j+7g4Y/MvkrpVd6/pWLB7Rljf6NmfVsWusPhFDTEo2/9t2kcVBEYzs5MQ4Txca1DHVdaj/SVGUEi0sKSkpXL58GShuJXrttdc0ZTY2Npw+fbrc41KrFc7HpWkSotCYVP7SSISpkT6ejWzxaWZH96Z2OFlX/p+1EFWZJEhCCCHEQ7qckM7XwVFsPROn+UDboWEdXvJpVO0ed6pnZcLMvs155YkmbDgdy/dHormalMW3h6L5/sg1+rauxyQvV9o7V74R0/744w9+/vlntm3bRmhoKHXq/BljQEAAb775Jl5eXri4uFRYTKlZ+Ry8ksSB8CQOXknidma+VnnTuub4NLOne1M7HnOpg7GBtBIJUVEkQRJCCCFK6dT1FL7aH8Xey4mabd2b2vGSTyM6uVpXq8To72oZ6TOmc0NGd3ImOCKRFYejORKZzPaz8Ww/G08759pM8nKlb6t6lablbO3atSxduhSAbdu2MXbsWE1ZkyZNuHXrFnZ2duUag1qtcO5mcStRcEQiZ27c0WolMjPSp2tj2+KkqJmdzkY2FEJIgiSEEEI8EEVROBCRxFfBUZyITgGKJ3f1c3fgxe6NaF2/Zo3wpqen4onmdXmieV0uxafz/eFoNofFERpzh8mrQ6lfuxbjPV0Y0ckJywoYlCInJ4dt27axfft2vv76a615sQICAliyZAlGRkbcuHGjxLHllRylZOVzMCKJ4PBEDl65rRmw455mdS2KH5trZsdjDa0xMqgcCaUQNZ0kSEIIIcS/KFIr7Dwfz9fBUVyISwfAUF9FQPsGPN+9Ea62ZjqOUPdaOFjy0TAPXu/bjJ//iOGXP65z804OC3ZcYsnvEQx7zImJXV1xtim/vjMvv/wyP//8MwDDhw+nd+/emjJPT0/Wrl1L3759sbS0LLcYitQKZ2Pv3G0lSuJs7B2Uv7QSmRsb4NW4uC9Rt6Z2OEorkRCVkiRIQgghxH3kFRYRePomyw9eJfp28eSupkb6jO7kzDPebjV68tR/Ym9hwvReTXnJpxGbw26y4nA0EbcyWXn0Gj8eu0bvlnWZ5OVGR5c6D/0YYkpKCkFBQQwfPlzrHAMGDNAkSFu2bNFKkPT09Bg+fPij3dw/SM7M4+CVJILDkzgYkURqdoFWefN6Fvg0s8enmR0dGtbBsJI8diiE+GeSIAkhhBB/kZVXyK8nYvjuUDQJ6cWTu1rVMtRM7lrHzEjHEVZ+Job6jOjozPDHnDh05TYrDkdzICKJ3RdusfvCLdzrWzHJy5X+bRxKlTDMnj2bjz/+mMLCQpo3b46Hh4emrE+fPjz33HMMGTKEHj16lMdtAcWtRGE37nAgPJHgiCTO3UzTaiWyMDHAu4ktPk3t6dbUThJpIaogSZCEEEIIiueeWXn0GiuPXuPO3VaAupbGPOvtxqhOzphV8fl+dEGlUtGtafHjZFduZfD9kWtsPB3LuZtpTF0bxgc7L/O0Z/GAD7VNtRPPxMRE7O3ttbY5OTlRWFg8v9SGDRu0EiQzMzOWL19eLveRlJFX3JcoIolDV5I09eOelg6W+DSzw6eZPe2ca0srkRBVnLzbCyGEqNES0nL57tBVVp+IITu/CAAXG1Ne6N6Ioe3ry/DKZaRJXQsW+rvzWu+mrD4ew6o/rpOQnsuiXeF8sTeSgA71mdjVlUM7NrB06VJOnTrFjRs3cHR01Jxj6NChfPLJJwwdOpShQ4eWW6yFRWrCbtzRjDh3/ma6VrmliQHeTYoHV/Bpaoe9pbQSCVGdSIIkhBCiRoq+ncXyA1FsOB1LQVHxM1ItHSx5ybcR/Vo7oK9XfYfq1iUbc2Ne6dGE57q7sfVMPCsOR3MpPp2f/4jh5z9iaKCnz7lbeajVagIDA3n55Zc1xzo4OBAZGVkuw6gnZuRy4O7gCoev3CYtR7uVqHV9S3yaFvclautUu9IMYS6EKHuSIAkhhKhRLsSl8VVwFDvPxWvmoenkas1LPo3o3tSuWs9hVFmcOXOGNWvWsHPnTg4fPszZW7l8fziavZcTiVXXoe6o99FLj+eqYkVeYZFWK15ZvT6FRWpCb9whODyR4PAkzQiF91jVMizuS9TMnm5NbbG3kFYiIWoKSZCEEEJUe4qicCI6ha+CozgQkaTZ3qO5PS/5NqJDQ2sdRlfzfP3115r+Qrt27eLJJ5/Es5EtV5My+f5INOtP3iDX0oENsXDgg/083aUhTz3ujI258SNd91b6vVaiRA5duU1GbqFWeZsGVvg0LX50zqOBtBIJUVNJgiSEEKLaUhSFfZcT+So4ilPXUwHQU8GANo686NOIFg7lNydOTVdYWMiBAwfYuXMnH374Ifr6f7YCBQQEsHz5cvT09Lh48aJmu5udOfOHuPNa72b8euIGPx69RkJ6Lp8GRbB0fyRD29VnopcrTetaPFAMBUVqTl9PJTiieBjuS/HarUS1TQ3p1sROMy+R7SMmYEKI6kESJCGEENVOYZGa7eeKJ3e9nJABgJG+Hk8+1oDnu7nR0EYmdy1vEyZM0MxLNHjwYLy9vTVlPj4+fPvttwwaNKjESHUAtU2NeNGnEc94u7LjXHE/pbOxaawJucGakBt0a2rHJC9XujWxLXFsQlouByKKH5s7fOU2GXl/thKpVNCmvhXd785L5NGgtvQ1E0KUIAmSEEKIaiO3oIgNp2NZfuAqMSnZAJgZ6TOmc0MmebnKaGPlICsri0OHDtG3b1+t7X369NEkSBs3btRKkAwNDXnmmWf+89yG+noMblufQR6OnLyeyopD0ey5mMDBiOJJWZvYmzOuizMJaSoW7Y7gUGSyJiG+x9rMiG53+xJ5N7F95Mf0hBDVnyRIQgghqrzMvELWHY3hu8PRJGXkAcUfjCd4uvB0FxesTA11HGH19O677/Lxxx+Tk5NDeHg4TZs21ZQNGDCAkSNHMnToUPr16/dI11GpVHR0saajizUxydn8cDSadSE3uJKYydubLwL6wLW7+4JHg9qaeYnc61tJK5EQolRK3fvw4MGDDBw4EEdHR1QqFZs2bSqxz6VLlxg0aBBWVlZYWFjQuXNnYmJiNOUJCQmMHTuWevXqYWZmRvv27Vm/fv0j3YgQQoiaJzkrn+0xenT/+CALd14mKSMPRysT5gxsyeE3fHmlRxNJjspIRkZGiW1WVlbk5OQAxRO3/lXt2rX59ddfGT58OBYWD9Zn6EE425gyZ2Arjr3Zg7f7t8DZuhYWhgqDPRz4bGRbTr3di00vd2Vqz6a0dZJH6IQQpVfqBCkrKwsPDw++/PLL+5ZHRUXh5eVF8+bNCQ4O5syZM7zzzjuYmPz5WMPYsWMJDw9ny5YtnDt3Dn9/f0aMGEFoaOjD34kQQogaJSopkz6fHWbPTT3ScwtpZGfGR0+2Ifh1XyZ0dcXUSB6SKAtr166lR48e2NnZkZycrFXm7++Pvb09zz33HD4+PhUal6WJIc94u7F3mjfzHyvi4yfdGdy2PtZmRhUahxCi+in1X49+/fr9a1P5W2+9hZ+fH4sWLdJsc3Nz09rn2LFjfP3113Tq1AmAt99+m8WLF3P69GnatWtX2pCEEELUMPmFaqauCSMtp5B6tRTeHtwWvzb10ZPWgjJ36tQp9u3bB8DmzZuZOHGipszV1ZX4+Hj09GQ4bCFE9VGmX6+p1Wq2b9/OzJkz6dOnD6Ghobi6ujJ79myGDBmi2c/Ly4u1a9fSv39/ateuzbp168jLy/vHb5/y8vLIy8vTrKenFw/TWVBQQEFBwX2PEdXfvdde6kDNJXWg5locdIVzN9OwqmXASy1zeaKpNUVFhRQV6TqyqunKlSts3LiRoKAgtm/fjrHxnwMZDB48mI8++gg3NzcURbnv71uRDn/w8j4gpA6Isn7tVYqiKA99sEpFYGCgJvlJSEjAwcEBU1NT5s+fj6+vL7t27eLNN99k//79dO/eHYC0tDRGjBjB7t27MTAwwNTUlPXr19OrV6/7Xmfu3LnMmzevxPbVq1djamr6sOELIYSogqLS4YsL+iiomNC0iLY2D/1nTNy1ZMkSgoODgeKnOh577DFNmVqt5vr167i4uKBSSQudEKLyyc7OZvTo0aSlpWFp+ejz25V5CxIUf9s0bdo0ANq2bcvRo0dZtmyZJkF6++23SU1N5ffff8fW1pZNmzYxbNgwDh06hLu7e4nzzp49m+nTp2vW09PTcXJywtfXFxsbm7K8BVGFFBQUEBQURK9evTA0lE7YNZHUgZonI7eARUuPoZCLfztHXh/YTOrAA1IUhVOnTrFnzx5mz56tlewUFhZqEiRFUfDz89NRlKUn7wNC6oD4e//IR1WmCZKtrS0GBga0bNlSa3uLFi04fPgwUDyIw5dffsn58+dp1aoVAB4eHhw6dIilS5eybNmyEuc1NjbWau6/x9DQUH4RhNQDIXWgBpm/8QI37+TibG3K/4a4Y6hX3HokdeC/jRkzhl9++QWA/v37a7US+fn58fHHHzN06NAS/YarCqkDQupAzVXWr3uZ9qo0MjKiY8eOhIeHa22PiIigYcOGQHETGFCiQ6e+vr6mBUoIIYT4u61n4tgYehM9FSwe4YG5sYxSdz8FBQUcO3asxPZu3bpplv8+JHetWrWYMWNGlU2OhBCiLJX6r0tmZiaRkZGa9ejoaMLCwrC2tsbZ2ZnXX3+dESNG0K1bN00fpK1bt2qa7ps3b07jxo15/vnn+fjjj7GxsWHTpk0EBQWxbdu2MrsxIYQQ1UfcnRzeCjwHwGTfxnRoaK3jiCqn9957j8WLF5Oamsr169dxdnbWlA0ZMoRNmzbh7+/P4MGDdRilEEJUbqVOkE6ePImvr69m/V7foHHjxrFy5UqGDh3KsmXLWLhwIVOmTKFZs2Zs2LABLy8voLgJbMeOHcyaNYuBAweSmZlJ48aN+fHHH6vUM89CCCEqhlqtMGPdGdJzC/Fwqs0rPZroOqRKIS8vj4SEBFJTU6lbty4ODg6oVCpSU1MB2LhxI1OnTtXsb29vz44dO3QUrRBCVB2lTpB8fHz4r4HvJk6cqDVPwt81adKkRPO+EEIIcT8rDkdz7GoytQz1WTKiLYb6NXvOnU2bNrFgwQJCQ0O1htf28fHhqaeewtzcnAEDBtC2bVvdBSmEEFWYPMAthBCi0roYl85Hu4v7tb47sCWutmY6jki3FEXhf//7H6GhoSXKgoODCQ4O5rPPPmPKlCk6iE4IIaqHmv01nBBCiEort6CIqWtDyS9S06tlXUZ2dNJ1SBUmLi6OpUuXMmTIEAoLCzXbN23apJUcOTs7M2nSJJo0+fOxw6lTpxIWFlaR4QohRLUiCZIQQohK6YOdl4m4lYmtuTEf+LvXqElKp06dyuTJk9m8eTMHDx7UbF+8eLFmecmSJVy/fp3vvvuOy5cv8+qrrwLFrUxffPFFhccshBDVhSRIQgghKp0DEUmsPHoNgI+GtcHGvORceNXB5cuX+fLLL0v07fX399cs79u3D4C0tDQOHToEQLNmzbQeo9PT02PBggWYm5sDsGXLlvIOXQghqi1JkIQQQlQqKVn5vPbbGQDGdWmIbzN7HUdUPsaPH0+LFi145ZVXuHjxolZZ//79mTNnDmfOnOG9994DICMjQ1PevHnzEi1qZmZmmjkH09PTyzl6IYSoviRBEkIIUWkoisLsjWdJysijsb05s/q10HVIj0ytVnPhwoUS29u3b69Z/vvIrhYWFsydO5c2bdpoEiFbW1uMjIwAOHTokGbi9XuuX7/OpUuXAGjQoEGZ3oMQQtQkkiAJIYSoNH47GcvuC7cw1FexZERbahnp6zqkR7Jo0SKcnZ1xd3fn1q1bWmVDhw6la9eufPrpp4wfP/4/z2ViYsKwYcMASElJYcyYMcTFxQEQERHBqFGjUKvVADz99NNleyNCCFGDSIIkhBCiUrienMXcrcUtLTN6N6N1fSsdR1Q695KTv0pLS+PmzZsoisLmzZu1ypycnDh8+DDTpk3D2dn5ga7xxhtvYGxc3B8rMDAQJycn6tevT7NmzTh27BgAdnZ2vPjii494N0IIUXNJgiSEEELnCovUTF0bRnZ+EY+7WvOst5uuQ3pgQUFBjBs3joYNG5KTk6NV5u/vj6GhIX5+fri4uDzytdzd3dm4cSOmpqZAcVJ2rxUJwN7enp07d2JvXz37bQkhREWQiWKFEELo3Jf7IwmNuYOFiQGfjmiLvl7VGdJ77dq1rFq1CoDdu3czZMgQTVn79u1JSkrCyqrsWsP8/PwIDw9n2bJlBAYGkpqaSt26dRk9ejSTJk3C2tq6zK4lhBA1kbQgCSGE0KnTMal8sS8SgPlDWlO/di0dR1RSamoqq1atYvz48SUepbs3JLeFhQXx8fFaZSqVqkyTo3saNGjA/PnzuXDhAnFxcYSGhvL6669LciSEEGVAWpCEEELoTGZeIdPWhlGkVhjc1pHBbevrOqT7Gj9+vGZuoeeff54uXbpoynr27Mm2bdvo2bOnpn+QEEKIqktakIQQQujMe1svcj05m/q1a/G/wa11HQ6xsbH8/PPPJbYPHTpUs7xjxw6tMiMjI/r37y/JkRBCVBPSgiSEEEIndp1PYO3JG6hU8MlwD6xqGeo0nmeffZbvvvsOAE9PT9zc/hwoYtCgQUybNo2AgACt1iMhhBDVj7QgCSGEqHC30nOZvfEsAM93a0RnN5sKvX5MTEyJbY0bN9Ys/33iVmtraz799FO6du2Knp786RRCiOpM3uWFEEJUKLVa4bXfzpCaXUArR0um92paYdf+7LPPaNGiBY0aNSI1NVWrLCAgAHd3d+bOncvgwYMrLCYhhBCVizxiJ4QQokKtOnaNQ1duY2ygx2cj22JkUHHf1V2/fp3Lly8DsG3bNsaOHaspa9y4MWfPnq2wWIQQQlRO0oIkhBCiwkTcyuD9ncUJylv9W9DY3qLMr3H48GEmT55M69atyc/P1yoLCAhApVLh7e1NnTp1yvzaouLl5eWVeJ2FEOJRSAuSEEKICpFXWMSra8LIL1Tj08yOsZ0blst1vv76a1avXg1AcHAwvXv31pR16dKFuLg46tWrVy7XFhUjLy+P7777jmXLlnH+/HkAWrRowQsvvMBzzz2HiYmJjiMUQlRl0oIkhBCiQny6J4JL8elYmxmx6Mk2qFSqhz5XdnY2mzZt4rXXXkNRFK2ygIAAoHj47YiICK0yPT09SY6quIyMDHr06MHkyZM1yRHApUuXePXVV/Hx8eHOnTu6C1AIUeVJC5IQQohydzTqNt8cugrAB/7u2Fs82jf8w4YN08xH5OLiolXWt29fVq9eTf/+/bG0tHyk64jK57nnnuPIkSOa9TZt2pCZmcnVq8X16/jx40yaNKnESIRCCPGgpAVJCCFEuUrLLmDGujMoCozq5ETvVg/egpOSksKWLVtKbB8wYIBm+fjx41plpqamjBo1SpKjaig6Opq1a9cCYGVlxeHDhzl58iSffvophw8fxtraGoCNGzeWaD0UQogHJQmSEEKIcqMoCm9tOkd8Wi6utma8M6DlAx/70ksvYW9vz+DBg7l586ZW2dChQ5k0aRJbtmzhySefLOuwRSW1YcMGzSOVr732Gl27dtWUderUiTfeeEOzvn79+gqPTwhRPUiCJIQQotxsCrvJtrPx6OupWDyiLaZG93+yOyUlpcQ2e3t7ioqKAAgMDNQqq1evHt999x19+/bF0NCw7AMXldLt27c1y126dClR/tdtSUlJFRKTEKL6kQRJCCFEubiRks27my4A8GqPJrR1ql1in2+++YZOnTrRoEEDMjMztcr8/f1xcXFhxowZdO/evSJCFpWcnZ2dZvnYsWMlyv+67a/7CiFEaUiCJIQQoswVqRVmrDtDRl4hHRrW4SWfRvfdLzQ0lJCQEHJycti5c6dWmbu7O1evXuXjjz/G3d29IsIWlZy/v79m9MOPPvqIw4cPa8qOHz/OBx98oFkfNmxYhccnhKgeJEESQghR5pYdiOLEtRTMjPR5prUh777zNt7e3ppH5u7x9/cHwMPDAwMD7cfvVCrVIw0FLqofV1dXRo4cCUB6ejre3t506NCBqVOn4u3tTWpqKlBcr5o0aaLLUIUQVVipE6SDBw8ycOBAHB0dUalUbNq0qcQ+ly5dYtCgQVhZWWFhYUHnzp2JiYnR2ufYsWM88cQTmJmZUbt2bXx8fMjJyXnoGxFCCFE5nItNY3FQ8Qhicwe14tvFC1m4cCGHDx/WGp4ZwMfHhytXrhAWFsbQoUN1Ea6oYpYvX46Xl5dm/dy5c1y7dk2z/vjjj/P999/rIDIhRHVR6gQpKysLDw8Pvvzyy/uWR0VF4eXlRfPmzQkODubMmTO88847WrNaHzt2jL59+9K7d29OnDhBSEgIkydPRk9PGrSEEKIqKiwsZO/evbwz9z1eXRtKoVrBz70eT3ZooJm4VU9Pj9DQUK3jDA0Nady4sS5CFlWUhYUFv//+O1999RVt2rTRbG/ZsiVffPEFwcHBWFlZ6TBCIURVV+qJYvv160e/fv3+sfytt97Cz8+PRYsWaba5ublp7TNt2jSmTJnCrFmzNNukKVwIIaquQYMGsXPnTqx7vYhF+yzqWhqzYIg7KpWKAQMGsHz5coYMGYK9vb2uQxXVgLGxMS+++CIvvvgiWVlZ7Ny5k8GDB8uIhkKIMlHqBOnfqNVqtm/fzsyZM+nTpw+hoaG4uroye/ZshgwZAkBiYiLHjx/nqaeewtPTk6ioKJo3b86CBQu0msz/Ki8vj7y8PM16eno6AAUFBRQUFJTlLYgq5N5rL3Wg5pI6UPGysrI4deoU3bp109ru6+tLcHgSFu37A/DB0NaYG6koKCjA1NSUCRMmAGX/WkkdECqVCkNDQ6kDNZi8D4iyfu1Vyr0Z1x7mYJWKwMBATfKTkJCAg4MDpqamzJ8/H19fX3bt2sWbb77J/v376d69O3/88QddunTB2tqajz/+mLZt27Jq1Sq++uorzp8/f9+WpLlz5zJv3rwS21evXo2pqenDhi+EEKIUVqxYwe7duyksLGTlypVYWlpqyq7GJfHFFUvURmZ42eUzrLE8Mi2EEKJiZGdnM3r0aNLS0rT+Nj2sMm9BAhg8eDDTpk0DoG3bthw9epRly5bRvXt3zT7PP/+85hvFdu3asXfvXr7//nsWLlxY4ryzZ89m+vTpmvX09HScnJzw9fXFxsamLG9BVCEFBQUEBQXRq1cveayihpI6UH5ycnKoVauW1raDBw+ydetWTfm90cQUReH5X0JRG92mqb05y154HGND/QqJU+qAkDogpA6I5OTkMj1fmSZItra2GBgY0LJlS63tLVq00MxV4ODgAHDfff4+0t09xsbGGBsbl9huaGgovwhC6oGQOlCGfvrpJ3788UdOnz5NfHy81nvv8OHD+emnnxgyZAjt27fX/Mx/OX6d/eG3MdLX47NR7TA3Nfmn05cbqQNC6oCQOlBzlfXrXqYJkpGRER07diQ8PFxre0REBA0bNgTAxcUFR0fH++7zb4M/CCGEKH+///47e/fuBSAoKIgBAwZoyjp16kR8fDz6+n+2DkUlZfLetosAzOzbjBYOj/5ogxBCCKFLpU6QMjMziYyM1KxHR0cTFhaGtbU1zs7OvP7664wYMYJu3bpp+iBt3bqV4OBgoLjf0uuvv86cOXPw8PCgbdu2/Pjjj1y+fJn169eX2Y0JIYS4v4iICDZs2MCxY8fYvHmz1mSsAQEBrFq1Cjc3N7Kzs7WOU6lUWslRQZGaaWvDyC1Q07WxDRO7ulbYPQghhBDlpdQJ0smTJ/H19dWs3+sbNG7cOFauXMnQoUNZtmwZCxcuZMqUKTRr1owNGzZojVA3depUcnNzmTZtGikpKXh4eBAUFESjRo3K4JaEEEL8mylTprB7926g+D29Y8eOmrLevXsTGhqKh4eHVuJ0P5/9foWzsWlY1TLk42Ee6On9+/5CCCFEVVDqBMnHx4f/Gvhu4sSJTJw48V/3mTVrltY8SEIIIcqOoiiEhIRw7NgxXn31Va2ygIAATYJ05MgRrQTJxMSEtm3b/uf5Q66l8FVw8dMEC/3dcbCq9R9HCCGEEFVDmfZBEkIIUTkMGDCAHTt2ADBkyBBNP9B76+np6fj7++PqWvrH4tJzC5i2Ngy1AgHtG+Dn7lBmcQshhBC6JhNVCCFEFVZQUEBoaGiJ7V26dNEsb9y4UavMzs6OGTNmPFRyBDB3ywViU3Nwsq7F3EEt//sAIYQQogqRBEkIIaqoWbNmUbduXTp37kx6erpW2ZNPPknfvn359ttvGTNmTJldc9vZODaevomeChYPb4uFiQypK4QQonqRR+yEEKIKKCoq0hpBDiArK4vU1FQAtm3bxujRozVlzZs3Z+fOnWUaQ3xaDm8FngfgZd/GPOZiXabnF0IIISoDaUESQohKbP369Zq+QoWFhVplAQEBmJubM2LECFxcXMo1DrVaYca6M6TlFODRwIopPZqU6/WEEEIIXZEWJCGEqMTWrVtHYGAgAAcOHKBHjx6aMm9vb5KSkjAxMSn3OL4/Es3RqGRqGeqzeERbDPXl+zUhhBDVk/yFE0IIHbt58yZLly5l3LhxJaZRCAgIAMDe3p7ExEStMn19/QpJji7GpbNoVzgA7wxoiZudeblfUwghhNAVaUESQggde+qppzhw4AAAM2fOpFWrVpqy/v37c/DgQTw9PUv0QaoIuQVFTF0bSn6Rmp4t6jKqk1OFxyCEEEJUJGlBEkKICnL58mVWrlxZYru/v79mec+ePVpl5ubmeHt76yQ5Ali0K5yIW5nYmhvzYYA7KpVKJ3EIIYQQFUVakIQQogIMGTKEzZs3o1Kp6Nu3L/Xq1dOUBQQEkJycTEBAAO7u7jqMUtvBiCS+PxINwEdPtsHG3FjHEQkhhBDlT1qQhBCiDKnVaiIjI0tsv/fYnKIobN68Wausfv36zJs3jzZt2lSaFprUrHxe++0MAGM7N8S3ub2OIxJCCCEqhiRIQghRRubOnUvDhg3x8PAgOztbq+zJJ5/E09OTTz75hP79++sowgejKAqzN54jMSOPRnZmvOnXQtchCSGEEBVGHrETQoiHoChKidae2NhYYmNjgeK+REOGDNGUtWvXjiNHjlRkiA/tt1Ox7LqQgIGeis9GtqOWkW76PwkhhBC6IC1IQghRCjt37mTcuHG4u7ujVqu1ygICAjA0NMTPz486deroKMJHcz05i3lbLgAwvXdTWte30nFEQgghRMWSFiQhhCiFr776im3btgHwxx9/4OnpqSnr2bMnSUlJWFmVb1KhVqsJCgpiz549ZGdn4+rqypgxY3B0dHyk8xYWqZm2Noys/CI6uVrzfLdGZRSxEEIIUXVIC5IQQvxNamoqq1atYurUqSXK7k3camFhQXR0tFaZoaFhuSdHZ86coVWrVvTt25dPP/2UZcuW8cYbb9CwYUOmTZtGYWHhQ5976f4oTsfcwcLYgE+He6CvVzkGjBBCCCEqkrQgCSHE3wwYMICjR48C8Morr9Co0Z8tKUOGDMHOzo6ePXtibFyxw15HRETg6+tLampqibLCwkKWLFlCVlYW33zzTanPHRqTyuf7rgDw3pDWNKhj+sjxCiGEEFWRtCAJIWqs2NhYAgMDS2wfPHiwZvne43T31K5dm/79+1d4cgQwa9YsTXLk4eHB2rVr+eOPP5g1axaGhoYAfPvtt5w8ebJU583KK2Ta2jCK1AqDPBwZ0q5+mccuhBBCVBXSgiSEqJFGjBjBunXrMDAwIDExUWtQhSeffJL4+HgCAgK0+hjpUnx8vGb+pLp163Lo0CEsLCwAePzxx3FwcODVV18FYPny5Tz22GMPfO73tl3kWnI2jlYmvDe4ddkHL4QQQlQh0oIkhKj2EhISSmxr0KABUPxo2tatW7XK3NzcWLx4MV5eXujpVY63yQsXLmhGzRs5cqQmObpn0qRJmuWwsLAHPu/uCwmsCbmBSgWfDG+LlalhmcQrhBBCVFWV4y+/EEKUgw8//JAWLVrQokUL8vPztcr8/f1xd3dn7ty5dO3aVUcRPri/Jmp/vxeAgoKC++77bxLTc5m14SwAz3Vzo0sjm0eMUgghhKj6JEESQlRb586d4/Lly9y5c4f9+/drlXl6enL27FnmzJmjNQhDZeXh4YGRkREAv/76K4mJiVrlX3zxhWa5U6dO/3k+RVF4bf1ZUrMLaOlgyfReTcs2YCGEEKKKkgSpCiksLGTNmjX4+vpiY2ODvb09gwYNYteuXSiKouvwhNCJCxcuMHXqVLp161bi9yAgIACVSoW3tzf6+vpaZSpV1RrC2sbGhuHDhwNw584dOnXqxJIlSwgMDGTcuHG8++67mn1feOGF/zzfqmPXORiRhLGBHp+NbIuxgf5/HiOEEELUBDJIQxWRmZnJ4MGD2bdvn9b2rVu3snXrVsaOHcsPP/xQ4kOgENXdunXrOHPmDFA8R1Dbtm01Zf369SMuLo569erpKLqy9cEHH7B//35u3rzJ9evXmTZtWol9Zs+eTatWrf71PFduZfD+jksAvOnXgiZ1Lf51fyGEEKImkRakKmLChAlayVG9evWwtrbWrP/000+88847ughNiHKXk5NDYGAgc+fOLVHWuXNnAIyMjDh37pxWmYmJSbVJjgDq16/P4cOH8fHxKVFmZWXFokWLWLBgwb+eI6+wiFfXhJFXqKZ7Uzue7tKwnKIVQgghqiZpQaoCLl26xPr164HiD0G//vorffv2paioiJ9//plnn32WwsJCPvvsM9544w2srKx0HLEQZcvX15fjx48D8Mwzz2hGoAPo0qULXl5eDBo0CEtLS12FWGFcXFzYv38/586dY8+ePWRlZeHm5sbQoUMxMzP7z+M/DYrgYnw61mZGfPRkmyr3qKEQQghR3qQFqQpYvXq1Zvndd9+lX79+qFQqDAwMGD9+PM888wwA2dnZbNq0SUdRCvHoUlJS2Lt3b4ntffv21Szfmwvontq1azNixIgakRz9lbu7OzNmzODdd99lzJgxD5QcHYtK5puDVwFY6O+OvaVJeYcphBBCVDmSIFUBcXFxmuUePXqUKO/Zs+d99xWiKnn66aepW7cuAwYMIDMzU6ts+PDhTJo0iR07dvDss8/qKMKqLS27gOnrwlAUGNnRiT6tqs+jh0IIIURZKnWCdPDgQQYOHIijoyMqleq+LRaXLl1i0KBBWFlZYWFhQefOnYmJiSmxn6IomtYQafn4Z7Vr19Ys/72PBcDZs2c1y/J4nagKMjIySmwzNzensLCQ3Nxcdu7cqVXWsmVLvvvuO/r166cZ6lqUzjubzxOflouLjSnvDGip63CEEEKISqvUCVJWVhYeHh58+eWX9y2PiorCy8uL5s2bExwczJkzZ3jnnXcwMSn5KMeSJUvk+fcHMGjQIM3yvHnziI2N1ayfO3eOzz//HCieHHLgwIEVHp8QD+qLL77g8ccfp0mTJhQVFWmV+fv74+LiwowZM2jdurWOIqyeNoXeZMuZOPT1VCwe0RYzY+l+KoQQQvyTUv+V7NevH/369fvH8rfeegs/Pz8WLVqk2ebm5lZivzNnzvDpp58SEhKCg4PDv14zLy+PvLw8zXp6ejpQPHP8X2ePr666dOlC+/btOX36NJGRkTRu3JhevXqRm5vLvn37UKvVQPGcL/Xq1asRPxNAc5815X6rg3379nHixAkAgoOD6datm6bM29ub8PBwzZcmD/K6Sh34bzfv5PD2pvMAvOzjRmsH82r185I6IKQOCKkDoqxf+zL9GlGtVrN9+3ZmzpxJnz59CA0NxdXVldmzZzNkyBDNftnZ2YwaNYovv/zygYbgXbhwIfPmzSuxff/+/ZiampblLVRazz//PG+//TZJSUnk5eWxbds2rXI3NzcGDx7Mjh07dBSh7gQFBek6BPEXkZGRHDt2jJiYGN566y2tMldXV83/hw4dKtHX6GFJHbg/tQJfXtAnM0+Fi7mCS3Y4O3aE6zqsciF1QEgdEFIHaq7s7OwyPZ9K+fvU86U5WKUiMDBQk/wkJCTg4OCAqakp8+fPx9fXl127dvHmm2+yf/9+unfvDhR/2C8qKuK7776773n+7n4tSE5OTsTHx2NjY/Ow4Vc5iYmJfPTRR/z444/cuXMHAEdHRyZNmsS0adMwNzfXbYAVrKCggKCgIHr16oWhoaGuwxF3de/enWPHjgHF/eOaN2+uKcvMzOTWrVs0atSoTK4ldeDfLT8YzcdBVzAz0mfzy11oaF39vlCSOiCkDgipAyI5ORkHBwfS0tLKZFTbMm9BAhg8eLBmhve2bdty9OhRli1bRvfu3dmyZQv79u0jNDT0gc9rbGyMsbFxie2GhoY16hehfv36LFmyhEWLFhETE4O+vj7Ozs7o6+vrOjSdqmn1oDIoLCzkwIEDnDt3jqlTp2qVPfnkkxw7dgw9PT1Onz6Nu7u7pqxOnTrUqVOnzOOROlDS+ZtpLNkbCcCcQa1oXLd6D+AidUBIHRBSB2qusn7dyzRBsrW1xcDAgJYttUdIatGiBYcPHwaK+yBERUVpjcwGxf1nvL29CQ4OLsuQqiUjIyMaN26s6zBEDebl5cXx48fR09Pjqaeews7OTlM2fPhwzM3NGTJkCPb29jqMsubKyS/i1TWhFKoV+raqx7AODf77ICGEEEIAZTwPkpGRER07diQ8XPsZ94iICBo2bAjArFmzOHv2LGFhYZp/AIsXL+aHH34oy3CEEI8oOztbM6jCX917XFatVpeYuLVBgwY899xzkhzp0Ps7LhGVlIW9hTEL/d1ltFAhhBCiFErdgpSZmUlkZKRmPTo6mrCwMKytrXF2dub1119nxIgRdOvWTdMHaevWrZqWoXr16t13YAZnZ2dNB24hhO49++yzrF69Gj09PZKSkrSG6h8+fDjR0dEEBATg5+enwyjF3+2/nMhPf1wH4ONhHtQxk3mjhBBCiNIodYJ08uRJfH19NevTp08HYNy4caxcuZKhQ4eybNkyFi5cyJQpU2jWrBkbNmzAy8ur7KIWQpSp/Pz8EhOwFhQUaEaFCQoK0ppjq0OHDqxbt65CYxT/7XZmHq+vPwPAhK4udGtq9x9HCCGEEOLvSp0g+fj48F8D302cOJGJEyc+8DkfYSA9IcQj+O6771izZg1Xr14lKipK61GsgIAAduzYwZAhQ3B2dtZhlOJBKIrCrA1nuZ2ZT9O65rzRt/l/HySEEEKIEmQ6dSFqsA0bNrB3714AQkJC6NSpk6asX79+xMfH1/hREquKX0/c4PdLiRjp67FkRDtMDOV1E0IIIR5GmQ7SIISofCIiIli4cCHjx48vURYQEAAUTzR8+/ZtrTIDAwNJjqqIq0mZvLftIgCv92lGS8dHnwNCCCGEqKmkBUmIam7kyJGaecfmzp2Li4uLpuzJJ5/ksccew8PDQ0Y6q6IKitRMWxtGTkERno1smOQlg90IIYQQj0JakISoBhRFISQk5L5D5d9rJQJKzDNWu3Zt2rZtK8lRFfb53iuciU3D0sSAT4Z7oKcnr6UQQgjxKKQFSYhqwMvLi6NHj2JoaIi/vz9WVlaaspEjR2JsbIy/vz9ubm46jFKUtZBrKSzdXzztwvv+7jhY1dJxREIIIUTVJy1IQlQhBQUFXLp0qcT2Dh06aMq3bdumVdaoUSNee+01SY6qEbVa4cej1xi74jhqBfzb12dAG0ddhyWEEEJUC9KCJEQVMWXKFH755RcAEhISMDQ01JQNHz6cyMhI/P396dOnj65CFBUgPi2H1387y+HI4kE1vJvYMm9QKx1HJYQQQlQfkiAJUQmp1Wr09LQbeG/dukVKSgoABw8epEePHpoyLy8vduzYUaExioqlKAqbw+J4Z/N5MnILMTHU402/Fox5vKH0OxJCCCHKkDxiJ0Ql8uuvvzJ06FDat29fYgLlgIAAzM3NGTlyJLVr19ZNgEInUrPyeXn1aaauDSMjtxAPp9psn+LN011cJDkSQgghypi0IAlRiSxfvpwDBw4AcOHCBVq3bq0pGzJkCIMGDcLExERX4Qkd2Hf5Fm9sOEdSRh4Geiqm9GjCSz6NMNCX77eEEEKI8iB/YYWoYHFxcSxdupRp06aVKLs3JLe9vT3Xrl3TKjMyMpLkqAbJyitk9sZzTFx5kqSMPBrbmxP4Ulem9GgiyZEQQghRjqQFSYgK1qtXLy5evIhKpeKNN96gXr16mrKRI0fi4eFB165d0dfX12GUQpdOXkth+rozxKRkAzDJy5XX+zTDxFDqhBBCCFHe5GtIIcrJ5cuXWb9+fYntQ4cOBYo73e/evVurzM7Ojm7duklyVEPlFRbxwc7LDFt+jJiUbOrXrsXqZx/nnQEtJTkSQgghKoi0IAlRDnx9fQkODsbU1BQ/Pz9MTU01ZaNGjUJfX5+AgADc3d11GKWoTC7FpzNtbRiXEzIAeLJDA94d2BJLE8P/OFIIIYQQZUlakIR4BGq1mhs3bpTY3rhxYwCys7NLtBK1atWKefPm0aZNG1QqGYGspitSK3wdHMWgLw9zOSEDazMjlo3pwMfDPCQ5EkIIIXRAWpCEeEhvvPEGq1evpqioiNjYWK15i4YNG8alS5fw9/fn8ccf12GUojK7npzFjHVnOHk9FYCeLeqy0N8dOwtjHUcmhBBC1FySIAnxkC5dukRsbCwAf/zxB56enpqy3r1707t3b12FJio5RVH49cQN5m+/SHZ+EebGBrw7sCXDOjSQVkUhhBBCxyRBEuJfbN26lfXr1xMTE8P+/fu1ygICAti1axe9evWSQRXEA0tMz+WNDWfZH54EwOOu1nw8zAMna9P/OFIIIYQQFUESJCH+xfz58zlx4gQAUVFRNGrUSFM2bNgwhgwZgpWVla7CE1XMjnPxvBV4jtTsAowM9JjZpxkTu7qipyetRkIIIURlIYM0iBovNTWVVatWMW/evBJl9yZutbCw4MKFC1plpqamkhyJB5KWXcDUNaG89MtpUrMLaOVoydbJXjzj7SbJkRBCCFHJSAuSqPE6d+5MREQEBgYGTJkyhTp16mjKnnrqKVq1akXPnj0xNpaO86L0Dl+5zWu/nSEhPRc9Fbzk05gpPZpgZCDfTwkhhBCVkfyFFjXGzZs32bNnT4ntAwYMAKCwsJDt27drldWvX5/+/ftLciRKLSe/iLlbLjBmxXES0nNxtTVj/YuevNanmSRHQgghRCUmLUiiRujXrx+7du3CysqKxMREjIyMNGWjR49GURT8/f3p0qWLDqMU1UXYjTtMXxvG1dtZAIzt3JDZfs0xNZK3XCGEEKKyk7/WotpJTk7GxsZGa9u99bS0NPbt20ffvn01ZR06dKBDhw4VGqN4eIqiEBwczKpVq7h+/TpZWVncvHmTp59+GnNzc53GVlCk5ot9kSzdH0mRWqGupTGLnvSge1M7ncYlhBBCiAcnCZKoNubNm8eaNWvIy8sjKipKaz6ZgIAAzp07h7+/Py1atNBhlOJRpKSk8OSTT5YYcv3EiRO8++67/Pbbb/j6+uoktiu3Mpi2LozzN9MBGOThyP8Gt6K2qdF/HCmEEEKIykQSJFFtHD58mMuXLwMQFhZGu3btNGVDhgxh6NChugpNlIHCwkIGDRrEkSNH7luenJzMgAEDOHbsGG3atKmwuNRqhR+OXuPDXZfJL1RjVcuQ+UNaM9DDscJiEEIIIUTZkZ7CospQFIX9+/czefJk/P39S5QHBASgUqnw9vYmJydHq+yvrUmiatq8ebMmObK3t+eXX34hMTGRjz76iB49egCQnZ3N3LlzKyymm3dyeOq747y37SL5hWq6N7Vjz7RukhwJIYQQVVipE6SDBw8ycOBAHB0dUalUbNq0qcQ+ly5dYtCgQVhZWWFhYUHnzp2JiYkBih+ReeWVV2jWrBmmpqY4OzszZcoU0tLSHvlmRPWmUql4depUvv5uJVsPhLA39AqF6j/LR48eTVxcHAcPHsTT01N3gYpysWLFCs3yDz/8wOjRo6lduzZNmjRh48aNODg4AMWJVGJiYrnGoigK60/F0nfxQY5dTaaWoT7zh7Rm5YSO1LU0KddrCyGEEKJ8lfoRu6ysLDw8PJgwYYJmEs2/ioqKwsvLi0mTJjFv3jysrKy4dOkSJibFHxri4uKIi4vj448/pmXLlly/fp0XXniBuLg41q9f/+h3JKqcIrVCSlY+tzPzSM7MJy4lgyOnzxF7Ow3X5m24nZlX/C8jn8x+83HqV5zXv7AxGnNDfS4ZRjDq8YY0srPE0tJSx3cjysuVK1cAMDc31xpkA6BWrVoMGjSI5cuXo1aruXr1Kvb29uUSR3JmHm8GnmP3hVsAtHeuzafD2+Jia1Yu1xNCCCFExSp1gtSvXz/69ev3j+VvvfUWfn5+LFq0SLPNzc1Ns9y6dWs2bNigWW/UqBELFixgzJgxFBYWYmAg3aKqg7zCouKkJ6M48Um6m+QkZ+ZrJTzJWXmkZOWjVv5+Bn3AmlOnYv+2vTg5sjDWR09PRVpOId8dvsZ3h6/RycWaER2d8HN3oJaRfgXcpahI9+aiysnJIT09ndq1a2uVJyQkaJbvfSFT1oIu3mL2xrPczszHUF/F1J5Neb6bGwb68rSyEEIIUV2UaTaiVqvZvn07M2fOpE+fPoSGhuLq6srs2bMZMmTIPx6XlpaGpaXlPyZHeXl55OXladbT04tHiSooKKCgoKAsb0H8i+z8Qm5n5t9NcvJJvtfqk/XnenJmHrcz80nPLSzVuVUqqGNqiK2ZMck3o4m5coGirDsMG9gXny4dsDEzwtbcCFtzY6zNjDA20CMnL4/Pf9tHlGLPgSvJnLiWwolrKczZcoFBHvUY3qEBrRylRam66N69OxcuXKCoqIj58+ezcOFCze//iRMn2LZtG1DcP6lJkyZl+t6QkVvI+zvDWX/6JgBN7c356MnWtHSwRFEXUaAuKrNridK59zrL34KaS+qAkDogyvq1VymKUuK7+wc+WKUiMDBQk/wkJCTg4OCAqakp8+fPx9fXl127dvHmm2+yf/9+unfvXuIcycnJtG/fnrFjxzJ//vz7Xmfu3LnMmzevxPbVq1djamr6sOHXeIoCOUWQUXDvn4qM/OL/M/+67e5yvrp0Ax3oqxTMDcHCECwMlbv/g7mBwv5dW4i6EIqxks/ihfOwMNZH/+7pL168yL59++jSpQtt2rTB0NDwP691Jw9OJKn4I1GP5Lw/42xgptDZXk0HWwVTaZys0m7cuMGUKVO495bVqlUrHnvsMeLi4jhw4AD5+fkADB8+nNGjR5fZdSPT4JcofVLyVKhQ8HVQ8HNWYyiNRkIIIUSlkJ2dzejRozWNLo+qTBOkuLg46tevz6hRo1i9erVmv0GDBmFmZsavv/6qdXx6ejq9e/emTp06bNmy5R8/CN+vBcnJyYn4+PgSE4LWdEVqhTvZxS06t++17Py1lSczn9tZxY+6JWflU1BUupffxFAPWzMjbMyNsTU3wsbMCJu7LTu2d5eLW3uMsaplgEqlIjs7u0QiO3z4cM0AH7///jvdunUr9b0WFBQQFBREr169NHVHrVb4IzqFdadusufiLc39mRjq0a9VXYZ1aMBjDWvLqHZV1OLFi3njjTf+sbxLly7s3LmzTL44ySsoYvHeSL4/eh1FgQa1TfgwoDWdXKwf+dyi7NzvfUDULFIHhNQBkZycjIODQ5klSGX6nbqtrS0GBga0bNlSa3uLFi04fPiw1raMjAz69u2Lubk5gYGB/1qhjY2NNf0P/srQ0LBG/iIoisLWs/GcuXGnRL+e+/fn+XcWJgbYmRv/mejc+2dhhI2ZMXYWf243NdJ/oORCURQ+/vhjfvvtN7Kysrhw4YJW+bBhwwgLCyMgIICGDRs+0uv493rQvXk9ujevR2pWPoGhN1kTEkPErUwCw+IJDIvHzdaMER2d8G/fADuLkvVKVF4zZ87EycmJOXPmaAZtgOKBGyZOnMj777+PmdmjD5Zw/mYa09eFEXErE4ARjznxzsCWmBtLM2RlVVP/Hog/SR0QUgdqrrJ+3cv0r72RkREdO3YkPDxca3tERAQNGzbUrKenp9OnTx+MjY3ZsmVLuXWoro4ycguYuf4sO88n/OM+KhVYmxqVSHhszI2wu5v4FK8bY2NmhIlh2Q9ooFKp2Lx5MyEhIUDx0O8tWrTQlI8YMYJRo0aVa0tOHTMjJnq5MqGrC2E37rA25AZbzsRx9XYWC3de5qPd4fRqWZcRHZ3wbmKHvp60KlUFo0aNYsSIERw/fpyoqCjCw8OZOnVqmbQmFxapWXYgiiW/X6FQrWBrbsQH/m3o2bJuGUQuhBBCiKqg1AlSZmYmkZGRmvXo6GjCwsKwtrbG2dmZ119/nREjRtCtWzdNH6StW7cSHBwMFLcc9e7dm+zsbH7++WfS09M1gy7Y2dmhry+jj/2TywnpvPjzaaJvZ2Gor2J0J2ca1DHVtPTca/WxNjWqkFG1FEXh9OnTbNiwgVu3bmnNUwPFE7ceOXIEDw8PkpOTtcoq8nVWqVS0c65DO+c6vD2gJdvOxLEm5AZhN+6w83wCO88n4GhlwrDHnBj2WAMa1JF+bZWdnp4eXbp04bHHHmPHjh1l0pwefTuL6evCCI25A0DfVvVYMLQ1NubSyiiEEELUJKVOkE6ePImvr69mffr06QCMGzeOlStXMnToUJYtW8bChQuZMmUKzZo1Y8OGDXh5eQFw6tQpjh8/DkDjxo21zh0dHY2Li8vD3ku1tvF0LG8GniO3QI2jlQlLn2pPO+c6ug6LkSNHEhkZiZ6eHh988AF2dnaasqeffpqBAweWeJ11ydzYgJGdnBnZyZnLCemsDblBYOhN4tJy+WzvFT7fdwXvJnaM7OhEzxZ1MTKQnvjVnaIo/PzHdd7fcZmcgiIsjA2YO6gV/u3rS181IYQQogYqdYLk4+PDf43rMHHiRCZOnPjQx4s/5RYU8b9tF1l9PAYA7ya2fDayHdZmRhUWQ2FhIQcPHuTatWtar6tKpSIgIIAPP/wQRVE4duwYgwYN0pTb2NhU6kE0mtezZM7AVrzRtzl7Lt5izYkYjkYlczAiiYMRSdiYGRHQoQHDH3Oisb25rsMV5SAhLZeZG85yMCIJAM9GNnw0zIP6tWvpODIhhBBC6Ir0OK7EbqRk89Ivpzl3Mw2VCqY80YQpPZpUaF8ZRVFo1aoVERERmJubM3r0aK0+Y+PGjcPNzY3BgwdTt27V7KdhYqjPIA9HBnk4cj05i3Unb/DbyVgSM/L45uBVvjl4lY4udRjR0Zn+MglttbHlTBzvbDpPWk4BxgZ6vNG3OeM9XdCTvmhCCCFEjSYJUiW1/3IiU9eGkZZTQG1TQ5aMaItPM/tyvWZ2djZRUVG4u7trtqlUKjw9PYmIiCAzM5M9e/ZotRK1aNFCa/CFqq6hjRmv92nOtJ5N2R+exNqQGPZdTiTkWioh11KZt+UCg9o6MqqTM63rW+k6XPEQ7mTn8/am82w7Gw+Ae30rFo/woLG9hY4jE0IIIURlIAlSJVOkVvjs9wg+31c8EIZHAyuWPtW+XAcOUBSFp556ik2bNmFjY8P169fR0/uz782oUaPIzs4mICBAq/9ZdWagr0evlnXp1bIuCWm5bDgdy9qQG8SkZPPL8Rh+OR5DK0dLRnZ0YlDb+ljVkmFFq4Lg8ERmrj9LYkYe+noqJvs2ZvITjTGsgEFNhBBCCFE1SIJUiSRn5jF1bRiHrtwGYGznhrw9oAXGBmX7SFdhYSEGBn++9CqVijt37pCTk0NsbCwhISE8/vjjmvLevXvTu3fvMo2hKqlnZcLLvo15sXsj/riazJqQG+w6n8CFuHTe2XyB+dsv0d/dgREdnejkai0d+yuh7PxCFmy/xC93+/K52ZmxeHhbPJxq6zYwIYQQQlQ6kiBVEqeupzJ59Wni03KpZajPBwHuDG5bv8zOrygKy5cvZ/369WRkZGhGErwnICCAkydPMmTIkDIZMrk60tNT4dnYFs/GtiUmod0YepONoTdlEtpK6NT1VKavC+N6cjYA4z1deKNvc+lLJoQQQoj7kgRJxxRFYeXRayzYfolCtYKbnRnLxnSgad2y7Q+hUqn49ttvOX36NFA8pLqrq6umfMyYMYwfP17moXpADzIJbc8WdRnRyYluMgmtTuQXqvlsbwRfB0ehVsDByoSPnvTAq4mtrkMTQgghRCUmCZIOZeUV8saGs5rO4v3dHfjwyTaYGz/8yxIREcHGjRtJSkrik08+0SoLCAjg9OnTuLq6EhMTo5UgGRtLa8fD+PsktNvPxvHrieJJaHddSGDXhQQc7k5CO1wmoa0w4QkZTF0bxqX44kmoh7arz9xBraSvmBBCCCH+kyRIOnLlVgYv/HyKqKQsDPRUvOnXggldXR6p/4qiKPTo0YPY2FgMDQ159913sbL6c6S1CRMm0K9fP9q2bSv9ZMqBubEBIzo6M6Kj9iS08Wm5fL73Cl/su4JXY1tGdXKWSWjLSZFaYcXhq3y8O4L8IjV1TA1ZMNQdP3cHXYcmhBBCiCpCEiQd2Bx2k9kbz5GdX0RdS2O+eqo9HRpaP/DxiqJw8uRJrl27xrBhwzTbVSoV/v7+fP755xQUFHDw4EEGDhyoKXdwcMDBQT4oVoS/T0K7NiSGI5HJHLpym0NXbmNtZkRA+/qM6Ogkw0uXkRsp2cxYd4YT11IAeKK5PR8EuGNvYfIfRwohhBBC/EkSpAqUX6hmwfaL/HjsOgCejWz4fFQ7bM0f/PE2RVFwd3fnwoULWFtbM2TIEAwN/3xsaPz48Tg7OzN06FDc3NzK/B5E6fx1EtqY5GzWnozRTEL77aFovj0UzWMN6zCioxP92zhgaiS/kqWlKPDbqVgW7AgnK78IMyN93hnQkhEdnaSlVAghdCA3N5ekpKQKu55arcbJyYm4uDitaUpE9WJsbIy9ffnOCXqPfBqrIHF3cnjpl9OE3bgDwGTfxkzr1fRfO+8XFBQQExNDo0aNNNtUKhWtW7fmwoULpKSkcODAAXr27Kkpb9euHe3atSu3+xAPz9nGVDMJbXB4EmtCbrA/PJGT11M5eT2V/229yKC2jozs6Ezr+pby4f4B3M7M47twPc7/cRGAji51+GRYW5xtpK+XEELoQm5uLomJidSvX7/CBn5Sq9VYWVlhaWkpCVI1lpSURHp6eoWMtiwJUgU4GJHEq2tCSc0uwNLEgMUj2tKjRd1/3F9RFJ577jk2btyItbU1ERERWh+WR4wYQVpaGgEBAbRv374ibkGUIQN9PXq2rEvPlnW5lZ7L+lMlJ6Ft6WDJyE5ODPaoj5Vp9R5YQFEUsvOLSM8tICO3kPScgr8tF5KeW0B6TiEZucXrGbkFpOcUEJ+WS3a+Hob6Kmb0bsaz3m4yYqAQQuhQUlJShSZHouawtbUlNjZWEqSqTq1W+GJfJEv2RqAo0Lq+JV8/1QEna+1vtxVF0UqAVCoVkZGRpKSkkJKSwvnz53F3d9eUDx06lKFDh1bYfYjyU9fy/pPQXoxP593NF1iw/RJ+7g6MrMST0BYWqYuTmfsmNQUlyu6t39uWkVtIkVp56Os7miosn9AFd6cH78cnhBCi/EhyJMpDRX4GkgSpnKRm5TN1bRgHIoqfwR3VyZk5A1tiYlj8pqFWq1m9ejUbN24kMzOTPXv2aB1/b+LW/v37V8oPxaJs/X0S2k1hN1lz4gbhtzIIDL1JYOhNXO9OQhtQhpPQKopCboH6brJSQFrO/ZOZjLstOPcry84vKpNYDPRUWNYyxMLEAEuTv/1fy1Br+V6ZmaGKqNOHaF5PBroQQgghRNmQBKkcnLlxh5d+Oc3NOzkYG+ixYKg7T3ZooLWPnp4e77//PpcuXUKlUhEfH681wtyECRN45plnMDGREbhqmjpmRkzo6sp4T+1JaKNvZ/HBzst8vDucHi3sGdnRma6Nbcm5+3ja/R9D005wMvJKJjqFj9B681emRvqaxKVEovOXda3lv5TVMtQv9ZcBBQUFRMv3B0IIIYQoQ5IglSFFUfj5eAzvbb1IfpEaFxtT/tfHmXOHNvPejhTeeecdrf0DAgKYP38+dnZ2REREaCVIZmZmFR2+qGTuNwntmpAbhMbcYfeFW+y+cKvMrqWn4h9abwyxrPX3lpySZeYmBhjqS8dYIYQQQlR9kiCVkez8Qt4KPE9g6E0A+rSqy4cB7jR3a8itW7cwNTVlxowZmJr+2f/omWeeoXfv3nh6esrzuuJf/XUS2vCEDNaExBAYepM72QUAmBjqFScsmhaZ4uW/JjGWf2vJuVdmYWKImVHpW2+EEEIIUf5UKhWBgYEMGTKkQq7n4uLC1KlTmTp16gPtf+3aNVxdXQkNDaVt27blGltFkQSpDEQlZTJxxTGu38lHX0/FrL7NecbbFZVKxaBBg/j222/Jzs5m//799O/fX3Ncw4YNadiwoQ4jF1VRs3oWzBnYijf9WpCeU4CFiSFGBtJ6I4QQQjyKo0eP4u3tTa9evdi1a1epji1tUlGZhYSElPmTTCtXrmTq1KncuXOnTM9bXiRBekTbztzklZ+OoxgYo2Tf4ZdX+9C5ka2mfPz48Tg4OBAQEKA1Ep0Qj8pQXw+bUkwyLIQQQoh/9v333/PKK6/w3XffERMTg7Ozs65D0gk7Oztdh6Bz8rVzKajVahISEgAoKFLzv60XmfxrGIqBMbkx54j9fjJFCeFax3h6ejJv3jzatGkjjzCVEbVaTUhICDt37iQiIoKiorIZRU0IIYQQNVNWVhbr1q3jxRdfZMCAAaxcubLEPlu2bOGxxx7DxMQEW1tb/P39AfDx8eH69etMmzYNlUql+bw3d+7cEo+cLVmyBBcXF816SEgIvXr1wtbWFisrK7p3787p06cfOO6tW7dSu3Zt1Go1AGFhYahUKl5//XXNPs8//zyjRo3SrB89epRu3bpRq1YtnJycmDJlCllZWZpyFxcXlixZolm/fPkyXl5emJiY0LJlS37//XdUKhWbNm3SiuXq1av4+vpiamqKh4cHx44dAyA4OJgJEyaQlpam+fnMnTv3ge9RFyRBegBqtZpXX30VZ2dn+vTpQ0JaLqO++YPvj0QD4G2bi9v1bXz0v3do3LixjqOtvhRFYfny5TRp0oROnToxePBgZs6cSfPmzVm6dCmKUjajsQkhhBCibH366ac0aNCABg0aEBwcrFUWHR2tKXvllVdKHDto0CBN+d+tXLkSZ2dnWrVqxcaNGx86vrVr19KsWTOaNWvGmDFj+OGHH7Q+V2zfvh1/f3/69+9PaGgoe/fu5bHHHgNg48aNNGjQgP/973/Ex8cTHx//wNfNyMhg3LhxHDp0iD/++IMmTZrg5+dHRkbGAx3frVs3MjIyCA0NBeDAgQPY2tpy4MABzT7BwcF0794dgHPnztGnTx/8/f05e/Ysa9eu5fDhw0yePPm+51er1QwZMgRTU1OOHz/ON998w1tvvXXffd966y1ee+01wsLCaNq0KaNGjaKwsBBPT0+WLFmCpaWl5ufz2muvPfDPSBfkEbsHoKenx/Hjx7l58ybJ+jb0XRzMndwiLEwM+GSYB71b1YPXAnQdZrWmKArTp0/X+kbjnuvXrzN58mQuXLjA0qVLpaVOCCGEqGTS09O5ebN4IKu8vDytsqKiIk1ZampqiWOTkpI05X+XlZWlKcvOzn7o+FasWMGYMWMA6Nu3L5mZmezdu5eePXsCsGDBAkaOHMm8efM0x3h4eABgbW2Nvr4+FhYW1KtXr1TXfeKJJ7TWly9fTp06dThw4AADBgz4z+OtrKxo27YtwcHBdOjQgeDgYKZNm8a8efPIyMggKyuLiIgIfHx8APjoo48YPXq0pq9UkyZN+Pzzz+nevTtff/11iell9uzZQ1RUFMHBwZp7W7BgAb169SoRy2uvvabpaz9v3jxatWpFZGQkzZs3x8rKCpVKVeqfj65IC9JdarWaLVu2MG7cOEaMGFGi3N8/gDpdR1J35Hzu5BbRwsGSba94FSdHotzt2rVLKznq2bMnb731Fu3atdNs+/rrr9m8ebMOohNCCCHEv7G0tKR+/frUr18fY2Pt/rP6+vqasjp16pQ41s7OTlP+d2ZmZtSvXx9HR0etkYJLIzw8nBMnTjBy5EgADAwMGDFiBN9//71mn7CwMHr06PFQ5/83iYmJvPDCCzRt2hQrKyusrKzIzMwkJibmgc/h4+NDcHAwiqJw6NAhBg8eTOvWrTl8+DD79++nbt26NG/eHIBTp06xcuVKzM3NNf/69OmDWq0mOjq6xLnDw8NxcnLSSmw6dep03zjatGmjWb43dU1iYuID30dlIi1Id6lUKl599VWuXbuGgYEBKSkpWFtbA5CWXcB5665YerUEYFiHBrw3pDUmhjI0d0X57LPPNMtffvklL7/8MgUFBXTs2JGEhAReeOEFzX4VNQymEEIIIR7M9OnTmT59+n3LXF1diY2N/cdjt2zZ8o9l48eP5+mnnyY9PR1LS8uHim3FihUUFhZqJWCKomBoaEhqaip16tShVq1apT6vnp5eicf/CwoKSsSflJTEkiVLaNiwIcbGxnTp0oX8/PwHvo6Pjw8rVqzgzJkz6Onp0bJlS7p3786BAwdITU3VPF4HxQ0Czz//PFOmTClxnvsNSqEoygM/mWNoaKhZvnfMvb5RVU2Na0FKTU3lp59+0vrADcUvZEBA8WNytWrV4ty5cwCcv5nGgC8PcTAyFSMDPT4McOejYR6SHFUgtVrN3r17AWjQoIEmGbpn/PjxuLq6AsXP3pbmTUUIIYQQNVdhYSGrVq3ik08+ISwsTPPvzJkzNGzYkF9++QUobh2591nkfoyMjEoMGmVnZ0dCQoJWkhQWFqa1z6FDh5gyZQp+fn60atUKY2Njbt++Xap7uNcPacmSJXTv3h2VSkX37t0JDg7W6n8E0L59ey5cuEDjxo1L/DMyMipx7ubNmxMTE8OtW39OTh8SElKq+OD+P5/KrEYlSEVFRTRr1oynn36aOXPmlPgg/eyzz7Jt2zaSkpLo1q0ba07E4P/1UW6k5OBsbcrGFz0Z0bFmDvmoSwUFBRQWFgJQv379EpPq6unp4eTkBBR/0/H3Z5uFEEIIIe5n27ZtpKamMmnSJFq3bq3178knn2TFihUAzJkzh19//ZU5c+Zw6dIlzp07x6JFizTncXFx4eDBg9y8eVOT4Pj4+JCUlMSiRYuIiopi6dKl7Ny5U+v6jRs35qeffuLSpUscP36cp556qtStVff6If3888+avkbdunXj9OnTWv2PAN544w2OHTvGyy+/TFhYGFeuXGHLli33HRwDoFevXjRq1Ihx48Zx9uxZjhw5ohmkoTR9vl1cXDT9um7fvv1I/cUqQrVNkGJjYzl8+LDWNn19ffr06QNAWloa+/fv1ypv1qwZ/fv3R60y4PX1Z5m18Rz5hWp6trBn62QvWte3qrD4xZ+MjY1xdHQEip+d/ftzufHx8fzxxx8A2NraYm5uXuExCiGEEKLqWbFiBT179sTKquRnvICAAMLCwjh9+jQ+Pj789ttvbNmyhbZt2/LEE09w/Phxzb7/+9//uHbtGo0aNdLMI9SiRQu++uorli5dioeHBydOnCgxetv3339Pamoq7dq1Y+zYsUyZMgV7e/tS34evry9FRUWaZKhOnTq0bNkSOzs7WrRoodmvTZs2HDhwgCtXruDt7U27du145513NH2G/k5fX59NmzaRmZlJx44deeaZZ3j77bcBSgzo8G88PT154YUXGDFiBHZ2dlrJZaWklNKBAweUAQMGKA4ODgqgBAYGltjn4sWLysCBAxVLS0vF3Nxcefzxx5Xr169rynNzc5XJkycrNjY2iqmpqTJw4EDlxo0bDxxDWlqaAii3b98uUVZYWKh4eXkpgOLi4qKo1Wqt8j179ijTpk1TDh06pBQVFZU4PjopU+mz+IDS8I1tiuusbcrS/VeUoiJ1if1ExXrrrbcUQAGUdu3aKUePHlXy8vKURYsWKY899pim7PXXX9d1qOUuKytLWbFihfLMM88o48ePVz7++GMlMTFR12HpRH5+vrJp0yYlPz9f16EIHZE6IKQOVC4xMTEVfs2ioiIlNTX1vp/rRNk7fPiwAiiRkZEVfu1/ql+3b99WACUtLa1MrlPqQRqysrLw8PBgwoQJmj47fxUVFYWXlxeTJk1i3rx5WFlZcenSJa0sc+rUqWzdupU1a9ZgY2PDjBkzGDBgAKdOnSrx+NR/SUtL08r69fX1NU2T165dIzQ0lPbt22vKe/Xqdd+hCQF2X0jgtXVnyMgrxNbciM9HtcOzkW2p4hHlY8qUKaxYsYKEhARCQ0Px9PQssY+dnZ1m2MrqauPGjTzzzDMlhkF98803mTdvHm+88YYMcy6EEEKIMhMYGIi5uTlNmjQhMjKSV199la5du9KoUSNdh1ZuSp0g9evXj379+v1j+VtvvYWfn59W05mbm5tmOS0tjRUrVvDTTz9pxpb/+eefcXJy4vfff9c8AvcgOnfujI2NjebxqnsCAgJISEggICCAunXr/ud5CovUfLQ7nOUHrwLwWMM6LH2qPXUtH7zpUJQve3t7fv/9d/r378/169dLlDdo0IBt27ZpHsWrjnbs2MGwYcPuOyJMfn4+s2fPBmDWrFkVHZoQQgghqqmMjAxmzpzJjRs3sLW1pWfPnnzyySe6Dqtclekw32q1mu3btzNz5kz69OlDaGgorq6uzJ49WzP08qlTpygoKKB3796a4xwdHWndujVHjx69b4KUl5en1fE+PT0dgMjISCIjIzUzMN8zfvx4Jk6cqFn/+5CKf5WYkcfUdWcJuVb8jfxEz4a81rsJhvp6/3qcqHhNmzbl7Nmz/Pbbb/z2228kJiaiKArPPfcco0ePxtTUtNq+Zmq1milTpmiSowEDBjB16lTMzc1ZtWoVX331FVDciXTs2LEP9fxyVXTv9a6ur7v4b1IHhNSBykWtVlf40M7K3VHiFEWpssNKV2ZjxozRTKL7V7r4WavV6vv+rpf173+ZJkiJiYlkZmbywQcfMH/+fD788EN27dqFv78/+/fvp3v37iQkJGBkZFRiIrC6deuSkJBw3/MuXLhQa+biv2rZsiWbNm3SaqV6UJFpsPKKPhkFKoz1FUY3UuOhRBG0O6rU5xIVx9bWlhdffFFrW3BwsG6CqSBnz54lKqq4XrZo0YKJEyeSmZlJZmYmvXv35tq1a+zYsYP8/HzefvvtGjcXVFBQkK5DEDomdUBIHagcnJyc7jvgQUXIyMjQyXVFxUlOTi4xVDpQ5qPilXkLEsDgwYOZNm0aAG3btuXo0aMsW7ZMaxz2v1P+ZSKq2bNna00ulp6ejpOTE2FhYbRs2bLUcSqKwndHrvHV8UiK1ApN7c35cpQHrrZmpT6X0J2CggKCgoLo1auX1uRk1VFkZKRm+dVXX2XAgAFa5Q4ODuzYsQMontPBz8+vQuPTlZpUB8T9SR0QUgcql7i4uIeesPVhKYpCRkYGFhYW0g+3mrOxscHd3b3E9uTk5DK9TpkmSLa2thgYGJRIWlq0aKEZcrtevXrk5+drZia+JzEx8b4d76F4mGdjY+MS2xs0aFDqN8P03AJeW3eWPReLJ7zyb1ef+UNbY2pUpj8KUYEMDQ2r/R/Fv9b/vLy8Evf710dQjYyMqv3P4+9qQh0Q/07qgJA6UDno6emhp1exs8jc+4JepVJV+LVFxdLT07vv73lZ/+6XaS0yMjKiY8eOhIeHa22PiIigYcOGAHTo0AFDQ0OtpvD4+HjOnz//jwlSWbkYl86gLw6z5+ItjPT1WDC0NZ8M95DkSFR6f/3d+Prrr7WakhVFYfHixZr1Ll26VGhsQgghhBDVSakzg8zMTK3HfaKjowkLC8Pa2hpnZ2def/11RowYQbdu3fD19WXXrl1s3bpV00fEysqKSZMmMWPGDGxsbLC2tua1117D3d1dM6pdefjt5A3e3nSevEI19WvX4usx7WnToHa5XU+IstS+fXs6derEiRMnuHz5Mh06dOCll17C3NyclStXcvDgQQBq167NqFGjdBytEEIIIUTVVeoE6eTJk/j6+mrW7/UNGjduHCtXrmTo0KEsW7aMhQsXMmXKFJo1a8aGDRvw8vLSHLN48WIMDAwYPnw4OTk59OjRg5UrV5Z6DqQHkVtQxNwtF1gTcgMAn2Z2LB7eljpmRmV+LSHK0zfffIO3tzcZGRlcvnyZKVOmaJWrVCq++eYbzMykL50QQgghxMMq9SN2Pj4+KIpS4t/KlSs1+0ycOJErV66Qk5NDWFgYgwcP1jqHiYkJX3zxBcnJyWRnZ7N161acnJwe+Wb+LiY5m4Cvj7Im5AYqFczo1ZTvx3WU5EhUSR4eHhw8eJBOnTqVKHN1dWXz5s0MGzZMB5EJIYQQ1ZOPj4/WJPQuLi4sWbJEZ/GIilFtO9/svXSLaWvDSM8txNrMiM9GtsW7iZ2uwxLikbRt25bjx49z6tQpjhw5QmFhIe7u7vTo0UM6pgohhBAPafz48fz4448lth8/fpwWLVr843EqlYrAwMAaN71GdVftEqQitcKnQeEs3V88Z0w759osHd0ex9q1dByZEGWnQ4cOdOjQQddhCCGEENVG3759+eGHH7S22dnZlUsXkL8rKCiQURgrkWr1lXNSRh5jVxzXJEfjPV1Y+1wXSY6EEEIIIXRAURSy8wvL/V9OfpHWuqIopY7V2NiYevXqaf3r0aOH1iN2f+Xi4gLA0KFDUalUmnWArVu30qFDB0xMTHBzc2PevHkUFhZqylUqFcuWLWPw4MGYmZkxf/78Uscryk+1aUE6eS2Fl1ef5lZ6HqZG+nwQ0IZBHo66DksIIYQQosbKKSii5bu7K/y6F//Xp9yncQkJCcHe3p4ffviBvn37alqadu/ezZgxY/j888/x9vYmKiqK5557DoA5c+Zojp8zZw4LFy5k8eLFFdJKJR5clU+QFEVhxeFoPth5mUK1QmN7c5aNaU9jewtdhyaEEEIIIaqIbdu2YW5urlnv16/fv+5vZ1fct7127drUq1dPs33BggXMmjWLcePGAeDm5sZ7773HzJkztRKk0aNHM3HixLK8BVFGqnSClJFbyDurT7PjXAIAgzwcWejvjplxlb4tIYQQQohqoZahPhf/16dcr6FWq8lIz8DC0kIzYFEtw9K3yPj6+vL1119r1s3MzB5qbsFTp04REhLCggULNNuKiorIzc0lOzsbU1NTAB577LFSn1tUjCqdSYz9PoQbWSoM9VW83b8lT3dpiEql0nVYQgghhBCC4r425f2om1qtptBIH1Mjg0ca0dXMzIzGjRuXSTzz5s3D39+/RJmJiYnW9UTlVKUTpOspOTSwt+bLp9rT3rmOrsMRQgghhBA1iKGhIUVFRVrb2rdvT3h4eJkkW0I3qnSC1MXNmq8nemMtE78KIYQQQogK5uLiwt69e+natSvGxsbUqVOHd999lwEDBuDk5MSwYcPQ09Pj7NmznDt3TkarqyKq9DDfX4z0kORICCGEEELoxCeffEJQUBBOTk60a9cOgD59+rBt2zaCgoLo2LEjnTt35tNPP6Vhw4Y6jlY8qCrdgqSvJ/2NhBBCCCHEo1m5cuV9twcHB2utX7t2TWt94MCBDBw4sMRxffr0oU+ffx6c4mHmaRIVp0q3IAkhhBBCCCFEWZIESQghhBBCCCHukgRJCCGEEEIIIe6SBEkIIYQQQggh7pIESQghhBBCCCHukgRJCCGEEEIIIe6SBEkIIYQQQggh7pIESQghhBBCCCHukgRJCCGEEEIIIe4y0HUAQgghhBBC3JOWlsbu3bu5ffs29vb29O3bF3Nzc12HJWoQaUESQgghhBA6l5+fz4wZM6hfvz4jRozg5ZdfZtiwYdSvX5+3336bwsLCcrv2+PHjUalUvPDCCyXKXnrpJVQqFePHjy+369cEKpWKTZs26TqMByIJkhBCCCGE0KnCwkL8/f359NNPycrK0ipLT09nwYIFjBkzBrVaXW4xODk5sWbNGnJycjTbcnNz+fXXX3F2di6365aF/Px8XYdQrUiCJIQQQgghdGrlypVs374dAENDQ55//nlWrFjBxIkT0dfXB2Dt2rVs2LCh3GJo3749zs7ObNy4UbNt48aNODk50a5dO802RVFYtGgRbm5u1KpVCw8PD9avX68pLyoqYtKkSbi6ulKrVi2aNWvGZ599pnWt4OBgOnXqhJmZGbVr16Zr165cv34dKG7NGjJkiNb+U6dOxcfHR7Pu4+PD5MmTmT59Ora2tvTq1QuAixcv4ufnh7m5OXXr1mXs2LHcvn1b67hXXnmFqVOnUqdOHerWrcs333xDVlYWEyZMwMLCgkaNGrFz506t6z/IeadMmcLMmTOxtramXr16zJ07V1Pu4uICwNChQ1GpVJr1M2fO4Ovri4WFBZaWlnTo0IGTJ0/+xytV/iRBEkIIIYQQOvXVV19pljdv3syyZcuYOHEiK1as4JdfftGULV26tFzjmDBhAj/88INm/fvvv2fixIla+7z99tv88MMPfP3111y4cIFp06YxZswYDhw4AIBaraZBgwasW7eOixcv8u677/Lmm2+ybt06oLi1bMiQIXTv3p2zZ89y7NgxnnvuOVQqVali/fHHHzEwMODIkSMsX76c+Ph4unfvTtu2bTl58iS7du3i1q1bDB8+vMRxtra2nDhxgldeeYUXX3yRYcOG4enpyenTp+nTpw9jx44lOzsboFTnNTMz4/jx4yxatIj//e9/BAUFARASEgLADz/8QHx8vGb9qaeeokGDBoSEhHDq1ClmzZqFoaFhqX4O5UKpgtLS0hRAOXbsmK5DETqUn5+vbNq0ScnPz9d1KEJHpA4IqQNC6kDlEhMTU+pjMjMzFUABFHd39xLlarVaadiwoQIoBgYGilqt1iovKipSUlNTlaKiooeOe9y4ccrgwYOVpKQkxdjYWImOjlauXbummJiYKElJScrgwYOVcePGKZmZmYqJiYly9OhRreMnTZqkjBo16h/P/9JLLykBAQGKoihKcnKyAijBwcH/Gstfvfrqq0r37t016927d1fatm2rtc8777yj9O7dW2vbjRs3FEAJDw/XHOfl5aUpLywsVMzMzJSxY8dqtsXHx2t9zn6Y8yqKonTs2FF54403NOuAEhgYqLWPhYWFsnLlyvv+HO7nn+rX7du3FUBJS0t74HP9myo9il2XLl3o2LEjc+bMoX///roORwghhBBC/L+9ew+Kqm7jAP5dQJZLCMMitwLE0FEEFSQzNNECUZHGJMFLiDKWFRaX0cTU1OYVRh2tmVAUcwxtGDHvpSkoCig4XFcRSQgIKCWViIsotz3vH8COK2SisEfk+5nZGfacs+c8u/uscx7P7/ecbmpublb+bWRk1Gm9RCKBkZERysrK0NLSAoVCoRx219NMTEzg5eWF2NhYCIIALy8vmJiYKNdfv34dDx48UA5p69DU1KQyDG/nzp347rvvUFZWhvv376OpqQljxowBABgbG2PRokXw9PSEh4cH3N3d4evrCwsLi27F6uLiovI8Ozsb58+f77LjX3FxMYYNGwYAGDVqlHK5pqYmZDIZHB0dlcvMzMwAALdv337q/QKAhYWFch//JiwsDEuWLMH+/fvh7u6OOXPm4NVXX33sa9Shzw+xy8zMxMyZM7Fr1y6xQyEiIiKibjI0NISlpSUAIC0tDcXFxSrrr169iitXrgAAhg8f3mvFUYfAwEB8//33iI2N7TS8rqNJxMmTJyGXy5WP69evK+chHTx4EKGhoQgMDERCQgLkcjkWL16s0khh7969SE9Ph6urK+Lj4zFs2DBcvnwZAKChoQFBEFSO+3AR2UFfX79TbN7e3ipxyeVyFBUVYdKkScrtHh3CJpFIVJZ1DPXreK/Pst//aqqxfv165Ofnw8vLC0lJSbC3t8fRo0cf+xp16HaBlJKSAm9vb1haWnbZrq+jTeLDj/Hjx6tsU1lZCX9/f5ibm0NfXx/Ozs4qk9uelL29vfLvoKAg3Lhxo9v7ICIiIiLxSCQSLFmyBEBbgwNPT0/8+OOPKCsrQ1xcHGbOnKnctmO73jRt2jQ0NTWhqakJnp6eKuvs7e0hlUpRXl4OOzs7lYeVlRUAIDU1Fa6urvjkk0/g5OQEOzu7TkUfADg5OWHVqlVIS0uDg4MD4uLiAACDBg3CrVu3VLaVy+X/GbezszPy8/MxePDgTrE9Wkx1R0/td8CAAWhtbe20fNiwYQgNDUVCQgJmz56tMgdMLN0ukO7du4fRo0cjKirqX7eZNm0abt26pXycOnVKZb2/vz9u3LiBEydOIC8vD7Nnz4afnx9yc3O7FUtycjKCgoIAtP2gHp7gR0RERER9Q3BwMGxtbQG0Ddvy9fXF4MGDsWDBAlRUVABoK06WLl3a67FoamqioKAABQUFna5WGRgYYPny5QgNDUVsbCyKi4uRm5uL7du3IzY2FgBgZ2eHrKwsnDlzBoWFhVi7dq2yKQEAlJaWYtWqVUhPT0dZWRkSEhJQWFiIESNGAADeeustZGVlYd++fSgqKsK6detw7dq1/4w7KCgIf//9N+bNm4eMjAyUlJQgISEBgYGBXRYmT6qn9jt48GCcO3cOlZWVqK6uxv3797Fs2TJcuHABZWVluHTpEjIzM5Wfg5i6PQdp+vTpmD59+mO3kUqlMDc3/9f16enpiI6Oxrhx4wC0dQP5+uuvkZOTozJ+s0NjYyMaGxuVz2trawG0dQH58ssvsWvXLrS0tOD06dNdXoKkF1PHd83vvP9iDhBzgJgDzxeFQvFU9yoyMjLC2bNn4ePj0+XVkvHjx+PQoUPQ09PrtP+O4WiCIDz1fZIEQVB5fcd8m47nD6/fsGEDBg0ahMjISJSUlMDIyEh5NUihUODDDz9Ebm4u/Pz8IJFIMHfuXHz88cc4ffo0FAoFdHR0UFBQgNjYWFRVVcHCwgJBQUH44IMPoFAo4OHhgTVr1uDzzz/HgwcPsHjxYvj7++PatWsq7+/R92tubo7U1FSEh4fD09MTjY2NsLGxUV4Fe/i9dPUZPrqs47t82v0++plu2bIFy5cvx+7du/Hyyy/j119/xd27d7Fw4UL89ddfMDExwbvvvot169b96/eoUCi6/K339O9fIjw6yLE7L5ZIcPToUZVe7YsWLcKxY8egra0NIyMjuLm5YePGjTA1NVVuM23aNGhpaWHfvn0wMjLCwYMHsWTJEly5cqXLiVnr16/Hhg0bOi2Pi4uDrq4uAgICUFtbC5lMhj179jzt2yEiIiKiZ2BlZYUhQ4Y89esVCgWSk5Nx/PhxVFdXQyaTwcfHB66urt1ug00vnpKSEuUVxYc1NDRg/vz5qKmpwcCBA5/5OD1eIMXHx+Oll16CjY0NSktLsXbtWrS0tCA7OxtSqRQAUFNTAz8/P5w5cwZaWlrQ09PDoUOHOnUE6dDVFSQrKyvcunULhYWFcHNzAwBMnDgRSUlJT/t2qI9pbm5GYmIiPDw8no+e+aR2zAFiDhBz4Ply8+ZN5VwcdREEAXV1dTAwMGAR9YKrqKhQNvR4WMeVuJ4qkHq8zbefn5/ybwcHB7i4uMDGxgYnT57E7NmzAbQNqauursbZs2dhYmKCY8eOYc6cOUhNTVVpM9hBKpUqi6uHpaWlYcWKFcrnixcv5j+O/dCAAQP4vfdzzAFiDhBz4PmgoaEBDQ31NknuGI4lkUjUfmxSLw0NjS5/5z392+/1+yBZWFjAxsYGRUVFANom3kVFReHatWsYOXIkAGD06NFITU3F9u3bsXPnzifet4+Pj/Jve3t7zJs3r2eDJyIiIiKifqXXy+yqqipUVFQob37V0NDQduBHKnxNTc2nnljn6OiI06dPQ1dX99mCJSIiIiKifq3bBVJ9fb3yBlFAW6tCuVyO8vJy1NfXY/ny5UhPT8fvv/+OCxcuwNvbW9mVAmi7wZednR2WLl2KjIwMFBcXY+vWrUhMTFSZy/Qk3N3dceDAAWRlZal9vCsREREREb14uj3ELisrC1OmTFE+DwsLAwAEBAQgOjoaeXl52LdvH/755x9YWFhgypQpiI+Ph4GBAYC2MYKnTp1CeHg4vL29UV9fDzs7O8TGxmLGjBndiuXAgQOQyWTdfQtERERE1AukUinu3LkDExMTNkygHlVfXw8trV6fHQTgKQqkyZMn43GN786cOfOf+xg6dCgOHz7c3UMTERER0XPM1NQUtbW1+OOPP9R2TIVCgaqqKshkMjZpeIFpaWnBzMxMPcdSy1GIiIiIqF8YOHBgj7RaflLNzc2Qy+VwdHRkJ0PqESyziYiIiIiI2rFAIiIiIiIiascCiYiIiIiIqB0LJCIiIiIionZ9sklDRxe9uro6Tsbrx5qbm9HQ0IDa2lrmQT/FHCDmADEHiDlAdXV1APDYTtvd0ScLpKqqKgCAra2tyJEQEREREdHzoKqqCoaGhs+8nz5ZIBkbGwMAysvLe+RDoL6ptrYWVlZWqKioUGs7UXp+MAeIOUDMAWIOUE1NDaytrZU1wrPqkwVSx03ADA0N+UMgtd9vgZ4/zAFiDhBzgJgD1FM3CmaTBiIiIiIionYskIiIiIiIiNr1yQJJKpVi3bp1kEqlYodCImIeEHOAmAPEHCDmAPV0DkiEnuqHR0RERERE1Mf1yStIREREREREvYEFEhERERERUTsWSERERERERO1YIBEREREREbVjgURERERERNSuTxZIO3bsgK2tLXR0dDB27FikpqaKHRKpSWRkJF577TUYGBjA1NQUs2bNwo0bN8QOi0QUGRkJiUSCkJAQsUMhNfrzzz/x/vvvQyaTQU9PD2PGjEF2drbYYZEatbS0YM2aNbC1tYWuri6GDBmCr776CgqFQuzQqJekpKTA29sblpaWkEgkOHbsmMp6QRCwfv16WFpaQldXF5MnT0Z+fr44wVKveFwONDc3Y+XKlXB0dIS+vj4sLS2xcOFC3Lx5s9vH6XMFUnx8PEJCQrB69Wrk5ubizTffxPTp01FeXi52aKQGycnJCAoKwuXLl5GYmIiWlhZMnToV9+7dEzs0EkFmZiZiYmIwatQosUMhNaqursaECRMwYMAA/PLLL7h+/Tq2bt0KIyMjsUMjNdq0aRN27tyJqKgoFBQUYPPmzdiyZQu+/fZbsUOjXnLv3j2MHj0aUVFRXa7fvHkztm3bhqioKGRmZsLc3BweHh6oq6tTc6TUWx6XAw0NDcjJycHatWuRk5ODI0eOoLCwEO+88063j9Pn7oP0+uuvw9nZGdHR0cplI0aMwKxZsxAZGSliZCSGO3fuwNTUFMnJyZg0aZLY4ZAa1dfXw9nZGTt27MD//vc/jBkzBt98843YYZEahIeH49KlSxw90M/NnDkTZmZm2LNnj3KZj48P9PT0sH//fhEjI3WQSCQ4evQoZs2aBaDt6pGlpSVCQkKwcuVKAEBjYyPMzMywadMmLF26VMRoqTc8mgNdyczMxLhx41BWVgZra+sn3nefuoLU1NSE7OxsTJ06VWX51KlTkZaWJlJUJKaamhoAgLGxsciRkLoFBQXBy8sL7u7uYodCanbixAm4uLhgzpw5MDU1hZOTE3bv3i12WKRmEydOxLlz51BYWAgAuHLlCi5evIgZM2aIHBmJobS0FJWVlSrniFKpFG5ubjxH7MdqamogkUi6PcJAq3fC6R13795Fa2srzMzMVJabmZmhsrJSpKhILIIgICwsDBMnToSDg4PY4ZAaHThwANnZ2cjKyhI7FBJBSUkJoqOjERYWhi+++AIZGRn47LPPIJVKsXDhQrHDIzVZuXIlampqMHz4cGhqaqK1tRUbN27EvHnzxA6NRNBxHtjVOWJZWZkYIZHIHjx4gPDwcMyfPx8DBw7s1mv7VIHUQSKRqDwXBKHTMnrxLVu2DFevXsXFixfFDoXUqKKiAsHBwUhISICOjo7Y4ZAIFAoFXFxcEBERAQBwcnJCfn4+oqOjWSD1I/Hx8fjhhx8QFxeHkSNHQi6XIyQkBJaWlggICBA7PBIJzxEJaGvYMHfuXCgUCuzYsaPbr+9TBZKJiQk0NTU7XS26fft2p/8xoBfbp59+ihMnTiAlJQWvvPKK2OGQGmVnZ+P27dsYO3ascllraytSUlIQFRWFxsZGaGpqihgh9TYLCwvY29urLBsxYgQOHz4sUkQkhhUrViA8PBxz584FADg6OqKsrAyRkZEskPohc3NzAG1XkiwsLJTLeY7Y/zQ3N8PX1xelpaVISkrq9tUjoI/NQdLW1sbYsWORmJiosjwxMRGurq4iRUXqJAgCli1bhiNHjiApKQm2trZih0Rq9vbbbyMvLw9yuVz5cHFxwYIFCyCXy1kc9QMTJkzo1N6/sLAQNjY2IkVEYmhoaICGhuppjKamJtt891O2trYwNzdXOUdsampCcnIyzxH7kY7iqKioCGfPnoVMJnuq/fSpK0gAEBYWBn9/f7i4uOCNN95ATEwMysvL8dFHH4kdGqlBUFAQ4uLicPz4cRgYGCivJhoaGkJXV1fk6EgdDAwMOs0509fXh0wm41y0fiI0NBSurq6IiIiAr68vMjIyEBMTg5iYGLFDIzXy9vbGxo0bYW1tjZEjRyI3Nxfbtm1DYGCg2KFRL6mvr8dvv/2mfF5aWgq5XA5jY2NYW1sjJCQEERERGDp0KIYOHYqIiAjo6elh/vz5IkZNPelxOWBpaYn33nsPOTk5+Pnnn9Ha2qo8TzQ2Noa2tvaTH0jog7Zv3y7Y2NgI2tragrOzs5CcnCx2SKQmALp87N27V+zQSERubm5CcHCw2GGQGv3000+Cg4ODIJVKheHDhwsxMTFih0RqVltbKwQHBwvW1taCjo6OMGTIEGH16tVCY2Oj2KFRLzl//nyX5wABAQGCIAiCQqEQ1q1bJ5ibmwtSqVSYNGmSkJeXJ27Q1KMelwOlpaX/ep54/vz5bh2nz90HiYiIiIiIqLf0qTlIREREREREvYkFEhERERERUTsWSERERERERO1YIBEREREREbVjgURERERERNSOBRIREREREVE7FkhERERERETtWCARERERERG1Y4FERERERETUjgUSERERERFROxZIRERERERE7f4PBbt1i7qNAhIAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pylab as pylab\n",
"\n",
"def g_h_filter(data, x0, dx, g, h, dt=1.):\n",
" x_est = x0\n",
" results = []\n",
" for z in data:\n",
" # prediction step\n",
" x_pred = x_est + (dx*dt)\n",
" dx = dx\n",
"\n",
" # update step\n",
" residual = z - x_pred\n",
" dx = dx + h * (residual) / dt\n",
" x_est = x_pred + g * residual\n",
" results.append(x_est)\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)\n",
"print(weights)\n",
"print(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This should have been straightforward. I just subtituted the variable names `x0`, `dx`, etc., for the variable names in the weight gain code. Nothing else needed to change."
]
},
{
"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 clear once 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": 23,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
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QyI+IiIiIFMjJkydJTEwkMDCQ0NDQ677/6MQ0pm84zo/bTpKWnQtAWQ9n7mlWiftaVCLI2+261/RvAgICePfdd3nttdc4duwYJpOJKlWq4OJSuKm0LypTpoz19dGjR2nSpIlN+5EjRy67bmml8CMiIiIiV2Xu3Lm88cYb/PHHH9ZlrVu35tlnn73sqMO1ysrK4qeffmLx4sUcPXqUlStXMnjwYLJ9K/PVhih+238Ww8hbNyKwDMNah9OnUXncnO03VbW9ubq6UqtWLbtvt1u3bixYsACACRMmsHDhQtzc8sLfzp07+frrrwHw9PSkbdu2dt//jUbhR0RERET+06RJk3jppZfyLV+/fj09evTg7bffZty4cYXez6ZNm7jzzjs5c+ZM3gJHJ/akefJTygZcgmKt67WrEcADrcNpXc2/SKaqvlHcc889PPfccyQmJrJixQqqVq1Kr169OHv2LAsXLiQnJweAIUOG2Fx6V1op/IiIiIjIFS1btswm+NSvX5+mTZuyYcMGDhw4AMATTzxBixYtaNGixTXvZ+/evXTu3JnU1FScAyrjWTuSMnVvw7FMWQAs5kz8kg7z4+RRRAQX7tk4N4syZcrwww8/0KNHDzIyMjhz5gyffPKJzTrNmjXjtddeK6YKS5YC3f316quv0rRpU7y8vAgMDKR3794cPHjQZp0hQ4ZgMpls/jRv3tyuRYuIiIjI9TN16lTr61dffZWdO3fyxRdfsG/fPsaPH29te++99wq1n2f+7w0c6nYjZNiHhA77EJ/m/XEsUxYvxxwyNs/m9MdD+OvL8RzZsaFQ+7nZdOjQgY0bN3LHHXfg4HDpx3t/f3/Gjx/PypUrdb/P3wo08rNmzRpGjx5N06ZNycnJ4bnnnqNz587s27cPT89L86V37dqV6dOnW9/b64YuEREREbm+srKyWL58OQBhYWE89dRT1svMTCYTEydO5LPPPuPcuXP88ssvGIZRoMvQElKzWLw7hp+2RrMnfABlw/OWOzuaaF8jgPI5MTw1qCu/LszirjXfAfD555/TrVs3+x7oDa5hw4YsWLCA2NhYjh07hpubG3Xq1MHV1bW4SytRChR+li5davN++vTpBAYGsn37dpsbqFxdXQkODrZPhSIiIiJSbNLS0qwPx6xRowaOjraTCri6ulKtWjX++OMP0tPTyc3Nxcnpyj9ipmblsHxvLAt2nmH9kQRyLXmzFxiGhczoXdwaZOLb157CwwkWLz6Ds6MDffv2xc3NjczMTPbt21c0B3sTCA4O1s/hV1Coe36SkpKAvIco/dPq1asJDAzE19eXyMhIXnnlFQIDAy+7jaysLLKysqzvk5OTATCbzZjN5sKUJzewi9+9+kDppT4g6gOiPlAyeHh4UKZMGVJTU9m8eTMJCQk2N86fPXuWnTt3Ank/eBuGcdnvLCvHwrrDCfyyK4aVB+LJyrFY2+qX96ZB2RxeHdmP3LTzeAwYgIeTbR9IS0sjOzsbAGdnZ/WLUsLe37PJMC5OFFgwhmHQq1cvzp8/z7p166zLv//+e8qUKUOlSpWIiorihRdeICcnh+3bt1922O3fZg6ZNWsWHh4e11KaiIiIiNjRxx9/bL30rXHjxowcOZKAgABiY2P58MMP2bNnDwC9e/dmyJAh1s9ZDDiabGJ7gomdiSYyci9dDhfoZtDY38It/gaB7nm/EB82bBhpaWk4OTkxdepUKlSoYF3/u+++48cffwSge/fuPPTQQ9fhyKW4paenM2jQIJKSkvD2LvwkF9ccfkaPHs2iRYtYv369Tcf8XzExMVSqVIk5c+bQt2/ffO2XG/kJCwsjJiaGcuXKXUtpchMwm82sWLGCTp064ezsXNzlSDFQHxD1AVEfKDkOHTpEs2bNSEtLA/Lu9QkJCbk0HTXg6+vL9u3bqVChAvtiUvhlVwy/7o7lbPKln/OCvFzpUT+YnvVDqB3ile/eoKeffto6uYK3tzeDBw/GbDZz/Phx6+0XJpOJP//8kzp16hTxUUtJkJiYSEhIiN3CzzVd9jZmzBgWLlzI2rVrrxh8AEJCQqhUqRKHDx++bLurq+tlR4ScnZ11ohP1A1EfEPUBUR8oAerUqcOCBQvo06cPKSkpGIZhE3z8/Pz4fM4CfjmWy4J5GzkWn2Zt83Zzonu9EHo1LM+t4X44Ovz7ZAiTJk3i999/Z9euXSQnJ/PBBx/kW+fll1+mYcOGdj0+Kbns/Xe/QOHHMAzGjBnDvHnzWL16NeHh4f/5mcTERE6ePElISMg1FykiIiIixatjx44cOnSIadOm8eOPP5KYmIh/WFXqdrufC74RjFuZBOTdD+7q5MBttYPo1SCUyBoBuDo5Xnnjf/Px8WH16tWMHTuW2bNn29zvUb58eSZOnMiDDz5YFIcnpUSBws/o0aOZNWsWCxYswMvLi9jYvKfs+vj44O7uTmpqKpMmTaJfv36EhIRw/PhxJkyYgL+/P3369CmSAxARERGR6yM4OJgJzz1Pkz4P8t2WaDYdTWRjJhCbhqODidbV/OnVMJTOdYIp43pt82qVLVuWmTNn8sYbb7Bs2TI2b95Mjx496Ny583/OIifyXwrUgy4+LbZdu3Y2y6dPn86QIUNwdHRk9+7dfP3111y4cIGQkBDat2/P999/j5eXl92KFhEREZHrKyndzPfbTjBzYzSnL2RYlzeuVJZeDUPpXi8E/zL2e6ZMUFAQAwcOxMfHh06dOin4iF0U+LK3K3F3d2fZsmWFKkhERERESo5j8anM2Hicn7afIj07F4Byni7c06wi/ZuEEean2XnlxqEILSIiIiI2DMNgw5FEvtoQxe8H4qzLawZ7Max1OHc0CMXN+eru4xEpSRR+RERERASATHMu83ec5qsNURw6mwqAyQQdawYyrFU4LaqWyzc9tciNROFHREREpJQ7m5zJN5ui+W5LNOfT82ZY83BxZECTMAa3rEy4v2cxVyhiHwo/IiIiIqXU7lNJfLUhil93ncGcm3dvd3lfd4a2qkz/JmH4uOv5SnJzUfgRERERKUVyci2s2HeWrzZEsfX4eevyWyv7Max1ZW6rFYSTo0MxVihSdBR+RERERG4C+/fv59tvv+X06dN4e3vTo0cPbrvtNhwc8oJMUoaZH7aeZMbG49apqp0dTfSsH8rQVuHUq+BTnOWLXBcKPyIiIiI3sLS0NB544AG+//57m+UffPABdevW5b0vZ7EmxsSP/5iq2s/ThXubVeTe5pUI9HYrjrJFioXCj4iIiMgNymKx0LdvX5YvX56vza1SA87W6MXQuccxmfJGf2oGezGsVTh3NNRU1VI6KfyIiIiI3KDmz59vDT7e3t6Mf2ESLtWa88NfCcRm5AUew7AQYI7lvYd7aapqKfUUfkRERERuUNOmTQOTA27hjbjt4YnMTHImY/M5wAF3ZwfObV/Muc0/k5idRIP/u1vBR0o9TeUhIiIicoMxDIOdJy+w1602FUZ/TVD/l9ie4ECGOZcq/p5M6F6TzRNuo713PDnnz5CWlkZUVFRxly1S7DTyIyIiInKDiE5MY/6OM8zfeZqohDQca3YEwJJ+gaEd6tOvSRj1yvtYR3jS09Otn3V01D0+Igo/IiIiIiXYubRsFu06w7wdp/nzxAXrcndnRzzOH2bf4hlkHt9JUM0PqF9hlLV9//79LFmyBICAgACqVat2vUsXKXEUfkRERERKmExzLr/tP8v8HadZfTCeHIsBgIMJWkcE0KdRKJ1rB7N9iweRH/0JwJgxY9i2bRtdunRh3759fPDBB+Tk5ADw4IMP4uzsXGzHI1JSKPyIiIiIlAC5FoMtxxKZt+M0S/bEkpqVY22rV96H3o3K07NBCIFel57L07ZtW0aOHMmnn36KxWJh+vTpTJ8+3Wa79evX55lnnrluxyFSkin8iIiIiBSx+Ph4jh07hqurK7Vr18bFxcXatj8mmfk7TrNg5xlikzOty8v7utOnUXl6NwqlWqDXv277o48+IjQ0lLfeeovk5GTrcgcHB+68804+/fRTvL29i+bARG4wCj8iIiIiRWTXrl1MnDiRhQsXYrFYgLz7b+59aAzhkXeyaG88B2JTrOv7uDtze/0Q+jQqT+OKZXFw+O+pqR0cHHjhhRd4/PHHWbhwIadPn8bb25tu3bpRsWLFIjs2kRuRwo+IiIhIEVizZg3du3e3zrhmcvHAo0YrHOq0Y665HqaVxwBwcXKgY81AejcqT7saAbg6XdusbGXKlGHQoEF2q1/kZqTwIyIiImJnqamp3HnnnaRnmfGo3pJyt3TBqWJDLKZLwSbzxG6aBZn4euI4fNw1GYHI9aDwIyIiIqVaRkYGJpMJNze3/175KuTkWpj8xVyMW+8lrHoLHFw9AbAA1YPKcGugiXcfv4f0+FOs9PSESSPB3ccu+xaRK3Mo7gJERERErreMjAymTp1KzZo18fDwwN3dnXr16vHxxx+TnZ1d4O0ZhsH26PNMWriX5q+uZE6sP2Xq3YaDqyf+7g6MjKzKksfasGxsWybf05ZBvboCkJaWxrp16+x9eCLyLzTyIyIiIqXKuXPn6Ny5M9u3b7dZvmfPHkaPHs2cOXNYvHgxZcqU+c9tHTqbwoKdp1n41xlOnsuwLncwp5O0+3fS9q3hz90b8Ctb1uZzNWrUsL5OSUlBRK4PjfyIiIjIVdm1axcPPvggYWFhlC1bloYNG/LOO++QlJRU3KUVyJAhQ2yCT+PGjWnQoIH1/bp16xg5cuS/fv7kuXQ+Xn2ErlPX0vndtXy06ignz2Xg6eJI30blmT60KW3PL+Xcik/JOr2fpUuW5NvGokWLrK81I5vI9aORHxEREflPH374IY8++iiGYViXXbhwgSeeeIL333+f5cuXU7169WKs8Ors27ePX375BQB/f3+WLFlCkyZNAFi/fj3du3cnJSWF2bNnM2XKFGswSUjNYvHuGBbuPMO26PPW7Tk7mmhXI5BeDUPpWDMId5e8CQ1M99/HzOlfATB27Fh8fHzo1q0bycnJvPrqq6xevRqAiIgIWrRocb0OX6TUU/gRERGRK/r1118ZM2aM9b27uzvBwcFERUUBEB0dTbdu3di9ezceHh7FVeZV+emnn6yvJ0yYYA0+AK1bt2bcuHG89NJLWCwW5vw0j2rt+rFg5xnWH0kg15IX/EwmaFGlHHc0CKVb3RB8PPLP1BYZGUn79u1ZtWoV8fHx9OjRgzJlypCRkUFubq51vYkTJ+LgoAtxRK4X/W0TERGRK5o8ebL19bhx44iLi+PYsWPs2bOHunXrAnDs2DFmz55dXCVetfj4eOvr5s2b52tvfGsz3COa49/rGT6Lq8K4H/5izaF4ci0G9Sv48Pzttdg8viOzHmzO3bdWvGzwATCZTMydO5fWrVtbl6WmplqDj8lk4s033+See+6x8xGKyJVo5EdERET+1dGjR9myZQsA9erV46233sJkMgFQp04dvvjiC2uI+Pbbb3nggQeKrdarERgYaH29adMmWrRoQa7FYPOxRBbsPM28bdkE9n0egFygSoAnvRqU546GoYT7exZoX2XLlmXVqlUsXLiQL774gkOHDuHm5kb79u0ZNWoUtWrVsuehichVUPgRERGRf3XmzBnr644dO1qDz0XNmjWjTJkypKam2qxbUt155528+OKLAEx57zNOlW3IxhiD2OTMv9dwIiclgfQD6/jhzafo2Kh6vmMuCCcnJ/r27Uvfvn3tUL2IFJbCj4iIiPwrX19f6+vdu3fna4+KiiI1NTXfuiVVteo1iLz3MfZn+eEW3oifD/49PXV2Oin71pC2bw1ZJ/dy3333ctstNa68MRG54Sj8iIiIyL+qU6cOVapU4dixY6xcuZI5c+Zw9913A5Cens6jjz5qXbd3797FVOV/i0pIY87WE8zdfoqE8p1w/3t5xvGdpP61lPTDmyE3B8ibrOCTTz4pvmJFpMgo/IiIiMi/cnBw4PHHH7fO9jZw4EDefPNNIiIiWLlyJQkJCQB4eXmVuPt9Ms25LNsby5w/TrLpWKJ1eYCXK30aBJN7eB3f/zqbuAN7AWjYsCEjR45k6NChuLi4FFfZIlKEFH5ERETkikaNGsW2bduYOXMmAH/++Sd//vmntd3NzY0ff/zRZjKB4nT4bAqz/zjJzztOcSHdDORNT92uegB331qRDjUDcXZ0AOrywuMPk52dDaDAI1IKKPyIiIjIFTk4OPDVV18RGRnJ1KlT2bVrFwDOzs7069eP8ePHU79+/WKtMSM7l0W7Y5jzxwmbh5CG+LgxoEkYA5qGUd7X/bKfVegRKT0UfkREROQ/OTg4MHToUIYMGUJsbCwpKSmEhoZSpkyZYq1r75kk5vxxkvk7T5OSmXfPjqODiY41Axl4a0XaVg/A0eHaZ2sTkZuLwo+IiIhcNZPJREhICCEhIcVWQ2pWDr/8dYY5f5zgr1NJ1uVhfu7c3bQi/RtXINDbrdjqE5GSS+FHRERESjzDMNh1KonZf5zgl7/OkJadC4Czo4nOdYIZ2LQiLauWw0GjPCJyBQ4FWfnVV1+ladOmeHl5ERgYSO/evTl48KDNOoZhMGnSJEJDQ3F3d6ddu3bs3bvXrkWLiIhI6ZCeA99uOUH399fT66MNzNl6krTsXKr4ezKhe002j+/IR4NuoXWEv4KPiPynAo38rFmzhtGjR9O0aVNycnJ47rnn6Ny5M/v27cPT0xOAN954g3feeYcZM2ZQvXp1Jk+eTKdOnTh48CBeXl5FchAiIiJy80jJNLP6YDxL98SwfK8jZssBAFycHLi9Xgh3Nw3j1nA/TCaFHREpmAKFn6VLl9q8nz59OoGBgWzfvp22bdtiGAZTp07lueeeo2/fvgDMnDmToKAgZs2axYgRI+xXuYiIiFgZhsGxY8dITEwkMDCQypUrF3dJBRKblMmK/WdZvjeWzccSMecaf7eYqB5YhoHNKtKnUXl8PTQzm4hcu0Ld85OUlHeToZ+fHwBRUVHExsbSuXNn6zqurq5ERkaycePGy4afrKwssrKyrO+Tk5MBMJvNmM3mwpQnN7CL3736QOmlPiDqA1dvzpw5vP322/z111/WZU2bNuXpp5+mV69exVjZvzMMg8Nxqfy2P57fDsSx+3SyTXtlPzequWfgHLuH0Z17UKNGBUD9obTReUDs/d2bDMMw/nu1/AzDoFevXpw/f55169YBsHHjRlq1asXp06cJDQ21rvvQQw8RHR3NsmXL8m1n0qRJvPTSS/mWz5o1Cw8Pj2spTUREpNT45ptvmDt37r+233ffffTr1+86VvTvLAYcS4Hd5xzYfc5EYtaly9ZMGFT2gmru6Rxc+SNbfltoffgoQP369bnvvvuIiIgojtJFpJikp6czaNAgkpKS8Pb2LvT2rjn8jB49mkWLFrF+/XoqVMj7bczF8HPmzBmbKTAffPBBTp48me+yObj8yE9YWBgxMTGUK1fuWkqTm4DZbGbFihV06tQJZ2fn4i5HioH6gKgP/LclS5bYjOw0btyYJk2asHHjRnbv3m1dvmrVKlq1alUcJZKRncv6I4n8diCOVQfjOZ9+6be4Lk4OtKrqx201A+lQM4DctAu0b9+eI0eOXHZbbm5uLFiwgPbt21+v8qWY6TwgiYmJhISE2C38XNNlb2PGjGHhwoWsXbvWGnwAgoODAYiNjbUJP3FxcQQFBV12W66urri6uuZb7uzsrE4u6geiPiDqA1fw4YcfWl+/9dZbPPHEE8ClmVf/7//+z7peu3btrltdialZrNwfx/J9Z1l3OJ6sHIu1zdfDmQ41A+lcO4g2EQF4ul76UaT/Q0OtwcfLy4uBAweSmJjIjh07OHbsGJmZmdx3330cP34cd3f363Y8Uvx0Hii97P29Fyj8GIbBmDFjmDdvHqtXryY8PNymPTw8nODgYFasWEGjRo0AyM7OZs2aNbz++uv2q1pERKSUy8zM5LfffgOgUqVKPP7449Y2k8nEc889x8cff0xCQgKLFy/GMIwinR0tKiGNFftiWbHvLNujz2P5x3UlFcq607l2MJ1qB9G0clmcHPM/aePkyZP8/PPPAPj7+/Pnn38SHBzM4sWLmTlzJr169WLlypXExcXx/fffM2TIkCI7FhG5eRUo/IwePZpZs2axYMECvLy8iI2NBcDHxwd3d3dMJhNjx45lypQpREREEBERwZQpU/Dw8GDQoEFFcgAiIiKlUXp6OhevXI+IiMDBwTZQuLi4UKVKFRISEsjIyMBiseDo6Gi3/VssBrtOJ7F8b17gORyXatNet7y3NfDUDPb6z+C1evVqLJa8EaKHHnqIsLAw643OLi4uvPjii6xcuRKA3377TeFHRK5JgcLPJ598ApBv6Hz69OnWk9DTTz9NRkYGo0aN4vz58zRr1ozly5frGT8iIiJ25OPjg5eXFykpKWzatIkLFy7g6+trbY+JiWHHjh0AhISE2C34pGbl8MW6Y8zacoK4lEv37Do5mGhepRyd6wRxW60gQn0Ldllaenq69XVYWFi+9n8uy8jIuIbKRUSu4bK3/2IymZg0aRKTJk261ppERETkPzg6OnLPPffw6aefkpaWxoABA/j000+pUqUKBw8eZPjw4daRk/vvv7/Q+8vOsTBn6wneX3mYhNS8WdjKuDoRWSOAzrWDaFcjEB/3a782v2rVqtbX8+bNY+TIkTbtFy+JA6hSpco170dESrdCPedHREREis8TTzzBd999R0pKCitWrKBq1ar4+/uTkJBgXcfPz48xY8Zc8z4sFoNFu2N4a/lBohPzRmfC/T0Z16k6nesE4epknxGl9u3bU6lSJaKjo1m+fDmPPvooTzzxBFlZWXz++ee8+OKL1nWHDh1ql32KSOmj8CMiInKDqlatGr/88gu9e/fmwoULADbBJyAggEWLFlG+fPlr2v6GIwm8tuQAu0/nPdTcv4wrY2+L4K6mYThfZtKCwnB0dOSVV17h3nvvBeCDDz7ggw8+yLfe/fffT+3ate26bxEpPRR+REREbmCRkZEcOnSIL774gp9++onExEQCAgK4++67GTZsGGXLli3wNveeSeL1pQdZeygeyLu8bUTbKgxrHW4zNbW93XPPPZw7d45x48aRk5OTr/2uu+5i2rRpRbZ/Ebn5KfyIiIjc4AICAhg/fjzjx48v1HZOnkvn7eUHmb/zDADOjibuaVaJMR2qUa5M/mfyFYUxY8bQq1cvpk2bxpo1a4iPj6dFixY89NBDNG/evEin6xaRm5/Cj4iISCl3Li2bD38/wrebo8nOzZtuulfDUJ7oVIOK5Tyuez0VK1Zk8uTJmM1mFi9eTPfu3fWASxGxC4UfERGRUio9O4ev1kfx2ZpjpGTlXWbWJsKfZ7rWpG55n2KuTkTE/hR+RERESpmcXAs/bDvF1N8OWZ/VUyfUm2e71aRNREAxVyciUnQUfkREREoJwzBYtjeWN5Yd5Fh8GgBhfu482bkGPeuH4uCg+2lE5Oam8CMiIlIKbDmWyGtLD7DjxAUA/DxdeLRDNQY1q4SLk32nrRYRKakUfkRERG5iB2NTeGPpAVYeiAPA3dmRB9uE82DbKni5aRIBESldFH5ERERuQqcvZPDuikPM/fMUhgGODiYG3hrGox0jCPRyK+7yRESKhcKPiIjITeRCejafrD7K9I3Hyc7Jm7a6e71gnuxcgyoBZYq5OhGR4qXwIyIichNIyTQzc+Nxpq09RnJm3rTVzcL9eLZbTRpVLFvM1YmIlAwKPyIiIjew5EwzMzcc54v1USRlmAGoGezFM11r0q5GACaTZnATEblI4UdEROQGlJxpZvr643y5/tJIT9UATx7tGEGP+qE4atpqEZF8FH5ERERuIEkZZqZviOKr9VHW0FMtsAyPdozg9nohCj0iIleg8CMiInIDSMow89X6KL7aEEXK36En4u/Q012hR0Tkqij8iIiIlGBJ6Wa+3BDF9H+EnupBf4eeuiE4KPSIiFw1hR8REZES6EJ6Nl+tj2L6huOkZOWFnhpBXjzaMYJudYMVekREroHCj4iISAlyIT2bL/8OPal/h56awXmhp2sdhR4RkcJQ+BERESkBzqflhZ4ZG21Dz2MdI+ii0CMiYhcKPyIiIkVox44dfPPNN5w+fRpvb2969OhBjx49cHR0BPJCzxfrjzFjw3HSsnMBqBXizWMdq9G5tkKPiIg9KfyIiIgUgeTkZO69915++eUXm+VffPEFERERTJ/1I+sTXPl646XQUzvEm8dui6BTrSCFHhGRIqDwIyIiYmc5OTn06tWL1atX52tzcPcmPrQlg2YfweTsBuSFnrG3RdCpdhAmk0KPiEhRUfgREZESJTExkW+++YZt27Zx5swZoqOjGTx4MD4+PsVd2lWbN2+eNfiULVuWV155hWZtO/Lx74f4LTobnFwB8Mq5wDvDbuO2WoEKPSIi14HCj4iIlBgffPABTz/9NJmZmdZlq1atYsKECbz//vsMGzasGKu7ep9//jkAJicXnpj6DXudQnhvzlEyzSZwciUn7hjn1n5L3JndtJgUp+AjInKdOBR3ASIiIgAff/wxjz76qE3wuSgtLY0HHniAb7/9thgqK5hMcy77kpzw7/EkYWO+4/N98OuuGDLNFuqV9+HLwU1ok7mJjKN/kJGRwfHjx4u7ZBGRUkMjPyIiUuxSUlJ49tlnre8ffPBBHnjgAdauXcvOnTuZNWsWAOPGjaN///64uroWV6mXlZWTy/rDCSzaFcOKfWdxaj/a+g9sqI8bPRqE0r1eCA0q+GAymXgnKcn6WWdn5+IpWkSkFFL4ERGRYvfDDz+QkpICwH333ce0adMwm83Exsby2GOPkZqaysKFC4mPj2fhwoX079+/mCuG7BwLG44m8OtfMSzfF0tKZo61zSUnnYQdy0k7sI7HnhzJ4907Wtt27drFsmXLAAgKCqJKlSrXvXYRkdJK4UdERIrd7t27ra8HDx5s02YymRg8eDALFy4EYM+ePcUWfsy5FjYdTeTXXWdYtvcsSRlma1uglyvd64XQo34Imaf30+btLwAYN+5x/vhjC126dGHv3r189tln5ObmTW09YsQIjfyIiFxHCj8iIlLsnJwu/XOUmpqar/2fy/657vWQk2thS9Q5ft11hqV7Yjmffinw+JdxpXu9YG6vF0LTyn6Xns1TuRVjx45l6tSpAMyZM4c5c+bYbLdJkyY8/fTT1+swREQEhR8RESkBWrVqxdtvvw3Au+++y+23325ty8rK4oMPPrBZt6jlWgy2RCWyaFcMS/fEkpiWbW0r5+lC17rB3F4/hGbh5XD8l4eRvvPOO5QvX57XXnuNxMRE63JnZ2cGDRrE+++/j6enZ5Efi4iIXKLwIyIixa5nz55UqFCBU6dOsWbNGpo3b86QIUPYtWsXzz//PHv27AGgZs2atG/fvkhqsFgMth4/x6LdMSzeHUtCapa1rayHM13rBtOjfijNwv1wcvzvyVJNJhNPPvkkjzzyCEuXLuXUqVN4e3vTpUsXgoKCiuQYRETkyhR+RESk2Dk5OTF9+nS6d++O2Wxm+/btbN++3WYdd3d3vvrqK7s+Eycn18KfJy6weHcMi3fHEJdyKfD4uDvTpU4QPeqH0qJqOZyvIvBcjpubG71797ZTxSIiUhgKPyIiUiLcdtttrFixgtGjR7N3716btkaNGvHJJ5/QrFmzQu/n1Pl01h5KYO2heDYcTbCZpc3LzYkudfIuaWtV1R8XJz0OT0TkZqLwIyIiJUZkZCS7d+9m48aNbN26lX379jFkyBBatGhxzSM+Gdm5bD6WyJpD8aw9HM+x+DSbdl8PZ9rXCKRH/RBaR/jj6uRoj0MREZESqMDhZ+3atbz55pts376dmJgY5s2bZzOcP2TIEGbOnGnzmWbNmrF58+ZCFysiIjc/k8lEq1atuPXWW1m8eDFNmzYtUPAxDIODZ1NYeyieNYfi2Rp1nuxci7Xd0cFEwzBfIqsH0LZ6ADUDPXBxdsLBQaM8IiI3uwKHn7S0NBo0aMDQoUPp16/fZdfp2rUr06dPt753cXG59gpFRET+w/m0bNYdybuUbd3heM4mZ9m0l/d1p211f9pGBNCymj+5GSl89NFH9H7gS6Kjo3F0dCQyMpJHHnmE3r172/W+IhERKTkKHH66detGt27drriOq6srwcHB11yUiIjIleTkWthx8gJrD8Wz9lA8u04nYRiX2t2cHWhepRxtI/JGd6oGeFoDzdGjR+nYsSPR0dHW9XNzc/n999/5/fffGTZsGJ9//rlGgkREbkJFcs/P6tWrCQwMxNfXl8jISF555RUCAwMvu25WVhZZWZd+Q5ecnAyA2WzGbDZf9jNy87v43asPlF7qA/K/feDU+QzWHUlg3eFENh07R2pWjs36NYLK0LpaOdpE+NOkoi+uzpfu3cnJybH+t0ePHtbg4+DgwC233EJ8fLx12VdffUVERARPPPFEkR+jXJnOA6I+IPb+7k2G8c/flRXwwyZTvnt+vv/+e8qUKUOlSpWIiorihRdeICcnh+3bt+Pq6ppvG5MmTeKll17Kt3zWrFl4eHhca2kiInKDy86Fw8kmDlzI+xOXaXspmqeTQQ0fg5q+eX98ruIK602bNvH6668DUKFCBZ577jlCQkKwWCysXr2a999/HwBfX18+//xznJ2d7X5cIiJy9dLT0xk0aBBJSUl4e3sXent2Dz//KyYmhkqVKjFnzhz69u2br/1yIz9hYWHExMRQrly5ay1NbnBms5kVK1bQqVMn/fBRSqkPlF5nkzOZuekEs7eeJDUr17rc0cFEwwo+1tGduqHeODoU7N6ce+65hx9//BGAX375hS5duti0DxgwgPnz5wOwZMkSOnbsWLiDkULReUDUByQxMZGQkBC7hZ8in+o6JCSESpUqcfjw4cu2u7q6XnZEyNnZWZ1c1A9EfaAUOXQ2hWlrj7Fg52nMuXm/lyvrYtC5fhjtawbSoqo/Pu6F6wuJiYnW123bts3Xt9q0aWMNP+fPn1ffKyF0HhD1gdLL3t97kYefxMRETp48SUhISFHvSkREbjCGYbD52DmmrT3KqoPx1uW3VvZjWKuKZBzdRo/ba9vtHz9/f3/r6y1bttCpUyeb9n8+lkFXH4iI3HwKHH5SU1M5cuSI9X1UVBQ7d+7Ez88PPz8/Jk2aRL9+/QgJCeH48eNMmDABf39/+vTpY9fCRUTkxpWTa2Hp3lg+X3uMv04lAWAyQZfawTwUWYVbKpbFbDaz+Jh993vnnXfyww8/APD444+zePFiKlasiGEYfP/99/z0008ABAQEEBkZad+di4hIsStw+Nm2bRvt27e3vh83bhwAgwcP5pNPPmH37t18/fXXXLhwgZCQENq3b8/333+Pl5eX/aoWEZEbUkZ2Lj9uP8kX66I4cS4dAFcnB+5sXIHhbaoQ7u9ZpPvv3bs3ERERHD58mL1791K1alWaN2/O2bNnbS7Pfuyxxy57SbaIiNzYChx+2rVrx5XmSFi2bFmhChIRkZtPYmoWMzdF882m45xPz5u2tKyHM/e1qMz9LSrhX+b6BA1nZ2d++eUXOnbsyOnTp8nJyWH9+vU269xzzz08++yz16UeERG5vor8nh8RESm9jiek8fm6Y/y0/RRZORYAKvp5MLxNOP0bh+Hu4vgfW7C/GjVqsGPHDt577z2+/PJLYmNjAWjZsiWPPPIId911lx5wKiJyk1L4ERERu9tx4jzT1h5j6d5YLl4sUL+CDyPaVqVr3eACT1FtbwEBAUyePJmXX36Z1NRUXFxcdJmbiEgpoPAjIiJ2YbEY/H4gjmlrj/HH8XPW5e1rBPBQ26o0r+KHyVS8oed/mUwm3ZMqIlKKKPyIiEihZOXkMn/HaaatPcbR+DQAnB1N9GpYnofaVqF6kMKFiIiUDAo/IiJyTZLSzXy7JZoZG48Tn5IFgJerE4OaV2Roy3CCfdyKuUIRERFbCj8iInLVDMPgWEIas7acYM4fJ0jLzgUg2NuNB1qHc/etYXi56SnsIiJSMin8iIjIFSWlm9lwNIF1h+NZeyiB0xcyrG01g714sE0VejYIxcVJM6SJiEjJpvAjIiI2zLkWdp68wLpD8aw9nMCuUxew/OPxbi6ODrSoWo6hrSoTWT2gxE1iICIi8m8UfkRESjnDMIhOTM8b2TmcwKajiaRm5disUz2oDG0iAmgT4U/jMB9cHNHU0CIicsNR+BERKYWSMsxsOprA2sN5l7OdPJdh0+7n6ULrav60ifCnTUQAgV4uzJ49m+eGfcymTZswDIPw8HCGDx/O6NGj8fHxKaYjERERuXoKPyIipUBOroW/Tl1g7aG8sLPzpO2lbM6OJppU8qNNdX/aRgRQO8Qbh78fRJqTk8OAAQOYO3euzTajoqJ47rnnmDFjBr///jsVKlS4nockIiJSYAo/IiI3uIMHD/LRRx+xZMkSUlNTqVSpEoMHD6Z9z/5sO5XGusPxbDySSMr/XMpWLbAMbSLyws6t4X54ul7+n4SJEyfaBJ+IiAh8fX3Ztm0bhmFw+PBh+vTpwx9//KH7f0REpERT+BERuYF98cUXjBw5ktzcXEwu7rhVasBh70ZM3unE69FbbNb19XCmVTV/2kb40zoigPK+7v+5/ZSUFD744AMAnJyc+OGHH+jduzcmk4kDBw7QvXt3oqKi2LZtGytXruS2224rkuMUERGxB4UfEZEikpSUxMyZM/npp59ITEwkMDCQu+66i3vvvZcyZcoUevvLli1jxCNjca8ZiUeNlriH34LJycXabuTm4HA+mkf7d6JD7RDqlvfB0aFgIzPLly8nJSUFgMGDB9OnTx9rW82aNXnttde46667APjhhx8UfkREpERT+BERKQJbtmyhZ8+exMfHW5ft27eP1atXM3nyZBYtWkSDBg2uadsJqVks33uWl+YepMKY7zA5XjqVVyrnQe2y8Nu3H3B001KM7AzKtp5Ogy5Drmlf/6y/RYsW+dr/uSwhIeGa9iEiInK9KPyIiNhZdHQ0Xbt25cKFC9Zl7u7uZGTkzah2+vRpOnfuzK5duwgKCrqqbcYmZbJ0TwxL9sSy9fi5vMkK/KpiAkzJMTzapw3d6oVQI8gLk8nExtqutGo1D4BvvvmGIUOGXNOx+Pv7W19v3ryZBx54wKZ98+bN1tflypW7pn2IiIhcL3oct4iInb399tvW4NOmTRv27NlDeno6f/75J02aNAEgLi6ODz/88IrbOZGYzrS1R+nz8Qaav7qSSb/sY0tUXvAJ93Hk/JqZnJ72EL1d9/J4pxrUDPa2TjjQokUL66V1p06duuZj6dKlC15eXgDMmDGD+fPnYxh508QdPHiQZ555xrrugAEDrnk/IiIi14NGfkRE7MhisfDNN98AeaM9P//8s3X0pFGjRvz888+Eh4eTm5vLjBkzePnll20+fyQuhSW7Y1myJ5Z9McnW5SYTNK5Ylq51g+lSJ5jzp47QYMKPQN7ldP/rxIkTpKamAuDt7X3Nx+Pl5cXo0aN57bXXyMnJoU+fPtSoUYOyZcuyZcsWaxC65ZZb6Nix4zXvR0RE5HpQ+BERsaMLFy5YR31atmxpc9kYQFhYGI0aNWLbtm2cOnWKnJwcDsalsXRPXuA5EpdqXdfRwUSzcD+6/R14Ar3drG2hPnWoVKkS0dHRLF++nAULFtCrVy8AsrKyGDdunHXdO+64o1DH9H//938cOnSIn3/+Gcgb8fmnatWqMW/ePBwcdDGBiIiUbAo/IiJ25OHhgclkwjAMoqKiMAzD5tk3OTk5nDhxEpfQGnjXakOHd9Zx4ly6td3Z0USrav50qxtMp9rB+Hm6XG43ODo68thjj1lDTu/evWnVqhUREREsX76cM2fOWOsZPnx4oY7J2dmZH374gdmzZ/PRRx9Z7/OpVKkSw4cP55FHHsHX17dQ+xAREbkeFH5EROzIzc2NyMhIVq9ezbFjx/jss8/ynsNjMdh6/ByvzFyE852vE+KVNyJ04lw6rk4OtKsRQNe6wXSoGYSPu/NV7evRRx9ly5YtfP/99wBs2LCBDRs2WNtdXFyYM2cOISEhhT4uR0dH7r33Xu69916ys7PJycnB3d1dDzUVEZEbisKPiIidPfbYY6xevRqAR198nY82nSU7uD5ZJhegHE5eYMlKp3klL4Z0bEC7GgF4uBT8dOzo6Mh3331H27Ztee+99zh06BAADg4O9OzZk+eee46mTZva8cjyuLi44OJy+REpERGRkkzhR0TEziI7daPH42+y7ZwzrsHVSPl7eW5GChlHNpN+cBNj7+7ClLH/V+h9OTo6MmrUKB5++GGioqJITU2lfPnymnZaRETkMhR+RETsINdisOFIAj9sO8nyfWfJdqmFazBgySHt8BbSdq0g4/gO6tSqyfiXxnPPPffYdf8mk4kqVarYdZsiIiI3G4UfEZFCiE5M46ftp5i7/RRnkjKty2sGezGgSRi9GoZy+lg4iYmdCAwMpHbt2rpPRkREpJgo/IiIFFB6dg5Ldsfy4/aTbD52zrrcx92ZXg1DGdAkjDqhlx44Wq5+/eIqVURERP5B4UdE5CoYhsGfJy7w47aT/LorhtSsHCDv4aNtIgLo37gCnWoH4ebsWMyVioiIyL9R+BERuYK45Ex+3nGaH7ed5Gh8mnV5RT8P+jeuQL/GFQj1dS/GCkVERORqKfyIiPyP7BwLvx+I46ftJ1l1MJ5ciwGAu7Mj3euF0L9JBW6t7IeDg+7dERERuZEo/IhIqZOcnMyMGTP49ttvOXXqFN7e3vTs2ZNudw9jQ4zB/B2nSUzLtq7fuFJZ+jeuwO31Q/Byu7oHkIqIiEjJo/AjIqXK/v376dq1KydOnADA5OpJSlBDvj0byo8/HrOuF+DlSt9bytO/cRjVAssUV7kiIiJiRwo/IlLinD59mgMHDnDw4EHat2+Ps7N9RluSk5Pp2rUrp84m4lmnAx41WuJepTEmx7ztG7k5ZBz9gxfv7cTIXm1xcnSwy35FRESkZFD4EZESY/v27Tz//PMsXbrUuuy1115j+PDhvPjii5Qpc+0jMImpWTzz0Vwymw2jQqWGmBwvnf6q+rtjHN3ImplvYslIZknWTh7p264whyIiIiIlkMKPiJQIK1as4I477iAzM9Nm+fnz53nzzTdZtWoVv//+O15eXle9zbjkTJbtjWXx7li2RCViMQJxrxIIQCVfZ3o3rky3esHUCPIiJ6cNVRdN4+TJZJYsWUJ8fDwBAQF2PUYREREpXgo/IlLsUlJSuOuuu6zBp2LFivTq1YsdO3awZcsWzGYz27Zt45lnnuHjjz++4rZOX8hgye4Ylu6JZfuJ8xjGpTZLYjRJe1ZT5sIR1uz/0+Zzzs7OdOzYkRkzZmAYBjExMQo/IiIiNxmFHxEpdt9++y3nz58HoGvXrsyfPx8HBwcWL15MWFgYbdq0IT09nZkzZzJlyhR8fX1tPn88IY0le2JZuieGv04l2bQ1quhLt7rBdKsbQsfmDTl5+DDpTk4kJCTg7+9vs+7+/futr729vYvmYEVERKTYFPhu3rVr19KzZ09CQ0MxmUzMnz/fpt0wDCZNmkRoaCju7u60a9eOvXv32qteEbkJ/fMen8mTJ+Pq6mp9X69ePe677z4A0tPTWbduHQCHz6bw/srDdJ26lnZvreb1pQf461QSJhPcGu7HpJ612TS+A/NGteKhtlUJ8/OgZ8+eAOTk5PDUU0+Rk5Nj3c+3337Lli1bAKhTpw6VKlUq8uMWERGR66vAIz9paWk0aNCAoUOH0q9fv3ztb7zxBu+88w4zZsygevXqTJ48mU6dOnHw4MECXasvIqVHWlqa9XWVKlXytVetWhUA58Bwfj5sZurbqzkaf+kzjg4mWlYtR9e6wXSuHUyAl2u+bQCMGjWKDz/8kOzsbGbMmMGqVavo2LEj+/btY/Pmzdb1xo0bh8mkB5iKiIjcbAocfrp160a3bt0u22YYBlOnTuW5556jb9++AMycOZOgoCBmzZrFiBEjCletiNyUKleubH39yy+/cP/99wNgGLDzxAW+/iuZ0Ic+x7lsCKviANJwcXSgdYQ/XesG06lWEGU9Xf5zP1WrVmX69Oncf//95ObmEh0dzVdffWWzzvDhwxk6dKgdj05ERERKCrve8xMVFUVsbCydO3e2LnN1dSUyMpKNGzdeNvxkZWWRlZVlfZ+cnAyA2WzGbDbbszy5gVz87tUHSg7DMFi3bh07duzAZDLRtGlTmjdvbpcRknvuuYcvv/wSyBt1Scx155xPBAv/NJG0+Q+o0BxngJxsOtWrQNc6QbSv4Y+X26Xn/1xtX+nfvz+hoaG89tprLFu2zLq8du3aPProowwdOtTmcjgpPjoPiPqAqA+Ivb97u4af2NhYAIKCgmyWBwUFER0dfdnPvPrqq7z00kv5lq9atQoPDw97lic3oBUrVhR3CQLs2rWLadOmcerUKZvllStXZuTIkdSsWbNQ2zcMg/pNWxJl8celXkfeO+gBnAYcsWSlk3F0K+mHNjLijtZE+jrA6TOsO12oXfLwww8zcOBAzp8/j4eHB4GBgZhMJpYsWVK4DYvd6Twg6gOiPlB6paen23V7RTLb2//+JtgwjH/97fD48eMZN26c9X1ycjJhYWG0b9+ecuXKFUV5cgMwm82sWLGCTp064ezs/N8fkCKzfPly/u///u+yoyHHjx9n0qRJLFmyhFatWhV42zm5FtYcTuDnHWdIu+05/Cx581IbOWbSj2wmbe8qMqJ24IiFt99+m1GjRhX6eOTGofOAqA+I+oAkJibadXt2DT/BwcFA3ghQSEiIdXlcXFy+0aCLXF1dbWZ2usjZ2VmdXNQPipnZbGbEiBHW4NOsWTOGDx9OTk4On332GTt37iQzM5MRI0awf/9+HByubgLJQ2dT+Gn7KX7+8zQJqZcue61b3pvabskcWDaHo4d3k2Vk0euxMYwaNco66YGUPjoPiPqAqA+UXvb+3u0afsLDwwkODmbFihU0atQIgOzsbNasWcPrr79uz12JyHXwyy+/cPp03vVl7du3Z8WKFTg6OgIwbNgwWrduzdatWzl06BC///47t912279uKyndzMJdZ/hp20mbZ/H4l3Ghd8Py3NmkAjWD/362zoO3YzabWbx4Md27d9c/eCIiImIXBQ4/qampHDlyxPo+KiqKnTt34ufnR8WKFRk7dixTpkwhIiKCiIgIpkyZgoeHB4MGDbJr4SI3giNHjrB8+XJSU1OpVKkSPXv2vKHuZdu4caP19dixY63BB8DFxYUxY8ZYZ2bbtGlTvvCTazFYfySBH7edZPm+s2TnWABwcjDRoWYgdzauQPuagTg7FviRYyIiIiIFVuDws23bNtq3b299f/F+ncGDBzNjxgyefvppMjIyGDVqFOfPn6dZs2YsX75cz/iRUiU2NpYHH3yQX3/91Wa5r68v48eP56mnnrohniPzz/t8LhfaPD09L7vusfhU62VtscmZ1uU1g724s3EFejcqj3+Zyz+LR0RERKSoFDj8tGvXDsMw/rXdZDIxadIkJk2aVJi6RG5YCQkJtGnTxmaE9KILFy7wzDPPkJCQwBtvvFEM1RVM/fr1ra9nzJhhM7JjGAbTp0+3vo+oXY85f5zgx+2n2B593rrc18OZXg1C6d8kjDqh3jdE6BMREZGbU5HM9iZSmk2cONEafIKCghgzZgzVqlVj0aJFfPPNNwC8+eabDBw40HpvXEk1YMAAHn/8cZKTk/nuu+9wdnZmxIgR5Obm8uGHH/Lrr4twq1ifck17MHmPJ5k7dgPgYILI6gH0bxJGx1qBuDo5/seeRERERIqewo+IHaWmpvL1118DeZeJbdmyhUqVKgFw1113Ubt2bcaPHw/AJ598wrRp04qt1qtRpkwZ3njjDUaOHAnkjf7MmDEDJ58gPOt1pPzIL3DyyZvJMdNsoWqAJ/2bhNG3UXkCvd2Ks3QRERGRfBR+ROxo7969pKamAtC3b19r8LnokUce4fnnnyc3N9dmMoGS7OJIz1PPTsAU1ogy9TvjVunS5XCuDhb6Na1M/8YVaBjmq8vaREREpMRS+BGxo9zcXOvry00Q4OLigpOTE7m5uTbrlmT7Y5KJqxBJ1XHfk5z596QGhkFl9yxGdmlI7yaVcXPWZW0iIiJS8in8iNhRjRo1cHZ2xmw2M3fuXN544w18fHys7bNmzSIrK++hng0aNCiuMv9TalYOC3ee4futJ2yeyVPe150BTcK4s0kFyvu6F2OFIiIiIgWn8CNiR+XKlaNfv37MmTOHxMREIiMjef7554mIiODXX3/llVdesa774IMPFmOl+RmGwZ8nLvD91hP8uiuG9Oy8kSlnRxOdagdxV9OKtK7mj6ODLmsTERGRG5PCj4idTZ48meXLl3Pu3Dn++usv+vfvn2+dfv360aFDh2KoLr9zadnM23Ga77ee4NDZVOvyKgGeDGxakT636Jk8IiIicnNQ+BGxs6pVq7Jq1SoGDBjAwYMHbdpMJhNDhw7l448/LtaJASwWg41HE5mz9QTL954lO9cCgJuzA7fXC+XuW8NoUqmsJi8QERGRm4rCj0gRqF+/Pvv27WPp0qUsWbKE1NRUKleuzH333UeVKlWKra7YpEx+2n6S77ed5OS5DOvyuuW9uatpRXo1DMXbzbnY6hMREREpSgo/IkXEwcGB7t27071792KtIyfXwqqD8Xy/9QS/H4jDYuQt93JzonfD8tzVNIy65X2uvBERERGRm4DCj8hNKjoxje+3nuSn7aeIS8myLr+1sh93NQ2je70Q3F00RbWIiIiUHgo/IjcwwzD49ddf+eijj1i3bh1mC1SN7EtAs16cyLo0FXU5TxfubFyBAU3DqBpQphgrFhERESk+Cj8iN6jc3FyGDx/OjK+/xa1iPTxaD8GvZmsy3L05kQUYFlqE+3J/q2p0rBWEi5NDcZcsIiIiUqwUfkRuQKlZOTw65RN+TfAnbMy3OLhdGs3JSY4jddcKUnf9xsn61ek6Yp1mbRMRERFB4UfkhpGQmsVv+86yfN9Z1h9OIDu3Cp518maOK+NooectlehWLwS35Gj69n6BpJR4NmyIZ926dbRt27aYqxcREREpfgo/IiXYicR0lu+LZdneWLZFn8cwLrWZz50h/fAm2lbxYd7n7+DgcHF0J4DXXnuN++67D4DZs2cr/IiIiIig8CNSohiGwd4zySzfd5ble2M5EJti016vvA9d6gRxfs8aXnz9IQB63vP5P4JPnsjISOvr2NjYoi9cRERE5Aag8CNSzHJyLWw9fp7l+2JZvvcspy9cevioo4OJZuF+dKkTTKfaQYT65s3g9kPCDus6f/75Z75tbt++3fraz8+vCKsXERERuXEo/IgUg0xzLmsPxbN831lW7j/L+XSztc3N2YHI6gF0qRNMh5qB+Hq45Pt8586d8fDwID09na+++oo777yTDh06AHDy5EnGjx9vXbdfv35Ff0AiIiIiNwCFH5Hr5EJ6Nr8fiGPZ3ljWHkogw5xrbSvr4UzHWkF0rh1Em4iA/3z4qK+vLw899BBTp04lKyuLjh070qRJE8qWLcvq1asxm/PCVJ06dejSpUuRHpeIiIjIjULhR6QI5VoMFu2OYc4fJ9gSdY5cy6UZC8r7utO5ThCdawfTtHJZnBwL9hye1157jf3797Ns2TIAtm3bZtMeFhbG/PnzcXS8cpASERERKS0UfkSKgMVisHhPDO/9dpjDcanW5TWDvehcJ5jOtYOoE+pdqOfvuLq68ssvv/DFF1/w4Ycfsm/fPgD8/f0ZNmwYTzzxBIGBgYU+FhEREZGbhcKPiB1ZLAbL9sYy9bfDHDybN1Obt5sTw1qH06dReSqV87Tr/pydnXn44Yd5+OGHOXfuHGazGX9/f432iIiIiFyGwo+IHRiGwbK9Z5n62yHr9NRebk480Dqcoa3C8XF3LvIaNKubiIiIyJUp/EiptH37dn766ScSExMJDAxkwIAB1K9fv8DbMQyD3/bHMfW3Q+w9kwxAGVcnhrWqzAOtq+DjUfShR0RERESujsKPlCpnz55l4MCBrFq1ymb5K6+8Qvfu3fnmm2+uagTFMAx+PxDH1N8Os/t0EgCeLo4MbRXO8Dbhl52eWkRERESKl8KPlBopKSl07NiRvXv3XrZ98eLFdOnShXXr1uHm5nbZdQzDYPWheKauOMRfp/JCj4eLI4NbVubBNlXw81ToERERESmpCja3rsgN7MMPP7QGn5CQED799FP+/PNPPvjgA/z9/YG86aK//PLLfJ81DIO1h+Lp+8lGhk7fyl+nknB3dmRE2yqse7o9z3StqeAjIiIiUsJp5EdKBcMwmDZtGgAmk4kVK1ZQp04dABo1akSTJk1o0aIFANOmTWP06NHWz204ksi7vx1ie/R5ANycHbiveSVGRFbFv4xrMRyNiIiIiFwLhR8pFZKTkzl+/DgALVq0sAafi5o3b06dOnXYu3cvu3fvxmKxsDnqHFNXHOaP4+cAcHVy4J5mlRjZrgqBXpe/LE5ERERESi6FHykVHBwuXeGZlZWVr90wDOtyt7C6DPx8C1ui8kKPi5MDg26tyKh2VQn0VugRERERuVEp/Eip4OXlRe3atdm3bx/bt29n/fr1tG7d2tq+ZMkSTma4EHjXK7hXbsCWqHO4ODpw961hjGpXjWAfhR4RERGRG53Cj5QaDz/8MGPGjAGgW7dujBkzhltvvZWFG3az5JQjwfe+AYAjBnc3q8To9tUI9XUvzpJFRERExI4UfqTUePDBB/nxxx9Zu3YtqWnpvPv9CryPuOJepQmulcDIzaHshYMsfHUUFf3LFHe5IiIiImJnCj9Sari6uvL2V98zdupsognA0bMsAIYll4y9q+he2YFPP3jlX5/xIyIiIiI3NruHn0mTJvHSSy/ZLAsKCiI2NtbeuxK5KmeTM1mw8zQ//3maA7Ep4FkdR8DdIZcqjom0DbYw9MnxBAYGFnepIiIiIlKEimTkp06dOvz222/W946OjkWxG5F/lZGdy/J9scz98zTrD8djMfKWuzg6cFvtQPo2qkBkjQCcHfWcXxEREZHSokjCj5OTE8HBwUWxaZF/ZbEYbIk6x89/nmLJnlhSs3KsbY0rlaXvLeXpUS8UHw/nYqxSRERERIpLkYSfw4cPExoaiqurK82aNWPKlClUqVKlKHYlwtH4VOb9eZp5O05z+kKGdXmYnzt9G1WgT6PyVPb3LMYKRURERKQksHv4adasGV9//TXVq1fn7NmzTJ48mZYtW7J3717KlSuXb/2srCybh04mJycDYDabMZvN9i5PbhAXv/t/6wPn07NZvDuWeTtj+OtUknV5GVcnutcNok+jUBpX9MVkMl1xO1Jy/VcfkJuf+oCoD4j6gNj7uzcZhmHYdYv/Iy0tjapVq/L0008zbty4fO2XmyABYNasWXh4eBRlaXKDybHAvgsmtsab2HveRK6RF2wcMKjpa9A0wKBuWQMX3WImIiIiclNIT09n0KBBJCUl4e3tXejtFXn4AejUqRPVqlXjk08+ydd2uZGfsLAwYmJiLjtSJKWD2WxmxYoV3HbbbeyPy2D+zjMs2h3L+fRL6b9WsBd9GoXSo14wAV6uxVitFIWLfaBTp044O+s+rdJIfUDUB0R9QBITEwkJCbFb+Cny5/xkZWWxf/9+2rRpc9l2V1dXXF3z/+Dq7OysTl4KWSwW/vjjD3YePsHyg+d59+AWjp+7dB9PgJcrfRqVp0+j8tQKKfxfACn5dC4Q9QFRHxD1gdLL3t+73cPPk08+Sc+ePalYsSJxcXFMnjyZ5ORkBg8ebO9dyU0kJ9fCa1/8wFdLN5PpWwWXoKqAJ5zLwJFcutUrT/+mFWlVtRxOmp5aRERERK6B3cPPqVOnGDhwIAkJCQQEBNC8eXM2b95MpUqV7L0rucHFJWey+lA8aw7Gs2LPKbINL6jRCZe/2zOjd5G693fSD27gcLs2tOj/i4KPiIiIiFwzu4efOXPm2HuTcpPIybWw4+QFVh+MY/XBePaeSf5HqyO5GclkRv1JJdd0utQLY0PMMjbs34CRk8Py5ct57733eOqpp4qtfhERERG5sRX5PT9SusWlZLLmYDyrD8Wz7lA8yZk5Nu31K/iQcmgLG+d+QXbMIZ5/bgIvv/wmZrOZxQ1q8eKLL9KxY0cAPvroI8aNG4ejo6ZzExEREZGCU/gRu8rJtbDz5AVWH4xn9aE49pxOtmn39XCmTUQA7WsE0LZ6AP5lXKlS5X6yz0Th5ubGM888Y7N+mzZt6NixIytXriQ6Oppjx44RERFxPQ9JRERERG4SCj9SaPEpWaw5FM+qg3GsP5xAUobtw6jqlfehfY0AImsE0jDMF0cHk017RkbebG7e3t54enrm235oaKj1dWZmZhEcgYiIiIiUBgo/UmC5FoOdJ8+z+mBe4Pnf0R0fd2faRPjTvkYgbasH/OczeCIiIoiNjSUuLo7169fbTIuemprK4sWLgbypDitWrGj/AxIRERGRUkHhR65KXHImaw8nsPpgHOv+ZXSnXY0A2tUIoEEF3wLNyjZs2DDWrVsHwKBBg3j//ffp0KEDR44cYerUqSQmJgJw55134uPjY7+DEhEREZFSReFHLis7x8L26POsORTPmoNx7I9NsWl3Nsy0rFKWnk2q0ra6P4Febte8r4EDB/Lee++xc+dOTp06Rd++ffOtU6ZMGV544YVr3oeIiIiIiMKPWJ08l54Xdg7Fs/FIAmnZuTbtWTGHyIj6k8xj28k6c5BjJmj09tsENh5bqP26urqydOlSevXqxZYtW/K1BwQE8PPPP1OrVq1C7UdERERESjeFn1IsIzuXzVGJrDkYz9rD8RyLT7NpL1fGhezonURtXEzG8R1Y0pNwd3fHnJUFhgWLAY8//jjBwcHcfffdhaolKCiIjRs3smzZMr7++mtOnTpFZmYmQ4cO5f7776dMmTKF2r6IiIiIiMJPKWIYBkfjU1l9MG90Z0vUObJzLNZ2RwcTjSuWJbJGAJHVA4g/vIMOLzwNgL+/P1/OXkCPHj24cOECr7zyCu+88w4AL774IgMGDMDB4erv87kcBwcHunXrRrdu3fKe87N4Md27d8fZ2blQ2xURERERAYWfm15yppmNRxJZcyietYfiOX0hw6Y91MfNGnZaVvPH2+1S0HjgxW+sr999913uuOMOAPz8/Hj77bfZtm0ba9eu5fDhw2zevJmWLVten4MSEREREbkGCj83GYvFYF9M8t8TFcSz/cR5ci2Gtd3FyYFm4X5EVs+bma1qQBlMJtNltxUdHW19ffvtt+dr79GjB2vXrrWuq/AjIiIiIiWZws9NIC45kw1HE1h3KIG1h+NJSM22aa/i70nb6gFE1gigeXg53F0cr2q7/7zP5ujRozRp0sSm/ciRI5ddV0RERG5OmZmZxMfHX7f9WSwWwsLCOHPmTKEvr5eSLSAgADe3a589+Gop/NyAkjPNbD6ayMajiWw4ksDhuFSbdk8XR1pW888LPBEBVCzncU376dq1KwsWLABgwoQJLFy40Nopd+7cyTff5F0W5+HhQdu2bQtxRCIiIlLSZWZmEhcXR/ny5XF0vLpfpBaWxWLBx8cHb29vhZ+bWG5uLqdPnyYwMLDIA5DCzw0g05zLn9Hn2XA0gQ1HEtl16gL/uJINkwnqhHrTqpo/7aoH0rhSWVycCn+CuOeee3j++edJTExkxYoVVKtWjV69enH27FkWLFhATk4OAEOHDtXDR0VERG5y8fHx1zX4SOnh6OhI+fLlOXPmDGFhYUW6L4WfEijXYrDndBIbjiaw8UgiW4+fI+sfs7IBhPt70rJqOVpX86d5lXKU9XSxex1eXl788MMP9OjRg4yMDE6fPs3HH39ss06zZs147bXX7L5vERERKXkUfKSoXK++pfBThGJjY9m8eTNms5natWtTp06dy66XNwV1GhuPJrDhSAKbjiaSnJljs06Alyutq/nTsmo5WlXzJ9TXHYvFwqJFi7hv/Gfs2LEDk8lE06ZNGTlyJJ07d/7XiQwKokOHDmzcuJEXX3yRX3/9FcPIG3IqV64cDz30EM899xyenp6F3o+IiIiISFFT+CkCZ86cYdy4ccydO9d6aRhA8+bNefPNN2ndujWxSZlsOJIXdjYcTeBscpbNNrxcnWhetRyt/g471QJtZ2XLysrirrvust6Tc9Hp06eZP38+gwYNYubMmTg5Ff4rbtiwIQsXLiQ2NpajR4/i5uZG3bp1cXV1LfS2RURERESuF4UfOzt9+jQtW7bkxIkTNssdXD35K9FEn8lzqNIiibO2j9vBxcmBJpXK0urv0Z165X1wcvz3+3YeeeQRm+BTtmxZLBYLSUlJAMyaNYvg4GDefvttux1bcHAwwcHBdtueiIiISHFp164dDRs2ZOrUqQBUrlyZsWPHMnbs2GKtS4qWwo+djR492hp8AiIackuvB0hwDiQh1x1MeWHmbAY4mKBeeR9aVvOnVVV/mlQui5vz1V3reOLECb766isA3N3dmTFjBv369cMwDL799lseeughzGYzH330EePHj8ff379oDlZERESkhBsyZAgzZ87Mt3zLli3UqlXrXz9nMpmYN28evXv3LsLq5HpT+LGjqKgolv6xH9/IIXjVboODdxAHACyACVwyz5GwdyOZ0Tt5/YnhjBmR/8GhV2POnDlYLHkTIDz99NMMGDDA2jZkyBD++usvpk6dSlZWFj/99BMjR44s/MGJiIiI3KC6du3K9OnTbZYFBARcl5vszWYzzs7ORb4fuTqaML2Qci0Gf0Sd46Vf9tL7y90E3/8OPs3vxME7CFcnBzrVDuKt/g3YPL4j0/tX4fxvn5JxeDOb1/5+zfs8efKk9XWnTp3ytXfu3Nn6+vTp09e8HxEREZGbgaurq/Xy/Yt/Onbs+K+XuFWuXBmAPn36YDKZrO8BfvnlFxo3boybmxtVqlThpZdesrnH22Qy8emnn9KrVy88PT2ZPHlyER6ZFJRGfq5BTq6FzcfOsWRPDMv2niUh9eJkBY5YsjPIOLqVgW1q8+qYe/B0vfS/OD0kxPo6MzPzmvf/z2fq7N+/n1atWtm079u3z/ra29v7mvcjIiIi8m8MwyDDnFuk+7BYLGRk5+KUnWN9yKm7s6NdZrS9kq1btxIYGMj06dPp2rWrdYRo2bJl3Hvvvbz//vu0adOGo0eP8tBDDwEwceJE6+cnTpzIq6++yrvvvqvpwUsYhZ+rlJWTy4YjCSzZHcuK/We5kG62tnm5OdGpVhDlieepe/ti5GSzO7kdHk/cb7ON77//3vo6IiLimmvp2bMnr7zyCgCvvPIKXbt2pUKFCgAcPXqUt956y7pujx49rnk/IiIiIv8mw5xL7ReXXff97vu/Lni4FOxH2F9//ZUyZcpY33fr1u2K6wcEBADg6+trM9nTK6+8wrPPPsvgwYMBqFKlCi+//DJPP/20TfgZNGgQw4YNK1CNcn0o/FxBRnYuaw7Fs3RPDCv3x5GSdWlI08/Thc61g+haN5iWVf1xcXLAYrHw8YQKHDt2jNWrVzN8+HCeffZZfH19+fbbb3nppZesny/MX4hbb72Vli1bsnHjRo4fP05ERAS33347OTk5LF68GLM5L5h17dr1ijfyiYiIiJQG7du355NPPrG+9/T0ZODAgQXezvbt29m6dav1l9AAubm5ZGZmkp6ejoeHBwBNmjQpfNFSJBR+/kdqVg6/H4hj6Z4YVh2ItxnODfRypUudYLrVDebWcL98U1E7ODjwxhtvcOeddwLw1VdfWWdl+6eHHnqI6tWrX3ONJpOJWbNmERkZSXR0NJmZmcydO9dmnRo1auS7sU9ERETEXtydHdn3f12KdB8Wi4WU5BS8vL1sLnsrKE9PT6pVq2aXel566SX69u2br83Nzc1mf1IyKfwASelmVuw/y9I9Maw9nEB2jsXaVt7Xna518wLPLRXL4uBw5WtM+/XrxxdffMHo0aPJysrK1z506FA+/PDDQtdcqVIl/vjjD6ZMmcKMGTOsz/fx8/PjgQceYPz48ZQtW7bQ+xERERG5HJPJVODLzwrKYrGQ4+KIh4uTNfxcL87OzuTm2t7TdMstt3Dw4EG7BCkpHqU2/MSlZLJyfxyLd8ew6WgiORbD2hbu72kNPPXK+xT4proHHniA22+/na+++op169ZhNpupVasWw4cPp0GDBnY7hsDAQKZOncprr73GsWPHMJlMVK1aFRcXF7vtQ0RERKQ0qly5MitXrqRVq1a4urpStmxZXnzxRXr06EFYWBj9+/fHwcGBXbt2sXv3bs3qdoMoNeEnJ9fCzpMXWHUwjtUH49l7JtmmvXpQGbrVDaFbvWBqBHkVehaR4OBgJkyYUKhtXC03Nzdq1659XfYlIiIiUhq8/fbbjBs3js8//5zy5ctz/PhxunTpwq+//sr//d//8cYbb+Ds7EzNmjUZPnx4cZcrV+mmDj/xKVmsORTPqoNxrDsUT3Jmjk17qJuZ5hXcebhHcyKCff5lKyIiIiJyo5oxY8Zll69evdrm/fHjx23e9+zZk549e+b7XJcuXejS5d/vdTIM41/bpPjdVOEn12Kw8+R5Vh+MZ/XBeHafTrJp93Zzwu1CFIdWzyPl8B9Ep19gEzC3YkUmTZrE0KFDi6dwEREREREpcjd8+ElIzWLNwXhWH4pn3eF4m+fvANQt70276oE0q+jJo/f2Zuuf2/Nt48SJEwwbNoy4uDieeeaZ61W6iIiIiIhcRzdc+Mm1GPx16gKrD8Sx+lA8u07lH91pUz2AdtUDiKwRQKBX3rSDTz31FDv/Dj5eXl4MGzaMatWqsWjRIpYuXQrA+PHjueOOO/RsHBERERGRm9ANEX4SU7NYezieVQfyRnfO/8/oTp1Qb9rVCKBdjUAahfnme/5ORkYGX375JQAuLi5s3rzZOkHAI488wvjx43nttdcwDINPPvmE999///ocmIiIiIiIXDclNvzsOpXEzj8TWX0wjl2nk/jnvWNebk60jcgb2WlXPYBAb7d/3xCwZ88ezp8/D0CfPn3yzYz2zDPP8MYbb2CxWFizZo3dj0VERERERIpfiQ0/g2dsx8HVw/q+dsil0Z1bKuYf3bmS7Oxs6+ty5crla/fy8sLFxYXMzMzLPphURERERERufCU2/Hi6OtK+XjDtqgcSWSOAoP8Y3bmSatWq4eDggMViYd68ebz55pt4eFwKVvPmzSMzMxNA9/uIiIiIiNykrn74pIA+/vhjwsPDcXNzo3Hjxqxbt65An181rg0f39OYAU3DChV8AIKCgrjjjjsAiImJoVu3bqxZs4YzZ84wbdo0HnzwQeu6/3wtIiIiIiI3jyIJP99//z1jx47lueeeY8eOHbRp04Zu3bpx4sSJq96GcwEua7saL7/8Mp6engCsXbuWdu3aUb58eUaMGMGFCxcA6NSpE127drXrfkVEREREpGQokvDzzjvv8MADDzB8+HBq1arF1KlTCQsL45NPPimK3V2VunXrsmzZMoKDgy/b3rNnT+bOnYuDQ5ENhomIiIiISDGy+0/62dnZbN++nc6dO9ss79y5Mxs3brT37gqkVatWHDt2jBkzZnD33XfTo0cPRo8ezR9//MHChQvx8vIq1vpEREREbmYZGRnMnz+fjz/+mNmzZ5OYmFjk+xwyZAgmk4mRI0fmaxs1ahQmk4khQ4YUeR03M5PJxPz584u7jKti9wkPEhISyM3NJSgoyGZ5UFAQsbGx+dbPysqymWEtOTkZALPZjNlszrd+YTk5OTFo0CAGDRpks7wo9iXX7uL3oe+l9FIfEPUBUR8oWSwWCxaL5Zo/+8Ybb/D2229z7tw563I3NzcGDx7MW2+9ZTMZ1UXG3886MQzjmvdtGAZhYWHMmTOHt99+G3d3dwAyMzOZPXs2FStWLNT2i1p2djYuLi7FXcZ/Kkz/+Oc2/vfvu73//hfZbG8mk8nmvWEY+ZYBvPrqq7z00kv5lq9ateqyfwmkdFmxYkVxlyDFTH1A1AdEfaBkCAsLw8fHp8CfMwyDJ554gunTp+dry8zM5LPPPmPXrl38/PPPuLldfpKrlJSUAu/3IrPZTL169Th+/DjfffcdAwYMAODHH38kNDSUypUrYzabSU5OxjAM3n//faZPn87Zs2epWrUqTz31FL169QIgNzeXsWPHsnbtWuLi4qhQoQIPPPCAzajS+vXrmThxIgcOHMDJyYmaNWvy+eefU7FiRUaNGkVSUhLfffeddf3x48eze/dufv31VwB69OhBrVq1cHFxYc6cOdSsWZNFixZx4MABXnjhBTZt2oSHhwft27dnypQp1se49OjRg9q1a+Po6Mjs2bNxcXFhwoQJ9O/fn6effpqFCxfi7+/PG2+8QadOnaz7v5rt1qlTB1dXV7755htcXFwYOnQozz77LAD169cHoF+/fkBeP9m1axe7d+9mwoQJ7Ny5E5PJRJUqVXj33Xdp1KjRv35XiYmJ7Ny502ZZenp6wb/0K7B7+PH398fR0THfKE9cXFy+0SDI+8LHjRtnfZ+cnExYWBjt27e/7DN5pHQwm82sWLGCTp064ezsXNzlSDFQHxD1AVEfKFnOnDmDt7d3gT/322+/WYOPyWTi7rvvpkOHDuzatYsvvviCjIwMNm3axNdff82TTz5p81nDMEhJScHLy+uyv0S/Gs7Ozjg5OfHAAw/www8/MHz4cCBvgq7hw4ezevVqnJ2d8fb25vnnn2fevHl88sknREREsHbtWkaMGEHFihWJjIzEbDYTHh7OI488gr+/Pxs3bmTkyJFUrlyZAQMGkJOTw7333svw4cOZM2cO2dnZ/PHHH3h7e+Pt7W2t5Z//H11cXGyWOTk5MWfOHEaOHMn69esxDIO0tDR69uzJ8OHDee+998jIyODZZ5/lwQcf5LfffrP53FNPPcWWLVv44YcfeOKJJ1i2bBm9e/fmxRdfZOrUqTz88MMcP34cDw8PYmJirnq7jz/+OJs3b2bTpk0MGzaM9u3b06lTJ7Zu3UpwcDBffvklXbt2xdHREW9vbx5++GEaNmzIZ599hqOjIzt37sTX1/eKfahcuXLUq1fPZpndL400isCtt95qPPzwwzbLatWqZTz77LP/+dmkpCQDMBISEoqiNLlBZGdnG/Pnzzeys7OLuxQpJuoDoj4g6gMly4kTJ67pc3369DEAAzA+/vhjm7aNGzda2ypXrmzk5ubatOfm5hrnz5/Pt7wgBg8ebPTq1cuIj483XF1djaioKOP48eOGm5ubER8fb/Tq1csYPHiwkZqaari5uRkbN260+fwDDzxgDBw48F+3P2rUKKNfv36GYRhGYmKiARirV6++Yi3/9NhjjxmRkZHW95GRkUbDhg1t1nnhhReMzp072yw7efKkARgHDx60fq5169bW9pycHMPT09O47777rMtiYmIMwNi0adM1b9cwDKNp06bGM888Y30PGPPmzbNZx8vLy5gxY8Zl/z/8m8v1sYSEBAMwkpKSCrStf1Mkl72NGzeO++67jyZNmtCiRQumTZvGiRMnLnuj2b/Zs2cPbdu2veaULyIiIiLF7+KzHv38/KyjLhe1aNGCyMhI1qxZw/Hjxzlz5gwVKlQokjr8/f25/fbbmTlzJoZhcPvtt+Pv729t37dvH5mZmTaXhEHePTf/vFTr008/5YsvviA6OpqMjAyys7Np2LCh9RiHDBlCly5d6NSpE7fddhsDBgwgJCSkQLU2adLE5v327dtZtWoVZcqUybfu0aNHqV69OnDpEjQAR0fHfCMpF6/CiouLu+btAoSEhFi38W/GjRvH8OHD+eabb7jtttvo378/VatWveJnrociCT933XUXiYmJ/N///R8xMTHUrVuXxYsXU6lSpaveRrt27ahZsybPPvss999/v0KQiIiIyA3o4g3rnp6eODnl/9HT19c337pFZdiwYTzyyCMAfPTRRzZtF2/WX7RoEeXLl7dpc3V1BeCHH37g8ccf5+2336ZFixZ4eXnx5ptvsmXLFuu606dP59FHH2Xp0qV8//33PP/886xYsYLmzZvj4OBgncThossd88VnU/6ztp49e/L666/nW/efwep/Lw81mUw2yy7+PH3xWAuz3f+a3GDSpEkMGjSIRYsWsWTJEiZOnMicOXPo06fPFT9X1IpswoNRo0YxatSoQm3jwIEDDBkyhEOHDvHKK6/YqTIRERERuV5q167Npk2bOHnyJOvWraNt27bWtrNnz7J8+XIAvL2984UOe+vatSvZ2dkAdOnSJV+drq6unDhxgsjIyMt+ft26dbRs2dLmZ9yjR4/mW69Ro0Y0atSI8ePH06JFC2bNmkXz5s0JCAhgz549Nuvu3LnzP+9pu+WWW5g7dy6VK1e+bIC8VvbarrOzM7m5ufmWV69enerVq/P4448zcOBApk+fXuzhp8Q+0bN58+bW11OmTGHlypXFWI2IiIiIXIsHH3zQ+rp///589dVXREdHs3DhQm677TYyMjIAuP/++4t8SmdHR0f279/P/v37cXR0tGnz8vLiySef5PHHH2fmzJkcPXqUHTt28NFHHzFz5kwAqlWrxrZt21i2bBmHDh3ihRdeYOvWrdZtREVFMX78eDZt2kR0dDTLly/n0KFD1KpVC4AOHTqwbds2vv76aw4fPszEiRPzhaHLGT16NOfOnWPgwIH88ccfHDt2jOXLlzNs2LDLho6rZa/tVq5cmZUrVxIbG8v58+fJyMjgkUceYfXq1URHR7Nhwwa2bt1q/f9QnEps+Pn111958803re/ff//9YqxGRERERK7FPffcw6233grk3WvywAMPULlyZXr16mX9wT84ONg6dXJRuzjz2uW8/PLLvPjii7z66qvUqlWLLl268MsvvxAeHg7AyJEj6du3L3fddRfNmjUjMTHRZhTIw8ODAwcO0K9fP6pXr85DDz3EI488wogRI4C80aYXXniBp59+mqZNm5KSksL999//nzWHhoayYcMGcnNz6dKlC3Xr1uWxxx7Dx8cHB4dr/3HeXtt9++23WbFiBWFhYTRq1AhHR0cSExO5//77qV69OgMGDKBbt26XfbzN9WYy/vfCw2KWnJyMj48PCQkJ+Pj4UKFCBc6ePYurqysZGRm696eUMJvNLF68mO7du2t601JKfUDUB0R9oGQ5efIkYWFh1/TZc+fOMWDAgMteyVOjRg3mz59PzZo187VZLBaSk5Px9vYu1A/5cmO4XB9LTEzE39+fpKSka5pq/X8V2T0/9uDk5ERYWBhnz54lKysLi8WSb4hSREREREo2Pz8/VqxYwZYtW/juu++IiYnB19eXXr160b17d/18J9dNiQ4/J06cYMeOHUDe02L1F0NERETkxmQymWjevLnNfd0i11uJHT/cuXMnffr0sd5sNWTIkOItSEREREREbmglduTntttus74ODg62zskuIiIiIiJyLUrsyM9FYWFhLF++nMDAwOIuRUREREREbmAlNvy0bduWzz//nP3791OvXr3iLkdERERERG5wJfayt59//ply5coVdxkiIiIiAri6uhIfH4+/v78ePSJ2ZRgGCQkJuLq6Fvm+Smz4EREREZGSIzAwkOTkZE6dOnXd9mmxWEhMTKRcuXJ6zs9NzsfHxy7P8fkvCj8iIiIiclW8vb2vyw+oF5nNZnbu3Em9evX0oFuxC0VoEREREREpFRR+RERERESkVFD4ERERERGRUkHhR0RERERESoUSN+GBYRgApKSk6Ma2UsxsNpOenk5ycrL6QSmlPiDqA6I+IOoDkpKSAlzKCIVV4sJPYmIiAOHh4cVciYiIiIiIlASJiYn4+PgUejslLvz4+fkBcOLECbscoNyYkpOTCQsL4+TJk9d1Sk0pOdQHRH1A1AdEfUCSkpKoWLGiNSMUVokLPxcfYHW9HnQkJdv1fp6AlDzqA6I+IOoDoj4g9nrIrSY8EBERERGRUkHhR0RERERESoUSF35cXV2ZOHEirq6uxV2KFCP1A1EfEPUBUR8Q9QGxdx8wGfaaN05ERERERKQEK3EjPyIiIiIiIkVB4UdEREREREoFhR8RERERESkVFH5ERERERKRUKHHh5+OPPyY8PBw3NzcaN27MunXrirskuU4mTZqEyWSy+RMcHFzcZUkRWrt2LT179iQ0NBSTycT8+fNt2g3DYNKkSYSGhuLu7k67du3Yu3dv8RQrRea/+sGQIUPynRuaN29ePMWK3b366qs0bdoULy8vAgMD6d27NwcPHrRZR+eCm9vV9AGdB25+n3zyCfXr17c+0LZFixYsWbLE2m6v80CJCj/ff/89Y8eO5bnnnmPHjh20adOGbt26ceLEieIuTa6TOnXqEBMTY/2ze/fu4i5JilBaWhoNGjTgww8/vGz7G2+8wTvvvMOHH37I1q1bCQ4OplOnTqSkpFznSqUo/Vc/AOjatavNuWHx4sXXsUIpSmvWrGH06NFs3ryZFStWkJOTQ+fOnUlLS7Ouo3PBze1q+gDoPHCzq1ChAq+99hrbtm1j27ZtdOjQgV69elkDjt3OA0YJcuuttxojR460WVazZk3j2WefLaaK5HqaOHGi0aBBg+IuQ4oJYMybN8/63mKxGMHBwcZrr71mXZaZmWn4+PgYn376aTFUKNfD//YDwzCMwYMHG7169SqWeuT6i4uLMwBjzZo1hmHoXFAa/W8fMAydB0qrsmXLGl988YVdzwMlZuQnOzub7du307lzZ5vlnTt3ZuPGjcVUlVxvhw8fJjQ0lPDwcO6++26OHTtW3CVJMYmKiiI2NtbmnODq6kpkZKTOCaXQ6tWrCQwMpHr16jz44IPExcUVd0lSRJKSkgDw8/MDdC4ojf63D1yk80DpkZuby5w5c0hLS6NFixZ2PQ+UmPCTkJBAbm4uQUFBNsuDgoKIjY0tpqrkemrWrBlff/01y5Yt4/PPPyc2NpaWLVuSmJhY3KVJMbj4917nBOnWrRvfffcdv//+O2+//TZbt26lQ4cOZGVlFXdpYmeGYTBu3Dhat25N3bp1AZ0LSpvL9QHQeaC02L17N2XKlMHV1ZWRI0cyb948ateubdfzgJPdqrUTk8lk894wjHzL5ObUrVs36+t69erRokULqlatysyZMxk3blwxVibFSecEueuuu6yv69atS5MmTahUqRKLFi2ib9++xViZ2NsjjzzCrl27WL9+fb42nQtKh3/rAzoPlA41atRg586dXLhwgblz5zJ48GDWrFljbbfHeaDEjPz4+/vj6OiYL73FxcXlS3lSOnh6elKvXj0OHz5c3KVIMbg405/OCfK/QkJCqFSpks4NN5kxY8awcOFCVq1aRYUKFazLdS4oPf6tD1yOzgM3JxcXF6pVq0aTJk149dVXadCgAe+9955dzwMlJvy4uLjQuHFjVqxYYbN8xYoVtGzZspiqkuKUlZXF/v37CQkJKe5SpBiEh4cTHBxsc07Izs5mzZo1OieUcomJiZw8eVLnhpuEYRg88sgj/Pzzz/z++++Eh4fbtOtccPP7rz5wOToPlA6GYZCVlWXX80CJuuxt3Lhx3HfffTRp0oQWLVowbdo0Tpw4wciRI4u7NLkOnnzySXr27EnFihWJi4tj8uTJJCcnM3jw4OIuTYpIamoqR44csb6Piopi586d+Pn5UbFiRcaOHcuUKVOIiIggIiKCKVOm4OHhwaBBg4qxarG3K/UDPz8/Jk2aRL9+/QgJCeH48eNMmDABf39/+vTpU4xVi72MHj2aWbNmsWDBAry8vKy/2fXx8cHd3R2TyaRzwU3uv/pAamqqzgOlwIQJE+jWrRthYWGkpKQwZ84cVq9ezdKlS+17HrDTTHR289FHHxmVKlUyXFxcjFtuucVmmkO5ud11111GSEiI4ezsbISGhhp9+/Y19u7dW9xlSRFatWqVAeT7M3jwYMMw8qa4nThxohEcHGy4uroabdu2NXbv3l28RYvdXakfpKenG507dzYCAgIMZ2dno2LFisbgwYONEydOFHfZYieX++4BY/r06dZ1dC64uf1XH9B5oHQYNmyYNQMEBAQYHTt2NJYvX25tt9d5wGQYhlHYpCYiIiIiIlLSlZh7fkRERERERIqSwo+IiIiIiJQKCj8iIiIiIlIqKPyIiIiIiEipoPAjIiIiIiKlgsKPiIiIiIiUCgo/IiIiIiJSKij8iIiIiIhIqaDwIyIiIiIipYLCj4iIiIiIlAoKPyIiIiIiUioo/IiIiIiISKnw/6Bh0Vm437peAAAAAElFTkSuQmCC\n",
"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 they are much larger."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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 your initial guess for x to be 100."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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=0.02)\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": 28,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\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., 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 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."
]
},
{
"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 using `plot_g_h_results` or your own routine. Play around with different accererations and times steps. Explain what you see."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"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 + accel * (i**2) / 2 + 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=9.)\n",
"data = g_h_filter(data=zs, x0=10., dx=0., g=0.2, h=0.02)\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 the effect 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": 32,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"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_plots.figsize(y=4):\n",
" book_plots.plot_measurements(zs, color='k')\n",
" book_plots.plot_filter(data1, label='g=0.1', marker='s', c='C0')\n",
" book_plots.plot_filter(data2, label='g=0.4', marker='v', c='C1')\n",
" book_plots.plot_filter(data3, label='g=0.8', c='C2')\n",
" plt.legend(loc=4)"
]
},
{
"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": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\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",
"book_plots.plot_measurements(zs)\n",
"book_plots.plot_filter(data1, label='g=0.1', marker='s', c='C0')\n",
"book_plots.plot_filter(data2, label='g=0.5', marker='v', c='C1')\n",
"book_plots.plot_filter(data3, label='g=0.9', c='C3')\n",
"plt.legend(loc=4)\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 $g$ 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": 35,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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