{
"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": {
"scrolled": false
},
"outputs": [],
"source": [
"from __future__ import division, print_function\n",
"%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": {
"scrolled": false
},
"outputs": [
{
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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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average of measurements is 165.0190\n"
]
}
],
"source": [
"import numpy as np\n",
"measurements = np.random.uniform(160, 170, size=10000)\n",
"mean = measurements.mean()\n",
"print('Average of measurements is {:.4f}'.format(mean))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The exact number printed depends on your random number generator, but it should be very close to 165.\n",
"\n",
"This code makes one assumption that probably isn't true - that the scale is as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `numpy.random.normal()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements similar to how a real scale works."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average of measurements is 164.9996\n"
]
}
],
"source": [
"mean = np.random.normal(165, 5, size=10000).mean()\n",
"print('Average of measurements is {:.4f}'.format(mean))"
]
},
{
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"outputs": [
{
"data": {
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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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\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": {
"scrolled": false
},
"outputs": [
{
"data": {
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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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"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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\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": {
"scrolled": false
},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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7sIOa7DU8/8A0Hppxtct6Q4YMMV5XVFScpdZ2X0o8xats2bLFGD582LBhnd0c6YYUQ+IuxZC4SzEk7lIMndmBIzV8sv0QH20rYvOBE8mmyQQjkyP40ZDeWHO/Z+bvngTg29XhMOM2lzpWrlxpvI6Lizs7De/GlHiKiIiIiIjXO3CkxriNdkvBiSuUJhOMSongR0NimZzRm5gw5/ycNefF8HiPHlRUVPDmm28yduxY7rrrLnx8fFi5ciWzZ8826rj11lvP+v50N0o8xasEBQVhtVrx8VFoS/sohsRdiiFxl2JI3KUYOiG/rIaPtzuTza1Nkk2zCUb1ieDqIbFcmdGb6NCAZusGBQXxxBNP8PTTT+NwOLj//vv5xS9+QWBgIEVFRcb7rr76as4///yzsj/dmaZTERERERHxEg6Hg6KiIqxWK7Gxsfj6duwUHxs2bGDhwoWsWbMGq9VKeno6M2fO5Lrrruu0c/m8smo++uHK5vaDlcZyswnG9I3kqiGxTE7vTVSo/xnrstvtPPDAA7z22mstlo8bN46PPvqIHj16eKz9nakj8zIlniIiIiIi3VxdXR0vvfQSr7zyCvv37wcgPDycO++8k5///Of07t3bo9tzOBw88cQTzJ8/v8XySZMm8d577xESEuLR7Z5KbumJZDOr0DXZHJsayY+GxHJlem96hZw52TyZw+EgMzOTBQsWNEuwb7rppg5P7s8mJZ4iIiIiItKi6upqJk+ezNdff91ieUJCAl988QWpqake2+b8+fN5/PHHjZ8DAgLw9/d3Gd116tSpLFu2zGPbbMpud7C7+Bgrdxzmo22H2Fl0Itm0mE1cmBrJVRmxXJkeQ2Q7ks1zlRJPERERERFp0T333MPrr79u/HzxxRcTGhrKypUrqa+vB5xTf2zevNkj59e1tbUkJCRw5MgRAH7/+9/z4IMP4u/vz7/+9S/uuOMOIwHdunWry7Qj7eVwONhTXMX6fWU//DvCkeoGo/x4snn1kFgmpfcmItjP7W2ei5R4irRSfn6+8TB9UlJSZzdHuiHFkLhLMSTuUgxJWxQXF5OYmEhDQwPBwcF8/vnnxMbGYrVaKS0t5fbbbyc7OxuAFStWMGnSJLe3+f777zN16lQAbr75Zt5++22X8j/96U888sgjADzxxBO88MILbd6Gw+Egp6SKdfuOsD7HmWyWNUk0AQJ9LYzuG8FVGb2ZNLg3PZVsuq0j8zINdSVepby83Ji3Sn+spT0UQ+IuxZC4SzEkbfHJJ5/Q0OBMyO677z5Gjx5tzOPp7+/Pr3/9a6ZNmwbA8uXLPZJ4FhQUGK8nT57crLzpsgMHDrSqTofDwb7SatblnLiiWVpV7/KeAF8zFyRHMKZvBGNTIxkSH46fjy5UdRdKPEVEREREuqny8nLj9bBhw5qVN1129OhRj2wzNDTUeL1r165m5U2XNX1vUw6Hg9yymiaJZhnFx1wTTX8fMyOSezK2byRjUiMZlqBEsztT4ileZeDAgTgcDkwmU2c3RbopxZC4SzEk7lIMSVvExsYarzMzM5k+fbpLDC1atMgo99TItldeeSUWiwWbzcYrr7zC9OnTGTRoEOBMhJ955hnjvddccw3gTDTzympYv6+MdT8kmocrXRNNPx8z5yeFM7ZvL8b0jWB4Ujj+PhaPtFk6n57xFBERERHppqqqqoiPj6eyshKz2czrr7/Oz372M8xmM19++SXTpk2jpKQEgG+//ZYLLrjAI9u99dZbjWc7fXx8uOaaawgLC+ODDz4wBhZKHTaaX7/2DzbklrN+XxlFFXUudfhZzAxPCnde0ewbyXlJ4QT4KtHsTBpcSEREREREWvTss88yd+5c4+eoqCiCgoLIy8szll155ZV88sknHttmeXk5l156KVu2bDGWWcKiCUgeSkDiEIJShmEO7eWyjq/FxHmJPRnTN4IxqZGcn9RTiWYXo8RTRERERERaZLPZmDlzJm+88UaL5aNHj+Y///kPPXv29Oh2Kysrefb5F3h7XQ6mfuPxi0p2KfcxmxieGM6YvpGM/SHRDPTzXKLpcDhwOBzKGTxIiadIK1VWVhrPNISFhXV2c6QbUgyJuxRD4i7FkLSHw+Hgk08+YeHChXz99dfYbDYGDhzIfffdx2233Yafn+emGnE4HGw6cJS3N+Tz4dZC6hrtAFhMkBEXykUDohnTN5IRyT0J8vPskDJ2u52lS5eycOFC1q5di81mY9CgQcycOZOZM2cSHBzs0e2da5R4irTS8eHDfX19WxzZTeRMFEPiLsWQuEsxJO7qqBg6VtfIPzcX8vaGfHYWVRrLB/YO5ZbRSfx4eDw9An09tr2TNTY2csstt7Bs2bIWy4cMGcLKlSuJjo7usDZ4O83jKSIiIiIinWJbQQVvf5PHB5sLqWmwAc6pTq4eGsuto5M4P6nnWRmFefbs2S5JZ58+fQgJCWHbtm3Odm7bxrRp0/jiiy80KnQXpMRTvEpMTAw2mw2LRQ+qS/sohsRdiiFxl2JI3OWJGKqut/LvLYW8tSGfbQcrjOWpUcHcMjqZqefHEx7kudt3z6SiooKXX34ZcI6i+8477zBlyhRMJhObNm3immuuobCwkC+//JJ169Zx4YUXnrW2Seso8RSv4qn5qeTcpRgSdymGxF2KIXGXOzG0s6iStzfks3zTQarqrYBz2pPJGb25dXQSo/pEdMrVxI8//pjq6moA7rrrLqZOnWqUnXfeecybN48777wTgHfeeUeJZxekxFNERERE5BxW12jjw61FvLUhj035R43lKZFB3DI6iannJxAZ4t+JLYTi4mLj9bhx45qVX3TRRcbr4/OWSteixFNERERE5By05/Ax3tqQz/sbC6isc17d9DGbuDK9N7eMTmJs30jM5q7xrGRkZKTx+ttvv2X69Oku5d98843xOiIi4qy1S1pPo9qKiIiIiJwj6q02Ptl+iLfW5/NN7hFjeULPQG4elcS0CxKIDg3oxBa27MiRI8THx1NXV4e/vz8ffvghl19+OQB79+5l0qRJ7N+/H4DMzEwmTJjQia3tvjSdikgrZWVlGcOHp6end3ZzpBtSDIm7FEPiLsWQuKulGNpXUsXfv8ln2fcFlNc0AmAxm7hsYDS3jE7i4v5RXebq5qn813/9Fy+99JLx8/DhwwkNDWXNmjXY7c65REeOHMmGDRs0qm07aToVkVayWq1YrVZ1NtJuiiFxl2JI3KUYEncdjyGrHT7c6px3c21OmVEe1yOAm0YmcdPIRHr36HpXN0/lhRdeYPfu3axYsQKAzZs3u5Snpqby3nvv6Xeni1LiKV7F398fs9mMr2/HTV4s3k0xJO5SDIm7FEPirqONZv69o5aV+6o5WncQAJMJLk2L5tbRSUxIi8bSxa9utiQgIIB///vfvPHGGyxYsICtW7cCEB8fz913380jjzxCz549O7mVciptutV21apVLFmyhLVr13LgwAHCw8O54IILmDNnDiNGjDDed8cdd7Bo0aJm66elpbFr165my3WrrYiIiIiIe3JKqliYmcM/Nx/EZnee4keH+vPTkYncNCqJ+PDATm6hZ1VVVdHY2Eh4eLiucnpIl7nV9pVXXqGsrIxHHnmEwYMHU1JSwvz58xkzZgwrVqxg4sSJxnsDAwNZtWqVy/qBgd4V7CIiIiIinW1nUSULMvfy0bYijl9SGtcvkuljUrhsUDS+Fu+8mBMSEtLZTZA2aNMVz+LiYqKjo12WVVVV0a9fPzIyMli5ciXgvOK5bNkyqqqqWlWvrniKiIiIiLTNlgNHeTlzL5/tOGwsu3xQDA9N7MfwxPBObJl0V13miufJSSc4v2kYPHgwBw4ccLsxIiIiIiJyet/sP8LLmXv5cncJ4Hx+8+ohsTx4aT8GxYZ1cutEWub24EIVFRVs3LjR5TZbgNraWnr37k1JSQmxsbFcf/31/OpXv2r1hK5ZWVkkJycTFnbil6e+vt54RrRnz54kJSW5rLNnzx5qamoAGDZsmEtZaWkpBw86H65OSkpyefDYZrOxfft2wJnR9+3b12Xd/fv3U1lZCUB6ejo+PicO29GjR8nLywMgLi6OqKgol3W3bt2Kw+EgMDCQAQMGuJQdOHCAI0ec8yelpaUREHBiVLGqqipycnIAZ8IfGxvrsu6OHTuMYbIHDx7sUlZUVERxcTHgHN2r6W0IdXV1ZGdnA87JdRMTE13W3b17N7W1tZhMJoYOHepSVlJSQmFhIQDJycmEh5/4Js1qtZKVlQVAWFgYffr0cVl33759xrcnGRkZWCwWo6y8vJz8/HzA+XB4r169XNbdsmULAEFBQfTv39+lLD8/n/LycgAGDhxIWVkZNpsNi8VCSEiIMZ9TTEwMvXv3dlk3KysLq9WKv78/AwcOdCkrLCykpMTZmffr14/g4GCjrKamhj179gDOyYwTEhJc1s3Ozqaurg6LxUJGRoZLWXFxMUVFRQCkpKTQo0cPo6yhoYGdO3cC0KNHD1JSUlzWzcnJMe4iGDJkiMs3T2VlZRQUFACQkJDgMsmy3W5n27ZtgPOLotTUVJd6c3NzqaioAGDQoEH4+fkZZRUVFeTm5gIQGxvb7Mun7du3Y7PZCAgIIC0tzaWsoKCAsjLnCHr9+/cnKCjIKKuurmbv3r0AREVFERcX57Lurl27qK+vx8fHp9lUAocOHeLwYec3u3369PF4H2Gz2QgNDSU4ONhol/qIE7p7H+Hv72+UVVZWdkgfkZeXZ8R+dHS0+ggv6yOg488jCgsLjb9lpaWl6iPwrj6ivecRDoeDD7/by6tf5pJV0gA4p0O5fng8909IJSncj507d7KlGHx9fQkNDcVisRi/P+ojnLyhj2iqo84jOoLbieeDDz5IdXU1v/zlL41lw4YNY9iwYcYvy+rVq/nDH/7A559/zrffftuq+7GtVisn3wXscDhobGw0ylta53j5yex2u1F2fJ6fplpb78ltalqvzWZrsV6Hw9HiyHQ2m82tek+1r03rPXlfmx7Dluo9vq8tPaDd2no787MpKSkx/pAGBwef8RhardYWbx043WdzpmN4/LNpqex09Tbd17Z+5q09hi2t37RNJzvTvjY0NGC3211OAFqqt73HsKVj1Np63YnDiooKampqXP6QqY9w6u59xKna5Mk+ory83Gin+gjv7CM6+jyi6d+y4+dD6iO8p49o63mEw+Hg853FvJS5ly0HjgLgY4brh8bwyKTBJEY4E7KGhgaXfa2pqcHX19f4W6Y+om31dpU47KzziI7gVuI5e/Zs3nrrLV566SWXUW0fffRRl/ddccUVnHfeedxwww28/vrrzcpbbJiPT7NOy2QyGQe16TcBTdc51dDjTYclb6mDaG29J7epab0t/dL4+vricDharNdisbhVb9P/T1Xvyfva9Bi2VO/xfW3pD0Zr6+0qn82Z9vX4fp7pGLan3uPfVLel3uPrnq5ed4/hmfb1ZGfaVz8/P2w2W4ccQ7vd3ubfG0/E4an+oKiPcFIfgfH+0/0uN31fS/Wqj+i+fcTx1y21qTX1qo9QH9Ha8whMZj7aWsTLmXvZWeS8GubvY2ZS3yCuHxTCBYP70aNHULN1wZlInJxoqI9oW71dJQ47q4/oCG0aXKipZ599lrlz5zJv3jxmzZp1xvfb7XbCwsK4+uqr+cc//tGsTIMLiSdUV1fjcDgwmUwut7WItJZiSNylGBJ3KYbObVabnX9tKWRB5l5ySqoBCPazMH1sCndd1IeoUP8z1KAYkvbrMoMLHXc86Zw7d26rks7jHA6HkknpUOpcxV2KIXGXYkjcpRg6N9Vbbbz3/UFeWb2XA0dqAQgL8OHOcX24c1wK4UF+Z6jhBMWQdEVtTjyfe+455s6dy9NPP80zzzzT6vWWLVtGTU0NY8aMaesmRURERES8Um2DjXe+zee11fs4VFkHQGSwH3eN78P0McmEBrR8a6dId9OmxHP+/PnMmTOHyZMnc/XVV7N+/XqX8jFjxpCXl8ctt9zCT3/6U/r164fJZGL16tX88Y9/JD09nbvvvtujOyAiIiIi0t1U1VtZsj6Pv3y1j9Iq5yi1MWH+3HtxKjePSiLQ7+w8dydytrTpGc8JEyawevXqU5Y7HA7Ky8u566672LRpE4cPH0HlupMAACAASURBVMZms5GcnMxPfvITZs2a5TI0/HF6xlM8paamxnimoemw2yKtpRgSdymGxF2KIe9WUdPI39bm8tc1+6modQ5ol9AzkPsnpHLDiAT8fdxPOBVD0l4dmZe1e3AhT1LiKZ6yZcsWYwj6k+dXEmkNxZC4SzEk7lIMeafSqnr+7+v9vLkuj6p655QafXsF88Cl/fjx8Dh8LZ4771UMSXt1ucGFRERERES6E4fDQVFREVarldjY2FNOi+FJhw4d4pMvv2HVQQcbSn2ptzmv96TFhPLQxH78aEgsFvOpp2QS8SZKPMWrREZGnnJ+PJHWUAyJuxRD4i7FkGfV1dXx8ssvs3DhQvbv3w9AeHg4d955J08++SQxMTEe3Z7D4eCLLXuZ/cpS9jWE4BeTerwEv6oiHrk8jfuvuwhzByaciiHpinSrrYiIiIh4perqaiZPnszXX3/dYnlCQgJffPEFqampLZa3VqPNzjf7j/DZjsN8su0gh441GmUOh536/G1UbHiPuv0bCQgI4KOPPmLixIlubVOkI+hWWxERERGRNnr00Uddks6LL76Y0NBQVq5cSX19PQUFBfzkJz9h8+bNbT6xPlbXyOrdJXy24zCZu4qprLMaZfbGOupyN2Mu2s7UsWlEpQXw941V7MZ5BfbWW28lNzcXf39/T+2qSJenK54iIiIi4nWKi4tJTEykoaGB4OBgPv/8c0aPHg3AwYMHueyyy8jOzgZgxYoVTJo06Yx1Hq6s47Mdh/lsx2HW5ZTRYLMbZRHBfoyMC+DN3z5BXe5mYqMj2bRpE9HR0QA0NDRw1VVXsWrVKgDefPNNbrvtNk/vtohbOjIvU2YnIiIiIl7nk08+oaHBOT/mvffeaySdAPHx8Tz33HPGz8uXL2+xDofDQfahY7y8ag8/fvlrRj//OU//czurd5fQYLPTp1cw91zcl6X3jeXbX17OBfZd1O7dgMNazwMPPGAknQB+fn7MmjXL+Pl4AipyrtCttuJVsrOzjeHD09LSOrs50g0phsRdiiFxl2LIM8rLy43Xw4cPb1bedNnRo0eN11abne/yyo0rm/lHaowykwmGJ4ZzxeAYJg2OITUqBJPpxCBBtbW1xuvY2Nhm24yLizNe19XVtWOvWkcxJF2REk/xKnV1dTQ2NmKz2Tq7KdJNKYbEXYohcZdiyDOaJn6ZmZlMnz7dpTwzM9N43at3HJ9sL+LTH57XLK85MTiQn4+Zi/r14orBMVw2KJro0IBTbrN///7G62XLljFjxgyX8qVLl7b4Xk9TDElXpMRTvIrFYtHw4eIWxZC4SzEk7lIMecaPfvQjwsLCqKysZNGiRYwfP57bb78ds9nMV199xdPzXiBk2JUE9hvNJ4Gj+PeSjca64UG+TBwYzaTBMYzvH0Wwf+tOma+44goSEhIoKCjgP//5Dw8++CBPPPEEoaGhLFq0iHnz5gFgMpm44447OmK3AcWQdE0aXEhEREREvNLcuXN59tlnjZ+j+6YTOGAs9b0G4hc3AJPpxLlmUkQQVwyO4YrBMVyQ3BMfS/vOQ5csWdLs6urJHnzwQV5++eV21S/SkTSdioiIiIhIG82ePZuc/AKWf5tLyNArCEjMAOD4JCY+lQe55+ox/HhEHwbEuD6v2V633XYbFRUVPProozQ2NjYrnzlzJn/84x/d3o5Id6MrniIiIiLiVRwOB9/llfPutwf4aFsRNQ3OZx0ddjuNBdvpVVfAjCtH8sCdt+Dn59chbTh48CCvv/46a9aswWq1kp6ezsyZMxk2bFiHbE/EEzoyL1PiKSIiIiJnXW1tLVarlZAQz1xpBDhUUcd7GwtY9n0B+0urjeUpkUFMuyCRKefHE9sj0CPbEvFGutVWpJWKi4uNh+mbzp0l0lqKIXGXYkjc5c0xZLVaWbRoEQsXLmTjRudgPklJScycOZOHH36YHj16tLnOequNlTuKefe7A3y1pwT7D5dUgvwsXD0klhtHJnJBck+PJbfdgTfHkHRfSjzFqxQVFRnzVqmjlfZQDIm7FEPiLm+Nofr6eqZMmcLHH3/ssjw/P5/Zs2fz5ptv8vnnn5OQkNCq+rYfrGDZ9wX8c/NBjjaZ/mRUSgTTLkjgR0NiWz0arbfx1hiS7u3c/G0UERERkbPqySefdEk6hwwZQmhoKOvXr8dut7N7925uuOEG1q1bd8qrk+XVDfxz80GWflfAjqJKY3nvsACmjojnhhGJ9OkV3OH7IiJtp2c8xatUVFTgcDgwmUztul1HRDEk7lIMibu8MYbKy8uJj4+ntrYWf39/PvjgA6688koAsrOzufLKK8nLywPgiy++4JJLLjHWtdrsfLWnlKXfH+CzHYdptDlPXf0sZq5Ij+HGCxK5qF8vLOZz51baM/HGGJKzQ894irSSOldxl2JI3KUYEnd5Ywx9/PHH1NbWAs7pRI4nnQBpaWnMmzeP2267DYClS5dyySWXsK+kiqXfF/D+xgIOV9Yb78+ID2PaiER+PDyO8KCOGZG2u/PGGJLuT4mniIiIyDkqKyuLV199lTVr1tDY2EhGRgYzZ87k0ksv9ehgPKWlpcbrUaNGNSsfPXo0ACa/QHbUh3PDK2v5Lq/cKO8Z5Mv158UzbUQig+PCPNYuETl7lHiKiIiInGMcDge/+tWvmDt3rsvy7du388477/CTn/yEt99+m4CAAI9sLyoqyni9du1apk+f7tKWtz7bQOSP/pugtIvY5xfAvrxyzCaYkBbNtBEJXDYoBj8fPYIl0p3pGU/xKg0NDcbrjpoQWrybYkjcpRgSd52NGFq4cCEPPvig8bPJZMJisWC1Wo1l06dPZ/HixR7ZXkVFBXFxcdTU1ODr68u7777LyEsmsXzTQZas3cehqhPbjQ02c/v4AUw5P56YMM8kvuca9UPSXh2ZlynxFK+yZcsWY/jwYcOGdXZzpBtSDIm7FEPiro6Oofr6epKSkiguLgZgzpw5/M///A+BgYG88847PPDAA1RXVwOwc+dOBg4c6JHtPvHEE8z/35cJGnAhwRkTCUweCibnuZ69vobqXV+Raipm/Ydv6xzQTeqHpL00uJCIiIiIeMSKFSuMpHPKlCk8++yzRtntt9/O4cOH+fnPfw7AokWL+M1vfuPW9ux2B+v2lWEdcTMp/z0Ou9nXKKvL20rVtpXU7F7D4AH9+NfKlUo6RbyUEk/xKj169MBms2GxWDq7KdJNKYbEXYohcVdHx1Bubq7x+rrrrmtWft111xmJZ9P3ttXe4ire31jAPzcdpLCizrnQ7Eukn42G3V+z65PFWCsOM2DAAO75zTzuvfdeQkJC2r09OUH9kHRFSjzFq6SkpHR2E6SbUwyJuxRD4q6OjqHg4GDjdU5OTrPyffv2Ga/bmgiWVzfw762FvLfxIFsOHDWWhwX4cO2wOKacn8D5SeGYTNdhs/0Gu92Or6/vaWqU9lA/JF2REk8RERGRc8jll1+O2WzGbrezcOFC7rzzTvr06QNAdXW1y623TefbPJUGq50vsot5b2MBq3YV02hzDh9iMZuYMCCKqSMSmDgwmgBf16tvFotFV+REziEaXEhERETkHHPDDTfw3nvvARAYGMi0adMIDQ1l2bJlHD58GIDk5GT27NnT4hVJh8PBtoMVvL/xIP/aUsiR6hOjqKbHhTH1/ASuGx5HrxD/s7NDIuIRGtVWRERERDympKSE8ePHk52d3WJ5WFgYK1euZOTIkS7Liypq+eemQt7fWMCe4ipjeVSoPz85L54p58czsHdYh7ZdRDqORrUVaaWcnBxj+PDU1NTObo50Q4ohcZdiSNx1NmIoKiqKNWvWMGfOHBYvXkxVlTOJtFgsXHfddcybN49BgwYBUNNgZUXWId77/iBrcko5fsnC38fMlem9mXJ+PBf164WPRRcMugr1Q9IVKfEUr1JVVWV0tCLtoRgSdymGxF3Hjh2jsbERPz+/Dt1OZGQkCxYs4He/+x1bt27FarWSlpZGTEwMdruDtTmlvL/xIP/ZVkR1g81Yb1SfCKaeH89VQ2IJC1Ccd0Xqh6QrUuIpIiIi0snsdjvvv/8+CxYs4Ouvv8Zut9O3b18efvhh7r77boKCgjps2yEhIVx44YUA7Cup4sUV2SzfdJCDR2uN9yRHBjHlvAR+cl48SZEd1xYR8V56xlO8it1uN14rfqQ9FEPiLsWQtJXVauXWW2/l3XffbbF82LBhfPrpp0RHR3fI9qvrrXywuZCl3x9gU/6JKVBCA3y4ZmgcU8+PZ0RyT0wmU4dsXzxP/ZC0l57xFGklda7iLsWQuEsxJG01e/Zsl6QzOTmZkJAQsrKyANiyZQs33XQTq1at8mjyt+tQJW+tz2f5poNU1VsB5xQolwyIYsr58Vw+KKbZFCjSPagfkq5IVzxFREREOkllZSXx8fFUVVXh4+PDW2+9xbRp0zCZTHz//fdce+21FBUVAbB27VrGjh3r1vbqGm38Z3sRb63P57u8cmN5317B3DwqiR+fF0d0aIBb2xCR7ktXPEVERES80Mcff2yMKDtjxgxuvPFGo2zEiBHMmzePGTNmAPDOO++0O/HMLa3m79/k8+53ByivaQTAx2xiUnoMt41OZmxqpG6lFZEOpcRTvEpZWRl2ux2z2UxkZGRnN0e6IcWQuEsxJG1x+PBh4/VFF10EuMbQ+PHjjfLi4uI21W212Vm5s5i3NuTx1Z5SY3lcjwBuHpXETSMTiQ7T1U1vpH5IuqI2JZ6rVq1iyZIlrF27lgMHDhAeHs4FF1zAnDlzGDFihMt7N27cyM9//nPWr1+Pj48PEydO5MUXX6Rv374e3QGRpgoKCozhw9XRSnsohsRdiiFpi6Yx8t133zF9+nSXGNqxY4dRHhER0ao6D1XU8fdv8nnn23wOV9YDYDLBJQOiuG10MhPSojTnppdTPyRdUZsSz1deeYWysjIeeeQRBg8eTElJCfPnz2fMmDGsWLGCiRMnArBr1y4mTJjA8OHDeffdd6mrq2POnDmMHz+ezZs3ExUV1SE7IyIiItKdXHXVVQQEBFBXV8ef//xnrr/+eiPBPHDgAE8//bTx3htuuOGU9djtDr7eW8qS9Xl8vqsYm905hEdksB83jkzkllFJJEZoGhQR6TxtGlyouLi42VDeVVVV9OvXj4yMDFauXAnAjTfeSGZmJjk5OYSFhQGQl5dH//79efTRR/nd737nUocGFxJP0a0l4i7FkLhLMSRt9dBDD7FgwQLj56FDhxIaGsr69eux2WyA83nPb7/9ttlzmEeqG1j63QHe/iafvLIaY/noPhHcOiaZK9Nj8PfRyLTnGvVD0l4dmZd5ZFTbiRMncvDgQbKzs7FarYSFhXH77bfz6quvurzvyiuvZP/+/ezevdtluRJPEREROVfV1dVx3XXX8dlnn7VY3rdvXzIzM0lKSgLA4XDwfV45S9bn8fG2QzTYnHM2hvr7MHVEAreOTqJ/TOhZa7+IeI8uPaptRUUFGzduNG6zzcnJoba2lqFDhzZ779ChQ/nss8+oq6sjIOD0D7NnZWWRnJxsXDEFqK+vZ9euXQD07NnT6ICP27NnDzU1zm/7hg0b5lJWWlrKwYMHAUhKSqJnz55Gmc1mY/v27YDzwJ78HOr+/fuprKwEID09HR+fE4ft6NGj5OXlARAXF9fsNuKtW7ficDgIDAxkwIABLmUHDhzgyJEjAKSlpbkck6qqKnJycgCIjo4mNjbWZd0dO3YY9+4PHjzYpayoqMgYgCA1NZWQkBCjrK6ujuzsbMD5rEhiYqLLurt376a2thaTydTsMywpKaGwsBBwzjEWHh5ulFmtVmO+sbCwMPr06eOy7r59+4wgzsjIwGI58e1reXk5+fn5AMTHx9OrVy+Xdbds2QJAUFAQ/fv3dynLz8+nvNw5HPzAgQPx9/c3yiorK9m/fz8AMTEx9O7d22XdrKwsrFYr/v7+DBw40KWssLCQkpISAPr160dwcLBRVlNTw549ewDnszkJCQku62ZnZ1NXV4fFYiEjI8OlrLi42BgWPyUlhR49ehhlDQ0N7Ny5E4AePXqQkpLism5OTo4x8uGQIUNcOoCysjIKCgoASEhIcPl20263s23bNgBCQkJITU11qTc3N5eKigoABg0ahJ+fn1FWUVFBbm4uALGxsc3ueNi+fTs2m42AgADS0tJcygoKCigrKwOgf//+BAWduMWrurqavXv3AhAVFUVcXJzLurt27aK+vh4fHx/S09Ndyg4dOmQMxtGnTx/1EaiPUB/hpD7Cqbv2Ec8//zyXX345ixcvNn5XevfuzXXXXcett95KXV0dx+oa+eemg7y1IZ9dh06cGKZG+HLnRf2YckESQX7OutVHnKA+wkl9hFN37SPg7J5HdAS3E88HH3yQ6upqfvnLXwIYAdLSA/ARERE4HA7Ky8vPuHNWq5WTL8Y6HA4aGxuN8pbWOV5+MrvdbpTZ7fZm5a2t9+Q2Na33+O0wJ9frcDjw9fVtVmaz2dyq91T72rTek/e16TFsqd7j+9rSkOqtrberfDZn2tfGxkasVmuL3+Cc7rNpTb2NjY0tlp2u3uPrnqnelrT2GLa0ftM2nexM+9rQ0IDdbnc5AWip3vYew5aOUWvr7SpxqD6ieb1d5bNRH9G8XvURndtH3H777fz85z+noqICq9VKz5492bRpEzlHGvj7V4dYnbePmgbn8QjwNTMxNYyL48z0i/AlPT2WQD+fFutVH6E+omm9LVEf0bzerhKHnXUe0RHcSjxnz57NW2+9xUsvvdRsVNvTzQXVmnmifHx8mr3PZDIZB7XpNwFN12npoAOYzWajrKUOorX1ntympvW29Evj6+uLw+FosV6LxeJWvU3/P1W9J+9r02PYUr3H97Wlz6i19XbmZ9P0F/1M+3p8P890DE8Xh6eq12aztVh2unqb7uup6nX3GJ5pX092pn318/PDZrN1yDG02+1t/r3xVBwCxrMxTdvUmnrVR3TtPuJUbfJkH9G0TeojvLOP6OjziNDQUOoabby3sYDXM4+wu6zBeH+/6BBuHZ3ElPMTqCw9ZFzNUB/RffqIs3Uecfyc6PgxUR/Rtnq7Shx21nlER2j3M57PPvssc+fOZd68ecyaNctYnp2dzcCBA1mwYAEPPPCAyzpPPPEE8+fPp6amxuVSr57xFE/ZsmWLcevQybdAiLSGYkjcpRgSd+wtPsafPtrIqn3VVDU6T9F8LSYmZ8Ry6+gkRveJaNUX+HJuUz8k7dXlnvE8nnTOnTvXJekE57MAgYGBxr3gTW3bto1+/fqd8flOERERkXNFXaONT7Yf4u1v8vlm/xFjeXSwhTvG92PaiESiQv1PU4OISNfX5sTzueeeY+7cuTz99NM888wzzSv08eHaa6/l/fff54UXXiA01DmqWn5+PpmZmTz66KPut1rkFEJCQoxv+ETaQzEk7lIMSWvtLa7inW/yeW9jAeU1zmetzCYYkxTC5P4hjEnuwYD+/Tq5ldIdqR+SrqhNt9rOnz+fxx9/nMmTJ7eYdI4ZMwZwjiQ1cuRIzj//fJ566inq6uqYM2cOR44cYfPmzc1GY9KttiIiInIuqLf+cHVzQz4bmlzdjOsRwE0jk7hpZCK9e+jOMBHpHF1mHs8JEyawevXqU5Y3rer777/nySefZN26dfj4+DBx4kRefPHFZkMwgxJPERER8W45Jc6rm8u+d726OXFgNLeMTuKSAdFYzHp2U0Q6V5dJPDuKEk8RERHxNvVWGyuyDvP2hjzW7ztxdTO2RwA3jUzkppGJxPYI7MQWioi46nKDC4mIiIhIy/aXVvP3H65uHql2ToViNsGlac6rmxPSdHVTRM49SjzFq+Tm5hpzX6WkpHR2c6QbUgyJuxRD56YGq50VWc5nN9ftKzOW9w47cXUzLrx1VzcVQ+IuxZB0RUo8xatUVFRoFDdxi2JI3KUYOrfkNrm6WfbD1U3TD1c3bx6VxKVpUfhY2naLmmJI3KUYkq5IiaeIiIjISQ4fPswbb7zBmjVrsFqtpKenc/fddzNw4EAarHY+3eG8urk258TVzZgwf2Nk2vhWXt0UETlXaHAh8SoNDQ3Gaz8/v05siXRXiiFxl2Ko+3v99dd5+OGHqa+vd1nuEx7LxXf+gvKeA41nN00mmDAgiptHJTFxYHSbr262RDEk7lIMSXtpVFsRERGRs+Ddd9/lpptuOrHA7ENQ/9GEDJ9MYMp5xuLoUH/j2c2EnkGd0FIREc9T4ikiIiLSwWw2G3379uXAoRIC+5zPkMm3UhWWQlWDHQCHw07d/o1Ub1nBlk/eJrVPSqe2V0TE0zSdioiIiHQJ5eXlLF68mK+//hqr1UpGRgYzZsygT58+nd00txRX1vG/72VSN2oGicnDMPn4cgigwU50qD83XpBI4ddL+cPSuQAsWbyIZ555pjObLCLSreiKp3iViooKHA4HJpOJHj16dHZzpBtSDIm7vDmGlixZwn333Ud1dbXLcpPJxOOPP85vf/vbDv3bXV9fj81mIzAwEJPJ/Xkw9xZX8emOQ3y24zCb8o+6lEX4Wrlh7AAmDY7hvKSeWMwmduzYQXp6OgA333wzb7/9ttttaIk3x5CcHYohaS9d8RRppdzcXGP48GHDhnV2c6QbUgyJu7w1hpYvX8706dNbLHM4HPz+97/HbDbz29/+1qPbtVqtvPnmmyxcuJDvvvsOgJSUFGbOnMmDDz7YppNqu93BpgNHnclm1mH2lbom0HH+DWR9+ndq96znnv+5n1k/+rFLeXFxsfHa39/fjb06PW+NITl7FEPSFemSooiIiJyWzWbjscceM36+5ZZb2LRpE3v37mX27NlYLBYAXnzxRQoKCjy23YaGBq6//npmzJhhJJ3gPKn+5S9/yejRoyksLDxtHXWNNlbtOswv3t/KqOc/Z+ora3lt9T72lVbjazFxyYAofn19BhtmXcYbtwymcv1SGssO8MorCykrOzFVitVq5Te/+Y3x84QJEzy2nyIi5wJd8RSvEhsbi81mM06CRNpKMSTu8sYYyszMZP/+/YAz4VqyZIlxq+uvfvUrGhsb+e1vf4vNZuONN95g9uzZHtnuU089xUcffWT8PHjwYEJDQ/nmm29wOBxkZ2czdepU1q5d63LrbUVNI6uyD/Np1mFW7y6hpsFmlIUG+HBpWjST0mO4ZEAUoQG+RllMWBqTJk3i008/paCggPT0dGbMmEFoaChvvfUWWVlZAERFRbmOfOth3hhDcnYphqQr0jOeIiIiclovvfQS//Vf/wU457i8++67Xcq3b9/OkCFDAM89+1heXk58fDy1tbX4+fnxz3/+k6uuugqAnTt3MnnyZPLz8wFYvXo1qUNH8lnWIT7dcZgN+49gs584vekdFsAVg2OYlB7D6D6R+Pmc+vxi//79jBs3jqKiohbLfX19+fDDD5k0aZLb+ygi0tXoGU8RERHpNE0noD9y5Eiz8qbLPDVZ/ccff0xtbS0AM2fONJJOgEGDBvHrX8/jrsfmEDRgDA/9u4DKj11PlNJiQpmUHsMVg2MYEt+j1YMR9enTh3Xr1vHf//3f/Otf/8Jutxtlo0aNYv78+Vx00UUe2EMRkXOLEk8RERE5rfHjxxuvFy5cyD333EN4eDjgfP7zhRdeMMovvvhij2yztLTUeD169GgArDY73+aW8+mOQ/wnL5q4GS8BUAmYTXBBcoSRbCZHBrd728nJySxfvpwDBw6wfv16rFYr6enpDB061K19EhE5lynxFBERkdMaPHgwl156KZmZmeTl5TFkyBBmzpxJWFgYb775Jhs3bgQgIiKCn/70px7ZZlRUlPOFycyH3+5hZ8g2Ptl+iCPVDcZ77I111O3fxNjkEP763KNEhnh2pNnExEQSExM9WqeIyLlKz3iKV9m+fTsNDQ34+fmRkZHR2c2RbkgxJO7y1hjas2cP48aNo6SkpMVyi8XC8uXLufbaa93elt3uIHN7Prc8NR+/vqOwhPQ0ynoG+TKitx8r3niRg9+txGGt56uvvvKq21+9NYbk7FEMSXvpGU+RVrLZbNjtdmw225nfLNICxZC4y1tjqH///qxdu5aHHnqIFStWuJQNHTqU//f//h+XXXZZu+t3zrFZzr+3FPHxtiKKj9UTOPRKAGy1ldTsXkfEsX2Y64v5v+++Nda78MILGTduXLu32xV5awzJ2aMYkq5Iiad4lYCAACwWC76+vmd+s0gLFEPiLm+OoX79+vHJJ5+wd+9e1q5di9VqJSMjg5EjR7Z68J6mHA4Hmw8c5aOtzmSzsKLOKAsN8OGKQdFs+uAvfPGP18Bu4+RhjQYNGsSyZcvate2uzJtjSM4OxZB0RbrVVkRERM4ah8PB9oOVfLitkI+2FlFQXmuUhfj7cMXgGK4ZGstF/Xvh72PBZrPx97//nQULFrB+/XrAmQDPnDmT+++/n9DQ0M7aFRERr9OReZkSTxEREelQDoeDnUXH+HBrIR9tKyKvrMYoC/KzcNkgZ7J5yYAoAnxPPeG91WrFZrPh7+/ZQYRERMRJz3iKiIhIt7P78DE+3FLIh9uK2FdSbSwP8DVz2cAYrh4ay6Vp0QT6nTrZbMrHxwcfH526iIh0R+q9RURExGP2Flfx0dYiPtxayJ7iKmO5n4+ZS9OiuGZoHBMHRhPsr1MQEZFziXp98SoFBQXYbDYsFgsJCQmd3RzphhRD4q5zMYZyS6v5cGshH24tYtehE7do+VpMXDLAmWxeNiia0AANdNIa52IMiWcphqQrUuIpXqWsrIzGxkZ8fX3V0Uq7KIbEXedKDB08Wsu/Nhfy0bZCth+sNJb7mE1c1L8X1wyN44rBMfQIVLLZVudKDEnHUQxJV6TEU0REpJs6duwYb7/9NmvWrMFqtZKens4dd9xBfHx8h2zP4XCwbl8Zi9bm8tmOw9h/GJ7QYjZxYWok1wyN5cr03oQH+XXI9kVEpPvSqLbiVWpqX8m13gAAIABJREFUanA4HJhMJoKCgjq7OdINKYbEXWcrhpYuXcrdd99NZWWly3KLxcKsWbN49tlnPTa/ZU2DleWbDrJ4bR7Zh0/8vR7dJ4LrhscxOb03kSEaadZT1A+JuxRD0l6aTkVEREQMH330Eddeey2n+xM+Z84cnn32Wbe2k19Ww+J1ubz73QEq66wABPpamHJ+PD+7MIUBMZpDU0TEmyjxFBEREcD5NzMtLY29e/cCMHXqVB577DFCQ0NZvHgxL774Ig6HAx8fH/Ly8oiLi2tT/Q6Hg6/2lLJobS6rsos5fpaQHBnE9DHJTLsgUc9tioh4Kc3jKSIiIgCsXr3aSDovuugili5datxS+8ILL+BwOHjxxRexWq387W9/Y9asWa2qt6reynvfF7BoXa7LnJsXD4jijguTmTAgGrPZM7fuiojIuUeJp3iV6upq45mG4ODgzm6OdEOKIXFXR8dQVlaW8Xr69OnNnuO8/fbbefHFF5u991T2lVSxeF0ey74voKreeTttiL8PN4xIYPrYZFKjQjzYemkN9UPiLsWQdEVKPMWr7N271xg+fNiwYZ3dHOmGFEPiro6OIR+fE3+6Tx5Y6ORlvr4t3xJrtzv4Yncxf1ubx5e7S4zlfaOC+dnYFKacH685NzuR+iFxl2JIuiIlniIiIt3IuHHjjNevvvoq9957L6GhzkF+7Ha7cbXz5PcCVNQ2svS7A7y5Po+8shoATCaYmBbNzy5M4aJ+vXQ7rYiIdAglnuJVoqKisNlsWCyWzm6KdFOKIXFXR8fQkCFDuPjii/nyyy/Jyclh+PDh3HfffcbgQuvWrQMgPDycW265BYA9h4/xt7W5LN90kJoGGwChAT7cdEEi08cmkxypW/G6EvVD4i7FkHRFGtVWRETEQ+rr69m5cydWq5V+/foRHh7eIdvZuXMn48aNo7y8vMVys9nMO/94l7BB41i0Npe1OWVG2YCYEH52YQo/OS+eID99/ywiIidoOhUREZEurKKignnz5vF///d/HDlyBAA/Pz9uvPFG5s6dS2pqqse3uXPnTu6//35Wr17tsrx/+nCufnge35QHcPBoLQBmE1wxOIafXZjC2L6RzQYkEhERgS6WeB47doznnnuOzZs3s2nTJkpLS3nmmWeYO3euy/vuuOMOFi1a1Gz9tLQ0du3a5bJMiaeIiHRXR44cYcKECWzbtq3F8oiICFatWtVhA3xkZWWxZs0aDlbDft9kNhyyU2+1AxAe5MtPRyZx25gkEnoGdcj2RUTEe3SpeTzLysr485//zLBhw7j++uv5y1/+csr3BgYGsmrVqmbLREREvMVDDz1kJJ1+fn5ce+21hIaG8sEHH1BeXs6RI0eYOnUqu3btchmR1hMqahvZUhXKClsG3x8uB5zToQyODeOOC1O4bngcAb56xktERDpfm/8CJicnU15ejslkorS09LSJp9lsZsyYMW41UOT/s3ff4VFV6QPHv9PSJ4X0AgmQkEACoSoKSFEUEcRFFFeRFbFhW0VFV9eu6+padxcWXV0Bf7pYsLKAjV5UOiQhkAoJ6SGkZyZTfn+EXDJJIGVSJuH9PI+Pw5x7z5x7582Zeeeee05bJCcnK9OHx8TEdHdzRA8kMSTaIjs7m88++wyom8znl19+wWq1Ultby6JFi7jnnnvYv38/aWlprF27luuuu87u1zSZLWxLLWLN3mx+SMrHeObqpkatYlpsELeNi2B0uI8Mp+3BpB8S9pIYEo6ozYmnfJAJR2YwGKitrcVisXR3U0QPJTEk2uLHH3/EbK6bJfbee+8lOjqagwcPUltbi7OzM88//zzXXnstAOvWrbMr8UzOK+PLfSf5av9JCssNyvODAj24fmQY140IJdDTxb4DEg5B+iFhL4kh4Yg6dTq76upqgoKCKCwsJDg4mOuuu44XXniBPn36tLhvYmIi4eHheHp6Ks8ZDAbl/lAfHx/69etns09KSgpVVXXrkjW+l6aoqIiTJ08C0K9fP3x8fJQys9lMQkICUDeGecCAATb7ZmRkKAtyx8bG2gyVOn36NMePHwcgJCQEf39/m30PHTqE1WrF1dWVQYMG2ZRlZWUpk1BER0fj4nL2C0NFRQVpaWkABAQEEBwcbLNvUlKS8kvWkCFDbMpyc3MpKCgAYODAgXh4eChlNTU1HD16FKi776hv3742+x47dozq6mpUKhXDhg2zKSssLCQnJweou/LdcLZGk8lEYmIiAJ6envTv399m3/T0dGW8eFxcnM303iUlJZw4cQKA0NBQ/Pz8bPY9ePAgAG5ubkRFRdmUnThxQpnVMSYmBq1Wi9VqRavVUlZWRkZGBgCBgYEEBQXZ7JuYmIjJZMLZ2bnJr4E5OTkUFtYtqh4ZGYm7+9mlBqqqqkhJSQHA19eXsLAwm32PHj1KTU0NGo2GuLg4m7KCggJyc3MBiIiIwMvLSykzGo0cOXIEAC8vLyIiImz2TUtLo6KiAqhbTqHhWPvi4mKys7MBCAsLw9fXVymzWCzKMEAPD48mk5xkZmZSWloKwODBg3FyclLKSktLyczMBCA4OJiAgACbfRMSEjCbzbi4uBAdHW1Tlp2dTXFx3UyaUVFRuLmdvb+ssrKS1NRUoG7K95CQEJt9k5OTMRgMaLVaYmNjbcry8vLIz88HoH///h3eR9TW1qJWq23+zqWPOKun9xHOzs5KWUf0EQ3nLKj/G6j/26ytrbX5G68/vrb0ESaNC98cyGHNvmwSc8qU7TxdNMwe2ZfrR4YRF+qJSqUiLS2NvAzpIzq7j4DO/x7R8LNM+og6PbWPgO75HmGxWNBqtTaxJt8j6vSGPqKhzuojOkOnJZ7x8fHEx8crfzBbtmzhrbfe4ueff2b37t02nVhzTCYTjec9qh++VF/e3D715Y1ZLBalrLlff1pbb+M2Nay3/lfvxvVarVZ0Ol2TMrPZbFe95zrWhvU2PtaG57C5euuPtbkr262ttzvfm4adS2lpaYvn0GQyNXuz9Pnem5bOYf1701zZ+epteKxtfc9bew6b279hmxpr6ViNRiMWi6XZdcI64hw2d45aW689cRgeHm7zoVvfptbUK32EY/cR52pTe/uIhl9w161bx/z58xkwYIDy5e/nn39Wyuu/oLfUR1TVGNmbZ+Ct3UlsTy/BZKlrt06jYkSgE5PCXZgyOIiYQZFN2it9RNf0EZ39PaLhZ9nevXulj6Dn9hHtrdfe7xE+Pj5NEkTpI9pWr6PEYXd9j+gMnZZ4Pvzwwzb/njp1KiNGjGDOnDn8+9//blLepGFabZNOS6VSKSe1uQkatFptsycd6n6Bri9rroNobb2N29Sw3ub+aHQ6nfKrZWMajcauehv+/1z1Nj7WhuewuXrrj7W5D4zW1uso701Lx1p/nC2dw/bUe65Fm89Xb/2+56vX3nPY0rE21tKxOjk5YTabO+Uc1v9a2956HSUOpY9oWq+jvDcd0UdMnDgRX19fiouL+fTTTxkxYgQLFy5ErVazceNG3nrrLWWf+fPnK/U27iOsVisHs0v5v+3ZfH+kiHLj2S8tw8K8uH5kGFcN9iP/RN2v0y7NrL8pfUTb6nWUOJQ+omm9jvLeyPeIpvVKH3Hh9BGdwa51PIuKivD39292OZXmWCwWPD09ueaaa/j0009tnpflVIQQQvREb731FosXL1b+7ezsjE6nU4a0Adxwww3KJEQN5ZZW89X+k6zZm01aYaXyfKCnM9eNCGXOyDCiAvWdewBCCCHEGQ61nIq9rFarJJRCCCF6jYceeoi8vDxee+01oO4eIYPh7OQ/V111FR9++KHy72qjme8T81izL5vtqUXU//zrrFUzLS6I60eGMS7SD41aJvMTQgjRe3Rp4vnFF19QVVUlS6yITpOXl6cMT2k8CYAQrSExJNpKpVLx6quvcsMNN7Bs2TK2bt2KyWQiOjqa+++/n2uuuQZQ8Ut6MWv2ZrPucC6VxrP301wU0YfrR4UyfWgwepfmh3CJC4v0Q8JeEkPCEbUr8Vy/fj2VlZXKZdikpCS++OILAKZPn05hYSE333wzN910E5GRkahUKrZs2cLbb79NbGwsd9xxR8cdgRAN5OfnK7P0SUcr2kNiSLTX6NGj+c9//qMsp6LT6fAOi+Ttn1P5cl822SXVyrZ9+7gye0QY148Mo5+v23lqFRci6YeEvSSGhCNqV+K5aNEiZVpfgM8//5zPP/8cqJsO2MvLi8DAQN58803y8/Mxm82Eh4fz4IMP8uSTT9pMKS2EEEL0JpVGC1syqtiWZSCpMFt53sNZyzVDg7l+VBijw31Qy1BaIYQQFxC7JhfqKDK5kOgoZWVlWK1WVCqVzbpMQrSWxJBoD7PFys60Ir7Ym82GhDwMprpZadUqGBfpx5xRYVw5JAhXp66ZOVD0bNIPCXtJDIn26lWTCwnRmaRzFfaSGBJtkVZYwZq92Xy57yR5ZTXK85EBHlw/MozfjQglyMvlPDUI0ZT0Q8JeEkPCEUniKYQQQrRBaXUt/zuUyxd7s9h34rTyvJerjmvjQ5gzKoxhYV7NrrEnhBBCXKgk8RRCCCFaYLZY2Z5axJq92XyfaDuUdlJ0ANePDOPywQG46GQorRBCCNEcSTxFr2IwGJR7Gpydnbu7OaIHkhgSDaUWVLBmXzZfNRpKGxXgwQ2jw7hueCgBnrZDaSWGhL0khoS9JIaEI5LEU/QqycnJyvTh8fHx3d0c0QNJDInS6lrWHsrhi73Z7G80lHbW8LqhtENDzz2UVmJI2EtiSNhLYkg4Ikk8hRBCXPDqh9J+cWYorfHMUFqNWsWkQf7MGRXGlMEBOGtlKK0QQgjRHpJ4il7Fx8cHk8mEViuhLdpHYujCklpQzhd7T/LV/mzyywzK84MCPbhhVF9mjQghQN+2WWklhoS9JIaEvSSGhCOSdTyFEEJcUEqravnuzFDaA1lnh9J6u+mYFR/CnFF9iQv1lFlphRBCXHBkHU8hhBDCDmaLlW0phXyxN5sfkvJthtJOjq4bSjs5RobSCiGEEJ1FEk8hhBC9ktliJSmnjLWHc/hq30kKys8OpY0O1HPD6DBmDQ/FXy8zPgohhBCdTRJPIYQQncpkMrF27Vp27NiByWQiNjaWuXPnotfrO/R16hPNX9KL+SW9mN8yT1FeY1LKfdx0zBoeypxRYcSGyFBaIYQQoivJPZ6iV0lJSVFupo+Kiuru5ogeSGKoY/38888sWLCArKwsm+f1ej2vvPIK9913X7vrNpktJOXWJ5qn2J1xinKDyWYbN52a4cGu3DR2ANOGheGk7fzPFYkhYS+JIWEviSHRXnKPpxCtVFVVpaxbJUR7SAx1nG3btjF9+nSMRmOTsvLycu6//35MJhN//OMfW1WfyWwh8cwVzV8zmk809c5aRvbzoirjADu/XsGRpN0csVr41t2defPm8dRTT9G3b98OOb5zkRgS9pIYEvaSGBKOSBJPIYQQHc5qtXLfffcpSedll13Gww8/jF6vZ9WqVaxatQqAxx9/nFtuuQU/P78mdZjMFhJyyvj1zNDZ3ZklVDRONF20XNy/D2MH+DJ2gC+h7nDVlVPZvXu3zXaVlZW8++67fP3112zatInBgwd30pELIYQQojky1FYIIUSH27lzJ+PGjQNg5MiR/Prrrzbryd1999289957ALzxxhssXrxYSTTr79Hc00yi6emi5aL+vowdUJdsDg72RKM+e6/mbbfdxsqVKwFQq9VceeWV6PV61q1bR2VlJQAxMTEkJCSg0cgMtkIIIURDMtRWCCFEj7J//37l8cKFC5ssYn733Xfz3vsf4BQ4kG9Tqjn4n9/Yk3mKSqPZZruWEs2G8vLy+Pjjj4G6D8lt27YRHx8PQGFhIVOmTCEhIYHk5GS+//57pk+f3pGHLIQQQojzkMRTCCFEh2s4Y6zJVHfVstZs4fDJUn5JL+aH/cX0ffC/qJ3dyAQyjxUC4OWq4yJl6GwfYoLOnWg2tmHDBuW1Fi1apCSdAP7+/rzwwgvMnj0bgG+++UYSTyGEEKILSeIphBCiw40ZM6bugUbHv77ZTkbAeDYeLaK0ulbZRu3shrm6nGgfNTdfMYaxA3yJCdKjbmWi2VhpaanyODY2tkl5XFyc8risrKxdryGEEEKI9pHEU/QqRUVFWCwW1Gp1s5OVCNESiSH7VRhM5DmFEvWHV6jxGUi1sxtfHcgFwE1rRVeSScavP1Jz4jC6ygK+OJmNt7e33a8bGhqqPP7xxx+ZP3++TfkPP/zQ7LYdTWJI2EtiSNhLYkg4Ikk8Ra9y8uRJZfpw6WhFe/T2GDp16hQrV65k+/btmEwm4uLiWLhwIQMGDLCr3tKqWn48ks+GhDy2phRiNFkgaChqwFRWSNWxXVQd24khOwmsFmW/Zf/+d4cknQDTp0/Hx8eHkpISPv74Yy6++GLuuusudDodGzZs4Omnn1a2nTdvXoe8ZnN6ewyJzicxJOwlMSQckSSeQghxgVi1ahWLFi2iqqpKee7bb7/llVdeYfHixbz22mttmrWuoLyGH5Pqks1dacWYLGcnSY/wdWNaXDBhFPLS4kc5mZxss6+/vz+vv/56k6uS9nBzc+Oxxx7jySefxGq18sADD/DUU0/h4uJCQUGBst3MmTMZPnx4h72uEEIIIVomy6mIXqWkpEQZWuLj49PdzRE9UG+NoTVr1jBnzpzzbvPYY4/x2muvnXeb7JIqvk/MZ0NCLnuOl9DwEyQmSM+0uCCmxQURHahXJhiyWq1s2rSJHTt2UFtbS1xcHLNmzcLZ2dnu42rMYrHwwAMPsGzZsmbLL7vsMr777js8PT07/LXr9dYYEl1HYkjYS2JItFdn5mWSeAohRC9nNpuJjIwkMzMTqBtm+thjj6HX61m5ciUvvfQSZrMZtVpNZmYmffv2tdk/vbCC9Ql5fJ+Yx6HsUpuy+L7eTIutSzb7+7l31SG1aMuWLSxbtswm2b3zzjuZM2dOk6VdhBBCCFFHEk8hhBDt9uOPP3LllVcCMHnyZH7++Web5U6efPJJXnnlFQBeeOEF/vznP3Mkt5wNCblsSMzjWH6Fsq1aBWMi+jAtLoirYoMI8Xbt2oMRQgghRKfpzLxMfvYVQoheLrnB/ZU333yzTdIJcMstt/DKK3/FKWQQ63Nd+On1zRwvPnsfqE6j4tKBfkyLC2LqkED8PDp+iKwQQgghejdJPEWvYjablccajaYbWyJ6qt4YQ05OTsrj4uJi5bHJbGF3ZgkfbD1J6L0fotX7kQNQXIWzVs3EQf5cPTSIKTGBeLnqur7hPVRvjCHRtSSGhL0khoQjksRT9CoJCQnK9OHx8fHd3RzRA/XGGLrsssuUx/969z2GXH4D2zMr+PFIPqcqjQBo9X5YDFUM81Nz37WXMjHaHzcn+Yhoj94YQ6JrSQwJe0kMCUck3yqEEKKX6x85iItn30mqQY8l8iIe+OKIUqYyVlKevIOqoztxK8/is8x03NzcurG1QgghhOiNJPEUvYper8dkMsmslaLdeksMVRhMbEwuYENCLpuSC6mOmoXHmTJTeTHVKbuoOrqTmqwEsFrQarWs/PprSTo7QG+JIdF9JIaEvSSGhCOSWW2FEKKXKK2q5ccjdWtsbk0pwmiyKGWh3q6MDXNh79fvs2XNCuBs1x8fH89bb73F5MmTu77RQgghhHAYspyKEEKIZhWWG/ghKY8NCXnsSivGZDnbpQ/wc2daXN0am0NDvZTZbNPS0ti1axcmk4nY2FhGjx7dZKZbIYQQQlx4JPEUQgihyC2tZkNCHusT8tiTeYoGuSYxQXqmxQVxdVwwgwI9JKEUQgghRKvJOp5CCHGBO1FcxfqEXNYn5HEg67RN2bAwLyXZ7O/n3k0tFEIIIYQ4N0k8Ra+SkZGh3Ezfv3//7m6O6IG6OoasVivFxcWYTCb8/f1t1ltLyS9nfULdMNqk3DLleZUKRvXzUYbRhvnIhECORPohYS+JIWEviSHhiCTxFL1KWVmZsm6VEO3RVTFkNBpZvnw5S5cu5dixYwD4+fkxe+GDhI6dwZa0UtIKK5XtNWoVYwf0YVpcMFcNCSTA06VT2yfaT/ohYS+JIWEviSHhiCTxFEKILlZVVcWMGTPYtGkTqNQ4hw7BNepinKLH8T1B8EsOADqNivGRflwdF8wVQwLp4+7UzS0XQgghhGifNk8uVF5ezosvvsiBAwfYv38/RUVFPPvsszz33HNNtt23bx9Llizhl19+QavVMmXKFF5//XUGDBhgs51MLiQ6islkwmq1olKpZO0q0S5dEUO33fswa3Yk4tJ/FK4Rw1G7eChlltoaatL34Wc4ya417+HlKslmTyP9kLCXxJCwl8SQaC+HmlyouLiY9957j/j4eK677jref//9ZrdLTk5m0qRJDB8+nM8++4yamhqeeeYZJkyYwIEDB/D397e78UI0Jp2rsFdnxJDBZGZPZglbjhXyc1IuaZ5X4Hv1FUq5t5uOy6L8GRWo4cV7f0/W0SQKgT07b+Xyyy/v8PaIziX9kLCXxJCwl8SQcERtjsrw8HBKSkpQqVQUFRWdM/F85plncHZ2Zu3atXh6egIwatQooqKieP3113n11Vfta7kQQjiw48WVbDlWyJajhexMK6a61qyUWa0WjDnHiA/U8cqDtzIszBuNum7ZE5fnn+Gmm24CYM2aNZJ4CiGEEKJXaHPi2Zo14UwmE2vXrmX+/PlK0gl1SevkyZP56quvJPEUQjiUvXv38q9//Yvt27djMpmIi4vjzjvv5Oqrr27V8JIqo4lf0ovZcrSQLccKySyusin31zszcZA/VWl7ePf5h7HUlPPaqlWM6Odjs92oUaOUx6dOneqYgxNCCCGE6Gadch0+LS2N6upqhg0b1qRs2LBh/Pjjj9TU1ODicu5ZGRMTEwkPD7dJXA0GA8nJyQD4+PjQr18/m31SUlKoqqr7shcfH29TVlRUxMmTJwHo168fPj5nv+yZzWYSEhKAujHMje9BzcjIoKysbimD2NhYm+ELp0+f5vjx4wCEhIQ0GUJ86NAhrFYrrq6uDBo0yKYsKytL+WIZHR1tcz4qKipIS0sDICAggODgYJt9k5KSlNnKhgwZYlOWm5tLQUEBAAMHDsTD4+z9YzU1NRw9ehSAPn360LdvX5t9jx07RnV1NSqVqsn7V1hYSE5O3aQn4eHheHt7K2Umk4nExEQAPD09m0zdnZ6erowXj4uLs1kyoqSkhBMnTgAQGhqKn5+fzb4HDx4EwM3NjaioKJuyEydOUFJSAkBMTAzV1dVYLBbUajVqtZqMjAwAAgMDCQoKstk3MTERk8mEs7MzMTExNmU5OTkUFhYCEBkZibv72bURq6qqSElJAcDX15ewsDCbfY8ePUpNTQ0ajYa4uDibsoKCAnJzcwGIiIjAy8tLKTMajRw5cgQALy8vIiIibPZNS0ujoqICgKFDh9okQ8XFxWRnZwMQFhaGr6+vUmaxWDh8+DAAHh4eDBw40KbezMxMSktLARg8eDBOTmfvKSwtLSUzMxOA4OBgAgICbPZNSEjAbDbj4uJCdHS0TVl2djbFxcUAREVF4eZ2dsmPyspKUlNTAfD39yckJMRm3+TkZAwGA1qtltjYWJuyvLw88vPzAejfv7/dfYTVauVPf/pTkx/D0tLS+Oabb7j66qtZvXq1Ekv1fYTVaiW1oIItxwrZcPAEB3MqqbWc3V+rVjE6woeL++np71JNhLeO0NAQNlo8+FdN3d/C1q1biY+Pt+kjtmzZotTh7u6uxL/0ER3TRzg7OytlZWVlndJH5OfnK+fB399f+oge3kfU68rvEadPn1Y+y06cOCHfI+hdfURXfI9wdXXFz88PtVqtnGfpI+r0hj6ioc7KNTpDpySe9UHSp0+fJmV9+vTBarVSUlJy3gOsvym6IavVSm1trVLe3D715Y1ZLBalzGKxNClvbb2N29SwXrPZ3GTf2tparFZrs9NZm81mu+o917E2rLfxsTY8h83VW3+szV3Zbm293fneHD9+XPkgjYiIaPEcmkymZq9mne+9aekc1r83zZWdr96Gx9rW97y157C5/Ru2qbGWjtVoNGKxWGy+ADRXb3vPYXPnqLX1tjYO33nnHZukU6fTodVqqa6uBmD9+vXccccdLFmyhMpaC3vzzfz7wCG2HC0kp7TGpi5/NzVXxIYwOSaQSwb6onfRcerUKdLT0zGZTJjNZqZPn45er6e8vJwPP/yQ8PBwrrzySnQ6Hb/88gtPPfWUUt/MmTOlj6Dz+u/WxGF7+ojc3FylPukjen4fUa8rv0c0/Cyr/z4k3yN6Tx/RFd8jTCYTZWVl6HQ6JfGUPqJt9TpKHHZXrtEZOvXO4/MNy21pyK5Wq22yjUqlUk5qczdNa7Xac65XpFarlbLmOojW1tu4TQ3rbe6PRqfTYbVam61Xo9HYVW/D/5+r3sbH2vAcNldv/bE29/60tl5HeW9aOtb642zpHLanXrPZ3GzZ+eqt3/d89dp7Dls61sZaOlYnJyfMZnOnnEOLxdLmv5u2xmFNTQ0vv/yy8u8HH3yQOXPm4OTkxNatW3nxxZcwuPnzfRYUbcgls1KNpUG/7axVM3aAL3F+aob4QKheS1yc7S+Vjf+W9Xo9Dz74IC+//DJms5mnn36av//977i7uyu/CgNcfvnljBw5UvklXvqIntNHNN6uuXqlj+gZfURD8j0C5XWkjzhbr6N+jzCbzU0SDekj2lavo8Rhd/URnaHNy6k0VFRUhL+/f5PlVI4ePUpMTAxLly7l3nvvtdnnscce44033qCqqkq53CvLqYiOUlhYqHTWMnOyaMlXX33F7NmzAZg7dy6rV68m5UQOO9NP8+uJMjYn51Nlse3IB/i7M3GQPxMH+TN2gC8uurZ31mazmT/84Q98/PHHzZaPHDmS77//vslwMdEzSD8k7CUxJOwlMSTay6GWU2mNgQMH4urqqozDUwtpAAAgAElEQVQHb+jw4cNERkae9/5OIdpLOlfRFvX3BGl9QvC8aDY3Lt/FnuOnGlzV1GIxVFFz/CCxvmpWvfoEffu4nbO+1tJoNHz00UfceOONLF26lB07dlBbW6tMaHTbbbdJH9mDST8k7CUxJOwlMSQcUacknlqtlpkzZ/Lll1/y2muvodfrgboveZs2beLhhx/ujJcVQohWMVusHMg6za81wQQvXIaTXz9+KACouwE/JkjPpOgAnIpTeeQPN4PFRNSdd3ZI0llPpVJx7bXXcu2113ZYnUIIIYQQjqpdief69euprKxULsMmJSXxxRdfADB9+nTc3Nx4/vnnGTNmDDNmzOCJJ56gpqaGZ555Bj8/Px555JGOOwIhhGiFaqOZ7alF/JiUx8bkAooqjIA7Tn7uWM0mzLnJ/HHOZH4/MY4wHzdKS0uZMuUWsNRNAjB9+vTuPQAhhBBCiB6sXfd4RkREKNP6NpaRkaFM8b53714ef/xxdu3ahVarZcqUKbz++utNpmGWezyFEJ2hsNzAxuR8fkwqYHtqITUN1jvRu2iZHB3AkZ8+5ef/+wdWYxVOTk7MmjULvV7P119/rUxBPnDgQJKTk5u9cV8IIYQQorfozLzMrsmFOooknqKjHDp0SJmCvrl1ZEXvZrVaSSus4IekfH5Kymd/1mka9nCh3q5MHRLI1CGBXNS/DzqNmlOnTjFx4kRlfa3GfHx82LhxI8OHD++ioxA9nfRDwl4SQ8JeEkOivXrc5EJCdBer1ar8Jy4MJrOFvcdL+OlIPj8m5ZNZXGVTPizMiysG1yWbMUH6JtOJ9+nTh+3bt/PSSy/xwQcfKMuX6HQ6brzxRp577jkiIyO77HhEzyf9kLCXxJCwl8SQcESSeIpexdXVFZ1OJ0Mie7lKg4mtxwr58Ug+m5ILKKk6u5izk0bNJQN9mTokkMsHBxDs5dpifV5eXvztb3/jxRdfZMOGDRgMBgYMGMCYMWM68zBELyX9kLCXxJCwl8SQcEQy1FYI0SPkl9UoVzV3phZjNJ+9X9PbTceU6ACuGBLIZYP88XCWD1ohhBBCiLaSobZCiAuKwWDg8y/WsOGXw+SpfCn36k9+re26lv36uCn3a44O90GrkR+qhBBCCCEclSSeQgiHkV9Wwz+/+JkP1+9CFTQYjfv4uoIzI2kDtVXMv3w4U4cEERXg0eR+TSGEEEII4Zgk8RRCdJsqo4lfM06xPaWIbSmFHMuvAEA78BIALMZqak4cpjr1V6pSf+V45Wlm6//KoMmPd2ezhRBCCCFEG8k9nqJXycrKwmw2o9Fo6Nu3b3c3RzRisVhJyi1j25lEc09mic29mlgtGPJSqcnYz1B/LU/cORcfL09WrVrF8uXLAXByciIrK4uAgIBOaaPEkLCXxJCwl8SQsJfEkGgvucdTiFY6deqUsm6VdLSOIbe0mm0pRWxPKWJ7ahGnKo025SFeLkyI8sffXMTjt12Hpaaciy66iE2f7USj0QBwySWXoNVq+ec//4nRaGTFihUsWbKkU9orMSTsJTEk7CUxJOwlMSQckSSeQogOVWU08Wv6KeWqZkpBhU25u5OGSwb6Mj7SjwmD/Bng545KpWLp0qVYaup+YVuwYIGSdNZbuHAh//znP4G6hbGFEEIIIUTPIYmn6FWio6OxWq0y6UwXslisJOaUsS21kG3Hith73Hb4rEoFw8K8uSzKj/GRfozo54OTtulwjYZDOGpqapqUN3yuM4fhSwwJe0kMCXtJDAl7SQwJRySJp+hVXFxcWt5ItInFYuHnn39m+/btmEwm4uLiGDvlanafKGdbahE7mhk+G+rtymWD/Bgf6c+4SF+83ZxafJ2xY8cqj999913uvvtuXF1dAbBarbzzzjvNbtvRJIaEvSSGhL0khoS9JIaEI5LJhYQQ57Rjxw4WLFhAasYJnPsNxbX/CFwiRuDk189mu7rhs35cNsiPCVH+RPi6tetX1rFjx/Lrr78CEBsby/33349er2fVqlX88MMPQF3fkJ2djaenp/0HKIQQQgghFJ2Zl0niKYRowmq18uVPO7nr2bfR9h2GS984VNqzVy2tFjPGvBSmDAnhoZuuYnhfb3Qa+/9eDx48yIQJE5r0Bw199NFHzJs3z+7XEkIIIYQQtiTxFKKVKioqsFgsqNVqPDw8urs5PUqFwcSO1CK2HCtky9FCTp6utin31lkY0gfyD2xm86fvYjFU4urqysmTJ/Hx8emwduzbt4877riD/fv32zwfFhbGm2++yQ033NBhr9UciSFhL4khYS+JIWEviSHRXrKcihCtlJaWpkwfHh8f393NcWhWq5XkvHI2Hy1ky7EC9mSWYLKc/R3KaqqlJusw3jW5fLXsJQaH+JwZPjuTBepTrFixgurqaj766CMefPDBDmvXyJEj2bt3L7/++is7duzAZDIRGxvLtGnT0Go7v8uSGBL2khgS9pIYEvaSGBKOSBJPIS4gpVW1bEutu6K55VghBeUGm/IIXzcmDvKnIvU33vrTvVhrDfz5739nSGgfm+3uvfdeVqxYAcDu3bs7vJ0qlYqxY8d26iRCQgghhBCi60jiKXqVgIAAzGZzkzUgL1QWi5WEnNIzVzUL2X+ihAYXNXHV1a2pOSnan8ui/Inwcwdg6dItWGvrktLmhlY0PL8OMFq/Q0kMCXtJDAl7SQwJe0kMCUckiafoVYKDg7u7Cd2uuMLA1pS6q5pbU5oudRIV4MHEQf5Mig5gdIQPLrqmH0ojR45UHr///vvcdddd6HQ65bnly5crj0eNGtUJR9F9JIaEvSSGhL0khoS9JIaEI5LJhYTo4UxmCwezTytXNQ+fLKXhX7WHs5Zxkb5MHBTAxGh/Qr1dW6zTarUyYsQIDh48CMD48eN56KGH0Ov1rFy5kk8++QSoWycsOzsbX1/fTjk2IYQQQgjRdWRWWyGEjbzSGuWq5raUQspqTDblQ4I9mRjtz6RB/owM92nXUic7duxgypQpGI3Gc27zj3/8g/vvv7/NdQshhBBCCMcjiacQF7jTVUZ2pRWzI62InWnFpBdW2pR7ueqYEOXHxEH+TBzkT4CnS4e87ubNm7nttts4fvy4zfOenp68+uqr3HPPPR3yOkIIIYQQovtJ4ilEKyUlJSnThw8ZMqS7m9NuVUYTv2WcYmdaMTvTikjMKbMZPqtWwUAfHVMGB3FVfF/iw7zRqFWd0haz2cy6detslja58cYbcXd375TX6269JYZE95EYEvaSGBL2khgS7SXreArRSrW1tdTW1nZ3M9rMaLJwIOs0O1KL2JVWzP6sEmrNtr8JDfRzQ12UwqEfPqcwaRcZhkq2OTuTPHcuzz77LAMGDOiUtmk0GmbOnMnMmTM7pX5H01NjSDgOiSFhL4khYS+JIeGIJPEUvUr9zKsNZ2B1RBaLlaTcMnak1g2d3Z15iiqj2WabUG9XxkX6culAP4b4ablx5lXKZD/1DAYDq1at4n//+x8bN25k2LBhXXkYvVJPiSHhuCSGhL0khoS9JIaEI5KhtkJ0AavVSnpRZd3Q2dQidqUXc7rK9pdIX3cnLhlYl2iOi/SlXx83VKq64bO33HKLMpOsTqdjxowZ6PV6vv32W06fPg1AZGQkycnJsmaXEEIIIYRoF7nHUwgHVl1djclkwsPDQ0kUAXJLq9mZemZCoNRi8spqbPbzcNZycf8+XDLQl3GRfkQH6lE3c5/myZMnCQ8Px2w24+3tzc6dOxk8eDAAJSUlTJkyhQMHDgDw9ddfM2vWrE48WiGEEEII0VvJPZ5COBiTycTKlStZtmwZ+/btA6BfZAxX3HIvvoMvZU9WOelFtjPPOmnUjAz3ZtxAPy6N9GNYmFerljn54YcfMJvrhuEuWrRISToBfHx8eP7555Vk83//+58knkIIIYQQwuFI4ilEGxkMBmbPns269RtwDh2M98Q/4BIxAgIH8HONGvbnAXUzzw4N9eLSSD/GDfRjdIQPLrq2D4Nt+KtTTExMk/KGzzX+hUoIIYQQQghHIImn6FVyc3Mxm81oNBqCg4M7vP5TlUbufPotftPEEvbArWhc9TblxqLj1GQepJ9zNVs+fx8vNye7XzMsLEx5vH79eubPn29Tvn79euVx37597X69C11nx5Do/SSGhL0khoS9JIaEI5LEU/QqBQUFyrpVHdHRWq11s89uSi5gY3IB+0+cxuo0FPczS2K5a+GKuBAmRfsTSCk3/+4+co8fpwQ4sHshEydOtLsN06dPx9fXl+LiYlavXs3IkSO57777cHZ25ptvvuGZZ55Rtm2clIq26+gYEhceiSFhL4khYS+JIeGIJPEUopFKg4kdqUVsOlrApuTCJpMCGQsyqE7bzdXxffno7RfRKBMChfHSSy9x6623AvD55593SOLp4uLCk08+ySOPPALAkiVLeOaZZ3BycqKsrEzZbs6cOcTFxdn9ekIIIYQQQnQ0STxFrzJw4EAsFkubZ946XlzJxjNXNX9NP4XRbFHKXHUaxkX6MjkmgIwda3n61QcAuPqOVQ2Szjpjx45VHhcXF9txJLYefvhhcnNzef311wGoqamhpuZsQnzllVeyYsWKDnu9C1l7Y0iIehJDwl4SQ8JeEkPCEUniKXoVDw+PVm1nNFnYk3mqLtk8WkB6oe0MtH37uDIlOoDJMQGMHeCrTAr0SZqPss3OnTuVq5v1duzYoTz29/dv72E0oVKp+Nvf/sYNN9zAsmXL2LFjByaTidjYWO68805mzpwpHy4dpLUxJMS5SAwJe0kMCXtJDAlHJOt4igtGYbnhzPDZAralFFFhMCllWrWK0RE+TIkJYEpMAAP9bdfkrFdaWkpISAhVVVXodDo+++wzZs2ahUql4tChQ1xzzTVkZ2cDsH37dsaNG9dlxyeEEEIIIYQ9OjMvk8RT9FoWi5XDJ0vZmFzApqMFHMoutSn3dXdiUnRdojlhkB+eLrpW1fvYY48pQ14BIiMj0ev17N+/X3lu/PjxbN26tdnkVQghhBBCCEckiacQrZR3qpxfM06xJaWYramnKKow2JQPDfVi8pmrmsNCvVCr254Y1tbWMnfuXL766qtmy2NjY/npp58ICgpq1zGI7lVTU4PVakWlUuHi4tLdzRE9kMSQsJfEkLCXxJBor87MyzrtHs/NmzczefLkZst27dplMwmLEG1ltVrJK6sh4WQZiTmlJOaUkZRTxsnT1TbbuTtpmBDlz5SYACZF+xPgaX/nq9Pp+OKLL1i9ejVLly5l165dWK1WBg0axJ133sk999wj91b0YEePHlWmoI+Pj+/u5ogeSGJI2EtiSNhLYkg4ok6fXOgvf/lLkwRUlnwQbWGxWMkoriQxpy7JTMopIzGnjFOVxma3D9FrGBXiyk0TYhkT0QcnbcdfOVer1dx8883cfPPNmM1mLBYLOl3rhuoKIYQQoueoqamhsLCwu5vRJjqdDq1Wi0qlIisrq7ubIxyMs7Mzvr6+aDSaLn3dTk88o6Ki5OqmaDWjycKx/PIzyeWZK5m5ZVQZzU221ahVRPp7EBviyZAQT2JDvPCyluOmBY1GQ9++fl3SZo1G0+V/uKLz9OnTB7PZLO+paDeJIWEviSHHUVNTQ0FBAaGhoT3q/TAajcpQWycnp+5ujnAgVquV6upqTp48ib+/P66url322rKciug2lQYTR3LLSDhZeuZqZhkpBeXUmpveduyiUxMT5EnsmQQzNsST6CC9sszJWb5d03jRa/Xt27e7myB6OIkhYS+JIcdRWFjY45JOQJJNcU4qlQo3NzeCg4OVH1W6Sqcnnvfddx833XQTbm5uXHLJJTz99NOMHz++xf0SExMJDw/H09NTec5gMJCcnAyAj48P/fr1s9knJSWFqqoqgCbj2YuKijh58iQA/fr1w8fn7HqMZrOZhIQEoO7m2QEDBtjsm5GRQVlZGVA3cYxWe/a0nT59muPHjwMQEhLSZO3GQ4cOYbVacXV1ZdCgQTZlWVlZnDp1CoDo6Gibm78rKipIS0sDICAggODgYJt9k5KSlLH7Q4YMsSnLzc2loKAAqFtAuOH9hjU1NRw9ehSo+0W18YfbsWPHqK6uRqVSMWzYMJuywsJCcnJyAAgPD8fb21spM5lMJCYmAuDp6Un//v1t9t2XeIxDWSWklxgptrhxJLecjOJKmpvaytNFqySXsaGeaMvzCNVr0Xu4ExUVZbPtiRMnKCkpASAmJgZnZ2elrKysjIyMDAACAwObTPaTmJiIyWTC2dmZmJgYm7KcnBxlWE1kZCTu7u5KWVVVFSkpKQD4+voSFhZms+/Ro0epqalBo9E0GVZeUFBAbm4uABEREXh5eSllRqORI0eOAODl5UVERITNvmlpaVRUVAAwdOhQm5u8i4uLlWVcwsLC8PU9m4BbLBYOHz4M1K3rNXDgQJt6MzMzKS2tm/F38ODBNh9WpaWlZGZmAhAcHExAQIDNvgkJCZjNZlxcXIiOjrYpy87Opri4GKgb+eDm5qaUVVZWkpqaCtStdxoSEmKzb3JyMgaDAa1WS2xsrE1ZXl4e+fn5APTv31/6CHpHH5Genq5MZhAXF2fzJa+kpIQTJ04AEBoaip+f7WiGgwcPAuDm5iZ9hPQR0kecIX3EWfb0EeXl5RgMBnQ6XZNbaqqrq5Wrio2vGhmNRkymumXbnJ2dbdprNpsxGOomP9RqtU2SxJqaGiwWS7P11tbWUltbC9Qllw1jyWKxUFNTA9SNxmp4LA3rBXB1dbWZed9kMmE0Gputt/4KGdTdatR4siKDwYDZXDcyzcXFxabvaVjv+c5hc/Xacw7P9940PIeN623LOWzYZzWu93znsLl6G57D8703zZ3D+j6rpXPY+L1Rq9WUlpZSVFTUbB/RGTot8fTy8uKPf/wjkyZNwtfXl9TUVP72t78xadIk/ve//3HVVVedd3+TyUTjCXetVqvyhtafxMb71Jc3ZrFYlLL6gGmotfU2blPDeusDpnG9Vqu12fv/zGazXfWe61gb1tv4WBuew+bqrT/W5pYBaW29BmMtB7JOsyO1iP0nSkg4WUZeWU2DrcuUR0GeLkT5uxDoVEt/by3jhoQTHxlm8/p79uRhMZva/N60dKy1tbWYTKZmZ+k633vTmnpra2ubLTtfvfX7tlRvc1ob383t37BNjbV0rEajEYvF0uwvwR1xDps7R62tV/oIx+0jHOW9kT6iab3SR0gf0bjeC72PaPhfY+d6vmF5S2Xnq9ee12zrvg3LzrVve+ptad/696szzq+9x9rWeluz7/les2F547+fznjP68vP9XnUGTot8RwxYgQjRoxQ/j1hwgR+97vfMXToUJYsWdJi4ll/Q3RDKpVK6Xgb/orQcJ9zTfCiVquVsua+RLS23sZtalhvcx+sOp0Oq9XabL0ajcauehv+/1z1Nj7WhuewuXrrj7W5D4xz1Wu1WjleXMVPmQYO5hk4XFBIhTGlyf4hei39fXRcGtOXuDBvYkM88fNwtv2l0se1yWu3971p6Vjrj7Olc9iees91b8756q3f93z12hvfLR1rYy0dq5OTE2azuVPOocViafPfjfQRTdvrCH1E43od5b2RPqJpvdJHSB/RuN4LvY9o+F9j9c+da83u863lfb59W3pNe+s9134t7dueelvaV61WN5totaXetr5ma4/1XPU6YptaU++59tXpdF02lLzL1/FctGgRy5cvp6qqSrn0Let49jxFFQZ2pBad+a+4yTImehctlw705eL+vgwN82JwsCcezp1/S/GxY8cwmUxotdomQ5KEaA2JIWEviSFhL4khx5GVldUj77mVdTxFazQX3z1yHc9zqc9zz5d9i45jMBj48ssv2bFjByaTidjYWObNm2dzb0prVBlN/JZxih2pRWxPLeZIbplNuU6jYlS4D+Mj/Rgf5U9ciCdaTdf/cFBdXa3csyJEe0gMCXtJDAl7SQwJe1kslnNeSRSiu3Rp4llSUsLatWsZPny4/PrSBdavX8+CBQuUSRbqPf7447z44ossXrz4nB2SyWzh8MnSM4lmEfuOn8Zotr1vYnCwJxOi/BgX6ceYCB/cnM6GU2ZmJrt27VKS3REjRnRJ53e+4SlCtIbEkLCXxJCwl8SQ6AorVqxgwYIFzZY98sgjvP7664SFhTFt2jTef/99AFJTU4mKiuKjjz5i3rx5AGzfvp2ffvqJxYsX20zmJURjnZZ43nzzzfTr14/Ro0fj5+dHSkoKb7zxBvn5+axYsaKzXlacsXHjRq699tpmb6Svrq7m0UcfxWw2s2TJEqDuSnRGUSU7UovYllLErvRiymts9w31dmV8pB/jovy4dKAvfh7OTepOT0/nwQcfZN26dTY3M48cOZI333yTiRMndvCR2mo8g54QbSUxJOwlMSTsJTEk7NV4xtXz+fDDD5vM3F0/k/R3331nM7t2c7Zv387zzz/PHXfcIYmnOK9OSzyHDRvGp59+yvLly6moqKBPnz6MHz+ejz76iDFjxnTWywrqksgHHnhASTqnTp3KI488gl6vZ9WqVbz77rsAPPvK6wRdPJPDBUZ2pBaRU1pjU4+ni5ZLB9YlmuMj/YjwdTvvr69paWmMGzeuyRVWgH379nHFFVfw7bffcvXVV3fg0Z5lNpvJzMzEZDLRr1+/Ll0QVwghhBCiJ4qLi2P06NHNljWcKLSrVVVVtSmBFo6v0xLPJ554gieeeKKzqhfnsX37dpKSkgC46KKLWL9+PRqNhiqjCYNvJMfc40guAaeA/jyzPl3Zz0mjrrtP80yiGRfqhUbd+mE+99xzj5J0hoSEsHDhQvR6PR9//DEHDx7EZDIxf/58Tpw40aFJYWVlJW+88Qbvvvuusj6Yh4cH8+bN46mnnmqyhp4QQgghhL2qjE1HlXW1hrc5dYbGQ20b+/Of/8zLL78MYDNJzbZt2xg/fjwA//3vf3nnnXc4dOgQGo2GcePG8eqrr9qslTtv3jzWrl3Lli1bePTRR/nll1+Ij49n+/btnXh0oqt1+eRCovMdOnRIefz7+bfzxb6TrD2Uyy/pxdSaraDrj9OZNb7djSXMu2LUmfs0++Dq1L7plI8cOcJPP/0E1C2svX//fvr06QPA4sWLmTFjBhs2bKCoqIhPP/2U2267za5jrFdWVsbUqVP57bffbJ6vqKhg+fLlfPXVV2zevLnJEBIhhBBCCHsMeeb77m4CmX+9xu46zGZzk1uzmlt6pjn33HMPJSUlLFu2jG+//RZ/f38AYmNjAXjhhRd47rnnuOOOO3j66acxGAy89tprjB8/nj179hAdHa3UVVNTw6xZs1i0aBF/+tOfumxtSdF1JPHshWrR4D5kEm6DL+PvWaFYsg4rZaHerkR7Wfj07y9Qc/wgt8yZxZ+mz7P7Nbdu3ao8vvfee5WkE+rW7XriiSfYsGEDAFu2bOmwxPOPf/yjknSq1WomTpyIu7s7GzdupKqqivz8fGbPnk1CQoIszyNapbCwUFljsf4DVIi2kBgS9pIYEvaqra1VHrc0O/LYsWOb3b81yWdYWJhypXPEiBE2o8wyMzN54YUXeOihh3jzzTeV56dOnUpkZCQvvPACH3/8sfK8wWDgxRdf5NZbb23xdUXPJIlnL1FTa2ZTcgHfHcrhp5y++M18FAALMCjAnVkjwrg6LogIXzfmzZtHVfI2oPnOpj2MRqPy2M/Pr0l5w+cMBkOHvGZeXp7SYen1erZu3YpKpaK2tpbFixfzwAMPkJiYyJEjR9iwYQPTp0/vkNcVvVtOTo6yjIF84RPtITEk7CUx1DMkvXBVdzfhnGpra5XlVFpKPFetWsXgwYNtnmvtFc/z2bBhA2azmfnz59tcUXV1dWXChAls3ry5yT6zZ8+2+3WF45LEswczmixsSynku4M5/JiUT6Xx7JAETVUxxfu/p+rINvTBXmjd7+fXPE/uXbmS77+vGxpSfx9kR2g4VOKTTz7h9ttvt5mI6L///a/yuKOGvW7YsEH5RW/RokUMHz6cgwcPAtCnTx9efPFFpQP75ptvJPEUQgghRIfp7Psru8rgwYPPObmQPern/TjXBEVOTk42//b09MTd3b3D2yEcR+/4i7mAmMwWfkk/xXcHc9iQmEdp9dmhFKHersyID2bmsBBqC9K57MP7qK2oIKE4i3vuuadJXcuWLeuwaa8vv/xywsPDOX78OBs3bmTBggU8+uij6PV6Vq5cyV//+legbjhsRw2zLS0tVR7X30sQHh6OxWJBrVbbzIRWVlbWIa8per+GMSREe0gMCXtJDAl7NU7qukP9aLevv/6a0NDQJuWNV0qQdWt7P0k8ewCLxcqe4yWsPZTDusO5FFWcHdYaoHfmmmHBzBgWwsh+3mf/aENHsGXLFhYuXMiBAwds6gsNDeWtt97ihhtu6LA2ajQaXn/9daXOlStXsnLlyibbLV68mH79+nXIazbsxH766Sfmz5+Pt7e38twnn3yiPK5fj0qIljSMISHaQ2JI2EtiSNirI4bKtpazc9267tXV1TbPT5s2DY1GQ1paGrNmzeqy9gjHJYmng7JarRzKLuW7gzmsPZRLXtnZNTZ93HRcPbTuyuZF/fucc8mTkSNHsm/fPnbt2sWOHTswmUzExcVx9dVXd0qHNGfOHP7zn/9w3333Nel8AB566CHlymdHmD59Ot7e3pw+fZr/+7//4+KLL+bOO+9Ep9Px/fff8/TTTyvbyo3qQgghhBAdb+jQoQC8/fbbzJs3D51OR0xMDAMHDuTZZ5/liSeeIDU1lauuugpvb2/y8vL47bff8PLy4plnnunm1ouuJImnA7FarRzNL+e7gzl8dzCXE6eqlDK9s5YrY4OYGR/MuEg/dJrWDb9RqVRceumlXHrppZ3VbBsLFixg5syZrFixQkl2Y2NjueOOO4iMjOzQ13Jzc+Oxxx7jqaeewmq1cv/99/Pkk0/i6uqq3FcAMGPGDIYPH96hrzABsYMAACAASURBVC2EEEIIIeput1qyZAkfffQRy5cvx2KxKOt4Pv3008TFxfHOO+/w8ccfYzAYCA4OZsyYMcyYMaO7my66mMpqtVq7uxEWi4Xy8nKb5/R6fa+7tyEjI4P33nvPJiG788478es/hLWHcvnuYA4pBRXK9q46DVcMCWTGsGAmDvLHRde+NTZ7M4vFwv3338+//vWvZssnTJjAd999h5eXVxe3TPRUJpNJmQmwK4cqid5DYkjYS2LIcWRlZSnLhfQkVqtViSG5d1KcS3Px3Zl52QXfm5WUlGAymfD19e3URPfNN99kyZIlymK4Gk9/Es0hrF22C+egQmU7J42aSdH+zIwP4fLBAb1mxrTOolarWbZsGXPnzmXp0qVs3rwZk8lEZGQkDz/8MDfccIN8aIs2SUxMVJYxiI+P7+7miB5IYkjYS2JI2Ku6ulpJPBtOtihEd7ogv5EbjUb+/e9/s2zZMpKSkgAIDAzkjjvu4OGHH8bX17dDX+/DDz/kkUceQesdjOegS3CLvhTnkLNLilgtZvzNRTxx85VcGRuIp8v511sSTU2cOJGJEydy8OBB+bAWQgghhBDCwVxwiWd1dTUzZ87k559/tnk+Pz+fl19+mU8++YRNmzYRHh5u92tZrVYSs0t45rNfCF7wD5wC+itlKqCvcw0J61ZQmriVE9VljLg3VZJOO3l6emIymeQqp2g3iSFhL4khYS+JIWEvjUajXPEUwlFccD3ao48+apN0jhkzBr1ez9atWzGZTGRkZDB79mz27NnTrj9Wq9XKwexSNiTksSEhl8ziKjTx16IBsFoYHxXAVXFBXDUkkABPF152SubPe9YCsGLFCl588cUOOtILU//+/VveSIjzkBgS9pIYEvaSGBL2ql/iRAhHckElnsXFxXzwwQcAuLq6sn79eiZOnAjUTfwzdepU0tLS2LdvH5s2bWLKlCmtqtdktrA7s4TvE/P4PjGP3NKzS59osFCe8htVx3by2h9v5d47Ztrse/311/PnP/8ZgLS0tI44TCGEEEIIIYRwKBdU4rlu3ToMBgMAd911l5J0Qt2viy+99BK///3vAVizZs15E0+DyczOtGI2HM7jxyP5nKo0KmXuThomxwRwdVwwx39Zx32vvgRAce6kJvVkZWUpj11dXe06PiGEEEIIIYRwRBdU4nnq1Cnl8ahRo5qUjx49utlt61UZTWw5WsiGxDw2Himg3GBSyrzddEwdHMi0uCDGRfopS5+ke0xGpVJhtVpZtmwZCxcuJCQkBACDwcBLL72k1HHFFVfYf5BCCCGEEEII4WAuqMQzMDBQebxt2zZuvfVWm/KtW7cqjwMCAgAora5lY3I+GxLy2HKskJpay9lt9M5MiwtiWmwQF/Xvg1bTdDmWAQMGMGPGDL777jvy8vIYMmQIt9xyC56enqxevZrMzEwAQkJCuP766zvycC9I6enpyoQMAwYM6O7miB5IYkjYS2JI2EtiSNjLYDAokwvJ/Z7CUVxQief06dPx8PCgoqKCDz/8kClTpnDjjTeiVqvZvXs3Tz31FABqN2/8L/kd8//zGztTizBZrEodffu4cnVcMFfFBjGirzdqdcsTEC1fvpzDhw+TmZlJaWkpy5Ytsyl3c3Nj9erVODk5dewBX4DKy8uV5VSEaA+JIWEviSFhL4khYS+z2Syz2gqHc0Elnp6enjz44IP85S9/wWQy8fvf/54lS5bg4eHBsewi3AZdQuCUS3EJi+X9A5VAJQCDAj2YFhfMtNggBgfr2/xHHBISwq5du3j88cdZvXo1RuPZ+0GnTp3Kq6++yogRIzryUIUQQgghhBDCYaisVqu15c06l8Vioby83OY5vV6PWt106Kq9TCYTt956K6tXr0bt7o1H7BTcYsbjHDzIZrv4MK+6ZU9igxjo79Fhr19cXMyePXswmUwMGTJEpkzvYGazWXms0Wi6sSWip5IYEvaSGBL2khhyHFlZWfTt27e7m9FmDb/en+uCyYoVK1iwYAEAmzZtYtKkSU3qiIqKIi0tjYkTJ7J58+bOaq5oQU5ODu+99x7XXXcdw4cP77B6m4vvzszLLqgrngBWlZrb/vwWZfG/J7FEBaozJ9FqIczFyPzJQ7lmeF9CvTtnhllfX1+uuuqqTqlbyAe0sJ/EkLCXxJCwl8RQ71VdXc1nn33G559/TlFREf7+/sydO5c5c+bg4uLSYa/TltF5er2eDz74oEniuWXLFtLS0tDr9R3WLtE+OTk5PP/880RERHRo4tnVLpjEMyW/nM/3ZvPlvmyKKoyABlQwsp83148M48rYIPz1cvO1EEIIIYToeAkJCcyYMYPjx4/bPL927VqeffZZ1q5dy+DBg7u8XXPnzuXjjz9m6dKleHp6Ks9/8MEHXHLJJZSVlXV5mzpSdXU1Li4ucr+rA+j4sawOpKymlk9+PcF1S3cw9a2tvLc1naIKI34eztx92QB+WnwZX947jlvGhkvSKYQQQgghOkVeXh5XXHFFk6SzXnp6OlOnTqWwsLCLW4ayhv1///tf5bnS0lLWrFnD7bff3mR7o9HISy+9RExMDM7Ozvj7+7NgwYImbf/000+58sorCQ4OxtXVlcGDB/PEE09QWVlps116ejo33XQTISEhODs7ExgYyOWXX86BAweUbVQqFc8991yTtkRERHDbbbcp/16xYgUqlYoffviB22+/HX9/f9zc3DAYDACkpKRw8803ExAQgLOzM4MHD2bp0qU2dW7evBmVSsUnn3zC448/TnBwMB4eHsycOZP8/HzKy8u566678PPzw8/PjwULFlBRUWFTR/0yisOHD8fV1RUfHx/mzJlDenq6zXaTJk0iLi6O3bt3M2HCBNzc3BgwYAB//etfsVgsSnvGjBkDwIIFC1CpVDbnozXnz1H0uiueFouVXzNO8fmeLNYl5CrLn2jUKqbEBHDj6L5MivZH18zSJ6LnKykpwWKxoFar8fHx6e7miB5IYkjYS2JI2EtiqPd56623yM/PB2DkyJH84x//4OKLL2bHjh088MADHDp0iJMnT/LPf/6T559/3u7XM5nOrjWv1Z7/676npydz5szhP//5D3fffTdQl4Sq1Wrmzp3L22+/rWxrsViYNWsW27ZtY8mSJVx66aUcP36cZ599lkmTJrFnzx5cXetuV0tJSWH69Ok89NBDuLu7k5yczKuvvspvv/3Gxo0blTqnT5+O2Wzmtddeo1+/fhQVFbFz505Onz7d7uO//fbbueaaa/joo/9v797DoqrzP4C/R2a4johcFIeroISigFpouoRm6ublUShd0UztV5bKoj1eUjPRytKKtrSH1Sy1JxXTdd1n85K7K2ZbWyym4v2ClwAxuYrDTZmZ7+8PHs5ymAEGh3EGe7+eh6fm+z3ny+ec+c5HvnO+53u+RGVlJVQqFc6dO4fBgwcjMDAQqamp8PX1xaFDh5CcnIzi4mKkpKTI2li2bBmGDRuGrVu34vr161i4cCESExOhVCoRFRWF9PR0nDhxAsuWLUPHjh2xbt06ad+XX34ZW7duRXJyMtauXYvS0lK8+eabGDx4MLKzs2WPePz1118xdepULFiwACkpKdi7dy+WLl0KjUaD559/Hv3798eWLVswc+ZMLF++HGPGjAEA+Pv7W+38WY2wA3q9Xty+fVv2o9frW9VGflmV+Phfl0Ts2gwR9No+6Wd46rfi06NXROGdGitFT/bk5MmTIisrS5w8edLWoVA7xT5ElmIfIkuxD9mP3Nxci9swGAzCx8dHABAqlUrcuHFDVn/t2jXh4OAgAAh/f3+Lf58QQlRWVoqKigpRWVnZ5DZbtmwRAERWVpY4cuSIACDOnDkjhBDiscceEzNmzBBCCBERESHi4uKEEEKkp6cLAGLPnj2ytrKysgQAkZaWZvJ3GQwGUVtbK44ePSoAiOzsbCGEEMXFxQKA+Oijj5o9HgAiJSXFqDwoKEhMnz7d6Jief/55o21HjRol/P39RXl5uaw8KSlJODs7i9LSUiGEkM7FuHHjZNvNnz9fABDJycmy8gkTJghPT0/p9Y8//igAiNTUVNl2eXl5wsXFRSxevFgqi4uLEwBEZmambNvevXuLUaNGSa/rz++WLVtk25l7/ppiqn+3xbisKXZ72W/z5s2orq5udpuaWj2+zi7AtM8z8bu1Gfjwn5eQW1oFtZMSiTGB2DtnMP756hN46YkQTqUlIiIiogdOq9VK01Aff/xxaDQaWX1wcDAGDBgAAMjPz5c9du9BiYuLQ2hoKDZv3ozTp08jKyvL5DTbffv2wcPDA+PGjYNOp5N+oqOj4evrK1v59urVq5gyZQp8fX3h4OAAlUqFuLg4AMD58+cBAJ6enggNDcX777+PDz/8ECdOnJCmmFrimWeekb2uqanB4cOHER8fD1dXV1nso0ePRk1NDX766SfZPmPHjpW9rr//tv6KY8Py0tJSabrtvn37oFAo8Nxzz8l+j6+vL6KiooxWB/b19UVMTIysLDIysslp2Q1Z6/xZi91OtV2yZAnS0tLwj3/8A97e3rK6MzfKsftYHv52sgDl1bVS+aAQT0x6NABP9+kGF0euCPdb5OfnJ01PIrof7ENkKfYhshT70MPFyckJCoUCQgjcuHEDQgjZQjcGgwEFBQUA6lY0bmlqrDlUKlWrtlcoFJg5cybWrVuHmpoahIWFITY21mi7W7du4fbt23B0dDTZTnFxMQCgoqICsbGxcHZ2xttvv42wsDC4uroiLy8PCQkJ0sUlhUKBw4cP480338R7772HBQsWwNPTE1OnTsXq1avve0Xdbt26yV6XlJRAp9Nh/fr1WL9+fbOx1/P09JS9rj/mpspramqgVqtx69YtCCFk02kbCgkJkb328vIy2sbJyanFC3CA9c6ftdjtwBMATpw4gUmTJuHw4cO4XVWLv528gV3H8nH+5v9W19J0csazA/zx7IAABHq52jBasgeNv6Qgai32IbIU+xBZin3o4eLk5ITY2Fh89913uHLlCr744gvZgjibNm1Cfn4+AGD48OFt8oVDaweeADBjxgysWLECGzZswOrVq01u4+3tDS8vL3zzzTcm6+sHOhkZGSgoKMC3334rXeUEYPK+w6CgIHz++ecAgEuXLmHXrl1YuXIl7t27hw0bNgCoO4f1CwQ1VFJSYjKOxivYdu7cGQ4ODpg2bRrmzp1rcp/u3bubLG8tb29vKBQK/Pvf/4aTk/GMS1NlljDn/NkLux14dunSBSWlZfjxejkSP/kXjv+qwz193aVjR4cOGBnRFZMeDcCQHt5w6MDlkYmIiIjIPiUnJ+O7774DULcy6e7duzFo0CD85z//kQ3ikpOTbRUi/Pz8sGjRIly4cAHTp083uc3YsWOxc+dO6PV6DBw4sMm26gd+jQdZGzdubDaGsLAwLF++HHv27MHx48el8uDgYJw6dUq2bUZGhtFqsk1xdXXFsGHDcOLECURGRjZ5xbYtjB07FmvWrMGNGzcwadKkNmmz/jy2dBW0qfNnL+x24PnEK2/jzkUtlB298dONurnuERp3THo0AOOjNfBwtV6HISIiIiJqKwkJCXjppZewadMmAMCBAwdw4MAB2TZJSUkYPXq0LcKTrFmzptn6yZMnY/v27Rg9ejTmzZuHmJgYqFQq5Ofn48iRIxg/fjzi4+MxePBgdO7cGa+88gpSUlKgUqmwfft2ZGdny9o7deoUkpKSMHHiRPTs2ROOjo7IyMjAqVOnsGTJEmm7adOm4Y033sCKFSsQFxeHc+fO4ZNPPkGnTp3MPraPP/4Yv/vd7xAbG4vZs2cjODgYWq0WOTk5+Prrr2Ur7VpiyJAhmDVrFmbOnIljx47hiSeegJubG27evInvv/8effv2xezZs1vVZmhoKFxcXLB9+3b06tULarUaGo0GxcXFZp0/e2G3A8/MMjcoOzpBX30HfrUF+Hz5i4jQmN+5iIiIiIjsgUKhwMaNGxEREYEPPvhAmloL1E2VXLRoEebMmWM0RdTeODg44O9//zs+/vhjfPnll3j33XehVCrh7++PuLg49O3bF0DdfYv79+/HggUL8Nxzz8HNzQ3jx4/HV199hf79+0vt+fr6IjQ0FGlpacjLy4NCoUBISAhSU1Pxxz/+Udpu0aJFuHPnDrZu3YoPPvgAMTEx2LVrF8aPH2927L1798bx48fx1ltvYfny5SgsLISHhwd69uzZ5gP+jRs3YtCgQdi4cSPS0tJgMBig0WgwZMgQo4WEzOHq6orNmzdj1apVGDlyJGpra5GSkoI5c+aYdf7shUIIIWwdhMFggFarlZX932c/4OCmd1CVk4nZs15CWlqajaKj9iQ7Oxu1tbVQqVSIioqydTjUDrEPkaXYh8hS7EP2Iy8vDwEBAW3apk6nQ2ZmJkpKSuDj44OYmBg4OLTtophVVVXSIkaurlwDhUwz1b9Njcs6duzYJvce2+0Vz+vpK1B18WcAxksiExERERG1R0qlEkOGDLF1GEQPnP0OPK9fBwD0798fTz75pG2DoXaj/tlMbbEUOf02sQ+RpdiHyFLsQ2SpDh06GD22hcjW7DqjBQcHY8+ePfzQkNl69uxp6xConWMfIkuxD5Gl2IfIUs7OzrYOgciI3T6ZeP78+Th27BiCg4NtHQoRERERERFZwKoDz4qKCsyfPx8ajQbOzs6Ijo7Gzp07zdp32bJl8PLysmZ4RERERERE9ABYdaptQkICsrKysGbNGoSFhWHHjh1ITEyEwWDAlClTrPmriYiIiIgsxnsl6WFkiwebWO1xKgcOHMCYMWOkwWa9kSNH4uzZs8jNzZWWjrbmsr3025KbmystyBAYGGjrcKgdYh8iS7EPkaXYh+xHYWEh1Gp1u3skyd27d6X/d3JysmEkZK+0Wi3u3btnNMPUmuMyq43s9u7dC7VajYkTJ8rKZ86ciYKCAmRmZlrrV9NvWFlZGUpLS1FWVmbrUKidYh8iS7EPkaXYh+yHl5cXiouLUVtba+tQWkWv10On00Gv19s6FLIzQghotVqUlZXBw8Pjgf5uq021PXPmDHr16mW0FHhkZKRUP3jwYGv9eiIiIiIiizg4OMDHxweFhYUwGAy2DsdsWq1WmiLcsWNHW4dDdsbV1RV+fn7S7NMHxWoDz5KSEoSEhBiVe3p6SvXNOXv2LIKCguDu7i6V3b17FxcuXAAAdO7c2Wj6yeXLl1FVVQUAiIqKktUVFxfjxo0bAIDAwEB07txZqtPr9Thz5gyAukvJjeO+du0a7ty5AwCIiIiQDaZv376NX375BQCg0Wjg4+Mj2/fUqVMQQsDFxQVhYWGyury8PJSWlgIAHnnkEdnS1xUVFbhy5QoAoEuXLujWrZts33PnzqG2thYqlQq9e/eW1d28eROFhYUAgNDQUKjVaqmupqYGFy9eBFD3XgQEBMj2vXTpEqqrq6FQKKQvCeoVFRWhoKAAABAUFCT7lkSn0+Hs2bMAAHd3d3Tv3l2279WrV6XL9n369JF19LKyMuTm5gIA/Pz84O3tLds3OzsbQN2HpPES87m5udI3wuHh4QgPD5cS7Z07d3Dt2jUAQNeuXeHr6yvb9+zZs9DpdHByckJ4eLisrqCgAEVFRQCAHj16wM3NTaqrqqrC5cuXAdR9E+rv7y/b9+LFi6ipqYGDgwP69OkjqyssLMTNmzcB1D0uqFOnTlLdvXv3cP78eQBAp06djFZ0vnLlCioqKgAAffv2lU15KCkpQX5+PgDA399fNm3CYDDg9OnTAAC1Wo3Q0FBZu9evX0d5eTkAoFevXnB0dJTqysvLpWfqduvWDV26dJHte+bMGej1ejg7O+ORRx6R1eXn50uf8549e8qmKVVWViInJwcA4OPjA41GI9v3woULuHv3LpRKJSIiImR1v/76K27dugUA6N69e5vnCCEEAgICZP2bOeJ/2nuOaDjlzFo5Ijg4GNeuXYMQAvn5+cwRD1mOAKz/d0TDf8uYI+rYQ47w8/OT7WvPf0d07NgRGo0GCoVCOibmiDoPQ45oyFo5whqsurhQczdit3STtk6nM7rpVQghTXXQ6XQm92lqKoTBYJDqTH1jZW67jWNq2K6p6Qy1tbUQQkClUhnV6fV6i9pt6lgbttv4WBueQ1Pt1h+rqffH3HZt+d40/EDV1NS0eA51Op3JOevNvTctncP698ZUXXPtNjzW1r7n5p5DU/s3jKmxlo713r17MBgMJr8xa4tzaOocmduuJf1QqVQa3RPDHFGnveeIpmJqyxyhVCqlWJgjHs4cYe2/IxrmH+YIebumtLcc8SD+jmj8N1HDdk1hjjBu1176oa3+jrAGqw08vby8TF7VrB9111/5bIpSqTRKWgqFQjqpjafw1peZOukA0KFDB6nOVIIwt93GMTVs19SHRqVSQQhhsl0HBweL2m3436babXysDc+hqXbrj9XUPxjmtmsv701Lx1p/nC2dw/tpV6/Xm6xrrt36fZtr19Jz2NKxNtbSsTo6OkKv11vlHBoMhlZ/buyxHzJHGLdrL+8Nc4Rxu8wRzBGN22WOYI5o2C5zxG8nR1iD1Va1nTVrFtLT01FWViY7ETt37kRiYiJ++OEH6R5PrmpLRERERERkW9Ycl1lt4Hnw4EGMHj0aO3fuxB/+8Aep/Omnn8apU6dkj1PR6/XSnPN6bm5uHHhSqzX8oPBmerof7ENkKfYhshT7EFmKfYjul8FgQGVlpaxMrVa3yVVRq021ffrppzFixAjMnj0bd+7cQY8ePZCeno5vvvkG27ZtkwVvauzb+ICJWqvxtzVErcU+RJZiHyJLsQ+RpdiHyFJtdZ3Salc8gbrVkl5//XXs2rULpaWlCA8Px9KlSzF58mTZdjqdjgNNIiIiIiIiO+Pm5mbyHtLWsurA01wceBIREREREdmfthp48iZKIiIiIiIisiq7uOJpMBiMnnejUChafNYnERERERERtQ0hhNE9nR06dLDvVW2JiIiIiIiIAE61JSIiIiIiIivjwJOIiIiIiIisyi4GnhUVFZg/fz40Gg2cnZ0RHR2NnTt32josaie+/fZb6Z7gxj8//fSTrcMjO6PVarF48WKMHDkSPj4+UCgUWLlypcltjx8/jqeeegpqtRoeHh5ISEjA1atXH2zAZHfM7UMzZswwmZfCw8MffNBkVzIyMvDCCy8gPDwcbm5u8PPzw/jx4/Hzzz8bbcs8RKaY24eYh6gpJ0+exJgxYxAYGAgXFxd4enri8ccfx7Zt24y2bas8ZPm6uG0gISEBWVlZWLNmDcLCwrBjxw4kJibCYDBgypQptg6P2ol33nkHw4YNk5X16dPHRtGQvSopKcGnn36KqKgoTJgwAZ999pnJ7S5cuIChQ4ciOjoau3btQk1NDVasWIHY2FicPHkSPj4+Dzhyshfm9iEAcHFxQUZGhlEZ/bb9+c9/RklJCebNm4fevXujqKgIqampGDRoEA4dOoQnn3wSAPMQNc3cPgQwD5Fpt2/fRkBAABITE+Hn54fKykps374d06ZNw/Xr17F8+XIAbZyHhI3t379fABA7duyQlY8YMUJoNBqh0+lsFBm1F0eOHBEAxO7du20dCrUDBoNBGAwGIYQQRUVFAoBISUkx2m7ixInC29tblJeXS2XXr18XKpVKLF68+EGFS3bI3D40ffp04ebm9oCjo/bg1q1bRmVarVZ07dpVDB8+XCpjHqKmmNuHmIeotQYOHCgCAgKk122Zh2w+1Xbv3r1Qq9WYOHGirHzmzJkoKChAZmamjSIjooeROY9q0ul02LdvH5555hm4u7tL5UFBQRg2bBj27t1r7TDJjvFxX2SpLl26GJWp1Wr07t0beXl5AJiHqHnm9CGi++Ht7Q2lsm5SbFvnIZsPPM+cOYNevXpJB1gvMjJSqicyx9y5c6FUKuHu7o5Ro0bh+++/t3VI1E5duXIF1dXVUh5qKDIyEjk5OaipqbFBZNTeVFdXw9fXFw4ODvD390dSUhJKS0ttHRbZofLychw/fhwREREAmIeo9Rr3oXrMQ9Qcg8EAnU6HoqIipKWl4dChQ3jttdcAtH0esvk9niUlJQgJCTEq9/T0lOqJmtOpUyfMmzcPQ4cOhZeXF3JycvD+++9j6NCh2L9/P0aNGmXrEKmdqc879XmoIU9PTwghUFZWhm7duj3o0KgdiYqKQlRUlHSv+dGjR/GnP/0Jhw8fRlZWFtRqtY0jJHsyd+5cVFZW4vXXXwfAPESt17gPAcxD1LI5c+Zg48aNAABHR0esW7cOL7/8MoC2z0M2H3gCaHbKEqczUUv69euHfv36Sa9jY2MRHx+Pvn37YvHixRx40n1jbiJLvPrqq7LXI0aMQL9+/fDss89i06ZNRvX02/XGG29g+/btWL9+PQYMGCCrYx4iczTVh5iHqCXLli3Diy++iMLCQnz99ddISkpCZWUlFi5cKG3TVnnI5gNPLy8vk1c166cAmBphE7XEw8MDY8eOxYYNG1BdXc3V26hVvLy8AJiecVFaWgqFQgEPD48HHRY9BOLj4+Hm5sZHPZFk1apVePvtt7F69WokJSVJ5cxDZK6m+lBTmIeoocDAQAQGBgIARo8eDQBYunQppk+f3uZ5yOb3ePbt2xfnz5+HTqeTlZ8+fRoAH4dB908IAYDfCFPrhYaGwsXFRcpDDZ0+fRo9evSAs7OzDSKjh4EQAh062PyfX7IDq1atwsqVK7Fy5UosW7ZMVsc8ROZorg81h3mImhITEwOdToerV6+2eR6yeY+Lj49HRUUF9uzZIyv/4osvoNFoMHDgQBtFRu1ZWVkZ9u3bh+joaP7DTK2mVCoxbtw4/PWvf4VWq5XKc3NzceTIESQkJNgwOmrP/vKXv6CqqgqDBg2ydShkY2+99RZWrlyJ5cuXIyUlxaieeYha0lIfagrzEDXnyJEj6NChA0JCQto8DylE/WUhGxo5ciSOHTuGtWvXokePHkhPeHDe8gAAAh5JREFUT8emTZuwbds2TJ061dbhkZ2bMmUKAgMD8eijj8Lb2xuXL19Gamoqrly5goMHD+Kpp56ydYhkZw4ePIjKykpotVq88MILmDhxIiZNmgSgbpqJq6srLly4gMceewz9+/fHkiVLpAcml5aW8sHt1GIfKioqwpQpUzB58mT06NEDCoUCR48exUcffYTQ0FBkZmbCzc3NxkdBtpKamoqFCxfi97//vckBQ/2AgHmImmJOH/rll1+Yh6hJs2bNgru7O2JiYtC1a1cUFxdj9+7d+Oqrr7Bo0SK89957ANo4D1n8lNE2oNVqRXJysvD19RWOjo4iMjJSpKen2zosaifeffddER0dLTp16iQcHByEj4+PiI+PF//9739tHRrZqaCgIAHA5M+1a9ek7Y4dOyaGDx8uXF1dhbu7u5gwYYLIycmxXeBkN1rqQ6WlpSI+Pl4EBwcLFxcX4ejoKHr27CkWL14sbt++bevwycbi4uKa7D+N/zRjHiJTzOlDzEPUnM2bN4vY2Fjh7e0tlEql8PDwEHFxceLLL7802rat8pBdXPEkIiIiIiKih5fN7/EkIiIiIiKihxsHnkRERERERGRVHHgSERERERGRVXHgSURERERERFbFgScRERERERFZFQeeREREREREZFUceBIREREREZFVceBJREREREREVsWBJxEREREREVkVB55ERERERERkVRx4EhERERERkVX9P77CtuAQeN55AAAAAElFTkSuQmCC\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": {
"scrolled": false
},
"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": {
"scrolled": false
},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"scrolled": false
},
"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": {
"scrolled": false
},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"scrolled": false
},
"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": {
"scrolled": false
},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution and Discussion"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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