{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Table of Contents](./table_of_contents.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# One Dimensional Kalman Filters"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"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": [
"Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a Kalman filter. We will do this exactly as we did the discrete Bayes filter - rather than starting with equations we will develop the code step by step based on reasoning about the problem. \n",
"\n",
"\"One dimensional\" means that the filter only tracks one state variable, such as position on the x-axis. In subsequent chapters we will learn a more general multidimensional form of the filter that can track many state variables simultaneously, such as position, velocity, and acceleration. Recall that we used velocity in the g-h filter to get better estimates than by tracking position alone. The same is true for the Kalman filter.\n",
"\n",
"So why not just jump into the multidimensional form of the filter? To be honest, the math is difficult, and my intuitive approach to developing the filter starts to break down. This math obscures the rather simple principles that allow the Kalman filter to work.\n",
"\n",
"So, in this chapter we learn how to use Gaussians to implement a Bayesian filter. That's all the Kalman filter is - a Bayesian filter that uses Gaussians. In the next chapter we will switch to a multidimensional form and the full power of the Kalman filter will be unleashed!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem Description\n",
"\n",
"As in the **Discrete Bayes Filter** chapter we will be tracking a moving object in a long hallway at work. Assume that in our latest hackathon someone created an RFID tracker that provides a reasonably accurate position of the dog. The sensor returns the distance of the dog from the left end of the hallway in meters. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
"\n",
"The sensor is not perfect. A reading of 23.4 could correspond to the dog being at 23.7, or 23.0. However, it is very unlikely to correspond to a position of 47.6. Testing during the hackathon confirmed this result - the sensor is 'reasonably' accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the true position; a position of 23 m would equally likely be measured as 22.9 or 23.1. Perhaps we can model this with a Gaussian.\n",
"\n",
"We predict that the dog is moving. This prediction is not perfect. Sometimes our prediction will overshoot, sometimes it will undershoot. We are more likely to undershoot or overshoot by a little than a lot. Perhaps we can also model this with a Gaussian."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Beliefs as Gaussians\n",
"\n",
"We can express our belief in the dog's position with a Gaussian. Say we believe that our dog is at 10 meters, and the variance in that belief is 1 m$^2$, or $\\mathcal{N}(10,\\, 1)$. A plot of the pdf follows:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import filterpy.stats as stats\n",
"stats.plot_gaussian_pdf(mean=10., variance=1., \n",
" xlim=(4, 16), ylim=(0, .5));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot depicts our uncertainty about the dog's position. It represents a fairly inexact belief. While we believe that it is most likely that the dog is at 10 m, any position from 9 m to 11 m or so are quite likely as well. Assume the dog is standing still, and we query the sensor again. This time it returns 10.2 m. Can we use this additional information to improve our estimate?\n",
"\n",
"Intuition suggests we can. Consider: if we read the sensor 500 times and each time it returned a value between 8 and 12, all centered around 10, we should be very confident that the dog is near 10. Of course, a different interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated random draws from a normal distribution. But that seems extremely unlikely - I've never seen a dog do that. Let's look at 500 draws from $\\mathcal N(10, 1)$:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean of readings is 10.021\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from numpy.random import randn\n",
"import matplotlib.pyplot as plt\n",
"\n",
"xs = range(500)\n",
"ys = randn(500)*1. + 10.\n",
"plt.plot(xs, ys)\n",
"print('Mean of readings is {:.3f}'.format(np.mean(ys)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks this way. The computed mean of the readings is almost exactly 10. Assuming the dog is standing still, we say the dog is at position 10 with a variance of 1."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Tracking with Gaussian Probabilities\n",
"\n",
"The discrete Bayes filter used a histogram of probabilities to track the dog. Each bin in the histogram represents a position, and the value is the probability of the dog being in that position.\n",
"\n",
"Tracking was performed with a cycle of predictions and updates. We used the equations \n",
"\n",
"$$\\begin{aligned} \n",
"\\bar {\\mathbf x} &= \\mathbf x \\ast f_{\\mathbf x}(\\bullet)\\, \\, &\\text{Predict} \\\\\n",
"\\mathbf x &= \\mathcal L \\cdot \\bar{\\mathbf x}\\, \\, &\\text{Update}\n",
"\\end{aligned}$$\n",
"\n",
"to compute the new probability distributions. Recall that $\\bar{\\mathbf x}$ is the *prior*, $\\mathcal L$ is the *likelihood* of a measurement given the prior $\\bar{\\mathbf x}$, $f_{\\mathbf x}(\\bullet)$ is the *process model*, and $\\ast$ denotes *convolution*. $\\mathbf x$ is bold to denote that it is a histogram of numbers, or a vector.\n",
"\n",
"This method works, but led to histograms that implied the dog could be in multiple places at once. Also, the computations are very slow for large problems.\n",
"\n",
"Can we replace $\\mathbf x$, the histogram, with a Gaussian $\\mathcal N(x, \\sigma^2)$? Absolutely! We've learned how to express belief as a Gaussian. A Gaussian, which is a single number pair $\\mathcal N(\\mu, \\sigma^2),$ can replace an entire histogram of probabilities:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import kf_book.kf_internal as kf_internal\n",
"kf_internal.gaussian_vs_histogram()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I hope you see the power of this. We can replace hundreds to thousands of numbers with a single pair of numbers: $x = \\mathcal N(\\mu, \\sigma^2)$. \n",
"\n",
"The tails of the Gaussian extend to infinity on both sides, so it incorporates arbitrarily many bars in the histogram. If this represents our belief in the position of the dog in the hallway, this one Gaussian covers the entire hallway (and the entire universe on that axis). We think that it is likely the dog is at 10, but he could be at 8, 14, or, with infinitesimally small probability, at 10$^{80}$. \n",
"\n",
"In this chapter we replace histograms with Gaussians:\n",
"\n",
"$$\\begin{array}{l|l|c}\n",
"\\text{discrete Bayes} & \\text{Gaussian} & \\text{Step}\\\\\n",
"\\hline\n",
"\\bar {\\mathbf x} = \\mathbf x \\ast f(\\mathbf x) & \n",
"\\bar {x}_\\mathcal{N} = x_\\mathcal{N} \\, \\oplus \\, f_{x_\\mathcal{N}}(\\bullet) &\n",
"\\text{Predict} \\\\\n",
"\\mathbf x = \\|\\mathcal L \\bar{\\mathbf x}\\| & x_\\mathcal{N} = L \\, \\otimes \\, \\bar{x}_\\mathcal{N} & \\text{Update} \n",
"\\end{array}$$\n",
"\n",
"where $\\oplus$ and $\\otimes$ is meant to express some unknown operator on Gaussians. I won't do it in the rest of the book, but the subscript indicates that $x_\\mathcal{N}$ is a Gaussian. \n",
"\n",
"The discrete Bayes filter used convolution for the prediction. We showed that it used the *total probabability theorem*, computed as a sum, so maybe we can add the Gaussians. It used multiplications to incorporate the measurement into the prior, so maybe we can multiply the Gaussians. Could it be this easy:\n",
"\n",
"$$\\begin{aligned} \n",
"\\bar x &\\stackrel{?}{=} x + f_x(\\bullet) \\\\\n",
"x &\\stackrel{?}{=} \\mathcal L \\cdot \\bar x\n",
"\\end{aligned}$$\n",
"\n",
"This will only work if the sum and product of two Gaussians is another Gaussian. Otherwise after the first epoch $x$ would not be Gaussian, and this scheme falls apart."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Predictions with Gaussians\n",
"\n",
"We use Newton's equation of motion to compute current position based on the current velocity and previous position:\n",
"\n",
"$$ \\begin{aligned}\\bar{x}_k &= x_{k-1} + v_k \\Delta t \\\\\n",
" &= x_{k-1} + f_x\\end{aligned}$$\n",
"\n",
"I've dropped the notation $f_x(\\bullet)$ in favor of $f_x$ to keep the equations uncluttered. \n",
"\n",
"If the dog is at 10 m, his velocity is 15 m/s, and the epoch is 2 seconds long, we have\n",
"\n",
"$$ \\begin{aligned} f_x &= v\\Delta t = 15\\cdot 2\\\\\n",
"\\bar{x}_k &= 10 + (15\\cdot 2) = 40 \\end{aligned}$$\n",
"\n",
"We are uncertain about his current position and velocity, so this will not do. We need to express the uncertainty with a Gaussian.\n",
"\n",
"Position is easy. We define $x$ as a Gaussian. If we think the dog is at 10 m, and the standard deviation of our uncertainty is 0.2 m, we get $x=\\mathcal N(10, 0.2^2)$.\n",
"\n",
"What about our uncertainty in his movement? We define $f_x$ as a Gaussian. If the dog's velocity is 15 m/s, the epoch is 1 second, and the standard deviation of our uncertainty is 0.7 m/s, we get $f_x = \\mathcal N (15, 0.7^2)$.\n",
"\n",
"The equation for the prior is \n",
"\n",
"$$\\bar x = x + f_x$$\n",
"\n",
"What is the sum of two Gaussians? In the last chapter I proved that:\n",
"\n",
"$$\\begin{gathered}\n",
"\\mu = \\mu_1 + \\mu_2 \\\\\n",
"\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
"\\end{gathered}$$\n",
"\n",
"This is fantastic news; the sum of two Gaussians is another Gaussian! \n",
"\n",
"The math works, but does this make intuitive sense? Think of the physical representation of this abstract equation. We have \n",
"\n",
"$$\\begin{gathered}\n",
"x=\\mathcal N(10, 0.2^2)\\\\\n",
"f_x = \\mathcal N (15, 0.7^2)\n",
"\\end{gathered}$$\n",
"\n",
"If we add these we get:\n",
"\n",
"$$\\begin{aligned}\\bar x &= \\mu_x + \\mu_{f_x} = 10 + 15 &&= 25 \\\\\n",
"\\bar\\sigma^2 &= \\sigma_x^2 + \\sigma_{f_x}^2 = 0.2^2 + 0.7^2 &&= 0.53\\end{aligned}$$\n",
"\n",
"It makes sense that the predicted position is the previous position plus the movement. What about the variance? It is harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information. We don't really know where the dog is moving, so the confidence should get smaller (variance gets larger). $\\sigma_{f_x}^2$ is the amount of uncertainty added to the system due to the imperfect prediction about the movement, and so we would add that to the existing uncertainty. \n",
"\n",
"Let's take advantage of the `namedtuple` class in Python's `collection` module to implement a Gaussian object. We could implement a Gaussian using a tuple, where $\\mathcal N(10, 0.04)$ is implemented in Python as `g = (10., 0.04)`. We would access the mean with `g[0]` and the variance with `g[1]`.\n",
"\n",
"`namedtuple` works the same as a tuple, except you provide it with a type name and field names. It's not important to understand, but I modified the `__repr__` method to display its value using the notation in this chapter. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"from collections import namedtuple\n",
"gaussian = namedtuple('Gaussian', ['mean', 'var'])\n",
"gaussian.__repr__ = lambda s: '𝒩(μ={:.3f}, 𝜎²={:.3f})'.format(s[0], s[1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can create a print a Gaussian with:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"𝒩(μ=3.400, 𝜎²=10.100)\n",
"𝒩(μ=4.500, 𝜎²=0.040)\n"
]
}
],
"source": [
"g1 = gaussian(3.4, 10.1)\n",
"g2 = gaussian(mean=4.5, var=0.2**2)\n",
"print(g1)\n",
"print(g2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can access the mean and variance with either subscripts or field names:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3.4, 3.4, 10.1, 10.1)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g1.mean, g1[0], g1[1], g1.var"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is our implementation of the predict function, where `pos` and `movement` are Gaussian tuples in the form ($\\mu$, $\\sigma^2$):"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def predict(pos, movement):\n",
" return gaussian(pos.mean + movement.mean, pos.var + movement.var)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's test it. What is the prior if the intitial position is the Gaussian $\\mathcal N(10, 0.2^2)$ and the movement is the Gaussian $\\mathcal N (15, 0.7^2)$?"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"𝒩(μ=25.000, 𝜎²=0.530)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pos = gaussian(10., .2**2)\n",
"move = gaussian(15., .7**2)\n",
"predict(pos, move)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The prior states that the dog is at 25 m with a variance of 0.53 m$^2$, which is what we computed by hand."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Updates with Gaussians\n",
"\n",
"The discrete Bayes filter encodes our belief about the position of our dog in a histogram of probabilities. The distribution is discrete and multimodal. It can express strong belief that the dog is in two positions at once, and the positions are discrete.\n",
"\n",
"We are proposing that we replace the histogram with a Gaussian. The discrete Bayes filter used this code to compute the posterior:\n",
"\n",
"\n",
"```python\n",
"def update(likelihood, prior):\n",
" posterior = likelihood * prior\n",
" return normalize(posterior)\n",
"```\n",
"\n",
"which is an implementation of the equation:\n",
"\n",
"$$x = \\| \\mathcal L\\bar x \\|$$\n",
"\n",
"We've just shown that we can represent the prior with a Gaussian. What about the likelihood? The likelihood is the probability of the measurement given the current state. We've learned how to represent measurements as Gaussians. For example, maybe our sensor states that the dog is at 23 m, with a standard deviation of 0.4 meters. Our measurement, expressed as a likelihood, is $z = \\mathcal N (23, 0.16)$.\n",
"\n",
"Both the likelihood and prior are modeled with Gaussians. Can we multiply Gaussians? Is the product of two Gaussians another Gaussian?\n",
"\n",
"Yes to the former, and almost to the latter! In the last chapter I proved that the product of two Gaussians is proportional to another Gausian. \n",
"\n",
"$$\\begin{aligned}\n",
"\\mu &= \\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
"\\sigma^2 &= \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n",
"\\end{aligned}$$\n",
"\n",
"We can immediately infer several things. If we normalize the result, the product is another Gaussian. If one Gaussian is the likelihood, and the second is the prior, then the mean is a scaled sum of the prior and the measurement. The variance is a combination of the variances of the prior and measurement. Finally, the variances are completely unaffected by the values of the mean!\n",
"\n",
"We put this in Bayesian terms like so:\n",
"\n",
"$$\\begin{aligned}\n",
"\\mathcal N(\\mu, \\sigma^2) &= \\| prior \\cdot likelihood \\|\\\\\n",
"&= \\| \\mathcal{N}(\\bar\\mu, \\bar\\sigma^2)\\cdot \\mathcal{N}(\\mu_z, \\sigma_z^2) \\|\\\\\n",
"&= \\mathcal N(\\frac{\\bar\\sigma^2 \\mu_z + \\sigma_z^2 \\bar\\mu}{\\bar\\sigma^2 + \\sigma_z^2},\\frac{\\bar\\sigma^2\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2})\n",
"\\end{aligned}$$\n",
"\n",
"If we implemented that in a function `gaussian_multiply()` we could implement our filter's update step as"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"𝒩(μ=10.800, 𝜎²=0.008)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def gaussian_multiply(g1, g2):\n",
" mean = (g1.var * g2.mean + g2.var * g1.mean) / (g1.var + g2.var)\n",
" variance = (g1.var * g2.var) / (g1.var + g2.var)\n",
" return gaussian(mean, variance)\n",
"\n",
"def update(prior, likelihood):\n",
" posterior = gaussian_multiply(likelihood, prior)\n",
" return posterior\n",
"\n",
"# test the update function\n",
"predicted_pos = gaussian(10., .2**2)\n",
"measured_pos = gaussian(11., .1**2)\n",
"estimated_pos = update(predicted_pos, measured_pos)\n",
"estimated_pos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Perhaps this would be clearer if we used more specific names:\n",
"\n",
"```python\n",
"def update_dog(dog_pos, measurement):\n",
" estimated_pos = gaussian_multiply(measurement, dog_pos)\n",
" return estimated_pos \n",
"```\n",
"\n",
"That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we won't use variable names with 'dog' in them. Also, this form obscures the fact that we are multiplying the likelihood by the prior.\n",
"\n",
"We have the majority of our filter implemented, but I fear this step is still a bit confusing. I've asserted that we can multiply Gaussians and that it correctly performs the update step, but why is this true? Let's take a detour and spend some time multiplying Gaussians."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Understanding Gaussian Multiplication\n",
"\n",
"Let's plot the pdf of $\\mathcal{N}(10,\\, 1) \\times \\mathcal{N}(10,\\, 1)$. Can you determine its shape without looking at the result? What should the new mean be? Will the curve be wider, narrower, or the same as $\\mathcal{N}(10,\\, 1)$?"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"𝒩(μ=10.000, 𝜎²=0.500)\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"z = gaussian(10., 1.) # Gaussian N(10, 1)\n",
"\n",
"product = gaussian_multiply(z, z)\n",
"\n",
"xs = np.arange(5, 15, 0.1)\n",
"ys = [stats.gaussian(x, z.mean, z.var) for x in xs]\n",
"plt.plot(xs, ys, label='$\\mathcal{N}(10,1)$')\n",
"\n",
"ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n",
"plt.plot(xs, ys, label='$\\mathcal{N}(10,1) \\\\times \\mathcal{N}(10,1)$', ls='--')\n",
"plt.legend()\n",
"print(product)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The result of the multiplication is taller and narrow than the original Gaussian but the mean is unchanged. Does this match your intuition?\n",
"\n",
"Think of the Gaussians as two measurements. If I measure twice and get 10 meters each time, I should conclude that the length is close to 10 meters. Thus the mean should be 10. It would make no sense to conclude the length is actually 11, or 9.5. Also, I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
"\n",
"\"Measure twice, cut once\" is a well known saying. Gaussian multiplication is a mathematical model of this physical fact. \n",
"\n",
"I'm unlikely to get the same measurement twice in a row. Now let's plot the pdf of $\\mathcal{N}(10.2,\\, 1) \\times \\mathcal{N}(9.7,\\, 1)$. What do you think the result will be? Think about it, and then look at the graph."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_products(g1, g2): \n",
" plt.figure()\n",
" product = gaussian_multiply(g1, g2)\n",
"\n",
" xs = np.arange(5, 15, 0.1)\n",
" ys = [stats.gaussian(x, g1.mean, g1.var) for x in xs]\n",
" plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(g1.mean, g1.var))\n",
"\n",
" ys = [stats.gaussian(x, g2.mean, g2.var) for x in xs]\n",
" plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(g2.mean, g2.var))\n",
"\n",
" ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n",
" plt.plot(xs, ys, label='product', ls='--')\n",
" plt.legend();\n",
" \n",
"z1 = gaussian(10.2, 1)\n",
"z2 = gaussian(9.7, 1)\n",
" \n",
"plot_products(z1, z2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you ask two people to measure the distance of a table from a wall, and one gets 10.2 meters, and the other got 9.7 meters, your best guess must be the average, 9.95 meters if you trust the skills of both equally.\n",
"\n",
"Recall the g-h filter. We agreed that if I weighed myself on two scales, and the first read 160 lbs while the second read 170 lbs, and both were equally accurate, the best estimate was 165 lbs. Furthermore I should be a bit more confident about 165 lbs vs 160 lbs or 170 lbs because I now have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
"\n",
"This becomes counter-intuitive in more complicated situations, so let's consider it further. Perhaps a more reasonable assumption would be that one person made a mistake, and the true distance is either 10.2 or 9.7, but certainly not 9.95. Surely that is possible. But we know we have noisy measurements, so we have no reason to think one of the measurements has no noise, or that one person made a gross error that allows us to discard their measurement. Given all available information, the best estimate must be 9.95.\n",
"\n",
"In the update step of the Kalman filter we are not combining two measurements, but one measurement and the prior, our estimate before incorporating the measurement. We went through this logic for the g-h filter. It doesn't matter if we are incorporating information from two measurements, or a measurement and a prediction, the math is the same. \n",
"\n",
"Let's look at that. I'll create a fairly inaccurate prior of $\\mathcal N(8.5, 1.5)$ and a more accurate measurement of $\\mathcal N(10.2, 0.5).$ By \"accurate\" I mean the sensor variance is smaller than the prior's variance, not that I somehow know that the dog is closer to 10.2 than 8.5. Next I'll plot the reverse relationship: an accurate prior of $\\mathcal N(8.5, 0.5)$ and a inaccurate measurement of $\\mathcal N(10.2, 1.5)$."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"prior, z = gaussian(8.5, 1.5), gaussian(10.2, 0.5)\n",
"plot_products(prior, z)\n",
"\n",
"prior, z = gaussian(8.5, 0.5), gaussian(10.2, 1.5)\n",
"plot_products(prior, z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The result is a Gaussian that is taller than either input. This makes sense - we have incorporated information, so our variance should have been reduced. And notice how the result is far closer to the the input with the smaller variance. We have more confidence in that value, so it makes sense to weight it more heavily.\n",
"\n",
"It *seems* to work, but is it really correct? There is more to say about this, but I want to get a working filter going so you can it experience it in concrete terms. After that we will revisit Gaussian multiplication and determine why it is correct."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Interactive Example\n",
"\n",
"This interactive code provides sliders to alter the mean and variance of two Gaussians that are being multiplied together. As you move the sliders the plot is redrawn. Place your cursor inside the code cell and press CTRL+Enter to execute it."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ipywidgets import interact\n",
"\n",
"def interactive_gaussian(m1, m2, v1, v2):\n",
" g1 = gaussian(m1, v1)\n",
" g2 = gaussian(m2, v2)\n",
" plot_products(g1, g2)\n",
" \n",
"interact(interactive_gaussian,\n",
" m1=(5, 10., .5), m2=(10, 15, .5), \n",
" v1=(.1, 2, .1), v2=(.1, 2, .1));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## First Kalman Filter\n",
"\n",
"Let's get back to concrete terms and implement a Kalman filter. We've implemented the `update()` and `predict()` functions. We just need to write some boilerplate code to simulate a dog and create the measurements. I've put a `DogSimulation` class in `kf_internal` to avoid getting distracted with that task. \n",
"\n",
"This boilerplate code sets up the problem by definine the means, variances, and generating the simulated dog movement."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"import kf_book.kf_internal as kf_internal\n",
"from kf_book.kf_internal import DogSimulation\n",
"\n",
"np.random.seed(13)\n",
"\n",
"process_var = 1. # variance in the dog's movement\n",
"sensor_var = 2. # variance in the sensor\n",
"\n",
"x = gaussian(0., 20.**2) # dog's position, N(0, 20**2)\n",
"velocity = 1\n",
"dt = 1. # time step in seconds\n",
"process_model = gaussian(velocity*dt, process_var) # displacement to add to x\n",
" \n",
"# simulate dog and get measurements\n",
"dog = DogSimulation(\n",
" x0=x.mean, \n",
" velocity=process_model.mean, \n",
" measurement_var=sensor_var, \n",
" process_var=process_model.var)\n",
"\n",
"# create list of measurements\n",
"zs = [dog.move_and_sense() for _ in range(10)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And here is the Kalman filter."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"PREDICT\t\t\tUPDATE\n",
" x var\t\t z\t x var\n",
" 1.000 401.000\t1.354\t 1.352 1.990\n",
" 2.352 2.990\t1.882\t 2.070 1.198\n",
" 3.070 2.198\t4.341\t 3.736 1.047\n",
" 4.736 2.047\t7.156\t 5.960 1.012\n",
" 6.960 2.012\t6.939\t 6.949 1.003\n",
" 7.949 2.003\t6.844\t 7.396 1.001\n",
" 8.396 2.001\t9.847\t 9.122 1.000\n",
" 10.122 2.000\t12.553\t 11.338 1.000\n",
" 12.338 2.000\t16.273\t 14.305 1.000\n",
" 15.305 2.000\t14.800\t 15.053 1.000\n",
"\n",
"final estimate: 15.053\n",
"actual final position: 14.838\n"
]
}
],
"source": [
"print('PREDICT\\t\\t\\tUPDATE')\n",
"print(' x var\\t\\t z\\t x var')\n",
"\n",
"# perform Kalman filter on measurement z\n",
"for z in zs: \n",
" prior = predict(x, process_model)\n",
" likelihood = gaussian(z, sensor_var)\n",
" x = update(prior, likelihood)\n",
"\n",
" kf_internal.print_gh(prior, x, z)\n",
"\n",
"print()\n",
"print('final estimate: {:10.3f}'.format(x.mean))\n",
"print('actual final position: {:10.3f}'.format(dog.x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is an animation of the filter. Predictions are plotted with a red triangle. After the prediction, the filter receives the next measurement, plotted as a black circle. The filter then forms an estimate part way between the two. "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from kf_book import book_plots as book_plots\n",
"from ipywidgets.widgets import IntSlider\n",
"\n",
"# save output in these lists for plotting\n",
"xs, predictions = [], []\n",
"\n",
"process_model = gaussian(velocity, process_var) \n",
"\n",
"# perform Kalman filter\n",
"x = gaussian(0., 20.**2)\n",
"for z in zs: \n",
" prior = predict(x, process_model)\n",
" likelihood = gaussian(z, sensor_var)\n",
" x = update(prior, likelihood)\n",
"\n",
" # save results\n",
" predictions.append(prior.mean)\n",
" xs.append(x.mean)\n",
"\n",
"def plot_filter(step):\n",
" plt.cla()\n",
" step -= 1\n",
" i = step // 3 + 1\n",
" \n",
" book_plots.plot_predictions(predictions[:i]) \n",
" if step % 3 == 0:\n",
" book_plots.plot_measurements(zs[:i-1])\n",
" book_plots.plot_filter(xs[:i-1])\n",
" elif step % 3 == 1:\n",
" book_plots.plot_measurements(zs[:i])\n",
" book_plots.plot_filter(xs[:i-1])\n",
" else:\n",
" book_plots.plot_measurements(zs[:i])\n",
" book_plots.plot_filter(xs[:i])\n",
"\n",
" plt.xlim(-1, 10)\n",
" plt.ylim(0, 20)\n",
" plt.legend(loc=2);\n",
"interact(plot_filter, step=IntSlider(value=1, min=1, max=len(predictions)*3));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I've plotted the prior (labeled *prediction*), the measurements, and the filter output. For each iteration of the loop we form a prior, take a measurement, form a likelihood from the measurement, and then incorporate the likelihood into the prior. \n",
"\n",
"If you look at the plot you can see that the filter estimate is always between the measurement and prediction. Recall that for the g-h filter we argued that the estimate must always be between the measurement and prior. It makes no sense to choose a value outside of the two values. If I predict I am at 10, but measure that I am at 9, it would be foolish to decide that I must be at 8, or 11."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code Walkthrough\n",
"\n",
"Now let's walk through the code.\n",
"\n",
"```python\n",
"process_var = 1.\n",
"sensor_var = 2.\n",
"```\n",
" \n",
"These are the variances for the process model and sensor. The meaning of sensor variance should be clear - it is how much variance there is in each measurement. The process variance is how much error there is in the process model. We are predicting that at each time step the dog moves forward one meter. Dogs rarely do what we expect, and things like hills or the whiff of a squirrel will change his progress. If this was a robot responding to digital commands the performance would be much better, and perhaps the variance would be $\\sigma^2=.05$. These are not 'magic' numbers; the square root of the variance is the distance error in meters. It is easy to get a Kalman filter working by just plugging in numbers, but if the numbers do not reflect reality the performance of the filter will be poor.\n",
"\n",
"```python\n",
"x = gaussian(0., 20.**2)\n",
"```\n",
"\n",
"This is the dog's initial position expressed as a Gaussian. The position is 0 meters, and the variance to 400 m$^2$, which is a standard deviation of 20 meters. You can think of this as saying \"I believe with 99.7% accuracy the position is 0 plus or minus 60 meters\". This is because with Gaussians ~99.7% of values fall within $\\pm3\\sigma$ of the mean.\n",
"\n",
"```python\n",
"process_model = gaussian(velocity, process_var)\n",
"```\n",
"\n",
"This is the process model - the description of how we think the dog moves. How do I know the velocity? Magic? Consider it a prediction, or perhaps we have a secondary velocity sensor. If this is a robot then this would be a control input to the robot. In subsequent chapters we will learn how to handle situations where you don't have a velocity sensor or input, so please accept this simplification for now.\n",
"\n",
"Next we initialize the simulation and create 10 measurements:\n",
"\n",
"```python\n",
"dog = DogSimulation(\n",
" x0=x.mean, \n",
" velocity=process_model.mean, \n",
" measurement_var=sensor_var, \n",
" process_var=process_model.var)\n",
"\n",
"zs = [dog.move_and_sense() for _ in range(10)]\n",
"```\n",
"\n",
"Now we enter our `predict() ... update()` loop.\n",
"\n",
"```python\n",
"for z in zs:\n",
" prior = predict(x, process_model)\n",
" likelihood = gaussian(z, sensor_var)\n",
" x = update(prior, likelihood)\n",
"```\n",
"\n",
"The first time through the loop `prior` is `(1.0, 401.0)`, as can be seen in the printed table. After the prediction, we believe that we are at 1.0, and the variance is now 401, up from 400. The variance got worse, which is what always happens during the prediction step because it involves a loss of information.\n",
"\n",
"Then we call the update function using `prior` as the current position.\n",
"\n",
"For this I get this as the result: `pos = (1.352, 1.990), z = 1.354`.\n",
"\n",
"What is happening? The dog is actually at 1.0 but the measured position is 1.354 due to sensor noise. That is pretty far from the predicted value of 1. The variance of the prior is 401 m$^2$. A large variance implies that confidence is very low, so the filter estimates the position to be very close to the measurement: 1.352.\n",
"\n",
"Now look at the variance: 1.99 m$^2$. It has dropped tremendously from 401 m$^2$. Why? Well, the RFID has a reasonably small variance of 2.0 m$^2$, so we trust it far more than the prior. However, the previous belief does contain a bit of useful information, so our variance is now slightly smaller than 2.0.\n",
"\n",
"Now the software loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 15.053 vs the actual position of 14.838. The variance has converged to 1.0 m$^2$. \n",
"\n",
"Now look at the plot. The noisy measurements are plotted with black circles, and the filter results are drawn with a solid blue line. Both are quite noisy, but notice how much noisier the measurements are. I plotted the prediction (prior) with red triangles. The estimate always lies between the prior and the measurement. This is your first Kalman filter and it seems to work!\n",
"\n",
"The filtering is implemented in only a few lines of code. Most of the code is either initialization, storing of data, simulating the dog movement, and printing results. The code that performs the filtering is very succinct:\n",
"\n",
"```python\n",
"prior = predict(x, process_model)\n",
"likelihood = gaussian(z, sensor_var)\n",
"x = update(prior, likelihood)\n",
"```\n",
"\n",
"If we didn't use the `predict` and `update` functions the code might be:\n",
"\n",
"```python\n",
"for z in zs:\n",
" # predict\n",
" dx = velocity*dt\n",
" pos = pos + dx\n",
" var = var + process_var\n",
"\n",
" # update\n",
" pos = (var*z + sensor_var*pos) / (var + sensor_var)\n",
" var = (var * sensor_var) / (var + sensor_var)\n",
"``` \n",
"\n",
"Just 5 lines of very simple math implements the entire filter!\n",
"\n",
"In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. The variance is plotted as a lightly shaded yellow area between dotted lines. I've increased the size of the process and sensor variance so they are easier to see on the chart - for a real Kalman filter of course you will not be randomly changing these values."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\t4.4502 2.6507 2.2871 2.1955 2.1712\n",
"\t2.1647 2.1629 2.1625 2.1623 2.1623\n",
"\t2.1623 2.1623 2.1623 2.1623 2.1623\n",
"\t2.1623 2.1623 2.1623 2.1623 2.1623\n",
"\t2.1623 2.1623 2.1623 2.1623 2.1623\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"process_var = 2.\n",
"sensor_var = 4.5\n",
"x = gaussian(0., 400.)\n",
"process_model = gaussian(1., process_var)\n",
"N = 25\n",
"\n",
"dog = DogSimulation(x.mean, process_model.mean, sensor_var, process_var)\n",
"zs = [dog.move_and_sense() for _ in range(N)]\n",
"\n",
"xs, priors = np.zeros((N, 2)), np.zeros((N, 2))\n",
"for i, z in enumerate(zs):\n",
" prior = predict(x, process_model) \n",
" x = update(prior, gaussian(z, sensor_var))\n",
" priors[i] = prior\n",
" \n",
" xs[i] = x\n",
"\n",
"book_plots.plot_measurements(zs)\n",
"book_plots.plot_filter(xs[:, 0], var=priors[:, 1])\n",
"book_plots.plot_predictions(priors[:, 0])\n",
"book_plots.show_legend()\n",
"kf_internal.print_variance(xs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we can see that the variance converges to 2.1623 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $\\sigma=1.47$ meters. Contrast this to the sensor's $\\sigma=2.12$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quickly converges to an estimate with lower variance than the sensor!\n",
"\n",
"This code fully implements a Kalman filter. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the endless pages of math in those books. So long as we worry about *using* the equations rather than *deriving* them the topic is approachable. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent beliefs with Gaussians, and they get better over time because more measurements means we have more data to work with."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise: Modify Variance Values\n",
"\n",
"Modify the values of `process_var` and `sensor_var` and note the effect on the filter and on the variance. Which has a larger effect on the variance convergence? For example, which results in a smaller variance:\n",
"\n",
"```python\n",
"process_var = 40\n",
"sensor_var = 2\n",
"```\n",
" \n",
"or:\n",
"\n",
"```python\n",
"process_var = 2\n",
"sensor_var = 40\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### KF Animation\n",
"\n",
"If you are reading this in a browser you will be able to see an animation of the filter tracking the dog directly below this sentence.\n",
"\n",
"\n",
"The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
"\n",
"When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x = 15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the first noisy measurement."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Kalman Gain\n",
"\n",
"We see that the filter works. Now let's go back to the math to understand what is happening. The posterior $x$ is computed as the likelihood times the prior ($\\mathcal L \\bar x$), where both are Gaussians.\n",
"\n",
"Therefore the mean of the posterior is given by:\n",
"\n",
"$$\n",
"\\mu=\\frac{\\bar\\sigma^2\\, \\mu_z + \\sigma_z^2 \\, \\bar\\mu} {\\bar\\sigma^2 + \\sigma_z^2}\n",
"$$\n",
"\n",
"I use the subscript $z$ to denote the measurement. We can rewrite this as:\n",
"\n",
"$$\\mu = \\left( \\frac{\\bar\\sigma^2}{\\bar\\sigma^2 + \\sigma_z^2}\\right) \\mu_z + \\left(\\frac{\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2}\\right)\\bar\\mu$$\n",
"\n",
"In this form it is easy to see that we are scaling the measurement and the prior by weights: \n",
"\n",
"$$\\mu = W_1 \\mu_z + W_2 \\bar\\mu$$\n",
"\n",
"\n",
"The weights sum to one because the denominator is a normalization term. We introduce a new term, $K=W_1$, giving us:\n",
"\n",
"$$\\begin{aligned}\n",
"\\mu &= K \\mu_z + (1-K) \\bar\\mu\\\\\n",
"&= \\bar\\mu + K(\\mu_z - \\bar\\mu)\n",
"\\end{aligned}$$\n",
"\n",
"where\n",
"\n",
"$$K = \\frac {\\bar\\sigma^2}{\\bar\\sigma^2 + \\sigma_z^2}$$\n",
"\n",
"$K$ is the *Kalman gain*. It's the crux of the Kalman filter. It is a scaling term that chooses a value partway between $\\mu_z$ and $\\bar\\mu$.\n",
"\n",
"Let's work a few examples. If the measurement is nine times more accurate than the prior, then $\\bar\\sigma^2 = 9\\sigma_z^2$, and\n",
"\n",
"$$\\begin{aligned}\n",
"\\mu&=\\frac{9 \\sigma_z^2 \\mu_z + \\sigma_z^2\\, \\bar\\mu} {9 \\sigma_z^2 + \\sigma_\\mathtt{z}^2} \\\\\n",
"&= \\left(\\frac{9}{10}\\right) \\mu_z + \\left(\\frac{1}{10}\\right) \\bar\\mu\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"Hence $K = \\frac 9 {10}$, and to form the posterior we take nine tenths of the measurement and one tenth of the prior. \n",
"\n",
"If the measurement and prior are equally accurate, then $\\bar\\sigma^2 = \\sigma_z^2$ and\n",
"\n",
"$$\\begin{gathered}\n",
"\\mu=\\frac{\\sigma_z^2\\, (\\bar\\mu + \\mu_z)}{2\\sigma_\\mathtt{z}^2} \\\\\n",
"= \\left(\\frac{1}{2}\\right)\\bar\\mu + \\left(\\frac{1}{2}\\right)\\mu_z\n",
"\\end{gathered}$$\n",
"\n",
"which is the average of the two means. It makes intuitive sense to take the average of two equally accurate values.\n",
"\n",
"We can also express the variance in terms of the Kalman gain:\n",
"\n",
"$$\\begin{aligned}\n",
"\\sigma^2 &= \\frac{\\bar\\sigma^2 \\sigma_z^2 } {\\bar\\sigma^2 + \\sigma_z^2} \\\\\n",
"&= K\\sigma_z^2 \\\\\n",
"&= (1-K)\\bar\\sigma^2 \n",
"\\end{aligned}$$\n",
"\n",
"We can understand this by looking at this chart:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import kf_book.book_plots as book_plots\n",
"book_plots.show_residual_chart()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Kalman gain $K$ is a scale factor that chooses a value along the residual. This leads to an alternative but equivalent implementation for `update()` and `predict()`:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def update(prior, measurement):\n",
" x, P = prior # mean and variance of prior\n",
" z, R = measurement # mean and variance of measurement\n",
" \n",
" y = z - x # residual\n",
" K = P / (P + R) # Kalman gain\n",
"\n",
" x = x + K*y # posterior\n",
" P = (1 - K) * P # posterior variance\n",
" return gaussian(x, P)\n",
"\n",
"def predict(posterior, movement):\n",
" x, P = posterior # mean and variance of posterior\n",
" dx, Q = movement # mean and variance of movement\n",
" x = x + dx\n",
" P = P + Q\n",
" return gaussian(x, P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Why have I written it in this form, and why have I chosen these terrible variable names? A few related reasons. A majority of books and papers present the Kalman filter in this form. My derivation of the filter from Bayesian principles is not unknown, but it is not used nearly as often. Alternative derivations naturally lead to this form of the equations. Also, the equations for the multivariate Kalman filter look almost exactly like these equations. So, you need to learn and understand them. \n",
"\n",
"Where do the names `z`, `P`, `Q`, and `R` come from? You will see them used in the rest of this book. In the literature $R$ is nearly universally used for the measurement noise, $Q$ for the process noise and $P$ for the variance of the state. Using $z$ for the measurement is common, albeit not universal. Almost every book and paper you read will use these variable names. Get used to them.\n",
"\n",
"This is also a powerful way to think about filtering. This is the way we reasoned about the g-h filter. It emphasizes taking the residual $y = \\mu_z - \\bar\\mu$, finding the Kalman gain as a ratio of our uncertainty in the prior and measurement $K = P/(P+R)$, and computing the posterior by adding $Ky$ to the prior. \n",
"\n",
"The Bayesian aspect is obscured in this form, as is the fact that we are multiplying the likelihood by the prior. Both viewpoints are equivalent because the math is identical. I chose the Bayesian approach because I think it give a much more intuitive yet deep understanding of the probabilistic reasoning. This alternative form using $K$ gives a deep understanding of what is known as the *orthogonal projection* approach. Dr. Kalman used that derivation, not Bayesian reasoning, when he invented this filter. You will understand more about this in the next few chapters."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Full Description of the Algorithm\n",
"\n",
"Recall the diagram we used for the g-h filter:\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We've been doing the same thing in this chapter. The Kalman filter makes a prediction, takes a measurement, and then forms a new estimate somewhere between the two.\n",
"\n",
"**This is extremely important to understand**: Every filter in this book implements the same algorithm, just with different mathematical details. The math can become challenging in later chapters, but the idea is easy to understand.\n",
"\n",
"It is important to see past the details of the equations of a specific filter and understand *what* the equations are calculating and *why*. There are a tremendous number of filters. They all use different math to implement the same algorithm. The choice of math affects the quality of results and what problems can be represented, but not the underlying ideas.\n",
"\n",
"Here is the generic 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. Compute scaling factor based on whether the measurement\n",
" or prediction is more accurate\n",
" 4. set state between the prediction and measurement based \n",
" on scaling factor\n",
" 5. update belief in the state based on how certain we are \n",
" in the measurement\n",
"\n",
"You will be hard pressed to find a Bayesian filter algorithm that does not fit into this form. Some filters will not include some aspects, such as error in the prediction, and others will have very complicated methods of computation, but this is what they all do. \n",
"\n",
"The equations for the univariate Kalman filter are:\n",
"\n",
"Predict\n",
"\n",
"$\\begin{array}{|l|l|l|}\n",
"\\hline\n",
"\\text{Equation} & \\text{Implementation} & \\text{Kalman Form}\\\\\n",
"\\hline\n",
" \\bar x = x + f_x & \\bar\\mu = \\mu + \\mu_{f_x} & \\bar x = x + dx\\\\\n",
"& \\bar\\sigma^2 = \\sigma^2 + \\sigma_{f_x}^2 & \\bar P = P + Q\\\\\n",
"\\hline\n",
"\\end{array}$\n",
"\n",
"\n",
"Update\n",
"\n",
"$\\begin{array}{|l|l|l|}\n",
"\\hline\n",
"\\text{Equation} & \\text{Implementation}& \\text{Kalman Form}\\\\\n",
"\\hline\n",
" x = \\| \\mathcal L\\bar x\\| & y = z - \\bar\\mu & y = z - \\bar x\\\\\n",
" & K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2} & K = \\frac {\\bar P}{\\bar P+R}\\\\\n",
" & \\mu = \\bar \\mu + Ky & x = \\bar x + Ky\\\\\n",
" & \\sigma^2 = \\frac {\\bar\\sigma^2 \\sigma_z^2} {\\bar\\sigma^2 + \\sigma_z^2} & P = (1-K)\\bar P\\\\\n",
"\\hline\n",
"\\end{array}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparison with g-h and discrete Bayes Filters\n",
"\n",
"Now is a good time to understand the differences between these three filters in terms of how we model errors. For the g-h filter we modeled our measurements as shown in this graph:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"scrolled": true
},
"outputs": [
{
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"book_plots.plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sensor A returned a measurement of 160, and sensor B returned 170. The bars are [*error bars*](https://en.wikipedia.org/wiki/Error_bar) - they illustrate the possible range of error for the measurement. Hence, the actual value that A is measuring can be between 157 to 163, and B is measuring a value between 161 to 179.\n",
"\n",
"I did not define it at the time, but this is a [*uniform distribution*](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)). A uniform distribution assigns equal probability to any event in the range. According to this model it is equally likely for sensor A to read 157, 160, or 163. Any value outside these ranges have 0 probability. \n",
"\n",
"We can model this situation with Gaussians. I'll use $\\mathcal{N}(160, 3^2)$ for sensor A, and $\\mathcal{N}(170, 9^2)$ for sensor B. I've plotted these below with the uniform distribution error bars for comparison."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xs = np.arange(145, 190, 0.1)\n",
"ys = [stats.gaussian(x, 160, 3**2) for x in xs]\n",
"plt.plot(xs, ys, label='A', color='g')\n",
"\n",
"ys = [stats.gaussian(x, 170, 9**2) for x in xs]\n",
"plt.plot(xs, ys, label='B', color='b')\n",
"plt.legend();\n",
"plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='g', capthick=2, capsize=10) \n",
"plt.errorbar(170, [0.015], xerr=[9], fmt='o', color='b', capthick=2, capsize=10);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using a uniform or Gaussian distribution is a modeling choice. Neither exactly describes reality. In most cases the Gaussian distribution is more realistic. Most sensors are more likely to return readings near the value being measured, and unlikely to return a reading far from that value. The Gaussian models this tendency. In contrast the uniform distribution assumes that any measurement within a range is equally likely.\n",
"\n",
"Now let's see the *discrete distribution* used in the discrete Bayes filter. This model divides the range of possible values into discrete ranges and assigns a probability to each bucket. This assignment can be entirely arbitrary so long as the probabilities sum to one.\n",
"\n",
"Let's plot the data for one sensor using a uniform distribution, a Gaussian distribution, and a discrete distribution."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from random import random\n",
"xs = np.arange(145, 190, 0.1)\n",
"ys = [stats.gaussian(x, 160, 3**2) for x in xs]\n",
"belief = np.array([random() for _ in range(40)])\n",
"belief = belief / sum(belief)\n",
"\n",
"x = np.linspace(155, 165, len(belief))\n",
"plt.gca().bar(x, belief, width=0.2)\n",
"plt.plot(xs, ys, label='A', color='g')\n",
"plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='k', capthick=2, capsize=10) \n",
"plt.xlim(150, 170);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I used random numbers to form the discrete distribution to illustrate that it can model any arbitrary probability distribution. This provides it with enormous power. With enough discrete buckets we can model the error characteristics of any sensor no matter how complicated. But with this power comes mathematical intractability. Multiplying or adding Gaussians takes two lines of math, and the result is another Gaussian. This regularity allows us to perform powerful analysis on the performance and behavior of our filters. Multiplying or adding a discrete distribution requires looping over the data, and we have no easy way to characterize the result. Analyzing the performance characteristics of a filter based on a discrete distribution is extremely difficult to impossible.\n",
"\n",
"There is no 'correct' choice here. Later in the book we will introduce the *particle filter* which uses a discrete distribution. It is an extremely powerful technique because it can handle arbitrarily complex situations. This comes at the cost of slow performance, and resistance to analytical analysis. \n",
"\n",
"For now we will ignore these matters and return to using Gaussians for the next several chapters. As we progress you will learn the strengths and limitations of using Gaussians in our mathematical models."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction to Designing a Filter\n",
"\n",
"So far we have developed filters for a position sensor. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. Following chapters will fill in the gaps. Still, let's get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 0.13 volts.\n",
"\n",
"We can simulate the temperature sensor measurement with this function:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"def volt(voltage, std):\n",
" return voltage + (randn() * std)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` method, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
"\n",
"As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `process_var = .05**2`. This is the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For a real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the later chapters.\n",
"\n",
"Let's see what happens. "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ETy855sGHVq5cqbS0NG3dulXLly9XXFycbDabtm/frpSUFIWGhqpTp05auHChli1bpvr16yszM1MTJ07U2rVrNXfuXHMm5QMHDqh+/fo6cOCABg8eLKlonFbjxo01Z84cff/996pTp462bNmie+65R7m5uXr77bdVr149sz6GYaigoMCljuHh4T4d7xUcHGz+AyqDDMETyBGsIkOwigzBKk9nyB8/OwD+ym/mhEhJSTGXg7rU/v37zZ4P27Zt08SJE/XVV1+psLBQnTp10pQpUzRw4EBz/4yMDDVp0kQjR47UwoULXc61fPlyPf3009q6davCw8PVs2dPPfPMM6WWgmJcFwAAAAB38NkBcJ/fNEL4Gy4kAAAAANxR0c8OeXl5OnHihDeqBnhFeHi4YmJi3OpdFDBzQkA6c+aMDMOQzWZTnTp1fF0dBCAyBE8gR7CKDMEqMgSrfJmhvLw8ZWVlKTExkSFFqBYMw9DFixd1+PBhxcbGKiIi4rL70wgRQDIyMliOCpaQIXgCOYJVZAhWkSFY5csMnThxggYIVCs2m02RkZFKSEgwG9guh7EFAAAAAOBFNECgOgoNDZXT6bzifvSECCAJCQkuy4sCFUWG4AnkCFaRIVhFhmAVGQJ8h0aIABIXF+frKiDAkSF4AjmCVWQIVpEhWEWGAN9hOAYAAAAAAPAKGiEAAAAAAJYtXLhQNputzH+PPfaYJCkpKUl33323ecyePXtks9m0aNEic9u6des0ffp0nT171uv3AVXPI8MxDh48qPT0dHXp0kUxMTGeOCUAAAAAIAAtWLBArVq1ctnWsGFDSdJHH310xWVR161bpyeffFJ33323ateuXWX1hG9UuBFi6tSpys3N1d/+9jdJ0ueff65BgwapoKBAdevW1VdffaW2bdt6vKKQtm3bpoKCAoWFhaldu3a+rg4CEBmCJ5AjWEWGYBUZglVkqGq1a9dOnTt3LrPsV7/6lZdr87MLFy4oMjLSZ7ePIhUejrFkyRK1adPG/H3q1Knq0KGDli5dquTkZP3lL3/xaAXxM4fDIafTKYfD4euqIECRIXgCOYJVZAhWkSFYRYZ859LhGJeaOnWqJk2aJElq1KiROZxj3fE8yT4AACAASURBVLp15j7vvvuuunXrpsjISNWqVUv9+/dXWlqay3nuvPNO1a1bV2lpaerTp49q1aqlvn37Vs2dQoVUuCfE4cOH1axZM0lSTk6ONm3apP/85z/q16+f8vLy9Oijj3q8kihSo0YNBQcHKzQ01NdVQYAiQ/AEb+XIbrdr2bJlWrBggfbv36+oqCj17dtX9913nxo3blylt42qxbUIVpEhWOWvGbpQYPd1FRQZZn3EvsPhkN3uel9CQtw77/33369Tp05p9uzZWrFihWJjYyXJ7G0/Y8YMTZ8+XXfffbcef/xx5efna+bMmbr++uu1efNmtWzZ0jxXXl6eBg8erLFjx2rSpEk0OvmJCifMMAw5nU5J0vr16xUcHKwbbrhBUtF6u9nZ2Z6tIUwln1BAZZAheII3cpSVlaWBAwdq06ZNLts3b96sF154QW+++abuuuuuKq8HqgbXIlhFhmCVv2aozROf+roKynj2Zsvn6NatW6lthYWFbjVEJCUlqVGjRpKKhm4kJSX9XLeMDM2YMUOPPPKIXnrpJXN7nz591KxZM82YMUPvvPOOuT0/P19PPfUU7xn8TIUbIVJTU/Xxxx/rpptu0nvvvaeuXbsqIiJCknT06FFFR0d7vJIAgF8Ou92uQYMGuTRA1KhRQ3l5eZKkgoICjRw5UvHx8erTp4+vqgkAAMrxz3/+U61bt3bZ5m5PiMtZtWqVHA6HRowY4dLTIiIiQj169NCaNWtKHfN///d/lm8XnlXhJNx3330aN26c/vnPf+r06dOaP3++WbZ+/XqX+SIAAKiojz76SN99950kKTExUfPmzVPfvn117NgxTZkyRQsWLJBhGJo2bRqNEACAamX7jH6+roJHtG7dutyJKa04fvy4pPIntwwLC3P5vXbt2oqKivJ4PWBNhRshxo4dq+joaH3zzTfq2rWr7rzzTrPs4sWLGjlypEcrCAD4ZXnrrbfMn9944w3161f0hiwhIUFvvvmmvvvuO6Wnp+vbb7/V7t271bx5c19VFQAAj/LEfAzVWf369SVJy5YtU2JiYqlym8122d/hHyqV8mHDhmnYsGGltr/xxhuWK4TyHTp0SA6HQ8HBwS5jowB3kSF4QlXn6MCBA5Kk4OBg9e/f36UsKChIAwcOVHp6uqSisaE0QgQerkWwigzBKjLk38LDwyUVfcldUv/+/RUcHKy9e/dq8ODBvqgaPKDCjRDBwcH69ttv1bVr11Jl33//vbp27cqso1UkJydHhYWFCg0N5WKJSiFD8ISqzlFxt0mHw6HMzEylpKS4lO/du9f8uWbNmh6/fVQ9rkWwigzBKjLk39q3by9Jevnll3XnnXcqNDRUrVq1UmpqqqZNm6aJEydqz5496tevn+rWratjx47pu+++U506dfTEE0/4uPa4kqCKHmAYRrllxatmAABQWSV7P0ycONFl4qlvvvlGS5culVTUJfOqq67yev0AAEDVuummmzRhwgQtXbpU119/vbp06aItW7ZIkh5//HEtXrxY27dv14gRI9SvXz9NnDhRBw8eVI8ePXxcc7jDZlyuVaEMQUFB2rhxo7p06VKqbM6cOZoyZYpycnI8VkFfcTqdOnfunMu2WrVqKSiowu02HnPhwgUZhiGbzabIyEif1QOBiwzBE6o6R8eOHVPTpk3NLpipqakaNGiQMjIytGLFCrPBe+rUqXrqqac8fvuoelyLYBUZglWezlBFPjscPHjQXIISqG7cybdbjRCzZs3SrFmzJBWN1Y2PjzfH6RS7ePGisrKydNttt2nx4sUWqu0f/LERAgB+KZYsWaJhw4a59IIo6aabbtInn3xS6rUIAABfoBECKOJOvt2aEyIuLk5t27aVVDQJWNOmTVW3bl2XfcLDw9W+fXs9/PDDlawuAABFbr31Vq1evVrTpk3Tl19+aW5v0KCBxo4dq4kTJ9IAAQAAEIAqPByjd+/eev3119WqVauqqpNfoCcEAPiHAwcOKCMjQ1FRUerQoUOpNcABAPA1ekIARTzWE6Kk1atXV7pCsCY3N9ccu1Y8ezxQEWQInuDtHCUnJys5ObnKbwfew7UIVpEhWEWGAN9xqxEiMzOzQidt3LhxpSqDy9uzZ4+5lFDHjh19XR0EIDIETyBHsIoMwSoyBKvIEOA7bjVCpKSkyGazuX1Sh8NR6QoBAAAAAIDqya1GiPnz51eoEQJVIzY2Vg6HQ8HBwb6uCgIUGYInkCNYRYZgFRmCVWQI8J0KT0z5S8HElAAAAADcwcSUQJEqmZiypLy8PJ06dUrR0dGqUaOGlVMBAOA3Tp06pYyMDEVERKh58+Z8UwYAAOAhlfpa/5tvvlGPHj1Uq1YtJSUlqVatWurZs6e+/fZbT9cPAACv2bZtm373u98pLi5OV111lVq3bq0mTZro2WefVUFBga+rBwAAEPAq3AixYcMG3Xjjjdq9e7fuvfdezZgxQ/fcc4927dqlG2+8URs3bqyKegIAUKXWrl2ra665Rh988IHsdru5/eDBg5o0aZJuvvlm5efn+7CGAAD4t4ULF8pms8lms2nNmjWlyg3DULNmzWSz2dSrVy+v1w8/O3LkiKZPn64tW7Z4/bYrPBzjiSeeUIcOHbR69WqXNXWff/559e7dW0888YQ+/fRTj1YSRXbu3GkuJdSqVStfVwcBiAzBE6pjjs6ePatbb71VFy5ckCTFxcVpwIABOnLkiD777DMZhqHPP/9c06dP1zPPPOPj2ga+6pgheBcZglXVLUNOp1MZGRnKy8tTo0aNVKtWLZ/Wp1atWpo3b16phoa1a9dq7969Pq8fihohnnzySaWkpKhTp05eve1K9YSYMGGCSwOEJEVFRWn8+PEMyahC+fn55j+gMsgQPKE65mjRokXKycmRJP3617/W/v37tWDBAn366af66quvFBJS1GY/Z84cs6EClVcdMwTvIkOwqrpkqKCgQC+++KKaNWum1NRUtW3bVrGxsbrrrru0a9cun9Xr9ttv15IlS3T27FmX7fPmzdO1116rxo0b+6hmnnHx4kWxvkPlVbgRwuFwKDw8vMyyGjVqyOFwWK4UyhYSEmL+AyqDDMETqmOOPv74Y/PnmTNnKjIy0vz9+uuv1+233y5JOn36tL755huv16+6qY4ZgneRIVhVHTKUn5+vW265RY899pj279/vsn3RokXq2rWrz74gvuOOOyRJ7777rrntzJkzWrJkicaMGVNq/4KCAv3lL39Rq1atFB4ertjYWI0ePVonTpxw2W/x4sXq27evEhISFBERodatW2vixInKzc112W/fvn0aNmyYGjZsqPDwcDVo0EA33XSTy9ADm82m6dOnl6pLSkqKRo0aZf5ePMTkv//9r8aMGaPY2FhFRkaaDVi7d+/W8OHDFRcXp/DwcLVu3VqvvfaayznXrFkjm82mf/3rX/rzn/+shIQE1axZU4MGDdLx48d17tw53Xvvvapfv77q16+v0aNH6/z58y7nMAxDs2fPVqdOnRQREaHo6Gjddttt2rdvn8t+vXr1Urt27bRp0yb16NFDkZGRatq0qZ599lk5nU6zPl26dJEkjR492hxCU/x4uPP4WVHhZ13Hjh31+uuva9CgQaXK5s6dq44dO3qkYiitbdu2vq4CAhwZgidUxxyVXFatuFvuvn371KBBA0VFRal169Zm+aXf6qDiqmOG4F1kCFZVhwxNnz7dZRh8r169lJCQoFWrVunUqVM6e/ashg4dqn379rk0rntD7dq1ddttt2n+/Pm67777JBU1SAQFBen222/Xyy+/bO7rdDo1ePBgff3115owYYK6d++uAwcOaNq0aerVq5c2b96siIgISUUf+AcMGKBHHnlEUVFR2rlzp5577jl99913+vLLL81zDhgwQA6HQzNnzlTjxo2VnZ2tb775RqdPn670fRozZoxuvvlmvf3228rNzVVoaKi2b9+u7t27q3HjxnrxxRcVHx+vTz/9VA899JCys7M1bdo0l3NMnjxZvXv31sKFC5WRkaHHHntMd9xxh0JCQtSxY0e9++67+uGHHzR58mTVqlVLf//7381j77vvPi1cuFAPPfSQnnvuOZ08eVIzZsxQ9+7dlZaWpgYNGpj7Hjt2TL///e/16KOPatq0aVq6dKkmTZqkhg0basSIEbrqqqu0YMECjR49WlOnTtXNN98sSUpKSqqyx8+FUUHLly83bDab0alTJ+OFF14w3nnnHeOFF14wrrrqKiMoKMhYsWJFRU/plxwOh3H69GmXfw6Hw9fVAgBUgWHDhhmSDEnGe++9Z4wcOdKQZAwZMsQwDMO4/vrrzfKNGzf6uLYAAH9Tkc8OmZmZlm/v/PnzRp06dQxJRkhIiLFmzRqz7OzZs0aPHj3M16158+ZZvj13LViwwJBkbNq0yVi9erUhydi2bZthGIbRpUsXY9SoUYZhGEbbtm2Nnj17GoZhGO+++64hyViyZInLuTZt2mRIMmbPnl3mbTmdTqOwsNBYu3atIclIS0szDMMwsrOzDUnGyy+/fNm6SjKmTZtWantycrIxcuTIUvdpxIgRpfbt16+fkZSUZJw5c8Zl+4MPPmjUqFHDOHnypGEYhvlYDBo0yGW/Rx55xJBkPPTQQy7bhwwZYtSrV8/8/dtvvzUkGS+++KLLfgcPHjQiIiKMCRMmmNt69uxZ5vuVNm3aGP369TN/L358FyxY4LKfu49fedzJd4WHY9xyyy1atGiRsrKyNH78eN15550aP368srKytGjRojJ7SAAA4M/uuusu8+cRI0borbfe0h/+cLvmzv27Jk2apHXr1kmSWrZsaXZfBADAV9atW6czZ85IKhr60LNnT7OsVq1amjlzpvn78uXLvV4/SerZs6dSU1M1f/58bd26VZs2bSpzKMbHH3+sunXratCgQbLb7ea/Tp06KT4+3mWVjX379mn48OGKj49XcHCwQkNDzfu+Y8cOSVK9evWUmpqq559/Xi+99JJ++OEHcxiCFbfeeqvL73l5efriiy80dOhQRUZGutR9wIABysvL04YNG1yOGThwoMvvxT0ti3silNx+8uRJc0jGxx9/LJvNpjvvvNPlduLj49WxY8dSK5HEx8era9euLts6dOigAwcOXPF+VtXjV1KFGyG2bdum4cOH69ChQ9q+fbu+/vprbd++XZmZmebYHwAAAkn//v11zTXXSJLs9gJJ0qJF7+u665roueeeNfebPn26bDabT+oIAECx4gYIqeyhJe3atStzX2+y2WwaPXq0Fi1apDlz5qhFixbq0aNHqf2OHz+u06dPKywsTKGhoS7/jh07puzsbEnS+fPn1aNHD23cuFF/+ctftGbNGm3atEn//ve/JRVNFll8u1988YX69eunmTNn6qqrrlJsbKweeughl+GXFZWQkODye05Ojux2u1555ZVS9R4wYIAkmXUvVq9ePZffw8LCLrs9Ly/PfIwMw1CDBg1K3daGDRtK3U5MTEyp+oeHh5uP0eVU1eNXUoXnhOjQoYM6d+6s0aNH64477qgWS9oEimPHjsnhcCg4OFjx8fG+rg4CEBmCJ1THHAUFBWn58uUaOrSvzp37UdnZUt26hiIjHUpOlg4csOm5557TsGHDfF3VaqE6ZgjeFUgZcjqdOnv2rGrUqKEaNWr4ujr4/wIpQ2VJTEw0f/7ss8/05z//2aX8v//9b5n7etuoUaP0xBNPaM6cOXr66afL3Kd+/fqKiYnRqlWryiwvXs7zyy+/1JEjR7RmzRqXnh9lzVOQnJysefPmSZJ++uknvf/++5o+fboKCgo0Z84cSUUfystaHaV4taxLXfolRHR0tIKDg3XXXXdp3LhxZR7TpEmTMrdXVP369WWz2fT111+XuUhEeQtHVJY7j58VFe4J8dprrykoKEjjxo1Tw4YNNXz4cH322WeWK4IrO378uI4eParjx4/7uioIUGQInlCdcuRwOLR161ZJUoMGIVqzZq6effZJ3XLL1WrSJE6NGzfSPff8n9avX65vvvmGlTE8pDplCL4RCBk6fPiwHn30UcXFxSk6OlqRkZHq1auX/v3vf7O0nx8IhAxdzrXXXqumTZtKkr744gvNmDFDFy5ckGEYWrdunR5++GFz35JDDr0tMTFR48eP16BBgzRy5Mgy9xk4cKBycnLkcDjUuXPnUv9atmwp6edGgEs/cM+dO/eydWjRooWmTp2q9u3b63//+5+5PSUlRT/++KPLvl9++WWpVSnKExkZqd69e+uHH34wv6i/9F9ZPRIqY+DAgTIMQ4cPHy7zdtq3b1/hcxY/jlfqHVHe42dFhXtCjB07VmPHjtWOHTu0YMECvfPOO3rvvfeUlJSkUaNGaeTIkUpNTfVI5QAAqCqnT5/W8OHD9fXXX+vbb5eqXbtohYWF6uabb3YZm5mZeUy9e9+nffsO67vvvtP3338fkN+aAfCeH374QX379nXpIm0YhtauXau1a9fq/vvv1+zZsxnehUoLCgrS448/rtGjR0uSpk2bpueee0516tTR0aNHzf2uueYa9e3b11fVlCQ9++yzly0fNmyY3nnnHQ0YMEAPP/ywunbtqtDQUB06dEirV6/W4MGDNXToUHXv3l3R0dG6//77NW3aNIWGhuqdd95RWlqay/l+/PFHPfjgg/rtb3+r5s2bKywsTF9++aV+/PFHTZw40dzvrrvu0uOPP64nnnhCPXv21Pbt2/Xqq6+qTp06bt+3WbNm6frrr1ePHj00duxYpaSk6Ny5c9qzZ48++ugjlxU7rLjuuut07733avTo0dq8ebNuuOEGRUVF6ejRo1q3bp3at2+vsWPHVuicqampioiI0DvvvKPWrVurZs2aatiwobKzs916/Kyo9MK4rVu31syZM/Xss89q5cqVeuuttzRz5kz99a9/ld1u90jl4KpJkyYyDIMXLFQaGYInVJccPf3001q5cqUk6bbb7ta2bYvLXC8+IaG+kpIaaN++w8rPz1dGRgaNEBZVlwzBd/w5Q+fPn9fAgQPNBojw8HBde+21yszM1L59+yRJc+bMUbt27crtwo2q588ZcteoUaOUmZlpLgN54cIFXbhwwSzv2LGjli1bpqCgCnd+96rg4GCtWLFCs2bN0ttvv61nnnlGISEhSkpKUs+ePc1v+WNiYvTJJ5/o0Ucf1Z133qmoqCgNHjxYixcv1lVXXWWeLz4+XqmpqZo9e7YOHjwom82mpk2b6sUXX9Qf//hHc7/x48fr7NmzWrhwoV544QV17dpV77//vgYPHux23du0aaP//e9/euqppzR16lRlZWWpbt26at68uTkvhKfMnTtX3bp109y5czV79mw5nU41bNhQ1113XalJKN0RGRmp+fPn68knn1Tfvn1VWFioadOm6YEHHnDr8bPCZnigP9iuXbu0YMECLVy4UCdOnJDD4fBE3XzK6XSWmnijVq1afv8kBgC458KFk+rR43odOHBEH374nHr16lzuvseP5+jee5/W3/8+TcnJvSUF7ptWAFXrjTfe0H333Sep6FvoZcuWKT4+XoZhaMGCBfrDH/4gqagr+J49exQcHOzL6sJDKvLZ4eDBg2rUqJHHbnvz5s167bXX9OWXXyovL0/NmzfXmDFjNHz4cOYhgde5k+9KN0KcO3dOixcv1oIFC7RhwwaFh4dr6NChGj16tH79619XqsL+hEYIAKjOzkjar4MHD8tud6hJk4pM2hUnyXNvHgFUL/369TMnBdy8ebOuvvrqcss3btxYqW8w4X982QgB+BN38l3hT9SrV6/WiBEjlJCQoHvvvVd2u12vvfaajh49qnfeeadaNEAAAKqXvLw8TZ069f+/QTwmaY8khxo1iq9gA4QkZUk6KenKkzkB+OUpHoZhs9lcuogXK14OWCp/Fn4AqM4qPCfETTfdpLi4ON1///0aM2aM2rRpUxX1Qhny8/PNsWueXoYFvwxkCJ4QaDk6cuSIhg4dqu+++05bt27U0qV/tdyrzencr6eeeknvvvuhNm7cWKFJrBB4GYL/8ecMxcXFSSqaiHLjxo3q1q2bS/m6devMn2NjY71aN/zMnzMEVHcVboRYunSpBg4cyPg1H9i5c6cKCwsVGhqqjh07+ro6CEBkCJ7gzzkqLCxUdna2GjRoYDY05Obm6qeffpIkff75OqWn71P79s0s3c6f/zxLL7zwtiRpxIgRWrp0KcP1KsCfM4TA4M8Z+t3vfqdVq1ZJKlpVbtmyZUpOTpbD4dBrr72m1atXS5KaNWtWZk8JeIc/Zwio7ir8jmnw4ME0QAAAvK6wsFDz58/XzJkzNX/+/FLlw4YNU1hYmBo2bKgTJ06Y25s3b6jFi59R06aJWr9+nuUGCEl64IHbFB1dW0FBQbr22msDenZ1AJ41bNgwJScnS5K2bNmi1NRUde3aVY0aNdLDDz9s7jdhwgQaLwH8IlV6iU54X3R0tOx2e5lLyAHuIEPwBF/lKCgoSHfffbcMw1DXrp01ZszvJNnNf5GRP8+zfOLERjVo0PT/lznUt28X7djxocLCQj1SlyZNEvXee3+VzSb16fN/YrWMiuFaBKv8OUMRERH65JNP1KdPHx09elQOh0ObNm1y2efRRx/V3Xff7aMaQvLvDAHVHc+6ANK4cWNfVwEBjgzBEyqTI6fTqczMTOXl5alRo0aKioqq4BmyFBx8VPXq1VZOzhllZx+VtMtljzZtEtS9ewfVr19XoaGFkvJdyj3VAFGsb9/icd5HJEVKYl4Id3EtglX+nqG2bdsqLS1Nr776qubPn69Dhw4pNDRUffr00UMPPaR+/fr5uoq/eL7OkMPhoHc5qp3CwkK3enhVeonO6o4lOlHdZGZm6qOPPtLJkycVHx+vIUOGMCEWqlxhYaFee+01vfrqq9q7d68kqUaNGho2bJimTJmiZs3cGRphl7RNkkPvvrtKYWGhSkior+7d/WkMb7Ck1srIOKoGDRooIiLC1xUC4EcKCwsVEhLC0C0POnPmjN59912lp6crJCRE1113nQYPHqzQUM82OLurIp8d8vLylJWVpcTERBoiUC0YhqGLFy8qOztbsbGxV3wfRCNEOWiEQHVx9uxZ3X///Vq8eLGcTqe5PSwsTPfdd59eeOEFhYWF+bCGqK7y8/M1ZMgQc4K2S9WpU0effvqpy3J1JW3btk1paWm6447rFRSUXZVV9Yj//GeTfv/7SRoyZIjmz5/Phw0AqAKGYejvf/+7pkyZotzcXJeyxMREzZ8/X3379vV6vSr62SEvL0/Z2dnioxiqi/DwcMXExLjVsOYXjRDnzp3TU089pS1btuiHH35Qdna2pk2bpunTp5fat7CwUK+88ooWLFigPXv2KDw8XG3atNELL7yg7t27u32bx48fV5s2bXTy5El98MEHuu2221zKaYRAdXDx4kX17t1bGzduLHefIUOGaMmSJdUm2+fOndPKlSuVlZWlmJgY9e/fX9HR0b6u1i/SpEmT9Oyzz5q/33DDDUpISNCqVat05swZSVJ8fLz27t2ryMjIUsf3799fn376qTp3bqMPPnhWKSkNvVb3isrJOa2UlFt0/vwFSdJbb72lESNG+LhWAFD9vPTSS3r00UfLLQ8NDdV///tf9erVy3uVEp8dgIrwi2dFTk6O3njjDfNbs/I4HA4NHTpUM2bM0B133KGVK1fqnXfeUf/+/Uu1hF7JuHHjVKNGDatV96rdu3drx44d2r17t6+rggDx6quvmg0QderU0YMPPqhXXnlFo0ePNtfEXrZsmZYsWeLLanqE3W7XlClTlJiYqNtvv11//OMfNXz4cCUmJuqRRx5Rfn7+lU8Ct7hzLbpw4YLmzJkjSQoJCdGXX36ptWvX6r333tOBAwd03XXXSZKOHTumxYsXlzp+06ZN+vTTTyVJJ06cUnx8TBXcE8+Jiamrf/xjiiRp8OD+Gjx4sFl28OBBvfnmm/r444914MABX1XRr/B6BqvI0C/TiRMnNHnyZPP3MWPGaM2aNfroo4/Uu3dvSUVfWD744INX7GFAhgDf8YuJKZOTk3Xq1CnZbDZlZ2frzTffLHO/V155RStXrtT69evVrVs3c/vNN99codtbsmSJPv30U7322msaOXKkpbp704ULF8z1jIErMQxDr7/+uvn7559/rtDQUBUWFqpHjx4aOHCgbr31VknS66+/rt/+9re+qqoLwzD01Vdfac6cOdq8ebMMw9DVV1+t+++/X7169Sqzi7vT6dSdd95Z5ofZixcvatasWdq1a5c++ugjv5oF22636+OPP9b69etlt9vVtm1b3X777apVq5avq3ZZ7lyLvv76a50+fVqSdMcdd5hvDqWiBrHnn3/e7L22fPlyjR492uX4Ll266NNPl2n8+PGaOHGkatQIr4J74lnDhvVT/fp1deONXRUUVCDprKRQbd68Qffcc48k6a9//asmTZrkctzgwYMVFRWldu3auby5rs54PYNVZOiX6Z///Kf5pcLYsWM1e/ZsGYYhm82m/v37q1u3bvr++++Vnp6ub7/99rK9pMkQ4Dt+0RPCZrO5NXZ21qxZuuGGG1waICrq5MmTGjdunJ5++mmfz4oLVKXs7Gzt379fknT99derc+fOLuVDhw5VUlKSJGnDhg1er19Z7Ha7xowZo169eum9997Tnj17tHfvXr3//vu68cYbNWLECBUWFpY6bsmSJWYDRHBwsO6++24tWLBADzzwgDnfxapVqzR//nyv3p/L+eKLL9S0aVMNHTpUL7zwgl5++WXdc889SkxM1OzZs31dPcuKGyAkqX379qXKS24rHppxqb59W+p//1uk22/3/tjeyvr1r69RUJBNUqak3ZK269ix/5nlDRo4/v/2DEmHVVBwUCtWrNC7776rjz9eIcnhg1oDQGD44YcfzJ9HjBihe++9Vy+//LKkol53Y8aMKXNfAP7Ff74SvIKDBw8qIyNDgwYN0uTJkzVv7faAoAAAIABJREFU3jzl5OSoZcuWmjBhgts9Gh566CE1adJEDz74oL766qsqrrVndezoTzPBw9+VnISyeOhFyQwZhmF+QC+5ry9NmjRJCxcuNH8vnln34sWLkqRFixapXr16mjVrlstxJT+0/+tf/9Lvfvc7SdKoUaM0ZMgQc4Kq2bNn6957763Ku+CWr776SgMGDFBBQUGpsnPnzmncuHEqLCzUww8/7IPaXZk716LExETz588++0zjx493Kf/ss8/Mnxs2LGuuh5OScqvFrOG9e3fW3LmTdexYjrp0aa6iHhJFsrKOmz/Hx0dK2iIpUVK8t6vpVbyewSoy9MtU8kvLxx57TOvXr1dISIiuueYade/e3eWLiivNxUCGAN8JmEaIw4cPSyqa7CspKUmvvvqq6tSpo3/84x8aNWqUCgoKzO6u5fnkk0/0/vvv63//+1+lJolJT09XcnKyateubW7Lz8/Xzp07JUnR0dGlelfs3r1bFy4UTVR26cUuOzvbvF+NGzd2mTzP4XBo27ZtkoomtWnatKnLsfv379fZs0VvZNu2bevSxfz06dPmuOOGDRuWWobxxx9/lGEYioiIUIsWLVzKDh48qJMnT0qSWrZs6TJvxvnz580l9uLi4pSQkOBy7Pbt281ubW3atHEpO3r0qLKysiRJqampqlmzplmWl5enXbt2SZLq1aunRo0auRz7008/6eLFi7LZbOrQoYNL2YkTJ3TkyBFJRcN66tata5bZ7Xalp6dLkmrXrq0mTZq4HLtv3z5zAqF27dq5fNg5deqUMjMzJRV9mKpfv77LsWlpaZKkyMhINW/e3KUsMzNTp06dkiS1atXKbACQilaqKO6d0KBBA8XHu37QSE9Pl91uV3h4uFq1auVSduTIEZ04cUKS1KxZM0VFRZllFy5cMMc0xsTEKCkpSbGxsYqPj9exY8e0Zs0arVixQk2bNlW7du0kSWvXrtW+ffskSS1atFBaWppSUlJUp04d87wFBQXasWOHpKIu9CkpKS512rt3r86fPy+p6Jvtks+rnJwcHTp0SJKUlJSkmJifx/Q7nU5t3bpVklSzZk2lpqYqOztbf//73yUVfZsxceJE3XLLLWrdurUWL16sBx54QAUFBXr99dd1yy23qH79+kpISFBsbKzWr18vqSgDrVu31oYNGxQdHa2WLVuqT58+6tSpk7Zs2aK0tDQ1bNhQ48aN05/+9CdzMkSHw6GoqCjZ7Xa1b99en3zySakPxjt37lR+fr5CQkLUtm1bl7Jjx47p+PGiD5NNmjS57DWiUaNGGjdunNkA0aVLF91xxx2KiorSunXr9Pbbb0uS/vznP+s3v/mN2QATaNeIlJQUNWnSRPv379dnn/0/9s47LIrjfeCfOw6QIqCADRuK7WuJ3aBYsaFi7yH2WGKvUWMiRo3GrsQSY29RsXeNsfdeUVEUkSa9c8Dd7e+PlRME9JBDDn/3eR4fj5ud2dm92Xdn3nnLv8ydOxcXFxcMDAx4/PgxU6dOVddzc3NTy4iYmBhq1aqJuXlAunuY2l8LC4sMz83r169JSkpCIpFkeB4jIyPVz03x4sXTubooFAr1M2BmZpZOcQLg7++vlt/ly5dPJyNiYmIIDg4GwNa2CIUKWaWr6+3tDYjpSCtXLkvlymXVZUFBwcTGxqjvU2zsBYKDw5FIJMTFxREYeBal0hKJpCzz5y9g4cKF6t9ImzIiLc+ePUMul2NgYKCWEamEhIQQFBSk7m9eyYi0+Pr6qi1oqlSpki7DT3R0NL6+voD4mxcpUiRd3UePHqFUKilQoACVKlVKV+bv7094eDgAFSpUSBcwNT4+nhcvXgBga2ubazJCP4/QzyN0ZR6RFl2REQ0aNGDbtm3vjkjBwECKTGZAQEAAcrmctWvXqutbWVlx//79LyYjUp9TPXr0fBqdcMfQhNSdWrlczrFjx+jRowetW7dm9+7d1K5dm99+++2j9aOjoxk2bBg//fRTBuGpKQqFIkOQG0EQSElJISUlBYVCkWmd1PLMrim1LLOdaE3b/bBPadtVKjOa9n6sXaVSmeN2M7vWtO1+eK1p72Fm7X7sHmrarq78Np+6Vk3voSbtSqVStWJOqVTyww8/sHPnTu7cucOSJUvo2rWrun7nzp0zbTdtn7LbX03vYWrd3bt3qxfm33//PZ06dUIikWBkZMTgwYMZN26cut7Ro0fVfRIEQf07mJubM3fuXPr160dcXBAQCoRSpowJqXP+oKAg4uICgEAgAPBHKg0gKSkJpVKJUpmAUpmYrWvV9LdRKBRcvXpVvTCoXbs269evp3HjxtSuXZstW7aoLTWSkpLYuXNnvpURAD///LO6bMaMGTRu3JjWrVvz3Xff8ebNG0BUwrRp0walUklQUBAuLi6MGfMDwcGB6e6hQqFAoVBkeh+USqW6/GNlGWUE6rLM7kNUgpKk5MzbValU6rqCkLFPH2tXqVSkqStgbm6Kg0Mpypcvqe5TcvJbhg3rx+bNm6lXr556IaRNGZGW1LLMrHM+1m7aurktI7Lq04d86lqTk5Nz9R7mVEZ8iH4ekbFd/Tziy8wjMms3r2WEm5sbZmZmWFpCXNwNHB3t+PXXPsTGxuLo6IiXlxcgKjQqVKjwxWWEHj16NCPfKCFSd0gqV65MmTJl1N9LJBLatGmDv7+/WkOeGT///DOGhoaMGjWKqKgooqKi1JrXhIQEoqKiPik8ZDJZhtgVEokEQ0NDDA0NMw14J5PJ1OUfIpVK1WWZWWZo2u6HfUrbbmamzB9r18DAIMftZnatadv98FrT3sPM2v3YPdS0XV35bT51rZreQ03bnTBhgnqXKiQkhLlz51KnTh0mTpyo3mWpX78+HTt2zLTdtH3Kbn81vYepdVN3jACaN2+eoV0XFxf157CwMHWfpFIpVapUAcQdoF27dvH8+XN+/90dQXiNv/8VAgOvY20NhoYSbGwsMTNLQSJ5CwQDb5FIQqlVqxJVq9rj4FAMQ8OIbF2rpr+NTCbjzp338QEGDx5MgQIF0rWb1l3k0aNH+VpGDBo0iF9//VVdnpCQkE5O16hRg4MHDyKVSjEwMGDt2rXEx8ezceMu/vhjc7p7KJPJkMlkmd4HAwMDdfnHyjLKCNRlae+DIAisvxRPp41G/HTKAlUmRoNSqVRdVyLJ2KfM2n3fJ1mauh+OF7FuWFg03t6+gLgDn7pjqW0ZkUpqWdrdQk3aTVs3t2VEVn36kE9dq5GRUa7ew5zKiA/RzyMytqufR3y5ecSH7eaVjHj79i3r1q3DysqS9etnUb48GBhAQsIb/vlnE4MHD+bevXuAaF0yZ86cPJERevTo0QyJoGNqu7CwMGxtbZk5cybu7u7q7xUKBZaWljg4OKhN2FJJzUUfGhqawdwtlWbNmnH+/PmPnjsyMlJthqeLuX7DwsJQqVRIpdIsr1OPng8JDAykT58+mcZA6dKlC5s2bUpnGpxXzJ07lxkzZgBiatGRI0emK1+7di3Dhg0DyCAfli1bxvjx45HJQKWSIJVKmTNnGLVqlWTlylVqc84hQ4YwYsRwDXojBWoA2o9HsHLlSkaNGgXAihUrGD16dLryGzdu0KBBA0C0CNmyZYvW+5BTsiuLrl+/zsqVKzlz5gxyuZwKFSowePBg3Nzc0plqL1q0iNmzfwNU+PgcxMbGKutGc4kkhcDP+2PYc/u9NUzveibM72b5kVq5Q0BACD17TuWPP8bi5NQV+PL3I7fQv8/05BT9GPr/w5kzZ+jTpw8hISEcPLiKjh3rc/z4CZYuXUJ4eAQpKfDOe4tq1aqxYcMG6tWr98l2tT2GdHHtoEePrpJvlBAAffv2Zc+ePXh7e6t9ygRBoHbt2sTGxqp9NTPj3r176aK1p343fvx43N3dadq0KU5OTmqNtC4Kkvv375OSIvpK6nowncDAQF6+fImJiQnVq1fPVHOenxEEgVOnTvH333/z5MkTZDIZTZo0YcSIERn8WHWFmzdvsnr1aiIjIylSpAjjxo1TWxDoAvfu3aNWrVqA6Nt85coVtY9+UFAQjRo1UvvBXr9+nfr166vrxsfH4+xcj8TEJ8TFgaEhpHF1BcDOrgRbt25N56v6ceyIjjbBwMAgne9xTrl586a679WqVePWrVtqf19BEBgwYIBa8eDh4aFWWOgSuSeLkggNvcT9+89o2bKBFtvVjJBYJcO3RnHHLwWpBHrXN+GfG4kIAszvakHv+qafbkTLpKaeExEDVqaaEudnuZqf3md6dBP9GPr/Q+pGA0D16g7cu7cDqVRKSkoKFy9exNv7FRERJXFycqJx48YaWyRoewzp4tpBjx5dRWcCUx4/fpz4+Hj1w+vl5cWePXsAaNeuHaampsyePZvjx4/Ttm1b3N3dsbCwYN26ddy/f5/du3er23r9+jXly5enf//+rF+/HoCaNWtmee6qVavSrFmz3Lu4/0fcuHGDmTNncuLECfV3RYoUYdiwYUybNk2d7SA/Ex8fT69evTh69Gi67x88eMDKlSuZPXt2Ol94XaFevXoYGRkgCCHExxfEy8tLp5QQNWvWpGnTppw/fx4/Pz8qVaqkjgtx4MAB4uPjAXB0dKR+/fpER0ezdetWRo4ciZlZLEePLmPKlJ/U5phpqVy5EosWLdJYAfH2bTiLFnnw11/7mDFjBlOmTNHaddatW5fatWtz584dHj16RKNGjRgzZgwWFhZs3ryZAwcOAKI5qZubm9bOmz/wx9bWKk8UEA/8Uxi6JZLgGBUWBST82deKJhWNsbMyYOHJOH49GEOV4oZ8U+rL5pNPP5kOABL57bfNnD79H/v27csQMFCPHj16vjbGju3JpUuHiYtLZNu22epFvaGhIS1atKBFC0NE60U9evTkF3TGEqJs2bLqSMwf8urVK7Xlw6NHj5g6dSoXLlwgJSWFmjVr8vPPP9OhQwf18b6+vtjb29O/f382pUn39yHnzp2jefPmeHp60r1793RluqjNjIyMVJuNpY2ArSscP36czp07Zxq0CKBJkyacOHEi3ysievTooVaQgZj+8sPAU2vXrv1ktpYvRXh4OK9fv6Z27RpER9/i9WsfeveexdOnL9i7dy9dunTJ6y6qefPmDY0bN85SFpQsWZKLFy8SGxtLt27deP78OStXuvPjj+LzLwgC9+7d59Spk0RERGJpaYGzszP169fPlq+mt/drKlfujiAIlChRglevXml11/nGjRs0a9ZMnfkiM/7++2+GDBmitXNqk9yRRXHAMy21JZKadUAul2NnZ5ch2nsqB+8lMmVPNEkKcChiwN/9CmFvk2oVJzBsWxT/eiVRwlLK4dE2WJvn3XvA0/M0PXuKmUXKly/PgwcP0kVnzy/o+vtMj+6jH0NfL7Gxse8yGSmAV0AMCQlyChQwymIe/nlKCG2PIV1cO+jRo6vojBJC19ALkuwRGRlJ2bJl1em+ypQpg6urKwEBARw6dEgdfXjy5MksWLAgL7uaI+7fv6+2qrGwsOCvv/6ie/fuxMfHs2jRIubMmQOIKc18fX0zDWr0JQkODqZVq1b4+/tz5sw6atUqy6JFW5k8eTkgLupfvHiRLv1XXvP27VtmzZrF1q1b1cFjzczMcHNzY+bMmRQvXhxPT0969uwJQNGi1vj4HMDMTLvKrS5dJnH8+BX69evP/PnzKVy4sFbbv3r1KoMGDVKn5kvF1taWxYsX8/3332v1fLrKrl27iIqKYvDgRshkSVppUy6Xs27dOvbt20d0dIz6+9q1azFixAhq164NgFIlsPBkHGvOi1Y2LSobs7y3JQULpJfzMXIVnf8M52WYkkYORmweWAiZQd4EILt58zGdOk0kKCiMBQvmMHmy7lld6dGjRzvExcWxdOlS7t+/z9q1a7X+HtI1BEFg5cqVuLu7c+XKaSpWNAAy39hKj25YQujXDnr0aI5eCZEFekGSPZYsWcLEiRMBcHV1Zc+ePeqd45s3b9KoUSNSUlKwtLQkICAgXW7qnCIIAleuXGH9+vV4e3tjbGxMs2bNGDJkSIYc5DllwoQJLF26FMg8qKCrqytHjhwBULsO5SVDhw7l77//BqBGjQrcvbsdiUSCm9sv3LzpxZEjB6lYMWtXpbwkPj6eZ8+eIQgClSpV+iAuQzgTJozl3Llb7N27AHt7O62f/+VLf8zMTChatAGQO0EJBUHg7NmzXLp0CYVCQbVq1ejUqZNGSqHHjx+zfPlyFi5cmI04F7pFfHw8FSpUICgoiP/9rxxXr27AwiJn8TcSE+WMGjUqU7ccAAMDKfPmzaNeo+aM/Seas89ExceIZmZMam2OgTRz5YL32xQ6r4wgIVlgeFMzproUzFE/c0JAQAibNh1m+vQhSCTl+JoCVurRo0fkxo0bdOnShcDAQGrWrMGlS1e0OnfSRVavXs2PP/4IiLEfrl3bhKlpgU/UAr0SQo+e/IdeCZEFekGSPVq3bs2///4LkGmsge+//55t27YBcPr0aZydnbVy3oSEBNzc3Ni/f3+GMmNjY9asWcOAAQO0ci6Abt26sW/fPiC9m1AqaTM4rF69muHDNcnEkHvEx0fStm1L/PwC+e+/1Tg4lAJALk8iIUFO4cI2QGVAtwPcyeXyd1kUBOANEEpKigKFQoGJiSYTlJxgDlTK5XNkj7QZNubPn85PP01CVJSI8mnp0qU0atSIevXq6XTKsN27d9OrVy8AOnVqyoEDi3Pc5vLly9myZSsAMpkBLVq0oGjRoly4cIHXr8U0sAaF7DFt7YFvBBjLYEF3SzrV/LQlzZEHiYzaEQ3AGjcr2lbL7bGnKWLAyocPH1KxYkWdsmzSo0dP9lGpVHh4eDBp0kQUCiWlSoGlpSGNGnVj3LiZVK5cmXPnzuHo6Jgvn3dBEPDz8yM8PFxtmQYQFxdN/fp1efLkBRMmfMf8+aMxNNQkfJ1eCaFHT35D/1TkI5RKpfqfrpFqNg+in/KHODg4ZHpsTunfv3+mCggQ/cEHDhzIoUOHtHa+tLsQPj4+CILA4MGD6dixI4sWLeLKlSvqcm1mVPg8kjAz8+fo0SVcvLgOB4dS6vFjaCijcGFLIAXwAVSfaCvvOHPmDA4ODly9egExZkAoAIaGsi+ggAAxVkH8FziP5rRu3UStXNiyZSeC4APcA17w6tVtJkyYQIMGDXB1dc2V82tLFvXs2ZPLlw/TuHEt/vhj9KcrfILERLlaHshkMjZt2sS8efMYN24cnp6etG7diuTCtQj9Zh6+EVDMQorncGuNFBAAHWqYMMRJjL8wcXc0L0IUOe6zdgjA2/s/mjRpQqdOnZDL5XndoU+iy+8zPfmDr20MpV6HUqlk0KDerFo1juLFlVhaQsGCYGSUws2bO3Fzq8O+fRtp1aoV5cqVU1s75hcSExMpVaoUZcuWfbdRIwfCgdeYm/uxd+889u5dwOLF4zVUQHw+X9sY0qMnP6FXQuQjHj16xN27d3n06FFedyUDZcqUUX8+fPhwujJBENQuCkAG64HP5ebNm+oAkebm5qxbt464uDhevnzJwIED1cdNmzYNbRn8uLi4qD//+uuvJCQkMGjQd5w4cYLJkyezfft2QFwAacvaIzt4e3u/W4AkIi7Yk7GwMKd06WKAqDh59uwZPj4+aWolIAgvWbBgATNnzvziff4YZ8+epVWrVgQEBNCjRw9CQt7kST8EIZiTJ0/i5eX1Rc+blJTEhg0buHjx4rtv4oAXVKiQzOjRvVi6dALXr296p5AQgGgOHNiurt+wYQ0+9Ke9cuXKRwNiaoL2ZJGChg1LcuHC31SqVDaHbcGTJ17ExopKzpYtW6azyJJKpVg3HEVsbXcEQ3MsU/w4NNqaGiWzF7dlqktBGtgbEp8sMGxrJHFJea/AU6lU9Oz5I1FRUZw8eZLp06fndZc+iS6/z/TkD76WMZSYmMicOXOoU6cOSUnxrF//Kw8femJuDjY24OpahfbtW1CwoLixIQgJjBkzDIVCQWBgIG/e+OXxFWQkNjaW/fv3M2XKFHbs2JGmRIWJiQILC1GZe/fuXRISbgO+QBiQTJUq9nTt2uKL9PNrGUN69ORHdCZFp578Tf/+/dm5cycAo0aNokCBAri4uBAeHo67uzu3bt0CxDSMNWpox2Ru48aN6s8LFixg8ODBANjb27N+/XqePHnCtWvX8PLy4saNGzRokPO0f926dcPOzo6AgACuXLlC7drl6NOnIZUq2fLoUSCWlgqMjaFdu64UL14UEF1VDA0Nad68ORMnTsw18/jbt2/TunVrHB3rs2/fbIyMNDuPIAgMHTqZdevE1JAVK1bku+++y5U+ZpfGjRvj5FSfCxeuUaOGAzKZwRfvg7f3a3r06MODB8/p06fPBxOq3OPFixc0adKEoKAgmjdvzJkza0lrkbF8+aRM67m5tcPCwoz9+8/RtWsd4CFgClgRFSWhadOmGBsbM3jwYJYvX/4lLuUjBAHa24FKq1yxsyuh/ixPEfh5fzR77xiABIwD/qWqcJoiBTdn+xwyAzF9p6tHOD6hSiZ7RrPqO6s8dXuRSqX8+ecUXFzGULGiPTNm6L4SQo8ePSJDhgxRv1eWLZvO+fM71WWLFi2gRQtxQR4fH8+kSZO4ceMm5uYp1KvnwJMngYwd2xoIAWwAKSkpKURERFC0aNEvfzHvCAgIoGvXrgC4uralb9/GiEr0RECgTZu6lCplTcOGNUhOTtEw7oMePXq+JvSWEPmIggULYmFh8S5tkW7RunVrnJycADEjQ4cOHTA3N6do0aKsWrVKfdysWbO0Nll/8eKF+nO3bt3SlUkkknTfpd/5/3xUKhWjRo2iYMGCFC0K5uYhHDp0AKUykFKloEgRcHIqz6JFw4B7xMTc5syZMxw7doxNmzZluPbQ0FCtmAEmJSXRqVMnIiIiOHr0BHPm/JXpcaamppiZmaVL6SeRSKhatZz6bz8/3dlVkcmC2bXLnQULxnDkyLJ3LiRfllKlihIYKLqA7N69O8v0odrG3r4sBQuKv9PZsxfx8nqoLpPL5Rw6dIhhw4bTpUsXvv/+e/7+ex1hYWHY2hZi8ODOHDmyjMqVy76rkQAEcvToOhQKBfHx8Ugkn+9KkFNZ9OzZMyCJVNcabVGihBigVJBIOX3xDs+Ckrnik0SfvyPYe0eOBAHTp2sx81pOKbvPD1prW9CAVW5WGBrA8UdJrL2QoK1L+GycnGpy5sxq/v13BYULR6DLLlag2+8zPfmDr2UMTZ48HIlEgoGBAc+fv+Tt2xAAnJyc1AoIEN1BJ0+e/O4z1KplyatXh7C2NkWMlfQQCGbHjm2ULVuWUaNG8eZN7lsPKpVKEhLSysBIKlaUqd/XV69eQxDeIr6HRKvUpUsncvLkn8ycORQrq7z7/b6WMaRHT35EbwmRjyhXrtynD8ojpFIpBw4cwNXVlatXrwLpdyVlMhl//vknHTt21No5TUze+3EHBAQQFxfHnDlzsLOzY9y4cfj7+2d67OcSHBxMly5duHbtGkuXTsPf/yoXLlxAqVRhYgK2tuZ07OjK0KFD373QBF6+fIa1tSUhIRE0a1YVeAoUfPfPnMGDB3Pp0iVatmzJX3/99dl5qo2Njdm2bS0uLl2pV+9/TJrklulxJUuWzPT7sWP74OsbRMOGNejZc9Rn9UH7BANvKVbMhsmT++VZL0xMCjBqVE+OH7/C5Mm/ZHkPc8Lz58+5e/fuu7SjSiAUA4MQpkzpw9Gjl/npp/7873/i8//mjT9jxozGzy/95NLL6wmbN4sxEBo3bpzpeSpVKsOgQR05dOgCXbp8A7wFsr9blhNZdOrUKdq0aUPfvh2ZO3cIZcuW+HQlIDRWiX+kksgEFRHxAhHxKiLiVUTGqwiPVxGZoCIy3oxo510oJCZESKS0WR6hrm9mqMTKaxHyN6Jri6trh8++BoDapY341dWCXw7E8MeJWKrbyWjokLcB4urVq/ruUyzwAnBAqRRQKBQ6F7xOl99n/x8JDg5m7969BAYGYmVlRceOHalUSbcC8n5IfhxDISEhJCcnv3uPyIE31KxpyooVk2jevC4xMSGMGiW6r1asWCFDfXt7e6RSCSqVQGxsLDY2aTPjKFAq/Zg37zfkcjkrV66kT58+lCpVKleuRRAEDhw4wC+//EKbNm1YvPhXIABIRCqFhQvHYG1tiaNjDZ0NkJwfx5AePV8L+uwYWaCPcPt5KBQKDh06xIYNG3jx4gUmJia0bNmS4cOHZxqwMid4eHgwZswYANq3b8/du3cJDAwEYPbs2SxcuJCYmBiMjIzw9/fH1tY2R+dLmzrK2toSX9/DJCUl4uf3BplMhoODQ6aBEgVB4OlTX4yMDClf/v0CVqlUYW3tTHR0LNbWhQkJCUEqfe9u8PbtW8zNzTVMyRUD+HDt2n1q1KiQQ9NGGWLGjC+/aDl27Bjbtm1j48aFGBsHf/HzZ4VCocDAwACJxA7QbtrXS5cu0bp1a6RSKX5+VylcWElWLgoJCQn06dM3nYLN1NSEhIT3Cj9DQxkbN27MkKEmLQqFAqlUilRqCFRFjCye+yiVSmrXrs2DBw8A2LZtNt995/KJWnDTN5neayNQZnNzX5IcgyQlBlliIKZP/8YgMQgQ3cLWrv0LA4OcufcIgsAkz2j23pFT2EzCkdE2lLD68i5DWaFUmtKv32wiIiLZv3//uwwzevS8Jzk5mfHjx/P333+TkpKSrqxDhw5s3LgRGxubPOrd14NSqWT58uXMmjWL5s2bceDAn4iWYOmn4M+fP6d37z4AVK9ejU2bNqUrv337NkOHihm4GjVqyIoVK9KVJyTI+fXXNaxZs5c6dapw/vwBwBYQn/1Hjx5hZGRExYoVc3xNb9++xd7ensTERIyNjXj2bA9+fj74+voikxlSp05trZxHM/TZMfToyW/olRBZoBckuk90dDSlS5cmJiYGgDJlivD6dQgGBhJKlizA69fiwqxfv35s3pxRAlUCAAAgAElEQVR93+8PEYQ4Bg36jv/+u87Bg4upVatyjtqLiIhm2LDfOX36Bm3bOvLPP38AFup/w4ePYePGjTg5ObFu3Trs7e3T1Q8ICMDOzg6IAl7y4WQmZxQAKuPvH0Tx4sVzvFjThMuXL9OqVSsSExNxdq7PwYOLMTPLuQWLdpEB1dGWJ5sgCNSrV4/bt28D8PvvI5k2bWCWx+/evZs//lgAiO4aM2fOpFq1agQHv2XJksWcOXMWgObNm7Fo0SINe2GNXF6MwMDAXN8VUigUrFmzBnf3Xyhbtjg3bmz+pExVqQQ6rQznYYACG3MpxS2lFDYT/xUyff857d93r51lyXx3UpKTMrRXs+Y3LF68GCsrq0zOln3kKQLdVofzOFDBN6UM2T2sMMYy3dj1Gzp0Ln//LWYL6dixIwcOHNDZHUk9Xx6VSkX37t2zzDAFUK1aNS5fvoyFhcUX7NnXx5YtW+jfv7/671On/qRVq28zHCcIAr179+bFC9GFdMiQwQwcOJACBQrw/PkLpk6diq+vLwBz5sxOFyw7LeHhUYSFRaUJ+GsGWNOx4yAOHz6Co6Mje/bsoUQJzSzRMieOKVPGsXDheipVKom1dRxyeVS6I2rW/IYZM37B3r5sZg1oEb0SQo+e/IZeCZEFekGSMy5cuMDo0aOpWLEiW7Zs0Yo7RGYcPnyYrl27YmmpoHRpCA4WfSUtLCApCczNK3L06BWOHTuGtbU1Li4unzkJjwBek5QkJyoqlqJFrbV2DUqlkqioWKyt3y+KBEGgXLnO+PoGYGRkREREGGZm730WPTw8GDt2LLt2radHj2/QrgJC5NIlb7p0GYObmxtLly7VevsfcvLkSbp06UJiYiI9e7Zix445X0T5kX3KIAYA0w5v3/rRqVMHTEyM2L9/0Uf9Y/v378+jR48B2LFjezpz6eTkZFxdOxIWFoZUKuG///775MJBEAQOHTrP+PF/Ym5ekDt37iCT5baXXgTR0Q95+zacihXLfPLoA3cTGbcrGnNjCecm22BjrtmYCAkJYd++fVy7do2kpCRKlLCjU6eONGrUSOvj6k2Egg4e4UQnCvSpb8K8rl8+dklmXLx4FxeXMSQnK/D03EWnTl3yukt6dIgDBw7QpYs4JoyNjRk7diwtWrTgwYMHLFy4kNBQMWbLL7/8wm+//ZaXXf0qOH16J6NHT8PJqSZz5ozIch5x6tQppk17H1zWzMyUQoUKp7OAK1OmNDt37sTIyEjj8799G46dXTuUSiUlS9rh6+uLgYFm8v7GjRts3rwZDw8PpFI5ottFDGFhUSxZ8hcnTniS1dTKysqSDRs2pMuipn30Sgg9evIbeiVEFuiiIHn16hUKhQKZTJZhV1yXePjwIU5OTsTExNCzZ3d27fLU+jni4uK4d+8eTk5OXL++h7Vr53Dv3n11ubGxES4u7Rg9ehQqlRnly7sQFRWFs7MzJ06c+ORCKy4ujlGjRjFt2jQqVTJHjE/w5ZDLkxg3bjEnT16jfPmSnD69GjAHLBCEgowbN50VK1Ygkxlw7dom6tTJ2vQ+LQEBASiVSgwMDN5ZUWROWFgUZcu6Eh8vWpNs27btC2TMSODqVU+WLdvOli2zMDbWfHL1JfHzi2TZsmPUrVuXvn375rA1JfCUxMQokpMVWFqaf/To1q1bEx4ega2tDSdOnMhQPnPmTI4cOQrArl07cXBw+Gh7KpWK+vX7c/v2E0BUbo0a9emYIJ8vi5SAFx+mDc0KeYqA8+JQAqJUTG5jzsjmH78/ecl57yQGbIxEEGBBNwt61jP9dKUvwMWLd4mMjKFjxw6AA7oSjzq/vM++Ztq0acOpU6cA0cqqR48e6rInT55QvXp1lEolxYoVw9/fX+eUwvlrDMkBL1JSUjA0/PTCf9OmTXh4/JlpWcmSdvz550pKlcpefKLo6DjWrz/Axo2HcXVtwu+/jwMKA9aACTNnziQpKYn+/func+ebNm0a8+fPB2DXruX07NlIXRYZGUX79u1IShJlesOGjrRt25aYmBh27drFmzei4uTbb79l5crMr0c7fJ4SQttjSBfXDnr06Cr6wJT5iJiYmHcvsC/jv/25KJVKzMxMiYmJoXXr/yGmjiqitfb9/Pzo2LEj3t7eXLiwnQYN7GnQYD2vXvni5/caIyMjqlatqt4FXrp0O1FRoolg6dIlPqmACAgIoF27djx48IArV85z/foGChX6sqaoBQoYs2bNdARBIC4uNaJ0LBCLRALXrp0BYPDgTtSqpXnwsPj4ePUL92PY2FixbNlEfvhhDq1aNaV9+/affzEakQQ8x9GxGo6O83L5XBkRBIGbN2/i6enJo0ePUKkEKlRwoFu3bjRt2lQ9gfDx8adSpW4olUqqVKlC7969czC5EAAfQI6JSQE0MRYyMTEFIoiKiiI2NjZDRO+0mU3SZkDJitTUjo6OA2ne3IlmzZpp1PPsyqKYmJh3z6MfmiogADZejicgSkVxSymDnTSJjZJ3NK1ozISW5iz+N44ZB2OoXNyQGiXzXlY3blzr3af3wSp1QRGRX95nXzM3b94EoGjRohkyTFWpUgVnZ2dOnTpFcHAw/v7+ubyTnX3y1xjyBwSNFBAAAwYMoF69euzevZurV6+SmJiInZ0dHTt2pGPHjpibZ18ha2lpzoQJbowf/x0pKQogBTE48VvkcgNWrFhOVFQ0Hh4ehISEqONRNW3akHc6CDZu3JVOCXH48CG1AqJTp4788ssvamtTV1dXevXqRXDwW65du8abN29yLUjm55K/xpAePV8XeiWEHq1Ts+b/uH59MzNmrKB371aIqaMigTLcuePFkSNHmDp1arbMCNOyZMkS7t8XrR7695/Ew4c7kUql2NuXzdTvcNy4vpQsWZTZs9fx22+9AV+gBCCePyoqKp1/uKWlJanuDW/fhvL0qS+Ojnlj5ieRSChYMP3iSxAEXF2dGDq0M4MGdco1H+8hQzpTuLAFrq5NMDTU/qIlOjqaO3fu0Ly5E+ANfH7KyJygVCqZM2cOhw4dTvd9WFgYV69eo1GjhvzxxwJMTApQvnxJHB2rc+nSPV69eoWXlxfVqlXL1vlWrFjBixcvWLJkLDJZ7KcrpKFhQ0d27/YkJUXBqlWrmDJlivr3P3PmDA8eiGk8y5YtS/HimgXQ/Pbb6ly/vol69b5BItHMoiY7+Pr6UrduXcaNG8q0aZ013k0Nj1Ox6mw8AJPbFKSAoe7HMhjZ3Iz7/imcfpLED1siaVO1ALbmUmwKSrE1l2Jb0ADbglKszaXp4kYkJSVx9OhRDhw4gK+vL4aGRtStW4eePXtSp04dLfZQVEScOvWSv/76m+3bt+uDVeoomiiLc0qqIaxUKs30PZL2WdUbzWafxMREnj59Sq1a5YDobNevWrUqs2bN0nq/JBIJRkbpF923bt0mLi4OgG7dWmNmpkDcHAimTZsS9O7dmmbN6jBoUKd09VKDDAP07ds33TgyNzenc+fOrFkjpgx/+PChzikh9OjRk3fo3TGyQBdNqhQKBYIgIJFIvoDf9ueiBJ4BiRlKUlIU1K8/mHv3HlOtWjWOHj1K6dKls32GpKRwnJ1bEhwcxuHDS6lSRTMTutR7JyIFinDmjBedOnVlypQpTJgw4Z3mPxZf34t899001q37ReP28wPiGAKJhGyOIQPEjBkFuHLlCvXq1cvRzoFcLqdt27ZcunSJTZvm4ubW8rPbyikrV65kw4aN6r/Nzc2QyWRERb2fNLZr58Ls2bMBOHXqGleu3GfkyOnY2pbN1rmOHTuGq6srKpUKF5eGHDq0JFu/w6tXr+jVqxfKd2kiypWzp0GDBrx8+ZLr12+oj5s2bSrdu3fPVt9EigCfniRqKosUCgXNmjXj8uXLAMyZM4Kffx6sUU9mHoxh89UEqpaQcXiUNVKp7ishAGLkKjr9Gc6rsMwznKRiaSLBtqAUS2MVvk9vEx/mhzQ5EklSJIYR9zFICgfgu+/6Mn78eK0pG0+dukbHjhNISkrGxcWFffv25YkiIn+8z748ycnJrFy5kqVLl3L9+nWNlYmfg7OzM2fOiFZ1Bw8eTJdC28fHhypVqpCSkoKNjQ1BQUE69zvp+hj67bffcHd354cfujF37vAP0mnqHiEhEezYcQJHxxo0aKCZcn3ChAmcP38BgIMHD2RIYb1161aWLVsOgLv7TFxdXTO0oVQquXLlChcuXCAuLo4iRYrSvn27bGbW+Dx3DG2PIV1cO+jRo6von4p8hEwmw9DQUOdetoIgcOnSJUTrgZdkpoAAuHz5Hg8fPgVAKoVixYp9xtkiMDZ+zf79C7l+fVO2FATpJ/EqVKpApkwZR1xcHL/++isHDx5ETJn1nLJli3Lp0vqvSgEBqWNI9hljSAm8IDDQm6ZNm1K2bFk8PDw+ux9r1qzh/PnzKJVKJkz4g+jouM9uKyfExsayY8c/ABgYSJkxYwanT//Hv//+y6JFCzE1FX0kjh07rvZtbd36W9zdh2Fr+/FFZmaIQSNFsVurVqVs/w729vZMnTpV/ffLl6/455+d6RQQbdu2oWvXrtnum0gokIggCB/d+cyOLHJ2bvHOUsmO0aN7adQLn1AF268nAPBzu4L5RgEBYFFAyr4R1szuZMHoFmb0rmeCc2VjapSUUcJSiuG7zeXoRIEXIUpuvxEIN6uNvExnEioMJL7aBGIariLZujYA27fvYOfOnVrrX4ECRhgYiGPQ1NQkz/z8dfV9ltfMnTuXCRMm8ObNG7p1a8GqVYvSuVlpk2HDhqk/9+7dm99++42rV/9j1apVNG3aVJ2yc8iQITr5O+nyGPLz82P+/PkIgsCGDfsJDY3M6y59kiJFCjNuXF+NFRBAurhDhw+ntyZUKBTqGEXisRUy1H/58iU9e/Zk3Ljx7Nu3n1On/mXbtm306dOXCRMmqK0zskIQBDZfiWeyZ8RnWevo8hjSo+drx8Dd3d09rzuhiwiCQHJyet9lY2NjfXqzTFiyZAl9+vQhKSmEFi2qZHmPypYtgatrY+7cecratVMpVcoWMdhi1vc0MTGR6dOnU69ePUxMIhD9KsHMzART05zt3iUmJvHw4XPu3fOmRo2KeHhMRiIJUZfrf+sPUbJokQdnz94iNjaW2rVr0aKF82e1VK9eXUJDfXjy5AUnT3pQvnz2Amxpi1OnTnH69H8AdO/ejR9+GIKBgWiabG9vj0Qi5cYNcYFvaWnxgWm8HDGgl+aTl2++qUCTJqUxMpKxZMnn7W5XqVKFGjWqExgYSHDwW/X3JUoUZ9iwYYwePTpHuy7e3k/4/vvRKJVKatas+dntgGjm3bx5JZydq9CzZyuNf+ef9kbzIkSJc2VjRrXQ3WCUWWFiJOGbUoY0LG9My/8VoFNNE/rUN2VwYzNGtzBjYCMzutcxoazsFbePrkIW5YWFKhjH6qUxMipAWKKMlOLNICUOWYw3z72f07t3b7XyICeUKVOcxo1rolKp2LJlHoaGRfiYDE4lISGB2NhY4uLi1L7ierSLXC5nz56N3L37CEGAxMQwnj//l/nzl3P//lOaNWumUawXTalcuTJXr17l5cuXKBQKHj8+x+XLW/D0PEZYmLibW6FCBTZu3JhrGa6yi5+fH3Fxce9izCQiKsh1bwFpYmKCmVkBrl69yogR3XBza5fXXcoVSpQooVaS3rt3j/j4eKysrHjxwoc//pjPw4eii2CVKpUZNmxourpBQcEMHjyIoKDMA3+/fv2aR48e0a6dS6bvtLgkFRN2x7D2QgJeQSnUKm1FWZu8lU36tYMePZqjd8fIAr1JlWY8ePCAmjVrqjXQZ8+uoVmzuh+tk94twhgoQ2ionNmzZzNr1iwKFSoEQFBQEJ06deLmzZu0bNmIY8cWaxzUKTs8e+ZLbGwCdev+T+ttf21cvnyPxYu3c+zYZV68OETJklUBW8CY5ORk9u3bR9euXTWI9/EKQQjHx8cfBwft+4g+Ckjh74vxxCQKKFQCShVp/gelSkChhLCISCIio0FiQKHCNsiMjFGqoHIxGesHFOLl82e4ubkB0KVLZ2bMmPHBmWwRhFIkJiZqsDhIAZ68+187BAQEEBISirm5GeXKlcvxrvbLl/5UrtydlBQFRYsWxdvb+5NpPj9OHGK8D81fM9deJtN7bQQGUjg5zgaHIrq3wNAWs2bNUscimT9/Hq1atSJJIfDz/hj23BYtyoz9j2P2dA2r/lzOt99+mwu9sADKc+bMOUaPHo1cLmfy5MkMHz483VFmZmYkJCRQrVo19cIiFV9fX27dukXXrl3178hs8PbtW4KCgqhZsyZKZTzDhrXn7t3zREaCsTGkihRBAD8/SEoyZ+zYscyePVtrixp3d3d13AFDQ6haFVQqePQIihQpxq1btz6aSelLERsby9y5c1m2bBldu3bmhx/a8vDhOWJjQaUqj6OjIy1b5p1bX+a8IjjYGxOTAp/MfJSf8fDwYNOmzVmWy2Qy1qxZQ61a6ZXas2fP4cCBA4BoUTFixHDKlSvH9evXWbVqFTEx4hx8/vz5tGqV/rd9FpzCiO1RvAxVIpPCtHZWDGrUMM8X+/q1gx49mvP1zu6+QqKiolCpVEil0nSBFPOSGjVq4OExnzFjpjFz5g+fVEDAhxYGSYA348bNZseOg3h6erJ3714aNmyIXC7n1atXAFy7dpfHj32oWVPzTBCaUqlSWa23qavExsaqx9CHmRU0oVGjmjRqVJPw8Cisra1IjawNlnh6nsPN7QeKFSuGh4dHhpgE7yNQvwEikEgkuaKA2HkjgV8PxZCsUZzLgmAm3odwOSAXYy1cepHMoXuJmAS/UB9pZpZ+EpmcnMKOHRtZtMiTFi1asGLFigytq1QqfHx8qFChPGJmAu0pIADs7Oy0ukAoV64kHTo0Zv/+sxgaGuLj40OtWrUyHPcpWSQGey0IvCI7CgiVSuD3YzEA9Klv8lUrIEB0z0mlbl1RdhrLJCzsbkHFojLmHYshqaQLStMS+AZFkhsqCIgBXiCXv8XLywuA0FAfIABQIf5+KgoUMCIhIQG5PJb3iiUVIGPOnNmsX7+VatWq8c8//2gUrFUX32dfCoVCwaJFi/j999+xs7PjwYOj/PvvDu7ePQ9A8eLG9O7dm5o1a/H06RO2bt2GUhlPXFwcc+fOJTk5mQULFmilL9OnT+LcuWPcvv2IIUOcKVHCnPPnvXnw4A7BwcHs3buXMWPGaOVcHxIREcHevXvx9/fHwsKC9u3bU7ly5UyPValUrFu3jqSkJP75Zxd37uzCxAQCAiA0VJxXzJ07l6lTp+b5QlQkDoigWDGbvO5IrjNy5EhkMhmbNm1CoUjvpmhtXZhZs37LoIBITEzkxInjAJiZmbJmzRoKFRLlQOnSpSlWrDjjxo0DYP/+femUEPvuJDJ9fzTyFChuKeXPvlbUKWOGJhZdH/L/WQ7p0ZPXfN0zvK+M169fqxdyuiMs4xg5siWOjnbZShWZloCAEI4cOQ1AUpKc8uXLA2BvX5T9+xcyaNBM9uz5gxo1MvoT6skeQUFB6qjrn6OESEVUQKQlGg8PMfhUcHAwRYqkn3ht2rSJ5cuXc/z4JooVy50sGPIUgV8PxrD7lriD7FzZmDbVjJFJJRhISfM/GBhIkEkhMjyMX36ehiAoKWhmivvMGdwNK8yqc/GsPhuDxZX16vabNWua7nyxsfGMHDmfhARRWebu7k7hwoXTHePu7s6iRYvYtm0RXbs2yJXr1jaLF4+jatVyTJ36E2ZmmT9zH5NFO3bsYOzYsWzcOI8OHTIqMD7G4QdyHvgrMDeWMK5l3u0cpk5KoQCi203ukPYZ9Pb2pkEDcYxIJBKGNjHjxn+enI5vgqLwNyx5mEzdRopcUszEYmoag7m5KcbGhhgayoH0JtLOznWJi0ugZMmiiFk2RN68CWbz5h3vPr/JEJguK3TzffZlMDAw4NChQ8TGxvL06VPWrv2LO3dOqsvnz59P48aNAWjc2AlHR0fath1AVJQou3r31iy2yqeJx8joJXv3ziMoKIxq1UT//ho1rnL06B0ALl68yOjRo7W6sFcoFMyYMYPly5cjl79/viZNmoSLiwsbNmz4IGaUgKVlCsOGuTJv3iZsbUVLEYkEEhLeHSEITJ8+HYVCwS+//KK1vmYXpVL5ziLtTZ714UsjlUoZMWIEPXr04OjRo7x69QojIyNq165NixYtMrWMDAwMRC5PAsDJyUmtgEjFyakRVlZWREVF4ePzEhDf8bMOx/DPDfEd37iCEct6WWFt/vlWBv+f5ZAePXmNXgmhJwfIAR9AoHbtzHcvNMHOrgiPH+/mxx/n062bM0WLxgNhwBucnKrj5bVbHzRIi6hywQFLEAQWLBiDh8cuXr0KpHFjS8RJWBFevQrE09OTe/fu0ahRe27e3ELhwpZaPf+bCAXDt0XxOFCBVAITW5szoqnZpwMaVrDjQq0inD17Dnk0zBjZk7qOzZAZ/8jLcGMKxhfBiDdUqVI5Q3wEa2srBg3qyJ9/7qZWrVqEhISkU0IcO3ZMnVGjZ88xeHvvpVy5vIl9kR3s7e2YPXsE4kIzCdFlSjNevXrFiBEjiImJwdX1B27e3KKxm5M8RWDBCXFxO6KZGTbmXz5gokqlYubMv3jx4g07dqxGIikLBKNU+vPyZQAVKmQ/m8/HaNasGSdPngJgxQoP/vyzknoyfuvWLR6eWINlgcPE1ZpJCEXosiqclX2taFJR899E877UJTb2Qpblu3fPz/T7kiWLcuTIMtzd19K2rSNWVsGIMa9FN57Xr19TqlQpvTlyGiSSGJYuHU2jRjcYMqQT3bs7s3XrEgDs7Erg5OSU7vhq1arRsmU1Llx4hFQqUK6cEjEWQvaeEUEQ+Ouvv+jZsyeFC0sQ01WrsLa2SqdYbtPGkWnTBmJnV4Qff/xVqwoIQRAYMmQImzdnbr5//Phx6tevT7169dixYwfGxnJEq5xEAgLu8L//iQqIatWq4uzszJs3Ebi770AmUyGXiy5OAwYMyJNUkGFhYTRs2JDx439g6NCmeRb0Na+wsbGhf//+Gh2b9t7Ex8dnKE9JSSEpSVRQyWQG+IUrGLFdfMdLJDDW2ZzRLcwwyEdBi/Xo0ZMe/awgH1GiRAlKlixJiRIl8qwPcrmcPn368PDhXUTzcu3sapcsWZSDB5fQr197IBJ4jWjqm91UknqyQhAE/vEqRJ/dhbn+tvCnK2QDiURCkya18fT8g6tXNyKRqIAQ4BH29kqsrUXn5g4dGlOoUE5iDGTk7NMkOniE8zhQQWEzCVsGFWJkc3ONMyr8/PMMHBxE6xuFQsm1i/8h8zsGQGLZrhQtWoT58+dnOhGfMqUfV65s4NKl/RnMiJ2dnXFz6wHAwoVj8oUCIj0CWe3mZSWLzM3NadasCQBubi7ZirOy6Uo8AVEqiltKGdQob4KLDRjgzpw569m58xTz5u0EpISFGeHiMoGGDQfh55d5ALXPpXnz5pQoIaZgfPr0Ka6uHZg4cRKDBw9m2LDhotVS3GsGlbpM3TKGxMoFBmyMZNPl+M+KBJ8bSCQS2rRx5MqVDUyfPgiIB54DT0lJCad58+bUqFEDT0/PdH3WhffZl8Df359Bgwa9cy1MRLw3L2jQoCK+vodYs2Y6RYoUVt8bmUyWqawxNDSkUCGwtARBiEVMhS0GwAsNDf1kP5KSkhg4cCAjRoyge/eOpKR4k/qOzYzffx/JyJE9kEheffS47HLmzBm1AkImkzF69GiOHDnCwoUL1dYPb968Yd++faxc6Y44z0jEx8eHhw8fYGwMpUuXYu3atbi6ujJsmBve3nuYO3cAIFoirFu3Tmv9zQ6//PILz58/58cfpzBz5l950of8gp1dSaytxXnI1atXef78ebryvXv3kZgoKiGsa3Sm/bt3fCFTCZsHFmJcS3OtKCD+v8ghPXp0Eb0SIh9ha2vL2bNnmTdvHuHh4V/8/CqVioEDB7Jz504aNWrMf/9d1Gr7EolER3w5vz5UKoEZB2LYeE1JbBL8dkLBtZfJn674GXwYPDQs7DW7dh1k2LCuLF06QWu/sVIlsOTfWAZuiiQ6UeCbUoYcGW2DU4Xs7RIXKmTFunXrGThwgHoXusDrg6BSoCj8DdMWbM7SxLxUqWI4OtZAjIuRHmPjZLZs+YmjR5cxblzfbF+fbhBNXFwA8+bNIzHxfepdW1tbihUrhq2tbbqjbW1tOHBgIRs3zmTlyp80Pkt4nIqVZ8TdsEmtC2JilDdyoFs30e9YKpWqswFMmzaNf/+9TFhYFL16TdPq4t/Q0JAlS5aozYATE+WcO3eOe/fuq4/59ttvmTx6MNt/KEz3OiaoBHA/HMvPB2JIUeqGIgJE+Z3+2Y9n69blvHr1isePH7Nu3bp0z35WY+hrwsvLi9KlS7Nx40amTh2NGJg2Rl0uuraI965ixYoAvH7tx507d9K18/LlS+7evQtAsWJFsbKyRFRoPGXt2j+pUKECZ8+e/WhfQkNDOX5c9ME/e/Yyp05d0/Aq5KRmpdIGa9asUX9evXo1K1asoH379kyaNIkrV65QoMD7MbRnz1H18/bs2TP1966urhgbG1OoUCFsbGywty9Njx6dKVJELP/w/n0JVCoVCe98Q8zNTRk5sucX70N+wtBQpk4lrVSqGDJkCCtWrODIkSPMmDGDxYsXIUikxDsM4ILgSqxcoHZpQ46OsdGqJdj/BzmkR4+uoldC5CPkcjlTp05h6dKllC9fnoCAgC96/tjYWHx8fABxt+Frjvb8NaFUCUzeE83264lIJFCjpIwUJQzfFolvWO7EZ0iLjY0V0dHnWLNmutZMsiPjVQzcFMmK/8SF6/ffmrJ7WGFKWH2e+WvBguaMGjWK48dPsHfvHvZvX43rN+IidPdDQw1aSAKiPvj7JRIJtGvnlG+Va2fP3qJy5dpMnz6dhQsXalAjGIkkngEDXLGw0Fw+rHtvqqcAACAASURBVPgvjtgkgaolZHSplbPUu5+PMZ06jWDJkiUcO3aM8ePHA7BgwQLKlStHkSK2zJunXd94EFMgbtu2jR49umNq+j4NYunSpZg0aSLLli3DyMhIHbBymktBJBLYcT2RfusjiYzX3i61tnFwKMW331YHYObMAaRdgAM6Y82RE1QqFXfu3GHBggVcvJhWMZ9CpUq2FCokup6dPn2J0NCILNtJXZABTJw4ka1bt/H48WM8PfcwYsSPpN6qzp27qMfg2bNX+fHHcURHR9OmTRu8vb2zbL9kyWIcPLgCK6uC7No1j/btnbI8NiOhPH9+GxcXFwIDA7NRLyOpKY8LFixI//79UalSx68Se3sjRo5sQpEiUKoUbNjwPshk2ufufR3SfKekWDHIK68fqVTK5s1ruHRpPWvWTKN48a8/IGVO6devH1WqiBaEcXHxbN68hZkz3Tl+/ARKw0LE1Pkdub0Y4HpQI1N2Dv38d7wePXp0D32KzizQxTQ7ly5donXrViQmynFxcebYsX/5nGjAOSEh4Tn9+g2nf/8OuLo2+aLn1pN9UpQC43dFc+SBHAMpLOlpSZuqBej1VwT3/VMob2vAvh+tsTTJP/rIB/4pjNgWSUCUigKG8HsXS7rW1n4Oe6/AFNqtCMdACucm2VCq8MfdghQKYwYNWsCQIQNp0qQIuRnQ8Evh5fWSb77pg0KhxNLSEn9/f8zN0ysX4uLiMDIywsgomeym4wTwCVXQZmkYChXsGFKIhg7aj3eQGYIg8OiRD9WrOyDGLyhHVj72Xl5eWFhYULKkCaIffe6QnJxMaGgoRkZG2NjYZKnwOO0lZ+zOaOKTBcpYG7C+fyGdzSQiCAI3bz6mfv3UjBlmQAmePAmgbdu21K5dm6lTp6qDcuY3Tpw4gYuLCwDDhw9i9epZiMoW0XJo6lQPDAykTJzo9tFYOCkpKQwbNoz79x9keUy5cvZs3LhR/QzGxSXQq9c0jh27zMSJP7Jo0cosaiYiujUkExMTly0FIcB//92gU6eJxMcn0rJlS06ePPnZc6HSpUvz5s0bLCws6NWrFwYGBqxePQfR2kLB1KlT+fdfMVD1zp07qVBBDJbp6+tLt27igtTOrgS7du1SWysBLFy4iH/+2YmvL0gkhbl27RoVKnzpYNbepA3aqg1UKoH9d+U88E+hVz0T/ldCE6V4/iE2No5FixZy4sQJdWaNlELVia/xE0ojK8yNJSzobkm76p9SThsCNXK9v59CF9cOevToKnolRBboqiAJCDjHzJnLGDOmNzVqVANKAKJf3YMHD6hevXou7rqGAn651LYebZOkEBi5PYrTT5IwNACPPla0rSa+yENilHRaGU5QtIrGFYzYMKAQhga6vVsvCAL/3EjE/VAMyUooa23AajcrqhTPvUnZ9+sjuPg8mYGNTJnpmnUsi+joOFq1+pGbN8UUhy9eHKB8+dyNARERr2LzlXiOPUyijLUBrasa06pKAQqZaVdGTZiwBG9vP5Yu/YsKFTLGePj+++958uQJ27f/SqVK2U8XOnRLJKe8knCubMz6AYW00eVPkpycwsiRf7Bx42FOndpOixY90Vyh64coC/OWp8EpDNkchX+kkoIFJLkWsDK36Nt3Jv/8cxSA8+fP0KRJc3VZaGgof/zxBzVr1qRhw4aUK1cur7oJQHh4OGfOnOH06dMMGTKEevXqISrbEoiPD6ZQoSqkpKTg4FCK58/3f/Z54uLimDVrFmfOZHStqF+/HnPmzMHa2jrd9wqFgk2bjjBoUEek0pKAGGNk1apVhISE4O4+HjFVrjJDm5oSHh5FjRp9CAwMpWLFipw9e/azfeg7duzI4cOH0323ebM7/fp1IDQ0jM6dOyGXJ2FmZsrJk6cwMXm/+Bw2bDi3bt0CwMHBgb59+1CoUCFOnjzJiRMnCQkB/3eeI927d8fT0/PzLviziEIM1K09bvkmM+twDA8D3lssOlc25sfmZtQpkzHjRH4mLCyMy1eucvSlNf8G2yMgoXIxGau+s6KcrSYKVr0SQo+e/IZeCZEFuihIHjx4gIGBN0ZGig80/KY8fBhNzZqNaNy4MQsXLnw3Sco5T548oUKFCshk8aRmwtCj+yQmCwzdGsnF58kYy2CNWyGaVzbm+fPn6hSdyWZl6bEmgoRkAbdvTZjdyUJn3QbkKWJMiz23xd3FVv8zZlEPy1y34LjgnUS/DZGYGkm4OtUWS9PMz6dSqahevTdeXi8xNJTx33+r/4+9s46O6lr78DOWTDJxgeDuTikUhxI80BaKuzulUCi0F2lLixTX4rQ4xa24uxcNEAgEiHsmk/Hz/XFgIDcJRCYh3G+etbJWZo7MPjP7nL33K7+X+vUzVp4yvTyPNrLijIatVzVoDcm3yaRQs6gdzSvY06yC0iqhq6/7i2jsLAaIzyKDwcCRI0eYMGECAPnyeREYuAd7+/RPji890dNpeTQyKRwa5ZVj3vwlS/5m2LAZAHh6evLo0SPc3dNrABGABxw4cIhPP62At3fOGE5SI1JtYvC6WK4+MyCVwCQ/Z3rVccy19/Fr9HoDvr6DuHr1AUlJOmJjT+Lq6g44Ao4cPHiOli3FnPoxY8Ywa9asZMffvHmTwoULpyiJaw2MRiNSqTTZWL9161Y6dRLLYk6aNIaffnpdPUZc2E+cuJR8+bzw9a1J6dJFstyGwMCnHDlymKioaFxdXfj8889TCN+mjRcHDtxh5MhvePz4MevX/0K3bi2z3Kbjx6+wadMh5s2bjUqVeaPQ/v378fPzQyYDkwkUChmTJ/ehYsV8rF69mhcvxDTTDh2+Zvz48cmODQgIoF+/fqjVKaspgHi+p08diYvT0LJlS3bt2pVqeUhrsnz5cipWLE+dOq68FgrNKsGxJqb/k8Cef8VoOmd7CZ8Ws+PkA52lutVnxe0Y1lhFvZJ2uf5+TwuN3szN5wauPzNw7ZmB60F64pLEC/z6E3FOkn59oMwZIV6PZQqFgsqVs27EyI1rBxs2ciu5M37TRqoIgmD5S46G8eO/w2w2c+rUKU6cOGEVI4Svry/Hjh2jdesWbN78H5ycPlSudu5Fozez4FgiggC1iiuoUdQOF+WHHWzUOjP91sZwKdCAg0LCql5ulhD3t/tQhfwK5nVyZdD6WNZfTKKkt5zeH6gqwbsIihLLb94LEctvjm3uxKAG6Si/aQXql7KjrI8c/1Aj6y9pGNY49TBmqVTKjh0zWbBgCx07+maLAeLOSwPLTyey/7YW06uU6EoF5PSqo+JFjIlDd7XcDzFy4YmeC0/0TNmbQJWCCppVsKdFRSUl0uVNSsmb6jTRgDfgZOlDxYoVo0yZkjx4EMCsWaMyZIAwmwV+OyBO1jp/6pCj6QSDBnVi374bnDhxmvnz52fAACGKqE2e/Ce//jqdJk1qcvDggg9WwcfLScaGAR78uFM00E3Zm0Ck2syYZk65emFiZ6dg5crx6PV6wsJiXukLGYA4II4bN05Z9q1WzQexSosj4IDRqKB27dpotVoaNWqUQpAxIiICV1fXDC8+t27dyrJly7h06RJnzpyhWrWqgAZQU7v2G6//iRPH+emnLsmOFUvaWo9ixYoycODATB4dSZUqLuh0okji/fuBVmnT559/yueff4ro8dcg/h4Zp1WrVnTt2pq7d/cTFgZubiZ27FjJjh1v9vHxyUv//v1THFuyZEmWL1/O5MmTefQoINk2Z2cnhg0bhlzuhYuLiiZNegPZa4B4/PgxI0aMQK/X07dvW1aunJil+y5JL7DsdCJ/nFKjNYBEAp1qODCmmRPezjICI40sO5XI9utJXHyi5+ITPZULyhnayIlm5e1zZEzMLIIg8DLWzLVnetHoEKTnfojRMpa9xslewkQ/Zzp9mrn+lZl2pT6vtmHDRnZjM0J8RDg4OCCVKlEokrs/BUGgb9+2PHr0HK1Wx4gRbREt8u8egLVaLWvWrOHKlSt4e3szY8aMV1vMgAZPT3FBun//QUaNsmflyolWv6aPmeBYEwP+iuFusBgquew0SCVQIb+cWsXsqFXcjppF7dL0nmcHcUlmeq+J4UaQASd7CWv7uFOj6Jt+YG9vj1wut9ToblZByfgWzkz7J4Gf9yVQxEtO4zK5J6T7hL+ObzbHEq8V8FRJWdjFNcc0A0AUQxvYQMXorXGsPa+hf30V9vLUJ3plyhTNUEWI9CAIAucf6/njVCJnHr3xstUvZceQhipql3jjBRvl60RQlJFDd3UcuqvlWpCBf1+If78fUlMyj4zmFZS0qKCkYoHUywC+nyAEoSzh4eEUKFCAatUqcO3aX2zdepCuXVtk6Ex7b2n594UBlZ2EUb45KXLriExWkk2btvL48WOqV6+eoaOjoqJYtWotIObKb9lyxCqe5szyWrCyhLeMGQfVLDqRiEQCo5vmbkPE62dRyZLOKbYNHPgV1auX5ebNB9SrVxax3K/IgwdP0GpFD3GePM6IxjF7QAnI6N27N4cOHaJYsWJcunQpWbSEXq8nICCAmzdv0rVr8oo1ISEvOH78OAAXLuyiWjV4XZqyUCEHfv55MDVrVqBevarW+xKyAUEQ6NNnLDExsaxePYk+fdpa+xMQ0zvKkV5t85iYGK5cuUKzZs2QSEJYs+ZHZsxQsGfPbszm5Iu/ihUr8Ntvv+HllbqwY5kyZdi0aRM3b97k6NFj6PU6ChUqRIcOHZOlbogaE9mrCbFo0SL0evG57O3tnun7TRAE9t7SMv1AAsFxYp+rWVTBpDYuVCzwJt2wmJec6e1d+cbXiRWnE9l4WcOtF6KRvlQeOUMbq2hTWYk8F6RW6o0Cd4PfRDhce2YgLD6loGh+VynVi9hRvbCCT4rYUS6fHLs0xtjswMHBAYVCYSsFb8PGB8CWjpEGuTek6j6iFyIlBoORJ09eUKZMUcTJgTeQjzVr/uLu3bv069ePcuXKWfY3Go24urqi0WgoWrQwgYGnEWu8awGBRYu2sGnTIRo1+oSxY3vi5pZysvj/letBegb+FUuk2oynSkrjsvZcearnWVTyvFuJBMr5yKlV3E40TBSzs3rO/muiE830WBXN3WAjrg4S/urrQZVC79dLEASBcdvi+ftaEk72EnYM9aB03g8vfnX0npZB62MxmaFaYQVLurmRzzXnlbENJoEGMyMIiTMzo71LjnhoTGaBf+5oWXYq0ZIPLJNC60pKBjVUUSEd4mThCSaO3tNx8K6WC4/1GN7qmgXcpDQtr6R9dQcqFUz/b337dgAjRy7k+vXbPHz4gLx54wB1Ri8PrUGgyewIXsaa+a6ZE8M/zz4jhNlsZubMv+jZszX585cBipDVwlBnzpyhWbNmTJ36PaNH++Waxf6qs4n8sk8ct0Z8rsr1hojM8OhREHPmbODBg2f4+dVj9Ojub21VULJkGx4/DsLJSUV8/AskEgdEg7yExYsXM3z4cACCgwPIl88Fsf8mcuXKdWrW7EWhQnkZN64nw4d3yvmLsxJ6vQGDwYhKZX3B3tckJCgZMeJ3/Pz8+Prrr9Pc7/r167Rv357Q0FDOn99MtWpvtHJCQkJeaTmEoVKpqF+/PpUrV7Ziny2FKDqbPRiNRpYv/42lS//i/PnVODtnPJLw9gsDP+2N5+oz0blUwE3KhFbOtK6kfO/3EKU2s+ZcIn9e0JCgFafyhTxkDGqg4utPHFAqcv7eP/9Yx9KTiVwK1KP/r+JbcilUyK+gehEFnxRRUL2wnRWrXdg0IWzY+NiwGSHSIPc+SNI2QqRGQoKOkiW/IDw8km+++YZ586YjGho0QCL163fh7NmbyOUyIiKO2gwN6WDnjSS+3x6H3ghlfeSs6OlmqZwQGmfiUqAYJnnpiZ4nkSnFwMr6vImUqFXMDk+nrPep8HgT3VfF8DDMiKdKyvr+7hkSbNQbBbqviuZyoIGC7jJ2D/O0Srsyy+VAPT1WRaMzwpdVlcz82jVHvSP/zYrTifx6IIGSeWQcHuWVbWGvWoPA39eSWHE6kaBose8oFdCphiP96zu+t0JHWsRrzZzwFyMkTvjrSTKIj32ZFLYM9EgWLfMuBg78lRUrdr7yPLZi9uwBmWrPH6fUTP9HjY+LlBPfeWcg7zclSUlajh27QkREDHnzetCqVfLSg76+Qzl27DI1a1bj1KnzKJXWSSsLDQ3Fx8cHeALEWOWc1uD/gyEiLQRBoGfPSdy9+wRnZxWnTi1/tUUC2PPNN7+zYMGfAGzfPpN27T63HGs0GgkNjaJgwbw53/CPjMjIWD77rDePH7/Azc2NW7duUahQoVT3HTlyJAsXLgSgZs0KXLy4Ngf7oyN37ph4+fIlzZs3z4bzJwAPMZvNGZ4bhieYmHVIzd/XkhAEcFBIGNJIxcAGqgwbD+K1ZtZf1LDqjIaoVyV7vZ2lDKivomstB5zss38svx6kZ/ZhNecC3kTseagkVC9sZzE4VC6oyNKz/t3YjBA2bHxs2IwQaZB7HyQZM0Ls23eGL7/8DpPJRJ06VTh3blWy7WfO3EAul1G1aun/CmX8OLkRpMfbWUZBd+t7zM1mgd8Pq1l6UhTF8i1nz7zOru8c4MPjRaPEa8NEQHhKo0T5fHLql7anQSk7ahS1SzPcPy2CY010WxlNYKSJvC5SNvT3yFR+fUyimS+XRPEsykSNIgo2DPDIcFuswb1gA52WR5OgFWhS1p4/erh98ModCVozdaZFkKATWNXLjSblrHuvxGnM/HVBw9rzbyaR7o4SetZ2pFcdFR5WjJ7RGgTOPNKx+qyGC0/0VMgvZ89wT2TpMKyEh0dTunQ7vvjCl0WLRuPsnPGokOhEMw1nit/l7A6utP/k/d7ahw+f8d1383j6NITp04cnMzRERMSQJ09TAFq1qsf+/UsRMw3Fv7ZtB7B371GkUikHDhzIhsWIGfDndUnG3MDbhoiRn6v49v+RIeJdTJr0B7dvB1C7diXat2+S7RVs/lcRBIHOnX9g69YjODk5sW3btjTvK53uBfXrt0Aigb//nkHhwj450kaj0cigQb+xdu0+8uTJQ0BAACqVNTWPBMT5WMbue51RYM25RBYdT0StE6ffX1ZV8n1L5yxH+iXpBbZc0bD8dKIlrcPVQULnmo50+CR7dHfuBhuYc1jNMX8dAAoZdK3pSM86jhT3kuXgc8dmhLBh42PDZoRIg9z7IMmYEQLECfymTYdwdXVi1Kiu7z/gI8RsFph+MIHlpzXIpdClpiMjmqjI42wdY4RaZ2bU5jiO3hcH2qGNVHzXzCnDHvFItYnLgQYuPRENE/6hyeMVlQpR9bp+KXsalLKnZJ53D+JBUUa6rIjmZayZAm5SNg7woIhn5icaAeFGvloSRYJWoF01JbM7uubo4iUoykj7P6KJSDDzaVEF6/p5fJCQ0tSYdiCBZacTqVVMwZZBnu8/IJ2EJ5hotySaFzGigaqgu4wB9R3pUMMBR7vse95Eqk00nhVJglbg169c6FYrfQaFv/8+Sv/+vzBoUDtmzvwmw587ZU88a89rKJ9Pzr4Rnu+9hwRBoHbtPly6dAeApUunM3hwX14bGUwmCQqFC4IgULNmTS5dupTs+JEjR3LhwgV+++03mjZtmuH2pg8tjx4dYtWqnUybNjxXLPhthggb2UlsbAIDBkxl+vTvKVHizX0lCMKrfmZGLGcbRVhYFG5uzhkSrrUG7dqNZedOUbj0999/57vvvsvyOSMjIzEajfj4SBEFU9PP0XtaftmfYEnbrFJQwaQ2zlYvt6k3Cuy6mcQfJxOTRWNWLaSg/ScOtK2szLJWVUC4kblH1Oy/LeqzyKTwdXUHRjRxyhYn0PuxGSFs2PjYsBkh0iA3PkieP3+OVPoAmUz3KgzYBoie3W+3xPLPHV2y9x0UEvrVc2RgQ1WWKlY8jzYy4K9Y/EON2MlhZntXvqxmnVzbSLWJcwF6Tj/UceaRnvCE5MJNPi5S0SBR2o66Je2TecQDwo10WxlNWLyZop6iSn6B9+RXhoaGWkJH0+pDZx/p6LUmBpNZrESRVkUIaxOeYOLrpdEERZso6yNnyyCPbC/BmRFC4kzUnxGB0Qy7h3mmS2/jfWgNAp2XR3PzuYECblLGtRBzgXNKWGzNuUR+2puAu6OEE99545bOiWl6+lFqPIkw0mxuJEYzbOzvnm6R0cuX7zB69B+cO3eRuXPnMmrUqGTbZ86cibOzM0WLFqVly5wXidy/fz9du3YhPj6BmTNHMnZszxxvQ2qsPJPI1P250xCR2T70sXDjxk22bdvGvXt3EQSBsmXL0r59e2rUqJFrfgPrkR/Ix4EDB5g4cSJHjuzDwyOG7I4Oel8fevDgKfXq9Wfs2OGMGPEDDg5ZG7fNZjOdOnXi0KFDTJ7cnxEjOmJnl75x4Mg9LQP+igXEVInvWzjTrpoyWytamMwCR+7p2HYtiRMPdJZKFHZyaFpeydfVHahfyi5D401QlJF5R9XsuqnFLIi6V22rKPmmiRPFM1mByTpkzgjx/PlzTCYTMpkszZSijJAb1w42bORWbEaINMiND5J///0XmewhdnZGSpcu/cHakZuIVJvo/2csN58bsJPBzK9dyesiZeYhNTeCRKEnN0cJQxs50bO2Y4a96lee6hm0LoboRAEvJynLe7pRvXDWvBYhISFs27aNU6dOkZCgxtvbi5YtW9KmTVuCNUrOPNRz+pGOy4F6dG8FSkgkYknG+qXsKZdPzpQ9Yjm+UnnkbOjvTh6X93sfHj58iNFoRC6Xv7MPrb+o4T+74gFY2s2NlpWyN1UnLslM5+XR3A8xUthDxrbBHum6npxm9NZYdlzX0rqSksXd3LJ0LrNZYOTmOPbd0uLqIGHXME+KeeXsJM5oEmi9IIoHYUZ6fObIL1+mT8Qtvf3obQRBoP+fsRzz1/F5WXtW905/WUxwQxCKExkZibe3dwaOyxn27dtHmzZtAKhUqSRXr65L9+Iku8mthojM9KGPAZPJxG+/TWPXrl2pbm/RogVTpkxBofhfUuOXsHr1Jfr1GwpAy5Z12bdvbrbPl9LTh7RaHUqlCqgIZG1MefDgAeXKlUMQBFxdnXj4cAd58ni89zitQcB3TiQvYky0r67kpy9cckSn4W0iEkzsvqll27WkZBGY3s5S2lVzoP0nyncKUofEmVhwTM3fV5MwvjJmNK9gz7dNnSjrkxuedZkzQvz7778YDAYUCgVVqlTJcity49rBho3cimzKlClTPnQjciOCIFhKL73G3t7+g07ewsLCkEqjkMnMeHpaLxw8OzCbBQ7f02E0C3g5Zc9iMiDcSJcVohijm6OE1b098C2vpJCHnE41HKiQX4F/qJHgWDNnHunZfj0JZ6WEsj7ydHkftl7VMGxDLIk6sezmpgFZrxpx/PhxBg8ezLVr14mNjUWj0RAZGcmFCxf5558D+PnWoWk1H9pVd2BAfRU1i9nh5SRFoxeIVJsJizdz5amBA7d1aPQC5fPJ2TjAA+90pp1ERUVZPEfv6kOVCyqI1Zi5+dzAMX8tDUvbkzebjAJag0DfNTH8+8KIl5OUzQM9KOCeOyfoRTxlrL+YxOMII19Vy1pI69yjatZdTEIhg1W93KlUMGdCle/du8fixYuZM2cO69evw4VoXtpV5c5LA03L26erL6W3H73NpstJrDyrQSGDP7q7Z0D4VAKUQCJRWDmn23qULl0as9lMnjx52LNnAY45WJb3fVQvYoeTvYTTj/RcCjQgIKZ8ZXUs8/f3Z/v27Zw8eZJHjx6RN29enJ3TL2ycmT70MbB48RI2b95seW1vb4dCIcdoFMPiAwICSEiIp27duh+qidmCl5cj69btR6NJomLFEnzxRcNsN7Skpw+JpRdfRxhmvlJGSEgIGzeuJCjoPtHRGpo0KUXVqiXJnz//e++lpScTOXRXh4+LlD/7uqPKYQMEgMpeLIXZ/TNHmpa3x14uISjaSJRa4NozA+suJnHcX4vBJFDYQ24RkIxIMDH7sJrRW+P497kRswANStuxsIsb/eursm1+l3FkQMZFZcPCwjCbzchkMqtEZOXGtYMNG7kVWyREGuRGa6ZYG/0+EkkS9vbpC2P+UCw8pmb2ETUSCXSt6cDY5s7pDvVOD+cf6xi8LpZ4rUARTxlrerunGgpoMgvsuJ7E3CNqi1BTcW8ZY5s506Ji6gODySww7UACK8+K2hstK9ozu6NrlvPz7969S9++/TAaRS+EVCrBw8ODyMgoyz7e3l5s3boVF5eUk6WweBNnHuk580jH+cd6SnjLWdbdLUMLYZ1OZ8nZfV8fMpoE+v0Zw6mHevK6SNk9zBMfK5fINJoEBq+P5eh9Hc72EjYP8khX+ckPSc/V0Zx+qKdXbUd++iJzk9pdN5IYtSUOgJlfu9CxRvaX/RQEgSVLlrB69ZoU2xIqjUPv04DqhaRsH+r93glTRvoRiAZDv4WRaA3wQytnBjZ4vzHhjeK8N1D4vft/aMxmMxKJBInEhKjdo+fFizDkchne3u7IZB92sp4sIqKJim99MxcRERERycSJ/+HKlavJ3pdKJfj5+fH999+nqwJJRvvQx0BsbCytWrVCp9Mjl8v47ruxfPFFWyQSCQcOHGDatGkYDEbkchn79u3LlVE9WeHYsctcvXqPceN65ciiK2N9SApUQKcT0tXf1Go127dvp1evXqxfv4ZffhmMk5MegwGSkuD1EF279mfMmDEjTQNpcKyJz2dHoDXAgi6utK2SfWVTM4reKHDygZiucdxfZ4lwUMhE4e38bjI2XkqyVFOqWUzBd82cqVksZ7U90kfmIiG0Wq2lD1mjclJuXDvYsJFbsUVCpEFutGbK5XLk8ljk8txtNzrxQMf4HfGW17dfGtlyRYOLUkr5/HKkWfwOt11LYvjGWJIM8EkRBev7eVAgDSEkqURChfwKun3miLtKyu0XBkLizOy/reXkAz2FPWQUfqvsYbzWzJD1sey4IYotjWyi4pcvXLCTzaQzcAAAIABJREFUZ30AmTFjJk+ePAGgefNmLFmyhIEDB9K0qS937twmMjISjUaDm5trqmGBTvZSyudX0LKikoGZrAMu9iH5K+/Qu5FKJTQpZ8+x+zqCok1cDNTzZTWl1SpVmM0C47bHsf+2Dns5rOnjQbUsprrkBHmcpey4ruVhmJFutRwzXHLs6lM9g9fHYhJgUEMVgxvmjObGtm3bWLhwkeW1UmmPk5MTWq0OedwDtAVbEJIgo5iXjLLvKe+akX6kNwr0WRtDcKyZuiXtmPqFS7qeo99+O4fVq/dSvXpTPDy83n+BHxjRACFBXOw4A9F06/YfBg36jV9+WcWQIV+jUr1ZgNy9+5j16w/w5MlLnJwccHfPvJc2PaQWEVG7RMYW//Hx8fTv34979+6n2CYI8ODBQx488KdZs2bvnXRnpA99LOzfv5+TJ08B0LFjRwYMGIBMJkMmk1G2bFmSkrTcvHkTs1nAy8ubKlXSXjQZTAI3nxvwcpKmq3JNbqB48QLUq1c1x+ZJGelDBoOB5cvX8eWXXalfvz4FC6ZdGWXnzp20atWKdevWYW+vYdWq77G3FyNZZDJ424bx4sULHj58SIsWLVK97gk74rkXYqRmUQU/tnbOVR5xmVRCiTxy2lRxoFstR3xcpESqzYTGmwkIN3EjyIDRLApozurgypimThTMpVGKmY2EkMvlKBQKqz2HcuPawYaN3IrNNGfDqgRFGflmUyyCAN1qObB5oAdl8sqJ0Qj8sDOeLxdHcT1I//4TpYIgCMw5ksB3f8dhMEHryko29PdIV1i3UiGhXz0Vp8d5M7KJCkc7Cf++MNBtZQw9VkVz+4WBZ1FG2i2J4uQDPfZyWNjFldFNna0iHJWQoOb0aXFy6uXlxZQpUyzho8WLF2fq1KmWfffvP/DOcwmCQFJSEjqd7p37WQMXpZRVvdzwUEm489JIv7WxXA/Sk9UAKkEQmPZPAtuva5FJYVFXN2oVz/0GCIA6Jewon09OkkFg/cWMVaoJijIycF0MehM0K2/P981zxgBhMBhZtepNed7hw4dx9Ogxjh49yqJFC/F0MOIQuBWAn/fEkKgzp3WqDDP7sJo7L8WUqdkdXNN1Pz16FMTixVv5++8j1KjxGYmJiVZrT87gCFQkNFRst0QiwdOzHGJUhzvgxLlzdxkzZh7du0/k+PGr7ziX9ehfX8V/WospEwuOJTL3SMJ7jkjOn3/+xbNnQQDkyePN+PHfs3LlSgYNGmgp8Xzu3HlOnDhh3YZ/IIxGIydOnOTHH//DsGHD+PHH/3Dy5ElLNNt/Exoaavk/tXSLevXevBcWFppiO4jPxmP3tTSfG0n7pdF0Wh5NdKL17sd3cfuFgeEbY7n0JHNjdG5m48aDDB06kbCwMMaNG/fOMSwpKYng4GAAZs6cb3nfz8+Pffv2cfHiBaZOnYqLi3gvnTt3nhs3bqQ4z8Unevbd0iKVwOS26TO+fig8naT0radi/0gv/vnGk371HGlW3p7lPdzYNcyD+qVsC2kbNmxYl9xq0rTxgYmPj2fv3r1cvnwZrVZLwYKFaNu2DZUrV05zIErSCwxaL6ZIVCusYFIbF+zlEvaN9GTdBQ1zj6i5/dJIuyXRdKzhwLgWTunOJ9QZBcZvj2PnqwiFzJbIdFZKGd3UmZ61HVl0PJENlzSvUhyicFBISDII5HWRsqKnO5ULWi8tICoqErNZnPTUqFEDO7vkC+6iRYuSP38+goNDCA8PS/UciYmJbN36Nzt37uDlS3GCVKZMaTp06EibNn7Z5lEs5CFneQ93uq6I5sITPe2WRFO5oJxetVX4VVFiL8/4xOSPU4msOCMu4Ge0d6Vp+ewVvrQmEomEQQ1VfLM5jj8vaBjQQJWuiJR4rZl+f8YSnShQsYCceZ3TtyC3BlevXiUiIhKAhg0b0KdPH8u22rVr8803I5nyyzR0+ZsSTT4WnUjk+xbpz+9Pi3MBOpadFhfiM9q7pjudJzAwGA8PV8LDoxk5cmSu1YJ4Nwp8fZuRL18BdDodMllyz2to6JvvIm/eakAZwAjoSUp6So8eE/jPf/pRtWoZq7aqf33xu5y6P4H5x8Tf5tum7/+tjUYju3eLYotyuZzly1dQqJB4TdWqVaV06dKMGSOWQNy+fTu+vr5WbXdO8/z5C0aP/pYnTwKTvX/w4EGKFy/GnDlzLdf/GkfHN/302bMg6tSpk2z7s2fPLP+n1qf9Qw1M3ZfA2YA3RoAbQQbaL41ibR/3LJVffh//3Nby7dZYtAY480jHwVFe5LNy+p01CY83sfB4IjEaM9Pbv1/osWvXFvz662oePQoiT548aDSaNJ4rGrp0qc7ChZVwdLQjNPQaEgmUK1eWKVMmW+Y/LVu2wGQyMnnyFAD27NlD9erVLWcxmgSm7BEjQrvUdMj1aYZvUy6fgol+H0d71WoNTk6OwP9GSpcNG/+fsEVCfESo1WrUajUaTca8rxnl5MmT+Pn5MWfOXM6ePcfVq9fYtWsXffv2Y/To0al+viAITNgRx/0QUVxwaTc3y+JUIZPQt56K49958fUnYjjy1qtJNJ4VydpziRhN7/aqx2rM9FgVzc4botd8ejsXxrXIWoSCl5OMKW1dOD7Gi3bVlEgkkGQQqFJQwZ7hnlY1QEDyCefTp4EptickJBAZGZli39dERkbSu3dvFi1aZDFAgBj+PHXqVEaNGpWuyAiNRpOpPlSjqB17R3jS4RMH7ORw64WRMX/HUWdaBLMPJxAaZ3r/SV6x5YqGGQfVAPzYytnSJ7KLY8cus3nzITZs+CfFths3/Jk1ax3Tp6/l7t3H6T5nq0pKCriJoas7b7y/DJ3RJDBsQyyPwo3kdZGysqd7ljVGMsLbhq3atWun2F67dm0kZgOqhysAUT8gMDJ1by+krx/FJJoZvVXUvehS04HmFdJvaGrW7DMCAq7zyy+/MHbs2HQfl9uYNm0ae/bs4dChQym2derUiU2bNjF37lyqVKkBOCFWAfGmb9/ZbN9+nLp1+3HgwFmrt6t/fRU/thIND/PTGRERFhZGTEwsAlJqfFYPZ8/8hMWbiFKLXvoGDRrg5SVGd/n7+7/3fJl9FuUEsbGxDBkyOIUB4jVPngQyZMhgYmNjk73/dqTDunV/ERb25r6LiopizZq1ltdvR0pEqk1M2BFHq/lRnA3QYyeDwQ1V7BrmQQE3KYGRJtotieZGJqMI34UgCCw6rmbIBtEAYS+HuCSBb7fEYTLnvtTPRJ2ZuUcSaPh7JOsuath3S8uio7HvPU6hkLNixY9cvLiWv/9ejUqlQq1WM2nSpFeRiAbgKaLuViJHjizmxx878VomoFGjRikcMJ9//rnl/5cvXybbtumyWIXC1UHCmGZZN+jaSI5Wq2PIkGnUrt0HjcYRKJWp86jVauLj41Gr1dZtoA0bNt6LLRLiI+Lx48fIZE+ztUTn9evX+f777y1K3v/N6dNnmDDhB+bNm5tsQP7zvIZdN9+E1qfm8fR2ljGrgytdajoweU88d14ambI3gc1XkviprUuq4fjPooz0WRPDk0gTzvYSlnR3o34p61m8C3nImdPJjUENDdx8buCLqhnXWUgPXl5elC1bFn9/f/z9H7B7926++OILQCzptmDBAvR6saRo/fr1kx0rCALjx4+3TIglEqhQoSJabRIBAeLC+cKFi8yZM5cJE8a/sx0vXrzIdFm8Mj4Kfu/gyviWzmy+omH9RQ0hcWYWHk9k6clEmldU0ruOIzWKKNKMljl4R8uEV3ohgxuqGJAOgcKs8uOPS7h06Q4gesPEtontO3fuFmPHiuG2BQvmo0KFsq+2vXuyr5BJ6FNXxdT9Caw4k0inGg5pGsUEQeCnvQmceaTHQSFhVS93qwt8vo+3PbRPnz5NsT0wUOxbiojL5OMZIaYi/Lw3gTV9Ui+j+b5+JAgC32+PIyzeTHFvGRP9MjoJd8TZuQj/+c9/Mnjcx0OZMmUoUyZllENCQgKBgaLHXCKRUrBgxvOc08Pre+/XA2JExIXHemRSCTqjgN4koDOIEWh6o4DOKKA1SElqsgukcvYD+38Ot5yrSVl7RnzuiNlsftXu9z9Ds/Isym62bNlCSIiYLlG0aFG+/XYUlStX5t9/bzFv3lyePn1GSEgoW7duZeDAgZbjSpUqRY0aNbh69SphYeG0a9eeRo0aIZNJOXHiBBqNaLCsWLEClSpVQmcUWHMukUXHE1HrxAV/60pKxrd0otArraKdwzzpuzaGOy+NdFkRzYLObjTLgEHvXfx3hGGfuo50q+VI20VRXHyiZ9npRIY2ypmUsfdhNAn8fS2JOUfURCSI/aygi4kX8TLWXNDRp77pvRWcGjb85NV/L9DpilOpUiWePn2Kvb09PXpUo0iRN9URnJwckwkVvp1qk9p7b4tdxiSamf3KsDemmRMeqpz39wmCwIMHD3j+/Dl2dnZUrlwFd/eslZXOTQwYMJX160XHwpAh01m7di2ZyRZ5/PixVUt02rBhI/3YIiFsJGPx4sUWA0Tjxo3YsmUzJ0+eYNKkiTg5iZORs2fPcv36dcsxV57qLarrP7Ry5rP35PZ/UsSO3cM8mfqlC64OEvxDjXRaHs2ozbGExb8xflx7puerJVE8iTSR31XKtiEeVjVAvE0ZHwWdPnXMFgMEiJPybt26Wl7//PMv9OzZk59//pmvvvqKHTt2AiCXy+jYsVOyY+/cucONGzcBMQ97y5Yt/PnnWrZs2cLixYuwtxe/7z17dhMT836PUFbxdJIyrLETZ8Z5s6SbGzWLKTCaYf8tLR3+iKb1gii2XtGgNST3ol14rGPk5ljMAnSq4cD3Law/uY2Pf+3NUALlgCrI5W8E/0ymKsAnQHWgOgpFccs2ozE/orp2JeD9td8713TAWSnhSYSJY/5pR6H8eV7DuosaJBKY19mVigVyPsy1Zs1PLf1k167d3L//xlOdkKBm8eIlgGh+GVJLLKN54oGOY/e1mfq8TZeTOHxPh0IGCzq7ZSLqI23RuP91XFxcOHHiBN26dWPDho1Urtwg2z5rQIM3ERGXnxq48ETP9SADd14aeRRuJCjaRGi8mRiNQJJBAtLkfgvZq5/1mL+OL5fE8LTwCIwuJSlfvny2tTm7EQSB3bt3A6I47/z586hXrx4uLi7Ur1+PefPmWwyOr/d7m59//on8+fMBovL+wYMH2b//gMUAkSePN7/88iv/3NHhOyeS6f+oUesEKhWQs3WQB4u7uVkMEAB5nGVsGehB4zL2aA0weH0sf13IukZKpNpE1xVvIgynfunC5DYulMwj56e2Yp+Yc1jNzecfVh9CEASO+2tpOT+KCTviiUgwU9hDxpJubqxsn0g5bwM6o4R5RzPiydZgb5/I11/7AWA2mzh7NqWmQ6VKlS2GiH/+OWgx1oLoPPjjjz8sr2vV+szy/5wjamI1AmV95HStmf2Vj/6bCxcu0K1bN7p168748RMYPXoMrVq1ZMqUKSmidz5WfvxxMCqVCqVSScOGDW16FTZsfITYqmOkQW5UuBUEAZVKg6OjHSqV9Qe2p0+fsmDBQkD0/ixfvgwvLy/s7e0pW7Ys3t5enDx5EhDLEDVu3JiweBPdVsag1gm0raLkh1bpU3+WSiRULigu/OO1Zu4GG/EPNbLpUhIKmYQXMSYGrY9FrYNKBeRsGuCRrfmwOUHJkiWJjo7h3r17AERERPDgwQNLOSepVMLEiROpVatWsuM2bNjA7du3ARgzZkyycPqCBQsSGxvL7dt3MJnMFCtWNFXv6mvMZgEHByWOjqos9yGpVEKpvHI61BAFrExmeBRuJDTezJH7OjZc0hCXJFDMS05QlIleq2NIMoiCjHM6ulpV8d1oNDJhwiKGDp1O9+5dUKkqIeaISlGpnKhbty5+fn58+mnNZKr9Hh4eNGjQgK5du1KnTh1cXV3FSe/x8wwb9gNKpYLy5Yun+pl2cgnxSQJXnxkIjTOlWmbzhL+OMX/HIQATWjrT6dOcn5ACKJVKwsPDuXfvPkajkV27dnLnzh3Onz/P9OnTefHiBQA+Pnn5ddI4koxSrj0z8O8LA11qOiL/r4oo7+pHAeFGBq2PwWiG8S2daVkpfV5bnU7PH39so3LlGsjl/3+NEAAKhYJ27dpRtmxZxEobSiAeEEhISLQYlKzBJ0XsqF/KjprF7PCrouTLag58/YkDHT91oGstR3rWdqRPXRUD6jvi8Gw7AXsn4fh4EwViDjDK14k2le15HhpNhMEZs6oQuoItcChQnQqFnd/pmbbms8iaaLU6Fi4Ux8FKlSrRs2fPZNtdXV04f/484eHhqNWJ9OrVM5kej5OTEy1atECrTeLp00AMBjGtSalU0qaNH91HTmXqMTuWn9EQnyRqEP3c1oWf2rpQ0CP1Mc5OLsGvspIItZnbL42ceKAnySBQt4RdpuYkD8MMdFkRw4NQI85KCSt7uuP3VunI8vnkBESYeBBq5MITPR1qOGCXCe2frHLnpYFvt8Sx6EQi0Ylm3BwljGvuzKwOrpTNp0AQBIp6SNh7F+4FG2ldWZmBqIM4atUqycuX4WzZMo1GjWqk2MPe3u7Vc/PeK02U3Tx//py7d+8yc+bvFjFKBwclP/00BaVSyb1gAxN2xCMgilvn9Lzl8OHDjB07NlnpbwCTyczDhw85ffo0zZs3e285yqioKKKiorGzU6BQ5DZ9CDe8vGpSqVIVxowZQ8uWLTN9JnFercLZ2Rln56ynzeTGtYMNG7kViZBVmfv/UXJvrd/7QPbk0J45c4ZRo74FoF+/vgwdOjTZdp1OR506Yh5rxYoVWbFqDV1WRHPtmYGyPnJ2DPXIdJ77rRcGJu2O5+ZzQ7L3fcvZs6CLa47mz2cngiCwb98+1q/fQEBAgOX9zz6rRZ8+fahRI+VEaNKkSZaKGVu3bqFEiRLJth8+fJgJE34AYNSob+jRo0ean3/hwi127TpJv35fULp0EWtcUjJiEs1suaph3QUNL2PFkFmpBBwUEhL1Ap8Vt2NtH3erR5yMHTufWbPWAdCkSRMOHTqETJa5lIczZ87QoIHofa5ZswIXL65NcwIRFm+i3owIDCbYMdSD6m+VGPUPNfD10mjUOoGONRyY0f7DqqNrNBqGDRvGrVu3U93u7OzE0qVLKVeuHGqdmc9nRRKeYGZscyeGNU5f1IreKPDVkijuBhupW9KOdX3d063dMnv2er77bh6FCxdizZq1yfKtbQAksmzZdH77bSV79syhSpWcT2FISFDTr19fHj9+kmKbyTE/ScU6ocvXGCTi87pJWXu+8XWyusZOdmIwGKld+zMEQTTy7tq1M9l9KwgCX375FS9evEAigYsXL6YpCpyUlMTTp08RBAGleyEWnTGx47oYXaRUwMAGKgY3VKV7fBMEgcUnEpl1WPT6t6miZFYH1wyJA598oGP4xljUOoEinjJW9XKnZJ6U7Y/TmGm1IJKXsWa+/sSBWR1c0/0ZWeVlrInZhxIspbLtZNCnroqhjVW4OqT8rgb+FcPhezp8y9mzslfqKWSZJSFBzeDBg/D3f5DqdrlcxvTp02ncuDGCINBpeTSXAw20rqxkcdecTX+IiYnFz88PrVb83sqWLUuTJp8TGRnJ/v37UavFCJq2bdswefLkFMcLgsCBAwfYuHGTRddFLpfj69uE3r37UKpUyZy7mLcICYlk7dq9jB/fB4mkIJkpxZlT5N61gw0buQ/bXWHDwtsVG6KiolJsf/s9pdKeqfsTuPbMgLNSwh/dMxNy/YbKBRXsGOLBzK9d8HzlyehT15FlPbJ23tyGRCKhTZs2bN68iT17drNx4wYOHz7E4sWLUzVAALi7v5lUvY6IeJtbt25Z/ndzS3vSExYWRZMmQ5g58y/q1u3HkycvsnAlqeOukjK4oROnxnrzR3c3ahe3wyxAol6gQn45K3q6ZUvKy+jRvfDxyYtcLqdNmzZZGvDr1atnyQ0ND48hPDw6zX3zusj4sqroQVxx+k2IdESCiX5rxQihz4rbMfXLD1+ezdHRkSVLljJ48CC8vLws79vZKfDza826desoV64cAE72Un54Faa/6HgiwbHpEx6dfVjN3eCMleMESErSMm3aGkCsSvC6fK2NN5w8eYXhw6cTFBRK3br9eP489RKP2YmzsxPLli2jXr16KbbZ68PpU/45R771oF11JVKJmKbRdlEU/dbGcOuFIZUz5j4UCjlVq1YFRN2Kw4cPJ9t+6NAhS+RQ1apV31mVyMHBgaIlynIkuDCtl2gsBoivqik5Psab0U2dMzS+SSQShn/uxJyOrsilsPdfLT1WRROneX8JT0EQWHsukb6vnks1iynYNdQzVQMEgKujlLmd3JBKYNu1JPb8+34B3qwSrzUz42ACjWdFWAwQX1RVcmyMFxNaOadqgAAY18IZmRSO3tdxOdC66SOv+3znzp1TROxUq1aVpUuX0rhxYwD23dJyOdCAUoHl+ZmT7Nmz22KAaNGiOevW/UXfvn0ZN24cGzdutLT/4MGDKdIyBEFg6tRfmTRpcjJhWaPRyMGDh+jVqycXLlzIuYt5xalT16hWrRs//LCYJUtOkZsNEDZs2MgYtkiINMi91szsi4RQq9U0b94CrVaLUqlk48YNFCkiessFQeCnn35i7959ANTp9gt7w6sBsLq3G5+XtV6JxQStmeBYE2V8Ph7vWXZy584devXqDYgClwsWzKdMmTIIgsC5c+cYO3Yser0Be3s7Dhw48E5DxM8/r2fy5HkAnD69gvr1q2V7+x+EGrjwWM8XVR1wzxaBLiegOOfOXUYQhFQXSBnl4MGDxMXF0b59OeTydy+eHoYZaDY3CokETozxwsdVRpcV0dwIMlDMS8bOoZ64OX7o50ZyjEYjz5+/wGDQkz9/fovey9sIgkCHP6K5+sxAmypKFnZ5t1fvXICObitjAFjWwy1D1TAA7twJZOzYleTLl5/Vq1dn6Nj/D4SEhPDVV19x6dIlxozpx6xZQz5oewIDn3Lq1EnUajVeXl74+vomM24FRhpZeFzNrhtaXhdZ+FgiI96OLpNIoFmzZlSqVIlbt25x5MgRXs+apk+fRtOmTZMdKwgCAeEmzgboOBeg5+ITvUV0snphBZPaOFO1UNbTac4+0jF4vRjRUDKPjLV9PCjonnr0l8Ek8NPeeNZfFA0JHWs4MPVLl3SlWMw5nMCC44k4KyUcGOmZTK/CWhhMAhsvaZh/TE10ovhd1Sqm4MfWLunuKz/sjGPjpSSqFRYdGtlh9E1MTOTevfvodFoKFSpkmR8BaPRmmsyOJCTOzOimToxskvOCnsOHD+fChYsAbNu2jWLFiibbPmPGDLZu/RuAefPmJhPB3rZtG9OmTbe8LlOmNIUKFebq1SvExopVjhwdHdi1a1eOGol37DhO+/bjAChWrBj3799PJgKa28i9awcbNnIfNiNEGuTeB0n2GSEApk2bzrZt2wAxz9HPz4+8efNy/Phx7t27D4DEozQJteagM8IoXydG+eYO9ez/VQRBYPDgwVy9es3yXtmyZdBqtTx9+qbufOfOnd5TztCL2FhXSpQowdmzxxCd3ukvrZlbSExMYsGCzYwd2wO5vABQgNfVLqxPFGLZtnfTZ00MJx7o6P6ZA3FJAnv/1eLqIGHnUE+Ke3+8WiZ3XhposygKQYDNAz3SFJ2NSTTTYn4kYfFmutR0YFq7zIRuFwB80Ov1yaKybLwhKSmJpUuX8s033yCThQEhH7pJ7+VjNEYIgsDEiRP555+Dae7TqlVLfv75ZyQSCWHxJs4F6C2Gh7D45JEJBdykjG/pjF9lpVUXx/dDDPRZE0NovBlvZylrerunEL6NSzIzbEMsZwP0SCSiNs2A+o7pbofRJNBxWTTXgwzUKKJg80CPFBoxWeFGkJ4xW+N4EimORSW8ZUxo6UyTchnLow+PN9Hw90iSDAJLu7mlW4vGWsw+nMDC44kUdJdxdLRXtolcv4tBgwZZ5gknT55IoXGwatUqlixZCsCMGdPx9fUFxPlu+/btCQp6Dojiqq1btwbEKLUffpjA6dNnABg6dAj9+vXLkesRyceYMbO5ffs2GzZswNvbOwc/O+Pk3rWDDRu5D5sRIg1y44Pk3r17SKUPsLMzUrx46mJ5WSUhIYEBAwbw6FFAqtsFO2dotpZonT2fl7VnZU+3dIdc28g80dHRDBkyNJmOxNvUq1eP33+fmWLxFhQUSuHCPkAeoBD37t2zlKMqX74Q8Aj4eB4BDx8+o127sdy9+4Tvv/+G6dPnZfMnCsBtxBryaXP+sY6uK2Isr+VS+KufO3VK5F6PTXr5cWccGy4lUdZHzr4RnshlEp48eWIpr1isWDEGrYvl8D0dxb1l7BvhmYkUKjugAv8LGYIBAQEcOnSIxMREihQpQps2bXB0zC7hxWiSkvxZvvxP7t+/jURiJE+evLRq1ZKaNWt+8BSgt0nNGFHGy0RpbzO1y3pSPr+cMnkVONjljjabTCbWrFnDpk2bLJ5gEFPe2nfuTsnaHTn/xMi5AD2Pwo3JjrWTQ82idtQtaUf9UvaUzyfPtnEyJM5EnzUx+IcaUdlJWNzNjUZlxOfO00gj/f6M4XGECUc7CfM7u9K0fMYX58+jjbScH4VaJ/CtrxPfWMHxIAgC6y8m8fO+eAwm8HKSMsrXic6fOqTbyPH2c6h48eLMOZLAgmOJFPWUcWS0FworGkveRVCUEd+5keiN8Ed3N1pUtI4BxGw2pzrnFAQh1Xt76tSp7Ny5C4Aff/yBdu3aJTtXt27dePjwEQCbNm20lMZ98uQJHTp0BOCTT6qzfPnyZOcNCQnBz68NAOXLl2PdunVWuLrUiYqKxdPTDZADRQFXDAYDUqk00zpP7yL5nCjrVX1y49rBho3ciq06RhrkRoXb4OBgIAKJxJht4XD29vY0b96c2Ng4AgOfYDK98ZSXLFUKB995PEtwoIinjD/7uOMuA2LJAAAgAElEQVTwP6TXkJtxcHDAz681Li6uhIQEExcnToorVqzA0KHDGD58WAoF699+W03HjuOpW7cxRYuKFTWCg4MxGMQFtY9PYcSBPo7nz0Nxdc39ES337z9l9uwNmM1mbt++T9++fVNNJbAeEkAgPj6EpCQdSmXqRoWC7jKO++sIf1W/fno7F1pUdEh1X2uQ/PeSAgK3bj1iyJDp6PUGChf2wcHBOgaQ6oXt2HJVw4sYM55OUqoWsiMiIgKjUVx4HX7syPIzYlnPP/t4UMA9/ZEfbyo9FAJUVmnvhyI0NJQuXbowYsQIDhw4wNGjR9m2bRtLlixBJpNRp04dq48f58/foFGjtuzYcZabN18QHx9MYOBD9u8/wOXLV2jQoAEODjnrEU4Ld0cpzSsoaVtVSYLWzINQA5EaKQ8jZRzz17H5ShJLTyay75aWa8/0BEWZ0BoEnJTSD2KYkEqlVK9enc6dO1OhUlXyVmiCW/UeaEv3ZFdQCXb/q+PmcwPRiWYkErGKU/tPHPjW14lfvnCl46eOfFrUjjwusmydNzgrpbStquTWCwOPI0zsvaXFx0WKWifQfVU0IXFm8rlKWd/fg8+KZ+6Z4OogJb+bjIN3Rc2FuiXtyO+W+QVhkl5g3PY4lpxMxCxAy4r2rO/vwadF7TJkrHn7OeTp6Umlggq2Xk0iOE6MDKlihbSX9DBuexwPw0zULWnHuOZOWf69BUFgz55TfPXVdzRqVIM8ecoC+QEjISEvqV27DwqFnIoVSyCXv/kd3N092LVLNEJcu3YVV1dXChQowMuXL/n999+5cuUqAOXKlaV///6WdgYFBbF79x4AGjZsQN26dZO1x9nZmY0bN6LX61EqlXTu3DlL15caL1+GM2HCInr3/omGDetSuHBDXo8JMpks2xbxyedEPlk+X25cO9iwkVuxRUKkQW60ZuZEJMTbxMXFcevWLbRaHQULFmDvs4IsOZmIg0LCjqEelMuXO0Npc5qXL8NRKu1eWe9zBoPBgEQiSVMUbcuWw3TuLOY0q1Qq/P39KViwYAqrvyAIzJkziQkTprNv3zyaNfss1fPlHtyZP38PK1asZPv27e8sR2oNIiIi+P33GSxbtowRIzoyderQNPc99VDHgL9iGNxQxeim2SNKdvjwRX79dTVXrtzl2bMjeHuXAzwBPZMmTeCXX+YCsGTJeIYM+dpqn7vuooaJu+JxUUo48Z03ceFPMRqNBKsVDN7pgNYgCrENbJB+Q4IgCNSp0xd3dzdmzlxCxYoVrdbenCYyMpLatWunGakEMHbsWGbOnGm1z7x//z41a9ZErVZb3nN2hlKl3uxToUJ5Vq1alQtL7MGFW4HcChYIjFEQnKTiXrCRSHXqAos+LlLK51dQIb+c8vkUlMsnp5CHzKplft8mPN7E9SAD157pufbMwJ2XBvT/lblWxFNG3ZJ21CtpT+3idtmkd5N+9EaB8dvjLIKOMimYzFCloIIVPd3I845yqenl2y2x7LyhpYCblH9GeeGizPg1B0YaGbI+Fv9QIzIpjG/hTP8MpIe8zX9HQgCsu6Bh4u54PFVSTo3zwsk+e3+XM4909FgVg0wK/3zjSem8Wb/X1q8/QI8ekwBo0qQxR44cs3w/Y8eOYtas+QBMnjyAKVMGWY4TBIHx48dz9OixNM8tlUpYuHAhn332Zqx/+fIlbdt+AUDJkiXYvHlzst/j/n1/unfvDohinCtXrsz0tRmNRu7ceYyPjyc+Pm80ZIKDIyhQQCy1mT9/fm7evJkjqRe2SAgbNj4cNiNEGuTeB0n2akKkxaG7WgatE9WU53d25Yuq2eflzUni4+PZs2cPZ8+eRaPRkCdPHlq39qN+/XrvVD2H12rSq5g8eRmrVk2kT5+2OdTq96PXG2jffhL79h1h5syZaWpFbN++na+/FherLi4qbt/e8ip9I3eQmJiESuWAGJFQAMiLIAhotVocHLK/D758+ZJixYphMBhwd3chKGgfTk5ph9abzUK2pieNHj2HuXM3AjBx4kR+/vlny7bGjRtz8uTJV+2+Rf78SiABEAgOjmD9+gN89VVjSpUqnOHPNZkF/BZGcT/EaNF8yEo5ToC//z5Kx47jAahUqRL//vvvR+stGjZsGEuWLAEgb968jBgxgpIlS7J///5kocvXr1+nWjXriMF26dKFzZs3A+LYpFI5cu7cRgICLjF79mwiI8VqRlOnTqVlyxZW+czsRBAEIhLM3A0xci/YwL1gI/dCDARGpq5bYyeHop5yinvJKO4tp7i3nGJeMkp4yzMkBGs0CfiHGrkeJBocrj0z8CIm5Wd6qCTULmFPvZJ21Ctply0CjVlFEARmH1az6IRYqad1ZSWzO7haTZ8gQWum1YIonkebaFtFyfzOrhm6Zw/d1fLd1jgSdAJeTlIWd3WjVho6M5nFYBJoNjeSwEgTIz9XMbpZ9lWpMJgEWs6PJCDcRJ+6jkxu42KV82q1EsqV+4qnT4No1KgRu3fvxsXFBUEQaNeuHbt27cLe3p6nT8/g4yPj7ZRKrVbL5MmTUzVEODgomTx5Ck2b+qbY1qdPH0v55u7duzFo0CAcHR0JDHzKDz9MsKRx/PDDBNq3b5+p69q58wQ9ekx6pes0lhEj+iIKS6sAJ4oVK01QUBAjR45kxowZH6U2UO5dO9iwkfuwGSHSIPc+SHLeCPE4wsgXi8R80L51HZlkpYH2Q3PhwkXGjx+fzJP4mvLlyzF37txkau//zfDhM1i8WFSaDgi4RokSXoAaSOLhw2e0aDGShg2r07Vrc5o2zekIg8Jotc78888/fPXVV2nuZTabadeuHbt372by5KFMntwn1ywE/f2f4us7lPnzv6d9+4GIk5Wcp3fv3mzevJmePVvx669D8fa2bh36tFCrNTg42L+VB+tKUJCBEiUqU7JkSSZPnvx/7J13fI3XG8C/994smVaiISKRGEHsWX72HhU0KLVX7a1oVVGqVs22ZtAiRdWeVXuUGjFCxEiMCNl73PX745UrV7Ykcun5fj4+cu/7nvM+573nPe85z3mGnlmsWq3mwoULXL58mfHjx6d8C0SyatUKRo2aBcDy5ZMYPTrn5rSXHiXTfXU4MhnsGVmMAzcSWX06jsLmMg6PlbKC5IS9e08xatQinjx5zoEDB2jfvn2OZTIEYmNjsbe3JzY2FnNzc3x9ffWi5s+fP59p06YBMGTIkDT+1m9DZGQkdnZ2KJVKihcvjq+vL9HR0bi4lAUecunSUYYPl6x2ateuzerVv+T6mgVFbJKGu89V3HyaxPErT7gdpCSKYmhkGSsBilrIKFvc6JVyQoFzcSNcbI1wLKogLknLtSeSwuFqoJLrT5QkKPWnQTIZVChhRM0yxtRyNKFWGWPKFMtft4q85C/fRCLiNXSrWSjPlaJXHyfj+Us4ag0s6W5D15pZK4NVai0Lj8ay+pSkHKnjZMzKXoUpkQfWGelx6GYiw7dEUshYxqnJxfPECiQ91p+NY87+GIpaSBZiGaUQzQylUsW9e4FUruwCKAB7wI5Dhw4THx9P165d0/S7S5cu4ePjw5AhQ4BkIBgIY/fuv7l48Sbjxn1GaGgwe/fu5fHjx5iamlK7dh06deqYYfasM2fOMm7cON1nMzMzbG2L8+TJ61Te9vYfsX379kxj3CQlJbNjx1+cOnWVWbOGUbJkijWDEVevBlCrlgcgBdLets1br+zVq1dxdHTMdN5l6Bju2kEgMDwMQgkRExPDnDlzuH79OteuXSM0NJSZM2eSXrgKpVLJihUr8PLy4v79+5iamlKpUiUWLVrExx9/nOE1nj9/zqpVqzh+/Dj+/v4kJydTrlw5hg0bxqBBg9IEvDHcgSRnSojo6GiOHTtGUNBzChUyo0GDBlSuXDnb5WOTNHisCuP+SzV1nY3ZMrjoOwv2lJ/cvXuXgQMHkpSUcU7x8uXLsWnTpgy18adPX6NlyxEolUpu3ryZypxcxbp1PzFkyFgA5s0bybRpA/TKPnr0DCenknk2qVWpVCQkJGFlZYEUzCn7MUNiY2M5ceIEnTq1QepfqqyKZIvExESOHj3K8ePHiYyMpHDhIrRq1ZJWrVplmWIrKCiE+vX78+TJC6ysrLh8+XK+u15kxNOnTzE2NqZEiXggPN+v9/JlOMuXe/PTTztZt24GXbt+ipQbXZrsX716lerVq+doLGrRogV///03AD4+B6la1Z63yYwy1juSPdcTcSyq4HG4VP5t0nFKyEhIcGbXroP06tXrvVngvcnFixdp0ECKudKnTx82b96sdzw2NpbChQujVqupUqUKN2/ezPU1fXx8qF69OgD9+vVj48aNqY5q0Wof0KJFLYKDoylTxpZDhw7l+poFycOHDxk/fjxPnz4DQIscjZktaotSFHOqQc0mXQiON+FhiIrg6PRdOgBkWg1aWdrnxspURo0yxtR8pXCoXtoYq7dwNfivsOJ4LIuPxWJhIuPg2GKUKZaxQigkRs2YbVFceCi9awc1MmdqO6t8nUdotVq6/iylSX77bD2ZExqrptnCUGKStMzvak3PujkPPnvs2EXGjVtCSEgE/v6nsLFxQ4rTlHO02mSqV6/OjRt3MDMz5caNbTm2evv9999ZuHAh6a0KSpSwY9WqVTg7O2dah6fnl+zcKVlhbN/+06uAl5aAKSqViipVqlCtWjXat29Pv379ciTf+4Dhrh0EAsPDIOwJw8LCWLNmDdWqVcPDwyNDfzO1Wk2XLl04e/YsU6ZM4eOPPyYuLo4rV64QFxeX6TWuXLnC5s2b6du3LzNmzMDY2JhDhw4xfPhwLl68+MHlpddoNKxevZpff/1Vb6H988+/4O5ehTlzvqN0aYcMy2u1Wv6+m8SPf8Vy/6WaEtaS6eSHoIAAWLt2re6+NGrUiHHjxuLo6Mj58xeYP/97goNfcO+eP8eOHdOlqtLHmMaNe7FunQmFCxd+w5/diJcvYzE1NSUpKYkmTXoArkim8bFERATj4uKBrW0R+vbtwMKFY3PVFqVSxeefz+DZs5ccObIPC4ucBS21tLSkU6dOrz65APfIbcYMf//7jBs3luDgF3rfnz17ljVr1rB06dJM45oUKWJFjRpuPHnygrJly2a4e/MucHBIeU7ejRLi6tW7zJ0rjUc//LCdLl0m6i3Qa9asmeM6V69ezZ9//smlS5dwd08xzY8BngCJ2a5nWjsrjvkm6RQQn9Ut9JYKCIDiFCpUhN69e79lecMgdfDe9FyETExMUCgUqNVqvXNzQ2ol3osXL944KiM21o5r12KJigJr64wX5e8DISEhfPHFF4SFvX72ZGhQJL5AkfiCmLCrPAo5yq+//oqlZVHikjQ8ClXzMFTFw5cq/rrkz92geFSFSqI1khaK8rinmEb70a6uA8O6fUw5u/zLXvEhMqKZBWf8k7gUoGSMdxQ7v0h/c+JKYDIjtkTyIlqDhYmMBZ/a0KFq/gdKlclkTG9vhecv4Wz/N4FBjSxwtcvb6e7Cw7HEJGlxL2WEZ+23cw1cu3Y3vr4PAfjuu80sXLjwreW5ffsed+8+AKBq1Uq4ujqTU0Vzjx49qFGjBt7e3pw7d56EhHg++ugjOnbsiIeHB9bWWVvBDh/eX6eEOH/+Hp6er+cjRkZG3L17N0cyCQSCDxeDsIRIEUEmkxEaGoqtrW26lhBLly5l4sSJnDt3Ti+oTnaIiIjA0tIyTYCuUaNGsWrVKh4/fkzp0qV13xuiNvP58+fIZHdRKJKxtc3cXG3hwoV4e/+e4fHixYuzadPGNNGA1Roth24lsupEHHeeSzviFiYyfh1chJqO759/XnpERETSunUrNBottrbF2bNnj96k/sqVKwwdKgV7Sm3KfO9eIOXLl0HyX3QBMg9AlZSUxKVLl6hXr56eNcW+fXv45BPJJHHMmD4sWzaO1Iv+S5duUbGiE9bW2XM/GDhwFl5e+wBo164dBw4cyHBX+fnz56jVahQKBfb29hnUGE5AwDlOnrxC//6dMjgnY0JCQundu5feouFNbG2Ls23bNooUyci1wQiVypVvvpnL2LFjKVGiRI7lyB/8geh8rN8YrdaW6tXbcufOHXr37s1PP/2Ub/Evnj+/z5dfjqVly7r07dsxW2V+ORXL/EOxlCkCv/ZR4FjybYKHKYAqGIgePFeEhYVhb2+PUqmkWLFiPHjwABub1zuvGzduZMAAyRKqR48eujgOuUGlUuHk5MSzZ8+QyWScP39e753YuXNn9u6Vot0bGyt4/PiAXhA4QyAkJBSNRo1crsj0ffbjjz/y229bAMk6bfz48bi5VeLatassXryEp08lc/Hx48fpguelsGXLFpYskYK1agGtaVHQKJErX7/bv/76a7p08cjj1n34PItU025pKNGJWkY2s2Bym9exF7RaLZvOx/PdgRhUGnC1U/DL50XyXBGQVR8asjmCY75JtKpkytq+eedG5/NEicdPYWi18MfwotQq8zZzIxMCAjRUrFiP6tWrs2zZMurVq5cruYKCgliyZAnNmjWjQ4d2QAjwAlAyYcISXF1L07Nna4oWzb1liFarZffuk9SoUQEnp5KADVLcpkJ89dVXNG/enAYNGuRjeuK8IXtzouxjiGsHgcBQMYinQiaTZcsUd9myZTRu3DjHCgiAIkWKpBshvG7dugC6iYwh8/LlS0JDQ4mIyHw39s6dOzoFhFwuw9PzU1auXMn06dN0u7qhoaG6QGogBVja8W88rX4MZdTWKO48l3KOD2tiwcnJxd+ZAkKj0fDkyVP8/f11aSizg7//Yx4+fIq0qMm8LwUHP0fzKlF9w4aN0rgG1KxZE2traUL19OlTtFotc+eux83Nk507LwLlyUoBAdJu5f/+97807hyWltZ06NABa2trWrfuAVRDUmrYolTKadVqJMWKtaBLl0nZavvo0Z9hY2ODmZkZo0ePzvRZevnyJcHBwbx8+TLDc86fv0vdugMYOHA2u3efzJYMqdm6dYtOAeHmVhEvrw1cvnyJdevWUb68FLo/JCQ0EyWZAiiHkZEF8+bNMyAFBGi1dhw7dpGrV/NmN0er1fLyZTjSUOwIVEEms2fDhg08fPgQLy+vfFNAPH36lPLla/DrrweZMmUF0dFpY6Okx9D/WfB1s3jmtoggMTYiR9d88OApM2b8TEyMBR+CAgKk1IApwV3DwsJo0qQJO3fuxMfHh7lz5zJixOuMKkOHDs2TaxoZGTF8+HBA6kNNmjRh4MCBLFq0iJYtW+oUEABz5owxOAUEQEREOGFhYZm+z9RqNfv2SQpWExNjVqxYQd26dbGysqRx48YsXrxId25KasIUYmJi+fnnn3Wfe33Wk11bVrPjt7V069ZV9/2KFctJTMy+NZBAolRhhc7N4aeTcVx85W4Rl6RhrHcU3+6TFBAdq5qxZ2SxPFdAQNZ96Mu2VshlcMw3icsBGbte5gSNRsu3+6LRaqFrDbNsKyAuXbrFlSt3kMb6kkBlnJyq8c8//3D+/PlcKyBAyiqxaNGiV9abciQ3PneePSvEsmXejBz5Aw0bDiK3e4937wZQp05funadzOzZm4CKSNae0rtq7ty5tGjRwuAVEJC9OZFAIMgfDEIJkR2ePHlCQEAA7u7uTJ8+nRIlSmBkZETlypXZtGnTW9f7999/Y2RkRPny5fNQ2oJl584/dH+PGTOWqVOn0qBBfbp168bGjV5YWUk77EePHuVlWCS/Xoin6cIQJu+M5mGIGptCMsa1tOTcVFumtbPC1ip/gjqlRq1W8/vvv9OtWzc8PDzo2fMzWrZsycSJk7hz506mZS9evEmDBgNo23YsISHFkXZYiwEyBg6cxYYNe3S5xEEKuJRCcHBwmvpiYmKIj4/Xnbtv32m+/vpnNBoNfftO5sGDR7lqa7Nmzdi/fz/h4eG0adMGadFdGHDk0qV4oqPjUKnUmJlZvjr2mjNnrhEY+DzVN3Jq1OjIkSNHOHDgAO3atcuVbAAnTpwgJCQMrVbL7Nlr0Wiyb86t1Wp1iwZjYyN+/PFHqlatilwup0aN6ixZsgSFQhp29u7doyun0WhYsGATsbEJSAoZw5u8BAQEUL16Y1q3HsU33+RNoL+5c9dTtepn/PNPKGBLypBcq1atVG4g+YODgwOtWrUCpGwqN29mnF4yNXK5jMbOKoqa53wiO23aSr77bj2uro24dOlSjssbKnPmzKFo0aKAFK/B09OT6tWr8/XXX5OQkADAp59+SrNmzfLsmhMnTqRJkyYAJCcn4+XlxeTJkzl+/HVU/EGDBvHll4uRxpf3j6ioKKKiJMujmjVrpQlY5+rqiqurCwCBgYF6i6ujR4+QkCApFzp3/oRJkybh7OyMq6sr06dPp2XLFq+uEa3LKiPIGR2qmtG9diG0Wil955XAZDxWhbPXJxEjOXzT0YoVn9lgkc9pMjPC1c6IHnWkhfG8gzG5XnwD7LiSwLXHSixMZHzZLnuZN5KTlfTp8w1jxixBq62MFHxSuifVqlXL511yGQcPntO9x3v06IZMpv9+DQ4OzVGNH31UjAcPpPgsmzb9ycOHb7qECQQCQda8N1tRz56lDHibcHBwYOXKldjY2LB27Vr69+9PcnLyq0jB2efoUcmPdOzYsRQrlrUf/e3btylTpoyeX1xSUpLOx61IkSI4OuoHAvL399ctaKtVq6Z3LDQ0VNcuR0dHPdN0tVrNrVu3AMmUq2zZsri4uADJyOWJPHv2TBcHo2zZsnrpJFPKyWTQokVzvWsWKVKEunXr8tfJ80SXbEfrFXFEvtoFKm4pp2d1DS2dozA3jqKQogzw2kogPj5eZzFSpEjRNOaP6eXsTiEk5LUFh4ODg56GPCEhgYkTJ/LPP/qLEo1Gy8mTJzl37izjx4+nZs2alCtXTu+c8PBwhgyZQ1hYFGFhUXz55YxX8T2cOH78Dl5e+/Dy2sfmzfs5eXKt7l5/9FEJgoNfcPHiRXbv3k2nTp1QKBRotVrWrl2LSiX5UlasWIFGjarRt29PNm/2ZsaMGZQtWxYfHx8AzM3N08j0+PFjIiIiXpWvqGdpER0dzaNHkhKjRIkSadxhwsPD6dmzJxcvXqR1665IVhJxQDQvXvjz2WfTePYslCpVyuLjswO5vBxgibu7O/7+/vj4+FCsWLE0C1g/Pz8SExORyWSUL19eb9Lz8uVLnj+XFBtOTk5Mnz4dX19fgoOD2br1W+7flxanlpaWlCxZUq/eJ0+ekpAg9W9XV1fi4+OJiJBSubq5uREREUFERAR2dnYULlwYe3t73NwqcevWLV6+DMHX1xdLSysWLNjKqlU7+OOP8xw4cJjY2DCdJYybm5ueNUlUVBQBAQEA2NvbY2dnpyfTrVu3UKvVmJmZpQlm+fTpU8LCpNSF5cqV0+uHcXFxurba2tqmaWtMTAwhISEAHDhwljt3HuHmJgXpCg0NJTxc6t8lS5bE0vK1K01ycrJOXisra+ztpd98z56TzJghKTOaNv2Effv20bKlfuq0nI4RqXn06BHR0dICrnLlynpjRGRkJIGBgQwePJjChQuzYMFEihd/vRvs7++PVqvF1NRUL9MDSIo7rVaLQqFIc+8zGyNevgznyJELOtnd3Nz0yj5//ly3G+Xi4qJ3DxMTE/Hz8wOgaNGieq5zAPfu3SMhIQGZTEbVqlX1joWEhBAUFARAmTJl9OKLqFQqbt++DYC1tXWaoGsPHz7UmdZWqVJFL4BxREQEjx8/BqBUqVKcOHECT09P7t27p1eHTCZjwIAB/PTTTzorpdyMEbdv30alUmFqasqhQ4f46quvWLdunZ4JcKlSpZgxYwbDhg179U1ZEhJu8+TJTeLiEilZskQaC6OAgACSk5ORy+W4urrqHQsPDyc0VFqo2NuX1CmyQQoWnSJvdsaIlLHHwcGBmJgYIiMjuXfvnm6MSEGj0RAY+DiVDGF69QYFBREVFa2Ty8TERHd/Y2JiuXr1mu7cN5Wz9+/fp1q1aro0ho8eBeiOvXjxQjf2lC7tSKFCr5XWCQkJPHnyBJDepba2+q5Ijx4FoFQmo1AoXr2vX/M2Y0QKjx8/1llrvLlhEhERSUiI9Nx89NFHevMTtVrNgwdSnABzc/M074XM5hExMTG694KtrW0a17mUMWJAdVMuB5jzKFRNt5+l9tlawPSmcVS2iyY5uYxe/87LeYSDgwMajQa5XE5SUhKBgYGA9CynPDfjW1qy+1oi1x4r8Tr2iP85q9O8syMiInRju729PVZWr5ULKpWKhw8f8iJWxqZrFvzlL/XfUc0tKGGt4OnTp7o5nouLi94YER0dTXBwMOvX7+fevcfcu/eY1as38MUXXwDk2zwi9RhRsWJFhgwZQt26ddm0aRNt2nTDx0eJTKbE1bUIWm0E5ct3o3x5RwYP7kzz5tL4aWNjoxsjoqJisbGxJCAggMREORqNPZMmTWHHjh189913ODs7p5lHpHZJS05O1m0m2djY4OTkpCfvgwcPdFnK3N3d9eYnYWFhuv7i4OCgN1fXaDS6QL+WlpZpnrmAgIAs5xFarRZbW9s0a4C3nUek9AWBQJA1740SIkWLm5iYyMGDB3UT41atWlG7dm1mz56dIyXE1atX6d69O/Xr1+f777/PVhmVSpVGk67ValEqlbrj6ZVJOZ5em1KOpbfb/Ga9xsbGqFQyChUqRGhoqO77tMr91zE23qw3Kl7DbeoT0WgwWhNr4hOhVGE5w5pY0L22OeEhz4mMVKFSkaatGo1Gd02NJm3AI5VKle49SDn/dVl9mby9vfUUEDVr1qBUqVJcuHCR0NBQlEoVy5evYPHiRWle1BqNhkWLpvL559Nxc5PSaqZw5MgJ3d+dOrXS/a1QKPD09GTFipUAzJs3jwsXLuDk5Mz58+fw9ZVelnK5jKZNW6FSubBmzUb69h1MixbS7ll2f/PM+kt6QepKly7NxIkTMTU1fZXFRIYUWdoSP7/7PHsmTX12UcQAACAASURBVLiLF7dDLq9IisVAVvUqlUqUSiVyuTxNcCm1Wq0nr0wmY/369a+UMsmEhj5DJlOiVqfto2/+5tJCQOqTISEhKJVKZDKZ7j6o1WrdhFmhkKPRaHj8OJgtWw4DcOXKda5fv46zs3OGz01WbU1OTkaj0aTJeJNeW3NSL0DPnj35669jzJw5gPLlXyscUz8bbz6PWq1Wd0ytfn2vGjWqTpMm9Th16h+dMuBNcjpGpCazfphSr52dHfPmzaN48RLAbSBJV1ar1eotSlKXTbk/qa2K3rwPb44RdnZF2bVrOZMnr+STTz7Rm+iD/m/zZluz+m1S2pqeK1J2683t+F21alXu3LnD4cOHOXz4MAEBAdjb29OtWzdat26dYb057YdKpRKVSoVcLqdQoUIsWbKEWbNmcfr0aR49eoSpqSnVqlWjUqVKqUrJ0GicuHhxH+PGfc+KFRPo3Vs/3kvKsyxLJ3uEWq1JdX/S7ia/7t9ZjxH37t1j165d+PvfR6vVULp0aZo2bZZmQQ9gampCmTKOBAY+5t49f06fPk3jxo111zp+/C8iI6VFRu3adVLfRZ3FFaBTxr2+hyq971L389R9+M226j/LGb8D09txf5sxIgW1Wp3hu1Wr1WT4bk2RKSN5U9f7pkyp5c2orVqtFjMzI5b3LEzXn8NQqqGeszEzWiQhT07K93nEm4rK9O6DnbWCIf8zZ/nfcay7bEqdUmlj+qS+D2/ew9hELRsuG7PL14xktQyZTArIO6iRRZqyaeWV2lq8uA22tsUIDQ3Xc7vIr3lE6jEihWrVqrFkyRKePHnyKpitERpNKXbvvkRMTBxXrtyhShUXGjeupJPdx+ceM2b8jK/vI+7c2U98vD3x8SbI5XImT57MtGnTdNfI7N2auq2ZzU8yuofZeQemVz61TG+S+h6amJjo9SXI3TxCIBBkj/dGCZGipaxYsaLezpxMJqNNmzZ8//33vHz5Ms3OXHpcu3aNVq1aUa5cOQ4ePJhlusAUjIyM0kxyZTKZLtZEehN2IyOjdGNRAMjlct2x9MzxjI2N0Wg0HDx4kAEDBnD+/HkqVgRHx2I0a9aMFi1aYmNjzZvz7vLly3P//gM0Gi1Hjhxh0KBBhMSoWX82nl8vxBEn/xhMQBH/jBmflqHXx8UwMZLp5Ehpx5ttTX1MLk87MKccS+8+yOWKVGVft1WlUrF9+3bd55kzv+GTTz4BpJfAtGnTOXnyJImJiZw5cyZNPBCZTNoF8PLyom7dunra93nz5lGpUiV2795N585DkEwgnwExdOjwCdu3H+LFiweo1RrdjhhAZCSYmUmmzHZ2TZDLLTE1NdUpIFJ+m4zamvo3z6y/pPdyMzY21p3zZp+wsrJi5MiRXLhwgTZtOpPaZSE79aYEX3oThUKRRt6UxWVysha12gkzs0Dkcplu1yl1W1PfAxMTE2rWrMmVK1d5/jyYc+fO0bRpU129u3b9yYsXkhKicuXKmJiYUKZMYU6f3kO7dn34/vvvadmyJQEBARk+N1m11cTEBLVanW759Nqak3v4+eefM3DgQKpUsQVex5HRf27SyptyTKF4fa+KFXPg6NFT/PjjUtq0aZPuAjo7YwTkvB+mrldqqwwoDdzXlU2xdkhPprcbI4yxt6/NunXr0h1zU/82b7Y1q98mpa3p3cPs1psX47dcLqd9+/a0b99eb5czs3pzM0akYGVlRYcOHQgKCtLt6L5Z7507dxk+/Dvi4+MZOHAuZcuWoUGD11YjRkZGaZ7vFBQKear7k/Yev+7facumjBFqtZr58+fzxx+79I77+Nzg4MGDDBw4iOHDv0hTtk2bNqxZI1mxTZo0iVatWlOpkhvnz1/g4sWLunN79OieqqQMN7dKHDhwEJACVDZu3Fh3z7RaDUePHtWdXaNGdd3fqfvwm23Vf5bT74dabfoLl7cZI1JQKBTp9k+prDzdd2tqmTKSN3W9b8qUWt6M2yqNEe4OxmwaUITAcDWetQoRGvKC6Oh3N49IuU5Gx4Y2sWDz+ViCYhQce1AI9zeylKe+DyllNRotf15LZMHhGF7ESC4dNUpp+a5bcSqXNE63bFp5pbZ+8klTPv10Alev+lCjRg3d8Xcxj3iTN9+B1tY21K5dm3///ZfPPx+FVmuCQhGJXC5nypTlHD0qPWNeXv/QpEkTjI0TUSgUaWJdZfZuTd3WjOTNzTw59f8ZyfQm+TmPEAgE2cMgsmOkJqPsGCqVChsbG1xdXXWTuxSmTZvG/PnzCQkJSeMz+ibXrl2jZcuWlClThuPHj2cYnd8QItyq1Wr69evHli1bdN9VrAgpc1o7O1t++eWXNObSt2/f5vNBo1EVdkNdtApWZf9HqLoYaq00OCpiHlHo0XY6Vbfk+3lz8rEFRkgporSEhERQrJhNmvt3585dXUTzRo0asmzZMr3jz54945NPOgPg7l6FNWvWsmnTfgYP9kAmK40UeCmnRDNjxpd8990vVKhQksKFo1EqY9Fq4cULCAoCB4cS3LzpS+HCRd+i/g+PpKQXDBs2mOLFC7NgwZhMn4O///6byZOn6D43bPgxVapUwcfnht6iYenSpfzvf42QfkMHYmNj0+xGGC5q4CY5TYH2GlOkYF6GpQdWKu+wbt1m+vfvqGeGnjeUA7JO8SbIH1QqFb1792b79u20bt2I3bvn58NvnDGLFy9m69ZtmZ4zdepUPD0/1ftOrVYzdepU/v77RAalwNPzU7788ku9BYBarcbDw4OgIMlEvGxZZz75pDNqtYo9e/bw+LHkVuHq6oK3t7dYPHzgbL4Qxzd7YihuKefk5OJYZhKn4t+AZGbvj+bGU8lCwbGoguntrWhT2fQt+0kZwPCCw6bG19cXNze3VO1L4J9/zlC/fhtKlSrFwoUL+eyzzwpUxvcBQ1g7CATvC+/NU2FkZETnzp25c+eOzncSJNOnw4cP4+LikqUC4vr167Rs2RIHBweOHTuWSXpAw+CHH37QU0CUK1eOmjVrYGQkaW1fvgxh/PjxJCcreRKuYtfVBKbtimLsETsimm4lpvoM4h278EJVHLVWhlHkXayuzcbm4mjslbcYM3pERpfOFdeu3X1l2ukCVEKrteHTT7+kZs3PdVr1FFL8AAGcnPT9sUHynTU1lTTukZExdOw4jqFD5/LVV1t4OwUEhIQksXTpbwA8fPiSjRu9WLt2DfPn/4CFheQz+/TpC9auXf9W9RsyiYmJJCQk5CgavFqtpm3bnmzatJ/Fi39j4cLNmZ7frFkzvejz586dZ/XqNXoKiI4dPWjUqCFSAFHpnr8/CgiQAobmbFKpVqtZvtyb5GQNUiRxw1JAXL58mWrVujJixHwWLMj8N05KSiIxMZGkpKRMz7txw5+FCzej0RRHKCAKFiMjI7Zs2cL8+fPZvfsIhQp9lHWhPOLFixe61KRGRkaMHz+OI0cOs2fPbnr37qU775dffiE5WT+LgUKh4Pvvv2fIkMHY2Oj3oeLFizNhwvg0CoiUcrNnz9a9Px4+fMTSpUtZsWKlTgFhbl6ImTNnGowCQq1Wc/HizVef5ICkBI+LSyApKW+yO2SHgIAgIiNjsj6xgDl37jp7957M1vvss7rmOBdXEBqrYe3puHTPeRqhZvS2SD79JZwbT1VYmsqY2s6SYxOK07aK2Vv2E3MMXQEBUKlSpTfaV4h69Vqza9cu7t+//8EqIN5mTiQQCPIGg7GEOHToEHFxccTExDBw4EA8PT3p3l0yr2zfvj3m5uY8ePCA2rVrU6JECb799lusra1Zt24du3fvZvv27bo0aYGBgbi4uNCvXz/Wr5cWkn5+fjRs2FDKX71pUxqFhYuLi55PakFrM5OSknBwcCA0NBSZTMa2bduoUKECRkb+REYFM//n7TyKsUFZpDIWZRoQkZTWZKyYURTxjy+gCLuFUaQvikTJDN7NrSJz585NY0GRF5w5c42mTYfRtWt71qzZTJEiRdi/fz+dOkn+x+XKOeLru11nfvj48WO6dJEWrK6urnh7b9N7EV69epUhQ6S0diVLVuTAAb9Xfqhm+Pr6pgkklx3UajXe3t588803tG3bllWr5gBBgJKHD7XUr9+WsWPHMn36dIOZnOYVPj4+KJVKjI2N0wRKzYylS5cyfvx4FAoFjx6dpHRpc9LzDU9Bq9Xi7f07v/32K8HBryNnlyxpT/36LZg/fxdz505gzJjZZJVS1VB58uQBy5Z9S/nyjgwd2jXL88eNW8yyZdto0qQRf/yxO1vBcN8lvr6+VKtWDZVKhbm5GU+fHqRIkfQVB/fu3dMFj8sos1BCQiK1a/fF1/chzZs35/fff89SUSx4l2iBh0CkLhZMfuHl5cXKlasAGDhwACNHjtTrQ+vWreP48b8BWLDgBz3Xt9QkJiZy9epVoqKiKVq0CDVr1sLYOHNl3s2bt1i0aCG3bt3W+7569epMmTI5TdC5guLkyX8ZN24Jt28/4NatI1So8D/ABJUqBA+PrsTGxvPnn4syfCbzBlO8vS8xbNhY2rf/mK1b5xr0O7B58yGcOHGNCRN6sHjx5CzPP3gzkRFbIjE3kXFycnHsXmX+ikvS8MupONacjiNJJbmm9KhdiImtLd86O9iWLYd4+PAZkybNplChtPFOBIbB286JMqKg1w4CwfuEwWzFDR8+XBfZGGDHjh3s2LEDkKK8Ozk54eLiwpkzZ5g6dSpDhw5FqVRSvXp19u7dS8eOHXVltVotarVaLwDOhQsXdNFsUxbEqfHy8qJ///751Lqcc+rUKV3Ub09PT3r06MG169eZfcKE2yHOxDlM1Z2bnARGcnB3MKaOkzF1nEyoXcaEIhYfERFhx5EjZjx/Xgozs0I0aFCfatWq5cvEIiEhkc8/n4FGo2Hnzv18/PFGxo8fT7FixahVqxZXrlxh3rzZGBlZApLW2dHRkSpVqnDr1i3u37/PwoULGT58OFZWVty+fZs5c167iwwb1pc2bUyZOXMue/fufSsFBEg7ZL1796Z79+6v0udZA0WAZMqWNcXPz8/grWTeNePGjaNcuXJcvXqV0qUbAUogBAjB2/sAXl77GD26B+3bN0QulyOTyfjss5507+7J7du3iYqKonDhItjYFKNGjc+JjY1n7NjvKFGiCj169Cjg1uWc58+f4+LihlKpxNHxIwYO/CRDv2CABw+esnq15At/7txFbt++rQuwZyhUqlSJ0aNHc+HCBVasGJPrxc5ff13izh0pgntYWFiaQJSCgkYGlCU+/jaenl9QpYoLc+eO0OvHN274s2vX3yQlKencuQn167vrjqlUKj75ZAImJsb06NGK7t1bpetbDegySgA0b55WwdCiRQudEiIlEn56mJmZ8fHHH+eole7uVdi0aRN+fn7cuXMHmUxG5cqV02QAKWhOnryCj4+UWWXSpKXs2yfdp4kTv+PAgbMAdOw4jrNn1+fp+9vPL4AKFZwAS8LCCvPFFxOIjo7F2/sonTs3oWfPNnl2rbxEqzWhZcv2nDhxjV9+2c3kyQP46KPMlZztqphSvbQx158oWfZXLHM6W0txH47E8CJaCnpYz9mYbzpZ68V9yClRUbFMmPAjL1+Gs2HDYa5evSrmFAKBQPAGBqOESO1ikRlVqlRh//79mZ7j5OSUJkJt//79DUrJkBUpCghAF025eLFiRCuDiEvWYm4CyqCrGEX64v6Rik1LvqSQSdqJSZEiRejZs+c7kblQITN+/HESgwfPpWrVqowZMwaABg0acOnSJQ4fPpwqVVoYEERYWAhKpR0qFRgZwe+/b+ePP3ZhY2NNWFi4ru6SJcvSqtUoTE2t6NGjT7qR1HOKfjAkGSnpSD/kyULRokUzDFCZFR06dKBDhw6vPhkDJQF7li0bzMWL/3L06EXOnFlHo0avg7wpFAq9lIlarZaRIz9jzpxfaN68OR4eHrlrUAFhb29P69atOXDgAC9ehHPtmh916lTO8HwXFwdOnPgdD49hzJ071+AUECnMmzcPExMT5PJI4FGG51lbW2cYxDCFTp0a8/ffuxg6dApbt27NdgBgwbsjISGRzp3H89df5zh48BzTpw/ExsYSaTyUcfPmQ2bNkoJClipVkvr16yG5CchQKGQcPnwBrVbLX39domXLetjapj92pv7tQ0Je4uZWUa8PpaRmffPcvKRChQoGY/WQFhMmT/6GtWsP8NFHHzFp0iTdkV69erFt2zYiIyP57ruxeaaA0Gg0fPvtGubO3cCff/7CJ58MplgxGWvWrKFHjx706tWZdu0a5sm1cktsbDyLFv1Kly7NqFatEmCPTGaLv/8SACpUcCIiIiZLJYRMJmN6eyu6rw7H+3IC158ouR2UV3EfXnPy5L+EhaVkban9Qc8p3ndyMycSCAS5w2CUEAJ9Umf5uHDhAiClb5zlEYKFaTLhDy8xftw3ALiWb52uAqIg6Np1IHXqdEcul+sN6ilR419THCjKvHkj2Lbtb8zNTSlZMglra2mHLSwsnIgISTHh7OzEihVHMTWVdlLzQgHxX6V06dJ5Wl9YWDgvX0rKInf3yjRs2AyIJMVVI8XcOgWZzIzZs5dTseL/6NSp03u9MJ02bRq1atVi5Mh22NlltWtmQ/36Nbl7t0m6qTgNhdcpN4siWbrEpnvem3np08eGpk1rcedOJzHBM1CMjIz0FkiJieWxsbHXfTY1fZDqWBHATfdZJpMiyCclJTFq1HBsbZ2AqHSvU7duXbZvlywbN2zYQN26dXV9KCIiAm/v33Xn1qlTJ906PhRUKhWrV+/Czq4onp6tkbI22WFhIef06dM4OzvrKffq1avHhQsXuHnzJs2adUTKYJN+TIOc8McffzNnzjoAevUaj69vGxwdHenevTulSpWiYcMGgC8paXsLihs3/GnTZhTBwWFcuHCPI0eOI8XkkeJmdejQgW7dGiGTPctWfXWdTWjpZspfd5K4HSTFfRjd3JL+Dc0xNcqbeVTnzk25ceM4X365iEWLFuVJnYL8Ia/nRAKBIPsYTEwIQ6Og/bqSk5MpXbq0bodo48aN9OnTB7ncjydP/Bg3bhwBAZL7yqJFi2jWrOk7kStziiNFgc4ecXFxlC5dmoiICMzMTDl+fDlnzx7n/Pnz3L0bjp9fPIUKmXLixCm93NoCw0KtVnPw4EGMjIxeWboogVAghAEDvubx42DGjfuMjh2bI5NVJMXi5MMhGvBP8+1rP/tCQAVSJs7vDwnAHYKCXlKyZE4Vf8ZAJYSe2/BRqVTs37+fe/fu6VzhUggODub69euYmZnh6uqKg4ODXtnw8HAuX75MzZo1XymH44Eg1OpwPD2n4unZgu7dW6HVavHw8OD582AA7O0/ok2btiQlJXLo0CEiIyXlRZ06tfnll1/eVdPfOVFRsTRoMIA7dx5RsmQJ7t27i4VFTpWSGqRYHlHcufMIN7e3c0vUamX07j0Pb+9dLF68mHHjxqVjARAH+JFZ/J/8JjExCTe3HgQEPMXIyIhbt26lY9GiBW4B2QveGRimYtzvUbjZGzG+5dvHfcgYU6Ay72u8I8HbU9BrB4HgfUIoITLAEAaSBQsW8OWXX+o+lylThjp1LHn06DYpv5qzsxPe3t6Z+qPnJ0lJydy69YBatWog7ZLl7P4EBQUxa9Ys7OzsmDPnayAIjSYUD4+J7Nt3BpBywy9cuDDPZRfkLyEhLyld2hEjIwUXLmzE3b0j0oL8Q+QO0gJMIikpmQ4dxtG/f2c+/3wSYJJhSUMlMDCQSZNGcPToKfz8/sjS1Blg/frdODiUoE2bvohsGIZNUlISmzdvZu3atfj6+mJkZESjRo0YMWIE7dq1y5VJ+u+/b6Znz34A9OnTns2bZ3Pz5k2GDx9OQkL6UehtbYuzYcMGSpYs+dbXfR/o3HkKe/dK8S927NihC6idM7Ts2rUGT88RzJgxiJkzh+bw9zIGXElMlHPhwgWaNWuWybnBxMc/ICAgiEqVyr6FrDkjKir2lUsQgBXggLf3Xnbs2MH8+fMpV65cBiXDycyF7N3iCtgUtBCCAsAQ1g4CwfuCeCoMmEmTJjFw4EDd58DAQG7deq2AKFnSnqVLlxaYAgJg2rSV1KvXn3nzdqJW51yfVbJkSVavXs3s2bORdg+ckcsrs23bb9SrV4+vv/6aBQsW5LncgvwnICCQ0qVLExcXT5s2Y7l5835Bi5SPlECr1RITE4dWq2Xw4DkcP36JPn2+YvHiFQUt3Fsxf/58du48SHR0HNOmrcry/Bs3/Bkx4gfath3NhAnfponLIzAcwsLCaNiwIUOHDuXy5cvExcURFRXFgQMH6NChA4MGDUKj0bx1/ceOndb93bevlOXK3d0dLy8v6tevr3eukZGC1q1bsXHjxg9KAREVFcvu3SeJjk5xaTIFXFi48GcaN27MxYsX31IBAY8eBdC79zg0Gg2zZq3lzz9PZFlm377TPHr0DCllpBtgjpmZWRYKCPDxeUHt2v1o3XoU4eHpu9vkBU+eBNOv30wqVOhGVJQSaSFfHjCnZ8+e/PHHH5koIACKEhgYwezZawtk7ElMTOLQoXNotdYIBYRAIBBkjbCVNWDkcjnr1q2jY8eOrFy5klOnTgFq7Oxs6datG56entjYFNzL7syZa/z441YAZs2aR7duPd868Jf+Lo45FhaOnDp16r2OGWCIZCe1YnpERUVx9+5dZDIZlSpVwtLSMssyderUwc/PjyNHjnD+/HlMTN4/a4DskJyczLZte1m0aC41a1Zg/foZWFhIFh/m5uY0bdq0YAV8S2bPns22bdswMTGmceMaescCAwN1wbxSUv2uW7eb5GQlID3Phpza77+MVqulR48eXLlyRfdd2bJliY2N1bn/eXl54ezszIwZM97qGmvXrqVXr17s3r2bFi36Irn2BFGuXDkmTZrGwYOnKV5cgUIhp1y5cnmSGs+QWLLkNyZPXo5Go+HPP5fi4dETsANklC9f+NW7/O1xdnZm3rx5TJw4kT59utOlS/MMz9VqtSxcuJmpU1fi5ubK+fP/YGOT/cwP06ZN484dKTbImDGL+O23OVmUeDu++uonfv31IAA//LCHefPqZ1FC/3126NAhpkyZQnJyMu7urnTpkrlyJa9ZsmQLX331E23bHmDlyp9wcXF5p9cXvB1vOycSCAS5R7hjZIAhmlRdu3YNmewu5uYYxGCpUqmYPftX5s79mR9//FGXDUNguOQ0J/bjx4/55ptv8Pb2JilJClBmYWHB559/zqxZsyhRokR+i2zwxMbG4ujoSEREBEZGCh492kupUtVZtmw7jo6OdO3ataBFfGtOnz5N1apVKVz4OandTdKbuGk0sHLlSbZt28nJkyeFAtFAuXDhgi7NZYkSJfjjjz9o2LAharWaTZs2MWTIEDQaDYULF+bZs2eYm5vn4dXjGTSoHxs27MTZ2Z7Fi0dSuXJZg3if5RSNRsOtWw84fvwSo0b1wNg4ZU/HiP37L9Op0xAARo4cycqVK/NFhr///ptGjRphYpIEPADUac6JjY2ndu0++Pm9jiE1ceLEbF/j2bNnVK1aFUfHUmzbNpOKFZ3yRng95Dx6lETFik2wsLDgu+++Y8SIEVmWSv0+CwwMpHPnzgA0aFCV8+c35IOc6RMcHIqLiwfx8YkoFAquXbuGu7t71gUFBU5O50RZYYhrB4HAUBFKiAwwxIHkxo0bKBT3MDFRZWGW+K6Qgs/5+NymatWqYufzPeDGjRu6F27q1Jnp4efnR5MmTXjx4kW6x52cnDhz5kyaYHX/Rb7++mvmzp1LgwZV+eWX76latX3Whd4rYpEC1En4+/vrlBCvxyJHwDbL1J2CgmXMmDGsWCG5CG3YsIEBAwboHe/Xrx+bN28GYOfOnXTr1i3Prv306VOcnJxQq9VYW1tw5MgSihWz1vWhAwfOcvduADVqVKB+fXfMzc2yqLHgGDp0LmvX/gnAuXPefPxxU6QYBubExMTQqFEjmjVrhoeHxzuyhkoA7hMYGEhMTBxVqri++l7G/fsa6tdvy9ixY/n6669z/K728fGhYsWKmJoGIwUdzj2vMycVAsoCZuzfv5+GDRtmO6Vl6veZu7s7bdu2pUYNd6ZO7UjhwlZZV5BHaLVadu48ycSJy/Hw8GD58uXv7NqC3JGTOVF2MMS1g0BgqAglRAYY7kCiHwCvYCmHCD73YaLVaqlVqxbXrl0DwMbGhm7duqFUKtm1axdxcVKKuJYtW3Ls2LGCFNUgePnyJffv3+fjj92AwnyYUdEDgLAMjtkg+XALDB1PT0927twJwMOHD3F21s+u4OXlpYtFtHLlSkaOHJln19ZqtZw8eZKZM2fSsmVLvvnma6TFczyQQK9eI9i27QAAN2544+7+uk9FR8cSHh5NmTL270zhfe9eIGfPXufq1busWDEl1XUt2LDhAIMGTQJg1qxZfPPNN+9Epsx49iyQ+vXrEBoaQc+edWnVqhFt246kaFFHwsLCKFasWC6voEGag6QfXDQ7KJUqpkxZxr17j9m3bxNyuTN5FZ7sdUaiADIeq/ILJ+LizF4p2MS86L+K4a4dBALDQzwVghzh6/uQ4OBQoARCAfHhcvr0aZ0CokKFCty/f5/169ezefNm/Pz8KFWqFAB//fUXt2/fLkhRDQI7O7tXJu5F+DAVEJCYWIy5c72YNk0yLddoNEyZsowHD4IBpwKVTZB9Uu8yX79+Pc3x1N8VLpzT9JGZI5PJaNasGadOnWL69OlIUxALwBZw5Pr1hwCYmJhQsWJT4COk94wRBw6cxdn5E4oWbc7mzfv16tVqtajVaV0RcoJKpUrz3cSJSxk0aA6rVu3g3r0YwAWoDlSkZUtPOnXqxLJly+jdu3eurp0X7Ny5ExeXCjx9GgKoOHXqPP37L6BUqQosXbqUokWL5sFV5IAzWi1cvHjzrWro0WMaS5du4+DBc8ydu5W8nIa+VhKVzNN6s8YCKIaFhYVQlZ1ligAAIABJREFUQAgEAkE2EUoIQbaJjY2nS5dJVK3ai4MHfQpaHEE+cujQId3fX331FcWLv07PWKpUKSZMmKD7fPDgwXcqm+Ddo1arqVevEV9/vYqFC3/l1q37LF/uzcKFv1K9ek927PizoEUUZJMuXbro/p4+fTrPnj3TfT537hxr164FwMzMjLZt2+aLDDKZLN2sTlu3bmX9+vXMnj0bY+MSQCkki7tqXL8eAUBkZAzFijkgmfFLU5jQ0EjMzRtRuXJ3Zs1ak205tFot48YtpkaNXtSq1efVtwokxUdJPv74dcDHCxcCkaycFAA4Ojqyd+9exowZU+BBCPfu3Uv37t11cXsSEyEgAJRKSExMZPz48SxbtixPrhUWlkC3bt/QoMEAjh27mOPyI0Z8hkwmw9jYGFtb2zyRKS0mgC3JycpU2UnyntfpZkvn2zUEAoHgQ0VkxxBkm5kzV3Pv3uNXf39L27bthInZB0ps7OuJm6trWjP71IHkUp8r+DBRKBR0796dGzduAHDy5BXWrdsNSL9/Xu+YC/KPNm3aULlyZW7fvs3du3dxcXGhRYsWREZGcv78ed15AwYMyAPz/ZxRvXp1qlevnu6xSpXcad++PdevX6d69bZICgqAZPz8TpCcrMTX9yEvX8YiLUKTdWXbtx9DVFQsbm7OrF37OiaCTCbj3LkbXL9+D4DIyFIULvyRrlzHjt1QKMxp0KABtWvXzocW5x61Ws2YMWN0aSk7deqEs7MzKpWK5ORk1q1bB0gKp379+mU73kJGbN++nT//lBTP/fp9i7//n7psQFljRcuWA1i5Uknt2rWpW7durmTJCI1Gw44dZ5g+fQpt2tTnp5+m5vk1wsOjcHfvSd++n/LVVwvIRsIogUAgEKRCKCHeI0JCQoAQjIyScz2ReBumTu2Pn99LTp48z9atW4UC4j0kJCREl1oxs10oR0dH3d8HDhygQYMGesf3739tDp2SolHwYTNx4kT8/PyYPHk4Dg5xdOjQjK++2oy9fUlatWpV0OIJsolcLufPP/+kWbNmPHv2jKSkpDTWTE2bNmXRokX5Kkd2x6IU+vXrR79+/dI5YkJSkhGVK1fG39+fChXqAe5I8QuS0GoTOH/+FlFR0Tx7FopMZg1YIpnQW9CgQXOuXPHF3d2doKBwPSWEu7u7wWc5OHbsGIGBUuaLpk2bsmfPnjQxM9atW0dCQgK//fYbo0ePztX1hg0bxu7du7ly5Qo///xVpgqIqKhYjh69iKdnSyTXmpKALFuZL7JDRn0oPDycwYOHEhsby5o1fzJ2bE8qVHDKk2umMHPmaoKCQpg//2eio2WsWrUqT+sXvBtyOg4JBIK8Q6wi3yOCgoJ48eLFK2XEu8fWtiz79h3h8uXLBpKdQ5BTgoKCePr0KUFBQZme16tXLxQKyex40aJFrF+/nuTkZBISEli2bJnOZNvc3DxPo+cLDBczMzM2b96Mu3sDgoOTCQ+35ssvp7Jw4cKCFk2QQ8qVK8eVK1eYMGGCnkLb1dWVJUuWcPjw4TxOzZmW7I5F2aFFixbcunWL+Ph4hg4d+upbOVCI6GgFFhbSNnWFClWA8kiLYRvAiK+++orIyEh8fHyoVKlSrmV516RYJ4FkvfKmAiIlyOib574tcrmczZs34+PjQ+fOAzI879at+9Sp05cePaZx6NBDJMuVvI2Xk1EfKl68OFOmTAGgSZNa5Ef49cKFrTAxMcHCwuJVfBPB+0hejkMCgSBnCEsIQTYxAcogk8lwc3MraGEE+YyDgwPDhg3jp59+IikpicGDBzNy5Eg0Gg1KpVJ33qRJk7CxsSlASQUFQXJyKbRaqR8Ii6j3kxIlSrB48WLmz59PcHAwxsbGlChR4r1OtaxQKHTK0xRsbGx49uwZsbGxREZGpilTokSJdyVevpC6vQkJCWmOx8fHp3tubtC/Z7ZA2o2RgwfP4e8vuW+OHj2Nu3e7pBsHJL+YMGECdevWpXXr2shkAXle/5w54+nX70tu3LipC9QsEAgEguwjUnRmgCGm2ZEmUHdQKJKwsno3ObAPHz5P8+Z1MTGpjGTCKnifiYyMRKPRIJfLs/TjT05OZsCAAWzdujXd4yNGjGDFihViEfofJCf9SCBID9GH8obz58/TsGFDAKpWrco///yDmZkZIM1jPDw82LdvHwAbN27MwKUlN2iAu1y+/C/u7q6YmZm+unYRunQZx+PHT/jjjz8oW7ZsHl83J30oP1KbixTlHwJ5PQ4Z4tpBIDBUhBIiAwx3IMmPl2lakpKSmTDhR376aQe1a1dj69YdwgXjP4hWq+XUqVOsWbOGq1evIpPJqFevHsOHD6devXoFLZ5AIBD8p9FqtdSoUQMfHyljlbu7O8OHD6dQoUJ4eXlx+vRpAIoVK8aTJ08oVCi7QSSzh0qlYt68Wcyc+R2jR/dg+fIpSNkibImOjsbY2DjPr5lzogH/XNWg1WrZu/cUjRvXpEgRR6R0rQKBPoa7dhAIDA+hhMgAwx1I3o0SIjY2njp1+nL3bgAACxYsYPLkyfl+XYFAIBAIBNnn33//pUmTJnquF6mRy+Xs3LlTLz1rXuHv70/VqlVJTEzkhx/GMWrUdMzNDS/An5/fEVau3MCPP07IsVvI/ftPGDp0LidO/Mu4cf358cc1gHH+CCp4rzHctYNAYHiIp0KQLpaWRdixYztFixZl7dq1TJo0qaBFEggEAoFA8Aa1a9fm5MmT6aY3dXZ2Zu/evfmigAApyGlKJhVv71PIZIbntrls2TIqV+7AypXbWb9+T47Lm5oac/HiLQBWrvyNgIBneS2iQCAQ/OcQgSnfI1QqFVqtEplMlecBnpKTlahUaszNzYAiQBmqVFEQEBDwzuJPCPIfqQ9pkclk7zRImODDQvQjQW4RfShvqVOnDlevXuWff/7hwoULqNVqqlWrRosWLfJ9F3bEiBFYWFjoUr6+K/eL7PahunXrolarAVi9ehdDh3bNQQBWI0qXrsPkyZP57bctLFq0SKSl/oAQ45BAUHAId4wMMESTKh8fHxSKe5iYqChfvnye1RsQEET37lMpX74Mv/66EZnMLs/qFhgWPj4+KJVKjI2NqVatWkGLI3hPEf1IkFtEHxLklpz0oQEDBuDi4sT48S2xsDBL9xytVsuePafw9j7C1q3zkMtLAPaAEQkJCcjlckxNTfO+IYICI6/HIUNcOwgEhopQ+/3HSU5W0qTJUB4/DubyZV+aNNnDkCFDClosgUAgEAgEgjzBy8vr1V9PgRfpnjNy5A/8/PNOADp06EmfPgN1xwo+uKZAIBB8WAjV3HuEtbU1lpaWWFhY5FmdJibGLFw4DQAXFxdq166dZ3ULDA9ra2tsbGywthapxQRvj+hHgtwi+pAgt7xdH7IHFOke6dKlte7vQ4f+yp1wgvcCMQ4JBAWHcMfIAMM1qcrL7BgywAGww8vLi65du2JjY5NHdQsEAoFAIBAYGi+IiPAlNDSScuUckYyC7QFbRo8eQ/PmzfHw8MhB3AiBQMJw1w4CgeEhlBAZYLgDSe6UEPv3nyEoKIShQ3sCZYG8s6oQCAQCgUAgMFRUKhUbN3oxZMhQALTax6TEfRAIcovhrh0EAsNDPBX/EbRaLVOnrqBTp/GMGrWQS5diEQoIgUAgEAgE/xWSkpKYMeMbAORyOT4+4QgFhEAgELx7hBLiP4JMJkOjkYxelEolv/66tYAlEggEAoFAIHh3WFhYsGnTJsqUKUPr1q0xMTEpaJEEAoHgP4lwx8gAQzSpevjwIXK5H0ZGyTg4OOSwtAlKZWlat+5C586dGTt2rPB3/A/y8OFDVCoVRkZGlC1btqDFEbyniH4kyC2iDwlyi+hDgtyS133IENcOAoGhImzQ3iNiYmJQKGIxMVHlsKQJUB5jY1OOHz8uBsP/MDExMbqc2ALB2yL6kSC3iD4kyC2iDwlyi+hDAkHBIVajHyghIRH07v01YWFxQHnAFEAoIAQCgUAgEAgEAoFAUGAId4wMMESTKrVaTUp2DIUi/TzXAKGhkTRv/gU3b96nalV3/vrrOLa2tu9MToHhIvUhicz6kECQGaIfCXKL6EOC3CL6kCC35HUfMsS1g0BgqAh3jPcIaYBM+Zcx4eFRhIZGvfo7gtjYWKGEEABioibIG0Q/EuQW0YcEuUX0IUFuEX1IICg4hBLiA6R8eRdOnvyLPn2GsGXLFpydnQtaJIFAIBAIBB8YKpWKAwcOcPbsWVQqFZUrV6ZHjx5YWVkVtGgCgUAgMGCEO0YGGK5JleSOkTFGSDEgCqHVakUGDIFAIBAIBHnOyZMn6d+/P4GBgXrfW1lZMW/ePEaNGlVAkgkEBYPhrh0EAsNDWEK8R0RERCCTRSKXJ2Jtba37Pjo6lt27T9K3rwdQDigEIBQQgjRERESg0WiQy+UUKVKkoMURvKeIfiTILaIPvd+cPXuWNv9v7+6joqrzP4C/R0CGZ4RBXVBwkQghkFwFNVyfwRY4Ci6VmqIeFw+iia0iYSuYlmWLUZaZuquoKB4faM1EyxXM8JgS6mo+YzBIxLMIKA8D9/cHh/uLBgQF5s7g+3XOnMN8v98787nwmTszH+73e/38UFdXp9ZXWVmJJUuWoK6uDm+++Wa3xcAcos5iDhFJh0UIHaJUKqGndw+9e6vEIkRlZTVefvkNnD37P+TlCVi1Kk7aIEmrKZVK8XJUfMOlp8U8os5iDukuQRCwePFisQDh4+ODN998E+bm5ti1axd27doFAHjrrbcwe/bsbluTijlEncUcIpIOzw/ScUeOfIezZ/8HANi4cROKiookjoiIiIh6qvPnz+Py5csAAE9PT5w6dQpBQUGYOHEiEhMTER4eDgCoq6tDYmKilKESEZGW4pkQOsTOzg4yWSV69aoV22bNCsAvv8iwfn08Tp48ib59+0oYIWk7Ozs78dRDoqeRn5+PgoICGBkZwcXFRepwSEfxWKS7Ll68KP48f/58GBgYtOgPCwvD559/DgDIysrqtjiYQ9RZzCEi6bAIoUMUCgUAa/z/wpS9ADhhxYpVmDs3jJfhpHY15RDRkztz5gzeeecdnDx5UmwbNGgQlixZgqVLl/JSZ/REeCzSXb9db6qhoUGt/7dt3bk2FXOIOos5RCQdlv50TE1NLe7evYemP91zAEwBgAUIIuo2+/fvx/jx41sUIAAgJycHf//73/HKK6+0+mWEiHqeESNGiD9v27YNtbW1Lfo/++wz8WcvLy+NxUVERLqDl+hsgzZeZqe2thZBQZORlXUNp06lwtV1RPsbERF1glKphLOzs/hFw9HREVOmTMHt27fx7bffiuPi4+O7dSV8ItIeXl5euHDhAgBg2LBhWLp0qbgwZUpKCgDAyMgI9+7dg5WVlZShEmmMNn53INJWLEK0QRsPJCtWrMA///lPAE1fBG7cuKE2F5OIqCvFxMRg/fr1AIDZs2djx44d4tSLY8eOwd/fHwDg4OCA7OxsTssgegZkZmZi7NixePjwYZtjtmzZgoULF2owKiJpaeN3ByJtxVeFDgkMDISLizPkcjl27NjBAgQ9scuXLyMzM1Nc2ZyoPceOHQPQNLd7w4YN0NPTE/PIzs4OkydPBgDk5ubi+vXrUoZKOoTHIt02fPhwnDp1CkOGDFHrUygU2LFjR7cXIJhD1FnMISLpcGFKHWJhYYHPPvsc9+7dw5///GepwyGiZ0Dzf3XMzMzQr18/tX5nZ2dxWsbv/wNERD2Xt7c3fvrpJ6SlpSEjIwP19fVwc3PD1KlTIZfLpQ6PiIi0GIsQOsTY2Bi9e/fGwIEDpQ6FdJSxsTFUKhX09fnSp46xt7fH3bt38eDBA5w9exYvvfSSmEcymQzHjx8Xx/LYRB3FY1HPIJPJMGHCBEyYMEHjz80cos5iDhFJh2tCtIHzuoiIgJ07d2LevHkAACcnJyQmJmLUqFEoLCzEypUrsWvXLgDAxIkT1a6eQURE9KzgdweijmMRog08kBARATU1NRg2bFiL9R4sLCzw4MEDNL996Onp4dSpU5wmRkREzyx+dyDqOL4qiIi6gCAIePjwIRobG6UOpUvJ5XKkpqbCxcVFbKuoqBALEL1798bu3btZgCAiIiKiDmERgoioE27duoXw8HBYWlrCxMQExsbGePXVV3Hu3DmpQ+syDg4OuHjxInbs2IFx48bB0dERHh4eiI6Oxq1btzBjxgypQyQiIiIiHcHpGG3QxlOqlEqluICOvb29ZHGQ7mIOda3jx48jODgYjx49UuuTyWT49NNPsWjRIgki617MI+os5hB1FnOIOqurc0gbvzsQaSu+KnRIeXk5ysrKUF5eLnUopKOYQ10nNzcX06dPFwsQJiYmGDNmDKytrQE0Tc+IiIhAenq6hFF2D+YRdRZziDqLOUSdxRwikg6LEERET2HTpk14+PAhAGDq1KnIz8/Hd999h/z8fCxbtkwct2HDBqlCJCIiIiLSOpyO0QZtPKWqtrYWgiBAJpPB0NBQsjhIdzGHuo6DgwOUSiUMDAyQn58PGxsbsa+hoQGOjo5QKpWQyWS4f/8+zM3NJYy2azGPqLOYQ9RZzCHqrK7OIW387kCkrbTiVVFZWYmoqCj4+vrCxsYGMpkMcXFxrY6tr6/Hxo0b4e7uDiMjI1haWmL06NE4e/Zsh54rOTkZnp6ekMvlsLW1RWRkJKqqqrpwb7qPoaEh5HI532zpqTGHuk5xcTEA4LnnnmtRgACaLlnp5eUFoGlaRllZmcbj607MI+os5hB11tPkUE1NDQ4dOoSNGzdi69atyMnJ6b4ASevxOEQkHX2pAwCA0tJSbN26FUOHDsW0adOwffv2Vsc1NDQgKCgI33//PaKiojB69GhUV1fjxx9/RHV1dbvPk5SUhNdffx0LFizARx99hFu3bmHlypW4du0avvnmm67eLSLqwRQKBfLy8nDnzh0UFxernQlx/vx58X6fPn2kCJGIiNBUDE5ISMC6detaFIVlMhmmTZuGLVu2oG/fvhJGSET0bNGKIoSDgwPKy8shk8lQUlLSZhFi06ZNSE1NRUZGBkaOHCm2+/v7t/scDQ0NWLFiBXx9fbFt2zYAwPjx42FmZoZZs2YhNTUVL7/8ctfsEBH1eCEhIdi4cSPq6uoQFhaGxMREmJubo66uDjExMVAqlQCAKVOmwMLCQuJoiYieXatWrcL69evV2gVBQEpKCq5du4aMjAxxYWEiIupeWrcmRElJCWxsbBAbG6s2JeOPf/wjBg0ahLS0tCd+3IyMDPj4+GDfvn147bXXxPb6+npYWVlhxowZ2Lp1q9je0NCgNk3DxMRE0nldv51nZmZmJlkcpLuYQ10nLy8PPj4+La6OMXToUNy8eROlpaXiuMOHD8PHx0eqMLsF84g6izlEndXRHLp69SomTJgg3g8KCoKvry9+/vln/Otf/xKP1wsWLMB7773XfQGT1unq41BjY6PamdmmpqbQ09Pr9GMT9TRacSZER+Tl5SEnJweBgYGIiYkR3zief/55REVFITQ09LHbX716FQDg4eHRot3AwAAuLi5if7PWajMdmfKhKb9f+IboSTGHOsfS0lLtuNGWnvy77sn7RprBHKLOelwOOTg4IDs7u9W+hQsXdvhxqGfrrr+9lv2vl0hr6EwRIj8/HwCQmJiIAQMG4NNPP4WFhQW2bduGuXPnoq6uDn/729/a3L650m1lZaXWZ2VlxcWJiIiIiIiIiLqZzhQhGhsbATStbHzs2DE4ODgAACZPnozhw4fjnXfeeWwRoplMJnuidiIiIiIiIiLqGlpxic6OaF4syMXFRSxAAE3FAz8/P9y7dw9FRUXtbv/budrNysrKWj1DgoiIiIiIiIi6js6cCTF48GAYGxu32tc83+pxi0a6u7sDAK5cuQJXV1exXaVS4caNG5gxY0aL8b169YKJiUmLNplMxjMmiIiIiIioBUEQ1NaAkHJBeyJtpjNFCH19fUydOhUHDx5ETk4OBg0aBKDpBX/8+HEMHjwYCoWize29vb3xhz/8ATt37sSrr74qth88eBBVVVUIDg5uMb5Xr148cBARERERERF1Ib24318HUyKpqam4fPkyrly5gv/85z/o27cvZDIZrl27hkGDBsHAwACenp7YuXMnvvzySygUCiiVSkRHR+P06dP44osvxDMccnNzoVAokJubi6lTpwJoKir069cPH374IQoKCmBmZoZvv/0WkZGRGDNmDNasWSPl7hMRERERERH1eFrzr/7w8HCEhIRg/vz5AIADBw4gJCQEISEh4loPgwcPxpkzZ+Dk5ISwsDBMnz4dBQUFOHLkCP7617+KjyUIAhoaGtDQ0NDiOV5//XXs3bsX586dg5+fH1avXo05c+bg8OHDmtvRp1BVVYXIyEjY2tpCLpfD09MTycnJUodFWqqyshJRUVHw9fWFjY0NZDIZ2qo1ZmVlYdKkSTA1NYWlpSWCg4Nx9+5dzQZMWuXUqVOYP38+XFxcYGJiAjs7O0ydOhU//vij2ljmD7Xl0qVL8Pf3h729PYyMjGBlZYVRo0Zhz549amOZR9QR27dvh0wmg6mpqVofc4hak56eLk6l/v3t3LlzLcaePHkSo0aNgrGxMRQKBebOnfvYteaIqHNkAi9gq/V8fX1x4cIFvP/++3B2dsbevXuxfft2JCUlYebMmVKHR1omJycHnp6eGDp0KJydnbF9+3bExsaqFSJu3LgBLy8veHp6Ijo6GjU1NVi9ejXKy8tx6dIl2NjYSLMDJKmQkBCUlpYiJCQErq6uKC4uRnx8PDIzM3HixAlMmDABAPOHHi89PR3Jycnw8fGBnZ0dqqurkZSUhOTkZKxduxZvv/02AOYRdUx+fj7c3NxgYmKCiooKVFVViX3MIWpLeno6xo8fj/feew/jx49v0ffCCy+IBa3Tp09j0qRJ8Pf3R0REBIqKirBy5Ur06dMHmZmZMDQ0lCJ8op5NIK329ddfCwCEvXv3tmifPHmyYGtrK6hUKokiI23V2NgoNDY2CoIgCMXFxQIAITY2Vm1cSEiIoFAohIqKCrEtJydHMDAwEKKiojQVLmmZwsJCtbbKykqhX79+wsSJE8U25g89DW9vb2HgwIHifeYRdURAQIAQGBgohIaGCiYmJi36mEPUlrS0NAGAcODAgceOGzFihODq6irU19eLbRkZGQIAYfPmzd0dJtEzSWumY1DrUlJSYGpqipCQkBbt8+bNwy+//IIffvhBoshIW3XkKi4qlQpHjx7F9OnTYW5uLrY7ODhg/PjxSElJ6e4wSUv17dtXrc3U1BSurq7Iy8sDwPyhp6dQKKCv37QmNvOIOmLPnj04ffo0Nm/erNbHHKLOys/Px4ULFzB79mzx2AQAo0ePhrOzM3OIqJuwCKHlrl69iiFDhrQ4MAKAh4eH2E/0pLKzs/Ho0SMxj37Lw8MDd+7cQU1NjQSRkTaqqKhAVlYW3NzcADB/qOMaGxuhUqlQXFyMzZs348SJE1i5ciUA5hG1r6ioCJGRkXj//fcxYMAAtX7mEHVEREQE9PX1YW5uDj8/P3z//fdiX/Pn6LZyiJ+ziboHixBarrS0FFZWVmrtzW2lpaWaDol6gOa8aSu3BEFAeXm5psMiLRUREYHq6mqsWrUKAPOHOm7RokUwMDBA3759sWzZMnzyySdYuHAhAOYRtW/RokV4/vnnER4e3mo/c4gex8LCAkuXLsUXX3yBtLQ0fPzxx8jLy8O4ceNw4sQJAO3nED9nE3UP/faHkNQed2p9e6fdEz0Oc4va849//ANJSUnYtGkT/vSnP7XoY/5Qe2JiYrBgwQIUFRXhq6++wuLFi1FdXY3ly5eLY5hH1JpDhw7hq6++wsWLF9vNA+YQtebFF1/Eiy++KN4fM2YMgoKC4O7ujqioKPj5+Yl9beUJ84eoe7AIoeWsra1brcKWlZUBaL1yS9Qea2trAK2fSVNWVgaZTAZLS0tNh0VaZs2aNVi3bh3effddLF68WGxn/lBH2dvbw97eHgDwl7/8BQDw1ltvITQ0lHlEbaqqqkJERASWLFkCW1tb3L9/HwBQV1cHALh//z4MDAyYQ/TELC0tERAQgC1btuDRo0ft5hA/ZxN1D07H0HLu7u64fv06VCpVi/YrV64AaLrEENGTGjx4MIyMjMQ8+q0rV67AyckJcrlcgshIW6xZswZxcXGIi4tDTExMiz7mDz0tLy8vqFQq3L17l3lEbSopKUFhYSHi4+PRp08f8bZv3z5UV1ejT58+mDVrFnOInoogCACaznJo/hzdVg7xczZR92ARQssFBQWhqqoKhw4datGemJgIW1tbeHt7SxQZ6TJ9fX0EBgbi8OHDqKysFNuVSiXS0tIQHBwsYXQktbVr1yIuLg5vv/02YmNj1fqZP/S00tLS0KtXLzg6OjKPqE39+/dHWlqa2s3Pzw9yuRxpaWlYt24dc4ieWHl5OY4ePQpPT0/I5XLY2dnBy8sLe/bsQUNDgzju3LlzuHnzJnOIqJvIhOZyIGktX19fZGZm4oMPPoCTkxP27duHbdu2Yc+ePZg1a5bU4ZEWSk1NRXV1NSorKzF//nyEhITglVdeAdB0SrSxsTFu3LiBESNGYNiwYYiOjkZNTQ1Wr16NsrIyXLp0CTY2NhLvBUkhPj4ey5cvx5QpU1otQIwcORIAmD/0WGFhYTA3N4eXlxf69euHkpISHDhwAPv378eKFSuwYcMGAMwjejJz587FwYMHUVVVJbYxh6gtM2fOhL29PYYPHw6FQoHbt28jPj4e2dnZSE1NxaRJkwAA6enpmDx5MgIDA7Fo0SIUFRUhOjoaFhYWyMzMhKGhocR7QtQDCaT1KisrhTfeeEPo37+/0Lt3b8HDw0PYt2+f1GGRFnNwcBAAtHr7+eefxXGZmZnCxIkTBWNjY8Hc3FyYNm2acOfOHekCJ8mNHTu2zdz5/VsG84fa8u9//1vFlw0KAAAFGklEQVQYM2aMoFAoBH19fcHS0lIYO3assHv3brWxzCPqqNDQUMHExEStnTlErVm/fr3g6ekpWFhYCHp6eoKNjY0QFBQknD9/Xm3sN998I4wcOVKQy+WClZWVMGfOHKGwsFCCqImeDTwTgoiIiIiIiIg0gmtCEBEREREREZFGsAhBRERERERERBrBIgQRERERERERaQSLEERERERERESkESxCEBEREREREZFGsAhBRERERERERBrBIgQRERERERERaQSLEERERK3Yu3cvEhISpA6DiIiIqEeRCYIgSB0EERGRtgkICMDVq1eRk5MjdShEREREPQbPhCAiIiIiIiIijWARgoiInknFxcUICwvDwIEDYWhoCBsbG7z00ks4efIkxo0bh6+//hq5ubmQyWTirVldXR3WrVsHFxcXcdt58+ahuLi4xXMMGjQIAQEBSElJgYeHB+RyORwdHfHJJ59oeneJiIiItAKnYxAR0TNpypQpyMrKwrvvvgtnZ2fcv38fWVlZcHV1hbu7O8LCwpCdnY2UlBRxm5EjR6KxsRH+/v44c+YMoqKiMHr0aOTm5iI2NhYWFhbIzMyEkZERgKYihEqlgp6eHuLi4tC/f38kJSUhKSkJH374IZYvXy7V7hMRERFJgkUIIiJ6JpmZmWHBggX46KOPWu1va02I5ORkzJgxA4cOHUJwcLDYnpmZiREjRmDz5s0IDw8H0FSEUCqVuHjxIoYOHSqO9fX1xQ8//ICCggIYGxt3/c4RERERaSlOxyAiomeSl5cXdu7ciXXr1uHcuXOor6/v0HZHjx6FpaUlAgMDoVKpxJunpyf69++P9PT0FuPd3NxaFCAAYObMmXjw4AGysrK6aneIiIiIdAKLEERE9Ezav38/QkNDsX37dowaNQpWVlaYM2cOfv3118duV1hYiPv376N3794wMDBocfv1119RUlLSYnz//v3VHqO5rbS0tOt2iIiIiEgH6EsdABERkRQUCgUSEhKQkJAApVKJI0eOIDo6GkVFRTh+/Phjt7O2tm5zjJmZWYv7rRU1mtusra07sQdEREREuodFCCIieubZ29tj8eLF+O9//4uMjAwAgKGhIR49eqQ2NiAgAMnJyWhoaIC3t3e7j/3TTz/h8uXLLaZk7N27F2ZmZhg2bFjX7QQRERGRDtCLi4uLkzoIIiIiTaqoqMDo0aNRWVmJsrIyFBQU4ODBg9i2bRsCAgIwffp0XL9+HceOHUO/fv0gCAIKCgpga2sLNzc3XLhwARs2bEBtbS0ePXqE3NxcnDlzBgkJCRAEAUOGDAEAJCQkwMTEBPv374elpSUKCwsRFxeHL7/8EmvXrsW4ceOk/UUQERERaRivjkFERM+c2tpaREZG4uzZs8jJyUF9fT3s7e3x2muvISoqCsbGxigvL0dYWBhOnjyJiooKCIKA5rdMlUqFjz/+GLt378bNmzehr6+PAQMGYOzYsVi+fDmcnJwANF0d44UXXsC8efMQGxuL27dvw9bWFm+88QaWLVsm5a+AiIiISBIsQhAREXWT5iLE0aNHpQ6FiIiISCvw6hhEREREREREpBEsQhARERERERGRRnA6BhERERERERFpBM+EICIiIiIiIiKNYBGCiIiIiIiIiDSCRQgiIiIiIiIi0ggWIYiIiIiIiIhII1iEICIiIiIiIiKNYBGCiIiIiIiIiDSCRQgiIiIiIiIi0ggWIYiIiIiIiIhII1iEICIiIiIiIiKN+D85Bd8wc1XL4AAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Variance converges to 0.005\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"temp_change = 0\n",
"voltage_std = .13\n",
"process_var = .05**2\n",
"actual_voltage = 16.3\n",
"\n",
"x = gaussian(25., 1000.) # initial state\n",
"process_model = gaussian(0., process_var)\n",
"\n",
"N = 50\n",
"zs = [volt(actual_voltage, voltage_std) for i in range(N)]\n",
"ps = []\n",
"estimates = []\n",
"\n",
"for z in zs:\n",
" prior = predict(x, process_model)\n",
" x = update(prior, gaussian(z, voltage_std**2))\n",
"\n",
" # save for latter plotting\n",
" estimates.append(x.mean)\n",
" ps.append(x.var)\n",
"\n",
"# plot the filter output and the variance\n",
"book_plots.plot_measurements(zs)\n",
"book_plots.plot_filter(estimates, var=np.array(ps))\n",
"book_plots.show_legend()\n",
"plt.ylim(16, 17)\n",
"book_plots.set_labels(x='step', y='volts')\n",
"plt.show()\n",
" \n",
"plt.plot(ps)\n",
"plt.title('Variance')\n",
"print('Variance converges to {:.3f}'.format(ps[-1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first plot shows the individual sensor measurements vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten larger and smaller results.\n",
"\n",
"Spec sheets are what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Values are often maximums - the spec is a guarantee that the performance will be at least that good. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that a sample falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution? Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
"\n",
"For example, I am looking at a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly $0.0\\%$ at low temperatures, and always nearly $+0.50\\%$ at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures lead to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
"\n",
"As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Animation\n",
"\n",
"For those reading this in a browser here is an animation showing the filter working. If you are not using a browser you can see this plot at https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/animations/05_volt_animate.gif."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
"\n",
"The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement.\n",
"\n",
"Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor $g$. The Kalman filter is doing exactly the same thing, except that the scaling factor $g$ varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example: Extreme Amounts of Noise\n",
"\n",
"With the dog filter I didn't put a lot of noise in the signal, and I 'guessed' that the dog was at position 0. How does the filter perform in real world conditions? I will start by injecting more noise in the RFID sensor while leaving the process variance at 2 m$^2$. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition say about the filter's performance if the sensor has a standard deviation of 300 meters? In other words, an actual position of 1.0 m might be reported as 287.9 m, or -589.6 m, or any other number in roughly that range. Think about it before you scroll down."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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