{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "view-in-github",
"tags": [
"no-tex"
]
},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "JoW4C_OkOMhe",
"tags": [
"remove-cell"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Note: you may need to restart the kernel to use updated packages.\n"
]
}
],
"source": [
"%pip install -q -U gtbook\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"id": "10-snNDwOSuC",
"tags": [
"remove-cell"
]
},
"outputs": [],
"source": [
"import numpy as np\n",
"from numpy.random import default_rng\n",
"rng = default_rng()\n",
"\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go\n",
"try:\n",
" import google.colab\n",
"except:\n",
" import plotly.io as pio\n",
" pio.renderers.default = \"png\"\n",
"\n",
"import gtsam\n",
"from gtbook import logistics\n",
"from gtbook.display import show\n"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {
"id": "8m7rpauo_4qD"
},
"source": [
"# Localization\n",
"\n",
"> We introduce three variations of Bayes filtering to solve the robot localization problem: Markov localization, and Monte Carlo localization, and Kalman filtering.\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Localization** is the process of estimating the robot's position using sensor data\n",
"and the history of executed actions.\n",
"In this chapter, the robot's position at time $k$ is denoted by $x_k$, so the localization problem\n",
"is to estimate $x_k$ at each time instant using the robot's history of sensor observations,\n",
"$z_1, \\dots z_k$, and commanded actions $u_1, \\dots , u_{k-1}$.\n",
"\n",
"As we have seen in Chapter 3, when we are able to exploit the Markov property, we need\n",
"not consider the entire sensor and action history at each time $k$; intstead, we can iteratively\n",
"compute a probability distribution for the state $x_k$ using only our belief about the state $x_{k-1}$,\n",
"the action $u_{k-1}$, and the sensor observation $z_k$.\n",
"This kind of iterative, online updating is referred to as filtering.\n",
"The input to the filter is the belief at time $k-1$, the action $u_{k-1}$, and the observation $z_k$.\n",
"The output of the filter is the new belief, a probability distribution for $x_k$.\n",
"Note that when taking this approach we abandon computing the full joint distribution\n",
"$P(X_1, \\dots X_k)$, and content ourselves to compute only the conditional distribution\n",
"for $X_k$ at time $k$.\n",
"In this chapter, the filters that we develop will be derived from Bayes theorem,\n",
"and the result is known as **Bayes filtering**.\n",
"\n",
"We begin the section with a general introduction to Bayes filters, and then develop\n",
"three specific algorithms, Markov localization, and Monte Carlo localization, and Kalman filtering.\n",
"These three algorithms reflect trade-offs in computational complexity versus accuracy and expressive\n",
"power. In particular, Markov localization relies on a grid-based representation that\n",
"can require significant computer memory as well as significant computation in the update\n",
"process.\n",
"Monte Carlo localization addresses each of these concerns by using a sampling-based approach,\n",
"at the expense of accuracy.\n",
"Kalman filters, on the other hand, provide an exact and optimal solution to the localization\n",
"problem, by only in the special case when the robot can be described as a linear system\n",
"and all uncertainties in motion and observation are Gaussian in nature."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A Running Example\n",
"\n",
"When introducing concepts related to localization, it will be useful to \n",
"have a short, ground truth trajectory for the robot that we can use to assess the quality of\n",
"solutions.\n",
"For this purpose,\n",
"consider a trajectory that starts at the bottom left of the map,\n",
"moves to the right, then up between the middle two shelves:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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x2
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"text/plain": [
"VectorValues: 14 elements\n",
" x1: 10 6\n",
" x2: 15 6\n",
" x3: 20 6\n",
" x4: 25 6\n",
" x5: 30 6\n",
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" x7: 40 6\n",
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" x13: 50 26\n",
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]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"left = [(10+i*5,6) for i in range(9)]\n",
"up = [(50,6+i*5) for i in range(1,6)]\n",
"N = len(left) + len(up)\n",
"indices = range(1, N+1)\n",
"x = {k:gtsam.symbol('x',k) for k in indices}\n",
"values = gtsam.VectorValues()\n",
"for i, state in enumerate(left+up): values.insert(x[i+1], state)\n",
"values\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note above we used a `gtsam.VectorValues` to store the ground truth trajectory, which will come in handy again when we simulate the measurements. Below we show this \"ground truth\" trajectory overlaid on the warehouse map we introduced before:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Ground truth trajectory displayed on the base map.\n",
"#| label: fig:logistics-ground-truth\n",
"ground_truth = np.array([values.at(x[k]) for k in indices])\n",
"logistics.show_map(logistics.base_map, ground_truth)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Bayes Filter\n",
"\n",
"> The Bayes filter is an iterative, one-step sum-product algorithm.\n",
"\n",
"The Bayes filter estimates the state of the robot at the *current time* \n",
"(denoted by index $k$ in our discrete-time representation), \n",
"given all the measurements and action history up to and including the current time. \n",
"To simplify notation, we define\n",
"$\\mathcal{Z}^{k}=\\{z_{1},z_{2},\\ldots z_{k}\\}$, i.e., all measurements\n",
"up to and including stage $k$. \n",
"Similarly, we define the controls\n",
"$\\mathcal{U}^{k}=\\{u_{1},u_{2},\\ldots u_{k-1}\\}$. \n",
"Note there is always one less control variable than there are measurements.\n",
"The Bayes filter computes the conditional probability distribution\n",
"$P(X_k | \\mathcal{Z}^{k},\\mathcal{U}^{k})$, which is also called the **filtering distribution**."
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Assuming that we are given a prior distribution for the initial state\n",
"of the robot, $P(X_1)$,\n",
"we can initialize the Bayes filter for time $k=1$ by using\n",
"the sensor observation $z_1$. Note that no action has yet been applied.\n",
"Thus, we have\n",
"\n",
"$$\n",
"P(X_1|\\mathcal{Z}^1=\\{z_1\\}, \\mathcal{U}^1=\\{\\}) \\propto L(X_1;z_1)P(X_1)\n",
"$$\n",
"\n",
"Given this, recursively assuming that we have a probability distribution\n",
"$P(X_{k-1}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k-1})$ over the previous state $X_{k-1}$, we proceed in two\n",
"phases:\n",
"\n",
"1. In the **prediction phase** we calculate a **predictive distribution**\n",
" $P(X_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k})$ on the current state $X_{k}$ given a control $u_{k-1}$. This is done by marginalizing out\n",
" the previous state $X_{k-1}$, by summing over all possible values\n",
" $x_{k-1}$ for $X_{k-1}$:\n",
"\n",
" $$\n",
" P(X_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k})=\\sum_{x_{k-1}}P(X_{k}|x_{k-1},u_{k-1})P(x_{k-1}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k-1}).\n",
" $$\n",
"\n",
"2. In the **measurement phase** we upgrade this predictive density to the **filtering distribution** $P(X_{k}|\\mathcal{Z}^{k},\\mathcal{U}^{k})$\n",
" via Bayes’ rule, given the measurement $z_{k}$:\n",
" \n",
" $$\n",
" P(X_{k}| \\mathcal{Z}^{k},\\mathcal{U}^{k})\n",
" \\propto L(X_{k};z_{k})P(X_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k}).\n",
" $$\n",
"\n",
"A keen observer will see that step 1 and step 2 above implement one step of the sum-product algorithm from Section 3.4, where in this case the previous state $X_{k-1}$ is eliminated. Step 1 is a sum, and step 2 is a product."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Markov Localization\n",
"\n",
"> Markov localization computes the filtering distribution at each time $k$ using a discrete grid.\n",
"\n",
"In principle, for a robot that translates in the plane, we take $x_k \\in \\mathbb{R}^2$,\n",
"and the belief associated to the state would be represented by a probability *density* function.\n",
"With **Markov localization** we approximate this continuous representation by using\n",
"a discrete grid to represent the workspace and assigning finite probability to each cell\n",
"in the grid.\n",
"In particular,\n",
"we assume a finite element discretization such that a density $p(x_k)$ over continuous states $x_k$ is approximated by a discrete probability distribution $P(X_k)$. \n",
"The only difference from the previous chapter, which also discussed discrete state spaces, is that in a finite element discretization the cardinality of the discrete states is typically much larger. Recall from section 4.1 that for our $100m \\times 50m$ warehouse example, even at a relatively course resolution of 1m by 1m cells, our state space had a cardinality of 5000 finite elements. \n",
"This makes reasoning over multiple time steps computationally challenging. \n",
"\n",
"By using this finite element discretization we can apply the Bayes filter, as is, on the discrete grid.\n",
"When applied to robot localization, because we are using a discrete Markov chain representation, this approach has been called **Markov Localization**. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### A 1D Example\n",
"Figure\n",
"1 below\n",
"illustrates the measurement phase for a simple 1D example. \n",
"\n",
"\n",
"\n",
"One-dimensional example of the measurement phase in Markov localization, the discrete version of the Bayes filter.\n",
"\n",
"\n",
"In this environment there are two doors, and the robot has a door sensor. The\n",
"predictive distribution $P(X)$ encodes the belief that the robot is\n",
"near the left door. The likelihood $L(X;z)$, where measurement (or observation)\n",
"$z$ indicates that the robot *did* perceive a door, \n",
"models the fact that the robot is more likely to be\n",
"near a door given $Z=z$, but also allows for the fact that the door\n",
"sensor could misfire at any location. Note that the likelihood is\n",
"un-normalized and there is no need for it to sum to 1. Finally, the\n",
"posterior $P(X|z)$ is obtained, via Bayes’ rule, as the product of the\n",
"prediction $P(X)$ and the likelihood $L(X;z)$, and is shown at the\n",
"bottom as a normalized probability distribution. As you can see, the\n",
"most probable explanation for the robot state is $X=5$, but there is a\n",
"second mode at $X=17$ due to the bimodal nature of the likelihood.\n",
"However, that second mode is less probable because of the prior belief\n",
"over $X$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Warehouse Example\n",
"\n",
"Let us apply Markov localization to the warehouse example, using *just* the proximity sensor for now. We start by initializing the finite element density representation with a Gaussian prior, centered around the ground truth location for $k=1$, but with a relatively large standard deviation of 5 meters:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"prior_mean = values.at(x[1])\n",
"prior_cov = np.diag([25,25])\n",
"prior = logistics.gaussian(logistics.map_coords, prior_mean, prior_cov)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Prior distribution over the robot's initial position.\n",
"#| label: fig:logistics-prior\n",
"logistics.show_map(prior/np.max(prior)+0.1*logistics.base_map)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With respect to implementation, the hardest and most computationally demanding part of the Markov localization algorithm is the prediction step.\n",
"Recall the formula:\n",
"\n",
"$$\n",
"P(X_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k})=\\sum_{x_{k-1}}P(X_{k}|x_{k-1},u_{k-1})P(x_{k-1}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k-1}).\n",
"$$\n",
"\n",
"Hence, for *every cell* in the predictive distribution grid, we need to sum over *all* cells in the previous image. Not only that, but for every one of these $5000^2$, i.e., *25 million* cell combinations $(X_k,x_{k-1})$ we need to evaluate the Gaussian motion model $P(X_{k}|x_{k-1},u_{k-1})$. With python for-loops, this will be rather expensive, so in the code below we build in two speed-ups:\n",
"1. We make the outer loop over the previous image, and threshold on the probability value\n",
" (i.e., if the probability value is less than a threshold, we set the value to zero in the output distribution);\n",
"2. We make use of the fact that the `logistics.gaussian` function is vectorized, i.e., we can process an entire row of the predictive image at a time.\n",
"\n",
"The fast code looks like this:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def prediction_step(previous, control, motion_model_sigma):\n",
" \"\"\"Calculate predictive density given control and control stddev.\"\"\"\n",
" cov = np.eye(2) * motion_model_sigma**2\n",
" predictive_density = np.zeros((50,100))\n",
" for i in range(50):\n",
" for j in range(100):\n",
" # Speedup 1: threshold on previous[i,j]\n",
" if previous[i,j]>1e-5:\n",
" previous_xy = logistics.map_coords[i,j]\n",
" mean = previous_xy + control\n",
" for k in range(50):\n",
" # Speedup 1: vectorize Gaussian evaluation over predictive row:\n",
" motion_model = logistics.gaussian(logistics.map_coords[k], mean, cov)\n",
" predictive_density[k] += motion_model * previous[i,j]\n",
" return predictive_density/np.sum(predictive_density)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we have *no* measurements at all, but have a perfect measurement model, our \"control tape\" just pushes the Gaussian density along:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"#| caption: Predictive density after taking 14 actions.\n",
"#| label: fig:logistics-predictive\n",
"motion_model_sigma = 2\n",
"current_density = prior\n",
"for k in indices[:-1]:\n",
" # prediction phase\n",
" control = values.at(x[k+1]) - values.at(x[k]) # ground truth control\n",
" current_density = prediction_step(current_density, control, motion_model_sigma)\n",
"# logistics.show_map(current_density/np.max(current_density) + 0.1*logistics.base_map)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Evolution of the predictive density (no measurements).\n",
"\n",
"\n",
"The figure above shows the result of purely predictive reasoning using a finite element discretization. As you can see, the density grows without bound, and also goes *inside* the shelves. Without any measurements, if we do not explicitly incorporate knowledge about the world (e.g., a map of obstacles),\n",
"the robot cannot rule out such situations.\n",
"\n",
"The measurement update step takes the predictive density $P(X_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k})$ and *upgrades* it to the posterior density:\n",
"\n",
"$$\n",
"P(X_{k}|\\mathcal{Z}^{k},\\mathcal{U}^{k}) \\propto L(X_{k};z_{k})P(X_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k}).\n",
"$$\n",
"\n",
"Note that this is so much simpler! We just have to code a pointwise multiplication and we are done. Because the ground truth trajectory never comes near any of the shelves, the proximity sensor is always `OFF`, and hence we multiply the predictive density with the corresponding `proximity_map_off` likelihood image:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"#| caption: Posterior density after taking 14 actions.\n",
"#| label: fig:logistics-posterior\n",
"predictive_density = prior\n",
"posterior_density = predictive_density * logistics.proximity_map_off\n",
"posterior_density /= np.sum(posterior_density)\n",
"for k in indices[:-1]:\n",
" # prediction phase\n",
" control = values.at(x[k+1]) - values.at(x[k]) # ground truth control\n",
" predictive_density = prediction_step(posterior_density, control, motion_model_sigma)\n",
" # measurement update phase\n",
" posterior_density = predictive_density * logistics.proximity_map_off\n",
" posterior_density /= np.sum(posterior_density)\n",
"# logistics.show_map(posterior_density/np.max(posterior_density) + 0.1*logistics.base_map)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Markov localization in action.\n",
"\n",
"\n",
"The figure above shows Markov localization in action! The measurement information has *literally* squeezed the predictive density to a posterior that fuses predictive information with the knowledge\n",
"(from the proximity sensor) that we cannot be anywhere near the shelves, or the wall. Note that the density is still spreading in the direction that the sensor does *not* yield information."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises\n",
"- In principle our motion model should have told us that we cannot move inside shelves. How would you change the prediction code to make this so?\n",
"- The full Markov localization algorithm takes *less* time than the code *without* the measurement update. We do more work yet have faster inference. Why?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Monte Carlo Localization\n",
"\n",
"> Localization with a particle filter is known as Monte Carlo Localization.\n",
"\n",
"The above finite element discretization of space is very costly, and most of the memory and computation is used to compute near-zero probabilities. \n",
"While there *are* ways to deal with this, switching to a sampling-based representation gets us more bang for the buck computation-wise. And, as we will see, it also leads to a very simple algorithm.\n",
"The sampling-based implementation of a Bayes filter is known as a **particle filter**.\n",
"Below we discuss it in a 2D context, but it is in fact rather general. \n",
"When used for robot localization, this technique is known as [\"Monte Carlo Localization\" or MCL](https://www.ri.cmu.edu/publications/monte-carlo-localization-for-mobile-robots/) {cite:p}`Dellaert99icra_mcl`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A particle filter approximates the Bayes filter by (a) replacing an explicit probability distribution by a set of samples, and (b) approximating the prediction step in the Bayes filter with a Monte Carlo approximation. We recursively assume that we have access to a sampling based approximation of the filtering density over the previous state $x_{k-1}$, as a set of $S$ *weighted* samples:\n",
"\n",
"$$\n",
"p(X_{k-1}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k-1}) \\approx \\{(x_{k-1}^{(s)}, w_{k-1}^{(s)})\\}_{s =1 \\dots S}\n",
"$$\n",
"\n",
"in which $x_{k-1}^{(s)}$ is the $s^{th}$ sample, and $w_{k-1}^{(s)}$ is its weight."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We then implement the process in two steps, called the *prediction* and *update* steps.:\n",
"\n",
"1. In the prediction step we approximate the predictive distribution\n",
" $p(x_{k}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k})$ by drawing $S$ *unweighted* samples from the following **mixture density** of motion model densities:\n",
" \n",
" $$\n",
" \\{ x_k^{(t)} \\}_{t = 1 \\dots S} \\sim \\sum_s w_{k-1}^{(s)} P(x_{k}|x_{k-1}^{(s)},u_{k-1})P(x_{k-1}^{(s)}|\\mathcal{Z}^{k-1},\\mathcal{U}^{k-1}).\n",
" $$\n",
"\n",
"2. In the update step, the measurement is used to convert this predictive density to a weighted sample approximation of the filtering distribution, by weighting each unweighted sample with the likelihood of $x_k^{(t)}$ given the measurement $z_{k}$:\n",
"\n",
" $$\n",
" p(X_{k}|\\mathcal{Z}^{k},\\mathcal{U}^{k}) \\approx \\{(x_k^{(t)}, L(x_k^{(t)};z_{k}))\\}_{t = 1 \\dots S}.\n",
" $$\n",
"\n",
"We initialize the algorithm with a set of $S$ samples from the prior, weighted by the likelihood on the first $x_1$ given the first measurement $z_1$:\n",
"\n",
"$$\n",
"P(X_1|\\mathcal{Z}^1=\\{z_1\\}, \\mathcal{U}^1=\\{\\}) \\approx \\{(x_1^{(t)}, L(x_1^{(t)};z_1))\\}_{t = 1 \\dots S}~\\text{with}~x_1^{(t)}\\sim p(X_1)\n",
"$$\n",
"\n",
"In the \"vanilla\" particle filter outlined above, the number of samples stays constant over time, but variants exist that adapt the number of samples to the complexity of the density over time, or even to the available computation. Used in that way, a particle filter can be used as a \"just in time\" algorithm."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will now describe the prediction and update steps in more detail, and illustrate the algorithm using our warehouse scenario."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The Prediction Step\n",
"\n",
"The prediction phase is the more complex of the two steps. \n",
"To illustrate how it works, we will us a simple example in which we represent\n",
"a Gaussian mixture density by a set of weighted particles.\n",
"A mixture density is simply a weighted sum of *component densities*, in this case a set of motion models. The weights define a probability mass function over the component indices and hence should sum to 1. Sampling from a mixture density proceeds in two steps:\n",
"\n",
"1. Pick a component according to the weight distribution.\n",
"2. Sample from the component.\n",
"\n",
"As a toy example, let us assume a *Gaussian mixture density* with just two Gaussian components, with weights 0.9 and 0.1, respectively:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"means = [gtsam.Point2(x,y) for x,y in [(20,25),(70,40)]]\n",
"covariances = [np.diag([sx**2,sy**2]) for sx,sy in [(5,10),(20,5)]]\n",
"data = [go.Contour(z=logistics.gaussian(logistics.map_coords, mean, cov), contours_coloring='lines',\n",
" line_width=2, showscale=False) for mean,cov in zip(means,covariances)]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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MG/25z6jMhLe8kADe8HFFSAuEjP5OunwoSmcMUIKdzwlDgAWvBkuDk9Y0gBinJljwxgm0hrfxF7xUTWGTFLmLqgLuQlFcioyMP7cgoZPMSNySqBXidiuJ264eQQkmt7QfpO2ALAdailqO8Gq4yHtBU3oI3kjDIjEsLRMUGbY32HF0e4S1PKmfKLuWPaaP+L9WD2e9AH1AF+h3nHiQ/7gSu6jet1+1jndcV/e27h5T/WHBq8F0seDVAGKcmmDBGyfQGt6m6WAb9q2pwar5P4gvAv+DSoVNvmIoxp4b+OpPw9v3WFPSkkA+29otdWiuaA4rbiliSxsVkAggYdvTiWDxjvC2ldfA3dweMFf2g42wVzeEnD9nYzvaymOvYqBmUaSdWBD28rRx+V1+Zu6fDmv/DDW3VHRtvAVvuE6Rv5we6Mg7TEI4UkSYbBFSBKcVpCDa2sOKwPTwSRs/rhLClyxbf/r67B7uzbF9exa8GswfC14NIMapCRa8cQKt8jaUdLZ5URVWv7m3ix83EUVusLilL/xwpb1k1JZe+VIJL6W+WpVTEtXlsQhed5Mdbbu9ItTZ1I623Z0VBFrLDsPV1ClomzdWRtWfRDrZmGpFclFnbVfrgHRYB3irX9DhL5pTQgjocCx6i+AN1T/pF6YKE1IQh0uco4c/igLTf7mluQkVCWYPr7pPMgtedfzE1Sx4NYAYpyZY8MYJdAy3oVd5a9/eG1Lknnx+AUbNHigsC4mwm5n80j646hCObqOIVtdXuTJ5jHyM2SXkZzx2XuP6C14ZffWPuDZ9XyFWCIlYf2Ebw7IRlyQNy4ExLSngciEEw0RGzek2JBVqtyFANP1u2uAde6ijaUNXId+2uxru5tAbVCi9r79I9hfIUhxTFDl5YCb6ZtqOmY0n/EUw+YPpMxXOEiEjwQOm9EP/0n7HbMk0FrxKV3zo81jwquPHglcDfvFsggVvPGkru9fat/Z5E8+C7Aqllw0GVVWYeFEB+uYmo7bRrqzBXngWfRlXr63GwVWHcWhNdcjtcClyK8Vt7qS+x0yiTktHtLVpYyWkVcBoABpDiLdIU2NMtSCp0FvP1ZxmRZJfFJMimqY0m+/y1PFdX/33wmnXpUv2Qw1wHGz0tU1/tx/0WjfoAaK1vDMy3rIpuki4Oc0GW2FfwTp5eD+YOqLJxlQbkoo6NwHRZWAaNUreYLJBkA0onAimbZr7T+qH/pNzcSx91ljwqlskLHjV8WPBqwG/eDbBgjeetMPfi/xoS/+2s0t1BaqsMO7c/IBIrtKyZL1jZN5edCdwaUMGitj2p4jTpN7/2pVErYzQSntBa/lhuJu7fwix5KbD0j8jQMRKAUvC6lgRUr1pfUXbF7KL0HzR4S+QZURZaRTZ2t87l/QwQlFyihD3djHsHwkmT3Cokmn+AnjQmXm9NgLMgjfalR94PgtedfxY8GrAL55NsOCNJ+3Ae8kKCx8/sSVgK1/y5J52y4iwdoVjQfDSl+r+z6pwaHU1flhMkU5nwOBJ4FIkacCU/r02oiQ9tCSM2g82iqQuJaI2Zaw32prWEXVNG18As8mA/GnDUFMfmEjWc6uP79wdAfLwpjW3oWpnjU8Ue8VxIxwUVa7ujCqHaiupIzJMSXnWXBLFfXvtwww9kNKblkOrDuPgmuoun1d605I7KReDz8rrVYlwLHi7W8WRf86CVx0/Frwa8ItnEyx440nbey9KQFv0xNaAaG5SuhlUV3LmLcUBhdVDfpFaTUixmXqdpYG+NPcvrkDFkqouHtzeLnDJV0v/tZQfViRsSdRKm4F1QIbwxlKU1phmDbmgYklai//K5Dv6E1CStCbtFJRcSPYVihB3J4ZJCFNkOLk4V0SE41V1IprZlQJ4/6dVXSLAtIUyvYUZNDu/xx9WWfBGM6tdz2XBq44fC14N+MWzCRa88aNN3tzVtPPZys7yT0VT+okyYpMuH6K4I70lwktR3ENrD2P/4kocWnO4SxWFgjPzep1FQUZtyV9rP1iP1rKaiEliJGxlshdFai0REr8iTWCvE7ytrXBXBZa08++/q6xc8XqM9kRDchKM+WE8x0kRfhbtjVSer0TwRrpF84bKDg+x9yGKfMVte46EvSR1XL6wRqQU9et10WDyAf/waYX4nAcnwlH0d9BZBaDPe7xrAbPgVbfIWfCq48eCVwN+8WyCBa++tMm2sPTvZVjz5h6fbYGiuePOzcM594zpNprb2yK8lP1dvaZGiFyK5PofMoo7aHYBBkzqHZnf5LUlGwJF3oToOBT6NTRVNaBILQkONcI23GrSQ/C6yztFqbuyEp7WNnF7T3NLgJj1tLTAE0Hc6vsJ0KB1IZA7a/UKwVzQ+XdjXh4MKcniRoasLBiyszW4KaBW8IbrBL1JoDVJAlisywhVJ4QILuyLlOG5SBmfF5f6w93Bo98B9Nkn+0PFZ4G/A6iSyuDZ+SL6WzArr7umVP+cBa86hCx41fFjwasBv3g2wYJXH9o+28JHlb6dgWjns3PvGaO6lFi8I7z0BVf5WRXK/7O3i1WBKikMOiuvVySa0etlEhMkIpo3VISN3FLUNrmor8i6JytCPCocRCN4pZCVItZfwLorK4AOYat25RqLisI2YRoe/mdq7+uh6HJl6Oiyp7YWnro6tbfwil8hhFPEn03Fw8X/jVnZMORkAQoiyXoJ3lCDk0l0VKLN6xWvCekRluXUSAinn1iAaOoKawI1RCP7F5P4rRbi178WMFkfBs3SV/yy4FU3qyx41fFjwasBv3g2wYJXW9pS6JJ9QR5UaeG0m0dotr1vPASvTDorf2cvaOte/4NeXQ46Kx89nb1NArdlQxWaNu4HvT4OFb2lyG3ScG/Uljy2PVUBwV/wkqD1tHgtBVLMxhKFNeQNhCHZK+gM2Vkw+kU2TcXFnVMWyUKg7fLXp7UggexpbYG7orO8WEB0O1rB7Bc9lqJYiP2kJFgGFfRoHV6lIlhaIShJMm1cQVgfuT6TE9iq9P7Sw7G/9UEv8cuCV92ssuBVx48Frwb84tkEC15taIcSulQ3N1bbQqRe6Sl46VUlidxgu0JvELkkABpW7g4rcGXdWvHFP74gLpHbcPPkL2rdFRUwtLXBuatM0WKTkVdjfh4Mycnidb18pU/CVqtX9oo6cwyfREJYRsNdu3aJkfii5gqFsblvDtx9skC2CWPfbOE91tI2ES1e8RajjN5iVHjfYoTwBJMApsoQlBDXkxFgaX0IFr9U8qzgzHyMvH646traLHijXUGB57PgVcePBa8G/OLZBAtedbTjKXRlT7UWvPTFtP3lMuyevydgA4jeIHLJg0sJZvVfl3exKJDApYgWfbmnjivokeitEFCVB+Cuq4VrVxnEK/na2oiLSgpaiiT6i1mjjjYCdas8ga/uiB7LqLG0WyixVhiHD/dG1nNyIOZSQ/+wUuL+UWCy8gRvrEEWCHr4o4fA9KmFPeYBpt8xu9/Zi93v7guwPVDC28jrR8T8togFr9KVEvo8Frzq+LHg1YBfPJtgwRsb7WChS4loM28uxqQrhsaUiBZNL7QSvPTlE2xZ6DMyE0U/HioSTtIKUqPplibn+kdx61fs7rKRA/lv+5xa2CMCl6K2JHBdFZXilXqkRDCyG5DFQEQEc3Jg7ZeDPiOGoNZh0oQTN6I/AfLwZtmbUL33IChCrEgMd1gkyB4h/ML5A8NXpNBhCPT5oehvuAgwJcClji9A9uxRPfKASEMm28O2l3dg/5IqX71faXkYed2IqCo9sOBVt4hY8Krjx4JXA37xbIIFb3S0ZdWFL1/YgbYG72YKM24aLpLRkjMt0TUW49lqBC95c7e/WoatL+3wfdlQZvWgWXkYdf0JUX3ZxNj9LpdJkVu/slxYFvwP2pUsY2qhiFJlTCvU6pbdtkPClgRud+LWX9gaC/KF3SBUya1okta67ZwGJ5gPbunSiunIHsDeErZ1U9XmqO/sTu8HT3r/sNd50nJB5/gf7rR+cKd5t1TuyaO7pDV3WTnctbUgywol4YmEwrbQG4tQNFiIYLJGkFVFo0oS3fEhCwT52xtWlKNpYwXczQ7fJRT9zZxWiIypReIz1hOHeOj+z96AWr+UCEsP3YWXdF+qkQWvulljwauOn7i66kirBq1wE/EgwIJXOeWNH1dh/v3f+8qL6eXR7a5HsQheeqW46emt4pWiPCiaO+qG2F8ndtfPSD+PJHJlFDdur2A7atJS7VmyJbjLQntthbjNz4epIF94aqOxIOgpeE21e2DoEKqmAx1Ctr0JpiN7fVNgPhi9WFUzv1peS+LXJ4BtKXDldIgzK/15mLiVHiK5O8EbaoxeS0udiAiLh6bKqpBVJ8j+YCwe7l1LRUVxiwKT+K1f4X2w9N8prqfFr7BVvbQL5fP3+h7Eyes76vpiFM4ZGnZrYxa86j5pLHjV8WPBqwG/eDbBgrd72mRf+Nft3/o2jKCtfy999CTNqi5034PAM6IRvFQwfsPTWwIqLZA3d9T1I5A7uW+0t1Z1fiSRmzFlGDKmFSFzapH+WeatrZDi1lVWFtKaIATJ8KKYxG0oSLEKXilmZfTV0HgIxsbDMNibYKrtFLTRToxzwJgul7iyhwK28DYW18Cx0d4GxqZqUJ/DHYamajEe/4OuMTYF/ls0N3YOKBGnu3JoPGmQ43JnD4XbqtymE4vgDdnPDp8wiWBadyEjwclJMMkocJwEMJXwE+J3RXlA8huJ36zZo3vE9iCrw2x8aovP60t2h8K5w0ImubHgjeaT0fVcFrzq+LHg1YBfPJtgwRuZ9qInt2HR496oGfl0ybpAXt2ePJQI3mChS7aForlDMfKG4rh7cymqVLdkK4I9ufEUucJ7u3lL2AiuN8qWJ147k/BAsncjA62OSILXJ2opOtsRmfWKvmpFt3dlDYHHluYVeQM7hay/QHXnRCf2FN04TicJFlIUk9An6wWVYvP7d+OR3TA6lL1ZJAHssabBlVcCdESJQ4lhzQRvCE4y+isiwWXlXaPAHQLYPHYcjMMLdbdAkPWhceVuHH73+4DIL22BnHXWaPSZNTLuCW/id9hTWwLsDmRzGHvnaN/vMBa86j6ELHjV8WPBqwE/vZrYs7IG5StrULWpDq31TlRtrvP5UOmehVO9XrqiU/th4JhMFE3ti6Q4+VL1GnOs7ZatqMHrd6wNsC9c8shJcfPpRup3JMFLReDXPfK9b5tfErqjrivGqOtGhH0tGCujSNfJL9Ca+d8H1Melurh9LzlJ90guvVp2l+2Gc9NGUBQ3eLMGEriUWU/1aqOxJsTKigRvest+1B+oFJFZ05HdMDRWdxulla/qhRc2LVf4Yen1vode7Wd7X+fz0UnAaG+GscPKYTqwSfxARseViGKKDkvfsSevBFkD83HInak7Ylqv3rcOoQUweX5NJSXeB7Kx3gi2XgdFfms/3drF9kA+X3oD02f2SL1uHbJdmeS2Z/4Pvp9L4TtifHzfUsV14HG4GQteDSCzh1cDiBo1Ubu/BV+/WIZ1b+0NELdKmz/l8sE49efFyCvR/5e+0j7peR4lpX38xFYs+5u3bmdP2xdCjTWU4A2O6NI2vyOvLxZRXUscH1pkNLdu8XZf1ynxLGv2KGSdNUrXKJEQDZs3w7F6bRebAlkUSCjoFcENnidKCiOhZTiyR/w/kv1AiloRnbWlwpVdKERXb0jc0vOz1lNtmymS3hEpllHiSGLYbU2BO7tQWCQ8OfT/Ibo/bPgE8MaOBzb/ZDhpfxg7FmYSvxq/jfCfl4YVu0HJpEeXdH6eyfLQ75KT4h71JZ8vWR38he/d9Vf31DJKiPuy4NVgGlnwagBRRRNt9Q6se3sfvnlzHw5sqfe1NHB0Bgqn9UPe2CxkD0oRIjanfzLMJgPqmx3YvaIGrfV2VG0+ivIVNdizqsZ3bdagFIw+Jw+n3jxcXJuIR8Xmevzr9rWo7GB29l2jhIWhtx3+gpe+BNY9vMG3UQRFdCf+7iRFGZseKN0AACAASURBVM5ajuvo4u04PP+7gFq59BqUIkJ6VleIJHJNJWM6ImJjdX0lLF65H9kL04HNIlEsbIJYei6cWUNEohX950nP1V04aTnHid6WjA6bancDDdUw11EkPnTlCiGCB5aIBDp6UAnlidaSF9kenB3i11N1IKBpU+lEmMeO1TXyS/57siXVfrI1wO+bNXskcq+epOuDbDBHKXyr19Tgv7ZeoiXm464tFrwaTDkLXg0gxtjEir+VYfHjW33RXFu6GWPOzcOPbg4dpY3k4RXR4Rd2YcuiAzha0VmuaNY9o3HqTUUJZXdY89Y+vPvb7wQ3iupe9VwpCnppVFsK3mWPbhD1LB0NTvSUdYGE7qHXVvtsC7QZRN85J6Hf3JN0TT5zrf3Wa1fY5Fd9IMkGE0W9xtGXf/QJVko/ciRwzQe2wnhgEyhaGMprS75a58ASIINEbSGMg8YiI9WCmvrQZauU3lvr84yuRljavG8z5GFpXh/2Nsb2SpjsBxV1w556EgxGY8hzXZaBcFsH+n7mNqXBkTRCUbvxOkl6eA8fOtLxQLNJCGBj7d6QSXUkel15Y3UXwOIhb9MmONbQmww/8UuR37FjYZkxXdeqD/QWp3bx1oCob08IX1oH7OFV92lgwauOn7iaBa8GEKNsgqKz/77jW9Tt9wrTYVP64kc3DxdiN9KhNGmtanM9vnpxF9a/7fVRJWWY8ZNnJnTbfpTD6JHT/RPTqNRYb/HqhoNxdF0t1jy0HjWbj3rneu5gTLz/pLhaF4KFLtkW+l8zSVgX9Doo0cexbLn4svf35FIk1zypVFeRa963VkRwzRTFDaqO4LYkw90R6aNEMadf4phkEWuVhlhYWtp2wuhqAvzErLllBwz0bwDMbTu8P+/FhyOpGB5Thugh/RmWjj+nnuz7N7cpXdcRREpa8z70bIGhZrd3TdR1lvuTnSI/sGtoqVgPevmtw4lfQ14eLJNLYZ44UTfLA/n0D81bg4aV5b76vvEWvix41X0EWPCq48eCVwN+0Tbx2ZPbseTxreKyPgUpuOzZCSicpszMr1Twyj6R8P3gvg0+uwN5fC98ePwxGe0lv+6/7vgGGxdVieHNfXh8j1dgiDT3VLJnw9NbseMVb0SOfLpTnyiNa3mxnhC6FM21L10a4MulmriWmTN18zCSoLFIkbtvbcC0CIFLr7PzSkQUV4mY0VLwmhxVMNsPwty2U4hYKWZjEbJuYyocyScEjM/RISpDrUW3LQ8ua+SHaHmdpfHbsMuZxmD0ixQbXQ2wtIWufxzpM+GyDoTLQn3qD7etwCuOTelojzAGpb9fo6nSIOwQJHyrOh6KggQw+bFJ+DqHTIJzSKnSLkR1Hj0QOteshXPt2oANMMjyYCkt1S05k+wOZGeqWfBd3IUvC96olkiXk1nwquPHglcDfkqbIMvBvGtW+Xy6Z941EmQ3iOaIVvDKtr996wd8cN/3aG90gvy917w65ZhKbKPauv+4ZqXw61K5sZ/PO7XH6uoqma/g6guld5eg+Nb4ZUvTa8xDr61B88ZK0V29I7oUuXIsXQ7nN2s7o7lJNphLS0U0N9RuZko4RjqHyoOZd34Jc9WmLhE7YVEYOgnhIrjd3TsWwSsitfYDwnJAotZor1QkCl2WAXCSKPWzCfgLVWdSMfSOjnbHo7uf09hlRNrSugNwNsLgaoS5w35B/2Z0N0dshmwSzqQTfBFiEvIkiJWOPRrBG9wREsD0VqDT9hJYV5hEr3PIZDgHjtYlOZHegpD4pVJ88qCor3XmTJhKJ3SHP6afk/A9OG81jry3wXc9RXzzbpmhm72JBW9MU9W5Jjwej0ddE3w1Wxr0XwMUaX3x4mXCcxptVNe/d7EKXmpDCO6rV+LA1gZhcbj5vRnHhOil5LRnLv7S59e96bWpyBmkvCC9/rPbeQeK6n77yPe+HdJo281pD5+MgpNzUNto170r9Nqy4onPfEKXPLp5t87QzbpAyTmOtWvhWvuN3xd1RzS3dKLm45Uil6K5/l5cGcV1Dp0sInLRbFgQqpORBK/00ZJ3ljyy5tadXXy1/m3KqKzbOkBEN50pI8Tr/2NByGo9gVIYS1FMf4erCbYIPmR/IexKOQHO5OKQ/mE1gjd4nGKdkSVmxxddH6ayh8I54nQ4aJ1pvKWy98FxWWDUNzlJvB2xTP+RLnYHaXWQlR1kVYe+F5+oufBlwavuE8URXnX8xNUseDWAGKEJf7FLlRdueX9GzJYCNYJXdvHt278V3l4SvRc8ciImXD5YXwAqWvcXu2PPzsNVz07sFbV1Qw2J6k+uunst6rbVi6S08b8Yg5HXFUPJxhMqEPkurXr+KxxZ8L34u97JaPTF3P7GWwHb+pomToBl5gzNo7kUfbNs+QiWnZ8HJB9ReTDH4FKvVWHIJC0Q+trwF7wkcG0Ny2Fp+hbm1h1ho7YiUps8QogxGaG1a/CqXtOB9eLGiDNFhEkMG9qrfH8OFxm2p54CR/opoEgwWSK0FLz+mGT017x3Ncw/dD7Y0Tnk+7WXnK+L7cG59hs4hDWoI9EtDsL3wF+Xo2GVd6MQ2sSi4K5ZSB2fr9mqYcGrDiULXnX8WPBqwC9SE/5ilxLTrp03JWaxS/fRQvBSO1L00p9//MyEXil6/cUuJadd9aw+XjotlgCJ3SVXfikqMPQZmYmpT5Yia7S3FrLegpciNPse+MhXYizn4vEYcM1kzaMzYjCtrbAv+hTO5cu92JJssMyYIYSu1vVFKYJrXf82rLu+9E2RFLnOE05X5MWNdW5THGVIa/kKzkOfhYzeksCiCK3Hlic8tSxsYyXd/XU+Idz4LSgiTBF1kyOw8oSIAqeeAmveLNQYSkQkXY9Den/N+9bAumup37rMhf3ky+EcMlH124Xgfou3KEuXdtodkpNgmzNXN6sD2aEOzluDlk1eO1TOnBORd+uPNMHJglcdRha86vix4NWAX7gmyDf74W+/F6/iT75ssEhOU3toJXipH5Q4Rwl0vVH0Hktil/y6q+5ZK8RuwZl5mPrExIAKDHoKXio0v//JJXA324VPd+hD5yOpSFkCZLRrkZLR2hfM93l0zdN/BOs5Z2sudCmb3rzriwCh6xw8EfaSC0NWVIh2HOHOtzUsg61+Kej/wVUR2jOmw5F2Cuxpp/S6clxajf9YakfYSprXwdK4Dlb6f1ACHXl/7X1Og5g3ncqniTcPu76AZfNC35sHqvfrKLkQjjHn6SJ87Ys+gbu8XEyVcfhwWOdcpPkbFbkO6G0RvTUSz7WFfTHkofNU1+9lwavuU8aCVx0/Frwa8AvVBInd/9zhzXrWSuxSW1oKXmrPv5+9JdJL1Rj+dPoS4TkmG8NN86bqNEvqm9397j6sutv7mpPKjVFkN/jQS/D6WxgypgzDoLtn6xLVpWxy+4L3ffYF2ubX9tMrNN8cgoQuRXT9N4KwF88UkTOtvZJyjsKJXLInGPqdjgbriWjPmKl+oejYgsHQCKNpOwx+9zAYqmAwVsLjccNgCF1bN7hL8ly3i5IrvSXEKEHG40mH999670FVJJKa1yOteTncdd8EJMhRZYi29BlozzlfN/ErIr6bF4J27KNDT+FLVgf7/Pm+yg6Wc87Wzd9L2xbvfWAhHNWNIG/v0AfPV2VxYMGr7jPEglcdPxa8GvALbsLfxqCl2NVD8PZG0fun05aIagy0ocSd78/stZ5dJWKX+GoteCm7uvyud30WBnrdSK8dNT9aW+FY/hUciz7xNp1kg3XuXJg1TkYLFrqUgOYouUD8pzb5LBSTcCLXkTQc7dkXiCiuIW1kj288QSLWaGiEFK9AA4xG7xsZo7ESBqO3PF+8D5dTJiOmw+321nGWItnlGikEck8c/h5eW8NSb7S+fllX8Zt9AVqzztXF9uBdy2/pL3yFtegTOJd7I7CG7GwR7dVjAxf6fbP/icU+by/V7869KjZ7GQtedZ8MFrzq+LHg1YCffxO0TfBjpyzS1Mbg377WEV7Ztoz09nT1hnfv+x7L/l6GrIIU/PrLWceE2D3hZ8Mx4YHwglNLwUv+ur0PLtTdwkC+wfY33gQlp9Ghh30hnkKXvJ+2IwuR1LgMJnvnbldS5LZlzggQQLGUJYvlV4nBVAmToQpGE70l8AraWMSs0xlsl4o9KuvtS+dhMDTAZNoZ1fDcrhPg8WTA7S6F25MHuPOhtxgOl7TmnfsPkVy3MED8irnPuRCtfc5TXPpMKQSxtjd/4Ety0yviK96+zH/PZ3MwjS2B7corNLcZ0bhp04rq1701rlPH5YtorzHNqhSJOI8Fb1S4upzMglcdPxa8GvDzb+Kp0z4XdXYpQe2W96dr3Lr2lgb/DspENqrT+4svzlCVXBfLwDd+XIV/XLtSXHrPF7N67VbB/pHdKU9MROElQyIOVyvBW7d4Gyqe/EzcK2VsPoY9FP0XjpJ5cXy62BfVpQ0jbD+9UlOfICWjJa1+WdQ9pUPPiG5y3UdIPvxGQOIZ2RVas85HW875YaN8egheitiaTd/AYNwmorYmc6CwDJ4btzsP9J/HkweP25sp73Z7q1H0pM2gs98k0LeJ/kiR7I1Kh98VziPGlC+EMI3J6Txds4iwkioN4SK/7Rkz0NLvCs2TD8NFfNtP+omSj6Lic5zLlomIL9rageQkJN1wgy4bV3gfuD8UG1bE4utlwat4SkOeyIJXHT8WvBrwk03QjmYr/l4u6uz+z5f6CEa9IrxyDE/N/EzU6S2c2g83v6dNZq4SxLSxxJ9mLkFbo7NX76BWvboGS670ZmcrEbt0nhaCl5LT9j30kbgvVWHI+y/tH6aobYrqypq6lrNmg/yBWh4kAJI+ewxGe4uuQtfavB4Z+x/yRXOpFi6J3PacCxT5OLUSvELkmt+D2fx5SAuC25Mm7ABu90jAQ0JwlIiIelzalYLScv6UtuUVxV5BTF5iEvhmc+id3Cga7HLOgcN1uqpxKxG8/v2niK83SbGj4git/4wZaBj0O30ivn5WBypn1jbrXk0tO6JU4L/e9EV7rVdeobn9iPiJqjC/W4i2PUdE6bLi569UHOllwav0ExT6PBa86vix4NWAHzXhn/x15xdn6Lahg96ClywZfzh5kdiRLZad4GLF+frta7H27R96dZIabSqxYMZHohrD2DtGYdwvxigarlrBS18wu255U9gYdPPr+ovdJBuSbrxR8wgRlRdLWv6sYEZVF9pm3KHpFz61S9n7aVX/C4rs0kGvrVv7XSnEbjSHGsErRa7J/DmMfj5bita6XBPgIVFL//Wg3zUaFlqeSxYOo4FsG9tEop3Z3Flyju7jE7+Oi6OO/EYreOW4RMLbkYVIqXlTWB6oxFnLgJ+jOedyLYcu2hIPfEv+AKOjFa7soWid9WvNEzLb//UGXN94Hy70Er0ij+BX7wjRmzG1EEMePE8RKxa8ijCFPYkFrzp+LHi14Oe3i5relQ70FryEY/eKGrw4xxv1uHnBdBRO06fMlURftqIGz8xZKrYMvnfprF67i9qym1eiYkkVaPe0WW/NULxy1Ahe/wQ1qsQw5KHohJvSTvoiuyR2b79NUwsD9cG2ZSFsq18W3WkffR7ap9ygtGuKz6PX1Rn7fy9KilFEV4iWvlcovt7/xGgFLwk5i+kLmC3zAiK5JHLptT1FMHt7pYOYQGlwET0YmMyfwWT+IsAO4XKeDqdjjuCn5IhV8Mq26WGJ3grIiC9tbNEw+H7Nk9uonFnywt+KHdzI29t63sOa15SOh+j1Poi/IewNSh/EWfAqWcnhz2HBq44fC14N+EnfrtYVGUJ1LR6Cl+4ra/RSEttv1p2jq59XVmU4+65ROPceZVFTDaYtqiao1u7yW1aKHdTO+2gW0gqUb22sRvBWPLkEdYu3ixq7I15Q/uowmsG1v/QyXJs2iyoMeohdiurKzSPapt8Oe/Fp0XSv23ODo7q0KUTj4N+pEipKBS+9urdY5gmxJg+yKTgdF7PI7Xbmup5gtr4Hk+mzgMivR/D8GRzOiyJaHtQKXtkb8eD0w0O+aG9T3i+jfkPQ3dCDRS99LrTeLVCUL3vjTdEV2w3X6VLBwd9qVfjE3G5LlrHg7W5lRP45C151/FjwquQnhaGevl3/LsZL8NI9X7hoOfasqsGYcwbimlenqCQV+nKZqEZVGR5af64u99Ci0femf4zmihaccv94sV1wNEesglcmqdE2wUVPXqrLhhIi2WXB+7qIXfpSJ7FLyWmUmGafcqPmYtffq6s2qus/p5EEL9W9NZu/gMX6XEA01+k8TUQkXc4zolkefG4IAoKxZQFM5gUBFSIo6utwXIPO0midF2sleKnF4GivXt7epOXP+HZs0+Nh0Pf5Tk5C8t13aV47m1jJ6g1Up7f4hSsibk7Bglfdx50Frzp+LHhV8KN6u0+f/rloIR6v/uk+8RS8tPEDJbGRn/eaVyZjzLnab9f592tWYtMnVb06UU1WZUjNT8HFX0UvymMRvPS6cMfVr4q1VXDXmcia7a13quVBJY3anvizaFLrCJCIYH10P0y1e4XYbT3/EU1f23oFye/Frmh0kFe3ftiTqqK63QleYVswvyaEmKGjEoGwLDguEhHInqo/q+Wa6I1tURTdZJ4Pi+UDX/fI60vM/as8aCl45Y0osS2t8s+6Rntt69+C7bt/i1vqIXrb//GS2JbYkJeH5Hvu0mWK9z2wUNTppXJlhU/ODXsPFrzq8LPgVcePBa8Kfi9e/BV2rzyMaTcV4cJHx6toSfml8RS81Cv/+rxaWxuoMsNDpywSg//Trot6bc1dGd1VWpUheDZjEby775qP5o2VulZkaP39I6LOrqixO3eO8kWo4MyUz/4oIruurCFonf0bTRNzSOz2Kb9FlBoTUd2+V6B5wM8V9Er5KcERXqvtj7BYX/M1QHVvXa45cNovVt4on6mKgDfq+yrMlvd9yYBkd2hrfVX4o/UQvNRhSmpLr/xfn7eXqjhEmwTZ3cD9Ezo1F72trWh9/El46uqgR+UVGhvlGmy7+mXh5430gM6Ct7uVEPnnLHjV8WPBGyM/KQTjZWWQ3Yy34KX7SmuD1sJ+6Yu7MP/+DSi9bDCueja2nXtinD7Fl0nvbqzRXbpRtIJXRnfJyjDqtesVl/xRPCiqktDh7zNkZSH5gfujubTbc2mb1ZTP/qRLZJdunnrwb0ir/ofmUV3/gfkLXvKV2mz3iR87HBfC5Zwb8pV6t2D4BM0IeL2+C0SpMxK9ra3zYfQUoG+mDYfq2jS7j39DFO2ltwp01I54XVF5u2g6IkUvJbI1Xf16NJd2ey5tJNP23F9Ejd6Ux/7Q7fmxnCAtWFSfl6wNoQ4WvLGQ7byGBa9Cfo1NLXC6XMjK7LrtY9WRVoWt8GlEwH83Nb1e9Ycj3ROC19+6oWXJNWln+OkzEzHp8sibN/TUyvv2oe+x49WyqMqQBfc1WsFb9dflOPLeBvSZNRKD7p6ly9Dbnvsr3GVlupQtkr7E9snXoX3MBZr2n3bNyt55lW6iQ3ZWCt7apg1ITrlE/HN7+6Mc0dV0NtU3Zku+TSS4kcXB3rZAV8FLvSV7Q+qRt+FIKkbtiH+pH0BQC2lv3wxj02G0nPswnAO1TeBte/YvokavXqXKaChb5rwgorwnvPazkF5eFrzqlgwLXj9+lQdrcPF1v8UVF5+OX97s3cmlpbUN9z7yIr5Y8Z34+7jRRXj2kTvQNzvTdyUL3ugWodxgQq/d1CL1picEL/VHjlnLDSnuGf6e2IL5gXXn9NpSZNLOcO7CWcga3fmZiWbFRCt4d1z9CuyHGlH8/BW6JKr5oj1JNqT88bFohqLo3LTXrhIbSzTP+bOmvl26efbOnworQ1PujZrbGPwHJwVvs+M8GE07YLdfBUf7bxSNn0+KHwGyOSSlzBUWB4f9v5CV8ivdIrw0KrLT0Bo0OQ6iKe9/Yi57F46QbdVLsG39CPbimWibfoemIH1vdbKzkfy732ratmxs/xNLcHTJduReVYr+13h3BfQ/WPCqw86Ct4MfRXB/+t+PoHxfFW644lyf4P3HGx/hPx8uxWvP3ofkJCtu/fX/YdjggXj4nutZ8Maw9iiR60+nfCKu1DLaqbQrPSV4/Tek0CKqXbG5Ho+fvgS9uTpD3dZ6fHz+EqixM9C8RiN428prsOvWN0UZspGvX6t0WUR1nqzRqYefT76WdQ4Yg5bzHo6qX92dLF8pU4Ja7Yg3ujtd1c9J8Can/BVOz7Nie9+2lvmclKaKqH4XU1JbUvK1gCcNqZaPUF2nb91wqgySVX6L2KDi8JjOcnRajJC23U57+xZRn7flshc135il9aGHhZc36bb/1nxjGRq/LFNGW58X/blr8hoLXnWrhAUv+fFcLtz2/57CgH45aGhqQcHAvj7Be+lND+CsmRNx00+9Bes/XboWv3zwr9j85T9hMBjEv3GEV/kinPezVdiy6ADiUXOXeuVscKBxRx2OfHNYdLJ5Rx2cTQ5knpIr/p4+sg9yJuTCnGFRPogYz/z6xTJ8eP9GZA1Kwa/XqdtyVm42UTSlH+58X/kmDjF2PabL5DbC0W40EXyzaAQv7VW/++75CPeFEdNAgi6Srzb1+NJLXfBLUZlB88QbABn7H0Ry3ce6RNaCudqsO2G2eRP52lpfYc+uFgtPxzYstsdgtb4OEyahodG7wYmeByVN2prXo67oBdhTT9b0Vikf3Q/zwS26fIbkw651zkUwz9D+9y4lr22Z+6LgMXbx7V24sOBVt1RY8AL4wzP/QtmeCrz4+K9w76N/CxC8E8+5BY/ce4MQvXRs3bkXP/75g1j54V+Qme4tns+CV9kilDuQ2dLN+H/r9d2MofK9vdgzbzsadxxV1LnkvBQUzCnC0KtG6Cp+Hzv5ExytaIHaHeWOBcEry5ENmzsYU5+MPakuGsEra1rmXDweef81XdHcR3tSyy9+KS5JeexRIDk52svDnu+LTlmS0XSN9v7Gvtsvgsl+QJeEoeBBpaReAoNxO1sZNFsd+jZE1obk1DNFuTh7+71w2K/R9YYycVIPa41M+tTjLYlj0SdwfLpYt2oNBH3TbO/24Sx4tV+Cx73gffO9z/HK25/g3y8+iMyMVBG9lRFej8eDktOuw18f+x/MmOItm1W+txIXXnsfPnv7zxjYP0f8W7vDpf3MJGCLT8z+AjuWV+OC+8bgovvHaj5CR70d21/ejrJ/l6G5osnXfu7k/ug/ub/4e7+xObBm2FC5okr8/dDqQ6jbUgtHo0P83ZphxagbR6Pw0iKkDlK+G5jSwXz/QQWe+8nXSMm04E87LkByH6vSSwPO++TZHXjt7nU4+79H4Oo/T4ipDb0vWv2njVj7xGaU3l2CyfeOi/l2RoMBRqMBTpe72zb2/H0l9r20CkNumIJhN03t9vxoT3DV1KLqnt/BlJ2NvCe9GedaHZ6KTXD+5zcwFJTA/OM/atWsaMfgbIBp9XTAlAbnlK81bTu4MRfmw+G5Fwbkw2ag2q8Zut6PG9eGgBvzYRfzlg6bYb02jYZpxdDwLUwbb4Q78xS4x76k6b0M7U2w//VywJYKy3+9rWnb7Tt2ofpPT8N2wnDk3vsLTduWjX171atoKqvBxHnXIHVEv4B72CwmXe55vDR63Aves664G0MK+mP40Hwx559/vR7paSk+GwNFeB/99Y2YPcMrKkJFeGvq24+X9RLzOMu+Poy/XLgMSekW/G7juZrWjHU0OLB73g6Uv7Idjka76CNFbEfdPg6D5hYG9JmihSaTAc2tzoB/r1lTje3PbsSRb6p9/z5ozjCMum0ckqPYBlcJoOfOX4rylTU4655ROPvXsWUSb/ioCs9f/TXGn5OPW/81Tclt437Od/+7Gd8/tRUn/mI0TvplScz3t1qMSLIY0dASOGehGqx6ZTUOzFuDgddMQt61k2O+Z6QLj97m/aLr89xTmrZvrNoM64e/hTtnGOyX/p+mbVNjWeu9v8PqTv5W87b9GzQYK2G2nSn+yWl/FR5X7NF9XTvKjQcQMFn/AKPpNbjdJ8DV/p6udGxHPkTKvofQnn0eWoY+pOm9jEf2wPrO/8Cd1g/2n/5d07adGzeh6W8vwTK2BKk336hp27Kx7y94Aa7mdpz4wa0wpQUGRKhsHB+xEzjuBe/b73+B+sZmH8H3Pvka2X0ycMGsKbjsotNBHt6zTyvFjVeeJ85hD29si01uMnHmXSMx657RsTUS4qqG7Uex/o6v0FrpncOsCbkY8d9jkV0a+GQsL+0uaY3a2ztvOyrf3ysuMadbMO7RSeh/RoFmfZbWjqQMM2LdjOJYsDT0hIdX1rLUsySZTFyhTG1DdrZm64IaSpv3UxgdrWi67AVNN5ugtvX0TQZDSEr6C0yWv8LjzkNL8xJNGXFj2hPwJa4BaG15V2xEoech/eR6bEIhd17To1IDWxr0XBX6t33cC95gxP6WBvrZ3/+1EO8sXCaqNKQk23DLvf/LVRqiXJd6eXf3vb4TWx/zvnpLH5GJ0b+ZEFboKhW88jwS0NR29ZeV4p+GXDUCo3+jXXKF3Iwi1gcAFryhF2E8k9a03k6YRuSrwTv6PLRPuSHKT1rk06VvsjnnMjTl/0rTtoMboyoN1uSL4cEO2NtvhcN+m67348ZjJyD8uylzYTBWwWK8HUfrb4m9MQVXitJku67SzU9OVRrID69nLV49PvuETm6aE67KDCetKVhgEU5hwRsEJ1jwNre04a7fP4/lqzeIM0tOGIZnH70TuX37+K7kpLXIi1CP6O7G+1aDEtOiFaPdRXiDR7L3tR3Y9kdvDeb0E/pg8itnaJLU5h/lfajswqg/xa31Dtxb/L647pnqS6O+Ph4XOOod+PdJ3j7+5LuLYMmMrRJGNElr/lnOY+bfrM8ua8uWwb7gfZhKxsB2o7ai1FS7B6kLfqVLWaV4bTpB802CNy21DO1u78YZ8YgaxmNNJ+I9ZIUGt3sEMqyLkEhw8AAAIABJREFUdK3DS/zkg1d76sk4WvSCpkh9u62l9UPTZd5qB1odtI04bSdOhx5vd6jdIwu+R9XzXyFjyjAMechbGcr/YMGrbjZZ8CrkR7YHh8MZsOGEvJQFb3iIekR3pdg1pZkx/g+To7IbRCt4aWRkc1j9s8/ganJqKnpllDfWig1/nLkEVVvrcceCmRg+Td/amQo/Jl1OW3L5MlSvPYzpL0zFoNl5MTUTjeClG+x7YCEaVu2JuCd9TB2RF7W2ouWh3wNt7bp88aXO/x+Y6vah5cx74RzStfi8mr53biusz05Xsm9y44n61j/Dante7OTV1voq1+JVM3k6XOtvZbC3zkd2+nhdBa/eD10pSx6D+YdvdClJJu0MpokTYPvplTrMBrDrljfRtrsm7O8uFrzqsLPgVcdPXM2CNzxELaO7VFN33R1fofabapDYnfzqmcgY2RlpVzKVsQheapcsDutuW47GnfWaid5v3/oB/7nj25jr8r573/dY9vcynH3XKJx7T2zJb0qYqTln+z93Yd3DG6CmNFm0glf6eFPH5aPwya7F29WMR14r63Hq8eVn2/IhbKv/CeeQUrSc+WstuutrI2CnKx13W5OClxJ6k1LmwGTaKWrxtrc9y6JX0xmNvTESu7ak2zpKkd0Kt/N2XbcWprXXp/xmWNrKdNnpz2hvRgptLWxv0d4DTw+5v38YaG1D0t2/gjHfm+Su5SHtDMZUC8YsCG0rYcGrjjgLXnX8WPBG4Cd3VdOq7q5/ZDcWsUtdjVXw0rUkuCnSq6XoVVOXd+PHVfjHtSuRPyYT9345S4OVrH0TTRXNeH/6IlgyzJiz7LyYbA3RCl6yNWy7+mWxJ33hE3OROl77Lyf/15tafwHKerw0G3psQCF3uqL2m3MuR8uAm+A2pWs6+f6C12CqRFLyXBgN3lKBTsdFcDrn8GYUmhJX3pjF8j4s1ueEZ5cOh+NC2Nseg8lo0E3wUmQ3/YeHxLbWLssA1IyicnXaHSR2kz+6X2zaomf9XWNREZJu/2/tOu7XktxWOFLCLQtedehZ8Krjx4I3Ar+3b/8W69/+QZNd1bQQu2oFb7DozZ6Yi0mvnK5qBckob+HUfrj5vR9F3dY9Re+hrdHZq20NK+9aiz3zf8DYO0Zh3C+ij0RHK3gJotyAwto/HcXPX6mLl9c+fwGcy7+CIS8PyfQlqOEmFNKLSGNpP/lytJ/0k6jXRqQL5DbDdI7LOhANgx7QdMcrf8FL9yDRa7E8B4ulU+hQxNflnAOH4yJNx8aNdSUg+Jvfh9nyqojo0uH2pMFpv9qXUKiX4E2r/ofw7Yq1ZhmA+mFPwpE0QrNp8he7rqwhaD3/EU23FHaXlaPtub+I/mr9cCshyC2FKbpb/MKVsPYPXbuaBa+6ZcOCVx0/Frxh+LXVO/DYKYvQ1uDEvevORvaglJhJV763BxvvWyOun/bu2VHbGPxvrCbC6/vl5Ofpzb94KMY9Gnu9V+L0h5MXob0xNk4fP74Fnzy5DaWXDcZVz/bOeqf+Ud5zF85CWpR1jWMRvDRXu25+A217jiBjaiGGPOgtK6j10fr4E/BUHYCpdCJsV16hafP+otdefJqI9mp5eKNuD4pXzHRoGe0NFryy3yS8zKYFMFtf80V8PZ40OOxXw+maA49L+2i8lsyOtbbM5i9gMn8Gs8WbPEqHyzUCTufP4LRfHDAcrQWvf1TXu74uQ8uAn2v6NoGSPJOWPSsiuyR222beAVf2MO2myc/KoNd2wmRlIO+uu9mOvFt/hJw5J4btPwtedVPLglcdP3E1e3i7QpSRy4GjM/CLpd4i9LEctWsPY811n4tLqR5u/sXqfplpIXipL/6JbGr7JSPh024qwoWPenf0U3oc2d+Mh05ZJE6/54tZKCjJVHppXM+TUd6CWXmY8WJ0O6DFKni9XyRvCGtD7lWl6H+NtglgBNBdWYm2Z58TCWx6iF7aJjVp2TOiNq9zQAnaZt2rafSKxiAT2YQY0ijaG07wykVHpbBMls9hNr8q/L3ykFFfp/N09vrG+An1RnNfg9n8uc+2QE2RdcHlnBvWSqKl4A2O6jYMflDTNwg0HhK7ZGMgz64ekV20tqL12b/AU1WlS0UW8fujyY7yu94ViWrhKjP4LwMWvDF+KDouY8Grjp+4mgVvV4gyWS3WCgTUInlmv5z9AZyNDgy/dQyKb1O/HbFWgpf6JyPPtDnFpFfOiDnyXLW5Hk+f/jloI4pYSpTJKO/wqf1wx3szNFjR2jdBUd6PzlsCZ6MTU56YiMJLhii+SayCl24g6/LSn4c8cB4ypgXuvKe4ExFOdK79BvY33hRn6CF6xRf7wt8K0evKHorW8x7WXPRqHe3tTvD646TkKZN5PkzmL3xRX/H5d1wEl/NMkPjlIzIBIXJNFM1dAKNph+9ktzsPTsfVcDrmdPsAoYXgjUdUlwbn//bDOXgi2mbcoe1nwk/sGvIGIvn22zS1LMkJqnhyCeoWb0fSsBwU/fnSbq1XLHjV/SZgwauOHwveEPy0SlZbc+0XoiID7Z42+VVtvvS0FLw09I3/b7XYlU1tjd6nZn6GA1sbEMsDAtXkfeDkj4SX98ZXpmLcubGV/9LgoxCxif2Lq7D8lpUigS0aa4MawUsdkrUtjalWjHrtum6/VGLhIETv/Pm6RXqFT3Hhb0W5MndaLlpn3avtq9uOQWsV7Y1G8EreMuprIsuDuXP7Y7I8uJxnwO2aJMSvx6Ntgl0s890brjGatsNsooeFIJEreJ0eMZobqv9qBW88orrUb9uWhbCtflkMQY/d1OitTfu/3hSRXT3FrqwmQ77doicvRVJR96UlWfCq++Sx4FXHjwVvCH4f3LcBK/5eripZbddzm1D2/BZRfuz0JRdpstkDdVVrwetfuUHNbmxqk9fWvLUP/7rjG2+UeN15SI5xkwcNPg4Rm1j285Wo+KwKWaMyMeuNmYqqNqgVvNSh8l/NR8umSiQV9kXRk5foInoD7A1jS7yeXg0T2fxFL42JktkcY87TNrIFIDja60gqRmu/K9GeMV2x/zIWweu/cLxe38+FmPO3PNA5tF2x250Pt7sUHnc+PJ48OJ0T9V66Pda+eBAwbYfRuB0wVIr/U1Q8+HA6T4PLdWYXb67SjscieE2OKiRXv4XkowthdHmT4fTw6lK7VL0kadlzMB/cLO7TPvk6tI/xbmyi1SES1F56SZQfi4fYpX4X3HUmsmaPUjQEFryKMIU9iQWvOn4seEPwe2D4ByJZ7c4vzkBeDJ5Sqnn79SWfCCvDpH+e0e12wdFModaCl+7t7+eNtb9qk9eoH09ftAzlqw6jN1sbaPe1xVcsxdHt9YpFrxaCV3jlfvWOSGKjSC+JXiURlWjWFp3rL3oN2dlC9BqHF0XbTMTzbategm3rR+IctzUFjpILdRG+FO1NqXkTRnezrz+tWeehPXMm2jMiW2fUCl5/AFL8Gk1rYTZ/GZZNpxAeCSADbhf9Px0u18heHxWmMRoNVeI/g5FE7TYAjSGFrQRAdgWXa4KwfbhdparHqFTwUj3d5KMfwXbkQ1FmTB60cxolpdlTtduCXQpd6/q3hY1BrHlLsrAwaL0pi+PTxaDNJcQ9qfzYjddr+sAqOVW/vlZUkaEjUgmyUAudBa+6X6UseNXxY8EbxE+LZDVpZci/aCjG/SH2CgihplYPwUv3kRHp5PxUnPrO2TFFpGXy2pl3jcSse0ZHvTL9rQ29eTOKaEWvFoJXfFE22bHngYUi0ktHdxnRUU9AxwVUo7ftHy+J6g10mHSI9poPbIF1/VswH9yiu/ClEma22oWwNa/3IXGb0tDa53y055wfssSUloI3eB684pAinttAr/UNhsouUeBQcycFsQceeNydCYxSGMtrXJ481dUizB0RWA+VZCMBJaKzjeIWBkOFiNQaYIDRtM1XJizceqPyYdRHimR73KPgpv90EPGRBC+JXFvDctjql8LWsKxzHRhT0Z45Q7wB0LLUWCihS/9G5fkcJRdo+laDorrtb7wJ+tzSYTlrNiznnB3rxz/sdfT7Z/+TS9CwcnfMv39Y8KqbFha86vix4A3i9+o1q7D1kwO44OFxOPXm4VHTlYlgWlsZZEf0ErzU/tdzFolNKWJNsJPbMGcNSsGv18X2C7dsRQ2embNUDPenz0zEpMuVJ4dFPVkqLggWvdNfnBq2XJlWgld2t+qvy3HkvQ3ir1mzRyLvlhm6WBzEVqTLlglfL5KTYD3nbJinT1dBreul8RS+9Po6qX4ZbLUU2fOWMqODKju0pc+Ao89MUJSPDj0FbziAviip0Rs9M5q8r/39/cCawtewMYrW0n8UkRZiFgXCrqGHsA3X7WDBG07k0vVkb6FIf2vW+RpS8DZF1gX/iC79G3l17SdfLvzrmh2trULoujZ5LRJkYbDNnav5Gxlqu628BvseXAj7oUaQZ3fogxfEtCEOC151s8+CVx0/cTVXafBClMlq9OeHdl2ApCh9pOSH/frST8Q2vmpLfQVPq2PfIXha2mB1OsSOQq1Gs/eLeZR2gtC/hNrMxReAor3RHnLntZsXTEfhtO6TGEK1v/TFXZh/v1fQ9eZSZf6ilxLZZr1xGrJGdy2rprXgJS5U6H3/k4tFyTLy9Q66e5YuFgeKGlECjLu8vONLNQ+2uXM0/1LtInwtyXCMvUgXqwMNhHy+9Eo7qWEZTI6DvmVIkV+yO7iyT0Ny7iTUNNui/Qjodr43GuyNsho7RLH4s2m7sA/Iw2isAv2n5qBatx5P5+YB3uisrDGcIaK0dMRT0HY3Hvq92M9Wg8aKJbAeXQZr87qAS6TIpfnVemc+upFYw1s+hHnfWt99dRG6VAFk+XLYyb7Q2gYk2WCZMUOXqC4NRCan0Z+pGsOQ358fdmOJ7uaIBW93hCL/nAWvOn7iaha8Xohfv1iGD+/fiNFnD8TP5k2Jmqy0BaSPyMSpC86J+vrgC9rW7UDrt9th37YPrsP1IdszpNhgGzUUyRNGIumUE2BIVfcFLas29D89Hyc/G/3OaUse34rPntyuKuGPBvr67Wux9u0fRBLbHe+d1mvr8yoRvXoIXmJEUZf9jy/2+Xrzbp2uOHkk2sXp2rQJ9vnvwVNXJy6lSK/1nLM09wgGC1+6F21aYT/5Mm2jY34Awolfce/UU2DvM0P4OrV+5R3tHPD5oQmQRcHSuA5JjctgsnttOPLQW+SKz8K+tbBuXuhLRiOPrnPoJO0juvSAQfaF+QtEBQY6TCVjYJ07B+S31/ogC0PVC8tE2TE6ci4ej7z/UveGhwWvulliwauOn7iaBa8X4lOnfY4DW+pxzSuTMSbK0lhaJqqRwD0671M4fzjkm11T30yY+vaBJT0JBgNgb2iDu7kVzv3VvnNI/GbdfBGSJpwQ86qgcXw1dxFcTc6YEu5klDzWmrz+HfeJ3nQz7ni/d4vepTevRPXaw6Jk2ZTHSzFodmdpNb0EL7GiL6XK55fh6BLvlxLtyjborlm6WByokL1j6TJQcow4kpNgmTkTluk/0kf4bv4A5h86s/lp4wrniNPF62G9Dp/tgURUU6fnV7A2pcGRegoc6afAmTTCZ3/Qqy/cblcCND/m1l0i2YxEbnAUF+TNzpgOR9oEEanXI5JLvSLbgmXXUlh2fiH+LNYHvZUouUBzjy61TW9a7Ave67QvZGXBOvdimMaqr+0eap1R/W+qsSstDHm3ztDkYZoFr7pPNQtedfxY8Hbw86+9+/vyC6OmKiOjahLVXDVHUT9vMSiySweJ3LRzJsE6aigsQ/qLfwv28NI17Vv3oWXZBti37xPnkM0h8+qzfNdEOxgZqc6emItJr0RfP1jW5I3lwSG4r7JyQ2+P9FK/5W5s9OcTri3G+DtHi7JlegpeyYteO1Y9v0xYHKiKQ79LTkLfi0/URfgG2xyk8DVPnKB5pMnrh3wL5r1rxMYVQlhYU0SGu3vgWDiHTNQ0AUjyFB5eWysaD6wSiU7WpvUB1gd5Hvl/Sfw6U04AlT9zJhfDZemddaSj/T3Q0+dTkqHRfgAmxwEhbs1tO3ylw/z75kgajvaMmXBlnYbMAWNxqK5Nl64LkbtvLcw7vxBbAcvDndZPRHOdQ0o1X4sU0SUfvfTp+uwLM2do/pBJ46HdHQ88/5UvMY0sDIPuma2ZXYoFr7qlyYJXHT8WvB38pJ3h5MsG47JnJ0RFlaKiS2d/KK6J1fva/OkaNLyzDJ6WdhiSrUg7exLSzpnSxaIQKWmtZfkG1M/7BJ5Wu1ccnzUJGZfMiNrmILzIlyxCa1ULTn7mVPQ/oyAqHmpYBt+IKje8+9vvfPaGSx45qdcmslHft/9zF9Y97PUfpxakYOrjpRg8vT9SbCbUNnrnRa+Dvqz2P/6Zr4oDCd/8W2egz2wqb6X9QV/G5COU/l66A+3UZikt1dzjSzV8Lbu+gHnHF2LzCv+DhIZrYAkcJDg0SgoKlbRG0UUSvpamb2Fu3RmQ+BZMl8Sv25rnE8IwpXNEOMQSFBFb+0GY23bC4GoSwpb+Ldia4BOXxlQ4kk+AI/VkOFNGiIi7jOIqLUsWzSeBdgk07/xSCF0ZyaXrpW3BWXwGnAPHRNNk9+e2tsK1aQvsS5f6rAviszVxgkgc1cO+QL87ql9b47MvUGJa3zknab6dOQve7qc/0hkseNXxE1ezpUGdnUFNdNfT3I4j//e28OnSkfyjcci4dIawL4Q6uqvSQO01LVqFxgVficvNg/uj329/FrXoldUmKHGNRHw0h5a2BnlfaW+gv59zzxicc5eyQufR9Furc+u21otoL9XqpWPMDSNw6q/Hocmk1R0it0OvIw/OW+MTvtb+6eh/9WRdha9jzRq4vuncXYy+lC0zp8M8caLmkShvpG0NTHvX+sqaSSK0dbFzYAlcQyfBOSB2IaK0SgP5f0n8GturYGleD7O9KmQk2H/GqBIElfQiawQdJN6o/JeTRLIpsXZhIz60oYOM1MLRIOwIBld9xAcGwSVpuHhoIO+0I30CXNYBEaPnWgheerAy7/sGxgObYN63BkZ7i2/qfCJ3yCTNa+gKEV1ZCcey5XBt3OitjEKVF7KyYKaHSJ0iumSJqnnvexx+9zu4m70P5FRblx6UjWlWzX9hseBVh5QFrzp+LHgp+Ye2ti32Rmijrc6gJrpL4vTwI68Kry5FdXN+dXm3VRe6E7xyOVBVh7rn3xMeX1O/TOQ+enPUonfprA9ElDeWihNaVGsIXtpyNzb693Hn5ImyZb11Rzbq48antmDTM1SAH0gvSMVJvx0f4O3V4KMbsQmyOVCBeEe1N4Nfb+FLVgfnmrWgbYplchvdV6+oL7XtFShrYd67GsYDm322ByEgrClwk/gdWCKicK7sYYqRKxW84Rq0Nq+HyV7lFcJtOwFXU0Ad4O46QslydHhMaSJK7PtcJxWDosX+f4+XSJbiVd7bJ2LpHzqELP3R4PKKWiWHuyNi6+4QsyRsacyxJAjGKnipFrRp7xqYD2wOsCqINZTWD47BpXANnax9JJduECaaSxtHmCeVCrGrxxFO6Pa/ZlLMFRiU9JMFrxJK4c9hwauOn7j6eI/wys0mYqnOoCa6W/PIPBHZNQ/KRdatFyvy3CoVvOLLkgT1w68I0RtLpFdGeWPx8srtmafdVIQLHx2vwSr1NkF1ev92zddoa3Qif0wmfvpsaa+t4ED9pWjv+ke+x8HVh0X/cyf1w5QnJoSt2asZKL+G4i186dYkekn8+tsdRLRq8iTo4fWVw6UqD6a9q73iJcj6EI0AVit4w80j1YY1iwhnA8wtO8VpFBkW/2/dEbArnJq1QJYKj6mzrFg0bYXzykbThjxXRGmpH1LEmtOFJSFWURupD0oFrxC4tE6qNvsqK/i36xw8Ea48sshM0swiE9xv8uQ6N26Ea/Nmb2kxOpJsMJeWimiuHrYFukUooZsyNh8DrpkUU13daNcEC95oiQWez4JXHT9x9fEueOUOYdFuNqEmulv34vtoXb5RRHb73n+tIrFLcxWN4KXz1YrexZPeialig9yEYuCYTPziyzM0WKWdTRzZ34y/X70SVVvrRdmyq54pxbgoq2po2qFuGqOktZ2vlGHVnzbA2egUlRxGXX8CRv5suEhqi9fRE8I3XNTXkJcHy+RSmEpKdPtyJ+sDCWDxepr+3+R96JCHEMDZhULcuAaOgTt7qC/pSC/Bq2SupSimc/2FMf1dimPZjpYiubu+uSwD4LR2JuTJqKy8jqKz4ndOjBHa7u7f3c9DCV5aA8Yje2E6sDlkBJfadGUN6bDB6BTF7eg4WRaca74RIlfuikY/8kVzx5Zobv+RzKRHt37Fbp91IZ5CV/aDBW93qzjyz1nwquMnrj7eBe8Dwz9AW4MT9647G9mDUhQTldUMoq3MEKvYpY5FK3jFF5BfpJdq9Wb/8idRjzH3tHyc8lx0dXl/V/QB2huj56qkc/7JbHT+jJ8X49y7R/dKi4Os0nCoohnfPPwd9sz/QQyRktrG3TkGhZdot3mIEnbBwldWdSDvnrV/bFFBJfcVGefk9d20yedRFKIuDuJXCItuBDCdQ0lv7pyhQL8iJBeeiDpDpm5RPiXMYj2H7AeUBBbLcax6ia2HtiLDVYfGH3bAdGQvjLW7Azy4koVP4OaVCMuL2xr9BjtKuVIk17WrrIvIld5csi3oFc2lPpKfv2bB976qC/RvPSF0myqaUb2mBqf+XJ8EWqXzcayfx4JXgxk8ngVv1eZ6PH365+hTkILfrI9uO9wlk9+Fs9ERVb3a5k/WoP41bx3Tvr+9plvPbvD0xiJ4qQ3y9NY8/Iqo4JA8fZyo16vkoIoNS6a8K06NtgKF3Kb5x89MwITLByu5XdTn+O/KRg8rcx8+sddFe4PLklWvrsGGp7aIur09LXxr3v1ObFwhj9Rx+ciePVq3BDd5H7I8UHKOa/OWgDmnL3+K+pqKh8M0vEi3iJcUwMYje8SrbSozRa+6wx1UA9id3g+e9P4iGuyxpkTlCY56YfMFIQmQZ9tYuxfGxsMwNFWLuRNR3I5auMEXUaKZ8HHnDIOLythpXVEh6IYUuXWX7YZz00a4yso67QodCWimsSXCm2vMl7vWaT/RFM2lutx1n24VdXTlQQ+0ent0g0dDQnfT01ux+11vUvbd9VdrP+DjqEUWvBpM9vEseGMtoSX9rdHsqkZ+XfLt0tHn5guRMj16b2usgjdY9GZePRupZ09StHqkT3nIVSMw+jcnK7qGToqVreIbdJxYsbker9+2Vlgc6KCEtjmPjEfOIP0iN9H0MVwdXvoSoMS25kpvJnhPRXxpx7bD879Dw8pyUcdXiMFUKzKnFYrSRElFsW0RrYgRJe2UlcG5cVOXyK/ox/DhPvFLr371PqgMFUUHzc3VsBzaAtfRQ12sEP59EBHhtFy4KCpsSxNimA41FSL0HmNvb98rYA/7RK2h8ZD4s/ng5ohdd2cPgSVrAFoyhghxSw8oWpWpC3tjsX7LQ0Zx6RpD3kCYhg/XXeSSN7dh5W7UrywPiOZactPFhhH95p6kS9WFcFyChS6dN2zuYFz6zxm9ffn16v6x4NVgeo5nwfvCRcuxZ1VN1Lurrbn2C9R+U624ggHZCqrve1FsEZw+50dIvzS23aLUCF5aKm3f7kDt//0btCtb7mM/D1v+zH9ZNWw/ihWXfAJzugWzVl+ieMXpUZ4s0s0p2vvx41tEQht5e0+75YReUb6su40ngoVvT3l86UuTvjCDo75U3SF9ahH6zh2vq+WB5pZ8ji4Sv2XlAQlvct7jJYD9PbwiqkivyJuqQeKLEp6kKOvuw0Bl0jzWNF90GBQZzvFWi6AKALoLsu46GOef+6Lo7c2+igimI7uB9paIkVr/boqHiQ6OxNKTniui7UqT1lQN2V/glu2CpypwK2NKPCOBaxo3Tryh0NOuQOMgkUsPqv7eXPp3iubSm5rU8fpFkkNxpCTd7f/c6YvoSqE77hdjRKIue3hVrT6w4FXHT1x9vAreWMuRyWQ1U5oZpy+5COaM7hOPaKvglk/XiooMuX+8OeZZUyt46ca1//s22tbtFHYKslUoOb6eswiNO+sVC3zZpixPducXZyCvJFPJrVSdQ97e12//Bps+8e41TzYHSmobPk3HKGU3Pe5O8MrLSfhue2mnr34vCd9Bs/Ix9s7Rca3qQP2h16I173q9f7KsGf17UmFfZJ81CulTC3UXv6JkU1mZN3pWVtZVXMgIcFEhjAUFMObnaSYwlCatUUTY0N4C04FNYhpJDNMRyR4RarlIYSyEcId1Qp5HP4Mt8G2Ff4Kdqg9MDBeHEvumI3sAv5q1ZDWQRzgvbbhbCxtCTqFP1JKNRHqrI/lt9RC89ADmqTwAZ9kukAfdP9nMN76iIiFuTePG6mpVkPcLJ3JpV7S+l5yEzKlFcY3mUr8qllRh28u7UL2mMzGUIrpS6Mq+s+CN4QPndwkLXnX8xNXHq+Dd8nEV5l27GsOm9MUt709XTHLrY+ux7/WdUJqsRv7Zw//vb6L9fn/4ueKKDKE6pIXgpWjzwTufEn5epdYKaeGINnlNlic7866RmHXPaMWM1Z5I5cteu30t6iq8doGetDkoFbxyzMEeX/r3gll5GHXdCOROjr9wp8SX2sVbAywP1CcZ+c2ePUpf24MEo0AAU0SNhC8JYBIhxry8mHzASgVvd+uUqkPQYaqlKGaz+E9uS6s0StzdPYJ/Tn5jtUe0IlXp/ShhzGNLE6dL+4eIeHdEwdVEvNUKXuG/rayCu6pKPGS5yYMb4iBrjRC4xcWa7ygYjmMkkZt99uj4PIAGdc5R78D+z6qw8ektaO74PWtON6No7lCMvKE45EM6C16ln5TQ57HgVcfvuBa8sZYjk8lq0949GxkjQ++I5j8tst6uGiuDbE8LwUtt0TbER1/8QFgbBjx1Z7ebUsSavCYfKvQoT6Zk6ZPBlSkVAAAgAElEQVTFgawOZHOgg3Zpm3nT8LhWc4hW8MpxkQ+OPL6yqgP9O/l8R11fjMI5Q+Na0kz2qWGF9Al2+n2l+E0Zl4/MaUXImFqoZGrUn9PaKgSKa9curwWisiKg+oO8QYAILqLXzFndRoK1ErxKBykjxXS+tE7Ia4Ojp/Tv0UaQlfZDyXmhrBjBUWgpYqm9uHhp6aHCaEDfTBsO1XXUtY0wGKoP7TlSB1fFfrirDnjXjqyH63cdVVMwkrgtyBd+cj2Tzfy7S29YWjZUdfHk0jkUye0pkUv3l7aF/Usq4Wjw/l5NzU/ByOuLhdiNVGqRBa+ST1j4c1jwquN3XAveP57yCer2tyCa1+2HPq/A+ju+htJkNSksTX0zkfuH6Hc7C55erQQvtVvz8DzYt+9Dylml6HPNWd2uJJm8NurXJ2Ho1Z27P3V34b2588Up0e5i1127Sn9OdXsXPb4Fa9/2lgOT/t54Cd9YBa8cH0VStnX44mSCG/2MypkNmp0vor89cZD4bdpQ0cX2IL4AhfgtROq4gvhEfzsA0CtoEaWrqPD+v7w8LBoSMCR+jTk5Xr9lVqcQjrfg1XL+ZFRZTZtUmk3Pcl1q+hbu2lCCVwjbllYRtRVr4kgtPFVeu1OXI8kGY773zYCI3ubH9nYg1rFRFLdpQyWaN1SgbXdNQDM9LXJlNHf7yztRt61e1BInsZtb2k8I3UGzlf0OYsEb6+rwXseCVx0/cfXxaGmQCVW2dDN+X36hYorRiD5hHfjF0/C0tCu2DnTXkdT6CphMBjSkqU9G8Lda9H/69m4T2KTYT85PFSXKlB6xJgYqbV/peVTN4d37vkf5Kq/PjPy9k64YpnvEV63g9R/f/sVV2P3OXlR81vmlTVHfgjPzUXTpUGSN1t8nHYo3VXqoX1GOhhXlAWXO6FxZ8SFt3CCkjM/T3/sb1EEpgj1HjkSMBMvLqC6wKTUFqWNOQKvRIqJ6/mJY6Xrj8+JDQD7UeMrLYXO2o2n3/rAR2845HgijsL/k94i4pX60bKxEE/33fQWaN1YGwDKmWpA2rgAZ04p6xJMrO0Pe3HL6fbOk8/dNd7aFSLPOglfdZ4IFrzp+x63gjXU7YWlnUFKTtvGdpWhc8BWsI4eg7/3KksOCp9N4eB9M6z6BsWwdDO2tAT/22JLhHn4K3MMnwDX8lJhWQt0L76P1q42KE9jkzmtKxi87tOTxrfjsye3QepvhmAbcsT3xR49v8QlfGfEtvWywLqXMtBS8csxkd6Avoe0v7/KVNaOfZY3KROGlQ0XUl7Kie+KQ1R4o+kv+X/+kN+oPeX8pezy5qF/cI8A+Hh12CHqVTVE/igaTh9NTVxcRGdkjvP95I8PGrGwYcrLENfEom9YT89mj96R56ojIkm2FDvLX0hHOhuDfXyoLJoWtsSBfzF28bAnB3CIJXDqXorgkcNPGF8S9uoJ/X+n3yv7FlfC3LNDPC87Mw6Cz8lVtlMOCV92niQWvOn7HreCNZVOEaOwMrpqjqP7N30R0N5YNJkjgWr58HYaGwFdbyB0MA+2eVu19PS8PEr+uqZfAeXL31oSA6/wS2JT0M5oIt7yPntsMq1n+lNjmL3yprdLLh+Ccu0drKnz1ELz+4yZP3baXd2D/kiqxdbE8SPwW/Xgo8s/sOfFLfSE/YiO9rv2+Ak0bK3y1fmU/KQJM4jftxAKkjctHUmG/uGeZ+/OkbHyzvQ2mQwfQVFUNT22dIjEs26AIsSElBYbkJJE8R4f4s9xsIMnvz2oW8LF6rZ+IFQL2/7N3JlBSVdfe/1fX0PNoDzSjyiA2iGFQQEAZZDIRcMREBZMIaIKKvjxBwS+DIOpKFMEhiO8Z0eSJkciQJ40oEAEFA/hEGWRQZuhBep6ru791bvdpqruq7j23zq1bt7r2XcsldJ2zz7n/fav51a599m4G2caKyha4FYHZi3pnwxYbB0fPHkhMS0RFWpZQnnYw5WPPPPvWw1+KAgfc+Ks7K4DL/otKcAVzS6q2/UFuSu+m3yFGfYAm4JVzMQGvnH4RC7yB5O/qgT0eOY0d0Q+pD4h1NeOudOYuh33/duWvjUmXoL77INQPGo/GpIxWrYWVckj7P0XU158iqvCUMr6+85VwT5mDxmjxFsktkWiBMmUt0H9FCob/Q7wzXajzeNXeJizVYevyb1tyfNnYHtdlYOSsnkp1B9kr2MDruT+W8nDqo9M+4TdzcGZI0x74PhkIVOw7jcqjBT4jwBwGYntmKCDM/mMH4sy8/OXwsvQIdripgUWDf/ih6f8MiKsqfZZNE9kzB2Q+lnWZa3spXed8XGamWij3Xu19IIwd/mooutBqdw0//KDowi89ANvKUHNeLfsZ10CJ1MbGeeXY6jm0JuIX0TEcblneLftQV3WsAA0VtV7TWQTXKoDLcnLzvijwGcllB9BYNNdfpQVRXXyNI+CVUY9yeOXUa54daTm8gebviqYzsOhu3iPLFHVFcmO5ExnAOlctQlTBSTS6YlE/7Fa4B7SGSn+H1pSI8IblsNVWoTEpHXVT5qAho5vQ8+FZpkwkysvTGkSrVLBNWCWPV00Qfrht34dnW6o6sDzfUbN64tqplwZc2cFM4BWBX17fN2tIJrrc2DEk1R4896kAw1EWDWOwUIjKr1vnM/KxrAawq0MSYntkKJFgR1Zi0PKBZQ6tcShmENxwuuleOBizP8vAsdAbOgwGeaZ/cJC1xcUqh8bYJVJJo+1tmgG87MMa+682v1QVbnkObgz75iLEKQpcJ/ZNUP4X+Ti58WyrernsdRbJzRqcge53XBbUcwAEvHJvTorwyumnzI404A0kf1dPOgOPmOqJ7rJcXeeaJUoKA4vq1k151CewqlVpUID53YVKtJelONRNmKXk+IpcfM8xA3sh7bGpqlP0RLq5IZ7Ha3Y9XpF7bzuGNa/Y9e5xbFl+pKWOLxvD0h1GzuyFzjobaIQKeNvCb97n+cphN89KD2xM5uAMdB3fEZnXZgb1Hzs9vvCMAlcfLfA6CMdt8XQIBhbRHRINiwbLAK+e+1RguDlqzOexMmueV2NzvrEvuyJ5x3r34288y4dlkdW2V6t0jeYXbSy/OS2tZWggAKt330YCL/sQ5s4rUw6V1Z4vQdXRQq/KCRefQSdiLs9EQnNeekyP9KB9ENOrCUtVOP95AU5/fKalVi63wSosdBnf0bB0BZG9EfCKqOR/DAGvnH7K7EgD3kCaIeiBvHMznteVu6tEZ3OXK4fSGtK7oO6uBX5TErTKkjHodWx5uyUlom7CTNT3GaH5lLAo77mZzyvjtKLSgaQ18DxevU0+NDce5AEs2svgl3duY8t16pOMUbN64aqJHYWivlYAXk+Z+IG3UyzS88XFzkhsDKv4wCI9Von+eu6bQTD7urj2fKmSG1n9Xb5XPjAfzw7GObOS4AnCeiLCZgJvkB/hiDEfCPAq0Vr2DcN3hQrY1p4v86qY4CkgS0tg3zKw54ql2lgJbtk+WRQ3b1c+8nYWtKqswF5j1RW6jO2IDkOzQvbNDgGv3NuRgFdOv4gEXv71+qwPrsflgi1nRZtN8Lq7oi2ElcjuqkUK7Nb3Ga5EZdUuLeDlcx17c+HY8lflr7WT5whFennesUiDjA193lVsi1Zr8Gzj/Fz+rQY8teaaYOkOW/98RIFf3sSCVXfod1Mnzaiv1YDXUzmWy3d+F8vlO438XYVe0V928I3l/nYYmoGsazNCnv7Q1uusIgSDYJYOwcCFAYu/lAg+l9UIZhc7JGdvPjAXFR/dql4wAa+57y8jVvMHvKw6ArtYtNZdVoPqYwWoY89KXpnfZVlKAovaxnZPV1JoXFlJIa2c4G+j7MMre9/m7cz3qqrA5rBUBVYjt8u4zpb49oaAV+5JJ+CV0y8igZcfoBIFr9JDxdhxWy5iO8Zh5Cb1mr28q5pIy17PnF0R2GXOEgVe5RN9M/Sy9IbaaYuUQ29qV+3BE2D7Z93Xslc8rjp2z+xtyN9yBv0WDUanKZcJPYWLB+Si+LS+Rh9Chk0etOvdE9j5P8dbypqx5XlNX1+lzawMvG2la4kQKV+Dehfo9wTglCuTQ1b6TMvlDH7rzpcpIFxfXqPkBqtFhLk9niLhSIxBWk4WKmvqlXxhdoW6eoTWPUfi6zz1wF1eg9rvCxEX7cD5nccVKdrWtvWlD4vYRiXEKOkILHLLwJZFbkNZMUHNjzwPl6UpFB0s9kpTYAfOMgenhzSKq7Z/Al65dykBr5x+EQe8LSWycpIwZ+uNQuodeflrHH1tP7rd0ws5TwzwO4c3crDFutDhpTma7Xodm9+B48uNmmkMngvqAV42z7nmRdiP7VWqN9RNfVLzfvPnLYf7VL5mo4wza77Hvvm7kDmqEwa+rJ0ywRYOpBSc5oZDOIBHffdtONsq15elPAz56aXoO7GjUt4snIC3rZz5Owtxfmce8nYWeqU/sLEsBSL1yhQlAsz+z/KBrX6x2sBNEFzQAsMs4te2XrC/++BQrEBw9ww4EqObgTgdjgT+Z+tCk9X9wyGW7ZNF7NkBMXZVHW3ylyjM8vuMu6o5on91J8VX7IOLPaF1RN+KmvBKCqyz2fnP870OmrE9szSFDoMzkTU0w9Rc3ED1IuANVLmmeQS8cvpFHPDyA2sDpnbF1GWDhNTbfmsuyr4txoClw5E1pukUsa+reOVGVG78AiKH1eynDsH53iLFTO20hcIVFfQCL4siu16fo1RvcI+626vqQ9v74CkZWofXqs5UYOu49XAkOjF2521COlqtAYXQpgUHsVzffRtOw7PCA5vK4Hf4PZdjyC1dYU9zClqz7jBPAL5wsKhV3V++ax4FTuzaBMPhAMF87zwy3FBQBlyoQFlhhRIdZpdIhNiX53g+MX/NE5LZz1yZSXB1SGw1VU++sdWeFpYX21DRBKb8Uj5ceJTq4vmynq/7KuWldW/OzKZcbUeCC7E9MhEXY4etVwdlGmtuEi4Xg9uiQ8XI21WIC/uLfEZvlXvyiOCySG6omssEqisBb6DKNc0j4JXTT5kdSYfW9B5Yc5fWYdPQ1YpOE/ffpao2P6yW8cxMOLtl+R2rQOiKOUrernvIFLiHiQGj8gsvxgGH3YaSijphz7NDca61S5TxWnCt5/Da1rHrUHW2EoPfHIO0a7Uje+F6cE1Y6OaB/uCXpT1cNbETBt91qe5KD3r3YNZ49hUr+2r1/Od5yoGZ4kMlPpdmEBzfOR5pfVKRNTgdqb1TLJcP7LlxtRxeDsVsfPV3BUpeKLvYQTp+aeURy/iH5yDrtcGg2tXBu/U0qx2r99LKgdVrz3M8h1j2M2XPWUnKyyzVgEVmld+DPmA2kENrMvsMdC7Luy0+yN43TZHbooNFqCu92DDG0y6rpJA1JB2pOanoMNh6OfR6NSDg1atY6/EEvHL6KbMjCXj1HljjFQlSB2ViyFuj/apdvftbXHjxPYgcVuOpDPWde6Nu6nxdHgwEeNkCF9fUTm3gh9eS7x2H+AmD/e7vwOK9OPHOYfR4sA96zr5K8z74wTV22Ov3R9VzoTWNhckABr/7N57B//3vWVSVXvyQosDvhI4Y/NPL2g38cpewKDCL/iqRKhUI5ukQHILjOsVZJmJl5KE1FvHkX8UzjTwhmf2dH7bzfKQDjSZb4W3B82I998IOf3FYbQLZpnxZfhmRN2tF4OUfCFkpQDW4ZakJaVemKq3B0/qy/6dY4pCZUc8TK/V45psSXD+pi1EmI9IOAa8Bbo8k4P1tj3WoLnXj90duRkyy9lfMolAnComeqQw1M17QPEjW1r2BAq8SVV75JGylP2imNnB4t2ckI2vJw36fMNEPA54G/l/3dagpc2PungnKQa9IuHgO7xe5Z/HVh6fRNueXV3voN7GTIZ3drKgpg+DyMxW48A37upYVwG9dDo3vmTXFSFX+4U8BT4kIRTTYSOA12h8sBzmQqwmsm/JhPS/WGEHv5fSIvOqdG6zxoQReFrWtPFOppCSUnypH0YFi5Tn3dXG45ZHb1BzrHv6U8RU74/DNhrM4sqNA+Z3Hfs+9U/RTGZMRP5eA14BHIFKAN5AOazx/V+1rez1pANErHlWaS+hNZeBuDhR42Xye2qBUbZixRLX98Ln7n0NjVS3U0jP0pHvw/euNsBvweIfchK9Da6yd8a7/+d4LftlmWTvjnsMyWg69hfwGgrQBHv3iEOwvJ5gtz0E4oXMcErokKGkRzkRX0KJgVgbeILkj7M0GG3h5nm356UqlfB/7BqPidIVfsGWCspxbHq3tMCQLcZ1jLfMtRjAcfvSzAnz14Vkc3ZGPM/tbA3/3oRl4brt4O/pg7C/cbRLwGuDBSAFevTmkokAnWnvXvn8bnLmvK53UamY05dTqvWSAVwGHVYtgP30I7v7j4R59j9/lecQ6bvy1SJk23u+47bdsQNnhEuE8Xr051Hr1seJ4rSoNDH7ZPxCs1NnZA63/kWBR8B7DMtDrukzhRhdW1EB0T0qk7HSVUhmC/bnidJXfaHDLh8DOcYjvFA8Ow+xrYVeSUypPmIBX1GPWGWcE8LIPYXVltUpeem2pW4Ha2tI6nxUSPO+cgS17BlnUln0gS+gUj8wh6dYRJ0g7Yb+7jn2W3xLF9VwmJtGBnsMylVrl7EN8bLITlMMr5wgCXjn9lNmRArx6qwRc+KIAu37+CbTyd0XTGXh0V7T7mS/XygKvrbQA0SseU1oPq0V5W3KSu2Yhc/FMv0+ZaMoHN7B9+VGsf2ofhs3ojkmLrjbg6bW+CS3g9bwDluvGvv47siPPq+IDG8eqPvQYlqlEgDv1TVbKnkXCxUGYRYFrS2qVMmkVZyq8GmX40oIBsDPJ1QLELiVtIkUZ6q+CBAFv+D1VWsDL0w7YnbHUA3ZxoFU7OOapBDtEpnyYYmkIEQS2XANPwD28I19JD/S8OuYkK7+brr6pM3r4aOpEwCv3viLgldMvooCXRxdvfrofhs/qoakcr7+rdSiLV2dQa8lrRHSXbVgWeJkNXptXK62CpzWo3Zfeerx6o+yaTgqDAXqAt+3t8Ogvy4M7wv6BKWv9DwyPAHfpm4Lu12W2uwNwIu5VonKldcpBOQbD7O8sKqeWItHWLjtAxyJ07GIwHJcWjWhnFBJ/lNoyNJzKq4no1h7GeEKsu9yNmmPlKK92K3m0LPWAXfm7fOeL+7p/HqmNb0494FCrfGgSOPPRHjTl96AcNNtfjCOfFeLI9nyc/qbIC3BTO8eh57B09ByW1RLFVdOAgFfuCSHgldMvooBXb/7ozumbUbQ7X7X+rmh1BueqZ2A/fRCBRnedlUcQVXMe8bXHYHOXodLVAw0xHVCT2F/3E8APzrEob83s1/3OF4lc663Hy/OoI6lSgwzwtnXO0R2FOLwjTznx7AuA2XieAxypANxWs7ZAzFMlFBjyc3hO603lCb8dhma2DGe5xfyyUtUJrfuxyus8pYDth+fKsj/XFDelGbBLiew3w6yeffPDYmwOSz1QPtzkpCI6ydXuc2tFdGKAe+Qz9sG6wGcOrqKXB+CyCK7eb5gIeEU84X8MAa+cfhEFvM8OzEXRqUrhCgGbhqyGu6wOIz+6GbHN0Z+2cvNmE2q5rlEFJ+BauQCNrljUzlQ/LNbWvqv0S8Sf/i+4yvb69HR9dDYqOt2PqoyJup4E11tPIqrwlCqAizah+Gjw+6gvd6vq5Lk5va2ddd2YBQcbCbxtb49HgFn05ciOwlYd3/jYHtdloOfwTPS8Lh3sz3R5K8BTJtgrLH+YfT0e7bLj+63nWwYHCsfcQNsIMc859twNzz9uu8NgHtCTeR74QS5fNngerOdrPIWA/yxQeOXzPSE2OsmJTgMvQUWVuyXdQIG0CIzOiviUVVFo+uDsH3DZQbPOfVmaQiY6XSWfQkXAK+IZAl45lTRmR0oOrx7Q4pFLe4ID43bd7lfB/Cdeh/tkHtIXTIPrym4+xzlzl8O+fzvq+wxH3YRZQr6Mqi9H0rdzEV32pTK+wR6PuqQBQNIVsLuSUFd0EK6yL2GvafoHuS6uJ8q6L1D+L3LxFAu1lsOe1Sc6/vUpv2ZFIuGek/VG2kXux8pjggm8be+b/SPGosAsB/j01yVeh+DYeJ4HzNIgOvZNicg0CK3nRSuHl5VZY1dNKUuhKGoxx3KL+aUnpUJrP3pe5znLeua0HSua0yqzhq+5Kb3ZgUOX8hLPlVX+nOxS6tSyy9mcQ9t2vlYOr9F7DTd7rILCmW+KFcA9/U0x2LdtbS8GuCxFodewLJ85uLL3TMArpyBFeOX0U2ZHAvDy3NHsnCTM2XqjpmoiNWbrC4uR98gy2GJdyH5jrk+bnl3VROvusvSFlAO/BoNeBrqVHaaiKvsuNNgTvHJ4Yws/RPzpNxTwZa+X9HoOtUnaaQ6eLYfV9pU/bzncp/KR9uidiBl0hc97FM115pPfmvY5DuSewx1LB2HQXV01fRHuA8wE3rZaKV9TNuf/sv+3rQLBx7PIb6e+KSAIblJEC3gDeSY5JPO5POfY0xbPP25rX/SAXiD7kp3DDnL5ungerOdrPIWA/8zIMl0EvBeV5nB76ptinPm62KtEGBvJqih06psaVMBt+1wQ8Mq92wh45fSLGODd/e5J/P3h3ciZkI3pK4dqqiYCcSJf+V+MpIp1VWOQe8mXtyqwWxfbA8V9XlVAll/+Dq0lHXsasYUblLHFOa8IRXp55FmtRFnZ+1tR9sE2qKVs8A8HmaM6YeDLIzS15dUybvxNb4x9PEdzfLgPCCXw+tLOMw+YRXqK/ORDcghO7xqnwHCnPilKaaFIuIIBvGbpxnOWZdYLxzSASARenpbAat6e+boIP5ys8Am37FngFRQ6X5WqvJ9ZqoLZFwGvnOIEvHL6RQzw6oWsPbO3IX/LGdUDayKHuvQcVmOQyyK7LMLLYPdCv5Ve3lWr0uAJvT/0/0crUPb1mLTkFielo2bGiz6fpNqDJ1C4cCUcKuXJSg8VY8dtuUqeM8t31rr2f3gWK+/bicuGpuOBtddrDQ/7160GvG0F5W0/+WE4NQhmhw079236B5ODcGqXON2HV6zu1HAGXqtrG6z9tWfgZbn6F1jO7f4S/HCyHBdOVoJFcf1dDG47X5WsvFfZf75KhAXLD2p2CXjlVCfgldMvYoCX541O+8sQ9Lmpo6ZqW8etB8vjHbZ6ApJ6N9XsbHvlzVmK+oISv93IeM1bNq9m9nLVzmZsTNJ3CxFb8CHqozvgwlUrfQKrVlkyBsws75fl8l646i3N+4xeMUdpN1w7eQ4aegz0Of7s3U8rP89+/XHY4qN9jtnQ513l5xP336W5Jq/UwEBp3p7233nH6sDry2EcgtlhOPbfDyercOxz9fJOLCIcl+xEJxZB6pOMtC7xIYkiaT6AAgMIeAVEstiQcAdeXgaM5dkWnqxU8m0Z5PrKteXSs6oJ7H3G8m4v6ZoQssit6KNAwCuqlO9xBLxy+kUM8PIKDY9sHoOOAl/laAGcSP6uY28uHFv+KnRYLf78KiSceEnJ2S3OedVvSoIW8LIocdrX05Sc3qqMm1B6+QLVJ0Rkj4VPr0TtoROqebz84JpaC2bPjeg5QGjAIx5SE+EIvP4EY1+hFp2sUkqjsX+MGQifYfU529QH9pzP4PeSrvFhBcIEvCF9ywS0eLgAry+w9VXj1lOEtmDLyoGxxjPhlmJEwBvQo90yiYC3WYryiioUlZQhLSUJ8XExXqqWlVfCXV+P1OREr9ci4dCaHsAS6bAmkr/rWjkfUQUnVaOnzBms9FjqwV8rfintvgBV6Tf5fVdoAS+b2HTo7VeIqq/QtOfZec1fTV6ex5t4ywgk3j7S5972PbkTZ9Yex5Xz+uPSe30fbvOcuGTkxzh3oBSzPrgel/voyCP3a8Fas9sT8Kopy3KDK0tqlYgwK3fE8gn9HZJjdljTDBadYukRcSkupWxaTJLLElFhAl5rvYdEdmM14GUpB5VK84aLaQhaYMuqJFzSNVZ5X7BKCTHJTku8H0T0FxlDwCuikv8xEQ+8lVXVuPvXC3H4u9MtKv3sljGYN/tu2O1RYK/PXbgcm3c0lbfql9MdyxY+jPS0iwnr7R14z35TgpdGf4KUznF4Yq/2V+jH3/4WB5/9Ep0mX4p+zwzx+fTx+rv+ILAFJF2xqHnIf3MHZjz9/26DveYcyjv9AhWd71d9R4gALzPAqjckHVuopEVo5fPymrz+0hp4cw1X725If2qaz/3xQ37d7umFnCcGaL6r9aaYaBq08IBIAV5/LmD5h+zrWZZ7yGoFV5XUqoKwJwyndY1Tvqq9hH112zUOZuULE/Ba+A3lZ2tmAy97rqtLa5Vnu7LUrRwaY4CrllvLt94WbFO7xra7PHhfbiLglXtfRTzwssjuX1blYvKEYeiYlY7Pdn+DB+a+gLeXPYkBV/XCG3/7X/x9/Va8vWw+YmNceHDei7isazaefvwXLcq3d+DV2872wOK9OPHOYdVopVb93ZZUge4DUDflUb9POQdTlrdb+KN/aL4bRIGXGeL5vFog7dixGo6da/ymXojU4xWJinvenN5DhJrCWHhApAOvGghXl9Qp6RHsa15+MMdf1QhPOzw6zHOG2WssdYL93YgoMQGvhd9QJgAvh1Z2OOyH05WoLG4CW3aJAC0bx6BWeT77sueSfXPBDnuGXxqCkU8CAa+cmhEPvG3lO3b8DCbdNx9r31yEHpd1wu0zfovxI6/BjLt/ogzduPULPPa7V/HNljdhs9mUn7V34OVwNWxGd0xadLXmEyeSj8oPcvlryOBc8yLsx/ZqthLm0V2tVAa+aT3Ay1MltKK8ItUa8h5ZivpC/wf03KV12DR0tbJNkYNr25cfxfqn9kHUJ5pOs/AAAl79zuG5wuwrYJYmwVIklK+HNfKF267EIDg2uamRAes2xy+WPsEvX93nCHj1+yzUM9QivDxvlu2Rpxkof/YAWa0DYm3vjz6X2rIAACAASURBVFVCYM8WK+/FcmkZ0DKwjXSoVXsOCHjl3iUEvM36nT5XgPfWbcHH2/bgptFDMPsXtyivXDPxASyc+0sFetl14PBx3DHzd/hs/StIToyPKOAVrfvKWwqP/fw2OJK86462lOrqkonMZ313Tov5072KtmrVGTiQikZ3mT09wMvGt0R5uz2Cig5T/b7bWqo1TFuIhgzvjnEXXliF6j2HkTJrEuKu9/2hQU+LYb1Rd7lfE6GdTcBrvP4ciHnOMFuBQzEDF5Eosa9dcUCOsgF2uw2XDrnYVCEuiRXqb12xhVo1G+9bfxY9oZWPOfLZxc521SW1yDtYilp3g/KyVr6sKpg1wyzPp+URWjbHKiW+zFPeuJUIeOW0JOBt1u/gkRNY/vZ67Nn3LW4Y+iP89rHpcDjs6Dvq53h18aO4YWgTpPAI8Mer/oTsrEuUnxVX1Mp5weKzX5q4RWm3OuNv16HfTzqp7rautBbr+v8djgQnJn91p8+xxf/cicI3c5E48mpkPdT0waLVdeIgGt55GsjsCvuMZ/2uF/t/D8Jeshe13R9FbWftcl7MkMthR1QUUF1bL6S6vXgvYr96EA0x2agcvMbvnIb1r6Fx3zZEjb0Xtmsneo374d0tuPD3fyH5x4OR+Qvv19mErT/dhMIv8nHDX8ciY8jFaJqvRU/vK8azwzeh01UpeGLHWKF7CddBDnuU0rmrssYdrrcQtvs+ua9YSZdg18Ftecr/WQ4x+zm/Du9QL7em5+Yv6RqH9K5NgQR2XdItHhndLjaOYT+7wiPS3DKuzTw9a1p9rOKD0iYf8OuHExUoPFXR6meHPm3yD7++3W6cX2ITnejSr+nDCoNX/uf4ZBe69mtqWXxJt9a+s7quodxfY4CLp8Q3fdtCV2AKEPC20a2krAI33vkfeOrRezFp3DAlwrto3v0Yd8MgZaSvCG9FVfv+h/hPEzbjyPYCPLZhFHqNUAex/J152PzTj5AxOAtj3h3n86k8/18fouifO5F+50hk/HS01xj31r+jfttqRF07EY7x033aiKo+h+jPJymvVV+/GY127+oZviY6HTZE2WyoqWuKYohc0Z/fjKjq86i96o+oT7/B55SGr/4F97rXYOs1EM6p/+k1pnL/9zi54E3E9bkUXRdezP/2HLj3D//GkTcPoc/D/dD3Ue3UkQcTVinTXyv3H3kWuT+rj3HYbWD/VdeK+8zq99Re93dCAeRa2G1ATXk9juy5GEFk0WRPUGYafLs9P+hSdL2qqYqFyMVyRrtenaY6tLGhETYWwla5Co6XK1U2RK8TXxV5Qa3oXNFxDFq7Xt0Ep/zq7fH7PIFV+hiU3hIMYB880rtd/PAhug6N01ZA/enxPz8+1qFtnEb4VYCA14c0N90zF7dMHKHk7bIc3gmjrsX9P/uxMjISc3h/22Mdqkvd+P2Rm5UyL2rXmTXfY9/8XaoVGnhd2vQF0+C60vvrf+eqRbCfPqRajizh+BLE572HqvSJKO3+lPBbXG9KAzPMa/zWpI5Aca/nfK6lVZ6MH1yzxUUje8XjPm2ItGP2nKinVJywQBYcSCkNFnSKxpYCzeHlqRbcPPs7q07hebFKFW0vmTQMq6vLc10998lTBTx/xnNg+c/0pg6YXaXB6rpbcX+U0iDnlYgH3i+/OYKDR07ixhEDkZIUj//9ZCcWPPdfWLn0SQzs1wsr/vpPvP/PfylVGuJio5UKDpFWpUEPWIlA27kZz6OxssZv5zGR/N2M3ePAmkQUXfkKapP6C78LAgFetg5bj12F/Vej3pXtc73oZTNhq61CzYwX0Jh0MXeRDz53/3NorKpF1ksPwZ7u3X1Ob6UGXpqsvdfiJeAVfrwtMzBQ4A3GDSjlr5rTMrTse+Y0a41Ve10pBddFPDpqhYNaBLwyHjdnLgGvnM4RD7xfH/wOv3riRVwoLmtRcu6vf4ppd4xX/l5RWY3f/OE1fLrzK+Xvfa+4DMsWPYJMD2Bpz1UaeBtb0Rq8e2ZvQ/6WMxiwdDiyxnT2ejpbIp2xLmS/Mdfr9YsVDy5BzYwlvsGy6FOkHJ6ntBAWKUXmaSQQ4GXzk449jdjCDShXObymVVlCK7LNgTfxihQM/4d2vWMCXrlffjQ7eApYCXiDd5ftyzIBr/X9ScAr56OIB14mX2NjI4pLy8Fq8nbIvAROh91LVZbbW1fnbtVwgg9qz8CrtxqAVkkyXqHBXxMG+/5tcOa+rtpOWAQ+/b0tAgXe6GbIrovriQtXveXTPK/H6+4/Hu7R93iN4c02ku8dh/gJg33a0GrJ7Dlp1UO7sXfVSdz8dD8Mn9VD7jeBhWdThNfCzvGzNQLe8PMZAa/1fUbAK+cjAl45/ZTZBLwXRdQqSVaRuwslb3+E2BH9kPrAZC/1HZvfgePLjXCPuhvuAb6jnDydQS29wGjgZfYydo9V2g37W9d+6hCc7y1CfefeqJs632sLvMVw3PhrkTKt6RuEthcHXn8l3TzHR0rzCQJeA35JmWyCgNdkwQ1YjoDXABGDbIKAV05gAl45/do98OptOqEVoeTQ56+lMD+wVnfnfNR36e3lnZZIa2wPXOi3Urf3Ao3wsoW0Isu2mkpEv9xUV7j6P9722ptWdJtN0IqQE/DqdjlNCIECBLwhEF1ySQJeSQFNmE7AKycyAa+cfhEDvCJNJ0oPFWPHbblI7JWM4R/4rjXL81jTHr0TMYOu8FKfH1jzBYwi0KnlThngFUlrUGtAUXciDwVPvg57RjKyljzsc6t6gFdvuomWNlZ9nSK8VvWM/30R8Iafzwh4re8zAl45HxHwyulHwOuhn0iVAbWDWyIH1ngrYZZHy/Jp9V4ywMvWytp1nbJkwaCPwFoOt720SqpptVQWqXLB1yTg1et9Gm+WAgS8Zilt3DoEvMZpGSxLBLxyyhLwyunX7oFXTyUAkRq8asAXdXQPXGuX+M2BdVYeQdrX0wOqzsAcZbOVIT52K6KibCiruAGNjWLNKjwfEd5quLT7AlSl3+T19LQcXBsyBe5ht3m9nvfIUtQXlvgtTRYI8Gb3ScacLWMMeJKtaYIivNb0i9quCHjDz2cEvNb3GQGvnI8IeOX0I+D10E8E1tSAVwsWeQMIvc0m2Bbtjn8jOmY2bLamIvaNjQmorX0C7topup6A+NNvIOHMf6Mi606UXzrHa25LlYnuA1A35VGv17VKk/EPDZmjOmHgyyM096anRrKmMYsOIOC1qGNUtkXAG34+I+C1vs8IeOV8RMArpx8Brw7g1Tq05cxdDvv+7aibMBP1fbxhjx8a8xdd9edKl+ttOKOfbQLdhmsQZeuERtsa5e/uusmoqX5G+ClwlX6J1IO/VtIpfJUn06rUcOGFVajecxj+cphF0kI8N0vAK+w6GmiiAgS8Jopt0FIEvAYJGUQzBLxy4hLwyunX7oGXtxWeu2cC0rrEqaql1XRCE3ibWwr7q9AQSP5udMyTcDjXKvuurZkLV9Qv4LDbUF6TC1fMk4iylaPefQ1qqpcJpzjwPN68wZ/51EPt4J1WlQoCXm9JKcJrwC8pk00Q8JosuAHLEfAaIGKQTRDwyglMwCunX7sHXj0RRK0KA7wGr786tFothbVAs60rY2Ifgt2xGQ2NCahrTl/wPLQWZT+E6NjpCvQ21F+B6qq3hKA3bd80OKuO+m1r3NJiePZyNEa3/pCgBbzsHrRKu3ne5+IBuSg+XQmRDyQGPOohMUHAGxLZpRYl4JWSLySTCXhDIruuRQl4dcnlNZiAV04/Al4P/bSAVwv21CKjLakEgvV3Ha41iI6er8BuTdVbaKhvqunbtkqDzX4G0dGzYbcfRl3dJNRWL9Z8IrRSK9RqCVfv/hYXXnwP/jrN6QVePYcKNW/MogMIeC3qGJVtEfCGn88IeK3vMwJeOR8R8MrpR8DroZ9WlzU14OW5rw3pXVA73TunNrbwQyQdWwjRA2tx8WNhizqLmppFrQ6m+SpLxqA3Lm6ccpCtquJjzSgvP7hW3ukXqOh8v9cT5FzzIuzH9qJ28hw09BjY6nWttA4CXu83JAGvAb+kTDZBwGuy4AYsR8BrgIhBNkHAKycwAa+cfu0aeM9+U4KXRn+C7JwkzNl6o6ZSWl/Fqx3Y0jrspQWZnptjqQqxcbehoaEjqio2tdq3vzq8LLXB4djtBci+bppHm2sS+6M45xWvIWrVJkSAd/stG1B2uATDVk9AUu8UVd0pwqv5WNKAEChAwBsC0SWXJOCVFNCE6QS8ciIT8Mrp166BV29jAy3gVSvJ5dibC8eWv6K+z3DUTWhqz+t58fq3xb2eRU3q9apec0Yvhsv1Dmpr70FdzRNCwMtTINzuUaipelndfnM9YH+VGtSAt7GiBudmPq/Y7/jXp3yuo5Ua4jmJgNeANzCZMFwBAl7DJQ26QQLeoEssvQABr5yEBLxy+hHweugnBbw7VsOxcw3cfho2cOAtuvIV1Cb1V/UaT2eorvqLUoHB8/IX4WVNKeIShihDK8t3aqY1qB2g02qgodVtTQ/wbnr+AD7+4yGItH424FEPiQlKaQiJ7FKLEvBKyReSyQS8IZFd16IEvLrk8hpMwCunHwFvs34i5bRUm05sfgeOLzfCPepuuAdM8PKKaIUGno/LDqtVle/ysqPWWpinNVRXLUW9W71zWfr/3Qp7zXkU9l+Neld2q3W00jMIePW96Qh49ellhdEEvFbwgr49EPDq0ysUowl45VQn4JXTj4DXIOBVq2zAlhAFXq3UBDXgdbpehiv6NZ+pEG0fE7WIc1TBCbhWLkBDRlfUTlvk9YRpdVs7sHgvTrxzGFfO649L771C9QmlCK8Bb2AyYbgCBLyGSxp0gwS8QZdYegECXjkJCXjl9CPgNQF4tQ6JebrQFfMEnM51SpOJutppuiK8rP1wTOx9Sk3eqsp/qD4ZKYfnIrpoG/zlFKuVWNMCXpEWzXxzBLwGvIHJhOEKEPAaLmnQDRLwBl1i6QUIeOUkJOCV069dAy+HqWEzumPSoqtVldJKaeCHtWyxLmS/MdfLllqEVw/w8vzdqsrVLbV3PRdTi/CycfGJfZThWnm8WlUjCHgNeGM1m6CUBuO0NMsSAa9ZShu3DgGvcVoGyxIBr5yyBLxy+kUE8IociNICXq1yXGpd1kRr8HoePKso2+/Ts1rAezGP1/vAWytwPv0GEs78N/zV4iXgNeCNRcBrnIgmWyLgNVlwA5Yj4DVAxCCbIOCVE5iAV04/At5m/c6s+R775u9Cp8mXot8zTdUOPC9R4K3+j7e95mpFU/kEnpLgdg9Suqv5urSAVyslgtvUgvDoFXNgK/0BNTNeQGNSRqutFP15Laq27UPKrEmIu947cq4npWH78qNY/9Q+DJjaFVOXDTLgabaeCYrwWs8nWjsi4NVSyHqvE/Bazydtd0TAK+cjAl45/Qh4m/XTgjQzgNfpWglX9HOqLYK1gJfb8FXD1/NR0UqzUEvR0GqxrKWl5z701ko24HE33QQBr+mSSy9IwCstoekGCHhNl1z3ggS8uiVrNYGAV04/Al5LAW9zlYWaB1FXOzugCK9IlJgZJuA14I0jaIKAV1AoCw0j4LWQMwS3QsArKFQIhxHwyolPwCunHwGvCcCrVRGBuzA6djYcji1Qq6OrFeG1AvDmfXIaex/ejtRBmRjy1mjVJ5QivAa8gcmE4QoQ8BouadANEvAGXWLpBQh45SQk4JXTj4DXAOC1lRYgesVjaEy6BDUzlnh5RLTLmsiBMy3gZYvzSg3+Dr4FO8KrdQDQUyACXgPewGTCcAUIeA2XNOgGCXiDLrH0AgS8chIS8MrpR8ArCLyVn36F4uXrEDf+WqRMG99Kda3OZKLAGxt3K6Ls38JfSTIFZmMccNhtKKmo8+t5EeBlk9WaYcjk8BLwtnYNpTQY8EvKZBMEvCYLbsByBLwGiBhkEwS8cgIT8MrpR8ArCLxqB7WMAl4RUCXgNeCBN9kEAa/JghuwHAGvASKabIKA12TBA1iOgDcA0TymEPDK6UfAS8CLvMGfeT1FFOE14I3VbIKA1zgtzbJEwGuW0satQ8BrnJbBskTAK6csAa+cfgS87RB4Y+Jugd1+GNVV6s0nKKXBgDePgAkCXgGRLDaEgNdiDhHYDgGvgEghHkLAK+cAAl45/Qh42yHwxiUMhs1WrtlemIDXgDePgAkCXgGRLDaEgNdiDhHYDgGvgEghHkLAK+cAAl45/Qh42yHwiuQCs9sm4DXgzSNggoBXQCSLDSHgtZhDBLZDwCsgUoiHEPDKOYCAV04/Al4LAW9swmBEaURm6dCaAQ+8ySYIeE0W3IDlCHgNENFkEwS8JgsewHIEvAGI5jGFgFdOPwJeQeBVay1sVJUGM+vw2mvPIf3L21Af3QGFP/qH11NEh9YMeGM1myDgNU5LsywR8JqltHHrEPAap2WwLBHwyilLwCunHwGvAcDLTMT86V7FUvV/vO3lEdE6vEYAr81+BnFx49DQ0BFVFZv8Ph3BbC1MdXhby07Aa8AvKZNNEPCaLLgByxHwGiBikE0Q8MoJTMArpx8BrwnAm3B8CeLz3kN5t0dQ0WGqX485oxfD5XoHtTVzUVc7zec4rZQGK7QWPrPme+ybvwudJl+Kfs8MUX1CqdOaAW9gMmG4AgS8hksadIMEvEGXWHoBAl45CQl45fQj4DUBeONPv4GEM/+N8k6/QEXn+/0Dr+tluKJfQ23Ng6irnR0Q8DpcaxAdPR9u9yjUVL0ckgjvkZe/xtHX9qPHg33Qc/ZVBLwuO+Ki7bhQVmvAu5VMmKEAAa8ZKhu7BgGvsXoGwxoBr5yqBLxy+hHwWgh47Y5PEBP7MNzuQaipeisg4HUKQDMzHF30KVIOz0NNYn8U57zitZZMDq8e4N3/4VmsvG8nciZkY/rKoQY8zdYzQSkN1vOJ1o4IeLUUst7rBLzW80nbHRHwyvmIgFdOPwLeZv208k7VDq0xE2o5vDzCW5F1J8ovnePXY1H2Q4iNuw2NDR1R6Sf/Viul4WIe8FLUu8f4XUsr6qx2P4VPr0TtoRNIXzANriu7ea2hB3g3PX8AH//xEG78TW+MfTzHgKfZeiYIeK3nE60dEfBqKWS91wl4recTAl5jfULAa4CeZ3+oMsCK9UzogSkt4K07kYeCJ1+Ho2sWMhfP9LpZ11tPIqrwFGqnLURDRmsI1Dog5mmM19CtLN+JxsZEr3W0gDcufixsUWdRVbkaDfW9CXgt8FgS8FrACTq3QMCrUzALDCfgtYATNLZAEV45HxHwyunXriO8er4u1wJeJtTZu59W9Or416e8VFdLAdADvFoRWjXgbanQ0JiAqvJdqk+G1kE6ivAa8MZqNkHAa5yWZlki4DVLaePWIeA1TstgWSLglVOWgFdOv3YNvHoqAAQTeHnN2wZ7AgoGfaTqsZYc3Np7UFfzhK4Ir+iBNWZUrVSaraYS0S/PQqMrFjUPve61B0pp0PemI+DVp5cVRhPwWsEL+vZAwKtPr1CMJuCVU52AV04/At5m/aSBd82LsB/bi9rJc9DQY6CXV9Ta+HoO5mXFGuqvQFWld0MItQivK+YJOJ3rVMua8bXUgFerkUbenKWoLyhB1ksPwZ6e4nWvO6dvRtHufAxYOhxZYzqrPqF60k4MeNRDYoKANySySy1KwCslX0gmE/CGRHZdixLw6pLLazABr5x+BLzN+lWdqcDWcesR2ykeIz+62aeqeY8sRX2hb9Bz7FgNx841cA+ZAvew27zmp//frbDXnEdh/9Wod2Wreq0lj7fyIzTWd2o1Vg144xIGw2Yr18zfZQbVAFwLeNVSO5htDryD3xyDtGszCHipLJkBv6XMNUHAa67eRqxGwGuEisG1QcArpy8Br5x+BLwe+m3o867yt4n77/KpqtpX+VrAK9ptjS0cHTsbDscW1NQsgrt2ihDw8goPWh3WmLGo+nJk7B6HBns8CgZ5d2Nz7M2FY8tfUd9nOOomzPLSwkjgXfXQbuxddRJ3LB2EQXd1NeBptp4JivBazydaOyLg1VLIeq8T8FrPJ213RMAr5yMCXjn9CHgNAt6oo3vgWrsE9Z17o27qfC+vaB0S85yglovrL8Lb0qXNT+6vp32tQ3Rq8M6rVdjTk5H10sM+nz49Ed4/T/4U339eiFkfXI/Lh6Ub8DRbzwQBr/V8orUjAl4thaz3OgGv9XxCwGusTwh4DdCzvZYlY9LMzWzKg30u/1ZNpbQivMUrN6Jy4xdIvncc4icMbmVPKw1AtBYvM2qzlSEuoaklb2WbtAZ/wKsnnSG28EMkHVuIqvSJKO3uXXHCsfkdOL7cCPeou+EeMKHVfWrVI2aDNw1ZDXdZHcZ+fhscSU5V3Ql4NR9LGhACBQh4QyC65JIEvJICmjCdIrxyIhPwyumnzCbgbRJx+y0bUHa4BMNWT0BSb+/DWGXvb0XZB9uQeMsIJN4+spXyttICRK94DI3RsaiZ7V3ZQCuq2taN/ABavXs0qquWtbzsC3idrpVwRT+n2qHN035LtNlPq2O1EmsiwKv1wcFzLwS8BryByYThChDwGi5p0A0S8AZdYukFCHjlJCTgldOPgNdDP62v4tWAl5lRq12rpzQZs8Vq6sbE3oooWznc7lGorV6sNKJoC7w8lYHNqa5S767Gb1Urn9i1cj6iCk76bKJRkbsLJW9/hNgR/ZD6wGSfTx8Bb2tZKKXBgF9SJpsg4DVZcAOWI+A1QMQgmyDglROYgFdOPwJeHcBbvftbXHjxPcQM7IW0x6Z6KR+9Yg5spT/4BEU2OGP3WETVVyi1eFlNXq2LHURjjSgY9LIyZdVVbyEuOhUOuw2llRfgil4Mh3OtYsbXATd/9tmBNXZwzV/FCDVw14L+lmoXHeMwctMkrVvUlXKiacyiAwh4LeoYlW0R8Iafzwh4re8zAl45HxHwyunX7oF3yciPce5AKR7ZPAYd+yarqnVg8V6ceOcwrpzXH5fee4XXWK2v89VSAZgxHlkt7vUsalKvF/Ici/RGR8+G3X4YjY0JsDW8BntUEuoaHkeU/Vs0NCagpuot1TbCngtdjDT7rtDQkpqRdAlqZizx2qNaHjMbLFLP2NOonhxrIcEsOIiA14JO0dgSAW/4+YyA1/o+I+CV8xEBr5x+7R549eSIHnn5axx9bT96PNgHPWdf5aVsfWEx8h5ZBltcNLJXPO71ulZpMn5wrdxP7qw/V7JDbCynl5Uq87zq63uhpuZlr1q9ao8EP7BWkzoCxb2e8xqqdfhOq8saAa+3+gS8BvySMtkEAa/JghuwHAGvASIG2QQBr5zABLxy+hHweujHgbfbPb2Q88QAn8qq1aDVql8bXfQpUg7PQ01ifxTnvKLbc+xwmtO1BjaUobZ2Mtx105W8Xj1X0rGnEVu4AeXdHkFFB++0jBZo7z8e7tH3eJnOf+J1uE/mIX3BNLiu7Ob1utaHBs8JF05V4rmBuUjpHIcn9rauBqHnnqw+loDX6h7y3h8Bb/j5jIDX+j4j4JXzEQGvnH7tHnj1NDYQiU6qdVvTio7yhg9MdNE83rbuVeu0JvIopP/fbbDXnMOFq95CXVxPrynO3OWw79/usyQZG6zVdEIP8H63oxDLb/kUlw1NxwNrxVI8RO7RamMIeK3mEe39EPBqa2S1EQS8VvOI934IeOV8RMArp1+7B95Nzx/Ax388hBt/0xtjH89RVUsEeNW+0rfVVCL65abOZNX/8bbPtQLJ4/U0JAO8Wvm7bB21POTGihqcm/k8bLEuZL8x1+f97XtyJ86sPY5+iwaj05TLVPUm4DXgzUsmgqIAAW9QZA2qUQLeoMpriHECXjkZCXjl9CPg9dDPXVqHTUNXw5HoxNidt/lUtujPa1G1bZ/P5hNsglalhvjzq5Bw4iW/TR+03CkDvCJrq1Vo0Dq0x/auVdrN8/52v3sSf394NwZM7YqpywZp3XrYvk4R3vBzHQFv+PmMgNf6PiPglfMRAa+cfu0eeDlU5UzIxvSVQzXV0qohq1WWy7nmRdiP7UXt5Dlo6DHQaz299XjbGpAB3rSvp8NZeQT+qkREFZyAa+UCNPqp0FD56VcoXr7Ob1k2ttet49aDlSbz17zD8370RN81HWfhAQS8FnaOn60R8Iafzwh4re8zAl45HxHwNutXUlaBmpo6ZKZ7dwhjQ8rKK+Gur0dqsvchp/bcaU3v1+Za3dZ4LV5X725If2qa19OrdeiLTUjbNw3OqqN+wVPtLREo8IqkM9j3b4Mz93XUdx+AuimPem1DC/bZBK0PDAS8cr/waLY5ChDwmqOzkasQ8BqpZnBsEfDK6RrxwFt4oQTTHn4GJ07nKUp279YRM+7+CW4ed53y98qqasxduBybd3yp/L1fTncsW/gw0tMu1qQl4L34EGp9JV93Ig8FT74OR9csZC6e6fX0ah1cYxNEUgv8vS0CBV6RNR2b34Hjy41wD5kC9zDvlI4LL6xC9Z7DSHv0TsQM8q5TzJtO2BMcGLfrds13Ni8ZN+0vQ9Dnpo6a48N1AEV4w89zBLzh5zMCXuv7jIBXzkcRD7z5hcVYk7sNk8YPQ3xsDN5+/yO8uSoXn36wFLExLrzxt//F39dvxdvL5it/f3Dei7isazaefvwXLcq3Z+BlN6mnuYFW8wlmT61SgcjBNR5tZbb0VmsIFHh5dQa1phe8pXDdnfNR36W31zuTlyTLeGYmnN2yvF4XOfTnOUlPjWS5XxOhnU3AG1r9A1mdgDcQ1UI7h4A3tPqLrE7AK6KS/zERD7xtpTl9rgDjf/qfeHvZkxhwVS/cPuO3GD/yGiXqy66NW7/AY797Fd9seRM2m035GQHvRRVFymrlz1sO96l8v7VoXW89iajCU/AHjmy1lMNzEV20zW89XCMjvK7SL5F68Neoj+6Awh/9w++7Se3Amhbos9fPrPke++bvQqfJl6LfM0M039nPDsxF0alKzN0zQzTr9wAAIABJREFUAWld4jTHh+sAAt7w8xwBb/j5jIDX+j4j4JXzEQFvG/0+2LANC577L2xbswxpKYm4ZuIDWDj3lwr0suvA4eO4Y+bv8Nn6V5CcGK/8LK+oWs4LFp/9wg2bcHZ/KR7bciM6XqXeXviHL/Lx+fRPkHZNJq5bOcbnnRX+8V1Usa/2H5iE+Bt+5DXG/uFyRO3fhobR96B+oO+GCqwJReKhuaiPzkbRAP8Q2tZ4XLQDdrsNZZV1wqonHHkaMYUfoqLzL1HV5X6f86JOHYT93UVo6NIb9Xct8BpTc/A48v+wEs6umejw3AM+bXy77GscefUb9PxVX1zxkHenuraTfpO+WvnRHwt9V8QQvkGLD4x22RHrikJxubjPLH5L7X57DHgT4hy4UFrb7u+1vdwgA97URBcKS2rayy21u/vISo1pd/dk5g0R8HqofeT70/jZrxZi+h3jMfsXt6CxsRF9R/0cry5+FDcMvVoZeez4GUy6bz4+XvUnZGddovysvqHRTJ+Zvtbi0R/j2235mPfxjeh9Q6bq+hf2X8C6seuQ0CUBt/vJQz33zsc4/7ct6PCzUci+50Yve3V7t6LyH6/A0XsQ4u/xXa9WmfSvHwNV54BrVwBp3hUdfG2UBeVZXF7UZbaqs2j8V1N033bDP9EY6ztXtvqTVajZ8j5cQ29C7I9/7rX0hU17ceLF1Uge0huX/797fWr4yX2f4NRHpzD6v0ej64SuqjpXFtfiVxnvIzbJidd+uMP0Z8LMBZm/2LcpDY3t+31mpqZmrBVFPjNDZkPXYNDb3v89M1Qwk40x/9AVuAIEvM3anTlfiHsfWoRrftQbz8ybAbs9SnmFRXgXzbsf425oqnPqK8Lb3lMaeLe1m5/uh+Gzemg+bVqVBrTq0dpKCxC94jE0RseiZvbrfteLP/0GEs78N2pSR6C413Oa+2ID9Obw8jWq0ieitPtTftfg+bv+yqkVr9yIyo1fIPGWEUi8faRPO9tvzUXZt8VCJcn0Vs8QEseigyilwaKOUdkWpTSEn88opcH6PqOUBjkfEfACOPr9Gfz80WcxevgAPPXoNDjs9hZVWQ7vhFHX4v6f/Vj5WSTm8Oqt96pVmqyl41hcNLJXPO7zCdZqQMEmebYaLuy/GvWubM13gx7gZfYv+fJWZZ2iK19BbVJ/n/Y9D9rVzF6OxmjvfFq1DnPcqNYHBc/F9dZH1hTGwgMIeC3sHD9bI+ANP58R8FrfZwS8cj6KeOD99tgp3PrLp/DjMUPw0C9vRVRUU2Q3LjZaqbm74q//xPv//JdSpYH97IG5L0RclYb9H57Fyvt2QrT5xJ7Z25C/5Yxqe9y8R5aivrAEWS89BLuP2sctJb76j4d79D1+n/KkY08jtnCDcOc1PcDbEkFO7I/inFf87kGr/i6byCtTZL/+OGzx0V62Sg8VY8dtuUjslYzhH0zUfFfr/RCiadDCAwh4LewcAt7wc46fHRPwWt+VBLxyPop44N2weRd+84fXvFRkdXiffXImKiqrldc/3fmVMqbvFZdh2aJHWjWoaO8pDXq/Phep1MBr0qbMmoS465vyoz0vXo+3IaMraqct8g+bteeQ/mXToa0LV72Furiequ8IUeAVje6yxZy5y2Hfvx3uUXfDPcD7kB2vPWxPT0bWSw/73B+v0JA5qhMGvjxC813N00zuWDoIg+5Sz/fVNGbxAQS8FneQj+1RhDf8fEbAa32fEfDK+SjigVdUPtaJra7O3arhBJ/b3oG3uqQOv+25Xrnd5/Jv1ZQs75PT2PvwdqQOysSQt0b7HF+Ruwslb3+EuPHXImXaeJ9jopfNhK22CjUzXkBjUobfdXkkllVsYNDbYE/wPzbGAYfdhpIK9RP/qQdmw1W2Vyg/OPrlmbDV+N8nv9fYEf2Q+sBkn3sT+ZDgOTFSavCyeybg1XzLWW4AAa/lXKK5IQJeTYlCPoCAV84FBLxy+imz2zvwsnvkzSd+f+RmxCQ7VVXjHcNiO8Vj5Ec3+xzLD67567jGJrVETv10LvM0zNsN1yYOQFHOy1LAm/TdQsQWfIgGezx+6P+BKkBHHd0D19olaEjvgtrpz/hct+jPa1G1bR+S7x2H+AmDfY7hHeoGLB2OrDGdNZ/K3/ZYh+pSN0T8oWnM4gMIeC3uIB/bI+ANP58R8FrfZwS8cj4i4JXTL2KAV29EkR/AGvv5bXAk+QZkrbxWDpONSemomfGiqqeaUhBuQVR9BSqy7kT5pXN8jtdKaYgt/BBJxxYqsFuc86pmioRzzYuwH9vrN52BbSJvzlLUF5TAX4c1NmbruPVgHxTYBwT2QUHt0htxN+ARD6kJAt6Qyh/Q4gS8AckW0kkEvCGVX2hxAl4hmfwOIuCV0y9igFdvaTIesRz85hikXes7HYFXLkh79E7EDLrCpydEqjXwic7KI0j7erry19LuC1CVfpOXTTXgFZnvabBVdQY/aRf1hcXIe2QZbLEuZL/hu6awu7QOm4Y2NZGYuP8uzSdSb061pkGLDyDgtbiDfGyPgDf8fEbAa32fEfDK+YiAV06/iAFeXhVg2IzumLTI+5BZWxkPLN6LE+8cxpXz+uPSe33DbNn7W1H2wTbVPF5eraG+z3DUTZil6S0eofUHvf6Al8FuyoFfKyXI1CLEnhsQqc5Q+elXKF6+DjEDeyHtsak+93/hiwLs+vknqjnPnhO3Lz+K9U/tw4CpXTF1WVN96PZ8EfCGn3cJeMPPZwS81vcZAa+cjwh45fSLGODVG1U8/va3OPjsl+g0+VL0e2aIT5VF8nijCk7AtXKB0oSidsYSnzVu2xpPOL4E8XnvKT+u6Hw/Kjvc2ZKH6wt42di4U28osKvVYMJzLd5som7CTNT38V1ZQSR/lx9Y63ZPL+Q8MUDziVw3/yvsWHEMN/6mN8Y+nqM5PtwHEPCGnwcJeMPPZwS81vcZAa+cjwh45fSLGOC9cKoSzw3MRUySA78/OklTNR61TLwiBcP/4V2qixs4d/9zaKyq9VuPl41zrloE++lDUAPLthvyjPSyqg1V2XehLqk/HBnXKFUaKgsOwFFxFPFn3oC95pwyXQ/stoC4KxY1D/nvBnduxvNorKxRvb99T+7EmbXHVaPhnvenN59a01kWH0DAa3EH+dgeAW/4+YyA1/o+I+CV8xEBr5x+EQO87EZ5pQaR0mRsvEjnMK16vMwOTx3Qqsnb1pUsTSH++BJEl32p6uWaxP6o7Hy/305qvia3VJBQaYwhUn+X2eYthdXynT33wCs0zN0zAWldvLu6GfBIW8oEAa+l3CG0GQJeIZksNYiA11Lu8LkZAl45HxHwyukXUcCrN7LIWwyrgZxIjisTmdfkrbtzPuq79NblNVfpl4gp+CccFUfgrDqqzK2L7YGGmGxUZfwYNanX67LHDqu5VsxRrb3LDIrkKIt+MPDcoN4PHrpuzoKDCXgt6BSNLRHwhp/PCHit7zMCXjkfEfDK6RdRwPvWtM9xIPccRLt7iXxV31LFIC4a2Sse9+sNx47VcOxcA9HDa/4MaZUlE3kcWvbSfQDqpjzqd0r+E6/DfTIPalUo9B5Y47nU2TlJmLP1RpHthv0YAt7wcyEBb/j5jIDX+j4j4JXzEQGvnH4RBby8UoPoYSnRdrn585bDfSpfFQxtpQWIXvGYordW5zU1l8oCr2d0Vy3aLFKOjO1T74G1/R+excr7diJnQjamrxxqwNNrfRMEvNb3UdsdEvCGn88IeK3vMwJeOR8R8MrpF1HAqxe2Sg8VY8dtuUojBX8d15iAIq132TieNysT5ZUF3pbobufeqJs63+/TI3pPe2ZvQ/6WMxDtsKb3Q4cBj3fITRDwhtwFujdAwKtbspBPIOANuQs0N0DAqymR6gACXjn9Igp4W75O75OMOVvGCCn30eD3UV/uVu0gxg932TTSGjyjvLXTFqIho5vQHjwHyQCvaHSXrcfTGVJmTULc9f7rFm8ashrusjqhDmvMrt60Et0CWXACAa8FnaKxJQLe8PMZAa/1fUbAK+cjAl45/SIKeNnN6j0wxSOY/RYNRqcpl/lVWyStgU3mEVa9FRv4wjLA61y7BPaje1CvEd0VTWdoiYB3jMPITdql3tg9LBn1Cc7tL8GsD67H5cPSDXh6rW+CgNf6Pmq7QwLe8PMZAa/1fUbAK+cjAl45/SIOeJeM/BjnDpTikc1j0LFvsqZ6Ig0omBHRFAAlyrrySdhKf4B7yBS4h92muQcjIrxRR/fAtXYJGl2xqJ2+CI1Jvtsl67kXUW0896/3A4cucSw6mIDXoo5R2RYBb/j5jIDX+j4j4JXzEQGvnH4RB7x6v1IXzeP1rNbQYckjsMVH+/WM/dQhON9bpLyuN7UhkAivZyqDe9TdcA/w30iD7SlvzlLUF5SoHsJj40Sj31yIs9+U4KXRnyCSKjSweyfgNeCXlMkmCHhNFtyA5Qh4DRAxyCYIeOUEJuCV0y/igJcfmho2ozsmLfKfm+opK8/jHbZ6ApJ6p/hVvPDplag9dAJaea/MgGPzO3B8uRF6UxsCAV7RVAYFwA+eQOHClbCnJyPrpYdVny7emGPs57fBkeTUfBJ3v3sSf394d0RVaCDg1XwsLDmAgNeSblHdFAGv9X1GwCvnIwJeOf0iDnj5wbXLhqbjgbViDRtE6vEyIXkTCkfXLGQunqnqmUBTG/QCr55UBrbhoj+vRdW2fYgbfy1Spo33ew8trZd7JWP4BxOFnsJ187/CjhXHIFoWTshoGAyiCG8YOKnNFgl4w89nBLzW9xkBr5yPCHjl9Is44K0uqcNve65HTJIDvz8qdtBKtB4vE/Pc/c+hsaoWGc/MhLNblnpEwiO1QbQDmx7gjSo4AeeqRUpHNZFUhsaKGpyf8xIaK2uQ9dJDsKf7j2YfWLwXJ945jG739ELOEwOEnkK9ne6EjIbBIALeMHASAW/4OanNjgl4re9CAl45HxHwyukXccDLbnjxgFwUn64UPrjmLq3DpqGrFa20vr4vXrkRlRu/QOyIfkh9YLKmd3jVhsboWKUurlapMlHgZRFkBrtRBSeFu7vxg3cxA3sh7bGpqnvfOm49qs5UQCvNw9MIP7D2+yM3IyZZOwVCU7wwGUDAGyaO8tgmRXjDz2cEvNb3GQGvnI8IeOX0i0jg1XtwjYm0c/pmFO3O12ywwA+vsTnZrz+ueniNu443pGDQ6x51L+r7jPDrVRHg9YzsNqR3Qd1dC9AYHaf5pIgeVmOgy4DXnuDAuF23a9plA/iBtZTOcXhir/qhOSGDYTSIgDeMnNW8VQLe8PMZAa/1fUbAK+cjAl45/SISeAM5uKanBNeFF1ahes9hJN4yAom3jxTyEIdeNth93a1wD73F5zwt4LXv3wZn7uvKXFZv1z3lUSHY1XNYTY8W/Ca2Lz+K9U/tw4CpXTF12SAhTdrLIALe8PMkAW/4+YyA1/o+I+CV8xEBr5x+EQm8gXRc41FNR6ITY3eq185tgceMZGQtUa904Om+VrDaZ7gS7W0bmVUDXseWd+DYu7EJdvsMR92EWcJPB6vMwPadfO84xE8YrDpv+625KPu2WDPa7Wlk1UO7sXfVSdz8dD8Mn9VDeF/tYSABb/h5kYA3/HxGwGt9nxHwyvmIgFdOv4gEXnbTgeSTbr9lA8oOlwiBXt4jS1FfWCJUoqwV9J46BMeaF2CrrUJj0iWoHzhRSXHg4NsWeFmubtTRvbDv2aDk67KrbsJM1bSIto8MB3RbrAsdXpqjmoYRSDoDW+/ZgbkoOiWeN23AY20ZEwS8lnGF8EYIeIWlssxAAl7LuMLvRgh45XxEwCunX8QCL68YMO0vQ9Dnpo5CKur5Kr9697e48OJ7sMVFQ6sRRdvFWQ6uffM7sJ8+1PJSfY+BaMzsBtclWYiKsqG64DxsJflgZcdYFQZ2MUCum/Ko5sG3tuvx6K5ICoYeDfg6F05V4rmBuYhOdOAPx8QqYwg5JEwGEfCGiaM8tknAG34+I+C1vs8IeOV8RMArp1/EAm8gebx60hqYsLwRhQhI+nIjg1n7N5/CfmyvqpfZwbT6QRPRwKBY4HCap7EWMBeI7rJ5gaQzRGrDCa4zAa8Bv6RMNkHAa7LgBixHwGuAiEE2QcArJzABr5x+EQu8geTxKsCnI62hJVUgLlppRKFW11bNjU1pC3tgK86Hs/IComxATWwaGlMy0dClNxqTMgJ+CnhlBpHucIGmM0Ry/i5zDAFvwI9nyCYS8IZM+oAXJuANWDrTJhLwyklNwCunX8QCL7vxQPJ49X6lzzuXxQy8AmmP3SntLa0qDXoWKHt/K8o+2AZHl0xkPqt9wE3vvfO9RHL+LgGvnifSOmMJeK3jC9GdEPCKKhW6cQS8ctoT8MrpF9HAG0geL49yMuG0mlCwMawub/685Ur3tfQF0+C6spuUx4wCXmVfT7yudFUT3RdvNjFg6XBkjeksdB+Rnr9LwCv0mFhuEAGv5VyiuSECXk2JQj6AgFfOBQS8cvpFNPAGWhuWN6Hot2gwOk25TNMDPJJq11mmzJdho4CXH1QT7Qh34YsC7Pr5J4jtGIeRm8QPngWqsaaoYTSAUhrCyFnNWyXgDT+fEfBa32cEvHI+IuCV0y+igZd3/0rtEod5e8S7f51Z8z32zd+FxCtSMPwfYvNYlNd9Kl9XM4pgAa/eg2psH/ue3Ikza4+j2z29kPPEAOGnLpCudsLGw2QgAW+YOMpjmwS84eczAl7r+4yAV85HBLxy+kU08LKbXzwgF8Wn9deH/Wjw+6gvd2PY6glI6p2i6QV+gI0NzHhmJpzdsjTnBAN4GytqcH7OS0oqg0iTCbYHd2kdtoxbB3dZHUZ+dDNiO8UL7b26pA6/7bleGfv7IzcjJtkpNK+9DSLgDT+PEvCGn88IeK3vMwJeOR8R8MrpF/HAG2gFgQOL9+LEO4fRafKl6PfMECEvFK/ciMqNX8DRNQsZC6arNnjwZ1A2pYGnMrh6d0P6U9OE9s0Pq6UOysSQt0YLzWGD9n94Fivv24nsnCTM2Xqj8Lz2NpCAN/w8SsAbfj4j4LW+zwh45XxEwCunX8QDL4eyy4am44G11wurqffwGjPMoqsFT/9FSW0IFHplgLdo+VpUfboPIh3VPIUI5LAam79u/lfYseIYbvxNb4x9PEdY2/Y2kIA3/DxKwBt+PiPgtb7PCHjlfETAK6dfxAOv59fuz+XfqkvNPbO3IX/LGfR4sA96zr5KaC6D3vwnlytthwMpVRYo8PLoMoPd9KfuE06pCPSwGhNjyahPcG5/CWZ9cD0uH5YupE97HETAG35eJeANP58R8FrfZwS8cj4i4JXTL+KBVwGzkR/j3IFS6GkzzOa1wGCneCW3VfSqO5GHwqf/opQqi72+H1JnTRadikCAt/LTr1C8fJ2yhmgJMr6hXfdtxoV/5+uCekWbCG8n7OlQAl7hx9syAwl4LeMK4Y0Q8ApLFbKBBLxy0hPwyulHwAsgkDbDXPatY9eh6mwlREuU8XmBQq9e4PWEXZFuap6PEwd6e4IDozdNhiNJ/NAZL0eWMyEb01cONeApDV8TBLzh5zsC3vDzGQGv9X1GwCvnIwJeOf0IeAEEWp6MicdLlLHKBXqivGyuZ+UG0UivHuCVgV22P16KTE/KBn8cqRzZxTcmAa8Bv6RMNkHAa7LgBixHwGuAiEE2QcArJzABr5x+BLzN+gVanoxNDzTKy+YyKC1ZmaukN7CDbKkPTFbNrxUBXtZFrWTlR6je861yd3oju2wOP5QXSHSXypG1flMS8BrwS8pkEwS8JgtuwHIEvAaIGGQTBLxyAhPwyulHwNusHy9PFkhFAZkoL1uepTdceGGVcpCNXSzam3LPBJ9ly9SAlx2IK9+4C+Ubdip1dtkBtdQHpiBm0BW6n5K9D21D3mZ9B/L4IlSOjIBX9wNnsQkEvBZziMB2CHgFRArxEAJeOQcQ8MrpR8DbrF8LpPVJxpwtY3SrKhPlZYspsLrhc5R9sE1Z2xYXjaTbb0D8+MGt9uIPeFm5sdLVWy9C84h+ynx7unZTjLY3K5O7y2wFWttYt+hhMoEivGHiKI9tEvCGn88IeK3vMwJeOR8R8MrpR8Drod//674ONWVuzN0zAWld4nQpm/fJaex9eDsciU6M+miSrgNengs1pSNsRPWewy0/ZuXLovt0g7NrBzB4Yr/YK6rdqC8oQfXB78FaBbOILrtYQwkGuq4ru+nav+fgQCszcBu/7bEO1aWB6Rjwpi08kYDXws7xszUC3vDzGQGv9X1GwCvnIwJeOf0IeD3045HJYTO6Y9Kiq3Uru3P6ZhTt1l/Cy9dCDGJL39+qNKkQuezpyUi87QbEXa9/3572W9IzOsZh+OqJusF997sn8feHd0d8dzVPTQl4RZ5ga40h4LWWP0R2Q8ArolJoxxDwyulPwCunHwGvh37f7SjE8ls+RWqXOMzbM0G3sqWHirHjtlxlHqvYwCo3yF4s1aFqzyHUHj8P94k8JbprswHu+kbYM5LhurSDkqMbSOpC2725S+uw/fZc5cCa3jJr3BavznDz0/0wfFYP2dtvF/MJeMPPjQS84eczAl7r+4yAV85HBLxy+hHwttGPV2sItDsYL+WVNboTBiwbYYB3WpsQqdIQ6KJHXv4aR1/bj9RBmRjy1mjdZqg6g2/JCHh1P0ohn0DAG3IX6N4AAa9uyUyfQMArJzkBr5x+BLxt9ONNKAZM7YqpywbpVpdFSTePXYv6cjcGLB2OrDGdddtQmxAs4PWMTg9+cwzSrs3QvW9qNkHAq/uhsegEAl6LOkZlWwS81vcZAa+cjwh45fQj4G2jH2+JG5PkwBN7JiImWby7GDd1/O1vcfDZL6UPsPlybbCAd/utuSj7thjd7umFnCcGBPRUPTswF0WnKnW3aA5osTCaRBHeMHJW81YJeMPPZwS81vcZAa+cjwh45fQj4PWh358nf4rvPy/EHUsHYdBdXQNSmB9gMzq1IRjAy1MZYgM8qMYE4t3qohMd+MOxSQFp1l4nEfCGn2cJeMPPZwS81vcZAa+cjwh45fQj4PWhX0ulgQBr8jKT7ODXtls3KKkNV87rj0vv1d/8wYwIL6+5y9YKNJWBzZWtcGHAY2xZEwS8lnWN340R8Iafzwh4re8zAl45HxHwyulHwOtHP16T95HNY9Cxb3JAKvPavGzysNUTkNRbfxOItgsbGeFl+cZbxq2Du6wOPR7sg56zrwroPj0PqwVSwzigRcNoEgFvGDmreasEvOHnMwJe6/uMgFfORwS8cvoR8PrRb938r7BjxTEEeniNmz2weC9OvHNYKVE2/P0JuuvaBhN4eYOJQKsy8L3xiPhlQ9PxwNrrDXgi25cJAt7w8ycBb/j5jIDX+j4j4JXzEQGvnH4EvH70M+LwGje9/ZYNKDtcgsQrUjDkL2OkoNeoCO+++TtxZs1x2BMcGL1pstSeloz6BOf2l0jlPBvwGFvWBAGvZV3jd2MEvOHnMwJe6/uMgFfORwS8cvoR8KroZ8ThNWZeaehw2wZUna1EpymXot+iIQF7zQjg5VFnBrtD3rpRKtWCN+ugw2r+XUrAG/DjHrKJBLwhkz7ghQl4A5bOtIkEvHJSE/DK6UfAq6If/6o+0M5rnqZZndud0z9WDrHJQK8s8PLWwWxvRtQJ5ofVbvxNb4x9PMeAp7H9mSDgDT+fEvCGn88IeK3vMwJeOR8R8MrpR8CroZ9s5zWjoVcGeFkuMYvusivQ1sGe98PTPtjP6LAaRXgN+FVkGRMEvJZxhfBGCHiFpQrZQAJeOekJeD30c9fXI8oWhagom5eqZeWVYK+nJid6vXb2hyo5L7Tj2bzz2uXXZWDWGvlWwbKR3kCBl+fsGgW7zA6P7soe7GvHj49yaxThDT8PE/CGn88IeK3vMwJeOR8R8DbrV1Vdi6mzfoeZ99yMn4wd2qJqZVU15i5cjs07vmyK7OV0x7KFDyM97WKpLQJe/w8hK7n1zIANqClzY9YH1+PyYelyTywAT+hlB9kGLhuhVHEQufQCL8sfZrCbt/lMk/8XDUanKZeJLKU6humyeOAGVJe6KbqroSYBr/TjZroBAl7TJZdekIBXWsKgGyDglZOYgBfAH/+8Cm++u0FR8rn5s1oB7xt/+1/8ff1WvL1sPmJjXHhw3ou4rGs2nn78Fy3KE/CqP4RGR3nZagx69z70qXKQzZHoVEA0a0xnzXeDHuBlTSX2LdipNMFgB9QGLbsBaddmaK4hMoBrkjMhG9NXXvyAJTI30sYQ8Iafxwl4w89nBLzW9xkBr5yPCHgBFJeUo7q2Fj/71dN4bOadrYD39hm/xfiR12DG3T9RlN649Qs89rtX8c2WN2GzNaU+EPCqP4TBiPKyFVn09asndyJ/S1P0Ne2aTPT81VWqUCoCvAxwj7z6tVJ2jF2JvZIx8OXrhaPIWm9Jz+iuUVFvrTXD+XUC3vDzHgFv+PmMgNf6PiPglfMRAa+HfuN/+p946Be3tgLeayY+gIVzf6lAL7sOHD6OO2b+Dp+tfwXJiU1foxPwaj+EwYjy8lWPv/0tDr/8tVLBQQHUK1Jw2bTeSjWHtpca8LKILgPdC//OV6axqO5l914RcAc1f6pQdFf7efEcQcCrTy8rjCbgtYIX9O2BgFefXqEYTcArpzoBrwrwNjY2ou+on+PVxY/ihqFXKyOPHT+DSffNx8er/oTsrEuUn9W5G+S8EAGzK4tr8Z8916GqtA5zPxqDK27INPSua0tqceCNAzj4xgHUldUptuM7J6DL+C7IHpaNrMFZcCW7lAOJLC5f39CojMn7PA95n5/HidwTKDpQpPzMmehE9zt7oM/9OYjvkmDoPgtPVODxXusUm88fnoT0bmK5x4ZuIsyMsW9SoqKA+vomn9FlfQWYz+xRgJt8Zn1nNe+QfWFpj4qCu57+PbOq05yOKKtuLSz2RcCrArzfCpjOAAAaUElEQVTsJRbhXTTvfoy7YZAy0leEt6CkJiycHepN5j67Hx89fxA9hmXgV+tvCNp2Tv3jOxxatk/J7217ORNdCvhWnC73es2R4ETvh/uhyy2Xw5nkDMr+/varf2P3uycw6K5u+NmrTd8a0KWuQLQzCjFOO0oqmz7I0GV9BZz2KMTHOlBcXmv9zdIOFQXsNhtSEp34oZR8ZtVHIiM52qpbC4t9EfBqAC/L4Z0w6lrc/7MfKyMphzfw55rlrr446hMUn640pY0uS1H44Yvz+OHfBSja3ZSm0PZKHZSpdEq75NpMoUNvgd89cPabErw0+hPFBNXdFVeSUhrEtbLKSEppsIonxPdBKQ3iWoVqJKU0yClPwMsOP9XXo7GhET+Z9gQemDYJP7lxKJxOh6Lsir/+E+//819KlYa42Gg8MPcFqtIg8cwZ2X0tkG24ahvQWO5GXZorkOlSc5ZP2YbvPivAsBndMWlRU4oMXdoKEPBqa2S1EQS8VvOI9n4IeLU1CvUIAl45DxDwAkrVBRa59bz+uXKxArYVldX4zR9ew6c7v1Je7nvFZVi26BFkpqe0DKdDa/oewiUjP8a5A6UIRTtdkSoN+u5GbPT+D89i5X07EZ3owJN7JyImOTgpE2K7Ca9RBLzh5S+2WwLe8PMZAa/1fUbAK+cjAl5B/UrKKlBX527VcIJPJeAVFLF52Hc7CrH8lk8Rk+TAI1tuRFqXOH0GJEaHCnifHZiLolOVuPnpfhg+q4fEHUTeVALe8PM5AW/4+YyA1/o+I+CV8xEBr5x+ymwCXv0ivjXtcxzIPYc+E7Mx7S3zGi+EAnh5GbLsnCTM2XqjfrEifAYBb/g9AAS84eczAl7r+4yAV85HBLxy+hHwBqjfhVOVYKkNRrYcFtmK2cDL7vOlUR8rLYSpyYSIh7zHEPAGplsoZxHwhlL9wNYm4A1MNzNnEfDKqU3AK6cfAa+EfjzymdolDnM2jzElr9Vs4OUH1QZM7Yqpy5pK29GlTwECXn16WWE0Aa8VvKBvDwS8+vQKxWgCXjnVCXjl9CPgldSPH2Azq3KBmcC7fflRrH9qHx1Uk3xGCHglBQzBdALeEIguuSQBr6SAJkwn4JUTmYBXTj8CXkn9PGvTTvvLEPS5qaOkRfXpZgEvu6/lU/6lpDKYcV9BFS3Exgl4Q+yAAJYn4A1AtBBPIeANsQMElifgFRBJZQgBr5x+BLwG6McjoWZUbTADeFmDjT9P+RTn9peAUhnkHxACXnkNzbZAwGu24vLrEfDKaxhsCwS8cgoT8MrpR8BrgH7MBK/akN0nGXO2jDHIqrcZM4D3vYd3Y8+7J8GqMjyw9gZTcpODJpgFDBPwWsAJOrdAwKtTMAsMJ+C1gBM0tkDAK+cjAl45/Qh4DdCPmfBsOzzwrq64c2lwDngFG3g983YZ7Hbsm2yQQpFrhoA3/HxPwBt+PiPgtb7PCHjlfETAK6cfAa8B+nETLO/1z5P/pZQqu2PpIAy6q6uB1ptMBRN4zc5HNlwcixok4LWoY1S2RcAbfj4j4LW+zwh45XxEwCunHwGvAfp5mtj97kn8/eHdyo8e2TzG8AhpsIDXs96uWRUnDJbesuYIeC3rGr8bI+ANP58R8FrfZwS8cj4i4JXTj4DXAP3amlg3/yvsWHFMaT08a42xaQHBAF7PQ2qXDU3HA2uvD4IqkWuSgDf8fE/AG34+I+C1vs8IeOV8RMArpx8BrwH6+TLBD7EZDb1GA68n7NIhteA8DAS8wdE1mFYJeIOpbnBsE/AGR1cjrRLwyqlJwCunHwGvAfr5MsFA8i/TPsf3nxcaGuk1EnhZzu57D+1Wyo8R7AbpQQBAwBs8bYNlmYA3WMoGzy4Bb/C0NcoyAa+ckgS8cvoR8Bqgn5qJVQ/txt5VJxXovXnhj6QPshkFvJ6NJQh2g/sQEPAGV99gWCfgDYaqwbVJwBtcfY2wTsArpyIBr5x+BLwG6KdlgkMvGydbvcEI4PWEXZaze9/KoVRrV8uJEq8T8EqIF6KpBLwhEl5iWQJeCfFMmkrAKyc0Aa+cfgS8BugnYsITesc+noMbf9NbZJrXGFng3f/hWbDGEqxlMHVRC8gFuicR8OqWLOQTCHhD7gLdGyDg1S2Z6RMIeOUkJ+CV04+A1wD9RE3wpg5s/OXXZeCOZQOR1iVOdLoyLlDgZTnF6576Sumgxi6CXV2ySw0m4JWSLySTCXhDIrvUogS8UvKZMpmAV05mAl45/Qh4DdBPj4nvdhTiL9M+U5pTsLzeSQt/BNaZTfQKBHhZVHf9U/tQdKoS0YkOjHs8B8Nn9RBdksZJKkDAKylgCKYT8IZAdMklCXglBTRhOgGvnMgEvHL6EfAaoJ9eEyzaylIcDuSeU6Zm90nGpIVX4/Jh6Zqm9AAvy9Vdv2AfvvusoGmdnCRMe/s63VFlzU3RAFUFCHjD7wEh4A0/nxHwWt9nBLxyPiLgldOPgNcA/QI1wSKv6xbsQ/HpSsVEapc4jJjVA1dO7OgXSrWAl3VMO7jhLP79PyeUcmPsoqhuoB4yZh4BrzE6mmmFgNdMtY1Zi4DXGB2DaYWAV05dAl45/Qh4DdBP1sSm5w+AtSTm4MvssRzfQXd1Q5+J2a0qKPgCXhYxPvZZIfZvONOSo8tBlwH0iFk9qQqDrJMk5hPwSogXoqkEvCESXmJZAl4J8UyaSsArJzQBr5x+BLwG6GeUCRbx/WbDWbD/sxxffrHIb2qXeMQmO3Bp/0sQZQPOHitF0ckqFJ2qUHJzPa+cCdnoc1Mn9G0Dy0btk+zoU4CAV59eVhhNwGsFL+jbAwGvPr1CMZqAV051Al45/Qh4DdDPaBMsYrv73RP45sOzOPtNcSv49bcWq6fb96aOyLnJfzqE0fske2IKEPCK6WSlUQS8VvKG2F4IeMV0CuUoAl459Ql45fQj4DVAv2CbYHm5xScrUVVSi4JDpYiKsiGuQ6yS5xuT7ETHvsnB3gLZl1CAgFdCvBBNJeANkfASyxLwSohn0lQCXjmhCXjl9CPgNUA/M01oHVozcy+0lpgCBLxiOllpFAGvlbwhthcCXjGdQjmKgFdOfQJeOf0IeA3Qz0wTBLxmqm3MWgS8xuhophUCXjPVNmYtAl5jdAymFQJeOXUJeOX0I+A1QD8zTRDwmqm2MWsR8Bqjo5lWCHjNVNuYtQh4jdExmFYIeOXUJeCV04+A1wD9zDRBwGum2sasRcBrjI5mWiHgNVNtY9Yi4DVGx2BaIeCVU5eAV04/Al4D9DPTBAGvmWobsxYBrzE6mmmFgNdMtY1Zi4DXGB2DaYWAV05dAl45/Qh4DdDPTBMEvGaqbcxaBLzG6GimFQJeM9U2Zi0CXmN0DKYVAl45dQl45fQj4DVAPzNNEPCaqbYxaxHwGqOjmVYIeM1U25i1CHiN0TGYVgh45dQl4JXTj4DXAP3MNEHAa6baxqxFwGuMjmZaIeA1U21j1iLgNUbHYFoh4JVTl4BXTj8CXgP0M9MEAa+ZahuzFgGvMTqaaYWA10y1jVmLgNcYHYNphYBXTl0CXjn9CHgN0M9MEwS8ZqptzFoEvMboaKYVAl4z1TZmLQJeY3QMphUCXjl1CXjl9CPgNUA/M00Q8JqptjFrEfAao6OZVgh4zVTbmLUIeI3RMZhWCHjl1CXgldOPgNcA/cw0QcBrptrGrEXAa4yOZloh4DVTbWPWIuA1RsdgWiHglVOXgFdOPwJeA/Qz0wQBr5lqG7MWAa8xOppphYDXTLWNWYuA1xgdg2mFgFdOXQJeOf0IeA3Qz0wTBLxmqm3MWgS8xuhophUCXjPVNmYtAl5jdAymFQJeOXUJeOX0I+A1QD8zTRDwmqm2MWsR8Bqjo5lWCHjNVNuYtQh4jdExmFYIeOXUJeCV04+A1wD9zDRBwGum2sasRcBrjI5mWiHgNVNtY9Yi4DVGx2BaIeCVU5eA9/+3d+fBclV1HsB/bEJIEBEULWusUsvCUkZ0SqDCgEBUBGURhOBEB5A1gcgSWSIUyBYQRcMOCmiFxSkFHBGUgQEmDCIyTIFYuOAoIDtJCBEwySRBrHutpMITkvfOPX26j376P0if3+/k83ud9+3bt+/t5ifwZvArWULgLamdp5fAm8exZBWBt6R2nl4Cbx7HXlYReLvpCrzd/ATeDH4lSwi8JbXz9BJ48ziWrCLwltTO00vgzePYyyoCbzddgbebn8Cbwa9kCYG3pHaeXgJvHseSVQTektp5egm8eRx7WUXg7aYr8HbzE3gz+JUsIfCW1M7TS+DN41iyisBbUjtPL4E3j2Mvqwi83XQF3m5+Am8Gv5IlBN6S2nl6Cbx5HEtWEXhLaufpJfDmcexlFYG3m67A281P4M3gV7KEwFtSO08vgTePY8kqAm9J7Ty9BN48jr2sIvB20xV4u/kJvBn8SpYQeEtq5+kl8OZxLFlF4C2pnaeXwJvHsZdVBN5uugJvNz+BN4NfyRICb0ntPL0E3jyOJasIvCW18/QSePM49rKKwNtNV+Dt5ifwZvArWULgLamdp5fAm8exZBWBt6R2nl4Cbx7HXlYReLvpCrzd/ATeDH4lSwi8JbXz9BJ48ziWrCLwltTO00vgzePYyyoCbzddgbebn8Cbwa9kCYG3pHaeXgJvHseSVQTektp5egm8eRx7WUXg7aYr8HbzE3gz+JUsIfCW1M7TS+DN41iyisBbUjtPL4E3j2Mvqwi83XQF3m5+Am8Gv5IlBN6S2nl6Cbx5HEtWEXhLaufpJfDmcexlFYG3m67A281P4M3gV7KEwFtSO08vgTePY8kqAm9J7Ty9BN48jr2sIvB20xV4h+n3/AvzY8mLL8Z6667zVyueeGbBMKt4Wr8FBN5+T2Dk/QXekZv1e4XA2+8JjLy/wDtys9IrBN5u4gLvSvzmL1gYx5z69bj1jnvbZ7733e+Ic089NDZ4/brLVgq83X4IS64WeEtq5+kl8OZxLFlF4C2pnaeXwJvHsZdVBN5uugLvSvwu+fYP46rrZsbl5x4Xo9Z6TUyaOj3e9tY3xylH7yvwdvvZ68tqgbcv7J2aCryd+PqyWODtC3unpgJvJ74iiwXebswC70r8dj/gi/HRbTaNAz69Y/vMG2f+T0w58YK4/7++Fausskr7/xzh7fZDWHK1wFtSO08vgTePY8kqAm9J7Ty9BN48jr2sIvB20xV4V+K36Q4T49Rj9mtDb/P45W8ejj0OPDF+ct35se46owXebj9/xVcLvMXJOzcUeDsTFi8g8BYn79xQ4O1M2PMCAm83YoF3BX4vvfRSbLztZ+OC04+Ircdu0j7zdw8/Hjvvc1zc/J2vxps3XL+bvtUECBAgQIAAAQI9FxB4h3GEd9rU/WO7rT/wqkd4ez4lDQgQIECAAAECBJIFBN6V0DXn8G6/7Wax/4SPt898pXN4k/UtJECAAAECBAgQ6LmAwLsS4ouvvD6uvv629ioNa49aMyYe87W/ukpDz6ekAQECBAgQIECAQLKAwLsSuj/OXxhHnnxh/PdP72ufufFGb4tzpx0Wb9zgdbGim1EkT8TCbAJ/+tNLMXfec7HGGqsv+4Lh0OJz5v4h1h61VvtmxqMOAa+7wZ3TM88+F813H5a/TnmzWzMbzJk9OWtubLjBerHqqn+54tDyDzMbzJnZVbqAwDtMuz88/8dYvHhJ+w/5cG5GMcyyntYjgTv/9xdx6PHntrNqHpu+711x5KQ92zcszeORx59uj9b//rGn2//e7WMfjBOm7B1rrL5aj3ak7EgEbrvzvjj4C9Nf9oVRr7uRCJZ7bvPG8tJ/+2FcdtWNMXfe8+0byLtvuKjdgJmVm8NIOjWzuvJ7N8fiJUva32u77rBVTDlovJmNBNFzqxMQeBNGNpybUSSUtSSjwE/v+WXMnjMvPjh2k1i4cFGcPH1GNL+YL/zSEW2XA486M8aMHhXTph4QT816JsYfdFKccMResdN2W2TchVIpAg/87tH4zORpbVha/gopXncpmr1f89WLvhvf/4/bY+Jeu8QO4zaPRYsXx5ve8Pq2sZn13n+kHX7xwMMx/qAT41vTp8Zm739XPPjIk7HTXl+Ib19wfGzy7neY2UhBPb8aAYE3YVTDuRlFQllLeihw3U0/iamnfSPuu+XSaE5T2WKnQ+KK846L92/8zrbrtLMvj6dmzW1PV/Hon8DsZ+bFnhNPiikHjo+TvjYjzjxh0rJLAnrd9W8ur9a5mdc2nzy8vVZ5c5Rw6MPMBm9md937q9j3iDPihivPiLe+ZcN2g1t94nNx9MH/0r7hN7PBm5kd5REQeBMch3MzioSylvRQoAm7v33o8bj64pOWXUt55jVnxRvWf13b9fKrb4prb7yj/XOP/ggsWLgo9jns9Nhq8/fG5H13jeZ1tnzg9brrz1xW1PWW2++JQ48/Jz61y7j4zYOPxZprrhE7b7dF7LzdP7fLzGzwZrZo0eLY7/NfiV//9pE4dL/d4oX5C+KmmXfHjHOOjdeOWdvMBm9kdpRJQOAdIaSbUYwQbACevvTo7iVnHhVjP/CeuPf+/2s/Ml/+bnnfvW5mXHTZtXHrVdMHYMd/f1toTjdpvhzaPJqQ23yJZvnA63U3mD8TzXmgp51zRfsGZaO3/0M88OCjcd43/z2+fPzE+Ni4zd24ZzDHFs3Vh5p/F0ettWbc/8BD7WU3P7ffbrHaqqua2YDOzLa6Cwi8CYbNL2I3o0iA68OSO+6+vz1f94tT9o7xO2/b7mDp3fJu+97Zy75N7ghvH4azXMtZc+bFtrsfHrvvuHWMHrVW+yczrroxttnife3RwubW3l53/Z3RK3VvAu93rr01fjDjtGV/3Hya0pw3f9bJk81s8EYWt9/18/YLu3def0F7RLf5N/LwE86LIyeOjz13GWdmAzgzW8ojIPAmOLoZRQJaH5YsvUnI0PMLmytuDD2H95Tpl8WsOc86h7cPc2paNl9Qu+Ka/3xZ97MvuSZ2/MjY2PHDY9vTHLzu+jScFbRdejWNn9186bIrnDRH6hcs/P84/7TDzWzwRhZnXXx13Prje172JuWQY89q32g2R+a9zgZwaLaURUDgTWB0M4oEtMJLmvNxjz394pg6eUKM2/KflnVfb90x7WWT9j/yK/HaMaPbI/Wu0lB4OMNsN/QcXq+7YcIVfNpzL8yPD+0xJfbe46Mxae9d2o/HJxx8Shx32L/GhF0/1H507sY9BQcyjFY/uuWuOOqUC+OiM6bElpv9Yzz6xOzY4dNHx1GTPhX77Lm9mQ3D0FPqFBB4E+a2optRJJSzpAcCJ0+/rP2odehj6dHehx55sv1Y77EnZ7dP+cT2W8aJn9+nvUmFx2AIDA28XneDMZehuxh6zesm6B4zeUKsvtpq7RVRXu3GPYP5t/nb31VzvvzXr/hBfP+GH7fXTV5nzKj2tKFDPrtre5TezP72fwb+Xv+GAm+HyS9/M4oOZSzto8DTs59tr8c7eu2/nDfqMfgCXneDN6MlL74YzWtp6ScoQ3doZoM3s2ZHTzw1J970xvVf8U5rZjaYM7OrdAGBN93OSgIECBAgQIAAgQoEBN4KhmSLBAgQIECAAAEC6QICb7qdlQQIECBAgAABAhUICLwVDMkWCRAgQIAAAQIE0gUE3nQ7KwkQIECAAAECBCoQEHgrGJItEiBAgAABAgQIpAsIvOl2VhIgQIAAAQIECFQgIPBWMCRbJECAAAECBAgQSBcQeNPtrCRAgAABAgQIEKhAQOCtYEi2SIAAAQIECBAgkC4g8KbbWUmAAAECBAgQIFCBgMBbwZBskQABAgQIECBAIF1A4E23s5IAAQIECBAgQKACAYG3giHZIgECBAgQIECAQLqAwJtuZyUBAgQIECBAgEAFAgJvBUOyRQIECBAgQIAAgXQBgTfdzkoCBAgQIECAAIEKBATeCoZkiwQIECBAgAABAukCAm+6nZUECBAgQIAAAQIVCAi8FQzJFgkQIECAAAECBNIFBN50OysJECBAgAABAgQqEBB4KxiSLRIgQIAAAQIECKQLCLzpdlYSIECAAAECBAhUICDwVjAkWyRAgAABAgQIEEgXEHjT7awkQIAAAQIECBCoQEDgrWBItkiAAAECBAgQIJAuIPCm21lJgAABAgQIECBQgYDAW8GQbJEAAQIECBAgQCBdQOBNt7OSAAECBAgQIECgAgGBt4Ih2SIBAgQIECBAgEC6gMCbbmclAQIECBAgQIBABQICbwVDskUCBAgQIECAAIF0AYE33c5KAgQIECBAgACBCgQE3gqGZIsECBAgQIAAAQLpAgJvup2VBAgQIECAAAECFQgIvBUMyRYJECBAgAABAgTSBQTedDsrCRAgQIAAAQIEKhAQeCsYki0SIECAAAECBAikCwi86XZWEiBAgAABAgQIVCAg8FYwJFskQIAAAQIECBBIFxB40+2sJECAAAECBAgQqEBA4K1gSLZIgAABAgQIECCQLiDwpttZSYAAAQIECBAgUIGAwFvBkGyRAAECBAgQIEAgXUDgTbezkgABAgQIECBAoAIBgbeCIdkiAQIECBAgQIBAuoDAm25nJQECBAgQIECAQAUCAm8FQ7JFAgQIECBAgACBdAGBN93OSgIECBAgQIAAgQoEBN4KhmSLBAgQIECAAAEC6QICb7qdlQQIECBAgAABAhUICLwVDMkWCRAgQIAAAQIE0gUE3nQ7KwkQIECAAAECBCoQEHgrGJItEiBAgAABAgQIpAsIvOl2VhIgQIAAAQIECFQgIPBWMCRbJECAAAECBAgQSBcQeNPtrCRAgAABAgQIEKhAQOCtYEi2SIAAAQIECBAgkC4g8KbbWUmAAAECBAgQIFCBgMBbwZBskQABAgQIECBAIF1A4E23s5IAAQIECBAgQKACAYG3giHZIgECBAgQIECAQLqAwJtuZyUBAgQIECBAgEAFAgJvBUOyRQIECBAgQIAAgXQBgTfdzkoCBAgQIECAAIEKBATeCoZkiwQIECBAgAABAukCfwb6Sini66EfwwAAAABJRU5ErkJggg=="
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Two Gaussian distributions that combine into a mixture density.\n",
"#| label: fig:logistics-mixture\n",
"fig = go.Figure(data=data); fig.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following code generates 100 samples, rather inefficiently:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Samples from a mixture of two Gaussian distributions.\n",
"#| label: fig:logistics-samples\n",
"component_indices = rng.choice(2, size=1000, p=[0.9,0.1])\n",
"samples = np.array([rng.multivariate_normal(means[s], covariances[s]) for s in component_indices])\n",
"fig.add_trace(go.Scatter(x=samples[:,0],y=samples[:,1], mode=\"markers\",\n",
" marker=dict(size=3, color=\"red\")))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see the first component is chosen much more often, which is exactly what we expect.\n",
"\n",
"Armed with this insight about sampling mixtures, we apply it below to code up the MCL prediction step:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def predict_samples(samples, weights, control, motion_model_sigma, size=500):\n",
" \"\"\"Create predictive density from weighted samples given control and control stddev.\"\"\"\n",
" weights /= np.sum(weights)\n",
" component_indices = rng.choice(len(samples), size=size, p=weights)\n",
" means = samples + control\n",
" cov = np.eye(2) * motion_model_sigma**2\n",
" return np.array([rng.multivariate_normal(means[s], cov) for s in component_indices])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Evaluating the Likelihood in the Update Step\n",
"\n",
"As before, we know that the ground truth trajectory stays away from obstacles at all times. However, we only have access to a likelihood *image*, not a function that evaluates the likelihood for an arbitrary coordinate. The following function calculates the correct cell for looking up the likelihood, and returns 0 likelihood if out of bounds:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"def likelihood_off(xy):\n",
" \"\"\"Calculate likelihood by looking up value in proximity_map_off.\"\"\"\n",
" j, i = np.round(xy).astype(int)\n",
" if i<0 or i>49 or j<0 or j>99: return 0.0\n",
" return float(logistics.proximity_map_off[i,j])\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### MCL Warehouse Example\n",
"\n",
"Now that we know how to do the prediction step and evaluate the likelihood function, we are able to implement the entire Monte Carlo localization method. First, let us obtain 500 samples from the prior:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: 500 samples from the prior density at the start.\n",
"#| label: fig:logistics-prior-samples\n",
"S=500\n",
"prior_samples = rng.multivariate_normal(prior_mean, prior_cov, size=S)\n",
"logistics.show_map(0.1*logistics.base_map, markers=prior_samples,\n",
" marker=dict(size=3,color=\"red\"))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare this sampling-based representation with the Markov localization representation of the prior above, and note they represent the *same* density, but using vastly different representations. In fact, they also use vastly different resources: for Markov localization we used 5000 cells, and here we use 500 samples, each represented as a two-dimensional vector. In higher-dimensional state spaces this difference is even greater: what would happen if we wanted to represent orientation as well?\n",
"\n",
"However, as discussed, we start off MCL with a set of *weighted* samples\n",
"$\\{(x_1^{(t)}, L(x_1^{(t)};z_1))\\}_{t = 1 \\dots S}$, which represents the posterior for $k=1$. We do this by weighting each sample from the prior with the likelihood:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: By weighting the samples with the likelihood, we get a representation for the posterior.\n",
"#| label: fig:logistics-posterior-samples\n",
"samples = prior_samples\n",
"weights = np.apply_along_axis(likelihood_off, 1, samples)\n",
"logistics.show_map(0.1*logistics.base_map, markers=samples,\n",
" marker=dict(color=\"red\", opacity=0.1, size=10*weights/np.max(weights)))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that all samples close to the wall and/or the shelves have disappeared, as they have zero weight. All remaining samples have the same weight."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"#| caption: Monte Carlo Localization in action!\n",
"#| label: fig:mcl_in_action\n",
"for k in indices[:-1]:\n",
" # prediction phase\n",
" control = values.at(x[k+1]) - values.at(x[k]) # ground truth control\n",
" samples = predict_samples(samples, weights, control, motion_model_sigma)\n",
" # measurement update phase\n",
" weights = np.apply_along_axis(likelihood_off, 1, samples)\n",
"# logistics.show_map(0.1*logistics.base_map, markers=samples,\n",
"# marker=dict(color=\"red\", opacity=0.1, size=10*weights/np.max(weights)))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Monte Carlo localization in action.\n",
"\n",
"\n",
"The figure above shows Monte Carlo localization in action! Comparing with Markov localization, we see that the results are consistent. Not only that, but if you look at the timing numbers, MCL runs at least an order of magnitude faster.\n",
"\n",
"\n",
"You might wonder about the samples that made it into the seemingly *wrong* aisles between the shelves. However, if we crank up the Markov localization visualization by a factor of 10, you will see that *in* fact the probability of being in those aisles is actually non-zero:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Markov Localization visualized with a heatmap.\n",
"#| label: fig:logistics-markov-heatmap\n",
"logistics.show_map(10*posterior_density/np.max(posterior_density) + 0.1*logistics.base_map)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MCL can be made to be *more* accurate than Markov localization, since the accuracy of the sample-based approximation can be increased by increasing the number of samples. Of course, we can also increase the resolution of the Markov localization representation, but at exponential cost. In contrast, the samples needed are proportional to the \"volume\" that the density occupies, an observation that underlies adaptive variants of the particle filter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Adding Range Sensing\n",
"\n",
"Finally, and this is will be rather easy in MCL, let us investigate the effect of adding range sensing. This time we won't have the luxury to know the entire measurement sequence in advance, as we did with proximity. Rather, the likelihood will have to be given the output of the RFID sensor. Remember that was either a beacon ID and a range $(i,r)$, or $(\\text{None},\\infty)$."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def likelihood_range(xy, rfid_measurement):\n",
" \"\"\"Calculate likelihood of xy given range measurement.\"\"\"\n",
" _id, _range = rfid_measurement\n",
" if _id is None:\n",
" j, i = np.round(xy).astype(int)\n",
" if i < 0 or i > 49 or j < 0 or j > 99:\n",
" return 0.0\n",
" return float(logistics.out_of_bound_map[i, j])\n",
" else:\n",
" sigma = 1.0 # In meters\n",
" range_for_xy = logistics.rfid_range(xy, logistics.beacons[_id])\n",
" return 0.0 if range_for_xy is None else np.exp(-1/(2 * sigma**2) * (range_for_xy - _range)**2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also use this to illustrate how to *globally* localize, without any prior information at all, except that we are *somewhere* in the warehouse. We can encode this knowledge as samples by uniformly sampling over the entire range for $x$ and $y$. This corresponds to assuming that the prior distribution on the initial state is\n",
"a uniform distribution, sometimes called the *uniform prior* assumption.\n",
"Because our knowledge is now so diffuse, we use 2000 samples instead of 500 to better approximate it:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: 2000 samples from an *uninformative* prior density at the start, i.e., we don't know where we are.\n",
"#| label: fig:logistics-uninformative-prior-samples\n",
"T=2000\n",
"prior_samples = rng.uniform(low=gtsam.Point2(0,0), high=gtsam.Point2(100,50), size=(T,2))\n",
"logistics.show_map(0.1*logistics.base_map, markers=prior_samples,\n",
" marker=dict(size=3,color=\"red\"))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first range measurement happens to be out of range, and we can see the effect on our estimate for the posterior $p(x_1|z_1)$ quite clearly:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Sample-based posterior after a single \"out of range\" measurement.\n",
"#| label: fig:logistics-posterior-samples-out-of-range\n",
"samples = prior_samples\n",
"range_measurement = logistics.rfid_measurement(values.at(x[1]))\n",
"weights = np.apply_along_axis(likelihood_range, 1, samples, range_measurement)\n",
"logistics.show_map(0.1*logistics.base_map, markers=samples,\n",
" marker=dict(color=\"red\", opacity=0.1, size=10*weights/np.max(weights)))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As expected, the likelihood has \"punched holes\" around the beacons, because we *know* we cannot have been near them. When we combine this with the proximity OFF measurement, we improve our posterior even more:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Upgrading the posterior with a single \"proximity=OFF\" measurement.\n",
"#| label: fig:logistics-posterior-samples-proximity-off\n",
"weights *= np.apply_along_axis(likelihood_off, 1, samples)\n",
"logistics.show_map(0.1*logistics.base_map, markers=samples,\n",
" marker=dict(color=\"red\", opacity=0.1, size=10*weights/np.max(weights)))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now ready to bring it all together by multiplying *two* likelihoods in every measurement update phase:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"#| caption: Global localization using Monte Carlo Localization.\n",
"#| label: fig:logistics-mcl-global\n",
"for k in indices[:-1]:\n",
" # prediction phase\n",
" control = values.at(x[k+1]) - values.at(x[k]) # ground truth control\n",
" samples = predict_samples(samples, weights, control, motion_model_sigma)\n",
" # measurement update phase\n",
" range_measurement = logistics.rfid_measurement(values.at(x[k]))\n",
" weights = np.apply_along_axis(\n",
" likelihood_range, 1, samples, range_measurement)\n",
" weights *= np.apply_along_axis(likelihood_off, 1, samples)\n",
"# logistics.show_map(0.1*logistics.base_map, markers=samples,\n",
"# marker=dict(color=\"red\", opacity=0.1, size=10*weights/np.max(weights)))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Global localization using MCL aided by range sensing.\n",
"\n",
"\n",
"The figure above shows global localization in action! At the onset, the robot is very confused as to where it might be in the warehouse, but it still has *some* knowledge. Then it moves within range of beacon $0$, which immediately localizes it, acting a bit like a GPS sensor, especially in combination with what was sensed before. After that the particular shape of the range likelihoods makes for some interesting antics, and at the end we are quite a bit more certain that the robot is in the center aisle. \n",
"\n",
"This example showed off *two* nice properties of Monte Carlo localization (and, for that matter, Markov localization):\n",
"1. We can reason about multi-model densities.\n",
"2. We can incorporate missing information/data, such as out of range measurements.\n",
"\n",
"To emphasize the latter point even more, note that for the last few time steps in the animation above we are *out* of beacon range, and you can see a bit of \"squeezing\" of the sample cloud at the very top, because of this."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Kalman Smoothing and Filtering\n",
"\n",
"> For linear systems with Gaussian uncertainty, the Kalman filter is both efficient and optimal.\n",
"\n",
"The final and mathematically most challenging approach we will discuss is Kalman smoothing and filtering. Ironically, while the math is more difficult, the circumstances in which these methods can be applied are more limited.\n",
"The math is only exact for (a) linear measurement and motion models and (b) Gaussian additive noise. \n",
"In addition, although there are ways to deal with nonlinear models, a more serious limitation is that the density on the state is restricted to Gaussian distributions.\n",
"\n",
"These methods are incredibly important in robotics. In spite of all their limitations, Kalman smoothers and filters are incredibly efficient, and are at the core of the navigation stack \n",
"(i.e., the software that handles everything from low-level sensor processing to higher-level localization)\n",
"of many systems, robots and otherwise. \n",
"In fact, the Kalman filter was implemented in the sixties on Apollo flight computers,\n",
"which had extremely limited computational hardware."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Factor Graphs and Least Squares"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"> When given measurements and actions, we can create a factor graph directly.\n",
"\n",
"**Kalman smoothing** is the equivalent of the Viterbi algorithm for hidden Markov model, but for continuous state spaces. \n",
"\n",
"In the continuous case, we build the factors directly from given control inputs and measurements.\n",
"A factor graph now encodes the negative log-posterior \n",
"\n",
"$$\\Phi(X)=\\sum_i \\phi(X_i) = \\frac{1}{2} \\sum_i \\|A_i X_i-b_i\\|^2.$$\n",
"\n",
"In the continuous case we use *minimization* of the log-likelihood rather than maximization over the probabilities. The main reason is because then inference becomes a linear least squares problem."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A least-squares problem is convex and can be solved in closed form. The linear terms within the square norm above are *sparse*, in the sense that $X_i$ is only a *subset* of the continuous variables $X$. For example, a simple sensor fusion problem on two scalar variables $x_1$ and $x_2$ would be one where both have a simple prior on them, resp. with $\\mu_1=3$ and $\\mu_2=7$, and we know that the difference between them is equal to $5$. This yields three factors that have to be minimized over $x_1$ and $x_2$:\n",
"\n",
"$$\n",
"\\Phi(X)= \\frac{1}{2} \\|x_1-3\\|^2 + \\frac{1}{2} \\|(x_2-x_1)-5\\|^2 + \\frac{1}{2} \\|x_2-7\\|^2.\n",
"$$\n",
"\n",
"This corresponds to the following \n",
"\n",
"|$X_i$|$A_i$|$b_i$|\n",
"|-|-|-|\n",
"|$x_1$|[1]|3|\n",
"|$x_1, x_2$|[-1 1]|5|\n",
"|$x_2$|[1]|7|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can collect all three matrices $A_1$, $A_2$, and $A_3$ into one sparse matrix $A$ and corresponding right-hand-side $b$:\n",
"\n",
"$$A=\\begin{pmatrix} 1 & 0 \\\\ -1 & 1 \\\\ 0 & 1 \\end{pmatrix}~~\\text{and}~~B=\\begin{pmatrix} 3 \\\\ 5 \\\\ 7 \\end{pmatrix}.$$\n",
"\n",
"You can convince yourself that the minimization problem can then be written as\n",
"\n",
"$$X^* = \\arg \\min_X \\Phi(X) = \\arg \\min_X \\frac{1}{2} \\|A X-b\\|^2$$\n",
"\n",
"which is now a *sparse* linear least-squares problem."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Setting the derivative to zero and solving for $X^*$ we obtain:\n",
"\n",
"$$\\begin{aligned}\n",
"A^T(A X^* - b) &= 0 \\\\\n",
"(A^T A) X^* &= A^T b \\\\\n",
"X^* &= (A^T A)^{-1} A^T b \n",
"\\end{aligned}$$\n",
"\n",
"This is known as a **system of normal equations**, and the last equation above is a closed from solution for it. \n",
"\n",
"Solving a linear least-squares problem this way can be expensive. The matrix $A$ can be very high dimensional, but luckily in many sensor fusion scenarios it is exceedingly *sparse*. Still, we have to proceed with some care, as in general the matrix $(A^T A)^{-1}$ is *not* sparse. The matrix $Q \\doteq A^T A$ is known as the **Hessian** or **Information Matrix** and has dimensions $n\\times n$ if there are $n$ scalar unknowns. In general, it takes $O(n^3)$ work to compute it, which is only 27 for $n=3$, but is already 1 *billion* for $n=1000$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Numerical Example\n",
"This method is trivial to implement in numpy for the small example above:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2.66666667 7.33333333]\n"
]
}
],
"source": [
"A,b = np.array([[1.,0.],[-1.,1.],[0.,1.]]), np.array([3.,5.,7.])\n",
"X_optimal = np.linalg.inv(A.T @ A) @ A.T @ b\n",
"print(X_optimal)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that in this simple sensor fusion example, a compromise solution is obtained: all factors are equally *unhappy*. We can compute the error vector as $A X^* - b$ and find that the errors is equally divided between all factors:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-0.33333333 -0.33333333 0.33333333]\n"
]
}
],
"source": [
"print(A @ X_optimal - b)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise\n",
"\n",
"What would make the errors *not* divide equally between factors?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sparse Least-Squares\n",
"\n",
"In practice we use *sparse factorization methods* to solve for $X^*$. In particular, *sparse Cholesky* factorization can efficiently decompose the sparse Hessian $Q$ into its matrix square root $R$\n",
"\n",
"$$A^T A=R^T R$$\n",
"\n",
"where $R$ is *upper-triangular* and sparse as well. There is one wrinkle: the sparsity of $R$ depends (dramatically) on the column ordering chosen for $A$, and the optimal ordering is hard to find (NP-complete, in fact). Hence, many heuristic ordering methods exist that are applied in practice.\n",
"\n",
"After we find $R$, which is where the heavy lifting occurs, we can efficiently solve for $X^*$ in two steps. First, we solve for an auxiliary vector $y$:\n",
"\n",
"$$\\begin{aligned}\n",
"(R^T R) X^* &= A^T b \\\\\n",
"R^T (R X^*) &= A^T b \\\\\n",
"R^T y &= A^T b\n",
"\\end{aligned}$$\n",
"\n",
"In the last line, $R^T$ is lower-triangular, and hence $y$ can be easily solved for proceeding from $y_1$ to $y_n$, via *forward-substitution*. We then turn around use the computed value of $y$ to solve for $X^*$ by *back-substitution*:\n",
"\n",
"$$R X^*=y.$$\n",
"\n",
"Both of these steps are $O(n^2)$ for dense matrices, but typically closer to $O(n)$ for sparse matrices.\n",
"\n",
"There is a deep connection between sparse factorization methods and the sum-product algorithm discussed in the previous chapter. In fact, sparse factorization *is* sum-product, where one continuous variable is eliminated at a time. The factor graph corresponding to a sparse least-squares problem corresponds to its sparsity pattern. In this graphical framework, the *product* is implemented by collecting all factors connected to that variable, and the *sum* is implemented by expressing the variable to be eliminated as a linear combination of its neighbors in the graph."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example with GPS-Like Measurements\n",
"\n",
"> We build a factor graph and then simply call `optimize`.\n",
"\n",
"GTSAM is built around state-of-the-art sparse factorization methods, and hence can very efficiently solve large sensor fusion problems, like the localization problem with GPS-like measurements.\n",
"Below we illustrate this with an example in code for the GPS-like measurements, which is easily tackled using optimization. Range measurements can also be handled."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We simulate measurements using the ground truth trajectory but with noise added, by creating a quick Bayes net do this for us. Remember from the previous section that the measurements are in centimeters, so the number $30$ below is the standard deviation of the measurement noise, in centimeters:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"measurement on [10. 6.] = [980.21898282 565.87931563]\n"
]
}
],
"source": [
"C = 100 * np.eye(2)\n",
"measurement_model_sigma = 30\n",
"z = {k: gtsam.symbol('z', k) for k in indices}\n",
"bn = gtsam.GaussianBayesNet()\n",
"for k in indices:\n",
" conditional_on_zk = gtsam.GaussianConditional.FromMeanAndStddev(\n",
" z[k], C, x[k], [0, 0], measurement_model_sigma)\n",
" bn.push_back(conditional_on_zk)\n",
"simulation = bn.sample(values)\n",
"print(f\"measurement on {values.at(x[1])} = {simulation.at(z[1])}\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice how the measurement is scaled by 100, and is corrupted by noise. Now we are finally ready to create a GaussianFactorGraph that will fuse the information from the prior, the measurements, and the motion models:"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"gfg = gtsam.GaussianFactorGraph()\n",
"\n",
"# The prior\n",
"p_x1 = gtsam.GaussianDensity.FromMeanAndStddev(x[1], values.at(x[1]), 0.5)\n",
"gfg.push_back(p_x1)\n",
"\n",
"# Create motion model factors from ground truth trajectory displacements\n",
"for k in indices[:-1]:\n",
" state = values.at(x[k])\n",
" next_state = values.at(x[k+1])\n",
" displacement = next_state - state\n",
" # |next_state - (A*state + B*u)|\n",
" gfg.push_back(gtsam.GaussianConditional.FromMeanAndStddev(\n",
" x[k+1], np.eye(2), x[k], displacement, motion_model_sigma))\n",
"\n",
"# Convert the conditionals in Bayes net from above into likelihood factors\n",
"for k in indices:\n",
" conditional_on_zk = bn.at(k-1)\n",
" measurement = simulation.at(z[k])\n",
" likelihood_on_xk = conditional_on_zk.likelihood(measurement)\n",
" gfg.push_back(likelihood_on_xk)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we show the factor graph, which looks exactly like the one for inference in an HMM, except we now have more states, and they are continuous. The two problems have essentially the same computational *structure*:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"position_hints = {'x': 1}\n",
"pos = {0:(0.35,1)}\n",
"pos.update({k:(k+0.5,1) for k in indices[:-1]}) # binary\n",
"pos.update({k+N-1:(k,0.5) for k in indices}) # unary"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#| caption: The factor graph for a Kalman smoother.\n",
"#| label: fig:logistics-factor-graph\n",
"show(gfg, hints=position_hints, factor_positions=pos)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can find the optimal solution, using the `optimize` method. In the Gaussian factor graph case, this solves a linear least-squares problem with a continuous variant of the max-product algorithm from Section 3.4:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"least_squares_solution = gfg.optimize()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we compare the estimated trajectory with the ground truth trajectory:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: Estimated trajectory using a Kalman smoother.\n",
"#| label: fig:logistics-estimated\n",
"estimated = np.array([least_squares_solution.at(x[k]) for k in indices])\n",
"logistics.show_map(logistics.base_map, estimated)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## GTSAM 102\n",
"\n",
"> A deeper dive in the GTSAM concepts used above."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Recall the `gtsam.GaussianFactorGraph` `gfg`:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#| caption: Factor graph for a Kalman smoother, again.\n",
"#| label: fig:logistics-factor-graph-again\n",
"show(gfg, hints=position_hints, factor_positions=pos)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also visualize the sparse $A$ matrix, which is called the **sparse Jacobian** of the system:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: The Jacobian matrix $A$ (and RHS $b$) corresponding to the above factor graph\n",
"#| label: fig:logistics_proximity_map2\n",
"A, b = gfg.jacobian()\n",
"px.imshow(np.abs(A), color_continuous_scale='Reds')\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"In fact, the deep connection between factor graphs and sparse linear algebra is this:\n",
"> Columns correspond to variables, and rows correspond to factors.\n",
"\n",
"You can make out, from the top:\n",
"- the first two rows correspond to the prior\n",
"- the two darker diagonals correspond to the motion model factors\n",
"- the single red diagonal corresponds to the measurements"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use the method `eliminateSequential` to use the linear-Gaussian sum-product algorithm (matrix factorization!) to turn it into a Bayes net, which encodes the multivariate Gaussian posterior:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#| caption: Bayes net representing a multivariate Gaussian posterior. \n",
"#| label: fig:bayes-net-gaussian-posterior\n",
"gaussian_posterior = gfg.eliminateSequential()\n",
"show(gaussian_posterior, hints=position_hints)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This Bayes net *is* the upper-triangular (DAG!) Cholesky factor $R$ we discussed above:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#| caption: The upper triangular matrix corresponding to the above Bayes net. \n",
"#| label: fig:upper-triangular-gaussian-posterior\n",
"R, d = gaussian_posterior.matrix()\n",
"display(px.imshow(np.abs(R), color_continuous_scale='Reds'))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed, here the correspondence is: \n",
"> Columns correspond to variables, and rows correspond to Gaussian conditionals.\n",
"\n",
"In general, the correspondence is about *block* columns, as variables in this case are two-dimensional, and *block* rows. For example, the first `GaussianConditional` in the `gaussian_posterior` Bayes net corresponds to the first two rows above, and can be shown like so:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First two rows are: p(x1 | x2)\n",
" R = [ 3.91933 0 ]\n",
" [ 0 3.91933 ]\n",
" S[x2] = [ -0.0637865 0 ]\n",
" [ 0 -0.0637865 ]\n",
" d = [ 37.6757 22.1659 ]\n",
" No noise model\n"
]
}
],
"source": [
"gaussian_posterior.at(0).print(\"First two rows are: \")\n"
]
}
],
"metadata": {
"colab": {
"authorship_tag": "ABX9TyNvmfi5Ca1zjvaaDmtt5TDb",
"collapsed_sections": [],
"include_colab_link": true,
"name": "S44_logistics_perception.ipynb",
"provenance": []
},
"kernelspec": {
"display_name": "Python 3.8.12 ('gtbook')",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.18"
},
"latex_metadata": {
"affiliation": "Georgia Institute of Technology",
"author": "Frank Dellaert and Seth Hutchinson",
"title": "Introduction to Robotics"
},
"vscode": {
"interpreter": {
"hash": "9f7376ced4243bb13dfcffa8a3ba834e0602aa8334cd3a1d8ba8d285f4628083"
}
}
},
"nbformat": 4,
"nbformat_minor": 1
}
![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\"){kind=icon}
![\"Splash](\"Figures4/S44-Warehouse_robots-08.jpg\")
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Localization** is the process of estimating the robot's position using sensor data\n",
"and the history of executed actions.\n",
"In this chapter, the robot's position at time $k$ is denoted by $x_k$, so the localization problem\n",
"is to estimate $x_k$ at each time instant using the robot's history of sensor observations,\n",
"$z_1, \\dots z_k$, and commanded actions $u_1, \\dots , u_{k-1}$.\n",
"\n",
"As we have seen in Chapter 3, when we are able to exploit the Markov property, we need\n",
"not consider the entire sensor and action history at each time $k$; intstead, we can iteratively\n",
"compute a probability distribution for the state $x_k$ using only our belief about the state $x_{k-1}$,\n",
"the action $u_{k-1}$, and the sensor observation $z_k$.\n",
"This kind of iterative, online updating is referred to as filtering.\n",
"The input to the filter is the belief at time $k-1$, the action $u_{k-1}$, and the observation $z_k$.\n",
"The output of the filter is the new belief, a probability distribution for $x_k$.\n",
"Note that when taking this approach we abandon computing the full joint distribution\n",
"$P(X_1, \\dots X_k)$, and content ourselves to compute only the conditional distribution\n",
"for $X_k$ at time $k$.\n",
"In this chapter, the filters that we develop will be derived from Bayes theorem,\n",
"and the result is known as **Bayes filtering**.\n",
"\n",
"We begin the section with a general introduction to Bayes filters, and then develop\n",
"three specific algorithms, Markov localization, and Monte Carlo localization, and Kalman filtering.\n",
"These three algorithms reflect trade-offs in computational complexity versus accuracy and expressive\n",
"power. In particular, Markov localization relies on a grid-based representation that\n",
"can require significant computer memory as well as significant computation in the update\n",
"process.\n",
"Monte Carlo localization addresses each of these concerns by using a sampling-based approach,\n",
"at the expense of accuracy.\n",
"Kalman filters, on the other hand, provide an exact and optimal solution to the localization\n",
"problem, by only in the special case when the robot can be described as a linear system\n",
"and all uncertainties in motion and observation are Gaussian in nature."
]
},
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"## A Running Example\n",
"\n",
"When introducing concepts related to localization, it will be useful to \n",
"have a short, ground truth trajectory for the robot that we can use to assess the quality of\n",
"solutions.\n",
"For this purpose,\n",
"consider a trajectory that starts at the bottom left of the map,\n",
"moves to the right, then up between the middle two shelves:"
]
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"outputs": [
{
"data": {
"text/html": [
"![\"\"](\"https://github.com/gtbook/robotics/blob/main/Figures4/markov-localization.png?raw=1\")
\n",
"![\"\"](\"https://github.com/gtbook/robotics/blob/main/Figures4/predictive.gif?raw=1\")
\n",
"![\"\"](\"https://github.com/gtbook/robotics/blob/main/Figures4/posterior.gif?raw=1\")
\n",
"![\"\"](\"https://github.com/gtbook/robotics/blob/main/Figures4/samples.gif?raw=1\")
\n",
"![\"\"](\"https://github.com/gtbook/robotics/blob/main/Figures4/global.gif?raw=1\")
\n",
"