From 7d3f9f9232ec5cc3a99e2c44b97736218c084021 Mon Sep 17 00:00:00 2001
From: Rajesh1505 <87649352+Rajesh1505@users.noreply.github.com>
Date: Tue, 7 Sep 2021 12:25:53 +0530
Subject: [PATCH 1/2] 1st commit
---
Copy_of_Guided_Project_Gradient_Descent.ipynb | 712 ++++++++++++++++++
1 file changed, 712 insertions(+)
create mode 100644 Copy_of_Guided_Project_Gradient_Descent.ipynb
diff --git a/Copy_of_Guided_Project_Gradient_Descent.ipynb b/Copy_of_Guided_Project_Gradient_Descent.ipynb
new file mode 100644
index 0000000..89dc2ca
--- /dev/null
+++ b/Copy_of_Guided_Project_Gradient_Descent.ipynb
@@ -0,0 +1,712 @@
+{
+ "nbformat": 4,
+ "nbformat_minor": 0,
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ },
+ "colab": {
+ "name": "Copy of Guided Project - Gradient Descent.ipynb",
+ "provenance": [],
+ "collapsed_sections": []
+ }
+ },
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "_wfP6xtQ5bNo"
+ },
+ "source": [
+ "# Gradient Descent for Optimization "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "M88APx1X5bNp"
+ },
+ "source": [
+ "## Introduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "hWZ1CROr5bNp"
+ },
+ "source": [
+ "### Gradient descent is an algorithm used to the find local minima of any differentiable function. More formally, given a differentiable function $f(x),$ the gradient descent algorithms helps us compute $x^*$ such that $f'(x^*) = 0$ and $x^*$ is a minimum of $f(x).$ A function can have many local minima $x_{1}^{*}, x_{2}^{*}, \\ldots, x_{k}^{*},$ the gradient descent algorithm will converge to one of them depending on the its starting position and learning rate (discussed below). \n",
+ "\n",
+ "### The name \"Gradient Descent\" hints at how this algorithm works. The algorithms requires 1) knowing the $\\textbf{gradient}$ (partial derivatives) of the function and 2) using the gradient to determine the direction of steepest $\\textbf{descent}.$ The idea is that we will begin somewhere on the function, for example $f(x_{1})$, and then climb down the function as quickly as possible towards the first valley (local minimum) where $f'(x^*) = 0.$ The gradient descent algorithm essentially describes the sequence of steps to take to go from $x_{1}$ to a local minimum $x^*.$\n",
+ "\n",
+ "### Gradient descent (or a variation) is very commonly used to train machine learning models by minimizing some objective function. Many of the objective functions in machine learning are hard to minimize analytically, but we can approximate the minimum using gradient descent. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "8QfdtIOD5bNp"
+ },
+ "source": [
+ "## Algorithm intuition \n",
+ "\n",
+ "### Suppose we have a single variable function $f(x)$ that has a single global minimum (for example a parabola that opens upwards) at $x^*.$ Our goal is to approximate $x^*$ through an iterative algorithm. The first step is to pick a starting point (initial value) for the algorithm, $x_{1}.$ We will randomly guess $x_{1}$ and note that either $x_{1} < x^*$, or $x_{1} > x^*$ (we can get really lucky and have $x_{1} = x^*,$ but this is very unlikely). Since $x^*$ is the global minimum, we know that $f(x^*) < f(x_{1}),$ that is our starting point is above the minimum. Starting at $x_{1}$ we want to take a sequence of steps to get down to $x^*.$ The gradient descent algorithm characterizes the set of steps to take to get from $x_{1}$ down to $x^*.$\n",
+ "\n",
+ "### Without loss of generality assume our starting position $x_{1} < x^*,$ and let us discuss how to get down towards $x^*.$ Recall that we can compute the gradient of $f(x)$ since we assume the function is differentiable. Suppose we find $f'(x_{1}) < 0,$ that indicates that if we take a step right to $x_{2} > x_{1}$ then we will move down the function since $f(x_{2}) < f(x_{1}).$ This is exactly what we want (moving down the function), so we want to take a step to the right of $x_{1}.$ But how large of a step should we take? Well it makes sense to say the step size will depend on the steepness of the descent. The steeper the descent at $x_{1}$, the larger the step size should be as it indicates we have a long way to go before getting to the minimum. More formally the step size will be proportional to the gradient at $x_{1}.$\n",
+ "\n",
+ "### Once we get from $x_{1}$ to $x_{2}$, we repeat the same logic as above. Suppose $f'(x_2) < 0$ again, so we need to take a step towards $x_{3} > x_{2}$ to further go down the function. Again our step size will be proportional to $f'(x_2).$ Repeating this process will result in a sequence of steps $x_{1}, x_{2}, \\ldots, x_{T}.$ For large values of $T$ we expect $x_{T} \\approx x^*.$ The diagram below more formally describes the intuition behind gradient descent."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "2buGN5YadfFV"
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "UJ-LpPwR5bNr"
+ },
+ "source": [
+ "### The diagram above formally shows a single step of the gradient descent algorithm from $x_{1}$ to $x_{2}$ To determine $x_{2}$ we take a step to the right of $x_{1}$ that is proportional to $f'(x_{1}).$ Mathematically speaking, the sign of $f'(x_{1})$ indicates the direction of the steepest ascent at $x_{1}$ (magnitude of $f'(x_{1})$ is measure of steepness), but since we want to descend (its called gradient $\\textbf{descent}$) we use $-f'(x_{1}).$ Gradient descent relies on a parameter $\\lambda$ called the learning rate, let us talk about this more. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "vbKscXZL5bNr"
+ },
+ "source": [
+ "### Thinking about the learning rate \n",
+ "\n",
+ "### The learning rate $\\lambda$ and the steepest descent $-f'(x_{1})$ together determine the step size towards the minimum. Hence the learning rate determines the size of the steps. If $\\lambda$ is large then we will take large steps down towards to the minimum. Similarly if $\\lambda$ is small it will take longer to converge towards the minimum as the step size is smaller. Does this mean we should pick a really large $\\lambda$ to coverge fast towards $x^*?$ No, this is not a good idea. $\\lambda$ too large or too small can cause covergence problems as illustrated by the diagram below."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "y4DwrV3gd21v"
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "Fe_mT9Yc5bNr"
+ },
+ "source": [
+ "### Note that $J(w)$ is the function that we want to minimize in the above diagram. On the left figure $\\lambda$ is very large which leads to taking very big steps. These big steps essentially have trouble locating the minimum because they are jumping over it. On the right figure $\\lambda$ is very small leading to tiny steps towards the minimum. The algorithm finds a minimum, but its only a local minimum (global minimum is ideal). For the right figure imagine the step size was a bit larger, then the algorithm could jump over the local minimum and possiblly converge into the global minimum. \n",
+ "\n",
+ "### So how you do pick the best $\\lambda$? This is often done using \"cross validation\" which will be discussed later on."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "sSDFRS9Y5bNr"
+ },
+ "source": [
+ "## Gradient descent algorithm \n",
+ "\n",
+ "### Single variable\n",
+ "\n",
+ "### Suppose we have a single variable and differentiable function $f(x).$ Given a initial value $x_{1}$ the gradient descent describes the steps required to coverge towards a local minimum $x^*$ such that $f'(x^*) = 0.$ In the above section we determined that $x_{2} = x_{1} - \\lambda f'(x_{1}),$ where $\\lambda$ is the learning rate parameter. This formula can be generalized to $$x_{t+1} = x_{t} - \\lambda f'(x_{t}),$$ for iteration $t.$ Given initial value $x_{1}$ and large number of iterations $T,$ this algorithm will generate $x_{1}, x_{2}, \\ldots, x_{T},$ where $x_{T} \\approx x^*.$ That is $x_{t+1}$ converges towards $x^*$ as $t$ gets very large. Notice that at convergence $f'(x_{t}) \\approx 0$ and hence $|x_{t+1} - x_{t}| \\approx 0.$ Therefore a common stopping criteria for gradient descent is to iterate until $|x_{t+1} - x_{t}|$ is a very small number. For example we can keep iterating gradient descent until $|x_{t+1} - x_{t}| < 0.001.$\n",
+ "\n",
+ "### Multiple variables\n",
+ "### Consider a multiple variable and differentiable function $f(x_{1},x_{2},\\ldots, x_{n}).$ Our goal is to apply gradient descent and find a minimum $(x_{1}^{*}, x_{2}^{*}, \\ldots, x_{n}^{*}).$ This function has partial derivatives stored in the gradient vector $(\\frac{df(x)}{dx_{1}}, \\ldots, \\frac{df(x)}{dx_{n}}).$ The direction of the gradient vector indicates direction of steepest ascent, and the length of the gradient vector is a mesuare of the steepness. We can easily generalize the gradient descent to multiple variables as follows:\n",
+ "\n",
+ "\n",
+ "$$\n",
+ "\\begin{bmatrix}\n",
+ " x_{1}^{t+1} \\\\ \n",
+ " \\vdots \\\\\n",
+ " x_{n}^{t+1}\n",
+ "\\end{bmatrix}\n",
+ "=\n",
+ "\\begin{bmatrix}\n",
+ " x_{1}^{t} \\\\ \n",
+ " \\vdots \\\\\n",
+ " x_{n}^{t}\n",
+ "\\end{bmatrix}\n",
+ "-\n",
+ "\\lambda\n",
+ "\\begin{bmatrix}\n",
+ " \\frac{df(x_{1})}{dx_{1,t}} \\\\ \n",
+ " \\vdots \\\\\n",
+ " \\frac{df(x_{n})}{dx_{n,t}} \\\\ \n",
+ "\\end{bmatrix},\n",
+ "$$\n",
+ "### where $t$ is the gradient descent itteration. Now the stopping criteria can depend on the euclidean distance between the now and previous itteration, that is stop if $\\sqrt{(x_{1}^{t+1} - x_{1}^{t})^2 + \\ldots + (x_{n}^{t+1} - x_{n}^{t})^2} < 0.001.$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "UOFaRc_l5bNr"
+ },
+ "source": [
+ "## Example: Minimizing single variable function\n",
+ "\n",
+ "### Consider the following single variable function $$f(x) = 0.1x^2 + sin(0.1x^2)$$ and suppose we find its minimum using gradient descent. Gradient descent requires us to compute the first derivative which is $$f'(x) = 0.2x + 0.2xcos(0.1x^2).$$ The plot for f(x) is shown below."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "CP6wYY7celwj"
+ },
+ "source": [
+ "# Matrix computations\n",
+ "from numpy import *\n",
+ "\n",
+ "# Plotting\n",
+ "from matplotlib.pyplot import *\n",
+ "\n",
+ "# Change size of figures\n",
+ "fig_size = [9,7]\n",
+ "rcParams[\"figure.figsize\"] = fig_size"
+ ],
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "W-gSocTW5bNs",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 458
+ },
+ "outputId": "b79a3def-4fad-408d-a604-280ef46e6cec"
+ },
+ "source": [
+ "# Define function f(x)\n",
+ "def f(x):\n",
+ " \n",
+ " # f(x) = 0.1x^2 + sin(0.1x^2)\n",
+ " return 0.1*x**2 + sin(0.1*x**2)\n",
+ "\n",
+ "# Plot function on given range\n",
+ "\n",
+ "# Second arguments allows for seperate points to be ploted on f(x)\n",
+ "def plotf(x, xdots, label):\n",
+ "\n",
+ " # Compute y-values\n",
+ " y = f(x)\n",
+ "\n",
+ " # Plot (x, f(x))\n",
+ " plot(x,y)\n",
+ " xlabel(\"x\")\n",
+ " ylabel(\"f(x)\")\n",
+ " title(label)\n",
+ " \n",
+ " # Plot points on f(x)\n",
+ " plot(xdots, f(xdots), 'bo')\n",
+ " show()\n",
+ " \n",
+ "# Plot f(x) from [-10,10]\n",
+ "x = arange(-10, 10, 0.1)\n",
+ "plotf(x, np.array([]), \"Single Variable Function\")"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "tags": [],
+ "needs_background": "light"
+ }
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "QMkG5tTU5bNs"
+ },
+ "source": [
+ "### Notice that f(x) has a global minimum at x = 0, but there are also seem to be two local minima near -5.5 and 5.5. Ideally we want to be able to start anywhere from [-10,10] and use gradient descent to go down towards the minimum of 0. We will see that finding the global minimum depends on initial starting point and learning rate. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "gZ0tTKsS5bNs"
+ },
+ "source": [
+ "# Derivative of f(x) is f'(x) (denoted by df below)\n",
+ "# f'(x) = 0.2x + 0.2xcos(0.1x^2)\n",
+ "def derivative(x):\n",
+ " return 0.2*x + 0.2*x*cos(0.1*x**2)"
+ ],
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "MyE6oBn95bNs"
+ },
+ "source": [
+ "### Now that we have defined $f(x)$ and $f'(x)$, let us run gradient descent for different initial values and learning parameters and try to compute the global minimum. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "D05eR7HO5bNs"
+ },
+ "source": [
+ "# Gradient Descent \n",
+ "def grad_descent(derivative,x_prev,learning_rate):\n",
+ "\n",
+ " # Deciding when to stop the algorithm\n",
+ " epsilon = 0.001\n",
+ "\n",
+ " # Iteration number\n",
+ " grad_iter = 1\n",
+ "\n",
+ " # Gradient descent update step\n",
+ " x_next = x_prev - learning_rate*derivative(x_prev)\n",
+ "\n",
+ " # Update the sequence where we store all the x_next\n",
+ " sequence = np.array([])\n",
+ " sequence = np.append(sequence,x_next)\n",
+ "\n",
+ " # Start my iteration \n",
+ " while abs(x_next - x_prev) > epsilon :\n",
+ "\n",
+ " # Setting x_prev to x_next\n",
+ " x_prev = x_next\n",
+ "\n",
+ " # Updating x_next \n",
+ " x_next = x_prev - learning_rate*derivative(x_prev)\n",
+ "\n",
+ " # Update sequence\n",
+ " sequence = np.append(sequence,x_next)\n",
+ "\n",
+ " # Update iteration\n",
+ " grad_iter = grad_iter + 1\n",
+ "\n",
+ "\n",
+ " return x_next,sequence,grad_iter"
+ ],
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "wAKOajaY5bNs",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 458
+ },
+ "outputId": "484804f9-be13-41c0-84ae-3df2a96fec4e"
+ },
+ "source": [
+ "# Output vector (min x-value, (x_1,..,x_T)) from gradient descent\n",
+ "\n",
+ "grad_output = grad_descent(derivative,5,1)\n",
+ "plotf(x,grad_output[1],\"Gradient Descent with alpha =1 and start point = 8\")"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "tags": [],
+ "needs_background": "light"
+ }
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "NVHYYscYcYQq",
+ "outputId": "d56ca718-f4a7-43d0-e696-2da7c9a64eab"
+ },
+ "source": [
+ "grad_output[1]"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ "array([4.81090413e+00, 4.50012309e+00, 3.99507105e+00, 3.21624014e+00,\n",
+ " 2.24427660e+00, 1.40230777e+00, 8.46789923e-01, 5.08509157e-01,\n",
+ " 3.05139493e-01, 1.83086341e-01, 1.09852011e-01, 6.59112224e-02,\n",
+ " 3.95467347e-02, 2.37280409e-02, 1.42368245e-02, 8.54209473e-03,\n",
+ " 5.12525684e-03, 3.07515410e-03, 1.84509246e-03, 1.10705548e-03])"
+ ]
+ },
+ "metadata": {
+ "tags": []
+ },
+ "execution_count": 28
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "9inbJKVjQAgd",
+ "outputId": "16ca7452-f3d4-404a-90c9-7b9c0da8f44c"
+ },
+ "source": [
+ "grad_output[2]"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ "20"
+ ]
+ },
+ "metadata": {
+ "tags": []
+ },
+ "execution_count": 33
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "6lN2-cxr5bNs"
+ },
+ "source": [
+ "## Using a small learning rate\n",
+ "\n",
+ "### The example below uses a smaller than ideal learning rate of $\\lambda = 0.1.$ Not only does this increase the number of gradient descent itterations to 105, but the algorithm coverges to one of the local minima. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "4ARHSuT85bNs",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 458
+ },
+ "outputId": "b0942bf3-5fe4-4503-ef1b-8f933e9f89cc"
+ },
+ "source": [
+ "# Initial value x1 = -8 and learn rate lambda = 1\n",
+ "grad_output = grad_descent(derivative,-5,0.1)\n",
+ "plotf(x,grad_output[1],\"Gradient Descent with lambda =0.1 and start point = -8\")"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "tags": [],
+ "needs_background": "light"
+ }
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "4EVrGpnXdG4e",
+ "outputId": "1110f3e2-5520-477c-9f5c-d7e5d202ba77"
+ },
+ "source": [
+ "grad_output[2]"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ "155"
+ ]
+ },
+ "metadata": {
+ "tags": []
+ },
+ "execution_count": 31
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "7Iiu6dAQ5bNs"
+ },
+ "source": [
+ "## Small learning rate but starting close to global minimum\n",
+ "\n",
+ "### The example below uses a small learning rate (for this context) of $\\lambda = 0.1,$ but starts the algoirthm at $x_{1} = -5.$ The key point is that the initial value is now slight beyond the local minimum. Hence even with a small learning rate we are able to eventually converge to the global minimum."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "3WKgyNeT5bNt",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 458
+ },
+ "outputId": "0d0eb7ac-dd6b-4b03-cb12-d97ad31722e0"
+ },
+ "source": [
+ "# Initial value x1 = -5 and learn rate lambda = 10\n",
+ "\n",
+ "grad_output = grad_descent(derivative,-5,1)\n",
+ "plotf(x,grad_output[1],\"Gradient Descent with lambda = 10 and start point = -5\")"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "tags": [],
+ "needs_background": "light"
+ }
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "g4tDyDvEdh4_",
+ "outputId": "6744fd43-d5ef-4a6b-a0a4-3a8679e88623"
+ },
+ "source": [
+ "grad_output[1]"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ "array([-3.01143616, 6.72279107, -4.14655271, 2.91878012, -6.76300996,\n",
+ " 4.89485449, 2.29724203, -6.26665275, -2.59482101, 6.65188675,\n",
+ " -2.87787679, 6.76986017, -5.02420532, -3.16954651, 6.56998637,\n",
+ " -1.50249925, 4.43125016, -1.03887977, 3.10454992, -6.64612123,\n",
+ " 2.77776915, -6.75995586, 4.83735732, 1.89203735, -5.43622563,\n",
+ " -5.24801587, -4.47009986, 0.7644714 , -2.29080396, 6.25588804,\n",
+ " 2.7088297 , -6.73226045, 4.32097251, -1.7977997 , 5.20722358,\n",
+ " 4.25882695, -2.20964135, 6.11255034, 4.0134673 , -3.69251039,\n",
+ " 5.21272267, 4.28807589, -2.01738673, 5.7225938 , 5.6211889 ,\n",
+ " 5.6193303 , 5.61787471, 5.61670025, 5.61573056])"
+ ]
+ },
+ "metadata": {
+ "tags": []
+ },
+ "execution_count": 37
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "UaxhaWkK5bNt"
+ },
+ "source": [
+ "## Initial value and learning rate are important\n",
+ "\n",
+ "### From the above exercises of changing the initial value and learning rate we can conclude that gradient descent is not guaranteed to converge to the global minimum. Having a really low learning rate can make convergence slower (more iterations before finding minimum) and make it more likely to get stuck at local minima. A very high learning rate may be even more problematic as gradient descent may never converge (try $\\lambda$ = 6 in the code). The initial value is also important for finding the global minimum. If we start close to the global minimum, we are more likely to find it in the above example even with a smaller than ideal learning rate.\n",
+ "\n",
+ "### The diagram below shows even with multiple variables different initial values can lead to different local minima from gradient descent."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "IT7IiypuhnfS"
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "ToQ5vmXp5bNt"
+ },
+ "source": [
+ "## Example: Minimizing multiple variable function\n",
+ "\n",
+ "### Let us consider the following straight forward bivariate function $$f(x,y) = x^2 + y^2 + 1.$$ Since this a function of two variables, we have have the following partial derivatives $$\\frac{df(x)}{dx} = f_{x} = 2x \\text{ and } \\frac{df(y)}{dy} = f_{y} = 2y.$$ Note that its easy to argue that the global minimum of $f(x,y)$ is (0,0) since $f(0,0) = 1$ and $f(x,y) \\ge 1.$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "sQZ-w8Be5bNt",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 418
+ },
+ "outputId": "cc21dfb8-1656-4505-d8a4-b33339659eae"
+ },
+ "source": [
+ "# Plotting in 3D\n",
+ "from mpl_toolkits.mplot3d import Axes3D\n",
+ "from matplotlib import cm\n",
+ "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+ "\n",
+ "# f(x,y) = x^2 + y^2 + 1\n",
+ "def f(x,y):\n",
+ " return x**2 + y**2 + 1\n",
+ "\n",
+ "# (X,Y) grid on [-5,5]\n",
+ "y = arange(-5, 5, 0.25)\n",
+ "y = arange(-5, 5, 0.25)\n",
+ "X, Y = meshgrid(x, y)\n",
+ "\n",
+ "\n",
+ "# z = x^2 + y^2\n",
+ "Z = f(X,Y)\n",
+ "\n",
+ "# Plot (X,Y) in 3D\n",
+ "fig = figure(1)\n",
+ "ax = fig.gca(projection='3d')\n",
+ "surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.RdBu,linewidth=0, antialiased=False)\n",
+ "\n",
+ "ax.zaxis.set_major_locator(LinearLocator(10))\n",
+ "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
+ "fig.colorbar(surf, shrink = 0.7, aspect=5)\n",
+ "show()"
+ ],
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "tags": [],
+ "needs_background": "light"
+ }
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "VpjQBORX5bNt"
+ },
+ "source": [
+ "## Finding global minimum using gradient descent\n",
+ "\n",
+ "### For this example the gradient descent algorithm is simplified to\n",
+ "\n",
+ "$$\n",
+ "\\begin{bmatrix}\n",
+ " x^{t+1} \\\\ \n",
+ " y^{t+1}\n",
+ "\\end{bmatrix}\n",
+ "=\n",
+ "\\begin{bmatrix}\n",
+ " x^{t} \\\\ \n",
+ " y^{t}\n",
+ "\\end{bmatrix}\n",
+ "-\n",
+ "\\lambda\n",
+ "\\begin{bmatrix}\n",
+ " 2x^{t} \\\\ \n",
+ " 2y^{t} \\\\ \n",
+ "\\end{bmatrix},\n",
+ "$$\n",
+ "\n",
+ "### where $t$ is the gradient descent iteration. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "rtT6_Mdg5bNu"
+ },
+ "source": [
+ "# Conclusion\n",
+ "\n",
+ "### Gradient descent is a first order (requires first derivative) optimization algorithm used to minimize a given objective function. The algorithm depends on the initial value and the learning rate. The idea behind gradient descent is that it takes a seqeuence of steps to go from the starting position to a local minimum. An initial value that is somewhat close to the global minimum is ideal. Too small a learning rate makes it more likely for the algorithm to get stuck at a local minimum. Whereas too high a learning rate makes it more likely that the algorithm will skip over the global minimum. As we discussed in this notebook, the gradient descent can be applied to any first differentiable function (single or multiple variabe) to approximate the minimums (can be local minimums) even if analytical ($f'(x) = 0$ solve for x) solutions are difficult."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "yE6Tc3m7EMSO"
+ },
+ "source": [
+ ""
+ ],
+ "execution_count": null,
+ "outputs": []
+ }
+ ]
+}
\ No newline at end of file
From 830590ccac4b4e7574808939c73a14d2f507da71 Mon Sep 17 00:00:00 2001
From: Rajesh1505 <87649352+Rajesh1505@users.noreply.github.com>
Date: Tue, 7 Sep 2021 12:27:06 +0530
Subject: [PATCH 2/2] Delete Copy_of_Guided_Project_Gradient_Descent.ipynb
---
Copy_of_Guided_Project_Gradient_Descent.ipynb | 712 ------------------
1 file changed, 712 deletions(-)
delete mode 100644 Copy_of_Guided_Project_Gradient_Descent.ipynb
diff --git a/Copy_of_Guided_Project_Gradient_Descent.ipynb b/Copy_of_Guided_Project_Gradient_Descent.ipynb
deleted file mode 100644
index 89dc2ca..0000000
--- a/Copy_of_Guided_Project_Gradient_Descent.ipynb
+++ /dev/null
@@ -1,712 +0,0 @@
-{
- "nbformat": 4,
- "nbformat_minor": 0,
- "metadata": {
- "kernelspec": {
- "display_name": "Python 2",
- "language": "python",
- "name": "python2"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 2
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython2",
- "version": "2.7.12"
- },
- "colab": {
- "name": "Copy of Guided Project - Gradient Descent.ipynb",
- "provenance": [],
- "collapsed_sections": []
- }
- },
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "_wfP6xtQ5bNo"
- },
- "source": [
- "# Gradient Descent for Optimization "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "M88APx1X5bNp"
- },
- "source": [
- "## Introduction"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "hWZ1CROr5bNp"
- },
- "source": [
- "### Gradient descent is an algorithm used to the find local minima of any differentiable function. More formally, given a differentiable function $f(x),$ the gradient descent algorithms helps us compute $x^*$ such that $f'(x^*) = 0$ and $x^*$ is a minimum of $f(x).$ A function can have many local minima $x_{1}^{*}, x_{2}^{*}, \\ldots, x_{k}^{*},$ the gradient descent algorithm will converge to one of them depending on the its starting position and learning rate (discussed below). \n",
- "\n",
- "### The name \"Gradient Descent\" hints at how this algorithm works. The algorithms requires 1) knowing the $\\textbf{gradient}$ (partial derivatives) of the function and 2) using the gradient to determine the direction of steepest $\\textbf{descent}.$ The idea is that we will begin somewhere on the function, for example $f(x_{1})$, and then climb down the function as quickly as possible towards the first valley (local minimum) where $f'(x^*) = 0.$ The gradient descent algorithm essentially describes the sequence of steps to take to go from $x_{1}$ to a local minimum $x^*.$\n",
- "\n",
- "### Gradient descent (or a variation) is very commonly used to train machine learning models by minimizing some objective function. Many of the objective functions in machine learning are hard to minimize analytically, but we can approximate the minimum using gradient descent. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "8QfdtIOD5bNp"
- },
- "source": [
- "## Algorithm intuition \n",
- "\n",
- "### Suppose we have a single variable function $f(x)$ that has a single global minimum (for example a parabola that opens upwards) at $x^*.$ Our goal is to approximate $x^*$ through an iterative algorithm. The first step is to pick a starting point (initial value) for the algorithm, $x_{1}.$ We will randomly guess $x_{1}$ and note that either $x_{1} < x^*$, or $x_{1} > x^*$ (we can get really lucky and have $x_{1} = x^*,$ but this is very unlikely). Since $x^*$ is the global minimum, we know that $f(x^*) < f(x_{1}),$ that is our starting point is above the minimum. Starting at $x_{1}$ we want to take a sequence of steps to get down to $x^*.$ The gradient descent algorithm characterizes the set of steps to take to get from $x_{1}$ down to $x^*.$\n",
- "\n",
- "### Without loss of generality assume our starting position $x_{1} < x^*,$ and let us discuss how to get down towards $x^*.$ Recall that we can compute the gradient of $f(x)$ since we assume the function is differentiable. Suppose we find $f'(x_{1}) < 0,$ that indicates that if we take a step right to $x_{2} > x_{1}$ then we will move down the function since $f(x_{2}) < f(x_{1}).$ This is exactly what we want (moving down the function), so we want to take a step to the right of $x_{1}.$ But how large of a step should we take? Well it makes sense to say the step size will depend on the steepness of the descent. The steeper the descent at $x_{1}$, the larger the step size should be as it indicates we have a long way to go before getting to the minimum. More formally the step size will be proportional to the gradient at $x_{1}.$\n",
- "\n",
- "### Once we get from $x_{1}$ to $x_{2}$, we repeat the same logic as above. Suppose $f'(x_2) < 0$ again, so we need to take a step towards $x_{3} > x_{2}$ to further go down the function. Again our step size will be proportional to $f'(x_2).$ Repeating this process will result in a sequence of steps $x_{1}, x_{2}, \\ldots, x_{T}.$ For large values of $T$ we expect $x_{T} \\approx x^*.$ The diagram below more formally describes the intuition behind gradient descent."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "2buGN5YadfFV"
- },
- "source": [
- ""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "UJ-LpPwR5bNr"
- },
- "source": [
- "### The diagram above formally shows a single step of the gradient descent algorithm from $x_{1}$ to $x_{2}$ To determine $x_{2}$ we take a step to the right of $x_{1}$ that is proportional to $f'(x_{1}).$ Mathematically speaking, the sign of $f'(x_{1})$ indicates the direction of the steepest ascent at $x_{1}$ (magnitude of $f'(x_{1})$ is measure of steepness), but since we want to descend (its called gradient $\\textbf{descent}$) we use $-f'(x_{1}).$ Gradient descent relies on a parameter $\\lambda$ called the learning rate, let us talk about this more. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "vbKscXZL5bNr"
- },
- "source": [
- "### Thinking about the learning rate \n",
- "\n",
- "### The learning rate $\\lambda$ and the steepest descent $-f'(x_{1})$ together determine the step size towards the minimum. Hence the learning rate determines the size of the steps. If $\\lambda$ is large then we will take large steps down towards to the minimum. Similarly if $\\lambda$ is small it will take longer to converge towards the minimum as the step size is smaller. Does this mean we should pick a really large $\\lambda$ to coverge fast towards $x^*?$ No, this is not a good idea. $\\lambda$ too large or too small can cause covergence problems as illustrated by the diagram below."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "y4DwrV3gd21v"
- },
- "source": [
- ""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "Fe_mT9Yc5bNr"
- },
- "source": [
- "### Note that $J(w)$ is the function that we want to minimize in the above diagram. On the left figure $\\lambda$ is very large which leads to taking very big steps. These big steps essentially have trouble locating the minimum because they are jumping over it. On the right figure $\\lambda$ is very small leading to tiny steps towards the minimum. The algorithm finds a minimum, but its only a local minimum (global minimum is ideal). For the right figure imagine the step size was a bit larger, then the algorithm could jump over the local minimum and possiblly converge into the global minimum. \n",
- "\n",
- "### So how you do pick the best $\\lambda$? This is often done using \"cross validation\" which will be discussed later on."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "sSDFRS9Y5bNr"
- },
- "source": [
- "## Gradient descent algorithm \n",
- "\n",
- "### Single variable\n",
- "\n",
- "### Suppose we have a single variable and differentiable function $f(x).$ Given a initial value $x_{1}$ the gradient descent describes the steps required to coverge towards a local minimum $x^*$ such that $f'(x^*) = 0.$ In the above section we determined that $x_{2} = x_{1} - \\lambda f'(x_{1}),$ where $\\lambda$ is the learning rate parameter. This formula can be generalized to $$x_{t+1} = x_{t} - \\lambda f'(x_{t}),$$ for iteration $t.$ Given initial value $x_{1}$ and large number of iterations $T,$ this algorithm will generate $x_{1}, x_{2}, \\ldots, x_{T},$ where $x_{T} \\approx x^*.$ That is $x_{t+1}$ converges towards $x^*$ as $t$ gets very large. Notice that at convergence $f'(x_{t}) \\approx 0$ and hence $|x_{t+1} - x_{t}| \\approx 0.$ Therefore a common stopping criteria for gradient descent is to iterate until $|x_{t+1} - x_{t}|$ is a very small number. For example we can keep iterating gradient descent until $|x_{t+1} - x_{t}| < 0.001.$\n",
- "\n",
- "### Multiple variables\n",
- "### Consider a multiple variable and differentiable function $f(x_{1},x_{2},\\ldots, x_{n}).$ Our goal is to apply gradient descent and find a minimum $(x_{1}^{*}, x_{2}^{*}, \\ldots, x_{n}^{*}).$ This function has partial derivatives stored in the gradient vector $(\\frac{df(x)}{dx_{1}}, \\ldots, \\frac{df(x)}{dx_{n}}).$ The direction of the gradient vector indicates direction of steepest ascent, and the length of the gradient vector is a mesuare of the steepness. We can easily generalize the gradient descent to multiple variables as follows:\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{bmatrix}\n",
- " x_{1}^{t+1} \\\\ \n",
- " \\vdots \\\\\n",
- " x_{n}^{t+1}\n",
- "\\end{bmatrix}\n",
- "=\n",
- "\\begin{bmatrix}\n",
- " x_{1}^{t} \\\\ \n",
- " \\vdots \\\\\n",
- " x_{n}^{t}\n",
- "\\end{bmatrix}\n",
- "-\n",
- "\\lambda\n",
- "\\begin{bmatrix}\n",
- " \\frac{df(x_{1})}{dx_{1,t}} \\\\ \n",
- " \\vdots \\\\\n",
- " \\frac{df(x_{n})}{dx_{n,t}} \\\\ \n",
- "\\end{bmatrix},\n",
- "$$\n",
- "### where $t$ is the gradient descent itteration. Now the stopping criteria can depend on the euclidean distance between the now and previous itteration, that is stop if $\\sqrt{(x_{1}^{t+1} - x_{1}^{t})^2 + \\ldots + (x_{n}^{t+1} - x_{n}^{t})^2} < 0.001.$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "UOFaRc_l5bNr"
- },
- "source": [
- "## Example: Minimizing single variable function\n",
- "\n",
- "### Consider the following single variable function $$f(x) = 0.1x^2 + sin(0.1x^2)$$ and suppose we find its minimum using gradient descent. Gradient descent requires us to compute the first derivative which is $$f'(x) = 0.2x + 0.2xcos(0.1x^2).$$ The plot for f(x) is shown below."
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "CP6wYY7celwj"
- },
- "source": [
- "# Matrix computations\n",
- "from numpy import *\n",
- "\n",
- "# Plotting\n",
- "from matplotlib.pyplot import *\n",
- "\n",
- "# Change size of figures\n",
- "fig_size = [9,7]\n",
- "rcParams[\"figure.figsize\"] = fig_size"
- ],
- "execution_count": null,
- "outputs": []
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "W-gSocTW5bNs",
- "colab": {
- "base_uri": "https://localhost:8080/",
- "height": 458
- },
- "outputId": "b79a3def-4fad-408d-a604-280ef46e6cec"
- },
- "source": [
- "# Define function f(x)\n",
- "def f(x):\n",
- " \n",
- " # f(x) = 0.1x^2 + sin(0.1x^2)\n",
- " return 0.1*x**2 + sin(0.1*x**2)\n",
- "\n",
- "# Plot function on given range\n",
- "\n",
- "# Second arguments allows for seperate points to be ploted on f(x)\n",
- "def plotf(x, xdots, label):\n",
- "\n",
- " # Compute y-values\n",
- " y = f(x)\n",
- "\n",
- " # Plot (x, f(x))\n",
- " plot(x,y)\n",
- " xlabel(\"x\")\n",
- " ylabel(\"f(x)\")\n",
- " title(label)\n",
- " \n",
- " # Plot points on f(x)\n",
- " plot(xdots, f(xdots), 'bo')\n",
- " show()\n",
- " \n",
- "# Plot f(x) from [-10,10]\n",
- "x = arange(-10, 10, 0.1)\n",
- "plotf(x, np.array([]), \"Single Variable Function\")"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "display_data",
- "data": {
- "image/png": "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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {
- "tags": [],
- "needs_background": "light"
- }
- }
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "QMkG5tTU5bNs"
- },
- "source": [
- "### Notice that f(x) has a global minimum at x = 0, but there are also seem to be two local minima near -5.5 and 5.5. Ideally we want to be able to start anywhere from [-10,10] and use gradient descent to go down towards the minimum of 0. We will see that finding the global minimum depends on initial starting point and learning rate. "
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "gZ0tTKsS5bNs"
- },
- "source": [
- "# Derivative of f(x) is f'(x) (denoted by df below)\n",
- "# f'(x) = 0.2x + 0.2xcos(0.1x^2)\n",
- "def derivative(x):\n",
- " return 0.2*x + 0.2*x*cos(0.1*x**2)"
- ],
- "execution_count": null,
- "outputs": []
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "MyE6oBn95bNs"
- },
- "source": [
- "### Now that we have defined $f(x)$ and $f'(x)$, let us run gradient descent for different initial values and learning parameters and try to compute the global minimum. "
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "D05eR7HO5bNs"
- },
- "source": [
- "# Gradient Descent \n",
- "def grad_descent(derivative,x_prev,learning_rate):\n",
- "\n",
- " # Deciding when to stop the algorithm\n",
- " epsilon = 0.001\n",
- "\n",
- " # Iteration number\n",
- " grad_iter = 1\n",
- "\n",
- " # Gradient descent update step\n",
- " x_next = x_prev - learning_rate*derivative(x_prev)\n",
- "\n",
- " # Update the sequence where we store all the x_next\n",
- " sequence = np.array([])\n",
- " sequence = np.append(sequence,x_next)\n",
- "\n",
- " # Start my iteration \n",
- " while abs(x_next - x_prev) > epsilon :\n",
- "\n",
- " # Setting x_prev to x_next\n",
- " x_prev = x_next\n",
- "\n",
- " # Updating x_next \n",
- " x_next = x_prev - learning_rate*derivative(x_prev)\n",
- "\n",
- " # Update sequence\n",
- " sequence = np.append(sequence,x_next)\n",
- "\n",
- " # Update iteration\n",
- " grad_iter = grad_iter + 1\n",
- "\n",
- "\n",
- " return x_next,sequence,grad_iter"
- ],
- "execution_count": null,
- "outputs": []
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "wAKOajaY5bNs",
- "colab": {
- "base_uri": "https://localhost:8080/",
- "height": 458
- },
- "outputId": "484804f9-be13-41c0-84ae-3df2a96fec4e"
- },
- "source": [
- "# Output vector (min x-value, (x_1,..,x_T)) from gradient descent\n",
- "\n",
- "grad_output = grad_descent(derivative,5,1)\n",
- "plotf(x,grad_output[1],\"Gradient Descent with alpha =1 and start point = 8\")"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "display_data",
- "data": {
- "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAG5CAYAAABcPzQJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi40LCBodHRwOi8vbWF0cGxvdGxpYi5vcmcv7US4rQAAIABJREFUeJzs3Xd81PX9B/DX+y57b0I2BAgrYQVQRAXcq1q3xdFhqdZfp6Mq/bXa1tbRX6sdVlHrjBP3rlpRARkJkIQdAtmE7D3v7vP74y4YIItwl8/37l7Px4MHSe5y39cll+R1n+/7vl9RSoGIiIhIF5PuAEREROTdWEaIiIhIK5YRIiIi0oplhIiIiLRiGSEiIiKtWEaIiIhIK5YRGlMiUiIiZzrevltEntSdydMN93UWke+KyFonbWvEt+XM7boDEblHRF7QncPZRCRFRNpExKw7C7kvlhE6TESuFpGNItIuIjWOt38sIuKK7Sml/qiUuvFEb0dE0kREiYjPENe5R0R6RaTV8W+viPxDRMaf6PZdxXGfJp3o7fT/Oo/ka+XJRGS8iLwjIlWOr0Oa7kzD6V/gT+A2nhGRPzgrU39KqTKlVIhSyjqCHC57/ImIv4g8JiKHRKRBRN4VkURnb4dcg2WEAAAiciuARwA8BCAewDgANwE4BYDfIJ/jbs+EXlFKhQKIAvBt2O9nnpELCTmdDcBHAC7THWSsuOHP6Wj9DMDJALIAJABoBPB3rYloxFhGCCISDuB3AH6slFqtlGpVdluVUsuVUt2O6z0jIv8SkQ9EpB3AUhG5QES2ikiLiJSLyD1H3fZ1IlIqIvUisvKoy45YthaRk0RkvYg0iUi+iCzpd9kaEfm9iKxzrGz8R0RiHBd/6fi/ybFcfPJQ91cp1auU2gHgKgC1AG7tt50LRWSbI8N6Ecnqd9mvRKTSsf09InKG4+Nmx66QYsdleSKS7Lhsqoh84nimtkdErux3e8+IyD9F5H3H520UkXTHZX33Kd9xn64a4PtWKiLzHG8vdzzjnOF4/wci8tYAX+dBv1Yi8mcRaRSRAyJy3mBfPxG5s9993Ski3x7iukpEfioi+0WkTkQeEhHTUdcZcLsi8j0R2eXYzn4R+dFg2xkppdQhpdSjADaP5PpD3Vdx7GYaIv8EEfnC8bmfAIgZcCP268aIyHuOx12DiHwlIiYReR5ACoB3Hd+vOxzXf01EqkWkWUS+7Pu+Oy47+uf0BwCWA7jDcRvvDpJh0O+VI8uvHY+5GhF5Tuy/N45Z7XDmz+pxmgDgY8f3uAvAKwBmDPM5ZBRKKf7z8n8AzgVgAeAzzPWeAdAM+2qJCUAAgCUAMh3vZwE4BOASx/WnA2gDcBoAfwB/cWznTMfl9wB4wfF2IoB6AOc7bussx/uxjsvXACgGMAVAoOP9+x2XpQFQQ+Xvv62jPv47ABsdb88BUANgIQAzgBsAlDiyZwAoB5DQb5vpjrdvB1DouI4AmAUgGkCw43O+B8DHcft1AKb3+3rWA1jguDwHwMv9sikAk4a4T88BuNXx9irH1+fmfpf9YoCv8zFfKwDfBdAL4IeO+30zgCoAMsh2r4D9macJ9kLXDmB8v9tae9R9+Bz21agUAHsB3DiS7QK4AEC642t6OoAOAHMHybQYQNMQ/xYfdX0fR7a0YR7zw93XofJ/Dftj3h/2n4FWDPAYdFz3TwAeA+Dr+Hdqv9spgeNnpt/1vw8g1HHbDwPYNszP6TMA/jDMfR3qe/V9APsATAQQAuANAM8P9JjCif+sfmeY72XKIJ+XDWCd4/sVBOBFAA+P9e9T/hvdP66MEGB/xlanlLL0fUC+WaHoFJHT+l33baXUOqWUTSnVpZRao5QqdLxfAOAl2P9wAMDlAN5TSn2p7Ksr/wv7MvlArgXwgVLqA8dtfQIgF/Zy0udppdRepVQngFcBzHbCfa+C/ZcvAKwA8LhSaqNSyqqUehZAN4CTAFhh/8U/XUR8lVIlSqlix+fdCODXSqk9yi5fKVUP4EIAJUqpp5VSFqXUVgCvw/4Hrs+bSqlNjq99znHepy/wzdf6VNj/oPW9f7rj8pEqVUo9oez7/Z8FMB72XXXHUEq9ppSqcnyfXgFQBHuhGswDSqkGpVQZ7H84rxnJdpVS7yulih1f0y8A/MdxPwfKtFYpFTHEv1ENyo7gvg6YX0RSAMwH8L9KqW6l1JcABlyRcOh1fG6qsq/cfaWUGvTEYUqpfyv7CmY37GVzVt9KhcMRP6fHcZcH+14tB/AXpdR+pVQbgLsAXC2Dz36M+mdVKfXiMN/LskE+tQj28l8JoAXANNifbJAbYBkhwP7sPKb/Lxal1CKlVITjsv6Pk/L+nygiC0XkcxGpFZFm2OdM+pZkE/pfXynV7ri9gaQCuMJRgJpEpAn2Z7v95zmq+73dAfsztBOVCKChX4Zbj8qQDPtqyD4AP4f9F3+NiLwsIgmOz0uG/ZngQPdp4VG3txz2WRVn3KcvAJwq9pkXM+y/9E8R+1BmOIBtx3Fbh3MopTocbw6YRUSul292ZTUBmIkhdkHgyMdMKeyPi2G3KyLnicgGx26LJtiL6VDbcboR3NfB8icAaHQ85vuUDrGph2BfefiPYzfJnUNkMovI/Y7dRy2wr5zgqFzlx37miAz2vUrAkflLYV9dGrCwwjU/q8P5J+xPGPpWJd8A8OEYbJecgGWEAPtycjeAi0dw3aOfrb0I4B0AyUqpcNiXmvtefXMQ9j/UAAARCYL9F8VAymFf9u3/DChYKXX/KDKNiGN/+EUAvuqX4b6jMgQppV4CDj9jWwx7yVAAHuj3eemD3Kcvjrq9EKXUzaPJezRHQeoA8BMAXyqlWmD/I7AC9l0lA61CndBpukUkFcATAP4HQLSjsG7HN9/zgST3ezsF9tWo4bbjD/sq0p8BjHNs54PBtiMipzpmEAb7N+CKyjAZRnNf+xwEECkiwf0+ljLYlR2rHLcqpSYC+BaAX4pjJgnHfs++A/vP6pmwl860vsj9b/LoTYwgMzD496oK9sd9/8sssO+WPR7D5hD7/NNQ38vBvo6zATzjWNnphn14dUG/eRUyMJYRglKqCcC9AB4VkctFJNQxsDYb9mcYQwkF0KCU6hKRBbD/ouyzGsCFIrJYRPxgXzId7DH3AoCLROQcxzO/ABFZIiJJI7gLtbDv/pk4gutCRHxEZBrsu5TiYd+vD9j/8NzkWO0REQkW+4BuqIhkiMgyxx/JLgCd+GaX05MAfi8ikx2flyUi0QDeAzBF7EO8vo5/8x3bHolDI7hPX8D+x7Jvl8yao94/2nF9rQYQDPsflFrAPmQK+2rBUG4XkUixD/X+DPbBwuH4wf4stxaAReyDoWcPdmXHbo2QIf71FU6ISIDjtgHA3/G+s+5rX55S2Hcz3isifiKyGPbiOyCxD05PEhGBfd7Dim8eX0c/DkJhf/JQD/tsxB9HEGkkjyVg8O/VSwB+Ifah3BDHNl9R/XbtjtCwjz+lVM4w38vBdtNsBnC9iISLiC+AHwOoUkrVHWdG0oBlhAAASqkHAfwSwB2w/+I6BOBxAL8CsH6IT/0xgN+JSCuA38C+q6DvNncAuAX21ZODsL/UrmKQ7ZfD/mzvbth/YZXDPhg67GPUsTx+H4B1juX0kwa56lUi0gb7L/t3YP9lPk8pVeW4nVzYhxH/4ci6D/YhRcD+x+t+2AdQqwHEwb7fHLCXmVdhn2loAfAUgEClVCvsf0Cvhv2ZZTXsqyl9fwiHcw+AZx336cpBrvMF7H+cvhzk/SMcx9dqQEqpnQD+D/bVtEOwDy+vG+bT3gaQB/tuo/dh//oMt51WAD+F/evaCHvJfed4sg6hE/bBagDY7Xh/oAyjua/9fQf2YegGAL+Ffah4MJMBfOrI9TWAR5VSnzsu+xOAXzu+X7c5bqcU9tmInQA2jCDLU7DPOzWJ41VWgxjse/VvAM/D/rg6AHsh/8kItnuEE338DeM2R64i2H+HnA/7S/jJDfRNaxMROZ2IKACTHbuUyMD4vSKduDJCREREWrGMEBERkVbcTUNERERacWWEiIiItDLUmTtjYmJUWlqa7hhERETkBHl5eXVKqdjhrmeoMpKWlobc3FzdMYiIiMgJRGSoIw8fxt00REREpBXLCBEREWnFMkJERERasYwQERGRViwjREREpBXLCBEREWnFMkJERERasYwQERGRViwjREREpBXLCBEREWnFMkJERERasYwQERGRViwjREREpBXLCBEREWnl8WWkvduCHVXNUErpjkJEREQD8NEdwNU+2l6NW1/Lx+S4EFwyJxGzkyOQFBmIiCA/+JoFPiYTfM0CEdEdlYiIyGVsNoVemw0Wq0KPxYbqli5UNHYi2N+MRekxWrN5fBlZNjUOf7hkJt7aWomHPt4z6PX8zCYkRAQgLSYYCyZE4ZLZiUiICBzDpERERCdOKYXNJY14r6AKuw624EBdBxrau2EbZAfB6VNitZcRMdLui+zsbJWbm+uy2z/U0oX9te0ob+xAS2cveq0KFqsNvTaF7l4rKho7UVzbht3VrRABlmbE4d5vzUByVJDLMhERETnLxzuqcd/7u1DW0IFAXzMyE8ORFhOE2FB/+JpN8DWb4GMS+JpNiA8PQGJEIJKjghAV7OeSPCKSp5TKHvZ63lRGRqq0vh1vbKnEk1/tBwCsvGA6rlmQzF05RERkSM0dvfjtO9vx1rYqTI0PxYrTJuKcGfEI9te7A2SkZcTjd9OMRmp0MH5x1hRckZ2EO1YX4O43C1HV1InbzsnQHY2IiOgIzR29uPqJDSg61IqfnzkZtyydBF+ze70+hWVkCEmRQXjhBwux8q1C/OPzfQj0M+OWpZN0xyIiIgIAtHVbcMPTm1Bc04anvjsfp0+J1R1pVFhGhmEyCf5wSSY6e6x46OM9iA3xx5Xzk3XHIiIiL2ezKdz0fB4KK5vxr+Vz3baIAF5wnBFnMJsEf75iFk6ZFI173t2BsvoO3ZGIiMjLPb2+BGv31eEPl8zE2TPidcc5ISwjI+RjNuHBy2fBLILbVufDNthrpIiIiFxsX00bHvxoN86cFoerPWC1nmXkOCRGBOI3F03HpgMN+Pe6A7rjEBGRF7JYbbj1tXwE+pnxx0szPeKVniwjx+nyeUlYmhGLhz8tQmN7j+44RETkZd7cWon88ibc+60ZiAsN0B3HKVhGjpOI4K7zp6G9x4LHv9yvOw4REXmRHosNj3xWhMzEcHxrVoLuOE7DMjIKU8aF4uJZCXhm/QHUtHbpjkNERF7i1dxyVDR24tazp3jE7pk+LCOj9PMzp6DXqvDo58W6oxARkRfo6rXi7/8twvy0SLd+Ge9AWEZGKS0mGFfMS8KLG8u4OkJERC73yuZyHGrpxq1nZ3jUqgjAMnJCfnR6OnqsNryyqVx3FCIi8mBKKTz7dQlmJ0fgpInRuuM4HcvICZgQE4xTJ8fgxU1lsFhtuuMQEZGHWl9cj/217bj+5FTdUVyCZeQEXXdSKg42d+HTXTW6oxARkYd6/utSRAb54vzM8bqjuATLyAlaNjUOCeEBeGFDqe4oRETkgQ42d+KTXYdw5fxkBPiadcdxCZaRE+RjNmH5SalYu68OxbVtuuMQEZGHeWljGWxK4dqFnrmLBmAZcYors5NhNglW51XojkJERB7EZlNYnVeB0ybHIjkqSHccl2EZcYLYUH+cMikG7+ZXQSmeQI+IiJwjr6wRVc1duGSO5xxtdSAsI07yrVkJqGjsxNbyJt1RiIjIQ7ybXwV/HxPOmh6vO4pLsYw4yTkzxsHPx4R3tlXpjkJERB7AYrXhg8KDOHPaOIT4++iO41IsI04SGuCLZRlxeL/wIKw27qohIqITs764HnVtPbjIg06INxiWESe6aFYCalu7sWF/ve4oRETk5t7Jr0Kovw+WZHjWeWgGwjLiRGdMi0Ownxnv5nNXDRERjV63xYqPt1fj7BnxHntskf5YRpwowNeMpVPj8OmuGti4q4aIiEZp4/4GtHZbcN5Mzx5c7cMy4mRnTItDXVs3CiqbdUchIiI39d/dNfD3MeGUSTG6o4wJlhEnWzIlDiYBPtt1SHcUIiJyQ0opfLrrEBZPikGgn+fvogFYRpwuMtgP2alRPHEeERGNyt5Dbaho7MQZ08bpjjJmWEZc4Ixpcdh1sAVVTZ26oxARkZv5bLd9ZX3Z1DjNScYOy4gLnDHN/gD6bDdXR4iI6Ph8tqsGMxPDEB8eoDvKmGEZcYH02BCkRgdxboSIiI5LfVs3tpQ14oyp3rOLBmAZcQkRwbKpcVhfXI+uXqvuOERE5Ca+LKqFUt+ssHsLlhEXOW1KLHosNuSWNOqOQkREbuKrojpEBvliZkK47ihjimXERRakRcHXLFi7r053FCIicgNKKazbV4dFk2JgMonuOGOKZcRFgv19MCclEmv31eqOQkREbqC4tg2HWrqx2EsOdNYfy4gLLZ4Ugx1VLWho79EdhYiIDG5tkX0lnWWEnOqUSTFQCvi6mGfxJSKioa3dV4+UqCAkRwXpjjLmWEZcaFZSOEL8fTg3QkREQ7JYbdiwv95rzkVzNJYRF/Ixm3DSxGisYxkhIqIh5Fc0oa3b4pW7aACWEZdbPCkaZQ0dKKvv0B2FiIgMam1RPUSAk9OjdUfRgmXExfqW3DYc4NwIERENbMP+ekyLD0NUsJ/uKFqwjLjYpLgQRAX7YdOBBt1RiIjIgHosNmwpa8TCiVG6o2jDMuJiIoL5aZEsI0RENKDCyiZ0W2xYOIFlhFxowQT73MjB5k7dUYiIyGA2Op6szk9jGSEX6mu7XB0hIqKjbTrQgElxIYgO8dcdRRuWkTEwbXwYQvx9WEaIiOgIVptCbkkjFnjxLhqAZWRMmE2CbM6NEBHRUXYdbEFbt8Wr50UAlpExs2BCFIpq2lDf1q07ChERGcQmzosAcHEZEZFfiMgOEdkuIi+JSIArt2dkfa13c0mj5iRERGQUmw40IDkqEAkRgbqjaOWyMiIiiQB+CiBbKTUTgBnA1a7antFlJkbA38fEXTVERAQAUEphc0mD16+KAK7fTeMDIFBEfAAEAahy8fYMy8/HhFlJEcgr48oIEREBJfUdqG/vQXYqy4jLyohSqhLAnwGUATgIoFkp9Z+jryciK0QkV0Rya2trXRXHEOamRmJnVTO6eq26oxARkWZbSu1PTuelRmpOop8rd9NEArgYwAQACQCCReTao6+nlFqllMpWSmXHxsa6Ko4hzE2JQK9VobCyWXcUIiLSbEtZI0L9fTA5LkR3FO1cuZvmTAAHlFK1SqleAG8AWOTC7RneXEf77WvDRETkvfJKGzE7JQImk+iOop0ry0gZgJNEJEhEBMAZAHa5cHuGFxPij9ToIGzh3AgRkVdr7erF3kOtmJvCXTSAa2dGNgJYDWALgELHtla5anvuYm5KJPJKm6CU0h2FiIg0yS9vhk19s2Lu7Vz6ahql1G+VUlOVUjOVUtcppbz+iF9zUyNR19aNikaeNI+IyFttKWuECDA7OUJ3FEPgEVjH2NwU+wMvj3MjREReK6+0EZPjQhAe6Ks7iiGwjIyxjHGhCPYzc26EiMhL2WwKW8sa+ZLeflhGxpiP2YRZyRFcGSEi8lL769rQ0mXBHA6vHsYyosHs5Ajsrm7lwc+IiLxQfrn9WFOcF/kGy4gGWUkRsNoUdlS16I5CRERjrLCyGYG+ZqTH8mBnfVhGNOhrwwUVTZqTEBHRWCusbMbMxDCYebCzw1hGNIgPD0BcqD8KKnhYeCIib2Kx2rCjqhkzE8N1RzEUlhFNspIikF/OlREiIm9SXNuOrl4bspJYRvpjGdFkVlI49te1o7mzV3cUIiIaI3275zO5MnIElhFNZjnmRrbzDL5ERF5je2Uzgv3MmBDD4dX+WEY06Vuiy+cQKxGR1yiobMaMhHAOrx6FZUSTiCA/pEYHoaCcKyNERN7AYrVhZ1ULMjkvcgyWEY2ykiK4MkJE5CWKatrQbeHw6kBYRjSalRSOg81dqGnt0h2FiIhcrNBxOAe+rPdYLCMa9Q2xclcNEZHnK6xsRoi/DyZEB+uOYjgsIxrNSAiDSXgkViIib2AfXg2DicOrx2AZ0SjIzwdTxoUin0diJSLyaL1WG3YdbOG8yCBYRjSb5RhiVUrpjkJERC6y91Areiw2zosMgmVEs6zkcDR19KK8oVN3FCIicpG+4dWspAjNSYyJZUSzWY4HJl/iS0TkuQormxEa4IPUqCDdUQyJZUSzjPhQ+PmYOMRKROTBCiubMTMhnMOrg2AZ0czXbML08WEcYiUi8lA9Fht2H2zl8OoQWEYMYHZyBLZXNsNq4xArEZGn2XuoFT1WDq8OhWXEALKSwtHRY8W+mjbdUYiIyMkKK/uGV1lGBsMyYgBZHGIlIvJYBRXNCAvwQQqHVwfFMmIAE2OCEeLvc/ilX0RE5Dm2VzYjMykcIhxeHQzLiAGYTIIZCWGHl/KIiMgzdFus2F3dgsxEHl9kKCwjBpGZGI5dB1tgsdp0RyEiIifZU92KXqtCJodXh8QyYhCZSeHotthQxCFWIiKPweHVkWEZMYi+l3xxVw0RkecorGhGeKAvkiIDdUcxNJYRg5gQzSFWIiJPU1jZjCwOrw6LZcQgTCbBdA6xEhF5jK5eK/ZUt/JgZyPAMmIgWRxiJSLyGHuqW2GxKWSxjAyLZcRAOMRKROQ5Chwr3ZkcXh0Wy4iBcIiViMhzFFY0ITLIF4kRHF4dDsuIgfQNsW5nGSEicnuFlS3ITIrg8OoIsIwYSN8QawFfUUNE5Na6eq3Ye6gVmYlhuqO4BZYRg+GRWImI3N+ugy2w2hQPAz9CLCMGk8UhViIit1fI4dXjwjJiMBxiJSJyf4UVzYgO9kNCeIDuKG6BZcRgOMRKROT+Ciubkckjr44Yy4jB8EisRETurbOnb3iVu2hGimXEgDITw7GzikOsRETuaOfBFtgUWEaOA8uIAWUmcoiViMhdFVY0AeDw6vFgGTGgvgcwd9UQEbmfwsoWxIT4Iz6Mw6sjxTJiQBxiJSJyX4WVTchMDOPw6nFgGTEgDrESEbmnjh4L9tW0ITOJBzs7HiwjBsUhViIi97Ozyj68msXh1ePCMmJQHGIlInI/PPLq6LCMGBSPxEpE5H4KK5oRF+qPcRxePS4sIwY1MSYYwX5mDrESEbmRgspmHl9kFFhGDMpkEsxIDOfKCBGRm2jvtqC4to27aEaBZcTAMhPDsesgh1iJiNzBjqoWKB55dVRYRgwsMzEcXb027KvlECsRkdEdHl5lGTluLCMG1jfEWlDBXTVEREZXWNGE+LAAxHF49bixjBgYh1iJiNxHYWXz4SeRdHxYRgyMQ6xERO6htasX++vakcXh1VFhGTE4DrESERkfh1dPDMuIwXGIlYjI+Pp2p3M3zeiwjBjc4SOxcoiViMiwCiqaMT48ALGh/rqjuCWWEYPrG2Ll3AgRkXFt55FXTwjLiMGZTIIZCRxiJSIyqhYOr54wlhE3kJnEIVYiIqPaUdkCgPMiJ4JlxA1wiJWIyLgKK5sA8JU0J8KlZUREIkRktYjsFpFdInKyK7fnqTjESkRkXAUVzUiMCER0CIdXR8vVKyOPAPhIKTUVwCwAu1y8PY/EI7ESERkXh1dPnMvKiIiEAzgNwFMAoJTqUUo1uWp7nqxviLWAZYSIyFCaO3tRUt+BTA6vnhBXroxMAFAL4GkR2SoiT4pI8NFXEpEVIpIrIrm1tbUujOPeZvJIrEREhrODZ+p1CleWER8AcwH8Syk1B0A7gDuPvpJSapVSKlsplR0bG+vCOO4tK4lDrERERlPAMuIUriwjFQAqlFIbHe+vhr2c0ChwiJWIyHgKK5uRFBmIyGA/3VHcmsvKiFKqGkC5iGQ4PnQGgJ2u2p6n4xArEZHxFFY082BnTuDqV9P8BECOiBQAmA3gjy7ensfikViJiIylqaMHZQ0dPNiZE/i48saVUtsAZLtyG95kZmI4XtxUCovVBh8zj1dHRKRTvmO3+ezkCM1J3B//ormRzKQwDrESERlEfnkTRDi86gwsI24kM9HevjnESkSkX355EybFhiA0wFd3FLfHMuJGOMRKRGQMSinkVzQhK4m7aJyBZcSNcIiViMgYKps6UdfWg9nJ3EXjDCwjbmZmYjh28kisRERa5ZfbnxTO4vCqU7CMuBkOsRIR6Zdf0QQ/swlT48N0R/EILCNuJpNHYiUi0i6/vAnTE8Lg58M/o87Ar6KbmRATwiFWIiKNrDaFwspmHl/EiVhG3IyZQ6xERFrtq2lDR48Vszi86jQsI24oMykcO6pa0MshViKiMZdf3gQAmMWX9ToNy4gbmpUcgW6LDXuqW3VHISLyOtsqmhAW4IO06GDdUTwGy4gbmuPYT7nV0c6JiGjs5JfbD3ZmMonuKB6DZcQNJUUGIjrYD9vKWEaIiMZSV68Vu6tbOS/iZCwjbkhEMDs5AtvKG3VHISLyKjuqmmG1Kc6LOBnLiJuanRyB4tp2NHf26o5CROQ1tjmOvMqX9ToXy4ibmp1i/0EoqOCuGiKisVJQ0YTx4QGICwvQHcWjsIy4qb4zRXJuhIho7OSXN3EXjQuwjLip8EBfpMcGYxtfUUNENCaaOnpQUt/Bk+O5AMuIG5udHIlt5U1QSumOQkTk8fIr+s7Uy1fSOBvLiBubnRKB+vYeVDR26o5CROTx8subIPLNCUvJeVhG3NhcxxDrljK+xJeIyNW2lDViUmwIQgN8dUfxOCwjbixjXCiC/czIK2UZISJyJZtNYUtpI7LTInVH8UgsI27Mx2zC7JQIlhEiIhcrrm1DS5cFc1NYRlyBZcTNzUuJxK6DLWjvtuiOQkTksfqe9M1LZRlxBZYRNzc3NRI29c0prYmIyPnyShsRGeSLCTE8U68rsIy4uTmOJUPuqiEicp28skbMS42ECM/U6wosI24uPNAXU8aFII+vqCEicomG9h7sr23HXO6icRmWEQ8wLzUSW0obYbPx4GdERM621fFkbx6HV12GZcQDzE2JREuXBcW1bbqjEBF5nLzSRviY5PA5wcj5WEY8QN90dy7nRoiInC6vtBEzEsIQ6GfWHcVjsYx4gAkxwYgK9kO6PoKYAAAgAElEQVRuCcsIEZEz9Vhs2FbexHkRF2MZ8QAigvlpkdhUUq87ChGRRymsbEK3xYaFE6J0R/FoLCMeYsGEaJQ3dOJgM0+aR0TkLJsO2Fec56exjLgSy4iH6Gvtmw40aE5CROQ5Nh2ox6S4EESH+OuO4tFYRjzEtPFhCPH3YRkhInISq00ht6QRC7iLxuV8RnIlEYkDcAqABACdALYDyFVK2VyYjY6D2STITotkGSEicpJdB1vQ2m3hvMgYGHJlRESWisjHAN4HcB6A8QCmA/g1gEIRuVdEwlwfk0ZifloUimra0NDeozsKEZHb21xif3LHeRHXG25l5HwAP1RKlR19gYj4ALgQwFkAXndBNjpOfe19c0kDzpkRrzkNEZF723SgAUmRgUiICNQdxeMNuTKilLp9oCLiuMyilHpLKcUiYhCZSeHw9zFxVw0R0QlSSmHTgQbOi4yREQ2wisjzIhLe7/00EfnMdbFoNPx9zJiTEoGNB3i8ESKiE1Fc24b69h4s4C6aMTHSV9OsBbBRRM4XkR8C+A+Ah10Xi0br5Ikx2FHVgqYOzo0QEY3W+mL7k7pF6TGak3iHEZURpdTjAG4E8DaA3wE4TSn1riuD0eicMikaSgEb9nN1hIhotNbtq0NSZCBSooN0R/EKI91Ncx2AfwO4HsAzAD4QkVkuzEWjlJUUgSA/M9btYxkhIhoNq03h6+J6LEqP1h3Fa4zoOCMALgOwWClVA+AlEXkT9lIyx1XBaHT8fExYMCEK64rrdEchInJLO6qa0dJlwSmTuItmrIx0N80ljiLS9/4mAAtdlopOyCnpMdhf247q5i7dUYiI3E7fvMjJXBkZM8Md9OzXIjLgKLFSqkdElonIha6JRqPV9wO0nqsjRETHbd2+OkyOC0FcaIDuKF5juN00hQDeFZEuAFsA1AIIADAZwGwAnwL4o0sT0nGbPj4MkUG+WLevHpfOTdIdh4jIbXRbrNhc0oCr56fojuJVhisjlyulThGROwDUwH44+BYALwBYoZTi+eoNyGQSnJwejfXFdVBKQUR0RyIicgtby5rQ1Wvj8OoYG66MzBORBADLASw96rJA2E+aRwa0KD0GHxRWo7i2HZPiQnTHISJyC2uL6mASYOFElpGxNFwZeQzAZwAmAsjt93EBoBwfJwM6fUosAGDNnhqWESKiEVqztwZzUyIRHuirO4pXGe7cNH9TSk0D8G+l1MR+/yYopVhEDCw5KgjpscH4Ym+t7ihERG6hprUL2ytbsCQjVncUrzPSl/be7Oog5HxLMuKwcX8DOnosuqMQERnel3vtr0BckhGnOYn3Gem5acgNLcmIRY/Vhq+LeTRWIqLhrNlTg5gQf0wfH6Y7itdhGfFgCyZEIdDXjDV7uKuGiGgoFqsNXxXV4fQpsTCZ+ArEscYy4sH8fcxYlB6NNXtroJTSHYeIyLDyK5rQ3NnLeRFNWEY83JKMWJQ3dGJ/XbvuKEREhrVmTy1MApw6meej0YFlxMP1DWJ9vrtmmGsSEXmv/+6uwZyUSEQE+emO4pVYRjxcclQQpsaH4j87DumOQkRkSBWNHdhR1YKzp4/THcVrsYx4gbNnxGNzaQPq2rp1RyEiMpy+J2tnz4jXnMR7sYx4gXNmjINSwKc7uTpCRHS0j3dUY8q4EEyICdYdxWuxjHiB6ePDkBQZiI93VOuOQkRkKPVt3dhc0oBzuCqiFcuIFxARnDMjHuv21aOtm0djJSLq89nuGtgUWEY0YxnxEufMiEeP1YY1e/iqGiKiPv/ZUY3EiEDMSOBRV3ViGfES81IjER3shw+3c1cNEREAtHVb8FVRHc6aPg4iPOqqTi4vIyJiFpGtIvKeq7dFgzObBOdlxuOzXYe4q4aICMDH26vRbbHholnjdUfxemOxMvIzALvGYDs0jEtmJ6Kr14b/cJCViAhvbatEUmQg5qZE6o7i9VxaRkQkCcAFAJ505XZoZOamRCIxIhBvb6vSHYWISKva1m6s21eHi2cncBeNAbh6ZeRhAHcAsA12BRFZISK5IpJbW8uzy7qSySS4eHYC1u6r4wHQiMirvVdQBZuyrxiTfi4rIyJyIYAapVTeUNdTSq1SSmUrpbJjY3m2RFe7ZE4irDaF9/K5OkJE3uutbVWYPj4Mk8eF6o5CcO3KyCkAviUiJQBeBrBMRF5w4fZoBKaMC8W08WF4i7tqiMhLldS1I7+8CZfMSdAdhRxcVkaUUncppZKUUmkArgbwX6XUta7aHo3ct+ckYFt5E/YeatUdhYhozL2aWw6TABfNYhkxCh5nxAtdNjcJfmYTXtxYpjsKEdGY6rXa8GpuBZZNjcP48EDdcchhTMqIUmqNUurCsdgWDS86xB/nzozHG1sq0Nlj1R2HiGjMfLLzEOraurF8YaruKNQPV0a81HcWpqCly4L3Cjg7QkTeI2djKRIjAnHaFL5gwkhYRrzUwglRSI8NxoubuKuGiLxDSV071u2rx9Xzk2E28dgiRsIy4qVEBN9ZmIqtZU3YUdWsOw4Rkcu9uKkMZpPgqvnJuqPQUVhGvNjlc5MQ7GfGE1/u1x2FiMilWrp68dLGMpw3Mx5xYQG649BRWEa8WHiQL76zMAXvFhxEeUOH7jhERC7zwoZStHZbcNPp6bqj0ABYRrzcDxZPhEmAJ7/i6ggReaauXiv+vbYEp02JxczEcN1xaAAsI14uPjwA356TiFdyy1HP89UQkQd6fUsF6tq6cdPpE3VHoUGwjBBWnJaObosNT609oDsKEZFT9VhsePyL/ZiVHIGTJ0brjkODYBkhTIoLwUVZCfj3ugOobu7SHYeIyGle2lSGsoYO/PyMyRDhy3mNimWEAAC3n5MBmw34yyd7dEchInKKlq5ePPJZERalR2NJBg9yZmQsIwQASI4Kwg2LUvFaXgV2V7fojkNEdMIeW1OMhvYe3HXeNK6KGBzLCB12y9JJCPX3wX3v74JSSnccIqJRq2jswFNrD+CS2QnITOIraIyOZYQOiwjywy/PmoKviurwxpZK3XGIiEZFKYW73iiE2SS4/dypuuPQCLCM0BGuPzkN2amRuPfdHahp4TArEbmfV3PL8VVRHe46byoSIwJ1x6ERYBmhI5hMggcvz0K3xYa739zO3TVE5FYONnfiD+/twkkTo7B8YaruODRCLCN0jImxIbj17Cn4dNchPLu+RHccIqIR6bHY8JMXt8JiU3jgsiyYeGZet8EyQgO6cfFEnDltHH7//i6sL67THYeIaFj3vLsDuaWNePDyLKRGB+uOQ8eBZYQGZDIJ/nrVLEyICcYtOVtQVs8T6RGRcT2/oRQvbizDzUvScdGsBN1x6DixjNCgQgN88cT12bAp4JonNqC0vl13JCKiY7y6uRy/eXs7lk2Nw21nZ+iOQ6PAMkJDmhATjJwbF6Kjx4KrHt+A/bVtuiMRER324sYy3PF6AU6dHItHl8+FmXMibollhIY1MzEcL/7wJPRYbfj2o+vx6c5DuiMRkZfrtlhxzzs7cPebhVg2NQ6rrpuHAF+z7lg0SiwjNCLTxofhzR8vQlJkIG58Lhe/f28n2rstumMRkRcqOtSKKx/7Gs+sL8H3TknDY9eyiLg7H90ByH2kRgfj9ZsX4b73d+GptQfw9rYq3Hr2FFw2Nwl+Puy1RORah1q68MhnRXh5UxlC/H3w2LVzce7M8bpjkROIkQ5qlZ2drXJzc3XHoBHIK23EHz/YhbzSRkQH++GyeUm4IHM8ZiSEwcfMYkJEztHS1Yuvi+vxel4FPttdAwFw7Ump+OkZkxEV7Kc7Hg1DRPKUUtnDXo9lhEZLKYUv9tbi5U3l+HTXIVhsCqH+PpidEoH02BCkRgchLMAXwf4+CPH3QbC/Gf4+ZphNArMJMInAbJLD/wf6mhEW6MsBNCIPYrMpdPRa0dFtQXuPFT0WG6w2BZtSsNoUrErBZrO/3d5jQWN7Lw61dmF/bTv2VLdiR1UzbAqICbE/6fnOghQeQ8SNsIzQmKpv68a64np8XVyPwsomHKhtR3uPdVS3FRHki8SIQCRHBmHq+FDMSAjHvNRIPgsiMiilFPbVtCG/ohnbK5tRXNuGysZOVLd0oWOUvwfGhfljYkwI5k+IwskTozEvNZK7g90QywhppZRCQ3sPWrssaO+xoL3bivZuC7otVlhtOOLZUN/bHT1WNHf2oq6tG5VNnSir78CB+nYoBYgAmYnhWJoRh0vmJGJCDJ8ZEY2lnBxg5UqgrAxISQF+/weF1AV1eK+gCl/urUO148Sagb5mTB4XgqTIQIwPD0RogA+C/MwI8rOvjvqZzUeujJoEZsfbQX5mRAb5ITbUH8H+HGn0BCwj5BHauy3YdbAFXxfX48uiWuSVNsKmgDkpEfjeKRNw/sx4zqgQuVhODrBiBdDR70DMJl8rIs8pwPh5NThtcixOnRyD7LQoTIgJ5q5WOoxlhDzSoZYuvL2tEi9vKsf+unYkRQbip8sm47J5SfwFSOQiaWlAaemxH48bb0FpqfBltTQolhHyaDabwqe7DuGfa4qRX96EqfGh+M1F07EoPUZ3NCKP0mOxwd9PAHVs2RcBbDYNochtjLSMcH2b3JLJJDh7Rjze+vEi/OM7c9DeY8F3ntiIu94oREtXr+54RB6hsKIZ3/rHWphDOwe8PCVljAORx2IZIbcmIrgwKwGf/OJ0/Oi0iXhlcxnO+euXyC1p0B2NyO3k5Nh3yZhMClHjenHGLfvR0N6D2+7uQVDQkdcNCgLuu09LTPJALCPkEQJ8zbjr/Gl448enwM/HhKtWbcDjXxTDSLshiYysb0i1tBRQStBY44vGj7KwImEJ7v9VBFatAlJT7btmUlOBVauA5ct1pyZPwZkR8jgtXb341eoCfLi9GhfNSsBDl2dxwI5oGIMNqaamAiUlY52GPAVnRshrhQX44tHlc/Grc6fi3fwqLH9yI+rbunXHIjK0srKBn5iWlY1xEPJKLCPkkUQENy9Jx6PL52J7ZTOueOxrVDUNPIRH5O3eK6jikCppxTJCHu38zPHIuXEhalu7ccVjX6O0vl13JCJDeXVzOX760lbMvawCgUFHro5wSJXGCssIebzstCi8tOIkdPRYcMVjX6OkjoWECABe2lSGO14vwOLJsVjzWDqeWCUcUiUtOMBKXmNPdSuuXvU1gvx88MqPTkJSZNDwn0Tkod7YUoFbX8vHkimxeOy6efD34ZA3OR8HWImOkhEfiud/sBAtXb1Y/uRG1LR26Y5EpMWHhQdx22v5WJQejX9dyyJC+rGMkFeZmRiOZ7+/ALWt3fje05vR1m3RHYloTG3YX4+fvbwNc1Ii8cT12XzZOxkCywh5nbkpkfjn8rnYXd2Km1/IQ4+FJ9cg77CnuhU/fC4XyVGBeOqGbAT5+eiORASAZYS81NKMOPzp25n4qqgOv3l7O4/USh6vrq0b339mMwJ9zXj2+wsQEeSnOxLRYSwj5LWunJ+MW5am4+XN5XhhwwCHniRyc/3PNZOaqrB/QxSeumE+h7fJcFhGyKvdelYGlk2Nw73v7sTG/fW64xA5zdHnmuloCEDjx1ko+CJcdzSiY7CMkFczmQQPXz0bKdFB+HHOFlTyKK3kIVauBDo6jvxYd5cJK1fqyUM0FJYR8nphAb544vps9Fhs+NHzuejsseqORHTCBjunDM81Q0bEMkIEID02BI9cMxs7qlpw5xsFHGglt5eYNPCrxHiuGTIilhEih2VTx+G2szPw9rYqvLiJTx/JfVltCgln7oP4HnkcHZ5rhoyKZYSon5tPT8dpU2Lxu3d3Ynd1i+44RKPy9/8W4VBcEX7622aea4bcAssIUT8mk+AvV85CWKAv/ufFrejo4RFayb1s2F+Pv31WhEvnJuLhldEoKQFsNqCkhEWEjItlhOgoMSH++OuVs1Fc24bfvbtTdxyiEWto78HPX96G1Ohg/P7imbrjEI0YywjRABZPjsHNp9sPiPZufpXuOETDUkrh9tfy0dDeg79fMwfB/jzUO7kPlhGiQfzirCmYmxKBu98oRFl9x/CfQKTR0+tK8NnuGtx1/lTMTOSBzci9sIwQDcLXbMIjV8+BCPCzV7bCYuUJ9ciYdh1swf0f7saZ0+Lw3UVpuuMQHTeWEaIhJEcF4feXzMTWsiY8/uV+3XGIjtFjseGXr+YjLNAHD1yWBRHRHYnouLGMEA3jW7MScEHWeDz86V7srOLLfclYHvlsL3YdbMGfLs1CdIi/7jhEo8IyQjQMEcEfLp6JiCA//PLVbei28HDxZAx5pY3415piXJmdhLOmj9Mdh2jUWEaIRiAy2A8PXJaJ3dWt+OsnRbrjEKGjx4LbXsvH+PBA/O+F03XHITohLCNEI7Rs6jhcsyAZj39ZjNySBt1xyMvd/+FuHKhrx5+vmIXQAF/dcYhOCMsI0XFYecF0JEUG4pev5qO9m0dnJT2+KqrFc1+X4geLJ+Dk9GjdcYhOGMsI0XEI8ffBny+fhfLGDjz08R7dccgLtXVbcOfrhUiPDcbt52TojkPkFCwjRMdp4cRo3HByGp79ugSbubuGxthDH+1GVXMnHrx8FgJ8zbrjEDkFywjRKNx+TgYSIwLxq9UF6Orlq2tobGwuacBzG0rx3UVpmJcaqTsOkdO4rIyISLKIfC4iO0Vkh4j8zFXbIhprwf4+uP/SLOyva8fDn/LVNeR6Xb1W/Or1AiRGBOK2s7l7hjyLK1dGLABuVUpNB3ASgFtEhK8/I4+xeHIMrspOxqovi1FQ0aQ7Dnm4v31WhP217fjTpZk8CR55HJeVEaXUQaXUFsfbrQB2AUh01faIdLj7gmmIDfXHHasL0GPhuWvINbZXNuPxL/fjinlJOHVyrO44RE43JjMjIpIGYA6AjQNctkJEckUkt7a2diziEDlNeKAv7rvEfjC0R9fs0x2HPFCv1YY7VhcgKtgPv76Ai8vkmVxeRkQkBMDrAH6ulDrmxB5KqVVKqWylVHZsLBs/uZ8zp4/DxbMT8M/P92FPdavuOORhnvhqP3YebMHvL56J8CAe3Iw8k0vLiIj4wl5EcpRSb7hyW0Q6/faiGQgL8MUdq/NhsXJ3DTlHcW0bHv60COdnxuPcmfG64xC5jCtfTSMAngKwSyn1F1dth8gIooL9cO/FM5Bf0Yyn1h7QHYfcXE4OkJqqMCkuGCX/WILMrkzdkYhcypUrI6cAuA7AMhHZ5vh3vgu3R6TVBZnjcfb0cfjLJ3uxv7ZNdxxyUzk5wIoVQFmZABD0Ngfitp/6ISdHdzIi1xGllO4Mh2VnZ6vc3FzdMYhGraalC2f+5QtMHR+Gl394Ekwm0R2J3ExaGlBaeuzHU1OBkpKxTkN0YkQkTymVPdz1eARWIieKCwvAry+cjk0HGvDipjLdccgNlZUN/ASxjA8n8mAsI0ROdsW8JCyeFIP7P9yNqqZO3XHIzUSPG/j0AikpYxyEaAyxjBA5mYjgT5dmwmpTuPvNQhhpVygZW21rNwIX7YTZ78hCEhQE3HefplBEY4BlhMgFkqOCcPs5GVizpxZvb6vSHYfcxD3v7EDAtEo8+HAvUlMBEfusyKpVwPLlutMRuQ7LCJGL3LAoDXNTInDvuztQ19atOw4Z3Efbq/F+4UH87IzJ+OXNASgpAWw2+9Aqiwh5OpYRIhcxmwQPXJaF9m4r7n13p+44ZGDNHb3437e3Y/r4MKw4baLuOERjjmWEyIUmjwvFT5ZNwrv5Vfhk5yHdccig7vtgJxrae/Dg5VnwNfPXMnkfPuqJXOxHp6djanwofv1WIZo7e3XHIYNZW1SHV3MrsOK0iZiZGK47DpEWLCNELubnY8KDl2ehtrUb93+4S3ccMpCOHgvufKMAE2OC8bMzJuuOQ6QNywjRGMhKisAPT52IlzaVY/2+Ot1xyCAe/GgPKho7cf9lWQjwNeuOQ6QNywjRGPnFWVOQFh2EO98oRGfPwAe2Iu+xuaQBz35dghtOTsWCCVG64xBpxTJCNEYCfM24/7IslDV04C+f7NEdhzTq7LHijtUFSIoMxB3nTtUdh0g7lhGiMXTSxGgsX5iCp9YewLbyJt1xSJP/+88eHKhrxwOXZSHY30d3HCLtWEaIxtid503FuLAA3LE6Hz0Wm+44NMbyShvx1LoDWL4wBYvSY3THITIElhGiMRYa4Iv7vj0Tew+14dE1+3THoTHU1WvFHavzkRAeiLvOn6Y7DpFhsIwQabBs6jhcPDsB//x8H/ZUt+qOQ2Pk4U+LUFzbjj9dmokQ7p4hOoxlhEiT31w4HaEBvrh9dT4sVu6u8XT55U1Y9WUxrspOxmlTYnXHITIUlhEiTaJD/PGHS2aioKIZ/1pTrDsOuVC3xYrbV+djXFgAVl7I3TNER2MZIdLo/MzxuGhWAh75rAg7qpp1xyEX+ftn+7D3UBv+eGkmwgJ8dcchMhyWESLNfvetGYgM9sOtr/LVNZ6osKIZ//qiGJfNTcLSjDjdcYgMiWWESLPIYD/cf2kmdle34m+fFemOQ07U1WvFL17dhtgQf/zmwum64xAZFssIkQGcMW0crpiXhEfX7OPB0DzIAx/txr6aNjx0RRbCg7h7hmgwLCNEBvG/F01HfFgAbn11G7p6ee4ad7duXx2eXleC7y5Kw6mT+eoZoqGwjBAZRFiALx68fBaKa9tx/4e7dcehE9Dc2YvbXsvHxNhg/IrnniEaFssIkYEsnhyDHyyegGfWl+Dz3TW649Ao/fbt7aht7cbDV81GoJ9Zdxwiw2MZITKY28/JwNT4UNy+Oh+1rd2649Bxeq+gCm9tq8JPlk1GVlKE7jhEboFlhMhgAnzN+Ns1c9DSZcEdq/OhlNIdiUaosqkTK9/cjlnJEbhlabruOERug2WEyICmjAvF3edNxed7avH8hlLdcWgELFYbfvbSVlhtCo9cNRs+Zv56JRop/rQQGdQNi9Jw+pRY3Pf+Luw9xJPpGd3fPitCbmkj7vv2TKTFBOuOQ+RWWEaIDEpE8NAVWQjx98FPX9rKl/sa2PriOvz98324Yl4SLp6dqDsOkdthGSEysLjQAPzflbOwu7oV97yzQ3cc6icnB0hLA0wmhaXZwQgsnYB7L56hOxaRW2IZITK4JRlxuGVpOl7eXI7X8yp0xyHYi8iKFUBpKaCUoKcpEAfemoY3X/PRHY3ILbGMELmBX5w5BQsnROHXb21HEedHtFu5EujoOPJjXZ2ClSv15CFydywjRG7Ax2zC36+Zg2B/M27O2YKOHovuSF6trOz4Pk5EQ2MZIXITcWEBeOTqOSiubcOv39zO449olJBkG/DjKSljHITIQ7CMELmRUybF4OdnTMEbWyuRs5FPw3XotlgRv6wI4nvk6lRQEHDffZpCEbk5lhEiN/M/yyZhaUYs7nlnBzbur9cdx+v8/r2dqIvfh1t/14rUVEAESE0FVq0Cli/XnY7IPbGMELkZs0nwyDVzkBIdhJtztqCisWP4TyKnWJ1XgRc2lOFHp03EQ3dGoqQEsNmAkhIWEaITwTJC5IbCAnzxxPXZ6LXa8MPn8jjQOga2ljVi5ZuFOHliNG4/J0N3HCKPwjJC5KbSY0Pwt2vmYHd1C25/rYADrS5U3tCBHz6Xi3FhAfjHd+bwvDNETsafKCI3tjQjDneeOxXvFx7EP/67T3ccj9TS1YsfPLsZPRYb/v3d+YgO8dcdicjj8HCBRG5uxWkTsbu6Ff/3yV4kRwXhkjk8N4qzWKw23JKzBftr2/Hc9xdgUlyI7khEHollhMjNiQjuvywTB5s7cdtr+YgO8cOpk2N1x3J7Sin89p0d+KqoDg9clolFk2J0RyLyWNxNQ+QB/H3MWHV9NibFheCm5/OwvbJZdyS398RX+5GzsQw3nZ6Oq+bzaGZErsQyQuQhwgJ88cz3FiAiyA/ffXozyur5kt/RemVzGf74wW5ckDked/CVM0QuxzJC5EHiwwPw7Pfno9dqww1Pb0J9W7fuSG7nvYIq3PlGIU6fEou/XjUbJpPojkTk8VhGiDzMpLhQPHVDNqqaOnH9vzehqaNHdyS38fnuGvz85W2YnxqFx66dBz8f/ookGgv8SSPyQNlpUXj8unkoqmnD8ic3spCMwIb99bjphTxMHR+KJ7+bjUA/s+5IRF6DZYTIQy3JiMOq6+ah6FAbrn2KhWQouSUNuPHZXKREBeG57y9EWICv7khEXoVlhMiDLcmIw+PXz8Pe6jZc99QmNHf06o5kOF/urcV1T21CXKg/nv/BQkQF++mOROR1WEaIPNzSjDg8ft087KluxXX/3oiGdq6Q9PloezVufDYXaTHBeOVHJyM+PEB3JCKvxDJC5AWWTo3DY9fNxZ7qVlz+r/Ve+7LfnBwgLQ0wmYDY8RZcv/IgZiSG4eUfnoTYUB7mnUgXlhEiL7Fs6jjk3LgQDR09uPRf61BQ0aQ70pjKyQFWrABKSwGlgLpqHzR8lIWLgk9CeBBnRIh0Yhkh8iLZaVF4/eZFCPA146rHN+Dz3TW6I42ZlSuBjqMWhKw9Zvzut3zVDJFuLCNEXiY9NgRv/HgR0uOCceNzucjZWKo70pgoK1ODfHyMgxDRMVhGiLxQXGgAXllxMk6dHIOVb27HXW8Uotti1R3LZYoOtcIvvGvAy1J42hki7VhGiLxUsL8PnrphPn68JB0vbSrDVY9vQHmD5w22flh4EN9+dD0SztyHgMAjV0eCgoD77tMUjIgOYxkh8mJmk+COc6fisWvnorimDef/7Su8X3BQdyyn6Oq14u43C3Fzzhakx4Vg3ZOT8OQTgtRUQARITQVWrQKWL9edlIhEqYH3o+qQnZ2tcnNzdccg8krlDR34yUtbsa28CZfOScRvL5rhtq8y2VrWiNtey0dxbTt+dPpE3HpWBs8zQ6SBiOQppbKHux5/OokIAJAcFYTXbjoZP102CW/nV+Gsv36Bj3dUw0hPWI7W/7ghaWnA089a8TC9G7cAAAqfSURBVKcPduGyf61HZ48Vz/9gAe46bxqLCJHBcWWEiI6xvbIZt72Wj93VrViaEYt7vjUDqdHBumMdoe+4If1frmvytSLynALc+F0z7r5gGs8xQ6TZSFdGWEaIaEC9VhueXV+Cv36yF71WhWtPSsX/LJtkmHO3pKXZD2B2tPgEKw5W8tghREbAMkJETnGopQt/+c9evJZXjmA/H1y/KBXfP2UCokP0Hj7dZFJQSo75uAhgs2kIRETH4MwIETnFuLAAPHB5Fj76+WlYPDkGj64pxikP/Bcr3yzE7uoWl2776JmQ55634cPCg7h61dcwhXYO+Dk8bgiR+3HpyoiInAvgEQBmAE8qpe4f6vpcGSEyvn01rXj8i/14J78K3RYb5qRE4JLZibggazxiRrBakpMD3HQT0NZ27GXR0fb/GxqAqCigpQXo7f3m8r6ZkIxTGpHRNgMv/zUOnR3frI4EBfHlukRGon03jYiYAewFcBaACgCbAVyjlNo52OewjBC5j8b2HqzOq8DrWyqwu7oVJgFmJUdgyZQ4LJwYhaykcAT5+RzxOTk5wLXXnth248ZbUVVhgtkkyMmxn3OmrMy+InLffSwiREZihDJyMoB7lFLnON6/CwCUUn8a7HNYRojc057qVnxQeBBr9taioKIJStkPqJYeG4xJcSFIiw5GXKg/vrc4FSe6d5gzIUTuY6RlxGe4K5yARADl/d6vALDQhdsjIk0y4kORER+KX5w1BU0dPdj6/+3da4xcdRnH8e+P1i0KDbulLRRapU0aEH1jXRs0aICSUhpD1aipvqBakwZNE3lhTEkTQsTEVKMvTFSC2ngJWryhDSkpRTC+MNRC0yu0dotFu/ai9qYhAqWPL85/m9NlZne2u2f+c/l9ksmePec/s8+T55yZZ8/5z8zfTvH8yyfZd/QML/zjDJv3HuONcwFcN+6/5TkhZp2nymakIZJWAasA3u5nGbO21/u2Hm69YSa33jDz/Lpz54ITr7zGjHXje2x/l4xZZ6ry3TSDwJzS77PTugtExMMR0R8R/TNmzKgwHDPL5ZJLlCa3vvmtuCPp6Skmtfq7ZMw6W5VnRrYB8yXNpWhClgOfrvDvmVmL6+2FU6fqby+/m8YTUs26R2XNSESclbQa2Ezx1t71EbG3qr9nZq3v5Eno67uwIentLdabWfeqdM5IRGwCNlX5N8ysvbjxMLPh/AmsZmZmlpWbETMzM8vKzYiZmZll5WbEzMzMsnIzYmZmZlm5GTEzM7Os3IyYmZlZVm5GzMzMLCs3I2ZmZpaVmxEzMzPLys2ImZmZZeVmxMzMzLJSROSO4TxJ/wReruChpwP/quBxW0035OkcO0c35NkNOUJ35OkcL847ImLGaINaqhmpiqTnIqI/dxxV64Y8nWPn6IY8uyFH6I48nWO1fJnGzMzMsnIzYmZmZll1SzPycO4AmqQb8nSOnaMb8uyGHKE78nSOFeqKOSNmZmbWurrlzIiZmZm1KDcjZmZmllXHNCOSPiFpr6RzkvqHbbtP0oCk/ZLuqHP/uZK2pnGPSuppTuQXL8W5I90OSdpRZ9whSbvTuOeaHed4SHpA0mApz6V1xi1J9R2QtKbZcY6HpG9I2idpl6THJPXWGdeWdRytNpKmpH15IB2D1zU/yosnaY6kZyS9kJ6DvlhjzC2STpf24/tzxDoeo+1/Knw71XGXpAU54hwPSdeXarRD0hlJ9w4b03a1lLRe0nFJe0rrpknaIulA+tlX574r0pgDklZUFmREdMQNeCdwPfAHoL+0/kZgJzAFmAscBCbVuP8vgOVp+SHg87lzGmP+3wTur7PtEDA9d4wXmdcDwJdGGTMp1XUe0JPqfWPu2MeQ42JgclpeB6zrlDo2UhvgC8BDaXk58GjuuMeY4yxgQVqeCvylRo63AI/njnWceY64/wFLgScAATcBW3PHPM58JwFHKT60q61rCXwIWADsKa37OrAmLa+p9bwDTANeSj/70nJfFTF2zJmRiHgxIvbX2LQM2BARr0bEX4EBYGF5gCQBtwG/Sqt+DHykyngnUor/k8DPc8eSyUJgICJeiojXgA0UdW8LEfFkRJxNvz4LzM4ZzwRrpDbLKI45KI7BRWmfbgsRcSQitqfl/wAvAtfmjSqLZcBPovAs0CtpVu6gxmERcDAiqvhU8KaKiD8CJ4atLh939V7z7gC2RMSJiDgJbAGWVBFjxzQjI7gW+Hvp98O8+YniSuBU6QWh1phW9kHgWEQcqLM9gCclPS9pVRPjmiir02nf9XVOJTZS43axkuK/y1rasY6N1Ob8mHQMnqY4JttOusT0HmBrjc3vl7RT0hOS3tXUwCbGaPtfJx2HUJylq/cPXrvXEuCqiDiSlo8CV9UY07SaTq7iQasi6Sng6hqb1kbE75odTzM0mPOnGPmsyM0RMShpJrBF0r7UKbeEkXIEvgc8SPFE+CDF5aiVzYtuYjRSR0lrgbPAI3UepqXr2O0kXQ78Grg3Is4M27yd4nT/f9O8p98C85sd4zh1zf6X5gzeBdxXY3Mn1PICERGSsn7OR1s1IxFx+0XcbRCYU/p9dlpX9m+KU4qT039mtcZkMVrOkiYDHwPeO8JjDKafxyU9RnHqvGWeRBqtq6TvA4/X2NRIjbNqoI6fAT4MLIp0sbbGY7R0HetopDZDYw6n/fkKimOybUh6C0Uj8khE/Gb49nJzEhGbJH1X0vSIaJsvXmtg/2v543AM7gS2R8Sx4Rs6oZbJMUmzIuJIupx2vMaYQYo5MkNmU8zLnHDdcJlmI7A8zdifS9HB/rk8ID35PwN8PK1aAbTLmZbbgX0RcbjWRkmXSZo6tEwxWXJPrbGtaNg1549SO/ZtwHwV74jqoTi9urEZ8U0ESUuALwN3RcQrdca0ax0bqc1GimMOimPw6XoNWStK81t+CLwYEd+qM+bqoXkwkhZSPPe2TcPV4P63Ebg7vavmJuB06TJAu6l7trnda1lSPu7qveZtBhZL6kuXyBendROv2bN6q7pRvFAdBl4FjgGbS9vWUszo3w/cWVq/CbgmLc+jaFIGgF8CU3Ln1GDePwLuGbbuGmBTKa+d6baX4rJA9rjHkN9Pgd3ALoqDZ9bwHNPvSynexXCwDXMcoLguuyPdht5Z0hF1rFUb4CsUzRfApemYG0jH4LzcMY8xv5spLiPuKtVwKXDP0LEJrE5120kxSfkDueMeY441979hOQr4TqrzbkrvamynG3AZRXNxRWldW9eSorE6AryeXic/RzEv6/fAAeApYFoa2w/8oHTflenYHAA+W1WM/jh4MzMzy6obLtOYmZlZC3MzYmZmZlm5GTEzM7Os3IyYmZlZVm5GzMzMLCs3I2ZmZpaVmxEzMzPLys2ImTWFpPelLzy8NH2i515J784dl5nl5w89M7OmkfRVik9cfStwOCK+ljkkM2sBbkbMrGnS99NsA/5H8THab2QOycxagC/TmFkzXQlcDkylOENiZuYzI2bWPJI2AhuAuRRferg6c0hm1gIm5w7AzLqDpLuB1yPiZ5ImAX+SdFtEPJ07NjPLy2dGzMzMLCvPGTEzM7Os3IyYmZlZVm5GzMzMLCs3I2ZmZpaVmxEzMzPLys2ImZmZZeVmxMzMzLL6Pwu2DVT6kXAYAAAAAElFTkSuQmCC\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {
- "tags": [],
- "needs_background": "light"
- }
- }
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "colab": {
- "base_uri": "https://localhost:8080/"
- },
- "id": "NVHYYscYcYQq",
- "outputId": "d56ca718-f4a7-43d0-e696-2da7c9a64eab"
- },
- "source": [
- "grad_output[1]"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "execute_result",
- "data": {
- "text/plain": [
- "array([4.81090413e+00, 4.50012309e+00, 3.99507105e+00, 3.21624014e+00,\n",
- " 2.24427660e+00, 1.40230777e+00, 8.46789923e-01, 5.08509157e-01,\n",
- " 3.05139493e-01, 1.83086341e-01, 1.09852011e-01, 6.59112224e-02,\n",
- " 3.95467347e-02, 2.37280409e-02, 1.42368245e-02, 8.54209473e-03,\n",
- " 5.12525684e-03, 3.07515410e-03, 1.84509246e-03, 1.10705548e-03])"
- ]
- },
- "metadata": {
- "tags": []
- },
- "execution_count": 28
- }
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "colab": {
- "base_uri": "https://localhost:8080/"
- },
- "id": "9inbJKVjQAgd",
- "outputId": "16ca7452-f3d4-404a-90c9-7b9c0da8f44c"
- },
- "source": [
- "grad_output[2]"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "execute_result",
- "data": {
- "text/plain": [
- "20"
- ]
- },
- "metadata": {
- "tags": []
- },
- "execution_count": 33
- }
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "6lN2-cxr5bNs"
- },
- "source": [
- "## Using a small learning rate\n",
- "\n",
- "### The example below uses a smaller than ideal learning rate of $\\lambda = 0.1.$ Not only does this increase the number of gradient descent itterations to 105, but the algorithm coverges to one of the local minima. "
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "4ARHSuT85bNs",
- "colab": {
- "base_uri": "https://localhost:8080/",
- "height": 458
- },
- "outputId": "b0942bf3-5fe4-4503-ef1b-8f933e9f89cc"
- },
- "source": [
- "# Initial value x1 = -8 and learn rate lambda = 1\n",
- "grad_output = grad_descent(derivative,-5,0.1)\n",
- "plotf(x,grad_output[1],\"Gradient Descent with lambda =0.1 and start point = -8\")"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "display_data",
- "data": {
- "image/png": "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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {
- "tags": [],
- "needs_background": "light"
- }
- }
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "colab": {
- "base_uri": "https://localhost:8080/"
- },
- "id": "4EVrGpnXdG4e",
- "outputId": "1110f3e2-5520-477c-9f5c-d7e5d202ba77"
- },
- "source": [
- "grad_output[2]"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "execute_result",
- "data": {
- "text/plain": [
- "155"
- ]
- },
- "metadata": {
- "tags": []
- },
- "execution_count": 31
- }
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "7Iiu6dAQ5bNs"
- },
- "source": [
- "## Small learning rate but starting close to global minimum\n",
- "\n",
- "### The example below uses a small learning rate (for this context) of $\\lambda = 0.1,$ but starts the algoirthm at $x_{1} = -5.$ The key point is that the initial value is now slight beyond the local minimum. Hence even with a small learning rate we are able to eventually converge to the global minimum."
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "3WKgyNeT5bNt",
- "colab": {
- "base_uri": "https://localhost:8080/",
- "height": 458
- },
- "outputId": "0d0eb7ac-dd6b-4b03-cb12-d97ad31722e0"
- },
- "source": [
- "# Initial value x1 = -5 and learn rate lambda = 10\n",
- "\n",
- "grad_output = grad_descent(derivative,-5,1)\n",
- "plotf(x,grad_output[1],\"Gradient Descent with lambda = 10 and start point = -5\")"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "display_data",
- "data": {
- "image/png": "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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {
- "tags": [],
- "needs_background": "light"
- }
- }
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "colab": {
- "base_uri": "https://localhost:8080/"
- },
- "id": "g4tDyDvEdh4_",
- "outputId": "6744fd43-d5ef-4a6b-a0a4-3a8679e88623"
- },
- "source": [
- "grad_output[1]"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "execute_result",
- "data": {
- "text/plain": [
- "array([-3.01143616, 6.72279107, -4.14655271, 2.91878012, -6.76300996,\n",
- " 4.89485449, 2.29724203, -6.26665275, -2.59482101, 6.65188675,\n",
- " -2.87787679, 6.76986017, -5.02420532, -3.16954651, 6.56998637,\n",
- " -1.50249925, 4.43125016, -1.03887977, 3.10454992, -6.64612123,\n",
- " 2.77776915, -6.75995586, 4.83735732, 1.89203735, -5.43622563,\n",
- " -5.24801587, -4.47009986, 0.7644714 , -2.29080396, 6.25588804,\n",
- " 2.7088297 , -6.73226045, 4.32097251, -1.7977997 , 5.20722358,\n",
- " 4.25882695, -2.20964135, 6.11255034, 4.0134673 , -3.69251039,\n",
- " 5.21272267, 4.28807589, -2.01738673, 5.7225938 , 5.6211889 ,\n",
- " 5.6193303 , 5.61787471, 5.61670025, 5.61573056])"
- ]
- },
- "metadata": {
- "tags": []
- },
- "execution_count": 37
- }
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "UaxhaWkK5bNt"
- },
- "source": [
- "## Initial value and learning rate are important\n",
- "\n",
- "### From the above exercises of changing the initial value and learning rate we can conclude that gradient descent is not guaranteed to converge to the global minimum. Having a really low learning rate can make convergence slower (more iterations before finding minimum) and make it more likely to get stuck at local minima. A very high learning rate may be even more problematic as gradient descent may never converge (try $\\lambda$ = 6 in the code). The initial value is also important for finding the global minimum. If we start close to the global minimum, we are more likely to find it in the above example even with a smaller than ideal learning rate.\n",
- "\n",
- "### The diagram below shows even with multiple variables different initial values can lead to different local minima from gradient descent."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "IT7IiypuhnfS"
- },
- "source": [
- ""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "ToQ5vmXp5bNt"
- },
- "source": [
- "## Example: Minimizing multiple variable function\n",
- "\n",
- "### Let us consider the following straight forward bivariate function $$f(x,y) = x^2 + y^2 + 1.$$ Since this a function of two variables, we have have the following partial derivatives $$\\frac{df(x)}{dx} = f_{x} = 2x \\text{ and } \\frac{df(y)}{dy} = f_{y} = 2y.$$ Note that its easy to argue that the global minimum of $f(x,y)$ is (0,0) since $f(0,0) = 1$ and $f(x,y) \\ge 1.$\n"
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "sQZ-w8Be5bNt",
- "colab": {
- "base_uri": "https://localhost:8080/",
- "height": 418
- },
- "outputId": "cc21dfb8-1656-4505-d8a4-b33339659eae"
- },
- "source": [
- "# Plotting in 3D\n",
- "from mpl_toolkits.mplot3d import Axes3D\n",
- "from matplotlib import cm\n",
- "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
- "\n",
- "# f(x,y) = x^2 + y^2 + 1\n",
- "def f(x,y):\n",
- " return x**2 + y**2 + 1\n",
- "\n",
- "# (X,Y) grid on [-5,5]\n",
- "y = arange(-5, 5, 0.25)\n",
- "y = arange(-5, 5, 0.25)\n",
- "X, Y = meshgrid(x, y)\n",
- "\n",
- "\n",
- "# z = x^2 + y^2\n",
- "Z = f(X,Y)\n",
- "\n",
- "# Plot (X,Y) in 3D\n",
- "fig = figure(1)\n",
- "ax = fig.gca(projection='3d')\n",
- "surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.RdBu,linewidth=0, antialiased=False)\n",
- "\n",
- "ax.zaxis.set_major_locator(LinearLocator(10))\n",
- "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
- "fig.colorbar(surf, shrink = 0.7, aspect=5)\n",
- "show()"
- ],
- "execution_count": null,
- "outputs": [
- {
- "output_type": "display_data",
- "data": {
- "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgwAAAGRCAYAAAAJlusPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi40LCBodHRwOi8vbWF0cGxvdGxpYi5vcmcv7US4rQAAIABJREFUeJzsnXl8HGd9/z9z76XdlSwfkhUfcXxGdpzYstNCuQIJIQQIIQmUFCihEKBA4ReSUHhBQ0sJR3+Um4AhB21pAw3kB68AIUkTWigxDjiRbFmHZVvWYVvH7urYc2bn98fqefTM7Mxe2tX5vF+vvKKdnZ0drbXzfOZ7fL6CaZrgcDgcDofDKYS40CfA4XA4HA5n8cMFA4fD4XA4nKJwwcDhcDgcDqcoXDBwOBwOh8MpChcMHA6Hw+FwisIFA4fD4XA4nKJwwcDhcDgcDqcoXDBwOBwOh8MpChcMHA6Hw+FwiiKXuT+3heRwOBxOpQgLfQKcyuERBg6Hw+FwOEXhgoHD4XA4HE5RuGDgcDgcDodTFC4YOBwOh8PhFIULBg6Hw+FwOEXhgoHD4XA4HE5RuGDgcDgcDodTFC4YOBwOh8PhFIULBg6Hw+FwOEXhgoHD4XA4HE5RuGDgcDgcDodTFC4YOBwOh8PhFIULBg6Hw+FwOEXhgoHD4XA4HE5RuGDgcDgcDodTFC4YOBwOh8PhFIULBg6Hw+FwOEXhgoHD4XA4HE5RuGDgcDgcDodTFC4YOBwOh8PhFIULBg6Hw+FwOEXhgoHD4XA4HE5RuGDgcDgcDodTFHmhT4DDqRTTNJHJZJBKpaAoCmRZhiRJEARhoU+Nw+Fwlh2CaZrl7F/WzhxOrchms8hkMtB1Hel0GgCoUJAkCYqiQJIkSJIEUeSBNA5nkcDV/BKGCwbOksI0Tei6Dl3XIQgCTNNEOp2mosA0TfofQRTFvAgEj0JwOAsC/+ItYbhg4CwZSFQhm83SRT+bzVoEgx27gJicnIQoiqivr6cCQhRFLiA4nPmBf9GWMLyGgbPoMU0ThmEgk8kAABULqVQKHR0dmJ6eht/vRygUQjgcRiAQoALCHk2YmpqCIAjw+/1IpVL0eVmW6X9cQHA4HE4+XDBwFjUk5cBGFQDg/Pnz6O3txdatW1FXV4dUKoVoNIqBgQFMTU1BVVWEw2GEQiEEg0FIkgTAWufAvkcmk6GCBIBFQPBCSg6Hw+EpCc4ixS2qoOs6Ojs7YRgGdu3aBVmWHVMSREBEo1FMTExAkiSEQiEYhgFN07Bx48aC722aJhUpwGwhJRcQHM6c4F+cJQwXDJxFB7njNwzDElUYHx9HZ2cnNm/ejKamppJqGAiZTAbRaBSDg4OIx+NQVRXBYBDhcBjhcBiqqhY8H3shpSRJlggE78TgcEqCC4YlDBcMnEUFiSqYpmkpbOzu7sbk5CRaW1vh9Xrp/qQQstQ7/uHhYei6jubmZsRiMUSjUcRiMWQyGdTV1VEB4fF4XI9pFxAXLlxAQ0MDfD4fbefknRgcjiP8S7GE4TUMnEWBvV2S3LFPTk6io6MDTU1N2L59e9UWYUmS0NDQgIaGBgA54TE5OYloNIru7m6kUilLIaXf76fvbRcD4+PjqKurQzqdRiqVApBr5eSFlBwOZznBBQNnwdF1HfF4HIqi0MXYNE2cOnUKFy5cwO7duxEIBKryXuTYdkRRRCgUQigUwsaNG2GaJqanpxGNRnH69GlMT0/D6/XSCATbiUGOW6iQkjzPGkpxAcHhcJYSXDBwFgwSVYhEIujv78fu3bsBAPF4HB0dHaivr8eBAwcWpD5AEAQEAgEEAgG0tLTANE0kEgnEYjEMDg5icnISiqIgHA4jnU7DMIy819sFhGEY0HWdbuOFlBwOZynBBQNnQbCbMJGagMHBQfT392Pnzp2or68v6Vik3qEU3CIMpbzO5/PB5/OhqakJwGwnxrlz59DZ2QlZlmkKIxQKQVEUy+vZcyRdGIlEgltaczicJQEXDJx5xaldUhRF6LqOP/7xj9A0DQcOHIAsl/6nWc6deTXv4jVNw9q1azE6OopNmzZBVVVaSHnmzBlks1ma5giHw9A0zXIebK0GERDJZBJAzmeisbERXq+XF1JyOJxFARcMnHnDzYRpfHwc4+PjuOyyy7B69eqyjlnJAlpJhKGUYyqKgsbGRjQ2NgLIdXxMTEwgGo1iaGjI0okRCoXg9XpdCylHR0dpuoMdrsWmMHghJYfDmU+4YODUnGImTKlUCvX19WWLBTfWXftJnPv5px2fq8UC63ZMSZJQX19PUyvZbBZTU1OIRqPo7e1FIpGA3++nhZRsJwaQK8QkdRBE5NgFBO/E4HA48wUXDJya4mbCFIlEcPz4cWzatAkNDQ3o7Oys6vsWEg21iDCUgiiKCAaDCAaD2LBhA+3EiMViOHPmDKampuDxeBAOh2l9B8HN0lrXdW5pzeFw5gUuGDg1w82EqaenBxMTE7jiiivg9XqRTCartoivu/aTVTnOfMB2Yqxfvx6maSKZTCIajSKZTKK9vR2qqloKKVnB4FRIST5zXkjJ4XCqDRcMnKpTignT/v376aImiuKcBMN8dEnMB4IgwOv1wuv14sKFC9ixYwcEQUA0GsXo6Cj6+vogCIKlkNKpE8OtkDIajcLr9aKuro4XUnI4nLLhgoFTVchsBzaqYJomTp8+jXPnzqG1tRV1dXWW18x1EScLnj26sOHGL6L/P++o+LiLAVVVsWbNGqxZswZAzuSKdGL09/cjm81aZmI4dWIQotEoTNOEpmm8kJLD4ZQNFwycquAWVSAmTOFwGAcPHnQMiVfrrl/1BZGOTxTcZzFHGEpBlmWsWrUKq1atAjDbiRGLxTA8PIx0Oo1AIEAFBNuJAbgXUqZSKSoweCElh8NxggsGzpyxmzCRRblUE6ZqLOIbbvyi5bHqC87peAtNqWkWt06MWCyGkydPIh6Pw+fzIRwOI5VKWT5nt0JK1tIa4IWUHA4nBxcMnIphowoAaPQgnU7j2LFjUBSlJBMmUgw5H9QqwrBYohZsJ8ZFF10E0zQRj8cRjUapJwQ7VCsYDBadieFWSMkFBIezsuCCgVMRTlEFIDfquaenB1u3bqV592LMZcExTRMb3/RP9LE9snDxrd9C37/cXvHxS2ExL5iCIMDv98Pv9yMej1P3SGJp3dPTA0mSaBdGKBSyCLxihZSZTAbxeBxr1qyx1EFwOJzlBxcMnLIoZMJ04sQJZDIZtLW1QVXVko9Z6V1/MplER0eH6/OyN3/C5VKvYZgLJM3h8Xiwbt06rFu3DkAuIhSLxTA+Po5Tp04BgKWVk/23tBdSJpNJDA0NIRQKOY725oWUHM7ygQsGTskQa+cXXngBu3fvtpgwdXZ2YuPGjWhubp6XxeH8+fPo7e3FLV9+zrJd9gagJ6Ys2yYnJxEIBJbUolWrtInTZ6CqKlavXk2dNkknRiwWw9mzZ2EYBrW0DofD8Hg8ltfzQkoOZ2XABQOnKOxoZtM0MTk5SesOent7EY1GsXfvXvh8vpqfiz2SATyXJxLYyILiCWD/hx/F99+9DZqmwePx0FTKYg+dL9Siau/EyGaztP6hq6sLqVSKWlrbI0mlFFKSOgnWUIoLCA5n8cMFA6cgTu2SgiBQE6Z169ahra1tXi740WgUx48fx4YNG7B+/XpcdMtXLc87pSAIbW1tSCaTGB4eRiQSwZEjR6CqKr1rthf/LUfKMbhiEUWRfk7kOGQmxsDAACYnJ9He3k7TGIFAgBdScjjLEC4YOK64mTClUil0dHQ4mjDVAtM00dfXh9HRUVx22WXw+/0F91c8AWSSU1A8swKCuCiuWrUKmUwG27dvRyqVQiQSwfnz5y3Ff042zMuBSgWDHUEQUFdXh7q6OoRCIQwNDWHDhg1UQExNTVExFgqFEAwGHS2t3QopgVxKw+v1wuPx8EJKDmeRwAUDJw83E6ZEIoGOjg6YpulqwlRt4vE42tvb0dDQgLa2NvqeLTd/xbKfb9V6pOMxx2OwkQd2wdQ0La/4j9gwnzx50nJnbe8eqDVLpTDTNE2Iogifzwefz4fm5mYAoDMxLly4gN7e3oKfpdNMjP7+fqxevRqhUAjAbCElt7TmcBYOLhg4FtxMmIaGhnDmzBns3LkTnZ2dNRcL5D1Pnz6NXbt25Rk/qb6Qo0AgUQVv/TpLXcOlH/gJjn31DfTYTthtmDOZDGKxGCKRSF73gH2OQy0W+GoviNWKMJRyTHsnRiaTQTQatXyWrKW1vRMDAK1vsI/2JiKFW1pzOPMLFwwcAO5RhXJNmKpBJpPBsWPHIEkSDh48mPeeF7/jQctj1RdyPVahuoZiKIqCxsZGNDY2AnCe4xAKhZBMJi3OiIuZhRIhiqJYOjEMw6Cf5eDgIDKZjKUTwzAM+jfoVkhJBATZh23l5HUQHE714YKB42rCNDIygu7u7rJMmObK2NgYTpw4gS1bttC7UzfsUQYSXXASCYon18ExFx+GQnMc+vr60NfXRxe9+vp6yyCoxcB8tmoWQ5IkNDQ0oKGhAUDub3BychLRaBTd3d2IxWJIp9NobGxEOByG3++3vI9TIaWu6xbhxgspOZzqwgXDCqaQCRNpn9u/f7/jwlft8LZpmujq6sLExAT27duX1+tPKBRdUPwhZKZnBYS3fg0yyTh93PaJp/DUXW1VO2cyx6Gurg7Nzc0IBAK0/bCzsxPpdDrPv6DUz2wxLe7zcUxRFKnT5MaNG9HR0YG1a9cilUrh9OnTmJ6ehtfrpZ+lUyeGvQ4im80ikUjkpThYPwjO8kQMtpjQk8V3XEKYibFfmqb56oU8By4YVigkpGuPKhATJtK66LQYkLv0ai0+U1NTiMfjUFUV+/fvr+i4JKpQKLoA1Nbp0d5+SAZBRaNR9PT0IJlMUv+CcDgMn89X8HddCnfEtRAh5LiBQACrV69GS0sLTNNEIpGgKYzJyUkoimJpiy2lE+PIkSPYs2cPrXvghZTLFCMFZecNC30WVSX9h0ONC30OXDCsMNyiCuWYMFVr0SXV8ENDQ/B4PNi8eXPB/be+52FImhdGKgFg1tWxmEhYKNhBUBs2bLD4F/T19SEej1sEhD3sXm0Wc4Sh2HEFQcjrxEilUohGoxgZGaGdGKylNVuUyhbwku1OdRC8kHL5IIjLqy16McAFwwqCOO4ZhmG5m5qamkJHRwfWrFlTkgmTKIrIZrNz8ikgXg4+nw8HDhzAs88+W3D/re952PLYKaKgzKQx0vFpZltOOCha7k99IWdJsP4F9kmSZ86cwdTUFA27G4axYjsvAJTkxKlpGtauXYu1a9cCmO1qIZ8nKUolIkLTNMv52lMYAFwLKbml9VJD4IKhBnDBsEJwM2E6c+YMhoeHcemllyIYDBY/EOa+6JKJltu2baNV80Bli4/i8SCTTNq2zUYXFE1GJqXTx6/84hEcelN1I3uVLiLsJMn169dbwu6pVArPPfccPB4PQqEQrZWYS969FgKEpLSqTUV/C7auFlKUGo1GMTQ0hEwmQ4dlhcNheL3ePPFQrJCSFRC8kJKz0uCCYZlTzIQpGAyWbcJEIgzlwhZT2idaFrrwukUXWBSHIkkSVSD/J9SqoHCusGH3oaEhXHHFFdRManh4GN3d3ZBl2TVvX8o5LpUIA/FamAukKJV4eGSzWRw+fBi6rqO3txeJRKJgSsipkNLN0poUVPJCykWCwCMMtYALhmWMYRiW8CqJDAwPD+PUqVPYuXMnbWsrh0oiDLFYDMeOHcNFF12ElpaWvEWmUCGl4vFZuh1IVIGIBF8oQKMIiiYjnXD2RJCVpXcBsRsgkbw9cVCUJIlGIILBYFGfjFos7rVKSVT7uGSq5oYNG2hNyfT0tCUl5PF4qICwR3QKWVr39PTg4osvhqIoea2cPAox/wgAhGVm7V4MQRC+B+C1AC6Yptk6s+0LAK4HkAZwEsBfmqYZnXnuYwBuA2AA+KBpmr8s9h5cMCxDSFRhcHAQ8XgcW7ZsAZDLzx4/ftzVEKlUyokwkDkQIyMjBedAkMJL+x3arg/9zPJY9RWeIwEAqleBmc0JGhJdYNMS7/tZFL9uLen0Fx1OeftoNIqxsTH09fVBEATXwr+l0qpZy+OyCIKAQCCAQCBAOzGIpfXQ0BDtxGA/T6dODCBXB0RcKVOpFFKpFIBZS2teSDnPCALElRdheADA1wA8xGz7FYCPmaapC4LwOQAfA3CXIAi7ALwZwKUAmgE8IQjCNtM0jUJvwAXDMoM1YWIXdmLCdMkll9DFplJKjTAkEgm0t7ejvr4eBw4cKBiuLXYRdYoy5O2juf85k+iCoi2Ni0ipi7vdQVHXdUSjUXrXbJomgsEg6uvrabFrtc+zVgvgfC+swsyAMq/Xi6amJgDW+SJ9fX0AQMUDaw9OUihuhZSpVIoKDF5IOT+stJSEaZq/FgRhk23b48zD3wF408zPrwfw76ZppgCcEgShF8ABAP9b6D24YFgmOLVLSpIEXddx7NixgiZM5VKKYBgaGsKpU6cc50C4HdMetSgUXSDFjE4iQdVkpBKZggJiuSLLcl7hH+kcmJ6exh//+EfLPIy5/j1Uo9ZgMWOfL+JkDx4MBpHJZJBOpy2fp1shZSaT4YWUtWZ51jA0CoJwhHn8bdM0v13G698J4D9mfl6PnIAgDMxsK8jKu6IuQ9xMmOLxOIaHh7F161bHuoFKKZSSyGQyOH78OARBwIEDBywh8ULYRcieO37uuq+TEPAHPUgzaQfNqyA7k5ZQZ6IK5DEAvPJLv8MTH76ypHNbKKrx78VaMEejUbS2ttK8PekcYN0ovV5vWcefj9RBtahGSsbNHnxkZIS6ewYCAcvnWczS2q2QkguIyhEACMtPyI6aprm/khcKgvBxADqAf53LCXDBsIQpZMJ08uRJXLhwAatWrcJFF11U1fd1Ewzj4+Po7OzExRdfTEO6peIUtZAVCXoml1JTNJn+THCLLuSek5BK6HnPs/usRJw6B9gZDqlUquCCZ2cpCYZSvB3KhXyemqZh7969FnfPkydPIh6Pw+fzWSytnToxnAopASAajcLn86Gurs5SB8EpxrKMMFSEIAjvQK4Y8ipz9iI7CIBdGFpmthVk5V45lzilmDC1trbi7NmzVX9v++KezWbR09ODiYkJXHHFFWXfpdqPaY8uEGEgKxIEMX9xIgLASQiQ6IIyk6aoBUtlwXS6w7bPcGDdKEtpPayVD0MtqIVgsMO6ewKwmHP19/djenoamqbRtFAwGCw4E2N8fBxALjViL6TkltYFWJ4pibIRBOHVAO4E8FLTNOPMU/8PwL8JgvB/kSt63ArgcLHjccGwBCFRBbsJE7FZJiZMU1NTFfklFINd3IlAWbt2bcVzINhjFktFkCiDkzhQNAmZlFGwsFFlvBlSqVTVJkouF1dGJzdKksIgQ6DYO2YuGApjN+cCQDsxzp07h56eHkiSRAspQ6GQpXspm83SyAKQX0gJWDsxeCHlLCtNMAiC8AMAL0Ou1mEAwKeQ64rQAPxq5m/id6Zp3m6a5jFBEB4GcBy5VMX7i3VIAFwwLCncTJiSySTa29tRV1eHAwcO0ItLpQZLxRBFEYZhoL+/HwMDA2htbS3ZJdINIhjszoy+oMfyGHAXC3b8Qc1SGKkx7ZYA8IbvtuOe/bmitcU6knqhcWo9JG6U/f39GB8fh8fjQTwed/QuWEzUsgW0HOzeGul0GrFYDOPj4zh16hQA0AhEJpPJa+UE3AspH3zwQXg8HrznPe+Z66+1tBGEFefDYJrmWxw2f7fA/p8B8Jly3oMLhiWCk7UzMNuNsGPHDlqIRXDqPKgGhmHg5MmTCIVCOHjw4JxmShAEQcBL/vG3rs+TRd8XUKFnsjPbchEF637u56JoEtIJa2fF/v37MTk5Sad0kpHU9fX1dCT1cqEaCybrRtnc3Iy+vj6agiLeBaqqWtwoF4uAqFWEYa7HVVU1rzU2FoshFoshEolgenra0tli/5tkCymnpqYQCoXy3mOlkSt6XFmCYT7ggmGR4xZVICZMoii6diPUIsJw4cIFDA8Po6WlBdu2bavacZ0WMtVbvMPCTSDM+i4U8GZQRUsOH5gtAoxEIjhx4sSyExC1SHNomoaGhgZa6ErcKM+fP28JuTuZH80ntRIMhmFU9XdiOzEmJyexbds2+pl2dXUhmUxaClPZMelkAuqKh9cw1AQuGBYxrAkTG1UYHR1FV1cXtmzZQsOaTlRTMBiGQS9WLS0tqKurq8pxCX/5H+fpz4omW4obnRZ9J6Hg5Opor2vwBTVLVOL6Q3/AT991BX3sJiDIxTqVStE2xPr6+iUvIOaKU9TC7kZpNz8SBMEiIOyOo7WaJlqreota1kaQGgYyxRSA45j0RCKB3/zmNxgZGYHH48E73/lO/OxnP8OaNWvQ0dEBAPjoRz+Kn/70p1BVFVu2bMH9999Pj/nCCy/gPe95DyYmJiCKIn7/+9/n/W2Pj4/jlltuwenTp7Fp0yY8/PDDqK+vh2ma+NCHPoTHHnsMPp8PDzzwAK644gosLCvS6bHmcMGwCLG3S5KLEVm0E4lESSZM1RIMZA5ES0sLdu7cSUcHV4sDn3rS9TnS5ZBOGfRnFnvNA1Caq6Os5j5TrUiLpb2LgLTNRSIRKiDIqG9N0yrqEFnKlJLmsJsfkTHUkUgkL2cfDochimJNFuBamUzVUjA4RS+cClPPnTuHF154AU888QSeeeYZ1NfX46abbsLjj88a/b3qVa/CZz/7WciyjLvuuguf/exn8bnPfQ66ruPWW2/F97//fVx22WUYGxtzjFjee++9uOqqq3D33Xfj3nvvxb333ovPfe5z+PnPf46enh709PTg2WefxXvf+96i4+prjsBTErWAC4ZFhltUgR3etHPnzpLulOYqGEzTxKlTp3DhwgXs2bMHgUBuSmQlw6eKIckiDH22NoHUKRBYseANqBZPhmKOjkQ4VGP4FNs2RwTE8ePHkclkLD4GJIWx3AVENcZQs+6JZ8+ehWEYSKVSuHDhAsLhsGWq6VxYrDUMhSi1s6WpqQkf/OAHceLECXzwgx9Ec3MzHnnkETz22GN0v6uvvpr+fOWVV+JHP/oRAODxxx/Hnj17cNlllwFAXi0U4dFHH8XTTz8NAHj729+Ol73sZfjc5z6HRx99FG9729sgCAKuvPJKOl21XC+WaiJwH4aawAXDIqGQCVNfXx/GxsYKDm9yYi7hVzIHIhwO582BqGaqwx5dmF3cRYgOngusOHA2bsp3dVQ12eICGQxpiCcyNLrwjh8exwM37aro/EVRhKZpaGxspOFZNyMkksJYTi1v1SiktLsnJpNJvPDCC5iensbg4CB0Xbe4UVaaBqqlYKhlXUY5n+/09DRt4bz++utx3333Oe73ve99D7fccgsAoLu7G4Ig4JprrsHIyAje/OY3484778x7zfnz56kIWLduHc6fz6URBwcHLeZwLS0tGBwcXFDBAPAIQy3ggmER4GbtTDwOVq9ejba2tnmrNh8eHkZfX5/r+OtqdV8USkWwONcmzP7pqprkmrJQGdOn+UAQBBqBICOUSQqjp6cHyWQSfr/fEoFYygKiFnUBgiBA0zRs3ryZvoe9EJWN4pQqwmpZ9LhYOkHi8TiNBLrxmc98BrIs461vfSuAXITnf/7nf/D73/8ePp8PV111Ffbt24errrrK9RiL3iyKFz3WBC4YFhASVbhw4QImJiawadMmiwnT4OAgLr300nlrkyJzIAAUnAMhiqJleE6lyIpoST2wNQdqESto8lonkSArkiWiwOL1zHgyzBwr4KntV4DNN7MCgjgpLnUBUQtvA/sxnQpRyWfIijCnrgGWpVj0WC7FuiQeeOAB/OxnP8OTTz5JP4uWlha85CUvoSmi17zmNfjDH/6QJxjWrl1LUw3Dw8O0JmX9+vUWR9mBgQFqUrVwcMFQC7hgWCDYdkkSYRAEAclkEh0dHfD7/VXzOCgFMgdi8+bNaG5uLrhvNWoY/vQf/svymIgFQ89ajJlK7ZDw2eoa2GP4ZkTBVHxW5IR9CqLM4/c92oVvvH57ub9G2TgVrNmtmAOBANLpNOLx+KIXELUSDIUWYLaOhIiw6elpRCIR2jXg8/moCCN21kuxhqFcCkUYfvGLX+Dzn/88nnnmGfh8Prr9mmuuwec//3nE43GoqopnnnkGH/7wh/Ne/7rXvQ4PPvgg7r77bjz44IN4/etfT7d/7Wtfw5vf/GY8++yzCIVCC56OgIAVZ9w0H3DBsADYTZgkSYJhGDQV4GTCVMtz6e3tRTQaLXkOxFxrGOxiwQ1vQGOGT+WbNLlFF1yPNyMc6jzzE10ohUJWzGR4kVvP/WKh2udTbiSAdaMknyGZ33DmzBlMT0/D4/FAFEV4PJ6qL/C1FCLlkslkoKoq3vKWt+Dpp5/G6OgoWlpacM899+Czn/0sUqkUXvWqVwHIFT5+61vfQn19PT7ykY+gra0NgiDgNa95Da677joAwLve9S7cfvvt2L9/P+6++27cfPPN+O53v4uNGzfi4YcfBpCLSDz22GO45JJL4PP5cP/991fvQ6gQXvRYGxb+irmCcDNhymazGBkZga7rZY2EnivT09Nob2/HmjVr6MWiFCqNMGSzWbz4H5+xbJMV0eK5UMj2uZhJE4vPIyOe1Gl0oRA+dfFcWMjip6oqdu/ebREQ5O6ZTWEstICYj5REudjnN5imiWQyib6+PsRiMRw5coS6UdbX18/ZznoxFlP+4Ac/yNt22223ue5/66234tZbb83bfujQIfrzqlWr8OST+XVHgiDg61//ekXnWTN4DUNN4IJhnihkwtTZ2QmPx4M9e/bMy7mYpomBgQGcPXu2ohqJSooep6am0N7eDlEWkdXZuoXZWgVtxtlRTxtFWyWJsGDTEME6zSIS1oY9mEzmahl8qoTJpE6jC07c+cs+fP6ai8v6vWqN0ywHJwFBFr/5FhC1EAzVXoAFQYDX60VdXR1WrVqFdevW0QFQw8PD6O7uhizLFjvrchbqxSIYamV4tVThgqH6cMFQY9yiCoZhoLu7G/F4HK2trTh9+nRNz4Fc1NPpNDo6OqBpWsU1EqIolnxxYsXJnb+eMaJwAf+BAAAgAElEQVSyiQY7rFhgPRfs7ZFAed0PrFjwqrmfjRnhE/DMLaozXxdrJwERj8epCRJpq3MbR11tFmOEwQ021eE0ACoajWJkZAS9vb2QJImaSTm5UbIYhlGxV8SGG78IAOj/zzscj1uJEFlsKauFwqktmzM3uGCoIcVMmFpaWrBjxw7qFlgLSL2BJEkYGRlBd3c3tm7dSiuc53LMYqTTaRw7dgyqqlKxwEKEgTegImsUXnBJRMFezBgnEYQZMeCUgiAph4BHwVRy7t0ddhbyAs2G31kBYR9HXV9fD8Mwqr4YL0TRYy2O6+RGGY1GLRMkWTtrNm041wiDk1gAyp9RUSuhtRQRBMGS6uRUBy4YakC5JkySJNVUMGQymbIspYtRSg0D6bq45JJLcPND3ZAkEYZhTUU4QeoU9HTWuRuCEQnkMUudRy6aeiDRhYAmI5ZI0+iCV5HwqafO4J5XbCz4uy1mnPL3RECk02kcPnwYPp+PpjDmGoGoRaviYmh/VBTFcYIkKaQ0TZOORc9kMhUJBhJdqMb5AjmzteXuLFoOXDxVHy4YqoybCdP09DQ6OjqwatWqPBMmURRhGIbbIedENpvFc889V5aldDEKCQbSdRGLxbBv374ZV75uyz4kSmDoVlHg9rNTIaRTJMFJJDSFvYjFZ0XBupAXscRslCHkVWEs49wvKyCGhoawf/9+JBIJRCIR2kFABhuFw2EEAoGy/kaWWkqi0kiA3Y3SMAwqIC5cuIDR0VGMjY3Rz7FUUe4WXSDvUU6EgUSTOJxawQVDlXCLKpimibNnz2JgYMC1wLAWY6hN08Tp06cxNTWFyy+/vKptmm7nG4/H0d7ejsbGRuzfvx+CIOClX/jvOb0XaYVMpQ0qEhqDGuLpnMAiEQWW2bZJ97qEwIwI8akSJlM6vPPkBLnQCIIAn88Hn89HIxCJRALRaBT9/f20BZF0YRQTEEuh6LEWx5UkCQ0NDWhoaICu61i9ejUEQUA0GsXQ0BAymYzFztp+518sulDJ+ZL6FU4OXsNQfbhgqAKmaSKTycAwDEtUIZlM4tixY/D5fAULDKt9wU0kEujo6EAwGMSqVauqHqZ06pIYGhrC6dOnsWvXLjoy9xVf+o1lH0kSIcmzF0A2iuDxKTRloWky0mlrxKVQe2Sh9AMwKxwCRTovyLG++NtB3PGnC+1UNz+wAqK5udlVQJAUhl1ALLUIQy2OaxgGZFmmAmHTpk2Wsej2mSLhcBiKP4TMdKzoccuJMBRzeVxRCOA1DDWAC4Y5YjdhIhekc+fO4eTJk9i+fTu1XJ0P7OZPL7zwQtWjF2yXhK7rFjtpUk1uFwtATiCQ4kZFk+h0SjblQCybVVWCVOQL7yQUnKIKAU3GFNNd0RTKtVuSYsimkMfi+riScRIQyWQSkUgEZ8+exdTUFBUQ4XC4JovwQhQ9zgWnSIB9LDrr6Ln79n8FADx2z6sxMDDg2s1SiWDgNQw5BHDBUAu4YKgQt3bJTCaDzs5OmKY5ryZMZOHOZrOW963WoCgWkmqJRqM4fvw4Nm3aZLGTZsUCGVvtVMDIjrS2E/DISDBpBwCIpw26yLNigXQ/OIkFkmooNboAAF5V4hXnMxAPA6/XaxEQ0WgUAwMDiMfjeOGFFywpjLkuyouh6LHax2UdPQmbNm3K62Zha0nKPV8eYWARIPLvb9XhgqEC3KIKY2NjOHHiBC6++OJ59VKPRCI4fvy44xyIWtRHCIKAqakpdHV1Ye/evZZCq1d+5bcQJaFgm6RbQWOdX0W6gD8D68joVWUk0joVCavrPEjM+DV4FYn+7HaM2VZL56/AQ8fGsA/nUF9fj/r6+qIzHVaKaQ4rIJqamjA9PY1t27ZRATE1NQVN0ywpjHIX6cVY9Fit425523cAALLqzfPTIKkgEsnJZrN0n1LcKHkNAwNPSdQELhjKoJgJ0/T0NNMZUHuy2SxOnjyJSCSCyy+/3LFCutqCIZlM4vnnn4dpmnndHq/8ym8dX1OoVkGfEQg+S8Rg9k5fdvjSl2KyxBYxksgBWxwZ8imIMWmIprAHU0kdXkaUbNq0CZFIBCdPnkQikaCWzPX19ZaRyis9EsEKCAB04RscHMTk5CQVEOFwuKSFbzEs7LU+btchqw2zPRUEAN3d3TBNE0NDQ5icnISiKFSIBYPBvPfkEQYrXDBUHy4YSiSbzWJsbIwWfZFFYmJiAh0dHVi/fj127Ngxp8WjnDsrMgdi9erVBedAVFMwkLqMbdu2oa+vr6SLpNsUSlKrIMsiFQ2A9Y7fp0o04kC8ExJpndnXPQXhhD2qUGz4lH2g0dTUFCKRCB2pHAgEUF9fD113HqW9mJjPCIhdQJAaCLLwFZvjsNSKHksVDDve/QMongDMbGkt1JIkIRwO0w6nVCqFaDSK8+fPo6enhz4fDoehqioXDAyCwLskasHimMm6iCFRhVQqhfb2dosJ08mTJ3H8+HHs2bMHGzdunNPFqFS7ZdKm+fzzz2Pnzp3YsmVLwfethmDQdR0dHR0YHh5GW1sbGhoa8s716q/9b97rinkpENjogibn/0kSsQBYRQIRB04igUQVinVQ5I4vWf5PhMR/dI7TfUgOesOGDdizZw/a2trQ0tKCTCaD8fFxdHV1obOzE+fOnUMqlSr6nisJj8eDpqYm7Ny5EwcOHMCOHTvg8XgwNDSEI0eO4OjRozh9+jRisRiy2WzNBMN8Fj0Wwh5dcMNuDa1pGtauXYvt27ejra0Nra2tCAQCOHv2LF7xilfgK1/5Ch5//HFcffXVWL16NVpbW+lrf/jDH+LSSy+FKIo4cuQI3f6rX/0K+/btw+7du7Fv3z489dRTjufi9vqxsTG8/OUvRyAQwF//9V+X/BnMB4K4vP5bDPAIQwGcTJgEQbCYMB04cKAqFyFi3lToWKzVMtuRUOy4cxEMJIJy0UUXoaWlhRY8ssd0Egts6sFOuE6jBY0Bj0yjCHW26IKdgCbT2gSnIsY1dZrF5dE6O8J6PPJ4ik1TeBWLqVMhBEFAMBhEMBhEJpNBKBSCqqqIRCLo7OxEOp2mToD19fVzdtecK4upiNM+xyGVSiESiWB4eBhdXV0wDAN1dXXweDyOofdKqVVKAqhNWqrY8CnWzvrw4cP4x3/8R2QyGQwODqK5uRnDw8N039bWVjzyyCN4z3veYzlGY2MjfvrTn6K5uRkdHR245pprMDg4mPdebq/3eDz4+7//e3R0dKCjo2OOv3F1WSx/78sJLhgcKGTC1N/fX9CEqVKKLeyVzoGoVDCYpokzZ85geHgYe/bsQSAQoM+xX0RWLIiigGzWzIsmsLUKdb7ZCAG5k1dl0RJZYMVCQ2BWXNDXscOplPyuCfb4U8nC6QIaVdCsaQqPVN7CwgqIjRs30j58UpCq67pFQFQ6rGguLNYLqKZpFgHR09MDIJcC6+7uLpq7L4eF+gx2vDs3blrSSm97LLet0jAMvOhFL8INN9yA06dP47WvfS19bufOnY6vufzyy+nPl156KRKJBFKpVJ7AdXu93+/Hi1/8YvT29pZ8nvNBrsZscf69L2W4YLDhZsKUSqWQSCQwOTlZ8ZTHQrjNk2CnWlYyB6KStkqSfgkEAjh48KDrBfqab/wub5uTWABytQr2u/xisOkHsqAXK2Z0Eg5sqsFe2FiMn/TE8Iat5QtDtg+fGPlMTEwgEolgcHAQhmHQaYj19fU1b79dSl0coigWzN2TUdTVEBDzzbGvvqHkfee7rfI///M/ccUVVyx4NKxa8KLH6sMFAwOJKriZMHm9XmzdurXqYgFwnicxOTmJjo4ONDc3V1xQWc4oamA2krFt2zY6eMeJe47mLmSCKMDMEjMmmf4MFG6TXGOxd1aQ1kmKIrdwWoob2dZLj0xfx26j+86IAhIpWB3ULFGGgEeGMXOO/pnaiOzM50OiHNkseVy9f2eyCIbDYWzevBmGYVABMTAwQAUE8TOoNospJVEM+7mS3P3atWsBuAuIcDiMYDBYk+/nXNj94ccAAN768gzc5tPp8dixY7jrrrvw+OOPV/T6xQgXDNWHCwYUN2HKZrNoa2tDR0dHzYZEsakDMgfi3Llz2L17tyUdUMlxSznnbDaLrq6ukiIZr/7ms3nb7NMn7VbO7ELNLvB1bBTB5WefKhUUCex7uEFTDbKE6XT1uxrKvYOXJIm2aAKzw4wikQi1ZO7p6aECopR6leVCMXFjFxDpdJoOgert7aWf7WISELI3gD9+7lVlvaZYTZOdSgXDwMAAbrjhBjz00EPYsmVL2a9flAjgxk01YOVchVwoZsLEmiFJklQzwUBSEslkEu3t7QgGgwXTAaVCxlsXYmpqCu3t7SVFMpzEAosgCnkhf7JYS6JgqU9gxUKDX0N6pkiSLW6ss0UXgFx0gtQ1kPdi6xxYHwc3SHTBI4uIZwwaXfApEqZSOo0uaLKIn5+axLWb61yPVY07d3aYEQAcPnwYDQ0NdKqkaZo0DB8KhcoWEEspwlBuKJ4t/gNmBcTIyAgVEOFwGLqul33XXoxiQpFEF5QKvFmKFT3aicfjZd9cRKNRXHfddbj33nvxohe9qNxTXLRwa+jasGIFQyETpp6eHkxOTuaZMLnVGVQDURQxMjKCCxcu0DkQ1Tqu2zmbpomBgQGcPXsWu3fvttjW2ikkFDxehUYP2EgCeUyo8ygwSvz8vIrVtKlQbQL7Pk4CYm2dhumMAc+MCFjt1xBnnCB9imQZcR3QZGQKOFXOF+w4ZV3XEY1GEYlEcOrUKQiCYBEQxRaWpSQY5nqubgJicHAQf/jDHyz+BaV8doUoRdyYWQOyUr5gKPdzIBGGt7zlLXj66acxOjqKlpYW3HPPPWhoaMAHPvABjIyM4LrrrsPevXvxy1/+El/72tfQ29uLT3/60/j0pz8NAHj88cexZs0avOtd78Ltt9+O/fv348c//rHj64GcwdnExATS6TR+8pOf4PHHH8euXbvK/n2ri8AFQw1YkYIhm80ik8lY2iWBXAvhsWPH0NzcjO3bt+d9WUsN75eLrusYHR2FoihVnz/hJhjYFs1iRZxOYoF0jWiatX6AhSzyKYc6BuKtkNazlhoFt5kPXlVCIm04ph3YuRPs/gDgL2Dk5JmJKngVCVNpHb6ZfTVJRMawRh0WGlmW0djYSAeZZTIZxGIxjI2Noa+vD4Ig0DD8XBfBhaba7Y9EQJw5cwZtbW1Ip9OIxWIYHR3FyZMnIYpixZ9doXMl0QVfKIDDn355VX6XQkxPTyMQCOAHP/iB4/M33HBD3rZPfOIT+MQnPuG4/6FDhyyvdXo9AJw+fbr8k6013LipJqwowWBvlyRfdNM0cerUKVy4cKFgzUAtUhKk7c7v96Opqanq1fJOgoGkWy655BKaB3bDLbLgLRBJsKcegNn0Q8ir0tQDYBUIq/wqFRd1jAhwEgn2YkagcAqCRBcqXfyfGYjjpS351tu1otidpaIoeQIiGo3SRZDcRZMIRK3GUNeCWp+rqqpYvXo1Leolnx0rvkqN3hQSDLKqQBCEgqZl1SSRSPBplQxLJaK2lFgxgsEtqhCPx9He3o6GhoaiJkzVFAzEKXJ8fByXX345zp8/X5N0BysYstksent7EYvFSpp5UUgssNjTEHV5j51FUEBzNm1ip0ayI67dogtkX4JTVMGnSJY0RL1XQSJj0DbNRp+aq2WY8V9o9CmYTBtUYHgcHCgXE4qiWBZBeyEgqWWJRqNVa0WspSNjtY9baGG3f3ZuAoJEINj6EbfjXn7Xr+jv4g3Mj+eGaZpLOrJUTXI1DAt9FsuPZS8YCpkwkfz9rl27Smplq5ZgICKlsbGRDnCqxVRJYLatkrzn6tWrsX///ooLG53EApCLKhhZM6/WgHQ72FMPBFUWC06otL+PW1rCr0iYzhiOYkGbY3RhKWLP409MTKCrq8tihkS6NEoZCOXEUpoqWc4xnQRELBbD+Pi4pX6EdK/YF2kiFgRBgKxK+NWHDpZ9vuVGb5aSz8a8sAJTEoIgfA/AawFcME2zdWZbA4D/ALAJwGkAN5umGRFyX9wvA3gNgDiAd5im+Ydi77GsBYOTtTOQ6+M+duwYNE0r2WIZmHvRo2maGBwcRH9/f55IqVVBpSiKmJycxNGjR0typyxHLIR9CnRbZIGl0FRJu7cCYVVAZQZOSXlighULjQENSd1dJKR0Z3GnMbULwGz0gEQXyONGn4J4JksfHx1JY+/q+XdorAaKosDj8WDHjh0AZu2YyUCoSkZSL6UIw1zmSDilf0gL7NjYGNLpNHp7e2kKg31PX4XRhUpEE3uN46zILokHAHwNwEPMtrsBPGma5r2CINw98/guANcC2Drz30EA35z5f0GWtWAwDCNPLJw/fx69vb1FjYmcmEvRIykyJIWNdpFSSvtjuWQyGTpZ8UUvelFRYVSOWLCLA3sHRMinWmscCtQqEFHAigGnDggWj4OpUoNXtYgE1njJp+QuvvFMltkm5XVLsI/LYand4dntmMlEyYGBAUxNTUHTNBqBIBNa7Sy1CEO1zpUVEI2NjTh37hzC4TAikQhe+fncTZogCPDVaXjiI+VHF8j58vTCXFh54sk0zV8LgrDJtvn1AF428/ODAJ5GTjC8HsBDZu7C9TtBEMKCIDSZpjmMAixrwcC2S+q6js7OThiGgba2toq8/CVJQjqdLvt1o6Oj6OrqKlhkWO2URDQaxbFjx7B+/XpIklRQLBTzVihFLACAJIowstm8yAIRC2k961iroMoiVKZGwGuZJcFEHBTJUjAJONcrzKYgRItAyD1n7Xxwiy6Q/ezPO7EULkzFFncyUZKMpE4kEohEIjh79iympqbg8XiogPD7/TStt1QiDLUaPJXNZi0dLIp2FpmUDlWToWgSnn/+eeqhwaYxilGuX4Su61xgMCzT8daNgiAcYR5/2zTNbxd5zVpGBJwDQBag9QDOMvsNzGxb2YIBAMbHx9HZ2YnNmzejqamp4ouRJEm47M+/QB9P/u6bBfcncyCmp6eLFhlWKyVhmib6+vowOjqKyy+/HIIgYHx83HHfcoUCkC8WwvZIgotYcHptOZD0gSqJFgc3knqYNVpyKngU6XPlRhDsouNERMeO+qX3tSl3EfZ6vfB6vWhuboZpmlRAnDlzBlNTU/D5fKirq4NhGFVf4JeaYCDHPfDJ/wKQcz2VVQn/dcefAsgt5rFYDNFolJpwERvwUCjk2BlV7vlOT0/PaY7EcmQZpiRGTdPcX+mLTdM0BUGYUyh06V35ysAwDHR1dWFiYgJXXHHFnFuO7Aq+7sr3QvYEEHn6C3n7kjkQTU1NJc2BqIbHQyKRQHt7O+rr62kxZSqVchQi1RALTuKANUAKe2drHNjUA2CtVQg4pCXciht9ioTkzL7UN8GWeohnslQk1HsVS5qCLXwk0QMieOhj0/rYHn1YaQiCAJ/PB5/Ph/Xr19Mi2pGRESQSCRw+fBh+v596Gfh8vjkt+Is9JWE/rv1cRUGAos3+ncmynGfC5SQgSARCUZSyIwzT09Pw+eav7XexIwiwdFitYM6TVIMgCE0ALsxsHwRwEbNfy8y2gixrwRCPx6FpWtGugFIRRRHPfu8DOPjOr9JtenIK9S/7KAAg8vQXLGOhW1tbC7on2o89lwgDGZC1c+dOai/sdFwyYdLt83ASCkCuwLGUSIIkCDBM02LpbIcVAqX8HPYqeeZPTh0PRCQ4Uc1BUqcms9hct7TEQzXv2gVBgN/vpwW1ra2tiMfjiEQi6OvroxbFpIjS6/WW/d6LqeixEGRhJ9EFAPCFNGgFCn7tAsI+R8Q0TXg8HtrdVYo3Szwe54KB48T/A/B2APfO/P9RZvtfC4Lw78gVO8aK1S8Ay1wwBIPBol4D5VCsrXLtdX8PAHjmn24qew5EpSkJXddx4sQJ6Lru6BJJBMPVX/vfoiE6J7EQ9uVfrAqlHQDkiQW3WgVWFDT4Zw2d/IqEpGGNIrA/s3f6pNaAFRRsCsIOiUCw0YN41qCPfYqEybRueQyAWkWT9ztx4oRleNRKhJ2/4vf74ff70dLSAtM0MT09jUgkgt7eXiSTyTwBMd/UOiUhKxL0jAF/UIOsSPj5+0qPHNvniBiGgYGBAYyMjKC9vT1vkqmTgJjraOvlyEqLMAiC8APkChwbBUEYAPAp5ITCw4Ig3AbgDICbZ3Z/DLmWyl7k2ir/spT3WNaCodoQwSB7ck6QenLK8nx6egKqP4iX/p8fQvHn2qsGHv5gSceuJCUxMTGBjo4ObNiwAevXr8+7K7vqn38LSS7+pSkUVbDjJhbYSZRsJIKNTARsaYlCHgweSaSiAbAKB68iOUQcrCKBTUPUexVLmqLBK+d1S2SZVEqdKiNTRLw1NTVhfHwcg4ODiMfjNJLkdkFfaGrVquh0TEEQEAgEEAgEcNFFF8E0TUxNTSESiaC7uxupVAqBQIAKrmqKejdqKRhueeAUAEDVZAiiUHErJUGSJPh8PqxatYqOQicpjLNnz1IBQVIYqqryCIMNAcKKEwymab7F5amrHPY1Aby/3PfggqEMiGCIPP0F1L/so1Q4OJGZjkHxh9By81egzOx36qF3uu5fTkqCjL8+f/489uzZY7GyfsWXfmO5iBu6SUWDmTVplIFc7EuNKgAlRBZcTJ3sP+c9xxzH7xBRAHJ39ik9S4sfyTayn91zoZQUBKlN8NlnScgiMuksfayI1tkSsihgQgxi8+YQNm/eTOcRTExM0JDyXCZL1oL5FAx2BEFAXV0d6urqsGHDBmSzWSogurq6kEqlUFdXV9OITS0FAwBLdOEnf7m3Kscl5+sUgZiYmKBtsHfddRdWrVoFWZYxMjJiaRf/8pe/jO985zswTRN/9Vd/hb/5m7/B0aNHcfvttyOZTEKWZXzjG9/AgQMHLO9/9OhRvPe978XExAQkScLHP/5x3HLLLQCAt771rThy5AhtEb/vvvsWn0jmNQw1YeGvZEuIQmkD1R9Eenqi4Os3v+17kL2zi3vPfTfTn0tNSaRSKbS3tyMQCODAgQN4+T/9ZvYY8uxsjGIXck2THb9QxQobabSggFiQbCOuWXGQl5ZgjhP2KMjMRBU0WaJ3+U71CiGPTIsfyf5OkKhCofoGJwKqbIk62CdaspA7QuKqSCZLss6AZDEMBoPLpv2tUhEiiiKCwSCCwSA2btyIbDaLyclJRCIRdHZ2Ynp6mqZ8wuEwNE2b87nWqujxLQ+dATAbXZDL/Dtzo1DRoyRJFnH14x//GN/4xjfw61//GjfffDMmJydx44034vrrr8d3vvMdHD58GKqq4tWvfjVe+9rX4s4778SnPvUpXHvttXjsscdw55134umnn7a8h8/nw0MPPYStW7diaGgI+/btwzXXXINwOIy3vvWt+Jd/+RcAwJ//+Z/j0KFDeO9731uV37taCOCCoRYsa8FQ7QsEiTBks1ko3gAyCWtKQvUHHV+XSU7RKAPLjg/8dPa1ZOH8wc8hzyyQMrPoitLs75LbPg3gPKQC/gBOaC7FiOyCb2TNgl82N7HgNuKaxatK9Dm/IiEz87M1mjB7Z68wv7fXsdCxtOJHjywiqc/WLtR7FMQzs7MiGnwKkpmsJYqQNkwoM3d5sgQYOujIbaXA5+M0WTIajWJkZAS9vb2QZXnOtszlspARhmKIoohQKERdEg8fPox169ZRJ0pd1xEMBqmAqMRDpRYRhpfc+z8AAFWTaCqisb469RnlnC9J/Vx77bW4++67kUwmMTAwgD/+8Y84ePAgTVW89KUvxSOPPAJBEDAxkbu5icViaG5uzjvmtm3b6M/Nzc1Ys2YNRkZGEA6H8ZrXvIY+d+DAAQwMDMzlV60JgjD7XeVUj2UtGKqNIAjQdR2///3v8duvvhV/+oF/BYA84cBGEezoiamCz1v2TRtUNGQNk4oGdnspKEVGRjv5IzjZOge0/CFT+a9zTj0YWdNxQJQiClQ02PEpIn2OpA8yWdOxvZEIAjexwP6/UgKqiKQ+e67nEsC6EtYH+2wCJ1vmYq6K1WCxCgY77KwGILd4khz+wMBASUWATudaK2EmiAIUTYaiyXjgpl1VOaZhGGWF+VkfBo/Hg0suuQSZTAYf//jHMTY2Bq/Xi8ceewz79+/HP//zP+Oaa67BHXfcgWw2i9/+9rcFj3348GGk02ls2bLFsj2TyeD73/8+vvzlL5f/C9YYHmGoDcteMBBHurlimiaGhoYQj8dx4MAByxwIxRuAmc1CsF2QzKwB1ec+u8FIJyCpuRUnPeMOVy6GkaVRBkPP0rSErIr0Ys5ut0cPyhELwOyQKSdYsRCytWGyYqFOk5HNWsP97PuQjgQn2EW/watYogYN3tk0BREQTmiSdRiVOlPjwUYXgJyoSRsm7NkOEl2oVH/YbZmJKVJ/fz81RUqn07S3vhqLcq2sq+fD5VIURSqoSBEgyeGTIkDWSbEaRkjFYKMLiiZD1SSsquJUynJ9GOLxOHXpJOzcuRN33XUXrr76avj9fuzduxeSJOGb3/wmvvSlL+HGG2/Eww8/jNtuuw1PPPGE43GHh4fxF3/xF3jwwQfzPr/3ve99eMlLXoI/+7M/K/8XrDXCyit6nA+WvWCoBul0GsePH4ckSfD7/VQsyB4/9OQ03a9Y5IA8r3h8yCTjrvvpGYOmJcpB0SQqDArhZIiU2+4+htqOW4Gjk5jwF+g60OTZDgWNOXcSKQhpsuPCX8rkSY/leNLM+c0+r8oC0kzEQJVyaYhyiGXmflGyuyrG43EcPXrU4mlAFsxKWxJr5Z64ELbY9hy+k4+B3Yq5VrMZSPRO0WQcunFn1Y5brsBJJBKObZW33XYbbrvtNgDA3/7t36KlpQUf+9jHaFTgpptuwrve9S7HY05MTOC6667DZz7zGVx55ZWW5+655x6MjIzgvvvuK/kc55NchGFpeaUsBbhgKMLY2BhOnDiBLVu2YN26dZbw3ZQGwE0AACAASURBVNCP70DzDV8EAItwAOBYs0DIJONQPLm8IisM2NSBObPwCiJgzixykizS/VlhwNY3uOEmEmafzy9uDHnzBYS9bdLpuOw2vzpzQRVFZLJZx1oFURAstQpuBYrktSlm1XdLT5D93aygSVSB/H82amB7PHO65HFAFZHSzYqjC8UgngaKomD37t2OLYlsR0E1CgIrpVZ1EeVi7yIgToqRSASnT5+m5xgOh6Hr+py7Vl7xf/8XQG5WgSAKVY8uAJVFGJwEw4ULF7BmzRr09/fjkUcewe9+9zt89atfxTPPPIOXvexleOqpp7B169a816XTadxwww1429vehje96U2W5w4dOoRf/vKXePLJJ+el/qZSeISh+ix7wVBpSiKbzaK7uxuTk5NF50AAuWiDaRgQbF9yM2tQTwYn3KIJiocVEvnPs2kGtr6B3a6qEu1IYFMR7M9e1blbolBUodS0RFCTwd6wu6Ue2FqFWaMkq7hw+pnUNaSMLBORUJCy+Vmw7ZFGkU4Ue5RBFQWkXX7X+cCpJZF0FBw/fhyZTIbm8+vr613z3ou56LHax3SyYu7q6sL09DSOHj1KayRI22s5CzMRCwBoKqI+5KlqdAEoP8LgJhhuvPFGjI2NQVEUfP3rX0c4HMZ3vvMdfOhDH4Ku6/B4PPj2t3Pzi44cOYJvfetbOHToEB5++GH8+te/xtjYGB544AEAwAMPPIC9e/fi9ttvx8aNG/Enf/InAIA3vvGN+OQnPzn3X7qKcGvo2rDsBUMlsHMgtm/fnncBYy9q9m6JQpGF3PPu5iqZlO5aoFgqqiZDLuH2t66M9ENuf3cfBfs2I2vmTZH0yCJtSywlncAS8syKC48s5hVJOkUkyHuENMWSDvHIIrLIvV6ViCdF7rm86MLMYe3RB/v21RsuxvToubJ+p2K4LZpsR8GmTZtoQSDJ52ezWboYspMRF+viPh/HlGUZHo8H4XAYq1atol0rY2Nj6OvrgyiK9DMrte1V8yq02NFXRgFyqVQrwvDf//3fedte/OIX47nnnsvbvn//fhw6dAgAcOutt+LWW291fC9d10s+r4ViJRo3zQdcMDCYpon+/n4MDQ25zoGgbo9MWNOpxRJAQWMnwJr/pOcwsxjq6SxkNbcyCaJAt8++1lqvUEp7ZbFpkXaxYGRNRxMnr+0CaRcPTmIBmJ0zwUIWe0UUoEj5NQdOx1FEwTKxkqAVuMCy7ZHpuc34shRUylR0VC8KUc6x2IJAILfQRKNRSzg+HA5XbRqq/TyX4lRJe9dKJpNBJBKhba9sjUQwGKSvI9EF8l3zBzUEPDK2ri1tXky551vu8CluDW1FWgJj55caXDDMQAyR/H4/Dhw4UNA0hb3wnvm327Hxz78FZaag0cwaEERbWsIwoPrdLypsZMEy5U5l0xKz/1TEHMbS/cB0S9hhfRJm0xJZWhTkVaSSTJyA4mLBYzsHu+2yNbVgFQhOaQnNIVriNLGSTUOQqIJSYOEh0QVlxm/BHl0g50wfz7xOse1H33NNM4A5KpEqIEmSJRxP7qaHh4cxMTGByclJx8WwEpZKhAEoLEQURcGaNWuo8VY6nUY0GsX58+fR09NDfTPIvAhFk2hHk0+V8H/+JN/HYK4YhlF2SoJ1fF3p8JREbVj2gqGUi8/58+fR29uL7du3U7MdN4oNoAJKjyw4oWeyc3aLs7spulFq+gHIFwpAcbFgd1/0MuKhlFoFViyEPHLBiZUkuuBUBOlVROjGbAGjX7GmNVRJQLllCqokUBGxmO9kyN00me/Q0tKCSCSCc+fOobu7G6qqWkykylmsayUYahVhKPVcVVW1CIhUKoXrv/187rmZ74wgCgh4ZGxc5a+JwKlWSmIlwwVD9Vn2gqEQZNJjJpNBW1tbSQ5yTkOi3IZRAcVbLYl4UJnIAvEoEAWBLrCiKFi8Cwisc2NJIqHA2N1ShULuOOWLBSD3Ozm1OwJAQJXowq1JoqM1NK1NYOoa7O2RgDUF4QZbm5BzdXR5bKt1KKEpZU7UwjOBLO6qqmLt2rVYu3YtACCZTNKZBJOTk/B6vVRA+P2FF8Ol1Ko5FyFCxIKeMeDxKVA1GQGPjDVBD/40exLPPz9Oa0bKFV2Fzrec43DBYIU7PdaGFSsYYrEYjh075jrp0Q2nCMPJ792KLe/8l4KRhWzWhOZVkEk5FwylUwYVDayBk/VnJl0xs3DqerakIsdCQgFAWYVbdrFAFvEsk1JguyO8tgU/W+KCSFox7e/jhCoLEGFthWTnUXmVnKOkm6WzXxGt3RGSWHDhlme6J0h0QREBAxIkszppifkK9Xs8HjQ1NaGpqQmmaVITqdOnT9O8OOsBwR5juaQkSkXVZDozos4jw6vkfFm2bdtGXSinpqZogeVcnTvLeV06na7IMnu5wosea8OyFwxOHQ59fX0YHR3FZZddVrYqLyUlUaiVkljIFqJS46a0nqVRBk0WoTrcXrN1DD7VuXYBKO6vQLAv4vmPZ2oszPznSFtk1jQt6QfNpfhRkQRkDOu+rI+CYavpKxRd8Moi9KyZdxcyW8uQK46UbbUObHRBFQWLMJJFAVXSCwuCIAjw+Xzw+XxYv349TNPE9PQ0IpEIent7kUgkLB4QS7XosRyu/cYRALkIH2ldbgp74FVl/MMrN+H3vx+hxltEdJGoTX9/P6anp+HxeEqO2lSKIAiL2hNhIeCCofose8HAEo/H0dHRgfr6erS1tVX0BXMTDCT1oDt0S6iajDQTWWCLHNmoAdnGRiFK8ZFgF3KnIkE7dQUES6lCASgsFiTB7txoTT2w9s/sfuxzuULIWatnO341v8XSSSTYCxUrDVWqktV/QpEEGLoJtuREkWVkFmHbWSWLO6l7IMONTNOkHhAnTpygi6GiKKivr6/KHW6tIgyVpCSIWABmupIkEb6Z78KaOmfDLEEQ8pw77VEbn89HBUQ1rL9rZfu9lOFFj7VhRQgG0zQxPDyMU6dOYdeuXbQFrRLc2tO6vv4GbH//T1xrFlQmssAKAjYVQVA02eYAmZ+KANzrC9xwmvZIcLeLLh5VYLeRtIS9wNHNcZkVBU61Cooogi2PcBJERAiQtAO7jcVuwuSbSUOQfWcfM89nrbUNhi0qkXN+zFY1X1rLGoa5IAiCZSz12bNnkUqlEI/HMTg4WNFQKKfzXOiiRzuqJkHTZIR9ClRZhFeVcdeLW0r6d3KK2sTjcUQiEZw6dapo2qccFsKme7HCh0/VhmUvGDKZDJ5//nmIooiDBw/O2RbWqejRCTNrQPNa70LSiQxUr0Id4vLOtULjJjYVkdJnWxFVWYTq0GrJ7uMtMy1RLAUB5NcsALmIQy4tkR91sI+xZlHl2bt68rvoWdPSFmnHTSwAs9EFtcLKxYCaa+l0O9/cewHpOVoeLJWLv9/vR1NTEx0K5TTTgQiIUqr+a1X0WG5KgkQXJDln/yzN/OdVZRpdqDRq4/f74ff70dLSQtM+0WgUJ0+epDMh0uk04vF4SQKCRxgc4BGGmrDsBUM8HrdMBpwrhWoYZDV3R6WnM3nPKZrsGllgRYKiScikDMsMiVLSEqxzY2ndEu7/9G6Ri3LFQkCVbR4Ms+dVp0l5NQeFnmOFD7vYy6JgERCW18xEFNQCF478GRKwPCbFkKVEEORFfH2ajwJFp5kO0WgU4+PjOHXqFARBoHfSoVDIcQFfDEWPr/32c5DkXLoJyHUi1XlyFuoBLRddKPeYbrBpHyIgYrEYYrEYent7kUwmEQgEqPByGj6WTCaLWtevNHjRY21Y9oIhHA5Xtd1IkiRkMvmCAACe++xV2PexJ6lwsEMiC+mUVXDYIwsKFRKMzwDzPLugl9PdUNTp0fY8KZAslIKg5+dg2GR/bHd5JLC20R6HgkavIlIBoYizbpFOizgpZiQigRULsk1UELFg7Y5wn1hJayEkq8jwiCZ0WI999uxZNDQ0VG089VxZiI4GWZbR2NhIvU2IIdKFCxfQ09NDax+IB4QoijUregTKi9oYukndVAMzYmF1nQdrgrNRw3K9Eko9R5LC2LNnj+vwMSIgPB4PpqenK55iupzhgqH6LHvBUG0kSUIymczbTi6CLIaRhWZrZ0wldGjefEtoQiZlOA6bKkZaN2hXhCqJSM+ssKos0vQD2yHBpjHc0hJ+RYLosN1RDFhqA5wjEcQamhUFrG00G+ZXC9yuS4IA9tqv2hZwFlkSoBtmnliw7OMSXbALA4IiABmbpiCnK2RzUaQtLevwh2O5gUdkPHVDQ0NJd4JLJcRcrghxMkSKRCIYGhrC5OQkNE2Dqqo0orYQQuu1387NWCBiQRIFyKKAgEdBnUdGU3D2369W4oYVIk7Dx4iAOHHiBD7/+c8jm80ilUpheHgYTU1N9Dhf+tKXcOjQIQiCgN27d+P++++nf38f/OAH8b3vfQ9TU/lF2ocPH8a73/1uALl/47/7u7/DDTfcgGQyiZe85CVIpVLQdR1vetObcM8991T9968GvOixNix7wVDtiw65CyIYhoGuri4kk0m0tbVB+el/AUCe34KZNaF6ZWSY6IKrJfSMBW25sM6Nbi6Olv0LRBzs8yCAwsWOpT5mxUKdNtsR4VHEvFoFw7SmGgrVK7DRC68suk7TVESrHwMxaWLJm1gpCdS0SYQ1uiFkc/9Ogp6CKc/cfRq5CFRra6vlDrGrqwupVArBYBANDQ0Ih8OunQVLwd9grsfUNM2SLkwkEujv70c0GsXhw4er3k1QjNd994+WxySyEPAoCGgyvKqEN24L0+cXogVUFEVL4en999+PH/3oR7jvvvvw9re/HaOjo3j5y1+Oj3zkI/jKV76C48ePw+v14uabb8a///u/4x3veAeOHDmCSCTi+v6tra04cuQIZFnG8PAwLrvsMlx//fXQNA1PPfUUAoEAMpkMXvziF+Paa6/FlVdeWfXPYK7wosfasOwFQ7VhaxjIVMv169dj586dEAQBR++9Bnvv/qVr8aKiSXn1DEB+ZIF0Q3g9hVMRXrW8f8JCIgEAPLJk8RrwSCKSNvtmeg5liAMg1+Fgt4YGcmKB4Far4JFnfRZkEXldF27RBSCX0mBFgl145ASBVQi4RRcIop5CdkYgCDMCgUQX6O9rJJCSvHl3iBMTE9RdMZvNIhQKUQFR7RB3Lam2CPF6vQiHw/B4PNiwYQPtJujr66OzEthugmrCigVREml0IexTEfLmogvrQ9b3nI8IQzE0TcOOHTuwd+9e3H///UilUuju7gaQqyFJJBJQFAXxeBzNzc0wDAMf/ehH8W//9m/48Y9/7HhMn292om4ymaT/xqTeAsgVk2cymUWRbnOERxhqAhcMZSJJEnRdR39/PwYHB12nWhKypklTEIRUIgPNm0tVOKUfyjFuSqR1KhrSRpYuuJos0tkLbiKBTUuokkgnQBqm1f64lGLHUsQCkG8NzYoFtlaBhV3gyUtJrULu3PPbKYulIFjTJvsAKnkm5UAeizOCwBRn5ggY6dz/sw5RIBfxQCCjlMPhMDZv3gxd1xGLxWhhIBlfret6VRekWrQr1jJq4dRN4JTLJwJC05x9EcpF0WQ6i6VuJrIAAKuDGt6w1WrGthgEA2CdVKlpGnbv3g0AuOOOO7BhwwZ4vV5cffXVuPrqq/HlL38Zr3vd6yypCyeeffZZvPOd78SZM2fw/e9/n3aXGYaBffv2obe3F+9///tx8ODBCn9LzlJk2QuGWjjRjY6OQhRF16mWxM45bYsiOG1nIwusDbSmSkgkyzcAYgsbyc+sMGDrGAIe2XVwkpsNs9N2p4JH+4RKg4kssM+JEJBFfvpgdkrk7HOFmj/sUQN76sHN2ZFgL1xUBDicVT40umCkAWNWVAAA9DQ0PY2U5uz6CeQKA9npkul0GqOjo0in0zhy5Ag0TaOL4lxshhdjSsIJt0XYKZdPTKSOHz8OXdcRDAbpZ1WOB8QND+ZmRWSNLEIBdcYlVURAy6Uk1gQ1hLT849Wi6BEoX4g4jbaORCJ49NFHcerUKYTDYdx000146KGH8MMf/hBPP/100WMePHgQx44dQ2dnJ97+9rfj2muvhcfjgSRJOHr0KKLRKG644QZ0dHSgtbW13F+x5ggQFvVQuKXKshcM1WRsbAzHjx+Hx+PBrl27XPc7fM9VOPCpJy0CAABSyQw0T254jVOdQjqlW15D0hF1lrREforCyWuhEIXSEsUEASs47EKBfT0ZnOU2iRKYHRAFwLVWgf1ZmjFOcktb2Le5zY0AcgLCabYELV400jBljUYXYGQAUZ6NLhgZCEbGKhCyem4fl+hCKaiqitWrV+PcuXO44oorkEwmMT4+jv7+fkxNTVXN5KcaLKQIIZGYUCiETZs2wTAMmuo5e/YsTNO0mEi5QcQCkIsupPXsTAulSMVCwCPnRReAxRNhcBpt/cQTT2Dz5s1YvXo1AOCNb3wjPvWpTyGRSOCSSy6hr7vkkkvQ29vreuydO3ciEAigo6MD+/fvp9vD4TBe/vKX4xe/+MWiFAwAaMSUUz1WhGAoxcegENlsFj09PZiYmMCePXsKfsGcMLOA+v/Ze/cwua76SnTt86pHVz/UekttSTa2sC3JyHq0YQYcM8YEiMfGhJgBQiDgMCFfSO5ALpjEhJDJjQ3XAZyHgz1mBg9m8DC+AZxgEsDYXwzBWDKW9bAsWZL1aL2l7lZ31+u89v3jnL3P3vvsU4/ualt21/q+/lR16pxTp1rVtVet3/qtn1KWkOOhZ/bfIJYiKm6QarUs5a2m2QzqYq6WJVQ0a6NUSxLi49FgJwj39V4Fx2zWQpnMcmiUx8BLDRkehiyY9anEyAiAeFXAEF5n4EokAgCIXwMMC/BZ2WJ65IEtmvl8HsuWLeMxw+Jsh1qt1rIs/0pRGKZbOjFNk/8eAPBSD4tkrlQq2L9/P8+AME2Tk4XAD1GI/0ZyloFS3oZJCCfqgxmD286XuRcs4EnEihUr8OSTT/LHHn30UXziE5/Axz/+cb5PqVTSfpa9+OKLuOCCC2BZFg4dOoTnn38eq1atwunTp2HbNgYGBlCtVvGjH/0In/70p6f/QmcRBLM/VXYuYk4QhpmgXC5jx44dWLx4MTZt2gTf91tKemRlBk/JXNDFQ4utljlhsW+Wm6BDb96SzJGMKGSVJXKWkSnd6aKkW/EzqGSB+RR0nI0t8CHkb/tse7qFMv1BqhIC9TYDK1Mw5EiIECaMeGKUHUSdDiIBACD5Eqhh8jIEABi1CVA7H6kLAIjvgipG1MLUCVRLMw8OU2c76GR59q163rx5M041bYbZKkl04rrFUk8QBHjmmWfQ19eHM2fOYP/+/fjC8wm5UslCb+xjKOWjVMf/eLG+pHS+KAysdVfEVVddhXe/+93YsGEDLMvClVdeyVsldXj44YexdetW/Pmf/zl++tOf4o477oBt2zAMA3fffTcWLFiA7du344Mf/CCCIEAYhrj55ptx/fXXT/t1zioItC3hXcwMXcKQAUopjh49isOHD2PNmjXo748+NFqZVgkAP/vja/Dv//LxlKmRlSWiqZVpUlF3A4k0MIjjqaXoZVaWaCHdkSFvmQ2jjcVERnl78w+xLEMjg6UhBQC0ZIHtz1QGtj0I05kJ0TkiZSSLLIj/GtMcK0lqk4Cdj9SFBvtQKzej0kQr0MnyYjQzEEnHg4ODCILgFaMwzAYJMU0TCxcu5BI9nt+e2q+Uj2ZFRK2UFkp5C/0N1L/ZVBjaIU3ValWbZPv5z3++YU6CmMFwww034IYbbgAAfOADH8AHPvCB1P5XXHEFnnnmmdT28xGRwtAlDJ1GlzBo4Hkedu3aBdM0MTw8LP3xGoYxrfIGDSnvjODPExse7ZypJQntQFQQWK1fRMExJc+ADqqiEFIKg7SW9ChuCzN+P+JCnrOSbAPLkA2GhKTVCJlcJNvZjAq2LWcmZQrV+KgDIw5MNTDcMqhpJ2ZGtwxqOi0t/sRPkwh2nsLECKp9Q03PAUw/uEmNZvY8D+Pj4zh9+jROnToF27ZRrVYxODiI3t7ejkxJfCWMt1bLHO/+RkIWom4Ii5scc7GyAETv53+3IDtEajYVhna6PiqVitQK2UWEroeh85gThKEdDwOTdy+66KKmrUfNoCs/AIDlpD9kqjVfa3IsZdRPs8A+7HRlCS8MOWnwAgrbJJJJUUXRNjO3N7oPpNUF3vVA9UZFgog06MoKBSE62hbIUKP5DrrMBVVVYIs5NVv8HTNCwI2PcRmiNgnqyDVkoz4Jak8/K6ATC7Ft2/xbteM4sG0bpmliZGQEU1NTyOfzGBwcnHYw0itJYWDnfM83d/DtpbzFOyIcy4zKc/GQqQU9DvpzFh9JrTObBkEwK2WfTpQk5jq6HobZwZwgDK0gDEMcOHAAo6Oj2LBhQ0eCYR7/5BtxzV/9NBXiJLZSFtrwKehKESIxaGfcddHOLku001LZjCyIKYnsvgixktLMg8BgGkSa3KArTzAYNEBIzIYlCDV4iXsU4vtGfSryKbD9vTqoLac6cnVByGZQz1McP4jKwKrM65hNUEp5B8aSJUtAKUW1Wk0FIzEC0WqE9SuFMBiGIZGFgmPGyoLJp7oWnOj2gh4HRdvEW1f1AlirNZuWSiX4vs/nZMzG9baKSqXS0Xk5rwoQ0vUwzAK6hAFRDXDHjh0YHBzEpk2bOiozWrYB34ts/2FIU2OtK1UPxbhUMR2TY9UNOFEQb6sQR0lnQbf4s7JEPk5pFBUHdX91/oNKDhyTIKTq/SQOWudVaBoNzfcVzIwGECJRFEy/xlUEEnhyyYF5EYjwewlcwIwimzkR8JN2yuhfWTUSo6FTpklMv1uiU1AXYnHI0fLly3kw0ujoKJ5//nm4risZKHW5Bq+UkkQYhvivzybvj1LeQhBSuHGw2fweh5scmRo3Tygf6symU1NT2LdvH0ZGRjAyMiK1cGbFfbeK6bRVdgmDDIJuSWI2MCcIQ6MPtePHj+PAgQO4/PLLeUtWpyGSBoacxkw1WfM5aRBLEeJciKJjYjIj0KmkdEjoyIGuLKG2SIotlbouCrULAmiNLACAQaKyhGxyjM6XNwlCzTHsMbGFMgippJCIKY1ZSBZ7/bRRAImZsckCT/w6aEwyOBlQkh+JX5NzGgAUz7yAyoJLGp775Ri8JAYjrVy5EmEYcgMlyzVgExJZhPUrRWH46D8e5L4e9vchqQtCKaLHNlG0TbxxebYngM1z6O3txYIFC9Df3y/FfQdBIP2u2i1bTEdh6JYk0uiWJDqPOUEYdPB9H7t370YQBBgeHm4rGY4Q0vIf9Y//4N/hLX/9b7Bi3ZzNkahVPeSnqSz0Kj6FdkoRDKwTIouF5zK6LkSywBSHVskCg44sqLCNRI2wNWULMSfejm/6gnqhmhlFkMCNjIyBoB4InQ9cVWCqQ+BFJRCVICgwvEoSHy3sw2/7DYjKLKPdhdgwjFSuwfj4OEZHR3HgwAGYpgnXdfmUyfM1wvp939oJQFagio4ZdUSYBjc5mgZBj2OhaJuSutAI7DNAjfsWu1UOHjwIAPx3yTIgGmE6Hoau6VHGXFQYCCH/BcAtiOxgOwD8NoClAB4EMB/A0wA+QCnNbvFqgjlJGM6dO4ddu3Zh5cqVWLZsWdvfaNjEylY/2JycxeOgxTkSDOMVDwPFaFu7JkegtbKEWD5o1DWgUw+yshp0bZONyAEQLfjM08AzGKhMCnjrI5G/JcgtlFG7pS0+Ht9mRED8dm+wbgdGCupTgCVIx14NaGehCtyIRCjzJST4Hgg8wBLk7dBHz6ndKC+6rPXnOg9gWRYWLFjAa/au62Lbtm04ffo0Dh48yCOsBwcH0dPTM22VQDQozhSMLDBEvgU78irEZEFUF3odE4Um6oKIrIVd7VZhZOvs2bPYv3+/FDLV19eX+hxhbaCtolqtdhUGFWRuDZ8ihCwH8AcALqeUVgkh3wbwnwC8A8CXKaUPEkK+CuAjAP5+us8zpwgDpRQHDx7EyZMn8brXvW7adT+WxdCK1Oj7EVHQpTnqIpqlWQ9KKUI9TjI8ZhCCnBVnPQSJhC9NbjQNLYEIabRgZxkgVbKg63zQkQUgapuU45+F8xhEO8OBHRsI5QyH+qAkWbCpKdeOUz4FHQRvAjVyXF0ggRd5EtRzGA3+z4MAJAgA4cOehD4obFldaFQSmSV0Wup3HAeO4+CSSy6B4zjcQHno0CEpwnpwcLAtA3GnrlMlC1GgmaWUJJKZEaU4bEtHmLPQ6pcGHdkaHx/HyZMnsXfvXjiOI80LCYKgLZWlWq12FQYFc1FhQLSeFwghHoAigOMA/gOA98WP3w/gz9AlDI1BCEGtVsOOHTvQ19eH4eHhGcmerYY3TUxMYOfOnbj311bgo98/xreX8hamaj7OVTz0x8qCbky1SB50aGRybAZGJLJQtA3tH1zOMqTkRduQkxjZNhFq94I8fTK75ZUdJz7eSB2RI5rr0bECiZBKEOK/MYx6WWqxZBkMKQhtlVSJhuYQCAKpToDaBalMUTzyNCoXbNS+jleKN0A8Z6FQQKFQSEVYi5MlWQdGI1NgJ0yPKllgJQhWlmBlMGZyLNrRSPd5BbtldWEm1+o4DhYtWoRFixYBiEZIM//D1NQUarUajh49ivnz57ek1nQqHfPVhlehh2EBIWSrcP9eSum9AEApPUoIuRPAYQBVAD9EVIIYp5SyD54RAMtncgFz4l129uxZ7Ny5E5deeimfCjgTNCMMlFIcOXIER48exRVXXIFSqYSccxJ1NzpmsuKhtyiXHoIwhBl/+KjtkxW3OTmpegE/zjAIQiW4KWcZLX17ykp5FD0NlCJFEhgkf4IhmxjVxxPFISINWW2V4m0DFCEIzFBYkIWBUGqmQookWCKBkDsmxO26c0TR0PKfDGGljCDg+1KzwPdP4WVQF2YLWSQkK8J6dHQUR48ebWgKnCmxyVIWgpCilLNQdBKjoxOX+o/wlAAAIABJREFU2gxCMK9gt+xdYOhUR0c+n8fSpUuxdOlSUErx1FNPwbIaZ0B00RgE5NWoMJyhlG7SPUAImQfgRgAXAhgH8H8AvK3TFzAnCENPTw82b94843YnBtM0EYbqUhjBdV3s2rULuVwuNf5al+aoDorSge0jljCYstAjKBNi14BYSrDib1Q1P+SkQWyRtE3COyeCEGA+xEZJj9oWxyY1QzX+WeQ0Ugqk0BHhmEJQU7yLRBbUgVBI1AX4ruxTYNuQ7pjINDLWp0CtJOmR1CZB7VwS2hSXMqTnjxUFCeUxoNArbSoc+DmqF71B+7ydxvkyWVI0BY6OjuLgwYMghPAFcSaLsI4sMDCyUIh/HMtA3jRgmwaKduRnWDP48hAGEYQQGIaB5cuX83bXcrmM8fFx7N+/H5VKhQ8c6+npQW9vLz+uCwFzzMMA4C0AXqSUngYAQsg/APj3AAYIIVasMgwBODqTJ+l8rul5iEKh0DGyAEQfgDqFYWxsDFu2bMGyZctw+eWXS2ThO78ty8+MBIgtkqWcJfkWWkHZnV5/fy7+oGw0N4L9iHBMojU2qmTBUe+bSekifby8n3rbpr6+XTIQVYYkylmC70okIUs94PfZ8a1EQbPnrJdT5+IEJEh7F2iTbomZTFZthPOlzMFMgRdffDE2bdqEK664Ar29vTh16hTGx8exa9cuHDp0CBMTEy3/LrLIQsGJ/qbYULaCoDDYpoFCxvu8FcxWNLQIptYMDQ1h3bp1GB4exgUXXADP83D77bdjw4YNmJiYwIMPPoiTJ08CAPbs2YP169fzn76+PnzlK1/B6OgorrvuOlxyySW47rrrMDY2lvm8ExMTGBoawu///u+nHrvhhhvO25HWDJGH4dX10wSHAbyeEFIk0R/ltQCeA/AYgHfH+3wQwPdm8nudE4Sh01BLEpRS7N+/H3v37sWGDRuwePFi7XG9eYt/kI1XPBQdk9dXAfDgInVfNginGbwgOV5MORMX/5xppHIXROTjmq4OuiRFndlRJAsqwcgiCwbRkwUVJHCjeeHSNs0C3GC8tGqGTBZ3OYOBqOeIF3qjrpASEYwU1Ct8E3Vr0WnLk8k2Lzp3Ye+/Ys+ePTh16hQ8TyBAs7C4dxqdUi1YhPVrX/ta9PX1YfXq1XAcByMjI9iyZQt27NiBkZERlMtl7evIIgulvM2VBRE9joV83CVRtM1pqQtA51tAWwHLy1ixYgVuv/12PPHEE8jn89i3bx/e+973YvPmzVi1ahW2bduGbdu24emnn0axWMRNN92EO+64A9deey1eeOEFXHvttbjjjjsyn+ezn/0srr766tT2f/iHf3jFdGSYhLyqfhqBUvoLAA8B+CWilkoDwL0APg3gE4SQfYhaK782k9/pnChJdBoiYWBmyoGBAWzevLmlDxBd7gIjDcyzkGV4FIlDPjYuit4E0WvAPA1eEMI22TyJpENCnSfB3pRiR0VIaeZIafXyVFXBatJiGcVGJ0Y0lvpoEQCUghICI0h7FQDouxcYAXAraa+BsL/WyCjuK0Y/a+6L5+NKRGUcyEWGOa4gCNdOPY26EN9etGiRFJDU29sL13U7+g12tsKgZiPpsVAooFQq8Zp+pVLhEdashXDevHn45ONnU8eLZEH0AjlWFP1cylvIW1FnUFRuMzDYpndhNtEusQuCAIODg7jttttw2223oV6vS4OrHn30UbzmNa/BypUr8b3vfQ+PP/44AOCDH/wgrrnmGnzhC19InfPpp5/GyZMn8ba3vQ1btyYeu6mpKXzpS1/Cvffei5tvvnl6L/AlQqQwzKmSBCilnwPwOWXzAQDDnXqOOUEYOv2hxgjDqVOn8MILL7Rspvyf730dfutbz/L7XFlQyIHOs9AIojehVfCo6AZW4qwYaZ3SoG5rRhbkMddJiJQhNFVKZEHwKhC/niIEunHTTBkwvKq0v0Q8QjXiWZ4NwYmBL3sdqFsFiQdOMQVBNTSG5UkQJRAsLE+AOMmcBup7WHr8l5h3+bXR0/g+Tp48ibNnz+Lpp5+Gbdu8u6BUKk37vTxbZY5OQxdh3dPTg56eHgwNDYFSisnJSfzu9w+njlWVhSCksYJnccJgGzFZMAgGCzaKtonX9M1sUmwn0S6xUydVqlMuH3zwQbz3ve8FAJw8eZIP1FuyZAkvYYgIwxCf/OQn8cADD+DHP/6x9NhnP/tZfPKTn3xltHCSxIvVRecwJwhDp0EIwdGjR2GaZttmStY+WXV9aSR1b87CZD27bq5TFnSo+yFXGUzBWyAqD43mSbB8BQPpDy21TJA1eVIlC2q2go4sAHE6I0tTDFwpaZGBGRpJ6PPSBPFdUNPit/njCpJuilhlaGO+g3g91ItNlcrxYbUMYkfvBVqv8e2JuiAQFUFpELdbloXBwUGMjo5i3bp1vOXu8OHDPN+AEYh2B6S9EoxxzRZMQgh+5x8PSQRbne7KfEDMt8CyFmyDcN9Cb86CQdrLXXgp0Mk5Eq7r4uGHH8btt9+eeowQov0933333XjHO96BoSF5FPu2bduwf/9+fPnLX+bplecz5qLC8FKgSxjaRLlcxqFDh1AqlXDllVdO+0NYzV2o+yF6c4lnAWiewwAkSoFICHQfgiKREOdJmIRoVYYQlJMGXdYCoJk82cTPwI5JIp+Tx7TTJGkIcSgU734AIo+CKaoGvuRtSA2Z8ipS6BJxq6BxAiPxM4yQ7LkziAWtlbnqwTwJ0uO+C+q7IEKnBvU9UN+D4eSl8oTz9MNwN94Q7SOoAWrLXblcxujoKM83aDYgij9vxkK8+K1/gpM//H8yj3s5kPU3JU6bZFBnrzCywJQFlurIyIIdpzoCOO/UBaB9I2WjWOgf/OAHkqdq8eLFOH78OJYuXYrjx4/zHAgRP//5z/HEE0/g7rvvxtTUFFzXRalUwsqVK7F161asWrUKvu/j1KlTuOaaa3iJ4/xD87p/F+2jSxjawLFjx3Dw4EEujU6HLNzz62vwyX/ag6lYTSg0cWez9slm5EEkBM0Q1XCb75tlPNQaHTUlCJLxeBT5rCcLxK/LIQ+izM8IBFMR3HRLJZBumZQfU7oifNnbwB8PPMDKcbLAyw7s+fw0QUBMBnTXlFIX4rIE1Z0H+kVTzDdYsWIFwjDExMQERkdHuf+hnZkFi9/6J9K/5xtxYNARBSCbLDBlQZofYZuwYsJQtE2UHBO9mrC0lxudVBi+9a1v8XIEEHU33H///bj11ltx//3348Ybb0wd881vfpPf/vrXv46tW7dyc+THPvYxAMDBgwdx/fXXn8dkoaswzBbOv7+YWcBMpVg2qCoMQwwPD2NsbKxhS1IrYB9uIhFoRg7EUkQzZUHshGDbG/kVGBplKbDHxOCmVpIe1ecV50mwTAVK0gSGLfiUGOkAJhWMJFBNPoZQimgLfl27+DPQeg2k0JOpLkT/RiSCWLakKATnzsLo6ZOOcX7xENyr3o1WIQ49AqL36djYGM6cOYP9+/fz8sbg4GBLMxouuCkywB35zqdbvobZxru/sT31t2AapCFZYOOrS3mLqwtA9DcTdQEZ6HUsHN/1FCZjA2W7JZ5OzrxQz9uuwqAjDOVyGT/60Y9wzz338G233norbr75Znzta1/DypUr8e1vfxsAsHXrVnz1q1/FfffdN/MXcL6g62GYFcwJwjATsHjnFStWYPny5SCEtBwN3Sp68xYma748R6JFw2M7yoI8T0IoSxiJfMdmSABRm6dJCLJO3yy8SUdQRP+CGMAEyIoAyeiOIDSMCUST2Qw6csDmPMT/d1EUtKAq1CYBO5kfQd0aSL6HqwvUc0FyBYm00Go5Gi4Vk4HQrUVDp/LFhCD4wgAqTQYDFdop7Z99C7gy/c2vFViWhYULF2LhwoXRyxH8D2fPnoXv+1i4cGHT+Q4X3PQF2D39OPDA707rOjqBd/6PbbA0b7wBISG1GVmwDYN3RFimAZMgbis24ZgEw8PDqRJPX18fJxCzHWGtQ6cUhp6eHpw9K3eRzJ8/H48++mhq302bNmnJwoc+9CF86EMfSm1ftWoVdu7cmdp+PqGrMMwO5gxhYPHDrYJSisOHD+PYsWM83pmhUdJjK/ir61+Lz/5wnxT53GjEtZjmWLRNVDw9WWm1W4K3UTbxRzgm0Vgf0y2VzRIexeMYGpIFvy4YHhOzIdGoC0TogCCBK7VXSvvxVsckwrkVhJPjILm8cH8MRqGHmxqZetDSeQrRBztTJCKVIU5/FElIhzoaRP/Djh07sHTpUlSrVezduxfX/9k/w+npg1ueyDz+ot/8KgC8ZMThhq89A8OwgZ3btI/rJrqqZCF6PCELBduEbRD0xqZH04gUtyUFANCXeMbGxppGWJ8vhKE72rqLlxJzhjC0A9d1sXPnTuTz+VS8M5Cd9NguWPuk2C3RiuFRLUeIQUtZZQn2bb8ZoWAfqjqYJCnviEqEipQZUtnRUBUBdl8sPQDJwk9DHsUMpIOXxNvErQgdE3oPg5TDEKsKrPOBVidBnHziWYihKzswhFPjMPI9kbrAtjGCoMldkM8rdktEt/u3/n8gC/SDqWaCnp4eLFiwABdccAGAfwYAThocoTxi9/Tz206xH5d+9FsAAKtQws67/mPHr+v6e5+GobzpLKHTpzdvCcpbY7JQcMw4lCkKZBLNjiXHiksS+jeuWOJhEdbj4+MYGxtLRVjncrlZIQztEpFqtTrtqbuvdnQFhs6jSxgUjI6OYvfu3bj44oszExs7UZL4r2+9GJ/94T5+v6AhD8wQGVKKom2i5utVjYoXtBxtK6oQQUglAsHKEuI8CYp0pwNDK+bHlskC1GAmcfKkpsVS7J5opCiI2xQvAycJnjB7AhBKEHFpwpO3B5PjqS4HDi0piI4Pq2UYTGWI96OVdC7DbOPC9/2ddN/p6YNVKMGvTjU9du0f/iMAwM5H1/zM5vaf/+13R2FApjbvO0Epb0nvH7UEAejJAgs8zQuEIWcZcKwodXSBHFWQCdM0MX/+fJ6x4nkexsbGcOrUKYyNjcH3fRw6dAiDg4MzysgQMR2FQdft0IW+NbyLmWHOEIZmJQkW7zw6OooNGzY0rPF2gjAEQcA/6KYU/0LBMVHVTKjMW1EaIiMSjcoTOqiJjo2gC2di0GYvaJIfG5IF3UwHRgKYPG8YchlCQy744m9YfF/DFcoUoTyCmnp1ELvxikHrNakMQWsVkLws+/IF30/KC2rJIZwcTxMEUamIjw0rkxJpgO/iiiP/imDNmobX2Q7Urh4dQbAK7Uf+br7tJ/y2HS/kljAcxIqJsCkoCFYTcluMg5YYSnk7URgEVSF6LCELRdtEGFIe9xzEt6NZJwYck6AQxYi2/TqBKMKajaWenJzEwYMH4TgOz8goFotSRsZ0CEQQBG0pDI26JOYyCLoKw2xgzhCGRqjVati+fTvmzZuHTZs2Nf2DnSlhKJfL2L59O4AodU1ncCw4JoJYWciCqCw065AQwcyMKrLaKLMeZ2WJVMqjhmw0JQtA1DYplh58UWWo804KiVxo9uXb2EwItwwIY6+5ogCkui64N4GpC0xtcBPPAqCoBSykqYG6wKCSA1FRmE11QdcGrCMITjEpR9g9/ZxUiPsydaFTYOWIUuxRYGRhoBiVjpqRhVLOQs4yJLJg8xZKAyXHimaaGAT9dmf8IWEYwnEcKSODRVjv27cPtVoNpVKJEwg1gbHReTvVVjnX0aK1qos2MOcJQ7vxzkBU65yu6ZFlOaxduxZv6OvDXz95hKsJjfwLAaUoNegbn048NBAPaGFqv0AkxNbJqIsifaxtpFtWm5UgxIU/ul+TTI0JKWClB6LvmKBhaigUDLPhuGqp9GA52S2aiDskxIXdrSUhTdzwqJCBapkbIDmxEAiC5IsQTY6eC1otg/T0SdvNR/4WwTvS0wJngtUfvj+1zc5HZMCrpUsSjCjY+Ty8Wi31OD+HZsqqpRndrqoLdk5WEwCgNy+bSNUSBJAmCwAkssCUhZxpgpDovVywDQDTNyuLUL0GWRHWo6OjeO655+D7Pg/ZGhgYyAzZCoJAMlc2Q5cwZIB0FYbZwJwlDGEYYs+ePahUKm3HOxuGMa0hMbt374bv+xgeHpY+FHT+hXy8iochlSZPMjByIJIEcVR1TviW4sS1YlFVaNbZoCsxJMfqtjVRFSDEOrPWSL8mPCYaGDPaKxVyAUUJklotQz/qmPATMyPExMXyBC87iDHOgFA+cPXEgO9XFZIedeqCQBD4bZb+mOWBgGyEJA9/GfSG/6Ldrx2ICkMWQbDzpYZeBjufl4gBDdv7G7BzJicMZvy+FcmC2imkIwqATBaKdqTE5ePI57ygLthm/GMQ9FgGeozOkAWguTmREIK+vj709fVh1apVCIIA586d422uAHgHhhiy1VUYOgMC0vUwzALmDGEQvwmzksDSpUtx6aWXznrG/tTUFHbs2IGhoSEMDQ01fL68ZaLmy+UOseygGh/bMTyKCoI4tZJVdS0jO07VFJIbxQ4Jk6T7nVPGRiixzoEr/SmrpYeEFNSSOGfVBAlEUyTZvqGfjnIWn5MhowQRujXJyMgUBh7AVG8l6TEiAyIx0W2jQQAad1GIJQvWshnd6VzOB6AvSTDiwO/H3RFWoQSn2MMVhawShEgenFz0exEVBKYwGE1KXWIXhBOHk/XHEyRNg0jjqVWyAICPbc9bkbmRJZlGikNEfCMy3bnfabvdDKZp8hAtQB+yNW/ePFQqFfT19TU5W4JuW2U2ugpD5zFnCAMDKwmsWbMG/f39zQ+YIY4ePYpDhw5h3bp16O3tTT3+B6+/AP/tl8ckk2PeMhFQpMoAIjlolSRkwTHlMgMrJYikIqRAvoGTvRWvQip5MRXNLMxtUNUEIFr8xRkRDcoIoKG0L09YZEpBrCqwxZ91OzCk/AVuLaViAEi6KXwPgBwFHT2nI6sLXrQtswQi+hgEdSFk5OWh/xfk3f939utuEVd8/DupbVY+2+jIiAIjBl7GcDRGFqTzNihHmJbBF341dKwVVQGQW4uLdhIDHdJouJpBogRSg0RdPnYHyQLQvjlRhRqyVa/XMTY2hhMnTmBiYgI9PT28hbOnpyfzS0alUpEyYrpI0PUwdB5zhjD4vo8dO6JMerUkMFvPt3v3blBKW3o+VpYQExjZh6KuLCGTh8alCCApGTTqfhChKzvwx5RAJ4MG+khmFRqVIHlMQxYQdzlwxSHD18DmPXj1xEOgmhXr2fX3UM1ckJId81JIE+CBCAsFS4MUyUA4OZZKhOSBT4JZNpgchxF3X9BYUQiqFZiCQS50o9cWfvsLMG6efmQzK6GZ8UjuwK2m9rHja/FqFe05evoSMmVp3iC67oe8kMyYi9/jrAwhTlUtKb4FkSz0F5XBUhqyULRN2CbhKoNJSGJ0zJuSmbYTaLd00Ay5XA5LlizB2NgYli9fDsuyeP5DuVxGKY6wHhwcRF5QfLo5DNno8oXOY84QhuPHj2P+/PlYvnz5rD/X5OQkduzYIcVJN4LaHsl8CWLZgHU+sA9HERUvlEhDI/gh5aTBIARhvJAY0Cc/igZMU/A1UER/kJbORNZqVHMMEnhyB4T6OA15QiPbn9/2qlIHRFiekEZME8VcJpYgxH95tDNb7Nn5Jsdlv4HvAor/gJOBJsFMHBlhTqEXLWreVBlmXihhhCFC10cnY4JMpyB1QTg9ifrVM6915U0sS8jlCPlqcxrFgZEEXo4wDSWkSVAYMsgC28bIgm1EZCEXZy5YJsGWJ3+OzZunERjRALOZ9GhZForFIorFIpYvXw5KKaampjA2NoY9e/agXq/j5MmTOHv2LOr1ekphWLVqFXp7e2GaJizLwtatUe7F3/zN3+Dv/u7vYJomfu3Xfg1f/OIXU8+fdWyrx58v6EZDzw7mDGFYsWIFfL9z3zIIIakPDUopjh49isOHD2eWIHR4/7rF+OaOk9rHGs2JENsnVWXB9WVDmqgs2Bm3dbCEccCpx1ohC01KCryrgYapMdK6Tgdp9LTgUZBaJQVQz+N+ALagS1HO4pwH6bjGyY7ijAnt8wqmSv5UE+dg9kQf7qzc4FeqEjlgpAFI1AUG9/4/h/PBP818zkb44DdOTCt7wdF1PzQhpypZYOjNpzsiGMRuB6AxWWDmRgCSd8E2DNgmgWVG72vHJOjXlEs6gTAMZ0Wl1BERQgh6e3vR29vLI6y3b9+OJ554Ai+++CKuueYaXH311XjLW96Ca665BgDw2GOPYcGCBfwcjz32GL73ve/h2WefRS6Xw6lTpzKvQT223ePPF3T5QucxZwhDp8GyGNgft+/7eO6550AImXHJQ5eTEGoyGRoZHlk5ghECUVkQlQvtsRkzJABAStUVOUkYSMQASKsFWWQBgDQzgu/LPjh9Lx0bLZKFuAOC1hOZnZcR3Fpq1oOqKrB/2fFqsiP3NjTwT4QaEyPPclBHW/PrEMiBQhRC14eZd0CV9t3afX+K/C1/nnkdzcAIAlGmcOraIkWyYAsLr6gk2Bqzo6OUHgBIxsXoMdncyMhCvzRcyuJ/B83IAlMXclbkzWHlCF+n8HQAL+csCcMwsH79eqxfvx4///nP8eijj+KnP/0pfvzjH2PdunXaY/7+7/8et956K8+DaDcdcqbHvxzoDqvsPObM77TTnRBieNPk5CSeeuopzJ8/H+vWrZsWWXj/usW8lRKIPkBzlgFP07rGyENR+PAMpzmwiLBar5l80AIyFzAJ4rQ8glCkEvHUSKIJYmqbLABRtoLvyvsyVcAXTYQCWdB8yw+VgUpsxDTf3/dko2FdrudrlQMlNjqcHI+vRc5TEK85qFY4WRDLDaFShvAmK9I+ABAGAerjk9Ft10fYwemoQEQGGCHIFQSfQcGWHmsEu8Vv7ypZKOVtlHKWZHAsCRHP7D4A/j4vxD8iWRD/BmzDgGkgfg9HqY49Rmd/ZyJmizC0c15KKSilKJVKePvb344777yTl0Df+ta3YuPGjbj33nsBAHv37sUTTzyBq666Cr/yK7+CLVu2aM+pO7ad488XkHjuzavp53xAV2GYJhhhOHLkCEZGRlITLacLXf5CzsqOghYDm0STo5jKqDM8thIP3Sj5MWvaY4ooeDXlcXWWhGiE9CQdUWybZODzH8JQDj9i6oAm+4D6bqpzIXUc+zeVwSC3WcrXIhOEsFbhJsagni6RZJUbAtdD4HqwCrlUGUJ3fPWe2zD1rj/EvHnzWiKnG279MexcVPbw6vL/j5OzYOcsbQeESAiYAtEse8FRyEFv3kIhDhxjioMjEGM1e6EgHN8bH8ei0Nn7XGyjtE0Cx2RkISK1BgEKlgHXDzo2+VPFTLsksjAdIqIuJj/96U+xfPlynDp1Ctdddx0uvfRS+L6P0dFRPPnkk9iyZQtuvvlmHDhwoKVjr7766paPP5/Q7ZLoPLqEYQbYvXt35kTL6SBnGagLOQtquWHSDdDrpKOgW4VYlsiKh27WRWGGnuxJUGY1iGibLGTsqzs3rVdBTDl5UfQihLUyiGEm3/AlM6SiKCjPzYmFkrmQGkolkIhQKW8A0QIfej4MWwg7CkL45RoM25IIhFh6ENWE+tgk7J6CdDwA9Dz0ZWzb/C4QQnh/f29vb9PFxs45yBVsThCcWF2wcxZvj/S9UEsWottC6YEpFMIizxb8Rt4bRhKS7AUDBcfk93uF52PnUclC0Ta5qsbIQt4k0ZApk8CqT2Dbc/swMDDAv4l3cnHrdJeEiFavM4sMMWP3okWLcNNNN+Gpp57C0NAQ3vWud/GSqWEYOHPmDG/rbHTs1Vdf3fLx5xPOYy7zisWcKUl0EhMTEzh79iwGBgawdu3ajn1wXL96Pi9FiB+4IY2mSookQeqqsA3kYyMaKx1kfbFij0c/SfukZRBYBuH97AD41D+LAAZoRBaA9BwHTfmhYQkCyCQLxK9nkgVar8T/Rgt+WC1L7ZKqKqCDqiS0A1qvpX0Jynn8SjWlLgQ1VyIHgevxckPgJsfXxyb5bXH/2vhkilwEro/V//og1q1bh2KxiGPHjmHr1q3Yvn07RkZGUKlUQCnF6z/3uLa8YMfKgg6WbTR8HNCbIQuaTgimLpRyFnrjHxGlvCUd1yOQ5JwV5SmIZIF1A4WUxuTAgGMkHREGAfLwUTPyuOiiixCGIer1OrZs2YLdu3fj5MmTcN0GWR4tYrZKEu3Add3UjIpyuYzJyUl++4c//CHWrl2Ld77znXjssccAROUF13VTxsasYwG0dPz5BIJocXs1/ZwPmDMKQye+XVBKceTIERw9ehSLFi3CvHnzOnBl2fCCELYpv1W8kKKkfDDXvJATBhGisbFVw6N6rJEx2S9FAADAd+U8hlCTz5AiFw2UBGZsNMyGHQmAUDoQEhJTKY2NjmPJjkIGA4C0iiEgWsR9EFZG0pgYmSKg3pauQVAXauOTcHqL2v11xzuOg8WLF2Px4sWglKJarWJ0dJQPQOL75Sy4mrKDLnRJRE9fsiA1mzIJRHMgRLNjwZYVB0djbgSAvphIGAaRlDUdWWBtlFEHT9zui0hlYKUINtvBtm2Mj49j3bp1fLbD0aNHEYYhj2YeGBhom/SfD4RBl/J48uRJ3HTTTQAiI/b73vc+vO1tb4Pruvjwhz+MtWvXwnEc3H///SCE4NixY7jlllvwyCOPZB4LAB/+8Ie1x5/PON+v75WIOUMYZgrP87Bz5044joPh4WEcOHBgxiOudWB+hXocD81aJ4u2gYoXKvsmH1itkAAVbOQ38yrwvIWsPzSBJFBiJGQg9IF40ZO2p45vVIIQlAS3mgpH4rerZcAw5G26/AO2wAsEIixPRMmPymAobmSMyxaSN8E0k+wGTXATPzcLWPJ8wAOIafAFPnA9hJ4Pu6cgKwrjk7CKeel4fo4YgeeDBiG8cg2Wpmvi3J2fQP8ffSn6HRLC+/eHhoaiAWnf/1e+r5Oz4BQsePX4vVWiESOvAAAgAElEQVQQSw3JbdLCe6nITIlSOULxI9iq2dFKtej2KYFNapKpGk6WM83YtxDFmFsG4iFTUfuv6VUQEKE0FYYghMAwDPT396O/vx8XXnghfN/HuXPnMDo6igMHDvBoZlbaabbYnC+EQQ1tuuiii/Dss8+m9nUcBw888EBq+7Jly/DII480PLbR8ectSNfDMBvoEoYWcO7cOezcuRMXXXQRli6NRlLPZGJlI1y1wMAvzoScODBM1gP05uSZElltlaJZkSkLOrVB3ZdB8jeIUyENMz3jQGd+bFB+AJqQBSVPQTslUiALYa0cxS4L26mGyLVSrtDBnziXSl408w5f1EPPR1j2pSwFZmDMQpZ3IWCdFDE5UI+p11w4fUUEri+pDWN/+QeY98d/nXqeX/nCz2Dn4wTRWvI7YT6ELLOjo7RQ+l4gqQtF7Tj29DbmVdBlL5SU0oT4Pm5EFhwrKqcxslCIHzMIkCMhXKK00GYs7JZlYf78+XxCLYtmPnr0KCYnJ1EoFDiBKBQKKQIxG4ShXYNmd/BUY3T5QufRJQwNQCnFoUOHcOLECVx55ZWS/Ce2VXbquVi5I798DR8y5YWUGx0ZRKLAFn9xIJQOYilCND/qYBkEpMHwI3HEtLxd8DiI6oO4T7tkAQDCQJuYqO2IqFf5oCfxeL6fMl9CVRVotRyZJ5XrFFshvcmKRBr4PsJ9d6LcWFEQyIGpmCIBwI2fI6uMASQJkABw9i9+H/Nv+9vMfe28qf3W3MinwEiCZZsSSWCqghjnzNSErGAmgEVAW7xLwiBR+YFxVpFEiGSBhZI5VqIs2PHIdZMQ5C0Cm8Qm2xYJgwoWzbxkyRJQSlGpVDA2NsZLO729vZxAOI7TUl5Cu2iXhHQJQzaipMeX+ypefZgzhKHdehYrQeRyOe4KFtFJwuD7Pnbt2gXTNDE8PIxf/OIXyA+tTV9TQFFSvsm5Qcg/gEXywJSDLGVBtDxI7ZbxbWqYCWmgNDW/AQAnBrqBUNquiemQBcTKAlMZNCOnw2qZew10x/NtasskIwlKeyTPUYjNiyyquVHLoztZhpXPSQSB3ZbaKaWshZgUlmswhP/XRkSkPjYlqRkAuNJ15vO/hwWfu5tvVxUEJ6PsoHY++F72+1rNVGi2X8Exk3ZKaRS7KUX3cq+DafD3oEgW8pYBy0xaJ5l/wTaixYH49ZS6ACQliXbA/A89PT28tMP8Dzt37kQQBFyRGBwc7BhxaJeETE1NdSdVNkDXw9B5zBnCACQ1+2YYHx/Hrl278JrXvAZLlizR7mOaJuqaXvt2weZOrFy5MnPOBTM6ii2XtuabSLyup45tVVlQIXcr6EZWuymVIdpX7ZDwIbZtqI9LZCFr/HTcJgmwMoURH5sOYKK1crolknks4n1Yi2W0jxwPHdTrUhlCBFu83YlyZm4C28ev1PSKgkgOhONVg2R9fEprgHQnK7B7lEyIIAQNApy67Xew6C/+G/7Dl34OILvswNQDHTlgjzFVgZUWJmt6wsQW+6Jj8o4HlSSwf3tsUzLyFu2oE8I0CCcLuThXQSULnCiQiCywNkrDr8OoTQD5tAmZUjrj0oHqfwiCAE899RTGx8dx8OBBPrp63rx56Ovrm/ZC1S5hqFQqXcKQga7CMDuYU4ShGSilOHjwIE6ePJkqQagwTXPGHgY2+loX+sTMjnVhochZBp8TIQY26WZD6MhDI7DMJ233g4jAjQiABkScG5GhPjQiC2K2QnS/QWdEGEpeBW27pJifYMnfypupCuxfvtBPVNLf7OPFPohJizuRDI1ix9XHp/jiHrgCaVDmR4Sery1ziMfTIOQ+B3ciUjTU9yANQpz8zEeAhbfwbXbOQi6fZC+IZQixC0KEzqcghjCJhkZRTdChlLP4+5KRBdbpw9ommdrQiCxEo6sZaYgCoAilILVJ1DRkAZgdrwEbzHTJJZcAiNobR0dHcezYMTz//PMoFosN/Q9ZaPdaq9Vqd7R1A3T5QufRJQwxXNfFjh07UCwWtSUIFYZhTLskEQQBdu/ejSAItHMnTNPExiUFPH2iyokDMzqW3QA98YetZQJ+AISgMDR/HrpyRFYpgoEaVsrkyBd5NkbatBLSoGudREwMhMWsoaoAaOdAMLDZD1KZwnNTZQqps6JWlmZIsO4KACl/gpqbkCoJiB0QSEoNXrnKQ5XUfaL90tuy0h6ZomD35Ju2UzKi5FWqMPM5ri4wfGDZf+Z/2KKCwIiCnTN5p4QIkST05q2UoqAzNupKFIOliAw5ZvpvSA10yitlCiBNFhyDgCIqszGyYJCIEBv1Mgy3DOT0EzZfim4Gx3Ek/wNrbd2/fz+q1WrK/5CFrsLQSZDutMpZQJcwABgbG8Nzzz2HSy65pOWhKtP1MJTLZWzfvh1DQ0MYGhrSfvtgZISRBEDukmCgNCINAMA+d0NKG/6heKFMGrQQSxGaiZHqPiIkYhAGgGFGqoVghGxEFsJqWRqMFOq8CMx7IJYekPYoqLcBpMhCO/BrdU5Kglp0DYFixvRrLgxhoWwn7VEEa6cEIn+EXSxIj9MwTBGJ0PNT27KyExrNgegVShE6Y2NRk+yYpS4AQL+QsQDEbZCWYHZ05GmUjESIZMESwsZMg8BGGIV81SZR7V2W+dwvdfujrrV1cnISY2Nj3P8wMDCAwcHBVP5Du9eqa6vsIgbpJj3OBuYUYVA9DJRSvPjiizh9+jQ2bNiAQqHQ4GgZ0yEMJ06cwIEDB7B27Vr09fVl7sdaNq9YXMT2k5XU40FIU9HQFIkEpzc/JvuKyoIwfiJZ7MX2SRryZEepvCDuI5Qi1BwGtcTRUFkQ2yUzFvqssdO6jghmhtR1WIS+B8OyU6WH5Pnl+yoxiLb5CDyfdzkEGnVBOqeSr8BIhORPiLsrkmPicsdkOVYT5PdcfWwSTp+8aDg5E66gIIh5CyJBLQnhSTpFYTrI8iowiGZHXSulShaA6F+TGx0jDwMJQxC3jFqxcdpgpyOh24Xof1i1ahWCIMD4+DjPfzBNk6sPvu+3rTCcz9HMXbz6MKcIgwhWgiiVSti8eXPb30LaIQxhGOL5559HvV7H5s2bYdtpN7d6blabFudLeEF6xLXqX9BNtwRkZaFt8yObCSG2S7LHdDkMum/xvmIQ9V3Zg5BBFmi9JqQtxuRCSX7UdkTwDghhtkOtAsOyeYukN1WWvuWHrg/DsThZ8Gv1qPMhPkejLolAOEeIKLhJTHt0a5UoeEkgB/XxZE6ESDbq45Mw84m3gCsNE+WoZKGoC/XxSX7uWy7+fQBJloKrlB4KGm8CA1MWmKrAFIWqF6RCmIBIVSgpWQtseBojC+z9mbOMlNkRSForAT1ZsI0o8pm1UVoGgeHVQEIfxKsDdm/m6wFmT2GY7lAr0zSl/AfXdTE2NoZjx45hbGwMhmEgl8th3rx5KBaLDclOtySRDUIpyCwNHpvLmJOEYXR0FLt3726rBKGiVdNjpVLB9u3bsWTJElx22WUtfdtR/RG6QT5Z+QvRHIkkvVG8rYUQzCSpAVmlCHG/rIwFNYdBzXRQOyEyUht5UFMQyJMpxf11HREaIsdICCMLrKSggpkJ+f3JshzKFCsKIkHwyzVYPXnJxxBU/BRB4NkMYl6DUG6gQaD4HYTfhSaPQVQx3Ikq7J60gbFvIDJM1us+igUlVTEuI4jpi6V8mswWbJOTiYKmHJGVvVAQMhZUs6MZEwWmNrRCFnKWEbX60hBGZQzVkr6DScRsBSx1SrUQo72PHz+OcrkMADhw4AAqlQp6e3v5cDHV/1Aul7umx0bISpztYtqYc4Rh//79OHv2LDZu3Ih8Pt/8gAy0ojCcOnUKL7zwAtasWYOBgYGWzy2mSL52fh57ziYLJDM6immMnDyg+ZAStq+F9B8TNe2EDBiWTAh0QU7xProcBkBjdNSUGagSqsRvK0OlmHdAnCQpnU+cGxGbHXneQvy7ZAu6mHngxxkIqnrg1xQjpPC4l3FMFgKNTyEU8xqUxyOPQxWGY6WIQn18Ck5f8q0yCm8KEAYhPrbm/wJb7tVWylzOksoO4lhp1adQVVot1RHUQNqzULRNri5YSimimGqlNPl717EIDBDuxdGRBW50DDwQrxq/5xrPFmGYDcIwW6pFGIYoFApYvnw5hoaGQCnl+Q+7du2C7/sYGBhAqVRCsVjMVBiCIMCmTZuwfPly/NM//RPe//73Y+vWrbBtG8PDw7jnnnu0Kufhw4dxyy234MiRIyCE4JFHHsGqVavwpje9iQ+lOnXqFIaHh/Hd736346+/08iMqH8VgxAyAOA+AGsRVao/DGAPgP8NYBWAgwBuppSOTef8c4ow7NmzB5RSbNq0qSO92VmEIQxDvPDCC5iamsLmzZsbOqN1UNULtsj7IUUQJkZHVoIQWygtMyEPTqOyg6a8wBEv9Fntk+J+un1IIOczUN9LEQ61E6IRWWh6O27HTDIbKpxghF4yHIpfdqwucEVAKEEA0bd+sVThTkTlBN3Cz8DaLnVpj9FzRK+vPj4JK97GiIxfrqaODTwffs3lXROhWIIYK8PUKAEishIcxbLDVE1vABUVhWjf5HaBj1eP46UbqFcsoVSnLgDgA9NEssBKGI4p+BYIYNNYqaIhjNokKgOrMp9XxGyMoZ5NwiB2TBFC0NfXh76+Psn/sG3bNnzmM5+B53mwbRuO42DTpk382LvuuguXXXYZJiYmAADvf//7+RyI973vfbjvvvvwsY99LPX8v/Vbv4U/+ZM/wXXXXYepqSn+Gp944gm+z6//+q/jxhtv7Phr7zzoXFUY7gLwz5TSdxNCHABFAH8M4FFK6R2EkFsB3Arg09M5+fkyNfMlwerVq7F69eqO/LFnKQy1Wo2z+Q0bNrRNFoA0GXnNvEhqVn0HAU1CmcT8BRUhTcZXW0TOXCCBB1Ca3BZAzfSiQwI3IhS6JMfQT1QFoigC7Jz1mkwIfK99siDun2GClJ4zSCKUg5ob+QxccXFu3jkhliCASJkA9C2TgbLwq4+L6kLo+gjj4VLsWkW4E9XU8QDgleuSugCkv/Wz0dEFx8SAYHBkikIpb2NJf4H7E3Q+BRGNOiHyZjKWXR3FnjMN3h4MgO/nxEOkgDRZsOKR1bZBYLGOiPoUjNokjOq5ljNQZkth6DQJAZq3VTL/w7XXXounnnoKl156KS6++GLcd9992LhxIx599FGMjIzg+9//Pm65JcnheMc73gFCCAghGB4exsjISOrczz33HHzfx3XXXQcAXMUQMTExgZ/85Cd45zvf2aFXPMug9NX10wSEkH4AVwP4WvTyqUspHQdwI4D7493uBzDt/8A5pTDMJDtBha6GeebMGezZsweXXXYZBgcHp31u3WAr0dBoIEq6U6GSB9sk8AL5jeZTuTOiEYjvSspAks8glCso1bZeUq/eVFVQOyGyyILkX8ggC6wdU5z5wBfwmgvDtrS+BUYWmLqgJjIGAtFQQ5nUEdZ+zRVGXcfnLVdTLZVB4KZKGqHnI6h5sHtyKSVDVBdoQIVIaRdmvMh/5lduA5C9qOsyFKTHBVVBpygAiaogkQElPEw0O6oGXSmgyUqIgng8Iwt2PDPCoEFMamPS4NfwyzED5w5uRS6X4wmLPT092r/JTiQ9qgiCYNYUhnbO67ou3vOe9/DyRRiGeM973oMvfvGLvIQgwvM8fOMb38Bdd92Vemzv3r0YGBjAu971Lrz44ot4y1vegjvuuEMiMN/97ndx7bXXNuzwOm9AX5UKwwJCyFbh/r2U0nuF+xcCOA3gfxBCXgfgaQB/CGAxpfR4vM8JAIunewFzijDMVnsVpRT79u3D+Pg4Nm3ahFxGrHCryDJU6kZYNxo+5QaJ4VHbPqnOh2CliAxPgnR8BvGSkhs9NxrspCk/SN6FLKIApM2O4uRKxdcgkgW/UpNIgleuwog//FRFQSUSnCQowUvpVkuff8AHnJzUeYeDSFjEsojYjhlqzIwA4jCmiOy5kzVYio+AhhSBGyBwA1h5K9UWyRQFXaskG/KU5WnQIW+liYjOjMtIAnuv8gFT8a6iAVcluCJZsAwCI4hKWcSrgHgRWagMrMJrYzsQC0g6ePAgyuWy1iD4SvIwTCe4iZkeCSH4wQ9+gEWLFmHjxo14/PHHU/v/3u/9Hq6++mq86U1vSj3m+z6eeOIJPPPMM1ixYgXe85734Otf/zo+8pGP8H2+9a1vScrF+Y5XoYfhDKV0U4PHLQAbAHycUvoLQshdiMoPHJRSSgiZdvvInCIMs4F6vY7t27djYGAAmzZt6ggp0Skhy0smTlYCsHESjChozY8Uqc4IjwJ2i5dGLYeTBkJDyfzI1QTTTEgDDXmQEzEMaWRzI6+C+nhTsqAeE4Z8CBVbnIlpJKFKDRQF1kKZ1S0hnpPtz84fnUeXs8DOre9uSN22089TG6/A7hG7MqLfsVv2YOfTBIMGFH/5q38GQD/zoTdvob8QnW+q7qNf6ZTQqQoMOrVCLTWI29TchZxlSDNPWPIje28SRGSBk1qVLARe9H4LQxC/BqNelq8vNgguX75cMgiygKR58+ahWq22ZThuBbPpYWiXMIjBTT/72c/w8MMP45FHHkGtVsPExAR+8zd/Ew888AA+//nP4/Tp07jnnnu05xoaGsL69etx0UUXAQDe+c534sknn+SE4cyZM3jqqafwne98Zwav8CXGq48wNMMIgBFK6S/i+w8hIgwnCSFLKaXHCSFLAZya7hN0CcMM4Ps+tm7dite+9rVYsKBxgEw7UEsSlUoFzz77LFau3cgTHYOQ8nY4lq+ga/cSyQMRshCaKQtNZ0ogI4MBkMKY+DZdh0RGDkPDtkvJ/yCTBUAmCTQIIwIhRDmLpQB3osIHQalBS1kJjIDoZ/DizAUxmVImFnx/D1I7JgDUhVZIKpSO6hN12MICHjKloezCyltcXcgCS2hUTY2lnMVbKSsZx4skoUcoKeRihUEtQajImQY3QjKyUOCZCwmpdQRVAUjIgk3i915MFohbiUoRXh3lRZdlvmbVIOj7Pg9IeuGFF3D48GGuPpRKpRkR+9lUGNo5r2qSvP3223H77bcDAB5//HHceeedeOCBB3DffffhX/7lX/Doo49mnn/z5s0YHx/H6dOnsXDhQvzkJz/Bpk3Jl9mHHnoI119//Yw6y15avCpLEg1BKT1BCDlCCHktpXQPgGsBPBf/fBDAHfG/35vuc8wpwtCpkgRLiKzX63jjG9/YVkJkKzBNE178bZW1Zq5duxb9vQ6OTSYLos1VBiT97o3Ig5WDoQYoCRCVBanFMk57VD0NqeNj9YDYThKc5MszJQC9ksCViUZkQcwl8BMVgX/rlzwE8tyHRkqCWHpQg5yk/eKFnyjRz1A6MQLPh2XKGQyhG/BESHnyZFJuCIR2RrfswhQWb1aiqE+4cEpx22hAEQaU+xOq8fX2FyNFoZS30ZuzODkQyw6LhKFTpbyFagMCktOUIxj6hXOKakLRNqVoXtsg/L6OLDhmZMgloR+RhcAFcePJol4N9NwpYP5rMq9DhWVZWLBgAc6cOYNly5Yhl8thdHQUhw8fxtTUFEqlEicQ7ZYQZ8vD0G5JotXwqN/93d/FypUr8YY3vAEA8K53vQt/+qd/iq1bt+KrX/0q7rvvPpimiTvvvBPXXnstKKXYuHEjfud3foef48EHH8Stt96a9RTnHyjmHGGI8XEA34w7JA4A+G1EzQ3fJoR8BMAhADdP9+SkzcSyV3R0VhiGfCGeLsSEyNHRUVx11VUd//A4fvw4KpUKfN/H1NQU1q1bx2uyJ8vy9dvKh69YiWASsBkKsyH8ukwGAKnjQZJ9A1FxyMhkEPcXY5nLE8L2ODZaIQ+qEpHqqMggC2Gcy8BIgFiGAJIFmZUfxH2Zd8CvJepEo7THVFCT5yF0fckAGbg+rIIjHUODUGrFZN0MVsGOjI/xAs3UAqfHQeAFCAPKr990TOk+Iwg0CGEVLNCA4m//0xegQgxS6hXaK/uLNqbickVJ0zapUxSAJJVRLDmwcoSqJjACwcgBy2YgJHqPGohafw0IagMjC0FESCOPjA/Dq0Z5C+VxVJavT73OVvDcc89hxYoVUsARpRRTU1MYHR3F6OgofN9Hf38/n++gDoNTcfr0aUxOTnL5vlN49tlncemll7ZEYCileNOb3oRt27a9rNHX08BLcrEb119Bf/7jR16Kp3rJkFt4wdNNPAyzjjmlMMwU4+Pj2LVrF0+I3LJly6x82wjDECMjIxgaGsKGDRukDwQ1/tkkkcLAEFAgp/gXAsOWSQMjCyIh0CkLGRBLESqD1I2kpmGQkAnDiLwHDciCrhWTmR1ZZ4VIEKTbrgfDNCVjo0gWAEhkoRV4lSoM25aSF9XjdVkN9YkqrIKNUPj2Xp+ow+mJFQLh/5GRBf6aAwq/6sOIVQaxZBGGFG7Zg2mb3MA4FQc1iR4FsQ23v8haKS1OEKZqvta7IKKomVSWU0KYAFldAGQPjWMSKSdEJAu2hiwQ3wXxqtHt6gTK0yQLgL58QAhBb28vent7sXLlSgRBgHPnznEDpWEYXH3o7e1NK3UvU1ulDq8wsvCS4lVoenzZ0SUMLYBSikOHDuHEiRO48soreX8yMyc2mw3RDsbGxrBv3z709/fjNa9JS7CDBQuj1bj1L6S8HBGEFDnLgC8sQiGlSaJjTALU4VDNQASToratMgy0WQjEchDWyqnttF6TlIiGqoJAPsQWTLUdkYGVH/xaXSpTRJcpGw7FEoKa9uiVaym/gQp3MiYImrRHtRShPr/oPwjcQCIHVNnPq/mcYIQB5WULGlD8z//8Jb5vSRPU1IwMlPKWVlUQSUJO10qZoS44FuEGXAZGFsSShEgW7JgsRL6FOAgsDKI0x3oZYTX9HmoHrfgNTNPkBAGIVMTR0VGMjIxgcnISxWKRP14oFGbV9NjqeV/qKZyvSHQJQ8cxpwjDdNi453nYuXMncrkchoeHpT/S6Y641oGRkpMnT2L16tUYHx/P3NcyCPyQZrZZBhTIscuM+QO1conpUaMsAHrlIfN6NQOfGj0mKQ/xpMuWyYKYrZBBFtjoaZ0BMnD9lLdB9SmI5QTxX6Yq+Iphkp1XPBdTFKLHoveFV/Nh2qyzIhoa5QchTMeUiEMYUHix+kCV7Iz6hMtJA5BkMRQdUzIviuFMKnQdD1kliIbblE6IvGVw8y1PcLTk+7p8EABpshB7ZAyvEplia2VUL3pD5mtqBdPJYXAcB0uWLMGSJUtAKUWlUsHo6Cj27t2Ler0Oy7JQLBZ50mKn0M61dgdPNUGLYUddtIc5RRjaxcTEBHbu3ImLLroIS5akB910ijD4vo+dO3fCcRxs3ryZt4dloS9nYiKeQihOnhQ7JziIwYkCCVxQ02kcCw0ApiOTCjGYiZ3LspMWyTCMSg3qlEqxE0IYh03dbJWBenKMtEgWgprLI59Fg6M69wGI5z2YhhS8JMZFA6LXQe2QUEoPWaSi5vGIZk4Q4k6GaD8W6KSYIt0QgRvCdIxMchC4AUJBLapN1GE6Jt//R5+5F3AD3vWggqkLVTeQlIYeIcBJ9SlUvFBbguD7m4bQQpkmq2orr1gS4YmOTchCZHoMQLwqyiuHM6+lVYRhOCPZnhCCnp4e9PT04IILLuCx77VaDc8++ywIIXw8dV9f30v2rb9cLncJQzN0FYaOo0sYNKCUYmRkBCMjI3jd614n9TqL6ARhmJycxI4dO3DhhRdi6dKlANpLpGSKQtIlIQ6iUhi2YXH/ATcxCoQCgNBi2dwcKqkGar6CTmUQiUEYRp0RvpcoDupC7ad9COJtGoSSVyFUPAo6iPHNzT7cmQGSP6+UyxBI54teU/T7FpWDRjkMbjmIsxXk/yf5+CTZ0a/6sRFS/0FYcMxUt0PBMSWSoAMjCUXb0JsdG/yeWMskUxMMEnVBEEVtEDsiCKUpskACLypDuJF3IZwcB5Y2vOyW0GnpXhw/vWjRInieh7GxMZw4cQJ79+5FPp+Xyhez5TFQMxi6SKPrYeg85hRhaOWP1/d9PPfcczAMA8PDww1NSLoI53Zw7NgxHDx4EFdccYXk4m7lvH25aKpg/CWWf+MTg5z42GpddHMTLwO17IQ0xG2V8Oup4CUVoVuTyUMYJMcIKgOgxjwLC7/yHJkGRy9dqhAXdb8aqRA87rlS462N0f3IzAi0ripE2wRfgsLr2GKvKgpApChEt9MQWyq9mi+1VEbPGQ2gCtwAVkEeNV11A25qLDgmNz5O1X30CUOqxKhmRgYqnv56dEoD64BQZ5owsDHU0e1ku0gWgLSyIJIF1MsIyxOorr5a+xztYraTHm3bxqJFi7Bo0SJQSnn65L59+1Cr1aT0yU6WL7oKQzPMvRyGlwJzijA0w9TUFLZv346VK1di+fLlTfefrsIQhiGef/55uK6L4eHhVBtXO0SEfTCL5QiDxtcUeIBpK/4FgTyIRkiNsiAFM2lKESSXj4ZJsQ4LdqxlR+UIjRmyUdIjIJsbAZkg6AZGiaUGX5PDoOuEyCpB6Foq5WtL/1+zsoMhyPGBG4IGPl/YgUhRqE/4UfCSoBDUJupw4mTHVtQEGlL8/PP/HRDSHNmAKVVdKOUsXkKo+dnEQGd2ZMflGg1DMhhJSFp6WRcEIEdHWwbhGSApshCbHUnoI6yWEYxNO4hOi05/y88iIYQQFItFFItFDA0NIQxDXl4cGRkBpZSXL/r7+2dEZLoehhbQJQwdx5wjDIQQbeDJ0aNHcejQIaxbtw69vb0tnWs6hKFarWL79u1YvHgxLrvsMu2HWavnLdgm3CBEEEvh/Jtf/HeiNTrGbY1ZoHYOhM2D0HgdqFvTBihJ+yidEAB4IJMYHa0SCrUTQoyYFskC64IQyYQvlCnYgizGRbPHo7RHG0Hse1DNjGqHROgGMByTk4XAS+Y3JNcWwChY2vTFLEVB9CfUY38CA58hMZ2z4DEAACAASURBVOXCKlhcXRAhtkaK6kIW5hVkpaHuR9eqMzbmNTMibMGDwAmCoiLwYCZlXgQhaE4WvCporYxwahzuVe/OfB3nA1pVLQzDQH9/P/r7+3HhhRfC932MjY3xMDZW2phO+aJcLndLEo3w6hw+9bJjzhEGFUEQYPfu3QiCQPttvxHaJQynT5/G3r17cfnll2PevHmZ+7Vb6mDKAjNAUsNMJzoKiz/vhiBGFIzDdmGLephWIYDEg0BsOyENseGRPca3Z3RCAJrAJoVMSJ0QClHgl6UhC0BEEtRuCZ67wFMfs9MudWBTIcWyAZCoCwDgTnmpkkN9wuWKAttXTHBkLZUA4rZKsYwRgIZRsiOLiaYhxa67/hcgXAdrjSzH28SgpogY6N9Hqqogt01GjzmWvPADkMiCYxDJZCuWJBwhsMkQR6erZMGPIqCp7yGsllFf/2va6z2fMN0yh2VZWLhwIRYuXAgg+vIwNjbGh2e5rosTJ05g3rx5TcObuh6GxiDoehhmA3OaMJTLZWzfvh1DQ0MYGhpqW7rMmiqpglKK/fv3Y2xsrKVplu0QBksgCwBA1G/2hgnixRG7TA0gpGHLUSvhTY2ClqILctPlhwZtlEA6vjmLLMjZC+k2S7mDgikPskmRmEamquCV65KqoINX9lL7sDAlKfq5nCz4fCz1lCeRA0YavLIHK2+lTJOu0HkBRMpSNSYIfbl0SqMIVhZQR01H21pb9BhZsAwiEIfkccsg0qRUSyiNkTCUVC7iu9H90E/IQm0KwbmzoGI66HmMToW1FQoFFAoFLFu2DLVaDbt27eL/BkGAgYEBnj6peqm6hKEFzMBf1oUec44wsJLEiRMncODAAaxZswb9/f3TOpdhGE2jpl3Xxfbt29HX19fyNEvDMFrOiTcIiQKa1HKEYcHwlG/yhpUYIfmIa8G/IJIEQaHQ5SNIbZXKY7wcEQaAYaaIATHNVCBPoEQ1ywpC62RBJhnsnB73OfD9s3IXhPZIUVVgyoCUncDNj2JCI2vVFAKYPLG0InsUkn1kciIOmKIBhVf2cPC/PwQ2rrSgJQDJtlLOQiU+Z8kRVYe0T0E8TuyIYNUKNU+BkQXLlIOaHJOAIHpPGjSIvuGpyoKGLNBqGbRaxo9qC1HcsqXhQnk+YLaMlLlcDqtWrcKqVasQBAEfnnXgwAFYlsXNkz09PV3C0BTdHIbZwJyLCgvDELt378bx48exefPmaZMFoHlJ4ty5c9iyZQtWrFiB1atXz0qLle/7IGHAlQVqmCCiBMzAzI58vzRXpLagfBjNP6ip7yaGR3WMNStRqKqC58kdEZ6fMiZ2miywc3IFwvWjjgNxzkP8AySLN//Xlf9likDgJnHObF+v5nOCIBoYRQ+CnDopJHMGFPUJuVzC5kew58kp/oKcZfIfFUXbRNE2tZ4E3TYRunlTlhGNnrZMwsmCbUStk4wsWCRWFvx6NETKr0lkgbAyROCCVs6B1msIa2W4m29CsVjEhg0bMDg4iNHRUfzyl7/EM888g0OHDmFqaqplEj3bmI1oaJWEmKaJ+fPn45JLLsHmzZtx+eWXw3Ec7N+/H5s2bcI3v/lNbNu2DUeOHAEAHDlyBG9+85tx+eWXY82aNbjrrrsAANu2bcPrX/96rF+/Hps2bcJTTz2Veu7HHnsM69ev5z/5fB7f/e53AQCPPvooNmzYgPXr1+ONb3wj9u3b19HXPWtgw6deTT/nAeacwrBz506USiVceumlM17AswgDpRRHjhzBsWPHpCjpToOVVFasWIFlSxanyhHUsCSPAoDIy8AVgDjAiBiJ0VHwL2SPldarKny7zgipGBxpGErSPaAQAjY4yjRAg7ApWWAEwTCMVEqjCDGdMSpLZBO+wA0Ev4HcDcHIQxTKJG8L3IBvExUFQ3AJ0ngehJ23UnMkvLLHj2c49cB3gPj3lYyYTs5XEtQK0VfA1IO8ZUjqgk5VEEmCWIYAkIp8Fv0KbD8SL+g8KMyvJb6YmCwgYMOlIuIYnDuLcOJscu3xQjl//nwAQL1ex+joKCcNYpsiG8j2UmM2FIZmcyRyuRyWLl2KpUuXYuvWrbjtttswNjaGW265BWfOnMFHP/pR/NVf/RU2bNiAyclJbNy4Eddddx0+9alP4XOf+xze/va345FHHsGnPvUpPP7449K53/zmN2Pbtm0AgNHRUVx88cV461vfCgD42Mc+hu9973u47LLLcPfdd+Mv/uIv8PWvf72jr3220PUwdB5zjjCsXbu2Y+fSEQYxx2Hz5s2zJqmePHkS+/fvx9q1a9HX1wfEo4CpaYOadqocQWjIiQJPfNSAmo7cTtkIYahtnYTlRB4GpjIEooyf9jukFAbN4ChAJgripEpfymZIkwWmPPhxCyYnGVWPL+IpQ6OiKkSvI4T43y2VHRT1IXreRGmgIQVM4XaM+kSdt1+KBMqv+TBtUyISedNATdhHVRv4dmWqZF0hZlkliGRbmkgzrmEqZQl2DSyMiU+bpGGaLLAyhFcHLU8grJVB3Rr8N/+29nUA8kJJKeVtijt37kQYhlL5Ql3EZ0uRmO1sh2Zg4VG/8Ru/gRtvvBG1Wg1TU1NYsGABAKC3txeXXXYZjh49CkIIJiYib8i5c+ewbNmyhud+6KGH8Pa3v51/yWn3+C5e3ZhzhKGT8x9U0+PU1BR27NiBCy64AENDQx15DhWUUrzwwguYnJzE5s2bkzAYpwC41XQpgobyaOoYJHAj/4LQQsnUCK4sGGaiLAhehJbmSCgqA++wENsqg1BqnVQjnpuRhegYMachzpXQtGM2GiQllh5oQAXFIPsbilR2iN9OYqkCAAzTkMoPonlRJALulCeQBiqVN0zFq8DGRVsCKegV1AWDpNWFnGk09SmIJIEPh9IYHIHEq8CfM/CEDpyELJB4eyZZqJbhveHm6HW3sLgTQtDX14e+vj6sWrUKvu9jfHwcZ86cwb59+5DL5bj6UCwWz4shUa2i3UmVoochn88jn8/zxw4ePIhnnnkGV111Fb7yla/gV3/1V/FHf/RHCMMQ//Zv/9bwvA8++CA+8YlP8Pv33Xcf3vGOd6BQKKCvrw9PPvlkm6/s5UK3rXI2MOc8DJ2EGOF84sQJbN++HWvWrJk1suC6Lp5++mkYhoENGzakkuNI6HNTIzUsaR6E9LhhSUOnUmjiXyBOXrpP3VpqPgSsOIzI81Ju5dD1Zb9BtQ6/Wk9mPSiPZ5EFOX0xDl9Skh5Fr0J0fOxpEIZDifeT50xIjfhv4IUpj0LohvDK8nmjkoPLbzOw/aLjhHTHspvyM9CAwq/5mPzfD6dMjnnL4D9Z26frU9DuaxAUbEMiCzb1OVkgfj0aSe0LbZNAQhYCl5MF6nug1TKCc0kpglLadonQsiwsWLAAq1evxvDwMFavXg3DMHDgwAFs2bIFe/bsge/7TY3J7WI61/r/s/fucXKUdbr4U1XdPfeZzC2ZMJdMQu7JZCaTREFBZXdZ0KOsgEGRXWBBj5fDHnDF+yKyCqiroL8D4mLWFdyVVY4iZxE8rOsGFXfBwMlckkkymUsyl8xMd8+lZ/pWt/f3R9X71lvV1T3dPd0dYPr5fPKZ6erqqurOdNVTz/f5Pt/lkCkJSWZ6XFpawrXXXotvfetbqK6uxiOPPIIHH3wQY2NjePDBB3Hrrbcm3ea5c+fQ19eHK664gi178MEH8eyzz2J8fBx/+Zd/aSMTr3mcb89B0cNQBA9JkqCqKk6cOIFIJGK/418hBEGwnUQWFhbQ39+PrVu3sj5uJ0hpFYTYomsUNHTN1iUBmG2WgsBqzrao5rh726SVt5CCcFAjpDNu2eUunycGzsdOr4Jt9HMKsqBGHbkMLP3RYWI0L/zOcoIaVZl3AqDlAdG2PtEIRJ/Iyg48eIJgvReu/ZJTFHSNMEVEiakQJcG16wKwOiOcA8aSlSYAk0Bw3gXngCjAUBJ8VE1weBeAxBZKm1dGU6zOG9VUF2jGAtEtsqAqIPGokbcQDkGPRaD96Ues95mDi3BZWRmam5vR3NwMXdcxOzuL+fl59Pb2AsB5GRKVLlaiMFAoioJrr70WN9xwA6655hoAwGOPPcYMkAcPHsSHPvShpNv8yU9+gquvvpqdw/x+P3p6evDmN78ZAPD+978fV155ZUbv67yBkMTwuCJWjFVHGHJ5Z0CT22pra7Ft27acbptmMYiiiPHxcYyNjaVnoKSqgulRSChHmM8TyWOVI0wI3hIQumyZREjB67ORBlcjpK4lzIUATN9B2BEJneBjUN0Njy5Ewe31/DIj/dHezUAvypREOE2G1v6Mz0AOKwltldY6mrUOHWXN2jMtAyPhuh2UsGxr9dQ1YnRqABDNqZRE04FfPo9S2KOdeY8CPzWSLztU+CTEksyJAOwlCCdZ4CEJZrojnQNBfTDU2KirgCqzFkrjp9EJQcsRlCzokUWjHBFZTPAt5GNIVGVlJSorK7Fnz56EIVFlZWW2IVGZIB/dTtkQBn7+DCEEt956K3bs2GFTAS644AK88MILeMc73oFf//rX2LJlS9JtPvHEE7j//vvZ49raWiwsLODUqVPYunUr/u3f/g07duzI8J2dP5BiDkPOseoIQ64QDAYxMDCAkpISbNq0KefbF0WRqRe6ri87CIuCVNRDCAcTyxEsGtpj64QAzG4K0yTJpzCy2GdbkiNHEpJ4GZwtlhTOYCbAbnA0HjvnPHBdG3xrYhKyoLnMkNBkDZqiJ3Q48AOiaC4C3/0gOYKNnEqEYgY1ARYBUbnBUZanQbfNmuBPZM6Tmq4RCFqiQkHLC6LjYpWq7FBqlhAo3MyMlCx4pOShTBSiZh89bnQ7mJ+zG1kwExxtZCEWgbY4n3Ac+Zb5kw2JOnXqFOLxOGpqalBXV4fa2tpl017zYabUdT2jlFmnwvDiiy/ihz/8ITo6OtDV1QUAuO+++/C9730Pt99+O1RVRWlpKR599FEAwJEjR/Dd734Xhw4dAmD4HsbGxvD2t7+dbdPj8eB73/serr32WoiiiNraWnz/+9/PxdstAIoKQz5QJAwZghCCkZERBAIB7N+/H6+++mre9vXqq6+iubkZbW1tGZ1MqapAJPO/V1McoU3mSZ5LgaQQyyoSQpVs2zYHTvGg6gIjG+bwKQpaZhC9HiszQdMSLpZqkqmU/DaM3zMjC8mQUKJwliocJQtbm6Uj0AngfA58uBMlFw4DIz/BkqoL7HOIqpB8Ikp+9SsAsMU78yoCP8uBD2fySQIUl7IIe543OEp2gyMPjyjAI5gqggary4a26mqq3dhIdJaxAMDwLMSj0JfmjfwNXYe+OAdy1ScS9lXIzgO3IVELCwusfVMURaY+VFVV5W1ENY9MFYZwOGxTGC655JKkROaVV15JWLZ//35GFgCgvb0dExMTCetdffXVuPrqq9M+rtcMCIqEIQ8oEoYMoCgK+vr6UF5ejv379+etDhoMBrGwsIBdu3Zh/fr1Gb9er14HMTSdWI7QLSKR8ByfyEinUYoS9JhFHihRsHkakmQyuJUiAECTE5enJgdOj0PmZIFe+A1vgtUBoSkaRPNCqTnk+0QTJK88SLZlvOeAz2twhjoBhqLAGyrlJc3uZ6AEI66Bxmi55S4AqSdJeh2dDqlGUvPP29QF/iWcVwEABCUG0FZKorPyFjU3AjDIgTmsjMTC0Bfnob/7dtfjyIfCkO426d0zne8iyzKbMLm4uIiKigpGIEpKSvJCIDIlTLFYzNYZUYQdBMTWzl1EbrDqCEO2X/ZQKIT+/n5s2rQJTU1NOT4qA7x6UV9fb7uDyBiUXYuSFf/MlSNY+6XoAZHtKgMdHJUMgq/UEerEvT4ZgTAv5JLPy0iD05+QygCZSeKjsdxOFng42yX5rgdREhNKD7QbgpoZbQRAM05MgqPkoOlGCyldl2gEiiy7Zi7EF2VIXGlBJwQN//kCe0z9C3z5gS9NlDlMjXSuiJvBEUitKrB1BLBcBYDzKlDSwJMFmrdAOyHiUdY5w8hCOIR4YDbpCee10HlA4fP50NTUhKamJhBCEA6HMTs7y0bSy7KMYDCY0+jqTBUGAK854+ZrCgQpPVhFZIdVRxiyATUddnZ25i2/XVVV9PX1obS0FPv378fAwEBGEyud0NdcAHF+MuHCL9DygaNjAoChMpjlCH25LIYkxMB2DA4CABgXfmfCI73ou5kcAYfRMUuyQCV/2gHBZx3weQlUheBNkoIoWGQhielRj5GEkgPRVGZgpDCmWlq+B80kA7KiwSuK0F1kZTefgs+T4mLvUA1sBkeTLCg6SXheJLw/gVMTeK8CYC9DcMOlXMlCJAQ9vAh5bh6eP/9C0mM+32FIySAIAjNPtrW1IRaLobe31zbjob6+ns14yJb0ZEIYXisR2a9tFD0M+UCRMKQAHX2t6zoOHDiQkSkpEywtLaG3txcbN25kJQg+4yFbJCQ26iqIx8tIA1MbPF6QmN234DZcyvY8F8AkSJLN1+BWjjBGPFvKgjOhEUjdOumMknadUplEVUhsp0xMceShOvwG1MjIKw+aoiWEKtHj5BUMaqa0pThypREA0AiBRgBN0+ETBTS//Dv2XFxLHCDFX5NKJbu6oCyjLlCUpTBLspRQ3U4SrPZJOmTMaKGkJYhkZEEJhSBd/7mUx/NaUhhSQRAElJSUsG6DXEVXZ3qsgiAUxFvxugUhIEXCkHOsOsKQ7pcsEomgp6cHzc3NaG1tTfm6lZzs6NTMjo4OVFVVseWZjLhOBq2+HVJwlD0WVMUgDPRCIHpAYkv2F+ma9UWjXgZJssoOfOBTivAnNn3SRWUA4EoWAItM2NsquajoZVQFJ5xkQXdRCujsB2emAl96cCoP/Dr2DgmRvQ8K+jvvUaDKgsbdLWqEIOrYvptPIVUpweld4IkD72OwqQrEManUBAv3on8PPAFVja4IIkeNGHBNs8hCPAY9sgioMrRoBOJ1n0l6vBSvVYVhuW2mE11dX1+PmpqalMeSTUmiiGVQLEnkHKuOMKSDmZkZDA4OYvfu3ctOs6QX9ky/7Lqu49SpU0kDn5yx09kgEomgih8mZaoLbCgVP7GSK0dY0dCJWQxO/wJgmSGpspCsfTKVR8G+Lk8KuDApvq0yCVlgfgQHIdAU3TVrgQ9rEhNKFULK3AW6Dr8dZ8nB2L993zohkE3iIgkAzxF29vwn+11WjSd4jwLPFUokvtRgrKPqZFl1IRXhEJSI8dNZkqDqAjU3KhaBTEYWlLk5xIILiM3NLXvBPJ+mx0yQioQki672+/0YHBxMiK7mjy0TciPLcs4C4t64KCoM+UCRMHBwzmlIR1KksykyIQzxeBy9vb2oq6vD3r17XU9qKy1JBAIBnDx5Ert27UJDbIq1WNp8C7oKwVcKPRyyvVbw+Kyx1TR3QZRY2SLZFEsKqdQHJRRhj2kpQvR5oMuq61wHnjw4VYUEopEhWXDCbUy18Xp714NTVeBLFfw6os/eNcGXHBiRcPEo0FKEJAhMafCKXFnBxaeQrNuBf97joi7wJIF6FXhVIaF8RaOdna243LqMINC/C44s6NEw4vOLWLrmdsyaBLy0tJTV+51hSa+XkoSmaWlvk0ZX06FQNPtheHgY0WgUVVVVqK+vR21tbUbnkHA4nLcJuG8YFNsq84IiYTBBL+K1tbXo7u5O++SV6TCr+fl5HDt2DNu2bWMnEjdkW5IghGB0dBR+vx/79+9HSUkJMDXFZTN4jQuFWzkCXKYCvWC7dExQlYEoCiBKtgmUbuoCYF30kwUz0fJDwvO2Tgl+GFUiUTDWTyQLbm2VutlWKSRpq9SdpIJTFZKtk+x3RddtHgVZ50mDQRwkAejsMwb70Iu7opOkHoVSm7pg/b7c3y1vbGSv0WR7B4QznIl6VWi4F08QYmHDr0DniagytPAi4nOLKP3Q36IUQGNjo2tYEp00WVtb+7oqSWRbOnBGVy8uLiIYDGJsbAxLS0s4c+ZMWtHV4XA4b+brNw5IsSSRB6w6wuB2Qp2bm8Px48eXvYi7IV0lgBCCsbExTE5Ooru7e9k42mymaqqqiv7+fvh8PltOhNq0HZ7JY9ZQKUd3hOD1sXKEtczLSINteiVLfFy+S8KZ4ggAktcDJZyoSmgOw6MR58wZBVdIFngkehWsXAQ+ldE58prPW6D70g0mYL7ebMMkBFAJREGAwp20NEKwpBL4RIGpC3S5U2kADOLgEQEut8nKTZAEqC6JkLR64eOIBvUpAJaqYFMUHF4U+pzRSmkmOAL2/3tdg07NjQ6yoIZjiPrnISgKu7iKopgQljQ/P4/Z2VmMjIyAEAKv14ulpaUVdRvweC2TEFEUUVNTw0qeL7/8MiorK9OKro5EIkWFYTkQFHMY8oBVRxgAgzQQQkAIwZkzZzA9PZ3WRdwN6XgNNE3DsWPHIAgCDhw4kNYdiiiKGU3ZoybNtrY2NDc3Jzwv6Cq9ZoBIPgia7FqOALhIaNpf7/FCjxklBqtEYcVFC6LIlAX+dx5OkyPbl6azz8+YMWHPhNCYGdIYO51JCcKZ1AgkehXUmH3QlPVaixDossbKDvy+KIGwTZk0L/iGgVE3yYFlbqTGRpq2SMnC20++DFU3SAMFbWTwiAYBoPkKJR6LNPCpjctUK9yNjXGDKFrqgqn4mNkcxgCpOJfmaXoVdM36XY4ZiY6xCJRQBJGZOVR/8pvQdR2aprFygyiK7CefpggAExMTCAaDGB0dRTgcRnV1NXs+23r9StSAVNvMR/6BIAgJ0dXBYDAhurqqqqqoMKSFYltlPrAqCQNgvxs/cOBA1ieB5ZQAeiFvaWlBa2trRtuNx+PLrwhjqtypU6dSmjSVlk54x3sAGBkMbi2TCeUIjy/x7rOkzB7U5ALNxX/gKfUx0kB0PWWCI2DvhrCWJc9XSPa8sxvCeN7ROWF2SdB2SLepkfy+aH6C5BETyg5UPaDgyQEtRWjEWO70JjrVBEkUoHHlC2dugjP+meUvQAdS+RRY0JLjb0CTXcyOpnqiGKUJIsdYdLgbWZAXw6j91IPWZ6brIIRA13X2j35feALh8XhQU1ODDRs2gBCCUCjE0hYBYxBSfX09qqur01YfXssKQyrw0dWtra226OoPf/jDmJ6eRnV1Nf7whz+gu7sbkiThlltuwTPPPIO1a9eiv7/ftr1vfvObuPPOO+H3+10V1E9/+tP4xS9+AV3Xcfnll+Pb3/42BEHAj3/8Y9x7773QNA3vfve78bWvfS2v7zunKE6rzAtWJWFYXFxEb28v2tvbccEFF6xoW6kIA72Q79q1C2vWrMlou+mUOgghGB4exuzsbFomTaLEIXhLjLtJczIln6FAVBmCx2cvR9DWSj6rgYuOViMWeaB+BE9piS2ZETAUBreJkm4GSFvrJHfBJzpxLQsYr0lubuR/dwYwOdskneADn5wkghoZ+bJD1MWnEOXzIzi1QdYNgvEng39gF3+qKtDpkJIoML+CogOlnBGyguue8JqL1SRvx2lq5HMVaLukQGdDcF4GIsdYFwR03SALqmzkYsgxkHAIWjwONRxDbH4RNbf/nW0/9OJK7/QpgdA0jSlLmqZBVTmiIghMrt+4cSObNDk5OYkTJ06wqOb6+nrDo5MEhJDzanrMFfjo6p///Od48skn8bOf/QwPP/wwXn31VRw8eBA333wzbrvtNtx44422146NjeH5559HW1ub67Z///vf48UXX2QjwC+55BK88MIL6OjowKc+9Sm88soraGxsxE033YR///d/xx//8R/n/f3mCsVplbnHqiMMNH7ZmXuQLdxKEpleyN2wnOmRJkOWlZVh3759aZ3E1I1vgmfkZW6BecevKhA8Xnt3BOdbSGDqKaKjKVFwMyvS4VNuBkgnmbDMkAILSmLPLVOCSFieZFolTxbUmGqLcuZbIdkAqbgGySOyDAUAjCzwvINXEixyQGzlBro+XZfvjkg2gdIrLt8l4dUtYkATGI03aFcVbHMhVPsypj6pslF20DUQsyQFVTbKU+ZzlCzIi+EEsuAGNwIRj8cxPT2N5uZmyLLMnqfqg3PSJI1qPn78OFRVRW1tLerq6rBmzRrb9+D1ojBkmtzo9Xqxb98+3HPPPSCEYHZ2FvX19RgdHU1Y9xOf+AS+/vWv48/+7M9ctyUIAmKxGGRZBiEEiqJg3bp1GB4expYtW9DY2AgA+JM/+RP89Kc/fR0RhqLCkA+sOsIgCAI6OztXnHFA4VQY6ICqioqKtC/kybab7BjD4TB6enqyU0hoicFjkBiiKLZsBao28EmPNtOj+bxmlksEyd2zwCPVOrR9knVJOEoRmqwxVQBwZDHwQ59cyEIq1cHN3MjPfQAsVQHggpYcgUs8UXBbBhikgO+G4J+/avQVZl50y0fgsxYk7nm+M0LkiIGgKSCSo+avyolmR5bayJEFNc7uyojpbbFaJs0OCdPc6CQL0WAI2dBv+n3ZsGED66Zwqg+878EZ1axpGubn5xEIBDA0NASfz8fUh3yoAZmOoU53m5kcJ+9hEAQB9fX1rus9/fTTaG5uRmdnZ9JtXXzxxbjssstY8NRtt92GHTt2YG5uDidPnsTo6ChaWlrw85//nJG51wWKbZV5waojDLkGXzpYXFxEX19fTgZUJStJ0FCpjo4OVFdXZ7zd3/hFvK1Rd01pJKpsH1/Nmx5p3Vq1qwWAaVaMJioLbuWGZMt1WWXzHNh65sVdEAWoMYcCQTsSdJKQp5Dwe8KYai55Uddt20vIZuCUBs1xJ8irBPT6rRHYQpkSWyhhWxewhkGpGmGTKd3Aex5ETYHuIAYWKVAAJeayPJEssGWaY0Q5wNplSTRskEdaojDJghwKQ43EEJ9bwtq7H0l63MkQDofR19eHrVu3MvMjYFcfqGlS0zRX74MkSaivr2cXTdq6efr0aSwsLCAWizEVIhcX+teCahGJRJY1PUYiEdx33314/vnnU653+vRpMudZuQAAIABJREFUDAwMMK/I5Zdfjt/+9re49NJL8cgjj+D9738/RFHEW97yFgwNDaV9jOcbBGRVliQEQZAAHAEwQQh5tyAIGwH8C4B6AK8A+AtCSNbMr0gYVgiqMExOTmJ0dBR79uxZ2ZRJE86SBCEEQ0NDmJ+fz7rMQbdLs/8F032ekNyoWqZHEgtD8FgXJkGUWIKamydBKvXZ1ARKINy6J6i6QNcRXeZLJI6d5mdNJCEILuZHqkzwr6dzH6xsBs2mWvAxzqnVA6stkh0DIZB1K8nR2ULpEwW87+yrbBlgEAevaHgVALtfwStY/gQvMT8vTWEXevPNsV/d2ictcqDZHpO41QFD5JilLDGSqNiyF5SlMNRoHGokhmgwlBVZWFhYwPHjx7F79+6kpUGqKgDu5klVVSEIgq11k886GBgYQHV1NUKhEM6cOcM6M+gk2GxaN/MVBpVJN0ckEkmqKlAMDQ1hZGSEqQvj4+Po7u7Gyy+/bLuZeeqpp3DRRRexc9Y73/lO/Od//icuvfRSvOc978F73vMeAMCjjz76+oquXr0Kw+0ABgDQu8mvAXiQEPIvgiB8F8CtADL/wppYlYQhl4lyoihifHwcJSUleNOb3pQzuZInDKqqore3FxUVFeju7l7RCUsURcS2XIKSgV+zZdTsCCSWKIznFVtWAyUKotcD1cxUECWJ+ReSKQv8c7qjZdT5Gmc5gWjEUYLg2xt123pOc6STLLjdedh8EarOxkfT7ge+lEBJgtOTIOu6LUshUVGwjum6sVcZMaDboR5G+tOZy8D4g4vyxAZCwYpvtj1PjY38KHOObJB4jGunVQzywKsKigJdjkGLyYwsKOFYVmQhEAjg9OnT6OrqSruV2c37wHdduLVuEkJQU1PD2oxlWcbs7CzOnj2LpaUlVFZWsuTJdAn4a4UwLJfD0NHRgZmZGfa4vb0dR44cSeiSaGtrw/e+9z187nOfAyEEL7zwAu644w4Ahpq5du1azM3N4Tvf+Q5+8pOfZPCuzjdWn4dBEIQWAP8NwL0A/lowLnR/BOCD5iqPAfgSioTh/CAWi2F4eBglJSXo6urKKRGhyoXbJMuVgBERXWcXCBtBUGVbOyVfjtBVBaLH65pbYNuHOS6aKgd86QIcT3CbJWEQA/e2SSC5qpCs28FJFujrRa6N0hbCxIHvfqCmRb7EQEsRTsOjUYowj5FTGthxU6VApPsxfvIeBUoiJEGApJnTICWfzchoIwlurZKUJLhNHdUUK60TBmmknRAkHjW6IPhERwdZkEMRLIxMoS5xyykxOTmJiYkJdHd3Z62SAcurD7Tzgi4XRRE+nw9NTU1oamoCIQRLS0sIBoNsUBTfupmMFOTLF7HSksT111+Pw4cPIxAIoKWlBffccw9uvfVW19cfOXIE3/3ud3Ho0CG8733vw69//Wt0dHRAEARceeWVTFW4/fbb0dNjtGJ/8YtfxNatW7N8h+cBb8zgpgZBEI5wjx8lhDzKPf4WgE8DzE5UD2CeEEJPtOMAEkN6MkCRMGQJmg5Jnd25zsEXRRGxWAy9vb056+ig29V1HXrXOyEefY4uNDok5BjLWRB8pcZcAP61Hi8bMMVUBp8Hihm2xJsb3ciApqgJygJFsvZJ0ScllAoAgyBYxCSxTGEfha0npDYytYEjFIIkMFOjW/dDVNMT7vrZ9ghPJKxlVinCUilunTrKQpgAgziUeKxgJi90lszIQ9BkSyngPAogLuTNpRRBlLixWc6/wsyuqmwpSDSkiw4VM8mCHApDV1TIoQhiwQVs+t6TiftNAhqSNjc3x7IDcgU39WF6ehrxeBxer5eRB0oyqApRVVWFqqoqNihqbm5u2aTFfIRBZaMwOAnDE088kfI1fAfF/v37cejQIQDGZ/b3f//3rq9Zbpuvbbwho6EDhJD9bk8IgvBuADOEkFcEQXhHvg6gSBgyBJ8OuW/fPkSjUZw7dy7n+xgZGUE0GsXb3/72nE6mEwSBJU9qYjO69ImELxbLXjCVB1s5wsWTIHm9jDTQLgdnZwQtOQiiaAtu0hjxMIhBQhxzErJg7EtLmPVAlxs/E08YJEWpwtkBQVUF5whq4yfYOtZziY/51/E+B9oeqboEM4E7bFHhSghKjHW38GCqAk8S1EQPg7FDmcvdMMmfc0qpKhuRz6oMLWb8U2NxRhYiM3No/dY/JRxHMhBCcOrUKaiqis7OzrznGExOTrLvp9frZYoDrzwA9tZNj8eDxsZG1qkRiUTY3AtZllFTU5PXzouVEoYiVj3eCuAqQRDeBaAUhofh2wDWCILgMVWGFgATK9nJqiQM2aoBqqri2LFj8Hg8LB1SluUVTZV0QlEU9Pb2oqqqCuXl5TkfY0sIQV9fH9avX2+k6r0yYj0piiDxmL3N0oyCpsoCnTiZDHy5gv+dT3JMTHm0tzUCdJaEqTJIgm3oE1+K0DXd1nbpRhac7ZL8erb5D7CTBfqTdjs4qx7JjJDJsqA0AnzMb0i8GgtqEgwTo6ZBl7wQ+e4GfgS5Yl3MbWWJZUgCNbiyzA2qGtBygzkLAlz+Bs1e4MmCHIpAV1TE5xczIgu6rqO/vx/l5eXYunVrzpU4HnTwWigUQldXl80M6SxfLNe6WVFRgYqKCrS2tkLTNCwsLCAYDCIYDCIWi6GxsRF1dXU5mXuRKQkpEoY0sYo8DISQzwH4HACYCsOdhJAbBEF4EsD7YHRK3ATg6ZXsZ1UShmwQDofR29uL1tZWtLS0sOXZDIlKBupXoG2ZgUAgJ9ulWFhYwNzcHLZs2YK2tjYQQqDufTekl5+yOiaoQ55efErKQMIhWzkCMEoSgiQyo6NRmoix5ygsBcHLSIPg0g3B1nd6FrgLO50lwcKcXOY6GC2e3Khsmivg0npJNALFNCoCfOBSKhUhsbXS2QHB/+4cNEXB+xVgHpJopi8Skfta0hZIPTlJA9yNjjxZcKoK/GPDu6AZBsd4jKV38mRBicSghqPw3/AJkIkJ1NfXo7S0NOUxqaqKnp4eNDY2Jk0azBV4FaOjoyPpBditfJFO6yYtT0SjUWzYsAHhcBijo6OIRCK2MdXZEPxMSxLhcDgnnVhvaBDCurlWOT4D4F8EQfgKgP8H4B9WsrEiYUgDMzMzOH36NHbt2pUwqyFXhGFqagrDw8M5a8t0YnJyEmfOnEFDQwOqq6vZCZIQAkmVWcmclSF8pSAR+2Aqvgyh0Yu/WWJItp4oiraY6IRER5cyRDIDozX7gVcPEg2SzuNxkgW37fNkgU9l5B8n637gX09fQ0F9DwDwP6dfYZ0JNEPBpihw5ECQI9wbsN6PTV1weS2Ro5b9wakqmJ4UphpRj4pJFKBrUCNR6IoKNRY3TY4yIwvrv/aPqA6HEQwGcezYMaiqytoUnSmL8XgcPT092LBhA9atW5fweecSuq7j+PHjKCkpwc6dOzO648+0dVPTNJSVlaGmpgYXXHBBwphqAOwzqaqqSutY8pHDUMTqjYYmhBwGcNj8fRjAm3K17VVJGNI9oRBCWADM/v37XV3dy0U4p7OPwcFBLC4u4sCBAzkvQei6jlOnTiEajeLAgQMYHByEqqqsjiuKIrS3vB/S73/MXiOYkyhZaUKUWEcFveBLPi8jDbTEkGx0NQ/N5oFQzNdJ0BTNVV1w5jAkIwtuXRu2soQLWaDGRqeywF5jMzIm64gQXF/vjIW+c/oPxl28OWJc1BQIpj+BSD56kAnvAXAfIGVTFFwioHnDIg8Sj9qinwHYWiaJpjOyoMkqIwsXfP0HAMBSFjds2MCMgtPT0zh58iTKysrQ0NCA8vJynDp1KiGQKR/QNA29vb2ora1Fe3v7iraVTusm/d7Qi7xzTLWiKJidncXExARCoRAqKipY62ayuReapmXUjl0kDGmAkJSdXEVkh1VJGNKBLMvo6+tDdXU19u3bl5RkrERhUBQFPT09qKmpQXd3d87ru7Iss5Pptm3bABgnxenpaXi9XttJR3vL+yH+5p9YSFPC5EoYZIEPZrIlPaZYJkgSNFq6MDsbjOXWuGrBEYtMl0te0eZfABK9Dm7LnTkMbkQBsJcTAHfvAgUfxGQts8hCqphoQZMNYuAikwqaDEGJgUjG15EnA4JiKQ2CWzcEB2cAFwA2KIxFO6uK8X9LCaBpeKQtk0YZwjQ7KiqUUBhL5xJHoANwNQqOj4/j1KlTKC0thd/vByEEtbW1eTE60u/PBRdcsOIhcm7g1QdN03D69GnmWUhWvvB6vVi3bh3WrVvH5l4Eg8GUcy80TUs5RMsJVVVX1JK6GkCI+01EEStDkTC4IBQKoa+vD1u2bMHatWtTrputwkBjpDdv3rzsPrKBc/tUam1paWHBOdFoFLW1tWhsbDRO6roG2rFrqQtiYhKk+UX0lJaw7ghdViH6PLbIaMnrgWLWw20zIFynVuoJpQKqIFD/Aq8uODsnNFm3OjBYzLNDnSAk5QwIfmiU87E9BlpgpYqE9+Gy/U9NvgiAa2+UfHYiYI6Utn4mKg02EsGbGrmsBPY+WbeDqQCFrQs+URU2J4I3NgKwkQUlHIW8GEE8FMe2H/084XgSjk8QEI1GMTc3h4svvhg+nw9zc3Pw+/0YHBxESUkJGhoaUF9fv2zoUDqIx+M4evQoNm7cmJfvDw9CCE6ePAlRFLF7924IguBqnnRr3eQVGU3TMDc3x75/JSUlqK+vRzweL3oSco7VGQ2dbxQJgwMTExM4e/Ysurq60pL9slEFzp07h5GRkbz5FaanpzE0NMS2z/sVSkpK0NLSgpaWFui6zk7qp06dQtmaTnTP97Dt0Fo3nWJJWyX57AUKb0WprRzhvFjz3RWGMdFSLpJNmeShu7RIGvuxMhv4E4SeorXSqSoAiWTB6VfglzlnR1jb5V9j/P65M78CoYZF08woRueN46UtknzJgZ8i6eJRAGCVi+i4cbqcGhjpY24uhBHSZO940WWVGRuNUoQxgpyShdhcFFt/+BTSgVsgU0NDA0sWjEQiCAaDOHnyJOLxONasWYOGhgbU1tZmnGsQiUTQ29uLbdu2oba2NqPXZgra5VFRUYFNmzax73sy82Sq1k1JkmyfSTQaZZ0Xs7OzCAaDqKurSzn3giZaFrEMigpDXrAqCYPbF07XdQwMDEBVVRw4cCDnE+noPgYHBxEOh9OKkaZ3MunKudRzEQqFmB+Cr7s6tyOKIhvcQyXlYf8abDz9K2PctddnuenpkCbmV/BCUxRbdwRgqQesO8LrZeUIvkxBSxOaoiekORqvtw+MMpa5j7jmj0+TdauV01QmiEa4tklzWw5Vwe05N7Jgj4e2nnMjDgmnK0eng8C1SBLRY0tuFGXqb/DajI5s7gOf0uhSiqCqgq09VlWgq4ox6EtRocmKaXCUbeQhE7KQbiBTeXk5ysvLWZsinTB5+vRp+Hw+m/qQ6oK4uLiI/v7+lDMocgXqj6irq8OGDRtSrptp6yYAlJWVoaWlBeFwmKkks7OzbO4F9T64zb0okoblUSQMuceqJAxOxGIx9PT0YN26ddiwYUNevoyyLKOnpwd1dXXYu3dvWvug5Y50CINz3gQAdsISBGHZ/fG952SAk8RFEdB11vlg8zC4mB01zsNAiQI/sto2s8EkBSy0yXVolF325xMg+fZJYz/2yZOAFcYEJJobk6kKTq+Cc3YE/9gt1AkwyMIXRv6v8VlQc6HHZ5/lwEHQVdcIZ0FTWHukTTGIWSUNazS55VOgy6mqAFWBFjeUBKoOqRFqjDTIgrwYhhyKQg7LaZOFbAKZ3CZMBoNBDA4OsjIZvVjyBISOXO7s7MxJWSMVaEtoU1MTm0WRLjJt3dQ0DV6vF5WVlUwxicfjtrkXVVVVWFhYQGtra8rv8i233IJnnnkGa9euRX9/f8LzhBDcfvvtePbZZ1FeXo4f/OAH7Hzx2GOP4Stf+QoA4G/+5m9w0003ZfS+X0sghEB/40VDn3esesIQDAZx4sQJ7NixI2+O7kw8ETwkSUrLHxEOh9HT08PmTfCtYemQBSe0P/0IpF8+YpAFIKFDQpBEaLICqdQHeTFie63k9SQMkvKU+aBGqQHSzFBQNHOeg8aWU/BmSNEnQndEO/Ptk4IouqY82lUFklRZcCML9Hnn7Ai63Fma4EsQ9H/rb4Z+YbQ3cp0RgirbchZE3segxNlyXmngyw6UGAi+UvZ/whQgvhThUBW0uEE46KAwLSabkzpVqOEYl+IYRXQuhh0/Xj7bRdd1HDt2DKWlpRm3MjpB77RpmYyqD8PDw/B4PGhoaIAgCJicnMTevXszMghmA1mWcfTo0Zy1hCZr3aTEIR6Ps+8rXb+kpATr169n3+fFxUX85je/wZ133olz587hrrvuwhVXXIGLLrrIplTefPPNuO2223DjjTe6Hstzzz2HwcFBDA4O4qWXXsLHPvYxvPTSS5idncU999yDI0eOQBAE7Nu3D1dddVXeSz75RNHDkHusSsIgCAJLhZuZmcG+ffuWDaFZDslqizT/IF1PBA9RFJftwKD+g46OjoR8hWzIQiwWM5IgO9+Llh7D7CZ4fNCiEdcOCU+pD2pMtkVBUylQ9HqhmnezbqOrKZgy4Lg4646BUU6jI/+cPfI58a7f2fLo1g7Jz4AwHtufj/IdGS6hTrpjP4wcmJ0RohIxDI+6aikNksQMjSxLwdH2CFjdDACgL5keiLjDjKoqlgphbkNZsiK9NUUxfxpEgbZQKuEYdEVNmyxQNauhoSHngUx0BDUl77FYDENDQ/D7/fD5fBgaGkJDQwPq6uryUjakauOFF16YMNkxF+DVB4/Hg8HBQfh8PpSXlyeduikIAqqrq/HRj34UV199NW655Rbs3bsXjz/+OL761a/imWeeYdt/29veZpsb4cTTTz+NG2+8EYIg4KKLLsL8/DzOnTuHw4cP4/LLL2ef++WXX45f/vKXuP7663P+GRQExbbKvGBVEgZd19HT04OSkhIW8bwS0NZK/gSm6zpOnjyJWCyWtSciVQcGJTx+vx8HDhyAz+ez+RWyIQsLCws4fvw4tm/fjtraWpBXLNOj6PUYhkfzp6e0hAUy8VHQuqzauiNEn4epC/yFnE9m5Kv9SU2PCR0UiZMqbcmPKQyN9mXWc3wbpZsi4RYNrTseA8Ddp/8PW8bCmGh+grMDQtNsOQr8XRHf0upMaAQ4JYEvZZi/U1XBmtmhsLKRoSrI0BUFalSGvBiDvKSkRRZoIFNbWxuampqWXX+lmJqagizLuPTSSyEIAhYWFhAIBDA6OmorbbjV+TMFNVNu374da9asydE7cAftvCCEsEmRyaZuAlb5IhwOY82aNbjmmmtwzTXXZLzfiYkJtLa2ssctLS2YmJhIuvz1jCJhyD1WJWEQBAEbNmzImdzmvLBTv0J9fT22b9+e9YksWUlC0zT09/fD6/Vi//79rA6abQkCMDo3xsbG0NXVxabzCX/219Cf+obVs6+oBmFQrIhnzaEu8GZH52RKZzmCehD4WRGiI9o5mdHRmbPAP9YdCgFgJwDJzIrpkAWnT8G57EsnfmqWIuydEeCUIltbZDwCAvsYccDdo8D/7toN4aIq0A4I+liJxKDLCmuhVGOGsrD7Z9ZdajLQC2ohApmogTcej9v8EbW1tbY6fzAYxMjICMLhMKqrq5n6kGkA2tLSEvr6+gpipiSEYGBgAJIkYdu2bSk7L5zmSb/fj1gsdThaEcZnXCxJ5B6rljDU1dWBuIwpzgZ8eNPCwgL6+/uxdetWNDY2rmi7biWJaDSKnp4eVvNdqV+BnpgjkQi6u7sTlBDx6juh/virEH0eeCpKoYZj9vwFqi5QUyTnYaB3t3w5Qnew/lRxzbqDCAAWgeAJB3svmqUauF3gk//u3hKZjEAA7mSBhTRRNcDjBXTV6ngQPRBkjhSoDgWBtjuavgU6cpzt0zlVEmCZCkxRUFRGFABYZlRmVLXIQjwUhxxW0iILVH0qxAWVdix5PB7s2rUr6d90SUkJC23SdR2hUAiBQABnzpyBIAis82K5iOaFhQUMDAxgz549eU9QpN6PsrIyXHjhhSmPy0kgFhYWcNddd+FNb8o+6be5uZlFWAPA+Pg4mpub0dzcjMOHD9uWv+Md78h6P68FOM81Rawcq5Iw5BqUMNAMh7179+bExe1ULmZnZzEwMICdO3caJYMV+hUURUF/fz+qq6uxZ8+epK/nx1E7SxKGImCX2Y3ShGGK5FsurUmS7kZHSgB406PkFaGE7UoFX85wqgv2FMdEEmBd/O0/l19vebLwlYEfA5ypUVAVgyB4DJOeoKsgqmKlaSp8AJOhKNDnAMNsyjof+NZJZ/yzqjBPCSUL7LGisowFLRY3VIWowpSFzmeew3KgHQy8+pQvaJqGvr4+1NTUoL29Pe2/aVEUsWbNGlZKkGUZwWAQZ86cYV0GlEDw6gMdYd3Z2Zn396brOkuP3bhxY0avnZ+fx3XXXYfbbrsNN9xwQ9bHcNVVV+Ghhx7CBz7wAbz00kuoqanB+vXrccUVV+Dzn/885ubmAADPP/887r///qz3c95RzGHIC1YtYaDGx1xAFEWcPn0aAHKa4UCJCCEEY2NjOHfuHDNorpQshMNh9Pf3o729fVknuPf6z0N54j722BncJPo8LNDJGREtcTkNdAy1xLVESj6JlSNoyYJoBKIk2pZTY6QgioCmWWOpWapj4p0+/3s6pQe3bAZ+uZtfgW7jK8f+2ShDiJ7EyZKmR0GPho1sC1UBiborDdrivLU8lrgO/zoawKSZOQpOVYGqDUokykiDEpahRg2y0PXcL7Eczp07h/HxcVsgU75AR7uvW7fONhE2G/h8PluXAVUf6N11fX09i0kvROcFzXSor6/P2CgaDAZx8OBB3HnnnXjf+96Xct3rr78ehw8fRiAQQEtLC+655x4oZmnwox/9KN71rnfh2WefxebNm1FeXo5//Md/BGAMzLrrrrtw4MABAMAXv/jFvJed8oqi6TEvEDK8aObmCvsagKIoKxoaRRGPx/H73/8e69atw44dO3Ka4UCz64PBIAgh2LlzJyMRK/Er0DvGXbt2ZSQvxx/7WwAGQZBDxoWLEgQ+myFRDrcuiHLYuqvmSwqUHPCJjvy6NNHR2RWhyRZ5oOqCUylwm/eQaoaE83k3RYHfz329j9mUAXbMfOmAUxPolEjRV2p7bPMw8K+NUk8Cp9Y4sjDkRXMmhBnKRLshqLHRCGhSEV8wyhDpkIXR0VHMzc1hz549GacxZopCTreUZRlDQ0OYnp6Gz+ezqQ/5IEUryXSYnp7Gddddh7vuugtXXXVVzo/tPKAgiVN7Lmgkz374vYXYVcHQ+reHXiGE7D+fx7BqFYZcYH5+HseOHUNtbS3Wrl2b88An6i9obW1lSXMrIQtUqZiZmcnqjrHkpi8i+v27ARlsZgQtSfAjranZiOYvSKVeazKlT0rohNB1wi76giRAjam2dRk5cCELFG5kIdnI6Uw8C6m8CvwyXiUQPF6WtCh4fTZVwPa+5Zj9OTWx7dT5WhqyBMA2NpyGYxnRzrQbImqUImTNIAshGfKSjH3//m+ux8P2aQYyKYqSUSBTtqC+nEKYKQHjIhyNRnHppZdCFEUsLi4iEAigp6cHhBDWeVFTU7Pi77SiKDh69ChaWlqwfv36jF577tw5HDx4EPfffz+uuOKKFR3HqkNRYcgLioQhS4yPj2NsbAx79+7F5ORk1hMrk2FhYQHj4+NYv3492tvbV2xupEYyQRDQ3d2d9UWA6Do0MzBJkERASSxJSKUlLH+BkgeeCNALfrJyhOSVXCdUilxpwjmB0hmy5NZKmdgWCdv6znhn/nRDUx2dZOHel75jXejN2RD6QtB87AVRZPuIaY5Y6EnIgk1dUO0KjjFF0jRH0hhuF1VBCcegyxp0TUc8ZHVDdP0qtWeBD2RKZTjMFWh3ws6dO9mI6HyBtiKHQiF0dXWx70B1dTWqq6uxadMm23jqgYEBVFRUMPUh07IFDYBqb2/PeEDW2NgYPvCBD+CBBx7AZZddltFrizBQJAy5x6olDNmeCPmZE29605sgSdKKRly7gZon29ra2DyIlfgV4vE4ent70dTUhJaWlhVdBMo/9GWE//4L7LHo9UDXZEtxEEXDDGk+9nDGR0EUoCm6LdZZ8kq20gPbLmd8pD4FOhtCT5K3wN/xO4OZ+LkQPOg6zphnJ9w6LL7y4rcAGHkJgtdrmRGpsVFVWLkBHq/dt0D9CR6f3avArUM7HzQu8IqSBTlkmCR5ogAYqoKmqNBlDUpMhRpVEQ/FEQ/F0fjDf0BPjzFcrL6+Hg0NDbYOgnwGMrlhfn4eJ06cKEh3AlXrZFlGR0dHUsLsHE+9tLSEQCCAvr4+6LqOuro6pj6kIt10mmY2AVAjIyP44Ac/iIcffhiXXHJJRq8twgRBTkrORdixaglDNkg2cyJXhIGGPcXjcRw4cAAzMzOIx+NJh0elg1AohGPHjmHbtm05k3srPnIvFh/6DESv8efD9/kDvKpgliu46ZR0XcknQja7H0RJ5OZI8DHP7uOsBUdWA3/RT2ZYdD5OVq5wPk7smjB++fILf2e8H1U22h8dg6CIqtjKEjpnZrRBla0pklz2go0kyIptGZ0qST9vGpJFiRk1NioxFcqSguhcDG/5wwsAwO6ig8Egzp49i8XFRVRXV6OmpgYTExPYsGFDQQKZ/H4/hoeH0dXVteKU1eXA5x5kEmMtCAKqqqpQVVWFjRs3QlVVzM7O4ty5czhx4gTKy8uZ+sC/h5WUWE6ePImbb74Zhw4dYgbEIjIHQbEkkQ8UCUOamJubYymIdGgOhSRJzImcLfjhVNu3bwdgEISpqSk2zS9TwjA1NYUzZ87kZVhP1W1fw8K3PwVREiGZaY5SqQ9KJOZakpB8EtSYCsknQV4y/QxeKbFMwZUjPGUeqFEVRNdt5QjArizwCY2SAESd2Q0ksfxAl9vdXvzOAAAgAElEQVR/2rshkpKFfzc6RqiSwOY68JkJ4UV7+yRfcuDzF/iuB5rKyJEF6lPgzaVWeqNRfmClCFmDzJOFsIJIIIq39b1o+zy8Xi+amprQ1NQEQghmZmZw4sQJeL1ejI+PIxqNoqGhISfpiW6gnRd79+7Ne+dFsvHU2cDj8WDt2rVYu3YtCCEIh8MIBAI4duwYVFVlkyVHRkawa9eujEssx48fxy233ILHH38cXV1dWR9nETDbKovDp3KNVUsYMjlxnD17FpOTk+ju7nbt1ZYkCfF43OWV6WFxcRF9fX3YvHkzOxlR+dPr9bIwGo/Hg8bGRjQ2NqbsGSeEYGhoCEtLS9i3b19eMvcBoOb2v8PCtz8FwIyADscgeS0fgxaLQxBFKxPAvPJ6yjxQluxBTqLPylvgyxEUtBzBShkeETKnRvDqAk8geLgpEcbUSeu5ZGQhAapilBlcIpsp2HMsiMme5sgrCiqfV6E4FAUu54L3KQBgXgVN0aBGVchhBZqsIR6K480v/keSg7ewuLiI4eFhdHd3o6qqKiE9saamJqezG86ePYtAIJByFHausJJWxuUgCAIqKytRWVmJ9vZ2qKqKyclJnDx5El6vFyMjI0x9SCffoaenBx/5yEfwox/9CLt3787psa5OFJMe84FVSxjSga7rOH78OHRdx4EDB5Ke4NIZEpUMU1NTGB4exp49e1BZWWnzK/BhNJs3b0YsFoPf78eJEycQj8dRX1+PxsZGm5tbVVX09/ejsrISnZ2deTetSbfeDfXRu43fS30caYibcyLAShJ8CBM1PEo+CQqnOFgmSDEhyVGX7cZHZwkimYfBbR0nIZAEAUqS1/Pr/+3zXwbRNAiSxAyM/NhpAK7pjM6yhBqxXkMzLSSf1whdklXboC5KuOj8B1aKCBsklVcVdFlHPBTHRf91GMvBLZApWXriyMgImxzZ0NCA8vLyjP62KImNRCI2w2G+oKoqjh49yt5LvhGJRDAxMYH9+/ejoqICkUgEwWAQAwMDkGWZeR9qa2sT3vuRI0fwV3/1V3jyySexbdu2vB/rqkAxuCkvKBKGJKB+haamJrS1taU8OWbjYaAmrFAohAMHDjBzYyq/QmlpKVpbW9Ha2gpN0xAMBjE5OYmBgQFUVVWhuroak5OTaG9vL1gdemhoCFvNNEEArCwhSJJZShCh6TorSXjKPLaShKZobIS1sUzk2iqt3ymo0qCplDRYhMAnCrZyBF+ecJYf3KZV0jFYyTwM9z53l1Fa8PiY3MkbFgFHuSEcAsyyBB/IZFMTZC6jgsu24EkCAGiObAvFNIrKS0ZqoxpVoSmaawnCDekEMrkR1mAwyKLEa2trUV9fj7q6upRqAfUQiKLIBi3lE7keT70cqHmTL/1VVFSgoqICbW1t0DQNc3Nz8Pv9GBwcRElJCWZmZtDW1oa5uTnceeedeOqpp7Bp06a8H+vqQdHDkA8UCYMLaATzjh070jItZUoYqBu9srIS3d3dADLPV5AkyVZPHR8fx9DQEHw+HyYmJiDLMrsTzDUIITZp2XfRRQje91cgmg5NM+ZJqJqRzQAY6YxE05mCwJck+JhoFgfNdVHYhko5Uh3pxdxZjuBJAyUR1rqJ5QrnaSUxARL4yr9+lut+SPQsOB9r4UWIZqcEYPkTjPesQPJ5bWmZTkWBD8CipQleUTB+KlCjRiCTJmsIT0fwR6dfwnIYHR3F7Ows9u7dm1GZobS0lM0d0HUd8/PzCAQCGB4ehtfrtakP7L2YcciVlZUr9hCkA0r0N2/enOA1ygfSiZaWJIl9NoChRvT09OC+++7D6dOncfXVV+PUqVNYv3593uOpiyhiJVi1hMHtxEUvhFNTUyyCOR0kmyrphnA4jJ6eHmzcuJHF1q50eNT4+DimpqZw8cUXo6SkBLFYDIFAgHVc1NXVsdLFSqVgXddx4sQJAMDevXvZ9uo//78Q+PL/MD4HXTdGXCsKRJ8HelTmTI2ipTSEFRs5ECXRGi5lLueNkfy6gN1fwBMFXmmgHgXe+OhUF/gB205PAwB8+alP2kdIm7CpCS4eBhrdzCsKSjhqzOOQrfkPvEfByFlQmaKgMrJgKQrGchXykpGvIIcVXHr0dwn7TzheLpBppWUBURRRV1fHCHU0GrX9zdGpkmNjY1i7dq1tdHK+UMjx1AAQCAQwNDSUcbR0eXk5mpubQQjBK6+8gqGhITz33HN45JFH8PTTy48YL2J5EFIcPpUPrNpoaF3XbZ0Nmqbh+PHjEAQBO3fuzOhkGg6HWS04Ffx+P06dOoWOjg5UV1evOF+BXrwJIdixY4frMWuahtnZWfj9fiwsLKCyshKNjY0JQ3jSgSzL6OvrY336bsc7c8/HmBQoSCKUUBhKOA5BErg2SsO8qGuEkQFLUdChKcbrlWQx0nEtqT+B74BwdkM4lYWo44SikMTwpruf+DgErynZi5bszvsWnEqDGokxdcWmIkRirBXVOUUSsMgBLU1QQhEPxW2fgRy2yhDRuRguO/lfWA58INPmzZvzeqevaRr8fj9OnjwJURRt0cv5uoNeXFxEf39/QaZpAsDMzAxGR0fR1dWVcafHL37xC3zjG9/Av/7rv2Yc6PQGQEGioXc3riH/+8/eUYhdFQw7/uHpYjT0awG0b/qCCy5Aa2trxifT5UoShBCMjIwgGAziwIED8Pl8KyYLsiyjt7cXjY2NKT0WkiSxzgpCCBYXF+H3+3H27FkmlTY2Ni5bulhaWkJ/fz82b96cMohm7d2PYOoLHzLet6ZBKvVB13Qo4ThTFzQNtmmUclhJIBTykgJBtDwMvAlSFAQAJEEN0IilHth/TyxH0OcVYikNPDRCcPcPP2y8D0U2SINu+ha4Tgc1EmXmTsBQE0SfB0TX2YUfMMiAKBkdIzZFgaY1upgdNVljJlH62fCqQiQUxxXDf0j6f8H2bZbA6uvrWcR4PiHLMkZHR7F7927U19cjHA4zA6CiKKitrUVDQwPWrFmTE/NjIcdTA/a20ExJ91NPPYWHH34Yzz77bEFKJqsWRdNjXrBqCQO9wAaDQZw4cYKNjM4GqQgDHddbUlKCffv2sY4KWoLI5oS5uLiIY8eOYcuWLRmddARBYDG4F154oWvpwu1EHggEcPr0aezevRuVlZXL7qfp3kOY+sKHWFuTt6IUxIyTBgDFLEVQomB4GhR4Sz2QwzI0zTI8Sj6LKEg+EUrc+Jx9ooAl1e5h4IkBnRGRrBzBGx3t3REGqfjiY7cYC2gnhPm8Fl6yVILFCESvh52Y5MUwJK/XmBAZ5rsgTAXCbD21lhvraDHZUFa4IV1Gx4MGTdYYWTDmQcQhLylpqQqANdSpra2tIEZYGvW8Y8cOVhZwGgBnZ2cxPT2NkydPJg0/She006MQ46kBI4V1amoqY/8HADzxxBN47LHH8OyzzxakZLKqQewTbIvIDVYtYaC58tPT0xn5FdyQjDBEo1EcPXoUra2taGlpYarCSiZNTk9PY3R0FB0dHSu+myotLUVLSwtaWlrYiXxqagonT55EZWUlGhoamDM+02FVTfceAgBMfvpmEE2Ht6IUSjgGT5kXRCeQlxR4TIIgSqLZPSHDU+qxWi9Nk6QtSprLXzC8Cny3hLV//jEf+8yTCGtda07EZ797AwRTCRDNm0dBNFoolaUwi7zm1QOAu/hDsQgC7P6F+PwiRJ/ZNWF6FGjEM98NwvsUaPcDbZtMV1UArJp+psQyWywsLOD48ePo6OhISiydihcffqRpGiOt1dXVy5JpWhYoxOhtwMiQCAaD6OrqyihDghCCxx9/HE8++SR+8YtfFKRkstpBQIoehjxg1RKGeDyOWCyGAwcOrFgWFQQBTi8I7bTYtWsX1qxZkxNz4/DwMEKhELq7uzOWQpeD80QeCoUwMDCAWCyGyspKTE5OorGxMWOScsHXf4CJT95odkl4oITj8JR6oGsE8VDcVBWMC6SnzCALztZLmhBJSYNXFBHTdGiE2AyOzrbKREJBbEqDsxzxme9cD8CQMilpAACNC1jSYakHgihCkxWoEY4ghKySghLhx1HH2U82TTJqEQMKGrykyzo0RYOuEShhOSNVAbAiwXft2oXq6uq0X5ct3DIdloNb+NHs7CxrFaaDnxoaGhIIweTkJCYnJ7MqC2SDkZERhEKhjKd3EkJw6NAhPPvss3jmmWfy0rVUhAsIQFzC24pYGVYtYSgtLWURzCsFf/F367RYqV9BVVUcO3YM5eXl6OrqyntrmqIoOH36NNavX4+2tjbIsoxAIIDBwUHEYjHU1taisbEx7Rp08zcfx8Qnb4Su6ZBKvczP4C31GMOkzC+2sqSwYVQGeTAuvrQswZckeAXBJ1plBp95OLIORih4TwPvY6BHrgH46wcPQpdViD77V0JeDLNSCmA3KQL2dkjqXwDgUBkS2yedZk9N1qApumkG1aGEFVaWmAsreO+ZI8t+zhS8TF+IC9TU1BTOnj274jt9Z/QyHfzU29sLXdfZwKyFhQUEAgHs3bs372mRNHAqFoulHFqV7LUPPfQQfvvb3+Lpp5/O+8yMIuzQiyWJnGPVEoZ8XHRpMiQhhCkXtAQBZDc8KhqNoq+vD62trVi/fn2uDzkB4XAYfX19uPDCC9HY2AjASP+j/fc0hIbWoCsqKtDY2IiGhoaUd3rN33wcY3f8OYiuw1PmtfkZqMpAZ0f4KnwGaXCoD/KSAskjIipbJQk+tIl6GoDEkoTMtb1S0qAD+PiX/5vR+klLSub1X/R5EsoOcigCySQEcijCvAwApybIKhsGBdhbJmmOAk8WdJ3Yuh/ociUsIxZT0y4/UJw7dw5jY2MFk+nHxsYwMzOD7u7unEaQOwc/0YFZAwMDiEQiaGxshN/vz6rbJ13QNlRN0zIe9U0IwTe+8Q309vbipz/9acajsYtYGUjR9JgXrNq2SsBwc2f4/pPid7/7HRvqQ3PrV1KCAIyBV9SQmekgm2xA70zTNTfSu0C/349gMAhBEGxdF8ne89n/+UEm+1O5HbACiZSwAkEUEjoEAHt7ZYw7ISyp1u986cGZ5siXLD70pSshiCJTBXglgS8ziF4P8xoIksh8CbQ7wmlwlBwqg9OfQDSdRWAbw7WIoTDIOtSYimhYzpgoAMCZM2cQDAaxZ8+evM0PoaAlsqWlpYzvvLPd3+DgIBRFwfbt25n3IRgMAgArXeRqYBY/4XLr1q0ZbVPXddx7770YHR3F448/XpCSyesIBWmr3LmmmvzzOy4qxK4Khu6n/+28t1UWCUMOCMP8/Dxefvll7Nu3D/X19Sv2KwDA+Pg4zp07h46OjoKM/6V3inv27Mn6zjQejyMQCCAQCCAajSYtXRBCcPa2622vlcMKlCXZ1hEAWAZA27KItYwnCnyuAk8MnNMrb/jsH0OQRIiSlURp7cMgLYwMhCK2MoWz1JDsOVpOseVHOMoQ9L1S0iQrGmZlDe1PPow1a9awoU/Lye70YirLcsYZItmAEIKTJ09C13Xs2LEj7yWy5S7esiwjGAwiEAhgaWkJ1dXVrPMiG+JElcLS0lJceOGFGZOFL37xi5idncWhQ4fyTtxehygYYfjhpW8uxK4Khv3P/KpIGM4nckEYxsfHMTY2Bk3T8Ja3vAWCIKw4jOnUqVNQVRU7duzIe41W13XbyT9XFxtauggEApibm2Oli7q6OgwNDQEAtm/fjrG/+iBrf5LDBmEQRQHxkAxBEhAPxZkSAVgEgp9UyROCZEoDAFz7ibdBEEXbUCwAjDjIoYg9U8EkD/QzUSJRrpTCGxrt7ZDs9yU5YTlTTZYUw9Qoa1DiGhYUDdeefQUAbLHLs7OzKCkpYXfQTkMhvbj5fD5s2bIl7xdvGgBVVlaW8cU02/1lMp6aEMI8DrOzs5AkiXkfKioqln09jbKurq7Gxo0bMz7WT3/609B1HQ8//HDev7uvUxSGMNRUk8ffeqAQuyoYDjz36yJhOJ9YCWGgF9p4PI6Ojg4cOXKEzYUAsvMr0CRFGrBTCHMjH+iTr/3R0sX09DTGxsbg9XrR3NzMui4EQcDoR9/P1o+H4pDDCuQlo+XSIA1WsJOyZOQ3AGB+BiBRYaBk4Z0feTNEkygIDlVBkETIixH2/2U8NrwLoikly6EwIxWAFbYE2NMoXdUQOjPDkV5JFYUFRcd1Y6+k/PwikQhTbhRFYa2HFRUV6O/vL1ggk6Zp6OnpKej+Vjqemo7rDgQCCIfDKZWblexP0zTccccdqKysxIMPPph3led1jIIQhh011eSxi8/rtTXnePP//Y+UhEEQhFYAjwNYB+Na/Sgh5NuCINQB+DGAdgCjAK4jhMxlcwyrmjAoipL2DAgesiyzEye9Czly5Aja29uzTq+jSYq82TCfcDM35hORSAR9fX3YuHEj1qxZg0AgAL/fz6YeNjY2ora2Fmc/fr2tfzo8EzEIg4ungUr7YTVRbbj0zztNNUGylAROXQAM74FgXjSsEkTYVWUw9mefJ8F7E5xlBvq8rlmmRiUsQ4lr0AjJyqMAgLUezszMYHp6GlVVVWhtbUV9fX1eTY6KouDo0aNobm4uyLhoRVFY+mqu9qfruk19oAOz6uvrUVJSgp6eHqxbtw4tLS0ZbVdVVXz84x9Hc3Mz7r///iJZSI3CEIbqKvKDN7+xCMNFvzq8HGFYD2A9IeRVQRCqALwC4L0AbgYwSwj5qiAInwVQSwj5TDbHUCQMGRKGUCiEvr4+bN26lWUW6LqOYDCIiYkJhMNhNuwpXfIwMzOD4eHhnIQxpQNqbty1a1dBQmTm5+dZJoUzE0DXdTb6d25uDuXl5azrYvx/3AAAtrt7AExdcKoFomRXEfjneOJA2xzt5CHmaJ+0Lvy8ugHYfQmyy7wLpi5wiggAhBQto/bIZKCBTJs3b0ZJSQkznQK5N/8B1gTITZs2FYRcFmo8NU06pX97NTU12LBhA2pra9MuJ8iyjA9/+MPYtWsX7r777rypdJqmYf/+/WhubsYzzzyTl30UCAUjDN/f3738iq8jvOU/fpNRSUIQhKcBPGT+ewch5JxJKg4TQrZlcwxFwpABYZiamsLw8DA6OztRUVHhmq/gvACmGvZEZ0zMz8+jo6OjIG7qsbExTE9Pr8jcmAlom9+ePXuWNW/S5D+/349AIADAuADGPnsHSqp9lkkxCWEAwK3jVBNitnWNUkc0YZu8agDYywwa55tQlpL4FhwlB40A7xrJTk1wQ6pAJpqXkY78ni6oElWoCZCFHk9NyUlbWxu8Xi/z3KTyjVDE43HcfPPNuOiii/DZz342ryXEBx54AEeOHEEoFCoShjSwvaqKfL97byF2VTC89Te/PQMgwC16lBDyqNu6giC0A/gNgN0AzhJC1pjLBQBz9HGmWNWEQVXVlEOjKKgLfWlpibWspRPGRGv3MzMzCAaDtjRFn8+HY8eOoaSkBFu2bMm7jEk9F5qmFcxJPzw8jMXFRezevTsrtzi9APKlC3L3ZyCaF/fSWouA8ORBXoxBEK3/D0N5sB47SQFgqQN0PaeiQJcr3HKnZ4FoOpS4hqimY0HR8ecTr2b8nlOBKkN79uxZNpApE+NkMlByUqgJkIUeTx2Px3H06FFceOGFCQPVIpEI8z64zVmJRqP4i7/4C1x++eW444478koWxsfHcdNNN+ELX/gCHnjggSJhSAPbK6vIPywzPfj1hkte/F1aCoMgCJUAXgBwLyHkZ4IgzPMEQRCEOUJIVoOTij0/y4AaA6urq7F3r8FY0x0exYfP0GFPfr8fx44dQygUQm1tLZqamgpibuzr60NdXV1BzJR0VLjP50NnZ2fW+/P5fKyGzZSbe76GWbN0UdXYCP9/vxWiJKKk2lBLmKqgEdalYLRQWsfgLDGIJrlQHETC1hIZTlQUqMpAY6rfM7ryckMyZBrIJIoi6urqUFdXB8AIAPP7/RgYGIAsy6xzoKamxvVveHZ2FqdOncoo6nklKPR46lgshqNHj2Lr1q3sM+JRXl6O8vJytLa2so6fmZkZ3HnnnZicnEQ0GsV73/vevJMFALjjjjvw9a9/HYuLi3ndzxsLq3OWhCAIXgA/BfDPhJCfmYunBUFYz5UkZrLdfpEwpMDS0hJ6e3uxadMmNDU1rThfobS0FFVVVRgfH0dnZydUVcXY2BgWFxdRU1PD2g5z2Y5FJeVNmzZh7dq1OdtuMlBD6Pr16zM2j6WCKIqor69nORe0dCHf/bcIh8OorKzEtm3bcPKqqwGAKQy8/8EqZVhqAa9EsGUu5QleTYjKhopw9egfCmJwo4FMK0lTLCsrQ1tbG5sYGQwGce7cOZw4cYK1vFLj5PT0NM6cOYO9e/cWJKFwfn4eJ06cKNh46kyVDDoGvqGhAQ888ABuvPFGNDc344UXXsDTTz+Nd73rXfjSl76Ul2N95plnsHbtWuzbtw+HDx/Oyz7ekFiFsyTMcsM/ABgghDzAPfV/ANwE4Kvmz6ez3kexJOFekpiZmcHp06fR0dGBqqqqnIQxTUxMYGJiIqGeTwjB/Pw8/H4/ZmdnUVpaaitdZItCmxtpp0ehpiNScrJ27VpWfw6Hw6itrWW1e/6C/sLOi+2GSMn+f2gzM7r4DzRNQ39/PyorK9PKBFgpChHI5EzrjMeN+Go6NC3f75EfWlWIWQt0/HY2Q7nm5+dx3XXX4WMf+xhuuOEGtr2enh689a1vzcfh4nOf+xx++MMfwuPxIBaLIRQK4ZprrsE//dM/5WV/BUBBShLbKirJ3+/oKMSuCobLXvmv5bokLgHwWwB9AKi88nkALwH4CYA2AGdgtFXOZnMMq5owaJoGVbXL0LT2Pjs7i87OTvh8vhUPj9J1HYODg4jH49i1a9eyCgK9e/b7/QDAyEOquGUnxsbGMDU1hT179hTkLjHTWOmVgionTnJCa/fUdFpWVsbuDlfyOciyjN7eXjQ1NeVUOUmGQgcy0XHvc3NzWLduHYLBIMLhcN6UL8AaT93V1VUQAy4te6Qav50MwWAQBw8exCc/+UkcPHgwT0eYGocPH8Y3vvGNoochDWwrryDf3ba7ELsqGP7o6MvnPbipWJLgoKoq+vv7UVJSgn379uVkeBT1D9TW1qadSV9RUYGKigq0t7cz49/p06cRjUZZy2ay2jOfFNnd3V2QtDkaY12ogUdzc3M4efKkKznha/eEEEQiEfj9fvT19YEQgvr6ejQ2NmbUdhiNRtHT01OwzApVVW2BWvkGHbKkqiq6urogiiKam5ttuQVDQ0Pw+Xys5XWlvoZCj6deWFjAwMBAVhM8Z2ZmcPDgQdx111246qqr8nSEReQapDitMucoKgymwhCJRNDT04O2tjY0NzfnpASR6zAm3ny1sLCAqqoqVnv2eDw2ctLe3l4wyTwej2Pnzp0FISfU/NfZ2ZmxYqAoCuu6oG2HNDAq2bHTToFCDQCjbX6Fmk6aiZIRjUbZ55eOcTIZzp49i0AggM7OzoL8zVCC2dnZmTHROXfuHA4ePIj77rsPV155ZZ6OcFWhIArD1rIK8p1NOwuxq4Lh8uNHzrvCsKoJg67rbGzuiRMnWN2WkgVN04x0wCwuvH6/H0NDQ3mT6AkhCIVCrPZMW702bdpUEMlc0zT09fWhqqqqYPX8kZERhEKhrNs0eThLF9Q3wpcuqLKTThtjLkDNeIXygNAoZEowM33t7Ows/H4/FhYWEoyTbqD/h4uLiwWZcAmAqSNdXV0ZE8yxsTF84AMfwAMPPIDLLrssT0e46lAwwvBw+/ZC7Kpg+NMTrxYJw/mEpmk4ffo0pqen2QllpX4FWguenZ1FR0dHQST62dlZDAwMYO3atQiFQtA0jUnvVVVVOb+Yx2Ix9Pb2FvQumE4r3LZtW17ICR8Ypes6fD4fotEouru7C+IBSRXIlA/Q6OX169ejubl5RduixkkaGgUgofTDj6feuXNn3gkmsDKPxMjICG644QY89NBDuOSSS/J0hKsShSEMpeXkf7W9sQjDlYP/r0gYzidmZ2cxMjLCHOiEEFaiyObuh+YPeL1ebN26tSB3UNQ/wJsbqWri9/uxtLTEpHdn10A2oBe27du3o7Y2q+yPjEDLLHQgUKHKLNQwmavExFTIJJApF4jH4+jp6UF7e3teWm3puGla+qmpqUE0GkV5eTm2b99eELIwNTWFsbExdHV1ZeyROHXqFG666SYcOnQIBw68sSYevgZQJAxZokgYzjNoSSIXfoVYLIa+vr6c5w8kA+28oC13yS5kbl0DVHrP9K5rZmYGIyMj6OjoKMiFLRqNore3Fxs3bixIhoSbkuFMTCwtLUVDQwMaGxtzojxMTU3h7NmzBesUoGWPZIFFuYaqqjh69Cj7jtGBT42NjXkLhJqYmMDU1BQ6OzszLl0dP34ct9xyCx5//HF0vcGSAl8jKAxhKCkn/19LVuMSXrN45/DR804YVnWXBJVKV0oWFhYWcPz48YLfdafTeeHsGqDSe09PDwRBYCfvVIE5hBBbeFAhXO2FNhvSzgRnGqYzMTEcDiMQCKC/v3/FpZ9cBDJlAtpWWKiyB/W5rF27lo2LpsbJEydOuEYurxTUUNnV1ZWxGtTT04OPfOQj+NGPfoTdu99YLXmrDf9/e2ce1eSdtv8rLFKVNUHAQmUXUSSAWqUu01qpQqJOsY5LX7G1jk57fr622mmdtlrbvuo4o9Y5U9tOp864zCi1vpIAIqL2tR7aKsVhURQUBUXWsC+yZHl+f3iepyAgJCZfCLk/5/SckoXnmxDzXM/3vu/r4gBwFuj0aGoseoehoqICWq0WTk5OBouFsrIy3Lt3DxMnTmRiocvHRPv4+Dx2kl97e7vQ9d7W1iac/Pj3A3hw1Z2fnw8AGDduHJMyi0qlwu3btxEaGsrkPeW36MeMGQMPD49+P+/h0k9/PQs4jkNhYSHa2towYcIEJu8pPynAKhG1P/HUfONkdXU16uvrMXLkSMEzwzZfUxcAACAASURBVJDdluLiYjQ0NBjUUJmZmYl169bh2LFjCAoaWlemgwwmOwyBw0Zwe90DWByKGfJ7VwZ8h8GiBUNqaiq2bNkCBwcHyGQyyOVyeHp69ks48LXu1tZWhISEMBkPq62tRUFBgUmuEB/uend0dISLiwvKy8sFPwAWteeSkhJUVVUhNDSUyU4GbwD1uFv0vGcB79ZpZ2cnlH46OxiyNmQCfhFgUqmUiZsiPxqqT49EfxonH/Xc27dv4/79+wYJsB9//BFvv/02Tpw4AT8/P72eS+gNI8EwnPvUdWgJhvnlV0kwDDT8VINSqURiYiKam5sxb948yGSyXr981Go1rl69CicnJ/j6+jL50u+pudFUcByHqqoq5Ofnw9raWhiZe/jkZ+xj3rhxQ+iiZ3nVbYrRV94wqrq6WihduLi4oKioCBKJRO8xRkPhDZKkUikTAcaHOj3uaCjfOFldXS3s3ri6ukIikXQR57xw12g0CA4O1vvf4oULF/Dee+9BoVAIZRPCpDARDAG2w7k9rv4sDsWMhRV5JBgGGzU1NTh58iSUSiUKCwsxc+ZMyOVyREZGwtbWFrm5ucIVMItGPP5E2l9baWNQX1+P69evCzsZD5/8+L4HfdwSHwXrjAYAQsDSw7kepkCtVqOyshKFhYWwsrIStt0fPvkZG97qOTQ0lMnnht+tMXY8dWfHydraWqFxUiKR4O7duxCJRAaN2545cwaffPIJEhMTey2bEEaHmWD4s2Ro7RbFVl4jwTCYaWtrw7lz56BQKHDx4kV4eXmhoKAAf//73xEZGWny42s0Gly5coXpTgbvpNjbifRht0QXFxfBLdGQXYH29nbk5ubC09OT2Zc23xgXGhrKpNmQt5YODAyEWCwWpi5qampgZ2cnCDBjCRe+R4J34GSxW8MynpqP6i4uLgbHcRg9erTejZMnT57Erl27kJSUZDLhX1JSgri4OFRWVkIkEmHNmjVYv369SY5lRjARDP62w7md4qElGBZXkWAwCziOw+7duxEfH4/p06cjPT0d7u7ukMvliI6Ohpubm9FP5sZsbuwPfB24qamp306KOp0OdXV1wshm59JFf7a/ewuQMhUDUfboy5Dp/v37ggDTaDRC3d7R0dGgzxQ/GmpjY9Pv7JLHhY+nZtVQqdPphB0pb29vvRsnExISsG/fPiQlJZn0c1deXi5krDQ1NWHSpElQKBQYP35oWRbrCTPBsN3Fl8WhmLFUdX3ABYNFj1X2lwMHDuDWrVv48ccfhfTKgoICKBQKxMXFgeM4REdHQyaTGaWRra6uTrCqZjX+xjfiSaXSfq/fysoKEokEEomkS0xyVlYWrK2tBfHQk2dDbW0tbty4wSzdUqvVIi8vDyNGjGB2IuVf46MCj0aMGIExY8ZgzJgx0Gg0qKmpQUlJCZqamuDo6CjYLfenpMCXdhwcHJjtSLGOp+btrPnxV+CXNNfOjZM5OTkAHjROisViODo6wsrKCvHx8Thw4ABSUlKMWjbpidGjRwtOqA4ODggODkZpaamlCwYmcAAoe8r40A5DP9Bqtb1+YXMch8rKSiQmJiIxMRFlZWWYPXs2ZDIZJk+erHftuLS0FKWlpUxq68Avsc3u7u546qmnjPZ729raugUV8VfOvAufIQFShsCP+Bn7NT4K3pDJ0NfIcVyXqQtbW9tHJkVqNBrhNbIwDgPYx1NrtVpkZ2f3+zXy5bP//Oc/ePfdd+Ht7Y3q6mqkpaUxsTTvTHFxMWbNmoWrV68yuQgYxDDZYfC1Gc597OzD4lDMiKvJH/AdBhIMRqapqQmnT5+GUqlEVlYWpk6dCplMhmefffaRAoDv9uZn81k2qZm6JKDRaFBbW4uqqiohKGvs2LFwdXU1+evk3SL9/PyYRFMDpumR4Ov21dXVUKvVXQSYWq1GdnY2vL29mZSvAPbTF7zo8/T01Ptkz3EcvvrqKyQmJmLSpEn4/vvvIRaL8dFHH2HatGkmWvEvNDc341e/+hXef/99xMbGmvx4gxxmguFDJx8Wh2LGq7UkGIY0arUa6enpUCgUOH/+PPz9/RETE4N58+Z1mfnnxzQdHR2ZTQnwW8msSgJ8bd3KygoeHh5C019PKZHGgrVbJCtDJr50wdftOzo6MGbMGHh7ezNp4rx79y5qamqYTV/wvg6GCCKO47Bv3z5cuHABx48fF0T73bt3YWtra/KdBrVaDblcjrlz52LDhg0mPZaZwEQw+Ng8wW129GFxKGasrisgwWAp6HQ6XLlyBQqFAqdOncKIESMQHR2NCRMm4IMPPsDhw4fh68umSYf3dJBKpUy2ktVqNXJzczFq1Khus+6dUyI5jutiVf04wol1oBNvyMQHj7EQfc3NzcjNzYW3tzdaW1tRU1Nj0qwGPp66ubkZISEhTJpG29vbkZ2dbdAOEd+snJ2djaNHjzIpfz18/JUrV0IsFmPv3r1Mjz2IYSIYvG2e4N538GFxKGasrSfBYJFwHIe7d+9iz549OHz4MEJCQjBjxgzI5XKEhoaa7It4IMoe+gRIdXR0CH0Pra2twsimvjkDZWVlKC0tZSaI+EY8FxcXZoZMvU0m8FkNKpUKarUaYrG4m923IQxEPDVvAmWIC6dOp8P27dtRVFSEQ4cOMSmbPEx6ejpmzpzZxap6+/btiImJYb6WQQQzwbDJ3ofFoZjxRgMJBovl4MGD+Oqrr3Ds2DGMGDFCMIsqKCjA9OnTMX/+fEyfPt1oX3R8EJC9vT38/f2ZfOHzoVyGlAS0Wq0wsllfXw97e3uhdNHbtjt/BdzY2IiJEycy2y7PycmBl5cXs0a66upqFBYW9jmZwPeOqFQqNDY2wsHBQZi60Kd0wXEcrl27xnRUk0/VNMQESqfT4cMPP0R1dTX279/PpExD9BsmgmGM9RPcO/beLA7FjHWNN0gwWCppaWmYMWNGt+3y9vZ2fPfdd1Aqlfjhhx8wYcIEzJ8/H3PmzDHYEKetrQ25ubnw8vJiZo5kzAApjuPQ1NQElUqFmpoaYWSz87Y7H5IlEokwbtw4Jie1zoZMLHwkgAez/ffu3dN794TjODQ2NgrvYX9LF509D1iNara0tCA3N9egsWKdTod33nkHWq0Wn3/+ORPRSOgFM8GwceTQEgxvNpFgIB6BTqfDzz//DIVCgTNnzkAikUAul0Mmk8Hd3b1fX9584x+r6G3gQUOZSqUyWYBUT9vu9fX1kEgkzE5qvLMhq4ZKwLjTF21tbVCpVN3GXjuXLvhSi0QiYZazwL+vEydO1LsZV6vV4q233sKIESOwd+9eJj0WhN4wEQxPWT/BvTViaGWDbGy+SYKB6B98B75CoUBycjLUarUQktXbFbVKpcKtW7eYNf4NhJNiS0sLsrOzYWtrC61WC2dnZ8Gq2lRXl7whE8v39datW7h//75Jmg21Wq0Q082XLlxcXFBWVsbUspsvYYWGhurtGKnRaPDGG2/A09MTO3bsILEweGEiGLysn+DWDx9aguGdFhIMhAFwHAeVSoWkpCQkJibizp07eO655yCTyTB16lSIRCIcPnwYEyZMYDYnPxABUg9HU+t0OtTX1wtW1cOHDxf6HozV/Pi4hkz6wnEc8vPzAYBJqYXjONTU1ODatWuwtrbuMvZqSnHEJ4dKpVK9S1hqtRqrV6/G+PHjsXXrViafPcJgmAmG//cEG5M2VvzhfiEJBuLxuX//PtLS0qBQKPDzzz9j+PDhcHZ2xqFDh0xufwsMTIAUn6jZW9gRx3FdRjaBXyyEDc07YB1axfcPjBw5kpkIezieurNjZ3t7OyQSCVxdXeHk5GS0q/iamhoUFhZCKpXq7W7a3t6OV199FVOnTsWmTZtILAx+mPyBPK2e4N4YYoLhg1YSDIQRqa+vx5IlS+Dr64snnngC58+fh7e3N2JiYhAdHQ2JRGL0L9Tm5mZcvXrVoNE3Q6mqqkJRUZFeJ5iOjg6hZt/W1iaMGzo7O/f5nrAyZOqMRqNBbm4uXF1dmfUP9BVPrdVqhamLhoYGODg4CDHThu5iqVQqFBUVGWQv3draihUrViAqKgpvvvkmiQXzgJlgWGvHxiKdFR+23SLBQBiP1157DXK5HC+++CKAX8yEEhIScOrUKQwbNgzz5s2DXC43SnMg6wApwDgNlT2d+HobNxwIQ6aBGNXUN566p8kVfuqiv6ULPlMkLCxM779lS0sLli1bhtjYWLz++uskFswHJn+oJ62e4NYMMcHwEQkGwphwHNfrFyfHcSgtLYVSqURiYiJqa2sxe/ZszJ8/H2FhYXpfNfPmSKGhocxq+Tdv3kR7e7tRr/J7GjfkSxe2traCIZO3tzfTkkBAQABcXV1NfjzAOPHUD5cuOhtG9fS3KisrE9xG9S3vNDU1YenSpVixYgVeffVVEgvmBSPBYMe9NmxoCYb/ab9NgoEYGBoaGpCSkgKlUom8vDw888wzkMvlmDlz5iO3hjmOw+3bt9HU1MTMHImv5Q8fPhwBAQEmPUHwIU+VlZVoamqCWCyGv78/7O3tTX5i4v0HgoODmfSeAKaJp354B4c33eJLFyUlJVCpVJBKpXp/furr6/Gb3/wGr7/+Ol5++WWjrJdgChPBMNrKjnvVdmgJhh0dAy8YLHb26NtvvxWuVDMzM7vct2PHDgQEBCAoKAinT5/u8flFRUWYOnUqAgICsGTJEnR0dLBYttFwcnLCsmXLEB8fj8uXL2PRokU4deoUZs6ciVdeeQXffvstGhoaujxHp9MhLy8PGo3GoC97Q1Cr1cjKyoKLiwsCAwNNftLmJyu0Wi3Gjx8PDw8PFBcX4+LFi8jPz0dNTQ10Op3Rj9vQ0IDc3FxMnDiRmVioqqrCrVu3EBERYdQodd5Ya/z48Zg2bRq8vb3R0tKCrKwspKeno6SkBGPHjtX781NTU4PY2FisX7/epGIhNTUVQUFBCAgIwB//+EeTHYcwHRwALccNqf8GAxa7w8AnJ65duxa7du3C5MkPhNu1a9ewbNkyZGRkoKysDHPmzMGNGze6fbn95je/QWxsLJYuXYrf/e53kEqleP311wfipRgVnU6H//znP1AoFEhLS4OzszNiYmLwzDPP4K233sLOnTsRERHBZC1tbW3IycnpVw6FsejNkKnzyGZtbS1GjhwpjBs+7tgqf5VvyEihobCOp+Z3phobG+Hq6oqamhq0tbX1Oy+kqqoKixcvxubNm7FgwQKTrVOr1WLs2LE4c+YMvLy8MGXKFBw9ehTjx4832TEtDCY7DB5WdtxKG08Wh2LGn9RFA77DYLEm68HBwT3erlQqsXTpUtjZ2cHX1xcBAQHIyMhAZGSk8BiO4/Ddd9/hyJEjAICVK1di69atQ0IwWFlZYfLkyZg8eTI++eQT3L59G//85z8xb948hIaG4syZM7Czs0NwcLBJpwX4EzfL7fnOhkwP1/KtrKwgFoshFovBcRyam5uhUqmQlZUFKysroe9BX6+CyspK3LlzBxEREUyCsoBf4qnDw8OZ7BJ1Dq4KCwuDSCTCU089JZQuKisrUVBQ0KsIKy8vx+LFi7F9+3bMmzfPpGvNyMhAQEAA/Pz8AABLly6FUqkkwWBucIB2yFzeDh4sVjD0RmlpKaZNmyb87OXlhdLS0i6PqampgbOzs9Cs1dNjhgIikQh1dXVITk7G6dOn4evri+TkZCEFcNasWZDJZIiMjDSqL0HnaGpDm/D0hT9xh4eH99nEKRKJ4ODgAAcHB/j5+aG9vR0qlQoFBQWCV0F/EiJLSkpQVVWFiIgIJr4OneOppVIpk/FQ3nhKJBJ1S7nsnAnysAgrKytDVlYWZsyYgQ8//BB79uzB7NmzTb7e0tJSPPXUL/P7Xl5euHTpksmPSxgXviRBGJchLRjmzJmDioqKbrdv27YNCxcuHIAVmR8qlQoKhUKIbX7llVfwyiuvoLW1FWfOnME333yDjRs3Ijw8HDKZDM8///xjneT56QvWV9wqlcrgE7ednR28vLzg5eUl2CyXlpbi+vXrcHR0FBr++Kt5/sTd1NSEsLAwZlf5N27cgFarxcSJE5lMFvApl8OGDeuzWfVhEVZVVYW8vDxs2LAB1tbWSEpKAgDMnDlzQKKqCfODdhiMz5AWDGfPntX7OZ6enigpKRF+vnfvHjw9u9bCJBIJ6uvrodFoYGNj0+NjhgrR0dE93j58+HAsWLAACxYsgFarxY8//gilUomdO3fC09MTMpkM0dHRGDVqVL9OThzHobi4GPX19YiIiGB2EuUzGsLDw41yxW1tbQ03Nze4ubmB4zg0NDQIyZ12dnYYNWoUGhoaIBKJEBoayvTEbWtri+DgYCbHfNyUy/r6eiQlJeHo0aMIDQ3F+fPn8b//+7/o6OgwaVmiP//+icEP7TCYBotteuR59tlnuzQ95uXlYfny5ULT4/PPP4+bN292O4EtXrwYixYtEpoeQ0ND8cYbbwj3L1myBAUFBQAefPk5OzsjOzu72/F9fHzg4OAAa2tr2NjYdJvYMDc4jsP169ehUChw8uRJWFlZITo6GjKZrNerTJ1Oh4KCAnAch3HjxjHZKtfpdLh+/TpsbGyYGTLxrphqtVoQD7xVtamOPxDx1FqtFleuXBH8K/Tl2rVrWLVqFQ4ePIjw8HATrLB3NBoNxo4di3PnzsHT0xNTpkzBkSNHMGHCBKbrGMIwaXoUiUSpANgYmbCjmuM40zbx9IHFCoaEhASsW7cOKpUKzs7OCAsLE0Yot23bhn/84x+wsbHB3r17havsmJgYfP3113jyySdx+/ZtLF26FLW1tQgPD8e//vWvXmvfGzduhJOTE7Zs2dLtPh8fH2RmZjIz6WEJx3GoqKgQzKIqKirw/PPPQy6XC7sIjY2NuHTpEgICAuDj48PshMbakIk/plgshre3Nzo6OoSEyJaWli5W1cYSTFqtFjk5OUztpfljurm5wctL/zn4nJwcrF27FkeOHEFISIgJVtg3KSkpePPNN6HVarFq1Sq8//77A7KOIQq5bJkxFisYWMFxHMaMGYPvvvsOgYGB3e4fyoLhYRobG5GamorExERkZ2cjPDwcmZmZeOONN/Daa68xWQNvu8wyKEutViM7O7vXY+p0OtTV1Qkpmw8bHRl6zJycHDz55JPMXqdGo0F2drbBx8zMzMS6detw7NgxBAUFmWCFxCCABIMZQ4LBxFy4cAEbNmzotdTg6+sLFxcXiEQirF27FmvWrGG8woHh2rVrWLhwIaRSKW7cuIHAwEDIZDLMmzfPZGOUra2tyMnJYWq7zHtJ+Pn5YdSoUX0+np8WqKqqEjIa+NJFfz0aOjo6kJ2dDR8fH2b+FbwoGjNmDNzd3fV+/k8//YSNGzfixIkTwkgjMSQhwWDGDOmmR1PTnymMo0ePYtmyZb3+jvT0dHh6eqKqqgpRUVEYN24cZs2aZbI1DwZKSkqwfPlyHD9+HFKpFDqdDjk5OVAoFHjxxRcxcuRIyGQyyOVyeHl5GaVk0Jshkynh0x+DgoLg4uLSr+d0nhbw9/dHW1sbVCoVrl+/DrVaLYxsOjo69vi+PBxPzQJeoPj6+vZLFD3MhQsX8N577yExMZFZ6YQgCP2hHQYTotFo4OnpicuXL/ernrt161bY29vj7bffZrC6gYPjONTU1PR4lc9PSyiVSiQlJaG5uRkvvPAC5HK5waFTvCHT44Qr6UtjYyPy8vL6nf7YHzQajdD30NTUBCcnJ4waNQpisRjW1tZ9xlObgscVKGfPnsXHH3+MxMREZqUTYkChHQYzhgSDCUlNTcWOHTvw/fff93h/S0sLdDodHBwc0NLSgqioKGzZssXkbnbmRG1tLZKTk5GYmIgbN25g5syZmD9/PiIjI/tV3+cNmaRSKZNUTaCrY6S+zo/9RafTCSObtbW1sLGxwf379xESEgKxWGySYz4MX+IxVKCcPHkSu3btQmJiokFlDMIsIcFgxlhs+BQL4uPju5UjysrKEBMTA+DByWzGjBmQSqV4+umnhRp+b2zduhWenp4ICwtDWFgYUlJSenzcUArPEYvFiIuLw/Hjx5GRkYGYmBicOHEC06dPx+rVq6FQKNDc3Nzjc0tKSnDv3j1EREQwEwtVVVUoLCxEeHi4ycQC8MCq2sXFBWPHjsW4cePQ0dEBDw8P3Lp1Cz///LPg6KjnBUG/aWlpQXZ2tsHW3QkJCfj0009x8uRJEgsEYSbQDoMZ0Z+ShaWE52i1WmRkZEChUODs2bNwc3ODXC5HTEwMXF1dsW3bNkRFRWHq1KlMfB2AB7bC5eXlzAKdgAc22oWFhZBKpULiZEdHB6qrq6FSqdDa2iqMbDo5ORnlveD7QQwtt8THx+PAgQNQKpX97u0ghgy0w2DGUNPjEMNSwnOsra0RGRmJyMhIwfZYoVBgxYoVqKiogK+vL1566SVmTorFxcVoaGhgFugEPNjNKC4uRnh4eBcb7WHDhgmjjXzAU3l5OfLz8+Hg4CCMbBpig93Q0IBr164ZlPPBcRwOHz6Mb775BidPnjRabwdBEGwgwWBmfPbZZzh06BAmT56M3bt3d7tCs8TwHJFIhKCgIKxbtw7p6el47rnn8NRTT+Gjjz5CaWkpnnvuOchkMkyZMsXoJ3M+ibGjowOhoaHMdjP4eOrw8PBH7mY8HPDU2NgIlUqF4uJi2NraCvfxuxOPor6+Hvn5+QgLC9M7hpvjOOzfvx/JyclITk5m1nxKEITxoJLEIONRo5rTpk2Dq6srRCIRNm/ejPLycvzjH//o8rjjx48jNTUVX3/9NQDg8OHDuHTpEj777DMm6x9I/vSnP8HDwwNxcXHCbc3NzUhLS0NCQgKysrKEXpFnn31W75Pew+h0OiFcKTAwkMluBvBLPHVoaOhjCaDW1laoVCqoVCpoNBq4urpi1KhRcHBw6PZa+ATRsLCwfomLznAch3379uHChQv49ttvH/t9J8waKkmYMSQYzJTi4mLI5XJcvXq1y+0//fQTtm7dKthc79ixAwDwhz/8gfkaBxsajQbp6elISEjA+fPn4efnh5iYGERHR+s9WcDnJTg7OwtJnqaG4zjcvn0bLS0tCAkJMepuhlqtFkY2m5ub4ezsLIxs1tTUoKioCGFhYXoniHIch927dyM7OxtHjx5l1nxKDFpIMJgxJBjMiPLycowePRoA8Omnn+LSpUuIj4/v8hh9w3N+//vfIykpCcOGDYO/vz/++c9/9tj1PtRCsnQ6Ha5cuQKFQoFTp05h+PDhiI6Ohlwu7zNfgrddHj16NLMkw87x1KZOnNTpdKivr4dKpUJVVRW0Wi38/f3h7u6ul2DQ6XTYvn07ioqKcOjQIWaNoP39TBMDAgkGM4YEgxmxYsUKZGdnQyQSwcfHB3/7298wevRolJWVYfXq1cKYpT7hOWlpaZg9ezZsbGzw7rvvAgB27tzZ7XFDOfOC4zjcu3cPCoUCiYmJqK+vx5w5czB//vxufQnt7e3IyclharvcOZ6aZemjrKwMpaWlGDt2LGpra1FdXQ2RSCSULh7Vh6DT6fDhhx+iuroa+/fvN6jB0lD6+5kmBgQSDGYMCQZCICEhAcePH8e///3vbvcNZcHwMHV1dUhJSYFSqcT169cxffp0zJ8/HxKJBFu2bMH+/fuZ2S7zOyGOjo7M0jyBBx4WKpUKUqm0S59Ee3u7MLLZ1tYmWFU7OTkJa9PpdHj33XehVqvxxRdfMJsa6YlHfaaJAYEEgxlDgoEQmD9/PpYsWYL/+q//6nafpYZktbe34//+7/+wf/9+nDt3DrNnz8avf/1rzJkzB46OjiY9Nh8VPWrUqC6TL6bmzp07qKurw8SJEx95stdqtULfQ2NjI+Lj4xEREYGMjAw4ODhg7969zKZGeuNRn2liQCDBYMbQWKUF0J+QrG3btsHGxgYvv/xyj7/DEkOyAMDOzg729vYoLCzETz/9hIaGBigUCuzduxcSiQQymQwymQweHh5GvfofiHhqjuMEh8j+jIhaW1vDzc0Nbm5u4DgOLS0t+PTTT5Gfn4+IiAh8/fXXkMvlJlm/MT7TBEHoB+0wEDhw4AD+9re/4dy5c/2yM7aUkCyeP//5z3j55Ze7nPg4jkNhYaEQktXR0YF58+ZBLpdj3LhxjyUeBiKemn89HR0dGD9+vN7rV6vVWL16NcaPH4+tW7fi9u3bSEpKQnFxMfbu3WuiVfeOvp9pghm0w2DGkGCwcFJTU7FhwwZ8//33vUYTU0jWo+E4DtXV1UhKSoJSqcSdO3fw7LPPQi6X4+mnn9ar4Y8PdGIZT81xHAoKCgAAQUFBeouF9vZ2vPrqq5g6dSo2bdrErM+iN/rzmSYGDBIMZgwJBgsnICAA7e3twslp2rRp+PLLL7tMXty+fRsvvvgigAdjm8uXL+9x8iI1NRXr16+HVqvF6tWrsWnTpi73t7e3Iy4uDpcvX4ZEIsE333zDzMOAJffv30daWhoUCgUyMzMxadIkyOVyPPfcc4+82uXjqYODg+Hk5MRkrY87gdHa2ooVK1YgKioKb7755oCLBaD3zzQxKBj4DwhhMCQYCKPQn9Crzz//HLm5ufjyyy8RHx+PhIQEfPPNNwO4atOj0Wjwww8/QKlU4rvvvsOYMWMgk8kQHR0NiUQinGDr6uqQn59vcKCTIeh0Oly9ehUjR46En5+f3if7lpYWLFu2DLGxsXj99dcHhVggBj30ITFjSDAQRqE/DpNz587F1q1bERkZCY1GAw8PD6hUKos50fBW0gqFAikpKbC1tUV0dDRGjRqFzz//HKmpqcwyFnQ6HXJzcw12qmxqasKSJUuwYsUKrFq1ymL+hsRjQx8UM2ZgZ56IIUNPoVelpaW9PsbGxgZOTk6oqalhus6BxMrKCiEhIfjggw/www8/4MiRIygtLcWmTZtgZ2eHXbt24fLly9DpdCZdh1arRXZ2NiQSiUFiob6+HosWLcJvf/tbvPbaayQWCMJCoLFKGsocbAAACOhJREFUghgARCIRLl68iMuXLwsBVqdOncIXX3yBK1euIDIyEnK5HDNnzjRq/oJGo0F2drbB45o1NTVYvHgxNm7ciMWLFxttXQRBDH5oh4EwCp6enigpKRF+vnfvXrechc6P0Wg0aGhoYDYJMBgRiUQ4deqU4JS4dOlSHDlyBJcvX8bixYtx+vRpzJo1CytXrsSxY8fQ0NDwWMdTq9XIysqCl5eXQWKhqqoKsbGxeO+990gsEIQFQj0MhFHoT+jVvn37cOXKFaHp8cSJEzh27NgArnrwo9PpkJWVhYSEBKSlpcHJyQkxMTGCIVJ/ywG8t4Ovr69Bo4bl5eVYvHgxtm/fTuO0xONA9SszhgQDYTR6Cr3asmULJk+ejAULFqCtrQ0rVqxAVlYWxGIx4uPj4efn98jfWVJSgri4OFRWVkIkEmHNmjVYv359l8ecP38eCxcuhK+vLwAgNjYWW7ZsMdnrHCh4J0aFQoGkpCS0trZi7ty5kMvlCA4O7tWZsa2tDTk5OQgICDBoR6ekpARLly7F7t27MXv27Md9GYRlQ4LBjCHBQAxqysvLUV5ejoiICDQ1NWHSpElQKBRdxjXPnz+PXbt2ITk5eQBXyp7q6mokJycjMTERt27dwqxZsyCXyxEZGSmYRVVWVqKoqAhBQUFwcXHR+xhFRUVYvnw59u3bhxkzZhj7JRCWBwkGM4Z6GIhBzejRoxEREQEAcHBwQHBwcLfpC0vF1dUVr7zyCk6cOIGLFy/ihRdewLfffotnnnkGa9aswVdffYU5c+bA1dXVILFw48YNLF++HH//+99JLBAEQTsMhPlQXFyMWbNm4erVq12SIs+fP49FixYJzXy7du3q0jthaWi1Wvz73//G73//e/j7+8PFxQVyuVzwfOhP38O1a9ewatUqHDx4EOHh4QxWTVgItMNgxtBYJWEWNDc3Y9GiRdi7d2+3WOmIiAjcuXMH9vb2SElJwa9//WvcvHlzgFY68OTk5GDPnj24cOECxo4di/z8fCgUCrz88ssQiUSIiYmBTCZDQEBAj+IhJycHa9euxZEjRxASEjIAr4AgiMEI7TAQgx61Wg25XI65c+diw4YNfT7ex8cHmZmZcHV1ZbC6wUdBQQGGDRsmNIHycByHiooKJCYmQqlUoqKiAs8//zxkMhkmTZoEa2trZGZmYt26dTh27BiCgoKYrnv37t14++23oVKpLPZvZwHQDoMZQ4KBGNRwHIeVK1dCLBb3GpNcUVEBd3d3iEQiZGRk4KWXXsKdO3fIgbAPmpqakJqaCqVSiezsbPj5+eHmzZtITk6Gv78/07WUlJRg9erVyM/Px+XLl0kwDF3oH6UZQ4KBGNSkp6dj5syZmDhxojA2uH37dty9excA8Lvf/Q6fffYZvvjiC9jY2GD48OHYs2cPnnnmmT5/t4+PDxwcHGBtbQ0bGxtkZmZ2uZ/jOKxfvx4pKSkYMWIEDhw4IDRgDjXUajUOHjyI8ePH9+u9MzYvvfQSNm/ejIULF1r07pAFQILBjCHBQFgsfZUuUlJS8Ne//hUpKSm4dOkS1q9fj0uXLjFe5dCHT/L8y1/+YvHlJAuABIMZQ02PBNELSqUScXFxEIlEmDZtGurr61FeXo7Ro0cP9NLMjjlz5qCioqLb7du2bcP27duRlpY2AKsiCEIfSDAQFotIJMILL7wAkUiEtWvXYs2aNV3u7y2BkwSD/pw9e7bH269cuYKioiJIpVIADzJIIiIikJGRAQ8PD5ZLJAiiD0gwEBZLeno6PD09UVVVhaioKIwbNw6zZs0a6GVZFBMnTkRVVZXwM5UkCGLwQk6PhMXCp2m6ubnhxRdfREZGRrf7+0rgJAiCsBRIMBAWSUtLC5qamoT/T0tL62ZStGDBAhw6dAgcx+HixYtwcnKicoSJKS4upt0FghikkGAgLJLKykrMmDEDUqkUTz/9NGQyGebNm4cvv/wSX375JQAgJiYGfn5+CAgIwG9/+1t8/vnnff7egoIChIWFCf85Ojp28484f/48nJychMd8/PHHJnmNBEEQxoTGKgnCRGi1Wnh6euLSpUvw9vYWbrfUdE2CAI1VmjW0w0AQJuLcuXPw9/fvIhYIgiDMFRIMBGEi4uPjsWzZsh7v++mnnyCVShEdHY28vDzGKyMIgtAfKkkQhAno6OjAk08+iby8PLi7u3e5r7GxEVZWVkK65vr16y06XZOwKKgkYcbQDgNBmIBTp04hIiKim1gAAEdHR9jb2wN40FipVqtRXV3NeokEQRB6QYKBIEzA0aNHey1HVFRUgN/Zy8jIgE6ng0QiYbk8giAIvSHBQBBGpqWlBWfOnEFsbKxwW+dxzePHjyMkJARSqRT//d//jfj4+B6juFetWgU3N7cu/hC1tbWIiopCYGAgoqKiUFdX1+MaDh48iMDAQAQGBuLgwYNGfoUEQVgi1MNAEIOUCxcuwN7eHnFxcbh69SoA4J133oFYLMamTZvwxz/+EXV1ddi5c2eX59XW1mLy5MnIzMyESCTCpEmTcPnyZbi4uAzEyyCIzlAPgxlDOwwEMUiZNWsWxGJxl9uUSiVWrlwJAFi5ciUUCkW3550+fRpRUVEQi8VwcXFBVFQUUlNTmayZIIihCwkGgjAjKisrBXtqDw8PVFZWdntMbymbBEEQjwMJBoIwU0QiUY+9DwRBEKaABANBmBHu7u4oLy8HAJSXl8PNza3bYyhlkyAIU0CCgSDMiAULFghTDwcPHsTChQu7PWbu3LlIS0tDXV0d6urqkJaWhrlz57JeKkEQQwwSDAQxSFm2bBkiIyNRUFAALy8v7N+/H5s2bcKZM2cQGBiIs2fPYtOmTQCAzMxMrF69GgAgFouxefNmTJkyBVOmTMGWLVu6NU8SBEHoC41VEgRBEKygphszxkbPx9MfmyAIgiAsECpJEARBEATRJyQYCIIgCILoExIMBEEQBEH0CQkGgiAIgiD6hAQDQRAEQRB9QoKBIAiCIIg+IcFAEARBEESfkGAgCIIgCKJPSDAQBEEQBNEnJBgIgiAIguiT/w9ojXP8rTkJoAAAAABJRU5ErkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {
- "tags": [],
- "needs_background": "light"
- }
- }
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "VpjQBORX5bNt"
- },
- "source": [
- "## Finding global minimum using gradient descent\n",
- "\n",
- "### For this example the gradient descent algorithm is simplified to\n",
- "\n",
- "$$\n",
- "\\begin{bmatrix}\n",
- " x^{t+1} \\\\ \n",
- " y^{t+1}\n",
- "\\end{bmatrix}\n",
- "=\n",
- "\\begin{bmatrix}\n",
- " x^{t} \\\\ \n",
- " y^{t}\n",
- "\\end{bmatrix}\n",
- "-\n",
- "\\lambda\n",
- "\\begin{bmatrix}\n",
- " 2x^{t} \\\\ \n",
- " 2y^{t} \\\\ \n",
- "\\end{bmatrix},\n",
- "$$\n",
- "\n",
- "### where $t$ is the gradient descent iteration. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "rtT6_Mdg5bNu"
- },
- "source": [
- "# Conclusion\n",
- "\n",
- "### Gradient descent is a first order (requires first derivative) optimization algorithm used to minimize a given objective function. The algorithm depends on the initial value and the learning rate. The idea behind gradient descent is that it takes a seqeuence of steps to go from the starting position to a local minimum. An initial value that is somewhat close to the global minimum is ideal. Too small a learning rate makes it more likely for the algorithm to get stuck at a local minimum. Whereas too high a learning rate makes it more likely that the algorithm will skip over the global minimum. As we discussed in this notebook, the gradient descent can be applied to any first differentiable function (single or multiple variabe) to approximate the minimums (can be local minimums) even if analytical ($f'(x) = 0$ solve for x) solutions are difficult."
- ]
- },
- {
- "cell_type": "code",
- "metadata": {
- "id": "yE6Tc3m7EMSO"
- },
- "source": [
- ""
- ],
- "execution_count": null,
- "outputs": []
- }
- ]
-}
\ No newline at end of file