tutorial.ipynb

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   "source": [
    "# Microjax: JAX in Two Classes and Six Functions"
   ]
  },
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   "cell_type": "markdown",
   "id": "4878a7a0-0a1a-4a53-aad4-82bbb50988da",
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   "source": [
    "## Introduction"
   ]
  },
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    "The goal was 100 lines. In practice it's a bit more than that, but not too much.\n",
    "\n",
    "We'll start with a preview of what we'll be building, review the theory that we'll need to understand the code, then step through the three main parts of the implementation.\n",
    "\n",
    "This is inspired by Andrej Karpathy's [Micrograd](https://github.com/karpathy/micrograd/tree/master), a PyTorch-like library in about 150 lines of code. Despite PyTorch's popularity, I prefer the way JAX works. I think of PyTorch as having a more *object-oriented* feel, while JAX has a more *functional* feel. I think you'll start to see right away in the preview why that is.\n",
    "\n",
    "This tutorial borrows heavily from Matthew J Johnson's great 2017 presentation on the predecessor to JAX, [autograd](https://github.com/hips/autograd): [Video](https://videolectures.net/videos/deeplearning2017_johnson_automatic_differentiation) / [Slides](https://www.cs.toronto.edu/~duvenaud/talks/Johnson-Automatic-Differentiation.pdf) / [Code](https://github.com/mattjj/autodidact). My main contribution is simplifying a bit and packaging it as a notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4197647c-3814-4472-96f4-e2bf8a5bf951",
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   "source": [
    "## Preview"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9f636412-ed36-4156-8eb3-e9c9de5faa47",
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   "source": [
    "from microjax import np, grad, jacobian"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e371faa2-34a0-4f00-80dc-3d5e12a02a58",
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   "source": [
    "First, a quick preview of what we're building. We've just imported the entire API of Microjax:\n",
    "* `np` is just a minimal wrapper around `numpy`. It has all the usual functions: `add`, `sub`, `sinh`, `cosh`, etc (`sin` and `cos` are also easy to implement but I'm trying to keep things minimal).\n",
    "* `grad` takes the gradient of a function\n",
    "* `jacobian` is a generalization of `grad`. I'll use `grad` where I can because it's more familiar.\n",
    "\n",
    "<details>\n",
    "    <summary>Aside: derivative, gradient, and Jacobian</summary>\n",
    "    \n",
    "* The derivative is only defined for univariate functions returning a scalar. $f'(x) = df/dx$\n",
    "    \n",
    "* The gradient generalizes the derivative: it's defined for multivariate functions which return a scalar. The gradient of a function taking $n$ arguments is an $n$-vector. $\\nabla f = \\begin{bmatrix} \\frac{\\partial f}{\\partial x_1}, ..., \\frac{\\partial f}{\\partial x_2} \\end{bmatrix}$\n",
    "\n",
    "* The Jacobian further generalizes the gradient and is defined for multivariate functions returning a vector. The Jacobian of a function from $n$ variables to an $m$-vector is an $m$ by $n$ matrix:\n",
    "\n",
    "$$\n",
    "f : \\mathbb{R}^n \\to \\mathbb{R}^m\n",
    "$$\n",
    "\n",
    "$$\n",
    "f(x) =\n",
    "\\begin{bmatrix}\n",
    "f_1(x) \\\\\n",
    "\\vdots \\\\\n",
    "f_m(x)\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "$$\n",
    "J =\n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial f}{\\partial x_1} & \\cdots & \\frac{\\partial f}{\\partial x_n}\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial x_1} & \\cdots & \\frac{\\partial f_1}{\\partial x_n} \\\\\n",
    "\\vdots & \\ddots & \\vdots \\\\\n",
    "\\frac{\\partial f_m}{\\partial x_1} & \\cdots & \\frac{\\partial f_m}{\\partial x_n}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "</details>\n",
    "\n",
    "We'll start by just plotting `tanh` to remind ourselves what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91121979-c4ab-43fd-a18b-b120e3ea17cb",
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy  # just for linspace\n",
    "\n",
    "x = numpy.linspace(-7, 7, 200)\n",
    "_ = plt.plot(x, np.tanh(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae4fd585-f53f-4e09-91f2-540731b8a613",
   "metadata": {},
   "source": [
    "Now, let's see what Microjax can do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a1e09f93-76a3-4caa-b323-98140a0ab28d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad(np.tanh)(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f404871-7ec6-4d29-8d62-0a8f0302c0c7",
   "metadata": {},
   "source": [
    "Did you see that? We took the gradient of a function (which is another function), and called that function with 0. In other words, the gradient of tanh at 0 is 1. Let's plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3c262ce1-4b8d-42c7-912d-93f757947a19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(\n",
    "    x, np.tanh(x),\n",
    "    x, jacobian(np.tanh)(x),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ef71713-495d-4f12-8eef-4b81cf03743d",
   "metadata": {},
   "source": [
    "(remember that `jacobian` is just a generalization of `grad`)\n",
    "\n",
    "<details>\n",
    "  <summary>Aside: Why didn't we just use <code>grad</code> then?</summary>\n",
    "<p>Try calling <code>grad(np.tanh)(x)</code> (go ahead and try).</p>\n",
    "    \n",
    "<p>You should see \"Gradient only defined for scalar-output functions. Output had shape: (200,)\". The problem is that <code>x</code> is a 200-array, i.e. it has shape <code>(200,)</code>, and <code>np.tanh</code> is a vectorized function so, given <code>x</code>, it will also return an array with shape <code>(200,)</code>. The gradient function is relatively simple because it only operates on scalar-valued functions, so we need the more general Jacobian here.</p>\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c140aed0-6119-402f-ad63-39b6cca44b25",
   "metadata": {},
   "source": [
    "What's more, we can take higher derivatives:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "995a56cd-2411-4f0e-8b4e-e2bfe50bf1fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(-0.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad(grad(np.tanh))(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27c352c0-ec4c-439a-9fbf-ea6540b4f065",
   "metadata": {},
   "source": [
    "We can do this as many times as we want. Here are the first four derivatives of `tanh` plotted (uncomment the next two or play with other functions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "24f1db05-7367-4fbd-bfc9-fbc045a5d50c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.plot(\n",
    "    x, np.tanh(x),\n",
    "    x, jacobian(np.tanh)(x),\n",
    "    x, jacobian(jacobian(np.tanh))(x),\n",
    "    x, jacobian(jacobian(jacobian(np.tanh)))(x),\n",
    "    x, jacobian(jacobian(jacobian(jacobian(np.tanh))))(x), \n",
    "    # x, jacobian(jacobian(jacobian(jacobian(jacobian(np.tanh)))))(x),\n",
    "    # x, jacobian(jacobian(jacobian(jacobian(jacobian(jacobian(np.tanh))))))(x),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42e969d-f0d0-4cd0-b9e5-b58340f95485",
   "metadata": {},
   "source": [
    "The amazing thing about Microjax is, that was the entire API. Use `microjax.np` as if it was just numpy and `grad` to take the gradient.\n",
    "\n",
    "<details>\n",
    "    <summary>Aside: Why <code>microjax.np</code>?</summary>\n",
    "    \n",
    "We'll cover this in more detail later, but the short version is that `jax.numpy` has the same API as `numpy`, but supports tracing the computation for backpropagation. `microjax.np` doesn't quite support the full API (because *micro*).\n",
    "</details>\n",
    "\n",
    "<details>\n",
    "    <summary>Aside: The Jacobian and other functions</summary>\n",
    "    \n",
    "You rarely need `jacobian` in real code (at least if you're writing neural networks).\n",
    "\n",
    "Aren't there other functions? Real JAX includes various other functions, e.g. `jacfwd` for a forward-mode evaluated Jacobian, `hessian`, `value_and_grad`. But `np` and `grad` are all you need to build a neural net.\n",
    "</details>\n",
    "\n",
    "Now that we've had a preview, let's take a few minutes to review some theory."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a99c5c2-5961-4bc8-8e20-cc6eeb99e92d",
   "metadata": {},
   "source": [
    "## Theory: Jacobians, Chain Rule, Forward- and Reverse-Mode"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3c33f100-75fa-4f8d-808c-90c76dc939e7",
   "metadata": {},
   "source": [
    "Assume that we have some function $F : \\mathbb{R}^{n} \\to \\mathbb{R}$. Let's say that $F$ is made up of a chain of functions, which we can individually differentiate: $F = D \\circ C \\circ B \\circ A$, more explicitly:\n",
    "\n",
    "$$y = F(x) = D(C(B(A(x))))$$\n",
    "\n",
    "$$\n",
    "y = D(c), \\quad \\textbf{c} = C(b), \\quad \\textbf{b} = B(a), \\quad \\textbf{a} = A(x)\n",
    "$$\n",
    "\n",
    "We'll sometimes use boxes to visualize the shapes of inputs and outputs:\n",
    "\n",
    "<img width=200 height=200 src=\"images/img1.png\" alt=\"Boxes of different sizes representing input and output\" />\n",
    "\n",
    "<details>\n",
    "    <summary>Aside: The Shape of $F$</summary>\n",
    "For now we're working in the simplified setting where $F$ returns a scalar, but everything still works if $F$ returns a vector.\n",
    "</details>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "40190ca3-9216-4e09-8971-1da6139daf77",
   "metadata": {},
   "source": [
    "Our goal is to evaluate the gradient of $F$.\n",
    "\n",
    "We write $F'(x)$ for the Jacobian matrix of $F$ evaluated at $x$. This is a matrix of partial derivatives. In this case it's just one row (because $F$ has a scalar output, with a vector input).\n",
    "\n",
    "$$\n",
    "F'(x) = \\frac{\\partial y}{\\partial x} =\n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial y}{\\partial x_1} & \\cdots & \\frac{\\partial y}{\\partial x_n}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "The chain rule tells us that we can write the Jacobian $F'(x)$ as the product of the other Jacobian matrices.\n",
    "\n",
    "<img src=\"images/img2.png\" width=\"500px\" alt=\"Boxes of different sizes representing Jacobian matrices\" />\n",
    "\n",
    "<details>\n",
    "<summary>Question: What are the sizes of the four boxes (representing the Jacobian matrices $D'(c)$, $C'(b)$, $B'(a)$, and $A'(x)$)?</summary>\n",
    "    \n",
    "* The first is 1 by the size of the output of C, or $1 \\times \\dim C$\n",
    "* $\\dim C \\times \\dim B$\n",
    "* $\\dim B \\times \\dim A$\n",
    "* $\\dim A \\times n$ (where $n = \\dim x$)\n",
    "</details>\n",
    "\n",
    "<details>\n",
    "<summary>Question: Does the order of multiplication matter?</summary>\n",
    "\n",
    "Yes! Different orders can have very different performance characteristics, both in terms of FLOPs and memory. This is an interesting and [well-studied problem](https://en.wikipedia.org/wiki/Matrix_chain_multiplication).\n",
    "</details>"
   ]
  },
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   "cell_type": "markdown",
   "id": "edb45251-a039-4c17-9479-f7559f5c813e",
   "metadata": {},
   "source": [
    "In practice, there are two common, simple ways to calculate the Jacobian.\n",
    "\n",
    "First is forward accumulation, where we start computing from the inputs to the outputs\n",
    "\n",
    "$$\n",
    "F'(x) =\n",
    "\\frac{\\partial y}{\\partial c}\n",
    "\\left( \n",
    "\\frac{\\partial c}{\\partial b}\n",
    "\\left( \n",
    "\\frac{\\partial b}{\\partial a} \\frac{\\partial a}{\\partial x} \n",
    "\\right) \n",
    "\\right)\n",
    "$$\n",
    "\n",
    "The big problem with forward accumulation is that if there are $n$ inputs and an $m$-dimensional internal state, then the Jacobian is $m \\times n$. Since neural networks are the main use for JAX, you should imagine that that's a *very* big matrix.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial b}{\\partial x} =\n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial b_1}{\\partial x_1} & \\cdots & \\frac{\\partial b_1}{\\partial x_n} \\\\\n",
    "\\vdots & \\ddots & \\vdots \\\\\n",
    "\\frac{\\partial b_m}{\\partial x_1} & \\cdots & \\frac{\\partial b_m}{\\partial x_n}\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
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   "cell_type": "markdown",
   "id": "e0748784-326f-4418-a814-8db85e456a9d",
   "metadata": {},
   "source": [
    "The alternative is reverse accumulation, where we start computing the Jacobian from the opposite end, the output.\n",
    "\n",
    "$$\n",
    "F'(x) =\n",
    "\\left( \n",
    "\\left(\n",
    "\\frac{\\partial y}{\\partial c} \\frac{\\partial c}{\\partial b}\n",
    "\\right) \n",
    "\\frac{\\partial b}{\\partial a} \n",
    "\\right) \n",
    "\\frac{\\partial a}{\\partial x}\n",
    "$$\n",
    "\n",
    "This turns out to be really efficient because neural networks (in training) typically have a scalar output, the loss. This means that each intermediate Jacobian is only as big as the internal state, in this case $1 \\times m$.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial y}{\\partial b} =\n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial y}{\\partial b_1} & \\cdots & \\frac{\\partial y}{\\partial b_m}\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
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   "source": [
    "So, most of the time, reverse accumulation is the right default."
   ]
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    "One thing we might want to do is, instead of building the entire Jacobian matrix, make a function which returns it multiplied by some vector.\n",
    "\n",
    "$$\n",
    "F'(x) v =\n",
    "\\frac{\\partial y}{\\partial c}\n",
    "\\frac{\\partial c}{\\partial b}\n",
    "\\frac{\\partial b}{\\partial a}\n",
    "\\frac{\\partial a}{\\partial x}\n",
    "v\n",
    "$$\n",
    "\n",
    "$$\n",
    "F'(x) v =\n",
    "\\frac{\\partial y}{\\partial c}\n",
    "\\left(\n",
    "\\frac{\\partial c}{\\partial b}\n",
    "\\left(\n",
    "\\frac{\\partial b}{\\partial a}\n",
    "\\left(\n",
    "\\frac{\\partial a}{\\partial x}\n",
    "v\n",
    "\\right)\n",
    "\\right)\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "Why would you want to do that? As we'll see when we reach the implementation, for our primitives it's typically *much* simpler to represent them as functions than as matrices. As a very simple example, given $f : \\mathbb{R}^n \\to \\mathbb{R}^m$, $f(x) = 2 x$, what's $\\frac{\\partial{f}}{\\partial{x}}$? Just $\\vec{2}$ of course. We wouldn't want to represent this as an $n$-dimensional matrix. We'll see something similar with other primitives where the matrix might be diagonal or otherwise quite inefficient to represent as a full matrix.\n",
    "\n",
    "We'll call these operators *Jacobian-vector products* (JVPs).\n",
    "\n",
    "What if you actually want the Jacobian, rather than this operator which gives us the JVP? Well, if $v$ is the vector $[1, 0, \\ldots]$, i.e. the first standard basis vector, or the first one-hot vector... then $F'(x) v$ is the first column of the Jacobian. So we can call the JVP with each of the standard basis vectors and build the Jacobian one column at a time.\n",
    "\n",
    "Remember that the Jacobian for a function $f : \\mathbb{R}^n \\to \\mathbb{R}^m$ is in $\\mathbb{R}^{m \\times n}$. In ML, $n$ is usually in the millions to trillions (the parameter count), while $m$ is usually 1 (the loss), our Jacobian has one row and *many* columns, so it would take forever to build the Jacobian this way.\n",
    "\n",
    "You can think of this as passing an identity matrix ($\\frac{\\partial x}{\\partial x}$), an $n \\times n$ matrix which has as columns each of the standard basis vectors.\n",
    "\n",
    "$$\n",
    "F'(x) =\n",
    "\\frac{\\partial y}{\\partial c}\n",
    "\\left(\n",
    "\\frac{\\partial c}{\\partial b}\n",
    "\\left(\n",
    "\\frac{\\partial b}{\\partial a}\n",
    "\\left(\n",
    "\\frac{\\partial a}{\\partial x}\n",
    "\\frac{\\partial x}{\\partial x}\n",
    "\\right)\n",
    "\\right)\n",
    "\\right)\n",
    "$$"
   ]
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    "Instead of multiplying it on the right (a JVP) we can also multiply the vector on the left (a *Vector-Jacobian Product* or *VJP*).\n",
    "\n",
    "$$\n",
    "v^\\top F'(x) =\n",
    "v^\\top \\frac{\\partial y}{\\partial c}\n",
    "\\frac{\\partial c}{\\partial b}\n",
    "\\frac{\\partial b}{\\partial a}\n",
    "\\frac{\\partial a}{\\partial x}\n",
    "$$\n",
    "\n",
    "$$\n",
    "v^\\top F'(x) =\n",
    "\\left( \n",
    "\\left( \n",
    "\\left( \n",
    "v^\\top \\frac{\\partial y}{\\partial c} \n",
    "\\right) \n",
    "\\frac{\\partial c}{\\partial b} \n",
    "\\right) \n",
    "\\frac{\\partial b}{\\partial a} \n",
    "\\right) \n",
    "\\frac{\\partial a}{\\partial x}\n",
    "$$\n",
    "\n",
    "In contrast to JVPs, VJPs calculate the Jacobian one row at a time. Since we're usually working with a single very big row, this is quite efficient (often with cost similar to the cost of calling $F$).\n",
    "\n",
    "We can think of this as passing an $m \\times m$ (usually $1 \\times 1$) identity matrix ($\\frac{\\partial y}{\\partial y}$), which has as rows each of the standard basis vectors.\n",
    "\n",
    "$$\n",
    "F'(x) =\n",
    "\\left( \n",
    "\\left( \n",
    "\\left( \n",
    "\\frac{\\partial y}{\\partial y} \n",
    "\\frac{\\partial y}{\\partial c} \n",
    "\\right) \n",
    "\\frac{\\partial c}{\\partial b} \n",
    "\\right) \n",
    "\\frac{\\partial b}{\\partial a} \n",
    "\\right) \n",
    "\\frac{\\partial a}{\\partial x}\n",
    "$$"
   ]
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    "<details>\n",
    "<summary>Aside: Non-chain composition</summary>\n",
    "\n",
    "Of course, not all computation is structured as a simple chain of function calls! We might actually have a DAG, where some functions take multiple arguments (which we'll call fan-in) and some functions return multiple results (fan-out).\n",
    "\n",
    "Handling fan-in is simple -- we just think of it as stacking the two inputs to get a version of $F$ with just one input. Then we can build separate Jacobians, one for each input.\n",
    "\n",
    "$$\n",
    "y = F(x_1, x_2)\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial y}{\\partial x_1} = F_1'(x_1, x_2)\n",
    "\\quad\n",
    "\\frac{\\partial y}{\\partial x_2} = F_2'(x_1, x_2)\n",
    "$$\n",
    "\n",
    "We can also handle fan-out easily. Think of this G function as duplicating its input $x$.\n",
    "\n",
    "$$\n",
    "G(x) =\n",
    "\\begin{bmatrix}\n",
    "x \\\\ x\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "I \\\\ I\n",
    "\\end{bmatrix} x\n",
    "$$\n",
    "\n",
    "What's the Jacobian of $G$?\n",
    "\n",
    "$$\n",
    "G'(x) =\n",
    "\\begin{bmatrix}\n",
    "I \\\\ I\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Well, we're getting partial derivative information from each of our outputs, and the Jacobian is just their sum.\n",
    "\n",
    "$$\n",
    "v^\\top G'(x) =\n",
    "\\begin{bmatrix}\n",
    "v_1^\\top & v_2^\\top\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "I \\\\ I\n",
    "\\end{bmatrix}\n",
    "= v_1^\\top + v_2^\\top\n",
    "$$\n",
    "</details>"
   ]
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   "source": [
    "## Implementation\n",
    "\n",
    "Phew! Enough theory, let's get into the code!"
   ]
  },
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   "cell_type": "markdown",
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    "There are three pieces we'll put together:\n",
    "\n",
    "1. Building a computation graph (\"tracing\")\n",
    "2. Defining a vector-Jacobian product (VJP) for each primitive\n",
    "3. Composing VJPs to get a VJP for the whole function"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### 1. Building a computation graph"
   ]
  },
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   "source": [
    "Let's look at an example function we might want to build the computation graph for. Here we'll focus on `neuron`, which uses `relu`."
   ]
  },
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    "def relu(x):\n",
    "    return (x + abs(x)) / 2\n",
    "\n",
    "def neuron(w, b, x):\n",
    "    z = w @ x + b\n",
    "    return relu(z)"
   ]
  },
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   "cell_type": "markdown",
   "id": "6ce7978b-dfb1-4939-88a6-77e7a84e39b0",
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   "source": [
    "Our strategy will be to *trace* the function by passing it *boxed* values instead of arrays.\n",
    "So, `w`, `b`, and `x` will be instances of `Box` (which we're about to define), rather than\n",
    "`np.ndarray`. You can of course\n",
    "still call `neuron` with Numpy arrays, but if `Box` supports `__add__`, `__matmul__`, `__div__`,\n",
    "and `__abs__`, then we should be able to put boxes in and get a box out. Our function will still\n",
    "compute a value, but it will also record the shape of the computation graph.\n",
    "\n",
    "Each time we need to call a primitive, we'll need to first unbox the value, call the primitive,\n",
    "and box the result on the other end.\n",
    "\n",
    "The goal is to build a graph of `Node`s mirroring the computation which actually took place.\n",
    "One will be created when (and *only* when) calling a primitive."
   ]
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  {
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   "execution_count": 8,
   "id": "d752d7ee-2864-4120-873a-ef917cad93ec",
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   "source": [
    "from dataclasses import dataclass\n",
    "from typing import Callable, Any\n",
    "\n",
    "class Box:\n",
    "    def __init__(self, value, trace_id, node):\n",
    "        self._value = value\n",
    "        self._node = node\n",
    "        self._trace_id = trace_id\n",
    "\n",
    "    def __add__(self, other):\n",
    "        return np.add(self, other)\n",
    "\n",
    "    def __sub__(self, other):\n",
    "        return np.subtract(self, other)\n",
    "        \n",
    "    # ... __div__, __abs__, etc\n",
    "\n",
    "@dataclass(frozen=True)\n",
    "class Node[T]:\n",
    "    \"\"\"A node in a computation graph.\n",
    "\n",
    "    parents and argnums should be the same length. There is one for each boxed argument.\n",
    "    args could be longer if there are non-Box arguments.\n",
    "    \"\"\"\n",
    "\n",
    "    parents: tuple[\"Node[T]\"]  # For each boxed argument, the node that produced it.\n",
    "    value: T  # The output of the primitive function.\n",
    "    fun: Callable[..., T]  # Wrapped primitive function\n",
    "    args: tuple[Any]  # All (unboxed) positional arguments\n",
    "    kwargs: dict[str, Any]  # Additional keyword arguments\n",
    "    argnums: tuple[int]  # Positional indices of boxed values\n",
    "\n",
    "    @staticmethod\n",
    "    def new_root():\n",
    "        return Node((), None, lambda x: x, (), {}, ())\n",
    "\n",
    "    # We have to override hash because dicts aren't hashable.\n",
    "    def __hash__(self):\n",
    "        return id(self)"
   ]
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    "This diagram shows what happens when we call `np.sum`.\n",
    "It shows both the nodes in the graph that ends up being built\n",
    "as well as the boxing and unboxing that we do around the primitive."
   ]
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    "<img src=\"images/img3.png\" width=\"700px\" alt=\"Unboxing and re-boxing a value around a primitive\" />"
   ]
  },
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   "cell_type": "markdown",
   "id": "0d386d5e-33cb-4183-a1cc-b8753d984f61",
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   "source": [
    "We also define a primitive function which does the boxing / unboxing and creates one `Node` in the graph."
   ]
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   "source": [
    "def primitive(f_raw):\n",
    "    def f_wrapped(*args, **kwargs):\n",
    "        argvals, argnums, parents = list(args), [], []\n",
    "        for i, arg in enumerate(args):\n",
    "            if isinstance(arg, Box):\n",
    "                argvals[i] = arg._value\n",
    "                argnums.append(i)\n",
    "                parents.append(arg._node)\n",
    "        raw_result = f_raw(*argvals, **kwargs)\n",
    "        if len(parents) == 0:\n",
    "            return raw_result\n",
    "        node = Node(parents, raw_result, f_wrapped, argvals, kwargs, argnums)\n",
    "        return Box(raw_result, trace_id, node)\n",
    "\n",
    "    return f_wrapped"
   ]
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   "source": [
    "<img src=\"images/img4.png\" width=\"700px\" alt=\"Computation graph\" />"
   ]
  },
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   "id": "d276b6b1-eacb-4bb5-b0e7-b15462840548",
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   "source": [
    "Earlier, in the theory section, we mentioned that functions didn't have to be a chain of primitives, they can also have fan-in and fan-out. The code we're writing now will actually work for any directed acyclic graph (DAG)."
   ]
  },
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   "cell_type": "markdown",
   "id": "c1b585bc-794f-4d11-bb50-0a47f440df4a",
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   "source": [
    "One important thing to note about the graph of `Node`s we've built: it doesn't contain any control flow! Any structure is recorded statically how it executed.\n",
    "\n",
    "Quiz:\n",
    "\n",
    "What does the graph for this function look like?\n",
    "\n",
    "```python\n",
    "def f(x):\n",
    "    import random\n",
    "    return np.cosh(x) if random.random() > 0.5 else np.sinh(x)\n",
    "```\n",
    "\n",
    "What about this function?\n",
    "\n",
    "```python\n",
    "def g(x):\n",
    "    for _ in range(5):\n",
    "        x = x + 1\n",
    "    return x\n",
    "```\n",
    "\n",
    "Expand the outputs of the next two cells to check your answer"
   ]
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    "from graphing import trace_and_draw\n",
    "\n",
    "def f(x):\n",
    "    import random\n",
    "    return np.cosh(x) if random.random() > 0.5 else np.sinh(x)\n",
    "\n",
    "trace_and_draw(f, np.array([0.5]))"
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    "def g(x):\n",
    "    for _ in range(5):\n",
    "        x = x + 1\n",
    "    return x\n",
    "\n",
    "trace_and_draw(g, np.array([0.5]))"
   ]
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    "There's one more function we need to finish tracing: `trace` itself.\n",
    "\n",
    "All we need to do is create a `Box` to pass into the computation, then unbox it at the end."
   ]
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    "def trace(start_node, fun, x):\n",
    "    \"\"\"(forward pass / build computation graph)\"\"\"\n",
    "    start_box = Box(x, trace_id, start_node)\n",
    "    end_box = fun(start_box)\n",
    "\n",
    "    if isinstance(end_box, Box):\n",
    "        return end_box._value, end_box._node\n",
    "    else:\n",
    "        # Output seems independent of input\n",
    "        return end_box, None"
   ]
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    "\"\"\"Advanced: the real definition of primitive and trace.\n",
    "\n",
    "What was the problem with the functions we just defined?\n",
    "They work perfectly fine if we only ever take a single grad:\n",
    "calling grad(np.tanh) will work.\n",
    "\n",
    "The problem arises when we take multiple gradients:\n",
    "e.g. grad(grad(np.tanh)). Here the outer `grad` is passsed\n",
    "a function returned by the inner `grad(np.tanh)`.\n",
    "This is a vjp (which we'll define below).\n",
    "This means we're going to trace, that is, pass `Box`es through a VJP which we've defined.\n",
    "We need to mark out boxes so that we end up building a compuation graph only\n",
    "of nodes from the same call to `trace`.\n",
    "\"\"\"\n",
    "\n",
    "def find_top_boxed_args(args):\n",
    "    \"\"\"Finds boxed arguments with largest trace_id.\n",
    "\n",
    "    Equivalent to finding the largest trace_id of any argument, keeping args\n",
    "    with the same, and dropping the remainder.\n",
    "\n",
    "    Args:\n",
    "      args: Arguments to function wrapped by primitive().\n",
    "\n",
    "    Returns:\n",
    "      top_boxes: List of (index, boxed argument). Arguments have same, largest\n",
    "        trace_id.\n",
    "      top_trace_id: trace_id of all elements in top_boxes.\n",
    "    \"\"\"\n",
    "    top_trace_id = -1\n",
    "    top_boxes = []\n",
    "    for argnum, arg in enumerate(args):\n",
    "        if isinstance(arg, Box):\n",
    "            if arg._trace_id > top_trace_id:\n",
    "                top_boxes = [(argnum, arg)]\n",
    "                top_trace_id = arg._trace_id\n",
    "            elif arg._trace_id == top_trace_id:\n",
    "                top_boxes.append((argnum, arg))\n",
    "    return top_boxes, top_trace_id\n",
    "\n",
    "def primitive(f_raw):\n",
    "    def f_wrapped(*args, **kwargs):\n",
    "        # Fetch boxed arguments with largest trace_id.  This ensures that the\n",
    "        # computational graph being constructed only consists of other nodes\n",
    "        # from the same call to trace().\n",
    "        boxed_args, trace_id = find_top_boxed_args(args)\n",
    "        if boxed_args:\n",
    "            # Replace some elements of args with corresponding unboxed values.\n",
    "            argvals = list(args)\n",
    "            for argnum, box in boxed_args:\n",
    "                argvals[argnum] = box._value\n",
    "            # Get nodes for each boxed argument.\n",
    "            parents = tuple(box._node for _, box in boxed_args)\n",
    "\n",
    "            # Get argument indices for each boxed argument.\n",
    "            argnums = tuple(argnum for argnum, _ in boxed_args)\n",
    "\n",
    "            # Calculate result of applying original numpy function.\n",
    "            #\n",
    "            # Note that we use a recursive call here in order to also augment\n",
    "            # outer calls to trace() with lower trace_ids.\n",
    "            ans = f_wrapped(*argvals, **kwargs)\n",
    "\n",
    "            node = Node(parents, ans, f_wrapped, argvals, kwargs, argnums)\n",
    "            return Box(ans, trace_id, node)\n",
    "        else:\n",
    "            return f_raw(*args, **kwargs)\n",
    "\n",
    "    return f_wrapped\n",
    "\n",
    "trace_id = 0\n",
    "\n",
    "def trace(start_node, fun, x):\n",
    "    \"\"\"(forward pass / build computation graph)\"\"\"\n",
    "    global trace_id\n",
    "    trace_id += 1\n",
    "    try:\n",
    "        start_box = Box(x, trace_id, start_node)\n",
    "        end_box = fun(start_box)\n",
    "\n",
    "        if isinstance(end_box, Box) and end_box._trace_id == start_box._trace_id:\n",
    "            return end_box._value, end_box._node\n",
    "        else:\n",
    "            # Output seems independent of input\n",
    "            return end_box, None\n",
    "    finally:\n",
    "        trace_id -= 1"
   ]
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   "source": [
    "Finally, we define `np` as a class, where we simply wrap each primitive.\n",
    "\n",
    "<details>\n",
    "    <summary>Why not a module?</summary>\n",
    "\n",
    "Just so I could include the definition of `np` in this notebook.\n",
    "</details>"
   ]
  },
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   "execution_count": 13,
   "id": "6803debd-440a-414d-9274-fb7c22ff87d1",
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   "source": [
    "class Np:\n",
    "    def __init__(self):\n",
    "        self.negative = primitive(np.negative)\n",
    "        self.exp = primitive(np.exp)\n",
    "        self.log = primitive(np.log)\n",
    "        self.multiply = primitive(np.multiply)\n",
    "        self.add = primitive(np.add)\n",
    "\n",
    "np = Np()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d84e6a6d-56fb-422a-8626-27c268c7f915",
   "metadata": {},
   "source": [
    "### 2. VJPs"
   ]
  },
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   "cell_type": "markdown",
   "id": "62c610ce-01d3-4406-b0a5-701fbacd4094",
   "metadata": {},
   "source": [
    "Now the setting is that we have some computation $a = A(x)$, with final loss $y$. Now, we get the derivative with respect to $a$: $\\frac{\\partial y}{\\partial{a}}$. We need to apply our vector-Jacobian product operator ($A'( x ) = \\frac{\\partial{a}}{\\partial{x}}$) to pull that derivative back to get $\\frac{\\partial y}{\\partial x}$."
   ]
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   "source": [
    "<img src=\"images/img5.png\" width=\"500px\" alt=\"Vector-Jacobian product\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7df245d0-ca19-40f1-9811-b2fc9265395e",
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   "source": [
    "\"\"\"\n",
    "Here are some example VJPs. Note that we're defining a different VJP for each argument.\n",
    "* g is the gradient we want to pull back\n",
    "* ans is the output from the function\n",
    "* x is the input\n",
    "\"\"\"\n",
    "\n",
    "primitive_vjps = {\n",
    "    np.negative: {0: lambda g, ans, x: -g},\n",
    "    np.add: {\n",
    "        0: lambda g, ans, x, y: g,\n",
    "        1: lambda g, ans, x, y: g,\n",
    "    },\n",
    "    np.multiply: {\n",
    "        0: lambda g, ans, x, y: y * g,\n",
    "        1: lambda g, ans, x, y: x * g,\n",
    "    },\n",
    "    np.exp: {0: lambda g, ans, x: ans * g},\n",
    "    np.log: {0: lambda g, ans, x: g / x},\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26cceb6b-ded8-408d-b2a2-4a7b32060d7d",
   "metadata": {},
   "source": [
    "### 3. Composing VJPs Backward"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "023827c2-7abc-4cf2-8cc2-6274ef7b849b",
   "metadata": {},
   "source": [
    "Now that we've defined our primitive VJPs, we can start with $\\frac{\\partial{y}}{\\partial{y}} = 1$, and keep pulling back the derivatives until we reach the start node."
   ]
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   "id": "3d8300e0-fb2a-4ffa-ad04-c0dbc7ce0df9",
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   "source": [
    "<img src=\"images/img6.png\" width=\"700px\" alt=\"Computation Graph\" />"
   ]
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6VXNlckNvbW1lbnQ+U2NyZWVuc2hvdDwvZXhpZjpVc2VyQ29tbWVudD4KICAgICAgPC9yZGY6RGVzY3JpcHRpb24+CiAgIDwvcmRmOlJERj4KPC94OnhtcG1ldGE+CtlP9IQAAAAcaURPVAAAAAIAAAAAAAABfQAAACgAAAF9AAABfQAAxZG34FQrAABAAElEQVR4AezdB5zURPvA8QeOevTeBUEQFPWvvCiCBREBpdkoUkSa0kQURBQUEQXBijRfulJEUEAsKPrSBBUUFBSQXkXaHb0ex/7zRBOSLXd7xx7s7v3m89GdmUyyyTdrzOXJzGTwGElICCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCBwUQIZCLxdlB8rI4AAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIGAKEHjjh4AAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIBACAQIvIUAkU0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggQOCN3wACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACIRAg8BYCRDaBAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAIE3fgMIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIhECAwFsIENkEAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgTe+A0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggEAIBAm8hQGQTCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCBB44zeAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQAgECLyFAJFNIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIEDgjd8AAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAiEQIPAWAkQ2gQACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggACBN34DCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCIRAgMBbCBDZBAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIE3vgNIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIBACAQJvIUBkEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggQeOM3gAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAIBAi8hQCRTSCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCBA4I3fAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIhECDwFgJENoEAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAgTd+AwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgiEQIDAWwgQ2QQCCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACBN74DSCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCAQAgECbyFAZBMIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIEHjjN4AAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIBACAQIvIUAkU0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggQOCN3wACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACIRAg8BYCRDaBAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAIE3fgMIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIhECAwFsIENkEAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgTe+A0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggEAIBAm8hQGQTCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCBB44zeAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQAgECLyFAJFNIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIEDgjd8AAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAiEQIPAWAkQ2gQACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggACBN34DCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCIRAgMBbCBDZBAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIE3vgNIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIBACAQJvIUBkEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggQeOM3gAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAIBAi8hQCRTSCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCBA4I3fAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIhECDwFgJENoEAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAgTd+AwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgiEQIDAWwgQ2QQCCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACBN74DSCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCAQAgECbyFAZBMIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIEHjjN4AAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIBACAQIvIUAkU0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggQOCN3wACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACIRAg8BYCRDaBAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAIE3fgMIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIhECAwFsIENkEAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgTe+A0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggEAIBAm8hQGQTCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCBB44zeAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQAgECLyFAJFNIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIEDgjd8AAgiElcDRo0fl77//lkyZMkmJEiUkW7ZsYbV/7AwCCISHgMfjkbi4ODlw4IDkzp1bihQpYl43wmPv2AsEEIhmgdOnT5v3KmfPnpVixYqZ16BoPl6ODQEEEAhWgPuzYKVohwACCCCAAALRLkDgLdrPMMeHQJgLnDlzRr766iuZPHmyfPfdd3Ls2DHXHhcuXFiaN28uTz31lJQtW9a1jAICCKQvgfj4eJk5c6ZMmjRJfvrpJ5+Dr1ChgnTs2FE6dOggefPm9VlOBQIIIJBagR9++EGmTJkin376qezfv9+1mVy5cknt2rWlZ8+eUqNGDdcyCggggEC0C3B/Fu1nmONDAAEEEEAAgdQIEHhLjRrrIIBASARWrFghbdu2lXXr1tnb0+Cavj2+adMmnwdbLVq0kH79+kmlSpXs9mQQQCB9COgD7y5duriC89dff73ExsbK2rVrXfUq0qdPH3n22Wclf/786QOIo0QAgTQR2LNnj3nt+eyzz+zta6BNrz/aQ3/r1q12vWY08PbSSy9JnTp1XPUUEEAAgWgU4P4sGs8qx4QAAggggAACoRAg8BYKRbaBAAIpFpg+fbo88sgj5nr6AGvw4MHSqFEjKVWqlL2tffv2mb3htLeb1RNO2y5evFhuvPFGux0ZBBCIXgEdsqh79+4yYsQI8yC1V5teL2rVqmX3ajt//rxs375dxowZI0OGDLEx9MH4okWLJF++fHYdGQQQQCBYgT/++EOqV69u34Noj7Y2bdpI5cqVJUOGDOZm9P5k+fLl0rVrV9m4caO96YkTJ8pjjz1ml8kggAAC0STA/Vk0nU2OBQEEEEAAAQTSQoDAW1qosk0EEEhSYP78+VK3bl2zTevWreWdd96RAgUKBFxnx44d5sMrfYCuSYNvP/74o1x77bVmmX8hgED0CvTv319eeeUV8wDfeustefLJJyVz5swBD3jJkiXSsmVL2b17t9mmatWq5jC2Og8cCQEEEAhWQHu6VaxY0Qy63XTTTeaQ2Ndcc03A1U+ePCnPPfec/ZKANvzoo4/M4bIDrsQCBBBAIEIFuD+L0BPHbiOAAAIIIIDAJRMg8HbJqPkiBBBQAX0wdfXVV5sPxRs2bCizZ8+WmJiYZHGOHz8u5cqVs4ef1LnfVq1aJSVKlEh2XRoggEBkCugQktqzRNObb75pzp8UzJHotaFKlSp209tvv93s+ZYxY0a7jgwCCCCQlIAG8KdNmyYlS5aUlStXit53BJPuv/9+cQ5L+e2335rzvwWzLm0QQACBSBDg/iwSzhL7iAACCCCAAAKXW4DA2+U+A3w/AulMYODAgebcJ3rYnTt3ll69eonO6xZM0jkEtIeclXT+pqFDh1pFPhFAIIoEdAgjHU7S6umqw0t269ZNcubMGdRRdujQQcaPH2+3/fzzz6VBgwZ2mQwCCCAQSECHtK5Zs6a5WAP3eu9y5513Bmruqt+8ebOUL1/ertPechq4IyGAAALRIMD9WTScRY4BAQQQQAABBC6FAIG3S6HMdyCAgClw9OhRyZMnj0tDh4FbsWKFqy5QQedxqlatmvz88892k0OHDtnzPNmVZBBAIOIFFixYIHfffbfrOPr06WPO7+aqDFDQYeKcPWL14bkOQ0lCAAEEkhO47bbbZNmyZa5m8fHxQc8XqUNOOl8M0uvZXXfd5doeBQQQQCASBbg/i8Szxj4jgAACCCCAwOUQIPB2OdT5TgTSqYD2OGnUqJHP0eubk8GmQYMGSd++fe3mOufTM888Y5fJIIBAdAhob1j979uZ7r33Xvnqq6+cVUnmNXCnD4ispEF+DfaTEEAAgUACcXFxUrBgQZ/FOresvvwTTFq6dKlosN9K9evXly+++MIq8okAAghErAD3ZxF76thxBBBAAAEEELjEAgTeLjE4X4dAehbQYd90+Ddnuv7662X16tXOqiTzM2fOlKZNm9ptdO6VXbt22WUyCCAQHQI6rKwOL+tMKR1etmvXrjJq1Ch7E+3atXMNP2kvIIMAAgj8K7BhwwapWLGij8eBAwf8BuR8GhoV3j1utc2WLVuCHlrb3zapQwABBMJBgPuzcDgL7AMCCCCAAAIIRIIAgbdIOEvsIwJRIuCciNs6pIULF9rzqFh1SX2uWrVKqlSp4mpy+PBhnyEsXQ0oIIBAxAlMmDBB2rdvb++3Btl1mNmiRYvadcllhg0bJj169LCbMdeSTUEGAQQCCJw7d84cpnb//v12iyFDhkjv3r3tcnIZ7cmfMWNGVzPtrau9dkkIIIBAJAtwfxbJZ499RwABBBBAAIFLKUDg7VJq810IICDr168X7bWWP39+qVevnlx11VUpUtE53XRdZ9Iec9pzjoQAAtElMH/+fNHh3UqXLi2NGzcOen4lS0GHdmvYsKFVlFy5conONUlCAAEEkhLQe41x48ZJYmKi3HHHHVK9evWkmvtddsMNN8iaNWvsZSNHjpQuXbrYZTIIIIBApApwfxapZ479RgABBBBAAIFLKUDg7VJq810IIHDRAv7eIte54xo0aHDR22YDCCAQXQLLli2T2267zXVQ8fHxKQ7guTZAAQEEEAhCoE6dOvLtt9/aLVM6VK69IhkEEEAgygS4P4uyE8rhIIAAAggggIBfAQJvflmoRACBcBXQ3ip58uRx7d6IESNE53IiIYAAAk6BefPmyX333eeskt9++020JwoJAQQQSEuBm2++2Rwe1/qOBx54QGbNmmUV+UQAAQTSrQD3Z+n21HPgCCCAAAIIpCsBAm/p6nRzsAiEp8DmzZvN4eT27dsnBw8elJiYGLnuuuukcuXKUqlSJbNs7fmGDRukYsWKVtH8fO655+T111931VFAAIHoE9Bh31auXCk6vKxeK3Q4uNy5c5uBNB1uVoekdKbx48dLhw4dnFXCPEsuDgoIIBCkwIEDB2TJkiWye/du8/pz5swZqVChgnm/ovcssbGxri3ptenYsWN2XdWqVWXFihV2mQwCCCAQLQLcn0XLmeQ4EEAAAQQQQCCUAgTeQqnJthBAIGgBfRg1bNgwmThxomzdujXgejVq1JBJkybZc8HpnAJ169Z1tX/55Zelf//+rjqrcHLDNjk6/0c5u2W7ZMiUWbJee5XkrnmzZLuyhNUk+U/jYf/pbX9JTJ6ckrmQe3655FemBQIIXKzAjh07zOD61KlTXQ+yvbf7+OOPyxtvvGEG43RZ3759ZdCgQa5m//vf/6RWrVquOi2cP3NWDn+5WE79vknO7T8gma8oKdlvqCD57jHmdjJeBgg2JcQflsT4o5K1dHHJkDlTsKvRDgEEwlBAHyZ/9NFH8t5777l6r3nvauHChUWvT7Vr1zYXHT9+3JxT0tlO72eWLl3qrLLz3KvYFGQQQCCCBLg/i6CTxa4igAACCCCAwCUXIPB2ycn5QgTSt4A+xJowYYL069dP9u/fb2PoEEyNGjUye6xojzcNxo0aNcp+0KVzAVSvXl3eeust6dWrl72eZgINNbl/7CdyZMZnrrZWofgbfSXH/7l7zlnLnJ8JB+Jl99OD5dy+vWZ10ZefkVw1bnQ2IY8AAmkkcPjwYTPgNmTIENc3PPnkk+b1oFSpUnLq1CmzB9zQoUPNa0rJkiXN4SQLFChgzv345Zdfutb1N9Tkmd375K/eQyTR6NHinbLferOUeLFzUEG0gx99KYcmTDc3keXKslJ6zADvzVFGAIEIEViwYIE8/fTTsmbNGnuPb7rpJmnXrp2UK1fODPDv2bNHZs6cKTNmzDDbvPPOO9KjRw+zZ9stt9xir6eZQENNcq/iYqKAAAIRIMD9WQScJHYRAQQQQAABBC67AIG3y34K2AEE0o+A9nJr3bq1fPbZhWBY/fr1zTfJy5Yt6xeiT58+og/ddbkOL9elSxeZPHmyq62+jd68eXNX3aEvFsvBYePMuvxPtJLctarJkXnfy6FJH9vtys7+r8TkdA8NZS/8N7Nv9HQ5OuvCg/vcD9aXIp3d3+W9DmUEELh4AR2CVq8PGzdutDf2/PPPS+/evSVv3rx2nZU5ffq02dtEg/R6PdDrQpEiRVwBfm27a9cu0eCclc6fPCU7Hn/JDK5nMR6mF3q6jWQukFd2Pd5PEo8dNZvlaX6/FG7/kLWK38/EYydk64OdXMuCuca4VqCAAAKXXcDj8cirr74qL730kr0veg/y4YcfivZa85e++OILadiwoblI71V++eUXad++vatpp06dZPTo0a467lVcHBQQQCACBLg/i4CTxC4igAACCCCAQFgIEHgLi9PATiAQ/QL6sLtBgwauN8cHDBhg9nzLmDFjQIBz586ZPeF0Eu7XXnvNfGil86s4kw7d5HwYdnLtZvmrxz89TZw92078ul729L4w7Fwwvde2t31BEnbvsr8uX7vmUvCR+naZDAIIhF5g8eLF5kNs5/xIc+fOtR9sB/pGnSdS53rT3rQffPCBtGnTxqepzsuUJUuWf+rPe2T3i8Pk1IqVkq3K/0nJgU/ZPdt2dBsoZzf8E/TLUqaMlB470GdbzoqjS3+VfQPedlZJ+a8npWiYStfKFBBA4JILaA9aHbJ2ypQp9nc3btzYvJ7kyZPHrvOX0blm9eUAHcr2yiuvFJ1j0pl02FtdbiXuVSwJPhFAIFIEuD+LlDPFfiKAAAIIIIBAOAgQeAuHs8A+IBDlAtu3bxcdcsk5tKS+Sa6Bt2CSPkwvWrRowKZHjhyx53QS40H6tkd7m71X8jRtLIU7Pmyvd8jo8Xbw7TF22Xu5veDfjL8eLCXe7S+xxjxxJAQQSBsBHRpSg/TO9M0330idOnWcVQHzc+bMMYd089egatWq5hBw1rIjC5bL/sEjJGPWbHLFB2+YPd2sZVsf7Gr3eNO6cnPHSsbs2azFPp97R02XY7Mv9I7NdsP1UurNZ33aUYEAAuEpoEH5e+65R77//nt7BzWIpi/+2MF6e4lvRnvKVa5cWdatW+e70KjR7dSrV++fZdyr+DWiEgEEwleA+7PwPTfsGQIIIIAAAgiEpwCBt/A8L+wVAlEjoG+P33bbbbJq1Sr7mB566CFzPpSkerrZjf/N3HrrrfLTTz95V0uFChVkw4YNdv2xn1bL3hfflJhcuaXM9HclY5bM9rI9r/1XTixaapfztHhQCrd9wC57Z44t+1X2vuzVg2XeJJFMMd5NKSOAQAgEdPginUPJ2dNt+PDh0q1bt6C3fvToUQnUM6V79+4ybNgwe1s7Hu8vZ7dtlQJd20j++2vb9Trn28627rkkr/pygmRwXE/sxv9mdnR8Uc4aLxlYKV/bZlKwhTuAaC3jEwEEwk9A547UOWOtpMNL/vzzz5I/f36rKtlPfalo4ED/vWP37t1rDn+rG+FeJVlKGiCAQBgJcH8WRieDXUEAAQQQQACBiBEg8BYxp4odRSAyBTp06OAz3JIOFVmiRIkUHdArr7wi/fv391mnXbt2ru3v6jlETq/5Q/I0M3q7dbjQ2+38mbOypUF71/qFn+8meWrd4qpzFrznd8t24w1Saqj7YbyzPXkEEEi9wIkTJ+Tmm2929Ra55ppr5Pfff5eUBOl1D+644w5XrxVrr3SOJp1nUtOJ3zfKnmf+eUDuPRfbwSmfy6EPZlirSUyhQlJ2mjsIby80Mn57xw57WWKvKedsRh4BBMJUQIeWtK4N1i5++umn8uCDD1rFoD4XLlxoDjXp3bhw4cKivfetxL2KJcEnAgiEuwD3Z+F+htg/BBBAAAEEEAhXAQJv4Xpm2C8EokBg0qRJ0rZtW9eRdOnSRUaOHOmqC6agc6VoEM87TZ48WVq1amVWJx4+KlubdDXzV0x4Q7KWujA85ZFFK2T/a8Ndq5ed9b7RMy6Hq85Z8OnBwvxuTh7yCIRUQK8Ves1wphkzZkiTJk2cVUHl9QG6c44ma6WtW7eacy9pee97U+XY519Ljpq3SfG+T1hNzM9trZ41h6u1KvM83FAKP9HUKvp80jvWh4QKBCJGQIeGvPbaa137q73ptT4mJsZVn1xBe+BXrFjRp1n79u1l3LhxZj33Kj48VCCAQBgLcH8WxieHXUMAAQQQQACBsBYg8BbWp4edQyByBRISEqRkyZKued30aJwPvlNydG+//bb07NnTZ5WDBw9KgQIFzPoTqzfInl6vSparK0jpES+62u7q85acXvmbXRd7261Son8Xu+yd8duD5T2jB0slerB4W1FG4GIF1q9fL9q7zZl0mDd9iJ0pUyZndVB5nSNO5yJxJh3CcuXKlXbVzh6D5Mza9VJsyPOS86YL331ywzb5q9tLdjvNlBo3RLKVLu6qcxZ85nejd6yThzwCYS3QsmVLmTZtmmsfNXCv9SlNOjSl9tz1Tl988YXUr1/frOZexVuHMgIIhKsA92fhembYLwQQQAABBBCIBAECb5FwlthHBCJQYPr06fLII4+49rxmzZqiwzClJuncTDrXkzPdc889Mn/+fLvKczZBjixYLtmvvcrV2y0h/ohsb+aeI6roq89Krluut9f1zvjtwfL1JDFef/duShkBBC5SoHPnzvL++++7tqLzJPXr189VF2zh6quvlo0bN7qaDx48WPr06WPXaYAtYc9+yVPTeEieIYNdb/WEsyqyXFlWSo8ZYBX9fvr2jn1ECj5yn9+2VCKAQPgI7NixQ8qUKeOzQzq0WmxsrE99chU6POXDD18Y5tpqf/LkScmePbtZ5F7FUuETAQTCXYD7s3A/Q+wfAggggAACCISzAIG3cD477BsCESxQpUoVWbVqlesI3n33XXnqqadcdcEW/G1vzJgx0rFjx2Q3ET/rW4kb/aHdLiZXbik7870kg2g+PViq/J+Uet23x529UTIIIJAqgf3790uRIkV81tXeadpLLaXp8OHDki9fPp/VdNi4SpUq+dS7KhITZUvjTnL+zGm7ukDXxyT//XfbZe+M396xwwdIbMWy3k0pI4BAmAk899xzMnToUNdeNW7cWObMmeOqC7agwf0hQ4a4mrdo0UKmTp3qqvNX4F7Fnwp1CCBwuQS4P7tc8nwvAggggAACCESLAIG3aDmTHAcCYSSwe/duKVWqlM8eaQ+U8uXL+9QnV3HkyBHJmzevTzP9g7BQoUI+9d4VO7u/JmfW/2lX53qgvhTt0twu+8v49GBpb/RgaU4PFn9W1CFwMQL+escWLlxY9u7da3REu9ATLdjv0F6wdevWdTX3HmbStdBROPHretnTe5CjRqTsJ6MkJk8uV52zQO9YpwZ5BCJLoFy5cuYQ2M69njBhgs/8tM7lSeV1mEkdbtKZnMNMOuu989yreItQRgCByynA/dnl1Oe7EUAAAQQQQCAaBAi8RcNZ5BgQCDMBf0Mt6XxNW7ZsSdWejhs3zqdnW7du3XyGnvS3cX/DTJYYZszVdk3gudroweJPkjoE0kbA3zCynTp1ktGjR6fqC/3N1zRjxgxp0qRJstvbO2yKHPviG7tdtiDmaqN3rM1FBoGIEtDgfrFixXz2eefOnX5fHvJp6FXx559/+vSqrVChgugcSRkzZvRq7S5yr+L2oIQAApdfgPuzy38O2AMEEEAAAQQQiGwBAm+Rff7YewTCUuCFF14QnU/Jmdq0aSOTJk1yVgWd9zfM5KZNm+Sqq65KdhuH5n0vB98eY7czh5n8ZIRIxsA9aejBYnORQSDNBfz1EJk4caI89thjKf7ugwcP+vSCLVmypGzbtk0yZcqU7Pa2PthVEo8dtdsV6NZW8jeuZZf9ZXx6x3ZoIQWb3euvKXUIIBBGAl9//bXce6/7v1Xtbbtv375U7aW/YSY/+OADefTRR5PdHvcqyRLRAAEELrEA92eXGJyvQwABBBBAAIGoEyDwFnWnlANC4PILdOjQQcaPH+/akZEjR0qXLl1cdcEUfv31V595npo2bSoff/xxMKvLnsFj5cSCJXbbHHVqSfFn29plfxl6sPhToQ6BtBHQYWl1eFpnWr16tVx//fXOqqDyw4cPF31D25nef/99eeKJJ5xVfvNn9xyQHW2ecS0rM3WYZC6c31XnLCQePS5bH+rsrJISI16R2KuvdNVRQACB8BOYMmWKtG7d2rVj2jNWe8imNJ05c8YM+h87dsxeVYN42nsua9asdl2gDPcqgWSoRwCByyXA/dnlkud7EUAAAQQQQCBaBAi8RcuZ5DgQCCOBZs2a+Ty4+vHHH6VatWop3ssnn3xSRowweqg5Ukoeym9t8YwkHjhgr13ouS6St/atdtlfZnvbFyRh9y57Ub6OLaVg03p2mQwCCIROIHfu3OJ8WK1bTkhICKqHmnMvPB6PVKxYUXQuSStpb7cNGzZIbGysVRXw8/B3P8qBIaPs5THG/JFlp71tl/1lji79VfYNuNAmY9ZsUu6z90ViYvw1pw4BBMJIQIPynTu7A+dDhgyR3r17p3gvP/nkE5/hbHW4XB02N5jEvUowSrRBAIFLKcD92aXU5rsQQAABBBBAIBoFCLxF41nlmBC4zAL+gmVxcXGSP3/gniP+dlkfxpcoUcL1UP7FF1+UV155xV9z37rz52VT3Tau+ismvCFZSxV11TkL9GBxapBHIO0Frr76alewTHu6aXA9pWnp0qVy++23u1b79ttvpXbt2q66QIWDk+fKoQ9n2otz3FFDir+Y9EPzvSM/kmNzvrLXyf6fG6XkYHevOXshGQQQCCuBmTNnivagd6a5c+dKw4YNnVVB5e+++25ZsGCB3bZGjRqyePFiIwYfRBCeexXbjQwCCISPAPdn4XMu2BMEEEAAAQQQiEwBAm+Red7YawTCWuCtt96SXr16ufZRe6OkND399NPy7rvv2qtVqFDBfCCfLVs2uy6pTOLho7K1SVdXk/LffJjk/G70YHFxUUAgzQUaNGggX375pf09OufSV19dCGbZC5LIaA857VG7atUqu1XHjh1lzJgL8zvaCwJk9r43VY59/rW9NN9jzaRgywZ22V/Gu3ds/idaSYGH6/prSh0CCISZwIoVK+SWW25x7VVqeufPnj1bHnzwQdd2tOdt+fLlXXWBCtyrBJKhHgEELqcA92eXU5/vRgABBBBAAIFoECDwFg1nkWNAIMwE1qxZIzfccINrr/766y8pXry4qy6pwg8//CD6xrgzLV++XHSi72CTd++1mFy5peyskUmuvmfoeDnx7SK7DT1YbAoyCKSJgM7/2K1bN3vbZcuWlS1bttjlYDJDhw6V5557zm6qcyvpEJN58+a165LL7B1uBN7mXgi8FXyqg+RrcGfA1c7uPSg7Wj/tWl5y5EDJXqGMq44CAgiEp4AG7AsUKODqVa/zu+k8b8GmQ4cOmUPc7t+/317l7bffFn1xKNjEvUqwUrRDAIFLKcD92aXU5rsQQAABBBBAIBoFCLxF41nlmBAIAwHv4UnGjRsn7du3D2rPdu/eLbfeeqvop5V0nreuXd2916xlSX1uuqe1vdicf+mLsXbZO3N6807Z1bmvqzr/E62NHix1XHUUEEAgdAJ79uwxh5R1bvHPP/8UvYYEk3R4Nx3mzZlS02sl7pP5Ev/fyfZmCnRrK/kb17LL3pm/BoySk0t/tKuZ382mIINAxAh0795dhg8fbu9vq1atZPLkC9cBe4GfzJkzZ+Shhx5y9dht3ry5uX6mTJn8rBG4inuVwDYsQQCByyPA/dnlcedbEUAAAQQQQCB6BAi8Rc+55EgQCCsBnSelcePG9j5VrVpV9GF4cvOd6B95Ok/T1q1b7XVTG3TTDezoOkDObtxsb6v0h29LlmKF7LKV0aGedjzeTxKNt9ediR4sTg3yCKSNQM+ePUV7iVhJe6+9/vrrVjHg5/fffy933HGHa/myZcukevXqrrpgCsd/+UP+fn6I3TRHrTuk+PMd7bIzc/Cjr+TQhI+cVZL95ipS8rUerjoKCCAQ3gK7du2SK664wrWTeh9SrFgxV513QXvLNWvWTHSYSSulNuim63OvYinyiQAC4STA/Vk4nQ32BQEEEEAAAQQiTYDAW6SdMfYXgQgS0IdSOmyTlfRh+uDBgyVDhgxWletT53nq1KlTSHq6WRs+snC57B80wipKrvp1pGiPC73gdMHJtZtl74D3fIJuZg+Wuf815oTLaK9PBgEEQi9w/PhxqVSpkuu/fQ3eN2zY0O+XnT17VkaPHi09ergDXakNuplfct4j2x7tLef27bW/s/SktyRLicJ22XM2Qfa9P8M1F5y1kN6xlgSfCESWwPvvvy+dO3e2d7pWrVoyZ84cyZUrl13nzKxdu9YcHnfRokV2ddOmTWXq1KmS0p5u1ga4V7Ek+EQAgXAS4P4snM4G+4IAAggggAACkSZA4C3Szhj7i0AECRw9elRatGjhGoapbt260qtXL9EecDlz5pRt27bJH3/8IWPGjJF58+bZR6dzNOncAg8//LBdl6pMYqLsfnmknPrpZ3t17cmS49b/k8RjJ+TUb+vl5JIf7GXODD1YnBrkEUhbAZ2T7b777nP1du3SpYt06NDBDMrpt2ubX3/91Qzgb9y40d6hatWqyahRo+TGG2+061KTOfH7RtnzzEB71Zh8+SRvi0YSUyCfnPlzm5xYvNwVmLMbGplSo1+VbFeVdlaRRwCBCBDweDwyYMAA8x9rdytUqCD9+vUTvWcpVKiQ/P3337Ju3TrRFwKcQ1Nq+4EDB0qfPn1SHXQzv5N7FYueTwQQCDMB7s/C7ISwOwgggAACCCAQMQIE3iLmVLGjCESmwLlz56R3797yzjvvBH0AgwYNkqeeekpiY2ODXifJhucSZf/E2XJkxmcBmxXo2kYOjftYzp85bbfJ38mY3+0h5nezQcggkMYCBw4cEB2uTedtCyaVLFnSHKJSA/SBetIGsx1nm5PrtsiBdz+Us9suDHfrXJ712kqS9eqycnTWl3Y1vWNtCjIIRKyAzu326KOPBr3/7dq1M4NuxYsXD3qdJBtyr5IkDwsRQODyCXB/dvns+WYEEEAAAQQQiFwBAm+Re+7YcwQiSmDnzp0yduxYmTVrlvnWuPfO67xu2tulTZs2yc6t4r1usGWzh9umHXJ25x5J+PugZC5aULJVKivZy5aSU1t2yl/dX3ZtqsyUdyRzkYKuOgoIIJD2Aj///LPZg23JkiWuHnD6zTr8W+3ataV+/fpmj9rs2bOHfoeMHjCnt+6WM8a14sz2PSJGOWv50hJrXC8yF8wnu3q/Kad/XW1/b446taT4s23tMhkEEIhMAe2pr0NGfvjhh6JDSh47dsx1INdcc405BK4OpX2xPWxdG3YUuFdxYJBFAIGwEuD+LKxOBzuDAAIIIIAAAmEuQOAtzE8Qu4dANArosE5xcXHmA628efOK/hOq3iqp9do/cZYcmTbbXj17tapScmB3u0wGAQQuj0CiMQTbvn37RHvPFihQQHLkyHF5duTfbz1/8rRsadzRtQ+lRr9mDDN5hauOAgIIRL6ABt60p4cG/PMZQ8+mdg63UElwrxIqSbaDAAIXK8D92cUKsj4CCCCAAAIIRLsAgbdoP8McHwLpUcB4UB83539y4vtfRM57JMedVZMcMvL82QTZ3ryHMefbUVur+Bt9Jcf/VbTLZBBAIDoFTu/YI/FTPpcE4zNTiSJSqGMTyVK8UMCDjft0vsS/P9lenrVSRbnivb52mQwCCCAQlAD3KkEx0QgBBNKnAPdn6fO8c9QIIIAAAghEkwCBt2g6mxwLAgiYAvvHfuIzn1upsa9LtjIl/ArFf75I4t4bby/LZMzXcuWk18XohmfXkUEAgegTSDh4SHY+1ts1t2PsbbdKif5d/B6sxwjSb2vVUxIPHbKXF37xKclzx3/sMhkEEEAgGAHuVYJRog0CCKRHAe7P0uNZ55gRQAABBBCIPgECb9F3TjkiBNK3gNHDbVPdR30Mir76rOS65Xqf+sTDR2W78SD9/JnT9rJAbe0GZBBAICoEDn48Tw6Nm+Y6lixXlpXSYwa46qyC9zBvZm+3d/qIxMRYTfhEAAEEkhfgXiV5I1oggEC6FeD+LN2eeg4cAQQQQACBqBIg8BZVp5ODQQCBs3sPyo7WT/tAXDljpGTKl9tdbzz42v3yCDn14wq7Pn+n1kkOS2k3JIMAAhEvsGfIeDnx3SLXceRqWE+Kdm/pqtPCqY3bZXfXF+36mEKFpPT7r0hM7px2HRkEEEAgGAHuVYJRog0CCKRXAe7P0uuZ57gRQAABBBCILgECb9F1PjkaBNK9QOLR47L1oc4uh3wdWkjBZve66sSYW2XP0AlyYsESuz5X/TpStEdru0wGAQSiW2Dv8GlybO48+yAzFSkqpYa/6BOkP7l+i/z97Ot2z9iMWbNJydEDJWupova6ZBBAAIFgBbhXCVaKdgggkB4FuD9Lj2edY0YAAQQQQCD6BAi8Rd855YgQSPcC29u+IAm7d0lMvnxS4u2+krVkEZfJeWOepj0DRsmpFb/Y9dmr3yIlXzICdgwZZ5uQQSDaBY4uXSX7BrxjHmaB7u0l/723i2RyDxt5fOU6+bvPYJtCg25FX+0pOf6vol1HBgEEEEipAPcqKRWjPQIIpBcB7s/Sy5nmOBFAAAEEEIhuAQJv0X1+OToE0qXA4e9+lANDRpnHnqPWHZL3wdqS7YpikhB3RE6sWieHp38uiQcOmMtjcuWWAt0fkzw1q6ZLKw4agfQscP70Gdn15Ktydvt2M1Cfv11TyXFzZcmYKZOc3rFHjsxdKCcWLbWJctxRQwp3a+HTI85uQAYBBBAIUoB7lSChaIYAAulOgPuzdHfKOWAEEEAAAQSiUoDAW1SeVg4KAQTi5yyQuJETk4TIdV9tKdSxicTkjE2yHQsRQCB6BRKPHJPdvYaawbdAR6nzuRV6up3kqlo5UBPqEUAAgRQLcK+SYjJWQACBdCLA/Vk6OdEcJgIIIIAAAlEsQOAtik8uh4ZAehdIiD8iR75ZZjxQ/0sSD8ZLhmxZJVOhApK1YhnJfev/SUyeXOmdiONHAAEV8Hjk2Irf5YQxrOS5v/aKx+gJF5M/r2QqXlhy3nydxFYqJ5IxA1YIIIBAyAW4Vwk5KRtEAIFoEeD+LFrOJMeBAAIIIIBAuhQg8JYuTzsHjQACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggEGoBAm+hFmV7CCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC6VKAwFu6PO0cNAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQKgFCLyFWpTtIYAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIpEsBAm/p8rRz0AgggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAqEWIPAWalG2hwACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggkC4FCLyly9POQSOAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCIRagMBbqEXZHgIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQLoUIPCWLk87B40AAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIBBqAQJvoRZlewgggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAulSgMBbujztHDQCoRcYMGCAvPzyy6HfcBhvceHChVKzZs0w3kN2DYHwFciQIUP47lwI90yvEXqtICGAQHgJpIdrEPcp4fWbY28QiASBu+66SxYtWhQJu3pR+8j92UXxsTICCCCAAAIIBCFA4C0IJJoggEDyAgTekjeiBQIIXBBIDw+99Wh5sHPhnJNDIJwE0sM1iMBbOP3i2BcEIkOAwFtknCf2EgEEEEAAAQTCX4DAW/ifI/YQAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgAgQIvEXASWIXEUAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEwl+AwFv4nyP2EAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIAIECLxFwEliFxFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBMJfgMBb+J8j9hABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQCACBAi8RcBJYhcRQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQTCX4DAW/ifI/YQAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgAgQIvEXASWIXEUAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEwl+AwFv4nyP2EAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIAIECLxFwEliFxFILwJHjx6Vv//+WzJlyiQlSpSQbNmypZdD5zgRQCCFAufOnZP9+/fL4cOHpVChQlKwYEHJkCFDCrdCcwQQQCD1Ah6PR+Li4uTAgQOSO3duKVKkiHkPk/otsiYCCCAQPQKnT582/7Y7e/asFCtWzLxORs/RcSQIIIAAAggggEDSAgTekvZhKQIIpKHAmTNn5KuvvpLJkyfLd999J8eOHXN9W+HChaV58+by1FNPSdmyZV3LKCCAQPoT2Lx5s0ybNk2mTp0qGzdu9AGoVq2a9OjRQx566CEefvvoUIEAAqEQiI+Pl5kzZ8qkSZPkp59+8tlkhQoVpGPHjtKhQwfJmzevz/LUVCQkJEhMTIxkzJgxNauzDgIIIHDJBH744QeZMmWKfPrpp+YLUs4vzpUrl9SuXVt69uwpNWrUcC4ijwACCCCAAAIIRJ0AgbeoO6UcEAKRIbBixQpp27atrFu3zt5hDa7p25CbNm3y+UOtRYsW0q9fP6lUqZLdngwCCKQPgVOnTsmrr74qgwYNch1w1apVRQP4a9ascdWXLFlSXnjhBfPht/agJSGAAAKhENCHyV26dHG9KHT99ddLbGysrF271lWv39enTx959tlnJX/+/Ml+/erVq2XOnDmyd+9e+euvv8zPHTt22PdDt99+uyxZsiTZ7dAAAQQQuBwCe/bsMa+Pn332mf31GmjTa6SOaLJ161a7XjMaeHvppZekTp06rnoKCCCAAAIIIIBAtAgQeIuWM8lxIBBBAtOnT5dHHnnE3GP9g2zw4MHSqFEjKVWqlH0U+/btM3vDaW83qyectl28eLHceOONdjsyCCAQ3QJHjhyRevXq2T1LGjZsKL1795abb75ZsmTJYh68DmG0fv166du3r3z55Zc2SPv27WXMmDH0ErFFyCCAQGoEdEjJ7t27y4gRI8zVtVeb3rvUqlXL7tV2/vx52b59u3nNGTJkiP01+tB50aJFki9fPrvOX+auu+4y2/lbpnUE3gLJUI8AApdb4I8//pDq1avbf7Npj7Y2bdpI5cqV7WHA9e+55cuXS9euXV2jFkycOFEee+yxy30IfD8CCCCAAAIIIBByAQJvISdlgwggkJTA/PnzpW7dumaT1q1byzvvvCMFChQIuIq+7a1/jOlDK00afPvxxx/l2muvNcv8CwEEolcgMTFR9GH0999/b/63//HHH8u9994b8ID14bgG2jp16mS36datm7z33nv2gx97ARkEEEAgSIH+/fvLK6+8YrZ+66235Mknn5TMmTMHXFt7prVs2VJ2795tttHeuTqkts4DFygNHDhQFixYIDrf7apVq3yavfzyy6L7QUIAAQTCSUB7ulWsWNEMut10003mFALXXHNNwF08efKkPPfcc/aLDNrwo48+MqcXCLgSCxBAAAEEEEAAgQgUIPAWgSeNXUYgUgX0D62rr77afBClvVZmz55tzlmS3PEcP35cypUrZw+3pHO/6UOpEiVKJLcqyxFAIIIFxo0bZw4XqYewdOnSoOcDGT58uNk7xTp0fVitD61JCCCAQEoFdAhJ7bWh6c033zTnJgpmG3qfUqVKFbup9ljTl4iCmaft0KFDPsNTauDu7rvvtrdHBgEEEAgHAX3JQOff1WG+V65cKfp3WjDp/vvvF+ewlN9++605/1sw69IGAQQQQAABBBCIBAECb5FwlthHBKJEQN/m1rH8NXXu3Fl69eolOq9bMEnnVdEeclbSOVOGDh1qFflEAIEoE4iLi5Mrr7zSHrbogw8+kFatWgX10FqHnrzuuutcQxnpvElFihSJMiUOBwEE0lJAe9HqcJJWr3sdXlJ70ebMmTOor+3QoYOMHz/ebvv5559LgwYN7HKgzC+//CLaS86ZdJi2YL/XuR55BBBAIK0EdAqAmjVrmpvXlwv0b70777wzqK/bvHmzlC9f3m6rveU0cEdCAAEEEEAAAQSiRYDAW7ScSY4DgTAX0KGT8uTJ49pLfai0YsUKV12ggs6dUq1aNfn555/tJvpGeN68ee0yGQQQiB6BAQMG+PRS++qrr5IcatJ59DrXm/MBt27PCvw725FHAAEEAgno0I/evcz69Oljzu8WaB1nvQ7B5uydH+w8bcOGDZMePXrYm9L7Hx1mm4QAAgiEk8Btt90my5Ytc+1SfHx8snNaWivokJPOFyn1mqtDjJMQQAABBBBAAIFoECDwFg1nkWNAIAIE9C3vRo0a+eypvk0ebBo0aJD07dvXbq7zrDzzzDN2mQwCCESPwA033CBr1qxxHZA+nNHersGkhIQEyZIli91U54fUXm+xsbF2HRkEEEAgKQHtma/3Gs6k80zqSwDBJg3c6cNkK+kLR9692axl1qf3EGz9+vUze5JYy/lEAAEELreAjkxQsGBBn93QlwT0ZYFgkg4jri8kWKl+/fryxRdfWEU+EUAAAQQQQACBiBYg8BbRp4+dRyByBHSoJR1yyZmuv/56Wb16tbMqyfzMmTOladOmdhudS2DXrl12mQwCCESPQO7cue1hJq2jCnaYNqu9zg25detWqyiTJ082h6u0K8gggAACSQjoENc61LUzpXSo665du8qoUaPsTbRr1841/KS94N/MuXPnzPnddGhJK33zzTdSp04dq8gnAgggcNkFNmzYIBUrVvTZjwMHDvgNyPk0NCq8ewVrmy1btgQ9FYG/bVKHAAIIIIAAAgiEiwCBt3A5E+wHAlEusHbtWqlcubLrKBcuXGjPC+BaEKCwatUqqVKlimvp4cOHfYawdDWggAACESnw6KOPmoEya+f1Lei5c+cGNcebtY53rxEd0uj111+3FvOJAAIIJCkwYcIEad++vd1GX/jRIa+LFi1q1yWX8R42Mrl5jHSOo//85z+uzXKv4+KggAACYSCgLwnoULr79++392bIkCHSu3dvu5xcRkc+yZgxo6tZSoYVd61IAQEEEEAAAQQQCDMBAm9hdkLYHQSiWWD9+vWivdby588v9erVk6uuuipFh6tzuum6zqQ95rTnHAkBBKJLQB/oaA817dV63XXXScOGDSVTpkwpOkh9+PPGG2/Y6zRp0kRmzJhhl8kggAACyQnMnz/fnF+tdOnS0rhx46DnLrK2q8Om6fXLSjrsrc57Gyi9++678vTTT9uLUzIfrr0SGQQQQOASCOjfZuPGjZPExES54447pHr16in+Vu+hxUeOHCldunRJ8XZYAQEEEEAAAQQQCDcBAm/hdkbYHwQQCCjg763IlA49F3DjLEAAgagTGDx4sLzwwgv2caV0eFt7RTIIIIBAKgWWLVsmt912m2vt+Pj4gAE8nQ9X722sRE9dS4JPBBCIRgEdRvfbb7+1Dy2lw/naK5JBAAEEEEAAAQTCTIDAW5idEHYHAQQCC+gb4nny5HE1GDFihOj8KSQEEEDAW+D555/3GVpSA/gkBBBA4FIJzJs3T+677z7X1/3222+ivTy8k/b0zZw5s6tae8zpULskBBBAIBoFbr75ZnMIX+vYHnjgAZk1a5ZV5BMBBBBAAAEEEIhYAQJvEXvq2HEEokNg8+bN5hBO+/btk4MHD0pMTIw5rJzOB1epUiWzbB2pv0m8eRPc0uETgegXOHnypCxdulT0uqHXiyNHjkipUqXM4Wb1IXaBAgVcCK1bt5YpU6a46nSd3Llzu+ooIBBOAosWLQp6d2rWrBl0WxqGRkCHVNN52HSoa70O6VBrek3Ra5D2qtUhKZ1p/Pjx0qFDB2eVBJrDSOeP04fQzpRU7zhnO/IIIIBAOAgcOHBAlixZIrt37zavkWfOnJEKFSqYf9/p0OGxsbGu3dTr57Fjx+w6hte1KcgggAACCCCAQIQLEHiL8BPI7iMQiQL6x9WwYcNk4sSJsnXr1oCHUKNGDZk0aZI9F5zOs1K3bl1X+5dffln69+/vqvMunEzwyLR1p+S3vedk/9FEOW90eCmeN0buLptFGpbLJhkzuNdYcyBBvtx8VtbtS5Azxrr5cmSUm4pnlmaVskverF6N3atSQgCBNBD44YcfzJ5rzuHX/H3Ne++9Z84LogF8Td5vUWvdqVOnJFu2bJoNKmnAf86cOfLnn3/Kpk2bzAfs+nD98ccfl7Jlywa1DRohEEjACrINGDDAbGKVA7X3V6/BNysAd+edd9p5f22pS73Ajh07zOvQ1KlTXQ+Jvbeo1wadW9IK8Pft21cGDRrkava///1PatWq5arTwttvvy09e/a0663hcU+cOGHOT6kvHuh1SK9h5cqVk+bNm4uecxICCCBwOQX0hYSPPvpI9D5MXyAIlAoXLix6Da1du7bZ5Pjx46LzXjqT/v2n17qUpNOnT4v2Lv7ll19k+/btotfrnDlzmtfJa6+9Vh555JGAw/um5HtoiwACCCCAAAIIpESAwFtKtGiLAAIXJaB/lE2YMEH69esn+/fvt7elQ4ronCb6lrg+MNdg3KhR+u7oeQAAQABJREFUo+w/3HR+FJ2s+6233pJevXrZ62kmuaEmP99yRkYuPi7nNdrmJ+XMGSOjG+WRIrEZzYDckJ9OyMK1p/y0/Kfqhbq5pWapLAGXswABBEInoD3b+vTpI59++qm9UX1o061bN/PN6aJFi0pcXJwsXrzYfNCtjRo3biyzZ88Wvd54D9mmy4MdalJ7s+gD8y+//FJX85usXiv6EGnmzJmSI0cOee2116RMmTJ+21OJgApocE0DbakJsgUrqC+laEruxRSzEf9KUuDw4cNmwG3IkCGudk8++aR5b6K9bjWgr9eMoUOHmvc3JUuWFB1OUnvhNmjQwOc6EmioSe+2GoTTwFrLli0DBvv0IfWHH37IiwCus0MBAQQulcCCBQvk6aefljVr1thfedNNN0m7du3MwJe+hLBnzx7zPmnGjBlmm3feeUd69OghK1askFtuucVeTzMpGWpSR0x5/fXXRXsWO3vNuTb4b8H6Tn/LqEMAAQQQQAABBNJEwHgARUIAAQTSXMCYn81jPBDX6Jf9jzFniWfLli0Bv9sYRtJsa/Qq8Rh/THmMYePsda3tGG9XBlx/6tpTnnvGHjD/aTIj3rNw5xnPkTPnPWsPJngenB5vL2vwYZzn9DmP56UlR+264StPeA6cTPQcO3veU2/CQbu+7viDnnOJAb+SBQggECIBY14jn//ejYfLnrNnz/r9BiNg7zHemjbX+e9//+sxeqj5rK/XkuSSEbDzGEF+17rGQ3SPEVjzGMMneYyhkzzdu3c3l+v3GQ+RXG2NB0nJfQXL06nAwoULPUbPNNfvxfp/WVp9GgE4j/5DSp2A0bvMYwyR5jpnxtyRHmN4Sb8bNAJwHiMQZrY3eqOZbYyXBVzr67netWuXz/p6bfP+Heg1y6ozHkZ7jJcMPEbvN8+qVas8Rm84e5m2+/vvv322SQUCCCCQVgLnjbcaX3nlFfs6pNcqvRYZvdUCfqUxcoHd3nhZwWMEzOyyda3r1KlTwPWtBXqvNnbsWPu+z1pX78F+/PFH8xq9bds2z2effeZp1aqV/R3Gi53WJvhEAAEEEEAAAQTSXEDf/CYhgAACaSqwc+dO1wMi/ePIeNvfo380JZUSEhI89957r/nHktGLxKMPv60/rKzPQH/c/ffXE3awbOKaEz5fs/3oOXu5Buce+vhCIO6TDafs9p3nHXG107a/7PX/4N9eiQwCCFyUwLvvvuv6b10ffK9fvz7ZbepDaevaMHr0aDtv1d1zzz1JbuPcuXM+Af4mTZqYD7q9V+zYsaPP9vV7Onfu7N2UcjoXuBwBN+s37/wkAJeyH6LRI9Hnoe7cuXOT3cjevXs9VrDtgw8+8HudMOY88tnOTz/95LetnsNp06b5tNcXAZzn9/bbb/dpQwUCCCCQFgLGnLuugJZei/QFS6OHcLJfN3jwYPPaZQy362nfvr3rOqbbMYbmTXIb+oJD06ZNXetVq1bNoy9K+Ev6t6L1YpZ+6r0eCQEEEEAAAQQQuBQCDDVp3N2REEAg7QR0nH0dQsQ5tORLL71kDrMVzLfqECI6nFygdOTIEXseFavN+rhz8tTsw2bxgSqx0vlG9yTeVrtGU+Ll9OnzVtH8vOOa7NKveg4zf+SMR5pMjnMt18KgBnnkP0Uz+9RTgQACFy/wwgsviPFQxt6QDi2pc3bocG7BpGeeeUZ0OCF/yeip4jPXktVOh6bUuZl0OFwrGb1yZdasWZIli+/wsjqfiO6b99BG48aNE+NBkrUJPtOxgA4lmdZDSqaGV4ehZAjKpOV0iFkd9tGZvvnmG6lTp46zKmBe54XU4dL8papVq5rDq3kve/PNN+XZZ5/1rpbly5eb81X6LDAqdLhLHXLbSkm1tdrwiQACCFyMgPHigBgvMsn3339vb0bnrNQ51vzdL9mN/s0YD7mkcuXKsm7dOu9FZlm3U69ePb/L9O++Bx98UHR4SysZL2naw31bddan97yZWq9DYl533XVWEz4RQAABBBBAAIE0EyDwlma0bBgBBHTOk9tuu02MIZFsjIceekh0fP+MGTPadcllbr31VjHeBPdpZvSCkQ0bNvjUP/LpIYk7lCiVy2SRt2vn9lluVTSdeUgOH0m0iubn9Fb5JX+2f/Zt17FEaf/xIdfyjBkzyOxH80v2TBlc9RQQQODiBXSeNOMtZteGUvog+bvvvjMfCLk28m9B54rTBzb+kgb7NOhnJQ2qGcNVSr58+awqn0+df8573idd5+qrr/ZpS0X6EQjXgJv3GTB64okx9KV3dbov69ySOj+RM6g+fPhwc27JYHGM4bUlT548fpsbQ9XKsGHDfJbdd9995oNr5wJrHklnnTM/ceJEcx4lq+6xxx4TrSMhgAACaSXgHfA3hpc05+XOnz9/0F+pL2EOHDjQb3uj17AUKVLEZ5m+INWwYUPXddIYctd8OSFbtmw+7ePj4815Nr0X6MtcVapU8a6mjAACCCCAAAIIhFyAwFvISdkgAghYAh06dDAnu7bK+mnMjyQlSpRwViWbN+YP8Pt2vk7arZNpO9PnW07L8IXHzarxzfJJqVwxzsWufIMP4+Xs2Qs93q6/Mou8ebc7UNdy9iE5EPdPcC5LlozS7fYcUu/KrK7tUEAAgYsX0Defr732WteGAj2gdjXyKhjDH0mOHP/0WvVaJMackqIPiLyTPoTRXijOpD3dAvVYsdqNGTNGnnjiCato9oDTB0YZMhCYt1HSWUZ7uGmPskhJ9H5znylj/jSzd5mzJ8Y111wjv//+e4peGNKt3nHHHa4eIdY3GXNVijFnrVU0P4353SRrVve9hQb1e/fu7WrnXfDumRfohSTv9SgjgAACqRGYMmWKz/UrqZeaAn2HvvihveS8k770pKOd+Ev+gnVJ9V7TFz/9Bdj0xQhjyEl/X0EdAggggAACCCAQUgECbyHlZGMIIGAJTJo0Sdq2bWsVzc8uXbrIyJEjXXXBFDS4pkE87zR58mQxJsx2Vbf57LD8feCcVCiVRUbUdQfRnA3jjSEmmxtDTTrTM3fn8gmqJRhxuV/3Jch5YyaBm4tlFqPDGwkBBEIsoMGyG2+8UTZu3Oja8o4dO+SKK65w1QVTyJ07t6u3iq5jzBEpxnyTPkExY64PM+Dn/G59g3r16tXJfpUxn5u8//77djt6m9gU6TITaUE36yQRfLMkxLxv0fsXZ9Je+sZcj86qoPIaXNOH1N5p69atcuWVV7qqtVe/9u53Ju2tkVSPW207ffp0eeSRR5yriV7TYmICv3TkakwBAQQQCFLA3wtSGuzX+pRec3TEkooVK/p8sw7VrUN2e6cffvhBatSo4arWUQecQ5O7FhoF7bWs94PO9Oqrr0rfvn2dVeQRQAABBBBAAIE0EyDwlma0bBiB9CuQkJBgPuR2zuumGv4eNgWj5G98fl3v4MGDPkOIWL3Yhj2QVyoVyBRw8wt3npXB84+6ls9pU0BiMxNZc6FQQOASCOhDlo4dO7q+ScvaoyylSecO8TeUrfYc8R4WUrf98ccfS/PmzV1fo8E0Z08210JHQeed0168VvLXk8Vaxmd0C9x1112iQ0yGIunwj8EMAanfF8rv1B4I6TmtX79etHebM2kPWX1AnClT4PsJZ3tnXueI0x5pzqRDWK5cudJZZeaHDh0qzz33nF0faB44u8G/GX/3R3v27JFixYp5N6WMAAIIXJRAy5YtZdq0aa5t6MsFWp/S9PPPP/udu/KLL74QnV/XmfS+rnr16j7TDuzatcv8e9PZ1juvLzVMnTpVdJjKunXrSuPGjb2bUEYAAQQQQAABBNJMgMBbmtGyYQTSr4C/N7D1IWJqH+rpcHM6v4oz6aTe8+fPd1aZ+UW7zsqJBI/UL+sessm74ZCfTsj//jhlV+fNEyMzmgSey8luSAYBBEIqoA9D9GG3s8eZfsHixYvNodpS+mU61KO/h87Lli0zH9w4txfou4PpaaK98cqUKePcnGzbts2nztWAQtQJaOBLe7pdTABM///Yv39/0yaYgJs/RN0HTdp77WJSeu795t2DVR11DqJ+/fqlilTnevS+rmnvDO2l4Z3q1asn33zzjV2dXE8Oq+Hjjz8uY8eOtYrmpw7TpsO1kRBAAIFQCfi759Ft6/C8sbGxKf4aHZ7y4Ycf9llPR0DInj27q/6zzz6T+++/31WnI57oyCckBBBAAAEEEEAgnAUIvIXz2WHfEIhQAR1PX8fVd6Z3331XnnrqKWdV0Hl/29OeMN49ZILeoNHwkU8PSdyhf+Zu0/XuuCa79Kvuf16olGyXtgggkDIB7zmKdG2deyMuLk4yZ86cso0Zrf1tTx9Cay8Q76GQ/A3vFiio770j3vOc6FCW+vY1Kf0IXOzQkmkV5ArX/QrnX4b20C9SpIjPLmrvNO2lltJ0+PBhv8NE6pBslSpVcm3O3/xu/np9uFb6t+AvuMdQk/6kqEMAgYsR0B652jPXmbT32Jw5c5xVQef15QLvUQhatGhh9k7z3ogG3TT45kxfffWV3Hvvvc4q8ggggAACCCCAQNgJEHgLu1PCDiEQ2QI67JoOv+ad9K3v8uXLe1cnWz5y5IjkzZvXp50+JCtUqJBPfTAVZ4x4W8OJB11Nn7snl9xdOulecq4VKCCAQEgE/PUy0bmRdNjG1CSdu2PQoEGuVfWB0euvv+6q04IGPqyeQtbCYF8S0HlIJkyYYK0mnTp1ktGjR9tlMtEtoD3cdHjJlCbt0ebs4ZbS9VPS/mICcNpDXfczvSR/PfU1YK89aDNkSPkQ1NojX4c1c6ZAw0wuX75cqlWr5mzqdyhtVwOjcOjQIcmfP7+rmhcAXBwUEEAgRALlypUzpwxwbk7vgbzn83YuTyp/8803iw436Uz+XjgI9BJDanvaOb+PPAIIIIAAAgggkNYCBN7SWpjtI5DOBPwNHaJzpGzZsiVVEv7mfurWrZvP0JMp2fiyvxJkwLwjrlVmG/O75WB+N5cJBQQuhYC/HhsfffSRz7xrweyL9vQoUaKEeM8vuXPnTr8vBNxwww2yZs0a16bXrl3rM8+Tq8G/Be0d4/wefXDfrFkzf02pi0KB1ARjLlcwK7UBuMu1v5fj5+JvSOuLCab7mwtpxowZ0qRJE5/DGzFihDz55JN2vQ69q9eh5NK8efPkvvvuczXT7ev3kBBAAIFQCQQawjvQvVVy3/vnn3/69PytUKGC6Dyb3nP0fv7559KoUSPXJh944AGZNWuWq44CAggggAACCCAQjgIE3sLxrLBPCESwwAsvvCA6h4kztWnTRiZNmuSsCjrvb5jJTZs2yVVXXRX0NrwbDv7xhCxce2F+t9y5Y+STpszv5u1EGYG0Fjh27Jjkzp3b52tS+9+4v2EmH3vsMZk4caLPd3g8Hp8HPDrEpfayTS6osnnzZp8evNu3b5fSpUv7fA8V0SeQ0kCW1cPtcvcg0x56KZmLTvc3tXOzRtpZ99f7Qq8bev1IaTp48KBPj3ztiaZzQGbKlMlncx06dJDx48fb9cG+XKTDd7/33nv2eppJ7T67NkIBAQQQcAh8/fXXPsM6ao9gnU8yNcnfMJMffPCBPProoz6bGzlypOg10ZmCHZnAuQ55BBBAAAEEEEDgcggQeLsc6nwnAlEs4P0ASQ9V/2jq0qVLio/6119/9ZlbpWnTpvLxxx+neFvOFZrOPCSHjxjjTf6bbq+UTV6skdMq8okAApdIQB9Ea49YZwo2+OVcx8r7mwfk999/l8qVK1tN7M/4+HgpUKCAXdZM/fr1RYc6Si7p8Eo61KSVLuYBlLUNPiNDIKVBt7Saxy21WpG+/6k97uTW0yGydahsZ1q9erVcf/31zqqg8sOHDxftQedM77//vjzxxBPOKjvfoEEDc25KqyLYHr/+9lnnsixWrJi1KT4RQACBixbwntNWN5ja3rVnzpwxX0zQF6+spPdQ2nsua9asVpX96W9uuSVLlsjtt99utyGDAAIIIIAAAgiErYDxxjcJAQQQCJmAERjzGBc81z8//vhjqrZvvOHo2o5u13gQlqptWSsdO3vec8/YA65/5m8/bS32+3ngZKKn53dHPF9uSbqd35WpRACBgAJGUMznv3FjXqSA7ZNa8Ndff/lsS69HgZIxpJFP+9deey1Qc1d9q1atXOsavWJcy42Aosd42cDzyy+/uOopRLaAEURznXfv/9d5l7V9OKZoOY5Q2hoBf59zm5CQkOKvOH/+vMcYMs21LaO3m8eYjyjgtqpWrepqv27duoBtrQWrVq1yraO/vRYtWliL+UQAAQRCJmDMX+tzvRkyZEiqtj9z5kyfben2A6WOHTv6tDfmtwzUnHoEEEAAAQQQQCCsBOjxZvylSkIAgdAJ6DwlOl+JM8XFxUn+/PmdVcnm9U1InavJ+Ubkiy++KK+88kqy6ybV4OttZ+Tt/114y1LbzjLmd8uZxPxu7/x8QuatPiWVy2SRt2v7DouX1PexDAEEAgto7wz979yZevbsKW+++aazKqj8oEGDpG/fvnZb7Tm3ceNGKVq0qF3nzGzdulXKlSvnrJJPPvlEHnroIVedd8G4i5M8efK4rk0ffvihtG7d2m766quvil6v3nnnHenRo4ddTyZyBXSIRh2qMdgU7vOjRdvxBHteArXznmtSe7ppj7eUpqVLl/r0xPj222+ldu3aATd16623yk8//WQv1x4hWbJkscv+MnqdfPvtt12LAvXudTWigAACCKRQwAiWiY444kxz586Vhg0bOquCyt99992yYMECu22NGjVk8eLFEhMTY9c5M9prXHtqO5Peh5EQQAABBBBAAIFIECDwFglniX1EIIIE3nrrLenVq5drj1PzB9LTTz8tOoa/lXTSbX0Ili1bNqvK5/O88XfYl1tPyx/7E6VozgzSrGJ2ifUKqD2/6Jis3HzGXjdXrhj5tFng+d30T7tGk+PlzJnz8uitOaXVtYG/394oGQQQCEogMTHRZ86joUOHyrPPPhvU+lajHTt2SJkyZayi+alDI7Vs2dJV5yzow23v64nRO1eqVavmbOaT9zcErgbxrrzySrutNV+UBjfuvPNOu55M5AokN++f88jCPehm7WtKg2+p+X+59V3h/uk93OO9994rX331VYp22+ghZ14/jN5o9npGbw0ZM2aMXfaX0evUtGnT7EXJOR8+fFiuuOIKV/D/YubStb+YDAIIIOBHYMWKFXLLLbe4lgRzv+RawSjMnj1bHnzwQVe1viBVvnx5V52zoPNWtmvXzq7Sl6qOHj1ql1OS0WF8+/XrJ5MnT5bq1aunZFXaIoAAAggggAACqRIg8JYqNlZCAIFAAmvWrJEbbrjBtdgYAk6KFy/uqkuq8MMPP4i+AelMy5cvF32YHShpgKzd54flr33n7CZlS2SR9++90EPt3HmRhh/ESWKitv4nJdeLbeaG0zL2++PGm5gZ5JNW+SWHVyDP2g6fCCCQOoGHH35YPv30U3tlnQ9S54UMNulDap2bbd68efYq+ha2vo2dXPKeI0kfmN94441JrqZvfevb31bynt9t//79UqRIEXOxMbycxMbGWk35jFCBlMyLpm/n9+/fP2KONJqPLSUnQa85xvDW9io69+SWLVvscjAZfWlA5yOykl4bNmzYIHnz5rWq/H7q78XZmz+568Yzzzxj9qa1Nqbf8+eff0q+fIFfIrLa8okAAgikVEBfKtA5cZ2jkMyYMcOc5y3YbRnDQ0rFihVF75GspL129UXLpNLKlSvlP//5j6tJML2CXSsYhc8//1waNWpkVmteX7YgIYAAAggggAACaS1A4C2thdk+AulQwHvIpnHjxkn79u2Dkti9e7fosEv6aSUdurJr165W0e+nvyEkNVg2r20Bu/3czadlxKLjdlkz1StmlZdvy+Wqswr7T56XtjMPS0KC8VkjpzxSid5ulg2fCIRKQINuGnyzkj5E/vvvvyVjxoxWVZKf3kNMau/Y77//XnQ7yaUOHTrI+PHj7WZffPGFGcSzK7wy+nDcO6jSpEkT0QdQVrIe4Acb/LPW4zN8BYLt7RZpQTdLPCXBt+R6Y1nbjLRPf8PeajBL72eCSTp0mg6h5kzB9gjxvgYm9b3+HkJHSg9Lpw15BBCILIHu3bvL8OHD7Z025ro1e47ZFUlkNFCmw3h/+eWXdqvmzZub62fKlMmuC5SpUqWKOHsSG/PnitYFm5xDZep+6/Dgwf5/PdjvoB0CCCCAAAIIIOBXwPgDmoQAAgiEVOCzzz7TLmX2P1WrVvWcO3cu2e8wesZ5jLfM7fV0G0bQLdn1tMHQn4577hl7wPVPq9kXJt8+dva8575Jca7l2r75J/F+t3/49HnP/dP+ad9kRrznvN9WVCKAwMUKGG9Se2666SbXf/fGEG9BbdaYC861nhF08+zduzeodbWRMXyta/1OnToFXNeYr83V1rrGOdcxhs706D7oMmPouIDbYkHkCBjBNL/n3Tr/1mfNmjUj56D87Knuv3UsSX2qR7QmoyeZy8DovRbUoS5ZssS1nvotW7YsqHW10dmzZz3GiwL2NvRa4y8ZQ9q62un3TJ8+3V9T6hBAAIGQCuzcudO+Rln/jzBeWEj2O/T69sADD7jWNYJuHr33CzYZQ4e71jeCZ0GtGh8f7zHmHrfXNXo1B/X3aFAbpxECCCCAAAIIIBCEgATRhiYIIIBAigWM4djsP3T0DzR9gHX+fODwldHTxFOyZEnXOsEG3XTnxq8+4RNUm7f1tLnfJ4ygW/vPD5vLNfj23MKjrrYHTyW6jm/r4XMeDbZpYK7h5DjPX8eSDxq6NkABAQRSJPDbb7+5/tvXh9BGr4+A2zhw4IDHGJLStU5Kg27Wxr0fCGkwzpmOHz/uefzxx+3vMuYbcT38Nnq22c2NYZPMdsYcJB5juDi7nkzkClgPGJP7jNwjvLDnwQTfIj3AeOFofXPGMGo+9yHGkLW+Df+tMXpxeIy5aO1rg/UbSUnQzdq43u9Y6+v1T69xzqTXSO8Xk4x5ipxNyCOAAAJpKjB69Gj7OqXXq1q1anmM+dYCfucff/zh8f7/iv59mJKgm7VxY54313cboxVYi3w+9UVO/bvTuqbq55AhQ3zaUYEAAggggAACCKS1AENNGndiJAQQCL2ATnzdokUL17AidevWlV69eonRA05y5swp27ZtE+OPMhkzZoxrfiYdIk6Ha3MOP5fcHu44ligdPz5kNytWKJN0qBIrG+PPydw/TsspY9jIjBkzyKD6uaVSgUzSbPohOX3amPTNSNmyZZSWVWMl1hjtZOnOBPl1yxmzPmfOGBnTOI8UzB7ckHfmSvwLAQRSJeCcf0M3YASv5PnnnxcdjkjnYjMCYLJu3ToxHmrLwIEDXXONtG7dWozeb0ENL+m9czqfkl6bdLua9Pqj33vNNdeIDmc0bNgwe06SOXPmSOPGjUXnJenZs6e9Kb2G7dq1y9wvrdT55urVq2cvJxOZAsEOwRipQ0x6n5VFixbJXXfd5V3tU47moQ11Trb77rtPjN5l9nHrvJM6LG2lSpXMOm3z66+/yuDBg2Xjxo12u2rVqsmoUaOSnSfSXsGRMXrLSufOnWXs2LFmrfEikrl9vQ7qMJbvvfee3VqH0zV6uqXqe+yNkEEAAQRSKGA8mBL9/6L+YyW9HvXr18+8jypUqJA5VLjeq+k8u86hKbW93rv16dNHghle0tq+9anDVerQ3nqvaCX9O/Oee+4x79cOHz4sP//8s+gQv84hLR977DFziPAyZcpYq/GJAAIIIIAAAghcMgECb5eMmi9CIP0JGMNLSu/evcUYNinog9f5mp566imJjY0Neh2r4aJdZ+XNhcfl7Nl/AmpWvX7myJFR3qiXR67KF2NWn0zwyNDlx+WHP/8Jsjnbar5CqSwy6K5ckjtLBu9FlBFAII0EdA4PDWw553hM6qtq1KghRo8T+c9//pNUs2SXHTp0SDR44ny47VxJ52vT7zF6nJjV+vBJg23GMJPOZmZeHyzpQyhS5AsEG3jT30O0JA28aQAuqWT0YBANvkVrMnqbmQF/DXgFkzRIpsF4fVnoYuYNMkYFMK9Deq0xet/5fLV+jzEcphg9cI17mhw+y6lAAAEELoWA0dtWHn300aC/yuitZgbdihcvHvQ6gRrqnJj6MsT+/fsDNTFf3NJ7SeslqoANWYAAAggggAACCKSxAIG3NAZm8wggIGLMC2C+xT1r1iyzx4q3ye23326+Yd6mTRspVqyY9+IUlc8bzz//t/OMbIhLlH3HE6Wo0WvttpKZ5bpCmcXo8OaTNsQnyo9/nZHtRxIlU8aMUs4IzFU32pfO9U+AzmcFKhBAIE0FNGCvbytrzw99e9n74Yr2SNNAmDFEpHnduJgH3d4HYswPJ19//bXs2LFD9O1qfdB99913y9VXX+3d1Cxrr5jFixfLpk2bJG/evGIMu3TRQUC/X0TlJRcINugWLb3dLGB6vVkSYl5/tAebMYebqwecttCeaLVr15b69eubvfuzZ89+YcWLzGkvXO1dq73p9HpYrlw50V4l2qMuNT1FLnJ3WB0BBBDwEdCRTaZOnSoffvihrF271udlAR01QO/VmjVrFvLeudpDePv27bJ+/Xr5/fffRfelYMGCUqRIESlfvrxUqVKFa6XPGaMCAQQQQAABBC6HAIG3y6HOdyKQjgW0Z0BcXJz5B5o+qNZ/QvngPB3TcugIRKWABsA0IJY5c2bzwUqWLFmi8jg5qPASCDbwFk293awzQK83S+LCpz7o3bdvnxkIK1CgAD3OLtCQQwABBMy/67S3sL6UkC9fPgJf/CYQQAABBBBAAAFDgMAbPwMEEEAAAQQQQAABBBwCwbwQEm293azDD7bXWzQGHS0DPhFAAAEEEEAAAQQQQAABBBC4GAECbxejx7oIIIAAAggggAACUSWQnnu7WScymF5vOs+bzvdGQgABBBBAAAEEEEAAAQQQQAABtwCBN7cHJQQQQAABBBBAAIF0LBBM4C1ae7tZpz0YAw26afCNhAACCCCAAAIIIIAAAggggAACbgECb24PSggggAACCCCAAALpWCCYoFO0B96CGW6SwFs6/o+EQ0cAAQQQQAABBBBA4P/ZuxdwOYoy4eNvOBEikHCTCCSoRETQXVaXzQILGnBVRNR9EITAkkUUPiUoiIC43E4AAVG5CAmukUses7tgXGHxhqIC4bJB1LhhFYRACCREEhLISQxIkpP55h3sPt1zeqarp2/V1f9+nnOmu6e7uupXNTXd9U7PIIAAAl0FCLx15eFJBBBAAAEEEEAAgToJmPy+Wx1+3wyHOrV6yooAAggggAACCCCAAAIIIJClAIG3LDVJCwEEEEAAAQQQQKDSAgScXq0+fuet0s2YzCOAAAIIIIAAAggggAACCJQoQOCtRHwOjQACCCCAAAIIIGCPgMlXLLr+NZNebRB48yR4RAABBBBAAAEEEEAAAQQQQCCZAIG3ZF5sjQACCCCAAAIIIOCoAL/vNlSxBCGHLJhDAAEEEEAAAQQQQAABBBBAIIkAgbckWmyLAAIIIIAAAggg4KyASeDt7rvvloMOOshZA69gBN48CR4RQAABBBBAAAEEEEAAAQQQSCZA4C2ZF1sjgAACCCCAAAIIOCpA4G2oYgm8DVkwhwACCCCAAAIIIIAAAggggEASAQJvSbTYFgEEEEAAAQQQQMBZAQJvQ1VL4G3IgjkEEEAAAQQQQAABBBBAAAEEkggQeEuixbYIIIAAAggggAACzgoQeBuqWgJvQxbMIYAAAggggAACCCCAAAIIIJBEgMBbEi22RQABBBBAAAEEEHBWgMDbUNUSeBuyYA4BBBBAAAEEEEAAAQQQQACBJAIE3pJosS0CCCCAAAIIIICAswIE3oaqlsDbkAVzCCCAAAIIIIAAAggggAACCCQRIPCWRIttEUAAAQQQQAABBJwVIPA2VLUE3oYsmEMAAQQQQAABBBBAAAEEEEAgiQCBtyRabIsAAggggAACCCDgrIBJ4G3atGnS39/vrIFXMCw8CR4RQAABBBBAAAEEEEAAAQQQSCZA4C2ZF1sjgAACCCCAAAIIOCpgcpfXQQcdJHfffbejAkPFIvA2ZMEcAggggAACCCCAAAIIIIAAAkkECLwl0WJbBBBAAAEEEEAAAacFRowY0bV8dQm8HXzwwaKByG6TBiDVgwkBBBBAAAEEEEAAAQQQQAABBIYECLwNWTCHAAIIIIAAAgggUHMBk4BTo9FwXikuAKkAdXBwvqIpIAIIIIAAAggggAACCCCAQOYCBN4yJyVBBBBAAAEEEEAAgaoKmATeXL/Ti6/crGrrJd8IIIAAAggggAACCCCAAAI2CBB4s6EWyAMCCCCAAAIIIICAFQImv23m+tdNmhhMmzZN+vv7ragzMoEAAggggAACCCCAAAIIIICATQIE3myqDfKCAAIIIIAAAgggUKqAyd1emkGXv2bR5GsmCbyV2kw5OAIIIIAAAggggAACCCCAgMUCBN4srhyyhgACCCCAAAIIIFC8gEngydWvmzS5201rxOXAY/EtjiMigAACCCCAAAIIxAmsWbNG/vjHP8rIkSNl3LhxMmrUqLhdeB4BBBAoTYDAW2n0HBgBBBBAAAEEEEDARgGT33lz9esm61x2G9sieUIAAQQQQAABBOoq8Morr8iPf/xjmT17tvz85z+XtWvXhijGjh0rkydPltNOO00mTJgQeo4FBBBAoGwBAm9l1wDHRwABBBBAAAEEELBKwPSuL9fuejMtN18zaVVzJTMIIIAAAggggIBzAg899JCccMIJ8sgjj/hl0+DazjvvLAsXLpQVK1b463Xm2GOPlfPOO0/22muv0HoWEEAAgbIECLyVJc9xEUAAAQQQQAABBKwR0N9208CTPppOrt31Zhp442smTVsI2yGAAAIIIIAAAggkFbjlllvkmGOOae02evRoueyyy+QjH/mI7Lrrrn5Sy5cvb90Np3e7eXfC6bZz586Vd77znf52zCCAAAJlCRB4K0ue4yKAAAIIIIAAAgiULtBLwC2YaVfuejMNunG3W7D2mUcAAQQQQAABBBDIUuDOO++UQw45pJXklClT5KqrrpIddtih4yGefvpp+fjHP+5/eE6Db/PmzZO3v/3tHffhCQQQQKAIAQJvRShzDAQQQAABBBBAAAFrBOKCbXonW39/v9EdcK7c9Wby225agdztZk0zJiMIIIAAAggggIBTAi+99JK89a1vlaVLl8qHP/xhue2226Svry+2jH/605/kzW9+s//1k/rbb/Pnz5dx48bF7ssGCCCAQF4CBN7ykiVdBBBAAAEEEEAAAasETANuGkzTSbfXgFTcVPXgG3e7xdUwzyOAAAIIIIAAAgjkLXDxxRfLBRdc0DrMySefLGeeeabo77qZTP/+7/8ueoecN5111lnyla98xVvkEQEEEChcgMBb4eQcEAEEEEAAAQQQQKAogaTBtvZ8md4JVtWvYDQNuqkLd7u1tw6WEUAAAQQQQAABBLIQWLNmjWyzzTahpCZOnCgPPfRQaF2nhU2bNsl+++0nv/rVr/xNXnzxRdl22239ZWYQQACBIgUIvBWpzbEQQAABBBBAAAEEChFIG3DzMpkkMFW14JvLZfPqj0cEEEAAAQQQQAAB+wV+8IMfyEc+8pFhGU3ywa9LL71Uzj33XD+NK664Qj7/+c/7y8wggAACRQoQeCtSm2MhgAACCCCAAAII5CaQVbCtPYMjRoxoX9Vx+e677xbvqyo7bmTJE0nK5ZXJe5w0aVJlymkJN9lAAAEEEEAAAQQQ6CBwww03yIknnhh6du+995YFCxaE1nVb+O53vytHHXWUv8n48eNlyZIl/jIzCCCAQJECBN6K1OZYCCCAAAIIIIAAApkL5BVw8zKq6Zv81pu3ve3Btzgvrxzeo97Jp4G2TgYajCMg52nxiAACCCCAAAIIIJBU4Pe//7381V/9VWi3pOfU8+fPl3322SeUxurVq4d9hWVoAxYQQACBnAQIvOUES7IIIIAAAggggAAC+Qlo8Gju3Lmij/rXPmkgqL+/3w8ItT+fdDnJ1zJq2rZ+7aRadQqgRZkEy5FkX/XXP524O67FwD8EEEAAAQQQQACBLgKPPvqo6F1r22+/vXzgAx+Q3XffvcvWw5/S33TTfYOT3jGnd84xIYAAAkULEHgrWpzjIYAAAggggAACCPQsoMEfDYLpY9SkwZ4sA27BY1Q9+JZF/pOmEfQjGBfUYB4BBBBAAAEEEEAgSwH9PbjNNtsslKT+dtyHPvSh0DoWEEAAgSIECLwVocwxEEAAAQQQQAABBFIJeMG2qIBbnsG29kzr3WJReWjfzlsO3jHmrSvjMWm+1VS/3idqSppWVBrBdQTkghrMI4AAAggggAACCPQisGbNmmFfKzl9+nQ55ZRTekmOfRBAAIFUAgTeUvGxMwIIIIAAAggggEBeAhrg8gJuUccoMuDmHV/zlOSrGr39ygrAxRl6+Wt/jPtNjayDb+3H94JxevciEwIIIIAAAggggEA9BZ544gmZN2+eLF++XFauXCl9fX3y13/9163fg9trr71ay57MY489Jnvuuae32Ho8++yz5ctf/nJoHQsIIIBAEQIE3opQ5hgIIIAAAggggAACxgLdgkVlBNvaM95r8E3TKSoA182wvTztyyZ5TGPQfrxOyyb56LQv6xFAAAEEEEAAAQSqKbB27Vr5+te/LjfddJMsWrSoYyEOOOAAmTVrlv9bcHfeeacccsghoe27nU++9NhTsubOebL+ycUyYuRrZIu37y5jDvp7GbXbuFAaXRcGB+XPTz0rfdtsLa/ZMfz7cl3340kEEHBegMCb81VMARFAAAEEEEAAAfsF4gJFNgTcgoppfutM0+k2CBA8TtL5OMe49JLkK61BXF70dzqYEEAAAQQQQAABBOohMNgMYt14441y3nnnyYoVK/xCH3744fKRj3xE3vjGN7bucNNg3HXXXSe/+tWvWts88MAD8g//8A9yxRVXyJlnnunvpzOdvmpyxbf+Swbm3B7a1lvY5avnylbvCN855z0XfNzw/Auy9PTLZOPy51qrd5r2eRl9wDuDmzCPAAI1FiDwVuPKp+gIIIAAAggggEDZAt0CRd7XDU6aNEl03rYpi8CTBrrSls8zVB+d73WK+3rJqHSzMIhKN0kAMGp/1iGAAAIIIIAAAghUR0DvcpsyZYrcfvtQMOywww6Ta665RiZMmBBZkC9+8Yty+eWXt55fsGCBTJ06VWbPnh3a9uabb5bJkyeH1r34w7my8uvXt9Zt/6njZMx79pOBO+6TF2d9x99uwm3flL6tt/SXo2aWf+MWWXPrj/ynxnz0MHn9yeFj+U8ygwACtRMg8Fa7KqfACCCAAAIIIIBAuQJeoKhTkMi2u9vitLL6vTMv0KjH02Bcp2nu3Ll+gK2TYad9o9an9c6q/F7eCLp5EjwigAACCCCAAALuCyxZskQ+9KEPycMPP+wXVj/cpXe+bbbZZv669pmNGze27oS744475JJLLpFvfOMbsnTp0tBm999/v+hXUnrTS79/Qp793IWtxeCdbet++6gs+8Kl3mZicvfa4hPOkQ1Ll/j7bPeJyfK6Yw7zl5lBAIF6CxB4q3f9U3oEEEAAAQQQQKAwAdcCbkG4vO78Ch4jj3kNuumdbmmnESNGpE3C35+vmPQpmEEAAQQQQAABBJwWWLx4sey7776hr5a84IILRM+tTably5fLTjvt1HHTgYEBGTNmzKvPb2rIU//yhdZXQ25z1D/J2JOO9Pd7sXnH28orZ/rL7c/7T/xlZnDtOln00U+HVo+7ul+2bP5OHBMCCCCgAgTeaAcIIIAAAggggAACuQm4HGxrR6ta8C3LO8u0nvXOt7RTlnlKmxf2RwABBBBAAAEEEMhP4OWXX5YDDzxQ5s+f7x/kiCOOkDlz5nS9083f+C8z+++/vzz44IPtq2WPPfaQxx57zF+/9sEF8tz5X5O+0WPkTbdcLZtt/hr/uWWXfFPW3XO/v7zNsR+VsScc7i+3z6x94Lfy3LQrQ6vfcscskZF9oXUsIIBAfQUIvNW37ik5AggggAACCCCQm0CdAm5BxKwCUME085jv5ffc4vKRReCRu93ilHkeAQQQQAABBBBwQ+DEE0+UG264IVQY/arIcePGhdbFLVx00UXS398/bLNPfOITofSXnHG5/Pnh38k2Rzfvdjtx6G63Ta+slyc/9MnQ/mP/9TOyzXv2Da0LLrT/vtuod/6N7PqVM4ObMI8AAjUXIPBW8wZA8RGokoAOZppM+rVZTAggUG8B+oty6r+uwbYo7SyCUFHppl2X9x1lacqd1ddepjXKa3+TfolzmLz0SdcToB16EjyWKWDSDjV/9Ill1hLHRiBfgVmzZskJJ5wQOsjUqVNlxowZoXUmCxq80yBe+zR79mw57rjjWqsHV6+RRR87pTX/hhu/KlvsOvT1lAP3PCQrLrk2tPuEW/+teWfcVqF1wYWnTzpf1je/JtOb+H03T4JHBBDwBAi8eRI8IoCAVQJ6MTZ37lzxLsq8R9NM6kWad6E2adIkf950f7ZDAIHqCHj9gw746+QtJymBBiN0or9oMST+p+bq38le+2P9FKrXLyc+QIV3SBOIyqrYRfvrV052agtxZco7MBh3/Cye98rOeUwWmqSRRkDbIu0wjSD7ZiFAO8xCkTQQcEtgw4YNMn78+NDvumkJFy1aJLvttlviwl555ZVyxhlnDNtv5cqVssMOO7TWr1vwmCw780uy+Vv3kDdOPz+07ZIvXiF//s3/+uu2PHB/Gdc/1V9un4n8fbdrpsmWe725fVOWEUCgxgIE3mpc+RQdAdsE9KKs28Bt2vx6A+tRX0GQNm32RwCBYgXy7i80UOEFK4otWXWO5g2keX1re849P31kktbvn6lZkVOZdTBixIhURa1aAM6r27zPY/hwQKpmVYud835/9Pp8zqdr0Zx6LiTtsGc6dkSgFgK33HKLHHPMMaGy6nmrfhV6L9Opp54q114bvmPtfe97n9x5551+co31G2Tgrl/Ka9++e+hutw0vDMjioz/jb6czO33pLBm9796hdcGFyN93+8kskT5+3y3oxDwCdRcg8Fb3FkD5EbBAoOi7AfSEzhuMtKD4ZAEBBBII5D2QE5WVKgUA1Ef7tzynuDrw+te885FnGfNIOxiI0jblDV7ncSwb6kDbid75ZjJ5Ft5jcB9dZ/MAf9zrIViWrOY9J5tdsior6ZgJ0A7NnNgqf4Gir+voD/OvU46AQB4C++yzj8yfPz+U9NVXXy2nnXZaaJ3pQlR6M2fOlJNOOik2iRdu/Zms+sa3/e36Ro+RCd+9pmsQ7bnrbpG1t/3I32fUPu+QXb88/I47fwNmEECglgIE3mpZ7RQagfIFyhggiCq17QN6UXlmHQJ1FLChz7C9v/AGu/STolkHvdTf+7oynW+fbAj0tOfJpmWvbjRPwXak63VS0yjX1pMG/9Rf/2y7GypY7m7FaDQa/tNR+wTN/A1LntH60rymqbe0RVAXnQjAtRhq+c+Gduj1P7TDWjbBVqFtaIeaERvfK+rbKig5Ap0Fli5dKrvuuuuwDR5//HF5y1veMmx93IqBgQHZdttth222YsUK2XHHHYetb1/xzKmXyCuP/sFfPfrww2SnqZP95aiZYb/v9slj5HWTPxi1KesQQKDGAgTealz5FB2BMgRsuTBrLzsXau0iLCNgh4CNfYaN/UUwWKGDoL1+TUt7rcf567F0sFUfmToLtN/t1m2AWs01yBk32RZk65TfYNuM2ibq9dRpn6hto9LMc13cayLPY3dL2wabbvnjuWwFaIfZepJabwK0w97c2AuBugt873vfkyOPPDLEMGHCBHnyySdD60wXrr/++mF3tn3mM58Z9tWTUelFfc3kuK83f6vtbZ1/qy3y992uvVC23HNC1CFYhwACNRYg8FbjyqfoCBQt0Gkgreh8dDseA1fddHgOgeIEdDDH9GvqistV+Ei29BdRfWvwDqJwrs2Wug2mEWwzM/S2aq+ftHXjpVulR30ta5tqn+JeQ+123v5x+3nbZf3YqRxZHydNennc8ZomP+ybvUAV2mFZr9HstUmxk0Cn/rnT9mWspx2Woc4xEYgXOOecc+Syyy4LbXj88cfLrFmzQutMF6K+ZnLhwoWy++67xybx4h33ycorZ/rbtb5m8r+mi2zW+beK+X03n4sZBBCIE2he/DMhgAACuQs0B2r1e6Qq8de8SMvdgwMggEBnAX0NVqW/0L6tzKmTVXPwPXG2dJ9ufbU+10u6iTPi2A7BOqrr+4u2m6jXtElV675BQy+dIi01D91eG16ebHks0sakDtkmGwHaYTaOpJJOgHaYzo+9EUCg0fjkJz857LxwxowZPdE0fyduWFpHHXWUcVrPXjqz8fh7j/P/nv3KjbH7/nHGzf72uu8zZ38tdh82QACBegpwx1vzCpkJAQTyE6jCXStRpW8OWvGbKVEwrEMgZ4EqfJI/iqCMPqPbp82bQQLjr5uMu7tN0+r21YhRHqwbEgh+zWTzcmPoiZrNtZ8PJH3NdGrvSdNJyt7puEnTKXr7vF2KLk/dj9f++qmKB+2wKjVllk/aoZkTWyGAQHeBo48+WubMmRPaaN68ebLffvuF1pksfPazn5Xp05t3qAWmBQsWyN577x1Y03l20bGfl8Hnn/c32PHsqbLte/f3l6NmFp9wjmxYusR/aruT/lled9QH/GVmEEAAAU+AwJsnwSMCCGQukOVglQ786uQ9thYi/ukFof5lNTU/1Rl7zKyORToI1FlAX7faZ2T1+vX6Cu+xk60OCmY1FTnAaNK/duu/4rzVjd9uS98ygvVUZPtIn/N8UvA8tH1p++xl8tII7qvpeW02uD7tfNSxek1T86eT99haiPinr80s+8FenSOyxqqSBGiHJcFz2JBA1duhFqbbeVGosCwggECuAlHBslWrVsn222+f6Lhr166VcePGiT560/nnny8XXXSRt9j9cdMmWXjI8aFt3nDjV2WLXXcKrQsuDK75kyw64uTgKhk3/SLZ8q27hdaxgAACCKgAgTfaAQII5CKQ9uLMG5hKM/CredAp7cA6g6W5NBESRcAX0EFmvdMtzaR9hndXltd/JElP8zB37tzWgHeaQe8i+gvTuwLVoX3QXcumfWNUGXV7/Zs0aVLrMYkf20YLBOuqiLYRnQu71qqJtjPv9dpL7rT96utVTYNTlsbBugsew3Q+WEadTzp5ZdT92suZNC0Gm5OK2bO9S+0wy9enPTVUj5xkcV2n/WCa8wuu6+rR1ihlPQSuuOIKOfPMM0OF7eVbIU4//XS5+uqr/XT22GMP0bvdRo0a5a/rNjO4eo0s+tgpoU3e8tNvd/19tzX3/1aWX3ilv89mW4ySN9/+byJ9ff46ZhBAAAFfoJ7fsEmpEUAgT4HmhdWw79ludjpG63Tf5gBR5tlrXuwbHb9TPnV/JgQQyF7Axtem5ilNvvLqx1Q/af+q+2if2m2/PPOrx6/rpO7B95S6OuRZ7k6vU13f69Reb8E6NJnP6/XUqawmedJt0pj0asl+vQvE9dtx9U477N2ePcMC3c4faIdhK5YQQMBMoBkcC50ja1/y7LPPmu38l60eeOCBYWn88pe/TJTGxoG1od9qe/LwqbH7P3v59aF9lnzxith92AABBOorIPUtOiVHAIE8BHq9OMtrgKC9jGkGrhi0atdkGYF0Ar2+HovqL7R0afKYTie8d6+DsN365CIdw6Wpx1Kw7fD+kW+dB629gWBt3724e/snfSzq9RRVVtO8aj/CVA0B0zpt364K7bCX12U1as29XGp7am9jJsu0Q/faAiVCIGuB5t1pof7l+uuvNz7EkiVLGuPHjw/t3/ydN+P9gxs+/t7j/EDaE4edGHxq2PzLC5/2t/X2W/ndnw7bjhUIIICAJ0DgzZPgEQEEUgv0MhhU1IVZe+E0r71cTDJo1S7JMgK9CehryWTwJrhNWf2FlrDX/q03nfBevVgF3YLzZRqGS+X+UtDd/dKWX0J9nUS9TnWd6dTLeUGS9E3zYbJdVFmDba7TPOcxJrrlbtNL3ZbVt/eSV22btMNy25jJ0Xup2zLbYS/9N+3QpCWwDQL5CNx+++2ha8GJEyc2Nm7cGHswvTNuwoQJoX17DbrpwRZPnRYKpr2ybEVkHja+ONB48mOfDW2rwbeXHnsqcntWIoAAAipA4I12gAACmQj0cnGm+5Q99ZJvLtLKrjWO74JAp0HhTut1QKXsqZf+Im0/p/1NJ5Mk68saDCu7zso6frCtpG0DZZWhqscN2gdfI3H10Gm/YBrt8zacDyQdbLahL61q2yoi31Vth0nzTTssojX1foyk9al9o+5T9tRLvm3ox8t24/gIlCVw1FFHha5zzj777MamTZs6ZueHP/xhZne6eQdZfdeDoWDaH6/6tveU/7judwsjg26tO+QGB/3tmEEAAQTaBQi8tYuwjAACiQWSDgzbNgCc9CKNwYLETYQdEAgJ6GuofQC727INgzleAbS/S5r/Xgd1kvatnQzps7zaK+4x2EZsar/FCZR/pKj3dq2XqPqI2rbT60nX2/aaSpr/KIPya4wcJK1HbYe9vr/kod1L/vPIB2mmE+ilHmmH6czZG4G6CgwMDDQOO+yw0HXhIYcc0vjZz37WWL16desOuIULFzZuu+22xqGHHhrabuzYsY3vfve76emad9ktOe/roeDbs5fObKy++6HGqu/f3Vh60XWh57yvmNTHJedclf74pIAAAk4LjNDSNS8gmRBAAIGeBUaMGGG8b3OQQJoXZ8bbF7XhhRdeKM0LTePD6bb9/f3G27MhAgi8KpD0tab9hfYbtk15lyNp+nE+nO7FCWX7fPB9EftsbZOkds8998jcuXOHvb8H38N1m4MPPtg42eC+xjsVsGHSPsPWchRAZeUhaIdWVkstMxV8/4oD4LouTojnEUAgTqD59ZLyhS98Qa666qq4Tf3nL730UjnttNNkyy239Nelmtk4KCtuuk0G5tzeMZkdTjleXrz+O7LplT/722z/6SmywxHv95eZQQABBIYJaOCNCQEEEOhVoHnBFfrkUbOT6bjcHOTp9TCF7edaeQqD40AIGAhoH9Ctjwg+p69Fmz5BHVW8pOWJSiNqXZJ0g2bd5m23jHKo6rpg/ek8U/kCwToJvk46rQ9uE5y3vT71dR7Mb9w8/UL5bdPLgUvnn9quXCqPV0d1eHSt3lwrTx3aIGWsr8DTTz/dOO+88xpve9vbIs9l3vWudzUuu+yyxrJly3JD2rjmT421v/l9Y9VtP2s8d93NjVW3/qyx7tEnG5teWd9Y98gTw+58W//c87nlhYTjBV5++eXG1772tUbzw2cNvXuSCQEbBbjjrXlFyoQAAr0JJPl0dXOwqjJ3iOkn3/WTxyZTc3BBmhd1JpuyDQK1F0jyKermSVMlvLLuB5OklwRI+yntr5h6F9C60SnubudgO+c9onfvPPZM8/qqynlM0junqtLX5tEebEkzSbt0tR3SV5bfGl1sh6rKdV35bYscIJBUQM9NVq1aJWvXrpVtt9229Rc8v06aXhbbr7jpVhn4z9v8pF6730QZf/Gp/jIzxQo88cQTcvTRR8v8+fNbB77//vvlgAMOKDYTHA0BAwECbwZIbIIAAtECpic/VRkk8EqZZNCKwWxPjUcEugskGdCp2gBcVoM6SYy6a0c/WzXX6FKUtzb4ntfpfS1Yh7w/lFdX3Y6s7/FaT/poOnWqb9P9i94uyXlM1cpWtGXexwv2GXHHqlpdJWmH9JdxtZ//88H3uG5Hox120+E5BBCohMDgoKz671/Iuvt+LbKpIVtNmtj1KyM3rd8giyd/TgbXrvGLt8tXz5Wt3rGnv8xMMVSqLtsAAEAASURBVAJPPfWU3HzzzXLuueeGDnjvvfdK867I0DoWELBBgMCbDbVAHhCooECSgYIqfpo6SfkYzK5gAybLhQu4OqDjQZoG3zoNLibpc7xjJn3sdOyk6dR1+6g2rAOQOnl3wQXrsWqDk62C1Oif6Wu2qvUYbItx1VrF87S4MlXledN6qmr/bVo+rS/Op8trtUnqqYr9RZLy0Q7La4ccGYGiBFZ867+G/Z7brt/6sox607jILLzwg3tk1TU3+M+N3GUX2W3Wl0VGjPDXMZOtwIYNG+Thhx+W5tdJSvNrSEXvcPvFL34h9913X+SBCLxFsrDSAgECbxZUAllAoIoCUQOQUeWo8sWL6UVaVQdDouqLdQjkIWD6WqrqALeaJflkf3u/aBoAyKJuqjhglkW5s0gj7n1P26/+eRPWnoR9j6Z9kua8yvVo2rdUue+1r3Uly1Fcv+KlVuV2aPp643zaq+3iH03bYfv5S/E57f2ItMPe7dgTAacEmne4LTzkX4YVaacvnSWj99172PrB1Wtk8XFnyKZX/uw/12lbfwNmUgs0f8tPxo2LDoRGJU7gLUqFdTYIEHizoRbIAwIVEzC9cHFhIMd00KrKF6IVa35kt4ICJgM6Lgy4mQbfgmU17WOyqnb6qt4lTdqxl3qwjr11PNojYHoe48LrxbSPqXJgx56WlSwnpu2wTufTtMNkbSiLrWmHwxVd6PuHl4o1CCCgAuufWylPTzl9GMZuc2bIyO3GhNc3g3RLp02Xl+c95K/f/tNTun4tpb8hM6kEgoG30aNHy5577in77befvPvd75bXv/71rcfgAQi8BTWYt0mAwJtNtUFeEKiIgMngowuDBF51mJSXQVZPi0cEwgKmAzquDLaZDnLroI7aaLAuz0n7puCky97XIgbXMx8vYPJe0J6KvhdOmjRJ2uuhfTuWixMwDZC7ch5jWl4Gmotrg96RTPqUurVDV8rr1XEVHmmHw2tJ37O1T2RCAAH3BAbX/EkWHXFyqGDbnXisvO7oQ0PrpPk7cMu+cqOsu+tef/3ow94vO31uir/MTL4CGzdulL6+vuY3eoa/0vM3v/mN/N3f/V3o4ATeQhwsWCRA4M2iyiArCFRBwHQQ3aUL5yQD6QyuVqEVk8ciBdpPlKOO7VJ/YTrIrX1Fp/5CAzUmU6f9TfZlm+QCJm25U6pefRP07CRU3HrT8xhXPgygsibnMdpGGWimHeYpYNIO9fguvfby9MwibfrDzop8GKGzDc8gUHWBxSecIxuWLpG+7baTcVeeK1uMf32oSJvWb5BlF14nLz/0a3/9a/9hXxl/QTNg1wwEMZUrQOCtXH+OnkyAwFsyL7ZGoPYCJgOPLg2ia4UnGUhn0Kr2LxEAAgJ1HNDR4jO4GGgEDs2avP+ZFFffI3UiCNdiKPyfST3W9TyGgebimiPtsLO1a6+/ziUt/xnaYec64MMInW14BoGqC6z++Tx5/vLrWsXY6j3vlm0/+l4Z9YadZcOqAVk3/xFZfcsPZPD551vP940eIzuc+nHZ5qCJVS+2M/kn8OZMVdaiIATealHNFBKBbARMB9FdvGBmID2bNkQq9RKo44CO1rBpsJ5B7mq9Hkzac5IScVdHEq1stjU9j3GxbkzOYxhozqadxaVCO7ynKxHtsCtPZk+atkOu6zIjJyEEELBI4IX/vktWzbipa45Gf/C9suNJH5O+rbfsuh1PFitA4K1Yb46WToDAWzo/9kagVgImF2guXpxpJTOQXqumTmEzEDB9zbjaZzDInUEjsiyJLANvBF3LqVyTOnS1TzLtk2mb+bdNk/cH2uHdogE4pvwEuK47OBaX/jCWiA0QqLTAhhcGZOCnD8j6xc/K4MoXZMSoLWTkjjvIFnu+Scbs/w7p22Z0pcvnauYJvLlas26Wi8Cbm/VKqRDIRaDOA1YKajJQwqd0c2l6JFpBgToP6Gh1mQ5yu3hnTQWbq1GWTd4DTRJiIM9EKftteE2ancfQPrNve+0pmvQlrgbe1MLkfNrl8re3h7KWaYcHt87VuvlzXddNh+cQQACBcgQIvJXjzlF7FGgO+DAhgAACsQLNgZhGs5uJ/YtNqMIbmBg0L9AKLaHmSY+pj0wI2CSg7TKuz2gOrNmU5czzYmLAazdz9twSjGvPJs+73uZzw88gYbWPqyPX60f7mziDss5jMqjiSiRh0g6LroOi4Wxuh3V5TzapA+0rXJ5MDIp+LWqe9Jj6yIQAAgggEC3w61//etj57L333hu9MWsRKFmAO96aZ5RMCCAQL1D3u1c8IZNPhzb7dW/zXB71U/s6aZ14880LNGleqLXW8w8BGwRseK2U7cCn+suugWyPb9Kmux2xOeAu/f393TbhuRwFOI8xuxNXzyX0nCLPSc9dtD508s5j8j53yrM8SdKmHb6qZdKf5t0mtO3NnTu31Qa9dliX82naoV3tUHOjdVK3dvhqLfAfAQQQSCbAHW/JvNi6ZIGSA38cHgEEKiJg8gld1z8prlWln0Jsdttd//L6lKKm2+n4eR2zIs2TbFomoO0x7nWibdn1CQd3atikLru1+Tq8P9pe253eP4P1Vof30mB5O83nVZfq26ke8jqmbemanE/XoR12agfBNpmXQ7d2mNcxq9gO6/C+RTu0rWWSHwQQQCBegDve4o3Ywh4B7nhrnt0zIYBAvIDJnRvNi1VpXsDEJ1bhLUw+IZqlg37yMfgJyE50WR6z0zFYj4CpgMnrpDmgU4u7f+I+1a99pr5+mewW0L5Y3wd7merS1nuxKXKfuNei5qV5iVZklko5VtHnc6bnMXWw1wqnHb7a7G1th3U5nzbxr8Nr0uR8Ncs2YdofZnnMUt5oOCgCCCCQowB3vOWIS9KZCxB4y5yUBBFwU4CBglfr1WTwNe1Auh5DJ5OAW2vD5j8u0DwJHm0QMBnIqEswgr7ThhaZPg8mfX/UUerSzqPKbtM6k/pL+95tU3m75cWkf057TqHeehyddN5kqsMgvzrwnvBqazB5TabtP/UY7V8lGdcW07b9uPRteZ52aN4O0743eH0g13W2tH7ygUD1BV566SWZPHmyPPbYY7Jx48bSCjRy5EjZa6+95D/+4z9kq622KiwfBN4Ko+ZAWQg0L3KYEEAAgViBZn/T9avjmhclsWm4sEHzgryrgzr1aqFp675x1lHP675MCNgiYNKO69JmsbClVabLh0nf39439/pekC6n7B0lYFJ/zUH+qF2dW5enhaZt0ue1v1Z0uQ5TnvZV8zOx6LUPTdMOdV/Xpzztq2aXpwXtsGqtgfwiUB2B22+/vacxo6jzryzWzZ8/v1A8vmqyUG4OllKAO96avQwTAgh0FyjiU6ndc2DXs3GfEm0OFBh/dZzaJvkEZCeJ5sWd6HGZELBBgK8wGqqFIu4uGToac3kJmLwPBo+d5H0guB/z+QiY1F/au2vyyXn2qWZtkdV5TPOaNvvCWpZi1vaWFS9xdjifTkyWyQ60wzAj7TDswRICCNgvsHz5cvnUpz4lS5YsKfWOty222EImTpwo06dPN7qjPytZ7njLSpJ0ihAg8FaEMsdAoOICXKCFKzDtBZp66pRFwK2VUPMfgTdPgkcbBAi8DdUCgbchiyrPmbwPBstXhyBCsLy2z5vUH4G3oVqMs1DPLM9h9Mh1eM3QDofamM5lcT6t7VAntc1iqsP5NO0w3FKyaIdJv9I0nIPhS3Voh8NLzRoEEEDATIDAm5kTW1kikPKOOXZHAIEaCDRP/mNvZa/LVzRpdTe7765/zTsdIluFOupzcfv38rymzYSALQIm7dyWvOadD+0b417TvH7zroX06Zu8D3r1TH2m9846BZP6q8t5TBoL3dekf/deC0kes65zG9NLY29jedLmKa59cD6dVjh6f9ph2IV2GPZgCQEEELBdgK+atL2GyF9QgDvemmdaTAgg0F2AT0aGfZJ8MlLtsv5UeDg3ry7pp9OZELBFwKQ9Nk9GbMlurvngjrdceQtL3OR9UDPTHNCU5mBxYfniQGYCJvWn/VZ/f79ZghXeKqkF5zHZVbZa6l+3qS7tUA04n+7WEvJ7jnYYtqUdhj1YqqdAUec/N9xwg2y99da1QH7jG98o++23Xy3KWnQhueOtaHGOl0aAwFsaPfZFoCYCeoGmXx3XbWKgYEhHB131z+TCdmgv5hColwCBt6H6JlgzZGHrHO+DttaMWb6ovyEnEwsveKzbMhUrwPn0kLfXDnUNbXHIpYg52uGQsrZD/dM2SDsccmHOLYGirkWuvvpqOf30093C61CaZcuWyc4779zhWVanESDwlkaPfYsWIPBWtDjHQ6CCAnqRQeBtqOJMPhmpF2h60cqEAALRAgTehlyKutgdOiJzSQXi3gfrNEiZ1M6G7ePqT/NYlzo0tfBMbKi/OuWhLu1Q65TzaXtbNu1wqG68wJuaMCHgqkBRr/nzzjtP7rvvPlcZ/XINDAzIHXfcQeDNF8l2hsBbtp6klq8Agbd8fUkdAScETAdpivqKgrJRTQYKdCBdJ+9H3/O+WPMuCsu24fgIqID2GfrXbSLwNqRD4G3IwtY5bc+dPoBS1GCFrTZVyFe3+vPyX5d6TGpR1HlM3udJXj2X/RhXzrq0Q60HzqfLa420wyF72uGQBXP1FJg0aZLoWAJTtgLr16+XzTffPNtESa0lQOCNhlAlAQJvVaot8opASQImgzR6suYFm0rKZmGHTXKBFsxUnoNXDNwHpZkvW0ADFNpvdJvq0mb5jbduraA6z3V6H6zTIHl1amt4TjvVX3DLutRlGgvtz3R//ct6qsOHMdStUwDf86zL+XQaizzbYR3OTdLYe+3UpUeu61yqTcqCAAJ1ECDwVodadqeMBN7cqUtKgkCuAnEXJXpwBk1erQKTwTuTwfgkFVqHgYIkHmxbrgCBtyF/E4s69J1DItWcixqoNOnrq1la93IdVX/tpaxLwMPk/COubavn3LlzRbfLaqpDP0g7HGotWbRDTc0knaGjxs/V5Xw67rquLv2hyWsyrj+kHca/rtgCAQSyFdi0aZNcfPHF8sQTT4jOlzX19fXJ7rvvLuecc46MHDmysGwQeCuMmgNlIEDgLQNEkkCgDgImg8d1uFg1ucA3uUDz2kxWg1d1sPfMeLRfIKuBDPtLGp/DuMEtTaEOA87xUnZv0d6m6zIoaXetJMsdr8VXvUzOY5KcU2h6Oum5T5qpLv0g7fDVVmLSDpOcT2fVDpO0/TTtvex9Ta7r6vCapB2W3RI5PgII9CLwk5/8RA499NBeds1ln/nz58s73/nOXNKOSpTAW5QK62wVIPBma82QLwQsEzC5QKvDxarJBVqvDmkGDXo9pmXNjOw4ItAepIgqVh0CFzhE1Xw11wXrsg5tt5q11D3XJucxdRhozjPwo+cx+lrRv6RTHezVxKQd1uGcLk+HNO2wDva0w6Heieu6IQvmEECgOgJ6p9sBBxwgK1asKD3TEydOlPvuu0+22GKLwvJC4K0wag6UgQCBtwwQSQKBOgiYXJjUYTAyzwGrYDsy8Q5uX5eBgmCZmbdboKjXis0KJq/jJJ/ot7msNuVNB/31a/C8wX/vsVsevbt1Ov3AvKahA8U60d92k7T3uTwH+u0t9fCcFdE36+sl6VdREngbqqs69DFFtEMVNXkfHpKvT/9u4lKH8xPaYbD1M48AAlUTGBwcLPWbUzbbbDPRv6InAm9Fi3O8NAIE3tLosS8CNRIIDjp2KrbrgTcTA7XJcvDIdPCqDoM0ndod6+0UYJDb7M6GOgxs5d1CtZ/UQUR9zHLygnH9/f2ttLVN09dmKVxcWqZtxPXzGJPB9qwN9Jg6ea+nTrWe5blTp2PYsF7bohfE75SfrOug03HKWm9zO6xLH087FP99Pe51kGXfpO4mH0qoSzuMs+d5BBBAIEqAwFuUCutsFSDwZmvNkC8ELBQw+VSgyxcKJgMFeQ6idxu8ctndwpcCWTIQMAm8uT64aNJnZjmgY1AtzmxiOniVVYG1reqfBuGY7Bfw2oc+6l+SyeXXpA3nMZ3qxGX3YPvT8scF3nR7l8/rbGiHahwVDHbZXcscnEzOUVz2oB0GWwPzCCCAQHUEHnzwQdl///1DGf75z38u//iP/xhaxwICVgg0L3KYEEAAASOB5qBjo9lxdf3TbVyd4squzzcv4gspvh4nmJ/mhXEhx+UgCJgKaJsMttFO86623fbXaKfym3qy3asC2l5M3os6eaddX1QfT30nE9B2kVXbcLWOTfskdSxias9PEce05RgmfZir7VDrwKQfLqr87e2wqPZvQ1s0aYdc13FdZ0NbJQ8IIIBAUGDmzJnDziWuvfba4CbMI2CNAHe8Nc/8mRBAwEygzp/SNflUpCo2e3czzIy20jrRryzp9LtEGR2GZBDoScDk09TNQZ3WJ/t7OoDFO5mUvTng599Bpa/lJJO+7k2n9rT1ri11r9KkZdB+uL0sZZVB604n7oBrMZTyz2sTevC4dqHtXevKpA252ifZeh6j+dKpTq8lkzvC1aToc0o9Zt6T7e2wTufT2m/W9e5LW9uh1gnXdXn3QqRfdYE1a9bIH//4Rxk5cqSMGzdORo0aVfUikf8OAo8++qisW7dO9Lfs1q9fLytWrJB7771Xrrnmmsg9Pve5z8mBBx4oY8eOlc0331z6+vrkzW9+s2y33XaR27MSgSIECLwVocwxEHBEwPQCzcVBq6SD6I5UOcVAIJVAXQcXTQd0NHjjBXBSQSfcufmJftF+ugqTvu+opz7aOGn91Wmgtsw68NqASXvw2nd7kFnTqOtAM+cxZbbe8LFN26H2L64FJGmH4bZQ5pJpO+S6rsxa4tgIIPDKK6/Ij3/8Y5k9e7bo1wmuXbs2hKJBlsmTJ8tpp50mEyZMCD3HQrUF9Osk9Wsl00wuvoel8WDf4gUIvBVvzhERqLSA6UB6lQZ24yokySC6awMkcTY8j0A3AdNBHdcGF5MMLJr2L92ckz5XlbsoTNtP0vLnsb1rbTgPo17S1DagrxGddL7bpBfW3nuwF3iL2t7kPMa1i3TTfqYqfUNUvVZtnUk71DK5VCe0Q/taKe2wc53wvt7ZhmcQKErgoYcekhNOOEEeeeQR/5AaXNt5551l4cKFrTug/CeaM8cee6ycd955stdeewVXM19RgalTp8o3vvEN/w42vYtN73TUv6hp48aNon96d5x3h9zb3vY2+f3vfx+1OesQKEageTLPhAACCBgL6G8fNHun2L/mxYpxmrZvWLfy2l4f5K9aAs0B7Nj+Ql9jrkza95n0GcHfkTHdxyTduG2q0jcXaRJnZvp8VWxtfq3p60IdTfoN3Ua3Db6WTMqm25vUadJ0TY5d1jYm5aX9Fls7tMPoawnaoZ3t0KV6oT8sto1xNAR6Fbj55pv987XRo0c3pk+f3njmmWdCyT333HONG2+8saHPe69tnZ8/f35oOxYQQACBsgS4463ZOzMhgEAyAdNPRzYHFaQ5MJYsccu2Nv10bvOC1P+kvWVFIDsIlCqgd6lonxE3ufAaSlNW074mzjHu+eYJZ9wmpT9v+h5jmtFu70Nxd1GZHsPbTo+l731MZgKev7Z/b77Tnl49tn99ZKftu603aWOu1KVp31KFvqFbnVbxOZN2qOWq0/k07bD4lkw7HG7uwjnp8FKxBoHqCNx5551yyCGHtDI8ZcoUueqqq2SHHXboWICnn35aPv7xj/vnks3gm8ybN0/e/va3d9yHJxBAAIFCBMqK+HFcBBCoroDpp3Sbg1bVLWQz5/rpzmZHHPtX9XJWupLIfCUE9DVi8lrS11yVp7Tl1L7VNA0Tz/ZtbO+rsiq/llPT0j/TSbfV9mfa77fbti8nObZpHl3ZTm20jkzaei91aeKkeWivs6hlPX6VJ9P2XPW+t6p1RDsMn2PTDstpybRD2mE5LY+jIhAtsG7dusb48eNb52kf/vCHG82vDozesG1t87ffGs3fe/PP73R+6dKlbVuxiAACCBQr4M53OxXrxtEQqL2AyYCZDmJVddDK9CJUy8hAQe1fDgDECCR5Pem2VZyyHOA2TSsqUNBtnc19VdoyewGarNqOtsO0ebLBW8uRtU1SY82Dl49u7VOf07wWlV89Tlx+9Hkb6jGpuW6fpP32kj77ZCNAOxwKelT1tZZNSyg3FdN2qNtVcdL3IJP+vsp9fhXrhTwjECVw0UUX+a/Xk08+ufHkk09GbRa5bvbs2f6++no+66yzIrdjJQIIIFCUAIG3oqQ5DgKOCbh+AWN6AaondEwIIBAv4PJrKskAt+nAYpI0TQeT4mupnC3SlFXblb4f5TmlyZ9pfeeR/+D7dNGDpXpsPabJ696rw7zrsd046BP3GiqzHtvzbbLsctlMyl+lbVyvq7jXlvd81V5jVWpjJnmlHQ4FgE282AYBBPIRGBgYCAXO9D1i4sSJxgcbHBxsbe+9t+jjiy++aLw/GyKAAAJZCzBinLUo6SFQIwGTATXvpKdKF9SaVy/fcY9VKleNmiZFtVAgyaCO9i1VmZL0F0nLlSTtqvZVSdpFsIxesKbIdtJrfWgZi56i8ppnHrSMekyT8wKv7spwaTcItqm4eRvy257/Tssm9eCVt0rl6lTeqq93tb6SlEv7D6ZyBZLUV5X6jaj3Q6//a3+kHZbbBjk6At///vcjx2GSyFxyySWhNK644ooku7MtAgggkKkAgbdMOUkMgfoJtF+wdFuuwsUMF2f1a8OUuDgB115fOvDUrc9rf66XgaokZu3Ha1+2sQ9uz2Pcsg4M9uKYZStPMjjplSfL43dLS2065S9LN02r27G8cuuj5seGeoty0zIE89pt3tYytJerU/1Hlc3GPqG9PHVYTtIOtR51e9unJO9dtEM7ajNpO6xCvdEO7Whb5AIBU4Hrr79+2HnZ3nvvbbp7a7s5c+aE0tDfi2NCAAEEyhIg8FaWPMdFwBEBly7SkgxW6bZMCCCQXMCV11mSwRwdKE0zQKX9bBK3qAH24DpNK01+ktd69B5FGkbnoPe1SfNexHtGXJ7S5sFrhyZtUbfR7fXP9inOLfjaSftaztNCrU3qxiuPlpvJHgHaoT11UeecaD/i9REmjzb3I0n6Q92WCQEEyhf43e9+N6wPSnou+Zvf/GZYGqtXry6/cOQAAQRqKUDgrZbVTqERyFag6oMFSQer9EKUCQEEehcwGcwJbmPbwE5ZfV7S4wYNO81rmmX4Ji1LGXmMa+E2lcFkgDHpwKK+N5q+P2ra+qfbV3GyqS578Uua/6RtoZc8sU9ygaT1qNvbNOnrv9N7Taf1NuWfvLwqQDukJSCAQJkCjzzySOPCCy9sXHvttY2FCxcmzsoLL7ww7L1owYIFidNhBwQQQCALAUaPs1AkDQQQaA3cdrqojlpvywBd0otLLYttAx00PwSqJtDL4JwNrzvNt/ZdUX1ap3VZ57vXPkv3i9vX2ybv9hSXj3ZLm4M5Sduylj3LKWmbjDt2kvRseR+PK5Pp82W/tk3z2b5d0teTvr6Y7BVI2g51exumXtqhzX27DaZl5iFpfVa5HWb9vlxmvXFsBBBoNDZt2jTsWu0HP/gBNAgggEApAlx5lcLOQRFwUyDpYIEO/pR5sZP0orLs/LrZaihVXQWq9vpLGmDR/iKvgaikdu1tTPePS8Pbpn3ftMtJHasyMJvk/S+rMsXVobbB9r/2Y+uy5t0k/7qNbq9/Lk5arnYvk2WthzImza9JvbWXoaz8lmFU1WNWqV5ph1VtZfH5rlI71NL08p5IfxjfDtgCgaoJDAwMDDufmz59etWKQX4RQMARAQJvjlQkxUDABoFeB610UKioC59eBwiKzKMNdUkeEChCoJdBkqJfi2n6DN03r8nULq5v1efj0tLnsypL3LGCQQLdtiqT+gTz3m1eBzPTTHqsXgZENU+6n+n+uq23fZr8VmnfJPUYrGNtq0W1V9P6C+bPmy8qj1Wqcxvz2ms71Houqo5phza2nGzzRDvM1pPUEECgdwH9yslvf/vbja9+9auNs88+u3HOOec0br755sb//d//NTZu3BhK+A9/+MOwc3LdhwkBBBAoQ4DAWxnqHBMBhwXSXKTlOWCQZoBA86WDj0wIIJC9gL62vEHhpI86wKiv7TymtH1GEYOfJnlMkg/dNq4+0phrfk3rOEm+86j/XtLUPJuWr9d2m8TQNC/B7bxAW6/568XNtn2S1GPQzpvPq+1qncS9Pr08RD3mlS/b6s+V/LjaDrUNM1VHIO17Tl79Ttr+kHZYnTZITusrsGbNmsbFF1/cmDBhQtfz6wMOOCD0W3A//elPh23frS9a94dFjT9e8x+Np0+7pPHMGV9pLL/x1sbLi5Ymg28G/15e+HRj/YpVyfZjawQQcF6AwJvzVUwBESheIO3FkA4Y6cmRppN2yiovafPB/ggg0FkgiwHGbhdUnY8cfiaL/sILXIRTznepm1+vR9Y04wb5k5p3y2cwUJA03V7LmMd+pmXsZdDPNO2gZdy85kPTzeL9Ng/PstLMwjoLV60X/Yt7LcbVs+aFqXoCWvdxdRv3PO2wevVuW45taYfqQn9oW+sgPwhkL6B3sM2cObMxduzY0Hvg4Ycf3rjpppsad911V2Pu3Lmt+YkTJ/rbPPDAA63MfO1rX/PXee+Rnb5qcvnM7zYef+9xkX9/+u2jRoXTYNuifz7TT2PN/fON9mMjBBCoh8AILWazM2JCAAEEMhe48MILpXnBnzrd5oCT6J9OkyZNaj12+tc8CZN77rmn9bT32Glbk/Wa//7+fpNN2QYBBFIIZNVfaBaC/U5cn6HH1SmL/kL7qeagUCu9ov9F+WXVf0WlHSyf10fH9ZUjRowI7hY5X6ZhZIZ6WHnwwQcbtSdtK1reuEnbptZBFm1Uj6XH1LoyOXZc3lx/3rQu4xzU2vOO65O885is6tu0ncWVgefLEyizHWqps2iLWb0flVcLHDnuXMBUqJf+UNOmHZoKsx0C1RVYu3atTJkyRW6//Xa/EIcddphcc8010rzzzV8XnPniF78ol19+eev5BQsWyNSpU2X27NnBTaT5tZQyefLk0LoXfzhXVn79+ta67T91nIx5z34ycMd98uKs7/jbTbjtm9K39Zb+ctTM8m/cImtu/ZH/1JiPHiavPzl8LP9JZhBAoH4C9YgvUkoEEChLoHmhrcH9Sv7ppyqZEECgOAF9zVW1v9C+ruypvb/Nug/T9NqP0V5f+nyURdx+XjplG2Z1fK883R6bg4+xhzN163ac9udMjhubsRptkEcdtNdJHstaz1n3ATWqduuKSju0rkpqmaGqtkPtY+kPa9lkKXSFBJ555pnG3nvvHboWbAb8G4ODg11LsWHDhsahhx7a2u+SSy5pjB8/PpSGvv7vv//+UBrrfrfQv0MteGfbn+Y/4q/XO+FM7l576uP/Gtrn+f/8YehYLCCAQL0FuOOt2QszIYBAvgJZfUIy31wOpa6fxGxenA2tYA4BBAoVqFqf0RyIsubO2KBd8xQ3t3rT4+ikZe80ec/p3VUmd7vZ5NipTKbrg/XQbR99r9H3nKgpq7tcotLOs21EHa/q60zr05ZyuvRassXUhnxUrR1yPm1Dq8k+D7TD7E1JEYG6CyxevFj23XdfWbFihU9xwQUXtL7xwV/RZWb58uWy0047ddxiYGBAxowZ8+rzmxry1L98QTYuf062OeqfZOxJR/r7vdi8423llTP95fbn/Sf+MjO4dp0s+uinQ6vHXd0vW75999A6FhBAoL4CBN7qW/eUHIFCBfTrQfRCLYuvCckz4wxW5alL2giYC1RhYEcHFW38yj6vn+0U0DGvBbMtta500v4zzeRaMMgk2Bg1MK31p0G3PKduAb88j1vltKvQJ6kv5zFVbmXxeS+if4jPRfwWtMN4oypvoe2Q67oq1yB5R8AegZdfflkOPPBAmT9/vp+pI444QubMmSObbbaZvy5uZv/995cHH3xw2GZ77LGHPPbYY/76tQ8ukOfO/5r0jR4jb7rlatls89f4zy275Juy7p77/eVtjv2ojD3hcH+5fWbtA7+V56ZdGVr9ljtmiYzsC61jAQEE6itA4K2+dU/JEShFwNaBK1sH0EupJA6KgCUCWQV0si6O9hden5F12lVPr9c6c3GQ1vSOtWAQrKj3SG2/3Nnd26utqDpKmjuvT9JHJvcFaIfu13EVSkg7rEItkUcE7BY48cQT5YYbbghlcunSpTJu3LjQuriFiy66KPIbSD7xiU+E0l9yxuXy54d/J9sc3bzb7cShu902vbJenvzQJ0OHGfuvn5Ft3rNvaF1wof333Ua9829k16+cGdyEeQQQqLkAgbeaNwCKj0BZArZcqDFQVVYL4LgIJBOwoc+gv0heZ/qpeP2Lm1y7203Lq+U2uXPNC4BpGzexirM0eV7bsndck+3ZZriADX2S5op+aXjd1GkN7bBOtW1vWWmH9tYNOUPAZoFZs2bJCSecEMri1KlTZcaMGaF1JgsavNMgXvs0e/ZsOe6441qrB1evkUUfO6U1/4Ybvypb7Dr09ZQD9zwkKy65NrT7hFv/rXln3FahdcGFp086X9Y3vybTm7b7xGR53TGHeYs8IoAAAkLgjUaAAAKlCuiFmk56t0OREwNVRWpzLASyEyhjcIf+ovf6M6kvF+9288RM7nrT9lVUwM3Llz4G77QLrmc+mYBJG0+WotnWLr9uzATYKihQVjvk/TFYC8xrO9SJ6zraAgIIxAls2LBBxo8fH/pdN91n0aJFsttuu8XtPuz5K6+8Us4444xh61euXCk77LBDa/26BY/JsjO/JJu/dQ954/TzQ9su+eIV8uff/K+/bssD95dx/VP95faZyN93u2aabLnXm9s3ZRkBBGosQOCtxpVP0RGwSaCICzUdHNC/SZMmtR5tKj95QQCBZAJFDDJqf2Hjb7glkyp3a5PfOXM5gKABNZO73vSOPy/4Nnfu3FCleeu9x9CTKRYIvKXAi9hV+ySto6zrKXgo7ZO8fim4nnkEPIEiz6f1/ZEJgSiBItsh13VRNcA6BOwXuOWWW+SYY44JZVTPcXr9RoZTTz1Vrr02fMfa+973Prnzzjv9YzTWb5CBu34pr3377qG73Ta8MCCLj/6Mv53O7PSls2T0vnuH1gUXIn/f7SezRPr4fbegE/MI1F2AwFvdWwDlR8BCAe9iLe0Alp646aSPXJS1KPiHgHMC2k94gYqs+gyCbdk1E5PAm4tfMxkUNLnrLWkQLBjc8dq/HtNb7z0G89E+n2Zwoz0tlsMCWZ/HeAEO77wmfDSWEIgWoB1Gu7C2WIGs2yHXdcXWH0dDIC+BffbZR+bPnx9K/uqrr5bTTjsttM50ISq9mTNnykknnRSbxAu3/kxWfePb/nZ9o8fIhO9e0zWI9tx1t8ja237k7zNqn3fIrl8efsedvwEzCCBQSwECb7WsdgqNQPUEdBAxOLioJdB17YNQGmDTqX19ayX/EECgFgJR/YVX8PZ+gz7Dk8n+Ua3j7vZy+W43TzSPwJuXtumj1oVOwfdRXdfrp4pbifHPWECtg/btO+rz3nkLfVK7DstZCnhBkLg0aYdxQjyfRiCqHQb7QS9t2qEnwSMCbgksXbpUdt1112GFevzxx+Utb3nLsPVxKwYGBmTbbbcdttmKFStkxx13HLa+fcUzp14irzz6B3/16MMPk52mTvaXo2aG/b7bJ4+R103+YNSmrEMAgRoLEHirceVTdASqLqCDmdyZUvVaJP8IFCugd2Alvbuo2By6czQdWIv7nZc6BN50MDEuAKlBF4Jg7rT9JCXR14m2Eeo/iRrbIoCAawKcn7lWo5QHgc4C3/ve9+TII48MbTBhwgR58sknQ+tMF66//vphd7Z95jOfGfbVk1HpRX3N5LivN3+r7W2df6st8vfdrr1QttxzQtQhWIcAAjUWIPBW48qn6AhUWcAbyGSwssq1SN4RKFbACwTRbxTj7nl3O1odgqDe+1U3B9pkNx23n/O+jtX1r1x1uxYpHQIIpBHw3id5L0yjyL4IVEfgnHPOkcsuuyyU4eOPP15mzZoVWme6EPU1kwsXLpTdd989NokX77hPVl4509+u9TWT/zVdZLMR/rr2GX7frV2EZQQQ6CRA4K2TDOsRQMBqgeCAbh0Gbq2uDDKHQEUEgv0Gg9z5V5oXUOh2pLrUAxbdWkF9nwv2SZzL1LcdUHIE6i5AX1j3FkD56yZw4oknyg033BAq9owZM2Tq1KmhdSYLv/3tb+Vv//ZvQ5seddRR8p3vfCe0rtPCssu+Jevuutd/eqv3v0d2OesEfzlqht93i1JhHQIIRAkQeItSYR0CCFgvEBzEZLDK+uoigwhYIUC/UWw1BL07HbkugTeT33mri0WntlDH9cHBZu70qGMLoMwIIKACwfMFrutoEwi4L3D00UfLnDlzQgWdN2+e7LfffqF1Jguf/exnZfr05h1qgWnBggWy9957B9Z0nl107Odl8Pnn/Q12PHuqbPve/f3lqJnFJ5wjG5Yu8Z/a7qR/ltcd9QF/mRkEEEDAEyDw5knwiAAClREIDlRpphmsqkzVkVEEShOg3yiePjiQFnX0OvXdBN6iWgDr2l8jDDjTJhBAoG4CnJ/VrcYpLwIiUcGyVatWyfbbb5+IZ+3atTJu3DjRR286//zz5aKLLvIWuz9u2iQLDzk+tM0bbvyqbLHrTqF1wYXBNX+SRUecHFwl46ZfJFu+dbfQOhYQQAABFSDwRjtAAIHKCbRfoGkBGKyqXDWSYQQKFYgKfNBv5FsF7UGF9qMReAuLcMdb2MP1pahzmWnTpkl/f7/rRad8CCCAgC8Q1RdyfubzMIOAkwJXXHGFnHnmmaGy9XIefPrpp8vVV1/tp7PHHnuI3u02atQof123mcHVa2TRx04JbfKWn3676++7rbn/t7L8wiv9fTbbYpS8+fZ/E+nr89cxgwACCHgCBN48CR4RQKAyAlGDuXUawK1MRZFRBCwSiOo3GOTOt4KizINHrFO/HRX4DVrofC8DDu1psFwdgag2UafXRHVqipwigECeAlHnCvSFeYqTNgLlCzz88MPyN3/zN6GMPPvss7LLLruE1nVb+J//+R854IADQpv88pe/lL//+78Preu20H73Wt/oMTLh1hnddpFlX7lB1v3sHn+b1/7dO2X8ZZ/3l5lBAAEEggIE3oIazCOAgPUCUZ+K9DLNoKUnwSMCCAQFOvUbDOwElbKfjxpMCx6lTv5RQZaghc7zHtYu4u7yPffcI9omoibu9IhSYR0CCLgo0On8TMvKe6KLNU6ZEBgSeOtb3yqPP/64v+L666+XT37yk/5yt5mlS5fK/vvvL/roTfo7b6ecEr57zXuu2+PC903xn27dvfbDb/nL7TN/fuIZWXLyuaHV239qiuxw5PtD61hAAAEEPAECb54EjwggUAmBboOXDFZVogrJJAKFC3QLANFv5Fcd3dz1qATewvYMMoY9XF7qNthcp9eFy3VM2RBAIF6g23kC52fxfmyBQJUFvv/978s//dM/+UWYOHGizJs3r/mNjd2/snHZsmXyrne9SxYtWuTv22vQTRN4+pQLZf3jT/hpvfHbV8rmO+/oL3sz+rWUT/+/82TwxRe9Va3H8TMultfu8abQOhYQQAABT4DAmyfBIwIIWC/Q7RPimnkGq6yvQjKIQOEC3Qa4NTP0G/lVSbcBtbrZd/vQiFcDBN48Cfcf414btAX32wAlRKDuAlzX1b0FUH4ERI4++miZM2eOT3H22WfLZZddJp3Ok370ox/Jpz/96UzudPMOOnD3L2XFpdO9RRl92Ptlp88N3QWnT7z0+yfkuQuvGRZ0a90h9/1vNn8TbjN/f2YQQACBoACBt6AG8wggYLVA3AC6Zp5PR1pdhWQOgcIFTPoNBrnzqZZOF83e0eoU9CTw5tU6jyZ9EucytBMEEHBdgL7Q9RqmfAjEC6xZs0aOPfZY0YCaNx1yyCFy5plnit4Bt/XWW8tTTz0lv/vd72TmzJlyxx13eJvJ2LFjZcaMGXLkkUf663qaGRyUpdNmyMsP/srffav3vFu22v8dMrh2nbz8v4/KS/f+j/9ccOa1f7+PjL/kc8FVzCOAAAIhAQJvIQ4WEEDAZoG4QVzN+7Rp06S/v9/mYpA3BBAoUMCk32CQO58KIdg05GrSDgkAD3m5PGcy2FynoLTLdU3ZEECgs4DJ+yLnZ539eAYBVwQ2btwoX/jCF+Sqq64yLtKll14qp512mmy55ZbG+3TdcOOgrLjpNhmYc3vHzXY45Xh58frvyKZX/uxvs/2nm7/vdgS/7+aDMIMAAsMECLwNI2EFAgjYKGAyUKX5ZrDKxtojTwiUI0C/UY67d1STwFsdBtXivk5LvXjv8lqN+48mg82qUIfXhvu1TQkRQCBKgPOzKBXWIVBvgWeeeUa+9a1vya233iqPPPLIMAz9XbcPfvCDcvzxx8vOO+887PksVrTucFv4tKx/Zpls+ONKec1Or5NRe02Q107YVV5+8hl59tRpocO86d+vkte8/nWhdSwggAACQQECb0EN5hFAwFoB0ws0LQCDVdZWIxlDoFABk8CPlyH6DU8iu0eTfrsOdynjkF2bqnpKJm3BK2MdXhteWXlEAIF6CSTpCzk/q1fboLQIqIB+C8SqVatk7dq1su2227b+TD+4lJfgiptulYH/vM1P/rX7TZTxF5/qLzODAAIIRAkQeItSYR0CCFgnkOREizsHrKs+MoRA4QImdxkFM8Ugd1Ajm3mTOqhDf20ywEj7y6bN2Z5Kkg8D1OG1YXt9kT8EEMhHgOu6fFxJFQEEDAWav+u26r9/Ievu+7XIpoZsNWli16+M3LR+gyye/Lnmb76t8Q+wy1fPla3esae/zAwCCCAQJUDgLUqFdQggYJWAyaBle4b5rZx2EZYRqJdA0n6DQe582ofJ4Jrr/bWJAZ/oz6f92ZSqSSC6Pb+0i3YRlhFAoOoCSc/PtLyunydUvU7JPwJVE1jxrf8a9ntuu37ryzLqTeMii/LCD+6RVdfc4D83cpddZLdZXxYZMcJfxwwCCCAQJUDgLUqFdQggYJWAyaBle4YZrGoXYRmBegnQb9hR3yb14Hp/bWLAoKId7TXPXPQy2MwHAvKsEdJGAIEyBEzeE9vz5fp5Qnt5WUYAgRwFmne4LTzkX4YdYKcvnSWj99172PrB1Wtk8XFnyKZX/uw/12lbfwNmEEAAgb8IEHijKSCAgNUCvXxCXAvEYJXV1UrmEMhVoJcBbs0Q/Ub21WLy1Xouu5u0Rb5mMvt2Z2OKvQw2azkIytpYm+QJAQR6EeC6rhc19kEAgSwF1j+3Up6ecvqwJHebM0NGbjcmvL4ZpFs6bbq8PO8hf/32n57S9Wsp/Q2ZQQABBJoCBN5oBgggYLWAyaBlpwLw6chOMqxHwG2BNP0Gg9zZtg3TQTZX+2uTYAuBt2zbnI2ppemTXH1t2FhP5AkBBPIVoC/M15fUEUAgXmBwzZ9k0REnhzbc7sRj5XVHHxpaJ83fgVv2lRtl3V33+utHH/Z+2elzU/xlZhBAAIE4AQJvcUI8jwACpQqYDFp2yiCDmZ1kWI+A2wJp+g0GubNvGyb14eJdb6YDjAR7s29ztqVo2hai8u3iayOqnKxDAAH3BUzOBzopcH7WSYb1CCCQVGDxCefIhqVLpG+77WTclefKFuNfH0pi0/oNsuzC6+Tlh37tr3/tP+wr4y9oBuz6+vx1zCCAAAJxAgTe4oR4HgEEShNIM1ClmWawqrSq48AIlCZAv1EafccDm9aJa4NqJgOMfECkY7Nx6gmTttCtwK69NrqVlecQQMBNAdNzgU6l57qukwzrEUAgqcDqn8+T5y+/rrXbVu95t2z70ffKqDfsLBtWDci6+Y/I6lt+IIPPP996vm/0GNnh1I/LNgdNTHoYtkcAAQT4qknaAAII2CuQ9gJNS8Zglb31S84QyEPA5DfF4o5LvxEnlPx5k8CDS4Nqpu9f3O2WvC1VbQ/TttCtXC69NrqVk+cQQMBdgSz6Qs7P3G0flAyBogVe+O+7ZNWMm7oedvQH3ys7nvQx6dt6y67b8SQCCCDQSYA73jrJsB4BBEoXMBmojcskg1VxQjyPgDsCpr8nFldi+o04oeTPmwZEXRlUM3n/4m635O2oinuYtv1uZaNP6qbDcwggUAUBk/fFuHLQF8YJ8TwCCCQR2PDCgAz89AFZv/hZGVz5gowYtYWM3HEH2WLPN8mY/d8hfduMTpIc2yKAAALDBAi8DSNhBQII2CCQxacivXJwR4EnwSMCbgtk1W8wsJN9OzENirpgbxpocSXImH1rcSdF03ZvUmLai4kS2yCAgI0CWZ2fadm4rrOxhskTAggggAACCEQJEHiLUmEdAgiULpDFpyK9QjBY5UnwiIDbAvQbdtevaUCqysE308FF7nazu61mlTvT9mByvCq/LkzKxzYIIOCuAOdn7tYtJUMAAQQQQACBzgIE3jrb8AwCCJQkkOUnxLUIDFaVVJEcFoECBbIc4NZs029kX3lJ+vYqBqaStMEqli/7FuF+ilkONqsWd3q432YoIQKuCSR57zcpO+dnJkpsgwACCCCAAAI2CBB4s6EWyAMCCIQEkgxehnbsssBdb11weAoBBwTy6DcY5M6+YZje9aZHrlK/nWRgkaBb9u3KxhTz6JOq9JqwsU7IEwIIFC9AX1i8OUdEAAEEEEAAATsECLzZUQ/kAgEEAgJZf0Jck2agMwDMLAIOCuTRbzDInX1DSRKg0qNXoQ5cLFP2NV+/FPMYbOZOj/q1I0qMQNUFOD+reg2SfwQQQAABBBDoVYDAW69y7IcAAqUKBO+aqMLAbKlYHBwBBFoC9Bt2NISkgSqbPzjhUlnsaB31ykUwOGdzO69XrVBaBBAoWoDzs6LFOR4CCCCAAAIIFCFA4K0IZY6BAAKZC3CBljkpCSLgvAD9hj1VHAw4mOTKxqCEC2UwsWeb/ASCbcjGNp5fyUkZAQQQGBLg/GzIgjkEEEAAAQQQcEeAwJs7dUlJEKiVABdotapuCotAJgL0G5kwZpZIMOhgkqhNgYkq593Emm2KEQi2I5vadzGl5ygIIIDAqwKcn9ESEEAAAQQQQMBFAQJvLtYqZUKgBgJcoNWgkikiAhkL0G9kDJpBcsE6MU2uzK8X1q+W1GCJPiaZGo1Gks3ZtiYCBN5qUtEUEwEEugoEzwXKfI/vmkmeRAABBBBAAAEEEgoQeEsIxuYIIGCHABdodtQDuUCgSgL0G/bVVtLfSPNKUPTdQb0G3DS/DCJ6tcZjuwCBt3YRlhFAoI4CnJ/VsdYpMwIIIIAAAu4LEHhzv44pIQJOCnCB5mS1UigEchWg38iVt+fEew2+6QE1AKdTf39/6zHrf2kCbpqXogOEWZef9PIVIPCWry+pI4BANQQ4P6tGPZFLBBBAAAEEEEgmQOAtmRdbI4CAJQJcoFlSEWQDgQoJ0G/YW1nBAEQvucw6AJc24KZlIOjWS03Wa59gu6e91KvuKS0CCAwJcH42ZMEcAggggAACCLgjQODNnbqkJAjUSoALtFpVN4VFIBMB+o1MGHNNJFhHvR7IC8Lp/iZ3wmmQTae5c+eKznvLrZU9/DvooINax9VHJgS6CRB466bDcwggUBeB4Hs/X89cl1qnnAgggAACCLgvQODN/TqmhAg4KcAFmpPVSqEQyFWAfiNX3swSDwYjMku0oIQ02KaDhkwImAgE2zp3vJmIsQ0CCLgowPmZi7VKmRBAAAEEEECAwBttAAEEKinABVolq41MI1CqAP1GqfyJDh4MSCTascSNCZyUiF/RQwfbOe2nopVIthFAILUA52epCUkAAQQQQAABBCwUIPBmYaWQJQQQiBfgAi3eiC0QQCAsQL8R9rB9KRiUsD2vfDWW7TVkZ/6CbZzAm511RK4QQCB/Ac7P8jfmCAgggAACCCBQvACBt+LNOSICCGQgwAVaBogkgUDNBOg3qlnhweCEbSXg99xsq5Fq5SfYtgm8VavuyC0CCGQnwPlZdpakhAACCCCAAAL2CBB4s6cuyAkCCCQQ4AItARabIoBAS4B+o9oNIRikKLskBNzKrgE3jh9s0wTe3KhTSoEAAskFOD9LbsYeCCCAAAIIIGC/AIE3++uIHCKAQIQAF2gRKKxCAIGuAvQbXXkq82QwWFF0pgm4FS3u9vGCbZnAm9t1TekQQKCzAOdnnW14BgEEEEAAAQSqK0Dgrbp1R84RqLUAF2i1rn4Kj0BPAvQbPbFZu1MwaJF3JgmK5C1cz/SDbZg2Vs82QKkRQECE8zNaAQIIIIAAAgi4KEDgzcVapUwI1ECAC7QaVDJFRCBjAfqNjEEtSU6DFzrdc889rb8ssqV3tunU398v3nxrBf8QyFCAwFuGmCSFAAKVFeD8rLJVR8YRQAABBBBAoIsAgbcuODyFAAL2CnCBZm/dkDMEbBWg37C1ZrLNlwbg5s6d20pU500nDbLpRKDNVIzt0goQeEsryP4IIOCCAOdnLtQiZUAAAQQQQACBdgECb+0iLCOAQCUEuECrRDWRSQSsEqDfsKo6yAwCtRcg8Fb7JgAAAgg0BTg/oxkggAACCCCAgIsCBN5crFXKhEANBLhAq0ElU0QEMhag38gYlOQQQCCVAIG3VHzsjAACjghwfuZIRVIMBBBAAAEEEAgJEHgLcbCAAAJVEeACrSo1RT4RsEeAfsOeuiAnCCAgQuCNVoAAAghwxxttAAEEEEAAAQTcFCDw5ma9UioEnBdgAN35KqaACGQuQL+ROSkJIoBACgECbynw2BUBBJwR4PzMmaqkIAgggAACCCAQECDwFsBgFgEEqiPABVp16oqcImCLAP2GLTVBPhBAQAUIvNEOEEAAAe54ow0ggAACCCCAgJsCBN7crFdKhYDzAgygO1/FFBCBzAXoNzInJUEEEEghQOAtBR67IoCAMwKcnzlTlRQEAQQQQAABBAICBN4CGMwigEB1BLhAq05dkVMEbBGg37ClJsgHAgioAIE32gECCCDAHW+0AQQQQAABBBBwU4DAm5v1SqkQcF6AAXTnq5gCIpC5AP1G5qQkiAACKQQIvKXAY1cEEHBGgPMzZ6qSgiCAAAIIIIBAQIDAWwCDWQQQqI4AF2jVqStyioAtAvQbttQE+UAAARUg8EY7QAABBLjjjTaAAAIIIIAAAm4KEHhzs14pFQLOCzCA7nwVU0AEMheg38iclAQRQCCFAIG3FHjsigACzghwfuZMVVIQBBBAAAEEEAgIEHgLYDCLAALVEeACrTp1RU4RsEWAfsOWmiAfCCCgAgTeaAcIIIAAd7zRBhBAAAEEEEDATQECb27WK6VCwHkBBtCdr2IKiEDmAvQbmZOSIAIIpBAg8JYCj10RQMAZAc7PnKlKCoIAAggggAACAQECbwEMZhFAoDoCXKBVp67IKQK2CNBv2FIT5AMBBFSAwBvtAAEEEOCON9oAAggggAACCLgpQODNzXqlVAg4L8AAuvNVTAERyFyAfiNzUhJEAIEUAgTeUuCxKwIIOCPA+ZkzVUlBEEAAAQQQQCAgQOAtgMEsAghUR4ALtOrUFTlFwBYB+g1baoJ8IICAChB4ox0ggAAC3PFGG0AAAQQQQAABNwUIvLlZr5QKAecFGEB3voopIAKZC9BvZE5KggggkEKAwFsKPHZFAAFnBDg/c6YqKQgCCCCAAAIIBAQIvAUwmEUAgeoIcIFWnboipwjYIkC/YUtNkA8EEFABAm+0AwQQQIA73mgDCCCAAAIIIOCmAIE3N+uVUiHgvAAD6M5XMQVEIHMB+o3MSUkQAQRSCBB4S4HHrggg4IwA52fOVCUFQQABBBBAAIGAAIG3AAazCCBQHQEu0KpTV+QUAVsE6DdsqQnygQACKkDgjXaAAAKoKYd/AAAFOUlEQVQIcMcbbQABBBBAAAEE3BQg8OZmvVIqBJwXYADd+SqmgAhkLkC/kTkpCSKAQAoBAm8p8NgVAQScEeD8zJmqpCAIIIAAAgggEBAg8BbAYBYBBKojwAVadeqKnCJgiwD9hi01QT4QQEAFCLzRDhBAAAHueKMNIIAAAggggICbAgTe3KxXSoWA8wIMoDtfxRQQgcwF6DcyJyVBBBBIIUDgLQUeuyKAgDMCnJ85U5UUBAEEEEAAAQQCAgTeAhjMIoBAdQS4QKtOXZFTBGwRoN+wpSbIBwIIqACBN9oBAgggwB1vtAEEEEAAAQQQcFOAwJub9UqpEHBegAF056uYAiKQuQD9RuakJIgAAikECLylwGNXBBBwRoDzM2eqkoIggAACCCCAQECAwFsAg1kEEKiOABdo1akrcoqALQL0G7bUBPlAAAEVIPBGO0AAAQS44402gAACCCCAAAJuChB4c7NeKRUCzgswgO58FVNABDIXoN/InJQEEUAghQCBtxR47IoAAs4IcH7mTFVSEAQQQAABBBAICBB4C2AwiwAC1RHgAq06dUVOEbBFgH7DlpogHwggoAIE3mgHCCCAAHe80QYQQAABBBBAwE0BAm9u1iulQsB5AQbQna9iCohA5gL0G5mTkiACCKQQIPCWAo9dEUDAGQHOz5ypSgqCAAIIIIAAAgEBAm8BDGYRQKA6AlygVaeuyCkCtgjQb9hSE+QDAQRUgMAb7QABBBDgjjfaAAIIIIAAAgi4KUDgzc16pVQIOC/AALrzVUwBEchcgH4jc1ISRACBFAIE3lLgsSsCCDgjwPmZM1VJQRBAAAEEEEAgIEDgLYDBLAIIVEeAC7Tq1BU5RcAWAfoNW2qCfCCAgAoQeKMdIIAAAtzxRhtAAAEEEEAAATcFCLy5Wa+UCgHnBRhAd76KKSACmQvQb2ROSoIIIJBCgMBbCjx2RQABZwQ4P3OmKikIAggggAACCAQECLwFMJhFAIHqCHCBVp26IqcI2CJAv2FLTZAPBBBQAQJvtAMEEECAO95oAwgggAACCCDgpgCBNzfrlVIh4LwAA+jOVzEFRCBzAfqNzElJEAEEUggQeEuBx64IIOCMAOdnzlQlBUEAAQQQQACBgACBtwAGswggUB0BLtCqU1fkFAFbBOg3bKkJ8oEAAipA4I12gAACCHDHG20AAQQQQAABBNwUIPDmZr1SKgScF2AA3fkqpoAIZC5Av5E5KQkigEAKAQJvKfDYFQEEnBHg/MyZqqQgCCCAAAIIIBAQIPAWwGAWAQSqI8AFWnXqipwiYIsA/YYtNUE+EEBABQi80Q4QQAAB7nijDSCAAAIIIICAmwIE3tysV0qFgPMCDKA7X8UUEIHMBeg3MiclQQQQSCFA4C0FHrsigIAzApyfOVOVFAQBBBBAAAEEAgIE3gIYzCKAQHUEuECrTl2RUwRsEaDfsKUmyAcCCKgAgTfaAQIIIMAdb7QBBBBAAAEEEHBTgMCbm/VKqRBwXoABdOermAIikLkA/UbmpCSIAAIpBAi8pcBjVwQQcEaA8zNnqpKCIIAAAggggEBAgMBbAINZBBCojgAXaNWpK3KKgC0C9Bu21AT5QAABFSDwRjtAAAEEuOONNoAAAggggAACbgoQeHOzXikVAs4LMIDufBVTQAQyF6DfyJyUBBFAIIUAgbcUeOyKAALOCHB+5kxVUhAEEEAAAQQQCAgQeAtgMIsAAtUR4AKtOnVFThGwRYB+w5aaIB8IIKACBN5oBwgggAB3vNEGEEAAAQQQQMBNgf8PAAD//xUVTAMAAEAASURBVOydB5zURPvHn4M7rgFH7yJIkaIioIgdu76IvWJ9FbtY/mIvYO8NCyroq9hFRUF9bYhYeVGw0qUjvR3cHVe4u/88e042yabubnaT7G8+n7skk8nMM9/JZmfnl2cmq1YEQgABEACBgBE45JBD6Ouvv45YPXXqVBo0aFDAagBzQQAEUk0Az41UE0d5IAACVgTuvPNOGjVqVCQJb0eOHGmVHOdAAARAIJQE0D8LZbOiUiAAAiAAAiCQ8QSyILxl/D0AACAQSAL4gRbIZoPRIJBWAnhupBU/CgcBENARgPCmA4JDEACBjCSA/llGNjsqDQIgAAIgAAKhJwDhLfRNjAqCQDgJ4AdaONsVtQIBLwngueElXeQNAiDglgCEN7fEkB4EQCCMBNA/C2Orok4gAAIgAAIgAAIQ3nAPgAAIBJIAfqAFstlgNAiklQCeG2nFj8JBAAR0BCC86YDgEARAICMJoH+Wkc2OSoMACIAACIBA6AlAeAt9E6OCIBBOAviBFs52Ra1AwEsCeG54SRd5gwAIuCUA4c0tMaQHARAIIwH0z8LYqqgTCIAACIAACIAAhDfcAyAAAoEkgB9ogWw2GA0CaSWA50Za8aNwEAABHQEIbzogOAQBEMhIAuifZWSzo9IgAAIgAAIgEHoCEN5C38SoIAiEkwB+oIWzXVErEPCSAJ4bXtJF3iAAAm4JQHhzSwzpQQAEwkgA/bMwtirqBAIgAAIgAAIgAOEN9wAIgEAgCeAHWiCbDUaDQFoJ4LmRVvwoHARAQEcAwpsOCA5BAAQykgD6ZxnZ7Kg0CIAACIAACISeAIS30DcxKggC4SSAH2jhbFfUCgS8JIDnhpd0kTcIgIBbAhDe3BJDehAAgTASQP8sjK2KOoEACIAACIAACEB4wz0AAiAQSAL4gRbIZoPRIJBWAnhupBU/CgcBENARgPCmA4JDEACBjCSA/llGNjsqDQIgAAIgAAKhJwDhLfRNjAqCQDgJ4AdaONsVtQIBLwngueElXeQNAiDglgCEN7fEkB4EQCCMBNA/C2Orok4gAAIgAAIgAAIQ3nAPgAAI+J7A9NVVERvHzSpTbP3l62nKft9BByv7fdrkRPb3bpdDA9vW7SsnsQMCIJDRBDCwk9HNj8qDgO8IQHjzXZPAIBAAgTQQQP8sDdBRJAiAQEIESmfNjVy/8eX3bfPJ27NnJE2h2Bb2q9u3vQgJQAAEQkEAwlsomhGVAIHwENCLbMv/Ed3irWFHIb5JMW54/4J4s8F1IAACISCAgZ0QNCKqAAIhIgDhLUSNiaqAAAjETQD9s7jR4UIQAIEUEWChTYpsFXPnJVRqbs8eJMW4VheclFBeuBgEQMDfBCC8+bt9YB0IZAwBFtzYoy1Roc0O2JC+BQRvODtKOA8C4SSAgZ1wtitqBQJBJQDhLagtB7tBAASSSQD9s2TSRF4gAALJIiDFtkSFNjt7is48MZIEIpwdKZwHgeARgPAWvDaDxSAQKgKpEtz00FiA4wAvOD0ZHINAeAlgYCe8bYuagUAQCUB4C2KrwWYQAIFkE0D/LNlEkR8IgEAiBFIluBnZyCIcBDgjMogDgWASgPAWzHaD1SAQeAJPzSyjyb9E12xLV4UgwKWLPMoFgdQTwMBO6pmjRBAAAXMCEN7M2eAMCIBA5hBA/yxz2ho1BQE/E0in4KbnAgFOTwTHIBBMAhDegtlusBoEAkvAL4KbEUAW4eABZ0QGcSAQDgIY2AlHO6IWIBAWAhDewtKSqAcIgEAiBNA/S4QergUBEEiUgJ8EN31dIMDpieAYBIJFAMJbsNoL1oJAYAnwlJJ3fFzse/shvvm+iWAgCMRNAAM7caPDhSAAAh4QgPDmAVRkCQIgEDgC6J8FrslgMAiEhsDyq+4lr9dwSxRWbs8e1Pz8k6iwX89Es8L1IAACKSYA4S3FwFEcCGQiAT97uRm1R8e2OTSsXwENFFsEEACB8BDAwE542hI1AYEwEIDwFoZWRB1AAAQSJYD+WaIEcT0IgIBbAuzlturG+9xeltb08H5LK34UDgJxEYDwFhc2XAQCIOCUQNBEN3W94P2mpoF9EAg+AQzsBL8NUQMQCBMBCG9hak3UBQRAIF4C6J/FSw7XgQAIxENg3UvvU/GbE+O5NO3XQHxLexPAABBwRQDCmytcSAwCIOCUAE8tOW5WGS0X20QCe59x6NMmh/ZuV7dv5onGZf60qq6839ZUJVw2lwvxjSkggEA4CGBgJxztiFqAQFgIQHgLS0uiHiAAAokQQP8sEXq4FgRAwA2BZIluPP1j3p49qVD8cbCaBpLL5FD+69ykTGsJ8S2CE/9AIBAEILwFoplgJAgEi0Ci67nJqR651mYim1MiUoyb/EuZ00ti0kF8i0GCCBAIJAEM7ASy2WA0CISWAIS30DYtKgYCIOCCAPpnLmAhKQiAQFwEeGrJjS+/n5Dwlay11tiWUiHCJeJ1lyxb4oKJi0AABBwTgPDmGBUSggAIOCGQyNSSUnBLVGwzszMR2zjPz4e1MMsa8SAAAgEggIGdADQSTASBDCIA4S2DGhtVBQEQMCWA/pkpGpwAARBIAoFE1nOTnm2tLjgpCZbEZpGoB167B2+x9LaLLRExIAACqSQA4S2VtFEWCIScQLyebl4Lbnrs8QpwbOe4wUX67HAMAiAQEAIY2AlIQ8FMEMgQAhDeMqShUU0QAAFLAuifWeLBSRAAgQQJLL/qXteebqn2KEtEgOv2xasJEsLlIAACXhGA8OYVWeQLAhlI4MhxG1zX+i4hZHnl4WZnTDwCHKadtKOK8yDgXwIY2PFv28AyEAg7ga+//pqmTZumqSbH8R+HQYMGRf54f+TIkbxBAAEQAIGMIID+WUY0MyoJAmkhEI+glc411OKxl0XCjqNvTQtfFAoCIGBNAMKbNR+cBQEQcEjArYjlF+8xt3YzDohvDm8KJAMBnxHAwI7PGgTmgEBICUiRTS2sxVNViHHxUMM1IAACQSOA/lnQWgz2gkAwCLgVsVLt5WZGMZ716NIpFprVA/EgAAJEEN5wF4AACCRMwK145UfhatjHxbR8dZVjFun01HNsJBKCAAhoCGBgR4MDByAAAkkkwCIbTx3JW6+CFOLgEecVYeQLAiCQDgLon6WDOsoEgXATiEd085vXmNs6QHwL9z2N2gWTAIS3YLYbrAYB3xAIg+gmYbqpi1889qTt2IIACNgTwMCOPSOkAAEQcEcgFYKbkUWjRo3ClJRGYBAHAiAQOALonwWuyWAwCPiaAHuMrbrxPsc2+lmwciu+tXvwFirs19Nx3ZEQBEDAWwIQ3rzli9xBINQEpgsPsTuEp5jTEAQvMYhvTlsT6UAgeAQwsBO8NoPFIOBXAukS3PQ8IMDpieAYBEAgaATQPwtai8FeEPA3geVX3UsVc+c5MtLPopusgBvxDeu9SWrYgoA/CEB480c7wAoQCCQBNyKVH6eXNIPupl5BEBPN6ol4EMg0AhjYybQWR31BIPkE5HSSXk4pGY/VEODioYZrQAAE/EAA/TM/tAJsAIFwEHAjUgVBdJOt4qZeEN8kNWxBIP0EILylvw1gAQgEkoAbcSpIoptsDKdrvmHKSUkMWxDwPwEM7Pi/jWAhCPiVgF883Oz4QICzI4TzIAACfiOA/pnfWgT2gEBwCSw84hxHxgdJdJMVciO+YcpJSQ1bEEgvAQhv6eWP0kEgsAScCm9BFN24UdxMowmvt8DexjA8wwhgYCfDGhzVBYEkEWAvNxa0ghIgvgWlpWAnCIAAE0D/DPcBCIBAMgg4FaaC7BHmdBrNINcxGfcC8gABvxCA8OaXloAdIBAgAk5Ft6B7gzkV34JezwDdejAVBBIigIGdhPDhYhDISAJBE91kIw0aNIimTp0qD7EFARAAAd8SQP/Mt00Dw0AgUAScersF3RssU+oZqJsPxoKACQEIbyZgEA0CqSZQVU20Zbv4J0JWFlGLwvqpNsFxeU6Ft8+HtXCcp18TOq0rvN782oKwCwSiBDCwE2WBPRAAAXsC6meGfWrzFCyCcRg5cmRka/Zv2rRpkVM8rWWy1pBj8U2Wb1Yu4kEABEAgnQTUz1o8s9LZEigbBIJLwKm3WxCnmNS3SumsubTqxvv00THH8HqLQaKJqNpUrBxnN25IWdn+HYNVDPXxTm3VDtqxrbTOwnpZlNOksY+tTZ1pEN5SxxolgYAlgRenl9CrX5coad4d3tK34tuR4zYodprtBHWKSaP6OFnvDV5vRuQQBwL+IoCBHX+1B6wBAb8SYNGLnxeJBBa7WGhLRPRiO1iMS3SaS0w9mUhL4loQAAGvCaB/5jVh5A8C4SfgxAssDKKbbEmnU052++JVeQm2KgKlC5fTH6dfrMR0efAOannEfsoxdtwTWPXmJ7T84dHKhf2nvE05TYuU40zdgfBm0fI1tURby2uUFEX59Ug4ImVMKKuspcpqAUGE3Owsys/JpNqnvpmf/6GE3vwmKry9eXlLatvYf29cOPUAC4O3m7wLnE45Ca83SQxbEPAnAQzs+LNdYBUI+IlAIlNLJkNsM2PBdnGIV4SD+GZGFvEgAALpJoD+WbpbAOWDQLAJZJK3m2wpp15vYRIbZd2TsS2Zt5j+HHq5klXnu2+m1oMPVo6x457AyvEf0sonxigX9v3v65TburlynKk7EN4sWv7rv8pp1LtblBSPntWM+u/UQDkO+84pL2ygDZt2RKrJ3jzjz8MHxss2D4rwlmnebrLN4fUmSWALAsElgIGd4LYdLAeBVBCI19PNS8FNX+9EBDiIb3qaOAYBEPADAfTP/NAKsAEEgksg07zdZEvB602ScL+F8Oaemd0VEN6MCUF4M+YSif103nZ64IPonK/3nt6U9u+ca3FFuE4d/+w6Kt5a5/HXpmU2vXVh8Nfr8nMLBUF4y0RvN3nPwOtNksAWBIJLAAM7wW07WA4CqSCQxYvsugzpWo+IBTgWCvnPTUiXvW5sRFoQAIHMIoD+WWa1N2oLAskkkInebpKfU6+3dg/eQoX9esrLsBUEILwl/zaA8GbMFMKbMZdILIQ3CG8Wt0fSTwVBeHPi9RWmtd30jezE2w/TTeqp4RgE/EMAAzv+aQtYAgJ+I6B+Pjixjb3cWMRKd4hnakyIb+luNZQPAiCgJqB+/uL5pCaDfRAAATsCToW3sK515sTrLbdnD+o4+lY7lBl1HsJb8psbwpsxUwhvxlwisRDeILxZ3B5JPxUE4c2J8BSmtd30jezE44+nZR03GAuI6tnhGAT8QAADO35oBdgAAv4j4Fa88tuUjW7t94to6L87ARaBAAikgwD6Z+mgjjJBIBwEMnWaSdl6Tr3ewio8Sg5utxDe3BKzTw/hzZhRKIW3qmqi7VU11DivnnGtHcZ6LbyVVtZSTv0salDfoUEJJNtWUUsFOVlU3wWSIE81ubW8hhrm1qN67mcMiqFcU0u0o7qWGmQnIbN/cuf2aJSrzS8Zwlu1mBm0Yodo6wbavGMqFUeEk6kWwy46OWHAaMMsPsZx6+ASEPANAQzs+KYpYAgI+IaAW9HKb6KbBMlTTvIzzmnwaz2c2o90IAAC4SGA/ll42hI1AYFUE3AivIVddHLCwKvpJmsqKomyxNhrg+ykNn1t1Q6q2bGD6ufnJZxvTXkFZWVni7/o4LvfhbcdJWWUXZBPyRrUZpb1GuQkzFJmUF1aRvULC+RhZJss4S1S94bavDUFBewgFMIbixjjftxGPyyspC3bqqlKCFoy5Apxo0WT+nRg9zw6skce7dLc+GHw0/JKmjCrTF4W2S5et4M2bNqhxPE6Zx1Nrj+tXwHt1bGBkla/s2prNX05fztNm19Bq0We28trqbZu+TQqKMiiji1zqHubbPpX73zq0crdh2HUJ8VU9k+dD+6WS4NFHpVCfHz/t1Ka8FMZbSquVspiHn3EOnWXHdiQOqvqcu9nxVS8PcqN7Z8xr1yphniO0t6CoVFoIuy/5cjUefjMW1dFL/1QqphywxGNqHlhfXprZim9N3O7ps1aNMumAbs0oGsPaSxETuUS253PxPp+Xy+ooIVrovdAfSG8dRD3wK5ts+n0/oXURcXPLkMWxMb/VEI/LamkhauqIvco57drhxzaR9h39l4Nadz0EnrzmxIlqzcvb0ltG1sbze381qwS+n1lFS1cXaWsycft3FncT3vslEvDBhYmRTR04u0V5mkmZcM4mW4T001KWtiCgL8IYGDHX+0Ba0Ag3QTcilVBmAJN/Zyz4wvxzY4QzoMACKSCgPq5FYTnbCqYoAwQAAF7Ak68vYrOPJFaXXCSfWYBTuFkuslkCW+VG7fQ2ve/pLK5i6ls/kKqWL0iQi5v5y5U0KsbNT2gP7U85kBbmitemEAVf6+LpGvYpzu1OekI2r58Na0a/yFt/mwq7Sgtjpxr0Lw15ffoRh0uOZ0a7dbNNl+ZYOPXP9GmKdOp9NfZVP730kh0o70GUOO9dqc2pxxJFes20p9DL5fJqfPdN1PrwQcrx17ulP61gla/OkkpYudrzqacJo1pzQdTaN07nwiuc5RzBbv2oqL9+1NHUf+sHGM9Q0ms2uH6b/luJpXOXqDkl11YJNqoBxX07EKtTziM8ju1V11hvVu7o5pWv/sZbZvxJ5X88jtVFW8gzq/R3v2p0T57UNuTj6C/3/iIVj4xRsmo739fp9zWzZVjs52NU2dQ8f9+E/fUImHrfKqp3B7JO7/nrlTYqyu1HXos5bZqZna57+MDL7y982spjfl8myIs2REff2lL6iiEOH144YcSekMleujP2x2fdXBDumjfhobJhk/YRH8sEm8BOAyXHdWITu9b6DA10aAH1ihpBwhxkYWoC1/ZqIgwykndzsf/15oK//GMOuShNY4Z6rLhlxto6g1t9NGeHX/wx3Z64uO6hzAX8vjZzeiD34SoKeLNQkshko0Z2pRaCIHOKpRX1dIdIm+16GiWfvgxjenkPvYqPAvDV7y1iZYLYcws7CbEt17tGtA73zkX3hZuqKIR72y2befGjerRE2c0MxWdzWzSxzsR3jJBcILwpr8zcAwCwSGAgZ3gtBUsBYFUEMjKcj5DQJAGg9XPOjuOQaqXXV1wHgRAIJgE1M8sPJOC2YawGgTSQcDJ+m6ZILylSoBkMWfJ7Y8oophZmzcddCh1vfvKGI8odfpfjr5AiF+rIlGN996HOt9yCc0++1rLvDvdPoLanHi4OpvY/dpaWjr6NVrzyuux5/6JyWvfiTredAktGH6zkiaVwtv6T7+jRbfco5Tde/xTtP7jabTu7XeVOP1OYa/dqMdTt1NOU2unF/ZAXHz/WNowabI+i5hjp3Vm77Z51z5A236eEZOHjGh62OFU2LsrrRz9nIwiO+Ftx7ZSWjTyGdr89VfKNUY79RrkU9dHbqdmB/QzOu37uEALb9P+KqeR725xBfm5C5obepR5Kbyd8eIGWrM+6jnnxGAW0B48oQk5GQ5QC2/9ujWgBat3UEnJP+50FoWFRXjr1C6HlgovMrvATB8STM0CT/155tj1tHWbPTuZx6F98umOY8wffJu319A5ov2dtIfMU26tPN4mCMH5mU+3yaSOto+d1Yz67WTulWmXiRPBKROmWHQiQGaC55/d/YLzIOBHAhjY8WOrwCYQSA8BN1NMBs0zzI0nH9Z7S8/9h1JBAASiBNA/i7LAHgiAgHMCEN7qWDkR3nJ79qCOo291DleXctG9z9P69ybqYs0Pc1u1o93ffZqyTaYMVAtv7C1XU1JClRvXmmf4z5m+n7xGuW1amKabP+Jh2vzVFNPzZiecilBm17uJ1wtvjffZl7b+70fbLFoMGUJd77zCNF319nL6Y+h1VL5skWka/YnWZ55Gna+/QB+tHFcVbxOC6PWK16BywsGOlfDGU33Ov+yOiOecg6wiSTpefxW1O/NfTpP7Jl2ghbdTx26g9RujglYXMW3fsAMaUo/WOdSwQT1aWbyDlorz0xZW0LQ/t0c8usyEtzViisplm8S8faowY1kFvaea0vBs4dW2u/BKMgqdmtWn1o2MvanUwlv/7rmRqQU7N8uhncU1HP7eUm3osXXHSU3oUJPpHdU2qIU3dTzv9xVCXI+2DWgn4eXH013OFQLVTDGFIge18PazmGpTLGOmCaM+2Ezb/5l+kr2mbj3WWLTKFh5v/RMQdDSFOjjQe7zJS9q1yqah+xRSd7FdJ9pz/PRSWrBcK8i9O7ylqdfb6G+20fuq9uZ8/7VXAR0i2qC94DdbeKy99ZNQ5MW0jurw/IXNaVcxVahReHjKVvpYTPepDuwdecAuuZHpH38S99jYr0qoWqzLpg9mwttycb+c+9x6TfKixvXokkGNqFebnMi6gfPXVtGYaSWazwdPu/nuxeZfUJoMDQ6OHLfBIFYblQnCm5N13sK+1p221XEEAsEhgIGd4LQVLAUBrwk49XYLmugmubkRFuFhIqlhCwIgkA4C6J+lgzrKBIHgE3AyxWLY13eTrWi3zlsiwtv6z4SH1s1RDy0uk73aWp92NOXv0oFqyrbT1tl/0cpHxmqElDbnDqVO15wrTdRs1cKb+kT7yy+ior16U/2CPNr2x0Ja/vCzkakHZZpWZ5xKu9xwoTzUbLf89CfNu2SEJq7VaSdT86MOoDwh1m0T02OuGvu2MvWiOmE6hTdpR6M+fanV0CFUsMtOVCWm9Fzz+mTa8u038nRk2/+rdyLTUmoi/zlYMfZd+nvMOM2pthecE5n+M7dtSyqdv4TWvvMpFf/wnSbN7hPGUmGXnTRx8mDZM2/Q6hfHy8PItuN1V1DR3ntE1vUr/mUerXzsBUNPRTPhjaet/O3EKzRiHk9b2f6qC6hxnx6U07woMu3o+g++og2To5577PnW99NXTOuvMdJHB4EV3taXVNOpT0fFh/ats+nV81uYrjvI3kzvCi+hY3rlU6uGxgKZvl0+Fet8PfBBdErDe09vSvuL9dHchpsnbYmsDXeGWAeuab5QqUzCF/PL6d6JUQ8+Hrwff579fKhGwhsLZY8Ke7u1iBWElm2upmeFyHT34CLLtb+Of3adMo0hr2/31oXxizYmVY4r2kh422vXXHrw+KZUX4WXpSye4nHO0ug0nxcc1pDO3Tt2SlC+P459Yq1mus0bjiuif4n7RR1qRKY3fbhFMxVlr04N6FkxlaM+GOV5v0i3r0ivDouFOHyJmBpUvTYhnzcT3i59cyPNWxYV//bvnUd3Dm5CLICqg5GtRnVSX2O2D7FJS8ZOhITwpuWFIxDwCwEM7PilJWAHCKSXgFNRKujeYJlSz/TeTSgdBEAgUQLonyVKENeDQGYSsBObmEqmCG9eiZA15RX0yzEXagQ1M5Fqx9YSmv3vm2n7koXKDdn30zcM1+fSC28sqvR6+VFq2GMX5VreKV24nP44/WIljgWavb59WzlW78y+4Fba9utMJarD1ZdSh/NOUI55h+sz55KRVPLHr5p4szppEiXpQO/xxtk2HzyYuo68nLKyVXqFmDZz/nXCg081FePON11DbYXgqQ/s7TbzkDM1ImXXh0dRi8MGapNW19Bfd4/RTEXJIuquj92gTSeOjPLsMfZRatK/tybt9mWraM75N2juEU5gJryteusTWv7QaCWPyDSaT48UglojJU7urJ00lZaMelAeEgupu9x0kXIchJ3ACm+//V1JV7+6SWF8VL98uvlI8yn/lIQudpIlvLkokoa+tIFWrYt68U29qY3tdJN64a1+dhZNvqoVFfyzfpub8tVpgyK88RpzH4r6Ns7TKU+iMr+vqqSrxkfvkyPFfXKLwX0y5vsSevvbEqX6e3RpQKNPjRXTOEGlcIw86lHtmngvXtSCuoh15NThebFu4JuqdQNZILt3iLHX4HjhSffSFO3UkUbC249CRLxZiIkysMD6/mWtYkQ3eX6LmOryxKfWKYJivF5vToS3TJpeEcKbvMOwBYFgEcDATrDaC9aCgFcEnHq71YofvEEP6ueeVV3CUFer+uEcCICAfwmon1PwwPVvO8EyEPAbATvhLREvL7/V1c4er4S35WPeEl5iLyvFtzzpBOpy26XKsX5ny8+zad7F1ynRbc47izpdfY5yLHf0wlvbYefRzpefKU9rtnMuv4u2Tv9BiRvw4ySql6t1aOCpC/8cermShtdx23NydL0x5YTY2b70b/rtJK3XXDqFNxYd+335uuG0nPp6mXkRrnzlA1r5ZLS+zY48kro/8H/qaiv7NZU76OeDTtWIdH3ef5HyO7VX0vDOyvEf0sonxihxLU85ibrcEhVBlRNiZ/WEz2jZ/Y+rowyFNxZnZx15jrbsya9QfvvWmmvVB3+ed5NGKN37u4nCI1LrJKNO77f9wApvi4SX0IViqkkZCgqy6JOrzBtKpnOzTYfwNuqTYvr69+2Kme8LQalZQaygpCQQO3rhjacyvGjfWK8u9TVO9oMivB20ex7dJTy+jAIPlxzywBrllJmgdrnOM+4B4Zk2UOeZpmQidu7+tJim/Bptp+HHNKaT+xSok5DeM230uc1oD5OpSrdV1NKQx9dqrjcS3vT3h5PpSG+dvIW+n10eyZtFyqk3tNGU4+QAwpuWEoQ3LQ8cgUBQCGBgJygtBTtBwDsCTr3AgjrFpJ6c0/XewlJfff1xDAIg4H8C6J/5v41gIQj4kQCEt2ireCW8/XbycI0H297fvk/1C7Vjn1Er6vZ+HXKpMo1g0X4HUM+nb9MnIb3w1v+rCYYeT3zhinHv0d/PjlXy6DPpZcrvoB3X1HtRdbjmMupw7vHKNfqdP84eQaVz/lSi0ym8WXpxiZcAp/c/RrHTTFCb/38PaTzjer74OBX17alcp99Z8uh/aO3rbyvRRvWfd+39tGXaNCXNbm88G+ORKE9Wl5bRTweeJA8jWyOPt41TZ9DC6+5Q0pkJiUoCsbP+ix9o0Y13KVG7vTFG2NFZOfb7TmCFN+EdSYc9FBVUGDR7FF12UCPqUKRyzUygBbwQ3raW1xBPLbiquDryt16sRaYOPy+ppI1iKkgZXr+sJbW3qY9eePt8RGvLKSRl3nbboAhvFx7eiM7Zq9C0OkcJQatCCFscOrXLoZfPjZ2+8+Tn1yvcnYhTes+zE/ctoKsPbqyx4cQx62hzsbhRRXCS5zkvb6AVa6LejkbC23liSsplYq05GT75v9a2no3/+V8JvTI16s33nhBzm9uIuTJ/uYXwJknUbSG8aXngCASCQgADO0FpKdgJAt4RcCq8hckDTP3ssyIbpjpb1RPnQAAE/EVA/YyCx5u/2gbWgICfCUB4i7aOJ8KbTvQp2LUX7fHmY9FCTfbUgo2Z55laeLOaPpKL0E832Pv1Z6hRzy6a0pc+9jKtee0tJc5q3TJOpF8PzUh4UjJL8o5+qsmdb76W2p56lGkps444jyo31jlqNN5nX+o1ZmRM2t9Pv5bKFs6NxLMH3YDpE2PSqCO2zBSeiRdFPRPbX3oh7XTxqeok9NupV9P2RfMd5zl72G20bdbPSh5GwtvKl4Vn3uioZ96uzzxITffto1xjtFP61wr647To9JJdHxpJLQ7f1yipL+MCK7wxzRETN9PP8ytiwObnZ9HuO+fSnjvlUL+dGlCPVrHrnMVcZBCRTOFtpRDaXvhuG33zR53nkUFxhlFvXdGS2jSyFhLVwhvX/b9XtzbMy21kUIQ3O6+v455ZR1u31QlgrVtk09vDYteqO+yRtVS9o06cc+I9uUSIp/9WeVwO6JFHD52g9bpT58lTQk66opVlE1z73ib6ZWF0PToj4e2YJ9fS9u11dnJmLCRyMJoJSabaJMTdkpK6+nPax89uRn07aN2yOd4qQHjT0oHwpuWBIxAICgEM7ASlpWAnCHhDwKnoFjbvL3i9eXM/IVcQAIHkEED/LDkckQsIZBoBCG/RFvdCeKtYu1Gs73ZWtBCxx8JPJNRExxhlAvkCV/nCxZr1vgbO/K/wRsiSySJbtfBW0K0n7fG2dppCdWK9l1SP5x+hJnvvpk5Ceo+v/lOFB11R7Jph8qK1H35FS+58SB5SOoW37k/dT83276vYot/59cQrqHzZokh0w9570G6vRu2WaX8+8HTaUVocOcxtuxP1/TjqISjTqLfbl6+m3074txLV4rgh1HXUFcox76jzzNu5C+058RnNef3BglufoE3//VSJNhLe/hr5DG2YPFlJw/Wp11A40hjcT5yI76naikrNVJPtr7yYdrpA612nZOjDnUALb7x+1bliTTQpqpjxZTHqmL4FdOWBjaie9rNudkkkPlnC2xfzy+neiVssyzI7abR2mD6tWnjr2DaHxp8X69Glv8bJcVCENzshyU54215VS8c8Wvf2AHNp1yqb3rggVpxTMyutrKXBj0Wv2alNNr16fvSacpHn0ao89efVecn9+z4vps9nbZeHpBfeqoQj5BEPa708lcQudu46tQkd1CXPxRVEEN60uCC8aXngCASCQgADO0FpKdgJAt4QcCq8yYEDb6xIT67q55+ZBYMGDSL2NkEAARAAgVQSUD+f4PGWSvIoCwSCTQDCW7T9vBDetvz0J827ZES0kDj3BvzwIdXLy9VcrRbeGu+9D/V6/k7NefVBjPD23MPUZMDu6iSk9vjiE0Zin/qCTd//QguG36xEpVN46z3+KWq0WzfFFv2OnfBWU15BM/aLTqvZqE9f6v2f+/XZaI6ry7bTTwecqMQ16rcX9R53j3JcI8SuGfsepxzrzysnVDtLnxhPa8a/ocQYCW9/nnMDlcz+XUkTz06b88+mTledHc+labkm0MIbE6sUXkrPCE+yT3/ZrkwnaEaSvZ1eEaJUXo4z9S0Zwht7Rl3w4gaq1b0M0KdrA+rcMptaN6xPBbnRNdy+nr9d4/XkVnjba9dceuTEpmYIXMWHUXhr2TybJlwUFcgYSBmLaE+sVdqoaVE9mniZtXfaDtGeh6umOtXny/flUUKYk+1u5mmnbpBHvtpKH80oU6L0wps+TyWhy50bjy+iY3rmu7oKwpsWF4Q3LQ8cgUBQCGBgJygtBTtBwBsCWbq3bY1KCZu3m6yjU683DHpLYtiCAAikigD6Z6kijXJAIFwEILxF29ML4W3rb/Npzr+vjhYS595e096j7Eba5YESEt7GPERN9tlDY41+LbqBs6KeV5qE/xxs+VlMtXhxdKrFtApvrz5NjXp3NTIzEqcW3gp77Ua7v/aIJi0Lbz8POoNqKuscOfK77Ep9JjypSaM/qN1RTf8bMFiJ1udbU1lFPx90mpKnmaedkoHYWfbsm7R63CtKlJHwpm8nJbGLnVann0K73DjMxRXpTRp44U3i42n1/lhVSb+srKSZyypp9rIqZepAmYa3QwYU0HWHatfiUp9X7ydDeLv0zY00T9giw+5dGtC9Q5pQ47yo2CbP8fbuT4tpyq9Rrye3wpvRlIfq/N3sZ4rwxkzUXoNFjevRh5dbC29rxPSNZzyzXsHZu3MDeub0Zsox7xwihDkpvDVvWp/eu6Sl5rz+4OZJW+jHOdGpSPXCmz5PnhLzmbPceze2FlOXFjRwJj5LG50Ib+xtOW5wkbwk1FsIb6FuXlQuxAQwsBPixkXVQMCGgFPhKYzebhKN+hko4/TbsAqP+nriGARAwD8E1M8miP/+aRdYAgJ+JwDhLdpCXghv+rW1mv3rXzHrgEUtMN/L79CG9NPPJVt4m3P5XbR1+g+KEQN+nET1cs2X2Fn/+fe06Ka7lfRBFt64EtP7Ha3UJb9zN+rz3lPKsdFOxTqx1NHRQ5VTTQ89jHZ95HrlmHdmDDxREd7spgPl9IvueY7Wv/8B70aCkfCmXv+PE/WZ+FLMNKR1V5v/z27ckHKamE8jan5les6ERnjT42Mh7vvF5fToZ1tpc3HU3ax+dhZNGdFan9zwOBnC21GPr1U88Xidr/cubUU5Fku2XfzGRlqwPCrUQXiLbZoP/thOT3xcN3ctn3Uz1aTeM03m/q/Ra6msrG5VNCf3yG9/V9LVr26Sl9OR/fLpliO1otOxT69T1lbLzc2iz661vu8uen0jLVwRbXsj4e1Usa7ceuFFySGZ6/kpFTHZgfAWBQMWURbYA4GgEcDATtBaDPaCQPIIOJlmMuyikxPxEdNNJu+eQ04gAALOCKB/5owTUoEACGgJ2AlvnLrbF69qLwrpkRcs2OtpxsAhCrEWQ8Q6YHdeoRwnspNs4W3RfS/Q+nffV0za86NXKa+dufPDqtc/ouWPPq2kD7rw9svgi6hi9YpIfbILi2ivb99W6ma0s23uIpp9VrQt25w7lDpdc64m6a9DLqXyv5dG4ho0b039voh6s2kS/nMwd/g9VPz9d8opI+Ft6ejXaM3Lr0XTfPoG5bbSOrEoJ0OyE1rhTbYPTyN4xtj1mnXgJl7diprmG3ucyet4q1+bbeTJTeiQbs7XxuI16E54cp2S5cG759OdFh5BLPv868m1tH17nQDEF/pFeHPisaVU1OMdL4S3c1/ZSMtXR0Wvd65sSa3ENKBm4Y2ZpfTCF9uU0xcc1pDO3buhcsw754k8l6nytLrvuMWPVom0fL2R8PZ/722iWQsr+XQkfPx/ranQpfeavNbt1s7Li/P7fJh2Gk+3ZQQh/VMzy2jyL9EpQY1sHiLWlBzev8DoFOJAAATSSAADO2mEj6JBIM0EILwRQXhL802I4kEABAwJoH9miAWRIAACNgSceHm1e/AWKuzX0yan4J+2E95ye/agjqNvdV3RWUecR5Ub10auc+L15LSAZAtvK1/+gFaOfk4pvvsT91Czg/ZSjvU7C24bTZs++USJDrrwNvviO2jbzzOU+vT74i1q0LyJcqzfWTPxS1p6d3TKyp1vuobanhb1muP0cy4ZSVt/+p9yaf+pEyinyMTTrLaWZh15vnKv8EVGwtvaSVNpyagHlTy7P3U/Ndu/r3Icxp3QC2/caKM+Kaavf49O3/ifi1tQ52bZtu35q/Bqukbl1XTxEY1oaP9C2+tkgo1lNXTy6Kjwtn/vvMg0k/K8fqsXlPh8OoW388dvpKWr6sSoHCHufCFEHj8EPadkeLzdOnkLfT87Os3jSfsV0lUHmTxQBISTn19PGzdXKzhGndKEBnXVirIjhVfeNOGdJ8N5hzSkf++jFefkuR+XVtDNb22Wh5GtkfA29scSen1aiZLusD3z6fajtZ52yskk7wwT9VGLk0bZ3yWE5YFiyskwBwhvYW5d1C3sBDCwE/YWRv1AwJyA+vNvlirM00zKOoODJIEtCICAXwion0uYatIvrQI7QMD/BNa99D4VvznR0tBMEN6ccCg680RqdcFJlqyMTuq9mLqPvo+aHdDPKKmruGQLbxunzqCF192h2NDk4IOpx+M3K8fqHV4TbcZ+x6ujKOjC26J7n6f170U/C+0vG0Y7XXSKpo7qg99Pv5bKFs5Voro//QA1229P5Zh3Fj84jta9/a4S1/GGq6jdGf9SjtU7W2aKNfMuiq6Zx+eMhLeS+UvpzzMvVS6NiLlvPeZ6ukklgwDsBFZ4q9xRS/PWVdEe7cznbGX+7El0xrgNtHZD3fR8HDdZTPnXSEz9Zxc2lFbTKU9F1/Hq3jGHXhjqfE2tGlH4oQ+uUYphr7EJF7fUT20bOV9cXkNnCDFH7e3GJ9IpvOnFqGfPb0692qRfVPFCePtTeKZdKTzUZGCh8Z3LWhp6Rn6/pIJufXuzTEo8jeQnV7em+jonyoUbquiicdE8GzasRxPEOm/5Odp7j++TYa9tpMV/Rz3uOHMj4Y09OI8XU1hWia0Mo89tZvs54LTTl1ZSnmi+Pdtbf2ZkvvothLc6IuCgvzNwDALBIYCBneC0FSwFgWQTyMrS9r+M8ofwVkcFA99GdwfiQAAEvCKA/plXZJEvCISbQOmsubTqxvssKxmvp5dlpj476aXwVjJvCf059DKlxrmt2tHu74wmXmfLKtRW7aANU/9HTfbejXKaFsUkTbbwVrujmtg7r6p4g1JWnw9fpvydxPpyurDyFeEd92TUO45PB11407dTTlEL2uODMYYealt++pPmXTJCocLTSPb970uUla2d9a1syd/0+8kXKuny2neiPSY8SfXycpW4yI4Y1J5z5d2aNfY43kh44/h5V99HW779hncjoeOI4dRu6GB5aLrdvmINlf21nJofMsA0jR9PBFZ4+2pBOd31/hYqalyPThlQSCftURAz5V6pECce+mKrxuuofetsev3fLRy3xSEPraHa6BJxdHT/fPr3wIbUqlF9sv/5TnTimHWaNeYG7cFrgTWmBmKtORl+X1VJ1wshp6IiKqbIc+kU3sZNL6HXvi6RphALRzcLj6Z+HRrEiEdKohTseCG8sdn6Nda4vmPPbU5tG0cfPlPEfXe3uO/U4dIjG9EZ/Yw9IfV5tmmZTS+e01y5V3eIe4unj/x9UXT6SJm3kfDG5yb/uZ0e/Si6xh3HHT9QTG14UGPK1ol/W4WgO/H3Mpowoyyy3twBu+XRPceauxtzXmYBa5vVkcGUm2Z3COJBwP8EMLDj/zaChSDgBQFMsRil6mTKTQhvUV7YAwEQ8J4A+mfeM0YJIBBGAhDe6lrV6yk3F93zHK1//wPlFuI1xDqNvIZaHL6vEid3yletp7XvfU7r35lEO0qLqevDo6jFYQPlaWWbbOGNM171+mSxbtszShlsZ6/xj1FB5/ZK3Kq3P6XlDz6hHMudoAtvXA+9dyILZT3H3Uu5raMORJu+m0ULrrpFVjuy7XT79dTmxMM0cfJAn2fD3feknmNGUv2C/EgSFjwX3vYkbfr8c3mJsjUT3ipWr6dfBp+jpOOdpocdTrvcejHlNGmsiWcBl21e8+ZHkak0uU57TtaKppoLfHgQeOFNzTQ/P4taN82OeB6J6UVpifBiUotmnPbmE4roqB51N4j6WrP9574vobe+jYpP6nRZKpHjiqMa0yl9Ytd0+mTOdnpoklYkYW+qLm2zaatYy23ztuoYLzd1GekU3li4PE5MlVktvAv1QV33woJ69NGVrfRJPDv2SnjTe73JCjRuVI9aFtWn5et2aDzN+Dzfcx8Nj/V2k9f+srKSrn1tkzxUti2bZwvxVXwxrN8Rc4/KRGbCG58/5+UNtGJN1ItTXsNCdHsxjWqxWF9wnZgKU+0Zx2m8Ft64jDCv8+ZkmsmOYqrNcUKgRgABEPAfAQzs+K9NYBEIpIKAE+Ft1KhRNHLkyFSYk9YywCKt+FE4CICAAQH0zwygIAoEQMARAbu1zTiTsE836YRBty9edcTTKNGOrSX06+ALI0Ka+ny9BvmU37ULNWjViipWr6HyJUuopjK63A6nTaXwxlNIzjri3Bg783YWNrZpRWV/zok5J+sTBuFN7/Um68b1z23flspmz9N4BPJ59mDc86OxMd5u8tptfy6k2ecOl4fKtrDXblSvQS6VzpkT0+YykZnwxudXjH2X/h4zTiZVtmxPXtddxDh5DVUsXkoV61Yp53gHwpsGh7cH0uPNTSmn7l9IVxxovm6XUV6VYhmvoS9uoA2bYkUOdfqzDm5IF+1r7Gp7rfBo+mVhpTq54T57WB0mPJI+nF6mnE+n8MZGsHD4sPCu0guYioFih0W4qTfEuu+q0yRz3yvhjW2curCc7vmw2FBs1NehhRC4Rp/RlNqpPOL0afj4i/nldO9ErZecPl194QHZv2suzZhXrpyyEt6qxH35+NRi+uRn7ZeacrHJTiLCG2fpxNsrzOu8ORHehvQV3of9Y0V4kyZBNAiAQAoJYGAnhbBRFAj4iADEpmhjgEWUBfZAAAT8QQD9M3+0A6wAgSAScOLtFebpJp1MM5mM+ldtKqa/Rj5Fxd9/5+o2SaXwxoZtX7ZKTKN4W4xgoze6zXln0ZpXXleiwyC8cWU2ff8LLb7pAVOBUamw2CnYtRft+sStGo849Xm5v+mbn2nBNbfJQ8Mtexc2OfQg2jB5snLeSnjjROv/+y0tufMxU+FOyUi1A+FNBcPr3XUl1fTqjFKaLqboW7/RWhTr0iGHrjqkEfWJc20rXoNrwq+l9OWc8ojXU2VVbYwQZSW8sb/YmzNLaeyUbTHXSU779sqj248uojdnldKrqukd0y28sX0by2rouW+30ZxVVbRpa6yHXpiEN67vWuGFOOK9zYYeZXye63vEnvl04+FFMeu68XmjwN50N0zYRGVlsd6D7FH3yGlNhehXQW9+E/WutBLeZBk8TeldH221FYZ77JxDR/TKp8N3zaOiPJWrpszI4dbJ+mZh9fhyIroxRghvDm8mJAOBNBDAwE4aoKNIEPABAYhN0UYAiygL7IEACPiDAPpn/mgHWAECQSTgZLpJrlciHl9+5uLE263ozBOp1QUnJaUaLJasfPI/lsJWRIQ5/GBqJqaibDpgd8rKEdN96YIXU03KIqqKt9HCGx6hrT/9T0YpW177rOPNl1F+x7Zi7brLlfiwCG9coYr1m+ivmx+jbbN+Vuqn3mFPxVZnnEg7X3mWqaebOj3vszfdwuvuE56NK/SniD3quj1yE23+fhatfGKMct5OeOOELOguvud52vz1V8p1RjsNe+9BzY4+kJofOpBy27Y0SuLbuMBONakmylMizllTFRFM1rAwJISxNmLKvZ2a5FDn5vWptViPzQ+hTNg5f10VLdxQRauLq6mpmKKxbeNs2q9zrrLmlx/shA11BCrFFJsLxFSQs9cIcbekhrq0yKaerXNoZ+HpFl2hzx2tDaXV9MvKqsh9sIuYbnLAzg2oRWHi9yevFbd4YxUtENNhLhFCdKO8rMjadO2LsiN25+fEa7G2fk7WeeMrwuj1Zia8bZz/A21c8D11H3J9BFaYp9rU3g04AoHgEcDATvDaDBaDQDIIQGyKUgSLKAvsgQAI+IMA+mf+aAdYAQKJEuA+RrLDoEGDLLN0KrwlU3yyNCiFJ514u7E5Xky1ydM6li5aQWXir3LNBspp2ZQatG5BeUIUKdi5HVG95IxBJoKTbdw2dzGViOkS6zcspKK9e1N+h9TN1paI7cm4tqayisoWr6TSBUupUohx+Z07UGH3nSm/fWvhURJf+1Rt2Urbfl9ApQuXUX6n9lTUv1fMumxx2S7WC6sQ91Hknlq8QpiXJaYHbUG54o9F0pwid7MXxmWDRxeFQnjziA2yBQEQMCCQqV5vRtNssug265HjFUrHXHwLffL8vcoxdkAABPxFAAM7/moPWAMCqSIAsSlKGiyiLLAHAiDgDwLon/mjHWAFCCRKQP1ZTjQvN9cP79yHhnfZ3faSsHm9pdrbzRYwEoAACMQQgPAWgwQRIAACVgQy0evNyttNLbxJbqNGjYrsjhw5UkZhCwIg4AMC6h+DU6dOJbs3KH1gMkwAARBIAgGITVGIYBFlgT0QAAF/EED/zB/tACtAIFEC6s9yonk5vZ5/0+3duDWtuvE+20vC5PXm1NstTHW2bWAkAAEfEoDw5sNGgUkg4HcCRt5fepvDtNabVX3Z623+pIeE+/b3egSRYxbhIMAZokEkCKScgPrHIIS3lONHgSCQNgIQm6LowSLKAnsgAAL+IID+mT/aAVaAQKIEnPQxEi1DXs8vUPLvORmWX3UvVcydJw9Nt2HxeoO3m2kT4wQI+IoAhDdfNQeMAYFgEDDzANNbP6RvAQ3vX6CPDtSxk6k1uUK3dP2Tpk2bRtLbTV9JGQ8RTk8GxyCQOgIY2Ekda5QEAn4i4GQgKFNelAELP92ZsAUEQIAJoH+G+wAEwkNA/Xn2qlZ60Y3LcbrWW27PHtRx9K1emZaSfOHtlhLMKAQEkkIAwltSMCITEMg8AlZeYGoadw0uooFtc9RRgdmPV2C88847TQU47iTyHwS4wNwGMDREBNQ/BOHxFqKGRVVAwIaAE7HJaBDHJttAnrbqo8gKZYoIKeuLLQiAQHoJoH+WXv4oHQSSScBJnyuR8qz6KE693oI8/aJT0Y0Zh8W7L5H7BdeCQLoJQHhLdwuEsPwXfiih0sqapNasX4cGdHDXvKTmicwSI+BUlOJSgii+uanf58NaGMLkwS0O3Dk0CladRqP0iAMBEEiMAAZ2EuOHq0EgqAScDAJBeIu2LvonURbYAwEQ8J4A+mfeM0YJIJBKAllZWZ4UZ9c/cer1xsa1e/AWKuzX0xM7vcrUTf2CLC56xc9pvhumTKeyhcucJneUrkHLZtTm5CMcpUWicBGA8Bau9vRFbQY9sCbpduzRpQGNPrVZ0vNFhokRcOr1FrT13qavrqI7Pi52BMfpdJpWb5hLYQ5ecI6QIxEIxE0AAztxo8OFIBB4Ak4GgWprawNfT7sKqJ+DZmnhEWxGBvEgAAJeEFA/l/D88YIw8gSB1BJQf6aTVbLTZ4NTrze2K2jim5N13SRveLtJEu63cy6/i7ZO/8H9hRZX5BS1oP5TX7NIgVNhJQDhLawtm8Z6/bi0kip2JNfjrXWj+tSzdTCnK0xjU3hetBuvMKcCledGOyjAqaDIWbn15oMXnIMGQBIQ8IiA+keg0x9vHpmCbEEABFJMQP35Nys6E54LECDNWh/xIAAC6SKgfj5nwnM4XZxRLgikioCTmQac2iKX6eCtk+DGKyxI6725ERTh7ebkTjFPU/rXCqpYt9E8QRxn6uXmUJP+veO4EpcEnQCEt6C3IOwHgTQTGCY8w5YLDzEnwe/iG3u6jZtVlpL6cGd02rRpJL3d9PxkPLzg9GRwDALxE8DATvzscCUIBJ2A+vNvVpdMGPC1E94yZcpNs3sA8SAAAqknoH4+Z8JzOPWEUSIIpJZAsoS3ePskbtZBC4L4BtEttfcvSgOBZBKA8JZMmsgLBDKUgBvxza/TTrrx3uNmTqaIaDUNJZfFIhwEOCaBAAKJEcDATmL8cDUIBJmAk0GgeAd4gsLFrr/B9UCfIyitCTtBIDwE0D8LT1uiJplLgPtZ3M/gbTJCov0RN2IV2+tHLzH23tv48vtUMXeeI6R+rIMjw5EIBEJMAMJbiBsXVQOBVBFwsyaatCmZwpXMM95tOkU3tc1OpqE8+OCDiQcGEUAABNwTwMCOe2a4AgTCQsCJ8MZ1DbO3hZ23m2xrHuzigJd+IhjwDwRAwGMC6J95DBjZg4BHBKTIlkzBjU1NVHST1Q2y+ObGa0/WF+u6SRLYgoB/CEB4809bwBIQCDQBt+IVV9YP4psbbz3ZQJ8PayF3PdtavZWOATHPsCPjkBPAwE7IGxjVCwwBowEau5dK+MUTs2B3rbxO/QyQcfot58XiW9iCVb/Cqq7oc1jRwTkQAIFkEFA/m8P88kMyWCEPEPADARbcjPpy0jbuS/HLO1ZpZFr9NlmiG+frZr03aYcfvMbiEd3aPXgLFfbrKauBLQiAgE8IQHjzSUPADBAIA4F4xTeu+/D+BSlFEI+XHht41+AiGtg2J2W2cmeVgxz40heczI6pPm8cg0DYCGBgJ2wtivoElYBT77Nk1E8tysk3s+3yra2ttUsSuPPxCm/qijJL/oP3vZoK9kEABBIlgP5ZogRxPQh4T8CJ2MZWsODGfQUO6s92JMLmnxfCezziG5uZDgHO7dSSEmc6bJVlYwsCIGBNAMKbNR+cBQEQcEkgHg8yLoK93zh4LcDFIw5GDBP/0u2hZzVoJoU5TAslWwtbEIgloP7x58UPu9gSEQMCIGBEIJXCmyyfvydZMOLngF0I20stVv0HNQtZb7uXfuQ16HtIEtiCAAgkQgD9s0To4VoQ8I6AndjGJbPIphbb1NY47e9Z5aHOL979eDzIZFmpELXiFdzYxlTYJ1lgCwIg4J4AhDf3zHAFCICADYFExC3OOtkCF3u3/bSqiib/UmZjufnpZNtkXpL9GR4Q404s/xkFOXBmdA5xIJDJBDCwk8mtj7r7jYD68+i1bervRaflhsnrzanwZlRniHBe353IHwRAQP1cxotRuB9AIL0EeIyV9OODAABAAElEQVRh2rRpkbEGs/EGN0KZ+vNtVDPOiz/3XodExDe2zQuBKxHBzSubvG4H5A8CmUYAwlumtTjqCwIpIpCo+MZmSi+4vdvluJ7ekcU2DuNmldHyf/YjEXH8S/X0kk5NtBsM44FGTAfllCbSZQIB9Q8/DOxkQoujjn4mwIM5/Jn0Oug/607LVYt1XtvoZf5ORTcn9WV2doNxXBceROM/9EG8bFnkDQLhIYD+WXjaEjUJLgH+juc+A2+NAn+vm3m2GaWXcZyfWX/PSd9D5pOMbaLiG9vAAhyHwj17ul5TjYU2Dhtffp8q5s6L7Mf7zwshMF5bcB0IgIA5AQhv5mxwBgRAIEECyRDf1CZ0FGur9Wljvr7ab2vqxLZEhTZZJpc3rF+Ba9FPXp/KrdXAmhwAwzSUqWwRlOVHAhjY8WOrwKZMJWA1EJMMJlYDROpngVVZetHOKq1fzzmtq5G3m12d5ACd2SCdvJ4H1jigHxLBgH8gAAI6AurnVBieu7rq4RAEfEuAv7/ld7mRkdyX4hCP4Ba58J9/WVlZ6sPIfqpFN2kAi1+rbrxPHia8ze3Zg/KECGcWyn+tE9sSFdrU+bd78BbXop/6euyDAAikjgCEt9SxRkkgkJEE2PMsGV5nqYbnp6kl3dSdO84c5CCX/tp0dXD1duAYBNJBAAM76aCOMkHAnID6M2meyv0Zu+86p6IfDzjxIHBQg9VLOeo62fFSpzXbt+t/yOtk/wQinCSCLQiAgPq7AMIb7gcQ8JaAndjGpVu9vBSPderPOF+fjH5HPHaor0mG95s6v1Tss8jXcfStqSgKZYAACCSJAIS3JIFENiAAAtYEku39Zl1aYmeDKrrpa2014IaBLz0tHGcCAfWPPgzsZEKLo45+J+BUAHNTD6eDOerngVX+QRXfrPoA+vrG4+2mz0N9zO3KU1LKvob6nHqf2fIfpqRUU8E+CGQeAfXzGP2zzGt/1Nh7AlJs45J43yjw93Ginm1G+XIcl8mfcw5++owHSXzD1JKR2wf/QCBwBCC8Ba7JYDAIBJeA38W3IE0t6eYu4ME37uzyn1FwOkhpdC3iQCBIBDCwE6TWgq2ZQIC/l+RATDLq62Ywx03ZQfuedCO6paJudv0Q2fZSqIM3nCSCLQhkBgH0zzKjnVHL1BPgvo78DjYq3UuxTV8ef869Evb0Zbk5DoL4BtHNTYsiLQj4iwCEN3+1B6wBgYwg4DcBLqyCm/5m4o631RvoGPDSE8Nx2AhgYCdsLYr6BJmA3WCQm7rFO3CkfibYledG1LPLy+vzRmupmJWZbG83s3JkPA8AcpB9Dhmv38rzEOH0ZHAMAuEjoH4WB+lZG76WQI3CQMCuf8V9Jv6Dt7m2tf0mwPG0ks3PPwlruWmbCUcgEDgCEN4C12QwGATCQyDdAlymCG5Gd4zd2/A84IXBLiNyiAsyAQzsBLn1YHsYCNgNBsVTRx484oHaeALbw88Fp8Hv341u+aa7Pk5FODlIiH6J0zsV6UAgWATQPwtWe8Fa/xFw8v3P36V+9DjzG00W4Mp/nUsVc+elxTQIbmnBjkJBwDMCEN48Q4uMQQAEnBJItQCXyYKbvk3sBr3SPSintxfHIJAIAQzsJEIP14JAfAScDAbFl3Od11SiYkxYxDe7F2r0jP32/c7twF75vOU/q8C24019K0I4BwLBIoD+WbDaC9b6gwB/V8rf8mbfmxDb4m8rFuA4FL85Mf5MXFwJwc0FLCQFgQARgPAWoMaCqSAQdgIswHGY/EvdNpn1ZbGNw7B+BTTwn/1k5h+GvKwG7XiQi0OiA5yRTPAPBNJEAAM7aQKPYjOOgBwMMhsIYiDqwSD1Z9MprGQKR1bff0b2JLNso/zdxgXdfqP6ysFE2f8wSsNx8jz6J2aEEA8C/ieg/g7AVJP+by9YmD4Csl/F35FyX2+Nun+lP4dj9wRKZ82lUuEB54UAx2IbB0wp6b5dcAUIBIUAhLegtBTsBIEMIzB9dRX9tKoqUuvf1lTRcnHsNEiRrU+bHNq7XZ3gBrHNKT1S3pyTg1n6KzkeA1x6KjgOAgEM7AShlWBjUAnwAJDVQBDXy2wwiK/lz6eTYJaHk2ut0rgVrzgvPwwQq59rVvWT55hfvFNzyjxSvYUIl2riKA8EUktA/Rzzw3M1tbVHaSBgT8CujyX7RpwT7yN4R0B6wnEJbsQ4KbLl7dmTCsUfh8J+ddvIAf6BAAiEkgCEt1A2KyoFAuElwIKcVYDAZkXH/TmrgUgpzEGEc88VV6SHAAZ20sMdpYaXgN1AENdcDgZZDQQ5Fd44Dy9FI/UzwmmrpetlFCfsjeoQ9EFtrreTKSn5XuE/TElpdBcgDgT8RUD97A36M8pfZGFNkAk4+Z7n7zn+Lc5bhPQRYK84qwCBzYoOzoFAuAlAeAt3+6J2IAACIJAUAlYCHBeQroHHpFQOmWQMAQzsZExTo6IeEvBqIEj9+TQyPxXfM1w3tiOekAr72C4n/M3sT5WNZuV7EQ9vOC+oIk8QSC0B9fMfwltq2aM0fxGQ3/FsFe8bBYhtRlQQBwIgAAL+JADhzZ/tAqtAAARAwJcE7Aa4eFAPb5f7sulglCCAgR3cBiAQHwE5EGQ2CMS5JjoQxHmbiV6pFIys7HBCzytb7V6AsbPNK7vsyk3lebs+irSFWXCAx34EA/6BQNoJoH+W9iaAAWkkIPtW/B0m9/XmJNrH0ueHYxAAARAAgdQQgPCWGs4oBQRAAARCR8BqEBCDWqFr7lBUCAM7oWhGVCJFBHjwx2oQiM2QA0FyPxHTuDwj4S1d3g/q50U89ZLfg/G+jCIH3+zawIlt6WLoxDav0jA/npJStoNZOXwP81+87WSWL+JBAAScE1A/bzPxeeWcFFKGiYBdPyuZfawwcUNdQAAEQCBIBCC8Bam1YCsIgAAI+JAADwpyMBvc4ni8Ve7DhstAkzCwk4GNjiq7ImA3CMSZeTkQpP6Mcjk8AJvOYPWCiVu7uD78Zxe4DfgvGYHLw9ovdSSlgGnHVvZl0G9Jxh2IPEDAGQH1sx/CmzNmSBVMAvwdJL+PjGog+wn47jaigzgQAAEQCB4BCG/BazNYDAIgAAK+JWA1SInBLN82W8YYhoGdjGlqVNQFAbtBIM5KCjhy30X2rpKyLfw59dMLG1bfa64ql+LEfmKY4qrbFsdtyoEZWQV5HiKcFSWcA4HECaB/ljhD5OBfAm76WVJ4829tYBkIgAAIgIAbAhDe3NBCWhAAARAAAUcE5Jt8/EPDKGBA0IgK4rwmgIEdrwkj/6AQcDMIxHVK1UAQ28XTA/pN6Aia+IbvWOefRKciHH8G+A9TUjpni5Qg4JQA+mdOSSFdUAjI38DyN7GR3fydAs82IzKIAwEQAIHwEIDwFp62RE1AAARAwHcE7Aa0eHAQg1i+a7bQGoSBndA2LSrmgIBfxTYHpvsmifoZ4hujdIZgmjYdEBeHUvjlLf9ZBfRfrOjgHAi4I6B+tuIZ5o4dUvuLAH93OBHb2GoW3hBAAARAAATCTQDCW7jbF7UDARAAAd8Q4B8hPFBlFPiHB//5zcvByFbEBZcABnaC23awPD4CdgNAnKv62cv7CNYE7F4osb7am7OyDdF+yeXrtK1l3wZ9mOTyR26ZQwD9s8xp6zDW1K6vJb+b4d0WxtZHnUAABEDAmgCEN2s+OAsCIAACIJBkAnYDWTyAhcGrJENHdhECGNjBjZAJBOwGgJiBFGrkfiZwSXYd7b7Lkl2eUX6yHeWgnlEaxCWHgNP25raQ7ZKckpELCISfAPpn4W/jsNXQTV8L39Fha33UBwRAAAScE4Dw5pwVUoIACIAACCSZAA9kyTfF9VnLeIhwejI4jpcABnbiJYfr/E7AzQAQ1wWDQMlrUWbP69LJ76zk5WyekxR20I7mjLw8I9uct/xnFrh9+A9TapsRQjwI1BFA/wx3QhAIOHn28zMfnm1BaE3YCAIgAAKpIQDhLTWcUQoIgAAIgIAFAbs3yXlAEwKcBUCcckQAAzuOMCFRQAjwABA/O+0G/uWzkweDELwlYPUySTJKxoBeMigmPw+7PowsUYqz8jMp47EFgUwngP5Zpt8B/q6/XX8L383+bj9YBwIgAALpJADhLZ30UTYIgAAIgICGAP+wsfIcwKCVBhcOXBLAwI5LYEjuOwJ2gz9ssBwAkvu+q0QGGCS/y7iqvM9/bgO3Iwcp0sjjSCT++ZYARDjfNg0M8zEB9M983DgZahp/b1u93CS/k/k7Wu5nKCpUGwRAAARAwIIAhDcLODgFAiAAAiCQPgJ2ngPwgktf2wS1ZAzsBLXlMttuu8EfpsODPhBo/H+fOBXgMIjn/7Z0YiG3N79MxFv+Mwvc3vyHKSnNCCE+7ATQPwt7CwejfvycthLbuBb8rIbYFoz2hJUgAAIg4AcCEN780AqwAQRAAARAwJSA3dvjEOBM0eGEjgAGdnRAcOhbAm4Gf7gSPBCEAAIg4G8Cdv0ZaT28+yUJbDOFAPpnmdLS/qun7G+xZbxvFCC2GVFBHAiAAAiAgBMCEN6cUEIaEAABEAABXxCw8oLDQJUvmsjXRmBgx9fNk/HGycEfs4EfBiQHf+R+xkMDABAIKAGIcAFtOJjtCQH0zzzBikwtCNj1uWR/i7cIIAACsQRKSkroxhtvpFdffZXmzp1L7du3j03kUQyXOWLECHrkkUfonHPO8agUZAsCySEA4S05HJELCIAACIBACgnYDVjBCy6FjRGgojCwE6DGyhBT7QZ+GIMc/JH7GYIG1QSBjCHAzwGr9W0lCH4W8B+mpJREsA0LAfTPwtKS/q6HXZ8Lz1h/tx+s8w+BTZs20eDBg2n69OnUqlUrmjNnDjVv3jxlBn788cd07LHHRsq7/fbbI1PEZmVlpax8FAQCbghAeHNDC2lBAARAAAR8RwBecL5rEt8ahIEd3zZNRhlmN/DDMHjwB2u2ZdRtgcqCgEKA+zX8nOA/qwBPfys6OBckAuifBam1gmUrP0flM9XMctnn4i0CCICANYE1a9bQYYcdFhHbGjVqFBHfevXqZX2RB2efeeYZuvLKKyM5X3755cTHCCDgRwIQ3vzYKrAJBEAABEDANQErAY4zgxeca6ShuwADO6Fr0sBUyM3AD1cKgz+BaVoYCgKeEuC+DQcpspkVJs9Lwd4sHeJBwI8E0D/zY6sE1ybZ5+Ia8L5RgNhmRAVxqSLw1Vdf0fz586mmpibhItnTq3Xr1tSpUyfaeeedqUWLFgnnaZZBRUVFRHT7/vvvI0mmTJlChx56qFlyz+PPPffcyFSXXBBPO3ndddd5XiYKAAG3BCC8uSWG9CAAAiAAAr4mYDdIxYNTmKbJ103omXEY2PEMLTI2ICAHfswGffgSOfAj9w2yQRQIgAAIRAjY9W8kJn6uqJ8tMh5bEPArAfTP/NoywbFL9rX4OSn39dbL5yJvEUAgXQS2bNlCTZs29ax4nvrxlltuoWHDhlFhYWFSy7nkkkvohRdeiOQ5btw4uvDCC5Oav9vMSktLacCAARHvO772k08+oWOOOcZtNkgPAp4SgPDmKV5kDgIgAAIgkE4C/ONLvgWut4N/dMkfYPpzOA4nAQzshLNd/VQrHuyxGvRhW9XPHd5HAAEQAAG3BPhZw+vC8Zb/rAJeOLKig3N+IID+mR9aIZg28PPPqt/F/Sz+w0uXwWzfMFpdXl5O7KnVoUMH+vHHH2ndunW0ePFi06ruvffehgIa5zN79mzatm2b4bU8DeQdd9xBPA1jQUGBYRo3kWPGjInkxdcMGTKEJk2a5OZyz9Ky52CPHj2U/BcsWEDdunVTjrEDAukmAOEt3S2A8kEABEAABDwnwD/IOJiJcByP6Zk8b4a0F4CBnbQ3QSgNsBv04UrzoI98xvA+AgiAAAgkk4BdP0eWJftB8nkk47EFgXQSQP8snfSDV7abfhf6XMFr30y0+K233qIzzzxTU3UWzpYuXUrNmjXTxOsPNm/eTIsWLaL333+f7r//fv1pOuKIIyIiWV5eXsw5pxHLli2LTGXJ6dmuuXPnUvv27Z1e7nm6CRMm0GmnnRYph+v7+eefe14mCgABpwQgvDklhXQgAAIgAAKhIMCDU3LgSV8hGY8BKT2ZcBxjYCcc7eiHWrgZ9GF7MfDjh1aDDSCQGQQgwmVGO4epluifhak1vamL7Hdx7rxvFLivxb/h0OcyooM4PxN47LHHYtYnGz58OI0ePdqV2UuWLKGbbrqJ3nnnHc11J554YiQuOztbE+/0gEVBFgc5PP3003TFFVc4vTRl6fbdd1+aPn16pLx3332XTj755JSVjYJAwIoAhDcrOjgHAiAAAiAQWgI8MMU/3Mx+vLEIBwEuXM2PgZ1wtWeqa8PPCvncMCtbDvrweQz8mFFCPAiAQKoI8HPLyZSU/LziP0zHlqqWQTlqAuifqWlgXxKQv9Gs+l783ILYJolhG1QCxx57LH388cca8ydOnEgnnHCCJs7pwYgRI+jRRx/VJOf12HhdNrfhu+++owMPPDByGXu7rVq1iho2bOg2G8/Tf/DBB8QCIwde546n70z2GneeVwIFhJIAhLdQNisqBQIgAAIg4JSAHJSS3m7662Q8RDg9meAdY2AneG2WboshtqW7BVA+CIBAMgnAGy6ZNJFXsgigf5YskuHIx67vJcU2ri3vI4BAkAlUVVVRgwYNYqrAa7+1bNkyJt5JxPbt22nPPfckXu9MHWbNmkV9+/ZVR1nuV1dX04ABA4iv43D99dfTQw89ZHlNuk6yrd27d1fWy+P17WSfJ102oVwQYAIQ3nAfgAAIgAAIgMA/BLhzJoU2PRT+Ycd/EOD0ZIJzjIGd4LRVOi21G/Bh29TPAt5HAAEQAIGgEZADUmb9HlkfeR79H0kE22QTQP8s2USDl5+bvhf6XcFrX1hsTuCnn36KiFvqFL169aLZs2ero1zvz5w5k/baay/Ndeeddx69/PLLmjirA56y8dRTT1WS/PXXX9SlSxfl2G87Y8eOpYsvvlgxa+vWrZE16ZQI7IBAGghAeEsDdBQJAiAAAiDgbwJ2g1E8CIUBKH+3oZF1GNgxooI4JuBmwIfTY9CHKSCAAAiEhQA/A3lKSimymdWLn338hykpzQghPh4C6J/FQy3417jpe6HfFfz2Rg2MCRit73bttdcSxycaeKrKDz/8UJPN33//Te3atdPEmR0cffTR9Nlnn0VODxkyhCZNmmSW1BfxZWVl1KZNG9q2bVvEnv/85z90/vnn+8I2GJG5BCC8ZW7bo+YgAAIgAAIOCFh5wckBKohwDkD6IAkGdnzQCD4ywc2AD5uNQR8fNR5MAQEQ8JQA9334Gcl/VgH9ICs6OOeUAPpnTkkFP518pshnjFGNuL/Fv63Q7zKig7iwEUj2+m5qPi+88AJdcskl6ii6//776aabbtLEGR0sW7aMOnXqpJz64osv6PDDD1eO/bpz++230z333BMxb++996YZM2b41VTYlSEEILxlSEOjmiAQVAKTF1XQM9NKqKam1rAKDRvWpzHHFVHrgnrESR6cXkpTZ283TMuRtxzVmAbt1MD0PE6AgBkBeMGZkQlOPAZ2gtNWXlnKAz5Wgz1crhzwkfte2YJ8QQAEQCAIBOz6P7IOEOEkCWzdEkD/zC2x4KW363+h7xW8NoXFiRPwYn03tVXTp0+nfffdVx1F55xzDo0fP14TZ3Rw33330a233ho51aFDB1q+fDllZWUZJfVV3JQpUzQC4e+//0677767r2yEMZlFAMJbZrU3agsCgSLwxpxyevmHkojNTYrq0+UDC6lf6xxaua2abv9ym3Ahr46cy82tR+8ObUb3/bCNfpxfEYk7rl8BndEzj/Kys+jU1zZRdXWdcFevXhZ9fH5zql8vUChgrI8I8A9Hq+mYMPDko8bSmYKBHR2QDDm0G+xhDBjwyZCbAdX0hABP6TN8+HB6//33ac6cOcQDNOkOffr0obZt29KYMWOoc+fO6TYnNOXb9YFkRfmZyn+YklISwdaKAPpnVnSCe86u/8XPCA7wbotgwL8MJODV+m4SJa/J1q1bN3kY2e6///703XffaeKMDngtt8WLF0dO8XSNPG1jEAKv61ZUVKSYyt597OWHAALpIgDhLV3kUS4IgIAlgRd+LaN3fy6LpBm6TwGdv3uBJv0yIbpd9PZmJa5x4/q0dWudEHfJQQ3p5O55kXOXf7qV/lpZqaTjnfuHFFF/IeAhgECiBPgtcCm0GeXF5zANpRGZ9MRhYCc93NNRqhzs4bJ53yjwgI/8fMrBH6N0iAMBEDAnsG7dOjrmmGNo1qxZ1KpVq4jw1rx5c/MLUnRGPu/Zpk8//ZT69u2bopIzpxh+tvKLSLzlP6sg+0rymWuVFucyj4D8vHLNp06dSvhODu49wM8CpzMLoJ2D286wPDkEvFzfjS1ctWoVtW/fXmNso0aNxLjZVk2c/oAFNxbeZOCXmC699FJ56PvtgAEDiEVNDphu0vfNFXoDIbyFvolRQRAIHoG5G3fQ1RO3RAw/sX8BXdZXK7rJGh0nPNnKy2vkYWR7UK98um2/wsh+cUUtnfrqRs15Prjv2CLaqw2EtxgwiIibgN00TDzghLe+48abtAsxsJM0lL7MSA72sHFmg8BykAdvV5s34Y4dOyJTydSvX988Ec6AgCCwYsWKyAA5D9DwQA6vo9GjRw9fsGEvvAMOOIB4iiEO/HY3v+WN4B0Bu76QLBkinCSBrSSA/pkkEcwt97nsRHjuf6Hvldr2Xb16NY0dO5Z+/vln2rJlCw0cOJCOPPJIzTR8Tixir6nq6mrq3r17IKYadFInv6Txcn03ruP8+fMN+2UlJSVUWFg3ZmbE4vXXX6ezzz5bOcUi1l577aUcJ3Nn4cKF9NFHHxHfZ4sWLSK2beedd6ZddtmFjjrqqEhfzm15N954Iz300EPKZcXFxdS4cWPlGDsgkEoCEN5SSRtlgQAIOCJw5nubaePmatqtUwN67HDzL8jTJmymLcV1Xm4y47fObkbN8upFDlcIr7gLVV5xHMlTTU48txnliykoEUDACwJWXnAYbPKCuPM8MbDjnFVQUkJsi6+l5s2bRxMmTKA1a9YQD8ysXLlS2XKOLKKsX7+ecnNz4ysAV7kiwANa3B4bN8a+LOQqo38S8xoc7Om10047Rf5at25NyRZSS0tLab/99lOErW+++YYOPPDAeMz17BoewGFPNxbh+J5mr7yuXbt6Vh4yjhJwKsLxYLwckI9ejb1MI4D+WTBbXPbBrF52gtiWnradNGkSHX/88YaFP/7443TNNdcYnlNHVlZW0tChQ+m9996LRLOY8cADD6iTYD8BAl6v78amsQfxoYceGmPlpk2bqGnTpjHxMuKyyy6j5557Th7S9u3bKS+vbkYpJTLBnYkTJ9Kjjz5K33//vWVOLBi/8847kf6sZULVSf39/8UXX7gWnFXZYRcEEiIA4S0hfLgYBEAg2QQmLyqnp6bWrev24ulNaadG5m/cHzt+E1VWRj3e9ujcgB45TCvUnTVxM63fWCfONWhQj648sJCO7oyBxGS3G/KLJWA36MQiHKZciuXmZQwGdrykm7q85UAPl2g12MPnMeDDFGLDKaecogykxJ6tE942b96cdLHGqCzEmQ+MJJPNddddR5dffnnkDeJE862pqaEzzjgjIhZyXq+99hqdddZZiWbryfUff/wx8RvlHPht/f/973/UpEkTT8pCpsYE+Dlt5w0jr8QMAZJEZm3RPwtOe8s+GPpf/m0z9vTmdU45XHTRRcRrXPGLVmqv7y+//JIOO+wwy0qovz85Yb9+/WjmzJmW1+CkcwJer+/Gljz77LN0xRVXxBjF/Th+ScssqNd3S/ZUjUuWLImsC8z3lwzcP+OxE/aq4xfH5s6dG/HUvOuuu4inNOfzP/zwAzmdynzt2rXUpk0bmX0k7zvuuEM5xg4IpJRALQIIgAAI+IjAuR9srj1i7PraKz4ttrRq4/bqSDpOK//+u7g85prK6tra/62qrP3x78ra6pqY04gAgZQQEANJteLL3fCPz/EfgvcExFv1ShuINwC9LxAlJI0Atxe3n7oN9Z8peR5ta49dvO0cYSl+TNcKTyDlcyGZirek7TNBiqQRWLZsWe3gwYMjbbLHHnsYtolsGzEgUSsGz5TPg7zv5VamM9teeOGFteIt64RsF4Mjyj0j3oZPKK9UXCwEeMVesR5drfAwTEWxKMOEgOz3mN2jMl6mM8kG0SEioP5ux3e4/xpW9sHkZ9Noy22Itkt/223YsKG2Q4cOke+8++67TzGIv/fV7Sa815RzZjvXX3+95hrupyAkj4Dw9tLw5fa59tprk1eAyIn7fOp2530xhaNlGcK7TXNNMm0Sgn1MH1eIg4b9UrEOXe0999yj2PLMM89Y2q0/qf59c+qpp+pP4xgEUkYAHm/iyYMAAiDgHwLSi+3JE5tQz+bZpoZNXV5J93+uXRT2g/OaU0GO+Zs7ppnhBAikiAC/ycVviPKfURCDTPCCMwITRxwz5jfs1YH5yiD3sfaeJOK/Lbeh9Bw1+8yIgZ6I4fBsi7/9eE23Zs2aRabjk7mMHj068jaqPMY29QTYO40Xs1eH0047jd566y3Lt5Q5Pb/JvHTpUvrggw+IPd304fzzz6cXX3xRTL9dNzW3/rzV8S+//BJ5653T8PSNvL5bixYtrC5J+zmeylMMGNJnn30WsWX8+PF0zjnnpN0uGEDKM15+J5sxkef5WY8QfALyO13202T7cs3U++ijpa+tnfbB0P9KXxsZlczeTezlxN5t/PmS00zz1MvqqZZ5+r4ff/zRKAslrn///pEpmmXEww8/TCNGjJCHCW3LysoinvO8Bhn3Q9MVsrOzqWfPnsRrmlmteeaFfV6v78Y29+7dm+bMmaMxn6eenDJliiZOfcBrrXXr1k2J4vuJp55MNPCUpTzjhjrw2m7cP9MHngqTvTZ5KnwZhHgWmXJSHttt1XWHt6YdLZz3kgCENy/pIm8QAAHXBL5eUUml4oWswbtYTwf54PRSmvLndiX/JkX16Z1TzeepVhJiBwR8QECKCerBBbVZHI/BBjUR630eHJDTWHFKOaBjfZX2LAs4UsQBey2bVB45HehhmzDYk5yW4TXe2rVrp8mM18LitbEQ0kfAaDpQJ1ND6S3mtuRnG69zpg5XXXUVPfnkk+oo233xamjku+nbb7+NpPXzFJP6ysyePZt22223SDQLhsLL0HJ9E/31OPaegPq73Op7nO9n/sN3tfdtkowSZFvKvq88dpu3bHe+DgKsW3rO03P7yBcFja7idkD/y4hM+uOEtxu1bNkyYsgff/yhfOdxxMsvv0z//ve/FSO5HYWHonKs3+HpxvmlLHWYPn067bPPPuqouPf1a3DFnVGSLkx1vzcV67uxuGkkJgovOBo3bpwpORblDj/8cOX8G2+8QWeeeaZyHM8O9xsPOuggzaW8bhuLaUaBp0d98MEHNaeGDBlCfN84DVye7K9yv0940Dm9FOlAIKkEILwlFScyAwEQSBWBM9/bTBs3163dxmUe1CufbtuvMFXFoxwQSBoB/nFrJsDJQQYMMMTithsYiL3CfQy3C9i75+b2CtmWfB3vGwX+LHDAYE8EQ1L/6d9A5R+n/KYpvwWMkB4C7KHFi97rxbLS0lIqKChwbRS/pX7DDTfEXLdgwQLNW80xCXQRb7/9duQNdY7mNTj4TeScnBxdKv8eHnfccTR58uSIgVdeeSU99dRT/jUWlsEbLsD3gJPv9USrhz5yogSj18v2suqDMW+I3VFmftxjoYIFC/Z2++677zQmHn300YrXN5+w+w7Ur+/G11RWVibtO5/X4LrkkktoxYoVafV4y83NJV7D7Omnn7adTYAZJCukYn03FlbZu00feOaE008/XR+tHL/00kvE4pwMZl5p8rzdlvuKvXr10vRpzz77bHr11VdNLz3hhBPoww8/1Jzn34BmYyaahP8cnHTSSTRx4kTlFL88hgACaSGQskktURAIgAAIJIlA+Y5aZV03ub7bl0tj13dLUnHIBgRSQkB0JCNrvYnOgDKXuXqfz3sVeE0GL/NPpt1sq/jxb8hIzSuZ+7JtklmPTM9LtqNVW/I5/uO0CN4RGD58uObzhPXdvGPtNGfx5rWmTfh5JgZPnF4ek664uDgmP86T1xdxGkpKSmp5fTn5bH3ggQecXuqbdOLNZ8V+rsfMmTN9YxsMsSYgv4fl/We2lemsc8NZrwjI73az9vEqPih9WK+4x5Ovk7ZCHywesum7Rogbke+4//znPxoj/v77b813H38OxdTLmjT6A/GyjuYarO+mJ5TYcSrWdxPTQ2raUD5/t2zZYmm83jbuOyUSjjrqqBg71q9fb5mlENk013D/c926dZbX6E9edNFFmjz053EMAqkiQKkqCOWAAAiAQLIIfLeyMkZ4K6msSVb2yAcE0k6ABxBk51i/9WJQSZbn54ELaaOeRyqPvWCf9psthQbIQR6IbSmE7qCo7t27a543Yn03B1chiZcEuA30z7Z77703oSLVopnMW7zx7jhP4TWnsclu0MRxxilOKNa1Ueoh1sxLcekoLhkE+LvESZ+Av2s4HadH8JaA/H6Xz5Z0bbm9EcwJyHay64fhM2PO0K9nxNSFyncbv2yjDo8//rhyjj+b3B/g9FZBrImlucbNizpW+eJcHQEWMvXPSeGdlTQ8wjuxVsxgEVOGmK7Rtoy7775bc91vv/1me41ZAhZ49fV00vfcvn17rfDgrD3vvPNq77rrrloxLb5ZEabxN954o6Zs04Q4AQIeE4Dw5jFgZA8CIJB8Avf9UKIR3k5+e1PyC0GOIOADAjyAYPXjOFkDDOoOcbLyTAY+/uHP9qjt88M+2+QnTslg7VUeTgd5+D7HQI9XrWCer9Fb0OxthZBeAux1qH/WiWmjEjLKSHi79NJLHeUppr6s3WWXXRSbnF7nKPMUJxJTFyn1YMbxDOak2GQUZ0OAv4+t+krys4TvbhuQcZyW3/GSsV+26KNFG5PbyK6d0AeL8grynpgSsPabb76JqYL0hJOfz1tuuSUmjTpCTDeu+Z7k62bMmKFOgv0ECLAoJttCvXXr0WVlgpHgxWWNHz/e6rLIuZtvvllj35IlS2yvMUpQU1NTu8cee2jyYhvmzp1rlDzpcQ899JCm7KQXgAxBwCEBrPEmPvkIIAACwSJw2oTNtKU4ur7bgT3z6Pb9GwarErAWBFwQ4DUXpk2bRmIgwfAqGc9zn7sNRmvMiR/glgtuuy0jnvRGdsWTj5fX+IGTl/WLN2+5Vghfb7VeCJ/ne5Y5IqSHAK/zoF4wHeu7pacd1KXu2LHDcA2V8vJy4rVI4gnCOy2yJpv+Wl4PxmjtN306MZAXWdtHxv/++++0++67y8NAbXn9vE6dOkXWp2PDef27ESNGBKoOMNacAPcdOMh+kVlKeT6efpNZnpkWf8ghh5h+x/uFBbdzprax7ItZ9cO4/4V12/xyt3pjB39f9+nTR5P5n3/+Sb1799bEqQ+M1ncTHnJY+1cNKYH9VKzvNmzYMHrxxRc1Vnbo0IEWLlxIeXl5mnj9wf/93/+R8JJUonk9PvHylnLsdEe8yEf9+/fXJOf19ISIq4nz6uC5554jMd2mkr3QSJR97IBASgk4FOiQDARAAAR8QWCbmFJSrusmt5/brO+2vqy69rovi2s/XoR14HzRiDAiIQJiEEHz9pboNCjH4ge0a08s9fXqfc4rXcGqjmob/bLPbxJnepBvU/N9Y9YufI7/wMs/dwt7LqnbC+u7pb9txICMpk24fXh9jETC888/H5Mn52v0ZrxROeeff75y/f7772+UJFBxF154oVIf9uRjjz6E8BHgvoST/gR/L3E6BGcE5Pe9+rvDz/uZ1LZO2gb9MGf3eVhS8TR96s8nTyFpF/TruzmZntAuT5yPEtCvocbtc+2110YTJLhnNJsFl/Haa685ylk/RePy5csdXadPdNttt2nuPbYh0WnT9WVYHT/xxBOa8q3S4hwIeEkAU016SRd5gwAIJJ3AfxeXxwhvLMZZhcdm1E1Nee0X2vnOra7BORDwOwG7ASUnAw2cRv1jTL/PP85THbhMvR1BOHbCO9UsvS5PDvBYtRmf4z9Oi+A/AuLtV83nDeu7pb+NjAZkeJ2LeANPGaVvZ36m8tRTPA2QXdi6davmHrn99tvtLvH9eZ5qSf29kug0nr6vMAyMfAfx97TV95W8JzgdvrOMbxq7fqNk6Lctt3tYA9+rsq9lxh39sLC2vn299NNMPvLII7YX6dd3e+yxx2yvQQLnBLxe3039spR8JvCUj2JGBUdGCs9xTR9JeEg6uk6fyGiayV9//VWfzLNjfT08KwgZg4ANAUw1KZ5ECCAAAv4gUCO+4j9eXE5/rqumNg2z6PQe+VSQk6Ux7uavt9HMvyqUuEaN6tN7pzdVjvU73Gs47tVNVFFRQ+fu25DO7m3tWq+/HscgEAQCVtMyikGSSBWMptqxuk7WW/xYT8m0kzwVDk9blIzANnPgLU+hYxR46k4OXC7/JSMwayPOycjbL3kwK75vOJhxk/yZhdz3i/2wI0pg6dKl1Llz52iE2ONpYfr27auJw0FqCRx77LHE0zypw48//kgDBw5URznaF78D6eSTT6aJEyfGpP/tt99IDIrExOsjPv/8cxIed0r0pEmTSLz9rhwHceevv/6ibt26KaaLN7BJrHmjHGMn/ATk95jsI5nVWJ5Px3d7VlYW+alf4aTPaMZRH899A/4z66NxevTT9NSix7L/xW0i96Nn6/aYL/pheiqZdbxo0SLq2rWrptJz5syhnj17auLUB5s3b6ZmzZqpo+jnn3+OmTJQkwAHjgnwlJ0NGjSISS/Wd6OWLVvGxLuNmD59Ou27774xl3355Zd02GGHxcQbRQhxlq6//nrlVLx9UP4O0weeTr1+/fr6aE+O9VNmcp8YAQTSQQDCWzqoo0wQAAFDAv+evIX+XrtDObdL+wb03DGNleMdNURDXtlI1dXRL83dOjWgxw6PplES/7MzYX45jf22RHzBZ9G7ZzejQp2Qp0+PYxAIMgG7gST9AI5Rh9is/uKN2sggidn5ROITHczhwQUOiQ4w2PGLFGLzj21hVmEKPKgj2VgN8HCdE22DMHHze13ElDN0zjnnKGbK9d044qOPPqIvvviC5s2bR8IrisR0fHTggQfS0KFDDQcMlEywkxABswGZyspKw3Xf7Ap75pln6Morr4xJ9tlnn9GRRx4ZE28Ucccdd9Ddd9+tnBJTGFG7du2U42TtrF69mt577z2aPXs2LViwIJJtjx49ImsQHnDAAckqRsmndevWxANdHI444ghigREhMwnI7zcpsplR4O93/kuFCMfftfJlJH3fzcw+L+MTXc9NzY334wnMxGq9Y6d5+oGnU1v16WR/zKovJu/PeDnry8RxcAno+3ncl2Mxziqkan037lty34JfhOH9dAUWgVic5JdvsrOzPTfDy/XdmCO/pMVlqAP34+T3nDrebH/s2LF08cUXK6fd9BnlRUYC7qGHHkpTpkyRSTzfimnF6aWXXlLK+X/27gTuirF//Pi3nUqLvfLYxeOpkKXklyhbSiEUkiX1ZMmSrZCokH0nKpU8hUIUUchWKkKpUEloIe37fv/nO/4zZ2bOuc+ZM2fus36u16vOrNdc8z5T99zX91oIvNkULKRbIEGPOHYjgAACaROw5myzPs96ebnr2u/M2xQ1zGSvL9a6jnGu/LVhR9HZQ1aY5wyfs8m5i2UE8lpAh50xKhY0Qh3zj+4zfiGPua+4c3S75ht2ilfOeGXRfXoPJVEmvcdUylVSVmHbx8tPXdU33nNi7S+p7yBe+diXuoB3KBqd382Y8DzmsITWv0UdstAIyqV+cXKIKWC0Ko76f1mHJEo2bd68uahv375Reen3OHDgwKSy0zndrO9/7733TupcPwcbPS+LjACwfQ3rWs7P7t27m1npEEXt27cv0vlmRo8e7Sf7Yo8xgsiua6oZCQH9eebnHUl//ulxJfXzz/sOouuZSHp/zn+LyS6rU0kYqYfXKJmyZcozyHeofvHexfS+S8o5SHk5J3sErrnmGte/X53XN1Eyejq5zimpuX/HjRvnuk4y/35L4lhjxIdENKHsjzWceFjzuw0ePDjKtHnz5r6HmLRu0Ai0ufIZOXKktcv3p77beb8nnTsunem8885zlSGd1+ZaCDgFmOPNqcEyAghkVMAKuFmf7d9eZZdH53GzgmjWfv1sN2qlfYxzYfXmnUXnDv8n6HbhGyuLEs9i4jybZQTyRyCVignvC7Ouh1mBErRs6axgCFpGtcq1ZFXuxKvg0X3p9M81w1wqrwZRnP/GnetGi9mit956q0jn9/r111+LvEEKY8iaXLrVnCmrzuXm/E50WStpkkmTJk0qql27dlQ+xx9/fJExXFQyWRVt2LDBlU+7du2SOj/RwcOGDSsyelra19Blo5de0W+//VZktJYu6t+/v71Pj3U+o3psKunFF1+081ZnDXqSEPAK6DuAn/cA6zjv+UHXi/s5rNdJZ/L+f+R3PV3ltNz9lst5XLrKGOT7st7HnOX1LvMuFkS2sM4xenO7fs4ZvX8SAnjn5XryyScTnhPkgHnz5rl+pnuf73Su6/tRuhrflNT8bvru5zUzejgW6Ty/ySZjOFJXXvq+lGzyvj9q2Z599tlks0npeOfPUZ3rkIRApgRyr1YoU1JcFwEESlzAGVDT5XEL/ml9vMEIunUcs9rsuabBtzsmrnX1fFu+aYerbAtWby/SYJvmcc6wFUWL1/mbSNaVCSsI5JlAKpUT3hf5MCorNA9vvonWM1nJELS82f4YWZU7zl9OvN+D7sukfbYb5mL5jKH8iv339+CDD0a1jt2xY0eRBuOcz8aiRYty8dazuszGXGouY/X2EyzTihUNlGpvMOd3pMsaoNJKE2NejaTv3ZgHzpVfmBVw2vLZWVat+Przzz+jyjh8+HDXcc5zog5OYoO3kkpbipMQiCfg9z3KOi5eXon2OZ9z77Lmn44U5L0nXWXz3r++y+RSeb3l13W9B/2T6H1MjyEh4EdAgw3O/z8SNTBZsWKF63g9t6R7gum7iTHMdsb+6PttupIxbHiUrxobw16nVARjXjdXIybNU4NuCxYsCJTv+vXrXeU0hiwPlI+zsZSWKdkRF6yLrlmzpsgYprLooosusjb5+nRev6R6bvoqCAcVvABzvBn/A5AQQCA7BM4YuNwuSI29ysrVx1aUuSu3y7uzNsumjTuldOlS8kCLKvLvPcpK29dWyebN/4wHvssupeXS4ytKRWNY7i9/3ybf/bLFzKdy5TLyUuuqsueupe18WUAAATHnDSlufgi/PkYFR+B5TvTa1twl6bie32skOi5Xy+29L70Pa6z/4p4Do+LHPI0527x6+bGucx7o3AfeZARvxBiaxbvZXNd9bdq0sfclO2eEfWKMBaNyQDp06CB///236MTrmUo6v4dObv/UU0/Jsccem9ZibNmyRXbZZZeoaxqtz6VChQpR23WDURkhOjfaunXrovZ36tRJWrVqJTqnRsWKFaP2+9mgc/0Zwzrah+q60VrbXg+60KNHD+nXr599ut6jUZksu+++u73NuWBUtogx1JFzU8rzsv34449iVEraeabyM83OhIWCEdCfnTrfmH7qn+KS/izVP02aNDE/izvOuV1/PuvzGC+V9PPqpwze8um/Yb3XTKZcLLc+P1ru4p4jNWXetkw+Vbl77aOOOkpmzpxp34DRy8ycz8ze4FkYMWKEOZevtdlouCNGw560zH1mXTOfP8Oe382IZojO5du1a1cXm87zNmbMGNlzzz1d25NZcc6DazSMEmMo+mRON4/Vd1Ath5V0Tr+7777bWvX1uXHjRvO9U/9/1HdFo0GYr/OWLFkitWrVso81hiwXo2Ghvc4CAmkVKPjQIwAIIJA1AhN/31LUYug/w0N6e7/psJHzVkZaa2svOJ3fzXuctX7dB2uK1mxhgMms+XIpSNYIaEtZ40UjlD9GxU+g+zIqEZK6ftDrBCqcj5O0PMkYZkP59XtX93j21n49lpTfAt6hI/V5fumll+Le9Pz5813PvfakCmtoHiOI58o7mX9fJXHs/fffH9eiJHZ++eWXMQ3UOdGfWAba0vfaa68t0uGcgqZnnnnGVSYtY6pJWzx7y5uojBMmTIg6R3tmppKMgKUrT51njoRAUAH9OR/v56v1zOtxid4JdL91fKLPkvh5ncz1tXx639mUcqH81jtZcd8v72PZ9ETlblm8c1zpEILFJe1VpL2knM+knk8KTyDWcOJB53fTkSu8369+dzoHrg7zmGryzr1rNA5LOkudE9r5PGnZkknLly8vcg6XOn36dN+ne69tBAB9n8uBCIQtwFCTYYuSHwIIpCSww4iVjV+4ueiZ6RuK7v5sbdGzxuf3f20t0u2x0k8rthcNnrnBDML1mbS+aPicTUUL10YCdLHOYRsChSyQbIWE84U51rLml0xK5vpa8VASlUrJlLe4Y5O5D3XLxH3oNa3Km1jfnW6z9meifMXZsr1kBXbu3Bk1JI0GaBIlne/N+xzFq8RJlJ9zvw6nqL9c69wimf6jE9EvXrzYWby0LGuwz+vrd14No0Vw0dSpU8050XTIRm8+RmvoQENNaoWQMy8dejKV9NNPP7ny07wff/zxhFlqYM5ZDl1ONGRWokw3bdrkyvOkk05KdAr7EfAloO8Hft4RrOO8mXqf9UTrmk9YSd8FEl3PuT/Ma4d1D5qP9f7jLGu8ZX0XKunkp0zZ/N5b0j7kH76A0VPS9e9Z50qNlXS4Rx2Kz/tvRBvfkMIR0GEm9f3Wazx69OikLqANoGIF3LSB1tChQ4vCGjpzwIABrrJ+//33SZVTD9bnyhvMNUYb8JWPziW93377mWXQhmTJDnnq/RlsjKjh67ochEBJCBB4KwlV8kQAAQQQQCBLBbwv/GGs+6148b4Ex7t2OipBUv2Kkrkfvdd0JKtiR/2K89V9VO6k49vIzmvMnj076tnQbYmSBqO8z9S4ceMSncZ+nwI6f4XX18/34s1eWzq3a9cuKq8uXboUadA1mXTFFVe48lm4cGEyp7uO1Wt75wnUiiI/rahHjRrlKoc6aSVWqsnpXbt27VSz43wEogT0Z7KfdwX9mazH+TnW+dxay3peGMnKz89nWNcMo9zF5ZGMZ0ncj/X9J3on0+NICIQt8Pvvv7t+dmrDHG9vKH23i/X+of8HJBvsCLv8uZqfNuz54YcfinQuWe2xP9iYQ9bZc8v5/6sxVGSRMYxjkTEMZdQfYzhj81xjeG4z2OYNYln5XHPNNUU6P1+YadasWa5nR+8hSDKGOnXlU9x8vpq3Bg3fffdd17uiBiuDzFXnnDNZ5zokIZBJgfTUAmXyDrk2AggggAACCJgCyVRAWC/zfj8TVVgkc22toMiVlA33pRU2apaoYkf3U7mTK09WyZXzhRdecP0SrC1J/STtleb9/0BbxJJSF9Aea15bDUolGyizSqKVF9qDy5tnt27drEN8fepE9s48jLlefJ0X66D333/flZfme+edd8Y6NGrb9ddf7zpXW+aHkazW1FoWv/8OwrgueRSugL4zxPtZ7fz3luxyqj/jk3mf0WNzJSXjHdY7kuYT77rWdxXW9XLlu6Cc6RfwDhnduHHjoldffbXImM+tSHvD67tGrP9rdLv2WCIlL6CBslimYW7T9xf9f1hHEiiJpO+RzmfjhhtuCHyZDz/80JWXll1HedDtOlqDBvW0cZgzsKjH6HMa5Bn0lj3ocJ6Bb5gTEfAIEHjzgLCKAAIIIIBAvgqE+cIfK694FTHJVOjkWkVEJu7NqtRJVLFjVe7k6zPNfSUvcOGFF7oqBPzObTV8+HDXefp/wMsvv5x8ATgjSkBbNXv/T9V5+FJJ77zzTlSeeg1tfew3tWjRwpXHtm3b/J7qOk4DiLGGwPRbYeSsjNF7CGv4q/r169v3pxVMJATSKaDvDsm8P3j/jyhuXfMMkorLz7s9aP5ByhTGOfq+5L2H4tb1nSlost7L4uXNO1lQXc5LRUADGNq4pLhnUxu3eH/eM79bcPHbbrutWOvivoN42/W708ZU+r6uw4d+8cUXoQ0pGe8uncON63uYBrSCJp1X1zuKQqx71h5u2kDQz2gIxZXF21tPexSSEMikAIG3TOpzbQQQQAABBNIkUBKVO7FemGNVyCRz7Vjnp4kopcvEC4A5ncKo1Il3Ld2nf7QCiISAV8DbClSfTb+91rS1q/NZ1mXtxURKXaB3795Rti+99FJKGWuQzPt96XrPnj195+sdfsr3iZ4DdW44b1m0EsdP+u2336LOTXWuOeu6zvvT1tUkBDIloO8+ybwref89edeTfZfye+1U3mEyZavX1Xcir1Fx68m8P+mx8d7J9Bq8k2Xym+faloAOf6i9i3QesLvvvrvooYceKvrkk0+KVq9ebQY5nL2b9LnVHnGkwhbwvrvpsJmppjVr1phz9A4aNKioe/fuRffdd585P7HOdbdkyZJUszfPdwY+GWYyFFIySVGAwFuKgJyOAAIIIIBALgj4rVQpriIime3eihm/1062oijb3P0aBanUiVexo/uo2Mm2pyE7y6NzTnifU7/ziDl7B1l5MP9HON+zDv1kmVqfc+bMSTlzDSZZ+Vmf2uPRb2revLnr/KCtnfv16+fKR8ty++23+yrGsGHDXOdq5WDQcngv6ByOkx5vXh3W0y3g913J+rec6NP7LhbvfhLlZe2Pl0e27/Prm8jNCrbpcZaL95N3smx/GiifU0ADcM5nWHtYpdLjyJk3y7kt4BytIJn3x0zd9bp161zDWj755JOZKgrXRcAWIPBmU7CAAAIIIIBA/go4f6FKx7Kz4sLP9XI96KZPjlbG+LlXp02sJ85vpQ4VO7H02BZPYODAga5n1G8QQ+f2ivVsb9iwId7l2OdDYP369VG2+r0End/NeclYQ0udfvrpzkPiLnuHJV27dm3c44vb6QxwWc+RVvT5Sd6hiVIdgtN5zdq1a9v2akVCIJMC+jPd+vcR5mei9yu/AalE+WTSzu+1/d6rvod5k/VuVtx3wzuZV4z1TAnoaATnnHNOUcOGDYtuueWWokTvajqspPO57tOnT6aKznWzTECHlHc+G4sXL86yErqLo6NFOMv7559/ug9gDYEMCJTSaxoPJgkBBBBAAAEE8ljg008/LfbujPmFit2nO+KdG2+fUQkh+seo6Iibv+7Ml9cRY8gMX/drVOCYNhaM5ajnW8vWPutTLTUZ4/u7zjU38hcCPgRuvPFGefrpp+0j27RpI6NGjbLXi1vQY4wgjGu3UVEjb731lmsbK8kLGAEoadasmetEI7gk//vf/1zbkl0xgmRStWrVqNM6duwoRgA2anusDUbQS4xhqexdRoWL1KxZ0173u1ClShUxWiG7Dtf1ypUru7bFWtlnn31k2bJl9q7+/fvLf//7X3s9lQVn3sbQl/LLL7+kkh3nIpCSQKlSpVI6P97J+h6m7w6xkp/rxjs/Vp7ZvM3P/er7lr6n6fsY72XZ/G1SNq/A+PHj5cwzz3RtNoIR0qlTJ9c2a+XHH38UYzg+a9X8NIb8kxo1ari2sVKYAkbjMDnkkEPs97AHH3xQjCEisxJD6xLq1KkjxogRZvm6desmjz32WFaWlUIVlgCBt8L6vrlbBBBAAAEE0iagFRannnpqwuvlU4WO33vWSh2rEixepY7iWcfqJwmBVATatm0rb7zxhp2FBuG6du1qrxe3cOWVV8qQIUNcuwcPHiwamAkjrVq1Sox5zuxf7MPIM2geRs8nuemmm+SAAw4ImkVS5+n/f/p/gDMZ8+7JGBu1HAAAQABJREFU1Vdf7dyU9PLrr78u7dq1izpPKyG0MsJPuvnmm8UYpsc+VCvojjjiCHvdz4LR0j4qwGYMWyrTp09PePrPP/8cdT1jzhGpV69ewnP9HOCsgDeGU5Jp06b5OY1jEAhdQP8P0P8LSjLFetfye918aRylvn7vOd53wXtZPB32ZVKgVatWMmbMGFcR7rzzTrn//vtd23TF6FlvNvzR312sdM8990S9k1j7+CxMgddee00uvvhi8+aNIczl119/lbJly2YdhjaWMObuNctljBwhxhzBUr169awrJwUqQAHjJYqEAAIIIIAAAgiELmBU8riGezBes2Kuh37hDGdoVMjEvM/i7j/Wds3D+AUiw3fC5fNNwPtsfvHFFwlvcdOmTa75EvR51aEQEw1dlDBjxwF9+/ZN+d9MrH9HQbcZFVSO0pXsYqxhGI0AV0oX3b59e1GsfNXjjz/+8J33448/7vpepk6d6vtc68AFCxa48tAy3HDDDdbuuJ/eIYNiDY1qVKIXPfPMM3HzibVz48aNrnJddNFFsQ5jGwJpEfD+3xz0/y4/5+m7mZWSPd46L9c//dy39xjey3L9Wy+M8sea23X06NExb/7555+P+jkY1hyqMS/IxpwU0KHPnT+jjAZ8WXkfrVu3tp/nF198MSvLSKEKU4A53grze+euEUAAAQQQKHEBb6VFrHVnBVCJFyhNF9CAWax7TbSNSp00fUEFfBmjJajr2Vy6dGlCjZEjR7rO0edYAzJhprFjx0YF9xL9eymp/RrcMXpVhXl7xealc6Z570PnGkt1freHH344Kl+9Tvv27YstS6wdxlCirnzGjRsX67C42xYtWuTKQ8uhlX1+kgbDnD7e4Ni8efPM/TpXW7Lpr7/+cuXdo0ePZLPgeARCE3A+5+lY1nevQm0cpV+asxI5njfvZaE94mSUJgGjR7jrZ5vO1aqNcbzJO+ev0es71AZV3uuxntsCM2fOtJ8rfU81RqrIqhvSeQ2t/8v138C2bduyqnwUprAFCLwV9vfP3SOAAAIIIFAiAoVcoaOgVOqUyGNFpikKGHN82L+Y6i+o2usnXtIAUOPGjV3naGtqY86HeKcF3qe/KGfyT6zKqcA34+PEDz/80GWr30mywTHvZb799tuoPDVfDSgmO8m8MRykK69HHnnEe7mE62pqVYZYn++++27C8zZv3hwVjPW2YH7uuefMvI0hTxPm5z1Ae+9Z5dFPY3hP7yGsI5AWAb/vS87nNZVlfT/x+46iZcvH5LeBFCMP5OO3n9/3dMstt9g/24ob1cDbOMeY463IT0Os/Jbj7hIJGHO72c/Wtddem+jwtO1fvXp1kQYDrZ+LU6ZMSdu1uRACfgSY483410lCAAEEEEAAgXAF/MyhYVTo2POchXv1zOfmd643o1JHjAqwzBeYEhSEgE6KrnN9WOn333+Xf/3rX9Zq1OeIESPkkksucW2fNGmSNGrUyLWNlWACd911lzzwwAOuk41W6NKxY0fXNr8rS5YsMefVnDt3btQpRmtgad68edT2eBuMygzX/BhGjzPRueOSTYcffrg4yzRhwgQ57bTT4majc8vpHHPONHv2bDEqCO1NZ599thi98GTYsGFiBCzt7X4WjF53ct1119mH6v/ZTZo0sddZQCBdAn7el5xlifXO4NzmfY6d+5z5OOc4dG53Lufze5rOQeyc28p539ay2ul7GgmBXBHQuVgbNGgg69atE2PIadF/w8cdd5zofKtGwxwxRixwPff6DmIE66R8+fK5couUM0MCRkMqadmypRiNxswSGKNVSIsWLTJUmshldU7kQYMGmRv086qrrorsZAmBLBAg8JYFXwJFQAABBBBAIN8E/FRo5HOFjn6ffgwIvOXbk5/d96NBCg1WWCleEG3FihVy0EEHmZU31vFaQXzPPfdYq3ymKHDssceaFWHObH766SfRQFUyyWhtKa+++qoZSNLKNm96++235dxzz/Vu9rV+1FFHiTHEkHms0dtRjDnifJ3nPOjGG2+Up59+2t40ePBgMXqp2eveBa3MOeecc7ybxZh7RkqXLm1uX7x4sWh5NBnDRorR2tlc9vtXhw4dzICddbzRi1MqVapkrfKJQNoE9F3BGRzzBs60IM79YRRMA0563XhJr5nPQScM4n377MtlgWnTppmNW2K9D1j3dfrpp4vRa1wOO+wwaxOfCCQUMIaYNAO5xvy95rHff/+96HtippIGkjVwrKlr166ud81MlYnrIuAVIPDmFWEdAQQQQAABBFIW8NOSWiuL8zn5qdTJ9+BjPn+/uXhvGrjQHkNW7yNj2BjRXnDepJU1Z5xxhhjDtdi79Bfap556Svz827ZPYqFYAe29VadOHdd+DR4Zw0EmZay9Fo0hf+S9995z5aUrmt/w4cOlWbNmUfv8btAKDa3YsNKyZctkr732slZ9ff78889yxBFH2Me2bt1aRo8eba87Fz766CPRCkFv0nvRAJuV7r//frn77rvlzDPPlA8++MDa7PvzkEMOEaviSHsFfPnll77P5UAEcl3ATy+7Qng/8fPzLN/fVXP9Wab8sQU2bdokxhy98vXXX8uvv/5qHqQjHOjPYu2ldOihh8Y+ka0IJBDQdzpjTkCzYZ6+m3333XdSs2bNBGeFv1sblZ1//vlmxvpM63q5cuXCvxA5IpCiAIG3FAE5HQEEEEAAAQTcAn4CTvneklpFcHA/F6xlh8CQIUPkyiuvtAujwQft2WYl7dGkvYH0+bXSTTfdZAZf/FRSWufwGRH4+++/RQNkOtST/pkxY4bZ0nzRokWRg4yl2rVrizHXmFSsWNG13blizH1mBue0Im3MmDFizOHi3G0vt2vXTp599lnZY4897G1BFt555x1Xbzk/w0TGuo4+c/rsWUmfL2fPHg0KP/roo6LBYE133HGHzJkzx7xH65ytW7ealSo6lJY15KSWr1WrVtYhvj6XL1/uCh727NlTevfu7etcDkIgHwT8BN4KoUc+IxPkw9PMPSCAQLoF5s2bJ02bNhV9j9X3Me1lmc5RAyZPnmwOpar3rUPi60gKDJea7qeA6/kVIPDmV4rjEEAAAQQQQMCXgJ8KnUJoSa1YiQIVhRCA9PXQcFBaBW6//XZ55JFHzGvutttu8thjj5mtVb/55hvRf5tW0n36y2ybNm2sTXwmKaABJW0JrD3F0pEuu+wyue2226Ru3bqhXE7Lvc8++9h5PfTQQ6LPT7Jpy5Yt5vCRGrjTpM9Wjx49RIfb1AocHYrS6onZp08fszeb9rg88cQT7Ut169ZNtKeaPq8aMNbhKvX5TDaNHz/e7Clnnae97FLpFWjlwycCuSLgJ+BUCD29/LyvFkIAMleeW8qJAALZI6DzCus75yeffCI6J3DVqlXTVjh9F9WGWjr8vf4pU6ZM2q7NhRBIVoDAW7JiHI8AAggggAACcQX8VGQUSuCNyq24jwo7MySgFarau0gDHLHmANGgyPXXX2/+ycTwMRliKZHLbtu2zRxS0goqhXmRgw8+WGrVqmXOr6HDM5588slSrVq1MC9h5qXzAur8gJpSGZZR51HTypK+ffuaeXn/ql+/vjz//PPSoEEDe5cOAXnxxRebrartjcaCDnOkvebi9Q50Hu9cdv6M0mGSdL64smXLOg9hGYG8FkjUKEhvvhACb/p/SKHPdZfXDzo3hwACJSqgPyd0Tug999yzRK/jzVxHQNB3yt133927i3UEsk6AwFvWfSUUCAEEEEAAgdwW8BNsKpQWxFjk9rOc76XXYQt1uEIduk/nAznggAPksMMOM3sZBQlo5LtXod6fd7jJmTNnptSjTod61J5v2mtNA7/ao06HnTzmmGNi9hJetWqV2aJa58XbuXOn1KtXzxxeMkiwTAOh++23n90DsVAagRTqs8t9RwsQbIqYYBGxYAkBBBBAAAEEwhcg8Ba+KTkigAACCCBQ0AJ+gk2F0JJaHwJnz4riHopCCUIWd/9sRwCB7BbwBqu6du1qDg2Z3aWOXbqRI0fKRRddZO+cP3++OXylvYEFBPJcwE+wqZAC0ol6/zEkeJ7/g+D2EEAAAQQQKEEBAm8liEvWCCCAAAIIFKIAgbfIt07gLWLBEgII5K5Ar169pHfv3vYNrF271pynzd6QIws6Z5zOHaepadOm8vHHH+dIySkmAuEIEHhzOxJ4c3uwhgACCCCAAALhCRB4C8+SnBBAAAEEEEDAECDwFnkMCLxFLFhCAIHcFdB50HSIRisNGDBArr76ams1Jz6/+eYbc244q7CTJk2SRo0aWat8IlAQAgTe3F8zgTe3B2sIIIAAAgggEJ4AgbfwLMkJAQQQQAABBAwBAm+Rx4DAW8SCJQQQyG2BRx99VG677TbzJnSetRkzZuTUDV1xxRUydOhQs8yXXXaZvPLKKzlVfgqLQBgCBN7cigTe3B6sIYAAAggggEB4AgTewrMkJwQQQAABBBAwBAi8RR4DAm8RC5YQQCC3BbZu3Sp169aVuXPnmjcyYcIEOe2003Liprw99hYtWiS1atXKibJTSATCFCDw5tYk8Ob2YA0BBBBAAAEEwhMg8BaeJTkhgAACCCCAgCFA4C3yGBB4i1iwhAACuS8wceJEc240vZODDz5YfvjhB6lYsWLW39j5558vb7/9tlnOfv36yR133JH1ZaaACJSEAIE3tyqBN7cHawgggAACCCAQngCBt/AsyQkBBBBAAAEEDAECb5HHgMBbxIIlBBDID4Err7xShgwZYt6MBrA0kJXN6fXXX5d27dqZRaxfv77o3G677LJLNheZsiFQYgIE3ty0BN7cHqwhgAACCCCAQHgCBN7CsyQnBBBAAAEEEDAE/ATetNfEKaeckvdeBN7y/ivmBhEoOIFNmzZJkyZN5Ouvvzbv/aOPPpJmzZplpYMOKXnkkUfKunXrZO+995bp06fLfvvtl5VlpVAIpEPAT+BN38/0Pa0QEoG3QviWuUcEEEAAAQQyI0DgLTPuXBUBBBBAAIG8FSDYFPlqE1Xo6JFFRUWRE1hCAAEEckBg6dKlcvTRR8uyZctkt912k8mTJ0udOnWyquRr1qyRRo0ayZw5c8xyTZkyRRo0aJBVZaQwCGRCgHeTf9T9vK/ee++90qtXr0x8TVwTAQQQQAABBHJcgMBbjn+BFB8BBBBAAIFsE6A1deQboXIrYsESAgjkl8CMGTOkcePGZm8y7UU2depUqVmzZlbc5NatW6Vly5YyYcIEszyvvfaatG3bNivKRiEQyLQAIxP88w0QeMv0k8j1EUAAAQQQyG8BAm/5/f1ydwgggAACCKRdgMDbP+R+HGhJnfbHkwsigECIArNnz5amTZuaPd90SMdp06ZJpUqVQrxCsKwuvfRSGT58uHny2LFjpUWLFsEy4iwE8lCAwNs/XyoOefhwc0sIIIAAAghkkQCBtyz6MigKAggggAAC+SJATy8RWlLny9PMfSCAQDyBP/74Qzp06CDa2GD16tVStWrVeIeX+D4dvlfLoH9GjhwpDRs2LPFrcgEEcknAT8OgQpjnjXfVXHpqKSsCCCCAAAK5J0DgLfe+M0qMAAIIIIBA1gvQiljEjwE93rL+UaaACCDgQ0CDXStWrJA999zTx9Elf8jKlSvNnncVKlQo+YtxBQRyTIDAm5gNBfQ9LV4qhOBjvPtnHwIIIIAAAgikJkDgLTU/zkYAAQQQQACBGAJ+gk75XqFBS+oYDwabEEAAAQQQQCDjAn7eUSZOnCj6rpaPiVEJ8vFb5Z4QQAABBBDILgECb9n1fVAaBBBAAAEE8kLAT2tqvdF8rdTxU6GT74HHvHiQuQkEEEAAAQTyUKDQG0j5CTwyKkEePvjcEgIIIIAAAmkUIPCWRmwuhQACCCCAQCEJ+KnUyNfgk597p0KnkP41cK8IIIAAAghkj0AhN5Dy0zhKvykdQpeEAAIIIIAAAggEFSDwFlSO8xBAAAEEEEAgroCf1tSaQb71eqNCJ+5jwU4EEEAAAQQQyAIBP42E8rGBlJ/7pnFUFjygFAEBBBBAAIEcFyDwluNfIMVHAAEEEEAgWwX8tqbOt0odKnSy9YmkXAgggAACCCBgCRRiAykaR1nfPp8IIIAAAgggUNICBN5KWpj8EUAAAQQQKGABv5U6+TKcDxU6Bfywc+sIIIAAAgjkkEAhNpCicVQOPaAUFQEEEEAAgRwXIPCW418gxUcAAQQQQCCbBQqpUsfvvTJ8UTY/sZQNAQQQQACBwhHw20AqH4YF99s4ive0wnn+uVMEEEAAAQRKUoDAW0nqkjcCCCCAAAIIiN9KnVyv6PDTilofh3zp3cejjQACCCCAAAK5LeC30ZDeZS4H3wi65fZzSukRQAABBBDIRQECb7n4rVFmBBBAAAEEckigECp1CiW4mEOPHUVFAAEEEEAAAR8Cft9hcnVOXr9BN6XK9UZgPr5uDkEAAQQQQACBNAkQeEsTNJdBAAEEEECgkAX8VuqoUa61qKZCp5CfbO4dAQQQQACB3BZIpoFULgam/I5IkIv3lttPHqVHAAEEEEAgvwUIvOX398vdIYAAAgggkBUCyVTq5FKLaoJuWfF4UQgEEEAAAQQQSEEgmQZSuRSgytf7SuGr5lQEEEAAAQQQSJMAgbc0QXMZBBBAAAEECl0gmSBVLgTfkrkf/e6Z263Q/wVw/wgggAACCGSvQL4FqfLtfrL3yaFkCCCAAAIIIBBLgMBbLBW2IYAAAggggECJCCRTCaIFyNZhJ5MNumXrfZTIl0ymCCCAAAIIIJBzAsmMTqA3l6093/Q+9D1NP/2kbL0PP2XnGAQQQAABBBDIXgECb9n73VAyBBBAAAEE8lIg2eBbtlWI5Hr58/Kh4qYQQAABBBBAIGWBZBsWZdsIBckGDxWMEQlSfmzIAAEEEEAAAQRiCBB4i4HCJgQQQAABBBAoOYEglSLZEHzTcifTgloFs6HcJfdNkjMCCCCAAAII5JtAssE3vf9s6Nmfq+XOt+eH+0EAAQQQQACBfwQIvPEkIIAAAggggEDaBYIE37RVtf7p1atX2ssbpDIn21qBpx2NCyKAAAIIIIBATgok27tfbzJTjY2CNIzKZHlz8oGg0AgggAACCCCQtACBt6TJOAEBBBBAAAEEwhAIEszS62rFjqZ0BOCCllHLx9BFqkBCAAEEEEAAgVwUCBJ80/tMVwAuaMAtnWXMxe+dMiOAAAIIIIBAOAIE3sJxJBcEEEAAAQQQCCCQSmCrpAJwqVTkWATZMOSSVRY+EUAAAQQQQACBZAWCjE7gvEZJBeBSfU8rqXI5751lBBBAAAEEEECAwBvPAAIIIIAAAghkVCCV4JtVcK1EadKkiTkUpbUt2c9UK3L0etZQmPpJQgABBBBAAAEEcl0gaM83677DaCil72ifffaZ6Kf+CZoIugWV4zwEEEAAAQQQSFaAwFuyYhyPAAIIIIAAAqELhBF8swqlQS8r8KXBuOJSGBU4zrypzHFqsIwAAggggAAC+SKQifc0vaamVAJtTn9GI3BqsIwAAggggAACJS1A4K2khckfAQQQQAABBHwLpNqq2veFQj6QoFvIoGSHAAIIIIAAAlklEGbwLZ03po2xdF5gq1FWOq/NtRBAAAEEEECgcAUIvBXud8+dI4AAAgggkJUCuVaxQwvqrHyMKBQCCCCAAAIIhCygvc+0kVSuJBpG5co3RTkRQAABBBDIPwECb/n3nXJHCCCAAAII5LxALgTftOW0Bt1ICCCAAAIIIIBAIQnkwnsaQbdCeiK5VwQQQAABBLJPgMBb9n0nlAgBBBBAAAEE/r9ANlbsMGQRjycCCCCAAAIIFLqAvqNp0gBXNiXe07Lp26AsCCCAAAIIFK4AgbfC/e65cwQQQAABBHJGIBsCcFTk5MzjQkERQAABBBBAIE0C2RKAo4dbmr5wLoMAAggggAACvgQIvPli4iAEEEAAAQQQyAaBTATgCLhlwzdPGRBAAAEEEEAg2wUy8Z5GwC3bnwrKhwACCCCAQGEKEHgrzO+du0YAAQQQQCCnBbRi59NPPzX/lMSNaLBNU69evcRaNjfwFwIIIIAAAggggEBcgZIOwNEoKi4/OxFAAAEEEEAgCwQIvGXBl0AREEAAAQQQQCC4gFbuaEolEGcF1zTQpslaN1f4CwEEEEAAAQQQQCBpAX03++yzz8zzUn1P03ezJk2a8I6W9LfACQgggAACCCCQCQECb5lQ55oIIIAAAgggUKICzoqe4i6klTeaCLIVJ8R2BBBAAAEEEEAgXAE/72h6RYJs4bqTGwIIIIAAAgikV4DAW3q9uRoCCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggECeChB4y9MvlttCAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBIrwCBt/R6czUEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIE8FSDwlqdfLLeFAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCQXgECb+n15moIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAJ5KkDgLU+/WG4LAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgvQIE3tLrzdUQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQTyVIDAW55+sdwWAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAegUIvKXXm6shgAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgjkqQCBtzz9YrktBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACB9AoQeEuvN1dDAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBDIUwECb3n6xXJbCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC6RUg8JZeb66GAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCQpwIE3vL0i+W2EEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEE0itA4C293lwNAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgTwUIvOXpF8ttIYAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIpFeAwFt6vbkaAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAngoQeMvTL5bbQgABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQSK8Agbf0enM1BBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACBPBUg8JanXyy3hQACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgggkF4BAm/p9eZqCCCAAAIIIIBAYIFffvlFOnfuLMuXL5cZM2YEzifsE4cNGya33nqrPProo3LZZZeFnT35IYAAAggggAACOSfwySefSKdOneTcc8+Vxx57LG3l//HHH6VBgwZy7bXXSu/evaV8+fJpuzYXQgABBBBAAIF/BAi88SQggAACCCCAAAIpCvz6669SpUoV2WOPPVLMqfjTv/vuO2nSpImsW7dOmjdvLu+//37xB6d5z3vvvSctW7Y0r9qzZ0+57777pFSpUmkuBZdDAAEEEEAAAQSyQ0AbJXXo0MEszMMPPyy33XZb2gr2+++/S506dcx3xjPPPFNGjRollStXTtv1uRACCCCAAAIIiBB44ylAAAEEEEAAAQRSELjiiitk6NChZg4bN26UXXfdNYXcYp86efJkOeuss8wKlPr168tnn32WdRUozz33nFx//fXmDWgLa10nIYAAAggggAAC6RLYuXOn/Pbbb7Jo0SLzjy4vXbpUqlWrJgcddJAceOCBcswxx0jVqlWLLdKOHTvM3mm1atWSSy+9tNjj4u1wvhN16dJFXnjhhXiHF7tP70fLU65cuWKPKW7HN998I8cff7y5Wz8/+ugjs5FYccezHQEEEEAAAQTCFSDwFq4nuSGAAAIIIIBAAQmMHz9etCWxlWbPni1HHnmktRrK58KFC6VevXpm0G3vvfcW7flWs2bNUPIOOxNt2a0tvDXpsJO33HJL2JcgPwQQQAABBBBAwCWg70YjR46UQYMGybJly1z7Yq3cfPPNZmOhgw8+OGr3ddddJ88//7ycfvrpou95yaaxY8fKOeecY56m74hjxoyJGzjbvn27vPTSS7JgwQIzSLhkyRLRPxow1FEONGnQrFmzZuZyMn+px9VXX22e0rp1a3nzzTelTJkyyWTBsQgggAACCCAQUIDAW0A4TkMAAQQQQACBwhbYsmWLGWTTihIr6Vwep556qrWa8ueGDRukUaNGMnPmTDMvnddNg3DZmrS8J5xwgsyZM8csog6HqcNikhBAAAEEEEAAgTAFtm3bJgMHDpQnn3xS5s6dGzNrDawdfvjhou9sX3/9tR3Isg4ePny4XHzxxdaqOVT2vffea67rZ69evex9fhZ0bjWrAVbt2rVl2rRpcXvXaZ6ff/65OZR4vPxTeb/s2LGjvPzyy2b2PXr0kAceeCDepdiHAAIIIIAAAiEJEHgLCZJsEEAAAQQQQKCwBHS+jjvuuMN10yNGjJB27dq5tgVdKSoqMvN64403zCwef/xx0Rba2Z5+/vlnOeKII+xiamXYYYcdZq+zgAACCCCAAAIIpCKgPcBuvPFGu6GPldduu+0ml19+uTm3mg4pWbZsWWuX6LCN2ljqww8/tIfG1p3W/Gs6HKQOlW2lZHuZrVq1So477jjzGprH1KlTzcZIVn7Ffc6fP19uuOEGWbt2rdnLzdmgyzpn/fr1UqlSJWs1qU8dBv3EE0+0G3Hpe+WFF16YVB4cjAACCCCAAALJCxB4S96MMxBAAAEEEECgwAX++OMP2X///aMUwgyOjRo1yq4Y0bk5dJ43ZwVS1MWzaIMO93TRRReZJQo6VFMW3Q5FQQABBBBAAIEsEND3Lw24vf32267S6FDcOsR1mzZtpGLFiq59sVZ0aMoLLrjADpJpIErfXZxJh3msXLmyc1Pc5a5du8qzzz5rHqMNs/r16xf3+OJ26jDd+j5ppZNOOkm+/PJLazXQpwb3rEZQGpzUue+qV68eKC9OQgABBBBAAAF/AgTe/DlxFAIIIIAAAgggYAu0bdtWrJ5o9kZj4fbbb5eHHnrIuSnQsrZO1qGRFi1aZJ6f7UNMxrpJbV09ZcoUc5cGEbUyjIQAAggggAACCAQR0B5krVq1iprDrUuXLubwickGkrSHWsOGDWMOU5lssGvWrFlSt25d87Y0CPjrr7/6CgDGctB71HnhrHTPPfeYQ2Ba60E/NZ8+ffqYp2uQ8Omnnw6aFechgAACCCCAgA8BAm8+kDgEAQQQQAABBBCwBD7++GM57bTTrFXXZ/v27WXYsGGubUFWdP6Nu+66yzw1V3uMjR49Ws477zzzHrQSSodOCjpMUhBDzkEAAQQQQACB/BB4/fXXo4by1p5b7777rpxyyimBb9I5uoAzk549e0rv3r2dm+Iun3HGGTJhwgTzmAcffFC6d+8e9/jidm7fvl3KlSvn2q35Fvfe6TowwcqSJUukVq1a9lHff/+9HHXUUfY6CwgggAACCCAQrgCBt3A9yQ0BBBBAAAEE8lhg69atZotmnbcsVtLKn4kTJ8ba5Xvb4sWLZb/99rOP11bPLVu2tNdzZWHHjh1Su3ZtexinsFps58r9U04EEEAAAQQQSF2gb9++ooEwZ9Kgmw6/WK9ePefmpJd13jedC27mzJmuc3UeOA2m+Uka/GvdurV96F9//SXa4ChI+vbbb+XYY491nbpmzRqpUqWKa1vQlc6dO8uAAQPM07VX3xdffCGlSpUKmh3nIYAAAggggEAcAQJvcXDYhQACCCCAAAIIOAV0zg2de0OT9kq78847nbvl4IMPll9++cW1LdkV5xwhGoBbuHChlClTJtlssuJ4rdzRSh4rrV27VrSyjIQAAggggAACCCQSeP755+W6665zHaZBrc8//9wcktu1I+DKm2++ac735jzdb7CrqKhIjjjiCHu4yquuukoGDRrkzCqp5aeeekpuuukm+xyd43fatGn2eqoLc+bMkf/85z92Np999pmcfPLJ9joLCCCAAAIIIBCeAIG38CzJCQEEEEAAAQTyWMDZE00rRa688sqYQ/RoJUzQpHO77bvvvrJu3ToziyeeeMJVARM030yd572fwYMHyxVXXJGp4nBdBBBAAAEEEMgRgfHjx8uZZ54ZVdqvvvrKnJstakfADdpg6tBDD7XPTibYNXnyZNGeY1b65ptvonqsWfv8fHrnd+vRo4fZ0MvPuX6PcV7j8ssvlyFDhvg9leMQQAABBBBAIAkBAm9JYHEoAggggAACCBSuwKWXXirDhw83e2z99ttvsmXLFqlRo0YUiN9W0lEnGhtee+01ufjii+1dK1eulOrVq9vrubigw0PpMFGakqnMysV7pcwIIIAAAgggkLqA9sxq2LCh3RDJylFHHXj00Uet1VA+t23bJuXLl7fz0tEM7r//fns93sI111wj/fv3Nw/RAJwOfxk0xZrf7f3335fmzZsHzTLmed6AZj68a8a8UTYigAACCCCQYQECbxn+Arg8AggggAACCGS/gA7Fo/O3aRo6dKh06NBBYlWQ6P558+a5Wk7rNr+pWbNm8sknn5iHd+zYUQYOHOj31Kw97uOPP5bTTjvNLp/Oo1K3bl17nQUEEEAAAQQQQMAS2LRpk9SpU8eeI9barsN56ztEpUqVrE2hfR5yyCH29caNGydnnXVWwrzXr1/vGj572LBh0r59+4TnFXeA9pbTBkrOVBJBsQ0bNkjlypXty+hwnhpAJCGAAAIIIIBAuAIE3sL1JDcEEEAAAQQQyDMBbQl99NFHi7a+1tbMOq9I6dKlzbvcZ599ZNmyZa471tbOzmGHXDvjrGgvugMPPNA+wgrw2RtydEHndatatapd+u7du8uDDz5or7OAAAIIIIAAAghYAv369RMdYtGbJk6caDeC8u5Ldf2MM86QCRMmmNmsWrVKqlWrljDLESNGyCWXXGIfN3/+fNEAXtCkw4t369bNPr1+/foyffp0ez3MhRNPPFGmTJliZsloBGHKkhcCCCCAAAIRAQJvEQuWEEAAAQQQQACBKIFnnnlGbrjhBnP7t99+K8ccc4x9zLHHHiu6zZlGjRolbdq0cW7ytawtpbUnnZV++OEHs8W3tZ7LnyeccIJ8/fXX5i1QwZPL3yRlRwABBBBAoOQEnPPpOq/SpUsXeeGFF5ybQl3WHm4ffvhhUkNi68gEL7/8slmO3XbbTXSo8VKlSgUuV8uWLeW9996zz7/99tvloYcestfDXNDApgY4reQ32GgdzycCCCCAAAIIJBYg8JbYiCMQQAABBBAIXaCoqMjsOaXDCv7000/y+++/y7/+9S/RAEWnTp1cPYRCvzgZ+hZYunSp1KxZ0zz++uuvFw3COdO5554r77zzjnOTPPvss3Lddde5tvlZ6dy5swwYMMA+VHvalS1b1l5PZWH6X9tk9M+b5fdVO2T95iKpWKGUHLlPObms7i6yX+Uyrqy37jDmmvtxk0xfuk0WG8fvWr6U1KxaRs4/YhdpUKOc61i/K3fccYc8/PDD9uGpzINnZ8ICAggggAACGRLQ97jJkyebw0MvXLjQHqZQh0PUXk9t27ZNqfdThm4r45fVBkjaEMmbfv31V9eoAN79qa4fddRR5jCW+r7iDEjFy1ff2xctWmQecs4558i7774b7/C4+7zzzOnBY8aMEQ3GzZgxw5wDePbs2aJDT+p76XHHHWf+vhB0HmAN8GneVtKgo/b6IyGAAAIIIIBAeAIE3sKzJCcEEEAAAQR8Cbz11lvSs2dPc+jCWCfsvffeovM86DCGGqzQip1///vf0qdPH6lYsWKsU9hWQgJXXHGFOaebtmTWoSC9FRzXXnttVAvsu+++2/yuki2Sc36Rpk2bis6NlmrasK1Irv9gjSz+a3uxWbU9oaJ0rPfPczVnxXbp8eFa2bRxZ8zja+1TVl48u5qUd8fqYh7r3KiVUa1bt7Y36XBOznnf7B0sIIAAAgggkMUCW7Zskeeee878s2DBgrgl1XeI/v37S4UKFeIex85/BGbNmhVzDtjTTz9dxo8fX6JM2pDqq6++krFjx0bNsxbrwn/88Yfsv//+9q6+ffvKXXfdZa8nuzBt2jRp0KCB6zQdulIDgW+++aZru3Pl0UcflVtuucW5ydfy8uXLZa+99rKPveeee+S+++6z11lAAAEEEEAAgdQFCLylbkgOCCCAAAII+BLQua5uvPFGGTJkiH38KaecIr179zbnENPWvDfffLPZelqH4zv//PNdc1xowO68886zz2WhZAV0rrbGjRubFxk8eLBoBZo3aTBUKyuc6aqrrpJBgwY5NyVcXrJkidSqVcs+7s4775T777/fXg+ysHLzTun87hpZu9bowmak0+vuKm0O30X2rVRahs7aJG9P32hn2+HEyvJ//yon17y5WnbsKJLdq5eRW06qLEfvXU5GGT3lBk9abx/bqn5Fud74k0z666+/ZN9997VP0codr5u9kwUEEEAAAQSyUOCzzz4T7Z0+d+5cu3QtWrQwh6OuW7eu2Ut95syZ8umnn4oGYjRddNFFonOBWXPD2ieyECWg7wX6XuVNr732mtmD0Ls9k+sjR440v1urDKn2GHvsscfk1ltvtbIzP2vXrm0+a9ogTwNw7dq1k1122UX0ndR5bNDg23/+8x+7EaC+7+ocxiQEEEAAAQQQCE+AwFt4luSEAAIIIIBAsQLasrRJkyb2L7h6oM7bcNttt7nmg1i/fr2cdNJJ5nA33syyseLBW8Z8Wd++fbvo/G1agdawYUOZNGlSzEqzgQMHmkP9OO/7zDPPlA8++MC5KeHyxIkTRXu5WWn06NGuHmLWdr+fy4wea51GrzZ7rlU2hpJ8oVVV2adiadfp3T5aK7MWbjW3lS5dSsqVKyVbtuyU3XYrI8POryYVjfVZy7dJt9FrXOfV2KusDG1dzbXNz0qVKlVk3bp15qEXXnihvPHGG35O4xgEEEAAAQQyLvDEE09It27d7HJoMETfy0499VR7m7WgDak0UKLBGU06VGC9evWs3XzGENChO7UHmTV0o3WIjjjw559/Zt2ID9porlevXlYx5e+//5Y999zTXk924eyzz5Zx48ZFnda8eXOzwZ4+b86kveseeOABe5MOXR/rWbQPiLFw2WWXyauvvmruUWdtIEhCAAEEEEAAgfAECLyFZ0lOCCCAAAIIxBTQ+Rj0l2EN4lhJezNpr6ZY6bvvvpP69etH7dK54A4//PCo7alu6N69uzmPxObNm1PNKvD5OpeZDq35/PPPS506dQLnE9aJWg5rnjYd9lODcLGSDkmk83o405FHHik6D0cySXtBXnnllfYp+qxo6/mg6doP1sr8RVuN4a1Ky8sXVJO9dnUH3TTfN+dulhc/j/Rk020agBvSrrrs+/+DdL2Nnm5f/uh+LoIG3pwtq/X5nj59ul6ShAACCCCAQNYKaEBIg2iPPPKIXcb99ttPtMHMoYceam+zFnR4cG1A5Uz6TnHNNdc4NyW9vHHjRrPH088//yzaOChTSd/XdPjz//3vf1KpUqXQijF16lSzoZM3w65du8rTTz/t3ZzxdWsoci1IqkGrrVv1fS16OFLt4aaBsTJlosf39o6UoD0v9Z00maSjbDz55JP2KatWrZJq1ZJvWGVnwAICCCCAAAIIuAQIvLk4WEEAAQQQQCBcgZ07d4q2YtUhaKzk55djDfR8++231imiLV21xW+pUqXsbWEsrFixIqUWumGUwZnHM888I9dff71zU9qXdVjEww47zOydpXO46VwuxaWvv/5aTjjhBNfuIBUw9957r2tuDZ1Pzjl3iOsCCVa+MAJufYzAm6YXL6wuB1WNrrDRfZ/+sVUeMOZzc6aTj9xV7m4UqUi7acJamfPbP73irOOaH7Wr3Hx85Bhre6LPk08+Wb744gvzsCBGifJnPwIIIIAAAmEL9OvXzzXst+Y/b968mEE33ed9f9Nt2lvupptu0sXAyTtXauCMQjpR31GPOeaYkHIT0UZgOhKEN73//vuivb6yLf3f//2fORqClksDsTrnW9A0ZcoUOfHEE12n6ygIeu+xAnLWgdpgbdmyZdZq3OfSPsix4O21R89MBw6LCCCAAAIIhCBA4C0ERLJAAAEEEECgOIFnn31WtLWuMy1cuFAOOOAA56ao5YsvvtgcwsjaocPBvPLKK9ZqqJ8aXNJeXVu2bAk132Qy0xbUNWrUkKFDh8oee+yRzKmhH3v11Vebc7RpcEi/q913373Ya/z+++8xv0ttmb7rrrsWe553R4cOHWTYsGH2Zu0lWb16dXs9mYXzRqyUDRt2St2DystjzaoUe+prP22Wl79093jT3m41jaEprfSZEZy73xGcO3S/8vLk6VWkfOQQ69CEnzpn4dtvv20fl8o92pmwgAACCCCAQAkJjB8/XnT4aGfSIaY7duzo3ORajtVA6qOPPpJmzZq5jkt2RRsF/fe//zUDPJns8aaBIJ2HWN9vY91rsvdlHV/cUIt6395hFq1zMvnpDHql2otfe1Pefvvt9u3o/eooF4neA71BXh3CW4fy9pu0YZmzsZv2mNPGgSQEEEAAAQQQCEeAwFs4juSCAAIIIIBAlIDO8XHwwQe7tt9yyy2ik6AnSocccogsWLDAPkwnUtdhbUglK+BsdZyock1LsmnTppjzjvgJrjrvpGXLlvLee+/Zm7Zt2yYajEw2Tf9rm/QY88+cbM+3qS6HVi8+Qnb35+tk2txIsFXndnuzbXSwb8n6HTJ7xXapt1e5qHnikilf586dZcCAAfYp+nwfdNBB9joLCCCAAAIIZIvA6tWrzZ7n1tykWi4NOOmQiPECTs6eUHrO6aefbo56EO8cPa7Qkw6lPnfuXBdDqj3JXJmFvOL8PrV32scffxz4CmeddZZrZAwd2lR7WiZK3t8VHn74YXPu6ETnWft1uND27dtbq2YDMOe6vYMFBBBAAAEEEAgkQOAtEBsnIYAAAgggkFhAe5K98MILrgNnzZolOtdVvBSrF9Uvv/wSFcSLlwf7khfQFuQNGjQwh/jUyrWvvvoq5rwa3pyrVKliDkvp3K4Vc94hKJ37vcs6B+Cnn35qb9Y5ZYKkEcZ8bIONedkOqllOXjy7atwsLhq5Slav2WEf4x1m0t4R0oJ3GCmdB0/nwyMhgAACCCCQbQJ33XWXPPDAA65i+elRtHjxYtFhs//++29z2EntRV++fHlXPqy4BfSdp3Tp6LloL7nkEnMuOffRmV/T98Vy5crZBWnTpo2MGjXKXk9mIdb8bjo8/RlnnBE3m1hm2ntNnz2/ady4ceZw+NbxL774omgjKRICCCCAAAIIhCNA4C0cR3JBAAEEEEDAJaBzPXjn6NJgzrRp01zHxVrxtkDN5ha/scqfq9teeuklcxgnLb/2TGzUqJGvW9EKF2/SuVjOOecc7+Zi1zVIp/PFaUrl+165eae8N3+LND2wvNRyDBnpvfCm7UXSesgK1+buZ1SRpvuXXOWgdyglHd5Uh0kiIYAAAgggkE0CS5YskVq1armKpMP/LVq0yBVwcR3ASmCB5cuXy1577RV1/uOPPy4333xz1PZMb9BekNroyko69KiOkhAkTZ48WU466STXqatWrZJq1aq5tnlXdC7gAw880LVZ5xHU+QT9JucoD3pOGHMR+r02xyGAAAIIIFAIAgTeCuFb5h4RQAABBNIuoMO96FAxzqQtp3v06OHcFHPZmmPM2qmtT7UVKqnkBLRlug7Z4xxSKpWraRCvU6dOvrPQXpBz5swxj9deYNobrCTTF4u2Sp8P1rou8fble0ilcqVc28Jc6d+/v1xzzTV2ljqk1GGHHWavs4AAAggggEA2CDz11FOiQQxn0l7bDz74oHMTyyEJzJs3T2rXrh2Vm/Yii9W4KerAgBu0t5nOm6fvInfeeafvXLyBwmQDXs4LPfTQQ6LPlpX8zhf35ptvygUXXGCdZn5qXs654lw7Y6zoKBx169a19zCsvU3BAgIIIIAAAqEIEHgLhZFMEEAAAQQQcAt45/jQvdOnTxf9hTpRck7YrseOGDFC2rVrl+g09qcgoAEhDQxp8s7LlyhbDdp5A3b33Xef3HPPPYlOtfdrz69vv/3WXNfr69CiJZkenrpBPvphk32JKlXKyKiLoud3sw8IYcFbkak9/I477rgQciYLBBBAAAEEwhM48cQTRXsDOdMXX3wh+m5HCl9Ae3jtvvvuURl//vnn0rhx46jtYW2whlps2LChOby433zXrFnj6pHWpUuXqKHl/eZ19tlni5bDSt26dZPHHnvMWi32Uxv3aSM/Zxo2bJhrzjbnvljL+t7pHHkgW3sYxio72xBAAAEEEMgFAQJvufAtUUYEEEAAgZwSWLFihey5556uMu+2226yevXqmHNYOA+cP39+VC8gHdrIO+SR8xyWUxPQ4T91bjdNQVr79uzZU/r27esqRLKVMCeffLJopZ4mfVbWrnX3RnNlHsLKxW+ukhWr0je/mxa5d+/e0qtXL7v0fuY7tA9mAQEEEEAAgTQIFPcOt3LlSilbtmwaSlCYl4g1X+5nn30m+n5UUqlt27ai8/bpu8m9997r+zLeedkuuugief31132fbx24c+dOM4DnbLz19ttvy7nnnmsdUuync4hy66AZM2ZIvXr1rNWEnxMnTpSmTZvax2kDNO0BSEIAAQQQQACBcAQIvIXjSC4IIIAAAgjYAtqTR38hdqYLL7zQ/OXeuS3W8pAhQ+TKK6+0d6Uy35edCQvFCuzYsUO0Zbt+Z9riedKkSQmDo97Mnn/+ebnuuutcm3V+N53nzW/ytnjWyphSpUpm2MdY87vddvpucvoBFfwWN9Bx2orbOfeI9upLtndhoAtzEgIIIIAAAj4FNHhx9NFHu45u3bq1jB492rWNlXAFnD3/rZzfeustOe+886zVUD/1HeTQQw818/zpp5/k8MMPTyp/5zvamWeeKR988EFS5+vBCxculIMOOsh1ns4vWKNGDdc278qff/4ZdYzOQajbneXynuddf+edd1xBvldeeUUuu+wy72GsI4AAAggggEBAAQJvAeE4DQEEEEAAgeIExowZI61atXLt1mFjNPCQKHXo0EF0qBgrXXXVVTJo0CBrtUQ+X331Vfn4449FW/BmMukQm7feeqvUrFkzbcV4+eWXpWPHjub1/A4F6i2cVgx55yDxO0eHldell14qw4cPt1bNoSsrV65sr4e5MPH3rfLgeHePureM+d0ql+D8blp+dVZvKy1btkz22msva5VPBBBAAAEEMi7w3nvvScuWLV3l0F7td911l2tbule0QU6fPn1ER0bQ5UylMmXKmAErnRMtzB6AVu8z532VZA8saz7lZBtKWeVz9tA7/vjjRUdPSDZ5G+r5HWpc39u9AbKuXbvK008/nVQR9PcN/b3DSn5721nH84kAAggggAAC8QUIvMX3YS8CCCCAAAJJCwwcOFA6derkOs/P3CBFRUWy7777igYkrDR06FDXL8WffPKJ6ITqWglUvXrqc3IVN6+Gdf10fz7zzDNy/fXXp+WyOmzUgQceaAa5dI437bkWJE2ePFlOOukk16na8vivv/5ybYu3ohV6DzzwgH2InxbP9sFJLvSZtF6++HGzfZaf+d1e+2mzfLt0m/Q5eTepUMY+NamF888/X7RSx0ol2avPugafCCCAAAIIJCPwv//9L2qerLFjx0qLFi2SySb0Y7VHVfPmzUPPN2iGOj/YMcccE/T0qPO0kZkGw5xJg0vaCyvspI3NTjvtNDPboPfhHOqxdu3a8vPPPyddzPHjx4v2lrPSJZdcIvr8JUre9yk9fs6cOfLvf/870amu/c8++6xowM5K33zzjWvON2s7nwgggAACCCAQTIDAWzA3zkIAAQQQQKBYAW8LUj1w6dKlZlCt2JOMHTrUjfeXZu9wfKeeeqp8+umnEtYvx86hFuOVLR37dG4z7XV22GGHpeNyZmWDVjrodX/99VfZY489Al3XOVyRM4Nt27b5bg0+YMAA6dy5s3367Nmz5cgjj7TXw1xo8/oqI9gYmd+t8b93kZ4nFd+7ToemPO+VlUYL+yIZ3K661KocLPJmPbt6L3pveo8kBBBAAAEEsknAGZSxyvX999/LUUcdZa1m5FN7umkjH2fjrIwUxLio9vDSBmUVKoQ3RPWGDRvM4ROd853p+1nYc+utWbNG6tSpIzp/co8ePVyNnpLxdI5UEHRu3o8++khOP/10+7I6F67OGxwvaaMubaTnTEHnmNNGfM7rMRKBU5VlBBBAAAEEUhcg8Ja6ITkggAACCCDgEtDJ4E855RTXtu3bt4sOzxMveVueeud308qCatWqmVloBUXFihXjZZfUPu19lMmhi3ROikQ+Sd1QgoOnTJlizu2mh7300ktRPRQTnO7ard9FrGEhFy9e7HvYTG+r55EjR8oFF1zguo6flYVrd8i4X7bI+q1FcsoB5eX4fcu5Tlu2cae0H77Sta1bs93krIOKrzx7/efNMuiL9VKuXGkZe/nuEnTmOR1K1KowZL4c11fACgIIIIBAlgjMmzdPtAeTMwWZA0zPnzVrljkUtfbkd/Yscuad7LI2mNIREjKVSpcunfRcuH7Lescdd8jDDz/sOlxHedAeXmGk9evXy1lnnWXO56vf8XfffRf4XVoDVhq4slKQkQq8De709wDvnMFW/tbngw8+KDrMpzMF6e2m5+uc0jq3tJUy+VxZZeATAQQQQACBfBIg8JZP3yb3ggACCCCQFQLae0rnaXCmRL/MalBN5wVbsGCBfZp3fjdrEvSmTZuac7LZB7KQlIAOr1mvXj2ztbN+6jBDqQb9Yk1mn8zwRd5ec0FaYU9avE3uG7fGZfHUedXk33uUtbf1/26jvDV9o72uC/F6se0wppE5zwjUbd68U845pqJ0PTZYsFcrpGrVqmVft3v37qKVRyQEEEAAAQSySWDLli3m/KPOnlfaoOrkk09Oqpj6c71Ro0Zmg5PbbrstKqCUVGYFcrC+Ax9yyCGuu9X3aQ0spdq7buPGjaLzuemQ7Toc+FdffRX1ru66cIIVHQLz8ssvt48aN26cGdSzN/hY0DJVqlTJPlKDedrrrbj0xx9/yP777+/a/cQTT8hNN93k2uZ3Ra2t3zuCzlPn91ochwACCCCAQCEKEHgrxG+de0YAAQQQKFEBbY2sLWmtX2b1YhrssXqreS+ulTzaA+jDDz907dI5x3TuMStZczqk8ku2lVehfm7evFnatWsnGsTU9O6775oVMal6HH744TJ37lxXNu+//35S87E4e4Tp0EPaCy6Z5B1CUs9t37CSdKizq5mNMVKktHltpWzYYETTHOmdK/aQXcvG7sf2+Ncb5IMZm4wKr9Ly1qW7i9HpLVB67733pGXLlva5Y8aMca3bO1hAAAEEEEAgwwLenlfJvnfNnDnTnBNOhzPU98GpU6cW+w6Y4VvNusuPGDFCdK4zZ9KhuPv37y+xGjk5jytuWedf0/nivv76a3N4cR31INXhvDXPI444wr6kztOrjaaSTc73x3hz2mkDvjZt2rjmytV3RZ37T3shJpu8czwTHE5WkOMRQAABBBBILEDgLbERRyCAAAIIIJC0wHPPPSc6tJCVtCJBAz7epENQ6nYdSsebnOfosIU69KQm7VF34IEHmsv85V9Ae13pPBiTJk2yT9IWzw0bNrTXgyzo0EU1a9Y05k1b5zrdz5BBzhO884WsXr3ad2WKBtXOGrTcmZ25fH/LqvZwky9+v1He/Mbd200P6nlWFWm8X/moc4fP2SxDJq83t3c/o4o03ZCCSKgAABvzSURBVD/6mKiTitlw3333yb333mvv/fvvv2XPPfe011lAAAEEEEAgWwS8vdD1/UsbU5Ur5x6+2Vtendv15Zdfli5dupi7dE42beCz++67ew9lPY6ABrD69evnOuKGG24w52Nz9hBzHRBjRYdQf/HFF+Xaa6819+pcbBMnTpRjjz02xtHJbdJAWNWqVe13v/POO0/eeuut5DIxjh40aJBcffXV5nlavj///DPm8JfeoS313VUb7FWpUiXpa+oJ2vOvWbNm9rnaIK1Vq1b2OgsIIIAAAgggkLoAgbfUDckBAQQQQACBKAENwmhrWm3trEmXNcjj/AV54cKF0r59ezMQpMPePPbYY2aLXCuzxx9/XG6++WZzLg/9hV5/KdZhcrQSh5RYQHu3ff/99zJ//nzRCeyHDh0adZJWpmmAVIfvPO6443y1pl67dq2Z58qVK835W5555hlX70brIvqdagtoHSZJ5+PTazmHW7SOsz61csiqrNNtOs/MoYceau2O+6mzvZw9eIXs2KFL/6RqVcvI6xdWN+dk++T3rdJv/FpzR6MjKsiUuVuNOf3+OfaE2hWk78m7WaeJbh46a6OMmPpPkK5V/YpyvfEnlaRzqlg9OvXfwuzZs1PJjnMRQAABBBAoUQHvUILa60ob1MQKvumQgTpXlg6hbL33aaMqDaqEOR9vid5wFmWuI0d07Ngx6r1N36seeugh8925bNmyxZZYA6CjRo0y52DTYSo1NW7cWF577TXfc+8Wm7ljR9u2beWNN94wt2jZ/vrrL8def4ubNm0yG9NZc+B6e85t3bpV+vTp45pPToNuOrRlcSNp+LmyzqWnPTutpGXXeyAhgAACCCCAQHgCBN7CsyQnBBBAAAEEXAI6DI3OmWD1hNJflP/73//KvvvuKzr0nlbgaNKAjAaGdLgZHY5P92nSgM39998vOizf8OHDzeFxtAJBjyclFrjxxhvl6aefTnzg/z9CA0NnnHFGwuOdFS0JD3YcoC2ZNWhXXJo1a5bUrVvX3q29IHV4Ub/pjonr5LtfttiHd2lSWSqUKSVfGEG3b+f/s/1Qo2fbc0YPt//N3iyvfPVPbzY94cTDK8iJxr6l63fI6B82y6aN/wxH6Ryq0s44yQVtca6VQ9a/Aw0ma1CZhAACCCCAQDYL6DvY3XffbRdRe7BdfPHFcvTRRxuNV3bKjBkzzEZV+p5m/YzTAI/21tL53UipCYwcOdIMwFm2Vm7agEdHMNBhPLWB0l577SU6V7IO+a3v06NHjzbn1tPj9d2rV69eou+E8YJ1Vt7JfOrwl84h4bW3mg4bnmz67rvvpEmTJvYzpA3CtMGSjtTw5JNPmnPcWXlqb0AdQaB8+eCjEGhe1vD1ukyDKFUgIYAAAgggEL4AgbfwTckRAQQQQAABW+DHH38053yw5hSzd/z/hdtvv92s1NGKAU3aalrnWdD53bxpwoQJctppp3k3s16MQLdu3UTnZdGkvrvuuqtUrlzZXNfhIbWVsbMyR4eW0mBnonTBBRfYQ4Na35uVt1Wpo9+jVgI582/RooWMHTs2bvb/+c9/7AqWTp06yUsvvRT3eOfObUas7LaP18qc37Y6N9vLZx21q9x8fCWzB5xu/GrJNnnwk3WyebN7zjfdV758aenyf5Wk5cEVdDWlpL3b6tSpY+cxbdo0MyBtb2ABAQQQQACBLBXQoEjXrl1dw1THKqr2nL/11luTmts1Vj5scwtoMEvflYcNG+bekWBN3880gKXv1NWrV09wdLDdWrYaNWrYJ7/66quiw4YHSRrE1VEPdP65WOnCCy80n68TTjgh1u6ktukw9zr8qfWOqiNu6DszCQE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    }
   },
   "cell_type": "markdown",
   "id": "6d1f83b2-f5e1-4681-bbb9-57c9e33a16ed",
   "metadata": {},
   "source": [
    "<details>\n",
    "    <summary>Aside: higer-order autodiff</summary>\n",
    "\n",
    "The backward pass is itself traceable! This is how higher-order autodiff (`grad(grad)`) works.\n",
    "\n",
    "![Screenshot 2024-07-29 at 4.26.53 PM.png](attachment:30d1f76b-e33f-4877-b52e-dea86260c3ea.png)\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "09e8fdf8-27e8-4e52-9fc7-3d84a36609b4",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "\"\"\"Import the full definitions of np and primitive_vjps\"\"\"\n",
    "from microjax import np, primitive_vjps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d1b1477-aa50-4dfe-bf02-025945d087f4",
   "metadata": {},
   "source": [
    "We previously defined the forward pass in `trace`. Now we have the graph and need to do the backward pass along the graph. This composes all of the primitive VJPs together to make a composite VJP for the entire function.\n",
    "\n",
    "Finally, to get the gradient, we just call this VJP with the $\\frac{\\partial{y}}{\\partial{y}} = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8da27b11-f4f6-4d0d-84e8-72f8d65a1b64",
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_pass(g, end_node):\n",
    "    outgrads = {end_node: g}\n",
    "    for node in toposort(end_node):\n",
    "        outgrad = outgrads.pop(node)\n",
    "        fun, value, args, kwargs, argnums = node.recipe\n",
    "        for argnum, parent in zip(argnums, node.parents):\n",
    "            vjp = primitive_vjps[fun][argnum]\n",
    "            parent_grad = vjp(outgrad, value, *args, **kwargs)\n",
    "            outgrads[parent] = add_outgrads(outgrads.get(parent), parent_grad)\n",
    "    return outgrad\n",
    "\n",
    "def make_vjp(fun, x):\n",
    "    start_node = Node.new_root()\n",
    "    end_value, end_node = trace(start_node, fun, x)\n",
    "\n",
    "    # This means that the output didn't depend on the input so the gradient is 0\n",
    "    if end_node is None:\n",
    "        def vjp(g):\n",
    "            return np.zeros_like(x)\n",
    "    else:\n",
    "        def vjp(g):\n",
    "            return backward_pass(g, end_node)\n",
    "\n",
    "    return vjp, end_value\n",
    "\n",
    "def grad(fun, argnum=0):\n",
    "    def gradfun(*args, **kwargs):\n",
    "        # Replace args[argnum] with x. Define a single-argument function to\n",
    "        # compute derivative wrt.\n",
    "        def unary_fun(x):\n",
    "            new_args = list(args)\n",
    "            new_args[argnum] = x\n",
    "            return fun(*new_args, **kwargs)\n",
    "\n",
    "        # Construct a vector-Jacobian product for the function\n",
    "        vjp, ans = make_vjp(unary_fun, args[argnum])\n",
    "        return vjp(np.ones_like(ans))\n",
    "\n",
    "    return gradfun"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90240599-fd71-49cf-972c-092c4e49d408",
   "metadata": {},
   "source": [
    "And that's it! `grad` is the main entrypoint so we now have a working Microjax!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39d69157-2632-47a4-907c-a0396c7efadb",
   "metadata": {},
   "source": [
    "## Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "013b36f8-01a1-4de1-bbf7-a6aedffd113d",
   "metadata": {},
   "source": [
    "Let's see a few examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "76e118fc-7170-4671-baac-5cf16166684c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from microjax import jacobian, np\n",
    "arr = np.array([1.,2.,3.])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cddc01ae-073a-4c62-972d-fc3d705c8bb8",
   "metadata": {},
   "source": [
    "Recall that the derivative of `exp` is `exp`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "80c9a0ec-122c-4c99-a15f-628cb8db3111",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 2.71828183,  7.3890561 , 20.08553692]),\n",
       " array([ 2.71828183,  7.3890561 , 20.08553692]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(jacobian(np.exp)(arr),\n",
    " np.exp(arr))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48ca83b7-6126-436c-b9e0-d31d1baa6b09",
   "metadata": {},
   "source": [
    "(Note that I'm using `jacobian` rather than `grad` because I'm using vectorized functions which return an array rather than a scalar. All of these are equivalent to just taking three derivatives in parallel.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e45cbb47-ee58-4d31-98fb-4c10dbb04afe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 3.71828183,  7.8890561 , 20.41887026]),\n",
       " array([ 3.71828183,  7.8890561 , 20.41887026]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(jacobian(lambda x: np.exp(x) + np.log(x))(arr),\n",
    " (lambda x: np.exp(x) + 1. / x)(arr))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07c2df06-5529-4b22-8308-ccab3fd66c5e",
   "metadata": {},
   "source": [
    "Let's revisit `f` and `g` from earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "335125c4-2862-4947-8dfd-97a555dccc06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.71828183,  7.3890561 , 20.08553692])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(x):\n",
    "    import random\n",
    "    return np.exp(x) if random.random() < 0.5 else np.log(x)\n",
    "\n",
    "jacobian(f)(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e6b96f94-1b81-4b55-9de1-0536198bba56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def g(x):\n",
    "    for i in range(5):\n",
    "        x = x + 1\n",
    "    return x\n",
    "\n",
    "jacobian(g)(arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c5cb8d9-d8ab-4f01-8c3e-588f8f12dee2",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "There were three main parts of the implementation:\n",
    "\n",
    "1. Build a computation graph:\n",
    "   `Box`, `Node`, `primitive`, and `trace`\n",
    "2. Define a vector-Jacobian product (VJP) for each primitive:\n",
    "   `primitive_vjps`\n",
    "3. Compose VJPs backward:\n",
    "   `backward_pass`, `make_vjp`, `grad`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb5c66f8-0880-4dd0-a725-160e8fd1704b",
   "metadata": {},
   "source": [
    "Where to go from here? There are a couple of important pieces still missing:\n",
    "\n",
    "First, we can only get the gradient for one array. This allows us to update, say,\n",
    "the weights in one layer. But we can't update a whole model at once. For that you'd need\n",
    "something like JAX's [pytrees](https://docs.jax.dev/en/latest/working-with-pytrees.html),\n",
    "which tell JAX how to update a whole container, for example, a model with many layers.\n",
    "\n",
    "Another important piece we're missing is around performance / accelerators. JAX has an\n",
    "[XLA](https://github.com/openxla/xla) backend, which makes it simple to compile and run\n",
    "computations on a GPU or TPU."
   ]
  }
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