{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(fixed-point-iteration)=\n",
    "# Solving Equations by Fixed Point Iteration (of Contraction Mappings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Sections 6.1.1 *Euler's Method* in {cite}`Sauer`\n",
    "- Section 5.2 *Euler's Method* in {cite}`Burden-Faires`\n",
    "- Sections 7.1 and 7.2 of {cite}`Chenney-Kincaid`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "In the next section we will meet {ref}`newtons-method` for root-finding, which you might have seen in a calculus course.\n",
    "This is one very important example of a more general strategy of **fixed-point iteration**, so we start with that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will often need resources from the modules numpy and pyplot:\n",
    "import numpy as np\n",
    "\n",
    "# We can also import items from a module individually, so they can be used by \"first name only\".\n",
    "# In this book this is done mostly for mathematical functions with familiar names:\n",
    "from numpy import cos\n",
    "# and some very frequently use functions for graphing:\n",
    "from matplotlib.pyplot import figure, plot, title, legend, grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-point equations\n",
    "\n",
    "A variant of stating equations as *root-finding* ($f(x) = 0$) is *fixed-point* form:\n",
    "given a function $g:\\mathbb{R} \\to \\mathbb{R}$ or $g:\\mathbb{C} \\to \\mathbb{C}$\n",
    "(or even $g:\\mathbb{R}^n \\to \\mathbb{R}^n$; a later topic),\n",
    "find a *fixed point* of $g$.\n",
    "That is, a value $p$ for its argument such that\n",
    "\n",
    "$$g(p) = p$$\n",
    "\n",
    "Such problems are interchangeable with root-finding.\n",
    "One way to convert from $f(x) = 0$ to $g(x) = x$ is defining\n",
    "\n",
    "$$g(x) := x - w(x) f(x)$$\n",
    "\n",
    "for any \"weight function\" $w(x)$.\n",
    "\n",
    "One can convert the other way too, for example defining $f(x) := g(x) - x$.\n",
    "We have already seen this when we converted the equation $x = \\cos x$ to $f(x) = x - \\cos x = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the two setups graphically: in each case, the $x$ value at the intersection of the two curves is the solution we seek."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_1(x): return x - cos(x)\n",
    "def g_1(x): return cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = -1\n",
    "b = 1\n",
    "\n",
    "x = np.linspace(a, b)\n",
    "\n",
    "figure(figsize=(12,5))\n",
    "title(\"$y = f_1(x) = x - \\cos(x)$ and $y=0$\")\n",
    "plot(x, f_1(x))\n",
    "plot([a, b], [0, 0])\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=(12,5))\n",
    "title(\"$y = g_1(x) = \\cos (x)$ and $y=x$\")\n",
    "plot(x, g_1(x))\n",
    "plot(x, x)\n",
    "grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fixed point form can be convenient partly because we almost always have to solve by successive approximations,\n",
    "or *iteration*, and fixed point form suggests _one_ choice of iterative procedure:\n",
    "start with any first approximation $x_0$, and iterate with\n",
    "\n",
    "$$\n",
    "x_1 = g(x_0), \\, x_2 = g(x_1), \\dots, x_{k+1} = g(x_k), \\dots\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proposition}\n",
    ":label: proposition-1-fpi-iterates-converge-to-fp\n",
    "\n",
    "If $g$ is continuous, and **if** the above sequence $\\{x_0, x_1, \\dots \\}$ converges to a limit $p$, then that limit is a fixed point of function $g$: $g(p) = p$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "From $\\displaystyle \\lim_{k \\to \\infty} x_k = p$, continuity gives\n",
    "\n",
    "$$\\lim_{k \\to \\infty} g(x_k) = g(p).$$\n",
    "\n",
    "On the other hand, $g(x_k) = x_{k+1}$, so\n",
    "\n",
    "$$\\lim_{k \\to \\infty} g(x_k) = \\lim_{k \\to \\infty} x_{k+1} = p.$$\n",
    "\n",
    "Comparing gives $g(p) = p$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That second \"if\" is a big one.\n",
    "Fortunately, it can often be resolved using the idea of a *contraction mapping*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Mapping\n",
    ":label: definition-mapping\n",
    "\n",
    "A function $g(x)$ defined on a closed interval $D = [a, b]$ which sends values back into that interval,\n",
    "$g: D \\to D$, is sometimes called a *map* or *mapping*.\n",
    "\n",
    "(*Aside:* The same applies for a function $g: D \\to D$ where $D$ is a subset of the complex numbers,\n",
    "or even of vectors $\\mathbb{R}^n$ or $\\mathbb{C}^n$.)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A mapping is sometimes thought of as moving a region $S$ within its domain $D$ to another such region, by moving each point\n",
    "$x \\in S \\subset D$\n",
    "to its image\n",
    "$g(x) \\in g(S) \\subset D$.\n",
    "\n",
    "A very important case is mappings that shrink the region, by reducing the distance between points:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proposition}\n",
    ":label: proposition-2-ivp-fpi-version\n",
    "\n",
    "Any continuous mapping on a closed interval $[a, b]$ has at least one fixed point.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "Consider the \"root-finding cousin\", $f(x) = x - g(x)$.\n",
    "\n",
    "First, $f(a) = a - g(a) \\leq 0$, since $g(a) \\geq a$ so as to be in the domain $[a,b]$ — similarly, $f(b) = b - g(b) \\geq 0$.\n",
    "\n",
    "From the Intermediate Value Theorem, $f$ has a zero $p$, where $f(p) = p - g(p) = 0$.\n",
    "\n",
    "In other words, the graph of $y=g(x)$ goes from being above the line $y=x$ at $x=a$ to below it at $x=b$,\n",
    "so at some point $x=p$, the curves meet: $y = x = p$ and $y = g(p)$, so $p = g(p)$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example}\n",
    ":label: example-1-x-4cosx\n",
    "\n",
    "Let us illustrate this with the mapping $g_44(x) := 4 \\cos x$,\n",
    "for which the fact that $|g_4(x)| \\leq 4$ ensures that this is a map of the domain $D = [-4, 4]$ into itself:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def g_4(x): return 4*cos(x)\n",
    "a = -4\n",
    "b = 4\n",
    "x = np.linspace(a, b)\n",
    "\n",
    "figure(figsize=(8,8))\n",
    "title(\"Fixed points of the map $g_4(x) = 4 \\cos(x)$\")\n",
    "plot(x, g_4(x), label=\"$y=g_4(x)$\")\n",
    "plot(x, x, label=\"$y=x$\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example has multiple fixed points (three of them).\n",
    "To ensure both the existence of a **unique** solution, and covergence of the iteration to that solution, we need an extra condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Contraction Mapping\n",
    ":label: definition-contraction-mapping\n",
    "\n",
    "A mapping $g:D \\to D$, is called a *contraction* or *contraction mapping* if there is a constant $C < 1$ such that\n",
    "\n",
    "$$|g(x) - g(y)| \\leq C |x - y|$$\n",
    "\n",
    "for any $x$ and $y$ in $D$.\n",
    "We then call $C$ a *contraction constant*.\n",
    "\n",
    "(*Aside:* The same applies for a domain in $\\mathbb{R}^n$: just replace the absolute value $| \\dots |$ by the vector norm $\\| \\dots \\|$.)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    ":label: uniformly-contracting\n",
    "\n",
    "It is not enough to have $| g(x) - g(y) | < | x - y |$ or $C = 1$!\n",
    "We need the ratio\n",
    "$\\displaystyle \\frac{|g(x) - g(y)|}{|x - y|}$\n",
    "to be *uniformly* less than one for all possible values of $x$ and $y$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:theorem} A Contraction Mapping Theorem\n",
    ":label: a-contraction-mapping-theorem\n",
    "\n",
    "Any contraction mapping on a closed, bounded interval $D = [a, b]$ has exactly one fixed point $p$ in $D$.\n",
    "Further, this can be calculated as the limit $\\displaystyle p = \\lim_{k \\to \\infty} x_k$ of the iteration sequence given by $x_{k+1} = g(x_{k})$ for *any* choice of the starting point $x_{0} \\in D$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "The main idea of the proof can be shown with the help of a few pictures.\n",
    "\n",
    "First, uniqeness:\n",
    "between any two of the multiple fixed points above — call them $p_0$ and $p_1$ — the graph of $g(x)$ has to rise with secant slope 1: $(g(p_1) - g(p_0)/(p_1 - p_0) = (p_1 - p_0)/(p_1 - p_0) = 1$, and this violates the contraction property.\n",
    "\n",
    "So instead, for a contraction, the graph of a contraction map looks like the one below for our favorite example,\n",
    "$g(x) = \\cos x$ (which we will soon verify to be a contraction on interval $[-1, 1]$):\n",
    "\n",
    "The second claim, about **convergence** to the fixed point from any initial approximation $x_0$,\n",
    "will be verified below, once we have seen some ideas about measuring errors.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An easy way of checking whether a differentiable function is a contraction\n",
    "\n",
    "With differentiable functions, the contraction condition can often be easily verified using derivatives:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:theorem} A derivative-based fixed point theorem\n",
    ":label: a-derivative-based-fixed-point-theorem\n",
    "\n",
    "If a function $g:[a,b] \\to [a,b]$ is differentiable and there is a constant $C < 1$ such that $|g'(x)| \\leq C$ for all $x \\in [a, b]$, then $g$ is a contraction mapping, and so has a unique fixed point in this interval.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "Using the Mean Value Theorem, $g(x) - g(y) = g'(c)(x - y)$ for some $c$ between $x$ and $y$.\n",
    "Then taking absolute values,\n",
    "\n",
    "$$|g(x) - g(y)| = |g'(c)| \\cdot |(x - y)| \\leq C |(x - y)|.$$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} $g(x) = \\cos(x)$ is a contraction on interval $[-1,1]$\n",
    ":label: example-2-x-cosx\n",
    "\n",
    "Our favorite example $g(x) = \\cos(x)$ is a contraction, but we have to be a bit careful about the domain.\n",
    "\n",
    "For all real $x$, $g'(x) = -\\sin x$, so $|g'(x)| \\leq 1$; this is almost but not quite enough.\n",
    "\n",
    "However, we have seen that iteration values will settle in the interval $D = [-1,1]$,\n",
    "and considering $g$ as a mapping of this domain,\n",
    "$|g'(x)| \\leq \\sin(1) = 0.841\\dots < 1$: that is, now we have a contraction, with $C = \\sin(1) \\approx 0.841$.\n",
    "\n",
    "And as seen in the graph above, there is indeed a unique fixed point.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The contraction constant $C$ as a measure of how fast the approximations improve (the smaller the better)\n",
    "\n",
    "It can be shown that if $C$ is small (at least when one looks only at a reduced domain $|x - p| < R$) then the convergence is \"fast\" once $|x_k - p| < R$.\n",
    "\n",
    "To see this, we define some jargon for talking about errors.\n",
    "(For more details on error concepts, see section {ref}`error-measures-convergence-rates`.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Error\n",
    ":label: definition-error\n",
    "\n",
    "The *error* in $\\tilde x$ as an approximation to an exact value $x$ is\n",
    "\n",
    "$$\\text{error} := \\text{(approximation)} - \\text{(exact value)} = \\tilde x - x$$\n",
    "\n",
    "This will often be abbreviated as $E$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:definition} Absolute Error\n",
    ":label: definition-absolute-error\n",
    "\n",
    "The *absolute error* in $\\tilde x$ an approximation to an exact value $x$ is the magnitude of the error:\n",
    "the absolute value $|E| = |\\tilde x - x|$.\n",
    "\n",
    "(*Aside:* This will later be extended to $x$ and $\\tilde x$ being vectors,\n",
    "by again using the vector norm in place of the absolute value.\n",
    "In fact, I will sometimes blur the distinction by using the \"single line\" absolute value notation for vector norms too.)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of $x_k$ as an approximation of $p$, we name the error $E_k := x_k - p$.\n",
    "Then $C$ measures a worst case for how fast the error decreases as $k$ increases, and this is \"exponentially fast\":"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proposition}\n",
    ":label: proposition-3\n",
    "\n",
    "$|E_{k+1}| \\leq C |E_{k}|$, or $|E_{k+1}|/|E_{k}|\\leq C$,\n",
    "and so\n",
    "\n",
    "$$|E_k| \\leq C^k |x_0 - p|$$\n",
    "\n",
    "That is, the error decreases at worst in a geometric sequence,\n",
    "which is exponential decrease with respect to the variable $k$.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:proof}\n",
    "\n",
    "$E_{k+1} = x_{k+1} - p = g(x_{k}) - g(p)$, using $g(p) = p$.\n",
    "Thus the contraction property gives\n",
    "\n",
    "$$|E_{k+1}| = |g(x_k) - g(p)| \\leq C |x_k - p| = C |E_k|$$\n",
    "\n",
    "Applying this again,\n",
    "\n",
    "$$|E_k| \\leq C |E_{k-1}| \\leq C \\cdot C |E_{k-2}| = C^2 |E_{k-2}|$$\n",
    "\n",
    "and repeating $k-2$ more times,\n",
    "\n",
    "$$|E_k|\\leq  C^k |E_0| = C^k |x_0 - p|.$$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:remark}\n",
    "We will often use this \"recursive\" strategy of relating the error in one iterate to that in the previous iterate.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Solving $x = \\cos x$ with a naive fixed point iteration\n",
    ":label: example-3-x-cosx-fpi\n",
    "\n",
    "We have seen that _one_ way to convert the example\n",
    "$f(x) = x - \\cos x = 0$ to a fixed point iteration is $g(x) = \\cos x$,\n",
    "and that this is a contraction on $D = [-1, 1]$\n",
    "\n",
    "Here is what this iteration looks like:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving x = cos(x) starting to the left, at x_0 = 0\n",
      "x_1 = 1.0\n",
      "x_2 = 0.5403023058681398\n",
      "x_3 = 0.8575532158463933\n",
      "x_4 = 0.6542897904977792\n",
      "x_5 = 0.7934803587425655\n",
      "x_6 = 0.7013687736227566\n",
      "x_7 = 0.7639596829006542\n",
      "x_8 = 0.7221024250267077\n",
      "x_9 = 0.7504177617637605\n",
      "x_10 = 0.7314040424225098\n",
      "Solving x = cos(x) starting to the right, at x_0 = 1\n",
      "x_1 = 0.5403023058681398\n",
      "x_2 = 0.8575532158463933\n",
      "x_3 = 0.6542897904977792\n",
      "x_4 = 0.7934803587425655\n",
      "x_5 = 0.7013687736227566\n",
      "x_6 = 0.7639596829006542\n",
      "x_7 = 0.7221024250267077\n",
      "x_8 = 0.7504177617637605\n",
      "x_9 = 0.7314040424225098\n",
      "x_10 = 0.7442373549005569\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp8AAAKqCAYAAAB8XzUWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAACHP0lEQVR4nOzdd3gUZcPF4d+mJ4Tee1EElKYBERAhgYTee68qIkhRXymfUkRRRMRCUQHpEHoNkNCRooCgNEFEBKTXQEL6fH/MS4SXAElIdrLJua9rL9lhd+dsZjccn5l5xmYYhoGIiIiIiB04WR1ARERERDIOlU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVT0lTfvrpJ5o3b06RIkVwd3cnb968VK1albfffjvJrzVjxgxsNhunTp2y63Ml7dm5cycjRozgxo0bdn1tKz9HqfWeH/W6I0aMwGazceXKlRRd5/960p9rYGAgzz33HJ6enthstlT9fCTE3uuzp9u3bzNgwAAKFCiAh4cHFStWZMGCBVbHkjRG5VPSjDVr1lCtWjVCQ0MZO3YswcHBfPnll1SvXp3AwEC7ZmnYsCG7du0if/78dl2vpI6dO3cycuTIVCufD3ttKz9HqfWeU/NnaQ+XL1+mc+fOPPXUU6xbt45du3axYcMGu74nR/8ZPkqLFi2YOXMmw4cPZ+3atVSuXJn27dszb948q6NJGuJidQCRu8aOHUvx4sVZv349Li7/fjTbtWvH2LFj7Zold+7c5M6d267rFMcSHh6Ol5fXIx+jz1Hac/z4caKjo+nUqRM1a9YE4Mcff7Q4VfoQFBRESEgI8+bNo3379gD4+vry999/8+6779K2bVucnZ0tTilpgiGSRjz33HNGlSpVEvXY7du3G35+foa3t7fh6elpVK1a1Vi9evV9j/nhhx8MwPjrr78MwzCMZcuWGYCxYcOGB15v0qRJBmD8+uuvCT53+PDhBmAcOnTIaNeunZElSxYjT548Rvfu3Y0bN2488HrLly83ypUrZ7i5uRnFixc3JkyYEP8aj3Pu3DkjU6ZMRtu2be9bvmrVKsPFxcUYOnRoYn5EyXL06FGjXbt2Rp48eQw3NzejcOHCRufOnY2IiIj4xyTmZ28YhnHp0iXj1VdfNQoVKmS4ubkZuXLlMqpVq2aEhIQ88Ngnec+PW8/dn/v/3jZv3mz88ccfRrdu3Yynn37a8PT0NAoUKGA0atTI+O233+5bx93X2Ldvn9GyZUsjW7ZsRr58+R752obx4Ofo3tdKzGcpuZ+jx+VK7DZM6usm5b0dP37caN++vZE7d27Dzc3NKF26tPHNN988NoNhJPxzTczrde3a9YHsNWvWfOR7SorEfJ4e9zNMiJW/E5KiV69ehre3txEdHX3f8nnz5hmAsWPHDouSSVqj8ilpRq9evQzA6Nevn7F7924jKioqwcdt2bLFcHV1NXx8fIzAwEBj+fLlRkBAgGGz2YwFCxbEP+5//4GKjo428uTJY3Ts2PGB13zxxReNF1544aHPvfsPRqlSpYwPPvjACAkJMcaPH2+4u7sb3bt3v++11q5dazg5ORm1atUyli1bZixatMioUqWKUaxYsUSVT8MwjJEjRxo2m83Yu3evYRiGsXnzZsPDw8Po169fgo+Pi4szoqOjE3V7mAMHDhje3t5GsWLFjClTphgbN2405syZY7Rp08YIDQ01DCPxP3vDMIy6desauXPnNr777jtjy5YtxvLly40PPvjggccl9z0ndj1nzpwx+vXrZwDG0qVLjV27dhm7du0ybt68aWzdutV4++23jcWLFxtbt241li1bZjRr1szw9PQ0fv/99/h13N3+RYsWNd577z0jJCTEWL58+SNf2zAeXT4f91l6ks/Ro3IlZRsm5XWT8t4OHz5sZM2a1ShXrpwxa9YsIzg42Hj77bcNJycnY8SIEY/MkNDPNbGvd+LECWPixIkGYHz88cfGrl27jK1btz7yPSVFYj5Pj/sZPkxyvx+PkxK/O+566aWXjMqVKz+w/NChQwZgfPvtt0+UVdIPlU9JM65cuWK8/PLL8SMBrq6uRrVq1YwxY8YYt27din/cSy+9ZOTJk+e+ZTExMUbZsmWNQoUKGXFxcYZhJPwP/6BBgwxPT8/7RmGOHDliAMbXX38dv+xh5XPs2LH3Ze7Tp4/h4eERv07DMIzKlSsbhQsXNiIjI+OX3bp1y8iZM2eiy2dYWJhRoEABo3bt2sbPP/9sZM6c2ejevft967nX5s2bExxNSeh278/jXn5+fka2bNmMS5cuPTRXYn/2hmEY3t7exoABAxL1fpPznpOyns8+++yR7/3e9xIVFWWULFnSGDhwYPzyu9v/gw8+SNJrP6p8Pu6z9KSfo4flSso2TMrrJuW91a1b1yhUqNADhatv376Gh4eHce3atUdm+N+fa1Je7+53ZdGiRYl6T0/iYZ+n5Kzvcd+PS5cuGQ0aNDC8vLyMkiVLGsHBwYl63ZT43XFXyZIljbp16z6w/Ny5c/GFX8QwDEMnHEmakTNnTrZv386ePXv45JNPaNq0KcePH2fIkCGUK1eOK1euEBYWxk8//USrVq3w9vaOf66zszOdO3fm7NmzHDt27KHr6NGjB3fu3LnvBKYffvgBd3d3OnTo8NiMTZo0ue9++fLliYiI4NKlSwCEhYWxd+9emjVrhpubW/zjvL29ady4caJ/Fl5eXowePZqNGzfi6+tL/fr1+f7777HZbAk+3sfHhz179iTqVqBAgQeeHx4eztatW2nTps1Dj1FM6s/+xRdfZMaMGYwePZrdu3cTHR2dou85ueu5V0xMDB9//DHPPvssbm5uuLi44Obmxh9//MHRo0cfeHzLli0T/dqP86jPUkp9jv7Xk35/EutR7y0iIoKNGzfSvHlzvLy8iImJib81aNCAiIgIdu/eneh1pfTrPYmkfp6S4nHfjzfffJN8+fJx+fJlxo0bR5s2bbh69epjX/dJf3f8r0d9Xx/3XZaMQyccSZpTqVIlKlWqBEB0dDTvvfceX3zxBWPHjuWtt97CMIwEzx6++4vxUb9wn3vuOSpXrswPP/zAa6+9RmxsLHPmzKFp06bkyJHjsdly5sx53313d3cA7ty5A8D169cxDIO8efM+8NyElj3KM888A5i/sGfMmPHIA/W9vb2pWLFiol733pO57rp+/TqxsbEUKlTooc+7+94S+7MPDAxk9OjRTJ06lffffx9vb2+aN2/O2LFjyZcvX4LrSMp7fpL13DVo0CAmTpzIe++9R82aNcmePTtOTk706tUrfpveKyXPWn/UZyk6OjrFPkf3Suo2TK5Hvbe7xfDrr7/m66+/TvD5SZmq6erVqyn6ek8iqZ+npHrY9+P27dssX76cP//8Ey8vL5o0aUKFChVYsWIFPXr0eORrPunvjnvlzJkzwc/PtWvXABL1O1YyBo18Sprm6urK8OHDATh06FD8L/Pz588/8Nhz584BkCtXrke+Zvfu3dm9ezdHjx5l3bp1nD9/nu7du6dI3uzZs2Oz2bh48eIDf3fhwoVEv86BAwdo1KgR1atX5/bt20yfPv2Rj9+6dSuurq6JuiU0N2KOHDlwdnbm7Nmzj3xvSfnZ58qViwkTJnDq1Cn+/vtvxowZw9KlS+nWrVuKvOfkrudec+bMoUuXLnz88cfUrVuXF198kUqVKj20rNhr5CalPkcJve6Tfn+eVPbs2XF2dqZbt24PHWFr0KCBZa/3JJL6eUqKR30//vjjD7y9vSlcuHD8snLlynH48OHHvu6T/u64V7ly5Th69CgxMTH3LT948CAAZcuWTcI7lvRMI5+SZpw/fz7BEZm7u6sKFChApkyZqFKlCkuXLmXcuHF4enoCEBcXx5w5cyhUqFD86MDDtG/fnkGDBjFjxgxOnjxJwYIFCQgISJH3kClTJipVqsTy5csZN25c/C7T27dvs3r16kS9xrFjx6hbty5Vq1ZlxYoVtG7dmhEjRtCpUyeyZs2a4HPu7jpLjIR2nXl6elKzZk0WLVrERx99lGABeZKffZEiRejbty8bN25kx44dKfKek7Ke/x2hvstms8X/3V1r1qzhn3/+4emnn07UOh/22k8iJT5HCeVKie/Pk75fLy8vfH192b9/P+XLl7/vsAKrXi+ltmFiP09JXd/jvh+3b98mS5Ys9z0nS5YsiSq9T/q7417Nmzfn+++/Z8mSJbRt2zZ++cyZMylQoABVqlRJ1Hok/VP5lDSjbt26FCpUiMaNG1O6dGni4uI4cOAAn3/+Od7e3vTv3x+AMWPG4O/vj6+vL++88w5ubm5MmjSJQ4cOMX/+/MeOTmXLlo3mzZszY8YMbty4wTvvvIOTU8rtBBg1ahQNGzakbt269O/fn9jYWD777DO8vb3jdz89zKlTp6hTpw6lSpViyZIluLq68sknn1C2bFk+/vhjPv300wSflzlz5vhDFZJr/PjxvPzyy1SpUoXBgwfz9NNPc/HiRVauXMm3335L5syZE/2zv3nzJr6+vnTo0IHSpUuTOXNm9uzZw7p162jRokWKvOekrKdcuXIAfPnll3Tt2hVXV1dKlSpFo0aNmDFjBqVLl6Z8+fLs27ePzz777JGHH/yvh7125syZE/0aCXmSz9Gjcj3p9ycl3u+XX37Jyy+/TI0aNXjjjTcoVqwYt27d4sSJE6xatYpNmzYl+rVS4vUe955sNhs1a9Zky5Ytj3ydxH6ekvIzTMz3w9vbm9DQ0PueFxoaet9xvQ+TEr877qpfvz7+/v688cYbhIaG8vTTTzN//nzWrVvHnDlzNMen/MvS051E7hEYGGh06NDBKFmypOHt7W24uroaRYoUMTp37mwcOXLkvsfenacwU6ZMhqenp/HSSy8Zq1atuu8xCZ1pfFdwcHD8GZzHjx9/4O8fdrb75cuXE7WOZcuWxc/PWKRIEeOTTz4x3nrrLSN79uwPff/nzp0znnrqKeOFF1544KzdV1991XB3d0/xs3H/15EjR4zWrVsbOXPmjM/erVu3BOf5fNTPPiIiwujdu7dRvnx5I0uWLIanp6dRqlQpY/jw4UZYWFiKvefErscwDGPIkCFGgQIFDCcnp/h5Fa9fv2707NnTyJMnj+Hl5WW8/PLLxvbt242aNWsaNWvWjH/uw7b/o17bMB59tntiPkvJ+RwlJlditmFyXjcp7+2vv/4yevToYRQsWNBwdXU1cufObVSrVs0YPXr0Y9f/JK+X0Nnuj3pPt27dMgCjXbt2j82V2M/To9Z3r8R+P27dumW4uroaZ86cif/7WrVqGdOmTXts5pR269Yt46233jLy5ctnuLm5GeXLlzfmz59v9xySttkMwzDs2nZFMqDo6GgqVqxIwYIFCQ4OtjqOOCh9juwvKCiIRo0a8euvv8aPWKZFrVu3JmvWrHz99dds3LiRzp0788cff6T6MbwiyaHd7iKpoGfPnvj7+5M/f34uXLjAlClTOHr0KF9++aXV0cSB6HNkvc2bN9OuXbs0XTwBJk2aRNeuXcmZMycFCxYkMDBQxVPSLI18iqSCNm3asHPnTi5fvoyrqysvvPACQ4cOpV69elZHEweiz5GIpEcqnyIiIiJiN5rnU0RERETsRuVTREREROxG5VNERERE7MYhznaPi4vj3LlzZM6c2W6XtxMRERGRxDMMg1u3blGgQIFHXrzFIcrnuXPn7rtmrYiIiIikTWfOnHnkleIconzeveTYmTNnHrh+bWqIjo4mODiYgIAAXF1dU319kvK0DR2btp/j0zZ0fNqGjs/e2zA0NJTChQs/9nK7DlE+7+5qz5Ili93Kp5eXF1myZNEXzkFpGzo2bT/Hp23o+LQNHZ9V2/Bxh0jqhCMRERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbEblU8RERERsRuVTxERERGxG5VPEREREbGbJJfPbdu20bhxYwoUKIDNZmP58uWPfc7WrVvx8fHBw8ODEiVKMGXKlORkFREREREHl+TyGRYWRoUKFfjmm28S9fi//vqLBg0aUKNGDfbv38/QoUN56623WLJkSZLDioiIiIhjc0nqE+rXr0/9+vUT/fgpU6ZQpEgRJkyYAECZMmXYu3cv48aNo2XLlkldfaqLi4NLl+DGDTdu3wY3N6sTSXJER0NEhDNhYeDqanUaSSptP8enbej4tA0dm2HAhSvh3LjhRlyc1Wnul+TymVS7du0iICDgvmV169Zl2rRpREdH45rAJzoyMpLIyMj4+6GhoQBER0cTHR2dqnkvXYijUBF3IPEFW9IiV6CR1SEk2bT9HJ+2oePTNnR8WYH61KwZTsGCqb+2xHa0VC+fFy5cIG/evPcty5s3LzExMVy5coX8+fM/8JwxY8YwcuTIB5YHBwfj5eWValkBbl5xAhqn6jpERERE7GXjlo3kyp76w5/h4eGJelyql08Am812333DMBJcfteQIUMYNGhQ/P3Q0FAKFy5MQEAAWbJkSb2gwO3QOOhl/vn0NwvJ4h5r7ou/e4s179tiY+P/TGwsREVBRIR5i4qCyEhsEREQGXnfMu7cwXbnDty+bd5u3cIWGZEi2Y3MWSBnTozcuSF3boy8eSF3bsiTx1yWN6/53zx5wNs7RdaZVkVHR7Np0yb8/PwSHF2XtE3bz/FpGzo+bUPHdPzacZosaMLF66Ew7jIAjRvUJnv21N+Gd/dUP06ql898+fJx4cKF+5ZdunQJFxcXcubMmeBz3N3dcXd3f2C5q6trqn8B3Dz+/XPmjs3Jms0OX7iYGLh1K76M3ncLDYXr1+HaNfN29eq/f757u3HDfJ1b4XDrApxKxDq9vCBfPihUyLwVLvzgf3Pnhof8D0JaFx0NHh6xZMuW+p8ZSXnafo5P29DxaRs6nmNXjtFsmT8Xo8/zXMEXOfzf5W5u9tmGiV1HqpfPqlWrsmrVqvuWBQcHU6lSJX2Y73JxgezZzVtyxMaaBfTqVbh8GS5eNG8XLjz45wsX4M4dCA+HkyfN28O4ud1fSIsUgRIlzFvx4uZyF7sMnouIiMgj/H7ld3xn+nLh9gXK5y3PiharKT7Q6lQJS3JzuH37NidOnIi//9dff3HgwAFy5MhBkSJFGDJkCP/88w+zZs0CoHfv3nzzzTcMGjSIV199lV27djFt2jTmz5+fcu8io3N2hpw5zdszzzz6sYZhjrBevAjnz8M//8DZs3DmzP3/vXDBPFTgUQXV2fnfQlq8+P3FtEQJM4+DjpyKiIg4iqOXj+I705eLYRepkLcCG7pswNPIZXWsh0py+dy7dy++vr7x9+8em9m1a1dmzJjB+fPnOX36dPzfFy9enKCgIAYOHMjEiRMpUKAAX331VZqcZilDsNkgc2bz9vTTD39cVJRZTu8tpX///W8ZPXXKPIb1r7/MW0KyZYNSpe6/PfMMlCwJHh4JP0dEREQS7cjlI/jO9OVS2CUq5qvIhs4byOmVk7Awq5M9XJLLZ61ateJPGErIjBkzHlhWs2ZNfvnll6SuSqzk5gZFi5q3hMTFmeX05EmzfN4tpXfvnztnHgrw00/m7V42m/m6d8toqVJQpgyULWueDCUiIiKPdfjSYfxm+XEp7BLP53uekM4h5PRK+HyatEQH7EnyODlBwYLmrUaNB/8+PBxOnIBjxx68hYaaI6enTsH69fc/L3dus4TevT33nHnLls0Ob0pERMQxHLp0CL+ZflwOv8zz+Z5nQ5cN5PDMYXWsRFH5lNTh5QXly5u3exmGeQmpY8fg+PF/C+nRo/Dnn+YJU5s3m7d7FSp0fymtUAGefVaXoBIRkQzn4MWD+M3y40r4FXzy+xDcOdhhiieofIq92WyQN695e+WV+/8uPNwsoYcO3X87e/bf27p1/z7ezc0sos8//++tfPl0P4epiIhkXL9d/I3as2pzJfwKlQpUIrhTMNk9kzlbjkVUPiXt8PICHx/zdq8bN+DwYbOIHj4Mv/0GBw7AzZvwyy/m7S6bDZ55BucKFXjawwObmxu8+KJ55r2IiIgD+/XCr9SeVZurd65SuUBlgjsHk80jm9WxkkzlU9K+bNmgenXzdpdhmCc27d9//+38eTh2DKdjx3gO4L9TfvHUU2YJvXt7/nnw9LTgzYiIiCTdgQsHqD2rNtfuXOPFgi+yvtN6hyyeoPIpjspm+3de0Xun7bp4EfbvJ3bvXi6sXUuBS5ewnThhHk/6559wd35ZZ2dzF/29hbRMGXO5iIhIGrL//H7qzK7DtTvXqFKwCus7rSerR1arYyWbyqekL3nzQr16xNWuzd5y5WjQoAGut2/D3r3w88/m7aef4ksq+/fDt9+az82UCSpVgqpVzVHWatUgh+McwC0iIunPL+d/oc6sOlyPuM5LhV5iXcd1Dl08QeVTMoLs2cHf37yBucv+7Nl/y+jPP5vl9PZt2LrVvN317LP/7vKvXt3cfa+rNomIiB3sO7ePOrPrcCPiBlULVWVdp3Vkcc9idawnpvIpGY/NZl6XvnDhf3fZx8bC77/D7t2wY4d5O34cjhwxb99/bz4ub15zRLR6dXj5ZfPYUU33JCIiKWzvub34z/bnRsQNqhWuxtqOa9NF8QSVTxGTs/O/E9r37Gkuu3wZdu78t4zu3Wvurl+2zLyBedJS9erg6wu1apm77VVGRUTkCez5Zw/+s/25GXmT6oWrs7bjWjK7Z7Y6VopR+RR5mNy5oWlT8wYQEWEW0LtldOdOuHoVNmwwb2BOF1W9ullEfX3NMurqatlbEBERx/LzPz/jP9uf0MhQXi7yMkEdgtJV8QSVT5HE8/Awd7W//LJ53zDMXfKbN8OWLebt6lUICTFvYJ7EdLeM1qoFlSuDi752IiLyoJ/O/kTAnABCI0OpUaQGQR2D8HZLfxdO0b+CIslls/27q75vX4iLM8voli1mId261SyjwcHmDSBLFnNE9O4JUCVL6gQmERFh15ld1J1Tl1tRt6hZtCarO6xOl8UTVD5FUo6T07/Xnr9bRg8f/ndUdMsWuHYNVqwwbwBFi/5bRGvX1pWYREQyoJ1ndlJvTj1uRd2iVrFarG6/mkxumayOlWpUPkVSi5MTlCtn3vr1M8+o37//393yP/4If/8NU6eaN5sNXnjh3zJavTq4u1v9LkREJBXtOL2D+nPrcyvqFr7FfFnVflW6Lp4ATlYHEMkwnJ3NE5CGDIFNm+D6dQgKgoEDzdFSw4B9++CTT/4dBW3a1JwE/8wZq9OLiEgK+/H0j9Sba454+hX3Y3WH9D3ieZdGPkWskikT1K9v3gDOnTPPmr87MnrxIqxcad7AHEFt0MC8Va2qs+hFRBzY9r+3U39ufcKiw6hdvDYr26/Ey9XL6lh2oZFPkbSiQAHo0gVmz4bz581d9B99ZE5q7+QEBw/Cp59CzZrmNFBt2sDMmWZJFRERh7Ht723xxdO/hD+r2q/KMMUTNPIpkjbZbFCxonkbOvTfs+aDgmDdOrhyBRYtMm9g7s5v3NjcTV++vM6gFxFJo7ae2kqDeQ0Ijw7Hv4Q/K9qtwNPV0+pYdqWRTxFHkDMntG9vjopeuGBeBvSDD8zSCebk98OHm2W1RAno3988rjQ62tLYIiLyr81/bY4vnnWfqpshiyeofIo4HmdnqFIFRo6EPXvMMjp9ujnq6ekJp07BV1+ZJy3lzQudOsHixXDrltXJRUQyrE1/baLhvIaER4dT7+l6LG+3PEMWT1D5FHF8efNC9+6wfLm5O37FCvN+rlzmGfVz50Lr1ub9Bg3Ms+fPn7c6tYhIhrHx5EYazWvEnZg7NCjZgGVtl+Hh4mF1LMuofIqkJ15e0KSJORJ64QJs3w7vvGNeSSkqCtauhd69oWBBqFEDvvxS0ziJiKSiDSc30Gi+WTwblmzI0jZLM3TxBJVPkfTL2dm8Dv1nn8GxY+alP8eMMXfZG4Y5yf2AAVCkiDl10+efm7vsRUQkRQT/GUzj+Y2JiImg0TONWNJmCe4uuniIyqdIRmCzQZkyMHiwebLSmTPmqGeNGubf7d5tjpAWLw6VK5tTOp04YXVqERGHtf7EeprMb0JETARNSjVhcevFKp7/pfIpkhEVKgRvvQXbtsE//8DEieDra84nunevWVJLloTnnzfnGlURFRFJtHUn1tF0QVMiYyNpWqopi1ovUvG8h8qnSEaXPz/06WNOzXT+vHlCkr+/udv+wAH4v/8zi2jlyuau+bNnrU4sIpJmrf1jbXzxbFa6GQtbL8TN2c3qWGmKyqeI/CtPHnjtNXNC+4sXYdo0qFvXLKJ795q75osUMa+yNGWKeXa9iIgAEPRHEM0CmxEVG0WLMi1Y2ErFMyEqnyKSsJw5oUcP84pK586Zu+Zfftk8WWnbNnjjDXPUtEEDc/J7zSMqIhnY6uOraR7YnKjYKFqWacmClgtwdXa1OlaapPIpIo+XJ4+5a377dvj7bxg71jweNCbGnL6pSxfzMa1awdKlEBlpdWIREbtZdWwVLQJbEBUbRatnWzG/5XwVz0dQ+RSRpClSBN59F375BX7/3bys5zPPQEQELFkCLVv+exzprl3mSKmISDq18thKWi5sSXRcNG2ea8O8FvNUPB9D5VNEkq9UKRgxwiyh+/aZx4QWKGBeWWnyZKhWzSymH34If/1ldVoRkRS14vcVtFrYiui4aNqVbcfcFnNVPBNB5VNEnpzNBi+8YE5of/q0ecJSp07mFZdOnIAPPoASJeCVV2DqVLh50+rEIiJPZNnRZbRaZBbP9mXbM7v5bFycXKyO5RBUPkUkZTk7m1M1zZ5tnjE/cybUrm0W1O3b4dVXIV8+aNcO1qwxjxsVEXEgS48upc3iNsTExdChXAdmNZ+l4pkEKp8iknq8vc2TkTZsMEdEP/nEvNJSRAQEBkKjRlC4sDmp/fHjVqcVEXmsJUeW0GaRWTw7le/ErGYqnkml8iki9lGoELz3Hhw+bM4Z+tZbkCsXXLhgXs6zVClzt/yMGRAWZnVaEZEHLDq8iLaL2xJrxNK5fGdmNJ2Bs5Oz1bEcjsqniNiXzQY+Pua15f/5BxYvNucKdXIyd8t3745L4cJUmDgR208/6Wx5EUkTFh5eSPsl7Yk1YulSoQs/NP1BxTOZVD5FxDpububUTGvWmPOHfvQRPPUUttu3KRYSgkuNGlC2rHlZz0uXrE4rIhlU4KFAOizpQKwRS7eK3ZjeZLqK5xNQ+RSRtKFQIRg6FI4fJ2bDBs7UqoXh6QlHjphTOBUsaBbV4GCIi7M6rYhkEAsOLaDDUrN4dq/YnWlNpql4PiGVTxFJW5ycMF55hV8GDCDm9GnzGvIvvmieFb90qXmt+ZIlzZOXLl60Oq2IpGPzDs6j49KOxBlx9KjYg6lNpuJkU3V6UvoJikjalTUrvP46/PQT/PYb9OtnLjt5EoYMMc+Ub9sWNm/WsaEikqLm/DaHzss6E2fE0ev5Xnzf5HsVzxSin6KIOIZy5eCrr+DcOZg+HapUgehoWLgQ/PygdGnz2NCrV61OKiIObvavs+m6vCtxRhyvvfAa3zb+VsUzBeknKSKOxcsLuneH3bth/37o3ducT/T48X+PDe3UyTxzXqOhIpJEMw/MjC+er/u8zuRGk1U8U5h+miLiuCpWNK8hf+4cfPuteYnPyEiYO9ecM7R8eXO55g0VkUSYcWAG3Vd0x8DgjUpvMKnhJBXPVKCfqIg4vsyZ4bXXYN8+2LMHevY0R0gPHTJHRgsWhIEDzevMi4gkYPr+6fRY0QMDgz6V+jCxwUQVz1Sin6qIpC+VKsHUqeYE9l98AU8/DTdvwoQJ5lnyDRpAUJCmaxKReNN+mUavlb0wMOhbuS/fNPgGm81mdax0S+VTRNKnbNlgwAA4dgzWroWGDc2rK9398zPPwPjxcP261UlFxELf7/ueXqvM4tnvxX58Vf8rFc9UpvIpIumbkxPUqwerV8Mff8Dbb5vF9M8/zT8XLGjusv/tN6uTioidfbfvO15b/RoA/av058t6X6p42oHKp4hkHE89BePGmbvkv//ePCHpzh3zzxUqQO3asGqVdsmLZABT9k7h9dWvAzCgygC+qPuFiqedqHyKSMbj5QW9esGBA+aUTG3agLMzbNoETZqYc4ZOnAi3b1udVERSweQ9k3ljzRsADHppEOPrjlfxtCOVTxHJuGw2ePllCAw0r5r0n/+Yu+T/+AP69jWvoPSf/8CZM1YnFZEUMvHnifQJ6gPA21XfZlzAOBVPO1P5FBEBKFIEPv3ULJrffGOeGX/jBnz2GRQvDu3amRPbi4jD+ubnb+i7ti8A71R9h8/8P1PxtIDKp4jIvby94c034fffzeM//fwgNtYcHa1a1bwtXAgxMVYnFZEk+Oqnr+i3th8A71V/j7H+Y1U8LaLyKSKSECcnaNQINm40jw3t1g3c3MzRz7ZtzZHRr77S1ZNEHMCE3RPov64/AIOrD2ZM7TEqnhZS+RQReZwKFeCHH+D0aRg+HHLnhlOnoH9/87jQ99+HS5esTikiCfhi1xcMXD8QgKEvD+Xj2h+reFpM5VNEJLHy5oURI+Dvv2HKFPPqSdevw+jR5jGjvXubJyuJSJowftd4BgUPAuD/avwfo/1Gq3imASqfIiJJ5ekJr79uHhe6ZAlUqQKRkfDtt1CqFLRsqZOTRCw2buc43g5+G4D3X3mfUb6jVDzTCJVPEZHkcnaGFi1g1y7Yts08RtQwYOlS88SkV17RpPUiFhi7YyzvhrwLwPCaw1U80xiVTxGRJ2WzQY0aZtE8fBh69ABXV3MC+yZNoGxZmDULoqOtTiqS7n3646e8t+E9AEbUHMGIWiOsDSQPUPkUEUlJzz4L06aZJyS99x5kzQpHj0LXruYZ8pMmmZf0FJEUN2b7GAZvHAzAyFojGV5ruMWJJCEqnyIiqaFAAfjkE/MM+U8+gTx5zBOV3nzTnLR+7FgIDbU6pUi68fH2jxm6aSgAH/p+yAc1P7A4kTyMyqeISGrKksUcAT11yrxyUtGicPGiuaxoUfjgA7hyxeqUIg5t9LbRDNs0DICP/D7i/175P4sTyaOofIqI2IOnpznq+ccfMHMmlC5tXr7zww/NEjpwIJw9a3VKEYczauso3t/8PgAf+33M0BpDLU4kj6PyKSJiT66u0KWLeWLSkiXg4wPh4TBhApQoAa++Cn/+aXVKEYcwcstIhm8xj+v8pPYnDKkxxOJEkhgqnyIiVnByMqdp2rMH1q+HmjXNs+GnTjXnCu3aFY4ftzqlSJpkGAbDNw9nxNYRAIytM5b3Xn7P2lCSaCqfIiJWstkgIAC2bIEff4T69SE21pyaqUwZ6NTJnMxeRID/Fs8twxm1bRQAn/l/xrvV37U4lSSFyqeISFpRvToEBcHPP5sT1sfFwdy55vRN7dubu+pFMjDDMPhg8wd8uO1DAD4P+Jx3qr1jcSpJKpVPEZG0pnJlc8L6ffugaVPzqkkLFkC5ctCmDRw8aHVCEbszDIP/2/R/jN4+GoDxAeMZVHWQxakkOVQ+RUTSqhdegOXLYf9+8/hQw4BFi6B8efP68QcOWJ1QxC4Mw2DoxqF8/OPHAEyoO4GBVQdanEqSS+VTRCStq1jRPDP+t9+gdWvzONGlS+H556FZM/j1V6sTiqQawzAYsnEIn+z4BIAv631J/5f6W5xKnoTKp4iIoyhXDhYuNHe7t2tnltAVK8xy2ro1HDlidUKRFGUYBu9teI9Pd3wKwNf1v+atKm9ZnEqelIvVAUREJImeew7mzzevjjRqFAQGwuLFsGQJcW3bc+WtkfDU03h5mf3UCtHREBHhTFiYObWpOB4rt6FhQFiYwcitI5h8+DNwgm/qf8ObL75p3yCSKlQ+RUQcVZkyZgkdOhSGD4dly7iyIJi8C+ZanQxwBRpZHUKeiNXb0AaMhHcmManNKN6o/IaFWSQlabe7iIijK1fOPAZ03z6oE2B1GpEU9an/Zyqe6YxGPkVE0osXXsBr2VzIbN69SG4yEQ6ubtCjB7z7LuTLZ5co0dHRrF+/nrp16+Kq/e4OyYptePcYz0k7foBxlwHoU62bXdYt9qPyKSKSjtx7jGem4BVk+niYefWkb8fDzEnw5pswZAjkzJmqOaKjwcMjlkyZdMyno7L3NjQMg/7r+jPp16/BzSt+uVXHLUvq0W53EZH0qlo12LwZNm40/xwRAZ9/DiVKwIcfwu3bVicUAczi2W9tP77++Wts2JjYYJLVkSQVqXyKiKR3fn7mdeODgsxpmUJDzTPln3oKvvoKIiOtTigZmGEY9A3qy8Q9E7FhY2qTqXSt2NXqWJKKVD5FRDICmw3q1zdPSpo/H55+Gi5dgv79oVQpmDkTYmOtTikZTJwRx5tBbzJp7yRs2JjedDo9nu9hdSxJZSqfIiIZiZOTOUH9kSPw7bdQoAD8/Td062ZetnPZMnOSRZFUFmfE0WdNHybvnYwNGz80/YFuFbtZHUvsQOVTRCQjcnWF116DEydg7FjInt0spC1awEsvwaZNVieUdCzOiKP36t58u+9bbNiY2WymdrVnICqfIiIZmaenOQXTyZPmZPVeXvDzz1C7NgQEwP79VieUdCbOiOP1Va/z/S/f42RzYlbzWXSu0NnqWGJHKp8iIgLZssFHH8Gff0LfvubIaEgIvPACdO5s7poXeUJxRhyvrnyVqfunmsWz2Sw6le9kdSyxM5VPERH5V7588PXX8Pvv0L69uWzOHHjmGXOE9Pp1a/OJw4oz4ui1shfTD0zHyebEnOZz6Fi+o9WxxAIqnyIi8qASJWDePNi7F3x9ISoKxo0zl48bZ84ZKpJIsXGx9FzZkx8O/ICzzZl5LebRvlx7q2OJRVQ+RUTk4Xx8zEnqg4KgbFm4ccMcAS1VyhwRjYuzOqGkcbFxsfRY2YMZB2aYxbPlPNqWbWt1LLGQyqeIiDza3TlCDxyAH36AQoXg9GnzWFAfH/PYUJEExMbF0n1Fd2b9OgtnmzPzW86nzXNtrI4lFlP5FBGRxHF2NucDPX4cPvkEsmQxC2lAANStC7/+anVCSUNi42Lpurwrs3+bjYuTC4GtAmn9XGurY0kaoPIpIiJJ4+kJ771nnhk/YIB5ZnxwMDz/PPTqBefPW51QLBYTF0OX5V2Ye3BufPFs+WxLq2NJGqHyKSIiyZMrF3zxhXlmfNu25pWRpk2DkiVx+vhjnHXN+AwpJi6Gzss6M+/gPFycXFjYaiEtyrSwOpakISqfIiLyZEqUgAULYOdOqFIFwsJwHjGC2n36YJs7VyclZSAxcTF0WtqJBYcW4OrkyuLWi2leprnVsSSNUfkUEZGUUbUq7NoF8+djFCmC59WruHTvbhbS7dutTiepLCYuho5LOxJ4ONAsnm0W07R0U6tjSRqk8ikiIinHZoN27Yg5eJAjnTtjZM5szhX6yivQqpV5nKikO9Gx0XRY0oGFhxfi6uTKkjZLaFKqidWxJI1S+RQRkZTn6ckfLVsSc+QIvP46ODnBkiVQpgy88445X6ikC9Gx0bRf0p5FRxbh5uzG0rZLaVyqsdWxJA1T+RQRkdSTNy9MmWJOyeTvD9HR8Pnn8PTT5vLYWKsTyhOIjo2m3ZJ2LDm6BDdnN5a1XUajZxpZHUvSOJVPERFJfeXKwfr15pWSypSBq1fhjTfghRdgyxar00kyRMVG0XZxW5YeXYq7szvL2y6nQckGVscSB6DyKSIi9nH3Skm//QZffQXZspl/9vWF1q3h1CmrE0oiRcVG0WZRG5b9vswsnu2WU79kfatjiYNQ+RQREftycYF+/eCPP8zRTycnWLzYHBH94AMIC7M6oTxCVGwUrRe1ZsWxFbg7u7Oi3QrqPV3P6ljiQFQ+RUTEGrlywaRJsH8/1KoFERHw4YdQqhTMm2dOWi9pSmRMJK0WtmLlsZV4uHiwsv1K6j5d1+pY4mBUPkVExFrly8OmTebZ8MWKwT//QMeO8PLLsG+f1enkvyJjImm5sCWrjq/Cw8WDVe1XEfBUgNWxxAGpfIqIiPVsNmjRAo4cgdGjwcvLvGJS5crQsydcvGh1wgwtIiaCFgtbsOaPNXi6eLK6/WrqlKhjdSxxUMkqn5MmTaJ48eJ4eHjg4+PD9sdcuWLu3LlUqFABLy8v8ufPT/fu3bl69WqyAouISDrm6QnDhsHx4+bop2HA9OnwzDPw5ZcQE2N1wgwnIiaCFoEtCPojyCyeHVZTu0Rtq2OJA0ty+QwMDGTAgAEMGzaM/fv3U6NGDerXr8/p06cTfPyPP/5Ily5d6NmzJ4cPH2bRokXs2bOHXr16PXF4ERFJpwoWhDlzYMcOczqm0FAYMACefx62brU6XYYRFRdF68WtWXtiLV6uXgR1DMKvuJ/VscTBJbl8jh8/np49e9KrVy/KlCnDhAkTKFy4MJMnT07w8bt376ZYsWK89dZbFC9enJdffpnXX3+dvXv3PnF4ERFJ56pVg59/Niekz5EDDh0yT07q0AHOnbM6Xbp2J/oOH//1MetPrjeLZ4cgahWrZXUsSQdckvLgqKgo9u3bx+DBg+9bHhAQwM6dOxN8TrVq1Rg2bBhBQUHUr1+fS5cusXjxYho2bPjQ9URGRhIZGRl/PzQ0FIDo6Giio6OTEjnJzJd3vWd9qbo6SSV3Pyep/XmR1KHtl3xp5XdYim/DHj2gaVOcPvgAp6lTsc2fj7FqFXHDhhHXrx+4uaXMegQwi2fzhc05cOsAmVwzsbLtSqoVrGa372Ra+Rw7Mit+hon9fCSpfF65coXY2Fjy5s173/K8efNy4cKFBJ9TrVo15s6dS9u2bYmIiCAmJoYmTZrw9ddfP3Q9Y8aMYeTIkQ8sDw4OxsvLKymRkywiwhkwLw22adMmPDx06TdHFhISYnUEeQLafkl37++w9evXW/47LMW3YcOGZC1VivLffUeO48dxHjKE8IkTOfjqq1yuUCFl15VBRcZF8vHJj/n19q94OHkwtOhQbh26RdChILtlSGufY0dkRZ8JDw9P1ONshpH4idTOnTtHwYIF2blzJ1WrVo1f/tFHHzF79mx+//33B55z5MgR6tSpw8CBA6lbty7nz5/n3XffpXLlykybNi3B9SQ08lm4cGGuXLlClixZEhs3WcLCIHt28/8ULl0KJ1s211Rdn6SO6OhoQkJC8Pf3x9VV29DRaPsl372/w65fjyZTJmtypPo2jIvDNns2zkOHYrt82VzUogWxY8dCkSIpv74MIjw6nBaLWrDp1Ca8Xb0ZWnQo/Zv3t/v3MK18jh2ZFX0mNDSUXLlycfPmzUf2tSSNfObKlQtnZ+cHRjkvXbr0wGjoXWPGjKF69eq8++67AJQvX55MmTJRo0YNRo8eTf78+R94jru7O+7u7g8sd3V1TfUvwL0vb4/1SerSNnRs2n5J9+DvMOuy/JshlUL06gWtWplXRZo4EaelSyFoHVcGfgRvvIFXdndsttRZdXpjGHD5Rhidl3Vjx5VNeHt4s7rtam4cvGHJ9zCtfY4dkRV9JrHrSFL5dHNzw8fHh5CQEJo3bx6/PCQkhKZNmyb4nPDwcFxc7l+Ns7MzAEkYdBUREXlQtmzmdeJ79YK+fbmy/Sh5xwyAMVYHc0SZgGVkGlqC9Z3mUDlfZYIO2m9Xu2QcST7bfdCgQUydOpXp06dz9OhRBg4cyOnTp+nduzcAQ4YMoUuXLvGPb9y4MUuXLmXy5MmcPHmSHTt28NZbb/Hiiy9SoECBlHsnIiKScZUvb07B9M1Eq5M4vMBWgVQrXM3qGJKOJWnkE6Bt27ZcvXqVUaNGcf78ecqWLUtQUBBFixYF4Pz58/fN+dmtWzdu3brFN998w9tvv022bNnw8/Pj008/Tbl3ISIiYrPh1bUN9DXvXiQPmQiDzFlg+HB49VX47543Md2Ouk3LhS3ZceIXGGceO1uzZGWLU0l6l+TyCdCnTx/69OmT4N/NmDHjgWX9+vWjX79+yVmViIhIot17jGembevINPA18/rw77wB86fC5MnmJTuF21G3ab2wATsubCdL5vyE/ne5jpOV1KZru4uISPr0wgvw008wcSJkzWqW0CpVoE8fuH7d6nSWuhV5i/pz67P99HayumdlVftVVkeSDETlU0RE0i9nZ7Ns/v47dOpkntY9eTKULg2zZ5v3M5jQyFDqza3Hj6d/JJtHNjZ02YBPAR+rY0kGovIpIiLpX758ZtnctMksnpcuQZcu4OsLR49anc5uQiNDqTenHjvP7CS7R3Y2dN5ApQKVrI4lGYzKp4iIZBy+vvDrr/Dxx+DpaZ4hX6GCeUJSRITV6VLVzYib1J1Tl11nd5nFUyOeYhGVTxERyVjc3GDIEDh8GBo2NC+CPWqUWUI3b7Y6Xaq4Wzx3n91NDs8cbOyykRfyv2B1LMmgVD5FRCRjKl4cVq2ChQvN3fLHj4OfH3TrBleuWJ0uxdyIuEHAnAB++uen+OL5fP7nrY4lGZjKp4iIZFw2G7RubZ6Q9MYb5v2ZM83jQmfNcvgTkm5E3CBgdgA///MzOT1zsqnLJirmq2h1LMngVD5FRESyZoVJk2DHDihbFq5eha5doU4d+OMPq9Mly/U71/Gf7c+ec3vI6ZmTjV02UiFfBatjiah8ioiIxKtaFX75BcaMAQ8P8+z4cuVg9GiIirI6XaJdu3ONOrPrsPfcXnJ55WJz180qnpJmqHyKiIjcy9UVBg82T0gKCIDISHj/fahYEX780ep0j3XtzjXqzKrDL+d/IbdXbjZ33Uy5vOWsjiUST+VTREQkISVKwLp1MHcu5Mljzgdao4Z5bOjNm1anS9DV8KvUnlWb/Rf2kydTHjZ33UzZPGWtjiVyn2Rd211ERCRDsNmgQweoVw/eew+mToUpU4hbsYorn0yFevXw8rL+euiGAWeuXKHVwlYcCTtAnsxm8Xw297PWBhNJgMqniIjI4+TIAd9/bxbR117jyokb5O1az+pU/yMXsIXcw59jc9dFKp6SZmm3u4iISGL5+sJvv0HfflYneahlbZepeEqappFPERGRpPD0xGvMB/CNefciuclEOPj6wVdfmZPX28mlsEs0mteII//8BeMuA1Ch8DN2W79Icqh8ioiIJNG9x3hm+nAomT4aCptXQ5VN8OGH0L8/ODunaoZLYZdovNiPIzcPkzd7CS4mkE0kLdJudxERkScxcKC5K75WLQgPh7ffNucL/e23VFvlxdsX8Z3py+HLhymQuQDrOq1LtXWJpDSVTxERkSdVsqQ5If3335tXS9qzB3x8zPlBIyNTdFUXbl/Ad6YvRy4foWDmgmzpuoWSOUum6DpEUpPKp4iISEqw2aBXLzhyBFq0gJgY88pIPj7w888psoq7xfPolaMUylKILd1UPMXxqHyKiIikpAIFYMkSWLQIcueGw4eJq1KVS2+O4NLfd7h9G8LCkna7fRsOnrxIja9b8Pul383i2XULT+d42up3K5JkOuFIREQkNbRqZR4H2r8/V+YFk3fSCJj0JC+YF9hJ/pEV2dJ1CU/leCpFYorYm0Y+RUREUkuuXOblOWfOTrGXXN5uuYqnODSVTxERkVTm1eLfqyFdJDe3ycTtYmW5HbSN27d56O34uXM89VkFeCd3/POfLVDMgncgknJUPkVERFLZffOCLptHpkI5yHTqMJka1CTTf94kU9wtMmXivtv12LM0WFyTP8N+o3CuXAm+logjUvkUERGxJ39/OHwYXn/dvD9pEpQtCyEh8Q85c/MMtWbU4sS1ExTLVoz1ndZbFFYk5al8ioiI2FuWLDBlCmzYAMWKwenTEBAAvXtz5uwRas2sxZ/X/6R4tuJs6bqFItmKWJ1YJMWofIqIiFildm04eBD69jXvf/sttvIVKLrvJCWyl2BLty0UzVbU2owiKUzlU0RExEre3vD111xYOY8zOVwodD2GTbPgwKEaFHHJaXU6kRSn8ikiImKxUzdOUfXkUJ59PYZ51bMAkPn7mVC+PGzfbnE6kZSl8ikiImKhv67/Ra0ZtTh14xT585ekZtARCA6GwoXh5EmoWRMGD7Y6pkiKUfkUERGxgGHAobN/8cp39fn78mWe9q7AmlZbyOZckLBq/oTtPkhY596EGZ6EfTPtvueJODJdXlNERMQCh86epHyREsDvAJwAnnnn3kdkBSb/9/av8MEj8R73Hnh42CeoSArTyKeIiIid/XntT+rNrff4ByZk4jfg4wN796ZsKBE7UfkUERGxoz+v/UnNGTU5F/EHz3z+An9euPjIS2zevg23bsHFi3Bxxlpy5XKCI0fgpZdg5EiIjrb6LYkkicqniIiIHdWdU5d/bv3Ds3meZdtraymRN+8Dl9b835u3N+TJA3m61sfp9yPQujXExsKIEVC9Ohw7ZvXbEkk0HfMpIiKSyu49SejCtZuULuDDqpZr8LblJSwsiS/mkROmB0L9VjBwIOw5TFjVOsCZB9YlkhapfIqIiKSy3878AZQ074y7zO/AU4Oe5BVtQJv/3oCof/8m/PhZvF8o9CQvLpKqtNtdREQkFf1+5XeaBTaz3wprvgKzZ2sIVNIsjXyKiIikkqOXj+I3y4/LxgXKfFKTxW0WUyR3bmy2lF2PYUD4oT/hzb7k+uUv6NIFli+HKVMgd+6UXZnIE1L5FBERSQVHLh/Bb6YfF8MuUj5/eTZ2WUIur1yptj7vl56Cn1bB2LEwfDgsXQo//gjffw9NmqTaekWSSrvdRUREUtiRy0fwnenLxbCLVMxXkU1dNqVq8Yzn4gJDh8LPP8Nzz8GlS9C0KfTsac7XJJIGqHyKiIikoEOXDlFrRi0uhV3i+XzPs6HzBnJ65bRviOefNyehf+cdsNlg+nSoWBF27rRvDpEEqHyKiIikkEOXDuE304/L4ZfN4tnFguJ5l4cHfPYZbNkCRYrAyZNQowZ88IEmphdLqXyKiIikgIMXD+I705fL4Zfxye/Dhi4byOGZw+pY8Mor8Ntv0KkTxMXBhx+aE9MfP251MsmgVD5FRESe0K8XfsV3pi9Xwq9QqUAlQjqHpI3ieVfWrOb0SwsWQLZssGePuWv+u+80JZPYncqniIjIEzh48SC1Z9Xm6p2rVC5QmZDOIWT3zG51rIS1bQsHD4KfH4SHw+uvmyckXbpkdTLJQFQ+RUREnkCDeQ24eucqLxZ8keDOwWTzyGZ1pEcrVAhCQuDzz8HNDVatgipVrE4lGYjm+RQREUmie/dUX78ZQaViNVnWfAWusVmTfq12SzjB64Ogmj/07EnYkb/i/8a4HQaZMlmYTdI7lU8REZEk2v3Xb0B58864y+wFCva1MlFylQN+vm9JeLXaeAd+AxUqWBNJ0j3tdhcREUmCfef20XJhC6tjpJ6Tf0LVqjiNG2eeHS+SwjTyKSIikkh7z+3Ff7Y/oU43qPRFQwJbLiBP9swpfq12ezMM8/wjrl8j15CasGwJzkOHUq1cOfOs+GLFrI4o6YjKp4iISCLs+WcP/rP9uRl5k+pFq7O24wIyu2e2OlaK8fYG8uSAJYtg+nSMt94i98GDGD4+MG0aNGtmdURJJ7TbXURE5DF+/udn6syuw83Im9QoUoO1Hdemq+J5H5sNevYk5qefuFGiBLZr16B5c3NaJsc4m0rSOJVPERGRR/jp7E/mrvbIUF4p+gpBHYPSb/G8V6lSbPv0U2Lfftu8/913UKkS7N9vbS5xeCqfIiIiD7HrzK744lmzaE3WdFiDt5u31bHsxnB1JW7MGHNe0Pz54fffzTlBx4/XyUiSbCqfIiIiCdh5Zid159TlVtQtahWrleGK533q1DGvD9+0KURHw9tvQ/36cP681cnEAal8ioiI/I8dp3fEF0/fYr6s6bCGTG4ZfOL1XLlg2TKYPBk8PSE4GMqXh9WrrU4mDkblU0RE5B4/nv6RenPrcTvqNn7F/VjdYTVerl5Wx0obbDbo3Rv27jUnob9yBRo3hv79ITLS6nTiIFQ+RURE/mv739upN8csnnVK1GFV+1Uqngl59ln46ScYMMC8/9VX8NJLcOyYpbHEMah8ioiIANv+3kb9ufUJiw7Dv4Q/K9utVPF8FHd3+OILc7d7rlxw4AD4+MCMGeas9SIPofIpIiIZ3tZTW+OLZ8BTAaxotwJPV0+rYzmGhg3h11/B19ecB7R7d+jUCUJDrU4maZTKp4iIZGib/9pMg3kNCI8Op97T9VQ8k6NAAXM6ptGjwdkZ5s2DF14wjw0V+R8qnyIikmFt+msTDec1JDw6nPpP12dZ22V4uHhYHcsxOTvDsGGwbRsUKQJ//gnVqsHnn2tOULmPyqeIiGRIG09upNG8RtyJuUODkg1Y2napimdKqFbNPP6zZUtzTtB33jF3zV+6ZHUySSNUPkVEJMPZcHIDjeabxbNhyYYsbaPimaKyZ4dFi2DKFPDwgHXrzKmZNmywOpmkASqfIiKSoQT/GUzj+Y2JiImg8TONWdJmCe4u7lbHSn9sNnj9ddizx5ya6cIFCAiAoUMhJsbqdGIhlU8REckw1p9YT5P5TYiIiaBJqSYsar1IxTO1lS1rFtDXXzenYBozBmrVgjNnrE4mFlH5FBGRDGHdiXU0XdCUyNhImpZqquJpT15e5i74wEDInBl27ICKFWHNGquTiQVUPkVEJN0L+iMovng2L92cha0X4ubsZnWsjKdNG9i/35yM/to1aNTIPCEpKsrqZGJHKp8iIpKurTm+huaBzYmKjaJFmRYEtgpU8bTSU0+ZI59vvWXe//xzeOUVOHXK0lhiPyqfIiKSbq0+vpoWC1sQFRtFyzItWdByAa7OrlbHEnd3+PJLWLYMsmUzrxP//POwfLnVycQOVD5FRCRdCjoeRItAs3i2frY181vOV/FMa5o1M3fDV6kCN25A8+bQvz9ERlqdTFKRyqeIiKRLHZZ2IDoumjbPtWFui7kqnmlVsWKwfbt57CfAV19B7dqWRpLU5WJ1ABERkZRiGP/+OSbClVYVu/Jd3alERbigU1qSJjoaIiKcCQsD11Tv7a4w4jN4qTa89hphB47F/82921TSB5VPERFJNxYdWAM0NO+Mu8xiYLGVgRyaK9DIzuusB5y+b0n4W4PxnjzSPE5U0gXtdhcRkXRhyZEl9FrVy+oYktJ+mAbVq8Nff1mdRFKIRj5FRMThLT6ymHaL2xHnEUvLaW/wdYNvyOztjM1mdTLHFR0dzfr166lbty6uqb/f/T6GAeHhwMaN5OoTB/v2mWfDz5wJTZvaNYukPJVPERFxaIsOL6L9kvbEGrF0rtiZH5p+g7OTs9WxHF50NHh4xJIpkz2O+XyQtzfQvjZU3w9t28Lu3ebZ8YMGwSefWBNKUoR2u4uIiMNaeHhhfPHsUqELPzT9QcUzvSlSBLZuNUsnwPjxULOmrg3vwFQ+RUTEIQUeCqTDkg7EGrF0q9iN6U2mq3imV25u5pWQli6FrFlh1y5zN/zatVYnk2RQ+RQREYcz/+B8Oiw1i2f3it2Z2niqimdG0Lw5/PILvPACXL0KDRrAsGEQE2N1MkkClU8REXEoc3+bS6dlnYgz4uhRsQdTm6h4ZiglSpjXhu/Tx7z/8cfg7w/nz1ubSxJN5VNERBzGnN/m0GV5F+KMOHo934vvm3yPk03/lGU4Hh4wcSLMn2+embRli7kbftMmq5NJIugbKyIiDmHWr7Posswsnq++8CrfNv5WxTOja9cO9u6FcuXg4kVzBHTMGIiLszqZPIK+tSIikubNPDCTbsu7YWDwus/rTGk0RcVTTKVKmdMwdetmls6hQ825QK9ftzqZPIS+uSIikqbNODCD7iu6Y2DQ26c3kxpOUvGU+3l5wfTp8P335mU4V68GHx/Yv9/qZJIAfXtFRCTN+mH/D/RY0QMDgzcqvaHiKQ9ns0GvXrBzJxQrZl6Os2pVmDbN6mTyP/QNFhGRNGnaL9PosdIsnm9WfpOJDSZi0/Uy5XFeeMGcjqlRI4iMNAtpjx5w547VyeS/VD5FRCTN+X7f9/Ra1QuAfi/24+v6X6t4SuJlzw4rVpjTMDk5wQ8/mKOgJ05YnUxQ+RQRkTTmu33f8drq1wB468W3+LLelyqeknROTjBkCISEQO7c8OuvUKmSWUrFUiqfIiKSZny791teX/06AP2r9GdCvQkqnvJk/PzME4+qVYObN6FZM3jvPV0VyUIqnyIikiZM3jOZ3mt6AzDwpYF8UfcLFU9JGQULmhPRDxxo3h87FurUMecGFbtT+RQREctN/HkifYLMyyW+XfVtPg/4XMVTUparK4wfDwsXmldF2rrVPDlp506rk2U4Kp8iImKpb37+hr5r+wLwTtV3+Mz/MxVPST2tW8OePVCmDJw7B7VqmZfqNAyrk2UYKp8iImKZr376in5r+wHwn2r/Yaz/WBVPSX2lS8PPP5tFNDoa+vaFLl0gPNzqZBmCyqeIiFjiy91f0n9dfwAGVx/MJ3U+UfEU+/H2hsBA+PxzcHaGOXPM6Zj+/NPqZOmeyqeIiNjdF7u+YMD6AQAMfXkoH9f+WMVT7M9mg0GDYMMGyJMHfvvNvCzn6tVWJ0vXVD5FRMSuvtj1BYOCBwEwrMYwRvuNVvEUa9WqBfv2wUsvmdMxNW4Mw4dDbKzVydIllU8REbGbz3d+Hl8833/lfT70/VDFU9KGQoXMM+DffNO8P2qUeYnOa9eszZUOqXyKiIhdfLbjM94JeQeA4TWHM8p3lIqnpC1ubvDNNzBzJnh4wLp15m74/futTpauqHyKiEiq+/THT/nPhv8AMKLmCEbUGmFtIJFH6dIFdu2CEiXg1Cnz6kgzZ1qdKt1IVvmcNGkSxYsXx8PDAx8fH7Zv3/7Ix0dGRjJs2DCKFi2Ku7s7Tz31FNOnT09WYBERcSyf/PgJgzcOBmBkrZEMrzXc4kQiiVCxIuzdCw0aQEQEdOsG/fqZUzPJE0ly+QwMDGTAgAEMGzaM/fv3U6NGDerXr8/p06cf+pw2bdqwceNGpk2bxrFjx5g/fz6lS5d+ouAiIpL2fbLjE4ZsHALAh74f8kHNDyxOJJIE2bPDqlXwwX8/t998A7Vrw4UL1uZycC5JfcL48ePp2bMnvXr1AmDChAmsX7+eyZMnM2bMmAcev27dOrZu3crJkyfJkSMHAMWKFXuy1CIikuYtvLCQeQfmATDadzTDXhlmcSKRZHBygpEjzWM/O3WC7dvNPy9dClWqWJ3OISWpfEZFRbFv3z4GDx583/KAgAB2PuTaqCtXrqRSpUqMHTuW2bNnkylTJpo0acKHH36Ip6dngs+JjIwkMjIy/n5oaCgA0dHRRKfycLf58q73rC9VVyep5O7nJLU/L5I6tP2SL638Dhu1dRTzLpjF88NaH/Kfqv/R9nQw+h7+j/r1YedOXFq1wnbsGMYrrxD71VcYPXpYnSxBVvwuSOxnJUnl88qVK8TGxpI3b977lufNm5cLDxmCPnnyJD/++CMeHh4sW7aMK1eu0KdPH65du/bQ4z7HjBnDyJEjH1geHByMl5dXUiInWUSEM9AIgE2bNuHhoTm+HFlISIjVEeQJaPsl3b2/w9avX2/J77AFFxaw4MICADrn70y5G+UICgqyew5JGfoe3s9l+HCe/+orCuzejUvv3pxaupSDr75KnKur1dHuY0WfCU/k5UlthmEYiX3Rc+fOUbBgQXbu3EnVqlXjl3/00UfMnj2b33///YHnBAQEsH37di5cuEDWrFkBWLp0Ka1atSIsLCzB0c+ERj4LFy7MlStXyJIlS2LjJktYGGTPbn6ALl0KJ1u2tPVhksSJjo4mJCQEf39/XNPYLwR5PG2/5Lv3d9j169FkymS/dRuGwajto/jox48A6JK/C5M7TdY2dFD6Hj5CXBxOY8fiNHw4NsMgrkoVYgMDoUABq5PFs6LPhIaGkitXLm7evPnIvpakkc9cuXLh7Oz8wCjnpUuXHhgNvSt//vwULFgwvngClClTBsMwOHv2LCVLlnzgOe7u7ri7uz+w3NXVNdW/APe+vD3WJ6lL29Cxafsl3YO/w+yzXsMwGL5leHzx/MTvE0pfK61tmA5oGz7E++9DpUrQoQNOP/2E00svweLFUL261ckAa/pMYteRpLPd3dzc8PHxeWAIPiQkhGrVqiX4nOrVq3Pu3Dlu374dv+z48eM4OTlRqFChpKxeRETSIMMw+GDzB3y47UMAxvmPY9BLgyxOJWIH9evDnj1Qtqx5BnytWjBpEiR+p3KGlOSplgYNGsTUqVOZPn06R48eZeDAgZw+fZrevXsDMGTIELp06RL/+A4dOpAzZ066d+/OkSNH2LZtG++++y49evR46AlHIiLiGAzD4P82/R+jt48GYHzAeN6u9rbFqUTs6OmnzQnp27SBmBjz8pw9e5pzg0qCkjzVUtu2bbl69SqjRo3i/PnzlC1blqCgIIoWLQrA+fPn75vz09vbm5CQEPr160elSpXImTMnbdq0YfTo0Sn3LkRExO4Mw2DoxqF8suMTAL6o+wUDXhpgbSgRK3h7w4IF5m74wYPhhx/g8GFzOqaCBa1Ol+YkuXwC9OnThz59+iT4dzNmzHhgWenSpXW2nIhIOmIYBkM2DuHTHZ8C8GW9L3mrylsWpxKxkM0G774Lzz9vjoL+/LNZRpcsMS/PKfF0bXcREUkSwzB4b8N78cXz6/pfq3iK3FWnjnlZznuPA5061epUaYrKp4iIJJphGLwb8i6f7fwMgG/qf0PfF/tanEokjSlRwjwOtGVLc7b3V181jwWNirI6WZqg8ikiIoliGAbvBL/D57s+B2Big4m8+eKbFqcSSaO8vWHRIhg92twlP2kS+PvDpUtWJ7OcyqeIiDyWYRgMWj+I8bvHAzC54WT6VE742H8R+S+bDYYNgxUrIHNm2LbNPA70l1+sTmYplU8REXkkwzAYuH4gE36aAMC3jb6ld6Xe1oYScSSNG5snID3zDJw5Y05EP2+e1akso/IpIiIPZRgG/df158ufvgTgu0bf8ZrPaxanEnFApUvDTz9BgwbmHKAdO5pnx8em/jXX0xqVTxERSZBhGPRb24+vf/4aGzamNp7Kqz6vWh1LxHFlywYrV5q74gHGjTPL6LVrlsayN5VPERF5gGEY9A3qy8Q9E83i2WQqPV/oaXUsEcfn7GyehLRoEXh5QXAwvPgiHDlidTK7UfkUEZH7xBlxvBn0JpP2TsKGjWlNptHj+R5WxxJJX1q1MqdjKlYM/vwTXnoJVq+2OpVdqHyKiEi8OCOOPmv6MHnvZGzY+KHpD3R/vrvVsUTSp/LlYc8eqFkTbt2CJk3g00/BMKxOlqpUPkVEBDCLZ+/Vvfl237fYsDGj2Qy6VuxqdSyR9C1XLggJgT59zNI5eDB06gR37lidLNWofIqICHFGHK+vep3vf/keJ5sTs5rPokuFLlbHEskYXF1h4kSYPBlcXMxpmGrUgLNnrU6WKlQ+RUQyuDgjjldXvsrU/VPN4tlsFp3Kd7I6lkjG07s3bNgAOXPCvn1QuTLs3m11qhSn8ikikoHFGXH0WtmL6Qem42RzYnbz2XQs39HqWCIZV82a5nGg5crBhQvm/RkzrE6VolQ+RUQyqNi4WHqu7MkPB37AyebE3BZz6VCug9WxRKR4cdi5E5o3h6go6N4dBg2CmBirk6UIlU8RkQwoNi6WHit7MOPADJxtzsxrMY92ZdtZHUtE7vL2hsWLYfhw8/4XX0DDhnD9urW5UoDKp4hIBhMbF0v3Fd2Z9essnG3OzG85n7Zl21odS0T+l5MTjBhx/4T0VarAsWNWJ3siKp8iIhlIbFwsXZd3ZfZvs3G2ObOg1QJaP9fa6lgi8iitWsGOHVC0KPzxh1lAg4OtTpVsKp8iIhlETFwMXZZ3Ye7Bubg4uRDYKpBWz7ayOpaIJEbFivDzz1C9Oty8CfXrw1dfOeSE9CqfIiIZQExcDJ2XdWbewXm4OLmwsNVCWj7b0upYIpIUefLAxo3QrRvExUH//ub0TNHRVidLEpVPEZF0LiYuhk5LO7Hg0AJcnFxY1HoRzcs0tzqWiCSHuztMnw7jxoHNBt99BwEBcPWq1ckSTeVTRCQdi46NpsOSDgQeDsTVyZXFrRfTrHQzq2OJyJOw2eDtt2HVKsicGbZsgRdfhCNHrE6WKCqfIiLpVHRsNB2WdmDRkUW4OrmypM0SmpZuanUsEUkpDRvCrl3mvKAnT8JLL0FQkNWpHkvlU0Qkneq2vBuLjyzGzdmNpW2X0rhUY6sjiUhKe+4580SkV16BW7egcWMYPz5Nn4ik8ikikk6tOLbcLJ5tltLomUZWxxGR1JIrF4SEQK9e5olIb78NffpYneqhXKwOICIiKScyJgpwA8A1NjsLGk+nVsEAwsLsmyM6GiIinAkLA1dX+65bUoa2oaNxgy++g5IVYfBgwmYvBiYDaW8QVOVTRCSdiIqNosOCXsAsAKI/PUuLT61K4wpotNWxaRs6Hhvw5n9v/wq/GU327Gnn/yBUPkVE0oHImEhaL2rN+hO7rI4iImlNGhu6VvkUEXFwkTGRtFrUitXHV+OWxYPZuzdTq7gvXl7mjCxWiI6OZv369dStWxfXNPYPnySOtqFjMwy4eTGUDT/uIFeuOlbHuY/Kp4iIA4uMiaTlwpas+WMNHi4erGq/ijolfK2ORXQ0eHjEkilTmht0kUTSNnR87u6eZMsWhVMaO708jcUREZHEioiJoMXCFqz5Yw2eLp6sbr+aOiXS1giHiMj/0siniIgDioiJoHlgc9adWGcWzw6r8SvuZ3UsEZHHUvkUEXEwETERNFvQjPV/rsfTxZM1HdbgW9z6Xe0iIomh8iki4kDuRN+hWWAzgv8MxsvVizUd1lCrWC2rY4mIJJrKp4iIg7gTfYemC5oScjKETK6ZCOoYxCtFX7E6lohIkqh8iog4gPDocJouaMqGkxvI5JqJtR3XUqNoDatjiYgkmcqniEgaFx4dTuP5jdn01ya83bxZ23EtLxd52epYIiLJovIpIpKGhUWF0Xh+Yzaf2oy3mzfrOq6jepHqVscSEUk2lU8RkTQqLCqMRvMbseXUFjK7ZWZdp3VUK1zN6lgiIk9E5VNEJA26HXWbhvMasu3vbWR2y8z6TuupWriq1bFERJ6YyqeISBpzO+o2DeY2YPvp7WRxz8L6Tut5qdBLVscSEUkRKp8iImnIrchbNJjXgB9P/0gW9ywEdwqmSqEqVscSEUkxKp8iImnErchb1J9bnx1ndpDVPSvBnYN5seCLVscSEUlRKp8iImlAaGQo9efWZ+eZnWTzyEZI5xAqFahkdSwRkRSn8ikiYrHQyFDqzanHrrO7VDxFJN1T+RQRsdDNiJvUm1uP3Wd3k90jOxu6bOCF/C9YHUtEJNWofIqIWORmxE3qzqnLT//8RA7PHGzovIHn8z9vdSwRkVSl8ikiYoEbETeoO6cuP//zMzk8c7Cxy0Yq5qtodSwRkVSn8ikiYmfX71wnYE4Ae8/tJadnTjZ22UiFfBWsjiUiYhcqnyIidnT9znX8Z/uz7/w+cnnlYmOXjZTPW97qWCIidqPyKSJiJ9fuXMN/tj+/nP+FXF652NRlE+XylrM6loiIXal8iojYwbU716gzqw77L+wnt1duNnXdRNk8Za2OJSJidyqfIiKp7Gr4VerMrsOBCwdUPEUkw1P5FBFJRVfCr1BnVh1+vfgreTLlYVOXTTyX5zmrY4mIWEblU0QklVwJv0LtWbX57eJv5M2Ul01dN/Fs7metjiUiYimVTxGRVHA57DK1Z9Xm4KWD5M2Ul81dN1MmdxmrY4mIWE7lU0Qkhd1bPPN552Nz182UzlXa6lgiImmCk9UBRETSk0thl/Cb5cfBSwfJ752fLV23qHiKiNxDI58iIink4u2L+M3y48jlIxTIXIDNXTfzTM5nrI4lIpKmqHyKiKSAC7cv4DfTj6NXjlIwc0E2d91MyZwlrY4lIpLmqHyKiDyhC7cv4DvTl9+v/E7BzAXZ0m0LT+d42upYIiJpko75FBF5AudvnY8vnoWyFFLxFBF5DI18iogk07lb5/Cd6cvxq8cpnKUwm7tu5qkcT1kdS0QkTVP5FBFJhnuLZ5GsRdjcdTMlspewOpaISJqn8ikikkT/hP6D70xf/rj2B0WzFmVz180Uz17c6lgiIg5B5VNEJAnOhp7Fd6YvJ66doGjWomzptoVi2YpZHUtExGGofIqIJNKZm2fwnenLn9f/pFi2YmzuulnFU0QkiXS2u4hIIpy+eZpaM2vx5/U/KZ6tOFu6asRTRCQ5NPIpIvIYf9/4G9+Zvvx14y9KZC/B5q6bKZK1iNWxREQcksqniMgj/H3jb2rNrMWpG6cokb0EW7puoXDWwlbHEhFxWNrtLiLyEKdunIovnk9lf0rFU0QkBWjkU0QkAX9d/wvfmb78ffNvSuYoyeaumymYpaDVsUREHJ5GPkVE/sfJ6yepNbOWiqeISCrQyKeIyD1OXj9JrRm1OBN6hmdyPsOmLptUPEVEUpDKp4jIf/157U9qzazF2dCzlMpZis1dN5M/c36rY4mIpCsqnyIiwIlrJ6g1oxb/3PqH0rlKs7nrZvJ557M6lohIuqNjPkUkw/vj6h/xxbNMrjIqniIiqUgjnyKSoR2/ehzfmb6cu3WOZ3M/y6Yum8jrndfqWCIi6ZbKp4hkWMeuHMN3pi/nb5/nudzPsanrJvJkymN1LBGRdE273UUkQ/r9yu/xxbNsnrIqniIidqKRTxHJcI5ePorfLD8u3L5AuTzl2NhlI7kz5bY6lohIhqDyKSIZypHLR/Cb6cfFsIuUz1uejV02kssrl9WxREQyDJVPEckwjlw+gu9MXy6FXaJC3gps7LKRnF45rY4lIpKh6JhPEckQDl06RK0ZtbgUdomK+SqqeIqIWEQjnyKS7h26dAi/mX5cDr/M8/meZ0OXDeTwzGF1LBGRDEkjnyKSrh28eBDfmb5cDr/MC/lfUPEUEbGYyqeIpFu/XvgV35m+XAm/gk9+HzZ0VvEUEbGayqeIpEu/XviV2rNqc/XOVSoXqMyGLhvI7pnd6lgiIhmeyqeIpDsHLhzAb5YfV+9c5cWCLxLcOZhsHtmsjiUiIqh8ikg688v5X/Cb6ce1O9eoUrAKwZ1UPEVE0hKVTxFJN345/wt1ZtXhesR1Xir0Eus7rSerR1arY4mIyD001ZKIpAv7zu2jzuw63Ii4QdVCVVnXaR1Z3LNYHUtERP6HRj5FxOHt+WdPfPGsVriaiqeISBqmkU8RcWg///MzAbMDuBl5k+qFq7O241oyu2e2OpaIiDyERj5FxGH9dPYn/Gf7czPyJi8XeVnFU0TEAah8iohD2n12NwFzAgiNDKVGkRoqniIiDkLlU0Qczq4zuwiYbRbPmkVrEtQxCG83b6tjiYhIIqh8iohD2XlmJ3Xn1OVW1C1qFavFmg5rVDxFRByIyqeIOIwdp3fEF0/fYr6sbr+aTG6ZrI4lIiJJoLPdRcQh/Hj6R+rNqUdYdBh+xf1Y1X4VXq5eVscSEZEk0siniKR52//eHl8865Soo+IpIuLAklU+J02aRPHixfHw8MDHx4ft27cn6nk7duzAxcWFihUrJme1IpIBbft7G/Xn1o8vnivbrVTxFBFxYEkun4GBgQwYMIBhw4axf/9+atSoQf369Tl9+vQjn3fz5k26dOlC7dq1kx1WRDKWe4tnwFMBrGy3Ek9XT6tjiYjIE0hy+Rw/fjw9e/akV69elClThgkTJlC4cGEmT578yOe9/vrrdOjQgapVqyY7rIhkHAdvHaTJwiaER4dT96m6rGi3QsVTRCQdSNIJR1FRUezbt4/BgwfftzwgIICdO3c+9Hk//PADf/75J3PmzGH06NGPXU9kZCSRkZHx90NDQwGIjo4mOjo6KZGTzHx513vWl6qrk1Ry93OS2p8XSR0hJ0L48OSHRBlR1C1Rl0UtF+FsOGt7OhB9Bx2ftqHjs/c2TOx6klQ+r1y5QmxsLHnz5r1ved68eblw4UKCz/njjz8YPHgw27dvx8UlcasbM2YMI0eOfGB5cHAwXl6pe6xXRIQz0AiATZs24eERm6rrk9QVEhJidQRJol9v/cpHJz8iyojCJ4sPPb17sil4k9WxJJn0HXR82oaOz17bMDw8PFGPS9ZUSzab7b77hmE8sAwgNjaWDh06MHLkSJ555plEv/6QIUMYNGhQ/P3Q0FAKFy5MQEAAWbJkSU7kRAsL+/fPfn5+ZMvmmqrrk9QRHR1NSEgI/v7+uLpqGzqKjX9tZMyiMUQZUVTKUongnsF4e2oCeUek76Dj0zZ0fPbehnf3VD9Okspnrly5cHZ2fmCU89KlSw+MhgLcunWLvXv3sn//fvr27QtAXFwchmHg4uJCcHAwfn5+DzzP3d0dd3f3B5a7urqm+g/v3pe3x/okdWkbOo7gP4Npvqg5ETERNHi6Ad29uuPt6a3t5+D0HXR82oaOz17bMLHrSNIJR25ubvj4+DwwfBsSEkK1atUeeHyWLFk4ePAgBw4ciL/17t2bUqVKceDAAapUqZKU1YtIOrX+xHqazG9CREwETUo1IbBFIK5O+sdORCQ9SvJu90GDBtG5c2cqVapE1apV+e677zh9+jS9e/cGzF3m//zzD7NmzcLJyYmyZcve9/w8efLg4eHxwHIRyZjWnVhHswXNiIyNpGmppixsvRBb3IOH8YiISPqQ5PLZtm1brl69yqhRozh//jxly5YlKCiIokWLAnD+/PnHzvkpIgKw9o+1NAtsRlRsFM1KNyOwVSBuzm5Ex+nsWhGR9CpZJxz16dOHPn36JPh3M2bMeORzR4wYwYgRI5KzWhFJR4L+CKJ5YHOiYqNoXro5ga0CcXXWrnYRkfRO13YXEbtbfXx1fPFsUaaFiqeISAai8ikidrXq2CpaBLYgKjaKVs+2YkHLBSqeIiIZiMqniNjNymMrabmwJdFx0bR+tjXzWsxT8RQRyWBUPkXELpb/vpxWC1sRHRdN2+faMq+liqeISEak8ikiqW7Z0WW0XtSa6Lho2pVtx5wWc3BxStb5jiIi4uBUPkUkVS09upQ2i9sQExdDh3IdmN18toqniEgGpvIpIqlm8ZHFtFlkFs+O5Toys9lMFU8RkQxO5VNEUsWiw4tot7gdsUYsnct3VvEUERFA5VNEUsHCwwtpv6Q9sUYsXSp04YemP+Ds5Gx1LBERSQNUPkUkRS04tIAOSzoQa8TStUJXpjeZruIpIiLxVD5FJMXMPzifjks7EmvE0r1id6Y1mabiKSIi91H5FJEUMe/gPDot60ScEUePij2Y2mSqiqeIiDxA5VNEntic3+bQeVln4ow4ej3fi++bfI+TTb9eRETkQTr1VESeyOxfZ9N1eVcMDF594VWmNJqi4ikiIg+lfyFEJNlmHpgZXzxf93ldxVNERB5L/0qISLLMODCD7iu6Y2DwRqU3mNRwkoqniIg8lv6lEJEkm75/Oj1W9MDAoE+lPkxsMFHFU0REEkX/WohIkkz7ZRo9V/bEwKBv5b580+AbbDab1bFERMRBqHyKSKJ9v+97eq3qBUC/F/vxVf2vVDxFRCRJVD5FJFG+2/cdr61+DYD+VfrzZb0vVTxFRCTJVD5F5LGm7J3C66tfB2BAlQF8UfcLFU8REUkWlU8ReaTJeybzxpo3ABj00iDG1x2v4ikiIsmm8ikiDzVpzyT6BPUB4O2qbzMuYJyKp4iIPBGVTxFJ0Dc/f8ObQW8C8G61d/nM/zMVTxEReWIqnyLygK9++op+a/sB8F719/i0zqcqniIikiJUPkXkPhN2T6D/uv4ADK4+mDG1x6h4iohIilH5FJF4X+z6goHrBwIw9OWhfFz7YxVPERFJUSqfIgLA+F3jGRQ8CIBhNYYx2m+0iqeIiKQ4lU8RYdzOcbwd/DYA77/yPh/6fqjiKSIiqULlUySDG7tjLO+GvAvA8JrDGeU7SsVTRERSjYvVAUTEOp/++CmDNw4GYETNEQyvNdziRCIikt5p5FMkgxqzfUx88RxZa6SKp4iI2IXKp0gG9NG2jxi6aSgAo2qN4oOaH1icSEREMgrtdhfJYEZvG837m983/+w7mmGvDLM4kYiIZCQqnyIZyKitoxi+xdy9/rHfxwypMcTiRCIiktGofIpkECO2jGDk1pEAjKk9hsEvD7Y4kYiIZEQqnyLpnGEYjNgyglHbRgHwaZ1P+U/1/1icSkREMiqVT5F0zDAMhm8ZzofbPgTgM//PeKfaOxanEhGRjEzlUySdMgyD9ze/z0fbPwJgnP843q72tsWpREQko1P5FEmHDMPg/zb9Hx//+DEA4wPGM7DqQItTiYiIqHyKpDuGYTB041A+2fEJAF/U/YIBLw2wNpSIiMh/qXyKpCOGYTB4w2DG7hwLwJf1vuStKm9ZnEpERORfKp8i6YRhGLy34T0+2/kZAF/X/5q+L/a1OJWIiMj9VD5F0gHDMHg35F0+3/U5AN/U/4Y3X3zT4lQiIiIPUvkUcXCGYfBO8DuM3z0egEkNJvFG5TcsTiUiIpIwlU8RB2YYBoPWD2LCTxMAmNxwMr0r9bY2lIiIyCOofIo4KMMwGLh+IF/+9CUA3zb6ltd8XrM4lYiIyKOpfIo4IMMw6L+uP1///DUA3zX6jld9XrU4lYiIyOOpfIo4GMMw6Le2HxP3TMSGje8bf0/PF3paHUtERCRRVD5FHIhhGPQN6sukvZOwYWNqk6n0eL6H1bFEREQSTeVTxEHEGXH0DerL5L2TsWFjetPpdKvYzepYIiIiSaLyKeIA4ow4+qzpw7f7vsWGjR+a/kDXil2tjiUiIpJkKp8iaVycEUfv1b35/pfvsWFjZrOZdK7Q2epYIiIiyaLyKZKGxRlxvL7qdabun4qTzYmZzWbSqXwnq2OJiIgkm8qnSBoVZ8Tx2qrXmLZ/Gk42J2Y1m0XH8h2tjiUiIvJEVD5F0qA4I45eK3vxw4EfcLI5Maf5HNqXa291LBERkSem8imSxsTGxdJrVS9mHJiBk82JuS3m0q5sO6tjiYiIpAiVT5E0JDYulh4rezDr11k425yZ22Iubcu2tTqWiIhIilH5FEkjYuNi6b6iO7N/m42zzZn5LefT+rnWVscSERFJUSqfImlAbFwsXZd3Ze7BuTjbnFnQagGtnm1ldSwREZEUp/IpYrGYuBi6Lu/KvIPzcHFyYUHLBbR8tqXVsURERFKFyqeIhWLiYuiyrAvzD83HxcmFha0W0rxMc6tjiYiIpBqVTxGLxMTF0GlpJwIPB+Li5MKi1otoVrqZ1bFERERSlcqniAVi4mLouLQjCw8vxNXJlUWtF9G0dFOrY4mIiKQ6lU8RO4uOjabj0o4sOrIIVydXlrRZQuNSja2OJSIiYhcqnyJ2FB0bTfsl7VlydAluzm4sabOERs80sjqWiIiI3ah8ithJdGw07Za0Y+nRpbg5u7Gs7TIalGxgdSwRERG7UvkUsYOo2CjaLW7Hst+XqXiKiEiGpvIpksqiYqNos6gNK46twN3ZneXtllPv6XpWxxIREbGEyqdIKoqKjaL1otasPLYSd2d3VrRbQd2n61odS0RExDIqnyKpJDImktaLWrPq+Co8XDxY0W4FAU8FWB1LRETEUiqfIqkgMiaSlgtbsuaPNXi4eLCy3Ur8n/K3OpaIiIjlVD5FUlhETAQtF7Yk6I8gPF08WdV+FbVL1LY6loiISJqg8imSgiJiImgR2IK1J9bi6eLJ6g6r8SvuZ3UsERGRNEPlUySFRMRE0DywOetOrMPTxZM1HdbgW9zX6lgiIiJpisqnSAq4E32HZoHNCP4zGC9XL9Z0WEOtYrWsjiUiIpLmqHyKPKE70XdouqApISdD8HL1IqhDEDWL1bQ6loiISJqk8inyBMKjw2m6oCkbTm4gk2smgjoG8UrRV6yOJSIikmapfIokU3h0OI3nN2bTX5vwdvNmbce1vFzkZatjiYiIpGkqnyLJEBYVRuP5jdl8ajPebt6s67iO6kWqWx1LREQkzVP5FEmisKgwGs1vxJZTW8jslpl1ndZRrXA1q2OJiIg4BJVPkSS4HXWbhvMasu3vbWR2y8z6TuupWriq1bFEREQchsqnSCLdjrpNg7kN2H56O1ncs7C+03peKvSS1bFEREQcisqnSCLcirxFg3kN+PH0j2Rxz0Jwp2CqFKpidSwRERGHo/Ip8hi3Im9Rf259dpzZQVb3rAR3DubFgi9aHUtERMQhqXyKPEJoZCj159Zn55mdZHXPSkjnECoXrGx1LBEREYel8inyEKGRodSbU49dZ3eRzSMbIZ1DqFSgktWxREREHJrKp0gCbkbcpN7ceuw+u5vsHtkJ6RyCTwEfq2OJiIg4PJVPkf9xM+ImdefU5ad/fiK7R3Y2dNnAC/lfsDqWiIhIuqDyKXKPGxE3qDunLj//8zM5PHOwofMGns//vNWxRERE0g2VT5H/un7nOgFzAth7bi85PHOwsctGKuaraHUsERGRdEXlUwSzePrP9mff+X3k9MzJxi4bqZCvgtWxRERE0h2VT8nwrt25hv9sf345/wu5vHKxsctGyuctb3UsERGRdEnlUzK0a3euUWdWHfZf2E8ur1xs6rKJcnnLWR1LREQk3VL5lAzravhV6syuw4ELB8jtlZtNXTdRNk9Zq2OJiIikayqfkiFdCb9CnVl1+PXir+TJlIdNXTbxXJ7nrI4lIiKS7ql8SoZzJfwKtWfV5reLv5E3U142dd3Es7mftTqWiIhIhqDyKRnK5bDL1J5Vm4OXDpI3U142d91MmdxlrI4lIiKSYah8SoZxKewStWfV5tClQ+Tzzsfmrpspnau01bFEREQyFJVPyRAuhV3Cb6Yfhy8fJr93fjZ33UypXKWsjiUiIpLhqHxKunfx9kX8Zvlx5PIRCmQuwOaum3km5zNWxxIREcmQnJLzpEmTJlG8eHE8PDzw8fFh+/btD33s0qVL8ff3J3fu3GTJkoWqVauyfv36ZAcWSYoLty/gO9OXI5ePUDBzQbZ03aLiKSIiYqEkl8/AwEAGDBjAsGHD2L9/PzVq1KB+/fqcPn06wcdv27YNf39/goKC2LdvH76+vjRu3Jj9+/c/cXiRR7kWfQ3/uf4cvXLULJ7dtlAyZ0mrY4mIiGRoSd7tPn78eHr27EmvXr0AmDBhAuvXr2fy5MmMGTPmgcdPmDDhvvsff/wxK1asYNWqVTz//PPJSy3yGOdvn+f9E+/zT+Q/FMpSiM1dN/N0jqetjiUiIpLhJal8RkVFsW/fPgYPHnzf8oCAAHbu3Jmo14iLi+PWrVvkyJHjoY+JjIwkMjIy/n5oaCgA0dHRREdHJyVykpkv73rP+lJ1dZIKzt06h/8cf7N4Zi5ESMcQimYumuqfHUk5d7eVtpnj0jZ0fNqGjs/e2zCx60lS+bxy5QqxsbHkzZv3vuV58+blwoULiXqNzz//nLCwMNq0afPQx4wZM4aRI0c+sDw4OBgvL6+kRE6yiAhnoBEAmzZtwsMjNlXXJynratRV3v/zfc5FniO3a27+r9D/cWzXMY5xzOpokgwhISFWR5AnpG3o+LQNHZ+9tmF4eHiiHpess91tNtt99w3DeGBZQubPn8+IESNYsWIFefLkeejjhgwZwqBBg+Lvh4aGUrhwYQICAsiSJUtyIidaWNi/f/bz8yNbNtdUXZ+knH9u/YP/XH/ORZ6jSJYiDCs4jE6NOuHqqm3oaKKjowkJCcHf31/bz0FpGzo+bUPHZ+9teHdP9eMkqXzmypULZ2fnB0Y5L1269MBo6P8KDAykZ8+eLFq0iDp16jzyse7u7ri7uz+w3NXVNdV/ePe+vD3WJynjbOhZ/Of6c+LaCYpmLUpIxxCO7DyibejgtP0cn7ah49M2dHz22oaJXUeSznZ3c3PDx8fngeHbkJAQqlWr9tDnzZ8/n27dujFv3jwaNmyYlFWKPNaZm2eoNaMWJ66doFi2YmzptoVi2YpZHUtEREQSkOTd7oMGDaJz585UqlSJqlWr8t1333H69Gl69+4NmLvM//nnH2bNmgWYxbNLly58+eWXvPTSS/Gjpp6enmTNmjUF34pkRKdvnsZ3pi8nr5+keLbibO66maLZdHKRiIhIWpXk8tm2bVuuXr3KqFGjOH/+PGXLliUoKIiiRYsCcP78+fvm/Pz222+JiYnhzTff5M0334xf3rVrV2bMmPHk70AyrL9v/I3vTF/+uvEXJbKXYHPXzRTJWsTqWCIiIvIIyTrhqE+fPvTp0yfBv/vfQrlly5bkrELkkU7dOIXvTF9O3ThFiewl2NJ1C4WzFrY6loiIiDyGru0uDufUjVPUmlGLv2/+zVPZn2JLty0UylLI6lgiIiKSCMm6truIVf66/ld88Xw6x9Ns7bZVxVNERMSBqHyKwzh5/SS1ZprFs2SOkmzpuoWCWQpaHUtERESSQLvdxSGcvH6SWjNqcSb0DM/kfIbNXTdTIHMBq2OJiIhIEql8Spr357U/qTWzFmdDz1IqZyk2d91M/sz5rY4lIiIiyaDd7pKmnbh2gpozanI29Cylc5VW8RQREXFwKp+SZv1x9Q9qzajFP7f+oUyuMiqeIiIi6YB2u0uadPzqcXxn+nLu1jmezf0sm7psIq93XqtjiYiIyBPSyKekOceuHKPWjFqcu3WO53I/p+IpIiKSjqh8Spry+5Xf8Z3py/nb5ymbpyybuqp4ioiIpCfa7S5pxtHLR/Gb5ceF2xcol6ccG7tsJHem3FbHEhERkRSkkU9JE45cPoLvTF8u3L5A+bzlVTxFRETSKY18iuXuFs9LYZeokLcCG7psIJdXLqtjiYiISCrQyKdY6tClQ/HFs2K+imzsslHFU0REJB3TyKdY5tClQ/jN9ONy+GWez/c8IZ1DyOmV0+pYIiIikopUPsUSBy8exG+WH1fCr/BC/hcI6RxCDs8cVscSERGRVKbd7mJ3v138Dd+ZvlwJv4JPfh8VTxERkQxE5VPs6tcLv+I304+rd65SqUAlFU8REZEMRrvdxW4OXDhA7Vm1uXbnGpULVCa4czDZPLJZHUtERETsSOVT7GL/+f3UnlWb6xHXebHgi6zvtF7FU0REJAPSbndJdb+c/yW+eFYpWIXgThrxFBERyag08impat+5fdSZXYcbETd4qdBLrO+0nizuWayOJSIiIhbRyKekmr3n9sYXz6qFqqp4ioiIiEY+JXXs+WcP/rP9uRl5k+qFq7O241oyu2e2OpaIiIhYTCOfkuJ+OvsTdWbX4WbkTV4u8rKKp4iIiMRT+ZQUtfvsbgLmBBAaGUqNIjVUPEVEROQ+2u0uKWbXmV3UnVOXW1G3eKXoK6zpsAZvN2+rY4mIiEgaopFPSRE7z+wkYE4At6JuUatYLYI6BKl4ioiIyANUPuWJ7Ti9g7pz6nI76ja+xXxZ3X41mdwyWR1LRERE0iCVT3kiP57+kXpz63E76jZ+xf1Y3UHFU0RERB5O5VOSbfvf26k3xyyetYvXZlX7VXi5elkdS0RERNIwlU9Jlm1/b6P+3PqERYdRp0QdFU8RERFJFJVPSbItp7bEF0//Ev6sbLcST1dPq2OJiIiIA1D5lCTZ/NdmGs5rSHh0OHWfqsuKditUPEVERCTRNM+nJNqmvzbRaF4j7sTcod7T9VjWdhkeLh5WxxIREREHopFPSZSNJzfScF5D7sTcof7T9VU8RUREJFlUPuWxNpzcQKP5jYiIiaBhyYYqniIiIpJsKp/ySMF/BtN4fuP44rmkzRLcXdytjiUiIiIOSuVTHmr9ifU0md+EiJgIGj/TWMVTREREnpjKpyRo3Yl1NF3QlMjYSJqWasriNotVPEVEROSJqXzKA4L+CIovns1KN2Nh64W4ObtZHUtERETSAZVPuc+a42toHticqNgompduzsJWKp4iIiKSclQ+Jd7q46tpsbAFUbFRtCzTksBWgbg6u1odS0RERNIRTTIvAKw6toqWC1sSHRdNq2dbMa/FPBVPERERSXEa+RRWHlsZXzzbPNdGxVNERERSjcpnBrf89+W0WtiK6Lho2j7Xlrkt5qp4ioiISKpR+czAlh1dRutFrYmOi6Zd2XbMaTEHFycdiSEiIiKpR+Uzg1p6dCltFrchJi6GDuU6MLv5bBVPERERSXUqnxnQ4iOLabPILJ6dyndiVrNZKp4iIiJiFyqfGcyiw4tot7gdsUYsncp3YkbTGTg7OVsdS0RERDIIlc8MJPBQIO2XtCfWiKVLhS4qniIiImJ3Kp8ZxIJDC+iwtAOxRizdKnZjepPpKp4iIiJidyqfGcC8g/PouLQjcUYc3St2Z2rjqSqeIiIiYgmVz3Ru7m9z6bysM3FGHD2f78nUJiqeIiIiYh2Vz3Rszm9z6LK8C3FGHL2e78V3jb/DyaZNLiIiItZRE0mnZv06iy7LzOL56guv8m3jb1U8RURExHJqI+nQzAMz6ba8GwYGr/u8zpRGU1Q8RUREJE1QI0lnZhyYQfcV3TEw6O3Tm0kNJ6l4ioiISJqhVpKOTN8/nR4remBg8EalN1Q8RUREJM1RM0knpv0yjZ4re2Jg8GblN5nYYCI2m83qWCIiIiL3UflMB77f9z29VvUCoG/lvnxd/2sVTxEREUmTVD4d3Hf7vuO11a8B8NaLb/FV/a9UPEVERCTNUvl0YFP2TuH11a8D0L9KfybUm6DiKSIiImmayqeDmrxnMm+seQOAgS8N5Iu6X6h4ioiISJqn8umAJv48kT5BfQB4u+rbfB7wuYqniIiIOASVTwfzzc/f0HdtXwDeqfoOn/l/puIpIiIiDkPl04F89dNX9FvbD4D/VPsPY/3HqniKiIiIQ1H5dBATdk+g/7r+AAyuPphP6nyi4ikiIiIOR+XTAXyx6wsGrh8IwJCXh/Bx7Y9VPEVERMQhqXymcZ/v/JxBwYMAGFZjGB/5faTiKSIiIg5L5TMNG7dzHO+EvAPA+6+8z4e+H6p4ioiIiENT+Uyjxu4Yy7sh7wLwwSsfMLLWSBVPERERcXguVgeQB33y4ycM2TgEgBE1RzC81nCLE4mIiIikDJXPNGbM9jEM3TQUgJG1RvJBzQ8sTiQiIiKScrTbPQ35aNtH8cVzVK1RKp4iIiKS7mjkM434cOuHfLDFLJujfUcz7JVhFicSERERSXkqn2nAqK2jGL7FPK7zY7+PGVJjiMWJRERERFKHyqfFRmwZwcitIwEYU3sMg18ebHEiERERkdSj8mkRwzAYsWUEo7aNAuDTOp/yn+r/sTiViIiISOpS+bSAYRgM3zKcD7d9CMBn/p/xTrV3LE4lIiIikvpUPu3MMAze3/w+H23/CIBx/uN4u9rbFqcSERERsQ+VTzsyDIP/2/R/fPzjxwCMDxjPwKoDLU4lIiIiYj8qn3ZiGAZDNw7lkx2fAPBF3S8Y8NIAa0OJiIiI2JnKpx0YhsHgDYMZu3MsAF/W+5K3qrxlcSoRERER+1P5TGWGYfDehvf4bOdnAHxd/2v6vtjX4lQiIiIi1lD5TEWGYfBuyLt8vutzAL6p/w1vvvimxalERERErKPymUoMw+Dt4Lf5YvcXAExqMIk3Kr9hcSoRERERa6l8pgLDMBi0fhATfpoAwOSGk+ldqbe1oURERETSAJXPFGYYBgPWDeCrn78C4NtG3/Kaz2sWpxIRERFJG1Q+U5BhGPRf15+vf/4agO8afcerPq9anEpEREQk7VD5TCGGYdBvbT8m7pmIDRvfN/6eni/0tDqWiIiISJqi8pkC4ow4+gb1ZfLeydiwMbXJVHo838PqWCIiIiJpjsrnE4oz4nhzzZtM2TcFGzamN51Ot4rdrI4lIiIikiapfD6BOCOOPmv68O2+b7Fh44emP9C1YlerY4mIiIikWSqfyRRnxNF7dW++/+V7bNiY2WwmnSt0tjqWiIiISJqm8pkMcUYcr696nan7p+Jkc2Jms5l0Kt/J6lgiIiIiaZ7KZxLFGXG8uvJVph+YjpPNiVnNZtGxfEerY4mIiIg4BJXPJIiNi6XXql7MODADJ5sTc5rPoX259lbHEhEREXEYKp+JFBsXS8+VPZn560ycbE7MbTGXdmXbWR1LRERExKGofCZCbFwsPVb2YNavs3C2OTO3xVzalm1rdSwRERERh6Py+RixcbF0W9GNOb/NwdnmzPyW82n9XGurY4mIiIg4JKfkPGnSpEkUL14cDw8PfHx82L59+yMfv3XrVnx8fPDw8KBEiRJMmTIlWWHtLTYulq7Lu8YXzwWtFqh4ioiIiDyBJJfPwMBABgwYwLBhw9i/fz81atSgfv36nD59OsHH//XXXzRo0IAaNWqwf/9+hg4dyltvvcWSJUueOHxq6x3Um7kH5+Li5EJgq0BaPdvK6kgiIiIiDi3J5XP8+PH07NmTXr16UaZMGSZMmEDhwoWZPHlygo+fMmUKRYoUYcKECZQpU4ZevXrRo0cPxo0b98ThU9vio4twcXJhYauFtHy2pdVxRERERBxeko75jIqKYt++fQwePPi+5QEBAezcuTPB5+zatYuAgID7ltWtW5dp06YRHR2Nq6vrA8+JjIwkMjIy/n5oaCgA0dHRREdHJyVykt2JjAE8AXBxcmVBi1k0erpRqq9XUtbd7aXt5pi0/RyftqHj0zZ0fPbeholdT5LK55UrV4iNjSVv3rz3Lc+bNy8XLlxI8DkXLlxI8PExMTFcuXKF/PnzP/CcMWPGMHLkyAeWBwcH4+XllZTISXb02mmgHwADigzA5YQLQSeCUnWdknpCQkKsjiBPQNvP8WkbOj5tQ8dnr20YHh6eqMcl62x3m812333DMB5Y9rjHJ7T8riFDhjBo0KD4+6GhoRQuXJiAgACyZMmSnMiJVt+AkuXXsfuX3Yzo8B/c3B4cmZW0Lzo6mpCQEPz9/RMcXZe0TdvP8WkbOj5tQ8dn7214d0/14ySpfObKlQtnZ+cHRjkvXbr0wOjmXfny5Uvw8S4uLuTMmTPB57i7u+Pu7v7AcldXV7v88JqUr43L2Ujc3OyzPkk99vrMSOrQ9nN82oaOT9vQ8dlrGyZ2HUk64cjNzQ0fH58Hhm9DQkKoVq1ags+pWrXqA48PDg6mUqVKaeLDbBhG/EisiIiIiKSuJJ/tPmjQIKZOncr06dM5evQoAwcO5PTp0/Tu3Rswd5l36dIl/vG9e/fm77//ZtCgQRw9epTp06czbdo03nnnnZR7F0/oUYcMiIiIiEjKSfIxn23btuXq1auMGjWK8+fPU7ZsWYKCgihatCgA58+fv2/Oz+LFixMUFMTAgQOZOHEiBQoU4KuvvqJly7QxdZGKp4iIiIj9JOuEoz59+tCnT58E/27GjBkPLKtZsya//PJLclYlIiIiIulIsi6vKSIiIiKSHCqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3LlYHSAzDMAAIDQ21y/qio6MJDw8nNDQUV1dXu6xTUpa2oWPT9nN82oaOT9vQ8dl7G97taXd728M4RPm8desWAIULF7Y4iYiIiIg8yq1bt8iaNetD/95mPK6epgFxcXGcO3eOzJkzY7PZUn19oaGhFC5cmDNnzpAlS5ZUX5+kPG1Dx6bt5/i0DR2ftqHjs/c2NAyDW7duUaBAAZycHn5kp0OMfDo5OVGoUCG7rzdLliz6wjk4bUPHpu3n+LQNHZ+2oeOz5zZ81IjnXTrhSERERETsRuVTREREROxG5TMB7u7uDB8+HHd3d6ujSDJpGzo2bT/Hp23o+LQNHV9a3YYOccKRiIiIiKQPGvkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbvJsOVz0qRJFC9eHA8PD3x8fNi+ffsjH79161Z8fHzw8PCgRIkSTJkyxU5J5WGSsg2XLl2Kv78/uXPnJkuWLFStWpX169fbMa38r6R+B+/asWMHLi4uVKxYMXUDymMldRtGRkYybNgwihYtiru7O0899RTTp0+3U1pJSFK34dy5c6lQoQJeXl7kz5+f7t27c/XqVTullXtt27aNxo0bU6BAAWw2G8uXL3/sc9JMlzEyoAULFhiurq7G999////t3FFIU20cBvC/cxvZIKEiGw4KQTODohqzJiGELCiQLiKhCIOCRkSrqFgUmRBERUKGdRFiNxqSIXRh4S5KZkWhTYgWGM6CURYrhJVFqc930Te/5vaZ59TeDfb8YBe+vmPPeDj639l2EAwG4fF4YLFY8ObNm6T7Q6EQ5s6dC4/Hg2AwiOvXr8NkMqGjo0NxcorR2qHH48H58+fx9OlTDA4O4sSJEzCZTHj27Jni5ARo7y9mdHQURUVFcLlcWLVqlZqwlJSeDqurq1FeXg6fz4fh4WE8efIEDx8+VJiafqW1Q7/fD4PBgMuXLyMUCsHv92PFihXYunWr4uQEAF1dXTh58iRu374NEUFnZ+eM+zNplsnK4dPhcMDtdsetlZaWwuv1Jt1//PhxlJaWxq3t27cP69atS1lGmpnWDpMpKytDfX39345Gs6C3v5qaGpw6dQp1dXUcPtNMa4d3795Ffn4+Pn78qCIezYLWDi9evIiioqK4tcbGRthstpRlpNmZzfCZSbNM1r3t/v37d+nv7xeXyxW37nK55NGjR0nv8/jx44T9mzZtkr6+Pvnx40fKslJyejqcbnJyUqLRqMyfPz8VEWkGevtraWmRoaEhqaurS3VE+g09Hd65c0fsdrtcuHBBCgsLpaSkRI4ePSpfv35VEZmm0dOh0+mUcDgsXV1dAkDev38vHR0dsmXLFhWR6Q9l0ixjVPpoGSASicjExIQUFBTErRcUFMjIyEjS+4yMjCTdPz4+LpFIRKxWa8ryUiI9HU536dIl+fLli2zfvj0VEWkGevp79eqVeL1e8fv9YjRm3Z+tjKOnw1AoJL29vTJnzhzp7OyUSCQi+/fvl0+fPvFzn2mgp0On0ymtra1SU1Mj3759k/HxcamurpYrV66oiEx/KJNmmaw78xmTk5MT9zOAhLXf7U+2Tupo7TDm5s2bcubMGWlvb5dFixalKh79xmz7m5iYkB07dkh9fb2UlJSoikezoOUYnJyclJycHGltbRWHwyGbN2+WhoYGuXHjBs9+ppGWDoPBoBw8eFBOnz4t/f39cu/ePRkeHha3260iKv0FmTLLZN0phIULF0pubm7CK7sPHz4kvCKIWbx4cdL9RqNRFixYkLKslJyeDmPa29tlz549cuvWLamqqkplTPofWvuLRqPS19cngUBADhw4ICI/BxkAYjQapbu7WzZu3KgkO/2k5xi0Wq1SWFgo+fn5U2vLly8XABIOh6W4uDilmSmeng7PnTsnFRUVcuzYMRERWblypVgsFtmwYYOcPXuW7wJmuEyaZbLuzKfZbJa1a9eKz+eLW/f5fOJ0OpPeZ/369Qn7u7u7xW63i8lkSllWSk5PhyI/z3ju3r1b2tra+BmlNNLa37x58+T58+cyMDAwdXO73bJs2TIZGBiQ8vJyVdHpX3qOwYqKCnn79q18/vx5am1wcFAMBoPYbLaU5qVEejocGxsTgyF+bMjNzRWR/86gUebKqFlG+VecMkDs8hLNzc0IBoM4dOgQLBYLXr9+DQDwer3YtWvX1P7Y5QkOHz6MYDCI5uZmXmopzbR22NbWBqPRiKamJrx7927qNjo6mq6nkNW09jcdv+2eflo7jEajsNls2LZtG168eIGenh4UFxdj79696XoKWU9rhy0tLTAajbh69SqGhobQ29sLu90Oh8ORrqeQ1aLRKAKBAAKBAEQEDQ0NCAQCU5fKyuRZJiuHTwBoamrCkiVLYDabsWbNGvT09Ez9rra2FpWVlXH7Hzx4gNWrV8NsNmPp0qW4du2a4sQ0nZYOKysrISIJt9raWvXBCYD2Y/BXHD4zg9YOX758iaqqKuTl5cFms+HIkSMYGxtTnJp+pbXDxsZGlJWVIS8vD1arFTt37kQ4HFacmgDg/v37M/5fy+RZJgfguXIiIiIiUiPrPvNJREREROnD4ZOIiIiIlOHwSURERETKcPgkIiIiImU4fBIRERGRMhw+iYiIiEgZDp9EREREpAyHTyIiIiJShsMnERERESnD4ZOIiIiIlOHwSURERETKcPgkIiIiImX+AfrDs8zFfD+8AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp8AAAKqCAYAAAB8XzUWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAACH3ElEQVR4nOzdd3hTZePG8W86aCllj7KXIqBMiyIgQoGWvfcqU0UEEdRXxk8ZIigqojIcgGwoexZo2Sh7KQIyVZBVdktL9/n9cV6qvKy2tDlNe3+uK5dNmuTcyZOU2zOeYzMMw0BERERExA6crA4gIiIiIhmHyqeIiIiI2I3Kp4iIiIjYjcqniIiIiNiNyqeIiIiI2I3Kp4iIiIjYjcqniIiIiNiNyqeIiIiI2I3Kp4iIiIjYjcqniIiIiNiNyqeIiIiI2I3Kp9jF7t27admyJUWLFsXNzQ0vLy+qVavGO++8k+TnmjFjBjabjT///NOuj5WkGTVqFM8++yzx8fFJfuy0adMoVKgQ4eHhKZJlx44djBgxgps3b6bI8yX2+a38vKXWa37U844YMQKbzcbVq1dTdJlJ8STveVLyp/Znyqpl2VNYWBj/+c9/8PPzI2/evNhsNkaMGGF1LLEDlU9JdWvWrKF69eqEhoYybtw4goKC+Oqrr6hRowYBAQF2zdK4cWN27txJgQIF7LrcjObChQuMGzeOUaNG4eSU9D8z3bp1I0uWLIwbNy5F8uzYsYORI0emavl80PNb+XlLrdec2u/lk7LXe27P9yGtv+fJde3aNb7//nuioqJo0aKF1XHEjlysDiDp37hx4yhRogTr16/HxeWfj1yHDh1SrFwkVt68ecmbN69dl5kRffXVV+TIkYNWrVol6/EuLi68/vrrfPTRR7z//vt4eHikcMKUERER8chs+rzZz92x0HvuOIoVK8aNGzcS1jZPnTrV6khiJ1rzKanu2rVr5MmT557iedf/rhX76aefqFu3LlmzZsXDw4Pq1auzZs2aRz7/8uXLsdlsbNy48b7fTZkyBZvNxq+//grcv0nu7ma2I0eO0LFjR7Jnz46Xlxc9e/bk1q1b9z3fihUrqFChAm5ubpQsWZKvvvoq4Tke5+LFi3h6etKhQ4d7bl+9ejWurq4MGzbssc+RXL///jsdO3bEy8sLNzc3ihYtir+/P1FRUQn3Sex7f+XKFV577TWKFCmCm5sbefPmpUaNGmzYsAGA6Ohopk2bRqdOne4b36S8B507dyY0NJQFCxY88rU9Ls+IESN47733AChRogQ2mw2bzcaWLVsAOHXqFD169KBUqVJ4eHhQqFAhmjZtyuHDh+9Zzt1xPnDgAG3atCFnzpw89dRTj3z+B20CTspnLrmft8e9Zkjedy0xzwtw+fLlx762kydP0qlTJ/Lly4ebmxtly5Zl0qRJj1z+v3M8aCzgwZvdk/o+Pi5/Yt+Hx0nMZy85y7Lyb01S3H0tkgEZIqmsd+/eBmD079/f2LVrlxEdHf3A+23ZssVwdXU1vL29jYCAAGP58uWGn5+fYbPZjAULFiTc78cffzQA448//jAMwzBiYmKMfPnyGZ07d77vOV988UXj+eeff+hjhw8fbgBG6dKljQ8//NAIDg42xo8fb7i5uRk9evS457nWrl1rODk5GbVr1zaWLVtmLFq0yKhatapRvHhxI7FfpZEjRxo2m83Yt2+fYRiGsXnzZsPd3d3o37//A+8fHx9vxMTEJOryMIcOHTI8PT2N4sWLG99++62xceNGY86cOUa7du2M0NBQwzAS/94bhmHUr1/fyJs3r/H9998bW7ZsMZYvX258+OGHCffbtm2bARiBgYFP/B6ULVvWaNWq1SPf08flOXfunNG/f38DMJYuXWrs3LnT2Llzp3Hr1i3DMAxj69atxjvvvGMsXrzY2Lp1q7Fs2TKjRYsWRubMmY3ff/89YTl3PyvFihUz3n//fSM4ONhYvnz5I5//fz9v/36ex33mnuTz9rjXnJTxTsrzJva1HTlyxMiePbtRvnx5Y9asWUZQUJDxzjvvGE5OTsaIESMe+doeNRaGcf93PCnvY2LzP+59SKzEfPaSu6yk/q1JrJT4m/QgV65cMQBj+PDhT5RPHIPKp6S6q1evGi+//LIBGIDh6upqVK9e3Rg7dqwRFhaWcL+XXnrJyJcv3z23xcbGGuXKlTMKFy5sxMfHG4Zx/z8uhmEYgwYNMjJnzmzcvHkz4bajR48agPHNN98k3Paw8jlu3Lh7Mvft29dwd3dPWKZhGMYLL7xgFClSxIiKikq4LSwszMidO3eiy2d4eLhRsGBBo27dusaePXuMrFmzGj169LhnOf+2efPmhPftcZd/vx//VqdOHSNHjhxGSEjIQ3Ml9r03DMPw9PQ03n777Yc+16effmoAxqVLl574PejcubPh5eX10GUlJo9hGMZnn332yPfo32JjY43o6GijVKlSxsCBAxNuv/tZ+fDDDxP9/I8qn4/7zD3p5+1Rrzkp452U503sa6tfv75RuHDh+wpUv379DHd3d+P69euPfG2PGov/fc+T8j4m5e9BUj5TifWwz15ylpWY71lISIjRqFEjw8PDwyhVqpQRFBT02OdNib9JD6LymbFos7ukuty5c7N9+3b27t3LJ598QvPmzTlx4gRDhgyhfPnyXL16lfDwcHbv3k2bNm3w9PRMeKyzszNdu3bl77//5vjx4w9dRs+ePblz5849BzD9+OOPuLm50alTp8dmbNas2T3XK1SoQGRkJCEhIQCEh4ezb98+WrRoQaZMmRLu5+npSdOmTRP9Xnh4eDB69Gg2btyIj48PDRs25Icffnjopidvb2/27t2bqEvBggXve3xERARbt26lXbt2D90PLqnv/YsvvsiMGTMYPXo0u3btIiYm5p7nu3DhAjabjTx58jzxe5AvXz5CQkKIjY194HMlJs/jxMbGMmbMGJ599lkyZcqEi4sLmTJl4uTJkxw7duy++7du3TpJz/8wj/rMpdTn7UGe9LuWGI96bZGRkWzcuJGWLVvi4eFBbGxswqVRo0ZERkaya9euRC3ncWOR3PfxcX8PUkpSP3tJkZjv2Ztvvkn+/Pm5cuUKn3/+Oe3atePatWuPfN4n/ZskAjrgSOyoSpUqVKlSBYCYmBjef/99vvzyS8aNG8dbb72FYRgPPEL17h+wR/1RfO6553jhhRf48ccfee2114iLi2POnDk0b96cXLlyPTZb7ty577nu5uYGwJ07dwC4ceMGhmHg5eV132MfdNujPPPMM4C5v9OMGTNwdnZ+6H09PT2pVKlSop73QfvU3rhxg7i4OAoXLvzQx919bYl97wMCAhg9ejRTp07lgw8+wNPTk5YtWzJu3Djy58/PnTt3cHV1feTrSux74O7ujmEYREZG3lOU/u1xeR5n0KBBTJo0iffff59atWqRM2dOnJyc6N27d8L4/1tKHUX9qM9cTExMin3e/ldSxzs5HvXa7hbNb775hm+++eaBj0/sVE2PG4vkfm8f9/cgpST1s5dUj/qe3b59m+XLl3P69Gk8PDxo1qwZFStWZMWKFfTs2fOhz/mkf5NEQAcciUVcXV0ZPnw4AL/99lvCH92LFy/ed98LFy4APHRN2l09evRg165dHDt2jHXr1nHx4kV69OiRInlz5syJzWbj8uXL9/3u0qVLiX6eQ4cO0aRJE2rUqMHt27eZPn36I++/detWXF1dE3V50LyGuXLlwtnZmb///vuRry0p732ePHmYMGECf/75J3/99Rdjx45l6dKldO/ePeH30dHRD52jMynvwfXr13Fzc3to8UxMnseZM2cO/v7+jBkzhvr16/Piiy9SpUqVhxYgexwgkVKft4c995N+1550+c7OznTv3v2ha8waNWqUqOd63Fik5vuYEpL62UuKx33PTp48iaenJ0WKFEm4rXz58hw5cuSRz/ukf5NEQOVT7OBB/8gBCZuVChYsSJYsWahatSpLly695//44+PjmTNnDoULF074v/iH6dixI+7u7syYMYMZM2ZQqFAh/Pz8UuQ1ZMmShSpVqrB8+XKio6MTbr99+zarV69O1HMcP36c+vXrU61aNTZv3kzz5s0ZMWLEA4+qv+tJN3FlzpyZWrVqsWjRoof+g/Yk733RokXp168fvr6+HDhwAIAyZcoAcPr06Sd+D86cOcOzzz770PcnMXng0WuubDZbwu/vWrNmDefPn0/0clN6zVhKfN4elulJv2tP+lo9PDzw8fHh4MGDVKhQIWGLyL8v/7vmMblS4n18mJQY88R+9pK6rMR8z27fvk22bNnueVy2bNm4ffv2I59bm90lJWiduKS6+vXrU7hwYZo2bUqZMmWIj4/n0KFDfPHFF3h6ejJgwAAAxo4di6+vLz4+Prz77rtkypSJyZMn89tvvzF//vzHruXIkSMHLVu2ZMaMGdy8eZN33303WROcP8yoUaNo3Lgx9evXZ8CAAcTFxfHZZ5/h6enJ9evXH/nYP//8k3r16lG6dGmWLFmCq6srn3zyCeXKlWPMmDF8+umnD3xc1qxZE3ZVSK7x48fz8ssvU7VqVQYPHszTTz/N5cuXWblyJd999x1Zs2ZN9Ht/69YtfHx86NSpE2XKlCFr1qzs3buXdevWJczpWbt2bQB27dpFhQoVkv0exMfHs2fPHnr16vXQ15aYPGCu0QFz/tFu3brh6upK6dKlyZo1K02aNGHGjBmUKVOGChUqsH//fj777LNH7qrwvx72/E/iST5vj8qUlPFO6vMm1ldffcXLL79MzZo1eeONNyhevDhhYWGcOnWKVatWsWnTpkQ/1+M86fv4MI96H2w2G7Vq1Xrs1EuJ/ewl5T1P7PfM09OT0NDQex4bGhr6yK0MkDJ/k/5t7dq1hIeHExYWBsDRo0dZvHgxAI0aNUqzc/zKE7LwYCfJIAICAoxOnToZpUqVMjw9PQ1XV1ejaNGiRteuXY2jR4/ec9/t27cbderUMbJkyWJkzpzZeOmll4xVq1bdc58HHUF8V1BQUMKRlidOnLjv9w872v3KlSuJWsayZcuM8uXLG5kyZTKKFi1qfPLJJ8Zbb71l5MyZ86Gv/8KFC8ZTTz1lPP/88/cd3fvqq68abm5uKXrE7IMcPXrUaNu2rZE7d+6E7N27dzciIyMT7pOY9z4yMtLo06ePUaFCBSNbtmxG5syZjdKlSxvDhw83wsPDE+5Xs2ZNo1GjRgnXk/MebNy40QCM/fv3P/R1JTaPYRjGkCFDjIIFCxpOTk4GYGzevNkwDMO4ceOG0atXLyNfvnyGh4eH8fLLLxvbt283atWqZdSqVSvh8Q/7rDzq+R91tHtiPnPJ+bwl5jUbRuLGO6nPm5TX9scffxg9e/Y0ChUqZLi6uhp58+Y1qlevbowePfqxy3/UWDzJ+5jUvwcPeh/CwsIMwOjQocNjX0diP3sPW9b/Ssr3LCwszHB1dTXOnTuXcJ/atWsb06ZNe2zulFSsWLEUOVpeHIvNMAzDHiVXJD2KiYmhUqVKFCpUiKCgIKvjpBlLliyhffv2/PXXXxQqVChZz9G1a1fOnDnDzz//nMLpHJc+bykjNd/HwMBAmjRpwi+//JKwxjKtatu2LdmzZ+ebb75h48aNdO3alZMnT6bqPr8ioM3uIknSq1cvfH19KVCgAJcuXeLbb7/l2LFjfPXVV1ZHS1NatWrFCy+8wNixY5k4cWKSH3/69GkCAgJSdPOrI9LnLWXY833cvHkzHTp0SPPFE2Dy5Ml069aN3LlzU6hQIQICAlQ8xS5UPkWSICwsjHfffZcrV67g6urK888/T2BgIPXq1bM6Wppis9n44YcfWLlyJfHx8Une9/bs2bNMnDiRl19+OZUSOgZ93lKGPd/Hzz77LMWfM7XkzZuXwMBAq2NIBqTN7iIiIiJiN5pqSURERETsRuVTREREROxG5VNERERE7MYhDjiKj4/nwoULCZP3ioiIiEjaYhgGYWFhFCxY8JEHmjpE+bxw4cI9558VERERkbTp3LlzjzxLnEOUz7unEDt37tx956JNDTExMQQFBeHn54erq2uqL09SnsbQsWn8HJ/G0PFpDB2fvccwNDSUIkWKPPZ0uw5RPu9uas+WLZvdyqeHhwfZsmXTF85BaQwdm8bP8WkMHZ/G0PFZNYaP20VSBxyJiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdJLl8btu2jaZNm1KwYEFsNhvLly9/7GO2bt2Kt7c37u7ulCxZkm+//TY5WUVERETEwSW5fIaHh1OxYkUmTpyYqPv/8ccfNGrUiJo1a3Lw4EGGDh3KW2+9xZIlS5IcVkREREQcm0tSH9CwYUMaNmyY6Pt/++23FC1alAkTJgBQtmxZ9u3bx+eff07r1q2TungREREReQzDgCs3I4iMdMYwrE5zrySXz6TauXMnfn5+99xWv359pk2bRkxMDK6urvc9JioqiqioqITroaGhAMTExBATE5O6gePjcapdm5dv3cLpiy+Id3YGZ2dwcvrnv3cvd3/n7Axubhju7uDmZl7c3f+5/Pt37u7g4QFZs2J4ekLWrP9cMmVK3deWgdz9nKT650VShcbP8WkMHZ/G0LH9cu4ULzxVFmhCSEgEOXKk/jIT+1lJ9fJ56dIlvLy87rnNy8uL2NhYrl69SoECBe57zNixYxk5cuR9twcFBeHh4ZFqWQFssbE027WL3Km6lAeLc3EhNnPm+y4xnp5EZ81q/tfTk5isWYm+e9t/f47x9MRwdrYgddoWHBxsdQR5Aho/x6cxdHwaQ8dzIeoCw46OAc4BELQxCM/MtlRfbkRERKLul+rlE8Bmu/cFG/9d//u/t981ZMgQBg0alHA9NDSUIkWK4OfnR7Zs2VIvKEB8PFELFvDLgQNULF8eZ4C4OIiPNy///dkWF/fP7bGxEB0NkZHmJSoKoqKw3b0eGfnP7+/cwRYRAbdvQ1gYhIWZ9wOcY2NxDgvDLSwsWdGNbNkgTx6MfPkgXz6M/PkhXz7w8jJvy5/f/K+XF3h6ptx7lgbFxMQQHByMr6/vA9euS9qm8XN8GkPHpzF0TMevHeeNuW9wI+ZWwm1+df3IkSP1x/DulurHSfXymT9/fi5dunTPbSEhIbi4uJA794PXL7q5ueHm5nbf7a6urnb5AsS0asVFd3cqN2qEiz2+cLGxZhH9VyFNuISGwo0bcP26ebl27Z+f715u3gTAFhoKoaHYzpx5/DI9PCB/fihc2LwUKXL/f/PmhYf8D4KjsNdnRlKHxs/xaQwdn8bQcRy/ehy/uX5cvH2R5/K+yJH/3m6vMUzsMlK9fFarVo1Vq1bdc1tQUBBVqlTRh/kuFxfImdO8JEdcnFlAr12DK1fg8mXzcunS/T9fugR37kBEBJw5Y14eJlOmewtp0aJQsqR5KVHCvN3FLivPRURE5BF+v/o7PjN9uHT7EhW8KrCi1WpKDLQ61YMluTncvn2bU6dOJVz/448/OHToELly5aJo0aIMGTKE8+fPM2vWLAD69OnDxIkTGTRoEK+++io7d+5k2rRpzJ8/P+VeRUbn7Ay5c5uXZ5559H0Nw1zDevkyXLwI58/D33/DuXP3/vfSJXNXgUcVVGfnfwppiRL3FtOSJc08Dr7mVEREJK07duUYPjN9uBx+mYpeFdngv4HMRh6rYz1Uksvnvn378PHxSbh+d9/Mbt26MWPGDC5evMjZs2cTfl+iRAkCAwMZOHAgkyZNomDBgnz99deaZskqNts/R9c//fTD7xcdbZbTf5fSv/76p4z++ae5b+sff5iXB8mRA0qXvvfyzDNQqpR51L+IiIg8kaNXjuIz04eQ8BAq5a/Ehq4byO2Rm/Bwq5M9XJLLZ+3atRMOGHqQGTNm3HdbrVq1OHDgQFIXJVbKlAmKFTMvDxIfb5bTM2fM8nm3lN69fuGCuSvA7t3m5d9sNvN575bR0qWhbFkoV848QEpEREQe60jIEerMqkNIeAiV81cmuGswuT2smK8nabTDniSPkxMUKmReata8//cREXDqFBw/fv8lNNRcc/rnn7B+/b2Py5vXLKF3L889Z17sMUGZiIiIg/gt5DfqzKzDlYgrVM5fmQ3+G8iVOZfVsRJF5VNSh4cHVKhgXv7NMCAkxCyhJ078U0iPHYPTp80DpjZvNi//VrjwvaW0YkV49llNzC8iIhnO4cuHqTOrDlcjruJdwJugrkEOUzxB5VPszWYz5xn18oJXXrn3dxERZgn97bd7L3///c9l3bp/7p8pk1lEK1f+51KhQrqfw1RERDKuXy//St1ZdbkacZUqBasQ1CWInJmTOVuORVQ+Je3w8ABvb/PybzdvwpEjZhE9cgR+/RUOHYJbt+DAAfNyl80GzzyDc8WKPO3uji1TJnjxRfPIexEREQf2y6VfqDurLtfuXOOFgi8Q1DWIHO45rI6VZCqfkvblyAE1apiXuwzDPLDp4MF7LxcvwvHjOB0/znMA/53yi6eeMkvo3UvlypA5swUvRkREJOkOXTpE3Vl1uX7nOi8WepH1XdY7ZPEElU9xVDbbP/OK/nvarsuX4eBB4vbt49LatRQMCcF26pS5P+np03B3fllnZ3MT/b8Ladmy5u0iIiJpyMGLB6k3ux7X71ynaqGqrO+ynuzu2a2OlWwqn5K+eHlBgwbE163LvvLladSoEa63b8O+fbBnj3nZvTuhpHLwIHz3nfnYLFmgShWoVs1cy1q9OuRynB24RUQk/Tlw8QD1ZtXjRuQNXir8Eus6r3Po4gkqn5IR5MwJvr7mBcxN9n///U8Z3bPHLKe3b8PWreblrmef/WeTf40a5uZ7nbVJRETsYP+F/dSbXY+bkTepVrga67qsI5tbNqtjPTGVT8l4bDbzvPRFivyzyT4uDn7/HXbtgp9/Ni8nTsDRo+blhx/M+3l5mWtEa9SAl1829x3VdE8iIpLC9l3Yh+9sX25G3qR6keqs7bw2XRRPUPkUMTk7/zOhfa9e5m1XrsCOHf+U0X37zM31y5aZFzAPWqpRA3x8oHZtc7O9yqiIiDyBvef34jvbl1tRt6hRpAZrO68lq1tWq2OlGJVPkYfJmxeaNzcvAJGRZgG9W0Z37IBr12DDBvMC5nRRNWqYRdTHxyyjrq6WvQQREXEse87vwXe2L6FRobxc9GUCOwWmq+IJKp8iiefubm5qf/ll87phmJvkN2+GLVvMy7VrEBxsXsA8iOluGa1dG154AVz0tRMRkfvt/ns3fnP8CI0KpWbRmgR2DsQzU/o7cYr+FRRJLpvtn031/fpBfLxZRrdsMQvp1q1mGQ0KMi8A2bKZa0TvHgBVqpQOYBIREXae20n9OfUJiw6jVrFarO60Ol0WT1D5FEk5Tk7/nHv+bhk9cuSftaJbtsD167BihXkBKFbsnyJat67OxCQikgHtOLeDBnMaEBYdRu3itVndcTVZMmWxOlaqUfkUSS1OTlC+vHnp3988ov7gwX82y//0E/z1F0ydal5sNnj++X/KaI0a4OZm9asQEZFU9PPZn2k4tyFh0WH4FPdhVcdV6bp4AjhZHUAkw3B2Ng9AGjIENm2CGzcgMBAGDjTXlhoG7N8Pn3zyz1rQ5s3NSfDPnbM6vYiIpLCfzv5Eg7nmGs86JeqwulP6XuN5l9Z8ilglSxZo2NC8AFy4YB41f3fN6OXLsHKleQFzDWqjRualWjUdRS8i4sC2/7WdhnMbEh4TTt0SdVnZcSUerh5Wx7ILrfkUSSsKFgR/f5g9Gy5eNDfRf/yxOam9kxMcPgyffgq1apnTQLVrBzNnmiVVREQcxra/tiUUT9+SvqzquCrDFE/Qmk+RtMlmg0qVzMvQof8cNR8YCOvWwdWrsGiReQFzc37TpuZm+goVdAS9iEgatfXPrTSa14iImAh8S/qyosMKMrtmtjqWXWnNp4gjyJ0bOnY014peumSeBvTDD83SCebk98OHm2W1ZEkYMMDcrzQmxtLYIiLyj81/bE4onvWfqp8hiyeofIo4HmdnqFoVRo6EvXvNMjp9urnWM3Nm+PNP+Ppr86AlLy/o0gUWL4awMKuTi4hkWJv+2ETjeY2JiImgwdMNWN5heYYsnqDyKeL4vLygRw9YvtzcHL9ihXk9Tx7ziPq5c6FtW/N6o0bm0fMXL1qdWkQkw9h4ZiNN5jXhTuwdGpVqxLL2y3B3cbc6lmVUPkXSEw8PaNbMXBN66RJs3w7vvmueSSk6GtauhT59oFAhqFkTvvpK0ziJiKSiDWc20GS+WTwbl2rM0nZLM3TxBJVPkfTL2dk8D/1nn8Hx4+apP8eONTfZG4Y5yf3bb0PRoubUTV98YW6yFxGRFBF0Ooim85sSGRtJk2easKTdEtxcdPIQlU+RjMBmg7JlYfBg82Clc+fMtZ41a5q/27XLXENaogS88II5pdOpU1anFhFxWOtPrafZ/GZExkbSrHQzFrddrOL5XyqfIhlR4cLw1luwbRucPw+TJoGPjzmf6L59ZkktVQoqVzbnGlURFRFJtHWn1tF8QXOi4qJoXro5i9ouUvH8F5VPkYyuQAHo29ecmuniRfOAJF9fc7P9oUPwf/9nFtEXXjA3zf/9t9WJRUTSrLUn1yYUzxZlWrCw7UIyOWeyOlaaovIpIv/Ilw9ee82c0P7yZZg2DerXN4vovn3mpvmiRc2zLH37rXl0vYiIABB4MpAWAS2IjoumVdlWLGyj4vkgKp8i8mC5c0PPnuYZlS5cMDfNv/yyebDStm3wxhvmWtNGjczJ7zWPqIhkYKtPrKZlQEui46JpXbY1C1ovwNXZ1epYaZLKp4g8Xr585qb57dvhr79g3Dhzf9DYWHP6Jn9/8z5t2sDSpRAVZXViERG7WXV8Fa0CWhEdF02bZ9swv/V8Fc9HUPkUkaQpWhTeew8OHIDffzdP6/nMMxAZCUuWQOvW/+xHunOnuaZURCSdWnl8Ja0XtiYmPoZ2z7VjXqt5Kp6PofIpIslXujSMGGGW0P37zX1CCxY0z6w0ZQpUr24W048+gj/+sDqtiEiKWvH7CtosbENMfAwdynVgbqu5Kp6JoPIpIk/OZoPnnzcntD971jxgqUsX84xLp07Bhx9CyZLwyiswdSrcumV1YhGRJ7Ls2DLaLDKLZ8dyHZndcjYuTi5Wx3IIKp8ikrKcnc2pmmbPNo+YnzkT6tY1C+r27fDqq5A/P3ToAGvWmPuNiog4kKXHltJucTti42PpVL4Ts1rOUvFMApVPEUk9np7mwUgbNphrRD/5xDzTUmQkBARAkyZQpIg5qf2JE1anFRF5rCVHl9BukVk8u1TowqwWKp5JpfIpIvZRuDC8/z4cOWLOGfrWW5AnD1y6ZJ7Os3Rpc7P8jBkQHm51WhGR+yw6soj2i9sTZ8TRtUJXZjSfgbOTs9WxHI7Kp4jYl80G3t7mueXPn4fFi825Qp2czM3yPXrgUqQIFSdNwrZ7t46WF5E0YeGRhXRc0pE4Iw7/iv782PxHFc9kUvkUEetkymROzbRmjTl/6Mcfw1NPYbt9m+LBwbjUrAnlypmn9QwJsTqtiGRQAb8F0GlJJ+KMOLpX6s70ZtNVPJ+AyqeIpA2FC8PQoXDiBLEbNnCudm2MzJnh6FFzCqdChcyiGhQE8fFWpxWRDGLBbwvotNQsnj0q9WBas2kqnk9I5VNE0hYnJ4xXXuHA228Te/aseQ75F180j4pfutQ813ypUubBS5cvW51WRNKxeYfn0XlpZ+KNeHpW6snUZlNxsqk6PSm9gyKSdmXPDq+/Drt3w6+/Qv/+5m1nzsCQIeaR8u3bw+bN2jdURFLUnF/n0HVZV+KNeHpX7s0PzX5Q8UwhehdFxDGULw9ffw0XLsD06VC1KsTEwMKFUKcOlClj7ht67ZrVSUXEwc3+ZTbdlncj3ojntedf47um36l4piC9kyLiWDw8oEcP2LULDh6EPn3M+URPnPhn39AuXcwj57U2VESSaOahmQnF83Xv15nSZIqKZwrTuykijqtSJfMc8hcuwHffmaf4jIqCuXPNOUMrVDBv17yhIpIIMw7NoMeKHhgYvFHlDSY3nqzimQr0joqI48uaFV57Dfbvh717oVcvcw3pb7+Za0YLFYKBA83zzIuIPMD0g9PpuaInBgZ9q/RlUqNJKp6pRO+qiKQvVarA1KnmBPZffglPPw23bsGECeZR8o0aQWCgpmsSkQTTDkyj98reGBj0e6EfExtNxGazWR0r3VL5FJH0KUcOePttOH4c1q6Fxo3Nsyvd/fmZZ2D8eLhxw+qkImKhH/b/QO9VZvHs/2J/vm74tYpnKlP5FJH0zckJGjSA1avh5El45x2zmJ4+bf5cqJC5yf7XX61OKiJ29v3+73lt9WsADKg6gK8afKXiaQcqnyKScTz1FHz+ublJ/ocfzAOS7twxf65YEerWhVWrtEleJAP4dt+3vL76dQDervo2X9b/UsXTTlQ+RSTj8fCA3r3h0CFzSqZ27cDZGTZtgmbNzDlDJ02C27etTioiqWDK3im8seYNAAa9NIjx9cereNqRyqeIZFw2G7z8MgQEmGdN+s9/zE3yJ09Cv37mGZT+8x84d87qpCKSQibtmUTfwL4AvFPtHT73+1zF085UPkVEAIoWhU8/NYvmxInmkfE3b8Jnn0GJEtChgzmxvYg4rIl7JtJvbT8A3q32Lp/5fqbiaQGVTxGRf/P0hDffhN9/N/f/rFMH4uLMtaPVqpmXhQshNtbqpCKSBF/v/pr+a/sD8H6N9xnnO07F0yIqnyIiD+LkBE2awMaN5r6h3btDpkzm2s/27c01o19/rbMniTiACbsmMGDdAAAG1xjM2LpjVTwtpPIpIvI4FSvCjz/C2bMwfDjkzQt//gkDBpj7hX7wAYSEWJ1SRB7gy51fMnD9QACGvjyUMXXHqHhaTOVTRCSxvLxgxAj46y/49lvz7Ek3bsDo0eY+o336mAcriUiaMH7neAYFDQLg/2r+H6PrjFbxTANUPkVEkipzZnj9dXO/0CVLoGpViIqC776D0qWhdWsdnCRisc93fM47Qe8A8MErHzDKZ5SKZxqh8ikiklzOztCqFezcCdu2mfuIGgYsXWoemPTKK5q0XsQC434ex3vB7wEwvNZwFc80RuVTRORJ2WxQs6ZZNI8cgZ49wdXVnMC+WTMoVw5mzYKYGKuTiqR7n/70Ke9veB+AEbVGMKL2CGsDyX1UPkVEUtKzz8K0aeYBSe+/D9mzw7Fj0K2beYT85MnmKT1FJMWN3T6WwRsHAzCy9kiG1x5ucSJ5EJVPEZHUULAgfPKJeYT8J59AvnzmgUpvvmlOWj9uHISGWp1SJN0Ys30MQzcNBeAjn4/4sNaHFieSh1H5FBFJTdmymWtA//zTPHNSsWJw+bJ5W7Fi8OGHcPWq1SlFHNrobaMZtmkYAB/X+Zj/e+X/LE4kj6LyKSJiD5kzm2s9T56EmTOhTBnz9J0ffWSW0IED4e+/rU4p4nBGbR3FB5s/AGBMnTEMrTnU4kTyOCqfIiL25OoK/v7mgUlLloC3N0REwIQJULIkvPoqnD5tdUoRhzByy0iGbzH36/yk7icMqTnE4kSSGCqfIiJWcHIyp2nauxfWr4datcyj4adONecK7dYNTpywOqVImmQYBsM3D2fE1hEAjKs3jvdfft/aUJJoKp8iIlay2cDPD7ZsgZ9+goYNIS7OnJqpbFno0sWczF5EgP8Wzy3DGbVtFACf+X7GezXesziVJIXKp4hIWlGjBgQGwp495oT18fEwd645fVPHjuamepEMzDAMPtz8IR9t+wiAL/y+4N3q71qcSpJK5VNEJK154QVzwvr9+6F5c/OsSQsWQPny0K4dHD5sdUIRuzMMg//b9H+M3j4agPF+4xlUbZDFqSQ5VD5FRNKq55+H5cvh4EFz/1DDgEWLoEIF8/zxhw5ZnVDELgzDYOjGoYz5aQwAE+pPYGC1gRankuRS+RQRSesqVTKPjP/1V2jb1txPdOlSqFwZWrSAX36xOqFIqjEMgyEbh/DJz58A8FWDrxjw0gCLU8mTUPkUEXEU5cvDwoXmZvcOHcwSumKFWU7btoWjR61OKJKiDMPg/Q3v8+nPnwLwTcNveKvqWxankiflYnUAERFJoueeg/nzzbMjjRoFAQGweDEsWUJ8+45cfWskPPU0Hh5mP7VCTAxERjoTHm5ObSqOx8oxNAwIDzcYuXUEU458Bk4wseFE3nzxTfsGkVSh8iki4qjKljVL6NChMHw4LFvG1QVBeC2Ya3UywBVoYnUIeSJWj6ENGAnvTmZyu1G88cIbFmaRlKTN7iIijq58eXMf0P37oZ6f1WlEUtSnvp+peKYzWvMpIpJePP88HsvmQlbz6mXykoUIcM0EPXvCe+9B/vx2iRITE8P69eupX78+rtru7pCsGMO7+3hO/vlH+PwKAH2rd7fLssV+VD5FRNKRf+/jmSVoBVnGDDPPnvTdeJg5Gd58E4YMgdy5UzVHTAy4u8eRJYv2+XRU9h5DwzAYsG4Ak3/5BjJ5JNxu1X7Lknq02V1EJL2qXh02b4aNG82fIyPhiy+gZEn46CO4fdvqhCKAWTz7r+3PN3u+wYaNSY0mWx1JUpHKp4hIelenjnne+MBAc1qm0FDzSPmnnoKvv4aoKKsTSgZmGAb9Avsxae8kbNiY2mwq3Sp1szqWpCKVTxGRjMBmg4YNzYOS5s+Hp5+GkBAYMABKl4aZMyEuzuqUksHEG/G8Gfgmk/dNxoaN6c2n07NyT6tjSSpT+RQRyUicnMwJ6o8ehe++g4IF4a+/oHt387Sdy5aZkyyKpLJ4I56+a/oyZd8UbNj4sfmPdK/U3epYYgcqnyIiGZGrK7z2Gpw6BePGQc6cZiFt1Qpeegk2bbI6oaRj8UY8fVb34bv932HDxswWM7WpPQNR+RQRycgyZzanYDpzxpys3sMD9uyBunXBzw8OHrQ6oaQz8UY8r696nR8O/ICTzYlZLWfRtWJXq2OJHal8iogI5MgBH38Mp09Dv37mmtHgYHj+eeja1dw0L/KE4o14Xl35KlMPTjWLZ4tZdKnQxepYYmcqnyIi8o/8+eGbb+D336FjR/O2OXPgmWfMNaQ3blibTxxWvBFP75W9mX5oOk42J+a0nEPnCp2tjiUWUPkUEZH7lSwJ8+bBvn3g4wPR0fD55+btn39uzhkqkkhx8XH0WtmLHw/9iLPNmXmt5tGxfEerY4lFVD5FROThvL3NSeoDA6FcObh501wDWrq0uUY0Pt7qhJLGxcXH0XNlT2YcmmEWz9bzaF+uvdWxxEIqnyIi8mh35wg9dAh+/BEKF4azZ819Qb29zX1DRR4gLj6OHit6MOuXWTjbnJnfej7tnmtndSyxmMqniIgkjrOzOR/oiRPwySeQLZtZSP38oH59+OUXqxNKGhIXH0e35d2Y/etsXJxcCGgTQNvn2lodS9IAlU8REUmazJnh/ffNI+Pffts8Mj4oCCpXht694eJFqxOKxWLjY/Ff7s/cw3MTimfrZ1tbHUvSCJVPERFJnjx54MsvzSPj27c3z4w0bRqUKoXTmDE465zxGVJsfCxdl3Vl3uF5uDi5sLDNQlqVbWV1LElDVD5FROTJlCwJCxbAjh1QtSqEh+M8YgR1+/bFNneuDkrKQGLjY+mytAsLfluAq5Mri9supmXZllbHkjRG5VNERFJGtWqwcyfMn49RtCiZr13DpUcPs5Bu3251OkllsfGxdF7amYAjAWbxbLeY5mWaWx1L0iCVTxERSTk2G3ToQOzhwxzt2hUja1ZzrtBXXoE2bcz9RCXdiYmLodOSTiw8shBXJ1eWtFtCs9LNrI4laZTKp4iIpLzMmTnZujWxR4/C66+DkxMsWQJly8K775rzhUq6EBMXQ8clHVl0dBGZnDOxtP1SmpZuanUsScNUPkVEJPV4ecG335pTMvn6QkwMfPEFPP20eXtcnNUJ5QnExMXQYUkHlhxbQibnTCxrv4wmzzSxOpakcSqfIiKS+sqXh/XrzTMllS0L167BG2/A88/Dli1Wp5NkiI6Lpv3i9iw9thQ3ZzeWt19Oo1KNrI4lDkDlU0RE7OPumZJ+/RW+/hpy5DB/9vGBtm3hzz+tTiiJFB0XTbtF7Vj2+zKzeHZYTsNSDa2OJQ5C5VNEROzLxQX694eTJ821n05OsHixuUb0ww8hPNzqhPII0XHRtF3UlhXHV+Dm7MaKDito8HQDq2OJA1H5FBERa+TJA5Mnw8GDULs2REbCRx9B6dIwb545ab2kKVGxUbRZ2IaVx1fi7uLOyo4rqf90fatjiYNR+RQREWtVqACbNplHwxcvDufPQ+fO8PLLsH+/1enkv6Jio2i9sDWrTqzC3cWdVR1X4feUn9WxxAGpfIqIiPVsNmjVCo4ehdGjwcPDPGPSCy9Ar15w+bLVCTO0yNhIWi1sxZqTa8jskpnVHVdTr2Q9q2OJg0pW+Zw8eTIlSpTA3d0db29vtj/mzBVz586lYsWKeHh4UKBAAXr06MG1a9eSFVhERNKxzJlh2DA4ccJc+2kYMH06PPMMfPUVxMZanTDDiYyNpFVAKwJPBprFs9Nq6pasa3UscWBJLp8BAQG8/fbbDBs2jIMHD1KzZk0aNmzI2bNnH3j/n376CX9/f3r16sWRI0dYtGgRe/fupXfv3k8cXkRE0qlChWDOHPj5Z3M6ptBQePttqFwZtm61Ol2GER0fTdvFbVl7ai0erh4Edg6kTok6VscSB5fk8jl+/Hh69epF7969KVu2LBMmTKBIkSJMmTLlgffftWsXxYsX56233qJEiRK8/PLLvP766+zbt++Jw4uISDpXvTrs2WNOSJ8rF/z2m3lwUqdOcOGC1enStTsxdxjzxxjWn1lvFs9OgdQuXtvqWJIOuCTlztHR0ezfv5/Bgwffc7ufnx87dux44GOqV6/OsGHDCAwMpGHDhoSEhLB48WIaN2780OVERUURFRWVcD00NBSAmJgYYmJikhI5We4uwx7LktShMXRsGr/kM98y1//+HINVb2GKj2HPntC8OU4ffojT1KnY5s/HWLWK+GHDiO/fHzJlSpnlCGAWz5YLW3Io7BBZXLOwsv1KqheqbrfvZFr5HDsyK97DxH4+klQ+r169SlxcHF5eXvfc7uXlxaVLlx74mOrVqzN37lzat29PZGQksbGxNGvWjG+++eahyxk7diwjR4687/agoCA8PDySEvmJBAcH221Zkjo0ho5N45d0kZHOgHl6w/Xr1+Pubu3pK1N8DBs3Jnvp0lT4/ntynTiB85AhREyaxOFXX+VKxYopu6wMKio+ijFnxvDL7V9wd3JnaLGhhP0WRuBvgXbLkNY+x47o3+/hpk2b7PIeRkREJOp+NsNI/ERqFy5coFChQuzYsYNq1aol3P7xxx8ze/Zsfv/99/sec/ToUerVq8fAgQOpX78+Fy9e5L333uOFF15g2rRpD1zOg9Z8FilShKtXr5ItW7bExk22mJgYgoOD8fX1xdXVNdWXJylPY+jYNH7JFx4OOXOa79mNGzFkyWJNjlQfw/h4bLNn4zx0KLYrV8ybWrUibtw4KFo05ZeXQUTERNBqUSs2/bkJT1dPhhYbyoCWA+z+PUwrn2NH9u/3MCQkghw5Un8MQ0NDyZMnD7du3XpkX0vSms88efLg7Ox831rOkJCQ+9aG3jV27Fhq1KjBe++9B0CFChXIkiULNWvWZPTo0RQoUOC+x7i5ueHm5nbf7a6urnb9Ath7eZLyNIaOTeOXdP9+u8z3z7os/2RIpRC9e0ObNuZZkSZNwmnpUghcx9WBH8Mbb+CR0w2bLXUWnd4YBly5GU7XZd35+eomPN09Wd1+NTcP37Tke5jWPseO6P73MPXfxMQuI0nlM1OmTHh7exMcHEzLli0Tbg8ODqZ58+YPfExERAQuLvcuxtnZGYAkrHQVERG5X44c5nnie/eGfv24uv0YXmPfhrFWB3NEWYBlZBlakvVd5vBC/hcIPGy/Te2ScST5aPdBgwYxdepUpk+fzrFjxxg4cCBnz56lT58+AAwZMgR/f/+E+zdt2pSlS5cyZcoUzpw5w88//8xbb73Fiy++SMGCBVPulYiISMZVoYI5BdPESVYncXgBbQKoXqS61TEkHUvSmk+A9u3bc+3aNUaNGsXFixcpV64cgYGBFCtWDICLFy/eM+dn9+7dCQsLY+LEibzzzjvkyJGDOnXq8Omnn6bcqxAREbHZ8OjWDvqZVy+TjyyEQ9ZsMHw4vPoq/HfLm5huR9+m9cLW/HzqAHxu7jtbq9QLFqeS9C7J5ROgb9++9O3b94G/mzFjxn239e/fn/79+ydnUSIiIon27308s2xbR5aBr5nnh3/3DZg/FaZMMU/ZKdyOvk3bhY34+dJ2smUtQOh/b9d+spLadG53ERFJn55/HnbvhkmTIHt2s4RWrQp9+8KNG1ans1RYVBgN5zZk+9ntZHfLzqqOq6yOJBmIyqeIiKRfzs5m2fz9d+jSxTyse8oUKFMGZs82r2cwoVGhNJjbgJ/O/kQO9xxs8N+Ad0Fvq2NJBqLyKSIi6V/+/GbZ3LTJLJ4hIeDvDz4+cOyY1ensJjQqlAZzGrDj3A5yuudkQ9cNVClYxepYksGofIqISMbh4wO//AJjxkDmzOYR8hUrmgckRUZanS5V3Yq8Rf059dn5906zeGqNp1hE5VNERDKWTJlgyBA4cgQaNzZPgj1qlFlCN2+2Ol2quFs8d/29i1yZc7HRfyPPF3je6liSQal8iohIxlSiBKxaBQsXmpvlT5yAOnWge3e4etXqdCnmZuRN/Ob4sfv87oTiWblAZatjSQam8ikiIhmXzQZt25oHJL3xhnl95kxzv9BZsxz+gKSbkTfxm+3HnvN7yJ05N5v8N1EpfyWrY0kGp/IpIiKSPTtMngw//wzlysG1a9CtG9SrBydPWp0uWW7cuYHvbF/2XthL7sy52ei/kYr5K1odS0TlU0REJEG1anDgAIwdC+7u5tHx5cvD6NEQHW11ukS7fuc69WbXY9+FfeTxyMPmbptVPCXNUPkUERH5N1dXGDzYPCDJzw+iouCDD6BSJfjpJ6vTPdb1O9epN6seBy4eIK9HXjZ320x5r/JWxxJJoPIpIiLyICVLwrp1MHcu5Mtnzgdas6a5b+itW1ane6BrEdeoO6suBy8dJF+WfGzutply+cpZHUvkHsk6t7uIiEiGYLNBp07QoAG8/z5MnQrffkv8ilVc/WQqNGiAh4f150M3DDh39SptFrbhaPgh8mU1i+ezeZ+1NpjIA6h8ioiIPE6uXPDDD2YRfe01rp66iVe3Blan+h95gC3kHf4cm7stUvGUNEub3UVERBLLxwd+/RX69bc6yUMta79MxVPSNK35FBERSYrMmfEY+yFMNK9eJi9ZiACfOvD11+bk9XYSEh5Ck3lNOHr+D/j8CgAVizxjt+WLJIfKp4iISBL9ex/PLB8NJcvHQ2Hzaqi6CT76CAYMAGfnVM0QEh5C08V1OHrrCF45S3L5AdlE0iJtdhcREXkSAweam+Jr14aICHjnHXO+0F9/TbVFXr59GZ+ZPhy5coSCWQuyrsu6VFuWSEpT+RQREXlSpUqZE9L/8IN5tqS9e8Hb25wfNCoqRRd16fYlfGb6cPTKUQplLcSWblsolbtUii5DJDWpfIqIiKQEmw1694ajR6FVK4iNNc+M5O0Ne/akyCLuFs9jV49ROFthtnRX8RTHo/IpIiKSkgoWhCVLYNEiyJsXjhwhvmo1Qt4cQchfd7h9G8LDk3a5fRsOn7lMzW9a8XvI72bx7LaFp3M9bfWrFUkyHXAkIiKSGtq0MfcDHTCAq/OC8Jo8AiY/yRN6ATsoMLISW7ot4alcT6VITBF705pPERGR1JInj3l6zpmzU+wpl3dYruIpDk3lU0REJJV5tPrnbEiXycttsnC7eDluB27j9m0eejlx4QJPfVYR3s2b8PhnCxa34BWIpByVTxERkVR2z7ygy+aRpXAuMv95hPBGrQnv9z5GaNh9jzkfep4Gcxtw+sYpCufO88DnEnFE2udTRETEnnx94cgRrvYbhdfsz2EG5uU+hQBzrtDlJ85RZYjdEoqkKq35FBERsbds2eDzzxN99yLZi6RiGBH7UvkUERGxgIfHPz9f7jnE3A+ULBzPkZ1XOmah+LhyHDt/jtu3772viKNT+RQREbHAPfuBfj2WsJVTuZ4rmmduhrJ1fgS/nqxCmey5yJJF+3lK+qLyKSIiYrG/bv5FtTNDefb1WObVyAZA1h9mQoUKsH27xelEUpbKp4iIiMUazGnAnzf/pECBUtQKPApBQVCkCJw5A7VqweDBVkcUSTEqnyIiIhYwjH9+Pnf1Kk97VmRNmy3kcC5EeHVfwncdJrxrH8KNzIRPnPbAx4k4IpVPERERCxw5/8c/Vz6/wql3D/FMwYJ4emJeCmXHc/YUPAnHiysJd40YPBIiIy1ILJIyVD5FRETs7PT107QIaJG8B0+aCN7esG9fimYSsReVTxERETs6ff00tWbU4lLcrzw9pjqHT18mLOzhp9i8fRvCwuDyZbg8Yy158jjB0aPw0kswciTExFj9kkSSROVTRETEjurPqc/5sPM86/UsP/VfRrmSXnh6QpYsD794ekK+fJCvW0Ocfj8KbdtCXByMGAE1asDx41a/LJFE0+k1RUREUtm/DxK6dP0WZQp6s6r1GjxtXoSHJ/HJ3HPD9ABo2AYGDoS9RwivVg84d9+yRNIilU8REZFU9uu5k0Ap88rnV/gdeGrQkzyjDWj33wsQ/c9vIk78jefzhZ/kyUVSlTa7i4iIpKLfr/6e/IOLkqPWKzB7tlaBSpqlNZ8iIiKp5NiVY9SZVYcrxiXKflKLxe0WUzRv3hQ/XaZhQMRvp+HNfuQ58Af4+8Py5fDtt5A3b8ouTOQJqXyKiIikgqNXjlJnZh0uh1+mQoEKbPRfQh6PPKm2PM+XnoLdq2DcOBg+HJYuhZ9+gh9+gGbNUm25Ikmlze4iIiIp7OiVo/jM9OFy+GUq5a/EJv9NqVo8E7i4wNChsGcPPPcchIRA8+bQq5c5X5NIGqDyKSIikoJ+C/mN2jNqExIeQuX8ldnQdQO5PXLbN0TlyuYk9O++CzYbTJ8OlSrBjh32zSHyACqfIiIiKeS3kN+oM7MOVyKumMXT34LieZe7O3z2GWzZAkWLwpkzULMmfPihJqYXS6l8ioiIpIDDlw/jM9OHKxFX8C7gzQb/DeTKnMvqWPDKK/Drr9ClC8THw0cfmRPTnzhhdTLJoFQ+RUREntAvl37BZ6YPVyOuUqVgFYK7BqeN4nlX9uzm9EsLFkCOHLB3r7lp/vvvNSWT2J3Kp4iIyBM4fPkwdWfV5dqda7xQ8AWCuwaTM3NOq2M9WPv2cPgw1KkDERHw+uvmAUkhIVYnkwxE5VNEROQJNJrXiGt3rvFioRcJ6hpEDvccVkd6tMKFITgYvvgCMmWCVaugalWrU0kGonk+RUREkujfW6pv3IqkSvFaLGu5Ate47Ek/V7slnOD1QVDdF3r1IvzoHwm/MW6HQ5YsFmaT9E7lU0REJIl2/fErUMG88vkV9gGF+lmZKLnKA3vuuSWiel08AyZCxYrWRJJ0T5vdRUREkmD/hf20XtjK6hip58xpqFYNp88/N4+OF0lhWvMpIiKSSPsu7MN3ti+hTjep8mVjAlovIF/OrCl+rnZ7Mwzz+CNuXCfPkFqwbAnOQ4dSvXx586j44sWtjijpiMqniIhIIuw9vxff2b7cirpFjWI1WNt5AVndslodK8V4egL5csGSRTB9OsZbb5H38GEMb2+YNg1atLA6oqQT2uwuIiLyGHvO76He7HrcirpFzaI1Wdt5bboqnvew2aBXL2J37+ZmyZLYrl+Hli3NaZkc42gqSeNUPkVERB5h99+7zU3tUaG8UuwVAjsHpt/i+W+lS7Pt00+Je+cd8/r330OVKnDwoLW5xOGpfIqIiDzEznM7E4pnrWK1WNNpDZ6ZPK2OZTeGqyvxY8ea84IWKAC//27OCTp+vA5GkmRT+RQREXmAHed2UH9OfcKiw6hdvHaGK573qFfPPD988+YQEwPvvAMNG8LFi1YnEwek8ikiIvI/fj77c0Lx9Cnuw5pOa8iSKYNPvJ4nDyxbBlOmQObMEBQEFSrA6tVWJxMHo/IpIiLyLz+d/YkGcxtwO/o2dUrUYXWn1Xi4elgdK22w2aBPH9i3z5yE/upVaNoUBgyAqCir04mDUPkUERH5r+1/bafBHLN41itZj1UdV6l4Psizz8Lu3fD22+b1r7+Gl16C48ctjSWOQeVTREQE2PbXNhrObUh4TDi+JX1Z2WGliuejuLnBl1+am93z5IFDh8DbG2bMMGetF3kIlU8REcnwtv65NaF4+j3lx4oOK8jsmtnqWI6hcWP45Rfw8THnAe3RA7p0gdBQq5NJGqXyKSIiGdrmPzbTaF4jImIiaPB0AxXP5ChY0JyOafRocHaGefPg+efNfUNF/ofKp4iIZFib/thE43mNiYiJoOHTDVnWfhnuLu5Wx3JMzs4wbBhs2wZFi8Lp01C9OnzxheYElXuofIqISIa08cxGmsxrwp3YOzQq1Yil7ZeqeKaE6tXN/T9btzbnBH33XXPTfEiI1ckkjVD5FBGRDGfDmQ00mW8Wz8alGrO0nYpnisqZExYtgm+/BXd3WLfOnJppwwark0kaoPIpIiIZStDpIJrOb0pkbCRNn2nKknZLcHNxszpW+mOzweuvw9695tRMly6Bnx8MHQqxsVanEwupfIqISIax/tR6ms1vRmRsJM1KN2NR20UqnqmtXDmzgL7+ujkF09ixULs2nDtndTKxiMqniIhkCOtOraP5guZExUXRvHRzFU978vAwN8EHBEDWrPDzz1CpEqxZY3UysYDKp4iIpHuBJwMTimfLMi1Z2HYhmZwzWR0r42nXDg4eNCejv34dmjQxD0iKjrY6mdiRyqeIiKRra06soWVAS6LjomlVthUBbQJUPK301FPmms+33jKvf/EFvPIK/PmnpbHEflQ+RUQk3Vp9YjWtFrYiOi6a1mVbs6D1AlydXa2OJW5u8NVXsGwZ5Mhhnie+cmVYvtzqZGIHKp8iIpIuBZ4IpFWAWTzbPtuW+a3nq3imNS1amJvhq1aFmzehZUsYMACioqxOJqlI5VNERNKlTks7ERMfQ7vn2jG31VwVz7SqeHHYvt3c9xPg66+hbl1LI0nqcrE6gIiISEoxjH9+jo10pU2lbnxffyrRkS7okJakiYmByEhnwsPBNdV7uyuM+AxeqguvvUb4oeMJv/n3mEr6oPIpIiLpxqJDa4DG5pXPr7AYWGxlIIfmCjSx8zIbAGfvuSXircF4Thlp7icq6YI2u4uISLqw5OgSeq/qbXUMSWk/ToMaNeCPP6xOIilEaz5FRMThLT66mA6LOxDvHkfraW/wTaOJZPV0xmazOpnjiomJYf369dSvXx/X1N/ufg/DgIgIYONG8vSNh/37zaPhZ86E5s3tmkVSnsqniIg4tEVHFtFxSUfijDi6VurKj80n4uzkbHUshxcTA+7ucWTJYo99Pu/n6Ql0rAs1DkL79rBrl3l0/KBB8Mkn1oSSFKHN7iIi4rAWHlmYUDz9K/rzY/MfVTzTm6JFYetWs3QCjB8PtWrp3PAOTOVTREQcUsBvAXRa0ok4I47ulbozvdl0Fc/0KlMm80xIS5dC9uywc6e5GX7tWquTSTKofIqIiMOZf3g+nZaaxbNHpR5MbTpVxTMjaNkSDhyA55+Ha9egUSMYNgxiY61OJkmg8ikiIg5l7q9z6bKsC/FGPD0r9WRqMxXPDKVkSfPc8H37mtfHjAFfX7h40dpckmgqnyIi4jDm/DoH/+X+xBvx9K7cmx+a/YCTTf+UZTju7jBpEsyfbx6ZtGWLuRl+0yark0ki6BsrIiIOYdYvs/BfZhbPV59/le+afqfimdF16AD79kH58nD5srkGdOxYiI+3Opk8gr61IiKS5s08NJPuy7tjYPC69+t82+RbFU8xlS5tTsPUvbtZOocONecCvXHD6mTyEPrmiohImjbj0Ax6rOiBgUEf7z5MbjxZxVPu5eEB06fDDz+Yp+FcvRq8veHgQauTyQPo2ysiImnWjwd/pOeKnhgYvFHlDRVPeTibDXr3hh07oHhx83Sc1arBtGlWJ5P/oW+wiIikSdMOTKPnSrN4vvnCm0xqNAmbzpcpj/P88+Z0TE2aQFSUWUh79oQ7d6xOJv+l8ikiImnOD/t/oPeq3gD0f7E/3zT8RsVTEi9nTlixwpyGyckJfvzRXAt66pTVyQSVTxERSWO+3/89r61+DYC3XnyLrxp8peIpSefkBEOGQHAw5M0Lv/wCVaqYpVQspfIpIiJpxnf7vuP11a8DMKDqACY0mKDiKU+mTh3zwKPq1eHWLWjRAt5/X2dFspDKp4iIpAlT9k6hz5o+AAx8aSBf1v9SxVNSRqFC5kT0Awea18eNg3r1zLlBxe5UPkVExHKT9kyib6B5usR3qr3DF35fqHhKynJ1hfHjYeFC86xIW7eaByft2GF1sgxH5VNERCw1cc9E+q3tB8C71d7lM9/PVDwl9bRtC3v3QtmycOEC1K5tnqrTMKxOlmGofIqIiGW+3v01/df2B+A/1f/DON9xKp6S+sqUgT17zCIaEwP9+oG/P0REWJ0sQ1D5FBERS3y16ysGrBsAwOAag/mk3icqnmI/np4QEABffAHOzjBnjjkd0+nTVidL91Q+RUTE7r7c+SVvr38bgKEvD2VM3TEqnmJ/NhsMGgQbNkC+fPDrr+ZpOVevtjpZuqbyKSIidvXlzi8ZFDQIgGE1hzG6zmgVT7FW7dqwfz+89JI5HVPTpjB8OMTFWZ0sXVL5FBERu/lixxcJxfODVz7gI5+PVDwlbShc2DwC/s03zeujRpmn6Lx+3dpc6ZDKp4iI2MVnP3/Gu8HvAjC81nBG+YxS8ZS0JVMmmDgRZs4Ed3dYt87cDH/woNXJ0hWVTxERSXWf/vQp/9nwHwBG1BrBiNojrA0k8ij+/rBzJ5QsCX/+aZ4daeZMq1OlG8kqn5MnT6ZEiRK4u7vj7e3N9u3bH3n/qKgohg0bRrFixXBzc+Opp55i+vTpyQosIiKO5ZOfPmHwxsEAjKw9kuG1h1ucSCQRKlWCffugUSOIjITu3aF/f3NqJnkiSS6fAQEBvP322wwbNoyDBw9Ss2ZNGjZsyNmzZx/6mHbt2rFx40amTZvG8ePHmT9/PmXKlHmi4CIikvZ98vMnDNk4BICPfD7iw1ofWpxIJAly5oRVq+DD/35uJ06EunXh0iVrczk4l6Q+YPz48fTq1YvevXsDMGHCBNavX8+UKVMYO3bsffdft24dW7du5cyZM+TKlQuA4sWLP1lqERFJ8xZeWsi8Q/MAGO0zmmGvDLM4kUgyODnByJHmvp9dusD27ebPS5dC1apWp3NISSqf0dHR7N+/n8GDB99zu5+fHzsecm7UlStXUqVKFcaNG8fs2bPJkiULzZo146OPPiJz5swPfExUVBRRUVEJ10NDQwGIiYkhxg6ru+8uwx7LktShMXRsGr/kM98y1//+HGPZFsJRW0cx75JZPD+q/RH/qfYfjaeD0ffwfzRsCDt24NKmDbbjxzFeeYW4r7/G6NnT6mQPZMXfgsR+VpJUPq9evUpcXBxeXl733O7l5cWlh6yCPnPmDD/99BPu7u4sW7aMq1ev0rdvX65fv/7Q/T7Hjh3LyJEj77s9KCgIDw+PpER+IsHBwXZblqQOjaFj0/glXWSkM9AEgPXr1+Pubv95ChdcWsCCSwsA6FqgK+VvlicwMNDuOSRl6Ht4L5fhw6n89dcU3LULlz59+HPpUg6/+irxrq5WR7vHv/8WbNq0yS5/CyISeXpSm2EYRmKf9MKFCxQqVIgdO3ZQrVq1hNs//vhjZs+eze+//37fY/z8/Ni+fTuXLl0ie/bsACxdupQ2bdoQHh7+wLWfD1rzWaRIEa5evUq2bNkSGzfZYmJiCA4OxtfXF9c09mGSxNEYOjaNX/KFh0POnOZ7duNGDFmy2G/ZhmEwavsoPv7pYwD8C/gzpcsUjaGD0vfwEeLjcRo3Dqfhw7EZBvFVqxIXEAAFC1qdLMG//xaEhESQI0fqj2FoaCh58uTh1q1bj+xrSVrzmSdPHpydne9byxkSEnLf2tC7ChQoQKFChRKKJ0DZsmUxDIO///6bUqVK3fcYNzc33Nzc7rvd1dXVrl8Aey9PUp7G0LFp/JLu32+X+f7ZZ7mGYTB8y/CE4vlJnU8oc72MxjAd0Bg+xAcfQJUq0KkTTrt34/TSS7B4MdSoYXUy4EF/C1J/DBO7jCQd7Z4pUya8vb3vWwUfHBxM9erVH/iYGjVqcOHCBW7fvp1w24kTJ3BycqJw4cJJWbyIiKRBhmHw4eYP+WjbRwB87vs5g14aZHEqETto2BD27oVy5cwj4GvXhsmTIfEblTOkJE+1NGjQIKZOncr06dM5duwYAwcO5OzZs/Tp0weAIUOG4O/vn3D/Tp06kTt3bnr06MHRo0fZtm0b7733Hj179nzoAUciIuIYDMPg/zb9H6O3jwZgvN943qn+jsWpROzo6afNCenbtYPYWPP0nL16mXODygMleaql9u3bc+3aNUaNGsXFixcpV64cgYGBFCtWDICLFy/eM+enp6cnwcHB9O/fnypVqpA7d27atWvH6NGjU+5ViIiI3RmGwdCNQ/nk508A+LL+l7z90tvWhhKxgqcnLFhgboYfPBh+/BGOHDGnYypUyOp0aU6SyydA37596du37wN/N2PGjPtuK1OmjI6WExFJRwzDYMjGIXz686cAfNXgK96q+pbFqUQsZLPBe+9B5crmWtA9e8wyumSJeXpOSaBzu4uISJIYhsH7G95PKJ7fNPxGxVPkrnr1zNNy/ns/0KlTrU6Vpqh8iohIohmGwXvB7/HZjs8AmNhwIv1e7GdxKpE0pmRJcz/Q1q3N2d5ffdXcFzQ62upkaYLKp4iIJIphGLwb9C5f7PwCgEmNJvHmi29anEokjfL0hEWLYPRoc5P85Mng6wshIVYns5zKp4iIPJZhGAxaP4jxu8YDMKXxFPq+8OB9/0Xkv2w2GDYMVqyArFlh2zZzP9ADB6xOZimVTxEReSTDMBi4fiATdk8A4Lsm39GnSh9rQ4k4kqZNzQOQnnkGzp0zJ6KfN8/qVJZR+RQRkYcyDIMB6wbw1e6vAPi+yfe85v2axalEHFCZMrB7NzRqZM4B2rmzeXR8XOqfcz2tUfkUEZEHMgyD/mv7882eb7BhY2rTqbzq/arVsUQcV44csHKluSke4PPPzTJ6/bqlsexN5VNERO5jGAb9Avsxae8ks3g2m0qv53tZHUvE8Tk7mwchLVoEHh4QFAQvvghHj1qdzG5UPkVE5B7xRjxvBr7J5H2TsWFjWrNp9Kzc0+pYIulLmzbmdEzFi8Pp0/DSS7B6tdWp7ELlU0REEsQb8fRd05cp+6Zgw8aPzX+kR+UeVscSSZ8qVIC9e6FWLQgLg2bN4NNPwTCsTpaqVD5FRAQwi2ef1X34bv932LAxo8UMulXqZnUskfQtTx4IDoa+fc3SOXgwdOkCd+5YnSzVqHyKiAjxRjyvr3qdHw78gJPNiVktZ+Ff0d/qWCIZg6srTJoEU6aAi4s5DVPNmvD331YnSxUqnyIiGVy8Ec+rK19l6sGpZvFsMYsuFbpYHUsk4+nTBzZsgNy5Yf9+eOEF2LXL6lQpTuVTRCQDizfi6b2yN9MPTcfJ5sTslrPpXKGz1bFEMq5atcz9QMuXh0uXzOszZlidKkWpfIqIZFBx8XH0WtmLHw/9iJPNibmt5tKpfCerY4lIiRKwYwe0bAnR0dCjBwwaBLGxVidLESqfIiIZUFx8HD1X9mTGoRk425yZ12oeHcp1sDqWiNzl6QmLF8Pw4eb1L7+Exo3hxg1rc6UAlU8RkQwmLj6OHit6MOuXWTjbnJnfej7ty7W3OpaI/C8nJxgx4t4J6atWhePHrU72RFQ+RUQykLj4OLot78bsX2fjbHNmQZsFtH2urdWxRORR2rSBn3+GYsXg5EmzgAYFWZ0q2VQ+RUQyiNj4WPyX+zP38FxcnFwIaBNAm2fbWB1LRBKjUiXYswdq1IBbt6BhQ/j6a4eckF7lU0QkA4iNj6Xrsq7MOzwPFycXFrZZSOtnW1sdS0SSIl8+2LgRuneH+HgYMMCcnikmxupkSaLyKSKSzsXGx9JlaRcW/LYAFycXFrVdRMuyLa2OJSLJ4eYG06fD55+DzQbffw9+fnDtmtXJEk3lU0QkHYuJi6HTkk4EHAnA1cmVxW0X06JMC6tjiciTsNngnXdg1SrImhW2bIEXX4SjR61OligqnyIi6VRMXAydlnZi0dFFuDq5sqTdEpqXaW51LBFJKY0bw86d5rygZ87ASy9BYKDVqR5L5VNEJJ3qvrw7i48uJpNzJpa2X0rT0k2tjiQiKe2558wDkV55BcLCoGlTGD8+TR+IpPIpIpJOrTi+3Cye7ZbS5JkmVscRkdSSJw8EB0Pv3uaBSO+8A337Wp3qoVysDiAiIiknKjYayASAa1xOFjSdTu1CfoSH2zdHTAxERjoTHg6urvZdtqQMjaGjyQRffg+lKsHgwYTPXgxMAdLeSlCVTxGRdCI6LppOC3oDswCI+fRvWn1qVRpXQGtbHZvG0PHYgDf/e/lHxK0YcuZMO/8HofIpIpIORMVG0XZRW9af2ml1FBFJa9LYqmuVTxERBxcVG0WbRW1YfWI1mbK5M3vXZmqX8MHDw5yRxQoxMTGsX7+e+vXr45rG/uGTxNEYOjbDgFuXQ9nw08/kyVPP6jj3UPkUEXFgUbFRtF7YmjUn1+Du4s6qjquoV9LH6ljExIC7exxZsqS5lS6SSBpDx+fmlpkcOaJxSmOHl6exOCIikliRsZG0WtiKNSfXkNklM6s7rqZeybS1hkNE5H9pzaeIiAOKjI2kZUBL1p1aZxbPTqupU6KO1bFERB5L5VNExMFExkbSYkEL1p9eT2aXzKzptAafEtZvahcRSQyVTxERB3In5g4tAloQdDoID1cP1nRaQ+3ita2OJSKSaCqfIiIO4k7MHZovaE7wmWCyuGYhsHMgrxR7xepYIiJJovIpIuIAImIiaL6gORvObCCLaxbWdl5LzWI1rY4lIpJkKp8iImlcREwETec3ZdMfm/DM5Mnazmt5uejLVscSEUkWlU8RkTQsPDqcpvObsvnPzXhm8mRd53XUKFrD6lgiIsmm8ikikkaFR4fTZH4Ttvy5hayZsrKuyzqqF6ludSwRkSei8ikikgbdjr5N43mN2fbXNrJmysr6LuupVqSa1bFERJ6YyqeISBpzO/o2jeY2YvvZ7WRzy8b6Lut5qfBLVscSEUkRKp8iImlIWFQYjeY14qezP5HNLRtBXYKoWriq1bFERFKMyqeISBoRFhVGw7kN+fncz2R3y05Q1yBeLPSi1bFERFKUyqeISBoQGhVKw7kN2XFuBznccxDcNZgqBatYHUtEJMWpfIqIWCw0KpQGcxqw8++dKp4iku6pfIqIWOhW5C0azG3Arr93kdM9Jxv8N/B8geetjiUikmpUPkVELHIr8hb159Rn9/nd5Mqciw1dN1C5QGWrY4mIpCqVTxERC9yMvEn9OfXZc34PuTLnYqP/Rirlr2R1LBGRVKfyKSJiZzfu3MBvjh/7Luwjd+bcbPTfSMX8Fa2OJSJiFyqfIiJ2dOPODXxn+7L/4n7yeORho/9GKnhVsDqWiIjdqHyKiNjJ9TvX8Z3ty4GLB8jjkYdN/pso71Xe6lgiInal8ikiYgfX71yn3qx6HLx0kLweednUbRPl8pWzOpaIiN2pfIqIpLJrEdeoN7sehy4dUvEUkQxP5VNEJBVdjbhKvVn1+OXyL+TLko9N/pt4Lt9zVscSEbGMyqeISCq5GnGVurPq8uvlX/HK4sWmbpt4Nu+zVscSEbGUyqeISCq4En6FurPqcjjkMF5ZvNjcbTNl85a1OpaIiOVUPkVEUti/i2d+z/xs7raZMnnKWB1LRCRNcLI6gIhIehISHkKdWXU4HHKYAp4F2NJti4qniMi/aM2niEgKuXz7MnVm1eHolaMUzFqQzd0280zuZ6yOJSKSpqh8ioikgEu3L1FnZh2OXT1GoayF2NxtM6Vyl7I6lohImqPyKSLyhC7dvoTPTB9+v/o7hbIWYkv3LTyd62mrY4mIpEna51NE5AlcDLuYUDwLZyus4iki8hha8ykikkwXwi7gM9OHE9dOUCRbETZ328xTuZ6yOpaISJqm8ikikgz/Lp5Fsxdlc7fNlMxZ0upYIiJpnsqniEgSnQ89j89MH05eP0mx7MXY3G0zJXKWsDqWiIhDUPkUEUmCv0P/xmemD6eun6JY9mJs6b6F4jmKWx1LRMRhqHyKiCTSuVvn8Jnpw+kbpymeozibu21W8RQRSSId7S4ikghnb52l9szanL5xmhI5SrClm9Z4iogkh9Z8iog8xl83/8Jnpg9/3PyDkjlLsrnbZopmL2p1LBERh6TyKSLyCH/d/IvaM2vz580/KZmzJFu6baFI9iJWxxIRcVja7C4i8hB/3vwzoXg+lfMpFU8RkRSgNZ8iIg/wx40/8Jnpw1+3/qJUrlJs7raZQtkKWR1LRMThac2niMj/OHPjDLVn1lbxFBFJBVrzKSLyL2dunKH2jNqcCz3HM7mfYZP/JhVPEZEUpPIpIvJfp6+fpvbM2vwd+jelc5dmc7fNFMhawOpYIiLpisqniAhw6vopas+ozfmw85TJU4bN3TaT3zO/1bFERNId7fMpIhneyWsnE4pn2TxlVTxFRFKR1nyKSIZ24toJfGb6cCHsAs/mfZZN/pvw8vSyOpaISLql8ikiGdbxq8fxmenDxdsXeS7vc2zqtol8WfJZHUtEJF3TZncRyZB+v/p7QvEsl6+ciqeIiJ1ozaeIZDjHrhyjzqw6XLp9ifL5yrPRfyN5s+S1OpaISIag8ikiGcrRK0epM7MOl8MvU8GrAhv9N5LHI4/VsUREMgyVTxHJMI5eOYrPTB9CwkOo6FWRjf4bye2R2+pYIiIZivb5FJEM4beQ36g9ozYh4SFUyl9JxVNExCJa8yki6d5vIb9RZ2YdrkRcoXL+ymzw30CuzLmsjiUikiFpzaeIpGuHLx/GZ6YPVyKu8HyB51U8RUQspvIpIunWL5d+wWemD1cjruJdwJsNXVU8RUSspvIpIunSL5d+oe6suly7c40XCr7ABv8N5Myc0+pYIiIZnsqniKQ7hy4dos6sOly7c40XC71IUNcgcrjnsDqWiIig8iki6cyBiweoM7MO1+9cp2qhqgR1UfEUEUlLVD5FJN04cPEA9WbV40bkDV4q/BLru6wnu3t2q2OJiMi/aKolEUkX9l/YT73Z9bgZeZNqhauxrss6srllszqWiIj8D635FBGHt/f83oTiWb1IdRVPEZE0TGs+RcSh7Tm/B7/ZftyKukWNIjVY23ktWd2yWh1LREQeQms+RcRh7f57N76zfbkVdYuXi76s4iki4gBUPkXEIe36exd+c/wIjQqlZtGaKp4iIg5C5VNEHM7Oczvxm20Wz1rFahHYORDPTJ5WxxIRkURQ+RQRh7Lj3A7qz6lPWHQYtYvXZk2nNSqeIiIOROVTRBzGz2d/TiiePsV9WN1xNVkyZbE6loiIJIGOdhcRh/DT2Z9oMKcB4THh1ClRh1UdV+Hh6mF1LBERSSKt+RSRNG/7X9sTime9kvVUPEVEHFiyyufkyZMpUaIE7u7ueHt7s3379kQ97ueff8bFxYVKlSolZ7EikgFt+2sbDec2TCieKzusVPEUEXFgSS6fAQEBvP322wwbNoyDBw9Ss2ZNGjZsyNmzZx/5uFu3buHv70/dunWTHVZEMpZ/F0+/p/xY2WElmV0zWx1LRESeQJLL5/jx4+nVqxe9e/embNmyTJgwgSJFijBlypRHPu7111+nU6dOVKtWLdlhRSTjOBx2mGYLmxERE0H9p+qzosMKFU8RkXQgSQccRUdHs3//fgYPHnzP7X5+fuzYseOhj/vxxx85ffo0c+bMYfTo0Y9dTlRUFFFRUQnXQ0NDAYiJiSEmJiYpkZPl7jLssSxJHRpDxxZ8KpiPznxEtBFN/ZL1WdR6Ec6Gs8bTgeg76Pg0ho7P3mOY2OUkqXxevXqVuLg4vLy87rndy8uLS5cuPfAxJ0+eZPDgwWzfvh0Xl8QtbuzYsYwcOfK+24OCgvDwsN++XsHBwXZblqQOjaHj+SXsFz4+8zHRRjTe2bzp5dmLTUGbrI4lyaTvoOPTGDo+e41hREREou6XrKmWbDbbPdcNw7jvNoC4uDg6derEyJEjeeaZZxL9/EOGDGHQoEEJ10NDQylSpAh+fn5ky5YtOZGTJCYmhuDgYHx9fXF1dU315UnK0xg6po1/bGTsorFEG9FUyVaFoF5BeGbWBPKOSN9Bx6cxdHz2HsO7W6ofJ0nlM0+ePDg7O9+3ljMkJOS+taEAYWFh7Nu3j4MHD9KvXz8A4uPjMQwDFxcXgoKCqFOnzn2Pc3Nzw83N7b7bXV1d7foFsPfyJOVpDB1H0OkgWi5qSWRsJI2ebkQPjx54ZvbU+Dk4fQcdn8bQ8dlrDBO7jCQdcJQpUya8vb3vW30bHBxM9erV77t/tmzZOHz4MIcOHUq49OnTh9KlS3Po0CGqVq2alMWLSDq1/tR6ms1vRmRsJM1KNyOgVQCuTvrHTkQkPUryZvdBgwbRtWtXqlSpQrVq1fj+++85e/Ysffr0AcxN5ufPn2fWrFk4OTlRrly5ex6fL18+3N3d77tdRDKmdafW0WJBC6LiomheujkL2y7EFn//bjwiIpI+JLl8tm/fnmvXrjFq1CguXrxIuXLlCAwMpFixYgBcvHjxsXN+iogArD25lhYBLYiOi6ZFmRYEtAkgk3MmYuJ1dK2ISHqVrAOO+vbtS9++fR/4uxkzZjzysSNGjGDEiBHJWayIpCOBJwNpGdCS6LhoWpZpSUCbAFydtaldRCS907ndRcTuVp9YnVA8W5VtpeIpIpKBqHyKiF2tOr6KVgGtiI6Lps2zbVjQeoGKp4hIBqLyKSJ2s/L4SlovbE1MfAxtn23LvFbzVDxFRDIYlU8RsYvlvy+nzcI2xMTH0P659sxrreIpIpIRqXyKSKpbdmwZbRe1JSY+hg7lOjCn1RxcnJJ1vKOIiDg4lU8RSVVLjy2l3eJ2xMbH0ql8J2a3nK3iKSKSgal8ikiqWXx0Me0WmcWzc/nOzGwxU8VTRCSDU/kUkVSx6MgiOizuQJwRR9cKXVU8RUQEUPkUkVSw8MhCOi7pSJwRh39Ff35s/iPOTs5WxxIRkTRA5VNEUtSC3xbQaUkn4ow4ulXsxvRm01U8RUQkgcqniKSY+Yfn03lpZ+KMOHpU6sG0ZtNUPEVE5B4qnyKSIuYdnkeXZV2IN+LpWaknU5tNVfEUEZH7qHyKyBOb8+scui7rSrwRT+/Kvfmh2Q842fTnRURE7qdDT0Xkicz+ZTbdlnfDwODV51/l2ybfqniKiMhD6V8IEUm2mYdmJhTP171fV/EUEZHH0r8SIpIsMw7NoMeKHhgYvFHlDSY3nqziKSIij6V/KUQkyaYfnE7PFT0xMOhbpS+TGk1S8RQRkUTRvxYikiTTDkyj18peGBj0e6EfExtNxGazWR1LREQchMqniCTaD/t/oPeq3gD0f7E/Xzf8WsVTRESSROVTRBLl+/3f89rq1wAYUHUAXzX4SsVTRESSTOVTRB7r233f8vrq1wF4u+rbfFn/SxVPERFJFpVPEXmkKXun8MaaNwAY9NIgxtcfr+IpIiLJpvIpIg81ee9k+gb2BeCdau/wud/nKp4iIvJEVD5F5IEm7pnIm4FvAvBe9ff4zPczFU8REXliKp8icp+vd39N/7X9AXi/xvt8Wu9TFU8REUkRKp8ico8JuyYwYN0AAAbXGMzYumNVPEVEJMWofIpIgi93fsnA9QMBGPryUMbUHaPiKSIiKUrlU0QAGL9zPIOCBgEwrOYwRtcZreIpIiIpTuVTRPh8x+e8E/QOAB+88gEf+Xyk4ikiIqlC5VMkgxv38zjeC34PgOG1hjPKZ5SKp4iIpBoXqwOIiHU+/elTBm8cDMCIWiMYXnu4xYlERCS905pPkQxq7PaxCcVzZO2RKp4iImIXKp8iGdDH2z5m6KahAIyqPYoPa31ocSIREckotNldJIMZvW00H2z+wPzZZzTDXhlmcSIREclIVD5FMpBRW0cxfIu5eX1MnTEMqTnE4kQiIpLRqHyKZBAjtoxg5NaRAIytO5bBLw+2OJGIiGREKp8i6ZxhGIzYMoJR20YB8Gm9T/lPjf9YnEpERDIqlU+RdMwwDIZvGc5H2z4C4DPfz3i3+rsWpxIRkYxM5VMknTIMgw82f8DH2z8G4HPfz3mn+jsWpxIRkYxO5VMkHTIMg//b9H+M+WkMAOP9xjOw2kCLU4mIiKh8iqQ7hmEwdONQPvn5EwC+rP8lb7/0trWhRERE/kvlUyQdMQyDwRsGM27HOAC+avAVb1V9y+JUIiIi/1D5FEknDMPg/Q3v89mOzwD4puE39Huxn8WpRERE7qXyKZIOGIbBe8Hv8cXOLwCY2HAib774psWpRERE7qfyKeLgDMPg3aB3Gb9rPACTG03mjRfesDiViIjIg6l8ijgwwzAYtH4QE3ZPAGBK4yn0qdLH2lAiIiKPoPIp4qAMw2Dg+oF8tfsrAL5r8h2veb9mcSoREZFHU/kUcUCGYTBg3QC+2fMNAN83+Z5XvV+1OJWIiMjjqXyKOBjDMOi/tj+T9k7Cho0fmv5Ar+d7WR1LREQkUVQ+RRyIYRj0C+zH5H2TsWFjarOp9Kzc0+pYIiIiiabyKeIg4o14+gX2Y8q+KdiwMb35dLpX6m51LBERkSRR+RRxAPFGPH3X9OW7/d9hw8aPzX+kW6VuVscSERFJMpVPkTQu3oinz+o+/HDgB2zYmNliJl0rdrU6loiISLKofIqkYfFGPK+vep2pB6fiZHNiZouZdKnQxepYIiIiyabyKZJGxRvxvLbqNaYdnIaTzYlZLWbRuUJnq2OJiIg8EZVPkTQo3oin98re/HjoR5xsTsxpOYeO5TtaHUtEROSJqXyKpDFx8XH0XtWbGYdm4GRzYm6ruXQo18HqWCIiIilC5VMkDYmLj6Pnyp7M+mUWzjZn5raaS/ty7a2OJSIikmJUPkXSiLj4OHqs6MHsX2fjbHNmfuv5tH2urdWxREREUpTKp0gaEBcfR7fl3Zh7eC7ONmcWtFlAm2fbWB1LREQkxal8ilgsNj6Wbsu7Me/wPFycXFjQegGtn21tdSwREZFUofIpYqHY+Fj8l/kz/7f5uDi5sLDNQlqWbWl1LBERkVSj8ilikdj4WLos7ULAkQBcnFxY1HYRLcq0sDqWiIhIqlL5FLFAbHwsnZd2ZuGRhbg6ubKo7SKal2ludSwREZFUp/IpYmcxcTF0XtqZRUcX4erkypJ2S2hauqnVsUREROxC5VPEjmLiYui4pCNLji0hk3MmlrRbQpNnmlgdS0RExG5UPkXsJCYuhg5LOrD02FIyOWdiWftlNCrVyOpYIiIidqXyKWIH0XHRdFjcgWW/L1PxFBGRDE3lUySVRcdF025RO1YcX4GbsxvLOyynwdMNrI4lIiJiCZVPkVQUHRdN20VtWXl8JW7ObqzosIL6T9e3OpaIiIhlVD5FUklUbBRtF7Vl1YlVuLu4s6LDCvye8rM6loiIiKVUPkVSQVRsFK0XtmbNyTW4u7izssNKfJ/ytTqWiIiI5VQ+RVJYZGwkrRe2JvBkIJldMrOq4yrqlqxrdSwREZE0QeVTJAVFxkbSKqAVa0+tJbNLZlZ3Wk2dEnWsjiUiIpJmqHyKpJDI2EhaBrRk3al1ZHbJzJpOa/Ap4WN1LBERkTRF5VMkBdyJuUOLgBYEnQ7Cw9WDNZ3WULt4batjiYiIpDkqnyJP6E7MHZovaE7wmWA8XD0I7BRIreK1rI4lIiKSJql8ijyBiJgImi9ozoYzG8jimoXAzoG8UuwVq2OJiIikWSqfIskUERNB0/lN2fTHJjwzebK281peLvqy1bFERETSNJVPkWQIjw6n6fymbP5zM56ZPFnXeR01itawOpaIiEiap/IpkkTh0eE0md+ELX9uIWumrKzrso7qRapbHUtERMQhqHyKJMHt6Ns0nteYbX9tI2umrKzvsp5qRapZHUtERMRhqHyKJNLt6Ns0mtuI7We3k80tG+u7rOelwi9ZHUtERMShqHyKJEJYVBiN5jXip7M/kc0tG0FdgqhauKrVsURERByOyqfIY4RFhdFwbkN+Pvcz2d2yE9Q1iBcLvWh1LBEREYek8inyCKFRoTSc25Ad53aQ3S07wV2DeaHQC1bHEhERcVgqnyIPERoVSoM5Ddj5905yuOcguGswVQpWsTqWiIiIQ1P5FHmAW5G3aDC3Abv+3kVO95wEdw3Gu6C31bFEREQcnsqnyP+4FXmL+nPqs/v8bnK652SD/waeL/C81bFERETSBZVPkX+5GXmT+nPqs+f8HnJlzsWGrhuoXKCy1bFERETSDZVPkf+6cecGfnP82HdhH7ky52Kj/0Yq5a9kdSwREZF0ReVTBLN4+s72Zf/F/eTOnJuN/hupmL+i1bFERETSHZVPyfCu37mO72xfDlw8QB6PPGz030gFrwpWxxIREUmXVD4lQ7t+5zr1ZtXj4KWD5PHIwyb/TZT3Km91LBERkXRL5VMyrGsR16g3ux6HLh0ir0deNnXbRLl85ayOJSIikq6pfEqGdDXiKvVm1eOXy7+QL0s+Nvlv4rl8z1kdS0REJN1T+ZQM52rEVerOqsuvl3/FK4sXm7pt4tm8z1odS0REJENQ+ZQM5Ur4FerOqsvhkMN4ZfFic7fNlM1b1upYIiIiGYbKp2QYIeEh1J1Vl99CfiO/Z342d9tMmTxlrI4lIiKSoah8SoYQEh5CnZl1OHLlCAU8C7C522ZK5yltdSwREZEMR+VT0r3Lty9TZ1Ydjl45SsGsBdncbTPP5H7G6lgiIiIZklNyHjR58mRKlCiBu7s73t7ebN++/aH3Xbp0Kb6+vuTNm5ds2bJRrVo11q9fn+zAIklx6fYlfGb6cPTKUQplLcSWbltUPEVERCyU5PIZEBDA22+/zbBhwzh48CA1a9akYcOGnD179oH337ZtG76+vgQGBrJ//358fHxo2rQpBw8efOLwIo9yPeY6vnN9OXb1mFk8u2+hVO5SVscSERHJ0JK82X38+PH06tWL3r17AzBhwgTWr1/PlClTGDt27H33nzBhwj3Xx4wZw4oVK1i1ahWVK1dOXmqRx7h4+yIfnPqA81HnKZytMJu7bebpXE9bHUtERCTDS1L5jI6OZv/+/QwePPie2/38/NixY0einiM+Pp6wsDBy5cr10PtERUURFRWVcD00NBSAmJgYYmJikhI5We4uwx7LkpR3IewCvnN8zeKZtTDBnYMplrWYxtOB6Dvo+DSGjk9j6PjsPYaJXU6SyufVq1eJi4vDy8vrntu9vLy4dOlSop7jiy++IDw8nHbt2j30PmPHjmXkyJH33R4UFISHh0dSIj+R4OBguy1LUsa16Gt8cPoDLkRdIK9rXv6v8P9xfOdxjnPc6miSDPoOOj6NoePTGDo+e41hREREou6XrKPdbTbbPdcNw7jvtgeZP38+I0aMYMWKFeTLl++h9xsyZAiDBg1KuB4aGkqRIkXw8/MjW7ZsyYmcJDExMQQHB+Pr64urq2uqL09Sxvmw8/jO9eVC1AWKZivKsELD6NKki8bQAek76Pg0ho5PY+j47D2Gd7dUP06SymeePHlwdna+by1nSEjIfWtD/1dAQAC9evVi0aJF1KtX75H3dXNzw83N7b7bXV1d7foFsPfyJPn+Dv0b37m+nLp+imLZixHcOZijO45qDB2cxs/xaQwdn8bQ8dlrDBO7jCQd7Z4pUya8vb3vW30bHBxM9erVH/q4+fPn0717d+bNm0fjxo2TskiRxzp36xy1Z9Tm1PVTFM9RnC3dt1A8R3GrY4mIiMgDJHmz+6BBg+jatStVqlShWrVqfP/995w9e5Y+ffoA5ibz8+fPM2vWLMAsnv7+/nz11Ve89NJLCWtNM2fOTPbs2VPwpUhGdPbWWXxm+nDmxhlK5CjB5m6bKZZDBxeJiIikVUkun+3bt+fatWuMGjWKixcvUq5cOQIDAylWrBgAFy9evGfOz++++47Y2FjefPNN3nzzzYTbu3XrxowZM578FUiG9dfNv/CZ6cMfN/+gZM6SbO62maLZi1odS0RERB4hWQcc9e3bl759+z7wd/9bKLds2ZKcRYg80p83/8Rnpg9/3vyTkjlLsqXbFopkL2J1LBEREXkMndtdHM6fN/+k9oza/HXrL57K+RRbum+hcLbCVscSERGRREjWud1FrPLHjT8SiufTuZ5ma/etKp4iIiIOROVTHMaZG2eoPdMsnqVylWJLty0UylbI6lgiIiKSBNrsLg7hzI0z1J5Rm3Oh53gm9zNs7raZglkLWh1LREREkkjlU9K809dPU3tmbf4O/ZvSuUuzudtmCmQtYHUsERERSQZtdpc07dT1U9SaUYu/Q/+mTJ4yKp4iIiIOTuVT0qyT105Se0Ztzoedp2yesiqeIiIi6YA2u0uadOLaCXxm+nAh7ALP5n2WTf6b8PL0sjqWiIiIPCGt+ZQ05/jV49SeUZsLYRd4Lu9zKp4iIiLpiMqnpCm/X/0dn5k+XLx9kXL5yrGpm4qniIhIeqLN7pJmHLtyjDqz6nDp9iXK5yvPRv+N5M2S1+pYIiIikoK05lPShKNXjuIz04dLty9RwauCiqeIiEg6pTWfYrm7xTMkPISKXhXZ4L+BPB55rI4lIiIiqUBrPsVSv4X8llA8K+WvxEb/jSqeIiIi6ZjWfIplfgv5jToz63Al4gqV81cmuGswuT1yWx1LREREUpHKp1ji8OXD1JlVh6sRV3m+wPMEdw0mV+ZcVscSERGRVKbN7mJ3v17+FZ+ZPlyNuIp3AW8VTxERkQxE5VPs6pdLv1BnZh2u3blGlYJVVDxFREQyGG12F7s5dOkQdWfV5fqd67xQ8AWCugaRwz2H1bFERETEjlQ+xS4OXjxI3Vl1uRF5gxcLvcj6LutVPEVERDIgbXaXVHfg4oGE4lm1UFWCumiNp4iISEalNZ+SqvZf2E+92fW4GXmTlwq/xPou68nmls3qWCIiImIRrfmUVLPvwr6E4lmtcDUVTxEREdGaT0kde8/vxXe2L7eiblGjSA3Wdl5LVresVscSERERi2nNp6S43X/vpt7setyKusXLRV9W8RQREZEEKp+Sonb9vQu/OX6ERoVSs2hNFU8RERG5hza7S4rZeW4n9efUJyw6jFeKvcKaTmvwzORpdSwRERFJQ7TmU1LEjnM78JvjR1h0GLWL1yawU6CKp4iIiNxH5VOe2M9nf6b+nPrcjr6NT3EfVndcTZZMWayOJSIiImmQyqc8kZ/O/kSDuQ24HX2bOiXqsLqTiqeIiIg8nMqnJNv2v7bTYI5ZPOuWqMuqjqvwcPWwOpaIiIikYSqfkizb/tpGw7kNCY8Jp17JeiqeIiIikigqn5JkW/7cklA8fUv6srLDSjK7ZrY6loiIiDgAlU9Jks1/bKbxvMZExERQ/6n6rOiwQsVTREREEk3zfEqibfpjE03mNeFO7B0aPN2AZe2X4e7ibnUsERERcSBa8ymJsvHMRhrPa8yd2Ds0fLqhiqeIiIgki8qnPNaGMxtoMr8JkbGRNC7VWMVTREREkk3lUx4p6HQQTec3TSieS9otwc3FzepYIiIi4qBUPuWh1p9aT7P5zYiMjaTpM01VPEVEROSJqXzKA607tY7mC5oTFRdF89LNWdxusYqniIiIPDGVT7lP4MnAhOLZokwLFrZdSCbnTFbHEhERkXRA5VPusebEGloGtCQ6LpqWZVqysI2Kp4iIiKQclU9JsPrEalotbEV0XDSty7YmoE0Ars6uVscSERGRdESTzAsAq46vovXC1sTEx9Dm2TbMazVPxVNERERSnNZ8CiuPr0wonu2ea6fiKSIiIqlG5TODW/77ctosbENMfAztn2vP3FZzVTxFREQk1ah8ZmDLji2j7aK2xMTH0KFcB+a0moOLk/bEEBERkdSj8plBLT22lHaL2xEbH0un8p2Y3XK2iqeIiIikOpXPDGjx0cW0W2QWzy4VujCrxSwVTxEREbELlc8MZtGRRXRY3IE4I44uFbowo/kMnJ2crY4lIiIiGYTKZwYS8FsAHZd0JM6Iw7+iv4qniIiI2J3KZwax4LcFdFraiTgjju6VujO92XQVTxEREbE7lc8MYN7heXRe2pl4I54elXowtelUFU8RERGxhMpnOjf317l0XdaVeCOeXpV7MbWZiqeIiIhYR+UzHZvz6xz8l/sTb8TTu3Jvvm/6PU42DbmIiIhYR00knZr1yyz8l5nF89XnX+W7pt+peIqIiIjl1EbSoZmHZtJ9eXcMDF73fp1vm3yr4ikiIiJpghpJOjPj0Ax6rOiBgUEf7z5MbjxZxVNERETSDLWSdGT6wen0XNETA4M3qryh4ikiIiJpjppJOjHtwDR6reyFgcGbL7zJpEaTsNlsVscSERERuYfKZzrww/4f6L2qNwD9XujHNw2/UfEUERGRNEnl08F9v/97Xlv9GgBvvfgWXzf8WsVTRERE0iyVTwf27b5veX316wAMqDqACQ0mqHiKiIhImqby6aCm7J3CG2veAGDgSwP5sv6XKp4iIiKS5ql8OqBJeybRN7AvAO9Ue4cv/L5Q8RQRERGHoPLpYCbumUi/tf0AeLfau3zm+5mKp4iIiDgMlU8H8vXur+m/tj8A/6n+H8b5jlPxFBEREYei8ukgJuyawIB1AwAYXGMwn9T7RMVTREREHI7KpwP4cueXDFw/EIAhLw9hTN0xKp4iIiLikFQ+07gvdnzBoKBBAAyrOYyP63ys4ikiIiIOS+UzDft8x+e8G/wuAB+88gEf+Xyk4ikiIiIOTeUzjRr38zjeC34PgA9f+ZCRtUeqeIqIiIjDc7E6gNzvk58+YcjGIQCMqDWC4bWHW5xIREREJGWofKYxY7ePZeimoQCMrD2SD2t9aHEiERERkZSjze5pyMfbPk4onqNqj1LxFBERkXRHaz7TiI+2fsSHW8yyOdpnNMNeGWZxIhEREZGUp/KZBozaOorhW8z9OsfUGcOQmkMsTiQiIiKSOlQ+LTZiywhGbh0JwNi6Yxn88mCLE4mIiIikHpVPixiGwYgtIxi1bRQAn9b7lP/U+I/FqURERERSl8qnBQzDYPiW4Xy07SMAPvP9jHerv2txKhEREZHUp/JpZ4Zh8MHmD/h4+8cAfO77Oe9Uf8fiVCIiIiL2ofJpR4Zh8H+b/o8xP40BYLzfeAZWG2hxKhERERH7Ufm0E8MwGLpxKJ/8/AkAX9b/krdfetvaUCIiIiJ2pvJpB4ZhMHjDYMbtGAfAVw2+4q2qb1mcSkRERMT+VD5TmWEYvL/hfT7b8RkA3zT8hn4v9rM4lYiIiIg1VD5TkWEYvBf8Hl/s/AKAiQ0n8uaLb1qcSkRERMQ6Kp+pxDAM3gl6hy93fQnA5EaTeeOFNyxOJSIiImItlc9UYBgGg9YPYsLuCQBMaTyFPlX6WBtKREREJA1Q+UxhhmHw9rq3+XrP1wB81+Q7XvN+zeJUIiIiImmDymcKMgyDAesG8M2ebwD4vsn3vOr9qsWpRERERNIOlc8UYhgG/df2Z9LeSdiw8UPTH+j1fC+rY4mIiIikKSqfKSDeiKdfYD+m7JuCDRtTm02lZ+WeVscSERERSXNUPp9QvBHPm2ve5Nv932LDxvTm0+leqbvVsURERETSJJXPJxBvxNN3TV++2/8dNmz82PxHulXqZnUsERERkTRL5TOZ4o14+qzuww8HfsCGjZktZtK1YlerY4mIiIikaSqfyRBvxPP6qteZenAqTjYnZraYSZcKXayOJSIiIpLmqXwmUbwRz6srX2X6oek42ZyY1WIWnSt0tjqWiIiIiENQ+UyCuPg4eq/qzYxDM3CyOTGn5Rw6lu9odSwRERERh6HymUhx8XH0WtmLmb/MxMnmxNxWc+lQroPVsUREREQcispnIsTFx9FzZU9m/TILZ5szc1vNpX259lbHEhEREXE4Kp+PERcfR/cV3Znz6xycbc7Mbz2fts+1tTqWiIiIiENySs6DJk+eTIkSJXB3d8fb25vt27c/8v5bt27F29sbd3d3SpYsybfffpussPYWFx9Ht+XdEorngjYLVDxFREREnkCSy2dAQABvv/02w4YN4+DBg9SsWZOGDRty9uzZB97/jz/+oFGjRtSsWZODBw8ydOhQ3nrrLZYsWfLE4VNTnBFHj1U9mHt4Li5OLgS0CaDNs22sjiUiIiLi0JJcPsePH0+vXr3o3bs3ZcuWZcKECRQpUoQpU6Y88P7ffvstRYsWZcKECZQtW5bevXvTs2dPPv/88ycOn1pi42OZ8NcEFhxZgIuTCwvbLKT1s62tjiUiIiLi8JK0z2d0dDT79+9n8ODB99zu5+fHjh07HviYnTt34ufnd89t9evXZ9q0acTExODq6nrfY6KiooiKikq4HhoaCkBMTAwxMTFJiZxksfGx+C/3Z/vN7bg6uTK/1XyaPN0k1ZcrKevueGncHJPGz/FpDB2fxtDx2XsME7ucJJXPq1evEhcXh5eX1z23e3l5cenSpQc+5tKlSw+8f2xsLFevXqVAgQL3PWbs2LGMHDnyvtuDgoLw8PBISuQkOxNxhpUnV+Jic+G9Yu/hcsqFwFOBqbpMST3BwcFWR5AnoPFzfBpDx6cxdHz2GsOIiIhE3S9ZR7vbbLZ7rhuGcd9tj7v/g26/a8iQIQwaNCjhemhoKEWKFMHPz49s2bIlJ3KSPHPqGXbs3cGwNsMeuGZW0r6YmBiCg4Px9fXVGDogjZ/j0xg6Po2h47P3GN7dUv04SSqfefLkwdnZ+b61nCEhIfet3bwrf/78D7y/i4sLuXPnfuBj3NzccHNzu+92V1dXu7x5fk/7EXsi1m7Lk9SjMXRsGj/HpzF0fBpDx2evMUzsMpJ0wFGmTJnw9va+b/VtcHAw1atXf+BjqlWrdt/9g4KCqFKlSpr4MBuGkbAmVkRERERSV5KPdh80aBBTp05l+vTpHDt2jIEDB3L27Fn69OkDmJvM/f39E+7fp08f/vrrLwYNGsSxY8eYPn0606ZN49133025V/GEHrXLgIiIiIiknCTv89m+fXuuXbvGqFGjuHjxIuXKlSMwMJBixYoBcPHixXvm/CxRogSBgYEMHDiQSZMmUbBgQb7++mtat04bUxepeIqIiIjYT7IOOOrbty99+/Z94O9mzJhx3221atXiwIEDyVmUiIiIiKQjyTq9poiIiIhIcqh8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjdqHyKiIiIiN2ofIqIiIiI3ah8ioiIiIjduFgdIDEMwwAgNDTULsuLiYkhIiKC0NBQXF1d7bJMSVkaQ8em8XN8GkPHpzF0fPYew7s97W5vexiHKJ9hYWEAFClSxOIkIiIiIvIoYWFhZM+e/aG/txmPq6dpQHx8PBcuXCBr1qzYbLZUX15oaChFihTh3LlzZMuWLdWXJylPY+jYNH6OT2Po+DSGjs/eY2gYBmFhYRQsWBAnp4fv2ekQaz6dnJwoXLiw3ZebLVs2feEcnMbQsWn8HJ/G0PFpDB2fPcfwUWs879IBRyIiIiJiNyqfIiIiImI3Kp8P4ObmxvDhw3Fzc7M6iiSTxtCxafwcn8bQ8WkMHV9aHUOHOOBIRERERNIHrfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbvJsOVz8uTJlChRAnd3d7y9vdm+ffsj779161a8vb1xd3enZMmSfPvtt3ZKKg+TlDFcunQpvr6+5M2bl2zZslGtWjXWr19vx7Tyv5L6Hfz/du4vpKk+DgP4Mz2zdJBQkS0HhqGZQfZnzFJCCFlQJF1EQhEWBY2IVlGxMDIhiIqEDOtCzG5mSYbRhYW7KJsWhTYhWmCoBVIWM4SV/VO/70Wvvk33qmfvu7PBng/swp+/g894OPrd2Txj2traoCgKVq5cGd6ANC21Hf748QOlpaVIS0vDrFmzsGTJEly/fl2jtBSM2g6dTidycnKQlJQEo9GIPXv2YGBgQKO09KfHjx9jy5YtWLRoEXQ6He7evTvtMVEzy0gMunXrluj1eqmurhav1yt2u10MBoO8e/cu6P6enh5JSkoSu90uXq9XqqurRa/XS0NDg8bJaYzaDu12u5w/f16eP38uXV1dcvLkSdHr9fLixQuNk5OI+v7GDA4OSnp6ulitVsnJydEmLAUVSodFRUWSm5srLpdLent75dmzZ9LW1qZhavqT2g7dbrfExcXJ5cuXpaenR9xutyxfvly2bt2qcXISEWlqapLS0lK5c+eOAJDGxsYp90fTLBOTw6fFYhGbzRawlpWVJQ6HI+j+EydOSFZWVsDa/v37Ze3atWHLSFNT22Ew2dnZUl5e/n9HoxkItb/i4mI5deqUlJWVcfiMMLUd3r9/X5KTk2VgYECLeDQDaju8ePGipKenB6xVVlaKyWQKW0aamZkMn9E0y8Tc2+4/f/5ER0cHrFZrwLrVasWTJ0+CHvP06dNJ+zdu3Ij29nb8+vUrbFkpuFA6nGh0dBR+vx9z584NR0SaQqj91dbWoru7G2VlZeGOSNMIpcN79+7BbDbjwoULSE1NRWZmJo4dO4Zv375pEZkmCKXDvLw89PX1oampCSKCjx8/oqGhAZs3b9YiMv1H0TTLKJr+tCjg8/kwMjKClJSUgPWUlBT09/cHPaa/vz/o/uHhYfh8PhiNxrDlpclC6XCiS5cu4evXr9i+fXs4ItIUQunvzZs3cDgccLvdUJSY+7UVdULpsKenB62trZg9ezYaGxvh8/lw4MABfP78mZ/7jIBQOszLy4PT6URxcTG+f/+O4eFhFBUV4cqVK1pEpv8ommaZmLvyOUan0wV8LSKT1qbbH2ydtKO2wzE3b97EmTNnUF9fjwULFoQrHk1jpv2NjIxgx44dKC8vR2ZmplbxaAbUnIOjo6PQ6XRwOp2wWCzYtGkTKioqcOPGDV79jCA1HXq9Xhw6dAinT59GR0cHHjx4gN7eXthsNi2i0v8gWmaZmLuEMH/+fMTHx096Zffp06dJrwjGLFy4MOh+RVEwb968sGWl4ELpcEx9fT327t2L27dvo7CwMJwx6V+o7c/v96O9vR0ejwcHDx4E8HuQEREoioLm5mZs2LBBk+z0WyjnoNFoRGpqKpKTk8fXli1bBhFBX18fMjIywpqZAoXS4blz55Cfn4/jx48DAFasWAGDwYD169fj7NmzfBcwykXTLBNzVz4TEhKwZs0auFyugHWXy4W8vLygx6xbt27S/ubmZpjNZuj1+rBlpeBC6RD4fcVz9+7dqKur42eUIkhtf3PmzMHLly/R2dk5/rDZbFi6dCk6OzuRm5urVXT6WyjnYH5+Pt6/f48vX76Mr3V1dSEuLg4mkymseWmyUDocGhpCXFzg2BAfHw/gnytoFL2iapbR/F+cosDY7SVqamrE6/XK4cOHxWAwyNu3b0VExOFwyK5du8b3j92e4MiRI+L1eqWmpoa3WoowtR3W1dWJoihSVVUlHz58GH8MDg5G6inENLX9TcT/do88tR36/X4xmUyybds2efXqlbS0tEhGRobs27cvUk8h5qntsLa2VhRFkatXr0p3d7e0traK2WwWi8USqacQ0/x+v3g8HvF4PAJAKioqxOPxjN8qK5pnmZgcPkVEqqqqJC0tTRISEmT16tXS0tIy/r2SkhIpKCgI2P/o0SNZtWqVJCQkyOLFi+XatWsaJ6aJ1HRYUFAgACY9SkpKtA9OIqL+HPwTh8/ooLbD169fS2FhoSQmJorJZJKjR4/K0NCQxqnpT2o7rKyslOzsbElMTBSj0Sg7d+6Uvr4+jVOTiMjDhw+n/LsWzbOMToTXyomIiIhIGzH3mU8iIiIiihwOn0RERESkGQ6fRERERKQZDp9EREREpBkOn0RERESkGQ6fRERERKQZDp9EREREpBkOn0RERESkGQ6fRERERKQZDp9EREREpBkOn0RERESkGQ6fRERERKSZvwAoNAfJBSMBIAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 1\n",
    "x = np.linspace(a, b)\n",
    "iterations = 10\n",
    "\n",
    "# Start at left\n",
    "print(f\"Solving x = cos(x) starting to the left, at x_0 = {a}\")\n",
    "x_k = a\n",
    "figure(figsize=(8,8))\n",
    "title(f\"Solving $x = \\cos x$ starting to the left, at $x_0$ = {a}\")\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g(x), \"r\")\n",
    "grid(True)\n",
    "for k in range(iterations):\n",
    "    g_x_k = g_1(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_1(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_1(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    print(f\"x_{k+1} = {x_k_plus_1}\")\n",
    "\n",
    "# Start at right\n",
    "print(f\"Solving x = cos(x) starting to the right, at x_0 = {b}\")\n",
    "x_k = b\n",
    "figure(figsize=(8,8))\n",
    "title(f\"Solving $x = \\cos(x)$ starting to the right, at $x_0$ = {b}\")\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g(x), \"r\")\n",
    "grid(True)\n",
    "for k in range(iterations):\n",
    "    g_x_k = g_1(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_1(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_1(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    print(f\"x_{k+1} = {x_k_plus_1}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In each case, one gets a \"box spiral\" in to the fixed point.\n",
    "It always looks like this when $g$ is *decreasing* near the fixed point.\n",
    "\n",
    "If instead $g$ is *increasing* near the fixed point, the iterates approach monotonically, either from above or below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Solving $f(x) = x^2 - 5x + 4 = 0$ in interval $[0, 3]$\n",
    ":label: example-4\n",
    "\n",
    "The roots are 1 and 4; for now we aim at the first of these,\n",
    "so we chose a domain $[0, 3]$ that contains just this root.\n",
    "\n",
    "Let us get a fixed point for by \"partially solving for $x$\": solving for the $x$ in the $5 x$ term:\n",
    "\n",
    "$$ x = g(x) = (x^2 + 4)/5 $$\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_2(x): return x**2 - 5*x + 4\n",
    "def g_2(x): return (x**2 + 4)/5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA9UAAAHGCAYAAAB6l6gDAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAAB6P0lEQVR4nO3deXhV5b33/8/eOzvzROaEJBDmeUqCgAIOFQVnbbVaBRH51aPH87Q8fWxt+zyn9jo9tj09re3RalsZROpQReqEClUGFawkhJkwBgIhIQTIPO1h/f5YITEmQHYIWTvJ+3U1V9zfvXby3emdBR/ute7bZhiGIQAAAAAA4DO71Q0AAAAAANBTEaoBAAAAAOgkQjUAAAAAAJ1EqAYAAAAAoJMI1QAAAAAAdBKhGgAAAACATiJUAwAAAADQSYRqAAAAAAA6iVANAAAAAEAnEaoBAAAAAOgkQjUAAAAAAJ1EqAYAwE81NDRo/vz5SktLU2RkpKZMmaJNmzZZ3RYAAPgKQjUAAH7K7XYrIyNDn3/+ucrLy/Uv//IvuvXWW1VbW2t1awAAoInNMAzD6iYAAEDHxMTEaN26dRo/frzVrQAAADFTDQDooX7+859r1KhR8nq9Pr1u8eLF6t+/v2pqai5TZ211ttevy8/PV11dnQYPHtxFnV3ciy++KJvNpvDw8DbPdeRn6fF4lJCQoN/97ndav369bDZbux9ffPHF5XwbPvvZz34mm81mdRsAgB6AUA0A6HFOnDihX//61/r5z38uu923P8rmzZunsLAw/frXv75M3bV2Kb1+VW1trR544AH99Kc/bTfgXg5FRUX6wQ9+oJSUlHaf78jPcuPGjTp16pTuvPPO5tp//ud/avPmza0+xowZ0+X9AwDQHQjVAIAe5/e//72io6NbBbWOCggI0He/+139/ve/75Z7ky+l13NcLpfuvvtujRo1Sj/+8Y99eu3VV1+tBx98sFPf95FHHtGMGTN0/fXXt/t8R36Wb775prKysjRgwIDm2tChQzVlypRWH931DwUAAHQ1QjUA9CF33nmnUlNT29TdbrcmTJhw3vDUFQzD0LPPPqtRo0YpODhYY8aM0erVq3Xfffdp9OjRHf46jY2NWrx4se67775WM7/FxcUKDw/Xt7/97VbHv/fee3I6nfrJT37SXPvOd76jyspKvfbaa5f+xjrRqy/9er1ezZ07Vw6HQ4sXL+62S5JXrFihDRs26I9//OMFj7vQz9IwDK1atUp33XVXl/R08OBBzZ8/X0OHDlVoaKj69++vW265RTt37mx13LlLt3fv3q17771XUVFRSkxM1EMPPaSKioo2X/f999/XhAkTFBQUpIyMDP3mN7/pcE9W/U75Mt4BAJeZAQDoM373u98ZkowjR460qv/qV78ygoKCjP3797d5jdfrNVwuV4c+LuS73/2u4XQ6jR/+8IfGRx99ZDz33HNGfHy80b9/f2PevHkdfg8bN240JBmrV69u89xTTz1l2Gw2IycnxzAMw1i3bp0RHBxsPP74422OHTlypHHnnXee9/t0xfu+UK8d7ffhhx82Zs6cadTV1Z33+1zIzJkzffr5GoZhnDx50oiNjTWee+45wzAMY968eUZYWNh5jz/fz/Kzzz4zJDWPq3Xr1hmSjISEBMPhcBgRERHGrFmzjE8//bRDfW3YsMH43//7fxtvvvmmsWHDBmPVqlXG7bffboSEhBj5+fnNx/37v/+7IckYPny48f/+3/8z1q5da/z2t781goKCjPnz57f6mv/4xz8Mh8NhXHXVVcZbb71lvPHGG0Z2draRnp5udOSvSVb+Tvky3gEAlw+hGgD6kNzcXEOS8corrzTXDh8+bISGhho///nP233NuSDUkY+CgoJ2v8Ybb7xhSDJeeumlVvWf/exnhiTjf/7nfzr8Hn71q18ZkoySkpI2z9XU1BgpKSnGddddZ3z55ZdGRESEMX/+fMPr9bY59jvf+Y6RmJh43u/TFe/7Qr12pN8jR44Ykozg4GAjLCys+WPjxo3tfr32wtqMGTOMuXPn+hTW7rrrLmPatGnNfVwsVJ/vZ/m9733PGDt2bPPjrVu3Gv/rf/0vY9WqVcbGjRuNJUuWGCNHjjQcDofx4YcfXrCn9rjdbqOxsdEYOnSo8f3vf7+5fi5U//rXv251/KOPPmoEBwe3Gg9XXHGFkZKS0uofLSorK42YmJgOhWqrfqcMw7fxDgC4fAIuw+Q3AMBPTZgwQZGRkfr888917733SpL+5V/+RWlpafrhD3/Y7msyMzO1ZcuWDn398y1o9Ytf/EJXXnml5s6d26o+bNgwSVJ2drYkqaGhQY888oj+8Y9/qKKiQqNGjdJvf/tbTZs2rfk1J06ckM1mU1xcXJvvExoaqv/4j//QQw89pGuuuUY33XST/vKXv7R7yXRCQoJKS0vldrsVEND2j8OueN8X6rUj/Q4YMECGDztfbtiwQddcc02b+saNG7V8+fJWtYKCAg0cOLDNsStXrtS7776rvLy8Dl9qfr6f5VtvvaWHHnqo+fHEiRM1ceLE5sfTp0/XHXfcobFjx+qJJ57QDTfccMHv43a79etf/1orVqzQwYMH5XK5mp/bu3dvm+NvvfXWVo/HjRun+vp6lZaWKjExUTU1NdqyZYseffRRBQcHNx8XERGhW265RS+99NJF37tVv1OSb+MdAHD5EKoBoA+x2+2aNm2aNm3aJEn661//qo8++kjr1q1TYGBgu68JDw/XhAkTOvT12wunJSUl2rZtm5555pk2zx07dkwBAQHNey673W5lZGTo888/V2pqql5++WXdeuutKiwsVGhoqCSprq5OTqdTDoej3R7OBXWbzaZly5ad97jg4GAZhqH6+vp2F8m61PfdkV596bcj2gtr3/3ud5WSkqJ///d/b1VvL6xVV1frscce0+OPP66UlBSVl5dLMu8Nl6Ty8nI5nU6FhYW1el17P8svv/xShYWFF72fOjo6WjfffLNeeOEF1dXVKSQk5LzHLlq0SM8995x++MMfaubMmerXr5/sdrsefvhh1dXVtTk+Nja21eOgoCBJaj727Nmz8nq9SkpKavPa9mrtseJ36qu6cvwAADqHhcoAoI+ZMWOGduzYocLCQi1atEjz5s3T1Vdffd7jN2zYIKfT2aGPI0eOtHn98ePHJUnJycltnluzZo3Gjh3bPEsYFham//f//p/S09Nlt9s1b948eb1eHThwoPk1cXFxamxsbHdv5G3btunmm2/WlVdeqerqai1ZsuS87+vMmTMKCgo676rTl/q+L9arr/12REREhLKyslp9REREKDY2tk29vcBXVlamkydP6r//+7/Vr1+/5o9XX31VNTU16tevn77zne+0eV17P8uVK1dq2LBhHdoq69xs/MVmWFesWKG5c+fqP//zP3XDDTdo8uTJysrKUllZ2UW/R3v69esnm82mkpKSNs+1Vzuf7v6dOqerxw8AoHOYqQaAPmbGjBnyeDy6+eab5fF4LrrS8aVeqpqQkCBJ2rNnT6v6Bx98oI8//lgLFy4879fLz89XXV2dBg8e3FwbMWKEJOnQoUMaN25cc33fvn264YYbNHXqVL399tv61re+pZ/97Ge6//77FRUV1eZrHz58WKNGjTrv9+6KS3TP12tn+u0OSUlJWrduXZv6L3/5S23YsEEffPBBu5eyt/ezXLlype6+++6Lfs+zZ8/qvffe04QJE1pdgt0em83WPNt8zvvvv6+ioiINGTLkot/r68LCwjR58mS99dZb+q//+q/m719VVaV33323w1+nu3+nJP8cPwDQZ1l7SzcAoLs1NDQYISEhhiRjyZIll/37eb1eY/LkyUZERITx7LPPGuvWrTP+4z/+wxgwYIAhyfjLX/7S7utqamqMrKws4z/+4z9a1QsLCw1Jxp/+9KfmWkFBgZGammpMnz7dqK2tNQzDMPbu3Ws4HA7jiSeeaPO1PR6PERUVZSxatKgL32lb7fXamX4vRWdW//66Cy1U1t7PMi8vz5DUvCr1Offee6/xwx/+0HjjjTeMdevWGX/+85+N4cOHGwEBAcbatWsv2sfcuXONoKAg43e/+53x8ccfG7/+9a+N+Ph4IzU11Zg5c2bzcecWKjt16lSr1y9durTN4l9r1qwx7Ha7cdVVVxmrVq0y3nzzTSM7O9tIS0vr0EJlhtH9v1PdOX4AABdHqAaAPsblchkpKSnG9OnTu22V4IKCAuPGG280wsPDjfj4eOPBBx80lixZYkgyDh8+3Ob4xsZG46abbjLmzp3bbo/Tp0835syZYxiGYZw4ccIYPHiwMWnSJKOioqLVcQsXLjSCgoLarKD88ccfG5KM3NzcrnuT5/HVXjvb76W43KG6vZ/lT3/6U2PAgAFtjn366aeNCRMmGFFRUYbD4TDi4+ONO+64w/jyyy871MfZs2eNBQsWGAkJCUZoaKhx1VVXGZ9++qkxc+bMTodqwzCMd955xxg3bpwRGBhopKenG7/85S+bv0ZHdOfvVHePHwDAxdkMw4dlRQEAPd5vfvMb/eQnP9G2bds0cuRIS3qoq6vTddddp8jISH344YetnvN6vfrOd76j2tparVy5st2FmlauXKl77rlHR48eVf/+/X3+/g888IAOHz6szz//vNPvoaMutVd/197PctSoUZo9e7b++7//28LOuo8//E4BAKxDqAaAPqC2tlbbt2/Xli1b9H/+z//RL37xC/3gBz/olu+dk5OjN998U1deeaUiIiK0f/9+/c///I/Kysr0+eefa9CgQa2OX7hwoQ4cOKAPP/zwvPfYGoahadOmKTMzU88++6xP/Rw6dEgjR47UJ598oquuuqrT76ujLqVXf9fdP0t/YuXvFADAv7BQGQD0AWvWrNEdd9yhpKQk/fjHP+7Wv/xXV1dr7dq1ev7551VXV6eUlBTNmTNH//f//t82K4IfPXpUL774ooKDg1stiPXBBx9o+vTpzY9tNpv+8pe/6J133pHX65Xd3vHNLAoLC/Xss892Wwi8lF79XXf/LP2Jlb9TAAD/wkw1AAAAAACd1Hv+uRwAAAAAgG5GqAYAAAAAoJMI1QAAAAAAdFKPWKjM6/XqxIkTioiIkM1ms7odAAAAAEAvZxiGqqqqlJKScsGFRntEqD5x4oTS0tKsbgMAAAAA0MccO3ZMqamp532+R4TqiIgISeabiYyMtLib83O5XFqzZo1mzZolp9NpdTvoARgz8BVjBr5izMBXjBn4ijEDX/WUMVNZWam0tLTmPHo+PSJUn7vkOzIy0u9DdWhoqCIjI/16cMB/MGbgK8YMfMWYga8YM/AVYwa+6mlj5mK3ILNQGQAAAAAAnUSoBgAAAACgkwjVAAAAAAB0EqEaAAAAAIBOIlQDAAAAANBJhGoAAAAAADqJUA0AAAAAQCcRqgEAAAAA6CRCNQAAAAAAnUSoBgAAAACgkwjVAAAAAAB0kk+h+vnnn9e4ceMUGRmpyMhITZ06VR988MEFX7NhwwZlZmYqODhYgwYN0gsvvHBJDQMAAAAA4C98CtWpqan65S9/qZycHOXk5Ojaa6/Vbbfdpt27d7d7fEFBgebMmaPp06crLy9PP/7xj/Vv//ZvWrlyZZc0DwAAAACAlQJ8OfiWW25p9fgXv/iFnn/+eX3xxRcaPXp0m+NfeOEFpaen65lnnpEkjRw5Ujk5OfrNb36ju+66q/NdAwAAAAB6Ho9btvz3FFZ/0upOuoxPofqrPB6P3njjDdXU1Gjq1KntHrN582bNmjWrVe2GG27Q4sWL5XK55HQ6231dQ0ODGhoamh9XVlZKklwul1wuV2dbvuzO9ebPPcK/MGbgK8YMfMWYga8YM/AVYwYdUlUs+7YVsuctV0BVsQbHXSeXa67VXV1QR8e0z6F6586dmjp1qurr6xUeHq5Vq1Zp1KhR7R5bUlKixMTEVrXExES53W6VlZUpOTm53dc9/fTTeuqpp9rU16xZo9DQUF9b7nZr1661ugX0MIwZ+IoxA18xZuArxgx8xZhBG4ah2Op8ZZR9rOTyXNnlkSTVB0Sqzhnj92Omtra2Q8f5HKqHDx+ubdu2qby8XCtXrtS8efO0YcOG8wZrm83W6rFhGO3Wv+rJJ5/UokWLmh9XVlYqLS1Ns2bNUmRkpK8tdxuXy6W1a9fq+uuvP+8sPPBVjBn4ijEDXzFm4CvGDHzFmEEb9ZWy73xd9q1LZSvb31z2pk+VN/MheQfN0oFPNvj9mDl3xfTF+ByqAwMDNWTIEElSVlaWtmzZot///vf605/+1ObYpKQklZSUtKqVlpYqICBAsbGx5/0eQUFBCgoKalN3Op1+/UM/p6f0Cf/BmIGvGDPwFWMGvmLMwFeMGahkp7TlRWnHG5KrxqwFhkvjvy1lPSR74mjZJRlNl1X7+5jpaG+dvqf6HMMwWt3//FVTp07Vu+++26q2Zs0aZWVl+fUPDwAAAADQAe4Gac87Zpg+9kVLPX6kNPlhaezdUrD/Xm3cFXwK1T/+8Y81e/ZspaWlqaqqSq+99prWr1+vDz/8UJJ52XZRUZGWL18uSXrkkUf07LPPatGiRVq4cKE2b96sxYsX69VXX+36dwIAAAAA6B5nj0q5S6WtL0u1ZWbNHiCNvEXKXigNmCZd4Jbf3sSnUH3y5Ek98MADKi4uVlRUlMaNG6cPP/xQ119/vSSpuLhYhYWFzcdnZGRo9erV+v73v6/nnntOKSkp+sMf/sB2WgAAAADQ03i90qGPzVnp/R9JMtfLUmR/KXO+NOkBKSLJ0hat4FOoXrx48QWfX7ZsWZvazJkztXXrVp+aAgAAAAD4idozUt7LUs4S6eyRlvqga6Tsh6VhN0qOS76zuMfqu+8cAAAAANA+w5CKcs1Z6V1vSZ6mdbSCo6QJ90tZD0lxQ6zt0U8QqgEAAAAApsZaadebZpgu3t5STx5v3is95i4pMNS6/vwQoRoAAAAA+rqyg1LOYmnbX6X6CrPmCDJDdPbDUv9JfWbhMV8RqgEAAACgL/K4pf0fmLPSh9e31PsNlLIWSBPvl0JjrOquxyBUAwAAAEBfUlUibV0u5SyVqk40FW3mgmPZD0uDr5Xsdktb7EkI1QAAAADQ2xmGdPRzc1Z677uS123WQ+OkSXOlzAelfgMsbbGnIlQDAAAAQG9VXynteN0M06fyW+ppU8xZ6VG3SgFB1vXXCxCqAQAAAKC3KdllLjy2/XXJVWPWnGHSuLul7AVS0lhr++tFCNUAAAAA0Bu4G8xLu7e8KBVubqnHDTdnpcffY+4zjS5FqAYAAACAnqz8mJS71Fx8rOaUWbMHSCNuNsP0wKvYDusyIlQDAAAAQE/j9UqHP5G2LJb2fygZXrMekSxlzjcXH4tMtrbHPoJQDQAAAAA9Re0ZadtfzTB9tqClnjHTnJUePltyOK3rrw8iVAMAAACAvyvKNYP0rpWSu96sBUVJE+6Tsh6S4odZ218fRqgGAAAAAH/UWCvtfstceOxEXks9aayUvVAa+00pMMy6/iCJUA0AAAAA/uX0ISlniZS3QqovN2uOQGn0neYl3qlZLDzmRwjVAAAAAGA1j1s68JE5K33ok5Z6dLqUtUCaeL8UFmddfzgvQjUAAAAAWKXqpJS3XMpZJlUebyrapKGzzFnpIddJdoeVHeIiCNUAAAAA0J0MQzq6yZyV3vuO5HWb9dBYaeIDUtZ8qd9AS1tExxGqAQAAAKA7NFRJ218zV/E+tbelnjrZnJUedZvkDLauP3QKoRoAAAAALqeTe6ScxWagbqw2a85Qaey3pOwFUvJ4a/vDJSFUAwAAAEBXczdK+e+as9JHP2+pxw0zFx4b/20pJNqy9tB1CNUAAAAA0FUqjku5y6Tcl6SaUrNmc0gjbzYv8R44ne2wehlCNQAAAABcCq9XOrzOnJXe/4FkeM16RLKU+aA0aa4UmWJpi7h8CNUAAAAA0Bm1Z6Rtr5j3S5853FLPmGHOSg+fIzmc1vWHbkGoBgAAAABfnMiTvnxR2vWm5K43a0GR0oT7pKyHpPjh1vaHbkWoBgAAAICLcdVJu94y95Y+sbWlnjhWmvywuZJ3YJh1/cEyhGoAAAAAOJ/Th6ScJVLeCqm+3Kw5AqXRd5iXeKdms/BYH0eoBgAAAICv8nqk/R+Zs9KHPm6pR6ebl3dPfEAKi7OuP/gVQjUAAAAASFJ1qbR1ubklVsWxpqJNGnq9OSs95BuS3WFlh/BDhGoAAAAAfZdhSIVfmLPSe96WvC6zHhIjTXpAypwvxWRY2yP8GqEaAAAAQN/TUCXt+Ju5t3Tp7pZ6arY5Kz3qdskZbFl76DkI1QAAAAD6jtK9ZpDe/prUWGXWAkKkcd+SshZIKRMsbQ89D6EaAAAAQO/mbpTy3zPD9NHPWuqxQ8xZ6fH3SiHRlrWHno1QDQAAAKB3qigyFx3b+pJUfdKs2RzSiDlmmM6YyXZYuGSEagAAAAC9h9crFWwwFx7b94FkeMx6eJKUOU+aNE+K6m9tj+hVCNUAAAAAer66s9K2V6WcxdLpgy31gdPNWekRN0kOp3X9odciVAMAAADouU7kmfdK73xTcteZtcAIacK95sJjCSOs7Q+9HqEaAAAAQM/iqpd2rzIv8S7KaaknjpGyF0hj75aCwq3rD30KoRoAAABAz3DmsJSzVMp72bzcW5Icgeae0tkPS2mTWXjMz+0qqtDv/7FfQ2TTHKub6SKEagAAAAD+y+uRDqw1Z6UP/kOSYdaj0qWs+dLEB6TweEtbxMVtO1au//n4gD7OL5UkHY6wa5HFPXUVQjUAAAAA/1N9ypyRzlkqVRQ2FW3SkOvNWemh10t2h6Ut4uJyj57VHz4+oA37T0mS7DbplnHJGqVjFnfWdQjVAAAAAPyDYUjH/mnOSu/+u+R1mfWQfuaMdNZ8KWaQpS2iY/55+LT+55OD+uxgmSTJYbfpjon99dg1Q5QaFajVqwnVAAAAANA1GqqlnX8zV/E+uaul3j/LnJUefbvkDLGsPXSMYRjafOi0fv/xAf2z4IwkKcBu0zczU/Xo1UOUHhsqSXK5XFa22eUI1QAAAACsUZpv7iu97VWpscqsBYRIY79pruKdMtHa/tAhhmHo0wNl+sPHB5Rz1FxALtBh193ZqXpk5mCl9gu1uMPLi1ANAAAAoPt4XFL+e+as9JFPW+oxg81Z6Qn3mpd7w+8ZhqH1+07p9x8f0LZj5ZKkwAC77pucru/OHKTkqL5xdQGhGgAAAMDlV1EkbX1Jyl0mVZ80aza7NHyOGaYzZkp2u6UtomMMw9DaPSf1P58c1M6iCklSsNOu71wxQN+dMUgJkcEWd9i9CNUAAAAALg/DkAo2mAuP5a+WDI9ZD0uQMh+UMudJUamWtoiO83oNfbS7RH/45KD2FldKkkKcDs2dOkAPTx+k+Iggizu0hk+h+umnn9Zbb72l/Px8hYSEaNq0afrVr36l4cOHn/c169ev1zXXXNOmvnfvXo0YMcL3jgEAAAD4t7pyafur5iXepw+01AdcZd4rPeJmKSDQsvbgG7fHq/d2FOu5dQd1oLRakhQW6NC8aQO14KoMxYb3zTB9jk+hesOGDXrssceUnZ0tt9utn/zkJ5o1a5b27NmjsLCwC7523759ioyMbH4cH88G7QAAAECvcmKbufDYjjckd51ZC4yQxn/bDNMJIy1tD75pcHv01tYivbDhkI6erpUkRQQHaP6VGXroyoGKDuUfRiQfQ/WHH37Y6vHSpUuVkJCg3NxczZgx44KvTUhIUHR0tM8NAgAAAPBj7nqlnvlcjmV/kIpyWuoJo80gPe5uKSjCuv7gs7pGj17bUqg/bzys4op6SVJMWKAWXJWhB6YOUGSw0+IO/csl3VNdUWHelB4TE3PRYydOnKj6+nqNGjVKP/3pT9u9JPychoYGNTQ0ND+urDSv13e5XH69p9m53vy5R/gXxgx8xZiBrxgz8BVjBh129ojseS8pYNsKZdaZ2ygZdqeMkbfIm/mQjNQrJJvNPJbx1CNU1bv1ypfHtGTTEZ2pMf8/S4wI0oKrBuqerP4KDTTj46WeH3rKeaaj/dkMwzA68w0Mw9Btt92ms2fP6tNPPz3vcfv27dPGjRuVmZmphoYGvfzyy3rhhRe0fv36885u/+xnP9NTTz3Vpv7KK68oNLR373EGAAAA+C3Dq8TKHcoo+4cSKnfKJjNK1DpjdCTuWhXGzlSDM8riJuGrGpe0ocSujcU21XnMfwiJCTL0jf5eXRFvKKCPLspeW1ur++67TxUVFa1uZf66Tofqxx57TO+//74+++wzpab6tmLfLbfcIpvNpnfeeafd59ubqU5LS1NZWdkF34zVXC6X1q5dq+uvv15OJ5dE4OIYM/AVYwa+YszAV4wZtKumTPbtf5V96zLZKo41l72DrpVr/Fx9WCBdP+sGxkwPc6qqQUs2HdUrXx5TbaO5MvuguDA9MiNDN49LktNxedJ0TznPVFZWKi4u7qKhulOXfz/++ON65513tHHjRp8DtSRNmTJFK1asOO/zQUFBCgpqu4Kc0+n06x/6OT2lT/gPxgx8xZiBrxgz8BVjBjIM6diX5nZYe/4ueRrNenC0NPF+Kesh2WMHy+5ySUdWM2Z6kKLyOv1pwyG9vuWYGtxeSdLI5Ej96zVDdOOYJDnstm7pw9/HTEd78ylUG4ahxx9/XKtWrdL69euVkZHRqeby8vKUnJzcqdcCAAAAuIwaqqWdb5jbYZ3c2VJPmSRlPyyNuVNyhljXHzqtoKxGz68/qLe2FsntNS9YnpgercevHaJrhifIZuueMN3b+BSqH3vsMb3yyit6++23FRERoZKSEklSVFSUQkLMX6wnn3xSRUVFWr58uSTpmWee0cCBAzV69Gg1NjZqxYoVWrlypVauXNnFbwUAAABAp53aZwbp7a9KDeZCwQoIlsZ8U8p+SOqfaW1/6LQ9Jyr1/IZDen/HCTVlaU0dFKvHrx2iqYNjCdOXyKdQ/fzzz0uSrr766lb1pUuX6sEHH5QkFRcXq7CwsPm5xsZG/eAHP1BRUZFCQkI0evRovf/++5ozZ86ldQ4AAADg0nhcUv775iXeR76y+HDMIClrgTThPin04jv9wD99WXBGz68/qHX7TjXXrh2RoMeuGaLMAf0s7Kx38fny74tZtmxZq8dPPPGEnnjiCZ+aAgAAAHAZVZ6Qcl+ScpdJ1ebVp7LZpWGzzb2lB10j2fvoks89nGEY+iS/VM+vP6Sco+ZWZ3abNGdssh6ZOVhj+rM6e1e7pH2qAQAAAPQQhiEVbDRnpfPflwxztWeFxUuT5kmZD0rRaZa2iM5ze7x6f2exnl9/SPklVZKkQIddd2X213dnDNbAuDCLO+y9CNUAAABAb1ZXLm1/TcpZLJXtb6mnTzNnpUfeKgUEWtYeLk29y6M3co/rzxsP6diZOklSWKBD35kyQAuuylBiZLDFHfZ+hGoAAACgNyreYc5K73xDctWatcBwafy3zfulE0dZ2x8uSWW9Syu+OKolnx1RWXWDJCkmLFDzpw3U3KkDFRXqv1tV9TaEagAAAKC3cNVLe942w/TxL1vq8SOlyQ9L4+6RgiKs6w+X7FRVg5Z+XqCXNx9VVYNbkpQSFayFMwbpnuw0hQYS8bobP3EAAACgpzt7RMpZKuW9LNWeNmt2pzTqVnNv6fSpEtsm9WjHztTqzxsP6285x9Tg9kqShiSE65GZg3XbhBQ5HSwsZxVCNQAAANATeT3SwY/NWekDayQ17dQTmSplPShNnCtFJFrZIbrA3uJK/XnjYb2z/YQ8TZtMj0+L1qNXD9b1IxNlt/OPJVYjVAMAAAA9Sc1pc0Y6Z4lUfrSlPvhac1Z66A2Sg7/m92SGYWjz4dP604bD2rC/ZY/p6UPj9C9XD9bUQbGyceWB3+C3DQAAAPB3hiEdzzFnpXe/JXkazXpwtDTxfinrISl2sKUt4tJ5vIY+2l2iP204pO3HKySZe0zPHpus784YpHGp0dY2iHYRqgEAAAB/1Vgj7XzTDNMlO1rqKRPNWenRd0qBodb1hy5R7/Lozdzj+sunh3X0tLlSe1CAXXdnpenh6RkaEMse0/6MUA0AAAD4m7ID0pbF0rZXpAZzxlIBwdKYu8y9pftnWtsfukR5baNe3nxUyzYd0eka8+qDqBCn5k0doLnTBiouPMjiDtERhGoAAADAH3jc0r7V5qx0wYaWer8MM0hP+I4UGmNdf+gyx8/WavFnBXp9yzHVNnokSf2jQ/Tw9AzdnZWmsCBiWk/C/1sAAACAlSqLpa3LpdylUlWxWbPZpWE3mmF60LWSne2SeoP2VvIemRypR2YO0k1jkxXAtlg9EqEaAAAA6G6GIR35zJyVzn9P8rrNeli8NGmelPmgFJ1maYvoGudbyfvKIbH67ozBmj40jpW8ezhCNQAAANBd6iuk7a+Z90uX7Wupp081Fx4beYsUwH20vYHb49UHu0r0l08Pa8dXVvKeMzZZ350xWGNToyzuEF2FUA0AAABcbiU7zVnpHW9IrhqzFhgujbtbylogJY2xtj90meoGt17fckxLPitQUXmdJCnY2bSS91WDlB7Lau29DaEaAAAAuBzcDdKet80wfeyfLfX4Eeas9Lh7pOBI6/pDlyqpqNfSTQV65Z+Fqqo3L+ePCQvUA1MGaO7UAYplJe9ei1ANAAAAdKWzR81Fx7a+LNWWmTV7gHlpd/ZCacA0iXtoe409Jyr14qfm4mPupsXHBsWF6eHpg3TnpP4Kdjos7hCXG6EaAAAAuFRer3ToY3NWev9HksxwpYgUKWu+NGmuFJFkaYvoOoZhaOOBMv1l42F9drCsuX5FRowWTh+ka0ckyG7nH076CkI1AAAA0Fk1p6VtK6ScJdLZIy31QVebl3gPmy05+Ct3b9Hg9uidbSf04qcF2neySpLksNs0e0ySFk4fpPFp0dY2CEvwGw4AAAD4wjCkolxzVnrXW5KnwawHRUkTvyNlPSTFDbW2R3Sp8tpG/fWfhVq26YhOVZn/f4cFOnRPdrrmXzlQaTEsPtaXEaoBAACAjmislXa9aYbp4u0t9aRx0uSF0phvSoGEq96k8HStlnxeoNe3HFOdyyNJSooM1oNXDtS9k9MVFeK0uEP4A0I1AAAAcCFlB6WcxdK2v5r7TEuSI0gafYcZpvtnsvBYL2IYhnKPntXizwr00e4SNa09ppHJkVo4PUM3j0tRYIDd2ibhVwjVAAAAwNd53NL+D8xZ6cPrW+r9BpqXd0+4XwqLtao7XAYuj1erdxZr8WcF2nG8ork+c1i8Fk4fpCuHxMrGP56gHYRqAAAA4JyqEmnrcilnqVR1oqlok4bdaC48Nvhayc4sZW9SXtuoV74s1PJNR1VSWS9JCgyw686J/TX/ygwNT4qwuEP4O0I1AAAA+jbDkI5+bs5K731X8rrNemisuRVW5nyp3wBre0SXO3SqWks/L9DK3KLm+6XjwoM0d+oAfeeKdMWGB1ncIXoKQjUAAAD6pvpKacfrZpg+ld9ST5siZS+QRt0mBRCsehPDMLTp0Gkt/qxAn+SXNtdHJkdqwVUZumV8soICHBZ2iJ6IUA0AAIC+5eRuM0hvf11y1Zg1Z5g07m4zTCeNtbY/dLl6l7m/9JLPC5RfYu4vbbNJ141I1ENXDdTUQdwvjc4jVAMAAKD3czeYl3ZveVEq3NxSjxtu3is9/h4pOMq6/nBZnKpq0Iovjuqv/zyqsupGSVJooEPfykzVg1dmKCMuzOIO0RsQqgEAANB7lR+Tcpeai4/VnDJr9gBpxE1mmB44ne2weqG9xZVa8lmB3t52Qo0eryQpJSpY86YN1Lez0xUVyv7S6DqEagAAAPQuXq90+BNpy2Jp/4eSYYYqRSSbi45NmitFJlvbI7qcx2to7Z6TWrapQF8cPtNcn5AWrQVXZejGMUlyOli5HV2PUA0AAIDeofaMtO2vZpg+W9BSz5hpzkoPny05mKHsbSpqXXo9p1AvbTqqovI6SZLDbtONo5P00FUZyhzQz+IO0dsRqgEAANCzFeWaQXrXSslt7jOsoChpwn1S1kNS/DBr+8NlceBklZZuOqJVW1u2xOoX6tS9k9N1/5QBSokOsbhD9BWEagAAAPQ8jbXS7rfMhcdO5LXUk8ZK2Qulsd+UAlmEqrfxeg19kl+qZZuO6LODZc31EUkRmn/lQN02ob+CnWyJhe5FqAYAAEDPcfqQlLNEylsh1ZebNUegNPpO8xLv1CwWHuuFKutdeiPnuJZvPqKjp2slSXabdP2oRM2/MkNXZMSwJRYsQ6gGAACAf/O4pQMfmbPShz5pqUenS1kLpIn3S2Fx1vWHy+bQqWq9tOmI3sw9rtpG8xLvyOCA5ku802JCLe4QIFQDAADAX1WdlPKWSznLpMrjTUWbNPR68xLvIddJdi717W28XkMbDpzSss+PaMP+U831oQnhevDKgbpjYn+FBhJj4D8YjQAAAPAfhiEVbjZnpfe8I3ldZj00Vpr4gJQ1X+o30NIWcXlU1ru0Mve4Xt58VIfLaiSZV/JfNyJB86/M0LTBsVziDb9EqAYAAID16iulHa+b90uX7mmpp04275UedZvkDLauP1w2+0qqtHzzEa3KK2q+xDsiKEB3Z6dp7tQBGhDLgnPwb4RqAAAAWOfkHnNWesfrUmO1WXOGSmO/JWUvkJLHW9sfLguXx6u1e05q+eYj+uLwmeb60IRwzZ1mXuIdHkRUQc/ASAUAAED3cjdKe98x95Yu3NRSjx1qzkqP/7YUEm1Ze7h8TlU16LUvC/XXfxaqpNLcU9xht2nWqETNnTpQUwaxijd6HkI1AAAAukf5MSl3mbR1uVRTatZsDmnETWaYzpjBdli9kGEY2lpYruWbj2j1zmK5PIYkKS48UN/OTtd9V6QrJTrE4i6BziNUAwAA4PLxeqXD68xZ6f0fSIbXrIcnSZkPSpnzpMgUS1vE5VHv8uid7Se0fPMR7SqqbK5PTI/WvKkDNXtskoICWL0dPR+hGgAAAF2v9oy07RUpZ7F05nBLfeB0c1Z6xE2Sw2ldf7hsjp2p1Yovjur1nGMqrzVXbw8MsOu28SmaO3WgxqZGWdwh0LUI1QAAAOg6RVvNWeldb0pu855ZBUVK4+81Fx6LH25tf7gsvIa0Yf8pvZZTpI/zS2WYV3grtV+I7p8yQPdkpalfWKC1TQKXCaEaAAAAl8ZVJ+16y1zF+8TWlnriWDNIj/2WFBRuXX+4bE5XN+i1L49qSZ5Dp7/Ia65PHxqneVMH6poRCXLYuU8evRuhGgAAAJ1z+pC5r3TeCqm+3Kw5AqVRt5uXeKdNZuGxXsgwDOUePasVXxzV6p0lavR4JdkUGRygb2am6f4p6RoUzz+ioO8gVAMAAKDjvB5p/0fmrPShj1vqUelS1nxp4gNSeLx1/eGyqW5wa1Vekf76xVHll1Q118f1j9To4LN68r7rFBkWbGGHgDV8CtVPP/203nrrLeXn5yskJETTpk3Tr371Kw0ffuF7YzZs2KBFixZp9+7dSklJ0RNPPKFHHnnkkhoHAABAN6ouNbfCyl0mVRxrKtqkId8wZ6WHXi/ZWcm5N9pbXKkVXxzV3/OKVNPokSQFO+26dXyK7p8yQCMTw7R69WqFBPL/P/omn0L1hg0b9Nhjjyk7O1tut1s/+clPNGvWLO3Zs0dhYWHtvqagoEBz5szRwoULtWLFCn3++ed69NFHFR8fr7vuuqtL3gQAAAAuA8OQCr8wZ6X3vC15zZWcFRIjTXpAypwvxWRY2yMuiwa3Rx/sLNGKL44q5+jZ5vqg+DDdf8UA3TUpVVGh5urtLpfLqjYBv+BTqP7www9bPV66dKkSEhKUm5urGTNmtPuaF154Qenp6XrmmWckSSNHjlROTo5+85vfEKoBAAD8UICnTvbcpdLWZVLp7pYnUrPNWelRt0tOLvPtjQpP1+qvXx7VGznHdaamUZIUYLdp1uhE3X/FAE0dHCsb98kDrVzSPdUVFRWSpJiYmPMes3nzZs2aNatV7YYbbtDixYvlcrnkdLbdn7ChoUENDQ3Njysrzc3iXS6XX/9L2Lne/LlH+BfGDHzFmIGvGDPwyal8actizdr1qhw7zO2wjIAQGaPvlCfzISl5fMuxjKlew+3xasP+Mr2y5Zg+PXi6eTuspMgg3ZOVqruzUpUQEWQe63a3eT3nGfiqp4yZjvZnM4xzvza+MQxDt912m86ePatPP/30vMcNGzZMDz74oH784x831zZt2qQrr7xSJ06cUHJycpvX/OxnP9NTTz3Vpv7KK68oNDS0M+0CAACgHTavW8kVucoo+1hx1fnN9eqgJBXEXadjMVfJFdD+bX7o2c40SF+U2vVFqU0VjS2zzyOivLoqydCofoYcTEqjD6utrdV9992niooKRUZGnve4Ts9U/+u//qt27Nihzz777KLHfv0SkXM5/nyXjjz55JNatGhR8+PKykqlpaVp1qxZF3wzVnO5XFq7dq2uv/76dmfgga9jzMBXjBn4ijGD86o8IXveS7LnvSxbTakkybA55Bl6g/7pHauJd/wvjQgM1AiL20TXOjcr/VrOcW08UCZv0/Rav1Cn7pyYonuz0zQg1rdJLM4z8FVPGTPnrpi+mE6F6scff1zvvPOONm7cqNTU1Asem5SUpJKSkla10tJSBQQEKDY2tt3XBAUFKSgoqE3d6XT69Q/9nJ7SJ/wHYwa+YszAV4wZSJK8Xqlgg7nw2L4PJMNcyVnhiVLmg7JNmicjNEFlq1fLGRjImOlFTpTX6bUtx/S3LcdUUlnfXJ86KFb3XZGuWaMTFRRwaat3c56Br/x9zHS0N59CtWEYevzxx7Vq1SqtX79eGRkXX+1x6tSpevfdd1vV1qxZo6ysLL/+AQIAAPQadWelba9KOYul0wdb6gOnS9kLpBE3S46mv5f5+T2O6Di3x6v1+07plS8LtX5fafOsdExYoL6ZmapvZ6dpUHy4tU0CvYBPofqxxx7TK6+8orffflsRERHNM9BRUVEKCQmRZF66XVRUpOXLl0uSHnnkET377LNatGiRFi5cqM2bN2vx4sV69dVXu/itAAAAoJUT28xZ6Z1vSu46sxYYIU24V8paICVwcXdvdKK8Tq9vOaa/5RxTcUXrWel7r0jXDV0wKw2ghU+h+vnnn5ckXX311a3qS5cu1YMPPihJKi4uVmFhYfNzGRkZWr16tb7//e/rueeeU0pKiv7whz+wnRYAAMDl4KqXdq8yw3RRTks9cYw5Kz32bimI2cne5tys9KtfFmods9JAt/L58u+LWbZsWZvazJkztXXrVl++FQAAAHxx5rCUs1TKe9m83FuSHIHmntLZC6S0KyT2F+51jp+t1Rs5x9vMSk8ZFKP7rhjArDTQDS5pn2oAAABYyOuRDqwxZ6UPfiypaQIkKl3Kmi9NfEAKj7e0RXS9RrdX/9h7Uq9tOaZPD5xq3le6X6jTnJWenK7BzEoD3YZQDQAA0NNUn5Lylks5y6SKltvuNOQbUvbD0tBZkp3Zyd7mYGmVXt9yTCu3FulMTWNzfdrgWN2TnaYbxyQxKw1YgFANAADQExiGdOyf5qz07r9L3qZVukP6SRPvl7IekmIGWdoiul5to1vv7SjW37YcU87Rs831xMggfSszTd/KStWA2DALOwRAqAYAAPBnDdXSzr9JWxZLJ3e11PtnmbPSo2+XnCGWtYeuZxiGdhyv0Gtbjund7SdU3eCWJDnsNl07IkHfzk7TzGHxCnDYLe4UgESoBgAA8E+l+ea+0ttelRqrzFpAsDT2m2aYTplobX/ocuW1jfp7XpFe23JM+SVVzfUBsaG6JztN35yUqoTIYAs7BNAeQjUAAIC/8Lik/PfMWekjn7bUYwabK3hPuM+83Bu9htdr6IuC03p9yzF9sKtEjW6vJCkowK45Y5N1d1aapgyKkY2V2wG/RagGAACwWkWRtPUlKfclqbrErNns0vA55r3Sg66R7Fzq25ucKK/TytzjenPrcR09XdtcH5kcqXsnp+m28f0VFeq0sEMAHUWoBgAAsIJhSAUbzIXH8ldLhseshyVImfOkzAelqFRLW0TXqnd5tGbPSb2Rc0yfHSxr3gorIihAt05I0bez0zWmfySz0kAPQ6gGAADoTnXl0vZXzUu8Tx9oqQ+40rzEe8QtUkCgZe2haxmGoZ1FFfpbzjG9s+2EKuvdzc9NGRSju7PMrbBCA/lrOdBT8dsLAADQHYq3m7PSO96Q3HVmLTBcGv9tKWuBlDjK2v7QpcqqG/T3vCK9kXNc+062LDrWPzpEd2Wm6puTUpUeG2phhwC6CqEaAADgcnHVS3v+bobp41ta6gmjzFnpcfdIQRGWtYeu5fJ4tX7fKb2Rc0yf5JfK7TWv7w4KsOvGMUn6Vmaapg2Old3O5d1Ab0KoBgAA6GpnCqTcpdLWl6W6M2bN7pRG3WZuh5U+ReK+2V7jwMkqvZF7XG9tLVJZdUNzfXxatL6VmapbxqcoKoRFx4DeilANAADQFbwe6eA/zFnpA2slNa1CFZkqZT0oTZwrRSRa2SG6UEWdS+/tOKE3co5r27Hy5npsWKDunNRf38pK07BErkIA+gJCNQAAwKWoKZPyXpZylkjlhS31wdea90oPu1Fy8Feu3sDt8erTA2V6c+txrd1zsnlPaYfdpmuGJ+jurFRdMyJBTgfbnwF9CWd4AAAAXxmGeY/0lhel3askT6NZD46WJt5v7i0dO9jSFtF19hZXamXucf1924lWl3cPSwzXtzLTdPvE/oqPCLKwQwBWIlQDAAB0VGONtPMNM0yX7Gypp0wy75Uec6fkDLGuP3SZsuoGvb3thFbmHtee4srmekxYoG4dn6K7JqWypzQASYRqAACAizu13wzS21+VGpoCVkCwNOabUvZDUv9Ma/tDl2hwe/Tx3lKtzD2u9ftPydO0erfTYdN1IxJ156T+unp4ggIDuLwbQAtCNQAAQHs8Lin/fTNMH/m0pR4zyLxXesJ9UmiMdf2hSxiGobxj5VqZe1zv7ShWRZ2r+bnxadG6a1J/3TIuRf3CAi3sEoA/I1QDAAB8VeUJKfclKXeZVF1i1mx2adhsc2/pQddIdmYqe7oT5XValVeklVuP6/CpmuZ6UmSw7pjUX3dN6q8hCazeDeDiCNUAAACGIRVsNGel89+XDI9ZD4uXJs2TMh+UotMsbRGXrrLepQ93lejveUXafPi0jKZdz0KcDt04Jkl3TUrV1MGxcti5TxpAxxGqAQBA31VXLm1/TcpZLJXtb6mnTzUXHht5qxTAZb89WaPbq437T2nVtiL9Y89JNTRtgyVJUwbF6K5JqZo9NlnhQfy1GEDncPYAAAB9T/EOc1Z65xuSq9asBYZL4+4xL/FOHG1tf7gkhmFoa2G5/p5XpPd2nNDZ2pb7pIckhOuOif1124QUpfYLtbBLAL0FoRoAAPQNrnppz9tmmD7+ZUs9fqQ0+WEzUAdxD21PVlBWo7/nFenv24p09HRtcz0uPEi3TUjRHRP7a3QK22AB6FqEagAA0LudPSLlLJXyXpZqT5s1e4A06jbzEu/0qRIhq8c6Xd2g93YUa1VekbYdK2+uhwY6dOPoJN0+sb+mDY5VgIPF5QBcHoRqAADQ+3g90sGPzVnpA2skNa1IFZkqZT0oTZwrRSRa2SEuQV2jR2v3ntTf84q0cf8puZv2k7bbpOlD43XHxP6aNTpRoYH8VRfA5ceZBgAA9B41p80Z6ZwlUvnRlvrga81Z6aE3SA7++tMTuT1ebTp0Wm9vO6GPdpeousHd/Ny41CjdPqG/bh6frISIYAu7BNAX8acKAADo2QxDOp5jzkrvXiV5Gsx6cLQ08X4p6yEpdrClLaJzzAXHzuqdbSf0/s5ilVU3Nj+X2i+kacGx/hqSEG5hlwD6OkI1AADomRprpJ1vmmG6ZEdLPXmCNHmhNPpOKZDVnXui/JJKvb3thN7dfkLHz9Y112PCAjVnbJJuHd9fWQP6yc5+0gD8AKEaAAD0LGUHpC2LpW2vSA0VZi0gWBpzl7kdVv9Ma/tDpxw7U6t3tp/Q29uKtP9kdXM9LNChG0Yn6ZYJKbpqSJycLDgGwM8QqgEAgP/zuKV9q81Z6YINLfV+GWaQnvAdKTTGuv7QKaeqGvT+jhN6e/sJ5RWWN9cDHXZdPTxet03or2tHJCgk0GFdkwBwEYRqAADgvyqLpa3LpdylUlWxWbPZpWE3mmF60LWSnZnLnqSy3qUPd5Xo3e0n9PnBMjUt3C27TZo2OE63jk/RDWOSFBXitLZRAOggQjUAAPAvhiEd+dSclc5/X/I2rfIcFi9NmitlPihFp1vaInxT2+jWx3tL9d6OE1q375Qa3d7m5yakReu2CSm6aRwrdwPomQjVAADAP9RXSNtfM++XLtvXUk+fam6HNfIWKSDIuv7gk3qXR+v3lerdHcX6ZG+p6lye5ueGJoTrtgkpumV8igbEhlnYJQBcOkI1AACwVslOc1Z6xxuSq8asOcOk8fdIWQukpDHW9ocOa3B79On+Mr2344TW7jmpmsaWIJ0eE6qbxyXr5nEpGpkcIZuNlbsB9A6EagAA0P3cDdKet80wfeyfLfX4Eeas9Lh7pOBI6/pDh7k8Xn12sEzvbS/Wmj0lqqp3Nz/XPzpEN41L1s3jkjW2fxRBGkCvRKgGAADd5+xRc9GxrS9LtWVmzR5gXtqdvVAaME0iePk9t8erLw6f0Xs7TujD3SUqr3U1P5cYGaQ5Y80Z6Ylp0ewlDaDXI1QDAIDLy+uVDn1szkrv/0hS03LPESlS1nxz8bGIJEtbxMV5vIa2HGkK0rtKVFbd2PxcXHigZo8xZ6SzB8YQpAH0KYRqAABwedSclratkHKWSGePtNQHXWNuhzVstuTgryL+zOM1lHPkjFbvLNYHu0pUWtXQ/Fx0qFOzxyTp5nEpuiIjRgEOtjYD0DfxJxkAAOg6hiEV5Zqz0rvekjxNISw4Sppwv5T1kBQ3xNoecUFuj1cHKmz693f3aM2eUyqrbgnSEcEBumF0km4el6wrh8TJSZAGAEI1AADoAo210q43zTBdvL2lnjROmrxQGvNNKTDUuv5wQefukX5/Z7E+2l2sMzUOScclSZHBAbp+VJLmjE3SVUPjFBTgsLZZAPAzhGoAANB5ZQelnMXStr+a+0xLkiNIGnOXeYl3/0wWHvNTLo9Xmw6d1gc7i/XR7hKd/cpiY6EBhuaMS9XN41M0bXCcAgOYkQaA8yFUAwAA33jc0v4PzFnpw+tb6v0GmvtKT7xfCo2xqjtcQKPbq88Plmn1zmKt2XNSFXUtQTomLFA3jE7UrJEJOpv/T91y82g5nU4LuwWAnoFQDQAAOqaqRNq6XMpZKlWdaCrapGE3mntLD75WsjOj6W8a3B59ur9Mq3cVa+2ek632kY4LD9QNo5N009hkTW5abMzlcmn1fgsbBoAehlANAADOzzCko5+bs9J735W8TYEsNM7cCivzQanfAEtbRFvVDW6t31eqD3eVaP2+U6puaAnSCRFBmj0mSbPHmttfOdj+CgAuCaEaAAC0VV8hbX/dvF/6VH5LPW2KOSs96lYpIMi6/tDG2ZpG/WPvSX20u0QbD5Sp0e1tfi4pMlg3jknSTeOSlZnej32kAaALEaoBAECLkl3mrPSOv0muGrPmDJPG3W0uPJY01tr+0EpJRb3W7CnRh7tK9M+CM/J4jebnBsaG6sYxybpxTJLG9Y8iSAPAZUKoBgCgr3M3SHveMcP0sS9a6nHDzVnp8feY+0zDLxSU1eij3WaQ3nasvNVzo5IjdcPoJN04JknDEsNlY+V1ALjsCNUAAPRV5YXmomNbl0u1ZWbNHiCNuNkM0wOvYjssP2AYhvYWV+nD3SX6aFeJ9p2savV85oB+unF0km4YnaT0WPYCB4Du5nOo3rhxo/7rv/5Lubm5Ki4u1qpVq3T77bef9/j169frmmuuaVPfu3evRowY4eu3BwAAl8LrlQ59Ys5KH/hIMpruu41IljLnm4uPRSZb2yPk8RrKPXpWa/eU6KPdJ1V4prb5uQC7TVMHx+qG0UmaNSpRCZHBFnYKAPA5VNfU1Gj8+PGaP3++7rrrrg6/bt++fYqMjGx+HB8f7+u3BgAAnVV7Rtr1upSzRDpb0FLPmGnOSg+fLTnYk9hKdY0ebTxwSmv3nNQn+aU6U9PY/FxQgF0zhsXrxtFJum5kgqJDAy3sFADwVT6H6tmzZ2v27Nk+f6OEhARFR0f7/DoAANBJhiFb0VZNPPoXBfzP/ye56816UJQ04T4p6yEpfpi1PfZxZdUN+mRvqdbsOalPD5xSw1dW7I4KceraEQm6flSirh4er9BA7toDAH/UbWfniRMnqr6+XqNGjdJPf/rTdi8JP6ehoUENDQ3NjysrKyVJLpdLLpfrsvfaWed68+ce4V8YM/AVYwYd4qqVbc/fZc9ZrICS7UpvKhuJY+XJfEjG6DulwLCmYxlL3a2grEb/yC/Vx3tPaeuxchktC3YrNTpY141M0DdGJChzQLScDnvTM0a3/d5znoGvGDPwVU8ZMx3tz2YYXz2V+8Zms130nup9+/Zp48aNyszMVENDg15++WW98MILWr9+vWbMmNHua372s5/pqaeealN/5ZVXFBrKAhwAALQnrL5EA8s+UfqZTxXoMbfD8tgCdCL6ChXEX6ezoYNZeMwCXkMqrJZ2nrFr51mbTta1/v8gNczQ2H5ejY0xlBLK/0UA4C9qa2t13333qaKiotWtzF932UN1e2655RbZbDa988477T7f3kx1WlqaysrKLvhmrOZyubR27Vpdf/31cjq5Lw0Xx5iBrxgzaMPrlu3AGtm3LpX98LrmshGVLm/mg2oY9S2t/TyPMdPN6l0ebT58Rh/nl+qT/FM6Vd1yf3SA3aYrMmL0jZHxum5EgpKj/GuhMc4z8BVjBr7qKWOmsrJScXFxFw3VltycM2XKFK1YseK8zwcFBSkoKKhN3el0+vUP/Zye0if8B2MGvmLMQNWl0taXpJxlUuXxpqJNGjpLyn5YtiHXyWF3yOlyScpjzHSDk5X1+iS/VB/vLdXnB8tU5/I0PxcRFKCZw+M1a3SSrh4er8hg////gjEDXzFm4Ct/HzMd7c2SUJ2Xl6fkZLbrAADAJ4YhFW42t8Pa847kbbrXKzRWmviAlDVf6jfQ0hb7EsMwtKuoUh/nn9THe0u1s6ii1fMpUcG6bmSirh+VqCmDYhUYYD/PVwIA9GQ+h+rq6modPHiw+XFBQYG2bdummJgYpaen68knn1RRUZGWL18uSXrmmWc0cOBAjR49Wo2NjVqxYoVWrlyplStXdt27AACgN2uokna8Lm1ZLJXuaamnTpayF0ijbpec/nUJcW9V1+jR5wfL9HG+ue3VycqW29VsNml8arSuG5Gg60YmamRyhGzcIA0AvZ7PoTonJ6fVyt2LFi2SJM2bN0/Lli1TcXGxCgsLm59vbGzUD37wAxUVFSkkJESjR4/W+++/rzlz5nRB+wAA9GIn90g5i6Xtr0mN1WbNGSqN/ZYZppPHW9tfH1FcUdfqsu6vbnsVGujQ9KFxum5koq4ZnqD4iLa3rwEAejefQ/XVV1+tC61ttmzZslaPn3jiCT3xxBM+NwYAQJ/kbpT2vmPOShduaqnHDpWyH5bGf1sKibasvb7A6zW0s6hCH+89qY/zS7X7RGWr5/tHh+i6keZs9BUZMQp2OizqFADgDyy5pxoAAHxN+TEpd5m0dblUU2rWbA5pxE1mmM6YwV5Ll1FFrUufHjyldfmntGF/qcq+slq3zSZNTIvWdSMTdd3IBA1P5LJuAEALQjUAAFbxeqXD68xZ6f0fSEbTZcXhSVLmg1LmPCkyxdIWeyvDMJRfUqV1+0q1Pv+UcgvPyuNtuRIvLNChGcPidd3IRF09PF5x4VzWDQBoH6EaAIDuVntG2vaKeb/0mcMt9YHTzVnpETdJDv/dYqSnqm5w6/ODZVq/r1Tr8k+ppLK+1fNDE8J1zYgEXT08XlkDYlitGwDQIYRqAAC6S9FWc1Z615uSuynQBUVK4+81Fx6LH25tf72MYRg6dKrGDNH7SvVlwRm5PC2z0cFOu64cHKerRyTo6mHxSosJtbBbAEBPRagGAOByctVJu94y95Y+sbWlnjhWyn5IGnu3FBRuXX+9TF2jR18cPq11TUH62Jm6Vs8PiA3VNcMTdM2IBBYZAwB0CUI1AACXw+lDUs4SKW+FVF9u1hyB0ug7zEu8U7NZeKwLGIahA6XV2rDvlDYeOKV/FpxR41e2vAp02HXFoJjmIJ0RF2ZhtwCA3ohQDQBAV/F6pP0fmbPShz5uqUelm7PSEx+QwuKs66+XqKh16bODZdqwv1Qb95e1uTe6f3SIrh4er2uGJ2jakFiFBvLXHQDA5cOfMgAAXKrqUmnrS1LuS1LFsaaiTRp6vTkrPeQbkp3LjDvL4zW0/Xi5Nu4/pQ37T2n7sXJ9ZaFuBQXYNWVQrGYMi9fMYXEaHB/OllcAgG5DqAYAoDMMQyrcbM5K73lH8rrMekiMNOkBKXO+FJNhbY89WElFvRmiD5zSZwfKVFHnavX80IRwzRwWrxnD4jWZe6MBABYiVAMA4IuGKmnH69KWJVLp7pZ6arY5Kz3qdskZbFl7PVW9y6MtR87o0wNl2rDvlPadrGr1fGRwgK4aGqeZw+I1fWi8UqJDLOoUAIDWCNUAAHTEyT3mvtLbX5Maq81aQIg07ltS1gIpZYKl7fU0Xq+hPcWV+uxgmT47UKYvj7ReYMxmk8anRjdf0j0+NVoBDvaNBgD4H0I1AADn426U8t8195Y++nlLPXaIOSs9/l4pJNqy9nqaovI6fXbglD49UKZNh07rTE1jq+eTIoObZ6OvGhKnfmGBFnUKAEDHEaoBAPi6iuNS7jJz4bGaUrNmc0gjbpKyF0gZM9kOqwMq613afOi0PjtQps8OlqmgrKbV82GBDk0dHKurhsTpqqEsMAYA6JkI1QAASJLXKxWsN2el962WjKZLkcOTpMwHpcx5UmSKlR36PZfHq7zCcnM2+mBZm1W6HXabxqdG6aqh8Zo+NE4T0qLl5JJuAEAPR6gGAPRtdWelba+YYfrMoZb6wOnmJd4jbpIcTuv682Ner6H8kiptOlSmzYdO64vDp1XT6Gl1zKC4MF01NE5XDYnTlMGxigzmZwkA6F0I1QCAvulEnrkd1s6VkrvOrAVGSBPuNRceSxhhbX9+yDAMFZTVaNOh09p86LQ2H257X3RMWKCuHBKn6UPidOXQOPVnlW4AQC9HqAYA9B2uOmn3KjNMF+W21BPHmPdKj71bCgq3rj8/VFRep00HzZnoTYdOq6SyvtXzoYEOTc6I0dRBsbpySJxGJUfKbue+aABA30GoBgD0fmcOSzlLpLwV5uXekuQINPeUzn5YSpvMwmNNyqobmgP05kNlOnK6ttXzgQ67Jg2I1rTBcbpySKzGpXJfNACgbyNUAwB6J69HOrDGnJU++I+WelSaufDYpHlSeLxl7fmLilqXvjxyRpsOlWnTwdPad7Kq1fMOu03jUqM0bXCspg2OU+aAfgp2OizqFgAA/0OoBgD0LtWnpLzlUs5SqeJYU9EmDfmGOSs99HrJ3ndDYXlto74sOKMvDp/RPwtOa09xpQyj9TEjkyObQnSssjNiWFwMAIALIFQDAHo+w5CO/dOcld79d8nrMush/aSJD0hZ86WYQZa2aJWztY3aftqmravz9eWRcuWXtA3Rg+LCNHWweU/0lEGxigkLtKZZAAB6IEI1AKDnaqiWdv7N3A7r5K6Wev8sc1Z69O2Ss2+tPn2mplFfFpzWF4fP6IvDp5VfUiXJIamw+ZjB8WGaMihWUwbF6oqMGCVEBlvWLwAAPR2hGgDQ85TmSzmLpW2vSo1N9wAHBEtjv2mG6ZSJ1vbXjcqqG5ou5z6tfx4+0+aeaElKCjF03dh0TR0Sp8kZMUqIIEQDANBVCNUAgJ7B45Ly3zNnpY982lKPGWwG6Qn3mpd793LHz9Zqy5Ez+rLgrLYcOaODpdVtjhmeGKErBsVoyqBYTUqN0D83fqw5c0bK6eTeaAAAuhqhGgDg3yqKpK0vSbkvSdUlZs1ml4bPMcN0xkzJ3ju3dPJ6DR0ordaXR85oS8EZ5Rw5oxMV9W2OG5EU0Xwp9+SMGMWGBzU/53K5urNlAAD6HEI1AMD/GIZUsMFceCx/tWR4zHpYgrkdVuY8KSrV0hYvB5fHq51FFdpScEZbjpxRztGzKq9tHYoD7DaN7h+lyQP7KXtgjLIHxqgfC4sBAGAZQjUAwH/UlUvbXzUv8T59oKU+4Cope4E04mYpoPcEyJoGt/IKy5tnovOOnVW9y9vqmBCnQxPTo5U90JyFnpgerdBA/vgGAMBf8KcyAMB6J7aZC4/teENy15m1wAhp/LfNMJ0w0tL2ukpJRb1yj55VztEz2nr0rHadqJTH23p/q+hQp7IGxGhyhjkTPaZ/lJyO3nl5OwAAvQGhGgBgDVe9tOfv5iXex7e01BNGm0F63N1SUIRl7V0qt8er/JIq5R492/xRVF7X5riUqGBlZ8Q0z0QPiQ+X3W6zoGMAANAZhGoAQPc6UyDlLpW2vizVnTFrdqc06jZz4bH0KZKt54XKijqX8gpbAvS2Y+WqbfS0OsZuk0YmRypzQL/mj9R+oRZ1DAAAugKhGgBw+Xk90oG15qz0wX9IarrkOTJVypovTZorhSdY2qIvDMPQ0dO1TZdyn9XWo2e1v7RKRusruRURFKCJA/opM72fsgb20/i0aIUH8UcvAAC9CX+yAwAun5oyaetyKWepVFHYUh98nTkrPewGye6wrr8Oqm5wa8excuUdK1deoTkLXVbd2Oa4AbGhrWahhyZEyMGl3AAA9GqEagBA1zIM6diX5qz0nr9LnqbwGRwtTbxfynpIih1sZYcX5PUaOniqujk85xWWa9/JtrPQgQ67xqZGKXNAP01KN0N0fERQ+18UAAD0WoRqAEDXaKiWdr5hbod1cmdLPWWSOSs95k7JGWJdf+dxpqZR246dVV6hGaC3HytXVYO7zXH9o0M0IT1aE9OiNTE9WqNTohTs9P9ZdgAAcHkRqgEAl+bUPjNIb39Vaqg0awHB0phvStkPSf0zre3vKxrdXuWXVDYF6LPKO1auo6dr2xwXGujQuNQoTUjrp4lNQTohMtiCjgEAgL8jVAMAfOdxSfnvm5d4H/m0pR4zSMpaIE24TwqNsa4/SR6vocOnqrX9eIV2HC/X9uMV2nuiUo0eb5tjhySEa0LTDPTEtH4alhiuAPaGBgAAHUCoBgB0XOUJKfclKXeZVF1i1mx2adhsc2/pQddI9u4Po4Zh6PjZOu1oCtDbjpVrV1GFar62pZUkRYc6zQDdNAs9Pi1aUSHObu8ZAAD0DoRqAMCFGYZUsNGclc5/XzKagmpYvDRpnpT5oBSd1q0tlVU3mLPPxyq0/Xi5dhyv0JmatqtxhzgdGts/SuNSozQuLVoTUqOVFhMiWw/cBxsAAPgnQjUAoH115dL216ScxVLZ/pZ6+jRzVnrkrVJA4GVv42xNo3adqNDOogrtPF6hHccrVFRe1+Y4p8OmEUmRGpcapfGp0RqXFqUh8VzGDQAALi9CNQCgteId5qz0zjckV9MiXoHh0vhvm/dLJ466bN/6dHWDdhZVaFdRhXYVVWpnUfsB2maTBseHtwTo1CiNTI5kNW4AANDtCNUAAMlVL+152wzTx79sqcePNGelx90jBUd26bcsrapvFZ53FVWouKK+3WMHxoZqdP+o5ku5x/aPUkQw90EDAADrEaoBoC87e0TKWSrlvSzVnjZr9gBp1G3mrPSAaea08CUwDEMllfXaVVTZFKLNS7lLqxraHGuzSRlxYRqTYgbn0f0jNTolioXEAACA3yJUA0Bf4/VIBz82Z6UPrJFkmPXI/lLWfGniXCkisVNf2u3x6nBZjfacqNSe4srmz+0tInbuEu6x/aM0pn+UxqREalRKJDPQAACgRyFUA0BfUXPanJHOWSKVH22pD7pGmrxQGnqD5Oj4HwvVDW7lF7cOz/klVWp0t90H2mG3aUh8uBme+0dqbH/zHuiwIP4YAgAAPRt/mwGA3swwpOM55qz07lWSp+mS6+AoaeIDUtZDUuzgi3wJQycrG7SnuKLVDPSR07XtHh8W6NColEiNSo5s+hyloYnhLCIGAAB6JUI1APRGjTXSzjfNMF2yo6WePMGclR59pxQY2uZltY1u7T9ZrX0lldpbXKV9JVXad7Kq3cu3JSkpMvhrATpS6TGhstvZBxoAAPQNhGoA6E3KDkhbFkvbXpEaKsyaI0gac5c0+WGpf6YkyeM1VFhWo/ymS7bzSyq1r6RKR8/UyjDaflmH3abB8WGtZp9HJkcoNjyoG98cAACA//E5VG/cuFH/9V//pdzcXBUXF2vVqlW6/fbbL/iaDRs2aNGiRdq9e7dSUlL0xBNP6JFHHulszwCAr/K4pX2rzVnpgg0t9X4ZUvYCnRn6TeVXOLW3oEr7Nm9XfkmV9p+sUr2r7b3PkhQXHqgRSZEanhSh4UkRGpEUoWGJEVy+DQAA0A6fQ3VNTY3Gjx+v+fPn66677rro8QUFBZozZ44WLlyoFStW6PPPP9ejjz6q+Pj4Dr0eAHAelcXS1uVS7lKpqliSZNjsKoqfoXWRt+qjupHK/6RWZe9sbfflQQF2DUs0Q7MZns0gHR/B7DMAAEBH+RyqZ8+erdmzZ3f4+BdeeEHp6el65plnJEkjR45UTk6OfvOb3xCqAcBXhqHw8j2qfPkV9Tv2D9kNtyTpjCL1ivsaveq+VkWF8U0Hn21+2YDYUA1PjNCI5MjmED0wNkwO7n0GAAC4JJf9nurNmzdr1qxZrWo33HCDFi9eLJfLJaez7X6kDQ0NamhoaH5cWVkpSXK5XHK5XJe34Utwrjd/7hH+hTGDC6mqd+lgaY0OlFarsLhEKUff0fSKd3Sdjjcf86V3uFa4r9eH3mw1yqnkqGDNSAjTkPhwDUkI19CEMA1NCG936yqvxy2vpzvfEazAeQa+YszAV4wZ+KqnjJmO9nfZQ3VJSYkSExNb1RITE+V2u1VWVqbk5OQ2r3n66af11FNPtamvWbNGoaFtV6v1N2vXrrW6BfQwjJm+yzCkikbpZJ1NJ+uk0jqbSpo+V7hsGmk7qgcca/Vvjs8VZjP/sbHGCNL7ukrrAq9TXXi6kkIMPRZqKCnEreCAaknVknFSOimdOCmdsPYtwk9wnoGvGDPwFWMGvvL3MVNb2/72oV/XLat/22ytLy80mpaW/Xr9nCeffFKLFi1qflxZWam0tDTNmjVLkZGRl6/RS+RyubR27Vpdf/317c7AA1/HmOk7GtxeFZ6u1aGyGh0+VaPDZU0fp2pU09h6ujhQLs22/1MPBP5DWfb9zfXy8EE6M/w72lqXqptvvlV3MGbQAZxn4CvGDHzFmIGvesqYOXfF9MVc9lCdlJSkkpKSVrXS0lIFBAQoNja23dcEBQUpKKjtQjlOp9Ovf+jn9JQ+4T8YM72DYRg6U9OoI6drdKi0RodOVTd91KjwTK083nb2qpK5XdWA2FBNjq7Wbe6PNPH0ewpuPGM+aQ+QRt4iZT+s6AFXKszt1s7Vqxkz8BljBr5izMBXjBn4yt/HTEd7u+yheurUqXr33Xdb1dasWaOsrCy//gECwPlU1bt0pKxWh8uqdaSsVgVl1So4XauCU9WqrHef93XhQQEaHB+mwQnhGhxvfgyJD9GAs1/IufV5af9HkpqCd0SKlPmglDlPikjqlvcFAAAA3/kcqqurq3Xw4MHmxwUFBdq2bZtiYmKUnp6uJ598UkVFRVq+fLkk6ZFHHtGzzz6rRYsWaeHChdq8ebMWL16sV199teveBQB0sXqXR4VnanX4VI0Kymp0pMz8fLisRmXVDRd8bUpUsDLizcXCBieEN39OiAhque2l9oyU97L08RLp7JGWFw+6RspeIA2bLTm65Q4dAAAAXAKf/8aWk5Oja665pvnxuXuf582bp2XLlqm4uFiFhYXNz2dkZGj16tX6/ve/r+eee04pKSn6wx/+wHZaACxX0+DW0dO1KjxTo6Ona3X0TK0KT9eqoKxGJyrqZLR/tbYkKS48UBlxYRoYG6aM+DBlNH0eEBOmkEBH+y8yDOl4jrTlRWnXW5KnKZwHR0kT7peyHpLihnT9GwUAAMBl43Oovvrqq5sXGmvPsmXL2tRmzpyprVu3+vqtAOCSGIahsurGltB8ulaFZ2p19LR5j3NZdeMFXx8RHKBBcWEaGBemjK98DIwLU2SwD7evNNZKu940w3Tx9pZ68ngpe6E05i4p0P93NgAAAEBbXFsIoEdrcHtUdLZOx8/W6dhZc6b56OlaHTldo2NnatusrP11/UKdSo8N04CYUA2IDVV6TGhzcI4NCzzvLgUdUnZQylksbfurVF9h1hxBZojOfljqP0m6lK8PAAAAyxGqAfg1l8er4vJ6HT9bq2Nna83wfKa2OUSfrLzw/c02m5QcGaz02FANiAkzP8eGamBsmNJiQhUV0sULJnrc0v4PzVnpw+ta6v0GSlkLpIn3S6ExXfs9AQAAYBlCNQBLuTxenays1/Fzs81fCcxFZ+tUXFGn8+xE1SzE6VBaTIhS+5kzzQNiz806hym1X4iCnee5x7krVZ2Uti6XcpdKlUVNRZs07EZzVnrwtZLdfvn7AAAAQLciVAO4bAzDUHmtS0XldTrR9FFcUf+Vx/Uqraq/aGgODLArtV+I0vqFmp9jQls9jrnUy7Q7yzCko59LWxZLe9+RvE3baYXGSZMekDLnS/0GdH9fAAAA6DaEagCdVtvoVklFvUqag3K9GZYr6lRUXqfi8nrVuS58T7MkBTrsSo4OVlq/0OYZ59R+5ue0mBDFhQXJbveje4/rK6Udr5uXeJ/Kb6mnTTFnpUfdKgUEWdcfAAAAug2hGkAbhmHoTE2jSirNwFxSWa+TTZ+LK+p1sqleWe/u0NeLCw9SSnSwUqJClBIdopToYPWPPvffIYoNC/Sv0Hw+J3ebQXrH36TGarPmDJPG3W3uLZ001tr+AAAA0O0I1UAfU9PgVmlVg0or61Va1dAckEsqzbBcXFGv0soGNXq8Hfp6oYEOJUU1heR2QnNSVHD33NN8ubgbzUu7t7woFW5uqccNN2elx99j7jMNAACAPolQDfQCXq+hs7WNZliuatCpqgaVVpnh+NRXH1c1qPYiW0x9VVx4oBIjg5UUGazEqGAlN31OigxWUlSwEiODFRkcYM39zJdb+TFz0bGty6WaU2bNHiCNuNkM0wOvYjssAAAAEKoBf+X2eHW21qXTNQ06Xd2osuoGlVU36nS1+fh0TUPTjHODyqob5L7Yal9fERroUEJEkOIjgppDc1JU00ekGZYTIoMUFNCDZ5g7w+uVDn9iLjy2/0PJaJqtj0g2Fx2bNFeKTLa2RwAAAPgVQjXQTTxeQ5V1Lp2pbdTZmkaVVTeqtLJWXxy3Kee9vTpT5/5KYG7U2dpGGR3PyZKkmLDA5rCcEBHc9DlICZFBig8PUkJksBIighQWxK9+K7VnpG1/NcP02YKWesZMc1Z6+GzJ0cX7WQMAAKBX4G/WQCe4PV6V17lUXtuoMzUunW0Kymdrv/rfTY+b/ru8znWekOyQjh1r9/vYbFJMaKBiwwMVGxak2PBAxYUHKTYsULHhQS0BOjJIceFBcjrYB9knRblmkN61UnLXm7WgKGnCfVLWQ1L8MGv7AwAAgN8jVKPP8ngNVdW7VFHX8lFZ52712Kx95b/rzZDc0VWv2xMRFKDoMKfiwoMUE+pU7ZmTmjBysBIiQxQbHqS4psAcGx6ofqGBcvSEVbF7ksZaafdb5sJjJ/Ja6knjzFnpsd+UAsOs6w8AAAA9CqEaPZLL41VNg1tV9eZHdYNb1Q2u1o/r3aqqd6mq+b/dqvxKiK66hGB8TlSIU/1CneoXZgZg86PlcUyYU9GhgYoJC1R0qFPRIYEKDGiZTXa5XFq9erXmfGOonE4uL76sTh+ScpZIeSuk+nKz5giSxtxphun+mSw8BgAAAJ8RqnHZuTxe1TZ6VNvoNj83eFTT6FZdo/m5tsF8ruZCxzR6zGDcYAblelfHtnvqiNBAh6JCnIoMdpqfQ8zPLR8BrWrRTcE5KsSpAC639m8et7ngWM5i6dAnLfXoAebl3RMfkMJiresPAAAAPR6hupczDEMujyGXx6tGt1cuj1cNTZ8bPV653IYaPR41ulsf09h0XIPbqwaXR/Uuj+pdXvOz2/zvOpen6bnW9XPHNrg8qnN5fFqV2lchTofCgwMUERRgfg4OUHhQgMKDnIr46uOmz18PzJHBzlYzx+glqk6aW2HlLpUqi5qKNmnoLHNWesh1kr2PrWwOAACAy4JQ3YX+84N9yj9k12d/3y2bzSbDkLyGZMhQ0//kNQwZTf9tNP+30XRsy3MeryG315DH65XbY8jjNeQxzM/nHru93q8c1/Jx7nGj2wzH/iLAblNooENhQQEKDXQoNDCg+XFIoENhX6uFBjoUFtj0XJCjOSiHB5lhOSwogIW50MIwpKObzHul974reV1mPTTWnJHOmi/1G2hpiwAAAOh9CNVdaFXeCZXX2aXSoosfbBG7TQoMsMvpsCuo6fO5x4EOu5wBdgU57HIG2JqPCXY6FOJ0KNjpUJDTruAA87+DnfaWzwEtz5879txzIU4zLDMjjMuivlLa8bq5ivepvS311MnmrPSo2yRnsHX9AQAAoFcjVHehR2ZmaMfuvRo+bLgCAhyy2SSbbLLb1PzfNptks9lkk1mz25pqaqo3HRfgsCnAbpOj6cP8b3tzrfmzwya7zaYAu735scNuk8NmawnLAWZgDgyws5I0eo+Tu80gveN1qbHarDlDpbHfkrIXSMnjre0PAAAAfQKhugstuHKgVlfs0ZyrB7GSM3A5uBulve+YYbpwU0s9dqg5Kz3+21JItGXtAQAAoO8hVAPwf+XHpNxl0taXpJpTZs3mkEbcZIbpjBlshwUAAABLEKoB+CevVzq8zpyV3v+BZDQtuheeJGU+KGXOkyJTLG0RAAAAIFQD8C+1Z6Rtr5h7S5853FIfON2clR5xk+Tg9goAAAD4B0I1AP9QtNWcld71puSuN2tBkdL4e82Fx+KHW9sfAAAA0A5CNQDruOqkXW+Ze0uf2NpSTxxrBumx35KCwq3rDwAAALgIQjWA7nf6kJSzRMpbIdWXmzVHoDTqdvMS77TJLDwGAACAHoFQDaB7eD3S/o/MWelDH7fUo9Kl7IekiQ9IYXHW9QcAAAB0AqEawOVVXSptXW5uiVVxrKlok4Zeb85KD/mGZHdY2SEAAADQaYRqAF3PMKTCL8xZ6T1vS16XWQ+JkSY9IGXOl2IyrO0RAAAA6AKEagBdp6FK2vE3cxXv0t0t9dRsc1Z61O2SM9iy9gAAAICuRqgGcOlK95pBevtrUmOVWQsIkcZ9S8paIKVMsLQ9AAAA4HIhVAPoHHejlP+utGWJdPSzlnrsEHNWevy9Uki0Ze0BAAAA3YFQDcA3FcfNRcdyX5JqSs2azSGNmGOG6YyZbIcFAACAPoNQDeDivF6pYL15ife+1ZLhNevhiVLmg9KkeVJUfys7BAAAACxBqAZwfnVnpW2vmGH6zKGW+sDpUvYCacTNksNpXX8AAACAxQjVANo6kWduh7VzpeSuM2uBEdKEe82FxxJGWNsfAAAA4CcI1QBMrjpp9yozTBflttQTx5iz0mPvloLCresPAAAA8EOEaqCvO3NYylki5a0wL/eWJEeguad09sNS2mQWHgMAAADOg1AN9EVej3RgjTkrffAfLfWodClrvjTxASk83rr+AAAAgB6CUA30JdWnpLzlUs5SqeJYU9EmDfmGOSs99HrJ7rC0RQAAAKAnIVQDvZ1hSMf+ac5K7/675HWZ9ZB+5ox01nwpZpClLQIAAAA9FaEa6K0aqqWdfzO3wzq5q6XeP8uclR59u+QMsaw9AAAAoDcgVAO9TWm+lLNY2vaq1Fhl1gJCpLHfNFfxTplobX8AAABAL0KoBnoDj0vKf8+clT7yaUs9ZrA5Kz3hXvNybwAAAABdilAN9GQVRVLuMmnrS1L1SbNms0vD55hhOmOmZLdb2iIAAADQmxGqgZ7GMKTD682Fx/Z9IBkesx6eKE2aJ2XOk6JSLW0RAAAA6CsI1UBPUVcubXvFvF/69MGW+oCrzHulR9wsBQRa1h4AAADQFxGqAX93YpsZpHe8IbnrzFpghDT+HvMS74SRlrYHAAAA9GWdutnyj3/8ozIyMhQcHKzMzEx9+umn5z12/fr1stlsbT7y8/M73TTQ67nqzdW7X/yG9OeZ0tblZqBOGC3d/Dvpf++VbvpvAjUAAABgMZ9nql9//XV973vf0x//+EddeeWV+tOf/qTZs2drz549Sk9PP+/r9u3bp8jIyObH8fHxnesY6M3OFEg5S6S8FVLdGbNmd0qjbjNnpdOnSDabtT0CAAAAaOZzqP7tb3+rBQsW6OGHH5YkPfPMM/roo4/0/PPP6+mnnz7v6xISEhQdHd3pRoFey/DKdmCNtHWpdPAfkgyzHpkqZc2XJs2VwhMsbREAAABA+3wK1Y2NjcrNzdWPfvSjVvVZs2Zp06ZNF3ztxIkTVV9fr1GjRumnP/2prrnmmvMe29DQoIaGhubHlZWVkiSXyyWXy+VLy93qXG/+3CP8SE2ZjLyX9Y09f1LAtrLmsnfQtfJmzpcxZJZkd5hFxhSacJ6Brxgz8BVjBr5izMBXPWXMdLQ/n0J1WVmZPB6PEhMTW9UTExNVUlLS7muSk5P15z//WZmZmWpoaNDLL7+s6667TuvXr9eMGTPafc3TTz+tp556qk19zZo1Cg0N9aVlS6xdu9bqFuCvDEP9ag4qo+xjpZR/KYfhVqCkRkeYCmNn6EjctaoJSpQOGtLBj6zuFn6M8wx8xZiBrxgz8BVjBr7y9zFTW1vboeNshmEYHf2iJ06cUP/+/bVp0yZNnTq1uf6LX/xCL7/8cocXH7vllltks9n0zjvvtPt8ezPVaWlpKisra3Vftr9xuVxau3atrr/+ejmdTqvbgT9prJZt10o5cpfKVrqruexJmqDtgdkacdeTcob679iG/+A8A18xZuArxgx8xZiBr3rKmKmsrFRcXJwqKioumEN9mqmOi4uTw+FoMytdWlraZvb6QqZMmaIVK1ac9/mgoCAFBQW1qTudTr/+oZ/TU/pENzi1X9ryorT9VanBvI1BAcHSmLuk7AXyJozTsdWrNTY0kjEDn3Cega8YM/AVYwa+YszAV/4+Zjram0+hOjAwUJmZmVq7dq3uuOOO5vratWt12223dfjr5OXlKTk52ZdvDfQcHpeU/74Zpo98Zbu5mEFS1gJpwn1SaIxZ8/P7SAAAAABcmM+rfy9atEgPPPCAsrKyNHXqVP35z39WYWGhHnnkEUnSk08+qaKiIi1fvlySuTr4wIEDNXr0aDU2NmrFihVauXKlVq5c2bXvBLBa5Qkp9yUpd5lU3XQ1h80uDZstZS+QBl0j2Tu1NTwAAAAAP+VzqL7nnnt0+vRp/fznP1dxcbHGjBmj1atXa8CAAZKk4uJiFRYWNh/f2NioH/zgByoqKlJISIhGjx6t999/X3PmzOm6dwFYxTCkgo3mrHT++5LhMeth8dKkeVLmg1J0mqUtAgAAALh8fA7VkvToo4/q0Ucfbfe5ZcuWtXr8xBNP6IknnujMtwH8V125tP01KWexVLa/pZ4+zZyVHnmrFBBoWXsAAAAAukenQjXQZxXvMGeld74huZqW2A8Ml8Z/27xfOnGUtf0BAAAA6FaEauBiXPXSnrfNMH38y5Z6/Ehp8sPSuHukoAjr+gMAAABgGUI1cD5nj0g5S6W8l6Xa02bNHmBe2j15oZQ+VbLZLG0RAAAAgLUI1cBXeT3SwY/NWekDayQZZj0yVcp6UJo4V4ro+J7sAAAAAHo3QjUgSTWnzRnpnCVS+dGW+uBrpeyHpaE3SA5+XQAAAAC0RkpA32UY0vEcc1Z69yrJ02DWg6OkiQ9IWQ9JsYOt7REAAACAXyNUo+9prJF2vmmG6ZIdLfXkCea90qPvlAJDLWsPAAAAQM9BqEbfUXZA2rJY2vaK1FBh1gKCpTF3mXtL98+0tj8AAAAAPQ6hGr2bxy3tW23OShdsaKn3yzCD9ITvSKEx1vUHAAAAoEcjVKN3qiyWti6XcpdJVSfMms0uDbvRDNODrpXsdktbBAAAANDzEarRexiGdOQzc1Y6/z3J6zbroXFS5jwp80EpOt3SFgEAAAD0LoRq9Hz1FdL218z7pcv2tdTTp5rbYY28RQoIsq4/AAAAAL0WoRo9V8lOc1Z6xxuSq8asOcOk8fdIWQukpDHW9gcAAACg1yNUo2dxN0h73jbD9LF/ttTjR5iz0uPukYIjresPAAAAQJ9CqEbPcPaolLtU2vqyVFtm1uwB5qXd2QulAdMkm83aHgEAAAD0OYRq+C+vVzr0sTkrvf8jSYZZj+wvZc6XJj0gRSRZ2iIAAACAvo1QDf9Tc1ratkLKWSKdPdJSH3S1OSs97EbJwdAFAAAAYD2SCfyDYUhFueas9K63JE+DWQ+OkibcL2U9JMUNsbZHAAAAAPgaQjWs1Vgr7XrTDNPF21vqyePNWekxd0mBodb1BwAAAAAXQKiGNcoOSjmLpW1/NfeZliRHkBmisx+W+k9i4TEAAAAAfo9Qje7jcUv7PzBnpQ+vb6n3G2juKz3xfik0xqruAAAAAMBnhGpcflUl0tblUs5SqepEU9FmLjiW/bA0+FrJbre0RQAAAADoDEI1Lg/DkI5+bs5K731X8rrNemicNGmulPmg1G+ApS0CAAAAwKUiVKNr1VdKO143w/Sp/JZ62hRzVnrUrVJAkHX9AQAAAEAXIlSja5TsMhce2/665Koxa84wadzdUvYCKWmstf0BAAAAwGVAqEbnuRvMS7u3vCgVbm6pxw03Z6XH32PuMw0AAAAAvRShGr4rL5Ryl5mLj9WcMmv2AGnEzWaYHngV22EBAAAA6BMI1egYr1c6/Im0ZbG0/0PJ8Jr1iGQpc765+FhksrU9AgAAAEA3I1TjwmrPSHkrpJwl0tmClnrGTHNWevhsyeG0rj8AAAAAsBChGu0ryjVnpXetlNz1Zi0oSppwn5T1kBQ/zNr+AAAAAMAPEKrRorFW2v2WufDYibyWetJYKXuhNPabUmCYdf0BAAAAgJ8hVEM6fci8vDtvhVRfbtYcgdLoO83tsFKzWXgMAAAAANpBqO6rPG5zwbGcxdKhT1rq0QPMy7snPiCFxVrXHwAAAAD0AITqvqbqpLkVVu5SqbKoqWiThs4yFx4bcp1kd1jaIgAAAAD0FITqvsAwpMLN5r3Se96RvC6zHhprzkhnzZf6DbS0RQAAAADoiQjVvVlDlbTjdXMV79I9LfXUydLkhdKo26SAIOv6AwAAAIAejlDdG53cY94rvf01qbHarDlDpXF3S1kLpORx1vYHAAAAAL0Eobq3cDdK+e+as9JHP2+pxw0z75Ue/20pOMq6/gAAAACgFyJU93Tlx6TcZebiYzWlZs3mkEbcZIbpjBlshwUAAAAAlwmhuifyeqXD68xZ6f0fSIbXrEckS5kPSpPmSpEplrYIAAAAAH0BobonqT0jbXvFvF/6zOGWesYMc1Z6+BzJ4bSuPwAAAADoYwjVPUHRVnNWetebkrverAVFShPuk7IekuKHW9sfAAAAAPRRhGp/5aqTdr1l7i19YmtLPXGsNPlhacw3paBw6/oDAAAAABCq/c7pQ1LOEilvhVRfbtYcgdLoO8xLvFOzWXgMAAAAAPwEodofeD3S/o/MWelDH7fUo9Kl7IekiQ9IYXHW9QcAAAAAaBeh2krVpeZWWLnLpIpjTUWbNOQb0uSF5me7w8oOAQAAAAAXQKjuboYhFX5hzkrveVvyusx6SIw06QEpc74Uk2FtjwAAAACADiFUd5eGKmnH38xVvEt3t9RTs817pUfdLjmDLWsPAAAAAOA7e2de9Mc//lEZGRkKDg5WZmamPv300wsev2HDBmVmZio4OFiDBg3SCy+80Klme6TSvdL7P5D+e6T0/iIzUAeESJPmSv/fBunhf0jjv02gBgAAAIAeyOeZ6tdff13f+9739Mc//lFXXnml/vSnP2n27Nnas2eP0tPT2xxfUFCgOXPmaOHChVqxYoU+//xzPfroo4qPj9ddd93VJW/C73gapX3vmrPSRz9rqccOMWelx98rhURb1h4AAAAAoGv4HKp/+9vfasGCBXr44YclSc8884w++ugjPf/883r66afbHP/CCy8oPT1dzzzzjCRp5MiRysnJ0W9+85veF6orT2hE8UoF/M8PpJpSs2ZzSCNukrIXSBkz2Q4LAAAAAHoRn0J1Y2OjcnNz9aMf/ahVfdasWdq0aVO7r9m8ebNmzZrVqnbDDTdo8eLFcrlccjqdbV7T0NCghoaG5seVlZWSJJfLJZfL5UvL3afmlAKey9TwpoXHjPBEeSfOlXfCXCky2TzG7bawQfijc+PZb8c1/A5jBr5izMBXjBn4ijEDX/WUMdPR/nwK1WVlZfJ4PEpMTGxVT0xMVElJSbuvKSkpafd4t9utsrIyJScnt3nN008/raeeeqpNfc2aNQoNDfWl5W41JXyk7F6XCuKuU0n0JBnVAdJneZLyrG4Nfm7t2rVWt4AehjEDXzFm4CvGDHzFmIGv/H3M1NbWdui4Tq3+bfvaJcyGYbSpXez49urnPPnkk1q0aFHz48rKSqWlpWnWrFmKjIzsTMvdwlU3Q2vXbdT111+vie3MwANf53K5tHbtWl1//fXtXrUBfB1jBr5izMBXjBn4ijEDX/WUMXPuiumL8SlUx8XFyeFwtJmVLi0tbTMbfU5SUlK7xwcEBCg2Nrbd1wQFBSkoKKhN3el0+vUPXQqX1BP6hL9hzMBXjBn4ijEDXzFm4CvGDHzl72Omo735tKVWYGCgMjMz20zTr127VtOmTWv3NVOnTm1z/Jo1a5SVleXXP0AAAAAAAC7G532qFy1apBdffFFLlizR3r179f3vf1+FhYV65JFHJJmXbs+dO7f5+EceeURHjx7VokWLtHfvXi1ZskSLFy/WD37wg657FwAAAAAAWMDne6rvuecenT59Wj//+c9VXFysMWPGaPXq1RowYIAkqbi4WIWFhc3HZ2RkaPXq1fr+97+v5557TikpKfrDH/7Q+7bTAgAAAAD0OZ1aqOzRRx/Vo48+2u5zy5Yta1ObOXOmtm7d2plvBQAAAACA3/L58m8AAAAAAGAiVAMAAAAA0EmEagAAAAAAOolQDQAAAABAJxGqAQAAAADoJEI1AAAAAACdRKgGAAAAAKCTCNUAAAAAAHQSoRoAAAAAgE4KsLqBjjAMQ5JUWVlpcScX5nK5VFtbq8rKSjmdTqvbQQ/AmIGvGDPwFWMGvmLMwFeMGfiqp4yZc/nzXB49nx4RqquqqiRJaWlpFncCAAAAAOhLqqqqFBUVdd7nbcbFYrcf8Hq9OnHihCIiImSz2axu57wqKyuVlpamY8eOKTIy0up20AMwZuArxgx8xZiBrxgz8BVjBr7qKWPGMAxVVVUpJSVFdvv575zuETPVdrtdqampVrfRYZGRkX49OOB/GDPwFWMGvmLMwFeMGfiKMQNf9YQxc6EZ6nNYqAwAAAAAgE4iVAMAAAAA0EmE6i4UFBSkf//3f1dQUJDVraCHYMzAV4wZ+IoxA18xZuArxgx81dvGTI9YqAwAAAAAAH/ETDUAAAAAAJ1EqAYAAAAAoJMI1QAAAAAAdBKhGgAAAACATiJU++iPf/yjMjIyFBwcrMzMTH366acXPH7Dhg3KzMxUcHCwBg0apBdeeKGbOoW/8GXMrF+/Xjabrc1Hfn5+N3YMq2zcuFG33HKLUlJSZLPZ9Pe///2ir+Ec07f5OmY4x+Dpp59Wdna2IiIilJCQoNtvv1379u276Os41/RdnRkznGv6tueff17jxo1TZGSkIiMjNXXqVH3wwQcXfE1PP8cQqn3w+uuv63vf+55+8pOfKC8vT9OnT9fs2bNVWFjY7vEFBQWaM2eOpk+frry8PP34xz/Wv/3bv2nlypXd3Dms4uuYOWffvn0qLi5u/hg6dGg3dQwr1dTUaPz48Xr22Wc7dDznGPg6Zs7hHNN3bdiwQY899pi++OILrV27Vm63W7NmzVJNTc15X8O5pm/rzJg5h3NN35Samqpf/vKXysnJUU5Ojq699lrddttt2r17d7vH94pzjIEOmzx5svHII4+0qo0YMcL40Y9+1O7xTzzxhDFixIhWte9+97vGlClTLluP8C++jpl169YZkoyzZ892Q3fwZ5KMVatWXfAYzjH4qo6MGc4x+LrS0lJDkrFhw4bzHsO5Bl/VkTHDuQZf169fP+PFF19s97necI5hprqDGhsblZubq1mzZrWqz5o1S5s2bWr3NZs3b25z/A033KCcnBy5XK7L1iv8Q2fGzDkTJ05UcnKyrrvuOq1bt+5ytokejHMMOotzDM6pqKiQJMXExJz3GM41+KqOjJlzONfA4/HotddeU01NjaZOndruMb3hHEOo7qCysjJ5PB4lJia2qicmJqqkpKTd15SUlLR7vNvtVllZ2WXrFf6hM2MmOTlZf/7zn7Vy5Uq99dZbGj58uK677jpt3LixO1pGD8M5Br7iHIOvMgxDixYt0lVXXaUxY8ac9zjONTino2OGcw127typ8PBwBQUF6ZFHHtGqVas0atSodo/tDeeYAKsb6GlsNlurx4ZhtKld7Pj26ui9fBkzw4cP1/Dhw5sfT506VceOHdNvfvMbzZgx47L2iZ6Jcwx8wTkGX/Wv//qv2rFjhz777LOLHsu5BlLHxwznGgwfPlzbtm1TeXm5Vq5cqXnz5mnDhg3nDdY9/RzDTHUHxcXFyeFwtJlhLC0tbfMvK+ckJSW1e3xAQIBiY2MvW6/wD50ZM+2ZMmWKDhw40NXtoRfgHIOuwDmmb3r88cf1zjvvaN26dUpNTb3gsZxrIPk2ZtrDuaZvCQwM1JAhQ5SVlaWnn35a48eP1+9///t2j+0N5xhCdQcFBgYqMzNTa9eubVVfu3atpk2b1u5rpk6d2ub4NWvWKCsrS06n87L1Cv/QmTHTnry8PCUnJ3d1e+gFOMegK3CO6VsMw9C//uu/6q233tInn3yijIyMi76Gc03f1pkx0x7ONX2bYRhqaGho97lecY6xaIG0Hum1114znE6nsXjxYmPPnj3G9773PSMsLMw4cuSIYRiG8aMf/ch44IEHmo8/fPiwERoaanz/+9839uzZYyxevNhwOp3Gm2++adVbQDfzdcz87ne/M1atWmXs37/f2LVrl/GjH/3IkGSsXLnSqreAblRVVWXk5eUZeXl5hiTjt7/9rZGXl2ccPXrUMAzOMWjL1zHDOQb/8i//YkRFRRnr1683iouLmz9qa2ubj+Fcg6/qzJjhXNO3Pfnkk8bGjRuNgoICY8eOHcaPf/xjw263G2vWrDEMo3eeYwjVPnruueeMAQMGGIGBgcakSZNabScwb948Y+bMma2OX79+vTFx4kQjMDDQGDhwoPH88893c8ewmi9j5le/+pUxePBgIzg42OjXr59x1VVXGe+//74FXcMK57Yg+frHvHnzDMPgHIO2fB0znGPQ3niRZCxdurT5GM41+KrOjBnONX3bQw891Px33/j4eOO6665rDtSG0TvPMTbDaLoLHAAAAAAA+IR7qgEAAAAA6CRCNQAAAAAAnUSoBgAAAACgkwjVAAAAAAB0EqEaAAAAAIBOIlQDAAAAANBJhGoAAAAAADqJUA0AAAAAQCcRqgEAAAAA6CRCNQAAAAAAnUSoBgAAAACgkwjVAAAAAAB00v8PN8puBVMJI0gAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 3\n",
    "x = np.linspace(a, b)\n",
    "\n",
    "figure(figsize=(12,5))\n",
    "title(\"$y = f_2(x) = x^2-5x+4$ and $y = 0$\")\n",
    "plot(x, f_2(x))\n",
    "plot([a, b], [0, 0])\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=(12,5))\n",
    "title(\"$y = g_2(x) = (x^2 + 4)/5$ and $y=x$\")\n",
    "plot(x, g_2(x))\n",
    "plot(x, x)\n",
    "grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = 10\n",
    "# Start at left\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "x = np.linspace(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_1 = 0.8\n",
      "x_2 = 0.9280000000000002\n",
      "x_3 = 0.9722368000000001\n",
      "x_4 = 0.9890488790548482\n",
      "x_5 = 0.9956435370319303\n",
      "x_6 = 0.9982612105666906\n",
      "x_7 = 0.9993050889044148\n",
      "x_8 = 0.999722132142052\n",
      "x_9 = 0.9998888682989302\n",
      "x_10 = 0.999955549789623\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_k = a\n",
    "figure(figsize=(8,8))\n",
    "title(f\"Starting to the left, at x_0 = {a}\")\n",
    "grid(True)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_2(x), \"r\")\n",
    "for k in range(iterations):\n",
    "    g_x_k = g_2(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_2(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_2(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_2(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    print(f\"x_{k+1} = {x_k_plus_1}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_1 = 1.6\n",
      "x_2 = 1.312\n",
      "x_3 = 1.1442688\n",
      "x_4 = 1.061870217330688\n",
      "x_5 = 1.0255136716907844\n",
      "x_6 = 1.010335658164943\n",
      "x_7 = 1.0041556284319177\n",
      "x_8 = 1.0016657052223\n",
      "x_9 = 1.0006668370036975\n",
      "x_10 = 1.000266823735797\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Start at right\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "x = np.linspace(a, b)\n",
    "x_k = b\n",
    "figure(figsize=(8,8))\n",
    "title(f\"Starting to the right, at x_0 = {b}\")\n",
    "grid(True)\n",
    "plot(x, x, \"g\")\n",
    "plot(x, g_2(x), \"r\")\n",
    "for k in range(iterations):\n",
    "    g_x_k = g_2(x_k)\n",
    "    # Graph evalation of g(x_k) from x_k:\n",
    "    plot([x_k, x_k], [x_k, g_2(x_k)], \"b\")\n",
    "    x_k_plus_1 = g_2(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g_2(x_k)], [x_k_plus_1, x_k_plus_1], \"b\")\n",
    "    # Update names: the old x_k+1 is the new x_k\n",
    "    x_k = x_k_plus_1\n",
    "    print(f\"x_{k+1} = {x_k_plus_1}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "\n",
    "The equation\n",
    "$x^3 -2x + 1 = 0$\n",
    "can be written as a fixed point equation in many ways, including\n",
    "1. $\\displaystyle x = \\frac{x^3 + 1}{2}$\n",
    "<br>\n",
    "and\n",
    "2. $x = \\sqrt[3]{2x-1}$\n",
    "\n",
    "For each of these options:\n",
    "\n",
    "(a) Verify that its fixed points do in fact solve the above cubic equation.\n",
    "\n",
    "(b) Determine whether fixed point iteration with it will converge to the solution $r=1$.\n",
    "(assuming a \"good enough\" initial approximation).\n",
    "\n",
    "**Note:** computational experiments can be a useful start, but prove your answers mathematically!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
