{
 "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": 1,
   "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",
    "# and some very frequently use functions for graphing.\n",
    "from matplotlib.pyplot import figure, plot, title, legend, grid\n",
    "from numpy import cos"
   ]
  },
  {
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_1(x): return x - cos(x)\n",
    "def g_1(x): return cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = f_1\n",
    "g = g_1\n",
    "a = -1\n",
    "b = 1\n",
    "\n",
    "x = np.linspace(a, b)\n",
    "\n",
    "figure(figsize=(12,5))\n",
    "title(\"$y = f(x) = x - \\cos(x)$ and $y=0$\")\n",
    "plot(x, f(x))\n",
    "plot([a, b], [0, 0])\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=(12,5))\n",
    "title(\"$y = g(x) = \\cos (x)$ and $y=x$\")\n",
    "plot(x, g(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 $g4(x) := 4 \\cos x$,\n",
    "for which the fact that $|g4(x)| \\leq 4$ ensures that this is a map of the domain $D = [-4, 4]$ into itself:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0YfXq1Tz33HNVDvme7TVSkbS0NHr37s0LL7xASkoKHTt2ZMmSJbz55psAZa/31atX8/PPP/O///2v0ufyBNzly5eXBaY9e/Zw8cUX07ZtW2bNmoXdbufZZ5+lU6dOTJo0iX/84x9nPIfL5WLFihXceeedlV4nNjb2nKbPeERGRlYYxj3D1r/+fy+88AIDBw6kT58+/PWvf6VVq1YcOXKEzz77jNdff53Y2NhqvY5zcnKq9XPiq3YU8SpTlzaJmMCzenvlypVnfYxn5esvv/xiREVFlds+prCw0OjRo4fRrFkz4/jx42X3796927jjjjuMRo0aGXa73UhJSTH69+9vPPXUU2d8/meffWZ06dLFCA8PN5o0aWI8++yzZSuRz8bzuNWrVxujRo0yYmJijNjYWOOmm24yjhw5csZjFy9ebFx00UVGnTp1jKioKKNv377G3Llzq/yaT7/GsWPHzvpYwzCMRx55xGjYsKFhtVoNwPjqq6+Me+65x+jSpYsRFxdnREVFGW3btjX+9re/GXl5eWf9GqtTd01XtVdU54IFC2r8tVb3e/xrlV2nspXTgwcPNjp27Fh2+/jx48add95ppKamGtHR0cbAgQONxYsXG4MHDzYGDx5c4bWq8xqpyO7du43LLrvMiImJMVJSUozbbrvNeOeddwzA2LVrl2EYhvHvf//biIqKMpKSkoykpCQjIiLCiI6ONsaPH3/Gcw0aNMi44oorDMMwjIMHDxotW7Y0LrjggnI7A9x9991GREREufb+7rvvyr4WX6vse2MYhrFp0yZjzJgxRlJSUtnP8W233WYUFhaWPeZsr+PCwsJq/5wEcjuKGIZhWAzDMHyedkXkvE2YMIGJEydy7Ngx0+Y7in+r7ddIQUEBw4YNIy4ujq+++gpwL8g5/fjRBx98kGbNmvHwww+fMYd01qxZ3HDDDezdu5dGjRrV+Nrjx49n165dVU7RCAVqRwl0GmoXEZFyVq1axccff8yAAQOIjY1l27ZtvPzyy2RkZJwRWmJiYs5YpBIdHU1cXFy5hUvXXnstvXr14plnnuGVV16pUS07d+5kxowZXp3CECjUjhLoFDxFRKSckydPMn/+fP773/9SUFBAw4YNueKKK3j88ccrXOnuMXny5Arvt1gsvPnmm3z22We4XK4zjnw8m/T0dF555ZWy41FDmdpRAp2G2kVERETEJ7SPp4iIiIj4hIKniIiIiPiEgqeIiIiI+IRfLy5yuVwcPHiQ2NjYWtvkWkRERERqj2EYnDhxgoYNG551wZtfB8+DBw+SlpZmdhkiIiIichb79u2r8hQ18PPgGRsbC7i/kLi4OK9fz+Fw8M0333DJJZdgt9u9fr1AorapmNqlcmqbiqldKqe2qZjapXJqm4r5ul1yc3NJS0sry21V8evg6Rlej4uL81nw9Gx+rBfwmdQ2FVO7VE5tUzG1S+XUNhVTu1RObVMxs9qlOtMitbhIRERERHxCwVNEREREfELBU0RERER8wq/neFaX0+nE4XCc9/M4HA7CwsIoLCzE6XTWQmXBo7baxm63Y7PZarEyERERCRQBHTwNw+Dw4cNkZ2fX2vPVr1+fffv2ad/QX6nNtklISKB+/fpqYxERkRAT0MHTEzpTU1OJjo4+7yDjcrk4efIkMTExZ90ANdTURtsYhkF+fj5Hjx4FoEGDBrVZooiIiPi5gA2eTqezLHQmJSXVynO6XC6Ki4uJjIxU8PyV2mqbqKgoAI4ePUpqaqqG3UVEREJIwKYrz5zO6OhokyuRmvJ8z2pjXq6IiIgEjoANnh6aJxh49D0TEREJTQEfPEVEREQkMCh4ioiIiIhPKHiKiIiIiE8oeEqVMjMzSU1NZc+ePdV6/OjRo3nhhRe8W5SIiIgEJAVPqdIzzzzDqFGjaNasWbUe/8QTT/D000+Tm5vr3cJEREQk4Ch4SqUKCgp4++23ueuuu6r9OV26dKFZs2ZMnTrVi5WJiIhIIFLwNEnjxo157bXXzrhv6dKlREdHs3fv3lq7zsaNG7nwwguJioqiW7duLFmyBIvFwrp16876ufPmzSMsLIx+/fqV3Td9+nQiIyM5cOBA2X133XUXXbp0IScnB4Arr7yS6dOn19rXICIiIsEhqIKnYRjkF5ec17+CYuc5fZ5hGDWqtW/fvqxcufKM2h944AEeeOABmjZtesZjJ02aRExMTJX/Fi9eXO4aGzdupG/fvgwaNIg1a9bwxBNPMHr0aOx2O+3btz9rjYsWLaJnz55n3HfjjTfStm1bnnnmGQAmTpzI119/zbx584iPjwegd+/erFixgqKiohq1iYiIiAS3gD0ysyIFDicdnvjalGtvevJSosOr35x9+/Zl8uTJZbc/+OAD0tPTeeSRR8o99p577uH666+v8vkaNWpU7r777ruPK664gqeffhqAdu3aMWXKFHbt2kV4eHjZ4/Lz82nfvj1jxozh+eefL7t/z549NGzY8IzntFgsPP3004wePZqGDRvy0ksvsXjx4jOu36hRI4qKijh8+HC5EC0iIiKhK6iCZyDp27cvDz/8MCdPnsRqtfLoo4/y1FNPERsbW+6xiYmJJCYm1uj59+zZww8//MCGDRvOuD8iIoKuXbuecd/TTz9Nnz59yj1HQUEBkZGR5e4fOXIkHTp0YOLEiXzzzTd07NjxjP/vOY89Pz+/RjWLiIhIcAuq4Bllt7HpyUvP+fNdLhcnck8QGxeL1VqzWQhRdluNHt+zZ09sNhs///wz3377LUlJSdxxxx0VPnbSpElMmjSpyuebN28egwYNKru9bt06wsPDy4XCzZs3c+utt5bd3r59O1u2bGHUqFHlQmpycjLHjx8vd62vv/6aLVu24HQ6qVevXrn/n5WVBUBKSkqVNYuIiEhoCargabFYajTc/Wsul4uScBvR4WE1Dp41FRkZSdeuXZk9ezZvvPEGc+fOrfSa5zLUbrPZKCkpobCwsKzXcuHChaxbt+6MHs+HHnqI5557jqVLl5Z7zu7duzNlypQz7vv5558ZM2YMr7/+Oh9++CGPP/44M2fOPOMxGzZsoHHjxiQnJ1dZs4iIiIQWny0ueuaZZ7BYLDzwwAO+uqTf69u3L//5z3+4+OKLGTZsWKWPS0xMpFWrVlX+8wxve/To0QO73c6f//xndu3axeeff86dd94JQLdu3QD49NNPadOmDW3atKnwupdeeikbN24s6/VMT09n1KhR/PWvf2X8+PE8+eSTzJo1i9WrV5/xeYsXL+aSSy4512YRERGRIOWT4Lly5UreeOMNunTp4ovLBYxu3boRFhbGc889V+vP3aBBA9555x0+/fRTunTpwjvvvMPtt99Oq1atyuaLLl++nA8//JBmzZrx0EMP8eabb/Lkk0+WPUfnzp3p2bMnH330EVlZWYwZM4ZRo0bx6KOPAu5wO2rUKB577LGyzyksLOSTTz7h7rvvrvWvSURERAKb14faT548ybhx43jzzTd56qmnvH25gDJ16lTuvfde2rZt65XnHzt2LGPHjgXc0wiGDh3KmDFjyv7/M888U7Yt0uTJk9mwYQNPPPHEGc/x+OOP89BDD3HnnXfy008/ERcXd8b///TTT8+4/fbbb9OnTx/69u3rjS9JREREzsblxOpymF1FhbwePH//+98zYsQILr744rMGz6KiojP2fvQcu+hwOHA4zmxAh8OBYRi4XC5cLlet1OrZi9PzvN7gcrk4duwY77zzDlu3bmXWrFleudaiRYs4duwY3bt3JyMjg+eff549e/ZUej2Xy1Xh133ZZZexbds29u/fT0JCwlnbxmaz8dJLL1X5GM+1HA4HNlvNFmX5G8/r8tevT1HbVEbtUjm1TcXULpVT21TAVYJlzu/ofWAnjoJhQIzXL1mT9rcYNd35vAY+/PBDnn76aVauXElkZCRDhgyhW7duvPjiixU+fsKECUycOLHc/dOmTSM6OvqM+8LCwqhfvz5paWln7Enp73788UeuvPJK2rRpwyuvvFJug/baMmfOHCZOnMihQ4dISUlhyJAhPP7446SmpnrlejVRXFzMvn37OHz4MCUlJWaXI1LrXAYsO2ph6RErJTX4u7JRHYMrm7hIiPBebSISvCyGkwv2vE7j7OW4sLGk9V/JivHOqOrp8vPzGTt2LDk5OeVGRsvX6KXguW/fPnr27Mk333xTtor6bMGzoh7PtLQ0MjIyyn0hhYWF7Nu3j2bNmlW41+S5MAyDEydOEBsbi8ViqZXnDBa12TaFhYXs2bOHtLS0WvvemcXhcDB//nyGDx+O3W43uxy/Eqptszsjj8c+3cTKPeW3IquOmIgw/nJpa27o0RirNbR+D4Xqa+Zs1C6VU9ucxlWC7dN7sG6ag2G1s6LpvXQe81eftEtubi7JycnVCp5eG2pfvXo1R48epUePHmX3OZ1OFi1axCuvvEJRUVG5YdaIiAgiIsr/qW+328s1nNPpxGKxYLVaa23rI8/wsOd55ZTabBur1YrFYqnw+xqogulrqW2h0jYOp4s3Fu3ipe+2U1ziIjrcxoPD29CxYfwZj3M6S1i+/Cf69u2DzXbqV3BhiZP/fLedNenZPPHZZr5Yf4Rnru1MixTvD5P5m1B5zdSU2qVyId82Tgd8cg9smgNWO87r3uHwDoMLfNQuNbmG14LnsGHDWL9+/Rn33X777bRr146HH3444Of2iYh4bDiQw18+/oVNh9zz0i9sk8KkazrRuG50ucc6HA4yNxv0aZ5Y7pf1ha1TeG/pHp77eis/7c7ispcW88eL23D3oOaE2fTHsIhUwOmAWXfCpk/BFg7Xf4DRYhjs+NLsyirkteAZGxtLp06dzrivTp06JCUllbtfRCQQFTqc/Pvbbby1eDdOl0FCtJ0nRnbgmu6NzmlKis1q4Y6BzRneoR6PfrKexdsz+MdXW/j8l4P847oudGoUf/YnEZHQ4XTAx3fA5s/cofOGKdDmUvDjxVb6E1pE5Bws25nJZS8u4vWFu3C6DEZ2acC3Dw7m2gsan/c86LTEaN6/ozfPj+lKfJSdjQdzuerVJTw7bwuFDmctfQUiEtBKimHmbaeFzqnu0OnnfHpk5g8//ODLy4mI1LqcAgfPztvM9BX7AKgfF8lTV3fi4g71avU6FouF0T0aM7hNChPmbuSLXw7xv4U7+XrjYZ65tjN9WyTV6vVEJICUFMPHt8OWz8EWATdOhdbDza6qWtTjKSJSTd9vOcIl/15YFjrH9WnCNw9eWOuh83QpsRG8OvYC3hjfg3pxEezOyOPGN5bzyOz15BVpOzKRkOPp6SwLndMCJnSCj3s8RUQC1eLtx7jrvVW4DGieXMfnvY6XdKxP35ZJPPPlFqavSGf6inSOnSjkjfE9Q27bJZGQVVIEH90K2+ZBWKQ7dLYaZnZVNaIeTxGRs9h/PJ8/TF+Dy4CrujVk3v8NMmWoOy7SzjPXdmbKnX0ID7Py7eajvLpgh8/rEBET/Dp03jQ94EInKHiKiFSp0OHkd1N+5ni+g86N4vnHdV2ItJu7HdzA1sn8/aqOALzw7TZ+2HrU1HpExMtKimDG+NNC54fQ8iKzqzonCp4iIpUwDIMnPt3A+gM51I2289+bLzA9dHrc0KsJN/VOwzDg/z5cy76sfLNLEhFvcBTCjJth+9cQFgVjZ0DLoWZXdc4UPEVEKjF9xT4+WrUfqwX+c1P3CjeEN9OEKzvSNS2BnAIHv/1gtbZaEgk2jkKYMQ62f3MqdLYYYnZV50XB0ySNGzfmtddeO+O+pUuXEh0dzd69e2vlGtOnTycyMpIDBw6U3XfXXXfRpUsXcnJyauUaIsFq7b5sJny2EYCHLm3LoNYpJldUXkSYjf+Ou4CkOuFsOpTLY59swDAMs8sSkdrgKIQPx8KOb8EeDeM+ghaDza7qvAVX8DQMKM47v3+O/HP7vBr+su/bty8rV648rXSDBx54gAceeICmTZue8dhJkyYRExNT5b/FixeXu8aNN95I27ZteeaZZwCYOHEiX3/9NfPmzSM+XiegiFQm42QRv5uymmKni0s71uN3g1uaXVKlGiZE8fJN3bFaYNbP+5nyU7rZJYnI+XIUwIc3wc7vSkPnTGh+odlV1Yrg2k7JkQ+TGp7zp1uBhHP95EcPQnidaj+8b9++TJ48uez2Bx98QHp6Oo888ki5x95zzz1cf/31VT5fo0aNyt1nsVh4+umnGT16NA0bNuSll15i8eLFFT5WRNxKnC7un7aGQzmFtEipw/Njup73SUTe1r9VMg9f1o5n5m3hybkb6dAgjh5N65pdloici+J8d+jc9QPY67hDZ7MBZldVa4IreAaQvn378vDDD3Py5EmsViuPPvooTz31FLGxseUem5iYSGJi4jldZ+TIkXTo0IGJEyfyzTff0LFjx/MtXSSoPff1VpbtyiQ63MbrN/cgNtJudknV8psLW7BufzZfrj/MvVNX8/n9g0iJjTC7LBGpieJ8mH4j7F7oDp03fwxN+5tdVa0KruBpj3b3PJ4jl8tF7okTxMXGYrXWcBaCvWaLDnr27InNZuPnn3/m22+/JSkpiTvuuKPCx06aNIlJkyZV+Xzz5s1j0KBB5e7/+uuv2bJlC06nk3r1vHe6ikgw+HL9IV5ftAuA50Z3pXW98n8I+iuLxcI/R3dl25GT7Dh6kvum/czUu/oQZguuGVUiQas4H6bfALsXQXgMjPsYmvYzu6paF1zB02Kp0XB3OS4X2J3u56hp8KyhyMhIunbtyuzZs3njjTeYO3dupWH3XIfaf/75Z8aMGcPrr7/Ohx9+yOOPP87MmTNrpX6RYLPj6An+PHMd4O49HNGlgckV1VxMRBj/u7kHV7+6hJ92Z/HsvC38v5EdzC5LRM6mOA+m3QB7FrtD582zoElfs6vyiuAKngGmb9++/Oc//2HkyJEMG1b56QPnMtS+Z88eRowYwV//+lfGjx9Phw4d6NWrF6tXr6ZHjx7nW7pIUDlR6OA3H6wmr9hJvxZJ/OXStmaXdM5apcbw/Jgu3DPlZ976cTdd0xIY1fXc576LiJedETpjS0NnH7Or8hqNwZioW7duhIWF8dxzz9Xq82ZlZXH55Zdz5ZVX8uijjwLQo0cPRo0axWOPPVar1xIJdIZh8OeZv7DrWB4N4iN5eWz3gB+evqxTA+4pXYn/8Kxf2HbkhMkViUiFik7C1DGnQuf42UEdOkE9nqaaOnUq9957L23b1m7vSmJiIps3by53/6efflqr1xEJBv9buIuvNh4m3GbltXEXkBwTHAtyHrqkDesPZLNkRya//WA1n943gLgAWSglEhI8oTN9KUTEwc2zIa2X2VV5XWD/WR+AXC4XR44cYdKkSWzdupWJEyeaXZJIyFq2M5Pnvt4CwN+u7ED3JsGzBVGYzcp/buxOw/hIdmfk8eeZ67S5vIi/KDoBU0efCp3jPwmJ0AkKnj63aNEiGjRowJQpU5g9e7Y2chcxidNl8LfPNuAyYHSPxozt3cTskmpdUkwE/xvfg3Cbla83HmHR9gyzSxKRohMwZTSkL4OIeBg/Bxr3NLsqn1Hw9LEhQ4bgcrnYtGkTffoE9zwOEX82++f9bDtykvgoO4+P7OD3m8Sfqy6NE7iln/s0tH/M24LLpV5PEdMU5sKU62DfcnfovOUTaBxaC34VPEUk5BQ6nPx7/jYA7h3Skvio4J77+PuhrYiNCGPToVzm/nLuex2LyHkozIEp18K+nyAyHm6ZA41CK3SCgqeIhKApy/dyMKeQBvGR3Nq/mdnleF3dOuH8dnALAP71zTaKS1wmVyQSYgpz4INrYf9KiEyAWz6DRheYXZUpFDxFJKTkFjp4ZcEOAB64uDWRdpvJFfnGHQObkxIbQXpWPtNXpJtdjkjoKMiGD66BA6sgqi7c+hk07GZ2VaYJ+OCpVZqBR98zMdMbC3eRne+gZUodrrugsdnl+Ex0eBh/GNYagJe/305eUYnJFYmEgLLQudodOm/5DBp0NbsqUwVs8LTb3XOy8vPzTa5EasrzPfN8D0V85WhuIW//uBuAP1/aLuA3iq+pG3ul0SwpmoyTxby1eLfZ5YgEt4Lj8MHVcPBniEqEW+dCgy5mV2W6gN1A3mazkZCQwNGjRwGIjo4+71WpLpeL4uJiCgsLKz03PVTVRtsYhkF+fj5Hjx4lISEBmy00hjjFf/zn++0UOJx0b5LApR3rmV2Oz9ltVv50SVvun76GNxbt5Oa+TUgKkg3zRfxKwXF4/2o4tBaik9w9nfU7mV2VXwjY4AlQv359gLLweb4Mw6CgoICoqKig3VrlXNVm2yQkJJR970R8ZU9GHh+u2AfAw5e1C9mf8RGdG/D6op1sOJDLKwt28LdRHc0uSSS45Ge5ezoPrXOHzlvnQj39nHkEdPC0WCw0aNCA1NRUHA7HeT+fw+Fg0aJFXHjhhRoG/pXaahu73a6eTjHF899spcRlMKRtCn1bJJldjmmsVgsPX9aO8W+vYOrydO4Y0Jy0xGizyxIJDvlZ8P5VcPgXiE4uDZ0dzK7KrwR08PSw2Wy1EmZsNhslJSVERkYqeP6K2kYC2fr9OXz+yyEsFvjLpe3MLsd0g1qnMKBVEkt2ZPLv+dt44YZuZpckEvjys+D9K+HweqiT4g6dqe3NrsrvaCKjiAS9f3zlPo/96m6N6NAwzuRq/MPDl7kD+CdrD7D5UK7J1YgEuLxMeO/00Pm5QmclFDxFJKj9uD2DH3dkYLdZeHB4G7PL8RtdGicwoksDDAOe+3qr2eWIBK68THdP55H1UCe1NHRqZKUyCp4iErRcLqOst3Ncn6aay/grD13SljCrhe+3HGXF7iyzyxEJPHkZ8N4oOLIBYurBbQqdZ6PgKSJB68sNh1h/IIc64Tbuu6iV2eX4nebJdbihVxoAz87brMMdRGri5DF36Dy6EWLqw21fQEpbs6vyewqeIhKUHE4Xz5cOId99YQuStV9lhf5vWGui7DZ+Ts9m/qYjZpcjEhjKQuem0tD5OSS3NruqgKDgKSJBacbKfezJzCepTjh3DWphdjl+KzUukjsGNgPccz2dLvV6ilTp5FF4byQc2wyxDdw9nQqd1abgKSJBJ7+4hJe+2w7A/Re1IiYiKHaO85rfDm5JQrSd7UdPMuvn/WaXI+K/ThyBySPh2BaIbVgaOjWNpyYUPEUk6Ly7ZA/HThSRlhjF2D5NzS7H78VF2vn9EPeb54vzt1HocJpckYgfOnHE3dOZsRXiGrmH15Naml1VwFHwFJGgcjyvmP/9sBOAPw1vS3iYfs1Vx/h+TWkYH8nBnEI+WLbX7HJE/MuJw6WhcxvENVboPA/6jSwiQeW1H3ZwoqiE9g3iuLJrQ7PLCRiRdhsPlO5z+sqCHeQUnP8xxCJBIfcQTB7hDp3xae7Qmah54+dKwVNEgkbGySLeK+2t+8tlbbFaLSZXFFiuu6AxrVNjyClw8O6S3WaXI2K+3EPuns7MHRDfpDR0Nje7qoCm4CkiQWPGyn0Ul7jo2jieIW1SzC4n4NisFu4f5l6dO+2ndBxOl8kViZgo96C7p/P00Fm3mdlVBTwFTxEJCk6XwbSf0gG4pV8zLBb1dp6LyzrWJzkmgqMnirSvp4SunAPu0Jm1ExI8oVMLFWuDgqeIBIXvtxzlQHYBCdF2RnRpYHY5ASs8zMpNvd2nGb2/bI+5xYiYIWd/aejcBQlN3VsmKXTWGgVPEQkKHyx3z+28oWcakXabydUEtpt6N8FqgeW7sth+5ITZ5Yj4TvY+d+g8vts9rH7bF+4eT6k1Cp4iEvD2ZOSxaNsxLBYY20dvEuerYUIUF7evB8CU5dpaSUJEWejcc1roTDO7qqCj4CkiAW/qT+5wNLhNCk2T6phcTXAY3889tDjr5wPkFZWYXI2Il2Wnu0Nn9l6o2xxu+xLiG5tdVVBS8BSRgFbocPLRKvcxj+P7ah5WbRnQMpnmyXU4WVTCnLUHzC5HxHuO7z0VOhNbwO1fQnwjs6sKWgqeIhLQ5q47SE6Bg0YJUQxpm2p2OUHDarUwrnTawgfL9mIYhskViXjB8b3us9ez0yGxpXt4PU4HT3iTgqeIBDTPHMSb+zbFpg3ja9WYHmlE2q1sOXyC1XuPm12OSO06vsfd05mTDkmtFDp9RMFTRALWun3ZrNufQ7jNyvU9NR+rtsVH27mqq3vI8X2d3y7BJGs3vDsCcvZBUuvS0Klt2HxBwVNEApZnC6URXRqQFBNhcjXBybPIaN6GQxw7UWRyNSK1IGuXu6czdz8kt3FvDh9b3+yqQoaCp4gEpON5xcxddxBwD7OLd3RqFE+3tAQcToOPVu0zuxyR85O50z2nM/cAJLeFWxU6fU3BU0QC0ser91NU4qJDgzguaJJgdjlBzbNbwNTle3G6tMhIAtTpoTOlXWlPZz2zqwo5Cp4iEnBcLoMppXt3ju/XVOeye9mILg1IiLZzMKeQ77ccNbsckZrL2OEeXj9xEFLaw61zIUa7YJhBwVNEAs7iHRnszcwnNjKMq7ppFaq3Rdpt3NDTfYLLBzrJSAJNxvbS0HkIUjsodJpMwVNEAs4HpSusR/doTHR4mMnVhIZxfZpiscCibcfYk5Fndjki1XNsm3t4/eRhSO1YGjpTzK4qpCl4ikhA2X88n++3HAG0qMiXmiRFM6SN+w1b57dLQDi2Fd4rDZ31OsGtn0GdZLOrCnkKniISUKb9lI7LgAGtkmiZEmN2OSHFs7XSzNX7KSh2mlyNSBWObint6TwC9TrDLQqd/kLBU0QCRlGJkxkr3Vv66Fx23xvcJpXGdaPIKXAw95eDZpcjUrGjm909nXlHoX7n0p7OJLOrklIKniISML7acJjMvGLqxUVwcXttg+JrNquFcX3cgV/D7eKXjmxy93TmHYP6Xdw9ndGJZlclp1HwFJGA4VlUNLZ3U8Js+vVlhut7NibcZuWX/Tms25dtdjkipxzZCO+NgvwMaNAVbvlUodMPefU393//+1+6dOlCXFwccXFx9OvXj3nz5nnzkiISpDYdzGXV3uOEWS3c1DvN7HJCVlJMBCO6uM+01tZK4jfOCJ3dYPwchU4/5dXg2bhxY5599llWrVrFqlWruOiii7jqqqvYuHGjNy8rIkHIs2H8pZ3qkxoXaXI1oc2zyGjuuoMczys2uRoJdXH56YRNvQbyM6Fhd7hljkKnH/Nq8Bw1ahRXXHEFbdq0oU2bNjz99NPExMSwfPlyb15WRIJMbqGDOWsOAFpU5A+6pyXQsWEcRSUuZq7W+e1iosPr6b/jWSwFWdDwAndPZ1Rds6uSKvhs52Wn08nMmTPJy8ujX79+FT6mqKiIoqKistu5ubkAOBwOHA6H12v0XMMX1wo0apuKqV0qV5ttM3NlOvnFTlql1OGCxrEB3d7B8poZ26sxj326iQ+W7eXWPmlYred/bGmwtE1tU7tU4vAvhE29DovzJM763XDdNBPC6oDayeevmZpcx2IYhuHFWli/fj39+vWjsLCQmJgYpk2bxhVXXFHhYydMmMDEiRPL3T9t2jSio6O9WaaI+CnDgGfW2ThSYGF0cyeD6nv1V5ZUU5ET/rbaRoHTwj3tnLSvq++L+E58/h767/gH4c48sqJbsqzVnymxKSeYJT8/n7Fjx5KTk0NcXFyVj/V68CwuLiY9PZ3s7GxmzZrFW2+9xcKFC+nQoUO5x1bU45mWlkZGRsZZv5Da4HA4mD9/PsOHD8dut3v9eoFEbVMxtUvlaqttlu/KYvy7q4gOt/HjnwcTGxnYR2QG02vmqS+38N6ydC5qm8LrN3c/7+cLprapTWqXXzm0lrBpo7EUZuNs2IOvku9m6GVXqW1O4+vXTG5uLsnJydUKnl7/DR4eHk6rVq0A6NmzJytXruSll17i9ddfL/fYiIgIIiIiyt1vt9t9+oLy9fUCidqmYmqXyp1v23y8xr1R+dXdG5EYG1VbZZkuGF4zt/RvznvL0lmw7RjHC5y1tugrGNrGG9QuwIGfYdp1UJgDjXvjunEGJd8tVttUwlftUpNr+HwjPMMwzujVFBGpTEGxk/mb3Oeyj+7R2ORq5NdapsTQvUkChgFfrD9kdjkS7A6shvevdofOtD5w8yyIiDW7KqkhrwbPRx99lMWLF7Nnzx7Wr1/PY489xg8//MC4ceO8eVkRCRLfbTlCfrGTxnWj6J6WYHY5UoEruzYE4LN1OkJTvGj/anj/GijKgbS+7tAZ6f0peFL7vBo8jxw5wvjx42nbti3Dhg3jp59+4quvvmL48OHevKyIBIm5pWFmVNeGWCznv2paat+Izg2wWmBNejb7svLNLkeC0f5V8MHV7tDZpD/c/LF6OgOYV+d4vv322958ehEJYrmFDhZsPQac6lUT/5MaF0nfFkks3ZnJ3F8Ocu+QVmaXJMFk30r44BooPgFNB8DYjyAixuyq5DzosGMR8UvfbDxCcYmLVqkxtKuv3g1/Nqr0D4O56zTPU2rRvhWnhc6BCp1BQsFTRPySZ87glRpm93uXd6pPmNXC5kO57Dh6wuxyJBikLz8VOpsNgnEKncFCwVNE/E7mySKW7MgATvWmif9KiA7nwjYpAHymXk85X+nLYcp1UHwSml/o7ukMr2N2VVJLFDxFxO98ueEwTpdB50bxNE/WG04guLJsuP0gXj6XRILZ3qXwwbWloXMw3DQDwnUiUTBR8BQRv3NqNXsDkyuR6rq4Qz0iwqzszshj48Fcs8uRQLRnCUwZDY48aDEEbvpQoTMIKXiKiF85lFPAyj1ZAIzsomH2QBETEcbF7esB2tNTzsGeH2HqmNLQOVShM4gpeIqIX/nil0MYBvRqVpeGCcFzRGYo8PRQf77uIC6XhtulmnYvPhU6Ww6Dm6aDXT/7wUrBU0T8yumr2SWwDGmbSkxEGAdzClmdftzsciQQ7F5UGjrzodXFcOM0hc4gp+ApIn5jT0Yev+zPwWa1cHlnze8MNJF2G5d0dA+3z9Vwu5zNroUw9XooKYBWw+GGqWCPNLsq8TIFTxHxG56w0r9lEskxESZXI+fC01P95fpDlDhdJlcjfmvXDzCtNHS2vgRumKLQGSIUPEXEb8z95dTZ7BKYBrRKpm60nYyTxSzblWl2OeKPdi6AaTdASSG0vlShM8QoeIqIX9hyOJdtR04SbrNyacf6Zpcj58hus3JF6TSJz9ZquF1+Zcd3MP1Gd+hscxnc8AGEaXQjlCh4iohf8AyzD26bQnyU3eRq5Hx4eqy/2niYohKnydWI39jxLUy/yR06214B17+v0BmCFDxFxHSGYTC39KhFrWYPfL2bJVIvLoIThSUs3HrM7HLEH2z/FqaPBWcRtB0BY95T6AxRCp4iYrp1+3NIz8onym5jWPtUs8uR82S1Wso2/5/7i85uD3nb58OHN7lDZ7uRMGYyhIWbXZWYRMFTREznmQs4vEM9osPDTK5GaoOn5/rbTUfILy4xuRoxzbZv4MOx4Cx2h87R7yp0hjgFTxExldNl8LlWswedLo3jaZoUTYHDyfxNR8wuR8yw9SuYMc4dOttfqZ5OARQ8RcRkK3ZncfREEXGRYVzYJtnscqSWWCwWRnmG29dpuD3kbJ0HM252h84OV8Hod8CmRYOi4CkiJvMckXlZp/pEhNlMrkZqk6cHe+G2o+TkO0yuRnxmyxcwYzy4HNDharjubYVOKaPgKSKmcThdzNvgWc3eyORqpLa1rR9L23qxOJwGX288bHY54gubP4ePbnWHzo7XKnRKOQqeImKaH7dnkJ3vIDkmnL4tEs0uR7xgVNfSzeR1dnvw2zwXZpaGzk7XwbVvgk2LBeVMCp4iYhrPpvEjOjcgzKZfR8HIM9y+dGcGx04UmVyNeM2mT2HmbeAqgc5j4Jo3FDqlQvpNLyKmKHQ4y4ZftZo9eDVNqkPXxvG4DPhyvRYZBaWNc2Dm7aWh83q4+n8KnVIpBU8RMcWCLUfJK3bSKCGKC5rUNbsc8SLPHxZzNdwefDZ+Ah/fAYYTutwI1yh0StUUPEXEFJ45fyO7NMBqtZhcjXjTyC4NsVhg1d7jHMguMLscqS0bZsHHd7pDZ9eb4OrXwKqdKaRqCp4i4nMnCh18v+UooGH2UFA/PpLezdyLxz5Xr2dwWP8xzLqrNHSOhateVeiUalHwFBGfm7/pCEUlLlok16FjwzizyxEf8PyBodXtQeCXmTD7bjBc0O1muOoVhU6pNgVPEfE5z1y/UV0bYrFomD0UXNG5ATarhY0Hc9l57KTZ5ci5+uUj+OQ37tDZ/Wa48mWFTqkRBU8R8ans/GIWb88ANMweShLrhDOwlftI1M91hGZgWjcDPvmtO3RecAuMehmsihFSM3rFiIhP/bD1GCUugzb1YmiVGmN2OeJDV3SuD8C3m4+YXInU2Nrpp4XOW2HkSwqdck70qhERn/KEjovb1zO5EvG1i9rVw2KB9QdyOJxTaHY5Ul1rp8Gc3wEG9LgdRr6o0CnnTK8cEfGZ4hIXC7ceA+DiDgqeoSYlNoJuaQkAfLdFvZ4BYc0UmHMvYEDPO2HECwqdcl706hERn1mxO4sTRSUkx4TTrXGC2eWICTw93d9uUvD0ez9/AJ/eBxjQ6y4Y8S+FTjlvegWJiM94htkvapeqTeNDlCd4LtmZSX5xicnVSKVWvweflYbO3r+BK54H7UAhtUDBU0R8wjAMze8U2tSLIS0xiuISV9nuBuJnVk+GuX9wf9znHrj8nwqdUmsUPEXEJ7YeOcH+4wWEh1kZ2DrZ7HLEJBaLhWHtNNzut1a9C3P/z/1xn9/BZc8qdEqtUvAUEZ/4brP7iMyBrZKJDg8zuRox0/DShWXfbzmK02WYXI2UWfk2fP6A++O+98Jlzyh0Sq1T8BQRn5i/ScPs4ta7eSKxkWFk5hWzdl+22eUIwIo34YsH3R/3uw8unaTQKV6h4CkiXnf0RGFZwBjWPtXcYsR0dpuVwW1SAG0m7xdWvAlfPuT+uN99cMlTCp3iNQqeIuJ1C7a4h9m7NI6nXlykydWIP/AMt3+n4Gmun14/FToH/J9Cp3idgqeIeN38Te7gqWF28RjSJhWb1cK2IyfZm5lndjmhafn/YN5f3B8PeAAunqjQKV6n4CkiXlXocPLjjtLTihQ8pVR8tJ1ezeoC8G3pwjPxoWWvwVcPuz8e+CBcPEGhU3xCwVNEvGrpriwKHS4axkfSvkGs2eWIH/H8IaLhdh9b9ip8/Yj740EPwbAnFDrFZxQ8RcSrvi+d33lxh3pY9OYmp/HM8/xpdxY5+Q6TqwkRS1+Brx91f3zhn+Gi/6fQKT6l4CkiXuMy4PstGmaXijVNqkOr1BicLoMftmm43euW/Ae+ecz98eCHYehjCp3icwqeIuI1+/Lg2Mli6oTb6NMi0exyxA+dGm5X8PSqJS/B/MfdHw/+Kwx9VKFTTKHgKSJesyHL/StmcNsUIsJsJlcj/mh4B/e+rgu2HsXhdJlcTZD68d8w/wn3x0MegaGPmFuPhDQFTxHxmg3H3T0qGmaXynRLq0tinXBOFJawau9xs8sJPov/Bd9OcH889DEY8ldTyxFR8BQRrziQXcDBfAtWCwxtq9OKpGI2q4WL2rlfH575wFJLFv8LvnvS/fFF/w8G/8XcekRQ8BQRL/GEiAuaJFC3TrjJ1Yg/u7j0GNVvtxzDMEwuJlgsfO600Pm4ewW7iB8IM7sAEQlO35UGz2Ht1NspVRvUOoVwm5X9xws4XGB2NUFg4T9hwdPuj4f9DQY9aG49IqdRj6eI1LoThQ5W7MkC4KK2KSZXI/6uTkQY/VslAafmBcs5+uHZU6Hz4gkKneJ3FDxFpNYt2paBw2mQGmnQIqWO2eVIABhWugDNsxOCnIMFz8APz7g/Hv4kDPyjufWIVEA/4SJS674tPQKxU11N2JPq8czz3HsSMk8WmVxNgDEMWDAJFj7rvn3JUzDg/8ytSaQSCp4iUqtKnC4WbHVvBt4xUfsySvU0iI+iY8NYDCws2JZhdjmBwzDcQ+sL/+G+fcnT0P9+c2sSqYKCp4jUqtV7j5Od7yAhyk7zWLOrkUDimQ+sbZWqyTDg+7/Doufcty+dBP3vM7cmkbNQ8BSRWuUZZh/SJhmb1olIDXh2QPhxRwaFDqfJ1fg5w3Bvl7T4X+7blz0L/X5vbk0i1aDgKSK1ynPm9kXttJpdaqZDg1jiww0KHC6W7cw0uxz/ZRju04h+fMF9+/J/Qt/fmVqSSHUpeIpIrdl57CS7MvKw2ywMbJVsdjkSYCwWS9mCtPmlPefyK4bhPnd9yYvu25c/B31+a2pJIjXh1eD5zDPP0KtXL2JjY0lNTeXqq69m69at3rykiJjo203usNC3RRKxkTqfQmrOEzy/23wEQ8cYnckwYP7jsPQ/7ttXPA99fmNuTSI15NXguXDhQn7/+9+zfPly5s+fT0lJCZdccgl5eXnevKyImMQzzD68Qz2TK5FA1TreIDrcxpHcIjYcyDW7HP9hGFi/ewKWvuy+PeJf0Ptuc2sSOQde7ZL46quvzrj97rvvkpqayurVq7nwwgu9eWkR8bGsvGJW7S09rUjHZMo5slthQMsk5m8+yvzNR+jcON7sksxnGHQ6MA3bsa/dt0e8AL3uNLcmkXPk07GwnJwcABITEyv8/0VFRRQVndo4ODfX/deuw+HA4XB4vT7PNXxxrUCjtqmY2uWUbzcewmVAu/qx1Iuxq20qoXapnKdNhrROdAfPjYe5f0hzk6symWHA14/QsjR0llz+L4xut4BeP4B+nirj63apyXUsho8m0RiGwVVXXcXx48dZvHhxhY+ZMGECEydOLHf/tGnTiI6O9naJInIe3t1qZW2WlUsbubiiiTaOl3N30gH/b5UNAwsTLiihboTZFZnEMOh8YAotjs0HYG3a7exNHmpyUSLl5efnM3bsWHJycoiLi6vysT4Lnr///e/54osv+PHHH2ncuHGFj6moxzMtLY2MjIyzfiG1weFwMH/+fIYPH47dbvf69QKJ2qZiahe3ohIXfZ5ZQF6xk1m/7UOXxvFqm0qoXSp3etvcPHkNP6dnM2FkO8b1aWJ2ab5nGFi//iu21W9jYGFtkztoe+NTes38in6eKubrdsnNzSU5OblawdMnQ+33338/n332GYsWLao0dAJEREQQEVH+T1u73e7TF5SvrxdI1DYVC/V2Wbr7GHnFTlJjI+jeNAmr9dTO8aHeNpVRu1TObrczvEN9fk7P5vttmdw2sKXZJfmWywVfPgSr3wYsOEe8SPrBunTSa6ZS+nmqmK/apSbX8OqqdsMwuO+++5g9ezbff/89zZuH+FwdkSD1femei8Pap54ROkXO1fAO7gVqy3dmkldUYnI1PuRywZd/glXu0MlVr2J0G2d2VSK1xqvB8/e//z1Tpkxh2rRpxMbGcvjwYQ4fPkxBQYE3LysiPrZwm/ts7aFttZpdakfLlBga142i2Oli+a4QOcXI5YIvHoRV7wAWuPo16K7QKcHFq8Hzv//9Lzk5OQwZMoQGDRqU/ZsxY4Y3LysiPpSemc+ezHzCrBb6tUwyuxwJEhaLhQvbuI9dXVT6h01Qc7ng8wdg9buABa75H3Qba3ZVIrXOq3M8deqESPBbtN0dCi5oUpfYSM2xktpzYetkpv2UzuLtGWaX4l0uF8z9A6z5ACxWuPp/0PUGs6sS8Qqd1S4i58XTG3VhG53NLrWrf6tkbFYLuzLy2JeVb3Y53uFywdz7T4XOa15X6JSgpuApIufM4XSxdKd7/p1nWFSktsRF2umelgCc6lkPKi4nfHY/rJniDp3Xvgldrje7KhGvUvAUkXO2Jj2bk0UlJNYJp1NDHW0otS9o53m6nPDpfbD2tNDZebTZVYl4nYKniJwzTxgY2CpZ2yiJV3iC59IdmTicQXIilssJc+6FddPAYoPr3lLolJCh4Cki58wz/KlhdvGWzo3iSYi2c6KohLX7ss0u5/y5nDDnd/DLh+7QOfpt6HSd2VWJ+IyCp4ick6y8YtYfyAHcq49FvMFmtTCwlfv1FfDD7c4S+OS38MuM0tD5DnS8xuyqRHxKwVNEzsni7ccwDGhXP5bUuEizy5EgFhTzPD2hc/1MsIbBmHeh49VmVyXicwqeInJOPHsraphdvO3C1u7X2C8HcjieV2xyNefAWQKf/AY2fFwaOidDh6vMrkrEFAqeIlJjhmGw2DO/s7WCp3hX/fhI2taLxTDgxx0Btpm8swRm3wUbZoHVDte/D+1HmV2ViGkUPEWkxrYeOcGR3CIi7VZ6NqtrdjkSAga1DsB5nk4HzLoTNn5yKnS2G2F2VSKmUvAUkRrzvPn3bZFEpN1mcjUSCsrmeW4/FhjHMXtC56Y57tB5wwfQ7gqzqxIxnYKniNTYom2l8zs1zC4+0rt5IhFhVo7kFrHtyEmzy6ma0wEf3w6bPgVbONwwBdpebnZVIn5BwVNEaqSg2MmKPVmAFhaJ70TabfRpkQT4+XB7STHMvA02zy0NnVOh7WVmVyXiNxQ8RaRGlu/OpLjERaOEKFqm1DG7HAkhnv1i/fbc9pJid0/nls/BFgE3ToM2l5hdlYhfUfAUkRrx9DYNap2MxaJjMsV3Bpf2sP+0O4uCYqfJ1fyKp6fz9NDZerjZVYn4HQVPEakR7d8pZmmVGkOD+EiKS1xl0z38QkkRfHQLbP0CwiLhpunQ+mKzqxLxSwqeIlJtB7ML2HH0JFYLDGipYzLFtywWS9mCNr+Z5+kJndvmnQqdrYaZXZWI31LwFJFq87zZd0tLID7abnI1Eor86vjMkiKYMR62fVUaOj+ElheZXZWIX1PwFJFq8yzq0DC7mGVAqySsFth+9CQHswvMK8RRCDNuhu1fQ1gUjJ0BLYeaV49IgFDwFJFqKXG6+FHzO8VkCdHhdGmcAFB2bKvPOQphxjjY/s2p0NliiDm1iAQYBU8RqZZ1+3PILSwhPspO19I3fhEznBpuN+HcdkchfDgWdnzrDp3jPoIWg31fh0iAUvAUkWrxzKkb2CoZm1XbKIl5BrdxL2z7cUcGTpcPj890FMCHN8HO78AeDeNmQvMLfXd9kSCg4Cki1eKZ3zmotVazi7m6Nk4gNjKMnAIH6/Zn++aijgKYfhPs/B7sdWDcx9B8kG+uLRJEFDxF5Kxy8h2s25cNaH6nmC/MZmVgK/cfQIt9MdxenA/Tb4RdC9yh8+aPodkA719XJAgpeIrIWS3ZmYHLcG/g3TAhyuxyRE7N8/T2AqPifJh+A+z6AcJj4OZZ0LS/d68pEsQUPEXkrDzzOz2bd4uYzRM81+7LJqfA4Z2LFOfBtOth9yJ36Bz3MTTt551riYQIBU8RqZJhGKeCZxvN7xT/0CghipYpdXC6DJbu8MJwe3EeTLsB9iyG8Fi4ebZCp0gtUPAUkSrtPHaSgzmFhIdZ6dM8yexyRMp4bbi96CRMHXMqdI6fDU361O41REKUgqeIVGlh6eKNPs0TiQq3mVyNyCmnzm3PwDBqaVslT+jcuwQi4mD8J5DWu3aeW0QUPEWkaprfKf6qT4tEwm1WDmQXsPNY3vk/YdEJmDoa0peeFjp7nf/zikgZBU8RqVShw8lPuzMBbaMk/ic6PIxezesCp/5AOmdFJ2DKaEhfBhHxMH4ONO55/kWKyBkUPEWkUqv2HKfQ4aJeXARt6sWYXY5IOZ6e+PM6t70wF6ZcB/uWu0PnLZ9A4x61VKGInE7BU0Qqdeq0ohQsFh2TKf7H0xO/fFcWRSXOmj9BWej8CSLj4ZY50EihU8RbFDxFpFKntlHSMLv4p3b1Y0mNjaDA4WTVnuM1++TCHJhyLexfAZEJcMtn0OgCr9QpIm4KniJSoSO5hWw5fAKLBQa10v6d4p8sFguDyla312C4vSAbPrgG9q8sDZ2fQsNu3ihRRE6j4CkiFfK8iXdpFE/dOuEmVyNSOc/BBgurGzw9ofPAaoiqC7d+ptAp4iMKniJSoUXb3ft3aphd/J17DjJsOXyCo7mFVT+44Dh8cDUc/NkdOm/5DBp09UmdIqLgKSIVcLkMftyu+Z0SGBLrhNO5UTxw6g+mChUch/evhoNrICoRbp0LDbr4pkgRARQ8RaQCmw7lcjzfQUxEGN3SEswuR+SsBrV2D7cvqezc9vwseP8qOLQWopPcobN+Z98VKCKAgqeIVMDz5t2neSJ2m35NiP8b0PJU8Cx3fGZZ6FwH0clw6+dQv5MJVYqI3lFEpJwlO92nFfXXanYJEBc0rUtEmJWjJ4rYeezkqf+RnwXvXwmHf4E6KXDb51Cvg3mFioQ4BU8ROUNxiYuVu7MAGNAqyeRqRKon0m6jZzP38ZlLdrj/cCIvE967Eg6vd4fOWz+H1PYmVikiCp4icoY16ccpcDhJjgmnbb1Ys8sRqbb+pw23k5fp7uk8sh7qpJaGznYmVygiCp4icoalpcPs/Vom65hMCSgDSqeGbN21G+O9kXBkA8TUg9u+UOgU8RNhZhcgIv5l6U73wqL+LTXMLoGlU8M4mkbk8brrSSxH90FMffeczuTWZpcmIqXU4ykiZfKKSliTng2cWiUsEijCCjKZFv407az7yAtPVugU8UMKniJSZsWeLEpcBo3rRtEkKdrsckSq7+RReG8kjRx7OGzUZULiPxU6RfyQgqeIlFlaun+nejsloJw4ApNHwrEtOOrU58bi/8fcA9EUlTjNrkxEfkXBU0TKLC3bv1PzOyVAnDgM742EjK0Q14iwO74kL6YZhQ5X2bQREfEfCp4iAsDxvGI2HcoFTm1LI+LXThx293RmbIO4xnDb51iSWpYtjFta2fGZImIaBU8RAWDZrkwMA9rUiyElNsLsckSqlnsIJo+AzO0Qn+ZeSJTYAji1I4PnBC4R8R8KniICnDqfXb2d4vdyD5aGzh0Q36Q0dDYv+9+e1/C6fdmcLCoxq0oRqYCCp4gAp+Z3DtD57OLPcg+6h9ezdp4KnXWbnfGQtMRomiRGU+IyWLFbvZ4i/kTBU0Q4mF3A7ow8rBbo0yLR7HJEKpZzwN3TmbUTEjyhs2mFDx1QukCu7Nx2EfELCp4iUtbb2aVxAnGRdpOrEalAzv7S0LkLEpq6j8GsJHTCqeH2pZrnKeJXFDxFpGz1r47JFL+Uvc8dOo/vdg+r3/aFu8ezCv1KX8ubD+WSebLIB0WKSHUoeIqEOMMwWFJ6Prvmd4rfyU4vDZ17TgudaWf9tOSYCNrVjwXcOzaIiH9Q8BQJcTuP5XEkt4jwMCs9mtY1uxyRUzyhM3sv1G0Ot30J8Y2r/eme4XbN8xTxHwqeIiFuaWlvZ8+mdYm020yuRqTU8b2loTPdvT/n7V9CfKMaPYVngZHnNS4i5vNq8Fy0aBGjRo2iYcOGWCwW5syZ483Licg5WLpD2yiJn8lOd2+ZlJ0OiS3dw+txDWv8NL2bJ2KzWtibmc/+4/leKFREasqrwTMvL4+uXbvyyiuvePMyInKOnC6jbP5bPy0sEj8QXXSMsA+uhJx0SGp1zqETIDbSTpfG8YBWt4v4izBvPvnll1/O5Zdf7s1LiMh52HQwl5wCB7ERYXRpFG92ORLqju9hwPansTiyIKk13DoX4hqc11MOaJnMmvRslu7I4PqeZ1+UJCLe5dXgWVNFRUUUFZ3a9iI3NxcAh8OBw+Hw+vU91/DFtQKN2qZigd4ui7YdAaBXs7oYLicOl7PWnjvQ28Zb1C6VOL4b2wdXYXdk4UpshXPcJxCVDOfZTn2aJfAK7iNhi4uLsVgstVOvD+k1Uzm1TcV83S41uY7FMAzDi7WcupDFwieffMLVV19d6WMmTJjAxIkTy90/bdo0oqOjvVidSGj67yYrW3KsXNPMyZAGPvlVIFJOnaIjDNj+DFGOLE5ENmRJq79SZE+oled2uOCRFTYchoVHupZQX28lIrUuPz+fsWPHkpOTQ1xcXJWP9asez0ceeYQHH3yw7HZubi5paWlccsklZ/1CaoPD4WD+/PkMHz4cu12nt5xObVOxQG6X4hIXD6/6HnBx18iBtKkXW6vPH8ht401ql1/J2knYlIexOLJwJbVhSYP7ufCK0bXaNrMzVrF0Zxb2xp24om/VG8/7I71mKqe2qZiv28UzQl0dfhU8IyIiiIiIKHe/3W736QvK19cLJGqbigViu/y8L5NCh4vkmHA6NKrrtSHIQGwbX1C7ABk7YMrVcOIQpLTDOXY2RYtW1XrbDGydwtKdWSzffZw7BrWstef1Nb1mKqe2qZiv2qUm19A+niIhaslOz2r25ICc9yYBLmO7e5/OE4cgpT3c+jnEpHrlUp6N5JfvysTp0pQSETN5tcfz5MmT7Nixo+z27t27Wbt2LYmJiTRpEnjDHSLBxHM++wBtoyS+dmwbvDcKTh6G1I5w62dQ5/wXElWmc6N4YiPDyC0sYcOBHLqmJXjlOiJydl7t8Vy1ahXdu3ene/fuADz44IN0796dJ554wpuXFZGzyCsqYe2+bEAbx4uPHdsG740sHzq9yGa10LeF+w+sJTrFSMRUXg2eQ4YMwTCMcv8mT57szcuKyFms2JNFicsgLTGKtEQt8xUfObbVPbx+8gjU6+Tep9PLodPD07O/TBvJi5hKczxFQtCpYXb1doqPHN3iDp15R6Fe59LQ6btpHp6e/ZV7sigqqb39akWkZhQ8RULQkh06JlN86Mim0tB5DOp3dg+vRyf6tIRWqTGkxEZQ6HDx895sn15bRE5R8BQJMVl5xWw65N5zrb96PMXbjmxyLyTKz4D6XeAW34dOcB9i0r/0D62lmucpYhoFT5EQ45nj1rZeLCmx5ffNFak1Rza6FxLlZ0CDrnDLp6aETg/P1JIlOxQ8Rcyi4CkSYjy9Pf1baZhdvOjwepg8EvIzoUE300MnnHrNr9ufw8miElNrEQlVCp4iIWZpaY+nFhaJ1xz6Bd67EgqyoOEF7tAZVdfsqmhcN5qmSdE4XQYrdmt1u4gZFDxFQsjB7AJ2Z+Rhs1ro08Lc3icJUofWwfulobNRDxj/CUQlmF1Vmf5lw+0KniJmUPAUCSGeuW3uk1x0rrHUsoNrS3s6j0Ojnn4XOoGyBUaa5yliDgVPkRBSNsyu+Z1S2w6ugfevgsJsaNwLxs+GyHizqyrHEzy3HD5Bxskik6sRCT0KniIhwjCMsoVFmt8pterAz6eFzt5ws3+GToCkmAja1Y8FYPkuDbeL+JqCp0iI2HksjyO5RUSEWbmgqfkLPSRIHFgN718NhTmQ1gdungWRcWZXVSXPKUaa5yniewqeIiHC09vZs1ldIu02k6uRoLB/Nbx/DRTlQFrfgAidcGqqiTaSF/E9BU+RELG0tHdHpxVJrdi/Cj642h06m/SDmz+GiFizq6qW3s2TsFkt7M3M50B2gdnliIQUBU+REOByGSwv3bewbwstLJLztG+le3i9KBea9IdxgRM6AWIiwujcyD0H1XOSl4j4hoKnSAjYcvgE2fkOosNtdGnsn4s+JEDsWwEfXAPFJ6DpQBg3EyJizK6qxvqVrm5X8BTxLQVPkRDgWb3bq1kidpt+7OUcpS8/FTqbDYJxHwVk6AToV9rzr5XtIr6ldyCRELCs9M3V08sjUmN7l8GU66D4pDt0jp0B4XXMruqc9WxWF7vNwoHsAvZl5ZtdjkjIUPAUCXJOl8FPnuCp+Z1yLvYuPRU6m18IYz8K6NAJEB0eRtfGCYCG20V8ScFTJMhtPpRLbmEJMRFhdGzo/1vdiJ/ZswSmjAZHHrQYAjfNgPBos6uqFZ6Fdss03C7iMwqeIkHO05vTu3kiYZrfKTWx50eY6gmdQ+GmD4MmdMKZC4wMwzC5GpHQoHchkSC3TMPsci52L4apY8CRDy0vgpumgz3K7KpqVY+mdQm3WTmcW8ieTM3zFPEFBU+RIFbidLFydxaghUVSA7sWngqdrS6GG4MvdAJE2m10a5IAaHW7iK8oeIoEsY0HczlRVEJcZBjtG2h+p1TDroUw7QYoKYBWw+GGqWCPNLsqr/GMBGiBkYhvKHiKBDHPMLvniECRKu1cANOud4fO1pfAjcEdOuHMBUaa5ynifQqeIkHM04ujYXY5q53fw/QboaQQWl8KN0yBsAizq/K67k0SCA+zcuxEETuP5ZldjkjQU/AUCVIOp4uVe0rnd2phkVRlx3cw/SZ36GxzOdzwQUiETnDP8+zRpC6gbZVEfEHBUyRI/bI/h/xiJ3Wj7bSrH2t2OeKvdnx7KnS2vQKufz9kQqeHZ0RgueZ5inidgqdIkPKs0u3TPAmr5ndKRbZ/C9PHgrMI2o6AMe9BWLjZVflcWfDUPE8Rr1PwFAlSnuDZt0WiyZWIX9r2DXx4kzt0thsJYyaHZOgE6NI4nki7lcy8YrYfPWl2OSJBTcFTJAgVl7hYtec4AP1aJptcjfidbV/DjHHgLIb2o0I6dAJEhNno2dT9B5q2VRLxLgVPkSC0bn82BQ4nSXXCaVMvxuxyxJ9s/Qpm3FwaOq+E0e+CzW52VaY7/fhMEfEeBU+RIOR58+zbIgmLRfM7pdTWeadCZ4erYPQ7Cp2lPPt5Lt+diculeZ4i3qLgKRKEyuZ3av9O8djyJcwYDy4HdLwGrntbofM0XRrHEx1uIzvfwdYjJ8wuRyRoKXiKBJmiEier95bO79T+nQKw5Qv46JbS0HktXPuWQuev2G1WejXTPE8Rb1PwFAkya9KzKSpxkRIbQcuUOmaXI2bbPPdU6Ox0HVz7JtjCzK7KL51+fKaIeIeCp0iQ0fxOKbPpM5h5G7hKoNNouOYNhc4qeBYY/bQrE6fmeYp4hYKnSJDx9NZomD3EbZxzKnR2vh6ueV2h8yw6NYwjJiKM3MISNh/KNbsckaCk4CkSRAodTtamZwOnem8kBG38BD6+AwwndLkRrvmfQmc1hNms9G6ueZ4i3qTgKRJEft57nGKni/pxkTRLija7HDHDhlnw8Z3u0Nn1Jrj6NbDazK4qYHhGCpZrnqeIVyh4igSRZacdk6n5nSFo/ccw6+7S0DkWrnpVobOGPAuMVuzOosTpMrkakeCj4CkSRDzDgxpmD0G/zITZpaGz281w1SsKneegQ8M44iLDOFFUwsaDmucpUtsUPEWCRH5xCev2ZwPQr4XOZw8pv3wEn/wGDBd0vxmufFmh8xzZrBZ6N9e2SiLeouApEiRW7TmOw2nQKCGKtMQos8sRX1k3Az75rTt0XnALjHoZrPrVfj50bruI9+i3k0iQKDsmU/t3ho61008LnbfCyJcUOmuBZ4HRqj1ZODTPU6RW6TeUSJA4fWGRhIC102DO7wADetwOI19U6Kwl7erHkhBtJ6/YyfoDOWaXIxJU9FtKJAicLCrhl/3uN0gtLAoBa6bCnHsBA3reASNeUOisRVarhT7az1PEK/SbSiQIrNyThdNlkJYYReO62r8zqP38AXz6e8CAXncpdHqJ9vMU8Q79thIJAst36pjMkLD6PfjsPtyh82644nnQfF6v6NfSvTPEqj3HKS7RPE+R2qLgKRIEys5n1zB78Fo9Geb+wf1x79/CFc8pdHpRm3oxJNYJp8DhLNumTETOn4KnSIDLLXSwoXQBRF/1eAanVe/C3P9zf9znd3D5PxQ6vcxisZQt1FuueZ4itUbBUyTArdydhcuAZknRNIjX/p1BZ+Xb8PkD7o/73guXPaPQ6SOeqSvaSF6k9ih4igQ4HZMZxFa8CV886P64331w6SSFTh/y/Eyt3nucohKnydWIBAcFT5EAt+y0jeMliKx4E758yP1xv/vgkqcUOn2sZUoMKbERFJW4WJOebXY5IkFBwVMkgGXnF7PpUC6gFe1B5afXT4XO/n9Q6DSJe56njs8UqU0KniIBbMXuLAwDWqbUITUu0uxypDYs/x/M+4v74wEPwPAnFTpNpP08RWqXgqdIANMwe5BZ9hp89bD744EPwsUTFDpN5lnZviY9m0KH5nmKnC8FT5EApoVFQWTZq/D1I+6PB/0Jhj2h0OkHmifXoV5cBMVOFz/vPW52OSIBT8FTJEBl5RWz5fAJQD2eAW/py/D1o+6PL/wzXPS4QqefsFgs2lZJpBYpeIoEqBW73W+CberFkBwTYXI1cs6W/Ae++X/ujy/8Cwx9TKHTz3hGFDTPU+T8+SR4vvbaazRv3pzIyEh69OjB4sWLfXFZkaDmGWZXb2cA+/FFmP+4++PBf4WLFDr9kednbO2+bAqKNc9T5Hx4PXjOmDGDBx54gMcee4w1a9YwaNAgLr/8ctLT0719aZGgVnY+u4JnQLIufQm+/Zv7xpBHYOgj5hYklWqSGE3D+EgcToNVe7PMLkckoHk9eL7wwgvceeed3HXXXbRv354XX3yRtLQ0/vvf/3r70iJBK+NkEduOnASgj4JnwGl9eC62BX933xj6GAz5q7kFSZUsFgt9NdwuUivCvPnkxcXFrF69mr/+9cxfqpdccglLly4t9/iioiKKiorKbufmujfGdjgcOBwOb5Zadp3T/yunqG0qZla7LN1+FIC29WKIDbf45fdFr5mKGYueo8OhmQA4Bz+Kq/8fQW0E+PdrplfTBGb/fIClOzJwXOTb+vy5XcymtqmYr9ulJtexGIZheKuQgwcP0qhRI5YsWUL//v3L7p80aRLvvfceW7duPePxEyZMYOLEieWeZ9q0aURHR3urTJGA89EuK0uOWLmwvovrmrvMLkeqqc3hT2l/aBYAmxqMZnv9K02uSKorsxCeXBOG1WLwbC8nETazKxLxH/n5+YwdO5acnBzi4uKqfKxXezw9LL+aLG8YRrn7AB555BEefPDBstu5ubmkpaVxySWXnPULqQ0Oh4P58+czfPhw7Ha7168XSNQ2FTOrXf7znyVAHjcM7c4lHer57Lo1odfMmayLn8O2xhM6x9Bs/H9orXY5g7+/Zt7evYgD2YUkt+vNoNbJPruuv7eLmdQ2FfN1u3hGqKvDq8EzOTkZm83G4cOHz7j/6NGj1KtX/s0yIiKCiIjy28LY7XafvqB8fb1AorapmC/b5eiJQnYey8NigQGtU/3++6HXDPDDs7DoHwA4L3qC7cdb0VrtUil/fc30a5nMx6v3s2JvDhd1aODz6/tru/gDtU3FfNUuNbmGVxcXhYeH06NHD+bPn3/G/fPnzz9j6F1Equ+nXe5Vte3rx5EQHW5yNVIlw4AFk+CHZ9y3hz+Jq98fzK1JzpnObRc5f14fan/wwQcZP348PXv2pF+/frzxxhukp6dzzz33ePvSIkFJ57MHCE/oXPRP9+1LnoL+92shUQDzrGxffyCHk0UlxET4ZLaaSFDx+k/NDTfcQGZmJk8++SSHDh2iU6dOfPnllzRt2tTblxYJSst1Prv/MwxY8DQses59+9JJ0O/35tYk561RQhRNEqNJz8pn5e4shrZLNbskkYDjk5OL7r33Xvbs2UNRURGrV6/mwgsv9MVlRYLOkdxCdmW453f2bp5odjlSEcOA7/9+Wuh8RqEziGi4XeT86Kx2kQDiebPr2DCO+ChNpPc7hgHfPQmL/+W+fdmz0O9ec2uSWtW3pfsPvmUKniLnRMFTJIAs1zGZ/ssw4NsJ8OML7tuX/xP6/s7UkqT2eeZWbziQQ26h5uuK1JSCp0gAWbZTC4v8kmHA/CdgyYvu21c8D31+a2pJ4h0N4qNolhSNy4CVu3Vuu0hNKXiKBIhDOQXsyczHaoFemt/pPwwD5j8OS//jvn3F89D7bnNrEq/yLOzz/CEoItWn4CkSIDzD7J0bxRMXqfmdfsEw4Jv/B0tfdt8e8S+FzhDgGXFYvlvBU6SmFDxFAoSG2f2MYcDXj8KyV9y3R/4bet1lbk3iE5451hsP5pKTr3meIjWh4CkSIMo2jtf+neYzDPjqEVj+mvv2yBeh5x2mliS+kxoXSYuUOhgG/KReT5EaUfAUCQD7j+ezL6sAm9VCr2aa32kqw4B5D8NP/3XfHvUf6Hm7uTWJz5UNt+/SAiORmlDwFAkAnje3zo3idUyfmQwD5v0FVrwOWODKl6HHrWZXJSbwDLdrP0+RmlHwFAkAZft3apjdPIYBX/4ZVrxBWei84BazqxKTeHo8txzOJTu/2ORqRAKHgqdIANDCIpO5XPDFn2Dlm4AFrnoVLhhvdlViopTYCFqlxmAYGm4XqQkFTxE/ty8rnwPZBYRZLfRsWtfsckKPywVfPAir3gYscPVr0H2c2VWJH9C57SI1p+Ap4uc8c8i6NI6njuZ3+pbLBZ8/AKvfBSxwzf+g21izqxI/0VfBU6TGFDxF/NzynZrfaQqXCz7/P/j5PbBY4ZrXoeuNZlclfqRvC/cOE1sOnyDzZJHJ1YgEBgVPET9mGEZZj2e/FskmVxNCXC6Yez/8/P5pofMGs6sSP5MUE0HberEA/KRz20WqRcFTxI+lZ+VzKKcQu81CD83v9A2XEz67D9ZMcYfOa9+ELtebXZX4KU+vp4bbRapHwVPEj3lWs3dLSyAq3GZyNSHA5YRP74O1U0+Fzs6jza5K/JhnCoznZ1VEqqbgKeLHyvbv1DZK3udywqe/h3XTwGKD695S6JSz6tPc/bO5/ehJMjTPU+SsFDxF/NTp8zu1f6eXuZww53ewbro7dI5+GzpdZ3ZVEgDq1gmnXX33PE8Nt4ucnYKniJ/anZHHkdwiwm1WLtD8Tu9xlsAnv4VfZpSGzneg4zVmVyUBRMPtItWn4CnipzynoXRrkkCkXfM7vcITOtfPBGsYjHkXOl5tdlUSYLSfp0j1KXiK+Kllmt/pXc4S+OQ3sOHj0tA5GTpcZXZVEoD6Nk/CYoGdx/I4mltodjkifk3BU8QPGYZRNmynjeO9wFkCs++CDbNKQ+d70H6U2VVJgIqPttOhQRxw6g9GEamYgqeIH9p5LI+Mk0WEh1nplpZgdjnBxemAWXfCxk/Aaofr34f2I82uSgLcqeF2bSQvUhUFTxE/5Ok16dGkruZ31iZP6Nw0xx06b/gA2o0wuyoJAv00z1OkWhQ8RfzQcm2jVPucDvj4dtj0KdjC4YYp0PZys6uSINGreSJWi3s3isM5mucpUhkFTxE/YxgGP+3S/M5aVVIMM2+DzXNPC52XmV2VBJH4KDsdG8YD6vUUqYqCp4ifcZ+AUkyk3UrXtHizywl8JcXuns4tn4MtAm6cBm0uNbsqCULaz1Pk7BQ8RfyMp7ekR9O6RIRpfud5KSmGmbeeGTpbDze7KglSfVskArB8t4KnSGUUPEX8TNk2SprfeX5KiuCjW2Drl+7QedM0aH2x2VVJEOvVLBGb1cLezHwOZheYXY6IX1LwFPEjLpfBT7vd27Fofud58ITObfMgLBJumg6tFDrFu2Ij7XRqpHmeIlVR8BTxI9uOniArr5gou43OjRLMLicwOQphxs2w7avS0PkhtBpmdlUSIjzD7ZrnKVIxBU8RP+J5s+rZrC7hYfrxrDFP6Nz+DYRFwdgZ0HKo2VVJCPFMkdEJRiIV0zubiB/xBE/t33kOHIUwYxzsmH8qdLYYYnZVEmJ6NkskzGph//EC9mXlm12OiN9R8BTxE06XUTYvbECrZJOrCTCOQvhwLOz4FuzRMG4mtBhsdlUSgmIiwuhaesythttFylPwFPETmw7mkltYQmxEGJ0axpldTuBwFMCHN8HO706FzuaDzK5KQlj/0oWBS3dmmFyJiP9R8BTxE543qT4tEgmz6UezWorzYfqNsPN7sNeBcR9Ds4FmVyUhrl9Z8MzEMAyTqxHxL3p3E/ETSz37d7bUMHu1eELnrh/cofPmj6HZALOrEuGCJu7FgUdPFLHzWJ7Z5Yj4FQVPET9QXOJiRen+nf21f+fZFefD9Btg90IIj4GbZ0HT/mZXJQJApN1Gz6Z1AQ23i/yagqeIH1i3P5sCh5OkOuG0rRdrdjn+rTgPpl0PuxedFjr7mV2VyBnK5nnu0AIjkdMpeIr4Ac+bU9+WSVitFpOr8WPFeTDtBtizGMJj4ebZ0KSv2VWJlNO/dGeKZbsycbk0z1PEQ8FTxA94huM0zF6F4jyYev2p0Dl+NjTpY3ZVIhXq0iiemIgwcgocbDqUa3Y5In5DwVPEZAXFTtakZwPQXwuLKlZ0EqaOgb0/QkQcjP8E0nqbXZVIpcJsVno31/GZIr+m4ClistV7j1PsdNEgPpJmSdFml+N/ykLnktNCZy+zqxI5K+3nKVKegqeIyTxvSv1aJmGxaH7nGYpOwJTrIH0pRMTD+DnQuKfZVYlUi2c/zxW7s3A4XSZXI+IfFDxFTLakdBhugIbZz1SY6w6d+5a7Q+ctn0DjHmZXJVJt7evHkRBtJ6/YyS/7s80uR8QvKHiKmCi30MH60jekflpYdEpZ6PwJIuPhljnQSKFTAovVaqFfC22rJHI6BU8RE63YlYXLgObJdWiYEGV2Of6hMAemXAv7V0BkAtzyGTS6wOyqRM6JZ1ulpVpgJAIoeIqY6tQxmertBNyh84NrYf/K0tD5KTTsZnZVIufMs8BodfpxCh1Ok6sRMZ+Cp4iJtH/naQqy4YNr4MAqiKoLt36m0CkBr0VyHerFRVBc4uLnvcfNLkfEdAqeIibJPFnElsMnAMrmgYWsguPwwdVwYDVEJcKtc6FBV7OrEjlvFoulbH9eDbeLKHiKmGbZLvebULv6sSTFRJhcjYkKjsP7V8PBNaWh8zOo39nsqkRqjWcqzRLt5ymi4CliFk/vR0ifVpSfBe9fBYfWQnSSu6dToVOCjGcqzS/7czhR6DC5GhFzKXiKmGRZWfAM0WH2stC5DqKT4dbPoX4ns6sSqXWN60bTNCkap8tg5Z4ss8sRMZWCp4gJDmYXsDsjD6sFerdINLsc38vPgvevhMO/lIbOuVCvg9lViXhN2fGZ2s9TQpyCp4gJPL2dnRsnEBdpN7kaH8vLhPeuhMProU4K3Pa5QqcEvX5aYCQCKHiKmGJpqA6z52W6ezqPrIc6qe7h9dT2Zlcl4nWenSs2HcrleF6xydWImEfBU8THDMNgWenq1pA6nz0vA94bBUc2uEPnbZ9DajuzqxLxiZTYCNrUiwFg+S71ekroUvAU8bE9mfkczCkk3GalR9O6ZpfjGyePuUPn0Y0QUw9u+wJS2ppdlYhPeXaw0LZKEsq8Gjyffvpp+vfvT3R0NAkJCd68lEjA8JxW1L1JAlHhNpOr8YE8T+jcBDH1S0NnG7OrEvE5z36emucpocyrwbO4uJgxY8bwu9/9zpuXEQkoobR/Z4Qjh7ApV8OxzRDbwB06k1ubXZaIKfq2SMJqgV3H8jicU2h2OSKm8GrwnDhxIn/84x/p3FkbQosAuFwGyz3Bs1WQLyw6eYQBO57BkrEVYhuWhs5WZlclYpr4KDudGsUDsGyXhtslNIWZXcDpioqKKCoqKrudm5sLgMPhwOHw/mkPnmv44lqBRm1TsZq2y9bDJ8jMKyY63EaHenWCtz1PHMY25WpiCw/iim2I8+Y5ENcEgvXrrQH9LFUuFNqmT7O6/LI/hx+3H2Nkp3rV+pxQaJdzpbapmK/bpSbXsRiGYXixFgAmT57MAw88QHZ2dpWPmzBhAhMnTix3/7Rp04iOjvZSdSK+88MhC5/ssdE+wcU97V1ml+MVEY5sBmx/htiiQ+TbE1nS+hHyI6r3BisS7DZnW/jfZht1ww3+doETi8XsikTOX35+PmPHjiUnJ4e4uLgqH1vjHs/KwuHpVq5cSc+ePWv61DzyyCM8+OCDZbdzc3NJS0vjkksuOesXUhscDgfz589n+PDh2O0htqn3WahtKlbTdvls6hrgGKP6tOWKgc29X6CvnThE2JSrsRQdwhXXiCWN/8iAkeP0mjmNfpYqFwptM6S4hLeeXsDxYujcbwhNEs/eqRIK7XKu1DYV83W7eEaoq6PGwfO+++7jxhtvrPIxzZo1q+nTAhAREUFERES5++12u09fUL6+XiBR21SsOu1S4nSxYvdxAAa1rhd87Zh7EKZcDVk7IT4N581zyF+6Ua+ZSqhdKhfMbRNvt9O9SQIr9xxnxd4cWtaLr/bnBnO7nC+1TcV81S41uUaNg2dycjLJycG/Glektm04mMuJohLiIsPo0ND7Pfg+lXsQJo8sDZ1N4La5ENMI2Gh2ZSJ+p1/LZFbuOc7SnZnc1LuJ2eWI+JRXV7Wnp6ezdu1a0tPTcTqdrF27lrVr13Ly5ElvXlbEL3n27+zbIgmbNYgmduUcgHevcIfOhCbuE4nqNjO7KhG/NaB0P89lOzPwwTILEb/i1VXtTzzxBO+9917Z7e7duwOwYMEChgwZ4s1Li/idZaXbKA1oFUQjBjn73T2dx3dDQlN36ExQD45IVbo1SSDSbiXjZDHbj56kTb1Ys0sS8Rmv9nhOnjwZwzDK/VPolFBTVOJk5Z4sAPq3DJL9O7P3weQR7tBZt5l7n06FTpGzigiz0atZIgBLd2g/TwktOqtdxAfWpmdT6HCRHBNBq9QYs8s5f9nppaFzz2mhM83sqkQCho7PlFCl4CniA0vKjslMwhLoG/cd3+sOndl7oW5zuO1LiG9sdlUiAcVzZO7yXZk4XZrnKaFDwVPEB5aVLiwK+GH243vdczqz0yGxBdz+JcQ3MrsqkYDTqWEcsRFh5BaWsPFgjtnliPiMgqeIl+UXl7AmPRs41csRkI7vcYfOnHRIbOkeXo9raHZVIgEpzGalTwsNt0voUfAU8bKVe45T4jJoXDeKJkkBevRr1u5ToTOplUKnSC3or3meEoIUPEW8bGmgD7OXhc59kNS6NHQ2MLsqkYDXv5X7d8LK3VkUl7hMrkbENxQ8RbxsWdnCogAcZs/a5V5IlLsfktu49+mMrW92VSJBoU1qLEl1wilwOFm3P9vsckR8QsFTxIty8h1sOOBeONAv0Ho8M3fCuyMg9wAkt4VbFTpFapPVaqFv6e+FJdrPU0KEgqeIFy3dmYHLgFapMdSLizS7nOrL3OkeXj9xEFLalfZ01jO7KpGgM7D0JLMftyt4SmhQ8BTxokWlbyaDWgfQMHvGDvfw+omDkNIebp0LMalmVyUSlDzBc82+bHILHSZXI+J9Cp4iXmIYBou3HwPgwtYpJldTTRnbS0PnIUjtoNAp4mVpidE0T66D02WwXKvbJQQoeIp4yd7MfPYfL8Bus9CnRaLZ5ZzdsW3u4fWThyG1Y2noDJDALBLAPCMiizXcLiFAwVPESzy9nT2a1iU6PMzkas7i2DZ4rzR01usEt34GdQJoeoBIAPMMt3t+Z4gEMwVPES9ZXDa/0897DY9tdQ+vnzwC9TrDLQqdIr7Ur2USNquFPZn57MvKN7scEa9S8BTxAofTVbZ/p1/P7zy6xR06845C/c6lPZ0Btu2TSICLjbRzQZMEQMPtEvwUPEW8YN2+bE4UlVA32k7HhnFml1Oxo5tLQ+cxqN/F3dMZHQBzUUWC0MBW7j9QNdwuwU7BU8QLPNsoDWiVjNVqMbmaChzZ5F5IlJ8BDbrCLZ8qdIqYaFAb9/SWJTsycLoMk6sR8R4FTxEv+LG018Iv9+88stG9kCg/Axp0g/FzFDpFTNalUTxxkWHkFpbwi47PlCCm4ClSy3IKHKzdlw3AQH+b33l4Q2lPZyY07A63zFHoFPEDYTYr/VtqWyUJfgqeIrVsWekxmS1T6tAoIcrsck45vB7eGwUFWdDwAndPZ1Rds6sSkVKe4XYdnynBTMFTpJb55TZKh345FTob9YDxn0BUgtlVichpPDtg/Jx+nBM6PlOClIKnSC1b7G/nsx9cWxo6j0OjngqdIn4qLTGapknRlLgMlu/KMrscEa9Q8BSpRXsz80jPysdus9C3hR/sh3lwLbx/FRRmQ+NeMH42RMabXZWIVMLzB+uP2lZJgpSCp0gt8vR2dm9SlzoRJh+TeXANvH9laejsDTcrdIr4O88UHS0wkmCl4ClSizybP19o9jD7gdWlPZ05kNantKfTTzeyF5EynuMzd2Xksf+4js+U4KPgKVJLSpwulu5wH5Np6sKi/avh/WtKQ2dfuHkWRMSaV4+IVFtcpJ1uaQmAVrdLcFLwFKkl6/bncKKohPgoO50amTSkvX8VfHA1FOVAk35w88cKnSIBxjPPU8PtEowUPEVqiWeYfWCrZGxmHJO5byV8cA0U5UKT/jBOoVMkEJUtMNLxmRKEFDxFaomp2yjtW3EqdDYdCONmQkSM7+sQkfPWtXECsRFh5BQ42HAgx+xyRGqVgqdILThRePoxmT4OnunL3aGz+AQ0GwTjPlLoFAlgYTYr/Vu5t2NbrG2VJMgoeIrUguW7juN0GbRIrkPjutG+u/DeZTDlOig+6Q6dY2dAeB3fXV9EvMKzQHGR5nlKkFHwFKkFP+40YZh971KYOtodOptfCGM/UugUCRKe3yVr0o9zsqjE5GpEao+Cp0gt+LF0G6WBvtpGac8SmOIJnYPhphkQ7sOeVhHxqqZJdWiSGI3DabBiz3GzyxGpNQqeIucpoxDSswoIs1ro2yLR+xfc86O7p9ORBy2Glg6vK3SKBJtTq9szTa5EpPYoeIqcp6057q2TLmhSl9hIu3cvtnsxTB0DjnxoeRHcNB3sUd69poiYwhM8lyh4ShBR8BQ5T1uy3cHT66vZdy08LXQOgxsVOkWCWb+WyVgtsCsjj6wis6sRqR0KniLnocTpYntpj6dXFxbt+gGm3QAlBdDqYrhxGtgjvXc9ETFdfNSp4zO3ZptwKIWIFyh4ipyH9QdzKXBaiIsMo0vjBO9cZOeCU6Gz9SVww1SFTpEQ4Vmw6JnSIxLoFDxFzoNn0n+/FoneOSZz5/cw/UYoKYTWl8INUxQ6RULIhaUjKVtzLDo+U4KCgqfIeVi6s3QbpVZeGGbf8R1MKw2dbS6HGz6AsIjav46I+K2uaQnERISRX2Jh06Fcs8sROW8KniLn6EShgzX73OcoD2hVy9so7fgWpt8EziJoewVc/55Cp0gIstus9G1eF9DqdgkOCp4i52jZzkycLoPkSIO02jwmc/t8mD62NHSOgDEKnSKhbGDpue0/7lTwlMCn4ClyjhaXnqHcLr4W511tnw8flobOdiNhzGQIC6+95xeRgOOZyvNzejZ5Oj5TApyCp8g5+nGHO3i2Tail4Lnt69LQWQztRyl0iggATRKjSIww3Mdn7s4yuxyR86LgKXIO9mXlszsjD5vVQuu4WgieW7+CD8eVhs4rYfS7YPPyKUgiEhAsFkvZyMqi7cdMrkbk/Ch4ipwDzzB7t8bxRIWd55NtnQczbgaXAzpcDaPfUegUkTN4RlY8v3tEApWCp8g5+HGHu9dhQMuk83uiLV/AjPHu0NnxGrjubYVOESmnTbyB1QI7jp7kUE6B2eWInDMFT5EacroMfiztdfCsNj0nmz+Hj25xh85O18G1b4HtfLtPRSQYRYdB50bxgHo9JbApeIrU0C/7s8ktLCE2MozOjeLO7Uk2z4WZt4KrBDqNhmveUOgUkSp5/tBV8JRApuApUkOe3s7+LZMIs53Dj9CmT2Hmbe7Q2XkMXPO6QqeInJVnas+SHRm4dHymBCgFT5EaWrD1KAAXtkmp+SdvnAMzby8NndcrdIpItXVLiyc2IoysvGJ+OZBjdjki50TBU6QGMk8WsWZfNgAXtUut2Sdv/AQ+vgMMJ3S5Ea75H1httV+kiAQlu81a9gfv95uPmFyNyLlR8BSpgR+2HsMwoH2DOBrER1X/EzfMho/vdIfOrjfB1a8pdIpIjQ0t/YP3uy1HTa5E5NwoeIrUwPelw+zDatLbuWEWzLrLHTq7jYOrXlXoFJFzMqRtChYLbDyYy+GcQrPLEakxBU+RanI4XSza6t6/86L21Qye6z8+LXTeDFe+rNApIucsOSaCbmkJwKn55iKBRMFTpJpW7sniRFEJiXXC6do44eyf8MtMmH03GC7ortApIrXjoralw+2bFTwl8Ch4ilTTgtI5VUPapmCzWqp+8LoZ8Mlv3KHzgltg1Mtg1Y+biJw/z4jLkh0ZFDqcJlcjUjN6JxSpJs9k/mHt6lX9wLXT4ZPflobOW2HkSwqdIlJrOjSIo35cJAUOJ8t3ZZpdjkiN6N1QpBp2Z+Sx61geYVYLg9okV/7AtdNgzu8AA3rcDiNfVOgUkVplsVjKej2/1+p2CTBee0fcs2cPd955J82bNycqKoqWLVvyt7/9jeLiYm9dUsRrPL/cezVLJC7SXvGD1kyFOfcCBvS8A0a8oNApIl5x+jxPw9ApRhI4vHZkypYtW3C5XLz++uu0atWKDRs2cPfdd5OXl8fzzz/vrcuKeIVnfuewSlazW9ZOhS8eAAzodRdc8TxYzjIPVETkHA1olUxEmJUD2QVsO3KStvVjzS5JpFq8Fjwvu+wyLrvssrLbLVq0YOvWrfz3v/9V8JSAcqLQwU+73fOoKjqtqEnGD4Stecd9o9fdcMVzCp0i4lVR4Tb6t0xiwdZjfL/lqIKnBAyfHhKdk5NDYmJipf+/qKiIoqKistu5ubkAOBwOHA6H1+vzXMMX1wo0odw2P2w5gsNp0CwpmrSEiDPawLXqXbrvc4dOZ8+7cQ2fBCUlZpXqV0L5NVMVtUvl1DYVq6xdBrdJZsHWY3y3+TB3DWhiRmmm02umYr5ul5pcx2L4aHLIzp07ueCCC/jXv/7FXXfdVeFjJkyYwMSJE8vdP23aNKKjo71dokiFpu2w8tMxK4MbuLi2mavs/qYZC+i2710AdqZcwoZG49TTKSI+k1UEE38Ow4LB0z2d1Klk+rmIt+Xn5zN27FhycnKIi4ur8rE1Dp6VhcPTrVy5kp49e5bdPnjwIIMHD2bw4MG89dZblX5eRT2eaWlpZGRknPULqQ0Oh4P58+czfPhw7Hb9BJ8uVNvG5TLo/8+FZOYV895tPejfMgkA6+p3sX31ZwB2plxKg9vexR4ebmapfidUXzNno3apnNqmYlW1y8hXlrL1yEn+NbozV3ZtYFKF5tFrpmK+bpfc3FySk5OrFTxrPNR+3333ceONN1b5mGbNmpV9fPDgQYYOHUq/fv144403qvy8iIgIIiIiyt1vt9t9+oLy9fUCSai1zdp92WTmFRMTEUa/VqnYw6yw8i0oDZ3O3vewobgfTcLDQ6pdaiLUXjPVpXapnNqmYhW1y7D29dh65CQLt2dyXc/QHG4HvWYq46t2qck1ahw8k5OTSU6uYh/D0xw4cIChQ4fSo0cP3n33XazaWkYCzPebjwAwqHUy4WFWWPEmfPmQ+3/2uw/X0L/BvHkmVigioeyidqm89sNOfth6lBKnizCb3mfFv3ntFXrw4EGGDBlCWloazz//PMeOHePw4cMcPnzYW5cUqXXfb3Vvo3RRu1T46fVTobP/H+CSpzSnU0RM1b1JXRKi7eQWlrB673GzyxE5K6+tav/mm2/YsWMHO3bsoHHjxmf8P212K4HgcE4hGw7kYrHA5XmfwoLH3P9jwP/BxRMVOkXEdDarhaFtU/lkzQG+33qUPi2SzC5JpEpe6/G87bbbMAyjwn8igWBBaW/n/0v8gRhP6Bz4R4VOEfErnv2Fv9+s4zPF/2kyiEglvt9ylDttX3JnXumiuEF/gmF/U+gUEb9yYZsUbFYL24+eJD0z3+xyRKqk4ClSgUKHk1Y73uVx+xT3HRf+GS56XKFTRPxOfJSdnk3rAvD9liMmVyNSNQVPkQoc+OIfPGx1h07jwj/D0McUOkXEbw1rXzrcvvWYyZWIVE3BU+TXfnyRlmv/AcC3qbdjuej/KXSKiF/zzPNcvjOTvCId2yv+S8FT5HQ//hu+/RsA/3ZchzHkEZMLEhE5u5YpMTRJjKbY6eLHHRlmlyNSKQVPEY/F/4JvJwDwL8do/msZw4BW2ppERPyfxWIp6/VcsEWr28V/KXiKACx6Dr57EoCfmt3Ly85r6d8yiehwr211KyJSq8rmeW45isulrQvFPyl4iix8Dr5/yv3xRY/zr8Ir3R+W9h6IiASC3s0TiQ63cfREERsP5ppdjkiFFDwltP3wD1hQGjqH/Y3snn9g1d4sAIa2VfAUkcAREWZjUOtkAL7TtkripxQ8JXQteAZ+mOT++OKJMOhBFm47hsuAtvViSUuMNrc+EZEaGtauHqB5nuK/FDwl9BgGLJgEC5913x7+JAx8AHDPjQK4qL16O0Uk8AxplwLAuv05HD1RaHI1IuUpeEpoKQud7n06ueQpGPB/AJQ4XfxQuvmy5neKSCBKjY2kS+N4AH7Yos3kxf8oeEroMAxY8DQs+qf79iVPQ//7y/73z+nZ5BQ4SIi20z0twZwaRUTOk+cPZ83zFH+k4CmhwTDg+7+7t00CuPQZ6H/fGQ/xDLMPaZNCmE0/GiISmDzzPH/cnkFRidPkakTOpHdXCX6GAd9NdG8QD3DZs9Dv3nIP+760d2CohtlFJIB1bBhHSmwEecVOVuzOMrsckTMoeEpwMwz3aUQ//tt9+7J/QN/flXvYvqx8th05ic1qYXCbFN/WKCJSi6xWCxeVbgf33Watbhf/ouApwcswYP4TsORF9+3Ln4O+91T4UM8we4+mdUmIDvdRgSIi3nHRaacYGYZOMRL/oeApwckwYP7jsPQ/7ttXPA99flPpwz3Bc5iG2UUkCAxslUy4zUp6Vj47j+WZXY5IGQVPCT6GAd/8P1j6svv2iH9B77srfXheUQnLdmUC2kZJRIJDnYgw+rRIBOC7zVrdLv5DwVOCi2HA14/Cslfct0f+G3rdVeWnfL/lKMUlLpomRdMqNcYHRYqIeN/wDu7V7fM2HDa5EpFTFDwleBgGfPUILH/NfXvki9DzjrN+2pfrDwFwRecGWCwWLxYoIuI7l3Wqj8UCa/dls/94vtnliAAKnhIsDAPmPQw//dd9e9R/oOftZ/20vKKSsvmdIzo38GaFIiI+lRobSe9m7uH2eevV6yn+QcFTAp9hwLy/wIrXAQtc+TL0uLVan/r9lqMUlQ6zd2wY5906RUR8bEQX9x/UX5SO7IiYTcFTApthwJcPwYo3KAudF9xS7U/3DLOP0DC7iAQhDbeLv1HwlMDlcsEXf4KVbwEWuOpVuGB8tT/99GH2KzTMLiJBSMPt4m8UPCUwuVzwxYOw6m3AAle/Bt3H1egpNMwuIqFAw+3iTxQ8JfC4XPDFH2H1u4AFrvkfdBtb46f54hcNs4tI8NNwu/gTBU8JLC4XfP5/sHoyWKxwzevQ9cYaP01eUQkLtmqYXUSCn4bbxZ8oeErgcLlg7h/g5/dPC503nNNTeYbZm2mYXURCwEgNt4ufUPCUwOBywdz7Yc0H7tB57ZvQ5fpzfjrPMLs2jReRUHCphtvFTyh4iv9zOeGz+2DNlFOhs/Poc346DbOLSKjRcLv4CwVP8W8uJ3z6e1g7FSw2uO6t8wqdAN9pmF1EQpBnuP1zDbeLiRQ8xX+5nDDnXlg33R06R78Nna4776f9UsPsIhKCPMPt6zTcLiZS8BT/5HLCJ/fALx+Whs53oOM15/20pw+ze/a2ExEJBamxkfRpruF2MZeC568YBhiGYXYZoc1ZAp/8FtZ/BNYwGPMudLy6Vp769GH2Dg00zC4ioWVEZw23hwJ/zjEKnqd5Z8keJq21sXZfjtmlhC5nCXzyG1g/szR0ToYOV9Xa02uYXURC2enD7fuyNNwerG6dvJr3t1vZ54dTKhQ8T7P50AmOFlr4dJ3+EjSFswRm3w0bZpWGzveg/ahae3oNs4tIqDtjuH2D3uuC0e6MPJbtymJNhoUou83scspR8DzNld3cYeTLDYcpLnGZXE2IcTpg1p2wcTZY7XD9+9B+ZK1eQsPsIiKnhtu/0DzPoDRnzQEA2iYYJMdEmFxNeQqep+nXPJE4u8HxfAeLth0zu5zQ4Qmdm+a4Q+cNH0C7EbV+Gc8w+4guGmYXkdB1aaf6WDXcHpQMw2DOWnfw7Jnsn/M8FTxPE2azckHpN+qT0m+ceJnTAR/fAZs+BVs43DAF2l5e65fRpvEiIm6psZH01nB7UFqzL5u9mflEh9vonKjgGRB6JruH2L/ddITcQofJ1QS5kmKYeRts/uy00HmZVy7lGWZvnlxHw+wiEvJGdGkIaLg92HiG2S9pn0qE/03vBBQ8y2lcB1qm1KGoxMVXG/QD6TUlxfDx7bDlc7BFwI3ToM2lXrvcF78cBOCKzvU1zC4iIe+yjhpuDzYOp4u569zvdZ41K/5IwfNXLBa4qqv7G+b5y0Fqmaen8/TQ2Xq41y6XV1TCD1vdc3Y1zC4iAimxERpuDzKLth3jeL6DlNgI+pV+b/2RgmcFRpVutbNsVyaHcgpMribIlBTBR7fA1i/cofOmadD6Yq9eUsPsIiLlabg9uHxS2lk2qktDwmz+G+/8tzITNa4bRe9miRgGfLb2oNnlBA9P6Nw2D8Ii4abp0Mq7oRM0zC4iUhENtwePE4UO5m86AsA13RuZXE3VFDwrcXXpN+4TDbfXjpIimDEetn11Wugc5vXLnjxtmH1E54Zev56ISKBIiY2gT/MkQMPtge6rDYcpKnHRMqUOnRr598iegmclRnRuQLjNypbDJ9h8KNfscgKboxBm3Azbv4awKBg7A1pe5JNLf7f5SNkwe/sGsT65pohIoLiidGrZF78oeAYyz96d13Rv5PcjewqelYiPtjO0XQpw6hsq58BRCDPGwfZvToXOFkN8dvkv13vOZtcwu4jIr5UNt+/P0XB7gDqcU8jSnZkAXNXNv4fZQcGzSp55Ep+uOYjL5Z8bsfo1RyF8OBZ2fOsOneM+ghaDfXZ5DbOLiFRNw+2B77N1BzAM6NWsLmmJ0WaXc1YKnlUY0jaVuMgwDucWsnx3ptnlBBZHAXx4E+z8DuzRMG4mNL/QpyVomF1E5Ow03B7YPlnjXkB7tZ8vKvJQ8KxCpN3GiC7a07PGivNh+o2w8/vTQucgn5fhGWYf0Vlns4uIVEbD7YFry+FcNh/KxW6zMCJA9qlW8DyLq0vnS8xbf5hCh9PkagKAJ3Tu+gHsdWDcx9BsoM/LOFlUwgJtGi8iclanD7d7/mCXwDCntLdzaNtUEqLDTa6mehQ8z6JXs0QaJURxoqiE7zYfNbsc/1acD9NvgN0LITwGbp4FzQaYUsp3m49QrGF2EZFq8Qy3K3gGDpfL4NPTVrMHCgXPs7BaLVzVzb0wRXt6VqE4D6ZdD7sXnQqdTfuZVo5naoRWs4uInN3pw+07j500uxyphp92Z3Eop5DYyDCGtks1u5xqU/CsBs9fEj9sPUpWXrHJ1fih4jyYdgPsWQzhsXDzbGjS17RyDmYXsHCbe5h9dI800+oQEQkUKbERDG3rDi8zVu4zuRqpDk8Hy4jODYi020yupvoUPKuhdb1YOjaMo8Rl8IWGIc5UdBKmXn8qdI6fDU36mFrSR6v24TKgb4tEmifXMbUWEZFAcWPvJgDMWr2f4hKXydVIVQodzrJpEYGymt1DwbOaPL2eWt1+mqKTMHUM7P0RIuJg/CeQ1tvUkpwug49K/1q/qfSXqIiInN3QtinUi4sgM6+47Nxv8U/fbznKiaISGsZH0rtZotnl1IiCZzWN6toQqwVW7z1Oeqa2m6DoBEwdDelLTwudvcyuikXbj3Ewp5CEaDuXdqxvdjkiIgEjzGZlTOn0pA9XpptcjVTFs+bkqu6NsFoDax2Dgmc11YuLZECrZEBHaFJ0AqaMhvRlEBEP4+dA455mVwXAhyvcvyyv6d4ooOa8iIj4gxt6uYPn4u0Z2tPTTx3PK+aHre5ddgJpNbuHV4PnlVdeSZMmTYiMjKRBgwaMHz+egwcPevOSXuXZ03POmgMYRogeoVl0AqZcB/uWu0PnLZ9A4x5mVwXA0ROFZVte3dhLw+wiIjWVlhjNwNJOFi0y8k9frD+Ew2nQoUEcbeoF3naBXg2eQ4cO5aOPPmLr1q3MmjWLnTt3Mnr0aG9e0qsu7VSfSLuVXRl5/LI/x+xyfC7MWYBt+vWw7yeIjIdb5kAj/widAB+v3k+Jy6B7kwTa1g+8H0YREX9wY293r+fM1fsocWqRkb/xrDUJxN5O8HLw/OMf/0jfvn1p2rQp/fv3569//SvLly/H4XB487JeExMRxiUd3PMGQ25Pz8Jc+u34J9YDKyEyAW75DBpdYHZVZVwuo+yv85vU2ykics6Gd6hHYp1wjuQWlZ0AJ/4hPTOfVXuPY7HAlaV7jAeaMF9dKCsri6lTp9K/f3/sdnuFjykqKqKoqKjsdm5uLgAOh8MnYdVzjaquNapLPT5bd5DP1h3gL5e0wm4LgWmyhblYp40mMX8nRmQCJWNnQUpH8KM/IJbtymRvZj51Imxc2iHZZ3/cVOc1E6rUNhVTu1RObVMxX7eLFbimWwPeXrKXaT/tYUhr/101HWqvmdk/uztY+rVIJDHKVunX7et2qcl1LIaXJys+/PDDvPLKK+Tn59O3b18+//xzkpKSKnzshAkTmDhxYrn7p02bRnR0tDfLrDanC55YbeNkiYXftnPSoW5wz/UMK8mj/87nqJu/i2JbHZa2epic6GZml1XOe9us/JxppX89Fze00NCQiMj5OFIAk9aGYcFgwgVOEiLMrkgMAyattXG00MK4lk56p/pP/sjPz2fs2LHk5OQQFxdX5WNrHDwrC4enW7lyJT17ulc5Z2RkkJWVxd69e5k4cSLx8fF8/vnnFR5jWFGPZ1paGhkZGWf9QmqDw+Fg/vz5DB8+vNJeWYAnv9jCB8vTGdWlPi+M6eL1ukxTmINt2mish9ZgRNXlhyZ/os9Vd1bZNmbIyitm4HMLcTgNPrmnL50aef+14lHd10woUttUTO1SObVNxcxql5veWsGqvdn830UtuW9oS59dtyZC6TWz/kAO1/7vJyLtVpb+ZQixkZUPWvu6XXJzc/n/7d15eJNV3j7wO0nbdN/oTle6QFkLFLAsKosgIrKMaIVhVV/xAoXX123UUXR0cGacmd+4DuglRRQoiIAgOFRlUWuBImWnQPfSndI23dI2eX5/pCllbEtLm+ck6f25Li9pSPp8e0iaO9/nOed4eXl1Knh2+VT7ypUrER8f3+F9QkNDW/7s5eUFLy8vREVFITo6GkFBQUhJSUFc3G/38Var1VCrf/uxytbWVtYn1K2O97uRQdiUkoukCyXQ6hVwVst2xYJ86q4DWx4ECk8CDp5oWvAVqk7kyv5v0Rl7zuShUSdhUIArhoe23U03NXMcF3PBsWkbx6V9HJu2yT0u88eEIDWnAl/+WoBVU/qb9XqRveE5s+eMYVH/ewb6wdPFoVOPkWtcunKMLicmY5C8HcbmauuupiUaFuiGMC8nZJXV4MC5IswdESi6pJ5VWw5smg0UngIc+xgmEvXpD8D8FhSWJAlbmycVxXOnIiKiHnPfEH+s+focrlbU4ccrZbgrylt0Sb1Wk06PPacMy1HOGW6Zk4qMTDYz5tixY3j//feRlpaGnJwcHDx4EPPnz0d4eHib3U5LolAoWtb0tLrZ7bXlwGezmkOnF7B4L+A3WHRV7TqRcx1XSqrhYKvCLAud4UdEZI7sbVUtS/YYN+cgMX66Uoay6gZ4OtlhQqRlfwAwWfB0cHDAV199hcmTJ6N///5YtmwZBg8ejMOHD7d5Ot3SzG7+xPHTlTLkXKsRXE0PqS0HPnsAKDrdHDr3AL4DRVfVoS3HDN3OGUP94Wpv3adZiIjkZjyTlHS+GKUayz5back2HzUE/5lD/S1+NR2TVT9kyBD88MMPuHbtGurr65GVlYWPPvoIffta5oKn/y2kjxPu7u8NSQISkrNFl9N9NdeAjQ8ARWcAJ29gyV6zD52VdY345ozh1MMjzQseExFRz4n2d8WwIHc06SXs+DVfdDm9Uu61WiRdMFzfuTAuRHA13WfZsVmwZePCAADbU/OhqbfgNcRqrhk6ncVnACcfw+l1n2jRVd3S12lXUd+oR6SPM0YEe4guh4jIKj3SvH974vG83rtdtEAJydmQJOCuKG9E+Fj+rnwMnt0wIdILET7OqNY2YVuqhX4SrCkDNs4Eis8aQueSvYDPANFV3ZIkSS2n2eNHB7e5PBcREXXfzGEBcLJTIausBimZ5aLL6VU09Y3Ylmp4r1s2PkxwNT2DwbMbFApFS9czITkLOr2FfRKsLjWEzpJzgLMvsOQbwLu/6Ko65czVSpwvrIKdSom5FrpfLRGRJXBS27Rsz7j1OCcZyWl7aj6qtU2I8HHGnZG3t6KQuWHw7KY5w/vC3dEWeeV1+K75GgyL0BI6zwPOfs2hM0p0VZ1m7HbeO9gPHk52gqshIrJu8aMMk4z2ny1CRW2D4Gp6B51eaplDsnRcqNWc2WPw7CYHOxXmN8/6+/SnLMHVdFJ1CbDxfqD0AuDibwidXpGiq+q0Gm0Tvk4zLGMVz0lFREQmNzTQDdH+rmho0lvfMoJm6vsLxcgtr4Wbgy3mDree9cIZPHvAwrgQ2CgVOJpVjrNXK0WX0zFNMZBwP1B6EXAJaA6dEaKr6pJvTheipkGH0D6OiOsnZqciIqLeRKFQtKwesvUYJxnJ4dOfDc2s+WOC4WCnElxNz2Hw7AH+bg64b4g/AGDDz9lii+mIpsjQ6SxLbw6de4E+5rn/bke2NF9j9PAoTioiIpLLrJi+sLdVIr1Yg5N5FaLLsWrnCiqRklkOlVKBRVawhFJrDJ49xDjbbM+pApRo6gVX0wZNkaHTWXYJcO0LLP3GIkNnepEGJ3MrYKNU4MGR1nPqgYjI3Lk52LY0WbiTkWkZm1j3DfGHv1vn9mW3FAyePSQmyB0jgt3RoNPjixQze0FWFQIJM4BrlwHXQEOn07Of6Kpuy5bmX3ZTon3h7WL5O2AREVmSR5rnNOw5VWjZ61ebsVKNFl+nGTZHWTYuVGwxJsDg2YOMXc8vjuagvlEnuJpmVQXNofMK4BZk0aGzvlHXclE7JxUREckvNsQDET7OqGvU4etTBaLLsUpfHM1Bg06P4cHuGG6Fm6MwePagewf5IcDNHmXVDdhjDi/IyquG0FmeAbgFN4dOy12A9tuzRaisa0RfdwdMiPQWXQ4RUa+jUCgQP+rGJCPqWdomHT5PyQFwY3dEa8Pg2YNsVEosGhsKAPj052yxs/5aQmcm4N4cOj1CxdXTA4yn2R+KDYJKyUlFREQizB0RCDuVEmeuVpr/Si4WZs+pQpRVN8DfzR73DvYTXY5JMHj2sPhRQXCwVeFCYZW4rcUq8w2h83pWc+j8BvCw7Flx5wuqcDSrHEoF8NAoTioiIhLF08kOUwf5AkDLAufUfZIktawHviguFLYq64xo1vlTCeTuaIffjTRs4Whcg0tWFXmtQmcIsGSfIXxauHe/vwzAOmf4ERFZmkeb5zTsPHkVOddqBFdjHY5mleN8YRXsbZUta6ZaIwZPE1gy1vCC/O5CsbwvyIrc5tCZbTitvnQf4G75T94LhVX49lwRFArg6cmWs8MSEZG1Gh7sgbuivKHTS/jg4BXR5VgFY7fzdyMC4e5ovVtBM3iaQISPM+7u7w1JkvE0xPUcQ+isyAE8wgydTjfrOCVt7HbOGOKPKF8XwdUQEREArJpiaATs+PUqcq/VCq7GsuVeq0XShWIAwFIrnVRkxOBpIsbTENtT802/1tn1HMPi8BW5hqWSlnwDuPU17TFlcqGwCvvPsttJRGRuRgR74M7mruf7By+LLseiJSRnQ5KAu/t7I8LHWXQ5JsXgaSLjI7wQ6eOMam0TtqXmm+5A17MNnc7KXMAz3KpCJ3DztZ3sdhIRmZdVk9n17C5NfSO2pRqWprLWJZRaY/A0EYVC0bKgfEJyFnR6EyytVJ5l6HRW5gF9Igyh0zWg548jyMWiVt3OSex2EhGZm5EhN7qevNbz9mxPzUe1tgkRPs6YEOkluhyTY/A0oTnD+8LD0RZ55XX4rvnajR5TntkqdEY2h07/nj2GYK27nf392O0kIjJHN7qe+ex6dpFOL7XMBVk2LgwKhfWvUc3gaUL2tirMH2NYysg4W61HXMswhM6qfMAryrA4vIt1LTR7sagK+84UAWC3k4jInI0M8cCESC80sevZZd9fKEZueS3cHW0xZ7j1XCbXEQZPE1t4RyhslAoczSrvmR0eWkLnVcCrP7DY+kIncPNMdnY7iYjM2+opN7qeeeXsenaWcb3v+aOD4WCnElyNPBg8TczPzR4zhhpOgW/4Obt73+xahmEikaYA8B7Q3On07X6RZia9SHOj28mZ7EREZm9kiCe7nl10rqASKZnlsFEqsDDOsncX7AoGTxkY1+Tac6oAJZr62/smZVeaQ2ehIXQu3gM4+/RglebjxrWdfux2EhFZCGPX88sT7Hp2hrEZ1dt25GPwlEFMkDtGhnigQafHvw9ldv0blF1uFTqjDafXrTR0phdp8M2ZQgDsdhIRWZLWXc8PD7Hr2ZHsshrsTrsKAC0r4PQWDJ4yMc76++yXbFwpqe78A0svGa7prC4CfAYZTq87e5uoSvFadzsH+LkKroaIiLrC+F63PZVdz468+c0FNOok3BnljZggd9HlyIrBUyZ3RnljSrQPmvQS/rT3PCSpE+t6lqYDG1uFzsVfA07Wu8ZXepEG+86y20lEZKliQ9n1vJUjl0rx3YVi2CgVePX+aNHlyI7BU0YvzxgIW5UChy+V4mB6Scd3LrnY3OksBnwHG67ptOLQCQDv/nAZkgRMH8xuJxGRpWrd9cy/zq5na406Pd7Yex4AsCguFBE+vW8eA4OnjMK8nFq2w/rT3gtoaNK3fceSi4ZOZ00J4DukOXT2kbFS+RlmsrPbSURk6WJDPTE+wjjDPUN0OWbl85QcXCmphqeTXUtA720YPGW2clIEvJzVyCqrwcbm3QpuUnLBMJGophTwG2I4ve7oKXudcmvd7Yz2Z7eTiMiSrZpi7HrmsevZrLymAf9MugQA+L+pUXBztBVckRgMnjJzsbfF8/f2B2CYSFOq0d74y+LzhtPrtWWA31BgUe8InZeK2e0kIrImo0I9MS6iD7uerfwjKR1V9U2I9ndF/Khg0eUIw+ApwIMjAjGkrxs02ia88590w43F5wyn12vLAP9hwKLdvSJ0AoYALknAvYPY7SQisharJkcBAL48wa7n+YIqbD6aCwB4beZAqJTWvyd7exg8BVAqFVjzwEAAwLYTebh8KqW503kN8I/pVaHzUjHX7SQiskajwwxdz0adhA8P9d6upyRJeGPvOeglwzbQd/Sz7jkbt8LgKcjIEE/MignAAOTAd9c8oK4cCBhhCJ0OHqLLk03rbufAAHY7iYisibHruT01D1cr6gRXI8a3Z4uQklkOtY0SL04fILoc4Rg8BXplZBO22L0FV6kK1z2GAgt3Ag7uosuSzWV2O4mIrNroME+MDW/uevbCPdzrG3V4a98FAMATd/ZDkKej4IrEY/AUpfAUvHc8CHdFNU7qIzCv5jnUqXrPel56vYQ39p6HJAHTBvmy20lEZKWMywYlHs/D2auVgquR1yc/ZiL/eh383eyx/O5w0eWYBQZPEQrSgI0PAPUV0PeNxQsOa3ClSoWPDveea2A2/pKNHy+XQW2jxHPTeOqBiMhajenXB/cO8kOTXsLqxDTUN+pElySLwsq6lhn9L04fAEc7G8EVmQcGT7kVnAQ+M4ROBI6GcuFOrL4/FgCw7nBGr5j5d6lYg7X7LwIAXp4RjQgfZ8EVERGRKf157hB4u6hxpaQabzf//rd2f9l/EXWNOsSGeOCBYQGiyzEbDJ5yuvor8NksoL4SCBoD/H4HYO+K6YP9MCbME9omfUsgs1baJh1WbU1DQ5Med0V5Y+EdIaJLIiIiE/N0ssM784YBABKSs3HoVttGW7gTOeXYlVYAhQJ4beYgKBS9d/mk/8bgKZerJ4DPZjeHzjtaQicAKBQKvDZzEJQK4JvThTiaeU1srSb0jwOXcKGwCp5OdvjbvKF8MRIR9RJ3RXljydhQAMBzX55GeU2D2IJMRK+X8Poew37s80YGYkigm+CKzAuDpxzyUw2hU1sJBMcBv/8SUN88kWhggCseGW3YyeD1Peeh00sCCjWt5IwyrP8xEwCwdu4Q+LjYC66IiIjk9OL0AYjwcUapRosXd5yGJFnfe92OX/NxOr8SzmobzmFoA4OnqeUdBzbNAbRVQPBYYMFvQ6fRM/dEwdXeBucLq5B4PE/mQk2rsrYR/7ftFCQJiB8VhGmD/ESXREREMrO3VeFf8TGwVSlw4HwxtqVa13udpr4Rf/nWsCPh05Mj4O2iFlyR+WHwNKW8YzdCZ8h4YMF2QN3+RJo+zmqsnmJYbPedA+morGuUq1KTkiQJr+w+i8LKeoT2ccQf7x8ouiQiIhJkUIAbnp3aH4DhDF92WY3ginrO+wevoKxaizAvJywZGya6HLPE4GkquUeBTXOBBg0QOgFYsK3D0Gm0MC4E4d5OKK9pwL++uyxDoaa3O60Ae04VQKVU4J8Px8BJzSUliIh6s8cm9MMd/TxR26DD6sQ0NOn0okvqtqyyGnz6UxYA4JUZ0bCzYcRqC0fFFHJTgM9bhc75iYCdU6ceaqtS4tWZgwAAn/6cha9PFZiyUpPLv16LP+46CwB4elIkhgf3nu1AiYiobSqlAn9/KAYu9jZIy6vA+xa+q1FlbSOe2JSKRp2EO6O8MWmAj+iSzBaDZ0/LSW7udFYDYXcC87d1OnQatZ759+y2U0jOKDNBoaan00t4ZtspaLRNGB7sjhUTuWsDEREZ9HV3wJuzBwMA3vvhCn7NvS64ottT36jD45tScam4Gr6uarw9dwhXbOkAg2dPyv4Z+PxBoLEG6Hc38EgiYHd7+7L+8f6BmD7YDw06PZ747AQuFlX1bK0yWH8kE8eyyuFop8L/ezgGNio+3YiI6IZZMX0xKyYAOr2E/01MQ7W2SXRJXaLXS3hmWxqOZZXDRW2DhKWjEeDuILoss8Yk0FOyfwK+mNccOicCj2y97dAJoOV6yNGhntBom7D402O4WlHXgwWb1tmrlfhHkmFm35qZgxDSp2tdXyIi6h3emDUYAW72yLlWiz81r39pCSRJwht7z2PfmSLYqhRYt2gkov1dRZdl9hg8e0LWjzdCZ/gk4JEtgG33P/HY26rw8aJYRPo4o7hKiyWfHkNlrfnPdK9r0GHV1pNo1EmYNsgX82IDRZdERERmys3BFv94OAYKBZCYmodvzxaJLqlTPv4xEwnJ2QCAvz8Ug7HhXmILshAMnt2Vebg5dNYC4ZOB+J4JnUZujrZIWDYavq5qXC6pxuObUlHfqOux728Kb++/gIzSGvi4qLF2LncnIiKijt3Rrw+euNMwD+APX51GSVW94Io6tjvtKv68z7DF9cv3RXMv9i5g8OyOzEPA5oeBpjogYgoQvxmw7fndePq6OyBh6Wi4qG1wLKscz2xLg95MdzY6mF6Cjb/kAAD+Nm8YPJ3sBFdERESW4Jl7ojDQ3xXXaxvx7JenzfZ9LvlKGZ7dfgoAsGxcGB6bwPU6u4LB83ZlHAQ2xxtCZ+RU4OEvTBI6jaL9XbFu0UjYqhTYd6YIb+w9b3ZbjZ3Kq8Cz2wwvxiVjQ3FXlLfgioiIyFLY2Sjxr/gYqG2UOHKpFH/ed8Hsto8+X1CFJzadQKNOwoyh/nhlRjTP6nURg+ftyPgB2GIMndOAhz83aeg0GhvuhXfmDQMAJCRn4+Pmfc/NwfbUPMxb9wuu1TQg2t8VL07n/rRERNQ1kb4ueHWmYXe7T37KwtKE46iobRBclUH+9Vos2XAMGm0TxoR54u/zhkGpZOjsKgbPrrryfXOnsx6Iuhd4eBNgI99erLNi+uLl+6IBAH/edxG7067Kduy2NOr0eG33WTz35Wk0NOkxJdoXiU/cAXtbldC6iIjIMi0YE4J/xcfA3tbQ+Xzg/Z+FLylYUduAJRuOo0SjRZSvM9YviuX73G1i8OyKK98BWx4BdFqg/33AQ5/JGjqNHpsQhmXjDNeUPLv9FJKviFlgvlSjxYKPj7Zc07l6SiTWLxwJV3tbIfUQEZF1mBXTFzueHItADwfkltdi7ofJ+OZ0oZBa6ht1ePyzVFwpqYafqz0Slo6GmwPf524Xg2dnXU4CtsxvDp0zgHkbhYROAFAoFHhlRjRmDPVHo07CE5tO4HyBvJ8G0/IqMPO9n3AsuxzOaht8vCgWq6dE8bQDERH1iEEBbtizcjzGRfRBbYMOKzb/ir98e1HW6z6NC9sfz74OF3sbJCwbxQXiu4nBszMuHQC2NofOAfcD8xIAG7GztZVKBf4+bxjGhBkWmF+y4RiOZ5fLcuxtqXl4aN0vKKqqRz9vJ+xaMQ73DPSV5dhERNR7eDjZYePS0fifO/sBAD46lCHbdZ8VtQ14ccdp7D9bBDuVEusXxmKAHxeI7y4Gz1u59B8gcQGgawCiZ5pF6DSyt1Vh/aJYRPk6o0Sjxbx//4L49b8gOaPMJDPedXrg9b0X8Hyr6zl3rRiHCB/nHj8WERERANiolHjpvmjZrvu8Vq3FX769iHFv/4DtJ/IBAP94eBjiwvuY5Hi9jY3oAsxa+rdA4u8BfSMQ/QDw4KeAyryu63BzsMXmx+/A3w9cwpcn8pCSWY6UzKOIDfHAU5MjcWekV48s9VBWrcUH51XI0OQBAP53ShSemhTBU+tERCSLWTF9Eenjgv/ZlNpy3efbcwb12PcvqarH+iOZ+OJoLuqaN2qJ9nfFc9OiMGkAz+r1FFk6nlqtFjExMVAoFEhLS5PjkN2Xvv9G6Bw42yxDp5GXsxpr5w7B4ecmYlFcCOxslEjNuY7Fnx7D7A+T8f2F4m51QNPyKjD7oxRkaBRwVtvgk0WxWDUlkqGTiIhkNTDAFXtWjsf4CC/UNujwdOJp7MlRduu6z8LKOqz5+hzG//UgPvkpC3WNOgwNdMPHi2Kx7+nxDJ09TJaO5/PPP4+AgACcOnVKjsN1myJ9H/DVo4bQOWgOMPdjsw2drQW4O+CNWYOxYmJE86e2HJzKq8CjG1MxKMAVT02KxNSBvh0Gxsq6RmSUViOjpBoZpTXIKK3G4UulaGjSw9dBwmePj0H/AHf5figiIqJWPJzskLB0FP72n3SsO5KJ7wqUmP3hLxge4oFwb2eE+zgjwtsZAe4OUHXwfpd/vRYfHcrA9tR8NOj0AIARwe54enIk7ory5sLwJmLy4Ll//34cOHAAO3bswP79+019uG7zqzgB1VcfAPomYPDvgDnrAZVlXZHg62qPP94/EMvvCscnP2Vi0y85OFdQheWfn0B/XxesnBSB4cHuhmBZUm0ImqWGoFmq0bb5PScP8MZUl0L083aS+achIiK6mY1KiT/cF40Bvk54fsdpXCyuxsXi6pvuo7ZRIszLCeE+zgj3dkaEjzPCvZ1gp1Likx+zsOPXfDQ1d0pHh3li1eRIjA3vw8BpYiZNVMXFxXj88cexa9cuODo63vL+Wq0WWu2N4FNVZbhwuLGxEY2NjSar00h/bjdGZb0PBXTQD5oL3cwPAL1k6HxaIHd7JZ6dEoFlccFI+CUHm1LykF6swVNbTnb4OF9XNcK9nNDP2wn9vJzQ388ZwwKc8f13hbL8O1gS43hwXH6LY9M2jkv7ODZt47i0b1q0F6pidHAIGYqc6/XIKK1BZmkNsq7VQNukx8UiDS4Wadp9/NhwT6y4ux9Gh3oCAJqamuQq3aTkfs505TgKyUQbfkuShPvuuw/jxo3DK6+8guzsbISFheHkyZOIiYlp8zFr1qzB66+//pvbN2/e3Kng2r2C9Rh/+S30qbmMPI84nAz5H0gK69qVoLYJOFyowJFCJbR6wNse8HGQ4OsA+DpIhj/bA/aW1eAlIiK6iV4CyrVAcZ0CxXXG/xv+XNukQLS7HtMC9QhzEV2pdaitrcX8+fNRWVkJV9eOl5zqcvBsLxy2dvz4cSQnJyMxMRFHjhyBSqXqVPBsq+MZFBSEsrKyW/4gPaFRU4acbS8h5PfvwlZt+r3XRdHrJeglCTaqzs8ta2xsRFJSEu655x7Y2pr/9a5y4bi0j2PTNo5L+zg2beO4tO92xqahSQ87G+teTVLu50xVVRW8vLw6FTy73NtauXIl4uPjO7xPaGgo3nzzTaSkpECtvnl3n9jYWCxYsAAbN278zePUavVv7g8Atra28rzYXLxwyX82ItT2fHG3Q7Z/CwvDcWkfx6ZtHJf2cWzaxnFpX1fGpjcNoVzPma4co8vB08vLC15eXre837vvvos333yz5euCggJMmzYNiYmJGDNmTFcPS0REREQWzmRX8wUHB9/0tbOzYXeb8PBwBAYGmuqwRERERGSmrPsiByIiIiIyG7LNXw4NDTXJ/uFEREREZBnY8SQiIiIiWTB4EhEREZEsGDyJiIiISBYMnkREREQkCwZPIiIiIpIFgycRERERyYLBk4iIiIhkweBJRERERLJg8CQiIiIiWTB4EhEREZEsGDyJiIiISBYMnkREREQkCwZPIiIiIpIFgycRERERyYLBk4iIiIhkweBJRERERLJg8CQiIiIiWTB4EhEREZEsGDyJiIiISBYMnkREREQkCxvRBXREkiQAQFVVlSzHa2xsRG1tLaqqqmBrayvLMS0Fx6ZtHJf2cWzaxnFpH8embRyX9nFs2ib3uBhzmjG3dcSsg6dGowEABAUFCa6EiIiIiDqi0Wjg5ubW4X0UUmfiqSB6vR4FBQVwcXGBQqEw+fGqqqoQFBSEvLw8uLq6mvx4loRj0zaOS/s4Nm3juLSPY9M2jkv7ODZtk3tcJEmCRqNBQEAAlMqOr+I0646nUqlEYGCg7Md1dXXlE7gdHJu2cVzax7FpG8elfRybtnFc2sexaZuc43KrTqcRJxcRERERkSwYPImIiIhIFgyerajVarz22mtQq9WiSzE7HJu2cVzax7FpG8elfRybtnFc2sexaZs5j4tZTy4iIiIiIuvBjicRERERyYLBk4iIiIhkweBJRERERLJg8CQiIiIiWTB4doJWq0VMTAwUCgXS0tJElyPcAw88gODgYNjb28Pf3x8LFy5EQUGB6LKEy87OxqOPPoqwsDA4ODggPDwcr732GhoaGkSXJtxbb72FsWPHwtHREe7u7qLLEerDDz9EWFgY7O3tMXLkSPz444+iSxLuyJEjmDlzJgICAqBQKLBr1y7RJZmFtWvXYtSoUXBxcYGPjw9mz56N9PR00WUJ99FHH2Ho0KEti6PHxcVh//79ossyO2vXroVCocDq1atFl3ITBs9OeP755xEQECC6DLMxceJEbNu2Denp6dixYwcyMjLw4IMPii5LuIsXL0Kv12PdunU4d+4c/vnPf+Lf//43XnrpJdGlCdfQ0IB58+bhySefFF2KUImJiVi9ejVefvllnDx5EhMmTMD06dORm5srujShampqMGzYMLz//vuiSzErhw8fxooVK5CSkoKkpCQ0NTVh6tSpqKmpEV2aUIGBgXj77beRmpqK1NRUTJo0CbNmzcK5c+dEl2Y2jh8/jvXr12Po0KGiS/ktiTq0b98+acCAAdK5c+ckANLJkydFl2R2du/eLSkUCqmhoUF0KWbnr3/9qxQWFia6DLOxYcMGyc3NTXQZwowePVpavnz5TbcNGDBAevHFFwVVZH4ASDt37hRdhlkqKSmRAEiHDx8WXYrZ8fDwkD755BPRZZgFjUYjRUZGSklJSdJdd90lrVq1SnRJN2HHswPFxcV4/PHHsWnTJjg6OoouxyyVl5fjiy++wNixY2Frayu6HLNTWVkJT09P0WWQGWhoaMCJEycwderUm26fOnUqkpOTBVVFlqSyshIA+DulFZ1Oh61bt6KmpgZxcXGiyzELK1aswIwZMzBlyhTRpbSJwbMdkiRhyZIlWL58OWJjY0WXY3ZeeOEFODk5oU+fPsjNzcXu3btFl2R2MjIy8N5772H58uWiSyEzUFZWBp1OB19f35tu9/X1RVFRkaCqyFJIkoRnnnkG48ePx+DBg0WXI9yZM2fg7OwMtVqN5cuXY+fOnRg4cKDosoTbunUrfv31V6xdu1Z0Ke3qdcFzzZo1UCgUHf6XmpqK9957D1VVVfjDH/4gumRZdHZcjJ577jmcPHkSBw4cgEqlwqJFiyBZ6SZYXR0bACgoKMC9996LefPm4bHHHhNUuWndzrgQoFAobvpakqTf3Eb031auXInTp09jy5YtoksxC/3790daWhpSUlLw5JNPYvHixTh//rzosoTKy8vDqlWr8Pnnn8Pe3l50Oe3qdVtmlpWVoaysrMP7hIaGIj4+Hnv27LnpDUGn00GlUmHBggXYuHGjqUuVVWfHpa0nc35+PoKCgpCcnGyVpzq6OjYFBQWYOHEixowZg4SEBCiV1vn57naeMwkJCVi9ejUqKipMXJ35aWhogKOjI7Zv3445c+a03L5q1SqkpaXh8OHDAqszHwqFAjt37sTs2bNFl2I2nnrqKezatQtHjhxBWFiY6HLM0pQpUxAeHo5169aJLkWYXbt2Yc6cOVCpVC236XQ6KBQKKJVKaLXam/5OFBvRBcjNy8sLXl5et7zfu+++izfffLPl64KCAkybNg2JiYkYM2aMKUsUorPj0hbjZxetVtuTJZmNrozN1atXMXHiRIwcORIbNmyw2tAJdO850xvZ2dlh5MiRSEpKuil4JiUlYdasWQIrI3MlSRKeeuop7Ny5E4cOHWLo7IAkSVb7HtRZkydPxpkzZ266benSpRgwYABeeOEFswidQC8Mnp0VHBx809fOzs4AgPDwcAQGBoooySwcO3YMx44dw/jx4+Hh4YHMzEy8+uqrCA8Pt8puZ1cUFBTg7rvvRnBwMN555x2Ulpa2/J2fn5/AysTLzc1FeXk5cnNzodPpWtbDjYiIaHlt9QbPPPMMFi5ciNjYWMTFxWH9+vXIzc3t9dcBV1dX48qVKy1fZ2VlIS0tDZ6enr/5XdybrFixAps3b8bu3bvh4uLSci2wm5sbHBwcBFcnzksvvYTp06cjKCgIGo0GW7duxaFDh/Dtt9+KLk0oFxeX31z/a5yLYVbXBQubT29hsrKyuJySJEmnT5+WJk6cKHl6ekpqtVoKDQ2Vli9fLuXn54suTbgNGzZIANr8r7dbvHhxm+Ny8OBB0aXJ7oMPPpBCQkIkOzs7acSIEVwaR5KkgwcPtvn8WLx4sejShGrv98mGDRtElybUsmXLWl5D3t7e0uTJk6UDBw6ILsssmeNySr3uGk8iIiIiEsN6L0AjIiIiIrPC4ElEREREsmDwJCIiIiJZMHgSERERkSwYPImIiIhIFgyeRERERCQLBk8iIiIikgWDJxERERHJgsGTiIiIiGTB4ElEREREsmDwJCIiIiJZMHgSERERkSz+P2XM7x8bWOw7AAAAAElFTkSuQmCC\n",
      "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\n",
    "$\\| \\dots \\|$.)\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",
    "Rhen 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": 5,
   "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 = 0.8575532158463934\n",
      "x_4 = 0.6542897904977791\n",
      "x_5 = 0.7934803587425656\n",
      "x_6 = 0.7013687736227565\n",
      "x_7 = 0.7639596829006542\n",
      "x_8 = 0.7221024250267079\n",
      "x_9 = 0.7504177617637604\n",
      "x_10 = 0.7314040424225099\n",
      "Solving x = cos(x) starting to the right, at x_0 = 1\n",
      "x_1 = 0.5403023058681398\n",
      "x_2 = 0.8575532158463934\n",
      "x_3 = 0.6542897904977791\n",
      "x_4 = 0.7934803587425656\n",
      "x_5 = 0.7013687736227565\n",
      "x_6 = 0.7639596829006542\n",
      "x_7 = 0.7221024250267079\n",
      "x_8 = 0.7504177617637604\n",
      "x_9 = 0.7314040424225099\n",
      "x_10 = 0.7442373549005569\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ya9euvec+DzqC+K7AwMD4Iy1PnDhx3+8fdrT7lStXErSMlStXGmXLljXc3NyMQoUKGZ9++qnxxhtvGNmyZXvo6z9//rxRvHhxo1KlSvcd3fvyyy8b7u7uyXrE7IMcPXrUaNu2rZEjR4747N27dzciIiLi75OQ9z4iIsLo27evUa5cOSNz5sxGhgwZjJIlSxrDhg0zwsLC4u9Xs2ZNo1GjRvHXk/IebN682QCM/fv3P/R1JTSPYRjGkCFDjHz58hlOTk4GYAQHBxuGYRg3btwwevXqZeTOndvw9PQ0XnzxRWP79u1GrVq1jFq1asU//mGflUc9/6OOdk/IZy4pn7eEvGbDSNh4J/Z5E/Pa/vjjD6Nnz55G/vz5DVdXVyNXrlxG9erVjVGjRj12+Y8aiyd5HxP79+BB70NoaKgBGB06dHjs60joZ+9hy/p/ifmehYaGGq6ursbZs2fj71O7dm1jxowZj82dnAoXLpwsR8uLY7EZhmHYo+SKpEXR0dFUqFCB/PnzExgYaHWcVGP58uW0b9+ev/76i/z58yfpObp27crp06fZsWNHMqdzXPq8JY+UfB8DAgJo0qQJP//8c/way9Sqbdu2ZMmShYkTJ7J582a6du3K77//nqL7/IqANruLJEqvXr3w9fUlb968XLx4kWnTpnHs2DEmTJhgdbRUpVWrVjz33HOMHj2aSZMmJfrxp06dYvHixcm6+dUR6fOWPOz5PgYHB9OhQ4dUXzwBpkyZQrdu3ciRIwf58+dn8eLFKp5iFyqfIokQGhrK22+/zZUrV3B1daVSpUoEBARQr149q6OlKjabjW+//ZY1a9YQFxeX6H1vz5w5w6RJk3jxxRdTKKFj0OctedjzfRw7dmyyP2dKyZUrFwEBAVbHkHRIm91FRERExG401ZKIiIiI2I3Kp4iIiIjYjcqniIiIiNiNQxxwFBcXx/nz5+Mn7xURERGR1MUwDEJDQ8mXL98jDzR1iPJ5/vz5e84/KyIiIiKp09mzZx95ljiHKJ93TyF29uzZ+85FmxKio6MJDAzEz88PV1fXFF+eJD+NoWPT+Dk+jaHj0xg6PnuPYUhICAULFnzs6XYdonze3dSeOXNmu5VPT09PMmfOrC+cg9IYOjaNn+PTGDo+jaHjs2oMH7eLpA44EhERERG7UfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbtR+RQRERERu1H5FBERERG7UfkUEREREbtR+RQRERERu0l0+fzhhx9o2rQp+fLlw2azsWrVqsc+Ztu2bVSuXBkPDw+KFSvGtGnTkpJVRERERBxcostnWFgY5cuXZ9KkSQm6/x9//EGjRo2oWbMmBw8e5P333+eNN95g+fLliQ4rIiIiIo7NJbEPaNiwIQ0bNkzw/adNm0ahQoX48ssvAShdujT79u1j3LhxtG7dOrGLFxEREZHHMAy4cjOciAhnDMPqNPdKdPlMrF27duHn53fPbfXr12fGjBlER0fj6up632MiIyOJjIyMvx4SEgJAdHQ00dHRKRs4Lg6n2rV58dYtnD7/nDhnZ3B2Bienf/5793L3d87O4O6O4eEB7u7mxcPjn8u/f+fhAZ6ekCkThpcXZMr0z8XNLWVfWzpy93OS4p8XSREaP8enMXR8GkPH9vPZkzxXvDTQhMuXw8maNeWXmdDPSoqXz4sXL+Lt7X3Pbd7e3sTExHD16lXy5s1732NGjx7NiBEj7rs9MDAQT0/PFMsKYIuJodnu3eRI0aU8WKyLCzEZMtx3ifbyIipTJvO/Xl5EZ8pE1N3b/vdztJcXhrOzBalTt6CgIKsjyBPQ+Dk+jaHj0xg6nnMR5/jPsdHAWQACNwfilcGW4ssNDw9P0P1SvHwC2Gz3vmDjf+t////2u4YMGcKgQYPir4eEhFCwYEH8/PzInDlzygUFiIsjctEifj5wgPJly+IMEBsLcXHm5X8/22Jj/7k9JgaioiAiwrxERkJkJLa71yMi/vn9nTvYwsPh9m0IDYXQUPN+gHNMDM6hobiHhiYpupE5M+TMiZE7N+TOjZEnD+TODd7e5m158pj/9fYGL6/ke89SoejoaIKCgvD19X3g2nVJ3TR+jk9j6Pg0ho7pt2u/8er8V7kRfSv+Nr+6fmTNmvJjeHdL9eOkePnMkycPFy9evOe2y5cv4+LiQo4cD16/6O7ujru7+323u7q62uULEN2qFRc8PKjYqBEu9vjCxcSYRfRfhTT+EhICN27A9evm5dq1f36+e7l5EwBbSAiEhGA7ffrxy/T0hDx5oEAB81Kw4P3/zZULHvI/CI7CXp8ZSRkaP8enMXR8GkPHcfzqcfzm+3Hh9gWezfU8R/53u73GMKHLSPHyWa1aNdauXXvPbYGBgVSpUkUf5rtcXCBbNvOSFLGxZgG9dg2uXIFLl8zLxYv3/3zxIty5A+HhcPq0eXkYN7d7C2mhQlCsmHkpWtS83cUuK89FRETkEY5fPY7PbB8u3r5IOe9yrG61jqIDrU71YIluDrdv3+bkyZPx1//44w8OHTpE9uzZKVSoEEOGDOHcuXPMmTMHgL59+zJp0iQGDRrEyy+/zK5du5gxYwYLFy5MvleR3jk7Q44c5uXppx99X8Mw17BeugQXLsC5c/D333D27L3/vXjR3FXgUQXV2fmfQlq06L3FtFgxM4+DrzkVERFJ7Y5dOYbPbB8uhV2ivHd5NvlvIoOR0+pYD5Xo8rlv3z58fHzir9/dN7Nbt27MmjWLCxcucObMmfjfFy1alICAAAYOHMjkyZPJly8fX331laZZsorN9s/R9U899fD7RUWZ5fTfpfSvv/4po3/+ae7b+scf5uVBsmaFkiXvvTz9NJQoYR71LyIiIk/k6JWj+Mz24XLYZSrkqcCmrpvI4ZmDsDCrkz1costn7dq14w8YepBZs2bdd1utWrU4cOBAYhclVnJzg8KFzcuDxMWZ5fT0abN83i2ld6+fP2/uCvDTT+bl32w283nvltGSJaF0aShTxjxASkRERB7ryOUj+Mz24Ur4FSrmqUhQ1yByeFoxX0/iaIc9SRonJ8if37zUrHn/78PD4eRJ+O23+y8hIeaa0z//hI0b731crlxmCb17efZZ82KPCcpEREQcxK+Xf6XO7DrxxXOT/yayZ8hudawEUfmUlOHpCeXKmZd/Mwy4fNksoSdO/FNIjx2DU6fMA6aCg83LvxUocG8pLV8ennlGE/OLiEi6c/jSYerMqcPV8KtUzluZwK6BDlM8QeVT7M1mM+cZ9faGl16693fh4WYJ/fXXey9///3PZcOGf+7v5mYW0YoV/7mUK5fm5zAVEZH065dLv1B3Tl2uhl+lSr4qBHYJJFuGJM6WYxGVT0k9PD2hcmXz8m83b8KRI2YRPXIEfvkFDh2CW7fgwAHzcpfNBk8/jXP58jzl4YHNzQ2ef9488l5ERMSB/XzxZ+rOqcu1O9d4Lt9zBHYNJKtHVqtjJZrKp6R+WbNCjRrm5S7DMA9sOnjw3suFC/Dbbzj99hvPAvxvyi+KFzdL6N1LxYqQIYMFL0ZERCTxDl08RN05dbl+5zrP53+ejV02OmTxBJVPcVQ22z/ziv572q5Ll+DgQWL37ePi99+T7/JlbCdPmvuTnjoFd+eXdXY2N9H/u5CWLm3eLiIikoocvHCQunPqciPiBlXzV2Vjl41k8chidawkU/mUtMXbGxo0IK5uXfaVLUujRo1wvX0b9u2DPXvMy08/xZdUDh6Er782H5sxI1SpAtWqmWtZq1eH7I6zA7eIiKQ9By4coN6cetyIuMELBV5gQ+cNDl08QeVT0oNs2cDX17yAucn+77//KaN79pjl9PZt2LbNvNz1zDP/bPKvUcPcfK+zNomIiB3sP7+fenPrcTPiJtUKVGNDlw1kds9sdawnpvIp6Y/NZp6XvmDBfzbZx8bC8eOwezfs2GFeTpyAo0fNy7ffmvfz9jbXiNaoAS++aO47qumeREQkme09txe/eX7cjLhJ9YLV2dB5A5ncM1kdK1mofIqAua/n3Qnte/Uyb7tyBXbu/KeM7ttnbq5fudK8gHnQUo0a4OMDtWubm+1VRkVE5AnsObcHv7l+3Iq8RY2CNfi+8/dppniCyqfIw+XKBc2bmxeAiAizgN4tozt3wrVrsGmTeQFzuqgaNcwi6uNjllFXV8tegoiIOJaf/v4Jv3l+hESG8GKhFwnoFJCmiieofIoknIeHuan9xRfN64ZhbpIPDoatW83LtWsQFGRewDyI6W4ZrV0bnnsOXPS1ExGR++3+ezf159UnJDKEmoVqEtA5AC+3tHfiFP0rKJJUNts/m+pffx3i4swyunWrWUi3bTPLaGCgeQHInNlcI3r3AKgSJXQAk4iIsOvsLurPq09oVCi1CtdiXad1abJ4gsqnSPJxcvrn3PN3y+iRI/+sFd26Fa5fh9WrzQtA4cL/FNG6dXUmJhGRdGjn2Z3Un1ef21G3qV2kNus6riOjW0arY6UYlU+RlOLkBGXLmpf+/c0j6g8e/Gez/I8/wl9/wfTp5sVmg0qV/imjNWqAu7vVr0JERFLQjjM7aDC/AbejbuNTxIe1Hdem6eIJ4GR1AJF0w9nZPABpyBDYsgVu3ICAABg40Fxbahiwfz98+uk/a0GbNzcnwT971ur0IiKSzLb/tT1+jWedonVY1yltr/G8S2s+RaySMSM0bGheAM6fN4+av7tm9NIlWLPGvIC5BrVRI/NSrZqOohcRcWA//PUDjeY3Iiw6jHrF6rG6w2o8XT2tjmUXWvMpklrkywf+/jB3Lly4YG6i//hjc1J7Jyc4fBg++wxq1TKngWrXDmbPNkuqiIg4jG1/bosvnr7FfFnTYU26KZ6gNZ8iqZPNBhUqmJf33//nqPmAANiwAa5ehaVLzQuYm/ObNjU305crpyPoRURSqa1/bqXxgsaER4fjV9yPVe1XkcE1g9Wx7EprPkUcQY4c0LGjuVb04kXzNKAffmiWTjAnvx82zCyrxYrBm2+a+5VGR1saW0RE/hH8RzCN5jciPDqc+sXrs7rD6nRXPEHlU8TxODtD1aowYgTs3WuW0ZkzzbWeGTLAn3/CV1+ZBy15e0OXLrBsGYSGWp1cRCTd2vLHFhovaMydmDs0eKoBqzqswsPFw+pYllD5FHF03t7QowesWmVujl+92ryeM6d5RP38+dC2rXm9USPz6PkLF6xOLSKSbmw6vSm+eDYq0YiV7Vem2+IJKp8iaYunJzRrZq4JvXgRtm+Ht982z6QUFQXffw99+0L+/FCzJkyYoGmcRERSUNCpIJoubEpETASNSzRmRbsV6bp4gsqnSNrl7Gyeh37sWPjtN/PUn6NHm5vsDcOc5H7AAChUyJy66fPPzU32IiKSLAJPBcYXzyZPN2F5u+W4u+jkISqfIumBzQalS8PgwebBSmfPmms9a9Y0f7d7t7mGtGhReO45c0qnkyetTi0i4rA2ntxIs4XNiIyNpFnJZixru0zF839UPkXSowIF4I034Icf4Nw5mDwZfHzM+UT37TNLaokSULGiOdeoiqiISIJtOLmB5ouaExkbSfOSzVnadqmK57+ofIqkd3nzQr9+5tRMFy6YByT5+pqb7Q8dgv/8xyyizz1nbpr/+2+rE4uIpFoBvwfEF88WpVqwpO0S3JzdrI6Vqqh8isg/cueGV14xJ7S/dAlmzID69c0ium+fuWm+UCHzLEvTpplH14uICADrT6yn5eKWRMVG0ap0K5a0UfF8EJVPEXmwHDmgZ0/zjErnz5ub5l980TxY6Ycf4NVXzbWmjRqZk99rHlERScfWnVgXXzxbl27NotaLcHV2tTpWqqTyKSKPlzu3uWl++3b46y8YM8bcHzQmxpy+yd/fvE+bNrBiBURGWp1YRMRu1v62llaLWxEdF02bZ9qwsPVCFc9HUPkUkcQpVAjeeQcOHIDjx83Tej79NEREwPLl0Lr1P/uR7tplrikVEUmjVh9fTeslrYmOi6bds+1Y0GqBiudjqHyKSNKVLAnDh5sldP9+c5/QfPnMMytNnQrVq5vF9KOP4I8/rE4rIpKsVh1fRdulbYmOi6ZDmQ7MbzVfxTMBVD5F5MnZbFCpkjmh/Zkz5gFLXbqYZ1w6eRI+/BCKFYOXXoLp0+HWLasTi4g8kZXHVsYXz45lOjK35VxcnFysjuUQVD5FJHk5O5tTNc2dax4xP3s21K1rFtTt2+HllyFPHujQAdavN/cbFRFxICuOraDdsnbExMXQqWwn5rSco+KZCCqfIpJyvLzMg5E2bTLXiH76qXmmpYgIWLwYmjSBggXNSe1PnLA6rYjIYy0/upx2S83i2aVcF+a0UPFMLJVPEbGPAgXgvffgyBFzztA33oCcOeHiRfN0niVLmpvlZ82CsDCr04qI3GfpkaW0X9aeWCOWruW6Mqv5LJydnK2O5XBUPkXEvmw2qFzZPLf8uXOwbJk5V6iTk7lZvkcPXAoWpPzkydh++klHy4tIqrDkyBI6Lu9IrBGLf3l/vmv+nYpnEql8ioh13NzMqZnWrzfnD/34YyheHNvt2xQJCsKlZk0oU8Y8refly1anFZF0avGvi+m0vBOxRizdK3RnZrOZKp5PQOVTRFKHAgXg/ffhxAliNm3ibO3aGBkywNGj5hRO+fObRTUwEOLirE4rIunEol8X0WmFWTx7VOjBjGYzVDyfkMqniKQuTk4YL73EgQEDiDlzxjyH/PPPm0fFr1hhnmu+RAnz4KVLl6xOKyJp2ILDC+i8ojNxRhw9K/RkerPpONlUnZ6U3kERSb2yZIE+feCnn+CXX6B/f/O206dhyBDzSPn27SE4WPuGikiymv/LfLqu7EqcEUfvir35ttm3Kp7JRO+iiDiGsmXhq6/g/HmYOROqVoXoaFiyBOrUgVKlzH1Dr12zOqmIOLi5P8/Ff5U/cUYcL1d6ma+bfq3imYz0ToqIY/H0hB49YPduOHgQ+vY15xM9ceKffUO7dDGPnNfaUBFJpDk/z6Hbqm7EGXH0qdyHaU2mqXgmM72bIuK4KlQwzyF//jx8/bV5is/ISJg/35wztFw583bNGyoiCTD70Gy6r+qOgcGrVV5lSuMpKp4pQO+oiDi+TJnglVdg/37Yuxd69TLXkP76q7lmNH9+GDjQPM+8iMgDfHfwO3qs7oGBQb8q/ZjcaLKKZwrRuyoiaUuVKjB9ujmB/RdfwFNPwa1b8OWX5lHyjRpBQICmaxKReDMPzqTXml4YGLz23GtMajQJm81mdaw0S+VTRNKmrFlhwAD47Tf4/nto3Ng8u9Ldn59+GsaPhxs3rE4qIhaafmB6fPHs/3x/JjacqOKZwlQ+RSRtc3KCBg1g3Tr4/Xd46y2zmJ46Zf6cP7+5yf6XX6xOKiJ29s3+b3h57csAvFn1TSY0mKDiaQcqnyKSfhQvDuPGmZvkv/3WPCDpzh3z5/LloW5dWLtWm+RF0oGv931Nn3V9ABhQdQBf1P9CxdNOVD5FJP3x9ITeveHQIXNKpnbtwNkZtmyBZs3MOUMnT4bbt61OKiIpYNq+afRd3xeAgS8MZHz98SqedqTyKSLpl80GL74IixebZ016911zk/zvv8Prr5tnUHr3XTh71uqkIpJMpuydwqvrXwXgrWpv8bnf5yqedqbyKSICUKgQfPaZWTQnTTKPjL95E8aOhaJFoUMHc2J7EXFYk/ZM4rWA1wB4u9rbjPUdq+JpAZVPEZF/8/KC116D48fN/T/r1IHYWHPtaLVq5mXJEoiJsTqpiCTCxJ8m0v/7/gC8W/1dxviOUfG0iMqniMiDODlBkyawebO5b2j37uDmZq79bN/eXDP61Vc6e5KIA5iwewJvbHgDgME1BvNpvU9VPC2k8iki8jjly8N338GZMzBsGOTKBX/+CW++ae4X+sEHcPmy1SlF5AG+2PUFAzYOAGDIi0P4pO4nKp4WU/kUEUkob28YPhz++gumTTPPnnTjBowaZe4z2revebCSiKQK43eNZ1DgIACG1hzKx3U+VvFMBVQ+RUQSK0MG6NPH3C90+XKoWhUiI+Hrr6FkSWjdWgcniVhs3M5xvBX4FgAfvPQBH/l8pOKZSqh8iogklbMztGoFu3bBDz+Y+4gaBqxYYR6Y9NJLmrRexAJjd4zlnaB3APjwpQ8ZUXuEimcqovIpIvKkbDaoWdMsmkeOQM+e4OpqTmDfrBmUKQNz5kB0tNVJRdK8z378jHc3vQvA8FrDGeGj4pnaqHyKiCSnZ56BGTPMA5Leew+yZIFjx6BbN/MI+SlTzFN6ikiyG719NIM3DwZgRO0RDKs9zOJE8iAqnyIiKSFfPvj0U/MI+U8/hdy5zQOVXnvNnLR+zBgICbE6pUia8fEPH/P+lvcBGFl7JB/W+tDiRPIwKp8iIikpc2ZzDeiff5pnTipcGC5dMm8rXBg+/BCuXrU6pYhD+/iHj/lP8H8AGOUzig9qfWBxInkUlU8REXvIkMFc6/n77zB7NpQqZZ6+86OPzBI6cCD8/bfVKUUczshtI+OL5yd1PmHoS0MtTiSPo/IpImJPrq7g728emLR8OVSuDOHh8OWXUKwYvPwynDpldUoRhzB863CGbTX36xxddzRDag6xOJEkhMqniIgVnJzMaZr27oWNG6FWLfNo+OnTzblCu3WDEyesTimSKhmGwbDgYYzYNgKAz+p9xuAXB1ucShJK5VNExEo2G/j5wdat8OOP0LAhxMaaUzOVLg1dupiT2YsI8L/iuXUYI38YCcBY37G8W+Ndi1NJYqh8ioikFjVqQEAA7NljTlgfFwfz55vTN3XsaG6qF0nHDMPgg+AP+OiHjwAY5zuOt6u/bXEqSSyVTxGR1Oa558wJ6/fvh+bNzbMmLVoEZctCu3Zw+LDVCUXszjAM/rPlP3y8/WMAxvuN563qb1mcSpJC5VNEJLWqVAlWrYKDB839Qw0Dli6FcuXM88cfOmR1QhG7MAyD9ze/zyc/fgLAl/W/ZGC1gRankqRS+RQRSe0qVDCPjP/lF2jb1txPdMUKqFgRWrSAn3+2OqFIijEMg8GbBvPpjk8BmNBgAm++8KbFqeRJqHyKiDiKsmVhyRJzs3uHDmYJXb3aLKdt28LRo1YnFElWhmHw3qb3GLNzDAATG07kjapvWJxKnpSL1QFERCSRnn0WFi40z440ciQsXgzLlsHy5cS178jVN0ZA8afw9DT7qRWioyEiwpmwMHNqU3E8Vo6hYUBYmMGIbcOZemQsOMGkhpN47fnX7BtEUoTKp4iIoypd2iyh778Pw4bBypVcXRSI96L5VicDXIEmVoeQJ2L1GNqAEfD2FKa0G8mrz71qYRZJTtrsLiLi6MqWNfcB3b8f6vlZnUYkWY3xHafimcZozaeISFpRqRKeK+dDJvPqJXKRkXBwdYOePeGddyBPHrtEiY6OZuPGjdSvXx9XbXd3SFaM4d19PKfs+A7GXQHg1erd7LJssR+VTxGRNOTf+3hmDFxNxk+GmmdP+no8zJ4Cr70GQ4ZAjhwpmiM6Gjw8YsmYUft8Oip7j6FhGLy54U2m/DwR3Dzjb7dqv2VJOdrsLiKSVlWvDsHBsHmz+XNEBHz+ORQrBh99BLdvW51QBDCLZ//v+zNxz0Rs2JjcaIrVkSQFqXyKiKR1deqY540PCDCnZQoJMY+UL14cvvoKIiOtTijpmGEYvB7wOpP3TsaGjenNptOtgja1p2UqnyIi6YHNBg0bmgclLVwITz0Fly/Dm29CyZIwezbExlqdUtKZOCOO1wJeY8q+KdiwMbP5THpW7Gl1LElhKp8iIumJk5M5Qf3Ro/D115AvH/z1F3Tvbp62c+VKc5JFkRQWZ8TRb30/pu6big0b3zX/ju4VulsdS+xA5VNEJD1ydYVXXoGTJ2HMGMiWzSykrVrBCy/Ali1WJ5Q0LM6I49V1r/L1/q+xYWNWi1na1J6OqHyKiKRnGTKYUzCdPm1OVu/pCXv2QN264OcHBw9anVDSmDgjjj5r+/DNgW9wsjkxp+Uc/Mv7Wx1L7EjlU0REIGtW+PhjOHUKXn/dXDMaFASVKkHXruameZEnFGfE8craV5h+cLpZPFvMoUu5LlbHEjtT+RQRkX/kyQMTJ8Lx49Cxo3nbvHnw9NPmGtIbN6zNJw4rzojj5TUvM+PgDJxsTsxtOZfO5TpbHUssoPIpIiL3K1YMFiyAffvAxweiomDcOPP2cePMOUNFEig2LpZea3ox89BMnGxOzG81n05lO1kdSyyi8ikiIg9XubI5SX1AAJQpAzdvmmtAS5Y014jGxVmdUFK5u8Vz1qFZONucWdBqAR3KdLA6llhI5VNERB7t7hyhhw7Bd99BgQJw5oy5L2jlyua+oSIPEBsXS4/VPZj982yzeLZeQPsy7a2OJRZT+RQRkYRxdjbnAz1xAj79FDJnNgupnx/Urw8//2x1QklFYuNi6baqG3N/mYuzzZlFbRbR7tl2VseSVEDlU0REEidDBnjvPfPI+AEDzCPjAwOhYkXo3RsuXLA6oVgsJi4G/1X+zD88HxcnFxa3WUybZ9pYHUtSCZVPERFJmpw54YsvzCPj27c3z4w0YwaUKIHTJ5/grHPGp0sxcTH4r/RnweEF8cWz9TOtrY4lqYjKp4iIPJlixWDRIti5E6pWhbAwnIcPp26/ftjmz9dBSelITFwMXVZ0YeGvC3FxcmFp26W0Kt3K6liSyqh8iohI8qhWDXbtgoULMQoVIsO1a7j06GEW0u3brU4nKSw6NppOyzux+MhiXJ1cWdZ2GS1KtbA6lqRCKp8iIpJ8bDbo0IGYw4c52rUrRqZM5lyhL70EbdqY+4lKmhMdG02nFZ1YenSpWTzbLaN5qeZWx5JUSuVTRESSX4YM/N66NTFHj0KfPuDkBMuXQ+nS8Pbb5nyhkiZEx0bTcXlHlh1dhpuzGyvar6BZyWZWx5JUTOVTRERSjrc3TJtmTsnk6wvR0fD55/DUU+btsbFWJ5QnEBUbRftl7Vl+bLlZPNutoMnTTayOJamcyqeIiKS8smVh40bzTEmlS8O1a/Dqq1CpEmzdanU6SYK7xXPl8ZW4Obuxsv1KGj/d2OpY4gBUPkVExD7uninpl1/gq68ga1bzZx8faNsW/vzT6oSSQFGxUbRb2o5Vx1fh7uzOqvaraFSikdWxxEGofIqIiH25uED//vD77+baTycnWLbMXCP64YcQFmZ1QnmEyJhI2ixpw+rfVuPu7M7qDqtpWKKh1bHEgah8ioiINXLmhClT4OBBqF0bIiLgo4+gZElYsMCctF5SlciYSNosbcPaE2vxcPFgTcc11H+qvtWxxMGofIqIiLXKlYMtW8yj4YsUgXPnoHNnePFF2L/f6nTyP5ExkbRe0pp1J9aZxbPDGvyK+1kdSxyQyqeIiFjPZoNWreDoURg1Cjw9zTMmPfcc9OoFly5ZnTBdi4iJoNWSVqz/fT0ZXDKwruM6fIv7Wh1LHFSSyueUKVMoWrQoHh4eVK5cme2POXPF/PnzKV++PJ6enuTNm5cePXpw7dq1JAUWEZE0LEMGGDoUTpww134aBsycCU8/DRMmQEyM1QnTnYiYCFoubknA7wFm8ey0jrrF6lodSxxYosvn4sWLGTBgAEOHDuXgwYPUrFmThg0bcubMmQfe/8cff8Tf359evXpx5MgRli5dyt69e+ndu/cThxcRkTQqf36YNw927DCnYwoJgQEDoGJF2LbN6nTpRlRcFG2WtWHDyQ1kcMnA+k7rqVO0jtWxxMElunyOHz+eXr160bt3b0qXLs2XX35JwYIFmTp16gPvv3v3booUKcIbb7xB0aJFefHFF+nTpw/79u174vAiIpLGVa8Oe/aYE9Jnzw6//moenNSpE5w/b3W6NO1O9B0++eMTAk8H4unqSUDnAHyK+lgdS9IAl8TcOSoqiv379zN48OB7bvfz82Pnzp0PfEz16tUZOnQoAQEBNGzYkMuXL7Ns2TIaN374RLSRkZFERkbGXw8JCQEgOjqa6OjoxEROkrvLsMeyJGVoDB2bxi/pzLfM9X8/R2PVW5jsY9izJzRvjtOHH+I0fTq2hQsx1q4lbuhQ4vr3Bze35FmOAGbxbLmkJYdCD5HRNSNr2q+hRv4advtOppbPsSOz4j1M6OcjUeXz6tWrxMbG4u3tfc/t3t7eXLx48YGPqV69OvPnz6d9+/ZEREQQExNDs2bNmDhx4kOXM3r0aEaMGHHf7YGBgXh6eiYm8hMJCgqy27IkZWgMHZvGL/EiIpwB8/SGGzduxMPD2tNXJvsYNm5MlpIlKffNN2Q/cQLnIUMInzyZwy+/zJXy5ZN3WelUZFwkn5z+hJ9v/4yHkwfvF36f0F9DCfg1wG4ZUtvn2BH9+z3csmWLXd7D8PDwBN3PZhgJn0jt/Pnz5M+fn507d1KtWrX42z/++GPmzp3L8ePH73vM0aNHqVevHgMHDqR+/fpcuHCBd955h+eee44ZM2Y8cDkPWvNZsGBBrl69SubMmRMaN8mio6MJCgrC19cXV1fXFF+eJD+NoWPT+CVdWBhky2a+ZzduRJMxozU5UnwM4+KwzZ2L8/vvY7tyxbypVStix4yBQoWSf3npRHh0OC2XtCT4r2C8XL14v/D7vNnyTbt/D1PL59iR/fs9vHw5nKxZU34MQ0JCyJkzJ7du3XpkX0vUms+cOXPi7Ox831rOy5cv37c29K7Ro0dTo0YN3nnnHQDKlStHxowZqVmzJqNGjSJv3rz3Pcbd3R13d/f7bnd1dbXrF8Dey5PkpzF0bBq/xPv322W+f9Zl+SdDCoXo3RvatDHPijR5Mk4rVkDABq4O/BhefRXPbO7YbCmz6LTGMODKzTC6ruzOjqvBeHl4sa79Om4evmnJ9zC1fY4d0f3vYcq/iQldRqLKp5ubG5UrVyYoKIiWLVvG3x4UFETz5s0f+Jjw8HBcXO5djLOzMwCJWOkqIiJyv6xZzfPE9+4Nr7/O1e3H8B49AEZbHcwRZQRWkvH9YmzsMo/n8jxHwGH7bWqX9CPRR7sPGjSI6dOnM3PmTI4dO8bAgQM5c+YMffv2BWDIkCH4+/vH379p06asWLGCqVOncvr0aXbs2MEbb7zB888/T758+ZLvlYiISPpVrpw5BdOkyVYncXiL2yymesHqVseQNCxRaz4B2rdvz7Vr1xg5ciQXLlygTJkyBAQEULhwYQAuXLhwz5yf3bt3JzQ0lEmTJvHWW2+RNWtW6tSpw2effZZ8r0JERMRmw7NbO3jdvHqJ3GQkDDJlhmHD4OWX4X9b3sR0O+o2rRa3YuepgzDO3He2VonnLE4laV2iyydAv3796Nev3wN/N2vWrPtu69+/P/3790/KokRERBLs3/t4ZvxhAxkHvmKeH/7tV2HhdJg61TxlpxAaGUqbJY3YeelHMmfKS8j/btd+spLSdG53ERFJmypVgp9+gsmTIUsWs4RWrQr9+sGNG1ans1RoZCgN5zfkxzM/ksU9C2s7rrU6kqQjKp8iIpJ2OTubZfP4cejSxTyse+pUKFUK5s41r6czIZEhNJjfgB1nd5DVIyub/DdROV9lq2NJOqLyKSIiaV+ePGbZ3LLFLJ6XL4O/P/j4wLFjVqezm5DIEBrMa8DOszvJ5pGNTV03USVfFatjSTqj8ikiIumHjw/8/DN88glkyGAeIV++vHlAUkSE1elS1K2IW9SfV59df+8yi6fWeIpFVD5FRCR9cXODIUPgyBFo3Ng8CfbIkWYJDQ62Ol2KuFs8d/+9m+wZsrPZfzOV8layOpakUyqfIiKSPhUtCmvXwpIl5mb5EyegTh3o3h2uXrU6XbK5GXETv3l+/HTup/jiWTFvRatjSTqm8ikiIumXzQZt25oHJL36qnl99mxzv9A5cxz+gKSbETfxm+vHnnN7yJEhB1v8t1AhTwWrY0k6p/IpIiKSJQtMmQI7dkCZMnDtGnTrBvXqwe+/W50uSW7cuYHvXF/2nt9Ljgw52Oy/mfJ5ylsdS0TlU0REJF61anDgAIweDR4e5tHxZcvCqFEQFWV1ugS7Wzz3nd9HTs+cBHcLVvGUVEPlU0RE5N9cXWHwYPOAJD8/iIyEDz6AChXgxx+tTvdY1+9cp97ceuy/sJ9cnrkI7hZMWe+yVscSiafyKSIi8iDFisGGDTB/PuTObc4HWrOmuW/orVtWp3ug63euU29OPQ5cOEDujLkJ7hZMmdxlrI4lco8kndtdREQkXbDZoFMnaNAA3nsPpk+HadOIW72Wq59OhwYN8PS0/nzohgF/X71Gm6VtOHL7ILkzmcXzmVzPWBtM5AFUPkVERB4ne3b49luziL7yCldP3sS7WwOrU/2fHEAwuYY9S3C3pSqekmpps7uIiEhC+fjAL7/A6/2tTvJQK9qtUPGUVE1rPkVERBIjQwY8R38Ik8yrl8hFRsLBpw589ZU5eb2dXAm7QpMFTThy7jSMuwJAhUIl7bZ8kaRQ+RQREUmkf+/jmfGj98n48fsQvA6qboGPPoI33wRn5xTNcDnsMk2X1+XIrV/xzlaMSw/IJpIaabO7iIjIkxg40NwUX7s2hIfDW2+Z84X+8kuKLfJy2GXqzK7Dr5d/JV+mfGzosiHFliWS3FQ+RUREnlSJEuaE9N9+a54tae9eqFzZnB80MjJZF3Xp9iV8Zvtw5MoR8mfKz9ZuWymRo0SyLkMkJal8ioiIJAebDXr3hqNHoVUriIkxz4xUuTLs2ZMsi7h4+yI+s304euWoWTy7q3iK41H5FBERSU758sHy5bB0KeTKBUeOEFe1GpdfG87lv+5w+zaEhSXucvs2HD59iZoTW3Hs8jEKZC7A1u5beSr7U1a/WpFE0wFHIiIiKaFNG3M/0Dff5OqCQLynDIcpT/KE3sBO8o6owNZuyymevXiyxBSxN635FBERSSk5c5qn55w9N9meclWHVSqe4tBUPkVERFKYZ6t/zoZ0iVzcJiO3i5ThdsAP3L7NQy8nzp+n+Njy8Hau+Mc/k6+IBa9AJPmofIqIiKSwe+YFXbmAjAWyk+HPI4Q1ak3Y6+9hhITe95hzIedoML8Bp26cpECOnA98LhFHpH0+RURE7MnXF44c4errI/GeOw5mYV7ukx8w5wpddeIsVYbYLaFIitKaTxEREXvLnBnGjUvw3QtmKZiCYUTsS+VTRETEAp6e//x8qecQcz9QMvJb1iy81DEjRcaU4di5s9y+fe99RRydyqeIiIgF7tkP9KvRhK6ZzvXsUTx9M4RtC8P55fcqlMqSnYwZtZ+npC0qnyIiIhb76+ZfvHBqCM/0iWF+jcwAZPp2NpQrB9u3W5xOJHmpfIqIiFiswbwG/HXrL/LmLUHtgKMQGAgFC8Lp01CrFgwebHVEkWSj8ikiImIBw/jn57NXr1I8YznWt9lKVuf8hFX3JWz3YcK69iXMyEDYpBkPfJyII1L5FBERscCRc3/8c2XcFU698zNP58uHlxfmJX8WvOZOxYswvLkSf9fwwSMgIsKCxCLJQ+VTRETEzk5dP0WLxS2S9uDJk6ByZdi3L1kzidiLyqeIiIgdnbp+ilqzanEx9hee+qQ6h09dIjT04afYvH0bQkPh0iW4NOt7cuZ0gqNH4YUXYMQIiI62+iWJJIrKp4iIiB3Vn1efc6HnKJ27NNv7r6BMMW+8vCBjxodfvLwgd27I3a0hTsePQtu2EBsLw4dDjRrw229WvyyRBNPpNUVERFLYvw8Sunj9FqXyVWZdm/VksnkTFpbIJ/PIATMXQ8M2MHAg7D1CWLV6wNn7liWSGql8ioiIpLBfzv4OlDCvjLvCcaD4oCd5RhvQ7n8XIOqf34Sf+BuvSgWe5MlFUpQ2u4uIiKSg41ePJ/3goqSo9RLMnatVoJJqac2niIhICjl25Rh15tThinGR0p/WYlm7ZRTKlSvZT5dpGBD+6yl47XVyHvgD/P1h1SqYNg1y5UrehYk8IZVPERGRFHD0ylHqzK7DpbBLlMtbjs3+y8npmTPFluf1QnH4aS2MGQPDhsGKFfDjj/Dtt9CsWYotVySxtNldREQkmR29chSf2T5cCrtEhTwV2OK/JUWLZzwXF3j/fdizB559Fi5fhubNoVcvc74mkVRA5VNERCQZ/Xr5V2rPqs3lsMtUzFORTV03kcMzh31DVKxoTkL/9ttgs8HMmVChAuzcad8cIg+g8ikiIpJMfr38K3Vm1+FK+BWzePpbUDzv8vCAsWNh61YoVAhOn4aaNeHDDzUxvVhK5VNERCQZHL50GJ/ZPlwJv0LlvJXZ5L+J7BmyWx0LXnoJfvkFunSBuDj46CNzYvoTJ6xOJumUyqeIiMgT+vniz/jM9uFq+FWq5KtCUNeg1FE878qSxZx+adEiyJoV9u41N81/842mZBK7U/kUERF5AocvHabunLpcu3ON5/I9R1DXILJlyGZ1rAdr3x4OH4Y6dSA8HPr0MQ9IunzZ6mSSjqh8ioiIPIFGCxpx7c41ns//PIFdA8nqkdXqSI9WoAAEBcHnn4ObG6xdC1WrWp1K0hHN8ykiIpJI/95SfeNWBFWK1GJly9W4xmZJ/LnaLeEEfQZBdV/o1Yuwo3/E/8a4HQYZM1qYTdI6lU8REZFE2v3HL0A588q4K+wD8r9uZaKkKgvsueeW8Op18Vo8CcqXtyaSpHna7C4iIpII+8/vp/WSVlbHSDmnT0G1ajiNG2ceHS+SzLTmU0REJIH2nd+H71xfQpxuUuWLxixqvRDvbJmT/Vzt9mYY5vFH3LhOziG1YOVynN9/n+ply5pHxRcpYnVESUNUPkVERBJg77m9+M715VbkLWoUrsH3nReRyT2T1bGSjZcXkDs7LF8KM2divPEGuQ4fxqhcGWbMgBYtrI4oaYQ2u4uIiDzGnnN7qDe3Hrcib/FioRf5vvP3aap43sNmg169iPnpJ24WK4bt+nVo2dKclskxjqaSVE7lU0RE5BF++vsnc1N7ZAg1C9VM28Xz30qW5IfPPiP2rbfM6998A1WqwMGD1uYSh6fyKSIi8hC7zu6KL54vFX6JgM4BeLl5WR3LbgxXV+JGjzbnBc2bF44fN+cEHT9eByNJkql8ioiIPMDOszupP68+oVGh1C5Sm4BO6at43qNePfP88M2bQ3Q0vPUWNGwIFy5YnUwckMqniIjI/9lxZkd88fQp4sO6juvI6JbOJ17PmRNWroSpUyFDBggMhHLlYN06q5OJg1H5FBER+Zcfz/xIg/kNuB11mzpF67Cuk4pnPJsN+vaFffvMSeivXoWmTeHNNyEy0up04iBUPkVERP5n+1/baTDPLJ51i9Zlbce1eLp6Wh0r9XnmGfjpJxgwwLz+1Vfwwgvw22+WxhLHoPIpIiICbPtzGw3nNyQsOox6xeqpeD6Ouzt88YW52T1nTjh0CCpXhlmzzFnrRR5C5VNERNK9rX9updGCRoRFh+FbzJc1HdaQwTWD1bEcQ+PG8PPP4ONjzgPaowd06QIhIVYnk1RK5VNERNK14D+CabygMeHR4dQvXp/VHVareCZWvnzmdEyjRoGzMyxYAJUqmfuGivwflU8REUm3tvyxJb54NniqAas6rFLxTCpnZxg6FH74AQoVglOnoHp1+PxzzQkq91D5FBGRdGnz6c00WdCEOzF3aPhUQ1a2X4mHi4fVsRxf9erm/p+tW5tzgr79trlp/vJlq5NJKqHyKSIi6U7QqSCaLDSLZ6MSjVQ8k1u2bLB0KUybBh4esGGDOTXTpk1WJ5NUQOVTRETSlcBTgTRb1IyImAiaPN2EFe1W4O7ibnWstMdmgz59YO9ec2qmixfBzw/efx9iYqxOJxZS+RQRkXRj48mNNFtoFs+mTzdlWdtlKp4prUwZs4D26WNOwTR6NNSuDWfPWp1MLKLyKSIi6cKGkxtovqg5kbGRNC/ZnGXtVDztxtPT3AS/eDFkygQ7dkCFCrB+vdXJxAIqnyIikuYF/B4QXzxblGrBkrZLcHN2szpW+tOuHRw8aE5Gf/06NGliHpAUFWV1MrEjlU8REUnT1p9YT8vFLYmKjaJlqZYsaaPiaanixc01n2+8YV7//HN46SX4809LY4n9qHyKiEiate7EOlotaUVUbBStS7dmcZvFuDq7Wh1L3N1hwgRYuRKyZjXPE1+xIqxaZXUysQOVTxERSZMCTgTQarFZPNs804aFrReqeKY2LVqYm+GrVoWbN6FlS3jzTYiMtDqZpCCVTxERSZM6rehEdFw07Z5tx4JWC1Q8U6siRWD7dnPfT4CvvoK6dS2NJCnLxeoAIiIiycUw/vk5JsKV1uX9+ab+DKIiXNAhLYkTHQ0REc6EhYFrivd2Vxg+Fl6oC6+8Qtih3+J/8+8xlbRB5VNERNKMpYfWA43NK+OusBxYbmUgh+YKNLHzMhsAZ+65JfyNwXhNHWHuJyppgja7i4hImrD86HJ6r+1tdQxJbt/NgBo14I8/rE4iyURrPkVExOEtO7qMDss6EOcRS+sZrzKx0SQyeTljs1mdzHFFR0ezceNG6tevj2vKb3e/h2FAeDiweTM5+8XB/v3m0fCzZ0Pz5nbNIslP5VNERBza0iNL6bi8I7FGLF0rdOW75pNwdnK2OpbDi44GD49YMma0xz6f9/PyAjrWhRoHoX172L3bPDp+0CD49FNrQkmy0GZ3ERFxWIt/XRxfPP3L+/Nd8+9UPNOaQoVg2zazdAKMHw+1aunc8A5M5VNERBzSol8X0XlFZ2KNWLpX6M7MZjNVPNMqNzfzTEgrVkCWLLBrl7kZ/vvvrU4mSaDyKSIiDmfh4YXxxbNHhR7MaDZDxTM9aNkSDhyASpXg2jVo1AiGDoWYGKuTSSKofIqIiENZcHgBXVZ2Ic6Io1fFXkxvNh0nm/45SzeKFTPPDd+vn3n9k0/A1xcuXLA2lySYvq0iIuIw5v0yj64ruxJnxNG7Ym++afqNimd65OEBkyfDwoXmkUlbt5qb4bdssTqZJIC+sSIi4hDm/jyXbqu6EWfE8UqlV/i66dcqnuldhw6wbx+ULQuXLplrQEePhrg4q5PJI+hbKyIiqd7sQ7Pji2efyn2Y2mSqiqeYSpY0p2Hq3t0sne+/b84FeuOG1cnkIfTNFRGRVG3WoVn0WN0DA4NXq7zKlMZTVDzlXp6eMHMmfPuteRrOdeugcmU4eNDqZPIA+vaKiEiq9d3B7+i5uicGBv2q9GNyo8kqnvJgNhv07g07d0KRIubpOKtVgxkzrE4m/0ffYBERSZVmHpxJrzW9MDB47bnXmNRoEjadL1Mep1IlczqmJk0gMtIspD17wp07VieT/1H5FBGRVGf6genxxbP/8/2Z2HCiiqckXLZssHq1OQ2TkxN89525FvTkSauTCSqfIiKSynyz/xteXvsyAG9WfZMJDSaoeEriOTnBkCEQFAS5csHPP0OVKmYpFUupfIqISKrx9b6v6bOuDwADqg7gi/pfqHjKk6lTxzzwqHp1uHULWrSA997TWZEspPIpIiKpwrR90+i7vi8Ag14YxPj641U8JXnkz29ORD9woHl9zBioV8+cG1TsTuVTREQsN2XvFF5d/yoAb1V7i3F+41Q8JXm5usL48bBkiXlWpG3bzIOTdu60Olm6o/IpIiKWmrxnMq8FvAbAO9XfYazvWBVPSTlt28LevVC6NJw/D7Vrm6fqNAyrk6UbKp8iImKZiT9N5PXvXwfg3erv8lm9z1Q8JeWVKgV79phFNDoaXn8d/P0hPNzqZOmCyqeIiFhiwu4JvLHhDQAG1xjMp/U+VfEU+/HygsWL4fPPwdkZ5s0zp2M6dcrqZGmeyqeIiNjdl7u/ZMDGAQC8/+L7fFL3ExVPsT+bDQYNgk2bIHdu+OUX87Sc69ZZnSxNU/kUERG7+mLXFwzcaB51PLTmUEbVGaXiKdaqXRv274cXXjCnY2raFIYNg9hYq5OlSSqfIiJiN5/v/JxBgYMA+OClD/jI5yMVT0kdChQwj4B/zTz4jZEjzVN0Xr9uba40SOVTRETsYuyOsbwd9DZgFs8RtUeoeErq4uYGkybB7Nng4QEbNpib4Q8etDpZmqLyKSIiKe6zHz/j3U3vAjC81nBG+oxU8ZTUy98fdu2CYsXgzz/NsyPNnm11qjQjSeVzypQpFC1aFA8PDypXrsz27dsfef/IyEiGDh1K4cKFcXd3p3jx4sycOTNJgUVExLF8+uOnDN48GIARtUcwrPYwixOJJECFCrBvHzRqBBER0L079O9vTs0kTyTR5XPx4sUMGDCAoUOHcvDgQWrWrEnDhg05c+bMQx/Trl07Nm/ezIwZM/jtt99YuHAhpUqVeqLgIiKS+n2641OGbB4CwMjaI/mw1ocWJxJJhGzZYO1a+PB/n9tJk6BuXbh40dpcDs4lsQ8YP348vXr1onfv3gB8+eWXbNy4kalTpzJ69Oj77r9hwwa2bdvG6dOnyZ49OwBFihR5stQiIpLqLbm4hAWHFgAwymcUQ18aanEikSRwcoIRI8x9P7t0ge3bzZ9XrICqVa1O55ASVT6joqLYv38/gwcPvud2Pz8/dj7k3Khr1qyhSpUqjBkzhrlz55IxY0aaNWvGRx99RIYMGR74mMjISCIjI+Ovh4SEABAdHU20HVZ3312GPZYlKUNj6Ng0fklnvmWu//s52rIthCO3jWTBRbN4flT7I96t9q7G08Hoe/h/GjaEnTtxadMG22+/Ybz0ErFffYXRs6fVyR7Iir8FCf2sJKp8Xr16ldjYWLy9ve+53dvbm4sPWQV9+vRpfvzxRzw8PFi5ciVXr16lX79+XL9+/aH7fY4ePZoRI0bcd3tgYCCenp6JifxEgoKC7LYsSRkaQ8em8Uu8iAhnoAkAGzduxMPD/vMULrq4iEUXFwHQNW9Xyt4sS0BAgN1zSPLQ9/BeLsOGUfGrr8i3ezcuffvy54oVHH75ZeJcXa2Odo9//y3YsmWLXf4WhCfw9KQ2wzCMhD7p+fPnyZ8/Pzt37qRatWrxt3/88cfMnTuX48eP3/cYPz8/tm/fzsWLF8mSJQsAK1asoE2bNoSFhT1w7eeD1nwWLFiQq1evkjlz5oTGTbLo6GiCgoLw9fXFNZV9mCRhNIaOTeOXdGFhkC2b+Z7duBFNxoz2W7ZhGIzcPpKPf/wYAP+8/kztMlVj6KD0PXyEuDicxozBadgwbIZBXNWqxC5eDPnyWZ0s3r//Fly+HE7WrCk/hiEhIeTMmZNbt249sq8las1nzpw5cXZ2vm8t5+XLl+9bG3pX3rx5yZ8/f3zxBChdujSGYfD3339TokSJ+x7j7u6Ou7v7fbe7urra9Qtg7+VJ8tMYOjaNX+L9++0y3z/7LNcwDIZtHRZfPD+t8ymlrpfSGKYBGsOH+OADqFIFOnXC6aefcHrhBVi2DGrUsDoZ8KC/BSk/hgldRqKOdndzc6Ny5cr3rYIPCgqievXqD3xMjRo1OH/+PLdv346/7cSJEzg5OVGgQIHELF5ERFIhwzD4IPgDPvrhIwDG+Y5j0AuDLE4lYgcNG8LevVCmjHkEfO3aMGUKJHyjcrqU6KmWBg0axPTp05k5cybHjh1j4MCBnDlzhr59+wIwZMgQ/P394+/fqVMncuTIQY8ePTh69Cg//PAD77zzDj179nzoAUciIuIYDMPgP1v+w8fbzTWe4/3G81b1tyxOJWJHTz1lTkjfrh3ExJin5+zVy5wbVB4o0VMttW/fnmvXrjFy5EguXLhAmTJlCAgIoHDhwgBcuHDhnjk/vby8CAoKon///lSpUoUcOXLQrl07Ro0alXyvQkRE7M4wDN7f/D6f7vgUgC/qf8GAFwZYG0rECl5esGiRuRl+8GD47js4csScjil/fqvTpTqJLp8A/fr1o1+/fg/83axZs+67rVSpUjpaTkQkDTEMg8GbBjNm5xgAJjSYwBtV37A4lYiFbDZ45x2oWNFcC7pnj1lGly83T88p8XRudxERSRTDMHhv03vxxXNiw4kqniJ31atnnpbz3/uBTp9udapUReVTREQSzDAM3gl6h7E7xwIwqeEkXn/+dYtTiaQyxYqZ+4G2bm3O9v7yy+a+oFFRVidLFVQ+RUQkQQzD4K3At/h81+cATG40mdeef83iVCKplJcXLF0Ko0aZm+SnTAFfX7h82epkllP5FBGRxzIMg0EbB/HF7i8AmNp4Kv2ee/C+/yLyPzYbDB0Kq1dDpkzwww/mfqAHDlidzFIqnyIi8kiGYTBgwwC+/OlLAL5u8jV9q/S1NpSII2na1DwA6emn4exZcyL6BQusTmUZlU8REXkowzB4c8ObfLXnKwC+afINr1R+xeJUIg6oVCn46Sdo1MicA7RzZ/Po+NiUP+d6aqPyKSIiD2QYBv2/78/EPROxYWN60+m8XPllq2OJOK6sWWHNGnNTPMC4cWYZvX7d0lj2pvIpIiL3iTPieC3gNSbvnWwWz2bT6VWpl9WxRByfs7N5ENLSpeDpCYGB8PzzcPSo1cnsRuVTRETuEWfE8dr615i6byo2bMxsPpOeFXtaHUskbWnTxpyOqUgROHUKXngB1q2zOpVdqHyKiEi8OCOOfuv7MW3/NGzY+K75d3Sv0N3qWCJpU7lysHcv1KoFoaHQrBl89hkYhtXJUpTKp4iIAGbx7LuuL1/v/xobNma3mE23Ct2sjiWStuXMCUFB0K+fWToHD4YuXeDOHauTpRiVTxERIc6Io8/aPnx74FucbE7MaTmHruW7Wh1LJH1wdYXJk2HqVHBxMadhqlkT/v7b6mQpQuVTRCSdizPieHnNy0w/OB0nmxNzW86lS7kuVscSSX/69oVNmyBHDti/H557DnbvtjpVslP5FBFJx+KMOHqv6c3MQzNxsjkxr+U8OpXtZHUskfSrVi1zP9CyZeHiRfP6rFlWp0pWKp8iIulUbFwsvdb04rtD3+Fkc2J+q/l0LNvR6lgiUrQo7NwJLVtCVBT06AGDBkFMjNXJkoXKp4hIOhQbF0vPNT2ZdWgWzjZnFrRaQIcyHayOJSJ3eXnBsmUwbJh5/YsvoHFjuHHD2lzJQOVTRCSdiY2LpcfqHsz5eQ7ONmcWtl5I+zLtrY4lIv/PyQmGD793QvqqVeG336xO9kRUPkVE0pHYuFi6r+7O3F/m4mxzZlGbRbR9tq3VsUTkUdq0gR07oHBh+P13s4AGBlqdKslUPkVE0omYuBj8V/kz75d5uDi5sLjNYto808bqWCKSEBUqwJ49UKMG3LoFDRvCV1855IT0Kp8iIulATFwM/iv9WXB4AS5OLixps4TWz7S2OpaIJEbu3LB5M3TvDnFx8Oab5vRM0dFWJ0sUlU8RkTQuJi6Griu7svDXhbg4ubC07VJalm5pdSwRSQp3d5g5E8aNA5sNvvkG/Pzg2jWrkyWYyqeISBoWExdD5xWdWfTrIlydXFnWdhktSrWwOpaIPAmbDd56C9auhUyZYOtWeP55OHrU6mQJovIpIpJGRcdG02l5J5YcWWIWz3bLaF6qudWxRCS5NG4Mu3aZ84KePg0vvAABAVaneiyVTxGRNKr7qu4sPboUN2c3VrRfQbOSzayOJCLJ7dlnzQORXnoJQkOhaVMYPz5VH4ik8ikikkat/m2VWTzbraDJ002sjiMiKSVnTggKgt69zQOR3noL+vWzOtVDuVgdQEREkk9kTBTgBoBLbFYWNp1J7fz1CQuzb47oaIiIcCYsDFxd7btsSR4aQ0fjBl98AyUqwODBhM1dBkwFUt9KUJVPEZE0Iio2ik6LegNzAIj57BytP7MqjSugta2OTWPoeGzAa/+7/CP8VjTZsqWe/4NQ+RQRSQMiYyJpu7QtG0/usjqKiKQ2qWzVtcqniIiDi4yJpM3SNqw7sQ63zB7M3R1M7aI+eHqaM7JYITo6mo0bN1K/fn1cU9k/fJIwGkPHZhhw61IIm37cQc6c9ayOcw+VTxERBxYZE0nrJa1Z//t6PFw8WNNhDb7FfayORXQ0eHjEkjFjqlvpIgmkMXR87u4ZyJo1CqdUdni5yqeIiIOKiImg9ZLWBPwegIeLB2s7rqVesdS1hkNE5P+pfIqIOKCImAhaLm7JhpMbyOCSgbUd11K3WF2rY4mIPJbKp4iIg4mIiaDFohZsPLWRDC4ZWNdpHXWK1rE6lohIgqh8iog4kDvRd2ixuAWBpwLxdPVkfaf11C5S2+pYIiIJpvIpIuIg7kTfofmi5gSdDsLT1ZOATgHUKlLL6lgiIomi8iki4gDCo8Npvqg5m05vIqNrRgI6B/BS4ZesjiUikmgqnyIiqVx4dDhNFzZlyx9b8HLz4vvO3/NioRetjiUikiQqnyIiqVhYVBhNFzYl+M9gvNy82NB5AzUK1bA6lohIkql8ioikUmFRYTRZ2IStf24lk1smNnTZQPWC1a2OJSLyRFQ+RURSodtRt2m8oDE//PUDmdwysbHLRqoVrGZ1LBGRJ6byKSKSytyOuk2j+Y3YfmY7md0zs7HLRl4o8ILVsUREkoXKp4hIKhIaGUqjBY348cyPZHbPTGCXQKoWqGp1LBGRZKPyKSKSSoRGhtJwfkN2nN1BFvcsBHYN5Pn8z1sdS0QkWal8ioikAiGRITSc35CdZ3eS1SMrQV2DqJKvitWxRESSncqniIjFQiJDaDCvAbv+3qXiKSJpnsqniIiFbkXcosH8Buz+ezfZPLKxyX8TlfJWsjqWiEiKUfkUEbHIrYhb1J9Xn5/O/UT2DNnZ1HUTFfNWtDqWiEiKUvkUEbHAzYib1J9Xnz3n9pA9Q3Y2+2+mQp4KVscSEUlxKp8iInZ2M+ImfnP92Ht+Lzky5GCz/2bK5ylvdSwREbtQ+RQRsaMbd27gN8+Pfef3kdMzJ5v9N1POu5zVsURE7EblU0TETm7cuYHvXF/2X9hPTs+cbPHfQlnvslbHEhGxK5VPERE7uH7nOr5zfTlw4QC5PHOxpdsWyuQuY3UsERG7U/kUEUlh18KvUW9uPQ5dPETujLnZ4r+FZ3M/a3UsERFLqHyKiKSgfxdP74zebOm2hWdyPWN1LBERy6h8ioikkKvhV6k3px4/X/oZ74zeBHcLpnSu0lbHEhGxlMqniEgKuBp+lbpz6vLLpV/I45WHLf5bVDxFRFD5FBFJdlfCrlB3Tl0OXz5MHq88BHcLplTOUlbHEhFJFZysDiAikpZcDrtMnTl1OHz5MHm98rK121YVTxGRf9GaTxGRZHI57DJ1ZtfhyJUj5MuUj+BuwTyd42mrY4mIpCoqnyIiyeDS7UvUmVOHo1eOkj9TfoK7BVMiRwmrY4mIpDoqnyIiT+ji7YvUmV2HY1ePUSBzAYK7BfNU9qesjiUikiqpfIqIPIELoReoM6cOx68ep0DmAmzttpXi2YtbHUtEJNVS+RQRSaILoRfwme3Db9d+o2DmggR3C1bxFBF5DJVPEZEkOB96Hp/ZPpy4doJCWQoR3C2YYtmKWR1LRCTVU/kUEUmkcyHn8Jntw+/Xf6dwlsIEdwumaLaiVscSEXEIKp8iIonw/8Vza/etFMlaxOpYIiIOQ+VTRCSBzt46i89sH07dOEWRrEXY2m0rhbMWtjqWiIhD0RmOREQS4MytM9SeXZtTN05RNGtRFU8RkSTSmk8Rkcc4c+sMtWfV5o+bf1AsWzGCuwVTKEshq2OJiDgkrfkUEXmEv27+FV88i2crztZuW1U8RUSegNZ8iog8xJ83/8Rntg9/3vzTLJ7dt1IgcwGrY4mIODSVTxGRB/jjxh/4zPbhr1t/USJ7CYK7BZM/c36rY4mIODxtdhcR+T+nb5ym9uzaKp4iIilAaz5FRP7l9I3T1J5Vm7MhZ3k6x9MEdwsmX6Z8VscSEUkzVD5FRP7n1PVT1J5dm79D/qZkjpIEdwsmb6a8VscSEUlTVD5FRICT109Se1ZtzoWeo1TOUgR3CyaPVx6rY4mIpDna51NE0r3fr/1OrVm1OBd6jtI5S6t4ioikIJVPEUnXTlw7Qe3ZtTkfep5ncj2j4ikiksK02V1E0q3frv6Gz2wfLty+wLO5nmVLty3kzpjb6lgiImma1nyKSLp0/Opxas+uzYXbFyiTu4yKp4iInah8iki6c+zKMXxm+3Dx9kXK5i7LFn8VTxERe9FmdxFJV45eOUqd2XW4FHaJct7l2Oy/mZyeOa2OJSKSbmjNp4ikG0cuH8Fntg+Xwi5R3ru8iqeIiAW05lNE0oVfL/9Kndl1uBJ+hQp5KrCp6yZyeOawOpaISLqjNZ8ikuYdvnQ4vnhWzFORzf6bVTxFRCyi8ikiadovl36hzhyzeFbKW4lN/pvIniG71bFERNItbXYXkTTr54s/U3dOXa7duUblvJUJ6hpEtgzZrI4lIpKuac2niKRJhy4eii+ez+V7jk3+m1Q8RURSAa35FJE0527xvH7nOs/nf56NXTaS1SOr1bFERASt+RSRNObAhQPUmV2H63euUzV/VQK7BKp4ioikIiqfIpJmHLhwgHpz6nEj4gYvFHiBjV02ksUji9WxRETkX7TZXUTShP3n91Nvbj1uRtykWoFqbOiygczuma2OJSIi/0drPkXE4e09tze+eFYvWJ2NXTaqeIqIpFIqnyLi0Pac24PvXF9uRtykRsEabOi8gUzumayOJSIiD6HyKSIO66e/f8J3ri+3Im/xYqEX+b7z9yqeIiKpnMqniDik3X/vxm+eHyGRIdQsVFPFU0TEQeiAIxFxOLvO7qL+vPqERoXyUuGXWN9pPV5uXlbHEhGRBNCaTxFxKDvP7owvnrWL1CagU4CKp4iIA1H5FBGHsePMjvji6VPEh3Ud15HRLaPVsUREJBFUPkXEIfx45kcazG/A7ajb1Clah3WdVDxFRByRyqeIpHrb/9pOg3lm8axbtC5rO67F09XT6lgiIpIESSqfU6ZMoWjRonh4eFC5cmW2b9+eoMft2LEDFxcXKlSokJTFikg69MNfP9BwfkPCosOoV6weazquUfEUEXFgiS6fixcvZsCAAQwdOpSDBw9Ss2ZNGjZsyJkzZx75uFu3buHv70/dunWTHFZE0pd/F0/fYr6s6aDiKSLi6BJdPsePH0+vXr3o3bs3pUuX5ssvv6RgwYJMnTr1kY/r06cPnTp1olq1akkOKyLpx+HQwzRb0ozw6HDqF6/P6g6ryeCawepYIiLyhBI1z2dUVBT79+9n8ODB99zu5+fHzp07H/q47777jlOnTjFv3jxGjRr12OVERkYSGRkZfz0kJASA6OhooqOjExM5Se4uwx7LkpShMXRsQSeD+Oj0R0QZUdQvVp+lrZfigovG04HoO+j4NIaOz95jmNDlJKp8Xr16ldjYWLy9ve+53dvbm4sXLz7wMb///juDBw9m+/btuLgkbHGjR49mxIgR990eGBiIp6f9NrkFBQXZbVmSMjSGjufn0J/5+PTHRBlRVMpUiV5evdgSuMXqWJJE+g46Po2h47PXGIaHhyfofkk6w5HNZrvnumEY990GEBsbS6dOnRgxYgRPP/10gp9/yJAhDBo0KP56SEgIBQsWxM/Pj8yZMyclcqJER0cTFBSEr68vrq6uKb48SX4aQ8e0+Y/NjF46migjiiqZqxDYKxCvDJpA3hHpO+j4NIaOz95jeHdL9eMkqnzmzJkTZ2fn+9ZyXr58+b61oQChoaHs27ePgwcP8vrrrwMQFxeHYRi4uLgQGBhInTp17nucu7s77u7u993u6upq1y+AvZcnyU9j6DgCTwXScmlLImIiaPRUI3p49sArg5fGz8HpO+j4NIaOz15jmNBlJOqAIzc3NypXrnzf6tugoCCqV69+3/0zZ87M4cOHOXToUPylb9++lCxZkkOHDlG1atXELF5E0qiNJzfSbGEzImIiaPp0Uxa3Woyrk/6xExFJixK92X3QoEF07dqVKlWqUK1aNb755hvOnDlD3759AXOT+blz55gzZw5OTk6UKVPmnsfnzp0bDw+P+24XkfRpw8kNtFjUgsjYSJqXbM6Stkuwxd2/G4+IiKQNiS6f7du359q1a4wcOZILFy5QpkwZAgICKFy4MAAXLlx47JyfIiIAAb8H0HJxS6Jio2hRqgWL2yzGzdmN6DgdXSsiklYl6YCjfv360a9fvwf+btasWY987PDhwxk+fHhSFisiacj6E+tptaQVUbFRtCzVkkVtFuHm7GZ1LBERSWFJKp8iIk9i3Yl1tFrciui4aFqVbsWi1otwddY+niIi6UGSzu0uIpJUa39bG1882zzTRsVTRCSdUfkUEbtZfXw1rZe0JjoumrbPtGVBqwUqniIi6YzKp4jYxarjq2i7tC3RcdG0f7Y9C1qreIqIpEcqnyKS4lYeWxlfPDuU6cC8VvNwcdIu5yIi6ZHKp4ikqOVHl9NuWTti4mLoVLYTc1vOVfEUEUnHVD5FJMUsO7qM9svaExMXQ+eynZndYraKp4hIOqfyKSIpYumRpXRY1oFYI5au5bqqeIqICKDyKSIpYPGvi+m4vCOxRiz+5f35rvl3ODs5Wx1LRERSAZVPEUlWi35dROcVnYk1YuleoTszm81U8RQRkXgqnyKSbBYeXhhfPHtU6MH0ptNVPEVE5B4qnyKSLOb/Mp8uK7sQZ8TRq2IvpjdT8RQRkfupfIrIE5v3yzz8V/kTZ8TRu2Jvvmn6DU42/XkREZH76V8HEXkic36eg/9Ks3i+UukVvm76tYqniIg8lP6FEJEkm31oNt1XdcfAoE/lPkxtMlXFU0REHkn/SohIksw6NIseq3tgYPBqlVeZ0niKiqeIiDyW/qUQkUSbeXAmPVf3xMCgX5V+TG40WcVTREQSRP9aiEiizDgwg95remNg8PpzrzOp0SRsNpvVsURExEGofIpIgk0/MJ3ea83i+cbzb/BVw69UPEVEJFFUPkUkQb7Z/w0vr30ZgDervsmXDb5U8RQRkURT+RSRx/p639f0WdcHgAFVB/BF/S9UPEVEJElUPkXkkabunUrf9X0BGPTCIMbXH6/iKSIiSabyKSIPNXXvVPoF9APg7WpvM85vnIqniIg8EZVPEXmgyXsmxxfPd6q/wxjfMSqeIiLyxFQ+ReQ+E3+ayOvfvw7AezXe47N6n6l4iohIslD5FJF7TNg9gTc2vAHA4BqDGV13tIqniIgkG5VPEYn35e4vGbBxAADvv/g+n9T9RMVTRESSlcqniADwxa4vGLhxIAD/qfkfRtUZpeIpIiLJTuVTRPh85+cMChwEwAcvfcBIn5EqniIikiJUPkXSubE7xvJ20NsADKs1TMVTRERSlMqnSDo2ZscY3t30LgDDaw1neO3h1gYSEZE0T+VTJJ369MdPeW/TewCMqD2CYbWHWZxIRETSAxerA4iI/X2y/ROGbhkKwEc+H/Gfl/5jcSIREUkvVD5F0pmPf/iY/wSbZXOUzyiGvjTU4kQiIpKeqHyKpCMfbfuID7d+CMAndT5hSM0hFicSEZH0Rvt8iqQTI7aOiC+eo+uOVvEUERFLaM2nSDowfOtwRmwbAcBn9T7j3RrvWpxIRETSK5VPkTTMMAyGbx3OyB9GAjDWdyxvV3/b4lQiIpKeqXyKpFGGYfBh8IeM2j4KgHG+43ir+lsWpxIRkfRO5VMkDTIMg/9s+Q+f/PgJAOP9xjOw2kCLU4mIiKh8iqQ5hmHw/ub3+XTHpwB8Uf8LBrwwwNpQIiIi/6PyKZKGGIbBkM1D+GzHZwBMaDCBN6q+YXEqERGRf6h8iqQRhmHw3qb3GLtzLAATG07k9edftziViIjIvVQ+RdIAwzB4J+gdPt/1OQCTGk7itedfsziViIjI/VQ+RRycYRi8FfgWX+z+AoDJjSbT77l+FqcSERF5MJVPEQdmGAaDNg7iy5++BGBq46n0rdLX2lAiIiKPoPIp4qAMw2DAhgF8tecrAKY1nkafKn0sTiUiIvJoKp8iDsgwDN7c8CYT90wE4Jsm3/By5ZctTiUiIvJ4Kp8iDsYwDPp/35/Jeydjw8a3Tb+lV6VeVscSERFJEJVPEQcSZ8TxesDrTN03FRs2pjebTs+KPa2OJSIikmAqnyIOIs6I47X1rzFt/zRs2JjRbAY9KvawOpaIiEiiqHyKOIA4I45+6/vx9f6vsWHju+bf0a1CN6tjiYiIJJrKp0gqF2fE0XddX7498C02bMxuMZuu5btaHUtERCRJVD5FUrE4I44+a/sw/eB0nGxOzG4xmy7lulgdS0REJMlUPkVSqTgjjpfXvMzMQzNxsjkxp8UcOpfrbHUsERGRJ6LyKZIKxcbF0nttb2YdmoWTzYl5LefRsWxHq2OJiIg8MZVPkVQmNi6WXmt6Mfvn2TjbnJnfaj7ty7S3OpaIiEiyUPkUSUVi42LpuaYnc36eg7PNmQWtF9Du2XZWxxIREUk2Kp8iqURsXCzdV3dn3i/zcLY5s7D1Qto+29bqWCIiIslK5VMkFYiNi6Xbqm7MPzwfZ5szi9osos0zbayOJSIikuxUPkUsFhMXQ7dV3VhweAEuTi4sar2I1s+0tjqWiIhIilD5FLFQTFwMXVd2ZdGvi3BxcmFJmyW0LN3S6lgiIiIpRuVTxCIxcTF0WdGFxUcW4+LkwtK2S2lRqoXVsURERFKUyqeIBaJjo+m8ojNLjy7F1cmVpW2X0rxUc6tjiYiIpDiVTxE7i46NptOKTiw7ugxXJ1eWtVtGs5LNrI4lIiJiFyqfInYUHRtNx+UdWX5sOW7Obixvt5wmTzexOpaIiIjdqHyK2ElUbBQdlnVg5fGVuDm7saLdCho/3djqWCIiInal8iliB1GxUbRf1p5Vx1fh5uzGyvYraVSikdWxRERE7E7lUySFRcVG0W5pO1b/thp3Z3dWdVhFg6caWB1LRETEEiqfIikoMiaStkvbsvbEWtyd3VndYTX1n6pvdSwRERHLqHyKpJDImEjaLG3DuhPr8HDxYHWH1fgV97M6loiIiKVUPkVSQGRMJK2XtGb97+vxcPFgTYc1+Bb3tTqWiIiI5VQ+RZJZREwErZe0JuD3ADxcPFjbcS31itWzOpaIiEiqoPIpkowiYiJotbgV35/8ngwuGVjbcS11i9W1OpaIiEiqofIpkkwiYiJosagFG09tJINLBtZ3Wo9PUR+rY4mIiKQqKp8iyeBO9B1aLG5B4KlAPF09Wd9pPbWL1LY6loiISKqj8inyhO5E36H5ouYEnQ7C09WTgE4B1CpSy+pYIiIiqZLKp8gTCI8Op/mi5mw6vYmMrhkJ6BzAS4VfsjqWiIhIqqXyKZJE4dHhNF3YlC1/bMHLzYvvO3/Pi4VetDqWiIhIqqbyKZIEYVFhNF3YlOA/g/Fy82JD5w3UKFTD6lgiIiKpnsqnSCKFRYXRZGETtv65lUxumdjQZQPVC1a3OpaIiIhDUPkUSYTbUbdpvKAxP/z1A5ncMrGxy0aqFaxmdSwRERGHofIpkkC3o27TaH4jtp/ZTmb3zGzsspEXCrxgdSwRERGHovIpkgChkaE0WtCIH8/8SGb3zAR2CaRqgapWxxIREXE4Kp8ijxEaGUrD+Q3ZcXYHWdyzENg1kOfzP291LBEREYek8inyCCGRITSc35CdZ3eS1SMrQV2DqJKvitWxREREHJbKp8hDhESG0GBeA3b9vYusHlnZ1HUTlfNVtjqWiIiIQ1P5FHmAWxG3aDC/Abv/3k02j2xs8t9EpbyVrI4lIiLi8FQ+Rf7PrYhb1J9Xn5/O/UT2DNnZ1HUTFfNWtDqWiIhImqDyKfIvNyNuUn9effac20P2DNnZ7L+ZCnkqWB1LREQkzVD5FPmfmxE38Zvrx97ze8mRIQeb/TdTPk95q2OJiIikKSqfIsCNOzfwnevL/gv7yemZk83+mynnXc7qWCIiImmOyqeke9fvXMd3ri8HLhwgp2dOtvhvoax3WatjiYiIpEkqn5KuXb9znXpz6nHw4kFyeeZiS7ctlMldxupYIiIiaZbKp6Rb18KvUW9uPQ5dPETujLnZ4r+FZ3M/a3UsERGRNE3lU9Klq+FXqTenHj9f+pncGXMT3C2YZ3I9Y3UsERGRNM/J6gAi9nY1/Cp159Tl50s/453RW8VTRETEjrTmU9KVK2FXqDunLocvH44vnqVzlbY6loiISLqh8inpxr+LZx6vPAR3C6ZUzlJWxxIREUlXtNld0oXLYZepM6cOhy8fJq9XXrZ226riKSIiYgGt+ZQ079LtS9SZU4ejV46SL1M+grsF83SOp62OJSIiki4lac3nlClTKFq0KB4eHlSuXJnt27c/9L4rVqzA19eXXLlykTlzZqpVq8bGjRuTHFgkMf5dPPNnys/WbltVPEVERCyU6PK5ePFiBgwYwNChQzl48CA1a9akYcOGnDlz5oH3/+GHH/D19SUgIID9+/fj4+ND06ZNOXjw4BOHF3mUG9E38J3v+0/x7L6VEjlKWB1LREQkXUv0Zvfx48fTq1cvevfuDcCXX37Jxo0bmTp1KqNHj77v/l9++eU91z/55BNWr17N2rVrqVixYtJSizzGhdsX+ODkB/wd+TcFMhcguFswT2V/yupYIiIi6V6iymdUVBT79+9n8ODB99zu5+fHzp07E/QccXFxhIaGkj179ofeJzIyksjIyPjrISEhAERHRxMdHZ2YyElydxn2WJYkvwu3L+A7z9csnpkKENQ5iMKZCms8HYi+g45PY+j4NIaOz95jmNDlJKp8Xr16ldjYWLy9ve+53dvbm4sXLyboOT7//HPCwsJo167dQ+8zevRoRowYcd/tgYGBeHp6JibyEwkKCrLbsiR5XI++zn9O/ofzkefJ5ZqL/xT4D7/t+o3f+M3qaJIE+g46Po2h49MYOj57jWF4eHiC7peko91tNts91w3DuO+2B1m4cCHDhw9n9erV5M6d+6H3GzJkCIMGDYq/HhISQsGCBfHz8yNz5sxJiZwo0dHRBAUF4evri6ura4ovT5LHudBz+M735XzkeQplLsTQ/EPp0qSLxtAB6Tvo+DSGjk9j6PjsPYZ3t1Q/TqLKZ86cOXF2dr5vLefly5fvWxv6/xYvXkyvXr1YunQp9erVe+R93d3dcXd3v+92V1dXu34B7L08Sbq/Q/7Gd74vJ6+fpHCWwgR1DuLozqMaQwen8XN8GkPHpzF0fPYaw4QuI1FHu7u5uVG5cuX7Vt8GBQVRvXr1hz5u4cKFdO/enQULFtC4cePELFLksc7eOkvtWbU5ef0kRbIWYVv3bRTJWsTqWCIiIvIAid7sPmjQILp27UqVKlWoVq0a33zzDWfOnKFv376Aucn83LlzzJkzBzCLp7+/PxMmTOCFF16IX2uaIUMGsmTJkowvRdKjM7fO4DPbh9M3TlM0a1GCuwVTOKsOLhIREUmtEl0+27dvz7Vr1xg5ciQXLlygTJkyBAQEULhwYQAuXLhwz5yfX3/9NTExMbz22mu89tpr8bd369aNWbNmPfkrkHTrzK0z1J5Vmz9u/kGxbMUI7hZMoSyFrI4lIiIij5CkA4769etHv379Hvi7/y+UW7duTcoiRB7pr5t/4TPbhz9u/kHxbMUJ7hZMwSwFrY4lIiIij6Fzu4vD+fPmn/jM9uHPm39SPFtxtnbfSoHMBayOJSIiIgmg8ikO5Y8bf+Az24e/bv1FiewlCO4WTP7M+a2OJSIiIgmU6HO7i1jl9I3T1J5dW8VTRETEgWnNpziE0zdOU3tWbc6GnOXpHE8T3C2YfJnyWR1LREREEknlU1K9U9dPUXt2bf4O+ZuSOUoS3C2YvJnyWh1LREREkkDlU1K1k9dPUntWbc6FnqNUzlIEdwsmj1ceq2OJiIhIEmmfT0m1fr/2e3zxLJ2ztIqniIhIGqA1n5Iqnbh2Ap/ZPpwPPc8zuZ5hi/8WvL28rY4lIiIiT0jlU1Kd367+hs9sHy7cvsCzuZ5lS7ct5M6Y2+pYIiIikgy02V1SleNXj8cXzzK5y6h4ioiIpDFa8ympxrErx6gzpw4Xb1+kbO6ybPbfTK6MuayOJSIiIslI5VNShaNXjlJndh0uhV2inHc5NvtvJqdnTqtjiYiISDLTZnex3JHLR/CZ7cOlsEuU9y6v4ikiIpKGqXyKpX69/Ct15tThcthlKuSpoOIpIiKSxmmzu1jm8KXD1J1TlyvhV6iYpyKb/DeRPUN2q2OJiIhICtKaT7HEL5d+oc6cOlwJv0KlvJVUPEVERNIJrfkUu/v54s/UnVOXa3euUTlvZYK6BpEtQzarY4mIiIgdaM2n2NWhi4fii2eVfFXY5L9JxVNERCQdUfkUuzl44WB88Xwu33MEdQ0iq0dWq2OJiIiIHWmzu9jFgQsHqDenHjcibvB8/ucJ7BJIFo8sVscSERERO9OaT0lx+8/vjy+eVfNXVfEUERFJx1Q+JUXtO7+PenPN4lmtQDUCu6p4ioiIpGcqn5Ji9p7bi+9cX25G3KR6weps6LKBzO6ZrY4lIiIiFtI+n5Ii9pzbg99cP25F3qJGwRp83/l7MrlnsjqWiIiIWExrPiXZ/fT3T/jO9eVW5C1eLPSiiqeIiIjEU/mUZLX77934zfMjJDKEmoVqqniKiIjIPbTZXZLNrrO7qD+vPqFRobxU+CXWd1qPl5uX1bFEREQkFdGaT0kWO8/uxG+eH6FRodQuUpuATgEqniIiInIflU95YjvO7KD+vPrcjrqNTxEf1nVcR0a3jFbHEhERkVRIm93liWz/azsN5zckLDqMOkXrsLbjWjxdPa2OJSIiIqmU1nxKkv3w1w/xxbNu0boqniIiIvJYKp+SJNv+3Eaj+Y0Iiw6jXrF6Kp4iIiKSICqfkmhb/9xKowVm8fQt5suaDmvI4JrB6lgiIiLiAFQ+JVGC/wim0fxGhEeHU794fVZ3WK3iKSIiIgmm8ikJtuWPLTRe0Jg7MXdo8FQDVnVYpeIpIiIiiaLyKQmy6fSm+OLZ8KmGrGy/Eg8XD6tjiYiIiINR+ZTHCjoVRNOFTYmIiaBxicYqniIiIpJkKp/ySIGnAmm2qFl88VzebjnuLu5WxxIREREHpfIpD7Xx5EaaLTSLZ9Onm6p4ioiIyBNT+ZQH2nByA80XNScyNpLmJZuzrN0yFU8RERF5Yiqfcp+A3wPii2eLUi1Y0nYJbs5uVscSERGRNEDlU+6x/sR6Wi5uSVRsFC1LtWRxm8UqniIiIpJsVD4l3roT6+KLZ+vSrVU8RUREJNmpfAoAa39bS6vFrYiOi6bNM21Y2Hohrs6uVscSERGRNEblU1h9fDWtl7QmOi6ats+0ZUGrBSqeIiIikiJUPtO5VcdX0WZpG6Ljomn/bHsWtFbxFBERkZSj8pmOrTy2krZL2xITF0OHMh2Y12oeLk4uVscSERGRNEzlM51acWwF7Za1IyYuho5lOjK35VwVTxEREUlxKp/p0LKjy2i31Cyenct2Zk7LOSqeIiIiYhcqn+nM0iNL6bCsA7FGLF3KdWF2i9kqniIiImI3Kp/pyOJfF9NxeUdijVi6luvKrOazcHZytjqWiIiIpCMqn+nEol8X0XlFZ2KNWLqV78Z3zb9T8RQRERG7U/lMBxYcXhBfPHtU6MGMZjNUPEVERMQSKp9p3Pxf5tN1ZVfijDh6VujJ9GbTVTxFRETEMiqfadi8X+bhv8qfOCOO3hV7822zb3GyachFRETEOmoiadScn+fgv9Isni9Xepmvm36t4ikiIiKWUxtJg2Yfmk33Vd0xMOhTuQ/TmkxT8RQREZFUQY0kjZl1aBY9VvfAwODVKq8ypfEUFU8RERFJNdRK0pCZB2fSc3VPDAz6VenH5EaTVTxFREQkVVEzSSNmHJhBrzW9MDB4/bnXmdRoEjabzepYIiIiIvdQ+UwDvt3/Lb3X9gag//P9+arhVyqeIiIikiqpfDq4b/Z/wyvrXgHgzapvMqHBBBVPERERSbVUPh3YtH3T6LOuDwADqg7gi/pfqHiKiIhIqqby6aCm7p3Kq+tfBWDQC4MYX3+8iqeIiIikeiqfDmjynsn0C+gHwFvV3mKc3zgVTxEREXEIKp8OZtKeSbz+/esAvFP9Hcb6jlXxFBEREYeh8ulAJv40kf7f9wfg3erv8lm9z1Q8RURExKGofDqICbsn8MaGNwAYXGMwn9b7VMVTREREHI7KpwP4YtcXDNg4AID3X3yfT+p+ouIpIiIiDknlM5Ubv2s8gwIHATC05lBG1Rml4ikiIiIOS+UzFft85+e8FfgWAB+89AEf+Xyk4ikiIiIOTeUzlRq7YyxvB70NwIcvfciI2iNUPEVERMThuVgdQO43ZscY3tv0HgDDaw1nWO1hFicSERERSR5a85nKfPrjp/HFc0TtESqeIiIikqaofKYin2z/hCGbhwAwsvZIPqz1ocWJRERERJKXNrunEh//8DH/Cf4PAKN8RjH0paEWJxIRERFJfiqfqcBH2z7iw63mWs5P6nzCkJpDLE4kIiIikjK02d1iI7aOiC+eo+uOVvEUERGRNE1rPi00fOtwRmwbAcBn9T7j3RrvWpxIREREJGWpfFrAMAyGbx3OyB9GAjDWdyxvV3/b4lQiIiIiKU/l084Mw+DD4A8ZtX0UAON8x/FW9bcsTiUiIiJiHyqfdmQYBh8Ef8DH2z8GYLzfeAZWG2hxKhERERH7Ufm0E8MwGLplKKN/HA3AF/W/YMALA6wNJSIiImJnKp92YBgGQzYP4bMdnwEwocEE3qj6hsWpREREROxP5TOFGYbBe5veY+zOsQBMbDiR159/3eJUIiIiItZQ+UxBhmHwbtC7jNs1DoBJDSfx2vOvWZxKRERExDoqnynEMAzeDnyb8bvHAzC50WT6PdfP4lQiIiIi1lL5TAGGYTBo4yC+/OlLAKY2nkrfKn2tDSUiIiKSCqh8JjPDMBi4cSATfpoAwNdNvuaVyq9YnEpEREQkdVD5TEaGYfDmhjeZuGciAN80+YaXK79scSoRERGR1EPlM5kYhkH/7/szee9kbNj4tum39KrUy+pYIiIiIqmKymcyiDPieD3gdabum4oNG9ObTadnxZ5WxxIRERFJdVQ+n1CcEcdr619j2v5p2LAxo9kMelTsYXUsERERkVRJ5fMJxBlx9Fvfj6/3f40NG981/45uFbpZHUtEREQk1VL5TKI4I46+6/ry7YFvsWFjVotZ+Jf3tzqWiIiISKqm8pkEcUYcfdb2YfrB6TjZnJjdYjZdynWxOpaIiIhIqqfymUhxRhwvr3mZmYdm4mRzYk6LOXQu19nqWCIiIiIOQeUzEWLjYum9tjezDs3CyebE3JZz6VS2k9WxRERERByGymcCxcbF0mtNL2b/PBsnmxPzW82nQ5kOVscSERERcSgqnwkQGxdLzzU9mfPzHJxtzsxvNZ/2ZdpbHUtERETE4ah8PkZsXCw9Vvdg7i9zcbY5s7D1Qto+29bqWCIiIiIOySkpD5oyZQpFixbFw8ODypUrs3379kfef9u2bVSuXBkPDw+KFSvGtGnTkhTW3mLjYum2qlt88VzUZpGKp4iIiMgTSHT5XLx4MQMGDGDo0KEcPHiQmjVr0rBhQ86cOfPA+//xxx80atSImjVrcvDgQd5//33eeOMNli9f/sThU1KsEUuPtT2Yf3g+Lk4uLG6zmDbPtLE6loiIiIhDS3T5HD9+PL169aJ3796ULl2aL7/8koIFCzJ16tQH3n/atGkUKlSIL7/8ktKlS9O7d2969uzJuHHjnjh8SomJi+HLv75k0ZFFuDi5sKTNElo/09rqWCIiIiIOL1H7fEZFRbF//34GDx58z+1+fn7s3LnzgY/ZtWsXfn5+99xWv359ZsyYQXR0NK6urvc9JjIyksjIyPjrISEhAERHRxMdHZ2YyIkWExeD/yp/tt/cjouTCwtbLqTJU01SfLmSvO6Ol8bNMWn8HJ/G0PFpDB2fvccwoctJVPm8evUqsbGxeHt733O7t7c3Fy9efOBjLl68+MD7x8TEcPXqVfLmzXvfY0aPHs2IESPuuz0wMBBPT8/ERE60P+78wZoTa3CxufBO4XdwPeVKwKmAFF2mpJygoCCrI8gT0Pg5Po2h49MYOj57jWF4eHiC7peko91tNts91w3DuO+2x93/QbffNWTIEAYNGhR/PSQkhIIFC+Ln50fmzJmTEjlRSpwswc69OxnaZugD18xK6hcdHU1QUBC+vr4aQwek8XN8GkPHpzF0fPYew7tbqh8nUeUzZ86cODs737eW8/Lly/et3bwrT548D7y/i4sLOXLkeOBj3N3dcXd3v+92V1dXu7x5fk/5EXMixm7Lk5SjMXRsGj/HpzF0fBpDx2evMUzoMhJ1wJGbmxuVK1e+b/VtUFAQ1atXf+BjqlWrdt/9AwMDqVKlij7MIiIiIulMoo92HzRoENOnT2fmzJkcO3aMgQMHcubMGfr27QuYm8z9/f3j79+3b1/++usvBg0axLFjx5g5cyYzZszg7bffTr5XISIiIiIOIdH7fLZv355r164xcuRILly4QJkyZQgICKBw4cIAXLhw4Z45P4sWLUpAQAADBw5k8uTJ5MuXj6+++orWrTV1kYiIiEh6k6QDjvr160e/fv0e+LtZs2bdd1utWrU4cOBAUhYlIiIiImlIkk6vKSIiIiKSFCqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3Kp8iIiIiYjcqnyIiIiJiNyqfIiIiImI3LlYHSAjDMAAICQmxy/Kio6MJDw8nJCQEV1dXuyxTkpfG0LFp/ByfxtDxaQwdn73H8G5Pu9vbHsYhymdoaCgABQsWtDiJiIiIiDxKaGgoWbJkeejvbcbj6mkqEBcXx/nz58mUKRM2my3FlxcSEkLBggU5e/YsmTNnTvHlSfLTGDo2jZ/j0xg6Po2h47P3GBqGQWhoKPny5cPJ6eF7djrEmk8nJycKFChg9+VmzpxZXzgHpzF0bBo/x6cxdHwaQ8dnzzF81BrPu3TAkYiIiIjYjcqniIiIiNiNyucDuLu7M2zYMNzd3a2OIkmkMXRsGj/HpzF0fBpDx5dax9AhDjgSERERkbRBaz5FRERExG5UPkVERETEblQ+RURERMRuVD5FRERExG7SbfmcMmUKRYsWxcPDg8qVK7N9+/ZH3n/btm1UrlwZDw8PihUrxrRp0+yUVB4mMWO4YsUKfH19yZUrF5kzZ6ZatWps3LjRjmnl/yX2O3jXjh07cHFxoUKFCikbUB4rsWMYGRnJ0KFDKVy4MO7u7hQvXpyZM2faKa08SGLHcP78+ZQvXx5PT0/y5s1Ljx49uHbtmp3Syr/98MMPNG3alHz58mGz2Vi1atVjH5NquoyRDi1a9N927iikyfYNA/jt3EY2SKjIhoNC0MygqMasSQghCwqkg0gowqCgEdEqKhZFJgRRkZBhHYjYifZJhtCBhTsomRWFNiFaYDgLRlmsEFYWpV7fQf/5b26f+b7ft2eDXT/YgY/P2DUuXr33bnv/gslkQnNzM4LBIDweDywWC96+fZt0fygUwvz58+HxeBAMBtHc3AyTyYTOzk7FySlGa4cejwcXL17Es2fPMDQ0hFOnTsFkMuH58+eKkxOgvb+YsbExFBUVweVyYc2aNWrCUlJ6OqyurkZ5eTl8Ph9GRkbw9OlTPHr0SGFq+p3WDv1+PwwGA65evYpQKAS/349Vq1Zh+/btipMTAHR3d+P06dO4c+cORARdXV2z7s+kWSYrh0+HwwG32x23VlpaCq/Xm3T/yZMnUVpaGrd24MABbNiwIWUZaXZaO0ymrKwM9fX1/3U0mgO9/dXU1ODMmTOoq6vj8JlmWju8d+8e8vPz8enTJxXxaA60dnj58mUUFRXFrTU2NsJms6UsI83NXIbPTJplsu5t9x8/fsjAwIC4XK64dZfLJY8fP056nydPniTs37Jli/T398vPnz9TlpWS09PhTFNTUxKNRmXhwoWpiEiz0Ntfa2urDA8PS11dXaoj0h/o6fDu3btit9vl0qVLUlhYKCUlJXL8+HH59u2bisg0g54OnU6nhMNh6e7uFgDy4cMH6ezslG3btqmITP9SJs0yRqWPlgEikYhMTk5KQUFB3HpBQYGMjo4mvc/o6GjS/RMTExKJRMRqtaYsLyXS0+FMV65cka9fv8rOnTtTEZFmoae/169fi9frFb/fL0Zj1v3Zyjh6OgyFQtLX1yfz5s2Trq4uiUQicvDgQfn8+TM/95kGejp0Op3S1tYmNTU18v37d5mYmJDq6mq5du2aisj0L2XSLJN1Zz5jcnJy4n4GkLD2p/3J1kkdrR3G3Lp1S86dOycdHR2yZMmSVMWjP5hrf5OTk7Jr1y6pr6+XkpISVfFoDrQcg1NTU5KTkyNtbW3icDhk69at0tDQIDdv3uTZzzTS0mEwGJTDhw/L2bNnZWBgQO7fvy8jIyPidrtVRKX/QKbMMll3CmHx4sWSm5ub8Mru48ePCa8IYpYuXZp0v9FolEWLFqUsKyWnp8OYjo4O2bdvn9y+fVuqqqpSGZP+gdb+otGo9Pf3SyAQkEOHDonIr0EGgBiNRunp6ZHNmzcryU6/6DkGrVarFBYWSn5+/vTaypUrBYCEw2EpLi5OaWaKp6fDCxcuSEVFhZw4cUJERFavXi0Wi0U2bdok58+f57uAGS6TZpmsO/NpNptl/fr14vP54tZ9Pp84nc6k99m4cWPC/p6eHrHb7WIymVKWlZLT06HIrzOee/fulfb2dn5GKY209rdgwQJ58eKFDA4OTt/cbresWLFCBgcHpby8XFV0+h89x2BFRYW8e/dOvnz5Mr02NDQkBoNBbDZbSvNSIj0djo+Pi8EQPzbk5uaKyP/PoFHmyqhZRvlXnDJA7PISLS0tCAaDOHLkCCwWC968eQMA8Hq92LNnz/T+2OUJjh49imAwiJaWFl5qKc20dtje3g6j0Yimpia8f/9++jY2Npaup5DVtPY3E7/tnn5aO4xGo7DZbNixYwdevnyJ3t5eFBcXY//+/el6CllPa4etra0wGo24fv06hoeH0dfXB7vdDofDka6nkNWi0SgCgQACgQBEBA0NDQgEAtOXysrkWSYrh08AaGpqwrJly2A2m7Fu3Tr09vZO/662thaVlZVx+x8+fIi1a9fCbDZj+fLluHHjhuLENJOWDisrKyEiCbfa2lr1wQmA9mPwdxw+M4PWDl+9eoWqqirk5eXBZrPh2LFjGB8fV5yafqe1w8bGRpSVlSEvLw9WqxW7d+9GOBxWnJoA4MGDB7P+X8vkWSYH4LlyIiIiIlIj6z7zSURERETpw+GTiIiIiJTh8ElEREREynD4JCIiIiJlOHwSERERkTIcPomIiIhIGQ6fRERERKQMh08iIiIiUobDJxEREREpw+GTiIiIiJTh8ElEREREynD4JCIiIiJl/gbTHwDCR/n49gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = g_1\n",
    "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(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(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g(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(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(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g(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": 6,
   "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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = f_2\n",
    "g = g_2\n",
    "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(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(x))\n",
    "plot(x, x)\n",
    "grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = 10\n",
    "g = g_2\n",
    "# Start at left\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "x = np.linspace(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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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\n",
      "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(x), \"r\")\n",
    "for k in range(iterations):\n",
    "    g_x_k = g(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(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": 10,
   "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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\n",
      "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(x), \"r\")\n",
    "for k in range(iterations):\n",
    "    g_x_k = g(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(x_k)\n",
    "    #Connect to the new x_k on the line y = x:\n",
    "    plot([x_k, g(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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
