{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Implicit Methods: Adams-Moulton"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "% TO DO\n",
    "\n",
    "% - Complete {prf:ref}`ode-ivp-7-2` of solving a stiff linear system, compared to solving with the same-degree Runge-Kutta method.\n",
    "\n",
    "% - Change the stiff examples to using the damped mass-spring with $K = D $ and $M \\ll 1$ (near the singular perturbation limit.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.7 *Multistep Methods* in {cite}`Sauer`.\n",
    "- Section 5.6 *Multistep Methods* in {cite}`Burden-Faires`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "So far, most methods we have seen give the new approximation value with an explicit formula for it in terms of previous and so already known) values;\n",
    "the general **explicit s-step method** seen in\n",
    "{doc}`ODE-IVP-7-multi-step-methods-Adams-Bashforth`\n",
    "was\n",
    "\n",
    "$$U_{i} = \\phi(U_{i-1}, \\dots U_{i-s+}, h), \\quad s > 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we briefly saw two **implict methods** back in {doc}`ODE-IVP-2-Runge-Kutta`,\n",
    "in the process of deriving the explicit trapezoid and explicit midpoint methods:\n",
    "the **Implicit Trapezoid Method** (or just the **Trapezoid Method**, as this is the real thing, before the further approximations were used to get an explicit formula)\n",
    "\n",
    "$$U_{i+1} = U_i + h \\frac{f(t_i, U_i) + f(t_{i+1}, U_{i+1}))}{2}$$\n",
    "\n",
    "and the **Implicit Midpoint Method**\n",
    "\n",
    "$$U_{i+1} = U_i + h f\\left( t + h/2, \\frac{U_i + U_{i+1}}{2} \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are clearly not as simple to work with as explicit methods, but the equation solving can often be done.\n",
    "In particular for linear differential equations, these give linear equations for the unknown $U_{i+1}$, so even for systems,\n",
    "they can be solved by the method seen earlier in these notes.\n",
    "\n",
    "Another strategy is noting that these are fixed point equations, so that fixed point iteration can be used.\n",
    "The factor $h$ at right helps; it can be shown that for small enough $h$ (how small depends on the function $f$),\n",
    "these are contraction mappings and so fixed point iteration works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This idea can be combined with linear multistep methods, and one important case is modifying the Adams-Bashforth method by allowing\n",
    "$F_i = f(t_i, U_i)$ to appear at right: this gives the Adams-Moulton form\n",
    "\n",
    "$$U_{i} = U_{i-1} + h (b_0 f(t_{i-s}, U_{i-s}) + \\dots + b_{s} f(t_{i}, U_{i}))$$\n",
    "\n",
    "where the only change from Adams-Bashforth methods is that $f(t_{i}, U_{i})$ term.\n",
    "\n",
    "The coefficients can be derived much as for Adams-Bashforth methods, by the method of undetermined coefficients;\n",
    "one valuable difference is that there at now $s+1$ undetermined coefficients, so all error terms up to $O(h^s)$ can be cancelled\n",
    "and the error made $O(h^{s+1})$: one degree higher."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $s=1$ case is familiar:\n",
    "\n",
    "$$U_{i} = U_{i-1} + h (b_0 f(t_{i-1}, U_{i-1}) + b_{1} f(t_{i}, U_{i}))$$\n",
    "\n",
    "and as symmetry suggests, the solution is $b_0 = b_1 = 1/2$, giving\n",
    "\n",
    "$$U_{i} = U_{i-1} + h \\frac{f(t_{i-1}, U_{i-1}) + f(t_{i}, U_{i})}{2}$$\n",
    "\n",
    "which is the (implicit) trapzoid rule in the new shifted indexing.\n",
    "\n",
    "This is much used for numerical solution of partial differential equations of evoluton type (after first approximating by a large system of ordinary differnetial equations).\n",
    "In that context it is often known as the **Crank-Nicholson method**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can actually start at $s=0$; the first few Adams-Moulton methods are:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "s = 0: b_0 &= 1\n",
    "\\\\\n",
    " &U_{i} - h f(t_i, U_i)) = U_{i-1} \\qquad &\\text{The backward Euler method}\n",
    "\\\\\n",
    "s = 1: b_0 &= b_1 = 1/2\n",
    "\\\\\n",
    " &U_{i} - \\frac{h}{2} f(t_i, U_i) = U_{i-1} + \\frac{h}{2} (F_{i-1} ) \\qquad &\\text{The (implicit) trapezoid method}\n",
    "\\\\\n",
    "s = 2: b_0 &= -1/12, b_1 = 8/12, b_2 = 5/12\n",
    "\\\\\n",
    "&U_{i} - \\frac{5h}{12}f(t_i, U_i) = U_{i-1} + \\frac{h}{12} (-F_{i-2} + 8 F_{i-1})\n",
    "\\\\\n",
    "s = 3: b_0 &= 1/24, b_1 = -5/24, b_2 = 19/24, b_3 = 9/24\n",
    "\\\\\n",
    "&U_{i} - \\frac{9h}{24}f(t_i, U_i) = U_{i-1} + \\frac{h}{24}(F_{i-3} -5F_{i-2} + 19F_{i-1})\n",
    "\\end{align*}\n",
    "\n",
    "The use of $F_{i-k}$ notation emphasizes that these earlier values of $F_{i-k} = f(t_{i-k}, U_{i-k})$ are known from a previous step,\n",
    "so can be stored for reuse."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The backward Euler method has not been mentioned before; it comes from using the backward counterpart of the forward difference approximation of the derivative:\n",
    "\n",
    "$$u'(t) \\approx \\frac{u(t) - u(t-h)}{h}$$\n",
    "\n",
    "Like Euler's method it is only first order accurate, but it has excellent *stability* properties, which makes it useful in some situations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} An equation with fast and slow time scales\n",
    "\n",
    "The equation\n",
    "\n",
    "$$ y'' + 101 y' + 100y = 0, \\quad y(0) = y_0, y'(0) = v_0 $$\n",
    "\n",
    "has the general solution\n",
    "\n",
    "$$ y(t) = A e^{-t} + B e^{-100t} $$\n",
    "\n",
    "With explicit methods, the time-step size has to be smal enought to resove the fast time scale, so $h$ of order $1/100$,\n",
    "but the second term decays very rapdly, and with some equations like this it is enough to resolve the dominant behavior of the $e^{-t}$ term,\n",
    "which some implict method can resolve with far larger step sizes.\n",
    "\n",
    "Let us compare how this is handled by the implicit trapezoid and explicit trapezoid methods.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system form is\n",
    "\n",
    "$$\n",
    "\\frac{d}{dt} \\left[\\begin{array}{c} u_1 \\\\ u_2 \\end{array}\\right] =\n",
    "\\left[\\begin{array}{cc} 0 & 1 \\\\ -100 & -101 \\end{array}\\right] \\left[\\begin{array}{c} u_1 \\\\ u_2 \\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trapezoid method is thus\n",
    "\n",
    "$$\n",
    "U_i - \\frac{h}{2}\\left[\\begin{array}{cc} 0 & 1 \\\\ -100 & -101 \\end{array}\\right] U_i =\n",
    "U_{i-1} + \\frac{h}{2}\\left[\\begin{array}{cc} 0 & 1 \\\\ -100 & -101 \\end{array}\\right]\n",
    "$$\n",
    "\n",
    "or"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left[\\begin{array}{cc} 1 & -h/2 \\\\ 50h & 1 + 101h/2 \\end{array}\\right] U_i\n",
    "=\n",
    "\\left[\\begin{array}{cc} 1 & h/2 \\\\ -50h & 1 - 101h/2 \\end{array}\\right] U_{i-1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"NumericalMethods.jl\")\n",
    "using .NumericalMethods: explicittrapezoid_system, approx3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "function f_fast_slow(t, u)\n",
    "    return [u[2], -K*u[1] - (K+1)*u[2]]\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "function y_fast_slow(t; t_0, y_0, v_0, K)\n",
    "    B = -(y_0 + v_0)/(K-1)\n",
    "    A = y_0 - B\n",
    "    return A*exp(-(t-t_0)) + B*exp(-K*(t-t_0))\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 100.0\n",
    "y_0 = 1.0\n",
    "v_0 = 0.0\n",
    "u_0 = [y_0; v_0]\n",
    "a = 0.0\n",
    "b = 0.5;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 200  # explicit trapezoid works\n",
    "#n = 50  # explicit trapezoid works, barely\n",
    "\n",
    "h = (b-a)/n\n",
    "t = range(a, b, n+1)\n",
    "M = [(1)   (-h/2);\n",
    "     (50h) (1 + 101h/2)]\n",
    "N = [(1)    (h/2);\n",
    "     (-50h) (1 - 101h/2)]\n",
    "U = zeros(n+1, 2)\n",
    "U[1,:] = u_0\n",
    "for i in 1:n\n",
    "    U[i+1,:] = M\\(N*U[i,:])\n",
    "end\n",
    "\n",
    "Y = U[:,1]\n",
    "y = y_fast_slow.(t, t_0 = 0.0, y_0=y_0, v_0=v_0, K=K)\n",
    "figure(figsize=[10,3])\n",
    "title(\"With K=$K, by trapezoid with step size h=$(approx3(h))\")\n",
    "plot(t, Y, label=\"y computed\")\n",
    "plot(t, y, label=\"exact solution\")\n",
    "legend()\n",
    "grid(true)\n",
    "\n",
    "Yerror = y-Y\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error\")\n",
    "plot(t, Yerror)\n",
    "grid(true)\n",
    "\n",
    "n_middle = n ÷ 2\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error, second half\")\n",
    "plot(t[n_middle:end], Yerror[n_middle:end])\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare to the explicit trapezoid method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/pGPHjgkAYtu2bU+9jrKGyZX3faPJ+7g0Xbp0EY0bN35qneL3f1ltPSMjQ9StW1e4ubmJO3fuCCEe/a7Q1dUVX3zxhVrde/fuCUtLS9G7d+9ynTM4OFitfObMmQKASEtLU5V9/PHH5fqcf/x1L/68iIqKKnHuoUOHCj09vafGN3Xq1BJxFAsKChINGzZUPW7QoIHo0KFDiXqpqakCQInhz4+7ceOGsLCwEL6+vqKoqEhtW79+/cSaNWvEwYMHxaZNm0THjh0FADF+/Pinxk5UXhwmR2+M6tWrw9PTUzXE58CBA9DR0UGzZs0AAK1atcK+ffsAQPVv69atn+ucrVu3hrGxseqxhYUFateujWvXrpVr/w4dOkAul2P06NFlDo2ytrZGbGxsuX4eH0ajqaf1KD2+rbz1nvc8murRowf09fVVj42NjfHOO+/g4MGDKCoqAgD07dsXtWvXVg31Ah7NjFerVi306dPnqcffuXMnWrdurfpLffFPx44dATxqb8WaNWuGqVOnYt68efj000/x4YcfYtCgQaUe94MPPlB73Lt3b+jq6qraaHn9888/aN26NVxcXDTa70Vr06YNqlevXqJ87969aNeuHUxNTaGjowOZTIbvv/8eWVlZJWa9cnNzg6enp1pZv379kJOTgxMnTgB49Hq4u7ujcePGaq9Hhw4dyhzqd/bsWbz77rto2rQpli9frmpve/fuRbVq1dCzZ0+1+sXDzJ42TGvfvn1lxlsebdu2xZUrV5CUlIS8vDwcPnwYb7/9Nlq3bo2IiAgAj3qL5HJ5mT3H5fXuu++qPfbw8EBeXt5TZx2rX78+qlevju+++w5LlixBYmKiRufU5H0DlO99XJomTZogISEBwcHB2L17N3JycjSK88GDB+jcuTPy8vLwzz//wMzMDACwe/duFBYW4qOPPlKLX19fH61atSr3bIGlPfcA1H5XTJw4sVyf80uXLi1x/LI+O8v7mVre/Svy+X379m106tQJQgisX78eUqn6V9M1a9agX79+aNGiBd577z2EhYWhS5cu+Omnn8o1ZJjoWThMjt4orVu3xpw5c5Camop9+/bBx8cHRkZGAB4lQ7Nnz0Z2djb27dsHXV3d5/5yUdq4aLlcjocPH5Zr/3bt2mHEiBHo3r07Wrdujb1796qGFRXT09ND48aNy3W84qETmii+hqysrBLbbt++DYlEovpiULNmTeTl5SE3NxeGhoYl6j4rGatZsybi4+NLlD948AAFBQWoUaOGxvEXe3LoXXFZQUEB7t+/D1NTU8jlcgwbNgyzZ8/GrFmzoFAosGHDBowePRpyufypx8/IyMCOHTvKHLr25LTFH3zwASZMmID8/HzVfTnliVtXVxc1a9Ys9fV4mlu3bsHGxkajfV6Gx4fMFYuJiUFQUBDeeust/P7776p7R7Zt24apU6eWeL+U9VoC/99OMzIycOnSpXK/Hqmpqaqpfrds2QI9PT3VtqysLFhaWpb4Mle7dm3o6uo+9bXIysqCo6NjmfE+S7t27QA8SngcHR2hUCjQpk0bZGRkYMqUKaptzZo1g4GBQbmOWZYnP6+K2/zTPq9MTU1x4MABTJ06FWPHjsWdO3dgZWWFIUOGYPz48c8cyqnp+6Y87+PShISEoFq1avjzzz+xZMkS6OjooGXLlpgxYwZ8fX2fGmNhYSF69uyJCxcu4ODBg7C1tVWLH0CZQ2if/GJflvI893Z2duV6Dz/eTp/1+f2sz9TH939yKO2T+5f1uXT79m0AKPVcd+7cQfv27ZGSkoK9e/eWa/g4AHz44YfYuXMnjh07pkqciSqKyRC9UYqTof3792P//v2q+4MAqBKfgwcPqiZWKE6UtKljx474+++/0a1bN1VC9PgvpatXr5b6Zas0+/btK7EezbPUq1cPBgYGOHXqVIltp06dQv369VV/qS2+V+jUqVPw9/dX1UtPT0dmZibc3d2feq5GjRph3bp1SE9PV/vSU3zuZ+3/NOnp6aWW6enpqb3On376KX766ScsX74ceXl5KCwsLPNejMeZm5vDw8OjzPWfrK2tVf8vKirCBx98gOrVq0Mul2PQoEE4cuSI2hfwx2OsU6eO6nFhYSGysrJKTbSfplatWqob2rWptL8Or1u3DjKZDDt37lT7q39ZE26U9VoC///lzdzcHAYGBmXe72Jubq76f05ODjp16gSlUomwsLASX6hr1qyJo0ePQgihFv/NmzdRWFiodqwn1axZ86nxPouNjQ0aNmyIPXv2wMHBAb6+vjAzM0Pbtm0RHByMo0ePIjo6GpMmTSrX8V6G4vetEAInT55EaGgoJk+eDAMDA4wZM+ap+2ryvgHK/z5+kq6uLkaPHo3Ro0fj7t272LNnD8aOHYsOHTrg+vXrJf5487ihQ4fiv//+Q1hYWIkevuLXftOmTbC3ty/zGC/CJ598oppw5Gke75Eq/sw8deqU2u+74rLyfCYX13383qfCwkKcO3dO7f7KRo0a4a+//kJhYaHafUNlfX4XTw6UlJSE//77r9T7msoi/jexSnmTTaKnYTJEb5SWLVtCR0cHmzZtwpkzZzBz5kzVNlNTUzRu3BgrV67E1atXyzWM5fG/3j3vX2WfpkOHDvj777/RtWtXVUJUnCwUD5MrDycnJ43Prauri3feeQdbtmzBzJkzVcP+kpOTsW/fPowaNUpV9+2334a+vj5CQ0PVkqHiWZq6dev21HN17doV48ePx8qVK/Hdd9+p7W9gYFDiRndNFN8UX/xl+969e9ixYwdatGih1mNmZWWFXr16YdGiRSgoKMA777yjuqn/abp06YKwsDDUq1ev1GFgj/vhhx9w6NAhhIeHo1q1amjZsiW++eYbtZmtiq1Zs0atR23Dhg0oLCzUOKnt2LEjVq9ejfPnz2vUDsrTO1BW/fK+JyQSCXR1ddVeh4cPH2L16tWl1j9z5gwSEhLUvpiuXbsWxsbGqkWSu3TpgmnTpqFmzZpP/WNBQUEBunfvjqtXr+Lw4cOl/uW9bdu22LBhA7Zt24bu3buryletWqXaXpbWrVtj5syZpcZbXu3atcOGDRtga2uLzp07AwAaNmwIOzs7fP/991AoFKoepLJo+jpWhEQigaenJ+bOnYvQ0FDVkMXi85d2bk3eN0D538dPY2Zmhp49eyIlJQUjR47E1atXy5zkYPz48VixYgVWrlxZ6nPcoUMH6Orq4vLly3jvvffKdf6KmjhxYrkm3nh8aHadOnXQpEkT/Pnnn/j6669Vz1F0dDTOnz+PkSNHPvVY/v7+sLKyQmhoqNpQ4U2bNuH+/fvo0aOHqqx79+74/fffsXnzZrW6K1euhLW1tdrvhOJE6MqVK4iIiICXl9czr+txq1evhkwme66h30Qq2r1liejV8/PzExKJROjo6KitmyOEEKNGjRISiUQAEBEREWrbSptAofjm1x9++EFER0eL2NhYkZ+fL4Qoe22EJ2+wLk1Za+OEh4cLAwMD4ezsrJq04HmEhYWJjRs3qm7i79Wrl9i4caPYuHGj6kZ0IR4tumpkZCRatmwpwsLCxJYtW4S7u/tTF10dO3as2L9/v5g1a5aQy+UlFl1duXKl0NHRKTExQfGiq7NmzRL79+8XY8eOLXXR1eLXo6y1kYoVP5e2traiefPmYsuWLWLTpk3Cz89P6OrqisOHD5fY5+jRo6qbkffs2VOep1KkpqYKe3t74ezsLBYtWiT+++8/sWvXLrFw4ULRuXNn1QKo4eHhQiqVqsVdfLP4li1bVGXFN7Xb29uLb775RoSHh4u5c+cKIyMj4enpqWpnQpRvAoUbN24IKysrUbt2bTFv3jzx33//ic2bN4shQ4aIs2fPqj1Xj0+gUPw8Dxs2TERGRorY2Fi1SUGeVJH3xH///adaWDE8PFz89ddfwsfHRzRo0KDEDe329vaiTp06ws7OTixfvlz8888/4oMPPhAAxIwZM1T17t+/L7y8vISNjY2YPXu2iIiIELt37xa///676NWrl4iOjhZCPJokAP+7ufvJRR2LF099+PCh8PDwEMbGxmLOnDkiIiJC/PDDD0Imk4lOnTqpXcuT7++0tDRRq1YtUadOHbFixQoRFhYmPvjgA2Fra1vudYY2b96sao8HDhxQlQ8cOFAAENWrVy9x03lpbcLe3l44OTmJ3bt3i9jYWNXzWtY6Q8+aUEAIIXbs2CE6duwoli5dKiIiIkR4eLgYPny4ACB+++03tXhq164ttm/fLmJjY8W5c+eEEOV/31Tkffy4Ll26iDFjxohNmzaJAwcOiFWrVgkHBwdhb28vCgoKSr3eDRs2lLng54kTJ1THnjZtmtDV1RXDhg0TW7duFfv37xfr168XX331lfj++++fGldZ6wy9yHWo9u3bJ3R1dUX37t1FRESEWLNmjbC1tS2x6OrVq1eFjo6O+OSTT9T2X716tQAghg4dKvbt2yd+++03YWZmVuaiq9WrVxe//fab2Lt3rxgyZEiJCV9yc3NVv4fnz59f5vtOiEcTSQwYMECsXr1a7Nu3T6xfv14EBQUJAGLixInP/dwQCcFFV+kN9O233woAwtfXt8S2bdu2CQBCT09PLRkQovRfTvn5+WLw4MGiVq1aqiSq+Bfpy0iGhBBiz549wsDAQDg5OT33Ctz29vZlzkj05BegY8eOibZt2wpDQ0NhYmIiunXrpvZL63Hz588XDRs2FHp6esLOzk788MMPqi8cxYq/BDz+xVsIIQoKCsQPP/wg7OzshJ6enmjYsKFYsGBBiXPs2LFDABBLlix56jUWP5czZswQkyZNEjY2NkJPT094eXmJ3bt3l7mfg4ODcHFxeeqxn3Tr1i3x5ZdfCkdHRyGTyUSNGjWEj4+PGDdunLh//75ITU0VtWvXFm3atFH78qpUKsU777wjzMzMSnxBPX78uHjnnXeEkZGRMDY2Fn379hUZGRlq5y1PMiSEENevXxeffPKJsLS0FDKZTFhbW4vevXurjldaMiSEECEhIcLa2lpIpdJnfkGryHtCCCGWL18unJychFwuF3Xr1hXTp08Xy5YtKzUZ6ty5s9i0aZNwc3MTenp6wsHBQcyZM6fEMe/fvy/Gjx8vnJychJ6enjA1NRWNGjUSo0aNEunp6arnrqz3wOPv06ysLDF8+HBhZWUldHV1hb29vQgJCVH7Mlkc35Pv78TERNG+fXuhr68vatSoIQYNGiT+/vvvcn/ZvXPnjpBKpaJatWpq76PimcJ69OhRYp/S2sSePXuEl5eXkMvlatf3PMnQuXPnRN++fUW9evWEgYGBMDU1FU2aNBGhoaFq9eLj40WzZs2EoaFhiRnPnvW+EaLi7+Nis2fPFk2bNhXm5uaqz6VBgwaJq1evlnm9xc9LaT/29vZqx9+2bZto3bq1MDExEXK5XNjb24uePXs+848pryIZEuLRH2ECAgJUbfCjjz4q8TlS/ByX9vtp7dq1wsPDQ+jp6QlLS0vx5Zdfinv37pWod+/ePfHll18KS0tLoaenJzw8PErMRPqsGVAfP//27dtF8+bNRa1atYSurq4wNjYWLVq0eGGLjxMJIYREiCdWtCMiqgK+/fZb/PXXX7h48aLafSYvwsmTJ+Hp6YmFCxciODj4hR67vCZOnIhJkybh1q1bT70n5U3j4OAAd3d3jRcvpqqt+N7IWbNmqdaSIiJ6EXjPEBFVSfv27cOECRNeaCJ0+fJlXLt2DWPHjoWVlZVq6mQiIiJ6PTEZIqIqqbyTRmhiypQpWL16NVxcXLBx48anzjBFREREVR+HyRERERER0RuJE7QTEREREdEbickQERERERG9kZgMERERERHRG+m1mUBBqVQiNTUVxsbGkEgk2g6HiIiIiIi0RAiBe/fuwdraGlJp2f0/r00ylJqaCltbW22HQURERERElcT169dhY2NT5vbXJhkyNjYG8OiCTUxMtBqLQqFAeHg4goKCIJPJtBoLVQ1sM6QpthnSFNsMaYpthjRR2dpLTk4ObG1tVTlCWV6bZKh4aJyJiUmlSIYMDQ1hYmJSKRoDVX5sM6QpthnSFNsMaYpthjRRWdvLs26f4QQKRERERET0RmIyREREREREbyQmQ0RERERE9EZ6be4ZIiIiIqKqo6ioCAqFQtth0AuiUCigq6uLvLw8FBUVvfTzyWQy6OjoPPdxmAwRERER0SsjhEB6ejru3r2r7VDoBRJCwNLSEtevX39la36amZnB0tLyuc7HZIiIiIiIXpniRKh27dowNDR8ZV+c6eVSKpW4f/8+jIyMnrrI6YsghEBubi5u3rwJALCysqrwsZgMEREREdErUVRUpEqEatasqe1w6AVSKpUoKCiAvr7+S0+GAMDAwAAAcPPmTdSuXbvCQ+Y0jvTgwYN45513YG1tDYlEgm3btj1znwMHDsDHxwf6+vqoW7culixZUqLO5s2b4erqCrlcDldXV2zdulXT0IiIiIioEiu+R8jQ0FDLkdDroLgdPc+9ZxonQw8ePICnpyd+/fXXctVPSkpCp06d0KJFC8TFxWHs2LH48ssvsXnzZlWdqKgo9OnTB/3790dCQgL69++P3r174+jRo5qGR0RERESVHIfG0YvwItqRxsPkOnbsiI4dO5a7/pIlS2BnZ4d58+YBAFxcXHDs2DH8/PPPeO+99wAA8+bNQ/v27RESEgIACAkJwYEDBzBv3jz89ddfmoZIRERERET0TC/9nqGoqCgEBQWplXXo0AHLli2DQqGATCZDVFQURo0aVaJOcQJVmvz8fOTn56se5+TkAHjUTabNaRpz72fj5q8dYKfUw6nzS1GkZwyl3AySmnVhVMcVFnU9YFLTCuBfROgxxW2WU4xSebHNkKbYZkhTL6PNKBQKCCGgVCqhVCpf2HFJ+4QQqn+ffG3r1q2LESNGYMSIES/0nEqlEkIIKBSKEvcMlbfdvvRkKD09HRYWFmplFhYWKCwsRGZmJqysrMqsk56eXuZxp0+fjkmTJpUoDw8P1+o41IL7t9Gr6NKjB7n/+wGADACJj/6bKUxxUbchblZzQmH1htAxs4PkFdxoRpVfRESEtkOgKoZthjTFNkOaepFtRldXF5aWlrh//z4KCgpe2HHpxfPw8MCnn36KTz/9VKP97t27V6JMqVQiLy9P1XnxohQUFODhw4c4ePAgCgsL1bbl5uaWsZe6VzKb3JPj+Yozx8fLS6vztHGAISEhGD16tOpxTk4ObG1tERQUBBMTkxcRdoU8fHAPx6J1kXThNKzNTYD8+0BuFgzvJaFW3jVYi5swl2TDvCgWyIkFcoDb10yRVL0pdJ3fRt0mXaBvZKq1+Ek7FAoFIiIi0L59e8hkMm2HQ1UA2wxpim2GNPUy2kxeXh6uX78OIyMj6Ovrv5Bj0sshlUqhr69f7u/VQgjcu3cPxsbGJb7Da3qs8srLy4OBgQFatmxZoj2VN/F66cmQpaVliR6emzdvQldXVzWlYll1nuwtepxcLodcLi9RLpPJtPohLzOrAc+27yMlPwxNOnUqEUvOvRxcPRmJ7AsHYJR+DA3yTqGGJBs17vwDRP2D/MivkWgcCKnHe3Bq0RN6BkZauhLSBm23X6p62GZIU2wzpKkX2WaKioogkUgglUpfyfTLL8qqVaswatQopKamqn3/fO+991CtWjWsWrWq1P1u3LiBr7/+GuHh4cjPz4eLiwsWLlwIf39/AMDixYvx888/4/r163B0dMT48ePRv39/1f4SiQRLlizBjh07sHfvXtjb22P58uWoVasWBg8ejNjYWHh4eODPP/9EvXr1AAATJ07Etm3b8Omnn+LHH39EVlYWOnfujN9//x1mZmYAgLfeeguNGzdWuyWlW7duMDMzQ2hoKN566y1cu3YNo0ePVnU+FHdmREZGYsyYMYiNjYW5uTm6d++O6dOnq6a6vnXrFoYMGYI9e/bA0tISP/74o+paXvRrLpVKIZFISm2j5W2zL70VBgYGluheDQ8Ph6+vryrIsuo0bdr0ZYf3ypkYm8Cj2dtoMXA6vEIioDMmCXGtV+KweR9cl1hBLlHA8/5BNIocAcWMeji+oB+uxO0F/tcAiYiIiF4nQgjkFhRq5UeU8/tVr169UFRUhO3bt6vKMjMzsXPnTgwcOLDUfe7fv49WrVohNTUV27dvR0JCAr799lvV/TRbt27FiBEj8NVXX+H06dMYNmwYBg4ciH379qkdZ8qUKfjoo48QHx8PZ2dn9OvXD8OGDUNISAiOHTsGAPj888/V9rl06RI2bNiAHTt24N9//0V8fDw+++yzcr8mW7ZsgY2NDSZPnoy0tDSkpaUBAE6dOoUOHTqgR48eOHnyJNavX4/Dhw+rnX/gwIG4evUq9u7di02bNmHRokWqxVErI417hu7fv49Lly6pHiclJSE+Ph41atSAnZ0dQkJCkJKSosqQhw8fjl9//RWjR4/GkCFDEBUVhWXLlqnNEjdixAi0bNkSM2bMQNeuXfH3339jz549OHz48Au4xMrNwMAAXq26Aa26QSiVOJsQhazotaibsRvWuAWf27uAv3fh2k573GrYB05BQ2Bcvba2wyYiIiJ6IR4qiuD6/W6tnDtxcgcY6j3767CBgQH69euHFStWoFevXgCANWvWwMbGBm+99Vap+6xduxa3bt1CbGwsatSoAQCoX7++avvPP/+MAQMGIDg4GAAwevRoREdH4+eff0br1q1V9QYOHIjevXsDAL777jsEBgZiwoQJ6NChA4BH36OfTMjy8vKwcuVK2NjYAAB++eUXdO7cGbNnz4alpeUzr7dGjRrQ0dGBsbGxWv1Zs2ahX79+GDlyJACgQYMGWLBgAVq1aoWFCxfi0qVL+PfffxEdHa3q/Vq2bBlcXFyeeU5t0bhn6NixY/Dy8oKXlxeARy+cl5cXvv/+ewBAWloakpOTVfUdHR0RFhaG/fv3o3HjxpgyZQoWLFigmlYbAJo2bYp169ZhxYoV8PDwQGhoKNavX696Et8UEqkULl7N0PzThbCYcAEJ7f9CtEkQHgo92Bddg+/ZmdCb54q4ue/hfPQuCM7CQkRERPRKDBkyBOHh4UhJSQEArFixAgMGDCjzHvf4+Hh4eXmpEqEnnT17Fs2aNVMra9asGc6ePatW5uHhofp/8S0kjRo1Uit7cnICOzs7VSIEPBqFpVQqcf78+fJcapmOHz+O0NBQGBkZqX46dOgApVKJpKQkXLhwAbq6uvD19VXt4+zsrBqeVxlp3DP01ltvPbVLMTQ0tERZq1atcOLEiacet2fPnujZs6em4by2dHSk8GzWCWjWCXeybuFE+DJYXFyH+sokeGXvAf7dg2vhdrjlNhDuHYdA39BY2yETERERacxApoPEyR20du7y8vLygqenJ1atWoUOHTrg1KlT2LFjR9nH/t89NE9TngnEHr/3pXhbaWVPm6q8uE7xv1KptMT3+fJMRa1UKjFs2DB8+eWXJbbZ2NggPj5e7TxVwSuZTY6eT/WatdCs7xgI5bdIPHEQ2UeWweN2OOyVybA/NQl3T83GSZueqNtpBMyt62o7XCIiIqJyk0gk5RqqVhkMHjwYc+fORUpKCtq1awdbW9sy63p4eOCPP/7A7du3S+0dcnFxweHDh/HRRx+pyiIjI1/IkLLk5GSkpqbC2toawKN1P6VSKRo2bAgAqFWrluo+IODRxBanT59WG56np6eHoqIiteN6e3vjzJkzasP9iimVSjRs2BCFhYU4duwYmjRpAgA4f/487t69+9zX9LJUnWk8CBKpFK6+byFwxGooRp7BkXpfIQUWMMN9NLkRCtOlvjgxpwcuxx3QdqhEREREr50PPvgAKSkp+P333/HJJ588tW7fvn1haWmJbt264ciRI7hy5Qo2b96MqKgoAMA333yD0NBQLFmyBBcvXsScOXOwZcsWfP31188dp76+Pj7++GMkJCTg0KFD+PLLL9G7d2/V/T9t2rTBrl27sGvXLpw7dw7BwcElEhYHBwccPHgQKSkpyMzMBPDonqWoqCh89tlniI+Px8WLF7F9+3Z88cUXAB7dQ9ShQwcMGTIER48exfHjxzF48OBy9ZJpC5OhKsqsujma9f8etcedQWzALzgtawSZpAjeOf+h3t/v4ty0QJzauw5CWfTsgxERERHRM5mYmOC9996DkZERunXr9tS6enp6CA8PR+3atdGpUyc0atQIP/30E3R0Hg3N69atG+bPn49Zs2bBzc0NS5cuxYoVK8qckEET9evXR48ePdCpUycEBQXB3d0dixYtUm3/5JNP8PHHH+Ojjz5Cq1at4OjoqNYrBACTJ0/G1atXUa9ePdSqVQvAo96uAwcO4OLFi2jRogW8vLwwYcIEWFlZqfZbvnw5bG1t0apVK/To0QNDhw5F7dqVd/IviSjvnIKVXE5ODkxNTZGdna3VRVeBR2Muw8LC0KmUdYZepvPxR3B33wJ43d0DPcmjVXivSu1wu/Gn8Hh7EHT1Sq7LRJWDttoMVV1sM6QpthnS1MtoM3l5eUhKSoKjo2OVXXS1ffv2cHFxwYIFC7QdSqmK1xkqvn/nVVEqlcjJyYGJickrW0Pqae2pvLkBe4ZeI06Nm8F/1HrcHnockZYf4r4wgIMyGd4nQpA53Q0x66bi4f3yrcZLRERERP/v9u3bWLduHfbu3avRmj1UuVWNu9VII5Z1HGA5fCGyb0/Eke3z4HT1T1iKW7A8NxN3zy3GSbv34fzuVzA1t3r2wYiIiIgI3t7euHPnDmbMmAEnJydth0MvCHuGXmOmNWqh2YCpqPZtIqJcJ+CGxBJmuAf/5N8h+8UTRxcNQUbyBW2HSURERFTpXb16FdnZ2S9kgoOXaeLEia98iFxVxmToDWBgWA2Bvb+G5djTiPWbg4s69WAoyYf/zQ2osSwAx+b3RcrlU9oOk4iIiIjolWIy9AbRlcng13kQ6o87hoTWoTil1xgySRF874TBclULHJ/TA8lnY7UdJhERERHRK8Fk6A0kkUrh2ao7Go09gLOdtyDOIAA6EgGfnP9gt74d4md1xuWEQ9oOk4iIiIjopWIy9IZz8WsLr+9242L3f3C8WksohQSNHxxGva1dcHJGe5w/tkfbIRIRERERvRRMhggA0MCzKXy+2YFrff5DrEl7FAkJPB7GwGnnezgzvRUSI3cCr8eSVEREREREAJgM0RMcXX3gN3oTUj48hKNmXVAgdOCWHw/X8A9wblpTnNq/CUKp1HaYRERERETPjckQlcquQSP4j1yDzE+iEWX+HvKFDM6KRDTaPwiXp/khPuJPKIuKtB0mEREREb1AEydOROPGjZ/7OKGhoTAzM3vu47xsTIboqaztGyLw8+XIHnocURZ9kSvkqF94CY2PfIZrU71wYtfvKCos1HaYRERERK89iUSCbdu2aTuMEhwcHDB//ny1sj59+uDChcq/niWTISqX2nXsEfjpEjz8LB6RdQbinjCAo/IavGO/RurURji27RcUFuRrO0wiIiIiqgQMDAxQu3ZtbYfxTEyGSCM1a1uj6ZB5UI44jUi7YbgLI9iKVPjGj8fN6e6I2fQzCvIeajtMIiIiohdKCIGZM2eibt26MDAwgKenJzZt2qTa1q5dO7z99tsQ/5tw6u7du7Czs8O4ceMAAEVFRRg0aBAcHR1hYGAAJyenEr0pALB8+XK4ublBLpfDysoKn3/+OYBHvS8A0L17d0gkEtXjJxUUFODzzz+HlZUV9PX14eDggOnTp6u2Jycno2vXrjAyMoKJiQl69+6NjIyMMq/7rbfewsiRI9XKunXrhgEDBqi2X7t2DaNHj0b16tWho6MDoPRhcosXL0a9evWgp6cHJycnrF69Wm27RCLBH3/8ge7du8PQ0BANGjTA9u3by4ztRWAyRBViWsMcTT+ZCZ1RpxBZ90tkwRTW4iaanJ6COz+54ei6acjLva/tMImIiKiyEwIoeKCdHw1myh0/fjxWrFiBxYsX48yZMxg1ahQ+/PBDHDhwABKJBCtXrkRMTAwWLFgAABg+fDgsLCwwceJEAIBSqYSNjQ02bNiAxMREfP/99xg7diw2bNigOsfixYvx2WefYejQoTh16hS2b9+O+vXrAwBiY2MBACtWrEBaWprq8ZMWLFiA7du3Y8OGDTh//jz+/PNPVeIkhEC3bt1w+/ZtHDhwABEREbh8+TL69Omj6aumsmXLFtjY2GDSpEk4d+4cUlJSSq23detWjBgxAl999RVOnz6NYcOGYeDAgdi3b59avUmTJqF37944efIkOnXqhA8++AC3b9+ucHzPovvSjkxvBGPTGmj60RTkPvgGUX//groX/oAFsmBxbgayzi1FfP2B8Og2EoZGZtoOlYiIiCojRS4wzVo75x6bCuhVe2a1Bw8eYM6cOdi7dy8CAwMBAHXr1sXhw4exdOlStGrVCnXq1MHSpUvRv39/ZGRkYMeOHYiLi4NMJgMAyGQyTJo0SXVMR0dHREZGYsOGDejduzcA4Mcff8RXX32FESNGqOr5+fkBAGrVqgUAMDMzg6WlZZmxJicno0GDBmjevDkkEgns7e1V2/bs2YOTJ08iKSkJtra2AIDVq1fDzc0NsbGxqnNpokaNGtDR0YGxsTEsLCxgYmJSar2ff/4ZAwYMQHBwMABg9OjRiI6Oxs8//4zWrVur6g0YMAB9+/YFAEybNg2//PILYmJi8Pbbb2scW3mwZ4heCMNqJgjsNw6m351BtOt4pKEWauIuAi7NRf7P7ogODcG9u1naDpOIiIhIY4mJicjLy0P79u1hZGSk+lm1ahUuX76sqterVy/06NED06dPx+zZs9GwYUO14yxZsgS+vr6oVasWjIyM8PvvvyM5ORkAcPPmTaSmpqJt27bPFeuAAQMQHx8PJycnfPnllwgPD1dtO3v2LGxtbVWJEAC4urrCzMwMZ8+efa7zPsvZs2fRrFkztbJmzZqVOK+Hh4fq/9WqVYOxsTFu3rz50uJizxC9UPoGhgjo/Q0K8r9EzK4lsD61GDYiDQFXFyFn3kpE2/aFS7dvYVrTQtuhEhERUWUgM3zUQ6Otc5eD8n9rLO7atQt16tRR2yaXy1X/z83NxfHjx6Gjo4OLFy+q1duwYQNGjRqF2bNnIzAwEMbGxpg1axaOHj0K4NGEAy+Ct7c3kpKS8M8//2DPnj3o3bs32rVrh02bNkEIAYlEUmKfssoBQCqVqu6DKqZQKCoU25PnKO28xT1pj++jfIlrXLJniF4KPbkcTXqMgOXYk4j1mYGrUluY4AECrv8B3QUeiP7tC9zOuKHtMImIiEjbJJJHQ9W08VNGAvAkV1dXyOVyJCcno379+mo/j/eyfPXVV5BKpfjnn3+wYMEC7N27V7Xt0KFDaNq0KYKDg+Hl5YX69eur9SoZGxvDwcEB//33X5lxyGQyFJVjnUcTExP06dMHv//+O9avX4/Nmzfj9u3bcHV1RXJyMq5fv66qm5iYiOzsbLi4uJR6rFq1aiEtLU31uKioCKdPn1aro6en98y4XFxccPjwYbWyyMjIMs/7qrBniF4qXZke/N4ZjqJOQ3A8fBXMYuejnjIJAamr8HDROhy16I563cbC3NpB26ESERERlcrY2Bhff/01Ro0aBaVSiebNmyMnJweRkZEwMjLCxx9/jF27dmH58uWIioqCt7c3xowZg48//hgnT55E9erVUb9+faxatQq7d++Go6MjVq9ejdjYWDg6OqrOM3HiRAwfPhy1a9dGx44dce/ePRw5cgRffPEFAKiSpWbNmkEul6N69eolYp07dy6srKzQuHFjSKVSbNy4EZaWljAzM0O7du3g4eGBDz74APPmzUNhYSGCg4PRqlUr+Pr6lnrtbdq0wejRo7Fr1y7Uq1cPc+fOxd27d9XqODg44ODBg+jUqRMKCgpKnVL7m2++Qe/eveHt7Y22bdtix44d2LJlC/bs2fMcr8zzY88QvRI6Ojrw6TgQjuNOIK75ElzQbQgDSQH8b66HyVIfxPw6AOnJlX9hLiIiInozTZkyBd9//z2mT58OFxcXdOjQATt27ICjoyNu3bqFQYMGYeLEifD29gYA/PDDD7C2tsbw4cMBPJpdrkePHujTpw/8/f2RlZWlmkyg2Mcff4x58+Zh0aJFcHNzQ5cuXdSG282ePRsRERGwtbWFl5dXqXEaGRlhxowZ8PX1hZ+fH65evYqwsDBIpVLVoq3Vq1dHy5Yt0a5dO9StWxfr168v87o/+eQTfPzxx/joo4/QqlUrODo6qk14AACTJ0/GtWvX4O3tDQuL0m+F6NatG+bPn49Zs2bBzc0NS5cuxYoVK/DWW28987l/mSTiyUGAVVROTg5MTU2RnZ1d5iwWr4pCoUBYWBg6depUYtwjPSKUSpw8uBWyI7PhqjgDAFAIHcTXeBt1uoyDdT03LUf4arHNkKbYZkhTbDOkqZfRZvLy8pCUlARHR0fo6+u/kGNS5aBUKpGTkwMTExNIpa+mv+Vp7am8uUGFIl20aJHqpD4+Pjh06NBT6y9cuBAuLi6qBaZWrVqltj00NBQSiaTET15eXkXCoypAIpXC86334BJyGKfbr8EpvcaQSYrgd2cXLFY1w7E5PXHtXJy2wyQiIiKi15jG9wytX78eI0eOxKJFi9CsWTMsXboUHTt2RGJiIuzs7ErUX7x4MUJCQvD777/Dz88PMTExGDJkCKpXr4533nlHVc/ExATnz59X25d/MXj9SaRSuDfrAjTrgrMxe1Cw9yd45sXCNycCyr/24IRxS1TvOA6Obv7aDpWIiIiIXjMa9wzNmTMHgwYNwuDBg+Hi4oJ58+bB1tYWixcvLrX+6tWrMWzYMPTp0wd169bF+++/j0GDBmHGjBlq9SQSCSwtLdV+6M3i0qQdPMfswcVuOxFn2AxSiYD3/QNw3BiEuJkdcSnuoLZDJCIiIqLXiEY9QwUFBTh+/DjGjBmjVh4UFITIyMhS98nPzy/Rw2NgYICYmBgoFArVGNT79+/D3t4eRUVFaNy4MaZMmVLmjWHFx83Pz1c9zsnJAfBofGtF5z5/UYrPr+04qioHtwDA7W9cTIxBdsRMeN87AK/cSODvd3Byty90Wn2Dhr7PtyBZZcM2Q5pimyFNsc2Qpl5Gm1EoFBBCQKlUvtS1Y+jVK56GoPj1fRWUSiWEEFAoFNDR0VHbVt52q9EECqmpqahTpw6OHDmCpk2bqsqnTZuGlStXlhjmBgBjx47FihUrsHPnTnh7e+P48ePo3LmzapVdKysrREdH49KlS2jUqBFycnIwf/58hIWFISEhAQ0aNCg1lokTJ2LSpEklyteuXQtDw/ItoEVVQ96dVFjc2InmikjoSh69ueIkrrhg+S7ktV0gkZZvjQAiIiLSLl1dXVhaWsLW1hZ6enraDoequIKCAly/fh3p6ekoLCxU25abm4t+/fo9cwKFCiVDkZGRCAwMVJVPnToVq1evxrlz50rs8/DhQ3z22WdYvXo1hBCwsLDAhx9+iJkzZyIjI6PUeciVSiW8vb3RsmVLLFiwoNRYSusZsrW1RWZmZqWYTS4iIgLt27fnjD0vUEpSIjLCZsDrzr/Qkzxa2OuczAV5AaPh2rwrJK9o5pKXgW2GNMU2Q5pimyFNvYw2k5+fj+TkZNjZ2fGP168ZIQTu3bsHY2NjSMq5mO3zys3NVbUnuVyuti0nJwfm5ubPTIY0GiZnbm4OHR0dpKenq5XfvHmzzDnFDQwMsHz5cixduhQZGRmwsrLCb7/9BmNjY5ibm5e6j1QqhZ+fn9q86k+Sy+UlLhp4tDJvZfmQr0yxvA4cGnrCoeFapCdfxNXt0+B1awecFWeBQ0NwMWomHviPgmfb9yGR6jz7YJUU2wxpim2GNMU2Q5p6kW1GR0dH9V2yVq1a0NPTe2VfnOnlUiqVKCgoQH5+/kufWlsIgYKCAty6dQs6OjowNDQscc7ytlmNkiE9PT34+PggIiIC3bt3V5VHRESga9euT91XJpPBxsYGALBu3Tp06dKlzCdKCIH4+Hg0atRIk/DoDWFp1wCWn6/ArdSruPT3T/BM34IGhReBI8G4Ej0Td31GoHHQR5DqajxZIhEREb1EUqkUjo6OSEtLQ2pqqrbDoRdICIGHDx/CwMDglSW4hoaGsLOze67kS+Nvi6NHj0b//v3h6+uLwMBA/Pbbb0hOTlatrhsSEoKUlBTVWkIXLlxATEwM/P39cefOHcyZMwenT5/GypUrVcecNGkSAgIC0KBBA+Tk5GDBggWIj4/HwoULK3xh9PqrZe2AWp8uQdbNCUjY9hM8UjagbtFVIGYUrh2bjVuNP0fjjoOgK+OYZCIiospCT08PdnZ2KCwsRFFRkbbDoRdEoVDg4MGDaNmy5SvpfdbR0YGuru5zJ14aJ0N9+vRBVlYWJk+ejLS0NLi7uyMsLAz29vYAgLS0NCQnJ6vqFxUVYfbs2Th//jxkMhlat26NyMhIODg4qOrcvXsXQ4cORXp6OkxNTeHl5YWDBw+iSZMmz3Vx9GaoWbsOAof+guys8YjaNgtu19fCXnkD9ifGICVuHlLdP4Vnl+HQk3PdKiIiospAIpFwyOZrRkdHB4WFhdDX169Sr2uFxhEFBwcjODi41G2hoaFqj11cXBAXF/fU482dOxdz586tSChEKqY1LRA46Gfk3A1B1N+z4Zy0GnVEOuqc+gHpp37FNdch8Hznc+gbVNN2qERERERUCVTd6beIymBiVhOBH0+D/OvTiK4/CpkwgyVuwT9xGu7NcMPRPyfiwb272g6TiIiIiLSMyRC9tgyNTBHw4UQYfXsGR53HIAM1UQt34H9pLhSz3RC1/FvkZN3UdphEREREpCVMhui1p29oBP/3Q1A9JBExjSbhhsQKZriPwOSl0FnQCNFLg5GZdk3bYRIRERHRK8ZkiN4YenJ9NHlvJKzGncZxv9m4InVANUkeAtLWwHiJD47+MgCpSSUXDiYiIiKi1xOTIXrj6OjqwqfzYDiOj0NCy6U4p+sCuUQB/6ytqB0aiNi5vXDt3HFth0lERERELxmTIXpjSaRSeLZ5H05jI3Em6C+c1PeBrkQJv+xw2K9rg7hZnXEp7qC2wyQiIiKil4TJEL3xJFIp3Jp2gseYvbjw7nbEVWsOAPB6cBj1/34HJ39qg8TIMAilUsuREhEREdGLxGSI6DENvVvB65tduNrnP8SaBqFQSOGRdxyu4X1xfnoznNy7nkkRERER0WuCyRBRKRxcfOE3aiNuDojC0ZrdkC9kcFYkwuPgUFyZ6o3jYctQVFio7TCJiIiI6DkwGSJ6CmtHZ/h/sRL3hh1HtOUHyBVy1CtKgk/MaKRObYTYLfNRkJ+n7TCJiIiIqAKYDBGVg7m1PQKGL4Liy1OIshuKbFSDrUiF38nvcWe6K6L/moqHD+5pO0wiIiIi0gCTISINmNa0QOAns6Az+gyi64/CLVSHBbIQcH4mHs5yRXToWOTczdR2mERERERUDkyGiCrAyKQ6Aj6cCOPvzuCo2wSkSixQAzkIuLoQkrnuiPp9BLIybmg7TCIiIiJ6CiZDRM9B36Aa/Ht9jdpjT+OY9wxcldrCWPIQgSmhMFzkheiFg5GefFHbYRIRERFRKZgMEb0AujI9+L47HHbjEhDXdCEu6DaEgaQAAbc2ouYyf8TO7Y2rZ49pO0wiIiIiegyTIaIXSKqjA6+gD9Fg7FGcarMKp+WNIZMUwS97NxzWt0X8zLdxLiZC22ESEREREZgMEb0UEqkUjVp2hXvIAVx4dztOVGsJpZCgcW4UnMN6InFqMyTsXccFXImIiIi0iMkQ0UvW0LsVvL/ZgRsf7EdM9S4oEDpwVZyG58FhuPqjF45tX4JCRYG2wyQiIiJ64zAZInpF7Bo2RpMRa3B36KMFXB8IfTgqr8L3xHe4M6sxii7t4VpFRERERK8QkyGiV6x2HUcEDF+EwhGnEe3wGW7DBNbiJnrcW4WieR6IWvEdsm/f0naYRERERK89JkNEWmJaoxYCBkyD4bdnEeU0BjdELVTHPQReWwLd+e6IXjwcGTcuaztMIiIiotcWkyEiLdM3NIJvz68R23gmYrxn4IrUAdUkeQjI+AvVf/dDzLy+uHY+XtthEhEREb12mAwRVRJSqQ68Og6C4/g4JLT6A2f0GkFPUoQmd8Ngu/YtxM3qjPPH9mo7TCIiIqLXBpMhokpGIpXCs3UvuI09jHOdNyPOsCmkEgGvB4fhtLM7zkxrgZP7N3NabiIiIqLnxGSIqBJz9msHr2//wbU+exFr1hEKoQO3gpPw2P8Jrkz1wfFdf3BabiIiIqIKqlAytGjRIjg6OkJfXx8+Pj44dOjQU+svXLgQLi4uMDAwgJOTE1atWlWizubNm+Hq6gq5XA5XV1ds3bq1IqERvZbsXXzgN3IdsgbHINrifeQKOeoVXYFP7FfImOaOoxtmIe/hA22HSURERFSlaJwMrV+/HiNHjsS4ceMQFxeHFi1aoGPHjkhOTi61/uLFixESEoKJEyfizJkzmDRpEj777DPs2LFDVScqKgp9+vRB//79kZCQgP79+6N37944evRoxa+M6DVkaVsfAZ8uRcEXJxFlNwx3YIw6IgP+iT/i/gxXRK0ci+w7mdoOk4iIiKhK0DgZmjNnDgYNGoTBgwfDxcUF8+bNg62tLRYvXlxq/dWrV2PYsGHo06cP6tati/fffx+DBg3CjBkzVHXmzZuH9u3bIyQkBM7OzggJCUHbtm0xb968Cl8Y0evMzNwSgZ/MhPzrM4h2+g7pqAVz3EVg0kLoznND9OLhSL9+SdthEhEREVVqGiVDBQUFOH78OIKCgtTKg4KCEBkZWeo++fn50NfXVyszMDBATEwMFAoFgEc9Q08es0OHDmUek4geMTQyRUDfsag59gxivaYjSWqvmpa75h9NEDu3F66cZg8rERERUWl0NamcmZmJoqIiWFhYqJVbWFggPT291H06dOiAP/74A926dYO3tzeOHz+O5cuXQ6FQIDMzE1ZWVkhPT9fomMCjJCs/P1/1OCcnBwCgUChUSZa2FJ9f23FQ1fHcbUYiReNOQyDeHoS4Q1shi1kE94IE+GWHA5vCkbDTF5LAz+Ec0AkSKedNeR3wc4Y0xTZDmmKbIU1UtvZS3jg0SoaKSSQStcdCiBJlxSZMmID09HQEBARACAELCwsMGDAAM2fOhI6OToWOCQDTp0/HpEmTSpSHh4fD0NBQk8t5aSIiIrQdAlUxL6bNGABuX+FM5hXUSf0HgYUx8Mw7BuwbgPP7HJBQszNkNr6QSnWefSiq9Pg5Q5pimyFNsc2QJipLe8nNzS1XPY2SIXNzc+jo6JTosbl582aJnp1iBgYGWL58OZYuXYqMjAxYWVnht99+g7GxMczNzQEAlpaWGh0TAEJCQjB69GjV45ycHNja2iIoKAgmJiaaXNYLp1AoEBERgfbt20Mmk2k1FqoaXl6b+Rw3rp5F2r9z4Zm5E06Sq3DKWojU27VxrcEAuHYcBkMj0xd4PnpV+DlDmmKbIU2xzZAmKlt7KR419iwaJUN6enrw8fFBREQEunfvriqPiIhA165dn7qvTCaDjY0NAGDdunXo0qULpP8brhMYGIiIiAiMGjVKVT88PBxNmzYt83hyuRxyubzU81SGFwCoXLFQ1fAy2ox9Aw/YN1iBO7fSEL9jDpyT18Fa3IT1hZm4e2ERjtv0QYN3RqOmhc0LPS+9GvycIU2xzZCm2GZIE5WlvZQ3Bo2HyY0ePRr9+/eHr68vAgMD8dtvvyE5ORnDhw8H8KjHJiUlRbWW0IULFxATEwN/f3/cuXMHc+bMwenTp7Fy5UrVMUeMGIGWLVtixowZ6Nq1K/7++2/s2bMHhw8f1jQ8IipD9VpWCPxkFh4++B5Hdy6CzbllqCMyEHBjGfIWrcJR886o0/Eb2NR313aoRERERK+ExslQnz59kJWVhcmTJyMtLQ3u7u4ICwuDvb09ACAtLU1tzaGioiLMnj0b58+fh0wmQ+vWrREZGQkHBwdVnaZNm2LdunUYP348JkyYgHr16mH9+vXw9/d//iskIjUG1Yzh3+c7FBV+hRMRq2F0fBEaFl6Af9Y2KFf/jRNGLVCt9Sg4+bbRdqhEREREL1WFJlAIDg5GcHBwqdtCQ0PVHru4uCAuLu6Zx+zZsyd69uxZkXCIqAJ0dHXh3XEgRIePcSb6XxQemgvPhzHwfnAQ2HkQibvdURDwBTze6gWpDidbICIiotcP59glesNJpFK4Ne0Ez+8icLXPf4g164gCoQNXxWk0PjQM16d6InbLfOTnlW9WFiIiIqKqgskQEak4uPjCb+Q63B16HNGWH+CeMIC98jr8Tn6PnJ9cEbVqArLvZGo7TCIiIqIXgskQEZVQu44jAoYvghh1BtH1RuAmaqAW7iDwygLozHNH9OLhyLhxWdthEhERET0XJkNEVCYTs5oI6D8ZZiFnEeP5I65K7WAkeYiAjL9Q43c/xM7thSunj2o7TCIiIqIKYTJERM+kJ9dHk+5fwG5cPBJaLsUZvUaQSYrglx2OupuCcGp6a5zcvxlCqdR2qERERETlxmSIiMpNqqMDzzbvw23sYVx4dztOGLVCkZCgUf4JeOz/BFd/bIyYrQs42QIRERFVCUyGiKhCGnq3gvfX25ExIBrRtXsjV8jhqLyGJgkTcO8nF0SFjsHdzHRth0lERERUJiZDRPRcrB2dERD8OxQjExFd90vcRA2Y4y4Cry6G3i8eOPrrQNy4dFrbYRIRERGVwGSIiF4I0+rmCPhoCsxCzuKY90+4rFMXhpJ8+GdugfXq5oib2Qlnj+7mfUVERERUaTAZIqIXSk+uD993P0Xdccdxut1qJBg0gVQi4JV7BC7/9MbFaf44HrYChYoCbYdKREREbzgmQ0T0UkikUrg3fxee30XgWp+9iKneBflChoaFF+ATMxI3p7kheu2PuJ9zR9uhEhER0RuKyRARvXT2Lj5oMmIN7n0ahyjbwbgDE1iLmwi4MAvKOa6IXhLMRVyJiIjolWMyRESvjLmlLQIHzYbBt2dx1G0CrkusYYJcBKSvQY3f/XBsTk9cPhmp7TCJiIjoDcFkiIheOX1DI/j3+hp1xp9GfPMlqkVcfXMiUG9LR5ye3goJezdAWVSk7VCJiIjoNcZkiIi0Rqqjg8bt+sJt7GFc7LoDx4zbolBI4Z4fD8+DQ3B9qidiNs9F3sMH2g6ViIiIXkNMhoioUmjg1RK+X21B5qAYRFv0xX1hAHvldTQ5NREPZrggavm3uHMrTdthEhER0WuEyRARVSqWdg0Q8OkSiNGJiG4wGumohZrIRmDyUhj82ghHF/THtXMntB0mERERvQaYDBFRpWRsWgMBH/wA83GJOOb3My7qNoC+RAH/29thv641Tv7UDqcObOEirkRERFRhTIaIqFLTlenBt/MQ1B8bg8QO6xBXrTmUQgKPvFg02jcQ1378331Fufe1HSoRERFVMUyGiKhKkEilcA3sCK9vdiHt4yhE1+6NB0IfDspkNDk1EQ9nuiDqj1HITL2m7VCJiIioimAyRERVTp26LggI/h1Fox7dV5SGWqiOHATeWA6TpV6IndsLlxKOaDtMIiIiquSYDBFRlWViVhMBH/yAWuMScSJgPs7KXKEnKYJfdjjqb+2EM9OaIy78TxQVFmo7VCIiIqqEmAwRUZWnK9OD99sD4DIuChfe3Y5jxm2hEDpwKzgFr8jPkDbVDdF/TcX9nDvaDpWIiIgqESZDRPRaaejdCr5fbcHtIbGIsv4I2agGG5GOgPMzoZzjiujFw5F27by2wyQiIqJKgMkQEb2WLGzqIXDoL5B9fRZHXcfhusQaJshFQMZfqL3cHyd+fgfnYiI4NTcREdEbrELJ0KJFi+Do6Ah9fX34+Pjg0KFDT62/Zs0aeHp6wtDQEFZWVhg4cCCysrJU20NDQyGRSEr85OXlVSQ8IiIVQyNT+Pf+FnXGn0ZCy99xSu4FHYmA9/2DcA7riYvT/HFs529QFORrO1QiIiJ6xTROhtavX4+RI0di3LhxiIuLQ4sWLdCxY0ckJyeXWv/w4cP46KOPMGjQIJw5cwYbN25EbGwsBg8erFbPxMQEaWlpaj/6+voVuyoioidIdXTg2aY3GoXsR1KvcMSYdUK+kKFh4QX4HvsGt6e5IGrVBGTfvqXtUImIiOgV0TgZmjNnDgYNGoTBgwfDxcUF8+bNg62tLRYvXlxq/ejoaDg4OODLL7+Eo6MjmjdvjmHDhuHYsWNq9SQSCSwtLdV+iIheBkc3fzQZ+RfuB8cjym4YsmAKC2Qh8MoCyOa74eivA3H9YoK2wyQiIqKXTKNkqKCgAMePH0dQUJBaeVBQECIjI0vdp2nTprhx4wbCwsIghEBGRgY2bdqEzp07q9W7f/8+7O3tYWNjgy5duiAuLk7DSyEi0kxNCxsEfjITRmPOIcbzR1yROsBQkg//zC2wXdMSCTOCcOrg37yviIiI6DWlq0nlzMxMFBUVwcLCQq3cwsIC6enppe7TtGlTrFmzBn369EFeXh4KCwvx7rvv4pdfflHVcXZ2RmhoKBo1aoScnBzMnz8fzZo1Q0JCAho0aFDqcfPz85Gf//9j/HNycgAACoUCCoVCk8t64YrPr+04qOpgm9EuqY4MXl2GQ3QaipNH/0VR1CJ45h6F58OjwN6jSNpvhwznj+AaNAgG1Yy1HS4AthnSHNsMaYpthjRR2dpLeeOQCCFEeQ+ampqKOnXqIDIyEoGBgaryqVOnYvXq1Th37lyJfRITE9GuXTuMGjUKHTp0QFpaGr755hv4+flh2bJlpZ5HqVTC29sbLVu2xIIFC0qtM3HiREyaNKlE+dq1a2FoaFjeSyIiKlVedjpq3IhA0/yDqCZ59IeXbFENkQatcc+mDeTG5lqOkIiIiMqSm5uLfv36ITs7GyYmJmXW0ygZKigogKGhITZu3Iju3burykeMGIH4+HgcOHCgxD79+/dHXl4eNm7cqCo7fPgwWrRogdTUVFhZWZV6riFDhuDGjRv4559/St1eWs+Qra0tMjMzn3rBr4JCoUBERATat28PmUym1VioamCbqbzuZ2fh3L9LYX95DaxFBgCgSEgQb9QceoHD4eTXHhLpq1+lgG2GNMU2Q5pimyFNVLb2kpOTA3Nz82cmQxoNk9PT04OPjw8iIiLUkqGIiAh07dq11H1yc3Ohq6t+Gh0dHQBAWXmYEALx8fFo1KhRmbHI5XLI5fIS5TKZrFK8AEDlioWqBraZyqe6uSUCP/wBRYXjEL9vA3SPLYV7fjx8HhwC9hzC5X11keU+EB5vD4K+QbVXHh/bDGmKbYY0xTZDmqgs7aW8MWj858zRo0fjjz/+wPLly3H27FmMGjUKycnJGD58OAAgJCQEH330kar+O++8gy1btmDx4sW4cuUKjhw5gi+//BJNmjSBtbU1AGDSpEnYvXs3rly5gvj4eAwaNAjx8fGqYxIRaZuOri4at+8H95ADSOq9B0drvIuHQg/1iq6gScIEPJzhjKjfR+JW6lVth0pERETlpFHPEAD06dMHWVlZmDx5MtLS0uDu7o6wsDDY29sDANLS0tTWHBowYADu3buHX3/9FV999RXMzMzQpk0bzJgxQ1Xn7t27GDp0KNLT02FqagovLy8cPHgQTZo0eQGXSET0Yjm6+sHRdTXuZqYjIWwhHK6shSUyEZiyAoqlq3DcpBWqtfoczr5ttR0qERERPYXGyRAABAcHIzg4uNRtoaGhJcq++OILfPHFF2Ueb+7cuZg7d25FQiEi0hozc0sEfDQFhYoJOLFnDfRP/AFXxWn43NsL7NyLC/82RI7HIHh0GAA9OReRJiIiqmxe/V2/RESvGV2ZHrw7DoTruCO41H0XYs06okDoomHhBfie+A45050QtfxbZKZf13aoRERE9JgK9QwREVHp6ns2BzybIyvjBi6E/YL619ajFu7APHkpChYvQ6xZW1Rv8+WjekRERKRV7BkiInoJalrYIHDgDJiGnMMxn5k4r+sEPUkh/LJ3o/7Wzjg7NRDHw1agUFGg7VCJiIjeWEyGiIheIj25PnzfGQan8TE432Urjpm0g0LowEWRCJ+Ykcia6oyoleNwNzNd26ESERG9cZgMERG9Ik6+beA7ejPuDjuBaJtBuA0TWCALgUm/Qv8Xd8TM/wBJZ45qO0wiIqI3BpMhIqJXrJa1AwIGz4Hhd+cQ23gqLunUg75EgSZ3dsJxYxDOTGuOE/9wCB0REdHLxmSIiEhL9A2qwa/b56g37hjOdtyAE0YtUSikcCs4Be+j/xtCFzoGWRk3tB0qERHRa4nJEBGRlkmkUrj4d4D31zuQOTgWUXUG/v8QuquLYbzIE7Fze+HCif3aDpWIiOi1wmSIiKgSsbStj8Ah81BtzHnEek3HBd2G/5uFLhwNt3fFhR/9EPv3IuTnPdR2qERERFUekyEiokpIrm8Iv67BaDg+Fhfe/RuxpkGqhVz94kJQMNsNuuc242bKFW2HSkREVGVx0VUiokquofdbgPdbyMq4gYv/LILj1XWwQBY6P/wbhSt24IRRc8ibfQrXgLchkfJvXEREROXF35pERFVETQsbBAyYhprjzuGY31zES1ygK1HC+8FBuIX3xdUfG+Poxp+Rez9b26ESERFVCUyGiIiqGF2ZHjyD+uNa4xBc7P4Pjtbsilwhh6PyGvzPTEHhz86IXjwMNy6d1naoRERElRqHyRERVWEOrn5o4NkU2XcyER22CDaX1sBGpCMgYx2Uq9cjwdAPaDIUjVr2gFRHR9vhEhERVSrsGSIieg2YVjdHwAffw3p8IhJa/o4EfT9IJQKeD2PgeWAwUn90Q/TaKci+k6ntUImIiCoNJkNERK8RqY4OPNv0hueYPbj+4WFE1+6DHBjCRqQh4MLPkM1zxdFfPkZSYqy2QyUiItI6DpMjInpN2dZvBNv6v+HBvbs4+u8fsDi7Eg7KZPhnbQM2bMMZPQ/kew+CR9t+0JXpaTtcIiKiV449Q0REr7lqxmbw7/U17Mcn4Ez7tThRrSUKhRRuBSfhHT0Ct6c6IWrFd8hMvabtUImIiF4pJkNERG8IiVQKt2ad4f3NDmQOjkVUnQG4DRPUxm0EXlsC06VeOP5zV5yJDINQKrUdLhER0UvHZIiI6A1kaVsfgUPmo9qY8zjmMxNnZa6QSYrgc38/3ML74tqPnji6fgbuZd/WdqhEREQvDZMhIqI3mFzfEL7vDIPLuChcfm83jtZ4F7lC/ujeorPTIJ3jwgkXiIjotcUJFIiICABQr1EA6jUKQM7dLET/sxRWF9fAXnlDNeFCoswdDxsPRKN2H0JPrq/tcImIiJ4be4aIiEiNiVlNBPQdC7vxp3C6/Z84YfRowgVXxWn4xH6FnOlOiPpjFNKvX9J2qERERM+FPUNERFQqiVQK92bvAM3ewc2UJFz+dyHqX9+EWrgD8xvLUfTHCsQZNYOu/1C4NesCqY6OtkMmIiLSCHuGiIjomWrXcUTgoJ9hNvY8TvjPwxk9T+hIBLweHEajvR8h5Ud3RK+dguzbt7QdKhERUblVKBlatGgRHB0doa+vDx8fHxw6dOip9desWQNPT08YGhrCysoKAwcORFZWllqdzZs3w9XVFXK5HK6urti6dWtFQiMiopdIpieHd8eBcBt7ENf67MVR8/dwXxjAVqQi4MLP0Jvvipj5H+BSwhFth0pERPRMGidD69evx8iRIzFu3DjExcWhRYsW6NixI5KTk0utf/jwYXz00UcYNGgQzpw5g40bNyI2NhaDBw9W1YmKikKfPn3Qv39/JCQkoH///ujduzeOHj1a8SsjIqKXyt7FB/6fL4fk63M46jYBSVIHGEgK0OTOTtTf2gnnf/RH7N+LkPfwgbZDJSIiKpXGydCcOXMwaNAgDB48GC4uLpg3bx5sbW2xePHiUutHR0fDwcEBX375JRwdHdG8eXMMGzYMx44dU9WZN28e2rdvj5CQEDg7OyMkJARt27bFvHnzKnxhRET0alQzNoN/r6/hMD4OZztuwDHjtigQOnAqPAe/uBA8nOGMqKVfIDXpnLZDJSIiUqNRMlRQUIDjx48jKChIrTwoKAiRkZGl7tO0aVPcuHEDYWFhEEIgIyMDmzZtQufOnVV1oqKiShyzQ4cOZR6TiIgqH4lUChf/DvD9agtyPk1AtMNnSIc5qiMHgWmrYBkagIQZQUjYuw5FhYXaDpeIiEiz2eQyMzNRVFQECwsLtXILCwukp6eXuk/Tpk2xZs0a9OnTB3l5eSgsLMS7776LX375RVUnPT1do2MCQH5+PvLz81WPc3JyAAAKhQIKhUKTy3rhis+v7Tio6mCbIU1V9jZjWtMSPh9MQqFiHI4f3AJZ3Ap45B+H58OjwMGjSD84DlfseqJu+2GoaWmr7XDfCJW9zVDlwzZDmqhs7aW8cVRoam2JRKL2WAhRoqxYYmIivvzyS3z//ffo0KED0tLS8M0332D48OFYtmxZhY4JANOnT8ekSZNKlIeHh8PQ0FCTy3lpIiIitB0CVTFsM6SpqtFmTADXETibnQ7TlH0IyDsES0kmLJOXQPHH74jR9cGN2m0gr+0CibTsz316MapGm6HKhG2GNFFZ2ktubm656mmUDJmbm0NHR6dEj83NmzdL9OwUmz59Opo1a4ZvvvkGAODh4YFq1aqhRYsW+PHHH2FlZQVLS0uNjgkAISEhGD16tOpxTk4ObG1tERQUBBMTE00u64VTKBSIiIhA+/btIZPJtBoLVQ1sM6SpqttmPkFe7n0c3bsGpol/wllxFs2KYoC0GCSnW+NG3d5o0H4wzGpaajvQ107VbTOkLWwzpInK1l6KR409i0bJkJ6eHnx8fBAREYHu3buryiMiItC1a9dS98nNzYWurvppdP63MJ8QAgAQGBiIiIgIjBo1SlUnPDwcTZs2LTMWuVwOuVxeolwmk1WKFwCoXLFQ1cA2Q5qqim1GZlod/t0/B7p/jiunj+LW/iVwu/UP7JAKu8vzkH9pIeLNWsO42VA4+baFRMol8V6kqthmSLvYZkgTlaW9lDcGjYfJjR49Gv3794evry8CAwPx22+/ITk5GcOHDwfwqMcmJSUFq1atAgC88847GDJkCBYvXqwaJjdy5Eg0adIE1tbWAIARI0agZcuWmDFjBrp27Yq///4be/bsweHDhzUNj4iIqpC67v6o6+6PB/fuImb3ctQ4+yfqF12GX3Y4EBaOpH8dcNOpH1zfHgJj0xraDpeIiF4zGidDffr0QVZWFiZPnoy0tDS4u7sjLCwM9vb2AIC0tDS1NYcGDBiAe/fu4ddff8VXX30FMzMztGnTBjNmzFDVadq0KdatW4fx48djwoQJqFevHtavXw9/f/8XcIlERFTZVTM2Q5OeoyGUI3Eh/hDuHlyCRnf2wFF5FY5npyE3cTZiagahRqtPUd+zmbbDJSKi10SFJlAIDg5GcHBwqdtCQ0NLlH3xxRf44osvnnrMnj17omfPnhUJh4iIXhMSqRQNvVsB3q2QfScTCf/+BsuLa+GgvI4mt3cAW3fgwo6GuOvWH42CBsKgmrG2QyYioiqMA7GJiKhSMq1ujoC+Y2E//iQS316vWsy1YeEFNEmYAMWshoheOBjXzh7XdqhERFRFVahniIiI6FWRSKVwDXgbCHgbWRk3cHH3UtgmrUcdkYGAWxuB9RuRqNcIuR4foVG7DyHXrxzLKxARUeXHniEiIqoyalrYIOCjKbAafxanWq9AXLXmKBRSuBacgu+xb5D7kxOiln6GlCtntR0qERFVAewZIiKiKkeqo4NGrXoArXrgZkoSLu9ejHrJG1EbtxGY9iew6k+c1PdFkfdANGrdG7oyPW2HTERElRB7hoiIqEqrXccRgZ/MRI1x5xHfbDES9P2gFBJ45B2DV+RnuD3VCVF/jELq1fPaDpWIiCoZ9gwREdFrQVemh8bt+wHt+yE16RyuRSyEU+o21MZt1L6xHMoVK3DSwBeFXh+jUevekOmVXLibiIjeLOwZIiKi1461ozMCh/4Co5CLOOE/D6fkXpBKBDzyYuEd9TmypzVE1O8jkJp0TtuhEhGRFrFniIiIXlt6cn14dxwIdByIlCtnkLxnCRqm/g1z3IV5SiiUoStx0sAbhY0/QqM2fdlbRET0hmHPEBERvRHq1HVD4NBfYBxyAScC5uOkvs//eouOwzt6xKPeot++QMqVM9oOlYiIXhH2DBER0RtFT64P77cHAG8PeHRv0Z7FaJCy7VFvUeoqYNUqnJJ7ocDzYzRq2xd6cn1th0xERC8Je4aIiOiNZe3ojMAh82E69gJOBP6Kk/+bia5Rfhx8Ykbi/vQGiFr6GW5cOq3tUImI6CVgzxAREb3xZHpyeHfoD3Toj9Sr53FtzxLUv7EVtXDn0bpFf/6J0/LGyPfoD/e2/SDXN9R2yERE9AKwZ4iIiOgx1g5OCBw8F9XHXUBc04VIMGgCpZDAPT8ePrFfIfcnJ0QvCcb1iwnaDpWIiJ4Te4aIiIhKoSvTg1fQh0DQh0i7dh5X9/yGete3oDZuIyB9DbBmDc7oeeChR380avche4uIiKog9gwRERE9g5W9EwIHzUaNcecR33wJ4g0CUCQkcCs4Cd9j3yD3p4aIXjwc187HaztUIiLSAHuGiIiIyklXpofG7foC7foi/folJEUsRd3kzbBAFgIy/gL++guJMnc8cP8A7u36w6CasbZDJiKip2DPEBERUQVY2tZH4CezYD7+AhJaLkWcYVMUCQlcFafhFxcCxayGOPrrQFxKOKLtUImIqAzsGSIiInoOOrq68GzzPtDmfdxMScLliKWwv7YF1iID/plbgK1bcGl7PWQ5vQ/n9p/AtLq5tkMmIqL/Yc8QERHRC1K7jiMCB/wEy/FncarNKhw3bo0CoYv6RZfhnzgVevNcEDu3NxKj/4VQKrUdLhHRG489Q0RERC+YVEcHjVp2BVp2xZ1baTgR8QcsL22AgzIZftm7gX934/pua6TU7YX67YfA3NJW2yETEb2RmAwRERG9RNVrWSGg3wQI5TicO7EPOUeWwf32HtgiFbaX50Nx6VecMGoKHd+P4d6iO3R0+auZiOhV4ScuERHRKyCRSuHs2xbwbYv7OXcQExEK07N/wanwPLwfHAIOHELGge9wxbY77NsOhbWDk7ZDJiJ67TEZIiIiesWMTKqjyXujAIxC0pmjyDjwB5xvhsECWbC4/geUK5bhpIE3FB794d6mDxd0JSJ6SZgMERERaZGjmz8c3fyR9/ABju1dC/2Tf8I9Px4eeceBmOO4E/M94iw6w+qtIbB38dF2uERErxUmQ0RERJWAvkE1+HYeAnQegpQrZ5H831LUS/kbtXH70YKu6//COZkrclz7wr39xzA0MtV2yEREVR6TISIiokqmTl0X1Kk7D4WKmYg/uAXi+Eo0ehANZ0UikDAB9+On4WjN9qjefDAaNG4BiZQrZRARVUSFPj0XLVoER0dH6Ovrw8fHB4cOHSqz7oABAyCRSEr8uLm5qeqEhoaWWicvL68i4REREb0WdGV6aNz2fXh9+w/uDotHlOPnuCGxhJHkIfxvb0fD7e8i6UcvRK/9EXdupWk7XCKiKkfjZGj9+vUYOXIkxo0bh7i4OLRo0QIdO3ZEcnJyqfXnz5+PtLQ01c/169dRo0YN9OrVS62eiYmJWr20tDTo6+tX7KqIiIheM+bW9gj8eCqsxyfiTPu1OGbSDvlChrrKqwi4MAvVfnXDiZ/fQcK+jSgqLNR2uEREVYLGw+TmzJmDQYMGYfDgwQCAefPmYffu3Vi8eDGmT59eor6pqSlMTf9/XPO2bdtw584dDBw4UK2eRCKBpaWlpuEQERG9UaQ6OnBr1hlo1hnZWRmI37MCNS9sQP2iy/C+fxA4cBA3D3yLy3XehW3rIbCp767tkImIKi2NkqGCggIcP34cY8aMUSsPCgpCZGRkuY6xbNkytGvXDvb29mrl9+/fh729PYqKitC4cWNMmTIFXl5eZR4nPz8f+fn5qsc5OTkAAIVCAYVCUd5LeimKz6/tOKjqYJshTbHNEAAYmtSAd4+vAHyF86ejcftIKFwy/0Vt3EbtlFDgz1Akytxxz6UP6rXoA4BthsqPnzOkicrWXsobh0QIIcp70NTUVNSpUwdHjhxB06ZNVeXTpk3DypUrcf78+afun5aWBltbW6xduxa9e/dWlUdHR+PSpUto1KgRcnJyMH/+fISFhSEhIQENGjQo9VgTJ07EpEmTSpSvXbsWhoZcj4GIiN5MykIFFGlxcLx9ED5FpyCVPPo1f1/oI0YvALdqt4DcvD4kUomWIyUienlyc3PRr18/ZGdnw8TEpMx6FUqGIiMjERgYqCqfOnUqVq9ejXPnzj11/+nTp2P27NlITU2Fnp5emfWUSiW8vb3RsmVLLFiwoNQ6pfUM2draIjMz86kX/CooFApERESgffv2kMlkWo2Fqga2GdIU2wyVx80bV3Bt33LYX9+KOiJDVX5NaoMUh/dQr81A1LCw0WKEVJnxc4Y0UdnaS05ODszNzZ+ZDGk0TM7c3Bw6OjpIT09XK7958yYsLCyeuq8QAsuXL0f//v2fmggBgFQqhZ+fHy5evFhmHblcDrlcXqJcJpNVihcAqFyxUNXANkOaYpuhp6nj6IQ6jjOgLJqGk5FhuH1gCfwVMbBX3oD9lfkovPwLTlULgMSrP9xavQeZXsnfq0T8nCFNVJb2Ut4YNJpNTk9PDz4+PoiIiFArj4iIUBs2V5oDBw7g0qVLGDRo0DPPI4RAfHw8rKysNAmPiIiISiHV0YFLwNvIbjQUD784gxj3H3Be1xm6EiW8ciPR+MinyJ7WENFLgnHt3Alth0tE9MpoPJvc6NGj0b9/f/j6+iIwMBC//fYbkpOTMXz4cABASEgIUlJSsGrVKrX9li1bBn9/f7i7l5zVZtKkSQgICECDBg2Qk5ODBQsWID4+HgsXLqzgZREREVFpjE2ro0nP0QBG49rZ40g7sAwN0nfCHHdhnr4GWLcG53RdkOPSBy7tPoaxaQ1th0xE9NJonAz16dMHWVlZmDx5MtLS0uDu7o6wsDDV7HBpaWkl1hzKzs7G5s2bMX/+/FKPeffuXQwdOhTp6ekwNTWFl5cXDh48iCZNmlTgkoiIiKg87F18YO/iA0XBXMTt3wjEr0GjB9FwLjwLnJqI3JPTEWvWGtUCBsDFvwMk0gqt1U5EVGlpnAwBQHBwMIKDg0vdFhoaWqLM1NQUubm5ZR5v7ty5mDt3bkVCISIiouck05PDK+hDIOhDZKYn41LEH7BO2gQ7ZQr8sv8Fdv+LG+FWuGHfA47tBsHCpp62QyYieiEqlAwRERHR68nc0g7m/SdDKCfi3PG9yIlcAbfbe2CDNNhcXYii3xfhpIEPChq9D/fWfaFvaKTtkImIKozJEBEREZUgkUrh7NcO8GuH3PvZiN2zGtXO/AVXxWl45B0DYo8hJ/Z7JNQMglngx2jo/RaH0RFRlcNkiIiIiJ7K0MgUft0+B7p9jhuXTuP6/mVwvLEdlsiEf9Y2YOc2XAuzQapDD9RvNwi1rB20HTIRUbkwGSIiIqJys6nvDpv6c6Es+hmnI3ciL3Y13LIP/G/togUoWvoLThr4QtHofbi16Qt9g2raDpmIqExMhoiIiEhjUh0duLfoCrToinvZtxGzZxWMz22Ai+IMPPJigdjY/w2ja4/qzQaiQeOWHEZHRJUOkyEiIiJ6LsamNdDkvZEARuL6pVO4sX+5+jC67dtwbact0hy6ox6H0RFRJcJkiIiIiF4Y2/qNYKs2jG4V3LIPwl55XTWMLsHAF4UefeHW+n0OoyMirWIyRERERC/c48Pocu5m4dR/xcPoEuGZFwvExCInZsL/htF9ggaNW3AYHRG9ckyGiIiI6KUyMauJJu+NAjDq0TC6fctQN2U7LJClGkZ3dact0h17oH7bQTC3ttd2yET0hmAyRERERK/Mo2F081BU+DNORe5C/rFVcM8+AAfldThcno+iSwuQYOiHwkb94Na6N4fREdFLxWSIiIiIXjkdXV00atkVaPloGN3JPSthcn4jnBWJ8HwYA8TEIDtmHBLMO6B60485Gx0RvRRMhoiIiEirTMxqoknP0QBG4/rFBNzYvxx1U3Y8GkaXuQXYvgXJO+sg1a4bHNoMhKVdA22HTESvCSZDREREVGnYNvCEbYP5KCqcjVORO5B/7E+4ZR+EnTIFdlcXQrlsEc7IPfDApRdc234II5Pq2g6ZiKowJkNERERU6TwaRtcdaNn90aKue9eg2tkNcCs4CbeCBCAhAQ/jJ+OYaUvIfT6Aa7N3oaPLrzVEpBl+ahAREVGlZmxaA026fwF0/wJp187j6r4VsLn2N2yRCt+cPcC+Pbi5rwYuW3WCVcuBcHDx1XbIRFRFMBkiIiKiKsPK3glWA36CUE7D+RP7cTd6NZwzd6M2bqN22p/A+j9xSaceMuv1QIO2A1DTwkbbIRNRJcZkiIiIiKociVQKJ982gG8b5Ofl4sSBzZAk/AW3B9GoX3QZ9S/MQuH52Yg3bIKiRu9zmm4iKhWTISIiIqrS5PqG8O7QH+jQH3dupSFu70pUv7gZDQsvoPHDaCAmGjkxY5FQox1M/fvDya8dp+kmIgBMhoiIiOg1Ur2WFfz7jAEwBtfOnUDqwVDUTd35aJru29uBf7bjxr+WuG77Luze+gR16rpoO2Qi0iImQ0RERPRasnf2hr2zN5RFc3E6ahcexq6B2919sEE6bJJ/A1b9hrMyN9xz6gmnth/BtLq5tkMmoleMyRARERG91qQ6OnBv/i7Q/F3k3s/Gsb1rIT+zAW55cXBRnAFOn0H+qWk4btwMut594daiB3RletoOm4heASZDRERE9MYwNDKF77ufAu9+iowbl5G0NxSWV7fCQXkdPvf3Awf3I+vgt7ho0RG1mn2Muu4BvL+I6DXGZIiIiIjeSBY29WDx0RQI5SRcOhWJzCMr0fDmv6iJbNTMWAdsWYekbfbIcOgKh9Yfw9K2vrZDJqIXjMkQERERvdEkUinqezZHfc/mUBTkI/7QVijj1sD9XiQcldfgeGUBlJd/wRm5B3Kd34NTmw9hYlZT22ET0QvAZIiIiIjof2R6cjRu+z7Q9n1k376F+L2rYXRhC1wLTsGtIAE4mYD8hCk4YdwUUs/34dqyB/Tk+toOm4gqqEKDYBctWgRHR0fo6+vDx8cHhw4dKrPugAEDIJFISvy4ubmp1du8eTNcXV0hl8vh6uqKrVu3ViQ0IiIiohfCtEYtNOk5Gq5jDyNtYAyiHD/DNakt5BIFvO8fQOMjnyJ3ej0c/eVjnIuJgFAqtR0yEWlI42Ro/fr1GDlyJMaNG4e4uDi0aNECHTt2RHJycqn158+fj7S0NNXP9evXUaNGDfTq1UtVJyoqCn369EH//v2RkJCA/v37o3fv3jh69GjFr4yIiIjoBbGyd0Lgx9NgN/4kLnUPQ7RFX2TCDGa4D/+sbXAO64m0Kc6I/mM0ki/EaztcIionjZOhOXPmYNCgQRg8eDBcXFwwb9482NraYvHixaXWNzU1haWlpern2LFjuHPnDgYOHKiqM2/ePLRv3x4hISFwdnZGSEgI2rZti3nz5lX4woiIiIhetEf3FzVDwKdLUH38ZZxqE4pY0w54IPRhLTIQcGMZ7Na2woUf/RD911Rkpl/XdshE9BQa3TNUUFCA48ePY8yYMWrlQUFBiIyMLNcxli1bhnbt2sHe3l5VFhUVhVGjRqnV69Chw1OTofz8fOTn56se5+TkAAAUCgUUCkW5YnlZis+v7Tio6mCbIU2xzZCm2GZeDufALkBgF+Tez0bMoU3QS9wM94fH0LDwAnB+JgrP/YwEAx/ku7wHp5a9YGhkqu2Qy41thjRR2dpLeePQKBnKzMxEUVERLCws1MotLCyQnp7+zP3T0tLwzz//YO3atWrl6enpGh9z+vTpmDRpUony8PBwGBoaPjOWVyEiIkLbIVAVwzZDmmKbIU2xzbxMVoDL57j4MAe6KUfhdC8SrpLL8MyLBeJi8eDED4iU+SG9ZiD0LF0hlepoO+ByYZshTVSW9pKbm1uuehWaTU4ikag9FkKUKCtNaGgozMzM0K1bt+c+ZkhICEaPHq16nJOTA1tbWwQFBcHExOSZsbxMCoUCERERaN++PWQymVZjoaqBbYY0xTZDmmKbedXeBwBcvXwaqYdXwy5lF2yQjlaFh4GMw8jMMMPFWkGoEfAhHCvpwq5sM6SJytZeikeNPYtGyZC5uTl0dHRK9NjcvHmzRM/Ok4QQWL58Ofr37w89PT21bZaWlhofUy6XQy6XlyiXyWSV4gUAKlcsVDWwzZCm2GZIU2wzr5aDsxccnL0glD/j3Il9yI7+Ew0zI2COuzC/tQHYsQHXdtkize5d2L31MawdnLQdcglsM6SJytJeyhuDRn+G0NPTg4+PT4nur4iICDRt2vSp+x44cACXLl3CoEGDSmwLDAwscczw8PBnHpOIiIioKpBIpXD2bQv/z1egWsglxLdYiuPGrZEnZLBXXkfA1YWwDm2CxKnNcHTjz8jOytB2yERvBI2HyY0ePRr9+/eHr68vAgMD8dtvvyE5ORnDhw8H8Gj4WkpKClatWqW237Jly+Dv7w93d/cSxxwxYgRatmyJGTNmoGvXrvj777+xZ88eHD58uIKXRURERFQ56cn1VQu73su+jZN718Dw3Ca45iXAVXEaOHMaBaenIa5aAIRHb7i26gV9g2raDpvotaRxMtSnTx9kZWVh8uTJSEtLg7u7O8LCwlSzw6WlpZVYcyg7OxubN2/G/PnzSz1m06ZNsW7dOowfPx4TJkxAvXr1sH79evj7+1fgkoiIiIiqBmPTGmjS/QsAX+BmShKu7AtFraS/Ua8oCV65R4DoI7gXNQanqr8Ffe8+cAnsDF2Z3rMOS0TlVKEJFIKDgxEcHFzqttDQ0BJlpqamz5zRoWfPnujZs2dFwiEiIiKq8mrXcUTtDycBmISkM0eRfvhPOKb9A0vJLfjd/QfY+w8y95rhcq12MPXvByfv1pVy4gWiqqRCyRARERERvTyObv5wdPOHsqgIZ4/tQU7MWjTM+u9/Ey9sAnZuQsouCyRbd4J18/6wd/HRdshEVRKTISIiIqJKSqqjAxf/DoB/BygK8pFw+G8o4tfDNfsQ6iADdVJWAOtX4LKOI27ZvwOHtz6CpV0DbYdNVGUwGSIiIiKqAmR6cni26Q206Y3c+9k4fmAjpGc2w+3BUdQrSkK9KwuAKwuQKHPHvQbd0LD1h6hey0rbYRNVakyGiIiIiKoYQyNT+HQeDHQejOysDMTvW4NqF7bCJf/UoxnpEk9DcWY6Egx9oXB9Dy5v9UE1YzNth01U6TAZIiIiIqrCTGtaoEnP0QBGI+PGZSTtXw3zpO2oX3QZng+PAsePIvfYBBw3aQYdz95wbdEdenJ9bYdNVCkwGSIiIiJ6TVjY1IPFhxMBTMS18/FIPbwatjd2wQZp8Lm3Fzi8F9mHv0JcjbYw8u0LF/8OkOroaDtsIq1hMkRERET0GrJ3agx7p8YQylm4EH8It6PXoP7N3TDHXfjf3g6Eb8fN8Bq4YtkR5oEfoF6jQE7VTW8cJkNERERErzGJVIqG3q0A71YoKizE6ahdyD2+Ds5396M2bqN2+hpg6xpc+9sGqbZdYNuiP2zqu2s7bKJXgskQERER0RtCR1cX7i26Ai26Ij8vF3EHt0Cc3ADXe5GwV96A/bUlwLUluKDbEJkO76BAaqftkIleKiZDRERERG8gub4hvII+BII+xL3s2zi17y/Iz22B28PjaFh4AQ0vzYZSSHB21jLcb9AVDd/6gFN102uHyRARERHRG87YtAb8un0G4DNkpl/H5f1/wvTSNjgXnoNbwUngzEkUnp6KkwY+yHfuBqe3+sLErKa2wyZ6bkyGiIiIiEjF3NIW5u+HQKH4GhvWr4KN8ipqX9uF+kWX4ZEXC8THoiDuB8RV84fSrQdcWvWCoZGptsMmqhAmQ0RERERUKrmxOfw6fQSZbAquX0zAjcNrYX19F+yV1+GVewSIPYLcmLE4ZtIMOo3eg0uL7tA3qKbtsInKjckQERERET2TbQNP2DbwhFBOR9LZWKRHroVd6j+ogwz43tsLRO7FvSNf45RZK8gb94JLs3cg05NrO2yip2IyRERERETlJpFK4ejmD0c3fwjlXFxMOISs6L9QN2M3aktuwy/7X+DAv7hzwBgXaraBkXcfOPt3gI4uv3ZS5cNWSUREREQVIpFK0cCrFRp4tYKyqAhnj0UgJ3Y9GmTuQQ3kwD/rbyDib9yKqI7LtdvDzO99OPm05uKuVGkwGSIiIiKi5ybV0YGL/9uA/9soVBTgdFQYcuM2wPnOftTCHdS6uQHYtQGpYbVxzbIDagX2Qz33ACZGpFVMhoiIiIjohdKV6cG9ZTegZTcU5Och/vA2FCZshGv2IVjjJqzTVgNbViN5ax2k2HSCdfMPYO/kpe2w6Q3EZIiIiIiIXho9uT4at30faPs+8nLvIe7AJogzW+B2Lwp2SIHd9d+Bv37HZakjbtp3hl2L/qhT11nbYdMbgskQEREREb0S+obG8Oo4EOg4EPdzbuPU/vWQnd0K19xjqKdMQr2kX4GkX3Fe1wl3HLvAoeUHsLStp+2w6TXGZIiIiIiIXjkjkxrwffdT4N1PkZ2VgQv718Lgwt9wyYuHU+F54OJ54OJsnJW5ItuxC+q26ofadRy1HTa9ZpgMEREREZFWmda0gN97owCMQmb6dVze/yeMr+yEc/4ZuCgSgQuJUJ6fhUQ9N+TU7YJ6rfqhlrW9tsOm1wCTISIiIiKqNMwtbWH+fgiAENxKScKVg2themUnnBWJcFWcBs6fhvLcDJyRu+N+vXdQr1VfmFvaaTtsqqKYDBERERFRpVSrjiNq9R0HYBwyblxC0sG/YJa0C86Ks3ArOAWcPYWixOk4LffAg/pdUK9lX5hb2mo7bKpCmAwRERERUaVnYVMfFv0mAJiAjOSLSDq0FtWTdsGp8DzcCxKAxAQUnZmG0/qeeFD/HTRo1Rc1atfRdthUyVVolatFixbB0dER+vr68PHxwaFDh55aPz8/H+PGjYO9vT3kcjnq1auH5cuXq7aHhoZCIpGU+MnLy6tIeERERET0GrOwa4CAD36A0/gYpA2MQXT9Ubig2xA6EgH3/Hj4n5kCk4XuODX9LcRsmoM7t9K0HTJVUhr3DK1fvx4jR47EokWL0KxZMyxduhQdO3ZEYmIi7OxKH6/Zu3dvZGRkYNmyZahfvz5u3ryJwsJCtTomJiY4f/68Wpm+vr6m4RERERHRG8TK3glW9hMBTERq0jkkH1qDmslhaFB4CY3y44DTcSg8NQUnDbyQ1+BdNGz1PszMLbUdNlUSGidDc+bMwaBBgzB48GAAwLx587B7924sXrwY06dPL1H/33//xYEDB3DlyhXUqFEDAODg4FCinkQigaUlGyYRERERVYy1ozOsHacAmILUK4lIPrQW5slhqF90GR55x4FTx6E4ORknDbyR5/QunFr1hWmNWtoOm7RIo2SooKAAx48fx5gxY9TKg4KCEBkZWeo+27dvh6+vL2bOnInVq1ejWrVqePfddzFlyhQYGBio6t2/fx/29vYoKipC48aNMWXKFHh5eZUZS35+PvLz81WPc3JyAAAKhQIKhUKTy3rhis+v7Tio6mCbIU2xzZCm2GZIU1W9zdSybYBa/X4A8AOuXT6D1Kh1qH39X9RTJsEjLxZIiEVB/ETEG/ggv+E7aNC8F4yrm2s77CqrsrWX8sahUTKUmZmJoqIiWFhYqJVbWFggPT291H2uXLmCw4cPQ19fH1u3bkVmZiaCg4Nx+/Zt1X1Dzs7OCA0NRaNGjZCTk4P58+ejWbNmSEhIQIMGDUo97vTp0zFp0qQS5eHh4TA0NNTksl6aiIgIbYdAVQzbDGmKbYY0xTZDmnpt2kyNQNysEYjj2WnQT4+FS24MGkiS0TgvBjgZg4KEiTih44Hrpk0gsfKCrrxyfJ+saipLe8nNzS1XPYkQQpT3oKmpqahTpw4iIyMRGBioKp86dSpWr16Nc+fOldgnKCgIhw4dQnp6OkxNTQEAW7ZsQc+ePfHgwQO13qFiSqUS3t7eaNmyJRYsWFBqLKX1DNna2iIzMxMmJiblvaSXQqFQICIiAu3bt4dMJtNqLFQ1sM2QpthmSFNsM6SpN6HNXL+YgPSo9bBK2Q1H5TVVeYHQxRlDXxQ06IIGzXuyx6gcKlt7ycnJgbm5ObKzs5+aG2jUM2Rubg4dHZ0SvUA3b94s0VtUzMrKCnXq1FElQgDg4uICIQRu3LhRas+PVCqFn58fLl68WGYscrkccrm8RLlMJqsULwBQuWKhqoFthjTFNkOaYpshTb3Obaauqy/quvoCmIVrZ48jNWodrG/8A3vldXg9jAZORqMg4QckGj4aSufUsg9Ma5b+nZceqSztpbwxaDS1tp6eHnx8fEp0f0VERKBp06al7tOsWTOkpqbi/v37qrILFy5AKpXCxsam1H2EEIiPj4eVlZUm4RERERERVYi9iw8CP5kF++9PI6n3HkTbDsFVqR30JEXwfBiDJgkTYLjABSd/aoOYTXNw+2aKtkOmF0Dj2eRGjx6N/v37w9fXF4GBgfjtt9+QnJyM4cOHAwBCQkKQkpKCVatWAQD69euHKVOmYODAgZg0aRIyMzPxzTff4JNPPlENkZs0aRICAgLQoEED5OTkYMGCBYiPj8fChQtf4KUSERERET2bo6sfHF39APyMa+dOIDVqPWrf2I16RUmPZqU7fRxFpyY/WuC1XmfUa/k+zC1LX2KGKjeNk6E+ffogKysLkydPRlpaGtzd3REWFgZ7e3sAQFpaGpKTk1X1jYyMEBERgS+++AK+vr6oWbMmevfujR9//FFV5+7duxg6dKjqviIvLy8cPHgQTZo0eQGXSERERERUMfbO3rB39gYwA9cvncKNI+tgnvwvGhRdgnt+PJAYD+WZaUiUuyPHsRPqtuyL2nUctR02lZPGyRAABAcHIzg4uNRtoaGhJcqcnZ2fOrPE3LlzMXfu3IqEQkRERET0StjWbwTb+o0ATH20wOuRv1D96j9wKjwP14JTwPlTwPkZOCdzxV2HjnBo0ReWdqXPjEyVQ4WSISIiIiKiN9mjBV4nAZiE9OSLuHp4HUyTwuCiSISzIhG4mAhcnI0Luv/X3r0HRVnvfwB/c1muuV5ALoKuiLgLZgpLKSLiDTjaxX7+CpU5ZKVnjtNxCpnphOJJPc4cx6aS04Q6nlHPZIlkBFKZQhdugZX8FvOOAgoihIQKxGm5fX9/9IOJH5g8K7vPg/t+zXz/2Ifvbu9neg/ymWf32Slo0izG+PCV8JkUKHds+n84DBERERER3QevCQHwivsbgL+hobYKVYVpGFF5DDrjWUzpLAcqyoGKf+KKnT9uTvgDfMNX/t8VJpIbhyEiIiIioiHi4eMHjxUbAWxEY301KgoOw7XiMwT+chqTuyowuSoVqEpFhZ0fGnxjMG72Smi0M+SObbU4DBERERERmYG71wS4x/4VwF/R1FCLKwXpcLryKYL+Y4B/VxX8r+0Bru3BVdsJqPOJgVfYckzU6WFjK+nbb+g+cBgiIiIiIjKzMR4+eOyZRACJuN1Yj/LCD+FY/gkC20oxsbsaE2v+BdT8C9W2Pqj1jsbYx56F/7QwDkZmxmGIiIiIiMiCRrl74bH/ehnAy7hzqxE/FKTD/tInCPr5e0zorsWE2gNA5gHcyPJAtcdCjNL/N6boF8DWzk7u6A8cDkNERERERDIZOdodoUv/AuAvaLnThB8KjsDuYjZ0rd9hHBow7sc04FgaGo+NQoXbPLhMXwbdrD9A5eAod/QHAochIiIiIiIFGDFyDEKf/DPw5J/xn9ZmGL7JQte5bGibi+CO23D/KQv4Kgu3v3oIl0dFQPXwUujCn4KTs6vc0YctDkNERERERArj/JAawTHPATHPod34C34o/gS/nMlCQFMBRqMZj97+HCj6HD8XJqB0xCwg6Clo5yzDQ+rRckcfVjgMEREREREpmIOjEx6Z/yww/1l0dXbg/He5aDZ8DL+bX8HT5ifoW/OA7/Jg/PY1lLmGoj3gcWjnxmKkm6fc0RWPwxARERER0TBhZ69C0OwlwOwlEN3dKC8rQNOpDPjW5cIXdZjRVgKcLkFn2es44zQdbf5L4D9nOdzHaeSOrkgchoiIiIiIhiEbW1tMCZkHhMyD6O5G1cVS1J88As/aE5jUdRXTjAbgvAHd5/6Biw6BuK2JwYTwFRjnp5M7umJwGCIiIiIiGuZsbG3hF/Qo/IIeBfAGaivOoqb4Q4y+dgLazovQdZwHrpwHruzEFTt/3PSNwrhZsdAE6uWOLisOQ0REREREDxgf/4fh4/8wgL+jobYKVYWH8VDl59AZf8DkrgpMvlYBXNuDa7a+uOG9CO6PPoPJj4Rb3Ze8chgiIiIiInqAefj4wWPFBgAbcOtmHa4UfgiHy58hsK0Umu7r0NT+G6j9N+qzxuKqxwKoQ5ZBG7oIdvYP/qjw4J8hEREREREBAEaP9cajy14B8Apa7jThTGEGbC5mQ9fyLbxsbsKrIR04no6fjo9ExegIOE5bCt3sJ+Do5CJ3dLPgMEREREREZIVGjBwD/RN/Ap74E35pa4WhKAud57KhvVMEN9yB261PgYJP0ZrvjLPqWYDuCUyZswwjRo6RO/qQ4TBERERERGTlnFweQnD0H4HoP6Kj3YgzJ4+j7Ycs+DXmwcOmCfqWr4Hvv0b7d6/htHMwjJOXYNKcZ+HuNV7u6PeFwxAREREREfVSOThi2tylwNyl6O7qwiVDPppKM+Fb/wXG4wam//I9cPZ7dJ/5Oy44BOGOJhreM5fJHdskHIaIiIiIiGhAtnZ20IYuAEIXAACuXfwf1J38CG7XcxDQeRmBHeeAK+eAKzvRjgkoNZZjVuyrMqcePA5DREREREQ0KBpdCDS6EAD/QH3NFVwt+hAjqo5DazyDAJtq3Lx9Xe6IknAYIiIiIiIiybzGT4bXyo0ANuJmfQ3yD7+DkDkr5I4liXV9qxIREREREQ25UW5eUPnNwfiAR+SOIgmHISIiIiIiskochoiIiIiIyCqZNAzt2rULfn5+cHJygl6vR2Fh4e/uNxqNSE5OhkajgaOjI/z9/bF///4+ezIyMhAUFARHR0cEBQUhMzPTlGhERERERESDInkYSk9PR0JCApKTk2EwGBAREYHFixejurr6rs+JjY3Fl19+iX379uHSpUtIS0uDTqfr/XlJSQmWL1+O+Ph4nD59GvHx8YiNjcW3335r2lkRERERERHdg+S7yb399ttYvXo11qxZAwBISUnBiRMnsHv3bmzfvr3f/uPHjyM/Px+VlZUYM2YMAGDixIl99qSkpCAqKgobNmwAAGzYsAH5+flISUlBWlqa1IhERERERET3JGkYam9vR2lpKZKSkvocj46ORnFx8YDPyc7ORmhoKN544w0cPHgQrq6ueOqpp7Bt2zY4OzsD+PXK0Pr16/s8LyYmBikpKXfNYjQaYTQaex83NzcDADo6OtDR0SHltIZcz39f7hw0fLAzJBU7Q1KxMyQVO0NSKK0vg80haRhqbGxEV1cXPD09+xz39PREfX39gM+prKxEUVERnJyckJmZicbGRrz00ktoamrq/dxQfX29pNcEgO3bt2Pr1q39jufk5MDFxUXKaZlNbm6u3BFomGFnSCp2hqRiZ0gqdoakUEpf2traBrXPpC9dtbGx6fNYCNHvWI/u7m7Y2Njggw8+wMiRIwH8+la7Z555Bqmpqb1Xh6S8JvDrW+kSExN7Hzc3N2P8+PGIjo6GWq025bSGTEdHB3JzcxEVFQWVSiVrFhoe2BmSip0hqdgZkoqdISmU1peed43di6RhyN3dHXZ2dv2u2DQ0NPS7stPD29sbPj4+vYMQAAQGBkIIgevXryMgIABeXl6SXhMAHB0d4ejo2O+4SqVSxP8AQFlZaHhgZ0gqdoakYmdIKnaGpFBKXwabQdLd5BwcHKDX6/td/srNzcXs2bMHfE54eDhu3LiB1tbW3mPl5eWwtbWFr68vACAsLKzfa+bk5Nz1NYmIiIiIiO6X5LfJJSYmIj4+HqGhoQgLC8PevXtRXV2NtWvXAvj17Wu1tbV47733AABxcXHYtm0bXnjhBWzduhWNjY149dVX8eKLL/a+Re6VV17B3LlzsWPHDixduhRHjx7FF198gaKiokHnEkIAGPwlMXPq6OhAW1sbmpubFTEZk/KxMyQVO0NSsTMkFTtDUiitLz0zQc+McFfCBKmpqUKj0QgHBwcREhIi8vPze3+2atUqERkZ2Wf/hQsXxKJFi4Szs7Pw9fUViYmJoq2trc+eI0eOCK1WK1QqldDpdCIjI0NSppqaGgGAi4uLi4uLi4uLi4tLABA1NTW/O0PYCHGvcWl46O7uxo0bNzBixIjfvfGCJfTczKGmpkb2mznQ8MDOkFTsDEnFzpBU7AxJobS+CCHQ0tKCcePGwdb27p8MMuluckr0288gKYVarVZEGWj4YGdIKnaGpGJnSCp2hqRQUl9+ewO3u5F0AwUiIiIiIqIHBYchIiIiIiKyShyGzMDR0RGbN28e8HuQiAbCzpBU7AxJxc6QVOwMSTFc+/LA3ECBiIiIiIhICl4ZIiIiIiIiq8RhiIiIiIiIrBKHISIiIiIiskochoiIiIiIyCpxGDLRrl274OfnBycnJ+j1ehQWFv7u/vz8fOj1ejg5OWHSpEnYs2ePhZKSUkjpTF1dHeLi4qDVamFra4uEhATLBSXFkNKZjz/+GFFRURg7dizUajXCwsJw4sQJC6YluUnpS1FREcLDw+Hm5gZnZ2fodDrs3LnTgmlJCaT+LdPjm2++gb29PWbMmGHegKQ4UjqTl5cHGxubfuvixYsWTHxvHIZMkJ6ejoSEBCQnJ8NgMCAiIgKLFy9GdXX1gPurqqqwZMkSREREwGAwYOPGjXj55ZeRkZFh4eQkF6mdMRqNGDt2LJKTkzF9+nQLpyUlkNqZgoICREVF4dixYygtLcX8+fPx5JNPwmAwWDg5yUFqX1xdXbFu3ToUFBTgwoUL2LRpEzZt2oS9e/daODnJRWpnety5cwfPPfccFi5caKGkpBSmdubSpUuoq6vrXQEBARZKPDi8tbYJZs6ciZCQEOzevbv3WGBgIJ5++mls37693/7XXnsN2dnZuHDhQu+xtWvX4vTp0ygpKbFIZpKX1M781rx58zBjxgykpKSYOSUpyf10psfUqVOxfPlyvP766+aKSQoxFH1ZtmwZXF1dcfDgQXPFJAUxtTMrVqxAQEAA7OzskJWVhbKyMgukJSWQ2pm8vDzMnz8ft27dwqhRoyyYVBpeGZKovb0dpaWliI6O7nM8OjoaxcXFAz6npKSk3/6YmBicOnUKHR0dZstKymBKZ8i6DUVnuru70dLSgjFjxpgjIinIUPTFYDCguLgYkZGR5ohICmNqZw4cOICKigps3rzZ3BFJYe7n90xwcDC8vb2xcOFCfP311+aMaRJ7uQMMN42Njejq6oKnp2ef456enqivrx/wOfX19QPu7+zsRGNjI7y9vc2Wl+RnSmfIug1FZ9566y38/PPPiI2NNUdEUpD76Yuvry9u3ryJzs5ObNmyBWvWrDFnVFIIUzpz+fJlJCUlobCwEPb2/PPR2pjSGW9vb+zduxd6vR5GoxEHDx7EwoULkZeXh7lz51oi9qCwzSaysbHp81gI0e/YvfYPdJweXFI7Q2RqZ9LS0rBlyxYcPXoUHh4e5opHCmNKXwoLC9Ha2oqTJ08iKSkJkydPxsqVK80ZkxRksJ3p6upCXFwctm7diilTplgqHimQlN8zWq0WWq2293FYWBhqamrw5ptvchgaztzd3WFnZ9dvCm5oaOg3Lffw8vIacL+9vT3c3NzMlpWUwZTOkHW7n86kp6dj9erVOHLkCBYtWmTOmKQQ99MXPz8/AMC0adPw448/YsuWLRyGrIDUzrS0tODUqVMwGAxYt24dgF/fiiuEgL29PXJycrBgwQKLZCd5DNXfMrNmzcL7778/1PHuCz8zJJGDgwP0ej1yc3P7HM/NzcXs2bMHfE5YWFi//Tk5OQgNDYVKpTJbVlIGUzpD1s3UzqSlpeH555/HoUOH8Pjjj5s7JinEUP2OEULAaDQOdTxSIKmdUavVOHPmDMrKynrX2rVrodVqUVZWhpkzZ1oqOslkqH7PGAwG5X08RJBkhw8fFiqVSuzbt0+cP39eJCQkCFdXV3H16lUhhBBJSUkiPj6+d39lZaVwcXER69evF+fPnxf79u0TKpVKfPTRR3KdAlmY1M4IIYTBYBAGg0Ho9XoRFxcnDAaDOHfunBzxSQZSO3Po0CFhb28vUlNTRV1dXe+6ffu2XKdAFiS1L++++67Izs4W5eXlory8XOzfv1+o1WqRnJws1ymQhZny79Jvbd68WUyfPt1CaUkJpHZm586dIjMzU5SXl4uzZ8+KpKQkAUBkZGTIdQoD4jBkotTUVKHRaISDg4MICQkR+fn5vT9btWqViIyM7LM/Ly9PBAcHCwcHBzFx4kSxe/duCycmuUntDIB+S6PRWDY0yUpKZyIjIwfszKpVqywfnGQhpS/vvPOOmDp1qnBxcRFqtVoEBweLXbt2ia6uLhmSk1yk/rv0WxyGrJOUzuzYsUP4+/sLJycnMXr0aDFnzhzx2WefyZD69/F7hoiIiIiIyCrxM0NERERERGSVOAwREREREZFV4jBERERERERWicMQERERERFZJQ5DRERERERklTgMERERERGRVeIwREREREREVonDEBERERERWSUOQ0REREREZJU4DBERERERkVXiMERERERERFaJwxAREREREVml/wXKqJRvNljjnAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(t_ET, U) = explicittrapezoid_system(f_fast_slow, a, b, u_0, n)\n",
    "Y = U[:,1]\n",
    "y = y_fast_slow.(t, t_0 = 0.0, y_0=y_0, v_0=v_0, K=K)\n",
    "\n",
    "figure(figsize=[10,3])\n",
    "title(\"With K=$K, by explicit trapezoid with step size h=$(approx3(h))\")\n",
    "\n",
    "plot(t, Y, label=\"y computed\")\n",
    "plot(t, y, label=\"exact solution\")\n",
    "legend()\n",
    "grid(true)\n",
    "\n",
    "yerror = y-Y\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error\")\n",
    "plot(t, yerror)\n",
    "grid(true)\n",
    "\n",
    "n_middle = n ÷ 2\n",
    "t_secondhalf = t[n_middle:end]\n",
    "yerror_secondhalf = yerror[n_middle:end]\n",
    "yerrormin = minimum([minimum(yerror_secondhalf), 0.0])*1.1\n",
    "yerrormax = maximum([maximum(yerror_secondhalf), 0.0])*1.1\n",
    "\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error, second half\")\n",
    "ylim(yerrormin, yerrormax)\n",
    "plot(t_secondhalf, yerror_secondhalf)\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Uu3bt0tChQ6/7nm3btqlNmzZ67rnnJEmxsbF6+umn9dprr9WzZAAAAACo2U09o5ObmytJCgoKqnafgQMHaubMmVqxYoXGjx+vzMxMLVy4UHfddVe17ykpKVFJSYntdV5enqSKS2YWi+VmSm5yrh1vcztu1A79gerQG6gOvYHq0BuoiSP1R21rMBmGYdTnCwzD0L333qtLly5p48aNNe67cOFCTZ06VcXFxSorK9M999yjhQsXVnt/36xZszR79uwq4/Pnz5e3t3d9ygUAAADgBIqKijRp0iTl5ubW+Px+vYNOQkKCli9frk2bNtU4rdvhw4c1evRoPf/88xo3bpzS0tL04osvqm/fvnrvvfeu+57rXdGJiYlRVlZWs5yMICkpSWPGjHGYB7/gOOgPVIfeQHXoDVSH3kBNHKk/8vLy1LJlyxsGnXrdujZt2jQtW7ZMGzZsqDHkSBUztQ0aNEgvvviiJKlbt27y8fHRkCFD9PLLLysiIqLKezw8POTh4VFl3Gw22/0Hay/N+dhxY/QHqkNvoDr0BqpDb6AmjtAftf3+Os26ZhiGnn32WS1atEhr165VbGzsDd9TVFRUZcVSV1dX2+cBAAAAQEOrU9BJSEjQRx99pPnz58vX11fp6elKT0/XlStXbPvMmDFDkydPtr2eMGGCFi1apLlz5+rUqVPavHmznnvuOfXr10+RkZENdyQAAAAAcFWdbl2bO3euJGn48OGVxhMTEzVlyhRJUlpams6dO2fbNmXKFOXn5+utt97SCy+8oICAAI0cOVJz5sy5ucoBAAAAoBp1Cjq1udVs3rx5VcamTZumadOm1eWrAAAAADiQpvbUyU2towMAAADAOZVbDe07f1kbjl/U+mOZijKZVP1KmI6HoAMAAABAkpSWe0Ubj2dp/fGL2nQiS7lXvl+cM9e3To/32x1BBwAAAGimii3l+u50jjYcv6gNyRd1PKOg0nZfTzcNbtdSg9oGyZKy305V1g9BBwAAAGgmDMPQyYsFWnfsojYkZ2n7qWyVlFlt200mqXt0gIZ2CNGwDi3VPTpAbq4uslgsWpFJ0AEAAADgIHKLLNp8Mqviqs3xi7qQW1xpe5ifh4a2D9HQDiEa3K6lAn3c7VRpwyLoAAAAAE7kh5MIbDh+UXtTLsv6gxnT3N1c1D82yBZuOoS1kMlksl/BjYSgAwAAADRx6bnFFbOjJV/UpuTKkwhIUtsQn6u3o4Wof2ywvNxd7VTprUPQAQAAAJqY2k4iMLRDxVWbqAAvO1VqPwQdAAAAoAk4m12odccu6ttjmdp2KlvFlsqTCHSLDtCw9hXhpkdMxSQCzRlBBwAAAHBAxZZybT+do3XHMrXu2EWdziqstN1ZJxFoKAQdAAAAwEGcyy7SuuMVwWbLyaxKV23cXEzq3TpQI+JDNaxDiOLDfZ1yEoGGQtABAAAA7OTaszbrjl3UuuOZOnWx6lWb4R1CNSI+RAPbtZSfp9lOlTY9BB0AAADgFkrJKdK64xe17mimtpzM1hVLuW2b69WrNsM7hmhEx1Cu2twEgg4AAADQiErKyrXj9CWtO5apb49l6uSPrtqE+npoeMcQDe8YqkHtWsrfi6s2DYGgAwAAADSw85eKKm5Hu/qsTVHpj67atArUsI4hGt4xRJ0j/Lhq0wgIOgAAAMBNKi2zaueZHH17dYa05MzK69qE+HpoeIeKqzaD23PV5lYg6AAAAAD1kJlXrG+PZWrNkUxtPpGlwh9ctXEx6eqzNhUzpHWO8JOLC1dtbiWCDgAAAFALVquhA6m5Wns0U2uPZupAam6l7S1bXHvWJkRD2oXI35urNvZE0AEAAACqUVBSpk3JF6+Gm4vKKiiptL17TIBGdgzVyPhQ3RbJVRtHQtABAAAAfuBsdqHWHKmYIW3bqWxZyg3bNh93Vw3tEKIR8aEa3jFEob6edqwUNSHoAAAAoFmzlFu188wlrT2aoTVHqy7a2SbYWyPjwzQyPlT9YoPk7uZip0pRFwQdAAAANDs5haVadyxTa45masPxi8ovLrNtc3MxqW+bII3qVHFLWlxICztWivoi6AAAAMDpGYahI2n5V2dJy9CelMsyvr8jTUE+7hreMUSj4sM0pENL+XkykUBTR9ABAACAU7pSWq4tJ7O05mimvj2aqbTc4krbO0f4aWR8qEZ2ClX36AC5MpGAUyHoAAAAwGmk5V7RmiMVV222nMxWSZnVts3T7KLB7VpqRHzFLWkR/l52rBSNjaADAACAJsswDB26kKdvjmRozZGqa9tEBXhVXLWJD9WAtsHyNLvaqVLcagQdAAAANCklZeXadipH3xzO0JojGbrwg1vSTCapZ0yARnUK0+hOYeoQ1kImE7ekNUcEHQAAADi8S4Wl+vZYpr45kqH1xy6qsLTcts3L7Koh7VtqdKcwjYgPVYivhx0rhaMg6AAAAMAhnc4q1DeHM5R0JEM7z+TI+oNZ0kJ9PTSqU5jGdA7VwLYtuSUNVRB0AAAA4BDKrYb2nLukpCMZ+uZwhk7+aOHO+HBfjelccUta1yh/uTBLGmpA0AEAAIDdFJaUaWPyRX1zJFNrj2Yqp7DUts3NxaTb44I1ulOoRnUKU0yQtx0rRVND0AEAAMAtlZ5brG+OZOibq1NAl/5gCmg/TzeNiA/V6E5hGtYxhIU7UW8EHQAAADQqwzB0OC1P3xyumEzgx1NAtwrytt2S1qdNoMyuLnaqFM6EoAMAAIAGV1Zu1XdncrT6UIaSDmco9fIV27ZrU0CP7hymMZ3C1C6UKaDR8Ag6AAAAaBBXSsu1IfmiVh1K19qjmbpcZLFt8zS7aEj7EI1hCmjcIgQdAAAA1NulwlKtOZqpVYfStTH5ooot3z9vE+ht1uhOYRp7W7iGtGcKaNxaBB0AAADUyflLRUo6nKFVh9K148wllf9ggZvoQC+N7RyucbeFqXfrQLnxvA3shKADAACAGhmGoWMZ+Vp1MEOrD6fr0IW8Sts7RfhpbOcwjbstXJ0ifHneBg6BoAMAAIAqyq2Gdp+7pFUH07X6cIbO5RTZtrmYpD5tgmzhhvVt4IgIOgAAAJAkWazSt8cuas3RLH1zJEPZP1i8093NRUPbt9TYzuEa1SlUwS2YTACOjaADAADQjOVesWjdsUx9fSBNa4+4qnT7Hts2P083jeoUpnG3hWlI+xD5ePCrI5oOuhUAAKCZSc8tVtKRDK0+lK6tJ7NVZptMwKRwPw+Nuy1cY28LV7/YIBbvRJNVp6Dz6quvatGiRTp69Ki8vLw0cOBAzZkzRx07dqzxfSUlJfrjH/+ojz76SOnp6YqOjtbMmTP1+OOP31TxAAAAqJ1z2UVaeShNXx9M155zlyttax/aQqM7hcg7J1lPPzRG7u7u9ikSaEB1Cjrr169XQkKC+vbtq7KyMs2cOVNjx47V4cOH5ePjU+37Jk6cqIyMDL333ntq166dMjMzVVZWdtPFAwAAoHrJGflaeTBdXx9M1+G0yjOl9WoVoHG3hWtM5zDFhbSQxWLRihXJzJgGp1GnoLNy5cpKrxMTExUaGqpdu3Zp6NCh1b5n/fr1OnXqlIKCgiRJbdq0qV+1AAAAqJZhGDp0IU9fH0zTyoPpOnmx0LbN1cWk/rFBGt+l4ra0MD9PO1YKNL6bekYnNzdXkmwB5nqWLVumPn366LXXXtOHH34oHx8f3XPPPfrTn/4kLy+vm/l6AACAZs9qNbQn5ZK+PpCulYfSdf7SFds2s6tJg9u11PguERrdOUxBPtyShuaj3kHHMAxNnz5dgwcPVpcuXard79SpU9q0aZM8PT21ePFiZWVl6ZlnnlFOTo7ef//9676npKREJSUlttd5eRWXWi0WiywWS31LbpKuHW9zO27UDv2B6tAbqA694RzKyq3acfaSVh3KVNKRTGXmf/97k6e5YhrocZ3DNKJjS/l6mm3bavp7pzdQE0fqj9rWYDIMw7jxblUlJCRo+fLl2rRpk6Kjo6vdb+zYsdq4caPS09Pl7+8vSVq0aJEefPBBFRYWXveqzqxZszR79uwq4/Pnz5e3NwtSAQCA5qfMKh3LNWlftkkHL5lUWPb9szSeroZuCzTUPchQpwBD7q52LBRoZEVFRZo0aZJyc3Pl5+dX7X71CjrTpk3TkiVLtGHDBsXGxta472OPPabNmzfrxIkTtrEjR46oc+fOOn78uNq3b1/lPde7ohMTE6OsrKwaD8YZWSwWJSUlacyYMTKbzTd+A5oV+gPVoTdQHXqjablSWq4NyVladThD3x7LUkHJ95M5BXqbNbpTqMZ2DtWAuGB5uN3cNND0BmriSP2Rl5enli1b3jDo1OnWNcMwNG3aNC1evFjr1q27YciRpEGDBunzzz9XQUGBWrRoIUk6fvy4XFxcqr0S5OHhIQ+Pqqvtms1mu/9g7aU5HztujP5AdegNVIfecFx5xRZ9ezRTXx9I17rjmSq2WG3bQn0r1rgZ36VijRu3Rljjht5ATRyhP2r7/XUKOgkJCZo/f76WLl0qX19fpaenS5L8/f1tt6DNmDFDqamp+uCDDyRJkyZN0p/+9CdNnTpVs2fPVlZWll588UU9/vjjTEYAAAAgKaewVN8cztDXB9O0+US2Ssu/DzfRgV6647Zwje8arp4xgXJxYfpnoDbqFHTmzp0rSRo+fHil8cTERE2ZMkWSlJaWpnPnztm2tWjRQklJSZo2bZr69Omj4OBgTZw4US+//PLNVQ4AANCEZReUaNWhDK04kKatp7JVbv3+aYK4EB+N7xKu8V0idFukH2vbAPVQ51vXbmTevHlVxuLj45WUlFSXrwIAAHA62QUlWnkoXSsOpGnbqZxK4aZzhJ/GdwnXHV3C1T7M145VAs7hptbRAQAAQM2yCkq08uC1cJOtH2QbdYny051dI3Rnlwi1aeljvyIBJ0TQAQAAaGA1hZuuUf4V4aZruFoHE26AxkLQAQAAaAAX86/elrY/TdtPVw433aL9bVduWgWzJiBwKxB0AAAA6ikzv1irDqZr+YE0fXc6h3ADOBCCDgAAQB38MNxsP52jH87V1P1auOkaoZggwg1gTwQdAACAG8jML9bKg+lavj9N3535UbiJCdBdXSumgibcAI6DoAMAAHAdmXnF+vrqlZsdPwo3PWICdFfXCI3vGq7oQMIN4IgIOgAAAFddzC/R1wfT9NV+wg3Q1BF0AABAs3a5qFQrD6bry/0XtPVk5dnSera6Fm4iFBXgZb8iAdQZQQcAADQ7+cUWJR3O0Jf7LmhjcpbKfpBuuscEaEK3igkFIgk3QJNF0AEAAM1CUWmZ1hzJ1Ff7L+jbYxdVWma1besU4acJ3SN0d9dIpoIGnARBBwAAOK1iS7nWH7+oL/dd0JojmbpiKbdtaxviowndI3V3t0i1C21hxyoBNAaCDgAAcCqWcqs2JWfpy/0XlHQoQ/klZbZtrYK8K67cdItUfLivTCaTHSsF0JgIOgAAoMkrtxradipbX+67oJWH0nW5yGLbFuHvqbu7RWhC90h1jfIn3ADNBEEHAAA0SVaroV3nLunLfRe04kC6sgpKbNtatvDQXV3DNaF7pHq1CpSLC+EGaG4IOgAAoMkwDEP7zufqq30XtPxAmtJyi23bArzNGt8lXBO6Rap/XLBcCTdAs0bQAQAADs0wDB1Jy9eX+y/oq/0XlJJzxbbN18NNY28L193dIzS4XUuZXV3sWCkAR0LQAQAADulsdqGW7b2gpfsu6ERmgW3cy+yq0Z3DNKFbhIZ2CJGn2dWOVQJwVAQdAADgMDLzi7V8f5qW7r2gvSmXbePubi4a0TFEE7pHamR8qLzd+RUGQM04SwAAALvKK7Zo1cF0Ldt3QZtPZMlqVIy7mKRB7Vrq3h5RGntbmPw8zfYtFECTQtABAAC3XLGlXOuOZWrp3gtaczRTpWVW27YeMQG6r0ek7uoWqRBfDztWCaApI+gAAIBbotxqaOvJbC3dm6qVB9MrLeTZNsRH9/WI0j09ItU62MeOVQJwFgQdAADQaK5NB710b6q+2p+mi/nfr3UT4e+pe7pH6p4ekeoc4cdCngAaFEEHAAA0uBOZBVq274KW7U3Vmewi23iAt1l3do3Qvd0j1bdNEAt5Amg0BB0AANAg0nKv6Kt9aVq6L1UHU/Ns415mV43pHKZ7e0RqSPsQubux1g2AxkfQAQAA9Xa5qFRfH0zX0r2p2n46R8bVGdNcXUwa2r6l7usZpdGdwuTjwa8cAG4tzjoAAKBOrpSW65sjGVq694LWH8+UpdywbevbJlD39IjSnV3CFdyCGdMA2A9BBwAA3FC51dC2U9latDtVKw+mqbC03LYtPtxX9/aI0oTuEYoO9LZjlQDwPYIOAACo1tH0PC3enaqley8oPa/YNh4d6KV7e0Tqnu5R6hjua8cKAeD6CDoAAKCS9NxiLduXqkW7U3U0Pd827ufppru7R+r+nlHq0zqQ6aABODSCDgAAUEFJmVYdTNfiPanafDLLNqmA2dWkkfGhur9nlEbEh8rDzdW+hQJALRF0AABopsrKrdp0IkuL96Rq9aEMXbF8/9xNn9aBur9XlO7qGqEAb3c7VgkA9UPQAQCgGTEMQykF0v+34qi+OpChrIIS27bYlj66v2eU7usRpVbBTCoAoGkj6AAA0AykXr6iJXtStWj3eZ286CbpnCQpyMddE7pF6P5e0eoe7c9zNwCcBkEHAAAnlVds0dcH0rRod8Vinte4mQyNvS1cD/SO0dAOITK7utixSgBoHAQdAACcSGmZVRuOX9TiPalKOpKh0jKrbdvtcUG6p1uEXFL36YF7ustsNtuxUgBoXAQdAACaOMMwtDflshbvSdWX+y7oUpHFtq19aAvd3ytK9/aIUlSAlywWi1Zk7LNjtQBwaxB0AABoolIvX9Hi3ee1aHeqTmUV2sZbtvDQvT0q1ru5LdKP524ANEsEHQAAmpCi0jJ9fSBdX+w+r62nsm3r3XiZXTXutjDd3ytag9oGy43nbgA0cwQdAAAcnNVqaPvpHH2x+7xWHEhTUen3690MiAvWA72jNb5LuHw8+GcdAK7hjAgAgIM6m12oL3ad16I9qTp/6YptvE2wtx7oFa37e0UpOpD1bgDgegg6AAA4kLxii1bsT9MXu89rx5lLtnFfDzfd3T1CD/SKVu/WgTx3AwA3QNABAMDOyq2GNp/I0sJd57XqULpKrk4J7WKSBrcP0YO9ozW2c5g8za52rhQAmo46BZ1XX31VixYt0tGjR+Xl5aWBAwdqzpw56tixY63ev3nzZg0bNkxdunTR3r1761MvAABO40RmvhbuStWSPalKzyu2jbcPbaEHekfr/p5RCvPztGOFANB01SnorF+/XgkJCerbt6/Kyso0c+ZMjR07VocPH5aPj0+N783NzdXkyZM1atQoZWRk3FTRAAA0VZeLSvXlvgtauDtV+1Iu28YDvM26p3ukHugVrW7R/tyaBgA3qU5BZ+XKlZVeJyYmKjQ0VLt27dLQoUNrfO/TTz+tSZMmydXVVUuWLKlzoQAANFWWcqvWH7uoL3af15ojmSotr7g1zdXFpBEdK25NGxEfKg83bk0DgIZyU8/o5ObmSpKCgoJq3C8xMVEnT57URx99pJdffvmGn1tSUqKSkhLb67y8PEmSxWKRxWKp7m1O6drxNrfjRu3QH6gOveEYjqTla/HeC1q2L03ZhaW28U7hvrq/Z6Tu6Rau4BYeFYOGVRaLtdFrojdQHXoDNXGk/qhtDSbDuLbUWN0YhqF7771Xly5d0saNG6vdLzk5WYMHD9bGjRvVoUMHzZo1S0uWLKnxGZ1Zs2Zp9uzZVcbnz58vb2+m0QQAOK4Ci7Qzy6TvMl2UWvT97WctzIb6tDTUL8SqqJrv9gYA1KCoqEiTJk1Sbm6u/Pz8qt2v3ld0nn32We3fv1+bNm2qdp/y8nJNmjRJs2fPVocOHWr92TNmzND06dNtr/Py8hQTE6OxY8fWeDDOyGKxKCkpSWPGjJHZbLZ3OXAw9AeqQ2/cWmXlVm08ka2Fu1O19uhFlVkr/h+i2dWkUfGhur9npIa0C5bZ1cXOldIbqB69gZo4Un9cu9vrRuoVdKZNm6Zly5Zpw4YNio6Orna//Px87dy5U3v27NGzzz4rSbJarTIMQ25ublq9erVGjhxZ5X0eHh7y8PCoMm42m+3+g7WX5nzsuDH6A9WhNxrXqYsF+nzXeX2x67wy87+/5bpbtL8e6h2tCd0jFeDtbscKq0dvoDr0BmriCP1R2++vU9AxDEPTpk3T4sWLtW7dOsXGxta4v5+fnw4cOFBp7B//+IfWrl2rhQsX3vD9AAA4moKSMq3Yn6bPdqZo59nvF/QM8nHX/T2j9FCfaMWHN6+7DwDAEdUp6CQkJGj+/PlaunSpfH19lZ6eLkny9/eXl5eXpIrbzlJTU/XBBx/IxcVFXbp0qfQZoaGh8vT0rDIOAICjMgxDO89e0mc7UrT8QJqKSsslVSzoObxjqCb2idbI+DC5u9n/1jQAQIU6BZ25c+dKkoYPH15pPDExUVOmTJEkpaWl6dy5cw1SHAAA9pSeW6wvdp/Xwl3ndTqr0DYe19JHD/WJ0U96saAnADiqOt+6diPz5s2rcfusWbM0a9asunwtAAC3TGmZVWuOZOiznSlaf/yirs4rIG93V93dLUIT+8Sod+tAFvQEAAd3U+voAADgLI6m5+mzHee1ZG+qcn6w5k2/NkF6sE+07uoaIR8P/tkEgKaCMzYAoNnKLbJo2b5Ufb7rvPafz7WNh/l56IFe0Xqwd7TiQlrYsUIAQH0RdAAAzYrVamjLyWx9tjNFKw+lq7TMKqlizZvRncI0sU+MhrRvKTcHWPMGAFB/BB0AQLOQklOkhbsqJhZIvXzFNh4f7quH+sTovh6RCm5RdQ03AEDTRNABADitYku5Vh1K12c7U7T5RLZt3M/TTff2iNLEPjHqEuXHxAIA4IQIOgAAp3MsPV+f7DinxXtSdbnIIkkymaRBbVvqoT7RGndbuDzNrnauEgDQmAg6AACnUFhSpq/2X9AnO1K059xl23ikv6ce6hOjB3tHKybI234FAgBuKYIOAKDJMgxD+8/n6pMdKVq2N1WFpeWSJDeXiokFftYvRkPah8jVhVvTAKC5IegAAJqc3CKLluxN1Sc7UnQkLc82HtvSRz/tG6MHekUrxJeJBQCgOSPoAACaBMMw9N3pHH2yI0UrDqSp5Oq00O5uLrqzS7h+1q+V+scGMbEAAEASQQcA4OCyCkr0xa7z+nRHik5lFdrG48N99bO+Mbq/Z7T8vc12rBAA4IgIOgAAh1NuNbTpRJY++e6ckg5nqMxqSJJ83F11T49I/bRvK3WP9ufqDQCgWgQdAIDDSMu9os92nNdnO1MqLerZIyZAP+8Xo7u6RaqFB/90AQBujH8tAAB2ZSm3au3RTH3y3TmtP35RVy/eyN/LrPt7Ruln/WIUH+5n3yIBAE0OQQcAYBdnsgr16c4ULdx1XhfzS2zjt8cF6ef9WrGoJwDgphB0AAC3TElZuVYeTNcn36Vo66ls23jLFh56sHe0fto3RrEtfexYIQDAWRB0AACN7kxWoRZ8d06f7zqvnMJSSZLJJA3rEKKf9W2lUZ1CZXZ1sXOVAABnQtABADQKS7lVSYcz9PH2s9p84vurN+F+nvpp3xj9tG+MIgO87FghAMCZEXQAAA0qJadIC747p892nldWQcWzNyaTNLxDiCb1b60RHUPkxtUbAEAjI+gAAG5aWblVa45m6uPt57Qx+aKMqzOnhfh66Kd9Kq7exAR527dIAECzQtABANRb6uUr+vS7c/p0Z4oy8r6fOW1I+5Z6uH8rjeoUxrM3AAC7IOgAAOqk3Gpo3bFMzd9+Tt8ey7StexPs466H+sTo5/1i1DqYmdMAAPZF0AEA1EpGXrE+3ZGiT747pwu5xbbxAXHBmtS/Yt0bdzeu3gAAHANBBwBQLavV0MYTWfp421mtOZqp8quXbwK8zXqwV7R+3r+V2oa0sHOVAABURdABAFRxMb9En+1M0Sc7zikl54ptvF+bIE3q30p3dAmXp9nVjhUCAFAzgg4AQFLF1Zutp7L18fazWn0oQ2VXr974ebrpJ72iNal/K3UI87VzlQAA1A5BBwCauZzCUn2+M0ULvjunM9lFtvGerQI0qV8r3d0tUl7uXL0BADQtBB0AaIYMw9CelMv6aOtZfbU/TaXlVklSCw833dczUpP6tVbnSD87VwkAQP0RdACgGSkqLdOyvRf04bazOnQhzzbeNcpfD/dvpQndI+XjwT8NAICmj3/NAKAZOHmxQB9tO6uFu84rv7hMkuTh5qIJ3SP16O2t1T0mwL4FAgDQwAg6AOCkyg1p1aEMLdh5XptPZNvGWwd765H+rfVg72gF+rjbsUIAABoPQQcAnExmXrE+2nZG/9ntqtxt+yRJJpM0Kj5Ujw5ooyHtWsrFxWTnKgEAaFwEHQBwAoZhaNupHH207axWHUq/OjW0SUE+Zv2sbyv9vF8rxQR527tMAABuGYIOADRhecUWLd6dqg+3ndWJzALbeO9WAersnq3/fni0Wnh52LFCAADsg6ADAE3QkbQ8fbjtrJbsSVVRabkkydvdVff1jNIj/VurfYiXVqxYIQ83FztXCgCAfRB0AKCJKCkr18qD6fpw61ntPHvJNt4utIUevb217u8VJT9PsyTJYrHYq0wAABwCQQcAHFzq5Suav/2sPt2RoqyCUkmSm4tJ424L1yO3t9btcUEymZhcAACAHyLoAIADsloNbTyRpQ+3ntXaoxmyGhXjYX4emtSvtX7WL0Zhfp72LRIAAAdG0AEAB5JbZNFnO1P00fazOptdZBsf1C5Yj97eWqM6hcnsynM3AADcCEEHABzA0fQ8/WfLGS3ek6pii1WS5Ovhpgd6R+uR21urXWgLO1cIAEDTQtABADspK7cq6XCG5m05o+2nc2zj8eG+mjygje7rGSlvd07TAADUB/+CAsAtllNYqgXfndPH287qQm6xJMnVxaRxt4XpsQFt1C+WyQUAALhZdbrR+9VXX1Xfvn3l6+ur0NBQ3XfffTp27FiN71m0aJHGjBmjkJAQ+fn5acCAAVq1atVNFQ0ATdHB1Fz99vN9uv3VNfrfVcd0IbdYQT7uShjRVhv/a4T+8XBv9Y8LJuQAANAA6nRFZ/369UpISFDfvn1VVlammTNnauzYsTp8+LB8fHyu+54NGzZozJgxeuWVVxQQEKDExERNmDBB27dvV8+ePRvkIADAUZWWWfX1wTR9sPWsdv1g7ZuuUf56bGAb3d0tQp5mVztWCACAc6pT0Fm5cmWl14mJiQoNDdWuXbs0dOjQ677njTfeqPT6lVde0dKlS/Xll18SdAA4rcz8Ys3ffk7zt59TZn6JpIq1b+7sGqHHBrZRr1YBXLkBAKAR3dQzOrm5uZKkoKCgWr/HarUqPz+/Tu8BgKbAMAztSbms/2w5oxUH0mQpr1j8JsTXQ5P6tdLD/VsplLVvAAC4JeoddAzD0PTp0zV48GB16dKl1u97/fXXVVhYqIkTJ1a7T0lJiUpKSmyv8/LyJEkWi0UWi6W+JTdJ1463uR03aof+cAwllnKtOJihD7ef04HUPNt4zxh/PXp7K43rHCZ3t4pHIm/V3xW9gerQG6gOvYGaOFJ/1LYGk2EYRn2+ICEhQcuXL9emTZsUHR1dq/csWLBATz75pJYuXarRo0dXu9+sWbM0e/bsKuPz58+Xt7d3fcoFgAZ3uUTalOGirRkmFZRV3IbmZjLUq6WhoeFWxbD0DQAADa6oqEiTJk1Sbm6u/Pz8qt2vXkFn2rRpWrJkiTZs2KDY2NhavefTTz/V1KlT9fnnn+uuu+6qcd/rXdGJiYlRVlZWjQfjjCwWi5KSkjRmzBiZzWZ7lwMHQ3/ceoZhaMfZS/pwW4qSjmSq3FpxCg3389CkfjGa2CdawT7udq6S3kD16A1Uh95ATRypP/Ly8tSyZcsbBp063bpmGIamTZumxYsXa926dbUOOQsWLNDjjz+uBQsW3DDkSJKHh4c8PDyqjJvNZrv/YO2lOR87boz+aHxXSsu1dG+q/rP1rI6kfX97Wr/YIE0Z2EZjO4fJzbVOM/bfEvQGqkNvoDr0BmriCP1R2++vU9BJSEjQ/PnztXTpUvn6+io9PV2S5O/vLy8vL0nSjBkzlJqaqg8++EBSRciZPHmy3nzzTd1+++2293h5ecnf378uXw8At9z5S0X6cOtZfbIjRblXKu4J9jS76P6eUZo8oI06RTSvq8wAADQVdQo6c+fOlSQNHz680nhiYqKmTJkiSUpLS9O5c+ds2/75z3+qrKxMCQkJSkhIsI0/9thjmjdvXv2qBoBGZBiGdp29pPc3n9bKg+m6eneaogO9NHlAa03sE6MAb/vfngYAAKpX51vXbuTH4WXdunV1+QoAsJvSMqtWHEjT+5tPa//5XNv4oHbBmjIwViPjQ+Xqwto3AAA0BTe1jg4AOIPsghLN335OH247a1vc093NRff3iNLUwW0UH87taQAANDUEHQDN1pG0PCVuPq0ley+otMwqSQr19dDkAa31836tFNyi6qQoAACgaSDoAGhWrFZDa49m6v3Np7XlZLZtvFu0vx4fFKs7u0bYFvcEAABNF0EHQLNQUFKmhTtTNG/LGZ3JLpIkuZik8V0iNHVQG/VuHSiTiedvAABwFgQdAE4tJadI87ac0Wc7UpRfUiZJ8vN008/7tdKjA1orOtDbzhUCAIDGQNAB4HQMw9D20zlK3HxaSYczbNNDx4X4aOqgWD3QK0re7pz+AABwZvxLD8BplJSV68t9aXp/02kdTsuzjQ/tEKKpg9poWPsQuTA9NAAAzQJBB0CTdzG/RB9vP6uPtp1VVkGpJMnT7KKf9IrW1IFt1D7M184VAgCAW42gA6DJOpiaq8TNZ/TlvgsqLa+YHjrC31OPDmitn/dtpUAfdztXCAAA7IWgA6BJKbca+uZIht7fdFrbT+fYxnu2CtDjg2J1R5dwmV2ZHhoAgOaOoAOgSSgsKdPCXef1/ubTOnt1emg3F5Pu7FoxPXTPVoF2rhAAADgSgg4Ah5aRV6x5W85o/vZzyr1ikST5e5n1cP+K6aEj/L3sXCEAAHBEBB0ADunwhTz9e+Mpfbn/gizlFfNDtwn21hODY/VA72imhwYAADXiNwUADsNqNbT++EX9e9MpbT6RbRvv1yZITw6J1ahOYXJlemgAAFALBB0AdldsKdeSPan696bTOpFZIElyvfr8zZODY9U9JsC+BQIAgCaHoAPAbrILSvThtrP6cOtZZRdWrH/TwsNNP+8Xo8cGtlF0oLedKwQAAE0VQQfALXcis0DvbTqlL3anqrSsYv2bqAAvTR3URj/tGyNfT7OdKwQAAE0dQQfALWEYhraezNa/N53W2qOZtvHu0f56ckicxncJlxvr3wAAgAZC0AHQqErLrFp+4IL+teG0DqflSZJMJmlMpzA9NTROfVoHymRiggEAANCwCDoAGkVukUXzvzun/2w5o/S8YkmSl9lVD/WJ1tRBsYpt6WPnCgEAgDMj6ABoUOeyi/T+5tP6bGeKikrLJUkhvh6aMrCNHu7fSgHe7nauEAAANAcEHQANYtfZS/r3xlNadShd1or1PRUf7qsnh8RpQvcIebi52rdAAADQrBB0ANRbudXQ6kPpenfjKe05d9k2PqxDiJ4aEqdB7YJ5/gYAANgFQQdAnRVbyrVw13n9e+MpnckukiS5u7ro/p5RemJIrDqE+dq5QgAA0NwRdADU2uWiUn249azmbTljW+DT38usyQNaa/KANgrx9bBzhQAAABUIOgBuKCWnSO9tOq1Pd6ToiqVigoGoAC89OSRWE/vEyMeDUwkAAHAs/HYCoFoHU3P17oZTWn4gTeVXZxi4LdJPvxgap7u6RrDAJwAAcFgEHQCVGIahzSey9c8NJ7UxOcs2PqR9Sz09tC0TDAAAgCaBoANAklRWbtXyA2n65/pTOpyWJ0lydTHp7m4RempInLpE+du5QgAAgNoj6ADNXFFpmT7dkaL3Np3W+UtXJEleZlf9rF+MHh8Uq5ggbztXCAAAUHcEHaCZyioo0QdbzuiDbWd1ucgiSQr2cdeUgW30yO2tFejjbucKAQAA6o+gAzQzZ7IK9a+Np7Rw13mVlFklSW2CvfXU0Dg90CtanmZXO1cIAABw8wg6QDOxN+Wy/rn+pFYeSpdRMYGauscE6FfD4jSmc7hcXZhgAAAAOA+CDuDErFZD645n6p/rT2n76Rzb+Kj4UP1iaJz6xQYxgxoAAHBKBB3ACZWWWbVs3wW9u+GkjmcUSJLMribd2yNKvxgapw5hvnauEAAAoHERdAAnUlBSpgXbz+m9TaeVnlcsSWrh4aaH+7fS1EGxCvf3tHOFAAAAtwZBB3AC2YWlmv/dKf1n61nlXqmYQS3Mz0OPD4rVz/u3kp+n2c4VAgAA3FoEHaAJu3D5ir447aL/3rlBxZaKGdTiWvrol8Pa6t6ekfJwYwY1AADQPBF0gCboRGa+5q47paV7U1VmdZFkVdcofz0zvK3G3sYMagAAAAQdoAnZm3JZ//j2hFYfzrCNtfezauZP+mpYxzBmUAMAALiKoAM4OMMwtOlEluauO6ktJ7Nt4+NuC9NTg9sodf9mDWobTMgBAAD4AYIO4KDKrYZWH0rXP9ad1IHUXEmSm0vFFNG/Gh6ndqG+slgsSt1v50IBAAAcEEEHcDClZVYt2ZOqdzac1KmLhZIkT7OLfta3lZ4aGqeoAC87VwgAAOD4XOqy86uvvqq+ffvK19dXoaGhuu+++3Ts2LEbvm/9+vXq3bu3PD09FRcXp3feeafeBQPOqrCkTP/eeEpDX/tW//XFfp26WCg/Tzc9N7KdNv/3SM265zZCDgAAQC3V6YrO+vXrlZCQoL59+6qsrEwzZ87U2LFjdfjwYfn4+Fz3PadPn9add96pp556Sh999JE2b96sZ555RiEhIXrggQca5CCApuxSYanmbTmj/2w9o8tFFWvghPp66MkhsZrUv7VaeHDhFQAAoK7q9BvUypUrK71OTExUaGiodu3apaFDh173Pe+8845atWqlN954Q5LUqVMn7dy5U3/5y18IOmjW0nKv6N8bT2vBd+dUVFouSWoT7K2nh7XVT3pFsQYOAADATbip/1Wcm1vxgHRQUFC1+2zdulVjx46tNDZu3Di99957slgsMpurrtheUlKikpIS2+u8vDxJksVikcViuZmSm5xrx9vcjtuZnbpYqH9tOqOl+y7IUm5IkjqF++rpobG647awijVwDKssVxcArQn9gerQG6gOvYHq0BuoiSP1R21rMBmGYdTnCwzD0L333qtLly5p48aN1e7XoUMHTZkyRb/73e9sY1u2bNGgQYN04cIFRUREVHnPrFmzNHv27Crj8+fPl7e3d33KBewupUBKSnXR/hyTDFVMBd3W19CYKKviAwwxOzQAAMCNFRUVadKkScrNzZWfn1+1+9X7is6zzz6r/fv3a9OmTTfc98fre1zLVtWt+zFjxgxNnz7d9jovL08xMTEaO3ZsjQfjjCwWi5KSkjRmzJjrXv2CYzMMQ9tPX9LcDae05WSObXxkxxA9PTRWvVoF3NTn0x+oDr2B6tAbqA69gZo4Un9cu9vrRuoVdKZNm6Zly5Zpw4YNio6OrnHf8PBwpaenVxrLzMyUm5ubgoODr/seDw8PeXh4VBk3m812/8HaS3M+9qbIMAytO3ZRf1+brN3nLkuSXF1Muqd7pJ4eFqf48IYN7PQHqkNvoDr0BqpDb6AmjtAftf3+OgUdwzA0bdo0LV68WOvWrVNsbOwN3zNgwAB9+eWXlcZWr16tPn362P2HBDQ0q9XQ6sPp+vvaEzp0oeL/Nri7ueinfWL0i6Fxigni1ksAAIBboU5BJyEhQfPnz9fSpUvl6+tru1Lj7+8vL6+K9T1mzJih1NRUffDBB5KkX/7yl3rrrbc0ffp0PfXUU9q6davee+89LViwoIEPBbCfsnKrvtqfpre/PaHkzAJJkre7qx7u30pPDYlTqJ+nnSsEAABoXuoUdObOnStJGj58eKXxxMRETZkyRZKUlpamc+fO2bbFxsZqxYoVev755/X2228rMjJSf/vb35haGk6htMyqxXvO6x/rTupsdpEkydfDTVMGtdHUQbEK8nG3c4UAAADNU51vXbuRefPmVRkbNmyYdu/eXZevAhxasaVcn+5I0T/Xn9SF3GJJUqC3WU8OidOjA1rLz5PbMgEAAOyJJdeBOigsKdPH28/q3Q2nlVVQsdZTiK+Hnh4ap5/3ayUfD/6TAgAAcAT8VgbUQu4Vi/6z5Yze33xal4sqFqmKCvDSL4e31UO9o+VpdrVzhQAAAPghgg5Qg+yCEr236bQ+3HpW+SVlkqTYlj761fC2ur9nlMyuLnauEAAAANdD0AGuIyOvWO9uOKX528/piqVcktQxzFcJI9vprq4RcnW5/mK3AAAAcAwEHeAHUnKK9M8NJ/XZjvMqLbdKkrpG+evZke00plOYXAg4AAAATQJBB5B06mKB/rHupJbsSVWZtWJ2wb5tAvXsyPYa2r6lTCYCDgAAQFNC0EGzdjQ9T29/e1LL91/Q1XyjIe1b6tkR7dQ/Lti+xQEAAKDeCDpolvalXNZb355Q0uEM29joTqFKGNFOPVsF2rEyAAAANASCDpqVXWdz9OaaE9pw/KIkyWSS7uwaoYTh7dQ50s/O1QEAAKChEHTQLOw4k6M3v0nWphNZkiRXF5Pu7RGpZ4a3U7vQFnauDgAAAA2NoAOntu1Utt78JllbT2VLktxcTHqwd7SeGd5OrYK97VwdAAAAGgtBB07HMAxtvRpwtp/OkSSZXU16qE+MfjWsrWKCCDgAAADOjqADp2EYhracrAg4352pCDjuri6a2DdavxreTlEBXnauEAAAALcKQQdNnmEY2picpb+tSdbOs5ckVQScn/WL0S+HtVUkAQcAAKDZIeigyTIMQ+uPX9Sba5K159xlSZK7m4sm9WulXw5rq3B/T/sWCAAAALsh6KDJMQxD645VBJy9KZclSR5uLnq4f2s9PSxOYX4EHAAAgOaOoIMmwzAMrTmSqb+tTdb+87mSJE+zix7p31q/GBanUF8CDgAAACoQdODwDMNQ0uEM/W1tsg6m5kmSvMyuenRAaz01JE4hvh52rhAAAACOhqADh2W1Glp9OEN/W5Osw2kVAcfb/fuA07IFAQcAAADXR9CBw7FaDa08lK6/rUnW0fR8SZKPu6seG9hGTw6JU5CPu50rBAAAgKMj6MBhWK2GVhxM09/XnNCxjIqA08LDTVMGttETg2MVSMABAABALRF0YHflVkPLD6Tp72uSlZxZIEny9XDT1EFt9PjgWAV4E3AAAABQNwQd2I3VauirA2l685vjOnmxUJLk6+mmxwfF6vFBsfL3Ntu5QgAAADRVBB3ccteewXnjm+M6nlFxBcffy6wnBsdqyqA28vMk4AAAAODmEHRwyxhGxSxqf006bptkwNfTTU8NiSPgAAAAoEERdNDoDMPQ2qOZ+us3x23r4LTwcNPjg2P1xOBY+XsRcAAAANCwCDpoNIZhaP3xi/pr0nHtO58rqWIdnKmD2uipIXFMMgAAAIBGQ9BBgzMMQ5tPZOv/ko5p97nLkiQvs6smD2ytp4e2ZR0cAAAANDqCDhrUtlPZ+r+k4/rudI4kycPNRY/e3lpPD2urEF8PO1cHAACA5oKggwax40yO/pp0XFtOZkuS3F1dNKl/Kz0zvK1C/TztXB0AAACaG4IObsruc5f016Tj2picJUkyu5r0s76t9MyItorw97JzdQAAAGiuCDqol/3nL+uvScf17bGLkiQ3F5Me6hOjhBFtFR3obefqAAAA0NwRdFAnB1Nz9cY3yfrmSIYkydXFpAd6RWnayPaKCSLgAAAAwDEQdFArR9Pz9EZSslYeSpckuZik+3pEadqo9opt6WPn6gAAAIDKCDqoUXJGvt5Yk6zl+9MkSSaTNKFbpJ4b1V7tQlvYuToAAADg+gg6uK6TFwv0tzXJWrbvggyjYuyurhH69ej26hDma9/iAAAAgBsg6KCSs9mFenNNspbsSZX1asAZd1uYfjO6gzpF+Nm3OAAAAKCWCDqQJKXlXtHf157QZztSVHY14YzuFKrfjO6gLlH+dq4OAAAAqBuCTjOXXVCif6w7qQ+3nVVpmVWSNLRDiF4Y00HdYwLsWxwAAABQTwSdZir3ikX/3nhK7206raLScklS3zaB+u3YjuofF2zn6gAAAICbQ9BpZopKy5S4+Yz+uf6k8orLJEldo/z1wtgOGtYhRCaTyc4VAgAAADePoNNMlJSVa/72c3r725PKKiiRJLUPbaEXxnbQuNvCCTgAAABwKi51fcOGDRs0YcIERUZGymQyacmSJTd8z8cff6zu3bvL29tbERERmjp1qrKzs+tTL+qorNyqT747pxH/u06zvzysrIIStQry1v9N7K6VvxmqO7pEEHIAAADgdOocdAoLC9W9e3e99dZbtdp/06ZNmjx5sp544gkdOnRIn3/+uXbs2KEnn3yyzsWi9qxWQ0v3pmr0/63XS4sO6EJuscL9PPX/3d9Fa14Ypp/0iparCwEHAAAAzqnOt66NHz9e48ePr/X+27ZtU5s2bfTcc89JkmJjY/X000/rtddeq+tXoxYMw9A3RzL1+upjOpqeL0kK8nHXM8Pb6pHbW8vT7GrnCgEAAIDG1+jP6AwcOFAzZ87UihUrNH78eGVmZmrhwoW66667qn1PSUmJSkpKbK/z8vIkSRaLRRaLpbFLdijXjvdGx20YhracytH/fZOs/ecrfl6+nm56YlAbPTaglVp4uEmyymKxNnbJuIVq2x9ofugNVIfeQHXoDdTEkfqjtjWYDMMw6vslJpNJixcv1n333VfjfgsXLtTUqVNVXFyssrIy3XPPPVq4cKHMZvN19581a5Zmz55dZXz+/Pny9vaub7lO63S+9NU5F53Iq7gT0d3F0NBwQyMjrfK5/o8YAAAAaJKKioo0adIk5ebmys/Pr9r9Gj3oHD58WKNHj9bzzz+vcePGKS0tTS+++KL69u2r995777rvud4VnZiYGGVlZdV4MM7IYrEoKSlJY8aMqRIMD6fl6a/fnNC641mSJLOrST/vG6NfDo1ViK+HPcrFLVZTf6B5ozdQHXoD1aE3UBNH6o+8vDy1bNnyhkGn0W9de/XVVzVo0CC9+OKLkqRu3brJx8dHQ4YM0csvv6yIiIgq7/Hw8JCHR9Vf1M1ms91/sPbyw2M/kVmgvyYd1/IDaZIkVxeTHuodrWmj2isqwMueZcJOmvN/G6gZvYHq0BuoDr2BmjhCf9T2+xs96BQVFcnNrfLXuLpWPBB/ExeTmqWUnCK9uSZZi3afl/Xqj+6e7pF6fkwHxbb0sW9xAAAAgAOpc9ApKCjQiRMnbK9Pnz6tvXv3KigoSK1atdKMGTOUmpqqDz74QJI0YcIEPfXUU5o7d67t1rXf/OY36tevnyIjIxvuSJxYbqk068sj+mzXeVnKKxLO6E5hemFsB3WKaF638gEAAAC1Ueegs3PnTo0YMcL2evr06ZKkxx57TPPmzVNaWprOnTtn2z5lyhTl5+frrbfe0gsvvKCAgACNHDlSc+bMaYDyndvlolK9vTZZ8/a4ymJNkSQNbtdSL4ztoJ6tAu1cHQAAAOC46hx0hg8fXuMtZ/PmzasyNm3aNE2bNq2uX9VsXSktV+KW03pn3UnlFZdJMqlnjL9evCNeA9u2tHd5AAAAgMNr9Gd0UHuWcqs+25miN79JVmZ+xaxzHUJbaFhQrl6c1E/u7u52rhAAAABoGgg6DsBqNbTiYJpeX31cp7MKJUnRgV6aPqaD7rwtVKtWfi2TyWTnKgEAAICmg6BjZxuTL+q1lcd0IDVXkhTs465nR7bTpP6t5OHm6hCrzwIAAABNDUHHTvalXNZrq45q84lsSZKPu6ueGhqnJ4fEqYUHfy0AAADAzeA36lvs5MUCvb76mFYcSJckubu66OHbW+nZEe0U3KLqIqkAAAAA6o6gc4uk5xbrzTXH9dnO8yq3GjKZpPt7Run50R0UE+Rt7/IAAAAAp0LQaWSXi0o1d/1Jzdt8RiVlVknS6E6henFcvDqG+9q5OgAAAMA5EXQaSdW1cKS+bQL133fEq0+bIDtXBwAAADg3gk4Du95aOB3DfPVfd3TUyPhQpokGAAAAbgGCTgOpaS2ce3tEydWFgAMAAADcKgSdBnCjtXAAAAAA3FoEnZvAWjgAAACAY+K38XpgLRwAAADAsRF06iCnsFT/u+ooa+EAAAAADo6gUweuLiatOJCucqvBWjgAAACAAyPo1IG/l1kv39dF4f6e6staOAAAAIDDIujU0YTukfYuAQAAAMANuNi7AAAAAABoaAQdAAAAAE6HoAMAAADA6RB0AAAAADgdgg4AAAAAp0PQAQAAAOB0CDoAAAAAnA5BBwAAAIDTIegAAAAAcDoEHQAAAABOx83eBdSGYRiSpLy8PDtXcutZLBYVFRUpLy9PZrPZ3uXAwdAfqA69gerQG6gOvYGaOFJ/XMsE1zJCdZpE0MnPz5ckxcTE2LkSAAAAAI4gPz9f/v7+1W43GTeKQg7AarXqwoUL8vX1lclksnc5t1ReXp5iYmKUkpIiPz8/e5cDB0N/oDr0BqpDb6A69AZq4kj9YRiG8vPzFRkZKReX6p/EaRJXdFxcXBQdHW3vMuzKz8/P7k0Fx0V/oDr0BqpDb6A69AZq4ij9UdOVnGuYjAAAAACA0yHoAAAAAHA6BB0H5+HhoT/84Q/y8PCwdylwQPQHqkNvoDr0BqpDb6AmTbE/msRkBAAAAABQF1zRAQAAAOB0CDoAAAAAnA5BBwAAAIDTIegAAAAAcDoEHTv4xz/+odjYWHl6eqp3797auHFjtfsuWrRIY8aMUUhIiPz8/DRgwACtWrWq0j7z5s2TyWSq8qe4uLixDwUNrC69sWnTJg0aNEjBwcHy8vJSfHy8/vrXv1bZ74svvlDnzp3l4eGhzp07a/HixY15CGgkDd0bnDecR11644c2b94sNzc39ejRo8o2zhvOo6H7g3OH86hLb6xbt+66f+9Hjx6ttJ/DnTsM3FKffPKJYTabjX/961/G4cOHjV//+teGj4+Pcfbs2evu/+tf/9qYM2eO8d133xnHjx83ZsyYYZjNZmP37t22fRITEw0/Pz8jLS2t0h80LXXtjd27dxvz5883Dh48aJw+fdr48MMPDW9vb+Of//ynbZ8tW7YYrq6uxiuvvGIcOXLEeOWVVww3Nzdj27Ztt+qw0AAaozc4bziHuvbGNZcvXzbi4uKMsWPHGt27d6+0jfOG82iM/uDc4Rzq2hvffvutIck4duxYpb/3srIy2z6OeO4g6Nxi/fr1M375y19WGouPjzdeeumlWn9G586djdmzZ9teJyYmGv7+/g1VIuykIXrj/vvvNx555BHb64kTJxp33HFHpX3GjRtn/OxnP7u5YnFLNUZvcN5wDvXtjZ/+9KfG73//e+MPf/hDlV9kOW84j8boD84dzqGuvXEt6Fy6dKnaz3TEcwe3rt1CpaWl2rVrl8aOHVtpfOzYsdqyZUutPsNqtSo/P19BQUGVxgsKCtS6dWtFR0fr7rvv1p49exqsbjS+huiNPXv2aMuWLRo2bJhtbOvWrVU+c9y4cbX+TNhfY/WGxHmjqatvbyQmJurkyZP6wx/+cN3tnDecQ2P1h8S5o6m7mX9XevbsqYiICI0aNUrffvttpW2OeO4g6NxCWVlZKi8vV1hYWKXxsLAwpaen1+ozXn/9dRUWFmrixIm2sfj4eM2bN0/Lli3TggUL5OnpqUGDBik5OblB60fjuZneiI6OloeHh/r06aOEhAQ9+eSTtm3p6ek31W+wv8bqDc4bTV99eiM5OVkvvfSSPv74Y7m5uV13H84bzqGx+oNzR9NXn96IiIjQu+++qy+++EKLFi1Sx44dNWrUKG3YsMG2jyOeO67fxWhUJpOp0mvDMKqMXc+CBQs0a9YsLV26VKGhobbx22+/Xbfffrvt9aBBg9SrVy/9/e9/19/+9reGKxyNrj69sXHjRhUUFGjbtm166aWX1K5dO/385z+/qc+E42no3uC84Txq2xvl5eWaNGmSZs+erQ4dOjTIZ8LxNXR/cO5wHnX577xjx47q2LGj7fWAAQOUkpKiv/zlLxo6dGi9PvNWIOjcQi1btpSrq2uVZJuZmVklAf/Yp59+qieeeEKff/65Ro8eXeO+Li4u6tu3L/93pQm5md6IjY2VJHXt2lUZGRmaNWuW7ZfZ8PDwen0mHEdj9caPcd5oeuraG/n5+dq5c6f27NmjZ599VlLF7dCGYcjNzU2rV6/WyJEjOW84icbqjx/j3NH03My/Kz90++2366OPPrK9dsRzB7eu3ULu7u7q3bu3kpKSKo0nJSVp4MCB1b5vwYIFmjJliubPn6+77rrrht9jGIb27t2riIiIm64Zt0Z9e+PHDMNQSUmJ7fWAAQOqfObq1avr9Jmwr8bqjett57zRtNS1N/z8/HTgwAHt3bvX9ueXv/ylOnbsqL1796p///6SOG84i8bqjx/j3NH0NNS/K3v27Kn09+6Q545bP/9B83ZtOr/33nvPOHz4sPGb3/zG8PHxMc6cOWMYhmG89NJLxqOPPmrbf/78+Yabm5vx9ttvV5rO7/Lly7Z9Zs2aZaxcudI4efKksWfPHmPq1KmGm5ubsX379lt+fKi/uvbGW2+9ZSxbtsw4fvy4cfz4ceP99983/Pz8jJkzZ9r22bx5s+Hq6mr8+c9/No4cOWL8+c9/tvtUj6i7xugNzhvOoa698WPXm1WL84bzaIz+4NzhHOraG3/961+NxYsXG8ePHzcOHjxovPTSS4Yk44svvrDt44jnDoKOHbz99ttG69atDXd3d6NXr17G+vXrbdsee+wxY9iwYbbXw4YNMyRV+fPYY4/Z9vnNb35jtGrVynB3dzdCQkKMsWPHGlu2bLmFR4SGUpfe+Nvf/mbcdttthre3t+Hn52f07NnT+Mc//mGUl5dX+szPP//c6Nixo2E2m434+PhKJyU0HQ3dG5w3nEddeuPHrveLrGFw3nAmDd0fnDucR116Y86cOUbbtm0NT09PIzAw0Bg8eLCxfPnyKp/paOcOk2EYhv2uJwEAAABAw+MZHQAAAABOh6ADAAAAwOkQdAAAAAA4HYIOAAAAAKdD0AEAAADgdAg6AAAAAJwOQQcAAACA0yHoAAAAAHA6BB0AAAAAToegAwAAAMDpEHQAAAAAOB2CDgAAAACn8/8DDEDS/tMrEi8AAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 48  # explicit trapezoid fails\n",
    "\n",
    "h = (b-a)/n\n",
    "t = range(a, b, n+1)\n",
    "M = [(1)   (-h/2);\n",
    "     (50h) (1 + 101h/2)]\n",
    "N = [(1)    (h/2);\n",
    "     (-50h) (1 - 101h/2)]\n",
    "U = zeros(n+1, 2)\n",
    "U[1,:] = u_0\n",
    "for i in 1:n\n",
    "    U[i+1,:] = M\\(N*U[i,:])\n",
    "end\n",
    "\n",
    "Y = U[:,1]\n",
    "y = y_fast_slow.(t, t_0 = 0.0, y_0=y_0, v_0=v_0, K=K)\n",
    "\n",
    "figure(figsize=[10,3])\n",
    "title(\"K=$K, by trapezoid with step size h=$(approx3(h))\")\n",
    "plot(t, Y, label=\"y computed\")\n",
    "plot(t, y, label=\"exact solution\")\n",
    "legend()\n",
    "grid(true)\n",
    "\n",
    "Yerror = y-Y\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error\")\n",
    "plot(t, Yerror)\n",
    "grid(true)\n",
    "\n",
    "n_middle = n ÷ 2\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error, second half\")\n",
    "plot(t[n_middle:end], Yerror[n_middle:end])\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(t_ET, U) = explicittrapezoid_system(f_fast_slow, a, b, u_0, n)\n",
    "Y = U[:,1]\n",
    "y = y_fast_slow.(t, t_0 = 0.0, y_0=y_0, v_0=v_0, K=K)\n",
    "\n",
    "figure(figsize=[10,3])\n",
    "title(\"With K=$K, by explicit trapezoid with step size h=$(approx3(h))\")\n",
    "plot(t, Y, label=\"y computed\")\n",
    "plot(t, y, label=\"exact solution\")\n",
    "legend()\n",
    "grid(true)\n",
    "\n",
    "yerror = y-Y\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error\")\n",
    "plot(t, yerror)\n",
    "grid(true)\n",
    "\n",
    "n_middle = n ÷ 2\n",
    "t_secondhalf = t[n_middle:end]\n",
    "yerror_secondhalf = yerror[n_middle:end]\n",
    "yerrormin = minimum([minimum(yerror_secondhalf), 0.0])*1.1\n",
    "yerrormax = maximum([maximum(yerror_secondhalf), 0.0])*1.1\n",
    "\n",
    "figure(figsize=[10,3])\n",
    "title(\"Error, second half\")\n",
    "ylim(yerrormin, yerrormax)\n",
    "plot(t_secondhalf, yerror_secondhalf)\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{prf:example} Comparing 4th order methods: Adams-Moulton vs Runge-Kutta (coming soon)\n",
    ":label: ode-ivp-7-2\n",
    "\n",
    "Implementing the $s=3$ case above, which is fourth order accurate, and compare it to the classical Runge-Kutta method {prf:ref}`runge-kutta`.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rather than implementing any of these in general, the next section introduces a strategy for converting these to explicit methods,\n",
    "much as in section {doc}`ODE-IVP-2-Runge-Kutta`\n",
    "Euler's method (Adams-Bashforth $s=1$) was combined with the trapezoid method (Adams-Moulton $s=1$) to get the explicit trapozoid method:\n",
    "an explicit method with the same order of accuracy as the latter of this pair."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "Coming soon."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.8.1",
   "language": "julia",
   "name": "julia-1.8"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
