{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error Control and Variable Step Sizes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.5 *Variable Step-Size Methods* in [Sauer](../frontmatter/references.html#Sauer)\n",
    "- Section 5.5 *Error Control and the Runge-Kutta-Fehlberg Method* in [Burden&Faires](../frontmatter/references.html#Burden-Faires)\n",
    "- Section 7.3 of [Chenney&Kincaid](../frontmatter/references.html#Chenney-Kincaid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Basic ODE Initial Value Problem\n",
    "\n",
    "We consider again the initial value problem\n",
    "\n",
    "$$\n",
    "\\frac{d u}{d t} = f(t, u) \\quad a \\leq t \\leq b, \\quad u(a) = u_0\n",
    "$$\n",
    "\n",
    "We now allow the possibility that $u$ and $f$ are vector-valued as in the section on\n",
    "[Systems of ODEs and Higher Order ODEs](ODE-IVP-4-system-higher-order-equations.ipynb),\n",
    "but omitting the tilde notation $\\tilde u$, $\\tilde f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error Control by Varying the Time Step Size $h_i$\n",
    "\n",
    "Recall the variable step-size version of Euler's method:\n",
    "\n",
    "Input: $f$, $a$, $b$, $n$ <br>\n",
    "\n",
    "$t_0 = a$ <br>\n",
    "$U_0 = u_0$ <br>\n",
    "$h = (b-a)/n$ <br>\n",
    "\n",
    "for i in $[0, n)$:\n",
    "<br>\n",
    "\n",
    "$\\qquad$ Choose step size $h_i$ somehow!\n",
    "<br>\n",
    "\n",
    "$\\qquad$ $t_{i+1} = t_i + h_i$\n",
    "<br>\n",
    "\n",
    "$\\qquad$ $U_{i+1} = U_i + h_i f(t_i, U_i)$\n",
    "<br>\n",
    "\n",
    "end for\n",
    "\n",
    "We now consider how to choose each step size, by estimating the error in each step, and aiming to have error per unit time below some limit like $\\epsilon/(b-a)$, so that the global error is no more than about $\\epsilon$.\n",
    "\n",
    "As usual, the theoretical error bounds like $O(h_i^2)$ for a single step of Euler's method are not enough for quantitative tasks like choosing $h_i$, but they do motivate more practical estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A crude error estimate for Euler's Method: Richardson Extrapolation\n",
    "\n",
    "Starting at a point (t, u(t)), we can estimate the error in Euler's method approximato at a slightly later time $t_i + h$ by using two approximations of $U(t + h)$:\n",
    "- The value given by a step of Euler's method with step size $h$: call this $U^{h}$\n",
    "- The value given by taking two steps of Euler's method each with step size $h/2$: call this $U_2^{h/2}$,\n",
    "because it involves 2 steps of size $h/2$.\n",
    "\n",
    "The first order accuracy of Euler's method gives $e_h = u(t+h) - U^{h} \\approx 2(u(t+h) - U_2^{h/2})$,\n",
    "so that\n",
    "\n",
    "$$e_h \\approx \\frac{U_2^{h/2} - U^{h}}{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step size choice\n",
    "\n",
    "What do we do with this error information?\n",
    "\n",
    "The first obvious ideas are:\n",
    "- Accept this step if $e_h$ is small enough, taking $h_i = h$, $t_{i+1} = t_i + h_i$, and $U_{i+1} = U^h$, but\n",
    "- reject it and try again with a smaller $h$ value otherwise; maybe halving $h$; but there are more sophisticated options too."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "\n",
    "Write a formula for $U_h$ and $e_h$ if one starts from the point $(t_i, U_i)$, so that $(t_i + h, U^h)$ is the proposed value for the next point $(t_{i+1}, U_{i+1})$ in the approximate solution — but only if $e_h$ is small enough!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error tolerance \n",
    "\n",
    "One simple criterion for accuracy is that the estimated error in this step be no more than some overall upper limit on the error in each time step, $T$.\n",
    "That is, accept the step size $h$ if\n",
    "\n",
    "$$|e_h| \\leq T$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A crude approach to reducing the step size when needed\n",
    "\n",
    "If this error tolerance is not met, we must choose a new step size $h'$, and we can predict roughly its error behavior using the known order natue of the error in Euler's method: scaling dowen to $h' = s h$, the error in a single step scales with $h^2$ (in general it scales with $h^{p+1}$ for a method of order $p$), and so to reduce the error by the needed factor $\\displaystyle \\frac{e_h}{T}$ one needs approximately\n",
    "\n",
    "$$\n",
    "s^2 = \\frac{T}{|e_h|}\n",
    "$$\n",
    "\n",
    "and so using $e_h \\approx \\tilde{e}_h = |U^{h/2} - U^{h}|$ suggests using\n",
    "\n",
    "$$s = \\left( \\frac{T}{|U^{h/2} - U^{h}|} \\right)^{1/2}$$\n",
    "\n",
    "However this new step size might have error that is still slightly too large, leading to a second failure.\n",
    "Another is that one might get into an infinite loop of step size reduction.\n",
    "\n",
    "So refinements of this choice must be considered."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Increasing the step size when desirable\n",
    "\n",
    "If we simply follow the above aproach, the step size, once reduced, will never be increased.\n",
    "This could lead to great inefficiency, through using an unecessarily small step size just because at an earlier part of the time domain, accuracy required very small steps.\n",
    "\n",
    "Thus, after a successful time step, one might consider increasing $h$ for the next step.\n",
    "This could be done using exactly the above formula, but again there are risks, so again refinement of this choice must be considered.\n",
    "\n",
    "One problem is that if the step size gets too large, the error estimate can become unreliable; another is that one might need some minimum \"temporal resolution\", for nice graphs and such.\n",
    "\n",
    "Both suggest imposing an upper limit on the step size $h$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another strategy for getting error estimates: two (related) Runge-Kutta methods\n",
    "\n",
    "The recurring strategy of estimating errors by the difference of two different approximations — one expected to be far better than the other — can be used in a nice way here.\n",
    "I will first illustrate with the simplset version, using Euler's Mathod and the Explicit Trapezoid Method.\n",
    "\n",
    "Recall that the increment in Euler's Method from time $t$ to time $t+h$ is\n",
    "\n",
    "$$K_1 = h f(t, U)$$\n",
    "\n",
    "whereas for the Explict Trapezoid Method it is $(K_1 + K_2)/2$, as given by\n",
    "\n",
    "$$\\begin{split}\n",
    "K_1 &= h f(t, U)\n",
    "\\\\\n",
    "K_2 &= h f(t+h, U + K_1)\n",
    "\\end{split}$$\n",
    "\n",
    "Thus we can use the difference, $|K_1 - (K_1 + K_2)/2| = |(K_1 - K_2)/2|$ as an error estimate.\n",
    "In fact to be cautious, one often drops the factor of $1/2$, so using approximation $\\tilde{e}_h = |K_1 - K_2|$.\n",
    "\n",
    "One has to be careful: this estimates the error in Euler's Method, and one has to use it that way:\n",
    "using the less accurate value $K_1$ as the update.\n",
    "\n",
    "A basic algorithm for the time step starting with $t_i, U_i$ is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$K_1 \\leftarrow h f(t_i, U_i)$\n",
    "\n",
    "$K_2 \\leftarrow h f(t_i + h, U_i + K_1)$\n",
    "\n",
    "$e_h \\leftarrow |K_1 - K_2|$\n",
    "\n",
    "$s \\leftarrow \\sqrt{T/e_h}$\n",
    "\n",
    "if $e_h < T$\n",
    "\n",
    "$\\quad U_{i+1} = U_i + K_1$\n",
    "\n",
    "$\\quad t_{i+1} = t_i + h$\n",
    "\n",
    "$\\quad$ Increase $h$ for the *next* time step:\n",
    "\n",
    "$\\quad h \\leftarrow s h$\n",
    "\n",
    "else:  $\\quad$ (not good enough: reduce $h$ and try again)\n",
    "\n",
    "$\\quad h \\leftarrow s h$\n",
    "\n",
    "$\\quad$ Start again from $K_1 = \\dots$\n",
    "\n",
    "end if"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, in practice one needs:\n",
    "\n",
    "- An upper limit $h_{max}$ on the step size $h$, partly because error estimates become unreliable if $h$ gets too large,\n",
    "and also becuase subsequent use of the results (like graphs) might need sufficiently \"fine\" data.\n",
    "\n",
    "- A lower limit $h_{max}$ on $h$, to avoid infinite loops and such.\n",
    "\n",
    "- Since we are using only an approximation $\\tilde{e}_h$ of $e_h$, and out of general caution,\n",
    "it is typical to include a \"safety factor\" of about $0.8$ or $0.9$, when computing the *next* time step: reducing the step size scale factor to $S = 0.9 \\sqrt{T/e_h}$.\n",
    "\n",
    "Incorporating these refinements:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$K_1 = h f(t_i, U_i)$\n",
    "\n",
    "$K_2 = h f(t_i+h, U_i + K_1)$\n",
    "\n",
    "$e_{h} = |K_1 - K_2|$\n",
    "\n",
    "$s = 0.9\\sqrt{T/e_h}$\n",
    "\n",
    "if $e_h < T$\n",
    "\n",
    "$\\quad U_{i+1} = U_i + K_1$\n",
    "\n",
    "$\\quad t_{i+1} = t_i + h$\n",
    "\n",
    "$\\quad$ Increase $h$ for the *next* time step:\n",
    "\n",
    "$\\quad h \\leftarrow \\min(0.9 s h, h_{max})$\n",
    "\n",
    "else: $\\quad$ (not good enough; reduce $h$ and try again)\n",
    "\n",
    "$\\quad h \\leftarrow \\max(0.9 s h, h_{min})$\n",
    "\n",
    "$\\quad$ Start again from $K_1 = \\dots$\n",
    "\n",
    "end if"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "\n",
    "Implement the above, and test on the two familiar examples\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "du/dt &= Ku\n",
    "\\\\\n",
    "&\\text{and}\n",
    "\\\\\n",
    "du/dt &= K(\\cos(t) - u) - \\sin(t)\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "($K=1$ is enough.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Partial Solution to Exercise 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib.pyplot import figure, plot, title, grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import sqrt\n",
    "\n",
    "def euler_error_control(f, a, b, u_0, errorTolerance=1e-3, h_min=1e-6, h_max=0.1, steps_max=1000, demoMode=False):\n",
    "    # Use Python lists rather than Numpy arrays; they are easier to \"increment\"\n",
    "    # Initialize variables holding the current values of t and U\n",
    "    steps = 0\n",
    "    t_i = a\n",
    "    U_i = u_0\n",
    "    t = [t_i]\n",
    "    U = [U_i]\n",
    "    h = h_max  # Start optimistically!\n",
    "    while t_i < b and steps < steps_max:\n",
    "        K_1 = h*f(t_i, U_i)\n",
    "        K_2 = h*f(t_i + h/2, U_i + K_1/2)\n",
    "        errorEstimate = abs(K_1 - K_2)\n",
    "        s = 0.9 * sqrt(errorTolerance/errorEstimate)\n",
    "        if errorEstimate <= errorTolerance:  # Success!\n",
    "            t_i += h\n",
    "            U_i += K_1\n",
    "            t.append(t_i)\n",
    "            U.append(U_i)\n",
    "            # Adjust step size up, but not too big\n",
    "            h = min(s*h, h_max)\n",
    "        else:  #Innacurate; reduce step size and try again\n",
    "            h = max(s*h, h_min)\n",
    "            if demoMode: print(f\"{t_i=}: Decreasing step size to {h:0.3e} and trying again.\")\n",
    "        # A refinement not mentioned above; the next step should not overshoot t=b:\n",
    "        if t_i + h > b:\n",
    "            h = b - t_i\n",
    "        steps += 1\n",
    "    # Convert out to Numpy arrays, so that they can be used as input to numerical functions and such:\n",
    "    t = np.array(t)\n",
    "    U = np.array(U)    \n",
    "    return (t, U)\n",
    "    # Note: if the step count ran out, this does not reach t=b, but at least it is correct as far as it goes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, U):\n",
    "    return k*U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import figure, plot, title, grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 1.0\n",
    "a = 1.0\n",
    "b = 3.0\n",
    "u_0 = 2.0\n",
    "def u(t):\n",
    "    \"\"\"Note: the input \"t\" must be a numpy array or a number; not a Python list.\"\"\"\n",
    "    return u_0*np.exp(k*(t-a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get a \"stop watch\"\n",
    "# This gives the \"wall clock\" time in seconds since a reference moment, called \"the epoch\".\n",
    "# (For macOS and UNIX, the epoch is the beginning of 1970.)\n",
    "from time import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_i=1.0: Decreasing step size to 9.000e-02 and trying again.\n",
      "\n",
      "With errorTolerance=0.01, this took 36 time steps, of average length 0.0556\n",
      "The maximum absolute error is 0.831\n",
      "The maximum absolute error per time step is 0.0231\n",
      "The time taken to solve was 0.000543 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorTolerance = 1e-2\n",
    "time_start = time()\n",
    "(t, U) = euler_error_control(f, a, b, u_0, errorTolerance, demoMode=True)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "\n",
    "steps = len(U) - 1\n",
    "h_ave = (b-a)/steps\n",
    "U_exact = u(t)\n",
    "U_error = U-U_exact\n",
    "U_max = max(abs(U_error))\n",
    "print()\n",
    "print(f\"With {errorTolerance=}, this took {steps} time steps, of average length {h_ave:0.3}\")\n",
    "print(f\"The maximum absolute error is {U_max:0.3}\")\n",
    "print(f\"The maximum absolute error per time step is {U_max/steps:0.3}\")\n",
    "print(f\"The time taken to solve was {time_elapsed:0.3} seconds\")\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Solution to du/dt={k}u, u({a})={u_0}\")\n",
    "plot(t, U, \".-\")\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Error in the above\")\n",
    "plot(t, U_error, \".-\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_i=1.0: Decreasing step size to 2.846e-02 and trying again.\n",
      "\n",
      "With errorTolerance=0.001, this took 119 time steps, of average length 0.0168\n",
      "The maximum absolute error is 0.265\n",
      "The maximum absolute error per time step is 0.00223\n",
      "The time taken to solve was 0.00047 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAy8AAAE/CAYAAABPZPyCAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABArElEQVR4nO3deXydZZ3//9d1kqZbUrqkLZRudGUHadlka8EFFXXGlUUdHREdcZsZt9FxGUcdZ8aHP/XrMiOguABFRQYEWYWKLC1toLSU7m3SfUly0jZNmybnXL8/zukhSZM2TXKa7fV8PPJoz33f576v8/Fwm3ev5Q4xRiRJkiSpp0t0dwMkSZIkqT0ML5IkSZJ6BcOLJEmSpF7B8CJJkiSpVzC8SJIkSeoVDC+SJEmSegXDiyRJkqRewfAiSW0IIUwOIcQQQmEH339DCOHRrm5XV+vs52zlfOUhhNd1xbl6ixDCf4QQPpOH854dQni2q88rSb2V4UVSnxdCuDSE8GwIYXcIoTqE8EwI4fwuvsZhASDGeEeM8Q1deZ3steaEEDZ39XmPsQ3XhxDubMdxXw8h/KaD13hP9n+3uhDC/Ha2qSKEsC+E8H8hhJEdue6xCiGMBj4A/G/2dVEI4ffZEBdDCHOO8v6RIYR7s+2uCCFcf2hfjHEpUBNCeGsH2vW5EMLLIYS9IYQNIYTPHeX4q0IIK7P1fjKEMOlYrylJ+WZ4kdSnhRCGAQ8A/w8YCZwM/BtQ353t6gPeDPwpz9eoBr4PfOdoB4YQziATHt4PjAXqgJ/ks3FNfBD4U4xxf5NtTwPvA7a34/0/Bg6SafcNwE+zn+eQO4CPdqBdgUyoGgFcDXwihHBtqweGUAr8AfgKmf9OFgN3d+CakpRXhhdJfd0MgBjjXTHGVIxxf4zx0ey/aBNCSIQQ/jX7L947Qwi/CiGc0NqJWg6HatGr8FT2z5oQQm0I4eIQwgdDCE83Of61IYRF2R6gRSGE1zbZNz+E8O/ZXqG9IYRHs79QtmzDUOAhYFz2OrUhhHEhhIEhhO+HELZmf74fQhjYxucoCCF8N4RQGUJYD7zlGD4nIYQE8Hrg4ezr92frVxVC+HKT464GvgS8N9vOl1prT1tijI/HGH8LbG3H4TcAf4wxPhVjrCXzS/g7Qggl7flMRxJCuD2E8M0mr1v2fL0J+EuTdh+MMX4/xvg0kDrKuYcC7wS+EmOszb7nfjIh7JD5wFVt/e/Zlhjjf8UYX4gxNsYYVwH3AZe0cfg7gOUxxt/FGA8AXwfOCSGceizXlKR8M7xI6utWA6kQwi9DCG8KIYxosf+D2Z+5wBSgGPhRB65zefbP4THG4hjjc013ZocwPQj8EBgFfA94MIQwqslh1wMfAsYARcBnW14kxriPzC/LW7PXKY4xbgW+DFwEnAucA1wA/Gsbbf0IcA3wGmA28K5j/KwXAOtjjJUhhNOBn5L5ZXtc9rONz7b1YeDbwN3Zdp6TrcVPQgg1bfwsPca2HHIGkAtHMcZ1ZHozZnTwfMfiLGBVB987A0jFGFc32fYSmc8DQIxxC9AAzAQIIXzxCPWrae0iIYQAXAYsb6MdLeu3D1jXtB2S1BMYXiT1aTHGPcClQARuAXaFEO4PIYzNHnID8L0Y4/rsv9j/C3Bt6KLJ6028BVgTY/x19l/C7wJWAk3nMvwixrg6O/zot2SCSHvdAHwjxrgzxriLzNC497dx7HuA78cYN8UYq4H/6MBnOTRk7F3AA9kej3oyPR7pI705xvjxGOPwNn7OPsa2HFIM7G6xbTdQ0sHzHYvhwN4Ovre97d6bvQ4xxu8coX7D27jO18n8f/4vOtkOSepWhhdJfV6McUWM8YMxxvHAmWR6CL6f3T0OqGhyeAVQSGb+QVdqeZ1D1zq5yeum8yPqyPxC2dHzV2S3tXXsphbHHoum812anSv7L/ZVx3i+rlALDGuxbRgdDxXHIknHf8lvb7tLgJqOXCCE8Akyc1/ekg2YnWmHJHUrw4ukfiXGuBK4nUyIgcx8iqarKk0EGoEdrbx9HzCkyesTm576KJdueZ1D19pylPe1prVrtfY52porsg2Y0OLYptr8nCGEE4GTgBdaO1cIYQiZoWNttjWE8D9N5uu0/GlrWNPRLCczXO7QNaYAA8kMGzziZ2qHo713KR0fnrYaKAwhTG+y7RyaDO8KIYwjM4xwVfb1l45Qv9qmJw8h/D3wReCqGOORVqhrWb+hwFTaHmYmSd3C8CKpTwshnBpC+OcQwvjs6wnAdcCC7CF3Af8YQjglhFDMq3M0Gls53RIyQ8oGhBBazhXZRWa41JQ2mvInYEbILOdbGEJ4L3A6mZXQjtUOYFSLhQXuAv41hDA6O9H/q0BbE9J/C3wqhDA+Owfoiy32L6Htz/lm4OEY46FQ8nvgmpBZjroI+AbN/79lBzA5O8kfgBjjx5rM12n5k5tjkV1YYBCZnrBECGFQCGFAG5/pDuCtIYTLsr94fwP4Q4zxUM/BkT7ToQn9H2zj3EuAN4fMksYnAp9psf9PwBUtzjcw23aAomzbQ8sTZ3uq/gB8I4QwNIRwCfB24NdNDpsDPHGo1yTG+O0j1C/XWxdCuIHM9/n1Mcb1bXy2Q+4FzgwhvDPb7q8CS7NhX5J6DMOLpL5uL3AhsDCEsI9MaHkZ+Ofs/p+T+UXxKWADcAD4ZBvn+gqZf41OkplTknvOSYyxDvgW8Ex24vRFTd8YY6wiM0n+n8kMq/o8cE2MsfJYP1D2F8q7gPXZa40DvklmedulwDIyPSPfbOMUtwCPkJmg/QKZX57b9TlpsURyjHE5cHP2mG3Z9zT9F/7fZf+sCiG8wLF5P7CfzIIAl2X/fsuhndmehsuatONjZELMTjLDrD7ens+UDV2jeDXQtvRrMrUqBx7l8CWEf0Um3Axusm1Vtr0nk6n1frI9Y9mek4eaHPtxYHC23XcB/5D9PIfcAPxPG207km+S+VyLmvTM5M4TQlieDThk50m9k8x3OEnmv5lWl1WWpO4UXv3HM0mS2pZdxGA7MDXG2HJyd68VQrgUuDnGeF0nzvFtYGeM8ftd1rDMec8CfhZjvLgrzytJvZXhRZLULiGEMcA7Y4w/7e62SJL6J8OLJEmSpF7BOS+SJEmSegXDiyRJkqReoaufIH1EpaWlcfLkycfzkm3at28fQ4cO7e5m9GnWOP+scf5Z4/yzxvllffPPGuefNc6/nlTjsrKyyhjj6Nb2HdfwMnnyZBYvXnw8L9mm+fPnM2fOnO5uRp9mjfPPGuefNc4/a5xf1jf/rHH+WeP860k1DiFUtLXPYWOSJEmSegXDiyRJkqRewfAiSZIkqVcwvEiSJEnqFQwvkiRJknoFw4skSZKkXsHwIkmSJKlXMLxIkiRJ6hUML5IkSVI/VlaR5IF1BymrSHZ3U47K8CJJkiT1U4vLq3nv/z7HPWsauOHWBT0+wBheJEmSpH7or2t2cdOvy2hMRyLQ0Jhmwfqq7m7WERV2dwMkSZIkHV/3v7SFT9+1hJh9HYABhQkumjKqO5t1VPa8SJIkSf3Io8u389nfLs0FlwRwxqgEd9x4EbMmjejOph2VPS+SJElSP7CovJrvPbqK59ZXM3X0UDYn99OYSjOgMMHfTCvq8cEFDC+SJElSn/fUql188PbnSUcoCIFv/s2ZFBUWsGB9FRdNGcXeDS91dxPbxfAiSZIk9WGvbN3DJ+e9SPrQODEiL2ys4ea503K9LfM3dFvzjonhRZIkSeqDyiqS/Pzp9Tz2yg6GDiykqDBBKjtMrKdPzG/LUcNLCOHnwDXAzhjjmS32fRb4b2B0jLEyP02UJEmSdCwWrq/i+lsXkkpHEgG+++5zGD6kKDdMrDfMb2lNe1Ybux24uuXGEMIE4PXAxi5ukyRJkqQO2rZ7P/949xJS2XFiAVi5fS+zJo1oNlSsNzpqz0uM8akQwuRWdv1/wOeB+7q6UZIkSZKOTVlFkt8u3shDy7ZT35hmQEEgnY69ephYSyHGePSDMuHlgUPDxkIIbwOuijF+OoRQDsxua9hYCOEm4CaAsWPHzpo3b14XNb1zamtrKS4u7u5m9GnWOP+scf5Z4/yzxvllffPPGuefNT66NclGvvN8Pansr/YfO7uI0sEJVlanOHVkAdNGFBzx/T2pxnPnzi2LMc5ubd8xT9gPIQwBvgy8oT3Hxxh/BvwMYPbs2XHOnDnHesm8mD9/Pj2lLX2VNc4/a5x/1jj/rHF+Wd/8s8b5Z42PbPf+Bv79J8+SivUAFAQoOekUbpw7rd3n6C017shqY1OBU4CXQggA44EXQggXxBi3d2XjJEmSJLWurCLJfUu28MjL26msracwEYixbw0Ta+mYw0uMcRkw5tDrow0bkyRJktS1ysqrufaWBTRkx4l9+2/PYuaJJb1+NbGjac9SyXcBc4DSEMJm4Gsxxtvy3TBJkiRJh6s72MhX71ueCy4FAZJ1B5k1aUSfDS2HtGe1seuOsn9yl7VGkiRJUqvKKpI8uGwrjy7fwebk/n4xTKyljsx5kSRJknQclVUkufZnz+V6W756zWmcM2FEnx8m1pLhRZIkSerBDjSk+Lc/Nh8mtr8h3S+GibVkeJEkSZJ6oLKKJA8t28Zjr+ygorquXw4Ta8nwIkmSJPUwLYeJffktp3HexP43TKwlw4skSZLUg+w/mOLf7n91mFgiwMHG/jlMrCXDiyRJktRD3L9kC9944BUqaw86TKwVhhdJkiSpm8UY+e6jq/jxk+sAKCpI8PW3nUGy7mC/HibWkuFFkiRJ6ka19Y18+d5l3Ldka25bKp0mWXeQm+dO68aW9TyJ7m6AJEmS1F/9bvEmLv3PJ7h/yVauO38CgwYkKAg4VKwN9rxIkiRJx1mMkW888Aq/eKYcyAwTe9fsCbxr9oR+v6LYkRheJEmSpOOosraez/3uJZ5ctSu3LZVOs2B9FTfPnWZoOQKHjUmSJEnHyS+e3sAV//Ukf11byUcuO8VhYsfInhdJkiQpzw42pvnc71/KTcofWJjg6jNP4uozT3KY2DEwvEiSJEl5UlaR5KFl23hi5U7WV+7LbW9MOUysIwwvkiRJUh6UlVdz7S0LaEhFAG64cCL3vLCZhsa0w8Q6yPAiSZIkdbHddQ186d6Xc8ElEWDc8MHcceNFDhPrBMOLJEmS1EXKKpL8dvEmHn9lBzV1BylMBGKMuZ6WWZNGGFo6wfAiSZIkdYGF66u44daFNKYjAfjPd57F1DEl9rR0IcOLJEmS1Elrd9byqXkv0ph+dZjYrtqDvOd8e1q6kuFFkiRJ6qCy8mp++pd1PLV6FwMHFDCgIJBORyfk54nhRZIkSeqAx1fs4KZfLSYdMz0tP3nvuYwYUuQwsTwyvEiSJEnH6OGXt/GZu5eQHSVGAFZt3+tzW/LM8CJJkiS101/X7OI7D61k+dY9TCkdypaa/TSmfG7L8WJ4kSRJktrhV8+V87X7lhOBwkTgO+88i4JEwmFix5HhRZIkSTqCAw0pvvvIKm59ekNuW4yRReVJh4kdZ4YXSZIkqRVlFUnuW7KFJ1buZHNyP288Yyx/WbWLBoeJdRvDiyRJktTC8xuquP6WhbnntnzlmtP48KVTKKtIOkysGxleJEmSpCbW7NjLp+569YGTBQEONKQBmDXJh052J8OLJEmSBCwqr+bHT6zl6XWVDPaBkz2S4UWSJEn93gNLt/LJu14kZh84+f33nstwHzjZ4xw1vIQQfg5cA+yMMZ6Z3fbfwFuBg8A64EMxxpo8tlOSJEnqUmUVSZ5bV0nVvoP8+rkKYpMHTq70gZM9UqIdx9wOXN1i22PAmTHGs4HVwL90cbskSZKkvCmrSHL9LQv47qOr+cUz5UwZPZSBhQkKAg4T68GO2vMSY3wqhDC5xbZHm7xcALyri9slSZIk5UU6HfnJk2upb8xMwg/A288dx0VTSh0m1sN1xZyXvwfu7oLzSJIkSXlTVpHk4Ze38fSaSlZs30siZLYXFSa4aEqpK4n1AiEeGtx3pIMyPS8PHJrz0mT7l4HZwDtiGycKIdwE3AQwduzYWfPmzetsm7tEbW0txcXF3d2MPs0a5581zj9rnH/WOL+sb/5Z4/zrihqvTjbyn8/Xk8r+xnrNlELOGV3Aquo0p44sYNqIgi5oae/Vk77Hc+fOLYsxzm5tX4d7XkIIf0dmIv9VbQUXgBjjz4CfAcyePTvOmTOno5fsUvPnz6entKWvssb5Z43zzxrnnzXOL+ubf9Y4/zpb47U7a/nSzxfmgktBgNOmT+Ujc6d1TQP7gN7yPe5QeAkhXA18AbgixljXtU2SJEmSOu/5DVX86Il1PLu+koEFCZ/b0ge0Z6nku4A5QGkIYTPwNTKriw0EHgshACyIMX4sj+2UJEmS2u2ess189vcv5Z7b8oP3vYYRPrel12vPamPXtbL5tjy0RZIkSeqU+sYUP3piLT9+cm2z57as8rktfUJXrDYmSZIkdbs7F1bw3UdXU73vIFfMKGXB+moaU2mHifUhhhdJkiT1arX1jXz+9y/xp2XbASgqCHzqqhl86iocJtbHGF4kSZLU65RVJFmwvooBBYHbnyln6+4DuX2pdGTB+iqHifVBhhdJkiT1KmUVSa6/ZQH1jWkAxo8YzLf/9iy+8cByGhodJtaXGV4kSZLUa8QYueWv63PBJQDvmT2e6y+cyMwTSxwm1scZXiRJktTjlVUkeejlbSxYV8XLW/cQQia4FBUmuGTaaABmTRphaOnjDC+SJEnq0VZVN/Lfjz5HYzqz9vHHLp/C604fy8IN1fay9DOGF0mSJPVYi8qr+dGSerKjxCgIUDJ4ALMnj2T25JHd2zgdd4YXSZIk9ThPrdrFdx9bxdLNuxlWBAMKAul0dDJ+P2d4kSRJUo8RY+T7j6/hB39eA0BBIvCxs4u48PxZTsaX4UWSJEndr6wiyUPLtrFwQxXLtux5dUeMrN+d5uNOxheGF0mSJHWz59ZV8v7bns9NyH/bueN4dPn23DNbTh1Z0M0tVE9heJEkSVK3+cvqXXx63ou54FIQYObYEv7u4sm5YWJ7N7zUza1UT2F4kSRJ0nFVVpHk8Vd2sGRTkufWVzPuhEHUFaRIpdO5CflNn9kyf0M3N1g9huFFkiRJx83zG6q4/paFuZ6W686fwNfffgYvb9njhHwdleFFkiRJx8XC9VXcfOcLueCSCDB+5BAGFhY062mR2mJ4kSRJUl49vmIH33t0Na9s20NpcZHPbFGHGV4kSZKUF42pNN/60wp+8Uw5AIWJwA+vfQ0DBxQ4REwdYniRJElSlymrSLJgfRUlgwq5Y8FGVu3Ym9sXY+TFTTXcPHeaoUUdYniRJElSlyirSHL9LQuob0wDUFpcxOevnskP/7wm98wWh4mpMwwvkiRJ6rT6xhQ/eHx1LrgE4P0XTeLjc6Zx4SmjHCamLmF4kSRJUoeVVSS5c2EFz66rYtvuAyRCZntRYYJLp48GcCUxdRnDiyRJkjrkgaVb+dRdL5KOmZ6Wf33Labxm4gh7WZQ3hhdJkiS1W1lFkqdW76S8qo4/vrSV7CNbSASob0zby6K8MrxIkiSpXRaXV3PdLQtoSGUSy6yJw3l56x4aU07G1/FheJEkSdJRLS6v5hN3vpALLokAV542li+95XSHiem4MbxIkiSpVWUVSR59ZTsvb9nDM2srGTmkiAEFgXQ65npaHCam48nwIkmSpMM8u7aSD/z8eRqzk1rePetk/u3tZ7Ji2157WtRtDC+SJEnKSacjf3hxC1+//+VccEkEmFxazJCiQnta1K0ML5IkSQLgN89V8P+eXMOOPfVMG1PMxuo6Uk7GVw9ieJEkSernyiv38YV7lrJwQzUAAwoC33nHWYQQHCKmHuWo4SWE8HPgGmBnjPHM7LaRwN3AZKAceE+MMZm/ZkqSJKkrlVUk+cuqnayv3Mcjy7cDmQdNRjJDxxZuqObmudMMLepREu045nbg6hbbvgj8OcY4Hfhz9rUkSZJ6gYXrq3jv/z7HD59YywNLt3H59NH89IZZDByQoCDgMDH1WEfteYkxPhVCmNxi89uBOdm//xKYD3yhKxsmSZKkrhVj5KGXt/Ole5c1m4x/3qQRvO70sdxx40UOE1OPFmKMRz8oE14eaDJsrCbGOLzJ/mSMsdVveAjhJuAmgLFjx86aN29eFzS782praykuLu7uZvRp1jj/rHH+WeP8s8b5ZX3zrzfUeG0yxdNbGllTk2JLbWT0YEgegHSEwgR8/vxBTBtR0N3NbFNvqHFv15NqPHfu3LIY4+zW9uV9wn6M8WfAzwBmz54d58yZk+9Ltsv8+fPpKW3pq6xx/lnj/LPG+WeN88v65l9Pr/EfX9rCtx9ZQrajhY/PmcI/v+FUlmyq6TW9LD29xn1Bb6lxR8PLjhDCSTHGbSGEk4CdXdkoSZIkdVxZRZI/r9jB+l37eOSV7RwaaFMQYOjAARQkgs9rUa/U0fByP/B3wHeyf97XZS2SJElShz2ztpK/+/nzuTktF00ZyYsba2j0eS3qA9qzVPJdZCbnl4YQNgNfIxNafhtC+DCwEXh3PhspSZKkI2tIpZn3/Eb+46GVzSbjXzZ9NJ9746m9ZoiYdCTtWW3sujZ2XdXFbZEkSdIxWlxezS+fK2fRhmq276nntJNKWLdrH6kmPS0OEVNfkfcJ+5IkSep6MUZ+8cwG/v3BFcSYecDkl998GjdedgovbOw9k/GlY2F4kSRJ6kXKKpLc++IWXtqUZNmWPbntiQAHU2lCcDK++i7DiyRJUi9x34tb+Mffvrrs8TVnncjjK3fS0OhkfPUPhhdJkqQeblN1Hd9/fA1/eGEzhx4vXhDgtHEn8KFLpzhETP2G4UWSJKmHenzFDn7y5Fpe2lxDQSLBW885iUeW72i27LFDxNSfGF4kSZJ6mOS+g3z9j8u5b8lWAAoSgR9d9xrecMaJlFUk7WlRv2V4kSRJ6gHKKpI8tXon23Yf4KFl29lb3/jqzhhZs7OWN5yBPS3q1wwvkiRJ3ezZtZV84OfP5x4ueeEpI7n2/In8y71LnYwvNWF4kSRJOs4ODf06b+Jwlm/dw/ceW50LLokAl88Yzd+edzITRw1xiJjUhOFFkiTpOCqrSHLDrQuob0jnVg476+RhrNpRSyrVvJfFIWJSc4YXSZKk4+RgY5r/+cs6DjSkc9uuPX8C33nn2U7El9rB8CJJkpRnC9dXcdvTG3hhY5LK2oOEAAEoKkzw7tkTAHtZpPYwvEiSJOXJwcY033tsFf/7l/VEIAT4yjWnce744SzYUG0vi3SMDC+SJEldqKwiyTNrK6mrb+SPS7expWZ/bl8CONCQZtbkkcyaPLL7Gin1UoYXSZKkLrJgfSXvv/V5GrIrh00fU8y/vuU0vvvoKpc8lrqA4UWSJKmTDjSkuHvRJv77kVW54JII8DevGceNl03hNRNHOBlf6gKGF0mSpA56dm0l3ys7wKan/kyyroHTTixh3a59pNKHellKASfjS13F8CJJknSM9h5o4DsPreSOhRsBSIQU33j7GXzg4skueSzlkeFFkiSpHcoqksxftZMdew7w8Mvb2XOgMbcvAHuzr+1lkfLH8CJJknQUf16xg5t+XUYqO5/lgskjeNes8Xz1/uUcbHAivnS8GF4kSZJaODT0a+rooTy7roo7Fm7MBZdEgCtmjuE9509k6pgS7np8Ede97nx7W6TjwPAiSZLURFlFkutvWUB9YxqAggTMmTGGp9dW0phq3ssya9II9k4tMrhIx4nhRZIkKeulTTV88Z6lueASgI9cNoUvvuk0J+JLPYDhRZIk9Wtl5dXcvXgTK7btYdmWPQwpKqAwEYgxMqAwwetPPxFwIr7UExheJElSv5RKR37y5Fq+9/hqYmY6Cx+4eBKfe+NMVu+otZdF6oEML5Ikqd8oq0jy9Jpd1B1M8cjy7ZRX1eX2FQQYO2wQJYMG2Msi9VCGF0mS1C88tWoXf//LRTRmVw2bOnoon33DDH705FoaGl3uWOoNDC+SJKlParrc8fMbkvx6QXkuuCQCvOO8k7l57nQunlrqEDGplzC8SJKkPqesIsl1tyzg4KHljgNcOr2UBeurmyx3XAo4EV/qTQwvkiSpz4gxMn/1Lr523/JccAnARy53uWOpL+hUeAkh/CNwIxCBZcCHYowHuqJhkiRJ7bVgfSW3P1PBy1t3szm5n5FDilzuWOqDOhxeQggnA58CTo8x7g8h/Ba4Fri9i9omSZJ0RFW19fz3I6uYt2gTkOll+dSV0/jEldNZtmW3vSxSH9PZYWOFwOAQQgMwBNja+SZJkiS1rawiyYPLtrGpqo6n1uyiPjs8DDIT8QcOKKCoMGEvi9QHdTi8xBi3hBC+C2wE9gOPxhgf7bKWSZIkNRFj5BfPbOCbD64gu2gYrz9tDNecPY4v/GGpyx1L/UCIhx4pe6xvDGEEcA/wXqAG+B3w+xjjb1ocdxNwE8DYsWNnzZs3rzPt7TK1tbUUFxd3dzP6NGucf9Y4/6xx/lnj/Ort9V2bTLG8KsXBVGTJrhRbal/9vSUBvGP6AK6ZWsTaZIqV1SlOHVnAtBEFx7WNvb3GvYE1zr+eVOO5c+eWxRhnt7avM+Hl3cDVMcYPZ19/ALgoxvjxtt4ze/bsuHjx4g5dr6vNnz+fOXPmdHcz+jRrnH/WOP+scf5Z4/zqzfV9bPkO/uGOstyzWSaPGsI154zj1r+uz/Wy3HHjRd0+NKw317i3sMb515NqHEJoM7x0Zs7LRuCiEMIQMsPGrgJ6RjKRJEm9zqFljEcOLeLZdVU8uHRrbnhYIsC7Z4/n5rnTmTtzjBPxpX6qM3NeFoYQfg+8ADQCLwI/66qGSZKk/mPh+ired9tCGlKZtDJkQAFvPuskHntlhw+VlJTTqdXGYoxfA77WRW2RJEn9zM49B/jNwo2ZoWDZ4BKAmy6fwmdeP8OHSkpqprNLJUuSJB2TGCN3Pb+JXz9Xzuode0lFOG/icF7esptUOvNQyctmjAbsZZHUnOFFkiQdFwcaUtz/0lb+Z/5a1lfWAVCQCPz4unN5y9nj7GWRdFSGF0mSlDdlFUkeWb6dHXsO8JfVu6ipa6C0uIgARIAYKa/KBBl7WSQdjeFFkiR1uVQ68vOnN/AfD736QMmLp4zkU1fNoKggcMNtC32opKRjZniRJEldoqwiyZMrd7J7fwPzV+9kU/X+3L5EgEunj+biqZmgcseNFzlETNIxM7xIkqROiTFy58KNfPW+5aSyD78+/aQS/un1M/jJ/LWt9rA4RExSRxheJEnSMSurSPLU6p3UHUzx1zWVrNy+N7cvEeAtZ4/j5rnTuGRaqT0skrqM4UWSJB2T3y3exBf/sIxUdjLLKaVD+NgVU7j9mXIaUs17WexhkdSVDC+SJOmIyiqS/HX1LuobUzyzroqlm3fn9iUCvGvWeG6eO53Xn36ivSyS8srwIkmS2vT7sk184Z5Xe1kmjBjMhy+ZzG8WbqQx18tSCtjLIin/DC+SJAkg95DIcyYMZ1N1HXc9v/GwXpZrL5jAzXOn8+azx9nLIum4M7xIkiTKyqu57taFHGxM57bNHFtiL4ukHsXwIklSP3Sol+XMccNYX7mPnzy5NhdcAnD9hRP55t+cSQjBXhZJPYbhRZKkfmZxeTXX37KQg6lXe1mmjR5Kzf4G0unIgMIE7zhvPCEEwF4WST2H4UWSpH5iS81+fr94M7c9vT4XXALwgYsn829vPyPXG2MPi6SeyvAiSVIftqKqkXvufIGN1XUs3bKbGOHsk09gxfY9uV6Wt507DrCHRVLPZ3iRJKmPiTGybMtufvLkOh5eXg9sIwDvnj2eT145nQkjh9jLIqlXMrxIktRH/HnFDn79XAXrd+1jY7KOgkTI7UsEmDRqKBNGDgHsZZHUOxleJEnqxeobUzyxYie3Pb2BxRVJAEKAmy6fwqXTSrnx9udJRbLLHI/q5tZKUucYXiRJ6mXKyqv5vyVb2bW3ngUbqqipa2BoUQEBiEACOGHwAC6fMZrPnz+I+uGTHB4mqU8wvEiS1EtsrdnPj59cy50LNxKz2y6ZVspHLjuFIUUFfODnz9PQmG7WyzJtRAFz5kzrvkZLUhcyvEiS1EOVVSR5avUuUjHyQkWS59ZXEeOr+wsCvHbqKObMHAPAHTde5CR8SX2a4UWSpB6mMZXm9mfL+fafVpDOhpUThw3kM1fNYPqYYv7pd0sO62EBJ+FL6vsML5Ik9QBl5dXct2QrVfvqWbihmsrag7l9iQDvv3gSN8+dDsDYEwbZwyKpXzK8SJLUjTZW1fHT+WuZt2hTbh7LhaeM5O8vGc0Pn1jTpIelNPcee1gk9VeGF0mSjqOyiiRPrNxBfUOaso1JXtxY02x/QYDLZ4zm43OnceGUUfawSFIThhdJko6D2vpGfvaXdfzoybW5eSwTRwzh81fPZErpUD5z9+HzWOxhkaTmDC+SJOVBWUWSZ9buorAgwfIte3h8xQ7qG9O5/YkA771gAh/PLmN8R4nzWCTpaAwvkiR1ocZUml8+V863H1xJKruu8bBBhbxn9gROPbGEf3/wFVcKk6QOMrxIktRJi8ur+X3ZZpJ1B1lcnqRqX/OVwj5y+RQ+eWVmpbBTTxpmD4skdZDhRZKkDogx8sLGGn7x9AYeWLYtt/2SqaO4ZHopP3x8DQ2pTA/La6e6UpgkdYVOhZcQwnDgVuBMIAJ/H2N8rgvaJUlSj1NWXs3/LdnK7v0HKauoYUvNfgpCyO0vCPDaaaV8fM40LjzFlcIkqat1tuflB8DDMcZ3hRCKgCFd0CZJknqMGCPLtuzmtqc3cP+SrblnscyaNIJ/fsMMRpcM5CO/WuxKYZJ0HHQ4vIQQhgGXAx8EiDEeBA4e6T2SJPUGh3pY9hxooKwiyebkfhKBXHApCHDlqWN4x3njAbjjxovsZZGk4yDEGI9+VGtvDOFc4GfAK8A5QBnw6RjjvhbH3QTcBDB27NhZ8+bN60x7u0xtbS3FxcXd3Yw+zRrnnzXOP2ucfz2lxukYWb87zWPlDSzcnsptn3JCgjkTChk+MPCjF+tpTENhAj5//iCmjSjoxha3T0+pb19mjfPPGudfT6rx3Llzy2KMs1vb15nwMhtYAFwSY1wYQvgBsCfG+JW23jN79uy4ePHiDl2vq82fP585c+Z0dzP6NGucf9Y4/6xx/nVnjReVV/OHF7awe/9BXtxYw7bdB0gEcg+RLAjwT2+Yyc1zM89iKatI9roeFr/D+WeN888a519PqnEIoc3w0pk5L5uBzTHGhdnXvwe+2InzSZKUdw2pNAvXV/Or58p59JUdue2zJ43gc2+cSWnxQG769eFzWMB5LJLU3TocXmKM20MIm0IIM2OMq4CryAwhkySpR3luXSW/W5x5DsuLm2qoqWugMNF8lbC5zmGRpB6vs6uNfRK4I7vS2HrgQ51vkiRJnbfnQANPrtzJ3c9v4tn1VbntV8wo5YYLJ1EyqJAP3b7IHhZJ6kU6FV5ijEuAVsejSZJ0vP15xQ7uXrSJnXvrWb51Nw2pyNCiVyfVFwS44JRRvOGMEwF7WCSpt+lsz4skScdd04nzI4YM4NFXdvCHFzazekctAAF427nj+MDFk4gR3nfbQntYJKkPMLxIknqVxeXVXH9rJozAq89eGTtsICH7OhFgxtgSZk0aCdjDIkl9heFFktRjHephOW/icPbVp3h8xQ7uf2krB7PBBeCq08bwjbefyfbdB7jh1gX2sEhSH2Z4kST1SH9esYOP/aaMhtSrzyMrHljIuROGs6i8mnQ6MqAwwcfnTOPk4YM5efhge1gkqY8zvEiSutXaZIrlT67lolNGMmRgIX9esYPHV+xkyaaa3DEBeNfs8Xzrb86iqDDR5sMi7WGRpL7N8CJJ6jbPravkO88foDGuys1XAThn/Alcd/4E7nlxC6lUZhjYtedPpKgwARhSJKm/MrxIko6LQ70lM8aUsKu2nidW7mT+qp00ZhNLBN54xlj+/e1nMmbYIADeNXuCw8AkSTmGF0lSXqXSkbsXbeKr971MY/rV+SsnDx/M608fy2PLtxOBAYUJbrp8ai64gD0skqTmDC+SpC5VVpHkyZU7KSwIbKjcx19W76KmriG3PwAfvGQyX73mdEII3Hrvn6kfPsneFUnSURleJEmdlk5HXt66mzsXbuTuxZuI2Q6WYYMKed3pY5k8aig/fnItjdn5K9ecPY4QAgDTRhQwZ860bmy9JKm3MLxIko5Z096VjVV1PLVmF5W1B5sdkwhw0+VT+MSV0wG4ZFqp81ckSZ1ieJEktUsqHVmyqYa7F23kd2Wbc70rJQMLuPK0scyZOZrhgwfwD3e8kHtQ5MVTS3Pvd/6KJKmzDC+SpDY9tnwH97ywmT0HGli+dQ+79zc0W9I4EeCjV0zN9a4APihSkpQ3hhdJUm4Z49dMGM7BVJq/rqnk0eXb2ZTcnzvmypmjeces8ZQMLOSjvylrtXcF7GGRJOWP4UWS+rF0OnLvi1v4wj1Lmy1jXFSYYNwJg3K9LAUBZk0eyTVnjwPsXZEkdQ/DiyT1E00fElmz/yBPr63kmbWVzSbaB+Cds8bz728/k1e27eGGWxfkelgumjIqd5y9K5Kk7mB4kaQ+rra+kTsWVPBfj6wi1aR3pbS4iEumlTJ+xGBu/euG3DLG110wkcFFBcyaNMIeFklSj2J4kaQ+pKwiyTNrKxk5pIidtfU8s7aSJZtqmoWWAHzg4sl87a2nk0hknrVy5aljWw0p9rBIknoSw4sk9XLpdOSVbXv47eJN/GZBBYdySgDOnjCcj10xhdElA/nOn1bSkO1dedu543LBBQwpkqTewfAiSb1MjJE/Lt3K/Uu2UlvfyMrte6mpa2h2TCLAJ+ZO45/eMDO37ayThzsETJLUqxleJKmHOjTB/qIpoxhTMpBn11Xy3Loq/rJ6F8kmYWXuzNG87dxxlAwcwCfuevUBkVfMHNPsfPauSJJ6O8OLJPVAjyzfzifufIGGVGz2UMjS4iLGDhtETV1Dbgnj2ZNH8revGQ+4hLEkqW8zvEhSNzrUuzJtTDH76htZsL6KBeur2VhdlzsmAq87bQxfuPpUpo0p5oWNNS5hLEnqlwwvktQNNlXXcffiTfz0yXWk4qsrgQ0fMoALTxnJ604bwx0LN+aWL/6HOdOYPrYEwCWMJUn9luFFkvKsrLyah5ZvZ0AisH1PPc9vqGZLzf5mx7S2fPFbzh7XZkCxh0WS1B8ZXiSpCzSdXP+aCcNZvXMvz2+o5pGXt/PMuqrcccMGFXLp9FJuunwKJYMK+dK9y3LDv1y+WJKkIzO8SFInPb+hivfd9jwNjWlCgMEDCth3MAVAycBXb7OJAB+9Ygo3z52e2zZp1FCHf0mS1E6GF0lqp0O9K+dMGE6MkUXlSRZtqGZReTWN2SdDxghTRhfzwddO5oJTRrJzzwFuuG1hk8n1pc3Oae+KJEntZ3iRpKPYsecAv120ie//eQ2p9KuT6xMBTh83jDeeMZZHX9lBOh0ZUJjg6287IxdIJowc4uR6SZK6iOFFkppYXF7NA0u3UVSYYNfeev66so7Kh//c7JgAvGvWeL72tjMozg4Lazrnxcn1kiTlR6fDSwihAFgMbIkxXtP5JklSfjUNGjNPLOGlTTUsLk/y5KqdLNlUkzvuhMEDmDYswceunEHxoEK+fv/y3PCvay+YmAsuYECRJOl46Iqel08DK4BhXXAuScqbGCMPLdvOp+9+Mffkesg8BDIEGDW0KHdsIsBNl5/CGWELcy6bAsD0MSUO/5IkqRt1KryEEMYDbwG+BfxTl7RIkrpAWUWSp9fsYuTQImrrU7ywMcmLG5NU1h7MHROBi6eO4mNXTOXcCcNZu7O2xZPrS9m7YUvueHtXJEnqXp3tefk+8HmgpPNNkaRj03T413kTh1NeVceLG5M89soOHl6+nSYPrueU0qFcPmM0pcUDuf3ZclLZJ9d/9g0zc4GktSfXz9/QTR9OkiQdJsSm/+9+LG8M4RrgzTHGj4cQ5gCfbW3OSwjhJuAmgLFjx86aN29ex1vbhWpraykuLu7uZvRp1jj/+nONl1U28oOyehpjZgL9oALYn3m0CoUBGrO3tgBcM2UA75zx6pCwtckUK6tTnDqygGkjCo54nf5c4+PFGueX9c0/a5x/1jj/elKN586dWxZjnN3avs6El/8A3g80AoPIzHn5Q4zxfW29Z/bs2XHx4sUdul5Xmz9/PnPmzOnuZvRp1jj/+nqND/WszJ40gsFFBSzZVJP7Wb9rX7Njzzr5BG64cCLnThzO3gONvL/Js1XuuPGiDg/36us17gmscX5Z3/yzxvlnjfOvJ9U4hNBmeOnwsLEY478A/5K9wBwyPS9tBhdJao8YI+VVdfzfi1v40ZNrmz1XBaC0eCDnThjORVNG8fvFm0ml04c9WwXw2SqSJPVBPudFUrd6/JUdPLhsG4kAO/fWs3Tzbnbvb2h2TADees44vvCmUxl3wiBCyKwT9s7zxvtsFUmS+pEuCS8xxvnA/K44l6S+pemk+lNKh7Jsy26Wbqph6ZbdLC6vJln3alCZPGoIbz7rJM6dcAIDChJ86d5luaFff/fayZw8fHCzcxtQJEnqX+x5kZQXu+sauPfFzXzzwRU0pjPPVGk6AGzK6KGcdMIgauoaiEBBgHfPnsDNc6fljpk0aqhDvyRJUo7hRVKnPbV6Fw8u3UpRYQHVdQd5ectuKqrqmh0TgStmjOajV0zhzJNPYNigAZRVJFs8V2VUs/fYsyJJkpoyvEg6qpZDv17espuXt+5m+ZY9lFVUs31Pfe7Y0SVFzJ40kvfMnsDgAQn+8+FVNGafqfKpq6Y3CyOtPVdFkiSpLYYXSa2KMbJjTz33LdnCfz+yqtWhXxNHDmHY4AHs2FOfG/r1wdee0mzo1zkTRhwxnNi7IkmS2svwIonF5dU8snw7wwYNoK4hxfKte3hl624qaw82Oy4Cc2aM5qbLp3DGuBM4YYhDvyRJ0vFjeJH6gabDvs4YN4w1O2p5ZdtuXtm6h+c3VLNi+97csQUBZp44jLkzx3DGuGEUFiT45gOv0JAd+vVJh35JkqRuYniR+rCq2nruX7KVb/3p1RW/QoBDz30cWlTA8CEDcscnAnz6ddP51FUzmp3ntJOGOfRLkiR1O8OL1Ac0ptI8uHQbj63YQWEiQbLuICu27WHn3vpmx0XgwlNG8oGLJ3PGuGFMGDGEFzfVNBv2dcm00Yed33AiSZJ6AsOL1As0HfY1edQQVm7fy4pte5i/rJ7vLvsrK7fvpTH16lT6SaOGcOn0Uk4/aRiFicB/PLQyt+LX5954qsO+JElSr2R4kXqApuHkUHg40JBi7c5aHl6+nZ/OX0cqHQ973wkDA2dPLOI1E4azuDyZW/HrPS0e9njW+OEO+5IkSb2e4UXqZovKq3nfrQs52JimIBE4f/IIduytp7xyH63kFebOHM2Nl01h5oklvLz4OebMudAVvyRJUr9geJGOg0zPSiXTx5RQVJhg9Y69rNpey+odmeFfjdmU0piOrNi+lwsmj+Sas05i5onDSKXTfP6epblg8okrpx8WRBz6JUmS+gPDi9QFmg77Om/icHbtrWf1jkw4eW5dJY+v3Els0YsydthAZowt4U1nnsjDy7eTSkeKChLc9nfnHxY+Th4x5KjBxN4VSZLU1xlepA6KMbJrbz1/WraNbz6YXYo4wJABBew7mModN2hAIhdcAnDtBRP5wtUzGT6kKHdMa3NemjKYSJIkGV6koyorr+axFTsYXTKQGGHtzlrW7KxlzY697DnQ2OzYGGHamGL+9jUnM2NsCdPHlrCxah833LYwN+zrXbPGNwsuYDiRJElqD8OL+r1DvR7nTx7BqOKBrN1Zy9qdtazbWctLm2tYt2tfs+NHDS1i2phi3nbuOKaPKSHG2Gwp4q++9YxmQWR0yUDno0iSJHUBw4v6tNaGY+2rb2T9rn2s3bWXp9dUcu+LW1pd1evEYYMYWJjIvU4E+Ic5U/ncG0897FiXIpYkSco/w4v6pBgjj76yg0/e+SINqTSJROCMk4axq7aebbsP5I4LgWbzUa4+80Q+esVUpo4eSsmgAYctQXzlqWNbvZ7hRJIkKf8ML+rVnllbySPLtzNyaBExwrpdtazftY8NlfvY3/DqpPlUOrKztp7XTh3F1NHF2Z+hVO2r54O/WJQLJzdeNoVzJwzPvc8liCVJknoOw4t6rKZzUUqLB7KhMhNK1lfuY/2uWlZt30uyrqHZeyaMHMyU0mIumjKKwoLA7c+Uk0pngsmPrz/vsPAxnZKjhhN7VSRJknoGw4u6Rcu5KOl0ZOvu/ZRX1rGhah8L11Xxp5e3tToXZcSQAZxSOpRxwwdTU9dAJDMf5dNXTefTr5vR7Ng3nnGiz0eRJEnqIwwvOm7S6ciOvQd4ZPl2vvXgChpTmeeijBs+mJ176znYmM4dW5gIueASgDedeSI3Xj6FU0YNZcTQzDLDLeejXDp99GHXNJhIkiT1HYYXdalUOvLYK9t5YuVO9lbW82zdCjZU7qOiah8VVXXUNwkokJksP2hAAR987WQmjxrKKaWZny3JumbPRvnwZVM4b2LzEOJ8FEmSpP7F8KJ2OzTUa9ak4YwuGcTGqjrKs6GkomofFdV1bKyqo7HJWK/CTRuYUjqUSaOGcsWM0UwaNZTGVLrZc1H+851nHxY8TjxhULuCiT0rkiRJ/YfhRcDhc1B21zVQUb2PjdV1VFTV8eLGJE+s3NnqHJShRQVMHDWUmWNLKC0uYtGGJJHMcK/PXDWdT1w5/bD3HO25KGAwkSRJUnOGl36gtQc1NqTSbK3Zz8bqOp5eU8mtT28glc7MQRk8oIC6g6lm5xhSVNB8DspZJ/LhS09h0qihjBpaRAghd61D81AKAlw8tbTVNhlMJEmSdKwML31UjJFde+t5fMVOvnb/yzSmIokQOPWkYmrqGtm2e3+rvSgxwoyxJbzlrJOYOGoIE0dmflZu39tscvyHL53S5rLCh4Z7DaypMKBIkiSpyxheeqkYI/NX7+KJFTsZUzKQAYUJNifr2FS9n03JOrYk9x82OT4VI8m6Bi6YPJKJI09mwsghTBg5hN37G/j0vBdzweQr15x+WOg4lsnxh3pV5s/fnJfPLkmSpP7J8NIDZYZ5VXLaScMYNXQgm5P72Zysy/25pWZ/qyt3nTB4ABNGDmbm2BKuOnUME0YOob4hzXcfXZWbHP//rjv8QY2Ak+MlSZLU4xlejrND808uOGUkJw8fzJaa/WxJ7mdLzX42J/ezYtseXtpUQysjuhg2qJDxI4YwedRQSgYN4IWKZO4BjZ+4chr/9PqZrV7zvEkjDCaSJEnq9QwvXaTlpPi6g41srdnPlpoDbK3Zz9aa/SzdXMNf11S2OtcEYOTQIgYUhFxwCcDfnDuOj1w+lZNHDOaEwQOaXa/pHJQrZoxps20GE0mSJPUFHQ4vIYQJwK+AE4E08LMY4w+6qmE9RWsrdTWm0uzcW58JJbsPsGhDNXc+vzGzWhdQPLCAvfXNV+sqSASGtlix6/Wnj+X6CycyfsRgxg0fzJCiwsNCyfsunszp44Yd1i4f0ChJkqT+pjM9L43AP8cYXwghlABlIYTHYoyvdFHb8qasIskD6w5SckrysF/60+lI5b56ttUc4Jm1lXzvsdW5JYSnjy1hz/4Gduw50GbvSQSmjinmDWecyMnDM6Fk3PDBjC0ZyEubdzcLJh+9YmqXTIyXJEmS+oMOh5cY4zZgW/bve0MIK4CTgR4dXsoqklx/ywIONqb5v3XP8ZazTyIdYfvu/WzbfYAdew7QkDo8mcQI+w+meO3UUsYNH8S44YM56YTMnzv2HOAjv1rcZLWuM466jLDzTyRJkqRjE2JsowvhWE4SwmTgKeDMGOOeFvtuAm4CGDt27Kx58+Z1+nqd8cC6g9yzpiE3ryQRoHRwYMTAwMjBgZEDE5k/BwX2NUR+ufwgqTQUJuDz5w9i2oiCVs+7NpliZXWKU0cWtHlMf1NbW0txcXF3N6NPs8b5Z43zzxrnl/XNP2ucf9Y4/3pSjefOnVsWY5zd2r5Oh5cQQjHwF+BbMcY/HOnY2bNnx8WLF3fqep1VVpHkhlsWUN+YpqgwwZ03XsisySOPeLzzSjpm/vz5zJkzp7ub0adZ4/yzxvlnjfPL+uafNc4/a5x/PanGIYQ2w0unVhsLIQwA7gHuOFpw6SlmTRrBHR+5iLseX8R1rzv/qIHEIVySJElSz9CZ1cYCcBuwIsb4va5rUv7NmjSCvVOLDCWSJElSL5LoxHsvAd4PXBlCWJL9eXMXtUuSJEmSmunMamNPk3lciSRJkiTlXWd6XiRJkiTpuDG8SJIkSeoVDC+SJEmSegXDiyRJkqRewfAiSZIkqVcwvEiSJEnqFQwvkiRJknqFEGM8fhcLYRdQcdwueGSlQGV3N6KPs8b5Z43zzxrnnzXOL+ubf9Y4/6xx/vWkGk+KMY5ubcdxDS89SQhhcYxxdne3oy+zxvlnjfPPGuefNc4v65t/1jj/rHH+9ZYaO2xMkiRJUq9geJEkSZLUK/Tn8PKz7m5AP2CN888a5581zj9rnF/WN/+scf5Z4/zrFTXut3NeJEmSJPUu/bnnRZIkSVIv0ufCSwjh5yGEnSGEl9vYH0IIPwwhrA0hLA0hnNdk39UhhFXZfV88fq3uXdpR4xuytV0aQng2hHBOk33lIYRlIYQlIYTFx6/VvUs7ajwnhLA7W8clIYSvNtnn97gd2lHjzzWp78shhFQIYWR2n9/jowghTAghPBlCWBFCWB5C+HQrx3g/7oR21tj7cSe0s8bejzuonfX1XtwJIYRBIYTnQwgvZWv8b60c07vuxTHGPvUDXA6cB7zcxv43Aw8BAbgIWJjdXgCsA6YARcBLwOnd/Xl64k87avxaYET27286VOPs63KgtLs/Q0//aUeN5wAPtLLd73EX1bjFsW8Fnmjy2u/x0Wt2EnBe9u8lwOqW30Xvx8elxt6P819j78d5rG+L470XH3uNA1Cc/fsAYCFwUYtjetW9uM/1vMQYnwKqj3DI24FfxYwFwPAQwknABcDaGOP6GONBYF72WLVwtBrHGJ+NMSazLxcA449Lw/qQdnyP2+L3uJ2OscbXAXflsTl9ToxxW4zxhezf9wIrgJNbHOb9uBPaU2Pvx53Tzu9xW/weH0UH6uu9+Bhl76+12ZcDsj8tJ7z3qntxnwsv7XAysKnJ683ZbW1tV+d8mEyaPyQCj4YQykIIN3VTm/qKi7PdwA+FEM7IbvN73MVCCEOAq4F7mmz2e3wMQgiTgdeQ+Re/prwfd5Ej1Lgp78edcJQaez/upKN9h70Xd1wIoSCEsATYCTwWY+zV9+LC7m5ANwitbItH2K4OCiHMJfN/lpc22XxJjHFrCGEM8FgIYWX2X8B1bF4AJsUYa0MIbwb+D5iO3+N8eCvwTIyxaS+N3+N2CiEUk/ll4zMxxj0td7fyFu/Hx+goNT50jPfjTjhKjb0fd1J7vsN4L+6wGGMKODeEMBy4N4RwZoyx6XzPXnUv7o89L5uBCU1ejwe2HmG7OiCEcDZwK/D2GGPVoe0xxq3ZP3cC95LpktQxijHuOdQNHGP8EzAghFCK3+N8uJYWwxT8HrdPCGEAmV9I7ogx/qGVQ7wfd1I7auz9uJOOVmPvx53Tnu9wlvfiToox1gDzyfRgNdWr7sX9MbzcD3wgu7LCRcDuGOM2YBEwPYRwSgihiMx/JPd3Z0N7qxDCROAPwPtjjKubbB8aQig59HfgDUCrKz3pyEIIJ4YQQvbvF5D5b7kKv8ddKoRwAnAFcF+TbX6P2yH7/bwNWBFj/F4bh3k/7oT21Nj7cee0s8bejzuonfcJ78WdEEIYne1xIYQwGHgdsLLFYb3qXtznho2FEO4is/JHaQhhM/A1MpOTiDH+D/AnMqsqrAXqgA9l9zWGED4BPEJmdYWfxxiXH/cP0Au0o8ZfBUYBP8nezxtjjLOBsWS6KyHz3bszxvjwcf8AvUA7avwu4B9CCI3AfuDaGGME/B63UztqDPC3wKMxxn1N3ur3uH0uAd4PLMuOtQb4EjARvB93kfbU2Ptx57Snxt6PO6499QXvxZ1xEvDLEEIBmWD92xjjAyGEj0HvvBeHzH9fkiRJktSz9cdhY5IkSZJ6IcOLJEmSpF7B8CJJkiSpVzC8SJIkSeoVDC+SJEmSegXDiyRJkqRewfAiSZIkqVcwvEiSJEnqFf5/bD9HQMV0myIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorTolerance = 1e-3\n",
    "time_start = time()\n",
    "(t, U) = euler_error_control(f, a, b, u_0, errorTolerance, demoMode=True)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "\n",
    "steps = len(U) - 1\n",
    "h_ave = (b-a)/steps\n",
    "U_exact = u(t)\n",
    "U_error = U-U_exact\n",
    "U_max = max(abs(U_error))\n",
    "print()\n",
    "print(f\"With {errorTolerance=}, this took {steps} time steps, of average length {h_ave:0.3}\")\n",
    "print(f\"The maximum absolute error is {U_max:0.3}\")\n",
    "print(f\"The maximum absolute error per time step is {U_max/steps:0.3}\")\n",
    "print(f\"The time taken to solve was {time_elapsed:0.3} seconds\")\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Solution to du/dt={k}u, u({a})={u_0}\")\n",
    "plot(t, U, \".-\")\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Error in the above\")\n",
    "plot(t, U_error, \".-\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_i=1.0: Decreasing step size to 9.000e-03 and trying again.\n",
      "\n",
      "With errorTolerance=0.0001, this took 380 time steps, of average length 0.00526\n",
      "The maximum absolute error is 0.084\n",
      "The maximum absolute error per time step is 0.000221\n",
      "The time taken to solve was 0.00111 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorTolerance = 1e-4\n",
    "time_start = time()\n",
    "(t, U) = euler_error_control(f, a, b, u_0, errorTolerance, demoMode=True)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "\n",
    "steps = len(U) - 1\n",
    "h_ave = (b-a)/steps\n",
    "U_exact = u(t)\n",
    "U_error = U-U_exact\n",
    "U_max = max(abs(U_error))\n",
    "print()\n",
    "print(f\"With {errorTolerance=}, this took {steps} time steps, of average length {h_ave:0.3}\")\n",
    "print(f\"The maximum absolute error is {U_max:0.3}\")\n",
    "print(f\"The maximum absolute error per time step is {U_max/steps:0.3}\")\n",
    "print(f\"The time taken to solve was {time_elapsed:0.3} seconds\")\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Solution to du/dt={k}u, u({a})={u_0}\")\n",
    "plot(t, U, \".-\")\n",
    "grid(True)\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "title(f\"Error in the above\")\n",
    "plot(t, U_error, \".-\")\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The explicit trapezoid method with error control <a name=\"ETMEC\"></a>\n",
    "\n",
    "In practice, one usually needs at least second order accuracy, and one approach to that is using computing a \"candidates\" for teh next time step with a second order accurate Runge-Kutta method and also a third order accurate one, the latter used only to get an error estimate for the former.\n",
    "\n",
    "Perhaps the simplest of these is based on adding error estimation to the Explicit Trapezoid Rule;\n",
    "omitting the step size adjustment for now, the main ingredients are:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$K_1 = h f(t, U)$\n",
    "\n",
    "$K_2 = h f(t + h, U + K_1)$\n",
    "\n",
    "(So far, as for the explicit trapezoid method)\n",
    "\n",
    "$K_3 = h f(t + h/2, U + (K_1 + K_2)/4)$\n",
    "\n",
    "**May 5:** not $... + (K_1 + K_2)/2$\n",
    "\n",
    "(a midpoint approximation, using the above)\n",
    "\n",
    "$\\delta_2 = (K_1 + K_2)/2$\n",
    "\n",
    "(The order 2 increment as for the explicit trapezoid method)\n",
    "\n",
    "$\\delta_3 = (K_1 + 4 K_3 + K_2)/6$\n",
    "\n",
    "(An order 3 increment — note the resemblance to Simpson's Rule for integration.\n",
    "This is only used to get:)\n",
    "\n",
    "$e_h = |\\delta_2 - \\delta_3 |, \\, = |K_1 -2 K_3 + K_2|/3$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, if this step is accepted, one uses the explicit trapezoid rule step: $U_{i+1} = U_i + \\delta_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step size adjustment\n",
    "\n",
    "The scale factor $s$ for step size adjustment must be modified for a method order $p$ (with $p=2$ now):\n",
    "- Changing step size by a factor $s$ will change the error $e_h$ in a single time step by a factor of about $s^{p+1}$.\n",
    "\n",
    "- Thus, we want a new step with this rescaled error of about $s^{p+1} e_h$ roughly matching the tolerance $T$.\n",
    "Equating would give $s^{p+1} e_h = T$, so $s = (T/e_h))^{1/(p+1)}$,\n",
    "but as noted above, since we are using only an approximation $\\tilde{e}_h$ of $e_h$\n",
    "it is typical to include a \"safety factor\" of about $0.9$, so something like\n",
    "\n",
    "$$s = 0.9 \\left( \\frac{T}{|\\tilde{e}_h|} \\right)^{1/(p+1)}$$\n",
    "\n",
    "Thus for this second order accurate method, we then get\n",
    "\n",
    "$$s = 0.9 \\left( \\frac{3 T}{|K_1 -2 K_3 + K_2|} \\right)^{1/3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**A variant: relative error control**\n",
    "\n",
    "One final refinement: it is more common in software to impose a *relative error* bound: aiming for $|e_h/u(t)| \\leq T$,\n",
    "or $|e_h| \\leq T|u(t)|$.\n",
    "Approximating $u(t)$ by $U_i$, this changes the step size rescaling guideline to\n",
    "\n",
    "$$s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/(p+1)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3\n",
    "\n",
    "Implement this\n",
    "[error control version of the explicit trapezoid method](#ETMEC),\n",
    "and test on the two familiar examples\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "du/dt &= Ku\n",
    "\\\\\n",
    "&\\text{and}\n",
    "\\\\\n",
    "du/dt &= K(\\cos(t) - u) - \\sin(t)\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "($K=1$ is enough.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourth order accurate methods with error control: Runge-Kutta-Felberg and some newer refinements\n",
    "\n",
    "The details involve some messy coefficients; see the references above for those.\n",
    "\n",
    "The basic idea is to devise a fifth order accurate Runge-Kutta method such that we can also get a fourth order accurate method from the same colection of *stages* $K_i$ values.\n",
    "One catch is that any such fifth order method requires six stages (not five as you might have guessed).\n",
    "\n",
    "The first such method, still widely used, is the\n",
    "[Runge-Kutta-Felberg Mathod](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%E2%80%93Fehlberg_method)\n",
    "published by Erwin Fehlberg in 1970:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$K_1 = h f(t, U)$\n",
    "\n",
    "$K_2 = f(t + \\frac{1}{4}h, U + K_1/4)$\n",
    "\n",
    "$K_3 = f(t + \\frac{3}{8} h, U + \\frac{3}{32} K_1 + \\frac{9}{32} K_2)$\n",
    "\n",
    "$K_4 = f(t + \\frac{12}{13} h, U + \\frac{1932}{2197} K_1 - \\frac{7200}{2197} K_2 + \\frac{7296}{2197} K_3)$\n",
    "\n",
    "$K_5 = f(t + h, U + \\frac{439}{216} K_1 - 8  K_2 + \\frac{3680}{2565} K_3  - \\frac{845}{4104} K_4)$\n",
    "\n",
    "$K_6 = f(t + \\frac{1}{2}h, U - \\frac{8}{27} K_1 + 2 K_2 - \\frac{3544}{513} K_3 + \\frac{1859}{4104} K_4 - \\frac{11}{40} K_5)$\n",
    "\n",
    "$\\delta_4 = \\frac{25}{216} K_1 + \\frac{1408}{2565} K_3 + \\frac{2197}{4104} K_4 - \\frac{1}{5} K_5$\n",
    "\n",
    "(The order 4 increment that will actually be used)\n",
    "\n",
    "$\\delta_5 = \\frac{16}{135} K_1 + \\frac{6656}{12825} K_3 + \\frac{28561}{56430} K_4 - \\frac{9}{50} K_5  + \\frac{2}{55} K_6$\n",
    "\n",
    "(The order 5 increment, used only to get the following error estimate)\n",
    "\n",
    "$\\tilde{e}_h = \\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5  + \\frac{2}{55} K_6$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This method is typically used with the relative error control mentioned above, and since the order is $p=4$,\n",
    "the recommended step-size rescaling factor is\n",
    "\n",
    "$$\n",
    "s = 0.9 \\left| \\frac{T U_i}{\\tilde{e}_h} \\right|^{1/5},\n",
    "= 0.9 \\left| \\frac{T U_i}{\\frac{1}{360} K_1 - \\frac{128}{4275} K_3 + \\frac{2197}{75240} K_4 + \\frac{1}{50} K_5  + \\frac{2}{55} K_6} \\right|^{1/5},\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Footnote:** \n",
    "Newer software often uses a variant called the [Dormand–Prince method](https://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method) published in 1980; for example this is the default method in the module `scipy.integrate` within Python package SciPy.\n",
    "This is similar in form to \"R-K-F\", but has somewhat smaller errors.\n",
    "\n",
    "The basic usage is\n",
    "\n",
    "    ode_solution = scipy.integrate.solve_ivp(f, [a, b], y_0)\n",
    "    \n",
    "because the output is an \"object\" containing many items; the ones we need for now are t and y,\n",
    "extracted with\n",
    "\n",
    "    t = ode_solution.t\n",
    "    y = ode_solution.y\n",
    "\n",
    "This defaut usage is synonymous with\n",
    "\n",
    "    ode_solution = scipy.integrate.solve_ivp(f, [a, b], y_0, method=\"RK45\")\n",
    "    \n",
    "where \"RK45\" refers to the Dormand–Prince method.\n",
    "Other options include `method=\"RK23\"`, which is second order accurate, and very similar to the above\n",
    "[explicit trapezoid method with error control](#ETMEC).\n",
    "\n",
    "Notes:\n",
    "- SciPy's notation is $dy/dt= f(t, y)$, so the result is called `y`, not `u`\n",
    "- The initial data `y_0` must be in a list or numpy array, even if it is a single number.\n",
    "- The output `y` is a 2D array, even if it is a single equation rather than a system.\n",
    "- This might output very few values; for more output times (for better graphs?), try something like\n",
    "\n",
    "`t_plot = np.linspace(a, b)`\n",
    "\n",
    "`[t, y] = solve_ivp(f, [a, b], y_0, t_eval=t_plot)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get an ODE IVP solve function, from module \"integrate\" within package \"scipy\"\n",
    "from scipy.integrate import solve_ivp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To read more about this SciPy function scipy.integrate.solve_ivp,\n",
    "# run this cell (in the notebook version of this page).\n",
    "help(solve_ivp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get a \"stop watch\"\n",
    "# This gives the \"wall clock\" time in seconds since a reference moment, called \"the epoch\".\n",
    "# (For macOS and UNIX, the epoch is the beginning of 1970.)\n",
    "from time import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, u):\n",
    "    return u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.0\n",
    "b = 2.0\n",
    "y_0 = [1.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time take to solve: 0.0010390281677246094 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_plot = np.linspace(a, b)\n",
    "time_start = time()\n",
    "ode_solution = solve_ivp(f, [a, b], y_0, t_eval=t_plot)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "print(f\"Time take to solve: {time_elapsed} seconds\")\n",
    "\n",
    "# The output is an \"object\" containing many items; the ones we need for now are t and y.\n",
    "# More precisely \"y\" is a 2D array (just as y_0 is always an array)\n",
    "# though with only a single row for this example, so we just want the 1D array y[0]\n",
    "# These are extracted as follows:\n",
    "t = ode_solution.t\n",
    "y = ode_solution.y[0]\n",
    "\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Computed Solution\")\n",
    "plt.plot(t, y)\n",
    "grid(True)\n",
    "\n",
    "y_exact = np.exp(t)\n",
    "errors = y - y_exact\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Errors\")\n",
    "plt.plot(t, errors)\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time take to solve: 0.009053945541381836 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAygAAAE/CAYAAACtuOf7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABdPUlEQVR4nO3dd3hUVfoH8O+Z9N57JYEAAdLp0kERQSl2xV5W1772ts2yrq7rz7X3LqKASG/Se0gjdBIgkx7SezIz5/dHEgwhZTKZm8wk38/z8Ah37r3nzGG8zJtz3vMKKSWIiIiIiIhMgaqvO0BERERERNSCAQoREREREZkMBihERERERGQyGKAQEREREZHJYIBCREREREQmgwEKERERERGZDAYoRERERERkMhigEBFRp4QQZ4UQtUKIqla/3uvrfhERUf9k2dcdICIiszBPSrm5sxOEEJZSSk2bYxZSSq2+jXT3fCIi6n84g0JERAYRQtwhhNgthPivEKIEwN+EEF8JIT4UQqwVQlQDmCaEGC6E2CaEKBNCHBFCXN3qHu2dP0cIcVQIUSmEyBFCPNlnb5KIiHodZ1CIiKgnxgJYAsAbgBWADwHcDGAOgLkAHAAkA/gCwOUALgOwUgiRIKU80XyP1udbAzgD4Hop5U4hhBuAQb33doiIqK8pNoMihPhCCFEohEg30v3WN//0bXWb498LIU4IIdKb27QyRntERHSRX5ufwS2/7m0+niul/J+UUiOlrG0+tlJKuVtKqQMQA8ARwL+klA1Syt8BrAZwU6t7XzhfSlkHoBFApBDCWUpZKqVM6qX3SEREJkDJJV5fAZhtxPu9CWBxO8e/BzAMwCgAdgDuMWKbRETUZL6U0rXVr0+bj6vbObf1MX8A6uZgpcU5AAEdnA8Ai9A0o3JOCLFdCDG+p50nIiLzoViAIqXcAaCk9TEhRHjzTMghIcROIcSwbtxvC4DKdo6vlc0AHAAQ2NO+ExGR3mQXx3IBBAkhWv97Ewwgp6N7SCkPSimvQdOysV8BLDVOV4mIyBz0dpL8JwAellLGA3gSwAfGunHz0q7FANYb655ERNRj+wFUA3haCGElhJgKYB6a8lYuIYSwFkLcIoRwkVI2AqgAwF29iIgGkF5LkhdCOAKYAOBnIUTLYZvm1xYC+Ec7l+VIKa/Qs4kPAOyQUu7saV+JiOgSq4QQrQOFTQBWdnWRlLKhedeuDwA8h6aZk9uklMc7uWwxgPeEEBYATgC41fBuExGRuRFNK6MUurkQoQBWSylHCiGcAZyQUvr14H5TATwppZzb5vhfAcQCWNhmnTMREREREZmRXlviJaWsAHBGCHEdAIgm0T29rxDiHgBXALiJwQkRERERkXlTbAZFCPEjgKkAPAEUAPgrgN/RtEe+H5r2y18ipWxvaVd799uJpt26HAEUA7hbSrlBCKFB044wLQn0y/W9JxERERERmRZFl3gRERERERF1R2/v4kVERERERNQhBihERERERGQyFNlm2NPTU4aGhipx626rrq6Gg4NDX3ejX+MYK49jrCyOr/I4xsrjGCuPY6wsjq/yTG2MDx06dF5K6dX2uCIBSmhoKBITE5W4dbdt27YNU6dO7etu9GscY+VxjJXF8VUex1h5HGPlcYyVxfFVnqmNsRDiXHvHucSLiIiIiIhMBgMUIiIiIiIyGQxQiIiIiIjIZDBAISIiIiIik8EAhYiIiIiITAYDFCIiIiIiMhkMUIiIiIiIyGQwQCEiIiIiIpPBAIWIiIiIiEwGAxQiIiIiol5UUdeIg2dL+robJosBChERERFRL/p0Ryau/3gvCivr+rorJokBChERERFRL0rOKoOUwL5MzqK0hwEKEREREVEvkVIiLbsMALA343zfdsZEMUAhIiIiIuolZ4trUFGngZWFwJ6M4r7ujkligEJERERE1EtaZk/mxwTgXHENcspq+7ZDJogBChERERFRL0lRl8HWSoXbJ4QCAPZyFuUSDFCIiIiIiHpJWnY5Rvq7INLPGR4O1tjDPJRLMEAhIiIiIuoFGq0OR3LLERXoCpVKYFy4B/ZmFENK2dddMykMUIiIiIiIesHJgirUNeoQHeQCABgf5oG88jqcLa7p456ZFgYoRERERES9oCVBPirQFQAwIdwDALjMqw0GKEREREREvSA1uwzOtpYI9bAHAAzydICvsy0T5dtggEJERERE1AtS1eWIDnKFEAIAIITABOahXIIBChERERGRwuoatThRUImoQJeLjo8L90BxdQNOFlT1Uc9MDwMUIiIiIiKFHcmtgFYnL+SftGAeyqUYoBARERERKawlQT66TYAS6GaPYHd77GEeygUMUIiIiIiIFJaWXQ5vJxv4uthe8tqEcA/szyyGVsc8FIABChERERGR4lLVZYgOcm33tfHhHqio0+BobkXvdspEMUAhIiIiIlJQeW0jMs9XI7pNgnyL8WHMQ2mNAQoRERERkYLSc8oB4JIE+RbezrYY7O3IPJRmDFCIiIiIiBSUeqGCfPszKEBTHsrBsyVo1Op6qVemiwEKEREREZGC0tTlCPGwh6u9dYfnTAj3QE2D9sJuXwOZXgGKEOKsEOKwECJFCJGodKeIiIiIiPqL1OyyS7YXbmvsIA8IAew5zWVe3ZlBmSaljJFSJijWGyIiIiKifqSwsg555XWdLu8CADcHawz3dWYeCrjEi4iIiIhIMWnqpgT5jrYYbm1CuAcOZZWirlGrcK9Mm74BigSwUQhxSAhxn5IdIiIiIiLqL9Kyy6ASwAh/5y7PnTDYAw0aHZLOlfZCz0yXkLLripVCCH8pZa4QwhvAJgAPSyl3tDnnPgD3AYCPj0/8kiVLlOhvt1VVVcHR0bGvu9GvcYyVxzFWFsdXeRxj5XGMlccxVlZ/Hd//JNahtE6HVy6z7/LcWo3En7fU4KowKywa0nFCvaFMbYynTZt2qL30EUt9LpZS5jb/t1AIsQLAGAA72pzzCYBPACAhIUFOnTq1p302im3btsFU+tJfcYyVxzFWFsdXeRxj5XGMlccxVlZ/HF8pJR7fsQmXR/pj6tQova6JPrkbuRqBqVMnGL0/5jLGXS7xEkI4CCGcWn4P4HIA6Up3jIiIiIjInKlLalFa04iooM4T5FsbH+aBVHUZquo1CvbMtOmTg+IDYJcQIhXAAQBrpJTrle0WEREREZF5aynQ2NUWw61NCPeERidx8GyJMp0yA10u8ZJSZgKI7oW+EBERERH1G2nZZbC2VGGor5Pe18SHuMHaQoW9GcWYNtRbwd6ZLm4zTERERESkgNTsckT6OcPKQv+v3HbWFogNdsXeAVwPhQEKEREREZGRaXUS6TnliNGj/klbE8I9kZ5bjvKaRuN3zAwwQCEiIiIiMrLThVWoadB2WUG+PePDPSAlsO/MwJxFYYBCRERERGRkLQnyUd1IkG8RE+QKWyvVgF3mxQCFiIiIiMjI0rLL4GRjiTBPh25fa22pwuhQd+zJOK9Az0wfAxQiIiIiIiNLyy7HyAAXqFTCoOsnhHviZEEViirrjdwz08cAhYiIiIjIiOo1WhzLq+hWgca2JoR7AAD2ZQ68ZV4MUIiIiIjIrEkpcc/XB/HLoey+7goA4HheJRq1EjEG5J+0GOHvDCcbS+wZgHkoDFCIiIiIyKzllddh87FCfLQ9A1LKvu7OHwnyBmwx3MLSQoWxYe7YOwDzUBigEBEREZFZS84qA9C0te/hnPK+7QyAVHU5PB2t4e9i26P7jA/3xNniGuSW1RqpZ+aBAQoRERERmbUUdSmsLVWwtlBheVJOX3cHadlliAp0hRCGJci3aMlDGWjbDTNAISIiIiKzlqIuw6gAF8wY7o1Vqblo1Or6rC9V9RqcLqoyqEBjW0N9nOBmbzXg8lAYoBARERGR2WrU6pCWXY6YIFcsiA1AcXUDdp4q6rP+pOeUQ0ogugf5Jy1UKoHx4R7Ym3HeJHJregsDFCIiIiIyWyfyK1Gv0SEmyBVTh3rDzd6qT5d5parLAADRPdjBq7Xx4Z7ILa/DueIao9zPHDBAISIiIiKzldwcEMQGu8LaUoV50f7YeLQAFXWNfdKftOxyBLrZwd3B2ij3a8lDGUjLvBigEBEREZHZSs4qhaejDQJc7QAAC2ID0KDRYd3hvD7pT2p2mdFmTwAgzNMBPs422DuACjYyQCEiIiIis5WiLkNM0B87ZsUEuWKQp0OfLPMqrqpHdmmtURLkWwghMD5sYOWhMEAhIiIiIrNUXtOIzKJqxAa7XjgmhMCC2ADsP1OC7NLezdtIa67BYowE+dYmhHvifFUDThVWGfW+pooBChERERGZpZTmiu2xbQKCBbEBAICVKbm92p80dTmEAEYGGG8GBQDGt+ShnB4YVeUZoBARERGRWUrJKoMQwKg2S6qC3O0xJtQdy5Kye3VZVGp2GQZ7OcLRxtKo9w1yt0eQu92ASZRngEJEREREZilZXYoIbyc42Vpd8tqCuABkFlUjLbu8V/oipbxQQV4JE8I8sf9MCbS6/p+HwgCFiIiIiMyOlBKpzQny7Zkzyg/WliqsSO6dZPnc8jqcr2pAdJBxl3e1GB/ugfLaRhzLq1Dk/qaEAQoRERERmZ1zxTUorWlETKsE+dZc7Kwwc7g3VqXmolGrU7w/aUYu0NjWhTyUjP6fh8IAhYiIiIjMTrK6FAAu2sGrrQWxgSiubsCOk0WK9yc1uxxWFgLD/JwUub+Psy3CvRwGRB4KAxQiIiIiMjspWWVwsLbAEO+OA4IpEV5wd7DG8l5Y5pWqLsNwP2fYWFoo1saEcE8cOFPSKzNCfYkBChERERGZnRR1GUYFusBCJTo8x9pShXlRfth0tADltY2K9UWnk0jPKTdqgcb2TAj3QE2DttcS//uKcfdAIyIiIiJSWF2jFkfzKnDPpLAuz10QF4iv957DusN5uHFMsCL9yTxfjcp6jWI7eLUYF+YBIYDFn++Hl5MN3B2s4eFgDXcHa7g72MDdwQruDjatjlnDw9Ea9tbm9ZXfvHpLRERERAPekdwKNGplhzt4tRYd6IIwTwcsT85RLEBJay4YqVSCfAs3B2u8fX00UtXlKKluQEl1A3LK6nA4p+nPjdr2tyC2tVLBw8EGVrp6rJ+oha2VcsvQjIEBChERERGZleSs5gR5PQIUIQQWxAbgP5tOQl1SgyB3e6P3Jy27HPbWFhjs7Wj0e7e1IDYQC2IDLzkupURlvQYlVQ0obg5eSqrrm35f1fTnjOx82FiafoYHAxQiIiIiMisp6jIEuNrB29lWr/PnNwcoK1Ny8ND0IUbvT2p2GUYGdJ4PozQhBJxtreBsa4VQT4d2z9m2bRuE6Ls+6sv0QygiIiIiolZSOinQ2J4gd3uMGeSO5Uk5kNK4ldgbNDocya1AtMIJ8gMJAxQiIiIiMhtFlfXILq3ttP5JexbGBiDzfDVSjbwD1smCSjRodIonyA8kDFCIiIiIyGykNFds784MCgBcOcoP1pYqrEjKNmp/UnspQX4gYYBCRERERGYjRV0KS5XAyIDuLalysbPCrOE+WJWWZ9RCh2nqcrjZWyHI3c5o9xzoGKAQERERkdlIzmqq2G7IVrkL4wJQUt2A7SeKjNaf1OwyRAW6mkXyublggEJEREREZkGrk0jLLu/28q4WkyO84OFgjRXJOUbpT02DBicLKpkgb2R6ByhCCAshRLIQYrWSHSIiIiIias/pwipU1WsMDlCsLFSYF+2PTccKUF7b2OP+HMmtgE6CCfJG1p0ZlEcBHFOqI0REREREnUlRNxdo7OYOXq0tiA1Ag0aHtYfzetyf1OaE/aggzqAYk14BihAiEMBVAD5TtjtERERERO1LUZfBxc4KgzooRKiPqEAXhHk5YEVSz5d5pWWXw9/FFt5O+hWMJP3oO4PyDoCnARhvywMiIiIiom5IzipDdFDPEtKFEFgUF4gDZ0ugLqkx+D555bVIPFvC5V0KEF1V0xRCzAUwR0r5oBBiKoAnpZRz2znvPgD3AYCPj0/8kiVLjN9bA1RVVcHR0bGvu9GvcYyVxzFWFsdXeRxj5XGMlccxVlZX41unkXhgcw2uDrfCgiHWPWrrfK0OT26vxcIhVrg6vHv3qmiQWJPRgC1qDaQEHoyxQbyPZY/601tM7TM8bdq0Q1LKhLbH9RnNiQCuFkLMAWALwFkI8Z2U8tbWJ0kpPwHwCQAkJCTIqVOn9rzXRrBt2zaYSl/6K46x8jjGyuL4Ko9jrDyOsfI4xsrqanz3ZhRDYh/mT47B1KHePW7v56y9SC6tx3+mTNFrRqa8thGf7czE57vOoK5Ri0VxgXhkxhAEudv3uC+9xVw+w10GKFLK5wA8BwCtZlBu7ewaIiIiIiJjSm5OkI8x0pKqhXEBeGbZYaSoyxAb7NbheTUNGny5+yw+3p6BijoNroryw+MzIzDY23RmIvob85iPIiIiIqIBLSWrDIM8HeDm0LPlXS2uHOWHl1cewYrknHYDlHqNFj/sz8L7WzNwvqoeM4Z544nLIzDCnzt2Ka1bAYqUchuAbYr0hIiIiIioHVJKJKvLcNlgT6Pd09nWCrMifbAqNRcvXhUJa8umvaM0Wh1+OZSNd7ecQm55HcaHeeDjxfGID+l4loWMi5XkiYiIiOgSO08V4Yr/7kBSVmlfdwW55XUoqqw3uEBjRxbGBaC0phHbTxZBp5NYmZKDmW9vx7PLD8Pb2Rbf3zMWP943jsFJL+MSLyIiIiK6xIqkHJwoqMRNn+zDf2+IwZxRfn3Wl5SsMgA9K9DYnklDvODhYI33tp7GfzaewPH8SgzzdcKntyVg5nDvHm1nTIbjDAoRERERXURKiX2ZxZg0xBMjA1zw4PdJ+HBbBroqT6GU5KxSWFuqMMzX2aj3tbJQ4eoYf6Sqy1Cv0eHdm2Kx9pFJmBXpw+CkD3EGhYiIiIguoi6pRW55HR6YNhjXxQfiyZ9T8cb64zhXXI1/zh8JK4ve/Rl3iroMI/2dL+SJGNMTsyIwaYgnJg/xgmUvvy9qH/8WiIiIiOgi+zKLAQDjw9xha2WBd2+MxUPTBmPJQTXu/PIgKuoae60vjVodDueUd7oVcE842Vph+jAfBicmhH8TRERERHSRfZnF8HS0RrhXU60PlUrgySuG4s1ro7AvsxiLPtgDdUlNr/TleF4l6jU6oyfIk+ligEJEREREF7Tkn4wN87gkD+O6hCB8c9cYFFTUYcEHu5GiLlO8PyktBRoZoAwYDFCIiIiI6IKW/JNxYR7tvj5hsCeWPzgBdtYWuOHjvVh3OE/R/iSry+DpaINANztF2yHTwQCFiIiIiC5onX/SkcHeTljx4ERE+jvjge+T8PF25Xb4SskqQ0yQK3fVGkAYoBARERHRBW3zTzri6WiDH+8dh6ui/PD6uuN4fkU6GrU6o/alvKYRmeerjV7/hEwbtxkmIiIiIgCd55+0x9bKAv+7MRYh7vb4YFsGsktr8P4tcXC2tTJKf1KyywAAscw/GVA4g0JEREREALrOP2mPSiXw9Oxh+PeiKOzNKMa1H+5BdqlxdvhKziqFEMCoQBej3I/MAwMUIiIiIgKgX/5JR64fHYSv7xqDvPI6zH9/D9JzynvcnxR1GSK8neBkpBkZMg8MUIiIiIgIgP75Jx2ZONgTyx+YABtLFe748kCPaqVIKZGiLuP2wgMQAxQiIiIi6nb+SUeG+Djh67vGoFErcceXB1BeY1jV+bPFNSiraUQME+QHHAYoRERERGRQ/klHBns74pPF8VCX1OLebxNRr9F2+x4tBRq5g9fAwwCFiIiIiHqUf9KesWEeePO6KBw4U4Knfk6DTte9OinJWWVwsLbAEG8no/SHzAe3GSYiIiKiHueftOeamABkl9bizQ0nEOhmh6dnD9P72hR1GUYFusBCxQKNAw1nUIiIiIhM3LYThbjpk32obej+Uil9GCv/pD0PTg3HTWOC8cG2DPywP0uva+oatTiaW4HYYDej9oXMAwMUIiIiIhNWXtOIp35Jw97MYmw8mq9IG8bMP2lLCIF/XjMCU4d64aWV6dh6orDLa47klkOjk9zBa4BigEJERERkwl5fdwwl1Q1ws7fC8qQcRdowdv5JW5YWKrx3cxyG+Trhoe+TcCS38xopyVllAFhBfqBigEJERERkovZknMeSg2rcM2kQbhoTjJ2nilBYWWf0dpTIP2nL0cYSX9wxGi52Vrjrq4PILavt8NxkdRkCXO3g7WyrWH/IdDFAISIiIjJBtQ1aPLf8MEI87PHYjAgsjAuATgK/peQatR0l80/a8nG2xZd3jkFNvRZ3fnkQFXXt10hJyWKBxoGMAQoRERGRCXpn80mcK67B6wtHwc7aAoO9nTAqwAUrko27zEvJ/JP2DPV1wkeL45FRVIUHvjuEBo3uotcLK+uQU1bLAGUAY4BCREREZGIOZ5fj052ZuHF0ECaEe144viA2AEdyK3CyoNJobSmdf9KeiYM98a9FUdh9uhjPLT8MKf+okZLSkn/CAo0DFgMUIiIiIhPSqNXhmWVp8HS0wXNzhl/02tUx/rBQCaMmy/dG/kl7ro0PxGMzh2BZUjb+b8upC8dT1GWwVAmMDHDp1f6Q6WCAQkRERGRCPt2ZiaN5FfjHNSPhYmd10WuejjaYPMQTK1Nyul2ZvT29mX/SnkdnDMG18YF4Z/Mp7MppykdJUZdhmJ8TbK0ser0/ZBoYoBARERGZiMyiKryz+RRmj/DF7JG+7Z6zIC4QeeV1F5Zm9URv55+0JYTAawtGYeJgD3yZ3oCdp4qQqi5DbBALNA5kDFCIiIiITIBOJ/Hs8sOwtVThH9eM6PC8yyN94GhjiWVGWObVF/knbVlbqvDhrfHwcxC4++tEVDdomSA/wDFAISIiIjIBPx7MwoEzJXjhquGd1v+wtbLAnFG+WJ+eh9oGbY/a7Kv8k7acba3weLwtXJuXtMUwQX5AY4BCRERE1Mfyy+vwr7XHMSHcA9cnBHV5/oLYQFQ3aLHxaL7BbV7IPxnUN/knbXnYqfDdPWPx1BVDEebp0NfdoT7EAIWIiIgGHCklbv50Hz7cltHXXYGUEi+tTEejTofXF47SK1gYO8gdAa52PdrN64/8k75b3tVWhI8T/jxtsEkETNR3GKAQERHRgJNRVI09GcX48UDWRTU4+sLaw/nYdLQAT8yKQIiHfjMHKpXANTH+2HmqCIWVdQa125J/0lcJ8kQdYYBCREREA86WYwUAgKySGpwqrOqzfpTVNOCvv6VjVIAL7po4qFvXLowLgE4Cv6XkGtT2vsxieDhYY7B33+afELXFAIWIiIgGnC3HChHgagcA2HS0oM/68cqaYyitacS/Fo2CpUX3vpYN9nbCqAAXrEju/jKvlvyTcX1U/4SoM13+nyCEsBVCHBBCpAohjggh/t4bHSMiIiJSQml1AxLPlWBhXACiA12wsY8ClF2nzuOXQ9m4f3IYRvgbVjV9QWwAjuRW4GRBZbeuM8X8E6IW+oTq9QCmSymjAcQAmC2EGKdor4iIiIgUsu1kIXQSmDHcB7MifZCqLkNBhWF5HIaqadDguRVpCPN0wCMzhhh8n6tj/GGhEt1Olmf+CZmyLgMU2aRlcaZV86++zSYjIiIiMtCWY4XwcrJBVIALZkX6XjjWm97eeBLqklq8vnAUbK0sDL6Pp6MNJg/xxMqUHOh0+n89Y/4JmTK9FjsKISyEECkACgFsklLuV7RXRERERApo1Oqw/WQRpg/1hkolEOHjiGB3e2zqQT2R7kpVl+GL3Wdw89hgjDXCDMaCuEDkldddmBXpCvNPyNSJ7mytJ4RwBbACwMNSyvQ2r90H4D4A8PHxiV+yZIkRu2m4qqoqODrypwNK4hgrj2OsLI6v8jjGyuMY6+dosRb/PliHR2JtEOdjCQD48Vg9tqg1eG+6PWwtO/7Cbowx1ugk/ranFlWNwGuX2cHequcBQoNW4pHfa5Dga4l7Rtl0eX5hjQ5P76jF4khrzAi26nH7xsLPsPJMbYynTZt2SEqZ0Pa4ZXduIqUsE0JsAzAbQHqb1z4B8AkAJCQkyKlTpxrcWWPatm0bTKUv/RXHWHkcY2VxfJXHMVYex1g/O1YdhbXlOfxpwVTYWzd9DbIJKsaGT/dB+gzD1FF+HV5rjDF+7/dTyK46iU9vS8CsSJ8e3au1eSWpWHs4D2MnTIKddedLxpYeVANIw21XjMMQHyej9aGn+BlWnrmMsT67eHk1z5xACGEHYCaA4wr3i4iIiMiopJTYcrwAE8I9LgQnADA61A2u9lbYdEzZ3bwq6xrx/tYMXDnS16jBCQAsiAtAdYMWG/VYqsb8EzJ1+uSg+AHYKoRIA3AQTTkoq5XtFhEREZFxZRRV41xxDWYMvzg4sLRQYfpQb/x+vBAarU6x9lel5qG2UYv7JocZ/d7jBnnA38W2y5oozD8hc6DPLl5pUspYKWWUlHKklPIfvdExIiIiImNqqR4/Y5j3Ja/NivRBWU0jEs+VKtb+T4lqRPg4IibI1ej3VqkErokNwM5T51FUWd/heax/QuaAleSJiIhoQNhyrBCRfs7wb64g39qkCC9YW6gUqyp/Ir8SqeoyXJ8QpNjMxcLYAGh1Er+l5nZ4DuufkDlggEJERET9Xkv1+BnDL509AQBHG0tMGOyBzccK0J0dTvX100E1rCwEFsYFGv3eLYb4OGFkgDNWJGd3eA7zT8gcMEAhIiKifq919fiOzIr0wbniGpwqrOrwHEPUa7RYkZyNWZE+cHewNuq921oQG4j0nAqcKqi85DXmn5C5YIBCRERE/d7mVtXjOzKzOXgx9jKvzUcLUVrTiOsTgox63/ZcHe0PC5XA8naS5Zl/QuaCAQoRERH1a41aHXac+KN6fEd8nG0RHeiCjUYOUH5KVMPfxRaThngZ9b7t8XKywaQhnliZnAOd7uKlasw/IXPBAIWIiIj6tYNnSlBZr+kw/6S1WZE+SFWXobCiziht55TVYuepIlwbHwiLToIjY1oQG4Dc8jrsO1N80XHmn5C5YIBCRERE/drmY4WwtlThsiGeXZ47K9L3wjXG8EtiNqQEruuF5V0tLo/0haONJVYk/bHMi/knZE4YoBAREVG/1VH1+I5E+Dgi2N0em/SoyN4VnU7i50NqTBzsgSB3+x7fT1921haYPdIX69LzUdugBcD8EzIvDFCIiIio38ooqmq3enxHhBCYOdwHuzOKUV2v6VHbezKKkV1a2yvJ8W0tjA1AVb0Gm5qLUzL/hMwJAxQiIiLqt7Y0L9Vqr3p8R2ZF+qBBo8POU0U9avunRDVc7KxwxQjfHt3HEOPCPODnYosVSU01UZh/QuaEAQoRERH1W51Vj+/I6FA3uNpb9Wg3r7KaBmw4ko/5Mf6wtbIw+D6GUqkErokJwI5T51FUWc/8EzIrDFCIiIioX2qpHj9Tj927WrO0UGH6UG/8frwQGq3OoLZ/Tc5Bg0aH60f3/vKuFgvjAqDVSby/9TTzT8isMEAhIiKifqmlevx0PfNPWpsZ6YOymkYknivt9rVSSvyUmI2RAc4Y4d9xYUilRfg4YWSAM77ZexYA80/IfDBAISIion5Jn+rxHZkc4QVrCxU2G7DMKz2nAsfyKnBDHyTHt7UgNhA6CeafkFlhgEJERET9jr7V4zviaGOJCYM9sOlYAaSUXV/Qyk+JWbCxVOHqmIBut2tsV0f7w0IlmH9CZoUBChEREfU73ake35FZkT44V1yDU4VVel9T16jFypRcXDnSFy52Vga3bSxeTjZ4/+Y4PHF5RF93hUhvDFCIiIio3+lO9fiOzGzOXdnUjWVe69LzUFmn6dPk+LZmj/RFuBeXd5H5YIBCRERERqHR6pCcVdrtJVHG1lI9fqKe1eM74uNsi+hAl24FKD8dVCPY3R7jBjEhnchQDFCIiIjIKL7acxYLPtiDu746iMKKuj7rR0v1eEN272prVqQPUtRler2fc8XV2JdZgusTAg3KeyGiJgxQiIiIyCh+S82Ft5MN9mQU4/J3dmBNWl6f9MOQ6vEdmRXZVAV+c/M9O/NzYjZUArg23nSWdxGZIwYoRERE/VBWcQ1eXpmOukZtr7R39nw10rLLce+kMKx5ZBKC3e3x5x+S8OiSZJTXNPZKH1oYUj2+IxE+jghyt8Omo/mdnqfVSfxyKBtTIrzg62Lb43aJBjIGKERERP3QRzsy8M3ec93Kn+iJNYebZkuuivLDYG9HLHtgAh6fGYHVaXm44p0d2HGyqFf6YWj1+I4IITBruC92ZxSjTtNxbs2Ok0XIr6jDDSaUHE9krhigEBER9TO1DVqsSskFACxPyu6VNlel5iIhxO3CrIWVhQqPzhyCFQ9OgIONBW774gBe+jUdNQ0aRfvRUj1+hhHyT1rMivRBg0aH9PMdz0b9dFANDwdrTB9mvHaJBioGKERERP3M+iN5qKzXYEyoO3acOo+iynpF2ztVUInj+ZWYF+1/yWtRga5Y88gk3DVxEL7ddw5XvbsLSVmlivWlpXr8KAOqx3dkdKgbXOyskFzYfoByvqoem48VYGFcAKwt+dWKqKf4fxEREVE/s/RgNkI87PHqgpHQ6iR+S81VtL1VaXlQCeDKUb7tvm5rZYGX50Xih3vHokGjw7Uf7sFbG06gQaMzaj8aND2rHt8RSwsVpg/zRkqRBhrtpX1ekZQDjU5yeReRkTBAISIi6kfOFVdjb2YxrosPxBAfJ0QFumBFsnLLvKSUWJ2ai3FhHvB26jw5fEK4J9Y9NgkL4wLx3tbTmP/+bpzIrzRaXxLP9rx6fEdmRfqguhFIPHfx7I+UEj8lqhEX7IrB3k5Gb5doIGKAQkRE1I/8cqhpq9tF8YEAgAWxAUjPqcDJAuMFAq0dya1A5vnqdpd3tcfZ1gpvXReNjxfHo6CiDvP+twuf7MiAVtfz4o7GqB7fkckRXrAUwOY2mw4kZZXhdGEVZ0+IjIgBChERUT/RstXt5Agv+Lk0JavPi/aHpUpgeVKOIm2uTsuDpUpg9oj2l3d15IoRvtjw+GRMGeqF19Yex02f7sPZ89UG98NY1eM74mhjiUgPC2w6VgAp/wimlh5Uw97aAldF6RegEVHXGKAQERH1E7tOn0deeR2uT/jjp/mejjaYEuGFX5NzjDJL0ZqUEqtSc3HZEE+4OVh3+3pPRxt8sjgeb14bhaO5FZj59na8+Othg6rQt1SPN+buXW3FelvgXHENThVWAQCq6zVYnZaLuVF+cLQxflBENFAxQCEiIuonlh5Uw83e6pIcjIVxgcivqMO+zGKjtpesLkNOWS3m9WD2QAiB6xKC8PtfpuDGMUFYckCNyW9uxRvrj3erwGNLpffpRqge35EYbwsAuFBbZk1aHqobtFzeRWRkDFCIiIj6gcoGiY1H8zE/NgA2lhYXvTZjuDecbC2xzMg1UVan5sHaQoVZI3o+a+HtbItX5o/Clr9MwRUjfPHR9gxM+vfveH/rab1qp/xuxOrxHXGzVSE60OVCgPJTohrhXg6IC3ZTrE2igYgBChERUT+wL1eDRq28aHlXC1srC8yN8sP69HyjFUrU6iRWp+Vi6lAvONtaGeWeABDi4YD/uzEWax+ZhNGh7nhzwwlMeXMbvt17tsNtiY1dPb4zsyJ9kKIuw56M8zh0rhQ3jA6CEMbb0piIGKAQERGZPSklduRoEBXoguF+zu2esyA2EDUNWmw4km+UNg+eLUFhZb3eu3d113A/Z3x+x2j88qfxGOThgJdWHsHMt7fj1+Qc6Nrk0ihRPb4jsyKbNgN4cmkqLFUCC+MCFW+TaKBhgEJERGTmjuRWQF2pw3XtzJ60SAhxQ5C7ndF281qdlgs7KwtFao60lhDqjp/uH4cv7xwNBxtLPPZTCua8uxNbWu2mpUT1+I5E+DgiyN0OueV1mDHcG56ONoq3STTQMEAhIiIycz8dVMNKBVzdyWyGSiWwICYAu0+fR4EBu2S1ptHqsPZwPmYM91ZkS9+2hBCYNtQbax6+DO/eFIvaRi3u/joR1360F7tPn8eOE0WYMcy41eM768us4U2zKEyOJ1IGAxQiIiIzVteoxcqUHMT7WMDFrvNckAVxgdBJYGVKz2ZR9mQUo6S6QbHlXR1RqQSujvbH5iem4NUFI5FdWoNbPtuPynqNort3tXXXZaF4bOYQTInovTaJBpIuAxQhRJAQYqsQ4pgQ4ogQ4tHe6BgRERF1bcORfFTUaTA5sOtE9UGeDogNdu3xMq/VablwsrHElAivHt3HUFYWKtwyNgTbn5qG564chtkjfDG5F/sS6GaPx2ZGwKIXZmyIBiJ95mU1AP4ipUwSQjgBOCSE2CSlPKpw34iIiKgLPydmI9DNDsPc9fuyvDAuEC/9mo6juRWI9G8/ob4z9Rot1qfnY9YIH9haWXR9gYJsrSxw/5TwPu0DERlflzMoUso8KWVS8+8rARwDEKB0x4iIiKhz6pIa7M44j+vig6DSc6vbuaP8YGUhsNzAmig7T55HRZ2m15d3EdHA0a0cFCFEKIBYAPsV6Q0RERHp7ZdDTUHGonj9f27o5mCNaUO9sTI1Fxpt+3VFOrM6LReu9la4bLBnt68lItKHaNmir8sThXAEsB3Aq1LK5e28fh+A+wDAx8cnfsmSJcbsp8Gqqqrg6OjY193o1zjGyuMYK4vjqzyOsfHppMRT22vh6yDw1Gi7bo3xoQIN/pdcjyfibRDlpf8uXPVaiUd/r8FYP0vcOXLgba/Lz7GyOL7KM7UxnjZt2iEpZULb43o9lYQQVgCWAfi+veAEAKSUnwD4BAASEhLk1KlTDe+tEW3btg2m0pf+imOsPI6xsji+yuMYG9+uU+dRXLcff1sQg6nR/t0a4/EaLb45vgUZWg88MjVW7zbXHs5DnTYJ98+Ox4QBOIPCz7GyOL7KM5cx1mcXLwHgcwDHpJRvK98lIiIi6srSRDVc7KwwK7L71dNtLC0wL9oPG47ko6peo/d1q9Ny4elog7FhHt1uk4hIX/rkoEwEsBjAdCFESvOvOQr3i4iIiDpQXtOI9UfyMT/G3+CdtBbEBqKuUYd1h/P0Or+qXoMtxwpx1Shfbq9LRIrqcomXlHIXAD6JiIjIpBRV1sPGSgVn267rf/Q3K1Nz0KDR4boEwyuZxwW7ItTDHsuTcvS6z5ZjBajX6Lh7FxEpjpXkiYjI7Oh0Eos+3IOHf0ju6670iaWJakT6OWNkgIvB9xBCYEFsIPadKUZOWW2X569KzYWfiy3igt0MbpOISB8MUIiIyOzsyyxGVkkNtp8sQmZRVa+126jVQavTb/dLpRzJLUd6TgVuGG347EmLBbEBkBL4NbnzyvLlNY3YfrIIc6P8oOLyLiJSGAMUIiIyO8uScuBgbQFLlcD3+7N6pU2dTuLq93ZjzKub8bffjiAtuwz6btVvTD8nZsPaQoVrYnq+1CrYwx6jQ92wIjmn0/ey4Wg+GrWSy7uIqFcwQCEiIrNSXa/BuvQ8zI3yx+yRvvg5UY3aBq3i7W49UYhjeRUI9rDHD/uzcPV7uzHz7e14f+tpvZZIGUO9RotfU3Jw+QgfuNpbG+WeC+MCcbqwCodzyjs8Z1VqLoLd7TGqB0vKiIj0xQCFiIjMyoYj+ahp0GJRfCAWjwtBRZ0Gq1JzFW/3811n4Otsi6X3j8fBF2bi1QUj4WZvjTc3nMDEf/2OGz/Zi6UH1aisa1SsD5uOFqCsphHX9yA5vq05o/xgbanC8qT2l3kVV9VjT0Yx5kX7oanyABGRshigEBGRWVmWlI0gdzskhLhhzCB3RPg44rv95xRt81heBfZkFOO2CSGwslDBxd4Kt4wNwS8PTMCOp6bh8ZkRyC+vw9PL0pDwymY89EMSfj9egEatzqj9WJqYjQBXO0w0YpFEFzsrzBrug1Wpue32d116PrQ6Lu8iot7DAIWIiMxGblkt9mQUY2FsIFQqASEEFo8LQVp2OVLVZYq1+8WuM7CzssDNY4IveS3Ywx6PzhyCrU9OxfIHJ+D6hCDsOn0ed32ViHGvbcHfVx3B4ezyHuer5JbVYuepIiyKDzR6HZIFsQEorm7AjpNFl7y2KjUXg70dMdTHyahtEhF1hAEKERGZjaZkbmBhXMCFY/NjA+BgbYFv9ykzi1JUWY+VKblYFB/Qad6HEAJxwW745/yROPD8THy8OB6jQ93x/b4szHtvFy7/7w58sesMymsMWwK27FA2pASuiw809K10aMpQL7g7WF+yzKugog4HzpZgXpQ/l3cRUa9hgEJERGZBSonlSdkYHeqGEA+HC8edbK2wIC4Aq1JzUVrdYPR2v9t3Dg1aHe6cOEjva6wtVbhihC8+Whx/IV/F3sYS/1h9FGNe24wnf05Filr/XcB0Oomlh9SYEO6BIHd7Q99Kh6wsVLg62h+bjhWgvPaPAGpNWh6kBOZG+xm9TSKijjBAISIis5CaXY6MomosjLt0BuHWcSGo1+jwy6Fso7ZZ16jFd/vOYfowb4R7ORp0j5Z8lZV/nojVD1+GhXGBWHs4D/Pf3425/9uFH/Znobpe0+k99p0phrqk1qjJ8W0tiA1Ag0aHtYfzLhxblZaLSD9ng987EZEhGKAQEZFZWJ6UDWtLFa6KuvSn+cN8nTEm1B3f7T8HnRELKf6Wkovi6gbcfZn+syedGRnggtcXjsL+52fgn/NHQquTeH7FYYx9bQte+jUdx/Mr2r3u58RsONlaYvZIX6P0oz1RgS4I93LAiuZlXuqSGiRnlTE5noh6HQMUIiLqsZLqBtQ0dD4L0BP1Gi1+S83F5ZE+cLa1avecW8eH4FxxDXaePm+UNqWU+GL3GQzzdcKEcA+j3LOFk60VFo8LwbpHJ2HZA+NxeaQPfkpUY/Y7O7Howz1YnpSNusam2i4VdY1YezgP18T4w9bKwqj9aE0IgYVxgThwtgTqkhqsaZ5JmdtOQEhEpCQGKERE1CPV9RrM+b+duPWz/YpVVt96vAhlNY1Y1EmC+OwRvvB0tMa3e42TLL/7dDGO51firssGKZYgLoRAfIg73r4hBvufm4EXrxqOkuoGPLE0FeNe34JX1xzFJ9szUa/RKbq8q8X82KbNB1Yk52BVai5iglwVyXkhIuqMZV93gIiIzNtH2zOQX1GH/Io6bDxagCtGGH8Z0rKkbHg52WBSJ/U/rC1VuHF0MD7YdhrZpTUIdOvZF+vPd2XC09EaV/fSEic3B2vcMykMd00chL2Zxfh+/zl8ufssNDqJYb5OvVLFPcDVDuPC3PH1nrMorm7AS3MjFW+TiKgtzqAQEZHBsktr8MmOTFwV5YdwLwe8ueEEtEbMAQGalo9tPV6I+TH+sLTo/J+tm8Y21Sn58UBWj9o8XViFrSeKcOu4EEWXVbVHpRKYONgTH9wSjz3PTsfzc4bh1QUje22b34VxgSiuboAQwFWjuLyLiHofAxQiIjLYG+tPQAjghTnD8dQVQ3G6sArLk4y7k9ZvKTnQ6GS7u3e1FeBqh+nDfPDTQTXqNVqD2/xqzxlYW6hw67gQg+9hDN7OtrhvcjjiQ9x7rc0rR/rCxlKF0aHu8HWx7bV2iYhaMEAhIiKDHDpXglWpubhvcjj8Xe1wxQhfRAe64J3Npy4keBvD8uQcRPo5Y7ifs17nLx4fgvNVDVifnm9Qe2U1DVh2KAfXxPjD09HGoHuYMydbK3x6WwJemT+yr7tCRAMUAxQiIuo2nU7iH6uOwsfZBn+aEgagKeH7mdnDkFNWi+/392yJVYtTBZVIyy6/qHJ8VyYN9kSIhz2+M7Cy/A8HslDbqMXdk4yztbA5mhzhhQgfp77uBhENUAxQiIio235NyUFqdjmemT0M9tZ/7LcyYbAnJg3xxPtbT6OyrrGTO+hnWVIOLFQC18ToH6CoVAK3jg3BwbOlOJbXfl2RjjRqdfhmzzlMHOyBYb76zdgQEZFxMUAhIqJuqWnQ4I31xxEV6IL57QQOT10xFCXVDfhs55ketaPVSaxIzsaUCC94OXVvqdW18YGwsVR1exZl7eE85FfUGa0wIxERdR8DFCIi6paPtmeioKIeL8+NhEp16c5SUYGuuGqUHz7bmYnzVfUGt7Mn4zwKKuqxSI/k+LbcHKwxL9ofK5Jz9J7JkVLi811nEOblgKkR3t1uk4iIjIMBChER6S23rBaf7MjA3Cg/JIR2vLPUE5dHoE6jw/tbTxvc1rJD2XC2tcSM4YYFC4vHhaCmQYsVyTl6nZ94rhRp2eW4c+KgdgMvIiLqHQxQiIhIb/9efxw6CTx75bBOzwv3csT1CYH4fl8W1CU13W6nql6D9UfyMTfa3+A6JNFBrogKdMG3e8/pVeH+851n4GJnhUXdSMgnIiLjY4BCRER6Scoqxa8pubhvUpheVdofmTEEQgDvbD7V7bbWHs5DXaPOoOVdrd06LgSnCqtw4ExJp+epS2qw8Wg+bh4bfFHSPxER9T4GKERE1CUpm7YV9nKywQNTw/W6xs/FDndMCMXy5GxkV+q61d7ypGwM8nRAXLCrAb39w7wof7jYWeHbLpLlv9x9FiohcPv40B61R0REPccAhYiIuvRbai5S1GV4+oqhcLDRf4bhganhcLSxxLJTDXpfoy6pwb7MEiyMDYAQPcsFsbO2wHXxgVifno/Cyrp2z6msa8TSRDWuivJj5XQiIhPAAIWIiDpV26DFv9Ydx8gA524vuXK1t8afpoQjuVCLQ+c6X2bV4tfmpPb5scbJBbllXAg0OomfDqjbfX1pYjaq6jXcWpiIyEQwQCEiok59siMTeeV1eHnuCIN2t7pzYiicrQXeWHeiy2R1KSWWJ+dgXJg7gty7znPRxyBPB0wa4okfDmRBo714qZlWJ/HVnjMYHeqGqEBXo7RHREQ9wwCFiIg6lFdei4+2Z2DOKF+MGdTxtsKdsbe2xDWDrXDgbAm2nSzq9NykrFKcOV+NhT1Mjm9r8bgQ5JXXYcvxwouObzqaD3VJLe6ayNkTIiJTwQCFiIg69Ob6E9DqJJ67cniP7jMl0BLB7vb49/oT0Ok6nkVZlpQDWysV5ozy61F7bU0f5g1/F9tLKst/vusMAt3scPkIX6O2R0REhmOAQkTUT0gpoS6pwbJD2dh5qkiv2h+dSVGXYXlyDu6eNKjHy60sVQJ/uTwCx/IqsCott91z6hq1WJ2ai9kjfOHYjUR8vdq3UOHmscHYeeo8MouqAABp2WU4eLYUd0wIhQULMxIRmQxu9k5EZKaklDhbXIP9mcXYf6YE+zOLkVv+x05Vw3ydcN/kMMyL9oeVRfd+HiWlxD9XH4Wnow0e1HNb4a7Mi/LHh9sy8J+NJ3HlSD9YW17cpy3HClFRp8GieOMu72px/eggvLP5FL7fn4WX5kbi811n4GhjiRtGBynSHhERGYYBChGRmZBSIqOoGvtaBSSFlfUAAE9Ha4wd5IE/hbljdKg7juRW4JMdGXhiaSre3HACd00chBvHBMHJ1kqvtlan5eHQuVK8sWiU3td0RaUSeGb2MNz51UH8lKjG4nEhF72+LCkbvs62mBDuaZT22vJ2ssXskb74OVGNW8eFYE1aHm4bH2q090dERMbBAIWIqAu1DVqsPZyHq6L8YGtl0Wvt6nQSpwqrsP9MMfZnlmD/mRKcr2oKSLydbDA2zAPjwtwxdpAHwr0cLqoZMtzPGYviArDtRBE+3pGBV9cew7u/n8LNY4Nx18RB8HHuuN5HXWPTtsKRfs64Nt64swtTh3phTKg73t1yCoviAi5UbS+qrMf2k0W4d1KYosutFo8Lweq0PNz99UHopMSdE0MVa4uIiAzDAIWIqAtvbjiBL3afwU+Janx+e0Kv/MR945F8PL/iMM5XNRU49HexxaQhnhg7yB1jwzwQ6mHfZRFDIQSmDfPGtGHeSMsuw8c7MvHpjkx8sesM5scE4L7JYRji43TJdZ/tzEROWS3eui7a6MGCEAJPzx6Kaz/aiy93n8Wfpw0GAKxMyYFWJ7Eozji1TzoyZpA7InwccbKgCrNH+BptK2MiIjKeLgMUIcQXAOYCKJRSjlS+S0REnVOX1PTaF8ujuRX4eu9ZJIS4IelcKW76dB++vnMMPBxtFGvzu33n8PLKdIzwd8Ezs4dhXJgHAt3selRVPSrQFe/fHIes4hp8tisTSxPV+PlQNqYP88Z9k8MwdpA7hBAoqKjDB9sycMUIH4wP9zDiu/pDQqg7Zg73xkfbM3DL2GC42ltjeVIOogJd2g2YjEkIgdsnhOKFFem4ZxK3FiYiMkX6ZE1+BWC2wv0gItLL0kQ1Jv17K346mKV4WzqdxEsr0+FqZ4XPbx+NT26Lx6mCKlz/8V7kldcavT0pJd7acAIv/pqOaUO98dP943BdQhCC3LueLdFXsIc9/nHNSOx5dgYenxmBFHUZbvxkH+a/vxtr0vLwxvrjaNTq8Pycnm0r3JUnrxiKqnoNPtyegWN5FTiaV4GFRqoc35WbRgdj0+OTkRBqWF0XIiJSVpcBipRyB4CSXugLEVGn6hq1eHvjSQDAP1cfQ06Z8YOE1n45lI1D50rx3JzhcLG3wvRhPvjmrjEoqKjHtR/uxZnz1UZrq1Grw9O/pOG9radx4+ggfLw4/kJ+hhLcHazx6Mwh2P3MdPxz/kiU1Tbizz8kYXlSDu6aOAghHg6KtQ0Aw3ydsSAmAF/tPosPtmXAUiVwdUzvBCgqlVB8poaIiAzHOihEZDa+2XsW+RV1ePPaKOikxLPL0npc66MjpdUNeH3dMYwOdbsoL2JsmAd+vHccahu1uO6jvTiaW9HjtqrrNbj3m0T8fCgbj80cgtcXjoJlN7cFNpSdtQUWjwvB73+Zig9vicPicSF4aPrgXmn78VkR0EmJVam5mDbMG+4O1r3SLhERmTahzz/uQohQAKs7y0ERQtwH4D4A8PHxiV+yZImx+tgjVVVVcHR07Otu9GscY+WZ8hiX10u42Chf5K66UeLpHTUIc7HAXxJs8XtWI7452oA7RlhjalDPktbbG9+v0uuxI0eDv0+wQ5DTpcFCbpUObyXWoVYj8US8LYa4Gba7V0W9xH8P1eFshQ63G+G9mKqOPsPfHa3H5iwNHo61QbwP923pCVN+TvQXHGNlcXyVZ2pjPG3atENSyoS2x40WoLSWkJAgExMTu91JJWzbtg1Tp07t6270axxj5ZnqGP+WmotHfkzG/90Yg2sUXp7z5objeH9rBtY8chlG+LtAp5O49fP9SFWXYcPjkxHoZnjSfNvxTc4qxcIP9+DuiYPw4tzIDq/LLq3B4s8PIK+8Fh8vTsCUCK9utXv2fDVu//IACirq8P7NcZgx3MfQt2DyOvoMV9Q14reUXNw0JpjV3HvIVJ8T/QnHWFkcX+WZ2hgLIdoNULjEi4gMUq/R4t/rjwMA/rHqKMpqGhRrq7CiDp/vOoOro/0xwt8FQFMewRuLogAAT/+SBp3OOEu9tDqJF39Nh7eTDR6bFdHpuYFu9lh6/3gM8nTEPV8fxNrDeXq3k6ouw6IP96CithE/3DuuXwcnnXG2tcKt40IYnBAR0QVdBihCiB8B7AUwVAiRLYS4W/luEZGp+3bvOWSX1uKFOcNRVtuI19ceV6ytd38/BY1W4i+XXxwwBLnb4/mrhmNPRjG+P2CcXb2+23cOR3Ir8PLcEXC06XrJkZeTDZbcNw7Rga546IckvXYX23qiEDd+sg921hb45YEJiAt2M0bXiYiI+gV9dvG6SUrpJ6W0klIGSik/742OEZHpqqhrxHtbT2PSEE/cOzkM90wahJ8S1difWWz0ts6er8aSA2rcPDa43Z2lbh4TjMsGe+L1tcegLqnpUVuFlXV4a8MJTBriiTmjfPW+zsXOCt/ePRaThnjhmWWH8cmOjA7PXZqoxj1fJyLMywHLH5yAcC/TWQtMRERkCrjEi6gfUWpHq7Y+2paBsppGPDN7GADg0RlDEOhmh+dXHEa9RmvUtt7aeAJWFqoOd5YSQuCNa6OgEgJP/ZLao6Ver689jnqNDn+/ekS3647YWVvg09sScNUoP7y29jje3HD8or8PKSX+t+UUnv4lDRPCPfDT/ePh7WRrcF+JiIj6KwYoRP3EoXMlmPTvrThwRtmyRfnldfhi9xlcE+OPkQFN+SD21pb45/yRyCiqxsfbM43WVnpOOVan5eGeSYM6/TIf4GqHF68ajn2ZJfhu/zmD2tqbUYwVyTn405QwhBk4q2FtqcK7N8XipjFBeH9rBl5eeQQ6nYS2ueDjfzadxILYAHx++2i9lo8RERENRPwXkqgfaNTq8PzydGSX1uIvP6dg/aOT4aDQF+B3Np+EVifx5OVDLzo+bag35kb54b2tpzE3ys/gL/mtvbH+ONzsrXDv5LAuz71hdBDWpufj9bXHMSXCq1uFBjU6iVdWpiPI3Q4PTutZDRALlcBrC0bB2c4KH2/PREVdI2obtNh4tAAPTA3H01cMNVpVeCIiov6IMyhE/cCXu8/gREEl7p8ShuzSWvxrnTIJ66cKKrE0UY1bx4UgyP3SbX1fnhcJG0sVXliR3uPlZntOn8fOU+fx52mD4WzbdW0QIQTeWDQKliqBp7q5q9fGs404XViFv80bAVsrw+qZtO3Lc1cOx9Ozh2JlSi42HSvA368egWdmD2NwQkRE1AUGKERmLresFu9sPoUZw7zx7OxhuGviIHy77xx2nz5v9LbeWH8CDtaWeHj6kHZf93ayxbNXDsPezGIsS8oxuB0pJd7YcAL+Lra4dVyI3tf5udjhpXmROHCmBF/vPavXNTlltfg1oxGXR/oYfavfB6cOxoe3xOHrO8fg9gmhRr03ERFRf8UAhcjM/XP1UeikxN+aE7ufumIowjwd8PQvaaisazRaOwfPlmDzsQL8aWo43B2sOzzvptHBiA9xw6trjqKk2rDaKOvT85GqLsNjsyK6PaNxXXwgpg31whvrj+PM+eouz//HqiOAbJr9UcKVo/wwuZsFHImIiAYyBihEZmzriUKsS8/Hw9OHXFhyZWtlgbeuj0ZeeS1eW3vMKO1IKfH62mPwdrLBnRNDOz1X1ZyDUVmnwatrut++RqvDmxtPYIi3IxbFBXb7eiEEXl8YBSsLFZ76ORXaTpZ6bT1eiA1HCnD1YKseVaInIiIi42GAQqSABo0O69Pzjb7lbmt1jVr8deURhHk54J5Jgy56LS7YDfdODsOPB9TYfrKox21tOFKApKwyPD4rAvbWXSffD/V1wn2Tw7AsKRt7Mrq31OyXQ9nILKrGU1cMNbi6uK+LLf42bwQSz5Xiy91n2j2nrlGLv/52BOFeDpgd2nWOCxEREfUOBihERqbTSTyxNAV/+u4QnvklTbHaJB9sy0BWSQ3+ec1I2Fheugzq8ZkRGOLtiGd+SUN5reFLvTRaHf694TjCvRxwXbz+MxqPzBiCYHd7vLAiHXWN+gVqdY1avLP5FOKCXTErsmf5IAvjAjBjmDfe3HACmUVVl7zeevwsDQyEiIiIyPgYoBAZkZQS/1xzFKvT8jB2kDt+TcnFe7+fNno7Z85X46NtGbg62h8TB3u2e46tlQXeui4aRVX1eGX1UYPbWprYNKPx9OxhsLTQ/5Fha2WBVxeMxJnz1fhgW8eV1Vv7es9Z5FfUGWW3KyEEXls4CrZWFniyzVKvM+er8dH2DFwT448JHYwfERER9Q0GKERG9NH2THy5+yzuvmwQltw3DgtjA/CfTSexOi3XaG1IKfHyynTYWKrw4lXDOz03OsgVD0wJx8+HsrHlWEG326pp0OC/m08iPsQNlxswozFpiBfmx/jjw22ncbqwstNzy2sb8cG2DEwd6oWxYR7dbqs9Ps62+NvVkUjKKsPnu5oKSEop8dffjsDGQoUX5nQ+fkRERNT7GKAQGckvh7LxxvrjuCbGHy/MGd6UrL1oFBJC3PCXpalIUZcZpZ21h/Ox89R5/OXyCHg7d1xdvcXDMwZjmK8Tnlt+GGU13dtV6/OdZ1BUWY/n5xg+o/Hi3EjYW1vi+eXpndYm+Xh7BirqGvH0FcMMaqcj82MCMCvSB29tPInThVVYl56PHSeL8ISe40dERES9iwEKGaSwsg7ZpTV93Q2TsfV4IZ5ZloZJQzzx5rXRUDXnNNhYWuDjxfHwdrbBPV8nIqestkftVNVr8I/VRzDC31nv+iA2lk1LvUqqG/D3Vfov9SquqsfHOzJxeaQP4kPcDe0yPB1t8PycYThwtgQ/H1K3e05BRR2+2H0G10T7I9Lf2eC22iOEwKsLRsLe2gJ/WZqCf6w6ikg/ZyzuRn0VIiIi6j0MUKjbquo1WPThHlz+3x1G2SHK3CVnleLB75MQ6eeMD2+Nh7Xlxf9beTja4IvbR6O+UYu7vzqIqnqNwW39d9NJFFbW45X5I7uVDzIywAUPTR+MFck52HAkX69r/vf7adQ0aPD07KGGdveC6+KDMCbUHa+tPY7zVfWXvP7ullPQ6iSemNXzttrj7WSLv189AqnZ5civqMM/uzl+RERE1Hv4L3Q/kFtWi9OFl+5SpJR/rjqKnNJa+LrY4u6vDmJPruFfuM1dRlEV7vrqILydbfDlnaPhaNP+FrxDfJzw3i1xOFVYhceWJHdam6MjR3Mr8NWes7hxdDBig926ff2fpw3GCH9nvLDicJcFFLOKa/D9/nO4YXQQBns7dbuttlQqgdcWjkRNg+aShP0z56ux5KAaN48JRrCHcrVIro72x92XDcJfZkUgPqT740dERES9gwGKmSupbsDCD/Zg/vu7291K1dg2HsnHT4lq3D8lHCv/PBGjQ93xSVo9PtuZqXjbpqagog63fX4AFiqBb+4aA09Hm07PnxLhhb/Ni8TmY4X417ruFTDUSYmXVqbDxc4Kzxg4o2FlocJ/ro9GeW0jXl6Z3um5b208AQuVwGMzIwxqqz2DvZ3wwJRw/JqSi52n/ph5e2vjCdhYqvDQ9CFGa6s9Qgi8NDcSD89Qth0iIiLqGQYoZkxKiad+TkVJdQMsVAIPfp+E2gblCgOer6rHc8sPY7ifMx6fGQEnWyt8dddoJPhY4JU1x/D6umOK1fzQV02DBuk55fgtNRf/3XQSD/+YjDn/txOjX92MV9cc7XLmQF/ltY24/YsDKKtpwFd3jkGIh4Ne1y0eH4o7JoTi051n8OOBLL3b25WjwaFzpXjuymFwtbc2tNsY5uuMx2ZGYHVaHtak5bV7zuHspvG7+7JB8DFyEvmD0wZjkKcDXvy1qTbK4exyrEnLwz2XDYKXU+cBHhEREQ0MXZeEJpP15e6z2HK8EH+dF4kwL0fc8eUBvPhrOt66LqrHNSTaklLi2WWHUVmvwQ83xFzIs7CxtMCDMTbYVuGFj7dnoqiyHm8sioKVguv7pZTIr6hDZlE1MoqqLvw3o7AKueV1F84TAgh0s0O4lyMC3ezw2a4z+PGAGvdMGoS7LxsEJ1vDqofXNWpx7zeJyCiqwpd3jMHIAJduXf/iVcOReb4aL/2ajhB3+y7rcJRWN2DpiQaMDnXDojj9CyV25P7JYdh4JB8vrUzH2DD3i2Z+pJT41/pjcLO3wv1TwnvcVlu2VhZ4df5I3PzZfvzv91NIyy6Hm70V7p0cZvS2iIiIyDwxQDFTh7PL8fq6Y5g53Bt3TAiFEAKPTB+C/9tyCmMGueGG0cFGbW9pohqbjxXgxauGY6jvxTkJKiHw96tHwMvRBv/ZdBKl1Q14/5Y42Fsb7+NVWt2AT3dmYsepIpwpqkZ1q5kiB2sLhHs7YmyYB8I8HRDu7YgwLweEejjA1uqPCusnCyrx9saTeGfzKXy95ywenDoYi8eHXHROV7Q6iceWpODAmRK8e1MsLhvS/SJ/lhYqvHdzLBZ9sAd/+u4Qfv3zRIR5OXZ4/hvrj6NGA/xz/sgLu4P1hKWFCm9dF42r/rcLL6w4jI9ujb8Q0O48dR67Txfj5bmRcDYwgOvKhMGeWBgXgA+3ZUAnmwI2Q4NFIiIi6n8YoJihyrpGPPRjEjwdbfDmtdEXvlw+MmMIkrJK8dLKIxgZ4IIR/t37yX5Hsopr8I9VRzE+zAN3TRzU7jlCCDw8Ywg8nWzwworDuPnT/fjyjtFwczB8ORLQ9F4/33UGn+88g6oGDcaHeeC6hCCEezsivDkY8Xay0WvGKMLHCR8tjkequgxvbTyBV9cew2e7MvHIjCG4PiGoy1mfpgJ/6Vh/JB8vzY3E1dH+Br8vZ1srfHHHaFzz/m7c9dVBrHhwYrtjdehcKZYcVGN2qBWG+Rpv+90hPk74y6wIvL7uOH5LzcU1MQHQ6ST+te44At3scMs44wa4bb14VSS2Hi+EvbWl3tslExER0cDAHJQO9HUuRUeklHjx13SoS2rwfzfGXvSl1kIl8M4NMXC3t8aD3yehvLaxx+1pdRJPLE2BSgi8dX10lz/Bv2lMMD68NR5H8ypw7Ud7DK77UdugxcfbMzD531vxzuZTmDjYExsem4wf7h2Hv109AovHhWDCYE/4ONt2ezlbdJArvr17LH68dxwCXO3wwop0zHx7O1am5HRaSPB/v5/Gd/uycP+UMNx9WfuBWncEudvjk8XxyC2rwwPfH0KDRnfR6xqtDi/+mg5fZ1vMH2z8GYZ7JoUhNtgVL688gsKKOqxMzcHRvAo8dcVQ2FjqP6tkCHcHayx/cCJ+vHdct2awiIiIqP9jgNKOA2dKEPW3jbj9iwPYdLTAoC1hlfLzoWysTMnFYzMjMGbQpcXzPBxt8P4tscgprcVTP6f2OND6eEcGEs+V4h/zRyDA1U6va64Y4Ytv7xqDwsp6LPpgD07kV+rdXoNGh2/2nsWUN7fi9XXHERXoilUPXYaPFscjwqfn2922Nj7cA8semIAv7kiAvbUlHl2Sgjnv7sSmowWXjNuPB7Lw9qaTWBgXgGdnG6/SeUKoO964dhT2ZZbgpV/TL2r3m73ncCyvAn+dFwlbS+PmFAFNAe1b10WjrlGLZ5al4a0NJzHC3xnzogyfGeqOQZ4Oim4rTEREROaJAUob2aU1eOC7Q3C2s8Lx/Arc+00iJr3xO97dcgqFFXVd30BBpwsr8deVRzA+zAN/nja4w/PiQ9zx3Jzh2Hi0AJ/tPGNwe0dyy/HfTSdx1Sg/zI8J6Na1Y8M88POfxkMnJa77aA8Oni3p9HyNVoeliWpMe2sbXl55BKGeDlh6/3h8fdcYjAo0zlK19gghMH2YD9Y8fBn+d1Ms6jU63PtNIhZ8sAd7Tp8H0LS18gsrDmPqUC+8scj4GxAsiA3Ew9MH46dE9YW/r4KKOry96SSmRHhh9khfo7bXWriXI56ePQxbTxQhp6wWz145zCh5LkRERESGYg5KKzUNGtz7TdNSm6V/Go9gd3tsOVaI7/efw9ubTuLdLadw+Qgf3DI2BBPCPYz+RbUzdY1aPPRDMuysLfDOjTGw6OJL5F0TQ5F4tgT/Wn8cMcGuGB166WxLV+09/lMK3Oyt8cr8kQa912G+zlj2wATc/sUB3PrZfrx3cxxmRfpcdI5OJ7HmcB7+u/kkMouqERXogtcXjsKkIZ69Or4qlcC8aH9cOdIXvxzKxv9tOYWbP9uPsYPckaIuw6hAV3xwS5xiu5M9PjMCmUXVeG3dMYR6OmBlSg4atDr8/eoRio/DnRNCsef0edhaW2DSEC9F2yIiIiLqCgOUZk01RdJwPL8CX9wxGuHNuyrNHumL2SN9cfZ8NX44kIWfE9VYezgfYZ4OuHlsMK6ND+xRXQp9vbLmKI7nV+LLO0frVZtCCIF/XxuF4+/txp+/T8KaRyZ1q87EWxtO4GRBFb66s2eJ7kHu9vjlgQm486uDuP/bRLy+cBRuGB0MKSV+P16ItzaexLG8Cgz1ccLHi+NxeaRPrwYmbVlaqHDjmGDMjw3A9/uz8MHW0whws8OXd4w26q5kbamal1tll9bgzz8koUGjw+MzIxDqqV99lZ62/dntCYq3Q0RERKQPBijN3vv9NNYczsNzVw7DtKHel7we6umA5+cMxxOzIrAuPQ/f7cvCK2uO4c0NJzA3yh+3jgtGTJCrIl+u1x1uau++yWHt9q0jTrZW+OCWOMx/fzceXZKMb+8e2+XMCwDsOX0en+06g8XjQjC1G+11xN3BGj/cMxYPfJ+EZ5YdxvH8SqSoy5CcVYYQD3v8340xmBvlr1ffeoutlQXuvmwQbh0XDCnRK4ncdtYW+PS2BFzz/m7YWlng/im9VxukL4NCIiIiotYYoADYcCQf/9l0EgtiA3BfFwXjbK0ssCA2EAtiA3EsrwLf7z+HFUk5WJaUjRH+zrhlbAiuifGHg41xhlZdUoOnl6UhOtAFT14+tNvXD/dzxivzR+KpX9Lw300n8eQVnd+jvLYRT/6cijBPBzw3x3jJ4A42lvj89gQ8/Usavtx9Fn4utnh94ShcGx+oaFHHnlJ6N6u2vJ1tsf6xyUAvBUVEREREpmbABygn8ivxxE8piG7OfejOT5KbvvyPwrNXDsevyTn4bt85PL/iMP694TjunxyO2yeE9GhZUKNWh0eWJAMS+N9NcReqt3fXdQlBSDxbive2nkZciCumD/Pp8Ny//3YEBZX1WPbABKMvabKyUOE/10XjpjHBiAp04RfwDrjYsWghERERDVym+6PrXlBa3YB7vjkIBxtLfLw4weAvzI42TcXm1j06CcseGI/YIFe8sf44Jv97Kz7bmYm6Rm3XN2nH25tOIjmrDK8tHNXj7Vj/fs0IDPdzxuM/pSK7tKbdc9ak5WF5cg4emjYYMUGuPWqvIyqVwJhB7gxOiIiIiKhdAzZAadTq8OD3SSgor8dHi+Ph69J14nlXhBCID3HHl3eOwbIHJmCorxNeWXMMU97cim/3nkW9Rv9AZcfJIny4LQM3jQnCvB5ULG9ha2WBD2+Jg04n8efvky7pS2FFHV749TCiA13w0PSOtzAmIiIiIlLSgA1QXll9FHszi/HawlGIC3Yz+v3jQ9zw/T3j8OO94xDsbo+XVh7B9Le246eDWWjU6jq9trCyDk8sTUGEjyNenjvCaH0K9XTAm9dFIzW7HK+uOXbhuJQST/2ShrpGLd6+Icakc0KIiIiIqH8bkN9EfzyQha/3nsM9lw3CtfGBirY1PtwDS+8fj2/uGgNPJxs8s+wwZr69HcuTstutUK/TSTzxUyqq6jV47+Y42FkbdynU7JG+uHfSIHyz9xxWpuQAAL7bn4XtJ4vwwpzhF7ZXJiIiIiLqCwMuQDl4tgQvr0zHpCGeePZK4+1S1RkhBCZHeOHXByfgs9sSYG9tiSeWpuLy/27H6rRc6FoFKh/tyMCu0+fx13kjEOHjpEh/np49DAkhbnhu+WFsPJKPV9ccxeQIL9w6LkSR9oiIiIiI9DWgApScslr86dtDCHSzx3s3xcGyl5cyCSEwM9IHax6+DB/cEgeVEHjoh2TMeXcnNhzJR+LZEvxn40lcFeWHG0cHKdYPKwtV0+yMlQXu+/YQbCwt8Oa1UayFQURERER9bsBsM1zToMG9XyeiQaPDp7clwMW+77ZyVakE5ozywxUjfLEqNRfvbD6J+789BEuVgL+rbbe3OzaEr4st3r0pFg9+n4R/LRylV3V6IiIiIiKlDYgARUqJp35Ow7H8Cnxx+2gM9jaNPAsLlcD82ADMjfLD8uQcLDuUjReuGg5n294JniYO9kTyS7OgMqEK7kREREQ0sOkVoAghZgP4PwAWAD6TUv5L0V4Z2ftbT2PN4Tw8e+UwTBvm3dfduYSlhQrXJwTh+gTllnV1hMEJEREREZmSLpMwhBAWAN4HcCWASAA3CSEile6YsSQVaPDWxpOYH+OP+yeH9XV3iIiIiIioE/pkiY8BcFpKmSmlbACwBMA1ynbLOE7kV+KTtHpEBbrgX4uYBE5EREREZOqElJfW4rjoBCGuBTBbSnlP858XAxgrpXyozXn3AbgPAHx8fOKXLFmiTI+74c2DtVBXaPG3ifZwtx1QG5b1qqqqKjg6mkZeT3/FMVYWx1d5HGPlcYyVxzFWFsdXeaY2xtOmTTskpUxoe1yfHJT2ph0uiWqklJ8A+AQAEhIS5NSpU7vbR6OLHt2AVVt2YuHs6X3dlX5t27ZtMIW/7/6MY6wsjq/yOMbK4xgrj2OsLI6v8sxljPWZVsgG0Dp7OxBArjLdMS43B2sEOxu3EjsRERERESlHnwDlIIAhQohBQghrADcC+E3ZbhERERER0UDU5RIvKaVGCPEQgA1o2mb4CynlEcV7RkREREREA45edVCklGsBrFW4L0RERERENMBxaysiIiIiIjIZDFCIiIiIiMhkMEAhIiIiIiKTwQCFiIiIiIhMBgMUIiIiIiIyGQxQiIiIiIjIZDBAISIiIiIikyGklMa/qRBFAM4Z/caG8QRwvq870c9xjJXHMVYWx1d5HGPlcYyVxzFWFsdXeaY2xiFSSq+2BxUJUEyJECJRSpnQ1/3ozzjGyuMYK4vjqzyOsfI4xsrjGCuL46s8cxljLvEiIiIiIiKTwQCFiIiIiIhMxkAIUD7p6w4MABxj5XGMlcXxVR7HWHkcY+VxjJXF8VWeWYxxv89BISIiIiIi8zEQZlCIiIiIiMhMmHWAIoSYLYQ4IYQ4LYR4tp3XhRDi3ebX04QQcfpeS3qN7y3N45omhNgjhIhu9dpZIcRhIUSKECKxd3tuPvQY46lCiPLmcUwRQrys77XURI8xfqrV+KYLIbRCCPfm1/g57oIQ4gshRKEQIr2D1/kc7iE9xpjP4h7SY4z5LO4BPcaXz+EeEkIECSG2CiGOCSGOCCEebecc83keSynN8hcACwAZAMIAWANIBRDZ5pw5ANYBEADGAdiv77UD/Zee4zsBgFvz769sGd/mP58F4NnX78OUf+k5xlMBrDbkWv7q/jgBmAfg91Z/5ue46zGeDCAOQHoHr/M5rPwY81ms/BjzWazg+LY5l89hw8bYD0Bc8++dAJw05+/F5jyDMgbAaSllppSyAcASANe0OecaAN/IJvsAuAoh/PS8dqDrcoyklHuklKXNf9wHILCX+2juevI55GdYP90dp5sA/NgrPesnpJQ7AJR0cgqfwz3U1RjzWdxzenyOO8LPsR66Ob58DhtASpknpUxq/n0lgGMAAtqcZjbPY3MOUAIAqFv9ORuX/kV0dI4+1w503R2ju9EUlbeQADYKIQ4JIe5ToH/9gb5jPF4IkSqEWCeEGNHNawc6vcdJCGEPYDaAZa0O83Pcc3wO9y4+i5XDZ7HC+Bw2DiFEKIBYAPvbvGQ2z2PLvmy8h0Q7x9puSdbROfpcO9DpPUZCiGlo+kfxslaHJ0opc4UQ3gA2CSGON/8Ehf6gzxgnAQiRUlYJIeYA+BXAED2vpe6N0zwAu6WUrX/Kx89xz/E53Ev4LFYUn8W9g8/hHhJCOKIpwHtMSlnR9uV2LjHJ57E5z6BkAwhq9edAALl6nqPPtQOdXmMkhIgC8BmAa6SUxS3HpZS5zf8tBLACTdOHdLEux1hKWSGlrGr+/VoAVkIIT32uJQDdG6cb0WZZAT/HRsHncC/gs1hZfBb3Gj6He0AIYYWm4OR7KeXydk4xm+exOQcoBwEMEUIMEkJYo+lD/Vubc34DcFvzrgXjAJRLKfP0vHag63KMhBDBAJYDWCylPNnquIMQwqnl9wAuB9Duzh0DnD5j7CuEEM2/H4Om/2eL9bmWAOg5TkIIFwBTAKxsdYyfY+Pgc1hhfBYrj89i5fE53DPNn8/PARyTUr7dwWlm8zw22yVeUkqNEOIhABvQtPvAF1LKI0KIPzW//hGAtWjaseA0gBoAd3Z2bR+8DZOl5/i+DMADwAfNz22NlDIBgA+AFc3HLAH8IKVc3wdvw6TpOcbXAnhACKEBUAvgRimlBMDPsB70HGMAWABgo5SyutXl/BzrQQjxI5p2OPIUQmQD+CsAK4DPYWPRY4z5LO4hPcaYz+Ie0GN8AT6He2oigMUADgshUpqPPQ8gGDC/5zEryRMRERERkckw5yVeRERERETUzzBAISIiIiIik8EAhYiIiIiITAYDFCIiIiIiMhkMUIiIiIiIyGQwQCEiIiIiIpPBAIWIiIiIiEwGAxQiIiIiIjIZ/w9qWpl5VnZyRgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Increase accuracy requirement.\n",
    "# \"rtol\" is a relative error tolerance, defaulting to 1e-3\n",
    "# \"atol\" is an absolute error tolerance, defaulting to 1e-3\n",
    "# It solve to the less demanding of these two,\n",
    "# so both must be specified to increase accuracy.\n",
    "\n",
    "t_plot = np.linspace(a, b)\n",
    "\n",
    "time_start = time()\n",
    "ode_solution = solve_ivp(f, [a, b], y_0, t_eval=t_plot, rtol=1e-12, atol=1e-12)\n",
    "time_end = time()\n",
    "time_elapsed = time_end - time_start\n",
    "print(f\"Time take to solve: {time_elapsed} seconds\")\n",
    "\n",
    "t = ode_solution.t\n",
    "y = ode_solution.y[0]\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Computed Solution\")\n",
    "plt.plot(t, y)\n",
    "grid(True)\n",
    "\n",
    "y_exact = np.exp(t)\n",
    "errors = y - y_exact\n",
    "figure(figsize=[14,5])\n",
    "plt.title(\"Errors\")\n",
    "plt.plot(t, errors)\n",
    "grid(True);"
   ]
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
