{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notebook for generating the module `numerical_methods_module`\n",
    "\n",
    "**Author: Brenton LeMesurier**,\n",
    "brenton.lemesurier@unco.edu and lemesurierb@cofc.edu\n",
    "\n",
    "A collection of functions implementing numerical algorithms from the course and book *Elementary Numerical Analysis*,\n",
    "and a module `numerical_methods_module` produced from that.\n",
    "\n",
    "**Last updated on April 11, 2021**\n",
    "\n",
    "Recent additions; most recent first:\n",
    "- a function `inverse` for computing the inverse of a matrix (but use this sparingly!)\n",
    "- versions of Euler's Method and the Classical Runge-Kutta Method for systems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Index\n",
    "\n",
    "The three main sections (so far) are\n",
    "\n",
    "- [Zero Finding](#Zero-Finding)\n",
    "- [Linear Algebra](#Linear-Algebra)\n",
    "- [Solving Initial Value Problems for Ordinary Differential Equations](#ODE-IVPs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"Zero-Finding\"></a>\n",
    "## Zero Finding: solving $f(x) = 0$ or $g(x) = x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisection1(f, a, b, N, demoMode=False):\n",
    "    '''Approximately solve equation f(x) = 0 in the interval [a, b] with N iterations of the Bisection Method.\n",
    "    By the way, a triple-quoted multi-line comment like this provides covenient documentation about what a function does,\n",
    "    so I encourage adding them. Try the commmand `help(bisection1)`\n",
    "    '''\n",
    "    c = (a + b)/2\n",
    "    for iteration in range(N):\n",
    "        if demoMode: print(f\"\\nIteration {iteration+1}:\")\n",
    "        if f(a) * f(c) < 0:\n",
    "            b = c\n",
    "        else:\n",
    "            a = c\n",
    "        c = (a + b)/2\n",
    "        if demoMode:\n",
    "            print(f\"The root is in interval [{a}, {b}]\")\n",
    "            print(f\"The new approximation is {c}, with backward error {np.abs(f(c)):0.3}\")\n",
    "        root = c             \n",
    "        errorBound = (c-a)\n",
    "    return (c, errorBound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by the Bisection Method.\n",
      "\n",
      "Iteration 1:\n",
      "The root is in interval [0.0, 1]\n",
      "The new approximation is 0.5, with backward error 0.378\n",
      "\n",
      "Iteration 2:\n",
      "The root is in interval [0.5, 1]\n",
      "The new approximation is 0.75, with backward error 0.0183\n",
      "\n",
      "Iteration 3:\n",
      "The root is in interval [0.5, 0.75]\n",
      "The new approximation is 0.625, with backward error 0.186\n",
      "\n",
      "Iteration 4:\n",
      "The root is in interval [0.625, 0.75]\n",
      "The new approximation is 0.6875, with backward error 0.0853\n",
      "\n",
      "Iteration 5:\n",
      "The root is in interval [0.6875, 0.75]\n",
      "The new approximation is 0.71875, with backward error 0.0339\n",
      "\n",
      "Iteration 6:\n",
      "The root is in interval [0.71875, 0.75]\n",
      "The new approximation is 0.734375, with backward error 0.00787\n",
      "\n",
      "Iteration 7:\n",
      "The root is in interval [0.734375, 0.75]\n",
      "The new approximation is 0.7421875, with backward error 0.0052\n",
      "\n",
      "Iteration 8:\n",
      "The root is in interval [0.734375, 0.7421875]\n",
      "The new approximation is 0.73828125, with backward error 0.00135\n",
      "\n",
      "Iteration 9:\n",
      "The root is in interval [0.73828125, 0.7421875]\n",
      "The new approximation is 0.740234375, with backward error 0.00192\n",
      "\n",
      "Iteration 10:\n",
      "The root is in interval [0.73828125, 0.740234375]\n",
      "The new approximation is 0.7392578125, with backward error 0.000289\n",
      "\n",
      "root=0.7392578125, backward error 0.000289\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    def f(x): return x - np.cos(x)\n",
    "    print(\"Solving by the Bisection Method.\")\n",
    "    (root, errorBound) = bisection1(f, a=-1, b=1, N=10, demoMode=True)\n",
    "    print(f\"\\n{root=}, backward error {np.abs(f(root)):0.3}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fpi(g, x_0, errorTolerance=1e-6, maxIterations=20, demoMode=False):\n",
    "    \"\"\"Fixed point iteration for approximately solving x = f(x),\n",
    "    x_0: the initial value\n",
    "    \"\"\"\n",
    "    x = x_0\n",
    "    for iteration in range(maxIterations):\n",
    "        x_new = g(x)\n",
    "        errorEstimate = np.abs(x_new - x)\n",
    "        x = x_new\n",
    "        if demoMode: print(f\"x_{iteration} = {x}, {errorEstimate=:0.3}\")\n",
    "        if errorEstimate <= errorTolerance: break\n",
    "    return (x, errorEstimate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fixed point iteration.\n",
      "x_0 = 1.0, errorEstimate=1.0\n",
      "x_1 = 0.5403023058681398, errorEstimate=0.46\n",
      "x_2 = 0.8575532158463934, errorEstimate=0.317\n",
      "x_3 = 0.6542897904977791, errorEstimate=0.203\n",
      "x_4 = 0.7934803587425656, errorEstimate=0.139\n",
      "x_5 = 0.7013687736227565, errorEstimate=0.0921\n",
      "x_6 = 0.7639596829006542, errorEstimate=0.0626\n",
      "x_7 = 0.7221024250267079, errorEstimate=0.0419\n",
      "x_8 = 0.7504177617637604, errorEstimate=0.0283\n",
      "x_9 = 0.7314040424225099, errorEstimate=0.019\n",
      "x_10 = 0.7442373549005569, errorEstimate=0.0128\n",
      "x_11 = 0.7356047404363473, errorEstimate=0.00863\n",
      "x_12 = 0.7414250866101093, errorEstimate=0.00582\n",
      "x_13 = 0.7375068905132427, errorEstimate=0.00392\n",
      "x_14 = 0.7401473355678758, errorEstimate=0.00264\n",
      "x_15 = 0.7383692041223231, errorEstimate=0.00178\n",
      "x_16 = 0.7395672022122561, errorEstimate=0.0012\n",
      "x_17 = 0.7387603198742112, errorEstimate=0.000807\n",
      "x_18 = 0.739303892396906, errorEstimate=0.000544\n",
      "x_19 = 0.7389377567153443, errorEstimate=0.000366\n",
      "\n",
      "root=0.7389377567153443, errorEstimate=0.0003661356815616301\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    def g(x): return np.cos(x)\n",
    "    print(\"Fixed point iteration.\")\n",
    "    (root, errorEstimate) = fpi(g, 0, demoMode=True)\n",
    "    print(f\"\\n{root=}, {errorEstimate=}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton(f, Df, x0, errorTolerance=1e-15, maxIterations=20, demoMode=False):\n",
    "    \"\"\"Basic usage is:\n",
    "    (rootApproximation, errorEstimate, iterations) = newton(f, Df, x0, errorTolerance)\n",
    "    There is an optional input parameter \"demoMode\" which controls whether to\n",
    "    - print intermediate results (for \"study\" purposes), or to\n",
    "    - work silently (for \"production\" use).\n",
    "    The default is silence.\n",
    "\n",
    "    \"\"\"\n",
    "    x = x0\n",
    "    for k in range(1, maxIterations+1):\n",
    "        fx = f(x)\n",
    "        Dfx = Df(x)\n",
    "        # Note: a careful, robust code would check for the possibility of division by zero here,\n",
    "        # but for now I just want a simple presentation of the basic mathematical idea.\n",
    "        dx = fx/Dfx\n",
    "        x -= dx  # Aside: this is shorthand for \"x = x - dx\"\n",
    "        errorEstimate = abs(dx)\n",
    "        if demoMode:\n",
    "            print(f\"At iteration {k} x = {x} with estimated error {errorEstimate:0.3}, backward error {abs(f(x)):0.3}\")\n",
    "        if errorEstimate <= errorTolerance:\n",
    "            iterations = k\n",
    "            return (x, errorEstimate, iterations)\n",
    "    # If we get here, it did not achieve the accuracy target:\n",
    "    iterations = k\n",
    "    return (x, errorEstimate, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by Newton's Method.\n",
      "At iteration 1 x = 1.0 with estimated error 1.0, backward error 0.46\n",
      "At iteration 2 x = 0.7503638678402439 with estimated error 0.25, backward error 0.0189\n",
      "At iteration 3 x = 0.7391128909113617 with estimated error 0.0113, backward error 4.65e-05\n",
      "At iteration 4 x = 0.7390851333852839 with estimated error 2.78e-05, backward error 2.85e-10\n",
      "At iteration 5 x = 0.7390851332151606 with estimated error 1.7e-10, backward error 1.11e-16\n",
      "\n",
      "The root is approximately 0.7390851332151606\n",
      "The estimated absolute error is 1.7012334067709158e-10\n",
      "The backward error is 1.11e-16\n",
      "This required 5 iterations\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    def f(x): return x - np.cos(x)\n",
    "    def Df(x): return 1. + np.sin(x)\n",
    "    print(\"Solving by Newton's Method.\")\n",
    "    (root, errorEstimate, iterations) = newton(f, Df, x0=0.,\n",
    "                                               errorTolerance=1e-8, demoMode=True)\n",
    "    print()\n",
    "    print(f\"The root is approximately {root}\")\n",
    "    print(f\"The estimated absolute error is {errorEstimate}\")\n",
    "    print(f\"The backward error is {abs(f(root)):0.3}\")\n",
    "    print(f\"This required {iterations} iterations\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def false_position(f, a, b, errorTolerance=1e-15, maxIterations=15, demoMode=False):\n",
    "    \"\"\"Solve f(x)=0 in the interval [a, b] by the Method of False Position.\n",
    "    This code also illustrates a few ideas that I encourage, such as:\n",
    "    - Avoiding infinite loops, by using for loops sand break\n",
    "    - Avoiding repeated evaluation of the same quantity\n",
    "    - Use of descriptive variable names\n",
    "    - Use of \"camelCase\" to turn descriptive phrases into valid Python variable names\n",
    "    - An optional \"demonstration mode\" to display intermediate results.\n",
    "    \"\"\"\n",
    "    fa = f(a)\n",
    "    fb = f(b)\n",
    "    for iteration in range(1, maxIterations+1):\n",
    "        if demoMode: print(f\"\\nIteration {iteration}:\")\n",
    "        c = (a * fb - fa * b)/(fb - fa)\n",
    "        fc = f(c)\n",
    "        if fa * fc < 0:\n",
    "            b = c\n",
    "            fb = fc  # N.B. When b is updated, so must be fb = f(b)\n",
    "        else:\n",
    "            a = c\n",
    "            fa = fc\n",
    "        errorBound = b - a\n",
    "        if demoMode:\n",
    "            print(f\"The root is in interval [{a}, {b}]\")\n",
    "            print(f\"The new approximation is {c}, with error bound {errorBound:0.3}, backward error {abs(fc):0.3}\")\n",
    "        if errorBound < errorTolerance:\n",
    "            break\n",
    "    # Whether we got here due to accuracy of running out of iterations,\n",
    "    # return the information we have, including an error bound:\n",
    "    root = c  # the newest value is probably the most accurate\n",
    "    return (root, errorBound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by the Method of False Position.\n",
      "\n",
      "Iteration 1:\n",
      "The root is in interval [0.5403023058681398, 1]\n",
      "The new approximation is 0.5403023058681398, with error bound 0.46, backward error 0.317\n",
      "\n",
      "Iteration 2:\n",
      "The root is in interval [0.7280103614676172, 1]\n",
      "The new approximation is 0.7280103614676172, with error bound 0.272, backward error 0.0185\n",
      "\n",
      "Iteration 3:\n",
      "The root is in interval [0.7385270062423998, 1]\n",
      "The new approximation is 0.7385270062423998, with error bound 0.261, backward error 0.000934\n",
      "\n",
      "Iteration 4:\n",
      "The root is in interval [0.7390571666782676, 1]\n",
      "The new approximation is 0.7390571666782676, with error bound 0.261, backward error 4.68e-05\n",
      "\n",
      "Iteration 5:\n",
      "The root is in interval [0.7390837322783136, 1]\n",
      "The new approximation is 0.7390837322783136, with error bound 0.261, backward error 2.34e-06\n",
      "\n",
      "Iteration 6:\n",
      "The root is in interval [0.7390850630385933, 1]\n",
      "The new approximation is 0.7390850630385933, with error bound 0.261, backward error 1.17e-07\n",
      "\n",
      "Iteration 7:\n",
      "The root is in interval [0.7390851296998365, 1]\n",
      "The new approximation is 0.7390851296998365, with error bound 0.261, backward error 5.88e-09\n",
      "\n",
      "Iteration 8:\n",
      "The root is in interval [0.7390851330390691, 1]\n",
      "The new approximation is 0.7390851330390691, with error bound 0.261, backward error 2.95e-10\n",
      "\n",
      "Iteration 9:\n",
      "The root is in interval [0.7390851332063397, 1]\n",
      "The new approximation is 0.7390851332063397, with error bound 0.261, backward error 1.48e-11\n",
      "\n",
      "Iteration 10:\n",
      "The root is in interval [0.7390851332147188, 1]\n",
      "The new approximation is 0.7390851332147188, with error bound 0.261, backward error 7.39e-13\n",
      "\n",
      "Iteration 11:\n",
      "The root is in interval [0.7390851332151385, 1]\n",
      "The new approximation is 0.7390851332151385, with error bound 0.261, backward error 3.71e-14\n",
      "\n",
      "Iteration 12:\n",
      "The root is in interval [0.7390851332151596, 1]\n",
      "The new approximation is 0.7390851332151596, with error bound 0.261, backward error 1.78e-15\n",
      "\n",
      "Iteration 13:\n",
      "The root is in interval [0.7390851332151606, 1]\n",
      "The new approximation is 0.7390851332151606, with error bound 0.261, backward error 1.11e-16\n",
      "\n",
      "Iteration 14:\n",
      "The root is in interval [0.7390851332151607, 1]\n",
      "The new approximation is 0.7390851332151607, with error bound 0.261, backward error 0.0\n",
      "\n",
      "Iteration 15:\n",
      "The root is in interval [0.7390851332151607, 1]\n",
      "The new approximation is 0.7390851332151607, with error bound 0.261, backward error 0.0\n",
      "\n",
      "The Method of False Position gave approximate root is 0.7390851332151607,\n",
      "with estimate error 0.261, backward error 0.0\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    def f(x): return x - np.cos(x)\n",
    "    print(\"Solving by the Method of False Position.\")\n",
    "    (root, errorBound) = false_position(f, a=-1, b=1, demoMode=True)\n",
    "    print(f\"\\nThe Method of False Position gave approximate root is {root},\")\n",
    "    print(f\"with estimate error {errorBound:0.3}, backward error {abs(f(root)):0.3}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def secant_method(f, a, b, errorTolerance=1e-15, maxIterations=15, demoMode=False):\n",
    "    \"\"\"Solve f(x)=0 in the interval [a, b] by the Secant Method.\"\"\"\n",
    "    # Some more descriptive names\n",
    "    x_older = a\n",
    "    x_more_recent = b\n",
    "    f_x_older = f(x_older)\n",
    "    f_x_more_recent = f(x_more_recent)\n",
    "    for iteration in range(1, maxIterations+1):\n",
    "        if demoMode: print(f\"\\nIteration {iteration}:\")\n",
    "        x_new = (x_older * f_x_more_recent - f_x_older * x_more_recent)/(f_x_more_recent - f_x_older)\n",
    "        f_x_new = f(x_new)\n",
    "        (x_older, x_more_recent) = (x_more_recent, x_new)\n",
    "        (f_x_older, f_x_more_recent) = (f_x_more_recent, f_x_new)\n",
    "        errorEstimate = abs(x_older - x_more_recent)\n",
    "        if demoMode:\n",
    "            print(f\"The latest pair of approximations are {x_older} and {x_more_recent},\")\n",
    "            print(f\"where the function's values are {f_x_older:0.3} and {f_x_more_recent:0.3} respectively.\")\n",
    "            print(f\"The new approximation is {x_new}, with estimated error {errorEstimate:0.3}, backward error {abs(f_x_new):0.3}\")\n",
    "        if errorEstimate < errorTolerance:\n",
    "            break\n",
    "    # Whether we got here due to accuracy of running out of iterations,\n",
    "    # return the information we have, including an error estimate:\n",
    "    return (x_new, errorEstimate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving by the Secant Method.\n",
      "\n",
      "Iteration 1:\n",
      "The latest pair of approximations are 1 and 0.5403023058681398,\n",
      "where the function's values are 0.46 and -0.317 respectively.\n",
      "The new approximation is 0.5403023058681398, with estimated error 0.46, backward error 0.317\n",
      "\n",
      "Iteration 2:\n",
      "The latest pair of approximations are 0.5403023058681398 and 0.7280103614676172,\n",
      "where the function's values are -0.317 and -0.0185 respectively.\n",
      "The new approximation is 0.7280103614676172, with estimated error 0.188, backward error 0.0185\n",
      "\n",
      "Iteration 3:\n",
      "The latest pair of approximations are 0.7280103614676172 and 0.7396270126307336,\n",
      "where the function's values are -0.0185 and 0.000907 respectively.\n",
      "The new approximation is 0.7396270126307336, with estimated error 0.0116, backward error 0.000907\n",
      "\n",
      "Iteration 4:\n",
      "The latest pair of approximations are 0.7396270126307336 and 0.7390838007832722,\n",
      "where the function's values are 0.000907 and -2.23e-06 respectively.\n",
      "The new approximation is 0.7390838007832722, with estimated error 0.000543, backward error 2.23e-06\n",
      "\n",
      "Iteration 5:\n",
      "The latest pair of approximations are 0.7390838007832722 and 0.7390851330557805,\n",
      "where the function's values are -2.23e-06 and -2.67e-10 respectively.\n",
      "The new approximation is 0.7390851330557805, with estimated error 1.33e-06, backward error 2.67e-10\n",
      "\n",
      "Iteration 6:\n",
      "The latest pair of approximations are 0.7390851330557805 and 0.7390851332151607,\n",
      "where the function's values are -2.67e-10 and 0.0 respectively.\n",
      "The new approximation is 0.7390851332151607, with estimated error 1.59e-10, backward error 0.0\n",
      "\n",
      "Iteration 7:\n",
      "The latest pair of approximations are 0.7390851332151607 and 0.7390851332151607,\n",
      "where the function's values are 0.0 and 0.0 respectively.\n",
      "The new approximation is 0.7390851332151607, with estimated error 0.0, backward error 0.0\n",
      "\n",
      "The Secant Method gave approximate root is 0.7390851332151607,\n",
      "with estimated error 0.0, backward error 0.0\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    def f(x): return x - np.cos(x)\n",
    "    print(f\"Solving by the Secant Method.\")        \n",
    "    (root, errorEstimate) = secant_method(f, a=-1, b=1, demoMode=True)\n",
    "    print(f\"\\nThe Secant Method gave approximate root is {root},\")\n",
    "    print(f\"with estimated error {errorEstimate:0.3}, backward error {abs(f(root)):0.3}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"Linear-Algebra\"></a>\n",
    "## Linear Algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic row reduction elimination and backward substitution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rowReduce(A, b):\n",
    "    \"\"\"To avoid modifying the matrix and vector specified as input,\n",
    "    they are copyied to new arrays, with the method .copy()\n",
    "    Warning: it does not work to say \"U = A\" and \"c = b\";\n",
    "    this makes these names synonyms, referring to the same stored data.\n",
    "    Also: this doe not modify the vlaue of U belwo th main diagonal,\n",
    "    since they are know to be zero, an wil bever be used;\n",
    "    to clean this up, use function zeros_below_diagonal.\n",
    "    \"\"\"    \n",
    "    U = A.copy()\n",
    "    c = b.copy()\n",
    "    n = len(b)\n",
    "    # The function zeros_like() is used to create L with the same size and shape as A,\n",
    "    # and with all its elements zero initially.\n",
    "    L = np.zeros_like(A)\n",
    "    for k in range(n-1):\n",
    "        for i in range(k+1, n):\n",
    "            L[i,k] = U[i,k] / U[k,k]\n",
    "            for j in range(k+1, n):\n",
    "                U[i,j] = U[i,j] - L[i,k] * U[k,j]\n",
    "            c[i]= c[i] - L[i,k] * c[k]\n",
    "    return (U, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Immediately updated to the following, but I leave the first version for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rowReduce(A, b):\n",
    "    \"\"\"To avoid modifying the matrix and vector specified as input,\n",
    "    they are copied to new arrays, with the method .copy()\n",
    "    Warning: it does not work to say \"U = A\" and \"c = b\";\n",
    "    this makes these names synonyms, referring to the same stored data.\n",
    "    This code leaves \"garbage values\" below the main diagonal\n",
    "    if needed, clean up with the function zeros_below_diagonal.\n",
    "    \"\"\"    \n",
    "    U = A.copy()\n",
    "    c = b.copy()\n",
    "    n = len(b)\n",
    "    # The function zeros_like() is used to create L with the same size and shape as A,\n",
    "    # and with all its elements zero initially.\n",
    "    L = np.zeros_like(A)\n",
    "    for k in range(n-1):\n",
    "        # compute all the L values for column k:\n",
    "        L[k+1:n,k] = U[k+1:n,k] / U[k,k]  # Beware the case where U[k,k] is 0\n",
    "        for i in range(k+1, n):\n",
    "            U[i,k+1:n] -= L[i,k] * U[k,k+1:n]  # Update row i\n",
    "        c[k+1:n] -= L[k+1:n,k] * c[k]  # update c values\n",
    "    return (U, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Further updated on March 7 as follows, adding `demoMode` and \"zeroing\" below the main diagonal in U when using that mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rowReduce(A, b, demoMode=False):\n",
    "    \"\"\"To avoid modifying the matrix and vector specified as input,\n",
    "    they are copied to new arrays, with the method .copy()\n",
    "    Warning: it does not work to say \"U = A\" and \"c = b\";\n",
    "    this makes these names synonyms, referring to the same stored data.\n",
    "    This code leaves \"garbage values\" below the main diagonal\n",
    "    if needed, clean up with the function zeros_below_diagonal.\n",
    "    \n",
    "    2021-03-07: added a demonstration mode.\n",
    "    \"\"\"    \n",
    "    U = A.copy()\n",
    "    c = b.copy()\n",
    "    n = len(b)\n",
    "    # The function zeros_like() is used to create L with the same size and shape as A,\n",
    "    # and with all its elements zero initially.\n",
    "    L = np.zeros_like(A)\n",
    "    for k in range(n-1):\n",
    "        if demoMode: print(f\"Step {k=}\")\n",
    "        # compute all the L values for column k:\n",
    "        L[k+1:,k] = U[k+1:n,k] / U[k,k]  # Beware the case where U[k,k] is 0\n",
    "        if demoMode:\n",
    "            print(f\"The multipliers in column {k+1} are {L[k+1:,k]}\")\n",
    "        for i in range(k+1, n):\n",
    "            U[i,k+1:n] -= L[i,k] * U[k,k+1:n]  # Update row i\n",
    "        c[k+1:n] -= L[k+1:n,k] * c[k]  # update c values\n",
    "        if demoMode:\n",
    "            # insert zeros in U:\n",
    "            U[k+1:, k] = 0.\n",
    "            print(f\"The updated matrix is\\n{U}\")\n",
    "            print(f\"The updated right-hand side is\\n{c}\")\n",
    "    return (U, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def zeros_below_diagonal(U):\n",
    "    \"\"\"Insert the below-diagonal zero values into U, ignored in function rowReduce.\n",
    "    These are needed to display U correctly,\n",
    "    and to demonstrate that the new system of equations Ux=c has the same solution as Ax=b.\n",
    "    \"\"\"\n",
    "    for i in range(1,len(U)):\n",
    "        for j in range(i):\n",
    "            U[i,j] = 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with `rowReduce`, this is immediately updated to the following, but I leave the first version for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def zeros_below_diagonal(U):\n",
    "    \"\"\"Insert the below-diagonal zero values into U, ignored in the function rowReduce.\n",
    "    These are needed to display U correctly,\n",
    "    and to demonstrate that the new system of equations Ux=c$ has the same solution as Ax=b.\n",
    "    \"\"\"\n",
    "    for i in range(1,len(U)):\n",
    "        U[i,:i] = 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "[[  1.  -3.  15.]\n",
      " [  5. 200.   7.]\n",
      " [  4.  11.  -6.]]\n",
      "b = [4. 3. 2.]\n",
      "Step k=0\n",
      "The multipliers in column 1 are [5. 4.]\n",
      "The updated matrix is\n",
      "[[  1.  -3.  15.]\n",
      " [  0. 215. -68.]\n",
      " [  0.  23. -66.]]\n",
      "The updated right-hand side is\n",
      "[  4. -17. -14.]\n",
      "Step k=1\n",
      "The multipliers in column 2 are [0.10697674]\n",
      "The updated matrix is\n",
      "[[  1.         -3.         15.       ]\n",
      " [  0.        215.        -68.       ]\n",
      " [  0.          0.        -58.7255814]]\n",
      "The updated right-hand side is\n",
      "[  4.         -17.         -12.18139535]\n",
      "U =\n",
      "[[  1.         -3.         15.       ]\n",
      " [  0.        215.        -68.       ]\n",
      " [  0.          0.        -58.7255814]]\n",
      "c = [  4.         -17.         -12.18139535]\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "#    A = np.array([[4. , 235. , 7.], [3. , 5. , -6.],[1. , -3. , 22.]])\n",
    "    A = np.array([[1. , -3. , 15.], [5. , 200. , 7.], [4. , 11. , -6.]])\n",
    "    print(f\"A =\\n{A}\")\n",
    "#    b = np.array([2. , 3. , 4.])\n",
    "    b = np.array([4. , 3. , 2.])\n",
    "    print(f\"b = {b}\")\n",
    "    \n",
    "    (U, c) = rowReduce(A, b, demoMode=True)\n",
    "    zeros_below_diagonal(U)\n",
    "    print(f\"U =\\n{U}\")\n",
    "    print(f\"c = {c}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backwardSubstitution(U, c):\n",
    "    \"\"\"Solve U x = c for b.\"\"\"\n",
    "    n = len(c)\n",
    "    x = np.zeros(n)\n",
    "    x[-1] = c[-1]/U[-1,-1]\n",
    "    for i in range(2, n+1):\n",
    "        x[-i] = (c[-i] - sum(U[-i,1-i:] * x[1-i:])) / U[-i,-i]\n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**UPDATE:** this was further updated on March 7 as follows, mainly to add `demoMode`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backwardSubstitution(U, c, demoMode=False):\n",
    "    \"\"\"Solve U x = c for b.\n",
    "    \n",
    "    2021-03-07: aded a demonstration mode.\n",
    "    \"\"\"\n",
    "    n = len(c)\n",
    "    x = np.zeros(n)\n",
    "    x[-1] = c[-1]/U[-1,-1]\n",
    "    if demoMode: print(f\"x_{n} = {x[-1]}\")\n",
    "    for i in range(2, n+1):\n",
    "        x[-i] = (c[-i] - sum(U[-i,1-i:] * x[1-i:])) / U[-i,-i]\n",
    "        if demoMode: print(f\"x_{n-i+1} = {x[-i]}\")\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_3 = 0.20742911452558213\n",
      "x_2 = -0.013464280057025185\n",
      "x_1 = 0.8481704419451925\n",
      "\n",
      "x = [ 0.84817044 -0.01346428  0.20742911]\n",
      "The residual b - Ax = [ 0.0000000e+00 -8.8817842e-16 -4.4408921e-16],\n",
      "with maximum norm 8.88e-16.\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    x = backwardSubstitution(U, c, demoMode=True)\n",
    "    print(\"\")\n",
    "    print(f\"x = {x}\")\n",
    "    r = b - A@x\n",
    "    print(f\"The residual b - Ax = {r},\")\n",
    "    print(f\"with maximum norm {max(abs(r)):.3}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LU factorization ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lu(A, demoMode=False):\n",
    "    \"\"\"Compute the Doolittle LU factorization of A.\n",
    "    Sums like $\\sum_{s=1}^{k-1} l_{k,s} u_{s,j}$ are done as matrix products;\n",
    "    in the above case, row matrix L[k, 1:k-1] by column matrix U[1:k-1,j] gives the sum for a give j,\n",
    "    and row matrix L[k, 1:k-1] by matrix U[1:k-1,k:n] gives the relevant row vector.\n",
    "    \"\"\"\n",
    "    n = len(A)  # len() gives the number of rows in a 2D array.\n",
    "    # Initialize U as the zero matrix;\n",
    "    # correct below the main diagonal, with the other entries to be computed below.\n",
    "    U = np.zeros_like(A)\n",
    "    # Initialize L as the identity matrix;\n",
    "    # correct on and above the main diagonal, with the other entries to be computed below.\n",
    "    L = np.identity(n)\n",
    "   # Column and row 1 (i.e Python index 0) are special:\n",
    "    U[0,:] = A[0,:]\n",
    "    L[1:,0] = A[1:,0]/U[0,0]\n",
    "    if demoMode:\n",
    "        print(f\"After step k=0\")\n",
    "        print(f\"U=\\n{U}\")\n",
    "        print(f\"L=\\n{L}\")\n",
    "    for k in range(1, n-1):\n",
    "        U[k,k:] = A[k,k:] - L[k,:k] @ U[:k,k:]\n",
    "        L[k+1:,k] = (A[k+1:,k] - L[k+1:,:k] @ U[:k,k])/U[k,k]\n",
    "        if demoMode:\n",
    "            print(f\"After step {k=}\")\n",
    "            print(f\"U=\\n{U}\")\n",
    "            print(f\"L=\\n{L}\")\n",
    "    # The last row (index \"-1\") is special: nothing to do for L\n",
    "    U[-1,-1] = A[-1,-1] - sum(L[-1,:-1]*U[:-1,-1])\n",
    "    if demoMode:\n",
    "        print(f\"After the final step, k={n-1}\")\n",
    "        print(f\"U=\\n{U}\")\n",
    "    return (L, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "[[  1.  -3.  15.]\n",
      " [  5. 200.   7.]\n",
      " [  4.  11.  -6.]]\n",
      "b = [4. 3. 2.]\n",
      "After step k=0\n",
      "U=\n",
      "[[ 1. -3. 15.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "L=\n",
      "[[1. 0. 0.]\n",
      " [5. 1. 0.]\n",
      " [4. 0. 1.]]\n",
      "After step k=1\n",
      "U=\n",
      "[[  1.  -3.  15.]\n",
      " [  0. 215. -68.]\n",
      " [  0.   0.   0.]]\n",
      "L=\n",
      "[[1.         0.         0.        ]\n",
      " [5.         1.         0.        ]\n",
      " [4.         0.10697674 1.        ]]\n",
      "After the final step, k=2\n",
      "U=\n",
      "[[  1.         -3.         15.       ]\n",
      " [  0.        215.        -68.       ]\n",
      " [  0.          0.        -58.7255814]]\n",
      "A=\n",
      "[[  1.  -3.  15.]\n",
      " [  5. 200.   7.]\n",
      " [  4.  11.  -6.]]\n",
      "L=\n",
      "[[1.         0.         0.        ]\n",
      " [5.         1.         0.        ]\n",
      " [4.         0.10697674 1.        ]]\n",
      "U=\n",
      "[[  1.         -3.         15.       ]\n",
      " [  0.        215.        -68.       ]\n",
      " [  0.          0.        -58.7255814]]\n",
      "L times U is \n",
      "[[  1.  -3.  15.]\n",
      " [  5. 200.   7.]\n",
      " [  4.  11.  -6.]]\n",
      "The 'residual' A - LU is \n",
      "[[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "#    A = np.array([[4. , 235. , 7.], [3. , 5. , -6.],[1. , -3. , 22.]])\n",
    "    A = np.array([[1. , -3. , 15.], [5. , 200. , 7.], [4. , 11. , -6.]])\n",
    "    print(f\"A =\\n{A}\")\n",
    "#    b = np.array([2. , 3. , 4.])\n",
    "    b = np.array([4. , 3. , 2.])\n",
    "    print(f\"b = {b}\")\n",
    "\n",
    "    (L, U) = lu(A, demoMode=True)\n",
    "\n",
    "    print(f\"A=\\n{A}\")\n",
    "    print(f\"L=\\n{L}\")\n",
    "    print(f\"U=\\n{U}\")\n",
    "    print(f\"L times U is \\n{L@U}\")\n",
    "    print(f\"The 'residual' A - LU is \\n{A - L@U}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ... and forward substitution ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forwardSubstitution(L, b):\n",
    "    \"\"\"Solve L c = b for c.\"\"\"\n",
    "    n = len(b)\n",
    "    c = np.zeros_like(b)\n",
    "    c[0] = b[0]\n",
    "    for i in range(1, n):\n",
    "        c[i] = b[i] - L[i,:i] @ c[:i]\n",
    "        # Note: the above uses a row-by-column matrix multiplication to do the same as\n",
    "        #c[i] = b[i] - sum(L[i,:i] * c[:i])\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forwardSubstitution(L, b, demoMode=False):\n",
    "    \"\"\"Solve L c = b for c.\n",
    "        \n",
    "    2021-03-07: aded a demonstration mode.\n",
    "    \"\"\"\n",
    "    n = len(b)\n",
    "    c = np.zeros(n)\n",
    "    c[0] = b[0]\n",
    "    if demoMode: print(f\"c_1 = {c[0]}\")\n",
    "    for i in range(1, n):\n",
    "        c[i] = b[i] - L[i,:i] @ c[:i]\n",
    "        # Note: the above uses a row-by-column matrix multiplication to do the same as\n",
    "        #c[i] = b[i] - sum(L[i,:i] * c[:i])\n",
    "        if demoMode: print(f\"c_{i+1} = {c[i]}\")\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c_1 = 4.0\n",
      "c_2 = -17.0\n",
      "c_3 = -12.18139534883721\n",
      "\n",
      "c = [  4.         -17.         -12.18139535]\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    c = forwardSubstitution(L, b, demoMode=True)\n",
    "    print(\"\")\n",
    "    print(f\"c = {c}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ... and finally backward substitution again, to complete the LU factorization method example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_3 = 0.20742911452558213\n",
      "x_2 = -0.013464280057025185\n",
      "x_1 = 0.8481704419451925\n",
      "\n",
      "The residual c - Ux for the backward substitution step is [0. 0. 0.]\n",
      "\t with maximum norm 0.0\n",
      "The residual b - Ax for the whole solving process is [ 0.0000000e+00 -8.8817842e-16 -4.4408921e-16]\n",
      "\t with maximum norm 8.88e-16\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    x = backwardSubstitution(U, c, demoMode=True)\n",
    "    print(\"\")\n",
    "    print(f\"The residual c - Ux for the backward substitution step is {c - U@x}\")\n",
    "    print(f\"\\t with maximum norm {np.max(np.abs(c - U@x)):0.3}\")\n",
    "    print(f\"The residual b - Ax for the whole solving process is {b - A@x}\")\n",
    "    print(f\"\\t with maximum norm {np.max(np.abs(b - A@x)):0.3}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rowReduceMaximalElementPivoting(A, b, demoMode=False):\n",
    "    \"\"\"Solve Ax=b by maximl element partial pivoting.\n",
    "    This version actually swaps rows rather than keeping track of pivot row indices.\n",
    "    \"\"\"    \n",
    "    U = A.copy()\n",
    "    c = b.copy()\n",
    "    n = len(b)\n",
    "    # The function zeros_like() is used to create L with the same size and shape as A,\n",
    "    # and with all its elements zero initially.\n",
    "    L = np.zeros_like(A)\n",
    "    for k in range(n-1):\n",
    "        if demoMode: print(f\"Step {k=}\")\n",
    "        # Swap rows if necessary\n",
    "        pivot_row = k\n",
    "        size_U_pivot_row_k = abs(U[k,k])\n",
    "        for i in range(k+1,n):\n",
    "            size_U_i_k = abs(U[i,k])\n",
    "            if size_U_i_k > size_U_pivot_row_k:\n",
    "                pivot_row = i\n",
    "                size_U_pivot_row_k = size_U_i_k\n",
    "        # swap rows?\n",
    "        if pivot_row > k:\n",
    "            if demoMode:\n",
    "                print(f\"swap row {k} with row {pivot_row}\")\n",
    "            row_temp = U[pivot_row].copy()\n",
    "            U[pivot_row] = U[k].copy()\n",
    "            U[k] = row_temp.copy()\n",
    "            #( U[k,:], U[pivot_row,:] ) = ( U[pivot_row,:], U[k,:] )\n",
    "            ( c[k], c[pivot_row] ) = ( c[pivot_row], c[k] )\n",
    "            if demoMode:\n",
    "                print(f\"After this row swap, the matrix is\\n{U}\")\n",
    "                print(f\"and the right-hand side is\\n{c}\")\n",
    "        # compute all the L values for column k:\n",
    "        L[k+1:,k] = U[k+1:n,k] / U[k,k]\n",
    "        if demoMode:\n",
    "            print(f\"The multipliers in column {k+1} are {L[k+1:,k]}\")\n",
    "        for i in range(k+1, n):\n",
    "            U[i,k+1:n] -= L[i,k] * U[k,k+1:n]  # Update row i\n",
    "        c[k+1:n] -= L[k+1:n,k] * c[k]  # update c values\n",
    "        if demoMode:\n",
    "            # insert zeros in U:\n",
    "            U[k+1:, k] = 0.\n",
    "            print(f\"The updated matrix is\\n{U}\")\n",
    "            print(f\"The updated right-hand side is\\n{c}\")\n",
    "    return (U, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "[[  1.  -3.  15.]\n",
      " [  5. 200.   7.]\n",
      " [  4.  11.  -6.]]\n",
      "b = [4. 3. 2.]\n",
      "Step k=0\n",
      "swap row 0 with row 1\n",
      "After this row swap, the matrix is\n",
      "[[  5. 200.   7.]\n",
      " [  1.  -3.  15.]\n",
      " [  4.  11.  -6.]]\n",
      "and the right-hand side is\n",
      "[3. 4. 2.]\n",
      "The multipliers in column 1 are [0.2 0.8]\n",
      "The updated matrix is\n",
      "[[   5.   200.     7. ]\n",
      " [   0.   -43.    13.6]\n",
      " [   0.  -149.   -11.6]]\n",
      "The updated right-hand side is\n",
      "[ 3.   3.4 -0.4]\n",
      "Step k=1\n",
      "swap row 1 with row 2\n",
      "After this row swap, the matrix is\n",
      "[[   5.   200.     7. ]\n",
      " [   0.  -149.   -11.6]\n",
      " [   0.   -43.    13.6]]\n",
      "and the right-hand side is\n",
      "[ 3.  -0.4  3.4]\n",
      "The multipliers in column 2 are [0.2885906]\n",
      "The updated matrix is\n",
      "[[   5.          200.            7.        ]\n",
      " [   0.         -149.          -11.6       ]\n",
      " [   0.            0.           16.94765101]]\n",
      "The updated right-hand side is\n",
      "[ 3.         -0.4         3.51543624]\n",
      "U =\n",
      "[[   5.          200.            7.        ]\n",
      " [   0.         -149.          -11.6       ]\n",
      " [   0.            0.           16.94765101]]\n",
      "c = [ 3.         -0.4         3.51543624]\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "    A = np.array([[1. , -3. , 15.], [5. , 200. , 7.], [4. , 11. , -6.]])\n",
    "    print(f\"A =\\n{A}\")\n",
    "    b = np.array([4. , 3. , 2.])\n",
    "    print(f\"b = {b}\")\n",
    "\n",
    "    (U, c) = rowReduceMaximalElementPivoting(A, b, demoMode=True)\n",
    "    zeros_below_diagonal(U)\n",
    "    print(f\"U =\\n{U}\")\n",
    "    print(f\"c = {c}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Added 2021-04-11\n",
    "def inverse(A):\n",
    "    \"\"\"Use sparingly; there is usually a way to avoid computing inverses that is faster and with less rounding error!\"\"\"\n",
    "    n = len(A)\n",
    "    A_inverse = np.zeros_like(A)\n",
    "    (L, U) = lu(A)\n",
    "    for i in range(n):\n",
    "        b = np.zeros(n)\n",
    "        b[i] = 1.0\n",
    "        c = forwardSubstitution(L, b)\n",
    "        A_inverse[:,i] = backwardSubstitution(U, c)\n",
    "    return A_inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Hilbert matrix H_2 is\n",
      "[[1.         0.5       ]\n",
      " [0.5        0.33333333]]\n",
      "and its inverse is\n",
      "[[ 4. -6.]\n",
      " [-6. 12.]]\n",
      "to verify, their product is\n",
      "[[1. 0.]\n",
      " [0. 1.]]\n",
      "\n",
      "The Hilbert matrix H_3 is\n",
      "[[1.         0.5        0.33333333]\n",
      " [0.5        0.33333333 0.25      ]\n",
      " [0.33333333 0.25       0.2       ]]\n",
      "and its inverse is\n",
      "[[   9.  -36.   30.]\n",
      " [ -36.  192. -180.]\n",
      " [  30. -180.  180.]]\n",
      "to verify, their product is\n",
      "[[ 1.00000000e+00  9.62193288e-16  1.40628250e-15]\n",
      " [ 0.00000000e+00  1.00000000e+00  0.00000000e+00]\n",
      " [-2.22044605e-17 -1.99840144e-15  1.00000000e+00]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it\n",
    "\n",
    "    def hilbert(n):\n",
    "        H = np.zeros([n,n])\n",
    "        for i in range(n):\n",
    "            for j in range(n):\n",
    "                H[i,j] = 1.0/(1.0 + i + j)\n",
    "        return H\n",
    "\n",
    "    for n in range(2,4):\n",
    "        H_n = hilbert(n)\n",
    "        print(f\"The Hilbert matrix H_{n} is\")\n",
    "        print(H_n)\n",
    "        H_n_inverse = inverse(H_n)\n",
    "        print(\"and its inverse is\")\n",
    "        print(H_n_inverse)\n",
    "        print(\"to verify, their product is\")\n",
    "        print(H_n @ H_n_inverse)\n",
    "        print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"ODE-IVPs\"></a>\n",
    "## Solving Initial Value Problems for Ordinary Differential Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic implementations of some basic methods\n",
    "\n",
    "(More to come.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use Euler's Method to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following two lines will need to change for the systems version\n",
    "    U = np.empty_like(t)\n",
    "    U[0] = u_0\n",
    "    \n",
    "    for i in range(n):\n",
    "        U[i+1] = U[i] + f(t[i], U[i])*h\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "    \n",
    "    def f_1(t, u):\n",
    "        \"\"\"The simplest \"genuine\" ODE, (not just integration)\n",
    "        The solution is u(t) = u(t; a, u_0) = u_0 exp(t-a)\n",
    "        \"\"\"\n",
    "        return K*u\n",
    "    def u_1(t): return u_0 * np.exp(K*(t-a))\n",
    " \n",
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 0.5\n",
    "    n = 10\n",
    "\n",
    "    (t, U) = euler(f_1, a, b, u_0, n)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=} — by Euler's method with {n} steps\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Euler's answer with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler_system(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use Euler's Method to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\n",
    "    Modified from function euler to handle systems.\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    \n",
    "    # Only the following three lines change for the systems version\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        U[i+1] = U[i] + f(t[i], U[i])*h\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jjtKmIRzlRy2EmCOEGOm42NeinRzax/kuWr25VTqqzo6xbyVApBAitN06Xkb7jaY63h8thDirO/snfuuWnHaUxVrRGiYHAu85Emek1k39SBffQ714HMehH1qJlkkI4XeUu7sPgDOEEDMdx8tjwBdSq6Js61K7rJP7FiuEuA3tWHzA8btGasM+HCnu0xzLNKB9748JIQKFENOBszhCQiA0fmi/dxz76NuZOHvgYccxORytLcon7V57F63Nypkc+/zdISllGdoN7GWO7/AatLZ9HVkIDBJCXO64DngLISYKIYZ2YZNr0G6EJqE16s3AUcKDVrLbkRIgre2Y7A6hdXX2czz0cXx3bTeZ76IlDIlCiAS0m7W3AaSUe4GtwCOO95yDVu3/ueO9Rz2WHet+yHE+HoLWhOHtI8R4uhBigCOutvND+3NE+2vb+47tntL22xPaUA3tb8QuE0IME0IEOOL6TEpp68T563dcksQ4TsJnoNUJZqPdUb2O1jCzI7ejZeBZaHWSHwJvHmMz69G6ipWjtYWYLzuuv/wFLdMsFkKUO567HMgRWhXETTjqcjvwJtoJZIVjPyx07SL8KPCO0IrXLjjWwsD9aMV36xyx/YT2A+vIa2hFcNvQegt90faC44C9Ay2BqEK7A/+mC3F35Gu06pkqtM/vXEcGfazv+q9oRYfZaO1yunuH1pFn0RrRlaMlVO3vIE1oP/5CtCL9WWi9nkBrx7NeCFGP9rncKaXMPsI2jnasFKN9HoVoJ4+bpJS7e75bANyG9hkWo31mH6ElYx2JQ6t2qUWr5lnO7y8i76E1qDv8s+9w3xz78BGQ5Th2E4D/oH1WPwoh6tA+78nd3LdktGPiqKU4UsoW4Fy0G5Y3u3jRuBwtwX0JrRSqCUdJHBwaB2umYzsZaPv/AVrpSTC/HStt8a4+xvaqhRANwA60KrrzpZTHOod15Ba0Y7oU7Tu42REfQogUR9xtpZmpjv1qu5NuwlHy40TL0c5RPwNPSa39EwBSytVo7dA2S61t49FcKP63RCrG8dr1aL0YK9Aa96/paAWO89zJaO3vCtF+K/9Eu4HrFEfiuBnIcBxvoPWEzJVSlh7hbW03KhVCiKO1IzuaPWjfVyLaebyJ30r9X0Fr6LoDrU3gd47n2lyE1oanCq3jxHxH8teZY/kRtAbIuWjf5b+PUvI2EO0aVI/2mbwoHWPloLXBfMhxfvij1No7noXWlKAMrWTmXn6fc7yHljAVo7WpvMPx/LHOX7/T1rJYUTpNCPEoWqOrIyV7fY7QBqh6X0qZdIxFe2t7/wTipJRXduO9bRfFcVLKfb0eXNfjeQgok1K+csyFDUAIsRVtCIeuNPLsk4QQv6B18X1d71gU43CUZL7fG8eFkQaKUxTlCBxFvT5od2MT0caK6O6w5jcDG4yQwABIKf+mdwxdIaUco3cM7sBRhTwO7Y5cUZxCJTGK4h6C0aoTEtBKUf4PrUqvS4QQOWgNnc/uxdgU5XeEEO+gHWN3tmt/oSi9TlUnKYqiKIrillzVO0lRFEVRFKVXqSRGURRFURS31KfaxERFRcm0tDS9w+i0hoYGAgMDj72gm/HU/QK1b+7IU/cLPHffPHW/oPf3bdOmTeVSyiON9O72+lQSk5aWxsaNG/UOo9OWLVvG7Nmz9Q6j13nqfoHaN3fkqfsFnrtvnrpf0Pv7JoTozNQubktVJymKoiiK4pZUEqMoiqIoiltSSYyiKIqiKG6pT7WJURRFUfqW1tZW8vPzsVgseofSKaGhoezatavL7/Pz8yMpKQlv7yPNa+qZVBKjKIqieKz8/HyCg4NJS0vjt4mhjauuro7g4OAuvUdKSUVFBfn5+aSnpzspMmNS1UmKoiiKx7JYLERGRrpFAtNdQggiIyPdprSpN6kkRlEURfFonpzAtOkL+9gRlcQoiqIoios9++yzNDY2dvl9b7/9NoWFhU6IyD2pJEZRFEVR2imqK2LW27Mori922ja6k8TYbDaVxBxGJTGKoiiK0s7jKx5n1cFVPLb8sV5ZX0NDA/PmzWP06NGMGDGCv/71rxQWFjJnzhzmzJkDwM0338yECROYNGkSjzzyyKH3pqWl8dhjjzFjxgw++ugjNm7cyKWXXsqYMWNoamrqlfjcmeqdpCiKoiiA/xP+WKy/NY59aeNLvLTxJfy8/Gh6sPsJw+LFi0lISOC7774DoKamhrfeeoulS5cSFRUFwBNPPEFERATV1dWcffbZbN++nVGjRgFa9+lVq1YB8Prrr/PUU08xYcKEbsfjSVRJjKIoiqIAWXdkccmISwjwCgAgwCuAS0deSvad2T1a78iRI/npp5+4//77WblyJaGhof+zzIIFCxg3bhwzZswgIyODzMzMQ69deOGFPdq+J1MlMYqiKIoCxAfHE+IbgsVmwc/LD4vNQohvCHFBcT1a76BBg9i0aROLFi3igQce4OSTT/7d69nZ2Tz11FNs2LABLy8vbr/99t91l/bUGbt7gyqJURRFURSHkoYSbhp/E+uuXcdN42/qlca9hYWFBAQEcNlll/HHP/6RzZs3ExwcTF1dHQC1tbUEBgYSGhpKaWkp33///RHX1f59iiqJURRFUZRDvrjwi0P/f2HeC72yzh07dnDvvfdiMpnw9vbmpZdeYu3atZx22mnEx8ezdOlSxo4dy/Dhw0lJSWH69OlHXNdVV13FTTfdhL+/P2vXrsXf379XYnRXKolRFEVRFCc65ZRTOOWUU3733IQJE7j99tsPPX777beB/512ICcn53fvO++88zjvvPOcFqu7UUmMonggm11itdux2iQ2KTELgdkk8DabMJv65sieiqJ4HpXEKIoB2e2SysYWyuqaKatrprz+t38rGlqot1ipb3b8WazUNVtpaLbSarNjtUukPPK6hQBvkwkvsyDAx4sQPy+C/LwI8vUi2M+LIF9vIgK9iQ721f6C/IgO9qWuRSKl7LPDmyuKYjwqiVEUnbRY7WSXN5BdXs/BykbyKpvIq2okr7KRvKomWqz2/3mPn7eJyEBfgv20hCMy0IfUyECCfL0I9DHj7WXCyyTwciQpXiatBMYuJa02idWmldC02iStNjuNLTbqLK2HkqGc8kbqLK1UNLTQ3MH2/7hiMUnh/iRHBJASEUByeADJEf6kRQXSLyoIHy/VV0BRFNdRSYyiOJmUkpyKRjILa9lbUse+0jr2ltSTU96A1f5bkUmInxfJEQEMjAnm+CExJIb5ExPiR1SQViISFeRDkK+XS0pCpJTUN1sPlQSV1TezZnMGgdGJ5FU2cbCykU25VdRZrIfeYzYJ0iIDGBQbzMDYYAbGBDE0PoR+UYGYVBWWoihOoJIYRelFUkqKaprYllfD9vxqtudr/9Y6LvZCQIojUTl5WCyDYoPpHx1ESkQAoQHeOkf/GyEEwX7eBPt50y86CICgyr3Mnj3sd8vVNLZysLKRrPJ69pXUs7ekjt3FdfyQUUxbfhbk68XwhBBGJ4cxMjGUUUmhpEQEqGopRVF6TCUxitIDbaUs67MqWJ9dyfJdTVT+8AsAXibB4Lhg5o1KYFRSKCMSQhkQE4S/j1nnqHtPaIA3IwNCGZn0+xFILa02ssoayCyqPZTMvb0m51AVWUSgD5PSIpiUrv0NjQ9RDY4VRekylcQoShcV11hYvreUVfsrWJ9VQWldMwBRQT70DzNx+8TBjE4OY1h8CH7enpOwdIWft5lhCSEMSwhh/vgkAFptdvYU17E9v4bNB6v4NbuSxRnaQGLBvl6MTwtnar9IZg2OZnBssCqpURSHoKAg6uvr9Q7DkFQSoyjHYLXZ2XywmqV7Slm2p4xdRbUAxAT7MqVfJJP7RTA5PZL+0YEsX76c2dPTdY7YmLzNJkYkhjIiMZRLJqcAUFTTxK/ZlazPrmR9VgXL9pTx5Pe7iQ3xZdagaGYNimHGgChDVbUpfUBREVx0EXzyCcT1bMoBxblUEqMoHbC02li2p4zFO4v4eXcpdRYrXibB+NRw/nTaEGar0oJeER/qz1ljEjlrTCKgJTUr9paxfG8Zi3cWs2BjPiYBE1IjOGVEHKcMjyUpPEDnqBWP9/jjsGoVPPYYvPhir6zy/fff57nnnqOlpYXJkyfz4osvEhoayp133snChQvx9/fn66+/JiAggOzsbC655BKsViunnnpqr2zfU+maxAghTgX+A5iB16WU/zjs9XuBSx0PvYChQLSUslIIkQPUATbAKqVU85IrPdLQbGXZnjIW7Sxi6e5SGltshAd4c+rwOI4fEsP0gVGE+KkSAWeKD/XnwokpXDgxBavNzrb8apbtKWNJZgmPL8zk8YWZjEgM4dThcZw6Io4BMcHHXqmidJa/P7SbeJGXXtL+/Pygqanbq921axeffPIJq1evxtvbm1tuuYUPPviAhoYGpkyZwhNPPMF9993Ha6+9xp133smdd97JzTffzBVXXMELL/TO1AeeSrckRghhBl4ATgLygQ1CiG+klIfmH5dS/hv4t2P5M4C7pJSV7VYzR0pZ7sKwFQ9js0tW7ivj880FLMksxtJqJyrIh3PGJjJ3ZDyT0yPwMquxT/TgZTYxPjWC8akR3HPyYHLKG/gho5jFGcU89eNenvpxL4Njgzl7bCJnjUkgIaxvzyGj9IKsLPjjH+Grr6CxEQIC4Jxz4KmnerTan3/+mU2bNjFx4kQAmpqaiImJwcfHh9NPPx2A8ePHs2TJEgBWr17N559/DsDll1/O/fff36PtezI9S2ImAfullFkAQoiPgbOAzCMsfzHwkYtiUzzcnuI6vticz5dbCiitaybU35v545M4fVQCE9MiVE8ZA0qLCuTGWf25cVZ/imss/JBRzNdbC/jn4t3864fdTEmP5JyxiZw6Mk6VmCndEx8PISFaaYyfn/ZvSEiP28VIKbnyyit58sknf/f8U089dahK2mw2Y7X+Nu6SqqruHD2TmEQgr93jfGByRwsKIQKAU4Hb2j0tgR+FEBJ4RUr56hHeewNwA0BsbCzLli3reeQuUl9f71bxdpZe+9VslawtsrIsz0pOrR2zgFHRZi7o78voGDPepgosBytYebD72/DU7wyMt2+pwB3DoDTNn7WFVtYUVnLf5xX8+cvtTIwzMzvJm0HhpmNeDIy2X73JU/etK/sVGhpKXV1dp9ftV1CAvOYaWq++Gu+33kLk52Ppwvs7MmXKFC666CKuv/56oqOjqaysPNTbqC22pqYmWltbsdlsTJ48mbfeeouLLrqIN95443fLHY3FYvHI7/to9ExiOjqzHGnGlzOA1YdVJU2XUhYKIWKAJUKI3VLKFf+zQi25eRVgwoQJcvbs2T0M23WWLVuGO8XbWa7er/2l9by/LpfPN+dTZ7EyJC6YR2Ylc+boBCKDfHt1W576nYGx9+0CtLvdbfk1fL4pn6+2FLC20MKAmCAunpTCuWMTCQ/06fC9Rt6vnvLUfevKfu3atet3s0If0zffAOADMG0aAD0t15s4cSJ///vfOffcc7Hb7Xh7ex9q69IWm7+/P97e3pjNZl544QUuueQSXn311UMzVndmH/z8/Bg7dmwPo3UveiYx+UByu8dJQOERlr2Iw6qSpJSFjn9LhRBfolVP/U8So/RNNrtkSWYJ767NYc2BCnzMJk4bGcflU1IZnxquimo9kBCCMclhjEkO44G5Q1i4vYiPfj3I4wsz+efi3cwbGc/V09MYlRSmd6hKH3ThhRdy4YUX/u659mO/zJ8/n/nz51NXV0d6ejpr16499Nqf/vQnl8XpbvRMYjYAA4UQ6UABWqJyyeELCSFCgVnAZe2eCwRMUso6x/9PBh5zSdSKoVlabXy2KZ/XV2aRU9FIYpg/9506mAsmJBPVy6UuinEF+HhxwYRkLpiQzK6iWj769SBfbC7gyy0FTEwL59oZ6Zw0LE61fVIUN6dbEiOltAohbgN+QOti/aaUMkMIcZPj9Zcdi54D/CilbGj39ljgS8fdtBfwoZRyseuiV4ymqqGF99bl8s6aHCoaWhidFMoLl4zj1BHqQtXXDY0P4bGzRnDvKYP5ZEMeb6/J4ab3N5MU7s9V09JItB6pFltRFKPTdZwYKeUiYNFhz7182OO3gbcPey4LGO3k8BQ3UFbXzCvLD/DB+oM0tdqYMziaG2f1Z3J6hKoyUn4n2M+b62b24+rp6SzJLOaNVdn87btdBHjBLrmXa6anERbQcbsZRVGMSY3Yq7ilivpmXlmRxbtrtUkFzx6TyE2z+zMoVg1+phyd2SQ4dUQ8p46IZ1teNY99to7nft7HGyuzuGxqKtfN6Ed0sKp69CRSSo+/qZGyb5YoqiRGcSuVDS286kheLK02zhqTyO3HD6BfdJDeoSluaHRyGLeP9SN+yHheWLqf11Zk8fbqHC6elMIts/sTE+Knd4hKD/n5+VFRUUFkZKTHJjJSSioqKvDz63vHq0piFLfQ1GLjzdXZvLTsAA0tVs4cncDtxw9kQIxKXpSeGxwXzHMXj+Wukwbx0rL9vL8ul483HOTq6encdFx/NQGlG0tKSiI/P5+ysjK9Q+kUi8XSrWTEz8+PpKQkJ0RkbCqJUQzNbpd8saWA//txD0U1Fk4aFst9pwxmoKo2UpwgPSqQf80fza1zBvDMkr28vPwA76/L5aZZ/bl6ehoBPuqU6W68vb1JT3efmeWXLVvW58Z66Qn1i1QMa9W+cv6+aBeZRbWMTgrl2QvHMLlfpN5hKX1AamQgz140lptm9+epH/bw7x/28NbqHP5w4kAumpis5tNSFINQSYxiOHmVjTy2MJMlmSUkhfvz3MVjOX1kPCbVVVpxsSFxIbx+5UQ25Vbyz8V7eOirnby3NpeHTx/GjIFReoenKH2eSmIUw2i22nhtRRbPL92PQHD/qUO4ZkYavl5mvUNT+rjxqRF8csMUfsgo5olFu7jsjfWcODSWB+cNJT0qUO/wFKXPUkmMYgjL95bx6DcZZJc3MHdkHA/NG0ZCmL/eYSnKIUJoXbNnD47hrdU5PP/LPk5+ZjlXTUvjzhMHEeSrTqeK4mrqV6foqqyumUe/zeC77UWkRwXy7jWTOG5QtN5hKcoR+XmbuXl2f84bn8j//bCX11dls3B7EY+cMZxThsd6bDdeRTEi1TpN0YWUki+35HPSM8tZklHCPScNYvEfZqoERnEbMcF+/HP+KD6/eRqh/t7c9P4mrntnI/lVjXqHpih9hkpiFJertNi59p2N3PXJNtKjAll05wxuP2GgavuiuKVxKeEsvH0GD84dytqsCk56egUvLz9Aq82ud2iK4vFUdZLiMlJKPtmQx19XNSFFMw+fPoyrpqWpCRoVt+dlNnH9cf2YOyqev36TwT++383C7YU8df5ohsSF6B2eongsVRKjuERlQws3vLeJP32xg5RgEz/84TiunZGuEhjFoySG+fPqFRN46dJxFFVbOOO/q3j+l32qVEZRnESVxChOt2JvGfd8uo2axlYemjeUftZcUiNVt1TFc502Mp5J6RH85ZsMnvpxL4szilWpjKI4gSqJUZzG0mrj8YWZXPHmr4T5e/PVrdO5bmY/TKr3htIHRAb58sIl43ixXanMy8sPYLf3zdmGFcUZVEmM4hRZZfXc+uEWdhXVcuXUVB6YOxQ/b9VwV+l75o6MZ3J6BA9+uZN/fL+blfvKePqCMcSqGbIVpcdUSYzS677fUcSZz6+muKaJN6+awF/PGqESGKVPiwzy5aXLxvGPc0eyObeaU59dwZLMEr3DUhS3p5IYpde02uw8vjCTmz/YzICYIL67YybHD4nVOyxFMQQhBBdNSuHb22eQEObP9e9u5KGvdmBptekdmqK4LZXEKL2iuMbCRa+u441V2Vw1LY0FN05V0wYoSgcGxATxxS3TuH5mOu+vO8g5L64hp7xB77AUxS2pJEbpsY05lZz+35XsKqrluYvH8uiZw/HxUoeWohyJr5eZB+cN462rJ1JU08QZz6/ix4xivcNSFLejrjRKj3y6MY+LX1tHkK8X39w2nTNHJ+gdkqK4jTmDY/j2thmkRwVyw3ubePL7XVjVmDKK0mkqiVG6xWaXPPFdJvd+tp1J6RF8det0BsQE6x2Worid5IgAPr1pKpdOTuGV5Vlc+vp6yuqa9Q5LUdyCSmKULquztHLdOxt4bWU2V0xN5e2rJxEW4KN3WIritny9zDxxzkievmA02/KrOev5VWQU1ugdlqIYnkpilC4prG7ivJfWsGJfOY+fPYLHzhqBt1kdRorSG84dl8RnN01DAvNfWsvinUV6h6QohqauPkqn7Smu49wX11BUbeHdayZx+ZRUvUNSFI8zIjGUr2+dzuC4YG56fzPP/bwPKdUov4rSEZXEKJ2yPquC819eg11KPrlxKtMHROkdkqJ4rJgQPz6+YQrnjk3k6SV7ue2jLWo8GUXpgJp2QDmmRTuK+MPHW0mO8OedayaRFB6gd0iK4vH8vM383wWjGRQXzD8X76akxsJrV0wgPFC1P1OUNqokRjmq99flcuuHmxmZFMpnN01TCYyiuJAQgptm9ef5i8exPb+G815eQ15lo95hKYphqCRGOaLXV2bx0Fc7OX5wDB9cN1ndASqKTuaNiue9aydRXtfMuS+tYWeB6rmkKKCSGOUI/vvzPv723S7mjYznpcvGqwkcFUVnk/tF8vnN0/Axm7jwlbWs2Fumd0iKojuVxCi/I6Xk3z/s5v+W7OXcsYn856IxagoBRTGIgbHBfHHLNFIiA7n2nQ18v0N1wVb6NtWwVzlESsnfvtvFG6uyuXhSCk+cPQKTSegdlnIEUkoqGloorrFQVGOhtM5CTVOr9teo/VvfbKXZaqfFaqfVpv1ZbRKTSeBlEpgd/3qZTQT6ehHs50WInxchft4E+3kRGeRLbIgvMcF+1DRL7HapjgmdxTp6Ll391q/c+uFm/jV/NPPHJ+kdlqLoQiUxCqBdEP++aNehWagfOWMYQqiLld7sdklRrYWssnqyyho44Pj3YGUjxTUWWjqYZ8fHbCI0wJtQfy0R8TGbDv3r42XCbBJICVa7ltBY7ZJWm52aplbyKxuptVips7TSbP3fdd+9/HsSwvxIiwzU/qICSY8KYEB0MMkR/uqYcZFQf2/eu3YyN7y3kT9+uo3GFitXTE3TOyxFcTmVxCgAPL1kL6+tzObKqakqgdGJ3S7JrmhgZ0ENO/Jr2FFQQ2ZhLXXN1kPLBPt60S86kNHJYZw2wo/4UD/iQv2JD/UjJsSXMH8f/LxNvfL9WVptVDS0UFJrobTWwqpNOwmJTSavqomc8ga+OljwP7ENiQ9mWHwIwxJCGJEYyuDYYLzUiM5OEejrxRtXTuS2D7fwl68zqLNYuXXOAL3DUhSXUkmMwgtL9/PfX/Zz0cRkHjljuEpgXKTVZmdnQQ2/Zlfya3YlG3IqqbVoSYGvl4mh8SGcNTaBIXEh9I8Oon90INHBvi77fvy8zSSG+ZMY5q89Lt/D7NlDDr0upaSyoYWcigb2ltSTWVjLrqJaPtuUT8NabWC2QB8zY1LCGJ8awYTUcMalhhPkq047vcXP28xLl43jngXb+PcPe7DZJXecMFDvsBTFZdTZpI97fWUW//5hD2ePSeCJc0aq9g5OllPewNI9pSzbU8aGnEoaW7SLfb/oQOaNimdsSjgjE0MZEBNk+DmphBBEBvkSGeTL+NSIQ8/b7ZKDlY1sy69mY04Vm3KreP6XfdglmE2CcSlhzBwYzcyBUYxKCsOsjrke8TabeObCMXiZBU8v2YvZJFSJjNJnqCSmD/tw/UH+9t0u5o6M46nzR6uLiRNYbXbWZ1fy064Slu0pI7u8AdCSlvnjk5icHsmk9Aiig311jrT3mEyCtCitvcxZYxIBbebzrXnVrD1Qwar95Tzz016eXrKXED8vZg6K5pThccwZHE2wn7fO0bsns0nw7/mjsdkl//5hD2aTNkieong6lcT0UT9kFPPQVzuYPTiaZy8cq9ot9CKbXbI+u4LvthexeGcxFQ0t+HqZmNo/kqumpTF7cDSpkYF6h+lSwX7ejtKXaO4DKhtaWL2/nJX7yvhldxnfbS/Cx2xi2oBIThkex8nDYokM8pzEzhXMJsH/na8lMv/4fjdeJoEqj1E8nUpi+qCNOZXc8dEWRiaF8eKl49Q4ML0ks7CWD3Y188dVP1Ne34y/t5kThsZw+qh4Zg2Kwd9HDRjYJiLQhzNGJ3DG6ARsdsmWg1X8kFHM4oxiHvhiBw99tZNZg6I5e2wiJw+LVYMtdpKX2cSzF47B7hgu4dIhPszWOyhFcSKVxPQx+0vruPadjSSE+fPmlRMI8FGHQE/UNLXyzbZCFmzIY0dBDV4CTh4RxemjEpgzWCUunWE2CSakRTAhLYI/zx1KZlEt324r4uutBfyyu5QgXy9OGxHH+ROSmZgWrhqeH4OX2cR/LhqLzb6ZDzJKGLcpn/PUODKKh1JXsD6kpNbClW9uwNts4p2rJ6ni+h7IKKzhrdU5fLutkGarnaHxITx6xjCiGnI4/eTxeofntoQQDE8IZXhCKPeeMpj1WRV8uaWA73cW8+mmfAbHBnPplBTOGZuo2s8chbfZxHMXj+WcZ37kvs+3E+rvzYnDYvUOS1F6nUpi+oiGZitXvbWB6sYWPrlxKimRajbqrrLZJUsyS3hzdTa/Zlfi721m/vgkLp6UwojEUACWLcvVOUrPYTYJpg2IYtqAKP561nC+3VbIe+ty+cvXGfzj+92cPTaRK6emMTguWO9QDcnXy8ztY/14abc3t364mfevm8zEtIhjv1FR3IhKYvoAu11y1ydb2VNcy5tXTTx0wVU6x9Jq49ONebyyIov8qiYSw/x5cO5QLpiYTKi/Kg1whQAfLy6cmMIFE5LZll/D++ty+XxTPh+uP8jswdHceFx/pvSLUFVNh/H3Erx11UTOf2Ut17y9gQU3TmVofIjeYSlKr1FJTB/wf0v28GNmCQ+fPozZg2P0DsdtNLXY+GB9Lq+uyKK0rplxKWE8NG8oJw6NVb25dCKEYExyGGOSte/i/XW5vLU6h4tfW8fopFBunNWfU4bHqeEC2okM8uW9aydz3otruOLNX/ni5mkkR6iSWMUzqDOxh/t6awEvLD3ARROTuWZ6mt7huIWmFhsvLz/AjH/+wt++20W/6EA+vG4yn988jVNHxKsExiDCAny47fiBrP7T8Txxzghqmlq55YPNnPTMcr7ZVojdLvUO0TASw/x579pJtFjtXP32BmqaWvUOSVF6hTobe7AtB6u497PtTEqP4LGzRqii9mOw2ux8suEgc55axj++383wxFA+vWkqH98wlWkDotTnZ1B+3mYunZzKz/fM5sVLx+FtMnHHR1s47T8rWbyzGClVMgMwMDaYly8bT055A7d+sJnWDiYPVRR3o5IYD1VaZ+HG9zYRG+LLy5eNV2PBHIWUWoPd0/6zkvs/30F8mB+f3DCFd6+ZpBpCuhGzSTB3ZDzf3zmT5y4eS6vNzk3vb+KM51exYm+Z3uEZwtT+kTx57khW7S/nL1/vVAme4vZUmxgPZLXZueOjLdRaWvnymulEBProHZJh7S2p45GvM1ibVUG/qEBevmwcpwyPU6UubsxkEpw5OoG5I+L4amshz/60lyve/JU5g6N5cN4wBsQE6R2irs6fkExORQMvLD1AelQgNxynpidQ3Jeut+dCiFOFEHuEEPuFEH/q4PXZQogaIcRWx99fOvvevuypH/eyLquSJ84eqXoiHEF9s5Unvstk7n9WkllUy2NnDeeHu47j1BHxKoHxEF5mE/PHJ/HzPbP489whbMyp4pRnV/DoNxlUNbToHZ6u7jlpMPNGxfPk97tZvLNY73AUpdt0K4kRQpiBF4CTgHxggxDiGyll5mGLrpRSnt7N9/Y5P2YU8/LyA1wyOUWN0tkBKSXfbCvkie92UVrXzEUTk7nv1CGqtMqD+XqZueG4/pw7Lolnluzl3bU5fLmlgHtPGcwlk1L0Dk8XJsc8SwVVTdyzYCv9o6czMFaNt6O4Hz1LYiYB+6WUWVLKFuBj4CwXvNdj5VY0cM+n2xiZGMpfTh+mdziGU1xj4dp3NnLnx1uJDfHjy1um8Y/zRqkEpo+ICvLliXNG8v2dxzE8IYSHvtrJeS+vIa+ubzZw9fM28/Jl4/H38eKG9zZRa1E9lhT3o2cSkwjktXuc73jucFOFENuEEN8LIYZ38b19RrPVxi0fbMYkBC9eOk5NmNeOlJJPNhzkpKeXs+ZAOQ+fPoyvbp3O2JRwvUNTdDA4LpgPrpvM0xeMJreikUfWNPHk97tobLHqHZrLxYX68dJl48irbOSuj7eqbumK2xF6tU4XQpwPnCKlvM7x+HJgkpTy9nbLhAB2KWW9EGIu8B8p5cDOvLfdOm4AbgCIjY0d//HHHzt933pLfX09QUGda4T48e4WFue0cuc4X8bGGLu9dlf2q6cqmuy8tbOFnRU2BoebuGaEL7GBzsvdXblvruaJ+1bfIvkgo4G1JYIof8G1I3wZGuk5NwCd/c5+ym3l/V0tnD3Am7MHGL9k0hOPxTa9vW9z5szZJKWc0GsrNBg9r3b5QHK7x0lAYfsFpJS17f6/SAjxohAiqjPvbfe+V4FXASZMmCBnz57dK8G7wrJly+hMvKv2lbN48Xoum5LCXWePdH5gPdTZ/eqp73cU8dfPt2O1w2NnDeeyyamYnDySq6v2TQ+eum9BPsv4Q8pI7v98O//c0Mg109O579TBHlGa2dnvbJaUNH66jS82F3D6tNGGnyzSU49F8Ox9cwY9q5M2AAOFEOlCCB/gIuCb9gsIIeKEo6uIEGISWrwVnXlvX1HZ0MLdC7YyICaIB+eqdjAAjS1WHvhiOzd/sJm0qEAW3TGTK6amOT2BUdzX5H6RLLpzJldMTeXN1dnMe24l2/Or9Q7LZYQQ/P2ckYxIDOHuBVvJr2rUOyRF6RTdkhgppRW4DfgB2AUskFJmCCFuEkLc5FhsPrBTCLENeA64SGo6fK/r90JfUkru+2w71Y2tPHfRWPx93P/OsacyC2s547+r+HhDHjfN6s9nN00jLSpQ77AUNxDg48VjZ43g/Wsn09hi45wX1/Dcz/uw9ZF2In7eZl64ZBx2CXd8tEWN6Ku4BV3HiZFSLpJSDpJS9pdSPuF47mUp5cuO/z8vpRwupRwtpZwipVxztPf2NR/9msdPu0q479TBDEtQ48F8sTmfc15cTZ3FyvvXTuZPpw1RIxUrXTZjYBSL/3AcZ4yK5+kle7n8jfWU1ln0DsslUiMDefLckWw+WM3TS/bqHY6iHJM6w7up/KpGnvguk+kDIrlmerre4eiqxWrnka93cveCbYxJDuO7O2YyfUCU3mEpbizU35tnLhzDv+aPYvPBKub+ZxWr95frHZZLnDE6gYsmJvPSsgNqugbF8FQS44aklDzwxQ4k8I9zR/Xpth6ltRYueW0d76zN5boZ6Xxw3WSig331DkvxAEIILpiQzDe3zSA8wJvL3ljP0z/u6RPVS4+cMZxBsUHcvWBrnymFUtyTSmLc0IKNeazcV84Dpw0hOSJA73B0s7OghjOeX0VGYS3PXTyWh04fhpdZHdJK7xoUG8zXt01n/rgknvtlP9e9s8HjB4bz9zHz/CXjqG+2cs+CbWqiSMWw1BnfzRTVNPG3hbuY0i+CSyen6h2Obn7eVcIFr6zFJASf3zyNM0cn6B2S4sECfLz49/mj+dvZI1i5r5yzX1jNgbJ6vcNyqkGxwTw4bxgr95Xz/rpcvcNRlA6pJMaNSCn58xc7sNol/zpvdJ+tRnpnTQ7Xv7uRftGBfHXrdNWoWXGZy6ak8sF1k6lubOXsF1azdE+p3iE51WWTU5g5MIq/L9pNTnmD3uEoyv9QSYwbWbi9iKV7yrj3lMGkRPa9aiS7XfK3hZk88k0Gxw+JYcGNU4kN8dM7LKWPmdwvkm9um05yeADXvL2BN1dl6x2S0wgh+Nf8UXibBXcv2Non2gMp7kUlMW6iztLK4wszGZkYypXT0vQOx+WsNjv3frad11dlc9W0NF65fAIBPsaeXkHxXEnhAXx281ROHhbLYwsz+dvCTI+ddyg+1J/HzhrB5oPVvLLigN7hKMrvqCTGTTy9ZC9l9c387ewRmPtYNVLb5Jafb87nrhMH8cgZw/rcZ6AYT4CPFy9eOp4rp6by+qpsbv94C5ZWm95hOcVZYxI4bUQczyzZy66i2mO/QVFcRCUxbiCjsIZ31uRw6eQURieH6R2OSzU0W7n27Y38mFnCI2cM484TB+KYiUJRdGc2CR49czh/njuE77YXccWbv1LT6Hk9l4QQPHHOSEL8vPnT59tVtZJiGKo83uDsdslDX+0kPMCHe08eonc4LtXQbOXKN39l88Eqnjp/NPPHJ+kdkltqsdopr2+m1tJKQ7ONxhYrDc22Q6UGbTmhEAI/LxNBvl4E+XkR6OtFiJ83kYE+fbYReWcIIbjhuP7EhfrzxwXbuPDVtbx/3WSigjxrvKKIQB/+csYw7vx4K++uzeHqPj7IpmIMKokxuE835bHlYDX/d/5oQgO89Q7HZRpbrFz99ga25FXz34vHMW9UvN4hGZbNLsmvaiSrvIHssgayyuvJrWikrK6Z0rpmKhtaerR+L5MgOtgXf1r4KG8jKREB9IsOon90EP2iA4kM9FGlY8CZoxMID/Dm+nc3cuEra/nguinEhXpWw/MzRyfwxeYC/v3DHk4eHkdimL/eISl9nEpiDKzJKvn3D3sZnxrOueMS9Q7HZZpabFz3zkY25lTy7EVjVQLTjt0uOVBWz/b8GnYUaH8ZhTVYWn+brC/Ez4u0qECSIwIYnxpOTLAfMSG+hPl7E+DrRaCPmQAfL/y8tdpkCWhjmUksrXbqm63UW6w0tFipbmyltM5CcU0zu3MLOVDWwNI9ZbRYf9teeIA3IxJDGZUUysjEMEYlhRIf6tcnE5uZA6N55+pJXPP2Bi54ZS0fXj+ZpHDP6UkohOBvZ4/g5GdW8JevdvL6lRP65PesGIdKYgxsUVYr5fWtfepEYWm1ccN7G1mbVcHTF4zu84PYSSnJKm9gzYEK1h2oYF1WBRWOkpUAHzPDE0K4ZFIqQ+KC6RcdSHpUIBFOKhlZtqyK2bNnYbNLCqubOFBWT1ZZA3uK69hRUMPLy7MOtZVIDPNnav9IpvWPZGr/SOJD+84d++R+kXxw/RSueGM9F7y8lg+vn+JRM6knRwRwz8mD+Nt3u1i0o1jdZCi6UkmMQRVUN7E4p5WzxyQwpo805rXZJXd8tIWV+8r51/xRnDO2b7aBsdrs/JpTyY8ZJSzJLKGgugmA+FA/Zg2OZkq/SMYmh9EvOkiXXlpmkyA5IoDkiABmD/7teUurjV1FtWzNq2Z9ViU/7Srhs035AAyICeLEobGcNCyWsclhHt/GZkxyGB/dMIXL3/iVS15bxyc3TvWoKUKumpbGV1sLePTbDI4bFEWwX9+p6laMRSUxBvXvxbsBuPfUvtGYV0qtAfOPmSU8esYwLpiQrHdILmWzS9ZlVfDF5gJ+3l1CdWMrPl4mZg6I4pY5/ZneP4rUyABDl8j5eZsZmxLO2JRwrp6ejt0u2VVcy9oDFSzbU8brK7N4efkBooJ8OHFoLGeOSWBKeqTHJjTDE0J5/9rJXPTqWi59fT0LbpzqMW1kvMwmnjh7JGe/uJr//rKfP88dqndISh+lkhgD2ppXzVdbCzmjn3efaTj37E/7+OjXg9wyuz9X9aFeD/tL6/l8cz5fbSmgqMZCsK8XJw2L5eThscwcGE2gr/v+RE0mwfCEUIYnhHLdzH7UNLWybE8pSzJL+HZbIR9vyCM+1I+zxiRy7rhEBsUG6x1yrxuWEMK7107mstfXc8nr6/jkhqkeM8v66OQwLhifzJursrlgQjIDYoL0Dknpg9z3DOmhpJQ8uWgXUUG+zO1n1jscl/hgfS7/+Xkf88cnce8pg4/9Bjdntdn5aVcJb6/JYV1WJWaT4LiBUfx57lBOGhaLn7dnfu+h/t6cNSaRs8Yk0tRiY8muEr7cnM9rjhKacSlhXDE1jdNGxuHr5TmfwZjkMN66eiJXvPErl7+xno9vmEJYgI/eYfWKe08dzKIdRTy2MJN3rp5o6JJCxTOpJMZgVu0vZ312JX89czj+LTl6h+N0y/aU8vBXO5kzOJonzx3p0SfBmqZWPlx/kPfX5VJQ3URimD/3nzqE88YnEhPsGdUMneXvY+bM0QmcOTqB8vpmvtpSwAfrD/KHT7by+EIfLpyYzOVTUz2mQfDEtAhev3ICV7+1geve2cj71032iGQ1KsiXO08cyN++28XPu0o5cVis3iEpfYwasddApJQ89eNeEsP8uWiS57cJ2V9az+0fbmFwXAjPXzIOb7NnHo6VDS089cMeZvzjF/65eDcpEQG8fNl4lt87m5tn9+9zCczhooJ8uW5mP36+exbvXTuJcanhvLz8AMf9ayn3f7adrLJ6vUPsFdMHRPHMhWPYmFvFHz72nMkUr5yWxoCYIB5bmOmx0y4oxqVKYgzk512lbMur5p/njfSo4vSOVDe2cN07G/D1NvHaFePduu3HkVTUN/PqiizeW5dLU6uN00bEceucAQxPCNU7NEMymQQzB0Yzc2A0eZWNvLYyi0825LFgUx5zR8Rz2/EDGBofoneYPTJvVDxFNUP523e7eHxhJo+cMcztSx+9zSYeOWMYl7/xK++syeHGWf31DknpQzzvyuGm7HbJUz/uIS0ygHPHeXbXYqtdcuuHmymstvDRDZ41GBhoXY3fXJ3NS0sP0NBi5YzRCdw2ZwADPbDhqrMkRwTw2FkjuP34gby5Opv31+ayaGcRZ49J5K4TB5ES6b7HzHUz+1FUY+GNVdnEh/p5xEV/5sBoZg2K5sVlB7hoYkqfGl1c0Zdnlt+7oUU7i9hdXMcfThzksdUqbT7d08Lq/RU8cc4IxqdG6B1Or7HbJasLWjn+qWX8a/EeJveL4Me7juM/F41VCUw3RQf7cv+pQ1h1//HceFx/Fu0o4oSnl/HI1zspr2/WO7xue3DuUOaNiufJ73fzY0ax3uH0ivtPHUKtpZWXlh/QOxSlD/Hsq6WbsNslz/28jwExQZzh4SPULt5ZxA+5Vq6cmsr5HjQWzO7iWua/vIbXdrQQGeTLR9dP4fUrJzIgRiUvvSE0wJs/nTaE5ffOYf74ZN5ff5A5Ty3jrdXZWG32Y6/AYEwmwf+dP5pRSaHc9clW9hTX6R1Sjw1LCOHsMYm8tTqbopomvcNR+giVxBjAz7tL2VtSz61z+usyAqur5JQ3cO+n20kPNfHneZ4xOFZji5UnF+1i3nOryKlo5NoRPnx963Sm9o/UOzSPFBfqx5PnjuSHPxzHmOQw/vptJvOeW8W6rAq9Q+syP28zr14+gQBfL65/dyNVPZyo0wjuPmkQUsKzS/bpHYrSR6gkRmdSSl5ctp+kcH/OGOW5pTCWVhu3fLAZk0lwy2hfj2i4vHp/OSc9vYJXVmRx3rhEfr57FjOTvD12BFojGRATxLvXTOLly8ZT32zlolfXcfeCrdQ0tuodWpfEhfrxyuXjKa6xcNtHm92yVKm95IgALp+ayqeb8thX4v6lS4rxqSRGZ+uzK9lysJobj+uHlwe3hXl8YSaZRbU8fcFoogPcez8trTYe+zaTS19fj6+XiQU3TuVf80cTHugZA5i5CyEEp46I46e7Z3HrnP58vbWQE59Z7nZtTMalhPP3c0eyen8F/3RMN+LObp0zgAAfL579WZXGKM7n3lcTD/DiMm0uGU9qH3K4n3eV8MH6g9xwXD9OGOreg2HtLKjhjP+u4s3V2Vw5NZXv7pjJpHTPaZzsjvx9zNx7yhC+vnU6kYE+3PDeJu74aAvVje5TPTN/fBJXTE3ltZXZLMks0TucHokI9OHKaaks2lGkSmMUp1NJjI52FtSwYm8ZV09P94jROztSUd/M/Z9vZ0hcMPecPEjvcLpNSsl7a3M458XV1FpaefeaSfz1rBH4+3jm9+aORiSG8s1tM7jrxEEs2lHE3P+sZENOpd5hddqD84YyIjGEexZsJa+yUe9weuTaGf3w9zbz3C/79Q5F8XAqidHR6yuzCPL14vKpqXqH4hRSSh74Yge1TVaevWiM27aDaWyx8odPtvLw1xnMHBjN4juP47hB0XqHpXTAx8vEnScO5ItbpuHtZeLCV9by3M/73GJ0XF8vMy9cMg4p4baPttBidd/2MRGBPlwxNY2F2wvZX+oZIy4rxqSSGJ2U1ln4bkcR509IIsTPMweG+nRTPj9mlnDfqYMZEueeI60eKKvn7BdW8+22Qu49ZTCvXzFBtX1xA6OSwlh4+wzOHJ3A00v2cunr6yits+gd1jGlRgbyr/mjtJG73bx9zPUz0/HzMvP8L6ptjOI8KonRyYfrD2K1S66cmqZ3KE5RXGPhsW8zmdIvgmump+sdTres3l/O2S+spry+hXevmcytcwaonkduJNjPm2cuHMNT549mW14NZ/53NdvyqvUO65hOGxnPFVNTeWNVNqv2lesdTrdFBvly+dRUvtlW6DHzXynGo5IYHbRY7by/7iBzBseQFhWodzi9TkrJw1/vxGq386/zRrvlhX/BhjyufPNX4kP9+Oa26cwYGKV3SEo3CCGYPz6Jz2+ehpdZcP4ra/lsU77eYR3TA6cNpV90IPd+to2aJvfqNt7e9TO1XpevrczSOxTFQ6kkRgeLdhRRXt/MldPS9A7FKRbvLGZJZolbznFjt0v+tXg3932+nan9I/ns5mkeN7dTXzQsIYRvbpvBhNRw/vjpNh77NtPQ7WT8fcw8c8EYSuuaefSbDL3D6bboYF/OG5fE55sL3HqaCMW4VBKjg7fW5NAvOpCZAzzv7r6mqZW/fJPB8IQQrp3hXtVINrvk/s+38+KyA1w8KYU3r5rose2V+qKIQB/evWYSV01L483V2dz24WYsrTa9wzqi0clh3H78AL7cUsCiHUV6h9Nt185Ip8Vq5921uXqHongglcS42I78GrblVXPl1DS3rGY5ln8u3k1FfTP/OHeUWw3e12K1c8dHW/h0Uz53njCQv58zwuMn4uyLvMwmHj1zOA/NG8r3O4u54o1fqW8xbonMrXMGMDoplAe/3EGFm5ZkDIgJ4sShMby/LpemFuMmjYp7UmdpF/tk40F8vUycPTZR71B63c6CGj769SBXTUtnZFKo3uF0mqXVxo3vbeS7HUU8OHcod500CCE8L8FsI6WkodlKcY2FfSV1bMqtYn1Wxe/+duTXkFPeQEV9s1t39T2S62b2478Xj2VrXjV/X99EYbUxJyz0Npt46vzR1DdbeeK7XXqH023Xz+xHZUMLn282fnskxb146R1AX9LUYuPrLYXMHRlPqL9nVVNIKfnrtxlEBPhw54kD9Q6n0yytNq5/dyOr9pfz93NGcsnkFL1D6hVSSkrrmtldXMfuolqyyhoorGmioFq7YFtau5aYRAb6EGy2MujgRpLCAxgcF8Sg2GAGxQYT6Ouep5EzRicQFeTLNW+t44JX1vLR9VNIjjBe+6eBscHcPKs/z/2yn3PGJTJzoPuNUTQpPYJRSaG8sSqbSyaleGQptKIP9zz7uKnvdxZR12zlwomeN8XAwu1FbMip4slzR7pNgtZqs3Pbh1tYua+cf80fxQVuPPVDi9XOjoIaNuRUsiG7ks0Hq6hqNxliVJAvieH+DIkL5vjBMUQF+xLi502wnxdBfl74tqs6k0BDs5X6Zit1FivVja0U11rYmVVATkUDK/eV09SuLUl6VCATUsOZmBbB+LRw+kUFuk1J1tT+kdw30Y9nt1q58JW1fHTDFFIjjddj8JY5A1i4vYgHv9zJD384zu1GihZCcO2MdO78eCsr9pUxe3CM3iEpHkIlMS70yYY80iIDmOxhc+00tdh4ctEuhieEuE0iYLNL7l6wjZ92lfD4WcPdJu72yuub+WV3KT/vKmHlvnIaHe0N+kUHctKwWIYnhDI4LpghccGEBfR8gL5lyyqYPXsWdrskr6qR3cV17CmuY3t+DT/tKuFTR9fl+FA/Zg+O4fghMUwfEEmAj7FPM+mhZj64bgKXv7GeC19Zx4fXT6ZfdJDeYf2On7eZv587koteXcezP+/lgdOG6h1Sl502Ip7HgzJ5f91BlcQovcbYZxcPkl3ewPrsSu47dbDb3KV21qsrsiissfDsRWMxu0ExsZSSh77awbfbCnngtCFc7kYDDtZaWvl+RxGfby5gQ04lUmpJw7njEpneP4oJaRFEB/s6NQaTSZAaGUhqZCCnDI8DtM/0QFkDG3IqWb6njG+3FfLRrwfx8TJxwpAYzhqTyJwh0YademJEYigfXj+Fy15fz8WvreOzm6YZrmppSr9ILpiQxBsrszl/fDIDYoyVaB2Lj5eJCyYk8/LyAxRUN5EY5q93SIoHUEmMi3y+KR+TgPnjkvQOpVdVNrTw2sosTh0e5zazOb+wdD8f/ZrHbXMGcOOs/nqHc0xSSn7NruT99Qf5MaOYZqudftGB3HnCQE4cGsvwhBDdE2MhBANighgQE8TFk1JosdrZkFPJkswSFm4v5PudxQT7eXH6qAQum5LC8ATjNfweGh/Ch9dP4YJX1nLZG+v59KapxAT76R3W79x36hC+31nM4wszefvqibp/71118aQUXlp+gI9/Pcg9Jw/WOxzFA6gkxgWklHy9rYDpA6KICTHWSbGnXlq2n8YWK388xT1mqP56awFP/biXc8YmGn5W7WarjW+3FfHW6mwyCmsJ9ffmwonJnDsuidFJoYa+gPl4mZg+IIrpA6J4aN5QVh+o4OstBXy5JZ+Pfj3IhNRwLp+aytyR8Ybqyj44Lpi3rp7Ipa+t58o3N/DxDVMM1cYrKsiXO08YyN++28XSPaUcPyRW75C6JDkigDmDY/h4Qx53nDDQUN+94p7UEeQCW/Kqyats4szRCXqH0quKapp4Z20u545LYkBMsN7hHNOGnEru/XQ7k9Ij+Md5Iw2bBDRbbbyzJoeZ/1zKHz/dRovVzpPnjmTdAyfw2FkjGJMcZtjYO+JlNjFrUDRPXziG9Q+cyEPzhlJW38ydH29l9r+X8f66XJqtxhk/ZFxKOK9eMZ79pXVc+/YGww2Id8XUNPpFB/L4wl1u2f39sikplNU182NGid6hKB5AJTEu8M3WQny8TJwyIk7vUHrVcz/vQ0rJH9ygS3VBdRM3vreJpHB/Xr18vCHbZrTa7HywPpfZ/17GI99kkBYVyLvXTOLHu47j4kkpbtcjpSOhAd5cN7MfS++ZzZtXTSAmxJeHvtrJcf9aylursw2TzMwcGM2zF45l08Eq/vjpNqQ0zoB4Pl4mHj59GNnlDbyzJkfvcLps1qAYEsP8+WRjnt6hKB5AJTFOZrNLvttRxJzB0R41hP3BikYWbMzn0smphp9bqNlq45b3N9FitfP6lRN6padOb1u1r5zT/rOSB7/cSXyoHx9cN5lPbpjCcYOi3arUpbNMJsHxQ2L54uZpfHDdZNIiA/nrt5mc9PQKFu0oMkTSMG9UPPefOoSF24t49qd9eofzO3MGxzBrUDTPL93vdhNEmk2Cc8clsmpfGSW1Fr3DUdycSmKcbF1WBWV1zZw52rNG6H15xQHMQnDzbOM3jP3rt5lsy6/hqfNHG67rbF5lIze+t5HL3lhPi9XOq5eP5/ObpzF9QJRHJi+HE0IwfUAUn9w4lXevmYS/t5lbPtjM+S+vZUd+jd7hceNx/Th/fBL/+XkfX28t0Duc37n3lMHUNLXy2gr3myH6nLGJ2CV8tcVYn6niflQS42Tfbisk0MfMCUM9Z1yE0loLn23MZ/6EJGIN3lD50415fLj+IDfN6s+pBqrOs9sl767N4ZRnV7Bibzn3njKYH+86jpOHx/WJ5KUjxw2KZtGdM3ny3JHkVDRy1gureHxhJg3NVt1iEkLwxDkjmZQewb2fbWd7frVusRxuRGIop4+K583V2ZTVude8Sv2igxiXEsbnm/MNUeqmuC+VxDiRzS5ZklnC8UNj8fN2//YMbV5flY3Vbuem44xdCnOgrJ6Hv97J1H6R/NFAPZHyKhu59PX1/OXrDManhvPTPbO4dc4AjzpGustsElw8KYWf75nFRZNSeGNVNic/s4Jle0p1i8nHy8TLl40nOsiXm9/fTHVji26xHO7ukwbRbLXzwtL9eofSZeeNT2JvST0ZhbV6h6K4MV2TGCHEqUKIPUKI/UKIP3Xw+qVCiO2OvzVCiNHtXssRQuwQQmwVQmx0beSds/lgFRUNLZw8zL26QR5NdWML76/L5YzRCaREGrctTKvNzl2fbMXP28yzF40xzIzaC7cXctp/VrKjoIZ/nDuSd6+ZpAb96kCovzd/P2ckn940FT9vE1e9tYGHv9qpW0+hiEAfnr9kLKV1Fu5ZsA273RilB/2igzh/fBIfrj9IgUEnsTyS00cm4ONl4rNNalJIpft0O7MLIczAC8BpwDDgYiHEsMMWywZmSSlHAY8Drx72+hwp5Rgp5QSnB9wNSzJL8DYLZg92vwnbjuS9tbk0ttgM3xbmuZ/3sT2/hr+fM9IQVV7NVhuPfL2T2z7cwqDYIBb/YSYXTUrps1VHnTUxLYJFd87kuhnpvLculzOfX8XuYn3u3MemhPPQvGH8vLuUl1cc0CWGjtxxwkAkkleXGyemzggN8ObEoTEs3F6IzSBJoeJ+9Lw9nQTsl1JmSSlbgI+Bs9ovIKVcI6WscjxcB7jNcLdSSn7MKGZKv0iCPaRXUqvNzvvrczluUDRD4kL0DueINuVW8sLS/Zw3Lom5I+P1DofiGgvnv7yWd9bmcv3MdD65carhe3QZia+XmYdOH8Y710yisqGVM59fzYIN+nTPvWJqKvNGxfPUD3vYlFupSwyHSwjz55yxiXy8Ic/t2sbMG5lAeX0Lv2Yb47NU3I+eSUwi0P5MlO947kiuBb5v91gCPwohNgkhbnBCfD2yv7SenIpGTh5unMakPbV4ZzEltc1cNS1V71COqNlq477PthMf6s+jZx5esOd6OwtqOOuFVRworeeVy8fz4LxhapTSbpo1KJrFf5jJpLQI7vt8O498vZNWm2sHexNC8I9zR5IQ5s/dC7bp2ui4vZtm9afVZufN1dl6h9Ilc4ZE4+dt4vudRXqHorgpoVfLcCHE+cApUsrrHI8vByZJKW/vYNk5wIvADCllheO5BClloRAiBlgC3C6lXNHBe28AbgCIjY0d//HHHzttn9pbeKCFz/a18sxsf8L9unfRqq+vJyjIOF2C/7auidoWyT9m+mPqQTWIM/frq/0tfLW/lbvH+zIq2vWzarTfty2lVl7a1kyQt+Cu8X4kB7t38mKU49Fml3y6t4XFOVYGh5u4dawfIT6uPR73VNr4x68WZiV7cdVw50642VkvbrWwvczG/80OINBb+zyM8p0dzfNbLOyrtvPM7M6fV9xhv7qrt/dtzpw5m4za5KJXSCl1+QOmAj+0e/wA8EAHy40CDgCDjrKuR4E/Hmub48ePl64y/6XVct5zK3q0jqVLl/ZOML1gR361TL1/oXx9ZVaP1+Ws/dpXUicH/nmRvP3DzU5Zf2e07duCDQdl+p8WyjP+u1KW1DTpFk9vMtLxKKWUX27Ol4MeXCRn/3upPFjR0O31dHe/nvguU6bev1D+squk29vuTRkFNTL1/oXy+V/2HXrOaN9ZR77ZWiBT718o12dVdPo97rBf3dXb+wZslDpd513xp+et4QZgoBAiXQjhA1wEfNN+ASFECvAFcLmUcm+75wOFEMFt/wdOBna6LPJjqLO0svlgNbMGeU6D3nfX5hDgY+b8CcZsliSl5M9f7sDfx8zDp+tbjfTe2hzu/Ww70wdE8fENUzxu0k+jOHtsIh9eP5nKhhbOfWkNGYWuHRzvnpMHMSQumPs/306tRf9Rc4clhDBzYBTvrs1xeTVbT8wZEoOvl4lFO1SVktJ1uiUxUkorcBvwA7ALWCClzBBC3CSEuMmx2F+ASODFw7pSxwKrhBDbgF+B76SUi128C0e09kAFNrtkxgDPSGIamq0s3F7EmaMTDDt1wrfbi/g1u5IHThtCdLB+xfuLs1t5+OsMThwaw2tXTCDAR00U70zjUyP47KapeJkEF76yjvVZFS7btq+XmX/NH0V5fTNP/bDHZds9mqunp1FS28zincV6h9JpQb5eWnunncVq4Duly3StpJdSLpJSDpJS9pdSPuF47mUp5cuO/18npQyXWjfqQ12ppdajabTjb3jbe41i1f5yAnzMjEsN0zuUXvHdjiIaW2yGLYWxtNr45/e7GZ4QwgUTknWL4711uXy8p4V5I+N56bLxavA6FxkYG8wXt0wjLtSPq97a4NJEZlRSGFdMTeO9dblsOVh17Dc42exBMaRGBvC2m00MeeKwWIprLWQWqYHvlK5x75aGBrVyXzlT+kUacqbk7vh0Yx79ogMZlxKudygdemNVNgXVTTw0bxgmkz7jrnyzrZC/fL2TMdHa4HqqB5JrxYf68+H1k0kI8+PqtzewIcd1XXbvOXkQscF+PPDFDt2rcUwmwZVT09iUW2WoKRKOpW0srWV7ynSORHE36kzby/IqG8kub2DGgCi9Q+kV2eUNbMipYv74JEMOzFZaZ+HFpfs5eVgsU/tH6hLD8r1l3P3JViamRXDLGF+VwOgkJtiPj66fopXIvPmry0pGgv28efTM4ewuruPdtbku2ebRzJ+QRKCP2a1KY2KC/RiZGMovu/WbXkJxT+ps28tW7y8HYOZAz0hiPt+Uj0nAeeOMWZX035/302y188Dcobpsf29JHbd+sJlBscG8fuUEfMzGS/T6kpgQPz6+fgqRQb5c+85GsssbXLLdU4bHMnNgFM/9vE/3uZVC/Lw5e2wii3YU0djqPm1M5gyJYcvBKqoajDM3lWJ8KonpZb9mVxIV5MOAGPcfw0BKyTfbCpk+IMoQQ/cfrrC6iU825HH+hGTSowJdvv2qhhaue2cj/j5m3rhqgmEbPfc1MSF+vHPNJACufPNXl4xiK4TgwXlDqbO08tzP+k/GeMGEZCytdn4tNsZgfJ0xZ3A0dgkr9qkqJaXzVBLTyzbkVjIhNcKQVS9dtbOgloOVjZw+Sv+h+zvy4rL9SCS3znH9PE6tNju3fLCZ4hoLr1w+nvhQNYmjkaRHBfLmVRMpq2vm2nc2uGTiyCFxWsPyd9fmuKwE6EhGJYUyODaYFfnuk8SMTgojMtBHVSkpXaKSmF5UXGMhr7KJCWnGbADbVd/tKMLLJDh5mPGmTmhfCqPHPERPL9nL2qwK/n7uSMM2eO7rxiSH8d+Lx7KjoIYHvtjhku67d588CB8vE/9avNvp2zoaIQTnT0giq8bOvpI6XWPpLJNJMH1AFGsOVKiu1kqnqSSmF210TAg3KT1C50h6TkrJdzu0qqTwQB+9w/kfLztm7L11zgCXb3vlvjJeXn6AiyYmM3+8MdsKKZoTh8Vy14mD+HJLgUsausYE+3HdjHS+31lMZqG+3YXPHpuIWcCCjfpMltkdU/pFUlbXzIEyfUuyFPehkphetDGnigAfM8PijTvDc2ftKKghr7KJeQasSqpubOHTjfmcPSaRxDDXVuOU1TVz1yfb6B8dxCNnDHfptpXuuW3OAE4aFsvfvtvlkjFkrp3Rj2BfL577eZ/Tt3U0UUG+jIo28+22Iux29yjZaOthuNaFY/0o7k0lMb1oQ04lY1PC8PKALrY/ZpRgNglOHhardyj/48NfD9LUauPameku3a6Ukge+2E6dpZXnLxmLv49njAPk6UwmwdMXjCY1IoA7P97q9N5DoQHeXD0jncUZ+pfGTIrzorjWwmYDDMTXGWmRAcSF+LHugEpilM5x/6utQTS12NhVVMt4D2kf8cvuUsanhhMWYKyqpBarnXfW5DBzYBRD4lxb4vXt9iJ+2lXKH08e7PJtKz0T7OfNfy4aS3l9Mw9+udPpbS6unZFOsJ/+pTFjYsz4eplYuN095iUSQjC1fyTrslS7GKVzVBLTSzKLarBLGJkUpncoPVZcow3/PWdwjN6h/I/vdhRSUtvMtTNcWwpT2dDCo99kMDo5jGtcvG2ld4xMCuXukwfx3Y4iPt9c4NRthfp7c9W0NH7ILNa1p5K/l2DO4BgW7SjC5i5VSv0iqWhoYW9Jvd6hKG5AJTG9ZEe+NoPuyMRQnSPpuWV7tC6Oxw8xXhLzwbqD9IsKdPkM4X9bmEmdpZV/nTcKs05TGyg9d+Nx/ZmcHsGj32RQXGNx6rYun5qKt8nEW6uznbqdY5k3Kp7SumaXTsXQE5P7aR0j2jpKKMrRqCSml+woqCUqyJfYEP1mUO4tv+wuJSHUj0Gxxhqwb39pHRtzq7hwYrJLx+HZlFvJF1sKuPG4/gyOC3bZdpXeZzYJ/jV/FK02O49+k+HUbcUE+3HmmAQ+3ZhPTWOrU7d1NCcMjcHHy8SPGSW6xdAVKREBRAT6sPVgtd6hKG5AJTG9ZGdBDSMTQ9x+kLtWm53V+8uZPSTGcPuyYGM+XibBuS6cAsFulzy2cBexIb7cPNv1g+opvS81MpA/nDiIxRnF/JBR7NRtXTsjnaZWGx9tOOjU7RxNgI8XU/tFsnSPewwiJ4RgTHIYW/Kq9Q5FcQMqiekFTS029pXWeURV0vb8GhpabMw02ASWLVY7X2zO5/ghMUQHu66066utBWzLq+a+U4YQ6Ovlsu0qznXdzHSGxAXzyNcZWKzOaysyND6Eaf0jeW9trq7dnI8fEkN2eYPuIwl31pjkMA6U1VNr0a8ES3EPKonpBZlFtdgljPCAJGadY3wGow3Yt2xPKeX1LVw4Mdll22y22njqhz2MSgrlnLGJLtuu4nzeZhNPnDOS4loL32c790J5yeQUCqqbWH2g3KnbOZq29m3uMqT/2JQwpITteTV6h6IYnEpiesFex7DeQz1gkLv12ZUMig0iMshYbXsWbi8iPMDbpQ16F2zMp7DGwr2nDMakGvN6nPGp4cwbFc/3Oa2U1Dqvke9Jw2IJD/Dm4w36jZybHBHAgJgglrpJEjPK0ctzi5uMb6PoRyUxvWBfST3+3maXjx7b21ptdjbmVDKlX6TeofyOpdXGT7tKOHVEnMsGEmy22nhx6X7Gp4Yzw2BVa0rv+dOpQ7Db4akf9jhtG75eZs4em8iSjBIqG5w70N7RzBkczfrsCppanD8ZZk+F+nvTLzqQbfmqJEY5OpXE9IJ9pXUMiAly+7v1nQU1NLbYmJxurCRm2Z4yGltszB3puikQPt2YT1GNhTtPGGi4Bs5K70mOCODEVG8+25zP/lLnTZR44cRkWmx2vtri3PFpjmZa/yhabdJtRu8dFh/C7mJ9RzxWjE8lMb1gf2k9A2OM1R25Ozblaie3ienGGnV40Q6tKmmqi0qI7HbJayuzGJMcxsyBqhTG083t542fl5kXlh5w2jaGxIUwLD6EhdsLnbaNY5mQFo7ZJA61ezO6ofEh5Fc1qca9ylGpJKaH6iytFNVYGGCwMVW6Y1t+DQmhfsQE++kdyiEtVju/7C7llOGuq0pauqeU3IpGrp2Rrkph+oAQH8FlU1L4emsBOU7svTNvVDybD1ZTUN3ktG0cTbCfNyMSQ90oidHGZNpb7LwSMsX9qSSmh/aXakNjD4xx/0HQtudXH2pQZxSbD1ZR32xljgtHD357TQ6xIb6cOiLOZdtU9HX9cf3wNpt4cdl+p21jnqM69Psd+s1jNKVfBFvzqt2iXUzb/GS7VBKjHIVKYnqoLYkZ4ObVSdWNLeRWNDIq2VjdxJfvLcPLJJjW3zVVSftL61i5r5zLp6Ti7QGzkSudExPsx/kTkvhqSyHl9c1O2UZaVCAjEkN0nYxxSr9IWm3SLXr9xIf6EeLnxe4i1S5GOTJ1lu6hvMpGTAKSwt27Z9J2Ry+A0QYriVm+p4zxqeEE+3m7ZHufOkYFvmhSiku2pxjHVdPSaLHZ+cSJXaFPGxHP1rxqSp3YpftoxiVr7d3cYTRcIQRD4kPYrUpilKNQSUwP5VU1ER/q7/Z37TsKtCTGSAP2ldZqs2nPGuyasWFsdslXWwuYPTiaKIONk6M434CYYGYMiOL9dblYbXanbKNtZvhle8ucsv5jCQ3wJi0ygO351bpsv6v6RweRVaZms1aOzL2vvAaQV9no9qUwALuL60gM8yfU3zUlHp2xLlubxdZV47SsOVBOSW2zS+dmUozlymlpFNVY+GmXcyZLHBofTEywL8v36JPEAIxODmObm4yEmx4VQFVjq64TaCrGppKYHsqraiQ5IkDvMHpsX0md4Wat3pRTSYCPmWEuGgn5y80FhPh5HRqiXel75gyOJjrYly82O2c8FyEEswZFs3JfmdNKe45lVFIYxbUWp45S3FvSIgMByKlwjzmfFNdTSUwPWFptlNQ2kxzu3kmM1WYnq6yBQbHG6mG1IaeKsSlhLula3Wqzs2RXCScPj8PP2+z07SnG5GU2cdboBJbuKaXKSaPrzh4cQ63FyjadqnTGOBrvb3ODdjFpUSqJUY5OJTE90DbeQ3KEe1cn5VY20mKzM9BASUydpZXdxbVMSHXNRJQbsiups1g5aVisS7anGNc54xJptUkWOqkr9JR+2jG93lFd6mptc7y5Q4PZlIgAhICc8ka9Q1EMSiUxPVBQpSUx7j5n0j7HBJZGqk7amleNXWqjjLrCj5kl+HqZ1Ai9CsPiQxgUG8S325wzum5kkC/9owPZmKNPN+cAHy+Swv0PTVxrZH7eZhJC/VVJjHJEKonpgbI6bTyJ2BDjjHDbHQfKtBNE/2jjJDFtvaVcMfielJKfdpUwY0AUAT5eTt+eYmxCCE4ZHsem3CqnVSlNTItgU24Vdrt0yvqPZVBs8KExrowuOcKfvEpVEqN0TCUxPVDmGBQrOti9u+PmVzUSFeRDoK9xLuC7ilzXWyqvson8qiaOG+SartyK8Z04NBabXbJsb6lT1j8hLYKaplb269R9eGBsEFllDbo1Lu6K+FB/it2gEbKiD5XE9EBZXTMBPmZDXfy7I6+yiUSDNU7eVVR7qO7e2dZla3PJTHHRBJOK8Y1MDCU62JefMp2TxIxPdQw6p9PIuQNjgmmx2cmpMH4JR2yIHyW1Ft1KrRRjU0lMD5TWNRPj5qUwoJXEJBtorBtLq42ssnqGxbumofH6rEoiAn08YiZypXeYTILjB8ewcl8ZNidcPFMjAgj0MbOrSJ92KW3TpLjDQHLxoX602iSVjc6p2lPcm0pieqCszuL2VUl2u6SguokkA5XE7Cupxy5xWUnM+uwKJqVFYDKpGauV30zpH0GtxcoeJ/TiMZm0IfUzC/WZF6jtpiW/Sp8Ztbuirc1hcY2qUlL+l0pieqCsrtntk5iSOgutNmmoUYezyrW7w/4uKBkpr28mv6rpUPG+orSZlK5VL653VDf2tqHxwewqrkVK11eTRAT6EOBjdoskJj5UJTHKkakkpgcqG1qICPTRO4weaTsxtJ0ojOCgo57eFYMItt0JD090TamP4j4Sw/xJCvdnfZZzxnMZFh9KncWqSyIhhCAp3J/8KuO3iYlrS2JU416lAyqJ6SYpJbUWKyEuml3ZWcrrtXpmI014mFvZSEywL/4+zh85N8ORxLhqagPFvUxIDXfayLqH2qWU6zMGSlJ4gFuUxIQFaOfYatUmRumASmK6qanVhs0uCTHQhIndUeHoJh5loGqxgxWNpEa6po1OZlEtiWH+hAW4d4ma4hzDE0IpqrFQ6YTxYtqO8YM6DeTmLiUxvl5mAnzMVKtJIJUOqCSmm2qbrAAE+7l39+pyRxITaaBqsYOVrptUc19JHUPijDPdgmIswxK0EjpnNMCNCfbFz9tErk7dnKODfKm1WGm22nTZfleE+XtT3aSSGOV/qSSmm+os2g/KE6qTgn29DDPpod0uKatvdkkbHSklBysbSXXMlKsoh2vrIZdRWNPr6xZCkBIRQK5Oo9FGOqqQqxqMnxyEBfiokhilQyqJ6aZaRxLj7iUxFQ0tRAQZpxSmuqkVm126pI1OeX0LjS02Utx8Ak/FeSICfYgK8iGrzDlVPikRAboNqR/p+N23lcYaWViAt2oTo3RIJTHdVGvRqpPcvU1MbVOrS4b276y2E6orkpiDjouHKolRjiY5IoA8J7UdiQ720y2JiHIkMRVOmh+qN4UFeFOlkhilAyqJ6abGZq0eOdDNJwxsbLEaah/KHZNqRrqgdKigWuuZYaQxchTjSYkIOJTw9rboIB8qG1qcMirwsUQGajcKFW5QEhPk60Vji/Hb7iiup5KYbmqxaT8oHy/3/gjrm20E+hqjPQxAueOuMNoFJTEVLiz1UdxXSkQAhdVNtDphssTIIF/sEl1KGdqqwuscpcpG5udtxtKqkhjlf7n3FVhHLVbthOZtdu+h6htbrIaawLLe0tbry/lVXJUNLZgEhqpOU4wnNsRPSzScUO3SlkDrUaXU9rtvaHGPJKZJJTFKB1QS000tNq34191LYhqabQQYqDqp0XFCdcVAdxUNLYQH+Kg5k5SjahuV2xkTEP42kJvre974epkQAprcoJrGz8uEpdWuyxQNirG59xVYR20lMb5m41TFdIfWJsY4+9B2Qg1wQUxVDS2EG2h8HMWYwgN8iK6vJP7MU6G4uFfX3Zas61HKIIQgwNvsFm1NfB1DQDRbe79KT3FvKonpprYkxt1LYqx2idlAVWKNrTa8zQJvs/M/16ZWm0uSJcW9hQd6c8fqjwjZuA4ee6xX1+3vuDjrVRoS4Ot1qPTTyNrGsWpuVUmM8nu6XoGFEKcKIfYIIfYLIf7UwetCCPGc4/XtQohxnX2vs3lKEmO3S8zCOElMU4vt0Ind2VqsdnxckCwpbszfnyHxoVy+9XuElPDSSyAE+PdOj7a2JFqvJMbXy+QWiUHbedYdRhfuiaK6Iu7ceifF9b1b4ufJdDuDCyHMwAvAacAw4GIhxLDDFjsNGOj4uwF4qQvvdSq7o27W3ZtT2KXEbKCdsNklXi5KLFqsdrdPQhUny8rCcv6FNHk5erAFBMCll0J2dq+s/lBJjE6NVoUAd2hlIv7nP57p8RWPs6NmB48t790SP0+mZ4vOScB+KWUWgBDiY+AsILPdMmcB70qtNdc6IUSYECIeSOvEe53K5Ci9kFI7EbgjKSV2qdWNG4mrGu+12OwEufmIy4qTxcfjGxEG9laknx/CYoGQEIiL65XVt/329EokBEI1ljUA/yf8sVgthx6/tPElXtr4En5efjQ9aPyZxvWk5xk8Echr9zgfmNyJZRI7+V4AhBA3oJXiEBsby7Jly3oUdJvcXK2nwtJly5xWklFfX99r8XakrTQpLzeHZcsKnbadwx1tvwoLm2lttTp1v9vU1jZBs+jVbTn7O9OTp+7bsfZreGYmLWecQeHpp5OwcCE+O3eS0UufQ7VFq8rZv3cvyyy9U7rT3rH2zWJporik2fDf696DWu+tNWvWEOZr8rhj8f0J7/NS1kssK12FjWZ8Tb7MjJrJzf1v9qj9dAY9k5iOrvyH3xIcaZnOvFd7UspXgVcBJkyYIGfPnt2FEI8sQ+6HfXuYedwsp1VJLFu2jN6KtyM2u4QfFpGWls7s2QOdtp3DHW2/fqnZiVd5oVP3u03krjX4e5uZPbvD/LdbnP2d6clT9+2Y+7ViBaDdOXHddQAcZekuKa6xwLKfGTJkMLMnpfTSWn9zrH0L2LCUmJgwZs8e2+vb7k3563IhcyfTpk0jJtjPI4/Fnxb+xM+lv2DCh1bZysCUgZx78rl6h2V4eiYx+UByu8dJwOHFAUdaxqcT73WqthoYuxsXxZpNApPAKSORdpdAq6JzBW+zoMVA+670PZ7Stk7puZKGEgYFnkto8xwmjsmkqL5I75Dcgp5JzAZgoBAiHSgALgIuOWyZb4DbHG1eJgM1UsoiIURZJ97rVO3bxLgzHy+ToS7kPl6mQz2/nL8tM7VNrh9kTFHaWB2DZppN+jQwb7ba8XWDxu1ufprtlC8u/IJLXltHeWUVL8y7Ve9w3IZuSYyU0iqEuA34ATADb0opM4QQNzlefxlYBMwF9gONwNVHe68r42+7c7K5eRbjY3Zd0tAZAT5eNLXasNmd32vK18uk5mNRdFXfrI3REqTT1B+WVptLRsfuKU8ZXPRYrHapSuW6qFO/HCHEP6WU9x/rua6SUi5CS1TaP/dyu/9LoMOUtKP3ulLbYGytVju48fyBPl5mQ42C2XYyb2q1Of3EHh7gzY58VRKj6KfOoh1/wTr1kmtqtR0aSM7I2m42/HyMX2rUEzaVxHRZZ4+Ikzp47rTeDMTdBOg4XHhv8nVh9U1nBDhm1G5odv4oouGBPlQ2tqgupopu9CyJkVJiabXj5wbVSZZWG0Lg8YNTakmMymK64qi/HCHEzcAtQD8hxPZ2LwUDq50ZmNG13b24w7wjR+PnbawqlUDHZJT1zVZinbytiAAfWqx2GltshprJW+k72pIYPY6/thJYXzcoiWlqseHnZTbcmFa9TZXEdN2xfjkfAt8DTwLth/avk1JWOi0qN9A20qaREoDuCPX3psZAjVtD/bVZfV0RU9vkjxX1LSqJUXRRXq+NNxUV5PqJSNsatbf95ozMYnWPtjs91dRqI8yzC5t63bE+LjNQi9Yupa7dH0KICOeGZmwBPr+13XBnIQZLYqKDtQZGZXXNTt9WQqg2/01BtRoRU9FHSa0FHy+TLolEZaOWQEW4wUzu7lLt1VONzVb8vFRRTFcc6/ZzE78NLpcCVDn+HwYcBNKdGZyR+TsamOk1cVtvCfX3JqusQe8wDnFlEpMcoSUxeVWNTCXS6dtTlMMV11iIC/HTpZqkskFLYsIDjJ/E1FusfaK0tKHFhq/nFzj1qqOmtlLKdCllP7SuzGdIKaOklJHA6cAXrgjQqDylTYzRqpMiAn0QwkUlMWH+mATkVzY6fVuK0pGSWguxIfp0b6xq0H737lASU9XY4hbJVk81tdjwM6uSmK7obPncREeXZgCklN8Ds5wTknsI8dOKf2stxkkAuiPU35taSyt2uzF66HibTUQE+FBW7/wkxttsIj7Un7wqVZ2k6KOwpok4R7Wmq7VVJ4UHGr9NTHVjK2EBxo+zJ1qsdlpsdvpAgVOv6mwSUy6EeEgIkSaESBVCPAhUODMwo2trFFrtOBG4q4hAH6TU7nSMIjbEj0IXtVPpFx3I/tJ6l2xLUdqztNrIr2oiPSpQl+2X1lowCa2XntFVN7V4fBLT1jTBV5XEdElnk5iLgWjgS8dftOO5PivQx4y3WVDV6N4lMbEhfgCU1Dq/5KOz0qICOFjhmiqeIXHB7Cmpw2qgqReUviG3ohEpoX+0PklMQXUTcSF+eBl87BUpJVWNrR5fndTYqnW391NtYrrkqEevEOIBIcRYKWWllPJOKeVYKeU4KeUf+noXayEEYQE+bl8S81sSY9E5kt+kRASSV9WozbLtZEPjQ2ix2skuN07jZqVvyCrTSgD7Rwfpsv2CqiYSw/WpyuqKplYbLVY7YR6exNRZtCTGX/VO6pJjpeDZwJ1CiC1CiLeFEBcKIcJdEZg7CA/wPtQ4zl3FhWpJTLGBkpi0yABabdIlVUpD40MAyCyqdfq2FKW9A44kRq/qpILqJhLDjJ/EVNS3dQX37Oqktt5iQT4qiemKY/VO+lhKeZWUcizwH6Af8IUQYoUQ4i9CiEkuidKgwgJ8DNWWpDtign0RQuvqaRSpkdpJPdcFVUr9o4Pw8TKxI7/G6dtSlPYyi2pJiQjQpeuwzS4prrGQ4AZJTFspsV4NoF2lqi2J8excrdd1ujJUSrlFSvmklHIOWhfrDOA6p0XmBsIDvKl28zYx3mYTkYG+hqpO6udoI9B2p+pMPl4mRieFsiG3yunbUpT2tufXMCopVJdtF1Y3YbVLksIDdNl+VxQ5brDiHaXGnqqtt1iwKonpkk4lMUKIjUKIW9uqkqSUtVLKz6WUNzg3PGOLDvaltM44F//uSgr3J6/KOGOlxAT7Eh7gzS4XVfFMTIsgo6CGxhbnTzqpKAAV9c3kVzXplsTsd9wgDIzVpz1OV7SVEsd5eBLTdkMc6K2SmK7obEnMRUACsEEI8bEQ4hTh6TNxdUJ8qD9Vja1uP39SWmQAOeXGSWKEEAxLCHFZO5WJ6RFY7ZItB6tdsj1F2VGgVV+OTAzTZfsHHMMKDNCpUXFXFNVYCPQxE+zhA6hUNrQQ4GPGR3Wx7pJOJTFSyv1SygeBQWiTQr4JHBRC/LUvz6HU1rPHSO1JuiMtKpDCmiZDJWND40LYU+yars/jU8MRAtZn9+kOd4oLbc6twiRgRGKILtvfV1JPZKDPofGujKy4tom4UH2mZnClqoa+MSpxb+t0mxghxCjgaeDfwOfAfLTJIX9xTmjGF2/Anj3dkRYZiJSQZ6Dh94clhNBstZNT4fyuzyF+3oxJDmP5nlKnb0tRANZmVTAyMZRgP31ace4vq2dAjPFLYQAKqi3Ee3ijXoCKhha3mALCaDrbJmYT8AywHhglpbxDSrleSvl/QJYzAzQyTyqJAQw1VsrwBK2twHYX9Ro6fnAM2/JrPKKNk2JsjS1WtuZVM7V/lC7bt9sle4vr3KI9DEBuRQOpkcZvgNxT2jxant3uxxmONdjd3UKIu4FPgO+AeODWds8jpTzX+WEakxHHWOmOdEeXZleUenTWgJgggn292OiiXkNzhsQAsGxPmUu2p/RdG3OqaLVJpvbXZ+b0nIoG6pqtjEzUp1FxV1Q1tFDd2KrbWDquVFxr8fgeWM5wrJKYYMffGOBmINHxdxMwzKmRuYEgXy+C/bwoctE8P84SGuBNdLAve4qNM4eQ2SQYlxrOphzXJDHDE0KIDfHll12qSklxrlX7y/EyCSak6jNuaFuj4lFJYbpsvyuyHTdWaZGencQ0tdiobmz1+B5YznCswe7+KqX8KxAFjJNS3iOlvAcYDyS5IkCjSw4P4KCB2pJ019D4EJd1ae6sCanh7Cmpo8YFY/EIIThpWCzL9pbS0Ky6WivO81NmCVP7R+oyyB3Atrwa/LxNDHSDNjHZZVoSk67T/FKu0laaH6eqk7qssw17U4D2Q9O2AGm9Ho0bSosKcMnIss42NC6Y/aX1tBpoIsTxadqd6uaDrimNOWtMIpZWO0syS1yyPaXv2V9aT1Z5AycNi9Uthu351QxPCDX8xI+gVX2ZhHaz6MmKarTSfFWd1HWdPYrfA34VQjwqhHgErYHvO84Ly32kRmqTFbr7LMhD40NosdnJKjNOu5gxyWF4mwXrsitcsr3xKeEkhPrxzbZCl2xP6XvaEuQTh+qTxLRY7ewsrHGL9jAAWeUNJIUH4ONl/ISrJ/rKgH7O0NlxYp4ArgaqgGrgainlk06My220TVZY5OY9lIbEBwMYqkopwMeL8anhrNhb7pLtmUyCM8YksGJv2aHJ2BSlN/2YWczIxFDd5izaUVCNpdXO5HT3GN5rd1Etg2KD9Q7D6YpUEtNtXZk7abOU8j+Ovy3ODMqdpBqwZ0939I8OwsdsMtxszrMGxbCrqJZSF/UAO2dsIla75MstBS7ZntJ35FY0sOVgNXNHxusWw7osbUDHSW6QxFhabWSXNzAs3vOTmPyqRiICfQjw8exRiZ3Bs8voXCDtUBLj3u1ivM0mhiWEsNVgQ+/PGhQNwIp9rimNGRIXwriUMD5Yn4uU0iXbVPqGLzYXIAScPTZBtxjWZVUwODaYyCBf3WLorD3FddilVtXt6XLKG0nrA2PhOINKYnooJtgXP2/ToVb07mxcSjjbC6oN1bh3aHww0cG+LN/ruvFbLp2cSlZZA2uzXNMWR/F8Umqle1P7Reo2+myrzc7GnCom9zN+KQz8VrXdF5KY3IoGj+9G7iwqiekhk0kwICaIfaV1eofSY2NTwrC02tldZJx9EUJw3MBoVuwtc1lyNW9UPGEB3nyw7qBLtqd4vo25VRysbOTccfqNTLE1r5qmVhtT+ukzyF5X7SqqJdDHTEqEZ5dQWFptFNZYDo2crnSNSmJ6weDYEHYXG+fC313jUl3bpbmzTh0RR01TK2sPuKZkxM/bzAUTklmcUWyo+aQU9/XBulyCfL04dUScbjH8srsUs0kwfYA+0x101a6iOobEh2AyefbEj23nmL4wtYIzqCSmFwyJC6asrtnte7QkhPoRG+LLFoMlMTMHRhHoY+b7nUUu2+bV09MwCXh9ZZ+dGkzpJWV1zXy3o4j545MI0mmAO4Clu0uZkBpOqL8+k052hdVmZ0eB+3QF74m2OetUdVL3qCSmFwyK01rP73Hz0hghBONSwtmQU2WoRq1+3mZOGBrLDxklLhuPJz7Un3PGJvLxhjzK65tdsk3FM33860FabZLLp6bqFkNBdRO7i+s4YWiMbjF0xe7iOppabYxNCdM7FKdrGyxVJTHdo5KYXjDkUBJjrO7J3TG1fyQF1U2Gm0ph7sg4KhtaWJ9d6bJt3nBcf1psdt5ane2ybSqepdVm54P1B5k5MIr+0foN8//Lbm1OsOOHuEcS01YaPC5Fn/mlXCmrvJ7wAG9CA4xfQmZEKonpBTHBvoQFeLOnxL1LYgCm9dfqy1fvN1bPnFmDYgjwMfPNVteNpjsgJohTh8fxzppct68qVPTx5ZYCimstXDMjXdc4lmSWkBIRoGsi1RWbD1YTHexLUrg+PblcaXdxHYPjPH8sHGdRSUwvEEIwJC6YXQbq1dNd/aMDiQ3xZc0B14zL0ln+Pmbmjoxn4fZCGltcN0Hj3ScNorHFygtL97tsm4pnsNklLy7dz4jEEGY7xjvSQ2VDC6v3lzN3ZDxCuEcj2c0HqxiXEuY28XaXlJK9xXUM7gOjEjuLSmJ6ycjEUDKLag01xkp3CCGY3j+KtQcqsNuN0y4G4PzxSTS02Fi8s9hl2xwYG8x545J4b20uBdVNLtuu4v4Wbi8kp6KR2+YM0PVivHhnMTa75PRR+o0U3BUV9c3kVjT2iaqkguomGlpsDI7z/LFwnEUlMb1kVFIYLVa72zfuBa1dTEVDi+GqxyalR5AaGcCnG/Ndut27ThoEAp5Zstel21Xcl80ueWHpfgbGBHHyMP26VYOWTPWLCmR4gntcKNumRpiQ5h6D8vVE2/VicJx7VPMZkUpiesmY5DAAtuVX6xpHb5g5UCv6XrbHdaPkdoYQgvnjklibVeHS8VsSwvy5aloan2/OZ7sHfL+K832+OZ+9JfXceeJAXcc5qW62sy6rgtNHuU9V0uoD5QT5ejE6yfO7V7fdKA5U1UndppKYXpIU7k9EoA/b8qr1DqXH4kL9GJ4Qws+7SvQO5X+cOz4Jk4CPfnXtaLq3HT+AqCBfHv5qJzaDVbMpxtLUYuPpH/cyOimUeTpO9giwrtCGXcIZo/Wbr6mr1uwvZ3J6BF5mz7887S2uIzHMnxA/1TOpuzz/KHERIQSjkkLZnl+jdyi94oShsWw+WGW4XjmJYf6cNCyWj349iKXV5rLthvh589C8oWzLr+GTDXku267ift5cnU1xrYU/zx2qa+mHlJIVBa2MTQlzmzv9guomcioameYmowr31O7iOgbFqqqknlBJTC8anRTG3pI6l/aecZaThsZil9oon0Zz1bR0qhpbXdrdGuDM0QlMTo/gXz/spkINgKd0oLTOwkvLDnDi0Fgm6zxH0eaD1RTWSy6ckKxrHF2xer/WK3L6APeY36knGlus7C2pY2RSmN6huDWVxPSiMclh2CVsy3P/0pgRiSHEhvjy827jVSlN6RfBkLhg3lqT49KRhYUQPH72CBqarTzyTYbLtqu4j78t3EWL1c6f5w7ROxQWbMjD1wynu1lVUlSQT5/ocpxRWItdwqg+MLWCM6kkpheNSw1HCNiQ47pRZZ1FCMHxQ2JZvqfMpdU2nSGE4KppaewqqnXpCL4Ag2KDufOEgSzcXsR32103l5NifCv3lfHNtkJunt2ffjoPKlffbOXb7YVMivPSdb6mrrDZJcv3ljFzYLTbNELuibb2k6OSVRLTEyqJ6UWh/t4MjQthfbaxRrvtrlNHxNHQYmPFXmP1UgI4a0wikYE+vLTsgMu3fdOs/oxOCuWhr3ZQVqeqlRSwtNp4+KudpEUGcPPs/nqHw6cb82hssTEn2T0SGNAGuKtqbHWb+Z16ant+DfGhfsQE++kdiltTSUwvm5QewabcKlqs7j3oHcC0/pFEBPrwrQFLHPx9zFwzI53le8vY4eLG1F5mE/93wWgaWmz86fPthposU9HHM0v2klPRyONnj8DP26xrLDa75O01OYxLCaNfmL6xdMVPu0rwNguO03F0Y1fanl/NqD7QjdzZVBLTyyanR2Bp1aaRd3feZhOnjojjp8wSQzZWvmJqKiF+Xjy/dJ/Ltz0gJpgHThvCz7tLeWOVmiCyL1ufVcGrK7O4eFLKoTGW9PTL7lJyKxq5dkY/vUPpkp93lTI5PbJPdDeuaWwlp6KRUapRb4+pJKaXTUrXRpn81cVtNZzljFEJNLXaDs2CayTBft5cNT2dHzJKdBkp+appaZwyPJZ/fL+bzY5Zd5W+pc7Syj2fbiMlIoCH5g3VOxwA3liVRUKoH6cMj9U7lE7LKW9gf2l9n6lKahsUdbRKYnpMJTG9LDLIlwExQR7TLmZSegQxwb58u8213Zk76+ppaQT6mHnuF9eXxggh+Nf80cSF+nH7h1uoMtiYOorzPfpNJoXVTTx9wWgCDdCAdkd+DeuyKrlyWppbDRb3k2NgzROHuk/i1RMbcyoxCRiTEqZ3KG7PfY5yNzI5PYIN2ZUe0S7GbBLMGxXP0t1lVDca7yIdHujD1dPT+W57ETt1qMIL9ffmhUvGUVbXzK0fbsaqRvPtMz7ZcJDPN+dz25wBjE81xjw/z/2yjxA/Ly6ZnKJ3KF3y3Y4ihsWHkBwRoHcoLrE+u5LhCaFu03PMyHRJYoQQEUKIJUKIfY5//2e6UiFEshBiqRBilxAiQwhxZ7vXHhVCFAghtjr+5rp2D45u5sBoGlpsHlPFcN64JFpsdr4xaGnMDbP6ER7gzT8X79Zl+6OTw3jy3JGsOVDBh7uMl+gpvW9nQQ0Pf53BjAFR3HniIL3DASCzsJYlmSVcO6MfwW7UriSvspEtB6vdamqEnmi22tiaV32o6YHSM3qVxPwJ+FlKORD42fH4cFbgHinlUGAKcKsQYli715+RUo5x/C1yfsidN21AJF4mYciuyd0xIjGU4Qkhhh1uP8TPm1vnDGDlvnJW7SvXJYbzxidx46x+/JJn5b21ObrEoLhGTWMrt3ywmYgAH/5z0RjMOk7w2N7zS/cR7OvFVdPT9A6lSxY6ej+ePkrfeaZcZWdBDc1Wu0pieoleScxZwDuO/78DnH34AlLKIinlZsf/64BdQKKrAuyJED9vxqWEs9xDkhiACyYkk1FYq0uVTWdcPjWVxDB//rF4F3adqnTuO2UIo6PNPPptJksyjTfSsdJzLVY7N3+wiaKaJl64dByRQb56hwTAnuI6Fu0o5qrpaYT6u08pDMC32woZmxLWp6qSACamqSSmN+iVxMRKKYtAS1aAozZJF0KkAWOB9e2evk0IsV0I8WZH1VF6O25QFBmFtR4zGNpZYxLw8TLx6UZjlsb4epn54ymD2FlQy+eb83WJwWwS3DzalxGJodz64WbWZ3lG425FI6Xkoa92sOZABf84dxTjU41z2vn3D3sI9vXimunpeofSJftL68ksquWMUX2jKglgQ3YlA2OCiAj00TsUjyCcNVCXEOInIK6Dlx4E3pFShrVbtkpK2eEZQQgRBCwHnpBSfuF4LhYoByTwOBAvpbzmCO+/AbgBIDY2dvzHH3/c7X3qipwaG4+utXD9SB+mJ3bvzqi+vp6gIOPMcPrSVgs7K2w8MzsAH3P3i9CdtV92Kfn7eguljXaenBlAoLfri/nr6+uRPoH8fX0T1c2SP03yIzXEfQYcOxqjHY+9pbP7tfBAC5/ta+XM/t6cO9A4F6A9lTae/NXC/EHenN7v93EZ/Tv7cl8L3xxo5enZ/oT7df6e2uj7dSQ2u+S2XxqZHO/FVcM7LsXr7X2bM2fOJinlhF5bodFIKV3+B+xBSzwA4oE9R1jOG/gBuPso60oDdnZmu+PHj5euYrPZ5bjHfpR3fLS52+tYunRp7wXUC1bvK5Op9y+UCzYc7NF6nLlfO/KrZdqfFspHvt7ptG0cTdu+5Vc1yil//0mOf/xHuae4VpdYepvRjsfe0pn9+uTXgzL1/oXy9g83S7vd7vygOslut8szn18lp/z9J9nUYv2f1438nVltdjn17z/Jy15f1+X3Gnm/jmZTbqVMvX+hXLit8IjL9Pa+ARulDtd5V/3pVZ30DXCl4/9XAl8fvoDQZgB7A9glpXz6sNfatwA7B9jppDi7zWTShs9evrcMq839u1oDTO0fycCYIN528ezRXTEiMZRLJ6fw7tocdhXV6hZHYpg/7183GZMQXPTqOnYX6xeL0jPfbCvk/i+2M3NgFP8+f5ShJidctKOYbXnV3HXSIN2nO+iq1fvLKayxcOHEZL1DcZkVe8sQAqYPiNQ7FI+hVxLzD+AkIcQ+4CTHY4QQCUKItp5G04HLgeM76Er9LyHEDiHEdmAOcJeL4++Uk4fFUt3Yyq8eMKs1OGaPnp5GRmEtm3KN2338jycPJtTfm4e+2olNx3Fb+kcH8cmNU/Exm7j41XVkFqpExt0sySzh7k+2MjE1glcvn4Cvl3ESBUurjX8s3sXg2GDOG5ekdzhdtmBjHmEB3pw0rG8McAewcl85o5LCCAswTnWku9MliZFSVkgpT5BSDnT8W+l4vlBKOdfx/1VSSiGlHCUP60otpbxcSjnS8dqZ0tFI2GhmDY7G18vEjxme01PlnLGJhPh58daaHL1DOaKwAB8emjeMTblVvKtzd+f0qEA+uXEK/t5mLn5tHRs9JKHtC37IKObWDzYzPDGUN66agL+PcRIYgBeX7ievsolHzxxumG7enVXV0MKPGSWcPSbRUImhM9U0tbI1r5rjBkbpHYpHUSP2OlGAjxczB0bxY0axYatfuirAx4uLJqWweGcxRTVNeodzROeOS2T24Gj+tXgPeZWNusaSGhnIJzdOJSLQh0tfX88PGcW6xqMc2xeb87nlg80MTwzh3asnGW7wuJzyBl5ensVZYxKY2t/9qia+3lpAi83OBRP6TlXS2gPl2Oyyz8zS7SoqiXGyk4fHUVhjYWeB51QlXD4lFSkl76zJ1TuUIxJC8PdzRmI2Cf70xXbdk8jkiAA+v3kaQ+NDuPn9Tby3zrifXV/33toc7l6wjcnpEbx/7WRCA4yVwEgpeeSbDHy8TDw41xiTTnaFlJIP1h9kVFIowxJC9A7HZVbsKyfI14sxyWF6h+JRVBLjZCcMicEk4MdMz7n7To4I4LSR8by/Lpeapla9wzmihDB//nTaEFbvr+CD9Qf1DoeIQB8+un4Kxw+J4eGvdvLoNxm0ekijb09gt0ue/H4XD3+dwYlDY3nzqomGmNTxcN/vLGb53jLuOmkQMSF+eofTZWsOVLCvtJ4rp6bpHYrLSClZsbeMKf0i8XajiTndgfo0nSwyyJeJaREs3uk5SQzAzbP6U99s5X2DlyhcMimFmQOj+Nt3mewvrdM7HPx9zLx82XiunZHO22tyuPyN9VTUe8aAiO6sscXKzR9s4pXlWVw2JYWXLxtnyN4+FfXNPPzVTkYmhnLl1FS9w+mWt1bnEBXkw+mj+8Y0AwC7i+vIr2rihKFHHddV6QaVxLjAaSPi2Fdaz55i/S+ivWVEYiizB0fz5qpsmlpseodzRCaT4P/OH02Ajxd3fLSVZqv+sXqZTTx8+jCevmA0mw9Wc+bzq9meX613WH1WRZOdC19Zx5LMEv5y+jAeP2sEXga9W37kmwxqLa08df5ow8Z4NLkVDfy8u4RLJqX0mQa9oPVyEwKVxDiB+/0K3NC8UQmYBHyzrUDvUHrVLbMHUNHQwicb9K+qOZqYED/+ed4oMotqeeqHPXqHc8i545L47KapSCk576U1vLYiS7d5n/qqpXtKeWRNE1ll9bx2xQSumZFuqHFg2vt+RxELtxdx5wkDGRwXrHc43fLu2lzMQnDpFPcsRequJZkljEkOIybY/ar/jE4lMS4QHezL9AFRfL21UPcGpr1pUnoEE1LDeXVFFi1WY7ftOGlYLJdNSeG1ldks3VOqdziHjEoK47s7ZjJncAxPLNrFVW9v8Jj5tozMarPz1A97uPqtDYT7mfj29hmcMNS445WU1TXz0Fc7GZEYwo2z+usdTrfUN1tZsDGPuSPjiXXDtjzdVVjdxI6CGk4e1tEsPEpPqSTGRc4ak0h+VRObD1brHUqvuu34ARTWWFhg0Ikh23tw7jCGxAXzh4+36t7tur3wQB9euXw8fzt7BOuzKjj12RV8t73IoxJeI8kpb+CiV9fx/NL9XDQxmYen+NEv2rjz8Njtkns+3UZ9s5X/O3+M2zYM/WBdLnUWK9fOcK9JKnvqp13aOGF9aVA/V3LPX4MbOmV4LD5eJr7dVqh3KL1q1qBoJqSG899f9mFp1b+9ydH4+5h55fLx2KXk5g82GSpeIQSXTUnl29tnkBDmz60fbuaG9zZRUmvROzSPYbdL3l2bw2n/WcnekjqevXAM/zhvVI8mM3WF11dlsWJvGQ+fPsxtq5EsrTZeX5XNjAFRjO5jXYyXZJbQLyqQATHGTZTdmUpiXCTYz5sTh8awcHuhx8ylBNrF94+nDKaktpn31hq7pxJoA889e+EYdhbU8vBXOw1X2jEoNpgvb5nGn+cOYcXeMk58ejnvrcvVdfoET3CgrJ7L3ljPX77OYFJ6BD/eNYuzxybqHdYxbc2r/v/27js+qip9/PjnzKT33hMIvSSEGnoTqYoKNhAUsVe+6Orqrltc3VXXuq6KqKhgAyuKiFiJ9B5K6CGEkEpCSO8z5/dHoj90EQIkuVOe94t5zWTm3vCc3CnPnHvOeXh65QEmJkQwY2Cc0eGct0+2ZVNYXstdo+3zVNj5Kq2qZ2PGCemFaUWSxLShy5KiKaqoY216kdGhtKhBHYIZ3jmEeSnplNfY7roxPxvTPZw5F3Xi423ZNjlF3MVs4rYRHflm7ggSovz56+dpXPLfNaw/7FjPm7ZQVdfA0yv3M+E/q9mdU8qTUxNZOHsAEf62PyajtKqeOYtTCffz4KmptlV48lw0WKzM/+kwvWMDGNzB/lYXvhDf7Mmn3qK5pJfzTCdva5LEtKHR3UIJ9HLl463ZRofS4h4Y15WTVfW8tTbT6FCa5f8u7sLF3cN49Mu9pNjQQN9TtQ/x5oNbBzJvRl/Kaxq47o1N3PHuNo4UVRodms2zWjXLduYy9vnVzEs5zGVJ0fz4h1FMT46zi2TAYtXcuySVvNJq/ju9j82tGnwuvtyVS/bJau4e3cku/vYt6ctdubQL9iIx2t/oUByWJDFtyN3FzNS+MXy7N9/hFjhLig1gfM9w3liTYReza8wmxYvT+tA13Jd7Pkhlf75tloVQSjEpMZIf/jCSP4ztwk9Np5ge+HgnWSdsZ3CyrdBa89PBQia/vJY5i1Px9XDho9sH89w1SYT6uhsdXrM9++0BVh8s5B+XJdCvXaDR4Zy3BouVl35Ip2u4L2O6OdcaKYXltaxLL2JyryinS97akiQxbezaAbHUWzRLUx1rzRiAhyZ0o6bewvPf2c5aLGfi7e7Cmzf2x9vdzM0Lt3K83HYH0Xq4mrl3TGd++uMoZg1uz7KduVz0XAp/+myX9MzQmLysPVTE9Dc2MuutzZRW1/PCtUl8NWc4yfFBRod3TpbvyuXVlMNMT47jOjseBwPwWWoOGUWV3De2CyY7q7R9ob5Oy8OqYXJSlNGhODRJYtpYl3Bf+sQF8OGWYzY3qPRCdQj1YdaQ9izZcow9uaVGh9Mskf6evDlrAMWVdcx+ewtlNj6mJ8zXg79N7sHqB0dz3cA4Pt2Ww0XPpXDrO1vZlHHC4Z5TZ2OxapbvyuWyl9cx881NHC6s5B+X9eTHP4xiSp8YzHb2wbk7u5QHP95F37gAHr2sh9HhXJDaBgsvfn+IXjH+jO/pfANbv9yZS9dwX7udUWYvJIkxwLX9Yzl0vILUYyVGh9Li5lzUmQBPVx5fvtduPlATov2ZN7MvB/LLuWXRVpuaev17Ivw9eOzyBNY+PJp7R3dia2Yx176+kckvr+X9TUdtPhm7UMfLa5iXks6oZ1dxzwepVNY28NTURNY+NJpZQ9rj5mJ/b23HiquYvXALQd5uzJ/Zz+6X5V+8KYuckmoeHN/V6U6n5JRUsyXzJJOdqD6UUezvle4ALk2KwsvNzIebbX+BuHPl7+XKfWO7sDGjmG/3FhgdTrON7hrG89f2ZktmMXe/v91uqkuH+Xpw/7iurH94DE9MSaS+QfPI0jSS//U99324g/XpRQ4zPbuuwcqq/ce56/1tDHnyR55eeYCYAC/mz+zLd/ePZJod1+Mpqarjxrc3U9dgYdFNA+yyOvWpquoaeHlVOoM6BDGsU4jR4bS5ZTsa1wO7tJecSmpttldn3gn4uLswuVcUy3bm8udLuuPvab8zD07nuuQ43t1wlH99tY+RXUJtshrw6VyWFEVZdT1/+TyNBz7eyfPX9Lab0xGebmauGxjH9ORYdueU8uGWYyzbkcvS1BxCfNwY2yOCiQkRDO4YbFcrvjZYrGzIOMHynXms3JNPaXU9gV6uzB7anunJcTa90m5z1dRbuO2dbRwrrubdm5PpFGb/px/eWnuEooo6Xrve+XphtNZ8vO0YA9oH0j7E2+hwHJ4kMQa5fnA7Ptx6jI+3HuOW4R2MDqdFuZhN/OOynly3YBMv/5jOA+O7Gh1Ss80c1I7S6nqe+eYAZqV45uoku0lkoHE2U6+YAHrFBPDXS3vw/b4Cvk7L54sdOSzenIWfhwtDO4UwtFMIwzqF0C7Yy+Y+ZHJKqll9sJCfDhSyLr2I8toGvN3MjO0RzqW9ohjeJcRue1x+q95i5Z4PtrM5s5j/Tu/DQAdYR6WgrIZ5KYcZ3zOcfu3sa1B1S9iedZKMwkrusNMaV/ZGkhiDJET7M6B9IO9sOMrsofF29UHZHEM6hTClTzSvrT7MFX2i7Orb5d2jO2Gxap7/7iAWrXnu6iRc7Kj34mcermYu7RXFpb2iqKm3sPpgId/tLWBdehFfp+UDEB3gSd92gSTF+NMrJoCEaD+83NrubaGuwcrBgnK2Z51k+9GTbMs6ybHiagAi/T24pFcko7qGMaqr/fToNVeDxcrcJTv4ft9xHr+8J5c5yCyWp1ceoMGieWSSfQ9MPl8fbcnGy83MJYkyHqYtSBJjoFlD2nPPB6mkHDhu0xV0z9cjl3Tnx/3HeWRpGktuG2Rz3/jPZM6YzphNime+OYBVwwvX2Gci8zMPVzPjekYwrmcEWmsyT1SxNr2I9elFbMss/qWml0k1lmboEOJNh1BvOoT6EBfkRZivO5X1Gq31OR/HmnoLeaU15JVUk1taQ1ZxFYcKyjlYUE7miapfxuyE+brTNy6QWYPbM6JLKJ3DfOzqOXMurFbNHz/dxVe783hkUneuH9ze6JBaxM5jJXy6PZs7RnYkLtjL6HDaXGVtA8t35XJpr0i83eXjtS3IX9lA43tGEOHnwcL1mQ6ZxIT4uPPwxG786bPdfLItm6v7xxod0jm5e3QnzCbFU1/vp67BwovT+jhEb4BSivgQb+JDvLl+UDugcWGuXdkl7MwuJf14ORmFlaxJL6Ku4dcDnN1/WkmQtxuebma83VzwcjPj5mJCa7BqjVVr6hqslNc0UFZTT3lNA1V1v57t9XOi1DnMhwkJEXSN8KNvXADRAZ4Om7ScymLV/OXz3Xy2PYf7x3bh1hGOcTpZa81jy/cS4uPO3U5WI+lnK3bnUVln4Ro7e6+zZ5LEGMjVbGLGwDie++4g6ccrHLLK6bX9Y/lkWzZPrNjH6G5hhPjYz6qpAHeM7Iib2cRjy/cy663NvDGrP34ejjUQGyDU150x3cN/lUxbrJrckmqyT1ZzvLyGDal78QuP4WRlHVX1FqpqGxOUitoGTEphUo0JkpebC+F+Hvh6uODn4UqAlyuR/p5EBngQ5e9JhL+HQySD56PBYuWBj3fy+Y5c7hndiXsv6mR0SC1m2c5cth09yb+vTMTXAV8jzfHxtmw6hHjb9SrL9kaSGINNHxjHSz+ms2h9Jo9fkWB0OC3OZFI8OTWRS/+7lr9+nsa8GX2NDumc3TQsnmAfNx74eCfXvraRRbPtfwpsc5hNitggL2KDGk8L+JccYtSo7gZHZb9qGyzMWZzKN3sKeHB8V+4e7TgJTGlVPY8v30dSjD9X9XPOXohDBeVsPlLMQxO6OUWPoq2w35P8DiLEx53Le0fx8bZjDldP6Wddwn25b2wXvk7LZ1nT2At7c3nvaN6cNYCjJyqZ+up60o9XGB2SsCNVdQ3c+s42vtlTwKOTezhUAgPw72/2c7KqjiemJjrcJIXmemfDUdxcTFw7wDmTOKNIEmMDbh/ZgZp6K4s2HDU6lFZz6/B4escG8Lcv9lBSYx8Lyf3WiC6hLLltEDX1FqbMW8dPBwuNDknYgePlNVz72kbWHirk6St7cePQeKNDalFbM4v5YFMWNw1tT88o56zWXF5Tz2fbs5ncK4ogbzejw3EqksTYgE5hvozrEc6i9ZlU1jYYHU6rcDGbeO6aJGrqLSzcU2c3JQl+q1dMAJ/fPZSYQC9mv72Zt9Yesdu2iNZ3sKCcKa809ty9cUN/rnGwb+l1DVb+vHQ30QGezL24i9HhGOaz7TlU1lm4YXA7o0NxOpLE2Ig7RnWktLqeJVscrxTBzzqG+vDg+K7sKLTw8dZso8M5bzGBXnxyx2Au7h7OY8v38qfPdlPbYPv1lkTbWp9exJWvrqfOYuWj2wc75AzE11cf5mBBBY9d3tNppxRrrXlnQyZJMf4kxQYYHY7TkSTGRvSNCyQ5Pog312T8z7RWRzJ7aDzdgkz8fdkeDhfa77gSb3cX5s/sxz2jO7FkyzGumb+BY8VVRoclbIDWmrfWHuH6tzYT4efB0ruGkBjjeKdZ9uWV8eIPh7gkMdIhE7TmWn/4BIcLK7nBQdb6sTeSxNiQO0d1JLe0xm4HvzaH2aS4vZc7Hq4m7v0g1a57MEwmxQPjuzJ/Zj8yiiq55L9rSD3umKcDRfNU11m478MdPLZ8Lxd1C+PTu4YQE+h4i77VNVi5/6Od+Hu6OeSsynOxcH0mQd5uXNJLVug1giQxNmRUl1C6RfgyLyXdYSoPn06gh4lnrkpib14ZT67Yb3Q4F2xCQgTL7x1GbJAXL26v5ckV++ymCrZoOceKq7jy1fV8sTOXP4ztwmsz+znkmkIAL/14iH15ZTw5NdGpB7IeLqzg+30FzBgY57RrHxlNkhgbopRi7sWdySisZNnOHKPDaVUX9wjnxiHtWbg+k+/3FhgdzgVrF+zNp3cO4aJYF15bncGUees4VFBudFiijSzbmcukF9eQfbKKt24cwL1jOmNy0KnGO46VMC/lMFf1i2FsD+c9jQSwYE0GrmYTs4a0NzoUpyVJjI0Z1yOC7pF+vPj9IYfujQH406Ru9Ij044FPdpJ90v7Hk3i4mrmhpzvzZ/Yjt6SGS15ay5trj2B18OPozCpqG3jg453MWZxK53AfvpoznNFdw4wOq9VU1TVw/0c7CPd152+TnbPA48+Ol9fw6bYcruoXY3crkTsSSWJsjMmkuO/izmSeqGJDnmOPr3B3MfPKjL5YLJo73ttGTb39jo851YSECFbOHc7wTiE8vnwvM9/cJIN+HVBq1kku/e8aPtuezZyLOvHR7YN/Wd3YUf3tiz0cKark2WuSHPZUWXMtWp9JvdXKrcMdo/aVvZIkxgaN7RFOQrQfX6TXO/zYivgQb56/tjdpOWX85fM0h1lzJczXgwWz+vPU1ER2Hith7As/8dpPh2lw8OPpDKrrLPxz+d7G6dMNVhbfOoj7x3W16yrnzbE0NZtPtmVz7+hODOkYYnQ4hqqobeDdDUcZ3yOC+BBvo8Nxao79qrNTSinuH9uFwmrNZ9vtdz2V5hrbI5w5YzrzybZs3tuUZXQ4LUYpxbTkOL67fyTDOoXy5Nf7mfzyOnYcKzE6NHGeNmacYMKLq1mw9gjTkuP45r4RDOwQbHRYrS6jsIJHlqaR3D6IOWM6Gx2O4ZZszqKspoHbR0ovjNEkibFRo7uG0cHfxH9/SLfracjNNXdMZ0Z3DeWxL/ew7Wix0eG0qKgAT964oR/zZ/aluLKWKfPW8cjS3Q5bK8sRnaio5eFPdzHt9Y1oDR/cOpAnpjhHteaaegv3fJCKu4uJF6f3dvgep7OpqbfwxpoMkuOD6BMn1aqN5tzPRhumlOLKzm7klFTzrgPXVPqZyaT4z7V9iArw5PZ3t5NTUm10SC1KKcWEhEi+u38kswa3Z8mWY4x6NoXXVx92iiTVXjVYrCxan8noZ1P4ZFs2t43owMq5w53qdMo/vtzD3rwynr06iUh/T6PDMdyHW45RUFbLXOmRsgmSxNiwniFmRnQJ5aUf0ymtqjc6nFbn7+XKghv6U9tg4aa3t1Be43ht9vNw5dHLevLN3OH0bxfIEyv2M+6F1axMy3OY8UCOYn16EZe+tJa/L9tDr5gAVs4dzp8ndcfLzXmW139/01EWbz7GnaM6OvWqvD+rqbcwLyWd5PZBDO7o+KcR7YEkMTbuTxO7UVZTzysp6UaH0iY6h/vy6ox+pBdWcM8HqQ47ELZTmC9vz05m0U3JuJlN3PHedi57eR2r9h+XZMZgu7NLuf7NTVy3YBPlNQ3Mn9mXd29OplOYr9GhtamtmcU8umwPo7qG8sC4rkaHYxN+6YW5uDNKOeY6QPZGkhgb1z3Sjyv7xrBwXabTTNMd1jmEf16RwE8HC/nHl3sd+kN9ZJdQvv6/4TxzVS9KquuYvXALU19dz5pDhQ7dblt0uLCCu9/fzuSX15KWU8pfLunOD38YyYSESKf7wCooq+HO97cTFeDJi9f2weygC/edC+mFsU3O0y9qx+4f24Uvd+by3LcH+M+0PkaH0yamJ8eRWVTJa6szaBfsxS0OvBaDi9nE1f1juaJPNB9vzeblHw9x/ZubSYoN4LbhHRjfM9zpB1O2psxSC3e9v42v0/LxdDUzZ0xnbh0e7xSDdk+npt7CHe9to7K2gfduHoi/l3P+HX7r516YF67p7XRJrS2TJMYORAV4ctOweF5NOczNwzo4ZEXc03loQjeyiqv451f7CPFx54o+0UaH1KpczSauGxjHlf0ak5kFazK4+4PtxAZ5csuwDlzdP8apxmO0Jq01m44UMy/lMKsP1uDrXsSdIzty07B4p1591WrVPPjJLlKzSnh1Rl+6RjjXKbTfU11n4ZVV0gtji+Qd0U7cOaojH205xqNf7uGTOwY7xTcBk0nxwrW9KanawgMf78TP04WLujn+4EJ3FzMzB7VjenIc3+0t4PXVh/n7sj089+0BpvaNYcbAODqHy4fL+aiqa+Dz1Fze2ZDJ/vxyQnzcuKqLK3+7brTTr0AL8My3B/hyZy4PT+zGxESpyvyzt9Yd4Xh5La/M6OsU7732RPqo7YSfhysPTejGtqMnWZrq2MUhT+Xhaub1G/rRPdKPu97fztZMx1pD5kzMJsWEhAg+u2son9wxmJFdw3h/01HGvrCaq+evZ2lqtsOUamhtB/LL+ceXexj4xA/8eelulFI8OTWRtQ9dxKUd3CSBAT7YlMWrKYe5bmAct49w3NO356q4so75KYe5uHs4A9oHGR2O+A3pibEjV/WL4f3NWTyxYj9je4Q7zTl7Xw9XFs4ewNXzN3DTwi18ePtgukf6GR1Wm+rfPoj+7YM4UdGDT7dns3jzMe77cCd//XwP43qGc3nvaIZ2DJaxM6coLK9l2c5cPtuezZ7cMlzNiokJkdwwuB392gXKN+pTpBw4zl+/SGNU11Aeu6yn/G1O8fKP6VTWNfDQBJmhZYskibEjJpPisct6csW8dfz3h0M8conzVJEN9nHn3VsGctWr67n+zU0svnWQU55SCfZx57YRHbllWAc2HjnBF6m5rEjL47PtOQR7u3FJr0jG9YggOT4INxfnS2gKy2v5fl8BK9PyWZtehMWqSYz25++TezA5Kcqpx7v8nh3HSrj7/e10Dffl5ev6SiJ8imPFVby7MZOr+8U65fuNPZAkxs4kxQZwbf9Y3l6XyTX9neuFFR3gyXu3DGTa6xuZ/sYmltw20OnW7viZyaQY0jGEIR1DeOyKnqQcKGTZzlw+3HKMdzYcxcfdhRFdQhjTLZxRXUMJdtAPb6016ccrSDlQyDd78tmWdRKtIS7Ii9tGdGBqn2ineo2cqwP55cx6azPBPu68PXsAPu7ykXCq5749gNmkuG9sF6NDEb/DkGesUioI+BBoD2QC12itT55mu0ygHLAADVrr/ueyv6N6cHxXVuzO49Ev9/DezQOdquu3Y6gPi28dxLTXNzLt9U0suW0QncJ8jA7LUO4uZsb3jGB8zwiq6yysSy/ih/0F/LDvOCt25wPQLcKXQR2CGdQhmIHxQQR6uxkc9fnLLalmw+ETrEsvYm16EcfLG2tQ9Yj0Y+6YLozrGU63CF+nel2cj6MnKpn55iY8XE28f8tAwv08jA7JpqTllPL5jlzuGtWRCH/529gqo9Luh4EftNZPKaUebvr5od/ZdrTWuugC9nc4wT7uPDC+K3/7Yg9f7Mh1+KnHv9UpzIcltw1k2uubmP7GRpbcNoiOoc6dyPzM083MxT3CubhHOFarZk9uGT8dPM7GjGKWbMli4fpMALqE+5AYHUCvGH8Sov3pEemHp5vZ2OBPo6ymnr25Zew4VkJq1kl2HCuhoKwxaQn2dmNIpxCGdQpmaKcQYgK9DI7WfuSVVjNjwSYaLFY+un0wsUHytzuV1pq/L9tDiI8bd4zqaHQ44gyMSmIuB0Y13V4EpHBuSciF7m/3Zgxsx2fbc3hs+V5GdAklyI6/WZ+PTmG+LL51INPf2Mj01zfy3i0D6SKnDX7FZFIkxviTGOPPPRdBXYOVXdklbDh8gu1ZJ/np4HE+3Z4NNM6Eig/xpkOINx1CfegQ6k3HUB9igzwJ8XbH1IortjZYrOSV1pBTUk1WcRXpxys4WFDOwfxycktrftmuXbAXgzsE0zs2gOT4YLpF+LZqXI7qeHkNMxdsoqSq3mnHlp3NFzty2Xb0JE9f2Utmrtk4o5KYcK11HoDWOk8pFfY722ngW6WUBl7TWr9+jvs7LLNJ8dSViVz637X886u9PH9Nb6NDanOdw31ZfOsgZizYxDWvbWDh7GR6xwYYHZbNcnMx/TLLCRq/beaX1bA7u5TdOaUcyC8no6iSVQeOU2/5/yUPXEyKMF93PKnjw+xtBHq74evhgp+HK74eLvh6uODuYsakFGaTwmxqrNpd12CltsFKbb2FmgYrVbUNnKyqp7iyluLKek5W1ZFfWkN+WQ0Wq/5VnB1DfUiOD6JzuC/dInzpHRvgsON62lJBWQ3T39hIfmkNC2cnO83CmeeioraBJ1bso1eMP1f1izE6HHEWqrXqsyilvgciTvPQI8AirXXAKdue1FoHnuZ3RGmtc5uSlO+Ae7XWq5VSJc3Zv+mx24DbAMLDw/stWbLkQprVpioqKvDxOfNpkk8P1vFlRj0P9PcgIcT2TgecTnPadS6OV1l5ZksN5XWaOX096BFs3N+hpdtmBItVU1itya+0UlStKanVnKzRFFXWU9ZgoqJeU10PDefx1uGiwMdN4eum8HGFAA9FiKeJkKbrYE9FqKdq01o9jnDMfs+pbSuusfLvzTWU1mru7+9Bl0D7eL84ndY8Zh8fqOOrI/X8ZZAHnQLa/m/U0m0bPXr0tp/HkzqiVktizvifKnUAGNXUixIJpGitzzgJXyn1KFChtX72fPYH6N+/v966dWtLNKFNpKSkMGrUqDNuU1NvYdKLa6i3Wvl27kibHNfwW81p17k6XlbD9W9u5khRJS9d14fxPU+XP7e+1mibrfht22rqLZTXNFBeU0+dxYrFqrFawaI1Vq1xM5vwcDXh7mLG3dWEl5sL3m5mmxtw6wzHLPtkFde9sYmTlXUsvCmZfu1O+53PbrTWMTtSVMn4F1YzOSmK565JavHf3xwt3TallEMnMUYtCLAMmNV0exbwxW83UEp5K6V8f74NjAPSmru/s/BwNfPk1ESOFVfzwvcHjQ7HMGF+Hnx4+yB6Rvtx53vb+HBLltEhOTwPVzOhvu50CPWhW4QfPaMax9/0jg2gb1wgCdH+dArzJTbIizBfD3zcXWwugXEGmUWVTHt9Iyer6nj3loF2n8C0Fq01j325BzcXkyxsZ0eMSmKeAsYqpQ4BY5t+RikVpZRa0bRNOLBWKbUT2Ax8pbVeeab9ndXADsFMT45jwZoMth11mpnm/yPAy433bh7IsM6hPPTpbp5euR+rte17GoWwFZmlFq58dT1VdRY+uGWQjBk7gxW781l1oJC5F3cmTKab2w1DBvZqrU8AY05zfy4wqel2BnDa/rzf29+Z/XlSN1YfLOSBj3fy1ZxhTlvt2NvdhTdn9edvX6QxL+UwWcVVPHt1Eh6utn+aTYiWtC69iKc21xDs68k7NyfLMgRnUFpVz9+X7SEh2o8bh7Q3OhxxDmR9aQfh6+HKM1f34khRJU99vd/ocAzlajbxxJREHp7YjeW78pixYBPFlXVGhyVEm1m+K5fZb28hxFPx2V1DJIE5i6dW7qe4spanpvaSsgt2Ro6WAxnSMYTZQ9vzzoajrDlUaHQ4hlJKccfIjrxyXV9255QyZd46DhaUGx2WEK1Ka82CNRncuziV3rEB/Gmgp6zEexabjxSzeHMWNw+LJyFappzbG0liHMxDE7rRMdSbBz/eRWl1vdHhGO6SXpEsvnUQlbUWrnhlHV/vzjM6JCFaRV2DlT8v3c0/v9rH+B4RvHNzMt6uMpD6TGobLPzps11EB3hKfSQ7JUmMg/FwNfP8Nb0prKjl0WV7jA7HJvRrF8jye4fRJdyXO9/fztMr9/9qcTUh7N3JyjpueGsTizcf457RnZg3o6+MA2uGV1Yd5nBhJf+8IsFpxxHaO0liHFBSbAB3j+7E0tQcvtiRY3Q4NiHCv3EK9vTkWOalHGb2wi2UVMk4GWH/0o9XMGXeOrYfLeGFa5N4YHxXKcfQDLuzS5m3Kp0rekcxupvTLfruMCSJcVBzLupE/3aBPLI0jcyiSqPDsQnuLmaenNqLJ6YksuFwEZe+tJbULOedki7s38q0fKa8so6K2gYW3zaIKX1kmfzmqKm38IePdxDs48Y/LkswOhxxASSJcVAuZhMvTu+DScG9i1Opa7AaHZLNuG5gHB/ePhit4er5G3jtp8OynoywKw0WK0+u2Mcd722jQ6g3n989VBaxOwcvfH+QgwUVPHVlL/y9pMCjPZMkxoFFB3jy9FVJ7M4p5emVzj3t+rf6xgWyYs5wxvYI58mv9zN74RaKKmqNDkuIszpeVsN1Czbx2uoMrh/Ujo/uGExMoJfRYdmNbUeLeX11BtOT4xjdVU4j2TtJYhzchIQIbhjcjgVrj/Dj/gKjw7Ep/l6uzJvRl39ekcCGjBNMfHENaw8VGR2WEL9r/eEiLnlpLbuzS/nPtb15/IoE3F1kAG9zVdU18IePdhId4Mkjl3Q3OhzRAiSJcQJ/ntSd7pF+/OGjneSVVhsdjk1RSjFzUDu+uHso/p6uzHxzE3//Io2qugajQxPiF3UNjaePZizYhK+HC5/fPZQr+kQbHZbd+ddX+8g80biKt4+7zEZyBJLEOAEPVzMvX9eHugYrd72/ndoGi9Eh2ZzukX58ec8wZg9tz6INR5n04hq2HS02OiwhSD9ezpR563htdQbXJcfx1b3D6Rrha3RYdufr3Xm8vymL20d0YFCHYKPDES1Ekhgn0THUh2evTiI1q4THvtxrdDg2ydPNzN8n92TxrYNosGqumr+BJ1fso6Zekj7R9rTWvLvxKJe+tJa80hreuKE//5qSiKebnD46V9knq3jo010kxfjzh3FSodqRSBLjRCYmRnL7yA68vymLj7ceMzocmzW4YzAr545g2oA4XludwcQX17AuXcbKiLaTdaKKGQs28dfP00iOD2bl3MZB6OLcNViszF2yA6uGl6b3xc1FPvYciRxNJ/PguK4M7RTMI5+nkZZTanQ4NsvH3YUnpyby3s0DsWrNjAWbuP+jHZyQGUyiFVmsmjfXHmH8f1azK7uUJ6YksvDGAYT5Sv2j8/XiD4fYevQk/5qSQFywzOJyNJLEOBkXs4n/TutDiLcbt7+7jZNS3fmMhnUO4Zu5I7hndCe+3JnLmOd/4qOtx2RdGdHiDhWUc9X89Ty+fC+DOwbz3f0juG5gnKy+ewHWpxfx8qp0ru4Xw+W9ZSC0I5IkxgkF+7jz6sx+FJbXcs/i7dRbZCG8M/FwNfPA+K58NWc4ncN8+OMnu5j66npZ7Ve0iIraBp5csY+JL64hs6iSF6f15s1Z/Yn09zQ6NLuWX1rDnCWpxId48+hlPY0OR7QSSWKcVFJsAE9MTWRd+gkeXbYHraVn4Wy6hPvy4W2DeeaqXuSUVDNl3nru/3AH+aU1Rocm7JDWmi925DDmuRReW53B1L7RfHf/SC7vHY1S0vtyIRpnYm6jqs7CazP74S3TqR2WHFkndlW/GNKPVzD/p8N0CvNh9tB4o0OyeSaT4ur+sUxMjGTeqnQWrDnC12n53DWqI7cM72B0eMJO7Msr4+/L9rD5SDGJ0f7Mn9mPPnFSNqCl/POrvWzPKuGV6/rSOVymozsySWKc3B/HdyWjsILHl++lfYi3LMPdTD7uLvxxQjemDYjjiRX7eO67g7yz8SgTYjVDGqwyA0KcVm5JNc9/d5BPt2fj7+nKE1MSuXZALGYZ99JiPtuezTsbjnLr8Hgu6RVpdDiilck7rZMzmRQvXNubbhF+3PtBKgcLyo0Oya7EBXsx//p+fHzHYOKDvXl3bx0XP/8TS1OzscjgX9GktKqeJ1fsY9SzKSzbkcstw+JJeWAU1w2MkwSmBe3NLePPS3czqEMQD03oZnQ4og1IEiPwdnfhzRv74+lm5qaFWzheLmM8ztWA9kF8ePsg7u/njo+7C/d9uJNJL67hy525ksw4scraBub/dJgRz6zi9TUZXJoYyY8PjOSRS3oQ4OVmdHgOpbiyjtvf20qApxsvTe+Li1k+3pyBHGUBQKS/Jwtu6M+JijpuWriFilqpHXSulFL0CnVh+b3DeGl6HxqsVu5dnMrYpmnZMgvMeZTX1PPKqnSG/ftHnvp6P0mxAXx173Cev7a3VJxuBbUNFu54dxvHy2qZf30/Qn3djQ5JtBFJYsQvkmIDmDezL/vyyrnzvW3UNciH7vkwmRSTk6L49r6RzJvRFw9XM3/8ZBejnknhnQ2ZVNdJGQNHVVpdz4vfH2LYv1fxzDcHSIoN4NM7h/DOTcn0iPIzOjyHpLXmkaVpbM4s5tmrk+gdG2B0SKINycBe8Suju4bx5NRE/vjJLh7+dBfPXZMk0z3Pk9mkmJQYycSECFIOFPLyqnT+9sUenv/uINMGxHHD4HZEBchaII4g60QVb68/wsdbs6mobeDi7uHce1EnkuQDtdW9tjqDT7Zl839jOjM5KcrocEQbkyRG/I9r+sdSUFrDc98dJMzPg4cnygC5C6GUYnS3MEZ1DWVL5kneXneE11cf5o01GUxIiOCmofH0jQuQZNHOaK3ZevQkb645wrd78zEpxSW9Irl1eAcSov2NDs8pfLMnn3+v3M+lvSKZe3Fno8MRBpAkRpzWPRd1Ir+shvk/HSbU152bh8kaMhdKKUVyfBDJ8UEcK67i3Y1HWbw5i6925dEj0o9pybFcnhSNv5er0aGKM6isbWD5rlze35TFruxS/D1duX1kR2YNbk+Ev9Q4aitpOaXMXbKDXjEBPHu19Bg7K0lixGkppXjs8gSKK+t4fPlevN3MTEuOMzoshxEb5MWfJ3Xn/8Z05rPUHJZszuJvX+zhX1/tY1JiJNMGxJIcHyRvzDZCa82u7FKWbMli2Y5cKussdA7z4fErEriybzRebvJW2paOV1l54O3NBHm78cb1/fBwNRsdkjCIvPLE7zKbFC9O60P1u1v509LdeLqZpYhaC/N2d+H6Qe24flA70nIaPyS/SM1laWoOcUFeXJYUxWW9o+giq44aIr+0huW7cvlsew5788rwcDVxaa8opifH0jcuUJJMAxRV1PLc1hoacGHJTcmE+UnvlzOTJEackZuLifkz+3Hj25u5/6OdeLqaGdczwuiwHFJCtD//jE7kkUk9WLE7j8935DAvJZ2XV6XTLcKXyUlRXJYURWyQTNFtTScr6/g6LZ9lO3PYdKQYrSEx2p/Hr0jg8t5R+HnI6T6jVNY2MPvtLZys0Sy5YwCdwnyMDkkYTJIYcVYermYWzBrAzAWbuOeDVN68sT/DO4caHZbD8nQzc2W/GK7sF0NheS0rduexbGcuz3xzgGe+OUC3CF/G9Qjn4h7hJET5Y5IVXy9YXmk13+87zvd7C1iXXkSDVdMh1Ju5Y7owOSmSDqHyYWm0ugYrd7y3jb15Zdzb252+UmtKIEmMaCYfdxcWzU5m2hsbufWdrbw1awBDOoUYHZbDC/V1Z9aQ9swa0p5jxVWsTMvnu30FvLwqnf/+mE64nztjuoczsksogzoE4+8pvQTNYbVq9uSW8f2+Aj7fUs3RlT8C0D7Yi5uHxTM5KYqeUX5yushGWK2ahz7dxZpDRTx9VS/CKg4bHZKwEZLEiGbz93Ll3ZuTmfHGJm5atIU3Zw1gqCQybSY2yItbR3Tg1hEdKK6sY9X+440fwqk5fLApC5OCXjEBDOsUwtBOIfRtF4C7iwx4hMaBuRlFlaw/fIL16UVsyDhBSVU9SkEnfxMPT+zGxd3D6RjqLYmLjdFa85cv0liamsOD47tyTf9YUlIkiRGNJIkR5yTEx50Pbh3IjAWbuGnhFt64oT8jusippbYW5O32yymnugYrqVknWZdexNr0Il796TAvr0rHzcVEYrQ/feMC6BsXSN92gYQ7ySDIugYre/PKSM06SWpWCZuPFJNf1lgTLNLfgzHdwhnaKZgRXUJJ27qBUSM7GhyxOB2tNY8t38sHm7K4a1RH7holx0n8miQx4pwF+7jzwa2DmLFgE7e8s5XXr+/HqK5hRofltNxcTAzsEMzADsHcP64r5TX1bMooZtORE2zPKmHRhqO8seYIANEBniRE+9E9svHSI9KPmEBPu+59qK6zcLCgnAP55ezLL2PHsRL25Jb9UjYjws+Dfu0CGdIpmCEdQ2gf7GXX7XUWWmue/uYAb6/L5Kah8Tw4vqscN/E/JIkR5yXI240PbhnIzDc3cds725h/fV8u6hZudFgC8PVw5eKmgb/QWBxvb24Z27NK2J51kn25ZXy7twDdVFzb192FLhG+tA/2Jj7Ei3bB3sSHeNMu2AtfG5mJY7Fq8stqOHqikmPFVRw9UcXhwgoO5JdztLjql7Z4uppJjPZn9pD29I4NoHdcAJH+UtrBHv33h3ReTTnMjIFx/PXS7pLAiNOSJEact0BvN96/ZSDXv7mZ29/dxvPX9JbaJTbI3cVMn7hA+sQFcjONKy9X1TU09lzklbMvr4yDBeWsTS/k0+21v9rXz8OFCH8Pwv080FW1bKndT7ifB/6ervh5uuLn4dp02wVvNxdczSZczeqsHzj1FiuVtQ2U1zRQUdt0qWngRGUdheW1jZeKWo6X1XC8vJack9XUnVIF3MWkiAvyonukH1f0iaZbhB/dInyJC/KS2VoOYP5Ph3nh+4Nc2TeGxy9PkARG/C5JYsQFCfBy4/1bB3Lzwi3MWZJKWU09Mwa2MzoscRZebi6/JDanqqpr4OiJKo6eqORIURV5pdUUlNWQX1ZLVpGFDXkZWKz6rL/frSmZcXUxYbVqLFaNRTdeN1j1Lz0nv8fbzUyorzuhvu70iPRjXM9w2gV5ExfkRbtgLyL9PXAxmy7kTyBs1Es/HOK57w4yOSmKp6/qJUmpOCNJYsQF8/Nw5Z2bBnLX+9t4ZGkapdX13Dmyo3x7skNebi6/jJf5rZSUFIaPGElxZR2l1fWU1dQ3Xjddquos1Fus1Fk09RYr9Q1W6ixWTEphNilcTI3XZpPC1WzCx90FHw8XfJuuvd1dCPZ2I8THHW93eWtyNlprnvv2IC+vSmdq32ieuSoJsyQw4izknUK0CE83M6/f0J8HPt7J0ysPUFJVz58mdpNExsGYTeqXHhIhWorWmidW7OONNUeYNiCWJ6YkSg+MaBZJYkSLcTWbeOGa3vh7uvL66gxOVtbxxNREXKXbXwjxO6xWzaNf7uGdDUe5YXA7Hp3cUxIY0WySxIgWZTIp/nFZTwK93Hjxh0Pkl9Uwb0Zfm5nlIoSwHQ0WK39eupuPtmZzy7B4HrlEZiGJcyNfkUWLU0px39guPH1lLzYcPsHV8zeQV1ptdFhCCBtSXWfhjve28dHWbOZc1EkSGHFeJIkRreaaAbG8deMAsk9WM+WV9ezNLTM6JCGEDSipqmPmm5v4Yf9xHr+8J/ePk4XsxPmRJEa0qhFdQvn4jsEAXPPaBn46WGhwREIII+WWVHP1/A3szi7llev6cv3g9kaHJOyYJDGi1XWP9GPp3UOICfRk9tub+SazHn22hUKEEA7nUEE5V766nvzSGhbdlMykxEijQxJ2TpIY0SYi/T355M4hXNw9nMX763jwk13UNliMDksI0UbWHCpk6qvrabBqPrx9MIM7BhsdknAAksSINuPj7sL8mf24vKMrn2zLZvrrGzleXmN0WEKIVvbuxqPc+PYWogM8WXrXEHpE/e9iikKcD0liRJsymRRTOrsxb0Zf9uWVc9lL69iVXWJ0WEKIVtBgsfLosj389fM0RnYJ5ZM7hxAT6GV0WMKBGJLEKKWClFLfKaUONV0HnmabrkqpHadcypRSc5see1QplXPKY5PavBHigkxKjOSTOwdjNimumr+BD7dkGR2SEKIFldfUc8s7W1m4PpNbhsXzxg398ZFyEqKFGdUT8zDwg9a6M/BD08+/orU+oLXurbXuDfQDqoClp2zyws+Pa61XtEXQomX1jPJn2T1DSW4fxEOf7ubBj3dSXSfjZISwdxmFFUydt561h4p4Ykoif7m0h9RBEq3CqCTmcmBR0+1FwBVn2X4McFhrfbQ1gxJtL9jHnUU3JTNnTGc+2Z7NlHnrOFJUaXRYQojz9O2efC5/eR1FFbW8c1My1w2MMzok4cCMSmLCtdZ5AE3XYWfZfhqw+Df33aOU2qWUeut0p6OE/TCbFPeP7cLbNw4gv6yGyS+t5evdeUaHJYQ4Bxar5tlvDnDbu9uID/Vm+ZzhDOkUYnRYwsGp1lqvQyn1PRBxmoceARZprQNO2fak1vq0iYhSyg3IBXpqrQua7gsHigANPA5Eaq1v+p39bwNuAwgPD++3ZMmS825TW6uoqMDHx8foMFrcmdp1otrKKztqySi1MibOhWu7uuFmtp9uaEc9ZuC4bXPUdkHbta2iTjN/Vy1pRRZGxLgws3vrvm7lmDXf6NGjt2mt+7fYL7Q1Wus2vwAHaEw8ACKBA2fY9nLg2zM83h5Ia87/269fP21PVq1aZXQIreJs7aqtt+jHvtyj2z20XI99PkXvyyttm8BagKMeM60dt22O2i6t26ZtqVkn9dCnftCd/7xCf7DpaKv/f1rLMTsXwFZtwOd8W12MOp20DJjVdHsW8MUZtp3Ob04lKaVOXeZxCpDWotEJQ7m5mPjrpT1YOHsAxZX1XPbyOhatz5RVfoWwIVar5rWfDnPVq+vRGj66YzDTk2X8i2hbRiUxTwFjlVKHgLFNP6OUilJK/TLTSCnl1fT4Z7/Z/2ml1G6l1C5gNHBf24Qt2tKormGsnDucoR2D+fuyPdy8aCtFFbVGhyWE0yssr+XGhVt48uv9jO0Rzoo5w+kdG2B0WMIJGTJpX2t9gsYZR7+9PxeYdMrPVcD/rE2ttb6+VQMUNiPEx523bhzAovWZPPH1fsa/sJp/XpHARKm5IoQhVh8s5P6PdlJeU8+/piRwXXKcVKAWhpEVe4XNU0px49B4vrxnGJEBHtz5/nbuXZzKyco6o0MTwmnU1Ft4YsU+bnhrM4Feriy7ZxgzBraTBEYYSpZPFHaja4QvS+8ayvyUw/z3x0NsOHyCJ6YkMK7n6SbBCSFayu7sUu7/aAeHjldw3cA4/npJDzzdzEaHJYT0xAj74mo2ce+Yznxx9zDCfN257d1tzF2SSrH0ygjR4uotVl747iBXzFtHeU0DC2cP4IkpiZLACJshPTHCLvWI8uPzu4fyyqp0XlmVzupDRTwyqTtT+0ZL97YQLeBAfjn3f7SDPbllTO0Tzd8n98Tfy9XosIT4FemJEXbLzcXEfWO7sHzOMNoHe/GHj3dy3RubyCisMDo0IexWbYOFF78/xOSX1pJfWsP8mf14/treksAImyRJjLB73SL8+OSOIfxrSgJpuaVM+M8aXvz+ELUNUkxSiHOx+Ugxk15cwwvfH2R8QgTf3jeCCQky5kzYLjmdJByCyaSYMbAdY3uE8/jyfbzw/UG+2JHDXyf3YHTXs5XmEsK5lVbV8+TX+1iy5RgxgZ68PXuAvG6EXZCeGOFQwnw9eGl6HxbOHoAGZr+9hZsWbpHK2EKchtaaL3bkMOb5FD7els1tIzrw7X0jJIERdkN6YoRDGtU1jMEdg1m4LpOXfkxn3As/cdPQeO65qBO+HnJuX4g9uaX848u9bD5STK8YfxbdlEzPKH+jwxLinEgSIxyWu4uZ20d2ZErfaJ5eeYDXVmfwWWoOD47rypX9YjCbZBaTcD7FlXU8++0BlmzOwt/TlX9NSWDagDh5PQi7JEmMcHhhvh48e3USMwe14x9f7uGPn+5iwdoMHprQjYu6hcmUbOEU6i1W3tt4lBe+O0hlnYVZQ9ozd0wXmXUk7JokMcJp9I4N4LM7h/B1Wj7PfHOAmxdtJbl9EA9N7Ea/doFGhydEq9Ba882eAp75Zj+HCysZ3jmEv13ag87hvkaHJsQFkyRGOBWlFJMSIxnbI5wPtxzjP98f4spX1zO+ZzgPju9KpzB5YxeOY3+xhRdfXU9qVgkdQr15/fp+jO0RLr2PwmFIEiOckqvZxMxB7ZjSJ5q31h7htdUZfLt3NZf2imLORZ3kW6qwa/vyynh65X5WHaghwg+emprIVf1icDHLhFThWCSJEU7N292Fe8d0ZsagdixYk8Gi9Zks35XLJYmRzBnTmS6SzAg7cqignJdXpbNsZy6+7i5c08WVx64fhYer1DoSjkmSGCGAIG83/jihG7cO78CCtRksXJfJV7vzmJQYyT2jO9E90s/oEIX4Xfvzy3jpx3RW7M7D09XM7SM6cufIjqRuXicJjHBoksQIcYpAbzceHN+NW4Z14M21R3h73RG+2pXHyC6h3D6iA4M7Bst4AmEz0nJKeenHQ3yzpwAfdxfuGtWRm4d1IMjbzejQhGgTksQIcRqB3m48ML4rtw7vwHubjvL2ukyuW7CJxGh/bhvRgYkJETK+QBhCa82GjBMsWHOEH/cfx9fDhTljOnPT0PYEeEnyIpyLJDFCnIG/lyt3j+7EzcPi+Tw1h9dXZ3Dv4lRigzyZPSSeK/vF4O8p62yI1ldvsfLVrjzeWJPBntwygr3d+MPYLtwwpL08B4XTkiRGiGbwcDUzLTmOa/rH8v2+Al5fncFjy/fyzDcHmNI3mhsGt6NbhIybES2vtLqeJZuzWLg+k7zSGjqGevPk1ESm9ImW8S7C6UkSI8Q5MJkU43pGMK5nBGk5pby74Sifbsvmg01ZJMcH0d+vgaEWK65yqklcoLScUt7beJQvduRSXW9hcIdg/jUlgVFdwjBJiQAhAElihDhvCdH+/PuqXvxpUjc+2nqMdzceZd6RWj46/CNX9o3m6v4xsnieOCfVdRa+3JnL+5uOsjO7FA9XE5cnRXP94HYkREtxRiF+S5IYIS5QgJcbt41onBXy0ic/sLcmgDebFtDrExfA1f1iuTQpEj+pni1OQ2tNWk4Zn27P5tPt2ZTXNNA5zId/XNaTK/pEy3gXIc5AkhghWojZpOgd5sLcUf0pqqjl89QcPtp6jD8v3c1jy/cwoWcEl/eOZljnEDndJMgrrebz1Fw+257NoeMVuJlNTEyMYMbAdgxoHyhT+YVoBklihGgFIT7u3DK8AzcPi2dXdikfbT3Glztz+XxHLgFerkxMiGByUhQD44Mxy/gGp1FeU893ewv4bHsO6w4XoTX0bxfIE1MSuSQxUipKC3GOJIkRohUppUiKDSApNoC/T+7JmkOFLNuZyxc7clm8+Rihvu5ckhjJhIQI+rcLlLVnHFBpdT3f7y3g67Q8Vh8sos5iJTbIkzkXdWZKn2jah3gbHaIQdkuSGCHaiJuLiTHdwxnTPZzqOgs/7j/Olztz+aBp+myAlysXdQtjXI9whncOxdtdXp726kRFLT/sO86KtDzWpRdRb9FE+nswc1A7JiVG0DcuUGYYCdEC5F1SCAN4upm5pFckl/SKpLK2gdUHC/lubwE/7j/OZ9tzcHMxMbRjMBd1D2dE5xDaBcu3dVtmtWrScktZtb+QVQeOszO7BK0hJtCT2UPjmZgQQVJMgCQuQrQwSWKEMJi3uwsTEyOZmBhJg8XKlsyTfL+vgO/2FrDqQBoAsUGeDOsUyojOIQzpGCJjJ2xAUUUtGzNOkHKgkJQDhRRV1KIU9IoJYO6YLozpHkbPKD8ZoCtEK5IkRggb4mI2MbhjMIM7BvOXS7qTeaKKtYcKWX2oiC935rJ4cxYmBYkxAQyMD6J/u0AGtA8iUAr+tbriyjo2ZZxgQ8YJNmac4GBBBQB+Hi6M7BrG6K6hjOgSSoiPu8GRCuE8JIkRwkYppYgP8SY+xJvrB7en3mJlx7ES1hwqYn16EQvXZfL66gwAOof50L99EMnxgfSJDaRdsJf0AFwAq1WTUVRBalYJO46VsO3oSfbnlwPg5Wamf/sgrugTzaAOwfSK9pcB2UIYRJIYIeyEq9nEgPZBDGgfxP1ju1BTb2FXdilbMovZklnM8qaeGmjsHUiI9icxxp/EaH96RQcQG+Qpic1paK3JPlnFvrxydmWXkJpVws7sEsprGgDwdXehd1wAk5OiGpOWGH9Z50cIGyFJjBB2ysPVTHJ8EMnxQQBYrJoD+Y0fxLtzStmdU8rbazOps1gB8PVwoUu4L13CfegU1njdJdyXMF93p0luSqvqSS+sYH9+GfvzytmfX0ZadhXV36wCwKSgW4Qfk5Oi6B0bQJ/YADqG+siAXCFslCQxQjgIs0nRI8qPHlF+TGu6r67BysGCcnZll7Int5RDxytYmZbPyapjv+zn5+FCfIg3sUFexJ1yiQ3yItLfw65OlVismqKKWnJLqskqruJIUSVHTzReZ56opKSq/pdtfd1d6Bbpy+AoF8b060a3CF+6R/rh5SZvi0LYC3m1CuHA3FxMJET7/6p4oNaaE5V1HCwo51BBBQcLyskqrmJ3Tikr0/JpsOpftjWbFMHeboT5uWOuq+Gb4l2E+noQ5utOsLcb/p6u+Hm6Nl57uOLj4dKiKxBrraltsFJaXc/JqjpKquopqarjZFXjz0XldRSU1ZBXWk1+aQ0F5bVYTolfKYjy96R9iBeTEiOJD24cY9Qt0pfogMbTaykpKYwa2K7FYhZCtB1JYoRwMkopQnzcCfFxZ0jHkF891mCxkldaw7HiKrKKq8g+Wc3x8hoKymrJKKvgu70FnKisQ+vf+93g4+aCh5sZN7MJd1dT07UZdxcTrmaF1mDVGq1BA2jQaOoarFTXWxovdVZqmm6fmpT8lpebmQh/DyL9PRjcMYRIfw8i/D2I8PMgLrixR8nD1dxyfzwhhE2RJEYI8QsXs4nYplNJQ37zWEpKCqNGjaLeYuVERR3FlXWU1dRTVl1PWU0DpdU/366npt5KXYOV2gYLtQ3//3ZNvRWTAoWi6R/KBAoT3t4uRLma8XQ14+HWeO3pasbTzYy/pyuBXm4EerkS4OVGoHfjz5KgCOHcJIkRQpwTV7OpsbfD38PoUIQQTs5+RuwJIYQQQpxCkhghhBBC2CVJYoQQQghhlySJEUIIIYRdkiRGCCGEEHZJkhghhBBC2CVJYoQQQghhlySJEUIIIYRdkiRGCCGEEHZJkhghhBBC2CVJYoQQQghhlwxJYpRSVyul9iilrEqp/mfYboJS6oBSKl0p9fAp9wcppb5TSh1qug5sm8iFEEIIYSuM6olJA6YCq39vA6WUGXgFmAj0AKYrpXo0Pfww8IPWujPwQ9PPQgghhHAihiQxWut9WusDZ9ksGUjXWmdoreuAJcDlTY9dDixqur0IuKJVAhVCCCGEzVJaa+P+c6VSgAe01ltP89hVwASt9S1NP18PDNRa36OUKtFaB5yy7Umt9WlPKSmlbgNuAwgPD++3ZMmSlm9IK6moqMDHx8foMFqco7YLpG32yFHbBY7bNkdtF7R820aPHr1Na/27wzbsnUtr/WKl1PdAxGkeekRr/UVzfsVp7jvnjEtr/TrwOkD//v31qFGjzvVXGCYlJQV7ire5HLVdIG2zR47aLnDctjlqu8Cx29YaWi2J0VpffIG/IhuIPeXnGCC36XaBUipSa52nlIoEjl/g/yWEEEIIO2PLU6y3AJ2VUvFKKTdgGrCs6bFlwKym27OA5vTsCCGEEMKBGDImRik1BXgJCAVKgB1a6/FKqShggdZ6UtN2k4D/AGbgLa31v5ruDwY+AuKALOBqrXVxM/7fQuBoizeo9YQARUYH0QoctV0gbbNHjtoucNy2OWq7oOXb1k5rHdqCv8+mGDqwV5yZUmqrIw7IctR2gbTNHjlqu8Bx2+ao7QLHbltrsOXTSUIIIYQQv0uSGCGEEELYJUlibNvrRgfQShy1XSBts0eO2i5w3LY5arvAsdvW4mRMjBBCCCHskvTECCGEEMIuSRJjsOZU5FZKdVVK7TjlUqaUmtv02KNKqZxTHpvU5o04jeZWGldKZSqldjfFvvVc9zdCM49ZrFJqlVJqX1PF9v875TGbOma/Vy3+lMeVUuq/TY/vUkr1be6+RmtG22Y0tWmXUmq9UirplMdO+9y0Bc1o1yilVOkpz7G/NXdfozWjbQ+e0q40pZRFKRXU9JgtH7O3lFLHlVJpv/O43b7ODKW1louBF+Bp4OGm2w8D/z7L9mYgn8a5/wCP0lh/yvC2nE+7gEwg5EL/LrbWNiAS6Nt02xc4CPSwtWPW9Hw6DHQA3ICdP8d5yjaTgK9pLAUyCNjU3H3toG1DgMCm2xN/btuZnptGX5rZrlHA8vPZ19bb9pvtJwM/2voxa4ptBNAXSPudx+3ydWb0RXpijHeuFbnHAIe11ra+aN+FVhq35UrlZ41Na52ntd7edLsc2AdEt1WA5+BM1eJ/djnwjm60EQhQjeU+mrOvkc4an9Z6vdb6ZNOPG2ksb2LrLuTvbvfH7DemA4vbJLILpLVeDZxpUVZ7fZ0ZSpIY44VrrfOg8YMPCDvL9tP43xftPU3dj2/Z0GmX5rZLA98qpbapxorj57q/Ec4pNqVUe6APsOmUu23lmEUDx075OZv/TbZ+b5vm7Gukc43vZhq/Cf/s956bRmtuuwYrpXYqpb5WSvU8x32N0uz4lFJewATg01PuttVj1hz2+jozVKsVgBT/nzpDRe9z/D1uwGXAn065+1XgcRpfvI8DzwE3nV+k56aF2jVUa52rlAoDvlNK7W/6xmKoFjxmPjS+yc7VWpc13W3YMTuN5lSL/71tWqTSfCtqdnxKqdE0JjHDTrnbJp+bNK9d22k85VzRNObqc6BzM/c10rnENxlYp39dcsZWj1lz2OvrzFCSxLQBfYaK3kqpc6nIPRHYrrUuOOV3/3JbKfUGsLwlYm6OlmiX1jq36fq4UmopjV2nqzG4UnlLtE0p5UpjAvO+1vqzU363YcfsNM5ULf5s27g1Y18jNadtKKV6AQuAiVrrEz/ff4bnptHO2q5TEma01iuUUvOUUiHN2ddg5xLf//RK2/Axaw57fZ0ZSk4nGe9cKnL/z/nfpg/Rn00BTjvy3QBnbZdSylsp5fvzbWAc/z9+W65U3py2KeBNYJ/W+vnfPGZLx+xM1eJ/tgy4oWn2xCCgtOk0WnP2NdJZ41NKxQGfAddrrQ+ecv+ZnptGa067Ipqegyilkml8rz/RnH0N1qz4lFL+wEhOee3Z+DFrDnt9nRnL6JHFzn4BgoEfgENN10FN90cBK07ZzovGNyH/3+z/LrAb2EXjEzvS6DY1t100jrbf2XTZAzxytv1t4dLMtg2jsct3F7Cj6TLJFo8ZjbMiDtI4A+KRpvvuAO5ouq2AV5oe3w30P9O+tnRpRtsWACdPOUZbz/bctIVLM9p1T1PcO2kcsDzEUY5Z0883Akt+s5+tH7PFQB5QT2Ovy82O8joz8iIr9gohhBDCLsnpJCGEEELYJUlihBBCCGGXJIkRQgghhF2SJEYIIYQQdkmSGCGEEELYJUlihBBCCGGXJIkRQgghhF2SJEYI0WqUUo8rpf7vlJ//pZSaY2RMQgjHIYvdCSFaTVMF78+01n2VUiYaVzlO1qfUKBJCiPMlBSCFEK1Ga52plDqhlOoDhAOpksAIIVqKJDFCiNa2gMZaNxHAW8aGIoRwJHI6SQjRqpoq7+4GXIHOWmuLwSEJIRyE9MQIIVqV1rpOKbUKKJEERgjRkiSJEUK0qqYBvYOAq42ORQjhWGSKtRCi1SilegDpwA9a60NGxyOEcCwyJkYIIYQQdkl6YoQQQghhlySJEUIIIYRdkiRGCCGEEHZJkhghhBBC2CVJYoQQQghhlySJEUIIIYRd+n8PhufYhMeBgwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "    \n",
    "    def f(t, u):\n",
    "        return np.array([ u[1], -(k/M)*u[0] - (D/M)*u[1]])\n",
    "\n",
    "    M = 1.0\n",
    "    k = 1.0\n",
    "    D = 0.1\n",
    "    u_0 = [1.0, 0.0]\n",
    "    a = 0.0\n",
    "    b = 8 * np.pi # Four periods\n",
    "\n",
    "    n=10000\n",
    "    (t, U) = euler_system(f, a, b, u_0, n)\n",
    "    y = U[:,0]\n",
    "    Dy = U[:,1]\n",
    "\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"U_0, = y with {k=}, {D=} — by Euler with {n} steps\")\n",
    "    plt.plot(t, y)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('y')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"U_1, = dy/dt with {k=}, {D=} — by Euler with {n} steps\")\n",
    "    plt.plot(t, Dy)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('dy/dt')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"U_0=y and U_1=dy/dt with {k=}, {D=} — by Euler with {n} steps\")\n",
    "    plt.plot(t, U)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('y and dy/dt')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "    if D == 0.:\n",
    "        plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by Euler with {n} steps\")\n",
    "    else:\n",
    "        plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by Euler with {n} steps\")\n",
    "    plt.plot(y, Dy)\n",
    "    plt.xlabel('y')\n",
    "    plt.ylabel('dy/dt')\n",
    "    plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "    plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def explicitTrapezoid(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the Explict Trapezoid Method (a.k.a Improved Euler)\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following two lines will need to change for the systems version\n",
    "    U = np.empty_like(t)\n",
    "    U[0] = u_0\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h, U[i]+K_1)*h\n",
    "        U[i+1] = U[i] + (K_1 + K_2)/2.\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zZlcVa3dXszf4hPj4GOjRLkDPdgF6pMfQMz1ATrId15lLmnO+miPlKzzKV3iUr/BEM18jR46c7+4FdW1rsAfb3c+vb5uZbTKz3GDvdS6wuY5mxUDXkOU8oCTkGOOBS4FRHqz23X0/sD/4fr6ZrQL6AvPqiG8CMAGgoKDACwsLG/pIx0VRURHROndLpHyFR/kKT0vLV3W1s2ZbWe1Y7kXFu3inZBdvfF5TdbdLjK29eXJgXgandU2nU7vEJiu6W1q+ok35Co/yFR7lKzzNNV+RDhGZAowH7gq+vlRHmw+BfDPrCWwAxgFfh9rZRX4OjHD38oM7mFk2sN3dq8ysF5APrI4wVhGRZikQsNqnVF5xes3MJZVV1SzfVMqi4p21UwZOmLmayuDMJdlpCQzsEpy1pGvNEJPMFM1cIiLSHERaYN8FPGtm1wPrgKsBzKwzNdPxjQ7OEHIr8AY10/Q94e6Lg/s/ACQA04I9MQen4xsO/NbMKoEq4GZ33x5hrCIiLUZsTIB+ndvRr3M7xg2tWbfvQBWfbdzNouLgjZTFu3hr2ebaJ1LmtU/itLwMTs1LZ2Bw9pK0xLjofQgRkTYqogLb3bcBo+pYXwKMDlmeCkyto12feo47GZgcSWwiIq1NYlwMp3drz+ndDt3qsmffAT7dsLvmRspgT/ern2wEwAx6ZaXU3ECZl87Arhn0y21HYpxmLhEROZ40KauISAuWlhjH2b07cHbvDrXrtpdVHDae+72VW3n+4w0AxAaMvjlpnNb10ENxDg47ERGRpqECW0SklclMiafwpI4UnnRo5tQvdu0LDiupKbynfvIFz3xQM4NqYgycVzyP4X2zGZGfTbcOydEKXUSkVVCBLSLSBnRKT6RTeicu6l8z66q7s257OQuLd/HCe5/w2cbdtU+i7JmVwvD8LIb3zeasXh30BEoRkTDpqiki0gaZGd07pNC9QwrtdixnxIgRrNlaxszlW5i5YivPzitm4pzPiY8JUNCjPcP7ZjM8P5tTctOO65zcIiKtgQpsERHBzOiVnUqv7FS+dW5P9ldWMW/tDmYu38I7y7dw12tLueu1pXRMS+C8/GyG983ivPxsTQ0oIlIHFdgiInKUhNiY2se+/2L0KWzava+2d3vG0k1M/qgYMxjYJb2md7tvNqd3zdBj3kVEUIEtIiKNkNMukasLunJ1QVeqqp1PNuyq7d1+8O2V/OWtlaQlxHJun6xgwZ1FXnvdLCkibZMKbBERCUtMwBjUNYNBXTP4t1H57Np7gNkrtzJzxRbeWbaF1xd/AUDv7JTa3u2zenYgKV7zb4tI26ACW0REIpKeFMclp+Zyyam5uDurtpTyzvKtzFy+hb+/v46/zVpLfGyAM3tmMjy/puDum5OqmyVFpNVSgS0iIk3GzOjTMY0+HdO4flhP9h2o4oM124Pjt7dw59TPuHPqZ3Rql8jwvjXDSYb1ySIjWTdLikjroQJbRESOm8S4mNphIgAlO/fy7ootzFy+ldc//YJn5xUTMDita0Zt7/agrhnEBNS7LSItlwpsERE5YTpnJHHNGd245oxuVFZVs7D40M2Sf3lrBffPWEG7xNjaqQCH980mNz0p2mGLiIRFBbaIiERFbEyAId3bM6R7e350QV92llfw3sqttQX3q59sBKBvTmpt7/bQnpkkxulmSRFp3lRgi4hIs5CRHM+lAztz6cDOuDvLN5XWjt1+au7nPP7eGhJiA5zVqwPD+2Yzom8WvbN1s6SIND8qsEVEpNkxM07qlMZJndK4YXgv9lZUMXfNttre7d+9soTfAV0ykmqGkuRnc06fLNKT4qIduoiICmwREWn+kuJjGHlSR0ae1BGA4h3lzAxOBfjKwo0888F6YgLG6V0zam+qPLVLum6WFJGoUIEtIiItTl77ZL5+Zje+fmY3DlRVs2D9ztre7fumL+feactpnxzHsPxshudnMaJvNh3bJUY7bBFpI1Rgi4hIixYXE+CMHpmc0SOTn1x4EtvLKmqnApy5YgsvLywB4OROaYwI9m4X9GhPQqxulhSR40MFtoiItCqZKfGMGdSFMYO64O58tnFP7WPcn5i1hkdnriY9KY6vnpbL2CFdOS0vXTdKikiTUoEtIiKtlpnRr3M7+nVux80jelO2v5I5q7bx8qIS/jmvmKfnrqN3dgpXDcnjytPz6JSuYSQiEjkV2CIi0makJMRyfr8czu+Xw+59B5i6aCOTPyrmnteX8Yc3ljGsTxZjh+RxYb9OJMVrCImIfDmBSHY2s0wzm2ZmK4Kv7etpd7GZLTOzlWZ2e8j6X5vZBjNbEPwZHbLtF8H2y8zsokjiFBEROVK7xDjGDe3GP28+h3d+VsgPvpLP6i1l3DZpAWfcOZ2fP7eID9dux92jHaqItDCR9mDfDsxw97uChfPtwM9DG5hZDPAgcAFQDHxoZlPcfUmwyX3u/scj9ukHjAP6A52B6WbW192rIoxXRETkKN07pPDjC/ryw1H5vL9mO5M/KublRSX8Y956undI5srT87hycBe6ZiZHO1QRaQEiLbDHAIXB9xOBIo4osIGhwEp3Xw1gZpOC+y2hfmOASe6+H1hjZiuDx5kTYbwiIiL1CgSMs3t34OzeHfjNZf15/dMvmPxRMfdNX85905dzVq9M+icf4Iz9laQkaJSliNTNIvnVl5ntdPeMkOUd7t7+iDZjgYvd/bvB5euAM939VjP7NfAtYDcwD/iJu+8wsweAue7+dHCfvwKvuftzdcRwI3AjQE5OzpBJkyZ96c8TidLSUlJTU6Ny7pZI+QqP8hUe5Ss8ylfDtu6tZnZJJbM2VLKp3ImPgYKcWIZ1ieXkzAABzUJSL32/wqN8hSea+Ro5cuR8dy+oa1uD//02s+lApzo23dHI89d11TlY1T8M/C64/Dvgf4DvNLDP4SvdJwATAAoKCrywsLCRYTWtoqIionXulkj5Co/yFR7lKzzKV+OMBdydx198i9WezSsLNzK7ZB9dMpK44vTOXDUkj55ZKdEOs9nR9ys8yld4mmu+Giyw3f38+raZ2SYzy3X3jWaWC2yuo1kx0DVkOQ8oCR57U8ixHgNeaWgfERGRaDEz8tvHcEPhQH711f68uWQTk+cX81DRSh54eyVDurfnqsF5/MvAXNKT4qIdrohESUSziABTgPHB9+OBl+po8yGQb2Y9zSyempsXpwAEi/KDrgA+DTnuODNLMLOeQD7wQYSxioiINJnEuBguO60zE78zlDm/GMXtl5zM7r0H+I8XPmHondP5wTMfU7RsM1XVmoVEpK2J9A6Nu4Bnzex6YB1wNYCZdQYed/fR7l5pZrcCbwAxwBPuvji4/z1mNoia4R9rgZsA3H2xmT1LzY2QlcAtmkFERESaq5x2idw8ojc3De/FJxt28dz8YqYsLOHlhSV0TEvgisFdGDs4j/yctGiHKiInQEQFtrtvA0bVsb4EGB2yPBWYWke7645x7DuBOyOJT0RE5EQyMwbmZTAwL4M7/uUU3l66mefmF/P4u2t49J3VDMxL56rBeVx2Wmfap8RHO1wROU40x5CIiMhxkBAbw8UDcrl4QC5bS/fz0oISnptfzK+mLOb3ry5h1Mk5XDUkj8KTsomLiXTEpog0JyqwRUREjrOs1ASuH9aT64f1ZEnJbiZ/VMxLCzbw+uIv6JASz5hBXbhqSBf6d06Pdqgi0gRUYIuIiJxA/Tq3o1/nftx+ycm8s2wLkz8q5um5n/PErDWc3CmNsUPyGDOoC9lpCdEOVUS+JBXYIiIiURAXE+D8fjmc3y+HneUVvLywZgjJ71/9jP/32lIK+2Zz1ZA8Rp3SkYTYmGiHKyJhUIEtIiISZRnJ8Vx3dg+uO7sHKzbtYfJHG3jh42JmLN1MelIcl51W8yCb0/LSMT01UqTZU4EtIiLSjOTnpHH7JSfzs4tO4r2VW5k8v5hn563nf+d+Tu/sFK4akseVp+fRKT0x2qGKSD1UYIuIiDRDMQFjRN9sRvTNZve+A7y6aCOT5xdzz+vL+OMbyzi3TxZjh+RxYb9OJMVrCIlIc6ICW0REpJlrlxjHtUO7ce3QbqzdWsbzHxUz+aMN3DZpAWkJsfzLwFyuGpJHQff2GkIi0gyowBYREWlBemSl8OMLT+KH5/dl7pptTJ6/gSkLS5j04Xp6dEjmysF5XDm4C3ntk6MdqkibpQJbRESkBQoEjHN6Z3FO7yx+O6Y/r336BZPnF3PvtOXcO205Z/XKZOyQrlwyoBMpCfrnXuRE0t84ERGRFi4lIZaxQ/IYOySP9dvLeeHjDUz+qJif/nMhv3zpUy4e0InrzurO6d3aRztUkTZBBbaIiEgr0jUzmX8blc8PvtKH+Z/v4Ln5xby6aCPPf7SB8/Kz+OH5+QzpnhntMEVaNRXYIiIirZCZUdAjk4IemfzXpf3437mf89jM1Vz18BzO7dOB20b1ZWhPFdoix0Mg2gGIiIjI8ZWSEMvNI3rz7s9HcsfoU1j2RSlfe3QO4ybMYfaqrbh7tEMUaVVUYIuIiLQRyfGx3DC8F+/++0h+eWk/Vm8p4+uPvc81j87lvRUqtEWaigpsERGRNiYpPobvDOvJzH8fyW8u68+67eX861/fZ+wjc3hn+RYV2iIRUoEtIiLSRiXGxTD+nB688++F/O7yAWzcuZfxT3zAFQ/N5u2lm1Voi3xJKrBFRETauITYGK47qztFPxvJf19xKlv27OfbT37ImAdnMX3JJhXaImFSgS0iIiIAxMcG+PqZ3Sj6WSF3X3UqO8or+O5T87j0L+/x+qdfUF2tQlukMVRgi4iIyGHiYgJcc0Y33vpJIX+8+jTK9ldy89PzGf3nd5n6yUYV2iINiKjANrNMM5tmZiuCr3U+IsrMLjazZWa20sxuD1n/DzNbEPxZa2YLgut7mNnekG2PRBKniIiIhC8uJsDYIXlM//EI7rvmNCqqqvn+/33ExffP5OWFJVSp0BapU6Q92LcDM9w9H5gRXD6MmcUADwKXAP2Aa82sH4C7X+Pug9x9EDAZeD5k11UHt7n7zRHGKSIiIl9SbEyAK07PY9qPRnD/uEFUO/zgmY+56E8zeWnBBhXaIkeItMAeA0wMvp8IXF5Hm6HASndf7e4VwKTgfrXMzICvAc9EGI+IiIgcJzEBY8ygLrz5w+E88PXTiTHjtkkLuODed3j+o2Iqq6qjHaJIs2CR3BlsZjvdPSNkeYe7tz+izVjgYnf/bnD5OuBMd781pM1w4F53Lwgu9wAWA8uB3cB/uvu79cRwI3AjQE5OzpBJkyZ96c8TidLSUlJTU6Ny7pZI+QqP8hUe5Ss8yld4lK9Dqt2Zv6mKKasOsH5PNR2Tja/2iuPszrHEBgxQvsKlfIUnmvkaOXLk/IO165FiG9rZzKYDnerYdEcjz291rDuyqr+Ww3uvNwLd3H2bmQ0BXjSz/u6++6gDuU8AJgAUFBR4YWFhI8NqWkVFRUTr3C2R8hUe5Ss8yld4lK/wKF+H+wrwk2pn+mebuH/GCv766W7eLInhlsLeXDk4j9nvzVS+wqDvV3iaa74aLLDd/fz6tpnZJjPLdfeNZpYLbK6jWTHQNWQ5DygJOUYscCUwJOSc+4H9wffzzWwV0BeY11C8IiIicmIFAsaF/TtxQb8c3lq6mftnrOD25z/hL2+t5PzOVZxdWUVCbEy0wxQ5YSIdgz0FGB98Px54qY42HwL5ZtbTzOKBccH9DjofWOruxQdXmFl28OZIzKwXkA+sjjBWEREROY7MjFGn5PDSLefyt2+fQXZaAhOXVDDyD0X875y17DtQFe0QRU6ISAvsu4ALzGwFcEFwGTPrbGZTAdy9ErgVeAP4DHjW3ReHHGMcR9/cOBxYZGYLgeeAm919e4SxioiIyAlgZow8qSMvfP8cflqQQG5GEv/10mJG/OFtnpy1RoW2tHoNDhE5FnffBoyqY30JMDpkeSowtZ5jfKuOdZOpmbZPREREWigzY0BWLLdcdTZzVm3jTzNW8OuXl/Bg0SpuGt6Lb5zZnaR4DR2R1kdPchQREZHjysw4p08Wz950NpNuPIs+2an8/tXPOO+et5gwcxXlFZXRDlGkSanAFhERkRPmrF4deObGs3j2prM5Jbcd/z11KcPufpuHi1ZRul+FtrQOKrBFRETkhBvaM5P/vf5MJn/vHE7tks7dry9l2N1v8eDbK9mz70C0wxOJiApsERERiZoh3dsz8TtDefGWcxncrT1/eGMZw+5+mz/PWMGuvSq0pWVSgS0iIiJRN6hrBk986wxevnUYZ/TI5N5pyxl291vcO205u8pVaEvLogJbREREmo1T89J5fHwBr/xgGOf2zuLPM1Zw7t1v8cc3lrGjrCLa4Yk0igpsERERaXYGdEnnkeuG8Npt5zGibzYPFq1k2N1vcffrS9lWuj/a4YkcU0TzYIuIiIgcT6fktuPBbwxm+aY9/OWtlTzyziomzl7LdWd157vn9SI7LSHaIYocRT3YIiIi0uz1zUnjL9eezrQfjeDCfjk89u5qzrvnLX73yhI279kX7fBEDqMCW0RERFqMPh1T+dO405n+4xH8y6mdeXL2Ws67+21+PWUxm3ar0JbmQQW2iIiItDi9slP5n6+dxowfj2DMoM7879zPOe+et/nlS59SsnNvtMOTNk4FtoiIiLRYPbJSuGfsaRT9tJCrBnfh7++vo/APRdzxwifq0ZaoUYEtIiIiLV7XzGT+35UDKfpZIVcX5PHsvPWcf+87/OPDdbh7tMOTNkYFtoiIiLQaee2TufOKU5n2oxH0y23Hzyd/wr/+9X3Wby+PdmjShqjAFhERkVanR1YKz9xwFr+/fAAL1+/iwvtm8sR7a6iqVm+2HH8qsEVERKRVCgSMfz2rO2/+aDhn9crkt68s4epHZrNy855ohyatnApsERERadU6ZyTxxLfO4L5rTmP11jJG3/8eD7y1ggNV1dEOTVopFdgiIiLS6pkZV5yex/Qfj+CC/jn88c3lXPbALD7dsCvaoUkrpAJbRERE2oys1AQe/PpgHr1uCNtK9zPmwVnc/fpS9h2oinZo0oqowBYREZE256L+nZj2oxFcNbgLDxetYvT97/Lh2u3RDktaiYgKbDPLNLNpZrYi+Nq+nnZPmNlmM/u0sfub2S/MbKWZLTOziyKJU0RERORI6clx3DP2NJ6+/kwqqqr52qNz+NVLn1K6vzLaoUkLF2kP9u3ADHfPB2YEl+vyJHBxY/c3s37AOKB/cL+HzCwmwlhFREREjjIsP4s3fjicb53Tg6fmfs5F983kneVboh2WtGCRFthjgInB9xOBy+tq5O4zgbp+71Lf/mOASe6+393XACuBoRHGKiIiIlKnlIRYfvXV/jx389kkxgUY/8QH/OTZhewsr4h2aNICWSSPDzWzne6eEbK8w93rGybSA3jF3Qc0tL+ZPQDMdfeng+v/Crzm7s/VcdwbgRsBcnJyhkyaNOlLf55IlJaWkpqaGpVzt0TKV3iUr/AoX+FRvsKjfIWnJearosp5edUBXl1zgNQ447p+8ZzRKfaEnLsl5iuaopmvkSNHznf3grq2NfhtMbPpQKc6Nt0RaWDHOm0d6+r8n4C7TwAmABQUFHhhYeFxDKt+RUVFROvcLZHyFR7lKzzKV3iUr/AoX+Fpqfm6cBTcXLKLf39uEQ8u2M0lA9rzmzH96ZiWeFzP21LzFS3NNV8NFtjufn5928xsk5nluvtGM8sFNod5/vr2Lwa6hrTLA0rCPLaIiIjIl9a/czov3nIuj727mj9NX8HsVdv4r0v7cdXgLpjV1RcoUiPSMdhTgPHB9+OBl5po/ynAODNLMLOeQD7wQYSxioiIiIQlLibA9wv78Npt55HfMZWf/nMh4//2IcU7yqMdmjRjkRbYdwEXmNkK4ILgMmbW2cymHmxkZs8Ac4CTzKzYzK4/1v7uvhh4FlgCvA7c4u6aAV5ERESiond2Ks/edDa/uaw/89Zu56L7ZvLUnLVUV3/5e9mk9YpoxL67bwNG1bG+BBgdsnxtOPsHt90J3BlJfCIiIiJNJRAwxp/Tg6+c3JH/eOETfvnSYl5eWMLdVw2kV7ZuTJRD9CRHERERkTB0zUzmqe8M5Q9jB7Lsiz1cfP+7PFy0isqq6miHJs2ECmwRERGRMJkZVxd0ZfpPRvCVkzpy9+tLufyhWSwp2R3t0KQZUIEtIiIi8iV1TEvkkeuG8PA3BvPFrv1c9sB7/M+by9hfqVvH2jIV2CIiIiIRuuTUXKb/eDiXDerMX95ayb/8+T3mf74j2mFJlKjAFhEREWkCGcnx3Pu1Qfzt22dQvr+SsY/M5jcvL6a8ojLaockJpgJbREREpAmNPKkjb/54BNed1Z2/zVrLRX+ayayVW6MdlpxAKrBFREREmlhqQiy/HTOAZ286m9hAgG88/j63T17Err0Hoh2anAAqsEVERESOk6E9M3nttvO4eURv/jm/mAvve4dpSzZFOyw5zlRgi4iIiBxHiXEx3H7Jybz4/XNpnxzPDU/N49a/f8S20v3RDk2OExXYIiIiIifAqXnpTLl1GD+5oC9vLt7E+fe+w0sLNuCux623NiqwRURERE6Q+NgAPxiVz6v/NoweWSncNmkB10+cx8Zde6MdmjQhFdgiIiIiJ1h+ThrP3XwO/3VpP+as2saF987k7++vo1q92a2CCmwRERGRKIgJGNcP68kbPxzOqXnp/McLn3DPh/tYu7Us2qFJhFRgi4iIiERRtw7J/N93z+SuK0/l893VXHz/TB6buZqqavVmt1QqsEVERESizMwYN7Qb/z0siWF9srlz6mdc+fBsln2xJ9qhyZegAltERESkmWifGOCxbw7hz9eezvrt5Vz6l3f50/TlVFRWRzs0CYMKbBEREZFmxMy47LTOTP/xCEafmsufpq/gq395j4Xrd0Y7NGkkFdgiIiIizVBmSjz3jzudv44vYNfeA1zx0Cz+e+pn7K2oinZo0gAV2CIiIiLN2KhTcnjzx8MZN7QbE2au5pL7ZzJ39bZohyXHoAJbREREpJlrlxjHf19xKn+/4UwcGDdhLne88Al79h2IdmhSh4gKbDPLNLNpZrYi+Nq+nnZPmNlmM/v0iPV/MLOlZrbIzF4ws4zg+h5mttfMFgR/HokkThEREZHW4JzeWbx+23C+O6wnz3ywjgvvm8nbSzdHOyw5QqQ92LcDM9w9H5gRXK7Lk8DFdayfBgxw94HAcuAXIdtWufug4M/NEcYpIiIi0iokxcfwn5f2Y/L3ziEtMZZvP/khP/rHAraXVUQ7NAmKtMAeA0wMvp8IXF5XI3efCWyvY/2b7l4ZXJwL5EUYj4iIiEibcHq39rzyg/O4bVQ+Ly8s4YJ73+G9FVujHZYQeYGd4+4bAYKvHSM41neA10KWe5rZx2b2jpmdF0mQIiIiIq1RfGyAH13Ql1f+bRhZqQmM/9sHPPPBumiH1eaZ+7Efw2lm04FOdWy6A5jo7hkhbXe4e33jsHsAr7j7gDq23QEUAFe6u5tZApDq7tvMbAjwItDf3XfXse+NwI0AOTk5QyZNmnTMz3O8lJaWkpqaGpVzt0TKV3iUr/AoX+FRvsKjfIVH+QpPJPnaW+k8vGA/i7ZWcUnPOK7uG0fArIkjbF6i+f0aOXLkfHcvqGtbbEM7u/v59W0zs01mluvuG80sFwh7lL2ZjQcuBUZ5sNp39/3A/uD7+Wa2CugLzKsjvgnABICCggIvLCwMN4QmUVRURLTO3RIpX+FRvsKjfIVH+QqP8hUe5Ss8kebrgpHV/PaVJTw153OqkjL507hBJMc3WO61WM31+xXpEJEpwPjg+/HAS+HsbGYXAz8HLnP38pD12WYWE3zfC8gHVkcYq4iIiEirFhsT4LdjBvCrr/Zj+mebuObRuWzavS/aYbU5kRbYdwEXmNkK4ILgMmbW2cymHmxkZs8Ac4CTzKzYzK4PbnoASAOmHTEd33BgkZktBJ4Dbnb3o26SFBEREZGjffvcnjz2zQJWbSnl8gdnsaTkqFG2chxF9DsDd98GjKpjfQkwOmT52nr271PP+snA5EhiExEREWnLRp2Swz9vPpvrn5zH1Y/M5oGvD2bkyZHMRyGNpSc5ioiIiLRS/Tun89Kt59IzO4XrJ37IxNlrox1Sm6ACW0RERKQVy2mXyLM3nc1XTs7hV1MW8+spi6mqPvYschIZFdgiIiIirVxyfCyPXjeE7w7ryZOz13LDU/Mo3V/Z8I7ypajAFhEREWkDYgLGf17aj99fPoB3lm/h6kfmULJzb7TDapVUYIuIiIi0If96Vnf+9q0zKN5ezuUPzuKT4l3RDqnVUYEtIiIi0sYM75vN5O+fQ1xMgK89Ooc3Fn8R7ZBaFRXYIiIiIm1Q35w0XrzlXE7qlMbNT8/nsZmrCT5UWyKkAltERESkjcpOS2DSjWcxekAud079jP944VMOVFVHO6wWr/U+nF5EREREGpQYF8Nfrj2dHlnJPPj2KtZvL+fBbwwmPSku2qG1WOrBFhEREWnjAgHjZxedzB/GDuT9NdsY+/Bs1m8vj3ZYLZYKbBEREREB4OqCrjz1nTPZvGc/lz84i/mf74h2SC2SCmwRERERqXV27w48//1zSE2M5drH5vLywpJoh9TiqMAWERERkcP0zk7lhe+fy2l56fzgmY954K0VmmEkDCqwRUREROQomSnxPP3dM7ni9C788c3l/PSfi6io1AwjjaFZRERERESkTgmxMdz7tdPo0SGF+6Yvp3hHOY9eN4SM5Phoh9asqQdbREREROplZtx2fj73jxvEx+t2csVDs1mztSzaYTVrKrBFREREpEFjBnXh7zecya69B7jioVl8sGZ7tENqtlRgi4iIiEijFPTI5IXvn0NmSjzfeHwuz39UHO2QmiUV2CIiIiLSaN07pPDC987ljB6Z/PjZhdz75jLNMHIEFdgiIiIiEpb05Dgmfmco1xR05c9vreTfJi1g34GqaIfVbGgWEREREREJW1xMgLuuOpWe2Snc9dpSNuwo57FvFtAhNSHaoUVdRD3YZpZpZtPMbEXwtX097Z4ws81m9ukR639tZhvMbEHwZ3TItl+Y2UozW2ZmF0USp4iIiIg0PTPj5hG9efgbg1lcspvLH5rFys17oh1W1EU6ROR2YIa75wMzgst1eRK4uJ5t97n7oODPVAAz6weMA/oH93vIzGIijFVEREREjoNLTs3lHzedzd6Kaq54aDazVm6NdkhRFWmBPQaYGHw/Ebi8rkbuPhMIZy6XMcAkd9/v7muAlcDQCOIUERERkeNoUNcMXrzlHDqnJzH+iQ+Y9MG6aIcUNRbJXZ9mttPdM0KWd7h7fcNEegCvuPuAkHW/Br4F7AbmAT9x9x1m9gAw192fDrb7K/Cauz9Xx3FvBG4EyMnJGTJp0qQv/XkiUVpaSmpqalTO3RIpX+FRvsKjfIVH+QqP8hUe5Ss8rSFfeyudhxbs55OtVYzuGcfYvnEEzI7LuaKZr5EjR85394K6tjV4k6OZTQc61bHpjkgDAx4Gfgd48PV/gO8Adf0p1Pk/AXefAEwAKCgo8MLCwiYIK3xFRUVE69wtkfIVHuUrPMpXeJSv8Chf4VG+wtNa8nXByGp+/fJinp67jurkDtx3zSCS4pt+tG9zzVeDBba7n1/fNjPbZGa57r7RzHKBzeGc3N03hRzrMeCV4GIx0DWkaR5QEs6xRURERCQ6YmMC/G7MAHpmpfL7V5dwzYQ5PP7NAjq2S4x2aCdEpGOwpwDjg+/HAy+Fs3OwKD/oCuDgLCNTgHFmlmBmPYF84IMIYxURERGRE8TMuH5YTx67roCVm0u5/MFZLP1id7TDOiEiLbDvAi4wsxXABcFlzKyzmU092MjMngHmACeZWbGZXR/cdI+ZfWJmi4CRwI8A3H0x8CywBHgduMXdNXu5iIiISAtzfr8cnr3pbKrcGfvwHN5eFtaAhxYpogfNuPs2YFQd60uA0SHL19az/3XHOPadwJ2RxCciIiIi0TegSzov3TKM6yd+yPVPfsivL+vPN8/uEe2wjhs9Kl1EREREjrtO6Yk8e9PZfOXkjvzypcX85uXFVFV/+dnsmjMV2CIiIiJyQqQkxPLodQVcP6wnf5u1lhuemkfp/spoh9XkVGCLiIiIyAkTEzD+69J+/O7yAbyzfAtXPzKHjbv2RjusJqUCW0REREROuOvO6s4T3zqD9dvLGfPALD4p3hXtkJqMCmwRERERiYoRfbOZ/L1ziIsJ8LVH5/Dm4i+iHVKTUIEtIiIiIlFzUqc0XrjlHPp2SuOmp+fz+LurcW/ZNz+qwBYRERGRqOqYlsikG87ikgGd+P2rn3HHi59yoKo62mF9aSqwRURERCTqkuJjeODawXyvsDd/f38d33nyQ3bvOxDtsL4UFdgiIiIi0iwEAsbPLz6Ze64ayJxV2xj78GzWby+PdlhhU4EtIiIiIs3K187oylPXD+WLXfu44qFZfLxuR7RDCosKbBERERFpds7pncXz3z+X5PhYxk2Yy6uLNkY7pEZTgS0iIiIizVKfjqm8eMu5nNolnVv+/hEPvr2yRcwwogJbRERERJqtzJR4nv7umYwZ1Jk/vLGMnz23iIrK5j3DSGy0AxAREREROZbEuBj+dM0genRI4f4ZK1i/vZxHrxsS7bDqpR5sEREREWn2zIwfXdCXP10ziI/X7eTKh2azqax59mSrwBYRERGRFuPy07vwfzecyY7yCn47dy8L1u+MdkhHUYEtIiIiIi3KGT0yefGWc+nRLkDn9MRoh3MUFdgiIiIi0uJ075DCz85IomM7FdgiIiIiIq2aCmwRERERkSYUUYFtZplmNs3MVgRf29fT7gkz22xmnx6x/h9mtiD4s9bMFgTX9zCzvSHbHokkThERERGREyXSHuzbgRnung/MCC7X5Ung4iNXuvs17j7I3QcBk4HnQzavOrjN3W+OME4RERERkRMi0gJ7DDAx+H4icHldjdx9JrC9voOYmQFfA56JMB4RERERkaiySJ7nbmY73T0jZHmHu9c3TKQH8Iq7D6hj23DgXncvCGm7GFgO7Ab+093free4NwI3AuTk5AyZNGnSl/48kSgtLSU1NTUq526JlK/wKF/hUb7Co3yFR/kKj/IVHuUrPNHM18iRI+cfrF2P1OCj0s1sOtCpjk13RBpYiGs5vPd6I9DN3beZ2RDgRTPr7+67j9zR3ScAEwAKCgq8sLCwCcNqvKKiIqJ17pZI+QqP8hUe5Ss8yld4lK/wKF/hUb7C01zz1WCB7e7n17fNzDaZWa67bzSzXGBzuAGYWSxwJVD7QHl33w/sD76fb2argL7AvHCPLyIiIiJyIjVYYDdgCjAeuCv4+tKXOMb5wFJ3Lz64wsyyge3uXmVmvYB8YHVDB5o/f/5WM/v8S8TQFLKArVE6d0ukfIVH+QqP8hUe5Ss8yld4lK/wKF/hiWa+ute3IdIC+y7gWTO7HlgHXA1gZp2Bx919dHD5GaAQyDKzYuBX7v7X4DHGcfTNjcOB35pZJVAF3Ozu9d4keZC7Z0f4eb40M5tX3zgcOZryFR7lKzzKV3iUr/AoX+FRvsKjfIWnueYrogLb3bcBo+pYXwKMDlm+9hjH+FYd6yZTM22fiIiIiEiLoic5ioiIiIg0IRXYTWdCtANoYZSv8Chf4VG+wqN8hUf5Co/yFR7lKzzNMl8RzYMtIiIiIiKHUw+2iIiIiEgTUoEtIiIiItKEVGA3wMyeMLPNZvZpPdvNzP5sZivNbJGZDQ7ZdrGZLQtuu/3ERR09jcjXN4J5WmRms83stJBta83sEzNbYGZt4qFCjchXoZntCuZkgZn9MmSbvl9Hb/9ZSK4+NbMqM8sMbmuL36+uZva2mX1mZovN7LY62ugaFtTIfOkaFtTIfOkaFtTIfOkaFmRmiWb2gZktDObrN3W0ab7XL3fXzzF+qJmTezDwaT3bRwOvAQacBbwfXB8DrAJ6AfHAQqBftD9PM8jXOUD74PtLDuYruLwWyIr2Z2hm+SoEXqljvb5fDbf9KvBWyHJb/H7lAoOD79OA5Ud+T3QNCztfuoaFly9dw8LI1xHt2/Q1LHhNSg2+jwPeB846ok2zvX6pB7sB7j4TONZDbsYAT3mNuUCG1Tw2fiiw0t1Xu3sFMCnYtlVrKF/uPtvddwQX5wJ5JySwZqoR36/66PvVsGs5+iFWbYq7b3T3j4Lv9wCfAV2OaKZrWFBj8qVr2CGN/H7VR9+vhvPVpq9hwWtSaXAxLvhz5Mwczfb6pQI7cl2A9SHLxcF19a2XQ66n5n+eBznwppnNN7MboxRTc3R28Fdkr5lZ/+A6fb+OwcySgYs5/IFVbfr7ZWY9gNOp6QUKpWtYHY6Rr1C6hgU1kC9dw47Q0PdL17AaZhZjZguAzcA0d28x169IH5UuNb+WOJIfY70AZjaSmn+choWsPtfdS8ysIzDNzJYGeyzbso+A7u5eamajgReBfPT9ashXgVnuHtrb3Wa/X2aWSs0/1D90991Hbq5jlzZ9DWsgXwfb6BoW1EC+dA07QmO+X+gaBoC7VwGDzCwDeMHMBrh76D04zfb6pR7syBUDXUOW84CSY6xv88xsIPA4MMbdtx1c7+4lwdfNwAvU/IqnTXP33Qd/RebuU4E4M8tC36+GjOOIX6221e+XmcVR84/5/7n783U00TUsRCPypWtYiIbypWvY4Rrz/QrSNSyEu+8Eiqjp1Q/VbK9fKrAjNwX4ZvBO1rOAXe6+EfgQyDeznmYWT81flinRDLQ5MLNuwPPAde6+PGR9ipmlHXwPXAjUOVNEW2JmnczMgu+HUvN3dhv6ftXLzNKBEcBLIeva5Pcr+N35K/CZu99bTzNdw4Iaky9dww5pZL50DQtq5N9HXcOCzCw72HONmSUB5wNLj2jWbK9fGiLSADN7hpq7oLPMrBj4FTUD7XH3R4Cp1NzFuhIoB74d3FZpZrcCb1BzN+sT7r74hH+AE6wR+fol0AF4KHjNrXT3AiCHml//QM338u/u/voJ/wAnWCPyNRb4nplVAnuBce7ugL5fdecL4ArgTXcvC9m1TX6/gHOB64BPguMYAf4D6Aa6htWhMfnSNeyQxuRL17BDGpMv0DXsoFxgopnFUPMfs2fd/RUzuxma//VLj0oXEREREWlCGiIiIiIiItKEVGCLiIiIiDQhFdgiIiIiIk1IBbaIiIiISBNSgS0iIiIi0oRUYIuIiIiINCEV2CIiIiIiTej/A/IpFDZ+0FnOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "  \n",
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.\n",
    "    n = 10\n",
    "\n",
    "    (t, U) = explicitTrapezoid(f_1, a, b, u_0, n)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=} — by the Explicit Trapezoid Method with {n} steps\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wxqwzxtzmjjxO+m16Oy20UvvU8ffh5sGxJPxtIKN7RPPugu2c/lQC787frvHSIiIiXqbSRbQxxgd4GRgKxAHjjDFxx+w2FIgt/5kIvFq+vRi4y1rbAegD3HSc59YoWmil9mtcL5DJo7vw5a0D6BwVysOfr+fGj1ZwuKDY6WgiIiJSTdzRE90LSLLWbrPWFgJTgBHH7DMCeN+WWQSEGWMirbW7rbUrAKy1h4ANQJQbMjnmv0W0eqJruw6RIXxwdS8eOLcD367fw+hXF5B8MNfpWCIiIlIN3FFERwHJR91P4feF8F/uY4xpAXQHFrshk2NSMnIJ8vchrK6f01GkGhhjuGZAK967qhe7s/I5/6VfWZC03+lYIiIiUsXcsRrI8SZDPnaA6J/uY4wJBmYAt1trs4/7JsZMpGwoCBERESQkJJxU2KqWuCWf+v6l/Pzzz05HOa6cnByPPXY13X3xvjy/Ip8Jby9mXHt/zmzme9y5wtUGzlMbOEvH33lqA+epDZxX2TZwRxGdAsQcdT8aSDvRfYwxfpQV0B9Za2f+0ZtYa98A3gCIj4+3AwcOrHTwqvBk4jzaRgcycOApTkc5roSEBDz12NUGw84o4o6piXy0YS/FQRH838iOBPj+72qHagPnqQ2cpePvPLWB89QGzqtsG7hjOMdSINYY09IY4w9cDMw5Zp85wGXls3T0AbKstbtNWTfd28AGa+0zbsjiOC204t3qBfrxxqU9uXVwG6YuS2bcG4tIP5TvdCwRERFxs0oX0dbaYuBm4BvKLgycZq1dZ4y53hhzffluc4FtQBLwJnBj+fb+wKXAYGPMqvKfYZXN5JSsvCKy8zVHtLdzuQx3nt2OV8b3YMPuQ5z/4nwSkzOdjiUitVzG4UJWJWdy8LDmrxepDu4YzoG1di5lhfLR21476rYFbjrO837l+OOla6RUTW8nRxnWOZIWDYKY+MEyLnx9IU+M7swF3aOdjiUitcC+QwWsTc0q+0nLYm1qNqmZeUcebxISSFzTEOIiQ+gQGUJc0xCah9fF5ao1H7kijnNLES1lfjuBqSdafhPXNIQ5N5/KjR8t546piWzYfYg+dbQwi4icGGstu7Pyy4vlbNaVF817swuO7NOyYRDdm4Vxad/mtGwYxK4Duazfnc36tGx+3ryPkvLFoOr6+9C+ST3imobgk11E6K4M2jcJoY6/zx+9vYj8CRXRbqTVCuV4woP8+eDq3vzri/W88cs2FjT0oVe/YoID9OcnIseXU1DMawlb+WTJLg6UD89wGWjTOJj+rRvSMSqUTk3LepjrBf7xlKr5RSUkpeewPi27rLDenc3slWkcKijmvfULcBkY2T2Ku89uR1N9dolUiD7F3SglI486fj6EB/k7HUU8jJ+Pi3+O6ESHyBDu+2wN1763jP9ceQqBfuoBEpH/Kim1TF+ezNPfbmbfoQLO6RhB/zYN6dg0lLjIivcaB/r50CkqlE5RoUe2WWuZ/tVPhDSPY+HWA3y8ZBdfrt7NNQNacsPANvoffJETpL8UN/ptZo7jzQ0sAnBxr2ZsS9rMm2sOcPPHK3l1Qg/8fNwxSY6I1HQLkvbzyJcb2LA7mx7Nwnjj0p50b1bf7e9jjKFRXRcDOzbhnI5NuPrUljz1zSZe/mkrU5cmc/uZbbn4lBh8dW4S+VP6C3GjlIw8jYeWv9SvqS//d35Hvt+wl799mkhpqcZIi3izbftyuOa9ZVzy1mKy84p4cVx3ZtzQr0oK6OOJCa/LC+O6M+um/rRsGMQDs9Yy5Pl5/LhxL2XzAojI8agn2o1SM/Po3izM6RhSA1zatwXZ+cU89c0mggN9eWREJ32DIeJlMnMLef6HLXywcCeBfj7cM6QdV/Vv6dgwr24xYUy7ri/frNvL5K82cNW7y+jfpgH3DetAx6ahf/0CIl5GRbSbHMovIjO3SNPbyQm7cWBrsvOLeP3nbYQE+nHPkPZORxKRalBUUsoHC3fy/A9bOJRfxNhTmnHnWW1pVC/A6WgYYxjSqQmD2zfmo8VlGc978VdG94jm7rPb0SQ00OmIIh5DRbSbaHo7qShjDJOGtOdQfjGvJGylXqAfNwxs7XQsEaki1lq+35DO43M3sG3/YU5t05AHzutA+yYhTkf7HX9fF1f2b8moHtG8/FMS787fwRer07h2QCuuP701Qbr4UERFtLukHNRCK1JxxhgeGdGJnPxinvh6IyF1fBnfu7nTsUTEzQqKS7j709V8nphG60ZBvHNFPIPaNfb4YVyhdfy4b1gHLu3TnCe+3siLPybx3fq9vHtlL/VKi9fThYVu8tsc0eqJlorycRn+fVFXBrdvzAOz1jJ7VarTkUTEjbLzi7jinaV8npjG3We35evbT2Nw+wiPL6CPFhNel5cu6cF7V/Ui+WAuo16Zz5a9h5yOJeIoFdFukpqZR6CfiwaaI1pOgp+Pi1fG96BXi3DumpbIDxv2Oh1JRNwgPTufsa8vYumOgzw3ths3D46t0dNant62EVOv60tRqWX0qwtYsv2g05FEHFNz/5I9TEpGHlFhmiNaTl6gnw9vXR5Px6Yh3PDRChZuPeB0JBGphK37crjglQXsOnCYd644hZHdo5yO5BadokKZeUM/GgYHMOHtxXy1ZrfTkUQcoSLaTcrmiNZ4aKmceoF+vHtlL5qH1+Wa95aSmJzpdCQROQkrd2Uw5tUF5BeVMGViX05r28jpSG4VE16X6Tf0o2PTEG78eAXvLdjhdCSRaqci2k1+W61QpLLqB/nz4TW9CQ/25/L/LGGzxh2K1Cg/btzLJW8uJqSOHzNu6Efn6No5x3J4kD8fX9OHM9pH8I8563ji641anEW8iopoNzhcUEyG5ogWN4oICeSjq/vg7+NiwluLST6Y63QkETkB05Ylc+37y2nTOJjp1/ejRcMgpyNVqTr+Prw2oQeX9G7GqwlbuWtaIoXFpU7HEqkWKqLd4Lc5oqPUEy1u1KxBXT68pjf5RSVc98Fy8otKnI4kIn/AWsvLPyVxz/TV9GvdgE8m9vGIxVOqg6+Pi0dHduKus9oyc2UqV7+3lJyCYqdjiVQ5FdFuoOntpKq0jajHcxd3Y/3ubB6ctVZflYp4oJJSyz/mrOOpbzYxsltT3r78FIK9bDESYwy3nBHLk2O6sGDrAca+vpD0Q/lOxxKpUiqi3SAlQ6sVStUZ3D6CWwe34dPlKUxZmux0HBE5Sn5RCbd8soL3F+5k4mmteOaibvj7eu9H60XxMbx1eTzb9h1m1CsL2Lovx+lIIlXGe//S3SglI48AXxeNgr3jqzupfred2ZYBsQ35x+x1rE7JdDqOiABZeUVc/s4S5q7ZwwPnduC+YR1wuTTN6aB2jZkysQ95hSWMeXUBK3ZlOB1JpEqoiHaD1Iw8ouprjmipOj4uw/MXd6dRvQBu+HAFGYcLnY4k4tVyC4u59O3FrNiVwfMXd+OaAa2cjuRRusaEMfPGfoTU8ePyd5aQlK5ZhqT2URHtBikZuUSFaSiHVK3wIH9eGd+DfYcKuG3qKkpKNT5axAmlpZbbp6xibWoWr4zvyYhutWMRFXdr3iCIj67pTYCviyvfXcqBnAKnI4m4lYpoN9BCK1JdusaE8Y/z4/hl8z5e+GGL03FEvNITX2/k2/V7eeDcOM6Ki3A6jkeLrl+XNy+LJz27gImaZUhqGRXRlZRbWMyBw4W6qFCqzSW9mjG6RzQv/LiFnzalOx1HxKtMWbKL13/ZxoQ+zbiyfwun49QI3ZvV59mx3Vi+M4O/TV9Nqb5Fk1pCRXQlpWpmDqlmxhj+NbIT7ZuEcPuUVVqIRaSazE/azwOz1jIgtiEPD++o62AqYFjnSP4+pD2fJ6bx3PebnY4j4hYqoispJVNFtFS/31YJK7WWGz7SV6QiVS0pPYfrP1xOy4ZBvDy+B74++visqOtPb8XY+Bhe+DGJGctTnI4jUmk6C1TSf+eI1phoqV7NGwTx7EXdWJuazT9mr3M6jkitdfBwIVe9u5QAXxfvXHEKIYF+TkeqkYwx/OuCTvRr3YBJM1ezeNsBpyOJVIqK6EpKycjF30dzRIszzoyL4KZBrZm6LJmpS3c5HUek1ikoLuG6D5axJzufNy6LJyZcHSaV4efj4tXxPWkWXpfrPlzO9v2HnY4kctJURFdSSvkc0ZpgX5xy51nt6N+mAQ/OXsfa1Cyn44jUGtZaJs1Yw9IdGfz7wq70aFbf6Ui1QmhdP/5zRS9cxnDlf5Zo3nupsVREV1LZ9HYaDy3O8XEZXri4Ow2C/Ln+w+Vk5uoDScQdXvwxic9WpnLXWW0Z3rWp03FqlWYN6vLmZT1Jy8rnug+WU1Cs6zqk5lERXUmpGXlaaEUc1yA4gFfG92Bvdj53TF2lKaREKmlOYhrPfLeZUd2juHlwG6fj1Eo9m4fz1JguLNlxkHtnrMFanbekZlERXQn5RSXszylQT7R4hO7N6vPQeXH8tGkfryQkOR1HpMZavjODuz9N5JQW9Xl8dGdNZVeFRnSL4s6z2jJzZSov/ajzltQsbimijTFDjDGbjDFJxphJx3ncGGNeKH98tTGmx1GPvWOMSTfGrHVHluqkmTnE00zo05zzukTy3PdbND5a5CQkH8xl4vvLiAwN5PVL4wnw9XE6Uq13y+A2jOoRxb+/28zsValOxxE5YZUuoo0xPsDLwFAgDhhnjIk7ZrehQGz5z0Tg1aMeexcYUtkcTkjJKFvkQj3R4il+W4glPMifO6au0vzRIhWQnV/EVe8upaiklHeuOIXwIH+nI3kFYwyPj+pMr5bh/G36apbvPOh0JJET4o6e6F5AkrV2m7W2EJgCjDhmnxHA+7bMIiDMGBMJYK39BaiRfzHqiRZPFFbXnyfHdGFLeg7//naT03FEaoSSUsstH69k+/7DvDahJ60bBTsdyasE+Prw+oSeRIXVYeL7y0nPznc6kshf8nXDa0QByUfdTwF6n8A+UcDuE30TY8xEynqxiYiIICEh4WSyutXCTYX4GFi/YiEba8iYuZycHI84dt6sutpgUIwvb83bToOC3bQP11fSR9PfgbM88fh/sa2QnzcXcXmcP4Upa0mo5QvqeWIbAFzbvpSHFxRy5es/cVd8IK4a8tl6Mjy1DbxJZdvAHUX08f4LP/YS2xPZ509Za98A3gCIj4+3AwcOrMjTq8SM3SuJDs9k8KBBTkc5YQkJCXjCsfNm1dUGp/QtZtgL8/hwi+Wr2/pTT6usHaG/A2d52vFfuSuDz75dyLldInl4XHevuJDQ09rgaK7Gu5g0cw2bXc24/vTWTsepMp7cBt6ism3gjuEcKUDMUfejgbST2KfGScnI1Xho8VhBAb78+8KupGXm8a8vNjgdR8QjZecXceuUlTQJCeSxCzQThycYe0oM53aO5OlvNrEqOdPpOCJ/yB1F9FIg1hjT0hjjD1wMzDlmnznAZeWzdPQBsqy1JzyUw1OlZOQRHabx0OK54luEc93pZcuCf79+r9NxRDyKtZYHZ60lLTOfF8Z1I7SOvq3xBMYYHhvVmYiQQG79ZCWH8oucjiRyXJUuoq21xcDNwDfABmCatXadMeZ6Y8z15bvNBbYBScCbwI2/Pd8Y8wmwEGhnjEkxxlxd2UzVIb+ohH2HNEe0eL7bz4ylfZN6TJq5mgM5BU7HEfEYM1ekMntVGredEUvP5uFOx5GjhNbx44Vx3UjNzOOBWWu1EIt4JLfME22tnWutbWutbW2tfbR822vW2tfKb1tr7U3lj3e21i476rnjrLWR1lo/a220tfZtd2SqammZZTNzRKmIFg8X4OvDs2O7kZVXxP2f6cNIBGD7/sM8NHstvVqGc9MgrUjoiXo2D+f2M2KZvSqNmSs0f7R4Hq1YeJI0vZ3UJB0iQ7jzrHZ8vW4Ps7SYgXi5wuJSbv1kJb4+Lp4b2w0fl8ZBe6obB7Whd8twHpy9lm37cpyOI/I/VESfpP8W0eqJlpph4mmt6Nm8Pg/NXnfkmxQRb/TvbzexJjWLJ0Z3oWmYzuGezMdleO7ibvj7urh1ykoKi0udjiRyhIrok5SSkYuvyxAREuh0FJET4uMyPHNRV0pKLX+bnkhpqYZ1iPf5ZfM+Xv9lG+N7N2NIpyZOx5ETEBlahydHd2FtajZPfbPR6TgiR6iIPkkpGXk0DaujrwGlRmneIIj7z+3A/KQDfLBop9NxRKrV/pwC7pyWSGzjYB44N87pOFIBZ3dswmV9m/PmvO0kbEp3Oo4IoCL6pKVm5hGlrwGlBrqkVzNOb9uIx7/awFaNMRQvUVpqufvTRLLzi3jxku7U8dcqnjXNfcM60L5JPe7+NJH0Q1oWXJynIvokaaEVqamMMTw5pgsBvj7cOS2R4hKNMZTa7z8LdpCwaR8PnNuB9k1CnI4jJyHQz4cXx3Unp6CYu6ZpSJo4T0X0SSgoLmFvdoFm5pAaKyIkkH+N7ERiciavJmx1Oo5IlVqbmsXkrzZwZocILu3T3Ok4UgmxEfV46LyOzNuynzfnbXM6jng5FdEnIS2z7Gsk9URLTTa8a1OGd23K8z9sYW1qltNxRKrE4YJibv1kJeFB/jw5pouW9a4FxvWKYWinJjz1zSYStSy4OEhF9ElIycgFtNCK1HyPjOhIg2B/7pqWqKmjpFb65+fr2H7gMM+O7UZ4kL/TccQNjDFMHtWFxvUCuHWKlgUX56iIPgmpmiNaaomwuv48OrIzm/Ye0rAOqXW+WJ3GtGUp3DiwNf1aN3Q6jrhRaF0/nh/XneSDuTw4a63TccRLqYg+CSkZefi4DE00R7TUAmfGRTC8a1Ne+mkLW/YecjqOiFukZeZx78w1dG8Wxu1ntnU6jlSBU1qEc9sZbZm1Ko0vVqc5HUe8kIrok5CSkUtkaCC+Pjp8Ujv8Y3gcwQG+3DNjNSW64l1qOGstk2auoaTU8vzY7vjpXF1r3TSoNV2jQ3lo9jr25xQ4HUe8jM4sJyElI09DOaRWaRgcwEPD41i5K5P3F+5wOo5IpUxdmswvm/cxaWh7mjXQLEq1ma+Pi6cv7EpOfjEPzlqLteoEkOqjIvoklC20ohOz1C4ju0UxsF0jnvx6E8kHc52OI3JSUjPz+NeXG+jTKpwJvTWdnTeIjajH7WfF8tXaPXyxerfTccSLqIiuoMLiUvZk56snWmodYwyPXtAZl4H7PlujHh2pcay1TJqxmlJreWpMV1wuTWfnLSYOaEXXmDAemr2WfYc0rEOqh4roCtqdlYe1mplDaqeosDrcM6Q987bsZ8aKVKfjiFTIlKXJzNuyn3uHticmXN8WehNfHxdPj+nC4YISDeuQaqMiuoJSjkxvpxO01E6X9mlOfPP6PPLFevXoSI2RmpnHo19uoG+rBozXMA6vFBtRjzvPbsvX6/bwuYZ1SDVQEV1Bvy20op5oqa1cLsPk0V3IKyzh4TnrnI4j8peOHsbx5JguGsbhxa4d0Ipu5cM60g/lOx1HajkV0RWUmpGHy0CTUM0RLbVXm8bB3HpGG75cs5tv1+1xOo7In/pkSfkwjmEdNIzDy/m4DE9f2JXcwhIe+EzDOqRqqYiuoJSMPCJD62jeUan1rju9Ne2b1OPB2WvJytOyuuKZUjJyefTL9fRr3YDxvZo5HUc8QJvGwdx1Vlu+Xb+XOYlahEWqjirBCkrJyCNKQznEC/j5uHhyTBf2HSpg8lcbnI4j8jtlwzjWAPDEaA3jkP+6ZkArujcL4x9z1mlYh1QZFdEVlJKRq/HQ4jW6RIdxzYBWfLIkmQVb9zsdR+R/fLxkF78maRiH/N5vwzryCku4X8M6pIqoiK6AopLf5ojWyVq8xx1ntqV5g7rcO3MNeYUlTscRASD5YC6PfbmB/m0aML63hnHI77VuFMzdZ7fju/V7mb1KwzrE/VREV8CerHxKLUSHqSdavEcdfx8eH9WZnQdyee77zU7HESkbxjFzNVA2jMMYDeOQ47vq1Jb0bF6/bFhHtoZ1iHupiK6AZE1vJ16qX+uGjOsVw5vztrE6JdPpOOLlPlq8i/lJB7jv3A76ZlD+lI/L8NSYLuQXlWglVnE7FdEVoIVWxJtNGtqBhsEB3DN9NUUlpU7HES+VfDCXx+du4NQ2DblEs3HICWjVKJi/ndOO7zek89lKrcQq7qMiugJSNEe0eLHQOn78a2QnNu45xOs/b3U6jnih0lLL32esxhjD5NGdNYxDTtiV/VsS37w+D89Zx14N6xA3URFdASkZuUSEBOLvq8Mm3unsjk04t3MkL/yQRFJ6jtNxxMt8tGQXC7Ye4L5hGsYhFePjMjw5pguFJaXcN1PDOsQ9VA1WQGpGnsZDi9d7+PyO1PH34d6Zqykt1QeRVI/fhnEMiC0bny9SUWXDOtrzw8Z0Zq7QsA6pPBXRFZCSkafeD/F6jeoF8MC5HVi6I4OPluxyOo54gd9m43AZw2TNxiGVcGW/FsQ3r8//fbFes3VIpbmliDbGDDHGbDLGJBljJh3ncWOMeaH88dXGmB4n+lxPUXxkjmj1RIuM6RnNqW0a8sRXG9mdled0HKnlpixNZn7SAe4d1p4oTTEqleByGZ4on63jgVlahEUqp9JFtDHGB3gZGArEAeOMMXHH7DYUiC3/mQi8WoHneoTdWfmUlFoV0SKAMYbHLuhMSanlAa0GJlUoLTOPR7/cQN9WDRh3imbjkMpr3SiYO89qy7fr9/Llmt1Ox5EazB090b2AJGvtNmttITAFGHHMPiOA922ZRUCYMSbyBJ/rEX6b3i4qTMM5RACaNajLXWe35YeN6XyxWh9E4n7WWu77bA0lpZYnRnfB5dIwDnGPq09tSdfoUB6avY4DOQVOx5EaytcNrxEFJB91PwXofQL7RJ3gcwEwxkykrBebiIgIEhISKhW6on5NLQIgdfNqElJr7lDynJycaj928r9qUxu0LLW0DHFx34yVmL2bCPavGUVObWqDmuhEj//81CISNhUyvr0/29YsYVvVR/Ma+huAC5uX8o/UQm586ydu6Fb9U9eqDZxX2TZwRxF9vE/NY7/b/aN9TuS5ZRutfQN4AyA+Pt4OHDiwAhErr+vhQgb3yeaUFuH4+dTcIjohIYHqPnbyv2pbGzTtkM3wF3/lx8z6PHNRN6fjnJDa1gY1zYkc//TsfG5N+Jn45vV55LK+6oV2M/0NlMmou4V/f7eZqxq155yOTar1vdUGzqtsG7ijGkwBjp5vKBpIO8F9TuS5HqF+kD/9Wjes0QW0SFXoEBnC9ae3ZuaKVH7ZvM/pOFILWGu5f9ZaCopLeXKMhnFI1bl+YGviIkN4YNZaMnMLnY4jNYw7KsKlQKwxpqUxxh+4GJhzzD5zgMvKZ+noA2RZa3ef4HNFxMPdPLgNrRoFcd9nazhcUOx0HKnhPl+9m+/W7+Wus9vSqlGw03GkFvPzcfHkmC5kHC7kkS82OB1HaphKF9HW2mLgZuAbYAMwzVq7zhhzvTHm+vLd5gLbgCTgTeDGP3tuZTOJSPUK9PNh8qgupGTk8e9vNzsdR2qwAzkFPDxnHV1jwrj61FZOxxEv0CkqlBsGtmbGihR+2pTudBypQdwxJhpr7VzKCuWjt7121G0L3HSizxWRmqdXy3Am9GnGfxZsZ3jXSLo3q+90JKmBHpqzjpz8Yp4a0wUfDeOQanLz4DZ8vXYP981cwzd3nEZIoJ/TkaQG0ABfEXGbvw9pT0S9QCbNWENhcanTcaSG+Xrtbr5cvZtbz2hD24h6TscRLxLg68NTF3Zlb3Y+j8/d6HQcqSFURIuI29QL9OORkZ3YtPcQr/281ek4UoNkHC7kgVnr6Ng0hOtOb+10HPFC3WLCuHZAKz5Zsov5SfudjiM1gIpoEXGrs+IiOLdLJC/9mERS+iGn40gN8cgX68nMLeSpMV01C5I45o6z2tKyYRB/n7FaF0nLX9KZSkTc7uHhHanj78OkGWsoLdWS4PLnfty4l5krU7lxUBvimoY4HUe8WKCfD0+O6UJqZh5PfbPJ6Tji4VREi4jbNaoXwIPnxbFsZwYfLt7pdBzxYFl5Rdw7cw3tIupx86A2TscR4ZQW4VzetwXvLtjBku0HnY4jHkxFtIhUidE9ohgQ25AnvtpIWmae03HEQz325Qb2HSrgqQu74O+rjyTxDPcMaUdMeB3umZ5IXmGJ03HEQ+mMJSJVwhjDYxd0ptTCA7PWUjbTpch/zduyj6nLkpl4Wmu6RIc5HUfkiLr+vjwxqgs7DuTy7Pea+16OT0W0iFSZmPC63HV2W37cmM7MFalOxxEPklNQzKQZa2jVKIjbz4x1Oo7I7/Rr05BLejfjrXnbWLErw+k44oFURItIlbqyf0vim9fn4c/XsTtLwzqkzGNzN5CWlcdTY7oQ6OfjdByR47p3aHuahARy9zQN65DfUxEtIlXKx2V4+sKuFJdY7pm+WsM6hMR9xXy8eBcTB7SiZ/Nwp+OI/KF6gX48fWFXtu0/zOSvNjgdRzyMimgRqXItGgZx37D2zNuyn4+X7HI6jjjo4OFC3llbSLuIetxxVlun44j8pX5tGnJV/5a8t3An87bsczqOeBAV0SJSLcb3bs6pbRry6Jcb2HUg1+k44gBrLQ/MWkNOoeXZsd00jENqjHuGtKNN42D+9ulqsnKLnI4jHkJFtIhUC5fL8MSYLvgYw92fJmoRFi80a1Uqc9fs4YJYPy2qIjVKoJ8Pz17Ujf05BTw0Z63TccRDqIgWkWoTFVaHh4bHsWTHQd6Zv93pOFKN0jLzeGj2OuKb12dYSz+n44hUWOfoUG4ZHMvsVWl8sTrN6TjiAVREi0i1GtMzmjPaN+bJbzaRlJ7jdBypBqWllr9NT6Sk1PLvi7riMsbpSCIn5aZBrekaE8YDs9aSnp3vdBxxmIpoEalWxhgeH9WZuv4+3PVpIsUlpU5Hkir23sIdzE86wIPnxdG8QZDTcUROmq+Pi2cu6kp+UQn3zNBsQ95ORbSIVLvGIYE8MqITicmZvP7LNqfjSBVKSj/E5K82ckb7xlx8SozTcUQqrXWjYO4d2oGETfs025CXUxEtIo4Y3rUp53aJ5LnvN7M+LdvpOFIFikpKuWNqInX9fXh8dGeMhnFILXFpn7LZhv71xQZ27D/sdBxxiIpoEXHMIyM6EVrHnzunraKwWMM6apsXf0xiTWoWj4/qTON6gU7HEXEbl8vw1IVd8PUx3PVp2Xh/8T4qokXEMeFB/jw+qjMb9xzihR+2OB1H3GhVciYv/5TEqB5RDOkU6XQcEbeLDK3DIyM6sXxnBq/9vNXpOOIAFdEi4qiz4iIY0zOaVxKSWJWc6XQccYO8whLunLqKJiGBPHx+R6fjiFSZEd2acm7nsmFp69KynI4j1UxFtIg47qHhcUSEBHLXtFXkF5U4HUcq6fGvNrBt/2GeurALIYGaE1pqL2MM/xrZibC6/tw5NVHnLy+jIlpEHBcS6McTo7uwdd9hnv5mk9NxpBJ+2byP9xfu5OpTW9KvdUOn44hUufpB/jw5pgub9h7i2e82Ox1HqpGKaBHxCKe1bcSEPs14e/52Fm874HQcOQlZuUXcM301bRoH87dz2jkdR6TaDGrXmEt6N+ONedt0/vIiKqJFxGPcO7QDMfXrcvf0RHIKip2OIxX04Oy17M8p4Lmx3Qj083E6jki1un9YB5qF1+WuT3X+8hYqokXEYwQF+PL0hV1JzcjjvplrtBpYDTInMY05iWncdkYsnaJCnY4jUu2CAnz594VdScvM46HZa3X+8gIqokXEo/RqGc6dZ7VlTmIaHy7a6XQcOQFJ6TncN3MNPZqFccPA1k7HEXFMfItwbhkcy8wVqXyyJNnpOFLFVESLiMe5cWAbBrVrxP99sV7T3nm4wwXFXP/hcgJ8Xbw8vge+PvpYEe926xmxnNa2EQ/PWUeizl+1ms52IuJxXC7Ds2O70bheIDd9tIKMw4VOR5LjsNby9xmr2bYvhxfHdScytI7TkUQc5+MyPD+2G43qBXCjzl+1mopoEfFIYXX9eXVCD/YdKuCOaaso1bK6Hued+Tv4YvVu/nZOe/q10XR2Ir+pH+TPK+PLzl+3TV2lZcFrKRXRIuKxukSH8eDwOBI27ePln5KcjiNHWbL9II/P3cDZcRFcf3orp+OIeJyuMWE8fH5Hftm8j+d/2OJ0HKkClSqijTHhxpjvjDFbyn/X/4P9hhhjNhljkowxk47afqExZp0xptQYE1+ZLCJSO03o3YyR3ZryzPeb+XXLfqfjCJCenc9NH68gJrwuT1/UFWOM05FEPNK4XjGM7hHNCz9s4aeN6U7HETerbE/0JOAHa20s8EP5/f9hjPEBXgaGAnHAOGNMXPnDa4FRwC+VzCEitZQxhkcv6EybRsHcNmUle7LynY7k1YpKSrn545Xk5Bfz2oSeWtZb5E/8tix4h8gQbp+6iuSDuU5HEjeqbBE9Aniv/PZ7wMjj7NMLSLLWbrPWFgJTyp+HtXaDtVZr/IrInwoK8OXVCT3IKyrhpo9XUFRS6nQkrzX5q40s2XGQyaM7065JPafjiHi8Ov4+vDahB6XWcsNHy8kvKnE6kriJqcxk4MaYTGtt2FH3M6y19Y/ZZwwwxFp7Tfn9S4He1tqbj9onAbjbWrvsT95rIjARICIioueUKVNOOrc3y8nJITg42OkYXk1tcPIW7S7mtcQCzmnhy7j2ASf9OmqDk7NkdzGvJBZwZjNfJsTp+NdkaoPqtzK9mOdXFHBatC9XdQpQG3iAE22DQYMGLbfW/m7Yse9fPdEY8z3Q5DgP3X9CCeF4g+UqXLlba98A3gCIj4+3AwcOrOhLCJCQkICOnbPUBidvIJBXdy3vLdzJyP5dGNo58qReR21QcVv2HuLdH+fTs3l9Xrm2D/6+J/9Fpo6/89QG1W8gUBy6kZd/2sp5veNozFa1gcMq+3fwl0W0tfbMP3rMGLPXGBNprd1tjIkEjjdqPgWIOep+NJBW4aQiIsD958aRmJLF36avpn1kCC0bBjkdqdY7lF/EdR8up66/Dy9f0qNSBbSIN7vzrHasSs7kgdlrue8Uf6fjSCVV9kw4B7i8/PblwOzj7LMUiDXGtDTG+AMXlz9PRKTC/MtXxvPzMdzw4XLyCjW+sCpZa7ln+mp2HsjlxXE9aBIa6HQkkRrLx2V44eLuNAjy56VVBWTmaiGWmqyyRfRk4CxjzBbgrPL7GGOaGmPmAlhri4GbgW+ADcA0a+268v0uMMakAH2BL40x31Qyj4h4gaiwOjw7thub9h7igVlrqcy1HfLn3py3ja/W7uHvQ9rRt3UDp+OI1HgNggN4ZXwPMvItd0zVQlI1WaWKaGvtAWvtGdba2PLfB8u3p1lrhx2131xrbVtrbWtr7aNHbf/MWhttrQ2w1kZYa8+pTB4R8R4D2zXmlsGxzFiRwrRlyU7HqZUWbj3AE19vYminJlw7QAuqiLhL92b1uaSDPz9t2sdLWkiqxtLANhGpsW47I5YBsQ15cPY6VqdkOh2nVtmTlc8tn6ygeYO6PHWhFlQRcbfBMb6M7NaUZ7/fzM+b9zkdR06CimgRqbF8XIbnxnajUXAAV/xnKUnph5yOVCvkFBRz3YfLyS0s4fUJPQkO+Mtr0EWkgowxPDaqM20b1+Pmj1awNjXL6UhSQSqiRaRGaxAcwEfX9MbHZRj/1mJ2HdCKYJWRV1jC1e8uZW1qFs+N7UZshBZUEakqdf19eefKUwip48elby9m0x51BNQkKqJFpMZr0TCID6/uTUFxKePfXqSlwU9SflEJEz9YxpIdB3nmoq6c3fF4SwSIiDtFhdXh42t74+fjYsLbi9m+/7DTkeQEqYgWkVqhXZN6vHdlLzIOFzH+rUUcyClwOlKNUlRSys0fr2Delv08MboLI7pFOR1JxGs0bxDER9f0pqTUMv7NRaRk6Bu1mkBFtIjUGl1jwnj78nhSM/O49O0lZOUVOR2pRiguKeX2Kav4fkM6j4zoyEXxMX/9JBFxq9iIerx/VS9yCooZ/9Zi9mbrGzVPpyJaRGqV3q0a8NqEnmxJP8SV/1nC4YJipyN5tNLSssVUvlyzmwfO7cClfVs4HUnEa3WKCuXdq3qx/1AB499arG/UPJyKaBGpdQa2a8wLF3dnVXImEz9YRn6RVjU8Hmst989ay8yVqdx1Vluu0VzQIo7r0aw+b19xCskHc/WNmodTES0itdLQzpE8NaYr85MOcPPHKykqKXU6kkex1vLPz9fzyZJd3DSoNbecEet0JBEp16dVA16/tOwbtSv+s4QcfaPmkVREi0itNbpnNI+M6Mj3G/Zy17RESrS8LlBWQD/5zSbeXbCDq/q35O6z2zkdSUSOMbBdY14c14PVKVlc895SfaPmgVREi0itdmnfFvx9SHvmJKbxwKw1WKtC+sUfk3g1YSvjezfjwfM6aDVCEQ81pFMTnrmoK4u3H+S6D5ZTUKxC2pNoGSoRqfVuGNianIIiXv5pK0H+vvQP8t5C+o1ftvLMd5sZ3SOaR0Z0UgEt4uFGdIsir7CESTPXcNsnq3jpku74+qgP1BOoFUTEK9x9djuu6NeCt37dzuyt3nmhzvsLd/DY3I2c1yWSJ8d0weVSAS1SE1zcqxkPnRfH1+v2cPenGprmKdQTLSJewRjDQ+fFkVNQzPTlKTT7bjO3nRGLj5cUklOX7uKh2es4Ky6CZ8d285p/t0htcdWpLckrKuGpbzbh7+vi0Qs64+clPdLp2fls3XeYvq0bOB3lf6iIFhGv4XIZJo/qzO7de3jhhy2s2JnBs2O70ahegNPRqkx+UQmTv9rIuwt2cFrbRrx0SXev+eAVqW1uGtSGgqISXvgxic17c3hxXHdiwus6HatKJWxK565pifj6GH65ZxABvj5ORzpCZ1IR8Sq+Pi6u6ezP5FGdWbrjIEOfn8f8pP1Ox6oSSek5XPDKAt5dsIMr+7fgzct6etQHkIhU3J1nt+PlS3qwNT2HYS/M46s1u52OVCUKi0t59Mv1XPGfpTSqF8CHV/f2uPOXimgR8TrGGC7u1YzZN/cntI4vE95ezDPfba414wyttUxbmszwF39lb3Y+b18ezz+Gd/S4DyAROTnndolk7m0DaNUomBs+WsEDs9bUqinwduw/zOhXF/DmvO1c2qc5s27qT2xEPadj/Y6KaBHxWu2bhPD5Lacyqns0L/ywhfFvLWJvdr7TsSolO7+IW6es4p4Zq+neLIyvbhvAGR0inI4lIm4WE16XT6/ry8TTWvHhol2MfHk+Sek5TseqtM9WpnDuC/PYdTCX1y/tySMjOxHo55kdACqiRcSr1fX35d8XdeXpC7uSmJzFsOfn8fPmfU7HOikrd2Vw7gvzmLtmN387px0fXN2biJBAp2OJSBXx93Vx37AO/OeKU0g/VMD5L/3K9OUpTsc6KTkFxdw5bRV3TE2kY9NQvrptAOd0bOJ0rD+lIlpEBBjTM5rPb+lPw+AALn9nCU98vZHiGrJUeGmp5ZWEJC58bSGlpTDtur7cNKiNZuAQ8RKD2jdm7q0D6BIdyt2fJnLn1FUcrkFLha9JyWL4i78ya2Uqt58Zy8fX9qZpWB2nY/0lFdEiIuXaNK7H7Jv7M65XDK8mbOXiNxaRlpnndKw/lZ6dz2XvLOHJrzdxTqcmzL1tAD2b13c6lohUsyahgXx0TR9uPzOWWatSGf7ir6xLy3I61p+y1vLWvG2MenU+eYUlfHJtH24/s22NWUymZqQUEakmgX4+PD6qC89f3I0Nu7MZ9sI8ftiw1+lYx/XTpnSGPj+PZTsPMnlUZ14a153QOn5OxxIRh/i4DLef2ZaPr+3D4cJiLnhlAe8v3IG1nnfR9P6cAq56dyn/+nIDA9s15qvbBtC7lWfNA/1XNE+0iMhxjOgWRZfoMG76aAVXv7eMi+KjuaxvCzpFhTodjfTsfF79eSv/mb+D9k3qMfWSPrRp7HlXrouIM/q0asDcWwdw96eJPDR7HfO27OfWwbF0igrBGGeHeZWUWn7YsJf7Z60lK6+I/xvRkUv7NHc818lQES0i8gdaNgxi5o39ePLrTXy4eCfTlqXQsWkIY0+JYUTXKELrVl+vb35RCd9v2MuM5Sn8vHkfpRYu69uc+4Z18Ngr10XEOQ2CA3j78lN4+9ftPP3tJr5bv5cOkSFcFB/NyG5R1A/yr9Y8SemHmL48lc9WprA3u4DWjYJ478pexDUNqdYc7qQiWkTkTwT6+fDQ8DhuO6NsnOHUpck8NHsdj365gSGdmjA2PoY+rRrgqoKL+Ky1rErOZPryFD5PTCM7v5jI0ECuP701o3pE06ZxsNvfU0RqD5fLcO1prbjolBg+T0xj2rJk/vn5eh6fu5Gz4iK4MD6aAbGNquwi5KzcIuasTmPG8hRWJWfi4zIMbNuIh4dHM7hD4xo/d72KaBGRExBa14/L+7Xg8n4tWJuaxdSlycxalcrsVWk0C6/LhT2jGRMfTWRo5a8o352Vx2crU5m+PIVt+w4T6OdiSMcmjO4ZTb/WDTXrhohUSGgdPyb0ac6EPs3ZsDubT5el8NnKFL5cs5vI0EBG94jmwvhomjcIqvR7FZeUMm/LfqavSOG79XspLC6lXUQ9Hji3AyO6RdGoXoAb/kWeQUW0iEgFdYoKpVNUKPef24Gv1+5h6tJk/v3dZp79fjOnt23E2FNiGNw+An/fE792O6+whG/X72H68hR+TdqPtdCrRTjXndaKYZ0jqReoCwZFpPI6RIbw0PA4Jg1tzw8b9jJ1WTKvJCTx0k9J9GkVzkXxMQztFEkd/4r1Em/ee4gZy1OYuTKVfYcKqF/Xj0t6NWNMz2g6NnV+LHZVUBEtInKSAv18GNk9ipHdo9h54DCfLkvh0+XJXP/hClwGfF0ujAGXMb/77Tpyv+z2ofxi8opKiAqrwy2DYxndI8otvUIiIsfj7+tiaOdIhnaOZHdWHjNXpDJtWTJ3Tkvk/s/WElrHD2PAAKb83FV23xzZ7iq/UVxi2XUwF1+XYWC7xozpGc3g9o0r1JFQE6mIFhFxg+YNgrj7nHbcfmYsv2zZx/KdGZRaKLUWa8sWRCm1YCm/b235T9nY5wBfH87p2ITeLcOrZHy1iMgfiQytw02D2nDjwNYs2X6Qr9buIbewGGvBUna+ovy2/e28VX7bApRf6DyyexQNg2vPcI2/oiJaRMSNfH1cDG4fweD2EU5HERGpEGMMvVs1qHHzNTulUv3sxphwY8x3xpgt5b+Pu0yWMWaIMWaTMSbJGDPpqO1PGWM2GmNWG2M+M8aEVSaPiIiIiEh1qOxglUnAD9baWOCH8vv/wxjjA7wMDAXigHHGmLjyh78DOllruwCbgXsrmUdEREREpMpVtogeAbxXfvs9YORx9ukFJFlrt1lrC4Ep5c/DWvuttba4fL9FQHQl84iIiIiIVDlTmfXUjTGZ1tqwo+5nWGvrH7PPGGCItfaa8vuXAr2ttTcfs9/nwFRr7Yd/8F4TgYkAERERPadMmXLSub1ZTk4OwcFaoMFJagPnqQ2cpePvPLWB89QGzjvRNhg0aNBya238sdv/8sJCY8z3QJPjPHT/CSUsmwXlWP9TuRtj7geKgY/+6EWstW8AbwDEx8fbgQMHnuDby9ESEhLQsXOW2sB5agNn6fg7T23gPLWB8yrbBn9ZRFtrz/yjx4wxe40xkdba3caYSCD9OLulADFH3Y8G0o56jcuB84AzbGW6xUVEREREqkllx0TPAS4vv305MPs4+ywFYo0xLY0x/sDF5c/DGDME+DtwvrU2t5JZRERERESqRWWL6MnAWcaYLcBZ5fcxxjQ1xswFKL9w8GbgG2ADMM1au678+S8B9YDvjDGrjDGvVTKPiIiIiEiVq9SFhU4xxuwDdjqdo4ZqCOx3OoSXUxs4T23gLB1/56kNnKc2cN6JtkFza22jYzfWyCJaTp4xZtnxrjCV6qM2cJ7awFk6/s5TGzhPbeC8yrZBZYdziIiIiIh4HRXRIiIiIiIVpCLa+7zhdABRG3gAtYGzdPydpzZwntrAeZVqA42JFhERERGpIPVEi4iIiIhUkIpoEREREZEKUhHtBYwxMcaYn4wxG4wx64wxtzmdyVsZY3yMMSuNMV84ncUbGWPCjDHTjTEby/8e+jqdydsYY+4oPw+tNcZ8YowJdDpTbWeMeccYk26MWXvUtnBjzHfGmC3lv+s7mbG2+4M2eKr8XLTaGPOZMSbMwYi13vHa4KjH7jbGWGNMw4q8popo71AM3GWt7QD0AW4yxsQ5nMlb3UbZyp3ijOeBr6217YGuqC2qlTEmCrgViLfWdgJ8gIudTeUV3gWGHLNtEvCDtTYW+KH8vlSdd/l9G3wHdLLWdgE2A/dWdygv8y6/bwOMMTGUrbq9q6IvqCLaC1hrd1trV5TfPkRZ4RDlbCrvY4yJBs4F3nI6izcyxoQApwFvA1hrC621mY6G8k6+QB1jjC9QF0hzOE+tZ639BTh4zOYRwHvlt98DRlZnJm9zvDaw1n5rrS0uv7sIiK72YF7kD/4OAJ4F7gEqPNOGimgvY4xpAXQHFjscxRs9R9kfaqnDObxVK2Af8J/yITVvGWOCnA7lTay1qcDTlPX47AayrLXfOpvKa0VYa3dDWUcL0NjhPN7uKuArp0N4G2PM+UCqtTbxZJ6vItqLGGOCgRnA7dbabKfzeBNjzHlAurV2udNZvJgv0AN41VrbHTiMvsKuVuXjbkcALYGmQJAxZoKzqUScZYy5n7Jhlx85ncWbGGPqAvcDD53sa6iI9hLGGD/KCuiPrLUznc7jhfoD5xtjdgBTgMHGmA+djeR1UoAUa+1v38JMp6yolupzJrDdWrvPWlsEzAT6OZzJW+01xkQClP9OdziPVzLGXA6cB4y3WrijurWm7H/oE8s/m6OBFcaYJif6AiqivYAxxlA2DnSDtfYZp/N4I2vtvdbaaGttC8oupPrRWqseuGpkrd0DJBtj2pVvOgNY72Akb7QL6GOMqVt+XjoDXdzplDnA5eW3LwdmO5jFKxljhgB/B8631uY6ncfbWGvXWGsbW2tblH82pwA9yj8rToiKaO/QH7iUst7PVeU/w5wOJeKAW4CPjDGrgW7AY87G8S7l3wJMB1YAayj7DNLSx1XMGPMJsBBoZ4xJMcZcDUwGzjLGbKFsZoLJTmas7f6gDV4C6gHflX8uv+ZoyFruD9qgcq+pbw9ERERERCpGPdEiIiIiIhWkIlpEREREpIJURIuIiIiIVJCKaBERERGRClIRLSIiIiJSQSqiRUREREQqSEW0iIiIiEgF/T/Bb2prH3NXEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "    \n",
    "    def f_2(t, u):\n",
    "        \"\"\"A simple more \"generic\" test case, with f(t, u) depending on both variables.\n",
    "        The solution for a=0 is u(t) = u(t; 0, u_0) = cos t + (u_0 - 1) e^(-Kt)\n",
    "        The solution in general is u(t) = u(t; a, u_0) = cos t + C e^(-K t), C = (u_0 - cos(a)) exp(K a)\n",
    "        \"\"\"\n",
    "        return  K*(np.cos(t) - u) - np.sin(t)\n",
    "    def u_2(t): return np.cos(t) + C * np.exp(-K*t)\n",
    "\n",
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = explicitTrapezoid(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} — by the Explicit Trapezoid Method with {n} steps\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def explicitMidpoint(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the Explicit Midpoint Method (a.k.a Modified Euler)\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following two lines will need to change for the systems version\n",
    "    U = np.empty_like(t)\n",
    "    U[0] = u_0\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h/2, U[i]+K_1/2)*h\n",
    "        U[i+1] = U[i] + K_2\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8+5HHs39ncN6z3vW8Nm4BbiOZD6DGmLvPv9/ijKW2OL3qScWZmtfek8aYCsYZ7vQ6znF7/kK5azwfyk55thGHZBgVv1nLaZwLFVYYY87gFL3rcd7IwRlsPxLnE/UOIJLLN06/Aa1xGvZLCuRU6ofT+3nAs+1RJHPrNWvtBuBJz3b34zQmCe/mMBKnoNqJ0zM9JsG8W0nwxuppSLviXOhzHGcs3p8J5m/2xPKvcU5BpfvdHjzbOYFz8VINnILmC5wrsQ/ijKX7NdFTKpL8OOEBQAOcMWhTSbA/XnoTpyh8Faf3+JxnGua/G8pX8sQ/A+eCl/k4p+F24VzUkmK81rlo5F2cC5i2Aqm9cf73OEMV/sY5fqd6pnnjZpyipC3/Xcke4SlWMM4XGyTsvU+PbXrjAM5xuQ/nGHgswQc3cAreysD4RKfYE/sRuM5zDE9IaaPW2lCcsYdfeba/jZTvarHWXNy7Ptg446h/xrnwaK9nyMOPwLAEvaYrgOo4PaIf4Fz8edkzBp4PjG1wercO4Bw3wUksd9azziWefb/cmGWsc+ebOZ5T7Zdb7rLthsfl/ndP4Zzx+BfneP+NVNxSMAnzcHobDxhjjqS0sHXGdyf3+voC53qNWcaY0zjvC408z/Mqjx49cG57uA/nOO1vrT3fOTIAp43YgdNGX+6sBTiFdD7+6+XdiPO+lFyv7/n9ucs4d0S43Jji5FTGafPO9+aewxmPft4TnpgO4bxHPO55b0pKQ5z32wicHD9jrd3hmfcOMMKT126pfO39hpO3fz0/5+9uVB2nHY3A+YD2jbU2xKu9Fq+YJIa8iaSZMeYToIy19nJXAadlvdNwLhZIrzsrZDpPD8Lv1trkbtvkUzy9UmtxhmHEuB1PdmOM2Q48aq2d43Ys3jLG9AYettY2dTuW9GScL474xTrXVIikG2PMTpzXTJZ7vWdHPvutL5I1GGeoQwBOj1pDnFNkaf52nssIwemdzLKsteE4t/jJEjy9ZMld0CVXwBhzJ84p1HluxyIiktOo+JUrVQjn1FE5nNNIn+HcRi1d2az1rVM5njFmAxdfGHTeo9baxENBchRjTAhwHXB/KsYqi4hIOtOwBxERERHJMXTBm4iIiIjkGCp+RURERCTHyNQxvyVLlrRVqlTJzE0CcObMGQoUKJDyggIoX2mhnHlH+fKO8uUd5cs7ypd3lC/vuJmv1atXH7HWXpV4eqYWv1WqVCE0NDQzNwlASEgIQUFBmb7drEr58p5y5h3lyzvKl3eUL+8oX95RvrzjZr6MMUl+BbeGPYiIiIhIjqHiV0RERERyDBW/IiIiIpJjuP4lFzExMYSHhxMZGZlh2yhSpAibNm3KsPVnN76Qr7x581KhQgX8/f1djUNERESyF9eL3/DwcAoVKkSVKlUwxmTINk6fPk2hQoUyZN3Zkdv5stZy9OhRwsPDqVq1qmtxiIiISPbj+rCHyMhISpQokWGFr2Q9xhhKlCiRoWcDREREJGdyvfgFVPjKJXRMiIiISEbwieLXbX5+ftSrV+/Cz8cff5xu6w4LC2PatGnpsq6CBQumuMzgwYM5e/bshccdO3bkxIkT6bJ9ERERkazO9TG/viBfvnyEhYVlyLrDwsIIDQ2lY8eOGbL+xAYPHsx9991H/vz5AdKt8BYRERHJDtTzm4yTJ09y7bXXsmXLFgB69OjBDz/8AMDjjz9OYGAgtWvXpn///hees2rVKm6++WZuuOEGbrrpJk6ePMnbb7/NmDFjqFevHmPGjLloGxs2bOCmm26iXr16XH/99WzduhWAzz//nDp16lCnTh0GDx58SWwhISF06tTpwuN+/foxfPhw/ve//7Fv3z6Cg4MJDg4GnG/VO3LkSLLr3blzJ7Vq1eKRRx6hdu3atG3blnPnzqVPEkVERER8jE/1/D4741nCDoSl6zrrlanHe7e8d9llzp07R7169S48fu211+jevTtfffUVvXv35plnnuH48eM88sgjAHzwwQcUL16cuLg4WrVqxbp166hZsybdu3dnzJgxNGzYkFOnTpE/f37effddQkND+eqrry7Z7nfffcczzzzDvffeS3R0NHFxcaxevZphw4axYsUKrLU0atSIFi1aUL9+/RT39emnn+bzzz9n/vz5lCxZ8qJ5ya23WLFibN26lVGjRvHDDz/QrVs3Jk6ceGFfRURERLITnyp+3ZLcsIc2bdrw+++/8+STT7J27doL08eOHcuQIUOIjY1l//79bNy4EWMMZcuWpWHDhgAULlw4xe02adKEDz74gPDwcLp27Ur16tVZvHgxd9xxBwUKFACga9euLFq0KFXF7+Ukt94uXbpQtWrVC8X/jTfeyO7du69oWyIiIiK7Tuxi3Yl1BBHkdigX8anid3D7wRmy3tOnT6fpefHx8WzatIl8+fJx7NgxKlSowI4dO/j0009ZtWoVxYoVo3fv3kRGRmKt9foOBT179qRRo0ZMnTqVdu3aMXToUKy1KT4vd+7cxMfHX3icmluCXW69efLkufC3n58fsbGxKa5PREREJDnhp8Jp+XNLTp05Rd9OfcmbO6/bIV2gMb+X8X//93/UqlWLUaNG0adPH2JiYjh16hQFChSgSJEiHDx4kOnTpwNQs2ZN9u3bx6pVqwCn4I6NjaVQoULJFt///vsv1apV4+mnn6ZLly6sW7eO5s2bM2HCBM6ePcuZM2cYP348zZo1u+h5lStXZuPGjURFRXHy5Enmzp17YV5y20vNekVERESu1L7T+wgeEcyRs0d4r/Z7PlX4go/1/Lol8Zjf9u3b06dPH4YOHcrKlSspVKgQzZs35/3332fAgAHUr1+f2rVrU61aNW655RYAAgICGDNmDE899RTnzp0jX758zJkzh+DgYD7++GPq1at3YSzxeWPGjOGXX37B39+fMmXK8Pbbb1O8eHF69+7NTTfdBMDDDz98yZCHihUr0q1bN66//nqqV69+0fy+ffvSoUMHypYty/z58y9Mb9CgQZLr3blzZ3qnU0RERHKogxEHaTmiJQciDjDrvllEbY9yO6RLmNScZk8vgYGBNjQ09KJpmzZtolatWhm6Xbe/rjer8ZV8ZcaxkV5CQkIICgpyO4wsQ/nyjvLlHeXLO8qXd5Sv5B0+c5igEUHsPLGTGffOoFnlZq7myxiz2lobmHi6en5FRERE5IocPXuU1iNbs+P4DqbdO41Skc04fNjtqJKmMb8iIiIikmbHzx2nzcg2bDmyhUk9JnFL+SA6doSePd2OLGnq+RURERGRNDkZeZK2v7Rlw+ENTLxnIq2rtQZg6FAoUwYOHnQ5wCSo51dEREREvHYq6hTtf23P2gNr+aPbH1SNa8/Uqc684GDw1ct21PMrIiIiIl6JiI6g468dWbV3Fb/f/TudanTijjsgNBT++Qfy5XM7wuSp+BURERGRVDsbc5ZOv3ViefhyRt05ijtq3QHA8OFw4IBvF76gYQ8AfPDBB9SuXZvrr7+eevXqsWLFissuHxQUROJbtiU2YcIENm7ceOHx22+/zZw5c9Il3svZt28fd911FwBhYWFMmzbtwrx33nmHTz/9NMV1lC1bNs3bHzFiBNWrV6d69eqMGDEiyWU+//xzrrvuOq6//npatWrFrl270rw9ERERyTznYs7RZVQXFu1exM93/Ey9gLt59lmIjYUiReDaa92OMGU5vvhdtmwZU6ZMYc2aNaxbt445c+ZQsWLFK15v4uL33XffpXXr1le83pSUK1eOcePGAZcWvxnt2LFjDBgwgBUrVrBy5UoGDBjA8ePHL1mufv36hIaGsm7dOu666y5efvnlTItRRERE0iYyNpI7xtzBvB3zGHbbMHrW7cmsWfDbb7Bnj9vRpV6OL373799PyZIlyZMnDwAlS5akXLlyAMydO5f69etTt25d+vTpQ1TUpd9SUrBgwQt/jxs3jt69e7N06VImTZrESy+9RL169di+fTu9e/e+UJQmt94qVarQv39/GjRoQN26ddm8efMl2+vYsSPr1q0DnCLy3XffBeCtt95i6NCh7Ny5kzp16hAdHc3bb7/NmDFjqFevHmPGjAFg48aNBAUFUa1aNf73v/8lm5c33niDG264gcaNG3MwlZdqzpw5kzZt2lC8eHGKFStGmzZtmDFjxiXLBQcHkz9/fgAaN25MeHh4qtYvIiIi7oiOi+ausXcxc/tMhnYZyv3XPwDAk0/Cxo1QtarLAXrB54rfoCBnzAhATIzz+JdfnMdnzzqPPXUcJ086j//803l85IjzePJk5/GBAylvr23btuzZs4caNWrwxBNPsGDBAgAiIyPp3bs3Y8aM4e+//yY2NpZvv/02Vftw880306VLFwYNGkRYWBhXX331hXkprbdkyZKsWbOGxx9/PMkhCs2bN2fRokWcOnWK3Llzs2TJEgAWL15Ms2bNLiwXEBDAu+++S/fu3QkLC7vwtcqbN29m5syZF3pmY2JiLtnGmTNnaNy4MWvXrqV58+b88MMPAPz666/Uq1fvkp/zwyz27t17Ua95hQoV2Lt372Vz9eOPP9KhQ4cUcyoiIiLuiImLofu47kzdOpXvbv2O5oX60KSJc2EbQMmS7sbnLZ8rfjNbwYIFWb16NUOGDOGqq66ie/fuDB8+nC1btlC1alVq1KgBQK9evVi4cOEVby+l9Xbt2hWAG2+8kZ07d17y/GbNmrFw4UIWL17MrbfeSkREBGfPnmXnzp1cm4qBNrfeeit58uShZMmSlCpVKsle3YCAADp16nRJHPfeey9hYWGX/Jzv0U7qq7KNMcnG8ssvvxAaGspLL72UYtwiIiKS+WLjY+n5Z08mbJ7Alx2+5NHAR4mMhNOnITLS7ejSJsW7PRhjfgI6AYestXUSzXsRGARcZa09kh4BhYT897e//8WP8+e/+HGRIhc/Llny4sdlyqRum35+fgQFBREUFETdunUZMWIE9erVS9VzExZ3kak4CpIqEBM6P/zCz8+P2NjYS+Y3bNiQ0NBQqlWrRps2bThy5Ag//PADN954Y6riPb/+y23D39//wn4lXObXX39l0KBBlyx/zTXXMG7cOCpUqEBIgn9AeHh4st/nPWfOHD744AMWLFhwUUwiIiLiG2LjY7l//P2M2ziOz9t+Tu/r+gFQpw6sWwd+fi4HmEap6fkdDrRPPNEYUxFoA+xO55gy1ZYtW9i6deuFx2FhYVSuXJmaNWuyc+dOtm3bBsDIkSNp0aLFJc8vXbo0mzZtIj4+nvHjx1+YXqhQIU6fPn3J8qldb3ICAgKoWLEiY8eOpXHjxjRr1oxPP/30oiEPKcWQVin1/LZr145Zs2Zx/Phxjh8/zqxZs2jXrt0l6/nrr7949NFHmTRpEqVKlUq3+ERERCR9xMXH0WdiH0avH80nrT/h7orPcd118P33zvysWvhCKopfa+1C4FgSs/4PeBm4fFemj4uIiKBXr14Xbr21ceNG3nnnHfLmzcuwYcO4++67qVu3Lrly5eKxxx675Pkff/wxnTp1omXLlhfdIuyee+5h0KBB1K9fn+3bt1+Yntr1Xk6zZs0oXbo0+fPnp1mzZoSHhydZ/AYHB7Nx48aLLnjLSMWLF+ett96iYcOGNGzYkLfffpvixYsDzq3eJk2aBMBLL71EREQEd999N/Xq1aNLly4ZHpuIiIikTryN55HJjzBy3UjeD36fl295mVKloHVraNTI7eiunEnpNDyAMaYKMOX8sAdjTBeglbX2GWPMTiAwNcMeAgMDbeL7427atIlaGfz9d6dPn6ZQoUIZuo3sxFfylRnHRnoJCQlJdoiHXEr58o7y5R3lyzvKl3eye77ibTyPT3mcIWuG8Hbzt3no6gGUKAEFCqRtfW7myxiz2lobeMl0b4tfY0x+YD7Q1lp7MqXi1xjTF+gLULp06RtHjx590fwiRYpwzTXXeLk73omLi8MvK/fPZzJfyde2bds4efKk22GkSkRExEW3vZPLU768o3x5R/nyjvLlneycL2st/9v2Pybsm0DPij15oPwj9OnTiGrVInjvvQ1pWqeb+QoODk6y+E3L1xtfDVQF1nouiqoArDHG3GStveTmYtbaIcAQcHp+E1f/mzZtyvBeRl/pycwqfCVfefPmpX79+m6HkSrZvScgvSlf3lG+vKN8eUf58k52zZe1ludnPs+EfRN4scmLDGwzEGMMgwfD1Vfno0GDoDSt1xfz5XXxa639G7hwlZI3wx5ERERExLdYa3llzisMXjGYZxo9wxPVB7JihaFxY7j7brejS38pXvBmjBkFLAOuNcaEG2MeSu8gUjP0QnIWHRMiIiIZz1rLm/PeZNDSQTwR+AT/1+7/eOwxQ/fuEB3tdnQZI8WeX2ttjxTmV7mSAPLmzcvRo0cpUaLEZb8QQXIOay1Hjx4lb968bociIiKSrb274F0+XPwhjzR4hC87fokxhmHD4OBBCAhwO7qMkZYxv+mqQoUKhIeHc/jw4QzbRmRkpAopL/hCvvLmzUuFChVcjUFERCQ7+3DRh7yz4B161+vN69d/xycf5+LVV6FcOecnu3K9+PX396dq1aoZuo2QkJAsc+GUL1C+REREsrdBSwbxxrw3uO/6+xjaeSgffZiLTz+Fnj2hcmW3o8tYqfmGNxERERHJJgYvH8zLc17mnjr3MOy2Yfjl8uONN+Cvv7J/4QsqfkVERERyjK9Xfs1zM5/jzlp38mHgz9xxW24OHABjIINPxPsMFb8iIiIiOcCQ1UPoN70fXa7twm93/sa+cH/WrIHwcLcjy1yuj/kVERERkYz1018/8eiUR+lYvSO/3jaWAL8AbrkFtm+HnHZPAPX8ioiIiGRjI9eO5OFJD9P26rZ81ewPGgXm4Y8/nHk5rfAF9fyKiIiIZFuj/h5F74m9Ca4azITuE4iNzEvlylC2rNuRuUfFr4iIiEg29PuG37l//P00rdSUH1tNIjf5yFcIpk1zOzJ3adiDiIiISDYzYfMEev7Zk8YVGvP77VNp36oAjzzidlS+QT2/IiIiItnIlH+m0O33btxY9kam3TuNwnkK0q8f1KvndmS+QcWviIiISDYxY9sM7hx7JzeUuYERrWeyb0dhCteEfv3cjsx3qPgVERERyQbm/DuH20ffznVXXcfM+2Zy161F2L0bNm0Cf3+3o/MdKn5FREREsriQnSF0GdWFGiVqMPv+2RTPV5xvvoHDh1X4JqYL3kRERESysMW7F9Ppt05ULVaV39rNZcrYkgDUrAnNmrkcnA9S8SsiIiKSRS3bs4wOv3agfOHyzH1gLiO/v4onn4S9e92OzHep+BURERHJglbtXUX7X9tTukBp5j0wjzIFy/D++7BsGZQv73Z0vkvFr4iIiEgWs2b/Gtr+0pYS+Urwe8cFvP1ceU6dcsb3Xn+929H5NhW/IiIiIlnI2gNraTOyDYXzFGZer3kc2FqeceNg40a3I8sadLcHERERkSxiw6ENtB7Zmny58zHvgflUKVqFKh1gxw4oXtzt6LIG9fyKiIiIZAGbj2ym1c+t8M/lzx+dFnB/p2osWODMU+Gbeur5FREREfFxW49upeWIlgDM6zWPYnFXEx0NMTEuB5YFqfgVERER8WHbj20neEQwMfExTL1zIdeWqIkxsHIl5NI5fK8pZSIiIiI+aueJnbT8uSXnYs8xqes8+natxQsvOPNU+KaNen5FREREfNCek3toOaIlp6JOMfeBudQvU5dbb4UWLdyOLGtT8SsiIiLiY/ae2kvwiGCOnjvKH53mUzq+AcbABx+4HVnWp+JXRERExIcciDhAy59bcvDMQWbeO4s3ejXgyBEICwM/P7ejy/pU/IqIiIj4iENnDtFyREv2ntrLjPtmcHOlJnz4IZw8qcI3vaj4FREREfEBR84eofXPrdl5YidjOs3i5N9NoRI0aeJ2ZNmLrhMUERERcdmxc8doM7INW49tZVKPScz+sSl33w0HDrgdWfajnl8RERERF52IPEHbkW3ZeHgjk+6ZROtqrWnyEXTrBmXKuB1d9qOeXxERERGXnIo6Rftf2rPu4DpGtJ9IyI/tiI6GAgWgaVO3o8ueVPyKiIiIuCAiOoIOv3Zg9f7VjL17LLn+bc/nn8Pq1W5Hlr1p2IOIiIhIJjsTfYZbf7uVFeErGH3XaG6veTvUhMaNoVIlt6PL3tTzKyIiIpKJzsacpcvoLizevZghbcYw4pW7WLfOmafCN+Op+BURERHJJJGxkdwx5g7m75jP8NuGE1T6TjZsgF273I4s59CwBxEREZFMEBUbxZ1j72TW9ll832EY999wPwCbNkGePC4Hl4Ok2PNrjPnJGHPIGLM+wbRBxpjNxph1xpjxxpiiGRqliIiISBYWHRdNt3HdmLZ1Gl+0/JHhz/bmo4+ceSp8M1dqhj0MB9onmjYbqGOtvR74B3gtneMSERERyRZORJ6g86jOTNoyia86fMWTN/ehZk249lq3I8uZUhz2YK1daIypkmjarAQPlwN3pXNcIiIiIlnetmPb6DyqM9uObeOrliO4t8YD+PnBTz+5HVnOlR4XvPUBpqfDekRERESyjZCdITQa2ohDZw4x+745/PnOA3TsCPHxbkeWsxlrbcoLOT2/U6y1dRJNfwMIBLraZFZkjOkL9AUoXbr0jaNHj77SmL0WERFBwYIFM327WZXy5T3lzDvKl3eUL+8oX95RvryT2nxN2T+FwVsHUz5feT6s8yHl85Vn6dISREfnIijocCZE6hvcPL6Cg4NXW2sDE09Pc/FrjOkFPAa0staeTU0QgYGBNjQ0NNVBp5eQkBCCgoIyfbtZlfLlPeXMO8qXd5Qv7yhf3lG+vJNSvuLi43hx1osMXjGYdle347ly44g+U5DOnTMvRl/i5vFljEmy+E3Trc6MMe2BV4AWqS18RURERLKzU1GnuGfcPUzfNp2nb3qaT9t+Rqvg3EREwK23Qi59u4JPSLH4NcaMAoKAksaYcKA/zt0d8gCzjTEAy621j2VgnCIiIiI+69/j/9J5VGe2HNnCV+2+4+H6j+LvB2PHOrcyU+HrO1Jzt4ceSUz+MQNiEREREclyFu1aRNexXYmLj2N6z1l8/lRLVpaC4cOhTBm3o5PE9A1vIiIiImk0PGw4fSf3pWqxqkzuMZkaJWoQ2hxKlQLn5Lj4GhW/IiIiIl6Ki4/jtbmvMWjpIFpVbcVjRccTubcQlIDX9NVfPk3Fr4iIiIgXTked5t4/72XyP5N5IvAJPg4aTO1a/tSvDxMnuh2dpETFr4iIiEgqHYg8wC0/3cLGwxv5os03PNXkcYyBmTOhYkW3o5PUUPErIiIikgpL9yzliTVPEJ8rnt+7zGTQE62IvQuefx5q1XI7Okkt3XhDREREJAUj144keEQw+fzysfzh5dx2fSuqV1dvb1aknl8RERGRZMTbeN6c9yYfLf6IoCpBNNn5MSWpSa5cMGKE29FJWqj4FREREUlCRHQE94+/nwmbJ/BIg0d4o/5X1Ljaj3Mn4P/+z+3oJK1U/IqIiIgksufkHrqM7sK6g+v4vM1gnm3yNMYYPv10DX37NnA7PLkCGvMrIiIiksCK8BU0/KEh249tZ0TL2fzy1DPMmOF8Y0XduqfIk8flAOWKqPgVERER8Rj19yhaDG9Bfv/8LHtoGXfUb0mhQuDn53Zkkl407EFERERyvHgbzzsh7/DewvdoVqkZjxaaQo1ihfH3h/nz9VXF2YmKXxEREcnRzsacpdeEXozbOI4H6z3II2W+5+bG/hz/Evr1U+Gb3aj4FRERkRxr76m93Db6NtbsX8Og1p/yws3PY4xh8mRo397t6CQjaMyviIiI5Eih+0Jp+ENDthzdwreN5zL2uRfYutXp5u3UCXKrizBbUvErIiIiOc7vG36n+bDmBPgFsLTPUtrXDObsWTh2zO3IJKPpM42IiIjkGNZa3lv4Hv1D+tOkws08V3oKdUsXA2DdOsilbsFsT/9iERERyRHOxZyj55896R/SnwdueIAn84fQrXMxpk935qvwzRnU8ysiIiLZ3v7T+7lt9G2E7gvl41Yf8/ItLxMfbyAe2rVzOzrJTPqMIyIiItnaX/v/4qahN7Hh8AYG1ZnLnAGvcPKkwc8P7r1XPb45jf7dIiIikm2N3zSepsOaYjAs6bOEhlcFs2MHHDjgdmTiFg17EBERkWzHWsvHiz/m9Xmvc1PZxgy4djL1ypSEMrBpE/j7ux2huEU9vyIiIpKtRMZG8sCEB3h93uv0rNuTTkcW0rl1STZvduar8M3Z1PMrIiIi2cbBiIPcMeYOloUv4/3g93m92eucOmUoXwauvdbt6MQXqPgVERGRbGHdwXV0HtWZw2cO827VEDb/0IL4W6BIEejTx+3oxFdo2IOIiIhkeZO2TOLmH28mLj6OxX0WUzqyBStXwqFDbkcmvkbFr4iIiGRZ1loGLRnE7aNvp2bxOvwWtJoGZRvQty+EhUHZsm5HKL5Gxa+IiIhkSVGxUfSZ1IeX57zM3bXvpv5fi7izXWmOH3fm58vnbnzimzTmV0RERLKcw2cO03VsVxbvXkz/Fv3p36I/224wNLsFihVzOzrxZSp+RUREJEtZf2g9nUd15kDEAV65agFmQXNMEFSv7vyIXI6GPYiIiEiWMW3rNG7+8WaiYqNY2HshZzY1Z+JEOHfO7cgkq1DPr4iIiPg8ay2Dlw/mxdkvUrd4Q35s+yc3li9Hvc8hJkbjeyX11PMrIiIiPi06Lpq+k/vy/Kznub3m7ZSavJiHupUjNtb5trb8+d2OULIS9fyKiIiIzzp69ih3jr2TBbsW8EazN3g3+F3mFM1FRATkVhUjaaDDRkRERHzSpsOb6DyqM+GnwumXfxG19jcll4G2bd2OTLIyDXsQERERnzNz20wa/9iYiOgI5j0QwsYZTRkxAqx1OzLJ6tTzKyIiIj7DWstXK7/i2ZnPcl3hRvzebQw1y1Xkjz+csb3GuB2hZHXq+RURERGfEBMXw5PTnuTpGU/Tsdpt5Bq+iP7PVQSgaFEICHA3PskeUuz5Ncb8BHQCDllr63imFQfGAFWAnUA3a+3xjAtTREREsrNj547R7fduzN0xl1dueYUPW33IkIhcXH2125FJdpOant/hQPtE014F5lprqwNzPY9FREREvPbP0X9oPLQxi3YvonfsUu4o9DG5TC4eewzatHE7OsluUix+rbULgWOJJt8GjPD8PQK4PX3DEhERkZxg7r9zaTS0ESciTzD1rhAW/NqE775zOyrJzoxNxWWTxpgqwJQEwx5OWGuLJph/3FpbLJnn9gX6ApQuXfrG0aNHp0PY3omIiKBgwYKZvt2sSvnynnLmHeXLO8qXd5Qv77iZr0n7JvHF1i+omKsOH974GuXyl+Hw4TwULx6Fn58rIaVIx5d33MxXcHDwamttYOLpGX63B2vtEGAIQGBgoA0KCsroTV4iJCQEN7abVSlf3lPOvKN8eUf58o7y5R038hUbH8vzM5/ny61f0qZMD7YN/IVtNhc9387UMNJEx5d3fDFfaS1+Dxpjylpr9xtjygKH0jMoERERyZ62HNnCAxMeYOXelbzY5EU+avUxr23LpbG9kmnSWvxOAnoBH3t+T0y3iERERCTbibfxfLXyK16Z8wr5cuend9RqnqvTgNx+MGiQ29FJTpLiBW/GmFHAMuBaY0y4MeYhnKK3jTFmK9DG81hERETkErtO7KL1z615ZsYztKzaknldNzLuywYMGeJ2ZJITpdjza63tkcysVukci4iIiGQj1lqGhw3nmRnPEG8tr1aZwIc9umCMYelSqFPH7QglJ9I3vImIiEi6OxhxkNvH3E6fSX2oX7Y+75XYzse9b2PhQuf7ievW1VcVizsy/G4PIiIikrP8sfEPHpv6GKejTvPBLV/yaqsniInORQEDTZu6HZ3kdOr5FRERkXRx/Nxx7vvzPu76/S4qF6nM3Xv2MuaFfsTG5CJPHujbF5+9f6/kHOr5FRERkSs2a/ss+kzsw4GIA7zT4h1eb/Y6s8r7U6OChjeIb1HxKyIiIml2JvoML81+iW9Dv+XawvVovz6MsmVK4h8Et97q/Ij4Eg17EBERkTRZsnsJN3x3A9+FfsfzjZ9n9RNLiTlZkmPH3I5MJHnq+RURERGvRMVG0T+kP4OWDqJCnuvotncXbzWqSIE8MH065FLXmvgwHZ4iIiKSamEHwmj4Q0M+WfIJfer1YWTz5YwfUZE5c5z5KnzF16nnV0RERFIUGx/LJ4s/YcCCARTzq0j/sit5p0tDAHbsgHLlXA5QJJX0+UxEREQu65+j/9D0p6a8Of9Nutbqyl0H1/PRUw3Zt8+Zr8JXshL1/IqIiEiS4m08X6/8mlfmvEIeW5Tvgv7k0RZ3cLwV3HOXil7JmtTzKyIiIpfYfXI3bUa24ekZT9OiUjCV/tzJHx/cgbVQrBg0a+Z2hCJpo55fERERucBay89rf+bpGU8TF2sY0mkIDzd4mNG5DVddpS+skKxPxa+IiIgAcOjMIfpO7svELRNpmP8uToz4lfINAjAGevRwOzqR9KFhDyIiIsKfm/6k9je1mbFtBp+2+ZSQfqOpVjmAgAC3IxNJX+r5FRERycEiYiN4YPwDjFw3kppx3Wi08XueerkoAQEwY4bb0YmkPxW/IiIiOdTs7bPpE9qHY9HHeLv529Q/9RaPDcnN1q1Qu7bb0YlkDBW/IiIiOcyZ6DO8PPtlvgn9hrKnW/FRrW95Kbg6AG1aQ4ECLgcokoE05ldERCQHWbpnKfW+r8e3od/yXOPnqLBoFN9+UJ2YGGe+Cl/J7tTzKyIikgNExUbxTsg7DFw6kDKRzZl0zzA6Xd+U308tpUWLq/D3dztCkcyhnl8REZFsbu2Btdw09CY+XvIxPa/ux+mv5jHtu6YAXHVVNKVKuRygSCZSz6+IiEg2FRsfy8AlA3kn5B2KmopM7jGZTjU68ZuBoCC3oxNxh4pfERGRbOifo//Qa0Ivlocvp3ncAML+9yZlOzgnfHv2dDk4ERep+BUREclG4m0836z6hpdnv0ze3Hn5retvtCt/D8/sMBreIIKKXxERkWxjz8k9PDjxQebumEvdAwOpuK8f97ycD2Ng5Ei3oxPxDSp+RUREsjhrLT+v/ZmnZzxNXHwc3936HTa0L2M2G06ehKJF3Y5QxHeo+BUREcnCDp05xKNTHmXCpgnU2Pser7brw4OB5bA3Qt++kEv3dRK5iF4SIiIiWdT4TeOp800dpm2dxkfBnxGw/A2mjy0HgDEqfEWSop5fERGRLOZE5Amenv40I9eNpNqhZ5j5al/qV7yOXrPQRW0iKdBnQhERkSxk9vbZ1P22Lr/9/RsPlfqOf78ZzJKJ1wFQtiz4+bkcoIiPU8+viIhIFnAm+gyvzHmFr1d9zdV+QSx76E8alm/IbRWgQwe3oxPJOlT8ioiI+Lhle5bxwIQH2HZsG832TOCvMV0o/YABoHNnl4MTyWJU/IqIiPioqNgoBiwYwCdLPqFCwcrM7zWfqiaInys7QxxExHsqfkVERHzQuoPruH/8/aw7sI4aS0MILN2EoOcDAHjrLZeDE8nCVPyKiIj4kNj4WAYtGUT/kP4Uz1ecST0msZoWREeDtc4tzEQk7VT8ioiI+IitR7fSa0Ivlm1fx9WrJ/H9241odW0xOr/jdmQi2YdudSYiIuKyeBvP1yu/pt739dh0ZBNDbh1G9KZ2rA8t5nZoItnOFfX8GmOeAx4GLPA38KC1NjI9AhMREckJth7dypPTnmT25sXUCh/ErP/dToUi5emxEQoWdDs6kewnzT2/xpjywNNAoLW2DuAH3JNegYmIiGRnx84d49kZz3LdN9exLHwZvQOmsOnnJ9n5d3lAha9IRrnSMb+5gXzGmBggP7DvykMSERHJvqLjovl65de8t/A9ThwuQKerPmDIkw9QukAZnuoMDRq4HaFI9pbm4tdau9cY8ymwGzgHzLLWzkq3yERERLIRay3jN4/nlTmvsO3YNtpUa8PxiX+y8VBBSr3k3MVBha9IxjPW2rQ90ZhiwB9Ad+AE8Dswzlr7S6Ll+gJ9AUqXLn3j6NGjryTeNImIiKCgzh+lmvLlPeXMO8qXd5Qv7/hivrac3sI3279h3bENlNj8HM/cXoamZRuwY0dB8uWLo2xZ9y6X8cV8+TLlyztu5is4OHi1tTYw8fQrGfbQGthhrT0MYIz5E7gZuKj4tdYOAYYABAYG2qCgoCvYZNqEhITgxnazKuXLe8qZd5Qv7yhf3vGlfO05uYfX573OL+t+4ar8V/Fy1d8Z+N4dlG8PwcHOj9t8KV9ZgfLlHV/M15UUv7uBxsaY/DjDHloBoekSlYiISBZ2Ouo0nyz5hM+WfUZceD06Fx3DL6+2p3CewtxeExo3djtCkZzrSsb8rjDGjAPWALHAX3h6eEVERHKi2PhYfvrrJ96e/zYHzxykZ92enAwdwt8zCpDvXWeZJk3cjVEkp7uiuz1Ya/sD/dMpFhERkSxr5raZvDj7Rdbv3k2FdV8yeUAdOgU24MDNkC8f+Pu7HaGIgL7hTURE5IpsOLSBDr92oP2v7Tkbc5avgkZzeO79HFrn3LqhTBkoUsTlIEXkgiu9z6+IiEiOdDDiIP1D+vPDmh/Iu60brf2WMuWNBuTJnYc7dzpFr4j4HhW/IiIiXjgXc47Bywfz0eKPOBd7jn4N+xF//GNC5uQjPgbIrcJXxJep+BUREUmFeBvP6PWjeW3ua+wOj6L80qmMeL8Sd7SszNkWEDAIcutdVcTnacyviIhIChbvXkzjoY259897KZGvBJPuH0vufc04s68yAPnzq/AVySr0UhUREUnG9mPbeWXOK/yx6Q+KbHiBBkfGsXJOBfxy5aL9Vt3BQSQrUvErIiKSyPFzx3l/4fv8b8WX+Pv5MyBoAIWKvcKs6Xk4ewYKFVLhK5JVqfgVERHxiImL4dvQbxmwYADHDual5OTNfDKgKH1aFMc2h+eedjtCEblSGvMrIiI5nrWWiZsnUufbOjwz5UXql6lP6HPTaFC1GsXzFQfAGJeDFJF0oZ5fERHJ0dbsX8MLs14gZGcIV4UNpOLfjzF1Q0Hy5DHMnOl2dCKS3lT8iohIjrT31F7emPcGI0LHUqJAUb7u+DWVAvsybWpuoqIgTx63IxSRjKDiV0REcpSI6AgGLhnIp0s/JfZ0cQr9tI/nX8zDEw3zAdDpVpcDFJEMpeJXRERyhLj4OEasHcEb897gwD5D9yZd+KjVR3wVU5RmTdyOTkQyi4pfERHJ9ub8O4cXZr3AuoPrqPDXEArNf5CvX89NiWLw2WduRycimUnFr4iIZFubDm/ipdkvMXXNaioWL83oO0dzXdduzJhhKFDA7ehExA0qfkVEJNs5fOYw74S8w/ervyd/XDnyfr+Dzr1z072O87ZXt67LAYqIa1T8iohIthEZG8mo3aMYtXQsZ/6tw+NdH6N/i/5MrJiXoCC3oxMRX6DiV0REsjxrLWM3jOXVua+y88ROaqz/he3je/L864arCsDDD7sdoYj4ChW/IiKSpS3bs4znZz3P8lXnqFmuDp9e34/7H7+Xhd2halW3oxMRX6OvNxYRkSxpx/EddB/XnZt/upmdhw6R/7cV1N88kRuL3UipUnDXXfpKYhG5lIpfERHJUk5GnuTl2S9z7WcNGT+qMG83f5utL6xlysQ8fPON3tZE5PI07EFERLKEmLgYhqwewjsL3uHo2aME7v+FVX/25O4BUDAAgoPdjlBEsgIVvyIi4tOstUzdOpUXZ73EliXVqV+1J7Oe6k2tYvVZ/zjUqeN2hCKSlaj4FRERn7X2wFpemPUCc3fMpXqR2pRePIqrY/NTv6wzmDcw0OUARSTLUfErIiI+Z9/pfbw17y1+CplL3r+eZ/CHt/NEo0fZ1cmfypXdjk5EsjIVvyIi4jNORJ7gi+VfMHDpQGLiYuhccCizV9xP0zwGfz+45hq3IxSRrE7Fr4iIuG73yd0MXj6YIaFDObOoDw2rf8SoAbdSrdjVHHgCypZ1O0IRyS5U/IqIiGvWHVzHoKWDGBX2J/hFcU+de9g46X1qHC/I1cWdZVT4ikh6UvErIiKZylrL/J3zGbhkIDO3zyQg7EnyLtzHqnWnqFW+IidaQpEibkcpItmVil8REckUsfGx/LHxDz5ZMpC/VuSnZMXjfNj6QwKDnmRcqcKUDHAq3qJF3Y1TRLI3Fb8iIpKhzkSf4ae/fuLz5Z+z88ROqpogzPB5PPpmHK81c96G2rRwN0YRyTlU/IqISIY4dOYQX638iq9Xfc2xRXdSwbzFhIEl6HxtZ2Y2NLRoobcgEcl8anlERCRdbTu2jc+Wfsaw5eOJ9j/EbTVvw6x/lxPhZehcA3IZ6NDB7ShFJKdS8SsiIuliRfgKBi0dxJ+b/sTvn67YcbuZGrKXDk2qEnU75MnjdoQiIip+RUTkCsTbeKZtncbAJYNYtMBQqEgcr3V5jR4PPM13xQKoW7EqoMJXRHyHil8REfFaVGwUv/39G58u+5SNhzdSPu81FJiwjg4dcvNBK38AvvrK5SBFRJKg4ldERFLtZORJvl/9PV+s+IJ9i4MpsutzRv50hO51urGutT/XXed2hCIil6fiV0REUhR+Kpwvln/Bt/MnciZgO62vaUnXG95g7ZGadK5i8PeDG290O0oRkZRdUfFrjCkKDAXqABboY61dlg5xiYiID1h/aD2fLv2U3/7+jbjw+vDTRgZ+u5uX7q9GfDzk6u92hCIi3rnSnt8vgBnW2ruMMQFA/nSISUREXGStZcGuBQxcMojpM6PIQ2Ee7/E4Tz/xHCNK5+bu1tUAyJXL5UBFRNIgzcWvMaYw0BzoDWCtjQai0ycsERHJbHHxcYzfPJ5PFg8kdP8qSua7igqr11ChaGm+6OBcxPbuuy4HKSJyhYy1Nm1PNKYeMATYCNwArAaesdaeSbRcX6AvQOnSpW8cPXr0lcSbJhERERQsWDDTt5tVKV/eU868o3x5J6PzFRUXxYyDMxi7Zyz7wgLxX/g+j77/C50qteTYoSKUKBFFQEDa3ivcoOPLO8qXd5Qv77iZr+Dg4NXW2sDE06+k+A0ElgO3WGtXGGO+AE5Za99K7jmBgYE2NDQ0Tdu7EiEhIQQFBWX6drMq5ct7ypl3lC/vZFS+jpw9wjervmHwrD84HrebRtdcy615PmHesOYMH2aoXDndN5kpdHx5R/nyjvLlHTfzZYxJsvi9kjG/4UC4tXaF5/E44NUrWJ+IiGSCf4//y+fLPuenv37i3PHCmMF7ePCpffz4UCWMMbx1v9sRiohknDQXv9baA8aYPcaYa621W4BWOEMgRETEB4XuC2XQ0kH8Pvk45mhNej1yDy/e/CJLrvWnbdvKGON2hCIiGe9K7/bwFPCr504P/wIPXnlIIiKSXqy1zNw+k08WfUrI7rkUzlOYuofmcGpLfYbcmpvcueG6R9yOUkQk81xR8WutDQMuGUshIiLuiomLYfT60QxaOoi/VxbFb/xoXh0yjddu60Zs38IULAi59TVHIpIDqekTEclGTkWd4ofVP/Dp9N85cPIIdWrl44t7n2LagTLce93DFM4D5HE7ShER96j4FRHJBvaf3s8XK77gu9DvOHnmLP5fHKJp03Ms/KIMxhiebu12hCIivkHFr4hIFrbp8CY+XfopP0/cQ+ymjtz9fFteuvklDjcpSt26RXURm4hIIip+RUSyGGstS/Ys4aOQz5m2fQL5AvLSOPfPbNt9O98EP0vJkkB5t6MUEfFNKn5FRLKIuPg4Jm6ZyKClg1i+5iTm5/n0eO1u/vdsGwr5lSTX1+Dv73aUIiK+TcWviIiPi4qL4vvQ7/l48lh2hp+j2g2H+N99L7HsZAmebd2DkvndjlBEJOtQ8Ssi4qP2nNzDsLBhDF4xmOMxx8k/YgOV85Rjy5BC5Pbz46kmbkcoIpL1qPgVEfEhZ2POMmHzBIaHDWf23BhY/iwN+9ZmYM/3KNy5FmXKGHL7uR2liEjWpeJXRMRl1lqWhS/jp9UjGDX5IGeLL6NKhfzcV/tdlizpwOPFyhJU5Sao4nakIiJZn4pfERGXhJ8KZ+TakQxb8wtbT2wk78m6RP60jsde287XT1fFkAtehAULzrodqohItqHiV0QkE52LOecMa1g7nFnbZsOIuZStUpth/3eMO2vdyfIO0KzZ1eTS/XlFRDKEil8RkQxmrWXF3hUMDxvOLxP3cmb7DVTusoW3W7zFsbM3UPea4vSu5yzbpo2roYqIZHsqfkVEMsjeU3sZuW4k309bws6AKeQPyM81J39lz98d+HvSuxQqmAuC3Y5SRCRnUfErIpKOImMjmbh5IsPChjH739nEb7gdxk7mtWFTeK1HC4guRN68+jIKERG3qPgVEblC1lpW7l3J8LDh/LZqBqdGf0GJRtfwxoM30bVXL5Y0h563daJQHiCP29GKiORsKn5FRNJo3+l9jFw7km8nhbJrXwT5ai2g6/V3sXZac55p0YmHg3MBUO9JlwMVEZELVPyKiHghMjaSSVsmMXTZGObum0C8jafI5FDKx1Rl44+5KZynMNzpdpQiIpIcFb8iIimw1rJq3yqGhw1n1PpRnJj3IGbhMF4cdz2PNO4JPatTqhQU1pAGERGfp+JXRCQZ+0/v55d1vzBk3iy2je9OQPA87r7lVhrXuIcDNxXkxVv6U7QoUMLtSEVEJLVU/IqIJBAVG8WkLZP4ZvZ0FuxchC22jRvz30Hefx7gx9d60LNrAWfBO9yNU0RE0kbFr4jkeNZaVu9fzbC/hjNq/W8cj4jAfHqYOs23M+63gtQoUYOopyFPngC3QxURkSuk4ldEcqwDEQf4Zd0vDA8bzobR95DrYCe6f3iM3vV6E3lTQerd0IBKniENeTSeV0QkW1DxKyI5SlRsFJP/mcw3s6YTMrkctukHNKnUmO6Ngsl/MpAfbm+Pnx9wtduRiohIRlDxKyLZnrWWNfvX8N2iMfyx9TeOx+2l2LbHIGQA4998iNuDq7gdooiIZBIVvyKSbR2IOMCv635l+NrhrN98Fr7ZQMNHrua956vQtFxrTg3MRdmyVdwOU0REMpGKXxHJVqLjopnyzxSG/TWcqd80wxY4QKO7C/Dtff3YXcRy3z2Pct01zrIF8rsbq4iIZD4VvyKS5Vlr+evAX3wTMo6xs//ldOUxlC1YlmvsRzSsUJZfHy7uLNjQ3ThFRMR9Kn5FJMs6dOYQP68Zxc/rf+TvQ3+Ta/o3mDXv8MfKh+hyfTC5nstNrlxuRykiIr5Exa+IZCnRcdFM/Wcqw9cOZ8rMs8SPGU3d15bwTcfHadKtJ7njAqhTp43bYYqIiI9S8SsiPi86LpqFuxbye9g0fhlahLNl5lCm9jYea/8EO07m5rO7xlKrlttRiohIVqDiV0R80snIk0zfNp3hM/9i8dYwzpSdRV4KE794D/c80JORz1Uld67c0N3tSEVEJCtR8SsiPmP3yd388fcUxi5aQ2jsCGLjY8n9w18UL/gIv03cSOtqrYl6Oj/FihV2O1QREcmiVPyKiGustYQdCGPsX9OZsed3wg6Ewfhh+G3/hOd+L8nt13Umb+e6VCjvR+nSzv3J8hdzN2YREcnaVPyKSKaKjosm9Fgov08dx+R/JrFnQSuY/D03fb6Uga17UqVJMPmiS9C+9cfkzg1UcjtiERHJTlT8ikiGOxF5gulbpzPpn0lMXribM7/9QEDXJ2gfXJ++93fmaI0YXr1nCqVLux2piIhkdyp+RSRD7D65m4mbJ/Ln2tks+K4rtvpkrgpcxO03dWN5SF6G3DuDls3zOgvf6W6sIiKSc6j4FZF0cX787sQtE/npJ9gTsR1u+IUaxa+lxPF23FurBZ+9UAm/XH6ElA8hqHk1t0MWEZEc6IqLX2OMHxAK7LXWdrrykEQkq4iOi2bBzgUMm72CWcvDOVr1ewyGQitDubZYUSYOeZNrS16L7QfGuB2tiIhI+vT8PgNsAnTvIZEc4ETkCSZvnMnwqRsJ9R/MqahT+E39AbP+OYaENOa22h0JeKYURYr8V/Cq8BUREV9xRcWvMaYCcCvwAfB8ukQkIj5n14ldjF41k5l7/mDR3nnELukHM/+PbkOiuK/5LdS4rzVFCuSjTJnebocqIiJyWVfa8zsYeBkodOWhiIivsNby14G/mLBxEpO3TSRsZT4YtpCKT6zghdtfoEn7u7CPxdGu3cfky+d2tCIiIqlnrLVpe6IxnYCO1tonjDFBwItJjfk1xvQF+gKULl36xtGjR6c92jSKiIigYMGCmb7drEr58l52yFlMfAxhJ8JYcnQJi8PXc/TbiRD4HXXbLOCmwi04PLsv3TqfoXz5yCveVnbIV2ZSvryjfHlH+fKO8uUdN/MVHBy82lobmHj6lRS/HwH3A7FAXpwxv39aa+9L7jmBgYE2NDQ0Tdu7EiEhIQQFBWX6drMq5ct7WTVn5++/O3HLRMZ/HkR0nv3kaz2Itle35fCvn9L33qvodU+RdN9uVs2XW5Qv7yhf3lG+vKN8ecfNfBljkix+0zzswVr7GvCaZ+VBOD2/yRa+IuIbdp3YxaQtk/jhl2OsX58LG/Q2pQqUolKep6ldpQ2jXn6VfP754B63IxUREUl/us+vSDZ3fvzusLkL+XNiDPtqvwwGim8aSrHtnZnwU2tuqdKIXC/mcjtUERGRDJcuxa+1NgQISY91iciVi46LZs7WBXz/xyZC/b5mX9Q/mNV9sZO/5+W7ivFQ6+ZUeqUGefKAMaXcDldERCTTqOdXJJs4EXmC31fPZtrW6czdP47T/9SD4Qtp+Nw5PnigNM37diLf91C27MNuhyoiIuIaFb8iWdiuE7v4Y/1kpv47ngWb/iZuYDgF2/3DPY9159YutxHTOYqO7V6hQAG3IxUREfENKn5FspDDZw4z/9+FLNwzn/k757Nx4DdQrAC1Ht7PS60eIjLvXnrd/hr1bvCM363tbrwiIiK+RsWviA87evYoc7YuYsm+eczfOZ/1P/aDQ7Up8NhwmlZqSuUOhqY1O/L6kw86T2jtbrwiIiK+TsWviA85du4YMzcuYcXhuczfOZ91Y26Dlf3I99p9NK18M9Vbl6dETGW+fvk4Abn9QTcXFBER8YqKXxEXnYg8wfT1S1l+cB4Lw+cSNuMGmDiUPC8/RdPrrqFXp5qY66P4v2eOUbRQgNvhioiIZHkqfkUy0cnIk8zYsIwlexax5NAM1iwtDD/Pwb/PZzRtVox+tzciotJeBjy1hUrl87gdroiISLaj4lckA52KOsXMDcuZv20pq05OZfWmI9jB2/DrMpGmtxfilTvbc6DIHl55chq1aniK3V7uxiwiIpKdqfgVSUeno04za+MKZv0dSlj0eEJ3ryP+4yPkumkDTR/Oz5udHmB/7l082uP/CKyf13lSZ3djFhERyUlU/IpcgYjoCGZtWMnQBbN4bftrrNq7irgv/8YUj+KWV6fyetCLnMu/m9taPE6zJs85T2rpbswiIiI5mYpfES+cjTnLzPUrGL/wH7YVHMGqfauI/XUcHOnDzQMX8cotr5C3bBRNqrekddCtzpNU7IqIiPgMFb8il3Eu5hyzNq5g1NQ97Cn9Pav2rSRmxgew4mlu+nIUL938ElfVLEP07uO8/OASjAFauR21iIiIJEfFr0gCkbGRzN20kpETw9ldbCSrj88jeuX9MHkodd+dzPNNnueaRo0pb+JoExxCbs8rKCQkxCl8RURExKep+JUcLSo2igXbVjLsj3D+DZjI2qgJRP0bCMMWc/UTq3nm9rrUa92Wok+doVXzseTR3cdERESyNBW/kqNExUaxdNdKho7Zx5aoEDYEDCfyRGH49CDlux6m36MVaHp7S/x7RNCq2Wfkzet2xCIiIpKeVPxKthYdF82qvav4btQe/j60jn+KD+ZcdCQMPEKJGwN4/K18BFcJJm+n0zRr9PR/xW4dV8MWERGRDKLiV7KVmLgYQveFMvSPHSzfsI+dVftzNuYsDF1KgfxX0/eLswRXCeaqLn40qH0HefPe4TzxWnfjFhERkcyh4leytCNnj7Bq7yr+nHWABQtgX72nOBNzBsYPw39PTx4buYfgqkFU7V6TWlWLkSdPQ7dDFhERERep+JUs41TUKUL3riZ0/yqmTI8mdPzNnOvaAXJHw8LXMYve5JFuG2l7XWNq9w6iapkS5Mnzhdthi4iIiA9R8Ss+6VzMOeZvWM/GkytZd2wFIXP92TPiPXiwL5TYRqn9jxJw5mqerfc/2t54LdWfbMBVhfMREDDI7dBFRETEh6n4FdfFxMWwevcGxswI50DAIjbHzuLv1QWI+2Ex9HyHsg3+ombV2yne5Aj9Ov3E7U1rUTJ/Sc+zH3U1dhEREclaVPxKpoq38Ww5soWlO1czbEh+jhWdw79FfiLqRFH47AD5Oi2lWfdSPNflZg4XXU/fe3/k5hvKOE9+wdXQRUREJBtQ8SsZxlrLjuM7Cd2/ipXhq/jto+YcLbSQ6MBPId7AyONUaBlJv2fzE1gukNim++jY/AOKF/d8VVond+MXERGR7EfFr6Sb3cf2M3vd3+yMX8SqfauY9/FTxHAa7u5BgF8A+Y7eQd0yreh3W20almtImWcKUqJ4T6CnswLdW1dEREQymIpfSZNj544xcekG5q3ax+kqo1i1bxX7vv8WTlTF78mPqF2qNjc0iKRy8Uq89kgodUvXJeDNALfDFhERkRxOxa+k6HTUadbsX8Mfs/YyZ0Z+Ilu8wI4T/8L0/4M1j1B90ACCqwRT8PE4yufx54WHT5HfPz885nbkIiIiIhdT8SsXORcTyYaTG9mwcgOTZp5m8S9BnL39Vsh/DFY+jpn9OR3bT+bRG/tSrkVDahSNo+H1G8mVy+3IRURERFKm4jcHi42PZf66LWw+FcqGU8uYvzCGf77+GHoOhwqrKLr/Dvxj7uTJ2gPo0LgqdZ5sSLkiefH3/9Ht0EVERETSRMVvDhFv49mwfysjJ4Zz0H8F23JNZXVYJFFfroauH1Kk4VTqlGtPnma7aFqzN68+PI6KhStijAGqux2+iIiISLpQ8ZsNWWvZfXI3K8JX8c3gAhwvvJhdpb7m5OkY+OgUuYNW0Og+w6PtgjiWL5QH7nqfVoEjyWVywbMQEhJBpSKV3N4NERERkXSn4jcLs9ay49AhVm7byqHca1h/aD0TPr6DUwEbiAp6yVlo3E6uqn+KHi/0ILBcIHlu2UGHJi9Totjrzvxb3YtfREREJLOp+M0iDp85zIbDGxg74TSbdpwgrt4PbDi8gWNfToHcMdD7GYrnK46/XxfqlK1Jn45fE1gukKufLU2JIt2B7m7vgoiIiIjrVPz6mH3HjzFvzb9EFAllw6ENTBtelz1hNYi5N9hZ4I+R5NrblMY3fMedte7EPn2YqsUr0af7fkoXKI152bi7AyIiIiI+TMWvS05GnmTj4Y1MXXCA2dPyU6jdZ2w8sp7945+B5c/C640pmC8fJQPeokKZfDzZ5jPqlKpNuV51uLZcOQICljgr6uzqboiIiIhkKSp+M9ixiAhmLN/B6QJ/8c+ptYTMLsC6n3sR+0BTKHQAQh+Bad9Q94YvaHttW4o9XIa8d2+gT4/tXHNVJc/dFgAaubofIiIiItmBit90cjbmLJsOb2LR+h38PrIoAfXHsiPXLHatug5+mwYPPk6eaqFU8utG2WpH6d7wbZrXq8DVj9ShavFc5Ms7ze1dEBEREcn2VPx66UxUJDOX72RfzEb2mVBWbTrIgg9eJab5a3DdH3CkBvy6kUr5pnFzuyb0qBZIVP1VdO/8M4HVK+OXy8+zpptc3Q8RERGRnEjFbzKi46L55+g//L1/I9/9XwliSi/naMWf2br/APbDk9DyZ3IHDeLqQrW5qsIJWt3UhS4d7qFWidpU/CiewgU/d3sXRERERCSRNBe/xpiKwM9AGSAeGGKt/SK9AsssMXExzAndxcb9/xJRdBnrD69n6muvEFlqCbbds85Cf+yjWKOdBDWoTffa3TldYgltm/ai1Y3vEOAXAM8CNHRvJ0REREQkVa6k5zcWeMFau8YYUwhYbYyZba3dmE6xpavYuDj+PbGdDYc2MGKYP7sOniCu8UA2H9lMzDfLoYDF3D+AasWqUa7WHqpfU4n7u/5K7atqU/WlYhTO/xDwkLOyYFd3RURERETSKM3Fr7V2P7Df8/dpY8wmoDzgU8Xv1H+mcu/bhzn1byHsI4GeiWPIE3UNrdtVosM1Hchd4RB1KlTitqAI8vvnh6fdjVlEREREMoax1l75SoypAiwE6lhrTyWa1xfoC1C6dOkbR48efcXb80bYiTAGjzlBvlM30OX+5VTJX4WKeatQMCBfpsaRlURERFCwYEG3w8hSlDPvKF/eUb68o3x5R/nyjvLlHTfzFRwcvNpaG5h4+hUXv8aYgsAC4ANr7Z+XWzYwMNCGhoZe0fbSIiQkhKCgoEzfblalfHlPOfOO8uUd5cs7ypd3lC/vKF/ecTNfxpgki99cV7hSf+AP4NeUCl8REREREbelufg1zleP/Qhsstbqvl4iIiIi4vOupOf3FuB+oKUxJszz0zGd4hIRERERSXdXcreHxYBJx1hERERERDLUFY35FRERERHJSlT8ioiIiEiOoeJXRERERHIMFb8iIiIikmOo+BURERGRHEPFr4iIiIjkGCp+RURERCTHUPErIiIiIjmGil8RERERyTGMtTbzNmbMYWBXpm3wPyWBIy5sN6tSvrynnHlH+fKO8uUd5cs7ypd3lC/vuJmvytbaqxJPzNTi1y3GmFBrbaDbcWQVypf3lDPvKF/eUb68o3x5R/nyjvLlHV/Ml4Y9iIiIiEiOoeJXRERERHKMnFL8DnE7gCxG+fKecuYd5cs7ypd3lC/vKF/eUb6843P5yhFjfkVEREREIOf0/IqIiIiIZO3i1xjzkzHmkDFmfTLzjTHmf8aYbcaYdcaYBgnmtTfGbPHMezXzonZPKvJ1rydP64wxS40xNySYt9MY87cxJswYE5p5UbsrFTkLMsac9OQlzBjzdoJ5OsYunf9SglytN8bEGWOKe+blqGPMGFPRGDPfGLPJGLPBGPNMEsuoDfNIZb7UhnmkMl9qvxJIZc7UhnkYY/IaY1YaY9Z68jUgiWV8sw2z1mbZH6A50ABYn8z8jsB0wACNgRWe6X7AdqAaEACsBa5ze398IF83A8U8f3c4ny/P451ASbf3wQdzFgRMSWK6jrGUl+0MzEvwOEcdY0BZoIHn70LAP4mPEbVhXudLbZh3+VL75WXOEi2f09swAxT0/O0PrAAaJ1rGJ9uwLN3za61dCBy7zCK3AT9bx3KgqDGmLHATsM1a+6+1NhoY7Vk2W0spX9bapdba456Hy4EKmRKYD0vFMZYcHWMp6wGMysBwfJq1dr+1do3n79PAJqB8osXUhnmkJl9qw/6TyuMrOTnu+II05Synt2HWWhvheejv+Ul8IZlPtmFZuvhNhfLAngSPwz3Tkpsu/3kI59PaeRaYZYxZbYzp61JMvqqJ57TPdGNMbc80HWOXYYzJD7QH/kgwOcceY8aYKkB9nJ6ThNSGJeEy+UpIbZhHCvlS+5WElI4xtWEOY4yfMSYMOATMttZmiTYsd2ZtyCUmiWn2MtMFMMYE47xxNE0w+RZr7T5jTClgtjFms6eXL6dbg/P1iRHGmI7ABKA6OsZS0hlYYq1N2EucI48xY0xBnDfQZ621pxLPTuIpOboNSyFf55dRG+aRQr7UfiUhNccYasMAsNbGAfWMMUWB8caYOtbahNd8+GQblt17fsOBigkeVwD2XWZ6jmeMuR4YCtxmrT16frq1dp/n9yFgPM4pixzPWnvq/Gkfa+00wN8YUxIdYym5h0SnC3PiMWaM8cd5k/3VWvtnEouoDUsgFflSG5ZASvlS+3Wp1BxjHmrDErDWngBCcHrDE/LJNiy7F7+TgAc8Vxs2Bk5aa/cDq4DqxpiqxpgAnIN4kpuB+gJjTCXgT+B+a+0/CaYXMMYUOv830BZI8mr+nMYYU8YYYzx/34TzmjqKjrFkGWOKAC2AiQmm5bhjzHPc/AhsstZ+nsxiasM8UpMvtWH/SWW+1H4lkMrXpNowD2PMVZ4eX4wx+YDWwOZEi/lkG5alhz0YY0bhXK1a0hgTDvTHGXCNtfY7YBrOlYbbgLPAg555scaYfsBMnCsOf7LWbsj0HchkqcjX20AJ4BtPexhrrQ0ESuOczgDnmPnNWjsj03fABanI2V3A48aYWOAccI+11gI6xpLOF8AdwCxr7ZkET82Jx9gtwP3A354xcwCvA5VAbVgSUpMvtWH/SU2+1H5dLDU5A7Vh55UFRhhj/HA+OI211k4xxjwGvt2G6RveRERERCTHyO7DHkRERERELlDxKyIiIiI5hopfEREREckxVPyKiIiISI6h4ldEREREcgwVvyIiIiKSY6j4FREREZEcQ8WviIiIiOQY/w+DwZO1CaTqvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "  \n",
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.\n",
    "    n = 10\n",
    "\n",
    "    (t, U) = explicitMidpoint(f_1, a, b, u_0, n)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=} — by the Explicit Midpoint Method with {n} steps\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "    \n",
    "    def f_2(t, u):\n",
    "        \"\"\"A simple more \"generic\" test case, with f(t, u) depending on both variables.\n",
    "        The solution for a=0 is u(t) = u(t; 0, u_0) = cos t + (u_0 - 1) e^(-Kt)\n",
    "        The solution in general is u(t) = u(t; a, u_0) = cos t + C e^(-K t), C = (u_0 - cos(a)) exp(K a)\n",
    "        \"\"\"\n",
    "        return  K*(np.cos(t) - u) - np.sin(t)\n",
    "    def u_2(t): return np.cos(t) + C * np.exp(-K*t)\n",
    "\n",
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = explicitMidpoint(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} — by the Explicit Midpoint Method with {n} steps\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the (classical) Runge-Kutta Method\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following two lines will need to change for the systems version\n",
    "    U = np.empty_like(t)\n",
    "    U[0] = u_0\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h/2, U[i]+K_1/2)*h\n",
    "        K_3 = f(t[i]+h/2, U[i]+K_2/2)*h\n",
    "        K_4 = f(t[i]+h, U[i]+K_3)*h\n",
    "        U[i+1] = U[i] + (K_1 + 2*K_2 + 2*K_3 + K_4)/6\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "  \n",
    "    a = 1.\n",
    "    b = 3.\n",
    "    u_0 = 2.\n",
    "    K = 1.\n",
    "    n = 10\n",
    "\n",
    "    (t, U) = RungeKutta(f_1, a, b, u_0, n)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = Ku, {a=}, {u_0=} — by the Runge-Kutta Method with {n} steps\")\n",
    "    plt.plot(t, u_1(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_1(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "    \n",
    "    def f_2(t, u):\n",
    "        \"\"\"A simple more \"generic\" test case, with f(t, u) depending on both variables.\n",
    "        The solution for a=0 is u(t) = u(t; 0, u_0) = cos t + (u_0 - 1) e^(-Kt)\n",
    "        The solution in general is u(t) = u(t; a, u_0) = cos t + C e^(-K t), C = (u_0 - cos(a)) exp(K a)\n",
    "        \"\"\"\n",
    "        return  K*(np.cos(t) - u) - np.sin(t)\n",
    "    def u_2(t): return np.cos(t) + C * np.exp(-K*t)\n",
    "\n",
    "    a = 1.\n",
    "    b = a + 4 * np.pi  # Two periods\n",
    "    u_0 = 2.\n",
    "    K = 2.\n",
    "    n = 50\n",
    "\n",
    "    (t, U) = RungeKutta(f_2, a, b, u_0, n)\n",
    "    C = (u_0 - np.cos(a)) * np.exp(K*a)\n",
    "    h = (b-a)/n\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"Solving du/dt = K(cos(t) - u) - sin(t), {K=}, {a=}, {u_0=} — by the Runge-Kutta Method with {n} steps\")\n",
    "    plt.plot(t, u_2(t), 'g', label=\"Exact solution\")\n",
    "    plt.plot(t, U, 'b:', label=f\"Solution with h={h:0.3}\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.figure(figsize=[12,4])\n",
    "    plt.title(f\"Error\")\n",
    "    plt.plot(t, U - u_2(t))\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta_system(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the (classical) Runge-Kutta Method\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following three lines change for the systems version — the same lines as for euler_system and so on.\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h/2, U[i]+K_1/2)*h\n",
    "        K_3 = f(t[i]+h/2, U[i]+K_2/2)*h\n",
    "        K_4 = f(t[i]+h, U[i]+K_3)*h\n",
    "        U[i+1] = U[i] + (K_1 + 2*K_2 + 2*K_3 + K_4)/6\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "\n",
    "    def f_mass_spring(t, u):\n",
    "        return np.array([ u[1], -(k/M)*u[0] - (D/M)*u[1]])\n",
    "    M = 1.0\n",
    "    k = 1.0\n",
    "    D = 0.1\n",
    "    u_0 = [1.0, 0.0]\n",
    "    a = 0.0\n",
    "    b = 8 * np.pi # Four periods\n",
    "    n = 100  # Should be enough now!\n",
    "\n",
    "    (t, U) = RungeKutta_system(f_mass_spring, a, b, u_0, n)\n",
    "    y = U[:,0]\n",
    "    Dy = U[:,1]\n",
    "\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"U_0, = y with {k=}, {D=} — by Runge-Kutta with {n} steps\")\n",
    "    plt.plot(t, y)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('y')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"U_1, = dy/dt with {k=}, {D=} — by Runge-Kutta with {n} steps\")\n",
    "    plt.plot(t, Dy)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('dy/dt')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "    if D == 0.:\n",
    "        plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by Runge-Kutta with {n} steps\")\n",
    "    else:\n",
    "        plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by Runge-Kutta with {n} steps\")\n",
    "    plt.plot(y, Dy)\n",
    "    plt.xlabel('y')\n",
    "    plt.ylabel('dy/dt')\n",
    "    plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "    plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For the future: an attempt to use the IMPLICIT Midpoint Method\n",
    "\n",
    "Solving for now with a few fixed point iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def FP_Midpoint_system(f, a, b, u_0, n=100, iterations=1):\n",
    "    \"\"\"Use a few iterations of a fixed point method solution of the Implicit Midpoint Method\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\n",
    "    Note:\n",
    "        - the default of iterations=1 gives the Explicit Midpoint Method\n",
    "        - iterations=0 gives Euler's Method\n",
    "        \"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following three lines change for the systems version — the same lines as for euler_system and so on.\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        K = f(t[i], U[i])*h\n",
    "        # A few iterations of the fixed point method\n",
    "        for iteration in range(iterations):\n",
    "            K = f(t[i]+h/2, U[i]+K/2)*h\n",
    "        U[i+1] = U[i] + K\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Demo\n",
    "if __name__ == \"__main__\":  # Do this if running the .py file directly, but not when importing [from] it.\n",
    "\n",
    "    def f_mass_spring(t, u):\n",
    "        return np.array([ u[1], -(k/M)*u[0] - (D/M)*u[1]])\n",
    "    M = 1.0\n",
    "    k = 1.0\n",
    "    D = 0.0\n",
    "    u_0 = [1.0, 0.0]\n",
    "    a = 0.0\n",
    "    b = 8 * np.pi # Four periods\n",
    "    n = 200\n",
    "    iterations = 2\n",
    "\n",
    "    (t, U) = FP_Midpoint_system(f_mass_spring, a, b, u_0, n, iterations=1)\n",
    "    y = U[:,0]\n",
    "    Dy = U[:,1]\n",
    "\n",
    "    plt.figure(figsize=[12,6])\n",
    "    plt.title(f\"U_0, = y with {k=}, {D=} — by FP_Midpoint_system with {n} steps, {iterations} iterations\")\n",
    "    plt.plot(t, y)\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('y')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "    if D == 0.:\n",
    "        plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by FP_Midpoint_system with {n} steps, {iterations} iterations\")\n",
    "    else:\n",
    "        plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by FP_Midpoint_system with {n} steps, {iterations} iterations\")\n",
    "    plt.plot(y, Dy)\n",
    "    plt.xlabel('y')\n",
    "    plt.ylabel('dy/dt')\n",
    "    plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "    plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "    plt.legend()\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
   ]
  }
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