{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(section-eulers-method)=\n",
    "# Euler's Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- {cite}`Sauer` Sections 6.1.1 *Euler's Method*.\n",
    "\n",
    "- {cite}`Burden-Faires` Section 5.2 *Euler's Method*.\n",
    "\n",
    "- {cite}`Chenney-Kincaid` Sections 7.1 and 7.2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# Shortcuts for some favorite commands:\n",
    "from numpy import linspace\n",
    "from matplotlib.pyplot import figure, plot, grid, title, xlabel, ylabel, legend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Examples\n",
    "\n",
    "A lot of useful intuition comes from the first four examples in \n",
    "{ref}`the chapter introduction <ODE-IVPs>`:\n",
    "- {prf:ref}`ode-integration` $\\displaystyle du/dt = f(t)$ (Integration),\n",
    "- {prf:ref}`ode-simplest-genuine` $\\displaystyle du/dt = K u$ (the simplest \"genuine\" ODE),\n",
    "- {prf:ref}`ode-nonlinear` $\\displaystyle du/dt = u^2$ (a nonlinear ODE)\n",
    "and\n",
    "- {prf:ref}`ode-stiff` $\\displaystyle du/dt = -\\sin t -K(u - \\cos t)$ (with fast and slow time scales)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(eulers-method)=\n",
    "## The Tangent Line Method, a.k.a. Euler's Method\n",
    "\n",
    "Once we know $u(t)$ (or a good approximation) at some time $t$, we also know the value of $u'(t) = f(t, u(t))$ there; in particular, we know that $u(a) = u_0$ and so $u'(a) = f(a, u_0)$.\n",
    "\n",
    "This allows us to approximate $u$ for slightly larger values of the argument (which I will call \"time\") using its tangent line:\n",
    "\n",
    "$$\n",
    "u(a+h) \\approx4 u(a) + u'(a) h = u_0 + f(a, u_0) h  \\text{ for ``small'' $h$} $$\n",
    "\n",
    "and more generally\n",
    "\n",
    "$$ u(t+h) \\approx4 u(t) + f(t, u(t)) h \\text{ for ``small'' $h$} $$\n",
    "\n",
    "This leads to the simplest approximation: choose a step size $h$ determining equally spaced times $t_i = a + i h$ and define — recursively — a sequence of approximations $U_i \\approx4 u(t_i)$ with\n",
    "\n",
    "$$\\begin{split}\n",
    "U_0 &= u_0\n",
    "\\\\\n",
    "U_{i+1} &= U_i + h f(t_i, U_i))\n",
    "\\end{split}$$\n",
    "\n",
    "If we choose a number of time steps $n$ and set $h = (b-a)/n$ for $0 \\leq i \\leq n$,\n",
    "the second equation is needed for $0 \\leq i < n$, ending with $U_n \\approx4 u(t_n) = u(b)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This \"two-liner\" does not need a pseudo-code description; instead, we can go directly to a rudimentary Julia function for Euler's Method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler_method(f, a, b, u_0, n):\n",
    "    \"\"\"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 = linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    u = np.empty_like(t)\n",
    "    u[0] = u_0\n",
    "    for i in range(n):\n",
    "        u[i+1] = u[i] + f(t[i], u[i])*h\n",
    "    return (t, u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See {ref}`eulers-method-exercise-1`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for {prf:ref}`ode-integration`, an integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For integration of -sin(t)\n",
    "\n",
    "def f_1(t, u):\n",
    "    \"\"\"For integration of -sin(x)\n",
    "    The general solution is\n",
    "        u(t) = cos(x) + C,\n",
    "        C = u_0 - cos(a)\n",
    "    \"\"\"\n",
    "    return -np.sin(t)\n",
    "\n",
    "def u_1(t, a, u_0):\n",
    "    return np.cos(t) + (u_0 - np.cos(a));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A helper function for rounding some output to four significant digits\n",
    "# TO DO: check Python syntax\n",
    "def approx4(x):\n",
    "    return round(x, sigdigits=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 3/4*np.pi\n",
    "u_0 = 3.0\n",
    "n = 20\n",
    "\n",
    "(t, U) = euler_method(f_1, a, b, u_0, n)  \n",
    "u = u_1(t, a, u_0)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is y = cos(x) + {u_0 - np.cos(a)}\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \".:b\", label=f\"Euler's answer for h={(b-a)/n:0.4g}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for {prf:ref}`ode-simplest-genuine`, some exponential functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_2(t, u):\n",
    "    \"\"\"For solving du/dt = K u.\n",
    "    The variable K may be defined later, so long as that is done before this function is used.\n",
    "    \"\"\"\n",
    "    return K*u\n",
    "\n",
    "def u_2(t, a, u_0, K):\n",
    "    return u_0 * np.exp(K*(t-a));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You could experiment by changing these values here;\n",
    "# for now I instead redefine them below.\n",
    "K = 1.0\n",
    "u_0 = 0.8\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "n = 40\n",
    "\n",
    "(t, U) = euler_method(f_2, a, b, u_0, n)\n",
    "u = u_2(t, a, u_0, K)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is $u = {u_0}\\\\ \\\\exp({K}\\\\ t)$\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \".:b\", label=f\"Euler's answer for h={(b-a)/n:0.4g}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You could experiment by changing these values here.\n",
    "K = -0.5\n",
    "u_0 = 3.\n",
    "a = 0.\n",
    "b = 2.\n",
    "\n",
    "(t10, u_10) = euler_method(f_2, a, b, u_0, 10)\n",
    "(t20, U20) = euler_method(f_2, a, b, u_0, 20)\n",
    "t = t20\n",
    "u = u_2(t, a, u_0, K)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is $y = {u_0} \\\\, \\\\exp({K} \\\\, t)$\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t10, u_10, \".:r\", label=f\"Euler's answer for h={(b-a)/10:0.4g}\")\n",
    "plot(t20, U20, \".:b\", label=f\"Euler's answer for h={(b-a)/20:0.4g}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for {prf:ref}`ode-nonlinear`: solutions that blow up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_3(t, u):\n",
    "    \"\"\"For solving du/dt = u^2\n",
    "    # The general solution is u(t) = 1/((a + 1/u_0) - t), = 1/(T-t) with T = a + 1/u_0\n",
    "    \"\"\"\n",
    "    return u**2\n",
    "\n",
    "def u_3(t, a, u_0):\n",
    "    T = a + 1./u_0\n",
    "    return 1./(T - t);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jVq1ahre3t1GhQgVj2LBhxhdffGEAxr59+2743IxQvnz5m1b1fuONN1KtpG4YhnH//fcb7dq1u+1rJ1UZT61y96VLl4xBgwYZAQEBhpeXl1GrVi1j7ty5GfCub+zgwYNGs2bNDD8/PwMwxo0b5zy3fPlyAzC2bNmS6f0QEcntLIZhGFkV2EVERERyimrVqvHQQw8xbtw4t3NJ062PHDniNi09L+rWrRt///33Dafpi4iISSFaREREJAXDMGjSpAl169Zl0qRJ2d2dTHXw4EGqVq3KihUraNq0aXZ3R0Qkx9M+0SIiIiIpWCwWpk2bRpkyZXA4HNndnUx19OhRJk2apAAtIpJOGokWERERERERSSeNRIuIiIiIiIikk0K0iIiIiIiISDrluH2iHQ4Hx48fp1ChQpm276WIiIiIiIhIEsMwuHTpEmXKlMFqvfFYc44L0cePHyc4ODi7uyEiIiIiIiL5zD///ENQUNAN2+S4EF2oUCHA7HzhwoWzuTc3lpCQwNKlS2ndujWenp7Z3R2RTKX7XfIT3e+SX+hel/xE97vcSHR0NMHBwc48eiM5LkQnTeEuXLhwrgjRvr6+FC5cWL+Ikufpfpf8RPe75Be61yU/0f0u6ZGeJcUqLCYiIiIiIiKSTgrRIiIiIiIiIumkEC0iIiIiIiKSTjluTXR62e12EhISsrUPCQkJeHh4EBsbi91uz9a+iGS2zL7fPT09sdlsGX5dEREREZGMlOtCtGEYnDx5kosXL2Z3VzAMg4CAAP755x/taS15Xlbc7/7+/gQEBOj3SURERERyrFwXopMCdKlSpfD19c3W/9h2OBxcvnyZggUL3nRDbpHcLjPvd8MwuHLlCqdPnwYgMDAwQ68vIiIiIpJRclWIttvtzgBdvHjx7O4ODoeD+Ph4ChQooBAteV5m3+8+Pj4AnD59mlKlSmlqt4iIiIjkSLkq+SWtgfb19c3mnohIZkj63c7uegciIiIiImnJVSE6idZLiuRN+t0WERERkZwuV4ZoERERERERkeygEC0ZzmKx8N13393xdSpUqMCECRPu+DoiIiIiIiIZRSE6i/To0QOLxeL21bZt2yzrw4gRI6hdu3aWvV56zZw5E39/f7fjmzdvpnfv3lnfIRERERERkTTkqurcuV3btm2ZMWOGyzFvb+9s6k3OV7JkyezugoiIiIiIiAuNRGchb29vAgICXL6KFi0KwMqVK/Hy8mLNmjXO9uPGjaNEiRKcOHECgCVLltC0aVP8/f0pXrw4jzzyCAcPHnR5jcjISJ566imKFSuGn58f9erVY9OmTcycOZN33nmHHTt2OEfBZ86cmWo/V65cSYMGDfDz88Pf35/77ruPI0eOOM9PnjyZu+++Gy8vLypXrsxXX32V5nteuXIlFouFixcvOo9t374di8XC4cOHWblyJc8++yxRUVHOfo0YMQJwn8599OhR/u///o+CBQtSuHBhOnXqxKlTp5znk0bav/rqKypUqECRIkV46qmnuHTp0g1/LiIiIiIiIul1yyF69erVPProo5QpUybVta+GYTBixAjKlCmDj48PYWFh/PnnnxnVXzeGYRATH5MtX4ZhZNj7CAsLY/DgwXTr1o2oqCh27NjB66+/zrRp0wgMDAQgJiaGIUOGsHnzZpYvX47VaqV9+/Y4HA4ALl++TLNmzTh+/Dg//PADO3bs4JVXXsHhcPDkk0/y8ssvU716dU6cOMGJEyd48skn3fqRmJjI448/TrNmzdi5cycbNmygd+/ezqrJCxcu5MUXX+Tll1/mjz/+oE+fPjz77LNERETc1vtu0qQJEyZMoHDhws5+DR061K2dYRg8/vjjnD9/nlWrVrFs2TIOHjzo9h4OHjzId999x6JFi1i0aBGrVq3igw8+uK2+iYiIiIiIpHTL07ljYmK45557ePbZZ3niiSfczo8ZM4bx48czc+ZMKlWqxKhRo2jVqhV79+6lUKFCGdLp5K4kXKHg+wUz/LrpET08+pbaL1q0iIIFXfs6fPhw3nzzTQBGjRrFr7/+Su/evfnzzz/p1q0b7du3d7ZN+XmHh4dTqlQpdu/eTY0aNZgzZw5nzpxh8+bNFCtWDICQkBBn+4IFC+Lh4UFAQEDa7yk6mqioKB555BHuvvtuAKpWreo8P3bsWHr06EH//v0BGDJkCBs3bmTs2LE0b978lj4PAC8vL4oUKYLFYrlhv3799Vd27tzJoUOHCA4OBuCrr76ievXqbN68mfr16wPgcDiYOXOm817r1q0by5cv57333rvlvomIiIiIiKR0yyPRDz30EKNGjaJDhw5u5wzDYMKECbz++ut06NCBGjVqMGvWLK5cucKcOXMypMO5WfPmzdm+fbvL14ABA5znvby8mD17NvPnz+fq1atulakPHjxI586dueuuuyhcuDAVK1YEzGnOYE6TrlOnjjNA345ixYrRo0cP2rRpw6OPPsrEiROd08kB9uzZw3333efynPvuu489e/bc9mumx549ewgODnYGaIBq1arh7+/v8toVKlRw+WNNYGAgp0+fztS+iYiIiIhI/pGhhcUOHTrEyZMnad26tfOYt7c3zZo1Y/369fTp08ftOXFxccTFxTkfR0ebo7sJCQkkJCS4tE1ISMAwDBwOh3MKcwFbgVseEc4oPh4+XOays083YhgGvr6+3HXXXW7nkj937dq1AJw/f56zZ8/i4+PjPPfoo48SFBTElClTKFOmDA6Hg1q1ahEbG4vD4aBAgQJu10vZhxudTxIeHs7AgQP55Zdf+Oabb3jjjTf45ZdfaNSokfM6ya/hcDiwWCxux5I/ttvtzsdJP++kNknHU+tX8p93ytdIOp/UxjAMPD093dqk7IvcnqT7Jz33++1K+jkmJCRgs9ky5TVE0iPp/39S/v+QSF6je13yE93v2aP79905c+UMb93/Fo2CGmV3d9J0K/dFhobokydPAlC6dGmX46VLl3YpTJXc+++/zzvvvON2fOnSpfj6+rocS5qKfPnyZeLj4zOo17fvMpcB0lW4KiEhgcTEROcfCVJz6NAhXn75ZSZOnMjChQvp2rUr33//PVarlfPnz7Nnzx7Gjh3rnLq8YcMGAK5evUp0dDShoaFMnz6dI0eOOAuWJedwOIiPj79hH5Lcfffd9O/fn/79+9O6dWtmzZpFtWrVCA0NZeXKlTz++OPOtqtXryYkJMTlukl9SvojwP79+6lSpQoAGzduBMw13NHR0djtdux2u1u/HA4HsbGxREdHU758eY4ePcru3bsJCgoC4K+//iIqKopy5coRHR1NXFyc23WS/sCQnvcs6ZOZhdri4+O5evUqq1evJjExMdNeRyS9li1blt1dEMkSutclP9H9nnUMw2Dx3sVEJUbR2qM15/3OZ3eX0nTlypV0t82ULa6SilAlMQzD7ViS1157jSFDhjgfR0dHExwcTOvWrSlcuLBL29jYWP755x8KFizoHHXNToZhcOnSJQoVKpTm+0vi6emJ3W53++F4eHhQokQJ7HY7AwYMoFWrVvTr14/27dtzzz33MH36dIYOHUrBggUpXrw4c+bMISQkhKNHj/L2228D4OPjQ+HChXn22WeZMGEC3bt357333iMwMJBt27ZRpkwZGjduTOXKlTl69Ch///03QUFBFCpUyG2LrUOHDjFt2jRn8bi9e/dy8OBBunfvTuHChRk+fDhPPfUUDRo0oGXLlixatIgff/yRpUuXuvy8kvpUu3ZtgoODGTduHO+++y779+9n8uTJAM4q21WrVuXy5cts3ryZe+65B19fX3x9fbFarRQoUIDChQvz2GOPUatWLfr378/48eNJTExk4MCBNGvWjGbNmgHmrAebzebSjwIFCmC1Wt3uJbl1t3K/367Y2Fh8fHx44IEHcsTvuORfCQkJLFu2jFatWuHp6Znd3RHJNLrXJT/R/Z71Dl88TNSOKDytnvRt35cCHjn3v+9uZdAtQ0N0UmGokydPOitKA5w+fdptdDqJt7d3qnsle3p6ut3cdrsdi8WC1WrFas3+3bmSprQm9elGLBYLv/zyC2XLlnU5XrlyZf766y9GjRrF4cOH+fHHH7FarZQpU4bp06fTqVMnWrduTe3atZk3bx6DBg2iVq1aVK5cmU8++YSwsDDn51GgQAGWLl3Kyy+/zCOPPEJiYiLVqlXjs88+w2q10rFjR7777jtatmzJxYsXmTFjBj169HDpT8GCBdm7dy//+c9/OHfuHIGBgQwcOJB+/fphtVrp0KEDEydOZOzYsQwePJiKFSsyY8YMWrRo4XKdpD55e3szd+5c+vXrR506dahfvz6jRo2iY8eOzjZNmzalb9++PP3005w7d463337buc1V8s/2u+++44UXXnC+57Zt2/Lpp586zycFu+Q/i9SOye25lfv9dlmtViwWS6q//yLZQfei5Be61yU/0f2edbad3gbAPQH3UMgn44tMZ6RbuScsxh3s02SxWFi4cKFzaq9hGJQpU4aXXnqJV155BTCnZ5YqVYoPP/ww1TXRKUVHR1OkSBGioqJSHYk+dOgQFStWzBGjVEnThAsXLqyQJnleVtzvOe13XPKvhIQEFi9eTLt27fQfWpKn6V6X/ET3e9YbunQo4zaMo1+9fnz+8OfZ3Z0bulEOTemWR6IvX77MgQMHnI8PHTrE9u3bKVasGOXKlWPw4MGMHj2a0NBQQkNDGT16NL6+vnTu3PnW34mIiIiIiIjkSr8d+w2ABmUbZHNPMtYth+jff//dZT/gpPXM3bt3Z+bMmbzyyitcvXqV/v37c+HCBRo2bMjSpUszZY9oERERERERyXkSHYlsObEFUIgmLCyMG80At1gsjBgxwrmmVURERERERPKXPWf2cCXhCoW8ClG5eOXs7k6G0kJeERERERERyVBJU7nrlamHzWrL5t5kLIVoERERERERyVB5dT00KESLiIiIiIhIBvvtuEK0iIiIiIiIyE1dSbjCrlO7AKhfpn429ybjKUSLiIiIiIhIhtl2Yht2w05AwQCCCgdld3cynEK0iIiIiIiIZJjk66EtFks29ybjKUTnIitXrsRisXDx4sXs7kqetW7dOmrWrImnpyePP/54hl67R48eGX5NEREREZGcZvPxzQA0KJP31kODQnSW6dGjBxaLxe2rbdu22dIfi8XC4cOHs+W1c7IhQ4ZQu3ZtDh06xMyZM7O7Ozd14cIFunXrRpEiRShSpAjdunW76R9ZDMNgxIgRlClTBh8fH8LCwvjzzz9d2sTFxfHCCy9QokQJ/Pz8eOyxx4iMjHRps3XrVlq1aoW/vz/Fixend+/eXL58OaPfooiIiIjkMnm5MjcoRGeptm3bcuLECZevuXPnZmkf4uPjs/T1ciK73Y7D4Uj13MGDB2nRogVBQUH4+/vf1vWz8jPu3Lkz27dvZ8mSJSxZsoTt27fTrVu3Gz5nzJgxjB8/nkmTJrF582YCAgJo1aoVly5dcrYZPHgwCxcuZN68eaxdu5bLly/z2GOPYbfbATh+/DgPPvggISEhbNq0iSVLlvDnn3/So0ePzHy7IiIiIpLDnbtyjoMXDgLmHtF5Uf4O0ZGREBFhfs8C3t7eBAQEuHwVLVoUgMOHD2OxWNi+fbuz/cWLF7FYLKxcuTLNa65fv54HHngAHx8fgoODGTRoEDExMc7zFSpUYNSoUfTo0YMiRYrw/PPPu13jwoULdOnShZIlS+Lj40NoaCgzZsxI8zWXLFlC06ZNnSOQjzzyCAcPHnSeT3ovCxYsoHnz5vj6+nLPPfewYcMGZ5sjR47w6KOPUrRoUfz8/KhevTqLFy8GoG7duowbN87Z9vHHH8fDw4Po6GgATp48icViYe/evYAZWl955RXKli2Ln58fDRs2dPnMZs6cib+/P4sWLaJatWp4e3tz5MgRl/eU1Odz587Rs2dPLBaLcyR61apVNGjQAG9vbwIDA3n11VdJTEx0PjcsLIyBAwcyZMgQSpQoQatWrdL87ADGjh1LYGAgxYsXZ8CAASQkJNywfVr27NnDkiVLmD59Oo0bN6Zx48ZMmzaNRYsWOT+blAzDYMKECbz++ut06NCBGjVqMGvWLK5cucKcOXMAiIqKIjw8nHHjxvHggw9Sp04dZs+eza5du5yf66JFi/D09OSzzz6jcuXK1K9fn88++4z58+dz4MCB23o/IiIiIpL7JU3lrlS8EkV9imZzbzJH3gnRMTHml2FcPxYfbx6Li3Nv+/nnUL48tGhhfp861TweG5v6dZOPXN5m6Mlou3btok2bNnTo0IGdO3fyzTffsHbtWgYOHOjS7qOPPqJGjRps2bKFN9980+06b775Jrt37+bnn39mz549TJ48mRIlSqT5ujExMQwZMoTNmzezfPlyrFYr7du3dxvdff311xk6dCjbt2+nUqVKPP30087wOWDAAOLi4li9ejW7du3iww8/pGDBgoAZSpPCmmEYrFmzhqJFi7J27VoAIiIiCAgIoHLlygA8++yzrFu3jnnz5rFz5046duxI27Zt2b9/v7MvV65c4f3332f69On8+eeflCpVyqWvwcHBnDhxgsKFCzNhwgROnDjBk08+ybFjx2jXrh3169dnx44dTJ48mfDwcEaNGuXy/FmzZuHh4cG6deuYMmVKmp9dREQEBw8eJCIiglmzZjFz5kyXaeN9+/alYMGCN/w6evQoABs2bKBIkSI0bNjQ+fxGjRpRpEgR1q9fn+rrHzp0iJMnT9K6dWvnMW9vb5o1a+Z8zpYtW0hISHBpU6ZMGWrUqMFvv5lTc+Li4vDy8sJqvf4/IT4+PgDOn5OIiIiI5D95fSo3gEd2dyDDXAtgnD4NJUua//7oI3jjDXjuOZg27XrbEiVcw7LDAX37Qp8+0LkzfP319XMVKsDZs/DHH1C9unls5kxIZUT3ZhYtWuQMikmGDx+earBNj48++ojOnTszePBgAEJDQ/nkk09o1qwZkydPpkCBAgC0aNGCoUOHujzXSPbHhqNHj1KnTh3q1TOnW1SoUOGGr/vEE0+4PA4PD6dUqVLs3r2bGjVqOI8PHTqUhx9+GIB33nmH6tWrc+DAAapUqcLRo0d54oknqFmzJgB33XWX83lhYWGEh4fjcDjYtWsXNpuNrl27snLlStq1a8fKlStp1qwZYE6/njt3LpGRkZQpU8b5ukuWLGHGjBmMHj0agISEBD7//HPuueeeVN+TzWYjICAAi8VCkSJFCAgIAODzzz8nODiYSZMmYbFYqFKlCsePH2f48OG89dZbzhAZEhLCmDFjbvi5ARQtWpRJkyZhs9moUqUKDz/8MMuXL3fOEBg5cqTbzyqlpPd58uRJtz8GAJQqVYqTJ0+m+tyk46VLl3Y5Xrp0aefo/MmTJ/Hy8nLOkkh+3VOnTgHmPTVkyBA++ugjXnzxRWJiYvj3v/8NwIkTJ27YfxERERHJu5JCdF7cHzpJ3gnRtyL5aPWNjmWw5s2bM3nyZJdjxYoVu+3rbdmyhQMHDvB1stBvGAYOh4NDhw5RtWpVAGc4Tku/fv144okn2Lp1K61bt+bxxx+nSZMmabY/ePAgb775Jhs3buTs2bPOEeijR4+6hOhatWo5/x0YGAjA6dOnqVKlCoMGDaJfv34sXbqUBx98kCeeeMLZ/oEHHuDSpUts27aNdevW0axZM5o3b+4c/V25cqXzDwdbt27FMAwqVark0se4uDiKFy/ufOzl5eXSn/Tas2cPjRs3dinNf99993H58mUiIyMpV64ccPPPOEn16tWx2WzOx4GBgezatcv5uFSpUqkG47SktmWAYRg33Uog5fn0PCd5m+rVqzNr1iyGDBnCa6+9hs1mY9CgQZQuXdrl/YmIiIhI/mEYhkaic5WkqsC+vtePDRsGgweDR4q3uXMnVK3qOkXbZoPdu+FaKHJKqmB9baoqALdZPMnPz4+QkJBUzyWNaCYfIb7ZWlmHw0GfPn0YNGiQ27lyyd6Hn5/fDa/z0EMPceTIEX766Sd+/fVXWrZsyYABAxg7dmyq7R999FGCg4OZNm0aZcqUweFwUKNGDbeCWp6ens5/J4WvpMD93HPP0aZNG3766SeWLl3K+++/z7hx43jhhRcoUqQItWvXZuXKlaxfv54WLVpw//33s337dvbv38++ffsICwtzXs9ms7Flyxa38JZ81N/Hx+e29qhLLVwm/YySH7/ZZ5wk+WeSdI3k0+D79u3L7Nmzb3iN3bt3U65cOQICApwjw8mdOXPGbaQ5SdII+8mTJ51/2ADzjxtJzwkICCA+Pp4LFy64jEafOXOGunXrOh937tyZzp07c+rUKfz8/LBYLIwfP56KFSvesP8iIiIikjcdvniYM1fO4Gn1pHZA7ezuTqbJO2ui/fzMr+SBx8vLPObt7dq2UiVzDXRS6LLZYMoU8/i1KdBu10229pMUQSgjlLw2BT35VNjkRcZSc++99/Lnn38SEhLi9uXl5XXLr9+jRw9mz57NhAkTmDp1aqrtzp07x549e3jjjTdo2bIlVatW5cKFC7f0WkmCg4Pp27cvCxYs4OWXX2Zasin3YWFhREREsHr1asLCwvD396datWqMGjWKUqVKOUfZ69Spg91u5/Tp026fQVJgvBPVqlVj/fr1Ln/cWL9+PYUKFaJs2bJ3fP2URo4cyfbt22/4lTSdu3HjxkRFRTnXKQNs2rSJqKioNGcSVKxYkYCAAJYtW+Y8Fh8fz6pVq5zPqVu3Lp6eni5tTpw4wR9//EGDBu5/USxdujQFCxbkm2++oUCBAjctrCYiIiIiedO6f9YBcG/gvRTwKHCT1rlX3hmJvlW9ekGbNnDgAISEQFBQpr9kXFyc21pVDw8PSpQogY+PD40aNeKDDz6gQoUKnD17ljfeeOOG1xs+fDiNGjViwIABPP/88/j5+bFnzx6WLVvGp59+mu5+vfXWW9StW5fq1asTFxfHokWLnCE1paJFi1K8eHGmTp1KYGAgR48e5dVXX033ayUZPHgwDz30EJUqVeLChQusWLHC5TXDwsKYOHEixYoVo1q1as5jn376KR06dHC2q1SpEl26dOGZZ55h3Lhx1KlTh7Nnz7JixQpq1qxJu3btbrlvyfXv358JEybwwgsvMHDgQPbu3cvbb7/NkCFDXIpqZZRbmc5dtWpV2rZty/PPP+8sZta7d28eeeQRZ9E1gCpVqvD+++/Tvn17LBYLgwcPZvTo0YSGhhIaGsro0aPx9fWlc+fOABQpUoRevXrx8ssvU7x4cYoVK8bQoUOpWbOmcwYAwKRJk2jSpAkFCxZk2bJlDBs2jA8++OC2twYTERERkdxt3VEzRN8XfF829yRz5d8QDWZwzoLwnGTJkiUuU2gBKleuzF9//QXAl19+Sc+ePalXrx6VK1dmzJgxLhWSU6pVqxarVq3i9ddf5/7778cwDO6++26efPLJW+qXl5cXr732GocPH8bHx4f777+fefPmpdrWarUyb948Bg0aRI0aNahcuTKffPKJS7hKD7vdzoABA4iMjKRw4cK0bduWjz/+2Hn+gQceAKBZs2bOadPNmjVjwoQJzqJiSWbMmMGoUaN4+eWXOXbsGMWLF6dx48Z3HKABypYty+LFixk2bBj33HMPxYoVo1evXjf9A0dW+frrrxk0aJDzPnnssceYNGmSS5u9e/cSFRXlfPzKK69w9epV+vfvz4ULF2jYsCFLly6lUKFCzjYff/wxHh4edOrUiatXr9KyZUu+/PJLlynzv/32G2+//TaXL1+mSpUqTJky5aZ7VIuIiIhI3pU0Et0kOO36SnmBxTCyoKLWLYiOjqZIkSJERUVRuHBhl3OxsbEcOnSIihUrOitPZyeHw0F0dDSFCxfOlFFJkZwkK+73nPY7LvlXQkICixcvpl27dm61DETyEt3rkp/ofs9cUbFRFP2wKAYGJ14+QUDBO19amZVulENTUvITERERERGRO7IxciMGBncVvSvXBehbpRAtIiIiIiIidyRpKndeXw8NCtEiIiIiIiJyh9b/sx7I++uhQSFaRERERERE7kCiI5GNkRsBjUSLiIiIiIiI3NDOUzuJSYihsHdhqpeqnt3dyXQK0SIiIiIiInLbkqZyNw5qjNWS9yNm3n+HIiIiIiIikmnyU1ExUIgWERERERGRO7Du6LUQXU4hWkRERERERCRN/0T9wz/R/2Cz2GhQtkF2dydLKETnIitXrsRisXDx4sXs7kqetW7dOmrWrImnpyePP/54hl67R48eGX5NEREREZHslLQe+p6AeyjoVTCbe5M1FKKzSI8ePbBYLG5fbdu2zZb+WCwWDh8+nC2vnZMNGTKE2rVrc+jQIWbOnJnd3bmpCxcu0K1bN4oUKUKRIkXo1q3bTf/IYhgGI0aMoEyZMvj4+BAWFsaff/7p0iYuLo4XXniBEiVK4Ofnx2OPPUZkZGSq14uLi6N27dpYLBa2b9/uci61e/6LL764k7csIiIiIjlIflsPDQrRWapt27acOHHC5Wvu3LlZ2of4+Pgsfb2cyG6343A4Uj138OBBWrRoQVBQEP7+/rd1/az8jDt37sz27dtZsmQJS5YsYfv27XTr1u2GzxkzZgzjx49n0qRJbN68mYCAAFq1asWlS5ecbQYPHszChQuZN28ea9eu5fLlyzz22GPY7Xa3673yyiuUKVMmzdebMWOGyz3fvXv323/DIiIiIpKjJIXoJsFNsrknWSdfh+jISIiIML9nBW9vbwICAly+ihYtCsDhw4fdRvIuXryIxWJh5cqVaV5z/fr1PPDAA/j4+BAcHMygQYOIiYlxnq9QoQKjRo2iR48eFClShOeff97tGhcuXKBLly6ULFkSHx8fQkNDmTFjRpqvuWTJEpo2bYq/vz/FixfnkUce4eDBg87zSe9lwYIFNG/eHF9fX+655x42bNjgbHPkyBEeffRRihYtip+fH9WrV2fx4sUA1K1bl3HjxjnbPv7443h4eBAdHQ3AyZMnsVgs7N27FzBD6yuvvELZsmXx8/OjYcOGLp/ZzJkz8ff3Z9GiRVSrVg1vb2+OHDni8p6S+nzu3Dl69uyJxWJxjkSvWrWKBg0a4O3tTWBgIK+++iqJiYnO54aFhTFw4ECGDBlCiRIlaNWqVZqfHcDYsWMJDAykePHiDBgwgISEhBu2T8uePXtYsmQJ06dPp3HjxjRu3Jhp06axaNEi52eTkmEYTJgwgddff50OHTpQo0YNZs2axZUrV5gzZw4AUVFRhIeHM27cOB588EHq1KnD7Nmz2bVrl9u9+PPPP7N06VLGjh2bZj/9/f1d7nkfH5/ber8iIiIikrNcjr/MjpM7AI1E50oxMeaXYVw/Fh9vHouLc2/7+edQvjy0aGF+nzrVPB4bm/p1kw9c3mbmyXC7du2iTZs2dOjQgZ07d/LNN9+wdu1aBg4c6NLuo48+okaNGmzZsoU333zT7Tpvvvkmu3fv5ueff2bPnj1MnjyZEiVKpPm6MTExDBkyhM2bN7N8+XKsVivt27d3G919/fXXGTp0KNu3b6dSpUo8/fTTzvA5YMAA4uLiWL16Nbt27eLDDz+kYEFzDUVYWJgzrBmGwZo1ayhatChr164FICIigoCAACpXrgzAs88+y7p165g3bx47d+6kY8eOtG3blv379zv7cuXKFd5//32mT5/On3/+SalSpVz6GhwczIkTJyhcuDATJkzgxIkTPPnkkxw7dox27dpRv359duzYweTJkwkPD2fUqFEuz581axYeHh6sW7eOKVOmpPnZRUREcPDgQSIiIpg1axYzZ850mTbet29fChYseMOvo0ePArBhwwaKFClCw4YNnc9v1KgRRYoUYf369am+/qFDhzh58iStW7d2HvP29qZZs2bO52zZsoWEhASXNmXKlKFGjRr89ttvzmOnTp3i+eef56uvvsLX1zfN9zxw4EBKlChB/fr1+eKLL9KcBSAiIiIiuctvx37DbtgJLhxMcJHg7O5OlvHI7g5klGv5i9OnoWRJ898ffQRvvAHPPQfTpl1vW6KEa1h2OKBvX+jTBzp3hq+/vn6uQgU4exb++AOqVzePzZwJqQzo3tSiRYucQTHJ8OHDUw226fHRRx/RuXNnBg8eDEBoaCiffPIJzZo1Y/LkyRQoUACAFi1aMHToUJfnGsn+2nD06FHq1KlDvXr1AHP0+kaeeOIJl8fh4eGUKlWK3bt3U6NGDefxoUOH8vDDDwPwzjvvUL16dQ4cOECVKlU4evQoTzzxBDVr1gTgrrvucj4vLCyM8PBwHA4Hu3btwmaz0bVrV1auXEm7du1YuXIlzZo1A8zp13PnziUyMtI5pXjo0KEsWbKEGTNmMHr0aAASEhL4/PPPueeee1J9TzabjYCAACwWC0WKFCEgIACAzz//nODgYCZNmoTFYqFKlSocP36c4cOH89Zbb2G1mn+HCgkJYcyYMTf83ACKFi3KpEmTsNlsVKlShYcffpjly5c7ZwiMHDnS7WeVUtL7PHnypNsfAwBKlSrFyZMnU31u0vHSpUu7HC9durRzdP7kyZN4eXk5Z0kkv+6pU6cA8/7p0aMHffv2pV69emmur3/33Xdp2bIlPj4+LF++nJdffpmzZ8/yxhtv3PA9ioiIiEjOt+rwKgCalmuaZpvISNi/H0JDISgoq3qWufJMiL4VyUerb3QsozVv3pzJkye7HCtWrNhtX2/Lli0cOHCAr5OlfsMwcDgcHDp0iKpVqwI4w3Fa+vXrxxNPPMHWrVtp3bo1jz/+OE2apL2m4eDBg7z55pts3LiRs2fPOkcWjx496hKia9Wq5fx3YGAgAKdPn6ZKlSoMGjSIfv36sXTpUh588EGeeOIJZ/sHHniAS5cusW3bNtatW0ezZs1o3ry5c/R35cqVzj8cbN26FcMwqFSpkksf4+LiKF68uPOxl5eXS3/Sa8+ePTRu3BiLxeI8dt9993H58mUiIyMpV64ccPPPOEn16tWx2WzOx4GBgezatcv5uFSpUqkG47Qk71cSwzBSPX6j56XnOcnbfPrpp0RHR/Paa6/d8DnJw3Lt2rUB8w8FCtEiIiIiud/KIysBaF6hearnw8Ohd29z0NJqNWf/9uqVhR3MJHkmRF++bH5PPqt02DAYPBg8UrzLnTuhalXXKdo2G+zeDdcykVPSAFvyZZw9etxeH/38/AgJCUn1XNKIZvIR4putlXU4HPTp04dBgwa5nSuX7I34+fnd8DoPPfQQR44c4aeffuLXX3+lZcuWDBgwIM11ro8++ijBwcFMmzaNMmXK4HA4qFGjhltBLU9PT+e/k8JXUuB+7rnnaNOmDT/99BNLly7l/fffZ9y4cbzwwgsUKVKE2rVrs3LlStavX0+LFi24//772b59O/v372ffvn2EhYU5r2ez2diyZYtLOAVcRv19fHxuGhJTk1q4TPoZJT9+s884SfLPJOkayac39+3bl9mzZ9/wGrt376ZcuXIEBAQ4R4aTO3PmjNtIc5KkEfaTJ086/7AB5h83kp4TEBBAfHw8Fy5ccBmNPnPmDHXr1gVgxYoVbNy4EW9vb5fr16tXjy5dujBr1qxUX79Ro0ZER0dz6tSpNPsoIiIiIjnf1YSrbIzcCECzCs3czkdGXg/QYH7v0wfatMn9I9J5Zk20n5/5lTzveHmZx1L8dz6VKpl/BUnKXDYbTJliHr82A9rtutZkn1SKHJQhSl6bg37ixAnnsZTbBaV077338ueffxISEuL25eXldcuv36NHD2bPns2ECROYOnVqqu3OnTvHnj17eOONN2jZsiVVq1blwoULt/RaSYKDg+nbty8LFizg5ZdfZlqyOfdhYWFERESwevVqwsLC8Pf3p1q1aowaNYpSpUo5R9nr1KmD3W7n9OnTbp9BUmC8E9WqVWP9+vUuf9xYv349hQoVomzZsnd8/ZRGjhzJ9u3bb/iVNJ27cePGREVFuaxT3rRpE1FRUWnOJKhYsSIBAQEsW7bMeSw+Pp5Vq1Y5n1O3bl08PT1d2pw4cYI//viDBg0aAPDJJ5+wY8cOZ5+SisJ98803vPfee2m+v23btlGgQIHbrnwuIiIiIjnDpmObiLfHE1gwkNBioW7n9+93HbQEsNvhwIEs6mAmyjMj0beqVy/zryAHDkBISNb8NSQuLs5traqHhwclSpTAx8eHRo0a8cEHH1ChQoV0rRsdPnw4jRo1YsCAATz//PP4+fmxZ88eli1bxqeffprufr311lvUrVuX6tWrExcXx6JFi5whNaWiRYtSvHhxpk6dSmBgIEePHuXVV19N92slGTx4MA899BCVKlXiwoULrFixwuU1w8LCmDhxIsWKFaNatWrOY59++ikdOnRwtqtUqRJdunThmWeeYdy4cdSpU4ezZ8+yYsUKatasSbt27W65b8n179+fCRMm8MILLzBw4ED27t3L22+/zZAhQ5yzBzLSrUznrlq1Km3btuX55593FjPr3bs3jzzyiLPoGkCVKlV4//33ad++PRaLhcGDBzN69GhCQ0MJDQ1l9OjR+Pr60rlzZwCKFClCr169ePnllylevDjFihVj6NCh1KxZ0zkDoFyKKRtJo/533303Qdd+mX788UdOnjxJ48aN8fHxISIigtdff53evXu7jWCLiIiISO6y8vBKAMIqhKU64zM01ByITDn7N42JublKvg3RYAbnrJxKsGTJEpcptACVK1fmr7/+AuDLL7+kZ8+e1KtXj8qVKzNmzBiXCskp1apVi1WrVvH6669z//33YxgGd999N08++eQt9cvLy4vXXnuNw4cP4+Pjw/3338+8efNSbWu1Wpk3bx6DBg2iRo0aVK5cmU8++cQZrtLLbrczYMAAIiMjKVy4MG3btuXjjz92nn/ggQcAaNasmfOXslmzZkyYMMFZVCzJjBkzGDVqFC+//DLHjh2jePHiNG7c+I4DNEDZsmVZvHgxw4YN45577qFYsWL06tUrx6zp/frrrxk0aJDzPnnssceYNGmSS5u9e/cSFRXlfPzKK69w9epV+vfvz4ULF2jYsCFLly6lUKFCzjYff/wxHh4edOrUiatXr9KyZUu+/PJLtynzN+Lp6cnnn3/OkCFDcDgc3HXXXYwcOZIBAwbc4bsWERERkeyWPESnJijInP3bp485Ap00+ze3T+UGsBhGVpTUSr/o6GiKFClCVFQUhQsXdjkXGxvLoUOHqFixorPydHZyOBxER0dTuHDhTBmVFMlJsuJ+z2m/45J/JSQksHjxYtq1a+dWy0AkL9G9LvmJ7veME5sYi/8H/sTZ4/hrwF9ULlE5zbaRkVk7+/d23SiHppSvR6JFRERERETk1myK3EScPY6AggFUKl4p1TaGYdaryurZv1lBw6ciIiIiIiKSbjdbDw3wyy/m6POIEVnXr6yiEC0iIiIiIiLplrQ/dLPy7ltbJfn1Vzh40JzOnddoOreIiIiIiIikS2xiLBv+2QCkXVQM4K23oFkzuLY7a56SK0N0DquFJiIZRL/bIiIiIjnbb8d+I84eR2m/0lQunnZBscKF4dFHs7BjWShXTedOqqJ35cqVbO6JiGSGpN9tVcwUERERyZnSsx46r8tVI9E2mw1/f39Onz4NgK+vb7b+4BwOB/Hx8cTGxmqLK8nzMvN+NwyDK1eucPr0afz9/W9pP2oRERERyTpJIfpG66GnToXERHj8cU3nzhECAgIAnEE6OxmGwdWrV/Hx8cm3f4WR/CMr7nd/f3/n77iIiIiI5CxxiXFsiLz5eugxY8yiYuXKKUTnCBaLhcDAQEqVKkVCQkK29iUhIYHVq1fzwAMPaPqp5HmZfb97enpqBFpEREQkB/vt2G/EJsZSyq8UVUpUSbWN3Q7PPgsrVsADD2RxB7NIrgvRSWw2W7b/B7fNZiMxMZECBQooREuep/tdREREJH+LOBwB3Hg99IkT0KQJdO9uFhfLi7SQV0RERERERG7q179/BaB5heapng8Ph/LloUUL83t4eFb2LusoRIuIiIiIiMgNXYq75FwP3equVm7nIyOhd29wOMzHDgf06WMez2sUokVEREREROSGVh1ZRaIjkYr+Fbm72N1u5/fvvx6gk9jtcOBAFnUwCylEi4iIiIiIyA0tO7gMSH0UGiA0FFIuk7bZICQks3uW9RSiRURERERE5IaW/W2G6NZ3t071fFAQTJtmBmcwv0+ZYh7Pa3JtdW4RERERERHJfJHRkew5uwerxUqLii3SbNerF7RpY07hDgnJmwEaFKJFRERERETkBpKqctcrU4+iPkVTbeNwgNVqBue8Gp6TaDq3iIiIiIiIpClpKnda66EBBg6Ehg3h55+zqlfZRyPRIiIiIiIikiqH4XCORKcVog0DFi+GI0fMf+d1CtEiIiIiIiKSql2ndnE65jR+nn40Dm6cahuLBdatg19+gbCwrO1fdlCIFhERERERkVQlTeVuVqEZXjavNNuVLQs9e2ZVr7KX1kSLiIiIiIhIqtKzHjq/UYgWERERERERN7GJsaw+shpIO0RfuQLPPw//+59ZoTs/UIgWERERERERN+uOriM2MZYyhcpQrWS1VNusXAnTp8OwYeba6PxAa6JFRERERETETdJU7gfvehBLGgm5QAH417+gYkWFaBEREREREcnHlh5cCqQ9lTs8HHr3NqdxW61QuTL06pWiUWQk7N8PoaEQFJTJPc4ams4tIiIiIiIiLo5fOs62k9uwYKHN3W3czkdGXg/QYH7v08c87hQeDuXLQ4sW5vfw8KzpfCZTiBYREREREREXP+//GYAGZRtQ0q+k2/n9+90LidntcODAtQfpStm5k0K0iIiIiIiIuPhp/08AtAttl+r50FD3YzYbhIRce3DTlJ17KUSLiIiIiIiIU7w93llU7OHQh1NtU6YM3HPP9cc2G0yZkmzZc2iouVA6OZeUnXupsJiIiIiIiIg4rTmyhsvxlyntV5o6gXVSbWO1wvbtsG8fHD9uZmOXumFBQfDAA+YeWJBKys69FKJFRERERETEafH+xYA5ldtqufHk5UqVzK9UffmlWUwsMBD+7//yRIAGhWgRERERERFJJmk9dFpTuRMTIT4efH1vcqGKFWHUqAzuXfbTmmgREREREREB4OD5g+w9txcPqwcP3vVgqm1Wr4YSJaBnzyzuXA6hEC0iIiIiIiLA9anc95e7nyIFiqTaJiICrl69wUUcDhg+HJYvNyty5zGazi0iIiIiIiIALD5wfT10WkaOhI4dwcsrjQabN8OYMfD553DmjFlULA9RiBYRERERERFi4mOIOBQBpL0eGsBigVq1bnChQoWgVy/w9oYCBTK4l9lPIVpERERERESIOBxBnD2OCv4VqFKiyu1fqFo1mD494zqWw2hNtIiIiIiIiPDTvutVuS0WS6ptOnSAp56C33/Pyp7lLArRIiIiIiIi+ZxhGDddD/3xx7BwIXzzDTRsaG4B7WbDBoiMzMSeZj+FaBERERERkXxux6kdHI06io+HD80rNHc7HxkJQ4def+xwQJ8+KfKyYUCPHhAcDD//nOl9zi4K0SIiIiIiIvncwj0LAWgb0hYfTx+38/v3m8E5ObsdDhxIdiA6GkqWBB8fuO++TOxt9lJhMRERERERkXzuu73fAfB4lcdTPR8aClara5C22SAkJFmjIkVg7Vq4eBEKF86srmY7jUSLiIiIiIjkY39f+Judp3Zis9jS3NrqwAHo3v36ls82G0yZAkFBqTT298+0vuYEGR6iExMTeeONN6hYsSI+Pj7cddddjBw5EkfKsX8RERERERHJdt//9T0AD5R/gOK+xVNt88knMGMGDBgAERFw+LC5FbTT5cuQkJD5nc0BMjxEf/jhh3zxxRdMmjSJPXv2MGbMGD766CM+/fTTjH4pERERERERuUML/zLXQ7ev0j7NNo0aQc2a8OyzEBaWygj0J59A6dIwYUKm9TOnyPA10Rs2bOD//u//ePhhcxpAhQoVmDt3Lr/n543EREREREREcqDTMadZ9886AP6vyv+l2e6VV8yvNEVEwIULULBgBvcw58nwEN20aVO++OIL9u3bR6VKldixYwdr165lQhp/kYiLiyMuLs75ODo6GoCEhAQScvh0gKT+5fR+imQE3e+Sn+h+l/xC97rkJ7rfU/f9nu9xGA7qBNQh0Dfw9j+fH3/Esm4dRo0auXJa9628b4thGEZGvrhhGPz73//mww8/xGazYbfbee+993jttddSbT9ixAjeeecdt+Nz5szB19c3I7smIiIiIiIiybz393tsjt7M0wFP82TAk27n4+KsHDpUhEqVLmDNw2Wpr1y5QufOnYmKiqLwTSqLZ3iInjdvHsOGDeOjjz6ievXqbN++ncGDBzN+/Hi6d+/u1j61kejg4GDOnj17085nt4SEBJYtW0arVq3w9PTM7u6IZCrd75Kf6H6X/EL3uuQnut/dXY6/TODHgcTZ49jy3BZqlqrp1ub77y107OhB48YOVq2yZ0Mvs0Z0dDQlSpRIV4jO8Oncw4YN49VXX+Wpp54CoGbNmhw5coT3338/1RDt7e2Nt7e323FPT89cc3Pnpr6K3Cnd75Kf6H6X/EL3uuQnut+vW7F/BXH2OO4qehd1ytTBYrG4tTlzBgoVgoYNrXh6pjIU/c8/8MQT0LEjDB0KqVwjN7iVeyLDQ/SVK1ewphjnt9ls2uJKREREREQkB/lu73cAPF758VQDdGQkVKkCW7dCsWJpXOTLL2HzZvPfw4ZlTkdzmAyf1f7oo4/y3nvv8dNPP3H48GEWLlzI+PHjad8+7XLpIiIiIiIiknUS7Aks2rcIgMerPO52PjwcypeHFi2gcmVYuDCVi4SHw8iR5r9//918nA9keIj+9NNP+de//kX//v2pWrUqQ4cOpU+fPrz77rsZ/VIiIiIiIiJyG1YeXsnF2IuU8C1Bk+AmLuciI6F3b0iaTOxwQJ8+5vE0GxlGKo3ypgyfzl2oUCEmTJiQ5pZWIiIiIiIikr3+++d/AXii6hPYrDaXc/v3X8/GSex2OHAAgoJupVHelIeLlIuIiIiIiEhKCfYEFvy1AIBO1Tu5nQ8NxW07K5sNQkJSNEq5jtqtUd6kEC0iIiIiIpKPrDi0gvNXz1PKrxQPlH/A7XxQEEydej1I22wwZUqKAebz580p3ElSbZQ3Zfh0bhEREREREcm5kk/l9rCmHgl79YI2bczZ2SEhqWRjf38YMgROnYLnnkujUd6kEC0iIiIiIpJPxNvjWfiXWWo7tancyQUF3SAXlysH48ZlcO9yB03nFhERERERySeW/72cC7EXKO1XmvvL3Z9qm549oX9/+PvvLO5cLqEQLSIiIiIikk/8d7c5lftf1f7lVpUbzKXOs2fD5MkQG5vGRebMgT17MrGXOZumc4uIiIiIiOQD8fZ4Fu658VTuwoXhxx9h9WqoVi2VBhcumEPVcXHw559pNMrbFKJFRERERETygWUHlxEVF0VgwUDuC74v1TYeHmZBsTZt0rjIhQvQujVERkLVqpnX2RxMIVpERERERCQfuNlU7shI2L/f3AI6zYJid90FP/wACQnu+0TnE1oTLSIiIiIiksfFJcbx3V/fAalP5Q4PNwtut2gB5cubj2/I0zPjO5lLKESLiIiIiIjkcb8c/IXouGjKFipLk+AmLuciI6F3bzAM87HDAX36mMddbN0Kly5lTYdzMIVoERERERGRPG7OrjkAdKzWEavFNQbu328G5+TsdjhwINkBhwPat4fSpWHjxkzubc6mEC0iIiIiIpKHRcdF8/3e7wHoWqur2/nQULCmSIY2G4SEJDtw/Dj4+ICXF9SunXmdzQUUokVERERERPKwBXsWEJsYS5USVbg38F6380FBMHWqGZzB/D5lSoriYkFB5t7QO3ZAgQJZ0/EcStW5RURERERE8rCvdn4FQNeaXbGkUlF7xw4ICDCnbx8+bI5Ap1qd22Ixq47lcxqJFhERERERyaMioyOJOBQBQJdaXVJtM3YsPPIIfPophIWlEqDPnbtedUwUokVERERERPKqubvmYmBwf7n7qeBfIdU2wcFQsiR0ct/5ytSpk7lwes2aTOtnbqIQLSIiIiIikkfN3jUbSL2gWJLRo+HYMWjQIJWTFy/C5s1w8KC5kbRoTbSIiIiIiEhetPPUTnae2omXzYuO1TresK2nZxon/P3hxAlzFFrroQGNRIuIiIiIiORJX+/8GoCHQx+mqE9Rt/OnTsG+fTe4QGQkRETAhQvQtm0m9TL3UYgWERERERHJYxyGg693mSE6rancH34IlSvDc8+lcjI83Bx5btHC/B4enom9zV0UokVERERERPKYVYdXcezSMfwL+PNw6MNu58PDYcIE899ffpkiI0dGQu/e4HCYjx0O6NPHPC4K0SIiIiIiInnNf3b+B4BO1Trh7eHtci4pIyftWmUYKTLy/v3XA3QSu93cSFoUokVERERERPKSS3GX+N+f/wOg2z3d3M7fNCOHhoI1RVS02SAkJBN6m/soRIuIiIiIiOQh//3zv8QkxFC5eGXuC77P7XyZMjfJyEFBMHWqeTDp5JQp5nHRFlciIiIiIiJ5yZfbvwSgZ52eWCwWt/NLloCHByQkmFO5U83IvXpBmzbm8HRIiAJ0MgrRIiIiIiIiecSeM3tY/896bBYbz9zzTKptVq6E+Hh47z1o0iSVjNyzJ/j5wbBhEBaWFd3OVRSiRURERERE8ogZ22cA8HClhwkoGJBqmwULYN06qFkTihRJcfLYMfjPf8xF0n37ZnJvcyeFaBERERERkTwgwZ7ArB2zAOhZu2ea7SwWaNo0jZOBgfDzz7B6NVSvngm9zP0UokVERERERPKAxfsXczrmNKX9StMutJ3b+YQEcy10Ksukr7NaoVUr80tSpercIiIiIiIieUD4tnAAnrnnGTxtnm7nP/zQXPs8YUIWdyyPUYgWERERERHJ5U5cOsHi/YsBsyp3SuHh8OabcPw4DBliPnbTvTt8+ilcvpzJvc3dFKJFRERERERyuf/s+A92w06T4CZUKVHF5VxkJPTuff2xYUCfPuZxp+3bzYJiQ4bApUtZ0ufcSmuiRUREREREcjHDMJx7Q/eq08vt/P794HC4HrPbzS2gnVtb3X03fPaZmawDAzO5x7mbQrSIiIiIiEgutuLQCvad20chr0J0qt7J7XxIiFkvLHmQttnM406FCkH//pnf2TxA07lFRERERERyscm/TwagW61uFPQq6HZ+3jyoWtUM0mAG6ClTko1Cyy3RSLSIiIiIiEgudfzScb776zsA+tXv53beMOCLL+Dvv2HsWKhb1xyBdgZohwP69YMOHcxtrawaZ70ZhWgREREREZFcavrW6dgNO03LNaVGqRpu5y0WWLbMrMbdvz/4+KRosGwZTJ1qDlcfOwYF3UeyxZVCtIiIiIiISC6U6Ehk6papAPSr5z4KneSuu+C999I4WakSvPiiuSZaATpdFKJFRERERERyoUX7FnHs0jFK+pbkiapP3PoFIiPh8GEYOlQLpG+BJryLiIiIiIjkQkkFxXrW6Ym3h7fLuchI6NoVnn3WXA/tJjwcypeHFi3M7+HhWdDjvEEj0SIiIiIiIrnMgfMHWHpwKRYs9Knbx+VceDj07n19S6uiRWH8+GQNIiNdGzgc0KcPtGmjEel00Ei0iIiIiIhILjPl9ykAtA1pS8WiFZ3HU+ZjgE8+MY877d/v2gDAbocDBzKxx3mHQrSIiIiIiEguEpsYy4ztMwD3gmLpysehoe5bWdls5t5XclMK0SIiIiIiIrnInF1zOHf1HOWKlKNdaDuXc+nKx0FB5rZWNtv1BlOmaCp3OilEi4iIiIiI5BKGYTBh4wQAXmjwAjarzeV8UBA0aWLuDw03yMe9epmVuSMizO+9emV21/MMFRYTERERERHJJSIOR7Dr9C78PP3oVcc9+G7bBmvXmqPRc+fCffelCNCrV8OuXWbZ7qAgjT7fBoVoERERERGRXGLipokAdL+nO0V9irqdr1QJPvsMjh6FJ59M5QJvvQWrVpmVxt5/P5N7mzcpRIuIiIiIiOQCB84f4Me9PwIwqOGgVNv4+UH//mlcwOGATp3gxAkYMCCTepn3aU20iIiIiIhILvDppk8xMGgX2o7KJSrf+gWsVjNh//WXpnHfAYVoERERERGRHC46Ltq5rdXghoPdzu/dCw88AHPmgGHc5GJJVcfktihEi4iIiIiI5HBfbvuSS/GXqFayGg/e9aDLufBwqFoV1qyBLl1g+vRULjB+PKxYkY6ELTejEC0iIiIiIpKD2R12Ptn0CQAvNnwRS7KR5MhI6N3bNRv362cedzp6FIYPh5YtzcrcckdUWExERERERCQH+2HvDxy6eIhiPsXoWqury7n9+816YcnZ7XDgQLJlz15e0LevuR90rVpZ0ue8TCFaREREREQkhzIMgw/XfQhA37p98fX0dTkfGmrWC0sepG02CAlJ1iggAD79VFO5M4imc4uIiIiIiORQa46uYdOxTXjbvFPd1uqPPyAszAzOYH6fMiWN4tsqKJYhFKJFRERERERyqKRR6GdrP0vpgqVdzhkGvPuuWS/s+echIsKcsd2r17UGly/DsGFw5EjWdjqPU4gWERERERHJgXad2sXi/YuxWqy83OTlVNuMHAlt28Jbb5kj0s4R6MhIeOUVGDsW2rXTVO4MpDXRIiIiIiIiOdBH6z8C4ImqTxBSLMTtvMViFtxu2TLFifBws2R30kLpevU0lTsDaSRaREREREQkhzkadZS5f8wF4JX7XnE7HxlpTt922coq6UTyAA3w9depNJTbpRAtIiIiIiKSw4zfMJ5ERyItKragXpl6LufCw6FcOWjRAsqXNx873WjPK8kQCtEiIiIiIiI5yLkr55i2dRoArzRxHYVOGmhOWuLscECfPskGmkND3aduu+15JXdCIVpERERERCQH+WzzZ1xJuMI9pe+h9d2tXc7ddKC5WDEoXPj6yRvueSW3QyFaREREREQkh4iOi2bCxgkADL9vOJYUo8qhoWBNkeJcBpo9PeH996FuXfjllxR7XklGUIgWERERERHJIT777TMuxF6gcvHKdKreye18UBBMnWoGZ0hloNnTE/r1g82boXVrjUBnAoVoERERERGRHOBy/GXGbxwPwOv3v47NanM5v2cPtGoFlSqZA8wRETcYaNaWVplGIVpERERERCQH+OL3Lzh75Sx3F72bp2s+7Xb+vffg11/h44/NAeawsGQDzWfPQrt2sGZNlvY5P/LI7g6IiIiIiIjkd1cSrvDR+o8AcxTaw+oa1SIj4eGHzX8PHZrKBT78EH7+GU6dgt9/10h0JlKIFhERERERyWbTtkzjdMxpKvhXoGutri7nwsPNba0cDrOoWPPmULt2igu8+CJcugTt2ytAZzJN5xYREREREclGsYmxfLjuQwBea/oanjZP57mkfaGTtrVy2xc6SVAQfPEFtGmTRb3OvxSiRUREREREslH41nBOXD5BcOFgut/T3eXcTfeFNoys6aQ4KUSLiIiIiIhkk9jEWN5f+z5g7gvt7eHtcj61jOyyL3SvXvDCC+ZaaMkSCtEiIiIiIiLZZPLmyRy7dIzgwsE8d+9zbudbtIAhQ64vc3bZF/rvv2HmTJg0CY4dy9J+52cqLCYiIiIiIpINLsVdYvTa0QC81ewtt1HoJOPGwUsvmVO4Q0KuBejISDhyBObONTeQvvfeLOx5/qYQLSIiIiIikg0mbprI2StnCS0W6rYW2jAgPh68r+XqoKBke0KnLNc9dWrWdjyf03RuERERERGRLHbh6gXGrh8LwDth77hV5B45Eu66yxxodpHuct2SWRSiRUREREREsthH6z8iKi6KmqVq8mSNJ53Hw8OhfHkYMQKOH4c5c1I88abluiWzKUSLiIiIiIhkoVOXTzFx00QA3m3+LlaLGctSDjID/PxzikHm0FD3C7qU65bMphAtIiIiIiKShUavGc2VhCs0KNuAxyo/5jyerkHmoCCYPDmNct2SFVRYTEREREREJIscvniYL7Z8AcCo5qOwJIVhzEFmq9U1SKc6yNy3LzzySIpy3ZJVFKJFRERERESyyOsrXifeHk+Lii148K4HXc7ZbODhYVblTnrsMsi8cyfUrGmOQruU65aspOncIiIiIiIiWeD3478zZ5dZKeyjVh+5jEIDrFljbm11772wYgUcPgy9el07uWUL1K4N7dpdT9mSLTIlRB87doyuXbtSvHhxfH19qV27Nlu2bMmMlxIREREREcnxDMNg2LJhAHSt1ZV7A+91a9OpE+zeDbNmQfPmKQaat20DT08oVgy8vLKo15KaDJ/OfeHCBe677z6aN2/Ozz//TKlSpTh48CD+/v4Z/VIiIiIiIiK5wuL9i1l5eCXeNm9GNR/lci4y0iwqFhp6gyLbzz0HYWHg55fpfZUby/AQ/eGHHxIcHMyMGTOcxypUqJDRLyMiIiIiIpIrJDoSeeXXVwAY1HAQ5f3LO8+Fh1/f1spqhalTk03hTknbWOUIGR6if/jhB9q0aUPHjh1ZtWoVZcuWpX///jz//POpto+LiyMuLs75ODo6GoCEhAQSEhIyunsZKql/Ob2fIhlB97vkJ7rfJb/QvS75SXbe7+Hbwtl9ZjdFCxRlaMOhzj6Y+0J74HCYa6MdDujTx6BFi0TnVG7L/PkY9etDuXJZ3u/85FbuC4thGEZGvniBAgUAGDJkCB07duS3335j8ODBTJkyhWeeecat/YgRI3jnnXfcjs+ZMwdfX9+M7JqIiIiIiEiWirXH0m9PPy4kXqBnmZ48Vur6vtC7dpXgzTfvc3vOu++upWbNc/icOkXLF17AAFaNH89lVePONFeuXKFz585ERUVRuHDhG7bN8BDt5eVFvXr1WL9+vfPYoEGD2Lx5Mxs2bHBrn9pIdHBwMGfPnr1p57NbQkICy5Yto1WrVnh6emZ3d0Qyle53yU90v0t+oXtd8pPsut/fXvU27697n4r+FdnZeyfeHt7Oc5GREBJyfSQawGYz2L//2kj0vn3Y+vUDmw37L7+YW1tJpoiOjqZEiRLpCtEZPp07MDCQatWquRyrWrUq8+fPT7W9t7c33t7ebsc9PT1zzf+Y56a+itwp3e+Sn+h+l/xC97rkJ1l5vx++eJjxG8cDMLb1WAr6FHQ5X7GiuQa6Tx+w25P2hbZQ0fMUrL1WaWzVKoiKwqqK3JnqVu6JDN/i6r777mPv3r0ux/bt20f58uXTeIaIiIiIiEjeM3TpUOLscTSv0Jz2Vdq7nPvtN/jkE+je3dwPOiLi2r7QhEP58tCihfn9yy9BOx3lKBk+Ev3SSy/RpEkTRo8eTadOnfjtt9+YOnUqU6dOzeiXEhERERERyZEiDkUwf898rBYrE9tOxJJsKvbRo/DMM7B3L5w8CaNHX9sT2qw0ZlYYg6RKY9CmTYpNoyU7ZfhIdP369Vm4cCFz586lRo0avPvuu0yYMIEuXbpk9EuJiIiIiIjkOImORF5c8iIAfev2pWbpms5z4eHmNO6kybslSiR74v791wN0ErsdDhzI5B7LrcjwkWiARx55hEceeSQzLi0iIiIiIpKjTdsyjV2nd1G0QFFGNh/pPJ5yoBnglVegU6drA82hoeZm0ckb2GzaHzqHyfCRaBERERERkfzq/NXzvBHxBgDvNn+X4r7FneduOtAcFGRWGrPZzMdmpTFN5c5hMmUkWkREREREJD96c8WbnL96nhqlatCnXh+Xc5cuubd3DjTHxIC3N/TqZa6BPnDAPKEAneMoRIuIiIiIiGSAzcc2M/n3yQB8+tCneFhd49Z4c7crLBYwjBQDzc+9CNu3w4wZULOmwnMOphAtIiIiIiJyh+wOO/1+6oeBQddaXQmrEObWZt48eOstGDAALlxINtB85gwsWGAejIrK8r7LrVGIFhERERERuUNTtkxhy4ktFPEuwthWY13ORUaa66FDQ80lz25KloTdu2HxYmjaNGs6LLdNhcVERERERETuwMnLJ/n38n8DMLrlaEoXLO08Fx4O5ctDixbm9/DwNC4SEAA9e2ZBb+VOKUSLiIiIiIjcgWHLhhEVF0XdwLr0qXu9mFhkJDz//PWK3A4H9OljHgfgjz9g69as77DcEYVoERERERGR27Ty8Epm75yNBQtfPPIFNqvNeW7/frOAWHLOLa0SE6FHD2jQAObMydI+y51RiBYREREREbkNsYmx9Flkjjz3q9ePemXquZwPDQVrisRls0GI3wlYsgTKlIFChcy53pJrqLCYiIiIiIjIbXh31bvsO7ePwIKBvNfyPbfzQUFmIbE+fcwRaJsNpnRdQ1CjMHNut9UKH35oroeWXEMj0SIiIiIiIrdox8kdjFk/BoDP2n2GfwF/57m9e+HZZ2HfPujVCw4fhogIOLzhBL2+CnNdJP3qq8kWSUtuoBAtIiIiIiJyCxIdifT6oReJjkSeqPoE7au2d54LD4eqVWHmTKhc2XwcFARhYRB0+a/rATqJc5G05BYK0SIiIiIiIrdg4saJbDmxBf8C/kxqN8l5PDISevd2LSbmUo3b39/9YjYbhIRkan8lYylEi4iIiIiIpNPB8wd5M+JNAMa2GktAwevrmffvv8lAc506MGgQWCzmY5sNpkwxh6ol11BhMRERERERkXRwGA56L+rN1cSrtKjYgp51erqcL1fOrBWWPEi7DTRPnAjDhpnJOiREAToX0ki0iIiIiIhIOnzx+xesOLQCHw8fpj4yFUvSiDKwfDm0bAkvvWQGZ0g20HzxD4iOvn4h5yJpBejcSCPRIiIiIiIiN3Hw/EGGLRsGwAcPfsDdxe4GzPXO+/fDm2/CkSMQE2NW43YONBe8CPc8bA5RL15sVh2TXE0hWkRERERE5AYchoNnv3+WKwlXCKsQxsAGAwGz8nbv3te3fH74YfjoIyhYMNkg85/HzJM2GwQHZ9+bkAyjEC0iIiIiInIDEzdOZM3RNRT0KsiXj32J1WJ1VuJOvuXzkiVw8aIZop2qV4cdO+DYsRQnJLfSmmgREREREZE07D27l3+v+DdgVuOuWLQikI5K3MkVLqxp3HmIQrSIiIiIiEgqEh2JdP+uO7GJsbS+uzW96/Z2nrv7bvf2zkrcR49Cixbw1VdZ11nJMgrRIiIiIiIiqRi9ZjSbjm2isHdhpj863aUad5ky0Lbt9bbOSty/hEOFChARAc88AxMmZHm/JXNpTbSIiIiIiEgKGyM3MnLVSAA+b/c5wUXMomBJ1bhDQ+Hnn2HrVnP3qpAQCCISyvcGw7h+oaFD4V//0nZWeYhCtIiIiIiISDKX4i7RZUEX7Iadp2s8TZdaXQD3atxTp0KvXsmeGHGDhdIK0XmGpnOLiIiIiIgk8+KSF/n7wt+UK1KOzx/+HCDVatx9+pjHAXP0+di17ayScy6UlrxCIVpEREREROSab3d/y4ztM7BarMxuPxv/Av5AOqpxjx0L3brB/febwRmSLZTWKHReouncIiIiIiIiQGR0JL1/NCtwv3rfq9xf/n7nudBQc5A5eZB2GWQ2DLPB00/D7Nlmug4JUYDOgxSiRUREREQk30t0JPL0/Ke5EHuBemXqMSJshMv5oCBzDXSfPuYItNsg8yuvwMMPQ7VqYLEoPOdhCtEiIiIiIpLvjVg5grVH11LIqxDznpiHp80TMNc8jx0LXbqYRcTatEk2yByQCHbL9enb1atn4zuQrKI10SIiIiIikq8tO7iM0WtGAzD9sencXexuwKzGXa4cTJwIDRrAJ5+YA8xhYdcGml9/HR56CM6ezb7OS5ZTiBYRERERkXzrxKUTdF3YFQODvnX70ql6J+B6Ne7kWz4PGZKsGvfx4zBpEixbBmvXZn3HJdtoOreIiIiIiORLdoedLgu6cDrmNLVK12J8m/HOc2lW495whqASf5iVxjZuhF9+gccfz9qOS7ZSiBYRERERkXzp3dXvEnE4Aj9PP/77r//i4+kDmKPPBQqkUo3b6iDkybpg/GOenDoVhg7Npt5LdtF0bhERERERyXd+3v8zI1eNBOCLR76gconKgDld+8UXoXlzePbZ5Fs+G0wx+hBk/GMecDjMUt3O+d2SX2gkWkRERERE8pVDFw7RZUEXDAz61etH11pdAbOQWO/e10efL12Cw4evVeM+vYGgJ6e7XshuN09qO6t8RSPRIiIiIiKSb1xNuMq//vcvLsReoEHZBnzc5mPgeiGx5NO35883v4eFQVCTcuYU7uRsNnOvK8lXFKJFRERERCTfeHHpi2w9sZUSviX4tuO3eHt4A7BvXxqFxA5cexAUZK6Bvj6/G6ZM0Sh0PqTp3CIiIiIiki8sO7eMmf/MxGqxMu+JeQQXCQbMQmJTp4LF4rqllc0GIf5nYe1f0LQp9OoFbdpcm98dogCdT2kkWkRERERE8rwNkRuYEjkFgFHNR9HyrpbOc6tWwTffmP9OmrFts8GUSQkE9X8MWrSA//3PPBEUdG1+twJ0fqWRaBERERERydMioyPpNL8TiUYi7Su3Z3jT4ebxSHM/6NBQmD4dYmKgQ4dkA83FEyEiGPbsgVq1svldSE6hEC0iIiIiInnW1YSrPD7vcU7FnKJCgQqEPxqO1WJ1qcSdtOXzoEHmc64PMvvAvHlw8KAKiImTpnOLiIiIiEieZBgGz/34HFtObKG4T3Feq/gaBb0KulXidtnyOTLSnNudtP+zxaIALS4UokVEREREJE8au34sc3bNwWaxMbf9XEp7lwZuUIl74k9Qvjw89RSUKwfTpmVDryWnU4gWEREREZE854e9PzD8V3Pt88S2EwmrEMbZswVYudJCoUKpbflsEDKu3/V0bRjQr9/1EWmRaxSiRUREREQkT9l6YitPz38aA4Pe9/amf/3+zJhh4fnnW9O6tQeNGkG3bim2fH5pL0HGP64XctkoWsSkwmIiIiIiIpJnHIs+xqNzH+VKwhVa3dWKSe0mceyYhX79bBiGBTAHm2fPhg0bzIrcIWWvEuRZAMZbXed522xaDy1uFKJFRERERCRPuBx/mUfnPsrxS8epVrIa/+34XzxtnuzfDw6HxaWt3W4G6LD7EqB9R/D0hEmT4IUXzJM2G0yZov2gxY1CtIiIiIiI5Hp2h50uC7qw7eQ2SvqWZNHTi/Av4A+Y+0BbrYZLkHYOMm/fDr/+albhfvNNOHw42UbRCtDiTiFaRERERERyNcMweHHJi/yw9we8bd58/9T3VCxakchI2L/fDNGTJ9vp18+Gw2FxHWQOqg+//AKXL8O995oXVHiWG1CIFhERERGRXG3MujF8tvkzLFj4qv1XNA5uTHj49b2grVaYPBmmTl1K+fItqVLFg6DSCYCneYFmzbK1/5K7qDq3iIiIiIjkWl/t+IpXl78KwMdtPqZj9Y5ERl4P0GB+79/fLMXdrJlB0Ir/QIMGcOJEdnVbcjGFaBERERERyZWWHVxGzx96AvBy45d5sdGLANcKibm2tdstnPsrEcuSJTB8uLkWeubMrO2w5Amazi0iIiIiIrnOthPb6PDfDiQ6EnmqxlOMaTXGec4sJJZityqrg6fH9sVjbKR58qGHzDAtcos0Ei0iIiIiIrnKvnP7aDO7DZfjL9O8QnNm/t9MrBYr//xjFgwDmDrVrMANYLMZfGH0IZhI84DDAUuXwvHj2fMGJFdTiBYRERERkVwjMjqSVl+14syVM9QJqMPCJxfi7eFNeDiULw99+0K5cmbbw4chIgIOj/qa54zprhey282trERukUK0iIiIiIjkCmevnKXVV604GnWUSsUrsaTrEooUKOIsJGYYZjvDgD59zH+HhUHQL+HuF3NuFC1yaxSiRUREREQkx7sUd4mHvn6Iv87+RVDhIJZ1W0Ypv1JAWoXEkg00f/cdjrAwHNZr8cdlo2iRW6PCYiIiIiIikqNdSbjCY/Me4/fjv1PCtwTLui2jXJFyREbCDz9AvXqpFBKzGYSEWMwHRYpgX7qUFf/5Dy3Ll8ejShUFaLltGokWEREREZEcKzYxlvbftGfl4ZUU8irEki5LqFKiCuHh5trnAQOgUSPo2jVZITGrwZSCQwnaNN/1WiVKYDRrpgAtd0Qj0SIiIiIikiPF2+Pp+L+OLD24FD9PP37u8jN1y9RNdQ3011/Dhu9OEbP/OCGbvibom/EwZi08/vj1dC2SARSiRUREREQkx0l0JPL0/KdZtG8RBTwKsKjzIu4rdx+Q9hromMeeJsyIMOd2P/YYzJihAC0ZTiFaRERERERylERHIs8sfIYFexbgZfPiuye/I8QjjIgIOHEC6tdPZQ00iYQY+8wHDgf89BNcuQLFimXPm5A8S2uiRUREREQkx0gK0HP/mIuH1YNvO35L5Ko2lC8PLVpAly7mDO3PPku+BtrBFPoQxLHrF9I+0JJJNBItIiIiIiI5QqIjka4LuvLNn9/gYfXgv//6L3X8HqV8b9dR5z17oF07OHzYzMkhP39G0JgvXS+mfaAlk2gkWkREREREsl2CPYHO8zvzzZ/f4Gn15NuO39K+avtU1z8bBvz9t1lkOywMgj58AXr2TDY0rX2gJfMoRIuIiIiISLZKsCfQeUFn/rf7f2aA7vQtdQv+HxERsGyZuf45OZsNQs5sgPj46wfDw82h6YgI83uvXln5FiQf0XRuERERERHJNrGJsXT6Xyd+3PcjXjYv5neaz6k1j7hM4S5cGGJizGXONhtMeWYdQU89AB06wNy54HEt1gQFafRZMp1CtIiIiIiIZIuY+Bge/+Zxfv37Vwp4FGBBpwXU9HnIbQ30pUuw6Ydre0A3DSDo4hX42gP8/cFiybb+S/6kEC0iIiIiIlkuKjaKh+c8zLp/1uHn6ceizosIq2BuY5XaGmiXPaCnToXNm6FmTYVoyXIK0SIiIiIikqXOXjlL29lt2XJiC/4F/Pm5y88E0YjFi2Hs2HTsAd2nj7nuWQFasoFCtIiIiIiIZJnDFw/TdnZb9p7bSwnfEizrtowtP9XmvmRTuH19IS7u2hpoq8EURxp7QGv9s2QDhWgREREREckSO0/tpO3stpy4fIJyRcqxpMsSCsVVpXeKNdCxsbBxo1lMLMTvJEGNZkLyKd7aA1qykba4EhERERGRTLfy8Erun3E/Jy6foEapGqzvuZ6qJauyZYv7GmiHA2KiEs09oOsHmmugtQe05BAK0SIiIiIikqm+3f0tbWa3IToumgfKP8CaZ9dgRJdlwgTo2tV9abPNahDSoyns3Gke6NVLe0BLjqEQLSIiIiIimWbSb5Po9L9OxNvj6VC1A790/YX5X/tTvjy89BJcvgwBAWCzGYD5fUrVCQQd2wTvvnv9QkFBmEPTGoGW7KU10SIiIiIikuEMw+CNFW8weu1oAPrX688nD33CieM2tzXQp0852OBoRAy+hDj+Jqj3UDgyBEaNyqbei6RNIVpERERERDJUgj2BPov6MGP7DABGNR/Fv+//N4mJFiZMcF8DbXdYicGXMFaBAQwZYk7b9vHJ6q6L3JRCtIiIiIiIZJjouGie+vYpfj7wM1aLlamPTKVNqV5ERMDIkbBqlbkG2jCuP8dGIiEcuH5AW1hJDqYQLSIiIiIiGeLvC3/z6NxH2X1mNz4ePnzzr284vfZRyl+bvm2xgLc39O4Nn39+bR9om8EUe1/XfaC1hZXkYCosJiIiIiIid2zNkTU0nN6Q3Wd2U6ZQGVY/u5o6fo+6rH82DEhMhFdegcOHjGvFti30mlwPrNeiibawkhxOI9EiIiIiInJHvtz2JX0X9SXBkUC9MvX4vOkPXNobyOTZqax/tsOB4dMIK7SFoC++MA/27QuPPGJO4Q4JUYCWHE0hWkREREREbovdYWf4r8MZt2EcAJ2qdyLs/H9oVMPbLTwnsVkNQuaMBCKhe3do3Ng8ERSk8Cy5QqZP537//fexWCwMHjw4s19KRERERESySHRcNP837/+cAXpEsxGMbTiPgf1SBmgDG4mAWUBsSre1BI17CWbPvh6gRXKRTB2J3rx5M1OnTqVWrVqZ+TIiIiIiIpKFDl88zKNzH+WP039QwKMA4xv9lyrGo3z1lfv0bbAwl6cpyRlCOEDQ7JPm9lUadZZcKtNC9OXLl+nSpQvTpk1jlDZJFxERERHJEyIORdDp206cvXKWwIKB9DTWMbB1xbSnb5NIYzZcr75tR9tXSa6WaSF6wIABPPzwwzz44IM3DNFxcXHExcU5H0dHRwOQkJBAQkJCZnUvQyT1L6f3UyQj6H6X/ET3u+QXutflVhiGwdiNY3lz5Zs4DAd1AurwWZPvaVo7yG36ttUKDocFm83gC0c/gozr21cZNhuJ5ctDFt93ut/lRm7lvsiUED1v3jy2bt3K5s2bb9r2/fff55133nE7vnTpUnx9fTOjexlu2bJl2d0FkSyj+13yE93vkl/oXpebibHH8MnRT9gUtQmAFsVa0KdUH3765hgOR3CK1hZe6b8av9JWAgNjuHebN8ZkKxaHA4fVyo6+fTm6cyfs3Jn1bwTd75K6K1eupLutxTAMIyNf/J9//qFevXosXbqUe+65B4CwsDBq167NhAkT3NqnNhIdHBzM2bNnKVy4cEZ2LcMlJCSwbNkyWrVqhaenZ3Z3RyRT6X6X/ET3u+QXutclPXad3sWTC57kwPkDeNm8mNh6Iq1L9GTOHBsffWTl0iUwDIuzvc3i4FCRewjYNB8qVjQPRkZiOXgQ4+67s20at+53uZHo6GhKlChBVFTUTXNoho9Eb9myhdOnT1O3bl3nMbvdzurVq5k0aRJxcXHYbDbnOW9vb7y9vd2u4+npmWtu7tzUV5E7pftd8hPd75Jf6F6XtMzeOZveP/bmauJVyhUpx/xO89nxcz1Ce18vIFamDJw6ZWC3m9O3p5T/gOC//4Dvv4dhw8xGFSteD9TZTPe7pOZW7okMD9EtW7Zk165dLseeffZZqlSpwvDhw10CtIiIiIiI5Dzx9nheWvISn//+OQBt7m7D1x2+5ur54jTs7VqB+9RJBxscjYjBlxDH3wT1GQhBX0PnztnUe5HMleEhulChQtSoUcPlmJ+fH8WLF3c7LiIiIiIiOcs/Uf/Q8X8d2XTMXP88uOpYHi4+mB//a+P77923sLI7rMTgSxirwAD+/W9zCyuRPCpT94kWEREREZHc47u/vqPXD704f/U8RQsUpZt9JZ88XYsJyYKzxQLJqyrZSCSEA9cP2O3awkrytCwJ0StXrsyKlxERERERkdtwNeEqQ34ZwhdbvgCgXpl6TGw8n/vvKecy8myxwHvvwZtvmlnZZjOYYu9zfQ9oAJsNQkKy+B2IZB1rdndARERERESyz65Tu6g/rb4zQPcLfY9RFdfz9eRyblO3DQMa7w7n8IFEIiLg8GELvaY3MYMzmN+nTNEotORpms4tIiIiIpIPGYbB55s/5+WlLxNnjyOgYABPx//KxG7VmexI/Tk27ITMfpugkEiC3n7bPNirF7RpY07hDglRgJY8TyFaRERERCSfOXvlLL1+6MUPe38AoF1oO96rN4u6VUukGH02sGHHjgc2Eply/9cEnS0Mjz3mesGgIIVnyTcUokVERERE8pEVh1bQbWE3jl86jpfNi3/X+pz6Hj35fq7Fbfo2WJjL05TkDCEcIGj9Sdi3D+66Kzu6LpIjKESLiIiIiOQDVxOu8vqK15mwcQIGBlVKVKFT3C+MbH997XNqlbcbs+F64TA7cPSoQrTkawrRIiIiIiJ53KbITXT/rjt7z+0F4Pl7n2do9QlUDfV1G3222a5V3rYaTHGo8rZISgrRIiIiIiJ5VFxiHCNWjmDM+jE4DAeBBQP5oMFsHAdbsPU3Uq2+PXculCwJISEWgv5XA4YlpWpV3hYBhWgRERERkTxp64mtdP+uO3+c/gOALjW70ODUF/RoVtA5ZdtiMTAMi/M5NhJp7LWDoLC65oGXXoKOHVV5WyQZhWgRERERkTwkwZ7A6DWjGbVmFImORIrF1+LF0Ek8FHw/jTq6rnnGcGDDuF59mz4ExbYG6l5vo8rbIi4UokVERERE8ohdp3bR4/sebD2xFYB7T3zG9mn9eNthYUSKomFgbmA1l47Xq29zDEp3y4aei+QeCtEiIiIiIrlcbGIso1aP4sN1H5LoSKRogaKMvPdLXmz7fzgc5nTtlAEaUqm+rcJhIjelEC0iIiIikotFHIqgz6I+7D+/H6LKcl/BZ5n4fwOJPlE6lX2fwWo1C4rZSGRKzc8I2n3S3LpKhcNE0kUhWkREREQkFzp35RzDlg1jxvYZABTZPYTob8eyzmGhwXvwwQfXA3MSmw02bICYGAjxO0NQ/Rch8gkVDhO5Bdbs7oCIiIiIiKSfYRjM3TWXqp9VZcb2GViw8EyFf3Pp27EY16ZuOxzw2mvwYYdN2EgEro08P7mC+vUhLAyC6geaFwwKunZAAVokPTQSLSIiIiKSSxy+eJh+P/VjyYElAFTyaMHAkImUttTgPymmbtvtUG/+axxmHwcIMQuHfXMSPjyswCxyBxSiRURERERyuLjEOMZtGMd7a97jSsIVvGxePBQ9nx/GPswgw4LFApYU1bdtVoMQxz6COHa9cJgdc+q2QrTIbVOIFhERERHJwRbvX8yLS17kwPkDEFWWWp7P88aDg3myTQVnaDYMM0TbrAZ2h8Wcut3jN4JmnoDkI9Sqvi1yxxSiRURERERyoL8v/M3gJYP5cd+PABT5cwjR88ey02HhyY9S2fPZgLnfWCg5/wtCEv8iaNRwaDIV+vQx53ar+rZIhlCIFhERERHJQa4kXOHDtR/y4boPiTtfAuuFljxd5/+Y8+1ADCP5ns8GYHE+z2Z10LixlaB/9TGHpQF69YI2bVR9WyQDKUSLiIiIiOQAhmHw/d7vGbxkMEeijsDWnvDjVByGja9npvYMC1bsOLCZ07eNfgTxNlhSBOWgIIVnkQykEC0iIiIiks12nNzBy0tfZvmh5QAEOupzctF058hzamwksoHGxOBnVt42jsGBLgrMIplMIVpEREREJJscv3ScN1a8wcztMzGiyuBxsRXP3teOsz8PZKHDPUA7R55tBlMc/ahv/H79pIqGiWQJhWgRERERkSwWEx/D2PVjGbN+DFcSrlybuj2NRMNK+CxwONyfY7PY2WA0IqZJa0K+eY+gXxpBnxkqGiaSxRSiRURERESyiN1h5z87/sMbEW9wPNIC5xtQvcxd7E42ddvhAIvFoKcRzkx6YMfDXPNMP+rPGADdu5v1xFQ0TCRbKESLiIiIiGSB5X8v5+WlL7Pj1A5n0TAMG3+mqLINYBgWujKbEYzgACHX1zxX6HK98jaoaJhINlCIFhERERHJRJuPbebfK/7Nr9v2wPlQ/PzCuLJoGoZhvdbCfe2zzWoQ4jhAEMcI4ti1g1rzLJITKESLiIiIiGSC3Wd288aKN1j418JrI89LwLARk8rIM4DV4sBhWK8tb7YQlPAGDByoNc8iOYxCtIiIiIhIBjp88TDvrHqHWauXY5y7GzzrYfkx5ciza5C2kcgGr+bE/G8xIXUKXcvKfeGRR7TmWSSHUYgWEREREckApy6f4r017/HF71+Q8Hs3+PEQGDYsFiOV/Z4t17erIpEp9KX+stFwfyHXZlrzLJLjKESLiIiIiNyBMzFnGLdhHJN+m0RMQgxElXUWDQNSCdDXRp5pTAx+ZtEwjoG9a1Z3XURug0K0iIiIiMhtOBNzhrHrx/LZ5s+c4bmypRsdK/Zn1LUAnZzVam5fZY4896E+v18/qaJhIrmGQrSIiIiIyC04HXPaGZ6vJFwBoMyOCRxfOIi9WHjPgtsUbpvVwYaNVmJiICQglqB1TaDPLBUNE8mFFKJFRERERNLhdMxpPlr3EZ///jlXzhaF8w2oVc2Xlxq9xLMjWpJUKMwwwIIDGwZ2PMyRZ6Mf9QPfvhaUC0KVXtCmjYqGieRCCtEiIiIiIjdwLPoY4zeMZ/Lvk7maePXadlXTwLDyh9XgzyHua54NbMylIyU5Y655No7BgS6uYVlFw0RyJYVoEREREZFU7Du3jzHrxvCfHf8h4UIpON+QamXKs/uH6SSNOjscFsaPB6vFwGG4blnVmA1mwTDQmmeRPEQhWkREREQkmS3Ht/DBug+Yv3s+BgZs6QmLzGrbeyyu+zuDWSxs6FD4eJwdu2HDZjOY0nUDQbNPgh2teRbJYxSiRURERCTfMwyDiMMRvL/2fX79+1dzm6rzzQiJ6sOBH5/k+npnC+AapG0k8mKnM7z4YuC1Jc4WgoLuh1GHteZZJA9SiBYRERGRfCvRkciCPQsY/dN/2LE7Bortx3LwOYwfp4Bh5UCqz7JgxY4Dm3O7qqCYbhAU6JqVteZZJE9SiBYRERGRfCcqNorwbeF8sukTjkS0hB+/B8MGGOYgs5F8yrb7yPMGGhODn1k0zHYSQt7J4ncgItlFIVpERERE8o3DFw/z3qJZfL3yN64W3mEe/HHqtQANYMEwUj4r2cizDaZ03UD92du0x7NIPqUQLSIiIiJ53sbIjYzfMJ5vZxfB+PGLa6HZwYOd/+BXZ4BOnY1ENvznADHBVa4tb9Z6Z5H8TCFaRERERPKkuMQ4vt39LeN++YZtf14Cz8vw48Zko85Wls+thdVqVthOYsGOFQM7Hs41z/WDu0FYleuNtN5ZJN9SiBYRERGRPCUyOpIpv09h6tapnF7zCPy40DnyDFaXtoYBL78MH398bXa2xc4U+tLG+JkDhGjNs4i4UYgWERERkVzPMAzWHF3DpN8mMX/jJhzn7gLPcinWO1tJdXuqJ07y4otB12Zn2wj6pRH0mUGQ/ZjWPIuIG4VoEREREcm1Lsdf5rNfv2fK0hUcsv4CB9rAor/N4GxxgGFN8YzUtqfqDEFB13Nyr17Qpo3WPItIqhSiRURERCTX2XZiG1O2TGHmDBtxCz8BowtgxxxtvjbSbKQ+8uy2PVXlVKZqa82ziKRBIVpEREREcoXL8Zf5fPkPhP+6mn3GIvPgwiPJpmunVmXbgtVq4HBYsFkdTOmm7alE5M4oRIuIiIhIjrb95Ham/D6FGTOs10adO4PFjqfvFRLSsz3VZzuIqVKXkBCrtqcSkTumEC0iIiIiOc7F2IvM3TWXLyIWsXP3FbDGwsK110edDRsJMQVJOV3bbXsqSz/qP/I2JM/KmqotIndAIVpEREREcgSH4eCb9euY/usq1l6eQfy+MPjxh2vB2TUsmywM4mM+s7yI3bCas7O7rqfNV1054KhIiPUQQVPfUmAWkQylEC0iIiIi2erQhUPM3D6TSVOucv6/74NxP/AaZmhOqq5tIbUiYcOab2PYwN85UKzBtdnZ98OodQRpuraIZBKFaBERERHJclGxUSzYs4BpK39mw44z4HkZ/rvx5kXCUm5P9VZPCGvgMltb07VFJDMpRIuIiIhIloi3xzN77Ur+s2IDG678h/i9zWHR3GvB2U7qwfm6VLenCklleyoRkUykEC0iIiIimcYwDNb/s56vd33Nf2Z4ELPgYzBaA2/gsqcz7uueLdixWq3YHZZr6521PZWIZD+FaBERERHJcH+d/YvJy3/kv2u2cdJrNUSXgfkbub7GOX3TtdvMe44DJRsnW+98WNtTiUi2UogWERERkQyx5a9TfLl8DWtjZrBzXQD8ONWcqm2x4+EdT6IzQKcu1enajd9xzcpa7ywi2UwhWkRERERu28nLJ5m/ez6ffBHDvpkvg/EvoAPmtOxrU7MNG4mxBUh1urbFkmx7Kk3XFpGcTyFaRERERG7JycsnWbBnAV+tiWDjznPgcQlmJq+sndqIs4WhjOFjhmDH4/p07W80XVtEcheFaBERERG5qVOXTzF95RL+t3Y7O+K/hYOt4cd514Kz6whzamxWgxeNSbxofMIBQjRdW0RyLYVoEREREXETGQmbdp5nr2MRy87NYNWCEIwfvwCjOzAWLBYwkkacLdx0qvYUC0G8DX36EGQ/punaIpJrKUSLiIiIiNPfF/7mtY8O8N8PWoJRDCxd4MGdsGwMLpW1jZTPTKWytstUbYBe0KaNpmuLSK6mEC0iIiKSjxmGwbaT25izYTU/rN/DoZidEJ5sfbNhw/LrGIyMqKwNmq4tIrmeQrSIiIhIPpNgT2D+xk3MW/U7q6O+5MKXDWDRlGvB2U7KPZwNw4oFO0ay4xbsWK1W7A6LKmuLSL6iEC0iIiKSD+z9O4a5q35nZ+J8lvxicHXBBDCaAi9ea5G0ntm9UJjNZvCB/VVe5f3rlbUt/WizcSQHYgJVWVtE8hWFaBEREZE8KDISVm45xkHLEv77QxS7v3wRjGZAU8yAnLwoWErJ1jdfKwrWiyo81ftuDjgqEmI9RNDUt6B+IC5RWVO1RSQfUIgWERERySPi7fGsPrKaDz89y68TO4JRFuiBa2i2pfl8nC0S2TB5BzFV6roUBQtq04YgjTSLSD6nEC0iIiKSix2/dJzZa1fyw4Y9bIv/L1fiY2DCUW4lNFuwY8Vwmapd/5G3QUXBRETcKESLiIiI5CKJjkQW/b6db9fsYHvC//hzVSVYMgGwgmUEvg98wZWbVNJOXhTManUwucta2n39jOtUbYVlEZFUKUSLiIiI5HDr/jjCt2t38JfjR1Yu9yZ24UQw6mFO1bbiXNds2Ihd3Q+LxcAwrq91Tm2kuc3GkfwVVZIjR5bzzDMt8By9TlO1RUTSQSFaREREJIfZfSCa+et2sp/FLFlicOabUWCUBx691iJ5JW1XDsPK0C7H+XhOAHbDem37qfW0+aqrW1Gw0gkJLF4caz5RU7VFRNJFIVpEREQkG0VGwl977VwpvIPtVxbx1UxPDsx65dr2U425eSVtVzYSefH/jvDiB2WS7TZ1P4zSSLOISEZQiBYRERHJQpGRsG+fgVFsH+H/i2Te+80xDBtY7oEH5/x/e/ceHWV57n389zyTCIIGNyAQCWqAIKgcNqdIaCyikC1Wq1sX8CoC7vAKlsLShbYseQvopkVsa1e1SsEiqBxEEQRLBKNFSAARkCAYFOSgRIMVFBKl0iTP/f6RZDIzmcwpMzmQ72ct/phDmHuWt+iP676vS3pnnmQqK8yRNQVLGlTeFMwrK1NpBoCoIEQDAADEUGVojr/0mJ5/9Qu9/Nt0ydiSukpKkbvKbFyysufJBAnOnk3BajyqTVgGgJghRAMAAERRQYF06JDUsv1XWvDqMS1+/DoZY0u6XNKVCnSf2cgl2zJyQmgK9tkPiRzVBoB6QIgGAACIUGVgTkmRzMXH9fifvtSixwdWhOb2kjoonHnNLpXqiYmfa/rzXVRWpoBNwbyiMke1AaDOEKIBAABCVBmau3Y1emn11/rNQ+3KA7NVJt3054r7zKGHZn9V5swZszR6hmgKBgANFCEaAACgBpWhuUtXRy+s+lKPP9xRxrElOZLayfM+s7LnKVhwtlQm27ICj55KSlKSaAoGAA0VIRoAAKBCZWhOuvJfWvRagZ6c3qXiaLaR1FGBj2aHeJ95B/eZAaAxI0QDAIAmqzI0X9ShUC+s+lILZvWtCM0XqLx7ds1NwHxxnxkAmgZCNAAAaBIqA/OVnUv0bfxH+uOzpytmNNsqP5rdXuE0AeM+MwA0TYRoAABwXqoMzW2TvtPzr36hv8zsWX6f2bKlm1ZUzGQOMzRznxkAmjxCNAAAOC8UFEgff/JvlbTK1ytrv9Py3/20osqcIKmnfJuAmVCagHGfGQDggxANAAAapS8++FJbN+xTUZcCrfzgQm16ZrRkLlBVYA50n9klW2VyPF6zVCbbtlXmWNxnBgDUKOoheu7cuVq9erU++eQTXXjhhUpLS9O8efN01VVXRfujAADAearyKHZKSnlGPX7caFveNyq6aLcOl23Wkcfi9HruY3LUUeWds6WwmoC5jJ4om67pmutdaX6fSjMAILCoh+jNmzdr8uTJGjBggEpLSzVjxgwNHz5c+fn5atmyZbQ/DgAAnAc8Q/PGjdL99xs5jiXLctQxfZMKcoZIpp2k/9IlffapKG+aRxXZCvA7V77Dp8q8wFKmumv0/V2oNAMAwhL1EL1hwwavx4sXL1a7du20e/duXX/99dH+OAAA0Ah5huaVa0/rkamtZBxLklPxjvL7y8bYKtgyVFVB2dLpvIdV1UXbP7/3mb2qzJKUqaSMDCrNAICwxPxO9JkzZyRJrVu39vv6uXPndO7cOffjoqIiSVJJSYlKSkpivbxaqVxfQ18nEA3sdzQl7PfoqwzNF3Yo0PI3TmrB7H4VTb8cSa1UFZL9hWPfSrMd5D6z0XN35+rmZWN12ElWF/uoEufPkOnTVu1V+c+24gfbty//5fVk08FeR1PCfkcg4ewLyxhjgr8tMsYY/fznP9d3332nnJwcv++ZPXu2HnvssWrPL1++XC1atIjV0gAAQJScPNlchYUXKTHxe7Vt+6OKD57VqfwSOV1P68uOX+gf7yRrz/JJ5V2xfSrNoTHyDNK27WjqdWv1zLZb3ZXmGTes1OX3tFVhYUslJv6gtm1/VPOTJ9WysFA/JCbqx7Zto/iNAQDnm7Nnz+ruu+/WmTNnlJCQEPC9MQ3RkydP1vr165Wbm6ukGo5I+atEd+rUSSdPngy6+PpWUlKi7OxsDRs2TPHx8fW9HCCm2O9oStjvgRUUSJ99ZqlrV6PsbEsPPOAqv79sOxrcbaO2fTJcjlyy5Kh/j19p5yfzKgJ0aHyPYt+jZVrmGquysooq83Nluu8+o4KdhTqy/Rt1HnSpkgYkxvAbn7/Y62hK2O8IpKioSG3btg0pRMfsOPeUKVO0bt06bdmypcYALUnNmjVTs2bNqj0fHx/faDZ3Y1orUFvsdzQl7PdylUexu3R1tHzNKT36UBsZp/IotqXKKrFxbOV+8l9Vj2Vr94F5CtYtO5TRUr/NsFR+ddlSUlL5/74kp12u5LTLY/a9mxL2OpoS9jv8CWdPRD1EG2M0ZcoUrVmzRu+9956Sk5Oj/REAACBKfEdJFews1KGcE+qYmqBTl/9T8xee09LfXl9xf1mS2qjqKHbw+8uOXLItI8dYHu8I1vSr+mipJNH3CwDQMEQ9RE+ePFnLly/X2rVrdfHFF+vEiROSpFatWunCCy+M9scBAIAw1DhKyjb6afd3tSX/BjlKlCVHva98XXmfT5NMoNDsy/v+skuleuLR7zX9iUtUVqYaK82MlgIANBZRD9Hz58+XJA0ZMsTr+cWLF2v8+PHR/jgAABBAZWhO7lKqpau/0cxp7T2OYkvuUVKOpffyb5TnUey9x6Yp3KPYY1IPaem2zlVV5nHblTknXaMnSVWF5eqVZgAAGouYHOcGAACx5+8o9idbvlKLXqX6ptMJLVns0hu/H1FRSbYldVA4o6RMREexu2nOzkJ9tvVrdR3cXkkD0iX5KSxTaQYANFIxnxMNAACio/K+ckp6B/19T1tNfiDO3RU7NSVLH3x6sxwlSjK6xFWo0077ejmKnTQgkW7ZAIDzFiEaAIAGwjMkJw1IVEGBtGvfGZnWB7Xt8f16KmtsxX3lMhmfrtjvf3qLqgKwpdNllwX9PI5iAwAQPkI0AAB1oNrRa4/Hl3V09PQ9GzVtxXA5SpStMl3V6R0dKLhBMq0k9ZXUX1X3lf3dU7aqPcNRbAAAoo8QDQBADNTUBdu2jQbfckS565PdDb7apM3Wd9tmyakIx45cOnC8qslXsOZe5TiKDQBAXSBEAwAQJt+qsuQ9X3nZ+3H6319dLuNY8u2C7TiWct7sLM8GX6e2zVL1oFy9suz9KkexAQCoD4RoAAB8FBRI+/a1Va9eUnKy913ljR8les1W/tmUd9V23y69+I9H3E29yoXeBVtyyVaZuxJdzruybFmObON4heSMOekeAZmj2AAA1AVCNACgyasekuPkOIM1a5bRLb3e1/q8AR4NvRx5zlZ+8883ytYNHgE4cAW5nM/Ra5f0xB27NH1VP3dIHpN2REt3dKs6ir3AVkavr/2G5EocxQYAIPYI0QCA85pvx2upvNJ88KDRJR2/0YYZOfrN67d7hOSqgOs4lt7MS1Wwhl5OkDvLvg29xmiZlrrGqqzMqgjIUmZmqkZ7VZK7aU6B51FsSSIkAwBQ3wjRAIBGzd9YqMr7ylkz3tMDL6W7O15PuOkpfdD5AuU9/4BkXJIulaU7ZCoryyF2vfZkW45kjFeQ9r2v7K+h15wMS75Xk30ryZy8BgCg4SFEAwAarJqqyJUh+a0ZWzTppcHukNyv8w7tPDpAMrakMlm63h2QHbn0t3emyrGsigAtSVbFvOVAfO4m+wbkBbaUk6OJLw4KcF+5ekOvJBGQAQBojAjRAIB6E6iKvPH/5ej+F9PcAXnaLUt16JpLtPb3I2SMrfJwmy730Wu5tPPIQHmOhTI+n+coTtWe9OEdko3frtfeAVlSZroyJvtv6uVGWRkAgPMCIRoAEBPBqsi+IXl4z+3auD+1IiCXydJgryry79ffLWWZiiqz5P+YdZCj1yqVbJccJ3DX66GzrtOyZTt0zz2pSk6uueu1J5p6AQDQNBCiAQARCaeKPP3WVSro3U4v/+4nMo6t8tnJP5FnFXnDvusUqIos2UGryKGMhVJ6uiZOVMCu1yUlJerZ81SNd5UBAEDTRYgGAPgVTki+ufc2ZX10XUUV2alWRf7dm3dKf3c8qsihzE72FkoVOdSxUBkZdL0GAACRIUQDQBMUKCAnJUl/G7dFEz0adl3fY7s2f5paUUUuk28Vef3eQaoKwbafgrFnM6+aRKOKHNpYKK4nAwCASBGiAaCR8w3AUuCQ7NvR+qaem5W9P91dRU6+cZ4+f/dX7pFNjlx674D3UevqGk4VmYAMAABiiRANAA2cb0j2DMgbP0rU/fdLjiPZtvTs/BL9uClb017JkKNEWXLUve1eHTjV0z32ybej9dv7rpdnFfnou79S9aAc5hgoqsgAAOA8RYgGgHoWekg2uqNvntbs6lURkMskOVV3jx3pgYku2cpwV5GNbB042dvj00KpIrtkq8z9e6jidwoUkqkiAwCApoIQDQBRFOyuse/rzz/vaNIkS45jybKMhl2bq3f2lTfsKq8aV4VXx7H0+q4+7sfGbyC25YS9au+A7HJJT9yxS9NX9QsjJFNFBgAATQMhGgBCFO7c45ED9+nVXdeWB2Tb0ZAem7T54yHuY9Y/6fUb5eyb7e5YbYylt/dVNeyK5O6xJUeWTC2ryFJmZqpGe81GDh6SCcgAAKApIEQDaLKCVYkDBeTH/nuVvuxzpRbM7uuee+w71umVD66Vu2rs2Nr08dCqx7K19aPZqvXdY5XJtm2VOZa7QqycHE18cVAtq8jVZyMTkgEAAAjRAM4T4R6jXrRIXneNb++zX298eLU7JA/otE07jl+n8nnGZdUC8szVd8iskdfcY79jnQI8duSSZRkZ4/l84JA8JvWQlm7r7NWwK2NOuncAzkxXxmSqyAAAALFAiAbQ4IQ7ssm3Sjxm0EEt3ZEix7Fk20Y399yut/amuo9RD+6wVrlf/8w9t9hxLK3+sKf78x25tOO459xjV7WAbOSSn9Rc7V3ewdnn7rFK9cSj32v6E5e4q8TBQ3I3zfE6Zl3esMs3AFNFBgAAiA1CNIA6F87IpoULJeV4h+Sbe+9Q1r4B7mPUUtU9YkcuvbQ9RZ7NuNbvrQrERrZyT9wqya6+MC/Rn3vsLyBnzknX6EkKKyT7BmQAAADUHUI0gFoJdoza9z2+I5uGX71Pb++/psaRTRMmlMpWmrtRliOX1u8dKM+5xtUFPkYt2bIsR8Z4/mzgqnF05h7XHJAJyQAAAI0DIRpowvwG3hqqxFde18b9+rFj/o9R3zXgI63a3bNiXJOjO6Zs1KUHPtHz2VMrRjYZ+Y5s2rC/pwKPbIrzM7IpvOZbkRyjjtXcYwIyAABA40aIBs4jYXWb3ijdf79x3xteuLA8ZHo+d/t/fqg3dvdx3yXu2vK0PjvrkjGSv2Zbr+70CMTG1uqnh8vWcI9xS/7Cb5CRTZYjy9RuZFNkx6iZewwAAIDqCNFAA1W7btPSvdcd1MvburirxEO77dW7h3qVd4K2HFlGHsemLU2YUCpZlnezrd195XmX+NAPvTxWWL3ZVvVA7PJTRfZVFyObIjtGTUAGAACAL0I0EAPVAm+QAOz7M8G6Tf+sz079/cN+7tdH/2ShVmyd4L7j6zjSi9s8mmvJpXcO9q5aoPE3jinOT7fpYMemfXkHYts2kuN4VZHra2QTx6gBAAAQDYRoIIiwxy35HJO+915LL79c1Uhr1IB8rdzR3R2AHx6xRMd6X6bX5t1U0W3aVDsm7dttet2HA+QZkF/JzXS/v0p4AdhWqWS55ASYWRzuMeoFCywpZ5tXFZmRTQAAAGjMCNE4r4UbgEMZt2S2bNHElwa7Q/BtfXdqbV5/GcdS+bglS56B98UXvRtprdhxtTwD8B+yxsh5y5LcnaItmaDdpb0fO3KF321aZbJlqsKt9YD05DxNnN66xrvEI67apazPUlVWZoV4jFp+qsiMbAIAAEDjRYhGgxZOo6xI5g3f2T9Pr3/Y291Nuvd/7NdH31aNWzJypGrjlgZ7jVt648P+qs24JcfvMWpfMeg2PWabMl4eo8+cZHW1jypp4Uwps7UyRvu/S3zFwNb66Juv9edepfr88/iQj1FLhGQAAACcPwjRiJnaBOBQGmWNHJCvV3f3KA/AttHAdnv1wYleMmHMG35tV295dpPO+7aqcVZdjVuyVSrZLjlOXXebTpfmbFWS98XiGu8Sl5SU6KOsPUpKkpKTg3xlAAAA4DxFiIZfsQ/AB/Tq7u7ue8NDrvxQm478p0zF6/dcv0hLc+4L2CjrlZ093I+NY2nHiT7u9UcvAPu82zKyjBN43JLPMekxWqalrrHuI9D+ArDS0zVxouq+2zQXiwEAAICwEKLPQ7EOwP/dN1+r83q4A3DG1Tu0Yf9AdwD+P+nPa3luZpAA3F2e94T/caSv1+vLtowPoVFWuAE4+Lzh4OOWqjfKCuWY9JwMK2gAzsig2zQAAADQ0BGi61m4ATdYoyzfe8C+Afi2nvu0bv+1ckx5AL651/t6K2+gx6ikBVqx9f8GDMCrPrzavX7HsfTW/lSv11fk/E8EAbj2jbKiMW84OuOWqh+TTlLwAExRGAAAAGj4CNG1ULCzUF+sLVLBpYVKTrs87AC8aLx3k6t70w7q5fe7uQPwmIEHtfT9qgB8U0qesj/rLWMsWbaj0dM36aJ/HNXf3v8f9z1g30ZYvgH4jX093et3HEvr867zev2V3AkRjEqKfgCOpFFWdAJwlMYtkYgBAACA85JljAnaF7guFRUVqVWrVjpz5owSEhLqezk1qgrArooAfNgjABvd0n2/1udf7X79xqt26p1PB8rIlmU7Gj5qjbJX3B7W0eLqj0tlyarh/m/kohKAZ/gG4INBAvDB6o2ylqSrwGdcUoFXwE0M+jqip6SkRFlZWRoxYoTi4+PrezlATLHf0VSw19GUsN8RSDg5lEp0BAp2FroDtFReeS2v+JZzHEtv5ntUfOVS9qdVR56NY2vjitulauE3vCPPUlzwyUj1VAEOv1N0dBplcU8YAAAAQCwRoiNwKOeEHPkGtfCOPKuiQl2bSrRtG8nx7hTtew+YAAwAAAAA0eN7+RUhSEnvIFtlPs/61oQDP3a5pHl37ZJLpeWPVapxaYfkclW9Pi7tUMDXFy60tHDcNq/3PD9um459bmnTJunYMWnJ1m469sE32vSnPB374Jvyx8dU4+uZS6oC8JAhVSE3aUCihjzYxx1yg70OAAAAAOcjKtERSBqQqIXjwuvyXG0M0gIpMzNVo8Oq8Pq+Lj+Nsqo3wqICDAAAAADRQYiOUOaSdA29/wv9fdFm/Szzp0pOiyAAK/yA66/pMyEYAAAAAOoGIboWkgYk6vJvEryOOIcbgAEAAAAAjQd3ogEAAAAACBEhGgAAAACAEBGiAQAAAAAIESEaAAAAAIAQEaIBAAAAAAgRIRoAAAAAgBARogEAAAAACBEhGgAAAACAEBGiAQAAAAAIESEaAAAAAIAQEaIBAAAAAAgRIRoAAAAAgBARogEAAAAACBEhGgAAAACAEBGiAQAAAAAIUVx9L8CXMUaSVFRUVM8rCa6kpERnz55VUVGR4uPj63s5QEyx39GUsN/RVLDX0ZSw3xFIZf6szKOBNLgQXVxcLEnq1KlTPa8EAAAAANCUFBcXq1WrVgHfY5lQonYdchxHX331lS6++GJZllXfywmoqKhInTp10vHjx5WQkFDfywFiiv2OpoT9jqaCvY6mhP2OQIwxKi4u1mWXXSbbDnzrucFVom3bVlJSUn0vIywJCQn8i4gmg/2OpoT9jqaCvY6mhP2OmgSrQFeisRgAAAAAACEiRAMAAAAAECJCdC00a9ZMs2bNUrNmzep7KUDMsd/RlLDf0VSw19GUsN8RLQ2usRgAAAAAAA0VlWgAAAAAAEJEiAYAAAAAIESEaAAAAAAAQkSIBgAAAAAgRIRoAAAAAABCRIgO4rnnnlNycrKaN2+ufv36KScnJ+D7N2/erH79+ql58+bq3Lmz/vrXv9bRSoHaCWevr169WsOGDdOll16qhIQEDRo0SBs3bqzD1QK1E+6f7ZW2bt2quLg49enTJ7YLBKIo3P1+7tw5zZgxQ1dccYWaNWumLl266IUXXqij1QK1E+5+X7ZsmXr37q0WLVooMTFR9913n06dOlVHq0VjRYgOYOXKlXrwwQc1Y8YM7dmzR+np6br55pv1xRdf+H3/0aNHNWLECKWnp2vPnj169NFHNXXqVL3++ut1vHIgPOHu9S1btmjYsGHKysrS7t27dcMNN+jWW2/Vnj176njlQPjC3e+Vzpw5o7Fjx+rGG2+so5UCtRfJfh85cqTeffddLVq0SJ9++qlWrFih7t271+GqgciEu99zc3M1duxYZWZm6uOPP9Zrr72mnTt3asKECXW8cjQ2zIkOIDU1VX379tX8+fPdz/Xo0UO333675s6dW+39v/71r7Vu3TodOHDA/dykSZO0d+9ebd++vU7WDEQi3L3uzzXXXKNRo0Zp5syZsVomEBWR7vfRo0crJSVFLpdLb7zxhvLy8upgtUDthLvfN2zYoNGjR+vIkSNq3bp1XS4VqLVw9/sf/vAHzZ8/X4cPH3Y/98wzz+jJJ5/U8ePH62TNaJyoRNfg3//+t3bv3q3hw4d7PT98+HBt27bN789s37692vszMjK0a9culZSUxGytQG1Estd9OY6j4uJi/ocLDV6k+33x4sU6fPiwZs2aFeslAlETyX5ft26d+vfvryeffFIdO3ZUt27d9PDDD+tf//pXXSwZiFgk+z0tLU0FBQXKysqSMUZff/21Vq1apVtuuaUuloxGLK6+F9BQnTx5UmVlZWrfvr3X8+3bt9eJEyf8/syJEyf8vr+0tFQnT55UYmJizNYLRCqSve7rj3/8o3744QeNHDkyFksEoiaS/X7o0CFNnz5dOTk5iovjP5toPCLZ70eOHFFubq6aN2+uNWvW6OTJk/rFL36hb7/9lnvRaNAi2e9paWlatmyZRo0apR9//FGlpaW67bbb9Mwzz9TFktGIUYkOwrIsr8fGmGrPBXu/v+eBhibcvV5pxYoVmj17tlauXKl27drFanlAVIW638vKynT33XfrscceU7du3epqeUBUhfPnu+M4sixLy5Yt08CBAzVixAg99dRTWrJkCdVoNArh7Pf8/HxNnTpVM2fO1O7du7VhwwYdPXpUkyZNqoulohHjr9Rr0LZtW7lcrmp/c/XPf/6z2t9wVerQoYPf98fFxalNmzYxWytQG5Hs9UorV65UZmamXnvtNd10002xXCYQFeHu9+LiYu3atUt79uzRL3/5S0nlIcMYo7i4OL399tsaOnRonawdCFckf74nJiaqY8eOatWqlfu5Hj16yBijgoICpaSkxHTNQKQi2e9z587V4MGD9cgjj0iSevXqpZYtWyo9PV1z5szhFClqRCW6BhdccIH69eun7Oxsr+ezs7OVlpbm92cGDRpU7f1vv/22+vfvr/j4+JitFaiNSPa6VF6BHj9+vJYvX87dITQa4e73hIQE7du3T3l5ee5fkyZN0lVXXaW8vDylpqbW1dKBsEXy5/vgwYP11Vdf6fvvv3c/d/DgQdm2raSkpJiuF6iNSPb72bNnZdveccjlckmqOk0K+GVQo1deecXEx8ebRYsWmfz8fPPggw+ali1bmmPHjhljjJk+fbq599573e8/cuSIadGihXnooYdMfn6+WbRokYmPjzerVq2qr68AhCTcvb58+XITFxdnnn32WVNYWOj+dfr06fr6CkDIwt3vvmbNmmV69+5dR6sFaifc/V5cXGySkpLMXXfdZT7++GOzefNmk5KSYiZMmFBfXwEIWbj7ffHixSYuLs4899xz5vDhwyY3N9f079/fDBw4sL6+AhoJjnMHMGrUKJ06dUqPP/64CgsLde211yorK0tXXHGFJKmwsNBr7lxycrKysrL00EMP6dlnn9Vll12mp59+WnfeeWd9fQUgJOHu9QULFqi0tFSTJ0/W5MmT3c+PGzdOS5YsqevlA2EJd78DjVm4+/2iiy5Sdna2pkyZov79+6tNmzYaOXKk5syZU19fAQhZuPt9/PjxKi4u1l/+8hdNmzZNl1xyiYYOHap58+bV11dAI8GcaAAAAAAAQsSdaAAAAAAAQkSIBgAAAAAgRIRoAAAAAABCRIgGAAAAACBEhGgAAAAAAEJEiAYAAAAAIESEaAAAAAAAQkSIBgAAAAAgRIRoAAAAAABCRIgGAAAAACBEhGgAAAAAAEL0/wFucd5EXT1BjwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 0.9\n",
    "u_0 = 1.0\n",
    "\n",
    "(t100, U100) = euler_method(f_3, a, b, u_0, 100)\n",
    "(t200, U200) = euler_method(f_3, a, b, u_0, 200)\n",
    "t = t200\n",
    "u = u_3(t, a, u_0)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is $u = 1/({a + 1/u_0} - t)$\")\n",
    "plot(t, u, \"g\", label=f\"Exact solution\")\n",
    "plot(t100, U100, \".:r\", label=f\"Euler's answer for h={(b-a)/100:0.2g}\")\n",
    "plot(t200, U200, \".:b\", label=f\"Euler's answer for h={(b-a)/200:0.2g}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is clearly a problem when $t$ reaches 1; let us explore that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 0.999\n",
    "u_0 = 1.0\n",
    "n = 200\n",
    "\n",
    "(t, U) = euler_method(f_3, a, b, u_0, n)\n",
    "T = a + 1/u_0\n",
    "tplot = linspace(a, b, 1000)  # More t values are needed to get a good graph near the vertical asymptote\n",
    "u = u_3(tplot, a, u_0)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is $u = 1/({T} - t)$\")\n",
    "plot(tplot, u, \"g\", label=f\"Exact solution\")\n",
    "plot(t, U, \":b\", label=f\"Euler's answer for h={(b-a)/n:0.4g}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly Euler's method can never produce the vertical asymptote.\n",
    "\n",
    "The best we can do is improve accuracy by using more, smaller time steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10000\n",
    "\n",
    "(t, U) = euler_method(f_3, a, b, u_0, n)\n",
    "T = a + 1/u_0\n",
    "tplot = linspace(a, b, 1000)  # More t values are needed to get a good graph near the vertical asymptote\n",
    "u = u_3(tplot, a, u_0)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is $u = 1/({T} - t)$\")\n",
    "plot(tplot, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \":b\", label=f\"Euler's answer for h={(b-a)/n:0.4}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for Solving for {prf:ref}`ode-stiff`, a stiff ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_4(t, u):\n",
    "    \"\"\"The variable K may be defined later, so long as that is done before this function is used.\n",
    "    The general solution is u(t) = u(t; a, u_0, K) = \\\\cos t + (u_0 - cos(a)) e^{-K (t-a)}\n",
    "    \"\"\"\n",
    "    return -np.sin(t) - K*(u - np.cos(t))\n",
    "\n",
    "def u_4(t, a, u_0, K):\n",
    "    return np.cos(t) + (u_0 - np.cos(a)) * np.exp(K*(a-t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With enough steps (small enough step size $h$), all is well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 2 * np.pi  # One period\n",
    "u_0 = 2.0\n",
    "K = 40.0\n",
    "n = 400\n",
    "\n",
    "(t, U) = euler_method(f_4, a, b, u_0, n)\n",
    "u = u_4(t, a, u_0, K)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is u = cos t + {u_0-1:0.4g} exp(-{K} t)\")\n",
    "plot(t, u, \"g\", label=f\"Exact solution for {K=}\")\n",
    "plot(t, U, \":b\", label=f\"Euler's answer for h={(b-a)/n:0.4g}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, with large steps (still small enough to handle the $\\cos t$ part),\n",
    "there is a catastrophic failure, with growing oscillations.\n",
    "\n",
    "As we will see, these are a characteristic feature of *instability*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 124\n",
    "\n",
    "(t, U) = euler_method(f_4, a, b, u_0, n)\n",
    "u = u_4(t, a, u_0, K)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is u = cos t + {u_0-1:0.3} exp(-{K} t)\")\n",
    "plot(t, u, \"g\", label=f\"Exact solution for {K=}\")\n",
    "plot(t, U, '.:b', label=f\"Euler's answer for h={(b-a)/n:0.3}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To show that the $K$ part is the problem, reduce $K$ while leaving the rest unchanged:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 10.0\n",
    "\n",
    "(t, U) = euler_method(f_4, a, b, u_0, n)\n",
    "u = u_4(t, a, u_0, K)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(f\"The exact solution is u = cos t + {u_0-1:0.3} exp(-{K} t)\")\n",
    "plot(t, u, \"g\", label=f\"Exact solution for {K=}\")\n",
    "plot(t, U, '.:b', label=f\"Euler's answer for h={(b-a)/n:0.3}\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variable Time Step Sizes $h_i$ (just a preview)\n",
    "\n",
    "It is sometime useful to adjust the time step size; for example reducing it when the derivative is larger,\n",
    "(as happens in Example 3 above).\n",
    "This gives a slight variant, now expressed in pseudo-code:\n",
    "\n",
    "Input: $f$, $a$, $b$, $n$ <br>\n",
    "$t_0 = a$ <br>\n",
    "$U_0 = u_0$ <br>\n",
    "for i from 1 to n <br>\n",
    "$\\quad$ Choose $h_i$ somehow <br>\n",
    "$\\quad t_{i} = t_{i-1} + h_i$ <br>\n",
    "$\\quad U_{i} = U_{i-1} + h_i f(t_{i-1}, U_{i-1})$ <br>\n",
    "end\n",
    "\n",
    "In a later section, we will see how to estimate errors within an algorithm,\n",
    "and then how to use such error estimates to guide the choice of step size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error Analysis for the Canonical Test Case, $u' = K u$.\n",
    "\n",
    "A great amount of intuition about numerical methods for solving ODE IVPs comes from that \"simplest nontrivial example\", number 2 above.\n",
    "We can solve it with constant step size $h$, and thus study its errors and accuracy.\n",
    "The recursion relation is now\n",
    "\n",
    "$$U_{i} = U_{i-1} + h K U_{i-1} = U_{i-1} (1 + hk),$$\n",
    "\n",
    "with solution\n",
    "\n",
    "$$U_i = u_0 (1 + hk)^i$$\n",
    "\n",
    "For comparison, the exact solution of this ODE IVP is\n",
    "\n",
    "$$u(t_i) = u_0 e^{K(t_i - a)} = u_0 e^{K ih} = u_0 (e^{kh})^i$$\n",
    "\n",
    "So each is a geometric series: the difference is that the *growth factor* is $G = (1 + hk)$ for Euler's method,\n",
    "vs $g = e^{kh} = 1 + hk + (hk)^2/2 + \\cdots = 1 + hk + O(h^2)$ for the ODE.\n",
    "\n",
    "Ths deviation at each time step is $O(h^2)$, suggesting that by the end $t=b$, at step $n$, the error will be\n",
    "$O(n h^2) = O\\left(\\displaystyle\\frac{b-a}{h} h^2\\right) = O(h)$.\n",
    "\n",
    "This is in fact what happens, but to verify that, we must deal with the challenge that once an error enters at one step, it is potentially amplified at each subsequent step, so the errors introduced at each step do not simply get summed like they did with definite integrals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Error and Local (Truncation) Error\n",
    "\n",
    "Ultimately, the error we need to understand is the **global error**: at step $i$,\n",
    "\n",
    "$$ E_i = u(t_i) - U_i $$\n",
    "\n",
    "We will approach this by first considering the new error added at each step, the **local truncation error** (or **discretization error**).\n",
    "\n",
    "At the first step this is the same as above:\n",
    "\n",
    "$$ e_1 = u(t_1) - U_1 = u(a+h) - U_1 $$\n",
    "\n",
    "However at later steps we compare the results $U_{i+1}$ to what the solution would be if it were exact at the start of that step: that is, if $U_i$ were exact.\n",
    "\n",
    "Using the notation $u(t; t_i, U_i)$ introduced <a href=\"#IVP_notation\">above</a> for the solution of the ODE with initial condition $u(t_i) = U_i$, the **location truncation error** at step $i$ is the discrepancy at time $t_{i+1}$ between what Euler's method and the exact solution give when both start at that point $(t_i, U_i)$:\n",
    "\n",
    "$$ e_i = u(t; t_i, U_i) - U_{i+1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error propagation in $u' = K u$, $K \\geq 0$.\n",
    "\n",
    "After one step, $E_1 = u(t_1) - U_1 = e_1$.\n",
    "\n",
    "At step 2,\n",
    "\n",
    "$$\n",
    "E_2 = u(t_2) - U_2 = (u(t_2) - u(t_2, t_1, U_1) + (u(t_2, t_1, U_1) - U_2)\n",
    "= (u(t_2) - u(t_2, t_1, U_1) + e_2\n",
    "$$\n",
    "\n",
    "The first term is the difference at $t=t_2$ of two solutions with values at $t = t_1$ being $u(t_1)$ and $U_1$ respectively. As the ODE is linear and homogeneous, this is the solution of the same ODE with value at $t=t_1$ being $u(t_1) - U_1$, which is $e_1$:\n",
    "that solution is $e_1 e^{y(t - t_1}$, so at $t=t_2$ it is $e_1 e^{kh}$.\n",
    "Thus the global error after two steps is\n",
    "\n",
    "$$\n",
    "E_2 = e_2 + (e^{kh})e_1:\n",
    "$$\n",
    "\n",
    "the error from the previous step has been amplified by the growth factor $g = e^{kh}$:\n",
    "\n",
    "$$\n",
    "E_2 = e_2 + g e_1:\n",
    "$$\n",
    "\n",
    "This continues, so that\n",
    "\n",
    "$$\n",
    "E_3 = e_3 + g E_1 = e_3 + g (e_2 + g e_1) = e_3 + ge_2 + g^2 e_1\n",
    "$$\n",
    "\n",
    "and so on, leading to\n",
    "\n",
    "$$\n",
    "E_i = e_i + g e_{i-1} + g^2 e_{i-2} + \\cdots + g^{i-1} e_{1}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bounding the local truncation errors ...\n",
    "\n",
    "To get a bound on the global error from the formula above, we first need a bound on the local truncation errors $e_i$.\n",
    "\n",
    "Taylor's theorem gives $e^{kh} = 1 + kh + e^{K \\xi} (kh)^2/2$, $0 < \\xi < K h$, so\n",
    "\n",
    "$$\n",
    "e_i = U_i e^{kh} - U_i (1 + kh) = U_i (e^{K \\xi} h^2/2)\n",
    "$$\n",
    "\n",
    "and thus\n",
    "\n",
    "$$|e_i| \\leq |U_i| \\frac{e^{kh}}{2} h^2$$\n",
    "\n",
    "Also, since $1 + kh < e^{kh}$,\n",
    "$|U_i| < |u(t_i)| = |u_0| e^{K(t_i - a)},$\n",
    "and we only need this to the beginning of the last step, $i \\leq n-1$, for which\n",
    "\n",
    "$$\n",
    "|U_i| < |u_0| e^{K(b - h - a)}\n",
    "$$\n",
    "\n",
    "Thus\n",
    "\n",
    "$$\n",
    "|e_i| \\leq \\frac{|u_0| e^{K(b - h - a)} e^{kh}}{2} h^2 = \\frac{|u_0 e^{K(b - a)}|}{2} h^2\n",
    "$$\n",
    "\n",
    "That is,\n",
    "\n",
    "$$ |e_i| \\leq C h^2 \\text{ where } C := \\frac{|u_0 e^{K(b - a)}|}{2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ... and using this to complete the bound on the global truncation error\n",
    "\n",
    "Using this bound on the local errors $e_i$ in the above sum for the global error $E_i$,\n",
    "\n",
    "$$ | E_i | \\leq C h^2 (1 + g + \\cdots g^{i-1}) = C \\frac{g^i - 1}{g-1} h^2 $$\n",
    "\n",
    "Since $g^i = e^{K h i} = e^{K (t_i - a)}$ and the denominator $g - 1 = e^{kh} - 1 > K h$,\n",
    "we get\n",
    "\n",
    "$$\n",
    "| E_i | \\leq  C \\frac{e^{K (t_i - a)} - 1}{K h} h^2\n",
    "\\leq \\frac{|u_0 e^{K(b - a)}|}{2} \\frac{e^{K (t_i - a)} - 1}{K} h, = O(h)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this global error formula is bulilt from three factors:\n",
    "\n",
    "- The first is the constant\n",
    "$\\displaystyle \\frac{|u_0 e^{K(b - a)}|}{2}$\n",
    "which is roughly half of the maximum value of the exact solution over the interval $[a, b]$.\n",
    "\n",
    "- The second\n",
    "$\\displaystyle \\frac{e^{K (t_i - a)} - 1}{K}$\n",
    "depends on $t$, and \n",
    "\n",
    "- The third is $h$, showing the overall order of accuracy: the overall absolute error is $O(h)$, so first order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A more general error bound\n",
    "\n",
    "A very similar result applies to the solution $u(t; a, u_0)$ of the more general initial value problem\n",
    "\n",
    "$$ \\frac{du}{dt} = f(t, u), \\quad u(a) = u_0 $$\n",
    "\n",
    "so long as the function $f$ is \"somewhat well-behaved\" in that it satisfies a so-called *Lipschitz Condition*:\n",
    "that there is some constant $K$ such that\n",
    "\n",
    "$$ \\left| \\frac{\\partial F}{\\partial u}(t, u) \\right| \\leq K  $$\n",
    "\n",
    "for the relevant time values $a \\leq t \\leq b$.\n",
    "\n",
    "(**Aside:** As you might have seen in a course on differential equations, such a Lipschitz condition is necessary to even guarantee that the initial value problem has a unique solution, so it is a quite reasonable requirement.)\n",
    "\n",
    "Then this constant $K$ plays the part of the exponential growth factor $K$ above:\n",
    "\n",
    "first one shows that the local trunction error is bounded by\n",
    "\n",
    "$$ |e_i| \\leq C h^2 \\text{ where now } C := \\frac{|u_0 e^{K(b - a)}|}{2}; $$\n",
    "\n",
    "then calculating as above bounds the global truncation error with\n",
    "\n",
    "$$\n",
    "| E_i | \\leq \\frac{|u_0 e^{K(b - a)}|}{2} \\frac{e^{K (t_i - a)} - 1}{K} h, = O(h)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### There is much room for improvement\n",
    "\n",
    "As with definite integrals, this is not very impressive, so in the next section on\n",
    "{ref}`section-runge-kutta-methods`\n",
    "we will explore several widely used methods that improve to second order and then fourth order accuracy.\n",
    "Later, we will see how to get even higher orders."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But first, we can illustrate how this exponential growth of errors looks in some examples, and coapr the the better behaved errors in definite integrals.\n",
    "\n",
    "This will be done by looking at the effect of a small change in the initial value, to simulate an error that arises there."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error propagation for {prf:ref}`ode-integration`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.0\n",
    "b = 2*np.pi\n",
    "u_0 = 1.0  # Original value\n",
    "n = 100\n",
    "\n",
    "(t, U) = euler_method(f_1, a, b, u_0, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now \"perturb\" the initial value in all cases by this much:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_u_0 = 0.1\n",
    "\n",
    "(x, U_perturbed) = euler_method(f_1, a, b, u_0+delta_u_0, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = u_1(t, a, u_0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "title(\"The solution before perturbing $u(0)$ was $u = \\\\cos(x)$\")\n",
    "plot(t, u, \"g\", label=\"Original exact solution\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer before perturbation\")\n",
    "plot(t, U_perturbed, \".:r\", label=\"Euler's answer after perturbation\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This just shifts all the $u$ values up by the perturbation of $u_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error propagation for {prf:ref}`ode-simplest-genuine`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 1.0\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "u_0 = 1.0  # Original value\n",
    "delta_u_0 = 0.1\n",
    "n = 100\n",
    "\n",
    "(t, U) = euler_method(f_2, a, b, u_0, n)\n",
    "(t, U_perturbed) = euler_method(f_2, a, b, u_0+delta_u_0, n)\n",
    "u = u_2(t, a, u_0, K)\n",
    "\n",
    "figure(figsize=[12,6])\n",
    "title(\"The solution before perturbing $u(0)$ was $u = {u_0} \\\\, \\\\exp({K} \\\\, t)$\")\n",
    "plot(t, u, \"g\", label=\"Original exact solution\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer before perturbation\")\n",
    "plot(t, U_perturbed, \".:r\", label=\"Euler's answer after perturbation\")\n",
    "legend()\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graphing the error shows its exponential growth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,6])\n",
    "title(\"Error\")\n",
    "plot(t, u - U_perturbed, '.:')\n",
    "U_perturbed\n",
    "grid(True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{exercise-start}\n",
    ":label: eulers-method-exercise-1\n",
    "```\n",
    "Show that for the integration case $f(t, u) = f(t)$,\n",
    "[Euler's Method](#eulers-method)\n",
    "is the same as the composite left-hand endpoint rule,\n",
    "as in the section [Definite Integrals, Part 2](integrals-2-composite-rules.ipynb).\n",
    "```{exercise-end}\n",
    "```"
   ]
  }
 ],
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  "kernelspec": {
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