L08.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lecture 8 - Root finding: Bracketing methods\n",
    "\n",
    "C&C Example 5.3-5.5\n",
    "\n",
    "Bisection and false position method on function:\n",
    "\n",
    "$$v(t) = \\frac{gm}{c}(1 - e^{-ct/m})$$\n",
    "\n",
    "Given $m = 68.1$ kg, $t = 10$ s, $v(t) = 40$ m/s\n",
    "\n",
    "- Solve for $c$ using initial bracket $[12, 16]$\n",
    "- Plot $log(|f(x)|)$ vs. number of iterations $n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "m = 68.1\n",
    "t = 10\n",
    "v = 40\n",
    "g = 9.81\n",
    "\n",
    "def f(c):\n",
    "    return g*m/c * (1 - np.exp(-c*t/m)) - v  # set f(c) = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisection(f, xl, xu, tol=1e-8):\n",
    "    \n",
    "    # check for valid initial bracket\n",
    "    assert f(xl) * f(xu) < 0, 'Choose xl,xu such that f(xl) * f(xu) < 0'\n",
    "    err = 9999\n",
    "    errors = [] # store errors to plot later\n",
    "    \n",
    "    while err > tol:\n",
    "        xr = (xl + xu) / 2\n",
    "        test = f(xl) * f(xr)\n",
    "        if test < 0:\n",
    "            xu = xr\n",
    "        elif test > 0:\n",
    "            xl = xr\n",
    "        err = np.abs(f(xr))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return xr, errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of root: 14.8011\n",
      "Iterations: 28\n"
     ]
    }
   ],
   "source": [
    "xr, errors_b = bisection(f, 12, 16)\n",
    "\n",
    "print('Estimate of root: %0.4f' % xr)\n",
    "print('Iterations: %d' % len(errors_b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The false position method will be the same except for the `xr` update:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def falseposition(f, xl, xu, tol=1e-8):\n",
    "    \n",
    "    # check for valid initial bracket\n",
    "    assert f(xl) * f(xu) < 0, 'Choose xl,xu such that f(xl) * f(xu) < 0'\n",
    "    err = 9999\n",
    "    errors = [] # store errors to plot later\n",
    "    \n",
    "    while err > tol:\n",
    "        xr = xu - f(xu) * (xl - xu) / (f(xl) - f(xu))\n",
    "        test = f(xl) * f(xr)\n",
    "        if test < 0:\n",
    "            xu = xr\n",
    "        elif test > 0:\n",
    "            xl = xr\n",
    "        err = np.abs(f(xr))\n",
    "        errors.append(err)\n",
    "    \n",
    "    return xr, errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of root: 14.8011\n",
      "Iterations: 9\n"
     ]
    }
   ],
   "source": [
    "xr, errors_f = falseposition(f, 12, 16)\n",
    "\n",
    "print('Estimate of root: %0.4f' % xr)\n",
    "print('Iterations: %d' % len(errors_f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The false position method converges faster for this problem. These implementations are not very robust. They should include a `maxiter` to catch cases where the iteration does not converge. We could have chosen a different stopping criteria based on the difference in `xr` values rather than the `f(xr)` value. Check root with scipy (docs [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.bisect.html)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.801135944990165"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.optimize as sopt\n",
    "sopt.bisect(f, 12, 16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "plt.semilogy(errors_b)\n",
    "plt.semilogy(errors_f)\n",
    "plt.ylabel('Log Error')\n",
    "plt.xlabel('Number of iterations')\n",
    "plt.legend(['Bisection', 'False Position'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Case Study 8.2 C&C\n",
    "Rain pH as a function of atmospheric CO2 concentration. Function defined below.\n",
    "\n",
    "Solve using bisection with initial bracket $[10^{-12}, 10^{-2}]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-27T04:05:57.254596Z",
     "start_time": "2020-03-27T04:05:57.176661Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of root: 2.34604E-06\n",
      "Iterations: 19\n",
      "pH = 5.63\n"
     ]
    }
   ],
   "source": [
    "KH = 10**-1.46\n",
    "K1 = 10**-6.3\n",
    "K2 = 10**-10.3\n",
    "Kw = 10**-14\n",
    "\n",
    "# Partial pressure of CO2 (ppm)\n",
    "# 1958: 315 ppm, 2003: 376 ppm, 2023: 423 ppm\n",
    "pCO2 = 315\n",
    "\n",
    "def f(H):\n",
    "    return K1*KH*pCO2/(H*1e6) + 2*K2*K1*KH*pCO2/(H**2*1e6) + Kw/H - H\n",
    "\n",
    "xr, errors_b = bisection(f, 1e-12, 1e-2)\n",
    "    \n",
    "print('Estimate of root: %0.5E' % xr)\n",
    "print('Iterations: %d' % len(errors_b))\n",
    "print('pH = %0.2f' % (-1*np.log10(xr)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using $p_{CO_2}=315$ ppm, we get `pH = 5.63`. Using the 2023 value $p_{CO_2}=423$ ppm, we get a lower value (more acidic), `pH = 5.57`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we try false position instead, it will be very slow to converge.\n",
    "```python\n",
    "xr, errors_f = falseposition(f, 1e-12, 1e-2)\n",
    "```\n",
    "Why? Let's look at the function over this bracket interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HAAAAAIDWE3igCYXeB3iiR+ABAAAAACADAg80wQQPAAAAAADtJPBAEwoJfzkmeAAAAAAAyILAA00omuABAAAAAKCNBB5oQj7f+0d4esoCDwAAAAAArSfwQBOKCYGnZIIHAAAAAIAMCDzQhHyu98DjFW0AAAAAAGRB4IEmJE3w9Ag8AAAAAABkQOCBJiR9g8cEDwAAAAAAWRB4oAmJEzxlgQcAAAAAgNYTeKAJhaQJnpLAAwAAAABA6wk80ISkwGOCBwAAAACALAg80ITECR7f4AEAAAAAIAMCDzQhn+s98JQEHgAAAAAAMiDwQBOKCRM8Ag8AAAAAAFkQeKAJeYEHAAAAAIA2EnigCSZ4AAAAAABoJ4EHmlBICjxlgQcAAAAAgNYTeKAJiYHHBA8AAAAAABkQeKAJhZzAAwAAAABA+wg80AQTPAAAAAAAtJPAA00QeAAAAAAAaCeBB5qQGHjKAg8AAAAAAK0n8EATTPAAAAAAANBOAg80QeABAAAAAKCdBB5oQiEn8AAAAAAA0D4CDzShWBB4AAAAAABoH4EHmpA3wQMAAAAAQBsJPNCEYtI3eMoCDwAAAAAArSfwQBPySYGnJPAAAAAAANB6Ag80oZD0ijYTPAAAAAAAZEDggSYUCr0Hnm7f4AEAAAAAIAMCDzQhaYKnR+ABAAAAACADAg80oZjwDR4TPAAAAAAAZEHggSbkEwJPhCkeAAAAAABaT+CBJiRN8ESY4gEAAAAAoPWK7X6ATrB3795YunRpvPjii/HKK6/EkCFD4thjj42JEyfGqFGjUt3rhRdeiF/96lfx8ssvx7Zt22LEiBExcuTImDx5cgwYMCDVvWidmhM8ZYEHAAAAAIDW6neB56/+6q/ivvvuqzo2cuTI+N3vftfwvTZt2hQzZ86M++67LzZv3tzrOZMnT47rr78+PvWpTzXzuBXz5s2Lm2++OZYvX97rz4cNGxaXXnppfOMb34ijjjqqT3vReiZ4AAAAAABop371iraHHnpov7jTrIULF8b48ePj9ttvT4w7ERHLli2LadOmxRVXXBHbt29veJ9t27bFZZddFtOnT0+MOxERmzdvjttvvz3Gjx8fixcvbngfspXPJQeeksADAAAAAECL9ZsJni1btsS1116byr0ee+yxmDp1auzZs6dyLJfLxSmnnBKjR4+OLVu2xKpVq+L111+v/Pyee+6Jt956Kx544IHI5+vrYqVSKS699NL42c9+VnX86KOPjokTJ8bhhx8ev/3tb2PVqlVR/v9e6/Xaa6/FhRdeGEuWLInTTz89hd+WVigWaryiTeABAAAAAKDF+s0Ez1e+8pV4+eWXIyLisMMOa/o+L730Ulx88cVVcWfKlCmxZs2aWLFiRcydOzcefvjheOmll+KWW26p+i7Oj3/847jhhhvq3utrX/taVdwZMGBA3HrrrfHSSy/F4sWLY+7cufHLX/4yVq9eHZMmTaqct3v37pg6dWq88sorTf+etFahxgSPV7QBAAAAANBq/SLwLFmyJL7//e9HRESxWIxvfOMbTd9r5syZ8eabb1bWkydPjiVLlsS4ceOqzjvkkEPiS1/6UsydO7fq+M033xwbNmw44D7r16+PW265perY/fffH9ddd110dXVVHT/ppJPikUceqYo8b7zxRsyaNavu34tsFWp8g6enLPAAAAAAANBaHR94tm/fHn/9139dWV9//fXxgQ98oKl7rV27Nu6+++7KuqurK2bPnh0DBw5MvGbq1Klx5ZVXVta7d++uK7zMmjUr9u7dW1nPmDEjLrzwwsTzBw0aFLNnz66KP3fddVesX7/+gHuRvVqBxwQPAAAAAACt1vGB5+tf/3r87ne/i4iI0aNHx4033tj0vebMmROlUqmyvvjii2Ps2LEHvO6rX/1q1Xru3Lmxa9euxPN37twZ8+bNq3mP3rz3ve+NqVOnVtbd3d0xZ86cA15H9mpO8Ag8AAAAAAC0WEcHnmXLlsV3v/vdyvqOO+6IQYMGNX2/BQsWVK2vuuqquq4bN25cfPjDH66st2/fHg8//HDi+YsXL44dO3ZU1pMmTYr3ve99de217zPNnz+/ruvIlgkeAAAAAADaqWMDz+7du+Mzn/lM9PT0RETElVdeGWeffXbT93v11VfjqaeeqqyLxWJMmTKl7uvPPPPMqvXChQsTz120aFHNa2s544wzolgsVtarVq2K1157re7ryUatwFMSeAAAAAAAaLGODTw33nhj/OY3v4mIiKOPPjr+1//6X3263+rVq6vWEyZMiMGDB9d9/eTJk6vWa9asqXuvSZMm1b3P4MGD4/3vf3/de9EehZzAAwAAAABA+3Rk4Fm5cmX8z//5Pyvrf/qnf4ojjzyyT/d85plnqtYnnnhiQ9ePGTOm5v3e6dlnn81sL9rDBA8AAAAAAO3UcYGnu7s7PvOZz0R3d3dERJx33nlx+eWX9/m+69atq1off/zxDV0/cuTIqvUbb7wRb7755n7nbd68OTZv3tynvfY9f+3atQ1dT+sJPAAAAAAAtFPxwKdk69vf/nblWzmDBw+O22+/PZX7btmypWo9fPjwhq4fMmRIDBw4MHbt2lU5tnXr1hg6dGjNfQ499NCGXgXX27Nt3bq1oetr2bhxY2zatKmha/aNYxwg8JQFHgAAAAAAWqujAs8zzzwT3/zmNyvrm266KUaNGpXKvbdt21a1HjRoUMP3GDRoUFXgefvtt1u2zzv1tk+zvve978WsWbNSu9/BqvYET0+GTwIAAAAAwMGoY17R1tPTE1dffXXs3r07IiI++MEPxpe+9KXU7r9veBk4cGDD99g3vOx7zyz3ob0KuVqBJ8MHAQAAAADgoNQxgeeWW26JX/ziFxERUSwW4//8n/8ThUKhZfvlavwDfX+8hmzVmuDpNsEDAAAAAECLdcQr2tavXx833HBDZX399dfHBz7wgVT3GDJkSNV6586dDd9j32v2vWeW+zTr85//fEyfPr2ha9atWxdTp05N7Rn+FORyucjnInp6+dyOvgMAAAAAQKu1PfCUy+X467/+69ixY0dERIwePTpuvPHG1PcReP5g+PDhMXz48NTudzAr5vOxp5f3sZngAQAAAACg1dr+irY777wz/u3f/q2yvuOOO/b7Bk0aDj/88Kr1pk2bGrp+27Zt+4WXI4444oD77NixI7Zv397QXhs3bjzgPrRfPuGvp6fcy1gPAAAAAACkqO0TPDNnzqz87+eff36ceOKJ8bvf/a7mNa+++mrVuru7e79rjj322Ojq6qqsx44dW/XzDRs2NPSc+54/bNiwGDp06H7nHXnkkTF06NB48803K8defPHFGDduXNN77fvsdIZiPh8R+0/r9DLUAwAAAAAAqWp74HnnVMzPfvazOOGEExq+x+9///v9rlu1alXVd3z2DSzr1q1raI/169dXrU866aTEc8eNGxfLli2r2quRwLPvXo1cS3byud6Pl7yiDQAAAACAFmv7K9qyMn78+Kr1008/XfnuTz2WLl1a8361frZ8+fK699m+fXs8/fTTde9F+xQLvf/5mOABAAAAAKDVDprAM2LEiJgwYUJl3d3dHU888UTd1z/22GNV649//OOJ55533nk1r63l8ccfj+7u7sp64sSJ8e53v7vu68lOPtf7CE+3CR4AAAAAAFqs7YFny5YtUS6XG/rv0UcfrbrHyJEj9zvnna9n+6OLLrqoav2DH/ygrmd87rnn4sknn6ysBw8eHOecc07i+eeee24MGjSosl6+fHk899xzde01e/bsqvW+z0znKCa8o62nXM74SQAAAAAAONi0PfBk6dOf/nQUCoXKev78+bF27doDXved73ynan3JJZfEwIEDE88/9NBDY9q0aTXv0Zvnn38+FixYUFkXi8W4/PLLD3gd7VFICDzdJYEHAAAAAIDWOqgCz9ixY+PKK6+srPfs2RMzZsyIXbt2JV7z4IMPVk3VdHV1xcyZMw+414033hgDBgyorGfPnh0PPfRQ4vm7du2Kq666Kvbs2VM5dvXVV8eYMWMOuBftkRR4TPAAAAAAANBqB1XgiYiYNWtWDB06tLJetmxZnH322fu9Qm337t1x6623xvTp06uOf+UrX4mRI0cecJ/Ro0fHl7/85apj06ZNi9tuu60q4kREPPvss3HWWWfFsmXLKseOPPLIukIS7ZM4wdMj8AAAAAAA0FrFdj9A1t7znvfE/Pnz49xzz62ElqVLl8ZJJ50UH/zgB2P06NGxdevWWLlyZWzatKnq2gsuuCBuuummuvf69re/HWvWrImFCxdGRMTevXvji1/8Ytx0001xyimnxGGHHRbr16+PlStXRvkdUx9dXV2xYMGCGDFiRAq/Ma2S0HeiR+ABAAAAAKDFDrrAExFx5plnxoIFC2LGjBmViFMul2PFihWxYsWKXq+57LLL4s4776z6hs+BFAqFmDt3blxzzTVx3333VY5v3LgxFi1a1Os1w4cPj7vvvjvOOOOMBn4j2qGY730AzgQPAAAAAACtdtC9ou2Pzj///Fi9enV87nOfq3pl275OO+20mDdvXsyZMycGDx7c8D5DhgyJe++9N+6///447bTTEs8bNmxYXHvttbF69eo477zzGt6H7OUTRnhKAg8AAAAAAC3WLyd4zjzzzKpXmjVr+PDhcfvtt8ctt9wSS5cujQ0bNsSrr74agwcPjuOOOy4mTpwYJ5xwQgpP/Ifv70ybNi1eeOGFWLlyZbz88suxffv2OOaYY2LkyJExZcqU6OrqSmUvslEUeAAAAAAAaJN+GXjS1tXVFR/96Ecz2euEE05ILRrRXokTPCnERwAAAAAAqOWgfUUb9FXiBE9J4AEAAAAAoLUEHmhSIWeCBwAAAACA9hB4oEkF3+ABAAAAAKBNBB5oksADAAAAAEC7CDzQpMTA4xVtAAAAAAC0mMADTUoMPCWBBwAAAACA1hJ4oEkmeAAAAAAAaBeBB5pUyPkGDwAAAAAA7SHwQJMKBYEHAAAAAID2EHigSSZ4AAAAAABoF4EHmlRM+gaPwAMAAAAAQIsJPNCkvMADAAAAAECbCDzQpMRXtJUFHgAAAAAAWkvggSYVCr0Hnm4TPAAAAAAAtJjAA01KmuDpEXgAAAAAAGgxgQeaVEj4Bo8JHgAAAAAAWk3ggSYlBR4TPAAAAAAAtJrAA00qmuABAAAAAKBNBB5oUj5pgqcs8AAAAAAA0FoCDzQpaYKnZIIHAAAAAIAWE3igSfmcV7QBAAAAANAeAg80KWmCp0fgAQAAAACgxQQeaFLSN3hM8AAAAAAA0GoCDzQpcYKnLPAAAAAAANBaAg80qZA0wVMSeAAAAAAAaC2BB5qUFHhM8AAAAAAA0GoCDzQpcYLHN3gAAAAAAGgxgQealDjBI/AAAAAAANBiAg80qZAzwQMAAAAAQHsIPNCkfMIET0ngAQAAAACgxQQeaFJR4AEAAAAAoE0EHmhS0jd4SmWBBwAAAACA1hJ4oEmJgccEDwAAAAAALSbwQJMKOYEHAAAAAID2EHigSSZ4AAAAAABoF4EHmiTwAAAAAADQLgIPNCkx8JQFHgAAAAAAWkvggSaZ4AEAAAAAoF0EHmhSrcBTNsUDAAAAAEALCTzQpEKu98ATEWGIBwAAAACAVhJ4oEnFQnLg8Zo2AAAAAABaSeCBJuVrTPAIPAAAAAAAtJLAA00q5pP/fEq+wQMAAAAAQAsJPNCkGn0nSiWBBwAAAACA1hF4oEkmeAAAAAAAaBeBB5pUqPHX093Tk92DAAAAAABw0BF4oEn5XC7xZ/oOAAAAAACtJPBAk2q9os0EDwAAAAAArSTwQJNq9B0TPAAAAAAAtJTAA00ywQMAAAAAQLsIPNCkmhM85XJ2DwIAAAAAwEFH4IEm1Z7gEXgAAAAAAGgdgQeaVMjlEn9WEngAAAAAAGghgQeaVCgkBx6f4AEAAAAAoJUEHmhSrQmeboUHAAAAAIAWEnigSYV8jQmesle0AQAAAADQOgIPNKlW4OkuCTwAAAAAALSOwANNqtF3omSCBwAAAACAFhJ4oEm5XC5xiqfUI/AAAAAAANA6Ag/0gcADAAAAAEA7CDzQB4WcwAMAAAAAQPYEHuiDogkeAAAAAADaQOCBPsgLPAAAAAAAtIHAA32Q+A2essADAAAAAEDrCDzQB4mBxwQPAAAAAAAtJPBAHxRyAg8AAAAAANkTeKAPkiZ4ugUeAAAAAABaSOCBPkgKPD0CDwAAAAAALSTwQB8UTfAAAAAAANAGAg/0QT5pgqcs8AAAAAAA0DoCD/RB0gRPyQQPAAAAAAAtJPBAH+RzAg8AAAAAANkTeKAPigWBBwAAAACA7Ak80AdJEzzdAg8AAAAAAC0k8EAfJH2Dp0fgAQAAAACghQQe6IN8QuAxwQMAAAAAQCsJPNAHiRM8ZYEHAAAAAIDWEXigDwomeAAAAAAAaAOBB/ogKfD4Bg8AAAAAAK0k8EAfFHImeAAAAAAAyJ7AA32QT5jgKQk8AAAAAAC0kMADfVAUeAAAAAAAaAOBB/ogcYKnLPAAAAAAANA6Ag/0QeIET0ngAQAAAACgdQQe6INCzgQPAAAAAADZE3igDwq+wQMAAAAAQBsIPNAHAg8AAAAAAO0g8EAfJAYer2gDAAAAAKCFBB7og8TAUxJ4AAAAAABoHYEH+sAEDwAAAAAA7SDwQB8Ucr7BAwAAAABA9gQe6INCQeABAAAAACB7Ag/0gQkeAAAAAADaQeCBPigmfYNH4AEAAAAAoIUEHuiDvMADAAAAAEAbCDzQB4kTPGWBBwAAAACA1hF4oA+SJni6TfAAAAAAANBCAg/0QSHXe+DpEXgAAAAAAGghgQf6oGCCBwAAAACANhB4oA+SAo8JHgAAAAAAWknggT4oJk7w9GT8JAAAAAAAHEwEHuiDfNIEjwEeAAAAAABaSOCBPjDBAwAAAABAOwg80Af5XNI3eDJ+EAAAAAAADioCD/RBsdB74Cl5RxsAAAAAAC0k8EAfJE3wdAs8AAAAAAC0kMADfVDM9/4n1FMWeAAAAAAAaB2BB/qgkPAX1F3yER4AAAAAAFpH4IE+KCRO8GT8IAAAAAAAHFQEHuiDxAmeHhM8AAAAAAC0jsADfZA4waPvAAAAAADQQgIP9EEhl+v1uAkeAAAAAABaSeCBPijkew88PeWIctmHeAAAAAAAaA2BB/ogKfBERJR6BB4AAAAAAFpD4IE+KNT4CyqZ4AEAAAAAoEUEHuiDQj75T8gEDwAAAAAArSLwQB8Ucl7RBgAAAABA9gQe6APf4AEAAAAAoB0EHugDgQcAAAAAgHYQeKAPBB4AAAAAANpB4IE+qBl4ygIPAAAAAACtIfBAHxRN8AAAAAAA0AYCD/RBXuABAAAAAKANBB7oAxM8AAAAAAC0g8ADfZDPCTwAAAAAAGRP4IE+qDnBUxZ4AAAAAABoDYEH+qDWN3i6SwIPAAAAAACtIfBAH9Sa4OkxwQMAAAAAQIsIPNAHhVoTPL7BAwAAAABAiwg80Ae1Ak+PwAMAAAAAQIsIPNAHhZwJHgAAAAAAsifwQB/kTfAAAAAAANAGAg/0UTEh8pjgAQAAAACgVQQe6KOkKZ5SWeABAAAAAKA1BB7oo6QJnlJJ4AEAAAAAoDUEHuijQs4EDwAAAAAA2RJ4oI8KhYTA4xs8AAAAAAC0iMADfZQ4wSPwAAAAAADQIgIP9FEh4Rs8PV7RBgAAAABAiwg80EdJgae7JPAAAAAAANAaAg/0UVLgKZngAQAAAACgRQQe6KPEwOMbPAAAAAAAtIjAA30k8AAAAAAAkDWBB/qokBN4AAAAAADIlsADfWSCBwAAAACArAk80EcCDwAAAAAAWRN4oI+KSYGnLPAAAAAAANAaAg/0Ud4EDwAAAAAAGRN4oI8KOYEHAAAAAIBsFdv9AL3ZuXNnPPfcc7Fhw4Z4+eWX4+233469e/fGu971rjjyyCNj/PjxcfLJJ0exmM7j7927N5YuXRovvvhivPLKKzFkyJA49thjY+LEiTFq1KhU9vijF154IX71q1/Fyy+/HNu2bYsRI0bEyJEjY/LkyTFgwIBU9yIbSd/g6RZ4AAAAAABokY4JPD/4wQ/i3/7t3+LJJ5+M3/72t9HT01Pz/CFDhsQll1wSX/ziF+MDH/hAU3tu2rQpZs6cGffdd19s3ry513MmT54c119/fXzqU59qao8/mjdvXtx8882xfPnyXn8+bNiwuPTSS+Mb3/hGHHXUUX3ai2wlBZ4egQcAAAAAgBbpmFe0/ff//t/jX/7lX2Lt2rUHjDsREdu2bYvvf//7ceqpp8bf/M3fRHd3d0P7LVy4MMaPHx+33357YtyJiFi2bFlMmzYtrrjiiti+fXtDe/zxOS+77LKYPn16YtyJiNi8eXPcfvvtMX78+Fi8eHHD+9A+JngAAAAAAMhax0zw7OvQQw+NMWPGxPHHHx/vete7oqenJzZv3hy//vWv49VXX62cVyqV4p/+6Z/id7/7XcybNy8KhcIB7/3YY4/F1KlTY8+ePZVjuVwuTjnllBg9enRs2bIlVq1aFa+//nrl5/fcc0+89dZb8cADD0Q+X18XK5VKcemll8bPfvazquNHH310TJw4MQ4//PD47W9/G6tWrYpy+Q8x4LXXXosLL7wwlixZEqeffnpd+9BeiRM8ZYEHAAAAAIDW6JjAM3jw4PjkJz8ZH//4x2Py5Mkxfvz4xJDyi1/8Im644YZ45JFHKsceeOCBuPnmm+Pv/u7vau7z0ksvxcUXX1wVd6ZMmRJ33nlnjBs3rnJs9+7dcccdd8Tf/u3fxt69eyMi4sc//nHccMMN8a1vfauu3+lrX/taVdwZMGBA3HzzzfHZz342urq6KsefeeaZuOaaayoTPrt3746pU6fGr3/96xgxYkRde9E+xYTAUzLBAwAAAABAi3TMK9pWr14dDz74YHzuc5+LCRMm1JySOe200+Lhhx+OK664our4P/zDP8Tu3btr7jNz5sx48803K+vJkyfHkiVLquJORMQhhxwSX/rSl2Lu3LlVx2+++ebYsGHDAX+f9evXxy233FJ17P7774/rrruuKu5ERJx00knxyCOPxKRJkyrH3njjjZg1a9YB96H98jmBBwAAAACAbHVM4BkwYEBD5+fz+fjud78bgwcPrhzbunVrPProo4nXrF27Nu6+++7KuqurK2bPnh0DBw5MvGbq1Klx5ZVXVta7d++uK7zMmjWrMvkTETFjxoy48MILE88fNGhQzJ49uyr+3HXXXbF+/foD7kV7FQsCDwAAAAAA2eqYwNOMd73rXft9p2bdunWJ58+ZMydKpVJlffHFF8fYsWMPuM9Xv/rVqvXcuXNj165diefv3Lkz5s2bV/MevXnve98bU6dOray7u7tjzpw5B7yO9kqa4OkWeAAAAAAAaJF+HXgiIoYNG1a1fvvttxPPXbBgQdX6qquuqmuPcePGxYc//OHKevv27fHwww8nnr948eLYsWNHZT1p0qR43/veV9de+z7T/Pnz67qO9kn6Bk+PwAMAAAAAQIv0+8Cz7/dwjj322F7Pe/XVV+Opp56qrIvFYkyZMqXufc4888yq9cKFCxPPXbRoUc1raznjjDOiWCxW1qtWrYrXXnut7uvJXj4h8JjgAQAAAACgVfp14Hn++efjySefrKxzuVx85CMf6fXc1atXV60nTJhQ9f2eA5k8eXLVes2aNYnn7rvXpEmT6t5n8ODB8f73v7/uvWi/xAmessADAAAAAEBr9NvA88orr8T06dOrvqkzbdq0GDVqVK/nP/PMM1XrE088saH9xowZU/N+7/Tss89mthftVzDBAwAAAABAxooHPqUzdHd3x5tvvhnPPvts/OQnP4k77rgj3nrrrcrPR48eHbfddlvi9evWrataH3/88Q3tP3LkyKr1G2+8EW+++WYMHTq06vjmzZtj8+bNfdpr3/PXrl3b0PVkKynw+AYPAAAAAACt0rGB57/8l/8St9xyS13nfvSjH40f/vCHMXz48MRztmzZUrWudW5vhgwZEgMHDoxdu3ZVjm3dunW/wLPvPoceemhDr4Lr7dm2bt3a0PW1bNy4MTZt2tTQNfvGMaoVckkTPD0ZPwkAAAAAAAeLjg089fjkJz8ZX/jCF+Kcc8454Lnbtm2rWg8aNKjh/QYNGlQVeN5+++2W7fNOve3TrO9973sxa9as1O5HRCHf+5sOS/oOAAAAAAAt0q8Dz8KFC6NUKsXAgQPjz//8z2ueu294GThwYMP7DRo0KN58883Ee6a5T6170lkKCV+yKpngAQAAAACgRRL+abr9/v7v/z5eeOGFyn/PPPNMPP7443HrrbfGX/zFX0RExN69e+OnP/1pfOQjH4nrrrsuSqVS3ffPJbxWq79eQ/vkE77BU/IJHgAAAAAAWqRjJ3iGDRsWw4YN2+/46aefHtddd1088cQTccUVV8SGDRsiIuK73/1u7Ny5M+66665e7zdkyJCq9c6dOxt+pn2v2feeWe7TrM9//vMxffr0hq5Zt25dTJ06NbVn+FNTTAo8JngAAAAAAGiRjg08B3L66afHo48+Gv/hP/yHeOONNyIi4vvf/3588pOfjAsvvHC/8wWePxg+fHgMHz48tfsRUUiYuCr1GOEBAAAAAKA1OvYVbfU44YQT4u///u+rjv2P//E/ej338MMPr1pv2rSpob22bdu2X3g54ogjDrjPjh07Yvv27Q3ttXHjxgPuQ+co5Hv/MxJ4AAAAAABolX4deCIi/uqv/qpq/Ytf/CK2bNmy33ljx46tWv/x1W712vf8YcOGxdChQ/c778gjj9zv+IsvvtinvfZ9djpLIeGvSOABAAAAAKBV+n3gGT58eFVQ6enpiRdeeGG/88aNG1e1XrduXUP7rF+/vmp90kknJZ6b9l773o/OkjjBo+8AAAAAANAi/T7wREQMGDCgar179+79zhk/fnzV+umnn44dO3bUvcfSpUtr3q/Wz5YvX173Ptu3b4+nn3667r1ov+QJnp5sHwQAAAAAgINGvw88u3btitdff73q2Lvf/e79zhsxYkRMmDChsu7u7o4nnnii7n0ee+yxqvXHP/7xxHPPO++8mtfW8vjjj0d3d3dlPXHixF5/HzpH8jd4Mn4QAAAAAAAOGv0+8DzyyCPR845JiUMPPTSOO+64Xs+96KKLqtY/+MEP6trjueeeiyeffLKyHjx4cJxzzjmJ55977rkxaNCgynr58uXx3HPP1bXX7Nmzq9b7PjOdp5Dr/bgJHgAAAAAAWqVfB56enp646aabqo6dd9550dXV1ev5n/70p6NQKFTW8+fPj7Vr1x5wn+985ztV60suuSQGDhyYeP6hhx4a06ZNq3mP3jz//POxYMGCyrpYLMbll19+wOtor0LCO9pKPT7CAwAAAABAa3RE4Ln11lvjlVdeaeiavXv3xtVXX101WRMR8YUvfCHxmrFjx8aVV15ZWe/ZsydmzJgRu3btSrzmwQcfrJqq6erqipkzZx7w+W688caqbwPNnj07HnroocTzd+3aFVdddVXs2bOncuzqq6+OMWPGHHAv2quQ632ER+ABAAAAAKBVOiLw3HXXXTFmzJi44oor4sc//nG8/fbbiefu3LkzfvSjH8XEiRP3e53Zf/yP/zH+4i/+ouZes2bNiqFDh1bWy5Yti7PPPnu/V6jt3r07br311pg+fXrV8a985SsxcuTIA/5Oo0ePji9/+ctVx6ZNmxa33XZbVcSJiHj22WfjrLPOimXLllWOHXnkkXWFJNqvmE8IPGWBBwAAAACA1ii2+wH+aOfOnXHPPffEPffcE7lcLk488cQYNWpUHHHEEdHV1RVvv/12bNiwIZ555pnYu3fvftdfcMEFceeddx5wn/e85z0xf/78OPfccyuhZenSpXHSSSfFBz/4wRg9enRs3bo1Vq5cGZs2bdpvj31fCVfLt7/97VizZk0sXLgwIv4wdfTFL34xbrrppjjllFPisMMOi/Xr18fKlSuj/I4Y0NXVFQsWLIgRI0bUvRftk08KPCWBBwAAAACA1uiYwPNO5XI51q5dW9f3cQYNGhQ33HBD/N3f/V3VK9FqOfPMM2PBggUxY8aMSsQpl8uxYsWKWLFiRa/XXHbZZXHnnXdWfcPnQAqFQsydOzeuueaauO+++yrHN27cGIsWLer1muHDh8fdd98dZ5xxRt370F4meAAAAAAAyFpHvKLtzjvvjBtuuCEmTZoUhxxySF3XvO9974ubbropnn/++fiv//W/1h13/uj888+P1atXx+c+97mqV7bt67TTTot58+bFnDlzYvDgwQ3tERExZMiQuPfee+P++++P0047LfG8YcOGxbXXXhurV6+O8847r+F9aJ/ECR7f4AEAAAAAoEVy5XJnjRns3bs3nn322Vi/fn38/ve/j23btsXevXtjyJAh8a53vStGjRoVEydOrBllGrVnz55YunRpbNiwIV599dUYPHhwHHfccTFx4sQ44YQTUtsnIuKFF16IlStXxssvvxzbt2+PY445JkaOHBlTpkyJrq6uVPdKy5o1a2L8+PGV9erVq+Pkk09u4xN1lp/9+pX4/D0r9zs+9NABservz2nDEwEAAAAAkIV2/vt5x72ibcCAATFhwoSYMGFCZnt2dXXFRz/60Uz2OuGEE1KPRrRXPtf7BE+3CR4AAAAAAFqkI17RBv1ZIeEVbT0CDwAAAAAALSLwQB8VEwKPCR4AAAAAAFpF4IE+yidN8HTW560AAAAAAPgTIvBAH5ngAQAAAAAgawIP9FE+13vgKZcjyqZ4AAAAAABoAYEH+qhY6D3wRESUTPEAAAAAANACAg/0UdIET4TXtAEAAAAA0BoCD/RR0jd4IiJ6vKINAAAAAIAWEHigjwo1Ao8JHgAAAAAAWkHggT6qFXh6BB4AAAAAAFpA4IE+MsEDAAAAAEDWBB7oIxM8AAAAAABkTeCBPirkTPAAAAAAAJAtgQf6qNYET0ngAQAAAACgBQQe6COBBwAAAACArAk80EfFWoGnLPAAAAAAAJA+gQf6KG+CBwAAAACAjAk80EeFnMADAAAAAEC2BB7oo0JB4AEAAAAAIFsCD/SRCR4AAAAAALIm8EAfFWp8g6db4AEAAAAAoAUEHuijWoGnpyzwAAAAAACQPoEH+sgr2gAAAAAAyJrAA32Uz+ciqfEIPAAAAAAAtILAAykoJrymTeABAAAAAKAVBB5IQT5hhEfgAQAAAACgFQQeSIEJHgAAAAAAsiTwQAryCYGnW+ABAAAAAKAFBB5IQdIET09Z4AEAAAAAIH0CD6SgYIIHAAAAAIAMCTyQgqTA0yPwAAAAAADQAgIPpKCQM8EDAAAAAEB2BB5IQaFgggcAAAAAgOwIPJACEzwAAAAAAGRJ4IEU5BO+wVMqCzwAAAAAAKRP4IEUFJMCT6kn4ycBAAAAAOBgIPBACvIJr2grGeABAAAAAKAFBB5IQbGQEHh6TPAAAAAAAJA+gQdSUEia4NF3AAAAAABoAYEHUlBI+AZPT9k72gAAAAAASJ/AAylICjzdPsIDAAAAAEALCDyQgqTAUzLBAwAAAABACwg8kILEwNPjIzwAAAAAAKRP4IEUFPK9/ymV9B0AAAAAAFpA4IEUFHof4DHBAwAAAABASwg8kAITPAAAAAAAZEnggRQUEv6STPAAAAAAANAKAg+koJg0wVMuZ/wkAAAAAAAcDAQeSEE+3/tHeEo9Ag8AAAAAAOkTeCAFRYEHAAAAAIAMCTyQgnyu98DTLfAAAAAAANACAg+koJDwl9Qj8AAAAAAA0AICD6SgkO/9T8kEDwAAAAAArSDwQAoSJ3jKAg8AAAAAAOkTeCAFxaQJnpLAAwAAAABA+gQeSEE+l+v1uAkeAAAAAABaQeCBFBQLvQeekm/wAAAAAADQAgIPpCBpgqdb4AEAAAAAoAUEHkhBMe8VbQAAAAAAZEfggRTkEwJPd0ngAQAAAAAgfQIPpMAEDwAAAAAAWRJ4IAWFpAke3+ABAAAAAKAFBB5IQVLg6RF4AAAAAABoAYEHUlDImeABAAAAACA7Ag+kIGmCpyTwAAAAAADQAgIPpEDgAQAAAAAgSwIPpCAx8JQFHgAAAAAA0ifwQApM8AAAAAAAkCWBB1JQyAk8AAAAAABkR+CBFJjgAQAAAAAgSwIPpEDgAQAAAAAgSwIPpEDgAQAAAAAgSwIPpCAx8JQFHgAAAAAA0ifwQApM8AAAAAAAkCWBB1JQyAk8AAAAAABkR+CBFBQKAg8AAAAAANkReCAFJngAAAAAAMiSwAMpKCZ9g6cs8AAAAAAAkD6BB1KQTwg85XJEjykeAAAAAABSJvBACpImeCJM8QAAAAAAkD6BB1KQNMET4Ts8AAAAAACkT+CBFNSc4BF4AAAAAABImcADKcjnkgNPt8ADAAAAAEDKBB5IQbGQHHh6BB4AAAAAAFIm8EAKCiZ4AAAAAADIkMADKcjX+AZPT1ngAQAAAAAgXQIPpKBYI/CY4AEAAAAAIG0CD6QgX+MVbb7BAwAAAABA2gQeSEGxYIIHAAAAAIDsCDyQgkKNCZ6SwAMAAAAAQMoEHkhBocY3eHrKAg8AAAAAAOkSeCAFtQJPd0ngAQAAAAAgXQIPpMAEDwAAAAAAWRJ4IAU1J3h8gwcAAAAAgJQJPJCCWoGnJPAAAAAAAJAygQdSUMgJPAAAAAAAZEfggRSY4AEAAAAAIEsCD6Qgl8tFUuMReAAAAAAASJvAAykp5nv/cyqVBR4AAAAAANIl8EBKEvpOlHp6sn0QAAAAAAD+5Ak8kJJCrvd3tJX0HQAAAAAAUibwQEoKCR/hMcEDAAAAAEDaBB5ISXLgyfhBAAAAAAD4kyfwQEoKCR/h6TbBAwAAAABAygQeSEkh4a+pp1zO9kEAAAAAAPiTJ/BASopJEzwlgQcAAAAAgHQJPJCShL5jggcAAAAAgNQJPJCSpAmekk/wAAAAAACQMoEHUpLP9X681KPwAAAAAACQLoEHUpI8weMVbQAAAAAApEvggZTkE0Z4ugUeAAAAAABSJvBASooJgaenLPAAAAAAAJAugQdSYoIHAAAAAICsCDyQksQJHoEHAAAAAICUCTyQkkLOBA8AAAAAANkQeCAlBRM8AAAAAABkROCBlCQFHhM8AAAAAACkTeCBlOQTAk+pLPAAAAAAAJAugQdSUkwKPCWBBwAAAACAdAk8kJJ8zgQPAAAAAADZEHggJYkTPL7BAwAAAABAygQeSElB4AEAAAAAICMCD6QkKfD0eEUbAAAAAAApE3ggJUmBp7sk8AAAAAAAkC6BB1KS+Io2EzwAAAAAAKRM4IGUFHK+wQMAAAAAQDYEHkhJoSDwAAAAAACQDYEHUmKCBwAAAACArAg8kJLEb/AIPAAAAAAApEzggZQIPAAAAAAAZEXggZQUkwJPWeABAAAAACBdAg+kJG+CBwAAAACAjAg8kJLECR6BBwAAAACAlAk8kJJ8rvfA0y3wAAAAAACQMoEHUlJImODpEXgAAAAAAEiZwAMpSQo8JngAAAAAAEibwAMpSZzgKQs8AAAAAACkS+CBlBSTJnhKAg8AAAAAAOkSeCAl+ZwJHgAAAAAAsiHwQEqKhd4DT8k3eAAAAAAASJnAAylJmuAReAAAAAAASJvAAylJ+gZPySvaAAAAAABImcADKcknBJ7uksADAAAAAEC6BB5ISdIET48JHgAAAAAAUibwQEoKSRM8vsEDAAAAAEDKBB5ISVLg6RF4AAAAAABImcADKSnkTPAAAAAAAJANgQdSYoIHAAAAAICsCDyQEt/gAQAAAAAgK8V2P0BvSqVSrFu3Lp555pl4+eWXY+vWrXHIIYfE0KFDY8yYMXHqqafG4MGDU91z7969sXTp0njxxRfjlVdeiSFDhsSxxx4bEydOjFGjRqW61wsvvBC/+tWv4uWXX45t27bFiBEjYuTIkTF58uQYMGBAqnuRnaTAUyoLPAAAAAAApKtjAs+LL74Y8+fPjyVLlsTjjz8eb731VuK5hUIhPvaxj8V1110Xn/jEJ/q076ZNm2LmzJlx3333xebNm3s9Z/LkyXH99dfHpz71qT7tNW/evLj55ptj+fLlvf582LBhcemll8Y3vvGNOOqoo/q0F9lLDDwmeAAAAAAASFlHvKLt8ssvj5EjR8bf/M3fxE9/+tOacSfiDxM+ixYtigsuuCD+8i//Ml577bWm9l24cGGMHz8+br/99sS4ExGxbNmymDZtWlxxxRWxffv2hvfZtm1bXHbZZTF9+vTEuBMRsXnz5rj99ttj/PjxsXjx4ob3ob0KueTAUzbFAwAAAABAijpiguf555/v9fhxxx0XY8eOjXe/+93R3d0d69evj6eeeip6enoq5/zkJz+JP//zP4+f//znccwxx9S952OPPRZTp06NPXv2VI7lcrk45ZRTYvTo0bFly5ZYtWpVvP7665Wf33PPPfHWW2/FAw88EPl8fW2sVCrFpZdeGj/72c+qjh999NExceLEOPzww+O3v/1trFq1qhIBXnvttbjwwgtjyZIlcfrpp9f9O9FeSRM8ERE95YhC8o8BAAAAAKAhHTHB804TJ06MW2+9NdatWxcvvfRSPProo3HvvffGvHnzYuXKlfHiiy/GZz/72aprnn/++Zg+fXrdUxIvvfRSXHzxxVVxZ8qUKbFmzZpYsWJFzJ07Nx5++OF46aWX4pZbbqn6Ls6Pf/zjuOGGG+r+fb72ta9VxZ0BAwbErbfeGi+99FIsXrw45s6dG7/85S9j9erVMWnSpMp5u3fvjqlTp8Yrr7xS9160V63A4zVtAAAAAACkqSMCTy6Xi0984hPx//7f/4uVK1fGddddF2PGjOn13OOOOy7uuOOO+O53v1t1/Iknnoj77ruvrv1mzpwZb775ZmU9efLkWLJkSYwbN67qvEMOOSS+9KUvxdy5c6uO33zzzbFhw4YD7rN+/fq45ZZbqo7df//9cd1110VXV1fV8ZNOOikeeeSRqsjzxhtvxKxZs+r6nWg/gQcAAAAAgKx0ROC5//774yc/+UmceuqpdV/z+c9/Pj71qU9VHfvhD394wOvWrl0bd999d2Xd1dUVs2fPjoEDByZeM3Xq1Ljyyisr6927d9cVXmbNmhV79+6trGfMmBEXXnhh4vmDBg2K2bNnV8Wfu+66K9avX3/AvWi/moHHN3gAAAAAAEhRRwSeUaNGNXXdF77whar1o48+esBr5syZE6VSqbK++OKLY+zYsQe87qtf/WrVeu7cubFr167E83fu3Bnz5s2reY/evPe9742pU6dW1t3d3TFnzpwDXkf7meABAAAAACArHRF4mjVx4sSq9c6dO2PLli01r1mwYEHV+qqrrqprr3HjxsWHP/zhynr79u3x8MMPJ56/ePHi2LFjR2U9adKkeN/73lfXXvs+0/z58+u6jvYSeAAAAAAAyEq/DjzFYnG/Y3v27Ek8/9VXX42nnnqq6vopU6bUvd+ZZ55ZtV64cGHiuYsWLap5bS1nnHFG1e+2atWqeO211+q+nvYoCjwAAAAAAGSkXweedevWVa2LxWIcddRRieevXr26aj1hwoQYPHhw3ftNnjy5ar1mzZq695o0aVLd+wwePDje//73170XnSGfE3gAAAAAAMhGvw48+37j5tRTT418PvlXeuaZZ6rWJ554YkP7jRkzpub93unZZ5/NbC86Q7HG/++VygIPAAAAAADp6beBZ9u2bXHXXXdVHbvoootqXrPvxM/xxx/f0J4jR46sWr/xxhvx5ptv7nfe5s2bY/PmzX3aa9/z165d29D1ZK9G34lSSeABAAAAACA9+3/Epp/4+te/Hq+++mplfcQRR8Q111xT85otW7ZUrYcPH97QnkOGDImBAwfGrl27Kse2bt0aQ4cOrbnPoYce2tCr4Hp7tq1btzZ0fZKNGzfGpk2bGrpm3zBG70zwAAAAAACQlX4ZeBYsWBC33XZb1bF/+Id/iGHDhtW8btu2bVXrQYMGNbz3oEGDqgLP22+/3bJ93qm3fZrxve99L2bNmpXKvahWc4Knpye7BwEAAAAA4E9ev3tF21NPPRX/6T/9p6pj55xzTlx77bUHvHbf8DJw4MCG9983vOx7zyz3obPUnODRdwAAAAAASFG/CjwvvvhifOITn6iKHSNHjox/+Zd/iVwu1/D9/tSuob0KNf5v1m2CBwAAAACAFPWbV7Rt3LgxPvaxj8Xvf//7yrFjjjkm/vVf/zWOPvrouu4xZMiQqvXOnTsbfo59r9n3nlnu04zPf/7zMX369IauWbduXUydOjWV/f+UFQrJgUffAQAAAAAgTf0i8GzevDnOPvvseP755yvHjjrqqFiyZEmMHTu27vsIPBHDhw+P4cOHp3IvqpngAQAAAAAgKx3/iratW7fGOeecE7/+9a8rx4YOHRr/+q//GieffHJD9zr88MOr1ps2bWro+m3btu0XXo444ogD7rNjx47Yvn17Q3tt3LjxgPvQWWp8gid6yuXsHgQAAAAAgD95HR143n777TjvvPPil7/8ZeXYu971rli0aFF84AMfaPh++077bNiwoaHr9z1/2LBhMXTo0P3OO/LII/c7/uKLL/Zpr0YmlWiPYo3C010SeAAAAAAASE/HBp7t27fH+eefH7/4xS8qx4YMGRILFy6MD33oQ03dc9y4cVXrdevWNXT9+vXrq9YnnXRSZnvtez86Tz75DW1RMsEDAAAAAECKOjLw7Ny5My644IJ44oknKscOPfTQ+OlPfxqTJ09u+r7jx4+vWj/99NOxY8eOuq9funRpzfvV+tny5cvr3mf79u3x9NNP170XnSGXy0UhofKUegQeAAAAAADS03GBZ9euXfHJT34yHnvsscqxgQMHxkMPPRR//ud/3qd7jxgxIiZMmFBZd3d3V0WkA3nnM0VEfPzjH08897zzzqt5bS2PP/54dHd3V9YTJ06Md7/73XVfT/sUcgIPAAAAAACt11GBZ8+ePXHxxRfHkiVLKscOOeSQeOCBB+Kss85KZY+LLrqoav2DH/ygruuee+65ePLJJyvrwYMHxznnnJN4/rnnnhuDBg2qrJcvXx7PPfdcXXvNnj27ar3vM9O5kiZ4eryiDQAAAACAFHVM4Onu7o5LLrkkFi5cWDk2YMCAmDdvXpx77rmp7fPpT386CoVCZT1//vxYu3btAa/7zne+U7W+5JJLYuDAgYnnH3rooTFt2rSa9+jN888/HwsWLKisi8ViXH755Qe8js6QFHi6SwIPAAAAAADp6YjAUyqV4tOf/nQ8+OCDlWPFYjHuu+++uOCCC1Lda+zYsXHllVdW1nv27IkZM2bErl27Eq958MEHq6Zqurq6YubMmQfc68Ybb4wBAwZU1rNnz46HHnoo8fxdu3bFVVddFXv27Kkcu/rqq2PMmDEH3IvOYIIHAAAAAIAsdETg+cxnPhNz586tOvatb30rJk6cGL/73e8a+q9WqPmjWbNmxdChQyvrZcuWxdlnn73fK9R2794dt956a0yfPr3q+Fe+8pUYOXLkAfcZPXp0fPnLX646Nm3atLjtttuqIk5ExLPPPhtnnXVWLFu2rHLsyCOPrCsk0TkSJ3h8gwcAAAAAgBTlyuX2jxbkEj5M34xHH300zjzzzAOe99hjj8W5555bFVpyuVx88IMfjNGjR8fWrVtj5cqVsWnTpqrrLrjggnjggQeqXvNWS6lUir/8y7+sevVcRMTw4cPjlFNOicMOOyzWr18fK1eujHf+n6KrqyuWLFkSZ5xxRl37tNKaNWti/PjxlfXq1avj5JNPbuMTda7/8A9LYtPbu/c7fstffSAu/MBxbXgiAAAAAABapZ3/fl7MZJcOdOaZZ8aCBQtixowZlYhTLpdjxYoVsWLFil6vueyyy+LOO++sO+5ERBQKhZg7d25cc801cd9991WOb9y4MRYtWtTrNcOHD4+77767I+IOjSkkxMqSCR4AAAAAAFLUEa9oa5fzzz8/Vq9eHZ/73OeqXtm2r9NOOy3mzZsXc+bMicGDBze8z5AhQ+Lee++N+++/P0477bTE84YNGxbXXnttrF69Os4777yG96H9kl7RJvAAAAAAAJCmjpjgaedb4oYPHx6333573HLLLbF06dLYsGFDvPrqqzF48OA47rjjYuLEiXHCCSekste0adNi2rRp8cILL8TKlSvj5Zdfju3bt8cxxxwTI0eOjClTpkRXV1cqe9EeAg8AAAAAAFnoiMDTCbq6uuKjH/1oJnudcMIJqUUjOksxKfC0/1NXAAAAAAD8CTmoX9EGacub4AEAAAAAIAMCD6QocYJH4AEAAAAAIEUCD6QonxN4AAAAAABoPYEHUlQwwQMAAAAAQAYEHkhRUuDpFngAAAAAAEiRwAMpSgo8PQIPAAAAAAApEnggRSZ4AAAAAADIgsADKSrkEiZ4ygIPAAAAAADpEXggRcVC74GnZIIHAAAAAIAUCTyQonzCBI/AAwAAAABAmgQeSFEx4Rs8Ag8AAAAAAGkSeCBF+YTA0y3wAAAAAACQIoEHUpQ0wdNTFngAAAAAAEiPwAMpMsEDAAAAAEAWBB5IUeIEj8ADAAAAAECKBB5IUSFnggcAAAAAgNYTeCBFBRM8AAAAAABkQOCBFCUFHhM8AAAAAACkSeCBFCUFnlJZ4AEAAAAAID0CD6QoMfCUBB4AAAAAANIj8ECK8jkTPAAAAAAAtJ7AAykqJk3w+AYPAAAAAAApEnggRYmvaBN4AAAAAABIkcADKRJ4AAAAAADIgsADKRJ4AAAAAADIgsADKUoMPGWBBwAAAACA9Ag8kKJCzgQPAAAAAACtJ/BAigoFgQcAAAAAgNYTeCBFJngAAAAAAMiCwAMpSvwGj8ADAAAAAECKBB5IkcADAAAAAEAWBB5IUTEp8JQFHgAAAAAA0iPwQIryJngAAAAAAMiAwAMpSpzgEXgAAAAAAEiRwAMpyucEHgAAAAAAWk/ggRQVCwIPAAAAAACtJ/BAipImeLoFHgAAAAAAUiTwQIoKCd/g6SkLPAAAAAAApEfggRQVEwJPd6kn4ycBAAAAAOBPmcADKUp6RZs3tAEAAAAAkCaBB1JULCR9g8cEDwAAAAAA6RF4IEWJEzz6DgAAAAAAKRJ4IEXFfO9/UqWyd7QBAAAAAJAegQdSlNB3otRTjrLIAwAAAABASgQeSFHSBE9ERI++AwAAAABASgQeSFGhxl9Utw/xAAAAAACQEoEHUlSoNcGj7wAAAAAAkBKBB1JUyOUSf2aCBwAAAACAtAg8kKJCPjnw6DsAAAAAAKRF4IEU1Qo8JngAAAAAAEiLwAMpqhV4SuVyhk8CAAAAAMCfMoEHUlQz8PQIPAAAAAAApEPggRQVBR4AAAAAADIg8ECK8gIPAAAAAAAZEHggRYWcwAMAAAAAQOsJPJAi3+ABAAAAACALAg+kqGbgKQs8AAAAAACkQ+CBFNUKPN0lgQcAAAAAgHQIPJCiWoGnxwQPAAAAAAApEXggRUXf4AEAAAAAIAMCD6QonxN4AAAAAABoPYEHUmSCBwAAAACALAg8kKK8wAMAAAAAQAYEHkhZ0hRPqSzwAAAAAACQDoEHUpY0xdNtggcAAAAAgJQIPJCypAmeHoEHAAAAAICUCDyQskLOBA8AAAAAAK0l8EDKCgUTPAAAAAAAtJbAAykzwQMAAAAAQKsJPJCyQtI3eMoCDwAAAAAA6RB4IGVJgae7JPAAAAAAAJAOgQdSlk94RVvJBA8AAAAAACkReCBlxUJC4PENHgAAAAAAUiLwQMoKSRM8Ag8AAAAAACkReCBlSd/g6fGKNgAAAAAAUiLwQMqSAk93SeABAAAAACAdAg+kzAQPAAAAAACtJvBAyhIneHyDBwAAAACAlAg8kLKkwFMSeAAAAAAASInAAykr5AQeAAAAAABaS+CBlJngAQAAAACg1QQeSJnAAwAAAABAqwk8kLLEwFMWeAAAAAAASIfAAykzwQMAAAAAQKsJPJCyosADAAAAAECLCTyQsnxO4AEAAOD/1969h9lV1/fi/8zsmcllAuQCCSHokJsEiLQJRyQhCILcPD4mamK4VC5HBLVWaut5pPUSArXgOdZHihWpRxv8nXJv0NIDBFGxlGBrLpSTECAhFyEBciOYezIz6/dHfsyPPTN7Zu/Za+2ZPXm9nmeex++a9V3f79pmf1iz3/u7FgBAtgQ8kLK6nIAHAAAAAIBsCXggZYVW8DQLeAAAAAAASImAB1KWK/AMnlYBDwAAAAAAKRHwQMoKBTxW8AAAAAAAkBYBD6QsV+AWba2JgAcAAAAAgHQIeCBldbnOA54WK3gAAAAAAEiJgAdSVltgBY+ABwAAAACAtAh4IGV1BZ7BI+ABAAAAACAtAh5IWW2BgKdZwAMAAAAAQEoEPJCyQit4WhMBDwAAAAAA6RDwQMqs4AEAAAAAIGsCHkhZwRU8Ah4AAAAAAFIi4IGU5WoKreBprfBMAAAAAADorwQ8kLJcbedvK/kOAAAAAABpEfBAynIF3lVW8AAAAAAAkBYBD6Ss0AqeFo/gAQAAAAAgJQIeSFmhFTwtVvAAAAAAAJASAQ+krOAKHvkOAAAAAAApEfBAynI1nW+3ggcAAAAAgLQIeCBludrOE56WVg/hAQAAAAAgHQIeSFnhW7QJeAAAAAAASIeAB1KWK/CuakkEPAAAAAAApEPAAykrtILHI3gAAAAAAEiLgAdSVmgFT7OEBwAAAACAlAh4IGWFn8FT4YkAAAAAANBvCXggZbmamk63t1jBAwAAAABASgQ8kLJcbaGAJ6nwTAAAAAAA6K8EPJAyAQ8AAAAAAFkT8EDK6goFPImABwAAAACAdAh4IGW1VvAAAAAAAJAxAQ+krOAKHgEPAAAAAAApEfBAymprOg94WpOIxG3aAAAAAABIgYAHUlaX6zzgibCKBwAAAACAdAh4IGWFVvBERDQLeAAAAAAASIGAB1JW6Bk8ERGtbtEGAAAAAEAKBDyQslwXAY8VPAAAAAAApEHAAynr6hZtrQIeAAAAAABSIOCBlNXlrOABAAAAACBbAh5ImRU8AAAAAABkTcADKavr4hk8LYmABwAAAACA8gl4IGW5LgKe5hYBDwAAAAAA5RPwQMq6CnhareABAAAAACAFAh5IWZcreDyDBwAAAACAFAh4IGVdruAR8AAAAAAAkAIBD6QsV2MFDwAAAAAA2RLwQMpyucIBT4uABwAAAACAFAh4IGVdreAR8AAAAAAAkAYBD6Ssq2fwtCQCHgAAAAAAyifggZR1GfBYwQMAAAAAQAoEPJAyt2gDAAAAACBrAh5IWW1tTRTKeAQ8AAAAAACkQcADGagrcJs2AQ8AAAAAAGkQ8EAGagss4RHwAAAAAACQBgEPZCBnBQ8AAAAAABkS8EAGCgU8zQIeAAAAAABSIOCBDBQKeFoTAQ8AAAAAAOUT8EAG6tyiDQAAAACADAl4IAO1NQIeAAAAAACyI+CBDFjBAwAAAABAlgQ8kIFaAQ8AAAAAABkS8EAGCq7gSQQ8AAAAAACUT8ADGSi0gqfZCh4AAAAAAFJQ19sT6CsOHjwYTz/9dPzud7+L1157LYYMGRLHHXdcTJkyJU444YRUx1q3bl08++yzsWnTpti1a1eMHj06mpqaYvr06VFfX5/qWPSOQit4WgU8AAAAAACkoM8GPGvXro3f/va3sWTJkvjtb38by5Yti507d7b9vqmpKdavX1/2OFu2bIl58+bFfffdF9u3b+90n+nTp8ef/dmfxSc+8YmyxnrwwQfjO9/5TjzzzDOd/n748OExd+7cuOmmm+Loo48uayx6V22NFTwAAAAAAGSnTwU8Tz75ZNxyyy2xZMmSgmFLmh599NG46qqrYvPmzV3ut3jx4li8eHFcfvnlceedd0ZjY2NJ4+zatSs+85nPxL333tvlftu3b4877rgjFi5cGHfddVdceOGFJY1D31GXs4IHAAAAAIDs9KmA59lnn43HH3+8ImM9+eSTMWvWrDhw4EDbtpqampg6dWqMGzcuduzYEcuXL4+tW7e2/f4f//Ef4/e//3389Kc/jdra4h5f1NLSEnPnzo1HHnkkb/sxxxwTU6ZMiaOOOipefvnlWL58eSTJoQ//33jjjZg5c2Y88cQTMWPGjBTOlkrLWcEDAAAAAECGikspetmAAQNi/PjxqR3v1VdfjY9//ON54c6ZZ54ZK1eujCVLlsT9998fjz/+eLz66qtx22235T0X5+GHH46vfe1rRY91ww035IU79fX1cfvtt8err74aixYtivvvvz+WLl0aK1asiGnTprXtt3///pg1a1a89tprZZ4tvSFX6Bk8iYAHAAAAAIDy9bmAp76+Pv7wD/8wrrnmmrjzzjtj6dKlsXPnzvhf/+t/pTbGvHnz4s0332xrT58+PZ544ok46aST8vYbMGBAfPGLX4z7778/b/t3vvOd2LBhQ7fjrF27Nm677ba8bQ888EB84QtfiIaGhrztJ598cvziF7/IC3m2bdsW8+fPL/q86DsKBTzNLQIeAAAAAADK16cCniuvvDJ+//vfx/Lly+OHP/xhXHvttTF16tS8FTTlWr16ddx1111t7YaGhliwYEEMHDiwYJ9Zs2bFlVde2dbev39/UcHL/Pnz4+DBg23tq666KmbOnFlw/0GDBsWCBQvywp8f/ehHsXbt2m7Hom8pFPC0WMEDAAAAAEAK+lTAM2zYsC6DljTcfffd0dLS0tb++Mc/HhMnTuy231e+8pW89v333x/79u0ruP/evXvjwQcf7PIYnXnPe94Ts2bNams3NzfH3Xff3W0/+paCAU9ra4VnAgAAAABAf9SnAp5KeOihh/LaV199dVH9TjrppHj/+9/f1t69e3c8/vjjBfdftGhR7Nmzp609bdq0mDRpUlFjtZ/TwoULi+pH31FbUyjgqfBEAAAAAADolw6rgOf111+P//zP/2xr19XVxZlnnll0/3POOSev/eijjxbc97HHHuuyb1fOOuusqKura2svX7483njjjaL70/vqrOABAAAAACBDh1XAs2LFirz2qaeeGo2NjUX3nz59el575cqVRY81bdq0osdpbGyM9773vUWPRd9T+BZtFZ4IAAAAAAD90mEV8Dz//PN57QkTJpTUf/z48V0e751WrVpVsbHoewoFPK1JUuGZAAAAAADQHx1WAc+aNWvy2u9+97tL6t/U1JTX3rZtW7z55psd9tu+fXts3769rLHa77969eqS+tO7CgU8zW7RBgAAAABACg6rgGfHjh157ZEjR5bUf8iQITFw4MC8bW+99Va34wwePLikW8F1NrfOxqHvytV2/tZyizYAAAAAANJQ19sTqKRdu3bltQcNGlTyMQYNGhT79u1ra+/cuTOzcd6ps3F6YvPmzbFly5aS+rRf+UT3cp0v4IkWK3gAAAAAAEjBYR3wtF+NU4xBgwbl3Zat/THTHKerY/bU97///Zg/f34qx6IwK3gAAAAAAMjSYXWLtvZqagoss6jSPvQduQLvLCt4AAAAAABIw2EV8AwZMiSvvXfv3pKP0b5P+2NWchz6roIreJIKTwQAAAAAgH7psLpFm4An4vOf/3zMmTOnpD5r1qyJWbNmpTL+4cIKHgAAAAAAsnRYBTxHHXVUXnvLli0l9d+1a1eH4GXo0KHdjrNnz57YvXt3NDY2Fj3W5s2bux2nJ0aOHBkjR45M5VgUVlfwGTyW8AAAAAAAUL7D6hZtEydOzGtv2LChpP7t9x8+fHgMGzasw34jRozosP13v/tdWWO1nzt9W22BZygJeAAAAAAASMNhFfCcdNJJee01a9aU1H/t2rV57ZNPPrliY7U/Hn1bXU7AAwAAAABAdg6rgGfy5Ml57eeeey727NlTdP+nn366y+N19btnnnmm6HF2794dzz33XNFj0fcUWsHTLOABAAAAACAFh1XAM3r06Dj11FPb2s3NzfFv//ZvRfd/8skn89oXX3xxwX0vuuiiLvt25amnnorm5ua29pQpU2LUqFFF96f31dV2HvC0JgIeAAAAAADKd1gFPBERH/vYx/La//AP/1BUvxdeeCH+/d//va3d2NgYF1xwQcH9L7zwwhg0aFBb+5lnnokXXnihqLEWLFiQ124/Z/q+2gIBT3OLgAcAAAAAgPIddgHP5ZdfHrlcrq29cOHCWL16dbf9vvWtb+W1P/nJT8bAgQML7j948OCYPXt2l8fozEsvvRQPPfRQW7uuri4uu+yybvvRt+QK3KLNCh4AAAAAANJw2AU8EydOjCuvvLKtfeDAgbjqqqti3759Bfv87Gc/y1tV09DQEPPmzet2rBtvvDHq6+vb2gsWLIh//ud/Lrj/vn374uqrr44DBw60bfv0pz8d48eP73Ys+pa6nGfwAAAAAACQnT4X8Lz66quxfv36Dj+vv/563n7Nzc2d7rd+/frYunVrl2PMnz8/hg0b1tZevHhxfOhDH+pwC7X9+/fH7bffHnPmzMnb/ud//ufR1NTU7bmMGzcurr/++rxts2fPju9973t5IU5ExKpVq+K8886LxYsXt20bMWJEUUESfU9toRU8Ah4AAAAAAFJQ19sTaG/GjBmxYcOGbvfbuHFjjB07ttPfXXnllR2eY/NOxx9/fCxcuDAuvPDCtqDl6aefjpNPPjlOO+20GDduXLz11luxbNmy2LJlS17fj3zkI3HzzTcXfT633nprrFy5Mh599NGIiDh48GD8yZ/8Sdx8880xderUOOKII2Lt2rWxbNmySN5x+66GhoZ46KGHYvTo0UWPRd9RV+AZPC1u0QYAAAAAQAr6XMBTKeecc0489NBDcdVVV7WFOEmSxJIlS2LJkiWd9rn00kvjhz/8Yd4zfLqTy+Xi/vvvj2uuuSbuu+++tu2bN2+Oxx57rNM+I0eOjLvuuivOOuusEs6IvqS2QMDT3CLgAQAAAACgfH3uFm2V9OEPfzhWrFgRn/3sZ/Nu2dbeGWecEQ8++GDcfffd0djYWPI4Q4YMiXvvvTceeOCBOOOMMwruN3z48Pjc5z4XK1asiIsuuqjkceg7Cq3gabWCBwAAAACAFPS5FTzr16+v6HgjR46MO+64I2677bZ4+umnY8OGDfH6669HY2NjjBkzJqZMmVLwVnClmj17dsyePTvWrVsXy5Yti02bNsXu3bvj2GOPjaampjjzzDOjoaEhlbHoXQVX8HgGDwAAAAAAKehzAU9vaWhoiA9+8IMVGWvs2LGphUb0TQVX8Ah4AAAAAABIwWF9izbISq7GCh4AAAAAALIj4IEM5KzgAQAAAAAgQwIeyEChgMcKHgAAAAAA0iDggQwUXMGTCHgAAAAAACifgAcyYAUPAAAAAABZEvBABgoFPC0CHgAAAAAAUiDggQzkagQ8AAAAAABkR8ADGcjlBDwAAAAAAGRHwAMZsIIHAAAAAIAsCXggAwWfwZMIeAAAAAAAKJ+ABzJQKOBJkohWq3gAAAAAACiTgAcyUCjgibCKBwAAAACA8gl4IANdBjxW8AAAAAAAUCYBD2QgVyPgAQAAAAAgOwIeyIBbtAEAAAAAkCUBD2Sgy4CnRcADAAAAAEB5BDyQgToreAAAAAAAyJCABzJQ21XA4xk8AAAAAACUScADGehyBY+ABwAAAACAMgl4IAO1NQIeAAAAAACyI+CBDNTlBDwAAAAAAGRHwAMZyHWxgqdZwAMAAAAAQJkEPJCBXBfP4GlNBDwAAAAAAJRHwAMZ6CrgaW4R8AAAAAAAUB4BD2TACh4AAAAAALIk4IEMdLmCxzN4AAAAAAAok4AHMlBbUzjgaRHwAAAAAABQJgEPZKDOLdoAAAAAAMiQgAcy0OUt2loEPAAAAAAAlEfAAxmoqamJQhmPFTwAAAAAAJRLwAMZKbSKp9kzeAAAAAAAKJOABzJSKOBpFfAAAAAAAFAmAQ9kJFdjBQ8AAAAAANkQ8EBGCq3gaRHwAAAAAABQJgEPZETAAwAAAABAVgQ8kJFcbedvr5ZEwAMAAAAAQHkEPJCRXIF3V0tra2UnAgAAAABAvyPggYzUFVrBI98BAAAAAKBMAh7ISIF8xwoeAAAAAADKJuCBjFjBAwAAAABAVgQ8kJHams63W8EDAAAAAEC5BDyQkcIreJIKzwQAAAAAgP5GwAMZqS2whKdZwAMAAAAAQJkEPJCRXIF3V2si4AEAAAAAoDwCHshIruAt2io8EQAAAAAA+h0BD2Qk1/kd2qKlVcIDAAAAAEB5BDyQkToreAAAAAAAyIiABzJSIN+xggcAAAAAgLIJeCAjBVfwJEmFZwIAAAAAQH8j4IGM1NZ2/hCe5lYBDwAAAAAA5RHwQEbqCgQ8rQIeAAAAAADKJOCBjNTWWMEDAAAAAEA2BDyQESt4AAAAAADIioAHMpLzDB4AAAAAADIi4IGMFAp4WhMBDwAAAAAA5RHwQEYKruBpEfAAAAAAAFAeAQ9kpFDA02IFDwAAAAAAZRLwQEZyNQUCHs/gAQAAAACgTAIeyEguJ+ABAAAAACAbAh7IiBU8AAAAAABkRcADGSn4DB4BDwAAAAAAZRLwQEYKBTytiYAHAAAAAIDyCHggI4UCnmYreAAAAAAAKJOABzLiFm0AAAAAAGRFwAMZydUIeAAAAAAAyIaABzJiBQ8AAAAAAFkR8EBGBDwAAAAAAGRFwAMZKRjwJAIeAAAAAADKI+CBjFjBAwAAAABAVgQ8kJE6AQ8AAAAAABkR8EBGamsEPAAAAAAAZEPAAxmpywl4AAAAAADIhoAHMmIFDwAAAAAAWRHwQEYKPoMnEfAAAAAAAFAeAQ9kpLZAwNPcIuABAAAAAKA8Ah7ISKEVPK1W8AAAAAAAUCYBD2QkV2gFj2fwAAAAAABQJgEPZKS2psAKHgEPAAAAAABlEvBARgrdoq3FLdoAAAAAACiTgAcyUlso4GkR8AAAAAAAUB4BD2TECh4AAAAAALIi4IGMFFrB0+wZPAAAAAAAlEnAAxkptIKnVcADAAAAAECZBDyQkVyNFTwAAAAAAGRDwAMZyRVYwRNhFQ8AAAAAAOUR8EBGugp4rOIBAAAAAKAcAh7ISJcreBIBDwAAAAAAPSfggYxYwQMAAAAAQFYEPJCRrgKeFgEPAAAAAABlEPBARgQ8AAAAAABkRcADGakT8AAAAAAAkBEBD2SktkbAAwAAAABANgQ8kJG62sJvr5ZEwAMAAAAAQM8JeCAjXeQ70dIi4AEAAAAAoOcEPJCRXFfP4LGCBwAAAACAMgh4ICNdBjyewQMAAAAAQBkEPJCRXI2ABwAAAACAbAh4ICN1XTyER8ADAAAAAEA5BDyQkS7yHQEPAAAAAABlEfBARrpcwZMIeAAAAAAA6DkBD2Sk6xU8rZWbCAAAAAAA/Y6ABzLS9TN4KjgRAAAAAAD6HQEPZKS2pvDvmq3gAQAAAACgDAIeyEhNTU3kCqQ88h0AAAAAAMoh4IEM5Wo6D3is4AEAAAAAoBwCHshQwRU8SVLhmQAAAAAA0J8IeCBDhQKe5hYBDwAAAAAAPSfggQxZwQMAAAAAQBYEPJChgit4WgU8AAAAAAD0nIAHMlQo4GkR8AAAAAAAUAYBD2QoVyPgAQAAAAAgfQIeyJAVPAAAAAAAZEHAAxkqFPC0JgIeAAAAAAB6TsADGSoU8DRbwQMAAAAAQBkEPJChgit4BDwAAAAAAJRBwAMZytVYwQMAAAAAQPoEPJChQit4WgQ8AAAAAACUQcADGRLwAAAAAACQBQEPZKhgwJMIeAAAAAAA6DkBD2SoYMDTIuABAAAAAKDnBDyQISt4AAAAAADIgoAHMpSr8QweAAAAAADSJ+CBDNXlBDwAAAAAAKRPwAMZqrWCBwAAAACADAh4IEN1hZ7BI+ABAAAAAKAMAh7IUG2BgKdZwAMAAAAAQBkEPJChQit4WhMBDwAAAAAAPSfggQxZwQMAAAAAQBYEPJChXE2BFTwCHgAAAAAAyiDggQwVukVbi4AHAAAAAIAyCHggQ4Vu0SbgAQAAAACgHAIeyFDBFTyJgAcAAAAAgJ4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      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1e-12, 1e-2, 100)\n",
    "y = f(x)\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The false position method assumes that the root is located near the side of the bracket with a function value closer to zero. However, that is not the case here: the root $~10^{-6}$ is much closer to $f(x_l)$. This will cause slow convergence for the false position method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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