{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c6ee0a39-d53c-4748-adf7-2257fd1784a6",
   "metadata": {},
   "source": [
    "# Exercise\n",
    "\n",
    "The cosmological growth factor describes the rate of growth of dark matter perturbations in the Universe and is defined as \n",
    "\n",
    "$D(a) = \\large \\frac{5 \\Omega_m}{2} \\frac{H(a)}{H_0} \\int_0^a \\frac{da'}{ (a' H(a')/H_0)^3}$,\n",
    "\n",
    "where $a$ is the scale factor, $\\Omega_m$ is the matter density parameter and $H(a)$ is the Hubble rate. In a flat Universe, after radiation domination, we can write $H(a)$ as:\n",
    "\n",
    "$ E(a) = H(a)/H_0 = \\sqrt{(\\Omega_m a^{-3} + \\Omega_{\\Lambda})}$,\n",
    "\n",
    "where $\\Omega_\\Lambda$ is the vacuum energy density (in a flat Universe, $\\Omega_{\\Lambda} = 1 - \\Omega_m$).\n",
    "\n",
    "1) Write a code to calculate the growth factor as a function of a, for given values of the cosmological parameters, using two numerical integration methods of your choice.\n",
    "\n",
    "2) Plot the growth factor in the scale factor range $a \\in [0.1,2]$ for the following values of $\\Omega_m$: $0.1$, $0.3$, $0.6$, $1$ (assume a present day expansion rate $H_0 = 67.4 \\, {\\rm km} \\, {\\rm s}^{-1}\\, {\\rm Mpc}^{-1}$). Make a panel with two plots, one for each integration method you chose. Set logscale on x-axis.\n",
    "\n",
    "3) Optional. For $a = 0.5$, compute the growth factor using the Simpson's rule with varying N and check the convergence rate of the result. Start by sampling the integration interval with ten points and then increase the sample size by a factor of $2$ at each step. How many steps do you need to achieve a final desired accuracy of $10^{-12}$ ?\n",
    "\n",
    "4) Do cosmic structures grow faster in a matter dominated Universe, or in a Universe with a cosmological constant?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edb92e75-438f-4e25-9f38-ec2e3d15578f",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "33d3600b-71fd-4a65-9cc3-006de24ccd4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import scipy.integrate as integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d2b4f01-86da-4935-9616-25459f7821bb",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5cf9dbc5-e4a4-4ebc-a992-c3bf5d1ed50d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def E2 (a, Omega_m):\n",
    "    Omega_L = 1. - Omega_m\n",
    "    return Omega_m * a**-3 + Omega_L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "97bb8f41-a768-4cc6-9212-65c0f5edd017",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-3, 1, 100)\n",
    "\n",
    "plt.plot(aas, E2(aas, 0.3), label=\"$\\Omega_m = 0.3$\")\n",
    "plt.plot(aas, E2(aas, 1.), label=\"$\\Omega_m = 1.0$\")\n",
    "plt.plot(aas, E2(aas, 0.), label=\"$\\Omega_m = 0.0$\")\n",
    "\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"$E^2(a)$\")\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "plt.legend(frameon=False)\n",
    "\n",
    "plt.loglog()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8adedb24-c380-40f2-aee4-8ac63ec64d7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def growth_integrand(a, Omega_m):\n",
    "    return (a **-3)* E2(a, Omega_m)**-1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b7936526-f63d-4c59-bf17-8185462dbac5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-3, 0, 100)\n",
    "\n",
    "plt.plot(aas, growth_integrand(aas, 0.3))\n",
    "\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"integrand\")\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcb357c5-5826-4f5d-b143-1c316093da5c",
   "metadata": {},
   "source": [
    "## numpy.trapz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d9857eed-10ca-4f01-8af0-c9b26f56fcb5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def growth_factor_trpz(a, Omega_m, sampling_points=100): \n",
    "    aas = np.linspace(1.e-9, a, sampling_points)\n",
    "    \n",
    "    # In order to vectorize the calculation later,\n",
    "    # we have to specify the axis on which to perform the integration.\n",
    "    # Otherwise, this leads to a lot of head-scratching during the tutorial!\n",
    "    integral = np.trapz(growth_integrand(aas, Omega_m), x=aas, axis=0)\n",
    "    \n",
    "    return 5./2. * Omega_m * np.sqrt(E2(a, Omega_m)) * integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "79967a43-2e47-49f5-9d97-8a020710d477",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.linspace(1.e-1, 2., 100)\n",
    "plt.plot(aas, growth_factor_trpz(aas, 0.3), label=\"$D(a)$\")\n",
    "plt.plot(aas, aas, label=\"$a$\")\n",
    "\n",
    "plt.loglog()\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"$a$\")\n",
    "#plt.ylabel(\"Growth factor\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8b92bbfe-ac27-4ff3-b9de-2c6b79a23ebd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = np.linspace(0, 10., 100)\n",
    "plt.plot(zs, growth_factor_trpz((zs+1)**-1, 0.3), label=\"D(a)\")\n",
    "plt.plot(zs, (zs+1)**-1, label=\"$a$\")\n",
    "\n",
    "plt.xlim(zs[0], zs[-1])\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"$z$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ec18ca84-8644-4f90-a431-dd3f75ad2a26",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2615/3474320013.py:2: RuntimeWarning: divide by zero encountered in power\n",
      "  return (a **-3)* E2(a, Omega_m)**-1.5\n",
      "/tmp/ipykernel_2615/1496804094.py:3: RuntimeWarning: divide by zero encountered in power\n",
      "  return Omega_m * a**-3 + Omega_L\n",
      "/tmp/ipykernel_2615/3474320013.py:2: RuntimeWarning: invalid value encountered in multiply\n",
      "  return (a **-3)* E2(a, Omega_m)**-1.5\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAAGwCAYAAABiu4tnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAABhSklEQVR4nO3dd1xTV/8H8E8GCUNAEUEREBxVEVyAijhqVdyj9VFbLa7WVou1Spe2P+fzVPvYVjtEq9VWbd2t+qi1KnXvgVK1uIviABGVvUJyf39cCERACCYkgc/79bovbs49ufnmmibfnnPuORJBEAQQERERkd6kpg6AiIiIyFIxkSIiIiKqICZSRERERBXERIqIiIiogphIEREREVUQEykiIiKiCmIiRURERFRBclMHYO40Gg3u378Pe3t7SCQSU4dDRERE5SAIAtLS0uDm5gap1HjtRkykynD//n14eHiYOgwiIiKqgDt37sDd3d1o52ciVQZ7e3sA4j+Eg4ODiaMhIiKi8khNTYWHh4f2d9xYmEiVoaA7z8HBgYkUERGRhTH2sBwONiciIiKqICZSpYiIiICPjw8CAwNNHQoRERGZKYkgCIKpgzBnqampcHR0REpKCrv2iIiILERl/X6zRYqIiIiogphIEREREVUQEykiIiKiCmIiRURERFRBTKRKwbv2iIiIqCy8a68MvGuPiIjI8vCuPSIiIiIzx0SKiIiIqIKYSBERERFVEBMpIiKicnjvvffg7+8PpVKJ1q1bl1jn4sWL6Nq1K2xsbFC/fn3MnTsXljwUWaVS4eOPP4afnx/s7Ozg5uaGUaNG4f79+zr1cnJy8O6778LZ2Rl2dnYYOHAg7t69q1PnyZMnCA0NhaOjIxwdHREaGork5ORKfDfGwUSKiIioHARBwLhx4zB8+PASj6empqJnz55wc3PDmTNn8N133+HLL7/EwoULKzlSw8nMzMS5c+cwY8YMnDt3Dlu2bMG1a9cwcOBAnXpTpkzB1q1bsWHDBhw9ehTp6eno378/1Gq1ts6IESMQHR2N3bt3Y/fu3YiOjkZoaGhlvyXDE+iZUlJSBABCSkqKqUMhIjI5jUYjZOSoTLJpNJpyx9m1a1fh3XffFT788EOhVq1agqurqzBr1iyDXINZs2YJrVq1Kla+ZMkSwdHRUcjOztaWzZ8/X3Bzcys19g4dOggff/yxTlliYqIgl8uF/fv3C4IgCBEREULjxo0FpVIpuLi4CEOGDCk1tp9++klwdHQUdu/eLTRr1kyws7MTevXqJdy/f78C77Rkp0+fFgAIt2/fFgRBEJKTkwUrKythw4YN2jr37t0TpFKpsHv3bkEQBCEmJkYAIJw8eVJb58SJEwIA4cqVKwaLrajK+v2WmzSLM2MRERGIiIjQyaaJiKq7LJUaPjP3mOS1Y+b2gq2i/D9bq1evRnh4OE6dOoUTJ05gzJgxCA4ORs+ePQEAffr0wZEjR555jvT09HK/3okTJ9C1a1colUptWa9evTB9+nTcunUL3t7exZ4zcuRIfPHFF5g/fz4kEgkAYOPGjXB1dUXXrl1x9uxZTJ48GT///DM6duyIx48flxlzZmYmvvzyS/z888+QSqV4/fXX8cEHH2Dt2rUAgLVr1+Ltt99+5jmWLVuGkSNHlngsJSUFEokENWvWBABERUVBpVIhJCREW8fNzQ2+vr44fvw4evXqhRMnTsDR0RHt27fX1unQoQMcHR1x/PhxNG3a9JnxmDMmUqUICwtDWFiYdh4KIiKyLC1btsSsWbMAAE2aNMHixYuxb98+bSK1YsUKZGVlGez1EhIS4OXlpVPm6uqqPVZSIjV8+HBMnToVR48eRefOnQEA69atw4gRIyCVShEXFwc7Ozv0798f9vb2aNCgAdq0afPMOFQqFb7//ns0atQIADBp0iTMnTtXe3zgwIE6CU1JCuJ+WnZ2NqZNm4YRI0Zo52ZKSEiAQqFArVq1ip0jISFBW8fFxaXY+VxcXLR1LBUTKSIiKjcbKxli5vYy2Wvro2XLljqP69Wrh8TERO3j+vXrGySuogpalQoI+QPNny4vUKdOHfTs2RNr165F586dERsbixMnTmDp0qUAgJ49e6JBgwZo2LAhevfujd69e+Pll1+Gra1tqTHY2tpqkyig+Pu2t7eHvb293u9NpVLh1VdfhUajwZIlS8qsLwiCzvsu6Ro8XccScbA5ERGVm0Qiga1CbpJN3x9cKyurYrFrNBrt4z59+qBGjRrP3PRRt27dYq0rBQlMaS08gNi99+uvv0KlUmHdunVo0aIFWrVqBUBMes6dO4f169ejXr16mDlzJlq1avXMu91Ket9CkTsH165dW+b7LugGLKBSqTBs2DDExsYiMjJSZ6bwunXrIjc3F0+ePCn23gved926dfHgwYNisT58+PCZ18YSsEWKiIiqJUN37QUFBeGTTz5Bbm4uFAoFAGDv3r1wc3Mr1uVX1ODBg/H2229j9+7dWLduXbE72eRyOXr06IEePXpg1qxZqFmzJvbv349XXnmlQnHq27VXkERdv34dBw4cQO3atXXq+vv7w8rKCpGRkRg2bBgAID4+HpcuXcKCBQsAiNcmJSUFp0+fRrt27QAAp06dQkpKCjp27Fih92EumEgREVG1pG/X3o0bN5Ceno6EhARkZWUhOjoaAODj4wOFQoERI0Zgzpw5GDNmDD755BNcv34d8+bNw8yZM5/ZmmZnZ4dBgwZhxowZuHz5MkaMGKE9tnPnTvzzzz/o0qULatWqhV27dkGj0TzX4Gx9uvby8vLwr3/9C+fOncPOnTuhVqu1rW5OTk5QKBRwdHTEG2+8gffffx+1a9eGk5MTPvjgA/j5+aFHjx4AgObNm6N3794YP348li1bBgB466230L9/f4seaA4wkSIiIiqXN998E4cOHdI+Lhj0HRsbCy8vLzg6OiIyMhJhYWEICAhArVq1EB4ejvDw8DLPPXLkSPTr1w9dunSBp6entrxmzZrYsmULZs+ejezsbDRp0gTr169HixYtDP8GS3D37l1s374dAIpNQnrgwAG8+OKLAIBFixZBLpdj2LBhyMrKQvfu3bFq1SrIZIXj2tauXYvJkydr7+4bOHAgFi9eXCnvw5gkgmDBU65WgspaPZqIiIgMp7J+vznYnIiIiKiCmEgRERERVRATKSIiIqIKYiJVioiICPj4+CAwMNDUoRAREZGZ4mDzMnCwORERkeXhYHMiIiIiM8dEioiIiKiCmEgRERERVRATKSIiIqIKYiJFRERUDu+99x78/f2hVCqLLZdS4OLFi+jatStsbGxQv359zJ07F0/f03Xo0CH4+/vD2toaDRs2xPfff18J0RvP48eP8e6776Jp06awtbWFp6cnJk+ejJSUFJ16T548QWhoKBwdHeHo6IjQ0FAkJyfr1ImLi8OAAQNgZ2cHZ2dnTJ48Gbm5uZX4bvTHtfaIiIjKQRAEjBs3DqdOncKFCxeKHU9NTUXPnj3RrVs3nDlzBteuXcOYMWNgZ2eH999/H4C4Ll/fvn0xfvx4/PLLLzh27Bjeeecd1KlTB0OGDKnst2QQ9+/fx/379/Hll1/Cx8cHt2/fxoQJE3D//n38+uuv2nojRozA3bt3sXv3bgDiosWhoaHYsWMHAECtVqNfv36oU6cOjh49ikePHmH06NEQBAHfffedSd5buQj0TCkpKQIAISUlxdShEBFROXXt2lV49913hQ8//FCoVauW4OrqKsyaNcsg5541a5bQqlWrYuVLliwRHB0dhezsbG3Z/PnzBTc3N0Gj0QiCIAgfffSR0KxZM53nvf3220KHDh1KfC21Wi3Ur19fWLp0qU55VFSUAEC4efOmNiYPDw9BoVAI9erVE959990y41+zZo3QoEEDwcHBQRg+fLiQmpparvdfHps2bRIUCoWgUqkEQRCEmJgYAYBw8uRJbZ0TJ04IAIQrV64IgiAIu3btEqRSqXDv3j1tnfXr1wtKpbJCv8GV9fvNrj0iIio/QQByM0yz6Tnt4erVq2FnZ4dTp05hwYIFmDt3LiIjI7XH+/Tpgxo1ajxz08eJEyfQtWtXKJVKbVmvXr1w//593Lp1S1snJCRE53m9evXC2bNnoVKpip1TKpXi1Vdfxdq1a3XK161bh6CgIDRs2BC//vorFi1ahGXLluH69evYtm0b/Pz8nhnrzZs3sW3bNuzcuRM7d+7EoUOH8Pnnn2uPz5s3r8xrc+TIkVLPXzB3k1wu175vR0dHtG/fXlunQ4cOcHR0xPHjx7V1fH194ebmpnNtcnJyEBUV9cz3Y0rs2iMiovJTZQLz3MquZwyf3AcUduWu3rJlS8yaNQsA0KRJEyxevBj79u1Dz549AQArVqxAVlaWwcJLSEiAl5eXTpmrq6v2mLe3NxISErRlRevk5eUhKSkJ9erVK3bekSNHYuHChbh9+zYaNGgAjUaDDRs24JNPPgEgjiuqW7cuevToASsrK3h6eqJdu3bPjFWj0WDVqlWwt7cHAISGhmLfvn347LPPAAATJkzAsGHDnnmO+vXrl1j+6NEj/Pvf/8bbb7+tLUtISICLi0uxui4uLkhISNDWefra1KpVCwqFQlvHHDGRIiKiKqlly5Y6j+vVq4fExETt49ISgechkUh0Hgv5rWhFy8tTp6g2bdqgWbNmWL9+PaZNm4ZDhw4hMTFRm+gMHToUX3/9NRo2bIjevXujb9++GDBggLY1qCReXl7aJAoofm2cnJzg5ORUnresIzU1Ff369YOPj482iS1Q0vsTBOGZ16akOuaGiRQREZWfla3YMmSq19anupWVzmOJRAKNRqN93KdPn2d2TwFAenp6uV+vbt26xVpOCpKTgpaW0urI5XLUrl271HOPHDkS69atw7Rp07Bu3Tr06tULzs7OAAAPDw9cvXoVkZGR+PPPP/HOO+/giy++wKFDh4pdgwJlXZt58+Zh3rx5z3y/f/zxBzp37qx9nJaWht69e6NGjRrYunWrzmvUrVsXDx48KHaOhw8f6lybU6dO6Rx/8uQJVCpVsZYqc1ItEqmXX34ZBw8eRPfu3XXuICAiIj1JJHp1r5kzQ3ftBQUF4ZNPPkFubi4UCgUAYO/evXBzc9N2+QUFBWnvUiuwd+9eBAQElJr0AOIdb//3f/+HqKgo/Prrr1i6dKnOcRsbGwwcOBADBw5EWFgYmjVrhosXL6Jt27YVei/6du2lpqaiV69eUCqV2L59O6ytrXXqBgUFISUlBadPn9Z2O546dQopKSno2LGjts5nn32G+Ph4bRfn3r17oVQq4e/vX6H3URmqRSI1efJkjBs3DqtXrzZ1KEREZCb07dq7ceMG0tPTkZCQgKysLERHRwMAfHx8oFAoMGLECMyZMwdjxozBJ598guvXr2PevHmYOXOmtmtqwoQJWLx4McLDwzF+/HicOHECK1euxPr165/52t7e3ujYsSPeeOMN5OXlYdCgQdpjq1atglqtRvv27WFra4uff/4ZNjY2aNCggX4XpAh9uvbS0tIQEhKCzMxM/PLLL0hNTUVqaioAoE6dOpDJZGjevDl69+6N8ePHY9myZQDE6Q/69++Ppk2bAgBCQkLg4+OD0NBQfPHFF3j8+DE++OADjB8/3qiLDj+vapFIdevWDQcPHjR1GEREZMHefPNNHDp0SPu4TZs2AMS5oby8vODo6IjIyEiEhYUhICAAtWrVQnh4OMLDw7XP8fb2xq5duzB16lRERETAzc0N3377bbnmkBo5ciTCwsIwatQo2NjYaMtr1qyJzz//HOHh4VCr1fDz88OOHTue2VVoSFFRUdouucaNG+scK7g2ALB27VpMnjxZe9fiwIEDsXjxYm1dmUyG33//He+88w6Cg4NhY2ODESNG4Msvv6yU91FREkHQ835SAzt8+DC++OILREVFIT4+Hlu3bsXgwYN16ixZsgRffPEF4uPj0aJFC3z99dc6/bLlcfDgQSxevFjvrr3U1FQ4Ojpqb+UkIiIi81dZv98mn0cqIyMDrVq10slKi9q4cSOmTJmCTz/9FOfPn0fnzp3Rp08fxMXFaev4+/vD19e32Hb/vokGRBIREVG1YPKuvT59+qBPnz6lHl+4cCHeeOMNvPnmmwCAr7/+Gnv27MHSpUsxf/58ADDoRF05OTnIycnRPi7o5yUiIiJ6mslbpJ4lNzcXUVFRxWaBDQkJ0c6Eamjz58/XLqjo6OgIDw8Po7wOERERWT6zTqSSkpKgVqtLnAVWn1lOe/XqhaFDh2LXrl1wd3fHmTNnSq07ffp0pKSkaLc7d+5UOH4iIiKq2kzetVceJc0Cq88sp3v27Cl3XaVSCaVSiYiICERERECtVpf7uURERFS9mHWLlLOzM2QyWYmzwBp7ltOwsDDExMQ8s/WKiIiIqjezTqQUCgX8/f11VusGgMjISO1MqERERESmYvKuvfT0dNy4cUP7ODY2FtHR0XBycoKnpyfCw8MRGhqKgIAABAUFYfny5YiLi8OECRNMGDURERGRGSRSZ8+eRbdu3bSPC2aAHT16NFatWoXhw4fj0aNHmDt3LuLj4+Hr64tdu3Y919T35cExUkRERFQWk89sbu44szkREZHlqTYzmxMRERFZKiZSpYiIiICPjw8CAwNNHQoRERGZKXbtlYFde0RERJaHXXtEREREZo6JFBEREVEFMZEqBcdIERERUVk4RqoMHCNFRERkeThGioiIiMjMMZEiIiIiqiAmUkREREQVxESqFBxsTkRERGXhYPMycLA5ERGR5eFgcyIiIiIzx0SKiIiIqIKYSBERERFVEBMpIiIiogpiIlUK3rVHREREZeFde2XgXXtERESWh3ftEREREZk5JlJEREREFcREioiIiKiCKpRI/fzzzwgODoabmxtu374NAPj666/xv//9z6DBEREREZkzvROppUuXIjw8HH379kVycjLUajUAoGbNmvj6668NHR8RERGR2dI7kfruu+/www8/4NNPP4VMJtOWBwQE4OLFiwYNjoiIiMic6Z1IxcbGok2bNsXKlUolMjIyDBKUOeA8UkRERFQWvRMpb29vREdHFyv/448/4OPjY4iYzEJYWBhiYmJw5swZU4dCREREZkqu7xM+/PBDhIWFITs7G4Ig4PTp01i/fj3mz5+PFStWGCNGIiIiIrOkdyI1duxY5OXl4aOPPkJmZiZGjBiB+vXr45tvvsGrr75qjBiJiIiIzNJzLRGTlJQEjUYDFxcXQ8ZkVrhEDBERkeWprN9vvVukYmNjkZeXhyZNmsDZ2Vlbfv36dVhZWcHLy8uQ8RERERGZLb0Hm48ZMwbHjx8vVn7q1CmMGTPGEDERERERWQS9E6nz588jODi4WHmHDh1KvJuPiIiIqKrSO5GSSCRIS0srVp6SkqKd5ZyIiIioOtA7kercuTPmz5+vkzSp1WrMnz8fnTp1MmhwREREROZM78HmCxYsQJcuXdC0aVN07twZAHDkyBGkpqZi//79Bg+QiIiIyFzp3SLl4+ODCxcuYNiwYUhMTERaWhpGjRqFK1euwNfX1xgxmgSXiCEiIqKyPNc8UtUB55EiIiKyPGY7jxQAJCcn4/Tp00hMTIRGo9E5NmrUKIMERkRERGTu9E6kduzYgZEjRyIjIwP29vaQSCTaYxKJhIkUERERVRt6j5F6//33MW7cOKSlpSE5ORlPnjzRbo8fPzZGjERERERmSe9E6t69e5g8eTJsbW2NEQ8RERGRxdA7kerVqxfOnj1rjFiIiIiILIreY6T69euHDz/8EDExMfDz84OVlZXO8YEDBxosOCIiIiJzpvf0B1Jp6Y1YEomkyi0Tw+kPiIiILI/ZTn/w9HQHRERERNWV3mOkisrOzjZUHEREREQWR+9ESq1W49///jfq16+PGjVq4J9//gEAzJgxAytXrjR4gERERETmSu9E6rPPPsOqVauwYMECKBQKbbmfnx9WrFhh0OCIiIiIzJneidSaNWuwfPlyjBw5EjKZTFvesmVLXLlyxaDBGcKdO3fw4osvwsfHBy1btsTmzZtNHRIRERFVEXoPNr937x4aN25crFyj0UClUhkkKEOSy+X4+uuv0bp1ayQmJqJt27bo27cv7OzsTB0aERERWTi9W6RatGiBI0eOFCvfvHkz2rRpY5CgDKlevXpo3bo1AMDFxQVOTk5cyoaIiIgMQu9EatasWZg0aRL++9//QqPRYMuWLRg/fjzmzZuHmTNn6h3A4cOHMWDAALi5uUEikWDbtm3F6ixZsgTe3t6wtraGv79/iYlceZw9exYajQYeHh4Vej4RERFRUXonUgMGDMDGjRuxa9cuSCQSzJw5E5cvX8aOHTvQs2dPvQPIyMhAq1atsHjx4hKPb9y4EVOmTMGnn36K8+fPo3PnzujTpw/i4uK0dfz9/eHr61tsu3//vrbOo0ePMGrUKCxfvvyZ8eTk5CA1NVVnIyIiIiqJXjOb5+Xl4bPPPsO4ceOM0qojkUiwdetWDB48WFvWvn17tG3bFkuXLtWWNW/eHIMHD8b8+fPLdd6cnBz07NkT48ePR2ho6DPrzp49G3PmzClWzpnNiYiILEdlzWyuV4uUXC7HF198UWnLwOTm5iIqKgohISE65SEhITh+/Hi5ziEIAsaMGYOXXnqpzCQKAKZPn46UlBTtdufOnQrFTkRERFWf3l17PXr0wMGDB40QSnFJSUlQq9VwdXXVKXd1dUVCQkK5znHs2DFs3LgR27ZtQ+vWrdG6dWtcvHix1PpKpRIODg46GxEREVFJ9J7+oE+fPpg+fTouXboEf3//YtMIDBw40GDBFZBIJDqPBUEoVlaaTp06VWh9wIiICERERFS5RZiJiIjIcPROpCZOnAgAWLhwYbFjEonEoImHs7MzZDJZsdanxMTEYq1UhhYWFoawsDBtHysRERHR0/Tu2tNoNKVuhm69USgU8Pf3R2RkpE55ZGQkOnbsaNDXIiIiItKX3i1SRWVnZ8Pa2vq5AkhPT8eNGze0j2NjYxEdHQ0nJyd4enoiPDwcoaGhCAgIQFBQEJYvX464uDhMmDDhuV63LOzaIyIiorLoNf0BAKjVasybNw/ff/89Hjx4gGvXrqFhw4aYMWMGvLy88MYbb+gVwMGDB9GtW7di5aNHj8aqVasAiBNyLliwAPHx8fD19cWiRYvQpUsXvV6noirr9kkiIiIynMr6/dY7kZo7dy5Wr16NuXPnYvz48bh06RIaNmyITZs2YdGiRThx4oSxYjUJJlJERESWxyznkQKANWvWYPny5Rg5ciRkMpm2vGXLlrhy5YpBgyMiIiIyZ3onUvfu3UPjxo2LlWs0GqhUKoMEZQ4iIiLg4+ODwMBAU4dCREREZkrvRKpFixYlLhq8efNmtGnTxiBBmYOwsDDExMTgzJkzpg6FiIiIzJTed+3NmjULoaGhuHfvHjQaDbZs2YKrV69izZo12LlzpzFiJCIiIjJLerdIDRgwABs3bsSuXbsgkUgwc+ZMXL58GTt27EDPnj2NESMRERGRWSpXi9S3336Lt956C9bW1oiLi0NISAh69epl7NhMivNIERERUVnKNf2BXC7H/fv34eLiAplMhvj4eLi4uFRGfCbH6Q+IiIgsT2X9fperRcrNzQ2//fYb+vbtC0EQcPfuXWRnZ5dY19PT06ABEhEREZmrcrVILV++HO+++y7y8vJKrSMIgsEXLTYHbJEiIiKyPGY3s3laWhpu376Nli1b4s8//0Tt2rVLrNeqVSuDBmhqTKSIiIgsj1l17RUMNvf19cVPP/2EoKAg2NjYGC0oc8DB5kRERFQWDjYvA1ukiIiILI9ZtUhxsDkRERFRcRxsXga2SBEREVkeDjY3E0ykiIiILI9Zde0BgL29vXaweXBwMJRKpdGCIiIiIrIEeq+1N3r06GqRREVERMDHxweBgYGmDoWIiIjMVLm69pycnHDt2jU4OzujVq1akEgkpdZ9/PixQQM0NXbtERERWR6z6tpbtGgR7O3ttfvPSqSqqknrolDHyQm1bK1Q09YKjrYKcd9GgZr5ZTVtFbBTyKrl9SEiIqqOyj3YvLoqyGg9pmyCVGlbZn0rmQSOBcmVjZhcFezXslPA0UZMumrZ6u7bMgEjIiIyGLNqkUpNTS33Catq99fsAT7IkVojOSsXKZkqPMnMRXKmStyycvEkU4XcPA1UagFJ6TlISs/R6/xWMgmc7BRoXs8BLes7wre+I1q614Srg5IJFhERkZkqV4uUVCot9495dZ5HKitXjeQsMcF6klmQcKmKJ19ZKiQXScRy1ZpSz1nHXgm/+o7araW7I1wcrA39NomIiKoEjUZAem4e7j14BB+veubRInXgwAHt/q1btzBt2jSMGTMGQUFBAIATJ05g9erVmD9/vnGitBA2ChlsFDao51j+dQgFQUCWSo3kTBUSUrPx970UXLibgov3UnA9MR0P03Kw/0oi9l9J1D7H1aEguaqJlu5i61Ud+6p/JyUREVV9Bb+LqVl5SM1WITVLhZQsVf5+nrj/9ONscUvJVCEtJw+CAGhyMislXr3HSHXv3h1vvvkmXnvtNZ3ydevWYfny5Th48KAh4zM5U961l5WrRkx8Ki7eTcbFe6m4eC8ZNxLToSnhX6yeo3Vhy5W7+Ld2DSZXRERUeQRBQLZKg7QcFdKy8/I3FdLz91OzC8vTn6qTmp2nTZBU6ucfvi1XZ+Pml/8yn5nNC9ja2uKvv/5CkyZNdMqvXbuG1q1bIzOzcjJAY4uIiEBERATUajWuXbtmNtMfZObmIeZ+Ki7cTcGleym4cC8FNx+mo6R/xfo1bXQSK7/6jqhlp6j8oImIyKwJgoCcPA0ycvKQkaNGek4eMnLzkJ5TmOikZeflJ0Sq/KQoP0l6qk5eSf+3XwEyqQQO1nI42FjB0cYKDtZWcLCRF9nP356q42hjBXtrOXKzMsxriZgCTZs2Rf/+/fHVV1/plL///vvYuXMnrl69atAATc0S5pFKzylIrpJx8Z7YLfjPw4wS63o4icnVS81c0b9lPVhbySo5WiIiMgSVWkx80osmP/mbdj+3sLzwuFiWmav7PEMlQAAgkQA1lHLYK+WwtxYTG3trOWoU2XfI36+RX8fBWg5H28Ik6XmnEzK7tfYK7Nq1C0OGDEGjRo3QoUMHAMDJkydx8+ZN/Pbbb+jbt69RAjUVS0ikSpKarcLf91K1rVYX7ybj1iPd1kLnGgqMbN8Ar3dowDFWREQGptaIY32ycsUtU5Wn3c9SqZFZbD+vlPKC/TztfkaO+pk3Kj0PGysZ7JRy1FCKf8VkR0x0xCTICjWK7ItJkVinIEmyU8ghlZr2jnOzTaQA4O7du1i6dCkuX74MQRDg4+ODCRMmwMPDwxgxmpSlJlIlSclS4e97KThz6wk2nIlDfEo2AEAhk2JgazeMDfZCCzdHE0dJRGRYGo2AXLUG2So1cvI0yFFpkJMn7mvL8tTIUWmQnf+3oCxbVXisWP38cxU+pyBhEv/m5Bkn0XmaUi5FDaUcdvlbDaUMtgp5fllBUqR73E7x1OOC4wo5ZCZOgAzFrBOp6qQqJVJFqdQa7L6UgB+PxeJ8XLK2vENDJ4wL9kb35q5V5j8mIiqbRiNAIwhQCwI0GiBPo4FaI2i3vKf2NYKAPHX+X40AtUYDdSnP0zz1fLVGfJ08tQa5agEqtQaqPA1UmiL7+cfy1OK+Si0mQ3lF9lVqDfLyn1/wWJUnIE+j0c7rp1JrDNplVVG2ChlsrGSwUcie2peXUi6DTf4xcV+m3S84VkMhh61SBiuZ3svmVgtMpMxEVU2kijoX9wQ/HbuFXRfjoc7/wvF0ssWYjl4YGuAOe2srE0dIZHx56oJWiMIWiFy1butFTp4auQV18suLJRj5SULRhEGt1i0rSELEpKV4YlI0WSmafGgEQCMUlIsDhAvOV3BMrREgCChSLh7TPs4/j1oQijzf1Fe/8kglgLWVDNZWMijl0vxNBqWVFNb5f4uWKeX59fL3rYuWyaWF58n/WzzxkcPaqvxzMZLhMJEyE9UhkSoQn5KFNSduY92pOKRkqQCIgwWHBXhgTEcveNYue4kcImMTBAGZueoSVxdIzshFcv6cM2Kyoy4hGdLkJ0O63TzVKZnQl0wqgUwiEf/mb3KpBNL8v8XKJRLIZYXPkUulkEoBuVSqrSeVSKCQS2Alk0IulWr3CzdJqfsKufgcK5kEVnIpFDIp5NLCfSuZFHKZRLtvJZNoEx45W2+qDSZSZqI6JVIFsnLV2HL+Ln48Goub+Xf/SSRAz+auGNfJG+29nfh/V2QQOXlqbTJUmBjlalcESM7IL88qLE8pYzUAQ7CSSXRaHZRWMihkUp3WCkXBj7ZcCpkExZMKSWGiIc1/XDT5kJaQnJSUsBQ9l/gXkErEREQmlUAigfa4WA5toiLNry+TSCCRFCQw+c8vOF9+7FKJ+FgiReH70L4G/3sny8NEykxUx0SqgEYj4MiNJPx4NBaHrj3UlvvUc8C4Tt4Y0KoelHJOn0AlU2sE3HmciRuJ6biemI7riWl4kJqNJxn5SyRlqZCZW/ElpRQyqXbR75q2VkX2FXCwEceWKOTSMhOip7t3FDKpye82IqLnx0TKTFTnRKqoG4lp+OnYLfx27i6yVWJrgHMNJV7v4ImR7Tl9QnWmUmtw+1GGmDA9KEia0nHzYTpyy3HXklQC1CxIhmwKkyExMbIqsl+QMClQy9YKNlbPN8cMEVVtZpVItWnTptxfWOfOnXvuoMwJEyldyZm5WH/6DlYfv4WE1MLpEwa1dsPYYG/4uPEaVVXZKjVikzJwPTEdNxLTcSMxDdcfpCM2KaPUu6IUcika1amBJi7i5u5ko02UCpIke6Xp55shoqqnsn6/y7Vo8eDBg40WgLkqukQMFappq8DEFxvhzc7e2H0pASuPxiL6TjI2R93F5qi7CGpYG+M6eeOlZi6cPsFCZebm4WZiBq4npmm75W4kpuP2o4xSB2TbKmRo4lIDjVxqoImLvZg4udaAey1bfg6IqEpj114Z2CJVtnNxT/Dj0Vj8cSlBO31Cg9oF0yd4oIayXPk6mUBKpgp/Xn6Aqw/ScP1BGq4npuPuk6xS6ztYy9HEVUyUGudvTVztUc/Bmq1KRGRWzKprrzpjIlV+95PF6RPWny6cPsHJToHVY9vBz50zppsLlVqDQ1cfYsv5u/gzJrHEO+Bq2ynykySxhalxftdcHXslxyURkUUw20RKrVZj0aJF2LRpE+Li4pCbm6tz/PHjxwYN0NSYSOkvMzcPW87dw8qjsYhNykBNWytseKsDmtXl9TMVQRDw9/1U/HbuLrZH38ejjML/bpvVtUeHhrV1kiYnO4UJoyUien5mNUaqqDlz5mDFihUIDw/HjBkz8Omnn+LWrVvYtm0bZs6caYwYycLYKuR4vUMDDGrthtCVpxF9JxmvrziFDW8FobFLDVOHV608SM3GtvP3sOXcPVx9kKYtd66hxODWbnilrTtvECAieg56t0g1atQI3377Lfr16wd7e3tER0dry06ePIl169YZK1aTYIvU80nJUmHEDyfx9/1UuDoosentIDSobWfqsKq0rFw19sYk4Ldz93D0+kPtAHGFXIqePq74V1t3dG7izBmeiahKM9sWqYSEBPj5+QEAatSogZSUFABA//79MWPGDMNGRxbP0cYKP7/RHq8tP4mrD9Iw4odT2Ph2B7jX4nIzhqTRCDhz6zG2nLuH3y/GIz0nT3ssoEEtvNLWHf1a1oOjDddNJCIyJL0TKXd3d8THx8PT0xONGzfG3r170bZtW5w5cwZKJSdlpOKc7BT45c32GL7sBP5JysDIFaew8a0g1HW0NnVoFu9WUga2nL+Hrefv4s7jwrvt3GvZ4JW27nilTX14ObMFkIjIWPROpF5++WXs27cP7du3x3vvvYfXXnsNK1euRFxcHKZOnWqMGKkKqGOvxNrx7TFs2QncfpSJkStOYuPbQXCuweRbXylZKvx+IR5bzt3F2dtPtOU1lHL086uHV9rWR6CXE6cjICKqBM89/cHJkydx/PhxNG7cGAMHDjRUXGaDY6QM687jTAxfdgL3U7LRrK491o/vgFq8Q6xMeWoNjlxPwq/n7iIy5oF26RWpBOjcpA5eaVsfIT51YaPg2odERIAZT39Q3TCRMrzYpAwMX3YCiWk58K3vgLVvduDYnVLE5E9Z8L/o+0hKz9GWN3W1xxD/+hjUuj5cHdhFSkT0NLNOpK5du4aDBw8iMTERGo3uZH5VbQoEJlLGcSMxDcOXncSjjFy08ayJn99ozxnQizhwJRH/3X0FVxIKpyyobafAwNZuGNLWHS3cHDgxJhHRM5htIvXDDz9g4sSJcHZ2Rt26dXW+zCUSCRctpnKLuZ+K1344iZQsFdp5O2H12HbsmgJw5PpDjFt1Biq1AIVMih4+LniljTu6Nq0DK05ZQERULmabSDVo0ADvvPMOPv74Y2PFZFBpaWl46aWXoFKpoFarMXnyZIwfP77cz2ciZVwX7iZj5A+nkJaTh85NnPHDqABYW1XfZOrC3WS8tvwkMnLV6OdXD5+97IuathxDRkSkL7NNpBwcHBAdHY2GDRsaKyaDUqvVyMnJga2tLTIzM+Hr64szZ86gdu3a5Xo+Eynji7r9GKErTyMzV43uzVyw9HV/KOTVr+UlNikD/1p6HI8ychHcuDZ+HBMIpbz6JpVERM+jsn6/9f61Gjp0KPbu3WuMWIxCJpPB1lac/DE7OxtqtRocX29e/Bs4YeXoQCjlUuy7koj3NpxHXgkL6VZlianZCF15Co8ycuFb3wHLQgOYRBERWQC9E6nGjRtjxowZGDNmDL766it8++23Opu+Dh8+jAEDBsDNzQ0SiQTbtm0rVmfJkiXw9vaGtbU1/P39ceTIEb1eIzk5Ga1atYK7uzs++ugjODs76x0nGVdQo9pYPioACpkUf1xKwPub/4JaUz0S3tRsFUb9eBp3n2TBq7YtVo1tx4H3REQWQu+uPW9v79JPJpHgn3/+0SuAP/74A8eOHUPbtm0xZMgQbN26FYMHD9Ye37hxI0JDQ7FkyRIEBwdj2bJlWLFiBWJiYuDp6QkA8Pf3R05OTrFz7927F25ubtrHDx48wCuvvIItW7bA1dW1xHhycnJ0zpWamgoPDw927VWSP2MeYMIvUcjTCBgW4I7PX2lZpSeWzFapMfrH0zgV+xjONZTYMrEjPGtz+RwioudltmOkjEkikRRLpNq3b4+2bdti6dKl2rLmzZtj8ODBmD9/vt6vMXHiRLz00ksYOnRoicdnz56NOXPmFCtnIlV5fr8Qj3fXn4NGAEI7NMDcQS2q5K3+ao2AsLXnsPvvBNgr5djwdge0cHM0dVhERFWC2Y6RKkoQBKOON8rNzUVUVBRCQkJ0ykNCQnD8+PFynePBgwdITU0FIF7Uw4cPo2nTpqXWnz59OlJSUrTbnTt3Kv4GqEL6tayHr4a1gkQC/HzyNj77/XKVG9cmCAL+b9sl7P47AQqZFMtHBTCJIiKyQBVKpNasWQM/Pz/Y2NjAxsYGLVu2xM8//2zo2JCUlAS1Wl2sG87V1RUJCQnlOsfdu3fRpUsXtGrVCp06dcKkSZPQsmXLUusrlUo4ODjobFT5Xm7jjvkv+wEAVhyNxVd7r5k4IsP6+s/rWH86DhIJ8M2rrRHUqHx3kRIRkXnRe0TrwoULMWPGDEyaNAnBwcEQBAHHjh3DhAkTkJSUZJSFi5/u1hEEodxdPf7+/oiOjtb7NSMiIhAREQG1Wq33c8kwXm3niZw8DWZt/xuLD9yAtZUUk15qYuqwntvPJ2/jm33XAQD/HuSLPn71TBwRERFVlN6J1HfffYelS5di1KhR2rJBgwahRYsWmD17tkETKWdnZ8hksmKtT4mJiaUOFjeUsLAwhIWFaftYyTRGd/RCtkqN+X9cwZd7r8HaSoY3O1vGHGYl2XUxHjP/dwkA8F73Jni9QwMTR0RERM9D7669+Ph4dOzYsVh5x44dER8fb5CgCigUCvj7+yMyMlKnPDIyssQYqGp6u2sjhPd8AQDwn98v4+cTt0wbUAUdv5mEKRuiIQjAyPaemNLD8lvXiIiquwrNI7Vp06Zi5Rs3bkSTJvr/MKSnpyM6Olrb/RYbG4vo6GjExcUBAMLDw7FixQr8+OOPuHz5MqZOnYq4uDhMmDBB79fSR0REBHx8fBAYGGjU16HyefelxnjnxUYAgBn/+xubzljWTQCX7qXgrTVRyFVr0LtFXcwd5Fsl70QkIqpu9J7+4LfffsPw4cPRo0cPBAcHQyKR4OjRo9i3bx82bdqEl19+Wa8ADh48iG7duhUrHz16NFatWgVAnJBzwYIFiI+Ph6+vLxYtWoQuXbro9ToVxSVizIcgCPj3zsv48VgsJBJg0bDWGNymvqnDKtPtRxkYsvQEktJz0N7bCavHtavW6wkSEVUGs55HKioqCosWLcLly+Jt6T4+Pnj//ffRpk0bY8RoUkykzEvBtAFrT8VBJpVg8WttzHqw9sO0HPzr++O4/SgTzes5YOPbHeBgbWXqsIiIqjyzTqSqEyZS5kejEfDRbxfwa9RdyKUSLAv1R/fmxr35oCLSslV4dflJ/H0/FR5ONvhtQke4OFibOiwiomrBrCbkLJjQsmD/WVtVwTFS5ksqleC/Q1piQCs35GkETPzlHI5cf2jqsHTk5Kkx4Zco/H0/FbXtFFgzrj2TKCKiKqhcLVIymQzx8fFwcXGBVCotcZBswdxOVW3eJbZImS+VWoNJ685hz98PYG0lxfQ+zTHE393kC/6qNQImbziP3y/Ew04hw4a3guDnzik0iIgqU2X9fpfrF2f//v1wcnICABw4cMBowRDpw0omxXevtcXbP5/FgasPMWv73/hiz1X8y98doUEN0KhOjUqPSRAEzNnxN36/EA8rmQTLQgOYRBERVWF6j5GKi4uDh4dHibON37lzB56engYN0NTYImX+cvM0WH86DqtP3MI/DzO05Z2bOGNUkBdeauYCmbRyphpYvP86vtx7DRIJ8O2rbTCglVulvC4REeky28HmRbv5inr06BFcXFyqTNde0SVirl27xkTKAgiCgGM3HmHV8VvYd+UBCj7Z9WvaIDSoAYYHeKCWncJor7/hdBymbbkIAJg9wAdjgr2N9lpERPRsZptISaVSPHjwAHXq1NEpv337Nnx8fJCRkVHKMy0TW6Qs053Hmfjl1G1sPHMHyZkqAIBSLsXAVm4Y3dELvvUN29225+8ETPwlChoBCOvWCB/2ambQ8xMRkX7MLpEKDw8HAHzzzTcYP348bG1ttcfUajVOnToFmUyGY8eOGSdSE2EiZdmyVWps/+s+Vh+/hb/vF95V2tazJkZ39EIf33pQyPWe4F/HqX8eIfTH08jN02B4gAc+H+LHWcuJiEzMrAabA8D58+cBiN0nFy9ehEJR2EWiUCjQqlUrfPDBB4aPkOg5WFvJMCzAA0P93XEuLhlrTtzCrovxOBeXjHNx0fh3jcsY0d4TI9t7wrUC0xNcSUjFm2vOIjdPgx7NXfHZy1z6hYioOtG7a2/s2LH45ptvqk3rDFukqp7EtGxsOH0Ha0/dxoPUHACAXCpBL9+6GB3khUCvWuVKhu48zsSQpceRmJaDQK9a+PmN9lz6hYjITJhd116BlJQUqNVq7XQIBR4/fgy5XF5lkg0ONq/6VGoN9v79AKtP3MLp2Mfa8mZ17TG6oxcGtXaDraLkRttH6TkY+v0J/JOUgaau9tj0dhAcbbn0CxGRuTDbRKpPnz4YMGAA3nnnHZ3y77//Htu3b8euXbsMGqCpsUWqergcn4o1J25j2/l7yFKJd546WMsxLMADoUEN0KC2nbZuRk4eRvxwEn/dTUH9mjb4bWJH1HXkrOVERObEbBMpJycnHDt2DM2bN9cpv3LlCoKDg/Ho0SODBmhqTKSql5RMFTZH3cHPJ2/j9qNMAIBEArz4Qh2M6uiFjo1q483VZ3HkehJq2Vph84SOaOxS+RN/EhHRs5ndYPMCOTk5yMvLK1auUqmQlZVlkKCITMXR1gpvdm6IccHeOHT9IdYcv4UDVx9qN3trOdKy82BjJcOPYwKZRBERVXN63/cdGBiI5cuXFyv//vvv4e/vb5CgiExNKpWgW1MX/DS2HQ5+8CLe7OQNh/wkSi6VYOnrbdHGs5apwyQiIhPTu2vv2LFj6NGjBwIDA9G9e3cAwL59+3DmzBns3bsXnTt3NkqgpsKuPSqQmZuHvX8/QP1aNgj0cir7CUREZDKV9futd4tUcHAwTpw4AQ8PD2zatAk7duxA48aNceHChSqVREVERMDHxweBgYGmDoXMhK1CjsFt6jOJIiIiLb1bpKobtkgRERFZHrMdbF5UVlYWVCqVThmTDSIiIqou9O7ay8zMxKRJk+Di4oIaNWqgVq1aOhsRERFRdaF3IvXhhx9i//79WLJkCZRKJVasWIE5c+bAzc0Na9asMUaMRERERGZJ7669HTt2YM2aNXjxxRcxbtw4dO7cGY0bN0aDBg2wdu1ajBw50hhxEhEREZkdvVukHj9+DG9vbwDieKjHj8U1yjp16oTDhw8bNjoiIiIiM6Z3ItWwYUPcunULAODj44NNmzYBEFuqatasacjYiIiIiMya3onU2LFj8ddffwEApk+frh0rNXXqVHz44YcGD9BUOI8UERERleW555GKi4vD2bNn0ahRI7Rq1cpQcZkNziNFRERkecxyZnOVSoVu3brh2rVr2jJPT0+88sorVTKJIiIiInoWvRIpKysrXLp0CRKJxFjxEBEREVkMvcdIjRo1CitXrjRGLEREREQWRe95pHJzc7FixQpERkYiICAAdnZ2OscXLlxosOCIiIiIzJneidSlS5fQtm1bANAZKwWAXX5ERERUrZQrkbpw4QJ8fX0hlUpx4MABY8dEREREZBHKNUaqTZs2SEpKAiBOyPno0SOjBkVERERkCcqVSNWsWROxsbEAgFu3bkGj0Rg1KCIiIiJLUK6uvSFDhqBr166oV68eJBIJAgICIJPJSqz7zz//GDRAIiIiInNVrkRq+fLleOWVV3Djxg1MnjwZ48ePh729vbFjM6mIiAhERERArVabOhQiIiIyU3ovETN27Fh8++23VT6RKsAlYoiIiCxPZf1+6z39wU8//WSMOIiIiIgsjt4zmxMRERGRiIkUERERUQUxkSIiIiKqICZSRERERBWk92BzQFxj7+DBg0hMTCw2OefMmTMNEhgRERGRudM7kfrhhx8wceJEODs7o27dujoLFUskEiZSREREVG3onUj95z//wWeffYaPP/7YGPEQERERWQy9x0g9efIEQ4cONUYsRERERBZF70Rq6NCh2Lt3rzFiISIiIrIoenftNW7cGDNmzMDJkyfh5+cHKysrneOTJ082WHBERERE5kzvtfa8vb1LP5lEgn/++ee5gzKGzMxMNG/eHEOHDsWXX35Z7udxrT0iIiLLY7Zr7cXGxhojDqP77LPP0L59e1OHQURERFXIc03IKQgC9GzQMonr16/jypUr6Nu3r6lDISIioiqkQonUmjVr4OfnBxsbG9jY2KBly5b4+eefKxTA4cOHMWDAALi5uUEikWDbtm3F6ixZsgTe3t6wtraGv78/jhw5otdrfPDBB5g/f36F4iMiIiIqjd5dewsXLsSMGTMwadIkBAcHQxAEHDt2DBMmTEBSUhKmTp2q1/kyMjLQqlUrjB07FkOGDCl2fOPGjZgyZQqWLFmC4OBgLFu2DH369EFMTAw8PT0BAP7+/sjJySn23L179+LMmTN44YUX8MILL+D48eNlxpOTk6NzrtTUVL3eDxEREVUjgp68vLyE1atXFytftWqV4OXlpe/pdAAQtm7dqlPWrl07YcKECTplzZo1E6ZNm1auc06bNk1wd3cXGjRoINSuXVtwcHAQ5syZU2r9WbNmCQCKbSkpKXq/HyIiIjKNlJSUSvn91rtrLz4+Hh07dixW3rFjR8THxz9fVveU3NxcREVFISQkRKc8JCSkXK1LADB//nzcuXMHt27dwpdffonx48c/cxmb6dOnIyUlRbvduXPnud4DERERVV16J1KNGzfGpk2bipVv3LgRTZo0MUhQBZKSkqBWq+Hq6qpT7urqioSEBIO+VgGlUgkHBwedjYiIiKgkeo+RmjNnDoYPH47Dhw8jODgYEokER48exb59+0pMsAyh6MLIgHi34NNl5TFmzJhy142IiEBERATUarXer0NERETVg94tUkOGDMGpU6fg7OyMbdu2YcuWLXB2dsbp06fx8ssvGzQ4Z2dnyGSyYq1PiYmJxVqpDC0sLAwxMTE4c+aMUV+HiIiILJfeLVKAeJfcL7/8YuhYilEoFPD390dkZKROkhYZGYlBgwYZ/fWJiIiInqVciVRqaqp2rFBZ0wHoO6YoPT0dN27c0D6OjY1FdHQ0nJyc4OnpifDwcISGhiIgIABBQUFYvnw54uLiMGHCBL1eR1/s2iMiIqKylGutPZlMhvj4eLi4uEAqlZY4Pqlg3JK+icfBgwfRrVu3YuWjR4/GqlWrAIgTci5YsADx8fHw9fXFokWL0KVLF71ep6K41h4REZHlqazf73IlUocOHUJwcDDkcjkOHTr0zLpdu3Y1WHDmgIkUERGR5TGrRYuLJkfe3t7w8PAo8U46zrlERERE1Yned+15e3vj4cOHxcofP34Mb29vgwRlDiIiIuDj44PAwEBTh0JERERmSu9EqrQ5nNLT02FtbW2QoMwBpz8gIiKispR7+oPw8HAA4uSYM2bMgK2trfaYWq3GqVOn0Lp1a4MHSERERGSuyp1InT9/HoDYInXx4kUoFArtMYVCgVatWuGDDz4wfIREREREZqrcidSBAwcAAGPHjsU333xT5e9g4zxSREREVJZyTX9QnXH6AyIiIstjVtMfPO3MmTPYvHkz4uLikJubq3Nsy5YtBgmMiIiIyNzpfdfehg0bEBwcjJiYGGzduhUqlQoxMTHYv38/HB0djREjERERkVnSO5GaN28eFi1ahJ07d0KhUOCbb77B5cuXMWzYMHh6ehojRiIiIiKzpHcidfPmTfTr1w8AoFQqkZGRAYlEgqlTp2L58uUGD9BUOCEnERERlUXvRMrJyQlpaWkAgPr16+PSpUsAgOTkZGRmZho2OhPihJxERERUFr0Hm3fu3BmRkZHw8/PDsGHD8N5772H//v2IjIxE9+7djREjERERkVnSO5FavHgxsrOzAQDTp0+HlZUVjh49ildeeQUzZswweIBERERE5kqveaTy8vKwdu1a9OrVC3Xr1jVmXGaD80gRERFZnsr6/dZrjJRcLsfEiRORk5NjrHiIiIiILIbeg83bt2+vXXevKuNde0RERFQWvZeI2bx5M6ZNm4apU6fC398fdnZ2Osdbtmxp0ABNjV17RERElqeyfr/1TqSk0uKNWBKJBIIgQCKRVLlFfplIERERWR6zXWsvNjbWGHEQERERWRy9E6kGDRoYIw4iIiIii6N3IrV9+/YSyyUSCaytrdG4cWN4e3s/d2BERERE5k7vRGrw4MHaMVFFFR0n1alTJ2zbtg21atUyWKBERERE5kbv6Q8iIyMRGBiIyMhIpKSkICUlBZGRkWjXrh127tyJw4cP49GjR/jggw+MEW+l4fQHREREVBa979rz9fXF8uXL0bFjR53yY8eO4a233sLff/+NP//8E+PGjUNcXJxBgzUF3rVHRERkecxyZnMAuHnzZokBOTg44J9//gEANGnSBElJSc8fHREREZEZ0zuR8vf3x4cffoiHDx9qyx4+fIiPPvpI2w12/fp1uLu7Gy5KIiIiIjOk92DzlStXYtCgQXB3d4eHhwckEgni4uLQsGFD/O9//wMApKenY8aMGQYPloiIiMic6D1GCgAEQcCePXtw7do1CIKAZs2aoWfPniXOem7pOEaKiIjI8pjtEjFFZWdnQ6lUQiKRGDIms6L9h9gwAQ616wI2NQHrmoBNreL7ihpAFb4WRERElsJsl4jRaDT47LPP8P333+PBgwe4du0aGjZsiBkzZsDLywtvvPGGMeI0vei1gLKMJEkqz0+saorJlT77VjbGjJ6IiIiMQO9E6j//+Q9Wr16NBQsWYPz48dpyPz8/LFq0qOomUsFTAVk2kPUEyEoGspN199W5gCYPyEwSN33JrQHb2oBLc6CuX/7WCnBqCFTBLlMiIqKqQO+uvcaNG2PZsmXo3r077O3t8ddff6Fhw4a4cuUKgoKC8OTJE2PFahLlahoUBECVWXKCVZ59QVN6AFZ2gGsLoF7L/OSqJeDiA1hZG/JtEhERVSlm27V37949NG7cuFi5RqOBSqUySFAWRyIBFHbi5lhfv+dqNEBumphUpT8AEi7mbxeAB38Dqgzg7mlx076eDHB+oUhylZ9g2ToZ9G0RERHRs+mdSLVo0QJHjhxBgwYNdMo3b96MNm3aGCwwU4uIiEBERATUarVxX0gqBawdxa1WA8CjXeExdR7w+CYQf0FMrAoSrMxHwMPL4nZhY2F9B3cxqSqaYNVswAHwRERERqJ3IjVr1iyEhobi3r170Gg02LJlC65evYo1a9Zg586dxojRJMLCwhAWFqZtGjQJmRyo01TcWg4VywQBSIsXk6qiCdaTWCD1rrhd+6PwHErHwqSqIMGq0wyQWZnmPREREVUhFZr+YM+ePZg3bx6ioqKg0WjQtm1bzJw5EyEhIcaI0aQsZh6p7BSxK7BogpV4GdCU0N0qUwBenQH/0UDTvkyqiIioyrGIeaSqA4tJpEqSlwskXS0cdxWf33qVk1JYx84FaDMSaDsacPI2XaxEREQGZLaJVMOGDXHmzBnUrl1bpzw5ORlt27bVLlxcVVh0IlUSQQAe3QCi1wHnfwEyEguPNewG+I8RW6nkCpOFSERE9LzMNpGSSqVISEiAi4uLTvmDBw/g6emJnJwcgwZoalUukSpKrQKu/gFErQJu7geQ/1GwqwO0Hgm0HQXUbmTKCImIiCrE7KY/2L59u3Z/z549OgOw1Wo19u3bBy8vL4MGR0YmswJ8Borbk1vAuZ+B8z+L0zAc+1rcvLuKrVTN+rOVioiI6CnlbpEqWJBYIpHg6adYWVnBy8sLX331Ffr372/4KE2oSrdIlUStAq7tEVupbvwJbSuVrTPQeoSYVLGVioiIzJzZdu15e3vjzJkzcHZ2NlZMZqXaJVJFJccVtlKlxReWe3UWE6rmAwC50mThERERlcZsE6nqplonUgXUecD1vfmtVJGFS9rYOBW2Ujk3MWWEREREOsw6kdq3bx/27duHxMREaDS668T9+OOPBgvOHDCRekryHfFuv3NrgLT7heUNOhW2UnEdQCIiMjGzG2xeYM6cOZg7dy4CAgJQr149SLj8SPVS0wPoNh3o8qE4hipqFXB9D3D7qLjZ1AJajRAn+6zT1NTREhERGZXeLVL16tXDggULEBoaaqyYzApbpMoh5V5hK1Xq3cJyz45Au/FAi5e53h8REVWqyvr9lur7hNzcXHTs2NEYsZClcqwPvPgxMOUCMGIz0LQfIJEBcceBX8cCOyaLdwMSERFVMXq3SH388ceoUaMGZsyYYayYDE4ul8PX1xcAEBAQgBUrVpT7uWyRqqDU+8CZFcDRReLgdO+uwLA1gE1NU0dGlkYQgLxsICcNyE4FclLFfe1WQlluRuXFJ5UBMqV4B6tM8dRfpTj/ms5fPevJFOKcb2zVJdKL2Y6Rys7OxvLly/Hnn3+iZcuWsLLSXfB24cKFBgvOUGrWrIno6GhTh1G9OLgB3WcC7u2AX8cBsYeAlT2BEZu4pl91pFYBj/8B0hKeSnpSiyRIaU9tKYX7mjxTvwMTkwBya8DKBrCyzf9bdL88ZdYlHHuqjkzBhI1IT3onUhcuXEDr1q0BAJcuXdI5xoHnVEzT3sAbe4B1w4Gka8CK7sCr6wDPDqaOjIxBrQIe3QQeXhG3xMvAw6vi+o6a5+3elQBKB0BpX7hZF31cZN/KFpDoPXKhAgQxycvLBdQ5Rf7mAOrcUv7mlFC/hOcJat3XycsSt6zHxns7EulTSZYtoLAt3LeyARR2pRwv53OkMuPFT2QCJp9H6vDhw/jiiy8QFRWF+Ph4bN26FYMHD9aps2TJEnzxxReIj49HixYt8PXXX6Nz587lfg2FQgE/Pz/Y2Njgs88+Q9euXcv9XHbtGUhagphMxUeL/9c7aAnQcqipo6KKyssFHucnTIlXChOnRzdKbz1S1AAcPZ5KfgoSoJISpKfKrOwAaWUkR2ZCo9ZNvPKyAFU2oMoEVFn5W/5+3lOPdfbLKMvNeCppMzKZUjf5khe0iFkX2bcp57H8VjZ5QWtbkXpy6+r1eaFizLZrz9AyMjLQqlUrjB07FkOGDCl2fOPGjZgyZQqWLFmC4OBgLFu2DH369EFMTAw8PT0BAP7+/iUulrx37164ubnh1q1bcHNzw6VLl9CvXz9cvHix1Iuak5Ojc67U1FQDvdNqzr4uMHYXsOUt4MpOYMub4g9x14/ZlWDOChKmgpalh5fFxOnxzWckTPbi1Bd1mgEuzcS/dZoBju78t9aHVCYmHLA1/mupVYXJVW5GkcQrozDxys3ULSupXm5m/nkyi5wvf79guSl1DpCVA2Q9Mf77klsXdonKFPmP8/8WjEMr2Ep8XLR+kec/65jUShzTJrUCZPIij+X8/FdR5W6ReuWVV8p1wi1btlQ8GImkWItU+/bt0bZtWyxdulRb1rx5cwwePBjz58/X+zX69OmDf//73wgICCjx+OzZszFnzpxi5WyRMhCNBtg3Gzj2jfjYbygwcDEn8TS1vFyxNelhfsJUkDiVJ2HSJkvNxcdMmOhpBTcM6CRgGYUtbAXHVFn5+5lPHct/rG15K+FYQcucOtfU77Z00qcSK23C9Yzkq2idoo+lMrErViLV3ZfIxP/+SiwvqF9SWcG+RLdc20VeJFXQSRuE0st0ysvxfEEQW0c16qf+akoo15RQT7c8NSMbjqPXmk+LlKOjo9GCKE1ubi6ioqIwbdo0nfKQkBAcP368XOd48uQJbG1toVQqcffuXcTExKBhw4al1p8+fTrCw8O1j1NTU+Hh4VGxN0DFSaVAz7mAUyPg93Dg4mZxtvRX1wJ21WP9RrOR+Vic/+uvDWK3XGndOwr7/GSpqZgsFSRODvWZMFH5SCSFXXK2TsZ9LY265IRMZ4xaka3Ex9n53anZ+c/L1h3HlpdT/FhetliuUeVP91JCG4UmL39MXZZxrwGJcipn5FK5E6mffvrJmHGUKCkpCWq1Gq6urjrlrq6uSEhIKNc5Ll++jLfffhtSqRQSiQTffPMNnJxK/w9ZqVRCqeRCvEbnPxqo1QDYOAq4c1IchD5iM1DnBVNHVvUlXAROLwcubNb9Qlc6FOmSa16YODm4MWEiyyGVAcoa4mZKGrWYUBUkVpq8Io/zipQ//ThP93mlnUOjLmzBETSFm+apxyWWFzy3pPolHNP577/IfpnlpdVFyeUFrWRSWZG/0qceP6v8qedn5QKfv1/Bf8DyM/kYqfJ4+m5AQRDKfYdgx44dcfHiRb1fMyIiAhEREVCrK3EQZnXT8EXgzT+BdUOBJ7eAFT2A4WvEcjIstQq4vAM4/YM4UWoBVz9x9vnGPZgwERmSNP8HHRy2YDKpqQCqeSLl7OwMmUxWrPUpMTGxWCuVoYWFhSEsLEw76p+MpM4LwJv7gQ0jxJapX4YA/b4SF0Cm55f2ADi3Gjj7I5AWL5ZJ5UDzgUC7t8RpKJg8ERFVmFknUgqFAv7+/oiMjMTLL7+sLY+MjMSgQYNMGBkZlF1tYPR24H+TgIubgB3viXMR9ZjD25crQhCAu2fE7ru/txXO32TnAgSMBfzHAg71TBoiEVFVYfJEKj09HTdu3NA+jo2NRXR0NJycnODp6Ynw8HCEhoYiICAAQUFBWL58OeLi4jBhwgSjxsWuvUomVwKvLAdqNwYOzgOOfyvOhP3KcnEyPyqbKhu49JuYQMVHF5a7twPavy22QskVJguPiKgqMvmEnAcPHkS3bt2KlY8ePRqrVq0CIE7IuWDBAsTHx8PX1xeLFi1Cly5dKiU+TshpAhc2A/97R7wjpl5r4LUNbEF5luQ7wNmVQNTqwlmvZUrA71/i+Ce3NqaNj4jIBCrr99vkiZS5YyJlInEnxXFTmY/E2+xHbATq+pk6KvMhCEDsYbH16eou8c4aQJw5PPANoM0oscuUiKiaYiJlJphImdDj2Pw1+q6Ky4P860dx7b7qLCcduLBBvPvu4ZXCcu+u4uDxF3qLE/oREVVz1WaJGHPFMVJmwMkbeGMvsGkUEHsI2PAa0Gse0H5C9bvTLOkGcOYHIHodkJO/bJGVHdD6NSBwvDhJJhERVTq2SJWBLVJmQK0Cfn9fvI0fAALfBHr/t+q3vGjUwPVIsfvu5r7CcqdGYutT69cAa07NQURUErZIERWQWQEDvgGcmwB7ZwBnVojdfkNXAdZVNLm9/iew631xolIAgAR4oZc4eLzhS5wWgojITDCRIssgkQAd3wVqeQNbxostND/2Egeh1/Q0dXSGlf4Q+HUckJMitji1CRUHkDuVvkYkERGZBv+3thQRERHw8fFBYGCgqUOhopr3B8b+AdjXAxJjgB9eAu6eNXVUhrVvtphE1W0JhF8Gen3GJIqIyExxjFQZOEbKTKXcE+/oe3ARkFsDg5cCvq+YOqrnd/esuIAzAIzbC3i2N208REQWqrJ+v9kiRZbJsT4wbrd4u39eNvDrWOD8WlNH9Xw0GmDXh+J+q9eYRBERWQAmUmS5lDWAV9cB7d4WH//xsdhSZamifwHunwMU9uI6g0REZPaYSJFlk8qA3vMB90AgNw34PVyc9dvSZD0B/pwt7r84DbB3NWk4RERUPkykSsHB5hZEKgMGLgZkCuDabnHhXktzYL64HI5zU3GBYSIisggcbF4GDja3IAf/CxycB9jWBsLOWM5acwmXgGWdxfXyRv0PaPiiqSMiIrJ4HGxOpK9OUwEXH7FlZ890U0dTPoIA/PGRmET5DGISRURkYZhIUdUhVwADvwMgAS5sFGcHN3eXfgNuHwPkNkDIZ6aOhoiI9MREiqoW9wCgwzvi/s4pQE6aScN5ppx0YO//ifud3wdqepg2HiIi0hsTKap6XvoUqNkASLkD7Jtr6mhKd/gLIC0eqOUlLn9DREQWh4lUKXjXngVT2ImLHAPA6R+AuFOmjackSTeAExHifq/5gJW1aeMhIqIKYSJVirCwMMTExODMmTOmDoUqolE3oPVIAAKw/V0gL8fUERUSBGD3x4BGBTTuCTTtY+qIiIiogphIUdUV8h/AzgVIugoc/tLU0RS6+gdw409AagX0/hyQSEwdERERVRATKaq6bJ2Avl+I+0cXivM1mZoqC9g9TdzvOAlwbmzaeIiI6LkwkaKqzWcQ0Kw/oMkTu/g0atPGc/w7IPk2YO8GdP7AtLEQEdFzYyJFVZtEAvT9ElA6igsCn1xquliS44AjX4n7If8WF10mIiKLxkSKqj6HemLiAgD7/wM8jjVNHHs+BfKygQadAN8hpomBiIgMiolUKTj9QRXTdhTg1RnIywJ2vCfeOVeZbh4ALm8HJDKgz385wJyIqIpgIlUKTn9QxUgk4txScmsg9hBw/pfKe+28XHE9PQAIfBOo61t5r01EREbFRIqqj9qNgG6fiPt7PwXSEirndU8vA5KuAbbOha9PRERVAhMpql46hAH1WgPZKcCuD43/emkJwMH/ivs9ZgE2NY3/mkREVGmYSFH1IpMDgxYDUrk4Zilmu3FfL3IWkJsGuLUFWr9u3NciIqJKx0SKqp+6fkDwe+L+rg+ArCfGeZ24k8CFDeJ+3y8BKf9zIyKqavjNTtVTl4+A2k2A9AfA3hmGP79GLSZpANAmFHD3N/xrEBGRyTGRourJyhoY+J24f/5n4J9Dhj1/1Cog4aI4EWj3WYY9NxERmQ0mUlR9NQgSpyMAgB2TgdxMw5w38zGwP38C0Jc+BWrUMcx5iYjI7DCRouqt+yzAoT7w5BZw4DPDnHP/v8VxVy4tgIA3DHNOIiIyS0ykqHqzdgD6LxL3Ty4B7kU93/nuRwNnfxL3+y4Q7xIkIqIqi4lUKbhETDXyQi/A91+AoAG2TwbUqoqdR6PJn5tKENfS8+pk0DCJiMj8SAShshcdsyypqalwdHRESkoKHBwcTB0OGUtGErA4EMh6DLz0f0CXCkzWGb0e2DYBsLIDJp0BHOsbPk4iIiqXyvr9ZosUEQDYOYuLCQPAoQXAw6v6PT87FYicKe53+YBJFBFRNcFEiqiA31CgcU9AnSt28Wk05X/uof8CGYmAUyMgKMx4MRIRkVlhIkVUQCIRB54ragB3TgJnV5bveQ+vAqe+F/f7/BeQK40XIxERmRUmUkRF1fQAeswW9/+cDSTfeXZ9QQD++AjQ5AFN+wJNeho7QiIiMiNMpIieFvAG4NEByE0Hdk4Vk6XSXN4O/HMQkCmBXvMqLUQiIjIPTKSIniaVisvHyBTAjUjg4uaS6+VmAns+FfeDJwNO3pUXIxERmQUmUkQlqfOCuLAxAPzxsTg9wtOOLgJS7gCOHkCn8MqNj4iIzAITKaLSBL8HuPqKc0vtnqZ77HEscOwbcT/kP4DCtvLjIyIik2MiRVQauULs4pNIxe69a3sKj+35BFDnAN5dAZ9BpouRiIhMiokU0bPUbwt0eEfc3zlVnHjzeiRwdRcglQN9FojTJhARUbXEFVWJytLtU+DKTuDJLWDvp8CtY2J5+wmASzOThkZERKbFFimisihsgQHfivvn1gCPbwJ2LkDXj00bFxERmVy1SKRiY2PRrVs3+Pj4wM/PDxkZGaYOiSxNw65Am9DCxz3nAtZcxJqIqLqrFl17Y8aMwX/+8x907twZjx8/hlLJJTyoAkL+AyReBhzdgZbDTR0NERGZgSqfSP3999+wsrJC586dAQBOTk4mjogslk1NYPw+U0dBRERmxORde4cPH8aAAQPg5uYGiUSCbdu2FauzZMkSeHt7w9raGv7+/jhy5Ei5z3/9+nXUqFEDAwcORNu2bTFvHpfxICIiIsMweYtURkYGWrVqhbFjx2LIkCHFjm/cuBFTpkzBkiVLEBwcjGXLlqFPnz6IiYmBp6cnAMDf3x85OTnFnrt3716oVCocOXIE0dHRcHFxQe/evREYGIiePUteXDYnJ0fnXKmpqQZ6p0RERFTVSAThWSuyVi6JRIKtW7di8ODB2rL27dujbdu2WLp0qbasefPmGDx4MObPn1/mOU+cOIE5c+Zg9+7dAIAvvvgCAPDhhx+WWH/27NmYM2dOsfKUlBQ4OHBwMRERkSVITU2Fo6Oj0X+/Td619yy5ubmIiopCSEiITnlISAiOHz9ernMEBgbiwYMHePLkCTQaDQ4fPozmzZuXWn/69OlISUnRbnfu3Hmu90BERERVl8m79p4lKSkJarUarq6uOuWurq5ISEgo1znkcjnmzZuHLl26QBAEhISEoH///qXWVyqVvKuPiIiIysWsE6kCkqeW4BAEoVjZs/Tp0wd9+vTR6zUjIiIQEREBtVqt1/OIiIio+jDrrj1nZ2fIZLJirU+JiYnFWqkMLSwsDDExMThz5oxRX4eIiIgsl1knUgqFAv7+/oiMjNQpj4yMRMeOHU0UFREREZHI5F176enpuHHjhvZxbGwsoqOj4eTkBE9PT4SHhyM0NBQBAQEICgrC8uXLERcXhwkTJhg1LnbtERERUVlMPv3BwYMH0a1bt2Llo0ePxqpVqwCIE3IuWLAA8fHx8PX1xaJFi9ClS5dKia+ybp8kIiIiw6ms32+TJ1LmjokUERGR5eE8UiYWEREBHx8fBAYGmjoUIiIiMlNskSoDW6SIiIgsD1ukiIiIiMycye/aM3cFDXZcvJiIiMhyFPxuG7vjjYlUGdLS0gAAHh4eJo6EiIiI9PXo0SM4Ojoa7fwcI1UGjUaD+/fvw97eXq9laSpDamoqPDw8cOfOnWo7fovXgNegAK8DrwHAa1CA1wFISUmBp6cnnjx5gpo1axrtddgiVQapVAp3d3dTh/FMDg4O1fY/lAK8BrwGBXgdeA0AXoMCvA7i77hRz2/UsxMRERFVYUykiIiIiCqIiZQFUyqVmDVrFpRKpalDMRleA16DArwOvAYAr0EBXofKuwYcbE5ERERUQWyRIiIiIqogJlJEREREFcREioiIiKiCmEgRERERVRATKTOyZMkSeHt7w9raGv7+/jhy5Eipdbds2YKePXuiTp06cHBwQFBQEPbs2aNTZ9WqVZBIJMW27OxsY7+V56LPdTh48GCJ7/HKlSs69X777Tf4+PhAqVTCx8cHW7duNfbbeC76XIMxY8aUeA1atGihrWNpn4XDhw9jwIABcHNzg0QiwbZt28p8zqFDh+Dv7w9ra2s0bNgQ33//fbE6lvQ50PcaVMXvBH2vQVX9PtD3OlS174T58+cjMDAQ9vb2cHFxweDBg3H16tUyn1dZ3wlMpMzExo0bMWXKFHz66ac4f/48OnfujD59+iAuLq7E+ocPH0bPnj2xa9cuREVFoVu3bhgwYADOnz+vU8/BwQHx8fE6m7W1dWW8pQrR9zoUuHr1qs57bNKkifbYiRMnMHz4cISGhuKvv/5CaGgohg0bhlOnThn77VSIvtfgm2++0Xnvd+7cgZOTE4YOHapTz5I+CxkZGWjVqhUWL15crvqxsbHo27cvOnfujPPnz+OTTz7B5MmT8dtvv2nrWNrnQN9rUBW/E/S9BgWq0vcBoP91qGrfCYcOHUJYWBhOnjyJyMhI5OXlISQkBBkZGaU+p1K/EwQyC+3atRMmTJigU9asWTNh2rRp5T6Hj4+PMGfOHO3jn376SXB0dDRUiJVC3+tw4MABAYDw5MmTUs85bNgwoXfv3jplvXr1El599dXnjtcYnvezsHXrVkEikQi3bt3SllniZ6EAAGHr1q3PrPPRRx8JzZo10yl7++23hQ4dOmgfW9rnoKjyXIOSVIXvhALluQZV8fvgaRX5LFS174TExEQBgHDo0KFS61TmdwJbpMxAbm4uoqKiEBISolMeEhKC48ePl+scGo0GaWlpcHJy0ilPT09HgwYN4O7ujv79+xf7v1Nz8jzXoU2bNqhXrx66d++OAwcO6Bw7ceJEsXP26tWr3Ne2Mhnis7By5Ur06NEDDRo00Cm3pM+Cvkr7Nz579ixUKtUz65jj58AQqsJ3QkVVle8DQ6lq3wkpKSkAUOyzXVRlficwkTIDSUlJUKvVcHV11Sl3dXVFQkJCuc7x1VdfISMjA8OGDdOWNWvWDKtWrcL27duxfv16WFtbIzg4GNevXzdo/IZSketQr149LF++HL/99hu2bNmCpk2bonv37jh8+LC2TkJCwnNd28r0vJ+F+Ph4/PHHH3jzzTd1yi3ts6Cv0v6N8/LykJSU9Mw65vg5MISq8J2gr6r2fWAIVe07QRAEhIeHo1OnTvD19S21XmV+J8j1qk1GJZFIdB4LglCsrCTr16/H7Nmz8b///Q8uLi7a8g4dOqBDhw7ax8HBwWjbti2+++47fPvtt4YL3MD0uQ5NmzZF06ZNtY+DgoJw584dfPnll+jSpUuFzmkOKhrvqlWrULNmTQwePFin3FI/C/oo6Zo9XW5pn4OKqmrfCeVVVb8PnkdV+06YNGkSLly4gKNHj5ZZt7K+E9giZQacnZ0hk8mKZcGJiYnFsuWnbdy4EW+88QY2bdqEHj16PLOuVCpFYGCg2f4fx/Nch6I6dOig8x7r1q373OesLM9zDQRBwI8//ojQ0FAoFIpn1jX3z4K+Svs3lsvlqF279jPrmOPn4HlUpe8EQ7Dk74PnVdW+E959911s374dBw4cgLu7+zPrVuZ3AhMpM6BQKODv74/IyEid8sjISHTs2LHU561fvx5jxozBunXr0K9fvzJfRxAEREdHo169es8dszFU9Do87fz58zrvMSgoqNg59+7dq9c5K8vzXINDhw7hxo0beOONN8p8HXP/LOirtH/jgIAAWFlZPbOOOX4OKqqqfScYgiV/HzyvqvKdIAgCJk2ahC1btmD//v3w9vYu8zmV+p2g19B0MpoNGzYIVlZWwsqVK4WYmBhhypQpgp2dnfYui2nTpgmhoaHa+uvWrRPkcrkQEREhxMfHa7fk5GRtndmzZwu7d+8Wbt68KZw/f14YO3asIJfLhVOnTlX6+ysvfa/DokWLhK1btwrXrl0TLl26JEybNk0AIPz222/aOseOHRNkMpnw+eefC5cvXxY+//xzQS6XCydPnqz091ce+l6DAq+//rrQvn37Es9paZ+FtLQ04fz588L58+cFAMLChQuF8+fPC7dv3xYEofg1+OeffwRbW1th6tSpQkxMjLBy5UrByspK+PXXX7V1LO1zoO81qIrfCfpeg6r4fSAI+l+HAlXlO2HixImCo6OjcPDgQZ3PdmZmpraOKb8TmEiZkYiICKFBgwaCQqEQ2rZtq3Nr5+jRo4WuXbtqH3ft2lUAUGwbPXq0ts6UKVMET09PQaFQCHXq1BFCQkKE48ePV+I7qhh9rsN///tfoVGjRoK1tbVQq1YtoVOnTsLvv/9e7JybN28WmjZtKlhZWQnNmjXT+WI1R/pcA0EQhOTkZMHGxkZYvnx5ieeztM9CwW3spX2+S7oGBw8eFNq0aSMoFArBy8tLWLp0abHzWtLnQN9rUBW/E/S9BlX1+6Ai/z1Upe+Ekt47AOGnn37S1jHld4IkP0giIiIi0hPHSBERERFVEBMpIiIiogpiIkVERERUQUykiIiIiCqIiRQRERFRBTGRIiIiIqogJlJEREREFcREioiIiKiCmEgRERERVRATKSIiIqIKYiJFREREVEFMpIioWpo7dy78/PxgZ2cHV1dXTJw4ESqVytRhEZGFkZs6ACKiyiYIAtRqNZYtW4b69esjJiYGo0aNQsuWLTFx4kRTh0dEFkQiCIJg6iCIiExtxIgRqFOnDr755htTh0JEFoRde0RU7dy+fRuTJk2Cr68vatWqhRo1amDTpk1wd3c3dWhEZGGYSBFRtZKUlIR27dohKSkJCxcuxNGjR3HixAnIZDK0bt3a1OERkYXhGCkiqlZ27dqFvLw8rF+/HhKJBAAQERGB3NxcJlJEpDcmUkRUrTg5OSE1NRXbt2+Hj48PduzYgfnz56N+/fqoU6eOqcMjIgvDweZEVK0IgoCJEydi3bp1sLGxweuvv47s7Gzcvn0bO3fuNHV4RGRhmEgRERERVRAHmxMRERFVEBMpIiIiogpiIkVERERUQUykiIiIiCqIiRQRERFRBTGRIiIiIqogJlJEREREFcREioiIiKiCmEgRERERVRATKSIiIqIKYiJFREREVEH/D7qvx7LZ7PrKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def residuals(aas, Omega_m, n1, n2):\n",
    "    integ_n1 = growth_factor_trpz(aas, Omega_m, sampling_points=n1)\n",
    "    integ_n2 = growth_factor_trpz(aas, Omega_m, sampling_points=n2)\n",
    "    \n",
    "    return np.abs(integ_n1 - integ_n2)/integ_n2\n",
    "\n",
    "aas = np.linspace(1.e-1, 2., 100)\n",
    "\n",
    "plt.plot(zs, residuals(zs, 0.3, 10, 200), label=\"n=10 vs n=200\")\n",
    "plt.plot(zs, residuals(zs, 0.3, 100, 200), label=\"n=100 vs n=200\")\n",
    "\n",
    "plt.semilogy()\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"Integration fractional difference\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d49fae12-331b-49a6-9326-5fe5ea087620",
   "metadata": {},
   "source": [
    "## scipy.integrate.romberg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "90c07e2a-c2e0-4bc3-80b3-8bf046564ba5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def growth_factor_romb(a, Omega_m):\n",
    "    integral = scipy.integrate.romberg(\n",
    "        growth_integrand, \n",
    "        1.e-6, a, \n",
    "        rtol=1.e-3,\n",
    "        args=(Omega_m,)) \n",
    "    return 5./2. * Omega_m * np.sqrt(E2(a, Omega_m)) * integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "85f7441b-29d8-4d2a-b6a5-862672d91939",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-1, np.log10(2), 100)\n",
    "\n",
    "plt.plot(aas, growth_factor_trpz(aas, .1), label = \"trapz\")\n",
    "plt.plot(aas, [growth_factor_romb(a, .1) for a in aas], label = \"Romberg\", dashes=[3,3])\n",
    "\n",
    "plt.loglog()\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"$D(a)$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad168996-6bf2-4df4-963a-b6b5b2570a38",
   "metadata": {},
   "source": [
    "## Simpson 1/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "10d7ea61-92dc-4998-85ad-39bd14060690",
   "metadata": {},
   "outputs": [],
   "source": [
    "def integrate_S13(f, a, b, tol, *args, dbg=False):\n",
    "    \"\"\"Simpson 1/3 integrator with error management via recursive subdivisions.\n",
    "    \n",
    "    Arguments:\n",
    "    f : callable\n",
    "        Integrand function. Must accept the integration variable as first argument\n",
    "        and return its value. Additional arguments can be specified as *args\n",
    "    a : float\n",
    "        Integral lower bound.\n",
    "    b : float\n",
    "        Integral upper bound.\n",
    "    tol : float\n",
    "        Desired relative tolerance.\n",
    "    dbg : bool\n",
    "        Prints additional information about the execution\n",
    "    \"\"\"\n",
    "    n = 2\n",
    "    \n",
    "    fafb = f(a, *args) + f(b, *args)\n",
    "    i_n = f((b-a)/2., *args)\n",
    "    I_2n = (fafb + 4.*i_n) * (b-a)/n /3.\n",
    "    \n",
    "    I_n = I_2n * (1+10.*tol)\n",
    "    \n",
    "    enum = 0\n",
    "    \n",
    "    while(np.fabs(I_n/I_2n-1.) > tol):\n",
    "        I_n = I_2n\n",
    "        n = 2*n\n",
    "        \n",
    "        # get the new sampling points\n",
    "        xs = np.linspace(a, b, n+1)\n",
    "    \n",
    "        # Calculate the function on the new even sampling points.\n",
    "        # the odd coincide with the ones calculated in all the previous steps.\n",
    "        # All the values of the function evaluated on the even points are summed.\n",
    "        i_2n = np.sum(f(xs[1::2], *args))\n",
    "        \n",
    "        # f(a) and f(b) appear without any coeffiecient,\n",
    "        # f(even points) = the one calculated in this cycle gets multiplied by 4\n",
    "        # f(odd points) = the ones calculated before gets multipled by 2\n",
    "        I_2n = (fafb + 4.*i_2n + 2.*i_n) * (b-a)/n /3.\n",
    "        \n",
    "        # the new points (even in this cycle) and the old points (odd in this cycle)\n",
    "        # will all be odd in the next cycle\n",
    "        i_n += i_2n\n",
    "        enum += 1\n",
    "        \n",
    "    if(dbg):\n",
    "        print(\"enum = \", enum)\n",
    "        print(\"number of function evaluations = \", n+1)\n",
    "    return I_2n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6fab0b8a-8ed9-4d35-a159-ce3aa93b7328",
   "metadata": {},
   "outputs": [],
   "source": [
    "def growth_factor_S13(a, Omega_m):\n",
    "    integral = integrate_S13(\n",
    "        growth_integrand, \n",
    "        1.e-6, a, \n",
    "        1.e-3,\n",
    "        Omega_m) \n",
    "    return 5./2. * Omega_m * np.sqrt(E2(a, Omega_m)) * integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fd7089da-fd21-4f97-aa97-64bca569b3c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-1, np.log10(2), 100)\n",
    "\n",
    "plt.plot(aas, growth_factor_trpz(aas, .1), label=\"trapz\")\n",
    "plt.plot(aas, [growth_factor_S13(a, .1) for a in aas], label=\"Simpson 1/3\", dashes=[3,3])\n",
    "\n",
    "plt.loglog()\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"$D(a)$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a250103f-1b37-4543-817c-51e91f6df839",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We can automatically vectorize the function,\n",
    "# to avoid using the list comprehension\n",
    "growth_factor_S13 = np.vectorize(growth_factor_S13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9303b6ca-8b21-4fd0-b3ef-5a73c6b28d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-1, np.log10(2), 100)\n",
    "\n",
    "plt.plot(aas, growth_factor_trpz(aas, .1), label=\"trapz\")\n",
    "plt.plot(aas, growth_factor_S13(aas, .1), label=\"Simpson 1/3\", dashes=[3,3])\n",
    "\n",
    "plt.loglog()\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"$D(a)$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abbd81c5-94f1-4e0d-b7f8-96b9a64b20e1",
   "metadata": {},
   "source": [
    "## Assignment 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4bf1801f-6c8a-4462-b9bb-c49903f03898",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-1, np.log10(2), 100)\n",
    "\n",
    "fig, axs = plt.subplots(1,2, sharex=True, sharey=True)\n",
    "\n",
    "for omega in [.1, .3, .6, 1.]:\n",
    "    axs[0].plot(aas, growth_factor_trpz(aas, omega), label=\"$\\Omega_m = %.1f$\" %omega)\n",
    "    axs[1].plot(aas, growth_factor_S13(aas, omega))\n",
    "\n",
    "axs[0].loglog()\n",
    "axs[0].set_xlim(aas[0], aas[-1])\n",
    "axs[0].legend(frameon=False)\n",
    "axs[0].set_xlabel(\"$a$\")\n",
    "axs[1].set_xlabel(\"$a$\")\n",
    "axs[0].set_ylabel(\"$D(a)$\")\n",
    "\n",
    "axs[0].set_title('Trapezoidal')\n",
    "axs[1].set_title('Simpson 1/3')\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91b46e2f-6cf2-4d3b-bfa9-dba93da7b81e",
   "metadata": {},
   "source": [
    "## Assignment 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "13b4b000-4108-40ac-9529-732bbb7d9bfd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "enum =  21\n",
      "number of function evaluations =  4194305\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.3609095056886648"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_tol = 1.e-12\n",
    "\n",
    "integrate_S13(\n",
    "        growth_integrand, \n",
    "        1.e-6, 0.5, \n",
    "        relative_tol,\n",
    "        0.3,\n",
    "        dbg=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d3ed25b-6a5b-411a-8cb9-c924000db009",
   "metadata": {},
   "source": [
    "## Numerical stability"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f66d9da-2c3a-48bd-8942-1c8dca9a10d5",
   "metadata": {},
   "source": [
    "The integrand can be simplified to avoid apparent singularities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b5cd2714-8452-4dd1-bb55-7da0272d8455",
   "metadata": {},
   "outputs": [],
   "source": [
    "def growth_integrand_2(a, Omega_m):\n",
    "    Omega_L = 1. - Omega_m\n",
    "    return (Omega_m + Omega_L*a**3)**-1.5 * a**1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "806c51de-c9d6-4400-85dd-bf3e6a46dc45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aas = np.logspace(-3, 0, 100)\n",
    "\n",
    "plt.plot(aas, growth_integrand(aas, 0.3))\n",
    "plt.plot(aas, growth_integrand_2(aas, 0.3), dashes=[3,4])\n",
    "\n",
    "plt.xlabel(\"$a$\")\n",
    "plt.ylabel(\"integrand\")\n",
    "plt.xlim(aas[0], aas[-1])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "126cfd34-0530-45c5-bce5-e27fae689a3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "enum =  15\n",
      "number of function evaluations =  65537\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.36090950568898855"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_tol = 1.e-12\n",
    "\n",
    "integrate_S13(\n",
    "        growth_integrand_2, \n",
    "        0, 0.5, \n",
    "        relative_tol,\n",
    "        0.3,\n",
    "        dbg=True) "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
