{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "058bacd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9fc0c673",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2D PLOTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7699c536",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input functions to plot\n",
    "twopi = 2*np.pi\n",
    "step = 0.05*twopi\n",
    "x = np.arange(0,twopi,step)\n",
    "y = np.cos(x)\n",
    "z = np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e0cddc91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Basic plot\n",
    "plt.plot(x,y)\n",
    "plt.plot(x,z)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "33c82884",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Embellishing\n",
    "\n",
    "#Changing line style, lineweight and colors\n",
    "cos=plt.plot(x,y,label='cos(x)',linestyle='dashed',linewidth=2,color='red')\n",
    "sin=plt.plot(x,z,label='sin(x)',linestyle='dashdot',linewidth=2,color='green')\n",
    "\n",
    "# Adding labels on x-y axis\n",
    "plt.xlabel('x',fontsize = 16) \n",
    "plt.ylabel('y', fontsize = 16)\n",
    "# Adding legend (after specifying \"label=\" in plt.plot above)\n",
    "plt.legend(loc='lower left', fontsize = 14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a6fb0853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot\n",
    "\n",
    "plt.scatter(x,y,label='cos(x)', marker = '^',color='blue')\n",
    "plt.scatter(x,z,label='sin(x)', marker = 'o',color='gray')\n",
    "\n",
    "# Change axis boundaries\n",
    "plt.xlim(-0.3,6.2)\n",
    "plt.ylim(-1.2,1.2)\n",
    "\n",
    "# Adding labels on x-y axis\n",
    "plt.xlabel('x',fontsize = 16) \n",
    "plt.ylabel('y', fontsize = 16)\n",
    "# Adding legend (after specifying \"label=\" in plt.plot above)\n",
    "plt.legend(loc='lower left', fontsize = 14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bcf492de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZkAAAEjCAYAAADg9HzdAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABon0lEQVR4nO3dd3hUVfrA8e+ZSZ/0CqEFQocICqIovYiKgIoFRYWVtYDuWrGuLpZd29p/grouICoCogIqgiiggCC999BJSO/JpMy8vz8miQmEJIRM7kw4n+eZJ8yt752Eee8p9xwlImiapmmaM5iMDkDTNE1rvHSS0TRN05xGJxlN0zTNaXSS0TRN05xGJxlN0zTNaXSS0TRN05xGJxnNrSmljiilVhodR0NTSs1USrn08wfuEKPmfDrJaC5HKdVGKfWxUmqvUipfKZWhlNqtlPpUKTXQ6Pg0Tas9D6MD0LSKlFI9gV+BYmAWsAvwBdoDI4AcYEWFXToA+m7ZNd0D3G90EJqxdJLRXM0/AT/gYhHZWnGFUupBoEnFZSJS2HChaedCRIpx3CxoFzBdXaa5mnZA2ukJBkBE7CKSUHFZVW0yZcuUUh2VUj8opXKUUllKqflKqUpJqnT7IKXUa0qpg0qpQqVUilLqS6VUm9oEXHqeqUqpXaXnyldKbVJK3VPFtlOUUqKU6qCU+rdS6kTpObcppa6tYnsfpdQbSqkEpVSBUmq9Uuqq2sR12nEGln4WaUopq1LqkFLqf0qp8ArbeCilniytmrSWbvutUiquiuPdVRpLplIqr/R4XyilIipsc0abTNmy0s98mlIqufRca5RSl1VxHqWUmlj6eeaXfr4rdLWp+9AlGc3VxAMdlFI3isg353GcZsBK4FtgMtANuA8IBMq/pJVSQcDvQEtgOo7quabAJOAPpVRPETlaw7kGAP2A74HDgAW4GfhYKRUuIq9Usc+nOO7y/wN4AQ8DC5RS7UXkSIXtvgSuB74DlgKxwDel56kVpdR9wDTgZOnPo6XXOwJoDqSWbvoFcAuwrHS7JsADwFqlVF8R2VJ6vDtK418FPA8UlB7vGiASSKlFWEtLt3sRCAMeBRYrpWJEJKfCdp8BtwHzgRmANzAWWFb6N7Kotp+DZhAR0S/9cpkX0BsowtHOsh/HF/9EoNNZtj8CrKximQC3nLb8g9LlHSssexfHl2S307ZtBWQDM2sRs6WKZSYcSS4L8KywfEppDN8DqsLyS0uXv1Jh2VWly2aeduzrS5dLLWJrDhQCu4HgquIs/Tm09JhzT4vrIqAEWFVh2Teln41HDeeeeXqMZcuAqactv7l0+X0Vlt1Quuze07b1ADbiSLSquhj0y/iXri7TXIqIrAV64LhTDgL+AkwFdiulVtW2CgtIEJF5py1bXvqzLTiqYnDcFf8GnFRKhZe9gDxgHRVKPdXEnFf279LqrTAgFPgJR8mpYxW7vSul35ilx9iAo1NDuwrbXF/6843TzrcA2FdTXKVuxlFSekFEMquI3V76zxtKf/7rtLi240iIfSpUhWXhaDcbXvoZ1sXbp70v+91UvP47cHwmC0773QTjKNnFnLa95oJ0dZnmckRkBzAeQCnVCugP/BXoCyxUSvUQkaIaDnOoimVppT/DSn9GlP77Ks5exWM/y/JySil/HCWUW4AWVWwSUsv40ivEBtCm9Pz7q9h2D46edTUp+xLeUsN2rUvPtaeKdTuBUaXbpAD/xlE9uABIU0r9CvwIzJXKVV3VqXT9IpJWmq8qXn8nIABIquY4UVT9+WguQicZzaWJoz1kllLqMxxtAFcCvYDVNexqq2adOu3nz8Br5xHmbOA64GMcpaJ0HFVM1wKPUHUHm7PFp87y7+q2q07ZdjV18651iUREDiilOgODS1/9gf8CLyil+olIfC2OUdvrTwFur+ZQO2sXtWYUnWQ0tyAiopT6A0eSaVZPh00BMoFAEfm5LgdQSgXjSDCficj9p60bcp7xxeMoZbXH0SGhoqqq4KpSVq12MXCghnMNw1F62H7aus6lP8s7G4ij6/ji0helPeN+wNGA/0AtY6vJARzXvk5EcuvpmFoD020ymktRSg1VSp1x86OU8uXP9pHd9XGu0vaIL4BeSqmbzhJPZA2HKbsjr1QSUEo1xVHFdz4Wlv6cfNqxr6d2VWXg6JVVBPxTKRV4+soKbSoLSn8+XbGdRSnVFRgJrBaRlNJl4Zxpc+nP0FrGVRuzcHxHVdU7D6VUVD2eS3MSXZLRXM3bQJhSahGwA8jH0c5xO4672lmlbTb15VkcpaN5Sql5OBr7i3D0LrsW2ERp+1BVRCRHKfUTcIdSqgDYULrvfTju/MPOtm9NRGSpUuo7YJxSKhRYgqML8304qom61uIYJ5RSD+PoWbdDKTULRxfmZjjaWe4GtorIstLrHwOEKKW+588uzFbg7xUO+5NSKgtH1eBxHA3x43FUyX1W1+utIvb5SqkZwINKqUtwdEBIxdFjrjeODhy17QiiGUQnGc3VPIrjy68PMBrHF1gWjiqc13B0ga03IpKllLoSeAxHw/0oHO0pJ3C0+3xSi8PcAbyK47mTcTiqeZ7F8RzMjPMM8VbgZRy94IbiSC6jcTw7UmOSARCRaUqpeBwlor/jeNYkAfgFR5IoMxZHiWQ88CaOHna/As+dltin4fis7sNRcknD0bHgbyJSccif8yYidyulVgD3Ak/j6Cl3qjTOp+vzXJpzqAq9FTVN0zStXuk2GU3TNM1pdJLRNE3TnEYnGU3TNM1pdJLRNE3TnEb3LqsgPDxcYmJijA5D0zTNrWzatClVRCKqWqeTTAUxMTFs3LjR6DA0TdPcilLqrNNh6OoyTdM0zWl0ktE0TdOcRicZTdM0zWl0ktE0TdOcRicZTdM0zWl0ktE0TdOcRicZTdM0zWl0ktE0TdOcRicZTdM0zWl0ktE0TdOcRicZTdM0zWl0kqkneoLR82e3240OQdO0eqaTTD0oLIROneCPP4yOxP0UFBQwZcoUIiIiMJvNBAYG8sgjj5Cenm50aJqm1QOXTzJKqX5KqUVKqZNKKVFKja/FPnFKqV+VUgWl+z2vlFLOivG//4WDB+Gxx5x1hsbJarXSp08fXnvtNVJTUwHIyclh6tSpXHLJJaSlpRkcoaZp58vlkwzgD+wEHgIKatpYKRUILAOSgEuBvwOTgUedEVxhIfzzn2CzwZYtsHatM87SOE2dOpU9e/ZgtVorLS8qKiIxMZHnn3/eoMg0TasvLp9kRGSxiDwjIvOB2lTajwX8gHEislNEvgZeAx51Rmnmv/91JBpvHzseXjYmT67vMzRe77//PgUFjvuG0381RUVFzJw5U7fTaJqba4yTlvUGVolIxVLPUuAlIAY4XHFjpdS9wL0ALVu2PKcTlZVi8vKg39B8Hn4uhcMHvFi2xpeLu/oSGuCDyVS7vPbtt3DRRRAbe04huIT4+HhmzZpFYmIiXbt25c477yQkJKTafUSE5ORkAIYNG0Z0dDQzZswof2+1Wjly5Ai5ubkEBgZWe6y8vDzmzJnD+vXrCQkJYezYscTFxdXPxWnaBWbXLjh+HK6+un6O1xiTTBPgxGnLkiqsq5RkRORj4GOAnj17nlMfsbJSDMDBvd7M+V8wF19WQK4tizU7szCbFEN7tsDb00yJzY7ZpM64YwdIS4PbboN+/eCnn84lAmOJCI899hjTpk3DZrNRXFyMn58fTz31FJ999hmjR4+utH1ubi7x8fHEx8dz9OhRWrRowb59+0hJSalUYomOjqZly5YopZg2bRqtW7cmNjaW2NhYgoODKx1z9erVDB8+HLvdTm5uLmazmffee48RI0bwxRdf4OHRGP/ENc15xo2D/fshMREslvM/nhI36nurlMoFHhSRmdVs8xNwXEQmVFjWCjgC9BaRdWfbt2fPnlLb6ZcLCyE6GqrqBBUWbmf+wgKimhXSqVUoABv2JpORW0hksC+Rwb6EB/vg5WEGYPJkeP99MJlgzRq4+OJahWC4Dz/8kMcee4z8/Pwz1vn5+bF69WoCAwOJj4/n0KFDJCUlla+LjY3l+PHjPPPMM1XuHxQUxD333EPfvn2Jj48nOzsbgNDQUGJjY+nWrRtms5l27dqRm5tb5fknTpzIf/7zn3q+ak1rvFauhOuuczyS8fzz8OSTtdtPKbVJRHpWua4RJplZQJiIDK+w7FJgPdBGRA6fbd9zSTL/93/w1FOOqrIzY4ArroDVq/9cdjw5h8S0fFKyCiixOT7z5hH+xIRF0LIl5OcLSimGDHGP0oyI0KxZMxITE89YFxkZyVVXXUWbNm0wmUyYzWZatmxJmzZtaNu2LVFRUSilKCoqYuDAgWzZsqW8bQbAx8eH5s2bs2HDBoKDgxER0tLSyktBR44cYdiwYSxatIipU6fSqVMntm7dSk5OTqU4/Pz8SElJwc/Pz+mfh6Y1Bj17wqZNjn8HBkJCQu1KM9UlGUTEbV5ALjC+hm0mAtmAT4VlzwAnKU2qZ3v16NFDamvwYBGT6ewvX1+RrKwz97PZ7ZKWVSB7jqbLoYQsefxxEYvFLp98fVTG3J0ufha7bN5c6zAMk5iYKD4+PgIIIF27dpUuXboIIIGBgfLAAw/IjTfeKPv375fCwsKzHsdqtcp//vMfadGihXh4eEhERIT84x//kKyqPrxSxcXFUlRUJD179pROnTrJlClTJDIyUgDx9PQsjykwMFDWrVvnjMvXtEZnxQoRi0WkR+88MZvt4ucn8uqrtdsX2Chn+V51+ZKMUsofaFv69nfgVWARkC4ix5RSrwC9RGRw6fZBwD5gJfAy0B6YCbwgIm9Wd65zKcnUh7Q0aNkSTGYbk55I5YqB+Wxa68uW3yL4bpG5weKoi9TUVJo1a0ZRURFms5mJEydy8OBBlixZUr5N8+bNOX78uNNiuOKKK1i7di0Wi4W8vDyUUowdO5aCggIWLVqEj48PK1asoEePHk6LQdMai7JSTGh4CS1iitm20bfWpZnqSjIu34UZ6AlsKX35Ai+U/vvF0vVNgfI+WSKSBQwFooGNwAfAm8BbDRdy7bz6KtjtkJtj5vXnIpn6RhgX9SzgujsS+GNTkdHhVSs8PJwuXbrg4eGBzWZj1qxZ/FShns/T05ObbrrJqTHcfvvt+Pn5kVdaZykiHD16lK5duzJhwgTCwsLo1q2bU2PQtMbg518L6XN1CiaTkJ7qwbaNvgCUlDiaBs6Hy5dkGlJDlmTKSjGnt3l36GLlyX8lk5XqzcMTohoklrpISEhg5syZbNiwgQULFpyxPiAggJ07d55zt/BzkZ2dTbt27UhNTa3UO61t27bcdNNN+Pr6MnbsWGLdsV+4pjWQo0k5bNybSlqyB8880JS0lMo9MmtTmnH3kkyj9M47UFQEPj6VX0fjfXh6YjTPPxbO7t1QVGLD7mI3Alu3bmX69On4+flxzTXX4O/vT0BAAH5+fvj7+9O8eXNWrlzp1AQDEBgYyNq1a+nQoQMWiwU/Pz8CAgI4efIkAQEBRERE8MUXX7B69Wr0zZSmVWazC9sOprL1YCo7N/vw7IPR5OV4nPGdlJ8Pn3xS9/PokkwFDVmS2bwZ1p21M7WjO/Mttwi7TiZiVoqeHSLx8jS2ncZms7F06VI2bNhA69atGT16NBaLBavVyo8//khKSgrt27enf//+VT4P5CwiwoYNG9i2bRsBAQFce+21BAYGUlRUxKJFi9i1axedO3dm1KhReHl5NVhcmubK1u9NIjEtn+jgIDb8GgKc/f9sv37QtevZj9VoujA7W0M3/NfG0aQctsen4eNl5tKOkQT7exsSR25uLl999RXHjh2jd+/eDBkyBJPJ9QvCIsLatWv5+eefCQ8P58477yQgIMDosDTNcOnZVgqKSmgW7n/ex6ouyejHoV1cq6gAAv28WL83iVU7EukeG06LyPP/ozgXJ06cYN68eRQUFDB69Gi6VndL42KUUlxxxRU0adKETZs2YamPR5g1zQ2JCEdO5WAtKqFTq1BCA30a5LyufyuqERLgzYBuzQjx92bv8QxstoYbNDI+Pp4ZM2bg4eHBX//6V7dKMBW1adOGm2++GZPJRF5eHmvXrtXtNNoFw2a3s/VgKtsPpZGVV9Sg7by6JOMmvL3MXNGlCdZiG2azCZtdKCmx4+3laKdZuBCKi+Fcew0XFxezYMECZs6cSU5ODgMGDGDixIk0bdoUgBYtWtCjRw8GDhyIr69vfV+WIbZu3crKlStp3749YWFhpKenM336dH744Qc8PDy47bbbGDNmjB4pQHNL06dD69YwcKDjfUFhCev3JpGZW0SHFsF0aBHcoG2muk2mAldskzmb7YfSSEzLo1fHKPy8vGnWzDGnTUIC1DYXZGRk0LdvX44ePVo+/pePjw+BgYE8//zz3HPPPY2yoVxKh6kJDw9nw4YNjBo1iqysrPIx1CwWC8HBwfz+++9O7yGnafUpM9MxpmJEBBw+DIKdXzafoLjEziXtImga5pzqYt2FuRFqGemPUorVOxL58tscrFZHl+gPP6z9McaNG8eBAwcqDTBptVrx9/fn5MmT7N692wmRG08pRXh4OFarlb///e+MHz++UjLJy8vj1KlTXHfddQZGqWnn7o03HINbpqfD/PlgNpno2jqMfhdFOy3B1EQnGTcV7O9N/27RhPh7E9IilTvuT6WoSHjxRSiocf5Qx8OUy5Yto6joz5EFmjRpAsChQ4eYOnUqixYtclb4LmH+/PkcPXqU1NRUxowZw6BBg8qrEWw2G4cOHWLDhg0GR6lptZOZCe++C3ax89eHk5m7IBe7HaLDLAT4GVcjoZOMG/P2NLN9dRO+mxdE/6tyiWhSUuvSzLZt2/D2/rM79ODBg7n33nuJjo4GICsri1WrVjkrdJewdu1aEhMTmTFjBlu2bKFfv37ccMMN5evtdjubN282MEJNq7033gCz2c6L75yi31V5eHqXMH++0VHphn+3VlgIzz+vSEsL5ZsvAslIc/w6X3wR7r+/+rYZi8VS3rsqLi6Ovn37smnTpkpD99c0I6W7CwwMxGw2U1JSwsKFC8nMzGTgwIEkJSWxZs0azGaz7vKsuQVHKUaY8FAaHeMKeeP5CNYs92ftckdnICMfadMlGTf2v/+B1er4tyPBCDfekcll/XJqLM307t0bs9lM06ZNGTlyJEePHmXx4sXlicff35/x48c7NX6jjRkzplJp7tdff2Xnzp0MGTKEtm3bUlJSwvDhw6s5gqa5hjfegKEjsxl0bS5zpgezZrnjWbqythkj6STjphylmMqTppnM0P3SAiY8lMZnXxZW2zbj6enJa6+9xm233UZ+fj7z5s3DZrMB4O3tTfv27bn22mudfBXG6tatG0OHDq3UNXvhwoUkJSVx00038eijjxISEmJghJpWs7K2GA9PYe2vfsydEVy+LjfXMfOuveEerTuDTjJuav58yMiAoKA/XwH+io/+E0lWppkHn05i7lclZ93fZrPh6elJUFAQP/74I2azmaCgIHx8fBg1ahQrV67EbHbtOW3qw7x58xg/fjw+Pj4EBQXh6+vLd999h4+PD61bt9YPbGou75NPHDedyxYG89EbkQQGqkrfC8ePw9KlxsWnn5OpwJ2ek8nIgD/+qHqd3VRIsV8iAX5eDOjeFJPpzAevfvjhBzZu3MgNN9xA586d2bBhA/n5+cTFxREZGenk6F1PVlYWmzZtwsPDg169epGcnIyfnx/h4eFGh6ZpZ1Vis7NqWxIFacGYbGdvhL3ySnDmkH167LJGKCQErr76bGu9OZkSzqb9KaRlW4kIrvzHt3nzZjZu3Ejv3r256KKLAEcbzYUsKCiIQYMGlb8ve25GRDh58iTNmzc3KjRNq5KIsOVAKtkFVi7vKUS5aM2uri5rpJpF+DO4R/MzEgxAaGgocXFxDBkyxIDI3MvWrVv53//+x7Fjx4wORdMqOXAyi4S0PDq3CiEqxHWHQNIlmUbM4uMJwKn0fDw9TARbPDGbzcTExBATE2NscG4iLi4Ou91OixYtjA5F08olpeez52gGzcIttG0WZHQ41dJJppGz24VdR9IpLCzi5M7ldOrUkT59+hgdltvw8PCgR48eAGRmZuLt7d1oBgrV3FdCWh5BFi+6tw1v0MEu60JXlzVyJpPi0o6RlNgEu4ef7pJbR8XFxUyfPp2vv/4au5H9QTUN6N42nCu6NMHD7Ppf4a4foXbe/H08uLRTE5q0743VM1J3y60DT09PBgwYQHx8PL/88ovR4WgXIBFh1+F08qzFKKUMn469tnSSaeSOHDnChx9+iI+piI4tgjmRkktyZi1G0NTOcMkll9CzZ09+//13duzYYXQ42gVm77FMDiZkkZzhXv9/dZtMI5aZmclXX32Fn58ffn5+tA/2Isjfm8gqepxptXP11VeTnJzMokWLCA8PL5/cTdOcKSEtj/0nMmkZ6U9MEyc+8OIEuiTTSBUXFzN37lxsNlv5GF1KKZqE+qGUIie/iDxrsdFhuh2z2cwtt9yCn58fc+fOJa/iuD6a5gTZeUVs3p9CsL83F8WGuXxD/+l0kmmERIRFixZx6tQpRo8eTVhYWKX1druwdncS6/ckUWLTjdjnymKxcOutt5KXl8dXX31VPuabpjnD3mMZeJhN9OoYidnI4ZTrSFeXuTmr1cpXX33F119/DcD1119PTEwMO3fuZNCgQbRr1+6MfUwmRffYMNbuTmLLgRR6dohk717FypUwcWIDX4Cbio6OZsSIEXz77bf8+OOPWK1W5syZQ2FhIddccw133nknAc4cx0NrtN5+G66/Hlq3dry/pH0E+YUl+Hq759e1HrusAncauwzg8OHD9OnTh+zs7PIplLt27cro0aNp1aoV48ePr7ZofeBEJruPZtCpZQj33RXMb7/BoUPQqlVDXYH7W7hwIdOnT2f58uXlvwOLxYKnpye//PILl1xyicERau5k1y7o2hVuvBHemZZL0zA/t+imXN3YZa4fvVYlEeGqq67i1KlT5V9uoaGhDB8+nKSkJF5++eUauyq3bRZEs3ALe45lkF1QgNkM//xnQ0TfeLz++uv8+OOP5Obmlif0vLw8MjMzGTJkCAW1mQtb00o9/bRjgrEsay6bD6QQn5BtdEjnTScZN7Vy5UpOnTpV6cHALl26ICLMmTOH5ORkfvrpp2qPoZSie9twfv85mB1bfCguhrlz4ehRZ0ffOOzevZstW7ZQXFxM69atmThxYqUqsuLiYubNm2dghJo72bULfv4ZYtoWcu9jqZw64UM7Fx8ypjZ0knFT69evx1o2LWapVatWMW3aNDIzM8nLy+OPs80FUMHWLSbefy2E4iKFt48dk8muSzO1tH79ekylDbF5eXlYrdby9wC5ubn8+uuvRoWnuZmnnwaT2c5T/04iO9PE8w9HcuCAe/Ukq4pOMm7K19cXDw9HQ2BMTAxRUVEA5OTkAI4xt2ozxtbkyY4pnP0sdt6ddZIb7sjUpZla8vX1LU8qycnJTJ8+naysrPL1Sin8/f2NCk9zI2WlmDETMgiPtPH6c5GkpZh55hmjIzt/Osm4qVGjRpX/e9iwYZXeg+N5jhtuuKHaY2zc6Jj4TATy80zs3urDDbdn0TymUJdmamHYsGEUF1d+1sjPz49Ro0YRFBSEn58fY8aMMSg6zZ08/bRjdsvv5gYy9bVwDuz2wWaDxYth3z6jozs/Osm4qVatWnHrrbfi5+fHrFmzyrswg+MOe+TIkVV2X66orBRTZsb/hZKbY+K+x1KZ95Xo0kwNgoODeeSRR/Dz+3MuD09PT7p06cKIESPo2bPnBT8ZnFazXbtg+XLBbheST3ny8w8V2/Vw+9KMTjJu7M0332TChAmICMXFxQQGBuLj48O4ceP4/PPPq913zx5YuRIsFggMdLwUZr74KIx2nYoYNiqbt95qmOtwZ//61794/PHH8fPzIzAwEBHht99+o23btrz55ptu93S21vD+/W+4YWwmL7yTRGiolP9/DAwEHx/49ls4ccLoKOvOLZ6TUUpNAiYDTYFdwMMisuos28YAh6tYdY2ILKnuPO70nExJSQkffvghkZGRDBs2jNWrVwNwxRVX1Go4/4IC+PFHOHPUesEckgRAx+goOnXSX5K1kZeXx6pVqyguLqZnz5788MMPZGRk8MADD1Qq6Wja6TZtLeJ47kmkwB9bVsQZ6z084NprwcvLgOBqqbrnZFw+ySilbgU+ByYBq0t//gXoLCJnzIlbIclcDWyrsCpdRIqqO5c7JZnly5ezatUq7rjjDmJjY+v12MUldjzMSt+Fn4ekpCQ+/vhj4uLiuP76640OR3NRIsKq7YnkWYsZdElzvN1k+P7TufvDmI8CM0XkvyKyR0T+BiQCNQ2AkiYipyq8qk0w7iQpKYk1a9bQrVu3ek8wAJ4eJpRSFBSWkJqlHyasi6ioKK688kq2bdtGfHy80eFoLupQYjYZuYXEtQlz2wRTE5dOMkopL6AHcPpThT8BV9Sw+zdKqWSl1Bql1E1OCdAAdrud7777Dh8fH6666iqnnmtrfCob9iZTWKwHgKyLfv36ERYWxvfff09RUaO5x9HqiV2Ew4k5RIb40izcYnQ4TuPSSQYIB8xA0mnLk4AmZ9knF3gcuAW4FvgFmKuUuqOqjZVS9yqlNiqlNqakpNRP1E60fv16Tp48ydVXX+30uv4uMaEU2+zsPJTm1PM0Vh4eHowYMYLMzExWrFhhdDiaizEpRf9u0VzcNrxRV027epIpc3rDkapimWNDkVQReVNE1onIRhF5HvgIeOIs238sIj1FpGdExJmNbq4kMzOT5cuX065dO7p27er08wX6edG+eTAnUvNISs93+vkao1atWnHppZdiMpn0tNdauey8Iux2wdPDhI+Xe46uXFuunmRSARtnlloiObN0U50/gOofGnFxIsL3338PwPDhwxvszqdd82ACfD3ZFp9KcYmee6YurrnmGoYOHdqo71a12isstrFmZyJb41ONDqVBuHSSKW2s3wQMPW3VUOD3czhUdxydBdxWfHw88fHxDB48mKCghhs0z2xyDKIZFuSDVF141GpQllyOHDnC5s2bDY5GM9rOw+kU2+y0jXb/wS9rwx3KaW8Bnyml1gNrgPuBaOBDAKXUK0AvERlc+n4cUAxsAezACOAB4MmGD73+xMbGcvPNN9OxY8cGP3dooA+hgT4Nft7GZsOGDaSkpNCtWzfM5sbZk0irXnJGPidScmnfPJhAiws/+FKPXD7JiMhcpVQY8A8cD2PuBK4VkbJBT5oCp/fj/QfQCkdV237gbhGp/hF4F2a1WvHx8aFz586GxpGdV8TBk1l0bxuOyaSrfs7V8OHD8fDw0AnmAlVis7M1Pg1/X0/atwg2OpwG49LVZWVEZKqIxIiIt4j0EJHfKqwbLyIxFd5/KiKdRcQiIoGljfpum2AOHjzIO++8w8mTJ40OhfzCEo6n5HLgZKbRobglPz8/vLy8KC4u5oQ7jxOi1UlhsQ0vDxPd24ZjvoBu0twiyVzIQkND6dy5c/lQ/kZqEupHs3AL+49nkpOvn/uoq8WLF/P555+XT8ugXRgsPp707xZN2AVW9ayTjIsLDQ1l5MiR5XPHGC2udRhms4mtB1N1l9w66tOnDzabjR9//NHoULQGYLcLe49lUFxiuyB7GOok46JOnDjBnDlzyMvLMzqUSry9zHRtHUp6TiHHU3KNDscthYWF0b9/f/bs2cOePXuMDkdzsoMns9h3PJO07EKjQzGETjIuyGaz8d1335GQkOAyJZiKWkT4071teKMeCsPZevfuTZMmTVi8ePEZ02hrjUdOfhH7jmcSHWahSeiFORq3TjIuaM2aNSQnJzN8+HC8vb2NDucMSilaRQVgNpmw2ey62qwOzGYzI0aMIC8vj2XLlhkdjuYEIsK2+DTMJkVcm1CjwzGM690mX4C2bdvG+vXr8fHx4fLLL+e3336jS5cudOjQwejQqpVnLWbNzlN0iQklMsjC779D//5GR+U+oqOjufzyy1m7di2xsbFs376d7OxsunbtSu/evS/I+vvGYPlyGDAAjiXnkJZtpXvb8EY/dEx1LtwrdwGnTp1i5MiR7Nq1CwCTycStt95Ks2bNnD7Ccn3w9fbAy8PEjkOpnNjhw733mNm9Gwx4XtRtDRw4kHXr1vHRRx8xa9YsioqKUEoRHR3N999/T/v27Y0OUTsHf/wBgwfD/PlwzXBf2jcPomWkv9FhGUpXlxmkuLiYPn36sGXLFvLz88nPz6djx460aNGCJUuW8MorrxgdYo1MyjHkTFGxnX0n0gF4+mmDg3IzM2fOZM6cOYSGhtKyZUvy8/PJy8vj4MGDXHHFFWRkZBgdonYOJk8u+yn4eHnSqVXoBV8i1UnGIAsXLiQ5OZmSkhIAAgICGDp0KIcOHWL9+vW8++67bvEcRbC/N7mpQfQZkkvcJQUsWQJ79xodlXuw2Wz84x//YM+ePXz00Uds3769fJ2IUFBQwP/+9z8DI9TOxR9/wKZNcHm/PP7yUBLfLtDzMIFOMoaZO3dupSQyfPhwTCYT3333HQCenp789ttvZ9vdZRQVweQHgkk84cGAYbkUF+vSTG3t2bOH/HzHFAqJiY7xW0NCQsrvfPPz85k9e7Zh8WnnZvJkUCY79z6ahiXAxpNPmLDrgct1kjFKcXFx+b+VUiQlJfHLL79Uqh4pK+W4sk8/haxME88+2JT3XwnHZkOXZmqppKSkUlVKREQEDzzwABdffHGlbTTXV1aKuWV8BsGhNqa+Hk5SkuLbb42OzHg6yRjk2muvxWJxPGciIqxYsYJ169aVry8qKuLyyy83KrxaKSqCZ5+FvDxIT/VARBEcWoKfv02XZmqhU6dOld6npKTw22+/ceDAAQC8vLy45pprjAhNO0eTJ0NIeBHDb8rm5+/9id/nTW6uY/mFXprRScYgY8eOxdvbm7i4uDN6EPn4+HDjjTe6xHhl1fn0U8ivMGGml7eddz49yV0T03Rppha8vb156KGHKk2j/dtvv5VXo3p6evLggw8aFZ5WS2WlmJvHZVJoVXzx3z+fiUlJ4YIvzegkYxCLxcLy5cu54oor6N27N+CoNrNYLPTp04f//ve/BkdYvZKSP0sxZYoKTfy0KIABw/KIaWflmWeMi89dTJkyhdGjR+Pr61s+ukOzZs34y1/+wty5c2nRooXBEWo1eeIJx83WR2+G8++nosjK+HMqh7LSzIX8vLJ+TsZA3bp14+233+brr7/Gz88Pi8XCLbfcwqWXXmp0aDWy2+G22+D0DnBmginIy+XJF9PIPBINXNjdN2tiNpuZNWsWTz31FLNnzyYtLY3u3buTnp5OVlaW0eFptXDVMKFtWxAxAb70urjy+tBQuJB7MSs9JMifevbsKRs3bmyQc2VlZeHj4+OSw8acr+PJuWw+kMLFbcNpGRVgdDhu6ffff2fZsmXcfvvttGvXzuhwtGrEn8ziaHIOfbo2xcvzwpyQTim1SUR6VrVOV5cZQERYsGAB06dPb5TjfjWPsBAS4E1Wnp5zpq4uu+wyQkNDWbp0KTabft7CVRUW2dh7PNMx+sUFmmBqopOMAfbu3cuRI0fo2bNno3waWCnFlV2bENcmzOhQ3JbZbGbYsGGkpaWxYcMGo8PRzmLPsQxsdjtdYy7cATBropNMAyspKeGnn34iMjKSHj16GB2O05hNjj+trLwi8q3FNWytVaVdu3a0bduWlStXuty8Qhpk5RZyNCmHNk0DCfDzMjocl6WTTANbu3YtmZmZXH311ZhMjfvjL7HZWb0jkR2H040OxS0ppbjqqqsoLi5mxYoVRoejnebwqWy8PEx0aBFsdCgurXF/y7mY7OxsVq1aRadOnWjdurXR4Tidh9lEu+ZBnErPJzmzwOhw3FJERASXXnopmzZt4tSpU0aHo1VwUWw4V8Y1xdNDt8VURyeZBvTLL79gt9sZOnSo0aE0mNjoQPx8PNh5OA17I+zk0BD69+9PaGgo6em6ROgKbDY7xSU2TEoRqKvJaqSTTAM5ceIE27dvp3fv3oSEhBgdToMxm0x0jQklJ7+YI6dcf1RpV+Tr68sDDzxA586djQ5FAw4mZPHz5hMUFutef7Whk0wDEBGWLFmCv78/ffv2NTqcBtck1I+oEF9stgt8EKfzYDKZEBF27NhRaXBVrWEVFJZw4EQW4YE+eOsuy7Win/hvAEophgwZQlFREV5eF17xWinFZZ2iGmV37YZ08uRJvvnmG4YPH07PnlU+96Y52e4j6YhAF91ludZ0kmkgMTExRodgKKUUIkJSRgF+Ph66LrsOmjdvzl133XXB/y0ZJS3byonUPNo3D8bPx9PocNyGri5zshUrVrB06dJG+WT/uSqxCZsPpLDjUJr+POqodevWKKUoKtKjKTS0U+n5+HiZadc8yOhQ3IpOMk5WUFCA1WrVVUWAp4eJji1DSM2ycio9v+YdtCodP36ct99+m+PHjxsdygWlS0wo/bs1w8OsvzbPhf60nOzaa69l5MiRRofhMmKaBBDg58nOI+nYLvTZnOooKioKT09PlixZokuEDaC4xE5egaOzhY+Xbuw/VzrJOMmJEyc4ceIEgC7FVGBSiq6tw8i3lhCfkG10OG7Jy8uLIUOGkJCQwLZt24wOp9HbfyKT5VtPYi3SU2HXhU4yTmC32/nuu+/45ptvsOu79TNEBvvSKioAXy/d76Su4uLiaN68OT///DOFhYVGh9No5RYUcyghi2bhFnz032ud6CTjBJs2bSI5OZmhQ4c2+vHJ6qp723BaRPobHYbbUkpx9dVXk5eXx6pVq4wOp9HadSQdpRSdW104D1DXN/0NWM8KCgpYsWIFMTExdOzY0ehwXJrdLhxKyCIjR9+J10WzZs3o1q0b69at00POOEFyZgGn0vPp0CJYl2LOg/7kzpOI8Ntvv7Fnzx7CwsLw8fHBarVy9dVX67aYGtjswv4TWfj55NE3rinLlysGDgRd+Ku9wYMHs3v3bpYsWUJAQAAnT56kVatWDB06FA8P/d/7XBUXw5o1MGCAYyh/f19P2kTrLsvnwy3+CpVSk4DJQFNgF/CwiJy1jkApFQf8H9ALSAc+Al6Seu6Ks23bNkaOHEl6ejo2m43IyEjGjRuHxWIhKiqqPk/VKHl6mOjcKoQtB1P5dV0eQ4b489VXcNNNRkfmPgICAoiIiODAgQPMnz+f+Ph4PDw88Pb2Zu7cuQwaNMjoEN3KjBlw//2wezd07BhMm+hAzCZ9s3g+XP6eUSl1K/Au8G/gYuB34EelVMuzbB8ILAOSgEuBv+NIUI/WZ1wJCQn079+fY8eOkZubS0FBAf369aOwsJDXX3+d+fPn1+fpGq0Wkf4E+3txIiMdH187kyeD7itRe2vXruXRRx9l+/btpKSkUFBQQE5ODqmpqYwYMYIdO3YYHaLbKCqCf/wDAgJtvP1/VuDPyfe0uqv1J6iUWqOUulMp5e3MgKrwKDBTRP4rIntE5G9AIjDxLNuPBfyAcSKyU0S+Bl4DHlX1WH/13nvvUVDw5xwp7du3JzY2lpUrV5KWlsYTTzyhn2GoBaUUpoIwAoJs3Dg2i9RU+OYbo6NyH88++yy5ubl88803JCUlVVpntVp58cUXDYrM/cycCfn5MGZCBsNuSWTHLt1luT6cS5ouBj4FEpRSbymlnN6qrZTyAnoAP5226ifgirPs1htYJSIVZ8laCkQDMfUV21dffVVpaI9+/fqRkpJSPh97YmIiJ0+erK/TNWrPPuHD3BnBbN/kQ24uujRTS3a7nV9//bX8vb+/P8OHD8fX17d8/Y8//mhUeG6lrBQTHlXEsFE5/LQwgOf/4RatCS6v1klGRAYAnXAkmruAXUqplUqpW5VSzhotLhww46j6qigJaHKWfZqcZfuydZUope5VSm1USm1MSUmpdWA2W+W5JL744gu++uqr8udiTCYTJSX6Tqgmf/wBmzbBl/8LYecWx5ejLs3UjohUKi37+fnRrVs3Wrb8syb59L9TrWqOUoww4e9p5OeZmP1JCEuWwN69Rkfm/s6pwlFE9onIo0AzYDyOBDAbOKGUelUp1ab+Q3Sc+rT3qoplNW1f1XJE5GMR6SkiPSMiImod0JAhQzCb/xxioqCggOTk5PL3FouFFi1a1Pp4F6rJk6Gs1tHH185fHkwjpl2BLs3Ugtls5qKLLip/n5yczNtvv82+ffvKl11++eVGhOZWykoxXS/J56KeVr78JIScbDPFxfD000ZH5/7q1KolIoUi8hnwELAKiACeAPYrpb5SSp2tlHGuUgEbZ5ZAIjmztFLm1Fm2p5p9ztnjjz+Ot3fVzVN+fn4888wzlZKQdqayUkzZzbjdBr0H5DHhoXTS0kWXZmrhhRdewM/Pr/x9WTths2bN8PPz45///KdRobmNsrYYX4udPdu9WbIwAACbDV2aqQ9lRe7avgBf4G5gPY4EsAv4G44v9nuAk8Av53rcas73B/Dxacv2A6+cZfuJQDbgU2HZM6VxqerO1aNHDzkX33//vfj5+YnFYhFAPD09xdfXVx588EGx2+3ndKwLUb9+Io4U8+frioG5smD1IblqVJbExIjoj7Fmr7/+uvj4+Ii3t7cAEhcXJ1OmTJF3333X6NBcXnGxSERExb9Be6W/R6VEbrjB6ChdH7BRzvK9WuuWrdJnT+7D0XvLAiwEnhSRFRU2+69S6hTw1Tlnu7N7C/hMKbUeWAPcj6MR/8PSuF4BeonI4NLtZwP/BGYqpV4G2gNPAS+Ufhj1Zvjw4SQmJvLFF1+wfft2mjRpwh133EFsbGx9nqbRuvpqaNv29KV+pCb6MOFvGWz+xYJSujRYk8mTJzN27FhmzZrFkSNHaNu2Ld7e3ogIJSUl+qHMatjtMP7uEnwDCzgR78+fNet/qlAjqdWBqu33rlLKDiQA/8VRskg8y3adgKkiMrDegnQ8jPkEjocxdwKPiMhvpetmAgNEJKbC9nHABzgexszAkZBerCnJ9OzZUzZu3FhfYWt1lJVbyMptCbRpGkhcmzCjw3FLhw4d4rPPPmPw4MH06dPH6HBc2uYDKZxMyWXwJc31jJd1pJTaJCJVzgl+Lrc4NwMLRKTa7ioisgeotwRTesypwNSzrBtfxbIdQL/6jEFrOEH+3lzUJoyIYF+jQ3Fbbdq0oUOHDqxatYpu3boREBBgdEguKSOnkOPJubRtFqQTjJOcSxfmr2tKMJpWX1o3DcTfV/+nPx9XXXUVJSUlLF++3OhQXJKIsONQGt6eZto3DzY6nEZLj5mguayiYht/7EnSUzXXUWhoKJdffjlbt27VDwZX4URKHhm5hXRuFYKnh/4qdBb9yWouy8NsIregmJ2H07Db9RA9ddGvXz8sFoueqrkKXp4mosMsel4jJ9NJRnNZJpOia+tQ8qwlHErUUzXXhbe3N4MHD+bEiRPs2rXL6HBcSlSIH5d2jNRTcjiZ7tuoubSoED+iQnzZdzyD5hH++HjpLs3nqnv37pSUlNChQwejQ3EJ+dbi8sZ+s1nfZzub/oQ1l9e1dVjpBGeZRofilpRSXHrppXh6euoqMxxTKh84mUVRiR63qCHoJKO5PH9fTy7tEEnHFsFGh+LWTp48yYcffkhmZqbRoRgmNauAhLR82jUPwtdbV+Q0BJ1kNLfQNMyCl6f5jJGHtdoLCAjAw8OD/PwLs7eeo8tyOr7eHrTVUyo3GJ1kNLdRUFjCr9sSSEjLMzoUtxQYGMhf//pXoqOjjQ7FEEeTcsjOL6JrTKhui2lA+pPW3EZZo/+uI+mU2HR9el0opSgsLOT3338vn/voQhHs701sdCBNw/xq3lirNzrJaG5DKUeX5oJCG/Ens4wOx23Fx8ezbNkyNm/ebHQoDSrY35uurcN0l+UGppOM5lbCg3yJDrNw4GQWBYV65tG66NSpE61atWL58uXl8880Zjn5RWw5kEJhsR4Vywg6yWhup0tMCALEJ+jSTF0opbj66qspKCjg119/NTocpxIRdh5OJyHtwuzs4Ap0H75astvtnDhxgrw83ehcXywWC82bN8dkOrd7HT8fT67s0oRg/6pnJtVq1qRJEy655BI2bNhAjx49OJepx91JUkYByZkFdI0JxdtTP8hrBJ1kaik1NRWlFB06dDjnL0XtTHa7nZMnT5KamkpkZGTNO5wmNNAHgBKbHbNJ6Xr2Ohg0aBC7du1i6dKljB07ttF9hna7sPNwGv6+nrRuGmh0OBcs/W1ZS5mZmURFRekEU09MJhNRUVFkZdW9yivfWszPm05wLDm3HiO7cFgsFvr37098fDwHDhwwOpx6dygxmzxrCV1bh2IyNa4E6k50SaaWbDYbnp56fpP65OnpSUlJ3Rvvfb09sPh4sOdoOtFhFjZuMBEXB/56UN1a69WrF5s2bWLp0qUcP36c/fv3ExYWxvDhw7FYLEaHd84yMuDgQbj0UmgW7og/KkR3Wa6txMRElixZQnFxMX369KFz587nfUydZM5BY6tOMNr5fp6OLs1h/LY9ga37Mxk4MJSHH4ZXX62f+C4EZrOZdu3asW7dOh577DH279+Ph4cHNpuNt956i/vuu8/oEM/J5Mkwdy4kJoK/vwdtm+kn+2ujuLiY+++/n9mzZ2M2/zmyRs+ePfn2228JC6v7NOi67kdzayEB3rSM9OdEWhaRTYt5/31ITzc6KveRkJDALbfcwrRp09i2bRsFBQXk5OSQn5/Po48+yvz5840OsdZOnIAvvoDmMYUsXJlIvrXY6JDcxqRJk5gzZw5Wq5W8vDzy8/MpKCjgjz/+YPDgwec1lJNOMlqtffjhh9x555212rawsJB27dqxd+9eJ0cFkf4hFFoVVw7KxW6H1193+ikbjXfffRer1UpSUhJApSqy/Px8nnzySbcZK27KFEdj/10T07CrIooKdW+y2khKSuLzzz+vcky7oqIi4uPj+eWXX+p8fJ1ktFrJy8vj+eefZ8qUKbXa3tvbm8cff5zJkyc7NzDgzTc8eOq+ZsyZHozVii7NnIP58+dTVFQEQIcOHXjkkUdo2rRp+fqEhAS3mLq5rBTTq28enbsVMndGCFM/0F9vtfHzzz/j4fFny0lQUOUqxtzcXL755ps6H1//FrRa+fzzz4mLiyM2NrbW+9x2220sX76cgwcPOi2ulBT48EM4etgTUEQ2LcbTy65LM7VUsePF0aNH2bhxIxkZGeXLTCbTeXXOaChTpoCvn40Jf08nfp8XP34bwKuvQq7ueFijir/fwMBAJk2aRJ8+fSptU3YjUhc6yTRCubm5PP7447Rp04aAgAC6dOnC6tWryc/P56GHHqJFixaEh4dz/fXXc+zYsfL95syZQ6dOnQgICCAqKorx48eXr1uwYAFDhw4tf5+QkEBUVBSff/55+bIJEyYwcOBAbDbH8B2BgYFceumlLFq0yGnX+sorUFabExRi491PT3L97Zm6NFNLQ4cOLb+LtVqtLFmyBKvVWr7e39+fFi1aGBVerZSVYq67JYvAIBv/92o4drvCZoP33jM6OtfXt2/f8kQzfPhwlFLs3LmzfH1AQADDhg2r8/F177LzsHpH4hnLmoVbaN00kBKbnXW7k85Y3zLSn5ZRARQW29iwN/mM9a2bBNAswp+CwhI27U8BoE9c0zO2q86ECRNISEjgl19+ISYmhoMHD6KU4pFHHmHr1q2sW7eO4OBgHnroIUaMGMHmzZspLCzkzjvvZOnSpQwaNIi8vLxKAyhu3ryZiRMnlr+Pjo7miy++4MYbb6RHjx5s2LCBH374ga1bt2I2/1kXHhcX57SBGMtKMWXfiVkZZn5b5s/IW7NYv8rC6697655mNZg8eTJffvllpbvZ8PBwRowYwZIlS3jyyScr/T5dkaMtBubOCGb3Vh8OH3CMBJGf7+hp+Pe/627t1WnTpg0DBw4kMTGRDh06sGTJkvKJ7ZRSBAQEcP3119f5+Lok08gkJyczb948PvzwQ1q3bo1Sinbt2tGmTRtmzZrFyy+/TLNmzbBYLLzzzjvs2bOH9evXA47nVvbu3Ut6ejoWi4W+ffuWHzcjI4PAwMpPTQ8ZMoRHH32UUaNG8eCDDzJ79myaNGlSaZvAwEDSnVSkePVVOL0UP2taCFkZZu55JJX33xcu4Ekga6VDhw7MmzcPPz+/8kZ/u91OVFQUf/nLX/jb3/5mcITVO3kSZs+2A3aKCk1sWlf5mZiCAl2aqY0ZM2ZwzTXXkJiYWP59EBAQQHR0NL/++ut5PSOoSzLnoboShofZVO16b09ztet9vT3OuQQDcOTIEQDat29faXlKSgpWq5U2bdqUL/P39ycyMpLjx4/Tu3dvFi9ezFtvvcWzzz5LmzZteOyxx7j99tsBCAkJITs7+4zz3X///bzyyitcfvnlDBo06Iz12dnZhIaGnvN11Eb37jBu3OlLzRzcFkavwclMeS0Luz3YKeduTIYPH05iYiKzZ89mx44dREZG0qtXL9avX8/27dvp3r270SGelckEL7+dSVSLPH5d2AxbyZn3zR07GhCYm1m7di2+vr5cf/31+Pv7U1hYyODBg7nuuusqdQqoC51kGpmYmBgADhw4UOlp3YiICLy9vTl8+HB5431ubi7Jycnlde4DBgxgwIAB2Gw2Fi1axOjRo7nsssuIjY3l4osvZvfu3YwcObL8mHa7nXHjxnHdddexdu1apk+fzt13310pnp07d3Ldddc55VrvvNPxOpOF9Xv9iB1uw0n5rdEJDAzk/vvvL38vIiQmJrJ06VLatm2Lv4vWN/kGFNK2axYtIv0Z+5GumKmL+Ph4tm3bRt++fRk0aBBXX311vR5f/1YamcjISG666SYmTZrEkSNHEBEOHjzIoUOHuOuuu3juuedISEggPz+fxx57jI4dO9KrVy+SkpL4+uuvycrKwmw2ExwcDFBeH3/99dfz888/VzrXyy+/zPHjx5k1axazZ8/m4YcfrtRgmJOTw/r16yslpoZyaYdIurau+1PKFzqlFCNGjKC4uJglS5YYHU6V7CJsPZiKl6eZLq313URdFBUV8f333xMWFka/fv2ccg6dZBqh6dOn0717d/r3709AQACjRo3i1KlTvP322/Ts2ZNLL72Uli1bkpiYyKJFizCbzdjtdj744ANiYmIICAjggQce4NNPPy0vGd15551s27aNQ4cOAbBixQr+85//8NVXX2GxWBgwYABPPPEEN998c/l0CF9++SUDBw6kXbt2Df4ZlA1Zk55jJSFNT89QFxEREfTt25ddu3axb98+o8M5w6GEbLLyirioTRheHq7dOcFVmUwm4uLiGDFixHlXi52NcpeneRtCz549ZePGjVWu27NnD506dWrgiFzLhx9+yJo1a/jss89q3LawsJCuXbuyaNGiaj83Z3+ua3YmkpVbxKBLmuHjpWuHz5XNZuOjjz6isLCQSZMm4e3tGnP4iAi/7zqFh9lEr46RelxBgymlNolIz6rW6ZKMVmv3339/rRIMOJ74P3DggOGJuVtsODa7sONQmqFxuCuz2czIkSPJzs4+r6FF6ptSiiu6NOGSdhE6wdSBzWZjzpw55TUTzqSTjNao+ft60qFlMAlp+STqarM6ad68Of369SM6OtroUABIzSqgsMiGUgpPD/0VVhc5OTmkpaVRWFjo9HPp+gOt0WsbHcTJlDy2H0ojPMhXfzHVwcCBA40OAQBrUQnr9yYTFuDDZZ2jjA7HbQUHB3P//fc3yIO2+n+b1uiZTIrubcNp0zQQs54hsc5EhA0bNrBmzRrDYthxKB2bzU7nmBDDYnBnIsIff/xBYWFhg43koJOMdkEICfCmXfNgPQ3veVBKcfz4cY4ePWrI8P+n0vNJSMujfYtgAvy8Gvz8jcGWLVtYsmRJg0zBUcalk4xSylsp9b5SKlUplaeUWqSUal7DPuOVUlLFy6eh4tZcV1J6Pqt3JGKz240OxS2NGDGC2267rcEb24tL7GyLTyXAz5N2zYIb9NyNRU5ODj/99BMxMTFcdNFFDXZel04ywDvAaOA2oC8QCHyvlKqpnJcPNK34EhFr9btoFwKlIC3byv7jWUaH4pY8PT1RSpGVlcX+/fsb7LwiQligD93bhuvSaB39+OOPlJSUcN111zXoTYLLJhmlVBAwAZgsIstEZDNwJ3ARMKSG3UVETlV8OTtezT1EhvjRIsKfAyczyc6r+xwZF7qlS5eWjxDRELw8zfTsEElogK6QqIs9e/awZ88eBgwYQFhYw46E4bJJBugBeAI/lS0QkePAHuCKGvb1VUodVUqdUEp9r5S6+GwbKqXuVUptVEptTElJqZfANdfWtXUonh4mthxMdZuphV3N0KFDERF++OEHp36GNruw+UAKOfn6hqCurFYrixcvJioqit69ezf4+V05yTQBbEDqacuTStedzT7gbmAUjmo2K7BGKVXl2CYi8rGI9BSRnhEREecftQvz9/dn7dq157TPU089xXPPPVerbVNSUmjVqhWpqaf/ylyLl6eZuNZhZOYWkph+5rzmWs1CQkIYOHAgBw4cYNeuXU47z4ETmRxPziW/0PVn53RVP//8M3l5eYwcOdKQuYEa/DkZpdTLwLM1bFZdp3wFnPXWSUTWAuXfpEqp34GtwN+Av9c60EYo9xznoj127BiffPJJrZ8KjoiI4Pbbb+eFF17g/fffr0uIDaZZuAVvTzPhQbr6pa4uu+wydu7cyY8//kibNm3w8/OreadzkJ1fxP4TmTSPsBAVUr/HvlAcPXqUTZs20bt3b8MepjWiJPMO0KmG13rgFGAGwk/bPxJHaaZWRMQGbAQafpRGNzdt2jRGjRp1xmRl1bn77ruZMWNGlXPPuBKlFBHBviilKCgsQUQoKIDSmaO1WjCZTIwcORKr1cpPP/1EUVERBw4c4Pjx43U+ZlERFBY6Gvq3HkzF02zSo2mfA5vNxsGDB8tHYI+Pjyc4OJgBAwYYFlODJxkRSRWRvTW88oFNQDFQPrF8afflTsDvtT2fcnSjuAg4c67kRuq9996jdevWBAQE0KxZM5555hnA8cW6evVqAGbOnEnbtm157733aN68OSEhIdx3333YKnzLLliwgKFDyz9+duzYQWBgIL/++ivgmE/mqquu4s4Kk7q0a9eO8PDwM6YFcFWZuYX8svkEJ1LyGDYMHnzQ6IjcS1k9/7Zt2+jRoweXXHIJ7du3p2PHjvz444/nfLw77oBbboFjyblk5BTStXUY3p56hOWaiAhvvPEGUVFRdO/enc6dO9O6dWuSk5O577778PIy7rkilx1WRkSylFL/A95QSiUDacBbwHag/BtMKfULsF5Eni59/09gHXAAR5fnv+NIMhOpZzNnzqxxm/bt23PFFVeUb9+9e3e6d+9Ofn4+8+bNq3H/su1ra//+/Tz11FNs2LCBLl26kJmZedYHr44ePUpSUhLx8fEcP36cXr160a9fP8aOHUtBQQF79+6tNPFZXFwc77zzDrfddhtbtmzhww8/5MSJE3z77beVjhsXF8fmzZu58cYbax23UYIsXgRavNhyII19B3zZsMHMc8+BiwzT5fJEhA8++ICWLVsyePBgpk6dSnFxMfv27WP06NF89tlnjB49ulbHOnAAvvvO8e/sFAvdYoXmERYnRt94TJo0iVmzZpGf72hjjIiIwGq1MmHCBNLT05k0aZJhsblywz/AI8A3wFxgDZALjCitAisTi+NZmDLBwMc4eqH9BDQD+onI+oYI2GgeHh6ICLt27SI3N5fg4GAuv/zyKrf19fXlxRdfxNvbm7Zt2zJ48GDKpjrIyMgAOKOq7O6772bYsGEMHTqUN998k/nz55fPDV8mMDCQ9PR0J1xd/VPKMeRMSYmd2/+aht0OL75odFTuY+3atSxbtoyFCxcSEBBAy5Yty9cVFBRw//33VyodV+eZZ6C4WEDZefYZEzFNAvUIy7Vw4MABZs6cWZ5gwNH7b+zYsRQWFjJ58uTyOZ4MISL6Vfrq0aOHnM3u3bvPus7VfP311zJkyBAJCAiQK6+8UpYuXSoiIoCsWrVKRERmzJghsbGxlfYbN26cTJgwQURE8vPzBZBt27adcfzNmzcLIHfddVeV57/uuuvk2WefrVWsrvC5/v67yJ33pcuC1Yfk4svyxMdH5ORJo6NyD3fffbcopQQQi8UiODrllL8CAgJk5cqVNR5n/34RHx+RvkNyZNqcY9KiVZHs3NkAF9AIPP/88+Lh4VHpc/f19ZXmzZuX/w7mzp3r1BiAjXKW71VXL8lodXDjjTeybNkyUlNTueWWWxg1alSlu5za8PX1pUOHDuzevbvS8oKCAsaNG8f48eNZsGBBlW0vO3fu5OKLz/poksuZPBm+nB7M0UOexLYv0qWZc5CUlFT+nEzZ3XLHjh3x9fUFHCXF2pRqn3kGIpoUcf/jqeRkmzmV4MHTTzsv7sYkOTmZkhJHF+/Q0FDMZjMFBQWcOHECgJKSEkNrFnSSaWT27dvHkiVLyM/Px9PTk6CgIJRSmEzn/qu+/vrrz0giDzzwAGFhYXzyySd88MEHjB07lsTEP/tUHDx4kJSUFIYMqWlQBtewdi1s2QIlxYon74tm/mfBFBXBp59CQoLR0bm+Sy65pNJsmYGBgdx0001ceeWVABQXF9c4cd2BA/DLCjtP/iuZkmLFG89FUFys+PlncOIjOI1Gt27d8PPzw9/fn/HjxzNq1KhK681ms6GTB+ok08gUFRXxwgsv0LRpU4KDg3nvvff4+uuv8fE59+dBJk6cyIIFC8q7I8+aNYvFixfz5ZdfYjabueOOOxgxYgS33357eb379OnTGT9+PEFBQfV6Xc4yeTKUFfKsBY7/Du27WBl7bxovvqhHA6jJvffeW6ndJDs7m08//ZQVK1ZgMpno0qULHTt2rPYYzzwjTHoihabNinn9uUhSkjwBR3dmXZqp2e23346Hhwe33norPj4+Z0zFEBYWRr9+/QyKDt0mU/HVWNpk6tOTTz4p//jHP2q1bUpKirRs2VKSk5NrfXwjP9fffxfx9BSByq+b7sqQBasPyQ23Z+q2mVqYNWuW+Pn5idlsrtQm0LJlS1mzZk21++7fLxIQaJOX30+Qa2/MOuN34eEhum2mBna7XT744AOZMmWKdO3atfx34O3tLcHBwbJ9+3anx0A1bTIu24VZcw2vvvpqrbcNDw/n6NGjToymfu3dC1FVTK74x4ogunYr5M7709l90IvoaN+GD86N3HnnnXTv3p3//Oc/rFq1Ch8fH8aNG0erVq1YsWIFMTExZ33afO9eCA4y8fEbTbDboflpE3koBfv2QZcuDXAhbmrjxo2kpKTQpUsXTp06RV5eHh4eHowZM4ZJkybRpEl1o3A5nxLRVQJlevbsKWVdeE+3Z88eQ+s1GytX/VxLbHZ+256AtchG/27RWHw8jQ7J7eTl5fHxxx8Djmq107u6Z+cVsftoOhe3i9APXNbR0aNHmTVrFrGxsYwZM6ZOba/1QSm1SUR6VrVOt8loWhU8zCYu6+go5hxKcO0hclyVxWJhzJgx5Ofn89VXX1V6Xqao2MYfe5PIzC3Cbtc3unWRlZXFvHnzCAkJ4cYbbzQswdTENaPSNBdg8fWkb1xTurYONToUt9W0aVNGjhzJ0aNHWbJkCQB2ETbuS8ZaWEKvTpH4euta+3NVXFzM3LlzKSkpYcyYMXXq2NNQ9G9X06pRNpd8QWEJKVkFtIwMMDgi9xMXF0diYiJr166ladOmeIW0IiXLSve24XoSsjqy2+0EBgbSv39/wsNPH0PYtegko2m1cOBkFocTs/HyMNMkVA87f66GDBlCcnIyP/zwA50vu4Z2bVvTKkon7LoQEby9vbn11lvdYtgdXV2mabXQuVUIQRYvNu1P1rM01oHJZGL06NEEBQVxePuvxIQbNyqwO4uPj2f69Onk5ua6RYIBnWQ0rVY8zCZ6dYrCZFKs35tMcYnd6JDcSmGRjSPJVm655Va6d++Gv78eXbkubDYbSilDh+4/VzrJaLX24YcfVpo7pjqFhYW0a9furNMMuCM/bw8u7RBJnrWYPUfdY5RpV2C3Cxv2JRGfkIVfYAhDhgzBZDJhtVrRj1DUTtnn1L59e/7yl7/oJKM1Pnl5eTz//PNMmTKlVtt7e3vz+OOPM3nyZOcG1sDCg3zp1TGKTq10j7Pa2nE4jbTsQrq3DSewtCNFVlYWU6dOZcOGDQZH5/pEhG+++Yb16x2zlbhLNVkZnWQaUGIixMbCqVNGR3LuPv/8c+Li4oiNja31PrfddhvLly/n4MGDToys4TUJ9cPTw4TNZic9x2p0OC7tyKlsjpzKoW2zIJpH+JcvDwwMpEOHDpXmn9GqtmrVKnbu3Fk+0rK70UmmAb30Ehw54vjpTLm5uTz++OO0adOGgIAAunTpwurVq8nPz+ehhx6iRYsWhIeHc/3113Ps2LHy/ebMmUOnTp0ICAggKiqK8ePHl687fSrmhIQEoqKi+Pzzz8uXTZgwgYEDB5Y/dBcYGMill17KokWLnHvBBtl5JJ3fd54iK8/REUDEMajjhayw0PE5ABSX2Nl9NIOIYF86twqptJ1SiuHDh5cPeVJUVISIkJSUVGn6gAtNSUkJJ0+eJDMzE3CMqr5ixQouuugievfubWxwdXW2Qc0uxJczB8hMSHBMygQivr4iiYnndbhq3XLLLdKnTx85dOiQ2O122b9/vxw4cEDuvfde6dWrl5w4cUJyc3NlwoQJctFFF0lJSYnk5eWJh4eH/PLLLyIikpubK7/99lv5MSMjI2XhwoWVzrNs2TIJCAiQ3bt3y6effipRUVGSeNqFPfjggzJ27NizxurOA48WFBbLkvVH5acNx6SwqESeekqkXz+jozKO3S5y0UUi//nPn8sycwulsKik2v2WLVsmr7zyirRr1068vb3F29tbWrVqJZ999pmTI3YdhYWF8uyzz0pQUJD4+vqKp6enDBs2TF5++WX56KOPpKioyOgQq4WetMx4L70E9tIOSTab80ozycnJzJs3jw8//JDWrVujlKJdu3a0adOGWbNm8fLLL9OsWTMsFgvvvPMOe/bsKa/r9fT0ZO/evaSnp2OxWOjbt2/5cTMyMs6YinnIkCE8+uijjBo1igcffJDZs2efMRifO03FfK58vDy4tGMk1qISft+ZzP/9n7B+Pfz+u9GRGWPxYsdglq+8YufQSccEZkEWL7xqGJds8+bNWK1WunXrRmFhIYWFhRw9epT77ruPf//73w0RuqFsNhvXXnstb731FllZWRQUFGA2m2nXrh1ZWVm0bdsWT0/3HTtPJ5kGkJgIM2b8WZVSVOR474y2mSNHjgCOXigVpaSkYLVaadOmTfkyf39/IiMjOX78OH5+fixevJglS5YQGxtLjx49mD17dvm2ISEh5fPKVHT//fdz9OhRLr74YgYNGnTG+uzsbEJDG28jeWiADxfFhpOVb+WmuzKwWh1z1FxoRODxx6GwULhrUho7jiSTmVtY434ZGRn885//5JdffqFr167lk50B5Ofn89JLL5GSkuLM0A23ePFi/vjjDwoKCgBHVeKNN95ISEgIc+fO5e9//7vBEZ4fnWQaQMVSTBlnlWZiYmIAOHDgQKXlEREReHt7c/jw4fJlubm5JCcn06JFCwAGDBjAokWLSE1N5R//+Ad33HEH8fHxAFx88cVnTMVst9sZN24c1113HQcOHGD69OlnxONuUzHXhb9HALP/G8JP3zmeYN+69cIrzSxeDMePw3U3Z9N/WC7ffhGMp/Kucb+vv/4as9nM6tWr2blzJ0OGDKFdu3bl65VSzJs3z5mhG27atGnk5uaWvx80aBDt27fnxx9/5NixYxw+fPiM/8/uRCcZJzu9FFPGWaWZyMhIbrrpJiZNmsSRI0cQEQ4ePMihQ4e46667eO6550hISCA/P5/HHnuMjh070qtXL5KSkvj666/JysrCbDYTHBwMOKZuhaqnYn755Zc5fvw4s2bNYvbs2Tz88MPs3LmzfH1OTg7r169n5MiR9XuRLua112DR3GASjnuilHDx5blMnnzhNFyLwOTJwg13pPPXh9L54zc/5s8K5oMPat63rIQNsHDhQpKSkhgzZgw9evQAoKCgoNGXZCpOX+7r60uPHj3YtGkTZdOOeHp6uvdncLbGmgvx5YyG/4kTRby85IwZ/8CxfNKkOh22WtnZ2fLQQw9Jy5YtxWKxSOfOnWXVqlWSm5srDz74oERHR0tYWJiMGDFCDh8+LCIiCQkJMnDgQAkODhZ/f3/p1KmTzJo1q/yYubm5Eh4eLvHx8SIisnz5cgkICJCdFaYtfOmll6Rjx46Sm5srIiIfffSRDB8+vNpY3bnhX0QkNVXEz+/P32nvAbmyYPUheeaVU7Jqtc3o8BrE99+LdOtRIN/8dkjufzxFPDztAiKBgSKlfwpnNX/+fAkICKg0o+bYsWNlypQpMmLECAkKCpIvvviiYS7EIHfeeaf4+/uLUkoACQsLK/83ID4+Pmd0qHE1VNPwb/gXuyu9nJFkmjWrOsGUvZo1q9NhDTFt2jS54447arWt1WqVtm3b1vi5uXuSmTz5z16DjpddRt6aKV//ekg+mX9ccvJdu1fQ+bIWlkjHjo5rj2lrrfS37ecn8tpr1e9fWFgoISEh5V+ogCilZNCgQTJlyhQZPXq0FBQUNMzFGGT16tXy+OOPS58+fSp9DoB4eHjI1VdfbXSINdJJxsAko1XPnT/X1NTTE8yfr7hL8mXW90dk4erDcio9z+hQneJ4co4sWHVYevbOP+tNVEBAzaWZlStXisViEQ8Pj0pfrt26dZPvvvtORBzz2DdWdrtdpkyZIi1btqyUYHx8fKRZs2aSkJBgdIg1qi7J6DYZTauj3bshMBDCws58JRz15eXJ0VjzvPAwN67/ZnYRdh5OY9P+FHKzvEhL9qzyMwgLA4sFamqz7t+/P1u3buWvf/0r0dHRREdHM378eObNm8d1112HiDB//vzyrvaNQXFxMT/88ANpaWkopfjnP//JzJkzGTZsGFFRUcTGxvL888+zc+dOmjZtanS450XPJ6NpddS3LyQlVbeFJyJNy8eaOp6cWz4kjbsqLLaxcV8yqVlWWjcNpGvvUMYOP/+xtNq2bcu0adOYNm3aGetKSkooKSnBfnoXTTeVlZXF3LlzSUxMJCoqirCwMAAGDhzIwIEDDY6u/ukko2lOVJZg8q3FbDmYgp+3J706RZYPFOluElLzSM8u5OJ24Q02S6inpydjxowpf3/48GFCQkLKe0C6k8OHDzN//nxsNhtjxoyhQ4cORofkdDrJaFoD8PPx5MouTdmwL4nftiVwSfsIosPcZ04Va1EJPl4exDQJICLYF3/fhn0CvSxZ22w2Fi5cSHFxMTfddBOtW7du0DjqSkRYt24dy5YtIywsjFtvvdXlp02uL+5bbtc0NxMW5EP/bs0I9PNiw95k9h7LqLTeboeEBIOCK3Xy5J8DXIJjLpjth9JYvvkk+dZilFINnmAqMpvN3HnnnVgsFj777DPWrl3r6MGE4+HgzZs3s3r1ajIyMmo4knMcO3aM3377rdLDk8XFxXz77bf89NNPdOjQgb/+9a8XTIIBXZLRtAbl6+3BlXFN2XEoDV+vyv/9Pv4YnnjC8UUf0DA1UZWkpDimopg1C265xVF62bgvmbTsQmKjA/Hxdo2vi7CwMCZMmMDChQv56aefyh8unjx5Mnl5eZjNZgoLC7nllluYOnUqFovzS4zx8fGMGzeOTZs24e3tTVFREe3ateODDz5g586dJCUlMWjQIPr06eN288GcL12S0bQGZjYpurcNp1UTRyZJTMsjNbOI554DqxXefdeYuP79bygpcYy9lpZl5ddtCWTmFtGjfQRdW4dhcqEvR29vb26++WYGDRrEzp07WbduHUVFReTm5pKVlYXVamXevHkMHjy4fOoJZ0lISKBXr16sXbsWq9VaPsjl9u3beeKJJ0hPT+f222+nb9++F1yCAZ1kNM1Qdruw60g6q3Yk0K1XLsXFjmFqcnIaNo6UFPjoI8eYeunp8OsfOZiUou9FTStNNuZKlFL07t2bhQsXEhAQwL333ltpUj2r1cquXbtYunSpU+N4/fXXycnJqdT7raw6bN26dWzatKnSeGwXGp1kLiD+/v6sXbv2nPZ56qmneO6552q1bUpKCq1atSI1NbUu4V2QTCZFrw5Nid/rxd+eSeHeR1NpFVvIu+827Nhnr7wixHaw0qRZMbm58MSkMPrGRRNkqXmQSyOtXbuWgwcP8vHHH5OVlcWYMWPw9/8zKebm5jJjxgynxvDFF19QXFxc/n7AgAHce++9BAUFISIsWrTIbWe1rA86yVxAcnNzz2l2vWPHjvHJJ58wuZZj10dERHD77bfzwgsv1DXEC9Lszz14aXJTfpgfyLU35vDS+wl8MM1OTg5k5xdRUFi7L6iMDBg9GkpHjK9RvrWYI6eyWbUtiR5XHePl/0vk6VeSMJuFpCQTixZWPw+MK8jJycFkMpGRkcH//vc/vvzyy/IRje+++24uu+yy8lkmq1NUVMRnn33G5ZdfTps2bbjuuutYsWJFtfuICGlpaXTo0IHbbrutfHqNTZs28fPPP5OVlVXp+Bcq12jJOwul1L3AbcDFQBDQWkSO1GK/0cBLQCwQDzwrIt86MdRq5ebm8sYbbzB16lTS0tIICwtj0qRJTJ48udJdl6uZNm0ao0aNOmOysurcfffdXHzxxfzrX/86p/0uVEVF8NxzkJ2l+O87YcybGUzbToVkZ5p5910YfEM6yZkFBPh6EhniS0SwL2GBPlWOIvDGG/DttzBtGjz66JnnKi6xk5VXSHiQLwBbD6aSkmXFmm9m/So/Nq3zZftGX2w2RW6uo23mppvA5MK3onFxcRQWOuatKS4u5tChQ4Dj2ZqsrCxsNhtXXHEFOTk5zJ49m9jYWGJjY2nRogUeHo6vv/z8fAYOHMiuXbvIy3NMtnb48GFWrlzJPffcw9tvv11+voKCAg4fPkx8fDzx8fFkZWUxdOhQ0tPT8fZ2lPrKRh8vExkZia+vb4N8Hi7pbOPNuMILeBh4uvSnADG12Kc3UAI8C3Qq/VkCXFbTvs4YuywnJ0e6dOkiPj4+Z4xL1KVLF8nJyanTcavz7rvvSkxMjPj7+0t0dLQ8/fTTIiICyKpVq0REZMaMGRIbGyvvvvuuNGvWTIKDg+Xee++VkpI/p8rt2LGjfPnll+Xvt2/fLgEBAbJy5UoREbHZbDJ06NAzBs1s1aqVfP3117WK1Z3HLqsP06aJWCxVj/vl7y+SkFwoB05kypqdibLo98OyYPUhWb39z7GscvKLxG63S3r6n8cJChLJz3eMiZWebZW9xzJk1fYEWbjmkCxYfah8OuSMHKscOV4ovr72s55/7lyDPphzcPXVV4unp+cZg0tSOqpzQkKCnDp1SmbMmCEvvviiTJkyRf71r3/J559/LmvXrpXHH3/8jP+fZS+LxSKLFy+WFStWyCeffCIvvPCCTJkyRV555RWZM2eObNiwQebOnSsWi6XK/f38/OSdd94x+iNyOtx9gEyg5zkkmbnAstOW/Qx8WdO+zkgyzz///Fn/gH18fOT555+v03HPZt++feLr61s+BH9GRoasXbtWRM5MMh4eHvLMM8+I1WqVAwcOSEhIiHz++eciIpKfny+AbNu2rdLx//e//0nTpk3l1KlTMmXKFOnUqVP50P5lrrvuOnn22WdrFe+FnGQKC0XCw6tOMGVTQbz00p/bl5TYJCk9T5Iy8kVEpKjYJgvXHJIf/zgqn8xJkqEjsqVF60IJC7fJm2+KHErIkgWrHYllxZYTsutwmiRn5IvN9udgkw8/LOLhcfYYWrYUsbn4jAUpKSnSrl078ff3L/+/5eXlJX5+frJgwYJK21qtVtm3b58sXrxY3n//fZkyZYpMmTJFHnnkERk5cmT5tAOdO3eWvn37CiADBw6Ujz/+WD755BNZvny5HDt2TGwVPhS73S6PP/64+Pn5iclkKh9J2mKxyM0331xp28aquiTj0tVlddQbeP+0ZUuBBw2IhalTp5ZPynQ6q9XKtGnT6rUNw8PDAxFh165dtGrViuDgYC6//PIqt/X19eXFF1/EbDbTtm1bBg8ezMaNGxk7dmz5w2ynV3ndfffdrFq1iqFDh3LkyBHWrVt3xnMIgYGBpKen19s1NVZZWdC+PTRvfvZtKv7pmM0mIkP8yt8rBd3bhnMyuYBk/wIeeNJR1fP2ixG8+KI/f5ngR4/2JiKCfPH2qrp9xWaDrl3Pfv7AQMjPBxeu1SU8PJwdO3bw1VdfMWPGDHJzc+nfvz8PPPAArVq1qrStt7c37du3L28/2bNnD3fffTctWrSgQ4cO5T3RWrVqRevWrVm9ejW7d+/m7rvvLp/A73RKKd544w1uvvlm3n//ffbu3UuLFi148MEHGThw4AXZbbmSs2UfV3pxbiWZIuCu05bdBRSeZft7gY3AxpYtW541U9f1jrvi5ENVvUwmU52OW52vv/5ahgwZIgEBAXLllVfK0qVLReTMkkxsbGyl/caNGycTJkwQkbOXZERENm/eLIDcddddVZ5fl2Qa1tNPi/j52aV1O6sMujZbIpsUicUi8uabRkfm+rKyssTLy6u89FH2/7LitAPt27c3OkyXhysN9a+UelkpJTW8BpznaU7v/6mqWObYUORjEekpIj0jIiLO87RnKhthta7r6+LGG29k2bJlpKamcssttzBq1Cjy8/PP6Ri+vr506NCB3bt3V1peUFDAuHHjGD9+PAsWLDhjSmaAnTt3cvHFF5/XNWi1k5EB770H+fmKwwe8Wb44gORTnuTlwYsv1r6n2YUqMDCQvn37ApTddAKUdzn29fXlvvvuMyS2xsKIfiPv4GiQr+51PhNHnAKanLYsEqh2UHZnmTRpEj4+PlWu8/HxYeLEifV6vn379rFkyRLy8/Px9PQkKCgIpRSmOnQRuv76689IIg888ABhYWF88sknfPDBB4wdO7bSHOUHDx4kJSWFIUOGnPe1aDV74w3HmGdVKSlx9DTTqvf2229X2cvT09OT6Oho7rnnHgOiajwaPMmISKqI7K3hdW633ZWtBYaetmwo8Pt5HLPOJk+eTGxs7BmJxsfHh9jY2Fo/g1JbRUVFvPDCCzRt2pTg4GDee+89vv7667MmuupMnDiRBQsWkJ2dDcCsWbNYvHgxX375JWazmTvuuIMRI0Zw++23lw/dMX36dMaPH09QUFC9XpdWtalTHT8DA8982WzwzjuGhucW4uLiWLNmDVdccQXe3t4EBATg4+PDTTfdxPr16wkwYiC5RkRVLCK6GqVUExylks7AF8BwIAE4JiLppdv8AqwXkadL318B/AY8B3wL3AC8CPQRkT+qO1/Pnj1l48aNVa7bs2cPnTp1qtN1lD0nM23atPLnZCZOnOjyz8mA44l/T09PXnrppRq3TU1NpUePHmzcuJHaVj2ez+eqwZEjUHoPUKWQEGjRosHCcXtJSUmkpaXRvHlz/ZzXOVBKbRKRnlWuc/EkMwX4ZxWr/iIiM0u3OQKsFJHxFfa7CXgZaMOfD2N+U9P5nJVktLPTn6umub/qkoxLd2EWkSnAlBq2iali2XxgvlOC0jRN02rNhQeM0DRN09ydTjKapmma0+gkcw5cuf3KHenPU9MaP51kasnHx4e0tDT9xVhPRBzDpNela7Wmae7DpRv+XUnz5s05ceIEKSkpRofSaPj4+NC8uoG7NE1zezrJ1JKnpyetW7c2OgxN0zS3oqvLNE3TNKfRSUbTNE1zGp1kNE3TNKfRSUbTNE1zGp1kNE3TNKdx6QEyG5pSKgU4eh6HCAdS6ykcozWma4HGdT2N6VqgcV1PY7oWqP31tBKRKode10mmHimlNp5tJFJ305iuBRrX9TSma4HGdT2N6Vqgfq5HV5dpmqZpTqOTjKZpmuY0OsnUr4+NDqAeNaZrgcZ1PY3pWqBxXU9juhaoh+vRbTKapmma0+iSjKZpmuY0OslomqZpTqOTjKZpmuY0OsnUA6XUJKXUYaWUVSm1SSnV1+iY6kIp1U8ptUgpdVIpJUqp8UbHVFdKqaeVUhuUUtlKqRSl1HdKqa5Gx1VXSqkHlFLbS68nWym1Vik13Oi46oNS6pnSv7f/MzqWulBKTSmNv+LrlNFx1ZVSqqlS6tPS/zdWpdRupVT/uh5PJ5nzpJS6FXgX+DdwMfA78KNSqqWhgdWNP7ATeAgoMDiW8zUAmApcAQwCSoCflVKhRgZ1Hk4ATwKXAD2B5cACpdRFhkZ1npRSlwP3ANuNjuU87QOaVnjFGRtO3SilgoE1gAKGA52AvwHJdT6m7l12fpRSfwDbReSeCssOAPNF5GnjIjs/Sqlc4EERmWl0LPVBKeUPZAHXi8h3RsdTH5RS6cDTIvKR0bHUhVIqCNiMI8k8D+wUkQeNjercKaWmADeJiNuWlMsopf4N9BeRK+vrmLokcx6UUl5AD+Cn01b9hOMOWnMdATj+3jOMDuR8KaXMSqkxOEqevxsdz3n4GMfN2HKjA6kHbUqrmQ8rpeYopdoYHVAdXQ/8oZSaq5RKVkptVUo9qJRSdT2gTjLnJxwwA0mnLU8CmjR8OFo13gW2AmsNjqPOlFJxpSXMQuBD4AYR2WFwWHWilLoHaAs8Z3Qs9eAPYDxwDY5SWRPgd6VUmJFB1VEbYBJwCBiG4//Nq8ADdT2gR/3EdcE7vc5RVbFMM4hS6i2gD9BHRGxGx3Me9gHdgWBgNPCpUmqAiOw0MqhzpZTqgKMNs6+IFBkdz/kSkR8rvldKrcPxJT0OeMuQoOrOBGysUNW/RSnVDkeSqVPHDF2SOT+pgI0zSy2RnFm60QyglHobuA0YJCKHjI7nfIhIkYgcFJGyL4GtwCMGh1UXvXHUAuxUSpUopUqA/sCk0vfexoZ3fkQkF9gFtDM6ljpIBHaftmwPUOeOTDrJnIfSu7BNwNDTVg3FvevKGwWl1LvA7TgSzF6j43ECE+COX8gLcPS+6l7htRGYU/pvty7dKKV8gI44vrDdzRqgw2nL2nMe82zp6rLz9xbwmVJqPY5f0P1ANI46c7dS2gOrbelbE9BSKdUdSBeRY4YFVgdKqQ+AO3E0ZGYopcpKm7mld5puRSn1KvADcBxHJ4bbcXTTdrtnZUQkE8isuEwplYfj78ytqv4AlFL/Ab4DjuGoxXgOsACfGhlXHb2Noz3pWWAujscy/g48U9cD6i7M9UApNQl4Akf/+J3AIyLym7FRnTul1ABgRRWrPhWR8Q0azHlSSp3tD/sFEZnSkLHUB6XUTGAgjqrZLBzPlbwhIkuNjKu+KKVW4r5dmOcA/XBUAaYA64DnROT0aie3UPqQ779xlGiO4WiLeV/qmCx0ktE0TdOcRrfJaJqmaU6jk4ymaZrmNDrJaJqmaU6jk4ymaZrmNDrJaJqmaU6jk4ymaZrmNDrJaJqmaU6jk4ymaZrmNDrJaJqmaU6jk4ymuSCllEUptVcptV4p5Vlh+VVKKbtSqs7ze2haQ9LDymiai1JKXYxjHKy3ReQppVQkjjHL1ovISGOj07Ta0UlG01yYUuoR4E3gKuBxHEPkdxORVEMD07Ra0klG01xY6dzqPwCDAC9gqIj8YmxUmlZ7uk1G01xY6fDqn+GYnGybTjCau9FJRtNcWOlka+8Am4FuSqmHjI1I086NTjKa5qJKq8o+xTEd8VAcyeY1pdRFRsalaedCt8lomotSSj0GvA4MEpFflVJeOHqbeQM9RaTA0AA1rRZ0SUbTXFBp9+V/A6+IyK8AIlIE3AbEAG8ZF52m1Z4uyWiapmlOo0symqZpmtPoJKNpmqY5jU4ymqZpmtPoJKNpmqY5jU4ymqZpmtPoJKNpmqY5jU4ymqZpmtPoJKNpmqY5zf8Dr1D9T2xzB7oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Points and lines\n",
    "\n",
    "plt.plot(x,y,label='cos(x)',linestyle='dashed',linewidth=1.5,color='lightsteelblue')\n",
    "plt.plot(x,z,label='sin(x)',linestyle='dashdot',linewidth=1.5,color='gray')\n",
    "\n",
    "# List of marker sizes\n",
    "size = [64 for i in range(len(x))]\n",
    "  \n",
    "plt.scatter(x,y,label='cos(x)', marker = '^',color='blue',s=size)\n",
    "plt.scatter(x,z,label='sin(x)', marker = 'o',color='black',s=size)\n",
    "\n",
    "# Change axis boundaries\n",
    "plt.xlim(-0.3,6.2)\n",
    "plt.ylim(-1.2,1.2)\n",
    "\n",
    "# Adding labels on x,y-axis\n",
    "plt.xlabel('x',fontsize = 16) \n",
    "plt.ylabel('y', fontsize = 16)\n",
    "\n",
    "# Change size of ticks on x and y-axis\n",
    "plt.xticks(size=14)\n",
    "plt.yticks(size=14)\n",
    "\n",
    "# Adding legend (after specifying \"label=\" in plt.plot above)\n",
    "plt.legend(loc='lower left', fontsize = 13)\n",
    "\n",
    "# Plot title\n",
    "plt.title('Sine and cosine', size = 18)\n",
    "plt.savefig('2dplot_example')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a8b2c1d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f95929537f0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Panel with 2 plots\n",
    "\n",
    "# Uses subplot and defines 2 plots with separate axes\n",
    "fig, axs = plt.subplots(2)\n",
    "axs[0].plot(x,y)\n",
    "axs[1].plot(x,z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7c2be678",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f95926f92b0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Horizontally stacked subplots\n",
    "fig, axs = plt.subplots(1,2,figsize=(9,3))\n",
    "axs[0].plot(x,y,label='cos(x)')\n",
    "axs[1].plot(x,z,label='sin(x)')\n",
    "\n",
    "axs[0].set_xlabel('x',fontsize = 16)\n",
    "axs[1].set_xlabel('x',fontsize=16)\n",
    "axs[0].label_outer()\n",
    "axs[1].label_outer()\n",
    "\n",
    "axs[0].legend(fontsize = 13)\n",
    "axs[1].legend(fontsize = 13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cb19a153",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Array of 4 subplots\n",
    "\n",
    "twopi = 2*np.pi\n",
    "step = 0.05*twopi\n",
    "\n",
    "# Defining functions\n",
    "x = np.arange(0,twopi,step)\n",
    "y = np.cos(x)\n",
    "z = np.sin(x)\n",
    "\n",
    "x1 = np.arange(-10,10)\n",
    "t = np.arctan(x1)\n",
    "s = np.exp(-x1)\n",
    "\n",
    "# Array of subplots\n",
    "fig, axs = plt.subplots(2,2,figsize=(7,4))\n",
    "\n",
    "# Plots in each panel\n",
    "axs[0,0].plot(x,y,label='cos(x)', color='red')\n",
    "axs[1,0].plot(x,z,label='sin(x)',color='blue')\n",
    "axs[0,1].plot(x1,t,label='arctan(x)',color='green')\n",
    "axs[1,1].plot(x1,s,label='log(x)',color='cyan')\n",
    "\n",
    "# x labels on bottom plots\n",
    "axs[1,0].set_xlabel('x',fontsize = 16)\n",
    "axs[1,1].set_xlabel('x',fontsize = 16)\n",
    "axs[0,0].set_ylabel('y',fontsize = 16)\n",
    "axs[1,0].set_ylabel('y',fontsize = 16)\n",
    "\n",
    "# Setting logscale on bottom left panel\n",
    "axs[1,1].set_yscale('log')\n",
    "\n",
    "axs[0,0].legend(fontsize = 9, loc='upper center')\n",
    "axs[1,0].legend(fontsize = 9)\n",
    "axs[0,1].legend(fontsize = 9, loc='upper left')\n",
    "axs[1,1].legend(fontsize = 9)\n",
    "\n",
    "axs[0,0].label_outer()\n",
    "# Removes tick labels from upper right panel\n",
    "axs[0,1].set_xticklabels([])\n",
    "\n",
    "# Overall title on top\n",
    "fig.suptitle(\"Plotting some functions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e0d863e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# CONTOUR PLOTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5fd187c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a 2d grid\n",
    "\n",
    "# This creates 10 linearly spaced points in the interval [-5,5]\n",
    "x = np.linspace(-5,5,10)\n",
    "# Same in y\n",
    "y = np.linspace(-5,5,10)\n",
    "\n",
    "# This creates a coordinate grid\n",
    "X,Y = np.meshgrid(x,y)\n",
    "# Let's check how it looks\n",
    "plt.scatter(X,Y,marker='o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "22a2c2f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<a list of 18 text.Text objects>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now we evaluate some functions on a grid and build contour plots\n",
    "\n",
    "# This creates 100 linearly spaced points in the interval [-5,5]\n",
    "x = np.linspace(-5,5,100)\n",
    "# Same in y\n",
    "y = np.linspace(-5,5,100)\n",
    "\n",
    "# This creates a coordinate grid\n",
    "X,Y = np.meshgrid(x,y)\n",
    "# Evaluate the function x^2 - y^2 on the grid (vectorized version)\n",
    "Z = X**2 - Y**2\n",
    "\n",
    "plt.xlabel('X',fontsize=16)\n",
    "plt.ylabel('Y',fontsize=16)\n",
    "# Note the Latex style syntax if you want to type formulas\n",
    "plt.title('Level contours of $Z = X^2 - Y^2$')\n",
    "\n",
    "# Plotting contour, '10' is the number of contour lines we ask to plot)\n",
    "curves = plt.contour(X,Y,Z,10)\n",
    "# Writes levels on the plot\n",
    "plt.clabel(curves)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "870f903f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sme contour plot as above but I am not using vectorization after meshgrid\n",
    "\n",
    "# This creates 100 linearly spaced points in the interval [-5,5]\n",
    "x = np.linspace(-5,5,100)\n",
    "# Same in y\n",
    "y = np.linspace(-5,5,100)\n",
    "\n",
    "# This creates a coordinate grid\n",
    "X,Y = np.meshgrid(x,y)\n",
    "\n",
    "###################################################\n",
    "# This part is different from box above\n",
    "\n",
    "# Compute x^2 + y^2 as scalar function in all the (x,y) points \n",
    "# and store in z coordinate\n",
    "z = [ ]\n",
    "for i in x:\n",
    "    for j in y:\n",
    "        z.append(i**2 - j**2)\n",
    "\n",
    "# Now turn z from list into array and reshape it to make\n",
    "# it become a 2-dim array with 1 to 1 correspondence with the \n",
    "# x,y grid\n",
    "z = np.array(z)\n",
    "Z = z.reshape(len(y),len(x))\n",
    "\n",
    "# The rest is as in the previous box...\n",
    "#########################################################\n",
    "\n",
    "plt.xlabel('X',fontsize=16)\n",
    "plt.ylabel('Y',fontsize=16)\n",
    "# Note the Latex style syntax if you want to type formulas\n",
    "plt.title('Level contours of $Z = X^2 - Y^2$')\n",
    "\n",
    "# Plotting contour, '10' is the number of contour lines we ask to plot)\n",
    "curves = plt.contour(X,Y,Z,10)\n",
    "# Writes levels on the plot\n",
    "plt.clabel(curves)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3c161ca4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<a list of 19 text.Text objects>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Filled contours\n",
    "curvesf = plt.contourf(X,Y,Z,10)\n",
    "\n",
    "plt.xlabel('X',fontsize=16)\n",
    "plt.ylabel('Y',fontsize=16)\n",
    "# Note the Latex style syntax if you want to type formulas\n",
    "plt.title('Filled level contours of $Z = X^2 - Y^2$')\n",
    "\n",
    "plt.clabel(curvesf,colors='black')\n",
    "#plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a4e0eeda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Density plot\n",
    "curvesf = plt.pcolormesh(X,Y,Z,cmap='gray')\n",
    "\n",
    "plt.xlabel('X',fontsize=16)\n",
    "plt.ylabel('Y',fontsize=16)\n",
    "# Note the Latex style syntax if you want to type formulas\n",
    "plt.title('Density plot of $Z = X^2 - Y^2$')\n",
    "\n",
    "#plt.clabel(curvesf,colors='black')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "88600e5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Density plot using imshow\n",
    "\n",
    "from pylab import imshow, show\n",
    "#imshow(Z,cmap='gray')\n",
    "\n",
    "imshow(Z,cmap='gray',extent=[-5,5,-5,5])\n",
    "\n",
    "plt.xlabel('X',fontsize=16)\n",
    "plt.ylabel('Y',fontsize=16)\n",
    "# Note the Latex style syntax if you want to type formulas\n",
    "plt.title('Density plot of $Z = X^2 - Y^2$')\n",
    "\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b5b8742",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Multivariate Gaussian contours\n",
    "\n",
    "from scipy.stats import multivariate_normal as multiv\n",
    "from scipy.linalg import det\n",
    "\n",
    "mean = [3.,3.]\n",
    "cov = [ [1.3, 0.7], [0.7, 2.1] ] \n",
    "# This produces a bivariate Gaussian function with mean and covariance given right above\n",
    "bivariate = multiv(mean, cov) \n",
    "\n",
    "x,y = np.mgrid[-6:12:3600j, -6:12:3600j]\n",
    "# Creates al possible (x,y) pairs to pass as coordinates to bivariate\n",
    "pos = np.dstack( (x,y) )\n",
    "\n",
    "#print(pos)\n",
    "\n",
    "# Evaluate bivariate in all x,y points\n",
    "z = bivariate.pdf(pos)\n",
    "#print(z)\n",
    "\n",
    "\n",
    "# Generatres X,Y grid for plotting\n",
    "#X,Y = np.meshgrid(x,y)\n",
    "\n",
    "contours=plt.contourf(x,y,z,levels=[0.000007,0.01,0.1])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9e30d73",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing maxwell class from scipy.stats\n",
    "from scipy.stats import maxwell\n",
    "\n",
    "# Distribution parameters\n",
    "kB = 1.380649*1e-23\n",
    "T = 3000\n",
    "u = 1.661*1e-27\n",
    "m = 4.*u\n",
    "\n",
    "# Number of data points to generate\n",
    "N = 100000\n",
    "# Generating N Maxwell distributed random variables and storing in vector data\n",
    "data = maxwell.rvs(loc=0, scale=np.sqrt(kB*T/m), size=N)\n",
    "\n",
    "print(data[1:100])\n",
    "\n",
    "# Producing and plotting a histogram of data with 100 bins; density = True means that we want\n",
    "# to normalize by dividing each column by the total number of counts\n",
    "plt.hist(data, bins=100, density=True, alpha=0.3, ec = 'black', histtype='bar')\n",
    "\n",
    "x = np.arange(0,np.max(data))\n",
    "# Generating and plotting the Maxwell pdf, for comparison with data histogram\n",
    "y = maxwell.pdf(x, loc=0, scale=np.sqrt(kB*T/m))\n",
    "\n",
    "#print(len(ticks))\n",
    "#print(ticks)\n",
    "\n",
    "plt.xlabel(r'$v \\, ({m/s})$', fontsize = 16)\n",
    "plt.ylabel('Frequency', fontsize = 16)\n",
    "\n",
    "plt.plot(x,y,label='Helium, T = ' + str(T) + ' K')\n",
    "plt.legend(fontsize = 14)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
