notebooks/09_IRASA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aperiodic and oscillatory components of the power spectrum\n",
    "\n",
    "This notebook demonstrates how to use YASA to separate the aperiodic (= fractal = $1/f$) components of the EEG power spectra using the IRASA method.\n",
    "\n",
    "Please make sure to install the latest version of YASA first by typing the following line in your terminal or command prompt:\n",
    "\n",
    "`pip install --upgrade yasa`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mne\n",
    "import yasa\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "sns.set_theme(style='white', font_scale=1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data loading\n",
    "\n",
    "Let's load 6 min of eyes open EEG data, sampled at 200 Hz. We use the [MNE library](https://mne.tools/stable/index.html), which includes various functions and utilities for reading EEG data and electrode locations. For a description of all the file formats supported by MNE, please refer to https://mne.tools/stable/auto_tutorials/io/20_reading_eeg_data.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chan = ['F4-A1', 'CZ-A2']\n",
      "Sampling frequency = 200.0 Hz\n",
      "Data shape = (2, 72000)\n",
      "Duration = 360.0 seconds\n"
     ]
    }
   ],
   "source": [
    "# Download the data\n",
    "raw_filepath = yasa.fetch_sample('resting_EO_200Hz_raw.fif')\n",
    "# Load data as a MNE Raw file\n",
    "raw = mne.io.read_raw_fif(raw_filepath, preload=True, verbose=0)\n",
    "\n",
    "# Extract data, sf, and chan\n",
    "data = raw.get_data(units=\"uV\")\n",
    "sf = raw.info['sfreq']\n",
    "chan = raw.ch_names\n",
    "\n",
    "# Let's have a look at the data\n",
    "print('Chan =', chan)\n",
    "print('Sampling frequency =', sf, 'Hz')\n",
    "print('Data shape =', data.shape)\n",
    "print('Duration =', data.shape[1] / sf, 'seconds')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**************\n",
    "\n",
    "## Calculate the original power spectrum\n",
    "\n",
    "For a primer on EEG spectral power please refer to https://raphaelvallat.com/bandpower.html or [08_bandpower.ipynb](08_bandpower.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(401,) (2, 401)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.signal import welch\n",
    "\n",
    "win = int(4 * sf)  # Window size is set to 4 seconds\n",
    "freqs, psd = welch(data, sf, nperseg=win)  # Works with single or multi-channel data\n",
    "\n",
    "print(freqs.shape, psd.shape)  # psd has shape (n_channels, n_frequencies)\n",
    "\n",
    "# Plot\n",
    "plt.plot(freqs, psd[1, :], 'k', lw=2)\n",
    "plt.fill_between(freqs, psd[1, :], cmap='Spectral')\n",
    "plt.xlim(1, 30)\n",
    "plt.yscale('log')\n",
    "sns.despine()\n",
    "plt.title(chan[1])\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.ylabel('PSD log($uV^2$/Hz)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen on the plot above, there is a strong alpha oscillatory peak around 10-11 Hz.\n",
    "\n",
    "## Extract the aperiodic and periodic component of the spectrum\n",
    "\n",
    "The Irregular-Resampling Auto-Spectral Analysis (IRASA) method ([Wen & Liu 2016](https://doi.org/10.1007/s10548-015-0448-0)) allows to separate the\n",
    "fractal and oscillatory components in the power spectrum of EEG signals.\n",
    "\n",
    "The steps are:\n",
    "\n",
    "1. Compute the original power spectral density (PSD).\n",
    "2. Resample the EEG data by multiple non-integer factors and their\n",
    "reciprocals ($h$ and $1/h$).\n",
    "3. For every pair of resampled signals, calculate the PSD and take the\n",
    "geometric mean of both. In the resulting PSD, the power associated with the\n",
    "oscillatory component is redistributed away from its original\n",
    "(fundamental and harmonic) frequencies by a frequency offset that varies\n",
    "with the resampling factor, whereas the power solely attributed to the\n",
    "fractal component remains the same power-law statistical distribution\n",
    "independent of the resampling factor.\n",
    "4. It follows that taking the median of the PSD of the variously\n",
    "resampled signals can extract the power spectrum of the fractal component,\n",
    "and the difference between the original power spectrum and the extracted\n",
    "fractal spectrum offers an approximate estimate of the power spectrum of\n",
    "the oscillatory component.\n",
    "\n",
    "**For more details on the IRASA method, please refer to**\n",
    "\n",
    "- Wen, H., & Liu, Z. (2016). Separating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal. Brain Topography, 29(1), 13–26. https://doi.org/10.1007/s10548-015-0448-0\n",
    "- https://github.com/fieldtrip/fieldtrip/blob/master/specest/\n",
    "\n",
    "**For another method to extract fractal noise, please refer to**\n",
    "- Donoghue, T., Haller, M., Peterson, E. J., Varma, P., Sebastian, P., Gao, R., ... & Voytek, B. (2020). Parameterizing neural power spectra into periodic and aperiodic components. Nature Neuroscience, 23(12), 1655-1665. https://doi.org/10.1038/s41593-020-00744-x\n",
    "- https://github.com/fooof-tools/fooof"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "28-Dec-24 14:10:28 | WARNING | The evaluated frequency range ends after the resampled Nyquist frequency (52.63Hz). Decrease the upper band (30.00Hz) or decrease the maximum value of the hset (1.90).\n"
     ]
    }
   ],
   "source": [
    "# Apply the IRASA technique\n",
    "freqs, psd_aperiodic, psd_osc = yasa.irasa(data, sf, ch_names=chan, band=(1, 30), win_sec=4, return_fit=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAHUCAYAAADm/FbiAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAdclJREFUeJzt3XV0FNf/xvH3RkjwAMVKcUhwJ7i7FWsJ7q6lpUhbilVoSynu3uIUd9IUd0pxGrQ4BCdu+/sjv8yXNAGSsMkm4Xmd03OyM3dnPrvZhmfv3LnXZDabzYiIiIiIxdhYuwARERGRpEYBS0RERMTCFLBERERELEwBS0RERMTCFLBERERELEwBS0RERMTCFLBERERELEwBS0RERMTCFLBERERELEwBSxK17t274+LiQo8ePaxdimHt2rW4uLiwaNEiix7X3d0dFxcXpk6damwbPnw4Li4uXLhwwaLnkvgVEBDAggUL4vw879Ln5f79+0ydOpVmzZpRtmxZihUrRqNGjZgwYQJPnjyJ1N7FxSVa/x05ciRGdTx48IBChQrh4uLC1q1bX9vWy8uLr7/+mmrVqlGkSBEqVarEkCFDuHnzZozOKQmDnbULEIktLy8vDh48SPLkydm/fz/37t0jS5Ys1i6LggUL0r9/f0qUKBHn56pduzbZsmXjvffei/NzSdxp3749165do2vXrtYuJUnYtWsXw4cPx9vbG1dXV5o2bQrAX3/9xdy5c1m/fj1Lly4lZ86cxnP69+//yuPdu3ePNWvWYGNjQ4YMGWJUy8aNGwkJCSF58uSsWbOGhg0bRtnOy8uLjz/+mLt371KpUiUaNmzItWvX2Lx5M/v27WPlypXkypUrRucW61LAkkRr06ZNhISE0L17d6ZOncqaNWte+0cyvhQsWJCCBQvGy7lq165N7dq14+VcEncePXpk7RKSjGPHjjFw4ECcnJxYuXJlpC86v/32G+PGjaNLly5s27YNBwcHAAYMGBDl8QIDA2ndujUAvXv3Jl++fDGqZ8OGDeTNmxdnZ2d27NjB7du3yZYtW6R2U6dO5e7duwwfPpwuXbpEeP7QoUMZP348s2bNitG5xbp0iVASrfXr15M2bVq6d+9O6tSpWbt2LVq7XOTdFRoayvDhwwkNDWXatGlR9iK3b9+exo0bc/v2bdauXfvGY3777becO3eOMmXKxPgL3Pnz5/H09KRixYrUrVuX0NBQ1qxZE2Vbd3d30qdPT6dOnSJsb9q0KTly5GD//v2EhobG6PxiXQpYkihdvHiRf/75hwoVKuDo6Ejt2rW5ffs2Bw4ciNDuyJEjuLi4sHr1apYuXUrt2rUpXrw4H3744Sv/uB46dIguXbpQunRpSpQogZubG9u3b4/Q5tatW7i4uDB58mS++eYbSpQoQbly5di2bdsrx2CdPn2avn37Uq5cOYoWLUrDhg2ZNWsWgYGBkWo4fvw4nTp1onTp0lSsWJHx48fj7+8fqd2rxtS4u7vToUMHypQpQ7ly5ejcuTPHjh2LzlvL48eP+e6776hZsybFihWjXr16/PLLL/j4+ERo9+DBgwjjRapVq8bXX3/NgwcPIrSbOnUqLi4uXL9+nR9//JHKlStTvHhxWrduzZkzZwgNDWXu3LnUrFmTEiVK8NFHH0Ua59KhQweqVq3K7du36d27NyVLlqRixYp8/vnn3LlzJ9JriGltV65cYeLEiVSvXp0iRYrQqFEjli9fHum4ZrOZ5cuX07x5c4oVK0bZsmXp3bs358+fj9Au/HO3du1a1qxZQ5MmTShatChVq1blhx9+wM/PD/jf5+j27du8ePECFxcXhg8fHq3f039F9/cG8Pz5c8aNG0flypUpVqwYzZs3Z9u2bVEe84cffqBBgwYUL16c4sWL06hRI2bNmkVwcHCMX+/r1KxZ843jn9703hw+fJhbt25Rrlw5Spcu/cp2vXv35osvvqBcuXKvPd727dtZsWIFTk5O/Pzzz9ja2r7xdbxs/fr1AFSpUoXq1auTPHly1q5dGykohYSE0KtXL/r374+NTeR/lpMlS0ZQUFCE91wSPl0ilEQp/A9X+HiGhg0bsm7dOlavXk3lypUjtV++fDkXL16kQYMGpE2bFnd3d0aMGMHt27cjXBpYvXo1I0eOJH369DRs2JAUKVLwxx9/MGjQIAYPHkzv3r0jHHfVqlUAtGnThqtXr1KiRAkOHToU6fzu7u4MGjQIGxsbateuzXvvvcfhw4f55Zdf2LdvHwsXLiRZsmQA7N27l759+5IsWTLq1auHra0t69atY/PmzdF6b2bPns3EiRPJkCED9erVw8HBgc2bN9O5c2fmzJlDpUqVXvlcLy8v3NzcuH37NuXKlaNevXqcP3+eWbNmcerUKebNm4ednR03btygTZs2PHz4kIoVK9KgQQP++ecfVq5ciYeHB8uXLyd79uwRjv3JJ5/w7NkzGjVqxN27d9mxYwfdu3enZs2a7N69m3r16hEQEMDGjRvp3bs327dvJ3PmzMbz/f396dixI3Z2drRu3ZorV66wceNGjhw5wurVq422saktPKjVrVsXOzs7Nm7cyOjRo7G1taVVq1ZGu2HDhrFhwwby589P69at8fPzY9u2bbRu3ZrZs2dToUKFCMf97bff8PT0pG7dulSpUoVdu3axYMECHjx4wM8//0yaNGno378/ixcvJiAggJ49e8bq8nJ0f2/hBg8ejIODAw0bNsTHx4dNmzbxySefkCxZMmrVqgXAixcvaNWqFXfv3qVmzZrUrl2bx48fs2vXLn755ReePXvGsGHDYvR6X6djx468ePHitW3e9N7s3bsXIMq/AS/Lnz8/+fPnf22bW7duMXLkSAC+//77GI/vDA4OZsuWLTg5OVGxYkXs7e2pUaMGW7duZd++fVSrVs1oa2trG6nnKtyVK1e4evUqOXLkMP5GSCJhFklkgoODzZUqVTKXLFnS7O/vbzabzeagoCBzhQoVzIULFzY/evTIaHv48GGzs7Oz2dnZ2bxt2zZj+8OHD821atUyFypUyHzt2jWz2Ww2371711ykSBFzgwYNzI8fPzba+vn5md3c3MwFChQw//PPP2az2Wy+efOm2dnZ2ezi4mK+cOFChPp+//13s7Ozs3nhwoVms9lsfvHihbls2bLmUqVKmc+ePWu0CwoKMn/22WdmZ2dn87Rp04zXVrNmTXOJEiWMc5nNZvO///5rrlixotnZ2dk8ZcoUY/uwYcPMzs7O5vPnz5vNZrP56tWr5kKFCpnr169vfvDggdHu+vXr5hIlSpgbN2782vf2888/j1B7uJEjR5qdnZ3NO3bsMJvNZnPHjh3Nzs7O5lWrVkVot3TpUrOzs7O5Y8eOxrYpU6aYnZ2dzTVq1DA/e/bM2P7pp5+anZ2dzaVKlTLfu3fP2D516lSzs7OzeenSpca29u3bm52dnc0tW7Y0+/n5Gdvnz59vdnZ2Ng8bNszYFtvaXv7cnDhxwuzs7Gz++OOPjW1bt241Ozs7mz/99FNzUFCQsf3GjRtmV1dXc5UqVcwBAQFms/l/n7uCBQua//rrL6Pt8+fPzeXLlzcXKlTI7O3tbWyvUaOGuXTp0ubYiu7vLfzz0rx58wjn37Vrl9nZ2dncu3dvY9vs2bOjfB/v3LljLlKkiLlSpUrGtpi+3rgyaNAgs7Ozs3nnzp1vdZygoCBzq1atzM7OzuZvv/02Vsf4888/zc7OzuavvvrK2Obu7m52dnY29+vXL1rHCAkJMXfq1Mns7OxsnjNnTqzqEOvRJUJJdA4cOICXlxd16tQxBqja2dlRv359goKC2LBhQ6TnlCpVivr16xuPM2TIQK9evQgODjYujWzcuJHAwEAGDhxIunTpjLaOjo4MHDiQ0NBQ1q1bF+G4OXPmpECBAq+t193dnWfPntGxY0cKFy5sbLezs+OLL77A0dGR33//HYBTp05x69YtmjdvjrOzs9E2R44cr/yG+7Lt27cTHBxM3759yZgxY4Q6hw0bRsuWLQkKCoryuYGBgezatYtcuXLRuXPnCPt69epF7969yZgxI3fv3uXw4cOUKVOGjz/+OEK7tm3bUrRoUeNSzctatGhBmjRpjMelSpUCoFGjRhF6qooVKwbA7du3I9X46aef4ujoaDzu1KkT2bJlY8eOHQQGBsa6tpYtW5I+ffoItaVJkyZCDeFjZ7788ssIvUHZs2endevW3L9/n4MHD0Y4btmyZSlZsqTxOHXq1JQsWZLg4GDu3bsX6fXFRnR/by/r2LEjKVOmNB5Xq1YNGxubCO9L5cqVGTNmDM2aNYvw3KxZs5I9e3YeP34cqZb4eL2vE94D9vJri41Jkybx999/U7hwYYYMGRKrY4T/HWrUqJGxrUqVKjg5ObF7924ePnz42uebzWa+/vprDh06RJEiRaL1/78kLLpEKIlOVH+4AJo0acLSpUtZs2ZNhLtwAFxdXSMdJ/wf8osXLwJw9uxZIGwM1qVLlyK09fX1jdA23AcffPDGesOfU7Zs2Uj70qdPT+7cublw4QIvXrww2hYpUiRS2/BAEp1zRTW4N/xOqFe5ceMGvr6+UT43W7ZsDB48GAAPDw8AypQpE+VxSpUqxZkzZ7h48WKE9ydHjhwR2iVPnhyI/B6Gh+b/jk0zmUyRzmlra0vhwoXZuXMnN27c4MaNG7GqLXfu3JHapkqVCm9vb+PxuXPncHBwYOnSpZHaXrt2DYALFy5QvXp1Y3tUt9WnTp0a4JVBN6ai+3t72X/rsre3J2XKlBHGaxUqVIhChQrh4+PDqVOn+Pfff7l+/Tpnzpzh33//JSQk5I3Hhei/3kWLFkXrEuHr7pp1cnIC4NmzZ689zuscOHCAefPmkTJlSiZNmhSry3Le3t788ccfZMyYMcLfnvDL/itXrmTdunWvnL8vODiYkSNHsnbtWrJnz86MGTN0eTARUsCSRMXb2xt3d3eAV/5xunz5Mn/99VeEQJIpU6ZI7cK/1Yf/Ixr+x33FihWvPP9//3CHh4E31Qxh/2BHJVOmTFy4cAE/Pz+eP38ORP0NPG3atG88V/jzX3Wu1wl/bW96bvjrCf+H87/C3+v/DspPkSJFlO2j+w9HunTpomwbPgfYixcvYl1bVMc1mUwR7kp98eIFwcHBTJs27ZU1/vfz8arjAha74zW6v7eXRedzGxAQwMSJE1m5cqUxSD1z5syULVuWdOnS4eXlFek5b/N6lyxZEmWv5cuaN2/+2oAVHprDg/brXLlyhbx580bY9vDhQ4YOHYrZbGbs2LGRvhSEu3DhgvF36GXh4zm3bdtGQEAAXl5erxw3tmbNmij/hvn5+TFo0CD27NlDrly5WLhwYYQeXkk8FLAkUdm+fTv+/v4ULVqUQoUKRdp/7do1jh49yurVqyMErICAgEhtw8NI+Lfe8ADg7u4eaRD02wgPS/+9gy2qOsIvoUX1TT68F+11wl+Dj49PhMucEBYqkiVLFuVdSi/XGdVdZ+HnT5EihdHu/v37Ubb77/tqKVH9Dl8+X7p06YzLVnFRW/hr3717d4yfG5ei+3uLqfHjx7Ns2TLq1atHu3btcHFxMd63Bg0aRBmw3kZ4z+jbqFKlCrNmzWL//v306tXrle1Onz7Nxx9/TOnSpVm2bBkQFgCHDRvGw4cP+eijj2jcuPErn3/hwoUog3Z4wAq/CefDDz80empf5uHhwfXr1zl27FiEnu1nz57Ro0cPTp06RaFChZg3b16MJzaVhEMBSxKV8MuDw4cPj/Iy0J07d6hVqxbbt2/nyy+/NLafOXMmUtu///4bgOLFiwNhS2W4u7tz5syZSAHr+vXrrFy5krJly1KzZs0Y1Rz+DfbEiRORvn17e3tz4cIFcubMSbJkyYxLg3/99RcfffRRhLbhlzBfx9nZGXd3d06fPh3p0ts333zDhg0b2Lp1a5QBMnfu3Njb23P69OlI++7fv0/VqlVp1aoVffr0MWqMyrFjxzCZTDGekPFNfHx8oux1OHXqFOnSpSN79uxGD0pc1Obi4sLx48fx8vKKNKZp9+7dnDx5kgYNGrxxTJ6lRff3Nm7cuBgdd/PmzWTIkIHJkycbvVAQFtTDp8Ywm80R9llbyZIlyZUrF0ePHuXEiROvnKph8eLFAFSsWNHYNnfuXPbv30++fPn46quvXnueFi1a0KJFiyj33bx5kxMnTpAjRw5++umnKNtkyZKFyZMns3r1aiNgBQQE0KtXL06dOoWrqyszZ86MVU+0JBwa5C6Jxu3btzl27BjZsmV75R/O999/n/Lly+Pr68uWLVuM7bt27eL48ePGYy8vL2bOnEmKFClo0KABEPZt09bWlkmTJkX4dh4cHMy4ceNYsGABT58+jXHdtWvXJnXq1Cxbtoxz585FOO63336Lv7+/sZRH0aJFyZcvH5s2bYoQEh48eBCtteoaN26MjY0Ns2bNirDe2o0bN9i2bRvZs2d/Ze+cg4MD9erV48qVK8b0E+HCZ5CuUKEC77//PuXKlePs2bPGt/9wq1ev5q+//qJcuXJxsmzRhAkTIozNWrBgATdv3qR58+bY2trGaW3NmzfHbDYzbty4CDU8ePCAUaNGMWfOnFgPrra3t4/1HEfR/b3F5rgBAQFGrx+EzdcU/pkFy40jsxRbW1vji9XAgQONL1HhQkJCmDlzJps3byZr1qzGwPFTp04xefJkUqRIwaRJk6LsdYquDRs2YDabadKkySvbNG/eHBsbG3bs2GH0Vk+cOJGTJ09SsmRJ5s6dq3CVBKgHSxKNl/9wve5bc4sWLTh48CCrV6/m888/B8LuBOzcuTP169cnVapUuLu78/DhQ8aNG2f0RuTKlYvPP/+c8ePH07hxY2rWrEnatGnZu3cvV65coUaNGnz44YcxrjtVqlR89913DB48mNatW1OnTh0yZMjA4cOH8fT0pEyZMsZYDJPJxHfffUfnzp3p1KkT9erVI1WqVOzatStal3ny5s1L//79mTJlCk2bNqVGjRqYzWa2bt1KQEAA48ePf+3zhw4dyokTJxg5ciQ7d+4kf/78nDlzhmPHjlG7dm1j3rGxY8fSrl07xowZw65du3BxccHT05MDBw6QKVOmGPeWRNexY8do2bIlFSpU4MqVK+zfv5/8+fPTr18/o01c1daiRQs8PDzYsWMH//zzD1WqVDHuQn369CmfffZZrC8tZ8qUievXrzNkyBAqV65Ms2bNuHXrFuvWrSNbtmyv7C0JF93fW0w0adKEBQsW0LJlS2rXrk1wcDD79+/n2rVrpE+fnsePH/P06dMoxzdaU9WqVRk3bhyjR4/Gzc0NV1dXChcujK+vL8eOHePq1atkzJiRWbNmGWP1Ro0aRXBwMEWLFmX79u2RJhZ+maur62snKN24cSPAa/9WZM2alQoVKnDgwAE2btxI3bp1jZsn8uTJw9y5c6N8Xs+ePaM1fk4SBgUsSTTCLw++KeTUqVOH1KlTc+bMGTw9PQFo1qwZmTNnZunSpTx9+pSCBQvy7bffRpjsD6BLly7kyZOHBQsWsHPnTkJDQ8mePTvDhw+nXbt2EW7Pj4m6deuybNkyZs6cyb59+wgMDCRHjhwMHTqUjh07Ym9vb7QtXrw4y5cvZ9KkSezevRuTyUTdunVp1qwZ7du3f+O5+vXrR+7cuVm8eDEbNmzAZDJRsmRJBg4caNw5+SqZM2dm9erVTJ06lT///JNDhw6ROXNm+vTpQ9++fY12uXLl4vfff2f69Ons3r2bY8eOkSlTJjp06ECfPn3ibNzIvHnzmDp1KitXriRt2rR07NiRAQMGRPi2H1e1mUwmpkyZwtKlS1m7di2rV6/G0dGRfPny0aVLl7daE/Lzzz/niy++YPv27Tx69IhmzZpx+/Ztpk2bhqur6xsDVnR/bzExePBgUqZMycaNG1m2bBnp06cnb968fPXVV1y5coXvvvuOPXv2RJoOIyFo1aoVJUuW5LfffuPEiROsXr2aoKAgcuTIQe/evenatWuEm0bCe+lOnjzJyZMnX3vs/v37vzJgnTx5kn///ZdixYq9cWHmFi1acODAAdasWUPmzJmN3sDwKVui0qlTJwWsRMRkttStLCIJ0JEjR+jYsSMdO3aMMCZLEpcOHTpw9OhRjh07FmEuraTO3d2d5cuXM3/+fGuXIiIxpDFYIiIJUPilXRcXF2uXIiKxoIAlIpIAhU8gGn7XpogkLhqDJSKSAOXMmdO4C1BEEh+NwRIRERGxMF0iFBEREbEwBSwRERERC1PAsqD27dtHa54iERERSdo0yN2C7t69a+0SREREJAFQD5aIiIiIhSlgiYiIiFiYApaIiIiIhSlgiYiIiFiYApaIiIiIhSlgiYiIiFiYApaIiIiIhSlgiYiIiFiYApaIiIiIhSlgiYiIiFiYApaIiIiIhSlgiYiIiFiYApaIiIiIhSlgiYiIiFiYApaFPXz4kKCgIGuXISIiIlakgGVhvr6+bNu2zdpliIiIiBUpYMWBEydOWLsEERERsSIFrDhw8uRJa5cgIiIiVqSAFQfOnj1LQECAtcsQERERK1HAigMBAQGcP3/e2mWIiIiIlShgxRFdJhQREXl3KWDFkb/++svaJYiIiIiVKGBZmMlkAhSwRERE3mUKWBaWLFkyAP79918ePXpk5WpERETEGhSwLMzBwcH4Wb1YIiIi7yYFLAsL78ECBSwREZF3lQKWhakHS0RERBSwLMzW1pYsWbIA8PfffxMSEmLlikRERCS+KWDFgVKlSgHg7e3N5cuXrVyNiIiIxDcFrDhQunRp42ddJhQREXn3KGDFgZIlSxo/K2CJiIi8exSw4kCxYsWwtbUFtGSOiIjIu0gBKw4kT56cQoUKAXDx4kW8vb2tXJGIiIjEJwWsOBI+0N1sNvP3339btxgRERGJVwpYcUTjsERERN5dClhxpGzZssbPBw4csGIlIiIiEt8UsOJIzpw5yZEjBwBHjx7Fz8/PyhWJiIhIfFHAiiMmk4mqVasCEBgYyOHDh61ckYiIiMQXBaw4VK1aNePn3bt3W68QERERiVcKWHGoUqVK2NiEvcV79+61cjUiIiISXxSw4lDatGmNuwk9PT25c+eOlSsSERGR+KCAFcdevky4b98+K1YiIiIi8UUBK46FD3QH2LNnjxUrERERkfiigBXHSpYsSerUqYGwcVghISFWrkhERETimgJWHLOzs6Ny5coAPHnyhLNnz1q5IhEREYlrCljx4OVxWLpMKCIikvQpYMWDlwOWpmsQERFJ+hSw4kGOHDnIlSsXAMeOHcPb29u6BYmIiEicUsCKJ+G9WMHBwRw8eNDK1YiIiEhcUsB6yc6dO3Fzc4uTY+syoYiIyLtDAQswm80sX76czz77DLPZHCfnqFixIra2tgD8+eefcXYeERERsT4FLGDcuHFs2bKFrl27xtk5UqdOjaurKwDXr1/H09Mzzs4lIiIi1qWABfTq1YvffvuNnDlzxul56tevb/y8Y8eOOD2XiIiIWI8CFpA5c+Z4OU+9evWMnxWwREREki4FrHiUPXt2ChUqBMDff//N3bt3rVyRiIiIxAUFrHj28mXCnTt3WrESERERiSsKWPHs5cuEClgiIiJJU5IIWHPmzKFSpUpR7rtz5w6DBw+mfPnylC5dmn79+nHz5s14rvB/ChcuTLZs2QA4cOAAz58/t1otIiIiEjcSfcDas2cPU6ZMiXLf06dP6dixI4cOHaJTp0707duXv//+m3bt2vH48eNI7Vu0aMGqVavitF6TyWT0YgUFBfHnn3/G6flEREQk/iXagGU2m/ntt9/o168fQUFBUbZZtGgRt27dYt68efTp04du3bqxcOFCHj58yNy5c+O54v/R3YQiIiJJW6INWG5ubowbN45y5cpRuHDhKNts3ryZEiVKUKRIEWObs7Mz5cuXZ/PmzfFVaiTlypXDyckJAA8PDwIDA61Wi4iIiFheog1Yd+7cYezYscybN4+UKVNG2v/s2TNu3rwZIVyFK1y4MA8ePODBgwfxUWok9vb21KxZE4AXL15w6NAhq9QhIiIicSPRBiwPDw/c3NwwmUxR7r9//z4Q9SSimTJlArDqPFQvT9ewfft2q9UhIiIilpdoA1ayZMleu9/HxweA5MmTR9rn6OgIgK+vr+ULi6bq1avj4OAAhE3XEBoaarVaRERExLISbcB6E7PZDPDKHq437YtrKVOmpHLlygDcu3eP06dPW60WERERsawkG7BSpEgBgJ+fX6R9/v7+AKRKlSpea/ovTToqIiKSNCXZgBU+maeXl1ekfeGD2+NrkedXqV27tvGzApaIiEjSkWQDVurUqcmRIwfnzp2LtO/cuXNkyZKFjBkzWqGy/8mcOTMlS5YE4MKFC9y4ccOq9YiIiIhlJNmABWF36p04cSJCyPL09OTw4cM0btzYipX9jy4TioiIJD1JOmB169aN9957j27dujF37lzmz59P165dyZw5M926dbN2eQDUrVvX+FkBS0REJGlI0gHLycmJZcuWUapUKWbMmMGcOXMoWbIkS5YsIX369NYuDwibWT5XrlwAHD58mKdPn1q1HhEREXl7dtYuwBJ+/fXXV+7Lnj07M2bMiMdqYsZkMlGnTh3mzp1LSEgIHh4etGjRwtpliYiIyFtI0j1YiYXGYYmIiCQtClgJQNmyZY3Fn//8808CAgKsW5CIiIi8FQWsBMDOzo5atWoB4O3tzeHDh61ckYiIiLwNBawE4uXLhDt27LBiJSIiIvK2FLASiGrVqhkLWO/cudNYS1FEREQSHwWsBCJVqlTG4s93797lzJkzVq5IREREYksBKwGpU6eO8fP27dutWImIiIi8DQWsBKR+/fqYTCYAtmzZYuVqREREJLYUsBKQTJky4erqCsDly5fx9PS0ckUiIiISGwpYCUzDhg2Nn9WLJSIikjgpYCUwDRo0MH5WwBIREUmcFLASmGzZslGyZEkALly4wNWrV61ckYiIiMSUAlYC1KhRI+PnrVu3WrESERERiQ0FrATo5XFYClgiIiKJjwJWApQzZ06KFCkCwKlTp7h165aVKxIREZGYUMBKoHQ3oYiISOKlgJVAaRyWiIhI4qWAlUDly5cPFxcXAI4fP87du3etXJGIiIhElwJWAvbyZUKtTSgiIpJ4KGAlYC9fJtQ4LBERkcRDASsBK1CgALly5QLgyJEjPH782LoFiYiISLQoYCVgJpPJuEwYGhrKzp07rVyRiIiIRIcCVgL38tqEuptQREQkcVDASuBKlChBlixZANi3bx8vXrywckUiIiLyJgpYCZyNjY3RixUYGIiHh4eVKxIREZE3UcBKBF6+TLht2zYrViIiIiLRoYCVCJQrV4506dIB8Mcff+Dv72/likREROR1FLASATs7O+rVqweAr68ve/futXJFIiIi8joKWImELhOKiIgkHgpYiUTlypVJlSoVADt37iQ4ONjKFYmIiMirKGAlEo6OjtSsWROAp0+fcvjwYStXJCIiIq+igJWI6DKhiIhI4qCAlYjUrFkTBwcHADZv3oyvr6+VKxIREZGoKGAlIqlSpaJu3boAPHz4kNmzZ1u5IhEREYmKAlYiM2TIEGxtbQGYOXMmXl5eVq5IRERE/ksBK5HJly8f7dq1A8DHx4dffvnFyhWJiIjIfylgJUKffvopKVOmBOC3337j8uXLVq5IREREXmZniYP4+/uzf/9+jhw5wrlz53j8+DHPnz/H0dGRLFmyUKBAASpVqkSVKlVIliyZJU75TsuYMSN9+vRhwoQJhISEMH78eObNm2ftskREROT/mcxmszm2T3706BFLlixhxYoVPH/+HLPZjI2NDalSpSJ58uQ8f/4cPz+/sBOZTKRJk4b27dvTsWNH0qZNa7EXkVDUqlULCFsvMK75+vpSuXJl7t+/D8D69espW7ZsnJ9XRERE3izWAeu3335j4sSJmM1mqlevTuXKlSlSpAh58uTB3t7eaBcYGIinpyd//fUX+/fv58CBAzg4ODBgwAA6d+6MyWSy2IuxtvgMWADLli3j888/B6B06dJs2LAhSb2fIiIiiVWsAlbr1q25efMmPXv2pGXLlsYSLtHx4MEDfv/9dxYtWkTu3LlZsWJFTE+fYMV3wAoODqZOnTp4enoCMG3aNJo3bx4v5xYREZFXi9Ug9woVKrBz5046deoUo3AFkClTJvr06cOuXbtwdXWNzenl/9nZ2TFy5Ejj8bhx43jx4oUVKxIRERGIZcAaNGiQcRdbbKVJk4ZPP/30rY4hYbO7h08+ev/+fU3bICIikgBYZJqGY8eOvXHCy6NHjzJt2jRLnE7+Y8yYMTg6OgIwf/5845KhiIiIWIdFAlaHDh1o2rQphw8ffmWbo0ePMn36dEucTv4jR44c9OvXDwgbl/Xll1/yFjeHioiIyFuy2ESjjx8/pnv37ixcuNBSh5QY6NOnDzly5ADg4MGDbNy40coViYiIvLssFrA++ugjnJ2d+fHHH/nss8/w9/e31KElGpInT86YMWOMx2PHjsXHx8eKFYmIiLy7LBawsmTJwvLly2nYsCFbtmyhdevW3L5921KHl2ioW7euMVXEvXv3mDp1qpUrihu+vr6EhIRYuwwREZFXsuhahA4ODvz88898+umneHp60rJlSw4ePBh2Ihstexgfxo4dayxHNHfu3CQXcletWoWzszNubm4EBQVZuxwREZEoxUnq6dmzJzNnziQoKIgePXqwcOFCUqRIERenkv/IlSsXXbp0AcLWiBw/fryVK7IcHx8fxo4di9ls5tChQ6xbt87aJYmIiEQpzrqVqlWrxqpVq/jggw/48ccf+fXXX+PqVPIfAwcOxMnJCYC1a9dy6tQp6xZkIb/++itPnjwxHk+ZMoXg4GArViQiIhK1OL1ulzdvXtasWUPFihWT3KWqhMzJyYnBgwcbj8eNG5fop23w9/dn9uzZEbZdu3aNDRs2WKkiERGRV7NIwFqyZMkr18BLnTo1c+fOZdCgQTRr1swSp5No6NixI7ly5QLg0KFD7Ny507oFvaWVK1fy4MEDAPLnz29snzx5sga8i4hIghOrxZ4lavG92PObbN26lR49egCQJ08ePDw8sLe3t3JVMRcUFETlypW5desWADt27GDUqFHGxLYzZsygadOm1ixRREQkAt3al4Q1aNCAcuXKAXD16tVEOw5u7dq1RriqWbMmRYoUiXAJdNKkSYSGhlqrPBERkUhi1YMV3lMT45OZTLi7u8fquYlBQuvBAjh58iSNGzcGIGvWrBw+fBg7OzsrVxV9ISEhVKtWjWvXrgGwfv16ypYti9lspnnz5hw7dgyAWbNm0aRJE2uWKiIiYojVv7QasJ54lCxZkjp16rBr1y7u3r3L9u3bjcCVGGzevNkIVxUrVqRs2bJAWFgfPHgwbdu2BcLGYjVq1EjzrYmISIIQq4B18eLFKLdPnTqVGTNmcOHChbcqSiyra9eu7Nq1C4AFCxYkmoDl5eXFjz/+aDweOHBghP1Vq1alZMmSnDx5kgsXLrBhw4ZX3mwhIiISnyz6dd9kMlnycGIhVapUMe68O3LkCGfPnrVyRW/m5eVFq1atuH79OgBlypShcuXKEdqYTCaGDBliPB47dizPnz+PzzJFRESipOsp7wCTyWTM7g6wcOFCK1bzZg8fPsTNzQ1PT08AsmXLxtSpU6MM8NWrV6devXoAPHjwgAkTJsRrrSIiIlFRwHpHfPTRR6RJkwaAdevW8fjx41e2DQoK4quvvuKjjz565eXguPLo0SPc3Nz4559/AHj//fdZvXo1OXLkeOVzxo4di6OjIxAWHhNDD52IiCRtCljviJQpU+Lm5gZAQEAAS5cujbJdaGgogwcPZuHChRw6dIiuXbvG22W3w4cP06JFCyPUZc2alTVr1pAzZ87XPu+DDz4wpm0IDQ1l+PDhmrZBRESsSgHrHdK5c2fjMtvixYsjreNnNpsZOXJkhEWU//33X4YNGxanS+3cvHmTXr160bJlSy5fvgxEP1yF69mzJ/ny5QPCpqZYtmxZnNUrIiLyJgpY75BcuXJRu3ZtAGPKhpdNmDCBRYsWAWBra0vKlCkB2LhxI8uXL7d4Pffu3eOHH36gevXqbN682dhepEgR1qxZYyz1Ex3JkiXju+++Mx5///33PHr0yJLlioiIRFusJhqdNm1alNuPHDnC8ePH6d+/f5Q9HiaTiX79+sW8ykQiIU40+l979+6lTZs2AGTOnJkKFSqQN29evL29IyymPHnyZJInT07Pnj0BcHR0ZOvWrbi4uPD8+XNWr17N1q1bKVq0KF9++WWUS/AcPnyYffv2kT17dvLmzUu+fPlImTIl7u7urFixgj///DPCpbwMGTIwfPhw3NzcsLW1jdXrGzBgAGvXrgWgRIkSLFq0iIwZM8bqWCIiIrEVq4BVoEABTCZTjC8bmUymJD1HVmIIWGazmRo1anDp0qVXthk3bhxdu3YFYMSIESxZsgQAZ2dnXF1dWbt2Lb6+vkb7Bg0aMGPGDJIlS2ZsW7FiBZ9//nmksVDJkiUjMDAwwjZ7e3u6devGoEGDjIH4sfXgwQNq1KjB06dPAciePTu//vprhAWi/8tsNrNt2zbu379P5cqVyZcvn6YcERGRtxKrgPXyGJ2YSsoTQSaGgAVw6NAhRowYwZUrVyIFoCFDhkRY58/Pz48mTZq8MRjXqVOH2bNnkyxZMmbMmBHhct2rvP/++7Rq1YrWrVuTPXv22L2YKFy4cIEOHTpw9+5dANKmTcu8efOoWLFipLZBQUF8+eWXEQb958iRg1q1alG9enVy5sxJpkyZSJMmjUKXiIhEW6wC1tKlS6lSpcprb51/FyWWgBXO39+ff//9l6tXr3Lt2jWyZ89O48aNIwWJy5cvU79+ffz8/ICwOxI/+ugjihcvzhdffIG/vz8QthBz3rx5mTt3rvHcDh06kD9/fi5fvszly5e5e/cuxYoVo3Xr1lSqVCnWlwLf5N69e3Ts2JFz584BYb1kn3/+OR06dDB6yZ4/f06vXr3Yu3fvG4/n6OhIlixZ6NmzJ506dYqTmkVEJOmIVcAqWbIk/v7+ZMuWjcqVK1OlShXKlStHqlSp4qLGRCOxBayYOHz4ML/99htlypShZcuWpE6dGoD9+/fTuXNnI3y9bPjw4fTv399qPT/e3t706dMHDw8PY1uqVKlo27YtDRs2ZPjw4caUEMmSJaNLly6cPXuWI0eORLrDMpydnR3nzp175z/rIiLyerEKWEFBQRw/fpwDBw6wf/9+/vnnH2xtbSlevDiVK1emUqVKFCtWLC7qTdCScsB6ncOHD9OhQwdjXJaNjQ0//PCDsRCzNQUHBzN69OjXzl7v5OTEwoULcXV1BeDFixfs3buXkydPcv/+fR48eMA///yDl5cXAGvXrqVcuXLxUr+IiCROsQpY//Xw4UP279/P/v37OXjwII8fP8bJyYmKFSsagStz5syWqDdBe1cDFsCxY8fo2bMnAQEBTJgwgYYNG1q7pAguXbrE3Llz+f33341LmhA2dcWvv/5Knjx5Xvv8ZcuW8fnnnwMwatQo4+5KERGRqFgkYP3X2bNn2b9/PwcOHODkyZOEhISQL18+KleuzLBhwyx9ugTjXQ5YAIGBgYSGhhrL1iREjx49YsmSJaxdu5b8+fMzYcIE0qdP/8bnnT171ljzsHnz5q+cqkRERATiKGC9zMfHh0OHDhmBa9euXXF5Oqt61wNWUhYUFISLiwsBAQHkyZOHffv2WbskERFJwOzi+gQpU6akdu3axgziIomRvb09hQoV4uTJk1y9epXnz5+/9ZxdIiKSdGmpHJFoKl68uPHzmTNnrFiJiIgkdDEOWM+fP2f37t389ddfkWZy9/X11dgUSbJevjP29OnTVqxEREQSuhgFrEuXLtGwYUP69u1L27ZtadmyJbdv3zb2+/r6Mn36dIsXKZIQvNyDderUKStWIiIiCV2MAtbPP/9MiRIlOH78OHv37iV79uy0adOG69evx1F5IglHvnz5SJ48OaAeLBEReb0YBaxTp04xaNAgUqRIQaZMmZg8eTINGjSgQ4cOXLt2La5qFEkQ7OzsKFKkCAD//vsvT548sXJFIiKSUMUoYAUGBkZa9mTEiBFGyLpy5YpFixNJaF4eh6WB7iIi8ioxCli5c+fm7NmzkbZ/8cUX1K9fn759+1qsMJGE6OWApXFYIiLyKjEKWHXq1GHz5s1R7vvqq6/48MMPI91ZKJKUvDzQXeOwRETkVeJ8Jvd3iWZyT/pCQkIoWLAgPj4+ZMuWjaNHj1q7JBERSYBiPdHoTz/9hJ+fnyVrEUnwbG1tKVq0KAC3b9/m4cOHVq5IREQSolgHrPnz59OwYUO2b99uyXpEEjxNOCoiIm8S64Dl5ubG/fv3GTx4MN26ddNcWPLO0ISjIiLyJrEOWGPGjGHNmjWUKFGCAwcO0KRJEyZOnIi/v78l6xNJcNSDJSIib/JWiz0XKlSI5cuX88MPP+Dk5MScOXNo2LAhO3futFR9IglOrly5SJMmDaCAJSIiUXurgBWuadOm7Nixg27duuHl5cWgQYPo3r07//77ryUOL5Kg2NjYGAPd7927x/37961ckYiIJDQWCVgAKVKk4PPPP2fjxo1UrlyZ/fv306RJE3755RcCAgIsdRqRBOHlcVi7du2yYiUiIpIQWSxghcudOzdz585lxowZZM6cmdmzZ9OgQQPc3d0tfSoRq2nYsKHx8/Tp0wkKCrJiNSIiktBYPGCFq1mzJlu2bGHQoEE8efKEAQMG0LNnz7g6nUi8KlmyJFWrVgXgxo0brFu3zsoViYhIQhJnASs0NJRbt26RO3du6tevj9lsZt++fXF1OpF498knnxg/T506lZCQEOsVIyIiCYqdJQ5y//59PD098fT05NKlS3h6enLlyhUCAwMBjPUJHR0dLXE6kQShXLlyVKhQgUOHDnH16lU2bdpEs2bNrF2WiIgkALEOWGPHjjXC1PPnzwEiLPScNWtWXFxcKFCggPFfzpw5375ikQTkk08+4dChQwBMmTKFDz/8EBsbG8xmM+vXr8fd3Z0uXbpQpkwZK1cqIiLxKdYBa9myZQA4ODhQqFChCEHKxcXFmCdIJCmrVKkSZcqU4fjx4/zzzz9s27aNQoUKMXz4cPbv3w/AwYMHOXDgAClSpLBytSIiEl9M5pe7nWJgy5YtFChQgNy5c2NjE2dDuRKVWrVqAfDHH39YuRKJT3/++Sft27cHIEuWLDx9+jTSigYjRoygf//+1ihPRESsINYBSyJTwHo3mc1mGjVqFGldwvfff5979+4RGhpK2rRpOXjwIE5OTtYpUkRE4pVFup4GDBjAzJkz2bNnD15eXpY4pEiiYTKZItxRaGNjQ8+ePdm9ezcff/wxAM+ePWPGjBlWqlBEROKbRXqwChQoEHYwkwmADBkyUKhQIQoWLEjhwoUpWLAg2bNnf9vTJHjqwXp3mc1mJk+ezMWLF+nbt6+xIPTt27epXLkygYGBODo6sn//frJmzWrlakVEJK5ZJGDdvXuXM2fOcPbsWc6ePcu5c+d49uxZ2An+P3SlTp2aggULsnjx4rc9XYKlgCVRGT16NHPnzgWgffv2/PDDD1auSERE4lqcjcG6efMme/bsYeXKlVy6dImMGTPy8OFDLly4EBenSxAUsCQqjx49omLFinh7e2Nra8vu3bvJkyePtctKlB4+fMjAgQMJDAykV69e1K5d2/gSJyKSkMT5IPfAwEBGjBjBixcv+Pnnn0mdOnVcns6qFLDkVX755RcmTJgAgLOzM7ly5SI4OJiQkBDy5MnDF198EeU0Drdv32bNmjXUrVuXggULxnfZCc6AAQNYu3at8djV1ZURI0bg6upqxapERCKLl7sI/fz8qFevHgMGDDAG/SZFCljyKt7e3lSsWJFHjx5Fub9evXrMnTsXW1tbY9utW7do0qQJDx48wNHRkQULFlCtWrX4KjnBOXnyJI0bN45yX+3atfnpp5/IlClTPFclIhK1eJnAKnny5FSoUIGVK1fGx+lEEpxUqVIxZsyYV84Zt2PHDr777jvj8bNnz+jQoQMPHjwAwN/fny5duryz4d1sNjNmzBjjsZubG/ny5TMeu7u7Gz2EIiIJgUUClru7O/fu3XttmxQpUnDlyhVLnE4kUWrevDnnz5/nxIkTnDp1ijNnzrB48WKj12rWrFksXbqUgIAAunXrhqenJwDJkiUDICAggO7du7Nz506rvQZr2bJlC8eOHQMgT548/PDDD/zxxx9MnDjReH8OHDhgzRJFRCKw2DQNJpOJdOnSUbhwYYoUKULhwoUpXLgwWbNm5caNG7Rt2xYbGxv27t1riboTJF0ilNhYsmQJI0aMAMDOzg5XV1cOHjwIhE15snbtWiZMmMCmTZsAsLe3Z+bMmTRo0MBqNVvKwYMHuX37Ni1btnxl715AQADVq1fnxo0bACxcuJC6desa+5s3b87Ro0cB+Ouvv8icOXPcFy4i8gaxXovwZYMHD+bcuXOcO3eOffv2sW/fPuPOHjs7O4KDgzGbzXTs2NESpxNJUjp27MjVq1eZO3cuwcHBRrhydHRk0aJF5MuXj2nTpmFnZ8e6desICgqiT58+7Nq1i/z581u5+tg7cuQIbm5uhIaGcuXKFYYPHx5luwULFhjhqlKlStSpUyfCfldXVyNgHT16lCZNmsRt4SIi0WDxQe7Pnj3j/PnznD17lgsXLnD16lXs7e2pXLkyffr0MbrzkyL1YElshYSE0K1bN3bt2gWEzR83b9486tevH6HNJ598YtxFV79+febPn2+Vet9WSEgIDRs25OzZs0DYZdA9e/aQI0eOCO0ePXpEpUqVePHiBSaTiR07dlC4cOEIbf744w/jy1u3bt0YO3Zs/LwIEZHX0FqEFqSAJW/Dx8eHjh07cuLECcaNG0eHDh0itfHz86NSpUrcv38fgPXr11O2bNn4LvWtLV++nCFDhkTY1qRJE2bNmmU8NpvNDBw40AiUbdq0iXIg+7NnzyhcuDBms5kiRYqwY8eOuC1eRCQa4uUuQhF5s5QpU7JmzRo8PT2jDFcQdkfuZ599Zjz+9ttvSWzfkV68eMH48eONxylTpgRg06ZNxkB2CBtrFR6uUqZMyeeffx7l8dKmTWss13X+/HlevHgRV6WLiERbrAJWnz59uH79+lud2NPTk169er3VMUSSGpPJ9MbL6C9PUXDs2DHjsmJ8MpvNzJo1i19++YXAwMAYPXfKlCk8fPgQgIYNGzJy5Ehj35gxYwgNDeXIkSMRpmWYMGHCawevlytXDoDQ0FBOnDgRo3pEROJCrAJWhgwZaNy4MSNGjIjx0jeHDh1i8ODBNG/enIwZM8bm9CLvNDs7O+OuQ4Dvv/+e4ODgeK1hzZo1jBs3jgkTJvDzzz9H+3nXr19n3rx5ADg4OPDVV1/Rpk0bXFxcgLDJRGfPnk2vXr2M19SnTx8+/PDD1x735Zncwwe8i4hYU6zHYB0+fJhRo0Zx48YN8uTJQ+XKlSlSpAj58uUjXbp0ODo68uLFC548ecLly5c5ceIEhw4d4u7du+TMmZMvvviCqlWrWvr1WJXGYEl8MZvNNGvWjOPHjwNhPTxt2rSJt3M3aNCAM2fOAGED1P/8809y5cr1xud269aN7du3A9C/f38jKO7evZt27dpFal+5cmWWLl2Knd3rb3i+c+eOMRatQoUKrFmzJiYvSUTE4t5qkHtISAjbt29n4cKFnD179pWLrprNZkwmE0WLFqVz5840aNAgSS7QqoAl8eno0aM0b94cgCxZsvDdd9/xwQcfkCNHjjhd8/PYsWM0a9YswrbX3dEYGhrKgQMHWLlyJevWrQMgU6ZM7Nu3j1SpUhntOnTogIeHh/H4gw8+YNu2baRPnz5adZUvX56bN2/i6OjIhQsXkvQdyyKS8L3VPFi2trY0atSIRo0acfPmTY4cOcL58+d59OgR3t7epE2blowZM5I/f36qVaumS4IiFuTq6krdunXZuXMn9+7do2vXrsa+jBkz8s0337xy7b63sXDhQuNnW1tb44vW3r17I/RKP378mIULF7Jq1Spu3boV4RjDhw+PEK4ARo4cyZ49ewgJCcHR0ZF58+ZFO1xB2Ptx8+ZN/P39OX36NGXKlInlKxQReXuapsGC1IMl8e3SpUvUr18ff3//SPvSpUvHoUOHLNqbde/ePcqVK0dwcDDvvfceQ4cOZejQoQA4Ozuza9cu7OzsOHjwIAMGDIi0hJaTkxM9e/ZkwIABUc7cvmLFClauXEn//v2N/5+i67fffmPYsGEAfPXVV/Tp0yeWr1JE5O1ZZCZ3EbGO/Pnz4+HhwdGjR7l16xY3btzgxIkTXLlyhSdPnjBv3jwGDx5ssfP9+uuvxuDzdu3a0aZNG5YvX87Jkyfx9PRk4cKFPH36lMmTJxvTR9jY2FCtWjXc3NyoW7cuDg4Orzx+69atad26daxqe3mg+5EjRxSwRMSqLNKDFZ0lcGxtbXF0dCRr1qyUL18+wlpiSYV6sCQhuHbtGtWqVSMkJITUqVNz6NAh0qVL99bHDQgIwNXVlYcPH2JnZ8fhw4fJmjUrf/311yuXp6lcuTI///wzH3zwwVuf/03MZjNFixblyZMnODk5cebMmVeubygiEtcs0oN19+5dnj9/zrNnz8IOamdH+vTp8fHxwcfHBwib3yc8yy1fvpwqVaowc+ZMbG1tLVGCiPy/3Llz4+bmxrJly3jx4gWzZs2KMK1DbG3atMmYv6pBgwZkzZoVgFKlSvHxxx+zevVqo62trS2ff/45ffv2jbf/x00mE2XLlmXnzp08ffqUS5cukSdPHpYtW8aSJUtwdnbm559/JkWKFPFSj4i82yzy9S58eYvSpUuzfPlyTp8+zd69ezlx4gSbN2+mWrVqpEuXjk2bNuHu7o6bmxv79u1j0aJFlji9iPzHJ598YtxFN3/+fCMYvY2XB7e/PKAeYMSIEaRJkwYIu/vv999/Z8CAAfH+BSp8wlGAGTNmULt2bb744gsuXrzIxo0b6dWrF0FBQfFak4i8myxyibBnz57cunWLDRs2YG9vH2l/YGAgzZs3J2fOnMyYMQMIG2vh5+fHhg0b3vb0CYYuEUpCMnLkSBYsWABAjx49GD16dKyPdeLECWOyz8KFC7Njx45IU614enpy/PhxGjVqRNq0aWN9rrfxcp2v0qJFCyZPnqzLhyISpyzyF+bYsWPUqFEjynAFYRMRVqpUiUOHDhnbSpYsyc2bNy1xehGJQv/+/XF0dARgyZIl3L1719jn7+8f7TUMjx8/Trdu3YzHXbt2jXIeO2dnZ9q2bWu1cAVQtGhR4zWHK1OmDN9//70xuH7t2rWMGTMm0a3hKCKJi0UCVooUKSLNc/Nf9+7dixDAQkNDXxnIROTtZc6cmS5dugBhA9Q/+ugjqlWrRsGCBcmbNy8lSpTgl19+4fHjx688xsqVK/n444/x8vICwu5abNq0abzUHxvJkiWjZcuWAOTKlYs5c+awfv16OnbsyIwZM4xeq3nz5jF9+vRoH/fcuXP88MMPLF++PE7qFpGkxyKXCD/99FN27NjBpEmTqFOnTqT9e/bsoW/fvlSvXp3p06cTFBTEhx9+SNq0aVmxYsXbnj7B0CVCSWgeP35M+fLljZtNopI8eXLatGlDhw4dSJUqFWazmZCQEBYuXMicOXOMdhUrVmT27NkxmvzTGsxmM9euXSNHjhyRlthZvnw5Q4YMMR6PGDGCfv36RdkjFxAQwJYtW1iyZAnHjh0zts+fP5/69etHar9y5Up+/fVX2rRpQ9u2bZPkahUiEn0WCVg3b96kVatWPH36lDJlylC0aFEyZsyIt7c3p0+f5uDBg6RMmZLly5eTM2dOmjRpwvXr1/nmm2+Mb5tJgQKWJESLFi3iyy+/BMJ6mzNlykS6dOk4ffo0ISEh0TpGp06dGDNmTJLodZ4+fTrfffed8bhz586MHTvWGJAfEBDAwoULmTFjBo8ePYr0/DJlykQaO3r37l0qVqxIYGAgAG3atOHbb7997ZxfAOvWrePw4cN06NCBIkWKRNpvNpu5cuUKTk5OvPfeezF+rSJiPRabyf3GjRt899137N27l9DQ0P+dwGSiYsWKfPXVV+TOnZsbN27QrFkz2rRpw+eff26JUycYCliSUD1//hwbG5sIy9PcvHmTuXPnsmzZMvz8/KJ8np2dHePGjYvWXHeJhdlsZtq0aYwfP97Y1qBBA6ZOncqff/7Jt99+y/Xr1yM8x8XFBR8fH2MoxPr1643FpQG+/vrrSGsxli5dmrlz55I5c+Yo63g5+Nrb2/PZZ59FmNbi8uXLjBw5kr1795IhQwY2bdpEzpw53/r1i0j8sPhSOU+ePOHcuXM8efKEVKlSUahQoQh/YMIXfk6KFLAkMXr8+DG//fYbZ86cAcLmsAoPY25ubpQuXdrKFcaN1atXM2TIEGNmeicnJ54+fWrsN5lMNG7cmM6dO1OuXDlWrVrFp59+CkDDhg2ZO3cuAPfv36dixYr4+/sbA+zDly7KkiULc+bMifQebt68md69e0caaF+mTBm+/fZb1q9fz9y5c43a4PULaotIwmPxgHXnzh0uXryIv78/Tk5O5M2b95Xf4JIaBSyRxGXPnj306NEj0hi1ChUqMHr06AiX7QICAqhQoQL379/HZDKxf/9+cuXKxejRo42w1bt3b5o2bUq3bt24c+cOEBbU2rRpw9ChQ8mYMSMHDx6kXbt2xuXEChUqcOTIkQg9/6+yfPnyCAtqi0jCZbGAdevWLUaOHMnhw4cjnsBkonz58owZM4bs2bNb4lQJlgKWSOJz9uxZOnTowIMHD8idOzcjR46kbt26Ufa0T5s2je+//x4IG7v1ySefUL58eaP36vDhw2TMmJGHDx/Ss2dPjhw5Yjw3VapUdO7cmcWLF/PixQsA3Nzc+Pnnnzl+/DiDBg3i33//Ndo7ODjQp08fMmfObMzEnz9/fnbt2pUkxsKJJHUWCVheXl60aNECLy8vihYtSqlSpciUKRPPnz/n6NGjnDx5kixZsrB27doEfwfS21DAEkmcXrx4wcWLFylevLgxA35Unj59StmyZfH19cXR0ZFmzZoZd0J3796dMWPGGG2DgoKYO3cukydPxtvbO9KxatWqxYIFC4w7HX18fBg3bhxr1qyhSpUqjBo1ily5chEaGsqHH37IyZMnARgzZgzdu3e35MsXkThgkYA1atQoVq5cyejRo2ndunWk/atXr2bkyJF06tTJImuiJVQKWCJJX1QD2h0cHDh48CBZsmSJ1N7Ly4uffvqJ5cuXG5cBS5UqxapVq0iePHmk9lGNU/37779p1KgRAGnSpGH//v1kyJDBUi9JROKARSYa3bNnD5UqVYoyXAF8/PHHVKpUScFDRBK97t27R1pmp127dlGGK4CMGTPy448/smPHDpo1a0aLFi1YvHhxlOEKiPLSZIkSJXBzcwPC7gj94Ycf3vJViEhcs0jAevjwIc7Ozq9t4+zszIMHDyxxOhERq8mRI4fRmwRhs8f36dPnjc8rVKgQ06dPZ+rUqbEaKjFixAhSp04NwLJly4y7PkUkYbJIwHrvvffw9PR8bZt//vmHdOnSWeJ0IiJW1bt3b6OnqW3btrz//vtxfs6MGTMyePBgIOwy4qJFi+L8nCISexYJWFWrVuXgwYP8/vvvUe5fvnw5hw4dolq1apY4nYiIVZUoUYKFCxfy1Vdf8fXXX8fbeTt27GhMFrt161YCAgLi7dwiEjMWu4uwWbNmPH78mDJlylCmTBlSp07N/fv3+euvvzh79iwZMmTg999/T9JzYmmQu4jEtYEDBxpfZl+1LqKIWJ/dm5u8WcaMGVmxYgVfffUVR44cibAwKkC5cuUYO3Zskg5XIiLxoXnz5kbAWrdunQKWSAJl8Znc7927x4ULF/D29iZlypQULFiQrFmzWvIUCZZ6sEQkrgUFBVGqVCkeP36Mo6Mjp06dirDGpIgkDBYZg/WyLFmyUKNGDZo0aULNmjXfmXAlIhIf7O3tadKkCRC25uH27dsj7N+zZw+1atXip59+skZ5IvL/YhWwvL29Y/2fiIi8nWbNmhk/b9iwwfj59u3b9OrVi4sXLzJp0iQuXLhghepEBGI5BqtMmTJRTob3JiaTifPnz8fmlCIi8v/KlClDtmzZuH37Nnv27OHRo0ekS5eOTz75xFjnEMLmyxo3bpwVKxV5d8UqYJUtW9bSdYiISDTZ2NjQtGlTZsyYQUhICJs3byYwMJCDBw9GaPf777/zxRdfvHLWeBGJOxYf5P4u0yB3EYkv586do27dugDkzZuXW7duGfNiFSlShLNnzwIwefJkPvroI6vVKfKusvggdxERiXuFChUif/78AFy5csUIV926deObb74x2i1btswq9Ym86xSwREQSIZPJFGGwO0D+/PkZMWIEZcqUMcLXkSNHuHz5shUqFHm3KWCJiCRSTZs2NX62s7NjypQpJE+eHJPJRNu2bY19S5cutUZ5Iu80BSwRkUQqd+7cdO/enbRp0/Ldd99RrFgxY99HH31EsmTJAFi9erXWLRSJZwpYIiKJ2JgxYzh//jzt2rWLsD19+vQ0bNgQgCdPnkSakFRE4pYClohIEvVy6NJlQpH4ZZHFnkNDQ7lw4QJeXl54e3uTIkUKsmfPTr58+WI1IamIiLy9ChUqkDt3bq5du8aBAwc4e/YsRYoUsXZZIu+EtwpYN2/eZMaMGezYsQM/P79I+9OkSUODBg3o1auX1iQUEYlnJpOJ9u3bG7O5d+vWjS1btvDee+9ZuTKRpC/Wlwj37NlD06ZNWbduHSEhIZQoUYJ69eoZizy7uLjg4+PDihUraNKkCXv37rVk3RZx9uxZWrZsSYkSJWjRooWW8RGRJKdTp07G4Pdbt27RrVs3/P39rVyVSNIXq5ncr169SosWLQgJCWHQoEG0b98eR0fHSO2ePXvGypUrmTFjBiaTiY0bN5I9e3aLFP62AgICqFOnDv3796d58+asWrWKuXPnsnPnTuPOm5jSTO4ikhDdvXuXxo0bc+/ePQBatGjBlClTNIRDJA7Fqgdr0aJFBAQEMH36dLp37x5luAJImzYtPXv2ZObMmfj5+bFkyZK3KtaSDh8+jL29Pa1atcLe3p527dqRLFkyjhw5Yu3SREQsKmvWrCxatMhYk3Dt2rVMmTLFylWJJG2xClhHjhzB1dWVqlWrRqt9hQoVKFOmDIcPH47N6eLEtWvXyJcvX4RtuXPn5sqVK1aqSEQk7hQtWjRCqPrxxx+1jI5IHIpVwHrw4AEFChSI0XMKFSrErVu3YnO6OOHr6xup583R0RFfX18rVSQiErcaNmzI8OHDjceff/45EyZMIBYjRUTkDWIVsPz9/UmVKlWMnpMqVaoENbAyefLkkWY29vf3J0WKFFaqSEQk7vXv358ePXoYj3/55RcGDx5MYGCgFasSSXpiFbDMZnOMB0fa2CSsOU3z5MnDtWvXImy7du0auXPntlJFIiJxz2QyMXr0aEaPHm38HV+9ejUdO3bk+fPnVq5OJOlIWKknHpUvXx4fHx+WLVtGUFAQy5Ytw8/Pj/Lly1u7NBGRONejRw9mz55tDJXYt28fXbp0ISQkxMqViSQNsZ5o9OLFi6xfvz7a7S9cuBDbU73SnDlzWLx4MQcOHIi0786dO/z0008cOnSIoKAgypcvz/Dhw41pIhwcHJg7dy6jRo3ip59+Infu3MycORMHBweL1ykikhA1atSITJky0aVLF548ecLhw4dZuHAh3bt3t3ZpIolerObBKlCgQIwvEYZfVrRU0NqzZw/9+vUjbdq0kQLW06dP+eijj/D29qZTp04kS5aMBQsWYGtry/r160mfPr1FavgvzYMlIonRoUOH+Oijj4Cwm3127dpFnjx5rFyVSOIWqx6s/v37W7qOaDObzSxdupTx48cTFBQUZZtFixZx69Yt1qxZY6y7VaVKFZo1a8bcuXMZNmxYfJYsIpKgVahQgS5durBw4UL8/f357LPP+P333xPc2FmRxCRWPVjW1KpVK06dOkXlypV58uQJ9+/fj9SDVbt2bd577z1WrFgRYXvXrl25dOkS+/bti5Pa1IMlIomVr68vtWvX5t9//wVg7NixdOvWzcpViSReb7XY8+sEBARw79493nvvPVKmTGmx4965c4exY8fSqlUrOnbsGGn/s2fPuHnzJtWrV4+0r3Dhwhw4cIAHDx6QKVMmi9UkIpLYpUiRggkTJvDxxx8D8N1331G4cGGuX7/Ovn37OHjwIL6+vuTPnx9nZ2ecnZ0pVaoUrq6uVq5cJGF6q4Dl4eHBrl276NSpkzHxqNlsZuLEifz222/4+/tjY2NDnTp1GDVqFOnSpXvrgj08PF67VuD9+/cByJw5c6R94aHq7t27ClgiIv9RsWJFOnfuzKJFi/D396dly5aR2pw8eZKTJ08aj7t168bYsWPjs0yRRCHWF9i//vpr+vXrx/r1640uZQibtG7u3Ln4+/tTsWJFKlSowM6dO+nQoYNFJrJ700LMPj4+AMaaWy8Lvx1Zs7WLiETtiy++IEeOHJG2p0qVyrgL+2Xz589n27Zt8VGaSKISqx4sDw8PVq1aRaFChfjss88oU6YMENZ7tGDBAkwmE+PGjTPuSvnjjz/o168fS5YsifPbf8OHlL3uLketIC8iErWUKVMye/Zshg0bRooUKahcuTKVK1emRIkS2Nvb4+vry6VLl9i5cyeTJk0CYMiQIZQoUYKsWbNat3iRBCRWAWvNmjU4OTmxZMmSCEvmbN++neDgYHLmzGmEKwgb/F2qVCm2b98e5wErfKkbPz+/SPvCl+qJ6TI/IiLvkmLFir2yVypFihQUL16cYsWK4enpydatW3n69CmDBg1ixYoVuvNQ5P/F6v+E06dPU7169UhB5eDBg5hMJmrWrBnpOcWLF49wKTGuZMuWDQAvL69I+x48eABEPT5LRESiz2Qy8eOPPxq9VgcOHGDWrFlWrkok4YhVwHr27FmkkBIaGsqJEyeAsDlV/svOzu6V81ZZUurUqcmRIwfnzp2LtO/cuXNkyZKFjBkzxnkdIiJJXbp06ZgyZYox7OKHH35g48aNnD17lhs3bvDs2TMS2UxAIhYTq4CVOnVqnjx5EmHb6dOn8fb2xs7OjrJly0Z6zvXr1y1yF2F01K9fnxMnTkQIWZ6enhw+fJjGjRvHSw0iIu+CihUr0q9fPwCCg4Pp06cP9erVo0KFChQqVIiGDRvy4sULK1cpEv9iFbCKFi3KwYMHCQ0NNbZt3rwZCOu9+u8dfF5eXuzfv5+iRYu+RanR161bN9577z26devG3LlzmT9/Pl27diVz5syaOE9ExMLCB7lH5fTp0yxatChe6xFJCGI1yL1Vq1b069ePTz/9lHbt2uHp6cnKlSsxmUy0a9cuQtvHjx/zySef4O/vz4cffmiRot/EycmJZcuW8f333zNjxgySJUuGq6srQ4cOjbN1CEVE3lX29vb8+uuv/P7773h5efHs2TOePn3K1q1bCQ0NZd68eXTv3j3K6XNEkqpYL5Uzbtw4li5dalx7N5vNtG3blq+//tpo07t3bw4dOkRAQAD169c3bulNqrRUjojI//Tu3ZtNmzYBYTPDd+rUycoVicSft1qL8MiRI+zevZvg4GAqVaoUaXmaunXr4u3tTbt27ejduze2trZvW2+CpoAlIvI/Z86coX79+gDkyJGDffv2YWcXZyu0iSQocbrYs7e39zs155QClohIRG3btmXPnj0ATJ8+nWbNmlm3IJF48lYzwt29e5fVq1czZ84cNmzYEOnOwncpXImISGThdxgCTJs2LcK0DaGhody9e1dTOUiSFOu+2smTJzN37lxCQkKMbY6OjgwbNozWrVtbpDgREUncKlasSMmSJTl58iQXLlzgzz//pHr16mzZsoWffvqJK1euULhwYfr27Uvjxo11CVGSjFhdIty4cSNDhw4lefLk1K5dm8yZM3Pjxg08PDwICQlhwYIFUU42mtTpEqGISGTbtm0zlkkrWLAgdnZ2nDlzJlK7Dz74gJ49e9KmTRtj2TORxCpWAatDhw78888/rFmzJsKq62fOnKF9+/ZUqVKFadOmWbTQxEABS0QkstDQUKpXr86VK1ci7cuUKZOxjFm49OnT07dvXzp16qSgJYlWrMZgeXp6Ur9+/QjhCsImIK1evTqnT5+2SHEiIpL42djYRBiLBVC4cGF+/fVX/vrrL1avXh1hDdvHjx/zzTffUKFCBWbPno2fn198lyzy1mIVsHx8fMiQIUOU+3LlyhVpsLuIiLzbWrZsSZcuXahatSozZsxg+/bt1KxZE5PJRMWKFfn1119xd3enWbNmxvyKDx8+ZOzYsdSuXTtSL5dIQhergBUcHPzKOa3s7e0JDg5+q6JERCRpsbOz45tvvmH58uU0bdoUG5vI//wULFiQ6dOn4+HhQZMmTYygdf36dWbNmhXfJYu8lbeapkFERMTSnJ2dmTVrFjt27MDBwQGAFStW4Ovra+XKRKJPAUtERBKkwoUL07RpUwCePXvG77//buWKRKIv1hOOXLx4kfXr10fafuHCBYAo9wGaxVdERKKta9eurFq1CoCFCxfSvn1749KhSEIWq2kaChQo8MoPePjh/rvfbDZjMpmMAJYUaZoGERHLa9q0KcePHwdg1apVVKpUycoVibxZrHqw+vfvb+k6REREotS1a1cjYC1cuFABSxKFOF3s+V2jHiwREcsLCgqifPny3Lt3DxsbGw4dOsQHH3xg7bJEXkuD3EVEJEGzt7enffv2QNis8EuWLLFyRSJvpoAlIiIJXvv27UmWLBkAS5cu1ezukuBp2XIREUnwMmbMSOPGjVm7di1Pnz6lWLFipE6dmhQpUpAmTRrKli1L48aNKV26dJSTmIrEN43BsiCNwRIRiTsnT56kcePGr22TJUsWGjVqRIcOHcifP388VSYSmQKWBSlgiYjErVmzZrF582a8vb3x8fHB19eX58+fExoaGqGdg4MDK1eupGzZslaqVN51ClgWpIAlIhL/nj59ys6dO9m8eTN79+4lKCgIgPTp07N582Zy5sxp5QrlXaQL1SIikqg5OTnRqlUrlixZwqlTp6hcuTIAjx8/pnPnzjx//tzKFcq7SAFLRESSjLRp0zJ79mzy5s0LgKenJ3369CE4ONjKlcm7RgFLRESSFCcnJxYvXoyTkxMAu3fvZvTo0VatSd49ClgiIpLk5M6dm3nz5mFvbw+ELbEzcuRIY3yWSFxTwBIRkSSpQoUK/PDDD8bjBQsW0K5dOx4/fmzFquRdoYlGRUQkyXJzcyMkJIQvvviCoKAgDhw4QKNGjZg/fz4ABw8e5MCBA5w9e5b333+fcuXKUbZsWcqUKUO6dOmsXL0kZpqmwYI0TYOISMJ07NgxunfvzsOHD6P9nLp16zJlyhRSp04dh5VJUqVLhCIikuSVLVuWrVu3UqxYsSj3p0yZMtK2nTt38vXXX8d1aZJEqQfLgtSDJSKSsPn5+TFq1Cg8PDwoVqwYFStWpGLFihQoUICHDx9y7Ngxjh49yvLly/Hx8QFg3rx5NGjQwMqVS2KjgGVBClgiIknDypUr+fTTT4GwGeH/+OMPMmXKZOWqJDHRJUIREZH/aNWqFfXr1wfCZoT//PPPUX+ExIQCloiIyH+YTCZ+/PFH3nvvPQDc3d1Zvny5lauSxEQBS0REJAoZMmRgwoQJxuNRo0Zx8eJFK1YkiYkCloiIyCvUqVOHtm3bAuDr60vjxo1ZtWqVlauSxEABS0RE5DVGjRpF4cKFgbC7EAcPHswnn3yCr6+vlSuThEwBS0RE5DVSpUrFhg0bjJ4sgNWrV9OwYUP++usvK1YmCZkCloiIyBskT56cn376iWnTphmTkl66dIkmTZrQrl07jh8/buUKJaFRwBIREYmm5s2bs23bNgoVKmRs2717N02bNqV169acOHHCitVJQqKAJSIiEgN58+Zly5Yt/PTTT2TPnt3Yvm/fPpo2bco333xDQECAFSuUhEABS0REJIaSJUtG27Zt2bdvHxMnTiRXrlwAmM1mZs6cScOGDTl37px1ixSrUsASERGJJXt7e9zc3NizZw9fffUVyZIlA+DixYs0atSI6dOnawb4d5QCloiIyFuys7OjT58+bNmyhYIFCwIQFBTEd999x7x586xcnViDApaIiIiFFCpUiC1bttC/f39j2/fff68Z4N9BClgiIiIW5ODgwIgRI+jRowcAAQEBDBgwQAPf3zEKWCIiInFg+PDhFChQAIDz58/z008/WbkiiU8KWCIiInHA0dGRKVOmGAPfZ82axaFDh6xclcQXBSwREZE4UrhwYYYOHQqETeEwaNAg7t69a+WqJD4oYImIiMShnj17UqFCBQBu375N2bJladasGbNmzeL69evWLU7ijMmsCTosplatWgD88ccfVq5EREQSktu3b1O3bl2ePn0aaV+NGjUYN24cuXPnjv/CJM6oB0tERCSOZcuWjZ07dzJw4ECcnZ0j7Pvzzz+pVasWP//8M/7+/laqUCxNPVgWpB4sERGJjitXrrBjxw4WLFgQYUxWrly5GDVqFHXq1MFkMlmxQnlbClgWpIAlIiIx4ePjw6RJk5gzZw7BwcHG9gIFCtCrVy+aNWtm3IUoiYsuEYqIiFhJypQp+fLLL9m5cyfly5c3tl+8eJHBgwdToUIFZs2aRVBQkBWrlNhQwBIREbEyFxcX1qxZw/z58yldurSx/d69e4wbN46OHTvy/PlzK1YoMaWAJSIikgCYTCbq16/Pxo0bWb9+PfXr1zfGYe3du5cWLVpw+/ZtK1cp0aWAJSIiksCULVuW+fPns3btWpycnAC4cOECTZo04ezZs9YtTqJFAUtERCSBcnV1ZdOmTeTKlQuA+/fv07x5c77//nuOHTtGSEiIdQuUV9JdhBakuwhFRCQuPHr0iC5dunDixIkI252cnKhevTpNmjShdu3a2NnZWalC+S/1YImIiCRwGTJkYOXKlXz88ccRtj99+pT169fTrVs3ypUrx8SJE7l3756VqpSXqQfLgtSDJSIicc3LywsPDw88PDzYs2cPL168iLDf1taWhg0bMmTIEPLly2elKkUBy4IUsEREJD4FBQWxd+9efvvtN9zd3QkNDTX22dra0r59ez799FPee+89K1b5blLAsiAFLBERsZbbt2+zdOlSli5dysOHD43tqVKlom/fvvTs2ZPkyZNbscJ3iwKWBSlgiYiItfn6+jJ79mxmzJiBr6+vsT1Xrlx888031KhRw4rVvTs0yF1ERCQJSZEiBYMHD+bgwYN06NABW1tbAK5fv0779u3p0aOHJiyNBwpYIiIiSVDGjBkZP3487u7uVKhQwdi+detWqlevzsqVK61YXdKngCUiIpKEOTs7s3r1aqZMmWIMdvf19eXTTz9l0aJF1i0uCVPAEhERSeJMJhMtW7Zk7969tG3b1tj+5ZdfMmfOHCtWlnQpYImIiLwj0qZNy48//sigQYOMbWPGjGHGjBlWrCpp0pz6IiIi7xCTycTQoUOxt7dnwoQJAHz77bfcu3eP9u3bkz9/fkwmk5WrTPw0TYMFaZoGERFJTKZOncr48eMjbMudOzcNGjSgWbNmFC5c2EqVJX66RCgiIvKOGjBgAKNGjTKmcgC4du0aM2bMoH79+mzYsMGK1SVu6sGyIPVgiYhIYnT79m22bdvG9u3bOXLkiLHkjqOjI5s2baJQoUJWrjDxUQ+WiIjIOy5btmx0796dNWvW8Pfff9O8eXMA/P396dGjB0+fPrVugYmQApaIiIgYMmTIwE8//UTRokWBsBngBwwYEGEhaXkzBSwRERGJIHny5MybN4906dIB4OHhwaRJk6xbVCKjgCUiIiKRfPDBB8yYMQMbm7Co8PPPPzN06FB27twZYRFpiZoCloiIiESpatWqDB8+3Hi8dOlSunTpQuHChWnTpg1btmxB98pFTQFLREREXqlv37706tWLZMmSGdsCAwPZu3cvPXv2xM3NjX/++ceKFSZMmqbBgjRNg4iIJFU+Pj4cOHAADw8PPDw8uH37trHP1taWLl268Nlnn5EmTRorVplwKGBZkAKWiIi8C8xmMzt37mT06NHcuHHD2J4tWzY2bdpE5syZ33iMkJAQLl26RLZs2UidOnVclmsVukQoIiIiMWIymahXrx4eHh4MGTIER0dHIGzC0pEjR772uSEhIaxfv56aNWtSq1YtGjdujI+PT3yUHa8UsERERCRWkidPzuDBg9m9ezfp06cHYMuWLWzfvj1S25CQEDZs2ECtWrXo168fly9fBuDy5cvMnj07XuuODwpYIiIi8layZ8/O2LFjjcdffPEFz549Mx4/fvyYVq1a0bdvXy5duhTp+TNnzuTBgwfxUmt8UcASERGRt9asWTNq1qwJwP379/n2228BuHLlCk2aNOHw4cNGW1dXV1asWEHnzp0B8PX1ZeLEifFec1zSIHcL0iB3ERF5l92+fZsaNWoYY6q+/PJLpk+fbqxlmClTJiZNmkTVqlUxmUw8fPiQSpUq4e3tja2tLR4eHuTLl8+Kr8By1IMlIiIiFpEtWzZGjBhhPP7222+NcFWwYEE2b95MtWrVMJlMALz33nv07dsXCBuj9f3338d7zXFFAUtEREQsplOnTpQuXTrCtmrVqrFu3TqyZcsWqX3Pnj3JkiULANu3b+fo0aOxPrfZbGbLli2sWLHC6otTK2CJiIiIxdjY2DBhwgRSpkwJQLt27Vi8ePEr57pKnjw5Q4YMMR6PHDmSVatWsXPnTo4cORJhQtPXefbsGT169KBnz5589tlnrFix4u1fzFvQGCwL0hgsERGRMLdv3+bx48cULVr0jW2Dg4OpW7fuK5fcadiwISNHjiRHjhxR7j99+jS9evWKMOlpmTJl2LBhQ+yKtwD1YImIiIjFZcuWLVrhCsDOzo7Ro0cbY7P+a+vWrVSvXp0ff/wRX19fIGzM1q1bt5g/fz5NmzaNEK4Ajh8/zq1bt97uRbwF9WBZkHqwREREYu/ixYtcvHiRp0+f8uzZMx4/fsyGDRvw8vIy2mTKlIlUqVJx69YtAgMDIzy/ZMmSFC1alCVLlgBhdzGGD6KPbwpYFqSAJSIiYlkvXrxg8uTJzJs3j6CgoFe269atG1999RV37tyhUqVKABQuXJidO3fGV6kRKGBZkAKWiIhI3Lh69Spjx47ljz/+wMHBgZw5cxr/1apVi8qVKxttGzVqxN9//w3Anj17rDK3ll28n1FEREQkhvLkycOiRYsICAggWbJkrxyvBdC0aVMjYG3YsIHPPvssnqr8Hw1yFxERkUTDwcHhteEKoEmTJkabDRs2YI2LdQpYIiIikqRkzZqV8uXLA2FrIZ47dy7ea1DAEhERkSTnww8/NH62xnxYClgiIiKS5DRu3BhbW1sgLGDF99I5ClgiIiKS5KRPn56qVasCYbPKnzhxIl7Pr4AlIiIiSVLTpk2NnydNmoS3t3ekNrt376Zx48YWP7cCloiIiCRJ9evXNxad3r17Nw0aNOD8+fMA+Pn58fXXX9OuXTtOnjxp8XMrYImIiEiSlDp1ambMmEHq1KmBsMlKmzRpwpQpU2jYsCHz58+Ps3MrYImIiEiSVbt2bbZt20aRIkUA8Pf354cffsDT0xMAR0dHxo0bZ/HzKmCJiIhIkpY7d242bNhAx44dI2wvXLgwW7dupWvXrhY/p5bKERERkSTP0dGR77//nooVK7Jo0SIqVqxI//79cXBwiJPzabFnC9JizyIiIgK6RCgiIiJicQpYIiIiIhamgCUiIiJiYQpYIiIiIhamgCUiIiJiYQpYIiIiIhamgCUiIiJiYQpYIiIiIhamgCUiIiJiYQpYIiIiIhamgCUiIiJiYQpYIiIiIhamgCUiIiJiYSaz2Wy2dhFJRdGiRQkJCSFr1qzWLkVERERiIGvWrPz2228WO556sCzIwcEBOzs7a5chIiIiVqYeLBERERELUw+WiIiIiIUpYImIiIhYmAKWiIiIiIUpYImIiIhYmAKWiIiIiIUpYImIiIhYmAKWiIiIiIUpYImIiIhYmAKWiIiIiIUpYImIiIhYmAKWiIiIiIUpYImIiIhYmAKWxInWrVvj4uIS6b+mTZtau7REZ86cOVSqVCnKff7+/kyYMIEaNWpQvHhx3NzcOHToUDxXmPi87j2dOHFilJ9dFxcXnj9/Hs+VJnynT5+mR48elClThqJFi9KsWTPWr18foY0+pzEXnfdVn9WY++eff+jZsyflypWjbNmyDBw4kH///TdCG0t9Xu0sVbTIyzw9PalevToNGzaMsN3Jyck6BSVSe/bsYcqUKaRNmzbK/Z999hl//vknbdu2JU+ePKxZs4bu3buzePFiypQpE8/VJg5vek89PT3Jnj07AwYMiLQvefLkcV1eonLlyhU6dOhA2rRp6d69OylTpmTr1q0MGzaMJ0+e0KVLF0Cf05iK7vuqz2rMXLt2jTZt2pA2bVp69epFSEgIixcvplWrVqxfv56sWbMCFvy8mkUs7NatW2ZnZ2fzsmXLrF1KohUaGmr+9ddfzYULFzY7OzubK1asGKnNwYMHzc7OzuaFCxca23x8fMy1atUyN2/ePB6rTRyi856azWZzjRo1zJ988kk8V5c49ejRw1yiRAnzvXv3jG0hISFmNzc3c4kSJcze3t76nMZCdN5Xs1mf1ZgaOHCguVixYuabN28a2y5evGh2dnY2f/PNN2az2bJ/V3WJUCzO09MTgLx581q5ksTLzc2NcePGUa5cOQoXLhxlm02bNmFvb0+rVq2MbSlSpOCjjz7i3LlzXL9+PZ6qTRyi8556e3tz584dfXajISQkhGPHjlGlShUyZ85sbLexsaFBgwb4+vpy4cIFfU5jKLrvqz6rMWdnZ0ejRo344IMPjG0uLi44OTlx8eJFwLJ/V3WJUCzu0qVLAOTLlw8AHx8fUqZMac2SEp07d+4wduxYWrVqRceOHaNsc/bsWXLnzk2KFCkibA8PD2fPniVXrlxxXWqiEZ339PLly5jNZuMfLT8/PxwcHLCx0XfR/7KxsWHjxo2YTKZI+x4/fgyAra2tPqcxFN33VZ/VmPv5558jbbt79y5Pnz7l/fffByz7d1W/CbG4f/75BwcHByZPnkzp0qUpVaoUVapUYcmSJdYuLdHw8PDAzc0tyj+y4e7fv0+WLFkibc+UKRMQFijkf6Lznob3vu7bt4/q1atTokQJSpcuzejRo/Hz84uvUhMFk8lE9uzZI/QGAPj6+vL777+TIkUKChUqpM9pDEX3fdVn9e08evSIPXv20LNnT1KkSEHXrl0By/5dVQ+WWNylS5cICAjg/v37fPfdd/j5+bF69Wq+/fZbnj59ysCBA61dYoKXLFmyN7bx8fGJciCro6MjgP7I/kd03tPwf7TOnDlD//79SZUqFXv27GH58uVcuXKFxYsXq4fgNcxmM1999RVeXl7069cPBwcHfU4tIKr3VZ/Vt9OyZUvu3r0LwJAhQ3B2dgYs+3dVAUsszs3NjZCQkAiXYT788EPatGnDnDlzaNOmDRkzZrRihe+G1/XUSNSqVKlC6tSp6dGjh3GJoH79+qRLl4758+eza9cu6tWrZ+UqEyaz2czo0aPZsmULrq6u9OnTJ1rP0+f09V71vuqz+nYGDx5MsmTJ2LZtGxMmTODWrVuMGTPmjc+LyedV8VYsrl27dpHGuNjY2ODm5kZQUBDHjx+3UmVJS4oUKfD394+0PXxbqlSp4rukRK9atWoMGjQo0viLtm3bAnD48GFrlJXgBQUFMWTIEFasWEGxYsWYOXMm9vb2gD6nb+N176s+q2+nadOmNGjQgClTptCgQQNWrFjBpUuXLPp5VcCSeJMhQwYgbCyBvL33338fLy+vSNsfPHgAEOEOJHk7+uy+mp+fH3369GHz5s24urqycOHCCP8I6XMaO296X19Fn9WYa9SoEQDnz5+36OdVAUss6s6dOzRq1IjJkydH2nf16lUAsmfPHt9lJUmFCxfm8uXLkb5tnTt3DoCiRYtao6xErXPnzsZg15fpsxu1oKAg+vfvz759+6hRowbz5s2LFAL0OY256Lyv+qzGzLNnz6hXrx7ffPNNpH0+Pj5A2DgrS35eFbDEorJmzcqzZ89YvXo1z549M7Y/e/aMRYsWkS1bNkqVKmXFCpOO+vXrExgYyIoVK4xtvr6+rFmzhmLFipEjRw4rVpc4OTk5cfDgQU6ePGlsCw0NZdq0adja2kZameBdN2XKFPbv30/NmjWZOnUqDg4Okdrocxpz0Xlf9VmNmbRp02Jvb8+mTZsi9FAFBgayZMkSUqRIQbly5Sz6edUgd7Eok8nEqFGj6N+/P61ataJNmzYEBgaycuVKHj16xNy5c7Gz08fOEqpUqUKVKlX46aefuHv3Lrlz52bVqlXcu3eP8ePHW7u8RGnIkCEcOHCAHj160KFDB9KnT8+OHTs4duwYn3zyCXny5LF2iQnGgwcPWLhwIXZ2dlSuXJmtW7dGalOhQgV9TmMouu+rPqsxN2bMGDp27EibNm1o06YNNjY2rF27lkuXLvHNN9/g5ORk0c+ryWw2m+Potcg7zMPDgzlz5nD+/Hns7OwoWbIkAwcOpHjx4tYuLdHp0KEDV69e5cCBA5H2+fj48Msvv7B161b8/PxwcXFh8ODBlCtXzgqVJh6ve08vXbrEpEmTOHLkCIGBgeTLl4+OHTvSrFmz+C80Adu+fTuDBg16bZu5c+dStWpVfU5jICbvqz6rMXfs2DGmTp3K6dOnAShSpAi9evWiSpUqRhtLfV4VsEREREQsTGOwRERERCxMAUtERETEwhSwRERERCxMAUtERETEwhSwRERERCxMAUtERETEwhSwRERERCxMAUtERETEwhSwRERERCxMAUtEXmvt2rW4uLi88T93d3drl/pOGD58eIT3/ciRI0DY8j8uLi7cunXrlc8N/11OnTr1rc6p37XIm2nVXRGJFldXV1xdXV+5P3fu3PFYjbi5uZExY0ayZcsW5+eqXbs22bJl4+jRoxw9ejTOzyeSFChgiUi0uLq6MmDAAGuXIf+vTZs2FCxYMF7OVbt2bWrXrs3UqVMVsESiSZcIRURERCxMAUtELGrq1Km4uLhw6NAhPv74Y4oUKUK9evXw8fEBwMvLi9GjR1O1alWKFClCzZo1+emnn/D29o50rDt37jB06FAqVKhAyZIl6du3L3fu3KFmzZp06NDBaBc+RujChQuRjuHi4kLTpk0jbDObzSxfvpzmzZtTrFgxypYtS+/evTl//nyEdkeOHMHFxYW1a9eyZs0amjRpQtGiRalatSo//PADfn5+kc7n7u5Ohw4dKFOmDOXKlaNz584cO3YMAD8/P0qVKkX16tUxm82RnjtixAhcXFy4fv36m99oC7h169Ybx9atXbs2XmoRSWp0iVBE4sSQIUPIkycPHTp0wMfHh5QpU3Lnzh3atGnD/fv3qVGjBnnz5uXChQvMmzePgwcPsnTpUlKkSAGEhatWrVrh5eVFjRo1yJ07Nx4eHnTs2BFfX9+3qm3YsGFs2LCB/Pnz07p1a/z8/Ni2bRutW7dm9uzZVKhQIUL73377DU9PT+rWrUuVKlXYtWsXCxYs4MGDB/z8889Gu9mzZzNx4kQyZMhAvXr1cHBwYPPmzXTu3Jk5c+ZQqVIl6tWrx9q1azl+/Dhly5Y1nhsQEMDOnTspUaIEuXLleqvXF11p0qShf//+kbb7+PiwaNEi7O3tKVSoULzUIpLUKGCJSLQcPXr0lXefNW/enA8++CDCtixZsrB48WJsbP7XUT569Gju37/PrFmzqF69urF9yZIlfPvtt0ybNo2hQ4cCMGHCBLy8vPjmm2/4+OOPARg0aBCdOnXi5s2bsX4d27ZtY8OGDTRu3JgffvgBO7uwP4M9e/bko48+YtiwYbi7u5MsWTLjORcvXmTp0qWULFkSgD59+lC3bl22b9/O2LFjSZkyJdeuXWPKlCnkyZOHJUuWkDFjRgA6depEs2bNGD9+PJs2baJp06asXbuWzZs3RwhYHh4eeHt78+GHH8b6tQEsXryYNGnSRLnvvz18adKkiTSuLjQ0lL59+2I2mxk9ejQFChR4q3pE3lUKWCISLa+7g8zV1TVSwKpTp06EcPXgwQP27t1LtWrVIoQrgPbt27NgwQLWrVvH0KFD8ff3548//iBv3rxGuAJwdHRk2LBhtGnTJtavY82aNQB8+eWXRrgCyJ49O61bt2bWrFkcPHgwQo1ly5Y1whVA6tSpKVmyJH/88Qf37t0jb968bN++neDgYPr27WuEK4CcOXMybNgw/P39CQoKoly5cmTLlo0dO3YwcuRIo4aNGzdib29Pw4YNY/3aICysvo1Jkybx559/0rZtW1q2bPlWxxJ5lylgiUi09O/fP0Z3Ef43cJ0/fx6z2czTp0+j7Amzt7fn7t273L9/n2fPnuHv70/RokUjtStRogSOjo4xfwH/79y5czg4OLB06dJI+65duwaE9fS8HLCiumSXOnVqAIKCgoCwXq7w+v6rdevWER43adKEWbNmsX//fqpXr87Tp0/Zt28fVatWJV26dLF5WYY//vgj0nsfbu3atYwYMeKVz92yZQuzZ8+mdOnSfPHFF29Vh8i7TgFLROLEf0PQ8+fPAfj777/5+++/X/m8p0+fGgPew8djvczGxuaVl8Ci48WLFwQHBzNt2rRXtnn27FmExy9fLgxnMpkAjMHq4a8vVapUb6yhWbNmzJo1i82bN1O9enW2bdtGUFBQpMH48encuXN88cUXZMqUicmTJ2Nvb2+1WkSSAgUsEYkX4WGpb9++DBo06LVtL1++DITdcfhf4b1gLwsPO6GhoRG2R3WXX4oUKUiZMiW7d++ObunREv76fHx8IvVC+fv7kyxZMuOSae7cuSlRogR//PEHgYGBbNu2jbRp01KjRg2L1hRdjx49ol+/foSEhDB16tQIlzhFJHY0TYOIxAsXFxcAzp49G+X+KVOmMGfOHAIDA8mVKxcpU6bk7NmzxiW4cJ6engQGBkbYFt7b8t9AdePGjSjruHfvXpThbffu3fzyyy/G5b6YcHZ2BuD06dOR9n3zzTcUL148wuD8pk2b4uvri7u7OydOnKB+/fpR9pTFtcDAQPr378/du3f5+uuvo7zEKSIxp4AlIvEie/bslC1blr1797J9+/YI+9avX8/06dPZt28fyZIlw87OjhYtWnD37l3mzZtntAsMDGTChAmRjp0nTx4A/vzzT2NbaGgos2bNitS2efPmmM1mxo0bFyGoPXjwgFGjRjFnzhxSpkwZ49fXuHFjbGxsmDVrFk+ePDG237hxg23btpE9e3ayZ89ubG/UqBH29vZMmDCB4OBgq10eHDt2LH/99Rdt27alVatWVqlBJCnSJUIRiTdjx46lXbt2DBo0iKpVq5I/f36uXbvG7t27cXJyYtSoUUbbTz75hCNHjjBp0iSOHDmCs7Mzhw4d4v79+5GO27hxYyZPnsz8+fO5efMmH3zwAQcOHODFixe8//77Edq2aNECDw8PduzYwT///EOVKlUIDg5m27ZtPH36lM8++yxCEIquvHnz0r9/f6ZMmULTpk2pUaMGZrOZrVu3EhAQwPjx4yO0T5s2LTVr1mTHjh1kz56d0qVLx/icb2vjxo2sXr2atGnT8sEHHzBz5kyCg4MjtClYsCC1a9eO99pEEjsFLBGJN3ny5GHt2rXMmDGDPXv2cOjQITJlykTTpk3p169fhGCTKlUqli5dyuTJk9m+fTsnT56kbNmyfPvttxGmbgB47733WLJkCRMnTmTv3r3Y29tTpUoVhg4dSq9evSK0NZlMTJkyhaVLl7J27VpWr16No6Mj+fLlo0uXLm8VJvr160fu3LlZvHgxGzZswGQyUbJkSQYOHEixYsUita9fvz47dux467mvYuvff/8Fwgb1//jjj1G2ad68uQKWSCyYzFGt1yAikkA9f/6csmXL4urqyq+//mrtct7KxIkTmT17Njt37iRnzpzRes7w4cNZt24d69evj7fFnsNNnTqVadOmMX36dIUukTfQGCwRESu4d+8ea9asoVy5ctEOVyKSeOgSoYhIPNq4cSOLFi3ixo0beHt7x2jy1pctX76cjBkzRrlMkaW5u7tz4cKFV87kLyKRKWCJiMSjLFmycPv2bRwdHRk6dGiE9QhjYuXKlUDUyxRZmru7O+vWrYvTc4gkNRqDJSIiImJhGoMlIiIiYmEKWCIiIiIWpoAlIiIiYmEKWCIiIiIWpoAlIiIiYmEKWCIiIiIWpoAlIiIiYmEKWCIiIiIW9n+OY5cGb4hChAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the aperiodic component on a linear-log scale\n",
    "plt.plot(freqs, psd_aperiodic[1, :], 'k', lw=2)\n",
    "plt.xlim(1, 30)\n",
    "plt.yscale('log')\n",
    "sns.despine()\n",
    "plt.title('Aperiodic component, chan = ' + chan[1])\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.ylabel('PSD log($uV^2$/Hz)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the oscillatory component on a linear-linear scale\n",
    "plt.plot(freqs, psd_osc[1, :], 'k', lw=2)\n",
    "plt.xlim(1, 30)\n",
    "sns.despine()\n",
    "plt.title('Oscillatory component, chan = ' + chan[1])\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.ylabel('PSD log($uV^2$/Hz)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot the oscillatory + aperiodic component on a linear-log scale\n",
    "# psd_combined = psd_aperiodic[1, :] + psd_osc[1, :]\n",
    "# plt.plot(freqs, psd_combined, 'k', lw=2)\n",
    "# plt.fill_between(freqs, psd_combined, cmap='Spectral')\n",
    "# plt.xlim(1, 30)\n",
    "# plt.yscale('log')\n",
    "# sns.despine()\n",
    "# plt.title('Aperiodic + oscillatory component, chan = ' + chan[1])\n",
    "# plt.xlabel('Frequency [Hz]')\n",
    "# plt.ylabel('PSD log($uV^2$/Hz)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit the fractal component (1/f)\n",
    "\n",
    "If `return_fit=True` (default), `yasa.irasa` [fits an exponential function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html) to the aperiodic power spectrum and return the fit parameters (intercept, slope), the $R^2$ of the fit, and the standard deviation of the oscillatory component.\n",
    "\n",
    "The aperiodic signal, $L$, is modeled using an exponential function in semilog-power space (linear frequencies and log PSD) as:\n",
    "\n",
    "$L = a + log(F^b)$\n",
    "\n",
    "where $a$ is the intercept, $b$ is the slope, and $F$ the vector of input frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "28-Dec-24 14:10:29 | WARNING | The evaluated frequency range ends after the resampled Nyquist frequency (52.63Hz). Decrease the upper band (30.00Hz) or decrease the maximum value of the hset (1.90).\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chan</th>\n",
       "      <th>Intercept</th>\n",
       "      <th>Slope</th>\n",
       "      <th>R^2</th>\n",
       "      <th>std(osc)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>F4-A1</td>\n",
       "      <td>3.351799</td>\n",
       "      <td>-1.297857</td>\n",
       "      <td>0.961306</td>\n",
       "      <td>1.012285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>CZ-A2</td>\n",
       "      <td>3.272062</td>\n",
       "      <td>-1.192108</td>\n",
       "      <td>0.855980</td>\n",
       "      <td>4.525508</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Chan  Intercept     Slope       R^2  std(osc)\n",
       "0  F4-A1   3.351799 -1.297857  0.961306  1.012285\n",
       "1  CZ-A2   3.272062 -1.192108  0.855980  4.525508"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs, psd_aperiodic, psd_osc, fit_params = yasa.irasa(data, sf, ch_names=chan)\n",
    "fit_params"
   ]
  }
 ],
 "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": "3.11.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}