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@ihrke
Created June 24, 2025 08:44
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Frequency spectrum of the accumulated tonic responses
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Frequency spectrum of the accumulated tonic responses \n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/home/mmi041/Dropbox/work/projects/pupil/pupil_algorithm/pypillometry/pypillometry\n"
]
}
],
"source": [
"import sys\n",
"sys.path.insert(0, \"../pypillometry\")\n",
"import pypillometry as pp\n",
"import numpy as np\n",
"import pylab as plt\n",
"print(pp.__package_path__)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"T=1000 # in seconds\n",
"fs=200 # in Hz\n",
"N=T*fs # in samples \n",
"tx = np.linspace(0,T,N)\n",
"\n",
"\n",
"def get_acc_pupil_response(mean_onset_diff, sd_onset_diff, T=T, fs=fs):\n",
" # Generate intervals between onsets\n",
" intervals = np.random.normal(mean_onset_diff, sd_onset_diff, size=int(T/mean_onset_diff))\n",
" # Ensure intervals are positive\n",
" intervals = np.maximum(intervals, 0.1) # Set minimum interval to 0.1s\n",
"\n",
" # Convert intervals to absolute onset times\n",
" event_onsets = np.cumsum(intervals)\n",
" # Remove any onsets that would exceed the total time T\n",
" event_onsets = event_onsets[event_onsets < T]\n",
"\n",
"\n",
" X = pp.pupil.pupil_build_design_matrix(tx, event_onsets, fs, npar=10.1, tmax=930)\n",
" sy = np.mean(X, axis=0)\n",
" return sy\n",
"\n",
"def plot_psd(sy, fs=fs, max_freq=5):\n",
" # Calculate power spectrum using FFT\n",
" freqs = np.fft.fftfreq(len(sy), d=1/fs)\n",
" power = np.abs(np.fft.fft(sy))**2\n",
"\n",
" # Convert power to dB\n",
" power_db = 10 * np.log10(power)\n",
"\n",
" # Plot only positive frequencies up to 10 Hz\n",
" mask = (freqs >= 0) & (freqs <= max_freq)\n",
" plt.plot(freqs[mask], power_db[mask])\n",
" plt.xlabel('Frequency (Hz)')\n",
" plt.ylabel('Power (dB)')\n",
" plt.grid(True)\n",
"\n",
"\n",
"def plot_psd_welch(sy, fs=fs, max_freq=5, nperseg=None, noverlap=None):\n",
" \"\"\"\n",
" Plot power spectral density using Welch's method - equivalent to plot_psd but with reduced noise.\n",
" \n",
" This function has the same interface as plot_psd() but uses Welch's method instead of raw FFT.\n",
" Welch's method reduces noise by segmenting the signal and averaging periodograms.\n",
" \n",
" Parameters:\n",
" -----------\n",
" sy : array_like\n",
" Input signal\n",
" fs : float\n",
" Sampling frequency (default: global fs)\n",
" max_freq : float\n",
" Maximum frequency to plot in Hz (default: 5)\n",
" nperseg : int, optional\n",
" Length of each segment for Welch method. If None, uses len(sy)//8\n",
" noverlap : int, optional\n",
" Number of points to overlap between segments. If None, uses nperseg//2\n",
" \"\"\"\n",
" from scipy.signal import welch\n",
" \n",
" # Set default parameters if not provided\n",
" if nperseg is None:\n",
" nperseg = min(len(sy)//8, 2048) # Use 1/8 of signal length, max 2048 points\n",
" nperseg = max(nperseg, 256) # Minimum 256 points for good frequency resolution\n",
" \n",
" if noverlap is None:\n",
" noverlap = nperseg // 2 # 50% overlap is standard\n",
" \n",
" # Calculate power spectral density using Welch method\n",
" freqs, power = welch(sy, fs=fs, nperseg=nperseg, noverlap=noverlap)\n",
" \n",
" # Convert power to dB (same as original plot_psd)\n",
" power_db = 10 * np.log10(power + 1e-12) # Add small constant to avoid log(0)\n",
" \n",
" # Plot only positive frequencies up to max_freq (same logic as original)\n",
" mask = freqs <= max_freq\n",
" plt.plot(freqs[mask], power_db[mask])\n",
" plt.xlabel('Frequency (Hz)')\n",
" plt.ylabel('Power (dB)')\n",
" plt.grid(True)\n"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate onsets with variable spacing\n",
"mean_onset_diff = 0.7 # mean time between onsets in seconds\n",
"sd_onset_diff = 0.2 # standard deviation of time between onsets in seconds\n",
"sy = get_acc_pupil_response(mean_onset_diff, sd_onset_diff)\n",
"plot_psd_welch(sy, nperseg=5000)\n",
"plt.title(f\"Mean onset diff: {mean_onset_diff} s, SD onset diff: {sd_onset_diff} s\")\n",
"plt.savefig(f\"../revision2/pics/psd_acc_pupil_response_{mean_onset_diff}.png\")"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Dw/HWW2/hxIkT2ucvXrwIQRDw3nvvlWkDzXLw0u1QXZpYGzVqVOa50NBQvesztMDAQPTs2RPPP/881qxZg+DgYPTs2bPKHz62trYoLCwsc72goED7fEWCgoIwefJkfPfdd/Dw8EBMTAy+/vrrMp8ffTRu3BirV69GWloaTpw4gY8++ghWVlYYM2YMtm7dWu16cnJyAACOjo4VltH8m5b379ekSZMyn08bGxt4enrqXHv48/nqq6+icePG6NOnD/z8/DBy5Ehs3rxZ554LFy5g8+bNZT6fPXv2BFCzz6fm/dS2z6fm81PRZ6yqIb/ScnNz0b9/f2RnZ+Ovv/7SJsCV+eSTT3Dq1Cn4+/vjsccew6xZs6r8pY5qhnOOyOSGDh2Kl19+GcnJyejTp4/OPIjS1Go1vLy8sGbNmnKf1/zHnpmZiS5dusDJyQlz5szR7ilz9OhRTJ06FWq1Wuc+mUxWbn1CNffReTixqkh1Xqdz5864dOkS/vrrL8TFxeG7777D559/jqVLl2L06NHa2N98803ExMSUW9/DyZo5GjRoEL799lvs3LmzwnYAAF9f33J70pKSkgCUzA2pzMKFCxEbG6v995g4cSLmzZuH/fv3VzkXqzIymQzh4eEIDw9HVFQUunXrhjVr1mgTiKqcOnUKgGH/rSv6fJbm5eWFhIQEbNmyBf/88w/++ecfrFixAsOGDcOqVasAlHyf9urVq8Kej8aNGxssZrH5+voCKPk8PTx3LSkpSaeXqzJFRUV4+umnceLECWzZsgXNmzev1n1DhgxBp06dsG7dOsTFxWHBggWYP38+/vzzzyrnS5J+mByRyT311FMYO3Ys9u/fj19//bXCcg0bNsTWrVvRoUOHSn8j27FjB9LT0/Hnn3+ic+fO2utXrlwxaNyBgYFQq9W4cOGCzkTnlJQUZGZmIjAwsEb1urm5YcSIERgxYgRycnLQuXNnzJo1C6NHj0ZwcDAAQC6XV/mDtLpJm+a9ACh3OO/cuXN6RG8amh6jqnpxIiIisH37dmRlZelMyj5w4ID2+apokph3330Xe/fuRYcOHbB06VJ8+OGHNX8DpWgm82oStqqoVCr8/PPPsLOzQ8eOHSssp/k3PXfuXJkJ4OfOnavx59Pa2hoDBgzAgAEDoFar8eqrr2LZsmV47733EBISgoYNGyInJ8egn0+g5P3Uts+n5vNz+PBhnUTo9u3buHnzJsaMGVNlHWq1GsOGDcO///6L3377DV26dNErBl9fX7z66qt49dVXkZqailatWmHu3LlMjgyMw2pkcg4ODvjmm28wa9YsDBgwoMJyQ4YMgUqlwgcffFDmueLiYu2xFJrfgEv3yBQVFWHJkiUGjbtv374AoD2GQOOzzz4DgEpXEVUkPT1d57GDgwNCQkK03fZeXl7o2rUrli1bVu4P0zt37mj/rtmJujrHdfj6+iIiIgKrVq3SSTji4+Nx5swZvd9HVS5duoRLly5VWa70+ynt+++/h0Qi0VmRk5aWhrNnz+rMDxo0aBBUKhWWL1+uvVZYWIgVK1agXbt2Fa5UA4CsrKwyuxyHh4dDKpWWO4xSlV27dkGpVJa5rpm7Vp3hIZVKhYkTJyIxMRETJ04sswqvtDZt2sDLywtLly7Vifeff/5BYmKiQT6fUqlUu8JM8xpDhgzBvn37sGXLljL3Z2ZmatvUzs5Oe606+vbti/379+PgwYPaa3fu3KmwJ/lRJCUl4ezZs+X+e5XWrFkzNGnSBMuXL4dKpdJe/+abbyCRSHSmCNy7dw9nz54tk9C/9tpr+PXXX7FkyRLtqr3qUKlUZery8vJCvXr1avT5pMqx54hEMXz48CrLdOnSBWPHjsW8efOQkJCA6OhoyOVyXLhwAWvXrsWiRYswaNAgtG/fHq6urhg+fDgmTpwIiUSC1atXV3uYrLpatmyJ4cOHY/ny5dqhvIMHD2LVqlUYOHAgunXrpnedYWFh6Nq1K1q3bg03NzccPnxYu1RX4+uvv0bHjh0RHh6Ol19+GcHBwUhJScG+fftw8+ZNHD9+HEDJb7UymQzz58/HvXv3oFAo0L17d3h5eZX72vPmzUO/fv3QsWNHjBw5EhkZGfjqq6/QrFkz7RwXQ6nuUv65c+diz5496N27NwICApCRkYE//vgDhw4dwmuvvaYzrLR48WLMnj0b27dv156r1a5dOwwePBjTp09HamoqQkJCsGrVKly9ehXff/99pa+9bds2TJgwAYMHD0bjxo1RXFyM1atXQyaT4ZlnntGWmzVrVpnXLc/8+fNx5MgRPP3009qE4ujRo/jxxx/h5uaG119/Xaf8vXv38NNPPwEoWR5/8eJF/Pnnn7h06RKee+65cn9JKE0ul2P+/PkYMWIEunTpgueff167lL9BgwZ44403Kr2/PKNHj0ZGRga6d+8OPz8/XLt2DV999RUiIiK0vadvvfUW/v77b/Tv31+7VUVubi5OnjyJ33//HVevXoWHhwdsbW0RFhaGX3/9FY0bN4abmxuaN29e4ZDS22+/rT32Y9KkSdql/IGBgTrz8gyhukv5AWDBggV44oknEB0djeeeew6nTp3C4sWLMXr0aJ0e5XXr1mHEiBFYsWIFYmNjAZT8YrVkyRJERUXBzs5O+++t8dRTT1V43E52djb8/PwwaNAgtGzZEg4ODti6dSsOHTqEhQsXPtL7p3KIuVSOLENFy7sfVtEO2cuXLxdat24t2NraCo6OjkJ4eLjw9ttvC7dv39aW2bNnj/D4449rN3V8++23hS1btpRZ2l7Rkunq7AotCCWbQM6ePVsICgoS5HK54O/vX+kmkA97eMnxhx9+KDz22GOCi4uLYGtrKzRp0kSYO3dumc3oLl26JAwbNkzw8fER5HK5UL9+faF///7C77//rlPu22+/FYKDgwWZTFatZf1//PGH0LRpU0GhUAhhYWHV2gRSEIy3lD8uLk7o37+/UK9ePUEulwuOjo5Chw4dhBUrVghqtVqnrGZTv4ffY35+vvDmm28KPj4+gkKhENq2bSts3ry5yte+fPmyMHLkSKFhw4aCjY2N4ObmJnTr1k3YunWrTrkpU6ZUazfkPXv2COPHjxeaN28uODs7C3K5XAgICBBiY2OFS5cu6ZR9eANNBwcHoVGjRsKLL75YZkPQqvz6669CZGSkdlPRyjaBfJimTTV+//13ITo6WvDy8hKsra2FgIAAYezYsUJSUpLOfdnZ2cL06dOFkJAQwdraWvDw8BDat28vfPrppzqf5b179wqtW7cWrK2tq7Ws/8SJE0KXLl302gRSA0ZYyq+xbt06ISIiQlAoFIKfn5/w7rvvlvme1XwvrFixoszrVPRV2esXFhYKb731ltCyZUvB0dFRsLe3F1q2bCksWbKkWjGTfiSCYOBfr4mIzNhjjz2GwMBArF27VuxQiMhImBwREVVTVlYWPD09kZCQUOnu40RUtzE5IiIiIiqFq9WIiIiISmFyRERERFQKkyMiIiKiUpgcEREREZXCTSD1pFarcfv2bTg6Ouq9HT4RERGJQxAEZGdno169epBKK+8bYnKkp9u3b1d6BAERERHVXjdu3KjyIGkmR3pydHQEUNK4lZ1zVBNKpRJxcXHaYzLIONjOpsF2Ng22s+mwrU3DWO2clZUFf39/7c/xyjA50pNmKM3JyckoyZGdnR2cnJz4jWdEbGfTYDubBtvZdNjWpmHsdq7OlBhOyCYiIiIqhckRERERUSlMjoiIiIhKYXJEREREVAqTIyIiIqJSmBwRERERlcLkiIiIiKgUJkdEREREpZhVctSgQQNIJBKdr48//linzIkTJ9CpUyfY2NjA398fn3zyiUjREhERUW1kdjtkz5kzBy+//LL2celtwrOyshAdHY2ePXti6dKlOHnyJEaOHAkXFxeMGTNGjHCJiIioljG75MjR0RE+Pj7lPrdmzRoUFRXhhx9+gLW1NZo1a4aEhAR89tlnTI6IiIgIgBkmRx9//DE++OADBAQEYOjQoXjjjTdgZVXyNvft24fOnTvD2tpaWz4mJgbz58/H3bt34erqWqa+wsJCFBYWah9nZWUBKDn7RalUGjR2TX2Grpd0sZ1Ng+1sGmxn02Fbm4ax2lmf+swqOZo4cSJatWoFNzc37N27F9OnT0dSUhI+++wzAEBycjKCgoJ07vH29tY+V15yNG/ePMyePbvM9bi4ONjZ2RnhXQDx8fFGqbc8KjUgkQDSqs/hMzumbGdLxnY2Dbaz6bCtTcPQ7ZyXl1ftshJBEASDvrqBTZs2DfPnz6+0TGJiIpo0aVLm+g8//ICxY8ciJycHCoUC0dHRCAoKwrJly7Rlzpw5g2bNmuHMmTNo2rRpmTrK6zny9/dHWloanJycHuGdlaVUKhEfH49evXqZ5MTntJxCRC/ag8cauOKboRHVOqnYHJi6nS0V29k02M6mw7Y2DWO1c1ZWFjw8PHDv3r0qf37X+p6jKVOmIDY2ttIywcHB5V5v164diouLcfXqVYSGhsLHxwcpKSk6ZTSPK5qnpFAooFAoylyXy+VG++YwZt2lnU25i+yCYvx79g72XMlEt1Avo79mbWKqdrZ0bGfTYDubDtvaNAzdzvrUVeuTI09PT3h6etbo3oSEBEilUnh5lfzQj4qKwowZM6BUKrWNFB8fj9DQ0HKH1MxdWs6DHrFPt5xDl0aekFri+BoREVEpZrPP0b59+/DFF1/g+PHjuHz5MtasWYM33ngDL774ojbxGTp0KKytrTFq1CicPn0av/76KxYtWoTJkyeLHL04MnKLtH8/fTsLm04liRgNERFR7VDre46qS6FQ4H//+x9mzZqFwsJCBAUF4Y033tBJfJydnREXF4fx48ejdevW8PDwwPvvv2+xy/jT7ydHDgor5BQW47O48+jdzAdWMrPJmYmIiPRmNslRq1atsH///irLtWjRArt27TJBRLWfZlgttn0DrDlwDZfTcvHn0VsY0tZf5MiIiIjEwy4CC6YZVgtwt8OrXUMAAF9sPY/CYpWYYREREYmKyZEFS88pSY48HKzxUlQgfJxscPteAf7vOOceERGR5WJyZMHS7w+rudkrYCOXoWdYyaq+6+m5YoZFREQkKiZHFkoQBKTdH1Zzty85TsXVruTPzHxujU9ERJaLyZGFyi1SoahYDQBwdyhJilzuJ0d385gcERGR5WJyZKE0Q2q2chnsrEsWLbrYlmyMmZlXVOF9RERE5o7JkYVKuz8ZW9NrBAAudiXJ0T0OqxERkQVjcmShNMv43R0enBv3YFiNPUdERGS5mBxZKM2wmmYyNvCg5yiTc46IiMiCMTmyUOkPrVQDHsw5yi4oRrFKLUpcREREYmNyZKHSc8oOqznfT44AzjsiIiLLxeTIQqXnlh1Ws5JJ4WhTsnKNex0REZGlYnJkodLLWa0GlNoIkpOyiYjIQjE5slDp5axWAzgpm4iIiMmRhSpvtRrwYN4RkyMiIrJUTI4skCAIpfY5Kn9YjXsdERGRpWJyZIGy8otRrBYAAG4P9Rxxl2wiIrJ0TI4sUNr9lWqOCisorGQ6z2n2OmLPERERWSomRxaoopVqwIMjRDjniIiILBWTIwuUodnj6KGVagCH1YiIiJgcWaC0+z1HD883Ajghm4iIiMmRBdIMq3mUM6zmzH2OiIjIwjE5skAPjg4pZ1jt/oTse0yOiIjIQjE5skCa3bErG1bLLiyGUqU2eiyCICCvqNjor0NERFRdTI4skHZ37HKG1Zzu9xwBxp+UrVILGLv6CCJmx+Niao5RX4uIiKi6mBxZoAdzjsoOq8mkEjjZWAEw/uGzi7ddRNyZFBSp1Nh3Od2or0VERFRdTI4sUEYlw2oA4Gpv/L2Odl9Iwxf/ntc+vnyHPUdERFQ7MDmyMCq1gIy8ijeBBB5MyjZWcpR8rwCT/ncMggD4OtsAAK6k5RrltYiIiPTF5MjC3M0rglByrBrc7CpIjoy415FSpcaEn48iPbcIYb5O+PiZFgCAy3eYHBERUe1gJXYAZFqaITUXOzmsZOXnxsbcJXvL6WQcvnYXjgorfPNiK9jKS852u3k3D4XFqjJnvREREZkae44sTJpmpVoF840A4w6rXUgpmVvUv6UvAt3t4emogIPCCmoBuJGRZ/DXIyIi0heTIwvz4NDZsivVNIw5rHbjbkkC5O9mBwCQSCQI8rAHAFzi0BoREdUCTI4sjGZYrdKeI80RIkYYVtP0Dvm72mmvBXuWJEeclE1ERLUBkyMLU9kGkBqaXbKNsc/RjYx8AA96jgBoe464nJ+IiGoDJkcWJk3bc1TxsJqxDp8tUKqQkl0AAPB3tdVe1yRH7DkiIqLagMmRhcnIqXyPI8B4E7JvZeZDEAB7a5nOBpQNPR0AcDk/ERHVDkyOLEx6rma1WsU9R8YaVtPON3Kzg0Qi0V5vcL/nKD23CPeMuCs3ERFRdZhdcrRx40a0a9cOtra2cHV1xcCBA3Wev379Ovr16wc7Ozt4eXnhrbfeQnGx5ZwKr1mtVtHRIcCDCdm5RSoUFasN9to37pbMN/IrNRkbABwUVvB2KknWrqSz94iIiMRlVptA/vHHH3j55Zfx0UcfoXv37iguLsapU6e0z6tUKvTr1w8+Pj7Yu3cvkpKSMGzYMMjlcnz00UciRm46VR0dAgCONnJIJIAglGwE6elYcS+TPjQ9RwFudmWeC/KwR0pWIS7fyUGEv4tBXo+IiKgmzCY5Ki4uxqRJk7BgwQKMGjVKez0sLEz797i4OJw5cwZbt26Ft7c3IiIi8MEHH2Dq1KmYNWsWrK0rThjMQbFKrd312rWCo0MAQCaVwNlWjsw8JTLzigyeHPm72ZZ5LtjTAfsvZ3BSNhERic5skqOjR4/i1q1bkEqliIyMRHJyMiIiIrBgwQI0b94cALBv3z6Eh4fD29tbe19MTAzGjRuH06dPIzIysky9hYWFKCws1D7OysoCACiVSiiVhp0fo6nP0PVqpOc+OFfNXl756zjblCRHadn5aOBmY5DXv55Rkvj4OlmXee1A15LXuJiSbbT3r2HsdqYSbGfTYDubDtvaNIzVzvrUZzbJ0eXLlwEAs2bNwmeffYYGDRpg4cKF6Nq1K86fPw83NzckJyfrJEYAtI+Tk5PLrXfevHmYPXt2metxcXGwsys7PGQI8fHxRqk3OQ8ArGAnExC/ZXPlhYtkACT4d9d+pJ4WDPL6l1NK6rxy6jA2XdZ9Lu2uBIAMJ64kY9OmWwZ5vaoYq51JF9vZNNjOpsO2Ng1Dt3NeXvWPqKr1ydG0adMwf/78SsskJiZCrS6ZODxjxgw888wzAIAVK1bAz88Pa9euxdixY2v0+tOnT8fkyZO1j7OysuDv74/o6Gg4OTnVqM6KKJVKxMfHo1evXpDL5QatGwAOXb0LHD8ELxd79O3bsdKyf6YdxbULaWgY1gJ9W9V/5NfOylcif992AMDQJ6JhZ6370QtLz8W3Z/cgXSlD797RkEol5VVjEMZuZyrBdjYNtrPpsK1Nw1jtrBn5qY5anxxNmTIFsbGxlZYJDg5GUlISAN05RgqFAsHBwbh+/ToAwMfHBwcPHtS5NyUlRftceRQKBRSKsnNu5HK50b45jFV3VmFJAulmb11l/a73V7PlFKoNEktSaknG7uFgDWf7snOOGng6wUoqQYFSjfR8Feq5lC1jaMb8N6QH2M6mwXY2Hba1aRi6nfWpq9YnR56envD09KyyXOvWraFQKHDu3Dl07FjSK6JUKnH16lUEBgYCAKKiojB37lykpqbCy8sLQEm3nZOTk05SZa40B8lWtoxfw9CHz2omYz+8jF9DLpMiwN0Ol+/k4vKdXJMkR0REROUxm32OnJyc8Morr2DmzJmIi4vDuXPnMG7cOADA4MGDAQDR0dEICwvDSy+9hOPHj2PLli149913MX78+HJ7h8yN5tDZylaqaRj68Nkbdytexq8RrD1GhGesERGReGp9z5E+FixYACsrK7z00kvIz89Hu3btsG3bNri6ugIAZDIZNmzYgHHjxiEqKgr29vYYPnw45syZI3LkpqFJjqrVc3T/CBFD7Vj94MDZinuEtAfQcjk/ERGJyKySI7lcjk8//RSffvpphWUCAwOxadMmE0ZVe9zVIznSzDky1LDadc0eRxUMqwElex0BPGONiIjEZTbDalQ1ze7YrtVIjpwNfPisZljNv5JhtQc9RxxWIyIi8TA5siDanqNqzDky5OGzarWAm/fPVavOnKNbd/MNeqYbERGRPpgcWRB9eo4MOSE7NbsQRcVqyKQS+DpXvNu2p6MCtnIZ1AJw8271N+siIiIyJCZHFuRubkmiU70J2SVl8opUKCxWPdLraobUfJ1tYCWr+CMnkUgQ6F7Ss3QtnckRERGJg8mRhSgsViGnsBhA9YbVnGytYCuXAYB2SKymNHscVTakptHAvWRo7Wo6J2UTEZE4mBxZCE2vkUwqgaNN1YsUJRIJQrxKVo9dTH20CdLVWammEejBniMiIhIXkyMLUXoDyOqeW9bIQMlRdfY40mDPERERiY3JkYV4cHRI9c+WCfEuSY4upGQ/0mtXZxm/BuccERGR2JgcWQh9jg7RaOTlCAC48Mg9R9VPjjQ9Rzcy8lCs4nJ+IiIyPSZHFkKfQ2c1Sg+rqdRCjV43t7AYyVkFAIDAaiRHPk42sLaSolgt4HZmQY1ek4iI6FEwObIQ2p4jPZIjfzc7WFtJUVisxq0arlhLTMqCIADeTgq4O1R9uK9UKtEmUZx3REREYmByZCH02R1bQyaVaHetvpBas3lHp29nAQCa13Ou9j2B94fWrjE5IiIiETA5shAZ989I06fnCAAaeT/avKNTt+4BAJrVr35y1MBd03PESdlERGR6TI4shKbnyF3f5OgRl/Of0vYcOVX7nkAP9hwREZF4mBxZiPQazDkCHiRHNek5KlCqtNsANGfPERER1RFMjixETeYcAUCj+3sdXUzJhiDot2LtfEo2itUC3OytKz1w9mGa5fzX0/NqvEqOiIioppgcWQBBEJCRp+k5qv4mkEDJ5GgrqQS5RSok3dNvaf2pWyVDas3qOUEiqd6u3EDJAbVymQRFKjWS7j3auW5ERET6YnJkAfKKVCgqLtlQUZ99jgBALpMiSLtiTb+htVO3SyZj6zOkBgBWMqn2HDZj7JR9/OY9HE+vfrJGRESWhcmRBdDscaSwksJWLtP7fs0BtPoeI3L6/ko1fZbxawS6G2evo5M37+GF7w/hh/Mybc8WERFRaUyOLEDp3bH1Gd7SqMmKNaVKjcRkzWTs6q9U03iw15Hheo7ScgoxdvVhFN7vRfvndLLB6iYiIvPB5MgCaHqO9B1S0wipwV5HF1NzUFSshqONFQKqcWzIw7Qr1tIM03OkVKkxfs1R3L5XAFt5ycd+y+lUvSeZExGR+WNyZAFqcq5aaaV7jqqbTGg3f9RzMrbGg72ODNNz9NGmRBy4kgF7axl+GtkWVhIB1zLycDa5Zjt/ExGR+WJyZAHSc+6vVNNzGb9GkIc9pBLgXr4Sd3IKq3VPTY4N0XlNzbBaRi7Uj7icP+50MlbsuQoA+OzZCLTwc0YTl5I6/znFoTUiItLF5MgCPGrPkY1cpp0DdDGlekNrmp4jfVeqadR3tYVMKkGBUo3U7OolZBX54+hNAEBs+waIaeYDAGjpXpIcbT6V9Eh1ExGR+WFyZAEycu+fq1bDniOg1Iq1asw7UqkFnEm633NUg8nYQMkWAn6utgAebcVasUqNvZfSAQBPRtTTXm/uKkAuk+B8Sg4u3anZ0ShERGSemBxZAO3u2HpuAFmaJjlKTKp6+fuVtFzkFalgK5chyMOhxq/5YMVazZOjE7fuIbugGE42Vmjh56K9bmcFRAW7AQA2c2iNiIhKYXJkAR7sjl3znqO2DVwBAOuO3cKNjMonSZ++v/ljWD0nyKQ132wx6P6KtUfZj2j3hTQAQIcQjzKxxIR5AwD+4dAaERGVwuTIAtx9xKX8ANAt1AuPB7uhsFiNORvOVFr20NUMAEDzejUbUtPoGuoFANh0MglKlbpGdey6cAcA0LGRR5nnejT1glRSknxVlfAREZHlYHJkAR51QjYASCQSzHmyOaykEsSfScG2synllkvNKsDawyUToLs39a7x6wElCY27vTXSc4uw+2Ka3vfnFBbj2PVMAECnEM8yz7vbW6NdkDsADq0REdEDTI7MnFot4G5eyYRst0eYkA0Ajb0dMbJjEABg1t9nUKBUlSmzZMclFBar0SrABZ3L6a3Rh1wmxYCWJZOo1x29pff9+y+lo1gtIMDNDgHu5W9E2Se8ZPVafGL5yR4REVkeJkdmLqtACdX9fYJcHjE5AoCJPRrB20mB6xl5WPbfZZ3nbmfm4+cD1wEAU6JDa7T548OeiqwPAIg7k4ycwmK97tX0NnWqJElr37Ck5+jkzXsoruHQHRERmRcmR2ZOc3SIo8IK1laP/s/toLDCu/3CAABLdlzEnlLDXYu3X0SRSo12QW7apONRtfBzRrCHPQqUamzRc+hr5/35RpUlR8EeDrC3liFfqcKlO4Y95JaIiOomJkdm7q4BVqo9rH8LX3Rp7InCYjVe+v4Aluy4iOvpefjt0A0Ahus1AkrmOg2833u0PqH6Q2u3M/Nx+U4upBIgqmHFyZFUKtFuVHn8ZuYjxUpEROaByZGZ024AacDkSCKRYNlLrTG4tR/UAvDJ5nN48uvdKFYL6NTIA48FuRnstQBgYERJcrTnYhpSsgqqdY9mCX8LPxc421a+v1NLfxcAJUNrRERETI7MnGYZv7sBkyOg5EiRTwa1wLynw2Etk2onfU/u1digrwMAAe52aB3oCrUA/N/x29W6Z1c15htphN/vOTrBniMiIgKTI7OXfL+nxdDJEVDSg/T8YwH4fVwUWgW4YHTHIEQGuBr8dYAHE7PXHat6aE2tFrRzoTo1KruE/2Et7++cnZiUjaJiTsomIrJ0TI7M3Nnkkt2lG3nX/BiPqrTwc8Gfr3bAu/3DjPYa/cJ9IZdJcPp2Fo5cu1tp2d0X05CRWwQHhRUiA1yqrNvfzRYudnIUqdQ4l5xtoIiJiKiuMpvkaMeOHZBIJOV+HTp0SFvuxIkT6NSpE2xsbODv749PPvlExKiN72xSyQ/7pr6Ptlu12FztrbW9R5/Hn6+07Le7SrYYGNTaD3JZ1R9xiUTyYGjtVuajBUpERHWe2SRH7du3R1JSks7X6NGjERQUhDZt2gAAsrKyEB0djcDAQBw5cgQLFizArFmzsHz5cpGjN468omJcuX9oaxOfup0cAcBr3RtBLpNg98U07L+cXm6Zs8lZ2HUhDVIJMOr+hpXV0cLvfnJ0g5OyiYgsndkkR9bW1vDx8dF+ubu746+//sKIESO0y8rXrFmDoqIi/PDDD2jWrBmee+45TJw4EZ999pnI0RvH+ZQcCALg4aCAp6NC7HAemb+bHZ5t6w8A+CzuPARBKFPmu11XAAC9m/vA3638XbHL0+L+vKMTt5gcERFZOrNJjh72999/Iz09HSNGjNBe27dvHzp37gxr6weTk2NiYnDu3DncvVv5PJa6KDGpZL5RU19HkSMxnAndGsHaSoqDVzPKnLeWmlWAv+7vhTS6U7Be9Wp6js6nZCO/qOyxKEREZDmsxA7AWL7//nvExMTAz89Pey05ORlBQbpDLd7e3trnXF3LrrQqLCxEYWGh9nFWVknCoVQqoVQqDRqzpj5D1Xvm/vyZxl72Bo9VLO52Mjzf1g+r9l3Hgi1n0S7QWdszuGLPZShVAloFuCDc16HC91xeO7vbyuDpYI07OUU4eSOjWhO5qXKG/jxT+djOpsO2Ng1jtbM+9dX65GjatGmYP39+pWUSExPRpEkT7eObN29iy5Yt+O233x759efNm4fZs2eXuR4XFwc7u+oP2+gjPj7eIPXsPSMDIEFhymVs2nTJIHXWBiFFgLVUhhM3szBjxWa08RAgkQCrjpa835Y26di0aVOV9Tzczl5yKe5Aiv/F70OSb9khO6oZQ32eqXJsZ9NhW5uGods5Ly+v2mVrfXI0ZcoUxMbGVlomOFh3CGXFihVwd3fHE088oXPdx8cHKSm6p69rHvv4+JRb9/Tp0zF58mTt46ysLPj7+yM6OhpOToad5KxUKhEfH49evXpBLq98V+eqCIKAd49tB1CMZ2M6oomP+QytAcB12/P4dvdVrL0iwx9XAR8nG+QVF8Df1RZTX+gImbTi40sqaudLtpdwetslqJ390LdvuAnehXkz5OeZKsZ2Nh22tWkYq501Iz/VUeuTI09PT3h6Vr2Rn4YgCFixYgWGDRtWplGjoqIwY8YMKJVK7XPx8fEIDQ0td0gNABQKBRSKspOZ5XK50b45DFH3zbt5yC4ohlwmQaivC+QGOHS2Nnm9VygKigVsP5eKm3fzcfteyWaXozsFw0ZRvQ0vH27nyAA3AJdw8nYW/+MzIGN+r9ADbGfTYVubhqHbWZ+6an1ypK9t27bhypUrGD16dJnnhg4ditmzZ2PUqFGYOnUqTp06hUWLFuHzzz8XIVLj0uxv1NDTAdZmlhgBgL3CCh8MbA4ASMkqwJFrd5FdoMSg1v41rjP8/qTsy2m5yC5QwtGG//kREVkis0uOvv/+e7Rv315nDpKGs7Mz4uLiMH78eLRu3RoeHh54//33MWbMGBEiNa4HK9Xq/v5GVfF2skHfcN9HrsfDQYH6Lra4lZmPU7eyENXQ3QDRERFRXWN2ydHPP/9c6fMtWrTArl27TBSNeM4ma3bGNq+5RsYW4e+CW5n52H85nckREZGFMr/xFgLwoOfIHHbGNqUujUvmt+04f0fkSIiISCxMjsxQfpFKe2yIJQyrGVKX0JLk6MTNTKTlFFZRmoiIzBGTIzN0LiX7/rEh1mZxbIgpeTvZoFk9JwgCsJO9R0REFonJkRk6a0GTsY2hW6gXAGD7OSZHRESWiMmRGXow34iTsWuiW5OSobX/zqWiWKUWORoiIjI1JkdmKFG7Uo09RzUR4e8KFzs5sgqKcexGptjhEBGRiTE5MjOCIGiH1bhSrWZkUol21dr2s6kiR0NERKbG5MjMJNzIRFZBMWzkUoR4OYgdTp3FeUdERJaLyZGZ+e3wTQBA3+a+ZnlsiKl0buwJiaRk/lby/XPbiIjIMvCnpxnJL1Lh/47fBgAMblPzM8YIcLO3RoS/CwBgxzkOrRERWRImR2bkn1NJyCksRoCbHdoFuYkdTp3XXTu0xuSIiMiSMDkyI78dvgEAGNzaD1KpRORo6r5uTUqSo10X0nA3t0jkaIiIyFSYHJmJa+m52H85AxIJ8ExrP7HDMQvN6jkhzNcJeUUqfPPfJbHDISIiE2FyZCZ+P1IyEbtTI0/Uc7EVORrzIJFI8FZMKABg1d6rnJhNRGQhmByZAZVa0CZHQ9qw18iQuoZ6om0DVxQWq/Hltgtih0NERCbA5MgM7L6YhqR7BXCxk6NXmLfY4ZiVkt6jJgCA3w7dwNW0XJEjIiIiY2NyZAbW7L8GABgYUR8KK5nI0Zifx4Lc0DXUE8VqAZ/Fn9f7fkEQcPr2PdzIyDNCdEREZGhWYgdAj+Z8SjbizqRAIgFefDxA7HDM1pvRodhx7g7+Pn4br3RpiLB6VR/NcurWPWw4kYSNJ2/jRkY+HG2ssOPNrnB3UJggYiIiqin2HNVxX2+/CADo3cwHIV6OIkdjvprXd0b/Fr4AgDkbTkMQhErLz998Fv2/2o2l/13CjYx8AEB2QTG+233F6LESEdGjYXJUh11Ny9XuiD2+W4jI0Zi/qb2bQGElxf7LGVh37FaF5Q5eycA3O0qW/vdp7oOvh7bCV89HAgB+3HuVeyYREdVyTI7qsKX/XYJaALqFeqJ5fWexwzF7/m52mNijEQBg7sZEZOaVTXIKlCpM/eMEAODZNv745sXW6NfCF/1b+CLM1wm5RSp8z94jIqJajclRHXU7Mx9/HC1Zvj+heyORo7EcL3cKRiMvB6TnFmH+5nNlnv88/jyupOXC20mBd/o11V6XSCTaxGrl3qu4l6c0WcxERKQfJkd11PKdl6FUCYgKdkfrQFexw7EY1lZSfDiwOQDgl4PXceRahva54zcy8e2uywCAj54Kh7OtXOfe6DBvNPFxRE5hMX7Yw94jIqLaislRHZR8rwC/HLwOAJjQnXONTK1dsDsG3z+i5fVfE/Dm2uOY9scJTPzfMagF4MmIeujRtOx+U1KpBK/d7+X7Yc8V3Mtn7xERUW3E5KiOUasFvLn2OAqL1Wgd6Ir2Dd3FDskiTe/bFK52ctzIyMfvR27if4du4Fp6HtztrTFzQLMK7+vT3AeNvByQXVCM1fuumi5gIiKqNu5zVMcs33UZuy+mwVYuw/xnWkAikYgdkkVys7fGL2Mex+4LaShWC1Dd/+rZ1Btu9tYV3ieVSvBKl4aYsvY4fjt8E+O7hfDfkIiolmFyVIck3MjEp1tKJgHPHBCGEC8HkSOybE18nNDEp+rNIB/WJ9wH7/11Ctcz8nDsRiZaBXDOGBFRbcJhtToiu0CJSf87hmK1gL7hPni2rb/YIVEN2VlbIfr+GXjrK9kviYiIxMHkqBa7kZGH/zt+Gx9tSsTgpftwLT0P9V1sMe8pDqfVdQMj6wMANpxIglKlFjkaIiIqjcNqtVDSvQLMjzuJjSeSdK5bW0nxxXMRcLaTV3An1RUdQzzg4WCNtJwi7LpwB92blF3dRkRE4mByVIsoVWpsuy3B9C/3IK9IBakECK/vjHA/Z7Twc0H7hu7wc7UTO0wyACuZFP1b1MPKvVex/thtJkdERLWI3snRlStXsGvXLly7dg15eXnw9PREZGQkoqKiYGNjY4wYLcLZ5CxMWHMUF+/IAKjQKsAFHwxsjmb1eCyIuRoYWR8r915F3Jlk5BQWw0HB31WIiGqDav9vvGbNGixatAiHDx+Gt7c36tWrB1tbW2RkZODSpUuwsbHBCy+8gKlTpyIwMNCYMZsld3sFkrMKYW8l4N0BzfFs20BIpZxXZM5a+jkjyMMeV9JyEXc6GU+38hM7JCIiQjUnZEdGRuLLL79EbGwsrl27hqSkJBw5cgS7d+/GmTNnkJWVhb/++gtqtRpt2rTB2rVrjR232fF0VOCboRGYEaHCoFb1mRhZAIlEgicj6gEA1nHVGhFRrVGt5Ojjjz/GgQMH8Oqrr8Lfv+wScoVCga5du2Lp0qU4e/YsgoODDR6oJXg82A32nGttUQZGlKxa23MxDanZBSJHQ0REQDWTo5iYmGpX6O7ujtatW9c4ICJL0sDDHhH+LlALwN8Jt8UOh4iI8Ij7HAmCgG3btmHjxo24e/euoWIisijPtCrpPfrjKIfWiIhqg2onR5mZmRg+fDjCw8Px8ssvIysrC506dULPnj0xYMAANG3aFCdOnDBmrERmaUDLepDLJEhMysKZ21lih0NEZPGqnRy9+eab2LdvH5577jmcPHkSvXv3hkqlwr59+3DgwAE0bdoUM2bMMGasVTp//jyefPJJeHh4wMnJCR07dsT27dt1yly/fh39+vWDnZ0dvLy88NZbb6G4uFikiIkAFztr9Li/z9G6YzdFjoaIiKq9lP+ff/7Bzz//jC5duiA2Nhb+/v7Ytm0b2rVrBwCYP38+nnjiCaMFWh39+/dHo0aNsG3bNtja2uKLL75A//79cenSJfj4+EClUqFfv37w8fHB3r17kZSUhGHDhkEul+Ojjz4SNXaybE+3qo/Np5OxPuE2pvZuAisZT/YhIhJLtf8HTklJQePGjQEA9evXh42Njc7KtYCAANy5c8fwEVZTWloaLly4gGnTpqFFixZo1KgRPv74Y+Tl5eHUqVMAgLi4OJw5cwY//fQTIiIi0KdPH3zwwQf4+uuvUVRUJFrsRF1DveBmb4072YXYdTFN7HCIiCxatXuO1Go1ZDKZ9rFMJtM5/FTsg1Dd3d0RGhqKH3/8Ea1atYJCocCyZcvg5eWlXT23b98+hIeHw9v7wVENMTExGDduHE6fPo3IyMgy9RYWFqKwsFD7OCurZE6IUqmEUqk06HvQ1GfoeklXbWxnCYB+4T5Yvf86fj98Ax2DXcUO6ZHVxnY2R2xn02Fbm4ax2lmf+vQ6r+C7776Dg4MDAKC4uBgrV66Eh4cHACA7O1ufqgxOIpFg69atGDhwIBwdHSGVSuHl5YXNmzfD1bXkB01ycrJOYgRA+zg5ObnceufNm4fZs2eXuR4XFwc7O+OccxYfH2+UeklXbWtn71wAsELcqST8YXMTtmZymkhta2dzxXY2Hba1aRi6nfPy8qpdttr//QYEBODbb7/VPvbx8cHq1avLlDG0adOmYf78+ZWWSUxMRGhoKMaPHw8vLy/s2rULtra2+O677zBgwAAcOnQIvr6+NXr96dOnY/LkydrHWVlZ8Pf3R3R0NJycnGpUZ0WUSiXi4+PRq1cvyOXcDdJYams7C4KA9cl7cfFOLlT1WqBvm7p9nEhtbWdzw3Y2Hba1aRirnTUjP9VR7eTo6tWrNYnlkU2ZMgWxsbGVlgkODsa2bduwYcMG3L17V5u0LFmyBPHx8Vi1ahWmTZsGHx8fHDx4UOfelJQUACXJXnkUCgUUCkWZ63K53GjfHMasmx6oje38TGt/zN98Fn8mJOGFqCCxwzGI2tjO5ojtbDpsa9MwdDvrU1et77j39PSEp6dnleU03WVSqe4cc6lUCrVaDQCIiorC3LlzkZqaCi8vLwAl3XZOTk4ICwszcORE+nu6VX18Fn8OR67dRcKNTET4u4gdEhGRxalWcvTll19Wu8KJEyfWOJhHERUVBVdXVwwfPhzvv/8+bG1t8e233+LKlSvo168fACA6OhphYWF46aWX8MknnyA5ORnvvvsuxo8fX27vEJGpeTvZ4ImW9fHH0ZtYvvMSlrzAo3iIiEytWsnR559/rvP4zp07yMvLg4uLC4CS3bM1myqKlRx5eHhg8+bNmDFjBrp37w6lUolmzZrhr7/+QsuWLQGUrLDbsGEDxo0bh6ioKNjb22P48OGYM2eOKDETlWdM52D8cfQmNp9KxrX0XAS624sdEhGRRalWcnTlyhXt33/++WcsWbIE33//PUJDQwEA586dw8svv4yxY8caJ8pqatOmDbZs2VJpmcDAQGzatMlEERHpL9THEV1DPbHj3B18t+sKPhjYXOyQiIgsit7b8L733nv46quvtIkRAISGhuLzzz/Hu+++a9DgiCzVmM7BAIC1R24gI5cblBIRmZLeyVFSUlK5Z5GpVCrtyi8iejRRwe4Ir++MAqUaP+67KnY4REQWRe/kqEePHhg7diyOHj2qvXbkyBGMGzcOPXv2NGhwRJZKIpFoe49+3HcN+UUqkSMiIrIceidHP/zwA3x8fNCmTRvtHkCPPfYYvL298d133xkjRiKL1Ke5D/xcbZGRW4QVe69UfQMRERmE3vsceXp6YtOmTbhw4QISExMBAE2aNNEeSktEhmElk2JSj0Z46/cT+Dz+PLo29kJYPcPuyk5ERGXVeBPIRo0aoVGjRoaMhYgeMqi1H+LOpCD+TApe//UY/p7QETZyWdU3EhFRjVVrWO3jjz9Gfn5+tSo8cOAANm7c+EhBEVEJiUSCj58Oh4eDAudTcjB/81mxQyIiMnvVSo7OnDmDgIAAvPrqq/jnn39w584d7XPFxcU4ceIElixZgvbt2+PZZ5+Fo6Oj0QImsjTuDgosGNwCALBiz1XsunCnijuIiOhRVCs5+vHHH7F161YolUoMHToUPj4+sLa2hqOjIxQKBSIjI/HDDz9g2LBhOHv2LDp37mzsuIksSrdQLwyLCgQAvLn2OHILy26nQUREhlHtOUctW7bEt99+i2XLluHEiRO4du0a8vPz4eHhgYiICHh4eBgzTiKLN71PU/x3/g6upefhu11XMKkn5/wRERmD3hOypVIpIiIiEBERYYRwiKgittYyvBUTigk/H8PynZfwwuMB8HDggclERIam9z5HRCSevs19EV7fGblFKizedlHscIiIzBKTI6I6RCqVYFqfJgCANQeu4Xp6nsgRERGZHyZHRHVMhxAPdGrkAaVKwGfx58QOh4jI7NR4E0giEs/U3k2w68JurE+4DXcHBZLu5eNSai7Sc4vgbGsFFztruNjK8UREPTwZUV/scImI6hS9kiOlUglbW1skJCSgefPmxoqJiKrQvL4znmhZD38fv43vd+ueu5aWUwggFwCw60Ia2jRwQ30XWxGiJCKqm/RKjuRyOQICAqBS8YRwIrG9268pAMBeYYWGnvZo6OUAL0cFsguKkZmnxLKdl3Dseia++vcCPn6mhcjREhHVHXoPq82YMQPvvPMOVq9eDTc3N2PERETV4OVkgy+fj6zweU9HBZ75Zi/WHrmJsV0aIsjD3oTRERHVXXonR4sXL8bFixdRr149BAYGwt5e9z/co0ePGiw4Iqq51oGu6N7EC9vOpuLz+POVJlJERPSA3snRwIEDjRAGERnDlOjG2HY2Ff934jZe7dYQTXycxA6JiKjW0zs5mjlzpjHiICIjaFbPGf3CfbHxZBIWxp3Ht8PaiB0SEVGtV6N9jjIzM/Hdd99h+vTpyMjIAFAynHbr1i2DBkdEj+6NXo0hlQDxZ1Jw7PpdscMhIqr19E6OTpw4gcaNG2P+/Pn49NNPkZmZCQD4888/MX36dEPHR0SPKMTLAU9F+gEAluy4JHI0RES1n97J0eTJkxEbG4sLFy7AxsZGe71v377YuXOnQYMjIsMY17UhgJLeo4upOSJHQ0RUu+mdHB06dAhjx44tc71+/fpITk42SFBEZFghXg7o2dQbAPDdrssiR0NEVLvpnRwpFApkZWWVuX7+/Hl4enoaJCgiMryxXYIBAH8evYXU7AKRoyEiqr30To6eeOIJzJkzB0qlEgAgkUhw/fp1TJ06Fc8884zBAyQiw2gT6IrIABcUqdRYtfeq2OEQEdVaeidHCxcuRE5ODry8vJCfn48uXbogJCQEjo6OmDt3rjFiJCIDkEgkGNu5ZO7R6n3XkFNYLHJERES1k977HDk7OyM+Ph67d+/GiRMnkJOTg1atWqFnz57GiI+IDKhXmDeCPOxxJS0Xvx66gVEdg8QOiYio1tE7OSooKICNjQ06duyIjh07GiMmIjISmVSC0Z2CMGPdKXy/6zKGPhYAW2uZ2GEREdUqeg+rubi4oHPnznjvvfewbds25OfnGyMuIjKSZ1r5wdtJgdv3CjDtzxMQBEHskIiIahW9k6OtW7eid+/eOHDgAJ544gm4urqiY8eOmDFjBuLj440RIxEZkI1chkXPRUImleCvhNv4Yc9VsUMiIqpV9E6OOnbsiHfeeQdxcXHIzMzE9u3bERISgk8++QS9e/c2RoxEZGCPB7tjRt+mAICPNiVi36V0kSMiIqo99J5zBJTsabRjxw7tV2FhIfr374+uXbsaODwiMpYRHRrgxM1MrE+4jQk/H8X/vdYR9VxsxQ6LiEh0eidH9evXR35+Prp27YquXbti6tSpaNGiBSQSiTHiIyIjkUgkmPd0C5xPycGZpCzM/Ps0vh3WRuywiIhEp/ewmqenJ/Ly8pCcnIzk5GSkpKRwUjZRHWVrLcOi5yIAAP8mpuB2Jr+XiYj0To4SEhKQnJyMadOmobCwEO+88w48PDzQvn17zJgxwxgxEpERNfJ2RLsgN6gF4LfDN8QOh4hIdHonR0DJcv4nnngC77zzDqZPn45Bgwbh0KFD+Pjjjw0dn16OHj2KXr16wcXFBe7u7hgzZgxycnRPIL9+/Tr69esHOzs7eHl54a233kJxMXcKJss2tF0AAODXQzegUnNpPxFZNr2Toz///BMTJ05EixYt4O3tjXHjxiEnJwcLFy7E0aNHjRFjtdy+fRs9e/ZESEgIDhw4gM2bN+P06dOIjY3VllGpVOjXrx+Kioqwd+9erFq1CitXrsT7778vWtxEtUFMMx+42smRdK8AO86lih0OEZGo9J6Q/corr6Bz584YM2YMunTpgvDwcGPEpbcNGzZALpfj66+/hlRakvMtXboULVq0wMWLFxESEoK4uDicOXMGW7duhbe3NyIiIvDBBx9g6tSpmDVrFqytrUV+F0TisJHL8EwrP3y3+wp+OXgdPZp6ix0SEZFo9E6OUlNr52+VhYWFsLa21iZGAGBrW7Iseffu3QgJCcG+ffsQHh4Ob+8H//HHxMRg3LhxOH36NCIjI8utt7CwUPs4KysLAKBUKqFUKg36HjT1Gbpe0sV2Lt/gVvXw3e4r2HY2FdfTsuHrbPNI9bGdTYPtbDpsa9MwVjvrU1+N9jlSqVRYv349EhMTAQBhYWF48sknIZOJd0ZT9+7dMXnyZCxYsACTJk1Cbm4upk2bBgBISkoCACQnJ+skRgC0j5OTk8utd968eZg9e3aZ63FxcbCzszPkW9DiTuOmwXYuK8RJhotZEsz733b09jfM3CO2s2mwnU2HbW0ahm7nvLy8apfVOzm6ePEi+vbti1u3biE0NBRASQLh7++PjRs3omHDhvpWWalp06Zh/vz5lZZJTExEs2bNsGrVKkyePBnTp0+HTCbDxIkT4e3trdObpK/p06dj8uTJ2sdZWVnw9/dHdHQ0nJycalxveZRKJeLj49GrVy/I5XKD1k0PsJ0rVlw/CVN+P4mEbHt83rsTZNKa71/GdjYNtrPpsK1Nw1jtrBn5qQ69k6OJEyeiYcOG2L9/P9zc3AAA6enpePHFFzFx4kRs3LhR3yorNWXKFJ1J1eUJDg4GAAwdOhRDhw5FSkoK7O3tIZFI8Nlnn2mf9/HxwcGDB3XuTUlJ0T5XHoVCAYVCUea6XC432jeHMeumB9jOZfVrWR8fbjqLpHsF+PnQLYzsGPTIdbKdTYPtbDpsa9MwdDvrU5feydF///2nkxgBgLu7Oz7++GN06NBB3+qq5OnpCU9PT73u0QyV/fDDD7CxsUGvXr0AAFFRUZg7dy5SU1Ph5eUFoKTbzsnJCWFhYYYNnKgOspHLMKF7I3yw4Qw+3HgGQR726NbES+ywiIhMSu/xJoVCgezs7DLXc3JyRF/ttXjxYhw9ehTnz5/H119/jQkTJmDevHlwcXEBAERHRyMsLAwvvfQSjh8/ji1btuDdd9/F+PHjy+0dIrJEIzs0wJA2flALwISfjyIxqfpd0URE5kDv5Kh///4YM2YMDhw4AEEQIAgC9u/fj1deeQVPPPGEMWKstoMHD6JXr14IDw/H8uXLsWzZMkycOFH7vEwmw4YNGyCTyRAVFYUXX3wRw4YNw5w5c0SMmqh2kUgk+HBgOKKC3ZFbpMKolYeQmlUgdlhERCaj97Dal19+ieHDhyMqKko7fldcXIwnnngCixYtMniA+vjxxx+rLBMYGIhNmzaZIBqiusvaSoqlL7bGU9/sweU7uXh1zVGsfSWKB0wTkUXQOzlycXHBX3/9hYsXL2qX8jdt2hQhISEGD46IxONsJ8eK2Lbos2gXDl+7i21nU7k5JBFZhGoPq6nVasyfPx8dOnRA27Zt8d1336Fnz54YMGAAEyMiMxXobo+XogIBAIv+vQBB4LlrRGT+qp0czZ07F++88w4cHBxQv359LFq0COPHjzdmbERUC4zpFAxbuQwnbt7DjnN3xA6HiMjoqp0c/fjjj1iyZAm2bNmC9evX4//+7/+wZs0aqNVqY8ZHRCJzd1Boe4++YO8REVmAaidH169fR9++fbWPe/bsCYlEgtu3bxslMCKqPV7uFAwbuRTHb2Tiv/PsPSIi81bt5Ki4uBg2NroHUcrlch7AR2QBPB0VeLEd5x4RkWWo9mo1QRAQGxurs1liQUEBXnnlFdjb22uv/fnnn4aNkIhqhTFdgrF6/zUcu56J7edS0b0JV64RkXmqds/R8OHD4eXlBWdnZ+3Xiy++iHr16ulcIyLz5OVog5ceL+k9evv3E0i6ly9yRERExlHtnqMVK1YYMw4iqgMmRzfG7otpOJucjVdWH8GvY6NgI5eJHRYRkUHpfXwIEVkuO2srLH+pDVzs5Dh+8x7eXX+K84+IyOwwOSIivQS422Hx860glQC/H7mJH/ZcZYJERGaFyRER6a1jIw9M69MEAPDBhjPo9ukOfBZ3DhdTs0WOjIjo0TE5IqIaeblTMMZ2Kdn/6Gp6Hr7cdhE9P9uJmX+dEjs0IqJHwuSIiGpEIpFgep+mOPJuL3zxbAS6N/GCRAKs2ncNvx26IXZ4REQ1xuSIiB6JvcIKAyPr44fYtngzOhQA8N5fp5CYxCE2IqqbmBwRkcGM69IQ3UI9UVisxmv/O478YrEjIiLSH5MjIjIYqVSCz4ZEoL6LLa5l5OGXS1KuZCOiOofJEREZlKu9Nb5+oRXkMgmOZ0gRn5gqdkhERHphckREBhfh74JhjwcAANYnJIkcDRGRfpgcEZFRDIyoBwDYcf4O7uUrRY6GiKj6mBwRkVGEejvAx1aAUiVgy+lkscMhIqo2JkdEZBQSiQStPdQAgP87flvkaIiIqo/JEREZTSuPkpVqey6mITW7QORoiIiqh8kRERmNhw3Q0s8ZagHYdIITs4mobmByRERG1b+FDwDgLw6tEVEdweSIiIyqb3MfSCXAseuZuJGRJ3Y4RERVYnJEREbl5ahAVEN3AMDf7D0iojrASuwAiMj8PdmyPvZcTMeify/gjyM34WZvDW9nG7zRsxFCvBzFDo+ISAd7jojI6HqH+8DTUYGiYjUup+Xi8LW72HgiCbP/74zYoRERlcGeIyIyOicbOXa93Q037+YhPacItzLz8eba49h1IQ3nkrMR6sPeIyKqPdhzREQmYSOXIcTLEe2C3fF0Kz/ENCtZxfbD7isiR0ZEpIvJERGJYnSnIADAuoRbSMspFDkaIqIHmBwRkShaBbiipb8LiorV+Gn/NbHDISLSYnJERKKQSCQY3bGk92j1vmsoUKpEjoiIqASTIyISTZ/mPqjnbIP03CL8ncA9kIiodmByRESisZJJEduhAQDgu92XIQiCuAEREYHJERGJ7Nm2AbC3luF8Sg7WHr4pdjhERHUnOZo7dy7at28POzs7uLi4lFvm+vXr6NevH+zs7ODl5YW33noLxcXFOmV27NiBVq1aQaFQICQkBCtXrjR+8ERUIWdbOSb2aAQA+GDjGSTfKxA5IiKydHUmOSoqKsLgwYMxbty4cp9XqVTo168fioqKsHfvXqxatQorV67E+++/ry1z5coV9OvXD926dUNCQgJef/11jB49Glu2bDHV2yCicozuFIyW/i7ILijGO+tOcniNiERVZ5Kj2bNn44033kB4eHi5z8fFxeHMmTP46aefEBERgT59+uCDDz7A119/jaKiIgDA0qVLERQUhIULF6Jp06aYMGECBg0ahM8//9yUb4WIHiKTSvDpoBawlkmx7Wwq1h27JXZIRGTBzOb4kH379iE8PBze3t7aazExMRg3bhxOnz6NyMhI7Nu3Dz179tS5LyYmBq+//nqF9RYWFqKw8MEGdVlZWQAApVIJpVJp0Pegqc/Q9ZIutrNp6NvODdxsMKFbMD7behGz/+802jVwgZejwpghmgV+nk2HbW0axmpnfeozm+QoOTlZJzECoH2cnJxcaZmsrCzk5+fD1ta2TL3z5s3D7Nmzy1yPi4uDnZ2docLXER8fb5R6SRfb2TT0aWc/NeBnL8PN3GK8vHw7Xm6ihlRixODMCD/PpsO2Ng1Dt3NeXl61y4qaHE2bNg3z58+vtExiYiKaNGlioojKmj59OiZPnqx9nJWVBX9/f0RHR8PJycmgr6VUKhEfH49evXpBLpcbtG56gO1sGjVt58ZtsvH0sgM4kwnccgzF2M5BxgvSDPDzbDpsa9MwVjtrRn6qQ9TkaMqUKYiNja20THBwcLXq8vHxwcGDB3WupaSkaJ/T/Km5VrqMk5NTub1GAKBQKKBQlO3al8vlRvvmMGbd9ADb2TT0befm/m6Y80QzTPvzJD7begGtGrihfUMPI0ZoHvh5Nh22tWkYup31qUvU5MjT0xOenp4GqSsqKgpz585FamoqvLy8AJR0yTk5OSEsLExbZtOmTTr3xcfHIyoqyiAxEJFhPNvWH0eu3cXaIzcx8Zdj2PBaJ/g424gdFhFZiDqzWu369etISEjA9evXoVKpkJCQgISEBOTk5AAAoqOjERYWhpdeegnHjx/Hli1b8O6772L8+PHanp9XXnkFly9fxttvv42zZ89iyZIl+O233/DGG2+I+daI6CESiQQfDGyOpr5OSMspwvifj0KpUosdFhFZiDqTHL3//vuIjIzEzJkzkZOTg8jISERGRuLw4cMAAJlMhg0bNkAmkyEqKgovvvgihg0bhjlz5mjrCAoKwsaNGxEfH4+WLVti4cKF+O677xATEyPW2yKiCtjIZfjmhVZwtLHCkWt38e2uy2KHREQWos6sVlu5cmWVu1kHBgaWGTZ7WNeuXXHs2DEDRkZExtLAwx6zBjTDlLXHsWT7JQxp4w8PBy7vJyLjqjM9R0RkmZ6KrI/w+s7IKSzG5/HnxQ6HiCwAkyMiqtWkUglm9GsKAPjl4HWcT8kWOSIiMndMjoio1ns82B0xzbyhFoCPNiWKHQ4RmTkmR0RUJ0zr0xRWUgl2nLuDnefviB0OEZkxJkdEVCcEedhjWFQDAMCs/zuN1OwCcQMiIrPF5IiI6oyJPULg6ajA5Tu5eHrJXlxMzRE7JCIyQ0yOiKjOcLGzxtqxUWjgboebd/PxzDd7cehqhthhEZGZYXJERHVKAw97/DGuPSIDXHAvX4kXvjuAfxNTqr6RiKiamBwRUZ3j7qDAz6MfR3SYN4qK1Zjw8zGcvHlP7LCIyEwwOSKiOsnWWoYlL7RC58aeyFeqMGrVISTdyxc7LCIyA0yOiKjOspJJ8fXQSIR6OyI1uxAjVx5GbmGx2GERUR3H5IiI6jRHGzm+j20DDwdrJCZlYeIvx6BWC2KHRUR1GJMjIqrz/Fzt8O2wNlBYSfHv2VTEneEEbSKqOSZHRGQWIgNcMbJjEABg1d6r4gZDRHUakyMiMhsvPh4ImVSCfZfTcTY5S+xwiKiOYnJERGajvostYpp5AwBW7b0mcjREVFcxOSIiszL8/vlr647dRGZekbjBEFGdxOSIiMzKY0FuaOrrhAKlGr8dviF2OERUBzE5IiKzIpFIENs+EADw475rUHFZPxHpickREZmdJyPqw8VOjpt383nuGhHpjckREZkdG7kMz7UNAAC899cprN5/DYXFKpGjIqK6gskREZmlkR0awM/VFilZhXhv/Sl0+WQHVu29ymE2IqoSkyMiMkteTjbYOrkLZj/RDD5ONkjOKsDMv0/jk81nxQ6NiGo5JkdEZLZs5DIMb98A/73dFe/0bQIAWLbzMnZfSBM5MiKqzZgcEZHZU1jJMKZzQwxtVzIPafJvCcjI5R5IRFQ+JkdEZDHe6xeGhp72SM0uxNQ/TkAQOP+IiMpickREFsPWWoZFz0XCWiZF/JkUrDlwXeyQiKgWYnJERBaleX1nvN07FADw4cYzSMkqEDkiIqptmBwRkcUZ2SEIrQJcUKBU46ttF8QOh4hqGSZHRGRxpFIJpvYuWb32v4M3cC09V+SIiKg2YXJERBapXbA7ujT2RLFawGfx58UOh4hqESZHRGSx3oopmXv09/HbSEzKEjkaIqotmBwRkcVqXt8Z/Vv4QhCAT7ecEzscIqolmBwRkUWbEh0KmVSCf8+m4uCVDLHDIaJagMkREVm0IA97DGnjBwB4+cfD2HuJR4sQWTomR0Rk8d6OaYIIfxfcy1di2PcH8ctBbg5JZMmYHBGRxXO1t8b/xjyOJ1rWQ7FawPQ/T2LO/52BWs3jRYgsUZ1JjubOnYv27dvDzs4OLi4u5ZaZOHEiWrduDYVCgYiIiHLLnDhxAp06dYKNjQ38/f3xySefGC9oIqozbOQyLHouAlN6NQYA/LDnCr7YyiX+RJaoziRHRUVFGDx4MMaNG1dpuZEjR+LZZ58t97msrCxER0cjMDAQR44cwYIFCzBr1iwsX77cGCETUR0jkUjwWo9GmP9MOADgy20XseHEbZGjIiJTsxI7gOqaPXs2AGDlypUVlvnyyy8BAHfu3MGJEyfKPL9mzRoUFRXhhx9+gLW1NZo1a4aEhAR89tlnGDNmjFHiJqK659m2AbiYmoNvd13Bm2uPo4G7PZrXdxY7LCIykTrTc2QI+/btQ+fOnWFtba29FhMTg3PnzuHu3bsiRkZEtc20Pk3RpbEnCpRqjPnxMO5kF4odEhGZSJ3pOTKE5ORkBAUF6Vzz9vbWPufq6lrmnsLCQhQWPvhPMSurZBddpVIJpVJp0Pg09Rm6XtLFdjYNc2jnzwY1x6BlB3AlPQ9jfjyEH0e0gY1cJnZYOsyhnesKtrVpGKud9alP1ORo2rRpmD9/fqVlEhMT0aRJExNFVNa8efO0Q3qlxcXFwc7OziivGR8fb5R6SRfb2TTqejs/7w98ninDsRv38OLieMQ2VkMqETuqsup6O9clbGvTMHQ75+XlVbusqMnRlClTEBsbW2mZ4OBgg72ej48PUlJSdK5pHvv4+JR7z/Tp0zF58mTt46ysLPj7+yM6OhpOTk4Giw0oyWrj4+PRq1cvyOVyg9ZND7CdTcOc2jmsVQZGrDqC4xlSHJc0wIy+4v3C9jBzaufajm1tGsZqZ83IT3WImhx5enrC09PTZK8XFRWFGTNmQKlUahs8Pj4eoaGh5Q6pAYBCoYBCoShzXS6XG+2bw5h10wNsZ9Mwh3bu2NgbC4dEYOIvx7By33X4uztgVMegqm80IXNo57qCbW0ahm5nfeqqMxOyr1+/joSEBFy/fh0qlQoJCQlISEhATk6OtszFixeRkJCA5ORk5Ofna8sUFRUBAIYOHQpra2uMGjUKp0+fxq+//opFixbp9AwREZXniZb1MK1PSY/RhxvPYNvZlCruIKK6qs5MyH7//fexatUq7ePIyEgAwPbt29G1a1cAwOjRo/Hff/+VKXPlyhU0aNAAzs7OiIuLw/jx49G6dWt4eHjg/fff5zJ+IqqWsZ2DcT0jDz8fuI63fz+J+Ddc4WpvXfWNRFSn1JnkaOXKlZXucQQAO3bsqLKeFi1aYNeuXYYJiogsikQiwfv9w3DwSgYupubg/b9P46vnI8UOi4gMrM4MqxER1QY2chkWDm4JmVSC/zt+G5tOJokdEhEZGJMjIiI9tfR3wbguDQEA764/xQ0iicwMkyMiohqY2KMRmvg4IiO3CDPWnYQgCGKHREQGwuSIiKgGrK2k+GxIBOQyCeLOpGDdsVtih0REBsLkiIiohsLqOWFSj0YAgJl/n8btzHyRIyIiQ2ByRET0CF7p0hAR/i7ILijG1D9OcHiNyAwwOSIiegRWMikWDmkJG7kUuy6k4af918QOiYgeEZMjIqJH1NDTAVN7l+ye/dGms7iSlityRET0KJgcEREZwPCoBogKdke+UoWh3+7H8RuZYodERDXE5IiIyACkUgk+e7YlGnraI+leAQYv24ffDt0QOywiqgEmR0REBuLrbIv14zugV5g3iorVePuPE5j2xwlcSMnmRG2iOoTJERGRATnayLHsxdaY3KsxJBLgf4duoNfnO9Ht0x2Yu/EMbmTkiR0iEVWByRERkYFJpRJM7NEIq0Y8hq6hnrCWSXE1PQ/f7rqCwUv3oUCpEjtEIqqEldgBEBGZq86NPdG5sSdyCovx37k7+GDDGSRnFWDt4Rt4KaqB2OERUQXYc0REZGQOCiv0a+GLV7uVHFa79L/LKCpWixwVEVWEyRERkYkMaeMPT0cFbmXmYz3PYiOqtZgcERGZiI1chjGdggEAS3ZcRLGKvUdEtRGTIyIiExraLgCudnJcTc/DxpNJYodDROVgckREZEL2CiuM7BAEAFi87SLUau5/RFTbMDkiIjKxYe0bwFFhhQupOXj5x8P47fANpGYXiB0WEd3HpfxERCbmbCvHxB6NMHdTIv49m4p/z6YCAB4PdsPsJ5oj1MdR5AiJLBt7joiIRPBy52D8PaEDJvVohBZ+zgCA/Zcz0P+rXfhi63ku9ScSEZMjIiKRtPBzwRu9GuPvCR2xZ1p39GzqDaVKwBdbL2DAV7ux/3K62CESWSQmR0REtUB9F1t8O6w1vno+Eu721jiXko3nlu/H88v3M0kiMjEmR0REtYREIsGAlvUQP7kLXnw8AHKZBPsup+O55fsx9Nv9SM3ipG0iU2ByRERUy7jZW+PDgeHY8VY3bZK091I6XvjuANJzCsUOj8jsMTkiIqql6rvY4sOB4djyemf4ONngQmoOXvz+IDLzisQOjcisMTkiIqrlgj0dsObldvBwUCAxKQvDfziIrAKl2GERmS0mR0REdUBDTwesGd0OrnZyHL95Dy99fxBpHGIjMgomR0REdUSojyNWj2oHZ1s5jt/IxMCv9+BCao7YYRGZHSZHRER1SPP6zvjz1fYIdLfDzbv5GLL8IM5mSsQOi8isMDkiIqpjGno6YN2rHdC2gStyCouxLFGKCb8k4M+jN3E3l5O1iR4Vz1YjIqqD3Oyt8dPodpi69jjWH0/CljOp2HImFTKpBMEe9rCSSSGVAFYyKQa08MXIDkGQStnDRFQdTI6IiOoohZUMnzzTHA3VN5Dv1hjbzt3B2eTsMvOQjt/IxH/n72DhkJbwcrQRKVqiuoPJERFRHSaRSBDgAPTtGYK3+zTFjYw8XEvPg1oQoBYEXLqTiwVbzmLXhTT0XbQLnw5uia6hXmKHTVSrMTkiIjIj/m528Hez0z7uGgp0aeyBCT8fw9nkbMSuOIQwXyc8GVEPA1rWQz0XWxGjJaqdmBwREZm5EC9HrB/fAR//cxY/7b+GM0lZOJOUhXn/nEVDT3v4udrBz9UW9Vxs4WpnDUcbKzjaWMHP1RYNPR0gkXCuElkWJkdERBbARi7DrCeaYVKPRvjnVDL+SriFA1cycOlOLi7dya3wPj9XW/Rs6o3oMG+0aeAGaysucibzV2eSo7lz52Ljxo1ISEiAtbU1MjMzdZ4/fvw4Pv74Y+zevRtpaWlo0KABXnnlFUyaNEmn3I4dOzB58mScPn0a/v7+ePfddxEbG2u6N0JEJCJXe2sMbReAoe0CkJpVgPMpObiVmYebd/NxO7MAWQVKZOUrkV1QjEt3cnDzbj5W7r2KlXuvwkYuRasAV7QLckebBq7wdbaBh6MCjgornd4lQRDY20R1Wp1JjoqKijB48GBERUXh+++/L/P8kSNH4OXlhZ9++gn+/v7Yu3cvxowZA5lMhgkTJgAArly5gn79+uGVV17BmjVr8O+//2L06NHw9fVFTEyMqd8SEZGovJxs4OVU8eq1vKJi7L6Qhq2JKdh2NhVpOUXYeykdey+l65RTWEmhsJJCqRKgVKmhEgT4ONkg0N0OQR72CHCzRz0XG9R3KRm6c7GTw8ZKxq0FqNaqM8nR7NmzAQArV64s9/mRI0fqPA4ODsa+ffvw559/apOjpUuXIigoCAsXLgQANG3aFLt378bnn3/O5IiI6CF21laIbuaD6GY+EAQBF1NzsP9KBvZfTseZ21m4k12InMJiFBarUVis1rk36V4Bku4VYP/ljArrt5XLYCMvGaYTAAgCIJdJ4KCwgv39LweFFeysZbC3toKttQzWVlJYy6SQy6SQSEruUQsCBABWUgmsZBLIpVJY30/YFHIpFFYySCUSyKQSyKQlK/wkKP0nIIEEUknJNakEkEpLPy4pp1apcCMHOHUrC1ZWuj8+NR1lUokEUmlJfSX1PngO96+V/A0P3V82UZRon6v0n0lTc7XL6svUnYDFxcXIFPnYwDqTHNXEvXv34Obmpn28b98+9OzZU6dMTEwMXn/99QrrKCwsRGHhg3+lrKwsAIBSqYRSadhTsTX1Gbpe0sV2Ng22s2mYsp0buNmggVs9PNe6nvZafpEKd3IKUawSILeSlCQtAG5nFuDa/W0FbtzNR9K9AtzOzEdyViGK1ULJvUoV8pWqMq+TllObd/m2wqcn94sdhNlzksswuL9xfsZWh9kmR3v37sWvv/6KjRs3aq8lJyfD29tbp5y3tzeysrKQn58PW9uyS1rnzZun7bUqLS4uDnZ2dmWuG0J8fLxR6iVdbGfTYDubRm1sZ2sAjQA0sgNgB8AXUAuAUg0Uqkr+VJbqcJJIgOL7zxWqJCjQ/r3kq0gtQbEaUAkl5TT3aDo21ELJcyoBKL5fRqkGitUSqISS3im18KCXCrj/9/t/0f79/vPq+38Kpf6sSOk6NPeV93ypPyqup5LHld1cWb2Vqel9xnwhudTwn+m8vLxqlxU1OZo2bRrmz59faZnExEQ0adJEr3pPnTqFJ598EjNnzkR0dPSjhIjp06dj8uTJ2sdZWVnw9/dHdHQ0nJycHqnuhymVSsTHx6NXr16Qy+UGrZseYDubBtvZNNjOpsO2Ng1jtbNm5Kc6RE2OpkyZUuVKseDgYL3qPHPmDHr06IExY8bg3Xff1XnOx8cHKSkpOtdSUlLg5ORUbq8RACgUCigUijLX5XK50b45jFk3PcB2Ng22s2mwnU2HbW0ahm5nfeoSNTny9PSEp6enweo7ffo0unfvjuHDh2Pu3Lllno+KisKmTZt0rsXHxyMqKspgMRAREVHdVmfmHF2/fh0ZGRm4fv06VCoVEhISAAAhISFwcHDAqVOn0L17d8TExGDy5MlITk4GAMhkMm0C9sorr2Dx4sV4++23MXLkSGzbtg2//fabzrwkIiIismx1Jjl6//33sWrVKu3jyMhIAMD27dvRtWtX/P7777hz5w5++ukn/PTTT9pygYGBuHr1KgAgKCgIGzduxBtvvIFFixbBz88P3333HZfxExERkVadSY5WrlxZ4R5HADBr1izMmjWrynq6du2KY8eOGS4wIiIiMis8JIeIiIioFCZHRERERKUwOSIiIiIqhckRERERUSlMjoiIiIhKYXJEREREVAqTIyIiIqJSmBwRERERlcLkiIiIiKiUOrNDdm0hCAIAICsry+B1K5VK5OXlISsriyc+GxHb2TTYzqbBdjYdtrVpGKudNT+3NT/HK8PkSE/Z2dkAAH9/f5EjISIiIn1lZ2fD2dm50jISoTopFGmp1Wrcvn0bjo6OkEgkBq07KysL/v7+uHHjBpycnAxaNz3AdjYNtrNpsJ1Nh21tGsZqZ0EQkJ2djXr16kEqrXxWEXuO9CSVSuHn52fU13BycuI3ngmwnU2D7WwabGfTYVubhjHauaoeIw1OyCYiIiIqhckRERERUSlMjmoRhUKBmTNnQqFQiB2KWWM7mwbb2TTYzqbDtjaN2tDOnJBNREREVAp7joiIiIhKYXJEREREVAqTIyIiIqJSmBwRERERlcLkqJb4+uuv0aBBA9jY2KBdu3Y4ePCg2CGZnZ07d2LAgAGoV68eJBIJ1q9fL3ZIZmnevHlo27YtHB0d4eXlhYEDB+LcuXNih2V2vvnmG7Ro0UK7UV5UVBT++ecfscMyex9//DEkEglef/11sUMxO7NmzYJEItH5atKkiSixMDmqBX799VdMnjwZM2fOxNGjR9GyZUvExMQgNTVV7NDMSm5uLlq2bImvv/5a7FDM2n///Yfx48dj//79iI+Ph1KpRHR0NHJzc8UOzaz4+fnh448/xpEjR3D48GF0794dTz75JE6fPi12aGbr0KFDWLZsGVq0aCF2KGarWbNmSEpK0n7t3r1blDi4lL8WaNeuHdq2bYvFixcDKDm/zd/fH6+99hqmTZsmcnTmSSKRYN26dRg4cKDYoZi9O3fuwMvLC//99x86d+4sdjhmzc3NDQsWLMCoUaPEDsXs5OTkoFWrVliyZAk+/PBDRERE4IsvvhA7LLMya9YsrF+/HgkJCWKHwp4jsRUVFeHIkSPo2bOn9ppUKkXPnj2xb98+ESMjMox79+4BKPnBTcahUqnwv//9D7m5uYiKihI7HLM0fvx49OvXT+f/ajK8CxcuoF69eggODsYLL7yA69evixIHD54VWVpaGlQqFby9vXWue3t74+zZsyJFRWQYarUar7/+Ojp06IDmzZuLHY7ZOXnyJKKiolBQUAAHBwesW7cOYWFhYodldv73v//h6NGjOHTokNihmLV27dph5cqVCA0NRVJSEmbPno1OnTrh1KlTcHR0NGksTI6IyGjGjx+PU6dOiTZvwNyFhoYiISEB9+7dw++//47hw4fjv//+Y4JkQDdu3MCkSZMQHx8PGxsbscMxa3369NH+vUWLFmjXrh0CAwPx22+/mXyomMmRyDw8PCCTyZCSkqJzPSUlBT4+PiJFRfToJkyYgA0bNmDnzp3w8/MTOxyzZG1tjZCQEABA69atcejQISxatAjLli0TOTLzceTIEaSmpqJVq1baayqVCjt37sTixYtRWFgImUwmYoTmy8XFBY0bN8bFixdN/tqccyQya2trtG7dGv/++6/2mlqtxr///su5A1QnCYKACRMmYN26ddi2bRuCgoLEDsliqNVqFBYWih2GWenRowdOnjyJhIQE7VebNm3wwgsvICEhgYmREeXk5ODSpUvw9fU1+Wuz56gWmDx5MoYPH442bdrgsccewxdffIHc3FyMGDFC7NDMSk5Ojs5vIFeuXEFCQgLc3NwQEBAgYmTmZfz48fj555/x119/wdHREcnJyQAAZ2dn2Nraihyd+Zg+fTr69OmDgIAAZGdn4+eff8aOHTuwZcsWsUMzK46OjmXmy9nb28Pd3Z3z6AzszTffxIABAxAYGIjbt29j5syZkMlkeP75500eC5OjWuDZZ5/FnTt38P777yM5ORkRERHYvHlzmUna9GgOHz6Mbt26aR9PnjwZADB8+HCsXLlSpKjMzzfffAMA6Nq1q871FStWIDY21vQBmanU1FQMGzYMSUlJcHZ2RosWLbBlyxb06tVL7NCIauTmzZt4/vnnkZ6eDk9PT3Ts2BH79++Hp6enyWPhPkdEREREpXDOEREREVEpTI6IiIiISmFyRERERFQKkyMiIiKiUpgcEREREZXC5IiIiIioFCZHRERERKUwOSIiEkFRURFCQkKwd+9eg9a7efNmREREQK1WG7ReIkvC5IiIHllsbCwkEkmZLzEOjKwrli5diqCgILRv3157TSKRYP369WXKxsbGYuDAgdWqt3fv3pDL5VizZo2BIiWyPEyOiMggevfujaSkJJ2v8g6dLSoqEiG62kUQBCxevBijRo0ySv2xsbH48ssvjVI3kSVgckREBqFQKODj46PzJZPJ0LVrV0yYMAGvv/46PDw8EBMTAwA4deoU+vTpAwcHB3h7e+Oll15CWlqatr7c3FwMGzYMDg4O8PX1xcKFC9G1a1e8/vrr2jLl9bS4uLjonJV348YNDBkyBC4uLnBzc8OTTz6Jq1evap/X9Mp8+umn8PX1hbu7O8aPHw+lUqktU1hYiKlTp8Lf3x8KhQIhISH4/vvvIQgCQkJC8Omnn+rEkJCQUGnP2ZEjR3Dp0iX069dPz1YGrl69Wm4vXemz7AYMGIDDhw/j0qVLetdPREyOiMgEVq1aBWtra+zZswdLly5FZmYmunfvjsjISBw+fBibN29GSkoKhgwZor3nrbfewn///Ye//voLcXFx2LFjB44eParX6yqVSsTExMDR0RG7du3Cnj174ODggN69e+v0YG3fvh2XLl3C9u3bsWrVKqxcuVInwRo2bBh++eUXfPnll0hMTMSyZcvg4OAAiUSCkSNHYsWKFTqvu2LFCnTu3BkhISHlxrVr1y40btwYjo6Oer0fAPD399fpnTt27Bjc3d3RuXNnbZmAgAB4e3tj165detdPRAAEIqJHNHz4cEEmkwn29vbar0GDBgmCIAhdunQRIiMjdcp/8MEHQnR0tM61GzduCACEc+fOCdnZ2YK1tbXw22+/aZ9PT08XbG1thUmTJmmvARDWrVunU4+zs7OwYsUKQRAEYfXq1UJoaKigVqu1zxcWFgq2trbCli1btLEHBgYKxcXF2jKDBw8Wnn32WUEQBOHcuXMCACE+Pr7c937r1i1BJpMJBw4cEARBEIqKigQPDw9h5cqVFbbXpEmThO7du5e5DkCwsbHRaUd7e3vByspKePLJJ8uUz8/PF9q1ayf0799fUKlUOs9FRkYKs2bNqjAGIqqYlbipGRGZi27duuGbb77RPra3t9f+vXXr1jpljx8/ju3bt8PBwaFMPZcuXUJ+fj6KiorQrl077XU3NzeEhobqFdPx48dx8eLFMj00BQUFOkNOzZo1g0wm0z729fXFyZMnAZQMkclkMnTp0qXc16hXrx769euHH374AY899hj+7//+D4WFhRg8eHCFceXn58PGxqbc5z7//HP07NlT59rUqVOhUqnKlB05ciSys7MRHx8PqVR3IMDW1hZ5eXkVxkBEFWNyREQGYW9vX+EwUulECQBycnIwYMAAzJ8/v0xZX1/faq9yk0gkEARB51rpuUI5OTlo3bp1uSu3PD09tX+Xy+Vl6tUshbe1ta0yjtGjR+Oll17C559/jhUrVuDZZ5+FnZ1dheU9PDy0ydfDfHx8yrSjo6MjMjMzda59+OGH2LJlCw4ePFju8FxGRobOeySi6mNyREQm16pVK/zxxx9o0KABrKzK/jfUsGFDyOVyHDhwAAEBAQCAu3fv4vz58zo9OJ6enkhKStI+vnDhgk5vSatWrfDrr7/Cy8sLTk5ONYo1PDwcarUa//33X5keHY2+ffvC3t4e33zzDTZv3oydO3dWWmdkZCS++eYbCIIAiUSid0x//PEH5syZg3/++QcNGzYs87ymZywyMlLvuomIE7KJSATjx49HRkYGnn/+eRw6dAiXLl3Cli1bMGLECKhUKjg4OGDUqFF46623sG3bNpw6dQqxsbFlho66d++OxYsX49ixYzh8+DBeeeUVnV6gF154AR4eHnjyySexa9cuXLlyBTt27MDEiRNx8+bNasXaoEEDDB8+HCNHjsT69eu1dfz222/aMjKZDLGxsZg+fToaNWqEqKioSuvs1q0bcnJycPr0aT1arcSpU6cwbNgwTJ06Fc2aNUNycjKSk5ORkZGhLbN//34oFIoq4yCi8jE5IiKTq1evHvbs2QOVSoXo6GiEh4fj9ddfh4uLizYBWrBgATp16oQBAwagZ8+e6NixY5m5SwsXLoS/vz86deqEoUOH4s0339QZzrKzs8POnTsREBCAp59+Gk2bNsWoUaNQUFCgV0/SN998g0GDBuHVV19FkyZN8PLLLyM3N1enzKhRo1BUVIQRI0ZUWZ+7uzueeuqpGm3UePjwYeTl5eHDDz+Er6+v9uvpp5/Wlvnll1/wwgsvVDq0R0QVkwgPD9gTEdVSXbt2RUREBL744guxQylj165d6NGjB27cuAFvb+8qy584cQK9evXCpUuXyp2YXlNpaWkIDQ3F4cOHy92Ek4iqxp4jIqJHUFhYiJs3b2LWrFkYPHhwtRIjAGjRogXmz5+PK1euGDSeq1evYsmSJUyMiB4BJ2QTET2CX375BaNGjUJERAR+/PFHve6NjY01eDxt2rRBmzZtDF4vkSXhsBoRERFRKRxWIyIiIiqFyRERERFRKUyOiIiIiEphckRERERUCpMjIiIiolKYHBERERGVwuSIiIiIqBQmR0RERESlMDkiIiIiKuX/Ae2gsJT68hn6AAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate onsets with variable spacing\n",
"mean_onset_diff = 3.0 # mean time between onsets in seconds\n",
"sd_onset_diff = 0.2 # standard deviation of time between onsets in seconds\n",
"sy = get_acc_pupil_response(mean_onset_diff, sd_onset_diff)\n",
"plot_psd_welch(sy, nperseg=5000)\n",
"plt.title(f\"Mean onset diff: {mean_onset_diff} s, SD onset diff: {sd_onset_diff} s\")\n",
"plt.savefig(f\"../revision2/pics/psd_acc_pupil_response_{mean_onset_diff}.png\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "pypil",
"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": "3.12.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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