{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lifetimes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate the lifetime of Rydberg states and analyze which transitions contribute to it. The calculations can be performed with a few lines of code; most of the code within this notebook is only needed for plotting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We import the libraries that we will use within the notebook and initialize PairInteraction's database."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install -q matplotlib numpy scipy pairinteraction\n",
    "\n",
    "from typing import Any\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pairinteraction as pi\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "if pi.Database.get_global_database() is None:\n",
    "    pi.Database.initialize_global_database(download_missing=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a quick example, we show how to calculate the lifetime of the Rubidium $|60S,m=1/2\\rangle$ state via `ket.get_lifetime`. At zero temperature, the lifetime is determined by the spontaneous decay. If the temperature is non-zero, black body radiation can drive transitions to neighboring Rydberg states, reducing the lifetime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The single-channel quantum defect theory can be inaccurate for effective principal quantum numbers < 25. This can lead to inaccurate matrix elements.\n",
      "The single-channel quantum defect theory can be inaccurate for effective principal quantum numbers < 25. This can lead to inaccurate matrix elements.\n",
      "The single-channel quantum defect theory can be inaccurate for effective principal quantum numbers < 25. This can lead to inaccurate matrix elements.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lifetime at T=0: 239.07 microsecond\n",
      "Lifetime at T=300K: 104.73 microsecond\n"
     ]
    }
   ],
   "source": [
    "ket = pi.KetAtom(\"Rb\", n=60, l=0, j=0.5, m=0.5)\n",
    "\n",
    "temperature = 300  # Kelvin\n",
    "lifetime_0 = ket.get_lifetime()\n",
    "lifetime = ket.get_lifetime(temperature, temperature_unit=\"K\")\n",
    "\n",
    "print(f\"Lifetime at T=0: {lifetime_0.to('mus'):.2f}\")\n",
    "print(f\"Lifetime at T={temperature}K: {lifetime.to('mus'):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transition rates contributing to the Rydberg lifetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To analyze which transitions contribute to the lifetime, we can obtain the transition rates from spontaneous decay (`ket.get_spontaneous_transition_rates`) and black body radiation (`ket.get_black_body_transition_rates`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The single-channel quantum defect theory can be inaccurate for effective principal quantum numbers < 25. This can lead to inaccurate matrix elements.\n",
      "The single-channel quantum defect theory can be inaccurate for effective principal quantum numbers < 25. This can lead to inaccurate matrix elements.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of possible spontaneous decay transitions: 180\n",
      "Number of considered BBR transitions: 235\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the transition rates\n",
    "kets_sp, transition_rates_sp = ket.get_spontaneous_transition_rates(unit=\"1/mus\")\n",
    "print(f\"Number of possible spontaneous decay transitions: {len(transition_rates_sp)}\")\n",
    "\n",
    "kets_bbr, transition_rates_bbr = ket.get_black_body_transition_rates(\n",
    "    temperature, \"kelvin\", unit=\"1/mus\"\n",
    ")\n",
    "print(f\"Number of considered BBR transitions: {len(transition_rates_bbr)}\")\n",
    "\n",
    "# Plot the transition rates\n",
    "fig, ax = plt.subplots(figsize=(6, 5))\n",
    "\n",
    "n_list = np.arange(0, np.max([s.n for s in kets_bbr]) + 1)\n",
    "rates_summed = {}\n",
    "for key, kets, rates in [\n",
    "    (\"BBR\", kets_bbr, transition_rates_bbr),\n",
    "    (\"SP\", kets_sp, transition_rates_sp),\n",
    "]:\n",
    "    rates_summed[key] = np.zeros(len(n_list))\n",
    "    for i, s in enumerate(kets):\n",
    "        rates_summed[key][s.n] += rates[i]\n",
    "\n",
    "ax.bar(n_list, rates_summed[\"SP\"], label=\"Spontaneous Decay\", color=\"blue\", alpha=0.8)\n",
    "ax.bar(n_list, rates_summed[\"BBR\"], label=\"Black Body Radiation (BBR)\", color=\"red\", alpha=0.8)\n",
    "ax.legend()\n",
    "\n",
    "ax.set_xlabel(\"Principal Quantum Number $n$\")\n",
    "ax.set_ylabel(r\"Transition Rates (1 / $\\mu$s)\")\n",
    "ax.set_title(\"Spontaneous and BBR Transition Rates vs $n$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lifetime scaling with the principal quantum number"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a more sophisticated example, we study how the lifetime scales with the effective principal quantum number $\\nu$. Our numerics reproduce the $\\nu^3$ scaling which one expects for states with a small angular quantum number $l$. For circular states, the lifetime scales as $\\nu^5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7d+ONN96Ag4NDpf33un2xePFivPvuu+jevTtsbW2xdu1aLFy4ECtWrMCIESOQm5uLg+W/HdRBcXExevbsiZdeegnOzs748ccfMXHiRLRt2xZhYWHG4zZv3ozZs2dX+1xarRZjxozB9OnTsW3bNmg0Ghw7dgyCIOCJJ57A2bNnsXv3bvz2m2FQWnmvG4lEgvfeew+tW7fG1atXMWfOHLz44otYs2YNIiIisGrVKixduhQXL14EADg6OgIA5s6di4SEBHzxxRfw9fXFt99+i+HDh+PMmTNo3749oqOjodFoEBcXBwcHByQkJBgfS0RNQIX1ckQRKMyUQ7W3BIU3PzQcI5PB9dFH4TFzBuT+/partZFiQGkod7QvrpoI5KUYjms9wGxPe+XKFYiiiI4dO9bp8QsWLMDYsWONX7/++ut44YUXMH/+fOO23r1717k+Pz8/LFq0yPj1vHnzsGfPHuzYscMkoLRv3x5vv/12tefJy8tDbm4uRo4cibZt2wIAOpWPhochWMhkskq3sRYsWGD878DAQLz++uuYNWsW1qxZA7lcDhcXFwiCYPK4GzduYOPGjbhx4wZ8fX0BAIsWLcLu3buxceNGvPnmm7hx4wbGjRuHLl26AADatGlTh3eHiKzSHb9wiiJQkK6A6pwjilQKAIAgEeHSUYBy9U+wCQiwbK2NGANKQ1FnmPe4GhLFqq7Y1FyvXr2M/52ZmYnU1FQMGTLkfssy0ul0ePPNN7Fjxw6kpKRAo9GgpKQE9vb2Jsf17Nnzrudxd3fHlClTMGzYMDzwwAMYOnQoHn/8cfj4+Nz1cb/99huWL1+OCxcuIC8vD1qtFsXFxSgsLKxUQ7kzZ85Ap9MhKMh0YFtJSQk8PDwAAM899xxmz56NX375BUOHDsW4cePQtWvXe70dRNQYXD8EMTcVBWkKqM45oSjLMCZOkIhwbVsAj05q2NjrAe01AAwodcUxKA2lpm2Jzdy+uH379hAEwTgQtrbuvC1kZ2d312MlEsO3052hqLS0YhdEU++88w5Wr16Nl156Cfv27UN8fDyGDRsGjca0rXNVt6cq2rhxIw4fPoyIiAhs374dQUFBJmNsKrp27RpGjhyJrl274uuvv8aJEycQExMDAJWe/05qtRpSqRQnTpxAfHy88c/58+exevVqAMCzzz6Lq1evYuLEiThz5gx69eqF999//56vgYismyiKyP8jFtd+VSIpzgNFWXIIUhFuQWq0HZUB7555hnACmP0XzuaGAaWhtIowzNZBdctiC4Czn9nbF7u7u2PYsGGIiYlBQUFBpf05OTk1PpeTkxMCAwNNpibfydPTE4BhunK5OwfMVuXgwYN45JFH8PTTT6Nbt25o06YNLl26VOOaKurevTuWLFmCQ4cOISQkBJ9//jkAQC6XV1oI8sSJE9Dr9Xj33XfRt29fBAUFITXV9DZcVY/r3r07dDodMjMz0a5dO5M/d94KCggIwKxZs/DNN9/ghRdewIYNG+r8uojIskS9Hnm//orEceOQ/NZWFGfLIUj1cO+oRruRGfDukQcbO73pg5rBejn1iQGloUikhqnEACqHlPptX1y+SnNYWBi+/vprXL58GefPn8d7772H8PDwWp3rlVdewbvvvov33nsPly9fxsmTJ41XBuzs7NC3b1+sWLEC58+fR2xsLP7zn//c9Xzt27fHr7/+ikOHDuH8+fOYOXMmMjJq/1tHYmIilixZgsOHD+P69ev45ZdfcPnyZeM4lMDAQCQmJiI+Ph4qlQolJSVo164dSktL8f777+Pq1avYsmUL1q1bZ3LewMBAqNVq7N27FyqVCoWFhQgKCsKECRMwadIkfPPNN0hMTMSxY8ewfPly/PjjjwAMY1v27NmDxMREnDx5Evv27TMZE0NEjYOo1yNv9x4kPjoWKfOeQ0nCeUjs7eERCrQbdRNeoXmQVQwm9fQLZ3PDgFImJiYGwcHB9zXg856CRwOPfwo4VxgX4exr2F5PfVDatGmDkydPYtCgQXjhhRcQEhKCBx54AHv37sXatWtrda7Jkydj1apVWLNmDTp37oyRI0fi8uXLxv2ffPIJtFotevbsiQULFuD111+/6/n+85//oEePHhg2bBgGDhwIb2/vOnWytbe3x4ULF4zTqGfMmIHo6GjMnDkTADBu3DgMHz4cgwYNgqenJ7Zt24Zu3bph5cqVeOuttxASEoKtW7di+fLlJueNiIjArFmz8MQTT8DT09M4UHfjxo2YNGkSXnjhBXTo0AFjxozBn3/+iZYtWwIwjK2Jjo5Gp06dMHz4cAQFBWHNmjW1fl1EZBmiTofcH3/E1dGjkbJgAUouXoTEwQEes2ai7d7f0GLpW5DZ6tHQv3A2J4J4v6Mom5i8vDy4uLggNzcXzs7OJvuKi4uRmJiI1q1bw9bWtu5PcpfGPtT8mO37iojum6jVIu+nn6Bauw6axEQAgMTJCe6TJsF90kRIy1oUAKim8aZfs1ovp6K7/QytLc7isYTy9sVERGQVRK0Wud//gKx166C5fh0AIHFxgceUyXB7+mlInZwqP4jr5dQrBhQiImq2RI0Gubt2QfXhepQmJQEApK6ucJ86FW4T/gHpvRos8hfOesOAQkRETc89bqXrNRrkfvMtstavR2nZ7D2puzs8npkGtyefhKQGrQ2ofjGgEBFR03KXRVn1bYch5+uvkbXhI2jLWiJIPZXweOYZuD3+OCTVNGikhseAQkRETUeFNXLK6bPTkPP6LGRdC4A2Ow8AIGvRAh7PPgvXx8dDwgHqVocBpQ448YnMid9PRGZSxaKseq2AW1fskXXBEbpiKYA8yLy94DFjBlzHjYNEobBYuXR3DCi1IJUa7l9qNJp7tn0nqqnCwkIAgI2NjYUrIWrk7liUVV96RzApMfzbbWOvhUewGi4vx0DSYbAlK6UaYECpBZlMBnt7e9y8eRM2NjbGtWeI6kIURRQWFiIzMxOurq7GAExEdaTOgK5UwK3LDsi+4ACdpiyYOGihDFbDJbAQghSAJtuydVKNMKDUgiAI8PHxQWJiIq6XzZMnul+urq4ma/gQUe3p8vKQvetPZH/vBb3G8MujjaMWyuB8uAQWQbjz90mukdMoMKDUklwuR/v27e+62i1RTdnY2PDKCdF90OXmIvvTLcj+9FPo8/MBSCB30kLZOR/OLSsEEwiG2TxcI6dRYECpA4lEwpbkREQWpL11C9mbN+PWls+gL1upXd6uLZSjw+CcvLJCMAG4Rk7jw4BCRESNhjY7G9kbN+HW1q3Qlw0wVwQFQTlnDpwefACCRAIkhFbTB6X5rpHTGDGgEBGR1dOqVMj6ZCNubdsGsagIAKAI7gTPOXPgOHiwIZiU4xo5TQIDChERWa3SjExkf/Ixbm3fAbG4GABgGxIC5Zw5cBw0EIIgVP1ArpHT6DGgEBGR1SlNT0fWho+Q8+WXEMsmJdh26wrP6Gg4DBhQfTChJoMBhYiIrEZpaipUGzYg96uvIZaWAgDsevSAMnoOHCIiGEyaEQYUIiJqGHdZYViTnIysD9cjZ+dOoCyY2PfuDWV0NOz7hDGYNENNMqAEBgbC2dkZEokEbm5u2Ldvn6VLIiJq3qpZYVgT+iJUe68g97tdgFYLALAP7wvl7NlwCAuzULFkDZpkQAGAQ4cOwdHR0dJlEBFRFSsMl+RJkXWkELkb3gJEw9URh379oIyeA/sePSxUKFmTJhtQiIjIClRYYbgkVwZVgiPybtjdDiYBgOfbW2HXncGEbrO61e7i4uIwatQo+Pr6QhAE7Ny5s9IxMTExCAwMhK2tLfr06YNjx46Z7BcEAVFRUejduze2bt3aQJUTEVElZSsMF+fIkHLIDVd/9kTedXtAFODoV4TAB2+iZb9U2LkWWLpSsjJWdwWloKAA3bp1w7Rp0zB27NhK+7dv346FCxdi3bp16NOnD1atWoVhw4bh4sWLaNGiBQDgwIED8PPzQ1paGoYOHYouXbqga9euDf1SiIiaveKz8VAdcEN+sp1xm5N/EZSd82Hrpr19oDrDAtWRNbO6gDJixAiMGDGi2v0rV67E9OnTMXXqVADAunXr8OOPP+KTTz7B4sWLAQB+fn4AAB8fHzz00EM4efJktQGlpKQEJSUlxq/z8vLM9VKIiJqtonPnoFqzFuq9ewHYARDhFFBsCCau2soP4ArDVIHV3eK5G41GgxMnTmDo0KHGbRKJBEOHDsXhw4cBGK7A5OfnAwDUajV+//13dO7cudpzLl++HC4uLsY/AQEB9fsiiIiasKK//kLSrNm4Nu4xQzgRBDi3BdqMUMG/360qwokAOPtxhWGqxOquoNyNSqWCTqeDl5dp0vby8sKFCxcAABkZGXj00UcBADqdDtOnT0fv3r2rPeeSJUuwcOFC49d5eXkMKUREtVR46hRUa9aiYP9+wwaJBC6jRsJj5kwois+WzeIRcOdMHq4wTHfTqAJKTbRp0wanT5+u8fEKhQIKhaIeKyIiaroKT5yAKiYGBYcMV7EhlcJl9GgoZ86APDCw7Kg2wOOfcoVhqpVGFVCUSiWkUikyMkwHU2VkZMDb29tCVRERNS+iKKLw2J9QrVmDwqNHDRtlMrg+OgYeM2ZAXtVVaK4wTLXUqAKKXC5Hz549sXfvXowZMwYAoNfrsXfvXsydO/e+zh0TE4OYmBjodDozVEpE1PSIoojCw4dxc80aFB0/YdhoYwPXsWOhnDEdNmUTFKrFFYapFqwuoKjValy5csX4dWJiIuLj4+Hu7o6WLVti4cKFmDx5Mnr16oWwsDCsWrUKBQUFxlk9dRUdHY3o6Gjk5eXBxcXlfl8GEVGTIYoiCg4chGrNGhSdOgUAEGxs4Dp+PDymPwsbHx8LV0hNkdUFlOPHj2PQoEHGr8sHsE6ePBmbNm3CE088gZs3b2Lp0qVIT09HaGgodu/eXWngLBER3R9RFKGOjYVqzVoU//UXAEBQKOD6xOPweOYZ2PDfXapHgiiK4r0Paz7Kr6Dk5ubC2dnZ0uUQEdWPu6wsLIoi1L//DlXMGhQnJAAABFtbuD35JDyemQaZp6clKycrZs6foVZ3BcVSOAaFiJqNalYWFh9cjvxUe6jWrEVJWesGwd4e7v94Cu5Tp0Lm4WGhgqk54hWUCngFhYiatCpWFhb1QH6yHVTnHFGSawMAkDg4wO3pp+E+ZTJkbm4WKpYaG15BISKi2quwsrCoB/KSDMFEk1cWTOSA+zOz4D55MqSurparlZo9BhQiouaibGVhUQ/kXbeDKsERmvyyYGKjh3sHNdyDCiAd3QNgOCELY0AhImomxJxU5F61gyrBCaVqwz//UrkhmLgFFUBqU3bbhysLkxVgQCnDQbJE1FSJGg1yvvsOWTEfoDTdMJ5EqtDBvWMB3NrdEUzKcWVhsgIcJFsBB8kSUVOh12iQ+803UK1fD21qGgBAagd4dMiDW7sCSGQV//kXDOvjLDjDFvRUJxwkS0RE1dKXlCDny6+QtWEDtGVrl0k9lVA++yxcuzpA8t2zVTyKKwuTdWFAISJqIvRFRcjZsQNZH30M7c2bAACZlxc8pk+H62PjILG1NRyokHNlYbJ6DChERI2cvrAQt77YjqxPPoFOpQIAyHx9oJwxAy5jx0Iil5s+gCsLUyPAgFKGg2SJqLHRqQtwa9vnyP5kI3S3bgEAbPz84DFrJlwfeQRCxWByJ64sTFaOg2Qr4CBZIrJ2uvx83Nq6FdkbN0GXmwsAsGnZEsqZM+EyehQEGxsLV0jNFQfJEhE1Q7q8PGRv2YLszZ9Cn5cHAJAHBkI5exacH34Ygoz/pFPTwe9mIiIrp8vJQfannyL70y3Qq9UAAHnbtlDOmgXnh0ZAkHLsCDU9DChERFZKe+sWsjduwq3PPoO+sBAAoGjfHso5s+H04IMMJtSkMaAQEVmCXlftLBptVhayN25E9ufbIJYHkw4doJwzB04PDIUgkViycqIGwYBCRNTQEnZV2YdE2+c/yNqfjFtffAGxuBgAYBscDGX0HDgOGsRgQs0KA0oZTjMmogaRsAvYMQnA7QmUpYUSZJ0sQM7Hr0HUGTq62nbpYggmUVEQBMFCxRJZDqcZV8BpxkRUb/Q6YFWI8cpJaYEEWeedkHPVHqLeEELsWgDK19bBITKSwYQaHU4zJiJqjK4fAvJSoVFLkXXeETmJ9kB5MFGWwDMkH/ZeGggtJQDDCTVzDChERA1E8/d5qI65IDfRHhANAcS+RQmUnfNh30JzO5OoMyxXJJGVYEAhIqpnmmvXoFr3IXJ37QL0DgAAB6/bwaQSR68GrpDI+jCgEBHVk5KrV6Fatw55P/wI6PUAAIcAQNlBBXtlFcEEgmFV4VYRDVsokRViQCEiMrOSy5ehWrsOeT//DJTNQ3AcOBDKObNhJ7tWNotHwJ0zeQxfAxi+gqsKE4EBhYjIbIovXoRq7Trk79lzO5gMGQLl7NmwC+lcdlRX4PFPq+yDguErgODRDV84kRViQCnDPihEVFfFCQlQrV2L/F9/M25zevBBKGfPgm2nTpUfEDwa6PhwtZ1kiYh9UCphHxQiqqmiM2egWrMW6n37DBsEAc4jhsNj1izYBgVZtjgiC2AfFCIiCyqKj8fNNWtQELffsEEigfPDD0M5ayYUbdtatjiiJoIBhYiohgpPnoQqZg0KDh40bJBK4TJyJDxmzoSiTWvLFkfUxDCgEBHdQ8GxY1CtWYvCI0cMG2QyuDwyGsoZMyBv1cqyxRE1UQwoRERVEEURhUePQvVBDAqPHzdstLGB65gx8Jg5A3J/f8sWSNTEMaAQEd1BFEUUHDwE1Zo1KDp5EgAg2NjA5bFxUD77LGz8/CxcIVHzwIBCRM2HXlft1F5RFFEQF4eba9ag+PRfAABBLofr44/D49lnYOPtbcnKiZodBhQiah4SdlXZHE0ctgLqDGeo1qxB8dmzAABBoYDbk0/A/ZlnYNOihYUKJmreGFCIqOlL2FXWXv522ydRBPITsqHa8QJKcmwAAIKdHdyeegoeU6dA5ulpoWKJCGBAMWInWaImSq8zXDkpCyeiCOQn20J1zskYTCQ2gNvkZ+A+bRpk7u4WLJaIyrGTbAXsJEvUxCTuBzaPhKgH8pJskZXghJLc8mCih1v7Arh3UEM243ug9QALF0vUuLGTLBFRDYm5qci7ZgfVOUdo8m8HE/cgQzCRyst+R1NnWLBKIqqIAYWImiSxtBS53/8A1QdrUJrqBgCQyPXw6KCGW/uC28GknKOXBaokouowoBBRkyJqNMjdtQuqD9ejNCkJACBVAO4d8gzBxKbiXW0BcPY1TDkmIqvBgEJETYJeo0HuN98ia/16lKYaphJL3d3h8cw0uIU6Q/L99CoeJRj+Gr7C2A+FiKwDAwoRNWr6khLkfPUVsjZ8BG16OgBA6qmExzPPwO2JJyCxszMcaKeosg8Khq8AgkdboHIiuhsGFCJqlPTFxcjZ8SWyPvoI2sxMAICsRQt4PPssXB8fD4mtrekDgkcDHR+utpMsEVkXBhQialT0hYW4tX0Hsj7+GDqVCgAg8/aGx4zpcB03DhKFovoHS6ScSkzUSDCgEFGjoC8owK1t25D1yUbosrMBADa+vvCYORMuj46BRC63cIVEZE4MKERk1XRqNW5t/RzZGzdCl5MDALAJCIBy1ky4jB4NwcbGsgUSUb1gQCEiq6TLy0P2Z58he/On0OfmAgBsWrWEctZsuIx8mMGEqIljQCEiq6LLzUX25k+RvWUL9Pn5AAB569ZQzpkN5xEjIMj4zxZRc8D/04nIKmhv3UL25s24teUz6AsKAADydm2hnD0bzsOHQ5Bytg1Rc8KAQkQWpc3ORvbGjbi19XPoCwsBAIqgICjnzIHTgw9AkEgsXCERWQIDSpmYmBjExMRAp9NZuhSiZkGrUiHr409w64svIBYVAQAUwZ3gOWcOHAcPZjAhauYEURQrLkzRrJlzqWiiZkmvu2sztNKMTGR/8jFufbEdYkkJAMA2JATKOXPgOGggBEGwUOFEdL/M+TOUV1CIyHwSdlXTTv4tlLqHIWvDR8j58kuIGg0AwLZbV3hGR8NhwAAGEyIywYBCROaRsAvYMQmA6UXZ0rRMqF6ci9xrzhC1hluodj16QBk9Bw4REQwmRFQlBhQiun96neHKyR3hRKOWIivBETmJ9oAoANDBvncvKKOjYd+nD4MJEd0VAwoR3b/rh4y3dTT5UqgSnJB7za4smAD2XiVQds6Hwz9nAK37WrJSImokGFCI6P6pM1CSJ0VWghNyr98OJg7exVB2VsPeU2M8joioJhhQiOi+lFy5AlXM98iLbXE7mPgUw7NzPuyUpaYHO3pZoEIiaowYUIioToovXoJq3Vrk794DiCIAAY5+xVB2zoede4VgAsEwm6dVhCVKJaJGiAGFiGql+Px5qNasRf6vvxq3OT0wFMphwbA9vqSKR5QNhh2+wqQfChHR3TCgEFGNFJ09B9XatVDv3WvYIAhwGjYMytmzYNuhg2FbG79q+qCsAIJHN3zRRNRoMaAQ0V0V/fUXVDFroI6NNWwQBDg/9BCUs2ZC0b696cHBo4GOD9+1kywRUU0woBBRlQpPnYIqZg0KDhwwbJBI4DJqJDxmzoSiTZvqHyiRAq0HNEyRRNRkMaAQkYnC48ehWrMGBYcOGzZIpXAZPRrKmTMgDwy0aG1E1HwwoBARRFFE4dFjUK1Zg8JjxwwbZTK4PjoGHjNmQB4QYNkCiajZYUAhasZEUUTh4cO4uWYNio6fMGy0sYHr2LFQzpgOGz8/yxZIRM0WAwpRMySKIgoOHIAqZg2K4uMBAIKNDVzHj4fH9Gdh4+Nj2QKJqNljQCFqRkRRhPqPP6BasxbFZ84AAASFAq5PPA6PZ56BjRc7vRKRdWBAIWoGRFGE+vffoYpZg+KEBACAYGsLt6eegse0qZB5elq4QiIiU002oBQWFqJTp04YP348/u///s/S5RBZhKjXI//X36BauxYlFy4AAAR7e7j/4ym4T50KmYeHhSskIqpakw0ob7zxBvr25bLu1DyJOh3y9+wxBJPLVwAAEgcHuD39NNynTIbMzc3CFRIR3V2TDCiXL1/GhQsXMGrUKJw9e9bS5RA1GFGnQ95PP0O1bh00f/8NAJA4OcF94kS4T5oIqaurZQskIqohiaULqCguLg6jRo2Cr68vBEHAzp07Kx0TExODwMBA2Nraok+fPjhW3rehzKJFi7B8+fIGqpjI8kStFjk7d+LqwyOR+s9/QvP335A4O0M5by7a7f0Nns/NYzghokbF6gJKQUEBunXrhpiYmCr3b9++HQsXLsSyZctw8uRJdOvWDcOGDUNmZiYA4LvvvkNQUBCCgoIasmyi+qXXAYn7gTNfGf7W6wAAYmkpcr7+Bn8/9DDSFi+B5to1SF1c4LlgAdr9vhee0dGQOjtbuHgiotoTRFEU6/rg0tJSpKeno7CwEJ6ennB3dzdnbRAEAd9++y3GjBlj3NanTx/07t0bH3zwAQBAr9cjICAA8+bNw+LFi7FkyRJ89tlnkEqlUKvVKC0txQsvvIClS5dW+RwlJSUoKSkxfp2Xl4eAgADk5ubCmf+wkzVI2FVphWDRwRc58rHI2nUUpSkpAACpmxvcp02F21P/gNTRwVLVElEzlpeXBxcXF7P8DK31GJT8/Hx89tln+OKLL3Ds2DFoNBqIoghBEODv748HH3wQM2bMQO/eve+rsKpoNBqcOHECS5YsMW6TSCQYOnQoDh82rBuyfPly4+2dTZs24ezZs9WGk/LjX331VbPXSmQWCbuAHZMAGH6P0OuA3Kv2UJ3XQVv4DQBAqlTCY9o0uD35BCT29hYslojIfGp1i2flypUIDAzExo0bMXToUOzcuRPx8fG4dOkSDh8+jGXLlkGr1eLBBx/E8OHDcfnyZbMWq1KpoNPp4FWhmZSXlxfS09PrdM4lS5YgNzfX+CcpKckcpRLdP73OcOUEIvQ6IPuSA/7+wQvpJ1yhLZRCZquDVzjQbs/P8Jg2leGEiJqUWl1B+fPPPxEXF4fOnTtXuT8sLAzTpk3DunXrsHHjRuzfvx/t27c3S6F1MWXKlHseo1AooFAo6r8Yotq6fgj67DTk/O2ArPOO0BZLAQAyOx08gvPh2qYQEimAzFNA6wGWrZWIyMxqFVC2bdtWo+MUCgVmzZpVp4LuRqlUQiqVIiMjw2R7RkYGvL29zf58RJaiLyzErc+/Rtb3LaArKQsm9looO6nhUh5Myqkzqj4JEVEjVudZPEVFRSgsLDR+ff36daxatQp79uwxS2FVkcvl6NmzJ/bu3WvcptfrsXfvXoSHh9/XuWNiYhAcHFwvY2eIakqnLoBq/QZcGTIUmVv2QFcihY2DFt69c9Du4Uy4ta8QTgDA0bzr5wQGBqJr164IDQ3FoEGDqjzmhx9+QIcOHdC+fXt89NFHxu1JSUkYOHAggoOD0bVrV3z55ZdmrY2Imo86z+J58MEHMXbsWMyaNQs5OTno2LEjbGxsoFKpsHLlSsyePbtOBanValy5Yuh82b17d6xcuRKDBg2Cu7s7WrZsie3bt2Py5Mn48MMPERYWhlWrVmHHjh24cOFCpbEpdWHOEchENaXLz8etrVuRvXETdLm5AACbgAAo2yTBxSsNgqSq/00FwNkXWHAGlVNL3QUGBuLs2bNwdHSscr9Wq0VwcDD27dsHFxcX9OzZE4cOHYKHhwfS0tKQkZGB0NBQpKeno2fPnrh06RIcHDiriKg5MOfP0DpfQTl58iQGDDDc9/7qq6/g5eWF69ev49NPP8V7771X54KOHz+O7t27o3v37gCAhQsXonv37saZOE888QT+7//+D0uXLkVoaCji4+Oxe/dus4QTooamy8vDzQ9icGXIUNxctRq63FzIAwPh+9YKtP35J7jOfwuCBACECo8s+3r4CrOGk5o4duwYOnfuDD8/Pzg6OmLEiBH45ZdfAAA+Pj4IDQ0FAHh7e0OpVCI7O7tB6yOipqHOre4LCwvh5OQEAPjll18wduxYSCQS9O3bF9evX69zQQMHDsS9LurMnTsXc+fOrfNzEFmaLicH2Z9+iuxPt0CvVgMA5G3bQjl7NpxHDIcgLQsdwaOBxz+t1AcFzr6GcBI82uy1CYKAqKgoSCQSLFiwABMmTDDZn5qaCj8/P+PXfn5+SCnrxXKnEydOQKfTISAgwOw1ElHTV+eA0q5dO+zcuROPPvoo9uzZg+effx4AkJmZ2ShvjcTExCAmJgY6nc7SpVATpr11C9kbN+HWZ59BXzaGS9G+PZTRc+D04IMQJFVc1AweDXR8GLh+yDAg1tELaBVRb1dODhw4AD8/P6SlpWHo0KHo0qULunbtWqtzZGdnY9KkSdiwYUO91EhETV+db/EsXboUixYtQmBgIPr06WMcpPrLL78Yb880JtHR0UhISMCff/5p6VKoCdJmZSHjnXdwZchQZK1fD31hIRQdO8LvvdVo/d1OOA8fXnU4KSeRGqYSd3nM8Pd9hJOHHnoIkydPNn69b98+KJVKYzgvvzri4+ODhx56CCdPnjR5vK+vr8kVk5SUFPj6+hq/LikpwZgxY7B48WJERETUuU4iat7qHFAee+wx3LhxA8ePH8fu3buN24cMGYL//e9/ZimOqLErzcxExoq3cGXIUGR//AnEwkLYdu4M/zUxaP3tN3Cu7qpJLSxbtgxBQUF48sknkZubi++//x7dunXDxx9/XOXxFW/JREVFoaioCEeOHEFBQQHy8/MBGAas//7775X6HoWFheHs2bNISUmBWq3Gzz//jGHDhgEARFHElClTMHjwYEycOPG+XhcRNW91vsWTlJSEgICASv1HwsLC7rsoosauNCMDWR99jJwdOyCWrfVk27UrlHNmwzEqCoJQcdBr3fz222/IzMzEiRMnsGbNGowZMwY5OTn48ssvq10w08/PD/v37zd+LZFIYGdnh8zMTGRkZODRRx8FAOh0OkyfPt049b58ULpMJsO7776LQYMGQa/X48UXX4SHhwcA4ODBg9i+fTu6du1qXIl8y5Yt6NKli1leLxE1H3WeZiyRSODu7o5u3bohNDTU+Eej0eC9997D5s2bzV1rg+A0Y7ofpampyProI+R8+RXE0lIAgF1oKJTR0XDo389swaTcO++8g/79+xtvsfbp0wfPPfdcpYGtd9qwYQMWLlxovFISHx+PXr16ITk5mQ0Piei+WHSxwHKJiYk4deoU4uPjcerUKezYsQOpqYZZBo3xBzsHydL90CSnIGv9euR8+y1QHkx69YRndDTs+/Y1ezAp17FjR+zatQvh4eHYvXs3BEHAW2+9hcGDB8PHx6fKx/j5+UGtViMvLw+Ojo54/vnnMWHCBIYTIrIqdQ4orVq1QqtWrTBmzBjjtsOHD2Py5Mn473//a47aGlR0dDSio6ON6Y+oJjRJSVB9+CFyd34HaLUAAPs+faCcMwcOfer/dueoUaOwd+9etGzZEoGBgfjmm2/w+++/o2/fvvjPf/6D6dOnV3pM+SDY5ORkbNy4Eenp6fjuu+/qvVYiotqo8y2e6vz88894+eWXcfz4cXOetsHwFg/VhObaNajWfYjc778Hyq66OUREQDlnNux79bJwdXenUqng6emJ4cOH49KlS4iLizPpa0JEVFdWcYtHo9FALpdX2t6+fXucO3fuvooislYlV69CtW4d8n74EdDrAQAOAwYYgkkjmV6vVCqhUChw/fp1xMbGMpwQkVWqc0BxdHREcHAwunfvjtDQUHTv3h2+vr54//33MXToUHPWSGRxJZcvQ7V2HfJ+/hkou+joOHAglHNmw66WTcysQXFxsaVLICK6qzrf4jlw4ABOnz6N06dPIz4+HmfPnjX+ozd8+HD06tULXbp0QZcuXdCxY0ezFl0f7hwke+nSJd7iIQBA8cWLUK1Zi/w7Vul2HDoEytmzYVehPwgRUXNnzls8ZhuDotfrcfHiRcTHxyM+Pt4YXjIzMxvVzBiOQSEAKE5IgGrtWuT/+ptxm9OwYVDOngXbRhC4iYgswSoDSnUyMjIa1UrDDCjNW9GZM1CtWQv1vn2GDYIA5xHD4TFrFmyraXxGREQGFhske+PGDbRs2bLGx6ekpHAAHjUKRfHxuLlmDQriyjqsSiRwfvhhKGfNhKJtW8sWR0TUDNVqEZDevXtj5syZd11QLzc3Fxs2bEBISAi+/vrr+y6Q6L7pdUDifuDMV4a/9bdvORaePIkbzzyLa08+ZQgnUilcHnkEbX78AX7vvM1wQkRkIbW6gpKQkIA33ngDDzzwAGxtbdGzZ0/4+vrC1tYWt27dQkJCAs6dO4cePXrg7bffxkMPPVRfdRPVTMIuYPdLQF7q7W3OvigImAnVj6dReOSIYZtMBpdHRkM5YwbkrVpZplYiIjKq0xiUoqIi/Pjjjzhw4ACuX7+OoqIiKJVKdO/eHcOGDUNISEh91NogOAalCUnYBeyYBMDwLS6KQGGmHKqzTii8qTAcY2MD10cfhceM6ZD7+1uuViKiJqBRDZJtLDjNuInR64BVIUBeKkQRKEhXQHXOEUUqQzARJCJcOgpQvvcrbBhMiIjMggGlHvEKShORuB/ippEoSFPg5jknFGcZuh4LEhGubQvg0UkNG3s9MPkHoPUACxdLRNQ0WEWreyJrJYoi1H/EQvWrEsXZZcFEqodb20K4d1LDxk5/+2B1hoWqJCKiu2FAoSZD1OuRv3cvVGvWouT8eQByQzBpXwiPjmrIbPWVH+TYeHr0EBE1Jwwo1OiJej3yf/nFEEwuXQIASOzt4RZUCPfAm5DZVtXJWACcfYFWEQ1bLBER1QgDCjVaok6HvN27oVq7FporfwMAJI6OcJv4NNwnTYIsbX/ZLB4B5TN5DATDX8NXABJpQ5dNREQ1UKtGbRXt378fTz/9NMLDw5GSkgIA2LJlCw4cOGCW4oiqImq1yN21C1dHjkLqC4ugufI3JE5OUEZHo93e39Bi/nzI3NyA4NHA458Czj6mJ3D2NWwPHm2ZF0BERPdU5ysoX3/9NSZOnIgJEybg1KlTKCkpAWDoJPvmm2/ip59+MluRRAAglpYi9/sfoPpwHUqv3wAASFxc4DFlMtyefhpSJ6fKDwoeDXR8GLh+yDAg1tHLcFuHV06IiKxanacZd+/eHc8//zwmTZoEJycnnD59Gm3atMGpU6cwYsQIpKenm7vWesU+KNZL1GiQu2sXVB+uR2lSEgBA6uoK92nT4PaPpyB1dLRwhUREBFjJNOOLFy8iMjKy0nYXFxfk5OTcT00WER0djejoaOObS5an12iQ+823yFq/HqWphlb1Und3eDwzDW5PPgmJg4OFKyQiovpS54Di7e2NK1euIDAw0GT7gQMH0KZNm/uti5oxfUkJcr76ClkbPoK27Eqc1FMJj2eegdsTT0BiZ2fhComIqL7VOaBMnz4d8+fPxyeffAJBEJCamorDhw9j0aJFePnll81ZIzUT+uJi5OzYYQgmN28CAGQtWsBj+nS4jn8MEltbC1dIREQNpc4BZfHixdDr9RgyZAgKCwsRGRkJhUKBRYsWYd68eeaskZo4fWEhbm3fgayPP4ZOpQIAyLy94TFjOlzHjYNEobBwhURE1NDuey0ejUaDK1euQK1WIzg4GI6NfMAi1+JpOPqCAtzatg1Zn2yELjsbAGDj6wuPmTPh8ugYSORyC1dIRES1YRWDZAGguLgYf/31FzIzM6HX601m7owezR4TVDWdWo1bn21F9qZN0JUNqLYJCIBy1ky4jB4NwcbGsgUSEZHF1Tmg7N69GxMnTkRWVlalfYIgQKerqr04NWe6vDxkf/YZsjd/Cn1uLgDAplVLKGfNhsvIhxlMiIjIqM4BZd68eXj88cexdOlSeHlxwTWqni4nB9mfbkH2li3Q5+cDAORt2kA5exacR4yAIOOKC0REZKrOPxkyMjKwcOFChhOqlvbWLWRv2oxbn30GfUEBAEDRvh2Us2fDadgwCFJ2cyUioqrVOaA89thj+OOPP9C2bVtz1mMxd3aSpfujzcpC9qZNyN76OcTCQgCAIigIyjlz4PTgAxAk97UEFBERNQN1nsVTWFiI8ePHw9PTE126dIFNhfEDzz33nFkKbGicxVN32ps3kfXJRtz64guIRUUAAEVwJ3jOmQPHwYMZTIiImjirmMWzbds2/PLLL7C1tcUff/wBQRCM+wRBaLQBhWqvNCMTWR9/hJztOyCWLRppGxIC5Zw5cBw00OR7g4iIqCbqHFD+/e9/49VXX8XixYsh4W/GzVJpejqy1m9AzldfQdRoAAC23brCMzoaDgMGMJgQEVGd1TmgaDQaPPHEEwwnzVBpSgpUGzYg9+tvIJaWAgDsevSAMnoOHCIiGEyIiOi+1TmgTJ48Gdu3b8e//vUvc9ZDVkyTlISs9euR8+1OQKsFANj37g1ldDTs+4QxmBARkdnUOaDodDq8/fbb2LNnD7p27VppkOzKlSvvuziyDppr16D6cD1yd+0CymY52Yf3hXL2bDiEhVm4OiIiaorqHFDOnDmD7t27AwDOnj1rso+/STcieh1w/RCgzgAcvYBWEYDE0J+k5Goisj5ch9zvfwD0egCAQ79+UEbPgX2PHpasmoiImrg6B5R9+/aZsw6yhIRdwO6XgLzU29ucfVHSeSFUv1xE3k8/AWWz0B2iIuE5ezbsQkMtUysRETUr7DHeXCXsAnZMAnC7DU5xjgyqg0XIX/8uAMNVMMfBg6GcPRt2XUIsUycRETVLtQooCxcuxGuvvQYHBwcsXLjwrsdyDIoV0+sMV07KwknxLRlU55yQn2xnPMQpEFD+35ewDWEwISKihlergHLq1CmUlk0rPXXqVLXHcQyKlbt+yHhbR68Fru9TQq+RABDhFFAMZed82LpqAYdblq2TiIiarVoFlDvHnWzevBn+/v6V+qCIooikpCTzVEf1Q51h/E+JDPDooEZJrgzKzmooXLRVHkdERNSQ6jwGpXXr1khLS0OLFi1MtmdnZ6N169ZcdM+aOZquQO0RrEaVF70cuVI1ERFZRp3bwFa3xqBarYatrW2dC6IG0CoCcPZF+UDYyuFEAJz9DMcRERFZQK2voJQPjhUEAUuXLoW9vb1xn06nw9GjRxHaCKeixsTEICYmpnlc+ZFIgeFvlc3iEXDnTJ7y0ILhK4z9UIiIiBqaIFZ3KaQagwYNAgDExsYiPDwccrncuE8ulyMwMBCLFi1C+/btzVtpAzHnUtFWr8o+KH6GcBI82nJ1ERFRo2TOn6G1Dijlpk6ditWrVze5H+LNKqAAd+0kS0REVBtWEVCaqmYXUIiIiMzEnD9D6zxIFgD279+Pp59+GuHh4UhJSQEAbNmyBQcOHLivooiIiKh5q3NA+frrrzFs2DDY2dnh1KlTKCkpAQDk5ubizTffNFuBRERE1PzUOaC8/vrrWLduHTZs2AAbGxvj9n79+uHkyZNmKY6IiIiapzoHlIsXLyIyMrLSdhcXF+Tk5NxPTURERNTM1TmgeHt748qVK5W2HzhwAG3atLmvooiIiKh5q3NAmT59OubPn4+jR49CEASkpqZi69atWLRoEWbPnm3OGomIiKiZqfNaPIsXL4Zer8eQIUNQWFiIyMhIKBQKLFq0CPPmzTNnjURERNTM1KoPyl9//YWQkBCTFYw1Gg2uXLkCtVqN4OBgODo61kuhDYV9UIiIiOrGYn1QunfvDpVKBQBo06YNsrKyIJfLERwcjLCwsEYfToiIiMg61CqguLq6IjExEQBw7do16PX6eimKiIiImrdajUEZN24coqKi4OPjA0EQ0KtXL0ilVa/bcvXqVbMUSERERM1PrQLK+vXrMXbsWFy5cgXPPfccpk+fDicnp/qqjYiIiJqpWs/iGT58OADgxIkTmD9/PgMKERERmV2dpxlv3LjRnHUQERERGdUqoCxcuBCvvfYaHBwcsHDhwrseu3LlyvsqjIiIiJqvWgWUU6dOobS01Pjf1REE4f6qug85OTkYOnQotFottFot5s+fj+nTp1usHiIiIqq9WjVqq4nk5GT897//xfr168152hrT6XQoKSmBvb09CgoKEBISguPHj8PDw6NGj2ejNiIiorqxWKO2msjKysLHH39s7tPWmFQqhb29PQCgpKQEoijCzBmMiIiI6pnZA8r9iouLw6hRo+Dr6wtBELBz585Kx8TExCAwMBC2trbo06cPjh07ZrI/JycH3bp1g7+/P/75z39CqVQ2UPVERERkDlYXUAoKCtCtWzfExMRUuX/79u1YuHAhli1bhpMnT6Jbt24YNmwYMjMzjce4urri9OnTSExMxOeff46MjIyGKp+IiIjMwOoCyogRI/D666/j0UcfrXL/ypUrMX36dEydOhXBwcFYt24d7O3t8cknn1Q61svLC926dcP+/furfb6SkhLk5eWZ/CEiIiLLqnUflLFjx951f05OTl1ruSeNRoMTJ05gyZIlxm0SiQRDhw7F4cOHAQAZGRmwt7eHk5MTcnNzERcXh9mzZ1d7zuXLl+PVV1+tt5qJiIio9modUFxcXO65f9KkSXUu6G5UKhV0Oh28vLxMtnt5eeHChQsAgOvXr2PGjBnGwbHz5s1Dly5dqj3nkiVLTHq65OXlISAgoF7qJyIiopqpdUCx9g6yYWFhiI+Pr/HxCoUCCoWi/goiIiKiWrO6MSh3o1QqIZVKKw16zcjIgLe3t4WqIiIiInNrVAFFLpejZ8+e2Lt3r3GbXq/H3r17ER4efl/njomJQXBwMHr37n2/ZRIREdF9qvNigfVFrVbjypUrxq8TExMRHx8Pd3d3tGzZEgsXLsTkyZPRq1cvhIWFYdWqVSgoKMDUqVPv63mjo6MRHR1t7IJHRERElmN1AeX48eMYNGiQ8evyAayTJ0/Gpk2b8MQTT+DmzZtYunQp0tPTERoait27d1caOEtERESNl9nX4mnsuBYPERE1Fjq9iGOJ2cjML0YLJ1uEtXaHVGK5BXvN+TPU6q6gWEpMTAxiYmKg0+ksXQoREdE97T6bhle/T0BabrFxm4+LLZaNCsbwEB8LVmYevIJSAa+gEBGRtdt9Ng2zPzuJij/Ay6+drH26h0VCilWvZkxERET1R6cX8er3CcZwIkjVEGxUAGDc9ur3CdDpG/f1B97iISIiakSOXs1CRvFVyD3OQ+Z0ARLbZGjzg1GcMhGAIaSk5RbjWGI2wtt6WLbY+8CAQkREZOWKtEU4lnYMscmx2JO4Dw5tVCb7BWkhDNHk9gDZzPxiNGYMKGU4SJaIiKxJekE64pLjEJsci6NpR1GiKzHuE/U20Ba0g07dEVp1R4jayv27WjjZNmS5ZsdBshVwkCwREZlTTacC6/Q6nM06i9ikWMQlx+HirYsm+30cfBDpH4kBfpF46bMCZOTqKw2SBQzXULxdbHHgpcENPuWY04yJiIgagXtNBVZr1DiUegixybE4kHIA2cXZxuMkggRdlV0RFRCFSP9ItHdtD0EwBI5XRhlm8QiASUgpjyPLRgVbtB+KOfAKSgW8gkJEROZQ3VRgiY0KMqfz6NwuBdfUZ6EVtcZ9TjZO6OfXD5H+kejv1x9utm53Pb+19UHhFRQiIiIrZjoVWAep/TXIHM9D5ngBEoVhgOuVfMOxgc6BiPKPQlRAFEJbhMJGYlOj5xge4oMHgr2tqpOsOTGglOEgWSIiMpe9l67ipngItn4XIHO4CEF6xwBXUQpdQWto1R3xfw8/iUdCutX5eaQSoVFPJb4b3uKpgLd4iIiotkRRxKVblxCXHIe45Dicvnka4h03d/RaB+OMG21Be0BvmGGz+slQPBLqZ6myzY63eIiIiCysWFuMY+nHjFOB0wvSTfbrin2gVXeCNr8j9MX+qKp5e2OfClyfGFCIiKjZqu1qwBkFGYhLiUNcUhyOpB1Bse72AFVbqS36+vRFZEAk+vn0x7gPEpCeW3zXqcBhrd3N/6KaCAYUIiJqlmoyC0Yv6nFWdRaxybHYn7wf57PPm5zD28EbUf6GacBh3mGwld2+IrJsFJr8VOD6xDEoFXAMChFR03fX1YAlxZg9Qoc84S/sT9lv0ptEgICunl2NoSTILcjYm6S657G2qcD1iWNQiIiI6qjiasAAINhkGacBSx0SseXq7RmdjjaOiPCNQFRAFPr79Ye7bc1vyzT1qcD1iQGlDKcZExE1D8cSs5GWWwCp/XVDIHE8D6nipskxeo0HHgwcjCdDhqFHix6wkdasN0lVmvJU4PrEWzwV8BYPEVHTlFOcg/0p+7Ht7B78lXUUgvT2bRdRlEBXGGiYdaPuCFHj2eSmADcE3uIhIiK6B1EUcSXnCmKTY429SfSiHgAgSAG91h46dQdDKCloD+jtTB7PKcCWxYBCRERNRomuBH+m/2lcETi1INVkf5BbEAb4ReLzfQ64qfKCWEVvEk4Btg4MKEREZFVq25skszAT+5P3IzY5FkfSjqBIW2TcJ5fI0cenj3HWjY+jYeZMR0XTXw24sWNAISIiq1HT3iTns84jNjkWscmxSMhKMDlHC7sWiAyIRJR/FMK8w2BvY1/peYaH+GDt0z0qPZd3E54C3NhwkGwFHCRLRGQZd+1NIpRgzkM65EvOIC45DlnFWXfsF9BF2QWR/pGICohCB7cOd+1NcqfaXq2hu+MgWSIialKq7k2Sfbs3if1VfHpHbxJ7mT36+fVDpH8k+vv1h9JOWafn5RRg68WAUoZ9UIiILMfYm8TuBqSOFyBzOg+pItPkGL3GHQ8EDsITnYehl1ev++pNQtaPt3gq4C0eIqKGk1uSiwMpB/D5mT04nXUEgvT2ANfbvUk6QqfuCL3GE6uf7M7eJFaMt3iIiKhREkURV3OvGga4JsUi/ma8SW8SUWsPbUEHaPM7QlsQxN4kzRgDChER1SuNToPj6ceNs25S1Ckm+9u5tkOkXxS2xTrg5k1v9iYhAAwoRER0D3WZ6aIqUhl7kxxKPVSpN0mYT5ixN4mvoy8AoJMte5PQbQwoRERUrZr0JQHKepNkn0dcUhxik2NxLuucyXk87TwN04D9o9DHpw97k9A9cZBsBRwkS0RkcNe+JABWP9UJjm7XEJcch7jkONwsMl0ROMQjxNgwrZN7J/YmaQY4SJaIiOpVVX1JgPLeJBcgc7yAf5+6Cgha4z57mT0ifCMQ6R+JAf4D2JuE7gsDChERVWLoS1IMQAepXRKk5Q3TbDNMjlPa+mJY60GI9I9EL69ekEvllimYmhwGFCIiMpFbkovfbuyGre9uyBwuQZAVGvcZepO0glbdCTp1R7z26AMY093fgtVSU8WAUoadZImouRJFEYm5iYhNjkVcchxOZZ6CTtTBxqVsv84OWnUHaNUdoVUHAfrbA1y9nO2qOSvR/eEg2Qo4SJaImgONToPjGccRlxyH2KRYJKuTTfa3dWmLG8mByM1qD11RAACpyf7yviQHXhrMAaxkxEGyRERUa+W9SeKS43Ao9RAKtbdv3dhIbBDmHYZI/0hE+kfC38nfOIuHfUnIEhhQiIiaKFEUcSH7gvHWzRnVGZP9SjulMZCE+4RX6k3CviRkSQwoRESNQE17gxSWFuJo2lHEJsdif/J+ZBaZrgjc2aOzoYNrQCQ6uXeCRKjcVv5Ow0N88ECwN/uSUINjQCEisnL36uaaqk41jCVJjsWxtGPQ6DXG4+xkdgj3CUdUQBQG+A2Ap71nrZ+ffUnIEhhQiIisWNXdXPXI1FzE/D070TLhOtKLEk32+jn6GdvK9/LuBYVU0ZAlE5kFAwoRkZUy6eYqKYLM4RJkThcgdbgISVlvkvQiQCJIEOoZagwlbV3b1ritPJG1YkAhIrJCoihi17l4qKS/wK7lBUjtr0EQ9Lf362yNvUnWjv0HHujYxoLVEpkfAwoRkZUo1ZXiROYJxCYZZt3cyL8BW6/b+3UlntCpOxq6uBa2QnlvksJi3sKhpocBhYjIgrKKsnAg5QBik2NxKPUQCkoLjPukggwl+a3LOrh2hFha9UDVFk62DVUuUYNhQCEiakCiKOLirYvGqyRnVGcg3jEE1t3W3TiWJMy7L4atPIr03OJKqwoDt7u5hrV2b7D6iRoKAwoRUT0r0hbhWNoxY8O0jELTFYE7uXdCVEAUIv0i0VnZ2aQ3ybJRwezmSs0SAwoRUT1IL0g39iY5mnYUJboS4z5bqS36+vZFlL+hN4mXg1e152E3V2quGFCIiO6iph1cdXodzmadNd66uXjrosl+Hwcf462b3t69YSur+bgRdnOl5ogBpUxMTAxiYmKg0+ksXQoRWYl7dXBVa9Q4lHoIscmxOJByANnF2cbjJIIE3Ty7Gde6ae/a/r56k7CbKzU3giiKVY29arbMuVQ0ETVeVXdwBSQ2KsiczqNzuxRcU5+FVtQa9znZOKGfXz9E+keiv19/uNm6NWzRRBZmzp+hvIJCRFSBSQdX6CC1vwaZ43nIHC9AolABAK7kG44NdA5ElH8UogKiENoiFDYSG0uVTdSkMKAQEVWw99JV3BQPwdbvAmQOFyFIbw9wFUUpdAWG3iTvPPwkxoR0s2ClRE0XAwoRNXuiKOLSrUvYn7IfsUmxOH3zNOz8bt/c0WsdoFN3gFbdCdqC9oDeMMBV0CotVTJRk8eAQkTNUrG2GMfSjxmnAqcXpJvs1xX7GAJJfkfoi/0BSCqdgx1cieoPAwoRNRsZBRmIS4lDXFIcjqQdQbHu9uwchVSBvj59DQNcfQdg3AcJ7OBKZEEMKETUZOlFPc6qziIuOQ5xyXE4n33eZL+3gzci/SIRFWDoTWInszPuWzYK7OBKZEEMKETUpKg1ahxOO4zYpFjsT9lv0ptEgICunl0R5R+FSP9IBLkFVdubhB1ciSyLAYWIGr2kvCTEJsciNjkWxzOOQ6u/3ZvE0cYREb4RiAqIQn+//nC3rfltGXZwJbIcBhQisho1bStfqi9FfGa8oa18ShwScxNN9rdybmVsK9+jRQ/YSOvem4QdXIksgwGFiKzCvdrK5xTnYH/KfsQlx+FgykHkl+Ybj5MJMvT06mlsKx/oEmiBV0BE5sSAQkQWV3VbeRGZxdfw3M+70eFCEm4Unode1Bv3uincMMB/ACL9IxHhGwEnuVNDl01E9YgBhYgsyqStvFAKqf1VyBwvQOZ4HhJ5DgDgWoHh2CC3IOMA1y7KLpBKpJYqm4jqGQMKEVnULxcuQSXEwdb/PGQOVyBISo37RL0MusK20OZ3wv9GPYWRnYMtWCkRNSQGFCJqUHpRj4SsBMOsm6RYnM8+D9s7ZuzqS52hVXeEVt0RuoJ2gCgHAOhKXSxUMRFZAgMKEdW7gtICHEk9gtjkWMQlxyGrOMu4T4AAbZE/tPkdoVV3gr7EB7fbod3GtvJEzQsDChHVi6T8JGMH1z/T/0Sp/vatG3uZPfr59TMMcPXpj0feO8228kRkggGFiMxCq9ciPjPeuPje1dyrJvv9Hf0xMGAgIv0j0curl0lvkmWjgtlWnohMNLmAkpSUhIkTJyIzMxMymQwvv/wyxo8fb+myiJqk3JJcHEg5gNjkWBxMOYg8TZ5xn1SQoodXD0T5R2GA/wC0dm7NtvJEVGOCKIpVXVVttNLS0pCRkYHQ0FCkp6ejZ8+euHTpEhwcHGr0+Ly8PLi4uCA3NxfOzs71XC1R4yKKIq7mXjUOcI2/GW/Sm8RF4YIBfgMQ5R+FCL8IOMtr9/9QTTvJEpF1MufP0CZ3BcXHxwc+Pobftry9vaFUKpGdnV3jgEJEpjQ6Df5M/9N46yZFnWKyv51rO0T5RyEqIApdlV3vqzcJ28oTUTmrCyhxcXF45513cOLECaSlpeHbb7/FmDFjTI6JiYnBO++8g/T0dHTr1g3vv/8+wsLCKp3rxIkT0Ol0CAgIaKDqiaxXba5O3Cy8if0p+xGbFIvDaYdRpC0y7pNL5AjzCTM2TPN19G2ol0BEzYjVBZSCggJ069YN06ZNw9ixYyvt3759OxYuXIh169ahT58+WLVqFYYNG4aLFy+iRYsWxuOys7MxadIkbNiwoSHLJ7JK91rnRi/qcT77POKSDFdJzmWdM3m8p52ncfG9Pj59YG9j39AvgYiaGasegyIIQqUrKH369EHv3r3xwQcfAAD0ej0CAgIwb948LF68GABQUlKCBx54ANOnT8fEiRPv+hwlJSUoKSkxfp2Xl4eAgACOQaEmo+p1bgBB0EDqcBlR3VVILDiOm0U3TfaHeIQgMsAQSjq5d6p2gCsRUblmOwZFo9HgxIkTWLJkiXGbRCLB0KFDcfjwYQCGQXxTpkzB4MGD7xlOAGD58uV49dVX661mIksyWecGgGCTDZnjRcgcz0NqfxWCRItjKsM+e5k9InwjEOkfiQH+A6C0U1qsbiKiRhVQVCoVdDodvLy8TLZ7eXnhwoULAICDBw9i+/bt6Nq1K3bu3AkA2LJlC7p06VLlOZcsWYKFCxcavy6/gkLUFBy+molMzQXIPc9D5ngBUtsMk/16jTu06o54ccBYTOw+CHKp3EKVEhGZalQBpSb69+8PvV5/7wPLKBQKKBSKeqyIqGHlluTiUOohxCbH4vfrcbAPzDfuE0UJdIWtDOvcqDtBr/EEIEApC2E4ISKr0qgCilKphFQqRUaG6W+BGRkZ8Pb2tlBVRJYliiIS8xKNA1xPZZ6CTtTd3q+zg1bdAVp1J2jV7QF95QGuXOeGiKxNowoocrkcPXv2xN69e40DZ/V6Pfbu3Yu5c+fe17ljYmIQExMDnU5374OJLKxUV4rjGceNvUmS8pNM9rdzbWcYS+IXibkbs5CRW8p1boioUbG6gKJWq3HlyhXj14mJiYiPj4e7uztatmyJhQsXYvLkyejVqxfCwsKwatUqFBQUYOrUqff1vNHR0YiOjjaOQCayNqoiFfYn70dcchwOpR5CobbQuM9GYoMw7zBE+kci0j8S/k7+xn2vjErjOjdE1OhY3TTjP/74A4MGDaq0ffLkydi0aRMA4IMPPjA2agsNDcV7772HPn36mOX52eqerIUoiriQfQGxybGIS47DGdUZk/1KO6UxkIT7hN+1N8m9+qAQEZmDOX+GWl1AsTQGFLKkIm0RjqYdNYaSzMJMk/2dPTobOrgGRKKTeydIBEmNz811boiovjXbPij1iWNQyFJS1amIS45DXHIcjqUfQ4nuduNAO5kdwn3CERUQhQF+A+Bp71nn5+E6N0TUmPAKSgW8gkL1TafX4YzqjGFF4ORYXL512WS/n6Ofsa18L+9eUEg5DZ6IGgdeQSFqZPI1+TiYehBxSXHYn7IfOSU5xn0SQYJQz1BEBUQh0i8SbV3bsq08ETV7DChEtVCbcRzXcq8Zx5KczDgJrag17nOSO6G/X39E+Uehn28/uNq6NtArICJqHBhQiGroXjNhSnWlOJF5wjie5HredZPHt3FpYxjg6h+J0BahkEn4vx8RUXX4L2QZDpKlu6luReAMtQrzvt+AsL/T8XfBSRSUFhj3ySQy9Pbqbbx1E+DMNZ6IiGqKg2Qr4CBZqkinF9H/rd/LrpyIkCjSIHO8AJnjBUjskiAIt/8X8rD1MA5w7evbFw42DpYrnIiogXGQLFEDOnAlDZm6eCi8DSsCS2xyTfbrivygVXfEq0PH44lu4bXqTUJERFVjQCGqQnpBunGdm8MpR2EfcLs3iai3ga6gXdniex0gag1LI9gjkOGEiMhMGFCIYOhNcjbrLGKTDLNuLt66aLJfX+oKbX5HaNWdoCtsA4g2lc7BFYGJiMyHAaUMB8k2P2qNGodSDyE2ORYHUg4guzjbuE8iSNDNs5thRWDfSExefwMZuSUNtiJwTk4Ohg4dCq1WC61Wi/nz52P69OmVjvvhhx/wwgsvQK/X46WXXsKzzz4LAEhKSsLEiRORmZkJmUyGl19+GePHjzdbfURE9Y2DZCvgINmm7XredcNVkpQ4nEg/YdqbxMYJ/fz6IdI/Ev39+sPN1s24r3wWD1D1isBrn+5h1kX3dDodSkpKYG9vj4KCAoSEhOD48ePw8Ljdql6r1SI4OBj79u2Di4sLevbsiUOHDsHDwwNpaWnIyMhAaGgo0tPT0bNnT1y6dAkODhy0S0T1h4NkiWqoVF+KUxmnjA3TruVdM9kf6ByIKP8oRAVEIbRFKGwklW/dAMDwEB+sfbpHpT4o3vW0IrBUKoW9vWF14pKSEoiiiIq/Sxw7dgydO3eGn58fAGDEiBH45Zdf8NRTT8HHxwc+PoaavL29oVQqkZ2dzYBCRI0GAwo1ObeKb+FAygHEJsfiYMpBqEvVxn0yiQy9vHoh0j8Skf6RaOXcqsbnHR7igweCvRtsReCcnBxERUXh8uXLeOedd6BUKk32p6amGsMJAPj5+SElJaXSeU6cOAGdToeAAPZhIaLGgwGFGj1RFHE557Jh1k1SLE7fPA3xjhsx7rbuGOA3AFEBUQj3CYej3LHOz9WQKwK7urri9OnTyMjIwNixY/HYY4/By8urVufIzs7GpEmTsGHDhnqqkoiofjCgUKNUrC3GsfRjxrbyaQVpJvs7unc0NkwLUYZY5fTfhx56CJ6enti8eTMAYN++fRg/fjwyMjIglUqNx3l5eaFbt27Yv38/HnvsMeN2X19fkysmKSkpCAsLM35dUlKCMWPGYPHixYiIiGiAV0REZD4MKNRoZBRkIC4lDnFJcTiSdgTFuttjQRRSBfr69DXeuvF28G7w+pYtW4Zt27ahR48e+PDDDxEXF4f//Oc/eO655/DMM89UOt7Pzw+JiYnGr6OiolBUVIQjR46gXbt2sLe3h5OTE3JzcxEXF4fZs2ebPD4sLAxnz55FSkoKXFxc8PPPP+Pll18GYLiqNGXKFAwePBgTJ06s3xdORFQPGFDKcJqx9dGLepxTnTMOcD2ffd5kv7eDt3Hxvd7evWEns7NQpcBvv/2GzMxMnDhxAmvWrMGYMWOQk5ODL7/8EkFBQVU+xs/PD/v37zd+LZFIYGdnh8zMTNjY2GDGjBnGwbHz5s1Dly5dAAChoaGIj4+HTCbDu+++i0GDBkGv1+PFF180zvI5ePAgtm/fjq5du2Lnzp0AgC1bthjPQURk7TjNuAJOM7YstUaNw2mHjbdu7uxNIkBAV8+uxlAS5BYEQaifAaq19c4776B///4IDw8HAPTp0wfPPfccJkyYUO1jNmzYgIULFyI/Px8AEB8fj169eiE5ORne3g1/BYiI6H5xmjFZPZ1erPFsl6S8JMQmxyI2ORbHM45Dq7/dm8TRxhERvhGICohCf7/+cLc1XzM0c+rYsSN27dqF8PBw7N69G4Ig4K233sLgwYON030r8vPzg1qtRl5eHhwdHfH8889jwoQJDCdERGBAoXqw+2xapX4hPnf0CynVlyI+M9641k1ibqLJ41s5tzIOcO3RogdspFX3JrEmo0aNwt69e9GyZUsEBgbim2++we+//46+ffviP//5T5VdYMunCCcnJ2Pjxo1IT0/Hd99919ClExFZJd7iqYC3eO5PecfVit9UgrQAModL6BuSgb8LTiBfk2/cJxNk6OnV0zjANdAlsEFrthSVSgVPT08MHz4cly5dQlxcnElfEyKixoa3eMgq6fQiXv0+oSyciJAoMiBzvACp43lI7W5AEETE3zIc66ZwwwD/AYj0j0SEbwSc5E4WrNwylEolFAoFrl+/jtjYWIYTIqI7MKCQ2Rz8Ow2Z2tNQeF2AzPE8JPIck/26Ym9o1Z2wdPBjeKpbP0gl0qpP1IwUFxff+yAiomaIAYXuS2ZhJvYn7y9bEfgQ7FuWGPeJehl0hW2hze8ErbojRK0rAMBJaMtwQkREd8WAUoZ9UGpGL+qRkJVgmHWTFFupN4m+1BlatSGQ6AraAqK80jlaONk2VLlERNRIcZBsBRwkW1lBaQGOpB4xNkzLKs4y7hMgoIuyCyL9I9HfLxLPbEhBRm5JpUGyhmMNq/8eeGlwvS2wR0RElsNBslTvkvKTjM3S/kz/E6X6UuM+e5k9+vn1Kwsl/aG0u73K7iujXDH7s5MQAJOQUh5Hlo0KZjghIqJ7YkAhAIBWrzXpTXI196rJ/gCnAET5RyEqIAo9W/SstjfJ8BAfrH26R6U+KN539EEhIiK6FwaUZiy3JBcHUg4gNjkWB1MOIk+TZ9wnFaTo4dXD2FY+0Dmwxm3lh4f44IFg7xp3kiUiIqqIAaUZEUURV3OvGge4xt+Mh17UG/e7KFwwwG8AovyjEOEXAWd53e8fSiUCwtt6mKNsIiJqhhhQmjiNToM/0/803rpJUaeY7G/v1t54laSrsiun/xIRkVVgQGmCbhbexP6U/YhNisXhtMMo0hYZ98klcoT5hBlDia+jrwUrJSIiqhoDShOgF/U4n30ecUmGqyTnss6Z7Pe08zQuvtfHpw/sbewtVCkREVHNMKA0UoWlhTiSdsQ4Ffhm0U2T/V2UXTDA3zCepJN7pxoPcCUiIrIGDChlGkMn2RR1CmKTYo29STR6jXGfvcweEb4RiPSPxAD/ASa9SYiIiBobdpKtwJo6yWr1Wvx18y9jB9crOVdM9vs5+mFgwEBE+keil1cvyKWV28oTERE1FHaSbUR0erFW/UByS3JxKPVQ2eJ7B5BbkmvcJxWk6N6iu3E8SWuX1rx1Q0RETRIDSj3afTatUkdVnwodVUVRRGJuovEqyanMU9CJt28zOcudjWNJInwj4KJwafDXQURE1NAYUOrJ7rNpmP3ZyUqL5qXnFmP21mN4fpQUhbKziE2KRbI62eSYdq7tjFdJunp2hUzCj4mIiJoX/uSrBzq9iFe/TzBdLE+aD6njRcgcz0PmcBkbLt8e4GojsUGYdxgi/SMR6R8Jfyf/hi+aiIjIijCg1INjidnG2zpS+ytQtNgDqV2SyTF6rRMi/SIxPvhB9PXpy94kREREd2BAqQeZ+bfHnECUGcOJrsgfWnVHaNUdoS/2xfCePTC4pZ+FqiQiIrJeDCj1oIWTrfG/dUUBKEp9DLqCIIha52qPIyIiotskli6gKQpr7Q4fF1sYJgBLoc3tZRJOBBhm84S1drdQhURERNaNAaUeSCUClo0KBgBU7FJS/vWyUcF37YdCRETUnDGg1JPhIT5Y+3QPeLuY3sbxdrHF2qd7GPugEBERUWUcg1KPhof44IFg71p1kiUiIiIGlHonlQgIb+th6TKIiIgaFd7iISIiIqvDgFImJiYGwcHB6N27t6VLISIiavYEURQrLhfTrJlzqWgiIqLmxJw/Q3kFhYiIiKwOAwoRERFZHQYUIiIisjoMKERERGR1GFCIiIjI6jCgEBERkdVhQCEiIiKrw1b3FZS3hcnLy7NwJURERI1L+c9Oc7RYY0CpID8/HwAQEBBg4UqIiIgap/z8fLi4uNzXOdhJtgK9Xo/U1FQ4OTlBEJrHqsN5eXkICAhAUlISu+daMX5O5sH38bam/l40hdfXmF5Dea0JCQno0KEDJJL7G0XCKygVSCQS+Pv7W7oMi3B2drb6/wGIn5O58H28ram/F03h9TWm1+Dn53ff4QTgIFkiIiKyQgwoREREZHUYUAgKhQLLli2DQqGwdCl0F/yczIPv421N/b1oCq+vMb0Gc9fKQbJERERkdXgFhYiIiKwOAwoRERFZHQYUIiIisjoMKERERGR1GFCakbVr16Jr167Ghj/h4eH4+eefjfuLi4sRHR0NDw8PODo6Yty4ccjIyLBgxbRixQoIgoAFCxYYt/FzurdXXnkFgiCY/OnYsaNxf3N7D1NSUvD000/Dw8MDdnZ26NKlC44fP27cL4oili5dCh8fH9jZ2WHo0KG4fPmyBSuuncDAwEqftyAIiI6OBmD9n7dOp8PLL7+M1q1bw87ODm3btsVrr71msp6NtX1G+fn5WLBgAVq1agU7OztERETgzz//NG+9IjUbu3btEn/88Ufx0qVL4sWLF8V//etfoo2NjXj27FlRFEVx1qxZYkBAgLh3717x+PHjYt++fcWIiAgLV918HTt2TAwMDBS7du0qzp8/37idn9O9LVu2TOzcubOYlpZm/HPz5k3j/ub0HmZnZ4utWrUSp0yZIh49elS8evWquGfPHvHKlSvGY1asWCG6uLiIO3fuFE+fPi2OHj1abN26tVhUVGTBymsuMzPT5LP+9ddfRQDivn37RFG0/s/7jTfeED08PMQffvhBTExMFL/88kvR0dFRXL16tfEYa/uMHn/8cTE4OFiMjY0VL1++LC5btkx0dnYWk5OTzVYvA0oz5+bmJn700UdiTk6OaGNjI3755ZfGfefPnxcBiIcPH7Zghc1Tfn6+2L59e/HXX38Vo6KijAGFn1PNLFu2TOzWrVuV+5rbe/jSSy+J/fv3r3a/Xq8Xvb29xXfeece4LScnR1QoFOK2bdsaokSzmz9/vti2bVtRr9c3is/74YcfFqdNm2aybezYseKECRNEUbS+z6iwsFCUSqXiDz/8YLK9R48e4r///W+z1ctbPM2UTqfDF198gYKCAoSHh+PEiRMoLS3F0KFDjcd07NgRLVu2xOHDhy1YafMUHR2Nhx9+2OTzAMDPqRYuX74MX19ftGnTBhMmTMCNGzcANL/3cNeuXejVqxfGjx+PFi1aoHv37tiwYYNxf2JiItLT003eDxcXF/Tp06dRvh8ajQafffYZpk2bBkEQGsXnHRERgb179+LSpUsAgNOnT+PAgQMYMWIEAOv7jLRaLXQ6HWxtbU2229nZ4cCBA2arl4sFNjNnzpxBeHg4iouL4ejoiG+//RbBwcGIj4+HXC6Hq6uryfFeXl5IT0+3TLHN1BdffIGTJ0+a3M8tl56ezs+pBvr06YNNmzahQ4cOSEtLw6uvvooBAwbg7Nmzze49vHr1KtauXYuFCxfiX//6F/78808899xzkMvlmDx5svE1e3l5mTyusb4fO3fuRE5ODqZMmQKgcfw/s3jxYuTl5aFjx46QSqXQ6XR44403MGHCBACwus/IyckJ4eHheO2119CpUyd4eXlh27ZtOHz4MNq1a2e2ehlQmpkOHTogPj4eubm5+OqrrzB58mTExsZauiwqk5SUhPnz5+PXX3+t9NsJ1Vz5b54A0LVrV/Tp0wetWrXCjh07YGdnZ8HKGp5er0evXr3w5ptvAgC6d++Os2fPYt26dZg8ebKFqzO/jz/+GCNGjICvr6+lS6mxHTt2YOvWrfj888/RuXNnxMfHY8GCBfD19bXaz2jLli2YNm0a/Pz8IJVK0aNHDzz11FM4ceKE2Z6Dt3iaGblcjnbt2qFnz55Yvnw5unXrhtWrV8Pb2xsajQY5OTkmx2dkZMDb29syxTZDJ06cQGZmJnr06AGZTAaZTIbY2Fi89957kMlk8PLy4udUB66urggKCsKVK1ea3fe6j48PgoODTbZ16tTJeMur/DVXnNXSGN+P69ev47fffsOzzz5r3NYYPu9//vOfWLx4MZ588kl06dIFEydOxPPPP4/ly5cDsM7PqG3btoiNjYVarUZSUhKOHTuG0tJStGnTxmz1MqA0c3q9HiUlJejZsydsbGywd+9e476LFy/ixo0bCA8Pt2CFzcuQIUNw5swZxMfHG//06tULEyZMMP43P6faU6vV+Pvvv+Hj49Psvtf79euHixcvmmy7dOkSWrVqBQBo3bo1vL29Td6PvLw8HD16tNG9Hxs3bkSLFi3w8MMPG7c1hs+7sLAQEonpj2OpVAq9Xg/Auj8jBwcH+Pj44NatW9izZw8eeeQR89VrtmG9ZPUWL14sxsbGiomJieJff/0lLl68WBQEQfzll19EUTRMxWvZsqX4+++/i8ePHxfDw8PF8PBwC1dNd87iEUV+TjXxwgsviH/88YeYmJgoHjx4UBw6dKioVCrFzMxMURSb13t47NgxUSaTiW+88YZ4+fJlcevWraK9vb342WefGY9ZsWKF6OrqKn733XfiX3/9JT7yyCONapqxKIqiTqcTW7ZsKb700kuV9ln75z158mTRz8/POM34m2++EZVKpfjiiy8aj7G2z2j37t3izz//LF69elX85ZdfxG7duol9+vQRNRqN2eplQGlGpk2bJrZq1UqUy+Wip6enOGTIEGM4EUVRLCoqEufMmSO6ubmJ9vb24qOPPiqmpaVZsGISxcoBhZ/TvT3xxBOij4+PKJfLRT8/P/GJJ54w6fvR3N7D77//XgwJCREVCoXYsWNHcf369Sb79Xq9+PLLL4teXl6iQqEQhwwZIl68eNFC1dbNnj17RABV1m3tn3deXp44f/58sWXLlqKtra3Ypk0b8d///rdYUlJiPMbaPqPt27eLbdq0EeVyuejt7S1GR0eLOTk5Zq1XEMU7WtURERERWQGOQSEiIiKrw4BCREREVocBhYiIiKwOAwoRERFZHQYUIiIisjoMKERERGR1GFCIiIjI6jCgEBERkdVhQCEiIiKrw4BCjZ4oipgxYwbc3d0hCALi4+Or3FZfBg4ciAULFtTb+e+HuWurj9dqze8fVY+fG9U3BhSyelOmTIEgCJX+DB8+HACwe/dubNq0CT/88APS0tIQEhJS5bb7Vd0/yN988w1ee+21+z7/3dz5HsjlcrRr1w7//e9/odVq7/o4c9fWEK+1KklJSZg2bRp8fX0hl8vRqlUrzJ8/H1lZWQ1eC2AdP5zLvydWrFhhsn3nzp0QBMFCVRGZj8zSBRDVxPDhw7Fx40aTbQqFAgDw999/w8fHBxEREcZ9VW2rL+7u7vX+HMDt96CkpAQ//fQToqOjYWNjgyVLllQ6VqPRQC6Xm722hnqtd7p69SrCw8MRFBSEbdu2oXXr1jh37hz++c9/4ueff8aRI0csUpc1sLW1xVtvvYWZM2fCzc3N0uWYRfn3LhGvoFCjoFAo4O3tbfLHzc0NU6ZMwbx583Djxg0IgoDAwMAqtwGAXq/H8uXL0bp1a9jZ2aFbt2746quvTJ5Hr9fj7bffRrt27aBQKNCyZUu88cYbmDJlCmJjY7F69WrjlYxr164BuP3b9Pr16+Hr6wu9Xm9yzkceeQTTpk0zeY571XG396BVq1aYPXs2hg4dil27dhlrmDt3LhYsWAClUolhw4aZ1FZu4MCBeO655/Diiy/C3d0d3t7eeOWVV+75+u98fMXzzZ07F3PnzoWLiwuUSiVefvll3LkG6e7du9G/f3+4urrCw8MDI0eOxN9//33P11suOjoacrkcv/zyC6KiotCyZUuMGDECv/32G1JSUvDvf//beGxgYCBWrVpl8vjQ0FCT11iTeu72Pt3te6Emzz9w4EDMmzcPCxYsgJubG7y8vLBhwwYUFBRg6tSpcHJyQrt27fDzzz/f870ZOnQovL29sXz58mqPqc+atFrtXT/7mnyvV/e9W9FDDz2EyZMnG7/et28flEoldDrdvd4maqQYUKhRW716Nf773//C398faWlp+PPPP6vcBgDLly/Hp59+inXr1uHcuXN4/vnn8fTTTyM2NtZ4viVLlmDFihV4+eWXkZCQgM8//xxeXl5YvXo1wsPDMX36dKSlpSEtLQ0BAQEmtYwfPx5ZWVnYt2+fcVt2djZ2796NCRMmGLfVpI6asLOzg0ajMX69efNmyOVyHDx4EOvWrav2cZs3b4aDgwOOHj2Kt99+G//973/x66+/3vX1383mzZshk8lw7NgxrF69GitXrsRHH31k3F9QUICFCxfi+PHj2Lt3LyQSCR599NFKQa4q2dnZ2LNnD+bMmQM7OzuTfd7e3pgwYQK2b9+O2izKXtN6qnufavK9cC+bN2+GUqnEsWPHMG/ePMyePRvjx49HREQETp48iQcffBATJ05EYWHhXc8jlUrx5ptv4v3330dycnKtajBHTff67Gv6vV6T710/Pz+kpKQYv46KikJRURGOHDlyX6+brJhIZOUmT54sSqVS0cHBweTPG2+8IYqiKP7vf/8TW7VqZfKYituKi4tFe3t78dChQybHPfPMM+JTTz0liqIo5uXliQqFQtywYUOVdURFRYnz58+/6/ZHHnlEnDZtmnHfhx9+KPr6+oo6na7GdVT3HjzyyCOiKIqiXq8Xf/31V1GhUIiLFi0y1tC9e/d71hwVFSX279/f5JjevXuLL7300j1ff3Xn69Spk6jX643bXnrpJbFTp07VnuPmzZsiAPHMmTNVnvNOR44cEQGI3377bZX7V65cKQIQMzIyRFEUxVatWon/+9//TI7p1q2buGzZshrXU15Tde/T3WquyfNXPLdWqxUdHBzEiRMnGrelpaWJAMTDhw9XW/ed3xN9+/Y1ft99++234p3/tNdXTff67Gv6vV7d925Fy5YtEzt06GCyzcPDQ/zmm2/u+VhqnDgGhRqFQYMGYe3atSbbajPu4MqVKygsLMQDDzxgsl2j0aB79+4AgPPnz6OkpARDhgypc50TJkzA9OnTsWbNGigUCmzduhVPPvkkJBJJjeuozg8//ABHR0eUlpZCr9fjH//4h8ll+p49e9aoxq5du5p87ePjg8zMzDq//r59+5oMygwPD8e7774LnU4HqVSKy5cvY+nSpTh69ChUKpXxSsWNGzdqPHhZvMcVktqMWahpPdW9T+Zw57mlUik8PDzQpUsX47byq1Y1fb633noLgwcPxqJFixq0prt99rX5Xq/J927FKyjx8fHIyclBeHh4DV8hNTYMKNQoODg4oF27dnV+vFqtBgD8+OOP8PPzM9lXPti24i2Euhg1ahREUcSPP/6I3r17Y//+/fjf//5XqzqqUx7S5HI5fH19IZOZ/u/r4OBQoxptbGxMvhYEAXq93iyvvyqjRo1Cq1atsGHDBuMYnZCQEJPbU9Vp164dBEHA+fPn8eijj1baf/78eXh6esLV1RUAIJFIKoWZ0tLSOtVT3ft0NzV5/urOfee28h/6NbkNBgCRkZEYNmwYlixZgilTplhFTbX5Xq/J966fnx/UajXy8vLg6OiI559/HhMmTIC3t3eN6qHGhwGFmoXg4GAoFArcuHEDUVFRVR7Tvn172NnZYe/evXj22Wcr7ZfL5fcckGdra4uxY8di69atuHLlCjp06IAePXrUqo7q3G9Iu5d7vf7qHD161OTrI0eOoH379pBKpcjKysLFixexYcMGDBgwAABw4MCBGp/bw8MDDzzwANasWYPnn3/eJESlp6dj69atiI6ONm7z9PREWlqa8eu8vDwkJiYav77fespV971wr+evTytWrEBoaCg6dOjQYDXd7bO/n+/1qpSHnOTkZGzcuBHp6en47rvv7vu8ZL0YUKhRKCkpQXp6usk2mUwGpVJZo8c7OTlh0aJFeP7556HX69G/f3/k5ubi4MGDcHZ2xuTJk2Fra4uXXnoJL774IuRyOfr164ebN2/i3LlzeOaZZxAYGIijR4/i2rVrcHR0hLu7u/HWzZ0mTJiAkSNH4ty5c3j66adrXYel3Ov1V+fGjRtYuHAhZs6ciZMnT+L999/Hu+++CwBwc3ODh4cH1q9fDx8fH9y4cQOLFy+uVV0ffPABIiIiMGzYMLz++usm04yDgoKwdOlS47GDBw/Gpk2bMGrUKLi6umLp0qWQSqXG/eaoB0C13wv3ev761KVLF0yYMAHvvfeeyfb6rOlun725v9fLA8oLL7yAS5cuIS4uDs7OzmZ5HWSdGFCoUdi9ezd8fHxMtnXo0AEXLlyo8Tlee+01eHp6Yvny5bh69SpcXV3Ro0cP/Otf/zIe8/LLL0Mmk2Hp0qVITU2Fj48PZs2aBQBYtGgRJk+ejODgYBQVFSExMdE4hflOgwcPhru7Oy5evIh//OMfdarDUu72+qszadIkFBUVISwsDFKpFPPnz8eMGTMAGG4vfPHFF3juuecQEhKCDh064L333sPAgQNrXFP79u3x559/4pVXXsHjjz+OzMxMiKKIsWPHYsuWLbC3tzceu2TJEiQmJmLkyJFwcXHBa6+9ZnK1wBz1ANV/L9zr+evbf//7X2zfvt1kW33WdLfPHjDv97pSqYRCocD169cRGxtb6bYRNT2CeK/RZ0RE1Rg4cCBCQ0Mr9dmob8uWLcPKlSvx66+/om/fvg363ETUMHgFhYganVdffRWBgYE4cuQIwsLCqrzVRkSNGwMKETVKU6dOtXQJRFSPeIuHiIiIrA6vixIREZHVYUAhIiIiq8OAQkRERFaHAYWIiIisDgMKERERWR0GFCIiIrI6DChERERkdRhQiIiIyOowoBAREZHVYUAhIiIiq8OAQkRERFbn/wHKbcYRm4IyjQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_list = list(range(30, 90, 5))\n",
    "\n",
    "\n",
    "def fit_function(x: np.ndarray, a: float, b: float) -> np.typing.NDArray[Any]:\n",
    "    return a * x + b\n",
    "\n",
    "\n",
    "# Calculate lifetimes for S states\n",
    "kets_s = [pi.KetAtom(\"Rb\", n=n, l=0, j=0.5, m=0.5) for n in n_list]\n",
    "nu_s = [ket.nu for ket in kets_s]\n",
    "lifetimes_s = [ket.get_lifetime(unit=\"mus\") for ket in kets_s]\n",
    "popt_s, _ = curve_fit(fit_function, np.log(nu_s), np.log(lifetimes_s))\n",
    "\n",
    "# Calculate lifetimes for circular states\n",
    "kets_circular = [pi.KetAtom(\"Rb\", n=n, l=n - 1, j=n - 0.5, m=n - 0.5) for n in n_list]\n",
    "nu_circular = [ket.nu for ket in kets_circular]\n",
    "lifetimes_circular = [ket.get_lifetime(unit=\"mus\") for ket in kets_circular]\n",
    "popt_circular, _ = curve_fit(fit_function, np.log(nu_circular), np.log(lifetimes_circular))\n",
    "\n",
    "# Plot the scaling of the lifetimes\n",
    "fig, ax = plt.subplots(figsize=(6, 5))\n",
    "\n",
    "ax.plot(nu_s, lifetimes_s, \"o\", label=\"S states\")\n",
    "ax.plot(nu_circular, lifetimes_circular, \"o\", label=\"Circular states\")\n",
    "\n",
    "fit_s = np.exp(fit_function(np.log(nu_s), *popt_s))\n",
    "fit_circular = np.exp(fit_function(np.log(nu_circular), *popt_circular))\n",
    "ax.plot(nu_s, fit_s)\n",
    "ax.plot(nu_circular, fit_circular)\n",
    "\n",
    "ax.text(nu_s[2], fit_s[2], rf\"$\\propto \\nu^{{{popt_s[0]:.2f}}}$\", verticalalignment=\"top\")\n",
    "ax.text(\n",
    "    nu_circular[2],\n",
    "    fit_circular[2],\n",
    "    rf\"$\\propto \\nu^{{{popt_circular[0]:.2f}}}$\",\n",
    "    verticalalignment=\"top\",\n",
    ")\n",
    "\n",
    "ax.legend()\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_xlabel(r\"Effective Principal Quantum Number $\\nu$\")\n",
    "ax.set_ylabel(r\"Lifetime ($\\mu$s)\")\n",
    "\n",
    "ax.set_xticks([30, 40, 50, 60, 70, 80, 90])\n",
    "ax.get_xaxis().set_major_formatter(plt.ScalarFormatter())\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
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