DAT/2_Stichprobenverteilungen.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Labor zu Stichprobenverteilungen und Standardfehlern\n",
    "## \n",
    "#### Literatur: \n",
    "- Bruce et al. Praktische Statistik für Data Scientists, Kapitel 1 bis Seite 27, Kapitel 2 bis Standardfehler\n",
    "- Sauer Moderne Datenanalyse mit R, Kapitel 17.1. 17.2\n",
    "- Python-Dokumentationen\n",
    "\n",
    "#### Sie werden hier:\n",
    "- kontinuierliche Daten visualisieren und zusammenfassen\n",
    "- erkunden, was bei wiederholter Messung passiert: Stichprobenverteilung und Standardfehler\n",
    "\n",
    "#### Lernziele:\n",
    "- kontinuierliche Daten in Histogrammen visualisieren und diese interpretieren können\n",
    "- Unterschied zwischen Verteilung der Messwerte und der Verteilung eines gesuchten Parameters (Stichprobenverteilung) verstehen\n",
    "- Stichprobenverteilung und Standardfehler kennen und interpretieren können\n",
    "- ein anschauliches Verständnis des zentralen Grenzwertsatzes haben\n",
    "\n",
    "#### Output (Abfrage über moodle):\n",
    "- Formulieren Sie eine Erkenntnis, die Sie bei der Bearbeitung des Labors gewonnen haben.\n",
    "- Formulieren Sie eine Frage, die bei Ihnen offen geblieben ist.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4735007",
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'statsmodels'",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mModuleNotFoundError\u001b[39m                       Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[1]\u001b[39m\u001b[32m, line 15\u001b[39m\n\u001b[32m     13\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnp\u001b[39;00m\n\u001b[32m     14\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mscipy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m stats\n\u001b[32m---> \u001b[39m\u001b[32m15\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mstatsmodels\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mapi\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01msm\u001b[39;00m\n",
      "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'statsmodels'"
     ]
    }
   ],
   "source": [
    "# Nötige Module importieren\n",
    "\n",
    "# Plotten\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "\n",
    "# Zum (einfacheren) Erstellen guter statistischer Plots:\n",
    "import seaborn as sns\n",
    "\n",
    "seaborn.set_theme()  # alle Plots (auch von matplotlib) im seaborn-Style\n",
    "\n",
    "# Numerische und statistisches Operationen\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81da0a5a",
   "metadata": {},
   "source": [
    "## 1. Kontinuierliche Daten in Histogrammen darstellen: Verteilung der Messwerte\n",
    "\n",
    "Wir nutzen wieder den NYC Flights Datensatz (ohne nans) und schauen uns die Verspätungen bei Ankunft `arr_delay` genauer an.\n",
    "\n",
    "Kontinuierliche Daten visualisiert man mit \"statistischen\" Plots: Histogramm, (empirische) Verteilungsfunktion, etc. Auch ein Boxplot zeigt immerhin 5 Quantile und damit nicht nur Lage und Streuung, sondern auch etwas von der \"Form\" der Verteilung der Daten.\n",
    "\n",
    "Beim Histogramm ist wichtig:\n",
    "- Daten werden in Klassen (Bins) zusammengefasst ⇒ geeignete Anzahl Klassen wählen\n",
    "- Histogramm ist eine flächentreue Darstellung ⇒ geeignete Normierung wählen (y-Achse)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "332a70c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/david/DATENV/lib/python3.12/site-packages/nycflights13/__init__.py:2: UserWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html. The pkg_resources package is slated for removal as early as 2025-11-30. Refrain from using this package or pin to Setuptools<81.\n",
      "  from pkg_resources import resource_filename as _rf\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from nycflights13 import flights\n",
    "\n",
    "fls = flights.dropna()\n",
    "\n",
    "sns.histplot(fls.arr_delay);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dccca170",
   "metadata": {},
   "source": [
    "#### a) Klassen beim Histogramm\n",
    "\n",
    "Testen Sie verschiedene Anzahl Klassen. Typische Faustregeln:\n",
    "- $2 \\sqrt{n}$\n",
    "- $< \\sqrt{n}$ für große Stichproben\n",
    "- $10\\log_{10} n$\n",
    "\n",
    "Bitte beachten: wichtiger ist der optische Eindruck!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d15c811e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "anzahl = len(fls.arr_delay)\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "n_bins1 = int(np.round(2 * np.sqrt(anzahl), 0))  # np.round(zahl, 0) rundet auf 0 Nachkommastellen, da #Bins ganzzahlig sein muss\n",
    "n_bins2 = int(np.round(np.sqrt(anzahl), 0))\n",
    "n_bins3 = int(np.round(10*np.log10(anzahl), 0))\n",
    "\n",
    "\n",
    "sns.histplot(fls.arr_delay, bins=n_bins1, ax=axs[0])\n",
    "sns.histplot(fls.arr_delay, bins=n_bins2, ax=axs[1])\n",
    "sns.histplot(fls.arr_delay, bins=n_bins3, ax=axs[2])\n",
    "#plt.xlabel('Arrival delay / min') #Um automatisch eine korrekte Beschriftung incl. Einheit zu erhalten, könnte man auch die Variable entsprechend benennen. Das ist Geschmackssache.\n",
    "#plt.ylabel('Number of flights') #Vorsicht bei der Beschriftung der Achsen. Je nach Normierung der y-Achse muss eine manuelle Beschriftung angepasst werden!\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d015c91",
   "metadata": {},
   "source": [
    "Was passiert beim Ändern der Klassenanzahl mit der y-Achse?\n",
    "\n",
    "#### b) Normierung beim Histogramm\n",
    "\n",
    "In matplotlib lässt sich die Normierung auf `density=True` und `density=False` stellen. Welchen Einfluss hat das?\n",
    "In seaborn sind über `stat = ...` die üblichen weiteren Möglichkeiten gegeben:\n",
    "https://seaborn.pydata.org/generated/seaborn.histplot.html:\n",
    "\n",
    "```\n",
    "    Aggregate statistic to compute in each bin.\n",
    "    \n",
    "        count: show the number of observations in each bin\n",
    "    \n",
    "        frequency: show the number of observations divided by the bin width\n",
    "    \n",
    "        probability or proportion: normalize such that bar heights sum to 1\n",
    "    \n",
    "        percent: normalize such that bar heights sum to 100\n",
    "    \n",
    "        density: normalize such that the total area of the histogram equals 1\n",
    "```\n",
    "Schauen Sie sich die verschiedenen Varianten an und überlegen Sie, was sie bedeuten. Häufig wird ohne genaueres Hinschauen \"count\" verwendet. Dann ist aber die Fläche nicht auf 1 normiert und der Vergleich mit der Dichtefunktion funktioniert nicht richtig. Daher: Wenn das Histogramm mit einer Dichtefunktion verglichen wird, sollte `stat=density` verwendet werden!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a20d379d7fce80e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6BD8/Py5fSURkw/g8rz1nZ2d07twZJ06cQP/+/XX97tmzJ0pKSlBSUlKrIEPnzp2xc+dOvP/++wgLC4OLiwsGDBjQ0N03cPToUZSXl0Oj0aCgoADHjh3Dvn374ObmhmXLlsHHx6fR+0RUHQYZiJq48ePHY9++fUhPT4dSqYSfnx+mTZuGhIQEXZuHH34Y48ePx44dO/DDDz9AEAQ88sgjEIvFWL58OZYuXYqdO3fi22+/RevWrfF///d/BktTffDBB2jevDl27NiBn376CX379sWnn36KIUOG6FVers7HH3+Md999F+vXr4cgCIiKikJKSgoeeOABs46JKf3794eXlxd27dqFl156Sbe9Y8eO2Lx5M5YsWYINGzagvLwcfn5+iI2N1bVp3749vvrqK3z88cdITk6GIAgIDw/Hhx9+qKuoDVQuN7Vs2TLMmzcPS5YsgY+PD+Li4iCVSnXrcNeVj48P5s2bh+TkZLzxxhtQq9VYu3YtmjVrBo1Ggx9//BGjRo2y+rRPIiIyjc/zuunevTtOnDiB7t2767b5+PigXbt2yMrKqlWQ4amnnsLff/+Nb7/9FqtXr0br1q0tEmRYt24dgMp3CHd3dwQHB2PKlCl48sknDYpjElkDkVDbyiRERHX0999/Y8SIEfjwww/x2GOPWbo7tfLZZ5/h22+/xZ49e8xWdNGSfv75Z8yYMQM//fQTWrRoYenuEBGRDbLF5zkRWQ5rMhCRWZSVlRlsW7NmDcRiMXr27GmBHtXPhAkTUFJSgh07dli6K2aRkpKCp59+mgEGIiKqlabyPCciy+F0CSIyi//+9784ffo0evfuDTs7O6SlpSEtLQ1jxozRraxgC1xdXXH48GFLd8NsNm3aZOkuEBGRDWkqz3MishxOlyAis0hPT8eyZctw8eJFlJSUoFWrVhg+fDgmTZoEe3vGM4mIiGwBn+dEdLcYZCAiIiIiIiIis2BNBiIiIiIiIiIyCwYZiIiIiIiIiMgsGGQgIiIiIiIiIrNg9RYLEgQBGg1LYlQlFos4LiZwbIzjuJjGsTGO42KcWCyCSCSydDeaFD7rTePfQ+M4LqZxbIzjuBjHcTGuMZ71DDJYkEgkgkJRgooKjaW7YjXs7cXw8nLluBjBsTGO42Iax8Y4jotp3t6usLNjkMGc+Kw3jn8PjeO4mMaxMY7jYhzHxbTGeNZzugQRERERERERmQWDDERERERERERkFgwyEBEREREREZFZMMhARERERERERGbBIAMRERERERERmYVVBRmysrIwZ84cDB8+HJ06dcKwYcOqbf/zzz8jJCTEaLvCwkLMnj0bvXr1QkREBKZOnYrr168btDt27BjGjBmD8PBw9O/fHytXroQg6C91IggCVq5ciX79+iE8PBxjxozBiRMn7upeiYiIiIiIiJoaqwoynD9/HgcOHEC7du0QHBxcbduysjIsWLAAzZs3N7p/2rRpSE9Px9y5c/HRRx8hIyMDEydOREVFha5NVlYWEhIS4OPjg+TkZMTFxWHp0qVYtWqV3rlSUlKwdOlSTJgwAcnJyfDx8UF8fDyys7Pv/qaJiIiIiIiImgh7S3fgTgMGDMBDDz0EAJg1axZOnz5tsm1ycjL8/PzQpk0bg3bHjx/HwYMHkZqaiujoaABAYGAghg4dij179mDo0KEAgNTUVHh5eeGTTz6BRCJBnz59kJeXhxUrVmD8+PGQSCQoLy9HcnIy4uPjMWHCBABA9+7dMWTIEKSmpmLu3LnmHwgiIiIiIiIiG2RVmQxice26c+nSJXzxxRd48803je5PS0uDVCpFVFSUbltQUBBCQ0ORlpam127gwIGQSCS6bUOHDoVCocDx48cBVE6nKCoqQmxsrK6NRCLBoEGD9M5FREREREREdK+zqiBDbb333nsYPnw4OnbsaHS/TCZDYGAgRCKR3vagoCDIZDIAQElJCa5evYqgoCCDNiKRSNdO+++q7YKDg5GTk4OysjKz3BMRERERERGRrbOq6RK1sW/fPhw/fhy7d+822UahUMDd3d1gu4eHh25qRWFhIQBAKpXqtZFIJHB2doZcLtedSyKRwNHRUa+dVCqFIAiQy+VwcnKq9/3Y2dlknKfBaMeD42KIY2Mcx8U0jo1xHBfTqsTmiYiIiOrMpoIM5eXlWLBgAaZMmQJvb29Ld8cspFJnS3fBKnFcTOPYGMdxMY1jYxzHhYiIiMj8bCrIsGbNGojFYjzyyCNQKBQAAJVKBY1GA4VCAScnJ0gkEkilUly7ds3geLlcDg8PDwDQZTpoMxq0lEolSktLde2kUimUSiXKy8v1shkUCgVEIpGuXX0pFKVQqzV3dY6mxM5ODKnUmeNiBMfGOI6LaRwb4zgupnl4ONe6PhIRERGRMTYVZJDJZMjKykKfPn0M9vXs2RNz587FuHHjEBQUhMOHD0MQBL26DBkZGejQoQMAwMXFBa1atdLVXLizjSAIuhoM2n9nZGTo1YCQyWTw8/O7q6kSAKBWa1BRwZfcqpr6uGw/lIlhfQPqdWxTH5v64riYxrExjuNiSBAs3QOipmNbegYA4NGoQAv3hIiocdnU54qJEydi7dq1ev9ER0ejdevWWLt2LQYMGAAAiImJgVwux+HDh3XHZmRk4K+//kJMTIxuW0xMDPbu3QuVSqXbtnPnTkilUkRERAAAunXrBjc3N+zatUvXRqVSYc+ePXrnIqoLgW/yREQ6Fy9exHPPPYeuXbsiKioKixYtglKprPE4QRCwcuVK9OvXD+Hh4RgzZgxOnDih1+bkyZN47rnnEBUVhS5duqBfv36YPXs2cnNz9dolJSUhJCTE4J8NGzaY81bpHqIRBGj4vCeie5BVZTKUlpbiwIEDAIArV66gqKhIV+CxV69eCA4ORnBwsN4x3333HXJzcxEZGanbFhERgejoaMyePRuvvfYaHB0d8emnnyIkJAQPP/ywrl1CQgK2bduGGTNmYNy4cTh37hxSU1Mxffp03bKWjo6OSExMRFJSEry9vdGhQwds2LABBQUFSEhIaOghISIiatLkcjni4uIQEBCApKQk5ObmYuHChSgrK8OcOXOqPTYlJQVLly7FzJkzERISgq+++grx8fHYunUr/P39AVRObwwKCsLo0aPRrFkzZGdn4/PPP8epU6ewZcsWvWWsnZycsGbNGr1raM9DREREtWNVQYZbt27hlVde0dum/fPatWv1Agk1Wbx4Md5//33MmTMHFRUViI6Oxptvvgl7+39vuV27dkhNTcXChQvxwgsvwNvbG1OnTkV8fLzeuSZOnAhBELBq1Srk5eUhNDQUqampfPEgIiK6Sxs3bkRxcTGWLVsGT09PAIBarca8efOQmJgIX19fo8eVl5cjOTkZ8fHxmDBhAgCge/fuGDJkCFJTUzF37lwAQHR0NKKjo3XHRUZGolWrVoiPj8fp06fRrVs33T6xWIyuXbs2xG0SERHdM6wqyNCmTRucPXu2TscsXLjQ6HZ3d3csWLAACxYsqPb4bt26YfPmzdW2EYlESExMRGJiYp36RkRERNVLS0tDnz59dAEGAIiNjcXbb7+N9PR0jBw50uhxx44dQ1FREWJjY3XbJBIJBg0ahJ9++qnaa2qvded0SSIiIjIPqwoyEBER0b1FJpPhiSee0NsmlUrh4+NjUJy56nHAvwWatYKDg7FmzRqUlZXpFWdWq9VQq9XIzs7Ghx9+iM6dO6N79+56x5aVlaF3795QKBQICAjAhAkT8OSTT97tLcLOzqZKYDUK7Zg05bERiyuLj9vb1/4e74VxqS+OjXEcF+M4LqbdsS5Cg2GQgYiIiCxGoVBAKpUabPfw8IBcLq/2OIlEore8NFAZoBAEAXK5XC/I8Mwzz+DYsWMAgC5dumDlypV6Uyjbtm2LmTNnolOnTigvL8e2bdvw1ltvobCw8K5rMEmlznd1fFPWlMfG2bmy3oeXl2udj23K43K3ODbGcVyM47hYBoMMRERE1OS99957KCwsRFZWFlJSUvDcc89hw4YNcHNzAwAMHz5cr32/fv2gUqmwfPlyPPvss3BwcKj3tRWKUqjVXC71TnZ2Ykilzk16bEpLK1dIyc8vrvUx98K41BfHxjiOi3EcF9M8PJwhFjdshgeDDERERGQxUqkUhYWFBtvlcjk8PDyqPU6pVKK8vFwvm0GhUEAkEhkcq51Wcf/996Nv377o378/Nm3aVG2WQmxsLH788UdcunTJYHWrulCrNaio4EuuMU15bDSayuUr63N/TXlc7hbHxjiOi3EcF0ONsbIuJ6kQERGRxQQFBRnUXigsLMSNGzcM6i1UPQ4AMjIy9LbLZDL4+fnpTZWoqnnz5mjZsiWysrLuoudERERkDIMMREREZDExMTE4dOgQFAqFbtvu3bshFosRFRVl8rhu3brBzc0Nu3bt0m1TqVTYs2cPYmJiqr3m1atXkZOTU+NS1Dt37oRUKkXbtm1reTdERETE6RJEZrYtvfKr2qNRgRbuCRGR9Rs7dizWrVuHyZMnIzExEbm5uVi0aBHGjh0LX19fXbu4uDjk5OTolqd0dHREYmIikpKS4O3tjQ4dOmDDhg0oKCjQmwIxZ84ceHl5ISwsDG5ubsjIyMAXX3yBZs2aYdSoUbp2I0eOxIgRIxAUFISysjJs27YNe/bswezZs++qHgM1TXzWExGZxiADkZlpGmOiExFRE+Hh4YE1a9bg3XffxeTJk+Hq6opRo0Zh+vTpeu00Gg3UarXetokTJ0IQBKxatQp5eXkIDQ1FamqqXoZCeHg4Nm/ejPXr10OpVKJVq1aIiYnBpEmT4OXlpWvXtm1brF69Gjdv3oRIJEKHDh3w4Ycf4rHHHmvYASCbxGc9EZFpDDIQERGRRQUHB2P16tXVtlm3bp3BNpFIhMTERCQmJpo8btSoUXoZC6YsXry4xjZERERUM9ZkICIiIiIiIiKzYJCBiIiIiIiIiMyCQQYiIiIiIiIiMgsGGYiIiIiIiIjILBhkICIiIiIiIiKzYJCBiIiIiIiIiMyCQQYiIiIiIiIiMgsGGYiIiIiIiIjILBhkICIiIiIiIiKzYJCBiIiIiIiIiMyCQQYiIiIiIiIiMgsGGYiIiIiIiIjILBhkICIiIiIiIiKzYJCBiIiIiIiIiMyCQQYiIiIiIiIiMgsGGYiIiIiIiIjILBhkICIiIiIiIiKzYJCBiIiIiIiIiMyCQQYiIiIiIiIiMgsGGYiIiIiIiIjILKwqyJCVlYU5c+Zg+PDh6NSpE4YNG6a3v6ioCElJSRg1ahR69OiBvn37YtKkSTh79qzBuQoLCzF79mz06tULERERmDp1Kq5fv27Q7tixYxgzZgzCw8PRv39/rFy5EoIg6LURBAErV65Ev379EB4ejjFjxuDEiRNmvXciIiIiIiIiW2dVQYbz58/jwIEDaNeuHYKDgw325+TkYNOmTYiKisLixYvx7rvvorCwEGPGjMHFixf12k6bNg3p6emYO3cuPvroI2RkZGDixImoqKjQtcnKykJCQgJ8fHyQnJyMuLg4LF26FKtWrdI7V0pKCpYuXYoJEyYgOTkZPj4+iI+PR3Z2dsMMBBEREREREZENsrd0B+40YMAAPPTQQwCAWbNm4fTp03r727Rpg59++gnOzs66bb1798aAAQOwfv16vPXWWwCA48eP4+DBg0hNTUV0dDQAIDAwEEOHDsWePXswdOhQAEBqaiq8vLzwySefQCKRoE+fPsjLy8OKFSswfvx4SCQSlJeXIzk5GfHx8ZgwYQIAoHv37hgyZAhSU1Mxd+7cBh4VIiIiIiIiIttgVZkMYnH13XFxcdELMACAq6sr2rZtqzcVIi0tDVKpFFFRUbptQUFBCA0NRVpaml67gQMHQiKR6LYNHToUCoUCx48fB1A5naKoqAixsbG6NhKJBIMGDdI7F5E5bUvPwLb0DEt3g4iIiBoIn/VE1FRZVZChPhQKBc6fP4+goCDdNplMhsDAQIhEIr22QUFBkMlkAICSkhJcvXpV7zhtG5FIpGun/XfVdsHBwcjJyUFZWZnZ74lIIwjQVKkNQkRERE0Hn/VE1FRZ1XSJ+vjwww8hEokwbtw43TaFQgF3d3eDth4eHropGIWFhQAAqVSq10YikcDZ2RlyuVx3LolEAkdHR712UqkUgiBALpfDycmp3v23s7P5OI9ZacfDlsdFLK4Mbtnbm74HsVhU4/6q52gKY9MQOC6mcWyM47iYViU2T0RERFRnNh1k2LJlCzZv3oyFCxeiZcuWlu5OvUilzjU3ugfZ8rg4O1dOv/HycjXZxslZUu3+6s5hy2PTkDgupnFsjOO4EBEREZmfzQYZDhw4gDlz5uCll17C448/rrdPKpXi2rVrBsfI5XJ4eHgAgC7TQZvRoKVUKlFaWqprJ5VKoVQqUV5erpfNoFAoIBKJdO3qS6EohVqtuatzNCV2dmJIpc42PS6lpUoAQH5+sck2ZaXKavcbO0dTGJuGwHExjWNjHMfFNA8P5xrrIxERERFVxyaDDCdOnMArr7yCESNG4JVXXjHYHxQUhMOHD0MQBL26DBkZGejQoQOAyiKSrVq10tVcuLONIAi6Ggzaf2dkZKBjx466djKZDH5+fnc1VQIA1GoNKir4kluVLY+LRlM5v7K6/ms0Qo37TZ3DlsemIXFcTOPYGMdxMWSp6eEXL17E/Pnzcfz4cbi6umL48OGYNm2aXmFmYwRBQEpKCtavX4+8vDyEhobi9ddfR9euXXVtTp48iU8//RTnzp2DXC5H8+bN0bdvX7zyyivw9fXVO9+xY8fwwQcf4O+//0azZs0wbtw4TJw40aDGExEREZlmc58rLly4gMTERPTu3Rvz5s0z2iYmJgZyuRyHDx/WbcvIyMBff/2FmJgYvXZ79+6FSqXSbdu5cyekUikiIiIAAN26dYObmxt27dqla6NSqbBnzx69cxEREVHdyeVyxMXFQaVSISkpCdOnT9dNhaxJSkoKli5digkTJiA5ORk+Pj6Ij49Hdna2ro1CoUBQUBDeeOMNpKam4uWXX8avv/6K559/HkqlUtcuKysLCQkJ8PHxQXJyMuLi4rB06VKsWrWqQe6biIioqbKqTIbS0lIcOHAAAHDlyhUUFRVh9+7dAIBevXpBEAQkJCTA0dERcXFxuiKOAODm5ob77rsPABAREYHo6GjMnj0br732GhwdHfHpp58iJCQEDz/8sO6YhIQEbNu2DTNmzMC4ceNw7tw5pKamYvr06bqvJ46OjkhMTERSUhK8vb3RoUMHbNiwAQUFBUhISGisoSEiImqSNm7ciOLiYixbtgyenp4AALVajXnz5iExMdEg20CrvLwcycnJiI+Px4QJEwAA3bt3x5AhQ5Camoq5c+cCAKKjoxEdHa07LjIyEq1atUJ8fDxOnz6Nbt26AQBSU1Ph5eWFTz75BBKJBH369EFeXh5WrFiB8ePH15hVQURERJWsKshw69Ytg+kP2j+vXbsWAHS1FrQvFFq9evXCunXrdH9evHgx3n//fcyZMwcVFRWIjo7Gm2++CXv7f2+5Xbt2SE1NxcKFC/HCCy/A29sbU6dORXx8vN65J06cCEEQsGrVKl06ZmpqKvz9/c1270RERPeitLQ09OnTRxdgAIDY2Fi8/fbbSE9Px8iRI40ed+zYMRQVFSE2Nla3TSKRYNCgQfjpp5+qvab2WndmMqalpWHQoEF6wYShQ4ciOTkZx48fR2RkZD3ujoiI6N5jVUGGNm3a4OzZs9W2qWm/lru7OxYsWIAFCxZU265bt27YvHlztW1EIhESExORmJhYq2sTERFR7chkMjzxxBN626RSKXx8fAzqJlU9Dvi3dpJWcHAw1qxZg7KyMr26SWq1Gmq1GtnZ2fjwww/RuXNndO/eHQBQUlKCq1evGpwrKCgIIpEIMpnsroIMXC7VkK0vJVvb5aqra8PlquuGY2Mcx8U4jotpjVFmyKqCDERERHRvUSgUkEqlBts9PDwgl8urPU4ikeit/ARUBigEQYBcLtcLMjzzzDM4duwYAKBLly5YuXKlLrtRu9JU1X5IJBI4OztX24/a4HKpptnq2NRmueqa2nC56vrh2BjHcTGO42IZDDIQERFRk/fee++hsLAQWVlZSElJwXPPPYcNGzbAzc2twa/N5VIN2fpSsrVZrrqmNlyuum44NsZxXIzjuJjWGMtVM8hAREREFiOVSnWZBHeSy+Xw8PCo9jilUony8nK9bAaFQgGRSGRwrHYqxP3334++ffuif//+2LRpExISEuDu7g4ABv1QKpUoLS2tth+1weVSTbPVsantctXVteFy1fXDsTGO42Icx8VQYyxXzUkqREREZDFBQUEGtRcKCwtx48YNgxoJVY8DKpeovpNMJoOfn5/eVImqmjdvjpYtWyIrKwsA4OLiglatWhn0IyMjA4IgVNsPIiIi0scgAxEREVlMTEwMDh06BIVCodu2e/duiMViREVFmTyuW7ducHNzw65du3TbVCoV9uzZg5iYmGqvefXqVeTk5OitEhUTE4O9e/fqrTixc+dOSKVSRERE1OfWiIiI7kmcLkFEREQWM3bsWKxbtw6TJ09GYmIicnNzsWjRIowdOxa+vr66dnFxccjJydEtT+no6IjExEQkJSXB29sbHTp0wIYNG1BQUICEhATdcXPmzIGXlxfCwsLg5uaGjIwMfPHFF2jWrBlGjRqla5eQkIBt27ZhxowZGDduHM6dO4fU1FRMnz5db1lLIiIiqh6DDERERGQxHh4eWLNmDd59911MnjwZrq6uGDVqFKZPn67XTqPRQK1W622bOHEiBEHAqlWrkJeXh9DQUKSmpuplKISHh2Pz5s1Yv349lEolWrVqhZiYGEyaNAleXl66du3atUNqaioWLlyIF154Ad7e3pg6dSri4+MbdgCIiIiaGAYZiIiIyKKCg4OxevXqatusW7fOYJtIJEJiYiISExNNHjdq1Ci9jIXqdOvWDZs3b65VWyIiIjKONRmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCysKsiQlZWFOXPmYPjw4ejUqROGDRtmtN3XX3+NwYMHIywsDI899hh++eUXgzaFhYWYPXs2evXqhYiICEydOhXXr183aHfs2DGMGTMG4eHh6N+/P1auXAlBEPTaCIKAlStXol+/fggPD8eYMWNw4sQJs9wzERERERERUVNhVUGG8+fP48CBA2jXrh2Cg4ONttmxYwfeeustxMbGIiUlBV27dsXLL79s8Ev/tGnTkJ6ejrlz5+Kjjz5CRkYGJk6ciIqKCl2brKwsJCQkwMfHB8nJyYiLi8PSpUuxatUqvXOlpKRg6dKlmDBhApKTk+Hj44P4+HhkZ2ebfQyIiIiIiIiIbJW9pTtwpwEDBuChhx4CAMyaNQunT582aLN06VI88sgjmDZtGgCgd+/eOHfuHD777DOkpKQAAI4fP46DBw8iNTUV0dHRAIDAwEAMHToUe/bswdChQwEAqamp8PLywieffAKJRII+ffogLy8PK1aswPjx4yGRSFBeXo7k5GTEx8djwoQJAIDu3btjyJAhSE1Nxdy5cxt2UIiIiIiIiIhshFVlMojF1XcnOzsbmZmZiI2N1ds+dOhQHD58GEqlEgCQlpYGqVSKqKgoXZugoCCEhoYiLS1Nty0tLQ0DBw6ERCLRO5dCocDx48cBVE6nKCoq0rumRCLBoEGD9M5FREREREREdK+zqiBDTWQyGYDKrIQ7BQcHQ6VS6aYvyGQyBAYGQiQS6bULCgrSnaOkpARXr15FUFCQQRuRSKRrp/131XbBwcHIyclBWVmZme6OiIiIiIiIyLZZ1XSJmsjlcgCAVCrV2679s3a/QqGAu7u7wfEeHh66KRiFhYVGzyWRSODs7Kx3LolEAkdHR4NrCoIAuVwOJyenet+TnZ1NxXkanHY8bHlcxOLK4Ja9vel7EItFNe6veo6mMDYNgeNiGsfGOI6LaVVi80RERER1ZlNBhqZIKnW2dBeski2Pi7Nz5fQbLy9Xk22cnCXV7q/uHLY8Ng2J42Iax8Y4jgsRERGR+dlUkMHDwwNAZRaCj4+PbrtCodDbL5VKce3aNYPj5XK5ro0200Gb0aClVCpRWlqqdy6lUony8nK9bAaFQgGRSKRrV18KRSnUas1dnaMpsbMTQyp1tulxKS2trA2Sn19ssk1ZqbLa/cbO0RTGpiFwXEzj2BjHcTHNw8O5xvpIDeXixYuYP38+jh8/DldXVwwfPhzTpk3Tq5tkjCAISElJwfr165GXl4fQ0FC8/vrr6Nq1q67NoUOH8PXXX+PPP//ErVu30Lp1a4wcORJxcXFwcHDQtZs1axa+++47g2ukpKQgJibGbPdKRETUlNlUkEFbF0Emk+nVSJDJZHBwcIC/v7+u3eHDhyEIgl5dhoyMDHTo0AEA4OLiglatWulqLtzZRhAE3fm1/87IyEDHjh31runn53dXUyUAQK3WoKKCL7lV2fK4aDQCAFTbf41GqHG/qXPY8tg0JI6LaRwb4zguhgTBMteVy+WIi4tDQEAAkpKSkJubi4ULF6KsrAxz5syp9ljtMtMzZ85ESEgIvvrqK8THx2Pr1q2694KNGzeirKwMU6dORatWrfDnn38iKSkJFy9exPvvv693Pn9/f3z00Ud620wtq01ERESGbCrI4O/vj4CAAOzevVu31CUA7Ny5E3369NF97YiJicHnn3+Ow4cPo2/fvgAqgwR//fUXnn/+ed1xMTEx2Lt3L1599VXdl4ydO3dCKpUiIiICANCtWze4ublh165duiCDSqXCnj17+FWDiIjIDDZu3Iji4mIsW7YMnp6eAAC1Wo158+YhMTERvr6+Ro+r7TLTc+fOhbe3t+64yMhIaDQaLF68GK+++qrePicnJ70sCCIiIqobqwoylJaW4sCBAwCAK1euoKioCLt37wYA9OrVC97e3pgyZQpmzpyJtm3bIjIyEjt37sTJkyfx5Zdf6s4TERGB6OhozJ49G6+99hocHR3x6aefIiQkBA8//LCuXUJCArZt24YZM2Zg3LhxOHfuHFJTUzF9+nRdwMLR0RGJiYlISkqCt7c3OnTogA0bNqCgoAAJCQmNODpERERNU1paGvr06aMLMABAbGws3n77baSnp2PkyJFGj6tumemffvpJt+3OIIJWaGgoBEHAjRs3jO4nIiKi+rGqIMOtW7fwyiuv6G3T/nnt2rWIjIzEsGHDUFpaipSUFKxcuRKBgYFYtmyZLvNAa/HixXj//fcxZ84cVFRUIDo6Gm+++Sbs7f+95Xbt2iE1NRULFy7ECy+8AG9vb0ydOhXx8fF655o4cSIEQcCqVat08z1TU1N1aZhERERUfzKZDE888YTeNqlUCh8fH4NpjVWPA4wvM71mzRqUlZWZnNZ47NgxSCQStGnTRm97VlYWunfvjvLycnTo0AEvvfSSXvZkfXAlE0O2vspLbVeSqq4NV5KqG46NcRwX4zgupjXGSlJWFWRo06YNzp49W2O70aNHY/To0dW2cXd3x4IFC7BgwYJq23Xr1g2bN2+uto1IJEJiYiISExNr7BsRERHVjUKhMFhSGqgs6KxdUtrUcfVZZjozMxNr167F2LFj4er67yo+oaGhCAsLw3333YfCwkJs2LABkydPxpIlSzBkyJB63x9XMjHNVsemNitJ1dSGK0nVD8fGOI6LcRwXy7CqIAORNduWngEAeDQq0MI9ISKi+ioqKsKUKVPQpk0bTJ8+XW9fXFyc3p8HDBiAsWPHYunSpXcVZOBKJoasdZWXrf+rzI4Z/kBQte1qs5JUTW24klTdcGyM47gYx3ExrTFWkmKQgaiWNJYqu05E1MRJpVKDJaUB/aWnTR1Xl2WmlUolJk+eDLlcjk2bNsHFxaXafonFYjz88MP48MMPq516UROuZGKatY1Nxe1fRmrqU21XkqquDVeSqh+OjXEcF+M4LoYa41caTlIhIiIiiwoKCjKovVBYWIgbN24Y1FuoehxQuYLUnYwtM63RaDBz5kycOXMGKSkpaNWqlRnvgIiIiLQYZCAiIiKLiomJwaFDh6BQKHTbdu/eDbFYjKioKJPH3bnMtJapZabnzZuHX375BZ9//jlCQkJq1S+NRoPdu3ejffv29c5iICIiutdwugQRERFZ1NixY7Fu3TpMnjwZiYmJyM3NxaJFizB27Fj4+vrq2sXFxSEnJ0e3PGVtl5lesWIFNm7ciISEBEgkEpw4cUK377777oObmxuuXLmCWbNm4ZFHHkG7du0gl8uxYcMGnD59GklJSY02FkRERLaOQQYiIiKyKA8PD6xZswbvvvsuJk+eDFdXV4waNcqgMKNGo4FardbbVptlptPT0wEAqampSE1N1Tteu0S2q6sr3NzcsHz5cty6dQsODg7o0qULUlJS8MADDzTQnRMRETU9DDIQERGRxQUHB2P16tXVtlm3bp3BttosM23suKo8PT2xfPnyGtsRERFR9ViTgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIbNi29AxsS8+wdDeIiIiogfBZT0S2xt7SHSCi+tMIgqW7QERERA2Iz3oisjXMZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIiIiIiIyCwYZCAiIiIiIiIis2CQgYiIiIiIiIjMgkEGIiIiIiIiIjILBhmIiIioTp5//nls27YNZWVllu4KERERWRl7S3eAiIiIbEt2djZeffVVuLi4YNCgQRg+fDj69OkDkUhk6a4RERGRhTHIQERERHXy448/4uTJk/jhhx+we/du/PDDD2jevDmGDRuGxx57DKGhoZbuIhEREVkIgwxERERUZ+Hh4QgPD8fs2bORnp6OH374AZs2bcLq1asRHByM4cOH49FHH0XLli0t3VUiIiJqRKzJQERERPUmFovxwAMP4MMPP8T+/fsxePBgXLhwAR9//DEGDBiACRMmYP/+/ZbuJhERETUSZjIQERHRXTl69Ch++OEH/Pjjj5DL5Wjfvj1GjBgBe3t7bNmyBS+++CImTZqEV155xdJdJSIiogZW70yGZ599FocPHza5/9dff8Wzzz5b39MTERGRFbtw4QI++eQTDBgwAOPHj8e+ffvw+OOP47vvvsO2bduQkJCAuLg4/PDDDxg1ahTWr19v6S4TERFRI6h3JsNvv/2G0aNHm9yfl5eH33//vb6nJyIiIis1fPhwnDt3DhKJBAMHDsTbb7+NBx54AGKx8W8XkZGR+Prrrxu5l0RERGQJd1WTobqlqrKysuDq6no3pzdp7969GD16NCIiIhAdHY1XXnkF2dnZBu2+/vprDB48GGFhYXjsscfwyy+/GLQpLCzE7Nmz0atXL0RERGDq1Km4fv26Qbtjx45hzJgxCA8PR//+/bFy5UoIgtAg90dERGTNpFIp3nnnHaSnp+OTTz7Bgw8+aDLAAAADBw7E3r17G7GHREREZCl1ymT47rvv8N133+n+vHz5cmzevNmgXWFhIc6ePYuYmJi772EVR44cwcsvv4wRI0Zg+vTpKCgowJIlSxAfH49t27bByckJALBjxw689dZbmDRpEnr37o2dO3fi5ZdfxldffYWuXbvqzjdt2jRcuHABc+fOhaOjIxYvXoyJEydiy5YtsLevHJ6srCwkJCQgKioK06ZNw9mzZ/HRRx/Bzs4OCQkJZr9HIiIia/bBBx/A29tb98ytqqysDHl5efDz8wMAODs7o3Xr1o3ZRSIiIrKQOgUZSktLkZ+fr/tzcXGx0S8XLi4uGDt2LCZPnnz3Paxix44d8PPzw4IFC3SZFN7e3oiLi8Pp06fRo0cPAMDSpUvxyCOPYNq0aQCA3r1749y5c/jss8+QkpICADh+/DgOHjyI1NRUREdHAwACAwMxdOhQ7NmzB0OHDgUApKamwsvLC5988gkkEgn69OmDvLw8rFixAuPHj4dEIjH7fVLTcz2/BL//cx0Pdfe3dFeIiO7KwIEDsWjRIjz66KNG9+/btw8zZszA33//3cg9I7KscpUa+/64jIgOPpbuChGRxdQpyPDUU0/hqaeeAgAMGDAAb7zxBgYOHNggHTOloqICrq6uelM13N3dAUA3fSE7OxuZmZl49dVX9Y4dOnQoFi1aBKVSCYlEgrS0NEilUkRFRenaBAUFITQ0FGlpabogQ1paGgYNGqQXTBg6dCiSk5Nx/PhxREZGNtj9UtOg1miQ9O0pXLlRDHmREu4uDpbuEhFRvdU0XVClUlU7fYKoqdpy4CJ+PnoZ6aevoUdI82qnFhMRNVX1Lvy4b98+c/aj1kaOHImtW7fiq6++wmOPPYaCggJ88skn6NSpE7p16wYAkMlkACqzEu4UHBwMlUqF7OxsBAcHQyaTITAw0OABEBQUpDtHSUkJrl69iqCgIIM2IpEIMpnsroIMdnZ8CbuTdjyscVzE4sqfE3v76vtmrN2BP3Jw5UYxAOCX41fwUI821Z7H2DmMjU1t+9SUWfPPjKVxbIzjuJhW3e9DRUVFUCgUuj8XFBQgJyfHoJ1CocDOnTvh48MvuXRvuXqrGL8cuwIAyLlZjEteTmjn627hXhERNb56Bxm0ioqKkJOTA4VCYfTLRs+ePe/2Enp69OiBZcuWYcaMGXjnnXcAAKGhofjvf/8LOzs7AIBcLgdQWZjqTto/a/crFApdFsSdPDw8cPr0aQCV9SWMnUsikcDZ2Vl3rvqSSp3v6vimyhrHxdm5MpPFy6v6gqZV2xWVqvDtgcqglbuLAwpLVDibLa/2PNVd686xqW2f7gXW+DNjLTg2xnFc6mb16tX47LPPAFQWfl6wYAEWLFhgtK0gCLrpirV18eJFzJ8/H8ePH4erqyuGDx+OadOm1TglURAEpKSkYP369cjLy0NoaChef/11vfpLhw4dwtdff40///wTt27dQuvWrTFy5EjExcXBwUE/s2zfvn1YvHgxMjIy4OfnhxdeeAFPPPFEne6F7k2b9l2AWiPA1ckexWUV+CerAG2a8/lMRPeeegcZ8vLyMH/+fOzZswdqtdpgvyAIEIlEZp+PeezYMfzf//0fnnzySfTr1w8FBQX4/PPP8cILL2D9+vUmi1BZK4WiFGq1xtLdsBp2dmJIpc5WOS6lpUoAQH5+cZ3affXTORSWKNG6uSsmPtYJc1f9jsyrChz/+yoCWkprdQ7A+NjUtk9NmTX/zFgax8Y4jotpHh7OJqc5REVFwcXFBYIg4MMPP8QjjzyCzp0767URiURwdnZG586dERYWVuvryuVyxMXFISAgAElJScjNzcXChQtRVlaGOXPmVHtsSkoKli5dipkzZyIkJARfffUV4uPjsXXrVvj7V9bA2bhxI8rKyjB16lS0atUKf/75J5KSknDx4kW8//77unMdPXoUL7/8MkaNGoXZs2fj119/xRtvvAFXV1cMGTKk1vdD955Tsls4efEW7MQivPZUNyz+5k/kKcohu1po6a4RETW6egcZ5syZg19++QXjx49Hjx49DL70N5T58+ejd+/emDVrlm5b165d0a9fP2zduhVjxoyBh4cHgMoshDvTNbVpntr9UqkU165dM7iGXC7XtdFmOmgzGrSUSiVKS0t17epLrdagooIvuVVZ47hoNJWZOjX168521/JK8PPvlcurjhlwH9q2cEfvTr749a9cbNp7ATPGdK3zte4cm9r26V5gjT8z1oJjYxzHxVB1pRYiIiIQEREBoLIQ9KBBgxASEmKW627cuBHFxcVYtmwZPD09AQBqtRrz5s1DYmIifH19jR5XXl6O5ORkxMfHY8KECQCA7t27Y8iQIUhNTcXcuXMBAHPnzoW3t7fuuMjISGg0GixevBivvvqqbt/y5csRHh6uy5Ts3bs3srOzsXTpUgYZyKQKtQYb954HAAzs3gZtWrjh8QeCkLrjb5zPlqO4TAVXJ9ZiIqJ7R70npKanpyMuLg6zZs3CQw89hF69ehn9x9wuXryIjh076m1r2bIlvLy8cOnSJQDQ1U/Q1lXQkslkcHBw0H3ZCAoKQkZGhsE0j4yMDN05XFxc0KpVK4NzaY+rWquB6E6bb6dOhgc3Q5egZgCAETFBEImAMxl5OJOZZ+EeEhHV3csvv2y2AANQWWC5T58+ugADAMTGxkKj0SA9Pd3kcceOHUNRURFiY2N12yQSCQYNGoS0tDTdtjsDDFqhoaEQBAE3btwAUPnx4MiRIwbBhKFDh+LixYu4fPlyfW+PmrgDJ3Jw9VYJ3Jwd8FhUAACgT+eWcHdxgEqtwc7DWZbtIBFRI6t3JoOTk5NF1rz28/PDX3/9pbftypUryM/P1/XH398fAQEB2L17Nx566CFdu507d6JPnz66+Z0xMTH4/PPPcfjwYfTt2xdAZfDgr7/+wvPPP687LiYmBnv37sWrr76qm7u5c+dOSKVS3VcdoqrOZOThxIWbsBOLMGbAfbrtLTydEdRKios5Cnyz/yJC47wgZvVpIrJiy5Ytg0gkwosvvgixWIxly5bVeIxIJKr1UtYymcyg7oFUKoWPj49BkL/qcQAMAv7BwcFYs2YNysrKTE6jPHbsGCQSCdq0aQMAuHTpElQqldFzaa+lbVtXLDJqyFoLsNa1yHOZSo3vD2YAAEb1C4bUzVHXpkugNw6fycXPRy/j4V5t0czDyeg5WOS5dqz1Z8bSOC7GcVxMa4xfO+odZHjsscfw888/4+mnnzZnf2o0duxYLFiwAPPnz8eAAQNQUFCA5cuXo1mzZnpfMqZMmYKZM2eibdu2iIyMxM6dO3Hy5El8+eWXujYRERGIjo7G7Nmz8dprr8HR0RGffvopQkJC8PDDD+vaJSQkYNu2bZgxYwbGjRuHc+fOITU1FdOnT6+xIBXdmzSCoEudHNCtDVo10y/8FOLviSs3i5F1rRBH/7mOXqHGU4GJiKyBNsgwceJESCQSswcZFAqF0WmXHh4e1RZYVigUkEgkcHR01NsulUohCALkcrnRIENmZibWrl2LsWPHwtW18r/PtS0aXR8sMmqatY1NXYs87/otG8WlKgS0kmJE//Z6v9AEtPbAxRwFrueXYueRS5g6JsLoOVjkuW6s7WfGWnBcjOO4WEa9gwyDBw/G77//joSEBIwZMwYtW7bUre5wp6pFoe7Ws88+C4lEgg0bNmDLli1wdXVF165dsXjxYnh5eenaDRs2DKWlpUhJScHKlSsRGBiIZcuWGWQeLF68GO+//z7mzJmDiooKREdH480334S9/b9D065dO6SmpmLhwoV44YUX4O3tjalTpyI+Pt6s90ZNR9a1Qly5WQxXJ3s8Fh1gsN9RYochkW3x/f8y8O0BGbp18IE9I61EZKX++eefav9sS4qKijBlyhS0adMG06dPb5RrssioIWstwFqXIs+KEiV++aNyGdcxA+6DQlGq16asTIXQdp64nl+Kn3+/hP4Rfmjj41bttVjk2TRr/ZmxNI6LcRwX06or8mwu9Q4yPPXUU7r/fejQIYP9DbW6hEgkwrhx4zBu3Lga244ePRqjR4+uto27u3u1y3BpdevWDZs3b65TX+nepKxQ45+sAgDAiAeCTBZ7erinP/Ydu4LrBaU4cCIHA7vXLw2XiMjWSaVSgwLLgH4hZlPHKZVKlJeX62UzKBQKiEQig2OVSiUmT54MuVyOTZs2wcXFRbfvzqLRd6paNLo+WGTUNGsbm7oUeT51MQ8aQUDX+5ojxN/T4BiNRoCnmyO6d/DBH+duYPPeC5g6KrxW12KRZ9Os7WfGWnBcjOO4GKquyLO51DvIcOeST0T0r7OX5FBWaODX3BX9IvxMtnOS2GN4VADW7TmHbekZ6NulJZwd6/1XkojIokpLS7Fjxw4olUo8+OCDdarbFBQUZFB7obCwEDdu3Ki2wLJ2X0ZGhl5RaJlMBj8/P72pEhqNBjNnzsSZM2fw1VdfoVWrVnrnatu2LRwcHCCTyfDAAw/onevOaxEBQG5eCa7nlxrUXTJm5INBOH7+Jk5cuIlz2QXo4O/ZOJ0kIrKQev9G8/jjj5uzH0RNwtVbxci4WvnVa+zA+2BXQyrSA/f74cffs3E9vxR7fs/G8OjAxugmEdFdmT17Nk6ePInt27cDqMwQePLJJ3H+fGUtGnd3d6xZswadOnWq1fliYmKwYsUKvdoMu3fvhlgsRlRUlMnjunXrBjc3N+zatUsXZFCpVNizZw9iYmL02s6bNw+//PILUlNTja6MIZFIEBkZiR9//BFxcXG67Tt37kRwcHC9iz5S01Oh1uB0Rj4A4KEebeDr7VJt+1bNXBEd3gppf+bgm/0X8foz3SBiwWciasI4CZzIjDbtuwBBAHy9nNElsFmN7e3txBgZU/l1bPdvlyAvVjZ0F4mI7tqRI0cwaNAg3Z+3b9+O8+fP46OPPsL27dvRvHnzWhWH1NIWYJw8eTIOHjyILVu2YNGiRRg7dix8ff8tjBsXF6d3XUdHRyQmJmLVqlVYs2YNDh8+jBkzZqCgoAAJCQm6ditWrMDGjRsxfvx4SCQSnDhxQvdPUVGRrt2LL76IEydOYO7cuThy5AiWLl2K7du3Y8qUKfUdKmqCfjl+BUWlKkgcxHi0b+0+DgyPDoTEXowLV+Q4cf5mA/eQiMiy6p3J8Prrr9fYRiQS1VjrgKipOC27hZMXb0EkAjoHGq7JbkqPji0QcOQSMq8VYnt6Jp5+uEMD9pKI6O7dvHlTbzrEzz//jC5dumDYsGEAgCeffBKpqam1Pp+HhwfWrFmDd999F5MnT4arqytGjRplUJhRo9FArVbrbZs4cSIEQcCqVauQl5eH0NBQpKamwt/fX9cmPT0dAJCammrQr7Vr1yIyMhIA0KNHDyQlJWHx4sX45ptv4Ofnh/nz5+utXkX3tqJSFX64vWRlaFsvuDjV7lXay90Rg3r6Y8fhLHxz4CLC76v5QwQRka2qd5DhyJEjBts0Gg1u3LgBtVoNb29vODtzyRC6N6g1GmzcdwEAENRKCncX48UejRGLRBjdLxgfbjyB/SeuYFBPpuQSkXVzdnbWFUisqKjAb7/9hmeeeUa339XV1Wghx+oEBwdj9erV1bZZt26dwTaRSITExEQkJibW6ThTBg4ciIEDB9a6Pd1btv4vA8VlFZC6OKBdS7eaD7hDbGRb7D9+BVdvlSD91LUG6iERkeXVO8iwb98+o9tVKhU2bdqENWvWYNWqVfXuGJEt2X88Bzk3i+Hm7IAObetegTw0wBtdAr1xOiMP36bJ0KpZ9fM7iYgsqXPnzti8eTMiIyOxb98+FBcXY8CAAbr9ly5dQrNm/FJLTcuVm8X45fgVAECXIO8611VwcXLAsL4B2LTvArYezEDfLr5cvpqImiSz/5fNwcEBzzzzDKKiovDuu++a+/REVqekTIXv/1dZfXzEA4GQ2NvV6zyj+gUDAH77+zoKisrN1j8iInObNm0a8vLy8MQTT2DZsmV4+OGHER7+79J8P/30E7p162bBHhKZ3+Z9F6ARBES0bw4fz/pl6w7o1hrNpI7ILyxHxtW6ZfsQEdmKBgufduzYEb///ntDnZ7IapyU3UJxWQV8vZzxYFfTS1bWpK2vO3p3rixw9ldmvrm6R0RkdmFhYdi1axeSkpKwdu1aLFmyRLdPoVDgqaee0iu8SGTrikpVOCW7BQB4soYlK6vjYG+HEQ9UFnw+l10ApUpdwxFERLan3tMlanLo0CHWZKB7wqVrlZXJOwV617hkZU0efyAIv/11HTcKylBSpjJH94iIGoS3tzceeughg+1SqVRvCUiipiDrWmXWQQsvZ/h63d2Uxj6dW2L3kUu4crMYObdKzNE9IiKrUu8gg6mlqQoLC/H777/jr7/+wgsvvFDvjhHZisxrCgBAO1/3uz6Xj6czglpLceGyHNcLyu76fEREDamoqAg5OTlQKBQQBMFgf8+ePS3QKyLzM+ezXiwWoWfHFrhyMAPX80vv+nxERNbG7EEGDw8P+Pv7Y968eXjyySfr3TEiWyAIArJyKzMZAloaf/HYfigTw/oG1PqcXQK9K4MMfPEgIiuVn5+Pd999F3v27DFYUhKo/G+jSCTC33//bYHeEZmfNpPBXM/6zkHe+P5gBm4UlEKt0dx1JiQRkTWpd5Dhn3/+MWc/iGzSjYJSlJZXwN5ODL/mrkbbGPu6V50ugc3w/f8qXzwq1BpWniYiq/PWW2/hl19+wfjx49GjRw9IpVJLd4moQWXeDjK0MxFkqOuzPrClFA72YqgqNJDlKNC+jefddpGIyGo0WE0GonuB9qXDv4WryWCASARsS88AADwaFVjjOQNauuu9eHTw9zRbf4mIzCE9PR1xcXH4v//7P0t3hajBFZepcFNeOYXRVJChrs96sVgEH08n5NwswWlZHoMMRNSk3HWQ4bfffsP+/fuRk5MDAPDz80O/fv3Qq1evu+4ckbXTpk/WNEdTU4cvHGKxCC08nXHlZjFOZ+QxyEBEVsfJyQmtW7e2dDeIGoX2Wd/cwwmuTg4m29XlWQ9UFpHMuVmC0xl5eDwm6K76SERkTeodZFAqlZgxYwZ+/vlnCIKgS5VUKBT44osvMGjQIHz88cdwcDD9H2MiW2cqfVL7RUMkqt95W3g54crNYpzJuIWRfPEgIivz2GOP4eeff8bTTz9t6a4QNThT9Rju+lnvWbkKW+ZVBYpKVXBz5jszETUN9Q4yfPbZZ/jpp58QHx+P+Ph4NG/eHABw69YtrFq1Cqmpqfjss88wbdo0c/WVyKoIgoBLudoXD8P5yBpBgAiAuB5vHz66F49CFJYo4e4iuau+EhGZ0+DBg/H7778jISEBY8aMQcuWLWFnZ2fQrnPnzhboHZF5ZeWarsdwN896Z0d7uLs4oLBEhTMZeYjs5Hu3XSUisgr1DjJs27YNjz/+uMF8zGbNmuHVV1/FrVu38MMPPzDIQE3WTXkZissqYCcWobWP8aKPd6rLFw9nR3tIXRygKFHhTGYeendqaYYeExGZx1NPPaX734cOHTLYz9UlqCnJvGb6g0JVdc1uaOHljMISFU5n3GKQgYiajHoHGW7cuIHw8HCT+8PDw7Fjx476np7I6mnTJ9v4uNV6BQjtFw8Ran77aOHlXBlkkDHIQETW5f3337d0F4gaRUlZhW5JaVNFH6vSPutro4WXMy5eUeBMRl6dV6ggIrJW9Q4ytGzZEr/99hvGjRtndP/vv/+Oli35ixE1XdWlT5pDCy9nXLiiwOm7ePGoS6VrIqLaevzxxy3dBaJGoX3WN5M6NUjNhGZSR0jsxSgoUuLKjWIE+NVvOdjthzIxrG+AeTtHRFRPtfv8asSIESOwa9cuzJkzBzKZDGq1GhqNBjKZDG+//TZ2797NlxBq0jJNFIIyF2+pEyQOYsiLlci+XlSvc2gEoc7VromI6uL69ev4559/UFJSYumuEJmdqaKP5mInFiOkrRcA4FTGrXqfh1kQRGRN6p3JMGnSJGRnZ2Pz5s34+uuvIRZXxis0Gg0EQcDjjz+OSZMmma2jRNZEEIR/l6+848Vjx+HMWh1/55xN7XtB1WwDO7EIHdt64eTFWziTkYeg1h5m6TsRkTn8/PPP+Oijj5CVlQUAWLVqFfr06YO8vDzEx8dj8uTJGDRokIV7SXR3tJkMbevxrAcqn/c7DmdCo6l82BvLLOwS6I1Tsls4Lctj5iERNQn1DjLY2dlh4cKFmDBhAtLS0nDlyhUAQOvWrRETE4OOHTuarZNE1iZPUY6iUhXsxCK0uaPoY12+JGjnbFZ3SOdAb5y8eAunM/LwaDRfPIjIOuzbtw9TpkxB165dMWzYMCxbtky3z9vbG76+vvj2228ZZCCbZyxrsa5ZA0INWYVdgryBvcD5ywUoV6rr11EiIitSpyBDeXk53nvvPbRv3x7jx48HAHTs2NEgoLB27Vps3LgRb7zxBhwcuOYvNT3al47WzV3hYG+4bJu5hAU1wwac54sHEVmVzz77DD169MC6deuQn5+vF2QAgK5du2LTpk0W6h2ReZSWVyA3r3IaUEPVXwKAlt4uaCZ1wi1FGf65lI+WvvWry0BEZC3qVJNh06ZN+O6779CvX79q2/Xr1w9btmzB119/fTd9I7JaWbkKAOZ76RCJKos2VeXr5YzmHk6oUAv4OyvfLNciIrpb58+fR2xsrMn9zZs3x61b9Z9fTmQNLt2eKuEtdYTURXLX59NOldQWZf53u6gymwHAqYv8e0NEtq9OQYZdu3bh4Ycfhr+/f7Xt2rZtiyFDhnAJS2qyMo3UY7hbxtIvRSIRugRWvnicvHjTbNciIrobzs7OKC0tNbk/Ozsbnp6ejdchogagq73ka75nvamCzP8+6xlkICLbV6cgw7lz59C9e/datY2IiMDZs2fr1Skia2aq6OPd0n7h2H5I/wtH58BmAIBTsjyzXYuI6G5ERkbi+++/R0VFhcG+GzduYPPmzYiOjrZAz4jMJ7OBlqrWFoO8U2g7b4hFIlzLK9FN0SAislV1qsmgUqlqXWPBwcEBSqWyXp0ismb5heUoLFFBLBLB38cNwL8rRdwtbTHIO4W284KdWITcvBJcu1UMx3ovPEtEZB7Tpk3DmDFjMGrUKAwZMgQikQgHDx7Er7/+ik2bNkEQBEyePNnS3SS6K1WXrzTXsx4wzF50cbJHcGspzl+W49jZ6+jd0cc8FyIisoA6/brSokULnD9/vlZtz58/jxYtWtSrU0TWTPvS4dfcBRKHyqKPptIfzcHFyR7BfpVFoI6fvd4g1yAiqougoCCsX78enp6eWLJkCQRBQGpqKpKTk9GhQwesX78ebdq0sXQ3ieqtTFmBa7duF328PV2iIZ/1wL9TJvisJyJbV6dMhr59+2Lr1q1ITExEs2bNTLa7desWtm7disGDB991B4msTVYDpU9Wp3NQM5y7LMcf/1xH71AG74jI8tq3b4/Vq1dDLpcjKysLgiDA398f3t7elu4a0V27lFsEAYCnmwQebo6Ncs0uQc3w3f8ycOLcDVSoNY1yTSKihlCnTIaJEyeivLwccXFx+PPPP422+fPPPzFhwgSUl5fj+eefN0snjfnuu+8wYsQIhIWFITIyEs8//zzKysp0+/ft24fHHnsMYWFhGDx4MLZs2WJwDqVSiQ8++ABRUVHo2rUrnnvuOchkMoN2Fy9exHPPPYeuXbsiKioKixYt4lSQe9i/a2Y33hJTuoJQF27yxYOILEqpVOLrr7/GtGnTMHLkSDz55JOYO3cuVq9ejf379/P5SE1ClgWe9e183eHm7IDS8gpcvCJvtOsSEZlbnTIZ/P39sXjxYvznP//B2LFj4e/vjw4dOsDV1RXFxcU4f/48Ll26BCcnJ3zyySdo27Ztg3R6+fLlSElJwaRJk9C1a1fk5+fj8OHDUKvVAICjR4/i5ZdfxqhRozB79mz8+uuveOONN+Dq6oohQ4bozjN//nzs3LkTs2bNgq+vL1asWIEJEyZgx44dcHev/Eotl8sRFxeHgIAAJCUlITc3FwsXLkRZWRnmzJnTIPdH1q0hij7WpF1Ld7i7OKCwRIULl+W4r7VHo12biEjr7NmzeOmll5CTkwNBEODu7g4XFxfk5eXhr7/+wu7du7FixQosX74cwcHBlu4uUb1ZImtRLK5cyvLXM7k4dfEWgv34rCci21SnIAMA9OvXDz/88ANSUlKwf/9+/Pzzz7p9LVq0wOjRozFx4sQal7msL5lMhmXLluHzzz/Hgw8+qNt+59SM5cuXIzw8HO+88w4AoHfv3sjOzsbSpUt1QYZr167hm2++wdtvv41Ro0YBAMLCwtC/f39s3LgREydOBABs3LgRxcXFWLZsmW45LrVajXnz5iExMRG+vr4Ncp9kncqUFZAXKyESAf4t3BrtumKRCF0Cm+HwmWs4JbvFIAMRNbri4mK8+OKLyMvLw/Tp0zF8+HC9Z2Bubi6+//57LF++HJMmTcLWrVvh4uJiwR4T1V9DLF9ZG2FBzSqDDLI8jHggqFGvTURkLvWqU9+mTRvMmzcPBw4cwNGjR3X/TktLwzvvvNNgAQYA+Pbbb9GmTRu9AMOdlEoljhw5opexAABDhw7FxYsXcfnyZQDAwYMHodFo9Np5enoiKioKaWlpum1paWno06eP3nrfsbGx0Gg0SE9PN+OdkS0oKKpMA/Zr5grH20UfG0tYcOWUiVMyrqFNRI3v22+/xdWrV5GcnIwXXnjBIMju6+uLxMRELF++HJcvX8Z3331Xp/PXd2qiIAhYuXIl+vXrh/DwcIwZMwYnTpzQa5OXl4f58+dj9OjR6NKlCyIiIoyea9asWQgJCTH45873Amr6KtQa5NwqBtC4mQxAZZABADKvKqAo4dQjIrJNdc5kqMrNzQ1ubo33RffPP/9Ehw4d8Pnnn2PdunUoLCxEly5d8Prrr+P+++/HpUuXoFKpEBSkH/3Vpm3KZDK0adMGMpkMzZo1g4eHh0G7b775RvdnmUyGJ554Qq+NVCqFj4+P0foNdWVnx/UI76QdD2scF7FYBHlx5QM/oJUU9vZivX0iUWXGgYDKNbAFAXe1DYDeNe5vX7mcVebVQpSUV0DqKoFYLDJoV7XP1e1vCqz5Z8bSODbGcVxMq255vv379yMqKgqRkZHVnqNPnz7o27cv9u3bh6effrpW172bqYkpKSlYunQpZs6ciZCQEHz11VeIj4/H1q1bdR89cnNzsXPnToSHh6NLly44e/asyfP5+/vjo48+0tvGqR/3FkWxEoIAeLhK4OXeOEUftTzdHRHQSorMqwr8lZGH3p1bNur1iYjM4a6DDI3txo0bOH36NM6dO4e3334bzs7OWLFiBeLj47Fnzx7I5ZWFcqRS/UI92j9r9ysUCl3dharttG207aqeCwA8PDz02tWXVOp81+doiqxxXJydJSgsUQEAOgU1g5eXq94+kQgQiUTQaAS94EF9twHQu4aXFxDoJ0VGjgIZuUXo190fzs4Sg3ZV+1zd/qbEGn9mrAXHxjiOS92cO3cO48ePr1Xb3r17Y+3atbU+d32nJpaXlyM5ORnx8fGYMGECAKB79+4YMmQIUlNTMXfuXABASEgIDh06BABISkqqNsjg5OSErl271rrv1PRosxYbO4tBq1tIC2ReVeA0gwxEZKNsLsggCAJKSkqwZMkSdOzYEQBw//33Y8CAAfjyyy8RHR1t4R7WjUJRCjVXC9CxsxNDKnW2ynEpLVXilrxyBZMWHk7Izy/G1v/JIBIB6tvBAbFIpPvfd2Yo1GcbAOTnF+uub2cnRreQFsjIUeDXUzm4P8gbpaVKg3ZV+1zd/qbAmn9mLI1jYxzHxTQPD2eIxcYzPORyOXx8fGp1nubNm9cpEG9qauLbb7+N9PR0jBw50uhxx44dQ1FREWJjY3XbJBIJBg0ahJ9++km3zdQ9ERmjCzLcrsewLT2j2iwfc+vWsQW+3X8BZzLyIGhfCIiIbIjNBRmkUik8PT11AQagspZCp06dcOHCBTzyyCMAgMLCQr3jFAoFAOimR0ilUhQVFRmcX6FQ6E2hkEqlBucCKl+2qk61qA+1WoOKCr7kVmWJcdl+KBPD+gaY3F9SVoEypRoiAK2bu6CiQoMKtUYvUAARDDIU6rsNgMEYdOvYAlt+uYBTsjwoVWpoNILRdlo17W9K+HfJNI6NcRwXQ9X9PqNUKmFvX7vXBjs7O6hUqlpft75TE7X7jE2RXLNmDcrKyuDk5FTrfgBAVlYWunfvjvLycnTo0AEvvfQSHnrooTqdg6zXtvQMAMCjUYEm28iLygEAAbczGTSCgEaMMaBToDckDmLIi5XIvm74rkpEZO1sLshw33334dKlS0b3lZeXo23btnBwcIBMJsMDDzyg21f1RSQoKAg3b940CBbIZDK9l5WgoCCDF5zCwkLcuHHD4KWGbFtNXwu0Lx0tm7nASWKZvzqhAc3g6GAHRbES2bl88SCixnXlyhWcOXOmxnbaIsu1Vd+piQqFAhKJBI6O+vPmpVIpBEGAXC6vU5AhNDQUYWFhuO+++1BYWIgNGzZg8uTJWLJkiUFB6bpg/Q9DFquNcjtaYKpWkSAIuqmRwW08YG8v1tVdqmutpdq0r9oXOzsxHOzt0CnAGyfO38RfWfm1qq8kFouadP0lgPV0TOG4GMdxMa0xMrNsLsjQv39/fPvtt/j7778RGhoKAMjPz8eZM2cwYcIESCQSREZG4scff0RcXJzuuJ07dyI4OBht2rQBAERHR0MsFmPPnj0YPXo0gMrshIMHD+Kll17SHRcTE4MVK1bovQDt3r0bYrEYUVFRjXXbZAUsPUcTABzsxQgN8MKJ8zdxOoOrTBBR41qyZAmWLFlSYztBECBqzPxyM7nzvQEABgwYgLFjx+otgV0frP9hWmOPTU21isoqBAgAPNwkCGrrDZFIpKu7VNdaS7Vpb6ovvTq3wonzN/HPpQJ0CW5WbZ8BwMlZck/UXwL498kUjotxHBfLsLkgw0MPPYSwsDBMnToV06dPh6OjI1auXAmJRIKnnnoKAPDiiy/i2Wefxdy5cxEbG4sjR45g+/bt+PTTT3XnadmyJUaNGoVFixZBLBbD19cXycnJcHd3x9ixY3Xtxo4di3Xr1mHy5MlITExEbm4uFi1ahLFjx5osREVNkzbIENBIa2aLRMancIQHN8OJ8zdxJiMPIW09G6UvRETvv/9+g527vlMTpVIplEolysvL9bIZFAoFRCLRXU9rFIvFePjhh/Hhhx/Wa+rFv/1h/Y+qLFUbpaZaRbnapSt93VFQUKI7pj61lmrbfvUPpwAAwx8I0o1LSJvKD1tnZLfQztcV9nbiausrlZUqm3T9JYD1dEzhuBjHcTGtuvpL5mJzQQaxWIyVK1fi/fffx5w5c6BSqdCjRw989dVXuoJUPXr0QFJSEhYvXoxvvvkGfn5+mD9/vl5hKAB488034erqio8//hjFxcXo1q0bvvjiC71VJzw8PLBmzRq8++67mDx5MlxdXTFq1ChMnz69Ue+bLE9eXDldQpvJsONwZoNf09gUDu0a2ucvyxHcWgp7poERUSN4/PHHG+zc9Z2aqN2XkZGhV6tJJpPBz8+v3kEBc2P9D9Mae2xqqlWUX1j5rG/r64aKCg12HM6sd62l2rc37FNzDyc093DCTXkZrueXoqW3S7XjpNEI98zPGP8+GcdxMY7jYqgx6snaXJABALy9vfHhhx9W22bgwIEYOHBgtW0kEglee+01vPbaa9W2Cw4OxurVq+vaTWpCFCVKlJarAQBtb2cyWKris6+3C3w8nXCjoAw3C8rQspmLRfpBRGQu9Z2a2K1bN7i5uWHXrl26IINKpcKePXsQExNz1/3SaDTYvXs32rdvbzUBC2pYct3KEpU/h5Z61otEInQJaob9x6/oggxERLbCJoMMRI3t0rXKNF5XZ3s4O1r+r02XwGb45fgV5BaUMshARDavtlMT4+LikJOTo1ue0tHREYmJiUhKSoK3tzc6dOiADRs2oKCgAAkJCXrX2L17NwDgwoULUKvVuj+HhYWhdevWuHLlCmbNmoVHHnkE7dq1g1wux4YNG3D69GkkJSU10kiQJakq1FCUaOsvuVm4N0CXQG9dkIGIyJZY/rclIhuQeTvI4OnmWEPLxhEWVBlkuJ5XCiGIa2gTkW2r7dREjUYDtVqtt23ixIkQBAGrVq1CXl4eQkNDkZqaCn9/f712r7zyitE/v//++xg5ciRcXV3h5uaG5cuX49atW3BwcECXLl2QkpKit1oVNV2XbxRDEACJvRjNpJbPXAlt5wU7sQjFZRUoKq39krBERJbGIANRLWRpgwyuEgv3pFJoOy/Y24lRUs4XDyJqGmozNXHdunUG20QiERITE5GYmFjtsWfPnq12v6enJ5YvX15jP6np0j7rPdwkVrE6irOjPTr4e+LvrHzk5jGbgYhsByvGEdVCVu6/Lx7WwFFih463V5bgiwcREdHds7asRaByRSkAyM0vsXBPiIhqj0EGohoUlapwU14GoPFfPEQiYFt6BralZxjsC9O9eDDIQEREdLd0WYsW+KCgXba6Km2Q4Za8DGXKikbuFRFR/TDIQFQD7UuHq5M9HOwb/6+MRhAgQMDW/8mw8ad/0311Lx6KMpSU8cWDiIiovlQVGly+UQTAklmLhs/6lt4ucHGyh0YA/s7Mt1C/iIjqhjUZiGqgnSrh6SbRZRZYYqqmRhD0ltLy9XKBq7M9iksr8FdmHnp0bNH4nSIiImoCcm4WQ60R4GAvhquTvdU860UiEXy9nJFxtRAnZbcQ0cGn8TtFRFRHzGQgqkGmrhBU5VQJjSBAY6F1s6tq6VW5fOXJi7cs3BMiIiLblXlNAQDwcK0s+mhNz3pfb2cAlc96wUr6RERUHQYZiGqQdfvFwxJzNGvS4vaLxynZLat5GSIiIrI1lqzHUJPmUifYiUXILyzH5RvFlu4OEVGNGGQgqkZxmQo3CiqLPlrLyhJ3aiZ1gp2dCPJiJS7dntZBREREdfPv1EjrWVlCy85OjOYeTgCAkxdvWrg3REQ1Y5CBqBqXbn/ZaO7hBIm9nYV7Y8hOLIKPx79plERERFQ3FWoNsq9XZghY4wcFQH/KBBGRtWOQgagambe/bAS0dLdwT0xryRcPIiKiesu5WYwKtQbOjvZwdbLOmui+t2swXbgiR1GpysK9ISKqHoMMRNXQztFsZyVBBpEI+OFght62Fl6VQYaMHAUUJUpLdIuIiMhmaQs8t/N1g8gSS0pUIRIBW/8nw7b0f5/3Lk72aN3cFYIAnMnIs2DviIhqxiADUTW0QYaAllIL9+RfVStLOzvao20LNwgATsuYzUBERFQXWbnW96w3trpFeHAzAKzLQETWj0EGIhNKylTIzS8FYD2ZDKaE6V48GGQgIiKqi8yr1pW1aIo2yHBKlgeNhitKEZH1YpCByARt+qSPpxPcnB0s3Jvq3R/cHABwWpYHtUZj4d4QERHZhsqij5XP+8BW1h1kCG7tAWdHexSVqpBxVWHp7hARmcQgA5EJmVY4VcKUID8pXJ3sUVJegYtX+OJBRERUG1duFKNCLcDF0R4+ns6W7k617O3E6BLoDYCZi0Rk3RhkIDJB+5UgwMq+bIhEwLb0DGw/9G9BKLFYhLAgTpkgIiKqi4xr/z7rraHo451EImDH4Uy9beGcHklENoBBBiITtHM0A60wk6H6glB88SAiIqqNzNsfFAJbWd+zHjAs9qz9oJCVW4iConJLdImIqEYMMhAZoShR4paiDID1F4LS6hLUDCIRcPlGEfJu952IiIhM035QCLCRZ73UVaKrHXGKHxWIyEoxyEBkhPalo6W3C5wd7S3cm9pxc3ZAsJ8HAOAkl7IkIiKqllKlxuUbxQCsN5PBmPDbxZ75rCcia8UgA5ERmde06ZO28WVDS7eU5QW+eBAREVUn+3oRNIIAqYsDvNwdLd2dWtNOjzyTkYcKNVeUIiLrwyADkRH/pk/azpcNALj/9ovHX1l5UFXU/sVjW3oGtqVn1NyQiIioidCtItVKanVFH6vTrqU7pC4OKFOqcf6yvE7Hbj+U2TCdIiK6A4MMREZkXLPuQlCm+Ldwg6ebBEqVBmez82t9nLFCkkRERE2ZbhUpG6nHoCUW3bmi1M06HVu1kCQRUUNgkIGoivzCcsiLlBCJAH9fNwCGS0hZK5FIxFUmiIiIauHOTAbAdp71ABB+3+26DHzWE5EVYpCBqArtclatm7vC0cEOgG1F/sOC+OJBRERUnTJlBa7evF308XYmgy096zsHeEEsEuHqrRLcKCi1dHeIiPQwyEBURUaVLxu2plOAF+zEIlzPL0VRqcrS3SEiIrI6WdcKIQDwcneEh5vtFH3UcnFyQPs2t1eU4kcFIrIyDDIQVaFbWcLG5mhqOTvao4O/JwAgN6/Esp0hIiKyQrqpEjb6rAfA6ZFEZLUYZCC6gyAI/64sYaOZDMC/q0zk5jOFkoiIqCpt0UdbK/B8J22Q4Z9L+VzKkoisis0HGYqLixETE4OQkBCcOnVKb9/XX3+NwYMHIywsDI899hh++eUXg+MLCwsxe/Zs9OrVCxEREZg6dSquX79u0O7YsWMYM2YMwsPD0b9/f6xcudKm5u5R7dySl6GoVAU7sQhtfNws3Z16C7v94nFTXsYXDyIioir+Lfpou5kMfs1d0UzqCFWFBjflZZbuDhGRjs0HGT7//HOo1WqD7Tt27MBbb72F2NhYpKSkoGvXrnj55Zdx4sQJvXbTpk1Deno65s6di48++ggZGRmYOHEiKioqdG2ysrKQkJAAHx8fJCcnIy4uDkuXLsWqVasa+vaokWnrMbRp4QYHe9v969HS2wUtPJ0hCGBBKCIiojsoK9S4fjvTL6Cl7WYyVK4oVVns+RqnRxKRFbHd36IAXLx4EevXr8eUKVMM9i1duhSPPPIIpk2bht69e+Odd95BWFgYPvvsM12b48eP4+DBg3jvvfcwdOhQDBw4EEuWLMHZs2exZ88eXbvU1FR4eXnhk08+QZ8+fTBhwgTEx8djxYoVUCqVjXKv1DgybTB9UiQCth/KrLJNpMtmyM1jkIGIrN/Fixfx3HPPoWvXroiKisKiRYtq9YwVBAErV65Ev379EB4ejjFjxhh8UMjLy8P8+fMxevRodOnSBRERESbPt2/fPjz22GMICwvD4MGDsWXLlru9NbIyBUWVP1c+nk5wc3awcG9qRyQCtqVnYFt6ht72O5/1zLAlImth00GG+fPnY+zYsQgMDNTbnp2djczMTMTGxuptHzp0KA4fPqx7aUlLS4NUKkVUVJSuTVBQEEJDQ5GWlqbblpaWhoEDB0IikeidS6FQ4Pjx4w1xa2QhtloIytiLxZ11GfjiQUTWTC6XIy4uDiqVCklJSZg+fTo2b96MhQsX1nhsSkoKli5digkTJiA5ORk+Pj6Ij49Hdna2rk1ubi527tyJZs2aoUuXLibPdfToUbz88svo2rUrUlJSEBsbizfeeAO7d+82y32SdSgoLAdge1kMGkGApsrzPLSdF+ztxCgpr0DO7SU5iYgszd7SHaiv3bt349y5c0hKSsKZM2f09slkMgAwCD4EBwdDpVIhOzsbwcHBkMlkCAwMhEgk0msXFBSkO0dJSQmuXr2KoKAggzYikQgymQyRkZHmvj2yAEEQdCtLaIMM29IzUOXHw2aEtPWEnViEMqUal3KL0M7GAidEdO/YuHEjiouLsWzZMnh6egIA1Go15s2bh8TERPj6+ho9rry8HMnJyYiPj8eECRMAAN27d8eQIUOQmpqKuXPnAgBCQkJw6NAhAEBSUhLOnj1r9HzLly9HeHg43nnnHQBA7969kZ2djaVLl2LIkCHmu2GyKG0mgzZr0Zaf9Y4OdujYzhOnZXk4ceEmWttwPSkiajpsMshQWlqKhQsXYvr06XBzM/yPqVwuBwBIpfoRau2ftfsVCgXc3Q1/8fLw8MDp06cBVBaGNHYuiUQCZ2dn3bnqy87OppNJzE47HpYYl5LyCpSWq+FgL0a7Vu6wE4sBEQARIBaJIKAyXVEQKv/d2Nu0wTCxWASxWKTXTgQR7KvUkLC3F8PX2xk5N0vw69+5CL69nrYxYrFId4ytseTPjLXj2BjHcTHNUr9opaWloU+fProAAwDExsbi7bffRnp6OkaOHGn0uGPHjqGoqEgvc1EikWDQoEH46aefdNvE4pr/v1YqlThy5Ahmzpypt33o0KHYvn07Ll++jDZt2tTxzsgaFRRpMxkq3wE1ggARKp+5tqhbBx+cluXh1zO5GNq7ncHHMyKixmaTQYbly5ejWbNmeOKJJyzdlbsmlTpbugtWyRLjUlReWUA0uLUHmjerfPFwdpbofsHXaAT9X+wtsA0AJI4OsHcwbPfj0csAgLGDQnT31N7fqzLIcOYaJj1xP+xN/FLl7Fw5FcjLy7WhhrfB8e+SaRwb4zgu1kMmkxk806VSKXx8fHSZhaaOA2CQbRgcHIw1a9agrKwMTk5OterDpUuXoFKpjJ5Ley0GGWxfuVKN0nI1RIBNZvhp6zAN6xug29aroy++3HMOV24WI/NaoU3VlSKipsnmggxXrlzBqlWr8Nlnn+myDEpKSnT/Li4uhodH5RfbwsJC+Pj46I5VKCpT4bX7pVIprl27ZnANuVyua6PNdNBeS0upVKK0tFTXrr4UilKoucSgjp2dGFKps0XG5fqtyrmM/i3ckJ9f+b9LS5W6jAJ1lQBAY28TiURwcnKAslwFVYXGaDsAur4DgKebAxwldpAXKbH/9yx0D2lh9N5LS5UGx9oKS/7MWDuOjXEcF9M8PJxr9dXf3BQKhUHGYGV/PKrNGFQoFJBIJHB0dNTbLpVKIQgC5HJ5rYMMtc2CrA9mzRiyVEaRvKTyedeymQvcXSsD7NrsQHNnI9b3HNo+CYLxdiLoZx5K3SRo3dwV2deLkH76Gtr7e5q8f7HYMPPRVjALzTiOi3EcF9MaI9nJ5oIMly9fhkqlwgsvvGCw79lnn8X999+Pjz/+GEDlV4c7v0jIZDI4ODjA398fQOWXj8OHD0MQBL3UsoyMDHTo0AEA4OLiglatWhl8ScnIyIAgCAZfPOpKrdagooIvuVVZYlzybxeCaufrpru2NosAIhhkGTT2Nu2PqEYjmGwHQH/cBMDfxxUXrihw4HgO7r+91FVVRo+1Mfy7ZBrHxjiOiyHWiG0YzJoxrbHHpqi0conykABvXfZeQ2Ut1vccAODo6GCyHSAyyDxs39YL2deLcOSvXEwe3RUSBzuj9+/kLLHprEWAf59M4bgYx3GxDJsLMoSGhmLt2rV62/7++2+8//77mDdvHsLCwuDv74+AgADs3r0bDz30kK7dzp070adPH90qETExMfj8889x+PBh9O3bF0Bl8OCvv/7C888/rzsuJiYGe/fuxauvvgoHBwfduaRSabXLYJHtUGs0ukJQtlZtuiZtfd1w4YoCJy/egrxYCQ9XSc0HERE1IqlUapAxCOhnFpo6TqlUory8XC+bQaFQQCQS1Snb8M4syDtVzYKsD2bNGLJURtGN/Mplnds0c2nwrMX6nEMA4OTkgPJyFQRBMNpOBJFB5qGniz2aSZ1wS1GGvUcy0btzS6P3X1aqtMmsRYBZaKZwXIzjuJjWGFmLNhdkkEqlJldz6Ny5Mzp37gwAmDJlCmbOnIm2bdsiMjISO3fuxMmTJ/Hll1/q2kdERCA6OhqzZ8/Ga6+9BkdHR3z66acICQnBww8/rGuXkJCAbdu2YcaMGRg3bhzOnTuH1NRUTJ8+XW9ZS7JdV2+VQK0R4CixQ8tmLpbujlm5u0gQ5CeFLEeBw6evYUhkW0t3iYhIz52rOmkVFhbixo0b1WYMavdlZGSgY8eOuu0ymQx+fn61nioBAG3btoWDgwNkMhkeeOABvXPdea36YNaMaY05NoIg6LIW27Zwb/CsxfqcQ5tMpNEIlctPG2kngmHmoSAAfbu0xLZDmThwIgc9TEyP1GgEm/9Z5N8n4zguxnFcDDVG1mKTnaQybNgwvPvuu9i+fTsSEhJw7NgxLFu2zCDzYPHixejbty/mzJmDGTNmICAgACtXroS9/b/xl3bt2iE1NRXXrl3DCy+8gFWrVmHq1KmIj49v7NuiBpJx9fbSlb7uNltdGqh8+diWnoFt6Rl626PDWgEA0k9drXxpISKyIjExMTh06JAuawCoXKpaLBYjKirK5HHdunWDm5sbdu3apdumUqmwZ88exMTE1KkPEokEkZGR+PHHH/W279y5E8HBwSz62AQUFClRrqos+ujva7tLPZp61keFVz7r/8rIQ56izBJdIyICYIOZDMZERkYaXfN69OjRGD16dLXHuru7Y8GCBViwYEG17bp164bNmzffVT/JemVeq0yPDWhVWejTltfM1giVXzx2HM7UbesV6osNe8+z8jQRWaWxY8di3bp1mDx5MhITE5Gbm4tFixZh7Nix8PX11bWLi4tDTk6ObnlKR0dHJCYmIikpCd7e3ujQoQM2bNiAgoICJCQk6F1j9+7dAIALFy5ArVbr/hwWFobWrVsDAF588UU8++yzmDt3LmJjY3HkyBFs374dn376aWMMAzWwzNsfFNxdHODoYNcknvV33kMLT2eE+HvibHYB0k9fw6N3rEBBRNSYmkSQgehuZV6tDDJof/nWrplty+7MWHBxskf3Dj749a9cHDx5lUEGIrIqHh4eWLNmDd59911MnjwZrq6uGDVqFKZPn67XTqPRQK1W622bOHEiBEHAqlWrkJeXh9DQUKSmpuqKPGu98sorRv/8/vvvY+TIkQCAHj16ICkpCYsXL8Y333wDPz8/zJ8/H7Gxsea+ZbKAjGuVQQZP98r6HU3hWa+9B9HtO4kOb1UZZDh1FcP6tNMrbE5E1FgYZKB7XoVag+zrtzMZbHDN7NqKCm+FX//KxZG/cjF24H1wsDdeeZqIyBKCg4OxevXqatusW7fOYJtIJEJiYiISExOrPdZYxqMxAwcOxMCBA2vVlmyL9oOCp1vTrafVI6QFvvzpHK7nl+L8ZTk6VLOcJRFRQ2GQge55V24Uo0ItwMFeDB/PprvMTWg7LzSTOuKWohzHzt1EZCffmg8iIiJqAgRB0E2N9HRzrKG1dRFVqOBUXAhJoRyOJYWwV6uh0aghFgSoxXZQubqhwsUNogJPOHp4omfHFjh48ioOnrzKIAMRWQSDDHTP0xZ99HKTNOm0QrFIhL5dWmHboUwcPHWVQQYiIrpn3JSXoahUBbEIkFrjUs6CAJdb1+Et+xstL5+Hc5YM7rlX4J57BS75N2t/GhcXTGnhh0GCG67tbwO73AEQhYejomMnwM12i10SkW1hkIHueZlV5mg2ZVHhlUEGbeVpb2ntl3cjIiKyVdosBqmrBHZiK/igIAjwvCyD36nf0OrUUbT8+xic5XnVHlLu6g6lqzvUDhIIIjEgEkFcoYJDWQkkxUWwV5ZBVFICl8wL6AYAWSeAY9srLycWoyL8fvTy7wyJfChUffpC8PJu8NskonsTgwx0z9PO0fSysfTJ+mDlaSIiuhdpsxYtOVVCVKGC36nfEXDkF7T7bT9c8m/o7deI7VDQJhDyDp1wq1UA5L5tUNzSH4pmvlC6e0AjtoNIVJmZqNZUri4hCJVLWoogwqPdW0GccwV2Vy7j9C/HcP3wcXQuuoL7CrJhl3sNDieOo8uJ48C2LyHY2UEV2QfKwUNRPjgWmqBgC40KETVFDDLQPU2pUuPyjWIA90YmA1D/ytPbD2ViGIMSRERkgzJ1QYZGniqh0aDlX8cQvG8r2v22H47FhbpdFRJHXA+5HzlhPXG1Sw/kB3dChaMTXFwkKClRQhAEvYACBNOXAQA4OUETFAxNUDB87o/EIsdDEARgYWJvtCzJg8Ovh3Dl+x/RPuMk7M+dheTQQUgOHYTb27NR0TkMZU+Owzb/SJR6NcejUYENOixE1LQxyED3tOzrRdAIAqQuDnCW3BurLdS38vSdS2ISERHZCo0gICv3dtHHRvqg4HrjKtrv3Yr2+7dBmntFt73UwxtZkf1xqfdAXOnUHRpHR102gtiMdaG8pU7oHOCN0xl5OHjqGkbGBKH8iSdxuGVPNI8KhDgrE457dkGyexccDh+E/ZlTcHv7FMaI7XCla29IprwE5ZChgN298W5ERObFIAPd07RzNANaSSEWi7AtPQNNuPYjAMBRYsfK00REdM/IzStBabkaEnsx3F0cIBIBOw5nmv9CgoAWZ/9E521fIeDXfRBr1AAApYsbLkYNxsV+jyC3w/2Avd2/GQrm74VOdHgrnM7Iw6HTVzEiOhDiO2pRaNoFoHTiiyid+CJE+Xlw3PodnDZvgMPR3+B/LB14Lh3qNv4onfA8yp55FoJ3swbsKRE1NQwy0D1NO0czoKU7gMqvHU08xgAAiA5rhYMnr+L3f67jqUHtLd0dIiKiBqP9oNDW112XLWDO7DyRWo3Awz+h0w9fosX507rtOV164NxDj+NSn4FQOjj9W0PBbFeuXkT75nBxtEeeohx/Z+Wjc6DxQo+ClzfKJiSgbEICftn8Czrs24rw/d/D7nI23Oa/DdeP3kfZ6HEomTINmgBOoyCimokt3QGixrAtPQPb0jMMtt+ZyXAvad/GA75ezihXqXH0nxs1H0BERGQDth/KNNimLfCs/aBgLiK1GsEHdmDkK0+g38ez0OL8aVQ4SHB24Ah8u/hr7Hznv7j44CNQOzqb9bq15WBvh8jOlctVHzx1tVbHKPza4egzU3Hr+N9QLPkcqrD7ISorg/O6L+DdpxvcX06E3YXzDdltImoCGGSge4JGEKCp8tWitLwCV29WFn0MNPOLh7UTiUSICmsFoPYvHkRERNbOWIZCxu2lqgPN9EFBpK7AfQd2YOTUkei/5A14XslEmbsH/hgzCZtW7sb/Js9FfjvryBKMvv2sP3buBkrKVLU/0NkZ5eOeQcHPaSjYugvKfgMgUqvhtHkDvKJ6wD3xOYhlFxuo10Rk6xhkoHvWpdxCCAC83B3hcQ8sXwnof+Hp26UlRCLgXHYBikvr8OJBRERkI9QaDS7larMW7/KDgiDA/2gaRrwyGv2WvAHPnCyUuXng6NMv45vknTg+ZhLKPI1PSWhMd2ZvBrR0R2sfV6gqNDjy9/W6n0wkgqpPFOSbv0f+7n0oHzIUIkGA03db4B3dE26v/Qei6/U4LxE1aQwy0D1LO1XCXF82bMGdX3i0lacB4NL1Ikt1iYiIqMFcvVkCpUoDJ4kdfL1d6n0e74x/EDs3EQ+/NxWel2Uoc/PA789Mxabknfhz1PNQubiZsdd3587sTZFIhKgutzMXT95d5mJFtx5QrN2IvL0HUf7QwxBVVMD5i/+iWa/74fLBexAVFdZ8EiK6JzDIQPesqkUfmyqRqPKrxvZDhjUposMrXzyyrxdxiUoiImpytFMlAlq612uJSJebuYhJegsjZoxD61O/ocJBglOPT8Dm5dtw8ol4qJxdzd3leqnuWd+nS0uIRSJkXFVAUay862upw8KhWP8NCr7bAVW37hCVFMP14w/g1bsbHL/eWFndkojuaQwy0D3r36KPTTvIABivSQH8W3m6tFyNGwVlFugZERFRw9E961vWLWtRVKFC2HerMfLl4ejwyzaIBAEXHhiCLcu+w9G46VC6Wl8WpKlnvYerBOHBlUtQZuWaL3NRFfUACnbtgzx1LdQBgbC7ngvp5Bfg+ehg2J/602zXISLbwyAD3ZOKy1S4nl8KoO4vHk3JnZWnL5nxxYOIiMgaZGqzFuvwQaHl6aN4fMZY9Fq7GA5lpcgNuR9bP1iH/dMXoqhF64bqaoO6M3OxQq0x34lFIigfHYG8//2GojfehuDiAofffoXnoAfh9up0iPJume9aRGQzGGSge5L2y4aPpxPcnB0s3BvLign3AwDk3CzGldurbRAREdm6CrUG2bdrDtVmqWqnglt4cMmbeOSt5+GdfRGlUi/8b8o72PbeF7jZIayhu9ugwoObQeoqQblKjQMncsx/AUdHlL4yA3npR1E2YiREGg2c16TCO6oHHL/ZxCkURPcYBhnoniTL0c7RvLeyGLRzNrVVpwGgXUt3tPR2gQBg0z6ufU1ERE1D5Vd7Aa5O9vDxcDLdUBDQ4advMfKl4Wh/YDsEkQh/Dx6Nb5Z9jwsDhwNi23tdFon0V5SytxNjeFQAAOD7/8lQXJflLOtA07oNCleuRsF3O1DRMRTiW7cgfWkiPMY9AfGlrAa5JhFZH9v7ryaRGZy8cBMA0LGtp2U7YgHG5mx2DvSCSAScluXhlIypjUREZPv+vP2s7+DvCZGJoo9uuVcQO28SHvj8HTiWFOJGcCf88ME6pCe+AaW7R2N21+yqFnSO6eoHdxcHFJdVYFt6ZoNeWxX1APJ//h+KZ70JQSKBZN/P8I6JhPPyZUBFRYNem4gsj0EGuufkF5bj4u1Mhq7tfSzcG+vg5uyAoNuppJv2XYBaY8b5mkRERBZw7NwNAEC3Dkae9RoNOu9Yj5GvPIHWJ4+gQuKE356bgR8WrsPN9l0auaeNw04sRlhQ5dLVe/+4jNy8koa9oESCkv/8H/L3H4ayTxREJSVwe3s2PGMHwu70qYa9NhFZFIMMdM85cfvLRrCfFF7ujiaXfGrKjE2bCGnrATdnB+TcLEZaPeZrVj0fERGRpVzPL8HlG8UQi0S4/77mes96jyuZGPrGc+iTuggO5WW42rk7vl28GWeGPwvBzs7CPTcfY896Xy8XhAU1g1ojYPMvF+p8zvo869X3tYf8ux0o/HgpNFIPOPx5HF6D+8Hlk0XMaiBqohhkoHuO9stGxO0vG6aWfGrqqt63g70dhkcHAgC++18GSuo4X/NeHUciIrI+x85VflAIaesJN2cHaAQBQkUFwr/9AiOmPwnfv09A6eSC9MQ3sGNeCgpbtbVwjxuGsWfzkwPug1gkwvHzN/F3Vv5dn69WxGKUjZ+A/PTfUR47DCKVCq4L58Nz6EDYnf2n7ucjIqvGIAPdU0rKVPjn9gPVaPrkPe7Brn5o1cwFRaUqbD/EAk1ERGSbjp/Xnyrhfu0yHnkzHr2+XAJ7lRKXI/piy5It+GfIaJss7Hg3Wjd3xYMRlStLbdp7HhpN430g0Pi2hGL1V1B8thIaD084nDgOr4cegPNnSwG1utH6QUQN6976ryrd805evAW1RkCrZi5o6e1i6e5YHXs7McYMuA8A8NPRbFzPb+D5mkRERGYmL1biwmU5ACDivmZw+motHv/Pk/D9508onV2R9vJc/DTncxT7tLJwTy1nRHQgnB3tcel6EdJPX23ci4tEKB89Fvlpv6J84CCIysvhNu9NeA6PhVh2sXH7QkQNgkEGuqccO1+ZPskshkoiEbDjcKbetrCgZugc6A21RsDXv/BhT0REtuXPCzchAOjiVoGAKc/BffrLkJSV4Gqn7vj20804P3BE5QPwHqGtzXBn/Sl3Fwke7RsAAPj2gAxlysavjaBp5QfF+m9Q+OkyaNzc4fDbr/AeEAWn1JUAp18S2TQGGeieodZodMszMsjwr6pLXIlEIowZcB9EIuCPczdw9lLd5msSERFZ0rFzN9Dr4m+Ys2QiHHfvhCCR4Miz07HrnZUoatHa0t2zCGO1FAZ2b4MWns6QFyux89dLlumYSISyp59F/oHDUD7wIEQlJXB/fSY8xj0Bce41y/SJiO4agwx0z7hRUIZypRpe7o4IaOlu6e5YtTY+bniwa+WL2Ma9F1jQkYiIbENhIfolv4O3ti6AszwfFaGdkf/jfpwaEdekVo4wBwd7MUb3r5wi+eNvl3BLXmaxvmj820L+9VYULlgEwckJkn0/w+vB3pDs2GaxPhFR/THIQPeMq7cq6wt0a+8D0T2UJllflfM17ZCVW4jDp/k1gYiIrJv9b0cw4j9PYtDJn6ARiVD80hTk//gL1J27WLprVqtbh+YI8feEqkKDLQcsPEVSLEbZ85OQ/1MaVF3CIc7Lg8dzT8Nt2mSIigot2zciqhObCzLs2rULL774ImJiYtC1a1cMHz4c33zzjUHK99dff43BgwcjLCwMjz32GH755ReDcxUWFmL27Nno1asXIiIiMHXqVFy/ft2g3bFjxzBmzBiEh4ejf//+WLlypcH1yLoJgoBreZVBhogOzS3cG9sgdZVgWJ8AAMCWAxdRodZYtkNERETGKJVwWfAOPB8bDO+bObju7oMf5qxEydz3ACcnS/fOqolEIowd2B4iAL/+lYu8wnJLdwnqkI4o2L0PJVOmQxCJ4Lx+Hbz6R8HutyOW7hoR1ZLNBRlWr14NZ2dnzJo1C8uXL0dMTAzeeustfPbZZ7o2O3bswFtvvYXY2FikpKSga9euePnll3HixAm9c02bNg3p6emYO3cuPvroI2RkZGDixImoqPi3+E1WVhYSEhLg4+OD5ORkxMXFYenSpVi1alVj3TKZQZ6iHEqVBq5O9ujg7wnAsAgSGXqohz+aezihoEiJ87crdRMRNYSLFy/iueeeQ9euXREVFYVFixZBqVTWeJwgCFi5ciX69euH8PBwjBkzxuB5DwC5ubmYMmUKIiIi0KtXL7zxxhsoKirSazNr1iyEhIQY/JOWlmau2yQzszv7DzxjB8J18UcQaTTY13kApjy7GC1HDNG1qVrgmPS1a+mOvmEtAQCnZXnW8SFNIkHxW/Mg/34n1G38YZeVCfehg4C33wZUKkv3johqYG/pDtTV8uXL4e3trftznz59UFBQgC+++AIvvfQSxGIxli5dikceeQTTpk0DAPTu3Rvnzp3DZ599hpSUFADA8ePHcfDgQaSmpiI6OhoAEBgYiKFDh2LPnj0YOnQoACA1NRVeXl745JNPIJFI0KdPH+Tl5WHFihUYP348JBJJ4w4A1Yt2qkR4cHPY21XG1jSCAE6a+Je2+jQAPBoVCKByvuaT/e/D59+fxvnLcuQpyuAt5VchIjIvuVyOuLg4BAQEICkpCbm5uVi4cCHKysowZ86cao9NSUnB0qVLMXPmTISEhOCrr75CfHw8tm7dCn9/fwCASqXC888/DwD4+OOPUVZWhg8++AAzZsxAcnKy3vn8/f3x0Ucf6W0LDg42492SWWg0cP7vCri++zZE5eXQeHvjr5nz8elNP3i4SRDoJ9U1tYpfmq2EsWc9AIyMCcbRf24gv7AcOTetZ/lqVZ8o5O8/BLdZM+H0zSbgnXfgvn0HFJ+thDq4vaW7R0Qm2Fwmw50BBq3Q0FAUFRWhpKQE2dnZyMzMRGxsrF6boUOH4vDhw7qvImlpaZBKpYiKitK1CQoKQmhoqN4Xi7S0NAwcOFAvmDB06FAoFAocP37c3LdHDUAQhH/rMdxeVYJfNYwzVn26e4gPOrTxgFojWH6+JhE1SRs3bkRxcTGWLVuGBx54AKNGjcKrr76KjRs3Ijc31+Rx5eXlSE5ORnx8PCZMmIA+ffrgk08+gaenJ1JTU3XtfvzxR5w/fx5LlizBgAEDMHToULz33nvYv38/Tp48qXdOJycndO3aVe8fd3cWC7Ym4qs58Hjycbi9OQui8nKUDxyE/AO/4sc2PQAAEe19IBaJmLFogrFnvZe7I2J7twUAnMnM+//27js8qjJ9+Pj3nOkpk0boJQkQDAJSREAQlKYIiquo7FpYG9hwLewroouirLqWnwquiohrx10XXZSqgtKL9ColhRJICOlt+nn/mMyQSYEE0rk/15UryTlnznnmmcncJ/fTcLrc9VG0CmnWMPLfm0vB3H9BeDj6bVuJGHYV5s/+JUtdCtFANbokQ0W2bt1KixYtCAkJISkpCfD2SiitY8eOOJ1Ojh07BkBSUhKxsbHlJgCMi4vzn6OoqIiTJ08SFxdX7hhFUfzHiYbt2KkCiuwuVFWhW6w3SSWtGlWnKAq3D/O2FmzYm86h4zkXdL4f1iX7W1GEEAK8Cf0BAwYQHh7u3zZq1Cg8Hg/r1q2r9HHbtm2joKAgoGHBaDQyYsSIcg0GXbp0CYjnAwcOJDw8nFWrVtXskxG1yrTwW++qA6t/QbNYyP/H/5H31X9xNW/B9kOnAejd2Tv3UkX/TIvKXXtFe8xGHcV2N0svcEnL2oj1zltuhV27cF412LvU5ZS/YL17PEpGRo1eRwhx4RrdcImytmzZwpIlS3j66acBb5dLAKvVGnCc73ff/ry8vApbJsLCwtizZw/gnRiyonMZjUYsFov/XBdCp2sSeZ4a46uPmqyXnYmZALSIsBAcZABAVRU0vN0GNc37XVXKbzvbvrre5kuIqaqCqiq1et0lG49w46AzibrO7cJp3yKEo+kFvPvtbp6bcDmtooID6llVveXT68/x2pXk9c55XBXVxnumqZC6qZjUS+Xqa+GdpKQkbrnlloBtVquV6Ojosyb0ffvKNgZ07NiRTz/9FJvNhtlsJikpqdwxiqIQGxtb7vxHjhyhT58+2O124uPjefjhhxk+fPiFPD1RA5S83DNd5gFnz17kv/cR7k7eJHhSai65hQ70OoVLOkTUZ1EbhYqGTZgMOrrGRLDt4GkWrk2mZVQQVyS0OK/z11pyp107Cr5bhOHd2QS/PAPT8qUYhvQn/51/4hhx3bkfL4SoE406yZCWlsYTTzxBv379uPvuu+u7OOfFarXUdxEapJqslx2HvS0bHVpZiYjw/mNsthjxeLSAf6wVRSm37Wz76mMbgNFkQG+o3euC4q8rn/7dW6HXnyIpNZc3vt7B65OvIirszOtksXiHFJV9XFlVPa665G+pclI3FZN6aTjy8vLKJfTBm/g/W0I/Ly8Po9GIyWQK2G61WtE0jdzcXMxm81kbFkqfPyEhge7du9OpUyfy8/OZP38+jzzyCO+88w7XXXf+/8BIQqu86iT79OvWEPTQRHTHj6GpKrYn/4rtr1NRDAb/jawv1reKCsJs8m71JeTrq6HgfM/hK7um1X45ITDp375FCNn5dpJP5jP3h32EBhnp3jHKv7+qDQpVbnioBv97xqDH+dhfyB86lOCJ96L7fT9hd9yG/c/3UvTiyxASUmPXbAwkcV4xqZfK1UWDQqNNMuTl5fHAAw8QHh7O7NmzUVXvGygsLAzw9kKIjo4OOL70fqvVSlpaWrnz5ubm+o/x3ZD4ejT4OBwOiouL/cdd2PMoxi1LA/rpdCpWq6XG6iUju5jkE97XPjLUSHZ2IQC2YgfuMv9Yq4pSbtvZ9tX1NkVRMJsNOOxOnC5PrV5XQfHXlY/b6ebJ2y7jpU+3kJ5VxLPvrePZCZcTYvH2Diku9s53UvZxZVX1uKqq6fdMUyJ1UzGpl8qFhVn88fRiNGHChIDfhw4dyvjx45k1a9YFJRkkoVW5s9aN3Q5/+xu88YY3QMXFoXzxBZYBAyj9KE3T/EMlOrQO8yexLRZjvTYUnO85AEwmQ501XpRO+gcFmejXvRVtW1hZsyOVWQt2MfPBK7mkQ6S/Tss+piK11aAApd4zV/WH7dvgmWfg7bcxffIxptW/wmefQak51y4W8jlTMamX+tEokww2m41JkyaRn5/Pv//974DWCV93yLJdI5OSkjAYDP6ZpuPi4tiwYQOaplF6Xobk5GTi4+MBCAoKolWrVuW6UiYnJ6NpWrmul+fD7fbgcslNblk1VS+/7fdOGNYszIxRr/LdqkR/9q5c671SftvZ9tX1ttLlru3rqgr+uipdF0EmPU/ddhkvf7GV1NOFvDl/O1PG98Jk1PlvjM71ulX1uOqSv6XKSd1UTOqlvPoavm61Wssl9CEw8V/Z4xwOB3a7PaA3Q15eHoqiBDQslF2u0nf+Vq1aVXp+VVUZOXIkr7/+un/oxfmQhFZ550r2qfv2Evzg/ej37AbAfucEiv7+KoSGQpkk9fGMAk6eLsSgU4kKMfLJ97tRFPwJ9PpqKDifc2iA2WzAbneiaVqdlPOzRXv89wHukhh9z6guZOcVsycpixfmbuS5u/vQJjqk3hoU4Czvmekz0V89nOBHHkRNSkIbPBjbY09ge3oalOnl1BRJ4rxiUi+Vq4sGhUaXZHC5XDz++OMkJSXx5Zdf0qJF4Fixdu3aERMTw7JlywLGUC5ZsoQBAwb4V4kYPHgw7733Hhs2bODKK68EvMmDffv2+Ze58h23YsUK/vrXv2IwGPznslqt9OrVq7afrrhA20paNlpGBQFnlq1USyWWRMV8daVp4M1FeOusWbiFp27vyatfbiPxRB7//G43j43rUa9lFUI0bqUnXfbJz88nIyPjrAl9377k5GQuueQS//akpCRat27tTwrExcVx8ODBgMdqmkZycnLAKlO1RRJalStXNx4Plg/fI/jvM7xLU0ZFkf/mbBzXj/Hur6Aef9t/CoCEmAh0qoLLHdjbr74aCs7nHL48n8ejeSeprouya56AxAMAGjxyU3de/3o7SSfyeO2r7TxzZ+96b1CAiv+eXFcOxr5qAyHPPo35319heftNDD8u9y51eWm3Gi9DQySfMxWTeimvLhoUGl2fyBkzZvDLL7/w4IMPUlBQwI4dO/xfvuUpJ0+ezKJFi5g1axabNm3i+eefZ9euXTz88MP+8/Tq1YtBgwYxbdo0li5dysqVK3nsscfo0qULI0eO9B933333kZWVxVNPPcWGDRv49NNPmTdvHg8++GDAspai4ckrcvhXQmgVGVS/hWli2kSH8JdbL8NoUNmTnMVHi/YhK3YIIc7X4MGDWb9+vX9oI8CyZctQVfWsSYDevXsTEhLC0qVL/ducTic//vgjgwcPDjj/77//TkpKin/bhg0byMnJYciQIZWe3+PxsGzZMjp37nzevRhE1alHjxB261hCpk/zLk05fCRZv248k2CoxLaD3tUFfMtUi5phMup4/NbLaN0smOx8O2/+eyd2R8NZ2rIszRpG/uwPyP3Xl3iiotDv20PEyCFYZr0F7oZbbiGaokbXk8G3lNWrr75abt+KFSto27YtY8aMobi4mLlz5/Lhhx8SGxvLu+++W67nwdtvv80rr7zC9OnTcblcDBo0iOeeew69/ky1dOjQgXnz5vHqq68yceJEIiMjeeyxx7j33ntr94mKC7bz0Gk0DTq0CCXI3Oje6g1epzZhPPqH7rzz311s3n+KmFah9IiLrO9iCSEaofHjx/P555/zyCOPMGnSJNLT03nttdcYP358QI/FCRMmcOLECX766ScATCYTkyZNYvbs2URGRhIfH8/8+fPJycnhvvvu8z/u2muvZc6cOUyePJknn3yS4uJiXnvtNa6++mp69PD2xEpNTWXq1KmMHj2aDh06kJuby/z589mzZw+zZ8+u2wq52Gga5s8/Ifj5Z1ELC9AsFgpmvIxtwr3nnKEsK8/GkbR8FKBnp2as3plaN2W+SIRYDDx1e09e/nwr6VlFbNjrYmD3lvVdrLNyjL6BrL79CJ3yGKZlSwiZ+TymH5eSN/sDPLEXPtRZCHFuje4/r5UrV1bpuFtvvZVbb731rMeEhoby8ssv8/LLL5/1uN69e/Of//ynymUUDYOvZaNXfDNpZa8l3eKiuH9MVz78fi8pJ/Mx1eAs0kKIi0dYWBiffvopL730Eo888gjBwcGMGzeOJ554IuA4j8eDu0yL5AMPPICmaXz88cdkZWWRkJDAvHnz/HMwARgMBj766CNmzpzJk08+iV6vZ8SIEUybNs1/THBwMCEhIbz//vtkZmZiMBjo1q0bc+fO5aqrrqrdCriIKcePEzb5IYyrfgHAeUV/8ma9jyeuY5Ue74v1ndqGYQ2WHqa1ISLUxFPje/LKF1vJLXSwef8pxg6KxaDX1XfRKqU1b07ep/Mxff0lIc8+jWHzRiKvGUjBiy9ju+vPdTO9vhAXMUWT/77qVXZ2oYwTKkWvV4mICL7gerE5XDz2zlpcbg8v3ncFWw+cqrNJm2pzdYmgICN2W+2vLlHphFQlnxa+NbV9Vm47zhc/esc7/2l4Z4Zf3q7sS+K3cK133PXYQRW3JpRdt/tcauo90xRJ3VRM6qVykZHBstxXLZD3Wnl6nULE//6D9vgTKPl5aGYzhdOmU/zAQ6Cr+j+vr8/fzv4j2dw+tBPXXtGeReuT6z1eX+jEj0FBRoqKHHU28WPF21TGXBkTUNdH0vL5++dbcLk1esdH89BNl6KrZPK4c8V6gEXrU8pd42zO97NbPXqE0Mcewrh+LQCOa4aR/8Y7eNq1r/I5GjKJaRWTeqlcXcR6uZMQTdKepCxcbg/Nwy20aVbzyyddrDyahqeCvOTQ3m25pH04AF/9fIiNe8svD3uh1xBCCNE0qCdPEHL7LXDffSj5eTgvv4LslesofvDRaiUYCoqdHDiaA0AvmY+hRlXUBtmhZSj9EpqjKt4eJJ8tO3BBPUXrqp3T074Dud8uouDFl9FMJoy/rCBicH/M8z4Ej/zzKURtkCSDaJK2HTozCVTpJUpF7YlvF0ZsK+9ysnMX7WPR+hRJFgghhDhD0zB/9TkRV/XD8POPYDJRNOPv5PywHHenztU+3c7Dp/FoGm2jQ2gebqmFAouymoVbuPySaBQF1uw6yT+/20ORzVnfxTo3VaX4wUfJ/mU9zn4DUAsLCH1mCuFjR6FLPFTfpROiyZEkg2hyXG4POw9nAt75GETtWbQ+xf+zoih0j4tkSM/WaBp8uzqJWf/dRUFxI7j5EEIIUat0iYcIu3kMoY8/gpqXi6v35bB9O/bJf6lW74XSzqwqIbG+Nv2wLtk/lBGgVVQw94/uil6nsO1gBi9+soWj6fn1WMKqc3fqTM7CpeS/8gZaUDCGTRuIuPpK7woULld9F0+IJkOSDKLJOXA0h2K7C2uwkY5twuq7OE2OonhvOBatTwa0Uj97Ew0TrruEe0ZdgkGvsisxkxn/2kzSibyzn1QIIUTT5HAQ9H+vEXH1lRjXrUELCqJgxsvkL/sZEhLO+7R2p5u9yVmALF1ZG0rHeo+moaGxeEOKf/+Abi155s4+NAszcyqnmJmfbWX1zhONY6JtVcV230Sy1mzCcfVQFLudkJnPE37dUHS7d9V36YRoEiTJIJoc/6oSnZuhylCJWlF63oSK5lC46rLWPHtXH5pHWMjMs/PKF1tZsfV4jd18lO5BIYQQomHS/7aJiOFXEfzqTBS7HcfQ4WSt2kjxQ4+C/sIWONubnIXD5aFZmJl2zUNqqMSitLLxvWwMj21l5fl7+nJZxyhcbg+fLP2djxfvx+50lz3VeSnbg6Kmedq1J/ff33lXMwkLx7BrBxEjhxD8t2dQChpHzwwhGipJMogmxaNpbD/kSzJ4WzZKZ95F3WnfIpTpE/rSp0s0bo/Glz8dZM73e3HWwAy/jaKlRAghLlJKdhYh/+8JwseMRP/7fjzNmpH3wTxy5y/A0yGmRq6x/eCZWK8oSkCvOlF3gs0GJo/rwbirO6IosG5PGjM/20J+0YUPlayTiaAVBfv4O8ha+xv2G25CcbsJmvNPIq68HNPCb0HuN4Q4L5JkEI1a2Sz3hj1p5BQ4sJh0JHSIAOQf0rqkKIG9DILMeh6+qRvjh3VGpyps3n+K1TtPkFfoqL9CCiGEqB1uN+bP/kXkgN5YPpmHomkU//FO7z9wN9/qDRLnqXRsOZVTzObfTwHQp4u3QUFWJqo7vqEUvvsvVVG4vn8H/t8fexEWbCQ1o5BVO0+QmlFYzyWtOq1FC/LmfUbO1wtwx8SiSzuJ9YE/E3bbTTIxpBDnQZIMolErfVNRZHPyzS+HARgzIAaDXt7e9aFsUkdRFEb2bcfTf+pNRKiJgmIXq3eeZP2ek/VUQiGEEDVNv/U3wkcNJXTKX1CzsnAldCXnf0soeOc9tMioCz5/6dgy/6eDOF0eEjpE0LmtzL1UHypK6nRpH8EL9/TlkvbhuN0aWw5k8OWPB2ukB2NdcQ4dQdbqTRT+9RnvcperfiFiyACCXp0JhY0naSJEfZP/wkST8d3qZPKKnLSKCmJE33bSdbKB6dQ2jOfv6Ut0uBm3R+OjRfv553e7OXFagrYQQjRWSkYGIY8/QsSoYRh2bMcTaqVg5qtk/7wG55WDavx6Ow6dZmdiJjpV4c6R8SxanyKxvgEJCzHx1Pie/uTPim3HeenTLexKPN14epaazRT99RmyV23Acc0wFIeD4P97jcgr+2D6z3zwNJ6kiRD15cJm3RGigTiSls/K7ccBuHNEPHqdikfTUEAmf6xjvm6UinJmKOMNA2MBsAYZGXBpCw4ey+XA0Ry2Hshg28EMBlzakhsHxco650II0VgUFRH04XtYZr2FWjJJnm38HRQ8NwOtefNauaTD6earnw8CMPKKdrSKCvbHelH3FMU775XH4w32vlivU1W6xkQQaTWxJymL4xkFvP3NLjq1CeMPg+P8w1kbOndcJ3K//hbjooWEvPAcumNHsT46CedHH1Dw4qu4+g+o7yIK0WBJTwbR6Gmaxhc/HUDT4IqE5iTERNZ3kS56vm6UvmWvSo+lVRSFLu3DmXHvFfTq3AxNg/V70nj2w418uux3iu01t061rEIhhBA1zO3G9PWXRA7oTfDLL6IW5OO8rBfZi34if9b7tZZgAFiy8Qinc21EWk3ceGVsrV1HVJ1WKtaXnSerZWQQL0/sz3VXtMegVzmcmsvr87fz+vztHE7NrbEy1OoqFIqC44abyFq3hYLnXsATEophx3YibryW0PsnoB5JqZ3rCtHISZJBNHpH0wtITM3DZNRx+9DO9V0cUSGt3PCVts1DmHxLD/424XK6xUXi9mis2nGCn7ccZ3dSJrk1MDlko+maKYQQjYDh15VEDB+M9bGH0J08gbttO/Le/4ic5b/guqJfrV67oNjJko1HARg/tDMmo65Wryeqz5dsKL2qV2iQkduGduIfDw5gWO+26FSF/Ueyefnzrazfm8aRtAtfKrJOJv00myl+7EmyNm6n+K570FQV8/ffETnwcoKn/RUlPb12ry9EIyNJBtGoOZxu9qVkAzB2YCwRoSaZi6GBquwmILaVlSdv68nUO3oT3y4cjwZJJ/J5+oP1fPPrYQqKL3wZLCGEEOfPsGEdYX8YTfhtN6HfuxuPNYyC6S+RtX4r9ltuA7V2byc1TWNXYiYut4dLYyP9K0rIEtUNU0UJ/vAQE3eMjOeVSf25qkcrVEUhPauYGZ/8xj+/201qI5mfSWvenII33yF7xVocQ65BcTgI+mgOUf0uI/jvM1Bysuu7iEI0CJJkEI3a/iM5OFwe2jQLZvjlbQFZxqoxKLvUJUB8u3Ce/lMvBnRrQXiIEYfTw9KNR/nr++uZt3gf+1Ky/OM+a0qtdrEUQohGTv/bJsLGjSV87CiM69agGY0UTXyIrM07KH70L2A210k5th86TXp2MXqdwp0j4lFK5lqS3moNW9mlLgGahVm45/oE/v5AP9pFB6MAWw9kMP2jTfzfv3ewYU8aNkfNDZuE2on17ku7kfvNQnL++z3OPpejFBUR9M6bRF7eg6C3XkcpuPAeGkI0ZjLxo2i0kk/mkVLSze7Okd7JHkVjovmDvm+yKEVRaB5uIfoyMzEtw/huTRLHThWwbnca63anER5ipH/XltidLjRN899oni9JRgkhRHn6LZsJfuNVjCt/BkAzGLD96W6KHn8KT5u2dVoWu8PN/JLJHq/r154WkUF1en1xYTya5m9YGHNljH97i8ggLr+kORNvjOZ/a5LZejCDPclZ7EnOwmhQ6R0fDZpGdMSFTwhdm7HeOfhqcq4agvHHZQS//CL6/XsJfuUlLO/Ppvj+Bym+f1KNLOEqRGMjSQbRKHk0jS9+PABA2+hgurT3zlQsXScbF9/Nh281Cl/SQFEUenZuRo9OURw+nsvGvWn89vspcgocLNvsHZN78Fgu/S9twcAerYmICK7PpyGEEI2fpmH8eTmW2W9j3Ljeu0mnw/bHOyl6fAqe9h3qpViLNqSQmWcnyKRn9IAY4EzMEI2JFrDylO/1axMdwiM3dyc9u4iNe9PZsDeNU9nFbNzrnePAZFAptrkZ0K0lnUqWxWxwFAXHtaNwjLgW0/8WEPT6K+gTDxP8xqsEvTeb4gn3UvzwZDwtWtZ3SYWoM5JkEI3Smp0nSD6Zj16ncGnsmaWQpOtk4+RfbrTMdlVRiG8XTny7cP44PJ7dSZls2JvG9oOnST1dyIJVSSxYlcSlcVH07tyMhA4RtIiwXHAPh7LK9rgQQogmw+nE9O03BL03C/3+fUBJz4Vxt3uTC7Fx9Va0tKwilm3yJpa7d4zEZPBO9ihLVDdOvtdN00ABlFKLj7aICGLsoFhuHBhD0sk8Nu5JZ83uE9idHn7eepyftx6nRWQQ1/RpR+c2obRvHoKuhucCueBYr6rYb74V+9ibMS7+nqC338SwZxdB78/GMm8OtvF3UjzxIdzxXWqw1EI0TJJkEI1OfpGD//6aCMAl7SOwmPTSqtHElO3dUHoN7t7x0SxYdZjo8CA27k3j96M57E3KZG9SJgBRVhMJMZFcGhOJ3eGukfLIsAohRFOjZGRg+fJTzJ9+jC71OACekFBsd99D8aSH8bRqXa/l0zSNL388gNuj0aNjFK2jgiTWNzGlY/2Z3g0KY66MoWPrMILMOjJyitFQ2H4wg/SsIr7+yduL1WLSc0n7cLrGRFJQ7CTYfOH/0tRYrNfpcNz4Bxw33IRx5U8EvfUGhs0bsXz2MZbPPsYx5BqKJz6EY9jIWp80VYj6IkkG0egsWJVEoc1F2+gQYluHAtKq0RSV7t1QNvAb9ToGX9aawZe1JqfQwa6kLDbtOcnBYzlk5tlZu+ska3edBGBPShaXxkTSNTaS+LZhGPS1s+xZ2fGmQgjR4Gga+i2bsXw8F9MP/0NxeJcK9kQ3p2jSw9gm3IsWFl6/ZSyx9UAGe1Oy0etU/jS8M5v3p+P2aEiUb1rK9244Q1UVWkQGMXZQHMV2FzsTT7MnJZudBzMotLnYfug02w+dBsBi0pGd7+DS2EgSOkQQGmSslfJWK9YrCo5hI3EMG4lh43os77+LcfkSjKt+wbjqF1yxcdjun4Tt9j+hWRvoUBAhzpMkGUSjkngilzU7TwDeyR73H8mq5xKJulK6xaO0ZmFmbhnamaG9WlNY5OTg8Rz2JmexLyWL4xmFHE0v4Gh6AUs3HcWgV4ltGUrHtmF0ah2G3eGusbXWzzVUR4ZcCCHqi5Kbg+l/32L+7F8Ydu/0b3f27kPxPQ9gH3tzna0UURU2h4v5Kw4BcH3/9jSPkMkeLxaVxXqLSc+gHq25YUhnMjMLSEzN9cf6A8dyKLa7WbPrJGt2nUQB2kQH06lNGB3bhNVYTwc4/1jv7H8lzv5Xoh5JwfLxXMxffoY+OYmQZ58meOYL2MeMxXbH3TgHDES664imQJIMotHweDS+WH4QDRjYrSXx7cIlyXCRKd1jxRfI/zCkIwDfr03m+v4d6B4XRfc470zO3/xyiLbNQ9mXnMXelCxyChwcPJ7LweO5/nMGm/Vk5Njo1CaMTm3CaN0sGFWt+QAvQy6EEHXK7cawaiXmf3+FackiFLsdAM1kwv6HcRTf+wCunr3ruZAV+2FdCtn5dpqFmbm+f/1MOCnqjy/WA+VWpvj6pwPYih2MHhBDbCsrY66MYcGqw2Tm2rAGm/wNDL6vX3d4G6aMepWj6YV0auuN9TEtQzEaar5n47livadDDIUz/k7hX5/B/M3XWD7+EP2B3zF/8zXmb7729m74013Yb/8Tnpatarx8QtQVSTKIBq10Rnj5b0c5kp6PxaRn3DWd6rlkor75VqZYuCYJS5CRimauNhv1DLi0JQMubYmmaaRlFXE4NZfE1FwOp+Zx4nQhhTYX6/eksX5PGgBmo46YlqG0aRZCq2ZBtIoKxuZwYzLUzbhJ6fEghDhvmoZ+1w5MC7/D9N9/o0s76d/lSuiK7fY7sI3/U4NbUq/0517yyTx+/O0YAH8aEV8r/wiKxsYb33U6BaPJgIbG4g0peDze+wC9TvUPqwDILXRw+Lgv1ueSdCIXh8vDjsOn2XHYO7xCpyq0ax5Cm+hgWjcLplVUMIXFToJqqMfDufywMwPih3HD6vvQb/0N81efY/pugbd3w99nEPzKSzgHXoX9pluwj76hwf3NCnEukmQQDZpH03B7PHy2/AC/bk8F4ObBcYQFG2W5SgF43yO+7otlx3aW7vFww8BYWkUFs/VABn8elQDAN78eIjvfTnRYkPdG5GQeNoeb34/m8PvRnIDrGPQq+1JyaBUV5L8haRFpIcpqRq+ruQTEuVpBJAkhhAigaeh3bMP0/f8w/bAQ3dEU/y5PRAS2W27DPv4OXN0va7DdsH2fe2t2neCLHw/i9mj07NSMnp2ayWSPAiiJ76XCo6ZplfZ4CAs2cuJ0ARaTjml39eHb1YnkFthp3SyEw6m5HD6eS26hg5S0fFLS8gOuo6oK2w9lemN9lDcB0TIyiGbhZszGmvu3yR/rFQXX5VdQcPkVFLz4CqYf/ofly88wbN6Icc0qjGtWEfL0kziGXIP9pltwXDsKLTzi7CcXogGQJINo0IpsTjb/nkFugQMFuGFgDNf0bgPIcpWianw9HkrfqPp+Nup1tIwMQkHhkvbhPHV7T45neOdwOJFZyMnThZzMLOJUTjFOl8d7c5KaG3B+RYGIUBOqonAqp5joMAvR4RaahZuJDrcQFmys0SU1ZdiFEAKbDcP6tRhX/Ihp2RJ0x476d2kWC47h12L7wzgcI64Fk6keC1o1breHXUlZHE0vAKBHxyjuG+NNBsvEzqLqzvRo9MX+xRtS0KkKUWFmHE437ZuH8PBN3cjMtZGcls/J04WcyCzkxOkiTpwuwOPROHaqgGOnCsqdPcRiwKBXST1dSLMwC9HhZpqFW4gOMxNZEw0OISHY/3gn9j/eiXokhaRZ8+i5/RcMe3ZhWvETphU/oel0OPtfiWPkKBzXXoc7Tnr2ioZJkgyiwdpx+DS/7jiJ0+UhxGLggRu60j0uSlo1xHkpfaNauvXDv0+BJRuPMObKGNq3CPXvW7whBbvDRUGxiy7tIziZWciJkuRDRk4xDpeHrDzvWOfTu9PKXdegV2kWZsbj0Qgy6zEZ9ESHl9ychFlqpWumrHQhRNOjHjuKccVPGFf8iHHNKpSiIv8+LSgI+4jrsN94E46hIyA4uB5LWj3pWUWs3nWSvEInigJ/uCqO6wd0YPH6FIn1otrKxvfSDVJnEg/eWN8s3OLft3hDCk5XFIU2F5fGRPlj/YnMIk5lF1Foc1FQ7ARg8/5T5a6rKBAZakZRIMisR1WUkgYHbxLCWs0GB0+HGHbffC8xb76E7vAhTP9bgOn779D/vh/jujUY162B56eR0yYG8003wujroFtvMMskqaJhkCSDaHDcbg/frDzMD+tTAIgINTLtzstZv+ckR9LypFVD1KLy8zoA6HQq4aFGTmUXodcpdGgZSrvmIYCGzeGmyO6isNhFu+YhZOTaOJ1TTEaOjax8G06Xh5OZZ/4ZSD4Z2DUz2KynWbiFyFATIRYDJ7MKMel1rNt9khCLgZAgA6EWAyEWIxZT1cYmV7WXjyQjhGi41OPHMKxb4+2xsG5twDAIAHfLVjiGe5fHc1wzDIIa3z8XG3af4K352yi2uzEaVB67pQddYyK94+01Wa5S1JaKY72iKIQGGTh2Kh9FgZZRQTSPsKAoUTicHorsTgqLXXRoaeV0bjGnc21k5Hi/O10eMvNs3hPl4u+V42PUqzQL9w6xDA0ykJ5VhNGgsmpHKiEWI6FBBn/MDzEbAiagdnfqTNGUqRRNmYqakozpx6UYly9Dv34t4akp8M9Z8M9ZhOv1uPr0xXHVEJxXDcHZpy8YjTLMUtQLSTKIBiW3wM4bX+9gV8nEPLGtQukeF8nGfWlywyHqREXzOpTdp3KmRcRo0GEy6oiymtE0aB5uJjrMTEIHGNW/A1l5NjJybfy85RhFNhfFdhcGvY6MnGIKip0U2lwUpuVzpMy40L0p2eXKplMV9DoVo0HlwNGckhsSIyGWkkRESUIiO9/O6dxiIkLNZ004yLKbQjQQDgf6/XvRb9uKYdsWDBvWl0sqaDodrj59sY+4Fsewkbgv7dZg51g4F5fbwze/HmbpRu8wj0irib6XRJNYMkmfELWtWrEe0OkUrMFGwkNMOF1uwkOMhAUb6djayugrY8grdJCRU8zyzUcpsrkosrsosrnwaBrZeXYcLo+3Z8TpwoBy7D+SU65sCt7eEIqisDspK7DBIchASP+bCL3mNvbuTKLz/s1cfXo/QRvWoKSkYNi0AcOmDfDGq2hmM64ePbm8VTynulyG2ukGPC1alruexHpRGyTJIBqMg8dy+GDhHnIKHJiNOv486hJOZhaWZJplHLpo+AJuWhRYvvmof/brmJahKIr3Rsb3dh5+eTsyS1pCcgodFBQ52Jl4GofTQ3iIifxiJwVFTgqKndidbtweDbfHjd3pLjcxZVmll+0KsZRqIbEYCLUYCQkykHIyj0370kv1lvB++WZzr+r8D3KDIkQ1OJ3oDh9Cv3c3+u1bMWzbin7PLv8Skz6aToerZy+cV16FY+AgXFf0RwsJreSkjUd2vp33F+7hcMlSwqP6t0evKuh0ivRUFI1C2VjvG9qjKN4VK0r3kFAVlev6tSczzxvrs/LsFBY72X4oA4fTQ6TVTH6xwx/rC20uNKDQ5gIoNw9UWSsMXfmgVVfUceOItZ2mT+oeuqXsIP7wdoLzczBs3kgPNnoPfu0p7K3aYuvZG63HZdCjB+7uPfB4PFVKWEqsF9UhSYYqSkxMZObMmWzfvp3g4GDGjh3L448/jtForO+iNXo2h4uV21L5dlUSHk2jfctQHr6pG83DLSxcm1TfxRPivJWd/drH1wvi5y3H/DcmvmRE97goFAV0qurfpmng8XhwuDWKbU4cLg9OpweHy4Pd6aZ1s2AKip0kn8zD4fRuczjdeDS8c0bk28nKt1dYxp2JmeW2GQ3exITbrWE0qKRmFBJk1mMxeb+CfN/N3p+z8+3o9Qq5BXaMBh1Gg4pOPTMBVlVuTGTohjjfOKtpGnPnzuWrr74iKyuLhIQEnnnmGXr27BlwXHp6OjNnzmTt2rUYDAZGjBjBM888Q0hISMBxK1eu5O233yY5OZnWrVszceJEbrnllvN/YoWFmN96A2XvHvT796E7fAjF6Sx3mCcsHFev3jh798HVtx/OfgOaRFLBx+3xsDsxi0+W7ievyInFpOPx8b1JaBfGgl8P13fxhDhvpXs+lKexdOORgMSDoihcGhvp/Rkl4D5AQ8Ph8OBweeO4zenB4XT7Y3vzCAtJJ/JK4rz3OJdbw+PRSDRGkRg7hP/EDoGrNdpkn+CSk79zyYkDdDl5gA6nj2I6eRzTyeOw9Ht/CW8NCuNYyzgOxnUhr00MBe3jsMd0RGneHIvZ4I/3mXk2DHqV7Hw7JoOK0aBDpyoBc02cK5ZLouLiIUmGKsjNzWXChAnExMQwe/Zs0tPTefXVV7HZbEyfPr2+i9copWcXsetwJrsST3PgWA4ut7fF9MpuLXniT334evl+6b0gmryKumT6lE5QaBooqoJFp2LUq2VaSbw9I8JDjLSKCvJvc7k9oICi6sgvsGNzuLk0JpL8YifbD57CXnLjEhpkpMB2pseE26PhcHrIcp5JSmTk2Kr0fH7ekur/WacqmEoSDk6XB52qsCsx05uE0Kv+ZITRoMOk15GSloeqKgH7THodRqN3v+/Y1TtPcH3/DpgMKnqdWm4iLbmBaZwuJM7OnTuXWbNmMWXKFLp06cKXX37Jvffey8KFC2nXrh0ATqeT+++/H4A333wTm83GP/7xD5566inmzJnjP9eWLVt49NFHGTduHNOmTWPjxo08++yzBAcHc911153fk0tPx/LSCwGbPCGhuBO64uzZC1evPrh698Ed27HRDn+oTEGxk91JmexKzGRPUqa/dbZd8xAeG9eDSzpG89miPfVcSiFqV7mhGRXsKz0M02BQMRpVVMWIu1Rjg68BwjtPRKmkBYBOR36BjWKbG4fLTXy7CLYeiCC5WwK/O7zbwnHQ4vAeWh09SPu0JOIykmmTlUpYUS5hSdshaXtAuQtMQaRGtCE1og3Hw1uht0aTbm3OP1ZGkxkShVvnneDSF5+NehW70832QxkY9bozcV6v8yclUtLy0KkKZqO+1OPO7Pcdv2ZnKjpV5YaBsRgMarneTRLrGz5JMlTB119/TWFhIe+++y7h4eEAuN1uZsyYwaRJk2jRokX9FrARcLk9HDyWw67ETHYmZpKeVRSwPzrcTJtmwbSKsvDD2kQ8miZJBiGqqKLeEori7X5sNhvQKRpocDq3GEWBSzpEBCQofDcroOH2gM3uwuHyYHN4v7s9Gk6nB6fbg9Pl/QoPNfnnmMjOt+Fya7g9Z/5m3R7NOya1VAeKvKLyrbelnWsIiM+yTWeW6/PddOlUBZ2q4PJ4UBSF1TtPoPrmsNB7580wG3WYDN75MLp3jga3B4NexVSy3aD3JnEMehWDXsfm/elc3bMNRoOKQadiKGm1UUtanVRVQVW8rVC+n8X5Od84a7fbmTNnDvfeey9//vOfAejTpw/XXXcd8+bN44UXXgBg+fLlHDp0iCVLlhAXFweA1WrlvvvuY9euXfTo0QOA999/nx49evDiiy8C0L9/f44dO8asWbPOP8lgNGIfdxvOLgm4E7riSrgUT9t2TS6hAN7k6PGMQnYePs2uxMxyXb2DzXpaRgbRLTaCjXvT2JmcJbFeiGqo6O9Fp1MxmvQompFgszcpYXO46NI+vFyCwtO9A25lNAddHva6PHiKiwhOOkSzlANEH0skMv0o0elHCc9OJ8ReRJe0Q3RJO1Tumm5FJSs4ggxrczJCm5EVEkF2UAQ5weHkBIWTHRxBWnA4eRYrmlK+j0dFc1FUZElJvPfNi6GqCjpVxe32xvpfd5zwxv+SRhiTUYe5ZK6s0zk2Lu0YhaJpGPQqZoO34cJYEuMNJfF+y/5TDOnV2r/NqPfeU/jiuqooqGpJ3FfO9DwRZydJhipYvXo1AwYM8N/4AIwaNYrnn3+edevWcfPNN9df4RoYm8NFToGDnHw7OYV2cvIdJKbmsjclC5vD7T9OUSDKaqZVVBAtIiyEBhnweP8PwiP3G0LUikqHbnDmJkSvU7CY9QQpoGlGfzKiotYU33AO3z4FcLo9eDzeZIXH48HjAbvLXbJN8393uTy4tZLvJdtdJfvcbk/J95Jtvt9Lfi79GaFp3iSmyx34vOyOMhvKSCkz0WZlVpXMbVFVvpsRVVFQShISLre3js0mPWqphIROVTDoVQqLnaiqQsvIIAx6HXp9SVJDr2DQ6VBUSDmZR1zrMP/NjULJd+VMjxadTuXQsRy6x0Wh13l/1+u8iRadeubngH2qis6/XSU8IoiqrWFSs843zm7bto2CggJGjRrl32Y0GhkxYgQ//fRTwPm7dOniTzAADBw4kPDwcFatWkWPHj1wOBxs2rSJKVOmBFzj+uuvZ9GiRRw/fpy2bdtW/8m1bUvRhx/jcnmq/9gGyunykFtoJ6fAQW6B93tqRgE7EzPJLjM0yxpkoGVkEC2jgogqWc5XUZDGBCFqUUV/W6V7SKqqgtmkQzVbcffqTUbv3pwq1UOS4mLC0o8RnnqEsBMphKanEnzqBCEZJwjJSEPnchJdkEl0Qfkhl6W5VR1FwWEUBYVSGBRKkTmEQksIhZZQCkwh5JtDvN+NQRQZzBTpTBTpTRTqTBTqzdgMZtw6PRreWIpbA858ltqdZ4/1R9KrGOt3Vi/W++rJn4hQS8V6o64k/gfGer1epaDIQfOIIG+CQ6f6txv0KjpFIflkHijQqU1YwFAaX6xX8DYgHTqWg6oqXNapWUmMrzi+63WlY3zJPlWpk1gvSYYqSEpKKjce02q1Eh0dTVJSw5gzwOlyY3d6/+g0TUOjpGWy9M+c+dDxaN7/6DW8X77j0Lz7XG6tZAyYG7vrzHgwh8vtHwdmc7jILXCQU3KDkVPSJbsy3ll5jbSK9N5oGEu6P7k9JdcWQjQaFc03oShKyT+zvmSErsIExQVvc3uv7XR78H6QnRnL6nJ7v4OC2+1B0/AnKLwJDW/CQlNU7HYnzpIkh7cnhsefBCmdECn987l4NA2PG6jgU83hcpz1sZl5Fc+b4XM4Ne+c1wfYk5xVpeMqMnfacFpGBZ/348/X+cZZ377SyQOAjh078umnn2Kz2TCbzSQlJZU7RlEUYmNj/ec4evQoTqezwnP5rnVeSYYa5PZ4KLZ746xWKm5rvt/LxHpvqNdKvhMQ6zW8S0Y7SmK8bwiV3en2b/Ntzyt0+BsOcgrsFBRX3ivJqFdJ6BCBqio0CzMTbNEHdusWQjR4bpOZ7A6dyWrfuXw8dnsIys3EejqNoPQTBGemYcnJJCgnE0tOJpbs097vednoPG5C87MIzT//uOTW6XGag3CaLThNFlxGEy69AbfeiEtvwGUw+n926gw4dXoceiMunQGX3ohN0eFExaWouFBxKipuVFyKgqvUdu+X4t2v6PCopb6rOjQUPCX/7WsoaAqAgqaUbEfxfhaX/Fz2WAcKRhSyjvq2Bx6rcWb7poPe7T5amQ9P393XkT3J5XrFaRUcd+Y83t/fmXEjLZrV7pw/kmSogry8PKxWa7ntYWFh5OaefdbXcwkLs3ChiXyny0NugR1LA5qD0tul6Ez2Ta9TvWv+nuu5lmTqtKbT4FOjFF8VSlYmgNRLJUpu6qVuyjjvevEmL3wPqvChWoU/ltmolbkJqOBxFRxXaZEquJbm+y+ybFkCjj+TbPZpFm451xVrxfnG2by8PIxGIyaTKWC71WpF0zRyc3Mxm83k5eURGlr+hqr0+X3fy5bD9/uFxPuaiPUakJVnw6JvOLduvhjvi/e+YUtVTSfIZ3fFzgxhEwEkplWsAdaLC8hHQ/F4UDxu73fNg+LR/D/j31byu6ahaBp4NO/2knPpSr7M9fd0mp6w2q/NhhOpLlKqWvFctNWh06mYTfJSCiGEEA1RTcR6gOYRQTVyHiGEEKI21UzUa+KsViv5+eXH9OTm5hIWFlYPJRJCCCGajvONs1arFYfDgd0eONQkLy8PRVH8j7VarRQUFJz1/L7vZcuRl5cXsF8IIYQQZydJhiqIi4srNyY0Pz+fjIyMcmM3hRBCCFE95xtnffuSk5MDticlJdG6dWvMZnOl59c0jeTkZP852rdvj8FgKHdcZfM+CCGEEKJikmSogsGDB7N+/Xp/awbAsmXLUFWVgQMH1mPJhBBCiMbvfONs7969CQkJYenSpf5tTqeTH3/8kcGDBwec//fffyclJcW/bcOGDeTk5DBkyBDAuypFv379WL58ecA1lixZQseOHet90kchhBCisVA0WT/onHJzcxk9ejSxsbFMmjSJ9PR0Xn31VW644QamT59e38UTQgghGrWqxtkJEyZw4sSJgOUpP/zwQ2bPns2UKVOIj49n/vz5rF27loULF9KuXTvAm3jwLYP55JNPUlxczGuvvUaXLl2YM2eO/1xbtmzh7rvv5rbbbmPUqFFs2rSJ9957j7feeitgmUwhhBBCVE6SDFWUmJjISy+9xPbt2wkODmbs2LE88cQTGI0NaEkHIYQQopGqSpy96667SE1NZeXKlf5tmqbx4Ycf8tVXX5GVlUVCQgLPPPMMvXr1Cjh/eno6M2fOZO3atej1ekaMGMG0adMICQkJOG7FihW8/fbbJCcn07p1ayZOnMi4ceNq98kLIYQQTYgkGYQQQgghhBBCCFEjZE4GIYQQQgghhBBC1AhJMgghhBBCCCGEEKJGSJJBCCGEEEIIIYQQNUKSDEIIIYQQQgghhKgRkmQQQgghhBBCCCFEjZAkgxBCCCGEEEIIIWqEJBmEEEIIIYQQQghRIyTJUMvWrVvHU089xfDhw+nSpQsvvvhihcc5HA7+8Y9/MHDgQHr27Mk999xDUlJSueMSExO555576NmzJwMHDuS1117D4XDU9tOoE1OnTqVLly7lvlavXh1wXFXrqqloyq95VX377bcVvjfeeOONgOO++eYbrr32Wrp3786NN97IL7/8Uk8lrh1Hjhxh+vTpjB07lq5duzJmzJgKj6tKPeTn5zNt2jSuuOIKevXqxWOPPcapU6dq+ynUiqrUy1133VXheygxMTHguKZUL0uXLuWhhx5i8ODB9OzZk7Fjx/Lf//4XTdMCjrvY3i+1QWJ91Umsr1hTfs2rSmK9l8T6ykm8r1hDjPf68342okrWrFnD77//Tt++fcnNza30uJkzZ7JkyRKmTp1KixYt+OCDD/jzn//M4sWLCQ0NBSA3N5cJEyYQExPD7NmzSU9P59VXX8VmszF9+vS6ekq1ql27duWCSceOHQN+r0pdNRUXw2teHR999FHAa9yiRQv/z4sXL+Zvf/sbDz74IP3792fJkiU8+uijfPnll/Ts2bMeSlvzDh06xKpVq7jsssvweDzlggdUvR4ef/xxDh8+zAsvvIDJZOLtt9/mgQceYMGCBej1jSs0VKVeAHr37s3TTz8dsK1t27YBvzelevnkk09o06YNU6dOJSIigvXr1/O3v/2NtLQ0Hn30UeDifL/UBon11SOxPtDF8JpXh8R6ifWVkXhfsQYZ7zVRq9xut//na665RpsxY0a5Y06ePKklJCRoX3/9tX9bdna21rNnT+3DDz/0b/vggw+0nj17atnZ2f5tX3/9tZaQkKClpaXVzhOoQ08//bQ2evTosx5T1bpqKpr6a15VCxYs0OLj47XMzMxKjxk5cqT25JNPBmy7/fbbtfvvv7+2i1dnSn+eVPb3UpV62LZtmxYfH6+tWbPGvy0xMVHr0qWLtnjx4looee2qSr3ceeed2sSJE896nqZWLxX9vTz33HNa7969/XV2Mb5faoPE+qqTWF9eU3/Nq0pivZfE+spJvK9YQ4z3Mlyilqnquat47dq1eDwerrvuOv+28PBwBg4cGNB9cPXq1QwYMIDw8HD/tlGjRuHxeFi3bl2NlruhqmpdNRXymlfNsWPHSElJYdSoUQHbr7/+ejZs2NBkupye6/OkqvWwevVqrFYrAwcO9B8TFxdHQkJCo/w7qsrnbFU0tXqJjIwsty0hIYGCggKKioou2vdLbZBYX7Mk1l98r3lVSKz3upg/uyXeV6whxntJMjQASUlJREVFERYWFrC9Y8eOAeMPk5KSiIuLCzjGarUSHR3dZMYpHjlyhD59+tCtWzduvvlmfv7554D9Va2rpuJieM2rY8yYMSQkJDBs2DDmzJmD2+0G8NdFbGxswPEdO3bE6XRy7NixOi9rfahqPSQlJREbG4uiKAHHxcXFNen31ebNm+nZsyfdu3fnzjvv5LfffgvYfzHUy9atW2nRogUhISHyfqljEuvPkFgf6GJ4zatDYv3ZyWf3uUm8r/9437gGnDRReXl5FY4vtFqtAWM78/LysFqt5Y4LCws76xjQxiIhIYHu3bvTqVMn8vPzmT9/Po888gjvvPOOvzWjqnXVVDT117yqoqOjmTx5MpdddhmKorBy5Urefvtt0tPTmT59ur8uytaV7/eLpa6qWg+V/R2FhYWxZ8+eWi5l/ejbty9jx44lJiaGU6dOMW/ePO655x4+//xzevXqBTT9etmyZQtLlizxj1OV90vdkljvJbG+vKb+mleVxPqqkc/us5N43zDivSQZqik/P79KM2y2a9cOo9FYByVquKpbVxMmTAjYPnToUMaPH8+sWbMCukyKi89VV13FVVdd5f990KBBmEwmPv30Ux588MF6LJloLB577LGA36+++mrGjBnDe++9x9y5c+upVHUnLS2NJ554gn79+nH33XfXd3EaPIn1VSexXtQUifWiJki8bxjxXpIM1bRs2TKee+65cx63ZMmScjMlV8ZqtVJQUFBue15eXkBXQavVSn5+frnjcnNzy3UpbAgutK5UVWXkyJG8/vrr2Gw2zGZzleuqqWhsr3ldGjVqFB9//DH79+/310V+fj7R0dH+Y/Ly8gAumrqqaj1YrVbS0tLKPf5iel8FBQUxZMgQli9f7t/WVOslLy+PBx54gPDwcGbPnu0f0yrvl8pJrK86ifUXrrG95nVJYn158tldPRLv6+c9I0mGarr11lu59dZba/SccXFxnD59utwLWHaMXkXjYfLz88nIyCg3lq8hqM+6aioa22teX3x1UfZ9kJSUhMFgoF27dvVVtDpV1XqIi4tjw4YNaJoWMO4uOTmZ+Pj4ui10A9IU68VmszFp0iTy8/P597//HdANUt4vlZNYX3US6y9cY3vN64vEei/57L5wTbFuGlq8l4kfG4BBgwahqio//vijf1tubi5r165l8ODB/m2DBw9m/fr1/qwTeFsQVFUNmAW0qfB4PCxbtozOnTtjNpuBqtdVU3GxvebVsWTJEnQ6HV27dqVdu3bExMSwbNmycscMGDDgounOXNV6GDx4MLm5uWzYsMF/THJyMvv27WuSf0cVKSoq4tdff6V79+7+bU2tXlwuF48//jhJSUl89NFHAWvNg7xf6prE+opJrL/4XvPqkFhfnnx2V4/E+/p5z0hPhlqWmprK7t27ASguLubo0aP+F9g39rBly5aMGzeO1157DVVVadGiBXPmzCE0NJTx48f7zzV+/Hg+//xzHnnkESZNmkR6ejqvvfYa48ePL/dmamxSU1OZOnUqo0ePpkOHDuTm5jJ//nz27NnD7Nmz/cdVta6aiqb8mlfHfffdR79+/ejSpQsAK1as4D//+Q933323v9vX5MmTmTJlCu3bt6dfv34sWbKEXbt28cUXX9Rn0WtUcXExq1atArx/MwUFBf7PkyuuuILIyMgq1UOvXr0YNGgQ06ZN4+mnn8ZkMvHWW2/RpUsXRo4cWS/P7UKcq158QXfEiBG0adOGU6dO8a9//YuMjAzeeecd/3maWr3MmDGDX375halTp1JQUMCOHTv8+7p27YrRaLwo3y+1QWJ91Uisr1hTfs2rQ2K9l8T6ykm8r1hDjPeKpmlaTT1BUd63337LM888U+G+AwcO+H92OBy89dZbLFy4kMLCQnr37s1zzz1XbvxiYmIiL730Etu3byc4OJixY8fyxBNPNPrsbU5ODs888wz79u0jMzMTg8FAt27dmDhxYsAkQFD1umoqmuprXh0zZ85kzZo1pKWl4fF4iImJ4dZbb+Wuu+4K6M71zTffMHfuXE6cOEFsbCxPPvkk11xzTT2WvGYdP36cYcOGVbjvs88+o1+/fkDV6iE/P59XXnmFn376CZfLxaBBg3juueca5Q3tueqlZcuWvPjiixw4cICcnBwsFgu9evXi0UcfpUePHgHHN6V6GTp0KKmpqRXuW7FiBW3btgUuvvdLbZBYXzUS6yvXVF/z6pBY7yWxvnIS7yvWEOO9JBmEEEIIIYQQQghRI2ROBiGEEEIIIYQQQtQISTIIIYQQQgghhBCiRkiSQQghhBBCCCGEEDVCkgxCCCGEEEIIIYSoEZJkEEIIIYQQQgghRI2QJIMQQgghhBBCCCFqhCQZhBBCCCGEEEIIUSMkySCEaBJmz55Nly5dzuuxU6dOZejQoTVcIiGEEELUJIn1QjQOkmQQQgghhBBCCCFEjZAkgxBCCCGEEEIIIWqEJBmEEHWmqKio0n3FxcV1WBIhhBBC1AaJ9UIISTIIIaolNTWVF154gWuvvZYePXrQr18/HnvsMY4fPx5w3LfffkuXLl3YvHkzL7zwAgMGDGDIkCEA3HXXXYwZM4Y9e/Zwxx13cNlll/F///d/VS7Dli1buOWWW+jevTvDhw/n66+/rvTYhQsXcvPNN9OjRw+uuOIKnnjiCU6ePHnOa8ybN4/x48fTr18/evTowc0338yyZcsCjrnzzju58cYbK3z8tddey3333Vfl5ySEEEI0FBLrz5BYL0T16eu7AEKIxmX37t1s376d0aNH07JlS1JTU5k/fz533303ixcvxmKxBBw/Y8YMIiMjeeSRRwJaN3JycnjggQcYPXo0N954I1FRUVW6/oEDB7jvvvuIjIxk8uTJuFwuZs+eXeHj33//fd555x1GjRrFuHHjyMrK4osvvuCOO+7gf//7H1artdLrfPbZZwwdOpQbbrgBp9PJ4sWL+ctf/sKcOXO4+uqrARg7dizPPfccBw8eJD4+3v/YXbt2kZKSwkMPPVSl5ySEEEI0JBLrJdYLcUE0IYSohuLi4nLbtm/frsXHx2vfffedf9uCBQu0+Ph47Y9//KPmcrkCjr/zzju1+Ph4bf78+dW+/sMPP6x1795dS01N9W87fPiwlpCQoMXHx/u3HT9+XEtISNDef//9gMcfOHBA69q1a8D2p59+WrvmmmvO+jwdDoc2ZswY7e677/Zvy8vL07p37669/vrrAce+9NJLWs+ePbXCwsJqPz8hhBCivkmsl1gvxIWQ4RJCiGoxm83+n51OJ9nZ2bRv3x6r1cq+ffvKHX/bbbeh0+nKbTcajdx8883Vurbb7Wbt2rUMHz6c1q1b+7d37NiRQYMGBRz7008/4fF4GDVqFFlZWf6vZs2a0aFDBzZt2lTl55mbm0t+fj59+vQJeI6hoaEMGzaMxYsXo2mav4xLly5l2LBhBAUFVev5CSGEEA2BxHqJ9UJcCBkuIYSoFpvNxpw5c/j2229JT0/3B1yA/Pz8cse3bdu2wvO0aNECo9FYrWtnZWVhs9no0KFDuX2xsbGsWrXK/3tKSgqapjFy5MgKz6XXn/3j75dffuH9999n//79OBwO/3ZFUQKOu+mmm1iyZAlbtmyhb9++rF+/ntOnTzN27NjqPDUhhBCiwZBYL7FeiAshSQYhRLW89NJLfPvtt0yYMIGePXsSGhqKoig88cQTATchPiaTqcLzlG49qA0ejwdFUZg7d26FrStna3nYsmULDz30EH379uX5558nOjoag8HAggULWLRoUcCxgwYNolmzZnz//ff07duX77//nujoaK688soaf05CCCFEXZBYL7FeiAshSQYhRLUsX76cm266ialTp/q32e32Cls2alpkZCRms5kjR46U25ecnBzwe/v27dE0jbZt2xIbG1ut6yxfvhyTycS8efMCWmAWLFhQ7lidTseYMWP47rvvmDJlCj///HOl3UaFEEKIxkBifSCJ9UJUj8zJIISolooC6ueff47b7a6Taw8aNIiff/6ZEydO+LcnJiaydu3agGNHjhyJTqfj3XffLdfqomka2dnZZ72OoigBz+n48eOsWLGiwuPHjh1Lbm4u06dPp6ioqNKlroQQQojGQGJ9eRLrhag66ckghKiWq6++moULFxISEkKnTp3YsWMH69evJzw8vE6uP3nyZNasWcMdd9zBH//4R9xuN1988QWdOnXiwIED/uPat2/P448/zptvvklqairDhw8nODiY48eP+1sgKlvbesiQIfzrX//i/vvvZ8yYMWRmZvLVV1/Rvn37gGv4dO3alfj4eJYtW0bHjh259NJLa+35CyGEELVNYr3EeiEuhCQZhBDV8uyzz6KqKj/88AN2u53evXv7g3RduOSSS5g3bx6vvPIKs2bNomXLlkyePJmMjIxyNwUTJ04kJiaGTz75hH/+858AtGzZkoEDBzJ06NBKrzFgwAD+/ve/M3fuXF5++WXatm3LlClTSE1NrfDGA7wtHK+//rpMAiWEEKLRk1gvsV6IC6FoFc3eIoQQolo+/fRTXnnlFVauXBmw5JYQQgghmgaJ9UJUjczJIIQQF0jTNP773//St29fuekQQgghmiCJ9UJUnQyXEEI0CIWFhRQVFZ31mMjIyAY1k3NRURErV65k06ZNHDx4kPfee6++iySEEEI0WBLrhbg4SJJBCNEgfPzxx7z77rtnPWbFihW0bdu2jkp0bllZWTz11FNYrVYefPBBhg0bVt9FEkIIIRosifVCXBxkTgYhRINw7Ngxjh07dtZj+vTpg8lkqqMSCSGEEKImSawX4uIgSQYhhBBCCCGEEELUCJn4UQghhBBCCCGEEDVCkgxCCCGEEEIIIYSoEZJkEEIIIYQQQgghRI2QJIMQQgghhBBCCCFqhCQZhBBCCCGEEEIIUSMkySCEEEIIIYQQQogaIUkGIYQQQgghhBBC1AhJMgghhBBCCCGEEKJG/H97YOH1dMdUsgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "x = np.linspace(-100, 200, 1000)\n",
    "\n",
    "sns.histplot(data=fls, x='arr_delay', kde=True, stat='count', ax=axs[0])\n",
    "sns.histplot(data=fls, x='arr_delay', kde=True, stat='density', ax=axs[1])\n",
    "axs[1].plot(x, stats.norm.pdf(x, loc=fls.arr_delay.mean(), scale=fls.arr_delay.std()),\n",
    "            color='red')  # Normalverteilung mit Mittelwert und Standardabweichung der Stichprobe, Dichte ist normiert auf 1\n",
    "\n",
    "axs[0].set_xlim(-100, 200)\n",
    "axs[1].set_xlim(-100, 200)\n",
    "axs[0].set_title('Histogram (count)')\n",
    "axs[1].set_title('Histogram with PDF')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "032695f4",
   "metadata": {},
   "source": [
    "## 2. Stichprobenverteilung: Verteilung der Parameter\n",
    "\n",
    "Bisher haben wir uns angeschaut, wie die Variable `arr_delay` verteilt ist. Normalerweise haben wir aber nicht alle Daten (die sog. Grundgesamtheit oder Population) vorliegen, sondern nur eine Stichprobe. Trotzdem wollen wir eine Aussage über alle Daten treffen, d.h. wir würden gerne anhand unserer Stichprobe einschätzen wie die Grundgesamtheit aussieht. Diesem Vorgehen nähern wir uns hier von Simulationsseite. Wir stellen uns vor, die Grundgesamtheit sind alle NYC Flüge aus 2013 aber wir hätten nur eine Stichprobe. Was könnten wir dann über die Flüge sagen?\n",
    "\n",
    "#### a) Stichprobenverteilung des Mittelwerts\n",
    "Zunächst versuchen wir aus einer Stichprobe des Datensatzes eine Aussage über die mittlere Verspätung im Jahr 2013 zu treffen. Dazu werden wir\n",
    "- eine Stichprobe ziehen und den Mittelwert berechnen.\n",
    "- nochmal eine Stichprobe ziehen $\\rightarrow$ Was ist anders?\n",
    "- ganz häufig Stichproben ziehen und eine Stichprobenverteilung für den Mittelwert erstellen\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "affa40e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample1 with mean 24.4: [-1.0, 11.0, -30.0, 73.0, 69.0]\n",
      "sample2 with mean 32.0: [-8.0, -22.0, 143.0, 47.0, 0.0]\n"
     ]
    },
    {
     "data": {
      "image/png": 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CPtW7c+fOSkxMVF5envbs2aN169ZJkpKSkpSfn6+5c+cqNTVVGRkZWrFihQ4ePKgxY8bEqBIAAFDX2Co0bd68WZI0e/bsCte98847SktLk8/nk9cbfELk2LFjZVmWlixZogMHDqhTp04qKChQenp6VNYNAADqPluFpvXr1591m+XLl1cYczgcys/PV35+fiSWBQAAYK9zmgAAAOyK0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGAg5NA0YsQIvf/++2e8/n/+5380YsSIUG8eAADAVkIOTR9++KH++c9/nvH6AwcOaOvWraHePAAAgK3U6O05h8Nxxut++OEHNWzYsCY3DwAAYBsJ1dn45Zdf1ssvvxy4vGDBAq1cubLCdqWlpdq+fbv69etX8xUCAADYQLVC05EjR/Tzzz8HLh86dEhOZ8UXq8455xwNGTJE48ePr/kKAQAAbKBaoWno0KEaOnSoJCk7O1v33XefBg4cGJGFAQAA2Em1QtPp1q9fH851AAAA2FrIocmvrKxMe/bskcfjkWVZFa7v3r17TacAAACIuZBD04EDB/Tggw/qrbfektfrrXC9ZVlyOBz6+uuva7RAAAAAOwg5NE2fPl0bNmzQ8OHDdfHFF8vtdodzXQAAALYScmjavHmz8vLy9Ic//CGc6wEAALClkD/csn79+jr33HPDuRYAAADbCjk0XXPNNXr77bfDuRYAAADbCvntuUGDBmnr1q0aM2aMbr75ZrVs2VIul6vCdueff36NFggAAGAHIYcm/4dcStKWLVsqXM9vzwEAgLok5ND08MMPh3MdAAAAthZyaLruuuvCuQ4AAABbC/lEcAAAgHgS8itN/+///b+zbuNwOPTQQw+FOgUAAIBthByaPvjggwpjPp9P+/btk9frVWpqqho0aFCjxQEAANhFyKFp/fr1lY6fOHFCzz//vJYtW6YlS5aEvDAAAAA7Cfs5TfXq1dOwYcPUp08fzZo1K9w3DwAAEBMROxG8Y8eO2rp1a6RuHgAAIKoiFpq2bNnCOU0AAKDOCPmcpnnz5lU6Xlpaqq1bt+qrr77S7bffHvLCAAAA7CTsoSklJUXp6emaOXOmfve734W8MAAAADsJOTR988034VyHJOmHH35QQUGBPv/8c+3YsUPt2rXTG2+8cdb9srOztXv37grj27ZtU1JSUtjXCQAA4k/IoSkSduzYoY0bN+rCCy+Uz+eTZVnG+w4aNEijR48OGktMTAz3EgEAQJyqcWj68MMP9e6772rPnj2SpFatWmnAgAHq0aNHtW8rOztbl19+uSRp2rRp+uKLL4z3bdq0qbKysqo9JwAAgImQQ9Px48f1+9//Xm+//bYsy5Lb7ZYkeTweLV26VFdccYUee+wx1atXz/g2nU7+FB4AALCnkEPT/PnztW7dOo0ePVqjR49W06ZNJUn79+/XkiVLVFBQoPnz52vSpEnhWmuVXn/9da1cuVL16tXTxRdfrClTpqhDhw41vt2EBPsGOZfr5NocDoccDsfJwX/9J4fkCFwIL/9c/vmj6fSao1GrXyxrPn3eWM0fTafu4xgvpIbC0TsqPcYjIYLHUqyPncrE4/EUT7VG8lAJOTS9/vrruu666/SHP/whaPxXv/qV/v3f/1379+/Xa6+9FpXQlJ2drczMTLVq1UpFRUV68sknNXToUL3yyitKT08P+XadToeaNGkYxpVGhsvlVEKCK2gsweU6w9bhmU+S3O7YfQ6Xy+UM1BjJWk+fT4ptzXaYP5pq8yvP4e4dlR3jkRCJY8kux05l7LimSImnWiPZO0IOTfv27VNmZuYZr8/MzNSqVatCvflquf/++wNfX3zxxerTp49ycnJUUFCgGTNmhHy7Pp8lj+dwGFYYGS6XU253A3m9PpWXe08OOk42vnKvVzI/j75avF6fJMnjORL4OlqCavZ6I16rXyxrlk7VHav5o8lfq8/nq7XBKVy9o9JjPBIi2DdifexUJh6Pp3iqNZK9I+TQ1LJlS3344Ye65ZZbKr1+69atatmyZcgLq4nmzZurW7du+vLLL2t8W+Xl9n+QWZYV+E3DwEvrlqr124fVnU/Svxp5bL4/lmWdau4RrDVoPsW2ZjvMH00RvksjLpz30+nHeCREsm/Y5dipjB3XFCnxVGske0fIUezaa6/VmjVrNH36dBUWFsrr9crn86mwsFB//OMftXbtWl133XXhXCsAAEDMhPxK07hx41RUVKSVK1fqhRdeCLwU5v98peuuu07jxo0L20Kro7i4WB9//LFyc3NjMj8AAKh7Qg5NLpdLs2fP1siRI7Vp06bAJ3Kfe+656tevnzp27Fjt2zxy5Ig2btwoSdq9e7fKysq0du1aSVKPHj2UmpqqvLw87dmzR+vWrZMkvfHGG9qwYYP69++v5s2bq6ioSIsWLZLL5dKoUaNCLQ8AACBItULTsWPH9Kc//Un/9m//puHDh0uSOnbsWCEgPfPMM3ruued03333Vetzmvbv36+77747aMx/+ZlnnlHPnj3l8/nk9Z46ITItLU179+7VQw89pNLSUjVq1Ei9evXSxIkTa/SbcwAAAKerVmh6/vnn9fLLL2v16tVVbjdgwAA9+uijysjI0NChQ41vPy0tTdu3b69ym+XLlwddzsrKqjAGAAAQbtU6EXzNmjW68sorz/oKTuvWrXXVVVdF7SMHAAAAIq1aoenbb79Vt27djLbt2rXrWV81AgAAqC2qFZpOnDhhfI5SvXr1dPz48ZAWBQAAYDfVCk3NmzfXjh07jLbdsWOHmjdvHtKiAAAA7KZaoemSSy7Rq6++qv3791e53f79+/Xqq6/qkksuqdHiAAAA7KJaoWns2LE6duyY8vLy9Pnnn1e6zeeff66RI0fq2LFjuu2228KySAAAgFir1kcOpKen64knntA999yjIUOGKD09XRkZGWrYsKEOHTqkHTt26B//+Ifq16+vxx9/XK1bt47UugEAAKKq2p8IPmDAAL322mtavHix3n33Xb399tuB65o3b66bbrpJY8eO5YMlAQBAnRLSn1FJS0vTzJkzJUllZWU6dOiQGjZsqOTk5LAuDgAAwC5C/ttzfsnJyYQlAABQ51XrRHAAAIB4RWgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwYKvQ9MMPP2j69OnKzc1V586dNXjwYKP9LMvSokWLNGDAAGVmZurmm2/WZ599FtnFAgCAuGKr0LRjxw5t3LhR5513ntq3b2+83+LFizVnzhyNHDlSCxcuVLNmzTR69GgVFRVFcLUAACCe2Co0ZWdna+PGjZozZ47OP/98o32OHTumhQsXavTo0Ro5cqR69+6txx9/XI0bN1ZBQUGEVwwAAOKFrUKT01n95XzyyScqKytTTk5OYCwxMVFXXHGFNm3aFM7lAQCAOGar0BSKwsJCSVK7du2Cxtu3b689e/bo6NGjsVgWAACoYxJivYCa8ng8SkxMVFJSUtC42+2WZVkqKSlR/fr1Q779hISz50qHwyGn0xHyHKHyz+lwOORw/Gt+/zIckkORWZN/Lpcr+pnbP6fD4YhKrX6xrPn0eWM1fzSduo9jvJAaMukdZ3P6490RyW9IBI8l/7rr1XPZ5vHr753VWZPPZ8myrEguKyJO7x2x+lkVTlXdD9HoHbU+NEWS0+lQkyYNz7qdz2fF9IHocjmVkOAKGktwuc6wdXjmkyS3u0HE5jBZg7/GSNZ6+nxSbGu2w/zRFMrb9XZh2jtMVXaMR0IkjqWURkny+SwlJ4f+5DVSqrOmWPf5mnK7G9T6GiSz+yGSvaPWhya3263jx4/r2LFjQa82eTweORwOpaSkhHzbPp8lj+dwldu4XE653Q204s1vtPdA1duGW4fzmuiqS9rK6/OpvNx7ctBxsvGVe71ShJ4Ueb0+SZLHcyTwdbT4v99er0/lXm/Ea/WLZc3SqbpjNX80+Wv1+Xy1NjiZ9A4TQY93/zEeCRHsG4kJTjmdjpj0yDNySC6nU16fz6je5qnn6JZBHWvl8ed/DJWVHVVycn173Q/VdLb7IRq9o9aHJv+5TLt27VLHjh0D44WFhWrVqlWN3pqTpPJyswOkeP8h7d5XVqO5qqtp43/VZinwcmXgpfXTxsLNf7snG3lsGohlWaeaXQRrDZpPsa3ZDvNHUy18JyRIOO8ny4rsW0OR7Bv+29t74LB+3Fsa1tsOlcPhUEKCS+XlXqN67XL814TPd7KGWPysChfT+yGSvaN2Po07zUUXXaTk5GStWbMmMHbixAm99dZb6tevXwxXBgAA6hJbvdJ05MgRbdy4UZK0e/dulZWVae3atZKkHj16KDU1VXl5edqzZ4/WrVsnSUpKSlJ+fr7mzp2r1NRUZWRkaMWKFTp48KDGjBkTs1oAAEDdYqvQtH//ft19991BY/7LzzzzjHr27CmfzyevN/i9/bFjx8qyLC1ZskQHDhxQp06dVFBQoPT09KitHQAA1G22Ck1paWnavn17ldssX768wpjD4VB+fr7y8/MjtTQAABDnav05TQAAANFAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADBAaAIAADCQEOsF/NLOnTv14IMP6tNPP1XDhg2Vm5urSZMmKTExscr9srOztXv37grj27ZtU1JSUqSWCwAA4oStQlNJSYny8vLUpk0bzZ07V8XFxZo9e7aOHj2q6dOnn3X/QYMGafTo0UFjZwtbAAAAJmwVmp577jkdOnRI8+bNU+PGjSVJXq9XM2fOVH5+vlq0aFHl/k2bNlVWVlbkFwoAAOKOrc5p2rRpk3r37h0ITJKUk5Mjn8+nzZs3x25hAAAg7tnqlabCwkLdcMMNQWNut1vNmjVTYWHhWfd//fXXtXLlStWrV08XX3yxpkyZog4dOtRoTQkJVedKl+vk9Q6HQw6Ho0ZzVVdgPkfw14ExRWY9/rn8tUfT6d/vaNTqF8uaT583VvNH06n7OMYLqaGz9Q4TUesvETyWKu1TsVbNemN9/NeEf81O58kaYvGzKlzOdj9Eo3fYKjR5PB653e4K4ykpKSopKaly3+zsbGVmZqpVq1YqKirSk08+qaFDh+qVV15Renp6SOtxOh1q0qSh0bYul1MJCa6Q5gmVy+kM/P/LuRNckVuL/4HpdjeI2Bwma/DXGMlaT59Pim3Ndpg/mpzO2vcDyq86vcNEtPpLJI6lqvpUrJnWa5fjvyaSk+tLis3PqnAxvR8i2TtsFZpq4v777w98ffHFF6tPnz7KyclRQUGBZsyYEdJt+nyWPJ7DVW7jcjnldjeQ1+tTebk3pHlC5fX5Av8H5nacbATlXq9kRWhe78l5PZ4jga+jJej77fVGvFa/WNYsnao7VvNHk79Wn89Xa4OTSe8wEbX+EsG+UWmfirVq1hvr478m/I+hsrKjSk6uH5OfVeFytvshGr3DVqHJ7XartLS0wnhJSYlSUlKqdVvNmzdXt27d9OWXX9ZoTeXlZgeIZVmyrAj/5K5kzpNfnPo68FLzaWORmvfkwRebBmJZ1qlmF8Fag+ZTbGu2w/zRFOXDKezCeT9Fur9Esm9U1qdirbr12uX4rwmf72QNsfhZFS6m90Mky7PV07h27dpVOHeptLRU+/btU7t27WK0KgAAAJuFpn79+mnLli3yeDyBsbVr18rpdKpPnz7Vuq3i4mJ9/PHH6tKlS7iXCQAA4pCt3p4bMmSIli9frvHjxys/P1/FxcV65JFHNGTIkKDPaMrLy9OePXu0bt06SdIbb7yhDRs2qH///mrevLmKioq0aNEiuVwujRo1KlblAACAOsRWoSklJUXLli3TrFmzNH78eDVs2FA33nijJk+eHLSdz+eT13vqRLa0tDTt3btXDz30kEpLS9WoUSP16tVLEydODPk35wAAAE5nq9AkSe3bt9fTTz9d5TbLly8PupyVlVVhDAAAIJxsdU4TAACAXRGaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADBCaAAAADNguNO3cuVOjRo1SVlaW+vTpo0ceeUTHjx8/636WZWnRokUaMGCAMjMzdfPNN+uzzz6L/IIBAEBcsFVoKikpUV5enk6cOKG5c+dq8uTJWrlypWbPnn3WfRcvXqw5c+Zo5MiRWrhwoZo1a6bRo0erqKgoCisHAAB1XUKsF3C65557TocOHdK8efPUuHFjSZLX69XMmTOVn5+vFi1aVLrfsWPHtHDhQo0ePVojR46UJHXr1k1XXXWVCgoKNGPGjOgUAAAA6ixbvdK0adMm9e7dOxCYJCknJ0c+n0+bN28+436ffPKJysrKlJOTExhLTEzUFVdcoU2bNkVyyQAAIE7Y6pWmwsJC3XDDDUFjbrdbzZo1U2FhYZX7SVK7du2Cxtu3b69ly5bp6NGjql+/frXX43Q6lJrasMptHI6T/992bRd5fVa156iJegknM++Y3AuiOrfLebLolJQGUZvzl6L9/T69Ziu6d7OkU4+zWM0fTf5anf/6ntdGJr3DRCz7S7jEqk+Fkx16Xk0lJ5/8GVibH0tn68PR6B22Ck0ej0dut7vCeEpKikpKSqrcLzExUUlJSUHjbrdblmWppKQkpNDkcDjkcpl985PPSaz27YdLrOZ2OmP3QmU81myH+aPJ4ai9oak6vcNELPtLuNSFGmrz8ecPEvFwP0Syd9TeRwAAAEAU2So0ud1ulZaWVhgvKSlRSkpKlfsdP35cx44dCxr3eDxyOBxV7gsAAGDCVqGpXbt2Fc5dKi0t1b59+yqcr/TL/SRp165dQeOFhYVq1apVSG/NAQAAnM5Woalfv37asmWLPB5PYGzt2rVyOp3q06fPGfe76KKLlJycrDVr1gTGTpw4obfeekv9+vWL6JoBAEB8sNWJ4EOGDNHy5cs1fvx45efnq7i4WI888oiGDBkS9BlNeXl52rNnj9atWydJSkpKUn5+vubOnavU1FRlZGRoxYoVOnjwoMaMGROrcgAAQB1iq9CUkpKiZcuWadasWRo/frwaNmyoG2+8UZMnTw7azufzyev1Bo2NHTtWlmVpyZIlOnDggDp16qSCggKlp6dHswQAAFBHOSyrrn/qCwAAQM3Z6pwmAAAAuyI0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA01RE7d+7UqFGjlJWVpT59+uiRRx7R8ePHY72sGnvppZfUoUOHCv/+8z//M2i7F154QYMGDVKXLl10zTXXaMOGDTFasbkffvhB06dPV25urjp37qzBgwdXup1JbaWlpbr33nvVo0cPde3aVRMnTtTevXsjXYIxk1qHDx9e6X29c+fOoO3sXmttUxd7B32DvhGpvmGrD7dEaEpKSpSXl6c2bdpo7ty5Ki4u1uzZs3X06FFNnz491ssLi6eeekqNGjUKXD79E+JXrVqlBx54QOPGjVOvXr20evVq3XXXXfrrX/+qrKysGKzWzI4dO7Rx40ZdeOGF8vl8quwj00xrmzRpkr777jvNmDFDSUlJeuKJJzR27Fi9+OKLSkiI/WFuUqt08k8iTZ06NWgsLS0t6LLda61N6nrvoG/QN/zCVquFWu/JJ5+0srKyrJ9//jkw9txzz1mdOnWyfvrpp9gtLAxefPFFKyMjw9q/f/8Zt7nyyiute+65J2js5ptvtm677bZIL69GvF5v4OupU6daV199dYVtTGr75JNPrIyMDOu9994LjO3cudPq0KGDtWrVqgisvPpMah02bJh1++23V3k7taHW2qSu9g76Bn3jdOGslbfn6oBNmzapd+/eaty4cWAsJydHPp9Pmzdvjt3CoqCoqEjff/+9cnJygsZ/85vf6P3337f12wxOZ9WHn2ltmzZtktvtDvqj1u3atVOnTp20adOm8C88BGer1VRtqLU2idfeQd+oHceSHfsGoakOKCwsVLt27YLG3G63mjVrpsLCwhitKrwGDx6sTp06aeDAgVq4cGHgbw/662vbtm3Q9u3bt9eJEydUVFQU9bWGi2lthYWFatu2rRwOR9B27dq1q3X3/4cffqisrCx16dJFw4YN09atW4Our0u12kFd7x30jVPoG+GpNfZvWqLGPB6P3G53hfGUlBSVlJTEYEXh06xZM02YMEEXXnihHA6H1q9fryeeeELFxcWaPn16oL5f1u+/XJvrN63N4/EEnbfhl5KSoi+++CLCqwyf7t27Kzc3V23atNHevXtVUFCgUaNGafny5erataukulOrXdTV3kHfoG9Eqm8QmmBrl156qS699NLA5b59+yopKUnLli3TuHHjYrgyhNvEiRODLg8YMECDBw/WX/7yFy1evDhGq0JtRN+IH9HuG7w9Vwe43W6VlpZWGC8pKVFKSkoMVhRZOTk58nq9+vrrrwP1/bJ+j8cjSbW6ftPa3G63ysrKKuxf2+//c845R/3799eXX34ZGKurtcZKPPUO+gZ945dCqZXQVAdU9r5saWmp9u3bV+F8hbrGX98v6y8sLFS9evWUnp4ei2WFhWlt7dq1065duyr8Ou6uXbvq3P0fT7VGQ7z2DvpGfB1L4ayV0FQH9OvXT1u2bAk8k5CktWvXyul0Bv22QF2xevVquVwude7cWenp6WrTpo3Wrl1bYZvevXsrMTExRqusOdPa+vXrp5KSEr3//vuBbXbt2qWvvvpK/fr1i+qaw+nw4cN699131aVLl8BYXa01VuKpd9A36BvhqJVzmuqAIUOGaPny5Ro/frzy8/NVXFysRx55REOGDAn6MLfaaMyYMerZs6c6dOggSXrnnXe0cuVKjRgxQs2aNZMkTZgwQVOmTFHr1q3Vs2dPrV69Wtu2bdOzzz4by6Wf1ZEjR7Rx40ZJ0u7du1VWVhZodD169FBqaqpRbV27dlXfvn117733aurUqUpKStJ//dd/qUOHDrryyitjUtsvna3WwsJCPfXUU7riiit07rnnau/evVq6dKn27dunP//5z4HbqQ211iZ1tXfQN+gbkeobDuuXr1ehVtq5c6dmzZqlTz/9VA0bNlRubq4mT55cq58xSdKDDz6o9957Tz/99JN8Pp/atGmjm266ScOHDw/69dEXXnhBixcv1p49e9S2bVvdc889uuyyy2K48rP78ccfNXDgwEqve+aZZ9SzZ09JZrWVlpbq4Ycf1rp161ReXq6+ffvq/vvvt80PvrPV2rJlS/3Hf/yHtm/froMHD6pBgwbq2rWr7rrrLmVmZgZtb/daa5u62DvoG/SNSPUNQhMAAIABzmkCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGgCAAAwQGhCnTZ37tzAn1KormnTpik7OzvMKwJQG9A7UBlCEwAAgAFCEwAAgAFCE2Lu8OHDZ7zuyJEjUVwJgNqE3oFoIzQhLHbv3q0ZM2Zo0KBByszMVM+ePTVx4kT9+OOPQdu99NJL6tChgz788EPNmDFDvXv3Vv/+/SVJw4cP1+DBg/XFF1/o1ltv1YUXXqjHH3/ceA0fffSRbrjhBnXp0kWXX365nnvuuTNu++qrr+r6669XZmamevToocmTJ+v//u//zjpHQUGBhgwZop49eyozM1PXX3+91q5dG7TNsGHDdM0111S6/6BBgzRmzBjjmoC6jt5xCr3D/hJivQDUDf/7v/+rTz/9VFdffbVatmyp3bt3a8WKFRoxYoRWrVqlBg0aBG0/c+ZMpaamavz48UHPFg8ePKixY8fq6quv1jXXXKNf/epXRvNv375dY8aMUWpqqiZMmKDy8nLNnTu30v0XLFigP//5z8rJydGNN96oAwcO6Nlnn9Wtt96qV155RW63+4zzPPPMM8rOztZvf/tbnThxQqtWrdLdd9+thQsXasCAAZKk3Nxc3X///fr222+VkZER2Hfbtm36/vvvdccddxjVBMQDege9o1axgDA4cuRIhbFPP/3UysjIsF5++eXA2IsvvmhlZGRYt9xyi1VeXh60/bBhw6yMjAxrxYoV1Z7/zjvvtLp06WLt3r07MPbdd99ZnTp1sjIyMgJjP/74o9WpUydrwYIFQftv377d6ty5c9D41KlTrcsuu6zKOo8fP24NHjzYGjFiRGDM4/FYXbp0sR599NGgbWfNmmVlZWVZhw4dqnZ9QF1F76B31Ca8PYewqF+/fuDrEydO6Oeff1br1q3ldrv11VdfVdj+d7/7nVwuV4XxxMREXX/99dWa2+v16u9//7suv/xytWrVKjDevn179e3bN2jbdevWyefzKScnRwcOHAj8a9q0qc477zx98MEHxnWWlJSotLRU3bp1C6qxUaNGGjhwoFatWiXLsgJrXLNmjQYOHKhzzjmnWvUBdRm9g95Rm/D2HMLi6NGjWrhwoV566SUVFxcHDnhJKi0trbB9WlpapbfTokULJSYmVmvuAwcO6OjRozrvvPMqXNe2bVtt3LgxcPn777+XZVm68sorK72thISqD4kNGzZowYIF+vrrr3X8+PHAuMPhCNru2muv1erVq/XRRx+pe/fu2rJli/75z38qNze3OqUBdR69g95RmxCaEBazZs3SSy+9pLy8PGVlZalRo0ZyOByaPHlyUBP0S0pKqvR2Tn82Fgk+n08Oh0OLFy+u9NlqVc/kPvroI91xxx3q3r27/vjHP6pZs2aqV6+eXnzxRb3xxhtB2/bt21dNmzbVa6+9pu7du+u1115Ts2bNdMkll4S9JqA2o3fQO2oTQhPC4s0339S1116radOmBcaOHTtW6TPFcEtNTVX9+vX1ww8/VLhu165dQZdbt24ty7KUlpamtm3bVmueN998U0lJSSooKAh6Rvviiy9W2Nblcmnw4MF6+eWXNWXKFL399ttnfFsBiGf0jmD0DnvjnCaERWUH9PLly+X1eqMyd9++ffX2229rz549gfGdO3fq73//e9C2V155pVwul+bNm1fhWaxlWfr555+rnMfhcATV9OOPP+qdd96pdPvc3FyVlJRo+vTpOnz48Bl/lRiIZ/SOiugd9sUrTQiLAQMG6NVXX1VycrJ+/etf67PPPtOWLVvUuHHjqMw/YcIEvffee7r11lt1yy23yOv16tlnn9Wvf/1rbd++PbBd69atNWnSJD322GPavXu3Lr/8cjVs2FA//vhj4BndmT4LpX///lq6dKluu+02DR48WPv379d///d/q3Xr1kFz+HXu3FkZGRlau3at2rdvr/PPPz9i9QO1Fb2D3lGbEJoQFvfdd5+cTqdef/11HTt2TBdddFGgSURDx44dVVBQoIcfflhz5sxRy5YtNWHCBO3bt69CU7r99tvVpk0bPf3005o/f74kqWXLlurTp0+Vf2Szd+/e+tOf/qTFixfroYceUlpamqZMmaLdu3dX2vikk88YH330UU7iBM6A3kHvqE0cVmVn2gEIi2XLlunhhx/W+vXrg36lGQCqQu+wJ85pAiLEsiz97W9/U/fu3Wl6AIzRO+yLt+dga4cOHaryj3JKJ38Dxk6/WXL48GGtX79eH3zwgb799lv95S9/ifWSgLhD70AkEJpga0uWLNG8efOq3Oadd9454wfexcKBAwf0+9//Xm63W+PGjdPAgQNjvSQg7tA7EAmc0wRbKyoqUlFRUZXbdOvW7YwfeAcgPtE7EAmEJgAAAAOcCA4AAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGCA0AQAAGDg/wMRtQwmS6lVSwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Wir ziehen zweimal eine Stichprobe, berechnen ihren Mittelwert und visualisieren die Stichprobe\n",
    "sample1 = fls.sample(5).arr_delay\n",
    "sample2 = fls.sample(5).arr_delay\n",
    "\n",
    "print(f\"sample1 with mean {sample1.mean()}: {sample1.tolist()}\")\n",
    "print(f\"sample2 with mean {sample2.mean()}: {sample2.tolist()}\")\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, sharex=True, sharey=True)\n",
    "sns.histplot(sample1, ax=axs[0])\n",
    "sns.histplot(sample2, ax=axs[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1feb7f85",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wir wiederholen das nun für verschiedene Stichprobengrößen je 1000x\n",
    "n_replics = 1000\n",
    "sample_sizes = [5, 30, 100]\n",
    "np.random.seed(123)\n",
    "\n",
    "means_by_sample_size = []\n",
    "\n",
    "\"\"\"\n",
    "Ich verwende hier list comprehensions, sie sind kompakter und schneller als Schleifen. Sie können stattdessen auch eine Schleife verwenden.\n",
    "https://www.w3schools.com/python/python_lists_comprehension.asp\n",
    "\n",
    "Beispiel:\n",
    ">>> numbers = [1, 2, 3, 4]\n",
    ">>> squares = [n**2 for n in numbers]\n",
    ">>> print(squares)\n",
    "[1, 4, 9, 16]\n",
    "\n",
    "Für jedes n aus sample_sizes tue 1000x:\n",
    "    - ziehe n Stichproben und  berechne den Mittelwert\n",
    "    - speichere die Mittelwerte in einer Liste\n",
    "    \n",
    "Als Resultat erhalten wir eine Liste, die 3 Listen (für die 3 Stichprobengrößen) mit jeweils 1000 Mittelwerten enthält.\n",
    "\"\"\"\n",
    "for sample_size in sample_sizes:\n",
    "    means_by_sample_size.append([flights.sample(sample_size).arr_delay.mean() for _ in range(n_replics)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "77874aae",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axs = plt.subplots(1, 3, figsize=(16, 5), sharex=True, sharey=True)\n",
    "\n",
    "fig.suptitle(\"Stichprobenverteilung des Mittelwerts\")\n",
    "\n",
    "for i, means in enumerate(means_by_sample_size):\n",
    "    sns.histplot(means, bins=64, kde=True, stat=\"density\", ax=axs[i])\n",
    "    axs[i].set_xlabel(r'$\\bar{x}$')\n",
    "    axs[i].set_title(f\"N={sample_sizes[i]}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "487f6a11",
   "metadata": {},
   "source": [
    "Diese Verteilungen des errechneten Parameters nennt man Stichprobenverteilung. In diesem Fall haben wir Stichprobenverteilungen für den Mittelwert erstellt.\n",
    "\n",
    "Was fällt Ihnen beim Vergleich der sog. Stichprobenverteilungen auf?\n",
    "\n",
    "Stellen Sie sich folgende Fragen:\n",
    "- wie relevant ist die Streuung in der Stichprobe für die Stichprobenverteilung?\n",
    "- wie relevant ist die Stichprobengröße für die Stichprobenverteilung?\n",
    "- wie relevant ist die Verteilung der Daten für die Stichprobenverteilung? (das schauen wir uns unten genauer an)\n",
    "- was ist der Unterschied zwischen der Verteilung der Daten und der Stichprobenverteilung?\n",
    "- gibt es für Sie eine Erkenntnis für die Praxis, z.B. bei der Analyse von Messdaten? \n",
    "    (Beispiel: Sie messen in einem Labor elektrische Kennzahlen und interessieren sich für den Mittelwert. Was geben Sie als Messergebnis an?) (Wir haben früher immer Mittelwert und Standardabweichung angegeben. Ist das sinnvoll? Überlegen Sie bessere Alternativen!)\n",
    "\n",
    "\n",
    "#### b) Berechnung des Standardfehlers\n",
    "Der Standardfehler (standard error (of the mean)) ist eine wichtige Kenngröße der Stichprobenverteilung und spielt eine zentrale Rolle bei Schätzungen. Lesen Sie im Buch nach welche Definitionen/Interpretationen es gibt.\n",
    "\n",
    "Berechnen Sie den Standardfehler als Streuung (Standardabweichung) der Stichprobenverteilung. Wie verändert sich der Standardfehler mit der Stichprobengröße? Vergleichen Sie den Wert mit der theoretischen Formel für den Standardfehler des Mittelwerts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91d64eb0e3b775a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#TODO: Berechnung des Standardfehlers für die unterschiedlichen Stichprobengrößen aus der Stichprobenverteilung und aus theoretischer Formel"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3e48c793591a5cc",
   "metadata": {},
   "source": [
    "#### c) Stichprobenverteilung für weitere statistische Größen\n",
    "\n",
    "Wie sehen Stichprobenverteilungen für andere statistische Größen aus? \n",
    "1. Wiederholen Sie die Analyse von oben für Median und Standardabweichung. Was fällt Ihnen auf?\n",
    "2. Untersuchen Sie den Einfluss der Verteilung der Daten auf die Stichprobenverteilung. Dazu können Sie sich Daten aus anderen Verteilungen generieren (z.B. exponentialverteilt, gleichverteilt etc.) und dann die Stichprobenverteilungen anschauen. Alternativ können Sie folgende Visualisierung nutzen: https://onlinestatbook.com/stat_sim/sampling_dist/index.html\n",
    "3. Sehen Sie einen Zusammenhang zum zentralen Grenzwertsatz?\n",
    "\n",
    "Hier gibt es viele Erkenntnisse zu gewinnen, spielen Sie mit den Parametern und lassen Sie sich überraschen!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56e5975f6fdafbd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: Stichprobenverteilung für Median und Standardabweichung\n",
    "# TODO: Einfluss der Verteilung der Daten auf die Stichprobenverteilung untersuchen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e1a9e01754ace26",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "source": [
    "## 3. Output \n",
    "Als Output aus diesem Labor sammeln Sie Ihre Erkenntnisse und offenen Fragen. Tragen Sie Ihre wichtigste Erkenntnis und Ihre \"größte\" Frage bis Dienstagabend auf moodle ein. Diese Antworten nutze ich zur Vorbereitung der nächsten Vorlesung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "392f73677803f15d",
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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