{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zufallszahlenlabor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Beispiel: Poisson-Verteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lage- und Streuungsmaße:\n",
      "Mittlere Tore Heim: 1.80, Standardabweichung: 1.34\n",
      "Mittlere Tore Auswärts: 1.30, Standardabweichung: 1.14\n",
      "Mittlere Tordifferenz: 0.50, Standardabweichung: 1.76\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(11)\n",
    "\n",
    "# gegebenen Parameter\n",
    "anzahl_fussballspiele = 1000000\n",
    "tore_heim_avg = 1.8\n",
    "tore_auswaerts_avg = 1.3\n",
    "\n",
    "# Erstellung einer Poison-Verteilung\n",
    "# Simulation der geschossenen Tore\n",
    "tore_heim = np.random.poisson(tore_heim_avg, anzahl_fussballspiele)\n",
    "tore_auswaerts = np.random.poisson(tore_auswaerts_avg, anzahl_fussballspiele)\n",
    "\n",
    "# Berechnung der Tordifferenz\n",
    "tordifferenz = tore_heim - tore_auswaerts\n",
    "\n",
    "# Plot der Verteilungen\n",
    "fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n",
    "\n",
    "# Verteilung der geschossenen Tore der Heimmannschaft\n",
    "values, counts = np.unique(tore_heim, return_counts=True)\n",
    "probs = counts / anzahl_fussballspiele\n",
    "axes[0].bar(values, probs, alpha=0.7, color='blue', edgecolor='black')\n",
    "axes[0].set_title('Verteilung der Tore (Heimmannschaft)')\n",
    "axes[0].set_xlabel('Anzahl Tore')\n",
    "axes[0].set_ylabel('Häufigkeit')\n",
    "\n",
    "# Verteilung der geschossenen Tore der Gastmannschaft\n",
    "values, counts = np.unique(tore_auswaerts, return_counts=True)\n",
    "probs = counts / anzahl_fussballspiele\n",
    "axes[1].bar(values, probs, alpha=0.7, color='green', edgecolor='black')\n",
    "axes[1].set_title('Verteilung der Tore (Gastmannschaft)')\n",
    "axes[1].set_xlabel('Anzahl Tore')\n",
    "axes[1].set_ylabel('Häufigkeit')\n",
    "\n",
    "# Verteilung der Tordifferenz\n",
    "values, counts = np.unique(tordifferenz, return_counts=True)\n",
    "probs = counts / anzahl_fussballspiele\n",
    "axes[2].bar(values, probs, alpha=0.7, color='red', edgecolor='black')\n",
    "axes[2].set_title('Verteilung der Tordifferenz')\n",
    "axes[2].set_xlabel('Tordifferenz')\n",
    "axes[2].set_ylabel('Häufigkeit')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Lage- und Streuungsmaße\n",
    "print(\"Lage- und Streuungsmaße:\")\n",
    "print(f\"Mittlere Tore Heim: {np.mean(tore_heim):.2f}, Standardabweichung: {np.std(tore_heim):.2f}\")\n",
    "print(f\"Mittlere Tore Auswärts: {np.mean(tore_auswaerts):.2f}, Standardabweichung: {np.std(tore_auswaerts):.2f}\")\n",
    "print(f\"Mittlere Tordifferenz: {np.mean(tordifferenz):.2f}, Standardabweichung: {np.std(tordifferenz):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Beispiel: Geometrische Verteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lage- und Streuungsmaße:\n",
      "Mittlere Tage seit letztem Fehler: 125.04\n",
      "Standardabweichung: 124.51\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(22)\n",
    "\n",
    "# Parameter für die geometrische Verteilung\n",
    "durchschnitt_tage = 125\n",
    "anzahl_maschinen = 1000000\n",
    "\n",
    "# Simulation der Tage seit letztem Fehler\n",
    "tage_seit_letztem_fehler = np.random.geometric(1/durchschnitt_tage, anzahl_maschinen)\n",
    "\n",
    "# Plot der Verteilung\n",
    "values, counts = np.unique(tage_seit_letztem_fehler, return_counts=True)\n",
    "probs = counts / anzahl_maschinen\n",
    "\n",
    "plt.bar(values, probs, alpha=0.7, color='purple', edgecolor='black')\n",
    "plt.title('Verteilung der Tage seit letztem Fehler')\n",
    "plt.xlabel('Tage seit letztem Fehler')\n",
    "plt.ylabel('Häufigkeit')\n",
    "plt.show()\n",
    "\n",
    "# Lage- und Streuungsmaße\n",
    "print(\"Lage- und Streuungsmaße:\")\n",
    "print(f\"Mittlere Tage seit letztem Fehler: {np.mean(tage_seit_letztem_fehler):.2f}\")\n",
    "print(f\"Standardabweichung: {np.std(tage_seit_letztem_fehler):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Beispiel: Binomialverteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 10000, p = 0.08333333333333333, size = 1000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lage- und Streuungsmaße:\n",
      "Mittlere Anzahl Kunden: 833.35\n",
      "Standardabweichung: 27.63\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(33)\n",
    "\n",
    "# Parameter für die Binomialverteilung\n",
    "anzahl_tage = 1_000_000\n",
    "anzahl_kunden_pro_tag = 10_000\n",
    "laden_oeffnungszeiten = 12  # Stunden\n",
    "zeit_kunden_einkaufen = 1  # Stunde\n",
    "p = zeit_kunden_einkaufen / laden_oeffnungszeiten  # Wahrscheinlichkeit, dass ein Kunde im Laden ist\n",
    "\n",
    "# Simulation der Anzahl der Kunden, die in einer Stunde einkaufen\n",
    "print(f\"n = {anzahl_kunden_pro_tag}, p = {p}, size = {anzahl_tage}\")\n",
    "anzahl_kunden = np.random.binomial(anzahl_kunden_pro_tag, p, anzahl_tage)\n",
    "\n",
    "# Plot der Verteilung\n",
    "values, counts = np.unique(anzahl_kunden, return_counts=True)\n",
    "probs = counts / anzahl_tage\n",
    "\n",
    "plt.bar(values, probs, alpha=0.7, color='orange')\n",
    "plt.title('Verteilung der Anzahl der Kunden im Laden')\n",
    "plt.xlabel('Anzahl Kunden pro Stunde')\n",
    "plt.ylabel('Häufigkeit')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Lage- und Streuungsmaße\n",
    "print(\"Lage- und Streuungsmaße:\")\n",
    "print(f\"Mittlere Anzahl Kunden: {np.mean(anzahl_kunden):.2f}\")\n",
    "print(f\"Standardabweichung: {np.std(anzahl_kunden):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Beispiel: Exponentialverteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DER0djT59+qCyshI5OTk4ePAgFi1ahIEDB5rdx6KiIowYMQLTpk1Djx49YG9vjx9++AFffPFFrTNIdYmOjsbOnTvx6KOPYtWqVfDy8sK///1vbN68Gc888wy6detW7zot9feCWgjr3otPREIIsWHDBgFA+Pr6mvz+999/FwsXLhTe3t5CLpeLtm3bCn9/f7F06VJRXFwshPjfU1T/+Mc/TNaxd+9e0aNHDyGXy42eDDx9+rQICwsT7du3F3K5XLi5uYmRI0eK+Ph4fYy5Tx2WlZWJF198UXh6egpbW1sxbNgwcerUqVqfOqz59Jqpdm7fvi1iYmJE+/bthUqlEoMGDRJqtVo4OjqK6Ojoug6tEEKIq1evikmTJonWrVsLe3t7MWnSJJGWlmbySUxzjkVtfa/Nd999J/7+97+Lvn37irZt2wqpVCratWsnxo4da/CUXjW1Wi1CQ0OFo6OjUCqVwsfHx2Cc1cf9999/N9ivul93Psn46aefir59+wqVSiU6dOggXnjhBfH5558bHePKykqxevVq4enpKRQKhejTp4/49NNPxbBhwwyeOhRCiOLiYrFs2TLRvXt3oVAohKOjo+jdu7eIjo4WeXl5+jgA4u9//7vR+O78u3D79m0RGRkp+vTpIxwcHIStra3o3r27WLFihSgpKdHvM2zYMNGrVy+jumbMmCG8vLwMyrKzs8W0adOEs7OzkMvlonv37uIf//iHwdOBdf17qfnvQwjz/l4QmSIRQggr5HdERPckLS0NgwcPxu7du42eICQielAw0SKiB15qairUajX8/f1ha2uL06dPY82aNXB0dMSPP/5o1lIIRETWwHu0iOiB5+DggIMHDyIuLg5//vknXFxcEBoaitWrVzPJIqIHGme0iIiIiCyEC5YSERERWQgTLSIiIiILYaJFREREZCG8Gd7KKisrcf36ddjb29/z6zyIiIjo/hBC4M8//4SHh0edCycz0bKy69evw9PT09rdICIioga4cuVKnW/nYKJlZfb29gCqTpSDg4OVe0NERETm0Gg08PT01P+O14aJlpVVXy50cHBgokVERNTE3O22H94MT0RERGQhTLSIiIiILISJFhEREZGFWD3R2rx5M7y9vaFSqeDv749jx47VGX/06FH4+/tDpVKhS5cuiI+PN4pJSkqCr68vlEolfH19kZycfE/tzps3DxKJBHFxcQblZWVlWLBgAVxcXGBnZ4cJEybg6tWr5g2ciIiImj2rJlr79u1DVFQUli5diszMTAwZMgShoaHIyckxGZ+VlYVx48ZhyJAhyMzMxJIlS7Bw4UIkJSXpY9RqNcLDwxEREYHTp08jIiICYWFhOHHiRIPa/fjjj3HixAl4eHgYfRcVFYXk5GQkJibi+PHjKC4uxvjx41FRUdEIR4eIiIiaPGFFjzzyiIiMjDQo69Gjh1i8eLHJ+BdffFH06NHDoGzevHli0KBB+u2wsDAxduxYg5iQkBAxderUerd79epV0aFDB3H27Fnh5eUl1q9fr//u5s2bQi6Xi8TERH3ZtWvXhI2Njfjiiy/qGLWhoqIiAUAUFRWZvQ8RERFZl7m/31ab0SovL0d6ejqCg4MNyoODg5GWlmZyH7VabRQfEhKCkydPQqvV1hlTXae57VZWViIiIgIvvPACevXqZdSX9PR0aLVag3o8PDzg5+dXa/+JiIioZbHaOloFBQWoqKiAq6urQbmrqyvy8vJM7pOXl2cyXqfToaCgAO7u7rXGVNdpbrtr166FTCbDwoULa+2LQqFAmzZtzO4/UHVfV1lZmX5bo9EAAHQ6HXQ6Xa37ERER0YPD3N9sqy9YWnOhLyFEnYt/mYqvWW5OnXXFpKenY8OGDcjIyKj3+wfv1v/Vq1fjlVdeMSo/efIk7Ozs6tUWERERWUdJSYlZcVZLtFxcXCCVSo1mf/Lz841mm6q5ubmZjJfJZHB2dq4zprpOc9o9duwY8vPz0alTJ/33FRUVWLRoEeLi4vDrr7/Czc0N5eXluHHjhsGsVn5+PoKCgmodd2xsLGJiYvTb1Uv4BwQEcGV4IiKiJqL6itTdWC3RUigU8Pf3R2pqKh5//HF9eWpqKiZOnGhyn8DAQHz66acGZQcPHkRAQADkcrk+JjU1FdHR0QYx1cmPOe1GRERg9OjRBu2EhIQgIiICTz/9NADA398fcrkcqampCAsLAwDk5ubi7NmzeOONN2odt1KphFKpNCqXyWSQyaw+wUhERERmMPs32/L35dcuMTFRyOVykZCQIM6fPy+ioqKEnZ2d+PXXX4UQQixevFhERETo43/55RfRqlUrER0dLc6fPy8SEhKEXC4XH330kT7m22+/FVKpVKxZs0ZcuHBBrFmzRshkMvHdd9+Z3a4pNZ86FEKIyMhI0bFjR3Ho0CGRkZEhRo4cKfr27St0Op3Zx4BPHRIRETU95v5+W3UKJTw8HIWFhVi1ahVyc3Ph5+eHlJQUeHl5AaiaIbpzbStvb2+kpKQgOjoamzZtgoeHB95++21MmjRJHxMUFITExEQsW7YMy5cvh4+PD/bt24eBAwea3a651q9fD5lMhrCwMJSWlmLUqFHYvn07pFLpPR4ZIiIiag4kQvz3bnKyCo1GA0dHRxQVFfEeLSIioibC3N9v3hTUjP3+++9GN+s5ODigXbt2VuoRERFRy8JEq5n6/fffMW3aMygsLDMod3ZWYs+eLUy2iIiI7gMmWs2URqNBYWEZlMpFsLX1BACUll5BYeFb0Gg0TLSIiIjuAyZazZytrSfs7Hz022VldQQTERFRo7Lauw6JiIiImjsmWkREREQWwkSLiIiIyEKYaBERERFZCBMtIiIiIgthokVERERkIUy0iIiIiCyEiRYRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgRERERWQgTLSIiIiILYaJFREREZCFMtIiIiIgshIkWERERkYUw0SIiIiKyECZaRERERBbCRIuIiIjIQphoEREREVkIEy0iIiIiC2GiRURERGQhTLSIiIiILISJFhEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEKYaBERERFZCBMtIiIiIgthokVERERkIVZPtDZv3gxvb2+oVCr4+/vj2LFjdcYfPXoU/v7+UKlU6NKlC+Lj441ikpKS4OvrC6VSCV9fXyQnJ9e73ZUrV6JHjx6ws7NDmzZtMHr0aJw4ccIgZvjw4ZBIJAafqVOnNuAoEBERUXNk1URr3759iIqKwtKlS5GZmYkhQ4YgNDQUOTk5JuOzsrIwbtw4DBkyBJmZmViyZAkWLlyIpKQkfYxarUZ4eDgiIiJw+vRpREREICwszCBJMqfdbt26YePGjThz5gyOHz+Ozp07Izg4GL///rtBn+bOnYvc3Fz95913323ko0RERERNlUQIIazV+MCBAzFgwABs2bJFX9azZ0889thjWL16tVH8Sy+9hAMHDuDChQv6ssjISJw+fRpqtRoAEB4eDo1Gg88//1wfM3bsWLRp0wZ79+5tULsAoNFo4OjoiEOHDmHUqFEAqma0+vXrh7i4uAYfg+p6i4qK4ODg0OB6arp8+TKmTImCk1Mc7Ox8AAAlJZdx82YUPvwwDj4+Po3WFhERUUtj7u+31Wa0ysvLkZ6ejuDgYIPy4OBgpKWlmdxHrVYbxYeEhODkyZPQarV1xlTX2ZB2y8vLsXXrVjg6OqJv374G3+3evRsuLi7o1asXnn/+efz55593GTkRERG1FDJrNVxQUICKigq4uroalLu6uiIvL8/kPnl5eSbjdTodCgoK4O7uXmtMdZ31afezzz7D1KlTcevWLbi7uyM1NRUuLi7676dPnw5vb2+4ubnh7NmziI2NxenTp5GamlrruMvKylBWVqbf1mg0AACdTgedTlfrfvVVWVkJmUwKmawSUmlVvTJZVVllZWWjtkVERNTSmPs7arVEq5pEIjHYFkIYld0tvma5OXWaEzNixAicOnUKBQUFeO+99/T3erVv3x5A1f1Z1fz8/NC1a1cEBAQgIyMDAwYMMNn/1atX45VXXjEqP3nyJOzs7Ezu0xClpaWYNi0EMlk2pNJ8AEBFRSl0uhBkZ2cjPz+/0doiIiJqaUpKSsyKs1qi5eLiAqlUajSLlJ+fbzTbVM3Nzc1kvEwmg7Ozc50x1XXWp107Ozs89NBDeOihhzBo0CB07doVCQkJiI2NNdm/AQMGQC6X49KlS7UmWrGxsYiJidFvazQaeHp6IiAgoFHv0crKysKSJRvh5DQarVp5AwBu3crCzZsbsXv3aHh7ezdaW0RERC1N9RWpu7FaoqVQKODv74/U1FQ8/vjj+vLU1FRMnDjR5D6BgYH49NNPDcoOHjyIgIAAyOVyfUxqaiqio6MNYoKCghrcbjUhhMFlv5rOnTsHrVYLd3f3WmOUSiWUSqVRuUwmg0zWeKfDxsYGOl0FdDobVFRU1avTVZXZ2Ng0altEREQtjbm/o1b9tY2JiUFERAQCAgIQGBiIrVu3IicnB5GRkQCqZn+uXbuGnTt3Aqh6wnDjxo2IiYnB3LlzoVarkZCQoH+aEACee+45DB06FGvXrsXEiRPxySef4NChQzh+/LjZ7ZaUlOC1117DhAkT4O7ujsLCQmzevBlXr17FlClTAFQ91bd7926MGzcOLi4uOH/+PBYtWoT+/ftj8ODB9+sQEhER0QPMqolWeHg4CgsLsWrVKuTm5sLPzw8pKSnw8vICAOTm5hqsbeXt7Y2UlBRER0dj06ZN8PDwwNtvv41JkybpY4KCgpCYmIhly5Zh+fLl8PHxwb59+zBw4ECz25VKpfjPf/6DHTt2oKCgAM7Oznj44Ydx7Ngx9OrVC0DVzNhXX32FDRs2oLi4GJ6ennj00UexYsUKSKXS+3H4iIiI6AFn1XW0iOtoERERNUUP/DpaRERERM0dEy0iIiIiC2GiRURERGQhTLSIiIiILISJFhEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEL4wrsWRqstQ3Z2tn7bwcEB7dq1s2KPiIiImi8mWi1IeXkhsrN/wYIFa/QvtnZ2VmLPni1MtoiIiCyAlw5bkIqKYuh0CigU0XByioNSuQiFhWXQaDTW7hoREVGzxBmtFkil6qh//2FZmZU7Q0RE1IxxRouIiIjIQphoEREREVkIEy0iIiIiC2GiRURERGQhTLSIiIiILISJFhEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEKYaBERERFZCBMtIiIiIgthokVERERkIUy0iIiIiCyEiRYRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgRERERWQgTLSIiIiILYaJFREREZCFMtIiIiIgshIkWERERkYVYPdHavHkzvL29oVKp4O/vj2PHjtUZf/ToUfj7+0OlUqFLly6Ij483iklKSoKvry+USiV8fX2RnJxc73ZXrlyJHj16wM7ODm3atMHo0aNx4sQJg5iysjIsWLAALi4usLOzw4QJE3D16tUGHAUiIiJqjqyaaO3btw9RUVFYunQpMjMzMWTIEISGhiInJ8dkfFZWFsaNG4chQ4YgMzMTS5YswcKFC5GUlKSPUavVCA8PR0REBE6fPo2IiAiEhYUZJEnmtNutWzds3LgRZ86cwfHjx9G5c2cEBwfj999/18dERUUhOTkZiYmJOH78OIqLizF+/HhUVFRY4GgRERFRkyOs6JFHHhGRkZEGZT169BCLFy82Gf/iiy+KHj16GJTNmzdPDBo0SL8dFhYmxo4daxATEhIipk6d2uB2hRCiqKhIABCHDh0SQghx8+ZNIZfLRWJioj7m2rVrwsbGRnzxxRe11lNbvUVFRWbvY46ff/5Z9O8/XowY8bMYP16I8eOFGDToK2Fr21MMGvSjGD9eiBEjqmJ+/vnnRm2biIiouTP391tmrQSvvLwc6enpWLx4sUF5cHAw0tLSTO6jVqsRHBxsUBYSEoKEhARotVrI5XKo1WpER0cbxcTFxTW43fLycmzduhWOjo7o27cvACA9PR1ardagPx4eHvDz80NaWhpCQkJM1lVWVoaysjL9tkajAQDodDrodDqT+zREZWUlZDIpZLJKSKVV9cpkAgqFXF8mk1XFVFZWNmrbREREzZ25v5tWS7QKCgpQUVEBV1dXg3JXV1fk5eWZ3CcvL89kvE6nQ0FBAdzd3WuNqa6zPu1+9tlnmDp1Km7dugV3d3ekpqbCxcVF3xeFQoE2bdqY3X8AWL16NV555RWj8pMnT8LOzq7W/eqrtLQU06aFQCbLhlSaDwDQaksRGjoDrVvnQS4vRkVFKXS6EGRnZyM/P7/R2iYiImruSkpKzIqzWqJVTSKRGGwLIYzK7hZfs9ycOs2JGTFiBE6dOoWCggK89957+nu92rdvX2v/7tb/2NhYxMTE6Lc1Gg08PT0REBAABweHWverr6ysLCxZshFOTqPRqpU3AKCw8CjOnNmB3r13wtm5F27dysLNmxuxe/doeHt7N1rbREREzV31Fam7sVqi5eLiAqlUajT7k5+fbzTbVM3Nzc1kvEwmg7Ozc50x1XXWp107Ozs89NBDeOihhzBo0CB07doVCQkJiI2NhZubG8rLy3Hjxg2DWa38/HwEBQXVOm6lUgmlUmlULpPJIJM13umwsbGBTlcBnc4GFRVV9ep0EpSXa/VlOl1VjI2NTaO2TURE1NyZ+7tptacOFQoF/P39kZqaalCemppaa6ISGBhoFH/w4EEEBARALpfXGVNdZ0ParSaE0N9f5e/vD7lcblBPbm4uzp49e9d6iIiIqGWw6jRGTEwMIiIiEBAQgMDAQGzduhU5OTmIjIwEUHWZ7dq1a9i5cycAIDIyEhs3bkRMTAzmzp0LtVqNhIQE7N27V1/nc889h6FDh2Lt2rWYOHEiPvnkExw6dAjHjx83u92SkhK89tprmDBhAtzd3VFYWIjNmzfj6tWrmDJlCgDA0dERs2fPxqJFi+Ds7Iy2bdvi+eefR+/evTF69Oj7dQiJiIjoAWbVRCs8PByFhYVYtWoVcnNz4efnh5SUFHh5eQGomiG6c20rb29vpKSkIDo6Gps2bYKHhwfefvttTJo0SR8TFBSExMRELFu2DMuXL4ePjw/27duHgQMHmt2uVCrFf/7zH+zYsQMFBQVwdnbGww8/jGPHjqFXr176etavXw+ZTIawsDCUlpZi1KhR2L59O6RSqaUPHRERETUBElF9NzlZhUajgaOjI4qKihr1ZvjLly9jypQoODnFwc7OBwBQUHAYp08/i75998HFpTdKSi7j5s0ofPhhHHx8fBqtbSIioubO3N9vq7+Ch4iIiKi5YqJFREREZCFMtIiIiIgshIkWERERkYUw0SIiIiKyECZaRERERBbC9660cFptGbKzsw3KHBwc0K5dOyv1iIiIqPlgotWClZcXIjv7FyxYsMbg/YvOzkrs2bOFyRYREdE9YqLVglVUFEOnU0ChiIaTUzcAQGnpFRQWvgWNRsNEi4iI6B4x0SKoVB31q8cDwH/fm01ERET3iDfDExEREVkIEy0iIiIiC2GiRURERGQhTLSIiIiILISJFhEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEKYaBERERFZCBMtIiIiIgthokVERERkIUy0iIiIiCyEiRYRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgRERERWQgTLSIiIiILYaJFREREZCFMtIiIiIgshIkWERERkYUw0SIiIiKyECZaRERERBbCRIuIiIjIQqyeaG3evBne3t5QqVTw9/fHsWPH6ow/evQo/P39oVKp0KVLF8THxxvFJCUlwdfXF0qlEr6+vkhOTq5Xu1qtFi+99BJ69+4NOzs7eHh44KmnnsL169cN6hg+fDgkEonBZ+rUqQ08EkRERNTcWDXR2rdvH6KiorB06VJkZmZiyJAhCA0NRU5Ojsn4rKwsjBs3DkOGDEFmZiaWLFmChQsXIikpSR+jVqsRHh6OiIgInD59GhEREQgLC8OJEyfMbvfWrVvIyMjA8uXLkZGRgf379+Onn37ChAkTjPo0d+5c5Obm6j/vvvtuIx8lIiIiaqokQghhrcYHDhyIAQMGYMuWLfqynj174rHHHsPq1auN4l966SUcOHAAFy5c0JdFRkbi9OnTUKvVAIDw8HBoNBp8/vnn+pixY8eiTZs22Lt3b4PaBYAffvgBjzzyCLKzs9GpUycAVTNa/fr1Q1xcXIOPgUajgaOjI4qKiuDg4NDgemq6fPkypkyJgpNTHOzsfAAABQWHcfr0s+jbdx9cXHobbQNAScll3LwZhQ8/jIOPj0+j9YeIiKg5Mff3W3Yf+2SgvLwc6enpWLx4sUF5cHAw0tLSTO6jVqsRHBxsUBYSEoKEhARotVrI5XKo1WpER0cbxVQnQw1pFwCKioogkUjg5ORkUL57927s2rULrq6uCA0NxYoVK2Bvb19rPWVlZSgrK9NvazQaAIBOp4NOp6t1v/qqrKyETCaFTFYJqbSqXplMQKGQ68tqblfFVO1XWVnZqP0hIiJqTsz9jbRaolVQUICKigq4uroalLu6uiIvL8/kPnl5eSbjdTodCgoK4O7uXmtMdZ0Naff27dtYvHgxpk2bZpC1Tp8+Hd7e3nBzc8PZs2cRGxuL06dPIzU1tdZxr169Gq+88opR+cmTJ2FnZ1frfvVVWlqKadNCIJNlQyrNBwBotaUIDZ2B1q3zIJcXG20DQEVFKXS6EGRnZyM/P7/R+kNERNSclJSUmBVntUSrmkQiMdgWQhiV3S2+Zrk5dZrbrlarxdSpU1FZWYnNmzcbfDd37lz9n/38/NC1a1cEBAQgIyMDAwYMMNn/2NhYxMTE6Lc1Gg08PT0REBDQqJcOs7KysGTJRjg5jUarVt4AgMLCozhzZgd6994JZ+deRtsAcOtWFm7e3Ijdu0fD29u70fpDRETUnFRfkbobqyVaLi4ukEqlRrNI+fn5RrNN1dzc3EzGy2QyODs71xlTXWd92tVqtQgLC0NWVhYOHz5810RowIABkMvluHTpUq2JllKphFKpNCqXyWSQyRrvdNjY2ECnq4BOZ4OKiqp6dToJysu1+rKa21UxVfvZ2Ng0an+IiIiaE3N/I6321KFCoYC/v7/RZbbU1FQEBQWZ3CcwMNAo/uDBgwgICIBcLq8zprpOc9utTrIuXbqEQ4cO6RO5upw7dw5arRbu7u53jSUiIqLmz6pTFjExMYiIiEBAQAACAwOxdetW5OTkIDIyEkDVZbZr165h586dAKqeMNy4cSNiYmIwd+5cqNVqJCQk6J8mBIDnnnsOQ4cOxdq1azFx4kR88sknOHToEI4fP252uzqdDpMnT0ZGRgY+++wzVFRU6GfA2rZtC4VCgcuXL2P37t0YN24cXFxccP78eSxatAj9+/fH4MGD79chJCIiogeYVROt8PBwFBYWYtWqVcjNzYWfnx9SUlLg5eUFAMjNzTVYU8vb2xspKSmIjo7Gpk2b4OHhgbfffhuTJk3SxwQFBSExMRHLli3D8uXL4ePjg3379mHgwIFmt3v16lUcOHAAANCvXz+DPh85cgTDhw+HQqHAV199hQ0bNqC4uBienp549NFHsWLFCkilUksdMiIiImpCrLqOFnEdLSIioqbogV9Hix5cWm0ZsrOz9dsODg5o166dFXtERETUNDXoZvhZs2bhzz//NCovKSnBrFmz7rlTZD3l5YXIzv4FCxaswZQpUZgyJQrTpj2D33//3dpdIyIianIalGjt2LEDpaWlRuWlpaX6G9epaaqoKIZOp4BCEQ0npzgolYtQWFhm9nohRERE9D/1unSo0WgghIAQAn/++SdUKpX+u4qKCqSkpKB9+/aN3km6/1Sqjvp7u+54YxARERHVQ70SLScnJ0gkEkgkEnTr1s3oe4lEYvL1MkREREQtUb0SrSNHjkAIgZEjRyIpKQlt27bVf6dQKODl5QUPD49G7yQRERFRU1SvRGvYsGEAqt6j16lTpzrfSUhERETU0pmdaP3444/w8/ODjY0NioqKcObMmVpj+/Tp0yidIyIiImrKzE60+vXrh7y8PLRv3x79+vWDRCKBqbVOJRIJKioqGrWTRERERE2R2YlWVlaWftHKrKwsi3WIiIiIqLkwO9Gqfg9gzT8TERERkWkNWrAUAD744AMMHjwYHh4e+te1xMXF4ZNPPmm0zhERERE1ZQ1KtLZs2YKYmBiMGzcON2/e1N+T5eTkhLi4uMbsHxEREVGT1aBE65133sF7772HpUuXQiqV6ssDAgLqfBqRiIiIqCVpUKKVlZWF/v37G5UrlUqUlJTcc6eIiIiImoMGJVre3t44deqUUfnnn38OX1/fe+0TERERUbNQr5Xhq73wwgv4+9//jtu3b0MIge+//x579+7F6tWr8c9//rOx+0hERETUJDUo0Xr66aeh0+nw4osv4tatW5g2bRo6dOiADRs2YOrUqY3dRyIiIqImqUGJ1s2bNzF37lzMnTsXBQUFqKysRPv27QEAP//8Mx566KFG7SQRERFRU9Sge7TGjRuH27dvAwBcXFz0SdbFixcxfPjwRuscERERUVPWoESrTZs2eOyxx6DT6fRlFy5cwPDhwzFp0qRG6xwRERFRU9agRCspKQklJSWYNm0ahBA4e/Yshg8fjieffBIbNmxo7D4SERERNUkNSrRUKhU+++wzXLp0CVOmTMGoUaPw1FNPYd26dY3dPyIiIqImy+yb4TUajcG2RCLBvn37MHr0aEyaNAnLly/Xxzg4ODRuL4mIiIiaILMTLScnJ0gkEqNyIQTi4+Px7rvvQggBiUSif/chERERUUtmdqJ15MgRS/aDiIiIqNkxO9EaNmyYJftBRERE1Ow0aMHSH3/80WS5RCKBSqVCp06doFQq76ljRERERE1dgxKtfv36mbxfq5pcLkd4eDjeffddqFSqBneOiIiIqClr0PIOycnJ6Nq1K7Zu3YpTp04hMzMTW7duRffu3bFnzx4kJCTg8OHDWLZsWWP3l4iIiKjJaNCM1muvvYYNGzYgJCREX9anTx907NgRy5cvx/fffw87OzssWrQIb775ZqN1loiIiKgpaVCidebMGXh5eRmVe3l54cyZMwCqLi/m5ubeW+/ogaDVliE7O9ugzMHBAe3atbNSj4iIiJqGBiVaPXr0wJo1a7B161YoFAoAgFarxZo1a9CjRw8AwLVr1+Dq6tp4PSWrKC8vRHb2L1iwYI3BAw7Ozkrs2bOFyRYREVEdGpRobdq0CRMmTEDHjh3Rp08fSCQS/Pjjj6ioqMBnn30GAPjll18wf/78Ru0s3X8VFcXQ6RRQKKLh5NQNAFBaegWFhW9Bo9Ew0SIiIqpDg26GDwoKwq+//opVq1ahT58+8PPzw6pVq5CVlYVBgwYBACIiIvDCCy/cta7NmzfD29sbKpUK/v7+OHbsWJ3xR48ehb+/P1QqFbp06YL4+HijmKSkJPj6+kKpVMLX1xfJycn1aler1eKll15C7969YWdnBw8PDzz11FO4fv26QR1lZWVYsGABXFxcYGdnhwkTJuDq1at3HXNTpFJ1hJ2dD+zsfGBr62nt7hARETUJDUq0AKB169aIjIzEunXrsH79esybNw/29vb1qmPfvn2IiorC0qVLkZmZiSFDhiA0NBQ5OTkm47OysjBu3DgMGTIEmZmZWLJkCRYuXIikpCR9jFqtRnh4OCIiInD69GlEREQgLCwMJ06cMLvdW7duISMjA8uXL0dGRgb279+Pn376CRMmTDDoT1RUFJKTk5GYmIjjx4+juLgY48eP5yuIiIiICEA9Lh0eOHAAoaGhkMvlOHDgQJ2xNROS2qxbtw6zZ8/GnDlzAABxcXH48ssvsWXLFqxevdooPj4+Hp06dUJcXBwAoGfPnjh58iTefPNNTJo0SV/HmDFjEBsbCwCIjY3F0aNHERcXh71795rVrqOjI1JTUw3afuedd/DII48gJycHnTp1QlFRERISEvDBBx9g9OjRAIBdu3bB09MThw4dMngik4iIiFomsxOtxx57DHl5eWjfvj0ee+yxWuPMfal0eXk50tPTsXjxYoPy4OBgpKWlmdxHrVYjODjYoCwkJAQJCQnQarWQy+VQq9WIjo42iqlOzhrSLgAUFRVBIpHAyckJAJCeng6tVmvQHw8PD/j5+SEtLa3WRKusrAxlZWX6bY1GAwDQ6XTQ6XS1tl9flZWVkMmkkMkqIZVW1SuTCSgUcn1ZzW3zY6rqrqysbNQ+ExERNRXm/v6ZnWhVVlaa/HNDFRQUoKKiwujJRFdXV+Tl5ZncJy8vz2S8TqdDQUEB3N3da42prrMh7d6+fRuLFy/GtGnT4ODgoO+LQqFAmzZtzK4HAFavXo1XXnnFqPzkyZOws7Ordb/6Ki0txbRpIZDJsiGV5gMAtNpShIbOQOvWeZDLi422zY2pqCiFTheC7Oxs5OfnN1qfiYiImoqSkhKz4sxOtNq2bYuffvoJLi4umDVrFjZs2FDve7JMqfkqHyFEna/3MRVfs9ycOs1tV6vVYurUqaisrMTmzZvrGIl5/Y+NjUVMTIx+W6PRwNPTEwEBAfokrjFkZWVhyZKNcHIajVatvAEAhYVHcebMDvTuvRPOzr2Mts2NuXUrCzdvbsTu3aPh7e3daH0mIiJqKqqvSN2N2YlWeXk5NBoNXFxcsGPHDqxdu/aeEi0XFxdIpVKj2Z/8/Pxa199yc3MzGS+TyeDs7FxnTHWd9WlXq9UiLCwMWVlZOHz4sEEi5ObmhvLycty4ccNgVis/Px9BQUG1jlupVJp84bZMJoNM1qDVNkyysbGBTlcBnc4GFRVV9ep0EpSXa/VlNbfNj6mq28bGplH7TERE1FSY+/tn9q9kYGAgHnvsMfj7+0MIgYULF8LW1tZk7Pvvv3/X+hQKBfz9/ZGamorHH39cX56amoqJEyfW2odPP/3UoOzgwYMICAiAXC7Xx6Smphrcp3Xw4EF98mNuu9VJ1qVLl3DkyBF9IlfN398fcrkcqampCAsLAwDk5ubi7NmzeOONN+46fiIiImr+zE60du3ahfXr1+Py5cuQSCQoKirC7du376nxmJgYREREICAgAIGBgdi6dStycnIQGRkJoOoy27Vr17Bz504AQGRkJDZu3IiYmBjMnTsXarUaCQkJ+qcJAeC5557D0KFDsXbtWkycOBGffPIJDh06hOPHj5vdrk6nw+TJk5GRkYHPPvsMFRUV+hmwtm3bQqFQwNHREbNnz8aiRYvg7OyMtm3b4vnnn0fv3r31TyESERFRy2Z2ouXq6oo1a9YAALy9vfHBBx8YzfLUV3h4OAoLC7Fq1Srk5ubCz88PKSkp+vco5ubmGqyp5e3tjZSUFERHR2PTpk3w8PDA22+/rV/aAahaTDUxMRHLli3D8uXL4ePjg3379mHgwIFmt3v16lX9Ehb9+vUz6PORI0cwfPhwAMD69eshk8kQFhaG0tJSjBo1Ctu3b4dUKr2n40JERETNQ4NusMnKymq0DsyfP7/WV/Vs377dqGzYsGHIyMios87Jkydj8uTJDW63c+fO+pvs66JSqfDOO+/gnXfeuWssERERtTwNSrRWrVpV5/cvv/xygzpDRERE1Jw0KNGq+e5ArVaLrKwsyGQy+Pj4MNEiIiIiQgMTrczMTKMyjUaDmTNnGjzJR0RERNSSNfil0jU5ODhg1apVWL58eWNVSURERNSkNVqiBQA3b95EUVFRY1ZJRERE1GQ16NLh22+/bbAthEBubi4++OADjB07tlE6RkRERNTUNSjRWr9+vcG2jY0N2rVrhxkzZiA2NrZROkZERETU1Fl9HS0iIiKi5qpR79EiIiIiov9p0IwWAPzwww/48MMPkZOTg/LycoPv9u/ff88dIyIiImrqzJ7Revvtt/UvkU5MTMTgwYNx/vx5JCcnQ6vV4vz58zh8+DAcHR0t1lkiIiKipsTsRGv9+vUoKSkBALz++utYv349PvvsMygUCmzYsAEXLlxAWFgYOnXqZLHOEhERETUlZidaWVlZcHZ2BgBcvnwZ48aNAwAolUqUlJRAIpEgOjoaW7dutUxPiYiIiJoYsxOtkSNH4ubNmwCANm3aoLi4GADQoUMHnD17FkDVgqW3bt1q/F4SERERNUFm3wzft29fyOVyAMD/+3//D4cPH0bv3r0RFhaG5557DocPH0ZqaipGjRplsc7Sg0OrLUN2drZBmYODA9q1a2elHhERET14zE607lyk9O2330ZpaSkAIDY2FnK5HMePH8cTTzzBdx22AOXlhcjO/gULFqyBUqnUlzs7K7FnzxYmW0RERP9Vr+UdNBoNAEClUkGlUum3IyMjERkZ2fi9owdSRUUxdDoFFIpoODl1AwCUll5BYeFb0Gg0TLSIiIj+q16JlpOTEyQSyV3jKioqGtwhajpUqo6ws/PRb5eVWbEzRERED6B6JVpHjhzR/1kIgXHjxuGf//wnOnTo0OgdIyIiImrq6pVoDRs2zGBbKpVi0KBB6NKlS6N2ioiIiKg54LsOiYiIiCyEiRYRERGRhdxzomXOzfFERERELVG97tF64oknDLZv376NyMhI2NnZGZTv37//3ntGRERE1MTVK9FydHQ02P7rX//aqJ0hIiIiak7qlWht27bNUv0gIiIianZ4MzwRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgRERERWQgTLSIiIiILYaJFREREZCFMtIiIiIgsxOqJ1ubNm+Ht7Q2VSgV/f38cO3aszvijR4/C398fKpUKXbp0QXx8vFFMUlISfH19oVQq4evri+Tk5Hq3u3//foSEhMDFxQUSiQSnTp0yqmP48OGQSCQGn6lTp9bvABAREVGzZdVEa9++fYiKisLSpUuRmZmJIUOGIDQ0FDk5OSbjs7KyMG7cOAwZMgSZmZlYsmQJFi5ciKSkJH2MWq1GeHg4IiIicPr0aURERCAsLAwnTpyoV7slJSUYPHgw1qxZU+cY5s6di9zcXP3n3XffvcejQkRERM2FVROtdevWYfbs2ZgzZw569uyJuLg4eHp6YsuWLSbj4+Pj0alTJ8TFxaFnz56YM2cOZs2ahTfffFMfExcXhzFjxiA2NhY9evRAbGwsRo0ahbi4uHq1GxERgZdffhmjR4+ucwytWrWCm5ub/lPzfZBERETUctXrXYeNqby8HOnp6Vi8eLFBeXBwMNLS0kzuo1arERwcbFAWEhKChIQEaLVayOVyqNVqREdHG8VUJ1oNabcuu3fvxq5du+Dq6orQ0FCsWLEC9vb2tcaXlZWhrKxMv63RaAAAOp0OOp2u3u3XprKyEjKZFDJZJaTSqnplMgGFQq4vq7nd0JiqskoAFfj1119RWVkJALC3t4eLi0ujjYmIiOhBYe5vttUSrYKCAlRUVMDV1dWg3NXVFXl5eSb3ycvLMxmv0+lQUFAAd3f3WmOq62xIu7WZPn06vL294ebmhrNnzyI2NhanT59GampqrfusXr0ar7zyilH5yZMnYWdnV6/261JaWopp00Igk2VDKs0HAGi1pQgNnYHWrfMglxcbbTc0BgB0Og2Ki0fhxx//gzNnfgIAyOU28PXtBoVC0WjjIiIiehCUlJSYFWe1RKuaRCIx2BZCGJXdLb5muTl11rddU+bOnav/s5+fH7p27YqAgABkZGRgwIABJveJjY1FTEyMfluj0cDT0xMBAQFwcHCoV/t1ycrKwpIlG+HkNBqtWnkDAAoLj+LMmR3o3XsnnJ17GW03NOZ/ZTvRrdtqODl1RWnpVZSVbcDu3SPh7e3daOMiIiJ6EFRfkbobqyVaLi4ukEqlRrNI+fn5RrNN1dzc3EzGy2QyODs71xlTXWdD2jXXgAEDIJfLcenSpVoTLaVSCaVSaVQuk8kgkzXe6bCxsYFOVwGdzgYVFVX16nQSlJdr9WU1txsac2eZVOoJpbIrdDoblJRUwMbGplHHRURE9CAw97fNajfDKxQK+Pv7G11mS01NRVBQkMl9AgMDjeIPHjyIgIAAyOXyOmOq62xIu+Y6d+4ctFot3N3d76keIiIiah6sOtUQExODiIgIBAQEIDAwEFu3bkVOTg4iIyMBVF1mu3btGnbu3AkAiIyMxMaNGxETE4O5c+dCrVYjISEBe/fu1df53HPPYejQoVi7di0mTpyITz75BIcOHcLx48fNbhcA/vjjD+Tk5OD69esAgIsXLwKA/unCy5cvY/fu3Rg3bhxcXFxw/vx5LFq0CP3798fgwYMtfuyIiIjowWfVRCs8PByFhYVYtWoVcnNz4efnh5SUFHh5eQEAcnNzDda28vb2RkpKCqKjo7Fp0yZ4eHjg7bffxqRJk/QxQUFBSExMxLJly7B8+XL4+Phg3759GDhwoNntAsCBAwfw9NNP67erFyJdsWIFVq5cCYVCga+++gobNmxAcXExPD098eijj2LFihWQSqUWO2ZERETUdFj95pn58+dj/vz5Jr/bvn27UdmwYcOQkZFRZ52TJ0/G5MmTG9wuAMycORMzZ86s9XtPT08cPXq0zjaIiIioZbP6K3iIiIiImismWkREREQWwkSLiIiIyEKYaBERERFZCBMtIiIiIgthokVERERkIUy0iIiIiCyEiRYRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgRERERWQgTLSIiIiILkVm7A9R8abVlyM7ONihzcHBAu3btrNQjIiKi+4uJFllEeXkhsrN/wYIFa6BUKvXlzs5K7NmzhckWERG1CEy0yCIqKoqh0ymgUETDyakbAKC09AoKC9+CRqNhokVERC0CEy2yKJWqI+zsfPTbZWVW7AwREdF9xpvhiYiIiCyEiRYRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgRERERWQgTLSIiIiILYaJFREREZCFMtIiIiIgshIkWERERkYUw0SIiIiKyECZaRERERBbCRIuIiIjIQmTW7gC1LFptGbKzs/XbDg4OaNeunRV7REREZDlMtOi+KS8vRHb2L1iwYA2USiUAwNlZiT17tjDZIiKiZomXDum+qagohk6ngEIRDSenOCiVi1BYWAaNRmPtrhEREVkEZ7TovlOpOsLOzgcAUFZm5c4QERFZkNVntDZv3gxvb2+oVCr4+/vj2LFjdcYfPXoU/v7+UKlU6NKlC+Lj441ikpKS4OvrC6VSCV9fXyQnJ9e73f379yMkJAQuLi6QSCQ4deqUUR1lZWVYsGABXFxcYGdnhwkTJuDq1av1OwBERETUbFk10dq3bx+ioqKwdOlSZGZmYsiQIQgNDUVOTo7J+KysLIwbNw5DhgxBZmYmlixZgoULFyIpKUkfo1arER4ejoiICJw+fRoREREICwvDiRMn6tVuSUkJBg8ejDVr1tTa/6ioKCQnJyMxMRHHjx9HcXExxo8fj4qKikY4OkRERNTUWTXRWrduHWbPno05c+agZ8+eiIuLg6enJ7Zs2WIyPj4+Hp06dUJcXBx69uyJOXPmYNasWXjzzTf1MXFxcRgzZgxiY2PRo0cPxMbGYtSoUYiLi6tXuxEREXj55ZcxevRok30pKipCQkIC3nrrLYwePRr9+/fHrl27cObMGRw6dKhxDhARERE1aVa7R6u8vBzp6elYvHixQXlwcDDS0tJM7qNWqxEcHGxQFhISgoSEBGi1WsjlcqjVakRHRxvFVCdaDWnXlPT0dGi1WoP+eHh4wM/PD2lpaQgJCTG5X1lZGcruuDGp+kZwnU4HnU5ndvt3U1lZCZlMCpmsElJpVb0ymYBCIdeX1dxuaEzD667qY2VlZaOOnYiIyNLM/d2yWqJVUFCAiooKuLq6GpS7uroiLy/P5D55eXkm43U6HQoKCuDu7l5rTHWdDWm3tr4oFAq0adOmXvWsXr0ar7zyilH5yZMnYWdnZ3b7d1NaWopp00Igk2VDKs0HAGi1pQgNnYHWrfMglxcbbTc0pqH7VVSUQqcLQXZ2NvLz8xtt7ERERJZWUlJiVpzVnzqUSCQG20IIo7K7xdcsN6fO+rZrrrvVExsbi5iYGP22RqOBp6cnAgIC4ODgcM/tV8vKysKSJRvh5DQarVp5AwAKC4/izJkd6N17J5ydexltNzSmofvdupWFmzc3Yvfu0fD29m60sRMREVmauUsTWS3RcnFxgVQqNZr9yc/PN5ptqubm5mYyXiaTwdnZuc6Y6job0m5tfSkvL8eNGzcMZrXy8/MRFBRU635KpVK/WOedZDIZZLLGOx02NjbQ6Sqg09mgoqKqXp1OgvJyrb6s5nZDYxped1UfbWxsGnXsRERElmbu75bVboZXKBTw9/dHamqqQXlqamqtiUpgYKBR/MGDBxEQEAC5XF5nTHWdDWnXFH9/f8jlcoN6cnNzcfbs2XrVQ0RERM2XVacRYmJiEBERgYCAAAQGBmLr1q3IyclBZGQkgKrLbNeuXcPOnTsBAJGRkdi4cSNiYmIwd+5cqNVqJCQkYO/evfo6n3vuOQwdOhRr167FxIkT8cknn+DQoUM4fvy42e0CwB9//IGcnBxcv34dAHDx4kUAVTNZbm5ucHR0xOzZs7Fo0SI4Ozujbdu2eP7559G7d+9an1QkIiKilsWqiVZ4eDgKCwuxatUq5Obmws/PDykpKfDy8gJQNUN059pW3t7eSElJQXR0NDZt2gQPDw+8/fbbmDRpkj4mKCgIiYmJWLZsGZYvXw4fHx/s27cPAwcONLtdADhw4ACefvpp/fbUqVMBACtWrMDKlSsBAOvXr4dMJkNYWBhKS0sxatQobN++HVKp1CLHqzmq+ZJpgC+aJiKi5sPqN8bMnz8f8+fPN/nd9u3bjcqGDRuGjIyMOuucPHkyJk+e3OB2AWDmzJmYOXNmnXWoVCq88847eOedd+qMI9NMvWQa4IumiYio+bB6okUtl+FLprsBAEpLr6Cw8C1oNBomWkRE1OQx0SKru/Ml0wBfNE1ERM2H1V8qTURERNRcMdEiIiIishAmWkREREQWwkSLiIiIyEKYaBERERFZCBMtIiIiIgthokVERERkIUy0iIiIiCyEiRYRERGRhTDRIiIiIrIQvoKHHjhabRmys7P12w4ODnzvIRERNUlMtOiBUl5eiOzsX7BgwRoolUoAgLOzEnv2bGGyRURETQ4vHdIDpaKiGDqdAgpFNJyc4qBULkJhYRk0Go21u0ZERFRvnNGiB5JK1RF2dj4AgLIyK3eGiIiogTijRURERGQhTLSIiIiILISJFhEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEK4vAM98GquFA9wtXgiImoamGjRA83USvEAV4snIqKmgYkWPdAMV4rvBgAoLb2CwsK3oNFomGgREdEDjYkWNQl3rhQPcLV4IiJqGngzPBEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEKYaBERERFZCJ86pCap5iKmXMCUiIgeREy0qMkxtYgpFzAlIqIHES8dUpNjuIhpHJTKRSgsLINGo7F214iIiAxYPdHavHkzvL29oVKp4O/vj2PHjtUZf/ToUfj7+0OlUqFLly6Ij483iklKSoKvry+USiV8fX2RnJxc73aFEFi5ciU8PDxga2uL4cOH49y5cwYxw4cPh0QiMfhMnTq1AUeBGqJ6EVNbW09rd4WIiMgkqyZa+/btQ1RUFJYuXYrMzEwMGTIEoaGhyMnJMRmflZWFcePGYciQIcjMzMSSJUuwcOFCJCUl6WPUajXCw8MRERGB06dPIyIiAmFhYThx4kS92n3jjTewbt06bNy4ET/88APc3NwwZswY/PnnnwZ9mjt3LnJzc/Wfd999t5GPEhERETVVVk201q1bh9mzZ2POnDno2bMn4uLi4OnpiS1btpiMj4+PR6dOnRAXF4eePXtizpw5mDVrFt588019TFxcHMaMGYPY2Fj06NEDsbGxGDVqFOLi4sxuVwiBuLg4LF26FE888QT8/PywY8cO3Lp1C3v27DHoU6tWreDm5qb/ODo6Nv6BIiIioibJajfDl5eXIz09HYsXLzYoDw4ORlpamsl91Go1goODDcpCQkKQkJAArVYLuVwOtVqN6Ohoo5jqRMucdrOyspCXl2fQllKpxLBhw5CWloZ58+bpy3fv3o1du3bB1dUVoaGhWLFiBezt7Wsdd1lZGcrueFFf9X1FOp0OOp2u1v3qq7KyEjKZFDJZJaTSqnplMgGFQq4vq7nd0BhL1m1eTNVYKysrG/UYEhER1cbc3xurJVoFBQWoqKiAq6urQbmrqyvy8vJM7pOXl2cyXqfToaCgAO7u7rXGVNdpTrvV/2sq5s4lBaZPnw5vb2+4ubnh7NmziI2NxenTp5GamlrruFevXo1XXnnFqPzkyZOws7Ordb/6Ki0txbRpIZDJsiGV5gMAtNpShIbOQOvWeZDLi422GxpjybrNiamoKIVWOwYXL140OD9SqRQKhaLRjikREVG1kpISs+KsvryDRCIx2BZCGJXdLb5muTl1NkbM3Llz9X/28/ND165dERAQgIyMDAwYMMBk/2NjYxETE6Pf1mg08PT0REBAABwcHEzu0xBZWVlYsmQjnJxGo1UrbwBAYeFRnDmzA71774Szcy+j7YbGWLJuc2Ju3kzH2bMb0bGjt0Fi5eysxLZtG+Di4tJox5WIiAiA2U+6Wy3RcnFxgVQqNZq9ys/PN5pJqubm5mYyXiaTwdnZuc6Y6jrNadfNzQ1A1cyWu7u7WX0DgAEDBkAul+PSpUu1JlpKpVK/9tOdZDIZZLLGOx02NjbQ6Sqg09mgoqKqXp1OgvJyrb6s5nZDYyxZtzkxZWUluHVLAolkAVq37gYAKC29gt9+ewslJSX680lERNRYzP3NttrN8AqFAv7+/kaX2VJTUxEUFGRyn8DAQKP4gwcPIiAgAHK5vM6Y6jrNabf6cuCdMeXl5Th69GitfQOAc+fOQavVGiRndP9UL/fAJR+IiOhBYdVLhzExMYiIiEBAQAACAwOxdetW5OTkIDIyEkDVZbZr165h586dAIDIyEhs3LgRMTExmDt3LtRqNRISErB37159nc899xyGDh2KtWvXYuLEifjkk09w6NAhHD9+3Ox2JRIJoqKi8Prrr6Nr167o2rUrXn/9dbRq1QrTpk0DAFy+fBm7d+/GuHHj4OLigvPnz2PRokXo378/Bg8efL8OIRERET3ArJpohYeHo7CwEKtWrUJubi78/PyQkpICLy8vAEBubq7B2lbe3t5ISUlBdHQ0Nm3aBA8PD7z99tuYNGmSPiYoKAiJiYlYtmwZli9fDh8fH+zbtw8DBw40u10AePHFF1FaWor58+fjxo0bGDhwIA4ePKh/olChUOCrr77Chg0bUFxcDE9PTzz66KNYsWIFpFKppQ8dERERNQFWvxl+/vz5mD9/vsnvtm/fblQ2bNgwZGRk1Fnn5MmTMXny5Aa3C1TNaq1cuRIrV640+b2npyeOHj1aZxtERETUslk90SKyFK22zGC5BwcHB750moiI7ismWtQslZcXIjv7FyxYsEb/lKezsxJ79mxhskVERPeN1V8qTWQJFRXF0OkUUCii4eQUB6VyEQoLy8xe94SIiKgxcEaLmrXqJR8A4I43HxEREd0XnNEiIiIishDOaFGLUfPmeIA3yBMRkWUx0aIWwdTN8QBvkCciIstiokUtguHN8f97H2Jh4VvQaDRMtIiIyCKYaFGLcufN8QBvkCciIsvizfBEREREFsIZLWrRuHo8ERFZEhMtarG4ejwREVkaLx1Si8XV44mIyNI4o0UtHlePJyIiS2GiRXQHLmpKRESNiYkW0X9xUVMiImpsTLSI/ouLmhIRUWNjokVUQ81FTYuLuQQEERE1DBMtojpwCQgiIroXXN6BqA5cAoKIiO4FZ7SIzHDn5cSalxIBXk4kIiLTmGgR1QOfTCQiovpgokVUD3wykYiI6oOJFlED8MlEIiIyBxMtonvEJxOJiKg2TLSI7lHNy4mlpVeQl/c6zpw5Ay8vL30cZ7mIiFoeJlpEjaT6cmJtN8zb2wP/+MdyODs7A2DiRUTUEjDRImpkpm6Y12jOIDPzeTz99DJeXiQiakGYaBFZyJ03zJeWZvPyIhFRC8REi+g+4uVFIqKWhYkWkRWYe3mxZuIFMPkiImpKmGgRWVFdlxdNJV4AZ72IiJoSJlpED5jq5Ktm4gVw1ouIqKmxsXYHNm/eDG9vb6hUKvj7++PYsWN1xh89ehT+/v5QqVTo0qUL4uPjjWKSkpLg6+sLpVIJX19fJCcn17tdIQRWrlwJDw8P2NraYvjw4Th37pxBTFlZGRYsWAAXFxfY2dlhwoQJuHr1agOOAlHtqhMvOzsfyOUOdyRfcbCxmY3MzAt4+ullmDIlSv+ZPHkWvv/+e1y+fBmXL1/GhQsX9H+u/vz+++/WHhoRUbNn1Rmtffv2ISoqCps3b8bgwYPx7rvvIjQ0FOfPn0enTp2M4rOysjBu3DjMnTsXu3btwrfffov58+ejXbt2mDRpEgBArVYjPDwc//d//4fHH38cycnJCAsLw/HjxzFw4ECz233jjTewbt06bN++Hd26dcOrr76KMWPG4OLFi7C3twcAREVF4dNPP0ViYiKcnZ2xaNEijB8/Hunp6ZBKpffpKFJLVJ9ZL622DNevZ6FDh4cgk/3vn3zNmbDy8nIoFAqDdjgzRkR0b6yaaK1btw6zZ8/GnDlzAABxcXH48ssvsWXLFqxevdooPj4+Hp06dUJcXBwAoGfPnjh58iTefPNNfaIVFxeHMWPGIDY2FgAQGxuLo0ePIi4uDnv37jWrXSEE4uLisHTpUjzxxBMAgB07dsDV1RV79uzBvHnzUFRUhISEBHzwwQcYPXo0AGDXrl3w9PTEoUOHEBISYrkDR1RDXfd63bjxHUpLX4NUutAiyVjNMiZsRET/Y7VEq7y8HOnp6Vi8eLFBeXBwMNLS0kzuo1arERwcbFAWEhKChIQEaLVayOVyqNVqREdHG8VUJ2fmtJuVlYW8vDyDtpRKJYYNG4a0tDTMmzcP6enp0Gq1BjEeHh7w8/NDWloaEy2yujtnve7cBhovGatZZumE7X7GMDkkosZgtUSroKAAFRUVcHV1NSh3dXVFXl6eyX3y8vJMxut0OhQUFMDd3b3WmOo6zWm3+n9NxWRnZ+tjFAoF2rRpY3b/gar7usrKyvTbRUVFAIA//vgDOp2u1v3qS6PRQCKpRGnpBQAaAEB5+WXI5TYoL7+IkhKd0XZDYyxZN2MsG2NjUwJAAxubWwbbACDE75BIVJBIJkCh8EB5+X+g011HZeWjUCg8/luPYZmpmNLSX3HmTDxmz14KhUIBna4ceXk5cHf31l9ir1lm7RgAsLeX4OWXY4z+jRNR0+Lo6AgnJ6dGr1ejqf5vpag7UFjJtWvXBACRlpZmUP7qq6+K7t27m9yna9eu4vXXXzcoO378uAAgcnNzhRBCyOVysWfPHoOYXbt2CaVSaXa73377rQAgrl+/bhAzZ84cERISIoQQYvfu3UKhUBj1cfTo0WLevHm1jnvFihUCAD/88MMPP/zw0ww+V65cqfU3XwghrDaj5eLiAqlUajT7k5+fbzSTVM3Nzc1kvEwm01+SqC2muk5z2nVzcwNQNWvl7u5ea0x5eTlu3Lhh8P948/PzERQUVOu4Y2NjERMTo9+urKzEH3/8AWdnZ0gkklr3qy+NRgNPT09cuXIFDg4OjVbvg6oljbcljRVoWeNtSWMFON7mrCWMVQiBP//8Ex4eHnXGWS3RUigU8Pf3R2pqKh5//HF9eWpqKiZOnGhyn8DAQHz66acGZQcPHkRAQADkcrk+JjU11eA+rYMHD+qTH3Pa9fb2hpubG1JTU9G/f38AVfdwHD16FGvXrgUA+Pv7Qy6XIzU1FWFhYQCA3NxcnD17Fm+88Uat41YqlQaLTwKwyJRmNQcHh2b7l9yUljTeljRWoGWNtyWNFeB4m7PmPlZHR8e7B9U532VhiYmJQi6Xi4SEBHH+/HkRFRUl7OzsxK+//iqEEGLx4sUiIiJCH//LL7+IVq1aiejoaHH+/HmRkJAg5HK5+Oijj/Qx3377rZBKpWLNmjXiwoULYs2aNUImk4nvvvvO7HaFEGLNmjXC0dFR7N+/X5w5c0Y8+eSTwt3dXWg0Gn1MZGSk6Nixozh06JDIyMgQI0eOFH379hU6nc6Sh80sRUVFAoAoKiqydlfui5Y03pY0ViFa1nhb0liF4Hibs5Y01ruxaqIlhBCbNm0SXl5eQqFQiAEDBoijR4/qv5sxY4YYNmyYQfzXX38t+vfvLxQKhejcubPYsmWLUZ0ffvih6N69u5DL5aJHjx4iKSmpXu0KIURlZaVYsWKFcHNzE0qlUgwdOlScOXPGIKa0tFQ8++yzom3btsLW1laMHz9e5OTk3MPRaDwt7S95SxpvSxqrEC1rvC1prEJwvM1ZSxrr3Vg90SLLuH37tlixYoW4ffu2tbtyX7Sk8baksQrRssbbksYqBMfbnLWksd6NRIi7PZdIRERERA1h9XcdEhERETVXTLSIiIiILISJFhEREZGFMNEiIiIishAmWs3U5s2b4e3tDZVKBX9/fxw7dszaXarTypUrIZFIDD7VK/QDVSvwrly5Eh4eHrC1tcXw4cNx7tw5gzrKysqwYMECuLi4wM7ODhMmTMDVq1cNYm7cuIGIiAg4OjrC0dERERERuHnzpsXH98033+Avf/kLPDw8IJFI8PHHHxt8fz/Hl5OTg7/85S+ws7ODi4sLFi5ciPLy8vs21pkzZxqd60GDBjXJsa5evRoPP/ww7O3t0b59ezz22GO4ePGiQUxzOrfmjLe5nN8tW7agT58++gU3AwMD8fnnn+u/b07n1ZzxNpfzahXWfOSRLKN6Qdb33ntPnD9/Xjz33HPCzs5OZGdnW7trtVqxYoXo1auXyM3N1X/y8/P1369Zs0bY29uLpKQkcebMGREeHm5yAdkOHTqI1NRUkZGRIUaMGGG0gOzYsWOFn5+fSEtLE2lpacLPz0+MHz/e4uNLSUkRS5cuFUlJSQKASE5ONvj+fo1Pp9MJPz8/MWLECJGRkSFSU1OFh4eHePbZZ+/bWGfMmCHGjh1rcK4LCwsNYprKWENCQsS2bdvE2bNnxalTp8Sjjz4qOnXqJIqLi/UxzencmjPe5nJ+Dxw4IP7973+LixcviosXL4olS5YIuVwuzp49K4RoXufVnPE2l/NqDUy0mqFHHnlEREZGGpT16NFDLF682Eo9ursVK1aIvn37mvyusrJSuLm5iTVr1ujLbt++LRwdHUV8fLwQQoibN28KuVwuEhMT9THXrl0TNjY24osvvhBCCHH+/HkBwOAtAWq1WgAQ//nPfywwKtNqJh/3c3wpKSnCxsZGXLt2TR+zd+9eoVQqLbKwYG2J1sSJE2vdp6mOVQgh8vPzBQD9AsjN+dyaGq8Qzfv8tmnTRvzzn/9s9ue15niFaN7n1dJ46bCZKS8vR3p6OoKDgw3Kg4ODkZaWZqVemefSpUvw8PCAt7c3pk6dil9++QUAkJWVhby8PIMxKZVKDBs2TD+m9PR0aLVagxgPDw/4+fnpY9RqNRwdHTFw4EB9zKBBg+Do6GjVY3M/x6dWq+Hn52fwEtSQkBCUlZUhPT3douO809dff4327dujW7dumDt3LvLz8/XfNeWxFhUVAQDatm0LoPmf25rjrdbczm9FRQUSExNRUlKCwMDAZn9ea463WnM7r/eL1V4qTZZRUFCAiooKuLq6GpS7uroiLy/PSr26u4EDB2Lnzp3o1q0bfvvtN7z66qsICgrCuXPn9P02Nabs7GwAQF5eHhQKBdq0aWMUU71/Xl4e2rdvb9R2+/btrXps7uf48vLyjNpp06YNFArFfTsGoaGhmDJlCry8vJCVlYXly5dj5MiRSE9Ph1KpbLJjFUIgJiYG/+///T/4+fnp+1Dd95pjaern1tR4geZ1fs+cOYPAwEDcvn0brVu3RnJyMnx9ffVJQXM7r7WNF2he5/V+Y6LVTEkkEoNtIYRR2YMkNDRU/+fevXsjMDAQPj4+2LFjh/6Gy4aMqWaMqfgH5djcr/FZ+xiEh4fr/+zn54eAgAB4eXnh3//+N5544ola93vQx/rss8/ixx9/xPHjx42+a47ntrbxNqfz2717d5w6dQo3b95EUlISZsyYgaNHj9baflM/r7WN19fXt1md1/uNlw6bGRcXF0ilUqPMPz8/3+j/JTzI7Ozs0Lt3b1y6dEn/9GFdY3Jzc0N5eTlu3LhRZ8xvv/1m1Nbvv/9u1WNzP8fn5uZm1M6NGzeg1Wqtdgzc3d3h5eWFS5cuAWiaY12wYAEOHDiAI0eOoGPHjvry5npuaxuvKU35/CoUCjz00EMICAjA6tWr0bdvX2zYsKHZntfaxmtKUz6v9xsTrWZGoVDA398fqampBuWpqakICgqyUq/qr6ysDBcuXIC7uzu8vb3h5uZmMKby8nIcPXpUPyZ/f3/I5XKDmNzcXJw9e1YfExgYiKKiInz//ff6mBMnTqCoqMiqx+Z+ji8wMBBnz55Fbm6uPubgwYNQKpXw9/e36DhrU1hYiCtXrsDd3R1A0xqrEALPPvss9u/fj8OHD8Pb29vg++Z2bu82XlOa8vmtSQiBsrKyZnde7zZeU5rTebW4+3DDPd1n1cs7JCQkiPPnz4uoqChhZ2cnfv31V2t3rVaLFi0SX3/9tfjll1/Ed999J8aPHy/s7e31fV6zZo1wdHQU+/fvF2fOnBFPPvmkyUepO3bsKA4dOiQyMjLEyJEjTT5a3KdPH6FWq4VarRa9e/e+L8s7/PnnnyIzM1NkZmYKAGLdunUiMzNTv+TG/Rpf9aPTo0aNEhkZGeLQoUOiY8eOjfrodF1j/fPPP8WiRYtEWlqayMrKEkeOHBGBgYGiQ4cOTXKszzzzjHB0dBRff/21wWPvt27d0sc0p3N7t/E2p/MbGxsrvvnmG5GVlSV+/PFHsWTJEmFjYyMOHjwohGhe5/Vu421O59UamGg1U5s2bRJeXl5CoVCIAQMGGDx+/SCqXoNGLpcLDw8P8cQTT4hz587pv6+srBQrVqwQbm5uQqlUiqFDh4ozZ84Y1FFaWiqeffZZ0bZtW2FrayvGjx8vcnJyDGIKCwvF9OnThb29vbC3txfTp08XN27csPj4jhw5IgAYfWbMmHHfx5ednS0effRRYWtrK9q2bSueffZZcfv27fsy1lu3bong4GDRrl07IZfLRadOncSMGTOMxtFUxmpqnADEtm3b9DHN6dzebbzN6fzOmjVL/9/Qdu3aiVGjRumTLCGa13m923ib03m1BokQQty/+TMiIiKiloP3aBERERFZCBMtIiIiIgthokVERERkIUy0iIiIiCyEiRYRERGRhTDRIiIiIrIQJlpEREREFsJEi4iIiMhCmGgR0QNh+/btcHJyskjdEokEH3/8caPW2blzZ8TFxdUZ8+uvv0IikeDUqVNYuXIl+vXrZ/D9zJkz8dhjjzVqv6odPnwYPXr0QGVlpUXqr4+ysjJ06tQJ6enp1u4K0X3HRIuIGkV+fj7mzZuHTp06QalUws3NDSEhIVCr1dbumtV4enoiNzcXfn5+eP755/HVV1/dt7ZffPFFLF26FDY2Vf+Z3759OyQSidFHpVJZvC9KpRLPP/88XnrpJYu3RfSgkVm7A0TUPEyaNAlarRY7duxAly5d8Ntvv+Grr77CH3/8Ye2uWY1UKoWbmxsAoHXr1mjduvV9aTctLQ2XLl3ClClTDModHBxw8eJFgzKJRHJPbWm1Wsjl8rvGTZ8+HS+88AIuXLiAnj173lObRE0JZ7SI6J7dvHkTx48fx9q1azFixAh4eXnhkUceQWxsLB599FGDuL/97W9wdXWFSqWCn58fPvvsM4O6vvzyS/Ts2ROtW7fG2LFjkZubq//uhx9+wJgxY+Di4gJHR0cMGzYMGRkZBvtfunQJQ4cOhUqlgq+vL1JTU436e+3aNYSHh6NNmzZwdnbGxIkT8euvv+q/r76k9+abb8Ld3R3Ozs74+9//Dq1Wa1DPrVu3MGvWLNjb26NTp07YunWrwfdnzpzByJEjYWtrC2dnZ/ztb39DcXGxUX/qaqe8vBwvvvgiOnToADs7OwwcOBBff/117ScDQGJiIoKDg41mqyQSCdzc3Aw+rq6u+u9NXQ7t168fVq5caVBHfHw8Jk6cCDs7O7z66qsAgC1btsDHxwcKhQLdu3fHBx98YFCPs7MzgoKCsHfv3jr7TtTcMNEiontWPVvz8ccfo6yszGRMZWUlQkNDkZaWhl27duH8+fNYs2YNpFKpPubWrVt488038cEHH+Cbb75BTk4Onn/+ef33f/75J2bMmIFjx47hu+++Q9euXTFu3Dj8+eef+jaeeOIJSKVSfPfdd4iPjze6XHXr1i2MGDECrVu3xjfffIPjx4/rk7ry8nJ93JEjR3D58mUcOXIEO3bswPbt27F9+3aDut566y0EBAQgMzMT8+fPxzPPPIP//Oc/+nbGjh2LNm3a4IcffsCHH36IQ4cO4dlnnzWo427tPP300/j222+RmJiIH3/8EVOmTMHYsWNx6dKlWs/HN998g4CAgFq/v1crVqzAxIkTcebMGcyaNQvJycl47rnnsGjRIpw9exbz5s3D008/jSNHjhjs98gjj+DYsWMW6xfRA0kQETWCjz76SLRp00aoVCoRFBQkYmNjxenTp/Xff/nll8LGxkZcvHjR5P7btm0TAMTPP/+sL9u0aZNwdXWttU2dTifs7e3Fp59+qm9DKpWKK1eu6GM+//xzAUAkJycLIYRISEgQ3bt3F5WVlfqYsrIyYWtrK7788kshhBAzZswQXl5eQqfT6WOmTJkiwsPD9dteXl7ir3/9q367srJStG/fXmzZskUIIcTWrVtFmzZtRHFxsT7m3//+t7CxsRF5eXlmtfPzzz8LiUQirl27ZjDuUaNGidjY2FqPi6Ojo9i5c6dBWfXxtbOzM/iMGTPGYEzr16832K9v375ixYoV+m0AIioqyiAmKChIzJ0716BsypQpYty4cQZlGzZsEJ07d66130TNEWe0iKhRTJo0CdevX8eBAwcQEhKCr7/+GgMGDNDPzpw6dQodO3ZEt27daq2jVatW8PHx0W+7u7sjPz9fv52fn4/IyEh069YNjo6OcHR0RHFxMXJycgAAFy5cQKdOndCxY0f9PoGBgQZtpKen4+eff4a9vb1+Jq5t27a4ffs2Ll++rI/r1auXwWxbzb4AQJ8+ffR/rr4sVx1z4cIF9O3bF3Z2dvqYwYMHo7Ky0uA+qbraycjIgBAC3bp10/e1devWOHr0qEFfayotLTV5k7u9vT1OnTpl8Nm2bVut9dSm5mzZhQsXMHjwYIOywYMH48KFCwZltra2uHXrVr3bI2rKeDM8ETUalUqFMWPGYMyYMXj55ZcxZ84crFixAjNnzoStre1d9695U7VEIoEQQr89c+ZM/P7774iLi4OXlxeUSiUCAwP1l/zujL2zjjtVVlbC398fu3fvNopt165dnX2puVRCXTFCiFpvNL+zvK46KisrIZVKkZ6ebpCMAajzxnoXFxfcuHHDqNzGxgYPPfRQrfvZ2NgYHcOa96UBMEge7+z3nUyN/48//jA4xkQtAWe0iMhifH19UVJSAqBq9ufq1av46aefGlzfsWPHsHDhQowbNw69evWCUqlEQUGBQXs5OTm4fv26vqzm8hIDBgzApUuX0L59ezz00EMGH0dHxwb3rSZfX1+cOnVKP34A+Pbbb2FjY1PnrN6d+vfvj4qKCuTn5xv1tfppxtr2O3/+fL373K5dO4OHDzQaDbKysu66X8+ePXH8+HGDsrS0NKOnC8+ePYv+/fvXu19ETRkTLSK6Z4WFhRg5ciR27dqFH3/8EVlZWfjwww/xxhtvYOLEiQCAYcOGYejQoZg0aRJSU1ORlZWFzz//HF988YXZ7Tz00EP44IMPcOHCBZw4cQLTp083mCkbPXo0unfvjqeeegqnT5/GsWPHsHTpUoM6pk+fDhcXF0ycOBHHjh1DVlYWjh49iueeew5Xr15tnAPy33ZUKhVmzJiBs2fP4siRI1iwYAEiIiIMnvSrS7du3TB9+nQ89dRT2L9/P7KysvDDDz9g7dq1SElJqXW/kJAQo8QHqJplysvLM/pUz6CNHDkSH3zwAY4dO4azZ89ixowZRjNpprzwwgvYvn074uPjcenSJaxbtw779+83eJABqEqUg4ODzRo7UXPBRIuI7lnr1q0xcOBArF+/HkOHDoWfnx+WL1+OuXPnYuPGjfq4pKQkPPzww3jyySfh6+uLF198ERUVFWa38/777+PGjRvo378/IiIisHDhQrRv317/vY2NDZKTk1FWVoZHHnkEc+bMwWuvvWZQR6tWrfDNN9+gU6dOeOKJJ9CzZ0/MmjULpaWlcHBwuPeDcUc7X375Jf744w88/PDDmDx5MkaNGmVwPMyxbds2PPXUU1i0aBG6d++OCRMm4MSJE/D09Kx1n7/+9a84f/680ZpZGo0G7u7uRp/qe8JiY2MxdOhQjB8/HuPGjcNjjz1mcM9cbR577DFs2LAB//jHP9CrVy+8++672LZtG4YPH66PUavVKCoqwuTJk+s1fqKmTiJM3dRARERN2osvvoiioiK8++671u4KAGDKlCno378/lixZYu2uEN1XnNEiImqGli5dCi8vr3rNGFpKWVkZ+vbti+joaGt3hei+44wWERERkYVwRouIiIjIQphoEREREVkIEy0iIiIiC2GiRURERGQhTLSIiIiILISJFhEREZGFMNEiIiIishAmWkREREQWwkSLiIiIyEL+Pz8iCnUzCLf+AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lage- und Streuungsmaße:\n",
      "Mittlerer Schaden: 2358.45 Euro\n",
      "Standardabweichung: 2362.62 Euro\n",
      "Maximaler Schaden: 37886.00 Euro\n",
      "Minimaler Schaden: 0.01 Euro\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# gegebene Parameter\n",
    "anzahl_schaeden = 21_961_000\n",
    "gesamt_schaden = 51_792_000_000 # Euro\n",
    "n = 1_000_000 # Anzahl der Simulationen\n",
    "\n",
    "# # Simulation der Schadenshöhe (Exponentialverteilung)\n",
    "schaden = np.random.exponential(gesamt_schaden / anzahl_schaeden, n)\n",
    "\n",
    "# # Plot der Verteilung als Histogramm\n",
    "plt.hist(schaden, bins=100, density=True, alpha=0.7, color='blue', edgecolor='black')\n",
    "plt.title('Verteilung der Schadenshöhe')\n",
    "plt.xlabel('Schadenhöhe (Euro)')\n",
    "plt.ylabel('Häufigkeit')\n",
    "plt.grid(axis='y', alpha=0.75)\n",
    "plt.show()\n",
    "\n",
    "# Lage- und Streuungsmaße\n",
    "print(\"Lage- und Streuungsmaße:\")\n",
    "print(f\"Mittlerer Schaden: {np.mean(schaden):.2f} Euro\")\n",
    "print(f\"Standardabweichung: {np.std(schaden):.2f} Euro\")\n",
    "print(f\"Maximaler Schaden: {np.max(schaden):.2f} Euro\")\n",
    "print(f\"Minimaler Schaden: {np.min(schaden):.2f} Euro\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Beispiel: Gammaverteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lage- und Streuungsmaße:\n",
      "Mittlerer Schaden: 2359.38 Euro\n",
      "Standardabweichung: 1179.87 Euro\n",
      "Maximaler Schaden: 11729.62 Euro\n",
      "Minimaler Schaden: 44.03 Euro\n"
     ]
    }
   ],
   "source": [
    "# gegebene Parameter\n",
    "anzahl_schaeden = 21_961_000\n",
    "gesamt_schaden = 51_792_000_000 # Euro\n",
    "avg_schaden = gesamt_schaden / anzahl_schaeden # Durchschnittlicher Schaden\n",
    "std_schaden = avg_schaden / 2 # Standardabweichung\n",
    "n = 1_000_000 # Anzahl der Simulationen\n",
    "varianz_schaden = std_schaden ** 2 # Varianz\n",
    "\n",
    "\n",
    "# Simulation der Schadenshöhe (Gammaverteilung)\n",
    "import numpy as np\n",
    "\n",
    "# shape ist p und scale ist 1/b\n",
    "shape = (avg_schaden ** 2) / varianz_schaden\n",
    "scale = varianz_schaden / avg_schaden\n",
    "\n",
    "schaden = np.random.gamma(shape, scale, n)\n",
    "\n",
    "# Plot der Verteilung als Histogramm\n",
    "plt.hist(schaden, bins=100, density=True, alpha=0.7, color='blue', edgecolor='blue')\n",
    "plt.title('Verteilung der Schadenshöhe (Gamma-Verteilung)')\n",
    "plt.xlabel('Schadenhöhe (Euro)')\n",
    "plt.ylabel('Häufigkeit')\n",
    "plt.grid(axis='y', alpha=0.75)\n",
    "plt.show()\n",
    "\n",
    "# Lage- und Streuungsmaße\n",
    "print(\"Lage- und Streuungsmaße:\")\n",
    "print(f\"Mittlerer Schaden: {np.mean(schaden):.2f} Euro\")\n",
    "print(f\"Standardabweichung: {np.std(schaden):.2f} Euro\")\n",
    "print(f\"Maximaler Schaden: {np.max(schaden):.2f} Euro\")\n",
    "print(f\"Minimaler Schaden: {np.min(schaden):.2f} Euro\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Beispiel: Log-Normalverteilung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lage- und Streuungsmaße:\n",
      "Mittleres Jahreseinkommen: 27520.03 Euro\n",
      "Standardabweichung: 16894.37 Euro\n",
      "Maximaler Jahreseinkommen: 467172.37 Euro\n",
      "Minimaler Jahreseinkommen: 1303.06 Euro\n"
     ]
    }
   ],
   "source": [
    "# gegebene Parameter\n",
    "avg_jahreseinkommen = 27_520 # Euro\n",
    "median_jahreseinkommen = 23_460 # Euro\n",
    "n = 1_000_000 # Anzahl der Simulationen\n",
    "\n",
    "# Simulation der Jahreseinkommen (Lognormalverteilung)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Berechnung der Parameter für die Lognormalverteilung\n",
    "mu = np.log(median_jahreseinkommen)\n",
    "\n",
    "# Berechnung von sigma mit der variable mu\n",
    "sigma = np.sqrt((np.log(avg_jahreseinkommen)- mu) * 2)\n",
    "\n",
    "jahreseinkommen = np.random.lognormal(mu, sigma, n)\n",
    "\n",
    "# Plot der Verteilung als Histogramm\n",
    "plt.hist(jahreseinkommen, bins=100, density=True, alpha=0.7, color='blue', edgecolor='blue')\n",
    "plt.title('Verteilung der Jahreseinkommen (Lognormalverteilung)')\n",
    "plt.xlabel('Jahreseinkommen (Euro)')\n",
    "plt.ylabel('Häufigkeit')\n",
    "plt.grid(axis='y', alpha=0.75)\n",
    "plt.show()\n",
    "\n",
    "# Lage- und Streuungsmaße\n",
    "print(\"Lage- und Streuungsmaße:\")\n",
    "print(f\"Mittleres Jahreseinkommen: {np.mean(jahreseinkommen):.2f} Euro\")\n",
    "print(f\"Standardabweichung: {np.std(jahreseinkommen):.2f} Euro\")\n",
    "print(f\"Maximaler Jahreseinkommen: {np.max(jahreseinkommen):.2f} Euro\")\n",
    "print(f\"Minimaler Jahreseinkommen: {np.min(jahreseinkommen):.2f} Euro\")"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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