{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "75b2af97",
   "metadata": {},
   "source": [
    "# Bonsai Algorithm\n",
    "\n",
    "The [Bonsai Algorithm](10.1103/PRXQuantum.4.030314) provides a method to create a TernaryTree encoding with the same toplogy as a target quantum computer."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cccca52",
   "metadata": {},
   "source": [
    "First we'll define a RustworkX graph representing the topology of the device (this can be obtained from most quantum SDKs.)\n",
    "\n",
    "Just like the original paper, we'll use a heavy-hex layout with 36 qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "41231598",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EdgeIndices[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import rustworkx as rx\n",
    "from rustworkx import visualization as rxv\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import ferrmion as fr\n",
    "\n",
    "graph = rx.PyGraph()\n",
    "graph.add_nodes_from(range(37))\n",
    "graph.add_edges_from_no_data(\n",
    "    [\n",
    "        (0, 1),\n",
    "        (0, 2),\n",
    "        (0, 3),\n",
    "        (1, 4),\n",
    "        (2, 5),\n",
    "        (3, 6),\n",
    "        (4, 7),\n",
    "        (4, 8),\n",
    "        (5, 9),\n",
    "        (5, 10),\n",
    "        (6, 11),\n",
    "        (6, 12),\n",
    "        (7, 13),\n",
    "        (8, 14),\n",
    "        (9, 15),\n",
    "        (10, 16),\n",
    "        (11, 17),\n",
    "        (12, 18),\n",
    "        (13, 19),\n",
    "        (13, 20),\n",
    "        (14, 21),\n",
    "        (14, 22),\n",
    "        (15, 23),\n",
    "        (15, 24),\n",
    "        (16, 25),\n",
    "        (16, 26),\n",
    "        (17, 27),\n",
    "        (17, 28),\n",
    "        (18, 29),\n",
    "        (18, 30),\n",
    "        (22, 31),\n",
    "        (26, 32),\n",
    "        (30, 33),\n",
    "        (31, 34),\n",
    "        (32, 35),\n",
    "        (33, 36),\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "421fd310",
   "metadata": {},
   "source": [
    "Let's plot a diagram of the device so we can see it's right.\n",
    "\n",
    "(This bit looks complicated but it's just to plot a nice-looking diagram so you can safely itnore it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cba744b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.array([0, -1]) * np.sqrt(1 / graph.num_nodes())\n",
    "s = np.array([1 * np.sin(45), np.cos(45)]) * np.sqrt(1 / graph.num_nodes())\n",
    "q = np.array([-1 * np.sin(45), np.cos(45)]) * np.sqrt(1 / graph.num_nodes())\n",
    "pos = {\n",
    "    0: [0, 0],\n",
    "    1: q,\n",
    "    2: s,\n",
    "    3: r,\n",
    "    4: 2 * q,\n",
    "    5: 2 * s,\n",
    "    6: 2.0 * r,\n",
    "    7: 2 * q - s,\n",
    "    8: 2 * q - r,\n",
    "    9: 2 * s - r,\n",
    "    10: 2 * s - q,\n",
    "    11: 2 * r - q,\n",
    "    12: 2 * r - s,\n",
    "    13: 2 * (q - s),\n",
    "    14: 2 * q - 2 * r,\n",
    "    15: 2 * s - 2 * r,\n",
    "    16: 2 * s - 2 * q,\n",
    "    17: 2 * (r - q),\n",
    "    18: 2 * r - 2 * s,\n",
    "    19: 3 * q - 2 * s,\n",
    "    20: 2 * (q - s) + r,\n",
    "    21: 3 * q - 2 * r,\n",
    "    22: 2 * (q - r) + s,\n",
    "    23: 2 * (s - r) + s,\n",
    "    24: 2 * (s - r) + q,\n",
    "    25: 3 * s - 2 * q,\n",
    "    26: 2 * (s - q) + r,\n",
    "    27: 3 * r - 2 * q,\n",
    "    28: 2 * r - 2 * q + s,\n",
    "    29: 3 * r - 2 * s,\n",
    "    30: 2 * (r - s) + q,\n",
    "    31: 2 * q - 2 * r + 2 * s,\n",
    "    32: 2 * (s - q + r),\n",
    "    33: 2 * (r - s + q),\n",
    "    34: 2 * q - 3 * r + 2 * s,\n",
    "    35: 2 * (s - q + r) - q,\n",
    "    36: 2 * (r - s + q) - s,\n",
    "}\n",
    "pos = rx.spring_layout(graph, pos=pos, fixed={*range(graph.num_nodes())})\n",
    "rxv.mpl_draw(graph, with_labels=True, pos=pos, node_color=\"orange\", node_size=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7132ddb3",
   "metadata": {},
   "source": [
    "## Root node\n",
    "\n",
    "The root node is set as the node for which its longest path is the shortest of all the nodes' longest paths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0fab01bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtXwaZOLi4qRPnz4SEREhQUFBsnz5co/nHceRCRMmSPXq1SUsLEy6desmhw8f9ll9AQCAf/FpkLlw4YI0b95c5syZk+Pz06dPl1mzZsm8efPkm2++kdKlS0uPHj0kLS2t0OsKAAD8T7Av37xnz55myYm2xsyYMUPGjRsnffv2Nds++OADqVq1qmm5eeSRRwq5tgAAwN/47RiZhIQEOXXqlOlOcgkPD5e2bdvK1q1bc90vPT1dUlJSPBYAABCYfNoiczUaYpS2wGSl667nchIbGysxMTEFXj8UnKixn+Wp3NGpva+rfGG8R2EcAwDAj1tkrld0dLQkJye7l8TERF9XCQAAFLUgU61aNfP4yy+/eGzXdddzOQkJCZFy5cp5LAAAIDD5bZCpU6eOCSzr1693b9PxLjp7qV27dj6tGwAA8A8+HSOTmpoqR44c8Rjgu3v3bqlYsaJERkbKqFGj5LXXXpP69eubYDN+/HhzzZl+/fr5stoAAMBP+DTIxMfHS5cuXdzro0ePNo8DBgyQhQsXyksvvWSuNTN48GA5d+6cdOzYUVavXi2hoaE+rDUAAPAXPg0ynTt3NteLyY1e7Xfy5MlmAQAAsGaMDAAAwLUQZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtQgyAADAWgQZAABgLYIMAACwFkEGAABYiyADAACsRZABAADWIsgAAABrEWQAAIC1gn1dAfhW1NjP8lTu6NTe173P9bwHAAB5QYsMAACwFkEGAAAUna6ljIwMWbhwoaxfv16SkpIkMzPT4/kNGzZ4s34AAADeCzIjR440QaZ3797SpEkTCQoKyu9LAAAA+CbILF68WJYsWSK9evXyTg0AAAAKa4xMyZIlpV69etf7fgAAAL4LMi+88ILMnDlTHMfxXi0AAAAKqmupf//+2Qb0fv7559K4cWMpUaKEx3NLly69nnoAAAAUTJAJDw/3WL///vvz/04AAAC+CDILFizw9vsCAAAU/hiZu+66S86dO5dte0pKinkOAADAb4PMpk2b5NKlS9m2p6WlyZdffumtegEAAHjvOjJ79+51/7x//345deqUx9V+V69eLTVq1MjrywEAABRekGnRooW5iq8uOXUhhYWFydtvv33jNQIAAPB2kElISDDXjqlbt65s375dbrrpJo+L5FWpUkWKFy+e15cDAAAovCBTu3Zt83jlTSIBAACsudfSypUrc9yuXU6hoaHm9gV16tTxRt0AAAC8G2T69etnQsuVtyhwbdPHjh07yvLly6VChQr5fXkAAICCm369bt06ad26tXlMTk42i/7ctm1bWbVqlcTFxcmvv/4qL774Yn5fGgAAoGBbZEaOHCn/+Mc/pH379u5tXbt2Nd1KgwcPlu+//15mzJghAwcOzO9LAwAAFGyLzI8//ijlypXLtl23/fTTT+bn+vXry5kzZ+RG6fVpxo8fb8bc6PTum2++WV599VXuvA0AAK4vyLRs2VLGjBkjp0+fdm/Tn1966SXT5aQOHz4stWrVkhs1bdo0mTt3rsyePVsOHDhg1qdPn871agAAwPV1Lb333nvSt29fqVmzpjusJCYmmuvLrFixwqynpqbKuHHj5EZ9/fXX5r169+5t1qOiomTRokXmOjYAAAD5DjINGzY0tyhYu3atHDp0yL3t7rvvlmLFirlnNnmDjsPR8Tj6Pg0aNJA9e/bIV199JW+99RZnDgAA5D/IKA0s99xzj1kK0tixY81dtW+55RZz1WAdMzNlyhR57LHHct0nPT3dLC66PwAACEzXFWTWr19vlqSkpGxX+n3//fe9VTdZsmSJfPjhh/LRRx9J48aNZffu3TJq1CiJiIiQAQMG5LhPbGysxMTEiL+KGvtZnsodndq7UMoDAFCkgoyGhMmTJ0urVq2kevXq5gJ4BUUHFWurzCOPPGLWmzZtKseOHTNhJbcgEx0dLaNHj/ZokfHGwGMAABAAQWbevHmycOFC+ctf/iIF7eLFi+5xNy7axXS1+z2FhISYBQAABL58B5lLly55XAyvIPXp08eMiYmMjDRdS7t27TIDfbnYHgAAuK7ryDz99NNmzEphePvtt+XBBx+UZ599Vm699VZz24NnnnnGXBQPAAAg3y0yaWlpZkr0F198Ic2aNZMSJUp4PO/NqdFly5Y1tzvQBQAA4IaDzN69e6VFixbm53379nk8V5ADfwEAAG44yGzcuDG/uwAAAPjHGBmXI0eOyJo1a+T33383647jeLNeAAAA3g8yv/76q3Tt2tXcMqBXr15y8uRJs/2pp56SF154Ib8vBwAAUHhB5vnnnzcDfI8fPy6lSpVyb3/44Ydl9erV118TAACAgh4jozeL1C4lvft1VvXr1zdX3QUAAPDbFpkLFy54tMS4/Pbbb1xRFwAA+HeQueOOO+SDDz7wmHKttwyYPn26dOnSxdv1AwAA8F7XkgYWHewbHx9vblfw0ksvyffff29aZLZs2ZLflwMAACi8FpkmTZrIoUOHpGPHjtK3b1/T1dS/f39zH6Sbb775+msCAABQ0C0yKjw8XP761796bPv3v/8tgwcPNrcvAAAA8OsL4uV0fZn33nvPWy8HAABQeEEGAACgsBFkAACAtQgyAAAg8Af76sykqzl37pw36gMAAOD9IKMzla71/OOPP573dwYAACisILNgwYIbfS8AAACvYowMAAAoWhfEw/8nauxnefoojk7tzUcGAEABoEUGAABYiyADAACsRZABAABFa4zM4cOHZePGjZKUlCSZmZkez02YMMFbdQMAAPBukJk/f74MHTpUKleuLNWqVZOgoCD3c/ozQQYAAPhtkHnttddkypQp8vLLLxdMjQAAAApqjMzZs2floYceyu9uAAAAvg8yGmLWrl3r/ZoAAAAURNfSrFmz3D/Xq1dPxo8fL9u2bZOmTZtKiRIlPMqOGDEiv3UAAAAouCDz97//3WO9TJkysnnzZrNkpYN9CTIAAMCvgkxCQkLB1wQAAKCgx8hMnjxZLl68mG3777//bp4DAADw2yATExMjqamp2bZruNHnAAAA/DbIOI7jcRE8lz179kjFihW9VS8AAADvXRCvQoUKJsDo0qBBA48wk5GRYVpphgwZkteXAwAAKLwgM2PGDNMaM3DgQNOFFB4e7n6uZMmSEhUVJe3atbvxGgEAAHg7yAwYMMA81qlTR9q3b5/t+jEAAAB+f6+lO++80/1zWlqaXLp0yeP5cuXKeadmAAAA3h7sq7OThg8fLlWqVJHSpUubsTNZFwAAAL8NMmPGjJENGzbI3LlzJSQkRN59910zZiYiIkI++OCDgqklAACAN4LMv/71L/mv//oveeCBByQ4OFjuuOMOGTdunLz++uvy4Ycfirf9/PPP8p//+Z9SqVIlCQsLM/d3io+P9/r7AACAIhBkfvvtN6lbt657PIyuq44dO0pcXJxXK3f27Fnp0KGDGVj8+eefy/79++XNN9+kCwsAAFzfYF8NMXrvpcjISLnllltkyZIl0qZNG9NSU758efGmadOmSa1atWTBggXubTprCgAA4LpaZJ588klzFV81duxYmTNnjoSGhsrzzz9vxs9408qVK6VVq1by0EMPmcHFt912m8yfP/+q+6Snp0tKSorHAgAAAlO+W2Q0sLh069ZNfvjhB9mxY4fUq1dPmjVr5tXK/fTTT2ZQ8ejRo+WVV16Rb7/9VkaMGGEuwOe6rs2VYmNjuecTAABFRJ6DTGZmpvztb38zrSR67ZiuXbvKxIkTpXbt2mYpCPqe2iKjA4mVtsjs27dP5s2bl2uQiY6ONsHHRVtktHsKAAAU4a6lKVOmmFaRMmXKSI0aNWTmzJkybNiwAq1c9erVpVGjRh7bbr31Vjl+/Hiu++iUcB2EnHUBAABFPMjoNWJ02vWaNWtk+fLlZnCvTrfWVpOCojOWDh486LHt0KFDBdYCBAAAAjTIaCtIr169PMbH6B2wT5w4UVB1M+Nxtm3bZrqWjhw5Ih999JH84x//KPCWIAAAEGBB5o8//jCzk7LS67tcvnxZCkrr1q1l2bJlsmjRImnSpIm8+uqr5i7cjz32WIG9JwAACMDBvo7jyBNPPGHGoGS9aeSQIUPMPZdcli5d6tUK3nvvvWYBAAC47iCT0ywhvXUAAACA3weZrFfXBQAAsPLKvgAAAP6CIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtQgyAADAWgQZAABgLYIMAACwFkEGAABYiyADAACsRZABAADWIsgAAABrEWQAAIC1CDIAAMBaBBkAAGAtggwAALAWQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtawKMlOnTpWgoCAZNWqUr6sCAAD8gDVB5ttvv5V33nlHmjVr5uuqAAAAP2FFkElNTZXHHntM5s+fLxUqVPB1dQAAgJ+wIsgMGzZMevfuLd26dbtm2fT0dElJSfFYAABAYAoWP7d48WLZuXOn6VrKi9jYWImJiSnwegEAAN/z6xaZxMREGTlypHz44YcSGhqap32io6MlOTnZvehrAACAwOTXLTI7duyQpKQkuf32293bMjIyJC4uTmbPnm26kYoXL+6xT0hIiFkAAEDg8+sg07VrV/nuu+88tj355JNyyy23yMsvv5wtxAAAgKLFr4NM2bJlpUmTJh7bSpcuLZUqVcq2HQAAFD1+PUYGAADA2haZnGzatMnXVQAAAH6CFhkAAGAtggwAALAWQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtQgyAADAWgQZAABgLYIMAACwFkEGAABYiyADAACsRZABAADWIsgAAABrEWQAAIC1CDIAAMBaBBkAAGAtggwAALAWQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtfw6yMTGxkrr1q2lbNmyUqVKFenXr58cPHjQ19UCAAB+wq+DzObNm2XYsGGybds2WbdunVy+fFm6d+8uFy5c8HXVAACAHwgWP7Z69WqP9YULF5qWmR07dkinTp18Vi8AAOAf/DrIXCk5Odk8VqxYMdcy6enpZnFJSUkplLoBAIDC59ddS1llZmbKqFGjpEOHDtKkSZOrjqsJDw93L7Vq1SrUegIAgMJjTZDRsTL79u2TxYsXX7VcdHS0ablxLYmJiYVWRwAAULis6FoaPny4rFq1SuLi4qRmzZpXLRsSEmIWAAAQ+Pw6yDiOI88995wsW7ZMNm3aJHXq1PF1lQAAgB8J9vfupI8++khWrFhhriVz6tQps13HvoSFhfm6egAAwMf8eozM3LlzzTiXzp07S/Xq1d3Lxx9/7OuqAQAAP+D3XUsAAABWtsgAAABcDUEGAABYiyADAACsRZABAADWIsgAAABrEWQAAIC1CDIAAMBaBBkAAGAtggwAALAWQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtQgyAADAWgQZAABgLYIMAACwFkEGAABYiyADAACsRZABAADWIsgAAABrEWQAAIC1CDIAAMBaBBkAAGAtggwAALAWQQYAAFiLIAMAAKxFkAEAANYiyAAAAGsRZAAAgLUIMgAAwFpWBJk5c+ZIVFSUhIaGStu2bWX79u2+rhIAAPADfh9kPv74Yxk9erRMnDhRdu7cKc2bN5cePXpIUlKSr6sGAAB8zO+DzFtvvSWDBg2SJ598Uho1aiTz5s2TUqVKyfvvv+/rqgEAAB/z6yBz6dIl2bFjh3Tr1s29rVixYmZ969atPq0bAADwvWDxY2fOnJGMjAypWrWqx3Zd/+GHH3LcJz093SwuycnJ5jElJcXr9ctMv5inclnfO7/7+Ft5f6wTx+Afn2sgnIe87sMxcB74Xfr/FcT3a9bXdRzn6gUdP/bzzz9r7Z2vv/7aY/uYMWOcNm3a5LjPxIkTzT4sfAb8DvA7wO8AvwP8Doj1n0FiYuJVs4Jft8hUrlxZihcvLr/88ovHdl2vVq1ajvtER0ebwcEumZmZ8ttvv0mlSpUkKCioQOur6bFWrVqSmJgo5cqVk6KiKB43x8x5DmT8fvP77Q+0Jeb8+fMSERFx1XJ+HWRKliwpLVu2lPXr10u/fv3cwUTXhw8fnuM+ISEhZsmqfPnyUpj0y7yofKEX9ePmmIuGoniei+pxc8z+JTw8/Jpl/DrIKG1dGTBggLRq1UratGkjM2bMkAsXLphZTAAAoGjz+yDz8MMPy+nTp2XChAly6tQpadGihaxevTrbAGAAAFD0+H2QUdqNlFtXkj/RLi29cN+VXVuBrigeN8dcNBTF81xUj5tjtleQjvj1dSUAAAAC7oJ4AAAAV0OQAQAA1iLIAAAAaxFkAACAtQgyXjRnzhyJioqS0NBQadu2rWzfvl0C1aRJk8yVkrMut9xyiwSauLg46dOnj7mypB7j8uXLPZ7XsfJ6aYDq1atLWFiYuaHp4cOHJZCP+Yknnsh27u+55x6xWWxsrLRu3VrKli0rVapUMRfgPHjwoEeZtLQ0GTZsmLlKeJkyZeSBBx7IdtXxQDvmzp07ZzvXQ4YMEVvNnTtXmjVr5r7oXbt27eTzzz8P2HOc1+O2/TwTZLzk448/Nhfv0ymLO3fulObNm0uPHj0kKSlJAlXjxo3l5MmT7uWrr76SQKMXX9RzqSE1J9OnT5dZs2bJvHnz5JtvvpHSpUub867/IAbqMSsNLlnP/aJFi8RmmzdvNl9g27Ztk3Xr1snly5ele/fu5rNwef755+Vf//qXfPLJJ6b8iRMnpH///hLIx6wGDRrkca71d95WNWvWlKlTp8qOHTskPj5e7rrrLunbt698//33AXmO83rc1p9nb97ksSjTm1gOGzbMvZ6RkeFEREQ4sbGxTiDSm3M2b97cKUr0z2XZsmXu9czMTKdatWrO3/72N/e2c+fOOSEhIc6iRYucQDxmNWDAAKdv375OIEtKSjLHvnnzZvd5LVGihPPJJ5+4yxw4cMCU2bp1qxOIx6zuvPNOZ+TIkU4gq1ChgvPuu+8WiXOc03EHwnmmRcYLLl26ZJKudiu4FCtWzKxv3bpVApV2oWj3Q926deWxxx6T48ePS1GSkJBgrjad9bzrfUG0WzGQz7vatGmT6Y5o2LChDB06VH799VcJJMnJyeaxYsWK5lH/vrXFIuu51q7UyMjIgDnXVx6zy4cffmhu4NukSRNzU96LFy9KIMjIyJDFixebFijtaikK5zin4w6E82zFlX393ZkzZ8wvx5W3TdD1H374QQKRflkvXLjQfJFpM2RMTIzccccdsm/fPtPnXhRoiFE5nXfXc4FIu5W0ub1OnTry448/yiuvvCI9e/Y0/9jr3eptpzemHTVqlHTo0MH8o670fOpNbK+8AW2gnOucjln9+c9/ltq1a5v/Ydm7d6+8/PLLZhzN0qVLxVbfffed+QLX7l8dB7Ns2TJp1KiR7N69O6DP8Xe5HHcgnGeCDK6LfnG56CAyDTb6h7BkyRJ56qmn+FQD2COPPOL+uWnTpub833zzzaaVpmvXrmI7HTeigTwQx3zl95gHDx7sca51ULueYw2wes5tpP/zpaFFW6A+/fRTc1NiHQ8T6BrmctwaZmw/z3QteYE2x+n/iV45ul3Xq1WrJkWB/l9MgwYN5MiRI1JUuM5tUT7vSrsW9W8gEM693tNt1apVsnHjRjNA0kXPp3Yhnzt3LuDOdW7HnBP9HxZl87nWVpd69epJy5YtzcwtHdg+c+bMgD7HVzvuQDjPBBkv/YLoL8f69es9mmp1PWsfZCBLTU016V2TfFGhXSv6D1zW856SkmJmLxWV867+/e9/mzEyNp97HdesX+ja3L5hwwZzbrPSv+8SJUp4nGttetdxYbae62sdc070/+iVzef6SvpvdXp6ekCe47wcd0CcZ1+PNg4UixcvNrNVFi5c6Ozfv98ZPHiwU758eefUqVNOIHrhhRecTZs2OQkJCc6WLVucbt26OZUrVzYzHwLJ+fPnnV27dplF/1zeeust8/OxY8fM81OnTjXnecWKFc7evXvNbJ46deo4v//+uxOIx6zPvfjii2YWh577L774wrn99tud+vXrO2lpaY6thg4d6oSHh5vf6ZMnT7qXixcvussMGTLEiYyMdDZs2ODEx8c77dq1M0ugHvORI0ecyZMnm2PVc62/43Xr1nU6derk2Grs2LFmVpYej/696npQUJCzdu3agDzHeTnuQDjPBBkvevvtt80fQcmSJc107G3btjmB6uGHH3aqV69ujrVGjRpmXf8gAs3GjRvNl/mVi05Bdk3BHj9+vFO1alUTZLt27eocPHjQ19UusGPWL7nu3bs7N910k5mqWrt2bWfQoEHWB/acjleXBQsWuMtoOH322WfNtNVSpUo5999/v/niD9RjPn78uPkyq1ixovndrlevnjNmzBgnOTnZsdXAgQPN76z+u6W/w/r36goxgXiO83LcgXCeg/Q/vm4VAgAAuB6MkQEAANYiyAAAAGsRZAAAgLUIMgAAwFoEGQAAYC2CDAAAsBZBBgAAWIsgAwB5oHd7v/LOyAB8jyADIF9Onz4tQ4cOlcjISAkJCTH3m+rRo4ds2bLFXSYoKEiWL1/ulU/26NGj5vVc93+5VrkqVarI+fPnPZ5r0aKFTJo0ySv1AeBfCDIA8uWBBx6QXbt2yT//+U85dOiQrFy5Ujp37mxuHOltejfi/NIQ88Ybb3i9LgD8E0EGQJ6dO3dOvvzyS5k2bZp06dJFateuLW3atJHo6Gi57777TJmoqCjzeP/995sWEte63h29b9++UrVqVSlTpoy0bt1avvjiC4/X17KvvvqqPP7441KuXDkZPHiw+67Mt912m3k9DU1X89xzz8lbb70lSUlJuZY5e/aseY8KFSpIqVKlpGfPnnL48OFsXUna6qTP67HkFNRWrFght99+u4SGhkrdunUlJiZG/vjjjzx/ngBuHEEGQJ5pANFFu43S09NzLPPtt9+axwULFsjJkyfd66mpqdKrVy9Zv369adG55557pE+fPnL8+HGP/bU1pXnz5qbM+PHjZfv27Wa7hh59vaVLl161jo8++qjUq1dPJk+enGuZJ554QuLj401r0tatW/XmuaZuly9fNs9/88038tRTT8nw4cNNl5aGttdee83jNTTQaRgaOXKk7N+/X9555x0TfqZMmZKnzxKAl/j6rpUA7PLpp5+auwOHhoY67du3d6Kjo509e/Z4lNF/WpYtW3bN12rcuLG5a7yL3qG3X79+HmUSEhLM6+3ateuqr5W13OrVq83duV13ZG/evLkzceJE8/OhQ4dMuS1btrj3PXPmjBMWFuYsWbLErD/66KNOr169PF5f7/AeHh7uXtc7CL/++useZf77v//b3BUeQOGhRQZAvsfInDhxwrRmaKvKpk2bTPeKtkZcjbbIvPjii3Lrrbea2T/asnPgwIFsLTKtWrW64TOig487duxoWnSupO8ZHBwsbdu2dW+rVKmSNGzY0DznKpP1edWuXTuP9T179phWH1crlS6DBg0yrUYXL1684WMAkDfBeSwHAG46JuTuu+82i4aFp59+WiZOnGi6bHKjIWbdunWm60i7fsLCwuTBBx/MNqC3dOnSXvmkp06dasLHmDFjCuTMaTDTMTH9+/fP8fMBUDgIMgBuWKNGjTymW5coUUIyMjI8yuj0bA06OnDWFQR0yvS1lCxZ0jxe+XrXooOQNWSMHTvWY7u2COmAXB0H0759e7NNB/IePHjQHIerjD6f1bZt2zzWtRVK99FQBsB3CDIA8ky/8B966CEZOHCgNGvWTMqWLWsGzU6fPt3MSMo6+0gH9Xbo0MFca0ZnB9WvX98M1NUBvjr7SFtyMjMzr/meel0Ybb1ZvXq11KxZ07R2hIeH56m+OvC2cePGpivJReuhddVuIB2gq8egYadGjRruYxgxYoSpu7Ye6bY1a9aY989qwoQJcu+995qZTdqyVKxYMdPdtG/fvmwDgwEUHMbIAMgzHQeiY0f+/ve/S6dOnaRJkyYmkGgomD17trvcm2++abqRatWqZaZNK50SrYFGW0E0zOg4Fm3VuBYNIbNmzTKhIyIiwiMwXUuDBg1M6EpLS/PYrjOqWrZsaYKIdj/p+OT/+7//My1J6j/+4z9k/vz5MnPmTDODau3atTJu3DiP19D6r1q1yjynU8l1H/1cdEo6gMITpCN+C/H9AAAAvIYWGQAAYC2CDAAAsBZBBgAAWIsgAwAArEWQAQAA1iLIAAAAaxFkAACAtQgyAADAWgQZAABgLYIMAACwFkEGAABYiyADAADEVv8P1Sqa1IsIlWgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distances = rx.distance_matrix(graph)\n",
    "plt.bar([*range(distances.shape[1])], np.max(distances, axis=1))\n",
    "plt.title(\"Longest Paths\")\n",
    "plt.xlabel(\"Start Node\")\n",
    "plt.ylabel(\"Path Length\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09ea1610",
   "metadata": {},
   "source": [
    "So for this graph, node 0 has the shortest path length and is therefore the root of the tree.\n",
    "\n",
    "To implement the algorithm, we'll build the graph out of Ternary Tree Nodes from `ferrmion`. By doing this, making an encoding from the graph is as simple as passing the root node to a `ferrmion.TernaryTree`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c963352e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ferrmion.encode.ternary_tree_node import TTNode\n",
    "from enum import Enum\n",
    "import numpy as np\n",
    "\n",
    "# First we find the root\n",
    "root_index = np.argmin(np.max(distances, axis=1))\n",
    "node_queue = [root_index]\n",
    "used_indices = {root_index}\n",
    "\n",
    "# Set values for the root node.\n",
    "nodes = [TTNode(parent=None) for _ in range(graph.num_nodes())]\n",
    "nodes[root_index].root_path = \"\"\n",
    "nodes[root_index].qubit_label = root_index"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60af1208",
   "metadata": {},
   "source": [
    "## Labelling Scheme\n",
    "\n",
    "At this point it's useful to define a preference for which branch we want to assign new nodes to.\n",
    "\n",
    "In the original paper there are two methods, which assign each of X, Y and Z in order of prefernce:\n",
    "- Homogeneous: [X, Y, Z]\n",
    "- Heterogenous: [Z, X, Y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "37d5c80d",
   "metadata": {},
   "outputs": [],
   "source": [
    "class LabellingTypes(Enum):\n",
    "    HOM = \"homogenous\"\n",
    "    HET = \"heterogenous\" \n",
    "\n",
    "labelling = LabellingTypes(\"homogenous\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5391d2ad",
   "metadata": {},
   "source": [
    "## Building the Tree\n",
    "\n",
    "To build the tree, we follow a bredth-first search, adding child nodes to each parent in the order defined by the Labelling type we have used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "92de9279",
   "metadata": {},
   "outputs": [],
   "source": [
    "while len(node_queue) > 0:\n",
    "    node = node_queue.pop(0)\n",
    "    parent = nodes[node]\n",
    "\n",
    "    match labelling:\n",
    "        case LabellingTypes.HOM:\n",
    "            chars = [\"x\", \"y\", \"z\"]\n",
    "        case LabellingTypes.HET:\n",
    "            chars = [\"z\", \"x\", \"y\"]\n",
    "\n",
    "    neighbors = list(set(graph.neighbors(node)).difference(used_indices))\n",
    "\n",
    "    for child in neighbors[:3]:\n",
    "        node_queue.append(child)\n",
    "        used_indices.add(child)\n",
    "\n",
    "    n_neighbors = len(neighbors)\n",
    "    for neighbor, char in zip(neighbors[:3], chars[:n_neighbors]):\n",
    "        parent.add_child(\n",
    "            char,\n",
    "            child_node=nodes[neighbor],\n",
    "            root_path=f\"{parent.root_path}{char}\",\n",
    "            qubit_label=neighbor,\n",
    "        )\n",
    "        nodes[neighbor].parent = parent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5db2b956",
   "metadata": {},
   "source": [
    "### Orphaned Nodes\n",
    "\n",
    "At this point we need to check if the tree covers all the nodes of our original graph (i.e. the tree _spans_ the graph).\n",
    "\n",
    "If not, then we attach orphaned nodes to the node closest to it which has space for another child."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "76f8cf83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tree spans the graph!\n"
     ]
    }
   ],
   "source": [
    "if len(used_indices) == graph.num_nodes():\n",
    "    print(\"Tree spans the graph!\")\n",
    "else:\n",
    "    print(\"Tree does not span the graph!\")\n",
    "    unused_indices = set(range(graph.num_nodes())).difference(used_indices)\n",
    "    for unused in unused_indices:\n",
    "        closest = np.argsort(distances[unused])\n",
    "        for used in closest:\n",
    "            used_node: TTNode = nodes[used]\n",
    "            for child_branch in chars:\n",
    "                if getattr(used_node, child_branch) is None:\n",
    "                    used_node.add_child(\n",
    "                        child_branch,\n",
    "                        child_node=nodes[unused],\n",
    "                        root_path=f\"{used_node.root_path}{child_branch}\",\n",
    "                        qubit_label=unused,\n",
    "                    )\n",
    "                    unused_indices.remove(used)\n",
    "                    break\n",
    "    if len(unused_indices) > 0:\n",
    "        print(\"Error, not all qubits assigned to nodes.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b458d57",
   "metadata": {},
   "source": [
    "## Creating an Encoding\n",
    "\n",
    "Now we can create a `TernaryTree` encoding from the root node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b168957c",
   "metadata": {},
   "outputs": [],
   "source": [
    "bonsai = fr.TernaryTree(graph.num_nodes(), root_node=nodes[root_index])\n",
    "bonsai.enumeration_scheme = bonsai.default_enumeration_scheme()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ed4225c",
   "metadata": {},
   "source": [
    "Let's see what this encoding looks like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8a837dbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ob6kXyu3gwYP49NNPVY+bJOYyNvDbb79lVeVDxuu+9dZb+Oabb9RqAwsWLFCJ46USExNVTEvyLr3sMunpnnvuUXHdsGFD1jFRkGBCSRQEyYwkkHLBjY+PVwuMy9i0/v37q9mzlxuHJjNtn3jiCdVzJLduSf9kExk6IAkmeUf2f5cxvPmR2+K//vqrinOZGS6L70tCKXEuCaaMaSWiwMWEkigAybp90rMjF9cff/xR3UqUXkbptenSpQu3tCNLkw9Bsn+8xL8Mz5Db4x07dlTxf+utt6JkyZL+LiIRXYIJJVGAkJ1qZGtEuYjK7dSzZ8+qLe6kh+b2229H6dKl/V1EItOdOnUKX3/9tXpfrF69Wq2r2qdPH/W+6NSpE4dvEAUIJpREfiS3+X7//fescZFHjx5VO9u4xkVWrVqVr48fyXhT1yQRmaHMxeD9S8avzpo1SyWXso+4TP6R4R/yfpFxmlyGiMh/mFAS+cH+/fuzLoyyTI3sauO6MDZp0oQXxgCRlpameoYlUZFFz2W3FwqMD2KbNm1S758vvvhCbTNav3599f6R8ZZVqlTxdxGJbIcJJQUPWcsu9QiQdgLIPA+EFAXCywPFgmOxadl1RRbKlougLJcSERGB3r17q1t3nTt35q27AI23FUvnIhQZaNv+pqCKNzuNt5TlhlxDReRDgAwVkeRSdui54oorEBSCvH0jYkJJgS15N5A4C0iKA5I2aI3tpaTRjYwFIlsC1fsDJfNePscfF7tly5api50smyIXu/bt22dNLgiai51dBHm82Z18aJs/f756v8n6l9KjnPNDW5EiRRBQGG9kIUwoKTA/qR9aAuycAhz+HnCEAE5ZfFvbbcMzR/bvRXUBag8DorvJdhzwx+24jRs3Zt2Ok4WwGzRokHU7TrbyowAS5PFGeQ8rcS23tW3bNlx55ZVZw0qaNm3qv2EljDeyKCaUFFjOHgDiBgFHlgGOUMBZiF0zXM+r2BloOR0oXtm0CQMyuUa+XBMGXAs0yy4rnDAQgII43sj7D3ibN2/Omvh25MgRXHvttVkT36pVq2ZeVTLeyMKYUFLg2P0p8NsjQEYa4EzXfzxHGBAaDjR7B6gxAEaQiRquJU1kwWtZ0kRuZcstNlk3jzvSBLAgjDfSvzSXrOsq71dZ51WW5rrxxhtVcilLc8luUoZhvJHFMaEk/5NbQPHPAwkvGHeOBmOAmPE+uSUpiyy7Fl3+3//+p8ZJuhZdlvXxuOhygAuyeCNjJCcnu20eIOMre/XqlbV5gGwm4BOMN7IJJpTkf1vHGntxd2kwFmg4Ps/bYrLVm4yzyuvnsn2ca1u4pKQkdRvbtS2c7D9MQSIA4o0Cy6FDh7LGW27duhWRkZG46667VHIpW0bmNVxFxkfLVqj5DmdhvJFNMKEk/5LbQHEDzTtfyxkeb0eOGjUKL7/8sppMIwskZxVv9+6scZG7du1SiaOMu5ILTUxMjHnlJkvFGwUuSSjl/S7rxEqiWbt2bfXBUb6qV8+e0S/jMmVyzzPPPIMXX3zR88EYb2QjTCjJf1L2A4vqAukp5p0zrATQc4fbxIn/+7//w7PPPqt6GYYPH46xY8di7ty5qrdi7dq1KFGihFrPTpJIWfKHu6UEqQCJNwoOskOSLD0k7YCsH5uSkoLWrVurduDOO+/E+PHj8fbbb6u7F9KGPP300+4HYLyRzTChJP+QcUUruwJHV/hmQkRBJk5U6AC0X6rGt73zzjsYOnRo1o9l3JRcIORiIuvWycXjlltuUUklBbEAiTcKTpJMyqLp0nMp68q6PlTK+GkXaUv++9//av9hvJENMaEk/zi4GFjdw3+133YRZiw/hvvvvz/XjwYPHowJEyaoZX/IIgIg3lCpu//OTz4jyw7JXYyPPvoo189mzJiBAQMGMN7IlsL8XQCyKVlEurDr/unlCMW+H57C/fdvy/Uj6XmQ2Z9MJi3Gz/GGnVOZUFqEtA1nzpxRbYXcychp4MCBSE1NxcO1v2W8ke2E+LsAZEOy3ZjsSOLh4j7le6Dao0DYvcDIWQad35mBKmHb0CqmIqKiotT2bC5ygVi4cKFBJya7xhsOLwWSEw06AZlN2oicyaS0IdKWyC5YFUueZbyRLbGHkswneyWrbevcL/Bb9gIjZgELRgDXVQNKFzeuCI6QUKyb9V8gZowaMynLAO3bt099FStWzLgTky3jTZ0/caaKNwp+spnBuXPnULVqVfUlywxlLR0U/wKQwHgj+2FCSeZLiru4V7K7hb8DsTWA7tmr9hhHzi/lkGu9w6HWkpOvJk2amHBysnO8UfCThc/zxHgjm+ItbzKXzH5M2iDfuD1cawQw+itg3S7A0Q+47738D7PjENB+IhAxEKj9BLB4s/a8zXu8LsjFcpClMd6I8UZkCvZQkrlSjwBpJ3I9vO55oNU4YEgnoH9roGRE/slki7HA8K7AtMHA1n1aAlokFKhXkOX+pBznDgPFogr3t1DgY7wR440xQKZgQknm8pBMCkkg9xwH2tQGKpYB+kwGVm0HOtYHvn7M/XcfmQHcFgtMuF37f80KwMy1wK4jQNGLEZ3f893Lk8SE0ubxdiED6PkacOwUEBYKjOkD3NHC+3jbnwTc+17ez3cvD+PN7vEWUQRoNxFIzwDSM4HhXYDBHbyPt5MpQKdJeT/fvTyMNzIPE0oyV+Z5jw9LL6OIqaL9K43kA22BT9e4/97e48CKbcCWSe6PS0PbqGr2//N6fu7ypBX8byBLxdvpc8Cb/YHGVwNHTgJNRwPdGwElIryLt7CQvJ+fuzyMN7vHW0RRYM0YoHg4kJIKNHgGuLU5EFnKu3grVSzv5+cuD+ONzMMxlGSukKIeH968F6hVMfsi3K4eUCrC8++pW9uV3B9P2A80qpb9/7yen7s82UsGkT3jLaqslgwK6R0vXwr4J8X7eMvv+bnLw3ize7yFhmjJoEhL14b5ukaUexNv+T0/d3kYb2Qe9lCSucLLe3xYGtKcPYx5CQkBMjK1L7m9KJZuARIOePf83OWJLMSTyKrxtjFRi60qkYWLt0ufn7s8jDdL8zLe5LZ124nabexX79Y+hBQk3vJ6fu7yMN7IPOyhJHNFVPTY6EqD2zhHD2NemlYHioQBo+YAu48B8zZoY45EgRNKKQcn5FhbAeLtn2RtcteHgwoXb56e74bxZn1exluZEtpt7cQ3gdnrgKOnChZveT3fDeONTMaEkswli/9Gxso3WQ9lZgLxXvYwRpcFpj0IzF0PNHoWmBMHDG6v3Wq8qnSBCnKxHGRpXsZb2gWg9xvAMzcD19cueLzl9fwcBWG82UEB27cKpbVb2T/tKFz7dunzcxSE8Uam4y1vMl9kS7etyeQ2T8rH3j+9fxvty2XEzEL0TsrOJVIOgt3jTcagDfwA6FAfuPeGgsfb5Z6vMN7s4zLxJr2JxYtqk2tOnQXW7ACGdPQ+3i73fIXxRn7AhJLMV70fEP98vr/S6SVgyz4gJQ2oPBT4ajjQ6hrkOYNSbhUV6Pmyc0n1/j74YyjY423tTq0nqGEV4NvftMc+HwLEVPUu3rx6PuPNPi4Tb3tPAA9N0ybSyIeRYZ3zjjVP8ebV8xlv5AcOp2xkTGS2ld2AI8tz7a9cGBWGAG/0B/q19vIJjlCgYmeg/WLd56YgwXgjxhuRoZhQkn8cXAys7uG/2m+7CKjU3X/nJ3Mx3ojxRmQoTsoh/4jupvUSOkwedSHni+qinZ/sg/FGjDciQzGhJP/Nhmw5HQg1eeHd0AigxTTt/GQfjDdivBEZigkl+U/xykCzd8w9Z7Op2nnJfhhvxHgjMgwTSvKvGgOABmPMOVeDsdr5yL4Yb8R4IzIEE0ryv5jxWrJnJDl+zDhjz0HBgfFGjDcin+Msbwocuz8FfnsEyEgDnOm+mYAjYzTltjp7JonxRv7E9o0sjgklBZazB4C4QcCRZdp6kYVZp9L1PJlFLhN/OGaSGG8UCNi+kYUxoaTAI2vtH1oC7JwKHF6qbSMmOz+ovSHy4sj+vaiuQO2h2lIxnM1NjDcKJGzfyKKYUFJgS04EEmcCSXFA0gYg7UTu3wkvD0TGanvoynaKJS/Zh5GI8UaBiO0bWQgTSgou5w6jSYNqeHrkY+h7931AeCRQLMrfpSKrOncYQx+6G0VCMjH5rXcZb2R4vM2eMQVT3nwNv6zfxHijoGLyNiVEOhWLQp3Y23DF1e2BMg1YnWSsYlGoXL+r9j3jjYxWLAplr74BVzdJZLxR0GEPJRERERHpwnUoiYiIiEgXJpREREREpAsTSiIiIiLShQklEREREenChJKIiIiIdGFCSURERES6MKGkoLF69eo8f3bihIcddIgYbxRE2MZRMGNCSUGjc+fOePLJJ3HhwgW3x5csWYKYmBi/lYusifFGjDki7zGhpKCxatUqzJ8/H7GxsUhISEBqaiqGDRuG3r17Y/jw4f4uHlkM440Yc0Te4045FFRSUlJUEvnll18iOjoaYWFhmD17Npo0aeLvopEFMd6IMUfkHfZQUlApXrw46tSpg/T0dBw4cADNmjVD7dq1/V0ssijGGzHmiLzDhJKCxt69e9GuXTtMnjwZ33zzDTZt2qRufTdu3Bjr1q3zd/HIYhhvxJgj8l5YAX6XyK8kcWzTpo1KIsuXL68e+/XXXzFq1Ci0b98eaWlpfIWI8UZBi20cBTOOoaSg8cEHH+Dhhx/2+LOVK1eqpJKI8UbBim0cBTMmlERERESkC295U9BwOp3IyMjI+n9ISIj6IjKKxJvEnXA4HAgNDWVlk2EyMzPVl4vEm8QdUTBgQklBQxrWbdu2qTGU0tDedtttTCjJULID0w8//KC+79SpEypUqMAaJ0M/wMybN0/926BBAzRq1Ii1TUGDt7wpqCQlJeGqq67Cfffdh08++cTfxSEbqFy5svpXlqkiMtr999+Pzz77DMeOHUNkZCQrnIIGE0oKHnLrMfUIUv7Zi+IRYXCEhgPh5YFiUf4uGVk43tJOHwQyzyO8WCnGGxkeb87U4zibfBIlSpVlvFFQYUJJgS15N5A4C0iKA5I2AGkncv+OJJWRsUBkS6B6f6BkdX+UlKyA8UaMN6JCYUJJgflJ/dASYOcU4PD3gCMEcMpAdW1yhGeO7N+L6gLUHgZEd5OBlyYWnIIS440Yb0S6MaGkwHL2ABA3CDiyDHCEAs7sWd1ecz2vYmeg5XSguDYGjojxRn7F9o0sjAklBY7dnwK/PQJkpAHOdP3Hc4QBMs6y2TtAjQG+KCFZCeONGG9EPsOEkgLjlmP880DCC8ado8EYIGY8b4ET443MxfaNbIKrQpP/GZ1MCjl+/Dhjz0HBgfFGjDcin2MPJfn/tmPcQPPO13IGb3/bGeONGG9EhmBCSf6Tsh9YVBdITzHvnGElgJ47OFHHjhhvxHgjMgxveZP/xhWtf1CbgGMmOZ/MIr+4PzPZBOONGG9EhmJCSf4h60zK0kC+mM1dEHI+Oa+cn+yD8UaMNyJDMaEk/5BFy2W9SH+Q8+6c6p9zk38w3ojxRmQoJpTkn+3tZAccD4uWT/keqPYoEHYvMHKWQeeX8x5eCiQnGnQCCiiMN2K8ERkuzPhTEF1C9uZW2yS6J5Rb9gIjZgELRgDXVQNKFzew5uT8iTOBmDF8eayO8UaMNyLDMaEk8yXFXdyb293C34HYGkD3xiaUQc4v5SDrY7wR443IcLzlTeaS2bZJG+Qbt4drjQBGfwWs2wU4+gH3vZf/YXYcAtpPBCIGArWfABZv1p63eY/XBblYDrI0xhsx3ohMwR5KMlfqESDtRK6H1z0PtBoHDOkE9G8NlIzIP5lsMRYY3hWYNhjYuk9LQIuEAvUqF6AsUo5zh4FiUYX7WyjwMd6I8cYYIFMwoSRzeUgmhSSQe44DbWoDFctoj51NA+o+CdzRAnitX/bvPjIDuC0WmHC79v+aFYCZa4FdR4CiOSI6r+e7lyeJCaWVeRlvVw8HrigGhDiAsiWAlaMLFm/5Pd+9PIw3S/My3hKPATe/Bhw9BYSGAHHjgRIR3sebPP+BDz0/3708jDcyDxNKMlfmeY8PSy+jiKmS/diLC4CWtdx/b+9xYMU2YMsk98eloW1U1f0xT8/PXR6TF1angI23deNy94wXJN48PT93eRhvluZlvA38AJh4B3DDtcA/yUB4kYLFW17Pz10exhuZh2MoyVwhRT0+vHkvUKti9qds+TQut7a7Ncr9e+rWdiX3xxP2A42qZf8/r+fnLk94of4Msla85cXbePO+PIw3u8fbtgNaTEkyKMqVBMJCvY+3/J6fuzyMNzIPE0oyV3h5jw9LQ5rzE7isQTmpb+7fCwkBMjK1L5elW4CEA949P3d5IgtUfLJmvDkcQNsXgOZjgFlrCx5veT0/d3kYb3aPN/mwKz3Zcsu7yXPASwsKFm/5PT93eRhvZB4mlGSuiIoeG11pcBtf/AS+4DegdpT2damm1YEiYcCoOcDuY8C8DdqYI+FqcPN7vhspByfkwO7xJn4eC2x8EfhuhHaBdt2i9Cbe8nu+G8ab9XkRb+kZwE9/Au/eD/wyDlger315G2/5Pd8N441MxoSSzCVdOZGx8k3WQ5mZQHyOT+BxfwFf/qJNdBg5G/hoJTBhvvaz6LLAtAeBueuBRs8Cc+KAwe21ge5Xlb7883MU5GI5yO7xJiqV0/6NKqutg7op0ft4y+/5OQrCeLMDL+JNYqVZdaBKpDb2UeJFEk5v4y2/5+coCOONTMdJOWS+yJZuWy/KbZ6Uj7N/POku7UvMWK3d7hl7a/bP+7fRvlxGzHRPDi73/KydcqQcBLvHW0oqkOkEShUDklO1SRF3tvA+3i73fIXxZh+XibfmNYBjp4F/U4DSxYA1O4CHO3gfb5d7vsJ4Iz9gQknmq94PiH/eZ4eT24tyq6jAO+VU7++zMlDwxtvR00Cfydr3MnZNeoSa1/Q+3rx6PuPNPi4TbzKB5qU7gRsnaNs7dI4BejbxPt68ej7jjfzA4XTKVhJEJlvZDTiyPNd+3oVRYQjwRn+gX2svn+AIBSp2Btov1n1uChKMN2K8ERmKCSX5x8HFwOoe/qv9touASt39d34yF+ONGG9EhuKkHPKP6G5aL6HD5FEXcr6oLtr5yT4Yb8R4IzIUE0ryD4cDp+tNRlq6Q40DMk1oBNBimjYbk+xDXu+W04FQkxd6ZrzZkx/iTQavOWUhc7Zv5CdMKMkvEhMTcX2nO/HYzLAcC2yYoNlUoHhlM89IgUJe92bvmHtOxpt9mRxvksM+920Z7DmWbto5iXJiQkmm++WXX9CiRQucO3cOj765EWgwxpwTNxgL1BhgzrkoMMnrz3gjC8bb8QpD8OX6oqptlTaWyGxMKMlUs2fPRvv27VGnTh2sX78edevWBWLGa8mekeT4MeOMPQcFh5jx+PGotiSAr4dbyHqUCuONcsSbGe3blR3eUW3qNddco9rYL774gq8BmYoJJZlCVqcaN24c+vXrhzvvvBM//PADypcvn32vpuF4oOUMIKyE7ybqyHHkeHJcOT7HTRKAefPno9OItVjyb184fBxv6c6iGPA+MP+vRow3Mr19u/LKK/Hjjz/ijjvuwD333IPx48ertpfIDEwoyXCpqakqkZTGbeLEifj0008RHh7u+fZQzx1AhQ7Z60UWhut5chw5Hm9z00V//PEHBg4cqC64Xf/7hc/jrUifv3C2wu0YMGAAduzYwXqnPNu3TKfDkPZN2tbPPvtMtbWuD/HSBhMZjetQkqGOHj2K3r17Y/PmzaqRkwv5Zckn6kNLgJ1TgcNLtW3EZOeHfG9QOi7ebnTCWaEzQusO15aKYa8kXXT69GnExsYiNDQUcXFxKFWqlK54y/q9qK5A7aFZ8XbmzBk1jk16hjZs2JB9HqKL8Zaa+A3WTLsTN9XPgCMkVFe85Wfu3Lnqw811112Hb7/9FldddRVfAzIME0oyTEJCAnr27Kk+HX/33XfqYl5gyYlA4kwgKQ5I2gCkncj9O+HlgchY/BNSG01vfxPjX/sU9913n0/+BrIGSe5uu+02dTtQkjwZw6s33tSezbJ9Z8nc+37++eefaN68OW666SZ8/fXXcPCDDeUgd2mkp3zvtlWomrFGd7zlR+K9V69eKFasGP73v/+hQYMGfC3IEEwoyRBLlixB3759Ub16ddWIVa1a1TcHPncYSEsCMtMAWXMtPBIoFpX1406dOiEtLQ0//fSTb85HlvB///d/ePbZZ1UvzS233OKzeMuPnKtPnz7q3E8//XThC0+W06ZNG5XgLV++3Gfxlp99+/apD/d79uxRvZZdu3bVfUyiXGQvbyJfevvtt50hISHOnj17Ok+fPm1q5X755ZfOEiVKOA8dOmTqeSlwLVu2TMXjc889Z/q5R40apc69fPly089NgengwYOqjZozZ46p55W2uEePHioep06dauq5yR7YQ0k+k56ejsceewzvvPMOHn/8cbz66qtqvJqZMjIyVA+lfPrnbUY6duwY6tWrh2bNmmHRokV+icfu3btj48aN2L59O8ewkRp+IcOAihYt6pd4fPLJJzF58mQMHTpU/RsWZvL2t2RZTCjJJ5KTk9WEG7mFM3XqVPznP/9hzZLfL9zyoUI+4Nx9990oV66cX8qRlJSEOXPm4L///W9WmYj86f3331cJZefOnfHVV1+hRIkSfEFINyaUpJtcJFNSUtC2bVs1XkwmIhAFikBI4gKhDEQ5yYd/GVe8atUqlVAyPkkvJpTks9vdmZmZ6jYOERXM+fPn+d4hv8RdSEgIb3uTT3BhcyrQzG1ZV9ITGYcT6Mmk9BJJ0kvWk5iYqF7bYN0VZPjw4di6dau/i0E2I212fmMod+3apYaMEHmDCSV5Zf/+/ejRo4dqYIKVLJfx0Ucf+bsYZMDuN02aNFFLowTjbTvZ3/6DDz5QE4jIWk6c8LCuZJB1IowYMYI77ZBXmFCSV6Tnp1KlSihdunTQ1Jirt0pu67z22mtqb1tZbJ2sJSoqSu0Lf/DgQQTj7j2y8PlTTz2l1lAla5Hx5DLDX+S8OxIMPen//vuvSiglNiMiItSwJqL8MKGkfC92rv2IZWFymSUbHx8fNI2iq7dq5syZqnfyzTffxJQpU/xdLPKxMmXKqAX0P/zww1xDGwI9Rt977z2sWbMma7F1DsmwDlm+7Morr8yKSxmr6HqNA7kn3fWekaWNZCiJLLslXLfGZUUPIk+YUJJHZ8+exQ033ICOHTuqLRNvvfVW1UBKQ+hqcAK1UXRdlE+dOoUnnnhC3bKRC/bgwYNV2flJ2xqk52flypU4cOCA2kpRYlY+BMkyPa6Lt6w+EGhc759ffvkFX375peo9b9WqlXpcyr1lyxa3D24UnMLDw9UOSdID/fnnn2c9LjEqS/V89tlnCESudl2WfxOy5JaQ+Pz4449VW8qdyMgTrmhKHhUvXhzz589XydcXX3yhbifu3LkTgwYNUhfBmJgYtGzZUn16rVatmukL9F7K1WDfe++9WcnEJ598ovaxlX1zc263x4V8g58kkrKtoXx4qFKlCo4fP67Gq0mPyj///KN6048cOYIHHngAEyZMQKCQhaVd75UVK1ao3lX50LZt2za1RemmTZvUv/LekkQkMjLS30UmHeS1lfV5ZWLL3r17sXjxYvUB6MyZMwG7HackjpL07t69W7WnrnG+cvtbEmFZY/jChQv+LiYFIC4bRF6THT+kF6h3794qqZQE88Ybb1Tfyxgbf5o+fTqeeeYZvPXWW6qxk0RSbifKRKKRI0eqCRvSW3X11VerHUsaN26MDh06+LXMpI9MEJOxk4cOHVLjZHv16oXmzZvjoYceUomlXBjlscqVK/u9quWDmbxfXLcPJbGQvZVlBx8ps0wWk/eSJMLDhg1T6wLKRCMKTtKDJz2QkkRKeyMxKqQ3WtqgLl26qA/tgXaXx/WBR8orvebSOykf2uS2vdylGjBggFpvmMgT9lCS12vkyXaGjRo1UtsrPvLIIypBu+KKK7J6BP1Jek4lwZBb3DVq1FAJpDTcctupX79+qvzR0dHqd6RXSP4OJpTB7ZprrlH/li1bVv0rvdDnzp1D165dEWiWLl2qktt3330XP//8s0p4Rc2aNVXiK4tMy4ecYJr0RnmTXrxrr71WfSh45ZVX1EoEsumDfHiQoUSSuAVaMilcvedyV0dW9pAP5vJh6JtvvkHr1q0Dfmk48i/2UJLXu3rIWnl///03Fi5cqBqZQLt1LGWScsutTxnvKROJpFdIen2kJ0su4pJkyu9Jz0GtWrX8XWTyIZl4JTEqt40rVKgQEB90cpo4caLalUR686U3Ur7k1rbr/XbpvxS8ZBzvpcMV+vbtq1aZkBiQyTqBZO3atSqJlLs8cnteJorJGHSZyCjDm2RYSc64ZIySJ0woyY3c6pCGsEiRIrkuyLIXsSRoP/zwQ9DVGhtD65MPCXJLedmyZao3JRDJDNmSJUtm/Z9JpPW5XmMZlyi9k5JYjho1CoFEkscWLVqocsqHcUksZbiQLBV3KbkFLsOKJGmWuz5ELoH1EZ78Smadym03uaXtqXdHxv3Iz4JRzh4f+Z7LswQvuZh5mqkvvSjSQykXxkCVM5nMGZc541P+NhlmQsHp0rbF1d7I8KD+/fsH5CoTMtRCloibN2+e2rFJxiFLMulp2S25Nsh14LrrrkNcXJxfykuBiT2UpMhM7vvvv1+N8ZHxMnKL2KrJiPS+njx5Uo2lpMAnPY6//vqrWmBZEi1ZAPzFF1/0OAbWCrfifvzxR4wZM0aNq5Qxay+//LJauqtz587+Lhp5wdW2uNqanFzbg/p7VYzLudz7SIYVySoL8r6cMWMG7rrrLlPLR4GJPZQ2Jw3H+PHj1S4yd955p7qdbbVkUgbAu27ryKQIGRMkY0EpOLz66qsYPXq0ml0qPTyyRqOMkfQk2JNJIX+brEUpS7bI3yzJpcwOpuDw119/qTZG2hppc3K2QdK7F+jJpDfvI7lGyLVCrhkyE1yW5gr0TQTIBE6yrXPnzjnvvvtuaQWcL774ojMzM9NpRWlpac6nnnrKWaxYMfW3ytf+/fv9XSzygsTkFVdcoV6zkJAQ9e+ECRMsX3fjx493+5tLly5t2fen1ezbty+rnSlevLjz6aefVm2QFUlMTpw4Uf2t99xzj7qmkH0xobSJv//+2/nQQw85T548qf5/5MgRZ6tWrZwRERHOr776yml1p06dcrZr1y6roU9NTfV3kcjLuHW9ZvLlcDicoaGhznfeecey9Sd/m/yN8rfm/Nt3797t76KRFySpcr1m0uZI22N1c+fOVdeS66+/3nn06FH1mFxr5Joj72GyB46hDHRyGyH1CJB2Asg8D4QUBcLLA8WiCnQY2TFEdo6RnRvk9pksTi6z+b777js1btIOZPxdmzZt1C1TWa/Q13VM+ShkHc+ZM8fj+CwZWyg74sgC4FYia7vKMleeJuVIXcgtxnwxlo3nRR3L0lANGzZUa47aZe1GWbNS1lqV9Yq//fZbtSawjAeWa49sPFEgjOOgxIQyECXvBhJnAUlxQNIGreG6lDRgkbFAZEugen+gZPV8B1DL8g4ySFzGxsj6kXXr1lVbvMlajXajBsun7fdpHZMxcfz444+rtfCEjD2TSQ233367WnZFViSwos2bN+Oll15SWy/KmDvX+DupizfeeMPw9oKgu44vVOmLImVq264qZUMJ2QFKZozLbHa5CyoJtWzde9mx+YzjoMeEMlDIJ7JDS4CdU4DD3wOOEMApy0/kN9DZkf17UV2A2sOA6G4yotrttyZNmqQmNeRczkJ2b3jyySdhKwbWMRlTx7J0iayNKsmk9HTITG+7LEgvkzvkffrxxx+rpFI+FMqFWWEsG491XCgSszn3KZcPRbIqg6xtyTq2NiaUgeDsASBuEHBkGeAIBZxaj0SBuJ5XsTPQcjpQvHJWb5ysz3f06FH3X3c41HIssgSLLRhYx2RcHd90y/1qz+P3338fUVH2HIIgCfWQIUPUMA15zzKWTcD2olBkqStZr/jSGd8VK1ZUWzm67a7GOrYcLhvkb7s/BRZeCxxdof2/MBfhnM+T48jx5LgAZs+e7ZZMut7QklD++eefsAWD65iMq+PlH/THggULbJtMCumZlDpQySRj2Xis40KTndRcSw7lTB6PHDmirkWsY2tjD6W/yCe4+OeBhBeMO0eDMah+y2fYs2evumUoiyPLYtCyh/D111+fa9cOyzGpjhEz3r63wFnHrGerYCz7xJkzZ9Sua7If+IoVK9RkHRmycfXVVyNx9262yRbGhNJfto41NtG5aHeJe7Hx/M1qoLTMvrMVk+oYDcYCDcfDlljHrGerYCwbQoZqLFy4UK1e0PHK1WyTLYwJpb9uqcQNNO98LWcANQbAVljHrGOrYCyzjq2AcWx5TCjNlrIfWFQXSE8x75xhJYCeO+wziYR1zDq2CsYy69gKGMe2wEk5Zo/RWf8gkJFm6mnV+WT2rR32WmUds46tgrHMOrYCxrFtMKE0k6zPJ0uqONNNPa06n5xXzm91rGPWsVUwllnHVsA4tg0mlGaSxZ5lnT1/kPPunArLYx2zjq2Cscw6tgLGsW0woTSLbCslO4d4WJ9vyvdAtUeBsHuBkbMMOr+c9/BSIDkRlsU6Zh1bRfJuTJmxFNWGZRjbLti8vWAds47Jd3IsW0+Gkn1g1fZy7gnllr3AiFnAghHAddWA0sUNLIOcP3EmEDMGlsQ6Zh1bxJalr5vXLti0vWAds47Jt5hQmiUp7uKexu4W/g7E1gC6NzahDHJ+KYdVsY5ZxxaxcOkP5rULNm0vWMesY/It3vI2a5Zb0gb5xu3hWiOA0V8B63YBjn7Afe/lf5gdh4D2E4GIgUDtJ4DFm7Xnbd7jdUEulsOCWMesY4uoVasWRk/f6XW7kBe2F6xjf2Ic2w97KM2QegRIO5Hr4XXPA63GAUM6Af1bAyUj8r84tBgLDO8KTBsMbN2nXWiKhAL1CrK8pJTj3GGgmMX2RmYds44tYt2P36BVbEOv2oW8sL1gHfsb49h+2ENpBg/JpJALxZ7jQJvawKmzQJvxQONnta9iA4Fvf8v+3UdmALfFAhNuB2pWAPo0B9rWBa6NBope/FgweQlQ/ymg3pPAo5/ms+xkWhLsWMcVywAfrcy7ji5Xx38eyn59PL1G7uWxbx2//6NWxw2eBmb+7P673sTxa4vyfr7l61jqs8g5t/q89z2g7GDg9jdz/+7CTUCdkcA1I4BpKwtWz30mez5urmNasJ4LUsd51ZOeOs71uI3reH8S0G6i1iY3fAb4ar3+OvZ4TAvWcaBhQmmGzPMeH5ZeRhFTBagTDWyepH39/DxQIhy4qYH2873HgRXbgMe6uj9f3lCNqmrfHz8NTF0GbJwIxL8MbEwE4v7KqzwmL6weIHWcXx15U8f5vUa5y2PPOo7fB8xep9Xxry9o9X0yxfs6zu/5tqhjqc/47Vn1KYZ3AT4bkvv30jO0CX0rRgG/vwS8ughIOuNdPed1XI/HPHEUdq3jvH6mp449Pm7BWPa2jsNCgDf7A9tfBZY9Azz2OZCSqq+OPR7zzEnf/5HkhgmlGUKKenx4816gVkWgxCW3tL7bCHSsn/24/J66tV3J/fcS9gONqrlfDFIvABfSgQsZwFVX5FWecNi1jvOqI2/rOK/XKHd57FnHfxwCWtUCIooCxYpqdbd0q/d1nN/zbVHHUk/b/naL2Xb1gFIe4mzD30D9ykClclovcbdGwLJ472PZ03E9HnPVRti1jvP6mZ469vi4BWPZ2zqOKgs0vlr7Xnoyy5cC/knRV8cej3kq1bd/IOXChNIM4eU9PixvmJyftFzmrgf6tsr+f0gIkJGpfbks3QIkHMh+/pVXACN7AFUfBaKHAp0aaLcIPJcnEpbjRR3nV0fe1HF+r1Hu8tizjhtUBlb9ofUq/puifX/wH+/rOL/n26KOpT637/UYc5c69C9QqWz2/+X7g/8WPJYve8zjybBrHedFTx3bJZYLU8dy10jqtEqk7+o465g16xesMFRgTCjNEFHR48VYLsSNL+n9On1Wm/XdvVH2Y02rA0XCgFFzgN3HgHkbtLElwvXGkouvLEG05y3g4FTtGGv+8FAWKYfVJuR4Wcf51ZE3dZzfa+TGxnUsE8Qe7QJ0eAm4dTLQshYQGuJ9Hef3fFvUsdRnwk40rlH4hScLEsuXFVYcKJLXrY7gFVB1bNFYLmgd/5OsTTT9cJDv6jjrmP8pbck6DjRMKM3gcACRsfJN1kOZmUC8h09aCzYCnWO0W34u0WWBaQ9qvWKNngXmxAGD22td+VeV1n7nhwSgVgWgXEntVmGPxp7GULrKYc86zq+OvKnj/F6jHAWxdR2LhzsCm14EVo7WblldU7FgdZzX8+1Qx5mZmYiPj0ejmHpu9exJ9MUeSRf5PrpMwWI5/2M6cPDsVYiOjoZd6zgveuo4FwvGckHrOO0C0PsN4Jmbgetr+6aO3Y7ZurUP/iq6HC4bZJbIlm5bL0p3fsrHuX9N3jwPdcj9eP822pfLiJnuF/Eq5bRes9Tz2qc6uVX4UHsPO19IOWxax5ero8vV8eVeI8XmdSyOndIafJkVL2Py3n+gYHWc3/OtXschISFISUkB4l8AEn73uFWrS2xNbTyZDAmQnXSWbAHG9C5YLOd7zBIOLPntDMZ80AV2reP8FLaO3UiuZcFYLkgdy0obAz8AOtQH7r3BN3XsdswbQy1Zx4GICaVZqvcD4p/P91dk6SC5gM577PKHk5m1ckvApeU12q4a1z0HhDi0CSO9mnrY+aJ6f9i1jr2qo3zq2KvXyOZ1LG55Q6snGYz/ycNAWGjB6viyz7d6HV9Sz51eArbsA1LSgMpDga+GA62u0erl9X5A+xeBTCfwVE8gspT39ZzXcbOPmYmnRo1AZKT1xvd5W8eX+1lh69jt8a7v4quvO6FVq/wGZVu3jtfu1HofG1bJXobt8yFATNXC17GMmcw+ZgZQ+gt8Pqs3YmJizPirbcvhdOa5WiH52spuwJHlhf5EnFOFIcAb/YF+3vbkO0KBip2B9othaaxj1rFVMJZZx1bAOLYNJpRmOrgYWN0DftN2EVCpOyyNdcw6tgrGMuvYChjHtsFJOWaK7qb1EjpMHmkg54vqop3f6ljHrGOrYCyzjq2AcWwbTCjNniXbcjoQavIitqERQItp2vmtjnXMOrYKxjLr2AoYx7bBhNJsxSsDzd4x95zNpmrntQvWMevYKhjLrGMrYBzbAhNKf6gxAGgwxpxzNRirnc9uWMesY6tgLLOOrYBxbHlMKP0lZryW7BlJjh8zDrbFOmYdWwVjmXVsBYxjS+Msb3/b/Snw2yNARhrgTPfNBBwZoym31e3YM+kJ65h1bBWMZdaxFTCOLYkJZSA4ewCIGwQcWaatF1mYdSpdz5NZ5DLxx05jJr3BOmYdWwVjmXVsBYxjy2FCGShkfflDS4CdU4HDS7Xt5WRHEOS37rwj+/eiugK1h2pLNNhhNndhsI5Zx1bBWGYdWwHj2FKYUAai5EQgcSaQFAckbQDSTuT+nfDyQGSstkepbENX8pL9qIh17G+MY9azVTCWWcd0WUwog8G5w2jZ5BoMHTIY/e8bBIRHAsWi/F0qazl3GE8/9iBO/nMUH3w0g3VsUB0v+XYmRo96Cj+tW4/iZaowjg1wNulvxDauhddfeRFduvViLBvh3GHc368XoiuUx4uTXmUdG1THn370Bj7+6D2s/imOdRwEmFAGiYyMDDgcDoSEcGK+UTIzMyFb24eGhhp2DruT+pV6ljiWeCbWcbBim2w8tsnBhQklEREREenC7i4iIiIi0oUJJRERERHpwoSSiIiIiHRhQklEREREujChJCIiIiJdmFAGuNWrV+f5sxMnPCx4TqzjAMVYZh1bAeOY9UyeMaEMcJ07d8aTTz6JCxcuuD2+ZMkSxMTE+K1cVsI6Zj1bBWOZdWwVjOXgw4QywK1atQrz589HbGwsEhISkJqaimHDhqF3794YPny4v4tnCaxj1rNVMJZZx1bBWA4+XNg8CKSkpKgk8ssvv0R0dDTCwsIwe/ZsNGnSxN9FswzWMevZKhjLrGOrYCwHF/ZQBoHixYujTp06SE9Px4EDB9CsWTPUrl3b38WyFNYx69kqGMusY6tgLAcXJpQBbu/evWjXrh0mT56Mb775Bps2bVK3vhs3box169b5u3iWwDpmPVsFY5l1bBWM5SDkpIBWpkwZZ8+ePZ3Hjx/Peuz8+fPOkSNHOosWLerXslkF65j1bBWMZdaxVTCWgw8TygD3/vvv5/mzFStWmFoWq2Ids56tgrHMOrYKxnLw4aQcIiIiItKFYyiJiIiISJcwfU8nM2RmZsrQBPV9SEgIHA4HK97AOpb6lXom35L6lXp2YSz7HuvYHGwvzI1ltsnBgVfNILB9+3a19qSsO8lk0hjScJUpUwYRERE4e/asQWexN4ndm2++WcXy999/z1g2qI6XLl2q6rhXr16sY4NIGyFthbQZOT8kkW9jWa55EstyDaTAxx7KQOd0okHNSEx7bTg6tr8BOBkPhJcHikX5u2TW4XQi7MJxLP7iZSSf+gcl0xOBc6xjX9cxUo/gs7efxNwvo9CtVWXg3GHGsa85neje/jq8PWEw7rnrdrYXRnA6UTL0DL6d8QLKXFEcYcl/sE02qL349tMXsOrH5WhQ2cn2IghwUk4gSt4NJM4CkuKApA1A2oncvyNJZWQsENkSqN4fKFndHyUNXqxj1rFVMJZZx1bAOA56TCgD6RPZoSXAzinA4e8BRwjglFsp2rg+zxzZvxfVBag9DIjuJvcKTCx4EGEds46tgrHMOrYCxrGlMKEMBGcPAHGDgCPLAEco4Mwo+DFcz6vYGWg5HShe2YiSBi/WMevYKhjLrGMrYBxbDhNKf9v9KfDbI0BGGuBM1388RxgQGg40eweoMcAXJQx+rGPWsVUwllnHVsA4tiQmlP7s6o9/Hkh4wbhzNBgDxIy37y1w1jHr2CoYy6xjK2AcWxqXDfIXo5NJIcePHwfbYh2zjq2Cscw6tgLGsaWxh9Jf3f1xA807X8sZ9rv9zTpmHVsFY5l1bAWMY8tjQmm2lP3AorpAeop55wwrAfTcYZ+JOqxj1rFVMJZZx1bAOLYF3vI2e/zI+ge1CThmkvPJLPKLWwtaGuuYdWwVjGXWsRUwjm2DCaWZZJ1JWRrIF7O5C0LOJ+eV81sd65h1bBWMZdaxFTCObYMJpZlk0XJZL9If5Lw7p8LyWMesY6tgLLOOrYBxbBtMKM2SvBtTZixFtWEZCLsXGDkL5pJFzw8vBZITYVmsY9axVTCWWcdWwDi2lTB/F8Autix9HSNmAQtGANdVA0oX90MhZJvGxJlAzBhYEeuYdWwVjGXWsRUwju2FCaVJFi79AbE1gO6N4T+y53dSHKyKdcw6tgrGMuvYChjH9sJb3iaoVasWRk/fiXW7AEc/4L73CnecHYeA9hOBiIFA7SeAxZu1423e4+0RnEDSBlgR65h1bBWMZdaxFTCO7YfrUJrg2N54tIptiCGdgP6tgZIR2ldBk8kWY4HhXYEBNwBb9wGDpwGnzwHJHwNFC9LX3OcQUCwKVsI6Zh1bBWOZdWwFjGP74S1vE5Qscg57jgNtagMVywB9JgOrtgMd6wNfP5b9eydTgE6TgPQMID0TGN4FGNxB+9kjM4DbYoEJt2v/r1kBmLkW2HUkO5nM67jibBpQ90ngjhbAa92TLJdQelvHHuujn7469vi62byOrx4OXFEMCHEAZUsAK0frj+Ncx7RgHRe0nhOPAQ98CBw9BYSGAHHjgRIR+uo51zHb7keJSlG2rOM/DwF9p+T4/2Hgi6FA72aFr2OPx3TORe9+w2HXOJ68BJi2UluyslMD4K37AIdDXxznOma3E3BYsL0IJEwoTbA1frv6N6aK9n9JOB5oC3y6xv33ShUD1owBiocDKalAg2eAW5sDyanAim3Alknuvy9vqEZVs/+f13HFiwuAlrUu/ifT5IXVA6iOPdYHgL3HC1/HHl+3Z44iskwD2LmO141z74nXU8cej2nBOC5oPQ/8AJh4B3DDtcA/yUB4Ef31nPuYTtvWcZ1oYPPFepR2WD7U3NRAXx17POaNTWHXOj5+Gpi6DNj2MlAkDLhxAhD3FxBdpvB17PGYG35Dqy4xxv3BxDGUZti87W/Uqqj1HIh29YBSHm55S2+AJCUiLV37ZCVN+ea9QJFQoF4l999P2A80qpb9/7yOK5/m5JZ5t0YXHwi5eBIb1rHH+tBZxx5fN0dR2LmOPT5fZxznYsE4Lkg9bzug1ackfqJcSSAsVF89ezxm0RKwmsLE8ncbtV4weY6vYjnrmKXKwM51LHd3Ui8AF9KBCxnAVVfor+Ncx7yqoi//PPKAk3JMsHn7XrdPVPmR26eNngUqDwOe7AGULwWEhAAZmdqXy9ItQMIB909qeZE1Lyf1zfFAeCTsXMe56gP66zjX6xado/vThnUst6vavgA0HwPMWuubOs51TAvGcUHqWT4YSW/tza8BTZ4DXlqgv549HtOC9VyQWHaZux7o28o3sZzrmDau4yuvAEb2AKo+CkQP1W5Py61tPXXs8ZjX+nOJFXtgQmmCzQk70biGdwtPlimhdfEnvgnMXqeNY2paXeu2HzUH2H0MmLdBG1siLvfGWvAbUDtK+1JCi1ly3Jm3dZyrPi7SU8e5Xre4MBw9HWLrOP55LLDxReC7EVpSIpPI9Nax2zG/C8XWXcdhRd7Ws/TA/PQn8O79wC/jgOXx2peees51zG1FsPznBNg5lsXps1CrdHS/eFdDbyy7HTM20tZt8r8pwMLfgT1vAQenanWy5g99dZzrmH+FYc2vu3z0l1FerHfVCzCZmZmIj49Ho5h60sfi9fMqlNa69X/aAUSXBaY9qH2alV6wOXHA4PbaQOerSud/HBmL8uUv2jidkbOBj1ZcwIQJE2DXOs5VHyuBCfP11XFOFUo70KhONH766SfYOY4rldP+jSqrrb26KVF/HWcf04Hurati06ZNsJqC1LPUR7PqQJVIbeyk1LPcJtRTz+7HdKB7m5rYvHkz7N4mL9gIdI4BIi6OZPFFe5F1zKgWsJqC1PEPCUCtCtrwimJFgR6NL46h1FHH7sd0oMcNtRAXZ901mAMFJ+UYLCQkBCkpKUD8C0DC79oWiHmQ3sjiRbVJHqfOAmt2AEM6aj/r30b7chkx07tPwpPu0r7EjDUOJJyLxdixY2HXOnarj9Xa7ZOxt+qrY7fX7ZwDa7alYkidOrBrHcvEpEynVh+uCWV3ttBXx27HTHNgxdZU3PlEfVhNQeq5eQ3g2GmtN6a0TAzbATzcQV89ux2zuANr/sjEwz3rwq517CJJzUMX69alsHXsfswQILIlrKYgdVylnNYrmXpe65Fc9QfwUHt9dex2zCIOrNqegYe6WatNDkRMKM1SvR8Q/7z6ttNLwJZ9QEoaUHko8NVwoNU1wN4TwEPTtIk4MrFjWGcgJo83j+sWYk55HTeLHLS0fGK0bx0XhLd1LJNysl+3TAwb+ShiYmJsW8dHT2tLeQgZ/yS9Cs1r6qtj6bHPPmYmBg97EM2bN4dleVHPMgHnpTu1GawSe9Lb1bOJ/vYi+5iZ6HxLG/Ts2RN2bi/kw/2Gv4F5HpYfK2wdZx8zE6jeH5blRR23vEbrXb/uOW1JMJmk1Kup/jrOPmYmOt58PXr16mXCH2xvXNjcTCu7AUeWe/WJ+HIqDAHe6A/0a+3lExyhQMXOQPvFsDTWMevYKhjLrGMrYBzbBhNKMx1cDKzuAb9puwio1B2WxjpmHVsFY5l1bAWMY9vgpBwzRXfTegkdJo80kPNFddHOb3WsY9axVTCWWcdWwDi2DSaUZpKF9FpOB0JNXpA5NAJoMU07v9WxjlnHVsFYZh1bAePYNphQmq14ZaDZO+aes9lU7bx2wTpmHVsFY5l1bAWMY1tgQukPNQYADcaYc64GY7Xz2Q3rmHVsFYxl1rEVMI4tjwmlv8SMh/NiUilLfhiWTMaMg23FjNfqwEisY9axGRjLrGMrMDCOZVU8xe5tsh8xofQXhwPvr43CgPeBTEeE7ybqyHHCSgAtZwANx9tj3GRe5G+XOmg5A+mIQIbTR3XBOvZYxyruGMfGYD0HbR1nymWWbbLBdRyq1qFcce4+Xvf8iAmln8i2VI8//jhKNXwEobfsAip0yF4vsjBcz5Pj9Nxhz9vceTgV2RuxE0oh4fhV2gOsY9+TeOu5A84K2hYXmYVN3hnHXtWzq71wonDthSw4r7C9uGwd620v1vwZhjNtf2WbbGAdh1TsiEnx96HH0LlISLDe3vPBgutQ+sHZs2cRGxurtqdav349ihUrpvXXH1oC7JwKHF4KOEIAZ+Zlbog7sn8vqitQe6i2RIOdeyU9eOyxxzBt2jT8sX07qoQmFKiOJTGS14l17J0ff/gBr4+8CTNGNcNV6Ru9jmMtAc2Es2JnhF47nHF8OU4n0vZ8izUf3YlO9dPhCAn1ur1wOjOwZDNQqf1LaNT1GbYX+dRxzjZZtv6UptVRgDb5eLm+uPr6IXjooYcxefLFrZ4ozzrWc907l5qqrqtOpxO//vqrdl0lUzGh9IMhQ4bg008/xW+//YZ69TxshZicCCTOBJLigKQNQNqJ3L8TXh6IjNX2gZWtu0pesh8VKVu2bEGTJk0wadIkPPXUUwWq45T04li74wI63TUaITXuZR17oX379jhz5oxq0B0pe7yO4xOoheZ3vo1X3pmLO+64g9Hrhblz56Jv377YHf8jqjvXet1eOK/uh2bt7kDp0qWxYsUK1rUXMk//jf/7Twxua1cJdSJPFqhNfvnll/Hcc89h06ZNaNiwIes7Lzna5JR9K1Ei7JzXdeyybds2NGvWDPfffz/effdd1rXJmFCabN68ebj99tvxwQcf4KGHHvLuSecOA2lJQGYa7h/0H0SUroT3ZnxrdFGDXmZmJm644Qb8+++/2Lx5M4oWLepVHSMkHAiPxI/rtqNTp07qFkr9+vXNLHpQ+vnnn1V9f/PNN+jdu7dXdYxiUVk/btGiBSpUqIDvvvvO3IIHqZtvvhnHjx9HXFxcgepZyGt06623qtesdWtv92+1L2kDYmJi8OOPP6JDhw5e1bHL+fPn0bhxY5QrVw5r1qzR7nhQvu666y5cOL0P82Z/6FUd5yTX1v/85z/qWisxTiZykmn27t3rLFOmjPO2225zZmZmFuoYzz33nHPkyJE+L5sVTZ8+Xe6bOFeuXFmo5ycnJzuLFy/unD9/vs/LZkVdu3Z1NmjQwJmRkVGo50+ZMsUZFhbmPHHihM/LZjVSR1JXU6dOLdTz5TWqX7++s1u3bj4vmxXNmzdPtQUpKSmFev6KFStUW/TJJ5/4vGxWJNc4udYVhlxbb731VnWtlWsumYc9lCbJyMhAu3btsG/fPtVbVrZsWbNObUtpaWlo2rSp6hmYOXNmoY9z4cIFFClSxKdlsyKpp5EjR6JNmzaFvmUtt8pliIIcgy7vp59+UvFdqlSpQt8yX7duHV599VXGuBekpzHfuxyX0a9fPxXfGzduRHi4ybul2cw///yj3htXX301Vq5cidDQQk76oQJhQmmi1157Dddff736IuMT+NTUVPXvFVdcweo2YXiBcDgc6quw5PVi429OXcnkBfkSvA1rvFOnTiEsLAwRERGMcRPIcA6Z9PrEE0+YcTpiQmkuabz1XGyJ9U1EwYvXANa3lbGHkoiIiIh04XQzHztxwsNyEmT4eEkiomDmGn5A5pDVEQ4cOMDq9iEmlD40btw4PProo/AHGS9oRzLI/dlnn/XLuf/44w/YkQxyN9v+/fvxww8/wI5SUlL8ct5PPvlETSIk48mENK6baO6Y7/79+2P06NEmntX6mFD6kMwo+/vvv2Gm06dPY9myZWrdLhmkbzd//fUXvvjiC8N7hqX3wDXxRF7jRx55BDfddBPs5ttvv0X37t1x8OBB03psVq1ahRtvvFF9YLMbSaQHDhyoZtFf2oNlVI+WtCOylt+gQYOwePFi2E1ebbiR9T1ixAj1dejQIdiNtKuy2oDr+0ulp6f7vB2XtkRWWpGJsuQ7TCh9qHnz5qrXKmcjrPfNIBcUuZgIeSPkfMNt375dzWB78MEH1W1f2dLRbmSJGZk5+f777xvW8LsG0stMWKnzUaNGqaWf7LiVWufOnVGnTh21lWVeFwBfkTqXHuj/+7//U0tuyQcnuzl58qSarTp//nxVHzlj26gJfmvXrsXnn3+ulhOSBaLtZOvWrWqB/R07duT6mdS3r5Mb1/JN0p4sXboU0dHRsJu9e/eqdvyrr75SbWzOGJfX45VXXvHZueQ13LVrF+bMmYM777xTLTYvy0EJDjnwARPXvLSsffv2OZOSkpwHDx509u7d2/naa685U1NT1cLY58+fV1/Hjx8v1LGrVq3qXLRokdtjv//+u7Nv377OIkWKODt27OhctmyZ085ef/1155133ulMS0tzHjt2zJmenu7cvXu3c926deqxglq1alWuBXFlIemnn37aWaxYMedNN93kXL9+vdOuZs6c6WzcuLHz8OHDWfWbkJDgnDVrlvPvv//WdWzXoujnzp1zvv32284SJUo4b7nlFueuXbvU4/La2s3YsWOd5cqVc27dujXrsf379zvfeecd5+LFi31yDtdGC19//bWzVKlSzv79+6s2Sx63U51Lm92rVy/Vrkp8u1y4cEHFtyy+70tr1651Xnnllc7HHnvMefbsWXWewm56EcwmT57svOKKK5wvv/yy+v8ff/zhHDNmjDMqKsrZqVMnn53nwIEDzhtuuEG9xpeSuid9mFDq9O677zqrVKmiLnwxMTFq9wqHw+Hs0qWLs3z58uox+dmCBQsKdXxJlOQN9f7776vE8cknn3TWq1dPPf7rr7+6vRkKu0NJMJoxY4bz/vvvdz788MPOGjVqqDpv1KiRs0mTJs7o6GhnyZIlnTfffHOhd3wZNGhQ1v+lcZPztG/f3vnVV19lPW6n+nYlMZJoSwJfoUIFFduSeEiyIx98ypYt6zx9+nSBjzt79uxc7w/ZmaRDhw7Ot956y4d/QfCSnT/kQ6TUh8T51VdfrXYC+f777312ju3bt6vYHz16tNPO5MNLu3bt1AfIPXv2OEeNGuVs2rSpMzIyUiU5heVKFF3txl9//eXs3LmzalsuZbe2RXz++efONm3aOO+66y61g5N8aJ02bZquY0qd56xLab/ltZUPwGLTpk3OuLg4Z79+/dS1lfQJ80Uvp53J3sVyC1CSc1mw9s8//8TgwYPVKv1Dhw5Vk2XkZ7169SrU8V966SWMHz9e3dKVY8nxq1WrpvYorVWrFpKTk1GsWDF129cu65zJ/sUy9qVJkybqNr/U83vvvaeGB3z88cfqNqzsu1u6dOlCHV+O99RTT6FGjRpo1aoVfv31VzVWUx5r2bKlGuck56hcuTLsQm5Hya1+qWPZgUhuzcltutjYWHz22WeoVKmSiseSJUsW+Ngy0/Kdd95RC9DLLUXZ73jixIno1q0bunbtqm6JHT16FPXq1VNjZUuUKIErr7wSVrdt2zY1ZlVuv8o4UtmTfvny5Rg7dqyKzZ49exb6vf7RRx+ptsQ1huz333/H/fffr9oRuRV47NgxdbuxYsWKKv7l1uAtt9wCO5A4vuaaa9StVvnq06cPevTogQceeEC1vYUl7be01a5F5KWtkh1dZGiBtNvyGssOOl9//bUa3zdmzBjYiby3ZRchGXIh19TVq1fjqquuUm1tYRfel7alSpUq6nuJZ2nbq1atqr6X4Rxy/Th8+LA6n7Q/0r65fp8KjutQGkAanw4dOvh0hX6ZBCEX2iNHjqgLzI8//qgea926tRpfVr16dTRs2FAlUnbcBk2WgJDGYuHCheoiqCe5lgZsw4YN6kIqDY8kTpLAyOPSyMnx5YIj41al4ZdkSBIqK5PxXZLIS0Itf3P58uXVLEn5980339R1bKlHmeQ0e/Zs1K1bF3v27MG5c+fUeE2p/6SkJNSuXVsllvK4XAjkImx1cuGTC6q8pwcMGKASjgULFqiEo2bNmroutJJAStvRu3dv9V6ShF0u5NJuyTFlW0dJ4GWWt7zP5IL7v//9TyXzVt7J5o033lCT/MqUKaNiW8btSmL3/PPP6zq2JI8y7njFihWqTuWDwjPPPINmzZqp8YOyPax8SJNEXj6oymsvMS7tutVJHT/++OMqDmX7Vok3+cAj17Xnnnuu0DEnH4JlfsG8efNUey5f3333nYp7IW24dMxIAtmoUSNd7yfSMKH0IVdAygwyCWZJSOQTqd4ew0sTI+mpkE+78slKziPLqcj3MutYlvqwC1e9yKQl+ZJkRxqht99+22fnkB4z6bWRyRG7d+9WPXCS2MisREmEZJLOww8/rHrT7FbvMrBdem0kiW/fvr2uY0qiKK+h9CjIEiqSoMsEN6l7ucBKPUuPs1xsZBauJLNW7omXOpYEL+e+5nLBlfe4tDFS53qTO0lqZLKPJE7SpjRo0ED1RMpdD5lVL8sVSUIryav00MsF2MokiZEkTj7cSM+4JNGSCEp7/vrrrxd6j3oX+bDkmjwpdS5xLneupJ4lkZeeUfngKvUt7we5dtjlLp9MhJIPilIH4ssvv8TTTz+tPvC8/PLL6u5fYcjdQulscE2albta0lbL8azeCeAPTCgN4Pr0L9330oj4MmHNa6/kxMRE1Ztjl9tSnhIcuSC88MILSEhI8On+3fn1dMrFwMq9Npdzzz33qA830gtg5QQvUPbtlg8zklTKEjNmzcC2wzAaIcmeJNauOxzyAadIkSKql+ybb75RPcPSa1tYckdJ2mhJZKTdkOE0nurWLvWdc+m74sWL5xq2JR+oJLHftGlToT/MyLGk17dChQrq9ZUhBXaua6NxDKVOngLy2muvxZAhQ3yaTIq8uuMl0ZRbI1a/PSK9JPIJ9tI6d30vF1ppsH2ZTOY8fs7zupaYsEMy6eqlzclVF9JTKMMvfNkoX1rPnr63G0kmJamUMXwyxlFuz/qKq15dSasrtl117Vou59IYsBpJNlzJpJBkUsji1zIEQMac6kkoJZG8tFfMVfc5b7e6loeSf11tnpVd2l67/n7plJE7E3rGqsuxJJkUrmQyZzuSsz2xc/viK+yhLCD5tCPjmWSsh9ymkHEZ0l1/aTAyOH1Pxu61bdtWTVCSW0Ny8bsUx8H4nozdlVugrh4bf9W5nEfeV55edyuSBM+1/mlOrrU/zahz12vuigG7ktvUkpCYEXvyust4ZRlKI4msTNwh47iu1XJrXK7lMs5VJqt9+umnasgHeY8jUAtIBsbLBAXpDZPueBm3J5M2Lv1kY/QnHbmoyJgqu+yOI3+n9MrIpAQZYySzL+WxSxejNfIiK+dyLTJvp0Vw5cOTrFogY+4k7lx14GJ0YuM6nyxILGOr7EL+VvmbRc46l/o2o87ltZZbvTJh4cknn4RduN7bOXcnkluyRieTci5p02TMoLRxMoFE2jwjNw8IJPK3yzXN7L9XrtUyTE2GIMg1Xa7tco2XCZhUMEwoC0i64OXWj7z5ZXaa9JQVdnmawpIB29LYyN6v33//PexAxja5GnfpLZAlbGQSgXyCN4OcW255ySxQ2Xrwrbfegl3IhVR2rJFbrfXr11ezYF29hUaTsWZTp05Vg+nldqOMp7ILGYMtf7Ms0yQrCZixp7drazp5jeXcffv2VcNI7NIrLGTVAnmPy05YO3fuNO3Do/QCS5smYzZdu57JayFtnx1IEifXNLm2yTXOTHINd83ql9dbrvFyraeCYUJZQDLhI+cnKLkdIct6yDgys8jsP5ndLUst2GWmmtwCuvRTpSyfJLMyL+0xM4KcLyoqSiWUS5Yssc3yTCLn2C5JqmXpqrwmh/ma9AzJ+nTSgyDvO3kN7EL+VvmbJYmWOpC6MJrrNZVVIySZcrHTciry3pb3uLzXZUylGXEuPXPSlkmbdun5Lm37rErGSso1Ta5tZs5wl2u3LLmXM3GX951c66lgrD3K+nLkk2fqESDtBJB5HggpCoSXB4rlfdGSnpqcCaW8+eXTpNya6tixo0kFh9prd/CDD6JR7auAk/Felz9Y6z9noyoXN/k0KYuZy6LDZg2klk+x0iP86KOPqqUuChM/AcXL8ksy4/r75ba3jGM1i7y2L774opqhKUu35Fx71Or175pEIEMOZKF3s8j7S5ZskfFk8v6SJbM8JjUWrX8ZKyrv7ylTpph290niWtb5lGWcZEKnrL3qus5I3ctET6vXf6NqRfHz8q/QqsOtphZDrt1yDc/5oUnqXq71+Qr2+jeA/SblJO8GEmcBSXFA0gYtGC4lQREZC0S2BKr3B0pWz/oUKZ+cXJMQ5F9ZJ0sae7kVGOjlDwiFLL8kj//973/Vj6XBnTRpkulDDfSUP2AUovwtOt6ldgeSCWj+7CGUtT9b1L8Sofu+tEX9Z5aLxeaTDdDkxtvgL9JTKbshyaLb69evt2X8m11+GTf57LPPqjZPyCREmaATLOXPV4CWX3ojZQF7+cDsurbLv7IkmttExAAtf6CwR0Ipf+KhJcDOKcDh7wFHCOCUT3/5/emO7N+L6gLUHoa4fWXR6vrr1U9lFw/ZFlHGNwVL+RHdTbp8YDoflH/DqRbo/d8PMGvWbN2LaBcY6z/o44flZ/0HW/ysXLkS/fr1w0cffoge14UEXfmD8f0r45YlmZctToWa+R0bGzTl9zfrJ5RnDwBxg4AjywBHKOAsxKzoi89LLdsWvSedwPBnXzVvZxQflh8VOwMtpwPFTdyDmuVn/TN++P5l+8P2M4iuXzKGViZHLZn3ESokjgre96/JrJ1Q7v4U+O0RICMNcKbrP54jDAgNB5q9A9QYAMOx/Kx/xg/fv2x/2H7y+sXrbxCwZkIpf1L880DCC8ado8EYIGa8MV3YLD/rn/HD9y/bH7afRuH1y7rXXz+y5loQRgeDkOPHjzPm2Cw/65/xA0Px/cv2h/FjzHuL1y//tj9+ZL0eSrlNHDfQvPO1nOHb298sP+uf8QPT8P3L9ofx47v3E69f/m1//MxaCWXKfmBRXSDd+B0lsoSVAHru8M1AW5af9c/44fuX7Q/bT7Pw+mWd628AsM4tb8mL1z+oDeA3k5xPZmHrzctZftY/44fvX7Y/bD/NxOuXNa6/AcI6CaWsEyVT+30xG64g5HxyXjm/Hiw/65/xw/cv2x+2n2bi9csa198AYZ2EUhYdlfWe/EHOu3OqvmOw/Kx/xg/8gu9ftj+MH33vIV6//Nv+BAhrJJTJuzFlxlJUG5aBsHuBkbNMPr8sWnp4KZCcWLjns/ysf8YP379sf9h+8vrF628QC4MFbFn6OkbMAhaMAK6rBpQu7odCyDZLiTOBmDEFfirLz/pn/PD9y/aH7SevX7z+BjNLJJQLl/6A2BpA98Z+LITs2SkbxhcCy8/6Z/zw/cv2h+2n3/D6FbT5QyAJ+lvetWrVwujpO7FuF+DoB9z3XuGOs+MQ0H4iEDEQqP0EsHizdrzNe7w9ghNI2lDg87L8rH/GD9+/bH/YfvL6xetvsAv6dSiP7Y1Hq9iGGNIJ6N8aKBmhfRW0MW8xFhjeFRhwA7B1HzB4GnD6HJD8MVC0IP24fQ4BxaJYftY/44fvX7Y/bD95/eL117D8IdAE/S3vkkXOYc9xoE1toGIZoM9kYNV2oGN94OvH3H/3tUXAJ6u17TOfuRno30Z7/JEZwG2xwITbtf/XrADMXAvsOqIlk/uTgHvfA46dAsJCgTF9gDtaaL+b63xpSQUKiJzlv5AB9HzN83nEwk3AE7OBzEzg6ZuBB9vrK7/Hx7sbV/68XpvLlT+/5+Z6TQ0qf34xoCd+cr2mBpX/ZArQaRKQngGkZwLDuwCDO+gvvzibBtR9UnvsNQPjJ9e5+ukrv8c6MbD8Vw8HrigGhDiAsiWAlaP113+uYxpY/sRjwAMfAkdPAaEhQNx4oESEvvLnOmbb/ShRyffl//MQ0HdK9vP+PAx8MRTo3azw5fd4TOdc9O433JD6n7wEmLZSW7KwUwPgrfu0dk9P/ec6ZrcTcBgQP3lde4We8vuy/Y8oArSb6LmN1HP9PZlP26u3/Q80QZ9Qbo3frv6NqaL9X16sB9oCn65x/734fcDsdcDGiermtLq93fM64NRZYMU2YMsk99+XQGhUVfs+LAR4sz/Q+GrgyEmg6WigeyOtMc11vsy0QpdfekTzOo8Eo0w8WvmcNulIftanGZCcWvjye3x85EmUKOP78uf12uw9fvny5/Vcj6/pkydQxoDy51WHJ84Uvv7Di3h4TZ8+isgyDXxe/lLFgDVjgOLhQEoq0OAZ4Nbm+uLH9bq+uABoWcvY+HdxO5eX8ZNX+T3WyTPG1L/LunHud1D0lN91XLdjGlj/Az8AJt4B3HAt8E+yFr96y5/7mE5Dyl8nGth8sYwS85KI39RAX/k9HvPGpoaU//hpYOoyYNvLQJEw4MYJQNxfQHSZwpf/7HkPx9zwG1p1ifFp+Xcf83ztLVNCX/17PK6O9j+iqOc2MrKUvutvXm2vHEdv+x9ogn4M5eZtf6NWxexGr109oJSHW95/HAJa1dKCplhRoFE1YOlWYPNeoEgoUK+S++8n7Nd+R0SV1YJZSC9o+VLAPyl5nC8kvNDlz+88G/4G6lcGKpXTLh7dGgHL4vWV3+Pjp1INKb/HuoJ35c/ruR5f0xW/GlL+vH6mp/49vqarNhpSfun9kQZNpKVrPRLSCOuNf/kULkNGpOxGxr/Hc+ksv8c6cRQ1rPwen6+z/nMxqP63HdDKKYmfKFdS6y3SU36PxyxawpDy5/TdRu1OhzzHV/WfdcxSZQwrvyQ1qReAC+lab+BVV+gvf65jXlXR5+XP69qrnq+j/L5u//NqI/Vef0PzOK4v2v9AE/wJ5fa9bj1ZeWlQGVj1h9b9/G+K9v3Bf4CQECAjU/tyWboFSDjg3kPmsjFR+90qkXmcKDzSJ+W/9DyH/gUqlc3+uXx/8F/flT/r8Zr1DSl/Xgpa/su+pseTDS9/zp/pqX+Pr6mB5Zd6avQsUHkY8GQPrWHWGz+y5uukvsbHv8dzFSJ+Lj1urjqJrmVY+eW2XNsXgOZjgFlrfVP+XMc0qP4lmZeL3s2vAU2eA15aoL/8Ho9pYPy4zF0P9G2lv/wej2lQ+a+8AhjZA6j6KBA9VLs9LbdW9ZTf4zGvbezz8ud17RV6ym9E+++pjfTF9fekh+P6ov0PNMGfUCbsROMal194sl5l4NEuQIeXgFsna7fN5JND0+pad/+oOVoX+rwN2pgIcWlAyy0ZmUX+4aA8ThJevsDjHzyV/7LnycEX5c96/D+lA7r8l31Na4cjNKKsoeW/9Gc+jZ+w4kCRKwwrv9xiklsziW9qt4pk3Jqe8i/4DagdpX0pocUMi59c54Jv6t+tTuLCcPR0iGH1//NYYOOLwHcjtORJJv/pLb/bMb8LxdZdxw0pv/Rk/fQn8O79wC/jgOXx2pee8uc65rYiWP5zgiHldzl9FmpFELll6qv3b9YxYyMNi39JmBb+Dux5Czg4VTvfmj/0lT/XMf8Kw5pfd/m8/Hlde4We8hvR/ntqI/PjbfnLeHPcQrT/gSaoE8rMzEzEx8ejUUw9+ax+2d9/uCOw6UVtMLx0U19TEYguC0x7UPuEKZ8g5sQBg9trXetXlc5+btoFoPcb2sDf62vncYLIWN3lz+s80Rc/EbnI9zJ+Rm/53R5v3dqw8ufF2/Jf/jV1oEiJK3HNNdcYVn5PP9NT/+6vqQMHz16F6Ohow8rvUqG0djvmpx36yi9juL78RRs7NnI28NGKC5gwYYIh5c91rpXAhPm+e/9WKO1AozrR+Omnnwwpv5BbW65beLLm3aZE/eXPPqYD3VtXxaZNmwwpv5ynWXWtZ0jGTkr55XafnvK7H9OB7m1qYvPmzYbVv1iwEegco90mFb6In6xjRl0yg8yH5f8hAahVQRsWILd3ezS+OIZSR/ndj+lAjxtqIS4uzpDye7r2+qL+fd3+e2ojfXH9zavt1dP+B6KgTihDQkKQkpKCHj17aTuNXIbMEhMyO0/GL3RpqP1fZpztnwKcmQ7MfRQ4dtr904WMeZDB4x3qA/fekMfBJR4jW+oqf37nia2pjcuQWwUyEHjJFv3ld3v8xlBDy5+fy5Xfq9f0sAMbdl1Aly5dDCl/fj8rbP27vaZpDiz57Yxh5ZdPxGfOad/LRLQ1O4A6UfrKP+ku7XnSw/FaPwcG3xaLsWPHGlJ+t3PdozXaY2/VV363OjnnwJptqahTp44h5ZfB+K5zuQbyy/gpPeV3O2aaAyu2pqJ+/fqGlL95Da1c0qslM1IlfupG6yu/2zGdDqz5IxN169Y1pPxut6Yvaeb0tv/aMUMMbT+rlNN6JVPPa7dX5fau3vev2zGdDqzanmFY/Od17dVTfl+3//m1kXquv0fzOK7e9j8QBf0sb6V6PyD+efVtp5eALfuAlDSg8lDgq+FAq4sfWm55Q3tBZQDuJw9rg8o9cd2Kclm7U/vk0bAK8O1v2mOfDwFiql5yvq7v4quvO6FVq1aFKn9+55Gyvt4PaP+iNL7AUz212Wd6yn/qXM7HM4DSX+DzWb0RExPj8/Jf7rXJr/z5PTf7Nc3EJzM+RFhYIULai/Jf7m/Lr/z5PTf7Nc3EU6NGIDIy0pDy7z0BPDRNGwwuDfSwzp7LXtDyZ5GDlpZP+oXgZfx4y9vyn7uQs04yMWzkowWPfS/Lf/S0tvSVkIRAEuLmNfWVX9qx7GNmYvCwB9G8eXNDyi/tz0t3ajOBpb6kR65nE33ll+NmHzMTnW9pg549expSfiHthCQz8y5ZTk5P+bOPmQlU71/wsntZ/pbXaL3C1z2nLRElE4B6NdVXfvdjZqLjzdejV69ehpTf22tvQcrvflz97X9+baSe6+/efI7rk/Y/gAT9wuZZVnYDjiwHnBm6D1VhCPBGf6Cft3eAHaFAxc5A+8WFPynLz/pn/PD9y/aH7adOvH4VTFpaGo58cR0qh+1AaIgzOOs/QFgnoTy4GFjdw3/nb7sIqNS98M9n+Vn/jB/4Dd+/bD8ZP7a6fmVkZODzzz/HuHHj0KDcPiwc6Qze9idABPUYSjfR3bQs32HyXXw5X1QX7fx6sPysf8YP379+bn+c0ltiJrafbvXP65fx8SN9aPPmzVPDW+6//340a9YMr3weH9z1HyCsk1DKgmwtpwOhBVvYV7fQCKDFNO38erD8rH/GD9+/fmx/Zid2RMq5jKzFnE3B9jOr/nn9MjZ+JJH8/vvv1Tjj22+/HVWrVsWvv/6Kr7/+GvVkMlsw5w8BwjoJpSheGWj2jrnnbDZVO68vsPysf8YPTMX3L1JTUzF48GD0e/BpfL23nRcLsLH+GT/Bdf1au3Yt2rVrh65duyI8PByrVq3C0qVLVe9kMJQ/WFgroRQ1BgANxphzrgZjtfMFafk/XFcRx0v5eNwG69828cPyB3/979u3DzfccIMaS/bxxx9j4PiVQVX+YK//XFh+n9b/77//jh49eqBNmzY4deoUFi1ahJ9//hlt27a1Zv37mfUSShEzXnuxjCTHjxkXtOU/euXDGPt1Jm688UYcOHDAtwdn/Vs+flj+4K//H3/8EU2bNsXx48dVD46MJwum8ueJ5bd9/f/555/o27cvmjRpgr/++gtz5sxRi/53794djsvdXg72+PEj68zy9mT3p8BvjwAZaYAz3TcDaGWMhXSLm/HJwuDy79q1C506dVILvP7www+oWTOPhfEKi/Wfb/0bjvXP+vdAmvxXXnkFo0aNQseOHTF79myUL1+e8XM5fP8GfPsjPe7jx4/HjBkzUKlSJTz//PMYMGBA4danDPb20w+snVCKsweAuEHAkWXaek+FWafS9TyZBSYDd80c82Bw+eUNeNNNN+HMmTNYvnx5gXbaCITyG47lZ/1bKH5Onz6teiLnz5+vEkrZKjM0NDRoyl9gLL8t6v/YsWN46aWX8N5776F06dJ47rnn8PDDDyMiIiIoym8V1k8ohfyJh5YAO6cCh5dq2zQ6M+UH+TzJkf17UV2B2kO1qf3+mI1lcPmPHj2qtnzav3+/GqhcqN02/Fh+w7H8rH8LxM+OHTvQp08fHDx4EJ999hl69+4dVOUvNJbfsvV/8uRJvPbaa3jzzTdVL+STTz6J4cOHo2TJkkFRfquxR0KZU3IikDgTSIoDkjYAaSdy/054eSAyVtubVbbTKnnJPoAWLP+///6rBi8nJCRg4cKFamxlMJXfNCw/6z8I40fW3Rs4cKBaKkV6JwuyZ3MglN9nWH5L1L/swT1lyhS8/PLLaqcbSSIlmSxXrlxQlN+q7JdQXurcYSAtCchMA0LCgfBIoNjFHeFtVv7k5GTVayED9OUCJAOYDcf69y/Wv6XrPz09Xd3+kzGTd9xxh5rJ7dPeG8aPf9ms/s+fP48PP/wQEydOxD///IOHHnpIxXdUlJ/+5mCvfx9jQkm51qS766671PIKMlhfLkJEFHxk9ra8l1evXq16ckaMGHH5Ga5EAUi2SZw5c6baJlHG/d97771qwk316vbp/QsGJu8zRIFOBjF/9dVXauC+XIxkss4DDzzg72IRUQHIDiC33Xab+oAok+3at2/P+qOgIzdQZYjGmDFj8Mcff6iYls6OevXq+btoZJt1KEmXIkWKqEH7cjth0KBB6vY3EQWHadOmqYWc5TagrL3HZJKCTb7bJDKZDFi85U35vqnfffdd1UMp21XJepVEFLjvV7nNfc011+Duu+/GW2+9pd63RMFExvDLklZr1qzB9ddfr5YDynNnGwooTCjpsjIzM5lMEgUBmYRz6NAh1aNDFGyxK8Os5I5Yo0aNVCLZrVs3jvsNIuxyossHST49ky+88IIac0lE5pBJCevWrfP4M1mLj8kkBXIv+p49ezz+TCaMyXJ1X375pffbJFJAYQ8lFbphkDf70KFDcfbsWXz00Uf577hBRD4h26VGR0ercc5EwUTGRN5www144403sq4hOXl6jIIHeyipUORNL7fCN2zYgCuvvJLJJJEJ5D1XokQJVKlSJWs5FaJAv5UtTpw4oVYNkQ9EwlPiyGQyuDGhpALJuQ6+3AovW7Zs1qKyO3fuxIoVK1ijRD504cIF9b6SrVHlPVetWjX8/fffWe9BokC0a9cuNGnSRO1iI3tty4ehU6dOqWsGWRPXoaQCJ5Sy1ZWMcfntt9+wcuVKnD59Wt3ylp12Dh8+rC5+smwJEen3+OOPY8GCBap3R5YAkg9uHTp0yNWjw9uFFEhq1KiB//73v3jvvfdw0003qfG9tWrVQt26dTnR06I4hpK8IhcrGfci217JPqpXXHEFjh49qvYAl22w5LZ3ly5dULRoUZQvX141HkSkn2w3J7e2586di8TERPU+lA9v/fr1Q+XKldGnTx/ExMSo9WP5vqNAc/LkSTWJTPbalsXJJX67du2Ka6+9Vv2cq4hYB6/65BXpCZELl0y8kVmk0kPy3XffqRl5sqWb7LDjYvft4Yl8ST6kiQEDBqh/5Q7BnDlz1O1E2Zt7xowZKFOmDBYuXIiaNWuy8imglC5dWs3YlvUl9+7di59++kmtDiLXjfvuu09NMCNrYA8lFZrspSprhiUkJLAWiQwmvZTyge7pp59WYyhl15Bz586pcWlyt0DW7iPyF1dHQl4Ta2699VbUrl0bL774ouqllA9CJUuWVMvOcakra+CIbtJ1K6Nx48ZuM/mIyDcu7el3TcCR29x//fWXes/Jbe6KFSsymaSA2CZRhkRduvKA3NIWBw8eVAmkfCiS29+yQoj0VjKZtA4mlKRrgeXixYur73OO3ZIGhcuZEBVOamqq2vL00p4e1/9l3LJcxOU9xzGT5E9yG7tdu3ZqTKRs89mwYcNcS8jJByGZrPnnn3+6baEo1w7XcA6yBiaUVGjffPONWtg8J7nQySfSHj164IcffmDtEhXwQ5os/Czjy7Zu3erxd1q3bq1uexP5y++//67aeFnNQ4ZcLFq0CD///DNatWrl8fflg8+DDz7o1pPONSeth2MoyZAeFhkv8+OPP6qZqbfccgtrmegy5P0iexnLwuUyNrlp06asMwoo0ss4duxY1a5fc801anLNHXfcwfVQSWEPJfmczPj+9ttvVSJ52223YebMmaxlojxIr/4rr7yCzp0747rrrsPGjRuZTFLA9ZxLD2P9+vXxyy+/YNq0adi+fTv69u3LZJKyMKEkQ8jYmC+++EItdSJLQ8jiti6rVq1SSw4R2Z0sVi49PHIL+5lnnsGSJUsQGRnp72IRKbLDzWOPPaZ6I6XNfv3119XC+oMGDeL4XcqF61CSYWRwtuygU6pUKbVjgoy1kbXzZOyN9GIeP37cbf1KIqtvoSizsl127Nih1naV2a8yHrl3795+LR9RzhU8XnvtNbz55psqcZTb3LKFoszSJsoLE0oylMzwmzx5slrc9tlnn1VJpkzakZ0+ZCHm22+/3fuDyTIqqUeAtBNA5nkgpCgQXh4opu0lTuRTPow3uTDLjlLr169Xi4/Pnz9f9d7Lkim//vor6tSpwxfP7gKgfZNd0KZMmYKXX35ZLaD/6KOP4qmnnkK5cuVMKwMFL07KIdNmBbZs2VJtIycksZSlJiSpzFfybiBxFpAUByRt0BrbS0mjGxkLRLYEqvcHSlY36K8gyzMg3s6ePavWjpTlfurVq6fiXhZ2llvdstMNe31sLEDaN2mXZQ1J+dDzzz//4KGHHsJzzz2HqCh+WCfvMaEkw8l2W7IA+unTp7MWuXUllYcOHcJVV12V+5P6oSXAzinA4e8BRwjglOflt6WjI/v3oroAtYcB0d1kbQrj/jCyBoPjberUqaqnJ+dC5a+++iqeeOIJLp1iRwHUvsl6wTJpcty4cWrizb333qt2QKtenR/KqeA4KYcMJ2MlJZGUr0sXQM81A/zsAWBlV2B1D+DIcq2RdcrOC5fbHzzH78nz5PlyHDkeUV4MjjcZNzlp0qRcu97I2GGuw2dDfmjfZBLN6NGj3XYzk3iUpaliYmIwcOBAtapAfHy82g6RySQVFnsoyRTSmMmuCv/73//U+LHExET1uIzNSUpK0n5p96fAb48AGWmA0wdbOTrCgNBwoNk7QI0B+o9H1mJCvH3++edqlYNLSe+8LFwut8DJJvzQvsmawDIR8o8//lBL/TzwwANYtmyZup0ty1N16dJF3eZu1qyZ/vKQ7TGhJL+QT81vv/22mvn9+WefAfHPAwkvGHfCBmOAmPG8BU7aLUcT4s3ZYBzKRUaqGbPSG+nqpZQPUbKjiCylVaVKFb4iVmdSvHlq34YNG6a28ZS7Q7IcVd26ddWONtdffz1eeuklt60QifRiQkn+t3WssY2tS4OxQMPxxp+HAptJ8ZZR7zmUvfFtVKpUSS0PJL1AzZs3VxN0eLvbRvzUvsmEx5tvvtntV6Kjo9VSbt26dWMMks8xoST/3waKG2je+VrO4O1vO2O8kQ3i7fDhw7j22mvVRMicypYtqybfcGUBMgIn5ZD/pOzXxhSZSc7HiTr2xHgjm8RbmzZtciWT0isuS1fJ8kBERuDC5uS/cUXrH9QGqJtJzhc3CGi/lOMp7YTxRjaKtzJlSqNGjRq4+uqrER4errbClV2a5IsTcMgovOVN/nFwsbb0hb+0XQRU6u6/85O5GG/EeCMyFG95k3/Ior6OUP+cW867c6p/zk3+wXgjxhuRoZhQkvmSd2PKjKWoNiwDYfcCI2eZfH5ZIPjwUiBZWwuTLI7xRow3IsNxDCWZbsvS1zFiFrBgBHBdNaB0cT+8CLKNWeJMIGaMH05OZmK8EeONyHhMKMl0C5f+gNgaQPfGfqx82RM3Kc6PBSCzMN7ITIw3sive8iZT1apVC6On78S6XYCjH3Dfe4U7zo5DQPuJQMRAoPYTwOLN2vE27/H2CE4gaUPhTk5Bg/FGjDcic3CWN5nq2N54tIptiCGdgP6tgZIR2ldBk8kWY4HhXYEBNwBb9wGDpwGnzwHJHwNFC9Lv3ucQUCyqoH8GBQnGGzHe2L6ROXjLm0xVssg57DkOtKkNRBQB2k0E0jOA9ExgeBdgcIfs3+0zGVi1HehYH/j6sezHH5kB3BYLTLhd+3/NCsDMtcCuI1oyeTIF6DTJ83FzHTMtiQmlhXkbb/uTgHvfA46dAsJCgTF9gDta6Is3j8fsznizMm/jLb82qrDx5vFxxhuZiAklmWpr/Hb1b0wVIKIosGYMUDwcSEkFGjwD3NociCyl/a40iA+0BT5dk/38vceBFduALZPcjysNbaOq2veliuV93FzHzDR54WEKyHgLCwHe7A80vho4chJoOhro3gg4cabw8ebxmCNPokQZBoHd4y2vmElOLXy8lSnh4fFnjiKyTAM/1ATZEcdQkqk2b/sbtSoCJSKA0BCt8RNp6drmEs4cv9uuHlDqktvhm/cCRUKBepXcH0/YDzSqpn2f33FzHTPk4i+SreMtqqyW+ImKZYDypYB/UvTFm8djnko15e+mwI63vH6mJ948Pu4oasrfTSTYQ0mm2rx9b9YnbSG3adpO1G7nvHq3dtHNT0gIkJGpfcltRLF0C5BwAIU7bnikD/4qslK8bUzU4qtKpHaB90W8ZR2zZn2j/lQKsnjz9DO97Vuux6NrmfWnE7GHksy1OWEnGtfIXnhSbtPI7Z3EN4HZ64Cjp/J/ftPqQJEwYNQcYPcxYN4GbcyRyNngenXc8PIcP2lxBY23f5K1lQc+HOS7eMs65n9KM94sriDx5ulneuPN7fG4MBw9zZuQZB5GG5kmMzMT8fHxaBRTTxYYcPtZhdLaLZ2fduR/jOiywLQHgbnrgUbPAnPigMHttVuKV5XO/fv5HjcyVudfRFaKt7QLQO83gGduBq6v7Zt4cztm69aG/r0UnO1bzp/5qn2rUNqBRnWi8dNPP/n6zyTKExNKMk1ISAhSUlLQo2cvtVONfKo+c0772amzwJodQB0vVrjo3wbYPwU4Mx2Y+yhw7LT7p3evjivtfWRLH/51FMzxJuPNBn4AdKgP3HuDb+LN7Zg3hjLeLK4g8Zbfzwobb26Pn3NgzbZU1KlTx7wKINvjGEoyX/V+QPzz2HsCeGiaNqBcLr7DOgMxORrOTi8BW/YBKWlA5aHAV8OBVtfkPpysQym3ilzyO67bMbu+i6++7oRWrVqZ8EdTIMfb2p1ab1DDKsC3v2mPfT7EPR4LGm8//5nzmBlA6S/w+azeiImJMekPp0CNt8u1fYWJtw1/53w8E8NGPspYI1NxYXPyj5XdgCPLAWeG7kNVGAK80R/o5+0dRUcoULEz0H6x7nNTkGC8EeONyFBMKMk/Di4GVvfwX+23XQRU6u6/85O5GG/EeCMyFMdQkn9Ed9N6CR0mj7qQ80V10c5P9sF4I8YbkaGYUJJ/OBxAy+lAqMkLi4dGAC2maecn+2C8EeONyFBMKMl/ilcGmr1j7jmbTdXOS/bDeCPGG5FhmFCSf9UYADQYY865GozVzkf2xXgjxhuRIZhQkv/FjNeSPSPJ8WPGGXsOCg6MN2K8EfkcZ3lT4Nj9KfDbI0BGGuBM980EHBmjKbfV2TNJjDfyJ7ZvZHFMKCmwnD0AxA0CjizT1osszDqVrufJLHKZ+MMxk8R4o0DA9o0sjAklBR7Z/uHQEmDnVODwUrWNGZyZ8oN8nuTI/r2orkDtodpSMZzNTYw3CiRs38iimFBSYEtOBBJnAklxQNIGIO1E7t8JLw9Exmp7JVfvD5TMsU8ZEeONAhXbN7IQJpQUXM4dRpMG1fD0yMfQ9+77gPBIoFiUv0tFVnXuMIY+dDeKhGRi8lvvMt7I8HibPWMKprz5Gn5Zv4nxRkGFCSUFnQsXLiAkJAShoaH+LgrZQHq6NkEsLMzkXZ3IljIyMpCZmYkiRYr4uyhEBcKEkoiIiIh04TqURERERKQLE0oiIiIi0oUJJRERERHpwoSSiIiIiHRhQklEREREujChpKCxevXqPH924oSHBc+JGG8URNjGUTBjQklBo3PnznjyySfVOpQ5LVmyBDExMX4rF1kT440Yc0TeY0JJQWPVqlWYP38+YmNjkZCQgNTUVAwbNgy9e/fG8OHD/V08shjGGzHmiLzHhc0pqKSkpKgk8ssvv0R0dLTavWT27Nlo0qSJv4tGFsR4I8YckXfYQ0lBpXjx4qhTp47aDu/AgQNo1qwZateu7e9ikUUx3ogxR+QdJpQUNPbu3Yt27dph8uTJ+Oabb7Bp0yZ167tx48ZYt26dv4tHFsN4I8YckffCCvC7RH4liWObNm1UElm+fHn12K+//opRo0ahffv2SEtL4ytEjDcKWmzjKJhxDCUFjQ8++AAPP/ywx5+tXLlSJZVEjDcKVmzjKJgxoSQiIiIiXTiGkoiIiIh0YUJJRERERLowoaSgsnHjRjgcDjRv3tzfRSEbkMXzIyIi1Jd8T2Q0WQpN2jhZxYIomHCWNwUPpxNN60Xj3ZeGoEe3m4CT8UB4eaBYlL9LRlbkdCLC+S8WfPYiQpCOiNRdgJPxRsbFG1KPYN70cfh+yf/QpEYR4Nxhtm8UNDgphwJb8m4gcRaQFAckbQDSTuT+HUkqI2OByJZA9f5Ayer+KClZAeONGG9EhcKEkgLzk/qhJcDOKcDh7wFHCODMlB/k8yRH9u9FdQFqDwOiuwEOh4kFp6DEeCPGG5FuTCgpsJw9AMQNAo4sAxyhgDOj4MdwPa9iZ6DldKB4ZSNKSlbAeCPGG5FPMKGkwLH7U+C3R4CMNMCZrv94jjAgNBxo9g5QY4AvSkhWwngjxhuRzzChpMC45Rj/PJDwgnHnaDAGiBnPW+DEeCNzsX0jm+CyQeR/RieTQo4fP87Yc1BwYLwR443I59hDSf6/7Rg30LzztZzB2992xngjxhuRIZhQkv+k7AcW1QXSU8w7Z1gJoOcOTtSxI8YbMd6IDMNb3uS/cUXrH9Qm4JhJziezyOX8ZB+MN2K8ERmKCSX5h6wzKUsD+WI2d0HI+eS8cn6yD8YbMd6IDMWEkvxDFi2X9SL9Qc67c6p/zk3+wXgjxhuRoZhQkvmSd2PKjKWoNiwDYfcCI2eZfH5Z9PzwUiA50eQTk18w3ojxRmS4MONPQeRuy9LXMWIWsGAEcF01oHRxP9SQbNOYOBOIGcOXx+IYb8R4IzIeE0oy3cKlPyC2BtC9sR8rX/b8TorzYwHILIw3MhPjjeyKt7zJVLVq1cLo6Tuxbhfg6Afc917hjrPjENB+IhAxEKj9BLB4s3a8zXu8PYITSNpQuJNT0GC8EeONyBxch5JMdWxvPFrFNsSQTkD/1kDJCO2roMlki7HA8K7AgBuArfuAwdOA0+eA5I+BogXpd+9zCCgWVdA/g4IE440Yb2zfyBy85U2mKlnkHPYcB9rUBiKKAO0mAukZQHomMLwLMLiD+++fTQPqPgnc0QJ4rZ/22CMzgNtigQm3a/+vWQGYuRbYdURLJk+mAJ0m5X1ct2N2T2JCaWEFiberhwNXFANCHEDZEsDK0frjLdcxGW+WVpB4SzwGPPAhcPQUEBoCxI0HSkToi7dcx2y7HyUqMaEkczChJFNtjd+u/o2pAkQUBdaMAYqHAympQINngFubA5Glsn//xQVAy1rZ/997HFixDdgyyf240tA2qqp9X6pY/sd1O2amyQurU0DH27px7j3mvog3t2My3iytIPE28ANg4h3ADdcC/yQD4UX0x1vuY3IDBzIPx1CSqTZv+xu1KmqfxOUTtDSKIi1d28wkZ/Mnn8jl9na3RjmevxcoEgrUq+R+3IT9QKNq2vf5HTfXMUMu/iLB7vHm8fk64y0XxpuleRtv2w5ocSWJnyhXEggL1RdvHo9ZtIQpfzeRYEJJptq8fW/WJ20ht28aPQtUHgY82QMon6O3SNannNTX/fkhIUBGpvblsnQLkHAAXh031zHDI33+N1JwxpvDAbR9AWg+Bpi11jfxluuYjDdL8zbe5IOt9Frf/BrQ5DngpQX6483jMRlvZCImlGSqzQk70bhG9sKTZUpot3cS3wRmr9PG/ogFvwG1o7SvnJpWB4qEAaPmALuPAfM2aGOORM4G19Nxcx0ztBjHT1qct/Emfh4LbHwR+G6EdjGWyV564i3XMb8LxdZdx0372ylw403GP/70J/Du/cAv44Dl8dqXnnjLdcxtRbD85wSzq4BsjAklmSYzMxPx8fFoFFNP+m7cflahtHZL56cd2v/j/gK+/EWb1DByNvDRSmDCfCC6LDDtQWDueu0T+pw4YHB7oGIZ4KrSuc+Z87i5jrniAiZMmGDSX0+BHG+iUjnt36iy2hqpmxL1xZv7MR3o3roqNm3aZNwfTEETbxIXzaoDVSK1sZMSb3K7W0+8uR/Tge5tamLz5s0m/fVETCjJRCEhIUhJSUGPnr3UTjXyqfrMOe1np84Ca3YAdS72Hk66C9g/BdjzFvDaPVqjOvZW7Wf922g/OzMdmPsocOy0+6f3vI7rdsx+Dgy+LRZjx45lDFhUQeJNJje4fpacqk2MqF9ZX7y5HTPNgRVbU1G/fn3zKoACNt6a19Di6N8USUS1n9WN1hdvbsd0OrDmj0zUrVuXUUCm4SxvMl/1fkD889h7AnhomjagXAaWD+sMxORoOL3lujXp4tVx5QelpSeBLM+LeDt6GugzWftexq/JB5jmNfXFm9yyzD5mJgYPexDNmzc3+q+lIIg3mYDz0p3AjRO0n3eOAXo20d++ZR8zE51vaYOePXua8AcTabiwOfnHym7AkeWAM0P3oSoMAd7oD/Rr7eUTHKFAxc5A+8W6z01BgvFGjDciQzGhJP84uBhY3cN/td92EVCpu//OT+ZivBHjjchQnJRD/hHdTesldJg86kLOF9VFOz/ZB+ONGG9EhmJCSf4hC/S1nA6EmryweGgE0GKadn6yD8YbMd6IDMWEkvyneGWg2TvmnrPZVO28ZD+MN2K8ERmGCSX5V40BQIMx5pyrwVjtfGRfjDdivBEZggkl+V/MeC3ZM5IcP2acseeg4MB4I8Ybkc9xljcFjt2fAr89AmSkAc5030zAkTGacludPZPEeCN/YvtGFseEkgLL2QNA3CDgyDJtvcjCrFPpep7MIpeJPxwzSYw3CgRs38jCmFBS4JHtHw4tAXZOBQ4vVduYwZkpP8jnSY7s34vqCtQeqi0Vw9ncxHijQML2jSyKCSUFtuREIHEmkBQHJG0A0k7k/p3w8kBkLBDZEqjeHyiZY58yIsYbBSq2b2QhTCgpuJw7DKQlAZlpQEg4EB4JFIvyd6nIqhhvxHgj8goTSiIiIiLShcsGEREREZEuTCiJiIiISBcmlERERESkCxNKIiIiItKFCSURERER6cKEkoiIiIh0YUJJRERERLowoSQiIiIiXZhQEhEREZEuTCiJiIiISBcmlERERESkCxNKIiIiItKFCSURERER6cKEkoiIiIh0YUJJRERERLowoSQiIiIiXZhQEhEREZEuTCiJiIiISBcmlERERESkCxNKIiIiItKFCSURERER6cKEkoiIiIh0YUJJRERERLowoSQiIiIiXZhQEhEREZEuTCiJiIiISBcmlERERESkCxNKIiIiItKFCSURERER6cKEkoiIiIh0YUJJRERERLowoSQiIiIi6PH/mJaK7UdeU/0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ferrmion.visualise import draw_tt\n",
    "\n",
    "draw_tt(bonsai, enumeration_scheme=bonsai.enumeration_scheme)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71ec5e20",
   "metadata": {},
   "source": [
    "# Inbuilt Function\n",
    "\n",
    "There is an in-built function in `ferrmion`, we only need to pass the initial graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5dbbb377",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eS71QTkeOHMGsWbNUj5sk5jI28Ntvv2VV5UHG67777rv45ptv1GoDixYtUonjtRISElRMS/Iuvewy6enBBx9UcV2/fn3WMVGAYEJJFADJjCSQcsGNj49XC4zL2LR+/fqp2bPXG4cmM22ffvpp1XMkt25J/2QTGTogCSa5R/Z/lzG8eZHb4r/++quKc5kZLovvS0IpcS4JpoxpJSL/xYSSyA/Jun3SsyMX1x9//FHdSpReRum16dy5M7e0I1OTD0Gyf7zEvwzPkNvjHTp0UPF/1113oWjRor4uIhFdgwklkZ+QnWpka0S5iMrt1IsXL6ot7qSH5p577kGJEiV8XUQiw507dw5ff/21el+sXbtWravau3dv9b7o2LEjh28Q+QkmlEQ+JLf5fv/998xxkSdOnFA72zjGRVaqVIl/Hx+S8aaOSSIyQ5mLwfuWjF+dM2eOSi5lH3GZ/CPDP+T9IuM0uQwRke8woSTygUOHDmVeGGWZGtnVxnFhbNSoES+MfiI1NVX1DEuiIouey24v5B8fxLZs2aLeP1988YXaZrRu3brq/SPjLStWrOjrIhJZDhNKChyyll3KcSD1NJBxGQgqBISVAQoHxmLTsuuKLJQtF0FZLiU8PBy9evVSt+46derEW3d+Gm+rls9HMNLRpt3tARVvVhpvKcsNOYaKyIcAGSoiyaXs0FO8eHEEhABv34iYUJJ/S9oHJMwBEuOAxE1aY3staXQjY4HI5kDVfkDR3JfP8cXFbsWKFepiJ8umyMWuXbt2mZMLAuZiZxUBHm9WJx/aFi5cqN5vsv6l9Chn/9AWGhoKv8J4IxNhQkn++Un96DJgzxTg2PeALQiwy+Lb2m4brtmyfi+qM1BzGBDdVbbjgC9ux23evDnzdpwshF2vXr3M23GylR/5kQCPN8p9WIljua2dO3fihhtuyBxW0rhxY98NK2G8kUkxoST/cvEwEDcQOL4CsAUD9gLsmuF4XrlOQPMZQEQFwyYMyOQa+XJMGHAs0Cy7rHDCgB8K4Hgj9z/gbd26NXPi2/Hjx3HzzTdnTnyrXLmycVXJeCMTY0JJ/mPfLOC3IUB6KmBP0388WwgQHAY0mQZU6w9vkIkajiVNZMFrWdJEbmXLLTZZN4870vixAIw30r80l6zrKu9XWedVlua67bbbVHIpS3PJblJew3gjk2NCSb4nt4DiXwJ2vOy9c9QbA8SM98gtSVlk2bHo8v/+9z81TtKx6LKsj8dFl/1cgMUbeUdSUpLT5gEyvrJnz56ZmwfIZgIewXgji2BCSb63fax3L+4O9cYC9cfneltMtnqTcVa5/Vy2j3NsC5eYmKhuYzu2hZP9hylA+EG8kX85evRo5njL7du3IzIyEvfff79KLmXLyNyGq8j4aNkKNc/hLIw3sggmlORbchsoboBx52s+0+XtyNGjR+P1119Xk2lkgeTM4u3blzkucu/evSpxlHFXcqGJiYkxrtxkqngj/yUJpbzfZZ1YSTRr1qypPjjKV9WqWTP6ZVymTO557rnn8Morr7g+GOONLIQJJflO8iFgSW0gLdm4c4YUAXrsdpo48X//9394/vnnVS/D8OHDMXbsWMyfP1/1Vqxfvx5FihRR69lJEilL/nC3lADlJ/FGgUF2SJKlh6QdkPVjk5OT0bJlS9UO3HfffRg/fjz++9//qrsX0oY8++yzzgdgvJHFMKEk35BxRau7ACdWeWZCRH4mTpRtD7Rbrsa3TZs2DUOHDs38sYybkguEXExk3Tq5eNx5550qqaQA5ifxRoFJkklZNF16LmVdWceHShk/7SBtyX/+8x/tP4w3siAmlOQbR5YCa7v7rvbbLMHMlSfxyCOP5PjRoEGDMGHCBLXsD5mEH8Qbynfz3fnJY2TZIbmL8fHHH+f42cyZM9G/f3/GG1lSiK8LQBYli0gXdN0/vWzBOPjDM3jkkZ05fiQ9DzL7k8mkyfg43rBnKhNKk5C24cKFC6qtkDsZ2Q0YMAApKSl4vOa3jDeynCBfF4AsSLYbkx1JXFzcp3wPVH4CCHkIGDnHS+e3p6NiyE60iCmHqKgotT2bg1wgFi9e7KUTk1XjDceWA0kJXjoBGU3aiOzJpLQh0pbILljlil5kvJElsYeSjCd7Jatt65wv8NsOACPmAItGALdUBkpEeK8ItqBgbJjzHyBmjBozKcsAHTx4UH0VLlzYeycmS8abOn/CbBVvFPhkM4NLly6hUqVK6kuWGcpcOij+ZWAH442shwklGS8x7upeyc4W/w7EVgO6Za3a4z1yfimHXOttNrWWnHw1atTIgJOTleONAp8sfJ4rxhtZFG95k7Fk9mPiJvnG6eEaI4AXvwI27AVsfYGH38/7MLuPAu0mAuEDgJpPA0u3as/but/tglwtB5ka440Yb0SGYA8lGSvlOJB6OsfDG14CWowDBncE+rUEiobnnUw2GwsM7wJMHwRsP6gloKHBQJ38LPcn5bh0DCgcVbDXQv6P8UaMN8YAGYIJJRnLRTIpJIHcfwpoVRMoVxLoPRlYswvoUBf4+knn3x0yE7g7Fphwj/b/6mWB2euBvceBQlcjOq/nO5cnkQmlxePtSjrQYxJw8hwQEgyM6Q3c28z9eDuUCDz0fu7Pdy4P483q8RYeCrSdCKSlA2kZwPDOwKD27sfb2WSg42u5P9+5PIw3Mg4TSjJWxmWXD0svo4ipqP0rjeS/2gCz1jn/3oFTwKqdwLbXnB+XhrZBpaz/5/b8nOVJzf9rIFPF2/lLwDv9gIZVgONngcYvAt0aAEXC3Yu3kKDcn5+zPIw3q8dbeCFg3RggIgxITgHqPQfc1RSILOZevBUrnPvzc5aH8UbG4RhKMlZQIZcPbz0A1CiXdRFuWwcoFu7699St7fLOj+84BDSonPX/3J6fszxZSwaRNeMtqpSWDArpHS9TDDiT7H685fX8nOVhvFk93oKDtGRQpKZpw3wdI8rdibe8np+zPIw3Mg57KMlYYWVcPiwNafYextwEBQHpGdqX3F4Uy7cBOw679/yc5YkswJPIrPG2OUGLrYqRBYu3a5+fszyMN1NzM97ktnWbidpt7Dcf0D6E5Cfecnt+zvIw3sg47KEkY4WXc9noSoPbMFsPY24aVwVCQ4DR84B9J4EFm7QxRyLfCaWUgxNyzC0f8XYmSZvc9dHAgsWbq+c7YbyZn5vxVrKIdls74R1g7gbgxLn8xVtuz3fCeCODMaEkY8niv5Gx8k3mQxkZQLybPYzRpYDpjwLzNwINngfmxQGD2mm3Gm8ska+CXC0HmZqb8ZZ6Bej1NvDcHcCtNfMfb7k9P1tBGG9WkM/2rWwJ7Vb2T7sL1r5d+/xsBWG8keF4y5uMF9ncaWsyuc2T/In7T+/XSvtyGDG7AL2TsnOJlINg9XiTMWgDPgTa1wUeap3/eLve8xXGm3VcJ96kNzGikDa55txFYN1uYHAH9+Ptes9XGG/kA0woyXhV+wLxL+X5Kx1fBbYdBJJTgQpDga+GAy1uQq4zKOVWUb6eLzuXVO3ngRdDgR5v6/doPUH1KwLf/qY99vlgIKaSe/Hm1vMZb9ZxnXg7cBp4bLo2kUY+jAzrlHusuYo3t57PeCMfsNllI2Mio63uChxfmWN/5YIoOxh4ux/Qt6WbT7AFA+U6Ae2W6j43BQjGGzHeiLyKCSX5xpGlwNruvqv9NkuA8t18d34yFuONGG9EXsVJOeQb0V21XkKbwaMu5HxRnbXzk3Uw3ojxRuRVTCjJd7Mhm88Agg1eeDc4HGg2XTs/WQfjjRhvRF7FhJJ8J6IC0GSasedsMlU7L1kP440Yb0Rew4SSfKtaf6DeGGPOVW+sdj6yLsYbMd6IvIIJJflezHgt2fMmOX7MOO+egwID440Yb0Qex1ne5D/2zQJ+GwKkpwL2NM9MwJExmnJbnT2TxHgjX2L7RibHhJL8y8XDQNxA4PgKbb3IgqxT6XiezCKXiT8cM0mMN/IHbN/IxJhQkv+RtfaPLgP2TAWOLde2EZOdH9TeELmxZf1eVBeg5lBtqRjO5ibGG/kTtm9kUkwoyb8lJQAJs4HEOCBxE5B6OufvhJUBImO1PXRlO8Wi1+zDSMR4I3/E9o1MhAklBZZLx9CoXmU8O/JJ9HngYSAsEigc5etSkVldOoahjz2A0KAMTH73PcYbeT3e5s6cginvTMIvG7cw3iigGLxNCZFOhaNQK/ZuFK/SDihZj9VJ3lU4ChXqdtG+Z7yRtxWOQqkqrVGlUQLjjQIOeyiJiIiISBeuQ0lEREREujChJCIiIiJdmFASERERkS5MKImIiIhIFyaURERERKQLE0oiIiIi0oUJJQWMtWvX5vqz06dd7KBDxHijAMI2jgIZE0oKGJ06dcKoUaNw5coVp8eXLVuGmJgYn5WLzInxRow5IvcxoaSAsWbNGixcuBCxsbHYsWMHUlJSMGzYMPTq1QvDhw/3dfHIZBhvxJgjch93yqGAkpycrJLIL7/8EtHR0QgJCcHcuXPRqFEjXxeNTIjxRow5Ivewh5ICSkREBGrVqoW0tDQcPnwYTZo0Qc2aNX1dLDIpxhsx5ojcw4SSAsaBAwfQtm1bTJ48Gd988w22bNmibn03bNgQGzZs8HXxyGQYb8SYI3JfSD5+l8inJHFs1aqVSiLLlCmjHvv1118xevRotGvXDqmpqfwLEeONAhbbOApkHENJAePDDz/E448/7vJnq1evVkklEeONAhXbOApkTCiJiIiISBfe8qaAYbfbkZ6envn/oKAg9UXkLRJvEnfCZrMhODiYlU1ek5GRob4cJN4k7ogCARNKChjSsO7cuVONoZSG9u6772ZCSV4lOzD98MMP6vuOHTuibNmyrHHy6geYBQsWqH/r1auHBg0asLYpYPCWNwWUxMRE3HjjjXj44Yfx6aef+ro4ZAEVKlRQ/8oyVUTe9sgjj+Czzz7DyZMnERkZyQqngMGEkgKH3HpMOY7kMwcQER4CW3AYEFYGKBzl65KRieMt9fwRIOMywgoXY7yR1+PNnnIKF5POokixUow3CihMKMm/Je0DEuYAiXFA4iYg9XTO35GkMjIWiGwOVO0HFK3qi5KSGTDeiPFGVCBMKMk/P6kfXQbsmQIc+x6wBQF2GaiuTY5wzZb1e1GdgZrDgOiuMvDSwIJTQGK8EeONSDcmlORfLh4G4gYCx1cAtmDAnjWr222O55XrBDSfAURoY+CIGG/kU2zfyMSYUJL/2DcL+G0IkJ4K2NP0H88WAsg4yybTgGr9PVFCMhPGGzHeiDyGCSX5xy3H+JeAHS977xz1xgAx43kLnBhvZCy2b2QRXBWafM/byaSQ48eP8+45KDAw3ojxRuRx7KEk3992jBtg3Pmaz+TtbytjvBHjjcgrmFCS7yQfApbUBtKSjTtnSBGgx25O1LEixhsx3oi8hre8yXfjijY+qk3AMZKcT2aRX92fmSyC8UaMNyKvYkJJviHrTMrSQJ6YzZ0fcj45r5yfrIPxRow3Iq9iQkm+IYuWy3qRviDn3TPVN+cm32C8EeONyKuYUJJvtreTHXBcLFo+5Xug8hNAyEPAyDleOr+c99hyICnBSycgv8J4I8YbkdeFeP8URNeQvbnVNonOCeW2A8CIOcCiEcAtlYESEV6sOTl/wmwgZgz/PGbHeCPGG5HXMaEk4yXGXd2b29ni34HYakC3hgaUQc4v5SDzY7wR443I63jLm4wls20TN8k3Tg/XGAG8+BWwYS9g6ws8/H7eh9l9FGg3EQgfANR8Gli6VXve1v1uF+RqOcjUGG/EeCMyBHsoyVgpx4HU0zke3vAS0GIcMLgj0K8lUDQ872Sy2VhgeBdg+iBg+0EtAQ0NBupUyEdZpByXjgGFowr2Wsj/Md6I8cYYIEMwoSRjuUgmhSSQ+08BrWoC5Upqj11MBWqPAu5tBkzqm/W7Q2YCd8cCE+7R/l+9LDB7PbD3OFAoW0Tn9nzn8iQyoTQzN+OtynCgeGEgyAaUKgKsfjF/8ZbX853Lw3gzNTfjLeEkcMck4MQ5IDgIiBsPFAl3P97k+f/6yPXzncvDeCPjMKEkY2Vcdvmw9DKKmIpZj72yCGhew/n3DpwCVu0Etr3m/Lg0tA0qOT/m6vk5y2Pwwurkt/G2YVzOnvH8xJur5+csD+PN1NyMtwEfAhPvBVrfDJxJAsJC8xdvuT0/Z3kYb2QcjqEkYwUVcvnw1gNAjXJZn7Ll07jc2u7aIOfvqVvb5Z0f33EIaFA56/+5PT9necIK9DLIXPGWG3fjzf3yMN6sHm87D2sxJcmgKF0UCAl2P97yen7O8jDeyDhMKMlYYWVcPiwNafZP4LIG5Wt9cv5eUBCQnqF9OSzfBuw47N7zc5YnMl/FJ3PGm80GtHkZaDoGmLM+//GW2/NzlofxZvV4kw+70pMtt7wbvQC8uih/8ZbX83OWh/FGxmFCScYKL+ey0ZUGt+HVT+CLfgNqRmlf12pcFQgNAUbPA/adBBZs0sYcCUeDm9fznUg5OCEHVo838fNYYPMrwHcjtAu04xalO/GW1/OdMN7Mz414S0sHfvoTeO8R4JdxwMp47cvdeMvr+U4Yb2QwJpRkLOnKiYyVbzIfysgA4rN9Ao/7C/jyF22iw8i5wMergQkLtZ9FlwKmPwrM3wg0eB6YFwcMaqcNdL+xxPWfn60gV8tBVo83Ub609m9UKW0d1C0J7sdbXs/PVhDGmxW4EW8SK02qAhUjtbGPEi+ScLobb3k9P1tBGG9kOE7KIeNFNnfaelFu8yR/kvXj1+7XvsTMtdrtnrF3Zf28Xyvty2HEbOfk4HrPz9wpR8pBsHq8JacAGXagWGEgKUWbFHFfM/fj7XrPVxhv1nGdeGtaDTh5HvgnGShRGFi3G3i8vfvxdr3nK4w38gEmlGS8qn2B+Jc8dji5vSi3ivK9U07Vfh4rAwVuvJ04D/SerH0vY9ekR6hpdffjza3nM96s4zrxJhNoXr0PuG2Ctr1DpxigRyP3482t5zPeyAdsdrtsJUFksNVdgeMrc+znXRBlBwNv9wP6tnTzCbZgoFwnoN1S3eemAMF4I8YbkVcxoSTfOLIUWNvdd7XfZglQvpvvzk/GYrwR443Iqzgph3wjuqvWS2gzeNSFnC+qs3Z+sg7GGzHeiLyKCSX5hs2G83UmIzXNpsYBGSY4HGg2XZuNSdYhf+/mM4Bggxd6ZrxZkw/iTQav2WUhc7Zv5CNMKMknEhIScGvH+/Dk7JBsC2wYoMlUIKKCkWckfyF/9ybTjD0n4826DI43yWFf+LYk9p9MM+ycRNkxoSTD/fLLL2jWrBkuXbqEJ97ZDNQbY8yJ640FqvU35lzkn+Tvz3gjE8bbqbKD8eXGQqptlTaWyGhMKMlQc+fORbt27VCrVi1s3LgRtWvXBmLGa8meN8nxY8Z59xwUGGLG48cT2pIAnh5uIetRKow3yhZvRrRvN7SfptrUm266SbWxX3zxBf8GZCgmlGQIWZ1q3Lhx6Nu3L+677z788MMPKFOmTNa9mvrjgeYzgZAinpuoI8eR48lx5fgcN0kAFixciI4j1mPZP31g83C8pdkLof8HwMK/GjDeyPD27YYbbsCPP/6Ie++9Fw8++CDGjx+v2l4iIzChJK9LSUlRiaQ0bhMnTsSsWbMQFhbm+vZQj91A2fZZ60UWhON5chw5Hm9z01V//PEHBgwYoC64Xf7zhcfjLbT3X7hY9h70798fu3fvZr1Tru1bht3mlfZN2tbPPvtMtbWOD/HSBhN5G9ehJK86ceIEevXqha1bt6pGTi7k1yWfqI8uA/ZMBY4t17YRk50f8rxBabt6u9EOe9lOCK49XFsqhr2SdNX58+cRGxuL4OBgxMXFoVixYrriLfP3oroANYdmxtuFCxfUODbpGdq0aVPWeYiuxltKwjdYN/0+3F43HbagYF3xlpf58+erDze33HILvv32W9x44438G5DXMKEkr9mxYwd69OihPh1/99136mKeb0kJQMJsIDEOSNwEpJ7O+TthZYDIWJwJqonG97yD8ZNm4eGHH/bIayBzkOTu7rvvVrcDJcmTMbx6403t2SzbdxbNue/nn3/+iaZNm+L222/H119/DRs/2FA2cpdGesoP7FyDSunrdMdbXiTee/bsicKFC+N///sf6tWrx78FeQUTSvKKZcuWoU+fPqhatapqxCpVquSZA186BqQmAhmpgKy5FhYJFI7K/HHHjh2RmpqKn376yTPnI1P4v//7Pzz//POql+bOO+/0WLzlRc7Vu3dvde5nn3224IUn02nVqpVK8FauXOmxeMvLwYMH1Yf7/fv3q17LLl266D4mUQ6ylzeRJ/33v/+1BwUF2Xv06GE/f/68oZX75Zdf2osUKWI/evSooecl/7VixQoVjy+88ILh5x49erQ698qVKw0/N/mnI0eOqDZq3rx5hp5X2uLu3bureJw6daqh5yZrYA8leUxaWhqefPJJTJs2DU899RTefPNNNV7NSOnp6aqHUj798zYjnTx5EnXq1EGTJk2wZMkSn8Rjt27dsHnzZuzatYtj2EgNv5BhQIUKFfJJPI4aNQqTJ0/G0KFD1b8hIQZvf0umxYSSPCIpKUlNuJFbOFOnTsW///1v1iz5/MItHyrkA84DDzyA0qVL+6QciYmJmDdvHv7zn/9klonIlz744AOVUHbq1AlfffUVihQpwj8I6caEknSTi2RycjLatGmjxovJRAQif+EPSZw/lIEoO/nwL+OK16xZoxJKxifpxYSSPHa7OyMjQ93GIaL8uXz5Mt875JO4CwoK4m1v8ggubE75mrkt60q6IuNw/D2ZlF4iSXrJfBISEtTfNlB3BRk+fDi2b9/u62KQxUibndcYyr1796ohI0TuYEJJbjl06BC6d++uGphAJctlfPzxx74uBnlh95tGjRqppVEC8bad7G//4YcfqglEZC6nT7tYVzLAOhFGjBjBnXbILUwoyS3S81O+fHmUKFEiYGrM0Vslt3UmTZqk9raVxdbJXKKiotS+8EeOHEEg7t4jC58/88wzag1VMhcZTy4z/EX2uyOB0JP+zz//qIRSYjM8PFwNayLKCxNKyvNi59iPWBYml1my8fHxAdMoOnqrZs+erXon33nnHUyZMsXXxSIPK1mypFpA/6OPPsoxtMHfY/T999/HunXrMhdb55AM85Dly2644YbMuJSxio6/sT/3pDveM7K0kQwlkWW3hOPWuKzoQeQKE0py6eLFi2jdujU6dOigtky86667VAMpDaGjwfHXRtFxUT537hyefvppdctGLtiDBg1SZecnbXOQnp/Vq1fj8OHDaitFiVn5ECTL9Dgu3rL6gL9xvH9++eUXfPnll6r3vEWLFupxKfe2bducPrhRYAoLC1M7JEkP9Oeff575uMSoLNXz2WefwR852nVZ/k3IkltC4vOTTz5RbSl3IiNXuKIpuRQREYGFCxeq5OuLL75QtxP37NmDgQMHqotgTEwMmjdvrj69Vq5c2fAFeq/laLAfeuihzGTi008/VfvYyr652bfb40K+gU8SSdnWUD48VKxYEadOnVLj1aRH5cyZM6o3/fjx4/jXv/6FCRMmwF/IwtKO98qqVatU76p8aNu5c6faonTLli3qX3lvSSISGRnp6yKTDvK3lfV5ZWLLgQMHsHTpUvUB6MKFC367HackjpL07tu3T7WnjnG+cvtbEmFZY/jKlSu+Lib5IS4bRG6THT+kF6hXr14qqZQE87bbblPfyxgbX5oxYwaee+45vPvuu6qxk0RSbifKRKKRI0eqCRvSW1WlShW1Y0nDhg3Rvn17n5aZ9JEJYjJ28ujRo2qcbM+ePdG0aVM89thjKrGUC6M8VqFCBZ9XtXwwk/eL4/ahJBayt7Ls4CNllsli8l6SRHjYsGFqXUCZaESBSXrwpAdSkkhpbyRGhfRGSxvUuXNn9aHd3+7yOD7wSHml11x6J+VDm9y2l7tU/fv3V+sNE7nCHkpye4082c6wQYMGanvFIUOGqAStePHimT2CviQ9p5JgyC3uatWqqQRSGm657dS3b19V/ujoaPU70iskr4MJZWC76aab1L+lSpVS/0ov9KVLl9ClSxf4m+XLl6vk9r333sPPP/+sEl5RvXp1lfjKItPyISeQJr1R7qQX7+abb1YfCt544w21EoFs+iAfHmQokSRu/pZMCkfvudzVkZU95IO5fBj65ptv0LJlS79fGo58iz2U5PauHrJW3t9//43FixerRsbfbh1LmaTccutTxnvKRCLpFZJeH+nJkou4JJnye9JzUKNGDV8XmTxIJl5JjMpt47Jly/rFB53sJk6cqHYlkd586Y2UL7m17Xi/XfsvBS4Zx3vtcIU+ffqoVSYkBmSyjj9Zv369SiLlLo/cnpeJYjIGXSYyyvAmGVaSPS4Zo+QKE0pyIrc6pCEMDQ3NcUGWvYglQfvhhx8CrtbYGJqffEiQW8orVqxQvSn+SGbIFi1aNPP/TCLNz/E3lnGJ0jspieXo0aPhTyR5bNasmSqnfBiXxFKGC8lScdeSW+AyrEiSZrnrQ+TgXx/hyadk1qncdpNb2q56d2Tcj/wsEGXv8ZHvuTxL4JKLmauZ+tKLIj2UcmH0V9mTyexxmT0+5bXJMBMKTNe2LY72RoYH9evXzy9XmZChFrJE3IIFC9SOTTIOWZJJV8tuybVBrgO33HIL4uLifFJe8k/soSRFZnI/8sgjaoyPjJeRW8RmTUak9/Xs2bNqLCX5P+lx/PXXX9UCy5JoyQLgr7zyissxsGa4Fffjjz9izJgxalyljFl7/fXX1dJdnTp18nXRyA2OtsXR1mTn2B7U16tiXM/13kcyrEhWWZD35cyZM3H//fcbWj7yT+yhtDhpOMaPH692kbnvvvvU7WyzJZMyAN5xW0cmRciYIBkLSoHhzTffxIsvvqhml0oPj6zRKGMkXQn0ZFLIa5O1KGXJFnnNklzK7GAKDH/99ZdqY6StkTYnexskvXv+nky68z6Sa4RcK+SaITPBZWkuf99EgAxgJ8u6dOmS/YEHHpBWwP7KK6/YMzIy7GaUmppqf+aZZ+yFCxdWr1W+Dh065OtikRskJosXL67+ZkFBQerfCRMmmL7uxo8f7/SaS5QoYdr3p9kcPHgws52JiIiwP/vss6oNMiOJyYkTJ6rX+uCDD6prClkXE0qL+Pvvv+2PPfaY/ezZs+r/x48ft7do0cIeHh5u/+qrr+xmd+7cOXvbtm0zG/qUlBRfF4ncjFvH30y+bDabPTg42D5t2jTT1p+8NnmN8lqzv/Z9+/b5umjkBkmqHH8zaXOk7TG7+fPnq2vJrbfeaj9x4oR6TK41cs2R9zBZA8dQ+ju5jZByHEg9DWRcBoIKAWFlgMJR+TqM7BgiO8fIzg1y+0wWJ5fZfN99950aN2kFMv6uVatW6paprFfo6TqmPBSwjufNm+dyfJaMLZQdcWQBcDORtV1lmStXk3KkLuQWY54Yy97nRh3L0lD169dXa45aZe1GWbNS1lqV9Yq//fZbtSawjAeWa49sPJEvjOOAxITSHyXtAxLmAIlxQOImreG6ljRgkbFAZHOgaj+gaNU8B1DL8g4ySFzGxsj6kbVr11ZbvMlajVajBsunHvJoHZN34vipp55Sa+EJGXsmkxruueceteyKrEhgRlu3bsWrr76qtl6UMXeO8XdSF2+//bbX2wuC7jq+UrEPQkvWtFxVyoYSsgOUzBiX2exyF1QSatm697pj8xnHAY8Jpb+QT2RHlwF7pgDHvgdsQYBdlp/Ia6CzLev3ojoDNYcB0V1lRLXTb7322mtqUkP25Sxk94ZRo0bBUrxYx+SdOpalS2RtVEkmpadDZnpbZUF6mdwh79NPPvlEJZXyoVAuzApj2ftYxwUiMZt9n3L5UCSrMsjalqxjc2NC6Q8uHgbiBgLHVwC2YMCu9Ujki+N55ToBzWcAERUye+Nkfb4TJ044/7rNppZjkSVYLMGLdUzeq+Pb73xE7Xn8wQcfICrKmkMQJKEePHiwGqYh71nGsgHYXhSILHUl6xVfO+O7XLlyaitHp93VWMemw2WDfG3fLGDxzcCJVdr/C3IRzv48OY4cT44LYO7cuU7JpOMNLQnln3/+CUvwch2T9+p45Yf9sGjRIssmk0J6JqUOVDLJWPY+1nGByU5qjiWHsiePx48fV9ci1rG5sYfSV+QTXPxLwI6XvXeOemNQ9c7PsH//AXXLUBZHlsWgZQ/hW2+9NceuHaZjUB0jZrx1b4GzjlnPZsFY9ogLFy6oXddkP/BVq1apyToyZKNKlSpI2LePbbKJMaH0le1jvZvoXLWvyEPYfPkONVBaZt9ZikF1jHpjgfrjYUmsY9azWTCWvUKGaixevFitXtDhhrVsk02MCaWvbqnEDTDufM1nAtX6w1JYx6xjs2Ass47NgHFsekwojZZ8CFhSG0hLNu6cIUWAHrutM4mEdcw6NgvGMuvYDBjHlsBJOUaP0dn4KJCeauhp1flk9q0V9lplHbOOzYKxzDo2A8axZTChNJKszydLqtjTDD2tOp+cV85vdqxj1rFZMJZZx2bAOLYMJpRGksWeZZ09X5Dz7pkK02Mds47NgrHMOjYDxrFlMKE0imwrJTuHuFifb8r3QOUngJCHgJFzvHR+Oe+x5UBSAkyLdcw6NoukfZgyczkqD0v3brtg8faCdcw6Js/Jtmw9eZXsA6u2l3NOKLcdAEbMARaNAG6pDJSI8GIZ5PwJs4GYMTAl1jHr2CS2LX/LuHbBou0F65h1TJ7FhNIoiXFX9zR2tvh3ILYa0K2hAWWQ80s5zIp1zDo2icXLfzCuXbBoe8E6Zh2TZ/GWt1Gz3BI3yTdOD9cYAbz4FbBhL2DrCzz8ft6H2X0UaDcRCB8A1HwaWLpVe97W/W4X5Go5TIh1zDo2iRo1auDFGXvcbhdyw/aCdexLjGPrYQ+lEVKOA6mnczy84SWgxThgcEegX0ugaHjeF4dmY4HhXYDpg4DtB7ULTWgwUCc/y0tKOS4dAwqbbG9k1jHr2CQ2/PgNWsTWd6tdyA3bC9axrzGOrYc9lEZwkUwKuVDsPwW0qgmcuwi0Gg80fF77KjwA+Pa3rN8dMhO4OxaYcA9QvSzQuynQpjZwczRQKAT482jWc10937k8ibBiHZcrCXy8Gqj7DFBnFPDELOelOa9Xx2Lystyf71we69bxBz9qdVTvWWD2z86/604dT1qS+/NNX8dSn6GXnOrzofeBUoOAe97J+buLtwC1RgI3jQCmr85fPfee7Pq4OY5pwnrOTx3nVk966jjH4xau40OJQNuJWpta/zngq43669jlMU1Yx/6GCaURMi67fFh6GUVMRaBWNLD1Ne3r55eAImHA7fW0nx84BazaCTzZxfn58oZqUEn7Pq/n5yyPwQur+0kdnzoPTF0BbJ4IxL8ObE4A4v5yv47zen7O8lizjuMPAnM3aHX068tafZ1Ndr+O83q+JepY6jN+V2Z9iuGdgc8G5/y9tHRtQt+q0cDvrwJvLgESL7hXz7kd1+UxT5+AVes4t5/pqWOXj5swlt2t45Ag4J1+wK43gRXPAU9+DiSn6Ktjl8e8cNbzL5KcMKE0QlAhlw9vPQDUKAcUueaW1nebgQ51sx6X31O3tss7/96OQ0CDyjmPe+3zc5YnDFatY7lgplwBrqQBV9KBG4vnr45ze37O8lizjv84CrSoAYQXAgoX0upu+Xb36ziv51uijqWedv7tFLNt6wDFXLyXN/0N1K0AlC+t9RJ3bQCsiHc/ll0d1+Ux12yGVes4t5/pqWOXj5swlt2t46hSQMMq2vfSk1mmGHAmWV8duzzmuRTPvkDKgQmlEcLKuHxY3jDZP2k5zN8I9GmR9f+gICA9Q/tyWL4N2HHYvefnLE8kTMeNOr6hODCyO1DpCSB6KNCxnnYbxd06zuv5OctjzTquVwFY84fWq/hPsvb9kTPu13Fez7dEHUt97jrg8n19raP/AOVLZf1fvj/yT/7bi+se81QSrFrHudFTx1aJ5YLUsdz1kTqtGOm5Os48ZvW6+SsM5RsTSiOEl3N5MZYLccNrehjPX9RmfXdrkPVY46pAaAgweh6w7ySwYJM2tkRc+8Zy9XwnUg6zTchxs44lQZFlmva/CxyZqtXTuj/cr+O8nu/EwnUsE8Se6Ay0fxW4azLQvAYQHOR+Hef1fEvUsdTnjj1oWK3gC0/mp724rpAIIDS3bvjA5Vd1bNJYzm8dn0nSJpp+NNBzdZx5zH+XMGUd+xsmlEaw2YDIWPkm86GMDCDexSetRZuBTjHaLT+H6FLA9Ee1nscGzwPz4oBB7bSu/BtLXP/52QpytRzWrOMfdgA1ygKli2q3U7s3zBoD6U4d5/X8bAWxdB2LxzsAW14BVr+o3bK6qVz+4ji351uhjjMyMhAfH48GMXWc6tmV6Ks9kg7yfXTJ/LUXeR/ThiMXb0R0dDSsWse50VPHOZgwlvNbx6lXgF5vA8/dAdxa0zN17HTMli098KroerhskFEimzttvSjd+cmf5Pw1efM81j7n4/1aaV8OI2bnfrvb1fMzd76Qcli0jiuW1noVUy5rn3zldupj7dyv4+s9X7F4HYuT57QGX1YekDF5H/wrf3Gc1/PNXsdBQUFITk4G4l8GdvzucqtWh9jq2ngyGRIgO+ks2waM6ZW/9iLPYxaxYdlvFzDmw86wah3npaB17ERyLRPGcn7qWFbKGPAh0L4u8FBrz9Sx0zFvCzZlHfsjJpRGqdoXiH8pz1+RpYPkArrgyesfTmbWyi2BfD1fdr6o2g9WrePmN2k7j9zyAhBk0yYu9Wzsfh279XyL17G4820tFmUw/qePAyHB+Yvj6z7f7HV8TT13fBXYdhBITgUqDAW+Gg60uEmrl7f6Au1eATLswDM9gMhi7tdzbsfNOmYGnhk9ApGR5hvf524dX+9nBa1jp8e7vIevvu6IFi3yGvhu3jpev0frfaxfMWupu88HAzGVCl7HMmYy65jpQIkv8PmcXoiJiTHiVVuWzW7PdSU98rTVXYHjKwv8iTi7soOBt/sBfd3tybcFA+U6Ae2WwtRYx6xjs2Ass47NgHFsGUwojXRkKbC2O3ymzRKgfDeYGuuYdWwWjGXWsRkwji2Dk3KMFN1V6yW0GTzSQM4X1Vk7v9mxjlnHZsFYZh2bAePYMphQGj1LtvkMINjgRWyDw4Fm07Xzmx3rmHVsFoxl1rEZMI4tgwml0SIqAE2mGXvOJlO181oF65h1bBaMZdaxGTCOLYEJpS9U6w/UG2PMueqN1c5nNaxj1rFZMJZZx2bAODY9JpS+EjNeS/a8SY4fMw6WxTpmHZsFY5l1bAaMY1PjLG9f2zcL+G0IkJ4K2NM8MwFHxmjKbXUr9ky6wjpmHZsFY5l1bAaMY1NiQukPLh4G4gYCx1do60UWZJ1Kx/NkFrlM/LHSmEl3sI5Zx2bBWGYdmwHj2HSYUPoLWV/+6DJgz1Tg2HJteznZEQR5rTtvy/q9qC5AzaHaEg1WmM1dEKxj1rFZMJZZx2bAODYVJpT+KCkBSJgNJMYBiZuA1NM5fyesDBAZq+1RKtvQFb1mPypiHfsa45j1bBaMZdYxXRcTykBw6RiaN7oJQwcPQr+HBwJhkUDhKF+XylwuHcOzTz6Ks2dO4MOPZ7KOvVTHy76djRdHP4OfNmxERMmKjGMvuJj4N2Ib1sBbb7yCzl17Mpa94dIxPNK3J6LLlsErr73JOvZSHc/6+G188vH7WPtTHOs4ADChDBDp6emw2WwICuLEfG/JyMiAbG0fHBzstXNYndSv1LPEscQzsY4DFdtk72ObHFiYUBIRERGRLuzuIiIiIiJdmFASERERkS5MKImIiIhIFyaURERERKQLE0oiIiIi0oUJpZ9bu3Ztrj87fdrFgufEOvZTjGXWsRkwjlnP5BoTSj/XqVMnjBo1CleuXHF6fNmyZYiJifFZucyEdcx6NgvGMuvYLBjLgYcJpZ9bs2YNFi5ciNjYWOzYsQMpKSkYNmwYevXqheHDh/u6eKbAOmY9mwVjmXVsFozlwMOFzQNAcnKySiK//PJLREdHIyQkBHPnzkWjRo18XTTTYB2zns2Cscw6NgvGcmBhD2UAiIiIQK1atZCWlobDhw+jSZMmqFmzpq+LZSqsY9azWTCWWcdmwVgOLEwo/dyBAwfQtm1bTJ48Gd988w22bNmibn03bNgQGzZs8HXxTIF1zHo2C8Yy69gsGMsByE5+rWTJkvYePXrYT506lfnY5cuX7SNHjrQXKlTIp2UzC9Yx69ksGMusY7NgLAceJpR+7oMPPsj1Z6tWrTK0LGbFOmY9mwVjmXVsFozlwMNJOURERESkC8dQEhEREZEuIfqeTkbIyMiQoQnq+6CgINhsNla8F+tY6lfqmTxL6lfq2YGx7HmsY2OwvTA2ltkmBwZeNQPArl271NqTsu4kk0nvkIarZMmSCA8Px8WLF710FmuT2L3jjjtULH///feMZS/V8fLly1Ud9+zZk3XsJdJGSFshbUb2D0nk2ViWa57EslwDyf+xh9Lf2e2oVz0S0ycNR4d2rYGz8UBYGaBwlK9LZh52O0KunMLSL15H0rkzKJqWAFxiHXu6jpFyHJ/9dxTmfxmFri0qAJeOMY49zW5Ht3a34L8TBuHB++9he+ENdjuKBl/AtzNfRsniEQhJ+oNtspfai29nvYw1P65EvQp2thcBgJNy/FHSPiBhDpAYByRuAlJP5/wdSSojY4HI5kDVfkDRqr4oaeBiHbOOzYKxzDo2A8ZxwGNC6U+fyI4uA/ZMAY59D9iCALvcStHG9blmy/q9qM5AzWFAdFe5V2BgwQMI65h1bBaMZdaxGTCOTYUJpT+4eBiIGwgcXwHYggF7ev6P4XheuU5A8xlARAVvlDRwsY5Zx2bBWGYdmwHj2HSYUPravlnAb0OA9FTAnqb/eLYQIDgMaDINqNbfEyUMfKxj1rFZMJZZx2bAODYlJpS+7OqPfwnY8bL3zlFvDBAz3rq3wFnHrGOzYCyzjs2AcWxqXDbIV7ydTAo5fvw4WBbrmHVsFoxl1rEZMI5NjT2Uvurujxtg3Pmaz7Te7W/WMevYLBjLrGMzYBybHhNKoyUfApbUBtKSjTtnSBGgx27rTNRhHbOOzYKxzDo2A8axJfCWt9HjRzY+qk3AMZKcT2aRX91a0NRYx6xjs2Ass47NgHFsGUwojSTrTMrSQJ6YzZ0fcj45r5zf7FjHrGOzYCyzjs2AcWwZTCiNJIuWy3qRviDn3TMVpsc6Zh2bBWOZdWwGjGPLYEJplKR9mDJzOSoPS0fIQ8DIOTCWLHp+bDmQlADTYh2zjs2Cscw6NgPGsaWE+LoAVrFt+VsYMQdYNAK4pTJQIsIHhZBtGhNmAzFjYEasY9axWTCWWcdmwDi2FiaUBlm8/AfEVgO6NYTvyJ7fiXEwK9Yx69gsGMusYzNgHFsLb3kboEaNGnhxxh5s2AvY+gIPv1+w4+w+CrSbCIQPAGo+DSzdqh1v6353j2AHEjfBjFjHrGOzYCyzjs2AcWw9XIfSACcPxKNFbH0M7gj0awkUDde+8ptMNhsLDO8C9G8NbD8IDJoOnL8EJH0CFMpPX3Pvo0DhKJgJ65h1bBaMZdaxGTCOrYe3vA1QNPQS9p8CWtUEypUEek8G1uwCOtQFvn4y6/fOJgMdXwPS0oG0DGB4Z2BQe+1nQ2YCd8cCE+7R/l+9LDB7PbD3eFYy6eq4Lo/ZLdF0CaW7dexwMRWoPQq4txkwqa++OnZ5TIvXcZXhQPHCQJANKFUEWP2i/jrOcUwT1nF+6znhJPCvj4AT54DgICBuPFAkXF895zhmm0MoUj7KknX851Ggz5Rs/z8GfDEU6NWk4HXs8pj2+ejVdzisGseTlwHTV2tLVnasB7z7MGCz6YvjHMfseho2E7YX/oQJpQG2x+9S/8ZU1P4vSd2/2gCz1jn/XrHCwLoxQEQYkJwC1HsOuKspkJQCrNoJbHvN+fflDdWgUtb/XR3X5TGfO4HIkvVgxTp2eGUR0LxG1v8PnCp4Hbs8ZobBi9f7YR1vGOfcE++JOnY6pgnrOL/1POBDYOK9QOubgTNJQFio/nrOeUy7Zeu4VjSw9Wo9SjssH2pur6evjl0e87bGsGodnzoPTF0B7HwdCA0BbpsAxP0FRJcseB27POam39Cic4z3XjBxDKURtu78GzXKaT0Hom0doJiLW97SGyCJn0hN0z5ZSVO+9QAQGgzUKe/8+zsOAQ0qZ/3f1XFdHtNWCFatYyGfbmUIQdcG2Z6vo45dHjPoaqVbtI5dPl9nHedgwjrOTz3vPKzVpyR+onRRICRYXz27PGahIjCbgsTyd5u1XjB5jqdiOfOYxUrCynUsd9BSrgBX0oAr6cCNxfXXcY5j3ljOky+PXOCkHANs3XXA6RNVXuQWdYPngQrDgFHdgTLFgKAgID1D+3JYvg3Ycdj5k5rbx4zO1jVnwTqWNUBf6+P8mN46znHMsEhYuY7ldlWbl4GmY4A56z1TxzmOacI6zk89y4cY6a29YxLQ6AXg1UX669nlMS0eyw7zNwJ9WngmlnMc08J1fENxYGR3oNITQPRQ7fa03NrWU8cuj3mzL5dYsQYmlAbYumMPGlZzb+HJkkW0Lv6Ed4C5G7RxTI2rat32o+cB+04CCzZpY0uEO29Yp2PGheDE+SDL1vGi34CaUdpXdnrqOMcxgwubcmxffuL457HA5leA70ZoSYlMItMbx07H/C4Y2/eeghm5W8/SA/PTn8B7jwC/jANWxmtfeuo5xzF3hmLlzztg5VgW5y9CrdLR7eodCL2x7HTM2EhLtxf/JAOLfwf2vwscmarVybo/9NVxjmP+FYJ1v+710Cuj3Jgvs/AzGRkZiI+PR4OYOtLH4vbzypbQuvV/2g1ElwKmP6p9mpWexnlxwKB22kDnG0u4X5ayJWxoUCsaP/30E6xaxzI258tftHFLI+cCH68GJizUV8c5jrnqCiZMmAArx3H50tq/UaW0tVe3JOiP46xj2tCtZSVs2bIFZpOfepb6aFIVqBipjZ2UepbbhHrq2fmYNnRrVR1bt26F1dvkRZuBTjFA+NXRQp5okzOPGdUMZpOfOv5hB1CjrDa8onAhoHvDq2ModdSx8zFt6N66BuLizLsGs7/gpBwvCwoKQnJyMhD/MrDjd20LxFxIb2REIW0izbmLwLrdwOAO2s/6tdK+HEbMdu+TsNMxL9mwbmcKBteqBavW8Wv3a19i5lrt9snYu/TVsdMx19mw41Isxo4dC6vWsUz+yrBrMeeYUHZfM3117HTMVBtWbU/BfU/Xhdnkp56bVgNOntd6Y0rI5LvdwOPt9dWz0zEjbFj3RwYe71EbVq1jB0lqHrtatw4FrWPnYwYBkc1hNvmp44qltV7JlMtaj+SaP4DH2umrY6djhtqwZlc6HutqruueP2JCaZSqfYH4l9S3HV8Fth0EklOBCkOBr4YDLW4CDpwGHpuuTcSRyTPDOgExubx5HLcQs3N1XJmUk3XMDAwb+QRiYmIsW8f54W4dOx1X/nAl5FM5LFvHJ85rS3kIGf8kvQpNq+urY+mxzzpmBgYNexRNmzaFletZJuC8ep82g1Xe39Lb1aOR/ljOOmYGOt3ZCj169ICV2wv5cL/pb2CBi+XHClrHWcfMAKr2g2m5UcfNb9J61295QVsSTCYp9Wysv46zjpmBDnfcip49exrwgq2NC5sbaXVX4PhKtz4RX0/ZwcDb/YC+Ld18gi0YKNcJaLcUpsY6Zh2bBWOZdWwGjGPLYEJppCNLgbXd4TNtlgDlu8HUWMesY7NgLLOOzYBxbBmclGOk6K5aL6HN4JEGcr6oztr5zY51zDo2C8Yy69gMGMeWwYTSSLKQXvMZQLDBCzIHhwPNpmvnNzvWMevYLBjLrGMzYBxbBhNKo0VUAJpMM/acTaZq57UK1jHr2CwYy6xjM2AcWwITSl+o1h+oN8aYc9Ubq53PaljHrGOzYCyzjs2AcWx6TCh9JWY87FeTSlnyw2vJZMw4WFbMeK0OvIl1zDo2AmOZdWwGXoxjWbFNsXqb7ENMKH3FZsMH66PQ/wMgwxbuuYk6cpyQIkDzmUD98dYYN5kbee1SB81nIg3hSLd7qC5Yxy7rWMUd49g7WM8BW8cZcpllm+zlOg5W61CuuvQwr3s+xITSR2RbqqeeegrF6g9B8J17gbLts9aLLAjH8+Q4PXZb8zZ3Ls5F9kLshGLYcepG7QHWsedJvPXYDXtZbYuLjIIm74xjt+rZ0V7YUbD2QhacV9heXLeO9bYX6/4MwYU2v7JN9mIdB5XrgNfiH0b3ofOxY4f59p4PFFyH0gcuXryI2NhYtT3Vxo0bUbhwYa2//ugyYM9U4NhywBYE2DOuc0PclvV7UV2AmkO1JRqs3CvpwpNPPonp06fjj127UDF4R77qWBIj+Tuxjt3z4w8/4K2Rt2Pm6Ca4MW2z23GsJaAZsJfrhOCbhzOOr8duR+r+b7Hu4/vQsW4abEHBbrcXdns6lm0Fyrd7FQ26PMf2Io86zt4my9af0rTa8tEmnyrdB1VuHYzHHnsckydf3eqJcq1jPde9Sykp6rpqt9vx66+/atdVMhQTSh8YPHgwZs2ahd9++w116rjYpi8pAUiYDSTGAYmbgNTTOX8nrAwQGavtAytbdxW9Zj8qUrZt24ZGjRrhtddewzPPPJOvOk5Oi8D63VfQ8f4XEVTtIdaxG9q1a4cLFy6oBt2WvN/tOD6NGmh633/xxrT5uPfeexm9bpg/fz769OmDffE/oqp9vdvthb1KXzRpey9KlCiBVatWsa7dkHH+b/zfv2Nwd9vyqBV5Nl9t8uuvv44XXngBW7ZsQf369VnfucnWJicfXI0iIZfcrmOHnTt3okmTJnjkkUfw3nvvsa4NxoTSYAsWLMA999yDDz/8EI899ph7T7p0DEhNBDJS8cjAfyO8RHm8P/Nbbxc14GVkZKB169b4559/sHXrVhQqVMitOkZQGBAWiR837ELHjh3VLZS6desaWfSA9PPPP6v6/uabb9CrVy+36hiFozJ/3KxZM5QtWxbfffedsQUPUHfccQdOnTqFuLi4fNWzkL/RXXfdpf5mLVu6u3+rdUkbEBMTgx9//BHt27d3q44dLl++jIYNG6J06dJYt26ddseD8nT//ffjyvmDWDD3I7fqODu5tv773/9W11qJcTKQnQxz4MABe8mSJe133323PSMjo0DHeOGFF+wjR470eNnMaMaMGXLfxL569eoCPT8pKckeERFhX7hwocfLZkZdunSx16tXz56enl6g50+ZMsUeEhJiP336tMfLZjZSR1JXU6dOLdDz5W9Ut25de9euXT1eNjNasGCBaguSk5ML9PxVq1aptujTTz/1eNnMSK5xcq0rCLm23nXXXepaK9dcMg57KA2Snp6Otm3b4uDBg6q3rFSpUkad2pJSU1PRuHFj1TMwe/bsAh/nypUrCA0N9WjZzEjqaeTIkWjVqlWBb1nLrXIZoiDHoOv76aefVHwXK1aswLfMN2zYgDfffJMx7gbpaczzLsd19O3bV8X35s2bERZm8G5pFnPmzBn13qhSpQpWr16N4OACTvqhfGFCaaBJkybh1ltvVV/k/QQ+JSVF/Vu8eHFWtwHDC4TNZlNfBSV/Lzb+xtSVTF6QL8HbsN537tw5hISEIDw8nDFuABnOIZNen376aSNOR0wojSWNt56LLbG+iShw8RrA+jYz9lASERERkS6cbuZhp0+7WE6CvD5ekogokDmGH5AxZHWEw4cPs7o9iAmlB40bNw5PPPEEfEHGC1qRDHJ//vnnfXLuP/74A1Ykg9yNdujQIfzwww+wouTkZJ+c99NPP1WTCMn7ZEIa1000dsx3v3798OKLLxp4VvNjQulBMqPs77//hpHOnz+PFStWqHW7ZJC+1fz111/44osvvN4zLL0Hjokn8jceMmQIbr/9dljNt99+i27duuHIkSOG9disWbMGt912m/rAZjWSSA8YMEDNor+2B8tbPVrSjshafgMHDsTSpUthNbm14d6s7xEjRqivo0ePwmqkXZXVBhzfXystLc3j7bi0JbLSikyUJc9hQulBTZs2Vb1W2RthvW8GuaDIxUTIGyH7G27Xrl1qBtujjz6qbvvKlo5WI0vMyMzJDz74wGsNv2MgvcyElTofPXq0WvrJilupderUCbVq1VJbWeZ2AfAUqXPpgf6///s/teSWfHCymrNnz6rZqgsXLlT1kT22vTXBb/369fj888/VckKyQLSVbN++XS2wv3v37hw/k/r2dHLjWL5J2pPly5cjOjoaVnPgwAHVjn/11Veqjc0e4/L3eOONNzx2Lvkb7t27F/PmzcN9992nFpuX5aAEhxx4gIFrXprWwYMH7YmJifYjR47Ye/XqZZ80aZI9JSVFLYx9+fJl9XXq1KkCHbtSpUr2JUuWOD32+++/2/v06WMPDQ21d+jQwb5ixQq7lb311lv2++67z56ammo/efKkPS0tzb5v3z77hg0b1GP5tWbNmhwL4spC0s8++6y9cOHC9ttvv92+ceNGu1XNnj3b3rBhQ/uxY8cy63fHjh32OXPm2P/++29dx3Ysin7p0iX7f//7X3uRIkXsd955p33v3r3qcfnbWs3YsWPtpUuXtm/fvj3zsUOHDtmnTZtmX7p0qUfO4dho4euvv7YXK1bM3q9fP9VmyeNWqnNps3v27KnaVYlvhytXrqj4lsX3PWn9+vX2G264wf7kk0/aL168qM5T0E0vAtnkyZPtxYsXt7/++uvq/3/88Yd9zJgx9qioKHvHjh09dp7Dhw/bW7durf7G15K6J32YUOr03nvv2StWrKgufDExMWr3CpvNZu/cubO9TJky6jH52aJFiwp0fEmU5A31wQcfqMRx1KhR9jp16qjHf/31V6c3Q0F3KAlEM2fOtD/yyCP2xx9/3F6tWjVV5w0aNLA3atTIHh0dbS9atKj9jjvuKPCOLwMHDsz8vzRucp527drZv/rqq8zHrVTfjiRGEm1J4MuWLatiWxIPSXbkg0+pUqXs58+fz/dx586dm+P9ITuTtG/f3v7uu+968BUELtn5Qz5ESn1InFepUkXtBPL999977By7du1Ssf/iiy/arUw+vLRt21Z9gNy/f7999OjR9saNG9sjIyNVklNQjkTR0W789ddf9k6dOqm25VpWa1vE559/bm/VqpX9/vvvVzs4yYfW6dOn6zqm1Hn2upT2W/628gFYbNmyxR4XF2fv27evuraSPiGe6OW0Mtm7WG4BSnIuC9b++eefGDRokFqlf+jQoWqyjPysZ8+eBTr+q6++ivHjx6tbunIsOX7lypXVHqU1atRAUlISChcurG77WmWdM9m/WMa+NGrUSN3ml3p+//331fCATz75RN2GlX13S5QoUaDjy/GeeeYZVKtWDS1atMCvv/6qxmrKY82bN1fjnOQcFSpUgFXI7Si51S91LDsQya05uU0XGxuLzz77DOXLl1fxWLRo0XwfW2ZaTps2TS1AL7cUZb/jiRMnomvXrujSpYu6JXbixAnUqVNHjZUtUqQIbrjhBpjdzp071ZhVuf0q40hlT/qVK1di7NixKjZ79OhR4Pf6xx9/rNoSxxiy33//HY888ohqR+RW4MmTJ9XtxnLlyqn4l1uDd955J6xA4vimm25St1rlq3fv3ujevTv+9a9/qba3oKT9lrbasYi8tFWyo4sMLZB2W/7GsoPO119/rcb3jRkzBlYi723ZRUiGXMg1de3atbjxxhtVW1vQhfelbalYsaL6XuJZ2vZKlSqp72U4h1w/jh07ps4n7Y+0b47fp/zjOpReII1P+/btPbpCv0yCkAvt8ePH1QXmxx9/VI+1bNlSjS+rWrUq6tevrxIpK26DJktASGOxePFidRHUk1xLA7Zp0yZ1IZWGRxInSWDkcWnk5PhywZFxq9LwSzIkCZWZyfguSeQloZbXXKZMGTVLUv595513dB1b6lEmOc2dOxe1a9fG/v37cenSJTVeU+o/MTERNWvWVImlPC4XArkIm51c+OSCKu/p/v37q4Rj0aJFKuGoXr26rgutJJDSdvTq1Uu9lyRhlwu5tFtyTNnWURJ4meUt7zO54P7vf/9TybyZd7J5++231SS/kiVLqtiWcbuS2L300ku6ji3Jo4w7XrVqlapT+aDw3HPPoUmTJmr8oGwPKx/SJJGXD6ryt5cYl3bd7KSOn3rqKRWHsn2rxJt84JHr2gsvvFDgmJMPwTK/YMGCBao9l6/vvvtOxb2QNlw6ZiSBbNCgga73E2mYUHqQIyBlBpkEsyQk8olUb4/htYmR9FTIp135ZCXnkeVU5HuZdSxLfViFo15k0pJ8SbIjjdB///tfj51Desyk10YmR+zbt0/1wEliI7MSJRGSSTqPP/646k2zWr3LwHbptZEkvl27drqOKYmi/A2lR0GWUJEEXSa4Sd3LBVbqWXqc5WIjs3AlmTVzT7zUsSR42fc1lwuuvMeljZE615vcSVIjk30kcZI2pV69eqonUu56yKx6Wa5IElpJXqWHXi7AZiZJjCRx8uFGesYliZZEUNrzt956q8B71DvIhyXH5Empc4lzuXMl9SyJvPSMygdXqW95P8i1wyp3+WQilHxQlDoQX375JZ599ln1gef1119Xd/8KQu4WSmeDY9Ks3NWStlqOZ/ZOAF9gQukFjk//0n0vjYgnE9bc9kpOSEhQvTlWuS3lKsGRC8LLL7+MHTt2eHT/7rx6OuViYOZem+t58MEH1Ycb6QUwc4LnL/t2y4cZSSpliRmjZmBbYRiNkGRPEmvHHQ75gBMaGqp6yb755hvVMyy9tgUld5SkjZZERtoNGU7jqm6tUt/Zl76LiIjIMWxLPlBJYr9ly5YCf5iRY0mvb9myZdXfV4YUWLmuvY1jKHVyFZA333wzBg8e7NFkUuTWHS+JptwaMfvtEeklkU+w19a543u50EqD7clkMvvxs5/XscSEFZJJRy9tdo66kJ5CGX7hyUb52np29b3VSDIpSaWM4ZMxjnJ71lMc9epIWh2x7ahrx3I518aA2Uiy4UgmhSSTQha/liEAMuZUT0IpieS1vWKOus9+u9WxPJT862jzzOza9trx+qVTRu5M6BmrLseSZFI4ksns7Uj29sTK7YunsIcyn+TTjoxnkrEecptCxmVId/21wcjg9DwZu9emTRs1QUluDcnF71ocB+N5MnZXboE6emx8VedyHnlfufq7m5EkeI71T7NzrP1pRJ07/uaOGLAquU0tCYkRsSd/dxmvLENpJJGViTvkPY5rtdwal2u5jHOVyWqzZs1SQz7IfRyBmk8yMF4mKEhvmHTHy7g9mbRx7Scbb3/SkYuKjKmyyu448jqlV0YmJcgYI5l9KY9duxitNy+yci7HIvNWWgRXPjzJqgUy5k7izlEHDt5ObBznkwWJZWyVVchrldcsste51LcRdS5/a7nVKxMWRo0aBatwvLez704kt2S9nUzKuaRNkzGD0sbJBBJp87y5eYA/kdcu1zSjX69cq2WYmgxBkGu6XNvlGi8TMCl/mFDmk3TBy60fefPL7DTpKSvo8jQFJQO2pbGRvV+///57WIGMbXI07tJbIEvYyCQC+QRvBDm33PKSWaCy9eC7774Lq5ALqexYI7da69atq2bBOnoLvU3Gmk2dOlUNppfbjTKeyipkDLa8ZlmmSVYSMGJPb8fWdPI3lnP36dNHDSOxSq+wkFUL5D0uO2Ht2bPHsA+P0gssbZqM2XTseiZ/C2n7rECSOLmmybVNrnFGkmu4Y1a//L3lGi/XesofJpT5JBM+sn+CktsRsqyHjCMzisz+k9ndstSCVWaqyS2gaz9VyvJJMivz2h4zb5DzRUVFqYRy2bJlllmeSWQf2yVJtSxdldvkME+TniFZn056EOR9J38Dq5DXKq9ZkmipA6kLb3P8TWXVCEmmHKy0nIq8t+U9Lu91GVNpRJxLz5y0ZdKmXXu+a9s+s5KxknJNk2ubkTPc5dotS+5lT9zlfSfXesofc4+yvh755JlyHEg9DWRcBoIKAWFlgMK5X7SkpyZ7Qilvfvk0KbemOnToYFDBofbaHfToo2hQ80bgbLzb5Q/U+s/eqMrFTT5NymLmsuiwUQOp5VOs9Ag/8cQTaqmLgsSPX3Gz/JLMOF6/3PaWcaxGkb/tK6+8omZoytIt2dceNXv9OyYRyJADWejdKPL+kiVbZDyZvL9kySyXSY1J61/Gisr7e8qUKYbdfZK4lnU+ZRknmdApa686rjNS9zLR0+z136ByIfy88iu0aH+XocWQa7dcw7N/aJK6l2t9ngK9/r3AepNykvYBCXOAxDggcZMWDNeSoIiMBSKbA1X7AUWrZn6KlE9OjkkI8q+skyWNvdwK9Pfy+4UCll+Sx//85z/qx9Lgvvbaa4YPNdBTfr9RgPI363C/2h1IJqD5sodQ1v5sVvcGBB/80hL1n1E6FlvP1kOj2+6Gr0hPpeyGJItub9y40ZLxb3T5Zdzk888/r9o8IZMQZYJOoJQ/T35afumNlAXs5QOz49ou/8qSaE4TEf20/P7CGgmlvMSjy4A9U4Bj3wO2IMAun/7yeum2rN+L6gzUHIa4g6XQ4tZb1U9lFw/ZFlHGNwVK+RHdVbp8YDgPlH/TuWbo9Z8PMWfOXN2LaOcb6z/g44flZ/0HWvysXr0affv2xccffYTutwQFXPkD8f0r45YlmZctToWa+R0bGzDl9zXzJ5QXDwNxA4HjKwBbMGAvwKzoq89LKdUGvV47jeHPv2nczigeLD/KdQKazwAiDNyDmuVn/TN++P5l+8P2M4CuXzKGViZHLVvwMcomjA7c96/BzJ1Q7psF/DYESE8F7Gn6j2cLAYLDgCbTgGr94XUsP+uf8cP3L9sftp+8fvH6GwDMmVDKS4p/CdjxsvfOUW8MEDPeO13YLD/rn/HD9y/bH7af3sLrl3mvvz5kzrUgvB0MQo4fP847x2b5Wf+MH3gV379sfxg/3nlv8frl2/bHh8zXQym3ieMGGHe+5jM9e/ub5Wf9M35gGL5/2f4wfjz3fuL1y7ftj4+ZK6FMPgQsqQ2keX9HiUwhRYAeuz0z0JblZ/0zfvj+ZfvD9tMovH6Z5/rrB8xzy1vy4o2PagP4jSTnk1nYevNylp/1z/jh+5ftD9tPI/H6ZY7rr58wT0Ip60TJ1H5PzIbLDzmfnFfOrwfLz/pn/PD9y/aH7aeReP0yx/XXT5gnoZRFR2W9J1+Q8+6Zqu8YLD/rn/EDn+D7l+0P40ffe4jXL9+2P37CFAnllEkvofK9yxHSLx0j5/igALJo6bHlQFJCwZ6ftA9TZi5H5WHpCHkIxr8Glp/1z/jh+5ftD9vPguD1y7fXXz8SggAnG7iPeH4iFj0VhFsqZ6BEhI8KItssJcwGYsbk+6nblr+FEXOARSOAWyrDN6+B5Wf9M374/mX7w/Yzn3j98u31158EfEK5ePFixNYqgW4Nz/q2ILJnp2wYXwCLl/+A2GpAt4bwHZaf9c/4KVAN8P3L9oftJ9tPX11//UlA3/KuUaMGXnzxRWzY+Q9sfe14+P2CHWf3UaDdRCB8AFDzaWDpVsDWF9i6Pz9HsQOJmwr2GmbswYa92jl99xpYftY/4ye/+P5l+8P2k9cvX11//U1Ar0N58uRJtGgei8EtDqBfS6BouPaV30BoNhYY3gXo3xrYfhAYNB04fwlI+gQolN8+3N5HgcJR7r+GA/FoEVsfgzvCP14Dy8/6Z/zw/cv2h+0nr19+f/31NwF9y7to0aLYf+AQWvUHypUEek8G1uwCOtQFvn7S+XcnLQE+XattnfncHUC/VtrjQ2YCd8cCE+7R/l+9LDB7PbD3eFYg5HZcl8dMTcxXQBQNvYT9p4BWNYEr6UCPScDJc0BIMDCmN3Bvs6zfXbwFeHoukJEBPHsH8Gg7917DoUTgofddHzfHMbt5r/y51aOe8uc4ppfqP68yFLT8Lh/3Uv2fTQY6vgakpQNpGcDwzsCg9vrK7/KYXowfcTEVqD1Ke3xSX33ld3lML5a/ynCgeGEgyAaUKgKsflF/+XMc04vlTzgJ/Osj4MQ5IDgIiBsPFAnXV/4cx2xzCEXKe778fx4F+kzJet6fx4AvhgK9mhS8/C6PaZ+PXn2He6X+Jy8Dpq/WlizsWA9492Ht2qOn/nMcs+tp2LwQP7ldf4We8uc4ro74Dw8F2k503Ubquf6ezaPt1Xv99TcBnVBu375d/RtTUfu//KH+1QaYtc759+IPAnM3AJsnqo5l1TXd4xbg3EVg1U5g22vOvy9B0KBS1v9dHTe3Y5bMyN/CqNvjd2W+BvlE804/oGEV4PhZoPGLQLcGWqMtwSgTd1a/oE3akZ/1bgIkpVz/NYQEuT5uWKiLYz57ApEl63m8/LnV44FTBS+/HDfHMb1U/7mV4fSFgpff5eMjz6JISc+Xv1hhYN0YICIMSE4B6j0H3NVUX/y4POZz3osf8coioHkNz8VPjmN6KX4cNoxz7gH3RPmdjunF8g/4EJh4L9D6ZuBMktZ+6C1/zmPavVL+WtHA1qtllJiXRPz2evrK7/KYtzX2SvlPnQemrgB2vg6EhgC3TQDi/gKiSxa8/Bcvuzjmpt/QonOMR8u/72Qu18oi+urf5XFHnUbJAraf4YVct5GRxfRdf3Nre+U4eq+//iagx1Bu3boVNapVzGzw2tYBirm4XfzHUaBFDS1gChcCGlQGlm8Hth4AQoOBOuWdf3/HIe13HFwdN7djIigsf69h59+oUU5rNKJKaW8aIT2uZYoBZ67uArXpb6BuBaB8ae3i0bUBsCLevdeQ23FdHnPNZq+UP7d61FN+l8f0Uv3n9jM95Xf5+LkUr5Rfen+kQROpaVqPhDTCesrv8pi2Ql4pv5BP/HJ7SeLUU/GT45heip9cn6+z/Dl4qfw7D2vllMRPlC6q9RbpKb/LYxYq4pXyZ/fdZu2OhjzHU/WfecxiJb1WfklqUq4AV9K03sAbi+svf45j3ljO4+XP9VqpM/5dHnfVrwUuf25tpN7rb3Aux/XE9dffBHxC2aB+/ev+Xr0KwJo/tK7nf5K174+cAYKCgPQM7cth+TZgx2HnHsr8HBNhkfl7DbsOuDzX5gStXBWvHu7oP0D5Ulk/l++P/JP/15D9uC6PeSrJK+XPjZ7yu+Sl+s/tZ54qf+bj1et6rfwSqw2eByoMA0Z11xpmveXPcczoGl4rv6zP+lof59/TW/4cx/Ri/MhtuTYvA03HAHPWe6b8OY7ppfJL4i0XvTsmAY1eAF5dpL/8Lo9pwPt3/kagTwv95Xd5TC+V/4biwMjuQKUngOih2u1pubWqp/wuj3lzQ4+XP9drpc76d3lcndcvV22kJ66/Z10c1xPXX38T8Allw0bNgLAyef5enQrAE52B9q8Cd03Wbm/Jp4bGVbWu/tHztO7zBZu08RDiegmly2PKp+t8jn/YumMPGlZzXnhSbv3IbO+PBl7/+fl5Ddc9bkgEEFo8cMsvceDl+r/2Z54of+bj/y7h1fLLLSa5NZPwjnarSMat6S2/0zHjQnDifJBXyr/oN6BmlPaVnZ7y5zhmcGGv1v/PY4HNrwDfjdCSJxm8r7f+nY75XTC27z3llfJLT9ZPfwLvPQL8Mg5YGa996Sl/jmPuDMXKn3d4pfwO5y9Craght0w99f7NPGZspNfiRxKmxb8D+98FjkzVzrfuD33lz3HMv0Kw7te9Hi9/btdfoaf8OY5bMwzB4aV0ld9VG5kXd8tf0p3jFuD6628CNqHMyMhAfHw8GjRsCETGymf1PH//8Q7Alle0gfDSRX1TOSC6FDD9Ue3TpXx6mBcHDGqndavfWOL6ZchxzJq1C/YaYupklj/1CtDrbW2A8a01s343+uonIgf5XsbPuPsaXB3X+Zg2HLl4I6Kjo71S/tzoKX8OKg7gtfLnVod6yu/0eMuWXi2/Q9kS2u2Yn3Z7rv7LlrChQa1o/PTTT14pv4wX+/IXbZzayLnAx6uBCQv1lT/HMVddwYQJE7xSfiG3thy38GTN2S0J+us/65g2dGtZCVu2bPFK+eU8TapqPUMydlLKL7f79JTf+Zg2dGtVXXUSeKv+xaLNQKcY7Tap8ET8Zx4z6poZZB4s/w87gBpltWEBcnu3e8OrYyh1lN/5mDZ0b10DcXFxXim/q+uvJ+o/67g2hBa5ATfddJOu8rtqIz1x/c2t7dVz/fVHAZtQBgUFITk5Gd27dwcim2srzedBZogJmZknYxc6X71TLrPNDk0BLswA5j8BnDx//d7JXI/ZpXvBXkOPnqr8MrZCBqm3rws81Nr5d2Ora+My5FaBDARets3915DbcZ2OmWrDst8uoHPnzl4pf14KWn4n0h5IHORDfsqf188KWn6nx28L9mr55RPxhUva9zIZbd1uoFaUvvI7HfOSDet2pqBWrVpeKf9r92tllN6USQ9qjfbYu/SV3+mYfW0YdHcsxo4d65Xyy2B8R105BvLL+Ck95Xc6ZqoNq7anoG7dul4pf9NqWrmkV0tmpEr81I7WV36nY9ptWPdHBmrXru3V9kfdmm7u2fZHO2aQV9+/FUtrvZIpl7Xbq3J7V+/71+mYdhvW7Er32vs3t+uvnvI7HfeYDZv2XtF1/cqrjdRz/T2Ry3H1Xn/9UUDP8s5UtS8Q/xI6vgpsOwgkpwIVhgJfDQdaXP3Acufb2h9TBt9++rg2oNwVx22o7HI7bo5j3tRfV/nX79E+4dSvCHz7m/ajzwcDMZW08r7VF2j3ijS+wDM9tNln7ryGvI6bdcwMPDN6BCIjI71SfpHX36eg5Xc6Zpf38NXXHdGiRQuPl/96r60g5T93Kfvj6UCJL/D5nF6IiYnxePkPnAYem64NBpcGelgn12XPT/kvXcl+zAwMG/lE/svuZvnzIz/xk0kqpYT0VMAr5T9xXlviSkhCIAlx0+r6yi/tTtYxMzBo2KNo2rSp19qfV+/TZgLL31t65Ho00ld+OW7WMTPQ6c5W6NGjh1fKL6StlmRmwTVLyukpf9YxM4Cq/fJfdjfL3/wmrVf4lhe0JaJkAlDPxvrK73zMDHS441b07NnTK+V39/qbn/I7HzcDn878CCEhIQUuf15tpJ7r74E8juuR668fCeiFzZ2s7gocX6lttK5D2cHA2/2Avvm5+2gLBsp1Atot9Xn5C/QaWH7WP+OH71+2P2w/LXj9Sk1NxfEvbkGFkN0IDrIH5vXXT5gnoTyyFFibv1vOHtVmCVC+W8Gfz/Kz/hk/8Bm+f9l+Mn4sdf1KT0/H559/jnHjxqFe6YNYPNIeuO2PnwjYMZQ5RHfVsnybwXfx5XxRnbXz68Hys/4ZP3z/+rj9sUtviZHYfjrVP69f3o8f6UNbsGCBGp7zyCOPoEmTJnjj8/jArn8/YZ6EUhZkaz4DCM7fwr66BYcDzaZr59eD5Wf9M374/vVh+zM3oQOSL6VnLuZsCLafmfXP65d340cSye+//16NM77nnntQqVIl/Prrr/j6669RRyazBXL+4CfMk1CKiApAk2nGnrPJVO28nsDys/4ZPzAU379ISUnBoEGD0PfRZ/H1gbbXWYCN9c/4Cbzr1/r169G2bVt06dIFYWFhWLNmDZYvX656JwOh/IHCXAmlqNYfqDfGmHPVG6udz5NYftY/4weG4PsXBw8eROvWrdVYsk8++QQDxq9m+8n4Mc316/fff1dLC7Zq1Qrnzp3DkiVL8PPPP6NNmzYBUf5AY76EUsSM1/5Y3iTHjxnnnWOz/H5T/167/cf4cav+vYb1jx9//BGNGzfGqVOnVA+OjCdj/TN+zPD+/fPPP9GnTx80atQIf/31F+bNm6cW/e/WrRts17u97AflD1TmmeXtyr5ZwG9DgPRUwJ7mmQG0MsZCusWN+GTB8vu0/nf+7xlUPvUmIsKDEQT9y2EwfvKJ8e+V+JEm/4033sDo0aPRoUMHzJ07F2XKuNi+lvXvlfp3G+s/3/UvPe7jx4/HzJkzUb58ebz00kvo379/wdanDPT69wFzJ5Ti4mEgbiBwfIW23lNB1slyPE9mgcnAXSPHPLD8Pqn/ixcvqlmAjW6+EfOfLgabrLHG+GH8B3j7c/78edUTuXDhQpVQylaTwcHBAVP+fGP5LVH/J0+exKuvvor3338fJUqUwAsvvIDHH38c4eHhAVF+szB/QinkJR5dBuyZChxbrm3TaM+4zg1NW9bvRXUBag7Vpvb7YjYWy294/T/77LN49913sX37dtSU/WEZP4z/AH//7t69G71798aRI0fw2WefoVevXgFV/gJj+U1b/2fPnsWkSZPwzjvvqF7IUaNGYfjw4ShatGhAlN9srJFQZpeUACTMBhLjgMRNQOrpnL8TVgaIjNX2ZpXttIpesxejL7H8XicDuWVpCbl1Ip90Wf+M/0B//8q6ewMGDFBLpUjvZH72bPaH8nsMy2+K+pc9uKdMmYLXX39d7XQjSaQkk6VLlw6I8puV9RLKa106BqQmAhmpQFAYEBYJFL66I3wgYPk9SnZPaNasmWqkNm/ejEKFCrH+/RnjP09paWnqQ5GMmbz33nvVTG6P9t6w/n3LYvV/+fJlfPTRR5g4cSLOnDmDxx57TMV3VJSPXnOg17+HMaEkymby5Ml4+umn8csvv6jEkihQyezt+++/H2vXrlU9OSNGjLj+DFciPyQf9GfPnq22SZSJNw899JCacFO1qnV6/wKBwfsMEfkv6c2RNcqGDh3KZJICmuwAcvfdd6tFy1euXIl27dr5ukhE+SY3UGWIxpgxY/DHH3+omJa1JOvUqcPa9EPsoSTK9ilYZrxeuXIFoaGhrBcKSNOnT8eQIUPQsGFDNXayQgXzziol8yaSK1asULezZehR586d1W1up51tyO+Yc2FzogJwLJ/CZJIC9SIsy6fIkA1ZGmjdunVMJinguLVNIvkl3vImIjIBGR8ps1zj4+PVbG6iQBtyJGN+pVe9QYMG6tZ2165dOe43gPCWN1mOLFoeERGhenQ4SYECjUxKOHz4MG699VZfF4UoX6TNPXDgAKpUqeJyyNG0adNQtmxZtSJBUBBvoAYaJpRkKUlJSXjwwQfVjMHixYv7ujhE+daxY0dER0erxcmJAoms79u6dWu8/fbbLj/Q80N+YONHALKUxMRExMXFqR1wiAJNRkYGihQpgooVK2b26hD5+61scfr0aVy4cEF9IBKu7g7xjlFgY0JJliI9OzI+580338y8QBP5M1l1YNWqVTh06JC6DVi5cmX8/fff6me8LUj+au/evWjUqJHaxUYmi0lbe+7cOZQqVcrXRSMvYUJJliENmszgliVVZOuu48ePq90WxLFjx1SvpTxO5E+eeuop9O/fHzExMWov7h9//BE33HBDjh4dq296Rv6lWrVq+M9//qPuCN1+++1qgk2NGjVQu3ZtfpA3KY6hJEt499131QLPcgH+888/8ddff6nB3zfddJP6v5D/b926lb0+5Fdkuzm5tT1//nwkJCSo8WcyFrhv375qWSBJMiXZlA9LISFcuIP8y9mzZ7Fhwwa117YsTi7xK0sC3XzzzZkf9NnTbg5sfcj0ZLcQ2X5Obr+cP39e7bYwZ84c9Zg0brLWmXxyDg8PZ8NGfsexn7z0UgrZZ37evHkqnmVv7pkzZ6JkyZJYvHgxqlev7uPSEjkrUaIEunXrptaXlBneP/30E15++WW1FejDDz+shiGRObCHkixJenoksZSLcf369dVjnGFIgbCT07PPPqvGUH799de4dOmSGpd24sQJNTaYyFccQy5ym1hz1113oWbNmnjllVfUB3lpe4sWLYqvvvqK66aaBMdQkuUaPJnkULVqVbVs0Ouvv575c84wJH9y7ZhIx21Buc0tQzZk9qzc5i5XrhyTSfJpnH7//fdqSaCPPvoox8oDjomPR44cUQmkfCiS29+bNm1SvZVchN88mFCSZTgSRsc4M5mcI+MqZTkLIn8aovHee+/l+IDj+P8///yjLuISxxwzSf60TaLc7XFsYZv9g5BMepSx6m3atMl8XDaXcAznIHNgQkmmJbO2pQdSenKy9/Y4LsytWrVSW32VKVPGh6Ukct4FRxZ+lvFlua2V2rJlS3Xbm8hXfv/9d3Tv3l21oTLkQrZJ/Pnnn9GiRQuXvy8ffB599FGnnnTeETIfjqEk03rnnXfUkiuyxIpMXujRo0eOcZKcYUj+QpYDkg84snC57GfcuHFjXxeJyIn0Mo4dO1atOCArZMjkGm6TSA7soSTTkjE7Msbs1KlTuOOOO9TyKnI7MXtvJZerIF+TeHzjjTfQqVMn3HLLLdi8eTOTSfK7nnPpYaxbty5++eUXTJ8+Hbt27UKfPn3YhlImJpRkWkePHnVaQHfRokWqt3Ljxo0+LReRg2xFJz08cgv7ueeew7JlyxAZGckKIr8gO9w8+eSTqjfyu+++w1tvvYU9e/Zg4MCBHL9LOXAdSjL1p+rsMw7lVrfcTpReSiKjyeoC0mPusHv3btVrLj3p33zzDXr16sU/CvnNYuSTJk1Sw4Zk/KPc5pYtFGWWNlFu2ENJgUNuVV86BpyNB85s1v6V/+ci+37HMvNQJjrIcisyK5HI0/GWF7kwR0VFZcbkwoUL1TIrEpu//vork0nyaLwVlGw9+3//939qWTVZK3Lo0KHYt28fXnjhBSaTdF2clEP+LWkfkDAHSIwDEjcBqS6W+AkrA0TGApHNgar9gKJV1cNysZbxaTJr9oMPPkCdOnWMLz9ZJt5yc/HiRbV2pCz3IzEoS6zIxVpudctkMfb6WJgX4q2g23vKGpITJ07EmTNn8Nhjj6kkUj4EEbmLCSX55yf1o8uAPVOAY98DtiDALmMhnRd6dmbL+r2ozkDNYWjV5xX07HmnWkSXS1SQt+MN0V1lXEWO35w6dSqeeOIJp8lgb775Jp5++mnGpRV5Od7yQ4YEzZ49G+PGjVNDhB566CG89NJLqoeSKL+YUJJ/uXgYiBsIHF8B2IIBu/OuC25xPK9cJ6D5DCCigjdKSmbg5XiTcZNVqlRRE8SymzJlirqdSBbjg/ZNJtF89tlnKml0LIQvH25k2MWYMWPwxx9/qG1oJ0yYwLs4pAvHUJL/2DcLWHwzcGKV9v+CNLbZnyfHkePJcYl8EG9ffvlljmRSyMxZWXaFLMQH7ZtMQJTJXrJ/9qxZs5y2SbznnnvUtocyhlf2heeQINKLCSX5xy2g7WOBuAFAWjJgT/PQcdO048lx5fjX7I1MFmVQvNkzMtStbpF9yEXp0qXVOMpixYp55rzk33zYvslwH1mMXMjSVLfddlvmNolr1qzB8uXL0aRJE8+UhyyPywaR78W/BOx42bvnUMe3AfXHe/c85P8MijdZA1XGqN18881qeSC5cEvPkEzQ4ZheC/FR+7Z48WI1ftchMTFRzdiWbRK7du3KGCSP4xhK8i25XSOfsI3SfCZQrb9x5yP/wngjC8TbsWPH1AeZ8+fPO/24VKlSavINVxYgb+Atb/Kd5EPAb0OMPaecTwbGk/Uw3sgi8daqVascyaT0isvSVbI8EJE38JY3+YaM99n4KJCeaux55Xwyy7Ldct1LblAAYbyRheKtZMkSqFatmlphQMZLFipUSO3SJF8cM0newlve5BtHlgJru/uu9tssAcp38935yViMN2K8EXkVb3mTb8iivrKemi/IefdkDVYnC2C8EeONyKuYUJLxkvZhyszlqDwsHSEPASPnGHx+Wcft2HIgKcHgE5NPMN6I8UbkdRxDSYbbtvwtjJgDLBoB3FIZKBHhgz+CbGOWMBuIGeODk5ORGG/EeCPyPiaUZLjFy39AbDWgW0MfVr7siZsY58MCkFEYb2QkxhtZFW95k6Fq1KiBF2fswYa9gK0v8PD7BTvO7qNAu4lA+ACg5tPA0q3a8bbud/cIdiBxU8FOTgGD8UaMNyJjcJY3GerkgXi0iK2PwR2Bfi2BouHaV36TyWZjgeFdgP6tge0HgUHTgfOXgKRPgEL56XfvfRQoHJXfl0EBgvFGjDe2b2QM3vImQxUNvYT9p4BWNYHwUKDtRCAtHUjLAIZ3Bga1z/rd3pOBNbuADnWBr5/MenzITODuWGDCPdr/q5cFZq8H9h7XksmzyUDH11wfN8cxUxOZUJqYu/F2KBF46H3g5DkgJBgY0xu4t5m+eHN5zG6MNzNzN97yaqMKGm8uH2e8kYGYUJKhtsfvUv/GVATCCwHrxgARYUByClDvOeCupkBkMe13pUH8Vxtg1rqs5x84BazaCWx7zfm40tA2qKR9X6xw7sfNccwMgxceJr+Mt5Ag4J1+QMMqwPGzQOMXgW4NgNMXCh5vLo858iyKlGQQWD3ecouZpJSCx1vJIi4ef+4EIkvW80FNkBVxDCUZauvOv1GjHFAkHAgO0ho/kZqmbS5hz/a7besAxa65Hb71ABAaDNQp7/z4jkNAg8ra93kdN8cxg67+Ilk63qJKaYmfKFcSKFMMOJOsL95cHvNciiGvm/w73nL7mZ54c/m4rZAhr5tIsIeSDLV114HMT9pCbtO0majdznnzAe2im5egICA9Q/uS24hi+TZgx2EU7LhhkR54VWSmeNucoMVXxUjtAu+JeMs8ZvW63nqpFGDx5upnetu3HI9H1zDqpROxh5KMtXXHHjSslrXwpNymkds7Ce8AczcAJ87l/fzGVYHQEGD0PGDfSWDBJm3Mkcje4Lp13LAyHD9pcvmNtzNJ2soDHw30XLxlHvPfJRhvJpefeHP1M73x5vR4XAhOnOdNSDIOo40Mk5GRgfj4eDSIqSMLDDj9rGwJ7ZbOT7vzPkZ0KWD6o8D8jUCD54F5ccCgdtotxRtL5Pz9PI8bGavzFZGZ4i31CtDrbeC5O4Bba3om3pyO2bKlV18vBWb7lv1nnmrfypawoUGtaPz000+efplEuWJCSYYJCgpCcnIyuvfoqXaqkU/VFy5pPzt3EVi3G6jlxgoX/VoBh6YAF2YA858ATp53/vTu1nGlvY9s7sFXR4EcbzLebMCHQPu6wEOtPRNvTse8LZjxZnL5ibe8flbQeHN6/JIN63amoFatWsZVAFkex1CS8ar2BeJfwoHTwGPTtQHlcvEd1gmIydZwdnwV2HYQSE4FKgwFvhoOtLgp5+FkHUq5VeSQ13GdjtnlPXz1dUe0aNHCgBdN/hxv6/dovUH1KwLf/qY99vlg53jMb7z9/Gf2Y6YDJb7A53N6ISYmxqAXTv4ab9dr+woSb5v+zv54BoaNfIKxRobiwubkG6u7AsdXAvZ03YcqOxh4ux/Q1907irZgoFwnoN1S3eemAMF4I8YbkVcxoSTfOLIUWNvdd7XfZglQvpvvzk/GYrwR443IqziGknwjuqvWS2gzeNSFnC+qs3Z+sg7GGzHeiLyKCSX5hs0GNJ8BBBu8sHhwONBsunZ+sg7GGzHeiLyKCSX5TkQFoMk0Y8/ZZKp2XrIexhsx3oi8hgkl+Va1/kC9Mcacq95Y7XxkXYw3YrwReQUTSvK9mPFasudNcvyYcd49BwUGxhsx3og8jrO8yX/smwX8NgRITwXsaZ6ZgCNjNOW2OnsmifFGvsT2jUyOCSX5l4uHgbiBwPEV2nqRBVmn0vE8mUUuE384ZpIYb+QP2L6RiTGhJP8j2z8cXQbsmQocW662MYM9Q36Qx5NsWb8X1QWoOVRbKoazuYnxRv6E7RuZFBNK8m9JCUDCbCAxDkjcBKSezvk7YWWAyFhtr+Sq/YCi2fYpI2K8kb9i+0YmwoSSAsulY2hUrzKeHfkk+jzwMBAWCRSO8nWpyKwuHcPQxx5AaFAGJr/7HuONvB5vc2dOwZR3JuGXjVsYbxRQmFBSwLly5QqCgoIQHBzs66KQBaSlaRPEQkIM3tWJLCk9PR0ZGRkIDQ31dVGI8oUJJRERERHpwnUoiYiIiEgXJpREREREpAsTSiIiIiLShQklEREREenChJKIiIiIdGFCSQFj7dq1uf7s9GkXC54TMd4ogLCNo0DGhJICRqdOnTBq1Ci1DmV2y5YtQ0xMjM/KRebEeCPGHJH7mFBSwFizZg0WLlyI2NhY7NixAykpKRg2bBh69eqF4cOH+7p4ZDKMN2LMEbmPC5tTQElOTlZJ5Jdffono6Gi1e8ncuXPRqFEjXxeNTIjxRow5Ivewh5ICSkREBGrVqqW2wzt8+DCaNGmCmjVr+rpYZFKMN2LMEbmHCSUFjAMHDqBt27aYPHkyvvnmG2zZskXd+m7YsCE2bNjg6+KRyTDeiDFH5L6QfPwukU9J4tiqVSuVRJYpU0Y99uuvv2L06NFo164dUlNT+RcixhsFLLZxFMg4hpICxocffojHH3/c5c9Wr16tkkoixhsFKrZxFMiYUBIRERGRLhxDSURERES6MKEkIiIiIl2YUFJA2bx5M2w2G5o2berropAFyOL54eHh6ku+J/I2WQpN2jhZxYIokHCWNwUOux2N60TjvVcHo3vX24Gz8UBYGaBwlK9LRmZktyPc/g8WffYKgpCG8JS9gJ3xRt6LN6Qcx4IZ4/D9sv+hUbVQ4NIxtm8UMDgph/xb0j4gYQ6QGAckbgJST+f8HUkqI2OByOZA1X5A0aq+KCmZAeONGG9EBcKEkvzzk/rRZcCeKcCx7wFbEGDPkB/k8SRb1u9FdQZqDgOiuwI2m4EFp4DEeCPGG5FuTCjJv1w8DMQNBI6vAGzBgD09/8dwPK9cJ6D5DCCigjdKSmbAeCPGG5FHMKEk/7FvFvDbECA9FbCn6T+eLQQIDgOaTAOq9fdECclMGG/EeCPyGCaU5B+3HONfAna87L1z1BsDxIznLXBivJGx2L6RRXDZIPI9byeTQo4fP86756DAwHgjxhuRx7GHknx/2zFugHHnaz6Tt7+tjPFGjDcir2BCSb6TfAhYUhtISzbunCFFgB67OVHHihhvxHgj8hre8ibfjSva+Kg2AcdIcj6ZRS7nJ+tgvBHjjcirmFCSb8g6k7I0kCdmc+eHnE/OK+cn62C8EeONyKuYUJJvyKLlsl6kL8h590z1zbnJNxhvxHgj8iomlGS8pH2YMnM5Kg9LR8hDwMg5Bp9fFj0/thxISjD4xOQTjDdivBF5XYj3T0HkbNvytzBiDrBoBHBLZaBEhA9qSLZpTJgNxIzhn8fkGG/EeCPyPiaUZLjFy39AbDWgW0MfVr7s+Z0Y58MCkFEYb2QkxhtZFW95k6Fq1KiBF2fswYa9gK0v8PD7BTvO7qNAu4lA+ACg5tPA0q3a8bbud/cIdiBxU8FOTgGD8UaMNyJjcB1KMtTJA/FoEVsfgzsC/VoCRcO1r/wmk83GAsO7AP1bA9sPAoOmA+cvAUmfAIXy0+/e+yhQOCq/L4MCBOONGG9s38gYvOVNhioaegn7TwGtagLhoUDbiUBaOpCWAQzvDAxq7/z7F1OB2qOAe5sBk/pqjw2ZCdwdC0y4R/t/9bLA7PXA3uNaMnk2Gej4Wu7HdTpmt0QmlCaWn3irMhwoXhgIsgGligCrX9QfbzmOyXgztfzEW8JJ4F8fASfOAcFBQNx4oEi4vnjLccw2h1CkPBNKMgYTSjLU9vhd6t+YikB4IWDdGCAiDEhOAeo9B9zVFIgslvX7rywCmtfI+v+BU8CqncC215yPKw1tg0ra98UK531cp2NmGLywOvl1vG0Y59xj7ol4czom483U8hNvAz4EJt4LtL4ZOJMEhIXqj7ecx+QGDmQcjqEkQ23d+TdqlNM+icsnaGkURWqatplJ9uZPPpHL7e2uDbI9/wAQGgzUKe983B2HgAaVte/zOm6OYwZd/UWC1ePN5fN1xlsOjDdTczfedh7W4koSP1G6KBASrC/eXB6zUBFDXjeRYEJJhtq660DmJ20ht28aPA9UGAaM6g6UydZbJOtTvtbH+flBQUB6hvblsHwbsOMw3DpujmOGRXr8NVJgxpvNBrR5GWg6Bpiz3jPxluOYjDdTczfe5IOt9FrfMQlo9ALw6iL98ebymIw3MhATSjLU1h170LBa1sKTJYtot3cS3gHmbtDG/ohFvwE1o7Sv7BpXBUJDgNHzgH0ngQWbtDFHInuD6+q4OY4ZXJjjJ03O3XgTP48FNr8CfDdCuxjLZC898ZbjmN8FY/veU4a9dvLfeJPxjz/9Cbz3CPDLOGBlvPalJ95yHHNnKFb+vMPoKiALY0JJhsnIyEB8fDwaxNSRvhunn5Utod3S+Wm39v+4v4Avf9EmNYycC3y8GpiwEIguBUx/FJi/UfuEPi8OGNQOKFcSuLFEznNmP26OY666ggkTJhj06smf402UL639G1VKWyN1S4K+eHM+pg3dWlbCli1bvPeCKWDiTeKiSVWgYqQ2dlLiTW5364k352Pa0K1VdWzdutWgV0/EhJIMFBQUhOTkZHTv0VPtVCOfqi9c0n527iKwbjdQ62rv4Wv3A4emAPvfBSY9qDWqY+/SftavlfazCzOA+U8AJ887f3rP7bhOx+xrw6C7YzF27FjGgEnlJ95kcoPjZ0kp2sSIuhX0xZvTMVNtWLU9BXXr1jWuAshv461pNS2O/kmWRFT7We1offHmdEy7Dev+yEDt2rUZBWQYzvIm41XtC8S/hAOngcemawPKZWD5sE5ATLaG012OW5MObh1XflBCehLI9NyItxPngd6Tte9l/Jp8gGlaXV+8yS3LrGNmYNCwR9G0aVNvv1oKgHiTCTiv3gfcNkH7eacYoEcj/e1b1jEz0OnOVujRo4cBL5hIw4XNyTdWdwWOrwTs6boPVXYw8HY/oG9LN59gCwbKdQLaLdV9bgoQjDdivBF5FRNK8o0jS4G13X1X+22WAOW7+e78ZCzGGzHeiLyKk3LIN6K7ar2ENoNHXcj5ojpr5yfrYLwR443Iq5hQkm/IAn3NZwDBBi8sHhwONJuunZ+sg/FGjDcir2JCSb4TUQFoMs3YczaZqp2XrIfxRow3Iq9hQkm+Va0/UG+MMeeqN1Y7H1kX440Yb0RewYSSfC9mvJbseZMcP2acd89BgYHxRow3Io/jLG/yH/tmAb8NAdJTAXuaZybgyBhNua3OnklivJEvsX0jk2NCSf7l4mEgbiBwfIW2XmRB1ql0PE9mkcvEH46ZJMYb+QO2b2RiTCjJ/8j2D0eXAXumAseWq23MYM+QH+TxJFvW70V1AWoO1ZaK4WxuYryRP2H7RibFhJL8W1ICkDAbSIwDEjcBqadz/k5YGSAyFohsDlTtBxTNtk8ZEeON/BXbNzIRJpQUWC4dA1ITgYxUICgMCIsECkf5ulRkVow3YrwRuYUJJRERERHpwmWDiIiIiEgXJpREREREpAsTSiIiIiLShQklEREREenChJKIiIiIdGFCSURERES6MKEkIiIiIl2YUBIRERGRLkwoiYiIiEgXJpREREREpAsTSiIiIiLShQklEREREenChJKIiIiIdGFCSURERES6MKEkIiIiIl2YUBIRERGRLkwoiYiIiEgXJpREREREpAsTSiIiIiLShQklEREREenChJKIiIiIdGFCSURERES6MKEkIiIiIl2YUBIRERGRLkwoiYiIiEgXJpREREREpAsTSiIiIiLShQklEREREenChJKIiIiIdGFCSURERES6MKEkIiIiIl2YUBIRERER9Ph/+zdMrtzA78cAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ferrmion.optimize import bonsai_algorithm\n",
    "\n",
    "bonsai = bonsai_algorithm(graph=graph, homogenous=True)\n",
    "draw_tt(bonsai, enumeration_scheme=bonsai.enumeration_scheme)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "612d6db9",
   "metadata": {},
   "source": [
    "or the heterogenous labelling, and optionally a maximum number of nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4a8f2dc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bonsai = bonsai_algorithm(graph=graph, homogenous=False, max_nodes=14)\n",
    "draw_tt(bonsai)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f862b9f",
   "metadata": {},
   "source": [
    "# Encoding a Hamiltonian\n",
    "\n",
    "We can encode a hamiltonian in the usual way, using the `TernaryTree` encoding we just created.\n",
    "\n",
    "Note that the number of qubits in the encoding is equal to the number of qubits in the original graph, even when you input a value for `max_nodes`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2a58f3d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "from pathlib import Path\n",
    "\n",
    "folder = Path.cwd().joinpath(Path(\"../../../python/tests/\"))\n",
    "with open(folder.joinpath(\"./data/h2o_sto-3g.json\"), \"rb\") as file:\n",
    "    data = json.load(file)\n",
    "ones = np.array(data[\"ones\"])\n",
    "twos = np.array(data[\"twos\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "84c2a655",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'ZIYYYIIZZIIIIXIIIIIIIIIIIIIIIIIIIIIII': (1.640297548266427e-08+0j),\n",
       " 'ZIZZIXYIZIXIIIIIIIIIIIIIIIIIIIIIIIIII': (-3.686346771541274e-08+0j),\n",
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       " 'XZYZXXYIXIYIIIIIIIIIIIIIIIIIIIIIIIIII': (8.885015986546761e-09+0j),\n",
       " 'IIIIIIIIIZIIZIIIIIIIIIIIIIIIIIIIIIIII': (0.2200397733437614+0j),\n",
       " 'YZXIZIIZIZIIIYIIIIIIIIIIIIIIIIIIIIIII': (-6.327747523109497e-09+0j),\n",
       " 'YZXIZIIZIIIIIYIIIIIIIIIIIIIIIIIIIIIII': (-3.072188755992133e-07+0j),\n",
       " 'ZIXZZIZIYIIXIIIIIIIIIIIIIIIIIIIIIIIII': (0.0001247385335499872+0j),\n",
       " 'YYXZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII': (0.003282532456907718+0j),\n",
       " 'YZYIZIIZIIIZIXIIIIIIIIIIIIIIIIIIIIIII': (1.505432923495098e-08+0j),\n",
       " 'YZZIXZZIZYIIXIIIIIIIIIIIIIIIIIIIIIIII': (-1.0612387392739578e-08+0j),\n",
       " 'IIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIII': (0.14713318244022264+0j),\n",
       " 'YZZIYXYIIIYXZIIIIIIIIIIIIIIIIIIIIIIII': (2.6857132619785154e-08+0j),\n",
       " 'ZXXZXIZIZIIYIIIIIIIIIIIIIIIIIIIIIIIII': (-0.0005906897714898403+0j),\n",
       " 'XYIZIIZYIIIZIXIIIIIIIIIIIIIIIIIIIIIII': (0.004584959583551752+0j),\n",
       " 'YZXIXIXIZIIZIIIIIIIIIIIIIIIIIIIIIIIII': (-5.368271948496131e-09+0j),\n",
       " 'ZIZZYZXXYYIIXIIIIIIIIIIIIIIIIIIIIIIII': (-1.4397538493886142e-08+0j),\n",
       " 'YYYIYIIZXIIIIXIIIIIIIIIIIIIIIIIIIIIII': (-4.009018053822631e-10+0j),\n",
       " 'IIIIIIXYIIIYIXIIIIIIIIIIIIIIIIIIIIIII': (-1.1082274893034266e-07+0j),\n",
       " 'IIIIYIIZYIIIIXIIIIIIIIIIIIIIIIIIIIIII': (2.3702939314246265e-07+0j),\n",
       " 'XZIZZIZXZIIZIIIIIIIIIIIIIIIIIIIIIIIII': (-1.505432923495098e-08+0j),\n",
       " 'YYXIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIII': (0.0017556821572203576+0j),\n",
       " 'YIZIZXIYIIZIIIIIIIIIIIIIIIIIIIIIIIIII': (-0.03498146595793702+0j),\n",
       " 'ZIZZIYXIXIIIZIIIIIIIIIIIIIIIIIIIIIIII': (0.007326677936559049+0j),\n",
       " 'XZIXYIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIII': (-0.026007683665143607+0j),\n",
       " 'XYIZIIXIZIIIZIIIIIIIIIIIIIIIIIIIIIIII': (6.881945697384798e-08+0j),\n",
       " 'IIIIYIYZZIIZZYIIIIIIIIIIIIIIIIIIIIIII': (0.00019258277957225466+0j),\n",
       " 'IIXYIXZIIIXZIIIIIIIIIIIIIIIIIIIIIIIII': (-0.0056398152645194535+0j),\n",
       " 'XYIZIIZIYIIZIIIIIIIIIIIIIIIIIIIIIIIII': (-0.004664385121536082+0j),\n",
       " 'YYXIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIII': (0.0055264031895712745+0j),\n",
       " 'IIIXIZZIIIZXIIIIIIIIIIIIIIIIIIIIIIIII': (-0.028744417919069638+0j),\n",
       " 'IIIIYIIYZZIIIIIIIIIIIIIIIIIIIIIIIIIII': (7.812829627745813e-08+0j),\n",
       " 'XZIZZIZYIIIXZIIIIIIIIIIIIIIIIIIIIIIII': (2.0678355084334222e-08+0j),\n",
       " 'IIYYIXZIIIYYIIIIIIIIIIIIIIIIIIIIIIIII': (0.004664385121536082+0j),\n",
       " 'IIIIIYIIIZZXIIIIIIIIIIIIIIIIIIIIIIIII': (3.336460876894293e-07+0j),\n",
       " 'ZIXYYIIZZIIIIYIIIIIIIIIIIIIIIIIIIIIII': (-1.640297548266427e-08+0j),\n",
       " 'XZYZZZYYIZIIIIIIIIIIIIIIIIIIIIIIIIIII': (0.003804304298248097+0j),\n",
       " 'IIIXYIZZYIIXIXIIIIIIIIIIIIIIIIIIIIIII': (2.7710446468664605e-08+0j),\n",
       " 'IXYIZYIXIIIIIIIIIIIIIIIIIIIIIIIIIIIII': (0.0018629150499428657+0j),\n",
       " 'YIXIZIIZIIIIIYIIIIIIIIIIIIIIIIIIIIIII': (1.0185732916363537e-08+0j),\n",
       " 'XZIZZIZYIIZXIIIIIIIIIIIIIIIIIIIIIIIII': (6.327596440655918e-08+0j),\n",
       " 'IIIIYIZZXIIIZYIIIIIIIIIIIIIIIIIIIIIII': (4.033626832746919e-08+0j),\n",
       " 'XZYZZXZZIIZYIYIIIIIIIIIIIIIIIIIIIIIII': (-0.0009533430025949679+0j),\n",
       " 'ZIZYYXIZZIXIIYIIIIIIIIIIIIIIIIIIIIIII': (5.3662020597575315e-09+0j),\n",
       " 'YZZXZXZXIIZYIIIIIIIIIIIIIIIIIIIIIIIII': (0.015632475168107188+0j),\n",
       " 'XZIZXIXIYIIIZIIIIIIIIIIIIIIIIIIIIIIII': (1.4448745105110505e-06+0j),\n",
       " 'XZIZYYZIIZZZIIIIIIIIIIIIIIIIIIIIIIIII': (6.810374460784758e-08+0j),\n",
       " 'XXIZYIXZYIIIZYIIIIIIIIIIIIIIIIIIIIIII': (-0.010284014113738468+0j),\n",
       " 'XZIZXIYIXIIIIIIIIIIIIIIIIIIIIIIIIIIII': (-1.4448745105110505e-06+0j),\n",
       " 'IIIYIIZIIZIYIIIIIIIIIIIIIIIIIIIIIIIII': (-0.02473750903395571+0j),\n",
       " 'ZIZZIZIIIZIZZIIIIIIIIIIIIIIIIIIIIIIII': (0.19925178925179549+0j),\n",
       " 'IIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII': (1.6537243288460575+0j),\n",
       " 'YXZIIZYIIXIYYIIIIIIIIIIIIIIIIIIIIIIII': (0.014616837616021673+0j),\n",
       " 'YZYXZIXXIIIIZIIIIIIIIIIIIIIIIIIIIIIII': (0.0034860696019765654+0j),\n",
       " 'ZIXZIIZIXIIYIIIIIIIIIIIIIIIIIIIIIIIII': (-0.0001247385335499872+0j),\n",
       " 'IIIIIIYYIIIYZYIIIIIIIIIIIIIIIIIIIIIII': (-1.1082274893034266e-07+0j),\n",
       " 'ZIZZYXXZYIYIZXIIIIIIIIIIIIIIIIIIIIIII': (-0.0009197248503949491+0j),\n",
       " 'YZZIXXIIYIXIIIIIIIIIIIIIIIIIIIIIIIIII': (-0.2282196033169116+0j),\n",
       " 'ZIZYIXIYIIYIIXIIIIIIIIIIIIIIIIIIIIIII': (0.00417227146923148+0j),\n",
       " 'ZIZYIXIIIIZIIZIIIIIIIIIIIIIIIIIIIIIII': (-1.919499197929779e-07+0j),\n",
       " 'YZZIZYIXIIIIIIIIIIIIIIIIIIIIIIIIIIIII': (0.3695921964533493+0j),\n",
       " 'ZYZZZZXYIXIIYIIIIIIIIIIIIIIIIIIIIIIII': (-6.26362927343161e-08+0j),\n",
       " 'YZYIZIYXIIIYZIIIIIIIIIIIIIIIIIIIIIIII': (0.0022644694973199754+0j),\n",
       " 'ZIZZIYZIIIIXIIIIIIIIIIIIIIIIIIIIIIIII': (-1.4448745105110505e-06+0j),\n",
       " 'ZIXZYIZZZIIZIYIIIIIIIIIIIIIIIIIIIIIII': (3.71881326193215e-09+0j),\n",
       " 'YZZIXYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII': (9.320333651911843e-08+0j),\n",
       " 'IIZIIZIIIIZIIIIIIIIIIIIIIIIIIIIIIIIII': (0.19925178925179549+0j),\n",
       " 'YZZIYZIIIZIIZIIIIIIIIIIIIIIIIIIIIIIII': (-0.001276799856755393+0j),\n",
       " 'XZIZZIYZIIIYIXIIIIIIIIIIIIIIIIIIIIIII': (-0.001723890321633336+0j),\n",
       " ...}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fham = fr.molecular_hamiltonian(ones, twos, 0.0)\n",
    "bonsai.encode(fham)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.1"
  }
 },
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}