ch4-qaoa.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "af9e9667-b296-40d9-80f2-52bb71e9df5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "from qiskit import *\n",
    "from qiskit.visualization import plot_histogram\n",
    "from scipy.optimize import minimize\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "f0e6c20d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def myplot(data):\n",
    "  fig = plot_histogram(data, figsize=(12, 6))\n",
    "  fig.set_facecolor('white')\n",
    "  return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "5220ead7-87cb-45db-bdbb-d8511150b9f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/03JH4kfs4Jf1x8oDamc8fG5FryKVjOvWa1p1/01tNd2e2GEqptYfKw+on/Hwbf3FIX39x/tciV5FKhnXA59t081Xt1b194kdquH1+mPlAc4wGr4j2ZzWPbJTJ/PuRa9idkNcz3/1el2Snvpfx8QOtXJ7/bHyAGcZDd/GJ3+uXe8er+uFLNVKxCxdtXiueu+69sM/I3Zwilvrj5UHOC9m6sJvHTqh/kzWk+hJUqFUnnwT/L8c0datW9XZ2amFCxdqy5YtWr9+vQ4cOKAdO3bozjvvJHqwrampSU8++aR6enrU1dWlrq4ujYyM1Hx/5XJZvb29am9v17Jly7R7926iBzjE2OL78lO79dzeI7bep1e3cknj//Jztf92F8sOrql3/bHyAHcZCV82N6Fr/vqnGi+Uqr7NyK5nNLr3/yn//js67w8+rQtv+kpN126IW3rjv3/Gdx9vhvCx+9wfz+UB3jDyq87dg8fVELd36cT585X+5Ead3/6Zuq49KxnXnsHjdd0HUI2Ojg7t3btXlmVpxYoV6uvrm/bvHj16VJ2dnXrggQe0fft2bd68megBLjESvv5MVicnCrZuM/v3P6nZl1+rWKq+V8zl8kX1Z7J13QdQrXM998dzeYD3jITvtYFhFav/LaejCqWyXh0YNnNxRNZU64+VB5hhJHxDI2MmLuub6yOaKuvvySef1O23366Pfexjam1tZeUBHjMSvomi2Y8HNX19RNfRo0fV09OjefPmqaOjQz/4wQ/00ksvmX5YQKQYCV8y7vy3JQTp+oieM5/Le+utt/SjH/3Isff9AaiekfA1N9l/HqNcKqpcyEulolQuqVzIq1yq7aPOark+UKuZnsuz88pPAM4wEr7VS+YrEbO3urI/e1qDD/+RRl79Pxrd94IGH/4jZX/2tO1rJ2KW1iyZb/t2gF3VvmLT6U99ATCzhImLtreklUrG9cF49W9pmLP2ds1Ze3vd146VCmpO8uIWuOvUT1/Zvn17VS9eqay/TZs2acWKFb78tncgDIwsvisXzVXe0PsZCmXpy7fdpFWrVumhhx7SwMCAkceBcKr3fXmsP8B9RsKXTiXVsbxZNn/bWbeYJd14RYsOv3NAmzdv1oEDB7R69WoiCEc4+b48nvsD3GPs2xm61i7VrETc02vOSsR119rLlEgktG7dOj3xxBM6fPgwEURd3Pr0FdYf4I5Ifx/fmQqFgnbu3KmtW7fqhz/8oRYvXqzOzk51dnZqyZIlrj9GBI9X36Tg9be9A2HGN7BPgwhiJqa+ScHtb3sHosBo+CRp6y8O6es/3qfchHvxSyXjeuCzbbr56taabk8EcSrT35fH+gPqY+w5vorOq1p0y6pWpZLuPN+XSsZ16zWtNUdPEs8JQpJ/vkmB5/6A+hhffNLkgfLgs/v19BuHHF1+leh97cblsiznX0LKEowO0ytvOqw/wD5fhE+ajN+2XRl1P7NP+UKprhe8JGKWGhIxdW+o/debdhHBcArKt6Lz3B9QPd+Er+JINqf7et9Ufyar8UJRdvoXsybfstDektZjG1dW/UIWpxHBcPDrypsO6w+oju/CV9GfOaGeVw6qb9+QGhIx5fLFKVdgImYp1RBXvlBSR1uzuq5bqvaWOd4/4GkQweAJysqbDusPmJlvw1eRzU1oz+Bx9WeyenVgWEMjY5oolpWMW2puatSaJfPV3pLWykVzlU4lTT/cGRFB/wvaypsO6w+Ynu/DF1ZE0F+CvvKmw/oDzkb4fIAImhWWlTcd1h9wOsLnM0TQO2FdedNh/QGTCJ+PEUH3hH3lTYf1BxC+wCCCzojaypsO6w9RRvgCiAjWJqorbzqsP0QV4Qs4InhurLyZsf4QNYQvRIjg2Vh51WH9IUoIX0hFPYKsvNqw/hAFhC8CohZBVl59WH8IO8IXMWGOICvPWaw/hBXhi7AwRZCV5w7WH8KI8EFScCPIyvMG6w9hQvhwlqBEkJXnLdYfwoLwYUZ+jCArzyzWH4KO8KFqfoggK88fWH8IMsKHmngdQVaeP7H+EESED3VzO4KsPH9j/SFoCB8c5WQEWXnBwvpDUBA+uKaeCLLygon1hyAgfPBEtRFk5YUD6w9+RvjguekieMMNN+gb3/gGKy8kWH/wK8IHowqFgl588UVt3rxZzz//vJqbm3XPPffotttu89Wb5VE71h/8Jmb6ASDajh07pu985zs6fPiwXn75ZX3/+9/X4OCgVq9erVWrVumhhx7SwMCA6YeJOnR0dGjv3r2yLEsrVqxQX1+f6YeEiGPxwYhzPZfnhzfLw3msP/gB4YPn7L5ikwiGC8/9wTTCB8848YpNIhgerD+YQvjgCTfel0cEg4/1BxMIH1zl1fvyiGCwsf7gJcIH15j69BUiGEysP3iF8MFxfvr0FSIYPKw/uI3wwVF+/oxNIhgcrD+4ifDBEX5aedUggsHA+oMbCB/q5ueVVw0i6G+sPziN8KFmQVt51SCC/sX6g1MIH2oS9JVXDSLoP6w/OIHwwZYwrrxqEEF/Yf2hHoQPVYvCyqsGEfQH1h9qRfhwTlFdedUgguax/mAX4cOMWHnVI4LmsP5gB+HDlFh59SGCZrD+UA3Ch7Ow8pxFBL3F+sO5ED58iJXnPiLoHdYfpkP4IImVZwIRdB/rD1MhfBHHyvMHIugu1h9ORfgijJXnT0TQHaw/VBC+CGLlBQcRdB7rD4QvYlh5wUUEncP6izbCFxGsvHAhgs5g/UUT4YsAVl64EcH6sP6ih/CFGCsveohg7Vh/0UH4QoqVByJoH+svGghfyLDyMBUiaA/rL9wIX4iw8lANIlgd1l94Eb4QYOWhVkTw3Fh/4UP4Ao6VB6cQwemx/sKF8AUUKw9uIoJTY/2FA+ELIFYevEQET8f6Cz7CFyCsPJhGBD/C+gsuwhcQrDz4DRFk/QUV4fM5Vh6CIOoRZP0FC+HzMVYegiiqEWT9BQfh8yFWHsIiihFk/fkf4fMZVh7CKkoRZP35G+HzCVYeoiQqEWT9+RPh8wFWHqIs7BFk/fkP4TOIlQecLswRZP35B+EzhJUHzCyMEWT9+QPh8xgrD7AvbBFk/ZlF+DzEygPqF5YIsv7MIXweYOUB7ghDBFl/3iN8LmPlAd4IcgRZf94ifC5h5QHmBDWCrD9vED4XsPIA/whaBFl/7iN8DmLlAf4WpAiy/txD+BzCygOCJQgRZP25g/DViZUHBJ/fI8j6cxbhqwMrDwgfv0aQ9eccwlcDVh4QDX6MIOuvfoTPJlYeEE1+iiDrrz6Er0qsPAAVfokg6682hK8KrDwA0zEdQdaffYRvBqw8AHaYjCDrr3qEbxqsPAD1MBFB1l91CN8ZWHkAnOZ1BFl/MyN8p2DlAXCbVxFk/U3P9+HL5ia0e/C4+jNZvTYwrKGRMU0Uy0rGLTU3NWr1kvlqb0nrykVzlU4la7oGKw+ACV5E0On158WZ7Dbfhq8/c0I9Lx9U3/4hNcRjyk0UVSid/VATMUupZFz5Ykkdy5vVtXap2lvmVH0dVh4AP3Azgk6sP6/OZC/4LnxHsjnd1/um+jNZjReKmuLnOq2YJc1KxNXektajG6/QgnRq2r/LygPgV25FsJb159WZ7CXfhK9cLmvbroy6n9mnfKE05b8kqpWIWWpIxNS9oU2dV7XIsqzT/j8rD0BQOB3Batefl2ey13wRvnK5rAef3a+n3zik3ETRsftNJeO6ZVWr7r9puSzLYuUBCDQnIzjT+vPqTDbFePjc+gFXpJJx3XpNq750zUWsPACh4UQEp1p/Xp3J99/U5vh9V8t4+Lb+4pC+/uN9rvyAK5JWWSdf+p7+9LrfY+UBCJ16I3jq+rvuz/5Sm//xoKtncioZ1wOfbdPNV7e6do2ZGA3fkWxO6x7ZqZN5937AFY1x6cW/XKdL0kQPQHjVGsGRkRHd81/+SjvPv15Wcpbrj3N2Q1zPf/V6I2ey0fBtfPLn2vXu8bqeNK1WImbpqsVz1XvXta5fCwD8wG4ENz75c73xzjFbr9yslckzOeb5FX/nrUMn1J/JehI9SSqUyurPZNWfOeHJ9QDAtEQioXXr1umJJ57Q4cOHtXnzZh04cECrV6/WqlWr9NBDD2lgYEDSR2eyR0ey0TPZ2OL78lO79dzeI579kKXJ95Tc2L5A37rlSu8uCgA+M9USTP/7r+hgIR2JM9lI+LK5CV3z1z/VeKFk63bF3Aca/sljGntnj2KpJs399H/SeW3X27qPWYmYXv9v/9a3H6UDAF4qFAr6h5++qHtfPKmSFbd1298887DG3nlLpYkxxc+bq6Y1n9cFn1hv6z5MnMlGftW5e/C4GuL2L32s79uy4km1fPn7unDDJg33Pa78++/auo+GREx7Bo/bvjYAhFEikdD5S9p1XqP9F7Q0renUpf/5f2vRV7fp4j/+mk689Hca/9e3bd2HiTPZSPj6M1mdnCjYuk0pP6aTv/4nzfnUnyjWkFJja5tmL1ut0X0v2LqfXL6o/kzW1m0AIMxqOZMlqeGixbISlaVmyZKlwvEjtu7DxJlsJHyvDQyraO+3nCoce09WLKbkvEs//LPkxUs0YXPxFUplvTowbO/iABBitZzJFcM7Htfgw5/X4Z4vKX7+PKUuu9rW7U2cyQlPr/Y7QyNjtm9TmsjJmjX7tD+LzZqtUj7nyfUBIKzqORPnr79b8z7zRY2/9yuNDe6VFbf/XJ3XZ7KR8E0U7b+eJpZMqTx+euTK4ycVa7D/ad+/+ue3ZVk32L4dAITRwi/2KDl3Qc23t2JxNba2aXTfC/pgz0/UdPVnbd2+libUw0j4knH7H06amHepyqWiJo699+GvO/NHB5S8aLHt+/r45cv0nvnP5gYAX1j3yIs68P5o/XdUKtl+jk+qrQn1MPIcX3OT/Y+oiTU0avbvX6sTL/+9SvkxjWX26+Tbr+m8NvvLrZbrA0BY1XImFkdPaHT/TpXyOZVLReUO7tLoL3eqcfEnPLl+PYwsvtVL5uv1gWO2P7VlXsfdGv7JY8p863bFUk2a33G3GmwuvkTM0pol823dBgDCrKYz2bL0wZ5/0PCOx6VySYn0xZq7rkuzL19j69omzmQj4WtvSSuVjOuDcXsvn42nLtDFn/+ruq6dapj8NmAAwKRazuT47LQuuX1z3dc2cSYb+VXnlYvmKl/ra2frlC+UtHLRXCPXBgA/itqZbCR86VRSHcubFfP4C3hjltTR1szHlQHAKaJ2Jhv7doautUs1K2Hvc+HqNSsR111rL/P0mgAQBFE6k42Fr71ljtpb0kp49E+MRMxSe0taKy7l+T0AOFOUzmRj4ZOkRzdeoYaENw+hIRHTYxtXenItAAiiqJzJRsO3IJ1S94Y2pZLuzutUMq7uDW1GvuIeAIIiKmey0fBJUudVLbplVatrP+hUMq5br2nVzVe3unL/ABAmUTiTjYfPsizdf9NyV37QlR/w125c7uj9AkBYReFMNvIN7FMpl8vatiuj7mf2KV8o2f5Ul1MlYpYaEjF1b2hj6QFADcJ8JvsmfBVHsjnd1/um+jNZjReKsvOzjlmTL49tb0nrsY0reU4PAOoUxjPZd+Gr6M+cUM8rB9W3b0gNiZhy+eKU/+JIxCylGuLKF0rqaGtW13VL1d4yx/sHDAAhFqYz2bfhq8jmJrRn8Lj6M1m9OjCsoZExTRTLSsYtNTc1as2S+WpvSWvlorl8IgsAuCwMZ7LvwwcAgJOMv6oTAAAvET4AQKQQPgBApBA+AECkED4AQKQQPgBApBA+AECkED4AQKQQPgBApBA+AECkED4AQKQQPgBApBA+AECkED4AQKT8f9Mt3marOQekAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "\n",
    "G = nx.Graph()\n",
    "G.add_edges_from([(0,3), (0,4), (1,3), (1,4), (2,3), (2,4)])\n",
    "nx.draw(G, with_labels=True, node_size=1000, pos=nx.bipartite_layout(G, [0,1,2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "ebe87eb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1320.88x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def qaoa(G: nx.Graph, thetas, measure):\n",
    "  rounds = len(thetas) // 2\n",
    "  gammas = thetas[:rounds]\n",
    "  betas = thetas[rounds:]\n",
    "\n",
    "  n = G.number_of_nodes()\n",
    "  qc = QuantumCircuit(n)\n",
    "  qc.h(range(n))\n",
    "  for i in range(rounds):\n",
    "    for e in G.edges():\n",
    "      qc.rzz(2 * gammas[i], e[0], e[1])\n",
    "    for j in range(n):\n",
    "      qc.rx(2 * betas[i], j)\n",
    "  if measure:\n",
    "    qc.measure_all()\n",
    "  return qc\n",
    "\n",
    "qaoa(G, [1, 0.5], True).draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "0286372a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cuts(G: nx.Graph, state: str):\n",
    "  score = 0\n",
    "  for i, j in G.edges():\n",
    "    if state[i] != state[j]:\n",
    "      score += 1\n",
    "  return score\n",
    "\n",
    "def expected_cuts(G: nx.Graph, counts: dict):\n",
    "  total_cuts = 0\n",
    "  total_samples = 0\n",
    "  for state, count in counts.items():\n",
    "    total_cuts += cuts(G, state) * count\n",
    "    total_samples += count\n",
    "  return total_cuts / total_samples\n",
    "\n",
    "def reverse_stats(stats):\n",
    "  reversed = {k[::-1]: v for k, v in stats.items()}\n",
    "  return dict(sorted(reversed.items()))\n",
    "\n",
    "def sv_to_stats(sv):\n",
    "  n = int(np.log2(len(sv)))\n",
    "  return reverse_stats({format(i, f'0{n}b'): np.abs(amp)**2 for (i, amp) in enumerate(sv)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "3410a9b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -5.865\n",
       "   maxcv: 0.0\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 115\n",
       "  status: 1\n",
       " success: True\n",
       "       x: array([1.71194052, 2.04247106, 0.94862923, 2.01243461, 0.40673912,\n",
       "       2.47837122, 6.12206167, 2.33731326, 4.00323295, 5.94832688])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f_sampling(G: nx.Graph):\n",
    "  backend = Aer.get_backend('qasm_simulator')\n",
    "  def execute(params):\n",
    "    qc = qaoa(G, params, True)\n",
    "    counts = reverse_stats(backend.run(qc, seed_simulator=0, shots=1000).result().get_counts())\n",
    "    return -expected_cuts(G, counts)\n",
    "  return execute\n",
    "\n",
    "initial = [0.81069872, 2.2067517, 0.83830696, 2.15579759, 0.37060699, 2.42068091, 6.1575306, 2.2453419, 3.85060091, 6.137845]\n",
    "res = minimize(f_sampling(G), initial, method='COBYLA')\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "6f0a1d9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = qaoa(G, res.x, True)\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "counts = reverse_stats(backend.run(qc).result().get_counts())\n",
    "myplot(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8a7823eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -5.990857943865554\n",
       "   maxcv: 0.0\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 368\n",
       "  status: 1\n",
       " success: True\n",
       "       x: array([1.75578287, 1.08357672, 1.11950429, 2.14525728, 0.6397307 ,\n",
       "       1.83865605, 0.96298038, 0.81942206, 1.10235353, 1.18187252])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f_sv(G: nx.Graph):\n",
    "  backend = Aer.get_backend('statevector_simulator')\n",
    "  def execute(params):\n",
    "    qc = qaoa(G, params, False)\n",
    "    counts = reverse_stats(backend.run(qc).result().get_counts())\n",
    "    return -expected_cuts(G, counts)\n",
    "  return execute\n",
    "\n",
    "initial = [1.0] * (G.number_of_nodes()*2)\n",
    "res_sv = minimize(f_sv(G), initial, method='COBYLA')\n",
    "res_sv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "8ac42053",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YAAAAoKYptyFfsGCBrrrqKkVFRWnBggVn3Pe6665zrDAAAACgJii3IR8+fLj27dunZs2aafjw4afdz+fzye/3O1ocAAAAUN2V25CfepoKp6wAAAAAzgrqOuQAAAAAnFWhc8grinPIAQAAgOBU6BzyiuAccgAAACB4QZ1DDgAAAMBZnEMOAAAAuIjrkAMAAAAuKvcV8uHDh+vQoUOB70/3NWLEiAr9wlmzZqlt27aKjY1VUlKSVqxYcdp9s7Ky9KMf/UhxcXGKjY1Vu3btNHnyZOXn55fYb9myZUpKSgrsM2fOnArVAgAAALgtrNchf/XVVzV+/HjNmjVLqampmjVrli6//HJlZWXpvPPOK7V/dHS0brnlFl188cU655xzlJGRobFjx6qwsFB/+tOfJElbt27V0KFDNXr0aM2fP18rV67UnXfeqaZNm2rYsGFnVS8AAAAQauU25E56+umnNWrUKI0dO1aSNGPGDC1evFizZ8/W1KlTS+3foUMHdejQIfBzmzZttHTp0hKvqs+ZM0fx8fGaMWOGJOmCCy7QqlWr9NRTT9GQAwAAwPOCflPnmjVr9POf/1zJyclKTk7WyJEjtWbNmnLvl5+fry+++EKDBw8usX3w4MH69NNPK/S7v/nmGy1evFj9+/cPbEtLSyuVOWTIEKWnp6ugoKBCuQAAAIBbgmrIX375ZfXs2VN79+7V0KFDNXToUO3fv1+XXHKJ5s+ff8b75uTkyO/3Ky4ursT2uLg47du374z3vfTSSxUbG6uOHTsqNTVVf/zjHwO37du3r8zMwsJC5eTkBDM8AAAAIOyCOmXlt7/9rR599FFNnjy5xPapU6fqd7/7nW6++eZyM3w+X4mfzazUth969dVXdeTIEWVkZOj+++/XE088oUmTJp0xs6ztkjR37lzNnTtXkrR3714tXbpUktSuXTvVr19fGRkZkqTGjRurS5cuWr58uSQpMjJSqampWrNmjQ4fPixJSk5O1v79+7Vz505JUseOHRUTE6PMzExJUrNmzdSpUyetXLlSkhQTE6PevXsrPT1dR48elSSlpKRo165d2r17tySpc+fOioiIUFZWliSpefPmatu2rdLS0iRJtWvXVkpKilatWqXjx49Lknr37q2tW7cGnthceOGF8vv9+uqrryRJLVu2VKtWrbRq1SpJUr169ZScnKy0tDTl5eVJklJTU/X1118rOztbkpSYmKi8vDxt3rxZktS6dWvFxcUpPT1dktSgQQP16NFDK1euVGFhoSSpX79+2rBhgw4cOCBJ6t69u6RGp5/Y/2/ZsmWBddC/f39lZGQE3kjco0cPHTx4UNu2bWOeQjhPR44c0ZYtWyRJCQkJOvfccwP/+WrUqJG6d+/OPDFPzBPzxDxV0XmSzldFFPdEzFNo5ulMfFbcvVZA3bp1lZGRUeK8bunkqSTdunVTbm7uae+bn5+vOnXq6JVXXilxRZa77rpLmZmZWrZsWYVqmD9/vsaMGaOjR48qMjJS/fr1U9euXTVz5szAPv/617/005/+VLm5uYqKijptVnJycmBhIDTGTit/n3n3hLoKAABqroo8Fks8HofamfrOoE5Z+dGPfhR49nSqpUuXljivuyzR0dFKSkrSkiVLSmxfsmSJLr300grXUFRUpMLCQvn9fkknn31/8MEHpTKTk5PP2IwDAAAAXlChDwYqdvnll2vSpElKT09Xr169JEmfffaZFixYoIcffrjcXzZhwgSNHDlSl1xyifr06aM5c+Zoz549GjdunCRp0qRJWr16tT788ENJ0ksvvaTY2Fh17dpV0dHRSk9P16RJkzR8+HDFxMRIksaNG6dnn31W99xzj26//XZ98sknevHFF/XKK68EfTAAAACAcCu3IR8+fHipbaeeh13sl7/8pe68884zZt1www06cOCApkyZor179yoxMVGLFi1SmzZtJJ08p/vbb7/9v+IiIzV16lRt3rxZZqY2bdrorrvu0r333hvYp23btlq0aJHuvfdezZ49W/Hx8Zo+fTqXPAQAAECVENQ55NUN55CHHueQAwDgLs4h9wbHziEHAAAA4KygP6nz4MGDWrx4sXbs2KH8/PwStz344IOOFQYAAADUBEE15J999pmuuOIKxcTE6LvvvlPLli21d+9excTEKCEhgYYcAAAACFJQp6zcf//9+tnPfqbdu3crNjZWH330kXbs2KHk5GRNnDgxVDUCAAAA1VZQDfm6det09913y+fzKSIiQnl5eYqLi9MTTzxRocseAgAAACgpqIY8Ojo68H1cXJy2b98u6eRHqO7Zs8fZygAAAIAaIKhzyHv06KHPP/9cnTp10oABA/S73/1O+/fv1/z589WtW7dQ1QgAAABUW0G9Qv7YY48pPj5ekjRlyhQ1bdpUv/zlL3Xo0KFSHxQEAAAAoHxBvUKenJwc+L5p06Z69913HS8IAAAAqEmCvg65JH377bfauHGjJOnCCy9Uu3btHC0KAAAAqCmCasgPHDigW2+9VW+//bZq1Tp5touZ6corr9QLL7ygxo0bh6RIAAAAoLoK6hzyMWPG6JtvvtGKFSt04sQJnThxQsuXL9fWrVs1duzYUNUIAAAAVFtBvUL+3nvv6cMPP1Tv3r0D2/r06aPnnntOP/7xjx0vDgAAAKjugnqFvGnTpqpbt26p7XXq1OF0FQAAAKASgmrIH3zwQd1zzz3avXt3YNvu3bv161//Wg8++KDjxQEAAADVXbmnrHTt2lU+ny/w89atW5WQkKCWLVtKOtmQx8bGKjs7W2PGjAldpQAAAEA1VG5DPnz48HDUAQAAANRI5TbkDz30UDjqAAAAAGqkSn0w0EcffaSsrCz5fD516dJFAwYMcLgsAAAAoGYIqiHfvXu3rr32Wn3xxReKj4+XJO3Zs0fJycl64403AtsAAAAAVExQV1n51a9+pYiICH3zzTfauXOndu7cqc2bNysiIkK/+tWvQlUjAAAAUG0F9Qr5kiVLtHTpUrVt2zawrV27dpo+fboGDhzoeHEAAABAdRfUK+SnDanlSAwAAABQ4wTVSQ8cOFC/+tWvtHPnzsC2HTt2aPz48bxCDgAAAFRCUA359OnTlZubq3bt2qlNmzZKSEhQ+/btlZubq+nTp4eqRgAAAKDaCuoc8saNG2v16tX6+OOPtWnTJpmZLrzwQv34xz8OVX0AAABAtVbhhtzv96thw4bKyMjQoEGDNGjQoFDWBQAAANQIFT5lJSIiQm3atFF+fn4o6wEAAABqlKDOIf/973+vBx54QDk5OaGqBwAAAKhRgjqH/KmnntLWrVvVsmVLtWrVSnXr1i1x+7p16xwtDgAAAKjugmrIhw8fLp/PJzMLVT0AAABAjVKhhjw3N1f333+/3nzzTRUUFGjgwIGaMWOGmjRpEur6AAAAgGqtQueQP/TQQ3rxxRd1xRVX6KabbtIHH3ygO+64I9S1AQAAANVehV4hX7Bggf7yl7/oxhtvlCT97Gc/U58+feT3+xURERHSAgEAAIDqrEKvkO/cuVN9+/YN/HzJJZcoMjJSe/bsCVlhAAAAQE1QoYbc7/crOjq6xLbIyEgVFhaGpCgAAACgpqjQKStmpptvvlkxMTGBbSdOnNDYsWNVp06dwLa3337b+QoBAACAaqxCDfktt9xSatvNN9/seDEAAABATVOhhvyvf/1rqOsAAAAAaqQKnUMOAAAAIDRoyAEAAAAX0ZADAAAALqIhBwAAAFxEQw4AAAC4iIYcAAAAcBENOQAAAOAiGnIAAADARTTkAAAAgItoyAEAAAAX0ZADAAAALqIhBwAAAFxEQw4AAAC4iIYcAAAAcBENOQAAAOAiGnIAAADARTTkAAAAgItoyAEAAAAX0ZADAAAALqIhBwAAAFxEQw4AAAC4iIYcAAAAcBENOQAAAOAiGnIAAADARTTkAAAAgItoyAEAAAAX0ZADAAAALqIhBwAAAFxEQw4AAAC4iIYcAAAAcBENOQAAAOAiGnIAAADARWFvyGfNmqW2bdsqNjZWSUlJWrFixWn3PXHihEaNGqVu3bopKipKAwYMKLXP0qVL5fP5Sn1t2rQphKMAAAAAnBHWhvzVV1/V+PHjNXnyZH355Ze69NJLdfnll2vHjh1l7u/3+xUbG6u7775bV1xxxRmzN2zYoL179wa+OnbsGIohAAAAAI4Ka0P+9NNPa9SoURo7dqwuuOACzZgxQy1atNDs2bPL3L9u3bqaM2eObrvtNrVq1eqM2c2aNVPz5s0DXxEREaEYAgAAAOCosDXk+fn5+uKLLzR48OAS2wcPHqxPP/30rPOTk5PVokULDRw4UB9//PFZ5wEAAADhELaGPCcnR36/X3FxcSW2x8XFad++fZXOLX6F/fXXX9eCBQvUuXNnDRw4UMuXLz/bkgEAAICQiwz3L/T5fCV+NrNS24LRuXNnde7cOfBz7969tW3bNj311FPq169fqf3nzp2ruXPnSpL27t2rpUuXSpLatWun+vXrKyMjQ5LUuHFjdenSJdDYR0ZGKjU1VWvWrNHhw4clnXxVfv/+/dq5c6ckqWPHjoqJiVFmZqakk6fRdOrUSStXrpQkxcTEqHfv3kpPT9fRo0clSSkpKdq1a5d2794dGE9ERISysrIkSc2bN1fbtm2VlpYmSapdu7ZSUlK0atUqHT9+PDDmrVu3Bp7YXHjhhfL7/frqq68kSS1btlSrVq20atUqSVK9evWUnJystLQ05eXlSZJSU1P19ddfKzs7W5KUmJiovLw8bd68WZLUunVrxcXFKT09XZLUoEED9ejRQytXrlRhYaEkqV+/ftqwYYMOHDggSerevbukRuXO4bJlywLroH///srIyNChQ4ckST169NDBgwe1bds25imE83TkyBFt2bJFkpSQkKBzzz1Xa9askSQ1atRI3bt3Z56YJ+aJeWKequg8SeerIop7IuYpNPN0Jj4zswrN0lnKz89XnTp19Morr2jEiBGB7XfddZcyMzO1bNmyM97/7rvvVmZmZmCxnMkjjzyif/7zn9q4ceMZ90tOTg4sDITG2Gnl7zPvnlBXAQBAzVWRx2KJx+NQO1PfGbZTVqKjo5WUlKQlS5aU2L5kyRJdeumljv6utWvXqkWLFo5mAgAAAKEQ1lNWJkyYoJEjR+qSSy5Rnz59NGfOHO3Zs0fjxo2TJE2aNEmrV6/Whx9+GLhPVlaW8vPzlZOTo6NHj2rt2rWSpIsuukiSNG3aNCUkJKhLly7Kz8/X/Pnz9eabb+r1118P59AAAACASglrQ37DDTfowIEDmjJlivbu3avExEQtWrRIbdq0kXTynO5vv/22xH2GDh2q7du3B36++OKLJZ0891w6eSrMfffdp927d6t27drq0qWL3nnnHQ0dOjRMowIAAAAqL2znkHsR55CHHueQAwDgLs4h9wZPnEMOAAAAoDQacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacgAAAMBFNOQAAACAi2jIAQAAABfRkAMAAAAuoiEHAAAAXERDDgAAALiIhhwAAABwEQ05AAAA4CIacg9YvHixOnfurA4dOujxxx/3TFYo8pzi5XF6NcvLtTFO9/O8muXl2hinu1lers3L43SSl8fp1WN2WlaDJSUluV2CFRYWWrt27ezbb7+1vLw869atm23YsMH1LKfyxjxT/pcbdYUqz6tZXq6NcVaOV2tjnJXj1dq8muXl2rw4zoo8Fgf7eOzFcYaqNqecqe/kFXKXrV69Wh06dFC7du0UHR2tG2+8UW+99ZbrWaHIc4qXx+nVLC/Xxjgrx6u1Mc7K8WptXs3ycm1eHqeTvDxOrx6zM6Ehd9nu3bvVunXrwM+tWrXS7t27Xc8KRZ5TvDxOr2Z5uTbGWTlerY1xVo5Xa/Nqlpdr8/I4neTlcXr1mJ0JDbnLzKzUNp/P53pWKPKc4uVxejXL6TyvZjmd59Usp/O8muV0nleznM6rCVlO53k1KxR5TvHyOL16zM6EhtxlrVq10s6dOwM/79q1S/Hx8a5nhSLPKV4ep1ezvFwb46wcr9bGOCvHq7V5NcvLtXl5nE7y8ji9eszOyNGz1Stg5syZlpCQYDExMdajRw9bvnz5Gfdft26d9evXz2JjYy0+Pt4eeeQRKyoqKrHP0qVLrUePHhYTE2Nt27a12bNnV6gWL7yps6CgwNq2bWtbtmwJvPEgMzPT9Syn8kLxpk4vjtPrWV6ujXFWjldrY5yV49XavJrl5dq8OM5QvKnTi+MMVW1OOVPfGRnO5v/VV1/V+PHjNWvWLKWmpmrWrFm6/PLLlZWVpfPOO6/U/ocPH9agQYPUr18/ff755/rqq680atQo1a1bV7/+9a8lSVu3btXQoUM1evRozZ8/XytXrtSdd96ppk2batiwYeEcXqVERkbq2Wef1ZAhQ+T3+zV69Gh16dLF9axQ5DnFy+P0apaXa2OclePV2hhn5Xi1Nq9mebk2L4/TSV4ep1eP2Zn4zMo40SZEUlJS1K1bN82bNy+wrWPHjho+fLimTp1aav/Zs2dr4sSJ2r9/v2rXri1JmjJlimbPnq1du3bJ5/Np4sSJWrBggTZv3hy435gxY7RhwwalpaWdsZ7k5GSlp6c7NDqUZey08veZd0+oqwAAoOaqyGOxxONxqJ2p7wzbOeT5+fn64osvNHjw4BLbBw8erE8//bTM+6Slpalv376BZlyShgwZoj179mjbtm2BfX6YOWTIEKWnp6ugoMDZQQAAAAAOC9spKzk5OfL7/YqLiyuxPS4uTh988EGZ99m3b59atWpVav/i29q2bat9+/bpxz/+cal9CgsLlZOToxYtWpS4be7cuZo7d64kadOmTUpOTj6rcTnpu+++U9OmTat1Vll5yfOdyzoboR5ndcxyOq8mZDmd59Usp/O8muV0nleznM7zapbTeV7NOl1eZR+Pq9o43VL8YnKZwnUi++7du01SqTdxPvzww9a5c+cy7zNo0CAbPXp0iW3btm0zSZaWlmZmZh07drQ//OEPJfZZunSpSbK9e/c6OILQc/JNpl7NcjrPq1lO53k1y+m8mpDldJ5Xs5zO82qW03lezXI6z6tZTud5NcvpPK9mhSIvVMJ2ykqTJk0UERGhffv2ldienZ1d6lXzYs2bNy9zf+n/Xik/3T6RkZFq3LixU+UDAAAAIRG2hjw6OlpJSUlasmRJie1LlizRpZdeWuZ9evfurRUrVujEiRMl9o+Pj1dCQkJgnx+e8rJkyRIlJycrKirK2UEAAAAADgvrBwNNmDBBL774op5//nlt3LhR48eP1549ezRu3DhJ0qRJkzRw4MDA/j/96U9Vp04djRo1SpmZmVqwYIEef/xxTZgwIfCJS+PGjdOuXbt0zz33aOPGjXr++ef14osv6r777gvn0Bxx2223Vfssp/O8muV0nleznM6rCVlO53k1y+k8r2Y5nefVLKfzvJrldJ5Xs5zO82pWKPJCJayXPZSkWbNm6U9/+pP27t2rxMREPfPMM+rXr58kadSoUVq6dGmJk97Xr1+vu+66S6tXr1ajRo00btw4PfjggyU+AnXZsmW69957tWHDBsXHx2vixImBJh8AAADwsrA35AAAAAD+T1hPWQEAAABQEg05AAAA4CIaco/y6plEXq1LorbK8GpdErVVhlfrAgCcGeeQAwBCrvih5tQ35HuBV+uSvFubV+uSqK0yvFqX5O3anEZD7iFmpr179+qNN95QdHS0OnXqpJYtWyo+Pl516tSRmQW9KP1+v3w+n2rVqvw/Q0JRl5drc6IuL9fGfFav2rw8nwCAiqEh95CZM2dq5syZys/P17Fjx5Sdna02bdro2muv1dixY3X++edXOGvLli1q165diW1+v1+1atUK+sHZybq8XJuTdXm5NuaT+QxXbZKUl5enTz75RB999JHatGmjjh07qm3btoqPj1dUVFSFnzCcut/Z1OP1urxcm1N1ebk25pP5dI3BMxo2bGgzZ860r776yszMtm/fbg899JC1bt3aYmNj7ZlnnrGCggIrKiqqUNaFF15okyZNsszMzBK3FRUVWVFRkX399deWl5cX1rq8XJuTdXm5NuaT+QxXbWZmN910kzVt2tR69uxpTZs2tYiICOvatatNnTrVDh8+XKGMYllZWaXqKSwsDCrD63V5uTYn6/Jybcwn8+kGGnKPWLhwobVp08YKCgrMzEotlj/+8Y/Wpk0bW7duXblZb731ljVs2NDGjBljPXv2tPj4eEtNTbU///nPtm/fvsB+devWtcWLF4etLi/X5mRdXq6N+WQ+w1Wbmdnf/vY3a9++vS1fvtyOHj1qZmaZmZl25513WoMGDax169a2ZMmSCtX22muvmc/nsz59+tgTTzxhO3bsKHG73++3I0eOVGisXq3Ly7U5WZeXa2M+mU+30JB7xIoVK6xjx462bNmywLb8/Hw7fvy4mZnt37/fUlNT7f777y83a/LkyTZ8+HDbtGmTrVu3zubNm2c///nP7YILLrBWrVrZNddcYxMmTLDatWuHtS4v1+ZkXV6ujflkPsNVm5nZiBEj7I477gj8fOoThoMHD9qwYcNs0KBBFXq1atiwYZaSkmJjxoyxrl27WsuWLe3yyy+3v/3tb3bs2DEzM3vnnXcsIiKiytbl5dqcrMvLtTGfzKdbaMg9Ij8/3/r06WPt2rWzBQsWlLnQfvazn9nYsWPLzfrXv/5l48ePL5GRnZ1ty5cvt6efftqGDRtmPp/Pbr/99rDW5eXanKzLy7Uxn8xnuGozM5s6dapdcskllp+fH9iWl5dnJ06cMDOzZcuWWYcOHezdd989Y05ubq796Ec/sqeeesqys7MtLS3Npk+fbsOHD7f27dtbQkKC3XLLLdazZ08bPnx4la3Ly7U5VZeXa2M+mU830ZB7yIEDB+zGG2+0zp0725AhQ2zKlCn26aef2pEjR2zatGnWuHFj++STT4LKLP5XdrGioiL77LPPzOfz2apVqypc10033WTnn3++Y3WZlf73emVr8+IxK67N6ePm1WNm5t215sQxK67Ni2vNy3+fa9eutfr169uQIUNs+fLlpW4/ceKENWrUyD7//PMz5hw+fNieeuope+6550ps37Vrl73//vv26KOP2oABA8zn81l6enq5dX355ZeerMus+h+zUNTm1WNm5t215tQxC0VtXj1moUZD7gF+vz/w/b59++z555+3G264wS655BJr1qyZ1apVyzp37mx//OMfy8364QN8scLCwsCbul566SWLi4sLqrZdu3bZ7Nmz7cYbb7TevXtbXFxcUHX9MO9Up77ZrKK1efmYnVqfE8fNi8fMzNtrzalj9sMsr601r/59niotLc0uu+wy69Kli1133XX21FNP2bp16yw9Pd1uvvlm69ixY4Wzimsp64nMQw89ZC1atKhw1meffWYDBw60xMREx+oq60lMsHWZ1YxjdmptThw3rx4zM++uNSeP2am1eW2tOf33GSpc9tAjtm3bpoYNG6qoqEiNGzdWXl6eNm7cqEOHDikmJkZNmjRRp06dKpzVoEEDHTt2TI0aNVK9evVK3L548WLl5OTo5ptvPmNOYWGhIiIiSlwi6PDhw8rKytLx48cVExOjxo0bq3PnzhWqq6y8H3r33XeVk5OjkSNHlpvnxWMmOXvcvHzMivO8ttacPmaSN9ea1/8+T7V582a99dZbWrlypXbu3KlNmzYpLy9PV199te644w4NGjTojPe3Mi5xZmYqKipSRESEJGnw4MHq0qWLnnnmmXLrKSoqUq1atZSZmamFCxdq9erV2rVrlzZs2BB0XVLpDy05td5g6jpVdT1mxXVIzh83rx0zyftr7WyP2Q9rOHWb22stlH+foUBD7rKVK1fq+eef18KFC3X06FF17dpVvXr10uDBgzVw4EDVqVOn0lndu3dXr1691K9fP/Xr109NmzatVI1+v19+v1+RkZGOfEiI3++XpMAfarCqwjGTnD1uXjpmZeV5ca2d7TGTqsZa89rfZ7G9e/fqyJEjqlu3buBJy5EjR/TNN9/IzBQdHa0OHTooNja23Kw9e/bo6NGjio2NVVFRkZo3b17ifgUFBXr++ed13XXXKS4u7oxZhYWFioyMLLHtu+++05YtWxQVFaXo6Gi1b99etWvXLreusrJOVVBQoHnz5mnYsGHl1iXVjGN2urxTBXPcvHrMTjdOL6w1J4+Z5N215vTfZ8iF78V4lOWCCy6wq6++2v7973/bRx99ZPfcc49169bNmjVrZtdff73t3LnTzEr+2zjYrLi4OLvxxhtt165dZnb6f5ufasiQIfbYY4/Zd999V2J7Xl5e4I0W//3vf0u86aIyeQUFBYF/k3///feBq0NUZpxuH7MzjbMyx82rx+xMeW6vNSeP2ZnG6fZa8/Lfp5nZzJkzrUePHhYTE2P16tWz1NRUmzhxYqnzQSty3E7Nql+/vvXv398mTZpk77//fuBNXpVRUFBQ4Wupl6ewsPCsr2tc046Z2dkft6pwzMy8tdacPGY/zPPqWnPi7zMcaMhdtGzZMmvatGmZC+Wtt96yxMRE69Kli+3ZsyesWStXrjSfz2ctWrQwn89nKSkp9uKLL5b4A83NzbXrr7++Qm/ucjLPq8fMzNlxevWYOZ3n1WPm9Di9esxCkffxxx9bfHy8/eY3v7GsrCxbtGiRjRkzxjp06GDNmze3Bx54oMJPcM+UFR8fb5MnTw5klXX++w/H2a1bN5s3b16pB/q8vLzAhyd999135TYjZ8oqfhJTnFWRRqAmHLPy8oI9bl49ZuWN08215uQxKy+vOv19hgsNuYtefvllu+CCCwKfIpWbm1viFa1vvvnG2rdvb3/5y1/CmvXII4/Y0KFD7bPPPrN//etfdv3119s555xjUVFR9pOf/MQ++OADS09PN5/PV6FPzHIyz6vHzOlxevWYOZ3n1WPm9Di9esxCkXfTTTeVeZnF/Px8mz17tjVt2tRGjx5dbo7TWT//+c+tVq1a1rx5c4uIiLAhQ4bYf/7znxL7rFy50oYMGVJuU+JkllnNOGZO53n1mJl5d605PU6vrjWn1224nP0Jh6i0K664QpI0b948SVLt2rUVFRUVOCe0ffv26t27tz777LOwZkVGRuq8885Tt27dNHz4cM2bN0/Lly/XtGnTdPjwYV199dXq2bOnrrjiCtWvXz+seV49Zk6P06vHzOk8rx4zp8fp1WMWirzo6GgdOnRIJ06ckCSdOHFChYWFioqK0rhx4zR16lR98skn2rBhQ1iztm3bpilTpuj999/Xc889J0kaMWKEGjRooFtvvVUZGRn65z//qT179pzxvFOns5wep1ePmdN5Xj1mTo/Tq8fM6TyvHrOwcvsZQU33wgsvWP369a19+/b22GOP2ZYtWwK3ZWRkWOvWre3VV18Na9axY8fsyy+/LLXd7/dbTk6Ovffee+bz+eydd96pUF1O5RX/m+qvf/2rNWjQ4KzG6WSW0+N0OsvM2XXmZJ5Xj5mX15pX/z6LLV682Bo3blxqLMWvRB07dsxat25tS5cuDVvW7t277dZbb7U5c+aY2clzSg8ePGirV6+2qVOnWnJyskVHR5vP57O33347bFlOj9PJLKfH6XSeF4+Z0+P08jFzMs/LxyycaMg9YN26dXbbbbdZYmKixcXFWefOnW3w4MHWpk0bu/LKK8Oa9cNzs/x+f4lrJJuZvfnmmxX+mFmn84qtXbvW7rjjDuvevbs1b978rI6Zk1lnUplxOpnl5DpzIs/JtRGqdWZW9daak+ss2LyioiI7fvy43XPPPRYREWEpKSk2e/Zsy8nJMTOz7777zv7yl79Y/fr1w5plZpaTk2M7duwotb2goMCys7Pt97//vTVs2DDsWcXjvPfeey0yMtKRY+ZEltPjdDLPy+vMyXE6meX02vDyWnN63YYLlz10WUFBgSIjI+X3+7V+/Xp9+eWX2rx5s3bv3q3Bgwfr6quvVoMGDcKeVVhYKJ/PV+LSZ8VLZdasWdq1a5emTp1a4XE6lWenXD/00KFDyszM1Ndff60tW7Zo165dGjRoUIXH6WRWRcycOTPo4+ZUlpNrw+k8J9eak1lVda05uc7OJm/RokX629/+prVr1+rAgQOKi4tTZGSk8vLyNGbMGN13332uZEllX9rxmmuuUUREhF5//XXXshYuXKh//OMfWrt2rbKzs89qnE5mnU5lx+lknpfXmeTNteb02qhqa83pdesUGnIXHDx4UP/5z3/0t7/9TU2aNFGbNm3UrVs3DRgwQK1bt/ZEVtOmTXXeeeepc+fOSk1N1fnnnx/Yz8x0/Pjxcq/B7HTeqfuf6cNLguFkVnmKiop04sSJoK/5XdksJ9eG03lOro1QrbPi+1S1tebkOqts3rFjx1S3bl3l5uYqIyNDmzZt0pYtW5SXl6df/OIX6tSpU4Wvc+5k1pEjR0qdB29mOnbsmH75y19q/Pjxuuiii8Kedera2Lt3r7KysrRjxw5t3bpVJ06cCGqcTmadydGjR4Mep9N5Xl1nkjfXmtNroyquNafXrZNoyF1w3XXXadOmTUpKStLhw4eVnZ2t48ePKy4uTtdff71uueWWCr/RINRZeXl5iouL07BhwzR69OigPnjEybw33nhDSUlJOu+88wLbioqKJCmQkZeXp5iYmLBmnS7vhwoKChQVFRXWLCfXhtN5Tq4Np9etV9eak2sjFHkbN27U008/rS+//FLt27dXmzZt1Lt3b/Xt21dNmjSpUEaoszp06KDzzjtPF110kfr27VviiWRF5sHJrB+qik/+KjPOs83z6jr7YZ5X15rTa6MqrjWn161jQn1ODErKysqyOnXqWEZGRmDbkSNHbMGCBXbDDTdYbGys3XbbbZaXl1futTbDmVW7dm27/fbbK5TldN6mTZvM5/NZbGysDRw40F5++WX773//W2KfwsJCmzdvnm3cuDFsWV6uzcm14XSek2vD6XXr1fn08ro1O3nZxk6dOlnfvn3tgQcesGuuucZSUlKse/fuNmzYMHv//ffLzQhXVq9eveziiy+2ESNG2HvvvedKlpnZvn377O9//7sdOHCgxPbiaySbnZyDiny4Sjiyfqj4Q6LK+7tyMs+r6+x0eV5Ya06uDafznFwbTq9bN9CQh9mcOXMsJSUl8C7kH14Dc+HChda0adMKfQCHV7Oczps6dar17t3b/v73v9vw4cOtXr161rBhQ7v55pvtww8/tIKCAtu8ebP5fD7bvn172LK8XJuX59OrWWbenU8vr1szs3HjxtmVV15Z4jrl+/btsxdeeMH69u1rderUseeff77cnJqSZWZ29913m8/ns0aNGtnw4cPtnXfeKdXEbN++3Z588slymxuvZjmd5+X59GptXp5Pr2a5hYY8zD7//HNr3rx5iQ8Ayc/PDzxry8vLsyFDhti9995bZbOcznvggQds3LhxgVfwtm7danPmzLG+fftaZGSktW3b1nr06GGJiYlhzfJybV6eT69mmXl3Pr28bs3MLr/8cnvwwQfNrOyPqZ4wYYKlpKTYsWPHyPr/evXqZQ888IC98MILNnDgQIuOjrYWLVrY3XffbV988YWZmf3ud7+z9u3bV9ksp/O8PJ9erc3L8+nVLLfQkLtgzJgx1qBBA3v44YfL/OS77t272/Tp06t0llN5fr/fVq5cafPnzy91W15enq1fv94eeugh8/l89sILL4Qty+u1mXlzPr2c5dX59PK6LTZt2jRr3bp1idNb8vLyAh9bvWHDBktISLCPPvqILDt5reThw4fbc889Z2Yn/7OzceNGe/zxx6179+5Wq1YtS0xMtDp16ti0adOqZFYo8rw6n16tzcvz6dUsN9GQu+SJJ56w+Ph4i4qKsoEDB9qzzz5rzz33nA0cONA6duxY4WflXs4KRV5ZH3O7bNky8/l8dvToUdeyvFrbk08+aa1atXLs+DuZ59WsYmWdY1jZ+fRqllN5W7ZssYsuusgSEhJK/Lei2Pr16y0qKqpC81ATso4ePWpvv/22ffbZZ6VuO3bsmK1atcpGjBhhERERlpubWyWzQpHn1fn0am1enk+vZrmJhtxF27Zts9mzZ9tVV11lzZo1s/POO89uvfVWW7FiRbXJCkWemZX40Jcnn3zyrD5Uxcksr9Tm9/sD32/YsMHmzJlj1157rTVv3rxSx9/JPK9mFRUVlcgrS0XnwKtZocozM/v+++9t3Lhx1qBBA6tbt65de+21NnPmTLvjjjusa9euNnLkSLJOk/3DUxLMzG655RZLTU2tFllO5h0+fNjuuusuO+ecc856DpzM8nptZmU/+a7sfDqd59WscOKyh2GUlZWlrKwsff/996pfv74uvfRStWrVKnD7oUOHdM4551ToEkJezQplbXXq1FGvXr3Utm3bEvusX79e9erVK7U9lFler+2HioqKlJ+fr9jYWB06dEj169cP6pKHoczzalZZMjIy1KBBg0rNQVXJOtu8zMxMvfvuu/rwww+1du1atWvXTjfffLOuu+46NW/enKzTMDMVFRUpIiJCx48f109+8hPdcccduvbaa6tN1tnknXq/EydOaP369Vq+fLk++ugjrVmzRm3btq3wHDiZ5eXaioqK5PP5TvtYG+x8Opnn1Sw30ZCHyeOPP66XX35ZmzdvVnx8vBo3biyfz6eePXvqpptuUq9evRQZGamioqJyr5ns1axQ1tayZUs1btxYtWrV0sUXX6yf/vSn6tOnT4WvL+1klpdr2759uxo3bqx69eqVebsFec1YJ/O8mlWRvGB4NSsUeUVFRXrrrbf03XffKTc3VwkJCerXr5/OPffcwD7ff/+9GjZsSNZp8lq2bKn+/furWbNmgX0KCwv1xRdfKCUlpUpmhSKvLH6/X7Vq1ZLP5wtqDkKd5fXaihUUFCg9PV29e/f2XJ5Xs0Iq/C/K1zw5OTlWr149mz17tpmZ7dixw/7973/br3/9a+vfv7+lpKTYxx9/XKWzwlnbgAEDrFevXoGs8v797mSWl2s7ePCgNWvWzK699lqbP3++bd++3fLz80vtt2LFCtu3b1+543Qyz6tZwebt2bOnSmaFIu/w4cM2YsQIa9KkiTVr1swuvvhiu/jii61Pnz72+9//3rKysgL7lnfN35qQVVZejx49LCkpyVJTU+23v/1tha757vUsp/Py8/Ptq6++Ou2l6oK5nrSTWV6urbysYDmZ59UsL6AhD4PZs2dbcnJymbetXbvWhg0bZvXr17dvv/22ymZ5ubaaMs4ZM2ZYo0aNbNCgQRYdHW1Nmza10aNH2+LFiy07O9v8fr/t2LHDOnbsWKEHRCfzvJrl5dq8PE4zsylTpli3bt1s9erVZma2ceNGe+mll+z222+3pKQku/LKKy07O7vcnJqSVV5ecnKyXXXVVY7U5maW03nPPPOM1alTx0aNGmVvv/227d27t9S56N9//70tWrSozCeYocrycm0VzVq4cGHgyi3hyvNqlhfQkIfBa6+9ZgkJCbZs2TIzK31d0ePHj1tKSorNnDmzymZ5ubaaMs4777zTbrvtNvP7/Xb48GF79tlnLSkpyXw+n3Xs2NF+97vf2YQJE6xhw4YVGqeTeV7N8nJtXh6nmVlqaqr97//+b6nthYWFtmzZMuvQoYMNGTKErCpQm5fH2atXLxswYIClpqZarVq1LCEhwe69915bsWJF4Dr6s2fPtpSUlLBmebk2xlm5cbqNhjwMjh07Zv3797err77a1q1bV+Y+ffr0sT/84Q9VNsvLtdWEcebn59tLL71kTz/9dKlXCDZv3my//e1vrUOHDubz+ezRRx8tty4n87ya5eXavDxOs5OX5Rw3bpxdeumlgVc6f/hk8oMPPrAuXbrY2rVra3yWl2vz8jizs7Otb9++9vLLL5uZ2c6dO+3RRx+1jh07ms/nsx49etjjjz9unTt3tl/96ldhy/JybYyzcuP0AhryECs+72vlypV28cUXW2RkpF111VX25ptv2pYtWyw9Pd2mT59u55xzjm3durVKZnm5tpoyTrOTTdfBgwfN7OQDYH5+fokHwY0bN1qtWrVs586d5WY5nefVLC/X5uVxmpmlpaVZu3bt7De/+U2Z5+rv2LHD6tata7t27SLL47V5dZx79uyxp59+2hYvXlzqtjVr1tidd95p5557rvl8vrBmebk2xlm5cXoBDXmYfP/995adnW3vvvuu/fSnP7WGDRtabGysJSQkWIcOHYL69CivZnm5tuo+zuLm/ptvvrH9+/eXuK34zaB/+MMfrHXr1hWqyck8r2Z5uTYvj7P4PgUFBTZ37lxr0qSJnXPOOTZmzBhbsmSJbdq0yV577TUbOXLkad8fUdOyvFybl8dpZpabm2vHjx83s5PruPir2OTJk+2iiy4Ke5aXa2OcwWd5AQ15CO3fv9+eeuopi4+Pt8TEREtOTrarr77annvuOdu8ebN9/vnn9vrrr1foShBezfJybTVxnBdddFHgTVN///vfS3zS4sKFC23p0qVhzfNqlpdr8/I4y3Lo0CF75plnrGfPnhYVFWXnnnuutWjRwn7yk5+U+cl5NT3Ly7V5dZynu8LIsWPHrHPnzvb444+7kuXl2hhn5cbpJq5DHkKjRo3Shg0bdNVVV+ncc8/VwYMHlZGRoU2bNik+Pl5//OMf1bNnzyqd5eXaavI4v/zyS23atEmtWrXS/fffr8GDB5/VOCub59UsL9fm5XFK0uHDh1W/fv0S13kvKirSiRMndPToUWVmZqpu3boVurZ0Tcjycm1VbZw/dOLECb366qu66aabFB0dHZYsL9fGOIPP8hS3nxFUV0VFRVa3bt3A1TOKt23bts1effVVGzRokLVv397WrFlTZbO8XFtNH+f27dvttddes0GDBlmnTp3OepyVyfNqlpdr8/I4i9122232/PPP27p16+z7778vc5/ic9XLu3ZyTcjycm1VfZyHDh0qtyans7xcG+MMPstLaMhDJDMz0xITEy0tLa3M2/Py8iwpKckeeOCBKpvl5doYZ/BZXq6NcQafFYq8f/zjH+bz+axhw4bWtm1bu+222+z111+3zZs3W25urpmZHTlyxH7yk5+c9qpBNSnLy7VVtXEuWLDAvvnmm0BWbm6uXX311bZ+/fqwZXm5NsZZuXF6CQ15iOTm5tpll11mvXr1sq+//rrMT1mcPn26de/evcpmebk2xhl8lpdrY5zBZ4Uib8yYMXb77bfbt99+a08++aQlJiZa7dq17aKLLrLJkyfbhx9+aLNmzbKoqCiyPF4b42ScVbE2p8fpJTTkIZSWlmbdu3e3Xr162V//+lfbsWNH4E1Ux44ds2HDhtnPfvazKp3l5doYJ+OsirV5dZwFBQX22GOP2cSJE0tsz8zMtPHjx1vLli2tcePGFhERYaNHj67xWV6ujXEyzqpYm9Pj9Boa8hBbv369XX/99RYbG2uNGze2K6+80n7xi19Y69at7ZJLLqnQvwK9nuXl2hgn46yKtXl1nAcPHrSNGzea2cnTXX54HvA///lP8/l89uWXX5Ll8doYZ/BZXq6NcQaf5TVcZSVMsrOz9c477+jNN99UbGysEhMTNWLECJ1//vnVJsvLtTFOxlkVa/PyOIsVFRXJzBQREaF58+Zp/Pjxys3NJasK1sY4K8ertTHOqoWG3AVFRUWqVatWtc5yOs+rWU7neTXL6TyvZjmd59WsUORJ0tNPPy2/36/777+fLBfyvJrldJ5Xs5zO82qW03lezQo3GnIAgCMKCgoUERHhSKNfE7KczvNqltN5Xs1yOs+rWU7neTUr3GjIAQAAABdVvacQAAAAQDVCQw4AAAC4iIYcAAAAcBENOQAAAOAiGnIAAADARTTkAAAAgIv+HykKEc1IvzFrAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = qaoa(G, res_sv.x, False)\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "sv = backend.run(qc).result().get_statevector()\n",
    "myplot(sv_to_stats(sv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "1fb8264c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.49083129,  0.46242808,  0.1783287 ,  2.27937851, -1.88497982,\n",
       "        -0.27836672,  2.50199742,  1.21554966,  1.99701902,  2.7590539 ]),\n",
       " -5.552,\n",
       " 1000)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.algorithms.optimizers import SPSA\n",
    "\n",
    "spsa = SPSA(maxiter=500)\n",
    "initial = [1.0] * (G.number_of_nodes()*2)\n",
    "res_spsa = spsa.optimize(len(initial), f_sampling(G), initial_point=initial)\n",
    "res_spsa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "3ca0e77b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = qaoa(G, res_spsa[0], True)\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "counts = reverse_stats(backend.run(qc).result().get_counts())\n",
    "myplot(counts)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}