02_GNN_vs_SA_for_MIS.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Graph Neural Networks versus Simulated Annealing for Maximum Independent Set\n",
    "\n",
    "#### Author: Ivan Carvalho (@IvanIsCoding)\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/IvanIsCoding/GNN-for-Combinatorial-Optimization/blob/main/02_GNN_vs_SA_for_MIS.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
    "\n",
    "In the previous notebook, we compared Graph Neural Networks (GNN) against Simulated Annealing (SA) on instances of the Max-Cut problem.\n",
    "\n",
    "In  this is notebbok, we will perform a similar benchmark but for the Maximum Independent Set (MIS) instead.\n",
    "\n",
    "Our benchmark is partly inspired by [Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set\n",
    "](https://arxiv.org/abs/2206.13211) by Angelini and Ricci-Tersenghi. They also criticize the baseline used by Schuetz et al. and share a greedy approach that beats the GNN. They also point that Simulated Annealing and Parallel Tempering, two heuristic methods, also beat the GNN.\n",
    "\n",
    "Let's verify those claims! We start by installing and importing the library we defined with the code from the previous notebooks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
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      "\u001b[?25h  Building wheel for gnn-for-co (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
     ]
    }
   ],
   "source": [
    "!pip install -q git+https://github.com/IvanIsCoding/GNN-for-Combinatorial-Optimization.git"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gnn_for_co.train import inner_solve_with_gnn, solve_with_annealing\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tqdm.notebook import trange, tqdm\n",
    "\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving MIS with GNNs: a tougher problem\n",
    "\n",
    "We reuse most of the code from the previous notebook, but we need to tweak how we find the MIS solution slightly.\n",
    "\n",
    "MIS instances are harder to solve than Max-Cut instances, at least from my experience from this notebook. MIS instances require more shots than Max-Cut to avoid truly suboptimal solutions (e.g. solution with no vertices). Hence we had to increase the number of shots considerably.\n",
    "\n",
    "To avoid wasting to much computational power on seeds that yield suboptimal results, we opt for an approach that:\n",
    "* Trains the GNN for $a$ epochs, where $a$ is small. We call this GNN a guess to see which landscapes are promising\n",
    "* Checks that the GNN has not converged to the solution with cost $0$ after $a$ epochs. If the cost is $0$, we discard and test a new seed.\n",
    "* Trains the GNN for $b > a$ epochs, where $b$ is large. This is the GNN we use at the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_with_gnn_mis(\n",
    "    G,\n",
    "    embedding_size,\n",
    "    hidden_size,\n",
    "    learning_rate,\n",
    "    epochs,\n",
    "    epochs_guess,\n",
    "    dropout_rate,\n",
    "    seed=2023,\n",
    "    verbose=False,\n",
    "    shots=5,\n",
    "    is_max_cut=True,\n",
    "):\n",
    "    lower_bound = -G.number_of_nodes() / 10.0\n",
    "\n",
    "    for k in range(shots):\n",
    "        solution = inner_solve_with_gnn(\n",
    "            G,\n",
    "            embedding_size,\n",
    "            hidden_size,\n",
    "            learning_rate,\n",
    "            epochs_guess,\n",
    "            dropout_rate,\n",
    "            seed + (k + 1) ** 3,\n",
    "            verbose,\n",
    "            is_max_cut,\n",
    "        )\n",
    "\n",
    "        if solution[\"energy\"] <= -1:\n",
    "            solution = inner_solve_with_gnn(\n",
    "                G,\n",
    "                embedding_size,\n",
    "                hidden_size,\n",
    "                learning_rate,\n",
    "                epochs,\n",
    "                dropout_rate,\n",
    "                seed + (k + 1) ** 3,\n",
    "                verbose,\n",
    "                is_max_cut,\n",
    "            )\n",
    "            break\n",
    "\n",
    "    return solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum Independent Set for d-Regular Graphs (d = 3)\n",
    "\n",
    "We revisit d-Regular Graphs to benchmark GNNs against SA, just like we did on our Max-Cut benchmark. \n",
    "\n",
    "We start with graphs that have $d = 3$ ranging from size 100 to 1000. Schuetz et al. do solve larger instances in their paper, but because MIS instances are more challenging to solve we opt to focus on these medium sized graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "d3_graphs = {\n",
    "    i: nx.convert_node_labels_to_integers(nx.random_regular_graph(d=3, n=i, seed=2023))\n",
    "    for i in range(100, 1100, 100)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(columns=[\"N\", \"MIS size\", \"Algorithm\"])\n",
    "gnn_results = []\n",
    "sa_results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a5e240e1b3254735b5692494094a6faa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 100, Anneling found 44.0\n",
      "N = 100, Graph Neural Networks found 37.0\n",
      "N = 200, Anneling found 89.0\n",
      "N = 200, Graph Neural Networks found 78.0\n",
      "N = 300, Anneling found 133.0\n",
      "N = 300, Graph Neural Networks found 114.0\n",
      "N = 400, Anneling found 177.0\n",
      "N = 400, Graph Neural Networks found 144.0\n",
      "N = 500, Anneling found 221.0\n",
      "N = 500, Graph Neural Networks found 183.0\n",
      "N = 600, Anneling found 266.0\n",
      "N = 600, Graph Neural Networks found 235.0\n",
      "N = 700, Anneling found 309.0\n",
      "N = 700, Graph Neural Networks found 269.0\n",
      "N = 800, Anneling found 352.0\n",
      "N = 800, Graph Neural Networks found 300.0\n",
      "N = 900, Anneling found 396.0\n",
      "N = 900, Graph Neural Networks found 334.0\n",
      "N = 1000, Anneling found 440.0\n",
      "N = 1000, Graph Neural Networks found 384.0\n"
     ]
    }
   ],
   "source": [
    "for i, G in tqdm(d3_graphs.items()):\n",
    "\n",
    "    annealing_sol = solve_with_annealing(G, num_reads=2000, is_max_cut=False)\n",
    "    model = annealing_sol[\"model\"]\n",
    "    sa_results.append(-annealing_sol[\"energy\"])\n",
    "\n",
    "    print(f\"N = {i}, Anneling found {sa_results[-1]}\")\n",
    "\n",
    "    embedding_d0 = int(np.sqrt(i))\n",
    "    embedding_d1 = embedding_d0 // 2\n",
    "    learning_rate = 0.005\n",
    "    epochs = 25000\n",
    "    epochs_guess = 100\n",
    "    dropout_rate = 0.05\n",
    "    gnn_sol = solve_with_gnn_mis(\n",
    "        G,\n",
    "        embedding_d0,\n",
    "        embedding_d1,\n",
    "        learning_rate,\n",
    "        epochs,\n",
    "        epochs_guess,\n",
    "        dropout_rate,\n",
    "        seed=2023,\n",
    "        verbose=False,\n",
    "        is_max_cut=False,\n",
    "        shots=500,\n",
    "    )\n",
    "\n",
    "    gnn_results.append(\n",
    "        -model.decode_sample(gnn_sol[\"solution\"], vartype=\"BINARY\").energy\n",
    "    )\n",
    "    print(f\"N = {i}, Graph Neural Networks found {gnn_results[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n, cut_size in zip(range(100, 1100, 100), gnn_results):\n",
    "    df.loc[len(df)] = [n, cut_size, \"Graph Neural Network\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n, cut_size in zip(range(100, 1100, 100), sa_results):\n",
    "    df.loc[len(df)] = [n, cut_size, \"Simulated Annealing\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
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4+flhaGiIq6srhoaGPHz4MFM+L168AFJ7ttIYPXo0jo6ONG7cWOrhBLCzs6N169bo6upibGxMgwYNsLOzQ19fnypVqvD5559rtT8AX375JWXKlMHKyop+/fpJ9xfkvT1Nz8iRI/n111+1ei0Bjh49SuXKlenevTv6+vrUr1+fdu3asW/fvjzUdipDhgyhTJky0jOjc+fO0nPP19cXpVLJvXv38pxehQoV6NWrV5bzZjZu3MiQIUOoVasW+vr6DBs2jBs3bki9FhlxcnLi77//BuDs2bMMHTpUquuzZ8/i5OQEpD6HBwwYQNWqVTEzM2PMmDGEhIRotVsjRozA1NRU69m4du1agoKC+OWXX6hWrRqQev+9fPmSBw8eoKenR4MGDShRokSeyw+QvccAlClThhcvXpCSkpKtc/H06VOsrKykbSsrK54+faqVRtqEqLQCmZubS+FGRkYkJCRI25UqVZL+6+rqUrFiRSm9HTt2sGbNGukkvHnzRrpBMh6bERcXF7744gtmzJjBkydPaNu2LePHjycpKQmVSpWpDNHR0dJ2+fLlpf8mJiZS3lnVRaVKlbQechnTygtWVlZ88sknLFiwgGrVqmFpaakVnpiYyI8//siJEyekoYWEhATUarVU1z179uTXX39l2LBhlC1bNtu88nt+ciN9XRkZGWltGxsbZ1lv2ZG+0TMxMZGOTavnNExNTaWuXEgdu/bz89M6D7q6ujx//lzaTl+nlStXlobF8nJsxushvV3p001/TT158oSnT59qDTWo1Wqt7Yx1lZycnOO9lxFvb2+8vb1RqVQcOnSIcePGYWNjQ+nSpUlJScHV1VWKq9FoMl1X2WFqaoq/vz+rV69m0qRJ2NvbM378eGrVqpVl/EmTJlGjRg2GDBkCpNZpfvKfNWsWixcvpkOHDlSpUoXhw4fTqlWrTG2Nrq4ulpaW+b6/cuPp06eULl1aqzG1srLi6tWr0nZ256patWpMnDiRgIAA7ty5g6urKxMmTKBixYp5yjv9df3ixYtc26b092ra/ZvxHszq/k1rE54+fUrVqlUBpKGj3r17aw1dZGxX7927x5w5c7h69SqJiYmo1WpsbW214mS8v9I/E/Lanqanbt26tGzZkhUrVmhdd0+ePOHy5cuZ7quML2M5kfE6DAoKYsuWLTx9+hQdHR3i4+O1njN54csvv6RNmzaZXg4iIiKYPXs2c+fOlfYJIYiOjqZy5cqZ0rGzs+P+/fvExMRw8+ZNli9fzuLFi4mNjdUq99OnT7WOr1y5MikpKVrtVlbPx6CgIPz8/LTCOnfuTFRUFGPGjOH169d4e3szevRoDAwM8lz+HFsshUKBoaEhhw4don379lnGsbCwICIiQnqDiYyMxMLCIs8GZCRtrgCkNj7R0dFYWFjw5MkTvv/+e4KDg1EoFNKbQnp0dHRyTLtfv37069eP58+fM2rUKFatWsWIESMwMDAgIiKC2rVrS2XIa0OQHgsLC6KiotBoNNKDKTIy8p0mXnbp0oWJEydqjS+nsXr1au7du8emTZuoUKECN27coEuXLoj/F6pVq9VMmTKFLl26sGHDBrp16yZ5owXBxMSEpKQkaTvf426FhIWFhdbYemJiojQPAlJvoNmzZ+Pg4JDp2LRJVZGRkVIDFRERIV2zeTk2OypUqEBkZKTWvZCGpaUlVapU4cCBA3kt5jtjYGBAhw4dWLlyJbdv36ZTp04YGhry119/Zemk5HbfALi5ueHm5kZSUhILFy5k8uTJbNiwIVO8FStWcO/ePa2wtN6f7PLPSPXq1VmwYAEajYYDBw4wcuRIzpw5g4WFheQAQmqDnN29WpBr1cLCglevXhEfHy85F/lpEz799FM+/fRT4uPjmTJlCvPnz+enn37K07Hpz0XZsmULrW3KSI0aNahYsSIHDx7M9XPhjNfHtGnTqF+/Pv/9738pUaIEwcHB0jyANNLfB+nvr4IwcuRIunbtqmWvpaUlTZo0Yc2aNVkeY2JiQmJiorSd1XWQvnznzp1j1apVBAcHU6dOHXR1dWnSpInUtuaVsmXL0r9/fxYuXKi139LSkmHDhuXZ8TExMcHW1pZ169ZRp04dDA0NUSgUBAcH88knn1CuXDkA6RmZRkREBPr6+pibm0vP1Kzu89WrVzN48GDKly9Pu3btgNT2Y/jw4QwfPpzHjx8zZMgQatSoQY8ePfJc/hyHQkqWLMnIkSOZMWMGhw4dIjExEZVKxbFjx5g3bx4AHTt2ZPny5cTGxhIbG8vSpUv59NNP82xARq5du8aBAwdISUlh7dq1GBoa0rhxYxITE9HR0ZEqcuvWrdIEx7xw+fJlLl26hEqlwsTEBENDQ3R1ddHT06N9+/b4+/sTHx/PkydPWLNmTb483jQaNWqEsbExq1atQqVScebMGY4cOYKXl1e+0/Ly8mL16tV06NAhU1hCQgJGRkaUKlWKly9fsmTJEq3wwMBAdHR0mD17NoMGDWL8+PGF8n2+jY0Nx44d4+XLlzx79izTZ7Efinbt2nH06FHOnTuHUqlk8eLFWm9YvXv3ZuHChdKNFhsby6FDh7TSWLZsmTRJdtu2bdI5ysux2dGhQwdWrFjBq1eviIqK4pdffpHCGjVqhJmZGStWrCApKQm1Ws2tW7e0hvJyonz58jx69Cjb8G3btnH06FHi4+PRaDQcO3aMO3fu0KhRIywsLGjevDlz5syRwh8+fCh1sZqbmxMdHa01AS89MTExHDp0iDdv3mBoaIipqalWj04ax44dY926dSxdulSruzW3/DOyc+dOYmNj0dXVpVSpUkBq70SHDh04duwYp0+fRqVSsXr1aqmhzUhu12pO9WlpaYlCoWDBggUkJydz8+ZNtmzZkqc24e7du5w+fRqlUomhoSFGRkZZ1lVeKMy2KSO6urpMmDCBJUuWsGnTJl69eoUQgvv372u95WZFQkICZmZmmJmZER4ezm+//ZYpTlBQEK9evSIyMpJ169a9UxuYkWrVquHl5aV1X7Vs2ZL79++zY8cOVCoVKpWKy5cvSy8eNjY2HDx4kMTERB48eMCWLVtyLZuenh7lypUjJSWFJUuWEB8f/072Dhw4kLCwMO7evSvt69WrFytWrJCeXXFxcYSGhkrhWV2XTk5O/PrrrzRp0gQAZ2dnrW2ATp06sXbtWh49ekRCQgL+/v506NAhV0e+du3arFq1ihkzZkgfGvz111/873//Q61WU6JECfT19fN9Deca29fXlwkTJrBs2TJcXFxo2bIl69evp3Xr1gB8/fXXNGjQQOqGtbW15euvv86XEenx9PQkJCSEJk2asHPnTgICAjAwMKB27dr4+vrSq1cvmjVrxq1bt7C3t89zugkJCXz//fc4OTnRqlUrypQpw6BBgwCYPHkyJiYmtG7dmj59+tCpUye6d++eb9sNDQ0JDAzk+PHjNG3alOnTpzNv3rxsu4xzwtjYmGbNmmWaKwLQv39/kpOTadq0KZ9//jlubm5S2NWrVwkODmbu3Lno6enx5ZdfAkjj7QWhc+fO1KtXDw8PD3x9fQulsXgX6tSpw5QpUxg7dixubm6UKlVKqyuvX79+ko0KhYKePXtmeoCnzfYfMGAAvr6+Ujd9Xo7NjuHDh2NlZYWnpye+vr5aPWp6enoEBgZy8+ZNPD09adq0Kd9//32eG60hQ4awfPlyHB0dtb5iSaNEiRIEBgbSqlUrHB0dmT9/PtOmTZO6SufNm4dKpcLLy4smTZowcuRInj17BkDTpk2pXbs2rq6uODs7Z0pbo9EQHByMm5sbTk5OnD17NtO3+pA6x+TFixd4eXlJX4ZMmTIl1/wzcuLECTp27IhCoWDWrFn4+/tjbGxMzZo1+emnn/jhhx9o2rQpf/zxB4GBgRgaGmZKI7drNbf6XLBgAU+ePMHNzY3hw4czYsQImjVrlqW96VEqlfz3v//F2dkZV1dXYmNjGTNmTK7HZUdhtU1Z4eXlxcKFC9m1axctW7akadOmjBo1ip49e2bbQw0wfvx49uzZg729PZMnT86yHfD09KRbt2506dKFli1b8tlnnxWKzX5+flrDJiVKlCAoKIiQkBDc3NxwdXVl/vz5kpPcv39/DAwMaNasGePHj8/1pTftq6V27drh4eGBkZFRnocMM1KiRAkGDx6s1Zvapk0bBg8ezJgxY7C3t6dTp04cP35cCh8+fDgTJkzA0dFRmn/VpEkTEhISJEci4zZA9+7d8fb2pm/fvnh6emJoaMjkyZPzZGe9evUIDAxk8uTJHDt2jJiYGEaOHImDgwNeXl44OTllGh3IDR2R3z6e90hAQAAPHjxg/vz5RW2KTDHl8ePHeHp6cu3atTzPXZCRkck71tbWHDhwoFCGX2X+mRTrJb1lZGRkZGRkPiyyYyEjIyMjIyNTaHxUQyEyMjIyMjIy/2zkHgsZGRkZGRmZQkN2LGQKncGDB2erUVBQPqT6X0adgX8CGTUv3ue52LBhA82aNUOhUOR7AaG8kFHv42OhOEhnF6Z8+Z07d+jWrVu2az0UxXn87LPP8rUcgUzhIjsWMu9EThLdq1atomvXrkVoXeYH7Pti27ZtWFtbay3N/THxvs6FSqVizpw5rF69mrCwsBxXd31feHh40KhRIxQKBc2bN2fChAn5WiX2Y+Jjly/PiUWLFjFo0KA8LbRWWOzdu5d27drh4OCAi4sL48eP1/p029fXt8ik6GVkx6LY8SEkcWWJ7rds376dMmXKaGkr/Bt4/vw5ycnJ0oqQ+UEIkUnt8l0JDAwkLCyMHTt2cP369UJZr+V9ktVCdf8U+fKsePr0KWfOnJHWNfpQ2Nvb89tvv3H+/HkOHTpESkqK1iqXnp6enDlzJtu1UmTeL7Jj8REwdepUrbXjAb766itpmdrc5LazkjXOSnY6o8w5pL71nTp1CshZrjo9uUl0px9CyK+0c24yx+k5evQoXbp0wd7eHnd3dwICAqSwvn37AqmLySgUCkmoKjvJYkh9a2zfvj0ODg7MmDEj12V8nzx5wtmzZ5kxYwYnT57UasTS6nr16tWSJP3WrVul8AkTJjB9+nSGDBmCQqGgR48eWmJROUlB51TujGQ8F717985WsvrRo0d88cUXksT99OnTs+zyv3fvnrSAUpMmTejXrx8AFy5coHv37jg4ONC9e3cuXLigZYe/vz+9evWicePGWa56ef36dbp27YpCoWDUqFH5eluvUKECrq6uklAdwMWLF+nVqxeOjo54e3tz5syZPJU1t/skIyNHjqR58+Y4ODjwxRdfaHXBT5gwgalTp/Lll19iZ2enZQN8vPLl27Ztw9PTE4VCgYeHh5bwWXpOnToliQymUZDzmFcsLS2lVZghdQG69EOkRkZG2NracvLkyULPWyYP5EsLVea98Pfff4sWLVpI0sEvX74UDRs2lCTic5PbzihrnJ3sdEbpaCG05aOzOy4juUl0p5cqzq+0c15kjtPkff/66y9x8+ZNoVarxY0bN4SLi4s4ePCgECKzDLYQOUsWP3/+XNjZ2YnQ0FChVCrFmjVrhI2NjZYtGVmyZIno3r27EEKITp06iaCgICksTZJ+4cKFQqlUiqNHj4pGjRqJly9fCiFSZb2dnJzEpUuXhEqlEmPGjBGjRo0SQuQuBZ2fcmc8FzlJVvfs2VPMmTNHJCcni7NnzwqFQpGtRHTGfF68eCEcHR3F9u3bhUqlErt37xaOjo4iNjZWssPd3V3cunVLqFQqoVQqtdJLTk4WLVu2FGvWrBFKpVKEhoaK+vXra0mfZyT9tRsZGSk6deokyUhHRUUJJycncfToUaFWq8XJkyeFk5OTeP78ea5lze0+ySidvXnzZhEXFyeSk5PFzJkzhbe3txQ2fvx4YW9vL86dOyfUarUkv53GxyhfnpCQoCX7HR0dLW7dupWlXXPmzBHTpk2TtvN7Hs+ePSscHByy/Z09ezbbOjl79qywt7cXdevWFY0bNxYnTpzQCv/hhx/E7Nmzc6xXmfeD3GPxEeDo6IiOjg7nzp0DYP/+/djZ2VGxYsU8yW1nlDXOTnY6N/J6XE4S3VnxrtLOueHs7Iy1tTW6urrUq1ePjh07Zqs/ATlLFh8/fpw6derQvn17DAwM6N+/v63V3ckAACAASURBVJYKY1bs3LmTTp06Aalr9WccDtHX18fPzw8DAwPc3d0xNTXVkl9u3bo1jRo1Ql9fH29vb+ltOzcp6PyWOz3ZSVZHRERw5coVRo4ciaGhIY6Ojnh4eOQpzTSbq1WrRpcuXdDX16dTp07UrFmTP/74Q4rTtWtX6tSpI0mCpydNxydtCeb27dvTsGHDXPP18/NDoVDg7u5OuXLlGDlyJJB6blq0aIG7uzu6uro0b96cBg0acOzYsQKXNSOfffYZJUqUwNDQkBEjRnDz5k3i4uKkcE9PTxwcHNDV1dV6s4ePV75cV1eX27dvk5SUhIWFhSQolpG4uDjMzMyk7fyeR0dHR86dO5ftL71qaVbHnj9/nuPHjzNo0KBM6qBmZma8fv062+Nl3h+yY/ERoKOjg5eXl3TT7969W1rTPr3cdtovMDBQS6UvoxzurFmzuH//Ph06dKB79+5ajXtO5Oc4b29vgoODJd2IxYsXc+LEiSzjvqu0c25cunQJHx8fmjZtioODAxs3bszx64Q0yeK0enRycpIkizNKsevo6OSoEXD+/HkeP35Mx44dgVTH4tatW1pd8WXKlNFaNjy9xDpklt5OC0svBZ322717tzTUkt9ypyc7yeo0qfC0fZBZTjonMkqaQ2aJ75zSe/r0KRUrVtSaAJg+vcGDB0v6I+m75ZcuXUpYWBi//PILd+/eleohIiKCffv2adXh+fPnefbsWYHLmh61Ws38+fNp3bo19vb2koOS/nzklHZ6+fI0/P39OXfuHPXr189Vvnzo0KE0b94ce3t7/P39M10H7yJfbmpqir+/Pxs3bsTV1ZUhQ4ZoqQmnp1SpUlr3bm7n8X1QsWJF3NzcMmmyJCQkSCJ2Mh8WWSzhI6FTp074+voyZMgQLl++zNKlS4G8yW1nnI2dnex0RilptVpNbGxsrseZmppmm3dGie70gmjvQl5kjtP49ttv6du3L6tWrcLIyIhZs2ZJDWtWM9Rzkix+8OCBJC8MbyW5s2PHjh0IIejSpYvW/u3bt2NjY5N9AfNAblLQOZX7XalQoQKvXr0iMTFResjkVP6MWFhYEBERobUvMjJS63rI6auBChUqEB0djRBCihcREUHVqlWB1K9bcsLJyYlu3boxd+5cli1bhqWlJZ07d2bmzJmZ4j558iTHsuZ2n6Rn9+7dHD58mDVr1lClShXi4uLyJbP9scqXu7m54ebmRlJSEgsXLmTy5Mls2LAhUzxra2utXpXczmNGzp07JwklZsXKlStz7LVIIyUlJVOvZ3h4eKEowcrkH7nH4iOhfv36lC1blu+//x5XV1fJ034Xue3sZKdr1KhBcnIyR48eRaVSsXz5cq3JXtkdl5GcJLoLSn5kjhMSEihdujRGRkZcvnxZq5u3XLly6Orqak0SzEmy2N3dndu3b3PgwAFSUlJYt25dtk5NcnIyoaGhzJgxgx07dki/yZMns2fPngLP2M9NCjqncr8rlStXpkGDBgQEBKBUKgkLC8tzTxek1t/9+/fZvXs3KSkphISEcOfOHVq2bJmn49O69NetW4dKpeLAgQNcuXIlX2Xo378/p06d4ubNm3h7e/PHH39w4sQJ1Go1ycnJnDlzhqioqFzLmtt9kp6EhAQMDQ0pW7YsiYmJLFiwIF82f4zy5TExMRw6dIg3b95gaGiIqalptrLZzZs35/r169IEzfyeR0dHR8LCwrL9ZedU7Nq1S3Jknzx5wsKFC7W+TEtOTubatWt5UqSVKXxkx+IjolOnTpw6dUoat4d3k9vOTna6ZMmSTJ06le+//54WLVpgYmKi1b2a3XEZyU2iuyDkR+Z46tSpLF68GIVCwdKlS+nQoYMUZmJiwrBhw+jduzeOjo5cvHgxR8nicuXKsWjRIkny+sGDB9jb22eZ76FDhzA2NqZLly5UqFBB+nXv3h21Wp3tkFBeyU0KOqdyF4T58+dz8eJFnJ2dWbhwIV5eXllKkmdF2bJlCQwMZM2aNTg7O7Nq1SoCAwO1Zu7nhKGhIQEBAWzfvh0nJydCQkJo06ZNvuwvV64cnTt3ZunSpVhaWrJs2TJ+/vlnXFxccHd3JygoSBpayKmsud0n6enSpQtWVla4ubnRsWPHPM9nSs/HJl+u0WgIDg7Gzc0NJycnabgzK8qXL4+zszOHDx8GCuc85oXw8HB69eqFnZ0dvXv3pkaNGvzwww9S+JEjR3BycqJixYqFnrdM7shaITIyMlkyatQoatasKU2ILM4Ux7J+KPnyO3fuMH78eLZs2fJBF8nKiR49ejBr1izq1q1b1Kb8K5F7LGRkZIDUdUwePnyIRqPh+PHjHD58+IMvfPSh+DeV9X1Tu3Zttm7d+tE4FQCbN2+WnYoiRJ68KSMjA6SOrY8YMYKXL19SqVIlaXJgceTfVFYZmQ+NPBQiIyMjIyMjU2jIQyEyMjIyMjIyhYbsWMjIyMjIyMgUGrJjISMjIyMjI1NoyJM388CSJUsICAhg9+7d1K1bF2tra+rWrSstGjNv3jysra2B1O+n582bh1qtxtbWlh9//FFr6eC88OJFAhrNP3fqi7l5CZ4/z36djX8Tcl1oI9eHNnJ9vKUgdaGrq0PZsma5R5T5IMiORS5cu3aNixcvZhK42bhxo5b4DqSuhDd58mTWr19P9erVmTRpEkFBQQwfPjxfeWo04h/tWAD/ePsLE7kutJHrQxu5Pt4i10XxQB4KyQGlUsmMGTOyXXUuI8ePH6dBgwZUr14dSF1COm3JaBkZGRkZmX8Dco9FDixatAhvb2+qVKmSKczHxwe1Wk2LFi0YMWIEhoaGREZGain5WVlZ5UvISUZGRkZG5p+O7FhkQ1hYGFevXmXs2LGZwo4ePYqlpSXx8fGMGzeOpUuXMnr06ELL29y8hNa2RqPh0aNHJCQk8E9YdSSdMvO/nuJUFwYGBlSsaEHp0qULlE6FCiULyaLigVwfb5HronggOxbZcPbsWcLDw/H09AQgKiqKQYMG8eOPP+Lq6gqkikX16NFDkre2tLTkzJkzUhoRERFYWlrmO+/nz+O1xhrj4l6SkqKmfPnK6Oh8/KNX+vq6pKRoitqMj4LiUhdCCFQqJY8fR/DqVSImJu82Ua5ChZI8exZXyNb9c5HrIxVDkjE10BCfYkCKyP9jSVdXJ9MLmUzR8fE/pYqIIUOGcPLkSY4cOcKRI0eoVKkSQUFBNGzYkKSkJABSUlLYv38/NjY2ALi5uXHlyhXu378PpE7wLAzlycTEeEqWLPOPcCpkiic6OjoYGhpRpkwF4uNfFrU5MsUEHR0djF/f5/X2WTxa+jWJh5ZjoowparNkCojcY5FP7t69y5QpU9DR0SElJQWFQsE333wDpPZgzJgxg6FDh6LRaLCxsWHSpEkFzlOjUaOnJ58qmaLHwMAQtTqlqM2QKSYYJccQs2U2IkUJQFL4eTSJryjR6TtUGBaxdTLvivy0yiNHjhyR/u/evTvbeK1bt34vKokfk3KgzL8X+TqUKUw0r6IkpyINZcQddBNjwaRSEVklU1DkvnWZj5JZs6axYsWy95L2gQOhjB7tl234hQvn6NrV673kLSMj8xYdI9PM+wyMQd+oCKyRKSxkx0KmyBk+fAjt27dCqVTmHrkQaNu2A/7+S6VtV1dHHj9+9EHylpGReYumpBWmNq5a+8p4+KA0LFtEFskUBvJQiEyREhkZweXLFzEzK8HJk8fx8Cj8YaT0pKSkoK8vX/YyMh8DKh0jjJv1wcTWDd3kOIRZBVJKWv0jPquXyR65hZUpUvbt24utbQPq12/Avn17snUs1q9fy6ZNGwAdBg8exty5M9m4cTtVqlQlPj4ef/95nDlzCiMjYz79tAv9+vmiq6tLSMhudu/ejo2NLfv2hdClS3eqVKnK7t07WL48CD+/LwEYMKA3Ojo6TJgwmbJlywHw22+/sn79WvT0dBkyxI+OHb2B1GEaIyPj/3eKwqhduw4zZ87j11/XEhq6h3LlyjFt2izq1q33QepQRuafjErPFMpZy5/eFiPkoRCZImXfvr20adOBNm06cObMaWJjn2eK89dfp/j99w34+y/j9993EBZ2Xivc338eCQnxbNq0kyVLVrBvXwghIbuk8OvXr2FlVZldu/bTv7+v1rFLl64EIDj4Nw4ePIGnZ1sAYmOfk5AQz44doUyYMJkFC+by+vVr6bg//jjIl19+xZ49hzAwMGTYMF/q1rVm795DtGzpSUCAf6HVkYyMjMw/iWLtWISHh7N06VKmT58ubd+8ebOIrZJJ49Kli0RFReLh0YZ69WyoXLkKBw/uyxTvyJGDeHl9Ss2atTA2NsbXd4gUplarOXz4AEOHDsfU1AxLSyt69fqCfftCpDjm5uX57LNe6OvrY2RknCfb9PT0GTBgMPr6+ri4uGJiYsrDhw+k8BYtWlGvng1GRka0aNESQ0NDOnTohJ6eHp6ebbl9+38FqBkZGRmZfy7F1rEIDQ2lb9++REdHs3PnTgDevHnDnDlzitgymTT27duDk1NTypQpA0CbNu0JDd2bKV5MTAwWFhWl7fT/X716SUpKCpUqvV3htFIlS2JinknbFSu+jZ9XSpcurTUXw9jYmMTEN9J22nAJgJGRcYZtIxITE/Odp4yMjExxoNjOsVi8eDFr1qyhXr16ksJovXr15B6Lj4Tk5CSOHDmIRqPB27sdkKomGx8fx+3bt7Tili9fnmfP3opuPH0aLf0vXboM+vr6REVFUqNGTQCio6MoX75CuhTktRdkZGRkPhTFtsciNjYWa2tr4O2iPjo6OvICPx8Jx48fRVdXj19+2cyaNetZs2Y969dvpnFjBfv2afdatGrVmpCQXdy/f4+kpCSCg1dJYXp6enh4tGHFimW8eZNAVFQkv/++nnbt8r4ORbly5kREPCm0ssnIyMj8mym2joWtra00BJLG3r17adSoURFZJJOe0NC9eHl9SqVKlTA3Ly/9unXrycGD+1Cr1VJcF5fmfPZZL0aOHMbnn3fB1rYhkKq2CTBq1DhMTEzo2bMzX389mDZt2ktfcOQFX98vmTVrKu3bt+Tw4YOFW1AZGRmZfxk6QhTPL4bDw8MZNGgQVapU4eLFizg7O3Pv3j1Wr15N9erVi9q8HMmobhoV9YBKlaoVoUX5430ret6/f49+/T7nyJFTH/2aFMVF3TQ9Bbke5U8KtZHr4y0FqQtZ3fTj4uNulQtArVq1CA0N5Y8//qBly5ZYWlrSsmVLzMzeTe5Zpmg5duwPXFyak5SUxPLli2ne3O2jdypkZGRk/o0U25Z5x44duLi44OWlPda+Z88eOnXqVERWybwrO3duY/bsaejq6mFnZ8+3304oapNkZGRkZLKg2A6F2NjYUKFCBRYtWoRCoZD229vbc+HChSK0LHfkoZDiQ3GsC3kopPCQ6+Mt8lBI8aHYTt40NjZm5syZ+Pn5sXnzZml/MfWjZGRkZGRkPgqKrWOho6NDixYtWL9+PWvWrOGHH35ArVbLn5vKyMjIyMi8R4qtY5HWM1GjRg1+//13Hj9+zMCBA7U+Y8wrS5Yswdramlu3UhduunjxIt7e3rRr1w5fX1+eP3+rb5FTmIyMjIyMTHGn2DoWzs7O0v+SJUsSGBhI48aNMTc3z1c6165d4+LFi1SuXBkAjUbDuHHjmDJlCvv378fR0ZH58+fnGiYjIyMjI/NvoNg6FoGBgVrbOjo6fPvttxw5ciTPaSiVSmbMmMG0adOkfVevXsXIyAhHR0cAevXqxb59+3INk5GRkfmY0CMF44THGESGYfT6PvpCWdQmyRQTitXnpsuXL+err74CYNGiRdnG++abb/KU3qJFi/D29qZKlSrSvsjISKysrKTtcuXKodFoePnyZY5haUJbeSHj7OanT3XR1/94fMCUFBVr1gRx8OB+9PT00NPTo2rVTxgy5CtJr6Mw7I2IiGDgwL7s35+7M7hyZSBBQStYtWotDRo0lPYlJiYycuToAtuSF86fP0dAgD/Bweu19uvr6xbIvvPnz5GSosLZ2eW92f7VV1/yxRc+uLq2yDWurq4uFSqUfOe8CnJscaQo6kMIDa/DDvEs9GdpX5nm3TBv9hm6hkYf3J405GujeFCsHIuoqKgs/78LYWFhXL16lbFjxxbUrHyT8XNTjUbzTp8snr4WxbZj4Tx/nYx5KSO6udfCxbZSge2bMWMaSUlJ/PxzMCVLlkQIwenTf3L37j2qVq2u9YmlRqN5Z40WtVoDiDyVXaMRVKpkybJlASxeHCjt02jydnxeSElJyXFRLrVagxBo5ZdWFwWx79y5syQmJuLg4JxjvHdFrVYjhECtzmtda975s0D580ptiqo+jJTPiT24Rmvfyz+3oV/DkWRTq2yOer/In5sWH4qVYzF9+nTp/48//ligtM6ePUt4eDienp5AqqMyaNAgfHx8iIiIkOLFxsaiq6tLmTJlsLS0zDbsQ3P6WhRrQ2+i/P8HxfPXyawNTVV2LYhz8ejRQ44f/4Nt20IoWTL17UJHR4dmzVylOCtXBhIeHk5CQjzR0VEEBq5h3brVXLx4AZVKRZkyZfjPf6ZQqZIlkZERDB7sQ/v2nTh37gxCCL79dgKNG79de+Tnn5fy119/kpSUxIQJU2jc2C5L29zdPTh37m/OnDmd5dv9r78Gc+zYEdRqNeXLWzB+/CTMzcsza9Y06tWzoXv3zwG0tmfNmoaenh4PHz7gzZs3BAdvYPr073n48AEqlZLKlavyn/9MoVSpUrnW3bvY9/LlS3bu3IZGo+Hcub/x9GxLQkI8pUqVok+ffhw+fJBp0yaya9d+ypYtx9ixI+nZsw9OTk0JDd3Db7/9go6ODlZWVfjuu4mULVuOkJDd7N8fiqmpKY8fP2TKlB+07Dh0aD8bN65n9uyftCTqZYoRyjeIlMxDHyIxDkyLwB6ZYsXH079eSLx584Y3b95I20IINm3axMyZM9m7d28OR2ozZMgQTp48yZEjRzhy5AiVKlUiKCiIwYMHk5SUxLlz5wDYuHEj7du3B6BBgwbZhn1oth0Ll5yKNJQpGrYdCy9Qurdu/Y8qVT7J9UF6/fpVpk6dxYYNWylVqhR9+w5g1ap1rF37G61bt2P58sVS3FevXlG7dh3Wrt3IqFHjmDZtEkqlUgpr0KARa9ZsYODALwkMXJxdlujo6DB0qB8//7w003ol+/eH8OTJE37+OZjVq9fj4tKcJUsW5qnMt2/f4r//DSA4eAMA33wzlqCgX1i37ndq1KjJ+vVr85TOu9hXq1ZtOnfuRvv2HQkO3oCPzwAcHJpw7txZAM6f/xtb24acP3+WlJQUrl+/RqNGdty9e4fAwCUsWLCUtWs3UrNmLfz9f5Lyu379CsOHj+KXXzZRp461tH/9+rXs3r2ThQuXyU5FMUaYlkO/VAWtfToGxuhm2Ccj8y4Uqx4LgNGjR9OhQwe6dOkCwNy5c9m+fTvOzs7MnDmT6OhofH193zl9XV1d5s2bx9SpU0lOTqZy5cr89NNPuYZ9aJ6/Ts7X/nfl3r27TJ/+PUlJSTRt2oxRo1KHjlxcmmv11Pz1159s27aZxMQ3mT75NTAwkGTO7e0dMTIy4uHDB5iZmWFiYkrz5m4A2No2zNUZaNbMlV9+WcORI4e09p88eZybN2/g69sXALU6hRIl8tZ12rKlJyYmJtL2vn17OHBgHykpKhITk6ha9ZM8pVNY9jVq1JipUyeiUqm4cuUSfn6jOHr0MBUqWFCzZi2MjY25cOEcLi7NKV++PACdO3djwIA+UhoNG9pRuXIVrXRXr15BxYqVmD9/kaQcK1M8UeqaUbbzaF7uX4Hq6X30S1ekbPuhJBuag7yIoEwBKXaOxbVr16SHuVKpZNOmTSxbtoymTZty+fJlvvvuu3dyLNJ/TWJvb8/u3buzjJdT2IfEvJRRlk6EeamCTcyqW9eax48fEhcXR8mSJalRoybBwRvYuvV3bt68IcUzMXnbnxoVFUlAwAJWrlyHlVVlrly5xPTp3+cpP0PDtw84XV1d1OqUXI8ZNmwEc+bMoFWr1tI+IQT9+/vSqVPnTPH19PS05rQoldr1Zmr61qm4dCmMHTu2snz5asqWLcuBA/vYtWtbnsryrvZlxMjImFq1anPo0H7Mzctjb+/IkiULqVDBAgeHJnmyIX2Z0rC1bcDZs2eIiorMl7Mk888kycSKUl3+g25yPMLQlCQdkyJxKpJUah4+S+Dc7RgsyppgZW6KvryQ4T+aYjcUkpiYKHXTX716FX19fZo2bQpAo0aNePbsWVGa98Ho5l4LwwxfZhjq69LNvVaB0q1a9RNcXd2ZO3cm8fHx0v7ExMRsj0lISEBf3wBzc3M0Gg07dmzVClepVBw8mPpZ7qVLYSQnJ1OtWvV3trFxYzuqVv1EShPA1bUF27dv4fXr10Cq03n7duqCZ5UrV+XmzWsAxMTEcOHC+WzTjouLw8ysBKVLl0apVLJ37673bp+ZmRkJCfFaaTg4NCEo6GccHJwwNDTEwsKC0NA9kmNhb+/I6dN/8vx5DAC7d++gSROnHO1ydm7G2LH/Ydy4b7h7t2BDZjL/DJQYkWRkTrJOZkfzg+Sv1rA29CZz1p1j2dbLTFt1hr+uP0Wn2D2Z/l0Uux4LCwsLbt68Sb169fjzzz9xcHCQwl6/fo2hoWERWvfhSJug+T6+Cpk0aRrBwasYPLgf+vr6lCxZkvLlK9C374As49eqVZtWrVrTt29PSpcug4tLcy5dCpPCS5cuze3bt9iwYR1CCKZNm1XgrvghQ/zw9f1C2m7fviOvXr1kxIghQOqXDV279qBOnbp4e3fh++/H07dvD6pW/YT69W2zTbdp02YcOBBK797dKF26DHZ2Cq5fv/Ze7WvRohUTJ45jwIA+eHq2xcdnAI6OTqxaFYijY6oj4eDQhCtXLlO/fgMAataszbBhwxk92u//J29WZty4ibna5eDQhIkTpzJhwhhmzpxL3br18l02GZm8EvUikTPXo7X2rd93k8a1zClpXOweT/8aip266ebNm1m4cCEKhYKTJ08SEBCAm1vqGH1ISAibNm0iODi4aI3MhX+TumnaVyF79x5+z1YVDbK6qTby56ba/Nvr41bEa+asO5dp/0/DXTEvkfeXQPlz04+LYucS9ujRg2rVqnH16lUGDBggrYIJYGRkxPDhw4vQOhkZGRmZNCqVNcXESJ/E5Ldzp2xrmlPaTJ48/E+m2PVYFAf+TT0WxZ3iWBdyj0Xh8W+vDx0diHyZxC+hN7kf+Rqn+hXp0qIWpU3y984r91h8XBS7HgsZGRkZmX8GQkCl0saM6WWHvoE+IkUtf+5aDJDn3srIyMjIFCl6QPkyRfO5q0zhIzsWMjIyMjIyMoVGsXUsZs6cmeX+WbNmfWBLZGRkZGRk/j0UW8di27asV0PctSv/CxrJaHPkyCEGDuzDgAF96NOnO9OmTZLCBgzoQ1JSUqHldeHCOQYN8sk13u3b/+Pw4YPvlEdkZAQdO3rmGGfKlP/QqVNrUlJyX/nzfREU9LO0pPnJk8dYunRRkdkiIyMjkx3FbvLmli1bgFQp6LT/aTx69KhIlEaLEzExMSxYMIegoF+pWLESQghu3/6fFB4cvKFIvoS4ffsWp06dwNOzTaGn/fr1K86ePcMnn1Tj5MljtGyZsxPyIXB1dcfV1b2ozZCRkZHJRLFzLHbu3AmkLhOd9h9SlSXLly/P3Llzi8q0D47y9imUZ7ci4p+jU8IcwybdMazTrEBpxsbGoKenT+nSqQ6ajo6O1uqMrq6OHDlyEkNDYz777FPatu3A+fNnefbsKcOGjeDly1gOHtzH69ev+c9/pmBnZ8+FC+dYunQRQUG/AGTaTiMlJYXvvhvFq1evSE5Opn59W8aNm8ibNwmsWhXImzcJDBjQBzs7BaNGjePatasEBgaQkJAAwODBwyR5961bN7Fp0wbMzMxwcXElJw4cCKVZs+Y4Obmwd+8uybFIW9zL27tbJln3tLAuXbpz6tTJTJLvp0+fZN261SQnKzEwMGDEiDE0aNCQ589jmDZtEgkJCSiVSpo1a87XX3+TyaaQkN2cOnWCmTPnceHCORYvXkD9+rZcu3YF0GH69NlUr14DSJWdP3LkIKVKlUahcOD8+bOZ6lZGRkamsCh2jsUvv6Q2mP7+/owePbqIrSk6lLdPkXwiGFJS5cdF/PPUbSiQc1G7dl3q17ele/eOKBQONGpkR7t2XpKjkRGVSsXPP6/hxo1rjBgxlK++GsnKles4fPggP/+8lOXLg/Kct56eHlOnzqR06TIIIZg5cyp79+6kS5fPGDx4mPSghVRNj/nzZ/PTT4spX748MTExfPllP9at+53o6CjWrVvNmjXrKVfOnPnz5+SY7969uxg+fDS2tg1ZuHA+MTHPKF8+VV46TdZ96FA/DhwIJTBwMcuXr5bCGjZsxJdffq0V9uTJY4KDg1iwIAAzsxLcvRvO2LEj2bZtLyVKlGTuXH9MTU1JSUlhzJjh/PXXKZo2zfmc3bsXzsSJU/juu0msXRvE2rVBTJ06k5Mnj3Pq1EmCg3/DyMiI778fn+f6lpGRkXkXip1jkcbo0aN58eIFx44dIyYmhsGDBxMdHY0QgkqVCq6X8bGjPLtVciokUpQoz24tkGOhq6vLjz/+l7t37xAWdoETJ46yYcMvrFu3kVKlSmeKnzY0UbduPZKSkvD0bAtAvXo2PHnyOF95azQafvvtV/766xQajZq4uDiMjY2zjHv16iUiIyMYO3aktE9HR4cnTx5x5cplmjVzpVw5cwA6d+7KH39kPT/j1q2bxMXFYW/viI6ODi1behAaugcfn4EAOcq6m5iY4uragpQUjVbYmTOnefLkMX5+Q6S4arWa2NjnmJiYsmzZIq5cuQwInj9/zu3bt3J1LD75pJrUc2Rr25A//zwBQFjYOTw8Wkuy7x06dCQ4OO/OuJXBJAAAIABJREFUnIyMjEx+KbaOxd9//82IESNo0KABFy5cYPDgwTx48IDVq1cTGBhY1Oa9d0T883ztzy81a9amZs3adO/ek759exAWdh53d49M8dJE3/T09LS200ug6+npI8TbORlKZQaH6P85eHAfly9fZNmylZiamrFu3WoePXqYZVwhoFatOixdujJTWOpDO2/s3buL+Pg4evTwBkClUmJiYiY5FjnJumcXJoTA2dmFyZNnZMovOHgVcXGvWbEiGCMjI+bOnZVJxj0rDA2NMuSlznMZZT48Ojo66KNCqItuMrCMzPui2H4VMnv2bBYuXEhQUBD6+qn+U+PGjbl8Oe8Pla+//hpvb2+6dOlCnz59uHHjBgAeHh60b9+ezp0707lzZ06cOCEdc/HiRby9vWnXrh2+vr48f144D/L8olPCPF/788qzZ0+5evVtHT59Gs3Lly+wtLR65zQrV65MRMQTXr9+jRCCQ4f2ZxkvPj6O0qXLYGpqRnx8vJbsuJmZmZaMe4MGjXj8+CEXLrwVOLpx4xpCCBQKB06f/pMXL2IB2LPn7Vyc9CiVSg4e3M+qVb+wZctutmzZzc6d+9HRQUudNb84OTXlzJnTWtLkN26kKqTGxcVhbl4eIyMjnj17ysmTx945HwCFwoGjRw+TlJSERqNh//6QAqUnU3AM1fHo3jlK3LYZPN2xEOOEx+jo6BS1WTIyhUax7bF48uQJLi4uANJNa2BgkK83ublz51KyZEkADh06xMSJE9m+fTsAixcvpm7dulrxNRoN48aN48cff8TR0ZFly5Yxf/58fvzxx8IoUr4wbNJda44FAPqGGDbpXqB01Wo1QUE/ExUViZGRMUJoGDz4qwLJa5cvX4FevfoyaJAP5cqVw87Onnv37maK1759J06cOE6fPt0pW7YcjRsrSE5OfZt3cHDit99+pX//3igU9owaNY45cxawdOkiFi36LykpKqysKjN3rj+1a9fBx2cgX301CFNTM1xcmmdp14kTR6lcuQpVqlTV2t+2bQf27t3FwIFfvlN5q1b9hClTfmDOnB9ITk4mJUVFw4aNsbGxpUePXkyePB4fn55UqFARB4cm75RHGq6u7ly5cpn+/XtRqlQpbG0bEhf379WmKGp0dUF19SivT6V+saZ69pA34Rco3+cHkowsitg6GZnCodiKkPXq1Qs/Pz/c3NxwcnLi77//5uTJk/z888/SBM/8sGPHDtatW8e2bdvw8PAgMDAwk2Nx+fJlJk6cyJ49ewCIjY3F09OTsLD8vd0WlgjZ+/gqJC8UR+Gtd+VjqIs3bxIwNTVDo9EwZ84PlC9fgSFDvn7n9GQRsnfHSB3H83VjESrt4a1ynUagsnIoIqs+DgpybcgiZB8XxbbHYsKECQwdOpSWLVuSlJTElClTOHLkCMuWLctXOpMmTeLPP/9ECMGqVauk/WPHjkUIgYODA2PGjKFUqVJERkZiZfV2SKBcuXJoNBpevnxZJOtnGNZp9kEcCZmPmx9+mEpUVATJyclYW9vwxRf9itqkfy86uugYGGVyLHR0i21TLPMvpNj2WABER/9fe/ceFlW1/gH8OzMwXIURBBwg9WhhmCkmSBZ4wQtmolbHNFM7mZlmSnksyVQUb4FmxwpTyzyaHs1bllpqaWpZGaammJp3EQZBbsptmMv6/cGP0QlFxJENe76f5/F5mLVm7/3uVy7vrL32Xpfx9ddfIyMjA1qtFn379q3xHSGbNm3C1q1b8cknn0Cn00Gr1aKsrAyzZs1CUVER5s2bh+3bt2PDhg1YsmSJZbu2bdtiz549d1VYHDv2J/z968+y6SRvGRkX8NBDraQOo966euh7XPnmY8trVQNv+A9NgGND+d+tRvZB1mWyn58fXn65/Dp4QUEBPD0r3w5ZXf3798fUqVORl5cHrVYLoPwOh8GDB2P06NEAAK1Wi4yMDMs2ubm5UCqVd1xU/P1SiNlslnw4/U7UheH/ukKOuTCbzTUesrb3SyEA4BDQDo3++Tb0549A7eUHhX8r5BvdADvPCy+FyIfs7grZtGmT1V0aqamp6Ny5Mx599FFER0fj7NnKkwJvpqioCDqdzvJ6165d8PT0hJOTk2XymxAC33zzDYKDgwEArVu3RmlpKQ4cKL8TYc2aNejVq5dNzkvGA0tUj5TfFsw7GO6GUaGG3qsllKHPwjPsSejVjaQOicimZDdisXTpUsydO9fyevLkyXjssccwfPhw/O9//0NSUlK1nmNRUlKC2NhYlJSUQKlUwtPTE4sWLUJOTg7Gjh0Lk8kEs9mMFi1aID4+HkD58wOSkpIQHx8PvV6PgIAAq1hqysFBjaKiq3Bz8+BtaSQJIQRMJiOuXcuDWn3zh5LRnblxVJJITmQ3xyIsLAz79++HUqmETqdD9+7dsW/fPmg0GhQWFqJnz574+eefpQ6zSn+/FGIyGZGXlw3j35+kWUcplUqYzfIa/q8pOeVCqVTBxcUd7u6eNS5weSnEmtT5MAMoKTPB2VEJlcQfWngpRD5kN2KhUqlgMBjg5OSEQ4cOoXnz5pY5Di4uLjZd0ru2qFQOaNRIK3UY1Sb1L8u6hLmguiq3qAzLvzmOo2dy0DzAEyP6PgStxhny+qhJUpDdHIsOHTrg/fffx4kTJ/D555+ja9eulr6zZ8/Cx8dHwuiIiKRXZjLj/TWHcPRM+ZOBz6YXYNay33CtlI8Yp7snu8LinXfewZ9//onnnnsOLi4ulrtCgPIl1SMjIyWMjohIennXypCeXWTVVlRqRFZ+iUQRkZzI7lKIn58fVqxYcdO+CRMm1HI0RER1j5NaBQeVEkaT9fwfV2fHW2xBVH2yG7EgIqKqadwc8XyvllZtvR9rBh8Pp1tsQVR9shuxICKi2xBAROvGaOHviez8EjRs4AR/bzfJ7wwheWBhQURkh1QKBQK9XRHo7Sp1KCQzsr0Ukp2dfUftREREdPdkW1hER0fftP3JJ5+s5UiIiIjsh2wLi5s9ULSwsJCPxCYiIrqHZDfHonPnzlAoFNDr9ejSpYtVX35+PkcsiIiI7iHZFRZz586FEAIjR45EUlKSpV2hUMDb2xvNmzeXMDoikpqDgxJCACaTPNZwIaprZFdYdOjQAQDw66+/wsXFReJoiKiuUMEIh7xzKD66CwpHJ7g+HAW9+30QXAaeyKZkV1hUUKlU+OKLL3D8+HEUFxdb9d04kkFE9sEh5zSubHjX8roodS98npuOUvf7JIyKSH5kW1hMnDgRJ0+eRNeuXdGoUSOpwyEiCTkozShM2WzdKMwoPXMAynZNYDZzSU8iW5FtYfHTTz9h586d8PDwkDoUIiIiuyHbwkKr1aKsrOyu9vHqq6/i0qVLUCqVcHV1xZQpUxAcHIxz584hLi4O+fn50Gg0SExMRLNmzQCgyj4ikobRrIR7WAxKLx673qhUwblFKEprebRCoQCulhhxOa8EOUVl8HRxhIOS8zxIPhTiZg98kIHPPvsM27Ztw7Bhw+Dt7W3V17Fjx2rt49q1a2jQoAEA4Pvvv0dycjK+/PJLDBs2DM888wz69euHr776Chs2bLCsqFpVX3Xl5BTW66FZH58GyM6+JnUYdQJzYU3KfKhggkPe2fLJm2oXuLbuIsnkTV1+KWYu+w0leiMAoFvYfRjQuQXUDrJ9rFC13M33hlKpgLe3u40jopqS7YjFypUrAQDz58+3alcoFNi5c2e19lFRVADXH66Vk5ODP//8E8uWLQMA9OnTBzNmzEBubi6EELfs8/LyssVpEVENmaCCqeEDcIpqCSGAUgluNzUJgc82H7MUFQCwMyUNHVtr0dyPfxhJHmRbWOzatcsm+3nnnXewb98+CCHw6aefQqfTwc/PDyqVCkD53Se+vr7Q6XQQQtyy704KCzlU3j4+DW7/JjvBXFiz53xczi3G2YyCSu3Xig12nZcKzIE8yLawAACDwYA//vgDWVlZ6N27t+W2U1fX6q/mN2vWLADApk2bkJSUhNjY2HsS6414KUQ+mAtr9p4PBYB2Qb44eDLLqt3bw8mu8wLwUoicyPai3smTJxEdHY3JkyfjnXfeAQCkpKRg0qRJNdpf//79sX//fjRu3BiXL1+GyWQCAJhMJmRlZUGr1UKr1d6yj4hIAeD56JZopi2/W03toMTwmIegbciH+ZF8yLawmDZtGsaNG4dt27bBwaF8YCYsLAy///57tbYvKiqCTqezvN61axc8PT3h7e2N4OBgbNmyBQCwZcsWBAcHw8vLq8o+IiIAaOjqiElD2+PdVx/Hgn93QeTDjaHiXSEkI7K9FHL69Gn069cPACwrmrq6ukKv11dr+5KSEsTGxqKkpARKpRKenp5YtGgRFAoFpk2bhri4OCxcuBAeHh5ITEy0bFdVHxERADgoFfD1cLL7S0MkT7ItLAICApCamoqHH37Y0nbkyBE0adKkWts3atQIa9euvWlfixYtsG7dujvuIyIikjvZFhaxsbF45ZVXMGjQIBgMBixevBhr1qzBjBkzpA6NiIhItmQ7x6Jr16749NNPkZubi7CwMKSnp+PDDz9ERESE1KERERHJlmxHLACgVatWmDZtmtRhEBER2Q1ZFRYLFiyo1vtq41kURERE9khWhUVmZqbla71ejx07dqB169YICAhARkYGjh49ip49e0oYIRERkbzJqrCYM2eO5es33ngD7733HqKjoy1tO3bswLZt26QIjYiIyC7IdvLm3r170b17d6u2qKgo7NmzR6KIiEhqAkB+sQEFJUbU8qKmRHZDViMWN2ratClWrVqFYcOGWdpWr15d7edYEJFtVTyoTiqFZSas23kKP/6RAZVSgZiIf6BnhyZwtvPlyolsTbaFxcyZM/Haa6/h008/hZ+fHy5fvgwHBwd8+OGHUodGZFcUCsCpWIey80eQYyyGc9N2KPNsArOovT/oSqUCv/15GT/+kQEAMJkFNu09ixaBGjzURFNrcRDZA9kWFq1atcL27dtx+PBhZGdnw8fHByEhIXB0dJQ6NCK74lSciStfTIcoKy1v+OVr+Ax4G6UNg2otBpMA9h3JqNT+x+kraPOPhjCZ6u9qwkR1jWwLCwBwdHREWFgYzGazpc1sNkOp5NAnUW1QKICytNTrRQUAQODqr1/C7ckJMJhVtRKHUgG0bNIQ5zKuWrU313rAbGZRQWRLsi0sjh07hoSEBJw8edKy8JgQAgqFAsePH5c4OiJ7ofhbUVFOlJUCovb+oAuzQPew+5Dy52XkXC2Pp7m/Bx5q7lWbYRDZBdkWFnFxcejatStmz54NZ2dnqcMhsktCCDg3bQP8shEQ10cO3cP6wFjLv3683NSYNiIcupxiqFQKaL1cOXGT6B6QbWGRnp6ON954Q/KZ6ET2rswjED7PvoNr+7+CubQI7qFPQjRuJclIgZtahfu1DWr/wER2RLaFRY8ePfDTTz8hMjJS6lCI7JpZKFHq2QIuvV6Hp4czcvLLpA6JiO4h2RYWer0er732Gtq3b49GjRpZ9SUlJd12+7y8PLz11lu4ePEi1Go1mjZtioSEBHh5eaFly5YICgqyTAJNSkpCy5YtAQC7du1CUlISTCYTHnroIcyZMwcuLi62P0GiesZoVkLp6ASAhQWRnMm2sLj//vtx//3313h7hUKBESNGIDw8HACQmJiIefPmYfbs2QCANWvWwM3NzWqboqIiTJkyBatWrUKzZs3wzjvvYOnSpXjttddqfiJERET1iGwLi7v9Y67RaCxFBQCEhIRg9erVVW6zd+9etG7dGs2aNQMADBo0CHFxcSwsiIjIbsi2sACAffv2YevWrcjNzcWiRYtw9OhRFBYWomPHjne0H7PZjNWrVyMqKsrSNnToUJhMJnTq1Aljx46FWq2GTqeDv7+/5T3+/v7Q6XQ2Ox8iIqK6TraFxeeff44VK1ZgwIAB2L59OwDA2dkZs2bNuuPCYsaMGXB1dcWQIUMAALt374ZWq0VhYSHefPNNJCcn44033rBZ7N7e7jbbl1R8fDjzvgJzYY35sMZ8XMdcyINsC4vly5fjv//9LwIDA/HJJ58AAJo3b45z587d0X4SExNx4cIFLFq0yDJZU6vVAgDc3d0xYMAALFu2zNK+f/9+y7YZGRmW996JnJzCev00QB+fBsjOviZ1GHUCc2GN+bDGfFx3N7lQKhWy+EAmF7J9OkxRUZHlj3rFsyyMRuMdrRUyf/58pKamIjk5GWq1GgBQUFCA0tJSy/62b9+O4OBgAEBkZCSOHj2K8+fPAyif4PnEE0/Y6pSIiIjqPNmOWISFhWHJkiUYPXq0pW3FihVWEzKrcurUKSxevBjNmjXDoEGDAACBgYEYMWIEpk6dCoVCAaPRiHbt2iE2NhZA+QhGQkICXnnlFZjNZgQHB+Odd96x/ckRERHVUQoh5Pmk/KysLIwaNQr5+fm4fPkyAgMD4ebmhsWLF8PHx0fq8KrESyHywVyUKyozIT27CAJAYy8XaFwduUYH+P1xI14KkQ/Zjlj4+vpiw4YNOHr0KNLT06HVatGmTRuubEpUy66WGpG08ndkXCkCALg4OSD+pXD4ejhJHBkR3Quy/itrNpthMBgAACaTCTIdnCGq005cyLMUFQBQojfi6x/Plq+pTkSyI9sRixMnTmDMmDEoKyuDn58fMjMz4eTkhOTkZDz44INSh0dkF5RKBXQ5RZXaL16+BpNZQMXagkh2ZDtiMWnSJDz//PPYu3cv1q9fjx9//BFDhgzBpEmTpA6NyG6YzQKtm3tXau/aPhCOrCqIZEm2hcX58+fxwgsvWG41VSgUGDZsmOVWUCKqHU193fFyv4fg6uwAB5UCTz7+D4QH+9XrCcpEdGuyvRTSuXNn7Nq1Cz169LC0/fDDD+jSpYt0QRFJRKGAZHdhOCgVePyhxgi53weOTg5wEGaANQWRbMm2sDCZTHjjjTfQunVrNG7cGJmZmUhNTUW3bt3w1ltvWd5XnSXUieorJ2MBzFmnYSrMhdq3BUyaJjBK8GNvNgu4OCrh4+3G2yuJZE62hUVQUBCCgoIsr++//35ERERIGBFR7XIyXUPB5vkwZF+wtHk9MRqKJo/yDikiumdkW1hwqXKydyI3zaqoAID83Z/Da3Ar6FVc7ImI7g3ZFhaA7ZZNJ6qPhFFfqc1cWgwIkwTREJG9kO1dIZ9//jmmTZuGZs2aISUlBUD5sukLFiyQODKi2qFq6A+Fg9qqzb1NVxgdPSWKiIjsgWwLi+XLl2PZsmUYOXKk5THeNVk2nai+0rv4odGzk+HUtDVUDbzg0fEpOLfvC5Pg8yOI6N6R7aUQWyybTlSfCQGUujeBW6/XoTCVwejgCr1Z6qiISO5kO2JRsWz6je5k2XQiuTAIB5QpXWFmUUFEtUC2IxaTJ0/GqFGjsG7dOhQVFSE6OtqybDoRERHdG7ItLCqWTT9y5AgyMjK4bDoREVEtkG1hAZTPrWjbti3atm17x9vm5eXhrbfewsWLF6FWq9G0aVMkJCTAy8sLhw8fxtSpU6HX6xEQEIC5c+fC27t8oaWq+oiIiOROIWT0CL7OnTtbJmpWZffu3bd9T35+Pk6ePGmZk5GYmIiCggLMnDkT0dHRmDNnDkJDQ7Fw4UKkpaVhzpw5MJvNt+y7Ezk5hfV6gSYfnwZ8bPP/Yy6sMR/WmI/r7iYXSqUC3t7uNo6IakpWIxZz5861fH306FFs2rQJQ4cOhb+/PzIyMrBy5Ur079+/WvvSaDRWEz1DQkKwevVqpKamwsnJCaGhoQCAQYMGoVu3bpgzZ06VfURERPZAVoVFhw4dLF8nJCRg6dKl8PPzs7R16tQJI0aMwPDhw+9ov2azGatXr0ZUVBR0Oh38/f0tfV5eXjCbzcjPz6+yT6PRVPt4cqi8fXz4yOgKzIU15sMa83EdcyEPsiosbpSVlQVXV1erNldXV1y+fPmO9zVjxgy4urpiyJAh+O6772wV4i3xUoh8MBfWmA9rzMd1vBQiH7ItLKKiojB69GiMHj0ajRs3hk6nw+LFixEVFXVH+0lMTMSFCxewaNEiKJVKaLVaZGRkWPpzc3OhVCqh0Wiq7CMiIrIHsr33cvr06QgJCUF8fDyeeuopxMfHo23btpg+fXq19zF//nykpqYiOTkZanX5mgutW7dGaWkpDhw4AABYs2YNevXqdds+IiIieyCru0Js6dSpU+jTpw+aNWsGZ2dnAEBgYCCSk5Nx8OBBxMfHW91S2qhRIwCosq+6eClEPpgLa8yHNebjOl4KkQ9ZFxZnz57FiRMnUFxcbNX+z3/+U6KIqoeFhXzUhVyYBGAwmeHiqILUP+51IR91CfNxHQsL+ZDtHItFixYhOTkZDz74oGXEASh/aFZdLyyIbEGhANJyivH5tyegu1KEzo8EIrrDfXB3ku2PPRHVAbL9DbN8+XKsW7cODz74oNShEEki51oZEpb+BqOpfPWxrfvOobjUgKE9g4D6OyBGRHWcbCdvOjs7o3nz5lKHQXbMEWUw5GfBUWGU5PgZV4osRUWFPQcvobBUmniIyD7ItrCIjY3FzJkzkZWVBbPZbPWP6F5SKADn4nQUbX0Pacmvoujb9+FSklnrcTipVZXa3F3VcFDJ9seeiOoA2V4KiYuLAwCsW7fO0iaEgEKhwPHjx6UKi+yA2ngVORsTYS6+CgDQXzyG3K/fg+eAaShTutVaHIE+7njgPg1OpeVb2l7s06pOTOIkIvmSbWGxc+dOqUMgOyWuZlmKigrGgmwoCq8AHrVXWLg4KhE7oC3OZ17D1aIy3OfnDm1DVxYVRHRPybawCAgIkDoEslMKp5sUDwoloHap9Vhc1Sq0asInvxJR7ZFdYbFgwYLbvic2NrYWIiF7ZXL1QYOwPriWssXS5vn4P2F0acS7MYhI9mRXWGRm1v4kOaIbGeEAh5A+aPSPECiK8yHcvGDyCIBRcNIkEcmf7AqLOXPmSB0CEYwKZxg198PnAT5ZkYjsCz9CERERkc2wsCAiIiKbYWFBRERENsPCgoiIiGxGdpM3b5Senn7TZdNjYmIkioiIiEjeZFtYLF68GAsXLkSLFi0qLZte3cIiMTER27dvR3p6OjZv3oygoCAAQFRUFNRqNZycnAAAEyZMQGRkJADg8OHDmDp1KvR6PQICAjB37lx4e3vb+OyIiIjqJtkWFp999hk2bNiA+++/v8b76NatG4YNG4bnn3++Ut8HH3xgKTQqmM1mvPnmm5gzZw5CQ0OxcOFCzJs3j7fAEhGR3ZDtHAuNRnPXj/UODQ2FVqut9vtTU1Ph5OSE0NBQAMCgQYOwbdu2u4qBiIioPpHtiMWkSZMwZcoUvPDCC5UuRfj7+9/1/idMmAAhBNq3b4/x48fDw8MDOp3Oat9eXl4wm83Iz8+HRsP1GuyNQgGUlhmhVCpgNvNZ3kRkH2RbWBgMBuzbtw9btmyxarfFsumrVq2CVqtFWVkZZs2ahYSEBMybN++u9nkjb293m+1LKj4+DaQOQVKXsq7h+/0XcfBkFsIfaoyu7e+Dv0/9/3+1BXv/3vg75uM65kIeZFtYTJ8+HePHj0fv3r2tJm/aQsXlEbVajcGDB2P06NGW9oyMDMv7cnNzoVQq73i0IiensF5/wvXxse/HWJeZzHj3899xIbM8B+cyruKPU1fw+rNt4ahUSBydtOz9e+PvmI/r7iYXSqVCFh/I5EK2cyxMJhOefvppuLm5QaVSWf27G8XFxbh2rfybXwiBb775BsHBwQCA1q1bo7S0FAcOHAAArFmzBr169bq7E6F6Jyu/1FJUVDh+Phc5V/USRUREVHtkO2IxfPhwLFmyBKNGjYJCUbNPiTNnzsSOHTtw5coVvPjii9BoNFi0aBHGjh0Lk8kEs9mMFi1aID4+HgCgVCqRlJSE+Ph4q9tNyb4obzEqoVLZ92gFEdkHhRCi/o65V6Fz5864cuUKHB0dK12K2L17tzRBVRMvhdRvRrPAx5tSceivbEtbZEgAXogOgrKGRa5c2Pv3xt8xH9fxUoh8yHbEgiMF9kmpMENddBmmgstQunrA3MAfBqVt59jcjoNSgeFPtsLxh/PwV1o+gps2RMsmGrsvKojIPsi2sOjQoYPUIVAtUygUcMhMRfbX/wGEGQDg9nBXOD06EAZF7RYXbk4qhD7QCE889g9+IiUiuyLbwmLBggW37IuNja3FSKi2qI1Xkfvdp5aiAgCKjv4Al1adAM9/SBgZEZH9kG1hkZmZafU6OzsbKSkp6N69u0QR0T1nKIW5+GqlZnPJVcBTgniIiOyQbAuLm63PsXfvXmzdulWCaKg2mJ09ofa/H2UZp683KpRQaRrDIF1YRER2RbbPsbiZiIgIfP/991KHQfeIAWp49hgJp8CWAACVe0M0emoC9C6+EkdGRGQ/ZDtikZaWZvW6pKQEW7ZsuaNFxaj+KXXyhVvvf6OB/iqEowvKVG6Q5w3VRER1k2wLix49ekChUKDiMR0uLi4IDg7Gu+++K3FkdK8ZoAacGpW/YFFBRFSrZFtYnDhxQuoQiIiI7I5dzbEg+2AUArlFZSgxmGv8OHciIqoZWY9YzJ49GydOnEBxcTGA8kXDFAoFUlNTJY6O7pW8ojJ8/OVRnL5UAA83NUY/3QZBAR5geUFEVDtkW1iMHz8ePXv2xOTJk22+bDrVTUYhLEUFAFwtKsPclQeQ+Orj8G7gJHF0RET2QbaFxZUrVxAbG8uhcDtyrdhgKSoqmAVwOa+EhQURUS2R7RyL/v37Y/PmzVKHQbXIWe0AjXvlAsLDTS1BNERE9km2IxYjR47EwIEDsXjxYnh7e1v1rVixQqKo6F5yVSsx6umHkbTyd8uy89GPNoVfQxeJIyMish+yLSzGjRuHwMBA9OjRA05OHAa3B0IAQQEeSHz1cVzOK4aHmxqNNS5wUPJyGBFRbZFtYXH8+HHs378fanXNh8ETExOxfft2pKenY/PmzQj41tbAAAAY8ElEQVQKCgIAnDt3DnFxccjPz4dGo0FiYiKaNWt22z6qBQLwdlfD252XP4iIpCDbORahoaE4c+bMXe2jW7duWLVqFQICAqza4+PjMXjwYGzfvh2DBw/G1KlTq9VHREQkd7IdsQgMDMTw4cPRo0ePSnMsYmNjq7WP0NDQSm05OTn4888/sWzZMgBAnz59MGPGDOTm5kIIccs+Ly+vuzwjIiKiuk+2hUVpaSm6dOkCg8GAzMxMm+1Xp9PBz88PKpUKAKBSqeDr6wudTgchxC37WFgQEZE9kG1hMWfOHKlDqDFvb3epQ7hrPj4NpA6hzmAurDEf1piP65gLeZBVYXHp0iUEBgYCqLxs+o3uu+++Gh9Dq9Xi8uXLMJlMUKlUMJlMyMrKglarhRDiln13Iien0HK7ZH2iUAAOCiM8PN2Rk1cqdTh1go9PA2RnX5M6jDqD+bDGfFx3N7lQKhWy+EAmF7IqLGJiYnDo0CEAlZdNr6BQKHD8+PEaH8Pb2xvBwcHYsmUL+vXrhy1btiA4ONhyqaOqPjlzNJcA6UdRePBblDTwgntoDPSeTSEEb/UkIrInCvH3v7xkMXPmTOzYsQNXrlxBw4YNodFosHXrVpw5cwZxcXG4evUqPDw8kJiYiObNmwNAlX3VVd9GLBQKBVTnfkTejk+vNypV8HkuAaVuAbfe0A7wE6k15sMa83EdRyzkQ7aFRV5eHho2bFip/eLFi2jSpIkEEVVffSss1ChFwdp4GPMvW7Vruv0LphZdJImpruAfDmvMhzXm4zoWFvIh2+dYxMTEYM+ePVZt//vf/zBgwACJIpIvASUUjpWfbqpw4EOqiIjsjWwLi1mzZmHy5MmYNm0aLly4gBEjRmDNmjVYvny51KHJjgFqeEY8a9WmdHaDQ+MHJIqIiIikIttLIQCQn5+PoUOH4vTp03jyyScxe/bsu3rEd22pb5dCAMBBYQJyzkF/7hCUrhqom7aB0c0P8v3uqh4OdVtjPqwxH9fxUoh8yHbEoqioCImJiSgsLMS//vUv7N27F19++aXUYcnWpTwDXl6WjkkHAvH6d86I33AJ1/QmqcMiIqJaJtvCom/fvjAajfj6668xceJELF++HCtXrsQrr7widWiyIwCs/v4v6A0mZOeV4FqxAWfTC3Au46rUoRERUS2TbWHx73//G3PnzkWDBuVPcgsODsb69eu50ug9YDCZkZ5VWKn9SkEJFHyMBRGRXZFtYdG7d+9KbU5OTnj77bcliEbenBxV6Nyu8vMqWvh72v0cCyIieyOrJ2/+3c6dO5GSkoK8vDyrJ3AmJSVJGJX8CLNA10cCkV+ox56Dl+Di7IhhTwQjwNtN6tCIiKiWyXbE4qOPPkJ8fDzMZjO2bdsGjUaDn376CR4eHlKHJkvuTioM7RmE92M74cN/d0H4gz5Qyfa7i4iIbkW2v/o3bNiAzz77DJMmTYKjoyMmTZqERYsW4dKlS1KHJl8CaODsAJ+GrvXudlkiIrIN2RYWV69eRVBQEADA0dERBoMBbdq0QUpKisSRERERyZds51g0adIEp06dwgMPPIAHHngAq1evhoeHBzw9PaUOjYiISLZkW1i8/vrryM/PB1B+6+mECRNQXFyM+Ph4iSMjIiKSL9kWFp07d7Z83bZtW3z33XcSRkNERGQfZFdYZGRk3PY9/v7+tRAJERGR/ZFdYREVFQXF/z/u8WbrqykUChw/ftwmx1Gr1XByKl8ufMKECYiMjMThw4cxdepU6PV6BAQEYO7cufD29r7r4xEREdUHsissHnzwQZSWluKpp55C37594evre8+O9cEHH1juPAEAs9mMN998E3PmzEFoaCgWLlyIefPmYc6cOfcsBiIiorpEdrebbtq0CR988AHy8/Px3HPPYeTIkdi6dSsMBgNUKhVUKtU9O3ZqaiqcnJwQGhoKABg0aBC2bdt2z45HRERU18iusACAoKAgTJw4Ebt27cK//vUv7N69GxERETh27JhNjzNhwgTExMRg2rRpuHr1KnQ6ndX8DS8vL5jNZsvdKfeSg4MSDg6y/O8kIqJ6RHaXQm50/vx5pKSk4PDhwwgODrbp47xXrVoFrVaLsrIyzJo1CwkJCejRo4dN9u3t7V7t9wqTAaVpJ1Dw+3ZAmOHxSDSc7wuG0lFtk1hqysengaTHr0uYC2vMhzXm4zrmQh5kV1jk5+dj69at+PLLL1FUVIR+/fph5cqVNr8TRKvVAgDUajUGDx6M0aNHY9iwYVZ3peTm5kKpVEKj0dzRvnNyCqv9SGznq+eQvSYBQPn7i0/uh8+zU1CqaXFHx7QlH58GyM6+Jtnx6xLmwhrzYY35uO5ucqFUKu7oAxndW7IrLCIjIxEYGIh+/fqhbdu2AIALFy7gwoULlvd07Njxro5RXFwMk8mEBg0aQAiBb775BsHBwWjdujVKS0tx4MABhIaGYs2aNejVq9ddHasqKpUSxal7UFFUVCg8vAPO3cfAaDTfs2MTERHdjOwKCx8fH+j1eqxduxZr166t1K9QKLBz5867OkZOTg7Gjh0Lk8kEs9mMFi1aID4+HkqlEklJSYiPj7e63fSeUlaeV6G4SRsREVFtUIibPeyBJHUnl0IcC84hd+0MQFSMTijg9exkGHgppE5gLqwxH9aYj+t4KUQ+ZDdiYU8UCgV+yXRFQOc34JF5AAphxjVtGI5luOIxLwWXLiciolrHwqIeU6kUOHDyChb+mY37/FpDoQAu/nIFDzUXiGgTwMKCiIhqHS/G12MmkxntH/QDAKRdvoaLmeXDiI+2bgyTiRM3iYio9rGwqMeEAB5q1hBRoYH4/+VRENnWHyH3NwJnzhARkRR4KaSec1Wr8Hz3IDzRsRkggIbualaLREQkGRYWMqAA4O0m7ZM2iYiIAF4KISIiIhtiYUFEREQ2w8KCiIiIbIaFBREREdkMJ2/WQUqlQuoQ7poczsFWmAtrzIc15uO6muaCOaxbuFYIERER2QwvhRAREZHNsLAgIiIim2FhQURERDbDwoKIiIhshoUFERER2QwLCyIiIrIZFhZERERkMywsiIiIyGZYWBAREZHNsLCgasvLy8PLL7+M6OhoxMTE4LXXXkNubi4A4PDhw+jbty+io6MxfPhw5OTkWLarqk8uPvroI7Rs2RJ//fUXAPvMh16vR3x8PHr27ImYmBhMmTIFAHDu3DkMHDgQ0dHRGDhwIM6fP2/Zpqq++u6HH35A//790a9fP/Tt2xc7duwAYD/5SExMRFRUlNXPBVDz85dTbmRPEFVTXl6e+PXXXy2v3333XfH2228Lk8kkunfvLlJSUoQQQiQnJ4u4uDghhKiyTy5SU1PFSy+9JLp27SpOnjxpt/mYMWOGmDVrljCbzUIIIbKzs4UQQgwdOlRs2rRJCCHEpk2bxNChQy3bVNVXn5nNZhEaGipOnjwphBDi+PHjIiQkRJhMJrvJR0pKisjIyLD8XFSo6fnLKTdyx8KCamzbtm3ihRdeEH/88Yd48sknLe05OTkiJCRECCGq7JMDvV4vnn32WZGWlmb5BWqP+SgsLBTt27cXhYWFVu1XrlwR7du3F0ajUQghhNFoFO3btxc5OTlV9tV3ZrNZdOjQQRw4cEAIIcRvv/0mevbsaZf5uLGwqOn5yzU3csXVTalGzGYzVq9ejaioKOh0Ovj7+1v6vLy8YDabkZ+fX2WfRqORInSbWrBgAfr27YvAwEBLmz3mIy0tDRqNBh999BH2798PNzc3xMbGwtnZGX5+flCpVAAAlUoFX19f6HQ6CCFu2efl5SXl6dw1hUKB//znP3j11Vfh6uqKoqIiLFmyBDqdzi7zUaGm528PuZETzrGgGpkxYwZcXV0xZMgQqUORzKFDh5CamorBgwdLHYrkTCYT0tLS0KpVK2zcuBETJkzA2LFjUVxcLHVokjAajVi8eDEWLlyIH374AR9//DFef/11u80H2ReOWNAdS0xMxIULF7Bo0SIolUpotVpkZGRY+nNzc6FUKqHRaKrsq+9SUlJw5swZdOvWDQCQmZmJl156CUOHDrW7fGi1Wjg4OKBPnz4AgLZt26Jhw4ZwdnbG5cuXYTKZoFKpYDKZkJWVBa1WCyHELfvqu+PHjyMrKwvt27cHALRv3x4uLi5wcnKyy3xU0Gq1NTp/e8iNnHDEgu7I/PnzkZqaiuTkZKjVagBA69atUVpaigMHDgAA1qxZg169et22r74bOXIkfvrpJ+zatQu7du1C48aNsXTpUowYMcLu8uHl5YXw8HDs27cPQPkM/pycHDRr1gzBwcHYsmULAGDLli0IDg6Gl5cXvL29b9lX3zVu3BiZmZk4e/YsAODMmTPIyclB06ZN7TIfFao6x5r2Ud2jEEIIqYOg+uHUqVPo06cPmjVrBmdnZwBAYGAgkpOTcfDgQcTHx0Ov1yMgIABz585Fo0aNAKDKPjmJiorCokWLEBQUZJf5SEtLw6RJk5Cfnw8HBwe8/vrr6Ny5M86cOYO4uDhcvXoVHh4eSExMRPPmzQGgyr767uuvv8Ynn3wChUIBABg3bhy6d+9uN/mYOXMmduzYgStXrqBhw4bQaDTYunVrjc9fTrmROxYWREREZDO8FEJEREQ2w8KCiIiIbIaFBREREdkMCwsiIiKyGRYWREREZDMsLIiqEBcXh/fff1+SYwsh8PbbbyMsLAz//Oc/a/34GRkZaNeuHUwmU60cb+rUqUhOTrbZ/lq2bIkLFy7YbH+1ZePGjXjuueekDoOoxlhYUL0SFRWFjh07Wj0aed26dRg6dKiEUd0bv//+O/bt24c9e/Zg/fr19/x4UVFR+Pnnny2v/f39cejQIcv6DPdaQkICxowZU6Nthw4dinXr1tk4IiKqCRYWVO+YzWasWLFC6jDu2J1+8k9PT0dAQABcXV3vUUTljEbjPd2/vWE+yd6xsKB656WXXsJnn32Gq1evVuq7dOkSWrZsafXL/cZPsxs3bsSgQYMwe/ZshIaGolu3bjh48CA2btyIzp07o2PHjvjyyy+t9pmXl4cXX3wR7dq1w5AhQ5Cenm7pO3PmDF588UV06NAB0dHR+Oabbyx9cXFxiI+Px8svv4yQkBDs37+/UryXL1/GqFGj0KFDB/To0QNr164FUD4KM3nyZBw+fBjt2rXDBx98YLVdWVkZQkND8ddff1nacnNz0aZNG+Tk5AAAfvjhB/Tr1w+hoaEYNGgQTpw4YXlvVFQUlixZgpiYGISEhGD8+PHIyMjAqFGj0K5dO3zyySeVcpmfn4+3334bERERCAsLw6uvvmrZX1XHWrJkCSIjI9GuXTtER0fjl19+qZSHinxVXHbav38/OnXqhM8++wwdO3ZEREQENmzYcNPt3n//fRw4cAAJCQlo164dEhISLH0///wzevbsidDQUEyfPh03Pg9w/fr1eOKJJxAWFoaXXnrJ6v/17zZt2oSuXbsiPDwcycnJVqM7H374IcaNG4cJEybgkUcewZdffokjR45g4MCBCA0NRUREBBISElBWVmbZX8uWLbFixQp069YN4eHhSExMhNlstjpmYmIiwsLCEBUVhT179twyNqI6R4q12olqqmvXrmLfvn1izJgxYv78+UIIIdauXSuGDBkihBAiLS1NBAUFCYPBYNlmyJAhYu3atUIIITZs2CCCg4PF+vXrhdFoFPPnzxedO3cW06ZNE3q9Xvz4448iJCREFBYWCiGEmDhxoggJCRG//fab0Ov1YsaMGWLQoEFCCCGKiopEp06dxPr164XBYBDHjh0THTp0EKdOnbJs+8gjj4gDBw4Ik8kkSktLK53P4MGDRXx8vCgtLRV//vmnCA8PFz///LMl1opj3UxcXJwlB0IIsXLlSjF8+HAhhBDHjh0Tjz76qDh8+LAwGo1i48aNomvXrkKv11vy2LdvX5GRkSFKSkqsclvh77l8+eWXRWxsrMjPzxdlZWVi//79tz3WmTNnRKdOnURmZqZlnxcuXLjp+UycONFyPr/++qsIDg4W//nPf0RZWZnYvXu3aNOmjcjPz7/ptjf+H1cICgoSI0eOFAUFBSI9PV2Eh4eLPXv2CCGE+O6770T37t3F6dOnhcFgEMnJyWLgwIE33fepU6dESEiISElJEXq9Xrz77ruiVatWllx98MEHolWrVuK7774TJpNJlJSUiKNHj4pDhw4Jg8Eg0tLSRK9evcSyZcusYhsyZIjIy8sT6enpomfPnlbfo61atRJffPGFMBqNYtWqVeLxxx8XZrP5pvER1TUcsaB6ady4cVi5ciVyc3PveNvAwEA888wzUKlU6N27N3Q6HcaMGQO1Wo2IiAio1WpcvHjR8v4uXbogLCwMarUab7zxBg4fPgydTofdu3cjICAAzzzzDBwcHNCqVStER0dj27Ztlm27deuG9u3bQ6lUwsnJySoOnU6HgwcPYsKECXByckJwcDAGDBiAr776qlrnERMTg61bt1peb968GTExMQCAL774AgMHDkTbtm2hUqnw1FNPwdHREYcPH7a8f+jQodBqtZZ1X6qSlZWFvXv3Yvr06fD09ISjoyM6dOhw22OpVCqUlZXhzJkzMBgMCAwMRJMmTap1fg4ODhgzZgwcHR3RuXNnuLq64ty5c9XatsLLL78MDw8P+Pv7Izw83DKSsmbNGowcORItWrSAg4MDRo0ahePHj9901GLbtm3o2rUrQkNDoVarMW7cOMv6HxVCQkLQvXt3KJVKODs7o3Xr1ggJCYGDgwMCAwMxcOBApKSkVIpNo9HA398fw4YNsyywBZTPb3n22Wct+czOzsaVK1fu6NyJpMJl06leCgoKQpcuXbBkyRK0aNHijrb19va2fF3xR/XGRcCcnJxQVFRked24cWPL125ubvD09ERWVhbS09Nx5MgRhIaGWvpNJhP69u1reV3Vss5ZWVnw9PSEu7u7pc3f3x+pqanVOo/w8HCUlpbijz/+gLe3N06cOIHu3bsDKL+jY9OmTVi5cqXl/QaDAVlZWdWK7e8yMzPh6ekJT0/PSn1VHatDhw6YNGkSPvzwQ5w+fRoRERGIi4uDn5/fbY+p0Wjg4HD9V5SLi4vVpN3q8PHxsdq+4v81IyMDs2fPRmJioqVf/P/S3AEBAVb7yMrKsvoecHFxqbTM/Y39QPnqru+++y5SU1NRUlICk8mEhx56yOo9N+Y/ICDA6v/mxu9HFxcXALjjcyeSCgsLqrfGjRuHp556CsOHD7e0VUx0LC0ttfzBzs7OvqvjZGZmWr4uKipCQUEBfH19odVqERYWhmXLltVov76+vigoKEBhYaElVp1OV60/ugCgUqnQq1cvbNmyBY0aNUKXLl0s+9FqtRg1ahRGjx59y+3//qm7Ko0bN0ZBQYFlZckb3e5YMTExiImJQWFhIaZOnYp58+Zh7ty51T72vVAR841F4K34+vpajZSUlpYiPz/f6j1/z+W0adPQqlUrvPfee3B3d8d///tfbN++3eo9Op0ODzzwAIDyQsfX17emp0NUp/BSCNVbTZs2Re/evfH5559b2ry8vODn54evvvoKJpMJ69evR1pa2l0dZ8+ePThw4ADKysqwYMECtG3bFlqtFl26dMH58+exadMmGAwGGAwGHDlyBGfOnKnWfrVaLdq1a4f58+dDr9fjxIkTWL9+fbX+2FWIiYnBt99+i82bN6NPnz6W9gEDBmDNmjX4448/IIRAcXExdu/ejcLCwlvuq1GjRrfMla+vLzp16oTp06ejoKAABoPBMrRf1bHOnj2LX375BWVlZVCr1XBycoJSaftfO1XFfjODBg3CkiVLcOrUKQDAtWvX8O233970vdHR0di1axcOHjyIsrIyfPjhh1aTQG+mqKgIbm5ucHNzw5kzZ7B69epK71m6dCkKCgqg0+mwYsUK9O7du9rxE9VlLCyoXhszZkylIeIZM2Zg6dKlCA8Px+nTp9GuXbu7OkafPn2QnJyM8PBwHDt2zPJp293dHUuXLsU333yDyMhIREREYN68eVaz/29n/vz5SE9PR2RkJF577TWMHTsWjz32WLW3b9u2LVxcXJCVlYVOnTpZ2h9++GHMmDEDCQkJCAsLQ8+ePbFx48Yq9zVy5Eh8/PHHCA0NxdKlSyv1JyUlwcHBAU888QQee+wxLF++/LbHKisrw3vvvYfw8HBEREQgNzcX48ePr/b5VdewYcOwfft2hIWFYebMmbd9f48ePTBixAiMHz8ejzzyCPr06YO9e/fe9L0PPPAApkyZgvHjxyMyMhKurq7w8vKCWq2+5f4nTpyILVu24JFHHsGUKVNuWjR069YNTz/9NPr3748uXbpI8hA0ontBIW5XehMRkUVRURHCwsKwfft23HfffTXaR8uWLbFjxw40bdrUxtERSY8jFkREt7Fr1y6UlJSguLgYiYmJCAoKQmBgoNRhEdVJLCyIiG5j586diIyMRGRkJC5cuID58+ff0eRXInvCSyFERERkMxyxICIiIpthYUFEREQ2w8KCiIiIbIaFBREREdkMCwsiIiKyGRYWREREZDP/B6vPEnDiHXGDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=df, x=\"N\", y=\"MIS size\", hue=\"Algorithm\").set(\n",
    "    title=\"Comparison of Maximum Independent Set size solutions from Graph Neural Networks \\n versus Simulated Annealing for d-Regular Graphs (d = 3)\",\n",
    "    ylabel=\"Maximum Independent Set Size\",\n",
    "    xlabel=\"Number of vertices in the graph\",\n",
    ")\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GNNs did not come on top again. This agrees with the claims by Angelini and Ricci-Tersenghi that reports that SA beats the GNN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum Independent Set for d-Regular Graphs (d = 5)\n",
    "\n",
    "The topolgy of the graph could affect the performance for both algorithms. For larger values of $d$, we expect smaller sizes for the MIS which might be harder to find. Hence, we try instances with $d = 5$ like in Schuetz et al.\n",
    "\n",
    "For $d = 5$, we will see that the GNN struggles more to find solutions compared to $d = 3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "d5_graphs = {\n",
    "    i: nx.convert_node_labels_to_integers(nx.random_regular_graph(d=5, n=i, seed=2023))\n",
    "    for i in range(100, 1100, 100)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(columns=[\"N\", \"MIS size\", \"Algorithm\"])\n",
    "gnn_results = []\n",
    "sa_results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0567525b885a4529820b5026ce10cd67",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 100, Anneling found 36.0\n",
      "N = 100, Graph Neural Networks found 30.0\n",
      "N = 200, Anneling found 74.0\n",
      "N = 200, Graph Neural Networks found 58.0\n",
      "N = 300, Anneling found 113.0\n",
      "N = 300, Graph Neural Networks found 89.0\n",
      "N = 400, Anneling found 149.0\n",
      "N = 400, Graph Neural Networks found -0.0\n",
      "N = 500, Anneling found 186.0\n",
      "N = 500, Graph Neural Networks found 153.0\n",
      "N = 600, Anneling found 223.0\n",
      "N = 600, Graph Neural Networks found 189.0\n",
      "N = 700, Anneling found 260.0\n",
      "N = 700, Graph Neural Networks found 218.0\n",
      "N = 800, Anneling found 298.0\n",
      "N = 800, Graph Neural Networks found -0.0\n",
      "N = 900, Anneling found 333.0\n",
      "N = 900, Graph Neural Networks found 274.0\n",
      "N = 1000, Anneling found 368.0\n",
      "N = 1000, Graph Neural Networks found 308.0\n"
     ]
    }
   ],
   "source": [
    "for i, G in tqdm(d5_graphs.items()):\n",
    "\n",
    "    annealing_sol = solve_with_annealing(G, num_reads=2000, is_max_cut=False)\n",
    "    model = annealing_sol[\"model\"]\n",
    "    sa_results.append(-annealing_sol[\"energy\"])\n",
    "\n",
    "    print(f\"N = {i}, Anneling found {sa_results[-1]}\")\n",
    "\n",
    "    embedding_d0 = int(np.sqrt(i))\n",
    "    embedding_d1 = embedding_d0 // 2\n",
    "    learning_rate = 0.005\n",
    "    epochs = 25000\n",
    "    epochs_guess = 100\n",
    "    dropout_rate = 0.05\n",
    "    gnn_sol = solve_with_gnn_mis(\n",
    "        G,\n",
    "        embedding_d0,\n",
    "        embedding_d1,\n",
    "        learning_rate,\n",
    "        epochs,\n",
    "        epochs_guess,\n",
    "        dropout_rate,\n",
    "        seed=2023,\n",
    "        verbose=False,\n",
    "        is_max_cut=False,\n",
    "        shots=500,\n",
    "    )\n",
    "\n",
    "    gnn_results.append(\n",
    "        -model.decode_sample(gnn_sol[\"solution\"], vartype=\"BINARY\").energy\n",
    "    )\n",
    "    print(f\"N = {i}, Graph Neural Networks found {gnn_results[-1]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n, cut_size in zip(range(100, 1100, 100), gnn_results):\n",
    "    df.loc[len(df)] = [n, cut_size, \"Graph Neural Network\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n, cut_size in zip(range(100, 1100, 100), sa_results):\n",
    "    df.loc[len(df)] = [n, cut_size, \"Simulated Annealing\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=df, x=\"N\", y=\"MIS size\", hue=\"Algorithm\").set(\n",
    "    title=\"Comparison of Maximum Independent Set size solutions from Graph Neural Networks \\n versus Simulated Annealing for d-Regular Graphs (d = 5)\",\n",
    "    ylabel=\"Maximum Independent Set size\",\n",
    "    xlabel=\"Number of vertices in the graph\",\n",
    ")\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
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    "As we can see in the plot above, SA consistently outperforms the GNNs. Moreover, for $N = 400$ and $N = 800$, the GNNs were unable to solve the problem after 500 shots. Surprisingly, the GNNs found solutions for larger graphs.\n",
    "\n",
    "Our results reinforce the points raised by Angelini and Ricci-Tersenghi. We elaborate further in the discussion.\n",
    "\n",
    "## Discussion\n",
    "\n",
    "Our results show again that the proposed GNN architecture is beaten by traditional methods like SA. Despite promising, the GNN struggles to solve the MIS problems sometimes. The same pros and cons we discussed in the Max-Cut notebook apply here.\n",
    "\n",
    "We found that the number of shots required to solve a MIS instance was considerably higher compared to the ones reported in the paper (which used only 5 shots). This could happen because of implementation details, but it still ignores the main point that the search landscape for the QUBO is challenging and perhaps the GNN architecture is not ready to navigate the cost landscape.\n",
    "\n",
    "Thus, as of now, Angelini and Ricci-Tersenghi are correct. GNNs find approximate solutions, but they do not beat current solvers. Further work is needed to make GNNs the best option possible.\n",
    "\n",
    "One particular improvement that needs to be made to improve MIS solutions is regarding the $\\mathcal{L}_{QUBO}$ loss function. Many times, the GNN finds the local minima of cost $0$ and gets stuck on it. Can we design a better $\\mathcal{L}_{QUBO}$ that avoids such scenarios? That remains an open question."
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    "## Conclusion\n",
    "\n",
    "Throughout this series of Jupyter notebooks, we implemented and verified the work of Schuetz et al. in [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://arxiv.org/abs/2107.01188). We were able to solve Max-Cut and MIS instances with the GNN.\n",
    "\n",
    "We were also able to benchmark the GNN and reproduce some criticism that targeted the paper by Schuetz et al. There were two other publications criticizing the baselines used by Schuetz et al.  Boettcher focused on the Max-Cut instances. Angelini and Ricci-Tersenghi focused on the MIS instances. Our benchmarks show that Simulated Annealing outperforms the GNN, which supports the work of the critics.\n",
    "\n",
    "GNN have proven useful in supervised learning tasks on graphs. For combinatorial optimization, the answer is less clear. The paper by Schuetz et al. contains clear and innovative ideas, but is undermined by its weak baseline that makes the algorithm appear the state-of-the-art, which is not the case.\n",
    "\n",
    "Hence, we end the notebook with a question: which improvements can be made to make GNN outperform those algorithms? We might need to tweak the type of graph layers, the activation functions, the cost functions, and maybe more to outperform more traditional algorithms."
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