01_GNN_vs_SA_for_Max_Cut.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Graph Neural Networks versus Simulated Annealing for Max-Cut\n",
    "\n",
    "#### Author: Ivan Carvalho (@IvanIsCoding)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/IvanIsCoding/GNN-for-Combinatorial-Optimization/blob/main/01_GNN_vs_SA_for_Max_Cut.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous notebook, we defined the architecture to use Graph Neural Networks to solve Combinatorial Optimization problems.\n",
    "\n",
    "In  this is notebbok, we will benchmark the quality of the solutions from our Graph Neural Networks against solutions obtained via Simulated Annealing (SA). Simulated Annealing is a common technique used to approximate QUBO solutions. We focus on the Max-Cut solutions first.\n",
    "\n",
    "Our benchmark is partly inspired by [Inability of a graph neural network heuristic to outperform greedy algorithms in solving combinatorial optimization problems like Max-Cut\n",
    "](https://arxiv.org/abs/2210.00623) by Boettcher. In his work, Boettcher argues that the GNNs can be outperformed by simple greedy algorithms and argues that Schuetz et al. overlooked trivial baselines when comparing the GNN results. Instead of implementing the greedy algorithm mentioned in Boettcher, I felt it would be more interesting to apply SA. SA is a general technique for QUBOs while the greedy algorithm is tailored for the Max-Cut problem.\n",
    "\n",
    "So let's get started! Firstly, we will install the `gnn_for_co` library we defined thanks to nbdev. That will allow us to reuse all the functions from our initial notebook."
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "Note that this notebook will also export some functions we will use in the third notebook. Don't worry about the cryptic comments too much, they are just nbdev directives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | default_exp train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "from gnn_for_co.core import (\n",
    "    create_train_state,\n",
    "    train_step,\n",
    "    get_classification,\n",
    "    create_Q_matrix,\n",
    "    create_max_cut_model,\n",
    "    create_mis_model,\n",
    ")\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import openjij as oj\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from tqdm.notebook import trange, tqdm\n",
    "\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving a QUBO instance using OpenJij's Simulated Annealing sampler\n",
    "\n",
    "Our baseline will be Simulated Annealing. More specifically, it will be [OpenJij](https://openjij.github.io/OpenJij)'s implementation of simulated annealing, the [SASampler](https://openjij.github.io/OpenJij/reference/openjij/sampler/sa_sampler/index.html).\n",
    "\n",
    "A very brief description of Simulated Annealing is that is a stochastic optimization process. SA generates candidate solutions $x_{1} \\rightarrow x_{2} \\ldots \\rightarrow x_{k}$ throughout its process. At each step, the algorithm uses randomness to generate a new $x^{\\prime}$. After, it either accepts the new value, $x_{i} = x^{\\prime}$, or rejects it, $x_{i} = x_{i-1}$, using the Metropolis-Hastings algorithm. The probabilities of the Metropolis-Hastings depend on the temperature $T_{i}$, which is annealed throughout the algorithm. Hence the name Simulated Annealing.\n",
    "\n",
    "The interface we will be using for this sampler shared among other samplers. It works by feeding a QUBO dict to the sampler and then performing a number of reads. Some other samplers that you might want to try to use are:\n",
    "* [D-wave's Neal Sampler](https://docs.ocean.dwavesys.com/projects/neal/en/latest/reference/sampler.html) - another implementation of simulated annealing\n",
    "* [D-Wave's Ocean Sampler](https://docs.ocean.dwavesys.com/en/stable/docs_system/reference/samplers.html#dwave.system.samplers.DWaveSampler) - runs on special quantum annealing hardware by D-Wave tailored to solve QUBO/Ising problems\n",
    "* [OpenJij's SQASampler](https://openjij.github.io/OpenJij/reference/openjij/sampler/sqa_sampler/index.html) - implementation of simulated quantum annealing also by OpenJij\n",
    "\n",
    "To demonstrate SA in practice, we reuse the same random graph from the previous notebook. We visualize the graph, then instantiate the SASampler. We feed the QUBO dictionary to the sample and retrieve the best solution the sampler found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.convert_node_labels_to_integers(\n",
    "    nx.fast_gnp_random_graph(n=100, p=0.05, seed=2023)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, pos=nx.spring_layout(G, seed=2023), with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = oj.SASampler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = create_max_cut_model(G)\n",
    "qubo_dict, offset = model.to_qubo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "response = sampler.sample_qubo(qubo_dict, num_reads=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-213.0"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "response.first.energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_color = [\"lightblue\" for i in range(G.number_of_nodes())]\n",
    "for x, val in response.first.sample.items():\n",
    "    if val == 1:\n",
    "        node_color[int(x[2:-1])] = \"yellow\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, pos=nx.spring_layout(G, seed=2023), node_color=node_color, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our SASampler seems to be working and it found a Max-Cut of 213 on the graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training GNNs and Sampling with Simulated Annealing\n",
    "\n",
    "\n",
    "Now that we know how to obtain solution to QUBO problems using both GNNs and SA, we write some code to automate the process for us.\n",
    "\n",
    "`solve_with_gnn` creates a Graph Neural Network and trains it using JAX + Flax. It is possible that sometimes the GNN will find clearly sub-optimal solutons (e.g. Max-Cut of zero). Hence, we add an option to re-run the GNN with a different seed up a couple times. In the paper by Schuetz et al., the authors report that 5 shots were enough.\n",
    "\n",
    "`solve_with_annealing` calls the SASampler from OpenJij. It is a short functiod and we keep the default parameters from OpenJij."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def inner_solve_with_gnn(\n",
    "    G,\n",
    "    embedding_size,\n",
    "    hidden_size,\n",
    "    learning_rate,\n",
    "    epochs,\n",
    "    dropout_rate,\n",
    "    seed=2023,\n",
    "    verbose=False,\n",
    "    is_max_cut=True,\n",
    "):\n",
    "    A = jnp.array(nx.to_numpy_array(G))\n",
    "    Q = create_Q_matrix(G, is_max_cut=is_max_cut)\n",
    "\n",
    "    rng = jax.random.PRNGKey(seed)\n",
    "    rng, init_rng = jax.random.split(rng)\n",
    "    rng, embed_rng = jax.random.split(rng)\n",
    "    state = create_train_state(\n",
    "        G.number_of_nodes(),\n",
    "        embedding_size,\n",
    "        hidden_size,\n",
    "        init_rng,\n",
    "        learning_rate,\n",
    "        dropout_frac=0.01,\n",
    "    )\n",
    "    node_embeddings = jax.random.uniform(embed_rng, [G.number_of_nodes(), embedding_size])\n",
    "\n",
    "    for epoch in trange(1, epochs + 1, disable=not verbose):\n",
    "        rng, dropout_rng = jax.random.split(rng)\n",
    "        state, metrics = train_step(\n",
    "            state=state,\n",
    "            node_embeddings=node_embeddings,\n",
    "            adj_matrix=A,\n",
    "            q_matrix=Q,\n",
    "            dropout_rng=dropout_rng,\n",
    "        )\n",
    "\n",
    "        if epoch % 25 == 0 and verbose:\n",
    "            print(\"train epoch: %d, cost: %.2f\" % (epoch, metrics[\"energy\"]))\n",
    "\n",
    "    classification = np.array(\n",
    "        get_classification(state.apply_fn, state.params, node_embeddings, A)\n",
    "    )\n",
    "    probs = state.apply_fn({\"params\": state.params}, node_embeddings, A)\n",
    "    solution = {f\"X[{i}]\": classification[i] for i in range(G.number_of_nodes())}\n",
    "    last_energy = metrics[\"energy\"]\n",
    "\n",
    "    return {\n",
    "        \"classification\": classification,\n",
    "        \"probs\": probs,\n",
    "        \"energy\": last_energy,\n",
    "        \"solution\": solution,\n",
    "    }\n",
    "\n",
    "\n",
    "def solve_with_gnn(\n",
    "    G,\n",
    "    embedding_size,\n",
    "    hidden_size,\n",
    "    learning_rate,\n",
    "    epochs,\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,\n",
    "            dropout_rate,\n",
    "            seed + (k + 1) ** 3,\n",
    "            verbose,\n",
    "            is_max_cut,\n",
    "        )\n",
    "\n",
    "        if solution[\"energy\"] <= lower_bound:\n",
    "            break\n",
    "\n",
    "    return solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def solve_with_annealing(G, num_reads, is_max_cut=True):\n",
    "    sampler = oj.SASampler()\n",
    "\n",
    "    if is_max_cut:\n",
    "        model = create_max_cut_model(G)\n",
    "    else:\n",
    "        model = create_mis_model(G)\n",
    "\n",
    "    qubo_dict, offset = model.to_qubo()\n",
    "\n",
    "    response = sampler.sample_qubo(qubo_dict, num_reads=num_reads)\n",
    "\n",
    "    return {\n",
    "        \"sample\": response.first.sample,\n",
    "        \"energy\": response.first.energy,\n",
    "        \"model\": model,\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Max-Cut for d-Regular Graphs (d = 3)\n",
    "\n",
    "With the solvers in hands, it is time to pitch GNNs against SA. We compare them on a benchmark of d-Regular Graps with d = 3. This was one of the types of graph used by Schuetz et al. on their original paper. d-Regular graphs are graphs in which every vertex has the same number of neighbors. Hence, we generate random instances where every vertex has 3 neighbors.\n",
    "\n",
    "For all instances, Schuetz et al. managed to beat their baseline. Let's check if this is what happens on this case too. We will run the code for graphs ranging from 100 to 2000 nodes and plot the Max-Cut value in a graph."
   ]
  },
  {
   "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, 2100, 100)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(columns=[\"N\", \"Max-Cut 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": "d5b719d2dcc1486e9dbdf0008e5a8312",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/20 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 100, Anneling found 138.0\n",
      "N = 100, Graph Neural Networks found 122.0\n",
      "N = 200, Anneling found 275.0\n",
      "N = 200, Graph Neural Networks found 241.0\n",
      "N = 300, Anneling found 413.0\n",
      "N = 300, Graph Neural Networks found 360.0\n",
      "N = 400, Anneling found 551.0\n",
      "N = 400, Graph Neural Networks found 490.0\n",
      "N = 500, Anneling found 689.0\n",
      "N = 500, Graph Neural Networks found 602.0\n",
      "N = 600, Anneling found 828.0\n",
      "N = 600, Graph Neural Networks found 727.0\n",
      "N = 700, Anneling found 965.0\n",
      "N = 700, Graph Neural Networks found 844.0\n",
      "N = 800, Anneling found 1103.0\n",
      "N = 800, Graph Neural Networks found 961.0\n",
      "N = 900, Anneling found 1242.0\n",
      "N = 900, Graph Neural Networks found 1085.0\n",
      "N = 1000, Anneling found 1381.0\n",
      "N = 1000, Graph Neural Networks found 1190.0\n",
      "N = 1100, Anneling found 1518.0\n",
      "N = 1100, Graph Neural Networks found 1345.0\n",
      "N = 1200, Anneling found 1657.0\n",
      "N = 1200, Graph Neural Networks found 1469.0\n",
      "N = 1300, Anneling found 1791.0\n",
      "N = 1300, Graph Neural Networks found 1567.0\n",
      "N = 1400, Anneling found 1935.0\n",
      "N = 1400, Graph Neural Networks found 1675.0\n",
      "N = 1500, Anneling found 2069.0\n",
      "N = 1500, Graph Neural Networks found 1808.0\n",
      "N = 1600, Anneling found 2207.0\n",
      "N = 1600, Graph Neural Networks found 1935.0\n",
      "N = 1700, Anneling found 2346.0\n",
      "N = 1700, Graph Neural Networks found 2063.0\n",
      "N = 1800, Anneling found 2488.0\n",
      "N = 1800, Graph Neural Networks found 2179.0\n",
      "N = 1900, Anneling found 2618.0\n",
      "N = 1900, Graph Neural Networks found 2298.0\n",
      "N = 2000, Anneling found 2761.0\n",
      "N = 2000, Graph Neural Networks found 2455.0\n"
     ]
    }
   ],
   "source": [
    "for i, G in tqdm(d3_graphs.items()):\n",
    "\n",
    "    annealing_sol = solve_with_annealing(G, num_reads=2000)\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 = 10000\n",
    "    if i < 1400:\n",
    "        dropout_rate = 0.01\n",
    "    else:\n",
    "        dropout_rate = 0.05\n",
    "    gnn_sol = solve_with_gnn(\n",
    "        G,\n",
    "        embedding_d0,\n",
    "        embedding_d1,\n",
    "        learning_rate,\n",
    "        epochs,\n",
    "        dropout_rate,\n",
    "        seed=2023,\n",
    "        verbose=False,\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, 2100, 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, 2100, 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=\"Max-Cut Size\", hue=\"Algorithm\").set(\n",
    "    title=\"Comparison of Max-Cut size solutions from Graph Neural Networks \\n versus Simulated Annealing for d-Regular Graphs (d = 3)\",\n",
    "    ylabel=\"Max-Cut Size\",\n",
    "    xlabel=\"Number of vertices in the graph\",\n",
    ")\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see above, GNNs did NOT come on top! This shows us that there are potential improvements that can be made to the GNN to improve the quality of its solution.\n",
    "\n",
    "The results are not necessarily bad. It is still neat that a GNN can approximat the solution with gaps between 10 to 20% of SA. Nevertheless, GNN might not be the silver bullet promised in the paper. In this point, our results agree with Boettcher that the baseline used by Schuetz et al. was weak."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Max-Cut for d-Regular Graphs (d = 5)\n",
    "\n",
    "We also benchmark GNN vs SA on d-Regular graphs for d = 5. The comparison for d=5 is also present in the paper by Schuetz et al. The authors also claim that GNN beats their baseline on this type of graph. \n",
    "\n",
    "The topolgy of the graph could affect the performance for both algorithms. Thus it is worthwhile to compare on this type of graph too and see the gaps between the algorithms."
   ]
  },
  {
   "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, 2100, 100)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(columns=[\"N\", \"Max-Cut 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": "fee88b8b10b347339fbae03c4743f743",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/20 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 100, Anneling found 205.0\n",
      "N = 100, Graph Neural Networks found 189.0\n",
      "N = 200, Anneling found 411.0\n",
      "N = 200, Graph Neural Networks found 371.0\n",
      "N = 300, Anneling found 623.0\n",
      "N = 300, Graph Neural Networks found 562.0\n",
      "N = 400, Anneling found 829.0\n",
      "N = 400, Graph Neural Networks found 739.0\n",
      "N = 500, Anneling found 1039.0\n",
      "N = 500, Graph Neural Networks found 904.0\n",
      "N = 600, Anneling found 1244.0\n",
      "N = 600, Graph Neural Networks found 1104.0\n",
      "N = 700, Anneling found 1455.0\n",
      "N = 700, Graph Neural Networks found 1269.0\n",
      "N = 800, Anneling found 1661.0\n",
      "N = 800, Graph Neural Networks found 1471.0\n",
      "N = 900, Anneling found 1871.0\n",
      "N = 900, Graph Neural Networks found 1659.0\n",
      "N = 1000, Anneling found 2081.0\n",
      "N = 1000, Graph Neural Networks found 1833.0\n",
      "N = 1100, Anneling found 2285.0\n",
      "N = 1100, Graph Neural Networks found 2027.0\n",
      "N = 1200, Anneling found 2492.0\n",
      "N = 1200, Graph Neural Networks found 2209.0\n",
      "N = 1300, Anneling found 2709.0\n",
      "N = 1300, Graph Neural Networks found 2371.0\n",
      "N = 1400, Anneling found 2915.0\n",
      "N = 1400, Graph Neural Networks found 2578.0\n",
      "N = 1500, Anneling found 3125.0\n",
      "N = 1500, Graph Neural Networks found 2775.0\n",
      "N = 1600, Anneling found 3327.0\n",
      "N = 1600, Graph Neural Networks found 2907.0\n",
      "N = 1700, Anneling found 3536.0\n",
      "N = 1700, Graph Neural Networks found 3102.0\n",
      "N = 1800, Anneling found 3746.0\n",
      "N = 1800, Graph Neural Networks found 3255.0\n",
      "N = 1900, Anneling found 3956.0\n",
      "N = 1900, Graph Neural Networks found 3467.0\n",
      "N = 2000, Anneling found 4169.0\n",
      "N = 2000, Graph Neural Networks found 3628.0\n"
     ]
    }
   ],
   "source": [
    "for i, G in tqdm(d5_graphs.items()):\n",
    "\n",
    "    annealing_sol = solve_with_annealing(G, num_reads=2000)\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 = 10000\n",
    "    if i < 1400:\n",
    "        dropout_rate = 0.01\n",
    "    else:\n",
    "        dropout_rate = 0.05\n",
    "    gnn_sol = solve_with_gnn(\n",
    "        G,\n",
    "        embedding_d0,\n",
    "        embedding_d1,\n",
    "        learning_rate,\n",
    "        epochs,\n",
    "        dropout_rate,\n",
    "        seed=2023,\n",
    "        verbose=False,\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, 2100, 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, 2100, 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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VHDx4MNM05cuXJygoSLoODg7OlaZOS8q3I0j+FR8aGkr58uV5+vQpkyZNYvLkyZw9e5bAwMB0v2oVCkWWeQ8YMICtW7cSEBDA33//zapVq7Czs8PU1DRdHSpUqJBr2cuXL09ISIi0jp2XvLp27cratWvp2rVrurg1a9bw4MEDNm/ezIULF6R1dPH/ziL0ej1Tpkyha9eubNy4UfoWVKlSJS5evCj9ATRp0oSTJ09mOUBYWFgQFxcnXace1LJ75gANGzZk2bJlnD59mtatWxt9B0vN7t272b17N4sWLcLU1BRIHrDNzc3ZvXs3gYGBBAYGcv78+UwVZLly5Zg5cyYnT55k+vTpTJ8+nYcPH6brp5B521hYWBh908vNYJfX/tSsWTPWrl3LyZMnqV69OpMnT85x2WnbIr/fzRQsLS1p1KhRjr4npZVp/vz5KBQK/P39uXDhAt9//73Ub1PLmUJQUFC+yDx48GDOnj3LtWvXpDAHBweqVKki9avAwEAuXrzIypUrgZz1g9T1y8kYlRPUajWfffYZP/zwg9GzcXBwYPjw4UbyXr58mc6dO2eal6urK/v27SMxMZEKFSrg6urK9u3befHiBY6OjgDS+JrCq1eviIqKMuqzGb3nP/zwA4cOHUq3uzujcTanFJpyK1WqFKNHj2bGjBkcPHiQuLg4EhMTOXbsGHPnzgWgU6dOLFu2jIiICCIiIliyZAnvvffea5d5/fp19u/fT1JSEuvWrUOtVtOoUSPi4uJQKBTY29sDsGXLlnTLDFlx5coVLl++TGJiIhYWFqjVapRKJSqVivbt27NgwQJiYmJ4+vQpa9euTbcUmBMaNmyIubk5q1atIjExkbNnz3L48GE6duyY67w6duzImjVr6NChQ7q42NhYzMzMKF26NFFRUfz4449G8b6+vigUCmbPns3gwYMZP3680a/p1HTp0oWKFSsyatQo7t27h8FgIDIyEl9fX2mjQ506ddi1axd6vZ7jx48bLSOVKVOGqKgooqOjM8w/ISGBnTt3Eh0djampKVZWVkYz2xRu3LjBt99+y5IlS6Q2huTZe8+ePZk9ezbh4eFA8sfxEydOZFjenj17pB9INjY2KBQKlEolLVq04O+//8bf35+kpCQCAgK4e/cuLVu2TJeHo6Mj586dIygoiOjoaJYvX24UX7Zs2UzPtOWlP4WFhXHw4EFevXqFWq3G0tIyw2eVU/L73UzN2LFj2bJlCytWrJDaJSQkxGgpKyNiY2OxtLSkVKlShIaGZjjwbdy4kZCQEKKiovD19X2t9yctpUuX5uOPP5Y2M0Hy+2plZcWKFSuIj49Hr9dz+/ZtaRnR0dGRY8eOERUVxfPnz9MN4mnJ6xiVmi5duqDT6Th58qQU1rNnTzZt2sTly5cRQvDq1SuOHj0qzYwy6pdubm78/PPP0vK8u7s7P//8My4uLtKsvXPnzmzdupWbN2+SkJDA/PnzadiwIVWqVMlSxvLly+Pn58f69evZuHEjkPk4m1MK9SjAoEGDmDBhAkuXLsXDw4OWLVuyYcMGWrduDcCnn35K/fr18fHxwcfHh3r16vHpp5++dnne3t4EBATg6urKjh07WLx4MaamptSsWZNBgwbRp08fmjRpwu3bt3F2ds5xvilLXW5ubrRq1QpbW1sGDx4MwOTJk7GwsKB169b07duXzp0706NHj1zLrlar8fX15fjx4zRu3Jjp06czd+5catSokeu8zM3NadKkSbpvhwAfffQROp2Oxo0b07t3b5o1aybFXbt2DT8/P+bMmYNKpZLOzaxYsSJTmf38/KhevTqDBg3CxcWFnj17EhkZKa2jT5w4kSNHjqDVavH395faHqBGjRp06tSJ1q1bo9VqM1zm27FjB15eXjg7O7Np0ya+//77dGkOHTrEy5cv6du3r7RsOmTIECB5qfGtt96iV69eODs7M3DgwEy/s1y9epWePXui0WgYMWIEEydOpGrVqtjZ2eHr68vatWtxd3dn1apV+Pr6GinSFJo2bUrHjh3x8fGhe/futGrVyih+wIAB7Nu3D1dXV2bOnJnu/tftTwaDAT8/P5o1a4abmxvnzp1j2rRp2d6XGfn9bqZGq9Wybt06zp07R7t27aTlYnd3d/r165fpfZ999hk3btxAq9UydOjQDHffde7cmUGDBtG6dWuqVavGiBEj8kXmAQMGGA20KpUKX19fbt26hbe3N40bN2bSpEmSsujSpQt16tTBy8uLQYMGZatk8zpGpUalUjF69GiioqKksAYNGvDtt98yY8YMXF1dadu2LVu3bpXihw4dyrJly9BqtZISd3V1JTY2VlqCdHFxIT4+XlJ2kLx68/nnnzNq1Cg8PT15/Phxljs2U1OpUiX8/PxYuXIlv/32W5bjbE5QiLTz+BLC4sWLefjwIfPmzStqUWRkZIoALy8vZs6cSZMmTYpaFJkiQDa/JSMjIyNT4pCVm4yMjIxMiaPELkvKyMjIyLy5yDM3GRkZGZkSh6zc/sUMGTKEbdu2FUjeBeWGIiPy6iKmKEhtIxIKti02btxIkyZN0Gg0uT7EmxPS2j0sLqS1y/lvJD9d09y9e5fu3bunO8uXQmG3Y0JCAu3bt8+Rx4+iQFZuxRxfX1+8vLzQaDQ0b97c6NDyqlWr6NatWxFKl36QLyi2bt1K7dq1c2XOqDApqLZITEzku+++Y82aNVy8eFGyEFOYeHl50bBhQzQaDU2bNmXChAkZWhv5N3Dq1Cn69++PRqPB3d2dLl26sGLFinQGlYsjP/zwA4MHD86RsYP8YuvWrTg6OhpZIzp79iyQfPSnR48emR4NKmpk5faaFIbLjW3btrFjxw78/Py4ePEiW7ZswcPDo8DLLY5s27YNW1vbTD0SlFTCw8PR6XTUrFkz1/cKIYws3OQFX19fLl68yPbt27lx40axHdBSyMjQwJ49exg9ejTvvfceR44c4ezZsyxYsIDQ0FAjSyapKS7urp49e8bZs2eNzoUWFk5OTkbWiFI8NQC89957bNu2TfIQUZx4o5Tb1KlTmTNnjlHYiBEjWLt2LZC1y4oUFzpjx47F2dmZbdu2ceXKFbp3746zszNNmjThv//9L5Cx083Uzv8yuy8tV69exdPTk2rVqgHJ5qB69+4txadezkvtEkSr1eLt7c2FCxfYunUrLVq0wMPDw2jZLO1SYFbLJ0ePHqVr1644OzvTokULI4eHKYdsXV1d0Wg0kimr33//nQ4dOuDq6srgwYONTPKcOnWK9u3b4+LiwowZMzJdZknh6dOnnDt3jhkzZnDy5Ekjk10pzzoz1yUTJkxg+vTpDB06FI1GQ8+ePY1clty7d4+PP/4YNzc32rVrZzQzzKreaUnbFlm5onn8+DEffvghGo2GgQMHMn369AyX3x48eED79u2l5ztgwAAga3c7/fv3Z8GCBfTp04dGjRplaP3kxo0bdOvWDY1Gw5gxY3I1aylXrhyenp7cvHlTCrt06RJ9+vRBq9Xi4+Mj/bLPrq7ZvSdpGT16NE2bNsXFxYUPP/zQyGLHhAkTmDp1Kp988glOTk5GMkCyov/uu+8YOXIkvXr1wtbWFkAyS5bi4zCz97x3795otVo8PT2ZMWOG0WBeu3Zt1q9fj7e3N+7u7syZMyfdj4q8uCWCZMeodevWNbL3mZd2zC8qVqyIjY1NpgaXi5Qc+w8oAfz555+iefPmkouZqKgo0aBBA8mtRFYuK1Jc6Bw4cEDo9XoRFxcnevXqJbZt2yaEECImJkZcvHhRCJGx+5XULiQyuy8t27dvF66urmLlypXiypUrIikpySg+tbuUFJcgv//+u0hKShLz588XLVq0ENOmTRM6nU6cOHFCODk5iZiYmHT3ptyf2oVGarcrf/zxh7h165bQ6/Xi5s2bwsPDQxw4cEAIkd6FixBCHDhwQLRu3VrcvXtXJCYmiiVLlojevXsLIYQIDw8XTk5OkiuitWvXCkdHx3RuX1Lz448/ih49egghhOjcubNYvXq1FJed65Lx48cLNzc3cfnyZZGYmCi++OILMWbMGCFEsruV5s2bi99//10kJiaK69evCzc3N3Hnzp1c1zttW2Tl2qhXr17iu+++EzqdTpw7d05oNJpM3RelLScn7nZatGghbt++LRITEyUXTynodDrRsmVLsXbtWpGQkCD27Nkj6tata+SOJS2p+25wcLDo3Lmz+Pbbb4UQQoSEhAg3Nzdx9OhRodfrxcmTJ4Wbm5sIDw/Ptq7ZvSdp3QX99ttvIjo6Wuh0OjFz5kzh4+MjxY0fP144OzuLwMBAyUVRau7evStq1aolHj9+nGk9U8pM+55fvXpVXLx4USQmJorHjx+L9u3bi7Vr10r31KpVS/Tr109ERkaKp0+fFohbou+++05MmzZNus5tO547d064uLhk+pfiziktW7ZsEY0aNRJubm6ibdu24scff0zntmzYsGFi3bp1WT7XouCNmrlptVoUCgWBgYEA7Nu3DycnJypUqJAjlxVOTk60bt0apVKJubk5JiYmPHr0iIiICKysrHBycsqRHDm9r0uXLkyaNImTJ0/Sv39/mjRpkuVyUJUqVejRowcqlYqOHTsSHBzMyJEjUavVeHp6olarM3W0mBXu7u7Url0bpVJJnTp16NSpE3/++Wem6Tdt2sTQoUOpUaMGJiYmDB8+nJs3b/L06VOOHz/Ou+++K7ki+uijj4ws22fEjh07JIOunTt3Trc0mZ3rktatW9OwYUNMTEzw8fGRZh1Hjx6lcuXK9OjRAxMTE+rWrUu7du3Yu3fva9U7NZm5ogkKCuLq1auSOxmtVouXl1eO8kyROTt3O926dePdd9/FxMREMhqdQoqtvo8++ghTU1Pat29v5Lw2M0aOHIlGo6FFixbY29szevRoILltmjdvTosWLVAqlTRt2pT69etz7NixPNc1Le+//z7W1tao1WpGjRrFrVu3jOyQent74+LiglKpNJrhANJGnNQumf7zn/+g1Wpp1KiRUZ9K+57Xr18fJycnTExMqFKlCr17907nWueTTz7B1taWSpUqMWDAAHbt2iXF5YdboujoaKysrKTr3LajVqs1MpKc9i+1Ca3UuLq64u/vz5kzZ1i0aBG7d+82sqkJyZb/UzuJLS68UcpNoVDQsWNHqeP5+/tLxl9z4rIircuNWbNm8ffff9OhQwd69OiRY39eubnPx8cHPz8/yTbgokWLMjX0m9rFSIodydSKIzO3I9lx+fJl+vfvT+PGjXFxcWHTpk1Z7toLCgqSlke1Wi1ubm4IIQgNDZVc+aSgUCgydIGRwvnz53ny5AmdOnUCkpXb7du3jZbFsnNdkvoZmJubS3FPnz7lypUrRm3u7+8vLXvmtt6pycwVzbNnz7CxsZHCIGMXIJmRE3c7WeX37NkzKlSoYLQpIXV+Q4YMkTYOpF4iW7JkCRcvXuSnn37i/v370nMICgpi7969Rs/w/PnzPH/+PM91TY1er2fevHm0bt0aZ2dnSUmmbo+s8k7ZiJPapUuKJ/S6desaLSOmfc8fPHjAsGHDaNq0Kc7OzixYsCBL1zqVK1c2Kic/3BKVLl3a6N3Nrh3zi6pVq1K1alWUSiW1a9dm5MiR7Nu3zyhNbGwspUuXzvey80rmnkNLKCmGVIcOHcqVK1dYsmQJ8I/Liv3792d6b9pdSm+//Tbz58/HYDCwf/9+Ro8ezdmzZ9O5t9Dr9UbbZTO7z9LSMtOyTU1N6dChAytXruTOnTtGBo5fh7SuZ7JyxfLll1/Sr18/Vq1ahZmZGbNmzZJe7ox2bqW408jIev3Dhw+NXBEJITL9mA/JPq2EEOnc9Wzbtk1ys/G6ODg44OrqKn1zTUtW9X5dypUrx4sXL4iLi5MGuqzqn5bM3O2k7g9Z7aYrV64coaGhCCGkdEFBQVStWhUgW5cibm5udO/enTlz5rB06VIcHBzo0qVLhkafnz59mmVds3tPUuPv78+hQ4dYu3YtVapUITo6GldX12y/16bwzjvvUKFCBQ4cOMCgQYOyTJv2+U2bNo26devyv//9D2tra/z8/NIN8MHBwdKsKzeudZo1a0azZs2Ij49n4cKFTJ48WbKKn5ratWsbzS6za8e0BAYGSobPM2LlytzEG3sAACAASURBVJWZzt5So1Ao0j3z+/fvZ/tMi4I3auYGULduXezs7Jg0aRKenp7SL47sXFZkxI4dO4iIiECpVEr5KJVK3nnnHXQ6HUePHiUxMZFly5YZfYDO7L60bN26VXJDYTAYOHbsGHfv3pUs7OcFR0dHDhw4QFxcHA8fPpQccWZEbGwsNjY2mJmZceXKFaMlF3t7e5RKpdHGhT59+rBixQrpg390dDR79uwBoEWLFty5c0dyRbR+/fpMFatOp2PPnj3MmDGD7du3S3+TJ09m165ded7J1rJlS/7++2+2b99OYmIiiYmJXLlyRfr1nFW9X5fKlStTv359Fi9eTEJCAhcvXsyVB+/cuNvJiJTltfXr15OYmMj+/fu5evVqrurw0Ucfcfr0aW7duoWPjw9HjhzhxIkT6PV6dDodZ8+eJSQkJNu6ZveepCY2Nha1Wo2dnR1xcXHMnz8/VzIrlUomTJjAjz/+yObNm3nx4gVCCP7++2/JzU5mxMbGYmVlhZWVFffu3eOXX35Jl2b16tW8ePGC4OBg1q9fnyPXOrlxS9S0aVNu3LghbRrJbTtqtVqjHY9p/zJTbMeOHZPez3v37rF06VK8vb2l+NDQUF68eJHjTzKFyRun3CB59nb69Gkjx3zZuazIiBMnTtCpUyc0Gg2zZs1iwYIFmJubU6pUKaZOncqkSZNo3rw5FhYWRksdmd2XFmtra3x9fWnVqhVarZZ58+Yxbdq0HP3Cyo6UtfomTZowfvz4LH1zTZ06lUWLFqHRaFiyZImRXzgLCwuGDx/OBx98gFar5dKlS7Rp04YhQ4bwxRdf4OzsTOfOnTl+/DiQrAx/+OEH/ve//+Hu7s7Dhw8zdeVx8OBBzM3N6dq1K+XKlZP+evTogV6vz3R5NqdYW1uzevVqAgICaNasGZ6ensybN08aYLOqd16YN28ely5dwt3dnYULF9KxY0fUanWO7s2Nu52MUKvVLF68mG3btuHm5kZAQABt2rTJlfz29vZ06dKFJUuW4ODgwNKlS1m+fDkeHh60aNGC1atXS8t8WdU1u/ckNV27dqVSpUo0a9aMTp06vdZg2rFjRxYuXMjOnTtp2bIljRs3ZsyYMfTq1UvalZoR48ePZ9euXTg7OzN58uQMFZe3tzfdu3ena9eutGzZkvfffz9beXLjlqhs2bK4u7tz6NAhIH/aMSf88ccf+Pj44OTkxNChQ2nTpg3Dhg2T4v39/enatWuO+29hItuWlJEpYsaMGUP16tWlTRolmZJY19q1a7N//37eeuutAi3n7t27jB8/nt9//71QD3JnRkJCAj4+PmzYsMHoe39x4Y2cucnIFCVXrlzh0aNHGAwGjh8/zqFDh4rkcG5h8CbVtaCpWbMmW7ZsKRaKDZJnj3v37i2Wig3ewA0lMjJFTVhYGKNGjSIqKoqKFStKGxZKIm9SXWWKF/KypIyMjIxMiUNelpSRkZGRKXHIyk1GRkZGpsQhKzcZGRkZmRLHG72hJDIyFoOh+H1yLFPGmvDwzM/XFTWyfHlDli9vyPLljbzIp1QqsLOzyj5hMeCNVm4GgyiWyg0otnKlIMuXN2T58oYsX94o7vLlB/KypIyMjIxMiUNWbjIyMjIyJY43elkyLUIIIiOfk5AQDxTdtP3ZM2U6T77FCVm+vJG1fArUanPs7MoVG0sUMjL/RmTlloqYmBcoFAoqVKiCQlF0k1oTEyVJScV3cJblyxtZySeEgaioMGJiXlCqlG0hSyZT0lGLOBKj4lApzNCXcF/VsnJLRVxcDPb2FYpUscm82SgUSkqVsiMiIlRWbjL5hlIhMA2/TdTBNYS/eI6VY1Ms3bsTb2pX1KIVGLJyS4XBoEelkh+JTNGiUplgMOiLWgyZEoQ6NoTnW+aASF4xiL1xAiEMmDUfTFIJncGVzFrlAfk7h0xRI/dBmfxGHxUkKbYUXt06g0niyyKSqOCRldsbzKxZ01ixYmmB5L1//x7+85+RmcZfuBBIt27ZeyuWkZHJOwqz9AevVda2CFXxczKaX8jK7Q3hs8+G0r59K8nLdEHTtm0HFixYIl17emp58uRxoZQtIyOTBtuqmFWrnypAgZ33IBKUlkUmUkEjf2B6AwgODuLKlUtYWVlz8uRxvLwK1llkUlISJiZy15KRKS4kqKywbjMc68hHKBPjoFQFEqwrUZIdnskj0BvA3r27qVevPnXr1mfv3l2ZKrcNG9axefNGQMGQIcOZM2cmmzZto0qVqsTExLBgwVzOnj2Nubk5nTt3ZcCAQSiVSgIC/PH334ajYz327g2ga9ceVKlSFX//7SxbtpqRIz8BYODAD1AoFEyYMBk7O3sAfvnlZzZsWIdKpWTo0JF06uQDJC+ZmpmZ/79ivkjNmu8yc+Zcfv55HXv27MLe3p5p02ZRq1adQnmGMjL/dhJU1lC2LuXKleL58+iiFqfAKfRlyR9//JHatWtz+/ZtAC5duoSPjw/t2rVj0KBBhIeHS2lfN07GmL17d9OmTQfatOnA2bNniIhI/6z++OM0v/66kQULlvLrr9u5ePG8UfyCBXOJjY1h8+YdLF26ir17AwgI2CnF37hxnUqVKrNz5z4++miQ0b1LlqwEwM/vFw4cOIG3d1sAIiLCiY2NYfv2PUyYMJn58+fw8uU/H7iPHDnAJ5+MYNeug5iaqhk+fBC1atVm9+6DtGzpzeLFC/LtGcnIyJQsClW5Xb9+nUuXLlG5cmUADAYD48aNY8qUKezbtw+tVsu8efPyFCdjzOXLlwgJCcbLqw116jhSuXIVDhzYmy7d4cMH6NjxPapXr4G5uTmDBg2V4vR6PYcO7WfYsM+wtLSiUqVK9OnzIXv3BkhpypQpy/vv98HExAQzM/McyaZSmTBw4BBMTEzw8PDEwsKSR48eSvHNm7eiTh1HzMzMaN68JWq1mg4dOqNSqfD2bsudO3/l4cnIyMiUZApNuSUkJDBjxgymTZsmhV27dg0zMzO0Wi0Affr0Ye/evXmKkzFm795duLk1xtY2+UBwmzbt2bNnd7p0YWFhlC9fQbpO/f+LF1EkJSVRsaKDFFaxogNhYc+l6woV/kmfU2xsbIy+zZmbmxMX90q6Tlm6BDAzM09zbUZcXFyuy5SRkXkzKLRvbj/88AM+Pj5UqVJFCgsODqZSpUrStb29PQaDgaioqNeOSxnEZUCni+fw4QMYDAZ8fNoByT8yYmKiuXPntlHasmXL8vz5M+n62bNQ6X8bG1tMTEwICQnmnXeqAxAaGkLZsuVS5SCfzZKRKUjUhlfw4ilC9wqVbUV0FuURQn7vMqNQlNvFixe5du0aY8eOLYzickyZMtZG18+eKTExKR6nI/JDjsOHj6NSqdiwYTOmpqZS+MSJ49m/PwCFQoFSqcDEREnr1m2ZNWs6HTt2wsHBgfXrVwOgUikwMzPF27sNq1YtY8qUGTx//oLNmzfSt29/TEyUKJUKFAqFkcxpw+ztyxAaGsTbb7/1//kqM6ynSpXcBqllyyg/lUqR5XMqLu2YGdnJp1QqKVeuVCFJk56iLDsnvGnyJUVHEhawmld3//9buFJFxd4Tsaze6LXyK+7PLz8oFOV27tw57t27h7e3NwAhISEMHjyY/v37ExQUJKWLiIhAqVRia2uLg4PDa8XlhvDwGCOnfQaDoVgY3M0vw7+7dvnTocN7lC1rvGTYrVsvfvhhHlqtGwaDICnJgJubB++/35uRI4ehUCgYOHAIAQG7UCpNSEoy8Pnn41i48Ht69HgPtdqM997rSocO75GUZMBgEAghjGROGzZo0CfMmDEFnU7HuHETsbNLtmmXtp56fXIbCCEk2TLKT68XGd6fn8+voMiJfAaDoch2tBX33XRvonzq8Lv/KDYAg56wfSux6TGVBEXOvnHnh3xKpSLdpKC4ohCi8E86eHl54evrS82aNWnbti3fffcdWq2WpUuX8vjxY/773/9iMBheKy43pFVuISEPqVjxrfyubq4pDoPz338/YMCA3hw+fDrdmbXiIF9WlAT5irIvvonKIz8pCPlMn5wjImCJcaBCSblBC4lXlc5VXm+KcivSc25KpZK5c+cydepUdDodlStX5vvvv89TnMzrc+zYETw8mhIfH8+yZYto2rSZfBhbRqYYoLJ1SBdmUcuNJFMrKL6/44qUIpm5FRfkmZsxX3wxiuvXr6BUqnBycubLLydQtmzZYiNfTikJ8skzt8x5E+VTosck+AqRB9dgiIvGvLqGUi36E29qn/3N+SifPHOT+Vcyf/7iohZBRkYmAwyoSKzkjH3fmij0CejNbIkXqqIWq1gjKzcZGRmZfwFCCHSqUqAC3tj1tpxTvPdLy8jIyMjIvAaycpORkZGRKXHIyk1GRkamEFAoQC3iMNdHo1LI64oFjfzNTUZGRqaAUSoMmD7/i6hDfiRFh2PdoAXmLu+hM5HNBRYU8sytGJOUlMTq1cv54IPu9OvXi48++oBJk77iwYP7+VpOcHAQnTp55yjt6tXLadzYmevXrxmF/fjjwnyVKSsuXAhk8OD+GcblRb4LFwL5888/8k3OjPjss6GcPHm8QMuQKX6oY4IJ2zqXpBehYEgi5vIh4s/vQqWUZ3AFhTxzywfOXA9h67F7hL/UUaa0Gd1b1MCjXsU85zt79nTi4+NZsWIdpUqVQgjBmTOnePTooWTAOAWDwYBCkWx/saCpWNGB5ct/ZNEi3wLJP6+evF9XvosXzxMXF4ebW+PXLjsr9Hp9geQrU/zRRzwl7RbHmGtHKefaBb2y5Nt5LApk5ZZHzlwPYd2eWyT8/6Hc8Jc61u25BZAnBff48SOOHz/C1q0BlCqV3PkVCgVNmnhKaVavXs6DB/eJjY0hNDQEX9+1rF+/hkuXLpCYmIitrS1ffz2FihUdCA4OYsiQ/rRv35nAwLMIIfjyywk0aqSR8lu+fAl//HGK+Ph4JkyYQqNGThnK1qqVN3/+eZazZ8/g7u6RLv7nn/04duwwer2esmXLM378RMqUKcusWdOoU8eRHj16Axhdz5o1DZVKxaNHD3n16hV+fhuZPn0Sjx49JDExgcqVq/L111MoXTp7U0OvI19UVBQ7dmzFYDAQGPgn3t5tiY2NoXTp0vTtO4BDhw4wbdo37Ny5Dzs7e8aOHU2vXn1xc2vMnj27+OWXn1AoFFSqVIWvvvoGOzt7AgL82bdvD5aWljx58ogpU741kuPgwX1s2rSB2bO/N3IxJFPyUJhZpgszKVUWg8I0g9Qy+YG8LJlHth67Jym2FBKSDGw9di9P+d6+/RdVqlTLdjC/ceMaU6fOYuPGLZQuXZp+/QayatV61q37hdat27Fs2SIp7YsXL6hZ813WrdvEmDHjmDZtIgkJCVJc/foNWbt2Ix9//Am+vosyKxKFQsGwYSNZvnwJaQ3c7NsXwNOnT1m+3I81azbg4dE0x0uWd+7c5n//W4yf30YAPv98LKtX/8T69b/yzjvV2bBhXY7yeR35atSoSZcu3WnfvhN+fhvp338gLi6uBAaeA+D8+T+pV68B58+fIykpiRs3rtOwoRP379/F1/dH5s9fwrp1m6hevQYLFvxjCu7Gjat89tkYfvppM+++W1sK37BhHf7+O1i4cKms2N4AFGXeQu1QM1WAElvvgbk2eiyTc+SZWx4Jf6nLVfjr8uDBfaZPn0R8fDyNGzdhzJhk90EeHk2NvCH88ccptm79jbi4V+mWwUxNTWnXriMAzs5azMzMePToIVZWVlhYWNK0aTMA6tVrkK1CatLEk59+WsvhwweNwk+ePM6tWzcZNKgfAHp9EtbWOTPX07KlNxYWFtL13r272L9/L0lJicTFxVO1arUc5ZNf8jVs2IipU78hMTGRq1cvM3LkGI4ePUS5cuUlj+UXLgTi4dFUMlPWpUt3Bg7sK+XRoIETlStXMcp31arllC9fkXnzfjByRSRTctGpSlGq4+cQ/gihi0VlX5kEa4dCPYytUEB0fBLRT19gYaKkmHuFyjOycssjZUqbZajIypQ2y1O+tWrV5smTR0RHR1OqVCneeac6fn4b2bLlV27duimls7D4Z7kjJCSYxYvns3LleipVqszVq5eZPn1SjspTq/8ZZJVKJXp9Urb3DB8+iu++m0GrVq2lMCEEH300iM6du6RLr1KpjGx5JiQYPzdLy38U2+XLF9m+fQvLlq3Bzs6O/fv3snPn1hzV5XXlS4uZmTk1atTk4MF9lClTFmdnLT/+uJBy5crj4uKaIxlS1ymF+vUbcPbsH4SEBOdKYcv8u0lQlYLy9QBIhEJVbAYBF+6EsXbXDeJ0SdSobMOnPRpiZ1lyf1yVcN1d8HRvUQN1mp9AahMl3VvUyFO+VatWw9OzBXPmzCQmJkYKj4uLy/Se2NhYTExMKVOmDAaDge3btxjFJyYmcuDAXiBZeeh0Ot566+3XlrFRIyeqVq0m5Qng6dmcbdt+5+XLl0Cy5+8Ur9+VK1fl1q3rAISFhXHhwvn0mf4/0dHRWFlZY2NjQ0JCArt37yxw+aysrIiNjTHKw8XFldWrl+Pi4oZaraZ8+fLs2bNLUm7OzlrOnDlFeHgYAP7+23F1dctSrsaNmzB27NeMG/c59+/nbflaRiYnhL6IZ+mWK8Tpkn+03nv6gvV7bpZohwLyzC2PpGwaKYjdkhMnTsPPbxVDhgzAxMSEUqVKUbZsOfr1G5hh+ho1atKqVWv69euFjY0tHh5NuXz5ohRvY2PDnTu32bhxPUIIpk2bledlsaFDRzJo0IfSdfv2nXjxIopRo4YCybs4u3Xrybvv1sLHpyuTJo2nX7+eVK1ajbp162Wab+PGTdi/fw8ffNAdGxtbnJw03LhxvUDla968Fd98M46BA/vi7d2W/v0HotW6sWqVL1ptsjJzcXHl6tUr1K1bH4Dq1WsyfPhn/Oc/I/9/Q0llxo37Jlu5XFxc+eabqUyY8AUzZ86hVq06ua6bjExOeRbxKl3Y5TthvNIlYW1WMtWA7PLmDXF5k7JbcvfuQ3nOqyS4lClKZJc3eUOWL/c8eBbDt2v+NAqrXM6KKR+7YarM+fGhf5PLG3lZUkZGRiYHmCVGYvr0PKp7RzGLfoiSf8+5xcplLPHWVpWuzUxVDO3aIFeK7d9Goc1HP/30U548eYJSqcTS0pLJkyfj6OiIl5cXarUaM7PkDRhjx46lWbPkXXuXLl1iypQpRt62y5Qpk22cTHocHCrly6xNRuZNxCwxiqjtc0mKDJbCynYbS0L5+vwb1r7UKiW9vWrS0rkKuiQ9ZUqZYWtp+q+Q/XUptJnbnDlz2LlzJ9u3b2fQoEF8880/3yUWLVrEjh072LFjh6TYDAYD48aNY8qUKezbtw+tVsu8efOyjZORkZHJb0T4QyPFBhB15GdMRXwRSZR7TJQKKttb4F7PARuLkq3YoBCVW4qVDYCYmJhszURdu3YNMzMztFotAH369GHv3r3ZxsnIyMjkNyIxvRLTv3qBIgdHZvKLlHNqYdE6kgwlXDPlA4W6TWbixImcOnUKIQSrVq2SwseOHYsQAhcXF7744gtKly5NcHAwlSpVktLY29tjMBiIiorKMi71gWYZGRmZ/EBVpioolCD+2QhkrWlLoqk1hbGfXi8EgX+F4bf7BroEPTWr2PBp94bYluBzanmlUJXbrFmzANi+fTtz585l5cqVbNiwAQcHBxISEpg1axYzZswotCXGtLt+nj1TYlJMju0XFzkyQ5Yvb2Qnn1KppFy5ojOoW5Rl54TClk8YaqLqM4mIoxvQvwynlKYNpZxaY2qTsRz5Ld/1++Es33ZVur775AUbD/zF+AGumKtzP4wX9/bND4rkgEPXrl2ZMmUKkZGRODg4AKBWq+nbty8jRowAwMHBgaCgIOmeiIgIlEoltra2WcblhrRHAQwGQ7HYQp6yVfzw4YP89NMahEi25lGrVh2mTUv+gTBwYF+WL1+DmVn+2Ka7cCGQJUt+YPXqn7JMd+fOXzx9+piWLVtnmS4jcnIcYcqUr7lw4Rzbt+99bc8AeT0KsHr1cuLi4vjsszGcPHmMy5cvMXLk56+d3+vIZzAYimw7eXHcyp6aIpOvVHWs3xuP0pBEgsqSqAQgAzkKQr6nz9Lnd/7WM0Kex2ClVuUqr7zI9286ClAoyi02NpaXL19Kiuzw4cPY2NhgZmYmmZcSQhAQEICjoyMA9evXJz4+nsDAQLRaLZs2baJ9+/bZxpUUwsLCmD//O1av/pkKFSoihODOnb+k+BTjwoXNnTu3OXPm5Gspt+x4+fIF586dpVq1tzh58hgtW+bMx1xB4unZAk/PFkUthkwxIRE1KNWFajoLwMY6vTm/ahVKY1bMVyiKkkJRbnFxcXz++efExcWhVCqxsbHB19eX8PBwRo0ahV6vx2AwUKNGDaZOnQokL8vMnTuXqVOnGm33zy6uKEi4c5qEc1sQMeEorMugdu2B+t0mecozIiIMlcoEG5vk2ahCoTCyYuHpqWX//uNYWlry/vvv0bZtB86fP8fz588YPnwUUVERHDiwl5cvX/L111NwcnJONzvLbLaWlJTEV1+N4cWLF+h0OurWrce4cd/w6lUsq1b58upVLAMH9sXJScOYMeO4fv0avr6LiY2NBWDIkOGSa54tWzazefNGrKys8PDwJCv2799DkyZNcXPzYPfunZJyS5nx+fh0T+eSJ6O4iROnUr9+IwDOnDnJ+vVr0OkSMDU1ZdSoL6hfvwHh4WFMmzaR2NhYEhISaNKkKZ9+mn52FhDgz+nTJ5g5cy4XLgSyaNF86tatx/XrVwEF06fP5u233wGSXQYdPnyA0qVt0GhcOH/+XLYzYRmZnFC5jCUtnatw9MITAMzUKob41MOkBJ9TyyuFotzKli3L5s2bM4zbvn17pvc5Ozvj7++f67jCJOHOaXQn/CAp2XWMiAlPvoY8KbiaNWtRt249evTohEbjQsOGTrRr11FSdmlJTExk+fK13Lx5nVGjhjFixGhWrlzPoUMHWL58CcuWrc5x2SqViqlTZ2JjY4sQgpkzp7J79w66dn2fIUOGc+bMSb79dg6QbANy3rzZfP/9IsqWLUtYWBiffDKA9et/JTQ0hPXr17B27Qbs7cswb953WZa7e/dOPvvsP9Sr14CFC+cRFvacsmXLAf+45Bk2bCT79+/B13cRy5atyTBuyZJFLFu2mqdPn+Dnt5r58xdjZWXN/fv3GDt2NFu37sbauhRz5izA0tKSpKQkvvjiM/744zSNG2fdZg8e3OObb6bw1VcTWbduNevWrWbq1JmcPHmc06dP4uf3C2ZmZkyaND7Hz1tGJjvMTJR80PpdvLVViI1PooKd5f+fU5N3TWZGyTQqVogknNsiKTaJpAQSzm3Jk3JTKpX897//4/79u1y8eIETJ46yceNPrF+/idKlbdKl9/ZuA0CtWnWIj4/H27stAHXqOPL06ZNclW0wGPjll5/544/TGAx6oqOjMTfP+NvetWuXCQ4OYuzY0VKYQqHg6dPHXL16hSZNPLG3Tz5c36VLN44cOZBhPrdv3yI6OhpnZy0KhYKWLb3Ys2cX/ft/DJClS57M4s6ePcPTp08YOXKolFav1xMREY6FhSVLl/7A1atXAEF4eDh37tzOVrlVq/aWNIOuV68Bp06dAODixUC8vFpLLns6dOiEn1/Of1DIFDwqhcAkPgySdAirsiTw7/KlZqpUUNn+Hy8gsmLLGlm55RERE56r8NxSvXpNqlevSY8evejXrycXL56nRQuvdOnUajWQPOtKfZ3afY1KZYJItZU5xVFpWg4c2MuVK5dYunQllpZWrF+/hsePH2WYVgioUeNdlixZmS4uWXHkjN27dxITE03Pnj4AJCYmYGFhJSm3rFzypI/T/79sAnd3DyZPnpGuPD+/VURHv2TFCj/MzMyYM2dWOhc8GaFW//PtI3VZMsUbE0M8hpuHCDuzFQx6TMu/jW2HkcSblStq0WQKCPlrZB5RWGds8iuz8Jzy/Pkzrl37Rzk8exZKVFQkDg6VsrgraypXrkxQ0FNevnyJEIKDB/dlmC4mJhobG1ssLa2IiYkxchljZWVl5IKnfv2GPHnyiAsXAqWwmzevI4RAo3HhzJlTREZGALBr144My0tISODAgX2sWvUTv//uz++/+7Njxz4UCoy8GuQWN7fGnD17xsitzM2byZ4FoqOjKVOmLGZmZjx//oyTJ4+9djkAGo0LR48eIj4+HoPBwL59AXnKTyZ/UUY95sWp38CQ/GMk8dnfxJzdiomi6HdHyxQM8swtj6hdexh9cwPARI3atUee8tXr9axevZyQkGDMzMwRwsCQISPy5BqlbNly9OnTj8GD+2Nvb4+TkzMPHtxPl659+86cOHGcvn17YGdnT6NGGnS65FmNi4sbmzb9zEcffYBG48yYMeP47rv5LFnyAz/88D+SkhKpVKkyc+YsoGbNd+nf/2NGjBiMpaUVHh5NM5TrxImjVK5chSpVqhqFt23bgd27d/Lxx5+8Vn2rVq3GlCnf8t1336LT6UhKSqRBg0Y4OtajZ88+TJ48nv79e1GuXIUcOx/NDE/PFly9eoWPPupD6dKlqVevAdHRxXc7/ZuG/kVIurD4+5ew8nxFkrJwt7YrFAp5SbEQkF3e5IPLm/zeLVkSXLYUJUUl36tXsVhaWmEwGPjuu28pW7YcQ4d++lryyS5vMud15FOH3SB861yjMPO3G2LZbjSJIn9/42cmX3R8En89jiLiZTx1qtlRuawlqmzMEBYE8jk3mRyjfrdJnrf+y/z7+fbbqYSEBKHT6ahd25EPPxxQ1CLJpGD/Nlb1mhN7/TgASsvSlPL8gPh8VmyZEaNLYvb6c4RGxElh/+mjoeE7diXegHFRISs3GZl84r//lT1TFFcSlJaom3yIRaM2iIQ4FKUroDO1KbTD2I9CY4wUG8C6gJvMHuaBWiWfVSsIZOUmIyPzRpCkljcbygAAIABJREFUMCPJOtV33UKcMSVksAwdG5+I3iBAVm4FgrxbMg1v8CdImWKC3AdLHlXLW2OiMh5uOzd9B0uz3NmFlMk5snJLhYmJmtjYl/LgIlNkCCGIjX2JiYm6qEWRyUfKllIzbYg7Tu+WpYK9Jf3b16GVc2WE7JetwJCXJVNhZ1eOyMjnxMREFakcSqUSg6H47kaU5csb2clnYqLGzk4+XJwWpUKg1kWgCwnDVFU62YjxvwQhoJKdBaPeb4heL1CbKI12asvkP7JyS4VKZULZsg5FLUaJ3IpdmMjylTxMhA7DrSM8P/k7GJIwq1Kb0q2HEq/Om7GE3KBQgC5JkKg3YG1m8lorPAoBJkqFrNgKAVm5ycjIFHtUUY+IPL5JutY9+YtXF3Zh6jEAvSj4DRkCwV9Polm18xpR0Tq8tFV4r+k7WJvJQ2hxRf7mJiMjU+xJCk9v/DvuzjlU+leFUn5olI45PwUS/iIevUFw4M/H7PnjIQp5BC22yE0jIyNT7FGVTv8NUl2xJgZVeieeBcGT5zHpwo6cf0JcQvH9tvumIys3GRmZ4k+ZtzGvqZUulebWlPLsRVIhWRixtjBNF1bOzkJ2FlqMKbQF408//ZQnT56gVCqxtLRk8uTJODo68uDBAyZMmEBUVBS2trbMmTOHt99+G+C142RkZEoWCSprLFsNwdqlEypFEnrLcuhMbQvtIHa1Cta8W9WWO4+Td1IrlQo+7iR7wi7OFJrh5OjoaEqVKgXAwYMHWbJkCdu2bWPAgAH06NGDLl26sGPHDrZs2cL69esBXjsup6Q1nFxcKO676WT58oYsX94oKvniEvU8fhZLXEISlctaUa60WYZ2IUvy8/s3GU4utGXJFMUGEBMTg0KhIDw8nBs3btC5c2cAOnfuzI0bN4iIiHjtOBkZGZmCwMJURa3KpWn0jj1lS2Ws2GSKD4W6j3XixImcOnUKIQSrVq0iODiYChUqSN6jVSoV5cuXJzg4GCHEa8XZ29sXZpVkZGRkZIohharcZs2aBcD27duZO3cun3/+eWEWn47iPL0uV65U9omKEFm+vCHLlzdk+fJGcZcvPyiSE4hdu3ZlypQpVKxYkdDQUPR6PSqVCr1ez7Nnz3BwcEAI8VpxuUH+5vZ6yPLljTdRPoUCzGKDiL99Bn10BBaOnhjK1CBJkXsTWq8rX6JB8CwqHl1CEuXtLChlblIgS4sluX3lb25piI2NJTg4WLo+fPgwNjY2lClTBkdHR3bt2gXArl27cHR0xN7e/rXjZGRkih9mr0IJ+3UG0X/68+rmKcK3zkERcp3CckQdn2jg531/MXnFGWb6nWPi8jM8e6krnMJlioQcz9xOnTrF7t27iYiIwNfXl6tXrxITE4OHh0e298bFxfH5558TFxeHUqnExsYGX19fFAoF06ZNY8KECSxdupTSpUszZ84c6b7XjZORkSleJIXeQSTGG4VFn/qN0u/XJYGCP4j9+HkMJy4H/VP2q0Q27PuL0e83lA/7llBypNx++ukn1q9fT8+ePdm3bx8A5v/X3p0HNHGmfwD/ziQknBJuw6EoFcQDQUFqKx54oF3Q7WGlrrrbVq3W2sPVag+hoq2i1nbb0lr3p90eVlsVtVorurrqbg+rRap4SxUVUFQOuXLO+/uDkhITQggkhPh8/iLvm8k8mRl4eN95532dnfHmm2+aldx8fX3x9ddfG60LCwvD5s2b27SOEGJfjD1xxJhQ/5yaDVpvt+8oDMouXK2AUi3AxYnSmyMy66x++umn+OSTTzBjxgzwfP0m3bt3x6VLl6waHCHEMTh1vg/cXWvUdRr0CNS8babP6uztZlAW29MfLhJKbI7KrDNbU1OjG6zB/d5JrtFo4ORkOCUNIYTcTekqh+/ENLj1HQ7n0Cj4jJ8LFtTPZs+KBfm4YlJSBMSi+r9fYUGeeHhYmM1mOCG2Z1a3ZFxcHNauXYtZs2bpyj777DPEx8dbLTBCiONgDFC4BcNp8JOQcAwqjWVZRSTiLVpHzUnEYWT/IMRG+EOlEeDtLoWYGm0Ozazk9vrrr2PmzJnYvHkzampqkJSUBDc3N3z88cfWjo8Q4kC0Wstm0ec4DjcqFdh/7ApuliswMi4EPYI6wUnUggzFAJkr9TbdK8xKbv7+/ti6dStOnjyJoqIiyOVyREVF6e6/EUKINd2qUiL9nz9BqdYCAPIu3MSzj0YhLtyXpsEiRpmVnT744AOcO3cOUVFRGDt2LKKjo8HzPNauXWvt+AghBAXFlbrE1mDzgQtQaimzEePMSm4fffQRnnrqKXz33Xd65WvWrLFKUIQQ+yPVVEJy4wScin6Bc90Nmz2ADQC8kZ3xHGeLpwhIB2VWt6REIsH69evx7LPP4ty5c3jxxRcBGH92hRDieKTqclRsXwFN+e8zDYnE8Ht8ERQeXW2y/+6BneAiFaNOqdGVTRwZDomIo25JYpRZLTeO49CzZ09s2bIFv/zyC5599lnU1NToHgsghDg24caFPxIbAGg1qPphC5w4bdMbtSEfdwkWT7sffx7SHYP7BeKVqXHoE+pFiY00yazk1tBC8/b2xieffAI/Pz9MmDABGo2mmS0JIR0dxwHaKsO1EjUV18EJapvEwBjg6yHBnwd3w4KpcegR6EGrYBOTzEpujzzyiO5nsViMxYsXY+rUqejXr5/VAiOE2AfGACd5uEG5W1QiNCIXm8Zij6t4EPtkVnJbtGiRQVlqaio+//zzNg+IEGJ/NJ4h8P7THIjcZOBETvAYmAJx+IOUbIjdanJAyaJFi7BkyRIAwMsvv9zkB6xYsaLtoyKE2BUt5wQheABkT0SCZxqoxJ2gamFe4zhAqRGgFQBXiYgGpBGrajK5BQcH637u0qWLTYIhhNgvxgAV7/r7i5ZtKwA4d6US//r2NO7UqvDQoFCMGBAMV4mozeMkBDCR3J555hndz88995xNgiGEOKbisjqs3PCL7vW2QwWQSkQYExdCXZvEKkzecysqKsL169d1r+vq6vDOO+9g1qxZWLt2LbRa2wwDJoR0XBwHFFyrMCjfe+QKFGr6G0Ksw2Rye+2113Dy5End64yMDHz77bcIDQ3F1q1b8Y9//MOsnZSXl2P69OlISkpCSkoKnnvuOZSV1Q8tjoiIQEpKCsaPH4/x48fj3Llzuu0OHDiAMWPGYNSoUXjxxRdRV1dnVh0hxDie5yBqyWTDbYAxwNPdcN22AG8XiG0cC7l3mLyyzp07hwcffBAAUFtbi927d+Pdd9/FggUL8OGHH+Lbb781ayccx2HatGnIycnBzp07ERISglWrVunqN23ahB07dmDHjh2IiIgAUL+G3KJFi7BmzRrs27cPbm5uWLduXbN1hBBDHMfBubYIQu5WqP+7DtLy8xAx2zyjBgBhQZ0Q6PvHgqEinkPqqAjzhmsTYgGT15ZarYara/0N5JMnT8LNzQ19+vQBAISFhaG8vNysnchkMr2136Kjo1FcXGxym8OHD6NPnz4IDQ0FUP/oQcPclqbqCCGGpLXFuLVpMap+/gY1+Ydwa/NbEN081/yGbcRDKsbCKbGY/5f+eH5CP7w16wGE+LrabP/k3mMyuQUHB+PIkSMA6rsBGyeosrIyuLi0/AFOQRCwceNGJCYm6sqmTJmC8ePH4+2334ZKpQIAlJSUIDAwUPeewMBAlJSUNFtHCNHHcYD62mkwjUqvvOqnbDhxtptlyF0qQmSIDNFhPvDzkNIq2MSqTE6c/Nxzz2H27NkICQnBb7/9pvfQ9v79+9G3b98W73DJkiVwdXXF5MmTAQAHDx6EXC5HdXU15s+fj6ysLLz00kst/lxL+Pi422Q/lvDz82jvEEyi+FrH1vFVnDeSSQQBHh5SiKSGLSg6fq1D8bU/k8lt5MiRyM7OxpkzZ9CrVy+EhITo6rp3747o6OgW7SwzMxOFhYVYs2aNbqFTuVwOAHB3d8eECRPwySef6MobWo0AUFxcrHuvqbqWuH272i6HIfv5eeDmzar2DqNJFF/rtEd8zoGRAC8GhD9aau7x41F2RwtAPxY6fq3jyPHxPGfXjYLGmr2f26VLFyQlJeklNgAYMGAAevToYfaOVq9ejfz8fGRlZUEikQAAKisroVAoAAAajQY5OTmIjIwEACQkJODkyZO4fPkygPpBJ2PHjm22jhBiSOkeCL/UNLj2Ggzn0Cj4/HkeWOfeLf6c9hhtSYglzFrPrbUuXLiAjz/+GKGhoUhNTQVQfz9v2rRpSEtLA8dx0Gg0iImJwQsvvACgviWXkZGBZ555BoIgIDIyEq+99lqzdYQQQ4xxULh3gWTodHAAVC1cwZrjgJt3lDhy6gbKq5V4sK8cXfzdIKJlr4id4tg9PMEbdUtahuJrnY4YX1m1Cq+v/REK1R8PXb88eQB6BnvaOrwOefzsCXVLEkLI785eKddLbADw9f7zoPlFiL0yK7nNmjXLaDnNOUmI4+M4QGukh0OjZaClsIm9MuueW+ORiY39/PPPbRoMIaRpUk0VWPlVMK0GIu8gKKU+NsktjAE9u3hBLOLqE9rvHhkWBjHPUX4jdslkcmuYO1KtVhvMI3n16lW9B6kJIdYjVZej8pu3ob59DQDASVzg+/giKFxt8zvo7ynF4umD8N2Pl1FRpcSY+7uiR5AnJTZit0wmt4YVARhjeqsDAPXPms2ZM8d6kRFCdLTFZ3SJDQCYqg7Vx3ZCOmw6tIL1b50zBshlzpiWHAkOgLaFoy0JsTWTyW3ZsmUAgJiYGDz++OM2CYgQoo/nOWjKrxuUa25egYuggRYSsz+L4zhwHCweJSxQUiMdhFn33AYNGoSrV68arbv74W5CSNsSBAZpSCSqfv5Gr9y19xBoeSlgRqLiOOBWlQq/XryF6loV+kf4I9DbBTw9p0YclFnJbdSoUeA4Do0fieN+/6U4c+aMdSIjhOhovbtDlvhXVP7vKzC1Cu79EuF03yAozWyB3apSIe2fP6FOWT/91vbDv+G1vw1EWOeO8cwSIS1lVnI7e/as3uubN2/igw8+QGxsrFWCIoTo03BScD2Gwye0PzgmQC3xhJKZd6+N44AzhWW6xNZgy4ELeHlSDKjtRhyRRXei/fz88Nprr2H16tVtHQ8hpAmMAUqxJxROXtCamdgaKFWGj1vXKTUQ2io4QuyMxcOsfvvtN9TV1bVlLIQQK2AM6NXNB/xdTbTxQ7pDTM024qDM6pacNGmS7h4bANTV1eHixYuYPXu21QIjhLQduZcz0qfdjx2HC3CnRoU/PdgNkV1k9JwacVhmJbcJEybovXZxcUHPnj0RGhpqjZgIcUhOTAG+6jpqawCJix9UvJvtds6AEB9XzHk0CgIDOMpqxMGZldwefvhha8dBiEOTaipRdWAdlJdPAADEXgHwGjcfCqmvTeNgAqMBJOSeYPKeW3Z2Nl566SWjdXPnzsWOHTusEhQhjkZbck6X2ABAU34Ddfn7wbfwrjfHQe8WASHEOJO/Wps2bcL06dON1s2YMQNffvmlVYIixJHwPAf1jQKDcmVhPkRMbdZncBxQVqPCf/NvYN8v11BSUQfqWCSkaSa7JQsLC9GrVy+jdT179sTly5fN2kl5eTlefvllXLlyBRKJBF27dkVGRga8vb2Rl5eHtLQ0KJVKBAUFYeXKlfDx8QEAi+sIsSeCwCAJ6gnk5uiVu/SIgwZOZn3G7SoV0v/vJ9Qo6p9V4zlg0dPx6Oprw/t2hHQgJltugiCgoqLCaF1FRQUEwbynZDiOw7Rp05CTk4OdO3ciJCQEq1atgiAImD9/PtLS0pCTk4PY2FisWrVKt29L6gixS/494BY1Avj9jpc0pDekPRPMGq3IcUD+pTJdYgPqZ9zK/k9BfSUhxIDJ5BYTE4OtW7carcvOzkZ0dLRZO5HJZIiPj9e9jo6ORnFxMfLz8yGVSnUznaSmpmLPnj0AYHEdIfZILXKHZNAk+E5ZhsAnM+E29gUonLzM2pbjONTUqQzKq2pVEGjUIyFGmeyWfO655/DXv/4VJSUlGD16NPz8/HDz5k3s3bsX2dnZ+PTTT1u8Q0EQsHHjRiQmJqKkpERvTThvb29da9HSOplMZnYsPj72O6+en59He4dgEsVnqfrr07mFWw2IDMCW/1zUa+mNH9IdAVb6nvZ7/OpRfK1j7/G1BZPJLSoqCuvXr8fKlSvx5ZdfQhAE8DyP6OhorFu3Dn379m3xDpcsWQJXV1dMnjwZ+/btszjwtnD7drXFS39Yk5+fB27erGrvMJpE8bWOJfH5eUjx+t8GYvOBC6hRaDA+oRsiu3hZ5Xs64vGzJUeOj+c5u24UNNbsc24xMTH48ssvoVAoUFlZCU9PTzg7t/T/znqZmZkoLCzEmjVrwPM85HI5iouLdfVlZWXgeR4ymcziOkIcEQegW4A75j8RA4EBYh40uwghJpj9lI2zszMCAgKwfPlyi3a0evVq5OfnIysrCxJJ/eKKffr0gUKhwLFjxwDUP3owZsyYVtURYk1OvAYSTtNu4zg4ACKOEhshzeEYa9mvSf/+/ZGbm9uinVy4cAHJyckIDQ3VtfqCg4ORlZWF3NxcpKen6w3p9/Wtn7XB0jpzUbekZe7F+ETQQHz7Iqp+zIagroPHwPFggX2h4aR2EV9bovhax5Hj60jdki1ObjExMTh+/Li14rEpSm6WuRfjk1b+hltfZeiV+aS8CJXcvBHDQP2oR4VGC2dnCaDR2G3r6148v23JkePrSMnNrLklG5s5c6Y14iDEbvE8B8XFowbl1bm74ZYSBbXQfO++hjGcLLiNL/achVKtxfgh3ZEQFQhnscWrThFCTDDrN6u8vFz38zPPPKP7+cqVK20fESF2SORs+N8q79IJzMybb1dLa/D+5l9RXqVErUKDjXvPI+/iLXoGmxArMSu5paSk4NChQ3plX375pcFSOIQ4IkFgkHTvD86p0Shhjod7bDI02uazE89zOH7hpkH53iNXYIe94oQ4BLO6Jd988028/vrrGDFiBJ588kksWbIEpaWlFj3ETUhHpHSVwzf1DaivnQbTqCAJ6Q2lRzDMmb2YMQY/mYtBeaCvG3ieA6MMR0ibM6vlNnToUOzcuRO//PILxowZA5lMhi1btqBnz57Wjo8Qu8AYoHDpDCE8EazXWCjcQ8CYeX2KjAF9u/vA2+OPkZVSJxGSH+xGiY0QKzGr5VZTU4PMzExUV1fjb3/7G7Zu3Ypt27Zh4sSJ1o6PELtSP8Kx5QlJ5uqE9KfjUXijGgAQ6OsKH3cpWjhYmRBiJrOS27hx49C/f39888038PDwwLhx4/Dyyy/jwIED+Pjjj60dIyEOwcNZjD5dZbqh2JTYCLEes7ol//73v2PlypXw8KifbDMyMhJbtmxBaGioNWMjhBBCLGJWy+2hhx4yKJNKpXjllVfaPCBCrEWqqQQruwbGtBB5B0Ph5N2i7ZUaATfK66AVGDp7u8DFSWSlSAkhrWX2Q9z79+/H0aNHUV5ertedsmLFCqsERkhbclbdRtm25dBW1g/J513c4TPhdSicO5u1fbVSgw+2nsD5K/WL9/p5uWDhlFh4uZq3kjYhxLbM6pb84IMPkJ6eDkEQsGfPHshkMvzvf/9Dp06drB0fIa3GcRxUl47rEhsACHXVqDuxHzzf/IhHjgNOXS7XJTYAuFleh//8chWcGdsTQmzPrOS2detWrF+/Hq+++iqcnJzw6quvYs2aNbh27Zq14yOk1Xieg/qW4Ww66tLLEHHND+rgeR4F1yoMyk9dKqOHsAmxU2Yltzt37iA8PBwA4OTkBLVajaioKBw9ajjfHiH2RqsV4HJfrEG5a++h0Ajmbd83zHDFiQf6yiGihhshdsms5NalSxdcuHABANCjRw9s3LgR27dvh6enp1WDI6StML8e8BzyBDgnKSASw2NgCvgu0WbPzN8j2BN/ejAUDb2Q9/fpjPhene1yVQlCiJkDSl588UVUVNR3y/z973/HvHnzUFtbi/T0dKsGR0hbUfMu4Hslwee++wEwqCWeUAnmN7ucxTweHdIdIwaEQCsweLlLzF/plxBic2Ylt6FDh+p+7tevH/bt22e1gAixFkEAlOLfexvM6I40wOpnGiGE2D+Tya24uLjZDwgMDDRrR5mZmcjJyUFRURF27typu4eXmJgIiUQCqbR+3r158+YhISEBAJCXl4e0tDS91bZ9fHyarSOEEHJvM5ncEhMTwf2+4JSxqYI4jsOZM2fM2tGIESMwdepU/OUvfzGoe++993TJroEgCJg/fz6WLVuG2NhYfPjhh1i1ahWWLVtmso6QpvA8h1qVFowBrhLeblfCJoS0nsnk1rNnTygUCjz88MMYN24c/P39Ld5RbKzhaDVT8vPzIZVKddulpqZixIgRWLZsmck64ricODX4mlsAEyC4+UENidnbqgWGY2dKsXHvOWi0Ah4Zdh8GR8lpJWxCHJTJ5LZ9+3acP38e27ZtwxNPPIGwsDCMHz8eo0ePhrOzs6lNW2TevHlgjGHAgAGYO3cuOnXqhJKSEr0uT29vbwiCgIqKCpN1MpnM7P36+Biurmwv/Pw82jsEk2wdn7ryJsr+/Rlqzv4AAHDpHg3fMdPh5GV8hpG74/spvwT/3JGve/3l3nPwkblgdHxX6wVtAp3f1qH4Wsfe42sLzQ4oCQ8Px4IFCzB//nx8//332LZtGzIyMvDpp5+id+/erQ5gw4YNkMvlUKlUePPNN5GRkYFVq1a1+nPNcft2tV0O5W6YNd5e2To+jgNEl4/rEhsA1P2WhzunfgTrOcqgy/zu+EQiHj+cMLx/vPenQgy4zxeCYMnoEsvR+W0diq91WhMfz3N23ShozOw+mcuXL+Po0aPIy8tDZGRkm029JZfLAQASiQSTJk1Cbm6urrzxgJaysjLwPA+ZTGayjjgekYiH4vKvBuWKi0chMuMKFgSGQF83g/KQAHdYsjYbIcT+mfzTUFFRgQ0bNuCxxx7D7Nmz4erqii+++AKff/45QkJCWr3z2tpaVFXV/wfBGMPu3bsRGRkJAOjTpw8UCgWOHTsGANi0aRPGjBnTbB1xPFqtAGlIpEG5c2iUWdNfMcbQP8IfskYrYbtIxRgV18UuW+6EkNYz2S2ZkJCA4OBgjB8/Hv369QMAFBYWorCwUPeeQYMGmbWjpUuXYu/evbh16xaefPJJyGQyrFmzBnPmzIFWq4UgCAgLC9M9GM7zPFasWIH09HS94f7N1RHHwxggDukHaUgklFfrR+c6BXSDpMcgKMxMTl6uTlj8dDyulNZ3RYf4u8PLzYlGTBLioDhmYjngxMRE0xtzHPbv39/mQdkK3XOzTHvFJ2EKcFXXAcbAPAKg4l2Nvo+OX+tQfK3jyPF1pHtuJltuBw4csFUchDRLxTkDnULbOwxCSAdAD/kQQghxOJTcSIfBcRyUWgFKLTNrkVFCyL3LrImTCWkrot/H7mu1LXu2TK1lyCu4iU37zkMrMDyWeB8G9vSHxJxnAQgh9xxKbsQmeE6ApPIKak8fBpgA195DoerUFYKZnQe/Xb+Dj7JP6l6v33kanVwliOrmba2QCSEdGCU3YhOSyiu4+VUGwOpbbDUnD8Fv4iIoPLs3u61IxOP7EyUG5f8+dhUx9/m2uBVICHF81KdDrE4k4lF76pAusdVjqDnxb4jNmLiYMQa5kRlGAn0MywghBKDkRmyEMSOtKzOfoBYEhoGRAXB3+WOhUBepGImxIdRqI4QYRd2SxOq0WgFufYahNv8wGs/l6BY1EgqNecnJ10OCjOn340ppNZjA0CXAHd7uEpphhBBiFCU3YhOqTl3gN3ERan7dByYIcI8eDZUs1OztGQNkrk6QhXrplRFCiDGU3IhNCBBB4dkdLiNnAwAUKk07R0QIcWSU3IhNMDBcvVWL734sBGMMY+8PRYifK3iOHsYmhLQ9Sm7EJq7eqsUb/3dE9/rn0zeQ/nQ8uvrRiEdCSNuj0ZLE6kQiHgdziwzK9x65YtajAIQQ0lLUciNm4ThAWncD2puXUVXMw9m7K5Qu/mYP6hCLDLsfxWLqkiSEWIdN/m3OzMxEYmIiIiIicP78eV35pUuXMHHiRCQlJWHixIm4fPlyq+uIdUhrinFrUzrKvvsIN3dl4damdEhrDWcNMUarFTCsfzAaz3XMccCouC7QmPkoACGEtIRNktuIESOwYcMGBAUF6ZWnp6dj0qRJyMnJwaRJk5CWltbqOtL2RCIOdacPg6kUujKmqoPizP/Mnp0/0NsFGTMGIen+rhg9sAsypg9CkI/xxUYJIaS1bJLcYmNjIZfL9cpu376N06dPIzk5GQCQnJyM06dPo6yszOI6Yh0cx0FbccOgXFNxw/ylZxgQ6OWCSSN64C+jwhHk7QLqlCSEWEu73XMrKSlBQEAARCIRAEAkEsHf3x8lJSVgjFlU5+1NM8Rbg0YjwLXPMNT9dlyv3LX3UKha2K1I02URQmzhnh5Q4uPj3t4hNMnPz6O9Q9CjdY8G99AslP/3a4Dj4JXwONzu6weRs30O5be343c3iq91KL7Wsff42kK7JTe5XI4bN25Aq9VCJBJBq9WitLQUcrkcjDGL6lrq9u1qCIL9zeHk5+eBmzer2jsMA1zI/ZClRsHZWYIqlQjKKgGosr847fX4NaD4Wofia53WxMfznF03Chprt4eMfHx8EBkZiV27dgEAdu3ahcjISHh7e1tcR6xHyxjOFVVi6aazWPTpSZwvugMtTe5ICLFTHGPW/wu1dOlS7N27F7du3YKXlxdkMhm+/fZbFBQUYOHChbhz5w46deqEzMxMdO9ev3ilpXUtQS038xVcr8Kb/zqqV7boyYHoFmB//8XZ4/FrjOJrHYqvde6VlptNkpu9ouRmHrGYR9a2fBw5dV2v/IEoOWaO6213z6rZ2/G7G8XXOhRf69wrye2eHlByrxFxAsSKMnAcB7XUC1pmXq80Y4Bbo4VCG7hBnIamAAAXSklEQVS7ONGyM4QQu0TJ7R4h0VZBeWw7Kk78BwDg0X8MnKIfglrU/H9hWq2AEbEhOJR7DdrfW7piEYdh/YNpaD8hxC5RcrsHcBwgXMlD9a/7dWVVv+yGd0A3IDjOrM+Qezlj6TODkHfhFnieQ1SYDwJkzo0X1iaEELtBye0eIBJxqD3zvUF53cWjcA6NN++eGQMCPJ0xJi4Evr7u9X32lNgIIXaK1hu5BwgCIAnuaVAukd8HrbZlGeoeHn9ECOlAKLndAwSBwTliMPhOvroykZcckm4DKFkRQhwSdUveIy7VuuFit6fQzbUaAIcL1a7oVeeGAEl7R0YIIW2Pkts9QCzmsefIFfw3r/FzalX4k8YVE4Z2t8tn/QghpDWoW/IeUVOnMlrGcbTwDCHE8VByuwdoNAKS7u9qUD40hp5TI4Q4JuqW7EA4DhBDDQ4cVKxlp657gAdenjwA2w//BhHP4eGhYQj2pZWwCSGOiZJbByFmSnBFJ1F1ZDs4kRgegx6D1i8CWs5wWixjRDyHnsGeWPCXmPoVsOk2GyHEgVG3ZAfBl55D2bcfQH3rGlQ3LuP29lUQV1xu8edwDJTYCCEOj5JbByAWcag5nmNQXnfuR4hEdAoJIeRu9JexA2AAeDeZQTnv6kkPYRNCiBGU3DoArZZB1HskwP9xi5RzkgJdB9AzaoQQYoRdDChJTEyERCKBVCoFAMybNw8JCQnIy8tDWloalEolgoKCsHLlSvj4+ACAyTpHw4s4rDuiwLAHXoR3XSEYL0KpUzDyT6owYShPw/kJIeQudpHcAOC9995DeHi47rUgCJg/fz6WLVuG2NhYfPjhh1i1ahWWLVtmss5RaRmw5JtSuDl7QGBAnbIUDw8No25JQggxwm67JfPz8yGVShEbGwsASE1NxZ49e5qtc0SClmHsoFDwPIcahQZ1Sg0kYh7xvTtTtyQhhBhhNy23efPmgTGGAQMGYO7cuSgpKUFgYKCu3tvbG4IgoKKiwmSdTGY48MIRBHm5YOkzg3Di4i2IRTz6hvnAv5MztdwIIcQIu0huGzZsgFwuh0qlwptvvomMjAyMGjXK6vv18XG3+j4s5efnYbSs731+7RCNIWPx2ROKr3Uovtah+NqfXSQ3uVwOAJBIJJg0aRJmzZqFqVOnori4WPeesrIy8DwPmUwGuVzeZF1L3L5dbdNuPan2DlhFCTieB/MMhIp3M/o+Pz+P+pWu7RTF1zoUX+tQfK3Tmvh4nrPrRkFj7Z7camtrodVq4eHhAcYYdu/ejcjISPTp0wcKhQLHjh1DbGwsNm3ahDFjxgCAyTp75awoRdm2TGirbgMAnPy7wfNPz0Pp5NXOkRFCiONp9+R2+/ZtzJkzB1qtFoIgICwsDOnp6eB5HitWrEB6errecH8AJuvsEc9zUJw6qEtsAKAuvQTt1XxwYQmg22aEENK22j25hYSEYPv27Ubr+vfvj507d7a4zt6IoEVd0VmDctX1Ajj1GErPqRFCSBuz20cBHInAiYHQgYblgb0hCJTYCCGkrVFyswFBYDjLhYEPi68v4HhwvUfhTJ0/eJ5OASGEtLV275a8V1Qwd/yrPB5DBiZAyzjsOVWLlGBP6pIkhBAroORmA4wxxPb0x6WSO3g3pwg8xyF5cDeEBXVq79AIIcQhUXKzETeJCH9NisCfE7qD4zh4uopp0VBCCLESSm42xAGQuTrVv6DERgghVkPJrQXE0ECkLAfH8VA7e0MrcO0dEiGEECMouZlJqq5E7Y9fofbsDwAvgkdcMpz6JkHNu7Z3aIQQQu5C49DNwPMclBd/rE9sACBoUXVkB1jpxfYNjBBCiFGU3MwghgbKcz8alCsunwDPU9ckIYTYG0puZtBABME3zLBcFtIO0RBCCGkOJTezcBDCh0Hk/seSOpxvKISAnrQSNiGE2CEaUGIGQWCAZyCK4l6Ai6IUDCIo3Toj2N0+Fg4lhBCij5KbmdykYoT16IayqkCIRDyCXZ1Ad9sIIcQ+UXJrAR6Ar4e0vcMghBDSDLrnRgghxOF06OR26dIlTJw4EUlJSZg4cSIuX77c3iERQgixAx06uaWnp2PSpEnIycnBpEmTkJaW1t4hEUIIsQMdNrndvn0bp0+fRnJyMgAgOTkZp0+fRllZWTtHRgghpL112AElJSUlCAgIgEgkAgCIRCL4+/ujpKQE3t7eZn2GPc8uYs+xARRfa1F8rUPxtY6l8dn792qswya3tuDl5dbeITTJx8e9vUMwieJrHYqvdSi+1rH3+NpCh+2WlMvluHHjBrRaLQBAq9WitLQUcrm8nSMjhBDS3jpscvPx8UFkZCR27doFANi1axciIyPN7pIkhBDiuDjGWIedHLGgoAALFy7EnTt30KlTJ2RmZqJ79+7tHRYhhJB21qGTGyGEEGJMh+2WJIQQQppCyY0QQojDoeRGCCHE4VByI4QQ4nAouRFCCHE49/QMJbZWXl6Ol19+GVeuXIFEIkHXrl2RkZEBb29vREREIDw8HDxf///GihUrEBERAQA4cOAAVqxYAa1Wi969e2PZsmVwcXGxSoyJiYmQSCSQSuvXrZs3bx4SEhKQl5eHtLQ0KJVKBAUFYeXKlfDx8QEAk3Vt6dq1a5g9e7budVVVFaqrq/Hzzz83Gbe148vMzEROTg6Kioqwc+dOhIeHA6hfsWLhwoWoqKiATCZDZmYmQkNDW1XXVvGZug4B2PRabOr4WXo+2/pcG4vP1HXYmtgtYepcWnqcbPX7bHWM2Ex5eTn76aefdK+XL1/OXnnlFcYYY+Hh4ay6utpgm+rqavbAAw+wS5cuMcYYe/XVV9n7779vtRiHDx/Ozp07p1em1WrZyJEj2dGjRxljjGVlZbGFCxc2W2dtS5cuZYsXL24yblvEd/ToUVZcXGyw/ylTprDt27czxhjbvn07mzJlSqvr2io+U9chY7a9Fps6fpacT2uc66bia6zxdWhp7JZq6lxaepza8/e5rVG3pA3JZDLEx8frXkdHR6O4uNjkNocPH0afPn10/72npqbiu+++s2aYBvLz8yGVShEbG6uLYc+ePc3WWZNKpcLOnTvx6KOPmnyfteOLjY01mPLN1IoVlta1ZXyWXIeAda5FY/GZYutrsbn4zL0OrRVfU+fS0uPUXr/P1kDdku1EEARs3LgRiYmJurIpU6ZAq9ViyJAhmDNnDiQSCUpKShAYGKh7T2BgIEpKSqwa27x588AYw4ABAzB37lyDGLy9vSEIAioqKkzWyWQyq8V44MABBAQEoHfv3k3G3alTp3aJz9SKFYwxi+qsNa2csesQsI9rsaXnsz3OtbHr0JLY2yK+xufS0uPUXr/P1kAtt3ayZMkSuLq6YvLkyQCAgwcPIjs7Gxs2bMDFixeRlZXVLnFt2LAB33zzDbZu3QrGGDIyMtoljuZs3bpV77/ljhK3vbn7OgTs41rsKOfz7usQaL/YjZ3Lexklt3aQmZmJwsJCvPvuu7qb9g1dH+7u7pgwYQJyc3N15Y27jIqLi6268kHDZ0skEkyaNAm5ubkGMZSVlYHnechkMpN11nLjxg0cPXoUKSkpJuNuKLd1fKZWrLC0zhqMXYcN8QPtey1acj5tfa6NXYeWxt5ad59LS49Te/y+WAslNxtbvXo18vPzkZWVBYlEAgCorKyEQqEAAGg0GuTk5CAyMhIAkJCQgJMnT+Ly5csAgE2bNmHs2LFWia22thZVVVUAAMYYdu/ejcjISPTp0wcKhQLHjh3TxTBmzBgAMFlnLdu2bcPQoUPh5eVlMu72is/UihWW1rU1Y9chYB/XoqXn09bn+u7rsDWxt4axc2npcWqP3xdroYmTbejChQtITk5GaGgonJ2dAQDBwcGYNm0a0tLSwHEcNBoNYmJi8Oqrr8LNrX4x1X//+99YuXIlBEFAZGQkli9fDldX1zaP7+rVq5gzZw60Wi0EQUBYWBhef/11+Pv7Izc3F+np6XrDg319fQHAZJ01JCUl4bXXXsOQIUOajdva8S1duhR79+7FrVu34OXlBZlMhm+//dbkihWW1rVVfO+++67R6zArKwvHjx+36bVoLL41a9ZYfD7b+lw3dX4Bw+sQsP212NTflKysLIuPk61/n62FkhshhBCHQ92ShBBCHA4lN0IIIQ6HkhshhBCHQ8mNEEKIw6HkRgghxOFQciN2YeHChXjnnXfaZd+MMbzyyiuIi4vDY489ZvP9FxcXIyYmRvfwtrWlpaW16awjERERKCwsbLPPs5Xs7Gw88cQT7R0GsRJKbsSoxMREDBo0CLW1tbqyzZs3Y8qUKe0YlXX88ssv+P7773Ho0CFs2bLF6vtLTEzEDz/8oHsdGBiI48eP6+aUtLaMjAy9JVtaYsqUKdi8eXMbR0RI26PkRpokCAI+++yz9g6jxVraAioqKkJQUJBVHoxvTKPRWPXz7zV0PIkplNxIk55++mmsX78ed+7cMai7du0aIiIi9P7ANP6vPjs7G6mpqXjrrbcQGxuLESNGIDc3F9nZ2Rg6dCgGDRqEbdu26X1meXk5nnzyScTExGDy5MkoKirS1RUUFODJJ5/EwIEDkZSUhN27d+vqFi5ciPT0dEyfPh3R0dE4cuSIQbw3btzAzJkzMXDgQIwaNQpff/01gPrW6Ouvv468vDzExMTgvffe09tOpVIhNjYW58+f15WVlZUhKioKt2/fBgD85z//wfjx4xEbG4vU1FScPXtW997ExESsXbsWKSkpiI6Oxty5c1FcXIyZM2ciJiYG//znPw2OZUVFBV555RUMHjwYcXFxePbZZ3WfZ2pfa9euRUJCAmJiYpCUlIQff/zR4Dg0HK+GLuAjR45gyJAhWL9+PQYNGoTBgwdj69atRrd75513cOzYMWRkZCAmJkZvQuAffvgBo0ePRmxsLBYvXozGc0Ns2bIFY8eORVxcHJ5++mm983q37du3Y/jw4YiPj0dWVpZeK/f999/H888/j3nz5qF///7Ytm0bTpw4gYkTJyI2NhaDBw9GRkYGVCqV7vMiIiLw2WefYcSIEYiPj0dmZiYEQdDbZ2ZmJuLi4pCYmIhDhw41GRvpYGy7fBzpKIYPH86+//57Nnv2bLZ69WrGGGNff/01mzx5MmOMsatXr7Lw8HCmVqt120yePJl9/fXXjDHGtm7dyiIjI9mWLVuYRqNhq1evZkOHDmVvvPEGUyqV7L///S+Ljo7WLYq5YMECFh0dzX7++WemVCrZkiVLWGpqKmOMsZqaGjZkyBC2ZcsWplar2alTp9jAgQPZhQsXdNv279+fHTt2jGm1WqZQKAy+z6RJk1h6ejpTKBTs9OnTLD4+nv3www+6WBv2ZczChQt1x4Axxr744gv21FNPMcYYO3XqFLv//vtZXl4e02g0LDs7mw0fPpwplUrdcRw3bhwrLi5mdXV1ese2wd3Hcvr06eyFF15gFRUVTKVSsSNHjjS7r4KCAjZkyBB2/fp13WcWFhYa/T4LFizQfZ+ffvqJRUZGsnfffZepVCp28OBBFhUVxSoqKoxu2/gcNwgPD2czZsxglZWVrKioiMXHx7NDhw4xxhjbt28fGzlyJLt48SJTq9UsKyuLTZw40ehnX7hwgUVHR7OjR48ypVLJli9fznr16qU7Vu+99x7r1asX27dvH9Nqtayuro6dPHmSHT9+nKnVanb16lU2ZswY9sknn+jFNnnyZFZeXs6KiorY6NGj9a7RXr16sa+++oppNBq2YcMG9uCDDzJBEIzGRzoWarkRk55//nl88cUXFi2YGRwcjEcffRQikQgPPfQQSkpKMHv2bEgkEgwePBgSiQRXrlzRvX/YsGGIi4uDRCLBSy+9hLy8PJSUlODgwYMICgrCo48+CrFYjF69eiEpKUlvEcURI0ZgwIAB4HkeUqlUL46SkhLk5uZi3rx5kEqliIyMxIQJE7Bjxw6zvkdKSopuPkEA2Llzp24m+K+++goTJ05Ev379IBKJ8PDDD8PJyQl5eXm690+ZMgVyuVw3958ppaWlOHz4MBYvXgxPT084OTlh4MCBze5LJBJBpVKhoKAAarUawcHB6NKli1nfTywWY/bs2XBycsLQoUPh6uqKS5cumbVtg+nTp6NTp04IDAxEfHy8rkW5adMmzJgxA2FhYRCLxZg5cybOnDljtPW2Z88eDB8+HLGxsZBIJHj++efBcZzee6KjozFy5EjwPA9nZ2f06dMH0dHREIvFCA4OxsSJE3H06FGD2GQyGQIDAzF16lTdxNRA/f3Oxx9/XHc8b968iVu3brXouxP7RIuVEpPCw8MxbNgwrF27FmFhYS3a1sfHR/dzwx/2xhOwSqVS1NTU6F537txZ97Obmxs8PT1RWlqKoqIinDhxQrc6MFB/X23cuHG616aWXiktLYWnpyfc3d11ZYGBgcjPzzfre8THx0OhUODXX3+Fj48Pzp49i5EjRwKoH+m4fft2fPHFF7r3q9VqlJaWmhXb3a5fvw5PT094enoa1Jna18CBA/Hqq6/i/fffx8WLFzF48GAsXLgQAQEBze5TJpNBLP7jT4GLi4veQCJz+Pn56W3fcF6Li4vx1ltvITMzU1fPGMONGzcQFBSk9xmlpaV614CLi4vBUiuN6wHg0qVLWL58OfLz81FXVwetVmuwcGjj4x8UFKR3bhpfjy4uLgDQ4u9O7BMlN9Ks559/Hg8//DCeeuopXVnD4AuFQqFLGjdv3mzVfq5fv677uaamBpWVlfD394dcLkdcXBw++eQTiz7X398flZWVqK6u1sXasFq2OUQiEcaMGYNdu3bB19cXw4YN032OXC7HzJkzMWvWrCa3v7v1YUrnzp1RWVmpWxWgseb2lZKSgpSUFFRXVyMtLQ2rVq3CypUrzd63NTTE3Pgfkab4+/vrtRgVCgUqKir03nP3sXzjjTfQq1cvvP3223B3d8e//vUv5OTk6L2npKQEPXr0AFCfbBtm6CeOjbolSbO6du2Khx56CJ9//rmuzNvbGwEBAdixYwe0Wi22bNmCq1evtmo/hw4dwrFjx6BSqfCPf/wD/fr1g1wux7Bhw3D58mVs374darUaarUaJ06cQEFBgVmfK5fLERMTg9WrV0OpVOLs2bPYsmWLWX9wG6SkpOC7777Dzp07kZycrCufMGECNm3ahF9//RWMMdTW1uLgwYOorq5u8rN8fX2bPFb+/v4YMmQIFi9ejMrKSqjVal03m6l9/fbbb/jxxx+hUqkgkUgglUr1FiBtK6ZiNyY1NRVr167FhQsXAABVVVX47rvvjL43KSkJBw4cQG5uLlQqFd5//329gSnG1NTUwM3NDW5ubigoKMDGjRsN3rNu3TpUVlaipKQEn332GR566CGz4ycdFyU3YpbZs2cbdNcsWbIE69atQ3x8PC5evIiYmJhW7SM5ORlZWVmIj4/HqVOndK0Od3d3rFu3Drt370ZCQgIGDx6MVatW6Y2Ka87q1atRVFSEhIQEPPfcc5gzZw4eeOABs7fv168fXFxcUFpaqrd+V9++fbFkyRJkZGQgLi4Oo0ePRnZ2tsnPmjFjBj766CPExsZi3bp1BvUrVqyAWCzG2LFj8cADD+DTTz9tdl8qlQpvv/024uPjMXjwYJSVlWHu3Llmfz9zTZ06FTk5OYiLi8PSpUubff+oUaMwbdo0zJ07F/3790dycjIOHz5s9L09evTAokWLMHfuXCQkJMDV1RXe3t56i6nebcGCBdi1axf69++PRYsWGU1cI0aMwCOPPII///nPGDZsWLs8qE9sj9ZzI4TYpZqaGsTFxSEnJwchISEWfUZERAT27t2Lrl27tnF0xN5Ry40QYjcOHDiAuro61NbWIjMzE+Hh4QgODm7vsEgHRMmNEGI39u/fj4SEBCQkJKCwsBCrV69u0YAcQhpQtyQhhBCHQy03QgghDoeSGyGEEIdDyY0QQojDoeRGCCHE4VByI4QQ4nAouRFCCHE4/w9fRegZKxKqcgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=df, x=\"N\", y=\"Max-Cut Size\", hue=\"Algorithm\").set(\n",
    "    title=\"Comparison of Max-Cut size solutions from Graph Neural Networks \\n versus Simulated Annealing for d-Regular Graphs (d = 5)\",\n",
    "    ylabel=\"Max-Cut Size\",\n",
    "    xlabel=\"Number of vertices in the graph\",\n",
    ")\n",
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    "The results put again SA at the top and GNNs at the bottom. The argument by Boettcher becomes stronger. Boettcher managed to beat the results by Schuetz et al. with a greedy algorithm. We also managed to beat them with a completely differnt baseline that was SA. This puts two algorithms ahead of GNN, while in the paper there are none."
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    "## Discussion\n",
    "\n",
    "We can discuss pros and cons of the GNN architecture in the following bullet points. It is important to highlight the achievements of Schuetz et al. But we can incorporate some criticism as did Boettcher.\n",
    "\n",
    "### Pros\n",
    "* Schuetz et al. proposed a new architecture that solves QUBO instances via unsupervised learning; this is remarkable; it is not straightforward how to approximate the solutions with gradient descent but the authors did it\n",
    "* Schuetz et al. solved large QUBO instances with up to $10^{6}$ nodes. We did not attempt to reproduce those specific results, but it is neat that the authors managed to train a  GNN on such large instances. Many solvers struggle with large instances, which was not the case for GNNs\n",
    "* There is room for improvement on the GNN architecture. We can improve the number of layers, the type of layer (e.g. use Graph Attention or other layers), and even tweak the smoothing of the cost function. So in terms of future work, Schuetz et al. is promising.\n",
    "\n",
    "### Cons\n",
    "\n",
    "* The current architecture of the GNN is not enough to solve the problems. The $k$-Hop neighbourhood for $k = 2$ and $k = 3$ does not capture the whole story and the GNN finds sub-optimal approximations.\n",
    "* The baselines in the paper were not adequate. This undermines the work by the authors. Even if GNNs are relevant, they are not the best. This needs to be clear.\n",
    "* Sometimes the GNN gets stuck on solutions with cost $0$. The authors handle them by running the GNN again with a different seed. This works, but is a sign that maybe the cost landscape for the problem is more challenging than they thought."
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    "# Maximum Independent Set instances\n",
    "\n",
    "After checking the results for the Max-Cut, let's jump into the MIS results of GNN vs Simulated Annealing on the next notebook.\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>"
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