TRA105_GPU_accelerated_Computational_Methods_using_Python_and_CUDA.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "gpuClass": "standard",
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ribesstefano/GPU-accelerated-Finite-Element-Method-using-Python-and-CUDA/blob/main/TRA105_GPU_accelerated_Computational_Methods_using_Python_and_CUDA.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Introduction\n",
        "\n",
        "This report document describes the work done within the course _TRA105 - GPU-accelerated Computational Methods using Python and CUDA_, held at Chalmers University.\n",
        "The main contributions are given by [Stefano Ribes](mailto:ribes.stefano@gmail.com), who developed all the high performance code, including this notebook, [Kim Louisa Auth](mailto:kim.auth@chalmers.se), who wrote an initial version of the FEM algorithm, and [Fredrik Larsson](mailto:Fredrik.Larsson@chalmers.se), who supervised the project.\n",
        "\n",
        "In the first part, we describe the FEM algorithm from a higher point of view. We then report a simple mechanism to generate \"large enough\" FEM problems. Then, we proceed to evaluate different solver strategies and select the best performing solver algorithm.\n",
        "At this point, we present three different implementation of the K-assembly step in the FEM algorithm. An additional K-assembly implementation based on cell coloring is proposed in the Appendix as a work in progress.\n",
        "In the end, we show an evaluation of the three different proposed K-assembly steps, before drawing our conclusions."
      ],
      "metadata": {
        "id": "eZKoAXVtSRs0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Code Setup\n",
        "\n",
        "This section installs the necessary dependencies and downloads the [Github repository](https://github.com/ribesstefano/GPU-accelerated-Finite-Element-Method-using-Python-and-CUDA).\n",
        "\n",
        "In order to run this notebook, please change the runtime type to GPU."
      ],
      "metadata": {
        "id": "tDSbPGTfaM-z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Methodology\n",
        "\n",
        "In this section, we cover our methodology, showing the implemented functions and algorithms to accelerate the FEM algorithm computation."
      ],
      "metadata": {
        "id": "aKv0ZM5sIUNh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install --upgrade matplotlib==3.4.0 -qqq"
      ],
      "metadata": {
        "id": "6ITn88TGS83V",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "91bada31-ce90-45a5-f405-fe9fadf80d92"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m10.3/10.3 MB\u001b[0m \u001b[31m39.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install pygmsh -qqq\n",
        "!pip install --upgrade scipy -qqq\n",
        "!pip install --upgrade jedi -qqq\n",
        "!pip install --upgrade --no-cache-dir gdown -qqq"
      ],
      "metadata": {
        "id": "VdEKRKx82JB4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b2dc91f7-3769-48ce-df98-6a018cd66b18"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/1.6 MB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[91m╸\u001b[0m \u001b[32m1.6/1.6 MB\u001b[0m \u001b[31m77.3 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.6/1.6 MB\u001b[0m \u001b[31m44.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "repository = 'GPU-accelerated-Finite-Element-Method-using-Python-and-CUDA'\n",
        "!git clone https://github.com/ribesstefano/{repository}.git"
      ],
      "metadata": {
        "id": "QRNzrZmM1ah9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a8693747-7b9f-48c9-fa79-306ff04746f7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cloning into 'GPU-accelerated-Finite-Element-Method-using-Python-and-CUDA'...\n",
            "remote: Enumerating objects: 186, done.\u001b[K\n",
            "remote: Counting objects: 100% (186/186), done.\u001b[K\n",
            "remote: Compressing objects: 100% (106/106), done.\u001b[K\n",
            "remote: Total 186 (delta 102), reused 137 (delta 73), pack-reused 0\u001b[K\n",
            "Receiving objects: 100% (186/186), 1.52 MiB | 7.89 MiB/s, done.\n",
            "Resolving deltas: 100% (102/102), done.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZnKn0w0Uugde"
      },
      "outputs": [],
      "source": [
        "%%capture\n",
        "%cd {repository}\n",
        "\n",
        "import pandas as pd\n",
        "import os\n",
        "import json\n",
        "\n",
        "from BasicFEM import *\n",
        "# Math and SciPy\n",
        "import math\n",
        "import scipy.sparse\n",
        "import scipy.sparse.linalg\n",
        "from scipy.sparse import coo_matrix\n",
        "# Profiling\n",
        "import time\n",
        "import timeit\n",
        "import cProfile\n",
        "import pstats\n",
        "# Plotting\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.tri as tri\n",
        "import seaborn as sns\n",
        "# Acceleration\n",
        "# !NUMBA_ENABLE_CUDASIM=1 # To run CUDA in simulation mode \n",
        "import numpy as np\n",
        "import numba as nb\n",
        "from numba import njit, prange\n",
        "from numba.typed import Dict\n",
        "from numba.core import types\n",
        "from numba.types import float32\n",
        "\n",
        "%cd .."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## FEM Problem Implementation\n",
        "\n",
        "In this section we define and visualize a simple FEM problem and its mesh, _i.e._, grid.\n",
        "\n",
        "The analyzed grid is defined as a mesh of 2D triangular cell elements, each referencing three nodes IDs. Each node is defined in a 2D coordinate system. We also limit our problem to two Degree of Freedom (DoF) per node.\n",
        "The length characteristic `lcar` of a grid can be adjusted in order to generate grids with different numbers of cells.\n",
        "\n",
        "We can create such a grid with the function `generate_grid`. The function exploits the Pygmsh Python library. The library  does show some limitations and bugs, and it's not ideal for generating large meshes. Nevertheless, it is a convenient way for checking the correctness of our implementation.\n",
        "\n",
        "A DoF handler object is instantiated given a grid and represents a useful wrapper of the FEM problem."
      ],
      "metadata": {
        "id": "VvrzNWWTaREK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "grid = generate_grid(lcar=0.5)\n",
        "dh = DofHandler(n_dofs_per_node=2, grid=grid)\n",
        "grid.plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "g72G2a2D29St",
        "outputId": "1c083c4f-b822-42a1-dbc6-7f3bdeae4f03"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The DoF handler allows us to define the _nodal forces_ vector $a$. The $y$ components of the top DoFs are set to $-0.1^{[2]}$.\n",
        "\n",
        "[2] Due to the limitations mentioned earlier, Pygmsh is unable to correctly identify all top DoFs. Because of that, the resulting nodal displacements will appear wrong in the top right corner. We haven't implemented a work-around for this issue, but we believe that such missing information would not make our implementation lose generality."
      ],
      "metadata": {
        "id": "EFtF2YubTRZ6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "top_dofs = dh.get_nodes_dofs(grid.nodesets['top'])\n",
        "a = np.zeros(dh.get_ndofs_total())\n",
        "a[top_dofs[:, 1]] = -0.1\n",
        "a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K_DgeKpZ32kf",
        "outputId": "cf40b78a-1569-46f2-9d13-251bb35c058c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. , -0.1,  0. , -0.1,  0. , -0.1,  0. , -0.1,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,\n",
              "        0. ,  0. ,  0. ,  0. ])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The DoF handler can also be used to extract the non-zero indexes of the global stiffness matrix $K$. Once the indexes are now, an empty Scipy sparse matrix can be instantiated."
      ],
      "metadata": {
        "id": "Glg5NWk9tXSR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def init_Kf(dh, as_dok=False):\n",
        "    if as_dok:\n",
        "        row_idx, col_idx, K_shape = dh.get_sparsity_pattern(return_shape=True)\n",
        "        K = scipy.sparse.dok_matrix(K_shape, dtype=np.float32)\n",
        "    else:\n",
        "        row_idx, col_idx = dh.get_sparsity_pattern()\n",
        "        K = scipy.sparse.csr_matrix((np.zeros(len(row_idx)), (row_idx, col_idx)))\n",
        "    f = np.zeros(len(row_idx))\n",
        "    return K, f\n",
        "\n",
        "K, f = init_Kf(dh)"
      ],
      "metadata": {
        "id": "9rxh0qQQ4Sqs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, we can wrap all the above information in a single function generating our selected FEM problem, accordingly."
      ],
      "metadata": {
        "id": "JLpI3KG5txaJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def generate_fem_problem(lcar=0.1, return_Kf=False, as_dok=False, grid=None,\n",
        "                         dh=None):\n",
        "    if grid is None and dh is None:\n",
        "        grid = generate_grid(lcar)\n",
        "    if dh is None:\n",
        "        dh = DofHandler(n_dofs_per_node=2, grid=grid)\n",
        "    # Prescribe a vector\n",
        "    a = np.zeros(dh.get_ndofs_total())\n",
        "    bottom_dofs = dh.get_nodes_dofs(dh.grid.nodesets['bottom'])\n",
        "    left_dofs = dh.get_nodes_dofs(dh.grid.nodesets['left'])\n",
        "    top_dofs = dh.get_nodes_dofs(dh.grid.nodesets['top'])\n",
        "    prescribed_dofs = (bottom_dofs[:, 1], left_dofs[:, 0], top_dofs[:, 1])\n",
        "    prescribed_dofs = np.concatenate(prescribed_dofs)\n",
        "    free_dofs = np.setdiff1d(range(dh.get_ndofs_total()), prescribed_dofs)\n",
        "    a[top_dofs[:, 1]] = -0.1\n",
        "    dofs = {\n",
        "        'bottom': bottom_dofs,\n",
        "        'left': left_dofs,\n",
        "        'top': top_dofs,\n",
        "        'prescribed': prescribed_dofs,\n",
        "        'free': free_dofs,\n",
        "    }\n",
        "    # Init weak form handler\n",
        "    weak_form = MomentumBalance(material=Elasticity(E=200e3, nu=0.3),\n",
        "                                thickness=1.0,\n",
        "                                element=CST())\n",
        "    if return_Kf:\n",
        "        # Init K and f components\n",
        "        K, f = init_Kf(dh, as_dok)\n",
        "        return K, f, a, weak_form, dh, dofs\n",
        "    else:\n",
        "        return a, weak_form, dh, dofs\n",
        "\n",
        "a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.5)"
      ],
      "metadata": {
        "id": "UD8er-uW8Br3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Generating Large Meshes\n",
        "\n",
        "The problem defined above is easy to investigate and therefore useful for inspecting the correctness of the different variations of our analysis.\n",
        "\n",
        "However, for testing our implementation for very large problems, _i.e._, when having a number of cells in the order of millions, we developed a function to generate random coordinates and then triangulate them via [Delaunay triangulation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Delaunay.html).\n",
        "\n",
        "In order to speed up some parts of the generation, we rely on Numba JIT compilation.\n",
        "To start with, we define as global variables the constant parameters of the FEM problem, _e.g._, the number of DoF per node. This will allow us for better handling of the array sizes within the jitted Numba functions."
      ],
      "metadata": {
        "id": "eVeW0uS5bm4G"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a, weak_form, dh, dofs = generate_fem_problem(lcar=0.5)\n",
        "\n",
        "n_dims = dh.grid.n_dim\n",
        "n_nodes_per_cell = dh.grid.get_num_nodes_per_cell()\n",
        "n_dofs_per_cell = dh.get_ndofs_per_cell()\n",
        "n_dofs_per_node = dh.n_dofs_per_node\n",
        "stiffness_shape = weak_form.material.stiffness.shape\n",
        "weights_shape = weak_form.element.weights.shape"
      ],
      "metadata": {
        "id": "3rod3w2p9YtZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, in order to populate the DoF information, we designed a custom Numba function `get_cells_dofs`. Note the use of `prange`: each cell can be processed independently, so we hint the compiler to parallelize over that dimension, _i.e._, axis."
      ],
      "metadata": {
        "id": "LK6SnrKtIzT7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@nb.jit(nopython=True, cache=True, parallel=True)\n",
        "def get_cells_dofs(cells, n_dofs_per_cell=n_dofs_per_cell, n_dofs=n_dofs_per_node):\n",
        "    n_cells = cells.shape[0]\n",
        "    dofs = np.empty((n_cells, n_dofs_per_cell), dtype=np.int32)\n",
        "    for i in prange(n_cells):\n",
        "        for j, nodeid in enumerate(cells[i]):\n",
        "                for d in range(n_dofs):\n",
        "                    dofs[i, j * n_dofs + d] = nodeid * n_dofs + d\n",
        "    return dofs"
      ],
      "metadata": {
        "id": "hryrOZPhtoKN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, the function is used to generate the FEM problems. The information about the grid, such as nodes coordinates, triangulation and sets, is stored on disk to be reused across multiple runs."
      ],
      "metadata": {
        "id": "C7vUHKEWJRRr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.spatial import Delaunay\n",
        "import os\n",
        "\n",
        "def generate_rand_fem_problem(n_nodes=int(3e3), filename='randgrid.npz'):\n",
        "    \"\"\"\n",
        "    If supplied, read filename containing compressed Numpy array.\n",
        "    \"\"\"\n",
        "    if os.path.isfile(filename):\n",
        "        print(f'File {filename} loaded.')\n",
        "        data = np.load(filename)\n",
        "        nodes = data['nodes']\n",
        "        cells = data['cells']\n",
        "        nodesets = {\n",
        "            'bottom': data['bottom'],\n",
        "            'left': data['left'],\n",
        "            'top': data['top'],\n",
        "        }\n",
        "    else:\n",
        "        nodes = np.random.rand(n_nodes, n_dims).astype(np.float32)\n",
        "        cells = Delaunay(nodes).simplices.astype(np.int32)\n",
        "        set_sz = int(0.2 * n_nodes)\n",
        "        nodesets = {\n",
        "            'bottom': np.random.choice(np.arange(n_nodes), size=set_sz).astype(np.int32),\n",
        "            'left': np.random.choice(np.arange(n_nodes), size=set_sz).astype(np.int32),\n",
        "            'top': np.random.choice(np.arange(n_nodes), size=set_sz).astype(np.int32),\n",
        "        }\n",
        "        np.savez_compressed(filename, nodes=nodes, cells=cells,\n",
        "                            bottom=nodesets['bottom'],\n",
        "                            left=nodesets['left'],\n",
        "                            top=nodesets['top'])\n",
        "    # Generate small mesh to be overwritten\n",
        "    grid = generate_grid(lcar=0.9)\n",
        "    dh = DofHandler(n_dofs_per_node=2, grid=grid)\n",
        "    # Update grid and dh with a much bigger random problem\n",
        "    dh.grid = Grid(nodes, cells, nodesets)\n",
        "    dh.cells_dofs = get_cells_dofs(dh.grid.cells)\n",
        "    # Generate the rest of the components\n",
        "    return generate_fem_problem(dh=dh)\n",
        "\n",
        "a, weak_form, dh, dofs_glob = generate_rand_fem_problem(n_nodes=int(3e3))"
      ],
      "metadata": {
        "id": "apzHdFRTvXXy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ac403e8d-714b-4ea7-b64d-8bdd38fa9e61"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "File randgrid.npz loaded.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Solver Evaluation\n",
        "\n",
        "We begin by identifying the best performing solver algorithm among the available ones provided by the SciPy and CuPy packages. For brevity, here we only report the final evaluation results, but the code implementation can be inspected at this [link](https://github.com/ribesstefano/GPU-accelerated-Finite-Element-Method-using-Python-and-CUDA/blob/main/test/profile_gpu_solvers.py)."
      ],
      "metadata": {
        "id": "qLR3c-tRxziz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import os\n",
        "\n",
        "df = pd.read_csv(os.path.join(repository, 'data', 'solver_evaluation_results.csv'))\n",
        "\n",
        "df['K dimensions'] = df['n_nodes'] * n_dofs_per_node\n",
        "df['Normalized Execution Time'] = df['Execution Time [s]']\n",
        "# NOTE: The cgs solver is just too much of an outsider, so we remove it\n",
        "df = df.drop(df[df['Solver'] == 'cgs'].index)\n",
        "\n",
        "for n_cells in df['Number of Cells'].unique():\n",
        "    selected_cells = df['Number of Cells'] == n_cells\n",
        "    exec_t = df.loc[selected_cells, 'Execution Time [s]']\n",
        "    max_t = df.loc[selected_cells, 'Execution Time [s]'].max()\n",
        "    df.loc[selected_cells, 'Normalized Execution Time'] /= max_t\n",
        "\n",
        "df_cpu = df[df['Device'] == 'Xeon']\n",
        "df_gpu = df[df['Device'] == 'GTX 1050']\n",
        "df"
      ],
      "metadata": {
        "id": "aiMfGABv3he9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "90e4cb8a-2bd2-4353-df8c-77747011d303"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Solver  lcar  n_nodes  Number of Cells  n_runs    Device  \\\n",
              "0    spsolve  0.50       29               38      20      Xeon   \n",
              "1       bicg  0.50       29               38      20      Xeon   \n",
              "2   bicgstab  0.50       29               38      20      Xeon   \n",
              "3         cg  0.50       29               38      20      Xeon   \n",
              "5      gmres  0.50       29               38      20      Xeon   \n",
              "6     lgmres  0.50       29               38      20      Xeon   \n",
              "7     minres  0.50       29               38      20      Xeon   \n",
              "8        qmr  0.50       29               38      20      Xeon   \n",
              "9    gcrotmk  0.50       29               38      20      Xeon   \n",
              "10     tfqmr  0.50       29               38      20      Xeon   \n",
              "11   spsolve  0.10      428              776      20      Xeon   \n",
              "12      bicg  0.10      428              776      20      Xeon   \n",
              "13  bicgstab  0.10      428              776      20      Xeon   \n",
              "14        cg  0.10      428              776      20      Xeon   \n",
              "16     gmres  0.10      428              776      20      Xeon   \n",
              "17    lgmres  0.10      428              776      20      Xeon   \n",
              "18    minres  0.10      428              776      20      Xeon   \n",
              "19       qmr  0.10      428              776      20      Xeon   \n",
              "20   gcrotmk  0.10      428              776      20      Xeon   \n",
              "21     tfqmr  0.10      428              776      20      Xeon   \n",
              "22   spsolve  0.05     1604             3052      20      Xeon   \n",
              "23      bicg  0.05     1604             3052      20      Xeon   \n",
              "24  bicgstab  0.05     1604             3052      20      Xeon   \n",
              "25        cg  0.05     1604             3052      20      Xeon   \n",
              "27     gmres  0.05     1604             3052      20      Xeon   \n",
              "28    lgmres  0.05     1604             3052      20      Xeon   \n",
              "29    minres  0.05     1604             3052      20      Xeon   \n",
              "30       qmr  0.05     1604             3052      20      Xeon   \n",
              "31   gcrotmk  0.05     1604             3052      20      Xeon   \n",
              "32     tfqmr  0.05     1604             3052      20      Xeon   \n",
              "33   spsolve  0.01    37836            74910      20      Xeon   \n",
              "34      bicg  0.01    37836            74910      20      Xeon   \n",
              "35  bicgstab  0.01    37836            74910      20      Xeon   \n",
              "36        cg  0.01    37836            74910      20      Xeon   \n",
              "38     gmres  0.01    37836            74910      20      Xeon   \n",
              "39    lgmres  0.01    37836            74910      20      Xeon   \n",
              "40    minres  0.01    37836            74910      20      Xeon   \n",
              "41       qmr  0.01    37836            74910      20      Xeon   \n",
              "42   gcrotmk  0.01    37836            74910      20      Xeon   \n",
              "43     tfqmr  0.01    37836            74910      20      Xeon   \n",
              "44   spsolve  0.50       29               38      10  GTX 1050   \n",
              "45        cg  0.50       29               38      10  GTX 1050   \n",
              "46     gmres  0.50       29               38      10  GTX 1050   \n",
              "47    minres  0.50       29               38      10  GTX 1050   \n",
              "48   spsolve  0.10      428              776      10  GTX 1050   \n",
              "49        cg  0.10      428              776      10  GTX 1050   \n",
              "50     gmres  0.10      428              776      10  GTX 1050   \n",
              "51    minres  0.10      428              776      10  GTX 1050   \n",
              "52   spsolve  0.05     1604             3052      10  GTX 1050   \n",
              "53        cg  0.05     1604             3052      10  GTX 1050   \n",
              "54     gmres  0.05     1604             3052      10  GTX 1050   \n",
              "55    minres  0.05     1604             3052      10  GTX 1050   \n",
              "56   spsolve  0.01    37836            74910      10  GTX 1050   \n",
              "57        cg  0.01    37836            74910      10  GTX 1050   \n",
              "58     gmres  0.01    37836            74910      10  GTX 1050   \n",
              "59    minres  0.01    37836            74910      10  GTX 1050   \n",
              "\n",
              "    Execution Time [s]  K dimensions  Normalized Execution Time  \n",
              "0               0.0001            58                   0.001739  \n",
              "1               0.0017            58                   0.029565  \n",
              "2               0.0012            58                   0.020870  \n",
              "3               0.0010            58                   0.017391  \n",
              "5               0.0013            58                   0.022609  \n",
              "6               0.0030            58                   0.052174  \n",
              "7               0.0013            58                   0.022609  \n",
              "8               0.0019            58                   0.033043  \n",
              "9               0.0021            58                   0.036522  \n",
              "10              0.0018            58                   0.031304  \n",
              "11              0.0017           856                   0.027732  \n",
              "12              0.0084           856                   0.137031  \n",
              "13              0.0060           856                   0.097879  \n",
              "14              0.0046           856                   0.075041  \n",
              "16              0.0110           856                   0.179445  \n",
              "17              0.0112           856                   0.182708  \n",
              "18              0.0033           856                   0.053834  \n",
              "19              0.0095           856                   0.154976  \n",
              "20              0.0097           856                   0.158238  \n",
              "21              0.0095           856                   0.154976  \n",
              "22              0.0110          3208                   0.063731  \n",
              "23              0.0299          3208                   0.173233  \n",
              "24              0.0213          3208                   0.123407  \n",
              "25              0.0149          3208                   0.086327  \n",
              "27              0.0671          3208                   0.388760  \n",
              "28              0.0264          3208                   0.152955  \n",
              "29              0.0063          3208                   0.036501  \n",
              "30              0.0313          3208                   0.181344  \n",
              "31              0.0286          3208                   0.165701  \n",
              "32              0.0382          3208                   0.221321  \n",
              "33              1.2001         75672                   0.042173  \n",
              "34              8.0172         75672                   0.281735  \n",
              "35              3.3653         75672                   0.118261  \n",
              "36              2.5096         75672                   0.088191  \n",
              "38             28.4565         75672                   1.000000  \n",
              "39              1.6956         75672                   0.059586  \n",
              "40              0.1698         75672                   0.005967  \n",
              "41              5.0055         75672                   0.175900  \n",
              "42              1.9213         75672                   0.067517  \n",
              "43             13.5836         75672                   0.477346  \n",
              "44              0.0575            58                   1.000000  \n",
              "45              0.0247            58                   0.429565  \n",
              "46              0.0143            58                   0.248696  \n",
              "47              0.0238            58                   0.413913  \n",
              "48              0.0161           856                   0.262643  \n",
              "49              0.0374           856                   0.610114  \n",
              "50              0.0613           856                   1.000000  \n",
              "51              0.0369           856                   0.601958  \n",
              "52              0.0706          3208                   0.409038  \n",
              "53              0.0660          3208                   0.382387  \n",
              "54              0.1726          3208                   1.000000  \n",
              "55              0.0457          3208                   0.264774  \n",
              "56              9.8619         75672                   0.346561  \n",
              "57              0.4239         75672                   0.014896  \n",
              "58              4.3324         75672                   0.152246  \n",
              "59              0.0720         75672                   0.002530  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-4b770c92-9f63-459d-b098-eb7c2bf15b4d\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Solver</th>\n",
              "      <th>lcar</th>\n",
              "      <th>n_nodes</th>\n",
              "      <th>Number of Cells</th>\n",
              "      <th>n_runs</th>\n",
              "      <th>Device</th>\n",
              "      <th>Execution Time [s]</th>\n",
              "      <th>K dimensions</th>\n",
              "      <th>Normalized Execution Time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0001</td>\n",
              "      <td>58</td>\n",
              "      <td>0.001739</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>bicg</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0017</td>\n",
              "      <td>58</td>\n",
              "      <td>0.029565</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>bicgstab</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0012</td>\n",
              "      <td>58</td>\n",
              "      <td>0.020870</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0010</td>\n",
              "      <td>58</td>\n",
              "      <td>0.017391</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0013</td>\n",
              "      <td>58</td>\n",
              "      <td>0.022609</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>lgmres</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0030</td>\n",
              "      <td>58</td>\n",
              "      <td>0.052174</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0013</td>\n",
              "      <td>58</td>\n",
              "      <td>0.022609</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>qmr</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0019</td>\n",
              "      <td>58</td>\n",
              "      <td>0.033043</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>gcrotmk</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0021</td>\n",
              "      <td>58</td>\n",
              "      <td>0.036522</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>tfqmr</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0018</td>\n",
              "      <td>58</td>\n",
              "      <td>0.031304</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0017</td>\n",
              "      <td>856</td>\n",
              "      <td>0.027732</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>bicg</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0084</td>\n",
              "      <td>856</td>\n",
              "      <td>0.137031</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>bicgstab</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0060</td>\n",
              "      <td>856</td>\n",
              "      <td>0.097879</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0046</td>\n",
              "      <td>856</td>\n",
              "      <td>0.075041</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0110</td>\n",
              "      <td>856</td>\n",
              "      <td>0.179445</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>lgmres</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0112</td>\n",
              "      <td>856</td>\n",
              "      <td>0.182708</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0033</td>\n",
              "      <td>856</td>\n",
              "      <td>0.053834</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>qmr</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0095</td>\n",
              "      <td>856</td>\n",
              "      <td>0.154976</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>gcrotmk</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0097</td>\n",
              "      <td>856</td>\n",
              "      <td>0.158238</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>tfqmr</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0095</td>\n",
              "      <td>856</td>\n",
              "      <td>0.154976</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0110</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.063731</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>bicg</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0299</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.173233</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>bicgstab</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0213</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.123407</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0149</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.086327</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0671</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.388760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>lgmres</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0264</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.152955</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0063</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.036501</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>qmr</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0313</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.181344</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>gcrotmk</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0286</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.165701</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>tfqmr</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.0382</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.221321</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>1.2001</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.042173</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>bicg</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>8.0172</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.281735</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>bicgstab</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>3.3653</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.118261</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>2.5096</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.088191</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>28.4565</td>\n",
              "      <td>75672</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>lgmres</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>1.6956</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.059586</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>0.1698</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.005967</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>qmr</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>5.0055</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.175900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>gcrotmk</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>1.9213</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.067517</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>tfqmr</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>20</td>\n",
              "      <td>Xeon</td>\n",
              "      <td>13.5836</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.477346</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0575</td>\n",
              "      <td>58</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0247</td>\n",
              "      <td>58</td>\n",
              "      <td>0.429565</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0143</td>\n",
              "      <td>58</td>\n",
              "      <td>0.248696</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.50</td>\n",
              "      <td>29</td>\n",
              "      <td>38</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0238</td>\n",
              "      <td>58</td>\n",
              "      <td>0.413913</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>48</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0161</td>\n",
              "      <td>856</td>\n",
              "      <td>0.262643</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0374</td>\n",
              "      <td>856</td>\n",
              "      <td>0.610114</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0613</td>\n",
              "      <td>856</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>51</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.10</td>\n",
              "      <td>428</td>\n",
              "      <td>776</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0369</td>\n",
              "      <td>856</td>\n",
              "      <td>0.601958</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>52</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0706</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.409038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>53</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0660</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.382387</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>54</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.1726</td>\n",
              "      <td>3208</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>55</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.05</td>\n",
              "      <td>1604</td>\n",
              "      <td>3052</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0457</td>\n",
              "      <td>3208</td>\n",
              "      <td>0.264774</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>56</th>\n",
              "      <td>spsolve</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>9.8619</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.346561</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>57</th>\n",
              "      <td>cg</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.4239</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.014896</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>58</th>\n",
              "      <td>gmres</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>4.3324</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.152246</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>59</th>\n",
              "      <td>minres</td>\n",
              "      <td>0.01</td>\n",
              "      <td>37836</td>\n",
              "      <td>74910</td>\n",
              "      <td>10</td>\n",
              "      <td>GTX 1050</td>\n",
              "      <td>0.0720</td>\n",
              "      <td>75672</td>\n",
              "      <td>0.002530</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-4b770c92-9f63-459d-b098-eb7c2bf15b4d')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-4b770c92-9f63-459d-b098-eb7c2bf15b4d button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-4b770c92-9f63-459d-b098-eb7c2bf15b4d');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In order to better visualize and compare different solvers' performance across different grid characteristic lenghts, the execution time as been normalized to the slowest recorded time.\n",
        "\n",
        "The following figure shows the solver algorithm performance running on a 8 cores Intel Xeon CPU processor."
      ],
      "metadata": {
        "id": "Ijla4IGGKjrr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.pyplot import figure\n",
        "\n",
        "figure(num=None, figsize=(10, 9), dpi=80, facecolor='w', edgecolor='r')\n",
        "\n",
        "ax = sns.barplot(data=df_cpu, y='Number of Cells',\n",
        "                 x='Normalized Execution Time', hue='Solver', orient='h')\n",
        "sns.move_legend(ax, 'upper left', bbox_to_anchor=(1, 1))\n",
        "\n",
        "for container in ax.containers:\n",
        "    ax.bar_label(container, padding=10)\n",
        "\n",
        "plt.grid(axis='x')\n",
        "plt.xlim([0, 1.1])\n",
        "plt.title(f'Normalized Execution Time of SciPy Sparse Linear Solvers on CPU')\n",
        "# plt.savefig(f'solvers_exec_time_cpu.png', bbox_inches='tight')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 625
        },
        "id": "5JKVCmzlVfUL",
        "outputId": "345e2be3-4e00-4243-b278-b3135988d3f9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x720 with 1 Axes>"
            ],
            "image/png": 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fZ9euXYwfP/6mZdWpU4d33nmHP/74g9zcXKKjo9myZYva81bmxve2paUlNjY26j3asWMHPXv2xM7ODisrK5577jkAo99DW1tbateubVTeqlWrWLJkCQ4ODnh7e/PDDz8Apc+quLgYrVarPquyXrWycz4IN75Hb3x/ln0r/vTTTxu9X86cOcPp06cBOHz4MP3796dp06ZYWVmp9+fvf3tu9zfhdu+PtLQ0GjZsaDRnomw41c3eh+PHj2fp0qVcv36dHTt2qMMdofTeZmZmqn8v69evj4uLCxYWFkbl/b3e77zzDr1792b8+PFYW1szbNiwm/YeVMbfCFtbW86fP09BQUGF6Td66aWXuHTpEhcuXODIkSNMmTJFTTM3N6+wV6uoqMjo74kQTxJpSIgq4erqyvjx4/nHP/5htL9sSMaNY6iLi4sxGAw4ODio+0xM7v+tu2rVKr788kuWLVvG+fPnuXTpEiEhIUZjxG/n9ddf58SJE/z000/UrFlT3d+kSRO6du1q9IE/JyeHa9eu0bRpU7RaLdnZ2Ubjfh/Usq9jx47F09OTevXqMW3aNKM6vfLKK0Z1ys3NVYfVODo6kpKSctPJkZaWlkZzPIqLi40++NzJM2nWrBkGg8FobkHZs77x+T5qbnfv/u5O38d3q127drz55pukpKSQnZ2No6Mj2dnZnD9//p7LvFGbNm3o0qULS5YsITw8nBdffPGWqxndyNTUlB49ejBs2DB1PH2ZG9/bly9f5vz582i1WgoLC+nXrx++vr4kJCSQm5urTny98fewovfWgAED+PXXXzl//jzvvPMOI0aMICEhgSZNmlCjRg3OnTtn9LyuXr3Kyy+/fA935e40adIEKG0s3Hj+K1euqL+Pw4YNo0WLFhw5coTc3Fx1KNHf//bc7d+5v78/mjVrRnZ2NtnZ2Wqeixcvkp2dfdP34eDBg7ly5Qq//vorixYtYujQoeoXHk2aNKF58+ZG13Xp0iWuXbtG586db1rv2rVr8+GHHxIXF8epU6cwMzMrN1SpTGX8jejTpw8mJiasXLnyno4v4+TkRGJiYrn9iYmJRl8aCPEkkYaEqDIffvghR44cUSeGQmmPQt++fZkyZQqZmZlcvXqV0NBQatSowYsvvvhAz5+Tk4OZmRm2trZoNBq2bdvGihUr7vj4jz76iI0bN/Lrr7+WW4I1MDCQQ4cOsWDBAq5cuaJ+O1g2afXpp5+mVatWvPXWW+Tn53PmzBlmz55939f0xRdfsGfPHlatWkVUVBTffvst69atA2DSpElERkaydu1aCgsLuX79OklJSfz6668A9OvXjwYNGjBp0iTOnz+PoigcO3aM1NRUADp06EB0dDRnz57l6tWrTJs2zejbuUaNGmFiYmI0Mf7vXnzxRczMzHj33Xe5evUqGRkZvPnmm/Tv31/9APYout29+7sH9T7+z3/+w3//+18uXrwIlH4ju2DBAlxcXGjYsCEdOnSgc+fOBAYGqt92Jycnc/z48fu61oULF7Js2TJCQkJumffNN99k79696nv8wIEDrFu3jmeffdYo3+zZs9W5BFOmTKFly5Z07tyZwsJCrl69SoMGDbC0tOTs2bMVLq/5dydPnuTnn3/m8uXLmJmZqR90TU1N6dq1K66urkycOFFt6GZnZxMVFcWVK1duWe61a9eMXvcyp6J58+YMHDiQV199Vf3dycvL45dfflGXGc3JycHKyop69epx8eJFo2+978bt3h8dO3bE1dWVyZMnk5ubS05ODq+++io6nQ5vb+8Ky6xZsyYjR47k888/JyoqyqhHavDgwRQVFTFjxgz1S5CsrKzbLjcbHR3N0aNHKS4upnbt2tSqVeumK3tVxt+IsknVb775JuHh4WrD+8yZM8yaNYtVq1bdUTkBAQH897//Zc2aNep795tvvuHIkSMVTtgW4kkgDQlRZaytrZk5c2a5b1OXL1+Oo6Mjnp6eaLVajh49ypYtW7C0tHyg5w8ICKBnz560b98eGxsbwsLC7moyXkREBGfPnsXZ2dlo9SYo/ce1e/duNm/eTIsWLahfvz59+vRR19c3MzPjp59+Ijk5GTs7O3r16mU0DOlWylZFuvF19uxZdu7cyYwZM4iMjMTGxgZnZ2cWL15MYGAgCQkJeHt7q5O6mzZtirW1NUOHDlU/7NSqVYutW7dy+fJl2rdvT7169RgxYoT6IeXNN9/Ey8uLtm3b0rp1a1q2bEnTpk3VetWqVYs5c+Ywfvx46tevz6RJk8rV3crKis2bNxMXF4dWq8XLy4uWLVvy3Xff3fF9rwq3u3cVeRDv43r16vHJJ5/QqlUr6tatS+fOnbGxsVGD12k0Gn788Ufs7Ox45plnsLS0pG/fvvc1hGfgwIFcu3YNKysrfH19b5t//Pjx2NnZUa9ePfz9/fH392fu3LlGecaNG8fzzz9P48aNSUhI4KeffsLMzIy6deuyaNEiZs+eTd26dXnhhRcYNmzYbc9ZWFjIxx9/rA4NmjJlCsuWLaNFixaYmpqyefNmateuzdNPP42lpSXu7u6sX7++wuGQZc6cOUOtWrWMXoGBgbe/YRX4/vvv8fLy4vnnn8fS0pLWrVvz7bffqj0OZUu2Wlpa0qlTJ1544YV7Os/t3h+mpqZs3LiRgoICWrZsSatWrSguLiY6OtpoyOffjR8/nq1bt9KsWTOjRqGlpSW7d+/GYDDQvn17rKys6Ny5M3/88cct65mcnMzAgQOpX78+TZs2JTMz86bxSyrrb8Q///lPli1bxurVq2nRogX16tWjZ8+edxUj5JlnnmHdunV8+eWX2NnZ4eDgQGRkJJs3b1aHXwnxpNEodzOOQwghxGPv6aefxs/Pj+nTp99XOSkpKTz11FMkJibKBy0hhHgMVV7UICGEENXOzz//zJEjR/jvf/9b1VURQgjxiJOGhBBCCKB0ouvVq1cJCwvDxsamqqsjhBDiESdDm4QQQgghhBB3TSZbCyGEEEIIIe6aNCSEEEIIIYQQd03mSPyPubk5jRs3rupqiHtUUFBQqRGZReWTZ1j9yTOs/uQZVm9PwvM7d+7cHUUpFw+HNCT+p379+mpAJ1H9bNq0iT59+lR1NcR9kGdY/ckzrP7kGVZvT8Lz02q1VV0FcQMZ2iSEEEIIIYS4a9KQEEIIIYQQQtw1aUgIIYQQQggh7prMkRBCCCGEENVeSUkJEh7twdBoNOrrVqQhIYQQQgghqq3CwkIMBgNFRUVVXZXHikajoX79+tja2mJiUvEgJmlICCGEEEKIastgMGBpaYm1tfVtv0EXd66oqIjMzExSU1N56qmnKswjDQkhhBBCCFEtlZSUUFRUhLW1NWZm8rH2QTI1NaVp06YkJiZSUlJSYa+ETLYWQgghhBDVUtmcCOmJqBxl9/Vmc0+kISGEEEIIIYS4a9KQEEIIIYQQ4g6tW7cOLy8vdDodbdq0oUePHpSUlNw0f0pKCvXr1394FXyIZDCZEEIIIYQQdyA9PZ3g4GAOHDhA8+bNATh48OBDHVpV1mi52UpKD1PV10AIIYQQQohqIDMzE1NTUxo2bKju8/T0RKPREBsbS+fOnXFzc6Njx478+eef5Y7/+OOPmTx5srp9+fJlGjZsyLlz5wCYO3cuHTt2xNPTE19fX1JTUwGYOXMmQ4YMoU+fPri6upKenl7JV3pnpEfif67foktKCCGEEEIINzc3unbtSvPmzXnuuefo3Lkzr7zyCo0aNWLw4MF8++239OnTh507dzJkyBCSkpKMjh89ejReXl785z//wcLCgrVr19K9e3caNWrE999/z8mTJ9m9ezempqYsX76cSZMm8d///heA3bt3c+jQIRo3blwVl14h6ZG4D4mJiXTu3BlnZ2e8vb05evRohfkiIiJo1aoVLVq0ICgoyChgys3SUlJS8PHxoV69euh0OqPylixZgk6nU182NjYMHjwYgOTkZHXcnqurK8OGDSM7O1s99rPPPsPV1ZV27doxaNAgLl26pKYNHToUe3t7NBqN0f78/Hyefvpp3N3dcXd3x9fXl5SUlPu7eUIIIYQQ1YyJiQlRUVHs2rULX19f/vzzT1xcXDh58iQmJib06dMHgK5du9K4cWP0er3R8c2aNcPDw4Po6GgAli5dSmBgIAAbNmxgy5Yt6ue4f//73xgMBvXYvn37PlKNCJCGxH0JCQkhODiYhIQEQkNDCQgIKJcnOTmZGTNmEBMTQ1JSEpmZmSxcuPC2aVZWVsyePZvvv/++XJmBgYHo9Xr11aRJE0aMGAGAvb09O3fuRK/Xc+TIEezt7Zk5cyYAmzdvZsmSJezevZtjx47h5eXF9OnT1XInTJhQ7g0PUKtWLbZs2UJcXBxxcXH06dOHf/zjH/d594QQQgghqqc2bdoQEhLChg0b6NSpE+vWrSuX52bzJsaOHcuSJUv466+/SEpKwtfXFyhdYvWf//yn+vkuPj6e+Ph49bi6detWzsXcB2lI3KOsrCxiY2MZOXIkAEOGDCEtLa1cF1ZkZCR+fn40adIEjUbDhAkT+OGHH26b1rBhQ7p27UqdOnVuWY+9e/eSlZWFn58fABYWFtSqVQuA69evk5+fr76R4+Li6Nq1K5aWlkBpy3b58uVqWb169cLW1rbcOUxMTNRjFEUhNzdX1msWQgghxBPnzJkzRnMfsrOzSU5ORqfTUVJSwubNmwHYtWsXGRkZ5UaVAAwcOJD9+/fzySefMHLkSDWQ3sCBAwkLC+PixYtAaWTpQ4cOVf5F3QeZI3GP0tLSsLOzUx++RqPBwcEBg8FAy5Yt1XwGg0Gd1Q/g6OiodlPdKu1ORUREMGrUKMzNzdV9hYWFdOzYkdTUVNzc3NTuMy8vLxYsWEBGRgaNGzdm5cqV5OXlcfHiRaNJQzfTq1cv4uPjadSoEZs2bbqregohhBBCVHfFxcV8+OGHJCcnU7t2bYqLixkzZgwDBgygadOmvP7660yZMoWaNWsSGRlJ3bp1OX/+vFEZFhYWvPTSSyxYsIDjx4+r+0eMGMGFCxfo3r27eq6xY8fi4eHxUK/xbkhDohrLz89n1apV7Nmzx2h/jRo10Ov1FBYW8tprrxEeHs7UqVPp3r07b7/9Nv369cPU1JRBgwYB3HFI+S1btlBSUsLHH3/Mxx9/zIIFCx74NQkhhBBCPKqaN29+0y9TO3TowK5du8rtd3R0NJp7CvDNN9/wzTfflMv7+uuv8/rrr5fbXzZM/VEjQ5vuUbNmzUhPT6e4uBgoHfJjMBhwcHAwyufg4KAu3QWlk6jL8twq7U6sXbsWFxcX2rVrV2F6jRo1CAwMNBq+NGnSJGJjY9m7dy8+Pj5otVqsrKzu+JwmJiYEBQUZlSmEEEIIIZ480pC4R7a2tnh6erJixQoAoqKi0Gq1RsOaoHTuRHR0NBkZGSiKQlhYGP7+/rdNuxMRERGMGzfOaF9qaipXrlwBSgOWrF27Fjc3NzW9bN3hK1eu8P777zN16tTbnicjI8No5afVq1cblSmEEEIIIZ48MrTpPoSHhxMQEMCcOXOwsrJiyZIlAIwfPx4/Pz/8/PxwcnJi1qxZdOnSBQAfHx9CQkIAbpl25coVnJ2dKSgoICcnB61Wy6hRo/jkk08AOHnyJHq9np9//tmoTocPH1ZXYiopKcHT05OvvvpKTe/duzclJSUUFhYyatQoo6AoL774InFxcQC4uLjQqlUrtm/fjsFgICQkhOvXr6MoCi1atFAbUEIIIYQQ4smkURRFqepKPAoaWltz8cKFqq6GuEebNm1S124W1ZM8w+pPnmH1J8+wensSnp9Wq+X06dPq9vXr10lISMDZ2RlTU9MqrNnj6Xb3V4Y2CSGEEEIIIe6aDG36HxMUDB+2v+fjHd6Pv30mIYQQQgghHhPSkKhCiYmJjBkzhvPnz1OvXj2WLl2Ki4tLuXwRERF8+umnlJSU0KNHDxYsWIC5uTlbt25l2rRpXL58GY1Gw4svvsinn36KiUlpR9Nnn33Gd999R0lJCa1bt2bJkiXUr18fKI174erqqnZTff3113Tr1g0oDa4yefJk9u/fj7m5Of379+fTTz+95XFnz54lMDCQlJQULCwsaNWqFWFhYTRq1Kiyb6MQQgghhBGvd5ZVSrkHPhtdKeXeLR8fH9544w0GDhxYpfWQoU1VKCQkhODgYBISEggNDSUgIKBcnuTkZGbMmEFMTAxJSUlkZmaycOFCABo0aMCqVas4duwYBw4cYNeuXSxbVvqLs3nzZpYsWcLu3bs5duwYXl5e6iTsMjExMWoY9rJGBKAGP0lISODo0aO88cYbtz3O1NSUGTNmcPLkSQ4fPoyTkxPvvPPOA7xbQgghhBDiUSINiSqSlZVFbGwsI0eOBEqXgk1LSyMpKckoX2RkJH5+fjRp0gSNRsOECRP44YcfAPDw8MDJyQmAmjVrotPpSElJASAuLo6uXbtiaWkJQN++fe8o9kNSUhKxsbG89dZb6r4mTZrc9rjGjRvTtWtXdfvpp59W6yKEEEII8aS4evUqw4cPp127dri7u9O7d2+2b9+Oq6sro0ePxtXVFS8vL/R6PVA6QqVLly64u7vTvn173nvvPQAuX77M2LFjcXV1xdXVlVmzZpU7V1paGra2thQWFqr7AgICmDdvHgD79++nR48edOjQAQ8PD9auXftAr1UaElUkLS0NOzs7Naq0RqPBwcEBg8FglM9gMNC8eXN129HRsVweKI31EBkZSb9+/QDw8vJiy5YtaoyKlStXkpeXx8WLF9Vjevbsibu7O2+99Rb5+fkAHDt2DK1Wy8SJE/Hy8qJ3794cOnTI6FwVHXej69evM3/+fAYMGHCPd0cIIYQQonr69ddfuXTpEseOHSMuLo5Vq1YBcPToUcaMGcORI0cIDQ3F398fRVGYP38+/fr1Iy4ujvj4ePXL3I8++oiCggIOHz7M3r172bBhA6tXrzY6V7NmzdDpdERHRwOljY/o6GhGjhzJpUuXCA4OZuXKlcTGxrJ582amTJnCmTNnHti1SkPiMZCbm0v//v2ZOnUqHTp0AKB79+68/fbb9OvXj06dOqlzFcoaLqmpqepwqHPnzqnDkIqLi9m3bx/+/v4cOHCAN998k379+lFUVHTL48ooisKkSZNo0KAB//jHPx7WLRBCCCGEeCS4u7tz/PhxJk2axOrVqzE3NwdKvwzu2bMnAC+99BIZGRmkpaXx7LPP8u233zJ9+nR+++03dT7rli1bCAoKwsTEhDp16jB69Gg2b95c7nyBgYFqLLO1a9fSo0cPrK2t2bVrF3/99RcvvPACOp2OXr16AaWxyB4UaUhUkWbNmpGenk5xcTFQ+gHcYDDg4OBglM/BwYHU1FR1OyUlxShPXl4evr6+DBgwwGg4EsCkSZOIjY1l7969+Pj4oNVqsbKyUssFqFOnDpMmTSImJkbd37RpU7p37w7ACy+8QGFhoVqHmx1X5vXXXyctLY3Vq1erk76FEEIIIZ4UTk5OHDt2DF9fX/78809cXV3Jzs4ul0+j0aDRaBgyZAh//vknrVu3VnsnKqLRaCrcP2jQIPbt20d6ejpLly4lMDAQKP1s6eLios5r1ev1GAwGevTo8cCuVT7pVRFbW1s8PT3VCNFRUVFotVpatmxplG/IkCFER0erQ5TCwsLw9/cHSruvfH198fX1VcfT3Sg9PR0ojZL9/vvvM3XqVKB0VaYrV64ApdGvV69ejYeHB1A6JMrKyorDhw8DsG/fPhRFoVmzZrc8DkobEUlJSaxfv54aNWo8sHslhBBCCFFdnD59Go1Gg5+fH3PnzkVRFNLS0khJSWHbtm1A6RzYxo0bo9VqSUxMpHHjxowePZp///vf7NmzB4BevXoRERGBoijk5+ezfPlyevfuXe58NWvWZNiwYcycOZNTp07h6+sLQOfOnUlOTmbLli1qXr1ebzSf4n7J8q9VKDw8nICAAObMmYOVlZXaLTV+/Hj8/Pzw8/PDycmJWbNm0aVLF6B0ua+QkBAA5s2bx759+8jPz2fdunUADBs2TF2dqXfv3pSUlFBYWMioUaOYPHkyACdOnCAkJASNRkNxcTGenp7qpByNRsN3331HUFAQV69excLCgqioKCwsLDh48OBNj/vzzz/5+uuvadOmDU8//TQATz31FOvXr39Id1MIIYQQourFx8fzz3/+E0VRKC4uZtSoUbi5ueHi4sLSpUt5/fXXqVGjBj/88AMajYbIyEhWrFhBjRo1KCkpISwsDIAZM2bw+uuv0759aZyzYcOG8dJLL1V4zsDAQDp27EhoaKi6RH+DBg3473//y9tvv82UKVMoKirCwcGBDRs2PLBr1SiKojyw0qoxG+uGHPxH03s+XgLSVa1NmzbRp0+fqq6GuA/yDKs/eYbVnzzD6u1JeH5arZbTp0+r29evXychIQFnZ2f1A/SjaPv27bzxxhvqSk3Vxe3urwxtEkIIIYQQQtw1aUj8TwnwcgOrO3o5vB9f7nU7iYmJdO7cGWdnZ7y9vTl69GiF+SIiImjVqhUtWrQgKChIXS1p69atdOzYkXbt2uHi4sLUqVMpKSlRj9u4cSNt2rShVatWDB48mNzcXDXtX//6F+3atUOn09GpUyf27dunpmVnZzNixAicnZ1xcXFh2rRpatry5ctxd3fH1dWVnj17Gi07W1BQwOTJk2nVqhXt27dX42EIIYQQQghjPj4+1a434k5IQ+Ihqcwo1pcvX2bcuHFs2LCBxMRE7O3t+eijj4DSSTULFixg37596PV6Jk+erM6VgJtHsT5x4gTvvPMOv/76K0eOHCEwMJCJEyeqx02bNg2NRkNCQgLx8fHMnTu3ku6cEEIIIYR4FElD4iGo7CjWv/zyCx4eHrRp0wYoXfa17DiNRkNRUZEaOO7SpUtotVrg1lGsjxw5gpubG3Z2dkBpZOxffvmFCxcukJ+fT0REBB9//LG6FNmdRL8WQgghhBCPD2lIPASVHcW6ouPKYlS4u7vz5ptv8tRTT6HVavniiy/4+uuvgVtHsXZ3d+fgwYMkJCQAsGLFChRFITU1lVOnTtGwYUPmzJlDhw4d6NatG7///vsDvGNCCCGEEOJRJw2JaqaiKNa3kpyczLp160hKSuL06dO8+eabDB8+HLh1FOtWrVoRFhbG6NGj6dChAxcuXKB+/fqYmZlRXFxMamoq7dq1IzY2lq+++orhw4eTmZlZ2ZcvhBBCCCEeEdKQeAgqO4p1RceV9YBERUXRvn177O3tgdJ1hv/8808KCwtvG8V66NCh7Nmzh9jYWCZOnMjVq1dp2bIlDg4OmJiYMGLECKB02NVTTz1FfLwsgSuEEEII8aSQgHQPwY1RrAMCAm4Zxbpr167MnDmTxo0b33EUa19fX1599VVOnDhBmzZtWLBggXqck5MTS5Ys4fLly9StW5eNGzfi7OxMjRo1jKJYu7m5GUWxhtLI2HZ2dly/fp3Q0FBeffVVateuTe3atenZsyebNm2ib9++JCcnk5ycTNu2bR/C3RRCCCGEuDXDh+0rpdw7jRum0WjIzs6mfv365dJ0Oh0xMTFYWlo+4No9fNKQeEgqM4q1paUlixYtYuDAgRQXF+Pq6sp3330HwKBBg9i/fz8dOnTAwsKCOnXq8P333wO3jmINpSs6paamUlBQwIsvvsicOXPU6wkLC2PcuHGEhoZiYmJCeHg4TZvee0A/IYQQQognweO0DKxEtv6fhtYNaTvzzr5R//O1Pyu5NuJuPQnRPB938gyrP3mG1Z88w+rtSXh+dxrZ+lHokZg+fTr//e9/yc/P54MPPlCHhN/YW3H8+HHeeOMN0tPTgdKVNydMmMCJEycIDAwkNzeX1q1bc/nyZV555ZUKwwdUpttFtpYeCSGEEEIIIR4wjUbDoUOH+Ouvv+jQoQNdunTB0dFRTS8uLmbAgAHMmjWLl19+GYDz588DMGrUKCZNmkRgYCDHjx/Hw8ODV155pSou45akIfE/JgrMWXvr2/HcHzseUm2EEEIIIUR1Nn78eKB0vuqzzz7LH3/8YdSQOHnyJNeuXVMbEQA2Njbk5uai1+sZPXo0AG3btqVr164Pte53SlZtqmSJiYl07twZZ2dnvL29OXr0aIX5IiIiaNWqFS1atCAoKIiioiKgdAUmHx8f6tWrh06nMzpmyZIl6HQ69WVjY8PgwYOB0mVfvby80Ol0uLq6MmzYMLKzs9VjP/vsM1xdXWnXrh2DBg3i0qVLatrQoUOxt7dHo9EY7c/Pz+fpp5/G3d0dd3d3fH191aB4QgghhBDi5sqC+D7sYyuTNCQqWUhICMHBwSQkJBAaGlrh2Lbk5GRmzJhBTEwMSUlJZGZmsnDhQgCsrKyYPXu2OkH6RoGBgej1evXVpEkTdfydvb09O3fuRK/Xc+TIEezt7Zk5cyYAmzdvZsmSJezevZtjx47h5eXF9OnT1XInTJhQ4USgWrVqsWXLFuLi4oiLi6NPnz784x//uP+bJIQQQgjxmClbWCclJYWYmBi6detmlN66dWtq167NDz/8oO47f/48VlZWuLu7s2LFCqC052Lnzp0Pr+J3QYY2VaKsrCxiY2P57bffgNLlXSdPnkxSUpLR0q+RkZH4+fnRpEkToPSD/Jw5c3j11Vdp2LAhXbt2Zfv27bc81969e8nKysLPzw9AXXkJSifK5OfnU7duXQDi4uLo2rWruuxY37598fHx4ZtvvgGgV69eFZ7DxMREPUZRFHJzcx/ZFrIQQgghnlx3Oim6Ml2/fh0PDw/y8/P56quvjIY1AZiZmfHjjz/y2muvMWfOHExMTJg0aRIhISEsW7aMsWPH8tlnn9GyZUu8vb0rXEq2qklDohKlpaWpgeGgtFvKwcEBg8Fg1JAwGAw0b95c3XZ0dMRgMNzVuSIiIhg1ahTm5ubqvsLCQjp27Ehqaipubm5ER0cD4OXlxYIFC8jIyKBx48asXLmSvLw8Ll68SMOGDW97rl69ehEfH0+jRo3YtGnTXdVTCCGEEOJxV7Yo6kcffXTTNCjtlSj7wvlGDg4O7N69G41GQ3JyMs888wxeXl6VV+F7JEObHgP5+fmsWrWKcePGGe2vUaMGer2ezMxM2rRpQ3h4OADdu3fn7bffpl+/fnTq1IlGjRoBqA2e29myZQvp6ekMHz6cjz/++MFejBBCCCHEE27Xrl3odDrc3d3p378/X3zxhRow+FEiDYlK1KxZM9LT0ykuLgZKW6AGgwEHBwejfA4ODqSmpqrbKSkp5fLcytq1a3FxcaFdu3YVpteoUYPAwECWL1+u7ps0aRKxsbHs3bsXHx8ftFotVlZWd3xOExMTgoKCjMoUQgghhBD3r3fv3uqc1CNHjhit7PQokYZEJbK1tcXT01OdLBMVFYVWqzUa1gSlcyeio6PJyMhAURTCwsLw9/e/4/NERESU641ITU3lypUrAJSUlLB27Vrc3NzU9LLAJ1euXOH9999n6tSptz1PRkaG0cpPq1evNipTCCGEEEI8OWSORCULDw8nICCAOXPmYGVlpc7gHz9+PH5+fvj5+eHk5MSsWbPo0qULAD4+PoSEhAClH/SdnZ0pKCggJycHrVbLqFGj+OSTT4DSmfx6vZ6ff/7Z6LyHDx9WV2IqKSnB09OTr776Sk3v3bs3JSUlFBYWMmrUKCZPnqymvfjii8TFxQHg4uJCq1at2L59OwaDgZCQEK5fv46iKLRo0UJtJAkhhBBCiCeLNCQqWevWrdm9e3e5/YsWLTLaDgoKIigoqFy+2rVrG4WCr6j8vLy8cvv79+9P//79b3pcfPzNVzP473//W+H+jh07cujQoZseJ4QQQgghnhwytEkIIYQQQghx16RH4n8UjQnx3m/fMk/8lJ/Unyf/5+bf9gshhBBCiKrT5esulVLun6/9eUf5NBoN2dnZFcZ+0Ol0xMTEqLG5HpQvv/wSf39/NS7ZrQQEBKDT6XjjjTfu65zSI/EQJSYm0rlzZ5ydnfH29ubo0aMV5ouIiKBVq1a0aNGCoKAgioqKANi6dSsdO3akXbt2uLi4MHXqVEpKSoDSoUrPPvssbdq0wdXVlbFjx3L16lW1zOzsbEaMGIGzszMuLi5MmzZNTdu7dy/u7u44OzvTo0cPzpw5o6Z99913tG/fHp1Oh4eHhzoX48KFC+h0OvXl7OyMmZkZFy9efOD3TQghhBDicaHX6x94IwJKGxIZGRkPvNxbkYbEQxQSEkJwcDAJCQmEhoYSEBBQLk9ycjIzZswgJiaGpKQkMjMzWbhwIQANGjRg1apVHDt2jAMHDrBr1y6WLVsGQM2aNZk/fz4nTpwgLi6O/Px8/vWvf6nljh07Fg8PDxISEjh69KjaAi0pKWHEiBF8+eWXJCQk0LdvXzXt4sWLvPbaa2zevBm9Xs/XX3+t1tna2hq9Xq++goODeeGFF+4ooJ0QQgghxONu7ty5eHh44OzszMqVK9X9Go2GS5cuAXD8+HH69OmDm5sbbm5uhIWFAXDixAmeeeYZXFxcGDx4ML1792bp0qVA6Tzbdu3aodPpaN++PXv37uXDDz/k7NmzDB8+HJ1Oh16v5/fff+eZZ57Bw8MDFxcXIiIijOp3+PBh9QvuMWPGGH0BfaekIfGQZGVlERsby8iRI4HSJV/T0tJISkoyyhcZGYmfnx9NmjRBo9EwYcIEfvjhBwA8PDxwcnICShsOOp2OlJQUAFq1aqUuxWpqaoq3t7ealpSURGxsLG+99ZZ6nrJurwMHDmBmZkb37t2B0sbOTz/9xLVr1ygpKUFRFHUy96VLl9BqtRVeX0VL0AohhBBCPKk0Gg2HDh3i119/5bXXXlM/l5UpLi5mwIABBAQEcPjwYQ4fPszQoUMBGDVqFMHBwRw9epSPP/6YP/74Qz1uypQp/P777+j1eg4ePIiLiwvvv/8+9vb2rF69Gr1ej06nw9PTk507d3Lo0CFiYmL48MMPjRbw2bt3L5s2beL48eNcvHiRL7744q6vURoSD0laWhp2dnZq9GiNRoODgwMGg8Eon8FgoHnz5uq2o6NjuTxQGtMhMjKSfv36lUvLz89n0aJFDBgwAIBjx46h1WqZOHEiXl5e9O7dW1196e/ns7S0xMrKirNnz2JjY0NYWBienp40b96csWPHqq3hG+3atYvs7OwK6yKEEEII8SQaP348AE5OTjz77LNGjQEoXcL/2rVrRsHmbGxsyM3NRa/XM3r0aADatm1L165d1Tw9e/Zk1KhRzJs3j+TkZOrWrVvh+S9cuMCwYcNwdXWlR48eXLhwgSNHjqjpL730EpaWlpiamjJu3Di2bNly19coDYlqKDc3l/79+zN16lQ6dOhglFZYWMjw4cPp3bs3gwYNAkpbvPv27cPf358DBw7w5ptv0q9fP3Xuxc3k5OQwb9489u3bR2pqKhEREQwaNIjCwkKjfBEREYwePVptJAkhhBBCCGMajeaBHBsVFcWnn35KUVERffv2ZdWqVRUeM2HCBLp27Up8fDx6vR5nZ2euXbv2QOsnDYmHpFmzZqSnp1NcXAyAoigYDAYcHByM8jk4OJCamqpup6SkGOXJy8vD19eXAQMGGA1VAigqKmL48OHY2dkxb948ozKbNm2qDl964YUXKCwsJDU1tdz58vLyyMnJwd7ens2bN1O/fn3atm0LlMamyM3NNcp/+fJl1qxZw9ixY+/3FgkhhBBCPDbKghCnpKQQExNDt27djNJbt25N7dq11SHsAOfPn8fKygp3d3c16O/JkyfZuXMnUPrl8KlTp+jQoQNvv/02Q4cOZd++fQBYWVmRk5OjlpWdnU3z5s3RaDT88ccfarDhMpGRkVy+fJnr16+zZMkSevXqddfXKA2Jh8TW1hZPT0/1TREVFYVWq6Vly5ZG+YYMGUJ0dDQZGRkoikJYWBj+/v5A6Yd2X19ffH19ee+994yOKy4uxt/fn4YNG7Jw4UKjVqWXlxdWVlYcPnwYgH379qEoCs2aNcPLy4uioiK2bdsGlEbi7t+/PzVr1sTJyQm9Xq+uALB7926Ki4tp1qyZWvbq1atxd3enTZs2D/iOCSGEEEJUX9evX8fDw4PevXvz1Vdf4ejoaJRuZmbGjz/+yJIlS2jfvj3u7u5ERUUBsGzZMv7v//4PV1dXQkND8fb2pn79+ly/fp2xY8fi6uqKTqfjwIED6hfLr7/+OkFBQepk608//ZRp06ah0+lYvHgxTz/9tNH5vb296dOnD23btqV+/fr3tBRstR2L0rt3bzIyMjAxMcHS0pKvvvpKXZ70vffeo6SkhOLiYt555x3GjBlT1dUFSj+kBwQEMGfOHKysrNSW6vjx4/Hz88PPzw8nJydmzZpFly6l6x/7+PgQEhICoA4zys/PZ926dQAMGzaM6dOns3r1atatW4ebmxseHh4AdOnShW+++QaNRsN3331HUFAQV69excLCgqioKCwsLABYsWIFISEhXLt2DXt7e5YvXw6Ap6cn06dPp0ePHpibm2NmZsaaNWuoWbOmek0REREVRuQWQgghhKgqdxrvobIoigLARx99dNM0KO2V+O2338rlcXBwYPfu3Wg0GpKTk3nmmWfw8vLCwsKi3FyLMuPHj1fnZZRJTEysMG9Fc17vhUa58WqqkUuXLqlBPtavX8/MmTPR6/VYW1uzfft23NzcSElJoU2bNpw7d+626/VaW9swK2DJHZ9fAtI9WjZt2kSfPn2quhriPsgzrP7kGVZ/8gyrtyfh+Wm1WqOVh65fv05CQgLOzs6YmppWYc0erN9++4133nkHKL3G6dOnG03Kflhud3+rbY/EjZECc3Jy1KE8N67Nm5ubi7W1tfrNuxBCCCGEEI+63r1707t376quxm1V24YEwOjRo9Wx/T///DMajYbVq1czePBg6tSpQ3Z2NuvWraNGjRrljv3888/5/PPP1e1rV6+Qk/ndHZ/745F3nvdmpq+IvO8yhBBCCCGEqArVerL1smXLSEtLY/bs2YSGhlJcXMzs2bNZt24dqamp/P7774waNYrz58+XO/att97i9OnT6qtmrZoVnOHRk5iYqEYh9Pb25ujRoxXmi4iIoFWrVrRo0YKgoCB1qdft27dTq1YtdDqd+iqLZLh161Y6duxIu3btcHFxYerUqZSUlAClE7379OmDjY2NUW8QlHal3lievb09np6eQGlMi6effhp3d3fc3d3x9fU1CsiyfPly3N3dcXV1pWfPnhXGzBBCCCGEEI+eat2QKDNmzBi2bdvGgQMHOHv2LM8++yxQOhtdq9WqwdceByEhIQQHB5OQkEBoaCgBAQHl8iQnJzNjxgxiYmJISkoiMzOThQsXqumtW7dGr9err1q1agHQoEEDVq1axbFjxzhw4AC7du1i2bJlAJibmxMaGlphsJI+ffoYlefp6cmIESMAqFWrFlu2bCEuLo64uDj69OnDP/7xD6A0/Ps777zDr7/+ypEjRwgMDGTixIkP+pYJIYQQQohKUC0bEpcuXeLs2bPq9oYNG7C2tsbR0ZH09HSOHz8OQFJSEqdOnaJ169ZVVdUHKisri9jYWEaOHAmULhWblpZGUlKSUb7IyEj8/Pxo0qQJGo2GCRMmGK1RfDMeHh44OTkBULNmTXQ6ndp7YGFhQY8ePcr1Rvzd2bNn1Z4gQF1VC0pXKcjNzVXnsxw5cgQ3Nzfs7OwA6Nu3L7/88gsXLly4sxsihBBCCCGqTLWcI5GTk8OwYcO4evUqJiYmNGrUiI0bN9K4cWMWLlzISy+9hImJCSUlJcyfP79c0LfqKi0tDTs7OzWCtEajwcHBAYPBYBSPwmAw0Lx5c3Xb0dHRaMjQqVOn8PT0xNTUlMDAQCZNmlTuXBkZGURGRrJx48a7quPSpUvp27cvtra2Rvt79epFfHw8jRo1YtOmTQC4u7tz8OBBdTWAFStWoCgKqampWFtb39V5hRBCCCHEw1UtGxLNmzdXo/j93csvv1wly2NVF56enpw+fZp69epx+vRp+vbti42NDS+99JKaJzc3l/79+zN16lQ6dOhwx2UrisLixYv56quvyqVt2bKFkpISPv74Yz7++GMWLFhAq1atCAsLY/To0RQXF/Piiy9Sv359taEkhBBCCHEvdjz7XKWU+9wfOyql3OqqWg5telI1a9aM9PR0iouLgdIP7gaDoVyPi4ODA6mpqep2SkqKmsfKyop69eoBpWsxv/zyy8TExKh58/Ly8PX1ZcCAAWqkxDu1Y8cOrl27dtM1rE1MTAgKClID3gEMHTqUPXv2EBsby8SJE7l69Wq5aN9CCCGEEOLRIw2JasTW1hZPT09WrFgBQFRUFFqtttwH7yFDhhAdHU1GRgaKohAWFoa/vz8A6enp6kpMeXl5bNy4UY2EffnyZXx9ffH19eW999676/pFREQQEBBgFLAkIyOD7OxsdXv16tW4ubmp2+np6UBpwJPQ0FBeffVVateufdfnFkIIIYR4VOzevZuuXbvi7u6Om5sbP/74I7t27UKn09G+fXvGjh2Lu7s727dvr+qq3hcZQ1LNhIeHExAQwJw5c7CysmLJktJo3OPHj8fPzw8/Pz+cnJyYNWsWXbp0AcDHx4eQkBCgtPHxf//3f5iZmVFcXMywYcMIDAwEYN68eezbt4/8/HzWrVsHwLBhw5g+fToAbm5unDt3jtzcXLRaLd27d1d7F3Jycli3bh3x8fFG9TUYDISEhHD9+nUURaFFixZqQwhg7NixpKamUlBQwIsvvsicOXMq8e4JIYQQQlSuixcvMnDgQCIjI+nWrRslJSWcP38eLy8vli1bRvfu3dm2bZv6Ga46k4ZENdO6dWt2795dbv+iRYuMtoOCgggKCiqXb/LkyUyePLnCsqdPn642Gipy+PDhm6bVq1eP/Pz8cvs7dux4y+V3f/nll5umCSGEEEJUN7t376Z169Z069YNKB3anZGRgZmZGd27dwege/futGjRoiqr+UDI0CYhhBBCCCEesrLl8Ksz6ZH4Hw0mDG5bfhnUm2k7vUcl1kYIIYQQQlRHnTt3JjExkZiYGHVoU+PGjSkqKmLHjh0899xz7Nixo1wcsOpIGhIPUWJiImPGjOH8+fPUq1ePpUuX4uLiUi5fREQEn376KSUlJfTo0YMFCxZgbm7O1q1bmTZtGpcvX0aj0fDiiy/y6aefYmJiQnx8PK+++ipZWVmYmZnRsWNHvvnmGzVqdXZ2NpMnT2b//v2Ym5vTv39/Pv30UwD27t1LcHAwV69eRavVsnz5cpo2bQrAd999x9y5czE1NUWj0fDxxx/Tt29fLly4QM+ePdU6X7lyhb/++ousrCwaNmz4EO6mEEIIIUTFqnKZ1gYNGrB+/XqmTJlCXl4eJiYmfPTRR6xatYpXX32VkpISvLy8aN269W0D/T7qZGjTQxQSEkJwcDAJCQmEhoYSEBBQLk9ycjIzZswgJiaGpKQkMjMzWbhwIVD6xly1ahXHjh3jwIED7Nq1i2XLlgGlkajnz5/PiRMniIuLIz8/n3/9619quWPHjsXDw4OEhASOHj3KG2+8AUBJSQkjRozgyy+/JCEhgb59+6ppFy9e5LXXXmPz5s3o9Xq+/vprtc7W1tbo9Xr1FRwczAsvvCCNCCGEEEI88Tp16sSff/7J4cOH0ev19O/fH3d3d+Li4tQvf3NycnB2dq7qqt4XaUg8JFlZWcTGxjJy5EigdInWtLS0ct1akZGR+Pn50aRJEzQaDRMmTOCHH34AwMPDAycnJ6C04aDT6UhJSQGgVatW6rKqpqameHt7q2lJSUnExsYaxYVo0qQJAAcOHDCa/BMSEsJPP/3EtWvXKCkpQVEU8vLyALh06RJarbbC64uIiGDcuHH3e5uEEEIIIR5LUVFR6nKwISEhLF++vNoveS9Dmx6StLQ07Ozs1KjNGo0GBwcHDAaDURwIg8FA8+bN1W1HR0cMBkO58jIyMoiMjGTjxo3l0vLz81m0aBGffPIJAMeOHUOr1TJx4kRiY2OxtrbmX//6Fx4eHuXOZ2lpiZWVFWfPnsXJyYmwsDA8PT1p2LAhV69eZcuWLeXOt2vXLrKzs+nXr9+93yAhhBBCiMdYQEBAhaNRqjPpkaiGcnNz6d+/P1OnTqVDhw5GaYWFhQwfPpzevXszaNAgAIqLi9m3bx/+/v4cOHCAN998k379+lFUVHTL8+Tk5KixJVJTU4mIiGDQoEEUFhYa5YuIiGD06NFqI0kIIYQQQjz+pCHxkDRr1oz09HSKi4sBUBQFg8GAg4ODUT4HBwdSU1PV7ZSUFKM8eXl5+Pr6MmDAAKOhSgBFRUUMHz4cOzs75s2bZ1Rm06ZN1eFLL7zwAoWFhaSmppY7X15eHjk5Odjb27N582bq169P27ZtAejfvz+5ublG+S9fvsyaNWsYO3bs/d4iIYQQQghRjUhD4iGxtbXF09NTjeocFRWFVqs1GtYEpXMnoqOjycjIQFEUwsLC8Pf3B0o/tPv6+uLr68t7771ndFxxcTH+/v40bNiQhQsXGq1N7OXlhZWVlRpQbt++fSiKQrNmzfDy8qKoqIht27YBpZGz+/fvT82aNXFyckKv15ORkQGUBlgpLi6mWbNmatmrV6/G3d2dNm3aPOA7JoQQQgghHmUyFuUhCg8PJyAggDlz5mBlZaWGRh8/fjx+fn74+fnh5OTErFmz6NKlCwA+Pj6EhIQAqMOM8vPzWbduHQDDhg1j+vTprF69mnXr1uHm5oaHhwcAXbp04ZtvvkGj0fDdd98RFBTE1atXsbCwICoqCgsLCwBWrFhBSEgI165dw97enuXLlwPg6enJ9OnT6dGjB+bm5piZmbFmzRpq1qypXlNERESFEbSFEEIIIcTjTaMoilLVlXgU2FjbEPPWmjvOLwHpHi2bNm2iT58+VV0NcR/kGVZ/8gyrP3mG1duT8Py0Wi2nT59Wt69fv05CQgLOzs6Ympqq++dP+alSzj/5P/0rpdxH1c3ubxkZ2iSEEEIIIcQjrGyO7aNGhjb9j4LC6qI/7vyAmRXnnTlz5oOpkBBCCCGEqJZ+/PFHpk2bRo0aNfD19SUiIoLY2Fh8fHwYOXIkW7duJS0tjenTp2NhYcHChQtJT0/n008/VefGajQa3n//fX7++Wd8fHx4//33eeutt4iLi+PatWt06tSJ+fPnU6NGDWbPns3KlSvVYes//vij0fL+lUV6JB4BiYmJdO7cGWdnZ7y9vTl69GiF+SIiImjVqhUtWrQgKChIXb519+7d6HQ6dDodLi4uhISEUFBQcNu0W5VZRlEUevToYRTCPTk5GS8vL3Q6Ha6urgwbNozs7GygdJUpU1NT9Zw6nY5Tp049yNslhBBCCPHIysrKYuzYsaxfv564uDjatGnDhQsX1PT8/Hx27drFtm3bePPNNzlz5gy7d+9m7dq1vPbaa0ZlmZqasn//fj777DOmTJlCt27d2LdvH3FxcZSUlDBv3jyys7OZO3cuBw8eRK/Xs2vXLho3bvxQrlUaEo+AkJAQgoODSUhIIDQ0tMJgJcnJycyYMYOYmBiSkpLIzMxk4cKFALi7u7N//370ej3x8fFkZWWxYMGC26bdqswyX3zxBS1atDDaZ29vz86dO9Hr9Rw5cgR7e3ujnhhLS0v0er36+vvxQgghhBCPqz179uDm5qauaDlmzBhq1Kihpg8fPhyAli1bUrNmTYYOHQpAhw4duHjxIpcuXVLz3ri8/oYNG/jss8/Q6XR4eHion9+srKxo1aoVI0eOJDw8nIsXLxotjFOZpCFRxbKysoiNjWXkyJFA6fKvaWlpJCUlGeWLjIzEz8+PJk2aoNFomDBhAj/88AMAtWvXxtzcHCgNSHf16lV1+ddbpd2qTICjR4+yYcMGpk2bZlQXCwsLatWqBZROwsnPzzdablYIIYQQQlTsxg/5pqam6rZGo0Gj0RjNh6hbt676s6IoREVFqV/Unjx5kvDwcExNTdmzZw9vvPEGWVlZdOrUiZiYmIdyLdKQqGJpaWnY2dmpUaE1Gg0ODg4YDAajfAaDwWism6Ojo1GelJQU3N3dsbGxoV69ekyaNOm2abcqs6ioiKCgIPUN+neFhYXodDpsbGxITExk1qxZalp+fj7e3t54enry4Ycfcv369fu5RUIIIYQQ1UanTp04fPgwJ0+eBEqX2S8sLLzvcgcOHMi//vUvtaGRnZ1NUlISeXl5ZGZm0q1bN2bMmEHXrl05dOjQfZ/vTkhD4jHh6OhIXFwcGRkZFBQUqHEmbpd2M7NmzWLw4MFqVOu/q1GjBnq9nszMTNq0aUN4eDgAdnZ2nDlzhv3797NlyxZiYmL4z3/+82AuUgghhBDiEWdra8uiRYsYOHAgOp2O+Ph46tatazTf9F588cUX1KpVC51Oh5ubGz179iQlJYWcnBwGDx5M+/btcXNzo6ioiDFjxjyYi7kNWbWpijVr1oz09HSKi4sxMzNDURQMBgMODg5G+RwcHIwmLaekpJTLA6VdYP7+/qxcuVKd9X+ztFuVuWPHDgwGA/Pnz6e4uJjc3FwcHR3Zv38/jRo1Uo+pUaMGgYGBBAUFMXXqVCwsLLC1tQWgYcOGjB07lu+//56pU6fe/80SQgghhLgDVR3voVevXgwaNAgonduwceNG6tevT0pKilG+8+fPG23fOKzp76He6taty/z58ys83549ex5Are+e9EhUMVtbWzw9PVmxYgUAUVFRaLVaWrZsaZRvyJAhREdHk5GRgaIohIWFqQ2FpKQkdbWlwsJC1q9fj5ub223TblVmTEwMqamppKSksHPnTqysrEhJSaFRo0akpqZy5coVAEpKSli7dq1aZlZWlnq+st6PskjbQgghhBBPgq+//hp3d3dcXV3597//zcqVK6u6SpVCGhKPgPDwcMLDw3F2dubTTz9lyZIlAIwfP57o6GgAnJycmDVrFl26dKFly5Y0atSIkJAQALZu3YqHhwfu7u54eHjQuHFjZsyYcdu0W5V5K4cPH6ZTp064ubnh5ubGuXPn+OqrrwDYuXOnej5PT0+aNGnC9OnTH/g9E0IIIYR4VL377rvExcVx5MgRdu3ahaenZ1VXqVJolL/3mzyhrK2ty63dey8kIF3V2LRpE3369Knqaoj7IM+w+pNnWP3JM6zenoTnp9VqOX36tLp9/fp1EhIScHZ2rnBxGHF/bnd/pUdCCCGEEEIIcddksvX/aDQK7Vx+vu9y1qwtLeOlYfvuuywhhBBCCCEeVdIj8QhJTEykc+fOODs74+3tzdGjRyvMFxERQatWrWjRogVBQUHq5Obdu3ej0+nQ6XS4uLgQEhJCQUGBelx8fDw+Pj60bduWtm3bqsvAbt++XV1OrOx19epVoHSORceOHWnXrh0uLi5MnTqVkpISAC5fvkyfPn2wsbEpt6TZpk2bjMqzt7d/bMcHCiGEEEI8iaQh8QgJCQkhODiYhIQEQkNDCQgIKJcnOTmZGTNmqGHRMzMzWbhwIQDu7u7s378fvV5PfHw8WVlZLFiwAIArV64wYMAAZs+ezfHjxzly5AjdunVTy23durUaKVGv16uRqxs0aMCqVas4duwYBw4cYNeuXSxbtgwAc3NzQkND2bJlS7l69unTx6g8T09PRowY8aBvmRBCCCGEqCIytOkRkZWVRWxsLL/99htQujTr5MmTSUpKMloKNjIyEj8/P5o0aQLAhAkTmDNnDq+++iq1a9dW8xUWFnL16lU0Gg0A33//PZ06daJr165AaUj2G+NB3MyNS7fWrFkTnU6nroFsYWFBjx49yq2J/Hdnz57l999/Z/Hixbe/EUIIIYQQ9+njkUMrpdzpKyLvKJ9GoyE7O/u+g9A96qRH4hGRlpaGnZ0dZmalbTuNRoODgwMGg8Eon8FgoHnz5uq2o6OjUZ6UlBTc3d2xsbGhXr16TJo0CYBjx45hYWFBv3790Ol0jB49mnPnzqnHnTp1Ck9PT7y9vdVejL/LyMggMjKSfv363dW1LV26lL59+6qB6oQQQgghxL27MXBdVZKGxGPG0dGRuLg4MjIy1IBwUPqG27JlC+Hh4Rw6dIimTZsyceJEADw9PTl9+jQHDx5k/fr1hIWFsWbNGqNyc3Nz6d+/P1OnTqVDhw53XB9FUVi8eDHjxo17cBcphBBCCFFN7Nq1C51OR/v27Rk7dizu7u5s374dAB8fH6ZMmcKzzz6Lg4MDM2bM4Oeff6Zr1644Ojry+eefq+U4OjoSGhpKx44dGTNmDEVFRUybNo2OHTui0+l46aWXyM7OBmDRokW0a9dOPe/evXsr5dpkaNMjolmzZqSnp1NcXIyZmRmKomAwGHBwcDDK5+DgwKlTp9TtlJSUcnmgNIy6v78/K1euxN/fHwcHB7p3707Tpk0BGDlypLrWtJWVlXqcVqvl5ZdfJiYmhpdeegmAvLw8fH19GTBgAG+99dZdXdeOHTu4du3aY7+utRBCCCHE3xUWFjJ8+HCWLVtG9+7d2bZtmxp4uExqairbtm0jNzcXR0dHsrOziYmJ4ezZs7Ru3ZqxY8eqQ6QuXLjA3r170Wg0zJkzhzp16rBvX+lKoR999BHvvfce33zzDVOmTOHEiRPY2dlRVFRktPjOgyQ9Eo8IW1tbPD09WbFiBQBRUVFotVqj+RFQOnciOjqajIwMFEUhLCwMf39/AJKSktQVnAoLC1m/fj1ubm4AvPTSS+zfv5/c3FwAfv75Z9zd3QFIT09XV2LKy8tj48aN6tyIy5cv4+vri6+vL++9995dX1dERAQBAQESJEYIIYQQT5wTJ05gZmZG9+7dAejevTstWrQwyjN06FBMTU1p0KABTk5O9OvXD41GQ9OmTWnUqJHRXNSAgAB1/uuGDRtYsWKFukLmDz/8QHJyMgA9e/Zk1KhRzJs3j+TkZOrWrVsp1yc9Eo+Q8PBwAgICmDNnDlZWVmqLdfz48fj5+eHn54eTkxOzZs2iS5cuQGmXWEhICFC6VOtXX32FqakpxcXF9OzZkxkzZgClPRnvvvsunTt3xsTEhKZNm6qrPUVFRfF///d/mJmZUVxczLBhwwgMDARg3rx57Nu3j/z8fHWY1LBhw5g+fToAbm5unDt3jtzcXLRaLd27d2f58uUA5OTksG7dOuLj4x/SHRRCCCGEeLSVNQTK1KxZU/3Z1NS03PaN8yFubBAoisLXX39N7969y50jKiqKAwcOsH37dvr27cvs2bPVL54fJGlIPEJat27N7t27y+1ftGiR0XZQUBBBQUHl8gUHBxMcHHzT8keNGsWoUaPK7Z88eTKTJ0+u8Jjp06erjYaKHD58+KZp9erVIz8//6bpQgghhBCPs9atW1NUVMSOHTt47rnn2LFjB0lJSQ+k7IEDB/LFF1/QtWtXateuzZUrV0hOTqZ169akpKTQoUMHOnTowPnz59m3b580JIQQQgghhKguLCwsWLVqFa+++iolJSV4eXnRunXrB7IsbGhoKAUFBTz99NNqL0doaCgtW7Zk7NixXLx4ETMzMxo1alRuXsaDIg2J/ynBhI81H91XGXFDZUKxEEIIIURVu9N4D5VFURT1Z3d3d+Li4gDYv38/mzZtwtnZGUBdvalMbGys0faNvRd/j9tlZmbGhx9+yIcfflju/H/88cf9VP+OyWTrKpaYmEjnzp1xdnbG29ubo0ePVpgvIiKCVq1a0aJFC4KCgtRJ1bt371Yn2bi4uBASEqLOzE9JScHHx4d69eqh0+mMyrvVcbc6XxlFUejRo4dRizo5ORkvLy90Oh2urq4MGzZMXYZMCCGEEOJJFBUVhbu7O25uboSEhLB8+XKjIMLVmTQkqlhISAjBwcEkJCQQGhpKQEBAuTzJycnMmDGDmJgYkpKSyMzMVCdKu7u7s3//fvR6PfHx8WRlZakB5aysrJg9ezbff/99uTJvddytzlfmiy++KLfqgL29PTt37kSv13PkyBHs7e2ZOXPmA7hLQgghhBDVU0BAAHFxcRw+fJiDBw/Sq1evqq7SAyMNiSqUlZVFbGwsI0eOBEqXdk1LSys3CScyMhI/Pz+aNGmCRqNhwoQJ/PDDDwDUrl0bc3NzoHTJ16tXr6rj5Bo2bEjXrl2pU6dOuXPf6rhbnQ/g6NGjbNiwgWnTphmVaWFhQa1atQC4fv06+fn55VYmEEIIIYQQjwdpSFShtLQ07OzsMDMrnaqi0WhwcHDAYDAY5TMYDDRv3lzddnR0NMqTkpKCu7s7NjY21KtXj0mTJt3R+W923K3OV1RURFBQEOHh4RXGhigsLESn02FjY0NiYiKzZs26w7shhBBCCCGqE2lIPAYcHR2Ji4sjIyODgoICNd5DZRw3a9YsBg8eTNu2bStMr1GjBnq9nszMTNq0aUN4ePhdXYsQQgghhKgepCFRhZo1a0Z6eroaaERRFAwGAw4ODkb5HBwcSE1NVbdTUlLK5YHSICX+/v6sXLnyrurx9+Nudb4dO3bw9ddf4+joSNeuXdVw7ufOnTMqs0aNGgQGBqrB6YQQQgghxONFln+tQra2tnh6erJixQoCAgKIiopCq9XSsmVLo3xDhgyha9euzJw5k8aNGxMWFqYGFUlKSqJ58+aYm5tTWFjI+vXrcXNzu+25b3Xcrc4XExOjlpGSkoJOp1OXI0tNTaVRo0bUrl2bkpIS1q5de0d1EUIIIYR4kI5/vLVSym07vUellFtdSY9EFQsPDyc8PBxnZ2c+/fRTNWDI+PHjiY6OBsDJyYlZs2bRpUsXWrZsSaNGjQgJCQFg69ateHh44O7ujoeHB40bN2bGjBkAXLlyBa1Wy7Bhwzh27BharZZ//vOftz3uVue7lcOHD9OpUyfc3Nxwc3Pj3LlzfPXVVw/8ngkhhBBCPA7Onj1Lt27dqroa90yj3Bgx4wnW0MaGZmF3NyTo7yQgXdXZtGkTffrI/a/O5BlWf/IMqz95htXbk/D8tFotp0+fVrevX79OQkICzs7ORovAPO49EsXFxepiPZXpZve3jAxt+h9TjUYaAkIIIYQQ4r5pNBpmz55NdHQ0mZmZfPnllxw/fpyoqChycnL49ttv8fHxUYeJX7p0ST3u448/ZsOGDZw7d47333+fwMBAoHSRnOHDh7Nt2zZatWrF0qVLmTFjBlu3bqWwsBBnZ2fCw8Np0KABixYt4vPPP6dGjRpcv36dRYsW8fTTTz/w65SGhBBCCCGEEA9Y3bp12bt3L7///jsDBgxg/vz5xMbGsnbtWt555x32799f4XEWFhbs27ePEydO4O3tzahRo9TehwsXLrB37140Gg1z5syhTp067Nu3D4CPPvqI9957j2+++YYpU6Zw4sQJ7OzsKCoqoqCgoFKuURoSQgghhBBCPGDDhw8HoEOHDuTn56sL13Ts2JHExMSbHjdixAgA2rRpg5mZGRkZGWi1WqA0SnZZsN8NGzaQk5NDVFQUUBrLy9HREYCePXsyatQo+vfvzwsvvICzs3OlXKM0JIQQQgghhHjAatasCaDOLbhxu2zp/1sdV1HeunXrqj8risLXX39N7969y5URFRXFgQMH2L59O3379mX27NlqQ+ZBklWbhBBCCCGEqGYGDhzIF198wZUrV4DS1TqPHj1KcXExp06dokOHDrz99tsMHTpUHf70oEmPhBBCCCGEeKw8KqsrVabQ0FAKCgp4+umn1eFOoaGhtGzZkrFjx3Lx4kXMzMxo1KiRGl7gQZOGhBBCCCGEEA/QjdEV6tata7St1Wq5fPkyULoSU9mKTX8/DuD8+fPqz2UBgMuYmZnx4Ycf8uGHH5Y7/x9//HE/1b9jMrRJCCGEEEIIcdekISGEEEIIIYS4a9KQEEIIIYQQQtw1aUgIIYQQQggh7po0JIQQQgghhBB3TRoSQgghhBBCiLsmy78KIYQQQojHysyZM6tVudWV9EgIIYQQQgjxCCsuLq7qKlRIGhJCCCGEEEI8QNHR0bRt2xY3NzemTp2KjY0NKSkpODo68t5779G5c2eaNWtGWFgYS5Ys4ZlnnsHR0ZFVq1apZWg0Gj744AO8vb355z//WYVXc3MytEkIIYQQQogHJCsri8DAQGJiYmjXrh0LFy7kwoULanp+fj67du0iKSmJ9u3bM336dHbv3s3+/fvp27cv/v7+al5TU1P2799fFZdxR6RHQgghhBBCiAdkz549uLm50a5dOwDGjRtHjRo11PThw4cD0LJlS2rWrMnQoUMB6NChAxcvXuTSpUtq3rFjxz68it8DaUgIIYQQQghRSTQajdF2zZo11Z9NTU3VbY1Gg0ajMZoPUbdu3YdTyXskDQkhhBBCCCEekGeeeYbDhw9z4sQJABYvXkxhYWEV16pyyBwJIYQQQgghHpBGjRqxePFiBg0aRI0aNfD19cXa2rqqq1UppCEhhBBCCCEeK1Ud72HAgAEMGDBA3Y6IiAAgJSXFKN/58+eNtm8c1qQoSuVV8AGRoU1CCCGEEEKIuyY9EkIIIYQQQlSiv/c8PC6kR0IIIYQQQghx16QhIYQQQgghhLhr0pAQQgghhBBC3DVpSAghhBBCCCHumky2/p/rJSV4vbPsno498NnoB1wbIYQQQghxr9as7Vgp5b40bF+llFtdSY9EFUlMTKRz5844Ozvj7e3N0aNHK8wXERFBq1ataNGiBUFBQRQVFQGwdetWOnbsSLt27XBxcWHq1KmUlJQAsGnTJnQ6nfqyt7fH09MTgPj4eKM0R0dHGjZsqJ6vd+/euLm5odPp6NatG4cOHQLg2rVrDBw4EGdnZ9zd3Xn++edJSkpSj/Px8eGpp55Sy/3iiy8q5b4JIYQQQjzJNmzYwJ49e+7p2KVLlzJw4MAHVhfpkagiISEhBAcHExAQQGRkJAEBAezfv98oT3JyMjNmzODgwYM0btyYAQMGsHDhQl599VUaNGjAqlWrcHJy4tq1a/Tq1Ytly5YREBBAnz596NOnj1pOv3796N69OwDt27dHr9eraZMnT0aj0ajba9asoX79+gCsX7+egIAA4uLiAAgODuaFF15Ao9Ewf/58xo8fz/bt29Vjv/jiiwf65hRCCCGEeNIUFxdjZnbzj+gbNmxAp9PRqVOnh1irikmPRBXIysoiNjaWkSNHAjBkyBDS0tKMvuEHiIyMxM/PjyZNmqDRaJgwYQI//PADAB4eHjg5OQFQs2ZNdDpduWiJAGfPnuX3339n1KhR5dKuXbvGypUrGTdunLqvrBEBkJOTozYyatasSd++fdXtTp06VXg+IYQQQogn3Y8//kjbtm1xd3cnNDQUGxsbUlJSOH78OH369MHNzQ03NzfCwsKA0pEdr7/+Os888wy9e/fm+vXrvPPOO7i6uuLq6sprr71GYWEhP//8M9HR0Xz22WfodDoWLVrE9u3bcXV1ZeLEibi5udG+fXsOHz5MQEAA7du35+mnn+bMmTPl6nj27Fm8vb1ZvHjxPV+nNCSqQFpaGnZ2dmprU6PR4ODggMFgMMpnMBho3ry5uu3o6FguD0BGRgaRkZH069evXNrSpUvp27cvtra25dLWrVuHk5MTOp3OaP/o0aNp1qwZM2bMYPny5RVew7x584xCvwNMmzaN9u3bM3z4cP7666+KL14IIYQQ4jGWlZXF2LFjWb9+PXFxcbRp04YLFy5QXFzMgAEDCAgI4PDhwxw+fJihQ4eqxyUkJPDHH3+wdetWFi5cyP79+zlw4AB6vZ5Tp07xxRdf0LdvX/z8/HjnnXfQ6/WMHz8egBMnTjB+/HgOHz7MwIED6dGjB9OmTSM+Pp4OHTrw5ZdfGtUxPj6e559/no8//pixY8fe87VKQ6Kay83NpX///kydOpUOHToYpSmKwuLFi416HG4UERFRYdqyZctIS0tj9uzZhIaGlkufM2cOSUlJfPLJJ+q+5cuXc+LECQ4fPky3bt0qbNQIIYQQQjzu9uzZg5ubG23atAFgzJgx1KhRg4KCAq5du8bLL7+s5rWxsVF/HjlyJObm5gBs2bKFgIAALCwsMDMzIygoiM2bN9/0nC1btsTLywuADh060LJlS/X8HTt2JDExUc179OhR/Pz8+P777+ndu/d9Xas0JKpAs2bNSE9Pp7i4GCj9wG8wGHBwcDDK5+DgQGpqqrqdkpJilCcvLw9fX18GDBjAW2+9Ve48O3bs4Nq1a0bzJcokJyezZ88eXnnllZvWc8yYMWzbto0LFy6o++bOncu6dev45ZdfqF27ttE1QWnvyuTJk/nrr7+MjhNCCCGEEDdXt27dm6bdOJ+1IjVr1lR/NjU1Lbdd9pkTwN7ensaNG7N169b7qG0paUhUAVtbWzw9PVmxYgUAUVFRaLVaWrZsaZRvyJAhREdHk5GRgaIohIWF4e/vD8Dly5fx9fXF19eX9957r8LzREREEBAQgKmpabm0xYsXM2jQIKM5EZcuXeLs2bPq9oYNG7C2tlZXdfr888/54Ycf2Lx5s9FxxcXFZGZmqttRUVE0btwYa2vru7sxQgghhBDVXKdOnTh8+DAnT54EYMWKFRQWFmJhYUHt2rXV+a4A58+fr7CMskV0CgsLKS4uZtGiRWrvgZWVFTk5OfdcvwYNGrB582Y2bNjAhx9+eM/lgKzaVGXCw8MJCAhgzpw5WFlZsWTJEgDGjx+Pn58ffn5+ODk5MWvWLLp06QKUTsQJCQkBSuco7Nu3j/z8fNatWwfAsGHDmD59OlA6UXrdunXEx8eXO3dJSQlLly5l2TLjuBk5OTkMGzaMq1evYmJiQqNGjdi4cSMajYbTp08zZcoUnJyc1BWgLCws2Lt3LwUFBbz44osUFBRgYmKCjY0N0dHRlXPjhBBCCCFuoyrjPdja2rJo0SIGDhyIhYUFzz//PHXr1sXGxoYff/yR1157jTlz5mBiYsKkSZPUz3Y3Cg4O5tSpU+ry/T4+PrzxxhsAjBo1ioCAADZs2MCrr75a7ovoO2Fpacmvv/7KoEGDeOedd/jss8/u6Vo1iqIo93TkY6ahtTVPjb232AcSkK7qbdq0qcIhXKL6kGdY/ckzrP7kGVZvT8Lz02q1nD59Wt2+fv06CQkJODs7VzgCo6rk5eVhaWkJlI7w+Oc//8nx48eruFZ373b3V3okhBBCCCGEeIC+/vprVq9ezfXr17GysmLlypVVXaVKIQ2J/zFBYb3lvXXrGD68t+OqO4f3yw+bup3ExETGjBnD+fPnqVevHkuXLsXFxcUoT0pKCgEBARw6dIinnnrKKIDe7t27mThxIgBFRUV07dqVr776CoAlS5Ywb948Ne/p06d59tln1aFfGzdu5O233+b69eu0b9+epUuXYmVlRXJyMkOHDuX69esUFxfTtm1bFi5cSIMGDbh8+TJDhgzhwIEDFBcXc+nSpbu+ZiGEEEI8Wd59913efffdqq5GpZPJ1uKhKovonZCQQGhoKAEBAeXyWFlZMXv2bL7//vtyae7u7uzfvx+9Xk98fDxZWVksWLAAgMDAQPR6vfpq0qQJI0aMAEonp48bN44NGzaQmJiIvb09H330EVC6esHOnTvR6/UcOXIEe3t7Zs6cCYC5uTmhoaFs2bKlcm6IEEIIIUQ1JQ0J8dDcaUTvhg0b0rVrV+rUqVOujNq1a6trLBcWFnL16tUKl0Tbu3cvWVlZ+Pn5AfDLL7/g4eGhrqk8adIkddUECwsLatWqBZSOBczPz1fLtLCwoEePHkarVAkhhBBCCGlIiIfoTiN6305KSgru7u7Y2NhQr149Jk2aVC5PREQEo0aNUhsdFUUJvzGWR2FhITqdDhsbGxITE5k1a9a9XqYQQgghxBNBGhKi2nF0dCQuLo6MjAwKCgrUORBl8vPzWbVq1U0jelekRo0a6PV6MjMzadOmDeHh4Q+62kIIIYQQjxWZbC0emhsjepuZmd00ovedqlu3Lv7+/qxcuZLJkyer+9euXYuLiwvt2rVT9zk4OBiFlk9JSTHqHSlTo0YNAgMDCQoKYurUqfdULyGEEEJULffITZVSbtzQO1ted+bMmUybNo2aNWty8eJF+vfvT35+vlHMr8eB9EiIh+ZOI3rfSlJSEkVFRUDpcKT169fj5uZmlCciIqJcb4Svry8HDx7kxIkTACxYsECNEp6amsqVK1eA0mB9a9euLVemEEIIIcSdmjVrFteuXQNg8+bN1K1bF71eX2mNiLKh2g+b9EiIh+pOInpfuXIFZ2dnCgoKyMnJQavVMmrUKD755BO2bt3KV199hampKcXFxfTs2ZMZM2awY8cOAE6ePIler+fnn382Oq+lpaUaZbK4uBhXV1e+++47AA4fPqz+YpeUlODp6akuKQvg5ubGuXPnyM3NRavV0r17d5YvX/4wbpcQQgghqpkJEyYA0K1bNxRF4a+//sLc3BydTsfcuXNxcXEhICCAtLQ07O3tsbGxoU2bNsycOZOZM2dy7Ngxrl69ysmTJ3F2dubTTz9lypQpJCcn4+XlxcqVKzExMSEgIAATExOSkpLIyspSvyx9mKQhIR6q1q1bs3v37nL7Fy1apP5cu3Zto6iVNwoODiY4OPiW5efl5VWYVtZQ+bv+/fvTv3//m5Z5+PDhm6YJIYQQQtwoLCyM8PBwYmJiqF+/PkuXLmXDhg1s2LABgGHDhtGxY0c2bdrEmTNn0Ol06qqSALGxsRw4cID69evj4+PD+PHj2bx5M7Vq1aJDhw788ssvvPjiiwAcOHCAnTt3qlG0HzZpSAghhBBCCPGQ/P7778ydOxeApk2blvuSs3fv3jRo0AAAT09PLCws1IaCh4cHiYmJat5hw4ZVWSMCpCGhKgFebmBV1dWoFH++9mdVV0EIIYQQQlTg7/Gwatasqf5sampabvvG+RB169at/Aregky2FhVKTEykc+fOODs74+3tzdGjRyvMFxERQatWrWjRogVBQUHqROiSkhLefvttXF1dadOmDePGjaOwsBCATZs2odPp1Je9vT2enp5qmd999x3t27dHp9Ph4eGhzne4cOGC0XHOzs6YmZlx8eJFAPbv30+XLl1wd3dHp9OxdetWtczp06erZep0OlatWlUp900IIYQQwtLSkpycnArTevXqxeLFiwFIT08nOjr6YVbtgZKGhKhQSEgIwcHBJCQkEBoaSkBAQLk8ycnJzJgxg5iYGJKSksjMzGThwoVAaQPj4MGDHDx4kOPHj2NiYsK8efMA6NOnD3q9Xn15enoyYsQIAC5evMhrr73G5s2b0ev1fP311+q5ra2tjY4LDg7mhRdeoGHDhiiKwqBBg5g1axZxcXGsWbOGgIAArl69CsA777xDfHw8er2e//73vwQHB3P+/PnKv5FCCCGEeOJMmTKF559/Hp1OR1ZWllHavHnz2LNnD+3atWP06NH06NGjimp5/2RokygnKyuL2NhYfvvtNwCGDBnC5MmTSUpKMlqqNTIyEj8/P5o0aQKUrlIwZ84cXn31VeLi4ujVqxc1atQA4IUXXmDmzJm88847Ruc6e/Ysv//+u9oyLykpQVEU8vLyaNKkCZcuXUKr1VZYz4iICD755BMAcnNzOXfuHL169QLA2dmZ+vXr88svvzB48GDq16+vHnf58mUURaGkpOQB3C0hhBBCPGruNN5DZfnggw/44IMPKkyzs7Nj06b/H+fi7bffVn+eOXOmUd6yuRRlblycZunSpfdf0fskPRKinLS0NKNgbRqNBgcHBwwGg1E+g8FA8+bN1W1HR0c1j5eXF9HR0eTm5lJUVMSaNWtISUkpd66lS5fSt29fbG1tAbCxsSEsLAxPT0+aN2/O2LFjK/xF2bVrF9nZ2fTr1w+AevXqYWdnx5o1a4DSYU4nT540OudXX31F69at8fT0ZOHCheo5hRBCCCHE3ZOGhKgUAQEB+Pr68txzz/Hcc8+p8xlupCgKixcvNgoel5OTw7x589i3bx+pqalEREQwaNAgdX5FmYiICEaPHm1U5o8//sjixYvx8PBg3rx5dO3a1Sj99ddf5+TJk+zatYs5c+Zw4cKFSrp6IYQQQog7M3fu3HI9EdWFNCREOc2aNSM9PV1dFUBRFAwGAw4ODkb5HBwcSE1NVbdTUlLUPBqNhpkzZ3Lo0CF27dpFu3btcHFxMTp+x44dXLt2jT59/n/34+bNm6lfvz5t27YFSmM85ObmGp3n8uXLrFmzhrFjxxqV5+7uzq+//sqhQ4dYsWIFZ8+eLXfOsnxNmzZl+/bt93B3hBBCCCEESENCVMDW1hZPT09WrFgBQFRUFFqt1mh+BJTOnYiOjiYjIwNFUQgLC8Pf3x+Aa9eukZ2dDcD58+f59NNPmTp1qtHxERERBAQEYGpqqu5zcnJCr9eTkZEBwO7duykuLqZZs2ZqntWrV+Pu7m4UvAVKVz4o8+2331KnTh11AtOxY8fUtFOnTnHo0CHatWt3bzdICCGEEI+EsqVTFUWp4po8nsru69+XqC0jk61FhcLDwwkICGDOnDlYWVmxZMkSAMaPH69GiHZycmLWrFl06dIFAB8fH0JCQoDSIUo+Pj6YmJhQUlLCP/7xD6Po0Tk5Oaxbt474+Hij83p6ejJ9+nR69OiBubk5ZmZmrFmzxmgN5YiICIKCgsrVeeHChaxcuRJFUWjbti3r169X3/hTp04lOTlZLXP+/Plqr4cQQgghqicTExPMzc25cOEC1tbWN/3AK+5eUVERmZmZ1KxZExOTivseNIo04QBoaN2QtjMfzw+WT0JAuk2bNhkNkRLVjzzD6k+eYfUnz7B6exKen1ar5fTp00b7CgsLMRgMaiwr8WBoNBrq16+Pra3tTRsS0iMhhBBCCCGqrRo1atCyZUt1CXlx/zQajfq6FWlI/I+JAnPWPvq347k/dlR1FYQQQgghHjk3+9ZcVB6540+AxMREOnfujLOzM97e3hw9erTCfBEREbRq1YoWLVoQFBSkdhEuWbIEnU6nvmxsbBg8eDBQulKTqampUfqpU6fUMjdu3EibNm1o1aoVgwcPJjc3t9x5AwIC0Gg0XLp0Sd23d+9e3N3dcXZ2pkePHpw5c0ZN++6772jfvj06nQ4PDw9+/vnnB3GbhBBCCCHEXZCGxBMgJCSE4OBgEhISCA0NJSAgoFye5ORkZsyYQUxMDElJSWRmZrJw4UIAAgMD0ev16qtJkyaMGDFCPdbS0tIovUWLFkDpMq3jxo1jw4YNJCYmYm9vz0cffWR03nXr1mFubm60r6SkhBEjRvDll1+SkJBA3759eeONNwC4ePEir732Gps3b0av1/P1119XeD1CCCGEEKJySUPiMZeVlUVsbCwjR44ESpdsTUtLIykpyShfZGQkfn5+NGnSBI1Gw4QJE/jhhx/Klbd3716ysrLw8/O77bl/+eUXPDw81GVaJ02aZFRmZmYmc+bM4fPPPzc67sCBA5iZmdG9e3egtCH0008/ce3aNXX8Y15eHgCXLl1Cq9XexR0RQgghhBAPwqM/KUDcl7S0NOzs7NQIzxqNBgcHBwwGg1FcCIPBQPPmzdVtR0dHDAZDufIiIiIYNWqUUS9Cfn4+3t7eXL9+nYEDBzJ9+nRMTU0rLLMs0J2ZmRlBQUH8+9//xtLS0ugcfz/O0tISKysrzp49i5OTE2FhYXh6etKwYUOuXr3Kli1bjGJICCGEEEKIyic9EuKO5efns2rVKsaNG6fus7Oz48yZM+zfv58tW7YQExPDf/7zn9uWtWjRIhwcHNSAcXcqJyeHefPmsW/fPlJTU4mIiGDQoEGy5JsQQgghxEMmDYnHXLNmzdReACiNUGgwGHBwcDDK5+DgQGpqqrqdkpJSLs/atWtxcXExightYWGBra0tAA0bNmTs2LHExMTctMyy3pFt27bx448/4ujoiKOjIwBubm4cOnSo3HF5eXnk5ORgb2/P5s2bqV+/vhpMrn///uTm5pKVlXW/t0oIIYQQQtwFaUg85mxtbfH09GTFihUAREVFodVqjYY1QenciejoaDIyMlAUhbCwMPz9/Y3yREREGPVGQOkcjLLegIKCAtatW4eHhwcAvr6+HDx4kBMnTgCwYMECtcyVK1eSlpZGSkoKKSkpABw+fBgPDw+8vLwoKipi27ZtQGmU7f79+1OzZk2cnJzQ6/VkZGQAsHv3boqLi2nUqNGDumVCCCGEEOIOyByJJ0B4eDgBAQHMmTMHKysrlixZAsD48ePx8/PDz88PJycnZs2aRZcuXQDw8fEhJCRELePkyZPo9fpyS63u3LmT999/H1NTU4qLi+nRowfTp08HSuc2LFq0iIEDB1JcXIyrqyvffffdbetrYmLCihUrCAkJ4dq1a9jb27N8+XIAPD09mT59Oj169MDc3BwzMzPWrFlDSUnJA7lXQgghhBDizmgUCQEIgE3DhkS5tq/qatyWBKSr2KZNm+jTp09VV0PcB3mG1Z88w+pPnmH19iQ8P61Wy+nTp6u6GuJ/ZGiTEEIIIYQQ4q7J0Kb/UTQmxHu/XdXVuK34KT9VdRUemsn/6V/VVRBCCCGEEDchPRLisZKYmEjnzp1xdnbG29ubo0ePlsuTkpKCj48P9erVQ6fTGaUtWbIEnU6nvmxsbBg8eLCa/tlnn+Hq6kq7du0YNGgQly5dKlf+Bx98gEajQa/Xl0tbsmQJGo2GDRs2qPt8fHx46qmn1HN+8cUX93r5QgghhBAPjTQkxGMlJCSE4OBgEhISCA0NJSAgoFweKysrZs+ezffff18uLTAwEL1er76aNGnCiBEjANi8eTNLlixh9+7dHDt2DC8vL3VieZl9+/axf/9+o4B6ZVJSUvj222/p1KlTubQvvvhCPeebb755j1cvhBBCCPHwSENCPDaysrKIjY1l5MiRQOmStmlpaSQlJRnla9iwIV27dqVOnTq3LG/v3r1kZWXh5+cHQFxcHF27dlUjcfft21ddTQrgypUrTJ48mfDw8HJllZSUMH78eL7++mssLCzu6zqFEEIIIR4F0pAQj420tDQ14B2ARqPBwcEBg8FwT+VFREQwatQozM3NAfDy8mLLli1qrI2VK1eSl5fHxYsXAZg6dSoTJ06kWbNm5cr6/PPP6dKlC15eXhWea9q0abRv357hw4fz119/3VN9hRBCCCEeJplsLUQF8vPzWbVqFXv27FH3de/enbfffpt+/fphamrKoEGDADAzM2Pz5s2kpqYyf/78cmUdOXKEqKgo/vjjjwrPtXz5cpo1a4aiKHzzzTf069ePY8eOVc6FCSGEEEI8INIjIR4bzZo1Iz09neLiYgAURcFgMODg4HDXZa1duxYXFxfatWtntH/SpEnExsayd+9efHx80Gq1WFlZsXXrVg4ePIijoyOOjo6cPn2avn378tNPPxETE0NKSgqtWrXC0dGRPXv2EBwczP/93/+p9YbSHpTJkyfz119/ceHChfu8G0IIIYQQlUsaEuKxYWtri6enJytWrAAgKioKrVZLy5Yt77qsiIgIxo0bV25/eno6UDof4v3332fq1KkAfPLJJ5w5c4aUlBRSUlLQarX8/PPP9O/fn4kTJ5Kenq6mderUiYULFzJx4kSKi4vJzMxUy4+KiqJx48ZYW1vfyy0QQgghhHhoHsmhTRcuXKBnz57q9pUrV/jrr7/IysrihRdeoKCgAIDi4mKOHj1KXFwcbm5uACxYsICvv/4aMzMzTExM2Lt3LzVr1qyS6xAPX3h4OAEBAcyZMwcrKyuWLFkCwPjx4/Hz88PPz48rV67g7OxMQUEBOTk5aLVaRo0axSeffALAyZMn0ev1/Pzzz+XK7927NyUlJRQWFjJq1CgmT558X/UtKCjgxRdfpKCgABMTE2xsbIiOjr6vMoUQQgghHoZHsiFhbW1ttAb/3Llz2bFjBw0bNmTv3r3q/sjISGbNmqU2In788UdWrlzJnj17qFevHufOnVMnyoonQ+vWrdm9e3e5/YsWLVJ/rl27NqdPn75lGXl5eRWmxcfH31E9UlJSbpq2fft29ec6deoQGxt7R2UKIYQQQjxKqsXQppsNM/n7/s8++4wPPviAevXqAdCoUSNMTU0fWj2FEEIIIYR4UjySPRI32rVrF9nZ2fTr189of1paGjt27DBax//YsWPExsYya9YsCgoKGD16NK+//nqF5X7++ed8/vnn6va1q1fIyfyuci5C3JOPR5Y+j+krIqu4JkIIIYQQ4u8e+R6JiIgIRo8ercYGKLN06VL69euHjY2Nuq+4uJjk5GT++OMPfv31V8LDw9m4cWOF5b711lucPn1afdWsJfMoHheJiYl07twZZ2dnvL29OXr0aLk8KSkp+Pj4UK9ePXQ6nVFaSUkJb731Fu3atcPNzY3u3burQe3i4+N59tlnadOmDa6urowdO5arV6+qaTqdTn05OjrSsGHDO6rXzz//jKenJzqdDldXV777Thq1QgghhHi0PdINicuXL7NmzRrGjh1rtF9RFJYsWVJuuJODgwMvv/wypqam2NjY0LdvX6M4AOLJEBISQnBwMAkJCYSGhhIQEFAuj5WVFbNnz+b7778vlxYdHc2ff/5JXFwchw8fpmfPnrz77rsA1KxZk/nz53PixAni4uLIz8/nX//6FwDt27dHr9err379+jFixIjb1ktRFEaOHMnSpUvR6/Vs3LiRkJCQm87TEEIIIYR4FDzSDYnVq1fj7u5OmzZtjPZv3bqV4uJinn/+eaP9r7zyCr/++isAV69eZfv27bi7uz+0+oqql5WVRWxsLCNHjgRgyJAhpKWlqT0KZRo2bEjXrl2pU6dOuTI0Gg0FBQVcu3YNRVHIzc1Fq9UC0KpVK3Vyv6mpKd7e3hVOrL527RorV65UG7u3q5dGo+HSpUsA5ObmYm1tjYWFxf3fECGEEEKISvJIz5GIiIggKCiowv2BgYGYmBi3g9566y1CQkJo164dGo2GIUOGMGzYsIdVXfEISEtLw87OTh0Kp9FocHBwwGAw3HE8if79+7Nt2zaaNGmCpaUlTZs2ZceOHeXy5efns2jRInXZ2ButW7cOJycnddjU7eq1evVqBg8eTJ06dcjOzmbdunXUqFHjHu+CEEIIIUTle6QbErt27apwf0XDUaB02ImMLRf3KzY2liNHjnDmzBmsrKyYNm0aEyZMUAPdARQWFjJ8+HB69+7NoEGDypVxs5XGKlJcXMzs2bNZt24dzz77LPv378fPz4/4+HijOUBCCCGEEI+SR3pokxB3q1mzZqSnp1NcXAyUzj8wGAw4ODjccRnLli2jR48e1K9fHxMTE8aMGcO2bdvU9KKiIoYPH46dnR3z5s0rd3xycjJ79uzhlVdeuaN66fV6zp49y7PPPguAt7c3Wq2WQ4cO3dM9EEIIIYR4GKQhIR4rtra2eHp6qr0HUVFRaLXaOx7WBODk5MTWrVspLCwEYOPGjbi6ugKlvQf+/v40bNiQhQsXotFoyh2/ePFiBg0aRP369e+oXmWNjOPHjwOQlJTEqVOnaN269T3dAyGEEEKIh+GRHtokxL0IDw8nICCAOXPmYGVlxZIlSwAYP348fn5++Pn5ceXKFZydnSkoKCAnJwetVsuoUaP45JNPePXVVzl+/Dju7u6Ym5vTpEkTwsLCgNIFANatW4ebmxseHh4AdOnShW+++QYoXTp26dKlLFu27I7r1bhxYxYuXMhLL72EiYkJJSUlzJ8//656UYQQQgghHjZpSIjHTuvWrdm9e3e5/YsWLVJ/rl27NqdPn67weAsLC7799tsK00aMGGG0pOvfmZiYkJaWdlf1Anj55Zd5+eWXb1quEEIIIcSjRoY2CSGEEEIIIe6a9Ej8jwYTBred9NDP23Z6j4d+TiGEEEIIIe6X9EhUQ4mJiXTu3BlnZ2e8vb05evRohfkiIiJo1aoVLVq0ICgoiKKiIgC2b99OrVq10Ol06uvq1asA7N69W93n4uJCSEgIBQUFQOn4/7feeot27drh5uZG9+7d1YBqycnJeHl5odPpcHV1ZdiwYWRnZ982DcBgMNC/f39at25Nu3bt+Prrryvt3gkhhBBCiAdDGhLVUEhICMHBwSQkJBAaGkpAQEC5PMnJycyYMYOYmBiSkpLIzMxk4cKFanrr1q3R6/Xqq1atWgC4u7uzf/9+9Ho98fHxZGVlsWDBAgCio6P5888/iYuL4/Dhw/Ts2ZN3330XAHt7e3bu3Iler+fIkSPY29szc+bM26YpisKgQYMYPXo0J0+e5NixY7z00kuVd/OEEEIIIcQDIQ2JaiYrK4vY2FhGjhwJwJAhQ0hLS1N7BspERkbi5+dHkyZN0Gg0TJgwgR9++OG25deuXRtzc3OgNOja1atX1SVONRoNBQUFXLt2DUVRyM3NRavVAqUTlMsaI9evXyc/P1897lZpv//+OxYWFkYRyBs3bnzP90cIIYQQQjwc0pCoZtLS0rCzs8PMrHR6i0ajwcHBAYPBYJTPYDDQvHlzddvR0dEoz6lTp/D09MTb21vtcSiTkpKCu7s7NjY21KtXj0mTSueO9O/fHx8fH5o0aYKdnR2///47H374oXpcYWEhOp0OGxsbEhMTmTVr1m3Tjh07RqNGjfD398fDw4NBgwbx119/PaC7JYQQQgghKos0JJ5Anp6enD59moMHD7J+/XrCwsJYs2aNmu7o6EhcXBwZGRkUFBSwbt06AGJjYzly5Ahnzpzh7Nmz9OzZkwkTJqjH1ahRA71eT2ZmJm3atCE8PPy2acXFxWzdupUZM2Zw6NAh+vTpI0ObhBBCCCGqAWlIVDNlUZCLi4uB0jkGBoOhXPAyBwcHUlNT1e2UlBQ1j5WVFfXq1QNAq9Xy8ssvExMTU+5cdevWxd/fn5UrVwKwbNkyevToQf369TExMWHMmDFs27at3HE1atQgMDCQ5cuX3zbNwcEBDw8PXFxcABg1ahQHDx5UJ4YLIYQQQohHkzQkqhlbW1s8PT1ZsWIFAFFRUWi1Wlq2bGmUb8iQIURHR5ORkYGiKISFheHv7w9Aeno6JSUlAOTl5bFx40Y1SnNSUpL6Ib6wsJD169fj5uYGgJOTE1u3bqWwsPD/tXfvcVVWef//XxtQNBMND4FukVBBQWCDYqbWjYdRK8XMY3na5gEzq8lptDuzW8s076b6amZgImZaaULlOM5tmVpqnkhBREtx5KQoTqkoCrJl//4gr197UIRUDvp+Ph48xn2tda3rc11Lm/1hXWstANauXUvbtm0BSE9P58KFC0Dx6k6ff/65cV5pZQ8//DBZWVkcO3YMgHXr1tGmTRtjnoaIiIiIVE3aR6Iaio6Oxmq1Mnv2bNzc3IiNjQVg7NixREREEBERgY+PDzNnzqRz584AhIeHExkZCRQnHx988AEuLi7YbDYGDRrE6NGjAdi4cSPz58/H2dkZm81G9+7dmT59OgDPPPMMBw8eJDg4mBo1auDh4UFUVBQA+/btY9q0aUBxshAaGsr8+fOvW1anTh2ioqJ49NFHsdvt1KtXj88++6wiHqOIiIiI3ACT3W63V3YQVUHDBg3ZMnnV9SveZNqQ7uZYv349vXr1quww5AaoD6s/9WH1pz6s3u6E/jObzWRlZVV2GPIbvdokIiIiIiLlplebfmPHzsrC7yv+wjMq4ZoV7MrmcyIiIiJy+9CIhFRJhw8fplOnTvj6+hIWFkZKSkqJOmlpaYSHhzvsdXHF5s2bqV27NhaLxfi5ePGiQx273W6sQvV7b731Fm3btsXf35/+/ftz5swZAJKTkx3a8/b2xt3d3TivoKCASZMm0apVKwIDA41NA0VERERuRxqRkCopMjKS8ePHY7VaWb16NVarld27dzvUcXNzY9asWZw9e5bnnnuuRBt+fn4kJiZe8xrvvvsuLVq0YM+ePcaxb775htjYWHbu3EndunWZNWsW06ZN4/333ycwMNChvUmTJhk7dAO89NJLmEwmDh06hMlk4sSJE3/8AYiIiIhUcWUakfj73/9Obm4uAH/7298YOHAg+/fvv6WByZ0rJyeHhIQE4zf6AwYMIDMzk9TUVId67u7udOnShTp16pT7GikpKXz55Ze89NJLDseTkpLo0qULdevWBeCRRx656n4Y+fn5rFixgjFjxgCQl5dHTEwMb7zxhpFceHh4lDsuERERkeqiTInEtGnTcHNzIykpieXLl/OnP/2Jp59++lbHJneozMxMPD09cXEpHjAzmUx4eXmRkZFRrnaOHDlCaGgoYWFhLFy40DheWFjIuHHjiI6OxtnZ2eGcdu3asWHDBmP/jRUrVnDu3Dl+/fVXh3rx8fH4+PhgsViMa7m7uzN79mzat2/Pgw8+yLfffvsH7l5ERESkeihTInHlC93XX3/N+PHjiYyMJC8v75YGJnIjQkNDycrKYs+ePXzxxRdERUWxalXx8r4zZ87k8ccfp02bNiXO69q1Ky+++CJ9+vShY8eONGrUCPj//w1cERMTY4xGANhsNtLT0/H39ychIYH58+czZMgQTp48eQvvUkRERKTylCmRuHz5Mjt37iQuLo6uXbsCGLsfi9xszZo1Izs7G5vNBhRPis7IyMDLy6vMbbi5uVGvXj2geM3pJ554gi1btgDw3Xff8d577+Ht7U2XLl3Izc3F29ubU6dOATBx4kQSEhLYuXMn4eHhmM1m3NzcjLaPHj3Kjh07ePLJJ41jXl5eODk5MWzYMABCQkK47777SE5OvrGHISIiIlJFlSmRmDVrFpGRkXTu3Jk2bdrw888/4+vre6tjkztU48aNCQ0NZfny5UDxTtxms5mWLVuWuY3s7GyKiooAOHfuHGvXriUkJASALVu2kJ6eTlpaGlu3bsXNzY20tDRj9CE7OxuACxcu8OqrrzJlyhSHtpcsWUL//v0dVntq2LAh3bt3Z/369UBxsnH06NGrjnqIiIiI3A7KtGpT37596du3r/HZz8+PuLi4WxaUSHR0NFarldmzZ+Pm5kZsbCwAY8eOJSIigoiICC5cuICvry8FBQWcOXMGs9nMiBEjmDNnDnFxcXzwwQe4uLhgs9kYNGgQo0ePLtO1e/bsSVFREZcuXWLEiBFMmjTJKCsqKmLp0qUsW7asxHlRUVGMGTOGqVOn4uTkRHR0NE2bNr05D0RERESkiik1kZg/f36pJ19tyU2Rm8HPz4/t27eXOL548WLjz3fddRdZWVkArF+/nl69ehllkyZNckgArsXb29vYJ+KK0l5HcnJyIjMz86plPj4+bNq06brXFBEREbkdlJpI7N2795plv18/X0RERERE7iylJhJXXie5E5hMdvwD1lV2GLelVZ8XP9fBg3ZVciQiIiIicrOUmkisWbOm1JMjIiJuajAi/+nw4cOMGjWKf//739SrV4+lS5cSEBDgUCctLY2//vWvDB48mPvuu89h9+nNmzfz8MMP4+fnZxzbvn07tWvXpqioiBdffJH/+7//w8XFhQYNGvDhhx/SsmVLkpOTeeaZZ8jJycHFxYUOHTrw/vvvU7t2bfLy8ujWrRv5+fkAeHp6EhUVhbe3NwAfffQRf/vb33B2dsZkMvHGG2/wyCOP3PJnJSIiIlKRSk0k3n333WuWmUwmJRJyy0VGRjJ+/HisViurV6/GarWye/duhzpubm6MGjWK1q1bM23atBJt+Pn5OSQXV6xZs4Zt27aRlJREjRo1mDVrFi+//DKrVq2iVq1aLFiwgKCgIC5fvsyTTz7J3LlzmTFjBrVr12bDhg3G7tfvvvsuzz//PF999RW//vorzz77LIcOHcLDw4OtW7fy+OOPk5OTc0uej4iIiEhlKTWR0MRRqUw5OTkkJCTw9ddfAzBgwAAmTZpEamqqw1Kw7u7utG3bFldX13K1bzKZKCgoID8/HxcXF3JzczGbzQC0atXKqOfs7ExYWBj79+8HiidcX0ki7HY7ubm5xpyhoqIi7HY7586dw8PDw1hNSkREROR2U6blX202G/PmzePIkSMsXLiQI0eOkJ6eTrdu3W51fHIHy8zMxNPT09hV2mQy4eXlRUZGRrn2lDhy5AihoaE4OzszevRoJk6cCBQva7xp0yY8PDyoW7cuTZs25bvvvitxfl5eHosXL2bOnDkOx3v06EFycjKNGjUy9o9o2LAhUVFRhIaG4u7uzsWLF9mwYcMffQQiIiIiVVaZNqSbNGkSP/30kzFC0aBBgxKbdIlURaGhoWRlZbFnzx6++OILoqKiWLVqFQAJCQns37+fY8eOcfz4cbp3786ECRMczr906RJDhgyhZ8+e9O/f36Fsw4YNZGdnM2TIEN544w0Azp49y7x589i1axfp6enExMTQv39/Ll26VDE3LCIiIlJBypRI7Nixgw8//JBatWoBUL9+fQoLC29pYCLNmjUjOzsbm80GFL9GlJGRgZeXV5nbcHNzo169egCYzWaeeOIJtmzZAsCyZcvo1q0b9evXx8nJiVGjRjm8zldYWMiQIUPw9PRk3rx5V23fycmJcePG8fHHHwPwzTffUL9+fWNH6759+5Kbm0t6enr5H4CIiIhIFVamROJKAnHF5cuXKSoquiUBiVzRuHFjQkNDWb58OQBxcXGYzeZyvdaUnZ1t/F09d+4ca9euJSQkBCjeQG7jxo3GaMHatWtp27YtUPw639ChQ3F3d2fRokUO+6acOHGC06dPG59XrlxJUFCQ0WZiYiInTpwAileIstlsNGvW7I8+BhEREZEqqUxzJIKCgli+fDlFRUWkpqYyd+5cwsPDb3FoIhAdHY3VamX27Nm4ubkZe5uMHTuWiIgIIiIiuHDhAsOHDweKXy0ym82MGDGCOXPmEBcXxwcffICLiws2m41BgwYxevRoAJ555hkOHjxIcHAwNWrUwMPDg6ioKKA4OYiPjycoKMhIPDp37sz7779PRkYGkZGRXL58GbvdTosWLYxkJzQ0lGnTptGtWzdq1KiBi4uLsQqUiIiIyO3EZLfb7derdP78ef7yl7/w5ZdfAvDYY4/xzjvvUKdOnVsdX4Vp2NCdhR+U/TfdUn63ckO69evX06tXr1vWvtx66sPqT31Y/akPq7c7of/MZjNZWVmVHYb8pkwjEnfffTfR0dFER0ff6nhERERERKQaKDWRWLJkCTabjfHjxzscX7RoETVr1sRqtd7K2CpUEU68YXq9ssO4LSUNLP9vR8q6o7XVamXv3r00bNiQI0eOGGWl7Wh9hd1up3v37uzZs4czZ84Yx9966y0++ugjioqK8PPzIzY2lvr165OcnMyIESOMemfOnCE3N5dff/0VgIKCAv7yl7+wfv16atWqRXBwsPHKk4iIiMjtptREYtGiRcb6+L83ZMgQevTocVslElK1lHVH61mzZnH27Fmee+65Em1ca0frK959911atGjBnj17jGPffPMNsbGx7Ny5k7p16zJr1iymTZvG+++/T2BgoEN7kyZNcpiE/dJLL2EymTh06BAmk8mYcC0iIiJyOyp11abLly8bS2f+Xr169bT8q9wyV3a0vjKBesCAAWRmZpKamupQz93dnS5duvyhuTopKSl8+eWXvPTSSw7Hk5KS6NKli7Fz9SOPPGIs7fp7+fn5rFixgjFjxgDFm9bFxMTwxhtvGMmFh4dHueMSERERqS5KTSSuvLJxNefOnbvpwYhA6Ttal8eVHa3DwsJYuHChcbywsJBx48YRHR2Ns7Ozwznt2rVjw4YNnDhxArvdzooVKzh37lyJfwvx8fH4+PhgsViMa7m7uzN79mzat2/Pgw8+yLfffvsH7l5ERESkeig1kQgNDWXJkiUljn/00UfGkpgiVVFpO1rPnDmTxx9/3Ng07ve6du3Kiy++SJ8+fejYsSONGjUCMJKaK2JiYozRCCjedyI9PR1/f38SEhKYP38+Q4YM4eTJk7fwLkVEREQqT6lzJObOnUuXLl34+uuveeCBBwD44Ycf+P7779m6dWuFBCh3nt/vaO3i4vKHd7S+4vc7Wg8ePJjvvvuOjIwMFixYgM1mIzc3F29vb3bv3k2jRo2YOHEiEydOBIp3dTebzQ7tHT16lB07dhAXF2cc8/LywsnJiWHDhgEQEhLCfffdR3JyMvfee++NPhIRERGRKqfUEQkfHx/27t2Lr68vX3/9NV9//TV+fn7s3buXFi1aVFSMcoe51Ttab9myhfT0dNLS0ti6dStubm6kpaUZow/Z2dkAXLhwgVdffZUpU6Y4tL1kyRL69+9P/fr1jWMNGzake/fuxuIER48e5ejRo1cd9RARERG5HVx3H4l7772X1157rSJiETGUdUdrX19fCgoKOHPmTJl3tL6enj17UlRUxKVLlxgxYgSTJk0yyoqKili6dCnLli0rcV5UVBRjxoxh6tSpODk5ER0dTdOmTW/OAxERERGpYsq0IZ1IRfPz82P79u0lji9evNj481133WXsbvmfu3lOmjTJIQG4Fm9vb4c9JACSk5OvWd/JyYnMzMyrlvn4+LBp06brXlNERETkdlDqq00iIiIiIiJXU+qIxDfffMOf/vQncnNzHSab3o6cTaY/tAOziIiIiMidqNQRiSubdYWHh1dELCIiIiIiUk2UOiJRWFjI3LlzycnJYf78+SXKn3vuuVsWmIiIiIiIVF2lJhIffvghH330ERcvXmTv3r0OZSaT6ZYGJiIiIiIiVVepicT999/P/fffT/PmzZk6dWpFxSQiIiIiIlVcmZZ/nTp1Krt27WLDhg1A8Tr77du3v6WBiYiIiIhI1VWm5V8XLVrEwIEDycnJ4dSpUwwYMMBhPX8REREREbmzlGlEYsGCBfz44480atQIgJdffpnu3bszduzYWxqciIiIiIhUTWXekO5KEvGffxYRERERkTtPmRKJVq1aMW3aNDIyMsjIyGD69Om0atXqVscmIiIiIiJVVJkSiaioKI4cOUJoaCjt2rUjNTWVDz744FbHJiIiIiIiVVSZ5kg0atSIzz777FbHIiIiIiIi1USZ50iIiIiIiIhcoURCRERERETKTYmEiIiIiIiU23UTicuXL9OjR4+KiEVERERERKqJ6yYSzs7OXLhwgaKiooqIR0REREREqoEyrdoUFhZGnz59GD58OHfffbdxPCIi4pYFJiIiIiIiVVeZEol9+/YB8OGHHxrHTCaTEgkRERERkTtUmRKJTZs23eo4RERERESkGinTqk02m423336biRMnAnDkyBE2btx4SwMTEREREZGqq0wjEpMmTeLy5cts3boVgAYNGjBkyBASEhJuaXAiIiIiIlI1lSmR2LFjB4mJiYSEhABQv359CgsLb2lgIiIiIiJSdZXp1aZatWo5fL58+bKWgxURERERuYOVKZEICgpi+fLlFBUVkZqayoQJEwgPD7/FoYmIiIiISFVVpkTinXfeYcuWLZw4cYJOnTrh5OTE3Llzb3VsIiIiIiJSRZVpjsTdd99NdHQ00dHRtzoeERERERGpBsqUSBQUFPDuu++yYcMGTCYTf/rTn3j++edxdXW91fGJiIiIiEgVVKZEYsKECfzyyy88++yzAMTGxvLTTz+xZMmSWxpcRbpcVES7vy6r7DAMP741slz1Dx8+zKhRo/j3v/9NvXr1WLp0KQEBASXqxcTE8Oabb1JUVES3bt1YuHAhNWrUACA5OZlnn32WkydPAvDGG2/w+OOPs337dp5++mkACgsL6dKlC/Pnz8fV1ZXY2FjmzZtntJ+VlcVDDz1EfHw8R48eZeDAgVy+fBmbzUabNm1YtGgR99xzD+fPn2fAgAH8+OOP2Gw2zpw5Y7SRnJzMM888Q05ODi4uLnTo0IH333+f2rVrl/cxioiIiMgtUqY5Etu3b+err76iX79+9OvXj7i4OH744YdbHZuUQ2RkJOPHj+fQoUNMnToVq9Vaos7Ro0eZPn06W7ZsITU1lZMnT7Jo0SIALly4QL9+/Zg1axYHDx5k//79PPjggwAEBweze/duEhMTSU5OJicnh4ULFwIwevRoEhMTjR8PDw+GDRsGQJMmTdi6dSuJiYns37+fJk2aMGPGDABq1KjB1KlT2bBhQ4k4a9WqxYIFC/jpp59ISkoiLy9Pc3JEREREqpgyJRINGjTg4sWLxueCggIaNmx4y4KS8snJySEhIYHhw4cDMGDAADIzM0lNTXWot3r1aiIiIvDw8MBkMjFhwgQ+/fRTAD755BM6duxIly5dAHB2dqZRo0YA3HXXXcaoxaVLl7h48SImk6lEHDt37iQnJ4eIiAgAXF1djVGEy5cvk5eXZ5zn6upKt27dqF+/fol2WrVqRVBQkBFHWFgYaWlpN/KIREREROQmK/XVpvnz5wPQunVr7r//fgYPHgwUfyENCwu79dFJmWRmZuLp6YmLS3F3mkwmvLy8yMjIoGXLlka9jIwMmjdvbnz29vYmIyMDgAMHDuDq6kqfPn3IysoiKCiIt99+20gm0tLS6NevH0eOHOHRRx9l4sSJJeKIiYlhxIgRRtIBxYlHhw4dSE9PJygoiDVr1pTr3vLy8li8eDFz5swp13kiIiIicmuVOiKxd+9e9u7dS1FREe3bt+df//oX//rXvwgNDeXy5csVFaNUAJvNxoYNG4iOjmbv3r00bdrUmBcBxUlHUlISJ06coKCggPj4eIfz8/Ly+OyzzxgzZozD8Zo1a5KYmMjJkydp3bp1uVb+unTpEkOGDKFnz57079//xm5QRERERG6qUkckYmNjKyoOuQHNmjUjOzsbm82Gi4sLdrudjIwMvLy8HOp5eXlx5MgR43NaWppRx8vLi65du9K0aVMAhg8fTq9evUpc6+6772bo0KGsWLGCoUOHGsc///xzAgIC8Pf3v2qMNWvWZPTo0YwbN44pU6Zc954KCwsZMmQInp6eDpO5RURERKRqKNMcCYB//vOfzJ8/n3feecf4kaqhcePGhIaGsnz5cgDi4uIwm80OrzVB8dyJNWvWcOLECex2O1FRUUYyMHjwYHbv3k1ubi4A69atIzg4GIDU1FQKCwuB4lGCL774wpjDcEVMTEyJ0Yj09HQuXLgAQFFREZ9//nmJ867GZrMxdOhQ3N3dWbRo0VXnY4iIiIhI5SrT8q9PPvkkBw8eJCQkBGdnZwB9uatioqOjsVqtzJ49Gzc3N2M0aezYsURERBAREYGPjw8zZ86kc+fOAISHhxMZGQkUj0i8/PLLxs7lTZs2NVZ02rhxI/Pnz8fZ2RmbzUb37t2ZPn26ce2ff/6ZxMRE1q1b5xDTvn37mDZtGlCcSISGhhrzbgCCgoI4deoUubm5mM1munbtyscff8zKlSuJj48nKCiIkJAQADp37sz7779/i56eiIiIiJSXyW63269XqXXr1qSkpBhJxO3IvUED7nvq3coOw1DefSTudOvXr7/qq1hSfagPqz/1YfWnPqze7oT+M5vNZGVlVXYY8psyvdrk7e1NQUHBrY5FRERERESqiTK92vT222/To0cPwsPDqVWrlnH81VdfvWWBVTQn7HxR963KDsOQ8VrViaWieL2aXNkhiIiIiEgZlWlE4r//+7+pWbMm+fn5nDt3zvgRqWyHDx+mU6dOjBkzhrCwMFJSUkrUSUtLIzw8nHr16mGxWBzKYmNjsVgsxk/Dhg15/PHHgeKdwNu1a4fFYqFt27YMGjSI06dPA5CcnMxDDz1E69atadu2LU899ZSxaWNeXh73338/wcHBBAcH07t3b2NDvdLKRERERKqTMo1I/Pzzz/z888+3OhaRcouMjGT8+PF4enpy7tw5rFYru3fvdqjj5ubGrFmzOHv2rDH5+4rRo0czevRo43Pbtm0ZNmwYAE2aNGHr1q3G7tzPP/88M2bMYN68edSqVYsFCxYQFBTE5cuXefLJJ5k7dy4zZsygdu3abNiwgbp16wLw7rvv8vzzz/PVV1+VWiYiIiJSnZRpRMLPz89YFlSkqsjJySEhIYHhw4cDxcvbZmZmkpqa6lDP3d2dLl26UKdOnVLb27lzJzk5OURERADg6upqJBGXL18mLy/PWK2sVatWxlK2zs7OhIWFGSMLTk5ORqJgt9vJzc01ziutTERERKQ6KdOIRO3atQkNDaVnz54OcyS0l4RUpszMTDw9PXFxKf5rbDKZ8PLyIiMjo8QeGmURExPDiBEjqFGjhnHs0qVLdOjQgfT0dIKCglizZk2J8/Ly8li8eDFz5sxxON6jRw+Sk5Np1KgR69evL3OZiIiISHVQphEJf39/RowYwb333ku9evWMH5HbRV5eHp999lmJTfVq1qxJYmIiJ0+epHXr1kRHRzuUX7p0iSFDhtCzZ0/69+/vULZhwways7MZMmQIb7zxRpnLRERERKqDMo1I/M///M+tjkOk3Jo1a0Z2djY2mw0oflUoIyMDLy+vcrf1+eefExAQgL+//1XLa9asyejRoxk3bhxTpkwBoLCwkCFDhuDp6cm8efOuep6TkxPjxo2jVatWLFy4sMxlIiIiIlVdmRKJ11577arHb6flX6X6ady4MaGhoSxfvhxPT0/i4uIwm81/+LWm/xyNSE9Pp1GjRtx1110UFRXx+eefG/MibDYbQ4cOxd3dnUWLFjnMczhx4gSurq7cc889AKxcudI4r7QyERERkeqkTInE75d6zc/PZ926dTzwwAO3LCiRsoqOjsZqtZKZmYmHhwexsbEAjB07loiICCIiIrhw4QK+vr4UFBRw9uxZzGYzI0aMMOY0/PzzzyQmJrJu3TqHtvft22es8lRUVERoaCjz588HihOA+Ph4goKCCAkJAaBz5868//77ZGRkEBkZyeXLl7Hb7bRo0YLly5cDlFomIiIiUp2Y7Ha7vbwn/fLLL1itVv7+97/fipgqRcMG7ux5vmllh3FHu5EN6davX0+vXr1uYjRS0dSH1Z/6sPpTH1Zvd0L/mc1msrKyKjsM+U2ZJlv/pwYNGvCvf/3rZsciIiIiIiLVRJlebbryOgcUr6e/a9cuPDw8bllQlaEIeOIet8oOo0rZ9uy2yg5BRERERKqoMo1I7N271/g5cOAAFouF1atX3+rYpBo6fPgwnTp1wtfXl7CwMFJSUkrUSUtLIzw8nHr16mGxWBzKNm7cSIcOHfD39ycgIIApU6ZQVFQEwNGjR2nXrh0Wi4W2bdsyaNAgTp8+XaJ9q9WKyWTizJkzxrGdO3cSHByMr68v3bp149ixYwAkJydjsViMH29vb9zd3W/eAxERERG5TZVpROLKBFaR64mMjGT8+PFYrVZWr16N1Wpl9+7dDnXc3NyYNWsWZ8+eNSYzX3HPPffw2Wef4ePjQ35+Pj169GDZsmVYrVaaNGnC1q1bjd2mn3/+eWbMmOGw9Gp8fLzDhnJQPFF62LBhfPjhh3Tt2pW//e1v/PnPf+bzzz8nMDCQxMREo+6kSZO007SIiIhIGZSaSHz//felnvzQQw/d1GCkesvJySEhIYGvv/4agAEDBjBp0iRSU1MdlmR1d3enS5cubN68uUQbV1ZAAqhVqxYWi4W0tDQAXF1djbLLly+Tl5fH3XffbRw7efIks2fPZtOmTSxevNg4/uOPP+Li4kLXrl2B4mTnlVdeIT8/32Gn9vz8fFasWMGmTZtu7EGIiIiI3AFKTST+8pe/lDhmMpk4fvw42dnZXL58+ZYFJtVPZmYmnp6euLgU/7UymUx4eXmRkZHxh/Z2OHHiBKtXr2bt2rXGsUuXLtGhQwfS09MJCgpizZo1Rtm4ceP43//9X+rWrevQTkZGBs2bNzc+161bFzc3N44fP46Pj49xPD4+Hh8fnxKvW4mIiIhISaXOkdi9e7fDz/r16+nSpQuXLl1i5syZFRWj3IFyc3Pp27cvU6ZMoX379sbxmjVrkpiYyMmTJ2ndujXR0dEA/POf/8TLy4tu3br94WtebVM6EREREbm6Mk22zs/PZ86cOfj7+wNw8OBBXnnllVsamFQ/zZo1Izs7G5vNBoDdbicjIwMvL69ytXPu3Dl69+5Nv379mDx58lXr1KxZk9GjR/Pxxx8DxZvHffXVV3h7e+Pt7Q1AUFAQe/fuxcvLi/T0dIf2z549S5MmTYxjR48eZceOHTz55JPlilVERETkTlVqIlFUVMSiRYto1aoVP/30Ezt37uSdd96hQYMGFRWfVCONGzcmNDTU2Kk5Li4Os9lcrteazp8/T+/evendu3eJZDU9PZ0LFy4AxX83P//8c4KCggCYOnUqmZmZpKWlGXMq9u3bR0hICO3ataOwsNCY+xAdHU3fvn0d5kcsWbKE/v37U79+/T96+yIiIiJ3lFLnSLRt25aCggJmz55NcHAwZ8+eZd++fUb5lS9xIldER0djtVqZPXs2bm5uxopfY8eOJSIigoiICC5cuICvry8FBQWcPXsWs9nMiBEjmDNnDvPmzWPXrl3k5eURHx8PwKBBg5g2bRr79u0zVnkqKioiNDTUYY+Ta3FycmL58uVERkaSn59PkyZNjJGMK20tXbqUZcuW3YInIiIiInJ7KjWRuHDhAiaTiVdffbVEmclk0u7WUoKfnx/bt28vcfz3qyjddddd19zeftq0aSWWhL2ib9++9O3bt0xx2O12h88PPPCAQxL8e05OTmRmZpapXREREREpVmoiceUVERERERERkd8r04Z0dwInO8z+vPo+jv/6/rvKDkFERERE7iBlWrVJbk+HDx+mU6dO+Pr6EhYWRkpKylXrxcTE0KpVK1q0aMG4ceMoLCwEiucWTJ48GX9/f4KCgujatSupqanGeRkZGfTt2xc/Pz/8/f157733gOIVktq1a4fFYqFt27YMGjSI06dPA5CcnMxDDz1E69atadu2LU899RQXL1402jx9+jTDhg3D19eXgIAAXnrpJaPso48+IjAwEIvFQkhICOvWrbvpz0xEREREiimRuINFRkYyfvx4Dh06xNSpU7FarSXqHD16lOnTp7NlyxZSU1M5efIkixYtAmDNmjVs27aNpKQk9u3bR/fu3Xn55ZeB4jkK/fv3Z+TIkfz8888cOHCAwYMHA9CkSRO2bt1KYmIi+/fvp0mTJsyYMQMo3s16wYIF/PTTTyQlJZGXl8fcuXONeJ566ilCQkI4dOgQKSkp/PnPfwaKl3R99tln+eabb0hMTOS999676v2IiIiIyM2hROIOlZOTQ0JCAsOHDwdgwIABZGZmOowoAKxevZqIiAg8PDwwmUxMmDCBTz/9FCiecF9QUEB+fj52u53c3FzMZjMA3377La6urgwaNMho69577wXA1dWV2rVrA3D58mXy8vIwmUwAtGrVylgNzNnZmbCwMGOuTmpqKgkJCQ57S3h4eADFoyN2u51z584BcObMGSMWEREREbn5qu+kALkhmZmZeHp64uJS/FfAZDLh5eVFRkaGw74PGRkZNG/e3Pjs7e1NRkYGULyK0qZNm/Dw8KBu3bo0bdqU774rnqtx4MABGjVqxNChQ/n555/x9vbm7bffxsfHB4BLly7RoUMH0tPTCQoKYs2aNSVizMvLY/HixcyZM8do02w28/TTT5OQkECDBg2YO3cuISEh1KtXj6ioKEJDQ3F3d+fixYts2LDh1jw8EREREdGIhPxxCQkJ7N+/n2PHjnH8+HG6d+/OhAkTALDZbGzcuJHp06ezd+9eevXqZbzaBMU7UycmJnLy5Elat25NdHS0Q9uXLl1iyJAh9OzZk/79+xtt7tq1i6FDh/Ljjz/ywgsv0KdPHwoLC8nLyzP2oEhPTycmJob+/ftz6dKlinsgIiIiIncQJRJ3qGbNmpGdnY3NZgOK5zRkZGTg5eXlUM/Ly4v09HTjc1pamlFn2bJldOvWjfr16+Pk5MSoUaOM3aO9vLwICQkhICAAgBEjRrBnzx5jovYVNWvWZPTo0Q4bxBUWFjJkyBA8PT2ZN2+eQyxNmzala9euADz88MNcunSJ9PR09uzZQ/369WnTpg1QPFqSm5vrELuIiIiI3DxKJO5QjRs3JjQ0lOXLlwMQFxeH2Wx2eK0JiudOrFmzhhMnTmC324mKimLo0KEA+Pj4sHHjRuO3/mvXrqVt27ZA8Zf8rKwsjh07BsC6deto06YNNWrUID09nQsXLgDFcxs+//xzY16EzWZj6NChuLu7s2jRImPuBEC7du1wc3MzNpbbtWsXdrudZs2a4eHhQWJiIidOnABg+/bt2Gw2mjVrdkuen4iIiMidTnMk7mDR0dFYrVZmz56Nm5sbsbGxAIwdO5aIiAgiIiLw8fFh5syZdO7cGYDw8HAiIyMBeOaZZzh48CDBwcHUqFEDDw8PoqKiAKhTpw5RUVE8+uij2O126tWrx2effQbAvn37jN2ri4qKCA0NZf78+QCsXLmS+Ph4goKCCAkJAaBz5868//77mEwmPvroI8aNG8fFixdxdXUlLi4OV1dXWrVqxbRp0+jWrRs1atTAxcWFVatWUatWrYp7oCIiIiJ3EJPdbrdXdhBVQUN3d+LaBlZ2GH/Ynb4h3fr16+nVq1dlhyE3QH1Y/akPqz/1YfV2J/Sf2WwmKyurssOQ3+jVJhERERERKTe92vQbu8mJ5LAXKzuMPyz5L3+v7BAqlef9RSy4w59BdTHp7b6VHYKIiIjcBBqREJEq7/Dhw3Tq1AlfX1/CwsJISUkpUWf79u1YLBYsFgsBAQFERkZSUFAAFM/FmTx5Mv7+/gQFBdG1a1eHzRfnzp2Lv78/FouFjh07smvXLgCSk5ONNi0WC97e3ri7uxvnFRQUMGnSJFq1akVgYKCxwaOIiMidQCMSIlLlRUZGMn78eKxWK6tXr8ZqtbJ7926HOsHBwezevZsaNWpQVFTEgAEDWLhwIS+88AJr1qxh27ZtJCUlUaNGDWbNmsXLL7/MqlWrSExMZOHChaSkpHD33XezfPlyJk2axK5duwgMDCQxMdG4xqRJkxxWEnvppZcwmUwcOnQIk8lkrBomIiJyJ1AiISJVWk5ODgkJCXz99ddA8ZLEkyZNIjU11WG54rvuusv486VLl7h48aLxpd9kMlFQUEB+fj4uLi7k5uZiNpuNsiubGt59992cOXPGKPu9/Px8VqxYYeyVkpeXR0xMDFlZWcZ1PDw8bs1DEBERqYKUSIhIlZaZmYmnpycuLsX/uTKZTHh5eZGRkVFi35O0tDT69evHkSNHePTRR5k4cSJQvEHhpk2b8PDwoG7dujRt2pTvvite6Sw4OJgXXniB++67D3d3d1xdXfn+++9LxBEfH4+Pjw8WiwWAI0eO4O7uzuzZs9mwYQO1a9dmxowZdO/e/RY+DRERkapDcyRE5Lbh7e1NUlISJ06coKCggPj4eAASEhLYv38/x44d4/jx43Tv3p0JEyYAcPToUeLj40lNTSUrK4sXXniBIUOGlGg7JiaGMWPGGJ9tNhvp6en4+/uTkJDA/PnzGTJkCCdPnqyYmxUREalkSiREpEpr1qwZ2dnZ2Gw2AOx2OxkZGXh5eV3znLvvvpuhQ4eyYsUKAJYtW0a3bt2oX78+Tk5OjBo1ynhFKS4ujsDAQJo0aQLA6NGj2bZtm7FjOxQnGzt27ODJJ580jnl5eeHk5MSwYcMACAkJ4b777iM5OfnmPgAREZEqqtITiZ49exIUFITFYuHBBx9k7969QOmrtHh7e+Pn52espLJy5Uqg+B3mxx57DF9fX4KDg/nTn/7ksDKLiFQ/jRs3JjQ0lOXLlwPFX/zNZnOJ15pSU1MpLCwEiudIfPHFFwQFBQHg4+PDxo0bjeRg7dq1tG3b1ijbtm0b58+fN8p8fX2pWbOm0faSJUvo378/9evXN441bNiQ7t27s379eqA42Th69Cht2rS5BU9BRESk6qn0ORKrVq0y/s/5iy++wGq1kpSUdN1VWlauXGm8q/x748eP5+GHH8ZkMrFgwQLGjh3L5s2bK+ZmROSWiI6Oxmq1Mnv2bNzc3IiNjQVg7NixREREEBERwcaNG5k/fz7Ozs7YbDa6d+/O9OnTAXjmmWc4ePAgwcHB1KhRAw8PD6KiogDo378/u3fvpn379ri6ulKnTh0++eQT49pFRUUsXbqUZcuWlYgrKiqKMWPGMHXqVJycnIiOjqZp06YV8EREREQqX6UnEr//Dd/Zs2cxmUxlXqXlP9WqVYtHHnnE+NyxY0f+9re/3bLYRaRi+Pn5sX379hLHFy9ebPx5/PjxjB8//qrnu7q68uGHH161zGQyMWfOHObMmXPVcicnJzIzM69a5uPjY7wiJSIicqep9EQCYOTIkcb/Ga9bt65Mq7SMHDkSu91Ohw4dePPNN2nUqFGJdufNm0e/fv0q7kZERERERO4QVSKRuPLKwEcffcTUqVN5/fXXS63//fff4+XlRWFhIa+88gqjRo1i3bp1DnVmz55Namoq33777VXbeOedd3jnnXeMz/kXL3D25Ec3eCfyn6YtX10h11m/fj2T3u5VIdcSERERkSow2fr3rqykYjabS12l5cr/1qhRgz//+c9s2bLFoZ2//e1vxMfH889//tNhk6rfmzx5MllZWcZPrdq1buGdSXmUNtH+irS0NMLDw6lXr16JuTKbN2+mdu3axmR8i8XCxYsXAdi4cSMdOnTA39+fgIAApkyZQlFRkXHuW2+9Rdu2bfH396d///6cOXPGKDOZTAQGBhpt/v7vXWllIiIiIrejSk0kzpw5w/Hjx43PX375JQ0aNCh1lZa8vDyHL3effvopISEhxud33nmHTz/9lG+++cZh/oVUH1cm2h86dIipU6ditVpL1HFzc2PWrFkOk2J/z8/Pj8TEROOndu3aANxzzz189tlnHDhwgB9//JEffvjBGBH75ptviI2NZfv27Rw4cIB27doxbdo0h3a3bNlitPnggw+WuUxERETkdlOprzadPXuWQYMGcfHiRZycnGjUqBFr167FZDJdc5WWkydPMmDAAC5fvozdbsfHx8f4IpiVlcVf/vIXfHx86Nq1K1A8yXLnzp2Vdo9SPmWdaO/u7k6XLl3KvSLX75POWrVqYbFYSEtLAyApKYkuXbpQt25dAB555BHCw8N5//33b+ymRERERG5DlZpING/enF27dl217FqrtPj4+Bh7Tfwns9mM3W6/qTFKxSrLRPuyOHLkCKGhoTg7OzN69GgmTpxYos6JEydYvXo1a9euBaBdu3YsXLiQEydOcO+997JixQrOnTvHr7/+iru7OwDdu3c3lhZ9/fXXqVOnjtFeaWUiIiIit5sqNUdC5GYIDQ0lKyuLPXv28MUXXxAVFcWqVasc6uTm5tK3b1+mTJlC+/btAejatSsvvvgiffr0oWPHjsZKYFeSmvT0dON1qFOnTvHXv/7VaK+0MhEREZHbkRIJqVKaNWtW6kT7snBzc6NevXpA8SjVE0884TD5+dy5c/Tu3Zt+/foxefJkh3MnTpxIQkICO3fuJDw8HLPZjJubG/D/T/KvU6cOEydOdGiztDIRERGR25ESCalSSptoX1bZ2dnGSkznzp1j7dq1xtyI8+fP07t3b3r37s0rr7xy1XMBLly4wKuvvsqUKVMAOH36NBcuXACKdzpeuXKl0WZpZSIiIiK3qyqxj4TI711rov3YsWOJiIggIiKCCxcu4OvrS0FBAWfPnmX48OGMHTuWOXPmEBcXxwcffICLiws2m41BgwYxevRooHiTwl27dpGXl0d8fDwAgwYNMlZn6tmzJ0VFRVy6dIkRI0YwadIkAH766SciIyMxmUzYbDZCQ0OZN2/edctEREREblcmu2YnA9CggTuTH+5W2WHcdipyQ7pevbQhXXWmPqz+1IfVn/qwersT+s9sNpOVlVXZYchv9GqTiIiIiIiUm15t+o0JJx5vU3KJ0D+qzTSNboiIiIjI7UsjElXI4cOH6dSpE76+voSFhZGSknLVejExMbRq1YoWLVowbtw4CgsLAdi+fTsWiwWLxUJAQACRkZEUFBQY5yUnJxMeHk6bNm1o06aNMUdg8+bN1K5d2zjXYrFw8eLF617vemXXup6IiIiIVH9KJKqQyMhIxo8fz6FDh5g6dSpWq7VEnaNHjzJ9+nS2bNlCamoqJ0+eZNGiRQAEBweze/duEhMTSU5OJicnh4ULFwLFqxD169ePWbNmcfDgQfbv38+DDz5otOvn50diYqLxU7t27eter7Sy611PRERERKo3JRJVRE5ODgkJCQwfPhyAAQMGkJmZSWpqqkO91atXExERgYeHByaTiQkTJvDpp58CcNddd1GjRg0ALl26xMWLFzGZTAB88skndOzYkS5dugDg7OxsbLhWmtKuV1rZH72eiIiIiFQPSiSqiMzMTDw9PY1dlE0mE15eXmRkZDjUy8jIoHnz5sZnb29vhzppaWkEBwfTsGFD6tWrx8SJxfM+Dhw4gKurK3369MFisTBy5EhOnTplnHfkyBFCQ0MJCwszRjGud73Syq53PRERERGp3pRI3Ga8vb1JSkrixIkTFBQUGPMSbDYbGzZsIDo6mr1799K0aVOefvppAEJDQ8nKymLPnj188cUXREVFsWrVqhuKo7TriYiIiEj1p0SiimjWrBnZ2dnYbDYA7HY7GRkZeHl5OdTz8vIiPT3d+JyWllaiDsDdd9/N0KFDWbFihXFe165dadq0KSaTieHDh7Njxw4A3NzcqFevHlC8PvMTTzzBli1brnu965Vd63oiIiIiUv0pkagiGjduTGhoKMuXLwcgLi4Os9lMy5YtHeoNGDCANWvWcOLECex2O1FRUQwdOhSA1NRUY9WkS5cu8cUXXxAUFATA4MGD2b17N7m5uQCsW7eO4OBgALKzsykqKgLg3LlzrF27lpCQkOter7Sy0q4nIiIiItWf9pGoQqKjo7FarcyePRs3NzdiY2MBGDt2LBEREURERODj48PMmTPp3LkzAOHh4URGRgKwceNG5s+fj7OzMzabje7duzN9+nSgeITg5ZdfplOnTjg5OdG0aVNjhaW4uDg++OADXFxcsNlsDBo0iNGjRwOUer3Sykq7noiIiIhUfya73W6v7CCqgoYNGrJl8o3NC/g9bUhXsdavX0+vXr0qOwy5AerD6k99WP2pD6u3O6H/zGYzWVlZlR2G/EavNomIiIiISLnp1abf2LGzsvD7m9fgjJvY1h1sxowZlR2CiIiIiFyFRiTktnP48GE6deqEr68vYWFhpKSklKiTlpZGeHg49erVw2KxOJQVFRUxefJk/P39CQoKomvXrsbGgOfPn6dXr140bNiQ+vXrO5x39OhR2rVrh8VioW3btgwaNIjTp0+XuLbVasVkMnHmzJkSZf/zP/+DyWQiMTHxj96+iIiISIVQIiG3ncjISMaPH8+hQ4eYOnUqVqu1RB03NzdmzZrFJ598UqJszZo1bNu2jaSkJPbt20f37t15+eWXAahRowZTp05lw4YNJc5r0qQJW7duJTExkf3799OkSZMSIyrx8fHG7uP/adeuXezevdthkz8RERGRqkqJhNxWcnJySEhIYPjw4UDxErWZmZnGiMIV7u7udOnShTp16pRow2QyUVBQQH5+Pna7ndzcXMxmMwCurq5069atxGjElbLatWsDcPnyZfLy8jCZTEb5yZMnmT17Nu+8806Jcy9cuMCkSZOIjo7+w/cuIiIiUpE0R0JuK5mZmXh6euLiUvxX22Qy4eXlRUZGRok9Oa6lb9++bNq0CQ8PD+rWrUvTpk357rvvynTupUuX6NChA+np6QQFBbFmzRqjbNy4cfzv//4vdevWLXHelClTePrpp2nWrFmZriMiIiJS2TQiIfIfEhIS2L9/P8eOHeP48eN0796dCRMmlOncmjVrkpiYyMmTJ2ndurUxwrB48WK8vLzo1q3kssDffPMN6enpxt4dIiIiItWBEgm5rTRr1ozs7GxsNhsAdrudjIwMvLy8ytzGsmXLjNeXnJycGDVqFJs2bSpXHDVr1mT06NF8/PHHAGzatImvvvoKb29vvL29AQgKCmLv3r1s3LiRPXv2GGVZWVk88sgj/P3vfy/XNUVEREQqkhIJua00btyY0NBQli9fDhTv2m02m8v8WhMU79i9ceNGLl26BMDatWtp27btdc9LT0/nwoULQPHKT59//jlBQUEArFixgszMTNLS0khLSwNg3759hISEMGfOHI4dO2aUmc1m1q1bR9++fctz6yIiIiIVSomE3Haio6OJjo7G19eXN998k9jYWADGjh1rzFm4cOECZrOZQYMGceDAAcxmM//93/8NwDPPPMN9991HcHAwQUFBfPvtt3zwwQdG+0FBQTzwwAPGJOwRI0YAxYlBx44dCQoKIigoiFOnTjF//vwKvnsRERGRiqHJ1nLb8fPzY/v27SWOL1682PjzXXfdRVZW1lXPd3V15cMPP7xm+/v27bvq8b59+5Z5FMFut1+z7MqIhYiIiEhVphEJEREREREpN41I/MZksuMfsK6yw7ijDB60q9znHD58mFGjRvHvf/+bevXqsXTpUgICAhzqpKWlYbVa2bt3L/fdd1+JXaKTk5N59tlnOXnyJABvvPEGjz/+OJs3b+bhhx/Gz8/PqLt9+3Zq165NbGws8+bNM45nZWXx0EMPER8fDxTPo3jxxRe5fPkygYGBLF26FDc3N86fP8+AAQP48ccfsdlsV93NWkRERKQ60oiEVCs3umv1hQsX6NevH7NmzeLgwYPs37+fBx980Cj38/MjMTHR+Lmywdzo0aMdjnt4eDBs2DAAzp8/z5gxY/jyyy85fPgwTZo04fXXXwdK3wlbREREpDpTIiHVxs3YtfqTTz6hY8eOdOnSBQBnZ2caNWpUrjh27txJTk4OERERAPzzn/8kJCSE1q1bAzBx4kQ+/fRToPSdsEVERESqMyUSUm2Utmt1WR04cABXV1f69OmDxWJh5MiRnDp1yig/cuQIoaGhhIWFsXDhwqu2ERMTw4gRI6hRowYAGRkZNG/e3Cj39vZ22MtCRERE5HakORJyR7HZbGzYsIEdO3bQpEkTXn75ZZ5++mlWr15NaGgoWVlZ1KtXz9gUrmHDhgwePNg4Py8vj88++4wdO3ZU4l2IiIiIVD6NSEi1cTN2rfby8qJr1640bdoUk8nE8OHDjaTAzc2NevXqAWA2m3niiSfYsmWLw/mff/45AQEB+Pv7O7SZnp5ufE5LS3MYORERERG5HSmRkGrjZuxaPXjwYHbv3k1ubi4A69atIzg4GIDs7GyKiooAOHfuHGvXriUkJMTh/JiYGMaMGeNwrHfv3uzZs4effvoJgIULFzJ06NA/dpMiIiIi1YR+ZSrVSnR0NFarldmzZ+Pm5mbsWv3uu+9SUFBAREQEFy5cwNfXl4KCAs6ePWvsPj1nzhy8vLx4+eWX6dSpE05OTjRt2pRFixYBxYnJBx98gIuLCzabjUGDBjF69Gjj2j///DOJiYmsW+e4THDdunVZvHgxjz32GDabjbZt2/LRRx8Z5Vd2ub6yE3bXrl35+OOPK+BpiYiIiNw6JntpW+zeQRo2dGfhB2X/zbbcuD+yj8S1rF+/nl69et209qTiqQ+rP/Vh9ac+rN7uhP4zm81kZWVVdhjyG73aJCIiIiIi5aZXm35ThBNvmF6v7DDuKG+sXn/T2vqLSz7B5WgvaeDt/RsbERERkVtNIxIiZXT48GE6deqEr68vYWFhpKSklKizceNGOnTogL+/PwEBAUyZMsWYwJ2cnMxDDz1E69atadu2LU899RQXL140zh04cCBNmjTBZDJx5swZ43heXh73338/wcHBBAcH07t3b9LS0gA4fvw4vXr1ws/Pj6CgIAYMGOCwL8Zzzz2Ht7c3JpOJxMTEW/JcRERE5M6kREKkjCIjIxk/fjyHDh1i6tSpWK3WEnXuuecePvvsMw4cOMCPP/7IDz/8wLJlywCoVasWCxYs4KeffiIpKYm8vDzmzp1rnDthwoSrftmvXbs2GzZsICkpiaSkJHr16sXzzz8PFO/MPX36dH7++Wf27duHj48Pf/3rX41zBw4cyNatWx02zBMRERG5GZRIiJRBTk4OCQkJDB8+HIABAwaQmZlJamqqQ72QkBB8fHyA4sTBYrEYowetWrUiKCgIKE4AwsLCjDKAHj160Lhx4xLXdnJyom7dukDx3hm5ubmYTCYA7r33Xrp06WLUvf/++x3afOihhzCbzTd28yIiIiJXoTkSImWQmZnpsMmcyWTCy8uLjIyMa+5jceLECVavXs3atWtLlOXl5bF48WLmzJlT5hh69OhBcnIyjRo1Yv36kvNBLl++zIIFC+jXr1+Z2xQRERH5ozQiIXIL5Obm0rdvX6ZMmUL79u0dyi5dusSQIUPo2bMn/fv3L3ObGzZsIDs7myFDhvDGG284lNntdiZOnMg999xjvPYkIiIicispkRApg2bNmpGdnY3NZgOKv7hnZGTg5eVVou65c+fo3bs3/fr1Y/LkyQ5lhYWFDBkyBE9PT+bNm1fuOJycnBg3blyJDe2ee+45MjMzWblyJU5O+mctIiIit56+cYiUQePGjQkNDWX58uVA8S7YZrO5xGtN58+fp3fv3vTu3ZtXXnnFocxmszF06FDc3d1ZtGiRMc/hek6cOMHp06eNzytXrjTmWkBxEpGamsoXX3xBzZo1/+gtioiIiJSLEgmRMoqOjiY6OhpfX1/efPNNYmNjARg7dixr1qwBYN68eezatYv4+HgsFgsWi8V4DWnlypXEx8eTkJBASEgIFouFZ555xmj/0UcfNSZGBwQEEB4eDkBGRgbdunUjKCiIwMBANm3aZCQ027Zt47333iMtLY37778fi8Xi8LpUZGSksQtor169rjmfQ0RERKS8THa73V7ZQVQF7g0b0ixqRWWHIX/QX1zyedtWq8z1tSFd1bN+/Xp69VK/VGfqw+pPfVi93Qn9d+WXY1I1aERCRERERETKTcu//sbZZNJvqaux9evXk3Sb/xZGREREpCrRiISIiIiIiJSbEgkRERERESk3JRIiIiIiIlJuSiRERERERKTclEiIiIiIiEi5KZEQEREREZFyUyIhIiIiIiLlpkRCRERERETKTYmEiIiIiIiUmxIJEREREREpNyUSIiIiIiJSbkokRERERESk3JRIiIiIiIhIuSmREBERERGRclMiISIiIiIi5aZEQkREREREyk2JhIiIiIiIlJsSCRERERERKTclEiIiIiIiUm5KJEREREREpNyUSIiIiIiISLkpkRARERERkXJTIiEiIiIiIuWmREJERERERMpNiYSIiIiIiJSbEgkRERERESk3l8oOoKq4XFREu78uuyVt//jWyFvSroiIiIhIZdGIRBV1+PBhOnXqhK+vL2FhYaSkpFy1XkxMDK1ataJFixaMGzeOwsJCh3K73U63bt2oX7++cSw5OZmHHnqI1q1b07ZtW5566ikuXrxolA8cOJAmTZpgMpk4c+aMw3kWi8X48fb2xt3d3Sjv2bMnQUFBWCwWHnzwQfbu3WuUPffcc3h7e2MymUhMTLyxhyMiIiIilU6JRBUVGRnJ+PHjOXToEFOnTsVqtZaoc/ToUaZPn86WLVtITU3l5MmTLFq0yKHOu+++S4sWLRyO1apViwULFvDTTz+RlJREXl4ec+fONconTJhw1S/7gYGBJCYmGj99+vRh2LBhRvmqVavYt28fiYmJTJ482SHmgQMHsnXrVpo3b/7HHoiIiIiIVClKJKqgnJwcEhISGD58OAADBgwgMzOT1NRUh3qrV68mIiICDw8PTCYTEyZM4NNPPzXKU1JS+PLLL3nppZcczmvVqhVBQUEAODs7ExYWRlpamlHeo0cPGjduXGqM+fn5rFixgjFjxhjHfj/qcfbsWUwmk/H5oYcewmw2l+0BiIiIiEiVpzkSVVBmZiaenp64uBR3j8lkwsvLi4yMDFq2bGnUy8jIcPgNv7e3NxkZGQAUFhYybtw4YmJicHZ2vua18vLyWLx4MXPmzClXjPHx8fj4+GCxWByOjxw5kk2bNgGwbt26crUpIiIiItWHRiRuUzNnzuTxxx+nTZs216xz6dIlhgwZQs+ePenfv3+52o+JiXEYjbhi2bJlZGZmMmvWLKZOnVruuEVERESkelAiUQU1a9aM7OxsbDYbUDxhOiMjAy8vL4d6Xl5epKenG5/T0tKMOt999x3vvfce3t7edOnShdzcXLy9vTl16hRQPGIxZMgQPD09mTdvXrniO3r0KDt27ODJJ5+8Zp1Ro0axadMmfvnll3K1LSIiIiLVgxKJKqhx48aEhoayfPlyAOLi4jCbzQ6vNUHx3Ik1a9Zw4sQJ7HY7UVFRDB06FIAtW7aQnp5OWloaW7duxc3NjbS0NBo1aoTNZmPo0KG4u7uzaNEih7kMZbFkyRL69+/vMCfizJkzHD9+3Pj85Zdf0qBBA4dVnURERETk9qFEooqKjo4mOjoaX19f3nzzTWJjYwEYO3Ysa9asAcDHx4eZM2fSuXNnWrZsSaNGjYiMjLxu2ytXriQ+Pp6EhARCQkKwWCw888wzRvmjjz5qTIwOCAggPDzcKCsqKmLp0qUlXms6e/Ysjz32GIGBgQQHB7NgwQLWrl1rJCmRkZGYzWaysrLo1atXiaRIRERERKoXTbauovz8/Ni+fXuJ44sXL3b4PG7cOMaNG1dqW97e3g77QQwbNsxh2db/9I9//OOaZU5OTmRmZpY43rx5c3bt2nXN86Kjo0uNUURERESqF41IiIiIiIhIuWlE4jdO2Pmi7lu3pO2M125Nu/L/u9zmr2S8FljZYZSb16vJlR2CiIiIyB+iEQmRaubw4cN06tQJX19fwsLCSElJKVFn48aNdOjQAX9/fwICApgyZQpFRUVG+dy5c/H398disdCxY0eH19IGDhxIkyZNMJlMDq/EJScnY7FYjB9vb2+HyfQ9e/YkKCgIi8XCgw8+yN69e40yb29v/Pz8jHNXrlx5k5+KiIiIVDSNSIhUM5GRkYwfPx6r1crq1auxWq3s3r3boc4999zDZ599ho+PD/n5+fTo0YNly5ZhtVpJTExk4cKFpKSkcPfdd7N8+XImTZpkJBMTJkxg4cKF3HvvvQ5tBgYGkpiYaHyeNGmSw4pfq1atMlby+uKLL7BarSQlJRnlK1euLLGBoYiIiFRfGpEQqUZycnJISEhg+PDhQPESwJmZmaSmpjrUCwkJwcfHB4BatWphsVhIS0sDindKLywsJC8vDyheuvfKKl0APXr0oHHjxqXGkZ+fz4oVKxxW7/r9csBnz54t97LCIiIiUr1oREKkGsnMzMTT0xMXl+J/uiaTCS8vLzIyMq65pO6JEydYvXo1a9euBSA4OJgXXniB++67D3d3d1xdXfn+++/LFUd8fDw+Pj4lRhhGjhzJpk2bAFi3bl2JMrvdTocOHXjzzTdp1KhRua4pIiIiVYtGJERuY7m5ufTt25cpU6bQvn17oHhn8vj4eFJTU8nKyuKFF15gyJAh5Wo3JiamxF4iAMuWLSMzM5NZs2YxdepU4/j333/Pvn372LNnDw0bNmTUqFE3dmMiIiJS6ZRIiFQjzZo1Izs7G5vNBoDdbicjIwMvL68Sdc+dO0fv3r3p168fkydPNo7HxcURGBhIkyZNABg9ejTbtm3j0qVLZYrh6NGj7NixgyeffPKadUaNGsWmTZv45ZdfAIz4atSowZ///Ge2bNlSthsWERGRKkuJhEg10rhxY0JDQ1m+fDlQnBSYzeYSrzWdP3+e3r1707t3b1555RWHMh8fH7Zt28b58+cBWLt2Lb6+vtSsWbNMMSxZsoT+/fs7zIk4c+YMx48fNz5/+eWXNGjQAHd3d/Ly8hxWf/r0008JCQkpz22LiIhIFaQ5EiLVTHR0NFarldmzZ+Pm5kZsbCwAY8eOJSIigoiICObNm8euXbvIy8sjPj4egEGDBjFt2jT69+/P7t27ad++Pa6urtSpU4dPPvnEaP/RRx81VlsKCAigVatWbN68GYCioiKWLl3KsmXLHGI6e/YsgwYN4uLFizg5OdGoUSPWrl2LyWTi5MmTDBgwgMuXL2O32/Hx8SlxvoiIiFQ/Jrvdbq/sIKqChg3c2fN808oOQ/6g/W3+StuD1W/jP21I9/9bv349vXr1quww5AaoD6s/9WH1dif0n9lsJisrq7LDkN/o1SYRERERESk3vdr0myLgiXvcKjuMSrft2W2VHcIfcnD9ev12X0RERKQCaURCbtjhw4fp1KkTvr6+hIWFkZKSUqJOWloa4eHh1KtXr8TeA6WVFRUVMXnyZPz9/QkKCqJr167G5mvJyck89NBDtG7dmsjISJ566ikuXrxonHv69GmGDRuGr68vAQEBvPTSS0bZwIEDadKkCSaTyWEisIiIiIiUjRIJuWGRkZGMHz+eQ4cOMXXqVKxWa4k6bm5uzJo1y2FSb1nK1qxZw7Zt20hKSmLfvn10796dl19+GSjesXnBggX89NNPLFy4kLy8PObOnWuc+9RTTxESEsKhQ4dISUnhz3/+s1E2YcIEEhMTb/jeRURERO5USiTkhuTk5JCQkMDw4cMBGDBgAJmZmcaowRXu7u506dKFOnXqlGijtDKTyURBQQH5+fnY7XZyc3Mxm80AtGrViqCgIACcnZ0JCwsjLS0NgNTUVBISEhz2T/Dw8DD+3KNHDxo3bnxjNy8iIiJyB1MiITckMzMTT09PXFyKp9uYTCa8vLzIyMi4Ke337duX8PBwPDw88PT05Ntvv+W1114rUS8/P5/FixfTr18/AA4cOIDZbObpp5+mXbt29OzZk717996UmEREREREiYRUcQkJCezfv59jx45x/PhxunfvzoQJExzqXLp0idmzZ9OzZ0/69+8PgM1mY9euXQwdOpQff/yRF154gT59+lBYWFgZtyEiIiJy21EiITekWbNmZGdnY7PZALDb7WRkZODl5XVT2l+2bBndunWjfv36ODk5MWrUKDZt2mSUFxYWMmTIENzd3Zk3b55x3MvLi6ZNm9K1a1cAHn74YS5dukR6evpNiUtERETkTqdEQm5I48aNCQ0NZfny5QDExcVhNptp2bLlTWnfx8eHjRs3cunSJQDWrl1L27ZtgeJRh6FDh+Lu7s7zzz+PyWQyzmvXrh1ubm7s27cPgF27dmG322nWrNlNiUtERETkTqd9JOSGRUdHY7VamT17Nm5ubsTGxgIwduxYIiIiiIiI4MKFC/j6+lJQUMDZs2cxm82MGDGCOXPmlFr2zDPPcPDgQYKDg6lRowYeHh5ERUUBsHLlSuLj4wkKCmLz5s3UrVuXzp078/7772Mymfjoo48YN24cFy9exNXVlbi4OFxdXQF49NFHSUpKAiAgIIBWrVqxefPmSnl+IiIiItWREgm5YX5+fmzfvr3E8cWLFxt/vuuuu665pX1pZa6urnz44YdXLRs2bBjDhg0DYP369fTq1cuhvF27duzcufOq5/7jH/+46nERERERKRu92iQiIiIiIuWmEYnfONlh9ufV+3H81/ffVXYIIiIiInKH0IjEHe7w4cN06tQJX19fwsLCSElJuWq9mJgYWrVqRYsWLRg3bpyxjGpRURGTJ0/G39+foKAgunbt6rAZ3dy5c/H398disdCxY0d27dpllA0cOJAmTZpgMpk4c+aMw/U+/vhjgoODadu2Ld27d3fYl+JaMf/yyy9YLBbjx9fXFxcXF3799deb9bhERERE5DdKJO5wkZGRjB8/nkOHDjF16lSsVmuJOkePHmX69Ols2bKF1NRUTp48yaJFiwBYs2YN27ZtIykpiX379tG9e3defvllABITE1m4cCG7du0iMTGRSZMmMWnSJKPdCRMmkJiYWOJ6P/30E3/961/5v//7P/bv38/o0aN5+umnrxtzgwYNSExMNH7Gjx/Pww8/jLu7+817YCIiIiICKJG4o+Xk5JCQkMDw4cMBGDBgAJmZmQ4jCgCrV68mIiICDw8PTCYTEyZM4NNPPwWKd7IuKCggPz8fu91Obm4uZrPZKCssLCQvLw+AM2fOGGUAPXr0oHHjxiXi2r9/P0FBQXh6egLwyCOP8M9//pNffvnlmjEfP368RDsxMTGMGTPmRh+TiIiIiFxF9Z4UIDckMzMTT09PXFyK/xqYTCa8vLzIyMhw2AciIyOD5s2bG5+9vb2NV4369u3Lpk2b8PDwoG7dujRt2pTvviueqxEcHMwLL7zAfffdh7u7O66urnz//ffXjSs4OJg9e/Zw6NAhfH19Wb58OXa7nfT0dOx2+1VjzsnJcWjjhx9+4PTp0/Tp0+fGHpKIiIiIXJVGJOSGJCQksH//fo4dO8bx48fp3r07EyZMAIpfiYqPjyc1NZWsrCxeeOEFhgwZct02W7VqRVRUFCNHjqR9+/b88ssv1K9f30geyiImJoaRI0eW6xwRERERKTslEnewZs2akZ2djc1mA8But5ORkYGXl5dDPS8vL9LT043PaWlpRp1ly5bRrVs36tevj5OTE6NGjWLTpk1A8S7XgYGBNGnSBIDRo0ezbds2Y5fq0gwcOJAdO3aQkJDA008/zcWLF2nZsuU1Y/79K1Lnz59n1apVPPXUUzfwdERERESkNEok7mCNGzcmNDSU5cuXA8Vf/M1ms8NrTVA8D2HNmjWcOHECu91OVFQUQ4cOBcDHx4eNGzcaycHatWtp27atUbZt2zbOnz9vlPn6+lKzZs3rxpadnQ3A5cuXmTp1Ks888wx33XXXNWO+kqxA8Y7XwcHBtG7d+kYej4iIiIiUQu993OGio6OxWq3Mnj0bNzc3YmNjARg7diwRERFERETg4+PDzJkz6dy5MwDh4eFERkYC8Mwzz3Dw4EGCg4OpUaMGHh4eREVFAdC/f392795N+/btcXV1pU6dOnzyySfGtR999FGSkpIACAgIoFWrVmzevBmAp556ivT0dAoKCnj00UeZPXt2qTH/frJ1TEwM48aNu3UPTUREREQw2e12e2UHURU0dHcnrm1gZYdxQ+7kDenWr19Pr169KjsMuQHqw+pPfVj9qQ+rtzuh/8xmM1lZWZUdhvxGrzaJiIiIiEi5aUTiNw0aNGSmNbayw5A/yPP+IrJ3Ki+uztSH1Z/6sPpTH1ZvrXrW1IiEVCj910JERETkDvXcc8/h7e2NyWQiMTGxssORakaJhIiIiMgdauDAgWzdutVh41mRstKqTSIiIiJ3qIceeqiyQ5BqTCMSIiIiIiJSbkokRERERESk3JRIiIiIiIhIud3SROKXX37BYrEYP76+vri4uPDrr78adTZu3IizszP/7//9P+PY4cOH+dOf/kRwcDABAQGsXLnSKPvHP/5Bu3btcHV15c9//rPD9YqKinj22Wdp0aIFLVu2ZMGCBbfy9kRERERE7li3dLJ1gwYNHJYS+9vf/sZ3332Hu7s7AGfPnuWll17ikUcecTjParUyevRoxo4dy6lTp2jfvj1dunShadOmtGrViiVLlvD5559z/vx5h/OWL1/OgQMHOHToEGfPniUkJISuXbsSEBBwK29TREREpFqKjIzkH//4BydOnKBXr17UrVuX1NTUyg5LqokKfbUpJiaGMWPGGJ8nTZrEK6+8QoMGDRzqJSUlGclFo0aNCA4ONkYlfH19CQ4OxsWlZA60cuVKxo0bh7OzM+7u7gwZMoRPP/30Ft6RiIiISPUVHR1NVlYWNpuNkydPKomQcqmwROKHH37g9OnT9OnTB4DVq1fj5OREREREibrt2rVj+fLlAPzrX//ihx9+IC0t7brXyMjIcFgH2dvbm4yMjJtzAyIiIiIiYqiwfSRiYmIYOXIkLi4unDhxglmzZrF58+ar1v3oo4/4y1/+gsVioXnz5nTv3v2qIxA34p133uGdd94xPudfvMDZkx/d1GuU17Tlqyv1+tXZ+vXrmfR2r8oOQ26A+rD6Ux9Wf+rD6m39+vWVHYLcYSpkROL8+fOsWrWKp556CoAff/yR7OxsLBYL3t7erF69mtdee41p06YBxSMJcXFxJCYm8tVXX3H27NkyzXPw8vIiPT3d+JyWloaXl9dV606ePJmsrCzjp1btWjfhTive4cOH6dSpE76+voSFhZGSknLVejExMbRq1YoWLVowbtw4CgsLAdi8eTO1a9d2mBR/8eJFoHjy+osvvkjbtm1p3bo1Y8aM4dKlS0Dxs3V2dnY478iRI8b15s6di7+/PxaLhY4dO7Jr1y6jzGQyERgYaJy3ZcsWAJKTkx3a8/b2NubTiIiIiEjVUiEjEitXriQ4OJjWrVsD8Oijj3Ly5Emj3Gq1YrFYjFWYTp48SaNGjXBycmL9+vUcOHCAJ5988rrXGTRoEB9++CGDBg3i7NmzrFy5krVr196Se6oqIiMjGT9+PFarldWrV2O1Wtm9e7dDnaNHjzJ9+nT27NnDvffeS79+/Vi0aBHPPPMMAH5+fg6T4q+IiYlhz5497Nmzhxo1ajB+/HjmzZvHX//6VwDq1q171fMSExNZuHAhKSkp3H333SxfvpxJkyY5JBNbtmyhfv36DucFBgY6tDdp0iRMJtMfezAiIiIicktVyIjEf06yvp6///3v+Pr64ufnx5tvvsm6deuoXbs2AN9++y1ms5l33nmHmJgYzGYza9asAWDEiBG0bt2aVq1aERYWxuTJkwkMDLwl91QV5OTkkJCQwPDhwwEYMGAAmZmZJSZKrV69moiICDw8PDCZTEyYMKFMk9CTkpLo0aMHNWvWxGQy8fDDD/Pxxx9f9zyTyURhYSF5eXkAnDlzBrPZXK57y8/PZ8WKFeX6eyMiIiIiFadCRiR++OGHUsuXLl3q8Hns2LGMHTv2qnW7d+9OVlbWVcucnZ15//33/1CM1VFmZiaenp7G/BGTyYSXlxcZGRm0bNnSqHe9SehHjhwhNDQUZ2dnRo8ezcSJE4HiSe/R0dFMmjSJ2rVrs2rVKodJ73l5eYSFhXH58mUee+wxpk2bhrOzM8HBwbzwwgvcd999uLu74+rqyvfff+8Qe/fu3bHZbHTv3p3XX3+dOnXqOJTHx8fj4+ODxWK5WY9LRERERG4i7Wx9hwsNDSUrK4s9e/bwxRdfEBUVxapVq4DiV8569+7Nf/3Xf/Ff//VfxoaCAJ6enhw7dozdu3ezYcMGtmzZwttvvw0Uv0oVHx9PamoqWVlZvPDCCwwZMsS4Znp6Oj/++CM//PADp06dMl6V+r3yjmKJiIiISMVSIlGNNWvWjOzsbGw2GwB2u52MjIwSE8xLm4Tu5uZGvXr1ADCbzTzxxBPG5GeTycSMGTPYu3cvP/zwA/7+/sakd1dXVxo3bgyAu7s7Tz31lHFeXFwcgYGBNGnSBIDRo0ezbds2Y6L2lWvXqVOHiRMnGuddcfToUXbs2FGmeTEiIiIiUjmUSFRjjRs3JjQ01NhzIy4uDrPZ7PBaExTPnVizZg0nTpzAbrcTFRXF0KFDAcjOzqaoqAiAc+fOsXbtWkJCQoDieQqnT58G4N///jdvvvkmU6ZMAYrnZ1xZ+amgoID4+HjjPB8fH7Zt22bsPL527Vp8fX2pWbMmp0+f5sKFC0DxqlArV640zrtiyZIl9O/fv8RkbBERERGpOipsHwm5NaKjo7FarcyePRs3NzdiY2OB4nkmERERRERE4OPjw8yZM+ncuTMA4eHhREZGAsXJxwcffICLiws2m41BgwYxevRoAM6ePUt4eDhOTk4UFRXx/PPP07dvXwC2bt3Kq6++irOzMzabjW7duhnL9/bv35/du3fTvn17XF1dqVOnDp988gkAP/30E5GRkZhMJmw2G6GhocybN8+4n6KiIpYuXcqyZcsq5gGKiIiIyB9istvt9soOoipo0MCdyQ93q9QYtCHdH7d+/Xp69dImStWZ+rD6Ux9Wf+rD6u1O6D+z2XzNRXek4unVJhERERERKTe92vQbE0483qZ42dM20yp3ZEJEREREpKrTiMRNcvjwYTp16oSvry9hYWGkpKRctV5MTAytWrWiRYsWjBs3zpiwXFrZ5s2bqV27NhaLxfi5ePEiUDyn4MUXX6Rt27a0bt2aMWPGGKsjQfEeEn379sXPzw9/f3/ee+89oHj48/ftNWnShNDQ0Fv1eERERETkNqNE4iaJjIxk/PjxHDp0iKlTp2K1WkvUOXr0KNOnT2fLli2kpqZy8uRJFi1adN0yAD8/PxITE42fKzt9x8TEsGfPHvbs2cPBgwdxcnIyJi/b7Xb69+/PyJEj+fnnnzlw4ACDBw8GoFevXg7thYaGMmzYsFv8lERERETkdqFE4ibIyckhISGB4cOHA8XLrWZmZpKamupQb/Xq1URERODh4YHJZGLChAl8+umn1y0rTVJSEj169KBmzZqYTCYefvhhPv74YwC+/fZbXF1dGTRokFH/3nvvLdHG8ePH+fbbbxkxYsQffgYiIiIicmdRInETZGZm4unpaez6bDKZ8PLyIiMjw6FeRkYGzZs3Nz57e3sbdUorAzhy5AihoaGEhYWxcOFC43i7du1Ys2YNubm5FBYWsmrVKtLS0gA4cOAAjRo1YujQoYSEhNC/f3/+9a9/lYh/6dKlPPLII8YGcyIiIiIi16PJ1tVAaGgoWVlZ1KtXj6ysLB555BEaNmzI4MGDsVqtpKen81//9V/Url2bHj168PXXXwNgs9nYuHEjO3bsICAggKioKAYPHkxCQoLRtt1uZ8mSJcyfP7+ybk9EREREqiGNSNwEzZo1Izs7G5vNBhR/Oc/IyMDLy8uhnpeXF+np6cbntLQ0o05pZW5ubtSrVw8oXj/5iSeeYMuWLUDx6MeMGTPYu3cvP/zwA/7+/gQEBBhthoSEGJ9HjBjBnj17HCZ4f/fdd+Tn59/2606LiIiIyM2lROImaNy4MaGhoSxfvhwo3i3abDbTsmVLh3oDBgxgzZo1nDhxArvdTlRUFEOHDr1uWXZ2NkVFRQCcO3eOtWvXEhISAkB+fj6nT58G4N///jdvvvkmU6ZMAeDhhx8mKyuLY8eOAbBu3TratGlDjRo1jJhiYmKwWq04OzvfqscjIiIiIrchvdp0k0RHR2O1Wpk9ezZubm7ExsYCMHbsWCIiIoiIiMDHx4eZM2fSuXNnAMLDw4mMjAQotSwuLo4PPvgAFxcXbDYbgwYNYvTo0QCcPXuW8PBwnJycKCoq4vnnn6dv374A1KlTh6ioKB599FHsdjv16tXjs88+M2I+e/Ys8fHxJCcnV8xDEhEREZHbhslut9srO4iqoGGDhmyZvArQhnTV0fr16/V6VjWnPqz+1IfVn/qwersT+s9sNpOVlVXZYchv9GqTiIiIiIiUm15t+o0dOysLvy/+MOP7yg3mDjdjxoxyn3Ps2DE6derEv//9b+rVq8fSpUuNSeZXpKWlYbVa2bt3L/fddx+JiYlGWWxsrLGRH0BWVhYPPfQQ8fHxpKWl0aJFCwIDA43yuLg4WrRoAcBbb73FRx99RFFREX5+fsTGxlK/fv1y34OIiIhIdaIRCbktzJ8//7o7i7u5uTFr1iw++eSTEmWjR4922Onbw8PDYafvunXrOpRfSSK++eYbYmNj2b59OwcOHKBdu3ZMmzbtlt2niIiISFWhREKqvZycHA4fPnzdncXd3d3p0qULderUKbW9nTt3kpOTQ0RExHWvnZSURJcuXahbty4AjzzyiLGzuIiIiMjtTImEVHuZmZncc889191ZvKxiYmIYMWKEwzK5eXl5hIWFERoaymuvvcbly5eB4p3FN2zYYCzbu2LFCs6dO8evv/564zcmIiIiUoUpkRD5nby8PD777DPGjBljHPP09OTYsWPs3r2bDRs2sGXLFt5++20AunbtyosvvkifPn3o2LEjjRo1AjCSGhEREZHblRIJqfaaNWvG6dOnr7uzeFl8/vnnBAQE4O/vbxxzdXWlcePGQPHrUU899ZSxszjAxIkTSUhIYOfOnYSHh2M2m3Fzc7vBuxIRERGp2pRISLXXuHFjWrRocd2dxcsiJibGYTQCiudgFBYWAlBQUEB8fLyxszgU7zwOcOHCBV599VVjZ3ERERGR25kSCbktPPfcc0RHR+Pr68ubb77psLP4mjVrgOIv+mazmUGDBnHgwAHMZjP//d//bbTx888/k5iYyJAhQxza3rp1KyEhIQQHBxMaGoqHh4fDykw9e/YkICCA4OBgunTpwqRJkyrgjkVEREQql17klttCs2bN2L59e4njixcvNv581113lbobpp+fH+fOnStx/PHHH+fxxx+/5nnJycnljFZERESk+tOIhIiIiIiIlJtGJH5jMtnxD1hX2WGUMHjQrsoOQURERESkBI1I3IYOHz5Mp06d8PX1JSwsjJSUlKvWi4mJoVWrVrRo0YJx48YZE4qh+HWd8PBw2rRpQ5s2bYiPjwcgNjYWi8Vi/DRs2NB47SctLQ1nZ2eH8iNHjgBw/vx5evXqRcOGDalfv75DHOvXr3c4p0mTJoSGhhrlAwcOpEmTJphMJs6cOXMTn5SIiIiI/FEakbgNRUZGMn78eKxWK6tXr8ZqtbJ7926HOkePHmX69Ons2bOHe++9l379+rFo0SKeeeYZLly4QL9+/Vi2bBldunTh8uXLxgZro0ePZvTo0UY7bdu2ZdiwYcbnunXrkpiYWCKmGjVqMHXqVNzd3QkPD3co69WrF7169TI+9+nTh65duxqfJ0yYwMKFC7n33ntv5LGIiIiIyE2kEYnbTE5ODgkJCQwfPhyAAQMGkJmZSWpqqkO91atXExERgYeHByaTiQkTJvDpp58C8Mknn9CxY0e6dOkCgLOzs7HR2u/t3LmTnJwcIiIirhuXq6sr3bp1KzEa8Z+OHz/Ot99+y4gRI4xjPXr0MPZxEBEREZGqQYnEbSYzMxNPT09jZ2WTyYSXlxcZGRkO9TIyMmjevLnx2dvb26hz4MABXF1d6dOnDxaLhZEjR3Lq1KkS14qJiWHEiBHUqFHDOJaXl0dYWBihoaG89tprXL58uVzxL126lEceeUSJg4iIiEgVp0RCSrDZbGzYsIHo6Gj27t1L06ZNefrppx3q5OXl8dlnnzls3ubp6cmxY8fYvXs3GzZsYMuWLbz99ttlvq7dbmfJkiUlNoQTERERkapHicRtplmzZmRnZ2Oz2YDiL+cZGRl4eXk51PPy8iI9Pd34nJaWZtTx8vKia9euNG3aFJPJxPDhw9mxY4fD+Z9//jkBAQH4+/sbx1xdXY2RBHd3d5566im2bNlS5ti/++478vPzHeZLiIiIiEjVpETiNtO4cWNCQ0NZvnw5AHFxcZjNZlq2bOlQb8CAAaxZs4YTJ05gt9uJiopi6NChAAwePJjdu3eTm5sLwLp16wgODnY4PyYmpsTIQU5OjrHyU0FBAfHx8YSEhJQ59piYGKxWK87OzuW7aRERERGpcEokbkPR0dFER0fj6+vLm2++SWxsLABjx45lzZo1APj4+DBz5kw6d+5My5YtadSoEZGRkUDxiMTLL79Mp06dCAoKYuPGjURFRRnt//zzzyQmJjJkyBCH627dupWQkBCCg4MJDQ3Fw8ODadOmGeVBQUE88MAD5ObmYjabHSZUnz17lvj4eJ566qkS9/Poo49iNpsBCAgIKLHqk4iIiIhUPJPdbrdXdhBVQcOG7iz8oOX1K1YwbUhXNuvXr9crUdWc+rD6Ux9Wf+rD6u1O6D+z2UxWVlZlhyG/0YiEiIiIiIiUmzak+00RTrxher2ywyjhjdXrKzuEauEvLvkE61lVa9WtD5MG3t6/9RMREbkejUiIiFSQw4cP06lTJ3x9fQkLCyMlJeWade12e4lNHNevX4/FYjF+mjRpQmhoKADJyckOZd7e3ri7uxvn9uzZk6CgICwWCw8++CB79+4tcc3Y2FhMJhNffvmlQxwzZszA19eXwMBAh13nRUTkzqYRCRGRChIZGcn48eOxWq2sXr0aq9XK7t27r1r33XffpUWLFuzZs8c41qtXL4f3n/v06WN8sQ8MDCQxMdEomzRpEiaTyfi8atUqIyn54osvsFqtJCUlGeVpaWl8+OGHdOzY0SGO+fPns2/fPvbv30/NmjU5ceLEH75/ERG5vWhEQkSkAuTk5JCQkMDw4cOB4iWYMzMzSU1NLVE3JSWFL7/8kpdeeuma7R0/fpxvv/3WYfWzK/Lz81mxYoXDEs2/H9k4e/asQ5JRVFTE2LFjee+993B1dXVo66233uLNN9+kZs2aAHh4eJTthkVE5LanREJEpAJkZmbi6emJi0vxQLDJZMLLy4uMjAyHeoWFhYwbN47o6OhS91RZunQpjzzyiLEJ5O/Fx8fj4+ODxWJxOD5y5EiaNWvG9OnT+fjjj43j77zzDp07d6Zdu3YO9XNzczl58iRfffUV999/P/fffz8rV64s762LiMhtSq82iYhUITNnzuTxxx+nTZs2pKWlXbWO3W5nyZIlzJ8//6rlV9swEmDZsmUAfPTRR0ydOpV169axf/9+4uLi+P7770vUt9ls2Gw2Ll68yM6dO0lLS6NTp060bt26xCaVIiJy59GIhIhIBWjWrBnZ2dnYbDagOBnIyMjAy8vLod53333He++9h7e3N126dCE3Nxdvb29OnTrlUCc/P/+q68UfPXqUHTt28OSTT14zllGjRrFp0yZ++eUXtmzZQlpaGq1atcLb25sdO3Ywfvx4PvjgA9zd3bn77ruN17G8vb3p3LnzNed1iIjInUWJhIhIBWjcuDGhoaEsX74cgLi4OMxmMy1bOm6EuWXLFtLT00lLS2Pr1q24ubmRlpZGo0aNjDoxMTFYrdarvvq0ZMkS+vfv7zAn4syZMxw/ftz4/OWXX9KgQQPc3d15+umnyc7OJi0tjbS0NDp27MiiRYt4+umnAXjiiSf4v//7PwB+/fVXdu3aRVBQ0E17LiIiUn3p1SYRkQoSHR2N1Wpl9uzZuLm5ERsbC8DYsWOJiIggIiLium2cPXuW+Ph4kpOTS5QVFRWxdOlS4xWm358zaNAgLl68iJOTE40aNWLt2rUOE66vZc6cOYwePZqFCxcCMHXqVDp06FCW2xURkducEgkRkQri5+fH9u3bSxxfvHjxVet7e3tz5swZh2P16tUjLy/vqvWdnJzIzMwscbx58+bs2rWrTDFu3rzZ4XODBg1Ys2ZNmc4VEZE7i15tEhERERGRctOIxG+cTSaSBpacuCjVw/r160m6ysRTqT7UhyIiItWLRiRERERERKTclEiIiIiIiEi5KZEQEREREZFyUyIhIiIiIiLlpkRCRERERETKTYmEiIiIiIiUmxIJEREREREpNyUSIiIiIiJSbkokRERERESk3JRIiIiIiIhIuSmREBERERGRclMiISIiIiIi5aZEQkREREREys1kt9vtlR1EVeDi4oKHh0dlhyF/0Pnz57n77rsrOwy5AerD6k99WP2pD6u3O6H/Tp06RUFBQWWHIb9xqewAqgoPDw+ysrIqOwz5g8xms/qvmlMfVn/qw+pPfVi9qf+kounVJhERERERKTclEiIiIiIiUm5KJH4zefLkyg5BboD6r/pTH1Z/6sPqT31Yvan/pKJpsrWIiIiIiJSbRiRERERERKTclEiIiIiIiEi53VGJxOHDh+nUqRO+vr6EhYWRkpJy1XoxMTG0atWKFi1aMG7cOAoLCys4UrmasvTfxo0b6dChA/7+/gQEBDBlyhSKiooqIVq5mrL+GwSw2+1069aN+vXrV1yAcl1l7cPk5GTCw8Np06YNbdq0IT4+voIjlaspS/8VFRUxefJk/P39CQoKomvXrqSmplZCtHI1zz33HN7e3phMJhITE69ZT99lpELY7yBdu3a1x8bG2u12u/3zzz+3t2/fvkSdf/3rX3ZPT097dna2vaioyN63b1/7ggULKjhSuZqy9N+ePXvsR44csdvtdvvFixftnTt3Ns6RyleWPrzi7bffto8dO9Zer169iglOyqQsfZiXl2e/77777Fu2bLHb7Xa7zWaz5+TkVGSYcg1l6b8vvvjC3qFDB/ulS5fsdrvd/vrrr9sHDRpUkWFKKb777jt7ZmamvXnz5va9e/detY6+y0hFuWNGJHJyckhISGD48OEADBgwgMzMzBK/ZVm9ejURERF4eHhgMpmYMGECn376aWWELL9T1v4LCQnBx8cHgFq1amGxWEhLS6vocOUqytqHACkpKXz55Ze89NJLFR2mlKKsffjJJ5/QsWNHunTpAoCzszONGjWq8HjFUVn7z2QyUVBQQH5+Pna7ndzcXMxmc2WELFfx0EMPXbc/9F1GKsodk0hkZmbi6emJi0vxZt4mkwkvLy8yMjIc6mVkZNC8eXPjs7e3d4k6UvHK2n+/d+LECVavXk2fPn0qKkwpRVn7sLCwkHHjxhEdHY2zs3NlhCrXUNY+PHDgAK6urvTp0weLxcLIkSM5depUZYQsv1PW/uvbty/h4eF4eHjg6enJt99+y2uvvVYZIcsfpO8yUlHumERC7iy5ubn07duXKVOm0L59+8oOR8ph5syZPP7447Rp06ayQ5E/yGazsWHDBqKjo9m7dy9Nmzbl6aefruywpIwSEhLYv38/x44d4/jx43Tv3p0JEyZUdlgiUgXdMYlEs2bNyM7OxmazAcUTOTMyMvDy8nKo5+XlRXp6uvE5LS2tRB2peGXtP4Bz587Ru3dv+vXrp815qpCy9uF3333He++9h7e3N126dCE3Nxdvb2/9RrsKKM9/R7t27UrTpk0xmUwMHz6cHTt2VEbI8jtl7b9ly5YZCx04OTkxatQoNm3aVBkhyx+k7zJSUe6YRKJx48aEhoayfPlyAOLi4jCbzbRs2dKh3oABA1izZg0nTpzAbrcTFRXF0KFDKyNk+Z2y9t/58+fp3bs3vXv35pVXXqmMUOUaytqHW7ZsIT09nbS0NLZu3YqbmxtpaWl6x74KKGsfDh48mN27d5ObmwvAunXrCA4OrvB4xVFZ+8/Hx4eNGzdy6dIlANauXUvbtm0rPF754/RdRipM5c3zrng//fSTvWPHjvZWrVrZ27VrZ9+3b5/dbrfbx4wZY//qq6+MeosWLbL7+PjYfXx87E899ZSxcoVUrrL036xZs+wuLi724OBg42fWrFmVGbb8Tln/DV5x9OhRrdpUxZS1D5ctW2YPCAiwBwYG2nv37m3PyMiorJDld8rSf/n5+faxY8faW7dubQ8MDLT/6U9/MlbDk8o3fvx4e9OmTe3Ozs72xo0b21u0aGG32/VdRiqHyW632ys7mRERERERkerljnm1SUREREREbh4lEiIiIiIiUm5KJEREREREpNyUSIiIiIiISLkpkRARERERkXJTIiEi1Ya3tzetW7c2NtQCaN++PZs3b660mMLDw/nyyy8BePXVV1mxYsVNa3vgwIEsXbr0qmUmk4nAwEAsFovx88svv9y0a5fF0qVL+emnn4zPa9as4YUXXrhp7T/yyCPGvf3+fh988EGioqJ46623btq1RESk/FwqOwARkfIoKCggJiaGyMjIP9yGzWbDxeXm/+fvtddeu+ltlmbLli3Ur1+/Qq/5e0uXLqV+/fq0bt0agIiICCIiIm5a++vWrTP+bDKZKv1+RUTEkUYkRKRamTFjBq+//joXLlwoUZaTk8Pjjz9OYGAgbdu2JTo62ijz9vZm6tSpdOjQgVGjRjFjxgwGDx5M37598fX1pU+fPuzfv59evXrh6+vLE088QVFREQCffPIJ999/PyEhIQQHB/P3v//9qrFZrVb+3//7f0Dxl+orv0339vbmvvvuA+DcuXOMGzeODh06EBQUxPjx440dhH/66Sc6depEQEAAjz32mLEzdHl8//33tGjRgl9//RWASZMmMW7cOAAOHz7Mo48+SlhYGEFBQSxYsMA4b/v27XTp0oXg4GCCgoL46quvjOeWmJho1LsyArR48WISEhJ44YUXsFgsrFu3jqVLl/LYY48Zdd966y0CAgIIDAxk2LBhnD17FijuwyFDhtC3b1/8/f3p1q2bEW9ZzZgxgz//+c9AcULTo0cPnnjiCfz9/enUqRMHDhygf//+tGnThp49e3L+/HkACgsLeemll+jQoQMWi4XBgwdz+vTpcl1bRESKKZEQkWolODiYrl278u6775Yoe/bZZ/Hz8yM5OZmNGzcya9YsduzYYZT/8ssv7Ny503j9KCEhgWXLlvHzzz9z7tw5xo4dy+rVqzlw4AAHDx7kn//8JwC9evVix44d7N27l6+++opx48ZRUFBQapxr1qwhMTGRrVu30qBBA2bOnAnAX/7yFx588EF27dpFUlISRUVFzJs3D4ARI0YwZswYUlJSeP311/nuu+9KvcaDDz5oJCtdu3YF4KGHHmLs2LFYrVZWrVrF1q1bee+997h8+TJPPPEEb7/9Nrt372bHjh0sWrSI3bt38+uvv/LYY48xZ84ckpKSSExM5MEHHyz12mPHjqV9+/a8++67JCYm8sgjjziU//Of/2TJkiVs27aN5ORk6tSpw0svvWSU79y5k6VLl3LgwAEaN27skPT9Ebt372bu3LkcOHCAFi1a0LdvX6Kiojh48CA1a9bko48+AoqTmzp16rBr1y4SExMJDAzklVdeuaFri4jcqfRqk4hUO6+//jodOnRgwoQJDsc3bNjAjz/+CEDjxo15/PHH2bBhAx07dgSKRwxMJpNRv2fPntxzzz0AhIaG4urqSt26dQEICQnh8OHDABw9epRhw4aRlZWFi4sLv/76K0ePHjVe6bkWm83GoEGD6N+/PyNHjgTgyy+/ZPv27bzzzjsAXLx4EWdnZ3Jzc0lMTMRqtQIQGBhIly5dSm3/Wq/6vPTSSzz88MOMHz+eXbt2UatWLQ4cOEBKSgpDhw416p07d44DBw6Qk5ODn5+fkTw4OTnh7u5e6rWvZ8OGDQwZMsSI7+mnn2bQoEFGee/evWnQoAEADzzwAMnJyTd0vQceeAAvLy+geNSksLCQe++9F4CwsDCjL7/88kvOnj1LXFwcAJcuXcLb2/uGri0icqdSIiEi1Y63tzdPPvkks2bNKrXe75MGgLvvvtvhc61atYw/Ozs7l/h8ZVL30KFDefPNNxk4cCAA7u7u5OfnXzfOCRMmYDabHX7jbbfbiYuLw9fX16Hu1V5j+s/4y+rcuXP861//ok6dOpw6dQpfX1/sdjvu7u4Oryld8Y9//OOabbm4uHD58mXjc1nu+2r+816u9az/qLL2pd1u57333qNnz543dD0REdGrTSJSTb3yyissX76c48ePG8d69OjBhx9+CMCpU6eIj4/nT3/60w1f6/Tp08Ych+XLl5fpnfrXXnuN48eP88EHHzgcf+yxx5g7d67xxfb06dOkpqbi5uZGSEgIy5YtAyAlJYWtW7f+oXjHjBnDsGHDWLVqFSNGjOCXX37Bz88PNzc3YmNjjXqpqan8+uuvdOrUicOHD7NlyxYAioqKjDkLLVu2ZOfOnQDs2rWLn3/+2Tjfzc3NmPfwn3r06MGqVauMBCk6OrpKfHl/7LHHePfdd405NhcuXCAlJaWSoxIRqZ6USIhItdSwYUOee+45srOzjWPz58/n4MGDBAYG0rVrV6ZNm8b9999/w9eaN28eAwcOJCQkhL179xqv0JTmf/7nfzhy5Ajt27fHYrEYcwjeffddateujcViISgoiO7du5OWlgbAsmXLWLRoEW3btuWVV17hoYceKvUav58jYbFY+Pnnn1mwYAG//vor06dPp3Pnzjz99NOMHDkSZ2dn1q5dS3x8PEFBQQQEBDBmzBguXrzIPffcwxdffMFLL71EUFAQoaGhbNu2DYBZs2bx/vvvExwczJIlSwgICDCuP378eGbPnm1Mtv69hx9+mNGjR/PAAw8QGBhIbm4uc+bMKc9jvyWmTp1KWFgY999/P0FBQXTs2PGqozQiInJ9Jrvdbq/sIEREREREpHrRiISIiIiIiJSbEgkRERERESk3JRIiIiIiIlJuSiRERERERKTclEiIiIiIiEi5KZEQEREREZFyUyIhIiIiIiLlpkRCRERERETKTYmEiIiIiIiU2/8H3vwmoiZTAtEAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now plot the normalized execution time of the different solvers running on a Nvidia GTX 1050 GPU. "
      ],
      "metadata": {
        "id": "oW5Ho0TLXC6O"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# figure(num=None, figsize=(10, 9), dpi=80, facecolor='w', edgecolor='r')\n",
        "\n",
        "ax = sns.barplot(data=df_gpu, y='Number of Cells',\n",
        "                 x='Normalized Execution Time', hue='Solver', orient='h')\n",
        "sns.move_legend(ax, 'upper left', bbox_to_anchor=(1, 1))\n",
        "\n",
        "for container in ax.containers:\n",
        "    ax.bar_label(container, padding=10)\n",
        "\n",
        "plt.grid(axis='x')\n",
        "plt.xlim([0, 1.1])\n",
        "plt.title(f'Normalized Execution Time of SciPy Sparse Linear Solvers on GPU')\n",
        "# plt.savefig(f'solvers_exec_time_cpu.png', bbox_inches='tight')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "0NhvN8qEV84R",
        "outputId": "0d48a41e-8b73-41f4-aeb9-c0d906dc8950"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see, for both devices, the `minres` solver is the best performing one, especially in the case of large matrix dimensions. We believe that the main reason for such result lies in the fact that `minres` is able to best leverage the symmetry and the sparseness of the stiffness matrix compared to the other solver algorithms."
      ],
      "metadata": {
        "id": "SH8JRPn8XBcR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## K-Assembly Implementation\n",
        "\n",
        "We now show different implementations for the K-assembly step. Given the chosen FEM problem, the stiffness matrix K is sparse by construction. This allows us to leverage different strategies for storing it.\n",
        "\n",
        "There exist several ways for storing sparse matrices, each with its own trade-offs. the Compressed Sparse Row (CSR) format, for instance, is well suited for efficient matrix computations, but it's not for accessing individual elements via indexing. This limitation can be overcome by the [COOrdinate (COO) format](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_matrix.html#scipy.sparse.coo_matrix): in practice three arrays contain the non-zero elements, rows, and columns indexes, respectively, of the matrix.\n",
        "\n",
        "Although not being optimal in terms of storage size, the SciPy and CuPy COO implementations have the advantage of automatically handle duplicate entries, _i.e._, at same coordinates, by summing them. This mechanism avoids manual handling of the reduction of the elements stiffness matrixes which share nodes together.\n",
        "Because of that, we decided to adopt the COO format during the assembly of the stiffness matrix, before converting it to CSR format for the subsequent solving step.\n",
        "\n",
        "In the following analysis, we solve the full FEM problem exploiting the MINRES solver algorithm.\n",
        "\n",
        "<!-- It allows fast indexing ($O(1)$ complexity) and  -->"
      ],
      "metadata": {
        "id": "3-rhRflJMC84"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Naive K-Assembly on CPU\n",
        "\n",
        "The naive K-assembly implementation mainly consists of a loop over each cell element. As expected, it is not well performant."
      ],
      "metadata": {
        "id": "P3T6-OZ6aXnh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@nb.jit(nopython=True, cache=True, parallel=True)\n",
        "def get_coo_indices(dofs):\n",
        "    block_sz, n_dofs_per_cell = dofs.shape\n",
        "    f_rows = np.empty(dofs.shape, dtype=np.int32)\n",
        "    f_cols = np.zeros(dofs.size, dtype=np.int32)\n",
        "    K_rows = np.empty((block_sz, n_dofs_per_cell, n_dofs_per_cell), dtype=np.int32)\n",
        "    K_cols = np.zeros((block_sz, n_dofs_per_cell, n_dofs_per_cell), dtype=np.int32)\n",
        "    for k in prange(block_sz):\n",
        "        for i, dof_i in enumerate(dofs[k]):\n",
        "            f_rows[k, i] = dof_i\n",
        "            for j, dof_j in enumerate(dofs[k]):\n",
        "                K_rows[k, i, j] = dof_i\n",
        "                K_cols[k, i, j] = dof_j\n",
        "    return (K_rows.flatten(), K_cols.flatten()), (f_rows.flatten(), f_cols.flatten())\n",
        "\n",
        "def naive_k_assembly_cpu(a, weak_form, dh, grid=None):\n",
        "    if grid is None:\n",
        "        grid = dh.grid\n",
        "    # Init element matrices\n",
        "    ndofs_cell = dh.get_ndofs_per_cell()\n",
        "    ke = np.zeros((ndofs_cell, ndofs_cell), dtype=np.float32)\n",
        "    re = np.zeros(ndofs_cell, dtype=np.float32)\n",
        "    # Setup K matrix and f vector in COO format\n",
        "    K_data, K_rows, K_cols = [], [], []\n",
        "    f_data, f_rows, f_cols = [], [], []\n",
        "    # Assemble K and f components\n",
        "    for cellid in range(grid.get_num_cells()):\n",
        "        ke.fill(0.0)\n",
        "        re.fill(0.0)\n",
        "        xe = grid.get_coordinates(cellid)\n",
        "        dofs = dh.get_cell_dofs(cellid)\n",
        "        ue = a[dofs] # NOTE: Not relevant as input for linear elasticity\n",
        "        weak_form.run_element_routine(ke, re, xe, ue)\n",
        "        K_tmp, f_tmp = get_coo_indices(dofs[None])\n",
        "        # Update K matrix components\n",
        "        K_data.extend(ke.flatten())\n",
        "        K_rows.extend(K_tmp[0])\n",
        "        K_cols.extend(K_tmp[1])\n",
        "        # Update f vector components\n",
        "        f_data.extend(re.flatten())\n",
        "        f_rows.extend(f_tmp[0])\n",
        "        f_cols.extend(f_tmp[1])\n",
        "    # Convert lists to COO matrices\n",
        "    # NOTE: Components at same indeces are automatically accumulated together\n",
        "    K_data = np.array(K_data, dtype=np.float32).flatten()\n",
        "    K_rows = np.array(K_rows, dtype=np.int32).flatten()\n",
        "    K_cols = np.array(K_cols, dtype=np.int32).flatten()\n",
        "    K = coo_matrix((K_data, (K_rows, K_cols)), dtype=np.float32)\n",
        "    f_data = np.array(f_data, dtype=np.float32).flatten()\n",
        "    f_rows = np.array(f_rows, dtype=np.int32).flatten()\n",
        "    f_cols = np.array(f_cols, dtype=np.int32).flatten()\n",
        "    f = coo_matrix((f_data, (f_rows, f_cols)), dtype=np.float32).toarray()\n",
        "    return K, f"
      ],
      "metadata": {
        "id": "Pz99Ps4E4Yz5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def run_solver(K, f, a, dofs, solver=scipy.sparse.linalg.spsolve):\n",
        "    K_free = K.tocsc()[:, dofs['free']].tocsr()[dofs['free'], :]\n",
        "    K_prescribed = K.tocsc()[:, dofs['prescribed']].tocsr()[dofs['free'], :]\n",
        "    f_glob = -K_prescribed @ a[dofs['prescribed']]\n",
        "    return solver(K_free, f_glob)"
      ],
      "metadata": {
        "id": "k-t3uxtGXNi_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.5)\n",
        "# dh.grid.plot(a.reshape(len(dh.grid.nodes), dh.n_dofs_per_node)[:, 1])\n",
        "K, f = naive_k_assembly_cpu(a, weak_form, dh)\n",
        "a[dofs_glob['free']], _ = run_solver(K, f, a, dofs_glob, solver=scipy.sparse.linalg.minres)"
      ],
      "metadata": {
        "id": "wzkSzODS45qj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_K(K, filename=None):\n",
        "    if K.shape[0] < 20000:\n",
        "        plt.spy(K)\n",
        "        if filename is not None:\n",
        "            plt.savefig(filename)\n",
        "        plt.show()\n",
        "\n",
        "plt.title('Global stiffness matrix')\n",
        "plot_K(K)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "iYiwTGdmrCoa",
        "outputId": "56979b85-42cf-406d-a094-ba369ddbe848"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_grid(a, dh):\n",
        "    if len(dh.grid.nodes) < 2000:\n",
        "        nodal_effects = a.reshape(len(dh.grid.nodes), dh.n_dofs_per_node).copy()\n",
        "        plt.title('X components')\n",
        "        dh.grid.plot(nodal_effects[:, 0])\n",
        "        plt.title('Y components')\n",
        "        dh.grid.plot(nodal_effects[:, 1])\n",
        "\n",
        "plot_grid(a, dh)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 545
        },
        "id": "7h04mYw-X486",
        "outputId": "2a6f5c97-8ab4-4b25-e845-a645dee25af8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Profiling\n",
        "\n",
        "This section about code profiling is reported for completeness, but its output is omitted for brevity.\n",
        "\n",
        "Please note that these two cells execution will take a considerable amount of time to complete, since the implementation is not efficient yet."
      ],
      "metadata": {
        "id": "MjKJIwUtxd_X"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# a, weak_form, dh, dofs_glob = generate_rand_fem_problem(filename=f'data/randgrid_n{int(3e3)}.npz')\n",
        "a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.09)\n",
        "print(f'Number of cells: {len(dh.grid.cells)}')\n",
        "print(f'Number of nodes: {len(dh.grid.nodes)}')\n",
        "K_dim = dh.get_ndofs_total()\n",
        "print(f'a dimensions: ({K_dim}, 1)')\n",
        "print(f'K dimensions: ({K_dim}, {K_dim}) (Total elements: {K_dim * K_dim})')"
      ],
      "metadata": {
        "id": "35tmiLF6xd_Z",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e24ee6f7-42cb-4a05-d46d-7fc20937d5bf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of cells: 264199\n",
            "Number of nodes: 132856\n",
            "a dimensions: (265712, 1)\n",
            "K dimensions: (265712, 265712) (Total elements: 70602866944)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Reset a, in case this code is called multiple times\n",
        "a = np.zeros(dh.get_ndofs_total())\n",
        "a[dofs_glob['top'][:, 1]] = -0.1\n",
        "# Init profiler\n",
        "profiler = cProfile.Profile()\n",
        "profiler.enable()\n",
        "# Run CPU functions\n",
        "K, f = naive_k_assembly_cpu(a, weak_form, dh)\n",
        "a[dofs_glob['free']], _ = run_solver(K, f, a, dofs_glob,\n",
        "                                     solver=scipy.sparse.linalg.minres)\n",
        "# Stop profiling\n",
        "profiler.disable()\n",
        "# Create statistics from the profiler, sorted by cumulative time\n",
        "stats = pstats.Stats(profiler).sort_stats('cumtime')\n",
        "# Print the 10 (inclusive) most expensive functions\n",
        "stats.print_stats(10)"
      ],
      "metadata": {
        "id": "_dYiqX6Vxd_b"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Batched K-Assembly on CPU\n",
        "\n",
        "As for-loops are very inefficient in Python, one optimization strategy is to refactor the code to eliminate explicit for-loop and instead embed them into Numba-optimized functions. In fact, we can take advantage of the fact that the element routine can be run independently on each cell before being eventually accumulated."
      ],
      "metadata": {
        "id": "MMSLg7LPQ3jJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Batched Element Routine on CPU\n",
        "\n",
        "In the following Numba functions, the vectors are defined with an additional first dimension, which indexes elements in the grid or in a batch. Numba has been utilized to optimize the remaining for-loops in the algorithm."
      ],
      "metadata": {
        "id": "XOr2eTapRxLS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@nb.guvectorize('(float32[:,:,:], float32[:])', '(b,c,n)->(b)', cache=True, target='parallel')\n",
        "def jacobi_det_cell3_2D(xe, detJ):\n",
        "    for i in prange(detJ.shape[0]):\n",
        "        detJ[i] = ((xe[i, 1, 0] - xe[i, 0, 0]) * (xe[i, 2, 1] - xe[i, 0, 1]) -\n",
        "                   (xe[i, 2, 0] - xe[i, 0, 0]) * (xe[i, 1, 1] - xe[i, 0, 1]))\n",
        "\n",
        "\n",
        "def jacobian_cell3_2D(xe, J):\n",
        "    # TODO(Kim): Not generally constant, could depend on iso_coord (xi)\n",
        "    J[:, 0, 0] = xe[:, 1, 0] - xe[:, 0, 0]\n",
        "    J[:, 0, 1] = xe[:, 2, 0] - xe[:, 0, 0]\n",
        "    J[:, 1, 0] = xe[:, 1, 1] - xe[:, 0, 1]\n",
        "    J[:, 1, 1] = xe[:, 2, 1] - xe[:, 0, 1]\n",
        "\n",
        "\n",
        "@nb.jit(nopython=True, cache=True, parallel=True)\n",
        "def assemble_B(dNdx, B):\n",
        "    \"\"\"\n",
        "    dNdx: (batch_sz, n_nodes_cell, n_dofs_node)\n",
        "    B: (batch_sz, n_nodes_cell, n_dofs_cell)\n",
        "    \"\"\"\n",
        "    for j in range(dNdx.shape[1]):\n",
        "        dNidx = dNdx[:, j, 0]\n",
        "        dNidy = dNdx[:, j, 1]\n",
        "        B[:, 0, 2 * j] = dNidx\n",
        "        B[:, 2, 2 * j] = dNidy\n",
        "        B[:, 1, 2 * j + 1] = dNidy\n",
        "        B[:, 2, 2 * j + 1] = dNidx"
      ],
      "metadata": {
        "id": "dnQMq-TdRNly"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The above functions are then utilized in the following element routine function, which also leverages efficient Numpy functions such as `einsum` and `matmul`. The idea is in fact to convert matrix-vector operations to matrix-matrix operations via _stacking_ all the vectors in a batch."
      ],
      "metadata": {
        "id": "akZOs1kfWTH7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def batched_element_routine_cpu(stiffness, thickness, weights, xe, ue, ke, re,\n",
        "                                detJ=None, J=None, B=None, dNdxi=None, dNdx=None):\n",
        "    batch_sz = xe.shape[0]\n",
        "    n_dofs_cell = ue.shape[1]\n",
        "    # Init local variables if not provided\n",
        "    if detJ is None:\n",
        "        detJ = np.zeros(batch_sz, dtype=np.float32)\n",
        "    if J is None:\n",
        "        J = np.zeros((batch_sz, 2, 2), dtype=np.float32) # Shape: (b, 2, 2)\n",
        "    if B is None:\n",
        "        # TODO(Stefano): For now, B doesn't depend on nqp\n",
        "        nqp = weights.shape[0]\n",
        "        B = np.zeros((batch_sz, dh.grid.nnodes_per_cell(), n_dofs_cell), dtype=np.float32)\n",
        "    if dNdxi is None:\n",
        "        dNdxi = np.array([[-1.0, -1.0], [1.0, 0.0], [0.0, 1.0]], dtype=np.float32) # Shape: (3, 2)\n",
        "    if dNdx is None:\n",
        "        dNdx = np.empty((batch_sz, *dNdxi.shape), dtype=np.float32)\n",
        "    # Get shape of gradients\n",
        "    jacobi_det_cell3_2D(xe, detJ)\n",
        "    jacobian_cell3_2D(xe, J)\n",
        "    JinvT = np.linalg.inv(J).transpose((0, 2, 1))\n",
        "    dNdx = np.matmul(JinvT, dNdxi.T).transpose((0, 2, 1))\n",
        "    # Get B\n",
        "    assemble_B(dNdx, B)\n",
        "    BT = B.transpose((0, 2, 1))\n",
        "    # Setup element routine\n",
        "    detJw = detJ * weights\n",
        "    dsde = stiffness\n",
        "    # Run element routine\n",
        "    epsilon = np.einsum('bij,bj->bi', B, ue)\n",
        "    sigma = np.einsum('ij,bj->bi', dsde, epsilon)\n",
        "    BTsigma = np.einsum('bij,bj->bi', BT, sigma)\n",
        "    BTdsdeB = np.matmul(np.matmul(BT, dsde), B)\n",
        "    re += BTsigma * detJw[:, None]\n",
        "    ke += BTdsdeB * detJw[:, None, None]\n",
        "    re *= thickness\n",
        "    ke *= thickness"
      ],
      "metadata": {
        "id": "vrvZDC1vRR_8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### K-Assembly on CPU\n",
        "\n",
        "Compared to the naive version, we also introduce a \"batched\" for-loop: instead of iterating over each cell element, we populate a batch accordingly, before feeding it into the batched element routine function. In order to efficiently populate the batch, we again exploit Numba and elements independence.  "
      ],
      "metadata": {
        "id": "NnTiOCGfR47R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@nb.jit(nopython=True, cache=True, parallel=True)\n",
        "def get_dofs(nodes, a, dofs, ue):\n",
        "    \"\"\"\n",
        "    Populate the dofs and ue based on the given nodes.\n",
        "\n",
        "    nodes: shape: (batch_sz, n_nodes_cell)\n",
        "    dofs: shape: (batch_sz, n_nodes_cell * n_dofs_per_node)\n",
        "    ue: shape: (batch_sz, n_nodes_cell * n_dofs_per_node)\n",
        "    \"\"\"\n",
        "    batch_sz, n_nodes_cell = nodes.shape\n",
        "    n_dofs = dofs.shape[-1] // n_nodes_cell\n",
        "    for i in prange(batch_sz):\n",
        "        for j, nodeid in enumerate(nodes[i]):\n",
        "            for k in range(n_dofs):\n",
        "                dofs[i, j * n_dofs + k] = nodeid * n_dofs + k\n",
        "        ue[i] = a[dofs[i]]\n",
        "\n",
        "@nb.jit(nopython=True, cache=True, parallel=True)\n",
        "def get_coo_indices(dofs):\n",
        "    batch_sz, n_dofs_per_cell = dofs.shape\n",
        "    f_rows = np.empty(dofs.shape, dtype=np.int32)\n",
        "    f_cols = np.zeros(dofs.size, dtype=np.int32)\n",
        "    K_rows = np.empty((batch_sz, n_dofs_per_cell, n_dofs_per_cell), dtype=np.int32)\n",
        "    K_cols = np.zeros((batch_sz, n_dofs_per_cell, n_dofs_per_cell), dtype=np.int32)\n",
        "    for k in prange(batch_sz):\n",
        "        for i, dof_i in enumerate(dofs[k]):\n",
        "            f_rows[k, i] = dof_i\n",
        "            for j, dof_j in enumerate(dofs[k]):\n",
        "                K_rows[k, i, j] = dof_i\n",
        "                K_cols[k, i, j] = dof_j\n",
        "    return (K_rows.flatten(), K_cols.flatten()), (f_rows.flatten(), f_cols.flatten())\n",
        "\n",
        "get_dofs.recompile()\n",
        "get_coo_indices.recompile()"
      ],
      "metadata": {
        "id": "U_gj9JI2Usya"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def batched_k_assembly_cpu(a, weak_form, dh, batch_sz=-1):\n",
        "    n_cells = len(dh.grid.cells)\n",
        "    n_dims = dh.grid.n_dim\n",
        "    if batch_sz <= 0:\n",
        "        batch_sz = n_cells\n",
        "    batch_sz = min(batch_sz, n_cells)\n",
        "    stiffness = weak_form.material.stiffness\n",
        "    weights = weak_form.element.weights\n",
        "    n_dofs_cell = dh.ndofs_per_cell(dh.grid)\n",
        "    K_shape = (dh.get_ndofs_total(), dh.get_ndofs_total())\n",
        "    f_shape = (dh.get_ndofs_total(), 1)\n",
        "    # Setup kernel inputs\n",
        "    dofs = np.zeros((batch_sz, n_dofs_cell), dtype=np.int32)\n",
        "    ke = np.zeros((batch_sz, n_dofs_cell, n_dofs_cell), dtype=np.float32)\n",
        "    re = np.zeros((batch_sz, n_dofs_cell), dtype=np.float32)\n",
        "    xe = np.zeros((batch_sz, dh.grid.nnodes_per_cell(), n_dims), dtype=np.float32)\n",
        "    ue = np.zeros((batch_sz, n_dofs_cell), dtype=np.float32)\n",
        "    # Assemble K and f components\n",
        "    for batchptr in range(0, n_cells, batch_sz):\n",
        "        actual_batch_sz = min(batch_sz, n_cells - batchptr)\n",
        "        dofs.fill(0)\n",
        "        ke.fill(0)\n",
        "        re.fill(0)\n",
        "        xe = dh.grid.nodes[dh.grid.cells[batchptr:batchptr+actual_batch_sz]]\n",
        "        # NOTE: The methods dh.grid.get_coordinates() and dh.get_cell_dofs() are\n",
        "        # implemented in Numba to handle multi-dimensional indexing and speed-up\n",
        "        # the nested for-loops\n",
        "        get_dofs(dh.grid.cells[batchptr:batchptr+actual_batch_sz], a, dofs, ue)\n",
        "        batched_element_routine_cpu(stiffness, weak_form.thickness, weights, xe,\n",
        "                                    ue, ke, re) #, detJ, J, B, dNdxi, dNdx)\n",
        "        # Update K and f COO components\n",
        "        K_idx, f_idx = get_coo_indices(dofs)\n",
        "        if batchptr == 0:\n",
        "            K_rows = K_idx[0]\n",
        "            K_cols = K_idx[1]\n",
        "            f_rows = f_idx[0]\n",
        "            f_cols = f_idx[1]\n",
        "            K_data = ke.flatten()\n",
        "            f_data = re.flatten()\n",
        "        else:\n",
        "            np.concatenate((K_rows, K_idx[0]))\n",
        "            np.concatenate((K_cols, K_idx[1]))\n",
        "            np.concatenate((f_rows, f_idx[0]))\n",
        "            np.concatenate((f_cols, f_idx[1]))\n",
        "            np.concatenate((K_data, ke.flatten()))\n",
        "            np.concatenate((f_data, re.flatten()))\n",
        "    # Convert lists to COO matrices\n",
        "    # NOTE: Components at same indeces are automatically accumulated together\n",
        "    K_data = np.array(K_data, dtype=np.float32).flatten()\n",
        "    K_rows = np.array(K_rows, dtype=np.int32).flatten()\n",
        "    K_cols = np.array(K_cols, dtype=np.int32).flatten()\n",
        "    K = coo_matrix((K_data, (K_rows, K_cols)), shape=K_shape, dtype=np.float32)\n",
        "    f_data = np.array(f_data, dtype=np.float32).flatten()\n",
        "    f_rows = np.array(f_rows, dtype=np.int32).flatten()\n",
        "    f_cols = np.array(f_cols, dtype=np.int32).flatten()\n",
        "    f = coo_matrix((f_data, (f_rows, f_cols)), shape=f_shape, dtype=np.float32).toarray()\n",
        "    return K, f"
      ],
      "metadata": {
        "id": "iNYW-jE8RwCB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "With this refactory, we can compare the batched implementation with the naive version."
      ],
      "metadata": {
        "id": "a7BW78ap3dBb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import timeit\n",
        "\n",
        "a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.09)\n",
        "fem = lambda: naive_k_assembly_cpu(a, weak_form, dh)\n",
        "naive_t = timeit.timeit(stmt=fem, number=10)\n",
        "# Reset a, then measure batched implementation time\n",
        "a = np.zeros(dh.get_ndofs_total())\n",
        "a[dofs_glob['top'][:, 1]] = -0.1\n",
        "# Force compilation\n",
        "K, f = batched_k_assembly_cpu(a, weak_form, dh, batch_sz=-1)\n",
        "fem = lambda: batched_k_assembly_cpu(a, weak_form, dh)\n",
        "batched_t = timeit.timeit(stmt=fem, number=10)\n",
        "print(f'Batched version over naive version speedup: {naive_t / batched_t:.2f}x')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rg2GHT1pz6QC",
        "outputId": "f1fa807f-d1b3-4fb0-8765-57cb34560026"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Batched version over naive version speedup: 451.93x\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see, the batched version is already showing a considerable speedup."
      ],
      "metadata": {
        "id": "PzroYFGw3nkq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Profiling\n",
        "\n",
        "This section about code profiling is reported for completeness, but its output is omitted for brevity."
      ],
      "metadata": {
        "id": "fnnUIvNob_aB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title\n",
        "# a, weak_form, dh, dofs_glob = generate_rand_fem_problem(filename=f'data/randgrid_n{int(3e3)}.npz')\n",
        "# a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.001)\n",
        "print(f'Number of cells: {len(dh.grid.cells)}')\n",
        "print(f'Number of nodes: {len(dh.grid.nodes)}')\n",
        "K_dim = dh.get_ndofs_total()\n",
        "print(f'a dimensions: ({K_dim}, 1)')\n",
        "print(f'K dimensions: ({K_dim}, {K_dim}) (Total elements: {K_dim * K_dim})')"
      ],
      "metadata": {
        "id": "-DKDF8_bb_aC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Reset a, in case this code is called multiple times\n",
        "a = np.zeros(dh.get_ndofs_total())\n",
        "a[dofs_glob['top'][:, 1]] = -0.1\n",
        "# Force compilation\n",
        "K, f = batched_k_assembly_cpu(a, weak_form, dh, batch_sz=-1)\n",
        "# Init profiler\n",
        "profiler = cProfile.Profile()\n",
        "profiler.enable()\n",
        "# Run CPU functions\n",
        "K, f = batched_k_assembly_cpu(a, weak_form, dh, batch_sz=-1)\n",
        "a[dofs_glob['free']], _ = run_solver(K, f, a, dofs_glob,\n",
        "                                     solver=scipy.sparse.linalg.minres)\n",
        "# Stop profiling\n",
        "profiler.disable()\n",
        "# Create statistics from the profiler, sorted by cumulative time\n",
        "stats = pstats.Stats(profiler).sort_stats('cumtime')\n",
        "# Print the 10 (inclusive) most expensive functions\n",
        "stats.print_stats(10)"
      ],
      "metadata": {
        "id": "fjvr785Tb_aF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Batched FEM on GPU\n",
        "\n",
        "The CuPy library has been developed as a GPU equivalent of Numpy and SciPy functions and features. Because of that, the aforementioned batched implementation can be easily be ported to CuPy functions. "
      ],
      "metadata": {
        "id": "VmuCSMFJc9x8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import cupy as cp\n",
        "import cupyx as cpx\n",
        "import cupyx.scipy.sparse.linalg\n",
        "from numba import cuda"
      ],
      "metadata": {
        "id": "pL3BwVK_dO7b"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Batched Element Routine on GPU"
      ],
      "metadata": {
        "id": "oB8dDkZAdU5X"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def cupy_jacobi_det_cell3_2D(xe):\n",
        "    return ((xe[:, 1, 0] - xe[:, 0, 0]) * (xe[:, 2, 1] - xe[:, 0, 1]) -\n",
        "            (xe[:, 2, 0] - xe[:, 0, 0]) * (xe[:, 1, 1] - xe[:, 0, 1]))\n",
        "\n",
        "\n",
        "def cupy_jacobian_cell3_2D(xe, J):\n",
        "    # TODO(Kim): Not generally constant, could depend on iso_coord (xi)\n",
        "    J[:, 0, 0] = xe[:, 1, 0] - xe[:, 0, 0]\n",
        "    J[:, 0, 1] = xe[:, 2, 0] - xe[:, 0, 0]\n",
        "    J[:, 1, 0] = xe[:, 1, 1] - xe[:, 0, 1]\n",
        "    J[:, 1, 1] = xe[:, 2, 1] - xe[:, 0, 1]\n",
        "\n",
        "\n",
        "def cupy_assemble_B(dNdx, B):\n",
        "    \"\"\"\n",
        "    B: (batch_sz, n_nodes_cell, n_dofs_cell)\n",
        "    dNdx: (batch_sz, 3, 2)\n",
        "    \"\"\"\n",
        "    for j in range(dNdx.shape[1]):\n",
        "        dNidx = dNdx[:, j, 0]\n",
        "        dNidy = dNdx[:, j, 1]\n",
        "        B[:, 0, 2 * j] = dNidx\n",
        "        B[:, 2, 2 * j] = dNidy\n",
        "        B[:, 1, 2 * j + 1] = dNidy\n",
        "        B[:, 2, 2 * j + 1] = dNidx"
      ],
      "metadata": {
        "id": "Xzset_tldU5a"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def batched_element_routine_gpu(stiffness, thickness, weights, xe, ue, ke, re,\n",
        "                                detJ=None, J=None, B=None, dNdxi=None,\n",
        "                                dNdx=None):\n",
        "    batch_sz = xe.shape[0]\n",
        "    n_dofs_cell = ue.shape[1]\n",
        "    # Init local variables if not provided\n",
        "    if J is None:\n",
        "        J = cp.zeros((batch_sz, 2, 2), dtype=cp.float32) # Shape: (b, 2, 2)\n",
        "    if B is None:\n",
        "        # TODO(Stefano): For now, B doesn't depend on nqp\n",
        "        nqp = weights.shape[0]\n",
        "        B = cp.zeros((batch_sz, dh.grid.nnodes_per_cell(), n_dofs_cell), dtype=cp.float32)\n",
        "    if dNdxi is None:\n",
        "        dNdxi = cp.array([[-1.0, -1.0], [1.0, 0.0], [0.0, 1.0]], dtype=cp.float32) # Shape: (3, 2)\n",
        "    if dNdx is None:\n",
        "        dNdx = cp.empty((batch_sz, *dNdxi.shape), dtype=cp.float32)\n",
        "    # Get shape of gradients\n",
        "    detJ = cupy_jacobi_det_cell3_2D(xe)\n",
        "    cupy_jacobian_cell3_2D(xe, J)\n",
        "    JinvT = cp.linalg.inv(J).transpose((0, 2, 1))\n",
        "    dNdx = cp.matmul(JinvT, dNdxi.T).transpose((0, 2, 1))\n",
        "    # Get B\n",
        "    cupy_assemble_B(dNdx, B)\n",
        "    BT = B.transpose((0, 2, 1))\n",
        "    # Setup element routine\n",
        "    detJw = detJ * weights\n",
        "    dsde = stiffness\n",
        "    # Run element routine\n",
        "    epsilon = cp.einsum('bij,bj->bi', B, ue)\n",
        "    sigma = cp.einsum('ij,bj->bi', dsde, epsilon)\n",
        "    BTsigma = cp.einsum('bij,bj->bi', BT, sigma)\n",
        "    BTdsdeB = cp.matmul(cp.matmul(BT, dsde), B)\n",
        "    re += BTsigma * detJw[:, None]\n",
        "    ke += BTdsdeB * detJw[:, None, None]\n",
        "    re *= thickness\n",
        "    ke *= thickness"
      ],
      "metadata": {
        "id": "lbCQ5k1edU5c"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### K-Assembly on GPU"
      ],
      "metadata": {
        "id": "Pp8mzUlTduGo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def batched_k_assembly_gpu(a, weak_form, dh, batch_sz=-1):\n",
        "    n_cells = len(dh.grid.cells)\n",
        "    n_dims = dh.grid.n_dim\n",
        "    if batch_sz <= 0:\n",
        "        batch_sz = n_cells\n",
        "    batch_sz = min(batch_sz, n_cells)\n",
        "    stiffness = cp.asarray(weak_form.material.stiffness)\n",
        "    weights = cp.asarray(weak_form.element.weights)\n",
        "    K_shape = (dh.get_ndofs_total(), dh.get_ndofs_total())\n",
        "    f_shape = (dh.get_ndofs_total(), 1)\n",
        "    # Assemble K and f components\n",
        "    for batchptr in range(0, n_cells, batch_sz):\n",
        "        actual_batch_sz = min(batch_sz, n_cells - batchptr)\n",
        "        # Init local variables for element loop (re-use them across iterations)\n",
        "        n_dofs_cell = dh.ndofs_per_cell(dh.grid)\n",
        "        dofs = np.zeros((actual_batch_sz, n_dofs_cell), dtype=cp.int32)\n",
        "        ke = cp.zeros((actual_batch_sz, n_dofs_cell, n_dofs_cell), dtype=cp.float32)\n",
        "        re = cp.zeros((actual_batch_sz, n_dofs_cell), dtype=cp.float32)\n",
        "        xe = cp.zeros((actual_batch_sz, dh.grid.nnodes_per_cell(), n_dims), dtype=cp.float32)\n",
        "        ue = np.zeros((actual_batch_sz, n_dofs_cell), dtype=cp.float32)\n",
        "        # Setup kernel icputs\n",
        "        xe = dh.grid.nodes[dh.grid.cells[batchptr:batchptr+actual_batch_sz]]\n",
        "        # NOTE: The methods dh.grid.get_coordinates() and dh.get_cell_dofs() are\n",
        "        # implemented in Numba to handle multi-dimensional indexing and speed-up\n",
        "        # the nested for-loops\n",
        "        get_dofs(dh.grid.cells[batchptr:batchptr+actual_batch_sz], a, dofs, ue)\n",
        "        xe_d = cp.asarray(xe)\n",
        "        ue_d = cp.asarray(ue)\n",
        "        batched_element_routine_gpu(stiffness, weak_form.thickness, weights,\n",
        "                                    xe_d, ue_d, ke, re)\n",
        "        # Update K and f COO components\n",
        "        K_idx, f_idx = get_coo_indices(dofs)\n",
        "        if batchptr == 0:\n",
        "            K_rows = cp.asarray(K_idx[0])\n",
        "            K_cols = cp.asarray(K_idx[1])\n",
        "            f_rows = cp.asarray(f_idx[0])\n",
        "            f_cols = cp.asarray(f_idx[1])\n",
        "            K_data = ke.flatten()\n",
        "            f_data = re.flatten()\n",
        "        else:\n",
        "            cp.concatenate((K_rows, cp.asarray(K_idx[0])))\n",
        "            cp.concatenate((K_cols, cp.asarray(K_idx[1])))\n",
        "            cp.concatenate((f_rows, cp.asarray(f_idx[0])))\n",
        "            cp.concatenate((f_cols, cp.asarray(f_idx[1])))\n",
        "            cp.concatenate((K_data, ke.flatten()))\n",
        "            cp.concatenate((f_data, re.flatten()))\n",
        "    # Convert lists to COO matrices\n",
        "    # NOTE: Components at same indeces are automatically accumulated together\n",
        "    K_data = cp.array(K_data, dtype=cp.float32).flatten()\n",
        "    K_rows = cp.array(K_rows, dtype=cp.int32).flatten()\n",
        "    K_cols = cp.array(K_cols, dtype=cp.int32).flatten()\n",
        "    K = cpx.scipy.sparse.coo_matrix((K_data, (K_rows, K_cols)), shape=K_shape, dtype=cp.float32)\n",
        "    f_data = cp.array(f_data, dtype=cp.float32).flatten()\n",
        "    f_rows = cp.array(f_rows, dtype=cp.int32).flatten()\n",
        "    f_cols = cp.array(f_cols, dtype=cp.int32).flatten()\n",
        "    f = cpx.scipy.sparse.coo_matrix((f_data, (f_rows, f_cols)), shape=f_shape, dtype=cp.float32).toarray()\n",
        "    return K, f"
      ],
      "metadata": {
        "id": "3z4aHVn0duGs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Profiling\n",
        "\n",
        "This section about code profiling is reported for completeness, but its output is omitted for brevity."
      ],
      "metadata": {
        "id": "YOgXQJXjduGv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# a, weak_form, dh, dofs_glob = generate_rand_fem_problem(filename=f'data/randgrid_n{int(3e3)}.npz')\n",
        "# a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.01)\n",
        "print(f'Number of cells: {len(dh.grid.cells)}')\n",
        "print(f'Number of nodes: {len(dh.grid.nodes)}')\n",
        "K_dim = dh.get_ndofs_total()\n",
        "print(f'a dimensions: ({K_dim}, 1)')\n",
        "print(f'K dimensions: ({K_dim}, {K_dim}) (Total elements: {K_dim * K_dim})')"
      ],
      "metadata": {
        "id": "Gk2B4WLmduGy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#@title\n",
        "from cupyx.profiler import benchmark\n",
        "\n",
        "# Reset a, in case this code is called multiple times\n",
        "a = np.zeros(dh.get_ndofs_total())\n",
        "a[dofs_glob['top'][:, 1]] = -0.1\n",
        "# init profiler\n",
        "profiler = cProfile.Profile()\n",
        "profiler.enable()\n",
        "# Run GPU functions\n",
        "K, f = batched_k_assembly_gpu(a, weak_form, dh, batch_sz=8196*16)\n",
        "a_gpu, _ = run_solver(K, f, cp.asarray(a), dofs_glob, solver=cpx.scipy.sparse.linalg.minres)\n",
        "a[dofs_glob['free']] = a_gpu.get()\n",
        "# Stop profiling\n",
        "profiler.disable()\n",
        "# Create statistics from the profiler, sorted by cumulative time\n",
        "stats = pstats.Stats(profiler).sort_stats('cumtime')\n",
        "# Print the 10 (inclusive) most expensive functions\n",
        "stats.print_stats(10)\n",
        "# K.nnz"
      ],
      "metadata": {
        "id": "e3ND3Ef5duGz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.title('Global stiffness matrix')\n",
        "plot_K(K.get())"
      ],
      "metadata": {
        "id": "F_Jw_jy15Sx6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot_grid(a, dh)"
      ],
      "metadata": {
        "id": "BdbZ13iu5fgX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Custom CUDA Kernel on GPU\n",
        "\n",
        "The CuPy implementation treats each function call as a single GPU kernel call. In this section we instead explore the design and implementation of a single custom kernel for the element routine function. This will also allow us to explore more fine-grained configurations in the kernel call, such as the grid size and the amount of threads per block. Our implementation will rely on Numba compilation targeting CUDA."
      ],
      "metadata": {
        "id": "6uvEmiM66gDC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Design Space Exploration (GPU)"
      ],
      "metadata": {
        "id": "mi9nKIpQQswE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Number of Blocks vs. Number of Threads"
      ],
      "metadata": {
        "id": "8KCK2N9LfF1Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sz2MB(sz):\n",
        "    return sz * 4 / (1024 * 1024)\n",
        "\n",
        "def sz2GB(sz):\n",
        "    return sz2MB(sz) / 1024\n",
        "\n",
        "def get_sizes(n_cells, batch_sz):\n",
        "    sizes = {}\n",
        "    B_sz = n_nodes_per_cell * n_dofs_per_cell\n",
        "    epsilon_sz = n_nodes_per_cell\n",
        "    sigma_sz = n_nodes_per_cell\n",
        "    BTsigma_sz = n_dofs_per_cell\n",
        "    BTdsde_sz = n_dofs_per_cell * n_dofs_per_cell\n",
        "    BTdsdeB_sz = n_dofs_per_cell * n_dofs_per_cell\n",
        "    sizes['Thread'] = (B_sz + epsilon_sz + sigma_sz + BTsigma_sz + BTdsde_sz +\n",
        "                       BTdsdeB_sz + 3)\n",
        "    sizes['Kernel'] = batch_sz * sizes['Thread']\n",
        "    sizes['Total'] = sizes['Kernel']\n",
        "\n",
        "    dofs = n_cells * n_dofs_per_cell\n",
        "    xe = n_cells * n_nodes_per_cell * n_dims\n",
        "    ue = n_cells * n_dofs_per_cell\n",
        "    sizes['Arrays'] = dofs + xe + ue\n",
        "    sizes['Total'] += sizes['Arrays']\n",
        "\n",
        "    K_sz = n_cells * n_dofs_per_cell * n_dofs_per_cell\n",
        "    f_sz = n_cells * n_dofs_per_cell\n",
        "    f_rows_sz = n_cells * n_dofs_per_cell\n",
        "    f_cols_sz = n_cells * n_dofs_per_cell\n",
        "    K_rows_sz = n_cells * n_dofs_per_cell * n_dofs_per_cell\n",
        "    K_cols_sz = n_cells * n_dofs_per_cell * n_dofs_per_cell\n",
        "    sizes['K - COO Format'] = K_sz + K_rows_sz + K_cols_sz\n",
        "    sizes['f - COO Format'] = f_sz + f_rows_sz + f_cols_sz\n",
        "    sizes['Total'] += sizes['K - COO Format'] + sizes['f - COO Format']\n",
        "    return sizes\n",
        "\n",
        "n_cells = int(3e6)\n",
        "batch_sz = n_cells\n",
        "used_GB = sz2GB(get_sizes(n_cells, batch_sz)['Total'] * 4)\n",
        "print(f'Estimated memory used: {used_GB} GB')"
      ],
      "metadata": {
        "id": "0SYUtTe0G1-G",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ba7e92a8-c424-4dcf-d6a8-c8d284f170a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Estimated memory used: 11.1311674118042 GB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "MaxGridDimX = 2147483647\n",
        "MaxBlockDimX = 1024\n",
        "MaxSharedMemoryPerBlock = 49152\n",
        "MaxRegistersPerBlock = 65536\n",
        "WarpSize = 32\n",
        "MaxThreadsPerBlock = 1024\n",
        "\n",
        "threadsperblock = 64\n",
        "blockspergrid = (batch_sz + (threadsperblock - 1)) // threadsperblock\n",
        "\n",
        "sizes = get_sizes(MaxGridDimX, MaxGridDimX)\n",
        "sizes['Thread'] * 4"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KrmnuUJaYI3A",
        "outputId": "27ff9986-de6c-4c48-bb28-b9a54093aab4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "420"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Element Routine CUDA Kernel"
      ],
      "metadata": {
        "id": "JnIxBE8Oa0U-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import cupy as cp\n",
        "import cupyx as cpx\n",
        "import cupyx.scipy.sparse.linalg\n",
        "from numba import cuda"
      ],
      "metadata": {
        "id": "lvxzYLDZYK3L"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The kernel needs to know arrays dimensions, _i.e._, shapes, at \"compile time\". In our case, they will depend on the dimensions of the FEM problem we are solving. Unfortunately, Numba support is very limited for advanced functions, _e.g._, matrix-matrix and matrix-vector multiplication. Because of that, we implement them as Numba CUDA device functions as follows."
      ],
      "metadata": {
        "id": "vbsbjeRB9Znf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def invert_2x2(A):\n",
        "    a, b, c, d = A[0, 0], A[0, 1], A[1, 0], A[1, 1]\n",
        "    detA = a * d - b * c\n",
        "    A[0, 0] = d / detA\n",
        "    A[0, 1] = -b / detA\n",
        "    A[1, 0] = -c / detA\n",
        "    A[1, 1] = a / detA\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def jacobi_det(xe):\n",
        "    return ((xe[1, 0] - xe[0, 0]) * (xe[2, 1] - xe[0, 1]) -\n",
        "            (xe[2, 0] - xe[0, 0]) * (xe[1, 1] - xe[0, 1]))\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def jacobian(xe, J):\n",
        "    # TODO(Kim): Not generally constant, could depend on iso_coord (xi)\n",
        "    J[0, 0] = xe[1, 0] - xe[0, 0]\n",
        "    J[0, 1] = xe[2, 0] - xe[0, 0]\n",
        "    J[1, 0] = xe[1, 1] - xe[0, 1]\n",
        "    J[1, 1] = xe[2, 1] - xe[0, 1]\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def B_operator(xe, B):\n",
        "    J = nb.cuda.local.array((2, 2), float32)\n",
        "    dNdxi = nb.cuda.local.array((3, n_dims), float32)\n",
        "    dNdxi[0, 0], dNdxi[0, 1] = -1.0, -1.0\n",
        "    dNdxi[1, 0], dNdxi[1, 1] = 1.0, 0.0\n",
        "    dNdxi[2, 0], dNdxi[2, 1] = 0.0, 1.0\n",
        "    jacobian(xe, J)\n",
        "    invert_2x2(J)\n",
        "    J = J.T\n",
        "    for i in range(dNdxi.shape[0]):\n",
        "        dNidx = dot(J[:, 0], dNdxi[i])\n",
        "        dNidy = dot(J[:, 1], dNdxi[i])\n",
        "        B[0, 2 * i] = dNidx\n",
        "        B[2, 2 * i] = dNidy\n",
        "        B[1, 2 * i + 1] = dNidy\n",
        "        B[2, 2 * i + 1] = dNidx\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def dot(a, b):\n",
        "    c = float32(0.0)\n",
        "    for a_elem, b_elem in zip(a, b):\n",
        "        c += a_elem * b_elem\n",
        "    return c\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def matmul(A, B, C):\n",
        "    for i in range(A.shape[0]):\n",
        "        for j in range(B.shape[1]):\n",
        "            C[i, j] = dot(A[i, :], B[:, j])\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def matvmul(A, B, C):\n",
        "    for i in range(A.shape[0]):\n",
        "        C[i] = dot(A[i, :], B)\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def macv(x, a, y):\n",
        "    for i, (x_elem, y_elem) in enumerate(zip(x.flat, y.flat)):\n",
        "        y.flat[i] = y_elem + x_elem * a\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def mulv(x, a):\n",
        "    for i, x_elem in enumerate(x.flat):\n",
        "        x.flat[i] = x_elem * a\n",
        "\n",
        "@cuda.jit(device=True, inline=True)\n",
        "def element_routine(thickness, xe, ue, weights, stiffness, re, ke):\n",
        "    '''\n",
        "    n_dofs_node = 2\n",
        "    n_nodes_cell = 3\n",
        "    n_dofs_cell = n_dofs_node * n_nodes_cell = 6\n",
        "    n_dims = 3\n",
        "\n",
        "    thickness: 1 [scalar]\n",
        "    xe: (n_nodes_cell, n_dims)\n",
        "    ue: (n_dofs_cell)\n",
        "    weights: (nqp) [number of quadrature points]\n",
        "    stiffness: (3, 3) ???\n",
        "    re: (n_dofs_cell)\n",
        "    ke: (n_dofs_cell, n_dofs_cell)\n",
        "\n",
        "    Jinv_t: (2, 2)\n",
        "    dNdxi: (3, 2)\n",
        "    B: (3, 6)\n",
        "    ue: (6,)\n",
        "    epsilon: (3,)\n",
        "    sigma: (3,)\n",
        "    dsde: (3, 3)\n",
        "    '''\n",
        "    B = nb.cuda.local.array((n_nodes_per_cell, n_dofs_per_cell), float32)\n",
        "    epsilon = nb.cuda.local.array((n_nodes_per_cell), float32)\n",
        "    sigma = nb.cuda.local.array((n_nodes_per_cell), float32)\n",
        "    BTsigma = nb.cuda.local.array(n_dofs_per_cell, float32)\n",
        "    BTdsde = nb.cuda.local.array((n_dofs_per_cell, n_dofs_per_cell), float32)\n",
        "    BTdsdeB = nb.cuda.local.array((n_dofs_per_cell, n_dofs_per_cell), float32)\n",
        "    # Computation\n",
        "    detJ = jacobi_det(xe)\n",
        "    B_operator(xe, B)\n",
        "    nqp = weights.shape[0]\n",
        "    for qp in range(nqp):\n",
        "        w = weights[qp]\n",
        "        matvmul(B, ue, epsilon)\n",
        "        matvmul(stiffness, epsilon, sigma)\n",
        "        matvmul(B.T, sigma, BTsigma)\n",
        "        matmul(B.T, stiffness, BTdsde)\n",
        "        matmul(BTdsde, B, BTdsdeB)\n",
        "        detJw = detJ * w\n",
        "        macv(BTsigma, detJw, re)\n",
        "        macv(BTdsdeB, detJw, ke)\n",
        "    mulv(re, thickness)\n",
        "    mulv(ke, thickness)"
      ],
      "metadata": {
        "id": "rbk-nFAgE9sP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's finally define a kernel which simply calls the element routine CUDA device function."
      ],
      "metadata": {
        "id": "pjqNt7zD8DPM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "@cuda.jit\n",
        "def elem_routine_kernel(thickness, stiffness_host, weights_host, xe_host,\n",
        "                        ue_host, re_host, ke_host):\n",
        "    # Thread ID in a 1D block\n",
        "    tx = cuda.threadIdx.x\n",
        "    # Block ID in a 1D grid\n",
        "    ty = cuda.blockIdx.x\n",
        "    # Block width, i.e. number of threads per block\n",
        "    bw = cuda.blockDim.x\n",
        "    # Compute flattened index inside the array\n",
        "    pos = tx + ty * bw\n",
        "    # Computation: make sure not to access elements outside the grid dimensions\n",
        "    n_cells = xe_host.shape[0]\n",
        "    if pos < n_cells:\n",
        "        element_routine(thickness, xe_host[pos], ue_host[pos], weights_host,\n",
        "                        stiffness_host, re_host[pos], ke_host[pos])"
      ],
      "metadata": {
        "id": "haby1iJw7gZC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### K-Assembly with CUDA Kernel on GPU"
      ],
      "metadata": {
        "id": "w8ORSsplYclX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Similarly to the previous solutions, the K-assembly wrapper function loops over the batches and call the CUDA kernel over them."
      ],
      "metadata": {
        "id": "rmTz5r59bve4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def naive_k_assembly_gpu(a, weak_form, dh, batch_sz=-1, threadsperblock=64):\n",
        "    n_cells = dh.grid.get_num_cells()\n",
        "    n_dims = dh.grid.n_dim\n",
        "    n_dofs_cell = dh.ndofs_per_cell(dh.grid)\n",
        "    n_nodes_cell = dh.grid.nnodes_per_cell()\n",
        "    if batch_sz <= 0:\n",
        "        batch_sz = n_cells\n",
        "    batch_sz = min(batch_sz, n_cells)\n",
        "    with cp.cuda.Device(0) as device:\n",
        "        if threadsperblock < device.attributes['WarpSize']:\n",
        "            threadsperblock = device.attributes['WarpSize']\n",
        "        if threadsperblock > device.attributes['MaxThreadsPerBlock']:\n",
        "            threadsperblock = device.attributes['MaxThreadsPerBlock']\n",
        "        if threadsperblock % device.attributes['WarpSize'] != 0:\n",
        "            threadsperblock -= threadsperblock % device.attributes['WarpSize']\n",
        "\n",
        "    # Init local variables for element loop (re-use them across iterations)\n",
        "    dofs = np.empty((batch_sz, n_dofs_cell), dtype=np.int32)\n",
        "    xe = np.empty((batch_sz, n_nodes_cell, n_dims), dtype=np.float32) \n",
        "    ue = np.empty((batch_sz, n_dofs_cell), dtype=np.float32)\n",
        "    ke = np.zeros((batch_sz, n_dofs_cell, n_dofs_cell), dtype=np.float32)\n",
        "    re = np.zeros((batch_sz, n_dofs_cell), dtype=np.float32)\n",
        "    # Specify CUDA kernel dimensions\n",
        "    blockspergrid = (batch_sz + (threadsperblock - 1)) // threadsperblock\n",
        "    # Move \"constant\" data to device (i.e. not depending on cell ID)\n",
        "    stiffness_d = cuda.to_device(weak_form.material.stiffness)\n",
        "    weights_d = cuda.to_device(weak_form.element.weights)\n",
        "    # TODO: Keep data on GPU if and only if they fit its memory!\n",
        "    keep_on_gpu = True\n",
        "    with cp.cuda.Device(0) as device:\n",
        "        free_bytes, total_bytes = device.mem_info\n",
        "        # print(f'GPU available memory: {total_bytes} B')\n",
        "        # print(f'GPU free memory: {free_bytes} B')\n",
        "\n",
        "    K_shape = (dh.get_ndofs_total(), dh.get_ndofs_total())\n",
        "    f_shape = (dh.get_ndofs_total(), 1)\n",
        "\n",
        "    # Run over batches\n",
        "    # NOTE: Each \"batch\" will become a \"grid\" from the kernel perspective.\n",
        "    for batchptr in range(0, n_cells, batch_sz):\n",
        "        actual_batch_sz = min(batch_sz, n_cells - batchptr)\n",
        "        # Setup kernel inputs\n",
        "        dofs.fill(0)\n",
        "        xe.fill(0)\n",
        "        ue.fill(0)\n",
        "        ke.fill(0)\n",
        "        re.fill(0)\n",
        "        xe = dh.grid.nodes[dh.grid.cells[batchptr:batchptr+actual_batch_sz]]\n",
        "        # NOTE: The methods dh.grid.get_coordinates() and dh.get_cell_dofs() are\n",
        "        # implemented in Numba to handle multi-dimensional indexing and speed-up\n",
        "        # the nested for-loops\n",
        "        get_dofs(dh.grid.cells[batchptr:batchptr+actual_batch_sz], a, dofs, ue)\n",
        "        xe_d = cuda.to_device(xe)\n",
        "        ue_d = cuda.to_device(ue)\n",
        "        re_d = cuda.to_device(re)\n",
        "        ke_d = cuda.to_device(ke)\n",
        "        # Run kernel\n",
        "        elem_routine_kernel[blockspergrid, threadsperblock](weak_form.thickness,\n",
        "            stiffness_d, weights_d, xe_d, ue_d, re_d, ke_d)\n",
        "        K_idx, f_idx = get_coo_indices(dofs)\n",
        "        if keep_on_gpu:\n",
        "            K_idx0 = cp.asarray(K_idx[0])\n",
        "            K_idx1 = cp.asarray(K_idx[1])\n",
        "            f_idx0 = cp.asarray(f_idx[0])\n",
        "            f_idx1 = cp.asarray(f_idx[1])\n",
        "            if batchptr == 0:\n",
        "                K_data = cp.asarray(ke_d).flatten()\n",
        "                f_data = cp.asarray(re_d).flatten()\n",
        "                K_rows = K_idx0\n",
        "                K_cols = K_idx1\n",
        "                f_rows = f_idx0\n",
        "                f_cols = f_idx1\n",
        "                K = cpx.scipy.sparse.coo_matrix((K_data, (K_rows, K_cols)), shape=K_shape, dtype=cp.float32).tocsr()\n",
        "                f = cpx.scipy.sparse.coo_matrix((f_data, (f_rows, f_cols)), shape=f_shape, dtype=cp.float32).tocsr()\n",
        "            else:\n",
        "                K_data = cp.asarray(ke_d).flatten()\n",
        "                f_data = cp.asarray(re_d).flatten()\n",
        "                K_rows = K_idx0\n",
        "                K_cols = K_idx1\n",
        "                f_rows = f_idx0\n",
        "                f_cols = f_idx1\n",
        "                K += cpx.scipy.sparse.coo_matrix((K_data, (K_rows, K_cols)), shape=K_shape, dtype=cp.float32).tocsr()\n",
        "                f += cpx.scipy.sparse.coo_matrix((f_data, (f_rows, f_cols)), shape=f_shape, dtype=cp.float32).tocsr()\n",
        "        else:\n",
        "            if batchptr == 0:\n",
        "                K_data = ke_d.copy_to_host().flatten()\n",
        "                f_data = re_d.copy_to_host().flatten()\n",
        "                K_rows, K_cols = K_idx\n",
        "                f_rows, f_cols = f_idx\n",
        "            else:\n",
        "                K_rows = np.concatenate((K_rows, K_idx[0])).flatten()\n",
        "                K_cols = np.concatenate((K_cols, K_idx[1])).flatten()\n",
        "                f_rows = np.concatenate((f_rows, f_idx[0])).flatten()\n",
        "                f_cols = np.concatenate((f_cols, f_idx[1])).flatten()\n",
        "                # Retrieve data from GPU and update K and f COO components\n",
        "                K_data = np.concatenate((K_data, ke_d.copy_to_host().flatten()))\n",
        "                f_data = np.concatenate((f_data, re_d.copy_to_host().flatten()))\n",
        "    # Convert lists to COO matrices\n",
        "    # NOTE: Components at same indeces are automatically accumulated together\n",
        "    if keep_on_gpu:\n",
        "        # K = cpx.scipy.sparse.coo_matrix((K_data, (K_rows, K_cols)), dtype=cp.float32)\n",
        "        # f = cpx.scipy.sparse.coo_matrix((f_data, (f_rows, f_cols)), dtype=cp.float32).toarray()\n",
        "        f = f.toarray()\n",
        "    else:\n",
        "        K_data = np.array(K_data, dtype=np.float32).flatten()\n",
        "        K_rows = np.array(K_rows, dtype=np.int32).flatten()\n",
        "        K_cols = np.array(K_cols, dtype=np.int32).flatten()\n",
        "        K = coo_matrix((K_data, (K_rows, K_cols)), dtype=np.float32)\n",
        "        f_data = np.array(f_data, dtype=np.float32).flatten()\n",
        "        f_rows = np.array(f_rows, dtype=np.int32).flatten()\n",
        "        f_cols = np.array(f_cols, dtype=np.int32).flatten()\n",
        "        f = coo_matrix((f_data, (f_rows, f_cols)), dtype=np.float32).toarray()\n",
        "    return K, f"
      ],
      "metadata": {
        "id": "MGlzNkuTw0fC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Profiling\n",
        "\n",
        "This section about code profiling is reported for completeness, but its output is omitted for brevity."
      ],
      "metadata": {
        "id": "_9LNgnOrYkLs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title\n",
        "# a, weak_form, dh, dofs_glob = generate_rand_fem_problem(filename=f'data/randgrid_n{int(3e3)}.npz')\n",
        "# a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.001)\n",
        "print(f'Number of cells: {len(dh.grid.cells)}')\n",
        "print(f'Number of nodes: {len(dh.grid.nodes)}')\n",
        "K_dim = dh.get_ndofs_total()\n",
        "print(f'a dimensions: ({K_dim}, 1)')\n",
        "print(f'K dimensions: ({K_dim}, {K_dim}) (Total elements: {K_dim * K_dim})')"
      ],
      "metadata": {
        "id": "trfwOzSGi8z8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Reset a, in case this code is called multiple times\n",
        "a = np.zeros(dh.get_ndofs_total())\n",
        "a[dofs_glob['top'][:, 1]] = -0.1\n",
        "# Reset memory pool, see: https://docs.cupy.dev/en/latest/user_guide/memory.html\n",
        "mempool = cp.get_default_memory_pool()\n",
        "mempool.free_all_blocks()\n",
        "\n",
        "profiler = cProfile.Profile()\n",
        "profiler.enable()\n",
        "# Run GPU kernel\n",
        "\n",
        "K, f = naive_k_assembly_gpu(a, weak_form, dh, batch_sz=8196*32, threadsperblock=1024*4)\n",
        "a_gpu, _ = run_solver(K, f, cp.asarray(a), dofs_glob, solver=cpx.scipy.sparse.linalg.minres)\n",
        "a[dofs_glob['free']] = a_gpu.get()\n",
        "\n",
        "# Stop profiling\n",
        "profiler.disable()\n",
        "# Create statistics from the profiler, sorted by cumulative time\n",
        "stats = pstats.Stats(profiler).sort_stats('cumtime')\n",
        "# Print the 10 (inclusive) most expensive functions\n",
        "stats.print_stats(10)\n",
        "K = K.get()\n",
        "K.nnz\n",
        "with cp.cuda.Device(0) as device:\n",
        "    free_bytes, total_bytes = device.mem_info\n",
        "    print(f'GPU available memory: {sz2GB(total_bytes / 4)} GB')\n",
        "    print(f'GPU free memory: {sz2GB(free_bytes / 4)} GB')"
      ],
      "metadata": {
        "id": "DDNGPsikqDeS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Evaluation\n",
        "\n",
        "In this section, we present the conducted experiments on the proposed solutions to the FEM algorithm. We then compare the obtained results and provide some discussions."
      ],
      "metadata": {
        "id": "Wfxevpkg8r-H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Setup\n",
        "\n",
        "We now download pre-computed 2D meshes with different numbers of nodes. There are six meshes in total, ranging from 3,000 nodes up to 30,000,000 nodes.\n",
        "The above implementations will be evaluated on the aforementioned meshes. \n",
        "\n",
        "<!-- https://stackoverflow.com/questions/9985912/how-do-i-choose-grid-and-block-dimensions-for-cuda-kernels\n",
        "\n",
        "https://www.nvidia.com/content/gtc-2010/pdfs/2238_gtc2010.pdf -->"
      ],
      "metadata": {
        "id": "0fw_j804W7fu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "!mkdir -p data\n",
        "!gdown --fuzzy https://drive.google.com/file/d/1_aknkiKgxuiK8RAB1RGGJ02ZvW9LfKat/view?usp=share_link -O data/randgrid_n3000.npz\n",
        "!gdown --fuzzy https://drive.google.com/file/d/1_sipbQHWOagsYDJUgff5-ijZt-OF0KRC/view?usp=share_link -O data/randgrid_n30000.npz\n",
        "!gdown --fuzzy https://drive.google.com/file/d/1Rh6QH1nt3eEp6h6lnfzlZKID1h9Lx8ez/view?usp=share_link -O data/randgrid_n300000.npz\n",
        "!gdown --fuzzy https://drive.google.com/file/d/16OO8DPnKH7v7VqHJcmRvkvETlodRQrHt/view?usp=sharing -O data/randgrid_n3000000.npz\n",
        "!gdown --fuzzy https://drive.google.com/file/d/1qmoLwlGw32bJVwrTCV4d8a_ucP3qRoCT/view?usp=sharing -O data/randgrid_n5000000.npz\n",
        "!gdown --fuzzy https://drive.google.com/file/d/1cpR1jW-nQ0f1O2XRmc1cvLEdSQRMLVz5/view?usp=share_link -O data/randgrid_n30000000.npz"
      ],
      "metadata": {
        "id": "Y3ycYAebQ0Qt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## CPU Specifications"
      ],
      "metadata": {
        "id": "hFmB8aL4H7_N"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!lscpu"
      ],
      "metadata": {
        "id": "gYDJh08FH-gf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "de2a06ca-2649-437e-c75f-0d4c647720e1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Architecture:                    x86_64\n",
            "CPU op-mode(s):                  32-bit, 64-bit\n",
            "Byte Order:                      Little Endian\n",
            "Address sizes:                   46 bits physical, 48 bits virtual\n",
            "CPU(s):                          2\n",
            "On-line CPU(s) list:             0,1\n",
            "Thread(s) per core:              2\n",
            "Core(s) per socket:              1\n",
            "Socket(s):                       1\n",
            "NUMA node(s):                    1\n",
            "Vendor ID:                       GenuineIntel\n",
            "CPU family:                      6\n",
            "Model:                           79\n",
            "Model name:                      Intel(R) Xeon(R) CPU @ 2.20GHz\n",
            "Stepping:                        0\n",
            "CPU MHz:                         2199.998\n",
            "BogoMIPS:                        4399.99\n",
            "Hypervisor vendor:               KVM\n",
            "Virtualization type:             full\n",
            "L1d cache:                       32 KiB\n",
            "L1i cache:                       32 KiB\n",
            "L2 cache:                        256 KiB\n",
            "L3 cache:                        55 MiB\n",
            "NUMA node0 CPU(s):               0,1\n",
            "Vulnerability Itlb multihit:     Not affected\n",
            "Vulnerability L1tf:              Mitigation; PTE Inversion\n",
            "Vulnerability Mds:               Vulnerable; SMT Host state unknown\n",
            "Vulnerability Meltdown:          Vulnerable\n",
            "Vulnerability Mmio stale data:   Vulnerable\n",
            "Vulnerability Retbleed:          Vulnerable\n",
            "Vulnerability Spec store bypass: Vulnerable\n",
            "Vulnerability Spectre v1:        Vulnerable: __user pointer sanitization and use\n",
            "                                 rcopy barriers only; no swapgs barriers\n",
            "Vulnerability Spectre v2:        Vulnerable, IBPB: disabled, STIBP: disabled, PB\n",
            "                                 RSB-eIBRS: Not affected\n",
            "Vulnerability Srbds:             Not affected\n",
            "Vulnerability Tsx async abort:   Vulnerable\n",
            "Flags:                           fpu vme de pse tsc msr pae mce cx8 apic sep mtr\n",
            "                                 r pge mca cmov pat pse36 clflush mmx fxsr sse s\n",
            "                                 se2 ss ht syscall nx pdpe1gb rdtscp lm constant\n",
            "                                 _tsc rep_good nopl xtopology nonstop_tsc cpuid \n",
            "                                 tsc_known_freq pni pclmulqdq ssse3 fma cx16 pci\n",
            "                                 d sse4_1 sse4_2 x2apic movbe popcnt aes xsave a\n",
            "                                 vx f16c rdrand hypervisor lahf_lm abm 3dnowpref\n",
            "                                 etch invpcid_single ssbd ibrs ibpb stibp fsgsba\n",
            "                                 se tsc_adjust bmi1 hle avx2 smep bmi2 erms invp\n",
            "                                 cid rtm rdseed adx smap xsaveopt arat md_clear \n",
            "                                 arch_capabilities\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## GPU Specifications\n",
        "\n",
        "<!-- Notes:\n",
        "\n",
        "* Threads per block must be a multiple of the warp size and must not exceed the max value\n",
        "* \"Fewer threads = more registers per thread\" -->"
      ],
      "metadata": {
        "id": "QSHERzSoYOsD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!nvidia-smi"
      ],
      "metadata": {
        "id": "hy7xERIeYR82",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "24427789-06d4-48b7-fd14-90724cf39a4a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wed Mar  1 10:36:51 2023       \n",
            "+-----------------------------------------------------------------------------+\n",
            "| NVIDIA-SMI 525.85.12    Driver Version: 525.85.12    CUDA Version: 12.0     |\n",
            "|-------------------------------+----------------------+----------------------+\n",
            "| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
            "| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |\n",
            "|                               |                      |               MIG M. |\n",
            "|===============================+======================+======================|\n",
            "|   0  Tesla T4            Off  | 00000000:00:04.0 Off |                    0 |\n",
            "| N/A   52C    P0    28W /  70W |      0MiB / 15360MiB |      0%      Default |\n",
            "|                               |                      |                  N/A |\n",
            "+-------------------------------+----------------------+----------------------+\n",
            "                                                                               \n",
            "+-----------------------------------------------------------------------------+\n",
            "| Processes:                                                                  |\n",
            "|  GPU   GI   CI        PID   Type   Process name                  GPU Memory |\n",
            "|        ID   ID                                                   Usage      |\n",
            "|=============================================================================|\n",
            "|  No running processes found                                                 |\n",
            "+-----------------------------------------------------------------------------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "with cp.cuda.Device(0) as device:\n",
        "    for k, attribute in device.attributes.items():\n",
        "        print(f'{k}: {attribute}')\n",
        "    print('-' * 80)\n",
        "    print('MaxThreadsPerBlock:', device.attributes['MaxThreadsPerBlock'])\n",
        "    print('MaxBlockDimX:', device.attributes['MaxBlockDimX'])\n",
        "    print('MaxGridDimX:', device.attributes['MaxGridDimX'])\n",
        "    print('MaxRegistersPerBlock:', device.attributes['MaxRegistersPerBlock'])\n",
        "    print('MaxSharedMemoryPerBlock:', device.attributes['MaxSharedMemoryPerBlock'])\n",
        "    print('MaxSharedMemoryPerMultiprocessor:', device.attributes['MaxSharedMemoryPerMultiprocessor'])"
      ],
      "metadata": {
        "id": "GU4mrPCzqrZ7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "618ea003-424c-4824-c7e4-1f965cb7cf1e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AsyncEngineCount: 3\n",
            "CanFlushRemoteWrites: 0\n",
            "CanMapHostMemory: 1\n",
            "CanUseHostPointerForRegisteredMem: 1\n",
            "ClockRate: 1590000\n",
            "ComputeMode: 0\n",
            "ComputePreemptionSupported: 1\n",
            "ConcurrentKernels: 1\n",
            "ConcurrentManagedAccess: 1\n",
            "CooperativeLaunch: 1\n",
            "CooperativeMultiDeviceLaunch: 1\n",
            "DirectManagedMemAccessFromHost: 0\n",
            "EccEnabled: 1\n",
            "GPUDirectRDMAFlushWritesOptions: 1\n",
            "GPUDirectRDMASupported: 1\n",
            "GPUDirectRDMAWritesOrdering: 0\n",
            "GlobalL1CacheSupported: 1\n",
            "GlobalMemoryBusWidth: 256\n",
            "GpuOverlap: 1\n",
            "HostNativeAtomicSupported: 0\n",
            "HostRegisterReadOnlySupported: 1\n",
            "HostRegisterSupported: 1\n",
            "Integrated: 0\n",
            "IsMultiGpuBoard: 0\n",
            "KernelExecTimeout: 0\n",
            "L2CacheSize: 4194304\n",
            "LocalL1CacheSupported: 1\n",
            "ManagedMemory: 1\n",
            "MaxBlockDimX: 1024\n",
            "MaxBlockDimY: 1024\n",
            "MaxBlockDimZ: 64\n",
            "MaxBlocksPerMultiprocessor: 16\n",
            "MaxGridDimX: 2147483647\n",
            "MaxGridDimY: 65535\n",
            "MaxGridDimZ: 65535\n",
            "MaxPitch: 2147483647\n",
            "MaxRegistersPerBlock: 65536\n",
            "MaxRegistersPerMultiprocessor: 65536\n",
            "MaxSharedMemoryPerBlock: 49152\n",
            "MaxSharedMemoryPerBlockOptin: 65536\n",
            "MaxSharedMemoryPerMultiprocessor: 65536\n",
            "MaxSurface1DLayeredLayers: 2048\n",
            "MaxSurface1DLayeredWidth: 32768\n",
            "MaxSurface1DWidth: 32768\n",
            "MaxSurface2DHeight: 65536\n",
            "MaxSurface2DLayeredHeight: 32768\n",
            "MaxSurface2DLayeredLayers: 2048\n",
            "MaxSurface2DLayeredWidth: 32768\n",
            "MaxSurface2DWidth: 131072\n",
            "MaxSurface3DDepth: 16384\n",
            "MaxSurface3DHeight: 16384\n",
            "MaxSurface3DWidth: 16384\n",
            "MaxSurfaceCubemapLayeredLayers: 2046\n",
            "MaxSurfaceCubemapLayeredWidth: 32768\n",
            "MaxSurfaceCubemapWidth: 32768\n",
            "MaxTexture1DLayeredLayers: 2048\n",
            "MaxTexture1DLayeredWidth: 32768\n",
            "MaxTexture1DLinearWidth: 268435456\n",
            "MaxTexture1DMipmappedWidth: 32768\n",
            "MaxTexture1DWidth: 131072\n",
            "MaxTexture2DGatherHeight: 32768\n",
            "MaxTexture2DGatherWidth: 32768\n",
            "MaxTexture2DHeight: 65536\n",
            "MaxTexture2DLayeredHeight: 32768\n",
            "MaxTexture2DLayeredLayers: 2048\n",
            "MaxTexture2DLayeredWidth: 32768\n",
            "MaxTexture2DLinearHeight: 65000\n",
            "MaxTexture2DLinearPitch: 2097120\n",
            "MaxTexture2DLinearWidth: 131072\n",
            "MaxTexture2DMipmappedHeight: 32768\n",
            "MaxTexture2DMipmappedWidth: 32768\n",
            "MaxTexture2DWidth: 131072\n",
            "MaxTexture3DDepth: 16384\n",
            "MaxTexture3DDepthAlt: 32768\n",
            "MaxTexture3DHeight: 16384\n",
            "MaxTexture3DHeightAlt: 8192\n",
            "MaxTexture3DWidth: 16384\n",
            "MaxTexture3DWidthAlt: 8192\n",
            "MaxTextureCubemapLayeredLayers: 2046\n",
            "MaxTextureCubemapLayeredWidth: 32768\n",
            "MaxTextureCubemapWidth: 32768\n",
            "MaxThreadsPerBlock: 1024\n",
            "MaxThreadsPerMultiProcessor: 1024\n",
            "MaxTimelineSemaphoreInteropSupported: 1\n",
            "MemoryClockRate: 5001000\n",
            "MemoryPoolSupportedHandleTypes: 1\n",
            "MemoryPoolsSupported: 1\n",
            "MultiGpuBoardGroupID: 0\n",
            "MultiProcessorCount: 40\n",
            "PageableMemoryAccess: 0\n",
            "PageableMemoryAccessUsesHostPageTables: 0\n",
            "PciBusId: 0\n",
            "PciDeviceId: 4\n",
            "PciDomainId: 0\n",
            "Reserved92: 0\n",
            "Reserved93: 0\n",
            "Reserved94: 0\n",
            "ReservedSharedMemoryPerBlock: 0\n",
            "SingleToDoublePrecisionPerfRatio: 32\n",
            "SparseCudaArraySupported: 1\n",
            "StreamPrioritiesSupported: 1\n",
            "SurfaceAlignment: 512\n",
            "TccDriver: 0\n",
            "TextureAlignment: 512\n",
            "TexturePitchAlignment: 32\n",
            "TotalConstantMemory: 65536\n",
            "UnifiedAddressing: 1\n",
            "WarpSize: 32\n",
            "--------------------------------------------------------------------------------\n",
            "MaxThreadsPerBlock: 1024\n",
            "MaxBlockDimX: 1024\n",
            "MaxGridDimX: 2147483647\n",
            "MaxRegistersPerBlock: 65536\n",
            "MaxSharedMemoryPerBlock: 49152\n",
            "MaxSharedMemoryPerMultiprocessor: 65536\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Evaluation Tests\n",
        "\n",
        "We begin be defining two wrapper functions."
      ],
      "metadata": {
        "id": "Dtx9oN6OHzvh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def solve_fem_problem_cpu(a, weak_form, dh, dofs_glob, batch_sz=-1,\n",
        "                          solver=scipy.sparse.linalg.minres):\n",
        "    K, f = batched_k_assembly_cpu(a, weak_form, dh, batch_sz=batch_sz)\n",
        "    a[dofs_glob['free']], _ = run_solver(K, f, a, dofs_glob, solver=solver)\n",
        "    return K, f, a\n",
        "\n",
        "def solve_fem_problem_gpu(a, weak_form, dh, dofs_glob, batch_sz=-1,\n",
        "                          threadsperblock=1024, batched=False,\n",
        "                          solver=cpx.scipy.sparse.linalg.minres):\n",
        "    if batched:\n",
        "        K, f = batched_k_assembly_gpu(a, weak_form, dh, batch_sz=batch_sz)\n",
        "    else:\n",
        "        K, f = naive_k_assembly_gpu(a, weak_form, dh, batch_sz=batch_sz,\n",
        "                                    threadsperblock=threadsperblock)\n",
        "    a_gpu, _ = run_solver(K, f, cp.asarray(a), dofs_glob, solver=solver)\n",
        "    a[dofs_glob['free']] = a_gpu.get()\n",
        "    return K, f, a"
      ],
      "metadata": {
        "id": "hAVC5TXorNgI"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The tests have been conducted over precomputed grids of up to 5 million nodes. The measurements were collected on different devices, namely an Intel 8-cores Xeon processor, an Nvidia Tesla T4 and an Nvidia RTX 2080 Ti.\n",
        "\n",
        "For the custom CUDA kernel implementation, we further explore different threads per block when launching the kernel. The amount of blocks launched is automatically adjusted accordingly.\n",
        "\n",
        "Additionally, the batch size is selected to be 8196 for the CPU solutions, and $8196\\cdot16$ for the GPU versions. In fact, we must break the computation into different batches, as the entire grid information would not fit into the GPU memory.\n",
        "\n",
        "NOTE: The above results may be slightly different from the one run below. The following evaluation will take a considerable amount of time to complete. Because of that, in the following section the pre-run results are loaded and plotted."
      ],
      "metadata": {
        "id": "jKy0R1WmAxhe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "\n",
        "n_threads = [2**i for i in range(6, 11)]\n",
        "n_runs = 10\n",
        "cols = ['Device', 'Batched/Custom Kernel', 'Num. Threads', 'Num. Runs',\n",
        "        'Time [s]', 'Avg. Time [s]', 'Num. Cells', 'Num. Nodes', 'K length',\n",
        "        ]\n",
        "# table = pd.read_csv(os.path.join(proj_dir, 'evaluation_results.csv'))\n",
        "table_data = []\n",
        "\n",
        "for n_nodes in [3 * 10**i for i in range(2, 7)] + [int(5e6), int(3e7)]:\n",
        "    print(f'Generating random Grid with {n_nodes} nodes.')\n",
        "    filename = os.path.join('data', f'randgrid_n{int(n_nodes)}.npz')\n",
        "    prob = generate_rand_fem_problem(filename=filename)\n",
        "    a, weak_form, dh, dofs_glob = prob\n",
        "    # ==========================================================================\n",
        "    # Evaluate batched version on CPU\n",
        "    # ==========================================================================\n",
        "    n_cells = len(dh.grid.cells)\n",
        "    n_nodes = len(dh.grid.nodes)\n",
        "    K_dim = dh.get_ndofs_total()\n",
        "    n_th = 8\n",
        "    fem = lambda: solve_fem_problem_cpu(a.copy(), weak_form, dh, dofs_glob, batch_sz=8196)\n",
        "    t = timeit.timeit(stmt=fem, number=n_runs)\n",
        "    print(f'[CPU] Processed Num Nodes:{n_nodes}, Num.Threads:{n_th} -> Avg.Time: {t / n_runs:.4f} s')\n",
        "    table_data.append(('CPU', 'Batched', n_th, n_runs, round(t, 2),\n",
        "                       round(t / n_runs, 2), n_cells, n_nodes, K_dim))\n",
        "    # Save temporary results\n",
        "    # table = pd.concat([table, pd.DataFrame(table_data, columns=cols)])\n",
        "    # table.to_csv('evaluation_results.csv')\n",
        "    # table.to_csv(os.path.join(proj_dir, 'evaluation_results.csv'))\n",
        "    # ==========================================================================\n",
        "    # Evaluate batched version on GPU\n",
        "    # ==========================================================================\n",
        "    n_th = -1\n",
        "    mempool = cp.get_default_memory_pool()\n",
        "    mempool.free_all_blocks()\n",
        "    fem = lambda: solve_fem_problem_gpu(a.copy(), weak_form, dh, dofs_glob, batched=True, batch_sz=8196*16)\n",
        "    t = timeit.timeit(stmt=fem, number=n_runs)\n",
        "    print(f'[GPU - Batched] Processed Num Nodes:{n_nodes}, Num.Threads:{n_th} -> Avg.Time: {t / n_runs:.4f} s')\n",
        "    table_data.append(('GPU', 'Batched', n_th, n_runs, round(t, 2),\n",
        "                       round(t / n_runs, 2), n_cells, n_nodes, K_dim))\n",
        "    # Save temporary results\n",
        "    # table = pd.concat([table, pd.DataFrame(table_data, columns=cols)])\n",
        "    # table.to_csv('evaluation_results.csv')\n",
        "    # table.to_csv(os.path.join(proj_dir, 'evaluation_results.csv'))\n",
        "    # ==========================================================================\n",
        "    # Evaluate custom CUDA kernel\n",
        "    # ==========================================================================\n",
        "    for n_th in n_threads:\n",
        "        mempool = cp.get_default_memory_pool()\n",
        "        mempool.free_all_blocks()\n",
        "        fem = lambda: solve_fem_problem_gpu(a.copy(), weak_form, dh, dofs_glob, threadsperblock=n_th, batch_sz=8196*16)\n",
        "        t = timeit.timeit(stmt=fem, number=n_runs)\n",
        "        print(f'[GPU - Custom Kernel] Processed Num Nodes:{n_nodes}, Num.Threads:{n_th} -> Avg.Time: {t / n_runs:.4f} s')\n",
        "        table_data.append(('GPU', 'Custom Kernel', n_th, n_runs, round(t, 2),\n",
        "                           round(t / n_runs, 2), n_cells, n_nodes, K_dim))\n",
        "        # Save temporary results\n",
        "        # table = pd.concat([table, pd.DataFrame(table_data, columns=cols)])\n",
        "        # table.to_csv('evaluation_results.csv')\n",
        "        # table.to_csv(os.path.join(proj_dir, 'evaluation_results.csv'))\n",
        "table = pd.DataFrame(table_data, columns=cols)\n",
        "table"
      ],
      "metadata": {
        "id": "-fVgmlaD88jd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Plotting\n",
        "\n",
        "We now show a series of graphs to visualize our results. We start from the normalized execution time of the different utilized devices. The normalization is carried out by normalizing according to the slowest implementation."
      ],
      "metadata": {
        "id": "zsfdG4InZZ7a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table = pd.read_csv(os.path.join(repository, 'data', 'evaluation_results.csv'))\n",
        "table"
      ],
      "metadata": {
        "id": "cfsw0qV_qeBr",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "outputId": "6575c41e-03d1-44c5-fd7d-f43e58890d9a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                  Device Batched/Custom Kernel  Num. Threads  Num. Runs  \\\n",
              "0               Tesla T4               Batched            -1         10   \n",
              "1               Tesla T4         Custom Kernel            64         10   \n",
              "2               Tesla T4         Custom Kernel           128         10   \n",
              "3               Tesla T4         Custom Kernel           256         10   \n",
              "4               Tesla T4         Custom Kernel           512         10   \n",
              "..                   ...                   ...           ...        ...   \n",
              "133  GeForce RTX 2080 Ti               Batched            -1         10   \n",
              "134                 Xeon               Batched             8         10   \n",
              "135  GeForce RTX 2080 Ti               Batched            -1         10   \n",
              "136                 Xeon               Batched             8         10   \n",
              "137  GeForce RTX 2080 Ti               Batched            -1         10   \n",
              "\n",
              "     Time [s]  Avg. Time [s]  Num. Cells  Num. Nodes  K length  \n",
              "0        0.79           0.08        5978        3000      6000  \n",
              "1        0.72           0.07        5978        3000      6000  \n",
              "2        0.75           0.07        5978        3000      6000  \n",
              "3        0.73           0.07        5978        3000      6000  \n",
              "4        0.74           0.07        5978        3000      6000  \n",
              "..        ...            ...         ...         ...       ...  \n",
              "133      3.69           0.37      599964      300000    600000  \n",
              "134    796.03          79.60     5999957     3000000   6000000  \n",
              "135     27.70           2.77     5999957     3000000   6000000  \n",
              "136   1222.63         122.26     9999958     5000000  10000000  \n",
              "137     44.95           4.50     9999958     5000000  10000000  \n",
              "\n",
              "[138 rows x 9 columns]"
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              "      <th></th>\n",
              "      <th>Device</th>\n",
              "      <th>Batched/Custom Kernel</th>\n",
              "      <th>Num. Threads</th>\n",
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              "      <th>0</th>\n",
              "      <td>Tesla T4</td>\n",
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              "      <td>-1</td>\n",
              "      <td>10</td>\n",
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              "      <td>3000</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Tesla T4</td>\n",
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              "      <td>64</td>\n",
              "      <td>10</td>\n",
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              "      <td>0.07</td>\n",
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              "      <td>3000</td>\n",
              "      <td>6000</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Tesla T4</td>\n",
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              "      <td>128</td>\n",
              "      <td>10</td>\n",
              "      <td>0.75</td>\n",
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              "      <th>3</th>\n",
              "      <td>Tesla T4</td>\n",
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              "      <td>10</td>\n",
              "      <td>0.73</td>\n",
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              "      <td>3000</td>\n",
              "      <td>6000</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Tesla T4</td>\n",
              "      <td>Custom Kernel</td>\n",
              "      <td>512</td>\n",
              "      <td>10</td>\n",
              "      <td>0.74</td>\n",
              "      <td>0.07</td>\n",
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              "      <td>3000</td>\n",
              "      <td>6000</td>\n",
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              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "    <tr>\n",
              "      <th>133</th>\n",
              "      <td>GeForce RTX 2080 Ti</td>\n",
              "      <td>Batched</td>\n",
              "      <td>-1</td>\n",
              "      <td>10</td>\n",
              "      <td>3.69</td>\n",
              "      <td>0.37</td>\n",
              "      <td>599964</td>\n",
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              "      <td>600000</td>\n",
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              "    <tr>\n",
              "      <th>134</th>\n",
              "      <td>Xeon</td>\n",
              "      <td>Batched</td>\n",
              "      <td>8</td>\n",
              "      <td>10</td>\n",
              "      <td>796.03</td>\n",
              "      <td>79.60</td>\n",
              "      <td>5999957</td>\n",
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              "    <tr>\n",
              "      <th>135</th>\n",
              "      <td>GeForce RTX 2080 Ti</td>\n",
              "      <td>Batched</td>\n",
              "      <td>-1</td>\n",
              "      <td>10</td>\n",
              "      <td>27.70</td>\n",
              "      <td>2.77</td>\n",
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              "    <tr>\n",
              "      <th>136</th>\n",
              "      <td>Xeon</td>\n",
              "      <td>Batched</td>\n",
              "      <td>8</td>\n",
              "      <td>10</td>\n",
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              "      <td>GeForce RTX 2080 Ti</td>\n",
              "      <td>Batched</td>\n",
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              "      <td>10</td>\n",
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              "      <td>4.50</td>\n",
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              "      <td>5000000</td>\n",
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              "<p>138 rows × 9 columns</p>\n",
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              "        buttonEl.style.display =\n",
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "            + ' to learn more about interactive tables.';\n",
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            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "table['Normalized Execution Time'] = table['Avg. Time [s]']\n",
        "\n",
        "for n_cells in table['Num. Cells'].unique():\n",
        "    selected_cells = table['Num. Cells'] == n_cells\n",
        "    max_t = table.loc[selected_cells, 'Avg. Time [s]'].max()\n",
        "    table.loc[selected_cells, 'Normalized Execution Time'] /= max_t"
      ],
      "metadata": {
        "id": "z5QmhaUkbbFo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "from matplotlib.pyplot import figure\n",
        "\n",
        "# figure(num=None, figsize=(10, 9), dpi=80, facecolor='w', edgecolor='r')\n",
        "ax = sns.barplot(data=table, y='Num. Nodes', x='Normalized Execution Time',\n",
        "                 hue='Device', orient='h')\n",
        "sns.move_legend(ax, 'upper left', bbox_to_anchor=(1, 1))\n",
        "for container in ax.containers:\n",
        "    ax.bar_label(container, padding=10)\n",
        "plt.grid(axis='x', alpha=0.5)\n",
        "plt.title('Normalized execution time for the different devices')\n",
        "plt.show()\n",
        "\n",
        "table_gpu = table[table['Device'].isin(['Tesla T4', 'GeForce RTX 2080 Ti'])].copy()\n",
        "# table_gpu = table[table['Device'] == 'GeForce RTX 2080 Ti'].copy()\n",
        "table_cpu = table[table['Device'] == 'Xeon'].copy()\n",
        "\n",
        "cpu_t = table_cpu['Avg. Time [s]']\n",
        "gpu_t = table_gpu['Avg. Time [s]']\n",
        "print(f'Average speedup CPU vs. GPU: {cpu_t.mean() / gpu_t.mean():.2f}x')\n",
        "# print(f'Highest speedup CPU vs. GPU: {cpu_t.max() / gpu_t.max():.2f}x')"
      ],
      "metadata": {
        "id": "rqMEwaZoqKIp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "c6d42f1a-7a55-49b3-92ed-507f0f90cc43"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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T4JjCw8NJTk7m5ptvpnbt2qSkpDjuRTV//vzL2pdSxU3ntCilypRKe3/GKflcvvVidkGV1Ozl/fv/UuC2Dhw4wKFDh+jf3z55d9++fZw4cYKXXnqJd955B4CQkBAGDhzICy+8wB9//MGjjz7K9u3bs42WpKtRowYff/wxffr0wcnJidtuu42///67QPEcPnyYRx99lFmzZjn2HxoaysiRI0lKSuKee+7B2dm5wP1T4Ozs3NLb2/tCSkqKODs7m+Dg4PgxY8YcvZLjuGbNmopffvllrZkzZ2rmmAtNWpRSZYpT8jmckxLzrXcJyOnXTlxc/tumO3fuHCdPnnSMrhw+fBiAI0eOOOrMmDGDsLAwANq2bcvFixc5ceIEbm5uue63W7dudOvWDYDPPvusQIlGYmIi9913HxMmTODWW291lLdt25a1a9cC8PPPP7Nnz54C909B+fLl03bt2hUJEBcX59K7d+9GiYmJztOmTTt0uftq167d+Xbt2p0v/CivH3p6SClVpqS5ViK1fNV8X+Uq5lzu7u5e4Jevry/JyclUrVqVevXqcerUKQICAqhXr54jngYNGjgm0u7cuZOLFy865qvk5tgx+5Wgp06d4qOPPuKxxx7Ls35ycjI9evSgf//+jiuKsu4rKSmJt99+myeffPKyj6myc3d3T/niiy+iv/rqK7e0tDRSUlIYOnSorUmTJn4+Pj7+kyZNqg3QtWvXRqGhodXSt+vZs6fnV199VWPp0qVV2rdv7wWQkJDg1KtXL08fHx9/Hx8f/5kzZ1YH+P7776sGBQX5+vv7+917772NEhISytTvcR1pUUqVKee87ylQPe+65fjr6KVs5bMv8z4ty5Yt47nnniM1NZUXXniBV199lTFjxrB48WK6d+/OlClTePzxx5k2bRoiwsyZMxERwD6xNjExkeTkZBYuXMjPP/+Mv78/I0aMYMuWLQCMGTPGMZF2w4YN9OjRg1OnTrFkyRLGjh3Ljh07mDt3LmvWrCE+Pp6ZM2cCMHPmTIKCgpg0aRJLly4lLS2NYcOG0aFDh8vqn8rM398/OTU1lbi4OJfvvvuuerVq1VK3b9++88KFC9K6dWvfbt26JT700EMn586dWyM4ODjh4sWLsm7duqqzZs06sHr16srp+3n55ZdvrFq1auqePXsiAY4fP+58+PBhlzfffPPGNWvW7KlatWraq6++Wu+///1v3cmTJx8uuR4XL01alFKqCHXp0oUuXbpkKhs/frzjvb+/P+vWrctx2+jo6BzLQ0JCcixv3bo1sbGx2cofeeQRHnnkkRy3mTRpEpMmTcpxnbo6v/zyS9Vdu3ZVXLx4cQ2AM2fOOEdGRlbo1atXwujRoz0uXLggCxYsqHbLLbecqVy5cqarqtasWVM1NDR0X/pynTp1UkNCQqr9/fffFW655RZfgEuXLknLli3PFm+vSpYmLUoppVQhiYyMdHV2dsbd3T3FGCNTpkw52LNnz2wToW699dYz33//fdXvvvuuRnBw8MmC7NsYw+233564ZMmS/YUfeemgSUs+6kgiP1Qpu3+FnKjQitpVNpZ0GCWmLPe/LPcdcu//wfFl5OdB/yUlHUGpc+jQIZfHH3+84aBBg445OTnRsWPHhI8//rhO165dz5QvX95s3bq1vKen56WqVaum9enT59SMGTNqb9u2rdK8efOis+7rzjvvTJw2bZrbl19+GQP200N33XXXuRdeeKHB9u3byzdp0iQpMTHRKTo6ulxgYGBSsXe2hJSpCTxKKaVUYUpKSnLy9fX19/LyCmjfvr3P3XffnTh58uRDACNHjjzh6+t7sWnTpn7e3t4Bjz/+eMNLly4JQI8ePRLDw8Or3H777YkVKlTIdsO9t9566/Dp06edvb29Axo3buy/bNmyKvXr10/59NNPo4ODgxv5+Pj4t2rVynfbtm0Vsm57PdORFqWUUldl8ODBLF26FDc3N7Zv317S4RSr1NTUTbmtc3Z2Zvr06XFAXNZ15cuXNwkJCREZy7p27Xqma9euZwCqVauW9v3330dn3a579+5nunfvvvOqAy+lSsVIi4hUEJFwEdkiIjtE5HWr/CYRWS8iUSLynYi4WuXlreUoa71nhn39n1W+W0Q6lVCXlFLqujFw4EDHvWaUKkqlImkBkoAOxphmQBDQWURuBd4GphljvIBTwBCr/hDglFU+zaqHiPgDwUAA0Bn4SET09o9KKXUV2rVrR82aNUs6DFUGlIqkxdilX9ZVznoZoAMw3yqfBTxgvb/fWsZaf7fYb3xwPxBqjEkyxuwHooBbir4HSimllLpapSJpARARZxGJAI4BK4C/gdPGmBSrSizgbr13B2IArPUJQK2M5Tlsk7GtJ0Rko4hsPHX2YhH0RimllFKXq9QkLcaYVGNMEGDDPjriW4RtfWaMaWWMaVWjcpmamK2UUkpds0pN0pLOGHMa+BVoC1QXkfQroGz8M0M7DvAAsNZXA+IzluewjVJKKaWuYaXikmcRqQNcMsacFpEbgI7YJ9f+CvQCQoEBwCJrk8XW8h/W+lXGGCMii4FvRWQqUB/wBsKLtTNKKXWd6du3L6tXr+bEiRPYbDZef/31Am3X8sXZLQszjk2T+ud6+THAkSNHnO+6667GACdOnCjn5ORkatasmQIQERGxM6f7pWT0/vvv19q4cWOl2bNnH8wvlgULFlR99dVXbQAHDx4s7+bmdqlChQppfn5+53/44YdogL1797o2a9YsYNSoUYfGjx9/tIDdLNNKRdIC3AjMsq70cQLmGmOWikgkECoibwCbgRlW/RnAHBGJAk5iv2IIY8wOEZkLRAIpwHBjTGox90Uppa4rOT0LKb8nT5eEevXqpe7atSsS4Pnnn69fuXLl1KJKFnr27JnYs2fPSIBbbrml8eTJk2PatWt3PmOdZ555xnbnnXcmFEX716tSkbQYY7YCzXMo30cOV/8YYy4CvXPZ1wRgQmHHqJRSqvRZu3Ztxeeff97j/PnzTjVq1Ej55ptvohs2bHjpjTfecPvqq6/qODs7Gx8fn4tLly7dl3G7b7/9ttrEiRNvvHTpklONGjVSvvvuu30eHh4pubWT1Zw5c6o3bNgwuVKlSmmF36vrV6lIWkrSCScn+taoWtJhlJhmFW9gi9H+F7d1z+T81N/ilBYdTQNPz5IOo8SU9f7n9oTp64kxhmeffbbBjz/+GFW/fv2Uzz//vMaoUaPc582bF/3+++/XO3DgwLYbbrjBnDhxItv9vDp27Hg2ODh4l5OTE1OnTq09fvz4ep9//nn2R2znICEhwWnKlCn1fvvttz2vv/56vcLv2fVLkxallFJlUlJSktPevXtv6NChgw9AWloaderUuQTQuHHjCz169Lipe/fup/v163c667b79+93feCBB2zHjx8vl5yc7OTh4VHghxa++OKL9Z9++umj1apV01GWy1Tqrh5SSmUXFhZG48aN8fLyYuLEibnWW7BgASLCxo32pxcnJyczaNAgmjZtSrNmzVi9erWjbnJyMk888QQ+Pj74+vqyYMECAKZOnYq/vz+BgYHcfffdHDhwwLFN586dqV69Ol27ds3Ubr9+/WjcuDFNmjRh8ODBXLp0qRB7r9SVMcbg5eV1YdeuXZG7du2K3LNnT+S6dev2Avz66697hw8ffvyvv/6q2Lx5c7+s39mnn366wVNPPXVsz549kdOnTz+QlJRU4N+nmzZtqjR27Fibu7t7088//9ztvffeu/HNN9+sU8jduy5p0qJUKZeamsrw4cNZvnw5kZGRhISEEBkZma3emTNneO+992jTpo2j7PPPPwdg27ZtrFixghdeeIG0NPsffx9++CFubm7s2bOHyMhI7rzzTgCaN2/Oxo0b2bp1K7169eKll15y7O/FF19kzpw52dru168fu3btYtu2bVy4cIEvvviiUI+BUleifPnyaSdPnnT55ZdfKgEkJSXJxo0bK6SmpvL333+7duvW7cyHH34Yd/bsWeeEhIRMp4jOnDnj3KBBg0sAM2fOrHU57W7atGl3XFzctri4uG2PP/74sREjRhx+5ZVXjhdez65fenpIqVIuPDwcLy8vGjVqBEBwcDCLFi3C398/U73XXnuN0aNHM2nSJEdZZGQkHTp0AMDNzY3q1auzceNGbrnlFubNm8fevXsBcHJyonbt2gC0b9/esf2tt97K119/7Vi+++67M43WpOvSpYvj/S233EJsbIFO/avrXH6XKBc1JycnQkND/3722WcbnDlzxjk1NVWGDRt2tGnTpkkPP/zwTWfOnHE2xshjjz12rHbt2pmuNH311VcP9e3b9+Zq1aql3H777WcOHjxYvqT6UZZo0qJUCSm3rhxyXnJc139D/1y3q1evHu+8845jOS4uDg+Pf+6ZaLPZWL9+faZt/vrrL2JiYrjvvvsyJS3NmjVj8eLF9O3bl5iYGDZt2kRMTAw+Pj6APdFZvXo1N998M9OnT6du3bqZ9jtjxgzuvffeAvf50qVLzJkzh/fee6/A2yhVFKZOnXoo/f3GjRt3Z12/adOmbGXPPvtsPPYblfLII4+cfuSRR04XpK3w8PBs+8opDpU/TVqUKiFyXnA6l/MZ2rhzhXej5rS0NJ5//nlmzpyZbd3gwYPZuXMnrVq1omHDhtx22204OzuTkpLC4cOHue2225g6dSpTp05l1KhRmU79fP3112zcuJHffvutwLE89dRTtGvXjjvuuKMwuqaUKmM0aVGqhJiKhjRyvnjAo7pHjuVgH2nJyN3dnZiYf54DGhsbi7v7P88BPXPmDNu3b+euu+4C4MiRI3Tv3p3FixfTqlUrpk2b5qh722234ePjQ61atbjhhht48MEHAejduzczZsxw1Pvll1+YMGECv/32G+XLF2xU/PXXX+f48eN8+umnBaqvlFJZadKiVAm59K/cr6CZ/czsAu+ndevW7N27l/379+Pu7k5oaCjffvutY321atU4ceKEY/muu+5i8uTJtGrVivPnz2OMoVKlSqxYsQIXFxfHXJj0+SkdOnRg5cqVjvLNmzczdOhQwsLCcHNzK1CMX3zxBT/99BMrV67EyUnn/yulrowmLUqVci4uLkyfPp1OnTqRmprK4MGDCQgIYMyYMbRq1Yru3bvnuu2xY8fo1KkTTk5OuLu7Zzr9M3r0aF555RWee+456tSpw1dffQXYrxA6e/YsvXvbbzrdoEEDFi9eDMAdd9zBrl27OHv2LDabjRkzZtCpUyeefPJJGjZsSNu2bQF48MEHGTNmTFEdEqXUdUqTFqWuA126dMl0hQ7A+PHjc6yb8eoeT09Pdu/OeY6gzWZjzZo12cp/+eWXXONYu3ZtjuUpKQW+u7lSSuVKk5Z81Kta75q4pXpJiY6OxrOM38q8LPdfKaWuJZq0KKWUKhEHxzdtWZj7azBmW573fYmKiip35513+v7111+RdevWTT1+/LhzUFCQ/6pVq3Y3btw4uTBjUUVDZ8QppZQqE7y8vC4NGjTo2HPPPWcDGDFihK1///7HNWEpPTRpUUopVWa89tprxzZt2lRp/PjxbuHh4ZXHjRt3dMeOHeXvuOMO74CAAL+WLVs23rx5cwWA3bt3u956660+Pj4+/m3btvXZu3evK0DPnj09Bw4c6NG8eXNfm83W9KuvvqpRsr0qOzRpUUopVWaUL1/evPXWW7Fjx471mDRpUkz58uXNY4891vCjjz46uGPHjp2TJk2KHTZsWAOAYcOGNejXr1/8nj17Ivv06RM/bNgwxw2Ujh49Wm7jxo27Fi1atHfs2LHuubeoCpPOaVFKKVWm/Pjjj9Xq1KlzaevWrRU6dOhwdvPmzZV79+59c/r65ORkAdi8eXOl5cuX/w0wbNiwk6+//rotvU737t1POzs707Jly4vx8fHlir8XZZMmLUoppcqM33///YY1a9ZUXbdu3a527do17tu37+kqVaqk7Nq1K/uj0fNQoUIFk/7eGJNXVVWI9PSQUkqpMiEtLY2nnnqq4aRJk2K8vb2Tn3766aOjRo1yt9lsyV9++WWN9Dp//PHHDQDNmzc/98UXX9QA+PTTT2u2atXqbEnGr3SkRSmlVAnJ7xLlwjZ16tTa7u7uyT169EgEGD169LHAwEC/SZMmxUycOPHGt99++8aUlBTp0aPHybZt21745JNPDvbv39/zvffeq1erVq2U2bNnRxdnvCo70WGtvNXxaGQaBI8r6TCKxKZJ/fOtU9ZvrlaW+1+W+w7a/6vtv4hsMsa0yli2ZcuW6GbNmp3IbRul0m3ZsqV2s2bNPLOW6+khpZRSSpUKmrSoAgsLC6Nx48Z4eXkxceLEbOvXrFlDixYtcHFxYf78+Y7yX3/9laCgIMerQoUKLFy4EIAhQ4bQrFkzAgMD6dWrF2fP2k8ZJyUl0adPH7y8vGjTpg3R0dEAfPPNN5n25eTkREREBGfOnMlUXrt2bZ577rmiPiRKKaWKkSYtqkBSU1MZPnw4y5cvJzIykpCQECIjM0+2b9CgATNnzuThhx/OVN6+fXsiIiKIiIhg1apVVKxYkXvuuQeAadOmsWXLFrZu3UqDBg2YPn06ADNmzKBGjRpERUUxcuRIRo8eDUC/fv0c+5ozZw433XQTQUFBVKlSxVEeERFBw4YNefDBB4vhyCillCoumrSoAgkPD8fLy4tGjRrh6upKcHAwixYtylTH09OTwMBAnJxy/1rNnz+fe++9l4oVKwJQtWpVwH7J4IULFxARABYtWsSAAQMA6NWrFytXrsx2WWFISAjBwcHZ2tizZw/Hjh3jjjvuuPIOK6WUuubo1UNlTKW9P+OUfA6A/v1/yba+Xr16vPPOO9nK4+Li8PBw3AwSm83G+vXrL7v90NBQnn/++UxlgwYNYtmyZfj7+zNlypRs7bm4uFCtWjXi4+OpXbu2Y7vvvvsuW+KU3kafPn0cCZBSSqnrg460lDFOyedwTkrEOSmRuLi4bK8jR44UWduHDx9m27ZtdOrUKVP5V199xaFDh/Dz8+O7774r0L7Wr19PxYoVadKkSbZ1oaGh9O3bt1BiVkopde3QkZYyJs21kuN9g9pVsq2vV69ejtu5u7sTExPjWI6NjcXd/fIetzF37lx69OhBuXLZ73jt7OxMcHAw77zzDoMGDXK0Z7PZSElJISEhgVq1ajnq55aYbNmyhZSUFFq2LNQn3iulisC/PvhXof5HXffMunzv+xITE+Py1FNPeWzevLlytWrVUsqVK2eef/75I/379z+d2za7d+92bdasWRNPT8+L6WURERE7M94VtyhkbPfSpUsSGBh47v3334/t2LGjD8CJEyfKOTk5mZo1a6YALF68OKp9+/aN//rrr8i6deumHj9+3DkoKMh/1apVuzM+yToqKqpcv379bjpx4kQ5EWHAgAHHX3vttWMAR48ede7Ro0ejuLi48u7u7kmLFi3aV6dOndT4+Hjn3r173xQXF+eampoqzzzzzJERI0bEA3zwwQe1Jk+efCPAqFGjDj/zzDPxGfvRsWPHm2NiYsqfP3/e6dSpUy7u7u7J1nYHXnrpJY/NmzfvKugx0aSljDnnfY/j/ewC3KclXevWrdm7dy/79+/H3d2d0NBQvv3228tqOyQkhLfeesuxbIzh77//xsvLC2MMixcvxtfXF4Du3bsza9Ys2rZty/z58+nQoYPjdE9aWhpz585l7dq1ObahoyxKqZykpaXRrVs3r4cffjh+yZIl+wH27NnjOm/evOr5bevh4ZF0ubf6B0hJScHF5cp/1aa3m5KSwu233+6zdOnSqulxPP/88/UrV66cOn78+KPp9QcNGnTsueees4WEhBwYMWKErX///sczJiwA5cqVY8qUKbG33377+VOnTjk1b97cv0uXLoktW7a8OHbs2BvvuuuuM2+++ebeV155pd6YMWPqffzxx3GTJk2q07hx4wurVq2KOnTokIufn1+ToUOHnkxISHB6++2362/atCnSycmJ5s2b+wcHB5+uU6dOanp7K1as+Btg6dKlVaZMmVL3119/jUpfdzkJC+jpIVVALi4uTJ8+nU6dOuHn58dDDz1EQEAAY8aMYfHixQBs2LABm83GvHnzGDp0KAEBAY7to6OjiYmJ4c4773SUGWMYMGAATZs2pWnTphw+fJgxY8YA9kuh4+Pj8fLyYurUqZkusV6zZg0eHh40atQoW5xz587VpEUplaMlS5ZUKVeunHnppZeOp5f5+Pgkv/rqq8fAnmAMHTrU1qRJEz8fHx//SZMm1c59b7Bo0aIqfn5+/j4+Pv69e/f2vHDhggC4u7s3HTZsmLu/v7/fl19+WWP+/PlV/f39/Ro3buzftm1bH4DExESn3r17ezZt2tTPz8/P/+uvv66eV1suLi60aNHiXFxcXJ4PZ3zttdeObdq0qdL48ePdwsPDK48bN+5o1joNGza8dPvtt58HqFGjRtrNN9984eDBg64AYWFh1YcOHRoPMHTo0Pjly5fXABARzpw545yWlkZiYqJT+ijVwoULq7Vr1y6xbt26qXXq1Elt165d4vfff18trxgzqlixYvOC1gUdaVGXoUuXLnTp0iVT2fjx4x3vW7duTWxsbI7benp6EhcXl6nMycmJdevW5Vi/QoUKzJs3L8d1d911F3/++WeO6/bt25dr/Eqpsm3btm03BAYGns9t/bvvvlu7WrVqqdu3b9954cIFad26tW+3bt0SRYSYmJjyvr6+/gCtW7c+++mnn8YMHTr0pp9//nl3YGBgUo8ePTwnTZpUZ8yYMccAatWqlRIZGbnz0KFDLi1atPBfvXr1Ll9f3+SjR486A7zyyis3tm/fPnHevHnRJ06ccG7VqpVf9+7dE6tWrZqWU2znz5+XTZs2VXr//fdjclqfrnz58uatt96K7dWrl/f333+/t3z58nmewtq9e7drZGRkxTvvvPMsQHx8vEvDhg0vAXh4eFyKj493AXjppZeOde7c2atu3bqB586dc/7yyy/3OTs7ExcXV85mszlGctzd3ZPzS6yuho60KKWUKpMeffTRBo0bN/Zv0qSJH8Avv/xSde7cubV8fX39mzdv7nfq1CmXyMjICvDPaZpdu3ZFzpkz5+CWLVsq2Gy2pMDAwCSAgQMHxv/vf/9zTBTs37//KYDVq1dXuuWWW874+vomA9StWzfVKq86bdq0G319ff1vv/32xklJSRIVFeWaNcb0ZKlu3brN3NzcLrVp0+ZCfv368ccfq9WpU+fS1q1bK+RVLyEhwenBBx+8eeLEiTE1a9bMliw5OTk5TssvXLiwWpMmTS4cPXp0a3h4eOQLL7zQ4OTJk8WeQ+hISz7qSCI/VJlU0mEUiYPj8+/XyZqtcDq5sRiiuTaV5f6X5b6D9p/+S0o6gkLXtGnTC4sWLaqRvjxnzpyDhw8fdmnVqpUfgDFGpkyZcrBnz56JGbfbvXt3tmQiP1WqVMlxxCSdMYb58+dHNWvWLCmveunJ0uHDh13atm3r+80331Tr169fQm71f//99xvWrFlTdd26dbvatWvXeODAgafSR04ySkpKkvvuu+/m3r17nxwwYMDp9PJatWqlHDhwoFzDhg0vHThwoFz6JN9Zs2bVevnll484OTnRpEmTJA8Pj6QtW7ZUcHd3v/Tbb785krW4uDjXO++880xefboaOtKilFLqqgwePBg3N7ccb0FwLenWrduZpKQkefvtt+ukl509e9bxe7Bjx44JH3/8cZ2kpCQB2Lp1a/nExMQcf082a9bsYlxcnOv27dvLA8yePbvWHXfcke2X9V133XUuPDy8yq5du1zBfnUOQPv27ROnTJlSNy3NntusW7fuhrxiv/HGG1PGjx8fO2nSpBtzq5OWlsZTTz3VcNKkSTHe3t7JTz/99NFnnnnGllO94ODghj4+Phezznnp1KnT6U8//bQWwKefflqrc+fOp8F+2ufnn3+uCvYrsPbt21fB19c3+YEHHkj47bffqh4/ftz5+PHjzr/99lvVBx54INek6mpdUyMtIlIBWAOUxx7bfGPMWBG5CQgFagGbgEeNMckiUh6YDbQE4oE+xphoa1//BwwBUoFnjTE/WeWdgfcAZ+ALY0z2h+gopZQqsIEDB/L000/Tv3/Br0iEgl2iXJicnJxYsmTJ38OHD/d4//3369WsWTOlYsWKqePGjYsFGDly5Ino6OjyTZs29TPGSM2aNS8tW7bs75z2VbFiRfPJJ59E9+7d++bU1FSaNWt2ftSoUcez1qtfv37K+++/H92jRw+vtLQ0atWqden333/fO3HixENPPPFEA19fX/+0tDTx8PBIynhVTU4eeeSR0xMmTKgfFhZWuXPnzmezrp86dWptd3f35B49eiQCjB49+lhgYKDfjz/+WPm+++5z1F+xYkXlhQsX1vL29r6QPk/n9ddfj+vTp0/C66+/frhHjx43N2zYsLa7u3vyDz/88DfAhAkTDvfr18/Tx8fH3xgj48aNi73xxhtTAF588cVDLVu29AN46aWXDqWfAisKkvXW6CVJ7CfPKhljzopIOeB/wAjgeeB7Y0yoiHwCbDHGfCwiTwGBxpgnRSQY6GGM6SMi/kAIcAtQH/gF8LGa2QN0BGKBDUBfY0yul7H5N6htwh7LNbG97p2o2YraZXiIvCz3vyz3HbT/af2X4OnpWeD60dHRdO3ale3btwMgIpuMMa0y1tmyZUt0s2bNThRqoOq6tGXLltrNmjXzzFp+TZ0eMnbp2WA562WADkD6Y4NnAQ9Y7++3lrHW320lPvcDocaYJGPMfiAKewJzCxBljNlnjEnGPnpzf9H2SimllFKF4ZpKWgBExFlEIoBjwArgb+C0MSbFqhILpN+K1R2IAbDWJ2A/heQoz7JNbuVKKaWUusZdc0mLMSbVGBME2LCPjPgWdwwi8oSIbBSRjafOXsx/A6WUUgWRlpaWpk8yVXmyviM5Xn11zSUt6Ywxp4FfgbZAdRFJnzRsA9LvUhYHeABY66thn5DrKM+yTW7lWdv+zBjTyhjTqkblPC9zV0opVXDbjx8/Xk0TF5WbtLQ0OX78eDVge07rr7Wrh+oAl4wxp0XkBuwTZt/Gnrz0wj4HZQCwyNpksbX8h7V+lTHGiMhi4FsRmYp9Iq43EA4I4G1djRQHBAMPF1f/lFLqetS3b19Wr17NiRMnsNlsvP766znWS0lJeezIkSNfHDlypAnX8B/NqkSlAdtTUlIey2nlNZW0ADcCs0TEGfsXeq4xZqmIRAKhIvIGsBmYYdWfAcwRkSjgJPYkBGPMDhGZC0QCKcBwY0wqgIg8DfyE/ZLnL40xO4qve0opdf0JCQnJVvbYY9l/57Rs2fIY0L0YQlLXqWsqaTHGbAWyPTzJGLMP+/yWrOUXgd657GsCMCGH8mXAsqsOVimllFLF6ppKWq5FJ5yc6FujakmHcVnWPZPzQwivRFp0NA0u414N15uy3P+y3HfQ/kdHR5d0CEplo+cUlVJKKVUqaNKiCAsLo3Hjxnh5eTFxYvanGqxZs4YWLVrg4uLC/Pnzs61PTEzEZrPx9NNPO8peffVVPDw8qFy5cqa6SUlJ9OnTBy8vL9q0aeP4a27FihW0bNmSpk2b0rJlS1atWuXYJjk5mSeeeAIfHx98fX1ZsGBBIfVcKaVUaaJJSxmXmprK8OHDWb58OZGRkYSEhBAZmfmpBg0aNGDmzJk8/HDOF1q99tprtGvXLlNZt27dCA8Pz1Z3xowZ1KhRg6ioKEaOHMno0aMBqF27NkuWLGHbtm3MmjWLRx991LHNhAkTcHNzY8+ePURGRnLnnXdebbeVUkqVQjqnpYwLDw/Hy8uLRo0aARAcHMyiRYvw9/d31El//oiTU/Ycd9OmTRw9epTOnTuzceM/z2m59dZbc2xv0aJFjBs3DoBevXrx9NNPY4yhefN/5l8HBARw4cIFkpKSKF++PF9++SW7du1yxFC7du2r6rNSSqnSSUdayri4uDg8PP65357NZiMuLtv99nKUlpbGCy+8wOTJk6+oPRcXF6pVq0Z8fHymOgsWLKBFixaUL1+e06dPA/bRnBYtWtC7d2+OHj2adbdKKaXKAE1a1BX76KOP6NKlCzabrdD2uWPHDkaPHs2nn34KQEpKCrGxsdx222389ddftG3bllGjRhVae0oppUoPPT1Uxrm7uxMT888zJGNjY3F3L9gzJP/44w/Wrl3LRx99xNmzZ0lOTqZy5co5TubN2p7NZiMlJYWEhARq1arlaLtHjx7Mnj2bm2++GYBatWpRsWJFHnzwQQB69+7NjBkzct2/Ukqp65eOtJRxrVu3Zu/evezfv5/k5GRCQ0Pp3r1gN6z85ptvOHjwINHR0UyePJn+/fvnmbAAdO/enVmzZgEwf/58OnTogIhw+vRp7rvvPiZOnMi//vUvR30RoVu3bqxevRqAlStXZppvo5RSquzIN2kRkX+JSCXr/SMiMlVEGhZ9aKo4uLi4MH36dDp16oSfnx8PPfQQAQEBjBkzhsWLFwOwYcMGbDYb8+bNY+jQoQQEBOS735deegmbzcb58+ex2WyOybdDhgwhPj4eLy8vpk6d6khypk+fTlRUFOPHjycoKIigoCCOHTsGwNtvv824ceMIDAxkzpw5TJkypWgOhlJKqWuaGGPyriCyFWgGBAIzgS+Ah4wxZeK6UzdPN+P9gndJh3FZCvOOuNHR0Y6rh8qistz/stx30P5fbf9FZJMxplXhRaRUwU4PpRh7ZnM/MN0Y8yFQpWjDUkoppZTKrCATcc+IyP8BjwJ3iIgTUK5ow7p21Ktar1BHLpRSSil1ZQoy0tIHSAIGG2OOADZgUpFGpZRSSimVRb5Ji5WoLADKW0UngB+KMiillFJKqawKcvXQ48B84FOryB1YWIQxKaWUUkplU5DTQ8OBfwGJAMaYvYBbUQallFJKKZVVQZKWJGNMcvqCiLgAeV8nrZRSSilVyAqStPwmIq8AN4hIR2AesKRow1JKKaWUyqwgScvLwHFgGzAUWAb8pyiDUkoppZTKKt/7tBhj0oDPrZdSSimlVInINWkRkW3kMXfFGBNYJBFdYw6fOkvLF2eXdBgAbJrUv6RDUEoppUpMXqeHugLdgDDr1c96Lcd+ikhd48LCwmjcuDFeXl45Pn15zZo1tGjRAhcXF+bPn59p3axZs/D29qZ9+/aOpzIDfPfddwQGBhIQEMDo0aMd5QcPHqR9+/Y0b96cwMBAli2zf0WSk5MZNGgQTZs2pVmzZo6nNZ8/f5777rsPX19fAgICePnll4vgCCillLqe5Jq0GGMOGGMOAB2NMS8ZY7ZZr9HAPcUXoroSqampDB8+nOXLlxMZGUlISAiRkZGZ6jRo0ICZM2fy8MMPZyo/efIkr7/+OuvXr2fhwoW8/vrrnDp1ivj4eF588UVWrlzJjh07OHLkCCtXrgTgjTfe4KGHHmLz5s2Ehoby1FNPAfD55/azitu2bWPFihW88MILpKWlATBq1Ch27drF5s2bWbduHcuXLy/qw6KUUqoUK8hEXBGRf2VYuK2A26kSFB4ejpeXF40aNcLV1ZXg4GAWLVqUqY6npyeBgYE4OWX+OH/66Sc6duxIzZo1qVatGh07diQsLIx9+/bh7e1NnTp1APj3v//NggULABAREhMTAUhISKB+/foAREZG0qFDBwDc3NyoXr06GzdupGLFirRv3x4AV1dXWrRoQWxsbNEdEKWUUqVeQR6YOAT4UkSqAQKcAgYXaVRlWKW9P+OUfC7Hdf37/5JpuV69erzzzjs51o2Li8PDw8OxbLPZWL9+fYFiyGnbuLg4OnfuzO7du4mOjsZms7Fw4UKSk+238Bk3bhz33HMPH3zwAefOneOXX+yxNmvWjMWLF9O3b19iYmLYtGkTMTEx3HLLLY79nz59miVLljBixIgCxaeUUqpsKsjVQ5uAZlbSgjEmocijKsOcks/hnJSY47q4uJzLi0uNGjX4+OOP6dOnD05OTtx22238/fffAISEhDBw4EBeeOEF/vjjDx599FG2b9/O4MGD2blzJ61ataJhw4bcdtttODs7O/aZkpJC3759efbZZ2nUqFFJdU0ppVQpkG/SYiUrY4F21vJvwHhNXopGmmulXNc1qF0l03K9evVyrevu7k5MTIxjOTY2Fnd39wLF4O7u7pgwm77tXXfdBUC3bt3o1q0bAJ999pkjAZkxYwZhYWEAtG3blosXL3LixAnc3NyYNm2aY1+33XYbPj4+juUnnngCb29vnnvuuQLFppRSquwqyOmhL4HtwEPW8qPAV8CDRRVUWXbOO/c5zrMv45Ln1q1bs3fvXvbv34+7uzuhoaF8++23Bdq2U6dOvPLKK5w6dYqEhAR+/vln3nrrLQCOHTuGm5sbp06d4qOPPmLu3LmAfVLvypUrGThwIDt37uTixYvUqVOH8+fPY4yhUqVKrFixAhcXF/z9/QH4z3/+Q0JCAl988UWB+6WUUqrsKkjScrMxpmeG5ddFJKKI4lGFxMXFhenTp9OpUydSU1MZPHgwAQEBjBkzhlatWtG9e3c2bNhAjx49OHXqFEuWLGHs2LHs2LGDmjVr8tprr9G6dWtSUlIYO3YsNWvWBGDEiBFs2bIFgDFjxjhGTaZMmcLjjz/OtGnTEBFmzpyJiHDs2DE6deqEk5MT7u7uzJkzB7CP3kyYMAFfX19atGgBwNNPP81jjz1WAkdLKaVUaSDG5P3sQxH5A3jRGPM/a/lfwGRjTNtiiK/E1fFoZBoEjyvpMICSublcdHQ0np6exd7utaIs978s9x20/1fbfxHZZIxpVXgRKVWwkZZhwKwMVw+dBAYWZVBKKaWUUlnlO9LiqChSFcAYU7KXsBQz/wa1TdhjN5Z0GCXmRM1W1D65saTDKDFluf9lue+g/U/rv0RHWtQ1J69nD+V4LkJEADDGXBsP5FFKKaVUmZDX6aHWuZR3B9wBTVqUUkoxePBgli5dipubG9u3by/pcNR1LK9nDz2T/gKeBdYDdwF/Ai2utEERqSAi4SKyRUR2iMjrVvlNIrJeRKJE5DsRcbXKy1vLUdZ6zwz7+j+rfLeIdMpQ3tkqixKRlzOU59iGUkqpKzdw4EDHfZqUKkp5PkNIRFxE5DFgJ/BvoJcxpo8xZutVtJkEdDDGNAOCgM4icivwNjDNGOOF/VEBQ6z6Q4BTVvk0qx4i4g8EAwFAZ+AjEXEWEWfgQ+BewB/oa9UljzaUUkpdoXbt2jlui6BUUco1aRGR4UAk0BLobIwZaIzZfbUNGruz1mI562WADsB8q3wW8ID1/n5rGWv93WKfWHM/EGqMSTLG7AeigFusV5QxZp8xJhkIBe63tsmtDaWUUkpd4/Ka0/IBcAy4HfhX+gRc7Jc9G2NM4JU2ao2GbAK8sI+K/A2cNsakWFVisc+bwfo3BnujKSKSANSyyv/MsNuM28RkKW9jbZNbG1njewJ4AqBejdxvq6+UUkqp4pNX0nJTUTVqjEkFgkSkOvAD4FtUbV0JY8xnwGdgv+S5hMNRSimlFHkkLcaYA0XduDHmtIj8CrQFqouIizUSYgPirGpxgAcQKyIuQDUgPkN5uozb5FQen0cbSimllLrG5TkRtyiISB1rhAURuQHoiH2i769AL6vaAGCR9X6xtYy1fpWx3xFvMRBsXV10E+ANhAMbAG/rSiFX7JN1F1vb5NaGUkqpK9S3b1/atm3L7t27sdlszJgxo6RDUtepgtzGv7DdiP2xAM7Yk6a5xpilIhIJhIrIG8BmIP1bPwOYIyJR2B8hEAxgjNkhInOxTxZOAYZbp50QkaeBnwBn4EtjzA5rX6NzaUMppdQVCgkJyVamDz9VRaHYkxbrcunmOZTvw37lT9byi0DvXPY1AZiQQ/kyYFlB21BKKaXUte+KkhYRGWeMGVfIsVyTTjg50bdG1Svadt0z6wo5muKXFh1NgzL8pNuy3P+y3HfQ/kdHR5d0CEplc6VzWjYVahRKKaWUUvm4oqTFGLOksANREBYWRuPGjfHy8mLixInZ1iclJdGnTx+8vLxo06ZNtr+EDh48SOXKlZk8eTIAu3fvJigoyPGqWrUq7777LgB9+vRxlHt6ehIUFJTjvj777DNH2eDBg3Fzc6NJkyaZ6m7ZsoW2bdvStGlTunXrRmJimXoQuFJKqWKSb9JiXYUzVUS+F5HF6a/iCK4sSU1NZfjw4SxfvpzIyEhCQkKIjIzMVGfGjBnUqFGDqKgoRo4cyejRozOtf/7557n33nsdy40bNyYiIoKIiAg2bdpExYoV6dGjBwDfffedY13Pnj158MEH89wX5P58kccee4yJEyeybds2evTowaRJk67qWCillFI5KchIy0IgGvsdcqdkeKlCFB4ejpeXF40aNcLV1ZXg4GAWLcp8RfaiRYsYMMB+9XevXr1YuXIl9iu5YeHChdx0000EBATkuP+VK1dy880307Bhw0zlxhjmzp1L3759HWW57Su354vs2bOHdu3aAdCxY0cWLFhwmb1XSiml8leQpOWiMeZ9Y8yvxpjf0l9FHlkZExcXh4fHP/fEs9lsxMXF5VrHxcWFatWqER8fz9mzZ3n77bcZO3ZsrvsPDQ3NlJikW7t2LXXr1sXb2xugQPvKKiAgwJFgzZs3j5iYmHy2UEoppS5fQZKW90RkrIi0FZEW6a8ij0wV2Lhx4xg5ciSVK1fOcX1ycjKLFy+md+/sV46HhIRkSmby21dOvvzySz766CNatmzJmTNncHV1vfxOKKWUUvkoyCXPTYFHsT8hOc0qS38qsyok7u7umUYoYmNjcXd3z7GOzWYjJSWFhIQEatWqxfr165k/fz4vvfQSp0+fxsnJiQoVKvD0008DsHz5clq0aEHdunUz7S8lJYXvv/+eTZv+uRgs674A6tev79hXTnx9ffn5558B+6miH3/88aqOhVJKKZWTgiQtvYFGxpjkog6mLGvdujV79+5l//79uLu7ExoayrfffpupTvfu3Zk1axZt27Zl/vz5dOjQARFh7dq1jjrjxo2jcuXKmZKMrKMp6X755Rd8fX2x2WyOsqz7Sk5OzjNhATh27Bhubm6kpaXxxhtv8OSTT152/5VSSqn8FOT00HagehHHUea5uLgwffp0OnXqhJ+fHw899BABAQGMGTOGxYvtF2sNGTKE+Ph4vLy8mDp1ao6XRWd17tw5VqxYke3qIMh9nktucnu+SEhICD4+Pvj6+lK/fn0GDRpU4H0qpZRSBSXpV5/kWkFkNRCI/UGESenlxpjuRRrZNcLN0814v+B9RdteD3fEjY6OxrOM3xW0rPa/LPcdtP9X238R2WSMaVV4ESlVsNNDBb+M5DpUr2q96yL5UEoppUq7fJMWvbxZKaWUUteCfJMWETmD/WohAFegHHDOGHNlTxFUSimllLoCBRlpqZL+XkQEuB+4tSiDUkoppZTK6rIemGjsFgKdiiYcpZRSSqmcFeT0UMZrZZ2AVsDFIotIKaWUUioHBbl6qFuG9ynYH554f5FEo5RSSimVi4LMadE7hSmllFKqxOWatIjImDy2M8aY/xZBPEoppZRSOcprpOVcDmWVgCFALaBMJC2HT52l5YuzSzqMbDZN6l/SISillFLFKtekxRgzJf29iFQBRgCDgFBgSm7bKaWUUkoVhTwveRaRmiLyBrAVe4LTwhgz2hhzrFiiU4UmLCyMxo0b4+XlleODFtesWUOLFi1wcXFh/vz5mdZ17tyZ6tWr07Vr10zlq1atokWLFjRp0oQBAwaQkpICwKRJkwgKCiIoKIgmTZrg7OzMyZMniYmJoX379vj7+xMQEMB7772XLY4pU6YgIpw4caIQe6+UUup6kGvSIiKTsD8k8QzQ1BgzzhhzqtgiU4UmNTWV4cOHs3z5ciIjIwkJCSEyMjJTnQYNGjBz5kwefvjhbNu/+OKLzJkzJ1NZWloaAwYMIDQ0lO3bt9OwYUNmzZrlqB8REUFERARvvfUWd955JzVr1sTFxYUpU6YQGRnJn3/+yYcffpgpjpiYGH7++WcaNGhQBEdBKaVUaZfXSMsLQH3gP8AhEUm0XmdEJLF4wlOFITw8HC8vLxo1aoSrqyvBwcEsWrQoUx1PT08CAwNxcsr+lbj77rupUqVKprL4+HhcXV3x8fEBoGPHjixYsCDbtiEhIfTt2xeAG2+8kRYtWgBQpUoV/Pz8iIuLc9QdOXIk77zzDvYbLyullFKZ5TWn5bLulqsKR6W9P+OUnNMc6Mz69/8lx/J69erxzjvvZCqLi4vDw8PDsWyz2Vi/fv1VxVm7dm1SUlLYuHEjrVq1Yv78+cTExGSqc/78ecLCwpg+fXq27aOjo9m8eTNt2rQBYNGiRbi7u9OsWbOriksppdT1qyA3l1PFyCn5HM5J+Q9kxcWV7GCXiBAaGsrIkSNJSkrinnvuwdnZOVOdJUuW8K9//YuaNWtmKj979iw9e/bk3XffpWrVqpw/f54333yTn3/+uTi7oJRSqpTRpOUak+ZaqUD1GtSukmN5vXr1spW5u7tnGgWJjY3F3d39ygLMoG3btqxduxaAn3/+mT179mRaHxoa6jg1lO7SpUv07NmTfv368eCD9idE/P333+zfv98xyhIbG0uLFi0IDw/PsT9KKaXKJk1arjHnvO8pUL3Zl3GfltatW7N3717279+Pu7s7oaGhfPvtt1caosOxY8dwc3MjKSmJt99+m1dffdWxLiEhgd9++42vv/7aUWaMYciQIfj5+fH88887yps2bcqxY/9ckObp6cnGjRupXbv2VceolFLq+qHzVsoAFxcXpk+fTqdOnfDz8+Ohhx4iICCAMWPGsHjxYgA2bNiAzWZj3rx5DB06lICAAMf2d9xxB71792blypXYbDZ++uknwH5ps5+fH4GBgXTr1o0OHTo4tvnhhx+45557qFTpn5GjdevWMWfOHFatWuW4JHrZsmXFdBSUUkqVdmKMKekYrml1PBqZBsHjSjqMbIrrjrjR0dF4enoWS1vXorLc/7Lcd9D+X23/RWSTMaZV4UWklI60KKWUUqqU0Dkt+agjifxQZVJJh5HNwfHFE9PJmq1wOrmxWNq6FpXl/pflvoP2n/5LSjoCpbLRkRallFJXZfDgwbi5udGkSZOSDkVd54osaRGRCiISLiJbRGSHiLxuld8kIutFJEpEvhMRV6u8vLUcZa33zLCv/7PKd4tIpwzlna2yKBF5OUP5ZbehlFLqygwcOJCwsLCSDkOVAUU50pIEdDDGNAOCgM4icivwNjDNGOMFnAKGWPWHAKes8mlWPUTEHwgGAoDOwEci4iwizsCHwL2AP9DXqsvltqGUUurKtWvXLttNJJUqCkWWtBi7s9ZiOetlgA5A+mOEZwEPWO/vt5ax1t8t9ofQ3A+EGmOSjDH7gSjgFusVZYzZZ4xJBkKB+61tLrcNpZRSSl3jinROizUiEgEcA1YAfwOnjTEpVpVYIP3WrO5ADIC1PgGolbE8yza5lde6gjaUUkopdY0r0qTFGJNqjAkCbNhHRnyLsr3CIiJPiMhGEdl46uzFkg5HKaWUUhTT1UPGmNPAr0BboLqIpF9qbQPirPdxgAeAtb4aEJ+xPMs2uZXHX0EbWeP9zBjTyhjTqkblClfWaaWUUkoVqqK8eqiOiFS33t8AdAR2Yk9eelnVBgCLrPeLrWWs9auM/Xa9i4Fg68qfmwBvIBzYAHhbVwq5Yp+su9ja5nLbUEopdYX69u1L27Zt2b17NzabjRkzZpR0SOo6VZQ3l7sRmGVd5eMEzDXGLBWRSCBURN4ANgPp3+4ZwBwRiQJOYk9CMMbsEJG5QCSQAgw3xqQCiMjTwE+AM/ClMWaHta/Rl9OGUkqpKxcSEpKt7LHHHiuBSNT1rsiSFmPMVqB5DuX7sM9vyVp+Eeidy74mABNyKF8GZHvi3pW0oZRSSqlrm97GPx8nnJzoW6Nqgeque2ZdEUdT/NKio2lQhh8aV5b7X5b7Dtr/6Ojokg5BqWz0Nv5KKaWUKhU0aSlBYWFhNG7cGC8vLyZOnJhtfVJSEn369MHLy4s2bdo4/vIJDw8nKCiIoKAgmjVrxg8//JBpu9TUVJo3b07Xrl0dZXfccYdjm/r16/PAAw8AcOrUKXr06EFgYCC33HIL27dvd2zz3nvv0alTJwICAnj33XcLvf9KKaXU5dCkpYSkpqYyfPhwli9fTmRkJCEhIURGRmaqM2PGDGrUqEFUVBQjR45k9OjRADRp0oSNGzcSERFBWFgYQ4cOJSUlxbHde++9h5+fX6Z9rV27loiICCIiImjbti0PPvggAG+++SZBQUFs3bqV2bNnM2LECAC2b9/O559/zsKFC9myZQtLly4lKiqqKA+JUkoplSdNWkpIeHg4Xl5eNGrUCFdXV4KDg1m0aFGmOosWLWLAAPsV2r169WLlypUYY6hYsSIuLvbpSBcvXiTjkwhiY2P58ccfc525n5iYyKpVqxwjLZGRkXTo0AEAX19foqOjOXr0KDt37qRNmzbccMMNuLi4cOedd/L9998X9mFQSimlCkyTlhISFxeHh8c/98az2WzExcXlWsfFxYVq1aoRH2+/F9769esJCAigadOmfPLJJ44k5rnnnuOdd97BySnnj3bhwoXcfffdVK1qn1zcrFkzRzISHh7OgQMHiI2NpUmTJqxdu5ZTp05x/vx5li1bRkxMTI77VEoppYqDJi2lVJs2bdixYwcbNmzgrbfe4uLFiyxduhQ3NzdatmyZ63YhISH07dvXsfzyyy9z+vRpgoKC+OCDD2jevDnOzs74+fkxevRo+vfvT+fOnQkKCsLZ2bk4uqaUUkrlSC95LiHu7u6ZRi5iY2Nxd3fPsY7NZiMlJYWEhARq1cr8fEc/Pz8qV67M9u3bWbduHYsXL2bZsmVcvHiRxMREHnnkEb7++msATpw4QXh4eKaJu1WrVuWrr74CwBjDTTfdRKNGjQAYMmQId999N56enrzyyivYbLYiORZKKaVUQehISwlp3bo1e/fuZf/+/SQnJxMaGkr37t0z1enevTuzZs0CYP78+XTo0AERYf/+/Y6JtwcOHGDXrl14enry1ltvERsbS3R0NKGhoXTo0MGRsKTvo2vXrlSo8M/zlE6fPk1ycjIAX3zxBe3atXOcOjp27BgABw8e5Pvvv+fhhx8uugOilFJK5UNHWkqIi4sL06dPp1OnTqSmpjJ48GACAgIYM2YMrVq1onv37gwZMoRHH30ULy8vatasSWhoKAD/+9//mDhxIuXKlcPJyYmPPvqI2rVr59tmaGgoL7/8cqaynTt3MmDAAESEgICATM8M6dmzJ0eOHKFixYp8+OGHVK9evVCPgVJKKXU5RJ8XmDc3Tzfj/YJ3gepej3fEjY6OxrOM3xW0rPa/LPcdtP9X238R2WSMaVV4ESmlp4eUUkopVUro6aF81Kta77ocQVFKKaVKGx1pUUoppVSpoEmLUkoppUoFTVqUUkopVSpo0qKUUkqpUkGTFqWUUkqVCpq0KKWUUqpU0KRFKaWUUqWCJi1KKaWUKhX05nL5OHzqLC1fnF3SYRTYpkn9SzoEpZRSqkjoSEsZFxYWRuPGjfHy8mLixInZ1q9fv54WLVrg4uLC/PnzHeUHDhygRYsWBAUFERAQwCeffOJYFxISQtOmTQkMDKRz586cOHECgNdee43AwECCgoK45557OHToEACrV6+mWrVqBAUFERQUxPjx4wG4ePEit9xyC82aNSMgIICxY8cW5aFQSil1jdOkpQxLTU1l+PDhLF++nMjISEJCQoiMjMxUx93dnZkzZ/Lwww9nKr/xxhv5448/iIiIYP369UycOJFDhw6RkpLCiBEj+PXXX9m6dSuBgYFMnz4dgBdffJGtW7cSERFB165dHckJwB133EFERAQRERGMGTMGgPLly7Nq1Sq2bNlCREQEYWFh/Pnnn0V8VJRSSl2rNGkpw8LDw/Hy8qJRo0a4uroSHBzMokWLMtWx2WwEBgbi5JT5q+Lq6kr58uUBSEpKIi0tDQBjDMYYzp07hzGGxMRE6tevD0DVqlUd2587dw4RyTM+EaFy5coAXLp0iUuXLuW7jVJKqeuXzmm5xlXa+zNOyecKXL9//19yXVevXj3eeecdx3JcXBweHh6OZZvNxvr16wvcVkxMDPfddx9RUVFMmjTJkZx8/PHHNG3alEqVKuHt7c2HH37o2ObVV19l9uzZVKtWjV9//dVR/scff9CsWTPq16/P5MmTCQgIAOyjQS1btiQqKorhw4fTpk2bAsenlFLq+qIjLdc4p+RzOCclFvgVFxeX6+vIkSOFGpuHhwdbt24lKiqKWbNmcfToUS5dusTHH3/M5s2bOXToEIGBgbz11luObSZMmEBMTAz9+vVznDZq0aIFBw4cYMuWLTzzzDM88MADjvrOzs5EREQQGxtLeHg427dvL9Q+KKWUKj00abnGpblWIrV81QK/3N3dc33Vq1cv077d3d2JiYlxLMfGxuLu7n7ZMdavX58mTZqwdu1aIiIiALj55psRER566CF+//33bNv069ePBQsWAPbTRumngbp06cKlS5cck3fTVa9enfbt2xMWFnbZ8SmllLo+6Omha9w573suq/7sy7jkuXXr1uzdu5f9+/fj7u5OaGgo3377bYG2jY2NpVatWtxwww2cOnWK//3vf4wcOZJatWoRGRnJ8ePHqVOnDitWrMDPzw+AvXv34u3tDcCiRYvw9fUF4MiRI9StWxcRITw8nLS0NGrVqsXx48cpV64c1atX58KFC6xYsYLRo0df1vFQSil1/dCkpQxzcXFh+vTpdOrUidTUVAYPHkxAQABjxoyhVatWdO/enS1btnD77bdz6tQplixZwtixY9mxYwc7d+7khRdeQEQwxjBq1CiaNm0KwNixY2nXrh3lypWjYcOGzJw5E4CXX36Z3bt34+TkRMOGDR2XSc+fP5+PP/4YFxcXbrjhBkJDQxERDh8+zIABA0hNTSUtLY2HHnqIrl27ltThUkopVcLEGFPSMVzT6ng0Mg2Cx5V0GAVW2DeXi46OxtPTs1D3WZqU5f6X5b6D9v9q+y8im4wxrQovIqV0TotSSimlSgk9PZSPOpLID1UmlXQYBXZwfOHGerJmK5xObizUfZYmZbn/ZbnvoP2n/5KSjkCpbHSkRSmllFKlgiYtSimlrsrgwYNxc3OjSZMmJR2Kus4VadIiItEisk1EIkRko1VWU0RWiMhe698aVrmIyPsiEiUiW0WkRYb9DLDq7xWRARnKW1r7j7K2lSttQyml1JUZOHCg3kNJFYviGGlpb4wJyjCL/GVgpTHGG1hpLQPcC3hbryeAj8GegABjgTbALcDY9CTEqvN4hu06X0kbSimlrly7du2oWbNmSYehyoCSOD10PzDLej8LeCBD+Wxj9ydQXURuBDoBK4wxJ40xp4AVQGdrXVVjzJ/Gft327Cz7upw2lFJKKXWNK+qkxQA/i8gmEXnCKqtrjDlsvT8C1LXeuwMxGbaNtcryKo/NofxK2shERJ4QkY0isvHU2YsF6qhSSimlilZRX/J8uzEmTkTcgBUisivjSmOMEZEivbvdlbRhjPkM+AzAv0FtvfueUkopdQ0o0pEWY0yc9e8x4Afsc1KOpp+Ssf49ZlWPAzwybG6zyvIqt+VQzhW0oZRSSqlrXJElLSJSSUSqpL8H7gG2A4uB9CuABgCLrPeLgf7WFT63AgnWKZ6fgHtEpIY1Afce4CdrXaKI3GpdNdQ/y74upw2llFJXqG/fvrRt25bdu3djs9mYMWNGSYekrlNFeXqoLvCDdRWyC/CtMSZMRDYAc0VkCHAAeMiqvwzoAkQB54FBAMaYkyLyX2CDVW+8Meak9f4pYCZwA7DcegFMvJw2lFJKXbmQkJBsZY899lgJRKKud0WWtBhj9gHNciiPB+7OodwAw3PZ15fAlzmUbwSy3c3oStpQSiml1LVNnz2UjxNOTvStUbXA9dc9s64Ioyl+adHRNCjDT7oty/0vy30H7X90dHRJh6BUNnob/xIUFhZG48aN8fLyYuLEidnWJyUl0adPH7y8vGjTpo3jh0h4eDhBQUEEBQXRrFkzfvjhB8c2p0+fplevXvj6+uLn58cff/wBQEREBLfeeitBQUG0atWK8PBwAIwxPPvss3h5eREYGMhff/3l2NfBgwd59NFH8fPzw9/f39H+ypUradGiBUFBQdx+++1ERUUV0RFSSiml/qFJSwlJTU1l+PDhLF++nMjISEJCQoiMjMxUZ8aMGdSoUYOoqChGjhzJ6NGjAWjSpAkbN24kIiKCsLAwhg4dSkpKCgAjRoygc+fO7Nq1iy1btuDn5wfASy+9xNixY4mIiGD8+PG89NJLACxfvpy9e/eyd+9ePvvsM4YNG+Zov3///jzxxBPs3LmT8PBw3NzcABg2bBjffPMNERERPPzww7zxxhtFfryUUkopTVpKSHh4OF5eXjRq1AhXV1eCg4NZtGhRpjqLFi1iwAD7RVC9evVi5cqVGGOoWLEiLi72M3sXL17EmuxMQkICa9asYciQIQC4urpSvXp1AESExMRER7369es72ujfvz8iwq233srp06c5fPgwkZGRpKSkcMcddwBQuXJlKlasmOe+lFJKqaKkc1pKSFxcHB4e/9wyxmazsX79+lzruLi4UK1aNeLj46lduzbr169n8ODBHDhwgDlz5uDi4sL+/fupU6cOgwYNYsuWLbRs2ZL33nuPSpUq8e6779KpUydGjRpFWloav//+e65xxMXFERsbS/Xq1XnyySc5evQo//73v5k4cSLOzs588cUXdOnShRtuuIGqVavy559/FsMRU0opVdbpSEsp1aZNG3bs2MGGDRt46623uHjxIikpKfz1118MGzaMzZs3U6lSJcdcmY8//php06YRExPDtGnTHKMxuUlJSWHt2rW88sorbNiwgX379jFz5kwApk2bxrJly4iNjWXQoEE8//zzRd1dpZRSSpOWkuLu7k5MzD+PQYqNjcXd3T3XOikpKSQkJFCrVq1Mdfz8/KhcuTLbt2/HZrNhs9lo06YNYD+llD6xdtasWTz44IMA9O7d2zERN7c4bDYbQUFBNGjQABcXFx544AH++usvjh8/zpYtWxxt9OnTxzFqo5RSShUlTVpKSOvWrdm7dy/79+8nOTmZ0NBQunfvnqlO9+7dmTXL/rDq+fPn06FDB0SE/fv3OybeHjhwgF27duHp6Um9evXw8PBg9+7dgP0qH39/fwDq16/Pb7/9BsCqVavw9vZ2tDF79myMMfz5559Uq1aNG2+8kdatW3P69Gni4+Md2/j7+1OjRg0SEhLYs2cPACtWrHBM9lVKKaWKks5pKSEuLi5Mnz6dTp06kZqayuDBgwkICGDMmDG0atWK7t27M2TIEB599FG8vLyoWbMmoaGhAPzvf/9j4sSJlCtXDicnJz766CNq164NwAcffEC/fv1ITk6mUaNGfPXVVwB8/vnnjBgxgpSUFCpUqMBnn30GQJcuXVi2bBleXl5UrFjRUd/Z2ZnJkyfTr18/ypUrR8uWLXn88cdxcXHh888/p2fPnjg5OVGjRg2+/DLbff+UUkqpQif2m8Sq3Lh5uhnvF7wLXP96u7lcdHQ0nmX8Bltltf9lue+g/b/a/ovIJmNMq8KLSCk9PaSUUkqpUkJPD+WjXtV6193oiVJKKVUa6UiLUkoppUoFTVqUUkopVSpo0qKUUkqpUkGTFqWUUkqVCnrJcz5E5Aywu6TjKEG1gRMlHUQJKsv9L8t9B+3/1fa/oTGmTmEFoxTo1UMFsbss32tARDZq/8tm/8ty30H7X9b7r65NenpIKaWUUqWCJi1KKaWUKhU0acnfZyUdQAnT/pddZbnvoP0v6/1X1yCdiKuUUkqpUkFHWpRSSilVKmjSopRSSqlSQZMWi4h0FpHdIhIlIi/nsL68iHxnrV8vIp4lEGaRKUD/nxeRSBHZKiIrRaRhScRZFPLre4Z6PUXEiMh1dRloQfovIg9Zn/8OEfm2uGMsSgX47jcQkV9FZLP1/e9SEnEWBRH5UkSOicj2XNaLiLxvHZutItKiuGNUKhNjTJl/Ac7A30AjwBXYAvhnqfMU8In1Phj4rqTjLub+twcqWu+HXS/9L0jfrXpVgDXAn0Crko67mD97b2AzUMNadivpuIu5/58Bw6z3/kB0ScddiP1vB7QAtueyvguwHBDgVmB9Scesr7L90pEWu1uAKGPMPmNMMhAK3J+lzv3ALOv9fOBuEZFijLEo5dt/Y8yvxpjz1uKfgK2YYywqBfnsAf4LvA1cLM7gikFB+v848KEx5hSAMeZYMcdYlArSfwNUtd5XAw4VY3xFyhizBjiZR5X7gdnG7k+guojcWDzRKZWdJi127kBMhuVYqyzHOsaYFCABqFUs0RW9gvQ/oyHY//q6HuTbd2tI3MMY82NxBlZMCvLZ+wA+IrJORP4Ukc7FFl3RK0j/xwGPiEgssAx4pnhCuyZc7s8GpYqU3sZfXRYReQRoBdxZ0rEUBxFxAqYCA0s4lJLkgv0U0V3YR9jWiEhTY8zpkgyqGPUFZhpjpohIW2COiDQxxqSVdGBKlTU60mIXB3hkWLZZZTnWEREX7MPE8cUSXdErSP8RkX8DrwLdjTFJxRRbUcuv71WAJsBqEYnGfl5/8XU0Gbcgn30ssNgYc8kYsx/Ygz2JuR4UpP9DgLkAxpg/gArYHyZYFhToZ4NSxUWTFrsNgLeI3CQirtgn2i7OUmcxMMB63wtYZYy5Xu7Ml2//RaQ58Cn2hOV6mtOQZ9+NMQnGmNrGGE9jjCf2+TzdjTEbSybcQleQ7/5C7KMsiEht7KeL9hVjjEWpIP0/CNwNICJ+2JOW48UaZclZDPS3riK6FUgwxhwu6aBU2aWnh7DPURGRp4GfsF9N8KUxZoeIjAc2GmMWAzOwDwtHYZ+4FlxyEReuAvZ/ElAZmGfNPz5ojOleYkEXkgL2/bpVwP7/BNwjIpFAKvCiMea6GGUsYP9fAD4XkZHYJ+UOvF7+YBGREOwJaW1rzs5YoByAMeYT7HN4ugBRwHlgUMlEqpSd3sZfKaWUUqWCnh5SSimlVKmgSYtSSimlSgVNWpRSSilVKmjSopRSSqlSQZMWpZRSSpUKmrSoUsV6yvKUDMujRGRcMcewOv3mciKyTESqX+X+7hKRpbmUJ4hIRIbXv6+mrcuI57YMy0+KSP+r3GfTDH04KSL7rfe/iEj3vJ6urZRS6fQ+Laq0SQIeFJG3jDEnLndjEXGxnh1VKIwxXQprX7lYa4zpWsRtZHUXcBb4HRz367gqxphtQBCAiMwElhpj5meocl3fD0cpVTh0pEWVNinAZ8DIrCtExFNEVonIVhFZKSINrPKZIvKJiKwH3rGWP7Ye/rfPGln4UkR2Wr9Q0/f3sYhsFJEdIvJ6TsGISLSI1LZGI9JHEvaLyK/W+ntE5A8R+UtE5olIZau8s4jsEpG/gAcv5wCISGurjxVEpJIVXxPr/ZciEi4im0Xkfqu+s4hMFpHt1nbPZIzdet/KGkHyBJ4ERlp9uUNExonIKKtekHXctorIDyJSwypfLSJvW23vEZE7LqM/A0VkeobPqiCfTY7HVSl1fdOkRZVGHwL9RKRalvIPgFnGmEDgG+D9DOtswG3GmOet5RpAW+zJz2JgGhAANBWRIKvOq8aYVkAgcKeIBOYWkDHmE2NMENAa+7N6ploJwX+AfxtjWgAbgedFpALwOdANaAnUy6Ovd2Q5PXSzMWaDFfMbwDvA18aY7difC7XKGHML0B6YJCKVgCcATyAow7HJrR/RwCfANGNMkDFmbZYqs4HR1n62Yb+DajoXq+3nspRfrjw/m9yO61W0p5QqJfT0kCp1jDGJIjIbeBa4kGFVW/4ZtZiD/Rd6unnGmNQMy0uMMUZEtgFHrdMXiMgO7L/gI4CHROQJ7P9PbgT8ga35hPce9sRhiYh0tbZZJ/ZHH7gCfwC+wH5jzF6rza+xJxY5ye300Hjsz825aB0HgHuA7umjItifkdMA+DfwSfppMWPMyXz6kCMrSaxujPnNKpoFzMtQ5Xvr303Yj+GVyu+zsZHzcVVKXec0aVGl1bvAX8BXBax/Lsty+lOq0zK8T192EZGbgFFAa2PMKevURIW8GhCRgUBD4On0ImCFMaZvlnpBBYw5L7WwPwuqnBXXOau9nsaY3Vnay20fKfwz2ppn3woo/TimcnU/W/L8bKz9ZzuuSqnrn54eUqWSNVowFxiSofh3/nmQZT8g66mNy1EVeyKQICJ1gXvzqiwiLbEnOY8YY9Ks4j+Bf4mIl1Wnkoj4ALsATxG52ap3Jb98PwVew36q522r7CfgGbGyFLE/mRtgBTBURFys8ppWeTT201MAPTPs+wxQJWuDxpgE4FSG+SqPAr9lrVcMcjuuSqnrnCYtqjSbAtTOsPwMMEhEtmL/hTriSndsjNkCbMaeYHwLrMtnk6eBmsCv1tyTL4wxx4GBQIgV0x+ArzHmIvbTQT9aE3GP5bHfrHNaeon98uNLxphvgYlAaxHpAPwX+8jLVutUyn+tfXwBHLTKtwAPW+WvA++JyEbsoxfplgA90ifiZolnAPa5MluxXw00Pp/jUuhyO67FHYdSqvjpU56VUkopVSroSItSSimlSgVNWpRSSilVKmjSopRSSqlSQZMWpZRSSpUKmrQopZRSqlTQpEUppZRSpYImLUoppZQqFf4ffb/0hNAN5EMAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average speedup CPU vs. GPU: 8.18x\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As expected, the GPU implementation is clearly superior in terms of performance, being as low as 3% of the CPU time and $8.2\\times$ faster than CPU on average, with a peak of $27.2\\times$.\n",
        "\n",
        "If we now investigate how the amount of threads per block influences the performance of the custom kernel, we see a negligible difference, as follows:"
      ],
      "metadata": {
        "id": "29wmfyVvCs1V"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# figure(num=None, figsize=(10, 9), dpi=80, facecolor='w', edgecolor='r')\n",
        "table_gpu = table[table['Device'].isin(['Tesla T4', 'GeForce RTX 2080 Ti'])].copy()\n",
        "table_gpu = table_gpu[table_gpu['Batched/Custom Kernel'] == 'Custom Kernel']\n",
        "\n",
        "ax = sns.barplot(data=table_gpu, y='Num. Nodes', x='Avg. Time [s]',\n",
        "                 hue='Num. Threads', orient='h')\n",
        "sns.move_legend(ax, 'upper left', bbox_to_anchor=(1, 1))\n",
        "for container in ax.containers:\n",
        "    ax.bar_label(container, padding=10)\n",
        "plt.grid(axis='x', alpha=0.5)\n",
        "plt.title('Execution time of the custom CUDA kernel')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "zCYUC_2jiN67",
        "outputId": "180ed416-f457-4ab3-9a05-32554ec6a766"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now focus on comparing the two proposed GPU versions."
      ],
      "metadata": {
        "id": "Gi3kMTLhJG_A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table_gpu = table[table['Device'].isin(['Tesla T4', 'GeForce RTX 2080 Ti'])].copy()\n",
        "table_gpu['Normalized Execution Time'] = table_gpu['Avg. Time [s]']\n",
        "\n",
        "for n_cells in table_gpu['Num. Cells'].unique():\n",
        "    selected_cells = table_gpu['Num. Cells'] == n_cells\n",
        "    max_t = table_gpu.loc[selected_cells, 'Avg. Time [s]'].max()\n",
        "    table_gpu.loc[selected_cells, 'Normalized Execution Time'] /= max_t\n",
        "\n",
        "# figure(num=None, figsize=(10, 9), dpi=80, facecolor='w', edgecolor='r')\n",
        "ax = sns.barplot(data=table_gpu, y='Num. Nodes', x='Normalized Execution Time',\n",
        "                 hue='Batched/Custom Kernel', orient='h')\n",
        "sns.move_legend(ax, 'upper left', bbox_to_anchor=(1, 1))\n",
        "for container in ax.containers:\n",
        "    ax.bar_label(container, padding=10)\n",
        "plt.grid(axis='x', alpha=0.5)\n",
        "plt.title('Batched versus Custom GPU kernels')\n",
        "plt.show()\n",
        "\n",
        "batched_t = table_gpu.loc[table_gpu['Batched/Custom Kernel'] == 'Batched', 'Avg. Time [s]']\n",
        "custom_t = table_gpu.loc[table_gpu['Batched/Custom Kernel'] == 'Custom Kernel', 'Avg. Time [s]']\n",
        "print(f'Average speedup Batched vs. Custom kernel: {custom_t.mean() / batched_t.mean():.2f}x')"
      ],
      "metadata": {
        "id": "coeCaLhH0SDs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "875ce0d6-e6d3-432b-d967-ff4287984147"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average speedup Batched vs. Custom kernel: 6.56x\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The batched GPU version is $6.6\\times$ faster on average, and the performance gap increases as the number of points increases. This suggests that the custom kernel implementation suffers from an inefficient memory managment.\n",
        "\n",
        "Finally, we can compare the performance of the two examined GPU devices."
      ],
      "metadata": {
        "id": "zh7mD13QJRou"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table_gpu = table[table['Device'].isin(['Tesla T4', 'GeForce RTX 2080 Ti'])].copy()\n",
        "table_gpu = table_gpu[table_gpu['Batched/Custom Kernel'] == 'Batched']\n",
        "table_gpu['Normalized Execution Time'] = table_gpu['Avg. Time [s]']\n",
        "\n",
        "for n_cells in table_gpu['Num. Cells'].unique():\n",
        "    selected_cells = table_gpu['Num. Cells'] == n_cells\n",
        "    max_t = table_gpu.loc[selected_cells, 'Avg. Time [s]'].max()\n",
        "    table_gpu.loc[selected_cells, 'Normalized Execution Time'] /= max_t\n",
        "\n",
        "# figure(num=None, figsize=(10, 9), dpi=80, facecolor='w', edgecolor='r')\n",
        "ax = sns.barplot(data=table_gpu, y='Num. Nodes', x='Normalized Execution Time',\n",
        "                 hue='Device', orient='h')\n",
        "sns.move_legend(ax, 'upper left', bbox_to_anchor=(1, 1))\n",
        "for container in ax.containers:\n",
        "    ax.bar_label(container, padding=10)\n",
        "plt.grid(axis='x', alpha=0.5)\n",
        "plt.title('RTX 2080 versus Tesla T4')\n",
        "plt.show()\n",
        "\n",
        "tesla_t = table.loc[table['Device'] == 'Tesla T4', 'Avg. Time [s]']\n",
        "rtx_t = table.loc[table['Device'] == 'GeForce RTX 2080 Ti', 'Avg. Time [s]']\n",
        "print(f'Average speedup T4 vs. RTX: {tesla_t.mean() / rtx_t.mean():.2f}x')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "vOP-_UthkULH",
        "outputId": "5439a12b-bcbf-4c72-9ebc-4630cade5ffd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average speedup T4 vs. RTX: 6.84x\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The RTX card is $6.8\\times$ faster on average than the T4 card. This might be due to different GPU architecture characteristcs, such as the number of CUDA cores (2944 in the RTX versus 2560 in the T4) and their core clock speed (around 1500MHz in the RTX versus 585MHz in the T4)."
      ],
      "metadata": {
        "id": "x_TBY3h-Tk2e"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Conclusions and Future Work\n",
        "\n",
        "In this work we proposed, designed and implemented different solutions for accelerating the FEM algorithm computation, to be run both in a multithreaded environment and on a GPU card.\n",
        "In our experiments, we show that the batched implementation is a viable and efficient solution, especially for the GPU case, which allowed us to achieve a top speedup of $28\\times$ over the CPU counterpart.\n",
        "\n",
        "Here is a list of possible future directions that can be explored and analyzed:\n",
        "\n",
        "* More advanced meshes, such as 3D meshes and/or more DoFs per cell\n",
        "* Efficient handling of the COO data and exploring and efficiently leverage DOK format to save space, _i.e._, manual implementation of the reduction phase\n",
        "* More in-depth analysis of the data movement and memory requirements of the algorithm. For example, use of shared memory in the custom kernel might improve its performance. See Numba on [shared memory](https://numba.readthedocs.io/en/stable/cuda/memory.html#shared-memory-and-thread-synchronization), and this [example](https://numba.readthedocs.io/en/stable/cuda/examples.html#cuda-matmul).\n",
        "* More advanced design space exploration of the custom CUDA kernel parameters\n",
        "* Analysis of the convergency rate of the solvers at different tolerance levels"
      ],
      "metadata": {
        "id": "2JImizAQNBI2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Appendix: Cell Coloring\n",
        "\n",
        "Cell coloring refers to a K-assembly mechanism in which cells not sharing nodes can be assigned to different color pools. This strategy allows then to update the global stiffness matrix color-wise without race conditions, since we are guaranteed to have non-overlapping updates.\n",
        "\n",
        "Unfortunately, this has remained a work in progress and it's included for future reference."
      ],
      "metadata": {
        "id": "OWBVDlautg8y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Coloring Strategies"
      ],
      "metadata": {
        "id": "mNkx9EXtPzkd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Graph Partitioning with PyMETIS\n",
        "\n",
        "Unfortunately PyMETIS, a Python wrapper to the METIS software, is producing colors with \"overlapping\" elements. Because of that, it is not possibile to use it as a partitioning algorithm."
      ],
      "metadata": {
        "id": "A4FP7ZEdqzDH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install pymetis -qqq"
      ],
      "metadata": {
        "id": "s7Aaxyfux_3F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import pymetis"
      ],
      "metadata": {
        "id": "9n-jLyKnuNQu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import defaultdict\n",
        "\n",
        "def create_adjacency_list_naive(cells):\n",
        "    # Create a defaultdict to store the adjacency\n",
        "    adjacency = defaultdict(set)\n",
        "    # Iterate through each cell in the graph\n",
        "    for i, cell in enumerate(cells):\n",
        "        for j, other_cell in enumerate(cells):\n",
        "            if set(cell).isdisjoint(other_cell):\n",
        "                if i != j:\n",
        "                    adjacency[i].add(j)\n",
        "    return adjacency\n",
        "\n",
        "def create_adjacency_list(cells):\n",
        "    # Create a defaultdict to store the cells that include a given node\n",
        "    node2cell = defaultdict(set)\n",
        "    for i, cell in enumerate(cells):\n",
        "        for node in cell:\n",
        "            node2cell[node].add(i)\n",
        "    cells_set = set(list(range(len(cells))))\n",
        "    # Create a defaultdict to store the adjacency\n",
        "    adjacency = defaultdict(set)\n",
        "    # Iterate through each cell in the graph\n",
        "    for i, cell in enumerate(cells):\n",
        "        nodes = set([c for node in cell for c in node2cell[node]])\n",
        "        adjacency[i].update(cells_set.difference(nodes))\n",
        "    return adjacency\n",
        "\n",
        "# Example usage\n",
        "grid = generate_grid(lcar=0.4)\n",
        "adjacency = create_adjacency_list(grid.cells)\n",
        "adjacency_naive = create_adjacency_list_naive(grid.cells)\n",
        "\n",
        "for k in adjacency_naive.keys():\n",
        "    # list(adjacency[k]).sort() \n",
        "    # list(adjacency_naive[k]).sort()\n",
        "    if adjacency_naive[k] != adjacency[k]:\n",
        "        # print(f'not matching: {adjacency[k]} vs. {adjacency_naive[k]}')\n",
        "        print('MISMATCH!!!', adjacency[k] - adjacency_naive[k])\n",
        "        if k > 10:\n",
        "            break"
      ],
      "metadata": {
        "id": "8Nsu2z4ABiBy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "grid = generate_grid(lcar=0.8)\n",
        "n_parts = 16\n",
        "# adjacency = create_adjacency_list(grid.cells)\n",
        "adjacency = create_adjacency_list_naive(grid.cells)\n",
        "\n",
        "n_cuts, membership = pymetis.part_graph(n_parts, adjacency=adjacency)\n",
        "\n",
        "print(f'n_nodes: {grid.get_num_cells() * grid.get_num_nodes_per_cell()}')\n",
        "print(f'n_cells: {grid.get_num_cells()} (n_parts: {n_parts}) - Cells per part: {(grid.get_num_cells() / n_parts) / grid.get_num_cells() * 100}%')\n",
        "print(f'n_cuts: {n_cuts}')\n",
        "print('-' * 80)\n",
        "\n",
        "for part in range(n_parts):\n",
        "    cells_part = np.argwhere(np.array(membership) == part).ravel()\n",
        "\n",
        "    nodes_idx_part = grid.cells[cells_part].flatten()\n",
        "    unique_nodes_idx_part = np.unique(nodes_idx_part)\n",
        "\n",
        "    if len(nodes_idx_part) != len(unique_nodes_idx_part):\n",
        "        nodes_part = grid.nodes[unique_nodes_idx_part]\n",
        "        nodes_idx_part.sort()\n",
        "        unique_nodes_idx_part.sort()\n",
        "        print(part, len(nodes_idx_part), nodes_idx_part)\n",
        "        print(part, len(unique_nodes_idx_part), unique_nodes_idx_part)\n",
        "        print(part, len(nodes_idx_part) - len(unique_nodes_idx_part))\n",
        "        nodal_values = np.random.randn(len(nodes_part))\n",
        "        nodes_x = grid.nodes[:, 0]\n",
        "        nodes_y = grid.nodes[:, 1]\n",
        "        # Plot the finite element mesh\n",
        "        for element in grid.cells[cells_part]:\n",
        "            x = [nodes_x[element[i]] for i in range(len(element))]\n",
        "            y = [nodes_y[element[i]] for i in range(len(element))]\n",
        "            plt.fill(x, y, edgecolor='black', fill=True)\n",
        "        plt.axis('equal')\n",
        "        plt.show()\n",
        "        print('-' * 80)"
      ],
      "metadata": {
        "id": "JCQjEKRfmO5K"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def color_cells(grid, n_colors=64):\n",
        "    \"\"\"\n",
        "    The returned partitions are already sorted (being sorted should help a bit\n",
        "    with cache locality...).\n",
        "    \"\"\"\n",
        "    adjacency = create_adjacency_list(grid.cells)\n",
        "    _, membership = pymetis.part_graph(n_colors, adjacency=adjacency)\n",
        "    partitions = []\n",
        "    for color in range(n_colors):\n",
        "        cellids_part = np.argwhere(np.array(membership) == color).flatten()\n",
        "        if len(cellids_part) > 0:\n",
        "            partitions.append(cellids_part)\n",
        "            # Check whether the nodes in the partition are all unique, and so\n",
        "            # non-overlapping\n",
        "\n",
        "            # nodes_part = grid.cells[cellids_part].flatten()\n",
        "            # unique_nodes_idx = np.unique(nodes_part)\n",
        "            # unique_nodes_part = grid.nodes[unique_nodes_idx]\n",
        "\n",
        "            nodes_idx_part = grid.cells[cellids_part].flatten()\n",
        "            unique_nodes_idx_part = np.unique(nodes_idx_part)\n",
        "            # nodes_part = grid.nodes[unique_nodes_idx_part]\n",
        "            # nodes_idx_part.sort()\n",
        "            # unique_nodes_idx_part.sort()\n",
        "            # if len(nodes_part) != len(unique_nodes_part):\n",
        "            if len(nodes_idx_part) != len(unique_nodes_idx_part):\n",
        "                if color != n_colors - 1:\n",
        "                    # raise ValueError('Overlapping nodes in two or more partitions.')\n",
        "                    print(f'WARNING. Overlapping nodes in partition n.{color}.')\n",
        "                else:\n",
        "                    print(f'WARNING. Overlapping nodes in last partition.')\n",
        "    return partitions\n",
        "\n",
        "grid = generate_grid(lcar=0.6)\n",
        "color_cells(grid, n_colors=8)"
      ],
      "metadata": {
        "id": "XTYzfKs82zw7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cd3ecdf3-1f58-4b48-b342-b6c8a3bed9dc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "WARNING. Overlapping nodes in partition n.2.\n",
            "WARNING. Overlapping nodes in partition n.5.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[array([ 1, 11, 19, 21, 28, 40, 61, 73, 76]),\n",
              " array([ 5,  7,  9, 18, 23, 38, 48, 56, 59, 67]),\n",
              " array([13, 16, 17, 22, 30, 31, 35, 68, 74]),\n",
              " array([ 4, 41, 43, 52, 53, 57, 58, 60, 62, 66]),\n",
              " array([ 2,  6, 10, 12, 24, 29, 46, 49, 70]),\n",
              " array([27, 33, 39, 42, 47, 51, 54, 65, 69, 75]),\n",
              " array([ 0, 15, 20, 25, 26, 32, 37, 44, 45, 71, 72]),\n",
              " array([ 3,  8, 14, 34, 36, 50, 55, 63, 64])]"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Naive Greedy Coloring Algorithm\n",
        "\n",
        "Greedy Coloring Algorithm, as described in these [lecture notes](http://paulino.princeton.edu/education_resources/GreedyColoring/GreedyColoring.pdf)):\n",
        "\n",
        "0. Set the maximum color size, _e.g._, according to the number of threads available\n",
        "1. Get the next element in the mesh\n",
        "2. Traverse all its neighbors, and see what colors cannot be used\n",
        "3. Pick the next available color\n",
        "4. If color is already full, go to 3\n",
        "5. Color this element with this color\n",
        "6. If this is not the last element, go to 1\n",
        "\n",
        "The greatest advantage of this coloring algorithm is that the colors will have at most $N$ elements, making is suitable to precisely map colors to GPU resources."
      ],
      "metadata": {
        "id": "_zZ0_FGPaCGO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import defaultdict\n",
        "\n",
        "grid = generate_grid(lcar=0.6)\n",
        "cells = grid.cells\n",
        "\n",
        "# Create a defaultdict to store the all cells to which a given node belongs to\n",
        "node2cell = defaultdict(set)\n",
        "for i, cell in enumerate(cells):\n",
        "    for node in cell:\n",
        "        node2cell[node].add(i)\n",
        "cell_neighbors = defaultdict(set)\n",
        "for i, cell in enumerate(cells):\n",
        "    for node in cell:\n",
        "        neighbors = node2cell[node] - {i} # Do not include the cell itself\n",
        "        cell_neighbors[i].update(neighbors)\n",
        "# # Init first element color\n",
        "# cells_colors = {0: 0} # {Cellid n.0: color n.0}\n",
        "# n_colors = 1\n",
        "# for i, cell in enumerate(cells):\n",
        "#     if i == 0:\n",
        "#         continue\n",
        "\n",
        "#     neighbors_colors = [cells_colors[neighbor] for neighbor in cell_neighbors[i] if neighbor in cells_colors]\n",
        "#     # for neighbor in cell_neighbors[i]:\n",
        "\n",
        "#     #     for neighbor_id in neighbors:\n",
        "#     #         neighbor_color = neighbors_colors[neighbor_id]\n",
        "\n",
        "\n",
        "# # cells_set = set(list(range(len(cells))))\n",
        "# # # Create a defaultdict to store the adjacency\n",
        "# # adjacency = defaultdict(set)\n",
        "# # # Iterate through each cell in the graph\n",
        "# # for i, cell in enumerate(cells):\n",
        "# #     nodes = set([c for node in cell for c in node2cell[node]])\n",
        "# #     adjacency[i].update(cells_set.difference(nodes))\n",
        "# # # return adjacency"
      ],
      "metadata": {
        "id": "dojzSejtaMYV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Greedy Coloring via NetworkX\n",
        "\n",
        "Coloring via NetworkX is fast and effective, but doesn't ensure that each color will contain a constant number of elements. Because of this, each color might have a different number of elements, eventually causing GPU under-utilization."
      ],
      "metadata": {
        "id": "MnEG2ck-toRM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import defaultdict\n",
        "\n",
        "@nb.jit(nopython=False)\n",
        "def get_neighbors(cells):\n",
        "    # Create a dict to store the all cells to which a given node belongs to\n",
        "    node2cell = defaultdict(set)\n",
        "    for i, cell in enumerate(cells):\n",
        "        for node in cell:\n",
        "            node2cell[node].add(i)\n",
        "    cell_neighbors = defaultdict(set)\n",
        "    for i, cell in enumerate(cells):\n",
        "        for node in cell:\n",
        "            neighbors = node2cell[node] - {i} # Do not include the cell itself\n",
        "            cell_neighbors[i].update(neighbors)\n",
        "    return cell_neighbors"
      ],
      "metadata": {
        "id": "rFBNNn3EuO1O"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "import networkx as nx\n",
        "\n",
        "grid = generate_grid(lcar=0.5)\n",
        "\n",
        "def color_cells(cells):\n",
        "    cell_neighbors = get_neighbors(cells)\n",
        "    coloring = nx.greedy_color(nx.Graph(cell_neighbors))\n",
        "    colored_cells = np.array(list(coloring.keys()))\n",
        "    colors = np.array(list(coloring.values()))\n",
        "    n_colors = colors.max() + 1\n",
        "    partitions = []\n",
        "    for color in range(n_colors):\n",
        "        partition = colored_cells[colors == color]\n",
        "        # print(f'cells in color n.{color}: {len(partition)}')\n",
        "        partitions.append(partition)\n",
        "    return partitions\n",
        "\n",
        "color_cells(grid.cells)"
      ],
      "metadata": {
        "id": "7vhSBA_xpP6C"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Colored FEM on GPU"
      ],
      "metadata": {
        "id": "YtZ-nBYD6sGS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "K, f, a, weak_form, dh, dofs_glob = generate_fem_problem(lcar=0.04, as_dok=True)\n",
        "print(f'Number of cells: {len(dh.grid.cells)}')\n",
        "print(f'Number of nodes: {len(dh.grid.cells) * dh.grid.get_num_nodes_per_cell()}')\n",
        "print(f'K dimensions: {K.shape} (total: {math.prod(K.shape)})')"
      ],
      "metadata": {
        "id": "gBZSKTy1KG8I",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca8ef637-7b81-4185-ff74-11dc620f6820"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of cells: 13488\n",
            "Number of nodes: 40464\n",
            "K dimensions: (13830, 13830) (total: 191268900)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "@nb.jit(nopython=True)\n",
        "def get_Kf_entries(K, f, dofs, ke, re):\n",
        "    \"\"\"\n",
        "    Populate ke and re entries from K and f based on dofs\n",
        "\n",
        "    dofs: shape: (block_sz, n_dofs_per_cell)\n",
        "    ke: shape: (block_sz, n_dofs_per_cell, n_dofs_per_cell)\n",
        "    re: shape: (block_sz, n_dofs_per_cell)\n",
        "    \"\"\"\n",
        "    color_sz = dofs.shape[0]\n",
        "    for k in range(color_sz):\n",
        "        for i, dof_i in enumerate(dofs[k]):\n",
        "            re[k, i] = f[dof_i]\n",
        "            for j, dof_j in enumerate(dofs[k]):\n",
        "                ke[k, i, j] = K.get((dof_i, dof_j), float32(0))\n",
        "\n",
        "@nb.jit(nopython=True)\n",
        "def set_Kf_entries(ke, re, dofs, K, f):\n",
        "    \"\"\"\n",
        "    Update K and f from ke and re based on dofs\n",
        "\n",
        "    ke: shape: (block_sz, n_dofs_per_cell, n_dofs_per_cell)\n",
        "    re: shape: (block_sz, n_dofs_per_cell)\n",
        "    dofs: shape: (block_sz, n_dofs_per_cell)\n",
        "    \"\"\"\n",
        "    color_sz = dofs.shape[0]\n",
        "    for k in range(color_sz):\n",
        "        for i, dof_i in enumerate(dofs[k]):\n",
        "            f[dof_i] = re[k, i]\n",
        "            for j, dof_j in enumerate(dofs[k]):\n",
        "                K[(dof_i, dof_j)] = ke[k, i, j]\n",
        "\n",
        "@nb.jit(nopython=True)\n",
        "def get_coo_matrix_components(Knumba):\n",
        "    nnz = len(Knumba)\n",
        "    data = np.empty(nnz, dtype=np.float32)\n",
        "    rows = np.empty(nnz, dtype=np.int32)\n",
        "    cols = np.empty(nnz, dtype=np.int32)\n",
        "    for k, (i, j) in enumerate(Knumba.keys()):\n",
        "        data[k] = Knumba[(i, j)]\n",
        "        rows[k] = i\n",
        "        cols[k] = j\n",
        "    return data, rows, cols\n",
        "\n",
        "def colored_k_assembly_gpu(K, f, a, weak_form, dh, return_numba_dict=False):\n",
        "    n_cells = dh.grid.get_num_cells()\n",
        "    n_dims = dh.grid.n_dim\n",
        "    n_dofs_cell = dh.ndofs_per_cell(dh.grid)\n",
        "    n_nodes_cell = dh.grid.nnodes_per_cell()\n",
        "    # Partition/color the cells\n",
        "    cellids_partitions = color_cells(dh.grid.cells)\n",
        "    color_sz = max([len(i) for i in cellids_partitions])\n",
        "    # Specify CUDA kernel dimensions\n",
        "    threadsperblock = 128\n",
        "    blockspergrid = (color_sz + (threadsperblock - 1)) // threadsperblock\n",
        "    # Init local variables for element loop (re-use them across iterations)\n",
        "    dofs = np.empty((color_sz, n_dofs_cell), dtype=np.int32)\n",
        "    xe = np.empty((color_sz, n_nodes_cell, n_dims), dtype=np.float32) \n",
        "    ue = np.empty((color_sz, n_dofs_cell), dtype=np.float32)\n",
        "    ke = np.zeros((color_sz, n_dofs_cell, n_dofs_cell), dtype=np.float32)\n",
        "    re = np.zeros((color_sz, n_dofs_cell), dtype=np.float32)\n",
        "    # Move to device the following data once for all colors\n",
        "    stiffness_d = cuda.to_device(weak_form.material.stiffness)\n",
        "    weights_d = cuda.to_device(weak_form.element.weights)\n",
        "    # The Dict.empty() constructs a typed dictionary required in Numba\n",
        "    Knumba = Dict.empty(\n",
        "        key_type=types.UniTuple(types.int32, 2),\n",
        "        value_type=types.float32,\n",
        "    )\n",
        "    # Loop over colors, fill GPU buffers and finally accumulate\n",
        "    for color, cellids in enumerate(cellids_partitions):\n",
        "        # Setup kernel inputs\n",
        "        dofs.fill(0)\n",
        "        xe.fill(0)\n",
        "        ue.fill(0)\n",
        "        xe = dh.grid.nodes[dh.grid.cells[cellids]]\n",
        "        # NOTE: The methods dh.grid.get_coordinates() and dh.get_cell_dofs() are\n",
        "        # implemented in Numba to handle multi-dimensional indexing\n",
        "        get_dofs(dh.grid.cells[cellids], a, dofs, ue)\n",
        "        xe_d = cuda.to_device(xe)\n",
        "        ue_d = cuda.to_device(ue)\n",
        "        # Setup kernel input-outputs (ke and re are accumulated)\n",
        "        get_Kf_entries(Knumba, f, dofs, ke, re)\n",
        "        re_d = cuda.to_device(re)\n",
        "        ke_d = cuda.to_device(ke)\n",
        "        # Run kernel\n",
        "        elem_routine_kernel[blockspergrid, threadsperblock](weak_form.thickness,\n",
        "            stiffness_d, weights_d, xe_d, ue_d, re_d, ke_d)\n",
        "        # Retrieve data from device\n",
        "        re = re_d.copy_to_host()\n",
        "        ke = ke_d.copy_to_host()\n",
        "        # Update Knumba and f components\n",
        "        set_Kf_entries(ke, re, dofs, Knumba, f)\n",
        "    if return_numba_dict:\n",
        "        return Knumba, f\n",
        "    else:\n",
        "        # Transform Numba matrix into Scipy sparse matrix in COO-format\n",
        "        data, rows, cols = get_coo_matrix_components(Knumba)\n",
        "        K = coo_matrix((data, (rows, cols)), dtype=np.float32).todok()\n",
        "        return K, f\n",
        "\n",
        "K_gpu, f_gpu = colored_k_assembly_gpu(K, f, a, weak_form, dh)\n",
        "print(f'K dimensions: {K_gpu.shape} (total: {math.prod(K_gpu.shape)}, nnz: {K_gpu.nnz})')\n",
        "K_gpu"
      ],
      "metadata": {
        "id": "avy8ZBv_7Vm9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.spy(K_gpu)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "lgbIzH5qelgu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "K_free = K_gpu.tocsc()[:, dofs_glob['free']].tocsr()[dofs_glob['free'], :]\n",
        "K_prescribed = K_gpu.tocsc()[:, dofs_glob['prescribed']].tocsr()[dofs_glob['free'], :]\n",
        "f_glob = -K_prescribed @ a[dofs_glob['prescribed']]\n",
        "scipy.sparse.linalg.minres(K_free, f_glob)"
      ],
      "metadata": {
        "id": "Vi84oSRjDS_g"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Converting Notebook to PDF\n",
        "\n",
        "The following two cells can be ignored for grading, as they just convert this notebook into a PDF file."
      ],
      "metadata": {
        "id": "pQI1nqgo39z7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive', force_remount=True)"
      ],
      "metadata": {
        "id": "ftzlAX5yTugG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "!apt-get update\n",
        "!apt-get install -y texlive-xetex texlive-fonts-recommended texlive-plain-generic\n",
        "!apt-get install -y inkscape\n",
        "!add-apt-repository -y universe\n",
        "!add-apt-repository -y ppa:inkscape.dev/stable\n",
        "!apt-get update -y\n",
        "!apt install -y inkscape"
      ],
      "metadata": {
        "id": "_PXT059d30qG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "import os\n",
        "import re\n",
        "\n",
        "document_name = 'TRA105 GPU-accelerated Computational Methods using Python and CUDA'\n",
        "pdf_dir = os.path.join(os.path.abspath(''), 'drive', 'MyDrive')\n",
        "pdf_dir = os.path.join(pdf_dir, 'Colab Notebooks', 'tra105')\n",
        "pdf_filename = re.escape(os.path.join(pdf_dir, document_name)) + '.ipynb'\n",
        "\n",
        "!jupyter nbconvert --to pdf --TemplateExporter.exclude_input=False $pdf_filename"
      ],
      "metadata": {
        "id": "mVgdQGHAtQJm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "5uxQbSfrVw1V"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}