GNN/message_passing.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "A6ROerFPE-pv"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from scipy.linalg import sqrtm\n",
        "from scipy.special import softmax\n",
        "import networkx as nx\n",
        "from networkx.algorithms.community.modularity_max import greedy_modularity_communities\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import animation\n",
        "%matplotlib inline\n",
        "from IPython.display import HTML"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5u3lquVTE-px"
      },
      "source": [
        "# Message Passing as Matrix Multiplication"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "9lBGkdPEE-pz",
        "outputId": "18f215bf-4d15-445c-8f13-f9956582e33a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1, 0, 0, 0],\n",
              "       [1, 0, 1, 0, 0],\n",
              "       [0, 1, 0, 1, 1],\n",
              "       [0, 0, 1, 0, 0],\n",
              "       [0, 0, 1, 0, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "A = np.array(\n",
        "    [[0, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 0]]\n",
        ")\n",
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "sMZUeUnRE-p0",
        "outputId": "4a971198-659a-4c54-a70a-d4f72f7308e3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2],\n",
              "       [3],\n",
              "       [4],\n",
              "       [5]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "feats = np.arange(A.shape[0]).reshape((-1,1))+1\n",
        "feats"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "jhuv6QCDE-p0",
        "outputId": "c522274c-d04f-4f33-a1cf-2a5c1a88ff9b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2],\n",
              "       [ 4],\n",
              "       [11],\n",
              "       [ 3],\n",
              "       [ 3]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "H = A @ feats\n",
        "H"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PdkZN39uE-p1"
      },
      "source": [
        "## Scale neighborhood sum by neighborhood size (i.e. average values)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "6DRSkGXoE-p2",
        "outputId": "e0d1680f-e29c-44ab-8c50-eddf6205d15f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0., 0., 0.],\n",
              "       [0., 2., 0., 0., 0.],\n",
              "       [0., 0., 3., 0., 0.],\n",
              "       [0., 0., 0., 1., 0.],\n",
              "       [0., 0., 0., 0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "D = np.zeros(A.shape)\n",
        "np.fill_diagonal(D, A.sum(axis=0))\n",
        "D"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "Ae9HfWvLE-p4",
        "outputId": "f865d7f9-743c-40f6-ec8e-038343512de0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.        , 0.        , 0.        , 0.        , 0.        ],\n",
              "       [0.        , 0.5       , 0.        , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.33333333, 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.        , 1.        , 0.        ],\n",
              "       [0.        , 0.        , 0.        , 0.        , 1.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "D_inv = np.linalg.inv(D)\n",
        "D_inv"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "gtuB8Sd9E-p5",
        "outputId": "ac9efeaf-8016-4f15-af79-1be9594da64e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.        , 1.        , 0.        , 0.        , 0.        ],\n",
              "       [0.5       , 0.        , 0.5       , 0.        , 0.        ],\n",
              "       [0.        , 0.33333333, 0.        , 0.33333333, 0.33333333],\n",
              "       [0.        , 0.        , 1.        , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 1.        , 0.        , 0.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "D_inv @ A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "dNEgOKx3E-p6",
        "outputId": "5cafd248-edb1-4b0d-fd9f-94f9b89eeec2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2.        ],\n",
              "       [2.        ],\n",
              "       [3.66666667],\n",
              "       [3.        ],\n",
              "       [3.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "H_avg = D_inv @ A @ feats\n",
        "H_avg"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qEGMrDLTE-p7"
      },
      "source": [
        "## Normalized Adjacency Matrix\n",
        "Ultimately want to define and build:\n",
        "\n",
        "$$ \\hat{A} = \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} $$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iRemhKtBE-p7"
      },
      "source": [
        "First, create $\\tilde{A}$:\n",
        "$$ \\tilde{A} = A + I $$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "moFUVpVIE-p7"
      },
      "outputs": [],
      "source": [
        "g = nx.from_numpy_array(A)\n",
        "A_mod = A + np.eye(g.number_of_nodes())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GomkJMaYE-p8"
      },
      "source": [
        "Then create $ \\tilde{D}^{-\\frac{1}{2}} $, where $D$ is the diagonal degree matrix:\n",
        "\n",
        "$$ (D)_{ij} = \\delta_{i,j} \\sum_k A_{i,k} $$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "mCg5pau2E-p8"
      },
      "outputs": [],
      "source": [
        "# D for A_mod:\n",
        "D_mod = np.zeros_like(A_mod)\n",
        "np.fill_diagonal(D_mod, A_mod.sum(axis=1).flatten())\n",
        "\n",
        "# Inverse square root of D:\n",
        "D_mod_invroot = np.linalg.inv(sqrtm(D_mod))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "4jDr9IDwE-p8",
        "outputId": "4d1b806e-fc6a-4776-a049-5d00a4d6b04c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2., 0., 0., 0., 0.],\n",
              "       [0., 3., 0., 0., 0.],\n",
              "       [0., 0., 4., 0., 0.],\n",
              "       [0., 0., 0., 2., 0.],\n",
              "       [0., 0., 0., 0., 2.]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "D_mod"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "Dgdhng6aE-p8",
        "outputId": "43158e90-4ba3-48f3-d240-440bd5159e10",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.70710678, 0.        , 0.        , 0.        , 0.        ],\n",
              "       [0.        , 0.57735027, 0.        , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.5       , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.        , 0.70710678, 0.        ],\n",
              "       [0.        , 0.        , 0.        , 0.        , 0.70710678]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "D_mod_invroot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oGrJ5PGXE-p9"
      },
      "source": [
        "I.e.: $\\frac{1}{\\sqrt{2}}$, $\\frac{1}{\\sqrt{3}}$, $\\frac{1}{\\sqrt{4}}$, ...etc"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "Y3GeDn7zE-p9"
      },
      "outputs": [],
      "source": [
        "node_labels = {i: i+1 for i in range(g.number_of_nodes())}\n",
        "pos = nx.planar_layout(g)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "dDasOplRE-p9",
        "outputId": "c90f0a1e-b496-48fd-dc31-623dcf3b5a2c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 807
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x1000 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, ax = plt.subplots(figsize=(10,10))\n",
        "nx.draw(\n",
        "    g, pos, with_labels=True,\n",
        "    labels=node_labels,\n",
        "    node_color='#83C167',\n",
        "    ax=ax, edge_color='gray', node_size=1500, font_size=30, font_family='serif'\n",
        ")\n",
        "plt.savefig('simple_graph.png', bbox_inches='tight', transparent=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "f4VF0OAsE-p9",
        "outputId": "f6133ff7-166b-49b0-82c0-9d873d4b5979",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: array([-0.875, -0.375]),\n",
              " 1: array([ 1.   , -0.375]),\n",
              " 2: array([0.375, 0.25 ]),\n",
              " 3: array([-0.5625, -0.0625]),\n",
              " 4: array([0.0625, 0.5625])}"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "pos"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6u7dvRRfE-p9"
      },
      "source": [
        "Create $\\hat{A}$:\n",
        "\n",
        "$$ \\hat{A} = \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} $$\n",
        "\n",
        "$$ (\\hat{A})_{i,j} = \\frac{\\tilde{A}_{i,j}}{\\sqrt{\\tilde{d_i} \\tilde{d_j}}} $$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "v71qXwj7E-p-"
      },
      "outputs": [],
      "source": [
        "A_hat = D_mod_invroot @ A_mod @ D_mod_invroot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I8nMXn9NE-p-"
      },
      "source": [
        "# Water drop"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "5vaK-qkOE-p-"
      },
      "outputs": [],
      "source": [
        "H = np.zeros((g.number_of_nodes(), 1))\n",
        "H[0,0] = 1 # the \"water drop\"\n",
        "iters = 10\n",
        "results = [H.flatten()]\n",
        "for i in range(iters):\n",
        "    H = A_hat @ H\n",
        "    results.append(H.flatten())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "o8iPiUddE-p-",
        "outputId": "54a6768c-f365-49ba-bb26-d47ebb6cfe21",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial signal input: [1. 0. 0. 0. 0.]\n",
            "Final signal output after running 10 steps of message-passing:  [0.18381719 0.20791335 0.20436693 0.13626176 0.13626176]\n"
          ]
        }
      ],
      "source": [
        "print(f\"Initial signal input: {results[0]}\")\n",
        "print(f\"Final signal output after running {iters} steps of message-passing:  {results[-1]}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "2qqYqv-DE-p-",
        "outputId": "b7f9a69a-255f-49c4-a4e1-8b640c14d6c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 837
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x1000 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, ax = plt.subplots(figsize=(10, 10))\n",
        "\n",
        "kwargs = {'cmap': 'hot', 'node_size': 1500, 'edge_color': 'gray',\n",
        "          'vmin': np.array(results).min(), 'vmax': np.array(results).max()*1.1}\n",
        "\n",
        "def update(idx):\n",
        "    ax.clear()\n",
        "    colors = results[idx]\n",
        "    nx.draw(g, pos, node_color=colors, ax=ax, **kwargs)\n",
        "    ax.set_title(f\"Iter={idx}\", fontsize=20)\n",
        "\n",
        "anim = animation.FuncAnimation(fig, update, frames=len(results), interval=1000, repeat=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "xyIena7GE-p-"
      },
      "outputs": [],
      "source": [
        "anim.save(\n",
        "    'water_drop.mp4',\n",
        "    dpi=600, bitrate=-1,\n",
        "    savefig_kwargs={'transparent': True, 'facecolor': 'none'},\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "MQFUkNrxE-p-",
        "outputId": "314f55fa-6219-44e5-de57-d61e864c581b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<video width=\"1000\" height=\"1000\" controls autoplay loop>\n",
              "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAIGZ0eXBNNFYgAAACAE00ViBpc29taXNvMmF2YzEAAAAIZnJlZQAASPttZGF0AAACrQYF//+p\n",
              "3EXpvebZSLeWLNgg2SPu73gyNjQgLSBjb3JlIDE2MyByMzA2MCA1ZGI2YWE2IC0gSC4yNjQvTVBF\n",
              "Ry00IEFWQyBjb2RlYyAtIENvcHlsZWZ0IDIwMDMtMjAyMSAtIGh0dHA6Ly93d3cudmlkZW9sYW4u\n",
              "b3JnL3gyNjQuaHRtbCAtIG9wdGlvbnM6IGNhYmFjPTEgcmVmPTMgZGVibG9jaz0xOjA6MCBhbmFs\n",
              "eXNlPTB4MzoweDExMyBtZT1oZXggc3VibWU9NyBwc3k9MSBwc3lfcmQ9MS4wMDowLjAwIG1peGVk\n",
              "X3JlZj0xIG1lX3JhbmdlPTE2IGNocm9tYV9tZT0xIHRyZWxsaXM9MSA4eDhkY3Q9MSBjcW09MCBk\n",
              "ZWFkem9uZT0yMSwxMSBmYXN0X3Bza2lwPTEgY2hyb21hX3FwX29mZnNldD0tMiB0aHJlYWRzPTMg\n",
              "bG9va2FoZWFkX3RocmVhZHM9MSBzbGljZWRfdGhyZWFkcz0wIG5yPTAgZGVjaW1hdGU9MSBpbnRl\n",
              "cmxhY2VkPTAgYmx1cmF5X2NvbXBhdD0wIGNvbnN0cmFpbmVkX2ludHJhPTAgYmZyYW1lcz0zIGJf\n",
              "cHlyYW1pZD0yIGJfYWRhcHQ9MSBiX2JpYXM9MCBkaXJlY3Q9MSB3ZWlnaHRiPTEgb3Blbl9nb3A9\n",
              "MCB3ZWlnaHRwPTIga2V5aW50PTI1MCBrZXlpbnRfbWluPTEgc2NlbmVjdXQ9NDAgaW50cmFfcmVm\n",
              "cmVzaD0wIHJjX2xvb2thaGVhZD00MCByYz1jcmYgbWJ0cmVlPTEgY3JmPTIzLjAgcWNvbXA9MC42\n",
              "MCBxcG1pbj0wIHFwbWF4PTY5IHFwc3RlcD00IGlwX3JhdGlvPTEuNDAgYXE9MToxLjAwAIAAAB03\n",
              "ZYiEABf//vfUt8yy7VNvtguo96KeJl9DdSUBm5bE7TqAAAADAAADAAADAAAoAvC2XGpYCTWuwAAA\n",
              "AwALqABqAAvIAa7Fv/+FI9h4gCmrhOnrywmZORQb5hksdk4nK18Pp2WlArR37m5LtFSSbr4yi+Ia\n",
              "7bLVO4gT34vZ6soXWM3QalFVLk2L1BpEa2lL4DWe/YkzdmeATDT8tcI0/xPwg+MfZ52XsQV2jArw\n",
              "WSOa34DknSb9QzT5Yc9UJNJuynURYuj5EUVOpNcXgi2+n7nmMwA42MBxAkRGTP6FuFdVhlM04Ivm\n",
              "Xl/+A+WVK9vIWf38l2IBA4KGOYOfKLU3dwd6lsvQgmnUZ6wQh2F2jmNEnBAdKyIfgUOdJV7OGOlZ\n",
              "u3uGqatCCVaHCB+fC2zPJK8gD0MGZ+i6bWl8ZgnROd0zr9QM56v/996Gy3Au4CPasE29jFRDy/0b\n",
              "9YR6Ju+AQA/CoTRF7PgE6LpvpXWjSecxEjiLyO3ydyHB4+hAGghygn7vcTvWMhU4E2NsUZLbOACy\n",
              "Dx2z67QIsn04QStnuWQTolnZEqdw7+LlL9HLxdZ1ErF+lnVvLxa1bmZRb7Koq3U0TwgLV0BopaGY\n",
              "opsFWGosUR9mteQ7jXZNBM1FIaNLoR55UkyYkVIam4ITQx0u07TuND3RL6hKFG04jnmzVd1dFlvf\n",
              "/txVoP1pV6yEhF1cUjnCTBu+M16F2betm9wBLq02q+MbjbKcXtX4HcCW/w5FlxfirHKtimZEsX1w\n",
              "dbgOg1rwWfISaxEw9pHQsVuPOTNsyn58vceXu7b4MYUomdS+RQjCyKjOPkjdQ230w3eF1yHd/obX\n",
              "tKT9NrjK1fFxYcD6a67cCqCQIKyZjlso+Rc4QTteBRDDhFA1HyviGU/wgXnanxjVjWX4OyM1B4Vk\n",
              "IkfEviWANVbtnCQLUAL19Ap4NUM3ZNiNdXq4O3kuT1eAUabjknCH1FaXTGVbMlac/pirMEMcrm8U\n",
              "RiYx2oAf3kNXwrRS6dzuwwQCu/Ewmr6jQ5NktwF5Y7bmd4uDrXQ95iNjezFGFd+3WmlO6nxx2xje\n",
              "+4My9trWi6BYeTVlEgnApZlCI6SQhUWR9mUvddyX2ZhWknlwTCyCl2pyWIBaRdUnykzneiwRkseQ\n",
              "85sG0pGihni9AE4ZvVOW/65En5pC6gj+jDkuDwrrFC27JHABuin/1iffvDNWgwQv/RzqjNr1OIbr\n",
              "3OKK304HwJDASbPUuY2G7qPATAKkKp2XYGuybp1hiFt99NmpTHg7QYC0xaN7TXpI5C3MAmK+xnvF\n",
              "0714aG/7+EyutgQu/c6nxMo1rv/jDjqF4uiKL/PCGSSvQ7/q5LOJpWU7D17Y0Wjbi76IeCf7vhbz\n",
              "dJDyOJGx77k6ufnkpkZtV3L61fznmts2hcwJFckZ7lA84iwA+uFsh4QsLIg4pcsXxwV8LNiy2LB3\n",
              "0Di4MYESR5O2Bdv//51Y75grgb6IZYcJjPZ3JUcEn6ZKsA+HWYnz3MfRrnyD+1udu+I2DNeHnr5z\n",
              "kdqHosoR+6QvYMBl5kcOEA1/xu84LCVL64Gvc2/w3KlCyx9zf5Vc2NiFAnDTz2WycVNtGt6AA7PN\n",
              "CyAX6pCsLukU6A01H+icSc0uOCgxkqJ4AhvT3t8j3Gdywde1USlUx6N4yhjBpJ3rXVuEFbh+thmF\n",
              "cChFkbR4PAdZ8U3biW0kbA+E8E6yHs4k4Q0JI3XjvE6fTHW9ZFq1gfnZoOg6sIcRv0rgHtvbMRyb\n",
              "tUBfYD7cfgU5PnblU7eWY4SI86SfUUgiq8If9U04I4D5PPjs0lkCOqr0saKRcOlw1SOV+pNcA0RY\n",
              "o3B60CQE5DvvPD2LqsKaTdMAYELoIqqzDd29Wyd8Qvcu8jI0g366hrtHEBulXx5uzLuLmD7kvwIY\n",
              "8hcCQkXHZsac7yz7yfoiDfk92UjmbAOnBQuaCl+F2EJ6j9+hHXeA9mgdwulRcN6xidFycVIpWRLd\n",
              "HXJkyZbxxpr5TTTAKmQ0TSAWry5WZ7TS1duuBcUsAAJOlC2YICTymIcO4uusir3wvCDX7tGKotGV\n",
              "Q4lGHkLV6Sa3zRImkPbhGQVDdX5K912hkm5M+80w9TnwAAAvOcytVKLYU0f67t5PuTkYXgaH5CL9\n",
              "1oR6UIUrZg4hBsUaWqC48+SA4sGYCyqUmJbsePMJ4S3xFfE7/dAOvLlQAAOI7ZK3smz+oqyepmnz\n",
              "5ix99dwDDeGfkExb+Wq0JsSiys7jH2UIf7ly98HZmWVIH4gJZ5iJ6rt3NYa09RAAB0AWPNCVjW8Y\n",
              "bZseGVRDExPrFKTsYBma8FyO8sMKRPgzUj0eocavsRlYMtLxx2ep+K+m0vO6yweLPKbjXHTjfpas\n",
              "e1+fwUmgAAgquRtmGayPLwQ/VzQGpNvEQ91sCd7zFhtaqy2d4eH5HTmdzH/e9LcqF1ahumn7rE73\n",
              "lxHNYZLZ3hJfWQyTgyEAAfzdrPKFjwcACGYgKxSsXAYl5Czr23cz18TujN/pzyuWNzyKGS7dLqqe\n",
              "HxeC0sbrOXi+oiQ/ISLG/r+/GQmSBgBoeJtAAAUAHP9uCLKeUVJPCukUn+A8KOIXioOnFfhWmI1k\n",
              "UMESaZM2xiM752W0gWf0bFnZ5Alsi3/c7XPHBZfKa8QAAC69suxGbyNyz/hxzUNG+n5Czvgk4IY7\n",
              "8W1LNmOUVFg6kPZxnA/SwiLu5wGUpWtI8WTze3MhA875mnnHhxoze+w/teti6R5G52mHATyVzD4Q\n",
              "EA/hAloQ+VctqWYb2eGLE/iCH84owULHsqJ4ei4w+8J4JfPbgT5cEO6aro6oi/IVFJIEs80fw6Eo\n",
              "KHf1OhQoRl8RRdcZVPJnn9R0qpxSdWDMSXx62yKOB57N1ujI0jHjDM+FSCFRR1d8Bi+CF+Ww+pXI\n",
              "5+owO5naoqgFKIXQLjN+WWtyC2oq5S7gAASE3BVeQO2r6d3nZPyVmoH5roNrt0VwGerf0TfYqFjB\n",
              "i32hIIlBjeSK2MgD9RKhfPIGzAuxGXBUKcp6Xsvi162QJGBtAwWdJSP5vNxH8Z5hxeihkEG02RUZ\n",
              "66uqBk4zixFbcdC2mW4y8qkOSOiQ6GzdZfmEAAAUlzrVlSi5N3V0FkaeG1qW0+FUawvliZj8mFkM\n",
              "3L3CfQtf1gePg5E6us4NmQMgjJTgOL/xIE9erO6TQCtM9FIfNzrEjIfjghhky4lcBmu1PjzlFGDz\n",
              "rFVGoeiUHrG9BDU8BKzWaAeyUOppxuvsv6dBI8JENMQXra3FPo+7/NoarAAAH2MxaSM9kvTMTgUt\n",
              "dTE84ZJl6A++BmRNQl/VgRzrn2jjmcUWFZlvAZk45mo5UwoHIZ7Zmn1/z8VdAQT4otwreYnDcOCL\n",
              "PasmXb2llMBHv5MdwDqNoC/6yYAQF+mUOWQ57NUzy4wzugcHjOfmRuYt0TtUzC/y7aI0Oxh3JDRQ\n",
              "Ti4k1Y+n2SI/XedsgqVy8JCjsgoR7KNqQu5a9tJULW0+u9oLeKVMX6JgzMZyxHVWX45n2Ox/g+wF\n",
              "PiJ5KmZMzyivvHU752k9MCVMuEIRUrtmYwO+syTTo98dx4eWV7GOdgtWYH4c76PrnjqFpFZi81Ys\n",
              "fpdRUDwPyKX4rgLg8vIjanREpdf14yNhTPHldA68KgV/bxcaKk70BXQJI/OhLmdeP7otJWPpWdRd\n",
              "o+NJ768Bp5btfizYd7rcQSpJPYftS7wam61kXisRQ+tP0mAW08ZErHgTQt/l8oR0cHBMoOAAGYHz\n",
              "SwICGy1CPvIR2wyu1LIpIRhlqSVF7fmkSCwFvXPZmRDdIWOZT8WBSWnrntvXqb0Xo2JJoMucS2hy\n",
              "8YRUWu1ldRRcr5vVmyEuk6BfRnnNxRiBOyMTyXWje4ELr60EQowamNpBUctbNQBrQoB1ikKBzOOK\n",
              "MWwp1z36bQgWlfWCk5sJ2YziBve0eViNRvPIlGoBjoi7vpQWgYDYqaFuDk+5dYfuWmBL/+OkR7ZQ\n",
              "oyysjQ7F4/TqJUm05JcMmMUsbP4Z6yrVjA4hZ+cc8xC3qyHvF11KpZoAACURuv1zcxAkDc1yUsSw\n",
              "reiSQEpSa8Fhc1VbqHm2M7noU0sLhoJb0yW3cp0cdc3prWuYVZcwBrkx17hwZaL9sGS6NE++NStt\n",
              "CvPPWndt24Hs0J9uGnMSYkK3+BDtn0wjiW9Q2Y3g5wqTBq8b1gbRqg/L4ICTGcxIkoySaRNvZGb7\n",
              "MnEBdI4e2yb0lJOF1FeSmO66/BBkC3Ia56yIIa8pbuVBjs/1zmZFgY+8ne22llnhWEfkBrt8KmKI\n",
              "y9gIPk4CRsChxPaLjtZXCwb3rljfvcEWlxiAR0AA1oYo96337aS0olhDEE6yMfNTtPOTaZUD78M4\n",
              "K4ZCyjRMlY9hry8yptvntfa1BacNTbU0MeT1feWSquM8faeJnETcuamQzvUU2lNMEakKSC4JkG/U\n",
              "sMnivhJSTNypfcihLz1InG1J/shczG84otyXQjwjIfNB6e9uBLIZwnwSSMsrW5KSPFXZyD9Wd0zU\n",
              "hznpftg3UB0dtsTnYh/4Mj9MPeNLL7cBNoiHgecXXh4wEKbw1d39bMJcumTLvLXZOp8ZKGiURVj5\n",
              "XVHokwEMW9mIAAXbr5R8hvU96Jc/ykis+AXX6znnfZ1wtcS+qtvD27UqlgKQ3XC+E1vHTXpTh0Yz\n",
              "u1+UxAArfn7ZN3M+Zn0kHsDNkQWJzLgJtVsJvscvEa1c7pmBMOh9QbtaLWuvwX9MpbdO4BuRfNXG\n",
              "N2cbcJRy4yGN+FK5VcfwIgUeLzST8gGMij7FfkSiNd+wNiuPHs2zbpaVC+3ZoPXuBATxSOZ1yBtx\n",
              "64bFGHRRc0lTUXLAJaog+azIg/DIDJmfv2jcsjIZnVeeNFIkPd/7qVKKehYp+UGOZFIsrPI39Lmn\n",
              "UAAG2BbqCZ6og0TaPu0Ly4pjEuxEttTcqTVcMaGV5dA+DZ7woIfBxY/a1jtOjup5VAh8uZdUHd3E\n",
              "cHkk6VgukM4I+W6L6N20wPKu2b9/mYG2MaP1rI90UzSliGNeST3MHvWvCkewefR7d9C9g/EpTabO\n",
              "ddMyfzGmcbdOd1sw3x+t6s5Z4bjp7mkx6fH7K7LC7j6faAXNlFQguxa3oOpz+CAEFm1NUfkWTjwS\n",
              "1Z4/FssuOwby50+qVorkFzzNVZqtHWHvIJXy2gcw7cX5Zr/eNjroeY1UOXq7qHkDrMUAA+rzqKpD\n",
              "gbGqRuZROLrkamNOzyijz5G5iWp6HqXKo52sAoYeu4mazdobtDZGB2Y3QDqzHrJ2ELajWWkUoVXp\n",
              "geNznoJaOWQBkcKPdd1ip7FDPbWwnSFELBAV1Dxmr4dpYzwdhJ/Rk/ntHcf1arZ0doGT+OREC2ff\n",
              "jsMdg9S79x497oU0o/3R9fxfVf+ILppCjW2tEGwyM2YDJtINz9kxzadde9hjKXDdP7vxKeSKJBLW\n",
              "7spbIQqll0mT6dS+BguM5+R0RTgfNuJFZrN/0Zml6aGzX1OPYx//j6/BZOISIAM+C6tL4NyHCZSo\n",
              "CbLknr7QSVM/OyPiEirb/vkz2jXuXPSKCm1hDGP54AfQ8iWazf2kY8c4vYDuVxEgFkU2MUHWG3ZE\n",
              "juoFrW2wB1rWgU3lHCxibF5g5VC9o+R8aAV/4Q/EzOr96NwUWCgDFFmYQHUpLNkqDxodBZT2fQ3e\n",
              "Vz46/kqwacoF4XZyDlEn/yt1xEMrxY/lUZYW2qdpBD46EPYNb+ORC5oiHmRmUzaQYSQqdwsqGQhi\n",
              "rdPk+Vo+zt6lBAayHph6y1Jo67CCKBm86IJbeaqyU7uq2RYY5hwWACzn+bOjV+y+of8kq4cjvcSb\n",
              "+1PtXXhaJ1wxsJmSJIt8Lk9wVhK3i6leWSmdZA3G6PANCRzptgs/aqgq9CQyBM/xhH9ywKQ8Rqe6\n",
              "SjkRIeP7ijjbJpBDTg3bwxmPQG/ESQ4S9Ed3MPXYBXVvka1GAbgb71JZRPbyoLrH/N/c4bFvhF3X\n",
              "IXW5M8NdDJl8eOMGSw7UZeLUfKEyXaXYIRxZ0Z6qBStebGqG/Sqf3rUXox/ztdgpNCx0/r0cUq3G\n",
              "JtqAvHSUKaUf6CwUmg5UIZRAZK3NaFaQ+M01rIAhAFC8pSGulezewscPg2flTNL8T+tDhVDvNNQh\n",
              "Em+1d/UGwJfDn0mDp1GBQ0AR4tzsmcq8ljwnUZma5N4cuzR2sybnGSvm19KmP3ewfujq/tmYDJqf\n",
              "TLosgzsxqd9A04uV/mQtz/n4arhOCmMY9cCZDg7KnK4Ib1Im2n54hYOh0jeV7R8uFl0xWL424jjl\n",
              "NSenG2ka+cIjbiiACr2gZxFIzfOdTXPql5cmbMpwoG8EFIVSeN5b/GvQItqIvelx8ZAls7uKqlUk\n",
              "df3KLakiefn7jmHLoAjplF4QmvxbqF/JCO4oLxVR3wDB50Q9UF4rPOJ6PDAQYD6oWOFfHGGTKyQp\n",
              "KBqKhL/SAnfQJmqhVlKb8NWgGqxuxw/yY/lIBZwvMm219UIrpZwq4M3PjDp3Yt4u6AvmDFD1sJsQ\n",
              "rJJqEqtI+cj1sZIj/G5ICu9Ug556kCC5KxVVePglmwup1L7c8JlwkOBl+XFyPMUYzwua2ugz0DPy\n",
              "wV1n9PiKIR6tT5HZct47T244GDvROIV+aNYgK8k7r6D2AZoOwM/J9ztws0LFcGg1X+yEmrXvAkO9\n",
              "OXCZE47p7r7uDMVv4kGV5R6b5lGfbI3BduNtYZkbRt4Nqmru3mogVLFSIR+s21+OKrNTYSy7Gmb/\n",
              "2O0DsmX6eIpDuz1omdE0QuH3GdfXvRUPHA7eWAAaoNlD3J8dVanFJuqQSjKA3m61TqhgpYBXXDW4\n",
              "bo8zMoTKi1cZdZZQ2CFUZL29pn7mR3oJySAJPRx2Qoxf1KlC37WdSt9oTirgoEwBJAJI2pf1rDT9\n",
              "cD0Dipn5Z/5O2UYbEgPn+nmol0WolQiiT0rvujtmRKxOmF1Yi2XM8dE6WXDZZy1vi/8R8iOGiKw3\n",
              "rGxh1lBfxk/3nvK/ZyErS/bOF5BN3QZ0kj2FEszGcqXrLaCdrrjHbhRzlQ28K0/uWetnKIthNqZX\n",
              "rm6ezKN3kOSNQKPQJgjgMFFNiFCy5qMlnxIiIrm3X3dBo/LbvYVxW9AOvSAPXZJTcCPlFy9Zf3QF\n",
              "uLnCP+Cocz+J4QWut8UHqKPcMSdfYx2mTr5S/SWPR2+QyOO1oAIe3qQEfTobur+qYAF96soZ8Bj7\n",
              "k4+sBdxfhO9CUTrTggcJLJo0NwKK1403HStqk5bZxZqqPWE93LXt9CalvNpXM3c10dwP5f4+FgX3\n",
              "PFFSpKay58/CPrabX8jxA+81avrim/52Yp60imD+oBh0XLn7nc0NI0OORr2L1XgVycOWwdci7jrR\n",
              "UzTyICUDd7jDuZqxo1nqeAKHg5/zkKRgdBNGsAPh96JuNFIzShORv7a82S7qI6CgJAC6bi5bQrQq\n",
              "s4lEYaoR9Inu3OOEfqj2qT921bBryiQioq5jHYI8EhVhlb6mbz9A8ifwsQszGgW1d5v2D0xo8+uG\n",
              "If5gtv3UvPZhC9mli1raEGL52tYjmHRrPyHmlmO5bm/TZJ6RUqxKwFcWR1kZZwBF8BL8VaDYpLbb\n",
              "LA3olDIIN/WY+HS6OPzWTJWdLCe/lkS5rmOG1lEGNOOHHcAMsu3ei/DvbcOi50yyMEl0HIpE9wlv\n",
              "l/Qqd1AE+2tQSDa4r2pd+6L/37TKzoVnZbUkkWr8DSPlwhp7X2PNY/w3l3V4GlgtmN9sW+QWYtye\n",
              "qrSpy3sDw9ezdym9iy4Nr3TCsAIKPq7dt5EbTNeNz58L7DErTM+a5Ikl8tiazzoLGqoI50oiCgBx\n",
              "NokQA3eEGk0LD5yAWdbyVwoHUGMSZ2gymgf99SraPiyXbPXY9InqDRukkIULQ4zUqY/R3tlv71K3\n",
              "wGSoVUAAHIWW7kSQ5Qmp/bIicaN73wg8a7GPToV8ajUs1p/rb8yguRwqXu5UMXMcZMLrPZPPtIAI\n",
              "znrniSlfV/TRTtlhTAACW7NZwUVDSSRj8RYXvjTiRg80fYfsxprUUooYUcTabuLdW4ooYrnhHMKa\n",
              "xqor5PSu8PMcTKeBixYAAGMBXx1ZpiIq9fOpiOWxu0w13X6kc2p7wx5uMAO/rWbF2NTvoWnqeHHP\n",
              "2kagLAOGdHQCqwOGeGDaKH7J+21+foAAcn+qPvYiACmhnbD0nUn6I0PxAVeubtkR0gcTFvdiWuqA\n",
              "mItiF4ekIRSNJE7KNL1RxjTIZClqL80AAMkaCLKy3+vQRtuyvljxMfTatazmpr5fkvUllNHfFmM1\n",
              "k74zrrqlXd4LGB7aOXa2fTC4fLchtC/8/NkQO5y3MJsAAAUiaQt/6gyxG/sh8rxFzbzJAl4kIRUU\n",
              "IDPZ8xENQ5mrDVA2+ExuENTlghxopgC0fHgDpJGVuvQYJn7FAAEGNT5oaGhKft3GNpMRkbgyO/8s\n",
              "kXa8WZcd7CoUazmsCPcaGsPHJSi9NmpJW0SxDVGhOykFo3AJ3J8QmpYA0IY9MkdwAAbHuQt/6g4x\n",
              "D4eZqwZbNqUAX3jLPJsjivrTDJPBE1gMWp1dJ0onRDitq6VoFkRfE5EWdlF82e/f9pEQ7zA/SxEM\n",
              "rCPMq4FBU0//PHr75TOHQVsfqGXrVFEz6qufPM79Kkz2G9RdiK3r1yX/zDc5skEbPZnExXnYhde/\n",
              "zwKigojNVjqeWh4zpnEA5F/l8ti6AJ3v30mx1+7D3tTN1uxexFKU4DPMzNBiNi6YAMX4xbfdWmsh\n",
              "DmVdJjyxPF96MCKYGK6QvRLD5PqIUb7yW419wsGp3Nnb6OCJtyz7eBOEkGfzdYe5zdPVCTc3NaRa\n",
              "nb3iUHV+prqDaTm9zMOKHbEuLo2zzbkTGWEZwrUmAoPkTB01v+elSXT/CBtggtM2jSaPGXthWBHf\n",
              "GHdp8tvK+dGdxUX0E/ZRfbvi92EkXJmgHPv2SPdyp+kc+AEhysXwH2k4/8mruLb7HBTGNDBXqZmd\n",
              "VN4c5FmKmPdROON94/tlnmOx16a4qYNmhXLxVsaPrvQ7Nw6N1KXnIE3vUGjbjVOZYAPEcIbcXSwM\n",
              "ToY/IgOdpXTQP2v1g9TE+NKsPMsNBD3eIjRsOjgOpzzJv0GNGLU3vZ3NXWn03lRZSgr/zipIdIYY\n",
              "anS/2taSjRErWtFbrxP5ipy/2hgJSzBVsLJbuntx8GUzTFPFNoN6lVXsOqz4gG8ijmUXwIDmLvBB\n",
              "l+563X6zSWqPIU5Rei9jOxwNWR+bdJDwyu+5oV2z37/32ljzNMMHKhul99DSk5XWTN3E8/A7T08G\n",
              "nqe13XlUhK03v85jaSyiy4U/k8NE7mD0F9RGLF8ZP2E1VQBHYTHXWn/cCAFrHxZ2BK08N8q+X1b2\n",
              "ZTu7GtTmN9TH/NzOih9JDDv+YCSA0od0ADEwTYgM7owvW23O8qG9UPJq+qLLzfUd1xbtENb4biYn\n",
              "0LAE1FwZrHeKaH0OUeBAAtixo2DT3wO5vpqYt7xipMKi4+MKOpWo9qb6D8dy9a2iKDqJ+4VAJIUm\n",
              "p1/xeDV/eEWqUlQDxyfudFzWzQgCPC8EzUijUOCgJZmS0g+LRuRXP+aarexnKxNc2k9INJxI2ReU\n",
              "l234A+cEZjl/Hgf/YPD8XwSkD2LdzEsAAuwRU47stLJ3l/cCt0f+iEyXVX0KOifV1t+DTCgdI/RU\n",
              "U4ttTOCCThlFrz2klVjisGuHsxdu36OqjvNsrpzEGKxzrQzF6tNUfiUW033+sr3GG5wQwr/XykZl\n",
              "4I7Ev1pGMPS+64wEBqLLMeTLJeltuVHG5jwkh2qLGpVP/cGoDhPqT7xpm+TdahDLkM9eOiQ4XfY8\n",
              "5iV10JhVZ2Zmv+9RK9aNo3bJp/SRCKw+I41MNxe4R4VQJKfqPEEaSfiI3FhfsCKdDEWmtI1OkiQ7\n",
              "tuZatKtnQA3XIwzdgR6NEutpH0Cne+C7XrAAC7wLnYJtQ3RtKlFkU/W5k2GZnRUaapAErP62kkuL\n",
              "Lh5ZLxrKrLQxiVpR4+s6rM7rNGbzbOmNbFCkq5nfbP6aYAIJk1oAAAMAAAMAAAMAAAMAAAMAAAMA\n",
              "AAMAAAMAAAMAABrxAAAOKUGaJGEYD6GVIAQFBf/+2qZYAACYOxSgAIVsQVWlay5C2TFxYbHlv6aU\n",
              "PssA/5qMiLTfTU/AM2QWDzkJeXefP0UVqz4hQL3APU8rnu6t2/G30h+URRkxzihxsNjM3ID1/AhX\n",
              "teyZcdmHSPXutJqxh3OZboZaU5yf8/3dVm9eC1DT3JDW/ccLbYScaaKLxRmB0tqAL7edVqWVCJFe\n",
              "WG5KnMTUF0NrV1uaO4ZKUughm/sCS4qig9ITWJsa8xBXhCU8wiUHkQMaVQkfPQVzveqOaJxEcPar\n",
              "RIPGQurNZyH1gwMa+ebu/zP78d7WPiaK9LKwNSMnEv5GeB4lcqgxTwwYjrd/DDyZLMQ8enQsuv9e\n",
              "FPclblE9Ri8jh1y06n+LpcMIK6rQzwfH5Kx+NplUh83rjVxsxpQ8TKKAZ/su5tjAtOT2YzzFsyP3\n",
              "cLZd2h+bleP8yJYrD7F9xd0P29J9DJ9Ect0Qmm2PoDHXL+956xI5Lo/cIwlGtbYLkUlPB1rWOvJR\n",
              "2dkaexrs6Qk4fQkYvn3APr9GeQZ7nqklR0Cqp0WgRQtPMjYoTvujP1iUdV352uiPEfHZqT2/C/eO\n",
              "S7tGe/QU1SEPn+yCcGm4xVHztS97DnNhcCN7w9X6su5aOOTK9XUXK1o7syYf9U+tHet6bhfayWGl\n",
              "KYb8G+7wMWMe+zXHJntx4p9LH7ExkcJt5KdiMQfSMQuT5kZJduqAnUPvWMAiXhufgTqt70KnNkCS\n",
              "KCm5jbydJMR37/0xtgUsb93/fueuJIj4BBEDdyHs93rMz5dGEfyjSCewkxiP4cA3PzzWhtft7iRi\n",
              "fgC3qRThFU95hh6fpSnjtv2/gLPH1lTU1APhDjtP65pxK0AlBce3Hq3CrX+Go1b3l4fwi5dctGW/\n",
              "gzDDizr65zXv2pIErsqZJTh1uqH9eUDsAQGQHiQZ4xPdLAkY0B/3pkun4eFSJLWWAQrBcrvOUWLL\n",
              "PhSKZ0aSDVNuMngtitiDCeB9bvHwRZ9TAJism3hB/zoZa3MqSA9NIl3PSNbFeYXoZYHpuLGqowfo\n",
              "KRIMNFjH55HgAA7ahe8CI8PNixzuanS/Lvk4D7Yjrq2jpvs9dsHA4PsPbHQyJ24tQjfPu6U7W5O8\n",
              "GcABnN8KQuU5q4VR0ekN4SfEZDFOkzs9i8fTP2WGQO/T7eWinyOA6IVg4riWxK+evOIOHizP874o\n",
              "Pk2j4G7nYuQc0krLZoryOnP15DSAsP61XlPE0oMANev83omAAAkeku+zASTtVCa3ek+ZgAAkcW4s\n",
              "GhLMnykwz1WvNQ+dmdnc3EPRs2okcjc5t4du0HxMp26FoLGGqfQU86Db+mdqLZRgyos2JOtAD9Va\n",
              "zDyUNKaSWa+ICxAhU7ZsavlCOngT8oWPoTjF/Kr5csPnQPLWd8OaTPPRqWsp2y6SEjHRZ5YzH5Nj\n",
              "v3YZ5N3KxRmKYmORRsMyaMMMkY7M35wA8cGzDxAKYyAYud6qfRWjXJ8qNTDbRCpKUf3TJ1/QTqS8\n",
              "8NbU9vLv4FfmSNQ3ADHYdqEyGiu2b9EJwYikD0e9c6GqspVkY3wvh8grF0WtnAG/2wumI0+fqa/p\n",
              "0JEgdwMpQXNiAAJ7xR9AC/L7ngK0xJj8tOx38Pn06LQK9c8XHmECAonrU5mBRvfnwe0lz5TGr9KM\n",
              "4WHEHquseQECfYT1CrNrqOnsmNBwxDbGw6ua49p2WPFGBoo5Z9XyO1SHsWQTjoKhPeJ1huJgH1cW\n",
              "mAeD2wIxEm+8Wa79z6JuCF7SsU0rteXdhZd4nBgG12MLQ10GrbHBBxPIbSV74KqZIRMWgFNrJuef\n",
              "4tknISbAKMj9Hm3/dSPYvftKEeLo8ca3ubVOl5z+AVXg4tpmaZVMjoEnR7Mzhf4Wuo0YE8MI71+1\n",
              "jLpuh4zhLX8vU+Dy3sG7hi/NxgPYUUo72Bl6A6F+u34pNdYQcqCPYtQycRay1aZ1KoxsnYbi9oyd\n",
              "PJadEA97vcPPwe3G27bskjk3OWrQ3DLJp6fwyPa3NnzACA40cBi3TUDkqtHqEbRoNj6DsVJOUp2n\n",
              "FKHkycAbeKbvvcMVWrbMfXB0CqVdRuLtGA8by0vhQnYbDDOiHv8FoIRnS05gQQxLPvOIhrSVyBQB\n",
              "aNHuIQgp18iXDXSrCzB0TR2/ApFPIlyfcjGtmAAJmM8mzB4oVqPCN5K0SsUj4zrDO0Q5O+k6Zfik\n",
              "SFikH1Cix2T2cBo/Xu7yCgyOOjQlzNG0ulzoWXq/EB0BqlDHSmbCx2Q4x6c/NuVrl4yBgHLE4nFM\n",
              "OrnPHXXcHDp8wOdwfXufWzF7lEvaMfXfi2prU4d9eujwVlcVDaunqrXuAcVGcaLd5YT9IzDSlcP4\n",
              "ycCV6FqC0HCSSk93F/IlLw16iky9J5hEgwD5T7LEQkk0BwFgY93ggquoO8lS2/CQHZiMuEqT8cl5\n",
              "7HXJyPEXHqml449mndipu7/ITPzp7woWOG1+MiXL4qZtms2hHUgyER0chPVsuTEcnFzyOznHn/EF\n",
              "+Ww6DPCQbOXSijCE+o+mOuBLGFW/cDGgFM83yejLXOzkaPnD8enFMiZ0NZXZ1hgttSuR7jeYhkJe\n",
              "u51NM+mVJ6xJail1HbQ0KE0v3hlXX13MHQ3NpDncacLvsCta46yHyOJXmT8kXyBibwTxbFi4j8Tb\n",
              "2Lgg5Lp3iT2ZNG+IyLjtp+QBQEiJLq8cDn5VbcIgb8Ob73uJ6/Fu58W921bp6hzdrlUNZfiZsiX5\n",
              "mY2VkCE/7jIZKYU1NJpSpACRsioIBNlh6l43Vf8hdcz/vatLM7grsNIwlpWLN1cm5L+/U5qfZ8Co\n",
              "Y+p5Id7VzlBepOLeVw1Ktq4ANNBzRwyB7rbb3H8jmQTPNxjpW3vTdI/LvT2uIUldukEvRHD6oB8C\n",
              "uxb6ZlHNhJMI+uh5LyQYzuljO4EkaSROkc8mxEQiRv7/BzBEPGknAThg5JWWPUI8iqtJo30Zagk9\n",
              "waQ7C1iRJKVp+CSuRYEDgQWsVqMKcalSH+o5rfkuigu/Ci1TNV0Dz/6jnVIzi9yYXxbXFs18RFR9\n",
              "0pwW3zj8ebaLT/IN77jjl82+BgKy2Crwfe/vAGysaqgpRYsEJIIMO26VKo1qp0pz/VQxbnoAAwbV\n",
              "mkVIFiJe1Rk/Un3nkhSPvrELzpl5qh0Jr5lOAFhjOc7qtyRn1lpv46wxLHGPG6zhK8Pqb9qjJjEz\n",
              "YVyKIsHC2aStArtV4bq/MlmlVUgAAESx7P9smWGpqN1V2a//7NQB6a//jcMf1ln0DR3YrwNgwWl4\n",
              "5/cqAGMTcK5+xNhYTb+cu1asumO765FqHSJ+zZDX/PFPknsUXBJ8HngejYsUbs4mStP28c6wRC8c\n",
              "V66Jpg3msCybV7cDkl5s/JRh1oZ7Us3qVJGBHZkKZiufyRoO/p3GZ2A6G/mBp4DepH+gwHD8SUdq\n",
              "5e4iQwDaL/EoJwJ0IKvwOKlz7AF+wRLjVPt6z49fZIaqkmqhYxdpHRscvvg67V7Ur1tKS6v10m21\n",
              "ku8e//8dXNT8Qwfx5BIn1newdtz/+ycoUkrUIw9SbELvjAvnsUzwfimhNGmFKfzQpj1RtTtDdU/c\n",
              "x3R3phyn9zLhGQSVtRmlg5Uz+DeFzyPJEtrtzbBNm31kt9h5ymbtHA79HjqEKQq6ACpuiqdMhjVX\n",
              "AU7DllnftUpDmCFRO8n60WWUtF75dOnOZh+4lth8xgYmMI9/CtYHzqtba6+CU9zl/sROqdyx/FDf\n",
              "TVULT7m1Brvmsnpyc5TbYBB2xUZQCl9xDeY3N5on5CBL/BaJmgb/qQvVMovuPgIrI1sg2dVZflb2\n",
              "2wQESPkT8bpG+i8PdP5QZFA5k+MRIZR68ysCLhXsOLwIMoryYv7Kwdmzs1TTc037oOZSdc821mnn\n",
              "Xq+Hp5iJwxPuqti3+xQzMBTk/gAfh8Why5XhXDW51IeLh8gSNJ5Yoi1JM3m65fkbEVxRNKCWJFpH\n",
              "VLlbW5RIs/5bOXSapwIbT+DUEO3aHi9zQqDgO5/0HJms+803MeHtrzpC3ItauUiNN59HgggDxnCv\n",
              "OXvfJwgRp/FN9t/rM4USFP4g+4M9VW8otIDG8V6+08VEVr7OH0dWa3Z3493459vScXssxvrj1sOl\n",
              "Ci3RlVXToQ2n4pWGcRgNTpmqPWOtcwxiCz2z8sqhY0yEitqa0ucwx+xcEShARNcCsf86W312fE1x\n",
              "WUPMT7bVMsFtrGD4EVBDlruK3IIQn4cTwVvPNS8vqnW5umSdeqD9kxta7qVGrJBPJODXTIjePwDT\n",
              "/fFmPgJ9iHeUWbCTlxvB3DRJ6u3Zbr5QSDZO1nqi1Km0xgrZG4VF8V84biKDFoMGTH3BPMdfZvl5\n",
              "O+PPtpElaBdoCwVQLbrxgq/NNJnWLl+98CAJ84WdPz1lEm+4mKTw0Hh7+ObIgN4q7SBniLuRuVxn\n",
              "MHGdKiy6cpVL8DUUpvRKO7/R/EJb5pDox2OEm65lX/rIvzXfG69MD8Oqo4w2PPCZS/ZKPQpbpxde\n",
              "pbB5cUiCMXw6cVmmUX5VX9+6OKEOZUwNbLOhWLjRVPTq3keOPYXGMxeTmf7kRg8BrBSyJIYhrwfs\n",
              "TGUVbt+eIuYy2G9jtuophZQ3paDGoEN5HIJBMJN3KsD8+eKX24BSIUY+etoJTk1CNC4BGyYOxl1s\n",
              "pSyoec9F7HsyT74wBa7HwRJyd9DKPVCVNyR/5IRk9qLO/kEK1BxNVm8VQL+cUJiJN9+OLIxJJiRE\n",
              "iKp7ftVZKP7ppeUCZG9jlzkTT9oXXm+4lh1wOX9dwj9JO/0iw2eXwg+3brMVoKzawmBOomnKObsu\n",
              "5OoEsQ6/MO5CKGbrl76jvQ6vqv3gH4dInNjHPp2Be7aQS1K09W0LaHfbN0R3TNAAAoYAAASeQZ5C\n",
              "eILfAAADAEEWmd45LHXah5QABu5/VSi0D3Jpwpde1KdCkuo7mjsF/FDpO457jDVmcCj042Toa0zr\n",
              "SMnjBC/SGywKJ+fYNSkkTxKfBLS6WHgkChO322PD9bTa8T88ErAOh5QSUzV9wi5PYO9m09Wba4bo\n",
              "R2+oXfygtxF+ghbZftydtSzwwbs1J9mhaq290RkQHbpQjcQZ9PrNAP0DLfbFcAS+NPZ+ZCwgh2n0\n",
              "4ALgocKeXpcoWdjUTsov/RYVey0pbarUCh5iJtR2S8hX8d3qsymwtriH+iMHyQ62RMoXKkAKE/Pm\n",
              "UCKbx3xMM244i77RdP5+Z4o9G+gkpI6w4ZUtyouMUxVOn8MEFwL/jgEZqkLq+NSmwacsCGkm0YhX\n",
              "7h6DfVDhgJHdOgBBeODBepb21RsegHgl3kPsuV9/kCGiKcxt6TyyIrxhRur5DLgu4kD0nXB3js0u\n",
              "OzLOOXlMrbNYgi2LHvfeuu9hsPVm9EMUfGbSgouP55z6OcEUvO2mSMvB9DeG73D2FiQFR4WBhVBN\n",
              "x64eOULAexvpseMVuZyhyc+eRzPFaFHHiN35syuTTlsieU8rgqjKNnBg79M7o5v3kePztDPQIVa5\n",
              "jWyArEpwiXFe4i0zTOHf3fIyg1PkYa8owTV9P7txPnZDlz+Jh9KRLYb5fQczv9vhHKhpdPOVvpSh\n",
              "7lGPDZGuRkK9KzXKojTwz/f8Yv/LitPnHm821sCgEL0mvZM35mdPRS7F6VII9/VXBxWuRUx0+lSn\n",
              "SoVCMKOM9K2vSezvHKAK54qeSUjny1aOk7IGCAEftWQt/JCzZSwmOU6yQOzID5jrBSCHz3sAFmju\n",
              "U96qrfF54qfE3ViVJ0ymf+zQedsrfX+pP4sEzJkdsimpJsDT51j4osxZlpbwbqNRdejSLtdsebI1\n",
              "8TgyHujGor2blxtrsaNDMwXDh5jwtK98R++IIVpzXXXav1081XWSRx/w9B9QyqLt2ECz7mm1Nyl6\n",
              "nfwYJGqJfWaRzNrERb1tHL46i5AIe+BI9sXAi7QGxLmFwuCbm8iwVl+fSMwWlfs5kop5oalPbAO5\n",
              "QuvYV+vuj3RT6slhDFLw4fEWLTrCbLOxQFSoA/VUqHQwAAADAACZgk95IgSh4/it41o+T0UdJfTE\n",
              "TRpMDR4K4MZOtj8XP0TBBN5K6qY5GbrSEhLkUZmrwn8PjuzBfAilB3TdFzstIP/CcB1/txDnfdFV\n",
              "RUKqEfX7oVz4VPXCvC98bBDFXbrI5dyPZGn90Z5+nozLGy9F2T4t1Kf7yWxl6vnHgIeNLypm9mM2\n",
              "UyG0qGRj1UetRFwpdVJ/pjslLKiDXPtUiXRwTT+MEQREQcMbefpl9pcLl/fNqlUCR3n9gUo70cmz\n",
              "5mEIUQppcGNmWgjIAZN+J6gkWlW8hc86JQD96KFk/F4RX6DoXigGVTfj0oZsXV1W4L6N+Vf5yln8\n",
              "w73YHHZKw8PwgC/E1NDy21nzeYFKXEi86Wj2VhgYX6W6mqFDp45Q97AlyBCfSgo7zFOMySaaGI07\n",
              "mSb/bXAD2gF9Fn7n3Ej6vNg4ST+70iCDH30qfM1t+cMDLgNUAAFpAAAEHQGeYXRBXwAAAwBcu9uy\n",
              "jaAEqyypdGGRcrsyd/i2cj4dAJSU9dBluQ6drZmkyohMYoy+GUs0Tw2tfRZ93hyARgwm0AMLk7v2\n",
              "H5xY3CW/hrYHbeqf94abTS/Xm1TKSb0in+882YXVjwyra8jOPfLsa5/1HiDAD6iecZLxKmx/1tQw\n",
              "AANxrySNjfKNFSwMrBYm/pd8MxCg0GsEBK0YIIAiIC+D0lYqlcF4nYhNnqAAAJCI2I/sh1sS0Cl6\n",
              "HUHkfC9roXZX4s8cALmSS6S86Fcm8RUkK0otsGsBnvTCtAmfHGaNwuUSC6kmeU08sxwYjsKOQv7o\n",
              "AaToVViXLfANTX/xP3hOEApiwOTsMl+uK14JVqLPQr/XuyFxDbGJwnjlD6X1blMXkoXvFUyTAHQ0\n",
              "iGkeNiEvANjec7+kc+23pjQWVANclkPA2p3iYicmYlihpMbheYoKnOUHKkyXDSrhxDGnz/JvH4kG\n",
              "88imUgSOtbIX6LQrWLAE48FwqNVlTgtPEIT3hkytd9FA83+V8rHNEDlIIR6cScp0Bqt0pj6BmwmM\n",
              "G7JlDbNfEwmilKGP1OO2zTVk6q7U7HK2Zg+OpkRYJ+ApVmlzqax18WpXwQpSWZo+nO4UAqxM3Gw4\n",
              "YX4oZyu58HGXw+rS5aMy1IdPKgyRRxhAC5Ec1enc2bxzRsXzN3lMmqZeGvbSE7pmQC5PAmXu57iP\n",
              "WmiuKhrCOe2UsGgPy9XG5U/7cMjZAQ5MpvYDzwrOV8Qbbd0epaPQtWmjjTESAF2ob72zELNoK1iu\n",
              "4Fb9VrGXMWtn31rBCzf20r3iKnW5g21DJhH9T9yqkprv9O+oEK64QkPjwf4CXIrsljRPm9axXEu0\n",
              "2r4Beo8IgATr7qDVlLiTmEOljPqCtdNN0bKF6QAFLUt3s6NEQ3JLO3Tvb4L5SAWwX0hWgtpNJsKZ\n",
              "FRMMgChfW7TdiuO7hmgL5eVbWzZIYyDnr2gYY0pueaPVOSj1bQlyNCMM/eiNvbTYkE+AWkUUJMOR\n",
              "ID8cAZFRV7IMDvcZBAo56NlNcIyrRFqi2+MicKqEbgff6qecFDkKTqEo5icNQTH5pb+SQ0+mF42I\n",
              "qBu5LinbHpNadFB9tIf62mI7u/IsPs3N8KgdetSGFHBXon7cJO0Bp4UcyVfOF+9RUv0RDzhHnvtw\n",
              "INdVrzMEmnka0WcjikBi3aHP7piWmdRPiCNG9i3qUPiz4jMEEFKpj3/JUptsavpSriQANK55WSjY\n",
              "nHIHxKz7xPc96wyPK4Bh1sr4I1OjorFUIvShd7PPqBrtBhergQMdVg0kHLqAHurfPrCtGZ9B20MP\n",
              "TN9rx4r+0hZNB3Rmf02N5RSP0NUErX+2lGhJp1f8NRsr1qmnpzPvqh5DyCt4jmyfsSEYabIXgzGy\n",
              "OecWAua5CrrSAAAf4AAAAbkBnmNqQV8AAAMAZq2jFmiX4PADcCUObwnPiDQ8tzNwkUS0+fB1bJUR\n",
              "XyP4EjfONtBcLvPbaXWI1/3OINpPz4j+whDR+vVKfFcXR6+xtAuUoqfgAc+PsZDeOsa57I9+1Db+\n",
              "Xn2MenBUttkx07gGPxaYeU7INOS5RrpYz+7fJlxvdjByxsIDZylRgB0pH0W8BC3AychGR07GH/Qv\n",
              "fy/FGIILnZeX+xaMVkwASAV2rD5p5LBhvqZxufwh3SjojVdHOYvLOBOG07uO6zhIf37ZRSMxRoi5\n",
              "IL1Bsye7kDYC6GrchpG+sdK+mv5dtr+1PTfxC/+et29Ob0cu0oI/4MFzIaReCiEEwiTILCEycFkf\n",
              "txVxs8PJRUGVbGrRKcy6Jc9vTiNgzcEQTNETn4GK6o+ePfa4ll2ZtJFSanoDq5sqAF9oR4iDbrev\n",
              "IV7kb3JD1VFdKHvbqfY7MKXHQ0MYG71VOS/qtjDaZ5WjIPvwa+4qxOubCnNH3BSSqicDhimfkaZn\n",
              "ZhYkPv/khK2DigiEWt8v8guC2j+cUfh3/VehLN/aGttuRRgJ1YsxfOjKSPHwOwNiBb+gdqx3iAAA\n",
              "Z8EAAAdSQZpoSahBaJlMCC///tqmWAAAjP8thhkEVYAcOfnlPrN++718YlVzC8xg2c0R76n0imq3\n",
              "kl3wPbiC8JTNWfAlSbuo38bI+GFOkDtPPnC92HGzHGzSnAklm4Bu2P1Ekm3xoHQV0I7HWwe0g+HC\n",
              "nfLEYiZ0Qr0WB3FAPqOa0ezNSmRNMyzCIFZ3oCNOF0ojxcGZv0Pvzsx+HJssYpzXJ2YMXAPgJlt8\n",
              "4yz59CnY0wqBmpLaf7nMahe+yPpJySf4baFgctZ5eTbU5oMcl5lbCoO6KsQwlZo5uCcvD5GzQAVK\n",
              "Jam0yUPBBxYhrjykrRc/aUd9Hdp0rX46Uv5/hGiTPA/f3OCnEYqkppzN95RjfdKa/9QglcqEy5Nn\n",
              "LyNieKJbG3180SewzhfDr5G6vDicw5XNDKTKr/nxDm1nJ1ToQ4lwGPoe5XF+uO3fBODifdAIGhjh\n",
              "0Iki3JVU/Kf4heiOFM7ye0kOETzMq1C4QdNrsEpcJDyVPdBjsBh/5jdwpsgs0REPSOULeC1GE8f+\n",
              "sAbaFuxEA1F4RPm1y3wzICHBSsi8v8dE2ijZ+XZ5icmVanY79Jlc7VJTCaefLGR3dGK96j11x7HC\n",
              "rFUePUsHPbMhqNWBYb9W/PIyoDje/s8uyv1d+aJ4kny9QpB7bYjta0uz6O4oUeEMDyKqm49RISZk\n",
              "esLykZIiZv60o4/AiZaaYUjVMVYFZPn2OpUWFKVcqVdV4XzZSxThMWcH0PQ+bQ7/fJC5ToqXZ/ij\n",
              "wtPXyPuHCibWhHPkI1iiCmDGwCjSMiUBlnEzoBIABeMDdq4tC7886RMbC+GjJSU7oPodC1pBte7d\n",
              "SqlABT/fKqPURaxW2ZI99YfQ3Y3pxrjge4sO/omgdK2Ww6aq38ttCcA7Dhav37m/FK8boZu+D003\n",
              "jVxxrxi8DmwRIkSsgvLnzLfHWs0tXmkWyvkU/2lYw1cZ5uxOc2nBE88hbeCRAsudup8+j6lQYVLM\n",
              "zKESEVXX3+uKMXmGM2Vc+BHEkbVkQ0dQmfGChp7Qy85vbZbSBAMAfCggZuojFP4rjMmU5UbOLz5+\n",
              "IeNWiENWwt7E+9WOaKslA8PU8URB2o+woatf570ocJb7QAA4N4BspUBCr+zqDzqsdLe+dCZxuinE\n",
              "xmUhpNcnJZGFhgkprGqH1P/qjCS1lEn9qVI4ExuTNlq3CLVxzTDrWOrZjsilQzqLKSnTHkbNJiiW\n",
              "8KnzvuvSrEBgSBn8Lwsf5G8IH/9+VILB2aMP/Mo0exYoF8w4j+U9UMy6ETC/UU2ovlBIWYDYXn6R\n",
              "92Stm70FVba3GyQGSEhaxBYkh+0FBjYOihWHnHJYUhlG+qPNv5tyCoLiCAEQx1tbi2ZiHmX6Wvyf\n",
              "CaarwxVl7jA+lVMg+md3qu/vcCVJJrB5UEvZ4Kh2vyxZV3cUwtZ6RoXSwVd8BsYqLvp6G9YcPtZ5\n",
              "KmkFQQ7hRAxuSgzbKvMmDapmlupzk2RM8EQOqQ6aeigAANr6/83oWMDpCBEwcT46mgasJ5/hglV5\n",
              "qjNOFi4TLKsUmh3f7HSwBdKeT8TJHg7mz/vEGe6cpalvgPkCvkCDJQJe75pUwnChLRdbcG5hbc6o\n",
              "MSvJ7dIcdOTIPZDzYhe8x+Q4q1lRK3x49FHpRRT37gr9cfTMKSGWXB1cfKCE8QeTfqn3oKN5U/mI\n",
              "GZ1OQDN2FEbi7EYPcS9hwzfQgWCDo2pDrAACwxjF/zP3lROMOCtDD24WHz+s0XCZ5T/90aHsEuQ6\n",
              "O3zF/ZH8iyDdkQDsImRr2bhVNuDC25s5gl6JwfWhQQl+/cMlYP7xGD9ZdJe+b7JuyYYIDqp2mtEJ\n",
              "cGbGYVDIzbMxo7z0nMiHjEiDO/pgAMZZUcj2iE16Sf8ZZRIYL+fVkQ3d+aOLcuGjV59MFdGPiJBB\n",
              "fNYN1tuq2IbzkgSBn0XMU1RZzdoomh5k4nGbA4ID0BDg4PvJg4XQvVJNN8AuytDCsnz6ZbedPBGj\n",
              "XL36kLdESMh1Qf+Nea6Gr8dDbNsDVYxUvLe+axb8nkxguchdt1hjztk2jDQeEb8pefiba3PgHylx\n",
              "80C/obj1WadH/3xGwDvC+EfsiJsC6TQYRmGeRCqKlXkX/TVSZ6la9h90NYtlA9rM8XRRMbMgcYkY\n",
              "1Si/B704WNOdD9pMDwrhWi9MeslQA8sCEjileVqrOnLDxuhOzzcD83RFueWqHUSBGWzL2NBZY0sX\n",
              "VHQpTHc12hBAgNcwdSdKuGn1FnenEzSw0ZmlorS2tM6pSggjyG6jpv2RqR7g8bW+cnsmNAen9VFY\n",
              "0VZbXWq4lDi0c0UN8K8kJpyEfPdJZ7grEc53VzqHd7kLOcG6D5PBx2Ta5hluR4wlW+aK95MUVibL\n",
              "PYGS/JyITtVCaulrRSh9oNOqNmKT6XWSBwgzqiCebcY/3l/M3U6/RJo0NhbYeHsz8FMmKn0uVaWj\n",
              "Ye284QDija+eFJpyG3TVQSzIJ30/LTE5+MNyUZ9JsPMVFFJV6kkoYE+fQTcFDHHVCuzngwAAEvEA\n",
              "AAHGQZ6GRREsFv8AAAMAQRYSU/RCSTXIKJJAQAiWfJEewzq698ir3cxIWr46lRht3UNIUlxHnNqQ\n",
              "X4b0fdflmQwWAqvRD54p8JhDPeOizhSJCuFKp4YL07ihWbVM/fSZmSyASFcq9DovwHa2R7Jq5zGw\n",
              "rD1x8HPoN0/Dycp8xMig6kCRmRFZkBl0kbdgRP7/twh2w49olsKALRMQJm6rNK7VyHnqfpLfmRVL\n",
              "n+pUAPDp+4gz+hp5IV5PLcr3dyVGjzywcabY8dR5wj8ZGIgi0+5+758q0BDL7RZHfojB8kNp4L9p\n",
              "o0Z548d/M+kxmHeYGNytnThQo9QoUbCvb52gctUAwKUoBoMmJ+Kbf6517qAScXTg7lGBD/XdbQxw\n",
              "R8g0u1O11TGnIuw/hloVJuPFAD5JabQZICAR/L+6oNJxaEDi+/IsF5JTcwByDC3J0/Vl5GlfVjgT\n",
              "DmQIbRKhVqQxhLAUcEPDrymQj96Qq4ncQMl2RCMxEjmw0CRrsSYHZXoCtaHvRywiPEqzIXn+18Ip\n",
              "ELAerg1QeOb+5RzLSBsI6aosoScCO8lffT6UBH8eLIjXA+ejk+8gnGnXNRo9fQ18aN15GC9gAADU\n",
              "gQAAAbIBnqV0QV8AAAMAZqpcTPH2oUACc19TylcmAbY3fS9rw6Z83ozpzsErq0MOpJMGxTXHquno\n",
              "PDk6ixpESq5xq/53u3sTAdi+amnpjvB0hlS0ccHFWHDHWorXbFC3NYhsaFjLimGqpcIU0Eyzmale\n",
              "5bssxy1OX36L4kfGopD0TpG+qIUuQxZkYEIG0E8XPpc3HUY+5ES7+/knjhV3hYrKuZpdD/JdVJYR\n",
              "+BBg36CG3+pmzJrowK5k2bqQt0Lhn+wzJMEMEZq7snPA9MdupqvmnFW6CJX0U3GdEJSG/jM9dtQQ\n",
              "e5ScWACqJ415C/BoTOIDerIdv+mv5dtwR1qL8g4+xQBkP6bMU3qt3vtIIyXzncDA0WDF5Cvu8CAE\n",
              "8CCeNVdzS4XfoU5FmgPlt1WX1rZYfTAa7kK5j2kwmAl8eACfNkS5zeWgyXSZFfXfIYwEpEEiukg/\n",
              "njUbf3tx/scUOhbMPqFUsDmvt9w87+oP48nRqVCbiaBr3kMbOZJU2xM+IjGcoKEb+XsfPMVhiTwG\n",
              "biNqImSzTxaayJ4egejQ2ez6Y19JwWOrHfjIMa5wrt57bL7AgAAH+QAAAXQBnqdqQV8AAAMAZq2j\n",
              "ESPSkAC5ZIvLUHnkXaRQftsjX6PT60aT9lmB0x56pVFlT06lIPJtelnblrXc3TwHD6ZOYT8hrByD\n",
              "OCAvAfkfo6pBJUt44gJGklDlYTaH55Rp4MV7pJcN94BBcISMq5SIghxH/TpWi8Y3qvHE+PFzPfNJ\n",
              "wtU7QMA1WGgwsHfhM2xcQHlA7uuUSy9HyEt2HSYWwli1u17D0tNwMnHvmrNASzC0g/7KlrPuut9W\n",
              "c36FXrKvZirbR7Xei+Z6hVqwS8YJVaDtWvCYamy/Ein9PUgjRSR4kO5EpbBS1ZH6H69FOUQeIBwx\n",
              "VtXv15kGtMdIf4tP5lD6V6r9a4U/PR8dpwtEYYPGtjhquMd791g1w4c7VDfm/aAMMvPJU7vT+lG8\n",
              "OnTFjXpSzC/Ft2WyhKFLwc1whcEx9yVx2v0YspcE/QLJcFP4+gEbLfdF4QC9lo+9EB3midnZH81Z\n",
              "q/c5eFWk58H90MdivIAACygAAAKHQZqqSahBbJlMFEwV//7WpVAAAJw4n+CU+Tu/Pw6dQ/+kW1Jq\n",
              "oAQiw/R6ww+ADIaqblGFynVTN9jOm41YwgjVPswh+W7iJjLnmXR9BnQljWw/bxnmXWf6Ub4Mj3Vw\n",
              "C1RUJcMHBRV7KlpfWYQsZb4vVFfPw5wA5sE7lB9MojQD1C5FcIdtkeMypo4koNxKH3o1Qnr81st/\n",
              "DRll/h2lYbp5FcZvBDfU2DtFNkJuof0YlTbiZ/c0QDkrOJ4IGnhYOJci0qSh/ws+8aCZfYiNHEnn\n",
              "cqNxLwWjoGPMsUViORx0RaHMRs7sj1HkRs8AbTuObi9WtuVbuEPwkCajRC8jiGBtLmZf9q3k326w\n",
              "PlU6YCRrkh0TPd4m3jyr2ogLLXtSc/QkxtnuvkfslXixW6ZYfu0ww1ndWnUfA97gH0RMS8cN9W4F\n",
              "lXE9sW7YCbqhZ5/eSq/XAxSC7ODMopbzK+WnjP0Qc+/JMHN9dzI/TpA1JrwWQKzZBvYvc/MJGRKy\n",
              "nnmsKHa4GyGZQngAHJvc4IgJt/lNdCQGD7631VJT9g/46KWTAaIULNM7gsZDyjskdu4E/AAjvNrR\n",
              "dQr6Uq9sl8jJ1A5//FL7jChJjvfAF4nGvGA3Hjp2D1pQm0Jc20V0aq4JQ7urzyPkepC09AkHZAAJ\n",
              "U4e/ut2x04EG4Hl+3mduJ4no1ergXM9OZKxXWDqKJy6u9rmu1G68uJiCgpYrKx3XuFz8o5VCGmEq\n",
              "XS0GWMygv6PnRWnBbNZukkzHxXO+q0QRREZy7xFowO7Psvh3cSAeoSchfYEmRikxlxLEhIlmFPiQ\n",
              "hpktVUoWKndrQrX0pt1P1tgxOZPOsn117eDuhgxyjVqECMKL+AAA6YAAAAF9AZ7JakFfAAADAGkt\n",
              "oqM5CQ0KYzQAlppGZasvGct5wEh0X0BYN7YjqKR3zA89wVOsENHQmwYZkXpNYJBIiih8niw5pSYQ\n",
              "WHu7MqVWsTmN8+O3tRT+J5v8i1DrPAx7anQ7F4jN2AtQgZWBi2excOMi+5AD/LVZBWJ7HprgKVeA\n",
              "AOapehZCKf4PTBceiGsdd3W65H1Mj0nb6ngfpk9ff8QPLIGOKqf/E2Obwz0jW6Skp/i/PXUf++8/\n",
              "fdkn2R2/ZvOYD/vM0KcxhfCIwlsDJ3D+ttR7WB2a5trP/3gYccPT7G58g2KZqJvhfINHLr75dTDj\n",
              "oL2v5Kf8vEyXrEXihWlulG4i7a0iCpnINPYJpwHtiwt86+jTsfKpDF/k9A8SrFSZ+PU3ZuFl36mI\n",
              "YYSoILc3lDvP54G/52OrXkbAZFUq6jZUvR6rcjHH6t9rI9W9dEazGEVd0Dt09AW1nOizsRh7jPL/\n",
              "Um/rsX5oqHWVGfnqJQ/UU3UNlXaBP2gAACvhAAADuG1vb3YAAABsbXZoZAAAAAAAAAAAAAAAAAAA\n",
              "A+gAACr4AAEAAAEAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAQAAA\n",
              "AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAALidHJhawAAAFx0a2hkAAAAAwAAAAAAAAAA\n",
              "AAAAAQAAAAAAACr4AAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAA\n",
              "AAAAQAAAAAPoAAAD6AAAAAAAJGVkdHMAAAAcZWxzdAAAAAAAAAABAAAq+AAAgAAAAQAAAAACWm1k\n",
              "aWEAAAAgbWRoZAAAAAAAAAAAAAAAAAAAQAAAAsAAVcQAAAAAAC1oZGxyAAAAAAAAAAB2aWRlAAAA\n",
              "AAAAAAAAAAAAVmlkZW9IYW5kbGVyAAAAAgVtaW5mAAAAFHZtaGQAAAABAAAAAAAAAAAAAAAkZGlu\n",
              "ZgAAABxkcmVmAAAAAAAAAAEAAAAMdXJsIAAAAAEAAAHFc3RibAAAALlzdHNkAAAAAAAAAAEAAACp\n",
              "YXZjMQAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAPoA+gASAAAAEgAAAAAAAAAAQAAAAAAAAAAAAAA\n",
              "AAAAAAAAAAAAAAAAAAAAAAAAAAAAABj//wAAADdhdmNDAWQAIP/hABpnZAAgrNlA/B/5ZYQAAAMA\n",
              "BAAAAwAIPGDGWAEABmjr48siwP34+AAAAAAcdXVpZGtoQPJfJE/FujmlG88DI/MAAAAAAAAAGHN0\n",
              "dHMAAAAAAAAAAQAAAAsAAEAAAAAAFHN0c3MAAAAAAAAAAQAAAAEAAABoY3R0cwAAAAAAAAALAAAA\n",
              "AQAAgAAAAAABAAFAAAAAAAEAAIAAAAAAAQAAAAAAAAABAABAAAAAAAEAAUAAAAAAAQAAgAAAAAAB\n",
              "AAAAAAAAAAEAAEAAAAAAAQAAwAAAAAABAABAAAAAABxzdHNjAAAAAAAAAAEAAAABAAAACwAAAAEA\n",
              "AABAc3RzegAAAAAAAAAAAAAACwAAH+wAAA4tAAAEogAABCEAAAG9AAAHVgAAAcoAAAG2AAABeAAA\n",
              "AosAAAGBAAAAFHN0Y28AAAAAAAAAAQAAADAAAABidWR0YQAAAFptZXRhAAAAAAAAACFoZGxyAAAA\n",
              "AAAAAABtZGlyYXBwbAAAAAAAAAAAAAAAAC1pbHN0AAAAJal0b28AAAAdZGF0YQAAAAEAAAAATGF2\n",
              "ZjU4Ljc2LjEwMA==\n",
              "\">\n",
              "  Your browser does not support the video tag.\n",
              "</video>"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "HTML(anim.to_html5_video())"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}