[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit TPU 42.64s (4) kkawchak.ipynb

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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "0f30a2d1-162e-46c9-e7ab-3d5699857813"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701146871.9722736\n",
            "Tue Nov 28 04:47:51 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "\n",
        "# !pip install pennylane pennylane-lightning-kokkos\n",
        "\n",
        "import time\n",
        "seconds = time.time()\n",
        "print(\"Time in seconds since beginning of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "6cfebd1e-3bd1-4d4c-c9f2-a1e38ebe1fee"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.2  0.11 0.08]\n",
            " [0.11 0.74 0.08]\n",
            " [0.08 0.08 0.23]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def create_data_point(n):\n",
        "    \"\"\"\n",
        "    Returns a random undirected adjacency matrix of dimension (n,n).\n",
        "    The diagonal elements are interpreted as node attributes.\n",
        "    \"\"\"\n",
        "    mat = np.random.rand(n, n)\n",
        "    A = (mat + np.transpose(mat))/2\n",
        "    return np.round(A, decimals=2)\n",
        "\n",
        "A = create_data_point(3)\n",
        "print(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fZNWu6j_jAmh"
      },
      "source": [
        "Let\\'s also write a function to generate permuted versions of this\n",
        "adjacency matrix.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "81480e81-c7f5-43a2-8a1e-5136c1727452"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.74 0.08 0.11]\n",
            " [0.08 0.23 0.08]\n",
            " [0.11 0.08 0.2 ]]\n"
          ]
        }
      ],
      "source": [
        "def permute(A, permutation):\n",
        "    \"\"\"\n",
        "    Returns a copy of A with rows and columns swapped according to permutation.\n",
        "    For example, the permutation [1, 2, 0] swaps 0->1, 1->2, 2->0.\n",
        "    \"\"\"\n",
        "\n",
        "    P = np.zeros((len(A), len(A)))\n",
        "    for i,j in enumerate(permutation):\n",
        "        P[i,j] = 1\n",
        "\n",
        "    return P @ A @ np.transpose(P)\n",
        "\n",
        "A_perm = permute(A, [1, 2, 0])\n",
        "print(A_perm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Js9CqRTZjAmi"
      },
      "source": [
        "If we create [networkx]{.title-ref} graphs from both adjacency matrices\n",
        "and plot them, we see that they are identical as claimed.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "d9a835f0-a22d-4de9-cdfa-d86ef0ba594b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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W5Zrz62wtMjIS/fv35zo7IhdlMBgA2P6ok2sFBgbiySefxH/+8x+cPHnSrp9FpCQMdtRoBw4cQH5+vl2CHWCZjl29ejWqq6vtcn0iEsdgMMDb2xvt2rWz+2dxrR25IwY7ajRJkuDt7Y1hw4bZ5fparRZFRUXIyMiwy/WJSByDwYC4uDhoNBq7fxa7duSOGOyo0SRJwrBhw+Dr62uX6/fv3x8RERHcHUvkgoxGo92nYa/06KOPIjAwkGvtyG0w2FGjVFVVYcOGDXabhgUAtVqNCRMmcJ0dkQsyGAx23zhxJXbtyN0w2FGj7Ny5EyUlJXYNdoBlnV1mZiaysrLs+jlE5Djl5eU4fvy4Qzt2APDII4+gRYsW7NqRW2Cwo0aRJAlBQUHo37+/XT9n9OjR8PT0ZNeOyIUcPXoUsiw7PNixa0fuhMGOGkWSJIwcORIeHh52/ZzAwEAkJiYy2BG5EEcddVKXRx99FC1atMDChQsd/tlEjsRgRw1WWlqKjIwMu0/DWmm1Wqxfvx4lJSUO+Twisi+j0YgWLVogPDzc4Z8dEBCAp556Cp9++ilOnDjh8M8nchQGO2qw9PR0VFVVYdSoUQ75PJ1Oh8rKSkiS5JDPIyL7sm6cUKlUQj6fa+3IHTDYUYNJkoTIyEh07drVIZ8XFxeHzp0789gTIhdhMBiETMNasWtH7oDBjhrMehsxR/60rdPpsGLFCsiy7LDPJCL7EB3sAEvXLigoiF07clkMdtQgBQUF2LNnj8PW11lptVqcOXMGe/bscejnEpFtXbhwAXl5ecKD3ZVdu+PHjwuthcgeGOyoQdavXw9Zlh0e7IYPH44WLVpwdyyRkzMajQDg0MOJ6/Pwww+za0cui8GOGkSSJHTu3NkhN+6+kpeXF8aMGcN1dkROznrUiRKCnbVr99lnn7FrRy6HwY4axLq+TgSdToedO3ciLy9PyOcTUfMZDAaEh4cjODhYdCkAuNaOXBeDHd3QiRMnYDQahQW78ePHAwBWrVol5POJqPmUsHHiSv7+/nj66afZtSOXw2BHNyRJElQqFZKSkoR8fnh4OAYOHMh1dkROTGnBDvhjrR3vRkGuhMGObkiSJPTr1w+hoaHCatDpdFizZg0qKyuF1UBETSPLMoxGoyLW112JXTtyRQx2dF2yLAtdX2el1Wpx8eJFpKenC62DiBrv7NmzKC4uVlzHDrB07UJCQti1I5fBYEfXlZmZidzcXOHBLj4+HlFRUdwdS+SErDtilRjsruzaZWdniy6HqNkY7Oi6JEmCl5cXhg8fLrQOlUoFrVbLdXZETshgMEClUqFjx46iS6nTnDlz2LUjl8FgR9clSRKGDh0KPz8/0aVAp9PBYDDUHHRKRM7BYDAgOjoavr6+okupk7Vr9/nnn7NrR06PwY7qVV1djQ0bNgifhrVKSUmBt7c3u3ZETkaJGyeuNWfOHISGhrJrR06PwY7qtWvXLly4cEExwc7f3x9JSUlcZ0fkZJR41Mm12LUjV8FgR/WSJAmBgYEYMGCA6FJqaLVabNy4ERcuXBBdChE1gNlshtFoVHywA4CHHnoIoaGheP3110WXQtRkDHZUL0mSMHLkSHh4eIgupYZWq0V1dTV++eUX0aUQUQOcPHkSFRUVThHsrF27L774AseOHRNdDlGTMNhRncrKyrBlyxbFTMNaxcTEoHv37pyOJXIS1s1OzhDsgD+6dlxrR86KwY7qtGXLFlRWViou2AGW3bErV66E2WwWXQoR3YDBYICHhwfat28vupQG8ff3xzPPPMOuHTktBjuqkyRJiIiIQI8ePUSXUotWq0V+fj527doluhQiugGDwYCOHTsqaknHjXCtHTkzBjuqk/U2YiqVSnQptQwdOhTBwcE89oTICTjDjthr+fn54ZlnnsF///tfZGVliS6HqFEY7KiWwsJC7N69W5HTsADg4eGBcePGcZ0dkRNwxmAHcK0dOS8GO6plw4YNkGUZo0aNEl1KvXQ6HX799Vfk5OSILoWI6lFZWYns7GynDHbs2pGzYrCjWiRJQlxcHKKjo0WXUq9x48ZBrVZj5cqVokshonocO3YMJpNJ8XedqM9DDz2Eli1bcq0dORUGO6rFur5OyVq2bIkhQ4ZwnR2RghkMBgDOc9TJtdi1I2fEYEdXOXXqFH7//XfFBzvAMh37yy+/oKKiQnQpRFQHg8EAPz8/REVFiS6lyR588EGEhYWxa0dOg8GOriJJElQqFZKSkkSXckNarRalpaXYuHGj6FKIqA7WjRNK3F3fUOzakbNhsKOrSJKE+Ph4hIWFiS7lhnr27Ino6GjujiVSKGe5R+yNPPTQQ2jVqhVee+010aUQ3RCDHdWQZdkp1tdZqVQqaLVapKWlQZZl0eUQ0TUMBoPTbpy4kq+vL5555hksXrwYR48eFV0O0XUx2FGNw4cPIycnx2mCHWBZZ3fs2DEcPnxYdClEdIWSkhKcPn3aJTp2gGWtXatWrbjWjhSPwY5qSJIET09PjBgxQnQpDZaUlARfX1/ujiVSmCNHjgBw3h2x12LXjpwFgx3VkCQJQ4YMgb+/v+hSGszX1xcpKSlcZ0ekMM5+1Eld2LUjZ8BgRwCA6upqrF+/3qmmYa20Wi3S09NRVFQkuhQiusxoNKJly5YIDQ0VXYrN+Pr64tlnn8XixYtrOpJESsNgRwCAX3/9FcXFxU4b7EwmE9asWSO6FCK6zFU2TlzrgQceYNeOFI3BjgBYpmEDAgIwcOBA0aU0Wrt27dC7d29OxxIpiPUMO1dj7dp9+eWX7NqRIjHYEQBLsEtMTISnp6foUppEp9Nh1apVMJlMokshIrhusAMsXbvw8HB27UiRGOwIly5dQnp6ulNOw1pptVoUFBRg+/btokshcnsFBQUoLCx02WDHrh0pGYMdISMjAxUVFU4d7AYNGoSWLVvy2BMiBTAajQBca0fste6//36Eh4fzbhSkOAx2BEmSEB4ejp49e4oupck0Gg3Gjx/PdXZECmA96iQuLk5wJfZj7dp99dVX7NqRojDYESRJQnJyMtRq5/7joNPpsG/fPpw8eVJ0KURuzWAwoE2bNk51JmZTsGtHSuTcf5NTsxUVFWHXrl1OPQ1rNXbsWGg0Gk7HEgnmyhsnruTr64vnnnsOX375Zc30M5FoDHZubsOGDTCbzS4R7IKDgzF8+HAGOyLB3CXYAZauXUREBLt2pBgMdm5OkiTExsYiJiZGdCk2odVqIUkSLl26JLoUIrckyzKMRqNLHk5cFx8fHzz33HP46quv2LUjRWCwc3OSJLlEt85Kp9Ph0qVLWL9+vehSiNxSTk4OysrK3KZjB1i6dq1bt2bXjhSBwc6NnT59GocOHXKpYNe1a1fExsZydyyRINYdse4U7K7s2lm/fiJRGOzc2Lp16wAAycnJgiuxHZVKBa1WixUrVkCWZdHlELkdg8EAjUbjMss7Guq+++5j144UgcHOjUmShD59+qBVq1aiS7EpnU6HEydO4MCBA6JLIXI7BoMBMTEx8PLyEl2KQ1m7dkuWLGHXjoRisHNTsiy73Po6q8TERPj7+3N3LJEA7rRx4lr33XcfIiMj2bUjoRjs3JTBYMCpU6dcMth5e3tj9OjRXGdHJIA7HXVyLXbtSAkY7NyUJEnw8PBAQkKC6FLsQqvVYuvWrSgoKBBdCpHbqK6uxtGjR9022AHA7NmzERkZiVdffVV0KeSmGOzclCRJGDx4MAICAkSXYhcTJkyA2WzG6tWrRZdC5Days7NRXV3t1sHO2rVLTU3F77//LrocckMMdm7IZDJh/fr1LjkNaxUVFYV+/fpxOpbIgdzxqJO6WLt2XGtHIjDYuaE9e/bg/PnzLh3sAMvu2NWrV6O6ulp0KURuwWg0wsfHB23bthVdilDs2pFIDHZuSJIk+Pv7Y9CgQaJLsSutVouioiJkZGSILoXILRgMBsTFxUGt5l8t1h2yXGtHjsbvPjckSRISEhJc/pypm266CeHh4Tz2hMhB3HlH7LW8vb0xb948fP311zh8+LDocsiNMNi5mfLycqSnp7v8NCwAqNVqTJgwgevsiByEwe5qXGtHIjDYuZmtW7fi0qVLbhHsAMs6u8zMTBw7dkx0KUQu7dKlSzhx4gSD3RXYtSMRGOzcjCRJCAsLQ+/evUWX4hCjR4+Gp6cnp2OJ7Ozo0aMA4LZ3najP7NmzERUVxbV25DAMdm5GkiQkJye7zeLmFi1aICEhgcGOyM541End2LUjR3OPv90JAFBcXIwdO3a4zTSslVarxfr161FaWiq6FCKXZTAYEBQUhFatWokuRXHuvfdetGnThl07cggGOzeyceNGmM1mtwt2Op0OFRUVkCRJdClELsu6cUKlUokuRXHYtSNHYrBzI5IkoUOHDoiNjRVdikN16tQJnTt35u5YIjsyGo2chr2Oe++9F23btmXXjuyOwc6NSJKElJQUt/yJWqvVYsWKFZBlWXQpRC7JYDBw48R1XNm1O3TokOhyyIUx2LmJM2fO4ODBg243DWul0+mQk5ODvXv3ii6FyOUUFRUhPz+fHbsbuOeee9i1I7tjsHMT69atAwAkJycLrkSM4cOHIzAwkLtjiezAaDQC4I7YG7F27ZYuXcquHdkNg52bkCQJvXr1QkREhOhShPDy8sLYsWO5zo7IDqxHnXAq9sa41o7sjcHODciyDL1e77bTsFZarRY7duxAfn6+6FKIXIrRaETr1q3RokUL0aUonpeXF55//nksXboUmZmZosshF8Rg5waOHDmCkydPun2wGz9+PABg1apVgishci3cONE4XGtH9sRg5wYkSYJGo0FCQoLoUoSKiIjAgAEDuM6OyMasZ9hRw1i7dsuWLWPXjmyOwc4NSJKEQYMGcZoElt2xa9asQWVlpehSiFyCLMsMdk1wzz33oF27duzakc0x2Lk4s9mMdevWuf00rJVWq8WFCxeQnp4uuhQil5CXl4eLFy8y2DXSlV27gwcPii6HXAiDnYvbu3cvCgsLGewu69u3L6KiojgdS2QjPOqk6e6++2527cjmGOxcnCRJ8PPzw+DBg0WXoggqlQoTJkzgsSdENmIwGKBSqdzuVoW2YO3affPNN+zakc0w2Lk4SZIwYsQIeHt7iy5FMXQ6HQwGQ02ngYiazmAwoH379vDx8RFdilO6++67ER0dza4d2QyDnQurqKjA5s2bOQ17jZSUFHh5eXE6lsgGuHGiedi1I1tjsHNh27ZtQ1lZGYPdNQICApCUlMRgR2QDDHbNd9dddyE6OhqvvPKK6FLIBTDYuTBJkhAaGor4+HjRpSiOVqvFxo0bcfHiRdGlEDktk8mEo0ePMtg1k7Vr9+233+LAgQOiyyEnx2DnwiRJQnJyMtRq/jZfS6vVoqqqCr/88ovoUoic1smTJ1FRUcG7TtiAtWvHtXbUXPwb30VduHAB27dv5zRsPWJjY9GtWzfujiVqBoPBAIBHndiCl5cXXnjhBXbtqNkY7FzUpk2bYDKZGOyuQ6fTYeXKlTCbzaJLIXJKBoMBnp6eaN++vehSXMKdd96J9u3bc60dNQuDnYuSJAnR0dGIi4sTXYpi6XQ65OXlYffu3aJLIXJKBoMBcXFx0Gg0oktxCdaunZ+fH6qqqkSXQ06Kwc5FSZKElJQUqFQq0aUo1tChQxEcHMzdsURNZDQaOQ1rY/feey+++OILhmVqMgY7F5SXl4f9+/dzGvYGPDw8MG7cOK6zI2oig8HAjRM2Zv1hnJveqKn4J8cFrVu3DgCQnJwsuBLl02q12L17N86cOSO6FCKnUlFRgezsbHbsiBSGwc4FSZKEHj16IDIyUnQpijdu3Dio1WqsXLlSdClETiUrKwtms5nBzoFKSkqwefNmGAwGnsFJ9WKwczGyLEOv13MatoHCwsIwePBgrrMjaiQedeI4ubm5mDt3Ltq1a4eHH34Yffv2xZ133sljUahODHYuJisrC8ePH2ewawSdToe1a9eioqJCdClETsNoNCIgIACtW7cWXYpLe++999C5c2esWbMGr7zyCv7973/j+++/R2hoKO68807R5ZECeYgugGxLkiSo1WokJiaKLsVpaLVazJs3D5s2bcLo0aNFl0PkFKwbJ7jz3j4qKyvx3HPP4fPPP8cTTzyBOXPmIDw8vOb5uLg4DB06FDt37sSAAQMEVkpKw46di5EkCQMHDkRQUJDoUpxGr1690K5dO+6OJWoEg8HAaVg7OnToEJYvX47XX38dTz/99FWhDrDczi0oKIgdU6qFwc6FmM1mrFu3jtOwjaRSqaDVapGWlgZZlkWXQ+QUGOzsa/v27QgPD8esWbPg6+t71XObN2/Go48+ipiYGERERAiqkJSKwc6F7Nu3D+fOnWOwawKdToesrCz8/vvvokshUryLFy/izJkzDHZ2VFVVhfLy8qtCXVZWFj744AO88cYbaNOmDd5++214eXkJrJKUiGvsXIgkSfDx8cGQIUNEl+J0kpKS4OPjg7S0NHTt2lV0OUSKduTIEQDg4cR29Mgjj2DhwoW46667kJiYCKPRiGPHjuHw4cPo0qULnnnmGfTo0UN0maRA7Ni5EEmSMGLECPj4+Iguxen4+fkhJSWFx54QNYD1qBMGO/v6+uuvERQUhGeffRY7duyAv78/XnrpJXz33XcYOHCg6PJIodixcxGVlZXYtGkTXnzxRdGlOC2tVovHHnsMRUVFCA4OFl0OkWIZDAaEhYUhNDRUdCkuLSEhAcOHD8c///lPAJbbIFrvIWsymaDRaCDLMncm01XYsXMR27dvR2lpKdfXNYNWq4XJZMLatWtFl0KkaNw44ThqtRre3t44ePBgzeYuk8kElUpV82+iKzHYuQhJkhASEoK+ffuKLsVpRUdHo1evXjz2hOgGGOwc6z//+Q9uvvlmLFu2DIDlDkNqtRoajQZ5eXlYuHAhXn31VSxYsAB79uwRXC2JxmDnIiRJQlJSUk2bnppGp9Nh1apVMJlMokshUiRZlmsOJybHGDt2LCZNmlQTpj08PFBdXY3HH38cHTt2xPfff4+NGzfim2++we23344ffvhBbMEkFIOdCygpKcG2bds4DWsDOp0O586dw44dO0SXQqRIBQUFKCoqYsfOgdq1a4f333+/5g4Tq1atQs+ePfHjjz/ilVdewaeffoo1a9YgMzMT99xzD5544gnBFZNIDHYuYNOmTaiurmaws4FBgwahZcuW3B1LVA/rjlgGOzEKCwvx7rvvIj4+HkuXLsWjjz6KPn361MzWJCUlwd/fH0ePHhVcKYnCYOcCJElC27ZtOdDagEajwfjx47nOjqge1mAXFxcnuBL3tGzZMmzatAnz5s3DoEGDah1Q/P7776OioqLWLcjIfTDYuQBJkpCSksLdUTai1Wrx22+/4dSpU6JLIVIcg8GAdu3awc/PT3QpbsloNGL69Ono3bv3VY9nZ2fjzTffxJ49e/D6668jMDBQUIUkGoOdkzt79ix+++03TsPa0NixY6HRaDgdS1QHo9HIjRMCde/eHatXr8bx48cBAEePHsV3332HJ554Au+++y7GjBlT8/cB733tnlQyf+ed2rJlyzBt2jScPn0aUVFRostxGYmJiQgKCsJPP/0kuhQiRenTpw+GDh2KDz74QHQpbisxMRGlpaW4cOECIiMjcerUKYSFhWHhwoU1oS4/Px+lpaWIiYkRXC05Gu884eQkSUK3bt0Y6mxMp9Nh/vz5uHTp0lU34SZyZ2azGUajEXfffbfoUtza8uXLkZ6ejr1798LLywvdu3fHn/70JwCWLt3HH3+Md955B7IsY+DAgXjxxRfRsWNHwVWTo7Bj5+Q6duyICRMm4N133xVdikvJzMxEjx49sHLlSowfP150OUSKcPLkSURHRyMtLQ1arVZ0OXQN68HRkydPRsuWLdGrVy9s27YNJ06cQHp6uujyyEG4xs6JHTt2DFlZWVxfZwfdunVDTEwMd8cSXcFoNALgUSdK8+GHH8LHxwe33347dDodCgoK8Mwzz2Du3Ln44IMPYDAYsHLlStFlkoMw2DkxSZKgVqsxcuRI0aW4HJVKBa1Wi7S0NC5AJrrMYDBAo9GgQ4cOokuhyzZv3oynn34a8+bNw8cff4yEhARkZGTUHEsTFBSEhIQE7Nu3T3Cl5ChcY+fEJEnCTTfdhODgYNGluCSdTof33nsPBw8eRM+ePUWXQyScwWBAbGwsPD09RZdClxkMBrRv3x533XUX2rdvjwEDBqC4uBj33HMPVq1ahe3bt+OHH37AtGnTRJdKDsKOnZMym80159eRfSQmJsLPz4/TsUSXWddwkXLIsgxfX1+0b9++5rGEhAS0b98ezz33HP7+97/jgQce4N8VboTBzkkdOHAAZ8+e5TerHfn4+GD06NE8z47oMgY75bnvvvtw7Ngx/Oc//4HJZEJxcTE+/PBDtG3bFsuXL8emTZuwYMEChISEiC6VHITBzklJkgRvb28MHTpUdCkuTavVIiMjA4WFhaJLIRKqqqoKx44dY7BToEWLFtXcP/buu+9GdnY2HnjgAQQGBqJNmza8vZib4Ro7JyVJEoYPH84z1uxsypQpaNeuHdcxktvLzs5GdXU17zqhQPfccw+io6OxevVqVFRUYPLkyRg3bpzoskgQnmPnhKqqqhAaGop58+bhueeeE12OyzOZTNBoNKLLIBJqxYoV0Ol0OHHiBNq1aye6HKqH2WyGWs3JOHfG330ntGPHDpSUlHB9nYMw1BFZ1tf5+vqiTZs2okuhesiyzFBHDHbOSJIkBAUFoX///qJLISI3UVJSgu7duzM4KJhKpRJdAikAp2Kd0K5du7B3717cd999okshIjfCaT7nwt8v98Rg54RMJhPUajV/OhPo4MGD+OWXX3D06FEMHjwYCQkJXHdERIohyzLy8vJw6dIlxMTEiC6HHIjBjqiBioqK8NFHH+GTTz7BsWPH0K5dO/Tq1Qtbt25F586dMX/+fIwdO1Z0mUREMJvN6Nu3L6Kjo/Hzzz+LLocciMGOqAFyc3MxZ84c/Pbbb5gyZQqmTJmC2NhYeHl5obi4GO+++y70ej1+/fVX0aUSEQEAlixZglmzZmHnzp246aabRJdDDsJgR3QDsizjmWeewZIlS7B06VIMGjQIXl5eV71m586dGDt2LI4fP47AwEBBlRIR/cFkMqF79+7o3Lkzu3ZuhKsqiW6gpKQEmzZtwqJFizBixIhaoQ4AfvzxRwwYMADV1dUCKiQiqk2j0eCll15CWloadu3aJbocchAGOwWrrq5GTk4OzGaz6FLcWmBgIPLz81FSUnLV4yUlJcjIyMAjjzyCN998E+PHj+f9GIlIUaZNm4YuXbpgwYIFokshB+EtxRRq/fr1WLRoETw8PDBt2jTMnDkTAFBYWIjQ0FDB1bmf++67D//6179w5swZdOzYEbm5uTh69CgyMzNhNpvx7rvv4qGHHhJdJhHRVaxdu5kzZ2Lnzp0YMGCA6JLIzrjGToGOHDlSc4/Sli1b4scff8TatWvx2Wef4fDhwwgJCcGTTz6JoUOHii7VbZSWluKbb77BCy+8gBYtWiA0NBReXl4YMmQIJk+ezIXJ5BIqKioAAN7e3vW+ZunSpaiqqsIdd9zhqLKomUwmE3r06IG4uDikpaWJLofsjMFOgV566SVkZGRAr9cDAJ599lmsXLkSgYGB0Gq12LBhA0pLS7FixQrenN6BZFmGSqXC8ePHcenSJXTt2lV0SUQ29eGHH+Lo0aPo2bMn2rdvj4iICISEhMDf3x++vr7w8PDA6NGjMWDAACxcuFB0udQIqampmDlzJnbs2MGunYtjsFOglJQUTJo0CXPnzgUATJkyBWazGd9++y00Gg3S09Px6KOP4vnnn8fUqVMFV+teTCYT8vLyEBUVVfNrlUrF093JJbRt2xZnz56Fh4cHLl26BD8/P7Rp0wYdO3ZE9+7dERcXh2eeeQb/+c9/OPY4GZPJhJ49e6Jjx47s2rk4/m2kMGazuWZr+qFDh3D06FGsWbMGt912W83N6IcPHw4AqKysFFmq2yksLMSQIUPw9NNP1zymVqthNpu5wYVcQmhoKL755huUlpYiLy8PP/74I2bPno3AwECsXLkSTz/9NC5evIhBgwaJLpUaybrWbsWKFdixY4focsiO2LFToF27dmHWrFmIiIhAWVkZAgMD0blzZ3z44YcAgKNHj6Jv377IyspCWFiY4Grdy5///GdERUXh4YcfrnVeXXFxMc6dO4fY2Fje7o2cTklJCZ599ll06NABTz75ZJ2vOXDgAPr27YuqqioHV0e2YO3axcbGYsWKFaLLITthsFMYWZYhyzLWrl0LSZKg0+ng5+eHBx98ELNnz4ZarcZXX32FVq1a4YcffhBdrtupqqqCp6dnza9zc3OxePFifPPNNygoKEDr1q1hMpnwwgsvYOLEiQIrJWock8mErKwsVFdXo1u3bjVjkfUfjUaDJUuW4JFHHkFxcbHocqmJvv76a8yYMQPbt2/HwIEDRZdDdsBg5wTKy8vx5ptv4q233oKnpydmzZqFRx99FF26dBFdmtsqLS3F66+/jv/+97/w8vJCcnJyzYLkrVu3Yvv27Vi4cCEmT54suFIi2zlx4gSys7ORkJAguhRqIpPJhF69eiEmJoZdOxfFYKcw5eXlyMvLw44dOxAdHV1rLcu5c+fQokWLOu9+QI6zcOFCfPHFF7jnnnswceJEdOjQAb6+vjWbKP7yl78gMzMTa9asEVwpUcNYO3M32ghk3R1Ozmvp0qWYPn06tm3bxvWSLojBTkH27duHV199FWvXrkVMTAyKiopQVVWFoUOHYsaMGRg3bhx8fX05sAp28uRJTJ48GZMmTcILL7xQ52veeOMNSJJUc2QNkTOy/vVgHW849rgGa9euQ4cOWLlypehyyMa4K1ZBHnjgAajVanz55Zf417/+hXfeeQePPfYYKioqsGDBArz//vsAwIFVsAsXLiA7Oxv33XdfredKSkrw448/4uWXX+YaO3IqWVlZOHfu3FW77VUqVc14U1RUhNGjR+P06dOiSiQbse6QXbVqFbZv3y66HLIxduwUorCwEG3atMG+ffvQqVOnmserq6tx/PhxfPvtt5g3bx4+//xz3HXXXQIrJQCIiIjAvHnz8Oijj6KiogKnTp1CVlYWNm3ahLVr1+Kmm27CP//5T/j6+oouleiGzp07h4kTJ6Jz586IiopCu3btEBUVhfDwcISFhSEkJARGoxHDhw9HdXU1f7h0AezauS7eK1YhTp06hc6dOyM3N/eqYOfh4YGOHTvi2WefRVlZGZYvX45Zs2bVnGlHYrzyyiv46KOP8Nprr2HgwIEoLS1FZmYmWrRogdtuuw33338/p83JaezZswfbtm1DixYtsHfvXhQWFkKWZfj7+6NVq1aIjo5GYWEhIiIi+OfZRWg0GsyfPx/Tpk3Dtm3bMHjwYNElkY0w2ClE165d0aFDB9xzzz3497//jYEDByIkJOSq1wQHB+PEiRMMdQrwwAMPYNCgQdi6dSsOHToEHx8fvPDCCxg1atRVr+NfguQMzpw5g4SEBCxevBjh4eEoLS1FVlYWMjMzsX//fhiNRmzatAkjR44UXSrZ0JQpU9C9e3e8/PLLWLVqlehyyEY4FasgOTk5mDt3Lg4fPowBAwYgJSUF7du3h4+PD/bv34/33nsPkydPrnfBPilDUVER/u///g8ZGRlITk7G7bffjg4dOogui6heGRkZ+P777zFjxgz069evztdMmjQJUVFR+OCDDxxcHdnTsmXLMG3aNGzdupVdOxfBYKcw+fn5WLZsGRYvXox9+/YhIiICYWFhMBqNeOqppzB37lwEBweLLpPwxw5Bk8mEL774Avv378ddd92FiooKzJo1CyNHjsSOHTsQGRnJY09I0aqrq1FYWIjg4OCao5RkWa65VV5VVRWGDRuGhx56CPfff7/IUsnGTCYTevfujejoaHbtXASDnYKVl5cjPT0dJSUlGDRoEFq3bs2pPYUpKCjAhAkTcPjwYYwYMQJGo7Hm/MHnn38excXFGDJkCN5//32MHz9edLlETXb+/Hn4+fnB29tbdClkY9988w1uv/12du1cBI87URhZlmEymWAymeDj44NRo0bhlltuQWRkJEOdAm3YsAG5ubn44YcfkJaWhi+++AJGoxGtWrWCr68vWrdujZEjR2L58uWiSyVqlpCQEIY6F2Vda7dgwQLRpZANMNgpjHV6T6PR1BwOevr06ZopEVKW/fv3o2/fvkhKSgIADBkyBDNmzMBHH30EALh06RLOnTuH1q1biyyTqMmqq6tx5swZVFVViS6F7EStVmP+/PlYs2YNtm7dKrocaiYGO4VRq9U1t/RRqVQoKSnB448/jvvvvx+cNVeeoUOHYvfu3aioqKh5LCQkBD4+PujXrx8SEhKwbds26HQ6gVUSXd+1Y4ssyzVBLjMzE7fddhv+/ve/iyiNHGTKlCno0aMHXn75ZdGlUDPxuBPBTCYTfvjhBxiNRuTm5iIkJATDhg3DsGHD4Ovri8rKSvj5+SEgIIBTsQo0ZswYeHp64m9/+xuSkpJw7tw5vPHGG/j4449RVVUFg8GA+Ph4DBkyRHSpRPVSqVSorKxEaWkpQkJCoFKp4OnpCcDyw2ZYWBjCw8MFV0n2ZO3a3Xbbbdi6dSvHLCfGzROC3X///fjxxx8REhKC2NhYlJWV4dy5c4iMjMTUqVPx4IMPArAEQJ5fp0zLly/Ha6+9hosXLyIwMBCDBw/GO++8Ay8vL5jN5hveVJ1IJLPZjM8//xybN29Gbm5uTbjr06cPkpOTa5YZkOszm83o3bs32rRpw538TozBTqBVq1bh3nvvxfLlyzFs2DAUFBTgxIkT2L9/P9atWwe9Xo+77roL8+fPrzmCgJQpPz8fW7ZsgUqlQkpKCgIDA0WXRNQg1lsV9urVC926dYOnpyfy8vJw+vRpFBYWYsaMGXj00Ufh5+cnulRygG+//Ra33XYbtmzZgqFDh4ouh5qAwU6gP//5z8jNzcWyZcvqfP6DDz7AwoULsXLlSvTq1cvB1RGRqysoKEBMTAy+/vpraLVaAJb1dcXFxcjOzsbPP/+MRYsWYfHixfjTn/4kuFpyBHbtnB/niATq06dPzT0ar2TN2vfffz+io6ORlpYmojwicnGHDh1CYGAgxowZU/OYSqVCcHAw4uPj8eKLL2Lu3LlYtGiRwCrJkaxr7dauXYuMjAzR5VATMNgJdMstt6B9+/Z45ZVX8PPPP+P8+fMA/gh2paWlOHr0KPr37y+yTCJyUcHBwYiIiMArr7yCS5cu1bnzPiIiAuXl5QKqI1FuvfVW9OzZk+faOSlOxQq2Z88ePPXUU1i3bh1iY2ORmJiI+Ph4nDp1CmvWrEFwcDA2bNggukwiclFvv/02PvzwQyQnJ2PMmDHo2rUrAgMDUVpaipUrV2LZsmWYMGEC5s+fL7pUcqDly5dj6tSpSE9Px7Bhw0SXQ43AYKcQR48exdKlS7F69WpkZWWhR48e6NevHx544AHExsaKLo8awHq4dHl5OXx8fESXQ9QgVVVVWLx4Mf7973/j4MGDMJvN8PPzQ2RkJMxmMyZPnoynnnoKLVu2FF0qOZDZbEafPn0QGRmJtWvXii6HGoHBTqHOnz+PkJAQ0WVQI73zzjv44IMPkJmZyXMHyemUlZXBYDDgzJkzKCgoQM+ePREfHy+6LBKEXTvnxGCnYNYOEDmPtLQ03HzzzTh8+DC6dOkiuhwioiYzm82Ij49HREQEfvnlF9HlUANx84SCMdQ5n+TkZPj4+HAnMxE5PesOWb1ej/T0dNHlUAOxY6cg1dXV0Gg0DHROTqvV4tKlS1i3bp3oUoiImoVdO+fDjp1CVFRU4B//+AcKCgpEl0LNpNPpsHnzZhQXF4suhajRTCaT6BJIQdi1cz7s2CmEXq/H6NGjsW/fPt5lwsmdOHEC7du3xzfffIOpU6eKLoeoUe644w5UVlbWe0cccj9msxl9+/ZFeHg4u3ZOgB07hZAkCeHh4ejZs6foUqiZoqOj0atXL66zI6f0+++/w9/fX3QZpCDs2jkXBjuFkCQJKSkpXF/nIrRaLVatWsVpLXIqsizDYDCgc+fOokshhbnlllvQu3dv3o3CCTDYKcD58+exe/dupKSkiC6FbESn0+Hs2bPYuXOn6FKIGuzs2bMoLi5msKNarF07SZKwefNm0eXQdTDYKcCGDRtgNpsZ7FzI4MGDERoaihUrVoguhajBjEYjADDYUZ1uueUW9OnTBy+//LLoUug6GOwUQJIkxMbGokOHDqJLIRvRaDQYP34819mRUzEYDACAjh07Cq6ElIhdO+fAYKcAkiRh1KhRossgG9Nqtdi7dy9OnToluhSiBjEYDIiOjoavr6/oUkihJk2ahD59+nCtnYIx2Al2+vRpHD58mNOwLmjs2LHQaDRYuXKl6FKIGoQbJ+hGrF27devWYdOmTaLLoTow2AkmSRIAICkpSXAlZGuhoaEYOnQop2PJaTDYUUNYu3Zca6dMDHaCSZKEPn36oFWrVqJLITvQ6XSQJAmXLl0SXQrRdZnNZhw5coTBjm5IrVZjwYIF7NopFIOdQLIsc32di9NqtSgrK8OGDRtEl0J0XadOnUJ5eTk6deokuhRyApMmTUJ8fDzX2ikQg51ABoMBp0+f5vo6F9a9e3d06NCBx56Q4ll3xLJjRw2hUqkwf/58rF+/Hhs3bhRdDl2BwU4gvV4PDw8PjBgxQnQpZCcqlQparRZpaWngbZlJyQwGAzw8PHjsEjWYtWvHtXbKwmAnkCRJGDJkCAICAkSXQnak0+lw/PhxZGZmii6FqF4GgwEdO3aEh4eH6FLISahUKixYsIBdO4VhsBPEZDJh/fr1nIZ1AyNHjoSfnx93x5KiGY1Grq+jRps4cSLX2ikMg50ge/bsQVFREYOdG/Dx8cGoUaO4zo4UjUedUFNYu3YbNmzgJjGFYLATRK/Xw9/fHwMHDhRdCjmATqfDli1bUFhYKLoUoloqKytx7NgxBjtqkokTJ6Jv375ca6cQDHaCSJKExMREeHl5iS6FHGDChAkwm81Ys2aN6FKIajl27BhMJhODHTUJu3bKwmAnQHl5OdLT0zkN60batGmDvn37cp0dKRKPOqHmuvnmm9G3b1+utVMABjsBtm7divLycgY7N6PVarF69WpUV1eLLoXoKkajEX5+foiKihJdCjkpa9du48aN7NoJxmAngF6vR1hYGHr16iW6FHIgnU6HwsJCbNu2TXQpRFcxGAzo1KkTVCqV6FLIibFrpwwMdgJIkoSUlBSo1fzf704GDBiAVq1acXcsKQ53xJItsGunDEwWDlZcXIydO3dyGtYNqdVqTJgwgevsSHEY7MhWbr75ZvTr1w/z58/n3XYEYbBzsA0bNsBsNjPYuSmtVosDBw7g+PHjokshAgCUlpbi9OnTDHZkE9au3aZNm9i1E4TBzsEkSUKHDh0QGxsruhQSYMyYMfDw8OB0LCnGkSNHAIB3nSCb0el06NevHxYsWMCunQAMdg4mSRJGjRolugwSJCgoCCNGjOB0LCkGjzohW2PXTiwGOwc6c+YMMjMzOQ3r5nQ6HdatW4fS0lLRpRDBYDAgNDQULVu2FF0KuRCdTof+/ftzrZ0ADHYOJEkSACA5OVlwJSSSVqtFRUUF1q1bJ7oUIm6cILuwdu02b96M9evXiy7HrTDYOZAkSejVqxfCw8NFl0ICde7cGXFxcVxnR4rAYEf2otVq0b9/f661czAGOweRZZnr6wiA5SdZrVaLFStWcLAj4YxGIzdOkF2waycGg52DHDlyBCdPnuT6OgJgWX9y6tQp7Nu3T3Qp5MYKCgpQUFDAjh3ZjVarxU033cSunQMx2DmIXq+Hh4cHEhISRJdCCpCQkICAgADujiWhjEYjAO6IJfu5smvHdcWOwWDnIJIkYeDAgQgMDBRdCimAl5cXxowZw3V2JJT1qJO4uDjBlZArmzBhArt2DsRg5wBmsxnr16/n+jq6ik6nw7Zt23D27FnRpZCbMhqNaNOmDQICAkSXQi7M2rVLT09n184BGOwcYO/evSgsLOT6OrrK+PHjIcsyVq9eLboUclMGg4EbJ8ghJkyYgAEDBrBr5wAMdg6g1+vh5+eHwYMHiy6FFKR169YYMGAA19mRMDzqhBzlyq6d9UxXsg8GOweQJAkJCQnw8vISXQopjFarxZo1a1BVVSW6FHIzsiwz2JFDjR8/nl07B2Cws7OKigps3ryZ07BUJ51Oh+LiYmzZskV0KeRmcnJyUFZWxmBHDmPt2m3ZsoVdOztisLOzbdu24dKlSwx2VKe+ffuidevW3B1LDsejTkiE8ePHY+DAgeza2RGDnZ3p9Xq0bNkSffr0EV0KKZBarYZWq+U6O3I4g8EAtVqNmJgY0aWQG7mya6fX60WX45IY7OxMkiQkJydDreb/aqqbVqvF4cOHcfToUdGlkBsxGAyIiYnh2l9yuHHjxrFrZ0dMG3Z04cIF7Nixg9OwdF2jRo2Cl5cXp2PJobhxgkSxdu0yMjLYtbMDBjs72rRpE0wmE4MdXVdgYCASExM5HUsOxWBHIo0bNw6DBg1i184OGOzsSK/XIzo6Gh07dhRdCimcTqfDxo0bcfHiRdGlkBuorq5GVlYWgx0Jc2XX7pdffhFdjkthsLMjSZIwatQoqFQq0aWQwmm1WlRWVnJaghzi+PHjqKqq4l0nSKixY8eya2cHDHZ2kpubiwMHDnAalhqkY8eO6Nq1K9fZkUMYDAYAPOqExLJ27bZu3cqunQ0x2NmJ9UbHycnJgishZ6HVarFixQqYzWbRpZCLMxgM8Pb2Rrt27USXQm6OXTvbY7CzE0mS0KNHD7Ru3Vp0KeQkdDodcnNzsWfPHtGlkIszGAzo1KkTj2Ei4VQqFV5++WV27WyI39V2IMtyzfo6ooYaNmwYgoKCuDuW7M5oNHIalhRjzJgxGDx4MObPn8+unQ0w2NlBVlYWjh8/zvV11Cienp4YO3Ys19mR3Vk7dkRKYF1rt23bNqxdu1Z0OU6Pwc4O9Ho9NBoNEhMTRZdCTkar1WLnzp3Izc0VXQq5qEuXLuHEiRPs2JGiWLt2XGvXfAx2diBJEgYMGIAWLVqILoWczPjx46FSqbBq1SrRpZCLOnr0KGRZZrAjRWHXznYY7GzMbDZj3bp1XF9HTdKqVSsMHjyY6+zIbnjUCSnVmDFjMGTIEK61ayYGOxvbt28fCgoKuL6Omkyr1WLt2rWorKwUXQq5IKPRiKCgILRq1Up0KURXsXbttm/fjjVr1ogux2kx2NmYXq+Hr68vhgwZIroUclI6nQ4lJSXYtGmT6FLIBVk3TvCOOKREo0ePxpAhQ7jWrhkY7GxMkiQMHz4c3t7eokshJ9W7d2+0bduWu2PJLgwGA6dhSbHYtWs+BjsbqqysxKZNm7i+jppFpVJBq9VynR3ZBYMdKd3o0aMxdOhQrrVrIgY7G9q+fTvKysq4vo6aTavV4siRIzUL3Ylsobi4GPn5+Qx2pGjWrt2OHTuwevVq0eU4HQY7G9Lr9QgJCUF8fLzoUsjJpaSkwMfHh107simj0QgAPJyYFG/UqFEYOnQo19o1AYOdDUmShOTkZGg0GtGlkJPz8/NDUlIS19mRTVk7wAx2pHTs2jUdg52NlJSUYPv27ZyGJZvR6XTYtGkTiouLRZdCLsJgMCAiIgJBQUGiSyG6oVGjRmHYsGHs2jUSg52NbNq0CdXV1Qx2ZDNarRbV1dU8hZ1shhsnyJlc2bXj3XgajsHORvR6Pdq2bcspDrKZ9u3bo2fPnpyOJZthsCNnk5KSwq5dIzHY2YgkSRg1ahQP/SSb0mq1WLlyJcxms+hSyMnJsgyj0cgfPsmpWLt2O3fuZNeugRjsbCA/Px/79u3jNCzZnE6nw9mzZ7Fz507RpZCTy8/Px4ULF9ixI6eTkpKC4cOHs2vXQAx2NrB+/XoAQHJysuBKyNUMHjwYISEhPPaEms26I5bBjpzNlV27lStXii5H8RjsbECv16Nbt26IiooSXQq5GA8PD4wfP57r7KjZDAYDVCoVOnbsKLoUokZLTk5m166BGOxswLq+jsgetFot9uzZg9OnT4suhZyYwWBA+/bt4ePjI7oUokazdu127drFrt0NMNg107Fjx3Ds2DGuryO7GTduHNRqNQczahZunCBnx65dwzDYNZMkSVCr1UhMTBRdCrmo0NBQDB06lOvsqFl41Ak5O5VKhZdffhm7du3i8pTrYLBrJr1ej5tuugnBwcGiSyEXptPpoNfrUV5eLroUckImkwlHjhxhsCOnl5SUhBEjRrBrdx0Mds1gNpuxbt06rq8ju9PpdCgrK8OGDRtEl0JO6OTJk6ioqGCwI6dnXWu3e/dudu3qwWDXDAcOHMDZs2e5vo7srnv37mjfvj0HMmoSHnVCroRdu+tjsGsGvV4PHx8fDB06VHQp5OJUKhV0Oh3S0tI4kFGjGY1GeHp6Ijo6WnQpRM1mXWu3e/fuWmuPzTJQXAlklwJ7zgMb8oFfcoE1uZZ/b8i3PJ5danmd2QWHU5XMvyWaTKvVoqKiAnq9XnQp5AZWrVqFCRMm4ODBg+jevbvocsiJ/PnPf8batWtx6NAh0aUQ2YQsyxg5ciRKSkqwa9culJpUyCoBjpUC1ZdTjQpAXQHnysc9VECMPxAbAAR4OKZ2e2PHromqqqqwadMmrq8jh0lKSoKfnx93x1KjcUcsuRrrWruLZg/879BZrMkFjpT8EeqAukPdtY9Xy5b3rckFNp8FCivtWbVjMNg10Y4dO1BSUsL1deQwPj4+SElJ4To7ajQGO3I1JhkI6zsSC3/cCpN/KID6g9yNWN93tgJYnw/sL7Jc31kx2DWRXq9HcHAw+vXrJ7oUciM6nQ5btmxBYWGh6FLISVRWViI7O5vBjlzG+UrLejlDiQoqtRpqjW3mUK1ZzlAC6PMsn+OMGOyaSJIkjBw5EhqNRnQp5EYmTJgAk8mENWvWiC6FnERWVhbMZjPvOkEuIa/csgGizGTfzymttnxOnhMeHcpg1wSlpaXYtm0b19eRw7Vt2xbx8fGcjqUG41En5CryyoEt5wAzmj7t2lAyLJ+z5ZzzhTsGuybYvHkzqqqquL6OhNBqtVi1ahVMJjv/yEouwWAwwN/fH5GRkaJLIWqy85VAxjn7B7prybB8rjNNyzLYNYFer0dUVBS6dOkiuhRyQzqdDoWFhdi2bZvoUsgJWDdOqFQq0aUQNYlJBrYXOD7UWZkB7Ch0ng0VDHZNIEkSUlJSOFCSEAMGDEBYWBiPPaEGMRqNnIYlp5ZZDJSaxAU7ACipBjIvCCygERjsGuncuXPYu3cv19eRMBqNBhMmTOA6O2oQg8HAjRPktAorLLtUlcBw0TnOuWOwa6T169cDANfXkVBarRb79+/HiRMnRJdCClZSUoKcnBx27MhpHbxguVOEEqgAHCwWXcWNMdg1kl6vR5cuXdCmTRvRpZAbGzNmDDw8PNi1o+syGo0AuCOWnFNJNZBfAVRWVODLhc/g/v5RmBHni2dvHoTfNv1yw/dvW/U93p5zOx4eFosZnfwwN7EL/vvKEygtLqr12s8X/AVPje+Hu3uGYkYnP/w5qRuWvb0Al0r/aBfKsNRTUm3DL9IOeK/YRoqLi8O4cePw3nvviS6F3Jz1FmMMd1SfZcuWYdq0aSgoKEBoaKjocogaZV+R5XZfbz8yHdtWLod29uOIjOmE9d9+gaO/7cSCZevRbeDwet9/T+8whEREYeDYWxDWJhonDu/H2q8+RER0LBat/BXevr41r31h8nDE9uqP1h3i4Ontg+wDe7Dum8/QsfdNeGX5JqjVlj6YCkBcANA72L5fe3O4yC1vHeP48eM4evQop2FJEXQ6HV544QWUlZXBz89PdDmkQEajEWFhYQx15HTMMnCsFDDs2YEtPy3FHc+/hUkPPQkASLz1Tvx1VE98ufBpLPwho95rPPHRcvQcMvKqx2J79cd7f7kLm39YglHT76t5/LXv02u9P6J9Ryx+7Ukc2bsDnfsNBmDp2h0rBXoGAWqlzBFfg1OxjSBJEtRqNUaOHCm6FCLodDqUl5dj3bp1okshheLGCXJWF6uAahnYtnI51BoNRs98oOY5Lx8fJE+bDcPurTiXc7Lea1wb6gBg0Lg/AQBOGw/dsIbwdh0AoNbUbbUMXFTwdCyDXSPo9Xr069cPISEhokshQufOndGxY0dOxVK9rGfYETmb81WWfx87uAdRsZ3hF9jiqufj4gcCALIP7m3UdYvO5gIAAkPDaj1nqq7GhcJzKMzNwd6Na/H1Wy/ANyCw5rOuqk/Bu2MZ7BpIlmWsW7eOx5yQYqhUKuh0OqSlpYFLZelasizj999/Z7Ajp3S+0rKe7XzeGQSH175rSsjlxwrzchp13R/efxNqjQZDtFNqPXd03y7c26cVHhjQBq/NGgtZlvHMZz8hMOTqpQwqAEUMds7v4MGDyMvL4/o6UhStVotTp05h//79okshhSkoKEBRURGDHTml4irLerbK8kvw9PKu9byXtw9w+fmG2vy/VEhLP8XNDzyByJjaSxTaduqOl1J/wdP/+QGT5jwNHz9/lJfWPkRPBlBU1eCPdThunmggSZLg7e2NYcOGiS6FqEZCQgICAgKQlpaG3r17iy6HFIRHnZAzqzJb/u3l44uqyopaz1dWlNc83xCZ2zfjg6dmIz5xLGY8/Xqdr/ELbIHeIyyzcgPHTsLm/6Vi0exJWLTqV3To3qfO+pSIHbsG0uv1GDp0KHx9G/aHiMgRvL29MXr0aK6zo1oMBgMAyxFNRM7GmptCIiJRlH+m1vPnLz8WGhF1w2tlZ/6GN2dPRLsuPfHER8uh8WhYT2vQ+MkAgC0/La23PiVisGuA6upqbNy4kevrSJF0Oh22bt2Kc+fOiS6FFMRgMKBt27Y8CoeckjWcdOgej5wsA8ouXn2jVuOe7Zbne8Rf9zq52Ufx2h3jENQyHPMWr4Svf0CDa6iqrIDZbEbZhdq3m1ByeFJybYqxc+dOXLx4kevrSJEmTJgAWZaxevVq0aWQgnBHLDkzz8vpZLB2CswmE35Z8nHNc1UVFVj/zefo1HcQwqLaAQDOnj6B00cOX3WN8/m5eHXmGKhVarzw1RoEtWxV52eVFhehuqr2ojnp6/8AAGJ731RvfUrENXYNoNfr0aJFC/Tv3190KUS1tG7dGjfddBPS0tIwa9Ys0eWQQhgMBgwdOlR0GURNEuQJFFYCnfsOwhDdVKS++RwuFOSjdYc4bFj+X5w9lY2H3/q05vXvPn4nMrdtxPKTf5wQ8Pod45B3IguT5jyNwzvTcXjnH4cQB4VFoE/CaADAwa0b8Nn8uRg8YQoiYzqhuqoSh3ZsxvZV36Nj75uQMPnqcVUFINjTvl9/czDYNYAkSRg5ciQ8GjgvT+RoWq0W//rXv1BVVQVPTwWPOOQQZrMZR44cwd133y26FKImCfECskot//3YPxdjaZsXsfH7L1FafB7tu/bGc5+nofvghOteIzvzNwDAjx8sqvVc98GJNcEuumsv9BiahJ1rf7Ss3ZNlRLTviCmPv4RJDz0FTy+vq94rAwj2qnVJxeC9Ym+grKwMISEh+Pvf/47HHntMdDlEddq1axcGDBiADRs2IDExUXQ5JNipU6fQrl07/Pzzz9DpdKLLIWq04kpAny+6ivqNirB0FZVIwbPEypCeno7KykquryNF69evHyIiIpCWlia6FFIA645YrrEjZyPLMn777Te8/uKzuFRyUXQ5dfJQAYEKnsBjsLsBvV6PyMhIdOvWTXQpRPVSq9XQarU89oQAWIKdRqNBTEyM6FKIGuTYsWNYuHAhevbsifj4eHz+2ac4e3A7oLBJRRWAGH9ArRJdSf0Y7G5AkiQkJydDpVLw7yIRLOvsDh06hKysLNGlkGAGgwGxsbFcb0mKdvbsWfz73//GsGHDEBsbi9dffx3x8fFYsWIFcnJycP+kUYDC/u6VAcQ2/MQUIRjsrqOwsBB79uzh+XXkFEaPHg1PT0927QhGoxGdOtW+ZRKRaCUlJViyZAm0Wi0iIyPx+OOPIyQkBEuWLEF+fj6WLFmCCRMmwNPTEwEeQLi3pUumBCpY6glQ8DQswGB3XevXr4csy1xfR04hMDAQiYmJXGdHPMOOFKWqqgorVqzAjBkzEBERgVmzZqG4uBjvvvsucnJykJaWhhkzZsDf37/We3sEWbpkSiDDUo/SKTx3iqXX69GpUye0a9dOdClEDaLT6fD000+jpKQEAQEKny8gu6iqqkJWVhaDHQllNpuRkZGB1NRUfPPNNygoKECPHj3wwgsvYPr06ejQoUODrhPqBXQOAAwl9q23IToHWupROnbsrkOSJHbryKlotVpUVlZCr9eLLoUEyc7ORnV1NYMdCXHgwAHMmzcPsbGxGDFiBNLS0jB79mz89ttv2L9/P5577rkGhzqr7kGAv0bclKwKlunX7i0EFdBI7NjV4+TJkzAajXjjjTdEl0LUYHFxcejSpQtWrFiBW265RXQ5JACPOiFHO3HiBL7++mukpqZi3759CAkJwdSpUzFz5kwMHz4canXzekgaFTCoJbAhX8y0rArAwFBLHc6Awa4ekiRBpVIhKSlJdClEjaLT6ZCamgpZlrmb2w0ZjUb4+PigTZs2okshF1ZQUIDly5djyZIl2Lx5M3x8fDBp0iS8+uqrGDduHLy8bDtnGeIFDA0DtpxzbLhTARgWZvl8Z8Gp2Hro9Xr07dsXoaGhokshahStVoszZ85gz549okshAQwGAzp16tTsLgnRtcrKyrBs2TJMnDgRkZGRePjhh+Hn54fFixcjPz8fS5cuxcSJE20e6qwifCwhSw3HTMuqAQwPA8J9HPBhNsTv/DrIsgxJknjMCTml4cOHo0WLFtwd66a4I5Zsqbq6GqtXr8add96JiIgITJs2Dfn5+fjHP/6BnJwcrF69GnfccQcCAwMdUk+EDzAyHPDT2PdzAjwsn+NsoQ5gsKvToUOHkJuby40T5JQ8PT0xduxYnmfnphjsqLlkWca2bdvw2GOPISoqCuPHj8eOHTvw9NNP48iRIzXPRURECKkvxAsY3dqyWxawXffOep3OgZZ7wTrT9OuVuMauDpIkwcvLC8OHDxddClGT6HQ63HXXXcjLyxM2+JLjlZWV4eTJkwx21CSHDx/GkiVLkJqaiqysLERFReHOO+/EjBkz0LdvX0Wt2dWogF7BQBtf4OAFIL/CEsyasv7O+r5W3pZz6pzhSJPrYbCrg16vx5AhQ+Dn5ye6FKImGT9+PFQqFVatWoW7775bdDnkIEePHgUA3nWCGuz06dNYunQplixZgj179iAoKAhTpkzBJ598gsTERGg0dp7zbKZQb2BEK6CkGsgqAY6VAtWX0119Qe/Kxz1Ulnu/xgYo/44SDeUiX4btVFdXY8OGDXjqqadEl0LUZK1atcKgQYOQlpbGYOdGeNQJNURRURGWL1+O1NRUbNiwAV5eXtDpdHjxxRcxfvx4+Pg438KyAA+gdzDQMwi4WA2crwSKKoGiKqDKDJhhWXvmqQaCPYFgL8tUa6AHoFZOI9ImGOyusXv3bly4cIHr68jpabVaLFq0CJWVlXbbpUbKYjAYEBwcjLCwMNGlkMKUl5cjLS0NqampWLFiBaqqqpCcnIxPP/0UkydPRlCQE9wrqwHUKiDI0/IPat+hzC1w88Q1JElCYGAgBgwYILoUombR6XS4ePEiNm/eLLoUchDrxgklrYUicUwmE/R6Pe655x5ERERg6tSpOHnyJP72t7/h9OnTNc+5SqgjC3bsrqHX65GYmAgPD/6vIefWp08ftGnTBmlpaexAuwmj0chpWDcnyzJ27dqF1NRULF26FLm5uYiLi8Nf/vIXTJ8+HV26dBFdItkZO3ZXuHTpEjIyMnh+HbkElUoFrVbLY0/ciPVwYnI/RqMRL7/8Mrp27YqBAwfi66+/xu23347t27fDYDBgwYIFDHVugm2pK2zZsgUVFRXsbpDL0Gq1+Pjjj3m2mRs4f/48zp49y99nN5Kbm4ulS5ciNTUVO3fuRGBgICZPnoz33nsPSUlJnHlyU/xdv4Jer0dERAR69OghuhQim0hJSYG3tzdWrFjBv/BdnNFoBMAdsa7uwoUL+P7777FkyRKsW7cOGo0GWq0WTz31FHQ6HXx9fUWXSIIx2F1BkiQkJydz4TG5DH9/fyQlJSEtLQ1/+ctfRJdDdmQ96oRTscqVk5OD5cuXw2w2Y8yYMejevXuD3ldRUYFVq1ZhyZIl+Pnnn1FZWYnExER8+OGHmDJlCkJCQuxcOTkTrrG77Pz589i9ezfX15HL0el02LRpEy5cuCC6FLIjo9GIyMhIh92zkxquuLgYDz74IHr06IGvv/4aK1asQFJSElauXFnve8xmM9avX4/7778frVu3xp/+9CccOXIEr732Gk6cOFHzHEMdXYvB7rINGzZAlmWuryOXo9VqUV1djbVr14ouheyIGyeUR5Yt9zf45ZdfsH79euj1emzduhXff/89unTpgtWrV6OioqLW+0wmE7p164bk5GRIkoRHHnkEBw8exJ49e/Dkk0+ibdu2jv5SyIlwKvYyvV6Pjh07on379qJLIbKpDh06oEePHlixYgWmTJkiuhyyE4PBgH79+okuw23t3r0bH374IXJzczFlyhRMnTq15raU//vf/9C9e3d06NABAGq6qqGhofD29q51LY1Gg2eeeQbdunXD4MGDuTyIGoUdu8skSWK3jlyWVqvFypUrYTabRZdCdiDLMnc+C7Rt2zbceeedKCwsRPfu3TFnzhw8/vjjyMrKAgD06tULBw8exEcffYSMjAzMmDEDJSUlSExMrPN6sizj3nvvxZAhQxjqqNEY7GC5CfLvv//O9XXksnQ6HfLz87Fr1y7RpZAd5ObmoqSkhMFOkIULF6Jt27b47rvv8Oabb2LZsmXYvXs3PvjgAwDA/fffj3feeQdbt25FcnIySkpKMHz4cNx888149tlna61/ZZij5mCwg6VbBwBJSUmCKyGyjyFDhiAkJARpaWmiSyE74FEn9lNeXo6CgoJ6n7eG6oSEhJrHRo8ejZtvvrlmB2zLli3Rp08fHD9+HF9++SV++uknvPPOO/joo4+wZs0afl+STTHYwbK+Lj4+njfOJpfl4eGBcePG8S4ULspgMECtViM2NlZ0KS5j06ZNGDJkCCIjIzFt2jS89dZbdb4uNDQUOTk58PHxQXV1NQDAx8cHCQkJKC8vr/me+/LLLxESEoJJkybVvDc+Ph5msxmlpaX2/4LIbbh9sJNlmevryC3odDr8+uuvyMnJEV0K2ZjBYED79u3rXIhPjXf27FnMnz8f/fv3x+rVqzFixAg888wzePfdd2EymWpeZzab4eXlhdatW2PXrl0oKyureS4mJgY9e/bE6tWrAQDt2rXDzp07kZmZWfOaXbt2IT8/H0OGDHHcF0cuz+2D3e+//46cnByuryOXN27cOKjV6uuenUXOiRsnbCsjIwN79+7FI488gkGDBuGll17CX/7yF6SmpiIjIwOAJdRZjzOZOnUqNm3ahOPHj9dco3Xr1ggODq4Je7fffjtiY2MxefJkzJ07F4mJiXj22Wfx1FNPoWfPno7/IslluX2wkyQJnp6eGDFihOhSiOwqNDQUQ4cO5XoeF8RgZ1vbt29Hv379EB4eXvPY9OnT4efnh++//77mMY1GAwCYMWMGzGbzVUsdfH19sWfPnprfF41Gg59++glPPfUUzp8/j3HjxmHHjh3461//6qCvityF2wc7vV6PwYMHw9/fX3QpRHan1Wqh1+tRXl4uuhSyEZPJhKNHjzLY2VCnTp2QmZmJysrKmsd69OiB7t27Y+fOnZBlGWq15a9PWZYREhKCO++8E19++SXefvttlJSU4LvvvoOXlxcGDhxY87rY2FjMmTMHX375JZ577jm0a9dOyNdHrs2tg53JZMKGDRs4DUtuQ6fTobS0FBs3bhRdCtnIiRMnUFlZybtO2NDIkSORn59fs9sYsHTg4uLiYDKZcODAgZrHL126BACYN28ebr31Vnz66afo0aMH7rzzTtx2220YOXIkAB5hQo7j1sHu119/RVFRETdOkNvo0aMHoqOjOR3rQgwGAwAedWJLMTEx6Nq1K5YvX37VLb+ioqJQWFgIb29vnDt3Dg899BDef/99AEBQUBBeeeUV/O9//8Onn36KixcvYsGCBTXTtUSO4tbBTpIkBAQE1LTKiVydSqWCTqfDihUrahZ+k3MzGAzw8vJCdHS06FJcyoMPPogff/wRW7durXksKysLhYWF6Ny5M0JDQ7Fr1y78/vvvV03Zdu7cGaNGjaqZqiVyNLf+k6fX65GQkABPT0/RpRA5jFarxbFjx3Do0CHRpZANGAwGxMXFsTPUBOfOnav3uXvuuQf9+/fHrFmzsGTJEixevBhfffUVXn75ZZjNZqjVavz000/45JNP4OXl5cCqia7PbYNdeXk5tmzZwvV15HaSkpLg6+vLw4pdhNFo5DRsIxQWFuKTTz7ByJEj0b59+3o3EgUGBuL999/H9OnT8c477+D555/HLbfcgpkzZ9Z046KiohxZOlGDeIguQJSMjAyUl5dzfR25HV9fX6SkpGDFylV44M9P4XwVcL4SKK4CqsyAGZaf+DzVQJAnEOIFhHgCgZ6Amuu/FcdgMGDKlCmiy1C0S5cu4eeff0ZqaipWrlwJk8mElJQUvP/++9ftdLZu3RqLFi3ChQsXEBQU5MCKiZrObYOdJElo1aoVD4Ykt1NSDdz21GtAqw7Q51seUwGoa8VdYSWQdfluRx4qIMYfiA0AAtx25FCWiooKZGdns2NXh+rqaqxbtw5LlizB//73P1y8eBEDBgzAW2+9hdtvvx2tW7du0HVUKhVDHTkVtx2e9Xo9kpOTucCV3EZhBXDwApBfAfjF9AauOH6hvm0UVz5eLQNHSgBjCRDuDfQIAkK5tEioo0ePQpZlBrvLZFnGzp07sWTJEixbtgx5eXno1KkTnnjiCcyYMYNHwpBbcMtgV1RUhF27duH+++8XXQqR3ZlkILMYMJRYOnMArgp1jWENemcrgPX5QOcAoHsQoOEUrRA86sTi999/R2pqKlJTU3HkyBFERkZixowZmDFjBvr3788z5MituGWw27hxI8xmM9fXkcs7XwlsLwBKL9+33FYHnFivYygBcsqBgaGWtXjkWEajEQEBAYiIiBBdisPl5ORg2bJlWLJkCXbv3o0WLVrg1ltvxYcffoiRI0dylzC5LbcMdpIkISYmBjExMaJLIbKbvHIg45ztwlx9SquBDfnA0DAgwsfOH0ZXsd4j1l06UsXFxfjuu++QmpqKdevWwdPTE1qtFs899xwmTJgAX19f0SUSCeeWwU6v17NbRy4trxzY4oBQB1g+Q4bl84Yx3DmUNdi5svLycqxcuRJLlizBihUrUFlZiaSkJHzyySe49dZbERwcLLpEIkVxu50DOTk5OHToEM+vI5d1vtIxnbprybB87vnKG76UbMRVg53JZMK6deswe/ZstG7dGrfeeiuys7Px+uuv4+TJk5AkCbNnz2aoI6qD23Xs1q1bBwBITk4WXAmR7Zlky5o6UTcLMwPYUQiMiuCGCnu7cOECcnNzXSbYybKMX3/9FampqVi6dClycnIQGxuLuXPnYvr06ejWrZvoEomcgssEO7MMXKzCDQ9b/b2wHKMm3oqWYa1El0xkc5nFf2yUEKWkGsi8APTi0V/Ndr1xraLcE69+vxlh3Tshu9R5D5E+cuRIzY7W33//HeHh4bj99tsxc+ZMDBw40G3WDxLZikp28juBl1QDWSXAsVLLOVtA/YetqiDDLFsOnORhq+RqCiuA9WdFV/GHpHCec9dUjR3X5MsH2TjLuJaXl1ezo3XHjh0ICAjAn/70J8ycORMpKSnw8FBw8UQK57TB7srDVusb8G7E+j4etkquYPNZy/lySviGVgFo5Q2MYGO8UVx5XLtw4QJ++OEHLFmyBHq9HhqNBuPHj8eMGTNw8803w8/PT3SJRC7B6YLdtYet2qJ463V42Co5q5JqYE1u/c9XVVRg6T9ewqbvvkRp8XlEd+uN6U+9hj4Jo6973W2rvkfGT8twZN9OFOXnIiyqHfqn6DDlzy/CPyj4hnWNba3szpFSuOq4VllZiVWrViE1NRU//fQTysvLkZCQgJkzZ+LWW29Fy5YtHV8UkYtzqmB37WGr9hDgwcNWyfnsK7Lc7qu+b+Z/PjId21Yuh3b244iM6YT1336Bo7/txIJl69Ft4PB6r3tP7zCERERh4NhbENYmGicO78farz5ERHQsFq38Fd7XOTdMBSAuAOgd3JyvzPW52rhmNpuxefNmpKam4ttvv8X58+fRu3dvzJw5E9OnT0e7du3sXwSRG3OaYHflYav2LFh1+R8etkrOwiwDP+f8sRbrWsY9O/DcxEG44/m3MOmhJwEAleXl+OuonmgRFo6FP2TUe+0DWzeg55CRVz22YflivPeXu/DQok8wavp9163NQwXcHOV8C/odxVXGNVmWsW/fPixZsgRff/01Tp06hfbt29fc1qtnz562/1AiqpNTnGNnPWzVDPuvH5Jh+Zwt5yyfS6R0F6vqD3UAsG3lcqg1Goye+UDNY14+PkieNhuG3VtxLudkve+9NtQBwKBxfwIAnDYeumFt1TJwsfqGL3NLrjCuHTt2DAsXLkTPnj0RHx+Pzz77DBMnTkR6evpVzxGR4yh+9Yvow1ZHhnNalpTtfNX1nz92cA+iYjvDL7DFVY/HxQ8EAGQf3IuwqIZPjxWdtSzmCwwNa1h9lZajhugPzjyunT17Ft9++y2WLFmCjIwM+Pn54ZZbbsGiRYswZswYeHryN5tIJEUHOx62SnRj5yuvv+D+fN4ZBIdH1no85PJjhXk5jfq8H95/E2qNBkO0U274WhWAokoA/o36CJfmjONaSUkJfvzxR6SmpmLt2rWQZRljx47FkiVLMHHiRAQEBNi1ZiJqOEVPxVoPWxW5CNB62CpdX2lpKbKzs3H48GEUFBTU+zpZlrF371688cYbuOOOO/Dss88iKyur5jnrtT777DMkJCTA29sbo0aNwunTpx3ydTij4qrrf49Ull+Cp5d3rce9vH1qnm+ozf9LhbT0U9z8wBOIjOl0w9fLAIpu0FF0N84yrlVVVWHFihWYMWMGIiIiMGvWLBQXF+P//u//cObMmZrnGOqIlEWxwa6wwrL1XwkMF4FC3v+yXgaDAbNmzUJ8fDyGDh2K++67D3v27AHwR1izKi8vx4YNG5Ceno4DBw4gNTUVeXl5V722rKwM586dw8SJEzFz5kycOnXKsV+Qk6kyX/95Lx9fVFVW1Hq8sqK85vmGyNy+GR88NRvxiWMx4+nXbVafO1H6uGY2m7FlyxY8/PDDiIyMhE6nw2+//Ybnn38eWVlZSE9Px8MPP4xWrXhAIZFSKXYq9uAF253n1FwqAAeLedhqXYqLi/HSSy8hKysLmZmZKCsrw/333485c+YgPT291gnynp6eGD16NKZOnYr09HS88sorNc9Zbx0UFhaGOXPmIDAwEF9++SVWr14Ns9k90oHZbMalS5dQWlpa809ZWdl1f9156qPwDQmv95ohEZEozK3d8TyffwYAEBoRdcO6sjN/w5uzJ6Jdl5544qPl0DTizgDu8TvXMEod16w/ZKWmpuL48eNo27YtZs+ejRkzZqB37968rReRE1FksCuptpy8DjT9YNU5Qzrg7KnjdT7XukMc3ttsrPO5QzvS8eKtIwAAn/12Fi1CwyDDUk9JNQ9bvdZvv/2GPXv24M0330RUlCUgvPHGG5g5cyaWL1+OadOmwWw2Q622NIc9PDzQo0cPAECrVq1QXl6Oqqqr5+pUKhUCAwMBAIGBgaisrER1tTK2VsqyjPLy8joDVkNC2I3ec+lSw6ZFvb294e/vDz8/Pzw7etZ1g12H7vE4kLEeZRcvXLWBwrhnu+X5HvHX/azc7KN47Y5xCGoZjnmLV8LXv3FTb4qdFnAw67imhDENQM24NnKsFhvXrkRISAimTp2KmTNnYvjw4TXfs0TkXBQZU7KuOH39vb/eXetg1YV3Tbjxwarz/4XysqvnPM6eOo6v33oBfRLG1Pkes9mMT196DD5+/igvK73qOdXlunjY6tXOnz+PgoICxMfH1zzWqlUrdO7cGbt378a0adNqvcdkMkGj0cDLywsmk6lWsANQEwYDAgIaFexkWUZlZWWzA1Z9vy4rK2tQ99DDwwP+/v5X/ePn51fz3yEhIVf9+trn6/q19TE/P7+rOqEb8oGC6ywVGKydgp8++jt+WfJxzTl2VRUVWP/N5+jUd1DNjtizp0+g8lIZ2sR1rXnv+fxcvDpzDNQqNV74ag2CWja+be3JfADgj3FNKWMaAJiqqzF61oP46yMPYty4cfDy4hEARM5OccHOLFtufC3DcrDqlp+WXnWwauKtd+Kvo3riy4VPX/dg1YHjbqn12PL/ew0AMOJPM+t8zy9LPkZBzkmkTL8PKz79v6uek2Gpq2cQD1u9Unl5+VUdNsDSZfPz86tZO3ctayfAz88PZrMZlZW1U4l16sff3x/V1dV1hr8r6fV63HrrrSgtLYXJdOMj/NVq9XUDVURExA0D1vV+7cgjH4I8LWul6pve69x3EIbopiL1zedwoSAfrTvEYcPy/+LsqWw8/NanNa979/E7kbltI5af/ONKr98xDnknsjBpztM4vDMdh3em//G5YRE37DKpAATz9Iuacc2goDENADQeHuiZPBE6HiJN5DIUF+yuPGz1egerpr45D+dyTjbq/K30H1MRHh2DrjcNrf255wux9K0XcPsTr6C4IL/O91sPW3X1M7lMJlNNd8rarerSpUudP81bO2pXhjONRgMPD4+azpbJZKpzWsfX17feYGfV0GAXFxeHl156qcFdL29vb5dZNxTiBWTVbsZc5bF/LsbSNi9i4/eW6b/2XXvjuc/T0H1wwnXfl535GwDgxw8W1Xqu++DEGwY7GUAwm0A145rSxjTAfcY1InehuGB35WGrtjxYNevAHpwyHsKtjz1f5/NL//4iglu1xuhZD2L5/71af30KOGxVluWrFtjbaprR+t/l5bWPps/KykJMTEytx6Ojo1FRUYFTp04hMtJyLppGo0Fubi4GDRoEALW6V1d24wDUhLYrg9aVr6lvuvZKHTp0wBNPPNGg/3+uJqQBfx69fHxw5wtv4c4X3qr3Na98u6HWY1d275qKB3z/Ma4pcUwDlDGuEZFtKC/YXXHYqi0PVt38vyUA6p6yyD60D78s+Qjz/rsSGo2m3ms09LBVWZZRUVFhk8X19V2jIby8vK7bwWrZsmWDphX9/PxqQtu1IiMj0b17d3z77bcYMGAAAODIkSPYtWsX5s+fDwDYsWMHWrRoga5du171Xi8vL3h4eODSpUs14c3Hx3K2Wnl5Oc6fP4+8vDzIsoz9+/fDbDYjNDQUcXFxDfr63UWgp+WerNe7rZgoHiogUHGjjONZxzWljWkAD5EmcjWKG3KvPGzVVgerms1mbPlpKWJ69kXbTt1qPf/ZS3PRN2k84hPrXoBsJQPYmWnAm+/Nv2EIa8gCe41Gc90pw8jIyCYtrrf+2xHrvFq2bIm5c+fiscceQ4cOHdCqVSv8+9//xtChQ5GcnIwLFy7g7rvvxrBhw/DJJ58AsHT/pk+fjsrKSpw4cQJz5szBvHnzMHLkSHz55ZeQZRl6vR4TJ06s6dzNnj0b3t7emDNnDt5++227f13ORK0CYvyBIyXKOEbDSgVLXVy79ce4prQxDeAh0kSuRnHB7srDTG12sOq2jSjMPQ3dfX+p9dyWn5bBsDsDb+sPNOhaJqiRl5cHf39/hIWFoX379k1aXO/n5wcvLy+nX+elUqlw9913w2w24+2330ZxcTFGjx6Nt96yTPn5+fnhtttuQ6dOf9ylIDAwEGPGjEFoaCgiIyPh6ekJT09PtG/fvuaao0aNQm5uLvz8/ODr63vDroO7iw0AjAo5+NZKhqUu+mNcU+KYdmV9ROT8FBfsrhxfbHGwKmCZslCr1Rg+aXqt5758/SkM1k6Fh6cX8k9mAwDKLhQBAM7lnER1ZSVCW//xOTEd47Bu3bqGfTFu5N5778W9995b63EPDw8sWLDgqsdatWqFV1+9/pofHx+fmmlZurEADyDcGzhboYyunQpAK2+e+2hlHdeUOKZdWR8ROT/FDbtX7p1s7sGqgOW8rm2rvkP3ISNrDWaAZaBL/yEV6T+k1nru6fH90KF7H/x9zd466yNSkh5BwPr6Nz86lAxLPWRhHTeUOKZdWR8ROT/FBbsrDzNtzsGqVr+uW4nS4iKMuKXuc56e/uR/tR5L/2kpMn5ehsf+tRgtI9vWWx+RkoR6AZ0DlHEv0s6BlnrIwjpuKHFMu7I+InJ+igt2Vx622pyDVa02/7AEnt7eGDzh1jo/r65DP49l7gUA9E0aX3P7HYCHrZLydQ8CTl8CykxipmRVAPw9gO4tbvhSt2Id15Q2pgEc14hcjeKC3bWHrTb1YFUAKLt4Ab9KK9AvWQv/Fs2fF+Jhq6R0GhUwqKXlNmOigt3AUEsd9IcrxzUljWkAxzUiV6OSZVkJa61rFFcCeoWsE6rLqAge5EnKl1cObDnn2HCnAjA8DAjnnpdaOK4RkaMobmWF9bBVJeJhq+QsInyAYWGWb3BHfDupwVB3PRzXiMhRFBfsrIetKm0M5GGr5GwifICR4YCfnY8ADPCwfA5DXf04rhGRoygu2AGWQ00VNT8MHrZKzinECxjd2rJbFrBdsLBep3OgZRqP94O9MY5rROQIimzA87BVItvRqIBewUAbX+DgBSC/4o/7MTeW9X2tvC3n1PFIk4bjuEZEjqC4zRNWhZXKOWwVAJLC+ZcYuYaSaiCrBDhWClRf/u6vL+hd+bjH5enE2ACGgabiuEZE9qbYYAcA+4uUc9hqL56iTy7GLAMXq4HzlUBRpeVG8FVmy+2l1LAcWhvsaTkKI8TLssCea7Gaj+MaEdmTon/u5mGrRPajVlmOuAjyBOAvuhr3wXGNiOxJkZsnrKyHrYpqEvCwVSKyNY5rRGRPig52gGUKaGiY4wdBFSzngHG3HxHZGsc1IrIXRa+xu1JeOZBx+SR9exeshmXw47lcRGRPHNeIyNacJtgBlkXe2wuAUpP9PiPAwzJNwZ9oicgROK4RkS05VbADAJMMZBZbdpU19Syua1mv0znQsqCYa0+IyJE4rhGRrThdsLMqrLDdYavhPGyViBSA4xoRNZfTBjsrHrZKRK6G4xoRNZXTBzsrHrZKRK6G4xoRNZbLBDsiIiIid6f4c+yIiIiIqGEY7IiIiIhcBIMdERERkYtgsCMiIiJyEQx2RERERC6CwY6IiIjIRTDYEREREbkIBjsiIiIiF8FgR0REROQiGOyIiIiIXASDHREREZGLYLAjIiIichEMdkREREQugsGOiIiIyEUw2BERERG5CAY7IiIiIhfBYEdERETkIhjsiIiIiFwEgx0RERGRi2CwIyIiInIRDHZERERELoLBjoiIiMhFMNgRERERuQgGOyIiIiIXwWBHRERE5CIY7IiIiIhcBIMdERERkYv4f+uM4VDNjSoeAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
        "\n",
        "# interpret diagonal of matrix as node attributes\n",
        "node_labels = {n: A[n,n] for n in range(len(A))}\n",
        "np.fill_diagonal(A, np.zeros(len(A)))\n",
        "\n",
        "G1 = nx.Graph(A)\n",
        "pos1=nx.spring_layout(G1)\n",
        "nx.draw(G1, pos1, labels=node_labels, ax=ax1, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G1,'weight')\n",
        "nx.draw_networkx_edge_labels(G1,pos1,edge_labels=edge_labels, ax=ax1)\n",
        "\n",
        "# interpret diagonal of permuted matrix as node attributes\n",
        "node_labels = {n: A_perm[n,n] for n in range(len(A_perm))}\n",
        "np.fill_diagonal(A_perm, np.zeros(len(A)))\n",
        "\n",
        "G2 = nx.Graph(A_perm)\n",
        "pos2=nx.spring_layout(G2)\n",
        "nx.draw(G2, pos2, labels=node_labels, ax=ax2, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G2,'weight')\n",
        "nx.draw_networkx_edge_labels(G2,pos2,edge_labels=edge_labels, ax=ax2)\n",
        "\n",
        "ax1.set_xlim([1.2*x for x in ax1.get_xlim()])\n",
        "ax2.set_xlim([1.2*x for x in ax2.get_xlim()])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "eUhWZ9_3jAmi"
      },
      "outputs": [],
      "source": [
        "import pennylane as qml\n",
        "\n",
        "def perm_equivariant_embedding(A, betas, gammas):\n",
        "    \"\"\"\n",
        "    Ansatz to embedd a graph with node and edge weights into a quantum state.\n",
        "\n",
        "    The adjacency matrix A contains the edge weights on the off-diagonal,\n",
        "    as well as the node attributes on the diagonal.\n",
        "\n",
        "    The embedding contains trainable weights 'betas' and 'gammas'.\n",
        "    \"\"\"\n",
        "    n_nodes = len(A)\n",
        "    n_layers = len(betas) # infer the number of layers from the parameters\n",
        "\n",
        "    # initialise in the plus state\n",
        "    for i in range(n_nodes):\n",
        "        qml.Hadamard(i)\n",
        "\n",
        "    for l in range(n_layers):\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            for j in range(i):\n",
        "            \t# factor of 2 due to definition of gate\n",
        "                qml.IsingZZ(2*gammas[l]*A[i,j], wires=[i,j])\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            qml.RX(A[i,i]*betas[l], wires=i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glOVsqRvjAmi"
      },
      "source": [
        "We can use this ansatz in a circuit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "e62af4a2-d500-4c14-a559-b680d4faaa79"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"lightning.kokkos\", wires=n_qubits)\n",
        "\n",
        "@qml.qnode(dev)\n",
        "def eqc(adjacency_matrix, observable, trainable_betas, trainable_gammas):\n",
        "    \"\"\"Circuit that uses the permutation equivariant embedding\"\"\"\n",
        "\n",
        "    perm_equivariant_embedding(adjacency_matrix, trainable_betas, trainable_gammas)\n",
        "    return qml.expval(observable)\n",
        "\n",
        "\n",
        "A = create_data_point(n_qubits)\n",
        "betas = np.random.rand(n_layers)\n",
        "gammas = np.random.rand(n_layers)\n",
        "observable = qml.PauliX(0) @ qml.PauliX(1) @ qml.PauliX(3)\n",
        "\n",
        "qml.draw_mpl(eqc, decimals=2)(A, observable, betas, gammas)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TIHRQVnDjAmi"
      },
      "source": [
        "Validating the equivariance\n",
        "===========================\n",
        "\n",
        "Let\\'s now check if the circuit is really equivariant!\n",
        "\n",
        "This is the expectation value we get using the original adjacency matrix\n",
        "as an input:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "62041984-2142-4833-8585-3b1dab34ebd4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 9.169869450541076e-05\n"
          ]
        }
      ],
      "source": [
        "result_A = eqc(A, observable, betas, gammas)\n",
        "print(\"Model output for A:\", result_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ncmkAwH-jAmj"
      },
      "source": [
        "If we permute the adjacency matrix, this is what we get:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "acafdf4a-216b-4c5c-ce83-43854a9e7d6b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.21804915149050919\n"
          ]
        }
      ],
      "source": [
        "perm = [2, 3, 0, 1, 4]\n",
        "A_perm = permute(A, perm)\n",
        "result_Aperm = eqc(A_perm, observable, betas, gammas)\n",
        "print(\"Model output for permutation of A: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZOIqQmysjAmj"
      },
      "source": [
        "Why are the two values different? Well, we constructed an *equivariant*\n",
        "ansatz, not an *invariant* one! Remember, an *invariant* ansatz means\n",
        "that embedding a permutation of the adjacency matrix leads to the same\n",
        "state as an embedding of the original matrix. An *equivariant* ansatz\n",
        "embeds the permuted adjacency matrix into a state where the qubits are\n",
        "permuted as well.\n",
        "\n",
        "As a result, the final state before measurement is only the same if we\n",
        "permute the qubits in the same manner that we permute the input\n",
        "adjacency matrix. We could insert a permutation operator\n",
        "`qml.Permute(perm)` to achieve this, or we simply permute the wires of\n",
        "the observables!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "MgYVIMP6jAmj"
      },
      "outputs": [],
      "source": [
        "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pb21hBrLjAmj"
      },
      "source": [
        "Now everything should work out!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "c4d85d8c-cd3f-4d41-d9cf-aa359daea0d2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.0619817888967175\n"
          ]
        }
      ],
      "source": [
        "result_Aperm = eqc(A_perm, observable_perm, betas, gammas)\n",
        "print(\"Model output for permutation of A, and with permuted observable: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0wblJk9mjAmj"
      },
      "source": [
        "Et voilà!\n",
        "\n",
        "Conclusion\n",
        "==========\n",
        "\n",
        "Equivariant graph embeddings can be combined with other equivariant\n",
        "parts of a quantum machine learning pipeline (like measurements and the\n",
        "cost function). [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf), for example, use such a\n",
        "pipeline as part of a reinforcement learning scheme that finds heuristic\n",
        "solutions for the traveling salesman problem. Their simulations compare\n",
        "a fully equivariant model to circuits that break permutation\n",
        "equivariance and show that it performs better, confirming that if we\n",
        "know about structure in our data, we should try to use this knowledge in\n",
        "machine learning.\n",
        "\n",
        "References\n",
        "==========\n",
        "\n",
        "1.  Andrea Skolik, Michele Cattelan, Sheir Yarkoni,Thomas Baeck and\n",
        "    Vedran Dunjko (2022). Equivariant quantum circuits for learning on\n",
        "    weighted graphs.\n",
        "    [arXiv:2205.06109](https://arxiv.org/abs/2205.06109)\n",
        "2.  Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone,\n",
        "    Patrick J. Coles, Frédéric Sauvage, Martín Larocca and Marco Cerezo\n",
        "    (2022). Theory for Equivariant Quantum Neural Networks.\n",
        "    [arXiv:2210.08566](https://arxiv.org/abs/2210.08566)\n",
        "\n",
        "About the author\n",
        "================\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "seconds = time.time()\n",
        "print(\"Time in seconds since end of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "HFTIJBPqph2f",
        "outputId": "a71fc2b5-aa17-409c-8e02-1c4bed2893d5"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701146914.607299\n",
            "Tue Nov 28 04:48:34 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      },
      "file_extension": ".py",
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "machine_shape": "hm"
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    "accelerator": "TPU"
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}