LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qulacs.simulator 25 qubit V100 320.99s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qulacs.simulator 25 qubit V100 320.99s (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e3803a22-5a3e-41b2-b0d4-51765bd8c6fc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695112250.5139697\n",
            "Tue Sep 19 08:30:50 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "# !pip install pennylane custatevec-cu11 pennylane-lightning-gpu\n",
        "# !pip install pennylane pennylane-qulacs --upgrade\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": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "3004a7f9-0a50-4164-fc30-07d907ecfe78"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.5  0.47 0.38]\n",
            " [0.47 0.22 0.23]\n",
            " [0.38 0.23 0.93]]\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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "f82e66b3-3aad-4c68-94dd-85c3201b7094"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.22 0.23 0.47]\n",
            " [0.23 0.93 0.38]\n",
            " [0.47 0.38 0.5 ]]\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": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "b24f9884-9641-4200-d37c-6949acf8b19c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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mhgwZws8//8zRo0ezOJ3IzamwE3EiP//8Mw8//DDt27dn3rx5WX7nXUREBIBG7MQt2Ww2LBbLHc2vu1yfPn0ICAhg4sSJWZRM5NapsBNxErNnz6Zbt248/PDDzJ49Gx+frO+AarVaARV24p727t3L+fPn77qwCwgIoH///nz11VdcvHgxi9KJ3BoVdiJOYPr06fTs2ZPHHnuM6dOn4+3tnS37iYiIIG/evAQFBWXL+4s4MrPZjLe3N/Xr17/r9xo8eDCxsbFMnz49C5KJ3DoVdiIObsqUKfTp04cnnniCqVOn4uWVfcs8ZNw4YTKp87C4H4vFQp06dbJk3mrp0qXp1KmTWp9IjlNhJ+LAvvjiC/r378+zzz7L119/jaenZ7buTz3sxF3Z7XYsFssdtzm5lrCwMPbs2cOaNWuy7D1FbkaFnYiDGjduHAMHDiQsLIyJEyfi4ZH9p6t62Im72rdvH5GRkXc9v+5yTZs2pXr16mp9IjlKhZ2IA/roo48IDw/n5Zdf5rPPPsuRS6M2m02Fnbgts9mMl5cXDRo0yLL3NJlMhIWFsWjRIg4dOpRl7ytyIyrsRBzMu+++yyuvvMIbb7zBBx98kGPz3U6fPk1SUpIuxYpbslgs1K5dO8uafWfo1asX+fPn5/PPP8/S9xW5HhV2Ig7CbrczYsQI3njjDUaNGsX//ve/HL2JQT3sxF3Z7XbMZnOWzq/LkCtXLp555hmmTJlCfHx8lr+/yH+psBNxAHa7neHDhzNq1ChGjx7Nm2++meMZMnrYacRO3M3+/fs5e/Zsls6vu9zAgQNJSEhg2rRp2fL+IpdTYSdiMLvdztChQ/nggw8YM2YMr776qiE5IiIiKFCgAHny5DFk/yJGsVgseHp60rBhw2x5/+LFi9O1a1fGjx+PzWbLln2IZFBhJ2Igm83G4MGD+eyzz5gwYQIvvPCCYVkyetiJuBuz2UytWrUICAjItn2EhYVx4MABVqxYkW37EAEVdiKGsdlsPPvss0yaNInJkyfz3HPPGZpHPezEHWVH/7pradCgAffffz9jx47N1v2IqLATMUBaWhpPPvkkU6ZMYerUqTz11FNGR1KrE3FLBw8e5NSpU9k2vy6DyWQiPDycFStW8Ndff2XrvsS9qbATyWGpqan07t2bGTNmMGPGDPr06WN0JNLS0jh69KhG7MTtZPf8uss9+uijhIaGMn78+Gzfl7gvFXYiOSg5OZkePXowd+5cZs+eTY8ePYyOBMCJEydITU3ViJ24HbPZzH333UfevHmzfV++vr4MGDCAadOmERMTk+37E/ekwk4khyQlJfHII4+waNEifvrpJ7p27Wp0pEwZrU5U2Ik7yan5dZcbMGAAycnJTJkyJcf2Ke5FhZ1IDrh06RIPPfQQK1euZMGCBXTq1MnoSFfIKOxKlixpcBKRnHPo0CFOnDiR7fPrLleoUCG6d+/O+PHjSUtLy7H9ivtQYSeSzRISEujYsSMWi4UlS5bQtm1boyNdJSIigkKFCpErVy6jo4jkGIvFgoeHB40aNcrR/YaFhREREcHixYtzdL/iHlTYiWSj+Ph42rVrx+bNm1m2bBktWrQwOtI1qYeduCOz2UzNmjUJDAzM0f3Wrl2b+vXrq/WJZAsVdiLZJDY2ljZt2rB9+3ZWrlyZo5d7bldERITuiBW3YsT8usuFh4ezdu1adu3aZcj+xXWpsBPJBtHR0bRq1Yp9+/axatUqGjRoYHSkG9KInbgbq9XKsWPHDPvC9fDDD1O0aFHGjRtnyP7FdamwE8li586do0WLFhw6dIg1a9ZQu3ZtoyPdUHJyMsePH9eInbgVi8WCyWTigQceMGT/3t7ePPfcc0yfPp3z588bkkFckwo7kSx09uxZmjdvzvHjxzPn7zi6Y8eOYbfbNWInbsVsNlOjRg2CgoIMy/D0009jt9uZPHmyYRnE9aiwE8kip06domnTpkRGRmI2m6levbrRkW6JetiJOzJyfl2G4OBgevXqxYQJE0hJSTE0i7gOFXYiWeD48eM0adKEuLg4LBYLVapUMTrSLbNarZhMJooXL250FJEcERERwZEjRxzihqawsDCOHz/O/PnzjY4iLkKFnchdioiIoHHjxiQnJ7Nu3ToqVKhgdKTbEhERQbFixfDx8TE6ikiOMHp+3eXuvfdemjRpotYnkmVU2InchUOHDtGkSRNMJhMWi4UyZcoYHem2Wa1W3TghbsVsNnPPPfeQP39+o6MA6a1PNm7cyB9//GF0FHEBKuxE7tD+/ftp0qQJfn5+rFu3zmmX44qIiND8OnErjjC/7nKdOnWiZMmSan0iWUKFncgd2Lt3L02aNCEwMBCLxULRokWNjnTH1MNO3MnRo0exWq0OMb8ug6enJ4MHD2bWrFmcOXPG6Dji5FTYidymnTt30rRpU0JCQli7di2FChUyOtIdu3TpEqdPn9alWHEbFosFgMaNGxuc5Er9+/fHy8uLL7/80ugo4uRU2Inchj///JNmzZpRvHhx1q5dS0hIiNGR7sqRI0cAtToR95HRiqhAgQJGR7lCvnz56NOnD5MmTSI5OdnoOOLEVNiJ3KItW7bQvHlzypUrx+rVqx3ug+FOZPSw04iduAtHm193uSFDhnD69GnmzJljdBRxYirsRG7Bhg0baNWqFdWqVeOXX34xtFt9VoqIiMDLy4tixYoZHUUk2x0/fjzzTnZHVKVKFVq1asXYsWOx2+1GxxEnpcJO5CbMZjNt27bl/vvvZ/ny5eTNm9foSFnGarVSokQJPD09jY4iku0cdX7d5cLDw/n999/ZvHmz0VHESamwE7mBVatW0a5dO+rXr8+SJUsICAgwOlKWUg87cSdms5mqVasSHBxsdJTrevDBBylXrpxan8gdU2Ench1Lly6lQ4cONG3alEWLFpE7d26jI2U59bATd+LI8+syeHh4MGTIEObOncuJEyeMjiNOSIWdyDUsWLCAhx56iLZt2/Lzzz/j5+dndKRsoR524i5OnjzJwYMHHXZ+3eX69u1Lrly5mDRpktFRxAmpsBP5jzlz5vDII4/QuXNn5syZg6+vr9GRskV8fDznz5/XpVhxCxnz65yhsMubNy9PPvkkX375JYmJiUbHESejwk7kMjNnzqRHjx48+uij/PDDD3h7exsdKdtEREQA6mEn7sFsNlO5cmWn6T05ZMgQzp8/z8yZM42OIk5GhZ3IP6ZOnUrv3r3p06cP3333HV5eXkZHylbqYSfuxGKxOMVoXYZy5crRrl07xo0bp9YncltU2IkAX331FU8++SRPP/0033zzjVu0/4iIiMDX19epl0QTuRWnTp1i//79Dn/jxH+Fh4ezY8cO1q1bZ3QUcSIq7MTtTZgwgWeffZbBgwfzxRdf4OHhHqdFRqsTd/l5xX1lFEbONGIH0LJlSypXrqzWJ3Jb9Btd3NqYMWMYPHgwQ4cOZdy4cZhMJqMj5Rj1sBN3YTabqVixotONTptMJsLCwpg/f37mnFiRm1FhJ27r/fff58UXX2T48OF8/PHHblXUgXrYiftwtvl1l3v88cfJmzcvEydONDqKOAkVduJ27HY7I0eO5LXXXuPtt9/m3Xffdbuizm63a8RO3MKZM2fYt2+f082vy+Dv789TTz3F5MmTSUhIMDqOOAEVduJW7HY7r7/+Om+//TbvvfceI0aMcLuiDiAmJoa4uDiN2InLc9b5dZcbNGgQcXFxfP/990ZHESegwk7cht1u56WXXuL999/nk08+Yfjw4UZHMkxGqxMVduLqLBYL5cuXp0iRIkZHuWOlSpWic+fOan0it0SFnbgFu91OWFgYY8aMYfz48QwdOtToSIZSDztxF2az2alH6zKEh4ezb98+Vq1aZXQUcXAq7MTl2Ww2BgwYwOeff86XX37J4MGDjY5kuIiICPz9/SlYsKDRUUSyTWRkJHv27HHa+XWXa9y4Mffee69an8hNqbATl5aWlkb//v2ZPHkyU6ZM4ZlnnjE6kkPIuHHCHecXivtwhfl1GTJanyxZsoS///7b6DjiwFTYictKTU3NXB7s+++/58knnzQ6ksNQqxNxBxaLhbJly1KsWDGjo2SJnj17UqBAAcaPH290FHFgKuzEJaWkpNCzZ09+/PFHZs2aRa9evYyO5FCsVqsKO3F5rjK/LoOfnx/PPPMM3377LXFxcUbHEQelwk5cTlJSEt26dWP+/PnMnTuXbt26GR3JodjtdiIiInTjhLi08+fPs2vXLpeYX3e55557jkuXLjF16lSjo4iDUmEnLiUxMZGHH36Y5cuXM3/+fDp37mx0JIcTGRnJxYsXNWInLs2V5tddrmjRojzyyCOMHz8em81mdBxxQCrsxGVcvHiRTp06sWbNGhYtWkS7du2MjuSQ1MNO3IHFYqF06dKUKFHC6ChZLiwsjL///ptly5YZHUUckAo7cQkXLlygffv2bNy4kaVLl9KqVSujIzmsjMXEdSlWXJmrza+7XL169ahduzZjx441Ooo4IBV24vTi4uJo27Ytf/zxBytWrKBZs2ZGR3JoVquVoKAggoKCjI4iki2ioqLYuXOny82vy5DR+uSXX35h7969RscRB6PCTpxaTEwMrVu3Zvfu3fzyyy80atTI6EgOL6OHnYirWr9+PXa73WVH7AAeffRRChUqpNYnchUVduK07HY727Zt49ChQ6xevZq6desaHckpqIeduDqLxULJkiVd+guMj48PAwYM4LvvviM6OtroOOJAVNiJ0zKZTDRp0oS9e/dy//33Gx3HaaiHnbg6V55fd7kBAwaQmprKN998Y3QUcSAq7MRh2Ww2UlNTb7iNh4cHwcHBOZTI+dlsNo4cOeLSIxni3mJiYti+fbvLzq+7XGhoKD169ODzzz8nLS3N6DjiIFTYiUN6+eWX6d27N82bN2fTpk1A+qVXuTunTp0iOTlZI3bistxhft3lwsLCOHLkCAsXLjQ6ijgIFXbiUJKSkqhbty7r1q2jSpUqeHp68sgjj5CYmKgF67NARg87jdiJq7JYLBQvXtxtvrzcf//9NGzYUK1PJJMKO3EYcXFxdO7cmeDgYMxmM2+88QYLFy7Ez8+Ps2fPGh3PJaiHnbi6jPl17vRFMCwsDIvFwo4dO4yOIg5AhZ04jEOHDlGhQgU++eQTcuXKBcDWrVvx8PDg3XffZciQIaxZs8bglM7NarUSHBxMQECA0VFEslxsbCzbtm1zi/l1l+vSpQvFihVj3LhxRkcRB6DCThxGzZo1GTx4MBUqVABg7dq1tGjRgqpVqxIaGsqWLVsYNmxY5pw7uX3qYSeubMOGDdhsNreZX5fB29ubQYMGMWPGDM6dO2d0HDGYCjsxVFJSEhcvXsz8c4UKFTCZTCQlJfHXX3/x2WefMX/+fEaNGsX69es5dOgQv//+u4GJnZt62Ikrs1gsFC1alLJlyxodJcc9/fTTmEwmvvrqK6OjiMFU2Ilh3n//fXr06EHdunUZM2YMJ06cyHzO19eXfv36ERYWhslkIi0tjZSUFEqVKoW/v7+BqZ2bRuzElbnj/LoMBQoUoHfv3kycOJGUlBSj44iBVNiJIR5//HG++eYb6tevT7NmzRgxYgRz5swByOzH5OPjk7m9p6cna9asISkpiapVqxqS2dmlpqZy7NgxjdiJS4qLi+PPP/90u/l1lwsLC+PEiRPMmzfP6ChiIC+jA4j7+eCDD9i/fz9Lly7NnE9XoEABPvvsMwYPHoyXV/phmfGt+/Dhw6xbt45BgwbxwQcfUL9+fcOyO7Pjx4+Tlpamwk5c0saNG0lLS3O7+XWXq169Os2aNWPs2LF0797d6DhiEI3YSY5KSEjg0KFDPProo5QtWzZzdK5Ro0b4+/tf1T09IiKCF198kVGjRjFlyhQGDx5sRGyXoB524sosFguFCxemfPnyRkcxVHh4OL/++qvmIrsxjdhJjvL39+fpp5+mZMmSeHp6Zq4m4ePjQ0xMDBcvXsTb2xsPj/TvHKVKleLFF18kJCQkc3RP7kxGD7uSJUsaG0QkG7jz/LrLdejQgdKlSzNu3Di+//57o+OIATRiJzmudu3ahISEYLPZMn8Jx8XF4eXlRa5cufDw8MBms2E2m7Hb7TRq1EhFXRawWq0UKVIEPz8/o6OIZKkLFy6wdetWt55fl8HT05PBgwcze/ZsTp06ZXQcMYAKOzGMh4dH5ohdWloahQsXxs/Pj5iYGO6//36+/vprrQ+bhSIiInQZVlyS5tddqV+/fvj4+PDll18aHUUMoMJOsk18fDxxcXFXPPbfQi3jz6dPnyZv3rwcOnSIWrVqkS9fPqZPn555SVbuntVq1Y0T4pIsFguhoaFUrFjR6CgOISgoiCeeeIJJkyaRlJRkdBzJYfrUlGwxaNAg2rVrR/Xq1XnttdfYuHEjkH6n6+XFXUbhduHCBX777Tfuv/9+6tevr6XDsoF62Imr0vy6qw0ZMoSzZ8/y448/Gh1FcpgKO8lyvXr1YvXq1Tz11FMMHDiQBQsW8NprrzF37lyAzIbD8O+I3YULF4iLi2PEiBGa8JsNkpKSOHnypEbsxOUkJCTw+++/a37df1SqVIk2bdowduxYTWlxM7orVrLUsWPH2LdvH19++WXmfJemTZsyceJERo0aRYECBWjWrBmenp4AnDlzhkKFCtGvXz/uv/9+2rdvb2R8l3X06FHsdrsKO3E5mzZtIjU1VfPrriE8PJx27dqxadMmGjZsaHQcySEasZMsd+zYMU6ePJn553r16jFo0CDKly/PBx98wJEjRwB44403GDx4MBERERQrVkxFXTZSDztxVRaLheDgYCpXrmx0FIfTpk0bKlSowLhx44yOIjlIhZ1kKV9fX8qVK8euXbu4dOlS5uN169alR48eHDt2jC1btgDg5eVFfHw8efLkMSqu24iIiMDDw4PixYsbHUUkS2l+3fV5eHgwZMgQfvrpJ44dO2Z0HMkhKuwkS4WEhNCzZ08+/vhjzGbzFc9169aNwMBAfvrpJwDefvttFi1aRIECBQxI6l6sVivFihXD29vb6CgiWebixYv89ttvugx7A0888QT+/v5MmjTJ6CiSQ1TYSZYbMmQI3bt358knn2Tjxo2kpqZmPle5cmUKFy6c+WcfHx8jIrqdiIgIza8Tl/Prr7+SkpKiGyduIE+ePPTr14+vvvrqiqso4rpU2Em2mDp1KjVr1qRHjx58+eWX/Pnnn6xfv55FixZpFQkDqIeduCKLxUKBAgWoUqWK0VEc2uDBg4mKimLmzJlGR5EcYLLrPmjJRk8//TR//vknR48exd/fnx49ejB69GijY7md0NBQnnvuOUaMGGF0FJEs07hxY4KDgzOnd8j1derUiYiICHbs2KH5iC5O7U4kW02ePJlTp05x6tQpfH19qVq1qtGR3M7Fixc5e/asRuzEpVy6dIktW7bw0UcfGR3FKYSHh9O1a1esVitlypQxOo5kIxV2kmXsdvs1vwkWLlz4inl1krMiIiIAtToR17JlyxaSk5M1v+4WNW/ePPMLtrg2zbGTLJGWlsaMGTOMjiHXkFHYacROXInZbCZ//vxUq1bN6ChOwWQykStXLq2/7Qb0Nyx3LTU1lb59+/LEE0+wZ88eo+PIf1itVry9vSlSpIjRUUSyjMVioXHjxipUspCm3LsGnRFyV1JSUujduzc//PADM2fO1Bw6B2S1WilRokTmMm4izi4xMZFff/1V/euymG6qcA2aYyd3LDk5mR49erB48WJ+/PFHHn74YaMjyTWoh524mt9++42kpCTNr8sCJ06c4KuvvuLw4cMUKlSINm3a0Lx5c42EOjH9zckdSUxMpGvXrixZsoR58+apqHNgVqtVN06ISzGbzQQFBVG9enWjozit48eP89hjj1GqVClmzpyJl5cXy5cvZ+jQoWpJ5eRU2Mltu3TpEp07d2bVqlUsXLiQDh06GB1JbkAjduJqMubXaXrB7bHb7dhsNiZOnEilSpU4ePAgM2bMYOPGjXz55Zfs2rWLt99+mw8//FDz7ZyYCju5LQkJCbRv354NGzawZMkS2rRpY3QkuYG4uDiioqJU2InLSEpKYtOmTZpfdwdMJhMHDx7kq6++Ijw8nEWLFvHoo48SEhKSubxjtWrVKFiwIFu2bDE4rdwpzbGTWxYfH0/79u3Ztm0by5cv54EHHjA6ktyE1WoF1MNOXMfvv/9OYmKi5tfdoUWLFpGcnMzgwYMpXLjwVf1Hp06dCqSv6y3OSYWd3JLY2FgefPBB9uzZw8qVK6lfv77RkeQWqIeduBqz2UxgYCD33nuv0VGc0sGDB6ldu3Zm0/iMom7Hjh3MmDGDH374gbfeeovAwEAjY8pdUGEnNxUVFUWbNm34+++/Wb16NbVq1TI6ktwiq9WKn58foaGhRkcRyRIWi4UHHnhA8+vuUO/evWnfvj0dO3akXbt2bNiwga1bt7J+/XrOnj3LM888Q8+ePY2OKXdBhZ3c0Llz52jVqhXHjh1j7dq11KhRw+hIchsy7ohVfypxBcnJyWzcuJFRo0YZHcVpPfDAAzz99NOMHDmS7t27U7FiRfLkyUO5cuUYNmyY5i66ABV2cl1nzpyhRYsWREZGYjabtXSPE9IdseJKtm7dyqVLlzS/7i599NFH9O/fn8jISBISEihZsuQVzeVtNpv62DkxFXZyTSdPnqRFixbExsZisVioVKmS0ZHkDlitVho1amR0DJEsYTabyZMnj64c3CUPDw+qVKkCpC8J6eXlRVpaGgCenp4q6pyc/vbkKseOHaNJkyZcuHBBRZ0Ts9vtGrETl5Ixv87LS2MSdysxMZGXXnqJF154AVBB50r0tyhXiIiIoHHjxqSmprJu3TrKly9vdCS5Q1FRUcTHx6uwE5eQkpLCxo0bNQcsi/j5+XH06FHOnj3LqVOngOuvFatmxc5FX3sk099//03z5s3x8fFhzZo1lChRwuhIchfUw05cyR9//EFCQoLm12Whzz77jDx58pAnTx7S0tJYsmQJ33//Pe3atcPX15cmTZrg5eWlu+qdjAo7AeCvv/6iRYsW5MmTh9WrV1O0aFGjI8ldUg87cSVms5mAgADuu+8+o6O4jCJFigD/jsj98MMPLFiwgIYNGzJnzhzGjRuHv78/gYGBVK9enT59+lC2bFkjI8st0KVYYffu3TRt2pSgoCDMZrOKOhdhtVoJCAggf/78RkcRuWsWi4VGjRppfl02MJlMeHp68vTTT+Pt7U3Pnj3ZuHEja9asYfz48djtdsaMGcPgwYONjiq3QIWdm9uxYwfNmjWjUKFCmM1mChUqZHQkySIZN06oh504u9TUVDZs2KD5ddnIbrfTuHFjatWqxTvvvAPAvHnzeP/994mLi6NRo0a0aNGC1NRUg5PKzeirjxvbunUrrVu3pkyZMqxcuVIjOy7GarXqMqy4hD///JMLFy5ofl02MplMeHl50b9/f5566ilOnjzJyZMnCQwMpEOHDjz66KO6muMkVNi5qc2bN9OmTRuqVKnCsmXLCAoKMjqSZDGr1Urr1q2NjiFy18xmM/7+/tx///1GR3FZx44dY968eaxbtw5/f3927NjB6NGjadCgQea6suIcdCnWDW3YsIFWrVpxzz33sHLlShV1Lkg97MSVWCwWGjZsiLe3t9FRXNZvv/3G2LFj8fHxoWvXrhw6dIiuXbtSuHBh7HZ75g0Wixcv1lqyDk4jdm5m7dq1dOjQgbp167Jo0SL8/f2NjiTZ4MyZMyQmJqrViTi91NRU1q9fz7Bhw4yO4tIeeugh7HY77du3J1euXPTu3ZuUlJSrGheXLVuWWbNm8cEHH1C8eHEDE8v1aMTOjaxcuZJ27drRsGFDFi9erKLOhanVibiK7du3Ex8fr/l12czT05NHHnmEXLlyYbPZaNq0Kd7e3lcUdXa7ncqVK9O5c2deeeUVA9PKjaiwcxNLliyhY8eOtGjRgoULF5I7d26jI0k2UnNicRVms5lcuXJRq1Yto6O4hbS0NDw8PDLXjrXZbJmXYW02GwD/+9//+PHHHzl//rxhOeX6VNi5gZ9//pkuXbrQrl075s2bh5+fn9GRJJtZrVby5ctHYGCg0VFE7krG/DofHx+jo7gFT0/PK/7t4eGByWQiPj4eT09PLly4QGhoKPfeey8jR440Mqpch+bYubgff/yRnj170rVrV6ZPn67Jx25CN06IK0hLS2PdunW8/PLLRkdxG2lpacyYMYPTp09z/PhxfHx82LFjB56enkRHR3PkyBFKlSrF9u3biYuL45NPPtHnioNRYefCpk+fzhNPPEHPnj359ttv1bHdjaiHnbiCHTt2EBcXp/l1OcjT05PNmzfzww8/cN999xEbG0uVKlXw8/OjfPnyPPnkkyQkJDBq1Cjsdjvx8fHqgepg9Envor799lv69+9P3759mTx5cuawuriHiIgIOnfubHQMkbtiNpvx8/Ojdu3aRkdxK2PHjmXixIlERUVlFm1paWn6HHESmmPngr788kv69evHM888w9dff62T0c2kpaVx5MgRjdiJ07NYLDRo0ABfX1+jo7iVjKs7GUWdzWbD09PzihspMv4tjkeFnYsZP348AwYMYMiQIUyaNOmKW9XFPZw8eZKUlBTdEStOLWN+ndaHzXn/XV8643Mk40aKa20jjkOf+i7k448/JiwsjJdeeomxY8fqxHNT6mEnrmDXrl3ExMSosBO5TSrsXMS7777Lyy+/zOuvv86HH36oos6NqYeduAKz2Yyvry9169Y1OoqIU1Fh5+TsdjsjRozgjTfeYNSoUbzzzjsq6tyc1WolJCRETajFqVksFurVq6e+myK3SYWdE7Pb7bz22muMGjWK0aNH8+abbxodSRyAetiJs7PZbKxbt05tThyQbppwfCrsnJTdbufFF19k9OjRjBkzhldffdXoSOIgrFarLsOKU9u9ezdRUVGaX+dA7HY7KSkpnD592ugochMq7JyQzWZjyJAhfPrpp3z++ee88MILRkcSB6IRO3F2ZrMZHx8f6tWrZ3QUuUyLFi0ICwszOobchAo7J2Oz2Xj22WeZOHEiX331FYMGDTI6kjiQlJQUjh07psJOnJrFYqFu3brkypXL6CjyD5PJRI8ePfj55585evSo0XHkBlTYOZG0tDT69evHlClT+Pbbb3n66aeNjiQO5tixY9hsNl2KFael+XWOq0+fPgQEBDBx4kSjo8gNqLBzEqmpqTz++ONMnz49cw1Ykf9SDztxdnv37uXcuXOaX+eAAgIC6N+/P1999RUXL140Oo5chwo7J5CcnEyPHj2YM2cOs2fP5rHHHjM6kjgoq9WKyWSiRIkSRkcRuSMWiwVvb2/q169vdBS5hkGDBhETE8OMGTOMjiLXocLOwSUlJdGtWzcWLVrETz/9RNeuXY2OJA4sIiKCIkWKaG1NcVpms5k6deqoD6ODKlOmDJ06dWLs2LFqfeKgVNg5sEuXLtGlSxdWrFjB/Pnz6dSpk9GRxMFZrVZdhhWnZbfbsVgsml/n4MLDw9mzZw9r1qwxOopcgwo7B3Xx4kU6deqE2Wxm8eLFPPjgg0ZHEiegHnbizPbt20dkZKTm1zm4pk2bUq1aNcaNG2d0FLkGFXYO6MKFC7Rr145ff/2VZcuW0bJlS6MjiZNQDztxZhaLBS8vLxo0aGB0FLkBk8lEeHg4ixYt4tChQ0bHkf9QYedgYmNjadOmDX/++ScrVqzQN1e5ZYmJiZw8eVKFnTgts9lM7dq18ff3NzqK3ETPnj3Jly8fEyZMMDqK/IcKOwcSHR1Nq1at2Lt3L6tWraJhw4ZGRxInktE0VJdixRlpfp1zyZ07N8888wzffPMN8fHxRseRy6iwcxDnz5+nRYsWHDp0iNWrV1OnTh2jI4mTsVqtgHrYiXPav38/Z86c0VUKJ/Lcc8+RkJDAtGnTjI4il1Fh5wDOnj1Ls2bNOH78OGazmfvuu8/oSOKErFYrnp6eFCtWzOgoIrfNYrHg6empKxVOpHjx4jz88MOMHz8em81mdBz5hwo7g506dYqmTZsSGRmJ2WymevXqRkcSJxUREUHx4sXx8vIyOorIbTObzdSqVYuAgACjo8htCA8P58CBA6xYscLoKPIPFXYGOn78OE2aNCEuLg6LxUKVKlWMjiROTD3sxFlpfp3zatCgAffdd59anzgQFXYGOXLkCE2aNCEpKQmLxUKFChWMjiROTj3sxFkdPHiQU6dOaX6dE8pofbJ8+XL++usvo+MIKuwMcejQIRo3bgzAunXrKFu2rMGJxBUkJydrxE6ckubXObfu3bsTEhLC+PHjjY4igMmuxd5y1P79+2nRogX+/v6sXr1aE90lS6WlpeHp6Wl0DJHb8tdff7FmzRqee+45o6PIHRoxYgSffPIJx48fJygoyOg4bk2FXQ7au3cvLVq0IH/+/KxatYrChQsbHUlExHAZd1R6eOgikrM6deoUJUuWZPTo0QwdOtToOG5NhV0O2blzJy1btqRQoUKsWrWKkJAQoyOJiIhkmd69e7Np0yYOHjyoKwcG0tejHPDnn3/SrFkzihUrxtq1a1XUiYiIywkPD8dqtbJ48WKjo7g1jdhls99++402bdpQoUIFli9fTr58+YyOJCIiki3q169P7ty5Wb16tdFR3JZG7LLRxo0badmyJVWqVOGXX35RUScibk9jCa4tPDycNWvWsGvXLqOjuC0VdtnEbDbTpk0b7rvvPlasWEHevHmNjiQiYjiTyWR0BMlGXbt2pUiRImpYbCAVdtlg1apVtGvXjvr167N06VItkSNZKjExkfnz5/Phhx9y6NAhAJKSktiyZQuHDx8mLS3N4IQiV7Pb7axevZqwsDAmTZp0xchdUlKSgckkK3l7e/Pcc88xffp0zp8/b3Qct6Q5dlls2bJldOnShebNmzNv3jz8/PyMjiQuJCkpiddff53PPvuMSpUqkZaWxpw5c3jrrbc4cuQIXl5edO/eXe0GxOFMnDiRr7/+muTkZPbu3cvIkSPp0KEDc+fO5fz583To0IEOHToYHVOyQGRkJMWLF+ftt99m2LBhRsdxOyrsstDChQvp1q0bbdu25ccff8TX19foSOJifvvtNx577DGmTp1KzZo1efPNN9m4cSNBQUE888wzbNmyhcmTJzN16lQeeugho+OKZCpXrhyDBw/m+eef548//iAsLIyUlBQ8PT2x2Wzs37+fadOm0blzZ6OjShbo168fv/zyC1arFS8vL6PjuBVdis0ic+fOpWvXrnTs2JE5c+aoqJNssW3bNkJDQ3nggQcICAjgnnvu4fTp08ydO5dHHnmEjz76iL59+zJ37lyjo4pkslqtREZG0r9/fwBq1qzJli1b6Nu3L7/++itbtmyhcePGrFq1ipSUFIPTSlYICwvj+PHj/Pzzz0ZHcTsq7LLAzJkz6dGjB926dWPWrFn4+PgYHUlcVFxcHEFBQcTHxwOwa9cuypUrR968ea+Ys5SammpURJGrbNiwgRo1amSuLLF69WoCAgJ48sknM+eE9ujRg82bN+Pt7W1kVMkiNWrUoHHjxowdO9boKG5Hhd1dmjZtGr1796Z37958//33GnKWbNWoUSOOHj3KK6+8wuDBg9m2bRtRUVFs2rQJk8mE1Wpl9+7d1KpVy+ioIply5cpFgwYNMr+QhISE8O2335IrV67MFQqsVit58uQxMqZksfDwcDZu3Mgff/xhdBS3ojl2d2Hy5Mk8++yzPPXUU3zxxRda51ByxOTJk/n888/JlSsXn3zyCXPmzGHnzp00bdqUxYsX4+vry5dffkmVKlWMjiqS6dy5cwQFBWV++bXZbJm/My9dukSbNm146KGHdOOPC0lNTaVcuXI0adKEadOmGR3HbbhsYWezQ3wKRKdAdDLEpkCKDWykD1N6e0CgN+TzgXzekMcbPG6jvdKECRMYPHgwgwYNYty4cSrqJEfY7XZMJhN2u53o6Gjy58/PiRMneP3119m0aRNlypRhzJgxKurEqbz33nt89913rFq1imLFihkdR7LQRx99xBtvvMHRo0cJDQ01Oo5bcLnC7kIqHL4A1gRI/ecnMwHX+iEvf9zLBKX9oUwABNzkauqnn37K0KFDGTp0KB9//LEabkqOunyk4/L/FnFUdrudmJgYUlJSCAkJyfyCksFqtRIREUGzZs0MTCnZITo6mmLFivHqq6/y1ltvGR3HLbhMYReVBHvi4GzS9Qu5m8l4XYgvVA2E/Ne4B2L06NEMHz6cYcOG8d5776mokxx19OhRFi5cSHx8PI8//jjFihXj+PHj/P7771SoUIGKFStqnqc4lN27d/P8889jtVqpVq0ab7zxBrVr176quBPXNWDAABYsWMCRI0d0c2EOcPrCLs0Oe2PhwIU7L+j+K+N9KgRAlUDwNKV/4/zf//7HiBEjMv/RLyXJSQcOHGDo0KFs2LCBoKAgatSowZNPPsno0aO5cOECuXLl4pVXXuGRRx4xOqoIAAkJCTRp0oRixYrRrl075s+fz5YtW9i4cSOVKlXKLO4WLFhA48aNtZ62i9q7dy9Vq1Zl+vTp9OrVy+g4Ls+pC7voZNhyHhKycQWlAC+onc/OJ6Pe4L333uPdd9/ltddey74dilzHiBEj2Lx5M1OmTCEoKIhevXoRERFB8+bN6dy5M2PGjOHIkSMsXLiQEiVKGB1XhB9++IH333+fjRs3Zt7x+thjj3Hs2DE2bNgAwIkTJ6hVqxZWq1Ur9biw1q1bExMTw5YtWzQoks2cdnLOmUQwn4WL2bwsZkKqnVWnUlm0bgsff/yxijoxzObNm2nUqBFFixbF39+ftLQ07rnnHsaMGUOTJk2YNGkS+fPnZ/369UZHFQHS182uW7cuefLkITk5GYD333+f2NhYvv76ayB9GUZvb28VdS4uLCyM33//nS1bthgdxeU5ZWF3JhE2nku/wzW7hxvtmMDkwVszVtB70IvZvDeR6zt37hyFCxfO/POuXbu4//77gfS2AkWKFOHcuXMEBAQYFVHkCl5eXgQHB5OcnIyPjw+pqamUKlWKvn378uWXX5KcnMzChQvp0qWL0VElm7Vr146yZcuqYXEOcLrCLjoZNp3L/oLucp6enpg8PNl0Ln3/IkaoXr06Xl5e2Gw2AGbNmkWPHj2A9A/Q+Ph4Tpw4QYUKFYyMKQKk37Hdtm1bzp07lzlhPuPGnmeeeYbk5GTGjx/Phg0bePTRR42MKjnAw8ODIUOGMHfuXE6cOGF0HJfmVHPs0uzwy+n0y69GhQ7wgpah6TdUiOSknTt3kpaWRs2aNa/5/Lx583j99dfZuXOnlmUSh3F578XL51YtWLCALl26EBgYSHR0tIEJJafExcVRtGhRwsPDeeedd4yO47KcqrDbFZN+96vRKuSB6oFGpxD5V1JSEhMmTMDT05Pw8HCj44gA3LClSWJiIn369CElJUULxbuRsLAwfvjhB44dO6Z5ldnEaQq7qCRYG2l0in81C7l2nzsREbmxyxtrx8TEEBQUZGwgyTEHDx6kYsWKfPPNNzz55JNGx3FJTlPYrY+EyCTjLsFezgQE+8IDwUYnEUl34cIFEhISCAkJUSsBcTg2mw2TyXTFsXn8+HEtH+amOnTowPHjx9m2bZt+X2UDp7h54kJq+ooSdiAlKYnv33uVp+8vQs9yuRjWsS471v1y0/fYvGweYwZ257mGZehZPjdhTSoybdSLJMTGXLFdfPR5FnzxEW92bUy/e4PpUzWI4Z3qsXHh7Mxt7KTnuZCatT+nyK2y2+2kpaVltpBYunQpHTt2ZOnSpQYnE7mah4fHFR/ghw8f5sknn1T7KDcVFhbGjh071JopmzjF2kOHL1tV4vOhfdm8dC7t+z9P4dLlWTtnKu890Y63Z6+lcp1G132PL199hnyhRWjcpTcFi5bg6F+7WDbtc/5cu5QPl/6Jb65cAOz/41d++PB1ajZrR9ewN/Dw9GLLsp/4dFAPjh/cS/cXRwLpeQ5fgHuCsv3HF8mUlpaWfpe2yYSnpyeenp4A+Pr6EhgYSMGCBQ1OKJI+QmexWPj77785duwYRYoUoX79+tx7771A+nHs7+9PcLAue7ijVq1aUblyZcaOHUvjxo2NjuNyHP5SrM0Oi05Cqh0ObvuN4Z3q8vjrH9F5wEsAJCcmMrRlNfIWDOG9+Zuu+z67fzVTrX7TKx4zz/2Oz194ggEfTqblY08BcOaoFQ8PD4KLlczczm63M/KxluzfupFvd57HL7c/AF4m6FgEPDSSLNksLS0Ns9nM2rVrOXDgAMnJyRQqVIiaNWvSsGFDqlWrZnREEQAuXrzIa6+9xldffUXBggUpX7488fHxJCQkUL58eXr16kW3bt2AK+faiXuZNGkSgwcP5tChQ5QqVcroOC7F4c+o+JT0og5g89K5eHh60qrXM5nP+/j50bxHfw788SvnTh677vv8t6gDqNs2vSnmiYP7Mh8LLVH6iqIOwGQyUafNQ6QkJXHmyOHMx1PtEK/LsZLN0tLS+OSTT2jfvj0LFizAz8+PvHnzcuzYMaZOncrAgQP58ccfSU3VwSjG++mnn1iwYAFLlizh6NGjTJ48mQ8//JCBAwdiMpl48cUXGTduHGlpaSrq3FifPn3ImzcvEydONDqKy3H4S7HRKf/+t3XPNoqUqUDuPHmv2KZcjToAROzZTsEixW/5vWMiTwOQJ//NL1/FnE3fNu9/to1OhkC1DJNstG/fPj7++GNmzJhB165dSU1N5eLFi0RFRXHo0CG+++47Bg4cSIkSJahXr57RccXNLVq0iPbt29OsWTMAypQpQ5kyZWjatCkDBw5kxIgRTJgwgU6dOmmkxo35+/vz1FNPMXnyZEaMGIG/v7/RkVyGw39dik5On88GEH3mFEEhha/aJt8/j0WdOXlb7z1/4gd4eHpSv/0jN9wuPjqK1bO+pnKdB8gX+u/+TUCMVqKQbLZz506Cg4Pp2rUrkN69P2/evJQqVYoWLVowbdo0OnTowEcffWRwUhGoVq0a27dv59ixq6+geHp68uqrr+Lj48Pq1asNSCeOZNCgQcTFxTF9+nSjo7gUhy/sYlP+bXGSnHgJbx/fq7bx8fXLfP5Wrf95JqtnfUPHZ16kcOny193OZrMxNqwXCXEx9P/f+CueswMxKdd+nUhWCQwMxNvbm0WLFl13m9DQUBITE3Mwlci19ejRg/Pnz/Pmm2+yZcsWLl268vdyUlISx44du+4KKuI+SpUqRefOnRk3bhwOPt3fqTj8pdgU27//7eOXi5TkpKu2SU5KzHz+Vuzdsp5JL/enRpM29Hzl3Rtu+82bQ9huXs6Qz76jVJV7b5hPJDs0bdqU6tWr89JLL/H333/TpEkTihQpgre3N/Hx8SxatIg1a9bQp08fo6OKUKFCBT777DOGDh3KzJkzuf/++2natCkVK1bkwIEDrFy5klq1anHfffcZHVUcQFhYGM2aNWPVqlW0atXK6DguweELu8vrpnyhhYk6ffXiwdFnTwGQP7TITd8vYu8OPujfieIVq/Hil3Px9Lr+/4IfPx3Jiu8m0mv4aJp0ffym+USyg7+/P2PHjuW9997jnXfe4cUXXyQwMJDAwEAKFCjA+fPneeyxx3j88WsfoyI5rU2bNuzZsweLxcLs2bP5+eefOX/+PNWrV6d58+YMHDjQ6IjiIJo0acI999zDuHHjVNhlEYcv7C6/VlyqSg12b1rLxfi4K26gOLhtS/rzVWvc8L1ORxzincfbElgghNe+W0ou/4Drbrts6gR+HPM27fs/T5fnXr2lfCLZwW63kz9/fj7++GM+/vhj/vrrL/766y9OnTpFUlISjRo1olatWkbHFLlKkyZNaNKkCZB+d3dUVJR618kVTCYTYWFhPP300/z999+UK1fO6EhOz+H72JnPwvl/blA4sG0Lr3Wqd0Ufu5SkJF5oWY08+Qrw/sLNAESeOErypYsULVcp832iz57mjS4NSUlK5J2fNxJSvNR197lx4WzGDulJw86PETb2+xsueVLAB5qG3P3PKSLiDux2u5aRkitcunSJ4sWL07t3bz777DOj4zg9hy/stkWDNeHfGyg+Gfgovy3/mQ5PvUChUuUwz53G39t/Y8QPq6lSL72D9VvdmrJ3s4W5x/790V5qU4OIvTvoPPAVSlaqfsU+AguGcm/j9CHgg9t+481HHiB3nkB6D/8AL+8re5lUvL8BoSXLAOl3xZbxhxr5sudnFxERcQevv/4648eP5/jx4+TNm/fmL5DrcvhLsfl84HDCv38e8ul3zCr6JpZ535MQG03JSvcw/NvFmUXd9UTs3QHAgkkfXvVclXpNMgu74wf3kpqcTNz5SCa+1O+qbQd98m1mYWcHgnzu8AcTEXEDKSkpeHur2afc2MCBA/nggw+YOnUqYWFhRsdxag4/YhebDKvOGp3i+lqGqkGx5CxdyhJn8dtvv7F7926eeOKJzHWNRa6nR48e/PHHH+zfv1+rktwFh/8/l8c7fU1WR+RlgjwOP+Yprubw4cMEBQWxZcsWo6OI3NDMmTN55513VNTJLQkLC+Pvv/9m2bJlRkdxag5f2HmYoLT/v6tPOAoT6bk8HC2YuDyr1UpsbCwFChQwOorIDZnN5sy7YkVupn79+tSqVYtx48YZHcWpOXxhB1Am4N+bJxyFnfRcIjktIiICk8lEiRIljI4icl1RUVHs3LmTpk2bGh1FnITJZCI8PJyVK1eyb98+o+M4Laco7AK8IMTXcUbtTKTnCdBlWDGA1WqlWLFi+Pjozh1xXOvXr8dut2vETm5Lt27dCA0NZfz48TffWK7JKQo7gKqBjjNqZyc9j4gRrFYrpUqVMjqGyA1ZLBZKliypY1Vui6+vLwMHDmTatGlER0cbHccpOU1hl98HKjjIpc8KedLziBghIiKC0qVLGx1D5IY0v07u1LPPPktKSgrffPON0VGcktMUdgBVAsHf07hLsibSL79WUe9EMZDValVhJw4tJiaG7du3a36d3JFChQrRo0cPPv/8c9LS0oyO43ScqrDzNEHdAkYVdnZMQJ386TlEjHDp0iVOnz6ty1vi0DS/Tu5WeHg4R44cYeHChUZHcTpOVdhB+koUDQrmbHGXlpaGLc1Gw4Lp+xcxypEjRwA0YicOzWKxULx4cR2ncsfuv/9+GjRooNYnd8DpCjuAUD9oWDA9fE4UeB7Y+V+v1nz3+cc5sDeR67NarQAasROHljG/TiukyN0IDw/HbDazc+dOo6M4Facs7CC9uGsaArmzuaF5gBe0KOxFxyb1ePnll5k2bVr27lDkBiIiIvDy8qJYsWJGRxG5ptjYWLZt26b5dXLXunTpQtGiRRk7dqzRUZyK0xZ2kH5ZtFWhf++WzarvhhnvUyFP+lqw+XzgnXfe4amnnqJ///4sXrw4i/YkcnusVislSpTQEk3isDZs2IDNZtP8Orlr3t7eDBo0iBkzZnDu3Dmj4zgNpy7sIP1GhupB0CwYgn3TH7vTAi/jdcG+0CwEqgf+e6OEyWRi0qRJdOrUiW7durFx48a7TC5y+9TDThydxWKhaNGilC1b1ugo4gKefvppTCYTX331ldFRnIbTF3YZ8vvCA8HQphCUCwCvy6q76xV6lz/uZUp/XZtC6e9zrT51Xl5ezJw5k7p169KhQwd2796dlT+CyE2ph504Os2vk6xUsGBBevXqxcSJE0lJSTE6jlNwmcIuQ4AX3BMEHYukX0a9Px+U8YcCPpDXK/35vF7pfy7jn/58y9D07e8JuvkyYX5+fixYsIBSpUrRpk0bIiIicuCnEkmnETtxZHFxcfz555+aXydZKiwsjBMnTjBv3jyjozgFk91ud5SVupzKmTNnaNiwIR4eHmzYsIGQkBCjI4mLi4+PJ2/evEyfPp1evXoZHUfkKsuWLaNdu3bs37+fChUqGB1HXEizZs1ISkpi06ZNRkdxeC43YpdTQkNDWblyJfHx8bRr1474+HijI4mLyxgd1qVYcVQWi4VChQpRvnx5o6OIiwkPD+fXX3/l999/NzqKw1NhdxfKlCnD8uXLOXjwIF26dCEpKcnoSOLC1MNOHJ3ZbKZp06aaXydZrmPHjpQqVUoNi2+BCru7dO+997Jo0SI2bNhA7969ta6dZJuIiAh8fX0pVKiQ0VFErnLhwgW2bt2qNieSLTw9PRk8eDCzZ8/m9OnTRsdxaCrsskDjxo2ZPXs28+bNY/DgwWjaomQHq9VKyZIl8fDQaSuOZ+PGjaSlpenGCck2/fv3x9vbmy+++MLoKA5NnxBZpHPnzkyePJkvvviCkSNHGh1HXJBanYgjs1gshIaGUrFiRaOjiIsKCgriiSeeYNKkSZr6dAMq7LJQv379GD16NCNHjmTChAlGxxEXY7VaVdiJw1L/OskJQ4YM4ezZs/z4449GR3FYKuyy2CuvvMLQoUMZMmQIs2fPNjqOuAi73a4eduKwEhIS+P333zW/TrJd5cqVad26NWPHjtW0p+tQYZfFTCYTH330Eb179+bxxx/nl19+MTqSuICYmBji4uI0YicO6ddffyU1NVXz6yRHhIeH88cff/Drr78aHcUhqbDLBh4eHnzzzTe0atWKLl26qO+O3LWMVicq7MQRmc1mgoODqVy5stFRxA20bduW8uXLM3bsWKOjOCQVdtnE29ubOXPmcO+99/Lggw/y119/GR1JnFhGc2JdihVHZLFYNL9OcoyHhwdDhgzhp59+4vjx40bHcTgq7LJR7ty5WbRoEYUKFaJNmzY6AOWOWa1W/P39KViwoNFRRK5w8eJFtmzZovl1kqP69u1L7ty5mThxotFRHI4Ku2yWP39+VqxYAUCbNm2IiooyOJE4o4wbJzQiIo5m8+bNpKSkaH6d5Kg8efLQr18/vvrqKy5dumR0HIeiwi4HFC1alJUrV3L27Fk6dOhAQkKC0ZHEyaiHnTgqs9lMgQIFqFKlitFRxM0MHjyYqKgoZs6caXQUh6LCLodUrFiRpUuXsnPnTrp160ZKSorRkcSJqIedOKqM+XVaEUVyWrly5Wjfvr1an/yHzsQcVLt2bX7++WdWrVpFv379sNlsRkcSJ2C324mIiNCNE+JwLl26xObNmzW/TgwTHh7Orl27sFgsRkdxGCrsclirVq2YPn06M2bM4MUXX9S3DLmpyMhILl68qBE7cThbtmwhOTlZ8+vEMC1atKBKlSpqfXIZL6MDuKNHH32Uc+fOMWjQIEJDQxk2bJjRkcSBZfSw04idOBqz2Uz+/PmpVq2a0VHETZlMJsLCwhg4cKCmrPxDI3YGee655xgxYgTDhw/n66+/NjqOOLCMHnb6hSWOxmKx0LhxY82vE0P17t2boKAgrdH+D52NBhoxYgQDBw7k2WefZf78+UbHEQdltVoJCgoiKCjI6CgimRITE/n11181v04M5+/vz1NPPcXXX3/NhQsXjI5jOBV2BjKZTIwfP56uXbvSo0cPTf6Ua8roYSfiSH777TeSkpI0v04cwqBBg4iPj+f7778HwGaH2GSISIBt0WA+C7+chhWn0/9tPpv+eERC+nY2F5rurjl2BvP09OT777+nffv2dOrUCYvFQo0aNYyOJQ5EPezEEZnNZoKCgqhevbrRUUQoWbIkXbp0Yfrc+TToMYCIiyZS/ynWTMC16raoZDj8T1tZLxOU9ocyARDg5JWRya7bMh1CfHw8zZo14/jx42zatIkyZcoYHUkcRIUKFejQoQNjxowxOopIphYtWhAQEMCCBQuMjiJCVBJsOBJNSu58YLeB6fYvSGYUgCG+UDUQ8vtkecwcoUuxDiJPnjwsW7aMwMBAWrduzenTp42OJA7AZrNx5MgRjdiJQ0lKSmLTpk2aXyeGS7PDrhhYGwmpuYPSH7yDog7+HdWLTIK1Z9PfN80Jh75U2DmQ4OBgVqxYwaVLl3jwwQeJjY01OpIY7NSpUyQnJ6uwE4fy+++/k5iYqPl1Yqjo5PT5cgf+uV/CTtaspZ1Ryx24AKvOpO/HmaiwczClSpVixYoVRERE0LlzZxITE42OJAZSDztxRGazmcDAQO69916jo4ibOpOYfgPExbTs3U9Cavp+zjjRR7EKOwdUrVo1Fi9ezG+//cZjjz1Gamqq0ZHEIBk97FTYiSOxWCw88MADeHp6Gh1F3NCZRNh4Dmxc+6aIrGQnfT8bzzlPcafCzkE1bNiQOXPmsGjRIgYOHKilx9yU1WqlYMGCBAQEGB1FBIDk5GQ2btyo+XViiOhk2HQu+wu6/7KTvl9nuCyrws6BtW/fnilTpvD111/zxhtvGB1HDKBWJ+Jotm7dyqVLlzS/TnJcmh22nM/5oi6DDfgtyvFvqHDybi2ur0+fPpw7d44XX3yR4OBgnn/+eaMjSQ7S2ofiaMxmM3ny5FG/Tclxe2MhIZvn1N3MhVTYGwfVA43NcSMq7JzA0KFDOXv2LC+88ALBwcH06tXL6EiSQ6xWK7Vr1zY6hkimjPl1Xl76+JCcE5X0792vRjsQD0VzOW6fO12KdRLvv/8+/fr1o2/fvixbtszoOJIDUlNTOXbsmEbsxGGkpKRofp0YYk8cWdTM5O6ZgD0O3I1MX7mchMlk4ssvv+TcuXN07dqV1atXU79+faNjSTY6fvw4aWlpKuzEYfzxxx8kJCRofp3kqAupcDbp+s+nJCUx65O3WPfT9yTERlOi8j089vI73Nu41Q3fd/aYt5nz6cirHvf29eWHv69/C6yd9DwXUh1z+TEHjCTX4+XlxaxZs2jTpg3t27dn/fr1VK1a1ehYkk3Uw04cjdlsJiAggPvuu8/oKOJGDl+4/nqvAJ8P7cvmpXNp3/95Cpcuz9o5U3nviXa8PXstles0uun7P/3eJHL5/9t5wMPj5m18TP/kuifoln6EHKXCzsnkypWLhQsX0qRJE9q0acOmTZsoUaKE0bEkG2T0sCtZsqSxQUT+YbFYaNSokebXSY6x2cGacP2i7uC239i4cBaPv/4RnQe8BECTrn0Y2rIa37/3Cu/N33TTfdRv/wh58xe8rVx20nNVCwQPR7lG/A/NsXNCQUFBLF++HB8fH1q3bs25c+eMjiTZwGq1UrhwYfz8/IyOIkJqaiobNmzQ/DrJUfEpkHqD9iKbl87Fw9OTVr2eyXzMx8+P5j36c+CPXzl38thN92G327kYH3fb/WJT7RDvgOsHqLBzUoULF2blypVER0fTrl07LlxwkNuFJMuoh504kj///JMLFy5ofp3kqOiUGz9v3bONImUqkDtP3iseL1ejDgARe7bfdB+DGpahT5VAHq+Uh7FhvYmJPHPr+RywYbHG051YuXLlWL58OU2aNOHhhx9m8eLF+Pg46P3XctvUw04cidlsxt/fn/vvv9/oKOJGopNvPL8u+swpgkIKX/V4vn8eizpz8rrvHRCYjwf7DqbCffXx9vVl32/rWT5tAn9v/40Plmy9qlj8LxMQkwz439rPklNU2Dm5mjVrsmDBAtq2bUufPn2YOXMmHh4aiHUFVqtVl73EYVgsFho2bIi3t7fRUcSNxKbceKWJ5MRLePv4XvW4j69f5vPX075/+BV/rteuK+XurcPYsF6s+G4iXQYNu2E2OxBzkxFFI6gCcAHNmjXjhx9+YM6cOYSHh2tdWReQlJTEyZMnNWInDiE1NZX169fri4bkuBTbjZ/38ctFSvLVvVCSkxIzn78dD3TpSVBIIXZuWJUl+Yygws5FPPzww0yaNInPP/+cd955x+g4cpeOHj2K3W5XqxNxCNu3byc+Pl6FneS4m9VN+UILE3P21FWPR//zWP7QIre9z4KFi3MhJuqWtnXAuk6XYl3JM888Q2RkJG+88QbBwcEMGDDA6EhyhzJanWjEThyB2WwmV65cWt5OctzNRp9KVanB7k1ruRgfd8WcuIPbtqQ/X7XGbe3Pbrdz9ngEpavWzJJ8RnDETHIXXnvtNcLCwnjuueeYO3eu0XHkDlmtVjw8PChevLjRUUSwWCw0aNBAN2dJjvO+SZVSr/0j2NLS+GXGV5mPpSQlsfbHbylfsy4Fi6T/Do08cZQTf/91xWtjz0de9X4rvptE3PlIajRtmyX5jKAROxdjMpn49NNPiYyMpFevXuTLl48WLVoYHUtuk9VqpVixYpqoLoZLS0tj3bp1vPzyy0ZHETcU6A1Ryde/gaJCzbrU79CNmR8MJ+78WQqVKod57jQij0fw3EffZG43/vk+7N1sYe6xf99pYL2SNOzYnRKVquPt68dfv29g48JZlKpag9a9n71pNhMQ5IC/olXYuSAPDw+mTp1KVFQUDz30EGazWS0KnIx62Imj2LFjB3FxcZpfJ4bI5wOHE268zZBPv2NW0TexzEtfK7ZkpXsY/u1iqtRrfMPXPdClF/v/2MTmZT+RkpRIwaIl6TzwFboOeR3fXLlvms0OBDngILbJrlsoXVZCQgItWrTg8OHDbNy4kfLlyxsdSW5RvXr1qFSpElOnTjU6iri5MWPG8PrrrxMTE4Ov79VtJUSyU2wyrDprdIrraxmaPqroSBzw6rBkFX9/f5YsWULBggVp3bo1J09ev1GjOBaN2ImjsFgs1K9fX0WdGCKPN3g52FqsGbxMkMcBr3uqsHNxBQoUYMWKFaSmptKmTRuio6ONjiQ3cfHiRc6cOaPCTgxns9lYv369lhETw3iYoLR/+nw2R2IiPZeHowVDhZ1bKF68OCtXruTkyZN07NiRixcvGh1JbiCj1Yl62InRdu7cSXR0tObXiaGKeifdcPUJI9iBMgFGp7g2FXZuonLlyixdupRt27axbNkyo+PIDaiHnTgKi8WCr68vdevWNTqKuCGbzcb333/PfVUqsHP9L9jS0oyOBKSP1oX4QoADXoYFFXZupW7duuzatYuuXbvecDvdT2Msq9WKt7c3RYrcfsd0kaxkNpupV68efn5+RkcRN2K321mxYgX33Xcfffr0oXbt2jxUqwIenp5GRwPSR+uqBhqd4vpU2LmZMmXK3HQbkyl90kCag3w7cjcRERGUKFECTwf5JSbuyWazsW7dOs2vkxz1xx9/0LJlS9q2bUvevHn59ddfmTt3LjXLl6SCg1z6rJAH8jtgm5MMDjqQKEbZuXMnS5cuZevWrRQrVoz+/ftTvXp1o2O5FavVqsuwYrjdu3cTFRWl+XWSIw4fPszrr7/OrFmzqFKlCgsXLqRDhw6ZAw0AVQLhxCW4mHb9hsXZyQT4e0GVvDfd1FAasZNMixYt4oEHHmDlypUkJiYSHR1NgwYN2L59u9HR3IrVatWNE2I4i8WCj48P9erVMzqKuLDIyEjCwsKoVKkS69at4+uvv2bHjh107NjxiqIOwNMEdQsYd4esCaiTPz2HI9OInQAwe/ZsevfuzcCBA3nhhRcyR4xSU1MZO3Ys33zzDR4e+h6QEyIiIm46D1Iku5nNZurWrUuuXLmMjiIuKCEhgU8//ZQPP/wQk8nEqFGjCAsLI3fuG6/4kM8HGhSEjedydtTOBDQsmL5/R6dPauHXX3+ld+/ehIeH88EHH1xxGbBQoUIcPXpUN1TkkLi4OKKionQpVgyl+XWSXVJTU/nqq68oX748//vf/3jqqac4fPgww4YNu2lRlyHUL73I8iBnRu88gEYFIcRJ7iFSYefmYmJiePXVV+natSuvvfbaFd/Oz507x/Lly6lRo4Ym8ucQq9UKqIedGGvv3r2cO3dO8+sky9jtdn7++WeqVavGs88+S/Pmzdm/fz9jxoyhQIECt/1+oX7QNARyZ/NHU4BX+n6cpagDFXZuLzo6miNHjvDwww+TP3/+zJG5mJgYxo8fT0BAAK1btzY4pftQDztxBBaLBW9vb+rXr290FHEBGzdupFGjRjz88MOULFmSP//8k+nTp9/1F9h8PtCqEJl3y2bV6F3G+1TIk74WrDNcfr2cCjs3d+HCBXx8fDLvfDWZTJw7d44vvviC+fPn06xZM9q0aWNwSvdhtVrx8/MjNDTU6CjixsxmM3Xq1LnlS2Mi17Jv3z4eeughGjVqxKVLl/jll19YsWIFNWvWzLJ9eJqgehA0C4bgf5YzvtMCL+N1wb7QLASqBzr+jRLXosLOzRUtWhQvLy8mT57MsWPHOHjwIC+99BJz586lcePGjB49GkifcyPZLyIiglKlSl11N5hITrHb7VgsFs2vkzt28uRJnnnmGapVq8aOHTuYMWMGW7dupWXLltm2z/y+8EAwtCkE5QLA67Jfodf7bXr5416m9Ne1KZT+Po7cp+5mdFesm8ufPz9z587lwQcfZPXq1ezatYvGjRvTs2dPhg4dCqQ3KtYcu5yhHnZitH379hEZGan5dXLbYmNj+fDDD/n000/JnTs3Y8aMYcCAAfj6+uZYhgAvuCcIqgVCfCpEJ0NMMsSkQIoNbKSPaHl7QJA3BPmkX2rN4wUeLvJ9WoWdULVqVbZu3cqxY8eIioqiVatWmc8lJSVlnpR2u/2qkSSbzUZaWhre3t45mtlVWa1WGjVqZHQMcWMWiwUvLy8aNGhgdBRxEklJSXzxxRf873//4+LFi7zwwgu88sorBAYat+6WhwkCvdP/wd+wGIZQYScAhISEEBISkvnnOXPm0KVLlyu+aSUkJGAymdi9ezd79uwhLi4Oi8VCXFwcr7zyiubi3SW73U5ERASPP/640VHEjZnNZmrXro2/v5t9Gspts9lszJo1izfeeIMjR47Qr18/3n77bYoWLWp0NLemwk6u8s477zBhwgQAunXrRnJyMtOmTePzzz8nX758JCcnky9fPrp06cLFixc5cOAAn376KY0aNdKHwV2IiooiPj5erU7EMBnz6/r162d0FHFwq1at4tVXX+XPP/+kc+fOLFmyhMqVKxsdS1BhJ9fwzDPPYDKZaNasGQDJycnMmTOHY8eOsWLFCgoVKgTA+vXr8fHx4f7772f48OGZRd21LtnKzanViRht//79nDlzRvPr5Lq2b9/Oq6++ysqVK6lfvz7r16/X9BEHo7ti5SohISG89tprFCxYEJvNRkBAABMnTqRYsWL07t0bgJUrVzJy5EjS0tJ49dVXqVu3bubr9+3bZ1R0p5bRnFiFnRjFYrHg6elJw4YNjY4iDiYiIoLevXtTs2ZNjhw5wrx58zL704ljUWEn15Qx4paxPmy5cuVYvHgxkZGR3HvvvYwdO5ZcuXIxfPjwzCamNpuN3bt3U61aNWbMmGFYdmdltVoJCAggf/78RkcRN2U2m6lVqxYBAQFGRxEHcf78eYYOHUrFihVZvXo1X375Jbt376ZLly66MuOgdClWbirj0mqJEiUYOnQo4eHhnDx5kqVLl1K7du3M7Tw8PKhWrRpTp06lX79+2O32zBE+ubmIiAhKly6tX5ZiiIz5dX369DE6ijiAS5cuMXbsWEaPHo3NZuPNN9/khRde0DxqJ6DCTm4qo9BYuHAhP/30EzVr1mTnzp3MmjWL2rVrXzWnrk+fPvj6+tKzZ09sNps+KG6RetiJkQ4ePMipU6c0v87NpaWlMXXqVEaMGMHZs2cZMGAAb775JsHBwUZHk1ukwk5uSWpqKkuXLuXkyZOMGzeOOnXqcP78eYArijqbzYaHhwfdu3fn/Pnz9O3bl3z58tGxY0ejojuNiIiIK3oIiuQkza9zb3a7ncWLFzNs2DD27t1L9+7deffddylbtqzR0eQ2aY6d3BIvLy8++eQTJk2aRIMGDfDy8iI0NBS73Q6Q+e+0tDRiYmJ44YUXWLBgAQBr164lNjbWsOzOIKOHnUbsxChms5n77ruPvHnzGh1FctjmzZtp0qQJnTp1olChQvz+++/MmjVLRZ2TUmEnt8zf3z9zTp3NZsNms2WO1plMJrZs2ZI5yXbx4sWULVuW/fv38/HHHxvagdwZnDlzhkuXLqmHnRhC68O6p/379/PII49Qv359YmNjWbZsGatWraJWrVpGR5O7oEuxckcy7pYFmDlzJmvWrGHatGk0aNCAp556imHDhuHn54e3tzc2m83ApM5BPezESIcOHeLEiROaX+cmTp8+zciRI5k8eTJFixblu+++o1evXlf8XhfnpcJO7tjq1asZNGgQUVFRVKxYkalTp9K2bVsKFChwxXb6ZXFzGT3sNGInRrBYLHh4eKgnmYuLj4/n448/5pNPPsHHx4cPPviAQYMG4efnZ3Q0yUIq7OSONWzYkPr16zNw4EBKlSp1xVqzWn3i9litVvLly6dL1mIIs9lMzZo1dfy5qOTkZL766itGjRpFXFwc4eHhDBs2jHz58hkdTbKBCju5Y35+fnz77bfXfE5F3e3RjRNilIz5dY8++qjRUSSL2e125syZw2uvvcbhw4fp27cvI0eOpHjx4kZHk2yka2QiDsBqteoyrBjCarVy7Ngxza9zMWazmbp169K9e3cqVarEzp07mTJlioo6N6DCTsQBaMROjGKxWDCZTDzwwANGR5EssGvXLtq1a0ezZs0wmUyYzWYWL15MtWrVjI4mOUSFnYjB0tLSOHLkiAo7MYTZbKZGjRoEBQUZHUXuwtGjR+nbty/33nsvBw8e5Mcff8zsTyfuRYWdZKuxY8eybds2o2M4tJMnT5KSkqJLsWIIi8WiD38nFh0dzSuvvEKFChVYtmwZn3/+OXv37qVbt26a6+ymVNhJtklOTmbGjBm0bduWv//+2+g4Dks97MQoERERHDlyRI2JnVBiYiIfffQRZcqUYeLEiQwbNoy///6b5557Dm9vb6PjiYFU2Em28fHxYcmSJeTLl482bdpw6tQpoyM5pIwediVLljQ4ibgbza9zPmlpaUybNo0KFSrw2muv0bNnTw4dOsTbb79Nnjx5jI4nDkCFnWSr4OBgVqxYQVJSEg8++CAxMTFGR3I4ERERhISE4O/vb3QUcTNms5l77rmH/PnzGx1FbsJut7N06VJq1qxJ3759qVu3Lnv37mXChAmEhoYaHU8ciAo7yXYlS5ZkxYoVHD16lM6dO3Pp0iWjIzkUq9Wqy7BiCM2vcw6///47zZs3p3379uTLl4/NmzczZ84cypcvb3Q0cUAq7CRHVK1alSVLlvD777/z2GOPkZqaanQkh6EedmKEo0ePYrVaNb/Ogf399990796dOnXqEBkZyeLFizP704lcjwo7yTH169dn7ty5LF68mGeffRa73W50JIegHnZiBIvFAqD5dTnsp59+4q233mL27NnExsbecNsBAwawadMmpkyZwo4dO2jfvr3udJWbUmEnOapdu3Z8++23TJkyhddee83oOIZLSUnh2LFjKuwkx1ksFqpXr07BggWNjuIWNm3aRPXq1QkPD+fw4cP07t2b4cOHc/r06Wtun5qaypQpUzhw4ABPPvkknp6eOZxYnJUKO8lxjz/+OGPGjGH06NGMGTPG6DiGOn78ODabTZdiJceZzWbNr8tBn332GQ0bNuTw4cNMnz6d8ePHs2rVKpKSkq65vZeXFyVKlCBXrlw5nFScnZfRAcQ9vfDCC5w9e5YXX3yR4OBgHn/8caMjGSKj1YlG7CQnHT9+nEOHDml+XQ7Ztm0bf/75J8OHD8fHxweAe+65h2LFimnEVLKcRuzEMO+99x79+vXjySefZMmSJUbHMYTVasVkMlGiRAmjo4gbyZhf17hxY4OTuJ7JkyczcuRI5s6dS3x8PAAlSpTA19eXlStXsnv3bqZOnUr79u3x9PRk1KhR7N+/3+DU4kpU2IlhTCYTX375JR06dKBbt25s2rTJ6Eg5LiIigiJFiuDr62t0FHEjFouFqlWrEhwcbHQUlzFp0iSKFCnCp59+ysGDB+nRowejRo0iMjKSAgUK8Oabb1KgQAH69u3Liy++yEsvvUSvXr1YtWoV/fr1Y9++fUb/COIiVNiJoby8vPjhhx+oXbs27du3Z/fu3UZHylHqYSdG0Py6rGO325k/fz4//vgjI0eOZNeuXUyfPp13332XpUuXZs6h69GjB++//z4pKSl8//33vP766/Tt25evv/4ak8nE6tWrDf5JxFWosBPD5cqVi4ULF1KyZEnatGnDkSNHjI6UY9TDTnLayZMnOXjwoObXZRGTyUSFChV477336NOnT+bdq2XLlqVChQqEhIRkbrtmzRq8vb1p2LBh5mN58+Zl9+7dBAUF5XR0cVEq7MQhBAYGsnz5cvz8/GjdujWRkZFGR8oR6mEnOU3z67Je5cqVqV+/fuaUilGjRtG7d28SEhJ48803+euvvwAoVaoUf/75J+vXrycqKorU1FTmzJlDlSpVqF+/vpE/grgQ3RUrDqNQoUKsXLmShg0b0q5dO9asWePSi1onJiZy8uRJjdhJjrJYLFSuXFnri96GS5cusXPnTipVqkRgYOBVz1/eNPjzzz9n8uTJfPLJJ/j4+PDtt9+ybt06Zs6cSc2aNXn00Ufp06cP9957L6dOneLSpUt89tlnlC1bNid/JHFhJrva/4uD2bZtG02bNqVOnTosXrzYZW8sOHDgABUrVmTNmjU0a9bM6DjiJipVqkSzZs2YNGmS0VEcXkpKCm+88QYTJ06kWLFiXLp0iY8++oj27duTO3dubDYbHh5XXvhKS0vDbrfj5ZU+brJp0yYGDRrE888/zxNPPEFsbCxbt25l8+bNlCtXju7duxvxo4kL06VYcTg1a9ZkwYIFrF+/nieeeIK0tDSjI2UL9bCTnHb69Gn279+v+XW3aP78+axYsYKff/6ZefPm0b59e4YNG8bEiRMBrirqMh7z8vLK/L2VnJzM7t27KVasGAB58uShRYsWvP766yrqJFuosBOH1LRpU3744QfmzJlDeHi4S64ra7Va8fT0zPyFL5LdMubX6Y7YG8v4fbN48WKCgoJo2bIllStXZsKECbRv355Zs2axbds2AGw22xWvzbgs6+npyfnz55kzZw7dunXLnEN3rWJQJCvpCBOH1aVLF7788ksmTJjA//73P6PjZLmIiAiKFy+eeclGJLtZLBYqVqxIoUKFjI7i0EwmEykpKcTGxlKzZs0rvlj27NmTvHnz8sUXXwBc9aVz7969fP/99wwfPpwqVaqwfft2hg4dSu7cuXP0ZxD3pU8UcWhPPfUUkZGRvPbaawQHBzNw4ECjI2UZtTqRnKb+dbfO29ubwoULs379emJjYzPbkdSpU4cGDRqwZs0aDh06RNmyZUlMTOTUqVOULl0af39/Vq9ezdmzZ/n666/p2LGjsT+IuB0VduLwhg0bxtmzZxk0aBAFCxakW7duRkfKEhEREVStWtXoGOImzp49y759+3jzzTeNjuI0hgwZQrVq1di8eTNt27bFbrfj4eFBrVq1+Omnnzhx4gRFihTh6aefJikpiW+//ZaSJUvyySefUKBAAaPji5vSpVhxeCaTiU8++YSePXtmLsHjCrTqhOQkza+7fVWqVOHBBx/k/fffJzIyMnP+XP369dm/fz/+/v7kypWL0NBQQkJCSElJwW63q6gTQ2nETpyCh4cH3377LVFRUXTp0oW1a9dSq1Yto2PdsQsXLhAZGalLsZJjLBYL5cuXp0iRIkZHcSpjxoyhZs2aTJw4kQEDBhAaGsrSpUupWbMm+fPnB+D999/Hx8fH4KQi6TRiJ07D29ubOXPmUK1aNR588EEOHDhgdKQ7lrFsmkbsJKdoft2dqVixIu+99x4//fQTLVq0oHv37gwePJiOHTtmfjFTUSeORIWdOBV/f3+WLFlCSEgIrVu35sSJE0ZHuiPqYSc5KTIykj179qh/3Q2cOnWKJUuWXLNvZlhYGD/++CP9+vUjNDSUDRs28Pbbb1+x4oSIo9ClWHE6+fPnZ8WKFTRo0IA2bdqwbt26zEsiziIiIgIfHx8KFy5sdBRxA+vWrQM0v+5a4uLi+OijjxgzZgyFCxdm3759eHp6XrGNyWSiUqVKVKpUyaCUIrdOI3bilIoVK8bKlSs5ffo0HTt25OLFi0ZHui1Wq5WSJUuqWankCIvFQtmyZdUM+zLJycmMHz+esmXL8vHHHxMWFsbWrVvx9va+aluNzIkz0aeKOK1KlSqxdOlSduzYwaOPPkpKSorRkW6ZethJTtL8un/ZbDZmzZpF5cqVef755+nUqRMHDx7k/fffz+xVJ+LMVNiJU6tTpw7z5s1j5cqV9O/f/6rlfRxVRESE5tdJjjh//jy7du3S/DpgzZo11KlTh8cee4yqVauyc+dOvvnmG41kiktRYSdOr3Xr1kybNo3p06fz8ssvO8W6suphJzlF8+tgx44dtG3blhYtWuDl5YXFYmHhwoVqEC4uSTdPiEt47LHHOHfuHGFhYYSGhvLKK68YHem6YmJiiImJ0aVYyREWi4XSpUtTokQJo6PkuCNHjvDmm28yffp0ypUrx9y5c3n44Yc1Z05cmgo7cRlDhgwhMjKSV199lYIFC9KvXz+jI11TREQEoFYnkjPccX5dVFQU7733HuPHjydfvnxMmDCBp5566po3Roi4GhV24lJGjhzJ2bNnefrppylYsCCdOnUyOtJVMnrYacROsltUVBQ7d+7khRdeMDpKjrh06RLjxo3j/fffJy0tjddff52hQ4cSEBBgdDSRHKPCTlyKyWRiwoQJnDt3ju7du7NixQoaN25sdKwrREREkDt3bkJCQoyOIi5u/fr12O12lx+xS0tL47vvvuOtt97i9OnTPPvss7z55puEhoYaHU0kx+nmCXE5np6ezJgxgwYNGtCpUyd27NhhdKQrZLQ60TwfyW4Wi4WSJUu67Oiw3W5nyZIl1KhRg379+tGgQQP27dvH559/rqJO3JYKO3FJvr6+/Pzzz5QtW5a2bdty+PBhoyNlUg87ySmuPL9uy5YtNGvWjA4dOlCwYEF+++03Zs+eTbly5YyOJmIoFXbisvLmzcuyZcsICAigdevWnDlzxuhIgHrYSc6IiYlh+/btLlfYHTx4kG7dulGvXj3Onz/PkiVLWLNmDbVr1zY6mohDUGEnLi0kJISVK1dy8eJFHnzwQeLi4gzNY7fbNWInOSJjfp2rNCY+c+YMgwYNokqVKmzZsoWpU6eyfft22rVrp2kNIpdRYScur3Tp0qxYsQKr1cpDDz1EYmKiYVnOnz9PQkKCRuwk21ksFooVK+b0x1p8fDxvv/02ZcuWZebMmbz33nvs37+fJ554Ak9PT6PjiTgcFXbiFqpXr86iRYv49ddf6dWrF2lpaYbkyGh14uwftuL4zGYzTZs2ddrRrJSUFCZOnEi5cuUYPXo0AwcO5NChQ7z88svkypXL6HgiDkuFnbiNRo0a8eOPP7JgwQKee+45Q5YeUw87yQmxsbFs27bNKefX2e125s6dS9WqVRk8eDAPPvggBw4c4KOPPiJ//vxGxxNxeCrsxK107NiRb775hq+++oq33norx/cfERFB3rx5yZcvX47vW9zHhg0bsNlsTje/zmKxUK9ePbp160a5cuXYvn07U6dOdcvl0ETulBoUi9t54okniIyM5OWXXyY4OJiwsLAc27fVaqV06dJOe3lMnIPFYqFIkSKULVvW6Ci3ZPfu3QwbNowlS5ZQq1Yt1qxZQ7NmzYyOJeKUVNiJW3rppZc4e/Ys4eHhFCxYkJ49e+bIfiMiInQZVrKds8yvO378OG+99RbTpk2jVKlSzJo1i27duuHhoYtJIndKZ4+4rQ8++IC+ffvyxBNPsHz58hzZZ8aInUh2iY+P588//3To+XUxMTG8+uqrlC9fnsWLFzN27Fj27dtH9+7dVdSJ3CWN2InbMplMTJ48mXPnztG1a1fWrFlD3bp1s21/NptNI3aS7TZu3EhaWppDzq9LTExkwoQJvPvuuyQlJfHyyy/z0ksvkTdvXqOjibgMfTUSt+bl5cXs2bO57777aNeuHfv27cu2fZ05c4akpCSN2Em2MpvNFCpUiPLlyxsdJVNaWhrff/89FStW5NVXX6V79+4cOnSIUaNGqagTyWIq7MTt5c6dm4ULF1K0aFFat27NsWPHsmU/6mEnOcFisTjM/Dq73c7y5cu577776NOnD7Vq1WLPnj1MmjSJQoUKGR1PxCWpsBMB8uXLx/Lly/Hy8qJ169acP38+y/ehHnaS3S5cuMDvv//uEPPr/vjjD1q2bMmDDz5I3rx52bRpEz/99BMVK1Y0OpqIS1NhJ/KPIkWKsHLlSs6fP0/79u25cOFClr5/REQEBQoUIE+ePFn6viIZNm3aZPj8ukOHDvHYY49Rq1YtTp8+zcKFC1m3bh3169c3LJOIO1FhJ3KZ8uXLs3z5cvbu3csjjzxCcnJylr231WrVaJ1kK7PZTGhoqCGjYpGRkYSFhVG5cmXWrVvH119/zY4dO+jYsaNDXBYWcRe6K1bkP+677z7mz5/Pgw8+SN++fZk+ffottWCw2SE+BaJTIDoZYlMgxQY20r9B1ej5PGVbHCciAfJ5Qx5v8NDnndyCmx1b3h4Q6A3nTP506vE4dkzk1KGVkJDAp59+yocffojJZGLkyJGEh4eTO3fuHEogIpcz2Y1YMFPECcydO5dHH32UwYMHM3bs2OuOOlxIhcMXwJoAqf+cTSbgWieWLS0VD8/071NeJijtD2UCIEBfseQabufYMmHHZk9v45MTx1ZqaipTpkzh7bff5ty5cwwaNIjXX3+dggULZs8OReSWqLATuYEvvviCgQMH8s477/D6669f8VxUEuyJg7NJ1/+wvZmM14X4QtVAyO+TBaHF6TnysWW325k/fz7Dhw9n//799OrVi//973+621vEQWicQOQGBgwYQGRkJG+88QbBwcE888wzpNlhbywcuEDm5a47/XaU8brIJFh7FioEQJVA8NQlWrfk6MfWxo0beeWVV9i0aROtWrXihx9+oGbNmnf+hiKS5VTYidzEG2+8wdmzZxk4cCAFipfFv0YLEtLSn8uq4e6M9zlwAU4mQp38kE+jd24lOhm2nMchj619+/YxfPhwFixYQM2aNVm5ciWtWrXKooQikpVU2InchMlkYuzYsXjkK0Ry+QaQagNT9t1QnpAK5rPQoCCE+mXbbsSBnEmETeeyrpi7nts9tk6ePMmIESOYMmUKJUqUYMaMGfTo0UPruYo4MM2xE7kFZxJh4zk7aTYbHh6eObJPE9BQxZ3LSz+2sr+ou9zNjq3Y2Fg+/PBDPv30U3Lnzs0bb7zBwIED8fX1zcGUInInVNiJ3ER0cvooh82AfXsATUN0WdZVOdqxlZSUxKRJk3jnnXe4ePEiL7zwAq+88gqBgYEGJBSRO6HxdJEbSLOnz3sy6tuPDfgtKj2HuBZHOrZsNhszZ86kcuXKvPjii3Tp0oWDBw/y7rvvqqgTcTIq7ERuYG9s+mR2I+uqC6mwN87AAJItHOXYWrYzgtq1a9OrVy+qV6/Orl27mDx5MkWLFjUwmYjcKRV2ItcRlZR+J6EjOBAPUVm3upkYzJGOrUv5SlCySg3Wr1/PggULqFKlitGRROQuaI6dyHWsj0zvAeYIJ4gJCPaFB4KNTiJZwZGOLew2QvxMPBCs5okirkAjdiLXcCE1vev/9T54U5KS+P69V3n6/iL0LJeLYR3rsmPdLzd939lj3uaR4qar/nms3I1vfbWTnudC6u3/LOJYLj+27vQ4AtiwYBYvP3gfj5Xzo9+9wUx8qT9xUeeu2Cbp0iUmvtSfF1pUo0+VQHpXDODF1vey5JuxpKakpG9k8uBskknHloiLUB87kWs4fOHGSzl9PrQvm5fOpX3/5ylcujxr50zlvSfa8fbstVSu0+im7//0e5PI5R+Q+edbaaFi+ifXPUG39COIg7r82LrT42jFd5OY/PpzVG/UgifeHMP5U8dZOmUsh3Zu5f2FW/DxS/+ikJx4iWMH9nBf83YEFyuFycOD/X9sYurIFzi4bQvPfz4T0LEl4kp0KVbkP2x2WHTy30XX/+vgtt8Y3qkuj7/+EZ0HvARAcmIiQ1tWI2/BEN6bv+m67z17zNvM+XQkU3ZEkjf/7S+W7mWCjkXAQ1fNnNLlx9adHkcpyck8dV8oJSvdw8g5Zkym9INh66rFjH6yI/1GjaPdk0NumOObN4ewbOrnTP7jFPlCCgE6tkRchS7FivxHfMr1izqAzUvn4uHpSatez2Q+5uPnR/Me/Tnwx6+cO3nspvuw2+1cjI/jdr9XpdohXpfMnNblx9adHkfH9u8mITaGBh27ZxZ1ALVadsDPP4CNC2fdNEdwsVIAXIyLyXxMx5aIa1BhJ/If0Sk3ft66ZxtFylQgd568VzxerkYdACL2bL/pPgY1LEOfKoE8XikPY8N6ExN55tbz6e5Yp3X5sXWnx1FKchIAPn65rnrOxy8X1t3bsNls/3lNMnFR5zh38hhblv3Mwq8+JrhYSQqVKndlPh1bIk5Pc+xE/iM6+cbz66LPnCIopPBVj+f757GoMyev+94Bgfl4sO9gKtxXH29fX/b9tp7l0ybw9/bf+GDJ1qs+5P/LBMQkA/639rOIY7n82LrT46hw6fKYTCb2b91I8+5PZj5+4tB+4s5HApAQG02efAUyn9uybB6fDX4s889l76nFcx9PwdPr348AHVsirkGFnch/xKbcuA1FcuIlvH2uXjPTx/ffCevX075/+BV/rteuK+XurcPYsF6s+G4iXQYNu2E2OxBzkxFFcVyXH1t3ehzlzV+Q+h0exTx3GkXLVaZu2y6cP32CKW8Nwcvbm9SUlKteW61BM96a+QsJcTHs2rCaiH07SLqUcMU2OrZEXIMuxYr8R8pNFu708cuVeTnscslJiZnP344HuvQkKKQQOzesypJ84rgu/7u7m+Po2dFfUrNZO7575yUGNSrLW480pkSl6tzfsiMAfrkDrtg+KDiUex5oSf32j/DM+5O4v0UHRvVsRfTZ09fNJyLOSYWdyH/c7LMtX2hhYs6euurx6H8eyx9a5Lb3WbBwcS7ERN3StvrsdV6X/93dzXHknzeQYVMWMGnzEUbNsTDp1wjCxn5P9NlT5C0QjH9g0A1z1G//CIkJF/h95YLr5hMR56TCTuQ/bnZSlKpSg5OHD3Ax/soFXA9u25L+fNUat7U/u93O2eMR5M1/a8tK6KR1Xpf/3WXFcRRctARV6jUmuFhJEmJjOLzrD+5p1PKmr8u4VHsxPva6+UTEOek8FvkP75ucFfXaP4ItLY1fZnyV+VhKUhJrf/yW8jXrUrBIcQAiTxzlxN9/XfHa2H8mt19uxXeTiDsfSY2mbbMknziuy//u7uY4upYZo4djS02lw1MvZD4WF3Xumi11Vv/wNZB+E8X18omIc9LNEyL/EegNUcnXv4GiQs261O/QjZkfDCfu/FkKlSqHee40Io9H8NxH32RuN/75PuzdbGHusX/faWC9kjTs2J0Slarj7evHX79vYOPCWZSqWoPWvZ+9aTYTEOR9lz+gGObyY+tujqOfJ4zm6P7dlK9ZF09PL35bMZ8d61by2MvvUK5G7czt1s2bzsrpX1CnzUOElijDpQvxbLesYOf6X6jVsiPVGzbP3FbHlohrUGEn8h/5fOBwwo23GfLpd8wq+iaWed+TEBtNyUr3MPzbxVSp1/iGr3ugSy/2/7GJzct+IiUpkYJFS9J54Ct0HfI6vrly3zSbHQjyuY0fRhzKf4+tOz2OSlSqzpblP7P1l4XY0tIoWfkehk76kQYdul2xXaXajdj/xyY2LPiB2HNn8PT0okjZijzx1pirVqfQsSXiGrSkmMh/xCbDqrNGp7i+lqHpIz/ifHRsiUh204wKkf/I452+bqYj8jJBHo2zOy0dWyKS3VTYifyHhwlK+6fPOXIkJtJzaZF256VjS0Symwo7kWsoE3Dj1SeMYCc9lzg3HVsikp1U2IlcQ4AXhPg6zsiKifQ8AbpU5vR0bIlIdlJhJ3IdVQMdZ2TFTnoecQ06tkQku6iwE7mO/D5QwUEuT1XIk55HXIOOLRHJLirsRG6gSiD4exp32cxE+iWyKnkNCiDZRseWiGQHFXYiN+BpgroFjP3wrZM/PYe4Fh1bIpIdVNiJ3EQ+H2hQMOc/gE1Aw4Lp+xfXpGNLRLKaVp4QuUVnEmHTufTJ5tl90niQ/sEb4pfNOxKHoGNLRLKKCjuR2xCdDFvOQ0Ja9u0jwCv9EplGU9yLji0RyQoq7ERuU5od9sbCgQvpl7Sy4gTKeJ8KedIns2vek3vSsSUid0uFncgdikqCPXFwNunOP4QzXhfim95LTG0nBHRsicidU2EncpcupMLhC2BNgNR/zqbrfRhf/rjXP+uGlglQ13+5Nh1bInK7VNiJZBGbHeJT0+dKxSRDTAqk2MBG+oR1bw8I8oYgn/Q5Tnm8tOi63BodWyJyq1TYiYiIiLgI9bETERERcREq7ERERERchAo7ERERERehwk5ERETERaiwExEREXERKuxEREREXIQKOxEREREXocJORERExEWosBMRERFxESrsRERERFyECjsRERERF6HCTkRERMRFqLATERERcREq7ERERERchAo7ERERERehwk5ERETERaiwExEREXERKuxEREREXIQKOxEREREXocJORERExEWosBMRERFxESrsRERERFyECjsRERERF6HCTkRERMRFqLATERERcREq7ERERERchAo7ERERERfxfy78jyz0NzThAAAAAElFTkSuQmCC\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": 24,
      "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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "15a3531a-89e7-4d81-a5d6-5822ee5a4d35"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"qulacs.simulator\", 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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "b28ef355-af8b-4fba-e030-e64299eb0b2d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -2.3968646467984435e-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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "5dd7622e-615a-4840-f403-2e73b48fbe88"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.11713966416462736\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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "52dcf7e7-8a27-4c61-b85a-c0e8a6793cbf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3813773084782757\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": "b1a79b79-9309-46f2-aa00-499c0c62f18b"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695112571.507541\n",
            "Tue Sep 19 08:36:11 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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  "nbformat_minor": 0
}