LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit A100 20.24s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit A100 20.24s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "e28ebed2-f6b0-4ce5-e6c3-c15e2e114b32"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1696311523.879999\n",
            "Tue Oct  3 05:38:43 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",
        "\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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "d75d96e9-1269-49ba-8d0a-b63eab3763dd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.61 0.57 0.64]\n",
            " [0.57 0.07 0.52]\n",
            " [0.64 0.52 0.09]]\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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "b70ba1db-cb99-4585-95dc-6deb1f80f419"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.07 0.52 0.57]\n",
            " [0.52 0.09 0.64]\n",
            " [0.57 0.64 0.61]]\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "f8a1aee6-b794-494e-fa10-79817e46783e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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xb98+LFiwANHR0Vi6dOlzlbpC1W0BWTWgip53ZnCw0r4OS0P58P0xXJ06dUJ6ejr27NlTdNu2bdugVqvRvXt3AIC1tXXRkGx8fDxq1aqFYcOGFRXGwYMHo3nz5jhz5gwA4LvvvsOePXuwadMmtG3bFqGhobC0tES1aiWv30tPptJoFyId/3cLIaDivxwVPi8hT7tq/Z9U7fGNDc/YEQmi0Wiwf/9+LFu2DKdOnYKPjw/WrVuHt956q9iwj664WgN9agC307SrMcsaniivwuP4OGon4pvanK3KwvfHMLVt2xYjR47EL7/8gsTERMTHx+O3337DV199hTZt2uDw4cPIy8uDTCaDg4MDPDw8SpQ0pVKJuLg49O7dGxqNBhs2bEBwcDBat26NuLg4XL16FVZWVkVTLQoKCnj1jWeQkg9cSAKytIugdXa2u/A4IZlATK52LqoxTVvgdidElUypVOLXX3/FsmXLcPPmTXTs2BHTpk3DkCFDSp3jow9PGrZ4VoXPM/ZhC0PE98ewpKSkYNOmTThw4ABsbGwwdepUdO7cGVKpFP369UNycjL27t1bVOYaNWqE7t27Y926dbC0tMTKlSuxdu1abN68Gd27d8fu3btx9OhR3Lp1C/fu3UNUVBQkEgny8/OxZ88eDBgwQPBXbPjicytn+oLk33+6uGvPrBsDFjuiSpKZmYkff/wRq1atwr1799C/f39MmzYN3bp1Ezaf5r8TjTUaDVQFSlhJS7aAxwuGKU00NmTlmQguAaD+d24W35/Kc+zYMSQlJeHVV18t+sXsxIkT+Oyzz2Brawtvb2+cO3cO77//Pj777LNSz8aPGjUKSUlJGDlyJAYPHlxsY+WCggIcOXIEW7duLbYnn6enZ7H988xJfK64BUfGUO5Y7Ij07OHDh1i7di2++eYbZGRk4PXXX8fUqVOLbX0gmloDZBQA3/38K+Iz8zF45NsltgZwkQIu1tohCUcr09kawBgUvj8p+UBqPpBaytYNLlLg/LEDWLVwDm5cOAtbG56iE+natWs4fvw4EhIS4Ofnh759+5b52N69e6Nhw4b49ttvS2yfolKpsHfvXixZsgR37txBWloaAO28vsaNG5fYfLlRo0Z6mcphKFLytVsEqQW8tgW0c1QNfViWxY5IT8LDw7Fy5Ups2LABFhYWeP/99zF58mTUq1dPdLQyDRo0CCqVCvv37xcdhSrg0qVLaN++Pc6cOYOuXbuKjkPPIDs7GyNHjkTLli2xaNGiJz5Wo9EgNja2xPV0b9++jYSEBACApaUlGjZsWOKKG40bN4a9vX1lfEl6o9IAh+PEbeoNaM+A965u2HNVWeyIdOzKlStYtmwZ5HI53Nzc8Omnn2L8+PE6u26lPvn4+GDAgAFYvXq16ChUAQUFBahatSq++OILzJw5U3QcqkSJiYm4c+dOidJ3//79osc0aNCgxPV0mzZtChcXF3HBy4GX4Xs2LHZEOqDRaHD06FEsXboUR44cgaenJ6ZMmYJ33323xHUhDVV+fj6qVKmCr7/+Gh9++KHoOFRBAwcORH5+Pg4dOiQ6ChmA9PR0BAcHFzu7d+fOHYSHh6Pwx3/NmjVLlD1fX194eHgYzH56yXnaLU0MRY9qhrsgyTxnXhLpSEFBAXbs2IFly5bhypUraNOmDbZt2wZ/f3+jm9gcHh4OlUqFxo0bi45Cz0Emk2Hu3LnIz88vdl1SMk9OTk7o0KEDOnToUOz2nJwcKBSKYmXv6NGj+O6771BQUAAAcHNzKzZ/r/DfderUqfTCdytdd1sAPS8JgFtpQDcP0UlKZ1w/eYgMRE5ODjZt2oQVK1YgPDwcvXr1wqFDh9C7d2+D+Q23vEJCQgCAxc7IyWQyZGdn49KlS+jSpYvoOGSg7Ozs0Lp1a7Ru3brY7UqlEmFhYcXO8F28eBGbN29Gbm4uAMDR0RFNmjQpUfoaNGhQYvGHLmQWaLf+AQBlXh5+XTkHp3b8jKy0FNRr2hKvT12EVt37PNOxzv6xHfvWr0HUnRuwlEpRp5EvXp+6CC269ix6zMHN/8M/544h7OoFJMbcg8z/HXyyelPR/Rpo82QWGOaqcwOMRGS4kpOT8e233+Krr75CUlIS/P398dtvv6Ft27aioz03hUIBBwcH1KxZU3QUeg6tW7eGk5MTTpw4wWJH5SaVStG0aVM0bdq02O0qlQpRUVElFm38/vvvyMjIAADY2toWW6lb+G9vb+/nOnsc/tiG3V9PHo3z+4MwYMwk1PRshOPyTQh8pz/mbT+Oph1efOJxtq+ah6A1C9BpgD9kw0dDVaBEtOImkuMeFHvcrv8tRU5mBrxbd0DKw9hSjyX5N1dLlwp/WXrDOXZEz+DevXtYtWoVfvjhB6hUKrz77ruYPHkyvL29RUfTmbFjx+Lq1au4fPmy6Cj0nAYMGAClUsl5dqR3Go0GDx48KDakW1j+kpKSAABWVlbw9vYuMaTbuHHjp85BVmuAPTHafRxDr17E9MEd8dbM5Rjy4ecAgPzcXEzu3RxO7tUQuOtcmccJuXIeM4d2wduzV2LQ+5898TUT7kfBvXY9SCQSvNnYAZ36+xc7Y1fISgIMqmV4Wz/xjB3RE9y8eRPLly/H1q1b4eDggEmTJuHTTz81yWs6KhQKDsOaCJlMhnnz5nGeHemdRCJBnTp1UKdOHfTpU3w4NCEhocSijY0bNyImJqbouZ6enqWu1HVycgIAZCgfbc59fn8QLCwt0eeND4pew9rWFj1HjsHWpTOQGHMP7rXqlppz749r4OJRAwPGTIRGo0Fudhbs7B1KfaxHnfrP9LUX/Lu/pLOBXf2NxY7oPzQaDU6fPo1ly5Zh3759qFOnDpYtW4axY8fC0dFRdDy9USgU6N27t+gYpAOcZ0eGwMPDA35+fvDz8yt2e1paWokzfEFBQYiIiCh6TO3atdG0aVP0GPEufPq9DolEgohbV1HLywdVHJ2KHc+7tXZhSOSta2UWu5tnj8KnbRfs3/AVdny1CBkpSXCpVgOvTpiJl0d/UuGvMSWfxY7IYKnVavzxxx9YunQpzp8/j2bNmuGnn37CyJEjTf6sR0pKChISEnjGzkS0adMGjo6OnGdHBsnZ2RmdOnVCp06dit2elZVVYqVuSt6jyxymxMfCpVrJOcCu/96WHB9T6utlpqYgPTkRiktncfPcMQyfNBcetevh2G8bsX72BFhaSfHSm+PK/XVIoL0SDAxs32cWOzJ7eXl5+OWXX7B8+XIoFAp069YNe/fuxcsvv1x07UdTp1AoAHBFrKmwsrJCt27dcOLECcyYMUN0HKJnYm9vjxdeeAEvvPBC0W0nHgJJ+do/5+fmQGpd8nJp1ja2RfeXJjdbu6txRkoSPvvmV3Qd/BoAoNMAf0zu0wI7vlpUoWKngfbyfobGPH5qEZUiLS0Ny5cvh5eXF8aOHYsmTZrg3LlzOHXqFAYMGGA2pQ54tNVJo0aNBCchXZHJZDh79iyUSgP8yUP0jJSPXRTW2tYOyvy8Eo/Jz8stur80hbdbSaXoNMC/6HYLCwt0HfQakmLvI+FB9HPnMxTm85OL6F+xsbEICAhAvXr1MHPmTPTr1w937tzBrl270LlzZ9HxhFAoFKhduzYcHEqfTEzG5/F5dkTG6vHe5Fq9JlJL2X6kcEsSt+q1Sj2Gg4sbrG1s4eBatcQ+e05VtQvhstJSnjufoWCxI7MREhKC999/Hw0aNMC3336LcePGITIyEuvXr0eTJk1ExxOKK2JNz+Pz7IiM1eMlpYFva8SEhyA7I73YY0KvXtDe36x16cewsECDZq2RnpQAZX5+sftS/p2X5+RWsctIGGKJMsRMRDp14cIFvPrqq2jSpAn27NmD+fPnIzo6GsuWLUOtWqX/hmduWOxMz+Pz7IiMlfSxltJpgD/UKhUOb1lXdJsyLw/Hf9uIRm06Fq2ITXgQjQdhwcWO02XQa1CrVDgR9FPRbfm5uTi9cwvq+PjCrUbFfhZIDbBFcfEEmSSNRoMDBw5g2bJlOHnyJBo1aoTvv/8eb731FmxtbUXHMygqlQqhoaEYO3as6CikY35+fpg/fz6USiWkUgPbk4HoGThLgeR87UIFnzYd0XngcGxdOh3pSQ9Ro4E3TgT9hIT7kRi/fH3Rc9ZOehu3z59E0L1H11/o88Y4HN32I9bP+hix4SFwr10Pp3b8jIQHUQjYuKfYa146vAeRt68DAAoKlIgKvoGg/1sEAGj30mA0aNoSgHZVrIsBfqxY7MjgJSQkIC4uDi1atHjqY5VKJbZv345ly5bhn3/+QYcOHbBjxw4MGTJEL9cwNAXR0dHIy8vjGTsTJJPJMG3aNFy6dMls54+ScXO1BsKzHv33hNWb8Wvt2Tj5u/ZasfWbtMT0jXvh26n7E49jY2eHeduP4ecvv8Cx7RuQl5OFBr6tMWPTPrSW9S322PP7dxQ7sxdx8yoibl4FAFStWaeo2GkAuBjgTli8pBgZrLNnz2Lu3Lm4c+cO3N3d4erqirVr15Za8DQaDbKzs9GiRQtERETg5ZdfxrRp09C9e3dIJAZ2vRcDc/DgQfTr1w/h4eHw9PQUHYd0qKCgAK6urpgxYwamT58uOg5RuaXlA0ceik5Rtt7VDW+DYgMcHSYCfvnlF3zyySfw9fXF8ePHMX/+fGg0Gnz88ccAtEXucRKJBPb29pg4cSKuX7+O/fv3w8/Pj6XuGSgUCtjY2KBevXqio5COcZ4dGTtHqfaarIbISgI4GuC4pwFGInN09epV2NraomnTpgC0V0Lo1KkTli9fDhsbG/j4+KB69erw8/NDamoqXFxcShxDo9Fg4sSJlZzc+CkUCnh7e3Oo2kTJZDLOsyOjZSEBPO2BsEzt0KehkECby8IASyfP2JFQP/30E1q0aIG2bdvi4MGDRbePHTsW//vf/2Bj82iX8ZCQEPj4+CAjI6PUY/HsXMVwRaxp4352ZOy8HAyr1AHaPF4Guu0nix0J8eeff8Le3h7z5s3DiBEjkJKSgkmTJhXdb2en3Slco9EU7Zx//vx5NGjQAHXrln6RZ6oYFjvT9sILL8DBwQEnT54UHYWoQhysgGo22rNkhkACbR4HAx3zZLEjIR4+fIj8/HwcPnwYs2fPhrOzMxISEoruL5xDJ5FIIJVKkZ2djUOHDmHChAkAALXaEPf7Nj5ZWVm4f/8+i50J4zw7MgXNnA3nrJ0G2jyGisWOKlVhYevevTu6dOmCGTNmYM2aNWjZsiVGjBiB119/Hffv3y8aVi0scFu2bIG9vT26dOkCAGZ1HVd9Cg0NBQAWOxMnk8lw5swZXjeWjJabNeBjIEOfPo7aPIaKPx1JL6KiohAeHg6VSgXgUUErLGy1a9fG4MGDsXv3bhw6dAhTp07FgAEDcP78ebz99ts4d+5c0bHUajU2b96MV199FY6OjggPD8f48eMhl8tLrI6l8lEoFAAAHx8fwUlIn2QyGbKysnD58mXRUYgqzNcZsLcUNyQrgXb41ddJUIBnxGJHOnXt2jV07twZLVq0gL+/P4YNG4bU1NQSZ9ikUil69+6NdevW4YcffsBbb72Fzz//HHv37kVBQQF27NgBQHtm7u+//8b9+/fh4eGBfv36oUmTJjh//jwaN27MBRPPSaFQwN3dHW5ubqKjkB4VzrPjcCwZM0sJ0LGq2GLXwU2bw5Cx2JHO5OXlITAwEI0bN8alS5ewaNEiXL58GR988AHCwsIAFJ8b5+vrizfeeAO1a9cuuq1Zs2Zwc3NDXFwcsrOzAQC7du1CVFQUFi5ciIYNG+LevXu4cuUKWrZsWblfoAniwgnzYGVlhRdffJHFjoyeqzXQxb3yy50EQFd37esbOhY70pnw8HAcOnQIw4YNg4+PD/r3749169YhNjYWP/74Y4nHS6VSWFk9WlakUqmgVCoRGhoKCwsLVKlSBQAwYsQIbN++HbGxsfjmm29QvXr1SvuaTB2LnfngPDsyFdVttSXLApVT8CwAvOgOVDOSy4yz2JHOhIeHo1atWqhTp07Rbb169ULnzp3x559/4uHDh7CwsEBBQUGx5+Xn50Oj0SA/Px+rV69GlSpVil3+qE2bNhg+fHilfR3mQqPRsNiZEc6zI1NS3RaQVQOq6HlfdQcr7esYS6kDWOxIhzp16oTQ0FA8ePCg6DZbW1t0794dUqkUe/fuBYBiZ+mUSiUCAwPx7rvvon79+tiwYQMmT54MX1/fSs9vbmJjY5GZmcliZyY4z45Mjas10KfGo9Wyujp7V3gcH0fttWCNYfj1cSx2pDNVq1ZFp06dsG3btqLVsADQqlUr2Nvb4+7duwCAS5cuYdmyZXjw4AGkUimaNGkCV1dX/PLLLwgODsbrr78u6kswKyEhIQC41Ym5kEqlePHFF7lRMZkUSwnQwgXo4QF4/HuhIvVjP3/Ko7DQedgAPaoBLZwNf6FEaVjsSKcmTJiAnTt34tq1a0W31a1bFykpKUX/febMGaxYsQJnzpwBALz22mtYvXo1XnrppcqOa9YUCgUsLS3h5eUlOgpVEs6zI1PlZgN08wC62Gdg/4b/g1qZV3RfWd3s8dutJIC3A9C3hvY4hrxP3dOw2JFOjRgxAp6enli1alXR5rf37t1Dbm4uatSoAQB45513sG3bNrz22msAeI1XURQKBTw9PWFtbcTfwahcZDIZMjMzceXKFdFRiPTi6L7d2LRgCjpJE9C7OtDWFfCyB6paA05W2jlzTlba//ay197fuzowqBbQ0sVwLxNWHhINd3glHfvzzz/x5ZdfIjo6Gu+//z5+//132NnZYc+ePdwvzYAMGDAAEomkaO4jmT6lUgk3NzfMmjUL06ZNEx2HSOeGDBmChISEYpvcmxuesaNy02g0OHDgAC5dulRihSsA9OvXD5s3b8aYMWNw/vx5DBo0CIcOHWKpMzBcEWt+pFIpunbtygUUZJLS09Nx8OBBs99FwQROOlJlUSqV+O2337Bs2TLcuHEDn332Gdq1a1ficRqNBp6enpgzZ46AlPQs8vLyEBERwWJnhmQyGb788ksolUpIpVLRcYh0Zs+ePcjLy4O/v7/oKELxjB09VVZWFr766is0atQIb775JmrVqoXjx49j5cqVpT6ec+YMX3h4ONRqNYudGeI8OzJVQUFB6NSpE+rWrSs6ilAsdlSmxMREzJ07F/Xq1cPkyZPRtWtXXLt2DQcOHIBMJmOBM2IKhQIAtzoxR23btoW9vT2HY8mkZGRk4MCBA2Z/tg5gsaNSREREYMKECahXrx6WL1+ON954A2FhYdiyZQtatWolOh7pgEKhgKOjIy/PZoYK97NjsSNTsnfvXg7D/ovFjopcu3YNo0aNQqNGjbBt2zZMmzYN0dHR+Oqrr9CgQQPR8UiHChdO8KyreSrcz660xU9Exkgul6NDhw6oX7++6CjCsdiZOY1Gg2PHjqFv375o06YN/vrrL6xZswZRUVGYO3cu3N3dRUckPeCKWPPGeXZkSjIzMzkM+xgWOzOlUqmKfsPp1asX4uPjsWXLFoSGhuKTTz6Bvb296IikRyx25o3z7MiU7Nu3D7m5uSx2/2KxMzO5ubn4/vvv0aRJE4wYMQKOjo74888/cfXqVYwaNQpWVtwBx9QlJSUhKSmJxc6McZ4dmRK5XI527drB09NTdBSDwGJnJlJSUhAYGIj69evjo48+QuvWrXHx4sWiYVjOtTIfISEhALgi1tz5+fnh9OnTnGdHRi0rKwv79+83+02JH8diZ+Lu37+PKVOmoF69eliwYAGGDRsGhUIBuVyO9u3bi45HAhRudeLt7S04CYnEeXZkCvbv34+cnBwOwz6Gxc5E3b59G++++y68vLywfv16TJgwAZGRkfjuu+/QqFEj0fFIIIVCgbp163IepZlr164dqlSpwuFYMmpyuRwvvPACvLy8REcxGCx2Jubs2bMYPHgwmjVrhsOHD2Px4sW4d+8eAgMDUaNGDdHxyABw4QQBnGdHxi87Oxv79u3jMOx/sNiZALVajT/++ANdu3bFiy++iLCwMGzcuBHh4eGYMmUKHB0dRUckA8JiR4VkMhnn2ZHROnDgALKzszkM+x8sdkYsPz8fGzduRPPmzTFkyBBIJBLs3r0bN2/exOjRo2FtbS06IhkYlUqFsLAwFjsC8Gie3dWrV0VHISo3uVyO1q1bc77wf7DYGaH09HSsXLkSXl5eeO+999CoUSOcOXMGZ86cweDBg2FhwbeVShcVFYX8/HwWOwLAeXZkvHJycrB3714Ow5aCDcCIxMfHY8aMGahXrx6mT5+OPn364NatW9i9eze6du0qOh4ZgcIVsT4+PoKTkCHgPDsyVgcOHEBWVhaHYUvBYmcEQkNDMW7cONSvXx9r167F2LFjER4ejo0bN8LX11d0PDIiCoUCtra2qFevnugoZCA4z46MUVBQEFq2bMlfUkvBYmfA/v77b/j7+6Nx48bYvXs35s6di+joaKxYsQJ16tQRHY+MkEKhQKNGjThcT0X8/PyQkZHBeXZkNHJycrBnzx4Ow5aB390NjEajwcGDB9GzZ0906NAB169fx//+9z9ERkZi+vTpcHV1FR2RjBhXxNJ/cZ4dGZuDBw8iMzOTxa4MJlns1BogLR+IzAKupgAnHgKH44CDcdp/n3iovT0yS/s4tUZ0YqCgoABbt25FmzZt0K9fP2RkZEAulyM4OBjjxo2Dra2t6IhkAljs6L+sra3RtWtXFjsyGkFBQWjRogW/l5XBpK74nlkAhGcCEVlAwb9lTQKgtN6WnA+EZ2n/bCUBPO0BLwfAoZL/j2RlZWHDhg1YuXIloqKi0LdvX6xevRoymYzXbyWdyszMRExMDL8ZUgkymQxLlixBQUEBrKxM6scCmZjc3Fz88ccf+Pzzz0VHMVgmccYuOQ84naA9IxeW+ajUAaWXuv/eXqDRPu9gnPY4yfn6TKuVmJiI+fPno379+vjss8/QtWtXXL16FX/++Sd69OjBUkc6FxISAgAsdlSCTCbjPDsyCocOHUJGRgaHYZ/AqH81U2mA22lASKb2zBxQdpF7msLnJeQBxx8CPg6ArzNgqeN+FRkZiVWrVmH9+vXQaDQYM2YMJk+eDE9PT92+ENF/cKsTKkvhPLuTJ0+iffv2ouMQlUkul6NZs2Zo2rSp6CgGy2jP2KXka+fLhWRq/1tX0+QKjxOSCRyJ176OLly/fh1vvPEGvL29sWXLFkydOhXR0dFYu3YtSx1VCoVCgWrVqsHFxUV0FDIwnGdHxiAvLw9//PEH9657CqMsdvG52gUQ2Sr9vk5WgfZ14nMr9nyNRoPjx4+jX79+aN26Nc6ePYvVq1cjOjoa8+bNg7u7u24DEz0BF07Qk3A/OzJ0hw8fRnp6Oodhn8Loil18LnA2EVBDd2fpyqKB9nXOJpav3KlUKuzYsQMdO3ZEz549ERsbi19++QWhoaGYMGEC7O3t9RWZqEwsdvQkMpkM6enpuHbtmugoRKWSy+Vo2rQpmjVrJjqKQTOqYpeSD5xL1H+h+y8NtK/7tGHZ3NxcrFu3Dk2bNoW/vz8cHBxw4MABXLt2DW+88QakUmml5CX6L41Gg5CQEBY7KlO7du1gZ2fH4VgySHl5edi9ezfP1j0Doyl2Kg1wIanyS10hNYCLydoc/5WamorFixejQYMG+PDDD9GyZUtcuHABx44dQ79+/bjClYSLiYlBVlYWix2VifPsyJAdPXoUaWlpnF/3DIym2N1OA7JU4oodoN0n73b6o/9+8OABPv/8c9StWxfz5s3DkCFDEBwcjKCgIHTo0EFcUKL/4IpYehacZ0eGSi6Xo3HjxmjevLnoKAbPKIpdct6j1a+ihWQAVxQReO+99+Dp6Ykff/wREyZMQFRUFL7//nv+4CSDpFAoYGVlBS8vL9FRyIBxnh0Zovz8fOzatQvDhw/nCNgzMIp97G6ll30FicqmVqmw81IIDh48iMDAQHzwwQdwcnISHYvoiRQKBby8vDjPk56offv2RfPs2rVrJzoOEQDg2LFjSE1N5TDsMzL4M3aZBcDDPG2pU+bl4efAaXi/bS2M8rZDwKCOuH7q8DMdJyn2AVZ+NAJvN3PBW02dsOS9IYiPCi/2mOO/bYJ/XUmZ/5zauQUWlpZo7dcX/4SG4/PPP2epI6PAFbH0LDjPjgyRXC5Ho0aN0LJlS9FRjILBn7ELz3x0tu7ryaNxfn8QBoyZhJqejXBcvgmB7/THvO3H0bTDi2UeIycrE/Ne64HsjDS88skMWFpJse/H1Zgz3A8rDl6Do2tVAIBvx+749P9+LvH8vT+uRuTt62jRtRcAbZ77+TZwq6KHL5hID0JCQvDKK6+IjkFGQCaTYdmyZVCpVLC0tBQdh8ycUqnErl278OGHH3IY9hkZdLFTa4CILG2pC716EWf/+BVvzVyOIR9qL/7r9+rbmNy7OX4O/AKBu86VeZyDm79FbEQoluy5CO/W2svlvNDjZXzWuzn++H4l3ggIBABUr++F6vWLz0HKy8nBDzPHo3mXnnCtVgOANk9EFtDcGbDg3zMycHl5eYiMjOQZO3omMpkMs2bNwrVr19C2bVvRccjMHTt2DMnJydzmpBwMeig2QwkU/Dux7vz+IFhYWqLPGx8U3W9ta4ueI8cg5PJfSIy5V+Zxzu8Lgner9kWlDgBqezdBi6698Nfe356Y4fKRPcjJzED3YW8Uu71AA2Rw4RgZgbCwMKjVahY7eiaPz7MjEi0oKAgNGzZEq1atREcxGgZd7FKUj/4ccesqann5oIpj8Tlt3q2124pE3rpW6jHUajWigm+gYcuSE4G9W3dAXNRd5GRmlJnh1M4tsLa1Q8eXSw5j6eo6skT6xK1OqDw4z44MhVKpxM6dO7katpwMu9jla+ezAUBKfCxcqtUs8RjXf29Ljo8p9RiZqclQ5uVV6LkZKcm4dvJPtOs9CHYOjsXukwBIZbEjI6BQKODs7Ixq1aqJjkJGws/PD6dOnYJKpecLchM9wYkTJ5CUlMRh2HIy6GKXpny0xUl+bg6k1jYlHmNtY1t0f2kKb5falHyu9CnPPb8/CAX5+ej2n2FYQJsrVVnyOUSGpnBFLH/jpWfF/ezIEMjlcnh5eaFNmzaioxgVgy52SvWjP1vb2kGZn1fiMfl5uUX3l6bwdmVeyecqn/Lc0zu3wMHFDW16vPzUfESGiludUHlxnh2JVlBQgJ07d8Lf35+/lJaTQRe7x3uTa/WaSH0YW+IxKf/e5la9VqnHcHBxg9TGptzPTXgQjTsXT6PzwOGwKmNTV/Y6MgYhISEsdlQuNjY26NKlC4sdCXPy5EkkJiZyGLYCDLrYPR6ugW9rxISHIDsjvdhjQq9e0N7frHXpx7CwQL3GLXD3xqUS94VevYDq9bxKzJ8DgDO7t0Gj0aDb0JLDsKXlIzJEiYmJSE5OZrGjcpPJZJxnR8LI5XI0aNCAW+5UgEF3E+lj6ToN8IdapcLhLeuKblPm5eH4bxvRqE1HuNeqC0B7pu1BWHCx43Qa4I+w638j7PqjcvfgrgI3zx1D54Gl/zZwZtdWuNeu98SNj6UG/X+PiCtiqeIK59ldv35ddBQyMyqVCr///juHYSvIoDcodpYCyfnahQo+bTqi88Dh2Lp0OtKTHqJGA2+cCPoJCfcjMX75+qLnrJ30Nm6fP4mge4+uLNvv7fE4uvUHLB49AIPHfQ5LKyn2/rAKLu7VMeiDKSVeNzr4JqLu3MCwjwPK/EslAeDCy26SgVMoFJBIJGjUqJHoKGRkHp9n98ILL4iOQ2bk1KlTSEhI4DBsBRn0OSdX60erYgFgwurNGDBmEk7+/jM2zP0UKqUS0zfuhW+n7k88jp2DI+bLT6Bpx+7Y8dUi/LpiNur7tsJ8+Uk4V/Uo8fjTu7YAAF4cMqrMY2oAuFhX5KsiqjwKhQL16tWDnV3pC4SIysJ5diSKXC5H/fr10b59+6c/mEqQaDQazdMfJkZaPnDkoegUZetdXXtWkchQDR06FDk5OTh48KDoKGSEFi1ahBUrViApKYnXjaVKoVKpULt2bbz55ptYsWKF6DhGyaDP2DlKASsDHV63kgCOBj2QTcQVsfR8/Pz8kJaWxnl2VGnOnDmD+Ph4+Pv7i45itAy62FlIAE/7R1efMBQSaHNZGFowoscUFBQgLCyMxY4qrEOHDrC1teVwLFUauVyOunXromPHjqKjGC2DLnYA4OVQfJ6dIdBAm4vIkEVGRkKpVHJFLFUY59lRZVKpVNixYwdXwz4ngy92DlZANRvDOWsngTaPA4dhycAVbnXCM3b0PLifHVWWc+fOIS4ujsOwz8ngix0ANHM2nLN2GmjzEBk6hUIBOzs71KlTR3QUMmIymYzz7KhSyOVy1K5dG506dRIdxagZRbFzswZ8DGTo08dRm4fI0CkUCvj4+MDCwig+5mSgCufZnTx5UnQUMmFqtbpoGJbfs56P0fzf83UG7C3FDclKoB1+9XUSFIConLgilnSB8+yoMpw7dw4xMTHclFgHjKbYWUqAjlXFFrsObtocRMZAoVCw2JFOcJ4d6VtQUBBq1aqFzp07i45i9Iym2AHaK1F0ca/8cicB0NVd+/pExiA9PR2xsbEsdqQTMpkMqampuHHjhugoZILUajWCgoLw6quvchhWB4zu/2B1W23JskDlFDwLAC+6A9VsK+HFiHQkJCQEALjVCekE97MjfTp//jwePHjAYVgdMbpiB2jLnawaUEXPV7hxsNK+DksdGRtudUK6ZGNjg86dO7PYkV7I5XLUrFkTXbt2FR3FJBhlsQO0w6J9ajxaLaurs3eqggJoNGr4OGqvBcvhVzJGCoUCNWrUgJMTV/uQbnCeHelD4TDsK6+8wmFYHTHq/4uWEqCFC9DDA/Cw0d5W0YJX+Lys2AjM9feDW+YDLpQgo8UVsaRrnGdH+nDx4kXcv3+fw7A6ZNTFrpCbDdDNA+hbA/B2AKweK2RldbPHb7eSaJ/XtwbwarPqiL97B/Pnz9dnZCK94opY0jXOsyN9kMvlqF69Ol588UXRUUyGSRS7Qg5WQEsXYFAt7TBqW1fAyx6oag04WWnvd7LS/reXvfb+3tW1j2/p8u/9Tk6YNWsW1q9fj+DgYNFfElG5qdVqnrEjnbO1tUXnzp25UTHpjEajKRqGtbTU86R5M2KSVzy1kADOUu0/sC//8z/66COsWbMGM2fOxI4dO3Sej0ifHjx4gOzsbK6IJZ2TyWRYs2YN1Go150PRc/v7778RHR3NYVgd4yezFDY2NliwYAF+//13XLhwQXQconLhiljSF5lMhpSUFM6zI52Qy+WoVq0aunfvLjqKSWGxK8Mbb7yBFi1aYNq0adBoNKLjED0zhUIBqVQKT09P0VHIxHCeHemKRqOBXC7nMKwesNiVwdLSEosXL8bJkyfx559/io5D9MwUCgUaNmwIKyuTnGlBAtna2qJTp04sdvTcLl++jKioKPj7+4uOYnJY7J6gf//+6NatG6ZPnw61Wi06DtEz4cIJ0qfC/ez4PZGeh1wuh7u7O/z8/ERHMTksdk8gkUiwdOlSXL9+Hdu2bRMdh+iZcKsT0ifOs6Pn9fgwLEcWdI/F7ik6d+6MoUOHYtasWcjLyxMdh+iJcnJyEBUVxRWxpDcdO3aEjY0Nh2Opwq5cuYKIiAiuhtUTFrtnEBgYiOjoaHz//feioxA9UVhYGDQaDc/Ykd4U7mfHYkcVFRQUhKpVq0Imk4mOYpJY7J5B06ZNMXr0aCxatAgZGRmi4xCViVudUGXgPDuqqMJh2GHDhnEYVk9Y7J7RvHnzkJ6ejpUrV4qOQlQmhUIBV1dXuLu7i45CJqxwnt0///wjOgoZmWvXruHu3bschtUjFrtnVLduXUyYMAErV65EfHy86DhEpSpcESuRlHWVZKLnx3l2VFFBQUFwc3NDjx49REcxWSx25TB9+nRYWlpi0aJFoqMQlYorYqkycJ4dVUThMOzQoUMhlUpFxzFZLHbl4ObmhoCAAHz//fcIDw8XHYeoGI1Gw2JHlcbPzw8nT57kPDt6Zjdu3EBoaCiHYfWMxa6cPv30U3h4eGD27NmioxAVk5CQgNTUVG51QpWC8+yovORyOVxdXdGrVy/RUUwai105ValSBXPnzsXWrVtx9epV0XGIinBFLFWmTp06cZ4dPbPCYdghQ4ZwGFbPWOwq4L333oOPjw+mT58uOgpREYVCAYlEAm9vb9FRyAzwurFUHjdv3kRISAiHYSsBi10FWFlZITAwEAcPHsTx48dFxyECoF0R26BBA9ja2oqOQmZCJpNxnh09E7lcDmdnZ/Tu3Vt0FJPHYldBr7zyCjp06ICAgABoNBrRcYi4cIIqHefZ0bN4fBjW2tpadByTx2JXQRKJBEuWLMHFixfx+++/i45DxGJHla5wnt3JkydFRyEDdvv2bQQHB3MYtpKw2D2HHj16oF+/fpgxYwYKCgpExyEzplQqcffuXa6IpUrFeXb0LORyOZycnNCnTx/RUcwCi91zWrx4MUJCQrBhwwbRUciMRUREoKCggGfsqNJxnh09TeEwrI2NjegoZoHF7jm1bt0ao0aNwrx585CdnS06DpkpbnVCovj5+SE5ORk3b94UHYUM0O3bt3H79m34+/uLjmI2WOx0YOHChUhMTMRXX30lOgqZKYVCAXt7e9SuXVt0FDIznTp1grW1NYdjqVRBQUFwdHTESy+9JDqK2WCx0wEvLy98+OGHWLJkCZKTk0XHITMUEhICHx8fSCQS0VHIzNjZ2XGeHZVJLpdj8ODB3IapErHY6cisWbOgUqmwePFi0VHIDHFFLInEeXZUmuDgYNy8eZOrYSsZi52OVKtWDVOmTMHatWtx79490XHIzLDYkUgymYzz7KiEoKAgODg4cBi2krHY6dCUKVPg5OSEefPmiY5CZiQtLQ3x8fHc6oSE4Tw7Ko1cLsegQYNgZ2cnOopZYbHTIUdHR8yePRubNm3C7du3RcchM8EVsSRa4Tw7blRMhUJCQnDjxg0OwwrAYqdj48aNQ/369TFjxgzRUchMFBY7nrEjkTjPjh4nl8thb2+Pfv36iY5idljsdMza2hoLFy7E7t27ce7cOdFxyAyEhISgVq1acHR0FB2FzJhMJkNSUhJu3bolOgoZgKCgIAwcOJDDsAKw2OnB66+/jlatWiEgIAAajUZ0HDJxXDhBhoDz7KhQWFgYrl27xmFYQVjs9MDCwgJLlizB6dOnsX//ftFxyMSx2JEhsLOzQ8eOHVnsCHK5HFWqVMHLL78sOopZYrHTk759+0ImkyEgIAAqlUp0HDJRarUaoaGhnF9HBoHz7AjQDsMOGDAAVapUER3FLLHY6YlEIsGSJUtw8+ZNbNmyRXQcMlH37t1DTk4Oz9iRQeA8OwoPD8eVK1c4DCsQi50edezYEa+88grmzJmDvLw80XHIBHGrEzIknGdHcrkcdnZ26N+/v+goZovFTs8CAwNx//59/O9//xMdhUxQSEgIrK2t0aBBA9FRiFClShXOszNzcrkc/fv3h729vegoZovFTs8aN26M9957D4sWLUJaWproOGRiFAoFvL29YWlpKToKEQDtcOypU6c4z84MRURE4PLlyxyGFYzFrhLMnTsXWVlZWLFihegoZGK4IpYMjUwmQ2JiIq++Y4aCgoJga2uLAQMGiI5i1ljsKkHt2rUxceJErFq1CnFxcaLjkAlRKBRcEUsGhfPszFfhMKyDg4PoKGaNxa6STJs2reiqFES6kJ2djejoaJ6xI4PCeXbmKTIyEn///Tf8/f1FRzF7LHaVxNXVFTNmzMC6desQFhYmOg6ZgNDQUABcEUuGx8/Pj/vZmZkdO3bAxsYGAwcOFB3F7LHYVaJPPvkENWrUwKxZs0RHIRMQEhICgMWODA/n2ZkfuVyOl19+mdesNgAsdpXIzs4O8+bNw/bt23H58mXRccjIKRQKVK1aFVWrVhUdhaiYzp07QyqVcjjWTERHR+PChQtcDWsgWOwq2TvvvIMmTZpg+vTpoqOQkeOKWDJUnGdnXjgMa1hY7CqZlZUVFi9ejMOHD+PIkSOi45ARY7EjQ1Z43ViNRiM6CumZXC5H37594eTkJDoKgcVOiCFDhqBz584ICAjg5GKqEI1Gw61OyKBxnp15uHfvHv766y8OwxoQFjsBJBIJlixZgsuXLyMoKEh0HDJC8fHxSE9P5xk7MlicZ2ceduzYAWtrawwaNEh0FPoXi50g3bt3R//+/TFz5kwolUrRccjIKBQKAFwRS4aL8+zMQ1BQEF566SU4OzuLjkL/YrETaPHixbh79y7Wr18vOgoZmZCQEFhYWKBhw4aioxCVSSaT4cSJE5xnZ6IePHiAs2fPchjWwLDYCdSyZUu8+eabmD9/PrKyskTHISMSFxcHT09P2NjYiI5CVCY/Pz/OszNhO3bsgFQqxeDBg0VHocdINPxVSqjIyEg0btwYc+bMwcyZM0XHISOSk5MDOzs70TGIypSTk4Ovv/4a7733HvdbNEHdunWDk5MT9u3bJzoKPYbFzgBMmjQJGzduRHh4OL/5EZFJKSgogKWlJSQSiegopEMxMTGoU6cONmzYgNGjR4uOQ4/hUKwBmDlzJjQaDQIDA0VHISLSKSsrK5Y6E/T777/D0tISQ4YMER2F/oPFzgB4eHhg6tSp+PrrrxEVFSU6DhER0RPJ5XL07t0brq6uoqPQf7DYGYjPPvsMrq6umDt3rugoREREZYqLi8Pp06e5GtZAsdgZCAcHB8yePRubN2/GzZs3RcchA8epsWTs0tPTceHCBcTExIiOQuVUOAw7dOhQ0VGoFFw8YUDy8/Ph6+sLX19f/PHHH6LjkIEp/KhqNBpYWPB3MjI+f/31FzZs2IAjR44gOjoa9evXh52dHUaOHInx48dz8ZiR6NGjB2xsbPDnn3+KjkKl4E8HA2JtbY1FixZhz549OHPmjOg4JFhubi7Cw8ORkZEBQHspusJ/Ht9egL+bkaFLTEzEO++8g5deegm3bt3C+++/j4MHD2LDhg145ZVXsG/fPixdulR0THoG8fHxOHXqFPz9/UVHoTLwjJ2BUavVaNeuHezs7HDmzBmuJjNju3fvxrx589C+fXs4OzujZs2aaNasGS5evIi5c+ciPj4eHh4eomMSPZFGo8HUqVMhl8uxZs0a9OzZs8Tlp3799VdMmzaNi8eMwHfffYdPPvkEcXFxcHd3Fx2HSmElOgAVZ2FhgSVLlqBv377Ys2cPd/Q2Y5GRkbh+/Trc3d2Rm5uLjIwM2NraIi4uDtWqVUNAQABsbW0xdOhQ9OnTR3RcolLdv38fJ06cwKJFizBs2LBSH5OZmQknJydkZmbCwcGhkhNSecjlcvTs2ZOlzoBxKNYA9enTB7169cL06dOhUqlExyFBhg8fjlGjRqFLly44fPgw5HI51q5dC3t7e9SoUQMZGRk4evQokpOTRUclKlOdOnVw+/ZttGrVqsR9aWlp2L9/P7744gsMHz6cpc7APXz4ECdOnOBqWAPHoVgDdenSJbRv3x4bNmzAu+++KzoOCZKXl4eXXnoJ3t7eWL9+PQCgYcOGWLx4MUaMGIHc3FwAgK2trciYRE/Uu3dvVKlSBbNnz4ajoyMiIiIQFhaGa9eu4eLFi2jfvj1Wr15dYoiWDMu6deswfvx4xMbGchqIAWOxM2AjRozA+fPnERISwh/cZkij0RTNsRw5ciQyMjKwZ88eODk54eDBg+jatavghETP5p9//sHSpUuxdetWNGzYEG5ubsjMzETNmjUxcOBAjBw5EjVq1BAdk56iT58+0Gg0OHLkiOgo9AQsdgYsJCQEvr6+WLp0KaZMmSI6DglQWO6SkpIwb9483LhxA6dPn8a9e/dQu3Zt0fGInllqaioSExNx+fJlSCQStGzZEk2aNBEdi55RYmIiatSogW+++Qbjxo0THYeegMXOwH344YeQy+W4e/cuXFxcRMchge7evYtZs2bB1tYWX3/9Nezt7UVHInpuarW6aBsfMlw//PADPvzwQ8TGxqJatWqi49ATsNgZuNjYWHh7e2PixIkIDAwUHYcqSUZGBlQqFRwdHWFpaVnsPrVazQ2Kyejs2bMHq1atwhdffIGXX34ZBQUFsLLixgzGom/fvlAqlTh27JjoKPQU/Olg4GrWrIlJkyZhzZo1vPSOGfnmm2+wd+/eosUR586dw4QJEzB+/Hj88ssviIuLE5yQqHycnJyQm5uLrKwsACiz1BXeT4YjKSkJR48e5WpYI8EzdkYgLS0NXl5eGD58OL777jvRcagSVK9eHd988w38/f2xefNmzJgxAz4+PlCr1YiMjESzZs2wfv16Tjgno6FWq5GUlFRiNaVKpUJCQgLi4uIQFhaGkydPYvTo0Wjbtq2gpPRf6enpWLp0KSZNmsTVsEaAxc5IrFy5EtOmTcPt27fh4+MjOg7pUXZ2Njw8PBAZGQk3Nze0adMG77zzDt544w04ODggODgYb731FoYOHYpFixaVGKolMkSFC4GUSiWUSiWqVKkCQLsR9w8//IDNmzcjLy8PiYmJeOWVVxAUFCQ4MRVSq9XQaDT8XmMkOBRrJD7++GPUqlULM2fOFB2F9Cw2NhZeXl64d+8e4uLikJycjNGjR6NGjRpwcHBAu3btsGrVKuzZs4ffaMloSCQSXLlyBWPGjMHff/9ddLubmxvy8/Oh0Wjw8OFDnDt3DkePHhWYlP7LwsKC32uMCIudkbC1tcWCBQsQFBRU7JsimZ569eqhR48eWLFiBVJSUtC8eXOcPn262GPCwsLAk+1kbKysrPDXX3/By8ur6DYnJyeMHj0a1tbWAIAXXngBeXl5CAsLExWTyKix2BmRt956C82aNUNAQAB/qJswqVSKd955B3fu3MGkSZOQlpaGyZMnY9myZdi1axe+/PJLbNq0CSNHjhQdlahcWrZsibi4ODx8+BAAii6ZqFQqYWVlhbNnz8La2hpeXl7YuHGjyKhERovFzohYWloiMDAQx44dw+HDh0XHIT3RaDRo27Ytdu3aBV9fX6SmpiI6OhpLlizBlClT8O2332LEiBGYOnWq6KhE5ebn54eff/4ZeXl5RcN727dvh7OzMxo1agQAmD9/PhdPVLIDBw7g5s2bomOQDnDxhJHRaDTo1q0bsrOzcenSJe5nZqIe36suJycHUVFRiIiIgFqtRrdu3eDk5CQ4IVHF7N+/H/PmzYOdnR1kMhnu3r2LP//8E1OmTMH06dNFxzNbderUgbu7O9atW4cOHToAKH5ZQzIeLHZG6OzZs3jxxRexdetWvP7666LjkJ7wmyqZqosXL+KLL75Afn4+3N3d0a9fP4wfP150LLO1d+9evPrqq+jVqxcePnyIlStXws/PT3QsqiAWOyM1ePBg3Lp1C3fu3CmadEymq/AMnlKpREJCAtzd3fm+k9GLiIiAm5sbnJ2di93+4MEDHDlyBO3bt4evr6+gdOajZ8+eaNmyJaZMmYJRo0bh6tWrWL16Nd5++23Y2NjwajdGhu+UkQoMDERERAR++OEH0VFIx/77u5ZGoymaZB4eHo5Ro0Zh0aJFIqIR6ZSnpyecnZ2L/s4X/jspKQkbNmzA4sWLRcYzC3l5eTh9+jTGjRuHunXrFv152bJl2L59OwCw1BkZvltGqnnz5njnnXewYMECZGZmio5DOiSRSJCfn4+HDx+ioKAAEokEUqm06D53d3dehJuMWk5ODuRyOc6dOwdA+/darVYXTT1o2bIlVq9ejf379yMxMVFkVJO3Zs0aeHl5oWnTpigoKAAAfPHFF3jppZcwevRojB8/HvHx8YJTUnlwKNaIRUdHw8fHBzNmzMCcOXNExyEdUKvVWLduHU6dOoXExERkZWXB2dkZLVu2RK9evdCnTx/REYmem1KphI2NDZycnDBmzBhMnz4d7u7uAIovHGrbti0mT56MN954Q2RckzZp0iTUq1cPkydPLjGvd8OGDVi2bBlefvllrF69WmBKKg8WOyM3ZcoUrFu3DuHh4byGnwmYNm0atm7dilatWqFJkyawsrJCXFwc7t+/j/j4eIwcORITJ06Eg4OD6KhEz6Vbt25wdHSEhYUFgoOD8emnn+K9994r+rsdExODkSNH4tVXX8XEiRMFpzUvheU6Pz8f27Ztw7vvvosvv/ySq5aNBIudkUtKSoKXlxfeffddrFmzRnQceg4ZGRmoVasWtm/fjv79+xe7PSoqCvv378fChQvx448/4rXXXhOYlOj5ff7554iMjERQUBA2bdqE5cuXQyqV4pVXXsHgwYOxZcsWyOVynDx5EvXr1xcd16wU1oLCs3f79+9H69atUatWLZGx6Bmx2JmAwMBAzJs3DwqFAp6enqLjUAVdvHgRQ4YMQUREBGxtbUt9zPz587F3715eVo6M3pUrVyCTyZCWlgaJRAKlUoklS5Zg3759uHz5MqpXr47p06dj/Pjx3PZHT1asWIHx48ejSpUqpd6vUql4jVgjxGJnArKysuDt7Y3evXvj559/Fh2HKkihUODNN99Et27dsGDBAtjb25f4gfbdd9/h66+/5g7xZBIsLCxw6tQpvPjii0Ul4uHDh7C2toaLi4voeCbtzJkz6N69O/Ly8iCVSlFQUIDo6GgEBwfDzc0N7du3h6WlJffTNEJWogPQ87O3t8fcuXMxfvx4TJ06FS1bthQdiSqgcePGeP/997Fq1SokJSWhX79+aNasGZydnZGVlYUDBw5ALpdj2LBhoqMS6cS4ceOQlJQEQHvJRLVaXWzFN0uF/qxduxYjR46EVCrFrVu38PXXX+P777+Ht7c3PDw80LNnT8yfP59bnRghnrEzEUqlEs2aNUOjRo2wb98+0XGoggoKCrB9+3Z8++23uHr1KvLz82Fra4tatWpBIpFg6NChmDp1atEKQiJjlpWVBUtLyzKnHpD+VKlSBefPn0fLli0xaNAg5OTkYPLkyXB1dcW+ffuwbNkyLF68GFOmTBEdlcqJxc6EyOVyjBgxAidOnODlYExAfn4+7t69i5iYGCQkJKBp06Zo1aqV6FhEZOT27duHQYMG4dKlS2jQoAHat2+P3bt3o3nz5kWPef/995GZmYlNmzbBxsZGYFoqLxY7E6LRaNChQwdYWlrir7/+4hAGERGVsGfPHixZsgRhYWFITExEx44dcfDgQTg6OqKgoABWVlb49ddfsWTJEly7dk10XConzrEzIRKJBEuWLEHv3r2xa9cuzsUiIqIS+vbti9atWyM4OBgnTpyAm5tb0RYnVlbaWnDixAk0atRIZEyqIJ6xM0EvvfQS7t27h3/++afoQ0pEZMiUSmXRpfOo8mRlZSEtLa3YHnVXrlzB4MGDsXnzZvTs2VNgOqoILncxQUuWLEFwcDB++ukn0VHoOWVnZ4uOQKR32dnZ+Pbbb3H//n3RUcyOvb19sVKXkJCAjRs3onv37ix1Ropn7EzU66+/jtOnTyM0NBR2dnai41AFde3aFa1bt8Y333wjOgqR3mRkZMDV1RXffPMNxo0bJzqO2SrcXiYrKwupqamoXbu26EhUATxjZ6IWLlyI+Ph4rF27VnQUeg4KhQI1atQQHYNIrxwdHdGuXTucPHlSdBSzo1Kpil1CLDk5Gfb29ix1RozFzkR5e3vjgw8+wOLFi5GSkiI6DlVAUlISkpKS0LhxY9FRiPROJpPhxIkT4CCS/t2/fx8JCQkAtBtDF+6gcPHiRbz55ptYv369yHj0nFjsTNjs2bORn5+PpUuXio5CFRASEgIALHZkFmQyGWJjYxEaGio6iklKTEzEN998g/r162Po0KEYOXIk3njjDfz666/IysoCoB0Sf/jwIZydnQWnpefBOXYmbs6cOVi+fDlCQ0NRp04d0XGoHDZt2oR3330XWVlZZV6km8hUFM6z+/bbb/HBBx+IjmNyxo4dW7Ta1cnJCQ8fPsSdO3cQHR0NT09PTJkyBV27dgUAqNVqXkrMiLHYmbj09HQ0bNgQQ4cOxQ8//CA6DpXD9OnTsXXrVkRFRYmOQlQpOnbsiIYNG2Lr1q2io5gcBwcH/PHHH8VWuoaHh+PMmTP44YcfkJCQgG3btqFNmzYCU5IusJKbOCcnJ8ycORMbNmxAcHCw6DhUDgqFAj4+PqJjEFUazrPTjzt37sDLy6vEDgleXl54++23cfToUVSpUgU7duwQlJB0icXODHz00UeoW7cuZs6cKToKlYNCoeD8OjIrnGenH56enqhVqxamTp2KsLCwEsXZ2toao0ePxv79+wUlJF1isTMDNjY2WLhwIX7//XecP39edBx6BiqVCmFhYSx2ZFa6du0KS0tLnDhxQnQUk2Jra4uFCxciOzsbb775JjZv3owHDx4gJycHAJCXl4e//vqLIwQmgsXOTIwaNQpdunRBTEwMhzmMQFRUFPLz81nsyKw4OTmhbdu2LHZ60L59e2zZsgUNGzbERx99hJYtW2LkyJH46KOP0LRpU9y9excBAQGiY5IOcPGEGcnPz4eFhQWvH2sEDhw4gP79+yMyMhL169cXHYeo0kybNg2//PIL7t+/X7S/GulWYmIi9u7di127dsHW1hbNmzfHK6+8Al9fX9HRSAdY7MxI4eViyPCtWbMG06dPR1ZWFrcdILNS+EtNSEgIGjVqJDqOyePWJqaH76YZYakzHgqFAo0aNeI3XDI7nGdXufg9xvTwHSUAwKFDh/DNN9/gp59+wq1bt0THMXtcEUvmivPsiJ4Pi52ZO378ONq1a4dhw4bh119/xZQpU/D6668jKChIdDSzFhISwmJHZsvPz4/72emRSqUSHYH0iMXOjI0fPx69evVC/fr1cfDgQfz222+4e/cuxowZg08//VR0PLOVmZmJBw8esNiR2ZLJZIiJiUFYWJjoKCZHqVTizJkzLM0mjMXODOXk5OD999/Hn3/+iS1btmDr1q148cUXUbNmTTg7O6N///5wcHDAhQsXREc1SyEhIQDAYkdm68UXX4SFhQWHY/Xg0KFDkMlkUCgUoqOQnrDYmaE7d+7gjz/+wNy5czF8+HDY2NgUu//kyZNITU3lNhuCFH7DZbEjc8V5dvojl8vRpEkTfn8xYSx2ZujGjRvw8vLCiBEjiu1pl52djY0bNyIwMBBjx45FjRo1BKY0XwqFAtWrV4ezs7PoKETC8Lqxupefn4/du3fD39+fuySYMBY7M+Tk5ITIyEhkZGQU3Xbu3Dl8+eWX+P7779GlSxeMHTtWYELzplAoeGkfMnuF8+zu3r0rOorJOHr0KFJTUzF8+HDRUUiPuEGxmercuTMsLS3RvHlzxMTEICMjA4mJiRgwYAACAgLg4uIiOqLZatu2LV544QX88MMPoqMQCZOeng5XV1d8//33/EVTR9577z2cPXsWwcHBPGNnwnjGzkzJ5XIMHz4cV65cgYuLC7p3746ff/4ZS5YsgYuLC9RqteiIZkmj0XCrEyJwnp2uKZVK7Nq1i8OwZoAXDTVTderUwcSJEzFx4sRit2s0Gmg0GlhYWBS7BJlSqYSFhQUsLS1FxDUbMTExyMzMZLEjgnY4duvWrbwcog4cPXoUKSkpHIY1AzxjR/jjjz9w/fp1ACgqdcCjS5DFxMTgxx9/xPLly4VlNBdcEUv0iJ+fHx48eMB5djoQFBQEb29vtGrVSnQU0jOesTNzf/31F8aOHYu3334brVq1KnbdwNTUVJw/fx4bN27En3/+iYyMDLRo0QIDBgwQmNi0KRQKWFlZwdPTU3QUIuEe38/O29tbdByjpVQqsXPnTowbN45nPs0Az9iZuc6dO2Pu3Ll47bXXAKDY1gI3b97EokWLcOTIEdy8eRNff/01PvjgA1FRzYJCoYCXlxekUqnoKETCOTs744UXXuA8u+d0/PhxJCcnw9/fX3QUqgQsdoSPP/4Y7du3BwDk5uYW3d6kSRP0798fNWvWRN26dTF+/Hg4ODhg5syZoqKaPIVCwWFYosdwP7vnFxQUBC8vL7Rp00Z0FKoELHYEAIiLi8OkSZNw5MiRotvc3d0xefJkeHh4YO7cuQCAlStXYuXKlcjJyREV1aRxRSxRcTKZjPPsnkNBQQF27tyJ4cOHcxjWTLDYEQDAxcUFZ8+eRXx8PABApVJBrVbD1tYWtWvXRlpaGlQqFQYOHIh79+7Bzs5OcGLTk5eXh8jISBY7osfwurHP58SJE0hMTOQwrBlhsSMAgK2tLUaMGIGlS5ciJycHlpaWsLCwQHZ2No4cOYIqVaoUbXXi4eEhOK1pCgsLg1qtZrEjekzhPLuTJ0+KjmKU5HI5GjRogLZt24qOQpWExY6KTJ06FS4uLhg7diz27NmDoKAgvPXWW6hduzbGjx9f7LEFBQWYPXu2oKSmiVudEJWO8+wqhsOw5onFjopZv349bG1tMWzYMEyePBnZ2dn47LPPUKtWrWLfVC0tLbFy5UoEBgYKTGtaFAoFnJ2deUaU6D9kMhnu37+P8PBw0VGMyqlTp5CQkMBNic0MrxVLpbp16xYsLCxQpUoV1K9fv9h9hbvA79u3D/7+/nj48CEcHR0FJTUdo0ePxp07d3DhwgXRUYgMSlpaGtzc3LBu3TqMGTNGdByj8dFHH+HAgQOIiIjgGTszwjN2VKpmzZqhadOmRaWu8NqxhaWuoKAAAwYMQI8ePTB69GiBSU0HV8QSlc7Z2Rlt2rThAopyUKlU+P3333ltWDPEYkdPVFBQAAAlLjNmZaW9aMmiRYuwc+dOXLp0SUxAE8I97IjKxnl25XP69Gk8fPiQw7BmiJcUoycqLHBxcXGws7PD1atXERkZiaioKJw6dQr29vYAgK+++gqbN28WGdWoJSYmIjk5mcWOqAwymQwrV65EeHg4GjZsKDqOwZPL5ahbty46dOggOgpVMhY7KlNqaiqWLl2KS5cuITc3F2FhYcjJyYGHhwcKCgrg5+cHBwcH/P7773B0dER+fj6sra1FxzZKXBFL9GSP72fHYvdkKpUKO3bswKhRozgMa4ZY7KhMLi4uiIuLQ5UqVdChQwe8+eab6N69OwoKCtCiRQvR8UyKQqGARCLhhc6JyuDi4lI0z44LKJ6scLN5DsOaJxY7eqINGzZAIpEULZp4nFqthoWFRan3UfkoFArUq1ePV/QgegKZTIbffvuN33OeQi6Xo06dOujYsaPoKCQAF0/QEz1e6v47afm/Cyqo4rgilujpZDIZ7t27h4iICNFRDJZarcaOHTvw6quvFn2PJvPCd52eqrC4scDpD1fEEj0drxv7dGfPnkVsbCyHYc0Yix2RYAUFBQgLC2OxI3qKx+fZUemCgoJQu3ZtdO7cWXQUEoTFjkiwyMhIKJVKFjuiZ+Dn58f97MqgVqsRFBTEYVgzx3eeSDBudUL07DjPrmx//fUXYmJi4O/vLzoKCcRiRxWiVCqhVCpFxzAJCoUCdnZ2qF27tugoRAavW7dukEgkHI4tRVBQEGrWrImuXbuKjkICsdhRhdy5cwfNmjVDXFyc6ChGT6FQwMfHh0MnRM+A8+xKx2FYKsR3nyqkXr16SExMxIIFC0RHMXrc6oSofHjd2JIuXLiA+/fvczUssdhRxbi4uGD69On44YcfEBYWJjqOUeNWJ0TlUzjPLjIyUnQUgyGXy1G9enUOwxKLHVXcJ598gho1amDWrFmioxit9PR0xMbGstgRlQPn2RWn0WiKhmEtLS1FxyHBWOyowuzs7DB//nxs374dly9fFh3HKIWEhADgilii8uA8u+IuXryIe/fucRiWALDY0XN6++230bRpUwQEBIiOYpQKtzrx8fERnITIuHCe3SNyuRzVqlVDt27dREchA8BiR8/FysoKgYGBOHLkCI4cOSI6jtFRKBSoUaMGnJycREchMip+fn6Ijo42+3l2hcOwr7zyCodhCQCLHenAkCFD0LlzZwQEBECtVouOY1S4IpaoYjjPTuvSpUuIioriMCwVYbGj5yaRSLBkyRJcvnwZQUFBouMYFa6IJaoYV1dXtG7d2uyLnVwuh4eHB7p37y46ChkIFjvSie7du2PAgAGYOXMmr0jxjNRqNc/YET0Hc59np9FoIJfLMWzYMFhZWYmOQwaCxY50ZvHixbh79y5+/PFH0VGMwoMHD5Cdnc1iR1RBMpnMrOfZXblyBZGRkRyGpWJY7EhnWrRogTfffBMLFixAVlaW6DgGr3BFLIsdUcUUzrM7efKk6ChCyOVyVK1aFTKZTHQUMiAsdqRTCxYsQHJyMtasWSM6isFTKBSQSqVo0KCB6ChERsmc59lxGJbKwmJHOtWgQQOMHz8eS5cuRWJioug4Bi0kJAQNGzbkN2Wi51A4z87cXL16FeHh4RyGpRJY7EjnZs6cCQAIDAwUnMSwcUUs0fOTyWSIiooyu3l2QUFBcHNzQ48ePURHIQPDYkc65+7ujqlTp+Kbb75BVFSU6DgGi8WO6PmZ4352jw/DSqVS0XHIwLDYkV589tlncHV1xdy5c0VHMUg5OTmIiopisSN6Tq6urmjVqpVZFbvr168jLCwM/v7+oqOQAWKxI71wcHDAnDlzsHnzZvzzzz+i4xicsLAwaDQaFjsiHTC3eXZyuRyurq7o1auX6ChkgFjsSG/ef/99eHl5YcaMGaKjGJzCrU58fHwEJyEyfuY0z65wGHbo0KEchqVSsdiR3kilUixatAh79+7FmTNnRMcxKCEhIXB1dYW7u7voKERGz5zm2f3zzz8IDQ3lalgqE4sd6dWIESPQpk0bTJs2zWwv+1OawoUTEolEdBQio+fm5oZWrVqZxUbFcrkcLi4uHIalMrHYkV5ZWFhg6dKlOHfuHPbs2SM6jsHgilgi3TKHeXaFw7BDhgyBtbW16DhkoFjsSO/69OmDXr16Yfr06VCpVKLjCKfRaFjsiHRMJpMhMjLSpOfZ3bp1CwqFgsOw9EQsdlQplixZgtu3b2Pz5s2iowiXkJCA1NRUFjsiHTKH68bK5XI4OTmhd+/eoqOQAWOxo0rRrl07DB8+HHPnzkVubq7oOEIVrohlsSPSHTc3N7Rs2dKkh2MLh2FtbGxERyEDxmJHlebLL79ETEwMvvnmG9FRhFIoFJBIJGjYsKHoKEQmxZTn2d2+fRt37tzhMCw9FYsdVZpGjRrh/fffx5dffonU1FTRcYQJCQlBgwYNYGtrKzoKkUkx5Xl2crkcjo6OeOmll0RHIQPHYkeVas6cOcjLy8OyZctERxGGCyeI9KN79+4mO89OLpdj8ODBHIalp2Kxo0pVs2ZNTJo0CWvWrEFMTIzoOEKw2BHph6nOs7tz5w5u3brFYVh6Jix2VOm++OIL2NnZYcGCBaKjVDqlUom7d++y2BHpiUwmM7kzdkFBQXBwcEDfvn1FRyEjwGJHlc7Z2RkzZ87Ejz/+WLRC1FxERESgoKCAxY5IT2QyGSIiIhAVFSU6is7I5XIMGjSI83LpmbDYkRDjx49HrVq1MGvWLNFRKlVhkfXx8RGchMg0mdo8O4VCgX/++YfDsPTMWOxICFtbWyxYsABBQUH4+++/RcepNCEhIbC3t0ft2rVFRyEySaY2z65wGLZfv36io5CRYLEjYd566y00a9YM06ZNg0ajER2nUigUCvj4+EAikYiOQmSy/Pz8TKbYyeVyDBw4EHZ2dqKjkJFgsSNhLC0tsXjxYhw/fhyHDh0SHadScEUskf6Zyjy70NBQXL9+Hf7+/qKjkBFhsSOhBg4ciK5duyIgIABqtVp0HL1jsSPSv+7duwOA0c+zk8vlqFKlCl5++WXRUciIsNiRUBKJBEuXLsW1a9ewfft20XH0Ki0tDfHx8Sx2RHpWtWpVk5hnFxQUhIEDB6JKlSqio5ARYbEj4bp27YpBgwZh1qxZyM/PFx1HbwpXxLLYEemfsV839u7du7h69SpXw1K5sdiRQQgMDERkZCTWrVsnOorehISEANBeM5eI9Ktwnl10dLToKBUil8thZ2fHYVgqNxY7MgjNmzfH22+/jYULFyIzM1N0HL1QKBSoVasWHB0dRUchMnnGPs9OLpdjwIABsLe3Fx2FjAyLHRmM+fPnIy0tDatWrRIdRS+4cIKo8hjzPLvw8HBcuXKFw7BUISx2ZDDq1auHjz/+GMuXL0dCQoLoODrHYkdUuYx1nl1QUBBsbW3Rv39/0VHICLHYkUGZMWMGLCws8OWXX4qOolNqtRqhoaEsdkSVSCaTITw83Ojm2cnlcvTv3x8ODg6io5ARYrEjg1K1alVMmzYN3377LSIiIkTH0Zl79+4hJyeHxY6oEnXr1g2Acc2zi4yMxKVLlzgMSxXGYkcGZ+LEiahatSrmzJkjOorOFG514uPjIzgJkflwd3dHixYtjGo4tnAYdsCAAaKjkJFisSODY29vj7lz52LLli24ceOG6Dg6ERISAmtrazRo0EB0FCKzYmzz7ORyOfr168fV81RhLHZkkMaMGQNvb29Mnz5ddBSdUCgU8Pb2hqWlpegoRGbFmObZRUVF4eLFixyGpefCYkcGSSqV4ssvv8T+/fuNan5MWbgilkgMY9rPbseOHbCxscHAgQNFRyEjxmJHBsvf3x/t2rXDtGnToNFoRMd5Lix2RGIUzrMzhmInl8vRt29fODk5iY5CRozFjgyWRCLBkiVLcOHCBezatUt0nArLzs5GdHQ0ix2RIMYwz+7evXs4f/48h2HpubHYkUHr1asXXnrpJcyYMQMFBQWi41RIaGgoAK6IJRJFJpPh7t27uHfvnugoZQoKCoK1tTUGDRokOgoZORY7MnhLlixBcHAwNm3aJDpKhYSEhAAAz9gRCWIM8+yCgoLQt29fODs7i45CRo7FjgxemzZtMHLkSMybNw85OTmi45SbQqFA1apVUbVqVdFRiMySu7s7mjdvbrDDsffv38e5c+fg7+8vOgqZABY7MgoLFy5EfHw81q5dKzpKuXHhBJF4hjzPbseOHZBKpRg8eLDoKGQCWOzIKHh7e2PcuHFYvHgxUlJSRMcpFxY7IvEMeZ5dUFAQXnrpJbi4uIiOQiaAxY6MxuzZs6FUKrFkyRLRUZ6ZRqNhsSMyAIY6zy4mJgZnz57laljSGRY7MhrVq1fH5MmT8dVXX+H+/fui4zyT+Ph4pKens9gRCebh4WGQ8+x27NgBKysrDsOSzrDYkVH5/PPP4eDggPnz54uO8kwKV8RyqxMi8WQymcGdsZPL5ejduzdcXV1FRyETwWJHRsXJyQmzZs3Chg0bEBwcLDrOUykUClhYWKBhw4aioxCZPZlMhrCwMIM54x8bG4szZ85wGJZ0isWOjM6HH36IevXqYcaMGaKjPJVCoYCnpydsbGxERyEye4Y2z+7333+HpaUlhgwZIjoKmRAWOzI6NjY2WLBgAXbu3Inz58+LjvNEXDhBZDgMbZ6dXC5Hr1694ObmJjoKmRAWOzJKo0aNQosWLRAQEACNRiM6TplY7IgMi5+fn0EUu7i4OJw6dYrDsKRzLHZklCwtLbF48WKcPHkSf/75p+g4pcrPz0d4eDiLHZEBMZR5djt37oSFhQWGDh0qNAeZHhY7Mlr9+/dH9+7dERAQALVaLTpOCREREVCpVFwRS2RADGWenVwuR8+ePXmpQdI5FjsyWhKJBEuXLsWNGzewdetW0XFKUCgUAMAzdkQGpFq1amjWrJnQ4diHDx/i5MmTHIYlvWCxI6PWqVMnDB06FLNnz0ZeXp7oOMUoFAo4ODigZs2aoqMQ0WNEXzd2586dkEgkGDZsmLAMZLpY7MjoBQYGIjo6Gt9//73oKMUULpyQSCSioxDRYwrn2T148EDI68vlcvTo0QPu7u5CXp9MG4sdGb2mTZvi3XffxcKFC5Geni46ThGuiCUyTCLn2SUkJOD48ePw9/ev9Ncm88BiRyZh3rx5yMzMxMqVK0VHKcJiR2SYRM6z27lzJwBwGJb0hsWOTEKdOnUwYcIErFy5EvHx8aLjICUlBQkJCSx2RAZK1Dy7oKAgyGQyVKtWrdJfm8wDix2ZjICAAEilUixatEh0FISEhAAAtzohMlB+fn4IDQ2t1Hl2iYmJOHbsGIdhSa9Y7MhkuLm5ISAgAN9//z3u3r0rNEvhVicsdkSGyc/PD0DlzrPbtWsXNBoNXnnllUp7TTI/LHZkUiZMmAAPDw/Mnj1baA6FQoE6derA3t5eaA4iKl21atXg6+tbqcOxQUFB6N69O6pXr15pr0nmh8WOTEqVKlUwb948bNu2DVevXhWWgwsniAxfZc6zS05OxtGjR7kpMekdix2ZnHfffReNGzfG9OnThWVgsSMyfDKZDKGhoYiJidH7a+3atQsqlYrDsKR3LHZkcqysrBAYGIiDBw/i2LFjlf76KpUKoaGhLHZEBq4y59nJ5XJ069YNNWrU0PtrkXljsSOTNGzYMHTs2BEBAQHQaDSV+tr37t1DXl4eF04QGbjKmmeXkpKCI0eOcBiWKgWLHZkkiUSCJUuW4O+//8aOHTsq9bULV8TyjB2R4auMeXa7d+/mMCxVGhY7MlkymQz9+vXDzJkzUVBQUGmvq1AoYGNjg3r16lXaaxJRxchkMoSEhOh1np1cLkfXrl1Rq1Ytvb0GUSEWOzJpS5YsQWhoKDZs2FBpr6lQKNCoUSNYWlpW2msSUcXo+7qxqampOHz4MIdhqdKw2JFJa9WqFUaNGoV58+YhOzu7Ul6TK2KJjEf16tXRtGlTvQ3H/vHHH1AqlXj11Vf1cnyi/2KxI5O3cOFCJCYm4v/+7/8q5fVY7IiMiz7n2cnlcnTp0gW1a9fWy/GJ/ovFjkyep6cnPvzwQyxduhTJycl6fa2srCzcv3+fK2KJjIi+5tmlpaXh0KFDHIalSsViR2Zh1qxZUKlUWLx4sV5fJzQ0FABXxBIZE33tZ7dnzx7k5+fD399fp8clehIWOzIL1apVw+eff461a9ciOjpab6/DrU6IjI++5tnJ5XJ07twZderU0elxiZ6ExY7MxuTJk+Hk5IR58+bp7TUUCgU8PDzg6uqqt9cgIt2TyWQ6PWOXnp6OgwcP8mwdVToWOzIbjo6OmD17Nn766Sfcvn1bL6/BhRNExkkmk0GhUCA2NlYnx9uzZw/y8vJY7KjSsdiRWRk3bhzq16+PGTNm6OX4LHZExknX8+yCgoLQsWNHblROlY7FjsyKtbU1Fi1ahN27d+Ps2bM6PbZGo2GxIzJS1atXR5MmTXQyzy4jIwMHDhzg2ToSgsWOzM7IkSPRunVrBAQEQKPR6Oy4cXFxyMzM5FYnREZKV/vZ7d27l8OwJAyLHZkdCwsLLF68GGfOnMG+fft0dlyuiCUybrqaZyeXy9G+fXs0aNBAN8GIyoHFjsxS3759IZPJMH36dKhUKp0cU6FQwNLSEl5eXjo5HhFVLl3Ms8vMzMSBAwe4KTEJw2JHZkkikWDp0qW4efMmfvnlF50cU6FQwMvLC9bW1jo5HhFVrho1ajz3PLt9+/YhNzeXw7AkDIsdma0OHTrg1VdfxZw5c5Cbm/vcx+PCCSLj97zz7ORyOdq2bQtPT0/dhSIqBxY7MmtffvklHjx4gP/973/PfSwWOyLjVzjPLi4urtzPzcrKwv79+zkMS0Kx2JFZa9y4Md577z18+eWXSEtLq/Bx8vPzERERwRWxREbueebZ7d+/Hzk5ORyGJaFY7MjszZ07F9nZ2VixYkWFj3H37l2o1WqesSMycs8zz04ul6NNmzZo2LCh7oMRPSMWOzJ7tWvXxsSJE7Fq1aoKb3PArU6ITEdF5tllZ2dj3759HIYl4VjsiABMmzYNNjY2WLhwYYWer1Ao4OTkhOrVq+s4GRFVNj8/PwQHB5drnt2BAweQnZ3NYVgSjsWOCICLiwumT5+OH374AWFhYeV+fuHCCYlEood0RFSZKjLPTi6Xo1WrVmjUqJG+YhE9ExY7on998sknqFGjBmbNmlXu53JFLJHpqFmzJho3bvzMw7E5OTnYu3cvh2HJIFiJDkBkKOzs7DB//nyMGTMGU6dORdu2bYvuU2uADCWQogRS8oE0JaBUA2pofzsaHLAKbrYWiMwCXKWAoxSw4Mk7IqPVo0dP3Il6gMis0j/zUgvAWQq4WgOXT51FTm4uix0ZBIlGl1dBJzJyBQUFaNmyJWrXro3Dhw8jswAIzwQisoCCfz8pEgClfWg0ajUkFtqT4FYSwNMe8HIAHPjrE5HRKPzMh6QqIbGSAtBAAkmpn/nHvxfkZmWiRXUHfuZJOBY7ov/YtWsXvpi/GMt+3Q+VfdUyi9zTFD6vmg3QzBlw45XGiAxWch5wKx14mFf2L29Pw888GQIWO6LHqDTA7TQNFOkaaDRqWFg+/6/ehd/sfRwAX2fAkkO0RAZD+5kHQjIrXuj+i595EonFjuhfKfnAhSQgS6W/13CwAjq4aeflEJFY/MyTKWKxIwIQnwucS9T+lq3PD4Tk33+6uAPVbfX4QkT0RPzMk6lisSOzF58LnE3U7zf3/5IA6Mpv9ERC8DNPpoz72JFZS8l/9Ft7ZdJA+7op+ZX8wkRmjp95MnUsdmS2VBrt/BpRp6zVAC4ma3MQkf7xM0/mgMWOzNbtNO2kaZHfYzMLgNvpAgMQmRF+5skcsNiRWUrO025vYAhCMoBkDs8Q6RU/82QuWOzILN1K105mNgQSALfSRKcgMm38zJO5YLEjs5NZoN1dXgNAmZeHnwOn4f22tTDK2w4Bgzri+qnDz3yss39sx4whnfGGjz3ebuaCGUO74J+zx4o95uDm/2HFh8PxYcd68K8rwdefjS52vwbaPJkFz/+1EVFJuvrMJ8U+wMqPRuDtZi54q6kTlrw3BPFR4cUec/y3TfCvKynzn1M7t/AzT3rFK9qR2Ql/bIf5ryePxvn9QRgwZhJqejbCcfkmBL7TH/O2H0fTDi8+8TjbV81D0JoF6DTAH7Lho6EqUCJacRPJcQ+KPW7X/5YiJzMD3q07IOVhbKnHkvybq6WLTr5EInqMLj7zOVmZmPdaD2RnpOGVT2bA0kqKfT+uxpzhflhx8BocXasCAHw7dsen//dziefv/XE1Im9fR4uuvQDwM0/6w33syKyoNcCeGKBAA4RevYjpgzvirZnLMeTDzwEA+bm5mNy7OZzcqyFw17kyjxNy5TxmDu2Ct2evxKD3P3viaybcj4J77XqQSCR4s7EDOvX3xyerN5V4nJUEGFQLsDCU8SIiE6Crz/yu/y3DL4HTsGTPRXi3bg8AeBAWjM96N8eQD7/AGwGBZT43LycHY1+ojkZtOmHO1kNFt/MzT/rAoVgyKxlK7Td4ADi/PwgWlpbo88YHRfdb29qi58gxCLn8FxJj7pV5nL0/roGLRw0MGDMRGo0GOVllz8r2qFMfEsnTv3MXaIAMDs0Q6ZSuPvPn9wXBu1X7olIHALW9m6BF1174a+9vT8xw+cge5GRmoPuwN4rdzs886QOLHZmVFOWjP0fcuopaXj6o4uhU7DHerTsAACJvXSvzODfPHkXDVu2xf8NXeK+VB95q4oixbWviwKavny8fV8oR6ZQuPvNqtRpRwTfQsGW7Evd5t+6AuKi7yMnMKDPDqZ1bYG1rh44vv1IyHz/zpGOcY0dmJSX/0VyblPhYuFSrWeIxrv/elhwfU+oxMlNTkJ6cCMWls7h57hiGT5oLj9r1cOy3jVg/ewIsraR46c1x5c4mAZCaD8C+3E8lojLo5jOfDGVe3lOfW9uhcYn7M1KSce3kn+jw0lDYOTgWu4+fedIHFjsyK2nKR5uT5ufmQGptU+Ix1ja2RfeXJjdbO+yakZKEz775FV0HvwYA6DTAH5P7tMCOrxZVqNhpAKQqn/owIioHXXzmC2+X2pR8rvQpzz2/PwgF+fno9p9hWICfedIPDsWSWVGqH/3Z2tYOyvy8Eo/Jz8stur80hbdbSaXoNMC/6HYLCwt0HfQakmLvI+FB9HPnI6Lnp8vPvDKv5HOVT3nu6Z1b4ODihjY9Xn5qPiJdYLEjs/L491DX6jWRWsr2I4VbkrhVr1XqMRxc3GBtYwsH16qwtLQsdp9T1WoAgKy0lOfOR0TPT1efeamNTbmfm/AgGncunkbngcNhJZU+NR+RLrDYkVl5/C98A9/WiAkPQXZG8Qs3hl69oL2/WevSj2FhgQbNWiM9KQHK/OIzn1P+naPj5Obx3PmI6Pnp6jNfr3EL3L1xqcR9oVcvoHo9rxLz5wDgzO5t0Gg06Da05DBsafmIdIF/p8isSB/7G99pgD/UKhUOb1lXdJsyLw/Hf9uIRm06wr1WXQDa37ofhAUXO06XQa9BrVLhRNBPRbfl5+bi9M4tqOPjC7capf/mX558RPT8dPWZ7zTAH2HX/0bY9Ufl7sFdBW6eO4bOA4eX+tpndm2Fe+16T9z4mJ950jUuniCz4izVXnxbA8CnTUd0HjgcW5dOR3rSQ9Ro4I0TQT8h4X4kxi9fX/SctZPexu3zJxF079Fe3n3eGIej237E+lkfIzY8BO616+HUjp+R8CAKARv3FHvNS4f3IPL2dQBAQYESUcE3EPR/iwAA7V4ajAZNWwLQrpBzKX20hogqSFef+X5vj8fRrT9g8egBGDzuc1haSbH3h1Vwca+OQR9MKfG60cE3EXXnBoZ9HFDmPpb8zJM+sNiRWXG1BsKzHv33hNWb8Wvt2Tj5+8/ISktB/SYtMX3jXvh26v7E49jY2WHe9mP4+csvcGz7BuTlZKGBb2vM2LQPrWV9iz32/P4dxc7sRdy8ioibVwEAVWvWKSp2GgAu1rr5OolIS1efeTsHR8yXn8DG+Z9hx1eLoFar0ayzDKPnrIZz1ZJTL07v2gIAeHHIqDKPyc886QMvKUZmJS0fOPJQdIqy9a6uPcNARLrBzzyZG47uk1lxlGqvz2iIrCSAI8+hE+kUP/NkbljsyKxYSABPe+3cFkMigTYXLwZOpFv8zJO5YbEjs+Pl8GgnekOhgTYXEekeP/NkTljsyOw4WAHVbAznN3gJtHkcOCRDpBf8zJM5YbEjs9TM2XB+g9dAm4eI9IefeTIXLHZkltysAR8DGQbxcdTmISL94WeezAWLHZktX2fA3lLc8IwE2qEYXydBAYjMDD/zZA5Y7MhsWUqAjlXFfpPv4KbNQUT6x888mQMWOzJrrtZAF/fK/0YvAdDVXfv6RFR5+JknU8crTxABiM8FziVqJzXr+wNhAe03+Gq2en4hIioTP/NkqljsiP6Vkg9cSAKyVPp7DQcr7VAMf2snEo+feTJFLHZEj1FpgNtpQEimduhEFx+OwuP4OGonTXN+DZHh4GeeTA2LHVEpkvOAW+nAw7yKf7MvfF41G+2eVdzegMhw8TNPpoLFjugJMguA8EwgIgso+PeTUtY3/cdvt/r3+pReDtxdnsiY8DNPxo7FjugZqDVARoF2Tk5qPpCqBJRqQA3txGipBeAiBVystXNpHK14cW8iY8bPPBkrFjsiIiIiE8F97IiIiIhMBIsdERERkYlgsSMiIiIyESx2RERERCaCxY6IiIjIRLDYEREREZkIFjsiIiIiE8FiR0RERGQiWOyIiIiITASLHREREZGJYLEjIiIiMhEsdkREREQmgsWOiIiIyESw2BERERGZCBY7IiIiIhPBYkdERERkIljsiIiIiEwEix0RERGRiWCxIyIiIjIRLHZEREREJoLFjoiIiMhEsNgRERERmQgWOyIiIiITwWJHREREZCJY7IiIiIhMBIsdERERkYlgsSMiIiIyEf8PSwXOiY3alF0AAAAASUVORK5CYII=\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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "4ce41b8b-1fd9-4df9-f099-9438c26a6435"
      },
      "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.gpu\", 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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "dfb308db-f49d-419f-e075-20c5a62f06ec"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.009071657139484242\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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "79324d9f-769f-4505-bcb1-a1e538de5285"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.49169229369148143\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": 32,
      "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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "47961217-b3c2-4607-eaf3-a7973ec74bdd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.5960710105733116\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": "3643ac13-3980-4b1d-b928-b1274cd01ba1"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1696311544.1228886\n",
            "Tue Oct  3 05:39:04 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": "A100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}