LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit CPU 173.99s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit CPU 173.99s (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "a0a15090-ea7a-460a-cad4-4924ac7fea07"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701188105.3023036\n",
            "Tue Nov 28 16:15:05 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "\n",
        "# !pip install Pennylane-Cirq\n",
        "# !pip install qsimcirq\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": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "80597c1f-bc03-4eb5-9385-8e50e05b4dfb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.78 0.5  0.88]\n",
            " [0.5  0.21 0.51]\n",
            " [0.88 0.51 0.33]]\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": 59,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "9d4ab176-df6d-490a-e84d-567f92fcd0bd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.21 0.51 0.5 ]\n",
            " [0.51 0.33 0.88]\n",
            " [0.5  0.88 0.78]]\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": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "935c8532-f30c-4b12-c3d2-bed468dd3af0"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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CrVu3kjdv3gx7lre3Nz4+PhqKFfFUsbGxaadDHD16lIoVKzJnzhxefvllpz0dIqOpsBMRR7HZbHTq1ImNGzfy448/ZspCs4CAAPXYiXia06dPM2XKFGbOnElMTAzNmjXjs88+o2rVqh6/d1t4eDiA5tiJyH0bM2YMs2fPZu7cudSqVStTnqnCTsRD2Gw2Nm7cSFhYGMuXLycoKIiOHTvSuXNnChYsaHQ8pxEeHo6/vz/Zs2c3OoqIuLAFCxbw3nvvMWzYMF577bVMe67FYtFQrIgrsdlsd9WrFh8fz6JFiwgLC2P//v2ULFmSjz/+mNatW5MlS5YMTOqaUvew8/SeSxG5d5s2beKNN96gTZs2DBkyJFOf7ek9dq6/Rb54lIsXL95xwREREcGQIUMoWLAgb7zxBvnz5+f777/n0KFDdOrUSUXdLURERGgYVkTu2bFjx3jhhReoVq0aM2bMyPQPiQEBAeqxE3FmUVFRjBs3jq+//prg4GBq1qzJG2+8QeHChW/ae3fixAmGDRvG4sWL8fX1TTsdokSJEgZ9B65Fp06IyL26ePEi9evXJ2/evHz11Vf4+vpmegaLxeLRPXYq7MSp/fHHH7zxxhvYbDaGDBlCREQEU6dOJSYmhokTJ95Q1CUnJ3P69Gk2b97MBx98wJtvvqm5YncpPDycMmXKGB1DRFxMfHw8L7zwAjExMWzfvt2wk3k8fShWhZ04FavVitlsJiUlBS8vL3744QeOHDnC7t27CQ4OBmDz5s3ExsaSmJh4w6dBb29vateuzfHjx/Hy8jLiW3B56rETkbtltVp5/fXX2bt3Lxs2bKBw4cKGZfH0HjvNsROnMG/ePJo3b06/fv3YsWNH2lEzR44coWTJkkRHRwP2xsNqtdKwYcP/7OJXUXdvrl27RnR0tObYichdeffdd1myZAnz58+nSpUqhmbx9B47FXZiqIMHDxISEsLw4cMpVqwYW7Zs4Y033mDFihUAPPPMM8TExNClSxeaNWtGlixZ2LFjBx9++CHTp08nPj7e4O/AvWhzYhG5WzNmzODDDz/ko48+olmzZkbH8fjFEyrsxBA2mw2A2bNnky1bNg4cOMCYMWOYNWsW+fLl45dffgGgXr16rFq1iipVqnDmzBmWLl3K7t27efrppwkLC+Pjjz8G7D15cv9SNydWYScid+L777/n7bff5p133qFnz55GxwE0FKvCTgxhMpmIjo7mzJkz5MmTh4CAAAAKFixIbGwsL7zwAmAvAP39/dmwYQOvvfYaDRo04KGHHmL48OFUrVqVjRs3AqQN3cr9UY+diNypgwcP0rx5c+rWrUtYWJjT7H2poViRDJKQkMDhw4fTetNSe+lSBQUFUa5cOVavXs2kSZMYMWIERYsW5dq1a3zzzTccOHAAs9nMkSNHOH36NNWqVUv72uvXr7N9+3aKFClCSkpKpn5f7iw8PByLxUK2bNmMjiIiTiw8PJwGDRpQtGhRFi9ejLe386zF9PSTJ1TYicNFRETwyiuvkCtXLl5++WWee+45Tp06le7TXGqR1717d+bPn8/69euZNWsW7777Ln379uWnn36icePGpKSk8Pjjj+Pr68uoUaNYvXo1p06dYsyYMfj6+tKqVSstlHAgnTohIrcTGxtLw4YNAVi5ciWBgYEGJ0pPPXYiDjZ16lQiIiJYt24dU6ZM4fLly7Rt25atW7cC9vlwqYVDUFAQZcuWZffu3SxYsIBu3brRtm1bFi1axPXr1/n8888BGDduHDExMfTp04fKlSuzadMmPvzwQ0JCQm7oCZR7p61OROS/JCcn07JlS44fP853333Hgw8+aHSkG3h6Yec8fafiFqKiovj6669p0qQJISEhACxatIjOnTszbdo0qlatesN8uPXr11O8eHEKFSqU9tqlS5cIDAwkKioKgBdffJEmTZqwa9cuihYtSt68edOuVe+S40RERKiwE5Gbstls9OjRgzVr1vDdd99RtmxZoyPdlMViITk5maSkJHx8fIyOk+nUYycOdenSJZKSkqhQoULaayVKlKBu3brs2bOHvXv3AvZPfalz47JkycK5c+dYuHAh165dIzY2lm+++YbcuXPzyiuvpN3H29ubJ598Ml1RJ44VHh6uPexE5KZCQ0P5+OOP+eSTT6hbt67RcW4pdTGep86zU2EnDlWsWDGio6M5ceJEutdr1KhBzpw5+fbbbwF7kZY6N65Zs2Y8++yzjBo1isaNG1OkSBHmzZvHgAEDyJ8/v4ZaM5GGYkXkZpYtW0bv3r3p168fb731ltFx/pMKOxEHa9KkCV999RVxcXFpr5UsWZK8efPyxx9/kJycnDZk+8cff2AymRg7dixr1qzhhRde4Ouvv+bIkSNpG11qqDVzxMXFcfXqVRV2IpLOzp07efXVV3nppZd4//33jY5zWxaLBcBj59mpsBOH69ChA7t3705bLAH2RRLJyckkJibi7e3NmjVrePvtt9N68AICAqhSpQpdunShevXqRkX3aNrDTkT+7dSpUzRq1Ijy5cvzxRdfuMSeoak9dirsRBykUqVK1KhRg9DQUA4dOgTYl8eHh4eTI0cOwH6iRJ8+fWjcuLGRUeUfUk+d0Bw7EQH7YrgGDRoQGBjI8uXL03rCnF1qTg3FityDWx3lNXbsWOLj46lXrx6TJ0+mVatWXLt2jR49egCQI0cO+vbty0MPPZSJaeW/6DgxEUmVmJjIiy++yPnz51m1ahV58uQxOtIdU4+dyF2y2WysW7eOxo0bM2vWLJKSkm64pkqVKsyePZs33niD5cuXkydPHr755hsKFy5sQGK5E+Hh4WTJkoWsWbMaHUVEDGSz2XjrrbfYsmUL33zzDSVKlDA60l3x9MJO+9jJHbt+/Trz588nLCyMX3/9lTJlypAnT56b7hNks9koWLAgI0aMMCCp3IvUPey0WEXEs40cOZIvvviCefPmUbNmTaPj3DUNxYrcxrlz5xg0aBAFChTgrbfeokiRIqxdu5aDBw/SpEmTm36NigPXoz3sRGTevHkMHTqUkSNH8uqrrxod556ox07kFrZv305YWBhLly7FYrHw5ptv0rVrV4oWLWp0NMkA2sNOxLP9/PPPvPnmm7Rt25ZBgwYZHeee+fv7A57bY6fCTtJJSkpi6dKlhIaGsnPnTooWLcr48eNp27Yt2bJlMzqeZKDw8HAef/xxo2OIiAGOHj1K06ZNqVGjBp9++qlLj7qYTCYsFot67MSzXbx4kenTp/PJJ58QHh5O7dq1WbFiBfXr1087IULcm86JFfFMkZGR1K9fnwceeICvvvoKX19foyPdt4CAABV24pl++eUXwsLCmDdvHiaTidatW9OtWzfKlCljdDTJRDExMcTExGiOnYiHuX79Ok2aNCEuLo61a9eSPXt2oyM5hMVi0VCseI6UlBRWrlxJWFgY69ev58EHH2To0KF06NCB3LlzGx1PDKBTJ0Q8j9VqpXXr1hw4cICff/6ZQoUKGR3JYdRjJx4hOjqa2bNnM3nyZE6ePMmTTz7JokWLaNas2U23LBHPoc2JRTzPgAED+Prrr1m2bBmVK1c2Oo5DqbATt/b7778zefJkZs+eTXx8PC+//DILFy4kJCTE6GjiJFJ77DQUK+IZPv30U8aNG8fEiRNvuW2VK9NQrLgdm83G2rVrCQ0NZdWqVeTKlYsePXrw9ttvq1dGbhAeHk5gYKBOnRDxAGvWrKFz58506dKF7t27Gx0nQ6jHTtzGtWvXmDdvHpMmTeLQoUOULVuWmTNn8sorr6Tt7SPyb9rDTsQzHDhwgObNm/P8888TGhrq0tua/JeAgAD12Ilr++OPP/jkk0+YPn06UVFRNGnShClTplCrVi23/cUVx1FhJ+L+zp49S4MGDShevDgLFy50662sLBYLly9fNjqGIVTYuTCbzca2bdsICwvjq6++IkuWLLRr144uXbpQpEgRo+OJC4mIiODBBx80OoaIZJCYmBgaNmyI2Wxm5cqVBAYGGh0pQwUEBHD27FmjYxhChZ0LSkxMZMmSJYSGhrJ7926KFStGaGgor7/+uuZIyT0JDw+nUqVKRscQkQyQnJxMixYtOHnyJFu2bPGIRVJaPCEuITIykk8//ZSpU6cSERHBc889x8qVK3n++ecxm81GxxMXZbPZNBQr4qZsNhvdunXjhx9+YNWqVTz22GNGR8oUWjwhTu3AgQOEhYWxYMECzGYzbdq0oVu3bpQqVcroaOIGYmJiiIuLU2En4oYmTJjA1KlTmTFjBnXq1DE6TqbR4gk3ZbVBTBJEJUFUIkQnQZIVrIAZ8DFDkA/k8IUcPpDVB8xOss4gJSWFFStWEBYWxs8//0yBAgUYPnw4HTp0IGfOnEbHEzeiUydE3NNXX31Fnz59GDhwIO3btzc6TqayWCzqsXMnsclwMhZOxUGyzf6aCbDd5NrLiXAyzv7P3iYonAWKBEKgQf9lrly5wqxZs5g8eTKnT5+mWrVqfPnllzRt2hRvb7f83yUGSz11whPm3Yh4iu3bt/Paa6/RokULRo0aZXScTKehWDdxOQEOXYXIhBsLuZsVdf9+PdkGx2Ph91jI6welgyCnb8bl/adjx44xadIkPv/8cxITE2nRogVLlizRhHbJcCrsRNzLyZMnady4MRUrVuTzzz/3yDnYqYsnbDabx2355RaFXYoNDkfDsVh7QQe3LuRuJ/XrLibA+kgoHgilgsArA34ubDYbP/74I2FhYaxatYo8efLQu3dvOnXqpD9kJdOEh4eTLVs2t9/+QMQTREVF0aBBA4KCgvjmm288dmP6gIAAbDYbCQkJHvffwOULu6hE2PEnxKXY//1eC7p/S73PsVgIj4eQnPa5eI4QFxfH3LlzmTRpEr/99hvly5dn9uzZtGzZ0uN+AMV4ERER+iAh4gYSEhJo1qwZkZGRbN++ndy5cxsdyTABAQGA/TQmT/tz1aULuwvxsPWS44q5W4lLhg2RUDU35LuPn48zZ87w8ccfM2PGDKKjo3nhhReYNm0aNWrU8LiuYnEe2upExPXZbDY6dOjA1q1bWbt2LcWKFTM6kqEsFguAR66MddnC7kI8bMmEog7sz7Bhf161uyzubDYbW7ZsISwsjGXLlhEYGEj79u3p0qULhQoVyqDEIncuPDycggULGh1DRO7D8OHDmTt3LgsWLKB69epGxzHcP3vsPI1LzqiMSsycnrp/s2F/blTi7a9NSEhg7ty5VK5cmRo1anDw4EEmTZrE2bNn+eijj1TUidOIiIhQj52IC5szZw7Dhw9n9OjRtGrVyug4TiG1sFOPnQtIsdnn1GV2UZfKCuy8DM/mu/mCigsXLjBt2jSmTp3KhQsXqFu3LqtWraJu3boeuTJJnFvqqROaYyfimjZs2ED79u1p164dAwcONDqO00gdivXEHjuXK+wOR/+9UMIosclw+Co8FvT3a/v27SMsLIyFCxfi7e2ddjpEyZIljQsqchtXr17l2rVr6rETcUG//fYbTZs2pVatWkydOlVztf/Bk4diXaqwu5xgX6XqDI7FQLBPMhtXLycsLIxNmzZRsGBBRo0aRfv27cmRI4fREUVuK3UPOxV2Iq7lwoUL1K9fnwcffJClS5fi4+NjdCSnosUTLuLQ1VufIJHZbFYrM1ZvZdBLL1G9enWWLl1KkyZNdDqEuBQdJybieq5du0bjxo2Jj49nw4YNBAUF3f6LPIx67FxAbLL9RImkhAQWjR/Cxq/mEhcdRcGSZWnVdxTlaj73n1+/Y/Uyfpg3jTNHfiHmyp9ky5mH4o8/wcs9h1Hw0TLprp09rCeHd/zMxT9Ok5gQT56HHqZqoxY07tgHSxb7Jq4ms5kSVWqyff8vVClX5maPFHF6OnVCxLVYrVZat27Nr7/+ysaNG3n44YeNjuSUVNi5gJN/nSoxpVdbtq9aSoN2PXigcDHWL/mcMa/XZ9ji9ZQMufUS7zNHfyFLUA7qt+tOtpy5uRJ5nnWLZzGgUQhjlm+jUKlyadeeOLiLkiE1ePrlN/Dx8+f0r/v45pMP+GXzT4xYujFtEYQJsDysok5cV3h4OEFBQWmNoIg4t379+rFs2TK++eYbKlasaHQcp+Xj44OXl5eGYp2V1Qan4uDYvp1sWbGI1oPG0aRTHwBqvdiGXs+WYe6Yfoz5Zust79G8x5AbXqvdqj0dQx7i+7lT6fj+tLTXR329+YZr8z1clDmj+nB8/06KP/4EYB8SPhUHZYLArDmr4oK0ObGI6/jkk08YP348YWFhNG7c2Og4Ti8gIMAje+xcYv+NmCRItsH2VUsxe3nx3Ktvpb3n6+/PMy3bcWzPNi6F/3FX9w3KnRc/SwBx0Vdue23eAoUAbrg22QYxyXf1WBGnoT3sRFzDd999R9euXenWrRvdunUzOo5LCAgIUI+ds4pKsv/91KF95C9SnICs2dK9/0j5EABOH9pP7vwF/vNecdFXSE5O4krkeb77LJRrMVd5rHrtG65LSU4m7uoVkhMTOXP0VxaOew9LYNa0Z6XLlwhBWpAkLig8PFybZYs4uX379tGiRQsaNmzIhAkTjI7jMiwWi0f22LlGYZdon88WdSGC7HlvnOSd46/XLl8Iv+29BjZ5gvATRwHwzxLIi93eo3bLdjdcd+Lgbt5t8mTav+cvWoL+s1aQNUfOdNeZgCuJQJY7/35EnEV4eDhVq1Y1OoaI3MLZs2dp2LAhJUuWZMGCBXh5eRkdyWV46lCsSxR20Un2+WyJ8dfx8fW74X1fP/vhrYnxt+9y7Tx+NtdjrnLhzEnWfzmbxPjrWFNSbjgV4qFipRiy4Efir8VxdM9Wftn8E/FxN26iZwOuJN3TtyViqNRTJzQUK+Kcrl69SoMGDfD29ubbb78lSxb1INwNi8WioVhnlWS1/93X30JSYsIN7ycmxKe9fzslKv7dC1etcUt6PGM/GeL1wR+luy4gazbK1ngWgJC6Tdi0bAFj2zVh7Oq96VbQ/jOfiCuJjo4mPj5ehZ2IE0pOTqZFixacPn2arVu3EhwcbHQkl+OpPXYusXgitW7Kke8BrkRG3PB+1F+v5cx3d39ABWbPQZmqz7Dpm/m3vbbK880A2LJi0S3zibgS7WEn4pxsNhudO3fmp59+4quvvqJ06dJGR3JJKuycWGrIQqXKE37yGNdirqZ7//d9O+zvly5/1/dOjL/OtavRt70uKTEBq9V602td4j+iyL/oODER5zRu3DimT5/Op59+yrPPPmt0HJflqUOxLlGT+PyV8okGL2FNSeHH+dPT3ktKSGD9l7MpVqFK2orYi+fOcO74kXT3iL4UecN9I/84zS9b1lK0bKW01+Kir5CcdOOkubULZwJQ5B/X/jufiCtRj52I81myZAn9+/dn0KBBvPnmm0bHcWme2mPnEnPsgnzgciIUr1CFJxs2Z8GHA7n6ZyTBhR5hw9IvuHj2NO+M+yzt+sk92nB4+88s/ePvU2V7PfcYj1WrTaHS5ckSlIPzp35n7aLPSElK4tWBH6Rdd2jbBmYN7cYT9V/igcLFSE5K5Ledm9ix+muKlq1EzWavpctmArJrqxNxQREREeTIkSPtsGwRMda2bdto3bo1rVq1YuTIkUbHcXnax86J5fCFk3H2f+46cQ6LHhzMz1/bz4p9+NGyDJy9klJP1PzPe9Rp/TZ7137H/g1ruB4XQ1CuvJSrWYdmXd7l4ZKPpV1X8NHHKF31aXb9sNw+d89mI9/DRXmpxxCadOqLj69vuvvagOy+iLic8PBw9daJOIkTJ07QuHFjKleuzOzZszGZdJzR/fLUfexMNpvNdvvLjBWdCD/dOJLqNJ7Npw2KxfU0b96cK1eu8OOPPxodRcSjXb58mSeffBKbzca2bdvIlSuX0ZHcwoABA1i6dCnHjx83Okqmcokeu6w+4G2yH9/lbLxNkNUl/iuKpBceHs4jjzxidAwRj5aQkMALL7zAn3/+yfbt21XUOZAWTzgxswkKZ7HPZ3MmJuy5zM4WTOQO6JxYEWPZbDbefPNNdu7cyYoVK/RBy8E8dfGESxR2AEUC7fPZnIkNey4RV5N66oTm2IkYZ+jQoSxYsIA5c+boaL8M4KmLJ1ymsAv0hrx+ztNrZ8KeJ1DDsOKCoqKiSEhIUI+diIFiYmJ4//33efnll42O4pYsFgsJCQmkpKQYHSVTuVRZUjoI1jvJIgob9jwirkibE4tkPKvVesM55P80ceJEXGD9ossKCAgA4Pr16wQGes7wmsv02AHk9IXiTvL/pnhWex4RVxQRYT+GT4WdSMa4ePHifxZ1qbStScZJ3aPT04ZjXarHDqBUEJy7DtdSjJlzZwKyeEOpbAY8XMRBUnvsdLC4iOPVrl2blJQU1q9fr8LNQKk9dp62gMLlCjsvE1TJBRsijSvsQnLac4i4qvDwcHLmzIm/v7/RUUTcyiuvvMLJkyfZtm2bijqDqbBzITl8oWpu2HIpc4s7E1Att/35Iq4sPDxcw7AiDvbWW2+xdetWNm3aRHBwML/99huXL18mOTmZokWL8tBDDxkd0aN46lCsS82x+6d8/vYiy0zmrJQ1A9VzQ151cIgb0B52Io61adMmZs6cSatWrShQoABz5szhxRdfpGXLljz77LO0bduWzz//3OiYHsVTe+xctrADe3H3VF4I8MrY5wR625+jok7chfawE3Gshx9+mCFDhjBz5kyaNm3K8OHD6d27N+vXr2f37t3kypWL6dOnc/DgQaOjeox/ror1JC45FPtPOXzhuWA4HA3HYu29d44Ynk1JScZsMlMim4lSQSbNqRO3Eh4ezlNPPWV0DBG3UbBgQTp37oyfnx9TpkyhS5cutGvXLu39999/n8cee4zt27dTtmxZA5N6jtShWPXYuSAvEzyWHZ7OA3n87K/dax2W+nV+8dEMbPIE+7+dp6JO3IrNZtNQrEgGyJMnD+3ateOTTz7hpZdeSnvdarVSoEABihUrhq+vJmlnFg3FuoGcflAjD9QNhkcCwfsfBdmtarN/vu5tsn9d3WBoUiIXFYoVol+/fly9ejUjY4tkqsuXL5OYmKjCTiQD5M2bl7p161KsWLG018xmM0ePHuX69evky5fPwHSexVMXT7j8UOzNBHpD2exQJghikiEqEa4kwpUkSLKCFXtF62OG7D6Q3dc+pJvVG8z/qPQ++ugjSpYsyYgRI/joo48M+m5EHCt1DzvNsRO5dykpKXh5/T3B+5+nTPxzG6GYmBhOnjxJs2bNqFOnDs8//3ymZ/VUZrMZPz8/j+uxc8vCLpXZBEE+9r/IcvdfX7BgQd59912GDRtGu3btKFmypMMzimQ2HScmcu/WrVvHsmXLOHLkCPXr1yckJIRq1aphNpvTFXc2m43ExESmTJnC0qVLqV69OlOnTjU4vecJCAjwuMLOrYZiM0Lv3r15+OGH6datm870E7egUydE7s369etp2LAh0dHRBAcHM2XKFPr378/EiRMBew9RUlISYD8qzM/Pj2bNmjFgwAC++OILI6N7LIvF4nFDsSrsbsPf35/Q0FB++uknli1bZnQckfsWERFBrly58PPzMzqKiMuIj49n8uTJdO/enTlz5jB37lyWL19OpUqVmDlzJiNHjgTAx8eHiIgIpk+fTlRUFCVKlKB58+YGp/dc6rGTm2rYsCENGjSgZ8+eHvcDIu5Hp06I3D1vb2/++OMPEhIS0l4rU6YMvXv3pnHjxqxYsSKtV27x4sW8++67LF++3Ki48peAgAD12MnNhYaGcv78eT744AOjo4jcFxV2InfHZrPh5eVFSEgI586d49KlS2nvFShQgI4dO/LAAw+kjep06dKFESNG0LZtW4MSSyqLxeJxHTIq7O7QI488Qp8+fRg7diwnT540Oo7IPdMediJ3x2QyYTKZqFOnTlrPXEpKCmAv+goVKkTfvn1ZsWIFe/fuxdvbm3feecfg1AIaipXbePfdd8mTJw89e/Y0OorIPdNxYiL3pkmTJrz//vv079+f0NBQYmJiMJnse2Rlz56dMmXKkC1bNoNTyj954uIJt97uxNGyZMnC+PHjadGiBatXr9Z+ROJyrFareuxE7kOPHj2w2Wz07t2bY8eOUa9ePR599FHGjh0LwEMPPWRwQvmngIAAjztkQD12d6l58+Y8/fTTdO/ePd0kWhFX8Oeff5KUlKTCTuQ+9OzZk+XLl3Pw4EE6d+5M06ZN+eWXX/jxxx/TbU4sxvPEoVj12N0lk8nE5MmTKVeuHBMnTmTAgAFGRxK5YxEREYA2Jxa5X40aNeLJJ58kOjqa+Ph4ChYsSNasWY2OJf/iiUOx6rG7B6VLl6Zr166MGjWKs2fPGh1H5I7pODERx8mdOzdFixaldOnSKuqclCf22Kmwu0fDhg0jS5Ys9O3b1+goIndMp06I3Bur1UpycrLRMeQuaR87uWNBQUF8+OGHLFq0iJ9//tnoOCJ3JDw8nDx58uDr62t0FBGX8euvv1K/fn2Sk5N1tKSL0T52clfatGnDE088QdeuXfVJTlyCVsSK3J2IiAgaNGhAREQEycnJadubiGvQUKzcFbPZzJQpU/j111+ZOnWq0XFEbkt72Incubi4OBo1akRycjLfffcdgYGBRkeSu5S6eMKTelpV2N2nihUr0qFDBwYPHkxkZKTRcUT+k44TE7kzKSkpvPLKKxw5coSVK1dqfzoXFRAQQEpKCklJSUZHyTQq7Bxg9OjRmM1mBg4caHQUkf+kwk7kzvTq1YuVK1fy5ZdfUqFCBaPjyD0KCAgA8KgFFCrsHCB37tyMGjWKWbNmsXPnTqPjiNyU1Wrl/PnzKuxEbmPSpElMmjSJyZMnU79+faPjyH2wWCwAHjXPToWdg3Ts2JHy5cvTpUsXrFar0XFEbnDp0iWSk5M1x07kP6xYsYIePXrQu3dv3nnnHaPjyH1K7bFTYSd3zcvLi8mTJ7Nr1y5mz55tdByRG6TuYaceO5Gb27NnD61ataJp06ZpZ7+Ka0vtsdNQrNyT6tWr89prrzFgwACioqKMjiOSjgo7kVv73//+R8OGDSlTpgxz587FbNYfj+5APXZy38aOHUt8fDxDhw41OopIOhEREZhMJvLly2d0FBGnEh0dTYMGDfD392fFihVpxYC4PhV2ct8eeOABhg4dyscff8zBgweNjiOSJvXUCR8fH6OjiDiNpKQkXnrpJc6dO8eqVav0wcfNaChWHKJbt24UK1aMLl26eNSmiOLctNWJSHo2m41OnTrx888/s2zZMkqWLGl0JHEw9diJQ/j6+jJp0iQ2bdrEokWLjI4jAqiwE/m3999/n1mzZjFz5kyeeuopo+NIBtA+duIwderUoVmzZvTp04fY2Fij44jonFiRf1i4cCGDBg1i6NChtGnTxug4kkF8fX0xmUzqsRPHGD9+PJcvX2bUqFFGRxHRObEif9m0aRNt27aldevWWujm5kwmEwEBASrsxDEKFSrEwIEDmTBhAkePHjU6jniwlJQUnTohAhw7dowXXniBqlWrMnPmTEwmk9GRJINZLBYNxYrj9O3blwcffJDu3btrIYUY5uLFi6SkpKiwE4926dIlGjRoQN68efn666/x9fU1OpJkAvXYiUNZLBZCQ0P5/vvvWbFihdFxxENFREQA2pxYPFd8fDxNmjQhOjqa7777jhw5chgdSTKJCjtxuMaNG1O3bl169OjhUd3B4jxST53QHDvxRFarlbZt27J3716+/fZbihQpYnQkyUQaihWHM5lMhIWFce7cOcaNG2d0HPFA4eHhOnVCPNZ7773Hl19+ybx586hSpYrRcSSTqcdOMkSJEiXo1asX77//PqdPnzY6jniY8PBw8uXLh7e3t9FRRDLVjBkzeP/99xk3bhwvvvii0XHEAAEBAeqxk4zx3nvvkTNnTnr37m10FPEw2sNOPNEPP/zA22+/zdtvv02vXr2MjiMGsVgs6rGTjBEYGMhHH33E119/zY8//mh0HPEg2sNOPM0vv/zCSy+9RN26dZk0aZK2NfFgGoqVDNWyZUtq1qxJt27dSExMNDqOeAgdJyaeJDw8nAYNGlC0aFEWLVqkKQgeTosnJEOZTCYmT57MsWPHmDRpktFxxEOosBNPERsbS6NGjbBaraxcuZKsWbMaHUkMph47yXBly5blnXfeYfjw4WnbUIhklJSUFC5cuKChWHF7KSkptGrVimPHjvHdd9/x4IMPGh1JnIAKO8kUI0aMwN/fn/79+xsdRdxcZGQkVqtVPXbi1mw2Gz169GD16tUsWbKEcuXKGR1JnISGYiVT5MiRgw8++IB58+axefNmo+OIG0vtFVZhJ+4sLCyMKVOm8PHHH1OvXj2j44gTUY+dZJo33niDypUr06VLF1JSUoyOI25KhZ24u2+++YZevXrRt29fOnbsaHQccTLax04yjdlsZsqUKRw4cIBPP/3U6DjipiIiIjCbzeTNm9foKCIOt2vXLl555RVefPFFPvjgA6PjiBNKHYq1Wq1GR8kUKuwMFhISwptvvsl7773HpUuXjI4jbij11AkvLy+jo4g41OnTp2nYsCHlypVjzpw5mM36I01uFBAQAEB8fLzBSTKHfgucwPvvv4/VamXQoEFGRxE3pK1OxB1duXKF+vXrExgYyPLly7FYLEZHEieV+rPhKcOxKuycQN68eRk5ciQzZsxg9+7dRscRN6PjxMTdJCYm8uKLL3L+/HlWrVqlaQbyn1J77DxlAYUKOyfx9ttvU6ZMGbp27eox8wAkc+g4MXEnNpuNjh07smnTJpYtW0aJEiWMjiROLrWwU4+dZCpvb28mT57M9u3bmTNnjtFxxI1oKFbcyejRo/n888+ZNWsWtWrVMjqOuIDUoVj12Emmq1WrFi1btqR///5ER0cbHUfcQHJyMhcuXFBhJ25h/vz5DB48mOHDh/Paa68ZHUdchIZixVDjxo0jLi6OYcOGGR1F3EBkZCQ2m02Fnbi8jRs38uabb/L6668zePBgo+OIC9HiCTHUQw89xHvvvcfkyZM5dOiQ0XHExaVuTqw5duLKjh49ygsvvED16tWZPn06JpPJ6EjiQtRjJ4br2bMnRYoUoWvXrthsNqPjiAvTqRPi6i5evEj9+vUJDg7mq6++wtfX1+hI4mJU2Inh/Pz8mDRpEuvXr2fJkiVGxxEXFh4ejpeXF3ny5DE6ishdu379Ok2aNCE2NpZVq1aRPXt2oyOJC9JQrDiFevXq0bhxY3r37k1cXJzRccRFRUREEBwcrFMnxOVYrVbatGnD/v37+fbbbylUqJDRkcRFeXt74+Pjox47Md7EiRO5ePEiY8aMMTqKuCjtYSeuauDAgXz11VfMnz+fkJAQo+OIiwsICFCPnRivSJEi9OvXj48++ojjx48bHUdckPawE1c0ffp0xo4dy/jx42natKnRccQNWCwW9diJcxgwYADBwcH06NHD6CjiglTYiatZs2YN77zzDp07d1a7Jw5Tp04djxnO9zY6gPy3gIAAJkyYwEsvvcTKlStp2LCh0ZHEheicWHElBw8e5OWXX6ZevXqEhoZqWxNxmC+++MLoCJnGZNN+Gk7PZrNRp04dTp06xa+//oq/v7/RkcQFJCUl4efnx/Tp02nfvr3RcUT+07lz53jiiSfIkycPGzduJDAw0OhIIi5JQ7EuwGQyMWnSJP73v/8xfvx4o+OIi7hw4YJOnRCXEBMTkzYasXLlShV1IvdBhZ2LKFmyJN27d2f06NGcOXPG6DjiArQ5sbiC5ORkWrZsyYkTJ1i1apV+XkXuk4ZiXcjVq1cpUaIENWrU4MsvvzQ6jji52NhYNm/eTK1atdI26BRxJjabjS5duvDpp5+yatUq6tSpY3QkEZenws7FzJ07lzZt2rB27VqeeeYZo+OIk0v99dYkdHFGEyZMoHfv3kyfPp0OHToYHUfELaiwczE2m40aNWoQFRXF/v378fHxMTqSiMhd+/rrr3nppZfo168fH3zwgdFxxM3ZbDYuXrzIuXPnOH36NLGxsfj6+pIzZ04qVapEjhw5jI7oMCrsXNC+ffuoWLEiEyZM0D5PIuJyduzYwVNPPUXjxo1ZuHAhZrOme0vGmjVrFpMnT+bo0aP4+/vj5+eHzWYje/bsPProo4wePZrSpUsbHdMhVNi5qHfeeYf58+dz9OhRgoODjY4jInJHTp06RZUqVShWrBhr167V9k2S4WbPnk337t3p1KkTL7/8MgUKFMDHx4e4uDgOHjzIsGHDCA4OZuHChW6xIluFnYu6fPkyxYsXp2HDhnz++edGxxERua2oqCiqVq1KUlIS27dvJ3fu3EZHEg9QtmxZOnToQNeuXW/6fmRkJCVKlGD37t0ULVo0k9M5nvq/XVTOnDkZPXo0X3zxBdu2bTM6jjgRfVYTZ5SYmMiLL75IZGQkq1atUlEnmebq1avkypXrP9/38vIiPj4+E1NlHPXYubCUlBRCQkIA2LlzJ15eXgYnEiPEx8ffMJx1/PhxLl68SL58+ShSpIhByUTsbDYbbdu2ZdGiRfz000/UqFHD6EjiQTp27Mjhw4cZO3YsJUqUIDk5mZSUFGJiYoiIiGDQoEEEBwfz6aef/mcB6CpU2Lm4bdu2UbVqVT799FPeeusto+OIASwWCzt37uSxxx4jISGBnj17sn37dvz8/PD396dDhw60aNFChb8YZvjw4QwbNoz58+fzyiuvGB1HPExUVBSvvfYaGzZs4PHHHydfvnwkJydz/fp1Tpw4Qf78+Zk8eTLlypUzOqpDqLBzA23btmXlypUcO3aMnDlzGh1HMpHNZsPHx4dz586RL18++vXrx7x58+jSpQu5cuVi8+bNzJ8/nw0bNlCzZk2j44oHSt17c9SoUQwaNMjoOOLBNm7cyJo1a4iIiMBkMpEvXz4ef/xxmjZtire3t9HxHEaFnRs4f/48xYsXp3Xr1nz88cdGx5FMdPbsWYoWLUpCQgIXLlwgJCSECRMm8OKLL6Zd89ZbbxEZGck333xjXFDxSBs2bKBOnTq0bt2amTNnaqNsMURycjJxcXEEBQXd8hqbzeY2P59aPOEGgoODGT58ONOmTWPfvn1Gx5FMdOrUqbTl+fHx8WTNmpW6deuSkpJCSkoKAA0aNOD33383MqZ4oCNHjtC0aVNq1qzJtGnT3OYPTXE948aNIyQkhM2bNwOQlJSE1WpN+wvc63QeFXZuokuXLjz66KN07dpVqyI9SHR0NFFRUTzyyCNUrFiRxMRELly4gJeXV9qcujNnzmivMMlUkZGR1K9fn/z587N06VKdkCOGKlasGDVq1EjrsfPy8sJsNmM2mzGZTG73Z6aGYt3IunXrqF27NnPnzuW1114zOo5kglOnTrFu3TquXbvG2bNnyZYtG82bN6d48eIAXLx4kb59++Lv78+0adMMTiue4Pr16zz99NOcPn2aHTt28PDDDxsdScSjqLBzMy+//DKbNm3i6NGjZMuWzeg4kklsNhuJiYlpW5/4+fkBsGfPHubPn0/Dhg155plnDE4p7s5qtfLyyy+zevVqfv75ZypVqmR0JBHA3kamjnBkzZo1bR/F//3vfyQmJvLII4+4zXCsCjs3c+bMGR599FE6d+7MuHHjjI4jBnKnycDiGvr27cv48eNZtmwZTZo0MTqOSJpNmzYxdOhQTp8+TYUKFRgwYADx8fEMHz6cxMREGjRoQLdu3bBYLEZHvW8q7NzQ6NGjGTZsGAcPHqRkyZJGxxEDXb58GS8vr/9cDSbiCNOmTePtt98mNDSU7t27Gx1HJM2xY8do27YtZrOZnj178t1333Ho0CEefPBBfH19yZs3L+vWraN79+506NDB6Lj3TYWdG4qPj6d06dIUKVKEH374Qb02HsJqtaZNArbZbHh7ezNgwAB27drFl19+6RY7qotzWrVqFY0aNaJz585MmjTJ6Dgi6SxbtoxRo0axatUq8uXLB0D79u05cOAAu3btAmDIkCHs2bOH7777zsioDqFVsW7I39+fsLAwfvrpJ5YtW2Z0HMkkZrM5bTVs6mabFosFi8Wi+ZaSYfbv30+LFi1o0KABEydONDqOyE3Fx8enFXVgXyn7T/ny5ePKlSuZnCpjuM9Wy5JOw4YNadCgAT179qRevXoEBAQYHUkygM1mIzw8nGXLlnHixAm8vLx48MEHKVWqFBUrVmTo0KFGRxQ3dvbsWRo0aECJEiVYuHChjq0Tp5QvXz5sNht79uyhYsWKnD9/nv379xMbG8u6desIDAxkzZo1lC5d2uioDqGhWDd2/PhxSpcuzYABAxg+fLjRccTBEhMTmTlzJl27duXhhx+mVKlSJCYmEhcXR1JSEo888gi9evXSykTJEDExMdSoUYOoqCi2b9/OAw88YHQkkZu6ePEinTt35tChQ3Tq1Ildu3Zx9OhRXn31VT755BNy5sxJSkoKM2fO5LHHHjM67n1TYefmBg0axPjx4zl8+DBFihQxOo440HfffUf37t3p378/bdq04eLFi8THx/Pnn39y+PBhpkyZQkJCAqtWraJgwYJGxxU3kpycTKNGjdi6dStbtmyhTJkyRkcS+U/nzp2jV69ebNy4kUKFCjFhwgSefPJJFi5cyJEjR6hfvz5VqlQxOqZDqLBzc3FxcTz66KNUrFhRZ4W6mcGDB7N7925Wr1590/djYmJo2LAh1apVY8yYMZmcTtyVzWbjnXfeYebMmaxatYrnnnvO6Egi98RqtWI2/73UIDk5OW1+sivT4gk3lyVLFsaPH8/y5ctZs2aN0XHEgXx9fbFarVy6dOmm72fNmpVcuXKRkJCQycnEnY0fP55p06Yxbdo0FXXiUq5cucKRI0f45ZdfSEhIwGw2c/LkSdatW8epU6fcoqgD9dh5BJvNRu3atTl79iy//PJL2qkE4tqOHj1KkyZNKFCgAAMGDKBMmTIEBQWRkpJCbGwsy5cvZ8qUKQwePJjmzZsbHVfcwNKlS2nevDnvvvsuo0ePNjqOyB0LDw+nbdu27Nixg+zZs9OhQwdat25Nx44duXz5MtmyZWPixImaYyeu49ChQ5QrV47Ro0fTv39/o+OIg+zZs4dBgwaxceNGAgMDeeCBB8iWLRs+Pj4cPnyYjh070qdPH7JmzWp0VHFx27dv5+mnn+aFF15g/vz56YawRJxdu3bt2LZtG+PHjwegf//+FCxYEB8fH5o1a8b8+fPx9vZm5cqVBie9fyrsPEjPnj2ZMWMGR48e5cEHHzQ6jjhIUlISJ06cYM+ePfz+++9cvnwZi8VCo0aNqF69utHxxA2cPHmSJ554guLFi/PTTz/h7+9vdCSRu1KwYEHmzp1LrVq1ANixYwdPPvkk165dw9/fnzNnzlC2bFkuXryIj4+PwWnvjwo7DxIdHU3x4sWpXbs2CxYsMDqOiLiAy5cvU7VqVVJSUti2bVva4ekiriQoKCjdCu7Tp09TpEgRrly5QrZs2YiMjKRYsWKcPXvW5Uc41JfuQYKCgvjwww9ZuHAhP//8s9FxRMTJJSQk0KxZMy5dusSqVatU1InLKl68ON999x1XrlwhISGBxYsX8+CDDzJ27Fi2bdvGsGHDeOyxx3CHvi712HkYq9VKtWrViIuLY+/evW6zCkhEHMtms9GmTRuWLFnC2rVrqVatmtGRRO7ZF198Qf/+/XnuuefIli0by5cvZ9KkSUyaNIlr165x+fJlxo0bxwsvvODy56ursPNAu3fvJiQkhLCwMLp27Wp0HHGgf+/LJHKvhg4dyogRI1i0aBEtWrQwOo7IfVu4cCFz5swhNjaWXr160bRpU86dO8dPP/1E4cKFqVmzptERHUKFnYfq2LEjX375JUePHiVv3rxGxxEHOXLkCJcuXaJatWou/6lT7ozVBjFJEJUEUYkQnQRJVrBin2vjY4YgH8jhCzl8IKsPmG/zo/HFF1/Qtm1bxowZw8CBAzPj2xDJdDabzS3bSRV2HurSpUsUL16cZs2aMXPmTKPjiIMMHDiQRYsWcerUKaOjSAaLTYaTsXAqDpL/asVNwM0a9H++7m2CwlmgSCAE3mQmxvr166lbty5t2rRhxowZbvkHn3guq9UKgMlkSvvZTi2D3OVnXWM2Hip37tyMGjWKzz77jJ07dxodRxwkPDyc/PnzGx1DMtDlBNh0Eb4/D8dj/y7q4OZF3b9fT7bZv+778/b7XE78+73Dhw/TtGlTnnrqKaZOneo2f9CJpDKbzZjN5nQ/2/8s8tyBeuw8WEpKChUrVsTX15ft27drbpYbeO6558iePTtLliwxOoo4WIoNDkfDsdhb98zdrdT7FA+E3PEXqPrkEwQGBrJ582aCgoIc8AQRyWz6k9yDeXl5MWXKFHbt2sXs2bONjiMOEBERoR47NxSVCD+etxd14Jii7p/3ORZrY+WZBPIUsm8JoaJOxHWpsPNw1atX59VXX2XgwIFERUUZHUfuU3h4OA888IDRMcSBLsTDhki4lpKRTzERlDc/A+asxi9vwYx8kIhhtm3bRt26dYmJiTE6SoZSYSeMHTuW69evM3ToUKOjyH24fv06UVFR6rFzIxfiYcsl+wrXjJ4z4+Xtjc1kZssl+3NF3M2VK1f44YcfuHr1qtFRMpQKOyF//vwMHTqUjz/+mIMHDxodR+5RREQEgAo7NxGVCFsvZXxB92827M+NSrztpSIuJSAgALB/CHZnKuwEgG7dulGsWDG6du3qFkeqeCIVdu4jxQY7/sz8oi6VFdh52Z5DxF1YLBYArl27ZnCSjKXCTgDw9fVl0qRJbNy4kUWLFhkdR+5BeHg4gObYuYHD0RCXYlxhB/Z98g6794iVeJjUHjsVduIx6tSpQ9OmTenTpw+xsbFGx5G7FB4ejr+/P9mzZzc6ityHywl/r3412rGY9Pvcibiy1B47DcWKR5kwYQKXL19mzpw5RkeRu5S6ObE7bbTpiQ5dte8v5wxMwKFoo1OIOIan9Njd5EAZ8WSFChVi3bp1VKlSxW3P0XNX2sPO9cUmQ2QCJCUksGj8EDZ+NZe46CgKlixLq76jKFfzuf/8+u2rv2brisUcP7iLK5HnyZ2/ABVrN+Sl7oPJEpQ93bVbVixm90/f8vu+HZw/fZxST9RixJIN6a6xYc8Tm3zz48dEXImnFHbqsZMbPPHEEzccuSLOT3vYub6Tf50qMaVXW1bOmECNpq/yxvAwzF5ejHm9Pr/t3PyfX/9p/7c4e/w3ajZ9jTdHTKL8U/VY/cUU3n3hSRL+Nfz0/dyp7PphObnzFyAwKMct72n6K5eIq/OUoVh9BpMbqKBzTeHh4ZQpU8boGHKPrDY4FQfH9u1ky4pFtB40jiad+gBQ68U29Hq2DHPH9GPMN1tveY/eny6lzJNPpXutyGMVmdLzdTZ9M59nW7VPe71b2FxyBj+I2WymZ+1b/9zYsOcqEwRmNQ3iwnx8fPDy8lKPnci/aWGFc0qdYyeuKSYJkm2wfdVSzF5ePPfqW2nv+fr780zLdhzbs41L4X/c8h7/LuoAqtRrCsC5339L93ru/AXu+HzoZBvEJN/RpSJOy2QyERAQ4PY9dirs5I4dO3aMFi1a0LJlS5566inGjRtndCT5y7Vr14iOjlZh58Kikux/P3VoH/mLFCcga7Z07z9SPgSA04f239V9r1w8D0DWnLnvL59Wx4obsFgs6rETAejduzclS5bk/PnzlC9fnscee4w5c+bQuXNno6MJf29OrDl2risq0T6fLepCBNnz3vj/Mcdfr12+EH5X9/3mkw8xe3nxZIOX7jmbCbiiwk7cQEBAgNsXdppjJ//pzJkzvPDCC5w9e5aZM2fSpEkTcubMCcDGjRtp2rQpvXv3pkiRIgYn9WypmxOrx851RSfZ57Mlxl/Hx9fvhvd9/fzhr/fv1KZlC1i76DOavN2PBwoXu+dsNuBK0j1/uYjTsFgsbj8Uq8JObik2Npa+ffuSLVs2vv/+eypUqJDu/cDAQIKDg+94no5kHBV2ri/Jav+7r7+FpMSEG95PTIhPe/9OHN6xial921G+Vl1e6TfaYflEXJl67MSj/fbbb6xevZrZs2ffUNRdu3aNDz74gPj4eJ104AQiIiKwWCxky5bt9heLU0qtm3Lke4DL58/d8H5UpH24PWe+2xfvpw8f4MN2jSlQogy9P12Kl/f9N/Wq68QdaPGEeLRTp05RunRpGjVqlO71X3/9lSFDhvD7778zceJEFXZOQKdOuL7UxrhQqfKEnzzGtZj0B7X+vm+H/f3S5f/zPudPn2BU63oE5crLu3NWYckS6NB8Iq5MiyfEo5UuXZr9+/ezceNGwN5L99lnnzFkyBC+//57WrZsSd26dQ1OKaCtTtyBz1+t8RMNXsKaksKP86envZeUkMD6L2dTrEIVcucvAMDFc2c4d/xIuntERZ5n5Kt1MJvMvDfve4Jy5XF4PhFXpqFY8WilS5emW7dudOrUCYvFwtWrV8mbNy+5c+dm/Pjx1KlTB0BHjzkBFXauL8gHLidC8QpVeLJhcxZ8OJCrf0YSXOgRNiz9gotnT/POuM/Srp/cow2Ht//M0j9saa+Nbl2PC2dO0uTtfhzZtZkju/4+qSIod750R5Id3r6RwzvsH9quXr5IwvU4loaNAqBUlZqUeqJm2rUmILtPRn3nIpnHYrEQHe3eByCrsJP/9OGHH9KoUSNWr17Nww8/TN68ealXrx7+/vYVelar9YbFEyr0Ml9ERATlypUzOobchxy+cDLO/s9dJ85h0YOD+flr+1mxDz9aloGzV6Yrtm7m9OEDACyfOvaG90o9UStdYffL1nUsmTg83TWLPhoMQPOeQ9M9ywZk972X70rEuXhCj53JZrPZbn+ZSHqJiYn4+t7Y0h86dIiDBw/SqlUrA1J5rqCgIN577z369u1rdBS5R9GJ8FOk0Slu7dl89l5FEVfWrVs3NmzYwMGDB42OkmE0a0Lu2OTJk3nvvfcAbijqoqKiWLlyJb169eLVV19l9Oj7315B7kxcXBxXr17VUKyLy+oD3k7a0e1tgqwa3xE34An72Kmwkzu2Zs0adu/ezalTp9K9HhERwRdffEGbNm2wWCxMmzaN4cOHc/LkSYOSepbUUydU2Lk2swkKZ7HPZ3MmJuy5zM4WTOQeeMJQrD6DyR2bOnUq169fp3DhwuleDwgIwGq1kpCQwMSJEylcuDBbtmyhZcuW7Ny506C0niN1c2IdJ+b6igTC77FGp0jPhj2XiDvQPnYi/1CwYEFKlChBTEwMa9asSXs9KCiId955h65du/LGG28AMH36dPbu3cvMmTONiusxdOqE+wj0hrx+ztNrZ8KeJ1BdAOImtI+dyE1MmzaNhQsXEhcXl/aar68vDRs2JDIykj179uDn58fBgwfTCj3JOOHh4WTJkoWsWbMaHUUcoHSQvZfMGdiw5xFxFwEBASQkJJCSkmJ0lAyjwk7uWkhICKtXr+aPP/5Ie81sNpOUlERERAT58uUDoGTJknh5eRkV02NERETo1Ak3ktMXijvB0KfNZqNYFis5tc2JuBGLxX7Wcnx8vMFJMo4KO7lrtWrV4qmnnqJXr15pCyl27drF6NGjqVChAsHBwQBphca1a9e4cuWKUXHdXnh4uObXuZlSQZDFy7ghWZvVSsSp3+nTqn7a4hwRdxAQEADg1sOxKuzknsybN4/o6GiaN2/OY489RseOHUlJSaFHjx54/+PA8ejoaL744gs++OADYmOdbFa4m9CpE+7HywRVchlX2HmZzTzqHc2vBw9Srly5dHNqRVyZCjuRW/D19WXhwoX069ePkJAQmjdvzrBhw2jcuHG664KCgsibNy+7du2iQ4cOBqV1byrs3FMOX6iaO/OLOxNQLTc8V7UyBw4coFKlSjz//PP079+fpKSkTE4j4lipQ7HuvDJWhZ3cs4IFC/Lyyy/z2WefMXDgQGrVqgXYjxn7599ffPFFKlWqxOLFi9m8efMt7yf3JnWOnbiffP72IstM5hR4ZqB6bshrPzGQPHnysHLlSj766CMmTJhAjRo1btjHUsSVqMdO5C6knk6Xenas2WzmzJkzNGvWjMmTJ9OnTx9KlChhZES3ExMTQ0xMjObYubF8/vBUXgjI4HVIgd7256QWdanMZjO9e/dmy5YtREZGUqFCBZYuXZqxYUQySGphpx47kds4derUDQskZsyYQdmyZTl9+jRr1qxh7Nix5MmTx5iAbkqnTniGHL7wXPDfq2Ud1XuXep/iWe1nweb4jxWwISEh7Nu3jzp16tC8eXPefvttt/7DUdxT6lCseuxEbmPRokW0bt0agBMnTlCvXj26dOlCt27dWLduHTVr1jQ4oXvS5sSew8sEj2WHp/NAHj/7a/da4KV+XR4/eDovPBZkv//tBAUFsXjxYj799FM+//xzqlSpwm+//XaPKUQyn4ZiRe5Q+/btWbVqVdp8uitXrrBhwwZGjBhB9uzZjY7ntlJ77DQU6zly+kGNPFA3GB4JBO9/FGS3qs3++bq3yf51dYPt97nbfepMJhNvvfUWu3btIiUlhUqVKjFr1qy0qRgizswTFk/ooBhxiDx58vD555/Ttm1bevbsyYgRI8iSJYvRsdxeeHg4gYGBOnXCAwV6Q9nsUCYIYpIhKhGuJMKVJEiyghX7J3cfM2T3gey+9qHWrN5gdsBYbpkyZdi1axfdunWjXbt2rF27lmnTpulnUZyaJwzFqrATh2nTpg2fffYZhw4dws/Pz+g4HkFbnYjZBEE+9r/I5M9SAQEBzJw5k9q1a9OxY0d27tzJokWLqFixYuYGEblDXl5e+Pn5uXVhp6FYcah58+Zx8uRJ9u3bZ3QUj6DCTpxBq1at2Lt3L0FBQTz55JOEhYVpaFaclsViceuhWBV24lAFChTgm2++oWjRokZH8Qjaw06cxSOPPMLWrVvp0qULPXr0oEmTJvz5559GxxK5QUBAgHrsRO5GqVKlyJkzp9ExPILOiRVn4uvry4QJE/j222/ZunUr5cuXZ9OmTUbHEkknICBAPXYi90vDMo5ns9k0FCtOqWHDhuzfv58iRYrw1FNPMXLkSFJSUoyOJQLYh2LVYydyH6xWK9evX+fo0aNGR3ErMTExxMXFqbATp/TQQw+xbt06Bg8ezNChQ6lTp07a9jwiRtJQrMh9MplMtGnThhdffFGHiDuQTp0QZ+fl5cWwYcNYt24dR44coVy5cqxZs8boWOLhtHhC5D6ZTCYGDRrE4cOH+fjjj42O4zZST53QHDtxdk899RT79++ncuXKPP/88/Tr108f8sQw6rETcYAKFSrQqVMnhg4dyoULF4yO4xZU2IkryZMnD99++y3jx48nNDSUGjVqcOrUKaNjiQfS4gkRBxk5ciTe3t4MGDDA6ChuITw8nGzZshEYGGh0FJE7Yjab6dWrF1u2bCEyMpIKFSqwdOlSo2OJh9HiCREHyZUrF2PGjOHzzz9n27ZtRsdxedrDTlxV5cqV2bdvH3Xr1qV58+a8/fbbbt2DIs5FQ7EiDtS+fXsef/xxunbtqu0P7pP2sBNXFhQUxKJFi5g+fTqff/45VapU4bfffjM6lngALZ4QcSAvLy8mT57Mnj17+Oyzz4yO49K0h524OpPJRIcOHdi1axcpKSlUqlSJWbNmad9LyVDqsRNxsKpVq/L666/z7rvvcvnyZaPjuCwVduIuypQpw65du3jllVdo164dr732GlevXjU6lrgpFXYiGeCDDz4gMTGRwYMHGx3FJdlsNs2xE7cSEBDAjBkzWLhwId9++y0VK1Zkz549RscSN6ShWJEMEBwczPDhw5k2bRr79+83Oo7LuXr1KteuXdMcO3E7LVu2ZN++fWTPnp0nn3yS0NBQDc2KQ6nHTiSDdOnShUcffZQuXbqo4b5LqXvYqcdO3FHRokXZsmULXbp0oWfPnjRp0oQ///zT6FjiJgICAkhJSXHbTbJV2IlhfHx8mDRpElu2bGH+/PlGx3EpKuzE3fn6+jJhwgS+/fZbtm7dSrly5di0aZPRscQNWCwWALfttVNhJ4aqXbs2L730En379tVk6buQek6shmLF3TVs2JD9+/dTtGhRnnrqKUaOHKmtkuS+BAQEACrsRDLM+PHjiY6OZuTIkUZHcRnh4eEEBQWlNVAi7uyhhx5i3bp1DB48mGHDhvHcc8+l9VqL3K3UHjt3XUChwk4MV7BgQQYNGkRoaChHjhwxOo5L0FYn4mm8vLwYNmwYa9eu5ejRo5QvX57Vq1cbHUtckHrsRDJB7969KViwIF27dtVCijugrU7EUz311FPs37+fypUrU79+ffr27UtiYqLRscSFqLATyQT+/v6EhYXx008/sWzZMqPjOD0dJyaeLE+ePHz77beMHz+esLAwatSowcmTJ42OJS5CQ7EimaRhw4bUr1+fXr16ue0nKUfRUKx4OrPZTK9evdiyZQuXLl2iQoUKLFmyxOhY4gLUYyeSiUJDQ4mIiODDDz80OorTstlsKuxE/lK5cmX27t3L888/z8svv0ynTp3ctidGHCO1sHPXnxMVduJUihUrRp8+ffjwww81tHIL0dHRxMfHq7AT+UtQUBALFy5kxowZzJkzh5CQEA4fPmx0LHFS2sdOJJO9++675MmTh169ehkdxSmlbvOgOXYifzOZTLRv355du3ZhtVqpVKkSs2bN0mIsuYGfnx8mk0mFnUhmyZIlC+PHj2f58uWsWbPG6DhOR6dOiNxa6dKl2bVrF6+99hrt2rXj1Vdf1ebnko7JZMJisWgoViQzNW/enKeffppu3bqRkJBgdBynoh47kf8WEBDA9OnTWbRoEStXruTxxx9n9+7dRscSJxIQEKAeO5HMZDKZmDRpEidPniQ0NNToOE4lIiKCHDlypM0TEZGba9GiBfv27SNHjhxUrVqV0NBQDc0KoMJOxBBlypShS5cujBw5knPnzhkdx2loDzuRO1e0aFG2bNlC165d6dmzJ40bN+bSpUtGxxKDaShWxCDDhg0jS5Ys9O3b1+goTkNbnYjcHV9fX8aPH8/KlSvZtm0b5cuXZ+PGjUbHEgOpx07EINmzZ+fDDz9k4cKFaoj/osJO5N40aNCAAwcO8Mgjj/D0008zYsQIUlJSjI4lBggICFCPnYhR2rRpwxNPPEGXLl1ITk42Oo7hdE6syL178MEHWbt2LUOGDGH48OE8++yzaQuSxHNYLBb12IkYxWw2M3nyZH799VemTZtmdBxDpZ46oTl2IvfOy8uLoUOHsm7dOo4dO0a5cuVYvXq10bEkE2koVsRglSpVon379gwePJjIyEij4xgmKiqKhIQE9diJOECtWrU4cOAAVapUoX79+vTp04fExESjY0km0OIJEScwZswYTCYT7777rtFRDKPNiUUcK3fu3Hz77beMHz+eSZMmUaNGDR1n6AHUYyfiBHLnzs3IkSOZNWsWO3fuNDqOISIiIgAVdiKOZDKZ6NWrF1u2bOHSpUtUqFCBL7/80uhYkoG0eELESXTs2JGyZcvSpUsXrFar0XEyXWqPXXBwsMFJRNxP5cqV2bt3L88//zwtWrSgY8eObtur4+m0eELESXh7ezNlyhR27drF559/bnScTBceHk7OnDnx9/c3OoqIWwoKCmLhwoXMmDGDuXPnEhISwuHDh42OJQ6moVgRJ1K9enVeffVVBgwYwJUrV4yOk6m0h51IxjOZTLRv355du3YB9sVbn332mY4jcyNaPCHiZMaOHcv169cZOnSo0VEylfawE8k8pUuXZufOnbz22mu0b9+eV155hYSEBKNjiQOox07EyeTPn58hQ4YwZcoUDh48aHScTKM97EQyV0BAANOnT2fRokWcP38eHx+f/7z+0qVLrF27lq+++iqTEsq9SF084Y69sCrsxGV1796dYsWK0bVrV7f85bwZDcWKGKNFixZ8//33/7loa+bMmbz00ku88MILjBw5kvz587N58+ZMTCl3ymKxABAfH29wEsdTYScuy9fXl0mTJrFx40YWL15sdJwMZ7PZNBQrYiBfX1+8vb1v+t7PP//MO++8Q6VKlfjpp5/YsWMHL774IsOHD3fL4sHVBQQEALjlcKwKO3FpderUoWnTpvTu3ZvY2Fij42Soy5cvk5iYqMJOxMnExMTQpk0bWrZsycCBA6lSpQp+fn60bt2aHTt2cOLECaMjyr+kFnbuuIBChZ24vAkTJnD58mVGjx5tdJQMlbqHnebYiTiX9957D4CRI0eSK1eutKkhJ06cIEuWLPqddUKpQ7HqsRNxQoUKFWLAgAGMHz+eY8eOGR0nw+g4MRHnc/r0aebNm0f//v0pWLAgYN8u5fLly6xdu5bKlSvr/FknpKFYESfXr18/HnzwQbp37+62Cyl06oSI8zlz5gzBwcFUrlwZk8mU9vrKlSvZs2cPtWrVuunv7Pnz51m5cmVmRpV/SO2x01CsiJOyWCxMnDiRNWvW8O233xodJ0NERESQO3du/Pz8jI4iIn/x9/cnPDw8rQcIYO3atSxevJjg4GB69OgBkO4DZ0pKCuvXr6dx48YEBQWpwDOAeuxEXECTJk2oW7cuPXr0cMtPYdrDTsT5FCxYkFKlSjFlyhQOHz7MsmXL6N69O8nJyYwcORIvLy9SUlLS9eYdPHiQ0NBQXn31VcaOHUuzZs145ZVX3Ha0wRmpsBNxASaTibCwMM6ePctHH31kdByH0x52Is4nODiYGTNmsHXrVho1akSnTp2oVKkSo0ePplKlSthstnRF3aVLl1i2bBm7du1izJgxdOzYkV9//ZVffvmFevXqGfideBZ3Hoq9+YY8Ii6qRIkS9OzZkzFjxtCmTRsefvhhoyM5THh4OKVKlTI6hoj8S6lSpThw4AD79+8nV65cFChQALAvrChUqFC6ws5kMlGsWDGeeeYZGjRowPDhw2natCm//PILly9fNupb8DhaFSviQt577z1y5sxJ7969jY7iUNqcWMS5lS9fPq2oCw0NpXnz5mzcuDHdNbly5eKVV15h5cqVtGzZkhEjRnDy5EkAcuTIkXbdrl27OHr0aOaF9zA+Pj74+Pi4ZY+dCjtxO1mzZmXcuHF89dVX/Pjjj0bHcQir1UpERITm2Im4iODgYAoWLJj2O3v16tW097y8vPD19eX111/nwoULrFu3DiCtZ+/YsWMsWrSIVq1a8c4772juXQaxWCzqsRNxFa1ataJGjRp069bNLfaQ+vPPP0lKSlKPnYiLaNmyJXPmzKFYsWJER0czevRojh8/DkBycjJms5ng4GDMZnO6oVqA4sWL06pVK3r06MG0adPo2rUrKSkpRnwbbi0gIECFnYirMJlMTJ48mWPHjjF58mSj49w3bU4s4nqyZMkC2Pes27p1Kx988AFxcXFp582GhYXxwAMPkD179rSvSe2dq1SpEpGRkWTPnp033ngDLy+vTM/v7iwWi4ZiRVxJuXLleOeddxg2bBgRERFGx7kvqfk1FCviekqUKMGsWbPYtWsXVapUYeDAgdSvX5/x48dTvnz5tNWw/1xBe+jQIYYMGcK7775LxYoVjYzvttRjJ+KCRowYgb+/P/379zc6yn3RqRMirq1YsWIcOHCAt956i9OnT+Pv78+oUaMYMWIEWbJkwWq1phV1NpuNt99+mypVqvDOO+8YnNx9uWthp+1OxK3lyJGD999/nw4dOtCxY0eqVatmdKR7Eh4eTp48efD19TU6iojch27duvH222/j4+OT7nWz+e9+lvHjx7N37162bNmS7kQLcSwNxYq4qDfffJPKlSvTpUsXl52ArK1ORNzHv4u6CxcupO1h99tvvzFkyBCGDh1KuXLljIjnMdy1x06Fnbg9s9nM5MmT2b9/P9OnTzc6zj3RcWIi7slms/H9999Tvnx5FixYQOfOnQkJCaFz585GR3N7AQEBbtljp6FY8QhVqlThzTffZNCgQTRv3pzcuXMbHemuhIeHU6ZMGaNjiIiDmUwm2rRpw2+//Ubbtm1JTk5m9erVGoLNBBaLhT///NPoGA6nHjvxGO+//z5Wq5X33nvP6Ch3TefEiri3999/n6NHj/LEE0/w8ssv89133xkdye1pKFbExeXNm5cRI0Ywffp09uzZY3ScO2a1Wjl//rwKOxE3V7hwYbZu3Uq/fv3YuHEjcXFxRkdya+66eEJDseJR3nnnHWbMmEHXrl3ZvHlzupVozurSpUskJydrjp2Ihxg0aBAJCQn4+fnd8J7VanWJdssVqMdOxA14e3szZcoUtm3bxty5c42Oc0d06oSI57lZUWez2ejXrx9vvfWWWxYkmc1dF0+osBOPU6tWLVq2bEn//v2Jjo42Os5tqbATkVSlSpVi3rx5hISEcOjQIaPjuDSLxeKWBbIKO/FI48aNIyYmhuHDhxsd5bYiIiIwmUzky5fP6CgiYiCTycSbb77J7t27MZlMVK5cmRkzZqSdLyt3R0OxIm7koYceYvDgwUyaNMnpP/Wmnjrx701NRcQzlSpVip07d9K6dWveeustWrVq5RKjD87GYrGQlJREcnKy0VEcSoWdeKyePXtSpEgRunXr5tSfeLXViYj8m8Vi4dNPP2Xx4sWsXr2axx9/nF27dhkdy6Wk7hXobvPsVNiJx/Lz8yMsLIx169axdOlSo+Pckgo7EbmVl19+mX379pErVy6qVavGhAkTsFqtRsdyCamFnbsNx6qwE4/2/PPP07hxY3r37u20e0bpnFgR+S9FihRh8+bNdO/end69e9OoUSMuXbpkdCynZ7FYAPXYibidiRMnEhkZyfvvv290lJvSObEicju+vr6MGzeO7777jp07d1KuXDl+/vlno2M5NfXYibipIkWK0K9fP8aNG8fx48eNjpNOSkqKTp0QkTtWv359Dhw4QPHixXnmmWcYNmwYKSkpRsdySppjJ+LGBgwYQHBwMD179jQ6SjoXL14kJSVFhZ2I3LH8+fPz008/MWzYMEaOHEnt2rU5d+6c0bGcTupQrHrsRNxQQEAAEyZMYOXKlU51+HZERASgzYlF5O54eXkxePBg1q9fz/HjxylXrpxTtW3OQEOxIm6uWbNm1K5dm+7duxMfH290HODvUyc0x05E7kXNmjXZv38/Tz75JA0bNqR3794kJiYaHcspaPGEiJszmUxMmjSJ//3vf0yYMMHoOIC9sNOpEyJyP3Lnzs2KFSuYOHEikydPplq1apw4ccLoWIZTj52IByhVqhTdu3dn9OjR/PHHH0bHITw8nHz58uHt7W10FBFxYSaTiR49erB161aioqKoUKECixcvNjqWofz9/QEVdiJub8iQIWTLlo0+ffoYHUV72ImIQ1WqVIm9e/fSsGFDWrZsSYcOHdyusLlTZrMZf39/DcWKuLts2bIxduxYvvzyS9avX29oFu1hJyKOli1bNubPn89nn33G/PnzqVy5Mr/++qvRsQwREBDgdoWtCjuRm3jttdeoWrUqXbt2JSkpybAcOk5MRDKCyWTizTffZPfu3ZjNZipXrsyMGTOc+tzsjBAQEKAeOxFPYDKZmDJlCocPH+bjjz82LIcKOxHJSKVKlWLnzp28/vrrvPXWW7Rq1Yro6GijY2Uai8WiHjsRT1GhQgU6duzI0KFDuXDhQqY/PyUlhQsXLqiwE5EMZbFYmDZtGl9++SWrV6/m8ccfZ9euXUbHyhQaihXxMKNGjcLb25sBAwZk+rMjIyOxWq2aYycimaJ58+bs37+f3LlzU7VqVcaPH4/VajU6VoayWCwaihXxJLly5WLMmDF8/vnnbN++PVOfnbo5sXrsRCSzFC5cmE2bNtGjRw/69OlDo0aNuHjxotGxMox67EQ8UPv27Xn88cfp0qVLph6mrcJORIzg6+vLuHHjWLVqFTt37qR8+fJs2LDB6FgZQoWdiAfy8vJi8uTJ7Nmzh1mzZmXacyMiIjCbzeTNmzfTnikikur555/nwIEDlChRgmeeeYahQ4dm6ofbzKChWBEPVbVqVdq0acPAgQO5fPlypjwz9dQJLy+vTHmeiMi/5c+fnx9//JHhw4czatQonnnmGc6ePWt0LIdRj52IB/vwww9JTExk8ODBmfI8bXUiIs7Ay8uLwYMHs2HDBk6cOEH58uVZuXKl0bEcQvvYiXiw4OBghg0bxrRp09i/f3+GP0+FnYg4kxo1anDgwAGqVq1Ko0aN6NWrF4mJiUbHui/ax07Ew3Xt2pUSJUrQtWvXDN+hPSIiQludiIhTyZUrF8uXLyc0NJQpU6ZQtWpVTpw4YXSse6ahWBEP5+Pjw+TJk9m8eTMLFizI0Gepx05EnJHJZKJ79+5s27aNK1euUKFCBRYtWmR0rHuixRMiQu3atXnppZfo27cvMTExGfKM5ORknTohIk6tYsWK7N27l0aNGtGqVSvat2/vcr1f6rETEQDGjx/PlStXGDlyZIbc/8KFC9hsNhV2IuLUsmXLxrx58/jss89YsGABlStX5tdffzU61h1LXTyR0VNrMpMKO5F7ULBgQd59910mTpzIkSNHHH7/iIgIAM2xExGnZzKZePPNN9mzZw9ms5nKlSszffp0lyiWLBYLVqvV5ReB/JMKO5F71KdPHwoWLEi3bt0c3oDp1AkRcTUlS5Zk586dtG3blo4dO9KyZUuio6ONjvWfAgICANxqOFaFncg98vf3JzQ0lB9//JFvvvnGofcODw/Hy8uLPHnyOPS+IiIZyWKxMHXqVL788kvWrFlDhQoV2Llzp9GxbslisQC41QIKFXYi96Fhw4bUr1+fnj17OvQTX0REBMHBwTp1QkRcUvPmzdm/fz958uShWrVqjB8/HqvVanSsG6jHTkTSMZlMhIaGEhERwdixYx123/DwcM2vExGXVrhwYTZv3kzPnj3p06cPDRs25OLFi0bHSkeFnYjcoFixYvTu3ZsPPviAU6dOOeSe2sNORNyBj48PY8eOZfXq1ezevZty5cqxfv16o2Ol0VCsiNzUoEGDyJMnD7169XLI/VTYiYg7qVevHvv37+fRRx+ldu3aDB06lOTkZKNjqcdORG4uS5YsfPTRR3zzzTesWbPmvu8XERGhwk5E3Er+/Pn58ccfGT58OKNGjaJ27dqcPXvW0EyphZ167ETkBi+//DJPPfUU3bt3v689kZKSkoiMjNQcOxFxO15eXgwePJgNGzZw8uRJypcvz8qVKw3LkzoUqx47EbmByWRi8uTJnDhxgtDQ0Hu+j06dEBF3V6NGDfbv30/VqlVp1KgRPXv2NGSTYA3Fish/KlOmDF26dGHEiBGcO3funu6hzYlFxBPkypWL5cuXExoayscff0zVqlU5fvx4pmbw8fHBbDZrKFZEbm3YsGFkyZKFfv363dPXpx4npsJORNydyWSie/fubNu2jejoaB5//HEWLlyYqc8PCAhQj52I3Fr27Nn54IMPWLBgARs3brzrrw8PD8fb25vcuXNnQDoREedTsWJF9uzZQ6NGjXjllVdo3749cXFxmfJsFXYicluvv/46VapUoWvXrne9pD88PJzg4GDMZv16iojnyJYtG/PmzWPWrFksXLiQypUr8+uvv2b4cy0Wi1sNxZpsjj69XEQA2L17NyEhIUyaNIkuXbqke89qg5gkiEqCqESIToIkK1iBiHNnib78JzUrlSOHL+Twgaw+YDYZ832IiGS23377jRYtWvD7778TFhZGhw4dMJkc0wj+u/1dv2MPuYPzky/4AcyAjxmCfHDZ9leFnUgGeuutt1iyZAnHjh0jT548xCbDyVg4FQfJf/3mmYCb/RL+83VvExTOAkUCIdA7c7KLiBjp+vXr9OrVi2nTptG8eXNmzJhBUFDQPd/PU9pfFXYiGejSpUsUL16cN7v1oUnnd4lMuHVDcjupX5fXD0oHQU5fx2YVEXFGS5YsoUOHDuTMmZNFixYREhJyV19/OQEOXcVj2l8VdiIZKMUG8zbsJaBoecwmEzhgKCG1gSkeCKWCwMuFhghERO7FqVOnaNWqFXv27OH999+nV69et52HnGKDw9FwLPbeC7p/c4X2V4WdSAaJSoQdf0Jcig17c+B4gd4QktM+F0RExJ0lJSXx3nvvMXbsWJ5//nm++OIL8uTJc9Nr/25/My6Ps7a/KuxEMsCFeNh6yf7JLiN/wUx//VU1N+Tzz8AHiYg4iTVr1tCmTRu8vb2ZP38+Tz/9dLr3Pb391X4KIg52IR62XLKvcM3oT0027M/Zcsn+XBERd1evXj32799PyZIlqV27NkOHDk3bVkrtr3rsRBwqKhE2RNp/2TObGXgqr/MNC4iIZISUlBTef/99hg4dSrVq1ZixYAmHyefx7a967EQcJMVmn9Nh1CclK7Dzsj2HiIi78/Ly4r333mPDhg38cS6ctf+LxWozoqxzrvZXPXYiDvLLFfvqK6MVzwqP3ftWTyIiLmfn+eucSfTDZPCJPc7Q/qrHTsQBLic4R1EHcCwGLicanUJEJHNcToA/ki2GF3XgHO2v8f8VRNzAoasZtaHJ3TMBh6KNTiEikjnU/qbnAodjiDi32GT7juYASQkJLBo/hI1fzSUuOoqCJcvSqu8oytV87j/vsX3112xdsZjjB3dxJfI8ufMXoGLthrzUfTBZgrKnu3bLisXs/ulbft+3g/Onj1PqiVqMWLIh7X0b9jyxya5x/I2IyL1KbX/vte3dsXoZP8ybxpkjvxBz5U+y5cxD8cef4OWewyj4aJl0184e1pPDO37m4h+nSUyIJ89DD1O1UQsad+yDJUsg4Bztr+bYidyng1fgeKz9F3pi51ZsX7WUBu168EDhYqxf8jknDuxi2OL1lAypfst7vFE2Nzny5Sek7gvkfrAgZ478wg/zppGvYBHGrtqLn8WSdu2Q5k9x8pc9PFKuMqcP7adgybLpCjuwf2p8JBDKZs+I71hExDmktr8T7rHtXRI6gj+OHaZwmQpky5mbK5HnWbd4FlGREYxZvo1CpcqlXftes+oUeawiwYUewcfPn9O/7mPdl7MoWrYSI5ZuTDsJw+j2V4WdyH2w2uDbcPuB0r/v28nAxlVoPWgcTTr1ASAxPp5ez5YhW+68jPlm6y3v8+u2DZR58ql0r21YOocpPV+n09gZPNuqfdrrl8L/IGfwg5jNZnrWLkPWnLlvKOzAfnB1o/xgdpYxChERB0ptf3/be+9t781cuXiBjiEP8UzLdnR8f9p/Xrvi0/HMGdWHMcu3UfzxJ9JeN7L91Rw7kfsQk2Qv6gC2r1qK2cuL5159K+19X39/nmnZjmN7tnEp/I9b3uffRR1AlXpNATj3+2/pXs+dv8Btz0gEe66Y5Dv4JkREXFBq+3s/be/NBOXOi58lgLjoK7e9Nm+BQgA3XGtk+6sZOCL3ISrp738+dWgf+YsUJyBrtnTXPFI+BIDTh/aTO3+BO773lYvnAciaM/e950uEIJ97/nIREaeV2v46ou2Ni75CcnISVyLP891noVyLucpj1WvfcF1KcjJxV6+QnJjImaO/snDce1gCs6Y9K10+g9pfFXYi9yEq0T6fwgZEXYgge94Hbrgmx1+vXb4Qflf3/uaTDzF7efFkg5fuKZsJuJIIZLmnLxcRcWqp7a8j2t6BTZ4g/MRRAPyzBPJit/eo3bLdDdedOLibd5s8mfbv+YuWoP+sFWTNkTPddUa2vyrsRO5DdNLfJ00kxl/Hx9fvhmt8/fzT3r9Tm5YtYO2iz2jydj8eKFzsnrLZgCtJt71MRMQlpba/jmh7O4+fzfWYq1w4c5L1X84mMf461pSUG6a9PFSsFEMW/Ej8tTiO7tnKL5t/Ij7uxk1MjWx/VdiJ3Iekf5xe4+tvISkx4YZrEhPi096/E4d3bGJq33aUr1WXV/qNdlg+ERF3ktq+OaLtLVHx7164ao1b0uOZkgC8PvijdNcFZM1G2RrPAhBStwmbli1gbLsmjF29N90K2n/my2xaPCFyH/75e5sj3wNciYy44Zqov17LmS//be93+vABPmzXmAIlytD706V4ed/fZy/VdSLirlLbN0e0vf8UmD0HZao+w6Zv5t/22irPNwNgy4pFt8yX2VTYidyHf/4CFSpVnvCTx7gWczXdNb/v22F/v3T5/7zX+dMnGNW6HkG58vLunFVpG146Kp+IiDtJbd/ut+29mcT461y7evsjJJISE7BarTe91qj2V+2+yH3w+cdv0BMNXsKaksKP86envZaUkMD6L2dTrEKVtFVZF8+d4dzxI+nuExV5npGv1sFsMvPevO8JypXH4flERNxJavt2P21v9KXIG+4b+cdpftmylqJlK6W9Fhd9heSkGyfNrV04E4Ai/7j23/kym+bYidyHIB/7gc82oHiFKjzZsDkLPhzI1T8jCS70CBuWfsHFs6d5Z9xnaV8zuUcbDm//maV//L03+OjW9bhw5iRN3u7HkV2bObJr89/PyJ0v3bE4h7dv5PCOjQBcvXyRhOtxLA0bBUCpKjUp9URNwL4qK7u2OhERN5Xa/t5P29vrucd4rFptCpUuT5agHJw/9TtrF31GSlISrw78IO26Q9s2MGtoN56o/xIPFC5GclIiv+3cxI7VX1O0bCVqNnstXTYj218VdiL3IYcvnIz7+9+7TpzDogcH8/PX9vMKH360LANnr0wrtm7l9OEDACyfOvaG90o9UStdYffL1nUsmTg83TWLPhoMQPOeQ9OeZQOy+97LdyUi4vz+2f7ea9tbp/Xb7F37Hfs3rOF6XAxBufJSrmYdmnV5l4dLPpZ2XcFHH6N01afZ9cNy+9w9m418DxflpR5DaNKpLz6+6RtbI9tfHSkmch+iE+GnG3vyncaz+bRBsYi4J7W/N6cZOCL3IauP/UxAZ+RtgqzqkxcRN6X29+ZU2IncB7MJCmexz6dwJibsuYw4gFpEJDOo/b05FXYi96lI4N+nTzgLG/ZcIiLuTO3vjVTYidynQG/I6+c8nxpN2PMEahhWRNyc2t8bqbATcYDSQc7zqdGGPY+IiCdQ+5ueCjsRB8jpC8WdZOizeFZ7HhERT6D2Nz0VdiIOUioIsngZNyRgwt79XyqbQQFERAyi9vdvKuxEHMTLBFVyGduwhOS05xAR8SRqf/+mwk7EgXL4QtXcmd+4mIBque3PFxHxRGp/7XTyhEgGuBAPWy/ZJ9Jm9C+YGXujktc/gx8kIuICPL39VWEnkkGiEmHHnxCXknHPCPS2d/87yydFERFn4Mntrwo7kQyUYoPD0XAs1t5d74hfttT7FM9qn6jrDHM6REScjae2vyrsRDLB5QQ4dBUiE+69gUn9urx+9n2SjF5SLyLiCjyt/VVhJ5KJYpPhZCycioPkv37zbtXQ/PN177/ORCwSqBMlRETuhae0vyrsRAxgtUFMsn0eyJVEuJIESVawYp+M62OG7D6Q3dc+fyOrt3EHSouIuBN3b39V2ImIiIi4Ce1jJyIiIuImVNiJiIiIuAkVdiIiIiJuQoWdiIiIiJtQYSciIiLiJlTYiYiIiLgJFXYiIiIibkKFnYiIiIibUGEnIiIi4iZU2ImIiIi4CRV2IiIiIm5ChZ2IiIiIm1BhJyIiIuImVNiJiIiIuAkVdiIiIiJuQoWdiIiIiJtQYSciIiLiJlTYiYiIiLgJFXYiIiIibkKFnYiIiIibUGEnIiIi4iZU2ImIiIi4CRV2IiIiIm5ChZ2IiIiIm1BhJyIiIuImVNiJiIiIuAkVdiIiIiJu4v8bY14EWe1KOQAAAABJRU5ErkJggg==\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": 61,
      "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": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "3dd0231b-07b8-4894-86a8-96ab86bcbb54"
      },
      "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(\"cirq.qsim\", 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": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "1c93bda4-7c89-4298-c232-f4e2e282ef32"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0008379860139395845\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": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "e5a1c37f-8e9d-4d24-d64e-a791a8f8e2d7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.48233570880256593\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": 65,
      "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": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "9bab9221-9369-4ce4-c438-3f124b478140"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4366201311349869\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": "8918e508-cae4-4e92-d2f4-60fa3ec4e4de"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701188279.293065\n",
            "Tue Nov 28 16:17:59 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
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      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
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    "colab": {
      "provenance": []
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