LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/default.qubit 25 qubit (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / default.qubit 25 qubit (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "7915c339-95bb-4e8a-9282-509c3eb8c403"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695144205.343889\n",
            "Tue Sep 19 17:23:25 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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "0cafacc2-5e6c-40e8-94e1-b9efb1bd98a0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.27 0.33 0.89]\n",
            " [0.33 0.16 0.17]\n",
            " [0.89 0.17 0.13]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "ae5162d0-397f-4728-bb26-aab4fbad0e55"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.16 0.17 0.33]\n",
            " [0.17 0.13 0.89]\n",
            " [0.33 0.89 0.27]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "061aecc8-ad24-4b32-c5db-aa5bbd3cf53d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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bt4+EhASeeuqpZAUvPj4eLy8vfvrpJwYNGsSoUaNo2LBh0jV6MTExnD17lsWLF/PDDz8wefJknnvuOYO+SueVYEvD32z9oaQTnARFxPmcPHmSKlWqUKxYMTZs2EDGjBnv+to7dQFsVjAlH9u6UxdwtpkIly52iaw2iIq3Xyt0zQLX7nC9UFZvyOpjn9IN8Pr3eqHVq1fTqFEjVq9eTYMGDYz8MpzSlStX+Oijj1i5ciUZMmRg4MCBvPDCC/j5+dGkSROuXr3KkiVLyJcvHwsXLqR48eI888wzSe+fPHkyX375JR9//DE1atS47diJJa958+b4+/vz9ddfa9HjhxBu0XWpIuJ8zGYzlStXxtfXl23btpE9e/YHet+tXeDgH+c4eOpPnq4QjJe3z327gDNxi2L3KGw2G8899xyRkZH89ttvKg6paO7cuVy+fJnevXvj7e3N8OHDWbNmDbly5aJs2bIkJCQwc+ZMevbsyYgRI/D39+fAgQOUKFECX1/fpGLXpUsXLly4wKxZs8iXL99tn2GxWChRogQlS5ZMWn+vbNmyFC9ePNkooTsxx6TPneSmf/6pksN+k5OIyKOIioqiZs2a/P333+zcuZPHH388RceZN28e7du3Jzo6+p6jfc7IiQYXjWEymQgNDaVatWosXryYtm3bGh3JZbRv3/62/x4wYADVq1dny5YtHD9+nAwZMrBkyRLq1q2Ll5cXFouFkSNHUrlyZZ577jkCAwNZtWoVX331FdOmTbvjHboxMTG0atWKQ4cOMWfOHM6fPw+Aj48PJUqUuK3slSlThrx587r8lHt6rv2YWBy3X7YvDaByJyIpZbFYeOmllzh16hRbtmxJcakD+6ifv7+/y5U60IjdA2vatClHjhzh2LFjyXZLkPQRExPDRx99xHfffcehQ4cICAigaNGi1K1bl379+uHn53ffY1y9epXDhw8nLbSc+M/16/bNBrNly5ZsZ43SpUu7zA4X2q1FRJyR1WqlY8eOLF68mLVr1yatrJBSAwcO5LvvvuPkyZOplNBxqNg9oEOHDvHUU08lTQ2K8aKjo4mMjCRPnjyPdByr1cqff/55W9k7ePAgJ06cwGq1V6DChQvfVvbKlClD0aJF8fJynkFvo/dUBPs1d460p6KIOId3332XSZMmsWjRIlq3bv3Ix+vYsSN//PEH27ZtS4V0jkXF7iF06NCB9evXc+rUqdsW3RXXFBMTw7Fjx27bRu3QoUOEhYUBJO2CcWvZK1u27D0XbTbSoWv2u1+NVjzAvmSAiMiDmDFjBn379mXatGn069cvVY5Zr149/P39WbZsWaocz5Go2D2EM2fO8MQTTzBq1ChCQkKMjiMGuXTp0m0je4cOHeLIkSPcuHEDgJw5c95W9sqUKUOpUqUMvZbjaixsvGTYxyfzfBAEakpWRO5jyZIltGnThgEDBvDee++l2nHLlStHlSpV+Oijj1LtmI5Cxe4h9enThzlz5nD69GntdCBJEhISOH36dLLCd+rUKWw2GyaTiaJFiya7fq9w4cLpcqf11ktwKda4KdhbmbAv9lk9p9FJRMSRbdq0iXr16tGqVSvmzJmTqufKPHny0KNHD0aMGJFqx3QUKnYPyWw2U6RIEd544w0mTpxodBxxcNHR0Rw9evS2snfw4EEuX74MQMaMGSlVqlSywpcjR45Uy3A93r4jRFxsLIumDGfLsrlER4RT4MmytH1nLE/VqHPP9+9a8y07vl/MqYN7uXYxjBx58/PMC415qe8wMmXJmvS6wzs3MfLl5+96nLbvjKVlnyFJ/10vt3Mt+iki6efQoUNUr16dChUqsGrVqlS9adFqteLj48OHH35Ijx49Uu24jkLFLgWGDx/Oe++9x6lTp5KtmyZyPzabDbPZfFvZS5zOjY2NBSB37tzJyt6TTz5JhgwPv17IwWv27b6mvtGWXauX0ui1fuQpVIyN33zFHwf2MnLxRp6sWO2u7+9cNgfZcuWlYr1m5MhXgHPHD/HjvE/IVaAwk1b/hu8/dyNfu2Tm4Nb1yd6/edlcDmz5kQkr91C0XAXAPmpX1B/KZn3oL0dEXNy5c+eoXLkyQUFBbN68mcyZM6fq8S9dukRQUBDfffcdzZo1S9VjOwIVuxSIiIigSJEitGzZkk8//dToOOIi4uPjOXXqVLK7c8+cOQOAp6cnxYsXT3Z37uOPP37XKQqrDVZegGO/7SGkaTDth7zHiz3eBsASE8NbtUuTOUcQ45fvuGuuwzs3Ubpyzdse27R0Dh/270iPSZ9Tu23Xe35dvasXw2Qy8cGWE7c97mWCJnmdc2V3EUkbV69epVq1aty8eZOdO3eSO3fuVP+Mw4cPU6ZMGXbs2EHlypVT/fhG00RICmTJkoXBgwczcOBABgwYQPHixY2OJC7Ay8uLEiVKUKJECV5++eWkx6Oiojhy5MhtU7nr168nPDwcAH9//2Rlr0yZMmTLlo2oOPveiLtWL8XD05M6r3RLOq5PhgzUavMaCyYO5vKFv8iRN/8dc/231AEE12/Oh/07cv7ksXt+TSf37SHs7Clefmtksufi/9neJ4v7bgAiIre4efMmTZs25eLFi+zYsSNNSh2QtLKBo65g8KhU7FKoV69eTJs2jWHDhrF48WKj44gLCwgIoFKlSlSqVCnpMZvNxoULF24b3du1axdffvklcXFxADz22GO06P4W1Tv248yRfeQtXJyMAbdPaRQtVxGAs0f237XY3cm1S/YTY0Dgva8F3Lp8PgDVm71yx+fDLSp2ImK/Aa1du3b89ttvbNy4MU0HTMxmM6BiJ/+RIUMGRo0axWuvvca7775L+fLljY4kbsRkMpEvXz7y5ctHgwYNkh6Pi4vj999/Typ7GQsWIyE+nnDz32QNSr6Qc7Z/HrtqvvBQn7/8o4l4eHpSudFLd31NQkICO1Yupmi5iuQpVDT51wBcswBaElLErdlsNt58801WrlzJ8uXLCQ4OTtPPM5vNZMqUyWXXo9WO9o+gQ4cOlChRgsGDBxsdRQQAb29vSpcuTdu2bRk/fjzV6jbGy9sbS8xNvH18k73ex9d+M4Yl5uYDf8bW7xbw06JZNOk2gDyFit31dYe2/cS1S2aqN7/zaJ0NuBb3wB8rIi5q/PjxfPzxx3zyySc0btw4zT/PbDa77GgdqNg9Ei8vL8aNG8e6devYuHGj0XFEkon7Z1NYnwx+xFlikz1viY1Jev5BHN29lY/feY1yz9Wj3cBx93zt1uXz8fD0pGqTu2//E2fEprUi4jBmz57N0KFDGT16NF273vtGrNSiYif31Lx5cypUqEBISAi6wVgcTWJvypYrD9cu/p3s+fB/HgvMlfe+xzp79AATX2tK/idKM+DTpXjeY5/c2Js32bP2O8pWq03WnHc/garXibivVatW0a1bN7p3787QoUPT7XPNZnOa3ZjhCFTsHpHJZGLChAns3r2bFStWGB1H5DaJ3+AFS5bjwukT3IiKvO35k/t2258vVe6exwk7+wdj29cnS/YgBs9ZjV8m/3u+/pf133PzetRdp2H/m09E3MuePXt4+eWXady4MTNnzsRkSr91jzRiJ/dVq1YtateuzeDBg0lISDA6jkgS73++wys1eglrQgLr53+W9FxcbCwbl3xJsaeDk+6IvXT+HOdPHb/tGOEXwxjzSl08TB4MnbeOLNnvvxfY1uUL8PXLSMX6zR8on4i4jxMnTtCoUSPKlSvHwoUL8fT0TNfPDwsLc+lip7tiU8n48eOpWLEic+fOpVOnTkbHEQHsS4lctUDxp4Op3LgVCyaGEHnlIrkLFmXT0q+59L+z9HpvVtLrP+jXgaO7NrP0r38vKxjXvj7mc6d5sedAju/dxvG92/49fo5cybYkiwq/yv5Nawhu0PKeI3smIKuWOhFxK2FhYdSvX58cOXKwcuVK/Pwe7Pre1GK1Wrl48aKKndxfhQoVeOmllxgxYgRt2rRJ0dZPIqktmw+cjrb/+5vT5rAo3zA2f2vfK/bxEmUJ+fIHSlaqcc9jnD16AIAVH09K9lzJSs8lK3Y7V31DfFwc1Zu1u+dxbUDW1Nv+UUQcXFRUFI0aNSI2NpaNGzcSGBiY7hmuXr1KQkKCSxc7bSmWin7//XdKlSrF5MmT6devn9FxRIiwwIaLRqe4u9q5tECxiDuwWCw0btyY3bt3s3XrVsqWLWtIjiNHjlC6dGm2bdtG1apVDcmQ1nSFSyp64okn6Ny5M+PGjSMyMvL+bxBJYwHe9j1ZHZGXCQI0ZyDi8qxWK6+99hqbN29m+fLlhpU6+HfXCd0VKw9sxIgRREVFMXXqVKOjiOBhgkKZ7NezORIT9lwejhZMRFJdSEgI8+bNY86cOTz//POGZnH17cRAxS7VPfbYY7z55ptMmTKFixcdeA5M3EZhf/v1bI7Ehj2XiLi2GTNmMGnSJKZNm0br1ndfrDy9hIWFkTFjRvz9XfcEpGKXBgYNGoSHhwfjx483OooI/l4Q5Os4o3Ym7Hn8NQ0r4tKWLFlCv379ePvttx3munNXX8MOVOzSRPbs2Rk4cCAff/wxZ8+eNTqOCKWyOM6onQ17HhFxXRs3bqR9+/a0a9eOiRMnGh0niYqdpFjfvn3Jli0bI0eONDqKCIE+UNxBZh6KB9jziIhrOnjwIM2aNeO5555j9uzZeHg4TtVQsZMU8/f3Z9iwYcyZM4fDhw8bHUeEklkgk6dxU7Im7NOvJTMbFEBE0ty5c+do0KABRYoUYdmyZfj4ONZvcSp28khef/11ChYsmK6bG4vcjacJgrMbW+wqBtpziIjruXr1KvXr18fX15fVq1cTEBBgdKRkzGazSy91Aip2acrHx4cxY8awYsUKdu7caXQcEbL5QJUc6V/uTEDVHPbPFxHXc/PmTZo0acKlS5dYu3atQ5Ynd9hODFTs0lzbtm0pW7YsISEhaJMPcQS5MthLlgfpU/A8gGo5IEi77Im4pISEBNq1a8f+/fv54YcfKF68uNGR7ig8PJy4uDgVO3k0icuebN68mR9//NHoOCKAvdzVDIKMnmn7Of5e9s9RqRNxTTabjd69e7Ny5UqWLFlCcHCw0ZHuyh0WJwYVu3TRsGFDqlWrRkhICFar1eg4IoB9WrRO7n/vlk2t0bvE4xQPsO8Fq+lXEdc1btw4PvnkEz777DMaNWpkdJx7UrGTVGMymQgNDWXfvn188803RscRSeJpgjJZ4fmckNPX/lhKC17i+3L6wvNBUCaLbpQQcWWzZ89m2LBhjB49mi5duhgd577cpdiZbLrwK900adKE48ePc/ToUby9vY2OI5LM9Xg4fR3OREP8P2cGE3de3PjWx73+2ZO2sL92lBBxB6tWreLFF1+ka9eufPzxx5hMjv9b3Pvvv09ISAjR0dFOkTeldApOR+PGjaNcuXLMnj2b7t27Gx1HJBl/LyibFUpngah4CLfANQvsPXqCBDwoVKQoHoC3B2T1hqw+9qnWAC/wcN3zpIjcYvfu3bz88ss0btyYmTNnOk1JSlzDzlnyppRG7NLZq6++ys8//8ypU6fImDGj0XFEHkiHDh04c+YMW7duNTqKiBjoxIkTVKlShSeeeIINGzbg5+dndKQH1qVLF44ePcquXbuMjpKmdI1dOhs9ejSXLl3igw8+MDqKyAOzWCwOt4K8iKSvsLAw6tWrR1BQECtXrnSqUgfusesEqNilu8KFC9O9e3cmTJhAeHi40XFEHkhcXJyKnYgbi4yMpGHDhlgsFtauXUtgYKDRkR6aip2kmaFDh2KxWJg0aZLRUUQeiMVi0Q0/Im7KYrHQsmVL/vjjD9auXUuBAgWMjpQiKnaSZnLnzk3//v15//33uXDhgtFxRO5LU7Ei7slqtdKlSxe2bNnCihUrKFOmjNGRUsRms7nFdmKgYmeYd955Bz8/P8aMGWN0FJH70lSsiHsaNGgQCxYsYO7cudSsWdPoOCl27do1LBaLQ+5hm9pU7AySJUsWQkJC+Pzzzzl58qTRcUTuSVOxIu7n/fff57333mPatGm8/PLLRsd5JO6yODGo2BnqjTfeIHfu3AwfPtzoKCL3pBE7EfeyZMkS+vfvzzvvvEPfvn2NjvPIwsLCABU7SWN+fn6MHDmSRYsWsW/fPqPjiNyVrrETcR8bN26kffv2tGvXjgkTJhgdJ1VoxE7STadOnShevDiDBw82OorIXWkqVsQ9HDx4kGbNmvHcc88xe/ZsPDxcoyaYzWZ8fX3JnDmz0VHSnGv8jTkxLy8vxo0bx9q1a9m0aZPRcUTuSFOxIq7vzz//pEGDBhQpUoRly5a51Pe8u2wnBip2DqFly5Y888wzhISEoB3exBFpxE7EtV25coX69evj6+vL6tWrCQgIMDpSqjKbzW5xRyyo2DkEk8nEhAkT2LVrF99//73RcUSS0TV2Iq7r5s2bNG3alMuXL7Nu3TqXLEDusjgxqNg5jNq1a/PCCy8wZMgQEhISjI4jchtNxYq4pvj4eNq2bcv+/ftZtWoVxYoVMzpSmggLC1Oxk/QXGhrKkSNHmD9/vtFRRG6jqVgR12Oz2ejduzc//PAD33zzDRUrVjQ6UprRiJ0YokKFCrRs2ZLhw4cTGxtrdByRJJqKFXE9Y8eO5dNPP+Xzzz+nYcOGRsdJMzabTcVOjDN27Fj++usvPv30U6OjiCTRVKyIa5k1axbDhw9nzJgxdO7c2eg4aSoiIgKLxaJiJ8YoUaIEnTt3ZuzYsURFRRkdRwSr1UpCQoKmYkVcxKpVq+jevTs9evRgyJAhRsdJc+60ODGo2DmkESNGEBkZybRp04yOIkJcXByARuxEXMDu3btp1aoVTZo04cMPP3SLdd0Si50r3u17Jyp2Dih//vy88cYbTJ48mUuXLhkdR9ycxWIBVOxEnN2JEydo1KgR5cuXZ8GCBXh6ehodKV1oxE4cQkhICGC/U1bESInFTlOxIs4rLCyMevXqERQUxPfff4+fn5/RkdJNWFgYPj4+ZMmSxego6ULFzkHlyJGDd955h5kzZ3Lu3Dmj44gb01SsiHOLjIykYcOGWCwW1q5dS2BgoNGR0pU7bScGKnYOrX///mTJkoWRI0caHUXcmKZiRZyXxWKhRYsWnD59mrVr11KgQAGjI6U7d1rqBFTsHJq/vz/Dhg3j66+/5ujRo0bHETelqVgR52S1WuncuTNbt25l+fLllClTxuhIhlCxE4fSrVs3ChQowNChQ42OIm5KU7Eizundd99l4cKFzJs3j5o1axodxzBms9lt7ogFFTuH5+vry+jRo/nuu+/YvXu30XHEDWnETsT5TJ8+ncmTJzN9+nRatWpldBxDacROHE67du0oXbo0gwYNwmazGR1H3IyusRNxLosXL6Z///4MHDiQPn36GB3HUDabjbCwMBU7cSyenp6MHz+eTZs2sX79eqPjiJvRVKyI89i4cSMdOnTg1Vdf1XJZ2O8Ijo2NVbETx9O4cWOqVKlCSEgIVqvV6DjiRjQVK+IcDhw4QLNmzahZsyazZs3Cw0M/4t1tcWJQsXMaJpOJCRMm8Ntvv7F06VKj44gb0VSsiOP7888/adCgAUWLFmXp0qX6fv2Hip04tOrVq9OwYUOGDh2aND0mktY0FSvi2K5cuUL9+vXJkCEDq1atIiAgwOhIDkPFThze+PHjOXnyJF9++aXRUcRNaCpWxHHdvHmTpk2bcvnyZdatW+dWy3o8CLPZjLe3N9myZTM6SrpRsXMyTz31FO3atWPUqFHcvHnT6DjiBjRiJ+KY4uPjadOmDfv372fVqlUUK1bM6EgOx922EwMVO6c0evRoLl68yIcffmh0FHEDusZOxPHYbDbeeOMNVq1axTfffEPFihWNjuSQ3G2pE1Cxc0pFihShW7duhIaGcu3aNaPjiIvTVKyI4xkzZgyfffYZX3zxBQ0bNjQ6jsNyt8WJQcXOaQ0dOpTY2Fjee+89o6OIi4uLi8PDwwNPT0+jo4gI8MUXXzBixAjGjh1Lp06djI7j0FTsxGnkyZOHfv36MX36dP7++2+j44gLs1gsGq0TcRA//PADPXr0oFevXgwePNjoOA5PxU6cyjvvvIOvry9jx441Ooq4MIvFouvrRBzArl27ePnll2natCkzZsxwqxsCUsJms2E2m93uTmEVOyeWNWtWBg0axGeffcYff/xhdBxxUXFxcSp2Igb7/fffady4MeXLl2f+/Pm6NOIBXL9+nZs3b2rETpxL7969CQoKYvjw4UZHERelqVgRY/3999/Ur1+foKAgvv/+e/z8/IyO5BTCwsIA91qcGFTsnF7GjBkZMWIECxYsYP/+/UbHERekqVgR40RGRtKwYUPi4uJYu3YtgYGBRkdyGu646wSo2LmEzp07U6xYMYYMGWJ0FHFBmooVMUZ8fDwtWrTgzJkzrFmzhgIFChgdyamo2InT8vb2ZuzYsaxevZotW7YYHUdcjKZiRdKfzWbDw8ODPHnysHz5csqUKWN0JKdjNpvx8vJyq+3EALyMDiCp46WXXqJ8+fKEhISwbds23S0lqUZTsSLpz2QyYbPZmDNnjs7nKWQ2mwkKCsLDw73GsNzrq3VhHh4ehIaGsmPHDn744Qej44gL0VSsSNqxWq13fc7Dw0Ol7hG441InoGLnUurUqcPzzz/P4MGDSUhIMDqOuAhNxYqkvs2bNxMSEkLTpk355ptvkrbuk9TjjosTg4qdSzGZTISGhnL48GEWLFhgdBxxERqxE0ldy5cvp3nz5vz11194eHjQunVrtm7danQslxMWFqZiJ84vODiY5s2bM3z4cGJjY42OIy5A19iJpJ4tW7bw2muvMWXKFObMmcP3339PnTp1OHfunGZaUplG7MRljB07lnPnzvHZZ58ZHUVcgKZiRVLH9evXWbx4MX369KFDhw5JF/XHxsaycuVKKlasyMiRI9m9e7fBSV2Dip24jJIlS9KxY0fGjBlDVFSU0XHEyWkqViR1+Pv707lzZ5o1a5a0Jdirr77KkSNHKF++PE2aNGH+/Pl89tlnuubuEV2/fp0bN26o2InrGDlyJBEREUyfPt3oKOLkNGInknqeffZZnnrqKQBOnjwJwM8//8zQoUMZOXIkgwcPZu7cufzvf/8zMqbTS1yc2B3vitU6di6qQIECvPHGG0yePJmePXuSI0cOoyOJk9I1diIpd/jwYfbu3UtUVBSVK1emQoUKSc8VKVKEzz//HD8/PxISEvD09CRbtmw8++yzZM2a1bjQLsBdd50Ajdi5tJCQEGw2GxMmTDA6ijgxTcWKpMxPP/1E7dq1WbhwISNHjmTIkCGcOnUK+HdniQwZMgDg6emJzWZj8eLF5M2bl8yZMxsZ3emFhYUBKnbiYnLmzMnbb7/Nhx9+yF9//WV0HHFSmooVeXg7duygVatWhISEsGbNGvbs2cOOHTv4888/AZIWHjaZTMTHx/P777/ToUMHdu/ezRdffIGXlybUHoXZbMbT05PAwECjo6Q7FTsX179/fzJnzsyoUaOMjiJOSlOxIg8nPDycGTNm8Prrr9O3b188PT0pWrQo1atXZ/v27QwdOpQ5c+YkvX7v3r10796dkydPsnfvXk3DpgJ33U4MVOxcXkBAAEOHDuXLL7/k+PHjRscRJ6SpWJGH4+3tTdu2bencuXPSY7169WLTpk2cPXuWXbt2MWnSJIYOHQpA5cqVGTduHOvXryd79uxGxXYp7rrUCajYuYXu3buTP3/+pJOIyMPQVKzIw/H396d+/fqUKFECsE/LLly4kPXr1zN79mzWr1/P888/z8aNG7l27RoAVatWJSAgwMDUrkXFTlyar68vo0aNYtmyZezdu9foOOJkNGIn8vB8fX2T/r1KlSqcPHmSatWqYbVaMZlMFCxYEKvVmnTzhKQus9nslkudgIqd23j11VcpWbIkISEhRkcRJ6Nr7EQeXeIUq4eHB1arld9++41SpUppNDyNuOs+saBi5zY8PT0ZP348P/30Exs2bDA6jjgRTcWK3J3Vak22x6vVak32usS7YCMiIujRowfbt29n7NixSTtQSOrSVKy4haZNm1KpUiUGDRqEzWYzOo44CU3FitzZgQMH6Ny5M3Xr1qVfv36sXbsWsI/K/bfsASxevJhu3bqxefNmtm7d6rZThWktOjqa6OhoFTtxfSaTiQkTJvDrr7+ybNkyo+OIk9BUrEhyhw8fpnr16sTHx/P000+zYcMGhg8fzsCBAwH7LMl/93sNDg6mRo0abNu2jfz58xsR2y24864ToGLndp577jnq16/PkCFDiI+PNzqOODibzUZcXJymYkVuYbVamT17Ns2aNWP+/PlMnjyZzZs307BhQ9atW0fv3r0B8PHxISEhgaVLl2I2mylYsCC9evUiZ86cBn8Frk3FTtzO+PHjOXHiBF999ZXRUcTBJZZ/jdiJ/MvDw4Pz589z6dKlpMeyZ89O//79adeuHbt27WLKlCkALF++nD59+vDpp59is9mSrrWTtJNY7Nx1qlvFzg09/fTTtGnThpEjR3Lz5k2j44gDS5xK0oidiF3i9cnPPPMMMTExnD59Oum5LFmy8Nprr1GmTBm+//57bDYbLVu2pGfPnrz++usqdekkcTsxd13sWcXOTY0ZMwaz2czMmTONjiIOLLHYacROxC6xnDVs2JB9+/YxZcoUbty4AdhLX44cORg6dChbt25l/fr1AAwbNow8efIYltndhIWFkTNnTrfcTgxU7NxW0aJF6dq1K+PHj09a+Vzkv+Li4gAVO5H/Kl26NAsWLODzzz9n6NChXL16Nan0+fr6UqZMGbJly2ZwSvfkzkudgIqdWxs2bBgxMTFMnjzZ6CjioDQVK3J3DRs2ZMGCBXzwwQf07NmTJUuWcOzYMaZOnUp4eDgFChQwOqJbUrETt5U3b1769u3LtGnTCAsLMzqOOCBNxYrc20svvcS2bdsICwvjnXfeoWnTpqxZs4bVq1e7dbkwkoqduLWBAwfi4+PD2LFjjY4iDkhTsSL3FxwczPfff8+mTZv49ttv2bZtG6VLlzY6lttSsRO3li1bNgYNGsRnn312291dIqCpWJEHlSVLFgoVKkSZMmXc9m5MR2E2m912qRNQsRPgzTffJEeOHIwYMcLoKOJgNGIncjubzXbHvWDFMdy4cYOoqCiN2Il7y5gxIyNGjGD+/PkcPHjQ6DjiQHSNncjtxo0bx6pVq7TftoNy910nQMVO/tGlSxeKFCnCkCFDjI4iDkRTsSL/+vzzzxk2bBhHjhzRYsMOSsVOxU7+4e3tzdixY/nhhx/Ytm2b0XHEQWgqVsRu5cqV9OjRg169evHuu+8aHUfuQsVOxU5u0apVK8qVK8egQYM0zSCARuxEAHbt2kXr1q1p1qwZM2bM0GidAzObzXh4eJAjRw6joxhGxU6SeHh4EBoayvbt21m9erXRccQB6Bo7cXfHjx+nUaNGPPPMM8ybNw9PT0+jI8k9mM1mcubM6dZ/Typ2cpt69erx3HPPERISoju/RFOx4tYuXLhA/fr1yZMnD99//z1+fn5GR5L7cPc17EDFTv7DZDIRGhrKoUOHWLhwodFxxGCaihV3FRERQcOGDYmPj2fNmjXa99VJhIWFqdgZHUAcT+XKlXnxxRcZNmxY0g92cU+aihV3FBsbS4sWLfjzzz9Zu3Yt+fPnNzqSPCCN2KnYyV2MGzeOs2fP8vnnnxsdRQyUOBXr5eVlcBKR9GG1WunUqRPbt29nxYoV2hrMyajYqdjJXZQqVYoOHTowZswYrl+/bnQcMYjFYsHb21t3AYrbeOedd1i8eDHz58+nRo0aRseRh6Rip2In9zBy5EjCw8N5//33jY4iBrFYLJqGFbcxdepUpk6dyowZM2jZsqXRceQhxcTEEBkZqWJndABxXAULFqRnz55MmjSJK1euGB1HDBAXF6diJ25h4cKFDBgwgEGDBtG7d2+j40gKJC5OnDt3boOTGEvFTu5p8ODBWK1WJkyYYHQUMUDiVKyIK/vpp5/o2LEjHTp0YPz48UbHkRQKCwsD3HvXCVCxk/sICgpiwIABfPDBB/zvf/8zOo6kM43Yiavbv38/zZs3p1atWnzxxRe6ntSJaTsxOxU7ua+33nqLgIAARo0aZXQUSWe6xk5c2dmzZ2nQoAHFixdn6dKlGp12cmazGZPJ5NbbiYGKnTyAzJkzM2TIEGbPns3x48eNjiPpSFOx4qouX75M/fr1yZQpE6tWrcLf39/oSPKIzGYzOXLkcPvlmVTs5IH06NGDxx57jGHDhhkdRdKRpmLFFd24cYMmTZpw9epV1q5d6/ZTd65CS53YqdjJA8mQIQOjRo1i6dKl/PLLL0bHkXSiETtxNfHx8bRu3ZpDhw6xevVqihYtanQkSSVms9nt74gFFTt5CO3bt6dkyZIMHjzY6CiSTnSNnbgSm81Gz549Wbt2LUuXLuXZZ581OpKkIo3Y2anYyQPz9PRk3LhxrF+/np9++snoOJIONBUrrmTUqFF88cUXfPHFF9SvX9/oOJLKwsLCVOxQsZOH9OKLLxIcHExISAg2m83oOJLGNBUrruKzzz5j1KhRjB8/no4dOxodR9KARuzsVOzkoZhMJiZMmMDevXv57rvvjI4jaUxTseIKvv/+e3r27Mkbb7zBoEGDjI4jaSAmJoaIiAgVO1TsJAVq1qxJ3bp1GTJkCPHx8UbHkTSkqVhxdjt37qRNmzY0b96c999/XwsQu6iLFy8CWpwYVOwkhcaPH8/x48eZM2eO0VEkDWkqVpzZ8ePHady4Mc8++yzz5s3D09PT6EiSRrTrxL9U7CRFnnnmGV5++WVGjBhBTEyM0XEkjWjETpzVhQsXqF+/Pnny5GHFihVkyJDB6EiShhKLnZY7UbGTRzBmzBj+/vtvPvroI6OjSBrRNXbijCIiImjYsCHx8fGsWbOGbNmyGR1J0lhYWBgmk4mcOXMaHcVwKnaSYsWLF+e1115j/PjxREREGB1H0oCmYsXZxMbG0qJFC/7880/Wrl1L/vz5jY4k6cBsNpM9e3a3304MVOzkEQ0fPpzo6GimTJlidBRJA5qKFWditVrp2LEj27dvZ8WKFZQuXdroSJJOtNTJv1Ts5JHky5ePPn36MHXq1KRrHMR1aCpWnMnbb7/NkiVLWLBgATVq1DA6jqQjFbt/qdjJI3v33Xfx8vJi3LhxRkeRVKapWHEWU6ZMYdq0aXzwwQe0aNHC6DiSzlTs/qViJ48sMDCQd999l08++YQzZ84YHUdSkaZixRksWLCAt99+m5CQEN544w2j44gBzGaz7oj9h4qdpIo+ffqQPXt2RowYYXQUSUUasRNH99NPP9GpUyc6duyoWQM3phG7f6nYSarIlCkTw4cPZ968eRw6dMjoOJJKdI2dOLL9+/fTvHlzXnjhBT7//HPtKuGmYmNjCQ8PV7H7h4qdpJquXbtSuHBhhgwZYnQUSSWaihVHdebMGRo0aMATTzzBN998o5FlN6btxG6nYiepxtvbmzFjxrBy5Uq2b99udBxJBZqKFUd0+fJl6tevT6ZMmVi1ahX+/v5GRxIDaTux26nYSapq3bo1Tz31FCEhIdhsNqPjyCPSVKw4mhs3btCkSRPCw8NZt24dQUFBRkcSg6nY3U7FTlKVh4cHoaGhbN26lbVr1xodRx5BQkICNptNxU4cRnx8PK1bt+bQoUOsXr2aIkWKGB1JHEThwoVV8v9hsmlYRVKZzWajZs2aRERE8Ntvv+Hhod8fnNHNmzfJmDEjc+fO5dVXXzU6jrg5m81Gt27d+Oqrr1i5ciX169c3OpKIQ9JPXEl1JpOJ0NBQDhw4wMaNG42OIykUFxcHoBE7cQgjR47kiy++YNasWSp1Iveg3XIlTVSpUoVt27ZRtWpVbDabliFwQhaLBVCxE+N9+umnjB49mtDQUDp06GB0HBGHphE7STNVqlQBUKlzUonFTnfFipFWrFhBr1696N27N++++67RcUQcnoqdpBkVOuemqVgx2o4dO2jTpg0tWrRg+vTpOqeIPAAVOxG5I43YiZGOHz9OkyZNqFixInPnzsXT09PoSCJOQdfYiSG2bt3K77//TubMmSlXrhzFixc3OpL8h66xE6NcuHCBevXqkSdPHpYvX06GDBmMjiQOxmq1YjKZNIp7Bxqxk3S1fft2qlatSr169Zg1axbdunWjdevWrFy50uho8h+aihUjRERE0KBBA6xWK2vXriVbtmxGRxIHER0dzbBhw7h48SIeHh6YTCZsNpsWw/8PFTtJN/369aNGjRoEBgbyww8/sGTJEk6ePEnbtm3p1auX0fHkPzQVK+ktNjaW5s2bc+7cOdauXctjjz1mdCRxIH/++Sfjxo2jfPny9O3bl99//12jdnegYidpLiYmhu7du/Pdd98xe/ZslixZQq1atcifPz85c+akRYsW+Pr6smvXLqOjyi00FSvpyWq10rFjR3bs2MH3339PqVKljI4kDub3338nZ86chISEsH79el588UVGjBjBoUOHjI7mUHSNnaS5o0ePsmLFCiZMmEC7du2SjQBt376d69evU7BgQWMCyh1pKlbS09tvv82SJUtYunQp1atXNzqOOKBTp07x5JNP8sYbb1CpUiWWLFnCN998w48//kjbtm1p1aoVuXLlcvvdjtz7q5d0ceDAAQoVKkTr1q1vK3UxMTHMmzePUaNG8corr5A7d24DU8p/aSpW0suUKVOYNm0aH3zwAS1atDA6jjios2fPki9fPgCeeeYZJk6cyOzZsylVqhRjx45Nunb75s2bBic1lkbsJM35+/tz7tw5bty4gZ+fHwC7d+9m1apVbNiwgeDgYF1j54A0FSvpYf78+bz99tsMHjyYN954w+g44sDOnj3LU089BUB8fDxeXl5UqlSJSpUqcfz4caZOnUr37t25efMmffr0MTitcUw23U4i6eDZZ5/F39+fsmXLcv78eSIiIjCbzdStW5dBgwaRM2dOoyPKf3z77be0bNmSK1euEBgYaHQccUEbNmygYcOGvPLKK8yePVsXwcs91a5dm3bt2tGlS5ekx6xWK0DS9OuRI0fIkiWLW994o2In6eLMmTMsXbqUefPmUbJkSQoVKkSzZs2oWLEiYP/mdPfrIhzNokWLaNu2LZGRkQQEBBgdR1zMvn37qFGjBtWrV2fFihWa8pf7iouLw2az3XUWQT9H7FTsxFCJaxDpm9HxzJ07lw4dOhATE4Ovr6/RccSFnDlzhsqVK5M/f342btyIv7+/0ZFEXIZ+mkq6W716Nb///jvAHUvdjRs3+PXXX9m5c6cR8eQfunlC0sLly5epV68eAQEBrFq1SqVOHlrigMB/Fye2Wq3Ex8cbmMwxqNhJutq8eTMdO3bk66+/BrjjSF1cXBwLFy6kb9++HD58OL0jyj8yZsxI0aJFNZoqqSY6OprGjRsTERHB2rVrCQoKMjqSOKHERYn/uzjxgQMHeP755w1M5hg0FSvpburUqTz33HM888wzyZ6Li4vD29ubS5cu8corrxAREcHu3bsNSCkiqSk+Pp7mzZuzceNGNm3axLPPPmt0JHEiV65cYeHCheTJk4fMmTMTEBBAQEAAmTJlImPGjGTKlInly5fTp08frly5YnRcQ2m5E0l3b731VrLHEhIS8PT0xNvbm/j4eKZPn86xY8fIkycPZ86coVChQgYkFZHUYLPZ6NGjB2vXruWHH35QqZOHtnfvXvr06cPjjz+O1WrFz88Pf39/MmfOTGBgIDlz5uTQoUM8/vjjRkc1nIqdGObmzZt4e3vj6emJp6cnYF/TasKECUk/COrVq6dvVBEnN3LkSGbNmsXXX39NvXr1jI4jTshsNlOuXDk++OADvL29OXv2LBcuXOB///sfYWFhnDlzhl9++YXGjRsbHdVwKnZiiJiYGJ577jmGDRtGkyZN+O233xg8eDDHjh2jfv36tGrVikqVKiVdWG2z2bTGlYgT+vTTTxk9ejShoaF06NDB6DjipPz8/MiWLRt+fn6UL18+aamsW7Vp04YMGTIYkM6xqNiJITJkyEC5cuV46623WL16NStXrqRs2bKMHz+eWrVqkSdPnqTXqtSJOKcVK1bQq1cvevfuzbvvvmt0HHFiNWvWJDAwkFy5cgH2azZNJtNtPx8iIyMpWbKkkTEdgm6eEEMVLFiQ8PBwRo0aRb169XjyySeTnrv1G9Zms7FgwQJeeeUVo6KKyEPYvn07tWvXpnHjxixatCjpcguRtBIZGYmXlxcZM2Y0OoqhVOzEUMuWLePll1/mwIEDlC5dGrjzCF10dDRBQUHMmjWLNm3aGBFVRB7QsWPHqFq1KmXLlmXt2rWaHhNJRyp2Yrjg4GAqVarE9OnT7zjlmlj0Zs6cyahRo7h48aIBKd3DlStXiI+Px8PDA09PTzJmzKgfyvJQLly4QOXKlcmcOTNbt24la9asRkcSN3Dt2jV8fHzcfrQOVOzEAfz5558cOnTonnczJe4BWLp0aRo2bMikSZPSMaHru3r1KsuWLeO7777jyJEjSSOkJUqUoGPHjrz44otGRxQnEBERQY0aNbh69So7d+50643YJW3cuuNE4kCAh4cHPXv25MKFCyxbtgwvL/e+fUBLyovhHn/88aRSl5CQcMfXJO5+8NlnnzF16lTCwsLSLZ+ri4yMZOTIkQwaNIh8+fJRqFAhsmTJQoMGDUhISKBt27b0798fAP0eKHcTGxtLs2bNOHfuHGvXrlWpkzRhMpmSZhQ8PDySfjb4+vri6+vr9qUOdFesOJjEC6wtFgs+Pj4cPXqUmJgYTpw4wd69e7HZbFitVsaNG8cHH3xgcFrX8NNPP7F582a2bduWdPPKW2+9xc2bN1mxYgUrV67k7bffpmLFirRt29bgtOKIrFYrHTp0YOfOnWzYsIFSpUoZHUlc0JUrV1i+fDl//vknPj4+5M2blyeeeIKnnnqK6dOnGx3PYajYicOIjo5m8eLF/Prrr1y/fp1ffvmF6OhoLBYLUVFRlC5dGm9vb4YPH05gYCCxsbH4+voaHdvpXbhwgaxZs/Lkk08m/ZkWLlyYuXPnAlCvXj1Wr17NmjVrVOwkGZvNxoABA/jmm29YunQp1apVMzqSuJj4+Hg+++wzBgwYQN68eSlSpAgxMTHExMRgMpl4+umn6devHyVKlDA6qkNQsROHkSlTJmbNmoXFYiF37tw0atSI8uXL4+/vT61atbh+/bo2DU8DgYGBWK1Wjh8/nnRiPHLkSNJ6UT4+Pvj5+emmFbmjKVOmMH36dGbOnEmLFi2MjiMuaPny5XzwwQeEhobSpk0bIiMjiY2N5fLlyxw6dIgPPviAgwcPsnz5cv2MQDdPiIOJiYkhQ4YMSVOxd5J4I4WkjrNnz9KnTx8iIyPp3r07W7ZsYcOGDQwZMoROnToRHh5O//79yZEjB5MnTzY6rjiQ+fPn8+qrrzJ48GDGjRtndBxxUX379uX8+fMsXbr0js+bzWaaNGlCq1ateOedd9I5nePRT0dxKIlLa/j4+GC1Wu/4GpW61FWwYEFGjx6Nj48PPXv25KeffuLdd9+lU6dOANy4cYMGDRrQsWNHY4OKQ9mwYQOdO3emU6dOjB071ug44uI8PT2Ji4u743O5cuUiS5YsxMTEpHMqx6QROxE3pxFQeVj79u2jRo0aVK9enRUrVuDt7W10JHFhu3fvpmXLllStWpW3336b4sWLkzFjRuLj44mOjmb58uVMmzaNSZMm0ahRI6PjGk7FTkSIjY3l/PnzZMiQgdy5c+Ph4cG1a9eIi4sjU6ZMWvRTkpw+fZoqVapQoEABfv75Z/z9/Y2OJG5g3bp1jB49miNHjpAjRw7y5s2Lv78/VquVX3/9ld69e/P222+TKVMmo6MaTsVOxM1ZrVZmzpzJF198QZYsWZgwYQLx8fH07NmTY8eO8fjjjzNp0iRatWpldFQx2KVLl6hatSo2m40dO3aQM2dOoyOJG7l06RJHjhzht99+4+zZs0RERJA5c2ZatWpFjRo1jI7nMFTsxGncaQ9ZeXTz589n9OjRNGrUiJiYGE6dOsWlS5eoWbMmr732GlOmTGHfvn188sknVKpUyei4YpDo6Ghq1arF2bNn2blzJ4ULFzY6kojcgS6sEYdns9mIi4tj165dRkdxSevXr6du3bpMnTqVjz76CG9vb4oVK8akSZMoXbo0M2bMIDAwkP379xsdVQwSHx9P69atOXr0KKtXr1apE3FgKnbi8EwmE6GhoTRs2JDw8HCj47icqKio266h8/T0JCgoKOmC+ICAAOLj47FYLEZFFAPZbDa6d+/OunXrWLZsGc8884zRkUTkHlTsxCl0796duLg4Jk2aZHQUl1OqVCkOHTrE3r17OXToEJcvX+bUqVOcOnUKgP3793Pz5k3y5MljcFIxwogRI5g9ezazZ8+mbt26RscRkftQsROnkCtXLvr378/777/PhQsXjI7jUjp16kR0dDSvvPIKzz33HE2aNCFjxoy8/vrrDB8+nObNm5MrVy5dX+eGPv30U8aMGcOECRNo37690XFEAPuCxEWLFmXbtm1GR3FIunlCnEZERASFCxfm5Zdf5uOPPzY6jktIvCHl/PnzrFixgsDAQFq0aEFcXBzDhg1jy5YtVKxYkUGDBlGgQAGj40o6Wr58OS1btuSNN97g/fff141L4jAOHDhAuXLl2LVrF8HBwUbHcTgqduJUJk+ezKBBgzh27BjFihUzOo5L0N3G8l/bt2+ndu3aNG7cmEWLFuHp6Wl0JJEkP/74I/Xq1ePMmTMULFjQ6DgOR8VOnMrNmzcpVqwY1atXZ+HChUbHcSn/LXiJ/52QkACgH+4OxmqDqDgIj4NwC0TEQZwVrNivsfH2gCzekM0HsnlDgDd4PEB/P3bsGFWrVqVs2bKsXbs2aZs/EUcxd+5cOnTowI0bN/Dz8zM6jsPRNXbiVPz8/Bg5ciSLFi1i3759RsdxKf8dtUv8ne+zzz6jSZMmnD592ohY8h/X4+HgNVh5ATZchF/D4Uw0XLFAZLz9+ch4+3+fibY/v+Gi/fUHr9mfv5vz589Tv3598uXLx/Lly1XqxCGZzWYCAgJU6u5CxU6cTqdOnShevDiDBw82OopLS9w/NioqiosXL6LBfWNdjYWtl2BdGJy6DvG3/HXc7W/m1sfjbfb3rQuzH+fqf1avuXbtGg0aNMBms7FmzRqyZs2ayl+BSOowm83kzp3b6BgOS1Ox4pSWLl1Kq1at2LhxIzVr1jQ6jkuIiYkhMjKShIQEvL298fX1xdfXFx8fH6OjubUEGxyNgBPXwcTdS9zDSDxOcX8omQXiLbHUr1+fAwcOsG3bNkqWLJkKnyKSNjp06MCZM2fYunWr0VEckoqdOCWbzUaFChXw9vZmx44duvj/Ef3yyy/Mnz+fgwcPcvnyZaxWK4GBgZQtW5auXbtStmxZ/RkbINwCu69AdELafUYmTxvLJ4fw9Ufvs379eqpVq5Z2HyaSCurWrUvmzJlZunSp0VEckoqdOK0NGzZQp04dli9fzosvvmh0HKe1adMm2rRpQ86cOalXrx758uXDarVy6dIl1q9fz759+1iyZAkvvfSS0VHdijkGdly2j6yl5Unaak0g3mLB989fafGCSp04vqeeeopq1aoxc+ZMo6M4JBU7cWq1a9fm77//5uDBg7prM4XKly9PzZo1mTp16h2fDw0NZc6cOWzbto3s2bOnczr3ZI6B7ZfTttDdymaz4mHyoGoOyKX7JcTB5c6dm169ejF8+HCjozgk3TwhTi00NJSjR48yb948o6M4rdOnT9OqVau7Pv/666/z559/Ji17Imkr3PLvSF16MZk8sGH/3HBtCSwOLCEhgUuXLpErVy6jozgsFTtxahUqVKBly5YMHz6c2NhYo+M4pWeeeYY5c+Zw4cIFrFZr0uM2mw2r1cratWvJmTOnlhZIBwk2+zV1Rk2jWIE9V+05RBzRlStXsFqtKnb34GV0AJFHNXbsWEqVKsUnn3xC3759jY7jdIYPH067du34888/qV69Ovnz58fX15eIiAj27t3LnDlzmDBhAv7+/kZHdXlHI9L2RokHcT0ejkZCmSzG5hC5E7PZDKDlTu5B19iJS+jatSsrVqzg9OnTBAQEGB3H6ezfv5/JkyezefNmoqKiSEhIwNPTk3LlytG/f3/dnJIOrsbCxktGp/jX80EQqJVuxMGsX7+eunXrcvr0aQoVKmR0HIekYicu4a+//qJYsWKEhIQwYsQIo+M4lf9uJWa1WrFarXh5aUA/PW29BJdijZuGvZUJyOkL1XManUTkdvPmzaN9+/ZER0eTMWNGo+M4JF1jJy4hf/789O7dmylTpnDpkgMNeziB/65P5+HhoVKXzq7Hw8V/Sl1cbCxzx7/L68/kpV1RPwY1CebAlvX3PcauNd8ytWdrelUtTLtiGenz3BN8PXoA0RHXbnvd4Z2beCm/6a7/LJsxDhv2PPfafkzECGazGX9/f5W6e9CInbiMK1euULhwYV577bW7Lt0h4ogOXrNv92UDpr3Rll2rl9LotX7kKVSMjd98xR8H9jJy8UaerHj3deY6l81Btlx5qVivGTnyFeDc8UP8OO8TchUozKTVv+H7z80v1y6ZObg1eVHcvGwuB7b8yISVeyhargImoKg/lM2aJl+ySIoMHDiQb7/9llOnThkdxWGp2IlLGTt2LGPGjOHkyZMUKFDA6DhOy2azER8fj5eXl3acSGNWG6y8YN/L9eS+PYQ0Dab9kPd4scfbAFhiYnirdmky5whi/PIddz3O4Z2bKF255m2PbVo6hw/7d6THpM+p3bbrPXP0rl4Mk8nEB1tOJD3mZYImecFD/xcQB9GxY0dOnTrF9u3bjY7isDQVKy6lX79+ZM2alZEjRxodxakdOnSIwYMHc+PGDaOjuLyoOHupA9i1eikenp7UeaVb0vM+GTJQq81rnPh1J5cv/HXX4/y31AEE128OwPmTx+6Z4eS+PYSdPUX15q/c9ni8DaI0HSsOxGw2647Y+1CxE5fi7+/PsGHD+Prrrzl69KjRcZzW8ePHmTx5MvHx+qme1sLj/v33M0f2kbdwcTIGZL7tNUXLVQTg7JH9D3Xsa5fCAAgIzHHP121dPh+A6s1eSfacFiwWR2I2m7WG3X2o2InL6datGwUKFGDo0KFGR3FacXH2tuHjo/Uu0lq4xX4XKkC4+W+yBuVJ9pps/zx21XzhoY69/KOJeHh6UrnR3ff5TUhIYMfKxRQtV5E8hYre9pwJuKZiJw4kLCxMxe4+VOzE5fj4+DB69Gi+++47du/ebXQcp2Sx2H+ae3t7G5zE9UXE/bvEiSXmJt4+vsle4+ObIen5B7X1uwX8tGgWTboNIE+hYnd93aFtP3HtkjnZNCzYc12LS/4eESNYrVZtJ/YAVOzEJbVr147SpUszaNAgdH/Qw7NYLJhMJjw9PY2O4vLi/t3FDZ8MfsRZkm+NZ4mNSXr+QRzdvZWP33mNcs/Vo93Acfd87dbl8/Hw9KRqk9b3zSdipCtXrpCQkKBidx8qduKSPD09GT9+PJs2bWL9+vuvASa3i4uLw8fHR3fEpoNbe1O2XHm4dvHvZK8J/+exwFx573u8s0cPMPG1puR/ojQDPl2K5z3WJIy9eZM9a7+jbLXaZM155x+W6nXiKBK3E1OxuzcVO3FZjRs3pkqVKoSEhNy2ub3cn8Vi0TRsOrn1JFywZDkunD7BjajI215zcp/9koKCpcrd81hhZ/9gbPv6ZMkexOA5q/HLdO/9fX9Z/z03r0fdcRr2TvlEjKRi92D0PSsuy2QyMWHCBH777TeWLl1qdBynkjhiJ2nP+5azcKVGL2FNSGD9/M+SHouLjWXjki8p9nQwOfLmB+DS+XOcP3X8tuOEXwxjzCt18TB5MHTeOrJkv/9+YFuXL8DXLyMV/1kW5X75RIykYvdgtG+QuLTq1avTsGFDhg4dSvPmzTUK9YAsFouKXTrJ4g1XLfYbFYo/HUzlxq1YMDGEyCsXyV2wKJuWfs2l/52l13uzkt7zQb8OHN21maV//Xv96Lj29TGfO82LPQdyfO82ju/d9u9n5MjFUzXq3Pa5UeFX2b9pDcENWt51ZM8EZNW3jDiIsLAwMmXKhL//vUei3Z2Knbi88ePHU65cOb788ku6det2/zeIpmLTUTYfOB3973+/OW0Oi/INY/O3c4mOCOfxEmUJ+fIHSlaqcc/jnD16AIAVH09K9lzJSs8lK3Y7V31DfFwc1Zu1u+sxbUBW9XtxEFrD7sFoSzFxC6+88gqbNm3i5MmT2jz6AQwaNIilS5dqP8Z0EGGBDReNTnF3tXPZRxVFjNapUydOnDjBjh1331pPdI2duInRo0dz8eJFPvzwQ6OjOAVNxaafAG/7nqyOyMsEAZrXEQehEbsHo2InbqFIkSJ069aN0NBQwsPDjY7j8DQVm348TFAo07+7TzgKE/ZcHo4WTNyWit2DUbETtzF06FAsFgvvvfee0VEcnu6KTV+F/f/dfcJR2LDnEnEUZrOZ3LlzGx3D4anYidvIkycP/fr1Y/r06fz9d/JFYOVfGrFLX/5eEOTrOKN2Jux5/DUNKw7CarVy8eJFjdg9ABU7cSvvvPMOGTJkYMyYMUZHcWi6xi79lcriOKN2Nux5RBzF1atXiY+PV7F7ACp24layZs1KSEgIn3/+OX/88YfRcRyWpmLTX6APFHeQqc/iAfY8Io5CixM/OBU7cTu9e/cmKCiI4cOHGx3FYWkq1hgls0AmT+OmZBPi44mLvMqTAY4ydihip2L34FTsxO34+fkxcuRIFixYwP79+42O45A0FWsMTxMEZzeq2NkwYWNImzp06/oasbGxhqQQuRMVuwenYiduqXPnzhQvXpwhQ4YYHcUhaSrWONl8oEqO9C93Jkw8l9ubUQP7s2DBAmrXrs2lS5fSOYXInZnNZvz8/LSd2ANQsRO35OXlxdixY1m9ejVbtmwxOo7D0VSssXJlgKo57Cfo9Ch4HkC1HBCUAV599VU2btzIiRMnqFixIocPH06HBCL3lrjUicnkKPeOOy4VO3FbLVu2pHz58oSEhKCd9W6nETvj5coANYMgo2fafo6/l/1zgjL8+1jlypXZs2cPmTNnpkqVKqxatSptQ4jcR1hYmKZhH5CKnbgtDw8PQkND2bFjBz/88IPRcRyKrrFzDNl8oE7uf++WTa2xisTjFA+w7wWb7Q5/1Y8//jjbt2+nVq1aNGnShKlTp+oXIDGMdp14cCp24tbq1KnD888/z+DBg0lISDA6jsPQVKzj8DRBmazwfE7I6Wt/LKUFL/F9OX3h+SAok8V+/Lvx9/fn22+/5d1332XAgAG8/vrrWCyWFH66SMqp2D04FTtxayaTidDQUA4fPsyCBQuMjuMwNBXreAJ9oXpOqJcbivqD1y2F7G7d7NbHvUz299XLbT/Og65Tlziy/fXXXzN37lzq1KnD5cuXU/pliKSIit2D04Yx4vaCg4Np3rw5w4cP5+WXX8bX19foSIbTiJ3j8veCslmhdBaIiodwC1yzwLU4iLOCFftv7N4ekNUbsvrYp1oDvMDjEeZyO3ToQNGiRWnWrBnBwcGsXLmSkiVLptJXJXJ3NptN24k9BI3YiQBjx47l3LlzfPbZZ0ZHcQi6xs7xeZggizcUzATlstlvgKiT2z4iVye3/b/LZbM/n8X70UpdoipVqrB3714yZcpE5cqVWbNmzaMfVOQ+wsPDiYuLI3fu3EZHcQoqdiJAyZIl6dixI2PGjCEqKsroOIbTVKzcTeJNFc899xyNGzdm+vTpuqlC0pQWJ344KnYi/xg5ciQRERFMnz7d6CiG01Ss3EtAQADfffcdb7/9Nv3796d79+66qULSTFhYGKBi96BU7ET+UaBAAd544w3ee+89t784XFOxcj+enp5MnDiRL7/8kq+++oq6dety5coVo2OJC9KI3cNRsRO5RUhICAChoaEGJzGWpmLlQXXq1Imff/6ZI0eOEBwczLFjx4yOJC7GbDaTIUMGAgICjI7iFFTsRG6RM2dO3n77bWbOnMm5c+eMjmMIm82mqVh5KNWqVWPPnj34+flRqVIl1q1bZ3QkcSGJS51oO7EHo2In8h/9+/cnc+bMjBo1yugohoiPjwfQiJ08lEKFCrF9+3aqV69Ow4YNmTFjhm6qkFShNewejoqdyH8EBAQwdOhQvvrqK7ecVoqLiwNU7OThZc6cmRUrVvDWW2/Rt29fevbsmfT/J5GUMpvNWurkIajYidxB9+7dyZ8/P0OHDjU6SrpLvLtRU7GSEp6enrz33nvMmjWL2bNnU79+fa5evWp0LHFiYWFhGrF7CCp2Infg6+vL6NGj+fbbb9m7d6/RcdKVRuwkNXTp0oUNGzZw4MABgoODOX78uNGRxElpKvbhqNiJ3MUrr7xCqVKlku6UdReJI3YqdvKoatSowZ49e/Dx8aFSpUr8+OOPRkcSJ6PtxB6eip3IXXh6ejJ+/Hh++uknNmzYYHScdKOpWElNhQsXZufOnVSpUoWGDRvy4YcfGh1JnMi1a9ewWCwqdg9BxU7kHpo0aULlypUZNGiQ29zhp6lYSW2ZM2dm5cqV9OnThzfffJNevXrppgp5IFqc+OGp2Incg8lkYsKECfz6668sW7bM6DjpQiN2khY8PT2ZOnUqn3/+OZ9//jkNGjTQTRVyX4nFTnfFPjgVO5H7qFGjBvXr12fIkCFJa7y5Ml1jJ2mpa9eurF+/nn379lGpUiVOnDhhdCRxYBqxe3gqdiIPYPz48Zw4cYKvvvrK6ChpTlOxktZq1qzJnj178PLyIjg42K2uYZWHExYWhq+vL5kzZzY6itNQsRN5AE8//TRt2rRh5MiR3Lx50+g4aUpTsZIeihQpws6dOwkODqZ+/fp89NFHRkcSB6TtxB6eip3IAxozZgxms5mZM2caHSVNaSpW0kuWLFn44Ycf6N27N2+88Qa9e/d2i8sd5MFpDbuHp2In8oCKFi1K165dGT9+PNeuXTM6TprRVKykJy8vL6ZPn86nn37Kp59+SsOGDQkPDzc6ljgIFbuHp2In8hCGDRtGTEwMkydPNjpKmtFUrBihW7du/Pjjj/zyyy9UqlSJkydPGh1JHID2iX14KnYiDyFv3rz07duXadOmERYWZnScNKEROzHK888/z+7duzGZTAQHB/Pzzz8bHUkMphG7h6diJ/KQBg4ciI+PD2PHjjU6SprQNXZipGLFirFr1y4qVKhA3bp1+fTTT42OJAax2WyEhYWp2D0kFTuRh5QtWzYGDRrEp59+yunTp42Ok+o0FStGy5o1K6tWraJXr1706NGDPn366KYKNxQREaHtxFJAxU4kBd58801y5szJ8OHDjY6S6hKnYlXsxEheXl7MmDGDjz/+mI8++ohGjRq59E1LkpwWJ04ZFTuRFMiYMSMjRoxgwYIFHDhwwOg4qcpiseDt7a11o8Qh9OjRg3Xr1rF3714qV67MqVOnjI4k6UTFLmVU7ERSqEuXLhQpUoQhQ4YYHSVVJRY7EUfxwgsvsHv3bqxWK8HBwWzcuNHoSJIOVOxSRsVOJIW8vb0ZO3Ysq1atYuvWrUbHSTVxcXG6cUIcTuJNFeXLl6du3bp89tlnRkeSNGY2m/Hx8SFr1qxGR3EqKnYij6BVq1Y8/fTThISEYLPZjI6TKjRiJ44qW7ZsrF69mu7du9O9e3f69eunmypcmLYTSxkVO5FH4OHhQWhoKNu3b2f16tVGx0kVFotFI3bisLy9vfnwww+ZOXMmH374IU2aNCEiIsLoWJIGtNRJyqjYiTyiunXrUrNmTUJCQrBarUbHeWSaihVn0KtXL9auXcuuXbuoXLkyf/zxh9GRJJVpceKUUbETeUQmk4nQ0FAOHTrEwoULjY7zyDQVK86idu3a7Nq1i/j4eCpWrMjmzZuNjiSpSMUuZVTsRFJBpUqVaNasGcOGDUta4NdZaSpWnMkTTzzBrl27ePrpp6lduzazZs0yOpKkEhW7lFGxE0klY8eO5c8//+Tzzz83Osoj0VSsOJvAwEDWrFlD165d6dq1K2+99RYJCQlGx5JHYLPZMJvN5M6d2+goTkfFTiSVlCpVivbt2zNmzBiuX79udJwU01SsOCNvb28++ugjPvjgA95//32aNm1KZGSk0bEkhaKiooiJidGIXQqo2ImkopEjRxIeHs77779vdJQU04idOCuTyUTv3r1Zs2YN27dvp3Llyi65n7M7CAsLA7Q4cUqo2ImkooIFC9KzZ08mTZrElStXjI6TIrrGTpxd3bp12bVrFxaLheDgYJdaQNxdaNeJlFOxE0llgwcPxmq1MmHCBKOjpIimYsUVlChRgt27d1OmTBleeOEF5syZc8/Xu8oC465CxS7lVOxEUllQUBADBgzggw8+4H//+5/RcR6apmLFVQQGBrJu3To6d+5MQkLCPdeZTNzdICoqKr3iyT2YzWa8vb3Jli2b0VGcjoqdSBp46623CAgIYNSoUUZHeWgasRNX4u3tzSeffELnzp3x8Lj7j7zZs2fTqFEjWrVqRZcuXdIxodyJ2WwmKChI24mlgIqdSBrInDkzQ4YMYfbs2Rw/ftzoOA9F19iJq7lfOXj11VeZOHEinp6evPTSS/z+++9UrFiRq1evplNC+S8tdZJyKnYiaaRHjx489thjDBs2zOgoD0VTseJORo4cybJlywgNDeXbb7+la9euzJkzh5iYGE6dOmV0PLelxYlTTsVOJI1kyJCBUaNGsXTpUvbu3Wt0nAemqVhxFzt27GDMmDFMnz6dZs2a4eXlBUCRIkU4ceIEJ0+eNDih+woLC1OxSyEVO5E01L59e0qWLMngwYONjvLANBUr7qJXr160aNGC9u3b33b93VdffcVjjz1G6dKlDUzn3jRil3IqdiJpyNPTk3HjxrFhwwY2bNhgdJwHoqlYcQf79u3DarXSqVMnMmbMmLTcyfHjx1m3bh2lSpUiT548Bqd0T4nbianYpYyKnUgae/HFFwkODiYkJMQp1srSVKy4i1OnTpEzZ07AfoPFpUuX+Prrrzlw4ABdunQhKCgo6XvWGb53XcX169e5efOmil0KqdiJpDGTycSECRP45Zdf+Pbbb42Oc1+aihV3EBgYSKlSpThx4kRSaRs1ahQ//fQTbdq04cUXXwTs3782mw2TyURkZCTffvstffr0YcCAAfzxxx9GfgkuK3FxYt0VmzIqdiLpoGbNmtSrV48hQ4YQHx9vdJx70lSsuIPHH3+cLl260LVrV2rVqkWuXLlYt24dL730EsOHDwdIWtA4cbmUhQsXMnr0aH799VcuXrzIU089xbx58wz7GlyVdp14NF5GBxBxF+PHj+eZZ55hzpw5Dr0AqqZixV307NmT6tWrs2HDBl5++WVatGhxxzKROGL3+++/4+fnx7Zt2zCZTCxYsIBx48ZRokQJnn32WQO+AtcUFhYGqNillIqdSDopX748rVu3ZsSIEbRr144MGTIYHemONGIn7qR06dK33f26du1a/v77bzp37pw0Unft2jXCwsIoUqQIERERSY8HBwdz7do1zp8/r2KXisxmM15eXtpOLIVU7ETS0ZgxY3jyySf56KOPeOutt4yOc0e6xk7c1fXr1wkNDSUuLo6qVatSvHhxTp06Rbdu3Th//jx58+Zl8+bNWCwWJk+ezKJFiwgMDCQiIsLo6C4lcTuxe20BJ3enYieSjooVK0bXrl0ZP348r732GlmyZDE6UjKaihV35e/vzxdffMHx48cpXrw4AFOmTMHT05NZs2ZRoUIFDh06ROvWrWnatCmZMmWiTp06tG/fHoCNGzcSHR1NbGwsLVu2NPJLcWpa6uTRqA6LpLPhw4cTHR3NlClTjI6STEJCAlarVSN24raKFStGkyZNAPv3Q1hYGN7e3lSrVg1fX1+effZZunbtSlBQED///DOhoaGYTCYmTpzISy+9xNtvv83EiRN56qmnOHfunMFfjXNSsXs0KnYi6Sxv3rz06dOHqVOnJt395Sji4uIANGIngn2B8dKlS+Pt7Z30vQGQL18+wsLCuHLlCr6+vhw+fJiQkBAmTZrEunXr2Lp1K+XKlaN9+/Zcv37dwK/AOZnNZi118ghU7EQM8O677+Ll5cW4ceOMjnIbi8UCoBE7kX906NCBo0eP0qxZM7Zu3crHH3/MhAkTeOyxx8iePTsAmzdvpmDBgjRo0IACBQrg6+vLwIEDuXTpksP98uYMNGL3aFTsRAwQGBjIu+++yyeffMKZM2eMjpMkcVRCxU7ErlixYhw5cgQ/Pz969+7NtGnTKFiwIMuWLUt6TdGiRUlISCBjxoxJd8xeunSJK1eukClTJqOiO62wsDAVu0egYidikD59+pA9e3ZGjBhhdJQkiSN2mooV+ZePjw9Lly5lyZIl7Ny5k8WLF+Ph4ZH0/VKrVi0KFSrEs88+y549e1i3bh1jxoyhbNmySYscy4O5fv06N27cULF7BCp2IgbJlCkTw4cPZ968eRw6dMjoOICmYkXu5YknniB79uwEBARw/fp1tm3bxrVr1/D29mbTpk00adKEXr160bdvXzZu3EidOnXImzev0bGdinadeHQqdiIG6tq1K4ULF2bIkCFGRwE0FSvyoM6fP8/MmTP58ccfkx6bNm0a3bp1I0+ePNSrV4+BAwcCJO1FK/enYvfotI6diIG8vb0ZM2YM7dq1Y/v27VStWtXQPJqKFXkwTzzxBMHBwXTs2JFDhw6RM2dOzGYz8+fPp0SJErz//vuAfb9ZLbT74BKLne6KTTmTTb9KiBjKarVSvnx5AgIC2LJlS9LF10Y4cOAA5cqVY8+ePVSoUMGwHCLOYtOmTYwbN47Y2FgiIyPp1q0bdevWpWjRoip1KfDJJ5/Qu3dvLBaL/uxSSCN2Igbz8PAgNDSUhg0bsmbNGho2bGhYFl1jJ/JwatasSbVq1TCZTMTHx+Pr65v0nIrJwwsLC9N2Yo9If3IiDqB+/frUqFGDkJAQQ++i01SsyMPz8vLC09NT3zepQGvYPToVOxEHYDKZCA0N5eDBgyxatMiwHLp5QiTl7jXKpGVPHoyK3aNTsRNxEFWqVKFp06YMGzYsaeQsvWkqViR1Wa1WvvrqK1q3bs2NGzeMjuPwVOwenYqdiAMZN24cZ86c4YsvvjDk8zUVK5K6PDw8CAwMZPXq1dSoUYPz588bHcmhqdg9OhU7EQdSunRp2rdvz+jRo4mOjk73z9dUrEjqa9q0Kdu3b8dsNlOhQgV++eUXoyM5LLPZrKVOHpGKnYiDGTVqFFevXmXGjBnp/tkasRNJG+XKlWPv3r0UKFCA6tWrs2TJEqMjOZzo6GiuX7+uEbtHpGIn4mAKFixIz549mThxIlevXk3Xz9Y1diJpJ3fu3GzatIkWLVrQunVrRo0apV0pbqFdJ1KHip2IAxoyZAjx8fFMnDgxXT83cSpWI3YiaSNDhgzMmzePsWPHMnLkSNq2bcvNmzeNjuUQVOxSh4qdiAMKCgpiwIABzJgxI10vtk5c7d3T0zPdPlPE3ZhMJoYMGcLSpUtZuXIlNWrU4MKFC0bHMpyKXepQsRNxUAMGDCBTpkyMHj063T7TYrFoGlYknbRs2ZKtW7fy999/U6FCBX799VejIxnKbDbj4eFB9uzZjY7i1FTsRBxU5syZGTx4MLNmzeLEiRPp8plxcXEqdiLpqHz58uzdu5fHHnuM6tWrs3TpUqMjGcZsNhMUFKQZg0ekYifiwHr16kWePHkYNmxYunyexWLR9XUi6SxPnjxs2rSJF198kVatWjFmzBi3vKlCa9ilDhU7EQeWIUMGRo0axZIlS9JlmkYjdiLG8PPzY8GCBYwePZrhw4fTrl07t7upIiwsTMUuFajYiTi4Dh06UKJECQYPHpzmn6Vr7ESMYzKZGDZsGN988w0rVqzgueee4++//zY6VrrRiF3qULETcXBeXl6MGzeOH3/8kZ9//jlNP0tTsSLGe+mll9i6dSvnz5+nYsWK7Nu3z+hI6ULFLnWo2Ik4gebNm1OhQgVCQkLS9NobTcWKOIZnnnmGvXv3kjt3bqpVq8a3335rdKQ0p2KXOlTsRJyAyWRiwoQJ7Nmzh+XLl6fZ52jETsRx5M2bl82bN9O4cWNatmzJuHHjXPamips3bxIVFaVilwpU7EScRK1atahTp07SrhRpQdfYiTiWjBkzsmjRIkaOHMnQoUNp3749MTExRsdKdYmLE+fOndvgJM5PxU7EiYwfP55jx44xd+7cNDm+pmJFHI/JZGLEiBEsXryYZcuWUbNmTcLCwoyOlaq060TqUbETcSLPPvssrVq1YsSIEWnyW7umYkUc18svv8yWLVs4d+4cFStWZP/+/UZHSjWJRVXF7tGp2Ik4mTFjxnDhwgU+/vjjVD+2pmJFHFuFChXYu3cvOXPmpGrVqml6zW16StxOLEeOHEZHcXoqdiJO5oknnqBLly6MGzeOyMjIVD22pmJFHF++fPnYunUrDRs2pHnz5oSGhjr9TRVms5kcOXJoO7FUoGIn4oSGDx9OdHQ0U6ZMSdXjaipWxDlkzJiRxYsXM3z4cAYPHkyHDh2c+qYKLXWSelTsRJzQY489xptvvsnUqVO5ePFiqh1XU7EizsPDw4NRo0axcOFCvvnmG2rVqpV0E4KzMZvNuiM2lajYiTipQYMG4enpyfjx41PtmJqKFXE+bdq0YcuWLZw5c4aKFSty4MABoyM9NI3YpR4VOxEnFRgYyMCBA/n44485e/ZsqhxTU7EizqlixYrs3buX7NmzU7VqVVasWGF0pIcSFhamYpdKVOxEnFjfvn3Jli0bI0eOTJXjacROxHk99thjbN26lXr16tG8eXMmTpzoNDdVaMQu9ajYiTixTJkyMXz4cObMmcPhw4cf+Xi6xk7EuWXKlIlvvvmGwYMHM2jQIDp16kRsbKzRse4pJiaGyMhIFbtUomIn4uS6du1KwYIFGTp06CMfS1OxIs7Pw8ODsWPHMn/+fBYvXswLL7yQqjdZpTbtOpG6VOxEnJyPjw9jxoxhxYoV7Ny585GOpalYEdfRrl07Nm/ezKlTp6hYsSKHDh0yOtIdqdilLhU7ERfQtm1bypYty6BBgx7pmhqN2Im4luDgYPbu3UvWrFmpUqUKK1euNDpSMonFTsudpA4VOxEX4OHhwfjx49myZQvr1q1L8XF0jZ2I68mfPz/btm2jdu3avPjii7z33nsOdVOF2WzGZDJpO7FUomIn4iIaNmxItWrVCAkJwWq1pugYmooVcU3+/v4sW7aMkJAQBg4cSJcuXRzmpoqwsDBy5MiBl5eX0VFcgoqdiIswmUyEhoayf/9+lixZkqJjaCpWxHV5eHgwbtw45s6dy4IFC6hduzaXLl0yOpaWOkllKnYiLqRatWo0btyYoUOHEhcX99Dv11SsiOt79dVX2bRpEydOnKBixYqpslTSo1CxS10qdiIuZty4cZw+fZpZs2Y91PtsNhvx8fEqdiJuoHLlyuzZs4fMmTNTuXJlVq1aZVgWFbvUpWIn4mLKli3LK6+8wqhRo7hx48YDvy9xhE9TsSLu4fHHH2f79u3UqlWLJk2aMHXqVENuqjCbzbojNhWp2Im4oFGjRnHlyhVmzJjxwO9JLHYasRNxH/7+/nz33XcMHDiQAQMG0LVrVywWS7pm0Ihd6lKxE3FBhQsXpnv37kycOJHw8PAHek/iyVzFTsS9eHh4MGHCBL7++mvmzZtHnTp1uHz5crp8dkxMDNeuXVOxS0UqdiIuKvEGiokTJz7Q6xOLnaZiRdxThw4d+Pnnnzl27BgVK1bk6NGjaf6ZiVudqdilHhU7EReVK1cu+vfvz/vvv8/58+fv+3pNxYpI1apV2bNnD/7+/lSuXJk1a9ak6edpO7HUZ7I50vLTIpKqIiIiKFy4MK1ateKTTz5Jetxqg6g4CI+DcAtExEF0TCynz57lsXz5yBbgTxZvyOYD2bwhwBs8TAZ+ISKSrqKionjllVdYtWoVkydPpl+/fphMKT8J3OmcE2eFqOvX+fPsGUqVKE7OTL4656QCFTsRFzdlyhTeffddjh07Rp5CxTh9Hc5EQ/w/3/km4E4ngVsf9zJBoUxQ2B/8tTi8iFtISEhg8ODBTJo0iddff50PP/zwoUf0r8ejc046U7ETcXE3b96kTrOXaffuOHIVL3vXk+r9JL4vyBdKZYFAzdiKuIWvvvqKbt26UaVKFZYtW0b27Nnv+56rsXAkEi7G3r3I3Y/OOSmjYifiwhJscDQCfo+yYU1IwDMV9mJMPNkW94eSWcBT0yUiLm/btm00b96cLFmysHLlSp588sk7vi7xnHPiesoL3X/pnPNwVOxEXFS4BXZfgeiEtPsMfy+oGGi/Fk9EXNuZM2do2rQp586dY/HixdSvX/+253XOcQy6K1bEBZljYNNFuJGGJ1iA6Hj755hj0vZzRMR4hQoVYvv27VSvXp1GjRoxY8aMpJ0qdM5xHCp2Ii7GHAPbL4OV1JkGuRcb9s/ZflknWhF3kDlzZlasWEH//v3p27cvPXr04ML1eJ1zHIiKnYgLCbfAjstpf3L9Lxv2zw1P352IRMQAnp6eTJ48mVmzZrFp7362XkzAls5nHZ1z7k7X2Im4iAQbrA+zT4UY9U3t7wW1c+niZhF3kGCD78/eJM7knSo3ZqWEzjnJacROxEUcjbBftGzkb2rX4+FopIEBRCTdHI0Aq7efYaUOdM65ExU7ERdwNda+vIAjOBEFVzU9IuLSdM5xXCp2Ii7gSKR9rSdHYAKORBidQkTSks45jksbdYg4uevx9tXdAeJiY1k0ZThbls0lOiKcAk+Wpe07Y3mqRp17HuP8H7/z49xPOLl/N2cO/0ZcbCwf7ThDUP6CyV775cj+HN29mUt/ncUSG0POxx6nSpPWNO3+Nn6Z/LFhz3M9XlsBibiixHOOI5xvAJ1z/kMjdiJO7vT1f39z/vCtTvzw+VSqN3+FzqPex8PTk/EdG3Jsz7Z7HuPErztZ8+UMYq5Hka/onVeUT/THwb08WbE6Lw8YRedR71O68vMs/2gC49rXx2q1AvY8px1kmkZEUlfiOcdRzjegc86tdFesiBOz2mDlBfvm2if37SGkaTDth7zHiz3eBsASE8NbtUuTOUcQ45fvuOtxosKv4uXtjZ9/ACs+mczcce/c9TfoO/n+0ynMGfs241fspHj5SoB9E+8mecHDUeZrROSRJZ5zjv3mWOcb0DknkUbsRJxYVJy91AHsWr0UD09P6rzSLel5nwwZqNXmNU78upPLF/6663ECsgXi5x+Q4hyJJ+ToiGtJj8XbICo+xYcUEQeUeM5xtPMN6JyTSLPRIk4sPO7ffz9zZB95CxcnY0Dm215TtFxFAM4e2U+OvPlT5XMT4uOJjrxGvMXCud8Ps/C9ofj5ByR9VlI+C2TxTpWPFBEHkHjOccTzDeicAyp2Ik4t3GK/tsQGhJv/JmtQnmSvyfbPY1fNF1Ltc/84+AuDX6yc9N95izzBu7O/JyBbYNJjJuCaBciUah8rIgZLPOc42vkGdM5JpGIn4sQi4v5dkNgScxNvH99kr/HxzZD0fGp5rFhJhi9YT8yNaH7/dQeHtm0gJvr2K5dtwLW4O79fRJxT4jnH0c43oHNOIhU7EScW9+9NYfhk8CPOEpvsNZbYmKTnU0vGgMyUrV4bgIr1XmTrdwuY9NqLTFrzGwVLPnXHfCLi/BK/px3xfHNrPnemmydEnNit57BsufJw7eLfyV4T/s9jgbnyplmO4AYtANj+/aK75hMR55f4Pe2I55tb87kzFTsRJ3brN3DBkuW4cPoEN6Ju3zjx5L7d9udLlUuzHHGWWKxWKzcib1/+XScYEdeS+D3tiOebW/O5M/0ZiDgx71u+gys1eglrQgLr53+W9FhcbCwbl3xJsaeDk+5Qu3T+HOdPHU/R50VHXCM+LvlFLD8t/AKAwmWfvWs+EXF+id/Tjni+uTWfO9M1diJOLIu3ffNrG1D86WAqN27FgokhRF65SO6CRdm09Gsu/e8svd6blfSeD/p14OiuzSz969+1yaMjI1jz5QcAHP9lOwBrvvqQTJmzkilLVhp06g3AkZ2bmD2iD5UavkSeQsWIj7NwbM9Wdq/5liJln6VGi1eTjmkCsrr5sgMiribxnONo5xvQOSeRip2IE8vmA6ej//3vN6fNYVG+YWz+1r534+MlyhLy5Q+UrFTjnseJjghn0eRhtz228rMpAOR87PGkE22BEmUoVeV59v64wn4tjc1GrseL8FK/4bzY4x28fXyS3m8DsvogIi7k1nOOI51vQOecRNpSTMSJRVhgw0WjU9xd7VxaLFTEleic4/g0Gy3ixAK87fsjOiIvEwRoTkDEpeic4/hU7EScmIcJCmWyX1viSEzYc7n7ZtwirkbnHMenYifi5Ar7/7v7hKOwYc8lIq5H5xzHpmIn4uT8vSDI13F+gzZhz+OvKRERl6RzjmNTsRNxAaWyOM5v0DbseUTEdemc47hU7ERcQKAPFHeQaYjiAfY8IuK6dM5xXCp2Ii6iZBbI5Gnc9IgJ+1RIycwGBRCRdKVzjmNSsRNxEZ4mCM5u7Em2YqA9h4i4Pp1zHJOKnYgLyeYDVXKk/4nWBFTNYf98EXEfOuc4Hu08IeKCzDGw47L9ouK0/gb3wH6CDcqQxh8kIg5L5xzHoWIn4qLCLbD7CkQnpN1n+HvZp0L0W7OI6JzjGFTsRFxYgg2ORsCJ6/api9T4Zk88TvEA+0XLur5FRBLpnGM8FTsRN3A1Fo5EwsXYlJ9sE98X5GtfM0rLC4jI3eicYxwVOxE3cj0eTl+HM9EQ/893/t1Ourc+7vXP/pCF/bW6u4g8OJ1z0p+KnYgbstogKt5+Tcw1C1yLgzgrWLFfmOztAVm9IauP/VqWAC9tri0iKadzTvpRsRMRERFxEVrHTkRERMRFqNiJiIiIuAgVOxEREREXoWInIiIi4iJU7ERERERchIqdiIiIiItQsRMRERFxESp2IiIiIi5CxU5ERETERajYiYiIiLgIFTsRERERF6FiJyIiIuIiVOxEREREXISKnYiIiIiLULETERERcREqdiIiIiIuQsVORERExEWo2ImIiIi4CBU7ERERERehYiciIiLiIlTsRERERFyEip2IiIiIi1CxExEREXERKnYiIiIiLkLFTkRERMRFqNiJiIiIuAgVOxEREREX8X8pyFydR5bqHgAAAABJRU5ErkJggg==\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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "7db17c57-bdd7-41cb-e04c-866b7ac74c1d"
      },
      "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(\"default.qubit\", 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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "b421c9a4-86e1-4c98-a080-0392e7353b8a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.003480064048607026\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "c28fe4e0-085e-411d-e049-ab56c5891cd0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.09016692505875779\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "0d818e87-fce7-4a9b-cb73-c8c1481ed6af"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.11221382688339102\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": "a3fb5fa9-5931-4542-c35f-ca00b57dd52a"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695144929.5385034\n",
            "Tue Sep 19 17:35:29 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
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        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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  "nbformat_minor": 0
}