recommender-systems/08_retrieval.ipynb

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      "source": [
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/PreferredAI/tutorials/blob/master/recommender-systems/08_retrieval.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/PreferredAI/tutorials/blob/master/recommender-systems/08_retrieval.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wzPrmZOMtXt1"
      },
      "source": [
        "# Recommendation Retrieval\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cBBggZxMmFG3"
      },
      "source": [
        "A typical recommender system has two phases.  In the first phase (preference learning), which can be done offline, we learn the model from observations.  In the second phase (retrieval), upon the appearance of a user, we retrieve the top-ranked recommendations for that user.  This latter phase needs to be done online.  In this tutorial, we investigate ways to speed up the retrieval phase by avoiding an exhaustive search over all items.  The focus is on matrix factorization-based recommender systems."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MqktDa7H2hKz"
      },
      "source": [
        "## 1. Setup"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "41oWCMUG2eC_",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703561113,
          "user_tz": -480,
          "elapsed": 5838,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "!pip install --quiet cornac==2.3.2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YqKrDcGH2k7E",
        "outputId": "ddf4ce77-1f4f-41f4-9275-b355d1e80331",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703562691,
          "user_tz": -480,
          "elapsed": 1562,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "System version: 3.11.12 (main, Apr  9 2025, 08:55:54) [GCC 11.4.0]\n",
            "Cornac version: 2.3.2\n"
          ]
        }
      ],
      "source": [
        "import os\n",
        "import sys\n",
        "import time\n",
        "import random\n",
        "import pickle\n",
        "from operator import itemgetter\n",
        "from collections import defaultdict\n",
        "\n",
        "import tqdm.auto as tqdm\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "import cornac\n",
        "from cornac.utils import cache\n",
        "from cornac.datasets import movielens\n",
        "from cornac.eval_methods import RatioSplit\n",
        "from cornac.models import PMF, BPR, IBPR\n",
        "\n",
        "print(f\"System version: {sys.version}\")\n",
        "print(f\"Cornac version: {cornac.__version__}\")\n",
        "\n",
        "SEED = 42\n",
        "VERBOSE = True"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MIFkpFiVs47-"
      },
      "source": [
        "## 2. Recommendation Retrieval is a Similarity Search Problem"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4WHXbb7TtCtG"
      },
      "source": [
        "The two phases of a matrix factorization-based recommender system are:\n",
        "1. **Learning phase:** derive a $d$-dimensional latent vector $\\mathbf{u}_i$ for each user $i$ and a $d$-dimensional latent vector $\\mathbf{v}_j$ for each item $j$. The user-item relationship is modeled using the inner product kernel, i.e., the user preference of user $i$ for an item $j$ is given by:\n",
        "\n",
        "$$\\hat{r}_{i,j} = \\mathbf{u}_i^T \\mathbf{v}_j$$\n",
        "\n",
        "2. **Retrieval phase:** given a user vector $\\mathbf{u}_i$, construct a recommendation list of $K$ items with the highest preference scores. This step requires $\\mathcal{O}(d \\times M)$ preference score computations for $M$ number of items.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1_OydLTFwg-J"
      },
      "source": [
        "### Probabilistic Matrix Factorization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-VsQWKF4whse"
      },
      "source": [
        "For the retrieval phase, the straightforward approach is to exhaustively compute the preference score for every item and maintain the top-$K$. Let us take a closer look through an example based on Probabilistic Matrix Factorization (PMF) [1].\n",
        "\n",
        "For PMF, the objective is to learn for each user $i$ a vector $\\mathbf{u}_i$ and each item $j$ a vector $\\mathbf{v}_j$, such that the following error function is minimized over the set of observed ratings $\\mathbf{R}$:\n",
        "\\begin{equation}\n",
        " \\mathcal{L} = \\sum_{r_{ui}\\in \\mathbf{R}}(r_{ui} - \\mathbf{u}_i^T\\mathbf{v}_j)^2 + \\lambda \\sum_{i = 1}^{N}||\\mathbf{u}_i||^2 + \\lambda\\sum_{j = 1}^{M}||\\mathbf{v}_j||^2,\n",
        "\\end{equation}\n",
        "where $\\lambda$ is a regularization term.\n",
        "\n",
        "We begin by running PMF on the Movielens 1M dataset.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "PSCJDcKTD6CK",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703564116,
          "user_tz": -480,
          "elapsed": 1424,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "# Load the MovieLens 1M dataset\n",
        "ml_1m = movielens.load_feedback(variant='1M')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eVhu7grbkysl",
        "outputId": "f29f001b-075a-4d7b-ca64-cafe5afb3076",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703787834,
          "user_tz": -480,
          "elapsed": 223716,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learning...\n",
            "epoch 0, loss: 46499.640708\n",
            "epoch 1, loss: 30998.520038\n",
            "epoch 2, loss: 26259.649251\n",
            "epoch 3, loss: 23518.953197\n",
            "epoch 4, loss: 21890.352186\n",
            "epoch 5, loss: 20891.838624\n",
            "epoch 6, loss: 20258.664548\n",
            "epoch 7, loss: 19839.733296\n",
            "epoch 8, loss: 19555.027505\n",
            "epoch 9, loss: 19353.265525\n",
            "epoch 10, loss: 19209.748147\n",
            "epoch 11, loss: 19091.622016\n",
            "epoch 12, loss: 19002.107503\n",
            "epoch 13, loss: 18922.031803\n",
            "epoch 14, loss: 18855.990579\n",
            "epoch 15, loss: 18799.360912\n",
            "epoch 16, loss: 18749.701542\n",
            "epoch 17, loss: 18703.444130\n",
            "epoch 18, loss: 18669.739487\n",
            "epoch 19, loss: 18628.281652\n",
            "epoch 20, loss: 18602.086991\n",
            "epoch 21, loss: 18568.658799\n",
            "epoch 22, loss: 18545.324010\n",
            "epoch 23, loss: 18516.599606\n",
            "epoch 24, loss: 18497.111461\n",
            "epoch 25, loss: 18473.562407\n",
            "epoch 26, loss: 18454.772496\n",
            "epoch 27, loss: 18436.231803\n",
            "epoch 28, loss: 18419.489569\n",
            "epoch 29, loss: 18402.149867\n",
            "epoch 30, loss: 18387.370057\n",
            "epoch 31, loss: 18371.641247\n",
            "epoch 32, loss: 18357.952066\n",
            "epoch 33, loss: 18344.552019\n",
            "epoch 34, loss: 18332.140419\n",
            "epoch 35, loss: 18319.598284\n",
            "epoch 36, loss: 18309.514574\n",
            "epoch 37, loss: 18297.204357\n",
            "epoch 38, loss: 18287.914280\n",
            "epoch 39, loss: 18279.047603\n",
            "epoch 40, loss: 18268.901466\n",
            "epoch 41, loss: 18261.625278\n",
            "epoch 42, loss: 18252.677630\n",
            "epoch 43, loss: 18244.326410\n",
            "epoch 44, loss: 18237.660108\n",
            "epoch 45, loss: 18228.602055\n",
            "epoch 46, loss: 18223.497865\n",
            "epoch 47, loss: 18214.232572\n",
            "epoch 48, loss: 18211.545393\n",
            "epoch 49, loss: 18200.904343\n",
            "epoch 50, loss: 18199.012207\n",
            "epoch 51, loss: 18190.769097\n",
            "epoch 52, loss: 18186.778938\n",
            "epoch 53, loss: 18181.981107\n",
            "epoch 54, loss: 18177.647265\n",
            "epoch 55, loss: 18171.850192\n",
            "epoch 56, loss: 18169.629079\n",
            "epoch 57, loss: 18162.964883\n",
            "epoch 58, loss: 18160.545500\n",
            "epoch 59, loss: 18154.592758\n",
            "epoch 60, loss: 18152.338580\n",
            "epoch 61, loss: 18146.442439\n",
            "epoch 62, loss: 18146.054928\n",
            "epoch 63, loss: 18137.896271\n",
            "epoch 64, loss: 18140.130187\n",
            "epoch 65, loss: 18131.401019\n",
            "epoch 66, loss: 18132.634177\n",
            "epoch 67, loss: 18127.061756\n",
            "epoch 68, loss: 18124.770038\n",
            "epoch 69, loss: 18122.192001\n",
            "epoch 70, loss: 18118.721448\n",
            "epoch 71, loss: 18115.873519\n",
            "epoch 72, loss: 18112.953857\n",
            "epoch 73, loss: 18110.863692\n",
            "epoch 74, loss: 18106.477187\n",
            "epoch 75, loss: 18105.173448\n",
            "epoch 76, loss: 18101.283214\n",
            "epoch 77, loss: 18100.181908\n",
            "epoch 78, loss: 18096.698893\n",
            "epoch 79, loss: 18092.888637\n",
            "epoch 80, loss: 18092.658595\n",
            "epoch 81, loss: 18087.066200\n",
            "epoch 82, loss: 18089.620375\n",
            "epoch 83, loss: 18082.313563\n",
            "epoch 84, loss: 18084.064516\n",
            "epoch 85, loss: 18077.944144\n",
            "epoch 86, loss: 18078.788412\n",
            "epoch 87, loss: 18074.763582\n",
            "epoch 88, loss: 18073.037961\n",
            "epoch 89, loss: 18071.554398\n",
            "epoch 90, loss: 18067.474385\n",
            "epoch 91, loss: 18067.850567\n",
            "epoch 92, loss: 18064.204387\n",
            "epoch 93, loss: 18063.386133\n",
            "epoch 94, loss: 18060.505470\n",
            "epoch 95, loss: 18057.835025\n",
            "epoch 96, loss: 18056.861527\n",
            "epoch 97, loss: 18054.046269\n",
            "epoch 98, loss: 18052.430863\n",
            "epoch 99, loss: 18050.162947\n",
            "Learning completed\n",
            "\n",
            "TEST:\n",
            "...\n",
            "    | Precision@10 | Recall@10 | Train (s) | Test (s)\n",
            "--- + ------------ + --------- + --------- + --------\n",
            "PMF |       0.1135 |    0.0237 |  217.1005 |   3.7782\n",
            "\n"
          ]
        }
      ],
      "source": [
        "# Instantiate an evaluation method\n",
        "ratio_split = RatioSplit(\n",
        "  data=ml_1m, test_size=0.4, rating_threshold=1.0, exclude_unknowns=False\n",
        ")\n",
        "\n",
        "# Instatiate a PMF recommender model\n",
        "pmf = PMF(k=100, max_iter=100, learning_rate=0.01, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "# Instantiate evaluation metrics.\n",
        "rec_10 = cornac.metrics.Recall(k=10)\n",
        "pre_10 = cornac.metrics.Precision(k=10)\n",
        "\n",
        "# Instantiate and then run an experiment.\n",
        "cornac.Experiment(\n",
        "  eval_method=ratio_split, models=[pmf], metrics=[rec_10, pre_10]\n",
        ").run()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "19yOmH88mv4V"
      },
      "source": [
        "### Exhaustive Search\n",
        "\n",
        "To retrieve the top-$K$ recommendation for a user $i$, we need to compute the inner product between the user's latent vector $\\mathbf{u}_i$ and that of every item $\\mathbf{v}_j$.  This is directly proportional to the number of items $M$ as well as the number of latent factors (dimensionality of the item vector) $d$, as we will see below."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kA9ZDTctoOcM"
      },
      "source": [
        "**Observation #1: Retrieval time scales linearly with the number of items**"
      ]
    },
    {
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          "user": {
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      "outputs": [
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          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/365 [00:00<?, ?it/s]"
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      "source": [
        "comp_time = []\n",
        "\n",
        "# For each user vector, we compute the inner product score to each item vector\n",
        "pmf_item_vect = pmf.V\n",
        "pmf_user_vect = pmf.U\n",
        "\n",
        "for incr_size in tqdm.trange(0, pmf_item_vect.shape[0], 10, disable=not VERBOSE):\n",
        "  start_time = time.time()\n",
        "  pred = np.matmul(pmf_item_vect[:incr_size, :], pmf_user_vect.T)\n",
        "  end_time = time.time()\n",
        "  comp_time.append((end_time - start_time) / pmf_user_vect.shape[0])"
      ]
    },
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      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
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            "image/png": 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1a9eiTZs2DsclHnPDhg1QKBR46KGHrP4+b948CIKAjRs3Wm0fM2aMVUbokksuAWDK9Fk+7+J229eJUqnEPffcY/5drVbjnnvuQUFBAX7//XcvHqVjCoXCnCE0Go0oKipCXV0dBg8ejIyMDK+OKb6G5s6da7V93rx5AIDvv//eantycrL5PQCYstg9e/Z0+N5pLG/Py4EDB3DixAnccsstKCwsNL8nKysrMWbMGPz8888wGo1O77ewsBAArN73QMOc1u+++w56vd7hbb/88ktERERg3Lhx5vs9f/48Bg0ahNDQUPNUgM2bN6O8vBxPPvmk3RxY8XW8b98+FBQU4L777rPaZ/LkyejVq5fduQHcf65JfZ8HBQVBrVZj+/btDsvibUVFReH8+fMu9xk9ejTatGmDzz//3LytuLgYmzdvxk033WTeFhkZiX/++cfhNB5vjR071qqCpl+/fggPD2/U67YpPje+/PJL9O7dG7169bJ6PY0ePRoArKaWAMDIkSORnJzsduxbtmxBbW0t5syZA7m84avz3XffjfDwcIevLV8SBAFr167FlClTIAiC1WObMGECSktL7T7Tbr/9dnOVCGB6XgVBsKsmuuSSS/D333+jrq4OQMP79ptvvnH5viciz1zQQffPP/+MKVOmIDExETKZzO/dIsW5O5b/9erVy6/3SeQL4txiS1FRUQ6/XHbs2NFuPwDmfU+ePAlBEPDMM8+gbdu2Vv+JwabYiEbUpUsXj8bbvXt3q99lMhm6detmN0+wXbt2VmWbAHD69Gl0797d6osVAPTu3dv8d/H/ExISzKXMop49e3o0VktZWVlITExEdHS018dwdMyePXtCqXQ+m+j06dNITEy0+uIL2D9mke05joiIAAB06NDB4Xbb10liYiJCQkKstvXo0QMAnM7l9NZHH32Efv36QavVIiYmBm3btsX333+P0tJSr453+vRpyOVydOvWzWp7fHw8IiMj3T5XgPP3TmN5e15OnDgBAJgxY4bde/K9996DTqeT9HwJNvP/R44cieuvvx5paWlo06YNrr76anz44YdW80dPnDiB0tJSxMbG2t13RUWF+bNA7D/gaq1m8bl39B7s1auX3bmR8rkm9X2u0WiwePFibNy4EXFxcRgxYgRefvllp0uDCYLg9kKaUqnE9ddfj2+++cb8nH311VfQ6/VWQfcTTzyB0NBQDBkyBN27d8f999/f6FJgf7xum+Jz48SJEzh06JDda0ncz9t/W5y9ttRqNbp27er3tenPnTuHkpISvPPOO3aPTbxwbPvYPHm+jUaj+T1+0003YdiwYbjrrrsQFxeHm2++GV988QUDcKJGuqDndFdWVqJ///6YNWuWec6cv/Xp0wdbtmwx/+7qizBRS+FJltnZvuIXcvEf7kcffRQTJkxwuK9tQGM5D9uX/HVcWzKZzGGnYtuGTa2Fs3Ps7tx7wllA4slztnLlStxxxx245ppr8NhjjyE2NhYKhQKLFi2yaiLnDamVB758Try9L6nvyf/85z8YMGCAw31tg05L4hxf2yBJJpNhzZo12L17N9avX49NmzZh1qxZeOWVV7B7926EhobCaDQiNjYWn376qcNj2wbFvuTJ55oUc+bMwZQpU/D1119j06ZNeOaZZ7Bo0SJs3brVbu52SUkJ2rRp4/aYN998M95++21s3LgR11xzDb744gv06tUL/fv3N+/Tu3dvHDt2DN999x3S09Oxdu1avPXWW/j3v/+NtLQ0rx6LlNetp+/RpvjcMBqN6Nu3L1599VWHf7cNOJvq34DGEt+j06dPd9o3xHbuuLfPd1BQEH7++Wds27YN33//PdLT0/H5559j9OjR+OGHH3z+viG6UFzQEd/EiRMxceJEp3/X6XR4+umn8dlnn6GkpAQpKSlYvHixwy7EUimVSsTHx3t9e6LWrmvXrgBMJdtjx471y32ImTuRIAg4efKkpIY2nTp1wh9//AGj0WiV7T569Kj57+L///jjj6ioqLAKSI4dO2Z3zKioKIdlmbbZkaSkJGzatAlFRUUus92elJonJSVhz5490Ov1VqWGljp16oQtW7agvLzcKttt+5h95ezZs6isrLTKWh0/fhwAzOWnYoWEbZdoRxklZ8/HmjVr0LVrV3z11VdW+9iW73vyfHbq1AlGoxEnTpwwVwIApiZHJSUlPnuuvJ1O4A2xjDg8PNyr96RYsZWdne3w75deeikuvfRSvPDCC1i1ahVuvfVWrF69GnfddReSkpKwZcsWDBs2zGUAJI4xMzPT7qKcSHzujx07Zi4nFh07dsyrc+PJ+1wc57x58zBv3jycOHECAwYMwCuvvIKVK1ea98nJyUFtba3V68eZESNGICEhAZ9//jmGDx+OrVu34umnn7bbLyQkBDfddBNuuukm1NbW4rrrrsMLL7yA+fPn+21JqqioKIdd3P2V9ZXyuZGUlISDBw9izJgxPn0PWb62xH/DANMKCdnZ2T79t8zRuNu2bYuwsDAYDAa//btpSS6XY8yYMRgzZgxeffVVvPjii3j66aexbdu2Jrl/okB0QZeXu/PAAw9g165dWL16Nf744w/ccMMNSE1NtftC74kTJ04gMTERXbt2xa233oozZ874cMRELV9sbCxGjRqFt99+G7m5uXZ/P3fuXKPv4+OPP0Z5ebn59zVr1iA3N9flRTbRpEmTkJeXZzWPsq6uDm+++SZCQ0MxcuRI8351dXVYtmyZeT+DwYA333zT7phJSUk4evSo1WM7ePCgXQno9ddfD0EQHGanLLM+ISEhDr/sOnL99dfj/PnzWLp0qdNjTpo0CQaDwW6fJUuWQCaTSXrePFFXV4e3337b/HttbS3efvtttG3b1tzZWQyyfv75Z/N+BoMB77zzjt3xQkJCHJY/ixkZy+duz5492LVrl9V+wcHBAOwDfEcmTZoEAHjttdestouZtcmTJ7s9hhSejKmxBg0ahKSkJPz3v/9FRUWF3d/dvSfbtWuHDh06mJe1ExUXF9tlK8VMulgufeONN8JgMOC5556zO25dXZ358Y8fPx5hYWFYtGiR3VrK4n0MHjwYsbGxWL58uVUJ+8aNG3HkyBGvzo3U93lVVZXduJKSkhAWFma3HJM4//iyyy5ze//iut7r16/HJ598grq6OqvScqBhTr1IrVYjOTkZgiCY59JXVVXh6NGjbueReyIpKQmlpaX4448/zNtyc3PtOvj7ipTPjRtvvBE5OTl499137W5fXV0tafULR8aOHQu1Wo033njD6jX9/vvvo7S01Gfve8Dx57tCocD111+PtWvXIjMz0+42vvh3U1RUVGS3zfZ9S0Seu6Az3a6cOXMGH374Ic6cOYPExEQApnLY9PR0fPjhh3jxxRc9PuYll1yCFStWoGfPnsjNzUVaWhouv/xyZGZm2s2lJApk//vf/zB8+HD07dsXd999N7p27Yr8/Hzs2rUL//zzDw4ePNio40dHR2P48OGYOXMm8vPz8dprr6Fbt264++673d72//7v//D222/jjjvuwO+//47OnTtjzZo12LlzJ1577TXze3XKlCkYNmwYnnzySZw6dQrJycn46quvHAZ/s2bNwquvvooJEybgzjvvREFBAZYvX44+ffqgrKzMvN8VV1yB2267DW+88QZOnDiB1NRUGI1G/PLLL7jiiivwwAMPADAFSVu2bMGrr76KxMREdOnSxdx8yNbtt9+Ojz/+GHPnzsXevXtx+eWXo7KyElu2bMF9992Hq6++GlOmTMEVV1yBp59+GqdOnUL//v3xww8/4JtvvsGcOXNcLknmjcTERCxevBinTp1Cjx498Pnnn+PAgQN45513zNn4Pn364NJLL8X8+fPNmf/Vq1ebm/1YGjRoED7//HPMnTsXF198MUJDQzFlyhRceeWV+Oqrr3Dttddi8uTJyM7OxvLly5GcnGwVXAYFBSE5ORmff/45evTogejoaKSkpDicP9y/f3/MmDED77zzDkpKSjBy5Ejs3bsXH330Ea655hpcccUVPnmOPBlTY8nlcrz33nuYOHEi+vTpg5kzZ6Jdu3bIycnBtm3bEB4ejvXr17s8xtVXX41169ZZzVX+6KOP8NZbb+Haa69FUlISysvL8e677yI8PNx88WLkyJG45557sGjRIhw4cADjx4+HSqXCiRMn8OWXX+L111/H1KlTER4ejiVLluCuu+7CxRdfjFtuuQVRUVE4ePAgqqqq8NFHH0GlUmHx4sWYOXMmRo4ciWnTppmXDOvcuTMeeeQRj58bqe/z48ePY8yYMbjxxhuRnJwMpVKJdevWIT8/37y0l2jz5s3o2LGj0+XCbN1000148803sWDBAvTt29cuQz5+/HjEx8dj2LBhiIuLw5EjR7B06VJMnjzZ/Hm1d+9eXHHFFViwYIHLdaM9cfPNN+OJJ57Atddei4ceeghVVVVYtmwZevTo4XWjQlekfG7cdttt+OKLL3Dvvfdi27ZtGDZsGAwGA44ePYovvvgCmzZtwuDBgz2+77Zt22L+/PlIS0tDamoqrrrqKhw7dgxvvfUWLr74YkyfPt1nj9PZ5/tLL72Ebdu24ZJLLsHdd9+N5ORkFBUVISMjA1u2bHEYLHvj2Wefxc8//4zJkyejU6dOKCgowFtvvYX27dtj+PDhPrkPogtSk/VJb+EACOvWrTP/Li4xEhISYvWfUqkUbrzxRkEQBOHIkSMCAJf/PfHEE07vs7i4WAgPDxfee+89fz88IkmcLRkWEhJit6/tUifikmGOlsyBg6WPsrKyhNtvv12Ij48XVCqV0K5dO+HKK68U1qxZ43I8rohLpXz22WfC/PnzhdjYWCEoKEiYPHmycPr0aat9R44c6XSZnfz8fGHmzJlCmzZtBLVaLfTt29dqCTBRYWGhcNtttwnh4eFCRESEcNtttwn79++3WzJMEARh5cqVQteuXQW1Wi0MGDBA2LRpk8Mld+rq6oT//Oc/Qq9evQS1Wi20bdtWmDhxovD777+b9zl69KgwYsQIISgoSADgdvmwqqoq4emnnxa6dOkiqFQqIT4+Xpg6daqQlZVl3qe8vFx45JFHhMTEREGlUgndu3cX/vOf/1gtISUIpnN5//33W21zdu7F8/Hll1+at4nP+759+4ShQ4cKWq1W6NSpk7B06VK7cWdlZQljx44VNBqNEBcXJzz11FPC5s2b7ZYMq6ioEG655RYhMjJSAGB+To1Go/Diiy8KnTp1EjQajXDRRRcJ3333ncPn/ddffxUGDRokqNVqq9eroyV99Hq9kJaWZn4+O3ToIMyfP99qCTxBMC0ZNnnyZLvH5WwJOVuejKmx50UQBGH//v3CddddJ8TExAgajUbo1KmTcOONNwo//vij27FmZGQIAKyWasrIyBCmTZsmdOzYUdBoNEJsbKxw5ZVXCvv27bO7/TvvvCMMGjRICAoKEsLCwoS+ffsKjz/+uHD27Fmr/b799lvhsssuE4KCgoTw8HBhyJAhwmeffWa1z+effy5cdNFFgkajEaKjo4Vbb71V+Oeff6z2kfq5JgjS3ufnz58X7r//fqFXr15CSEiIEBERIVxyySXCF198YXUsg8EgJCQkCP/617/cPqcio9EodOjQweGyfoJgWnprxIgR5vOWlJQkPPbYY0Jpaal5H/GcO1qCzpaj15IgmF7Ptp81P/zwg5CSkiKo1WqhZ8+ewsqVK/3y+vTkc6O2tlZYvHix0KdPH0Gj0QhRUVHCoEGDhLS0NKvnxNnjdGXp0qVCr169BJVKJcTFxQmzZ88WiouLrfZp7JJhrj7f8/Pzhfvvv1/o0KGD+bN8zJgxwjvvvGPex9n729m/p7bj/fHHH4Wrr75aSExMFNRqtZCYmChMmzZNOH78uJSniIickAmCH7q5tEIymQzr1q3DNddcAwD4/PPPceutt+LQoUN2TSNCQ0MRHx+P2tpat8tniN1ynbn44osxduxYLFq0qNGPgehCt337dlxxxRX48ssvMXXq1OYeDjkwatQonD9/3mGJJLVuY8aMQWJiIj755JPmHkqL9fXXX+OWW25BVlYWEhISmns4RETURFhe7sRFF10Eg8GAgoICqzVWLanV6kYt+VVRUYGsrCzcdtttXh+DiIioJXjxxRdx+eWX4/nnn/d5871AsXjxYjzwwAMMuImILjAXdNBdUVGBkydPmn/Pzs7GgQMHEB0djR49euDWW2/F7bffjldeeQUXXXQRzp07hx9//BH9+vXzqmnGo48+iilTpqBTp044e/YsFixYAIVCgWnTpvnyYRERETW5Sy65BLW1tc09jBbNtokfERFdGC7ooHvfvn1WTW/mzp0LAJgxYwZWrFiBDz/8EM8//zzmzZuHnJwctGnTBpdeeimuvPJKr+7vn3/+wbRp01BYWIi2bdti+PDh2L17t1/XISUiIiIiIqLmwzndRERERERERH7CdbqJiIiIiIiI/IRBNxEREREREZGfXHBzuo1GI86ePYuwsDDIZLLmHg4RERERERG1QoIgoLy8HImJiZDLneezL7ig++zZs+jQoUNzD4OIiIiIiIgCwN9//4327ds7/fsFF3SHhYUBMD0x4eHhzTwa5/R6PX744QeMHz8eKpWquYdDjcBzGRh4HgMHz2Xg4LkMHDyXgYHnMXDwXEpTVlaGDh06mGNMZy64oFssKQ8PD2/xQXdwcDDCw8P5Qm/leC4DA89j4OC5DBw8l4GD5zIw8DwGDp5Lz7ibtsxGakRERERERER+wqCbiIiIiIiIyE8YdBMRERERERH5CYNuIiIiIiIiIj9h0E1ERERERETkJwy6iYiIiIiIiPyEQTcRERERERGRnzDoJiIiIiIiIvKTZg26ly1bhn79+iE8PBzh4eEYOnQoNm7c6PI2X375JXr16gWtVou+fftiw4YNTTRaIiIiIiIiIs80a9Ddvn17vPTSS/j999+xb98+jB49GldffTUOHTrkcP9ff/0V06ZNw5133on9+/fjmmuuwTXXXIPMzMwmHjkRERERERGRe80adE+ZMgWTJk1C9+7d0aNHD7zwwgsIDQ3F7t27He7/+uuvIzU1FY899hh69+6N5557DgMHDsTSpUubeORERERERERE7rWYOd0GgwGrV69GZWUlhg4d6nCfXbt2YezYsVbbJkyYgF27djXFEImIiIiIyM8MRgG7sgrxzYEc7MoqhMEoNPeQiBpF2dwD+PPPPzF06FDU1NQgNDQU69atQ3JyssN98/LyEBcXZ7UtLi4OeXl5To+v0+mg0+nMv5eVlQEA9Ho99Hq9Dx6Bf4hja8ljJGl4LgMDz2Pg4LkMHDyXgYPnMjD44jxuOpSP5zccRV5Zw/f3+HAN/jWpFyb0iXNxS/Ilvielkfr8yARBaNZLR7W1tThz5gxKS0uxZs0avPfee/jpp58cBt5qtRofffQRpk2bZt721ltvIS0tDfn5+Q6Pv3DhQqSlpdltX7VqFYKDg333QIiIiIiIyGsHC2X44LhYiCuz+IspXJnVw4j+Mcx6U8tRVVWFW265BaWlpQgPD3e6X7NnutVqNbp16wYAGDRoEH777Te8/vrrePvtt+32jY+Ptwuu8/PzER8f7/T48+fPx9y5c82/l5WVoUOHDhg/frzLJ6a56fV6bN68GePGjYNKpWru4VAj8FwGBp7HwMFzGTh4LgMHz2VgaMx5NBgFLHrlZwA6B3+VQQZgY34wHr91BBRymYN9yJf4npRGrKJ2p9mDbltGo9GqHNzS0KFD8eOPP2LOnDnmbZs3b3Y6BxwANBoNNBqN3XaVStUqXkCtZZzkHs9lYOB5DBw8l4GD5zJw8FwGBm/O476sQquSclsCgNxSHfb/U46hSTGNHCFJxfeka1Kfm2YNuufPn4+JEyeiY8eOKC8vx6pVq7B9+3Zs2rQJAHD77bejXbt2WLRoEQDg4YcfxsiRI/HKK69g8uTJWL16Nfbt24d33nmnOR8GERERERE1QkF5jU/3I2pJmjXoLigowO23347c3FxERESgX79+2LRpE8aNGwcAOHPmDOTyhgbrl112GVatWoV//etfeOqpp9C9e3d8/fXXSElJaa6HQEREREREjRQbpvXpfkQtSbMG3e+//77Lv2/fvt1u2w033IAbbrjBTyMiIiIiIqKmNqRLNBIitMgrrYGjVmkyAPERWgzpEt3UQyNqtBazTjcREREREV2YFHIZFkxxvGyw2DZtwZRkNlGjVolBNxERERERNbvUlAQsmz4QQSqF1fb4CC2WTR+I1JSEZhoZUeO0uO7lRERERER0YUpNScC6jBxsOmxaJvjNaRdhUt8EZripVWOmm4iIiIiIWoyymjrzzz3iwhhwU6vHoJuIiIiIiFqMshq9+ecKnd7FnkStA4NuIiIiIiJqMUqrGwJty6w3UWvFoJuIiIiIiFqMMougu4JBNwUABt1ERERERNQiGI0CynUNgXY5g24KAAy6iYiIiIioRSivqYMgNPzOOd0UCBh0ExERERFRi2DZRA1geTkFBgbdRERERETUIlg2UQPYSI0CA4NuIiIiIiJqEcpsgu4KHYNuav0YdBMRERERUYtgm+lmeTkFAgbdRERERETUItjO6S5nIzUKAAy6iYiIiIioRRAz3eFaJQBmuikwMOgmIiIiIqIWQQy620UFA+A63RQYGHQTEREREVGLUFZtCrLbRQYBAMrZSI0CAINuIiIiIiJqEcRMd/soU9DN8nIKBAy6iYiIiIioRRAbqYmZ7mq9AXqDsTmHRNRoDLqJiIiIiKhFEDPdifVBNwBUssScWjkG3URERERE1CKIQXdMqBpalSlUYTM1au2UzT0AIiIiIiIioKGRWkSQCqEaFWr0Oq+DboNRwN7sIhSU1yA2TIshXaKhkMt8OVwiSRh0ExERERFRsxMEAWXiOt1BKoRplThfoUOFF+Xl6Zm5SFt/GLmlNeZtCRFaLJiSjNSUBJ+NmUgKlpcTEREREVGjGIwC9mQX4ffzMuzJLoLBKHh8DF2dEbX1TdMi6oNuACivb64mVXpmLmavzLAKuAEgr7QGs1dmID0z1+OxETUGM91EREREROQ166yyAh+f2OdVVlmcz62QyxCiViBUYwpVPMl0G4wC0tYfhqOQXwAgA5C2/jDGJcez1JyaDDPdRERERETkFV9mlcWgO1yrhEwms8h0Sw+692YX2Y3FkgAgt7QGe7OLJB+TqLEYdBMRERERkcfcZZUBU1ZZaqm5OJ87IkgFAAjVmP7fk6C7oNx5wO3NfkS+wKCbiIiIiIg85sussmlOeCEAQC6TwWAUzJnuCp30Od2xYVqf7kfkC5zTTUREREREHvNVVtm20/hf5ysxfPFWDOgQCQCo8CDTPaRLNBIitMgrrXGYgZcBiI8wLR9G1FSY6SYiIiIiIo/5Iqvsak74xsw8AJ6VlyvkMiyYkuzwb2LbtAVTktlEjZoUg24iIiIiIvKYmFV2Fr7KYFob21lWWcqccAAo83DJsNSUBCybPhBtQtVW2+MjtFg2fSDX6aYmx6CbiIiIiIg8ZplVdhZ4u8oqu5sTLsopqfZ4bKkpCVg6baDF73HY8cRoBtzULBh0ExERERGRV8SscnyEdQl5dLDabVZZ6pxwT8rLLVXpG24XrFKypJyaDYNuIiIiIiLyWmpKAnY8MRoh6obQYubwzm6zylLnhJfV6LErq1Dy0mOiCp3B/HNxVa1HtyXyJQbdRERERETUKHIZoKtrCIqP5pW7vY27OeGisuo6THt3N4Yv3or0zFzJY7Lsel5c5dm8cCJfYtBNRERERESNUmswos4iE51xuhjfHMhxmaGWMifcUl5pDWavzJAceFfqGoLuEma6qRkx6CYiIiIiokaptCjlBoDc0ho8vPqA2wy1sznhjoihe9r6w5JKzct1zHRTy8Cgm4iIiIiIGqUhq2wfDLvLUItzwru0CXF7PwJMAf3e7CIPxmSaF+7pnHAiX2HQTUREREREjVJa7TyTLCVDrZDLPOouLqXzueWcbkFwPUYif2LQTUREREREjfL7aTHz7DhwlpKhrq41OP2bLSmdzytqrZcaYwdzai4MuomIiIiIqFFyS3WS9nOVodbVmYLuNqFqp43VZAASIrQY0iXa7X1V2KzvXcJ53dRMGHQTEREREVGjaFXSwgpXGWox0/3wmO4A7HPm4u8LpiRLKkW3nNMNsIM5NR9lcw+AiIiIiIhat4bu4wIclZjL6vdxlqEWBAHVelPQPaFPPNqGaZC2/jBySxsy4/ERWiyYkozUlARJY6qoD7pVChn0BgHFVaZmanuzi1BQXoPYMNN4PJlLTuQNBt1ERERERNQoNRbzsWWw7mEuJUOtNwgQe6xp1QqkpiRgXHI8Hl9zEGszcjCmdyzeuW2wRwGyGHQnRgbhdGEVdmedxys/HLMK5BM8DOSJvMHyciIiIiIiapTK+qC7R7iAuHCN1d/iI7RYNn2gy8BWzHIDQJBKAcDU0XxAxygAgNJJd3ODUcCurEJ8cyAHu7IKrbqji0F3+6ggAMCajByrgBtwv5wZkS8w001ERERERI0iBrgJwcC3s0dg8Q8n8OHOUxjYIRJfzr7MbYa6pj7oVshlUCka8oJtQtQAgMIK+/nY6Zm5diXoYuZ6Qp9485zuxIggp/crFsOnrT+MccnxLDUnv2Cmm4iIiIiIGkUMcDUKU+A8qa8pq51bVmMVyDrLTItN1MQstygm1JQ1L6y0DrrTM3Mxe2WG08z1+oNnoTeYju0ujJaynBlRYzDTTUREREREjVKpMwXNWoUp0O0VHwbAFMwWV9YiKkTtMjPduU2I6fZ2Qbcp032+omFJMoNRQNr6w1bzxkVi5vqFDUfM2zQSO6tvPpyHoUkxkvYl8gSDbiIiIiIiahTLTDcAhGlV6BgdhDNF1Xh/x19QKRR4bctxu0BZzEw/NqEnAPulx9qEmDLd5TV10NUZoFEqsDe7yC7DbUkAkF9mCtKD1Qq0iwqW9Bg+2HkKQ7pEs6ka+RyDbiIiIiIiapTKWuugOz0z1xz4Lt2W5fR2Ymb6/R3ZAOzLy8ODlFDKZagzCiiqrEVCRBAKyp0H3LZCNEpc4mSZMluc203+wjndRERERETUKBUWme5Nh/Ixe2UGdHVGSbcV0DBnO0htHXTLZDJzibnYTC02TAupwjRKtAnVuN8RnNtN/tOsQfeiRYtw8cUXIywsDLGxsbjmmmtw7Ngxl7dZsWIFZDKZ1X9arfQ3HhERERER+VZV/ZxulRx4fsNRh/OtpbCd0w0AMfUl5uK87iFdohEf7vz7vwxAdLAKgCnTHVn/s1SeZNKJpGjWoPunn37C/fffj927d2Pz5s3Q6/UYP348KisrXd4uPDwcubm55v9Onz7dRCMmIiIiIiJbYqa7sBrIK9O52ds5h0G3TaZ78+E81NQZ7PYDGjqVXzuwPQAgVKNEkEoBT6rFPcmkE0nRrHO609PTrX5fsWIFYmNj8fvvv2PEiBFObyeTyRAfH+/v4RERERERkQTinG6dtIpyKzIA4UEqlFbrEeSg03gb87JhOvNSYc4y6ZHBKiy6ri+KKvWmcenqcPnL22CUkHqXAYiP0GKIxDngRFK1qDndpaWlAIDoaNcv9IqKCnTq1AkdOnTA1VdfjUOHDjXF8IiIiIiIyAGxe3mUtOnTZmICelzvWAD2jdQAICbElOk+V65zulSYSKOUY1xyvHk8f+SUuux0bjuOBVOS2USNfK7FdC83Go2YM2cOhg0bhpSUFKf79ezZEx988AH69euH0tJS/Pe//8Vll12GQ4cOoX379nb763Q66HQNJS5lZWUAAL1eD71e7/sH4iPi2FryGEkansvAwPMYOHguAwfPZeDguWzdauuM0BtMoXCPCAFx4RoUlOkkzeuOj9Dg6Ym9kHXONL1Uo5TZvQ4ig0why5HcMrcBdF6ZDrtOFqC40rN52eI4xvRsw9ch+J6USurzIxMEwds+Bz41e/ZsbNy4ETt27HAYPDuj1+vRu3dvTJs2Dc8995zd3xcuXIi0tDS77atWrUJwsLQ1+4iIiIiIyLFKPfDUPlNg/OqldcgskuGD42JBrWXWWLD6PTnSiLt7GSGXAd+dkWNzjhwj4o24vot1jfruAhk+y1IgMdiIs1XuC3Vv727AwUIZDhZJK+q9rZsBA9sIHs37JgKAqqoq3HLLLSgtLUV4eLjT/VpEpvuBBx7Ad999h59//tmjgBsAVCoVLrroIpw8edLh3+fPn4+5c+eafy8rK0OHDh0wfvx4l09Mc9Pr9di8eTPGjRsHlcqzjovUsvBcBgaex8DBcxk4eC4DB89l6/ZPcTWw7xdolHIoZMCjN4/FwONFeH7DUaumaqEaJSp0BkQFq1BcpYcyJBJXTr4UALB/w1Eg5wx6d0/CpPHdrY4fdOwcPsvaD3VQKFBV5XY84y+/BMe2ZQFFxZLGP33SCHRtG+LBIw58fE9KI1ZRu9OsQbcgCHjwwQexbt06bN++HV26dPH4GAaDAX/++ScmTZrk8O8ajQYajf3kEpVK1SpeQK1lnOQez2Vg4HkMHDyXgYPnMnDwXLZOtUZTKXeIxjQfW6VS4coB7TGxXzv8fPwcZq74DQDQOyEcv50qxqS+Cfh0zxkcL6iAXKGEQi5D/YpjCNHavwbiIkzVqTq9AQkRWuSV1rhspDa0WyyWbv9L+gOQK/i6c4LvSdekPjfN2kjt/vvvx8qVK7Fq1SqEhYUhLy8PeXl5qK6uNu9z++23Y/78+ebfn332Wfzwww/466+/kJGRgenTp+P06dO46667muMhEBERERFd0MTlwkLU1vk8hVyGK3rFonOMKWjed9qUeR7TOxZapRw1eiPe35GNXVmFqKnvfq510L1cXGe7oKIWN1/cweVYxvaKhUIug1rhOsyRAeZycr3Bi5brRB5o1kz3smXLAACjRo2y2v7hhx/ijjvuAACcOXMGcnnDm6a4uBh333038vLyEBUVhUGDBuHXX39FcnJyUw2biIiIiIjqVZqDbvvO4wDQMy4MpwqrIHaSyimuhqH+lxc3HAEAaJWm7/u23cvTM3Ox8FvTSkUGo4AlW04gMliF6loDdHUNwXKIRoFKnQERwaZO51W1Det4ywCrzLg4dTsqWI3CyloG3eR3zV5e7s727dutfl+yZAmWLFnipxEREREREZEnzEG3xj60SM/Mxc6sQqttz3xjv9xvTX0AfaKgwuq2jtbkLq3Sm7dd2S8Bt17SCYfOluL5748gr8xU6i5m3x8a0w1f7vvHqut5fIQWC6YkY3H6MRRW1qJOyiLeRI3QIhqpERERERFR61RZn1UW53SLnAXNrnx78CwWTOkDAE7X5LbcNjQpBkOTYlBSVQsAyCu1Drqv6BmLh8f0wN7sIhSU1yA2TIshXaKhkMvwyg/HAbC8nPyPQTcREREREUliMAp2AWylgzndBqPgNGh2paRKj73ZRQDgdk1uACiqMAXbcRFaAPZBd6jG1KhtaFKM3W2V9fO+xTXGifyFQTcREREREbmVnpmLtPWHrYLhhAhT4A0AwRaZ7r3ZRZKCZkcKyqXfTpwbnlAfdOeX1UBfZ0R5jR4AcDy/HF3bhkLhYBFulcK0rY6ZbvIzBt1EREREROSSs1LxvNIafHPgLADrTLcngbOt2DCt5H07RZs6o7cN1UAGoM4oYNDzmyHG0fev2o+EiCNYMCUZqSkJVrdVMdNNTaRZlwwjIiIiIqKWzVWpuOW2IHVDaOFJ4GypTagaQ7pEY0iXaCREaGGfn7Y2qlcsAGDLkXzztrKaOqt98kprMHtlBtIzc622K+uz33VGZrrJvxh0ExERERGRU1JLxf/8p8z8s9Sg2dYDo7tBIZdBIZdhwRTTksDOjqGUyxAZpEJ6Zi7uddGwTdyetv4wDBadysVMdx0z3eRnDLqJiIiIiMgpqaXiv/5VhIOFphBZStDsyIQ+8eafU1MSsGz6QMRHWGfN24Sq6/9fA6NgCqbdEWBqzCY2aQMAZf2c7lrO6SY/Y9BNREREREROeVIqvjZbbs4mOwuaEyK0eOuWi9C3XTgA4P9GdDH/LUhlvexYakoCdjwxGu/eNsi87dmrUgAAMaFqjxu2WV5AYKabmgobqRERERERkVNiqbiU4LZUL8Oyn/7CI+N7ATAFzeOS4x2uk/3D4Xz8mVOGIFVDSKK1CboBU9Z8bHIcQtQKVNYacCi3FAAQE6rxuGGb5QUEc/dyzukmP2Omm4iIiIiInLIsFZfi9a1ZVk3LxHWyrx7QDkOTYszLd0WFmMrEc0qqzftqlI7DE5lMhnZRQQCAP/6pD7pD1B5l4S2XNwMApZzdy6lpMOgmIiIiIiKXUlMS8MjY7pL3t21a5khMfdB9tj7oDlIpIJM5nwHePsq0PJhl0C21YZsMwIIpyVbrdYtzuvWc001+xqCbiIiIiIjcemB0d6eZaFu2TcscibIJurUq18duF2nKdJdW6wEA0aFqSQ3booJVWDZ9oP063XJxTjeDbvIvBt1EREREROSWQi5Dz7hQyfu7m28dHVwfdNfPFbdtomarfX15uahNiAaA84ZtkUEqPDK2O/b9a5xdwA0AKqWY6WZ5OfkXG6kREREREZEkkfWBrhTu5ltH12e6a+tMmWat2nXQ3c4m6BZvD7hu2OaMOKebjdTI3xh0ExERERGRJPr6ADkySIWS+jJvWzIA8TZNyxyxDJoB95lusbxcFBNqfXuxYZtU5u7lzHSTn7G8nIiIiIiIJBGbjt10cXvI4GgetSmAtW1a5oht0O1ouTBLYiM1UYwHWXdHlPXrdNdyTjf5GYNuIiIiIiKSRF/fkfzizjGO51GrgTdv7u9wDrWtyGA1LJuVu8t0twlVQ61ouEHWuQq3HdJdUcmZ6aamwfJyIiIiIiKSRCwvVynlGNsjzmoedUywEucO78aEPnGSjqWQyxAZpEJxlalM3V2me9OhPFjGxzNX/IaECC0WTEmWFOTbUik4p5uaBjPdREREREQkiVheLs6HFudRXz2gHS7pEg03FeV2oixKzF0tGZaemYvZKzPsMtt5pTWYvTID6Zm5nt0xGsrL2b2c/I1BNxERERERSSIG3WqFb8IIcdkwwHl5ucEoIG39YTgKjcVtaesPe1xqLl440HNON/lZo94tOp3OV+MgIiIiIqIWTswKq3wVdFtkuoOcLBm2N7sIuaXO1/wWAOSW1mBvdpFH963knG5qIh69WzZu3IgZM2aga9euUKlUCA4ORnh4OEaOHIkXXngBZ8+e9dc4iYiIiIiomdWay8v9EHQ7yXQXlDsPuL3ZT6RSiuXlzHSTf0l6t6xbtw49evTArFmzoFQq8cQTT+Crr77Cpk2b8N5772HkyJHYsmULunbtinvvvRfnzp3z97iJiIiIiKiJmcvLlR5O3nbCMujWOAm6Y8O0Drd7u59IJRcbqTHTTf4lqXv5yy+/jCVLlmDixImQy+3j9BtvvBEAkJOTgzfffBMrV67EI4884tuREhERERFRszJ3L2/CTPeQLtFIiNAir7TG4bxuGYD4CC2GdIn26L6VnNNNTURS0L1r1y5JB2vXrh1eeumlRg2IiIiIiIhaJnFOt9JHQXeUVSM1x8dUyGVYMCUZs1dmQAZYBd5ivn3BlGQoPGyd3tC9nEE3+Vej3y0GgwEHDhxAcXGxL8ZDREREREQtkCAI0ButlwxrrMhglfnns6XVTjuQp6YkYNn0gYiPsC4hj4/QYtn0gd6t081GatREJGW6Lc2ZMwd9+/bFnXfeCYPBgJEjR+LXX39FcHAwvvvuO4waNcoPwyQiIiIiouZkMAoQ6uNTXywZlp6Zi6fXZZp/f+fnbKw/mIsFU5IdBtGpKQkYlxyPvdlFKCivQWyYqaTc0wy3SCyR13NON/mZx++WNWvWoH///gCA9evXIzs7G0ePHsUjjzyCp59+2ucDJCIiIiKi5qe3yAg3dk53emYuZq/MQGFlrdX2vNIazF6ZgfTMXIe3U8hlGJoUg6sHtMPQpBivA26gYU53HcvLyc88frecP38e8fHxAIANGzbghhtuMHc2//PPP30+QCIiIiIian61FsFpY4Jug1FA2vrDDpuiidvS1h92WmruKyrO6aYm4vG7JS4uDocPH4bBYEB6ejrGjRsHAKiqqoJC4bjjIBERERERtW56q6Db+wzz3uwi5JY6X1NbAJBbWoO92UVe34cUSs7ppibi8ZzumTNn4sYbb0RCQgJkMhnGjh0LANizZw969erl8wESEREREVHzE4NulUIGmcz7oLug3HnA7c1+3jJ3Lzcy003+5XHQvXDhQqSkpODvv//GDTfcAI1GAwBQKBR48sknfT5AIiIiIiJqfvo6U0a4sfO5Y8O07nfyYD9vic3gmOkmf/M46AaAqVOn2m2bMWNGowdDREREREQtU6050924oHtIl2gkRGiRV1rjcF63DKalwIZ0iW7U/bgjNlLTM+gmP5MUdL/xxhuSD/jQQw95PRgiIiIiImqZ6ny0RrdCLsOCKcmYvTIDMsAq8BaPvGBKcqM6k0uhMgfdLC8n/5IUdC9ZssTq93PnzqGqqgqRkZEAgJKSEgQHByM2NpZBNxERERFRAPJVeTlgWnN72fSBSFt/2KqpWnyE1uk63b6mlIvl5Qy6yb8kBd3Z2dnmn1etWoW33noL77//Pnr27AkAOHbsGO6++27cc889/hklERERERE1K1+Vl4tSUxIwLjkee7OLUFBeg9gwU0m5vzPcIpVSbKTG8nLyL4/ndD/zzDNYs2aNOeAGgJ49e2LJkiWYOnUqbr31Vp8OkIiIiIiImp9l93JfUchlGJoU47PjeUJlXjKMmW7yL48vU+Xm5qKurs5uu8FgQH5+vk8GRURERERELYvex5nu5iYuGWYUAAOz3eRHHr9jxowZg3vuuQcZGRnmbb///jtmz55tXrObiIiIiIgCixh0q5WBEnQ3ZOzZTI38yeN3zAcffID4+HgMHjwYGo0GGo0GQ4YMQVxcHN577z1/jJGIiIiIiJpZrQ8bqbUEKnnD46hjprvZGIwCdmUV4psDOdiVVRiQVQcez+lu27YtNmzYgOPHj+Po0aMAgF69eqFHjx4+HxwREREREbUM/pjT3ZwsHwfndTeP9Mxcuw72CU3Ywb6peBx0i3r06MFAm4iIiIjoAtGwTndgZLotu6TrDYGXXW3p0jNzMXtlBmyf+bzSGsxemYFl0wcGTODtcdBtMBiwYsUK/PjjjygoKIDRaH1VaOvWrT4bHBERERERtQy+XKe7JZDJZFApZNAbBM7pbmIGo4C09YftAm4AEADIAKStP4xxyfFNtoScP3kcdD/88MNYsWIFJk+ejJSUFMhkrf9JICIiIiIi12oDrLwcAJRyOfQGA+qY6W5Se7OLrErKbQkAcktrsDe7qNmWlPMlj4Pu1atX44svvsCkSZP8MR4iIiIiImqBAm3JMKC+g7ke0BuZ6W5KBeXOA25v9mvpPH7HqNVqdOvWzR9jISIiIiKiFsq8ZFgABd3iY2Gmu2nFhml9ul9L5/E7Zt68eXj99dchCHxhEhERERFdKMRmYwGX6QbX6W5qQ7pEIyFCC2cTFWQwdTEf0iW6KYflNx6Xl+/YsQPbtm3Dxo0b0adPH6hUKqu/f/XVVz4bHBERERERtQy1dfXl5crAmtMNMOhuagq5DAumJGP2ygy7v4mvrgVTkgOiiRrgRdAdGRmJa6+91h9jISIiIiKiFioQ53SLTeHqjKzilcJgFLA3uwgF5TWIDTNlor0NjFNTErBs+kDMWX0ANXUNFz3iuU438OGHH/pjHERERERE1IIF4pxu8QICM93upWfmIm39Yauu4wmNDJBTUxIwsNMp/JpVBABYPn1gwCwTZsnrd8y5c+ewY8cO7NixA+fOnfPlmIiIiIiIqIUR53QrA2nJMDZSkyQ9MxezV2bYLfOVV1qD2SszkJ6Z6/Wxy2sM5p+7xYYGXMANeBF0V1ZWYtasWUhISMCIESMwYsQIJCYm4s4770RVVZVHx1q0aBEuvvhihIWFITY2Ftdccw2OHTvm9nZffvklevXqBa1Wi759+2LDhg2ePgwiIiIiIvJAIJeXM9PtnMEoIG39YTi6LCFuS1t/GAYvS/TLavTmn0uq9C72bL08fsfMnTsXP/30E9avX4+SkhKUlJTgm2++wU8//YR58+Z5dKyffvoJ999/P3bv3o3NmzdDr9dj/PjxqKysdHqbX3/9FdOmTcOdd96J/fv345prrsE111yDzMxMTx8KERERERFJFIhBt1IuBt3MdDuzN7vILsNtSQCQW1qD3VmF2JVViG8O5GBXVqHkILysOvCDbo/ndK9duxZr1qzBqFGjzNsmTZqEoKAg3HjjjVi2bJnkY6Wnp1v9vmLFCsTGxuL333/HiBEjHN7m9ddfR2pqKh577DEAwHPPPYfNmzdj6dKlWL58uacPh4iIiIiIJBAD00Ca020uLzcy0+1MQbnzgNvS/asyUGIRQEuZ7y0IAspq6sy/F1fVej/QFszjoLuqqgpxcXF222NjYz0uL7dVWloKAIiOdr4e265duzB37lyrbRMmTMDXX3/tcH+dTgedTmf+vaysDACg1+uh17fcKyni2FryGEkansvAwPMYOHguAwfPZeDguWwddHpTcCSXCQ7PVWs8j8r66wc1tXWtatz+ZnkuY4KlhYyWATfQMN/7zZv7Y0If+/gRACp1dVYZ8aKKmlZ1HqSOVSYIgke1FGPGjEFMTAw+/vhjaLVaAEB1dTVmzJiBoqIibNmyxfPRAjAajbjqqqtQUlKCHTt2ON1PrVbjo48+wrRp08zb3nrrLaSlpSE/P99u/4ULFyItLc1u+6pVqxAcHOzVWImIiIiILjTvHZXjz2I5buxqwLC4wCjHXn5EjiMlctySZMAlsYHxmHzNKABpGQqU1AINq2hbEp83x3+LVAMLBhrgqD9aiQ5YkNEQ1I9rZ8SVHVtP1UFVVRVuueUWlJaWIjw83Ol+Hme6X3/9dUyYMAHt27dH//79AQAHDx6EVqvFpk2bvB7w/fffj8zMTJcBtzfmz59vlRkvKytDhw4dMH78eJdPTHPT6/XYvHkzxo0bB5VK1dzDoUbguQwMPI+Bg+cycPBcBg6ey9bhq8IMoPg8LurfD5MGtrP7e2s8j98W78eRknPo3acvJl3cvrmH02LYnktV53w8uPqgw2ZqjoPthr+V1AJtky/FJV3sq5mP55cDGbvMv7dJ7IhJk5IbO/wmI1ZRu+Nx0J2SkoITJ07g008/xdGjRwEA06ZNw6233oqgoCBPDwcAeOCBB/Ddd9/h559/Rvv2rl/s8fHxdhnt/Px8xMfHO9xfo9FAo9HYbVepVK3iw6C1jJPc47kMDDyPgYPnMnDwXAYOnsuWTWzwHaR2fZ5a03lUKxUAAEEmazVjbkriubxyQHsolQo8ufZPqzLyyCCVXVm5I4VVdQ6f36o669/Lagyt6jxIHavHQTcABAcH4+677/bmplYEQcCDDz6IdevWYfv27ejSpYvb2wwdOhQ//vgj5syZY962efNmDB06tNHjISIiIiIix8Tu5YG4Tje7l7uXmpKA8xW1+NfXplWjpvRPxM0Xd8Ct7+1xe9vYMK3D7WU2AXtJdWA2UvO49eCiRYvwwQcf2G3/4IMPsHjxYo+Odf/992PlypVYtWoVwsLCkJeXh7y8PFRXV5v3uf322zF//nzz7w8//DDS09Pxyiuv4OjRo1i4cCH27duHBx54wNOHQkREREREEgXikmHiOt11XKdbkkpdQ2paq5Tj0q4xSIjQOi0wl8HUxXyIg9JyACiv71wuqz9AoC4Z5vE75u2330avXr3stvfp08fjJbuWLVuG0tJSjBo1CgkJCeb/Pv/8c/M+Z86cQW5urvn3yy67DKtWrcI777yD/v37Y82aNfj666+RkpLi6UMhIiIiIiKJAnHJMJVczHQ7D7oNRsGr9acDUVlNQ1BcVFkLhVyGBVMcz8EWA/EFU5KhcNRFzeJ4iRGmacqBGnR7XF6el5eHhAT7tdbatm1rFRxLIaVx+vbt2+223XDDDbjhhhs8ui8iIiIiIvJeIGa6xVJ5Z+Xl6Zm5SFt/GLmlDWtVS1l/OlCVW6ypXVhpKgVPTUnAsukD8cgXB1FdazD/PV7C8ySWl3eIDkJOSTVKAnSdbo/fMR06dMDOnTvttu/cuROJiYk+GRQREREREbUsteagO3DmdIsXEOqM9pnu9MxczF6ZYRVwAw3rT6dnepZwDASWc7CLKhsC5NSUBFxqUUL+zOTe2PHEaLcXJsrqg/iO0aalnCtrDaitC7xSf48z3XfffTfmzJkDvV6P0aNHAwB+/PFHPP7445g3b57PB0hERERERM3PnOlWBk6mu2FOt3Wm22AUkLb+sMMlsgSYSqfT1h/GuOR4p6XTgcgy020ZdANAQbnO/HP76GBJz4sYxLePCoZMBgiCqZmas8ZrrZXHQfdjjz2GwsJC3HfffaitNT3RWq0WTzzxhFXDMyIiIiIiChz6usCb0+2se/ne7CK7DLclAUBuaQ32ZhdhaFKMP4fYolgG3RW6OtToDdCqTMuu5ZfpHO7nijinOzJYhYggFUqq9Cip0jPolslkWLx4MZ555hkcOXIEQUFB6N69u8O1sImIiIiIKDAE4pxulVyc021d0lxQ7jzg9ma/pmQwCtibXYSC8hrEhpk6h/sqG2/ZSA0wZbsTI4OgNxhRWNkQdNsuBeb0eNWm4Dxcq0JUsNocdAcar9bpBkwN1YqKijBixAhoNBoIggCZ7MIprSAiIiIiagr+DKI8EYhzupVO5nRLzbS2tIysvxu/2WawxaD7fIUOlj2ybYNzZ8T9woOUiAhSAQCKA7CZmsdBd2FhIW688UZs27YNMpkMJ06cQNeuXXHnnXciKioKr7zyij/GSURERER0wWlJ3bPFec+BlOl21r18SJdoJERokVda43Betwym7tzO1p9uDmLjN9vxio3flk0f2OjXjJjB1qrkqNEbzR3MLUvLTftJLC+vP54p020KuksDMNPt8TvmkUcegUqlwpkzZxAcHGzeftNNNyE9Pd2ngyMiIiIiulC1tO7ZgVheLs5Pr7MpL7dcf9o2ry9l/emm5q7xG2Bq/NaYNcaNRgEVtaZgulN0CACgsMIUbOeXWb9GyyVnuuvLy4NUiAxWAzA1Ugs0Hr9jfvjhByxevBjt27e32t69e3ecPn3aZwMjIiIiIrpQNUUQ5QmjUUCdUcx0t4xA0xeUcufrdIvrT8dHWJeQx0dofZI19obBKGBXViG+OZCDXVmF5vPvSeM3b1XU1plLyDu3MSVfxQ7mBTZBt5TyckEQrDLdDeXlgZfp9ri8vLKy0irDLSoqKmIzNSIiIiIiH2hp3bP1FnOeA2nJsIbu5Y7Xhk5NScC45Hj0XZCOKr0Rchnwy+NXmG9nydXce1/My3c11UAncW3rxjR+EwNktUKOhIggALArL48MNnUgl1JeXq03mC/khAcpESVmuhl0A5dffjk+/vhjPPfccwBM3cyNRiNefvllXHHFFT4fIBERERHRhaaldc+2zAQH0pJh5nW6XVQMyADU1Ae1RgGo1BkQEWz9HLgKiAE0el6+u/nac8Z2l3ScxjR+KzeXgisRE2IKkIsqxKDb9Ni6x4bit1PFKNfp3V5oEANzpVyGIJUC4UGm0PRQTgne/+UvRIdqEB/efI0DfcnjoPvll1/GmDFjsG/fPtTW1uLxxx/HoUOHUFRUhJ07d/pjjEREREREF5SW1j1bb5FJDaQ53So3mW4AqKytg2VMfr5Sh4j6pl+A64D43pUZDo8pBsv/u+UiRIVoXGbA3U01kAH4bO8ZxIdrkV/mv8ZvYtAdplUhJtRU4WzOdJebMt3dYsPw26li5JXWYPjirS4vNDR0Lldh06E8vL7lBADgj5wy/JFT5vR2rZHH75iUlBQcP34cw4cPx9VXX43Kykpcd9112L9/P5KSkvwxRiIiIiKiC4rYPdtZfk8GUzDSVN2zxaBULkOrzzpaMi8Z5mBOt6jMZpmswoqGRl9S5t47ItT/98Bn+zHt3d14ePUBTHt3N4Yv3mrXIE/KVIO8Mh2mDeno8O++avwmlpeHaZWIrs90i2tzi3O6u8WGAgDOV9S6bQAoHk8hA2avzECJk7W9c5upcaAveXWZKiIiAk8//TS++OILbNiwAc8//zwSElrvlQciIiIiopbEsnu2rebonl0bgJ3LAUBlbqTmPNNdZhMMih27AfcBsTu2Ve2OOtNLnULQuU0wlk0fiBC1wmq7p43fDEYBe7KL8Pt5GfZkF5mbtZXrGpqexYTWl5dXWpeXd20T4vS44oWGp9b9ido6oznTXVKtd3mBQtSUjQN9zeN3TXp6Onbs2GH+/X//+x8GDBiAW265BcXFxT4dHBERERHRhUrsnt021LpZcXN0zw7ENboBi0ZqLoI526D7fGVDptvXc+oddab3ZKpBakoCrugVa97WISoIO54YjXHJ8Q67nttKz8zF8MVbMf2Dffj4hALTP9hnzr6Lc7DDtEpzp/H80hpsP5pv7ji+/4z7eLCoUo+LnvsBX+77G4DjzvG2fNF9vTl5/K557LHHUFZmqrH/888/MXfuXEyaNAnZ2dmYO3euzwdIRERERHShSk1JwAd3XGz+/d4RXbHjidHmgNvZElK+1rBGd+CUlgOAUmyk5irTbVde3pDp9secetsA09OpBmdLqs1/O19Rix8O5WH44q1uy9jdrQv/+2nTeEqr9bjt/T0ATA3m7lixz7zvG1tPSnqMlToDNmbmS9rXUlM1DvQ1jxupZWdnIznZVOqydu1aTJkyBS+++CIyMjIwadIknw+QiIiIiOhCVmsRECZGBZlLyl11zPZ1FjxQy8vVUuZ022a6LYJuMSDOK3XcwKwxxABTnGow20FTNkdTDc6WNLweqvUGzP7U/nZiIC1WTEhp1vbj0QIAwK9ZhY15WI3SVI0Dfc3jd41arUZVVRUAYMuWLRg/fjwAIDo62pwBJyIiIiIi36jRG8w/V9WafnaXlfR10yl9oJaXS5nTXWM7p7vWXGHw3R9ncfPFrhuYecsywByXHI8p/ewvpNhONaitMyK/PlgPUjk/V7Zl7FKatVXqDE7/7m9N3TjQ1zzOdA8fPhxz587FsGHDsHfvXnz++ecAgOPHj6N9+/Y+HyARERER0YWsutZg9bOUrGTa+sMYlxzvs0ZrYlCqVgZY0G2e0+2qkVr9+tRaJcpq6nAiv8JuOazIIJVd9+34+qoDQYBdtlkus2+iJrJd3stRRQMAtI/S4qfHRlud47zSGgiC6Tx1jgnBkbxyp4/Lsoy9NZRtN2XjQF/z+F2zdOlSKJVKrFmzBsuWLUO7du0AABs3bkRqaqrPB0hEREREdCGrqbMIuvUGSVlJXzedEtfpDrQ53SrznG7nxeHl9ZnuLm1Ny2GdPFdh9/zbBtyTUuLNc+8v7Rpj9bc3bh6ApdMGQgb7bLhtubizigYA+Ke4BpsP51lty6mfz90uMgjhQSq72zgirhHeUiU0Q+NAX/M4092xY0d89913dtuXLFnikwEREREREVED20y31KykL7OXgTqnWymvz3S7XKfbFFB3jQnGwb9LJB23Sm8wZ2Xzbc5DYmQQBneOxjL5QPzr60yct1j3O95iTr6rigbRgm8OIUyrwvkKHWLDtPi72DQNuF1kEBIjtNgj4cLL+XIdFJC5zL43pemXdkSXmBBEh2oQH27K+LfWDLdIUtBdWVmJkBDna641dn8iIiIiInLMdk63J0tI+UqgzulWK+sz3RLKy5UePPascxXmn/PLdFZ/E39PTUmARqnAzBW/mf+2dvZlSIwMAiBtDfD8ch1ufW+P+fdQjSm8axcZhCGdo/DF7/+4Hetz3x9xu483vA3iJ/dNxNCkGPc7tiKSXjndunXDSy+9hNxc5w0ZBEHA5s2bMXHiRLzxxhs+GyARERER0YWsWm9ZXl7n8RJSviAuqaUOsKDbnOmuc99ITeuiMZmtf4qrzRdL8stsmt1Z/G5bjZDv4m9SVOhMFwhOnivHixuPenx7qaTkncWA+4qebREZ7L7UvbU3S3NFUqZ7+/bteOqpp7Bw4UL0798fgwcPRmJiIrRaLYqLi3H48GHs2rULSqUS8+fPxz333OPvcRMRERERXRCqa40WPxs8XkLKF8TycmWAzekWH4/eRUpWDLoTI4IkHTNYJUeV3ojs85XonRCOc+W2me6GYNpyeS/ANBf/ovqfG1Op8PvpEq9vK0VUiBpFlbUO/xaqUZqDfwAY1q0N3ptxMZZuPYm3f84yd+C35K/XbUshKeju2bMn1q5dizNnzuDLL7/EL7/8gl9//RXV1dVo06YNLrroIrz77ruYOHEiFAqFv8dMRERERHTBqHawZFhqSgKWTR+I+V/9ieKqhiZe8X5apztQy8tV5nW63ZeXD+ocBaVchjoXAXpEkAqdY4Jw8J8yfPHb3xjfJx65pabmZkEqBar1BqugO8+mfPxsSbV5Ca+zxVUI0ypRXlOHluaZyb0RHxGEgvIatAnRADKY55Ufzi3Fc981lKy3izStLf/w2O54YHQ3LN16Eh/uzLZqPuev121L4VEjtY4dO2LevHmYN2+ev8ZDREREREQWLOd0W/6cmpIAfZ2AB1fvBwA8NqEH7h3ZzS+ZQn2ANlITH49RAIxGAXIHz52Y6Y4KVqNbbCiOuliG6/LubfDjkQIAwIe/nsKHv56Cpn6ZtZR24fjtVLFVoH22PiCPrs8c/5pViPd3ZLudy93cYsO0Tuddix3UReIcdQBWwbe4VFlsWGA0S3MlsN41REREREQBxrJ7uW1prmUWvH1UsN8Cl4Z1ugMrMLIsl3e0VrcgCCirz8iGB6nQIy7U5fG++yPX6pwAgK5+vni41jSvucCi3FwMwAd2jAIAbD1a0OIDbgCY9+VBpGc67vcVrrXO67aLsi/LV8hlGJoUg6sHtMPQpJiADrgBBt1ERERERC2adSM164Cusrah9LhSZz9X1ldq6wI00y1veDyOlg2rrDWYG4Lt/qsQW+qz2CJPno3fzxQDMAXagmA6qBhgX9Qx0oMjNRXnZfT5ZTWYvTLDYeBtuT64ViVHTIjaL6NrTQLrXUNEREREFGAsS8qrbTLdlpnvSp3/5v4G6pxuy0y3o3nd5fWl5Qo5MGf1AbtKA+czwe2V1M+9r9YbUK6rQ3mN3txwLMiDzugtgRiOp60/DIPNHPcwi0x3YmQQZLLAzmJL0brOLhERERHRBcZRIzWRZaBd4degOzAz3UqLsmZHmW6xiZoguMr7SicG1/mlNeYsd0SQCmplS2xG7TpYFmDK1O/NLrLaHqJWWvyssAvKL0SB9a4hIiIiIgowNTbl5WJpMmAddPs30y2u0x1YWUuZTAZV/WOqczCnW2yi5qu4Mbq+1DqvrCHoTojQIqltiG/uoBlYrieenpmLm97ZZf79z5wyDF+81en87wuFV0H3L7/8gunTp2Po0KHIyckBAHzyySfYsWOHTwdHRERERHShs53HXaNvCA4rLcvLa/1fXq4MsEw3ACjr53Xr6xxluvV227yVEKFF55hgAMCGP3PxxW9nAJjmPQ/qFA1/Xc+YeVknRIeo3eStvSeuJ56emYvZKzOQX2a9LnleqfP53xcKj981a9euxYQJExAUFIT9+/dDpzM9qaWlpXjxxRd9PkAiIiIiopbGYBSwK6sQ3xzIwa6sQr+W0NrO47YuN7csL/dfI7VALS8HGuZ1O+peLma6feHKfgnIOFMKAPhs79/4/s88AMCBv0sx5MUtHpWvSwmgEyK0WD59IBZclYIXr02RfDtxvwiVgPhwjdPbyOrvY0iXaBiMAtLWH3b4GFzN/75QeLRONwA8//zzWL58OW6//XasXr3avH3YsGF4/vnnfTo4IiIiIqKWJj0zF2nrD1st7ZQQocWCKclITUnw+f1ZZrYBU6Atlilbdixnebl3xAsJdfXZfINRMK8hffBvU5CsVcmh0xsbNa/73V+ynf5NbLLmivgaA+Dw9ffM5N6ICtE4XPs6NSUBy6YPtLudI+IZvr6LEQMH9sKDqw9CBus57eI+C6YkQyGXYVdWocvjWs7/dra+dyDzOOg+duwYRowYYbc9IiICJSUlvhgTEREREVGLJJbQ2gZfYgntsukDfR5425aXVzvpWM5Gat4Rm6nV6A14fcsJfLgzGyU2ZeWdY4JxLK/CLvhsChFBSrx16yBc2rVhPetxyfHmCwO2AbYzqSkJdrcrrqzFc99bB+LxEVo8PbEnDKd/x4Q+cQ6D9Xibi0yW87pdkbpfoPE46I6Pj8fJkyfRuXNnq+07duxA165dfTUuIiIiIqIWxV0JrQymDOS45Hi3AZAnXJWXVzbRkmG19fOdVcrAC7rFCwm3vrfH6YWLo3kVuGdEF3x7MNdtptjXSqvrIJfJrF5TCrnMq4yxo9tNSLEP4I2GOmw4bfq7o2DdNsgX53W7I3W/QONx0H333Xfj4YcfxgcffACZTIazZ89i165dePTRR/HMM8/4Y4xERERE1EpYluZKzcC1Fnuzi5q8hFYQBNTUmQLrcK0SZTV1VsuGWc7pbory8kDLdBuMAip0pqy2u0qBbw6cxc+Pj8bvp4tRUF6DU+er8NneM8gra3hNRIeoUFTpu3ngIn9miB0F4kaD+30sDekSjYQILfJKaxxelJLBlB0f0iW68QNuhTwOup988kkYjUaMGTMGVVVVGDFiBDQaDR599FE8+OCD/hgjEREREbUCTT3Xuak1Rwmtrs4IcYWwmFANymrqrDPdFnO6m6KRWiDN6U7PzMXCbw+htFraxYq8Mh2Wbc/Cw2O7m7c9MLqb1UWmvLIaPPL5AZ+PtaVniBVyGRZMScbslRlu539fiDy+VCWTyfD000+jqKgImZmZ2L17N86dO4fnnnvOH+MjIiIiolZAnOtsmwnOLa3BvSszsOGPs800Mt9pjhJayzW6o4JVAFzN6fZ9hlUUaJlu8fWaZ7O8lTtLthy3WvpKzABfPaAdhibFID7ct8GxZYfwlk5s1hYfYf0cxEdo/dLroDXxONMtUqvVSE5O9uVYiIiIiKgVcjXXWfTAZ/uxFDJM6td6v3g3RwmtmNVWK+QI1ZqCbrG83GAUrLLeNXoj6gxGv6ylLa7THQhBt5TXqyuu5u27e414ojVmiKXM/74QeRx019TU4M0338S2bdtQUFAAo816dhkZGT4bHBERERG1fO7mOgOAUQDuW5WB5fLWm/GyLKG15a8AScxqa1RyBKsUpm31gbZtV3PA1FgtIsi3gbHBKOB8hSkjnH2+Agaj0KqDKCmvV1dczdt3VWbtSmR9FYPl0mG2HcJbC2+bvAUyj4PuO++8Ez/88AOmTp2KIUOGQCZrvW84IiIiImo8T+Yw+6O7d1MSS2gf/Gy/OfsL+C9AEgPrIJUCQer6oLu+eVpVfWm5XGYKdPQGAZW6OkQEqXx2/7bz9Jduy8LajJxWGQyKfDHn3tUxnK2JbbmWdl5pNYoqaxEdqkF8eEN1BDPEgcnjoPu7777Dhg0bMGzYMH+Mh4iIiIhaGU/mMPu6u3dzSE1JQPuoo8g+XwUAeOe2QRjTO84vAZI4pztIbRl0mypNxW7bIWolFAoZSqr0PulgLnag33w4Dx/sPGX3d3+uSd4UfDHn3t0xvC2zbs3vC3LO46C7Xbt2CAsL88dYiIiIiKgVEuexSi3Z9efyR03FslN417YhfstIigF2kEphLi+v0tdnuutLz4M1CijlcpRU6d0ue+WOow70tvy5JnlTaMy8a0/m7bPMmkQeT/h45ZVX8MQTT+D06dP+GA8RERERtTLiPFapWvryR1KUVTfMvS2sqPXb/Yjl5Vqr8nLTtkqLTHeoRlm/zftlw5x1oHfEck3y1sby9erqcoHt31pjYzNqGTwOugcPHoyamhp07doVYWFhiI6OtvqPiIiIiC48qSkJeOuWi+AqFvHn8kcGo4BdWYX45kAOdmUVwmBsbO9o53R1BujqGpoJF1X6L+iucTin27RNzHSHaJQI0Zj+5m2mu7bOiKfWZXqc+W2tVQvOlrdKiNBi+fSBWM6lr8iHPC4vnzZtGnJycvDiiy8iLi6OjdSIiIiICAAwqV8iXqypw5Nf/Wn3N39mCR2VRCf4sfNzeY11YFvog6BbnEdtO/+32nJOt7m83LRNDLCD1QqolaZcmjdzutMzc/HUuj9RVOn5Ot+tuWrB3bxrLn1FvuJx0P3rr79i165d6N+/vz/GQ0RERESt2GVJbQDAbrkkf3X3FkuibTO0/mz2ZVlaDjQ+0+3qokGNubxcjuD6THeNOdNdX16uUUIjBt21ngXdzp4/d/yxJnlzcDXvmnOyyVc8Li/v1asXqqur/TEWIiIiImrlxKAvOkRtnjebEK7FjidG+zz4NRgFpK0/7DBgFLelrT/s81Jz20x3Y4JuZ/OoxYsGB86UABDndJvyZVXmOd2W5eWmv3lSXu7q+XOFc5uJPONx0P3SSy9h3rx52L59OwoLC1FWVmb1HxERXdiacl6lP7T28RM1NzH7GqpV4pIupixhnSD4JTjbm13ktsu2P5p9ldVYZ7q9LS+XctHgh8P5AOrndNeXl4sl5+ZMt1ph0UhNetDt7vlzhnObiTzjcXl5amoqAGDMmDFW2wVBgEwmg8HgfcdEIiJq3Zp6XqWvtfbxE7UEYvY12KKjdkVN49eOdkRqEy9fN/uyz3TrvDqOlIsGYuY6SKUwl5eLjdQqLJ7rILU4p1v6d3FPn5er+yfi5iEdObeZyEMeB93btm3zxziIiKiVa455lb7U2sdP1FJYZV+1pq+a1XoDDEbfZ7ulNvHydbMvcU63WilHbZ3R6yXDPAl6g9QN3csb1ukW53Q3/E1qebnBKOB8ufSLBXIZsHhqP2jrs+1EJJ3HQffIkSN9duc///wz/vOf/+D3339Hbm4u1q1bh2uuucbp/tu3b8cVV1xhtz03Nxfx8fE+GxcREXnGXYmkDKZ5leOS41tkdqS1j5+oJTFnui2WsQJMwWBEkMqn9zWkSzQSIrTIK61x+P71V7MvMdPdKToYJwoqvJ7T7cnFAK1leXmtabkyyzndYhZcSnm5o6oedxIitFApPJ6ZSkSQOKf7jz/+gNFoNP/s6j9PVFZWon///vjf//7n0e2OHTuG3Nxc83+xsbEe3Z6IiHyrueZV+kprHz9RS2KZ6dYoFVDXB2rerh/tikIuMzdrs+XPZl/inO7ObUIAAMVVtRAEz/s/iBcNnI1OBlPXcsC2vNwm061WIEQtrZGas8Zt7uSU1GD44q1Iz8z16HZEJDHTPWDAAOTl5SE2NhYDBgyATCZz+MHi6ZzuiRMnYuLEidJHWy82NhaRkZEe346IiPyjueZV+kprHz9RS1JZ2zDPGDA1VCuqrPVq/WgpUlMSsGz6QDzy+UFzgzHAt0uU2a6hXVJlymx3jgkGAOgNAspqPM/kixcNZq/MsPubGIj3iAvDH/+UWq3TXa03QBAEi3W6G7qXu3qeve1WLuJ0GyLvSAq6s7Oz0bZtW/PPzW3AgAHQ6XRISUnBwoULMWzYMKf76nQ66HQN81XEDut6vR56vd7ZzZqdOLaWPEaShucyMPA8uhYTLG22UkywstmfQ0fnsjWNnxrwfdkylVebAtIglQx6vR4hagWKKoGSihroox2XUzf2XI7p2QYpiWH47XQJAGB4UjTeu30QFHJZo18fmw7l4/kNR5FX1vB9Usw+RwerEKJWoLLWgILSSgQrQ7wa+5s398e/vj2MkqqGscaGafDM5F747Ld/AAAqmQClzBQuGwWgslpnDrA1CqB++jwqauqcPuY9EruVh2mVds3iAMvpNocwqnuMXQUB35OBg+dSGqnPj6RvGZ06dYJCoUBubi46derUqIE1RkJCApYvX47BgwdDp9Phvffew6hRo7Bnzx4MHDjQ4W0WLVqEtLQ0u+0//PADgoOD/T3kRtu8eXNzD4F8hOcyMPA8OmYUgEi1AiW1ABwWSgqIVAPnDu/GhiNNPDgnLM9laxw/NeD7smU5dEoOQI7cv09jw4ZsGHUKADJs3bELuZGuc6yNOZdZeab7AYBz589jU/pGr48lOlgowwfHxdmYDZ8NNXoDABl2HDgCrUyOSsjw/Zaf0CXM+/saGyvDmlMNc+CvbV8Fw+nfcbbA9LgO/3kQ8hwB4tf3bzdsQt55098OHcyAVmH62/nScmzYsAGA6bMtq0yGMj0QrgJKawHAfSM0RwG3yDTdRoeln6eje4Tj88n3ZODguXStqqpK0n6SG6l5M0/F13r27ImePXuaf7/sssuQlZWFJUuW4JNPPnF4m/nz52Pu3Lnm38vKytChQweMHz8e4eHhfh+zt/R6PTZv3oxx48ZBpfJt0xFqWjyXgYHn0T1V53w8uPogAFiVLsrq//f56/pjQp+4ZhiZNWfnsrWMnxrwfdky/frNISA3B31798CkUV3xydm9yDldguR+F2FiiuPGt409l3UGI+bu+RHiu1fQhGPSpMsa8zBgMApY9MrPABx1+DZ9Mhwq06JDGy0Kc8rRs99gjO3tfZ+hY1tOAqf+Mv8e3TkZky7rhLdP7QLKyzHs0osxonsbPPHbZugNAoaPGo1lWb8BVdW4YvhQhGqVWJL5K4xyNSZNugKbDuVjkU2GPipYBcA3mcuufQZgUj/rEnO+JwMHz6U0YhW1Ox53L29phgwZgh07djj9u0ajgUajsduuUqlaxQuotYyT3OO5DAw8j85dOaA9lEoFFnx7CPkWX/J8Oa/Sl2zPpTh+246+LXX81IDvy5alWm8KfMOC1FCpVAgPUgMAaurg9jx5ey7zyqtgMDZcLjtfWdvo18S+rEKrgNWRkmo9ushNJeWlNQaP7tN2nnhB/fJdwWoFqmoNOF5QCZVKhZo6UzPjUK3p+QxWK1FarUetUYaq+vnz4SEahGtN911ZW4cfj53Hg6sP2s3dLq5yH3CHaZQolzD/PiEyxOnj5XsycPBcuib1ufEo6H7vvfcQGhrqcp+HHnrIk0M22oEDB5CQwC9CREQtQWpKAvq2i8SwxVsBAJNS4vHmLQNbzTJbqSkJGNGjLZL/vQmAKSu044nRrWb8RC2BZUdtAAitb/AlJZDz1j/F1QCAyGAVSqr0KKqsRW2dEWql90tcSW2cqKq/j0IPlg1ztGSXONbLkmKw5UgBfj9djG8O5KC0vmmbuA53kEqB0mo9avQGVJqf64ZGanqDgIXfHvK6Wdqccd3x3i/ZTb4MG1Eg8yjoXr58ORQK5/NAZDKZR0F3RUUFTp48af49OzsbBw4cQHR0NDp27Ij58+cjJycHH3/8MQDgtddeQ5cuXdCnTx/U1NTgvffew9atW/HDDz948jCIiMiPLLsHh2qVrS5gFTNHgKkLcysbPlGzs1ynGzB9DgCmBl/+8k+xaV5lSmIE9mQXQm8QcL5Ch8TIIK+PKXUN7dgwUyb/t1NF2JVViCFdol1+7olLdtkGtLX1Ge3q+s+g7POVeHj1AfPf950qRp/ECPPM8j1/FaJGb7pNiEYJrcUFBncZelduvaQT2kUGYfbKDMjgaLqNf5ZhIwpkHgXd+/bt8+ma2Pv27cMVV1xh/l2cez1jxgysWLECubm5OHPmjPnvtbW1mDdvHnJychAcHIx+/fphy5YtVscgIqLmZblcjatmPC1VWXVD+WVtnRFVtQZzBomI3HOW6a7Q+a8Lspjp7hAdhL/OaXC2tAYF5Y0LusU1tJ1lfAEgIkiJn46fBwBsP3YO24+dQ4KLKSlSluzamVXocPuz3x3GG1tPmDucP/d9Q1fHHSfOYdHGo5IelyttwzTQqhTmZdg43YbINyR/i5DJfH81a9SoUS4btK1YscLq98cffxyPP/64z8dBRES+Yxl0l9W0vqVGymwuFBRV1roMum3nZbrLchEFOrt1us1Bt8HpbRpLDLrbRwWjbbjWFHSXSSsPd8bVGtqi0mr7C4uu1rLe/VehpCW7nClxMif7IYuMeGO0j2q4SJGakoBxyfH8fCPygVbVvZyIiFq+cj9mupsiwC2ttv5SW1xViw7RjpeYdDQv01WWiy4MF/qFmKr6z4AQjW2m2z+VLwajgMNnSwEA1bV1aBtqKvcWG5M1hpjxve/TDBglfhVuWMv6MMYlx5vPfXpmLp5c+2ejx+RPQSoFDEbBPGaFXIahSTHNPCqi1k9y0L1gwQK3TdSIiIj8VV7eVAFumU3QXeSkOZKzeZmuslwU+FrShZjmCv6dZrr9UPli+3wv3ZaF4Pqydl8E3QAwskes5IBbZFrLugZ7s4swNCnG6edFS/NrViGGL97KC4dEPia5peOCBQsQHOz4Sj8REZHIOuj2zZds8QurbVmmGOCmZ+b65H4A+5L44ir7oNvVvExxW9r6w1ZLGFHga8rXqZSxDF+8FdPe3Y2HVx/AtHd3Y/jirU0yBvOcbjHTrfVPptvZ8y02Q8w4XeTR8QxGAbuyCvHNgRzsyio0v3+zzlUAADRedELfefIcauuMbudxtyTN8XolCnTsDENERD5lOW/Tdn60N9wFuI7KOBujzGaOZnGl/YWDvdlFLudl2ma5yH+MArAnuwiFVXXNWsrd1K9TV5qzCqO2zgi9wXTP/pzTLaUh2W+niq1KpV1xVaGgq+8q3q99BI7mlnu09NnSbVn4aNcplNf4bz67rzX165XoQuD94oVEREQOWGa6a+uM0NU17sumJwGuL0jJdEtdv1fqfuSdTYfykZahwPQP9jV5NtdWU79OnWnuKoxqiyX3xDLvhky378rL3T3fAKCrM0p6vt1VKGzKzAMAdIsNRec2Iea/q5VySAlHPQm4U9qFS97Xn5rq9Up0oWDQTUREPmVbQtrYed1NHeCKc7qV9dkdR3O6pa/fK20/8lx6Zi4eXH0QJTanp7lKY1vKhZjmDv4r60vL1Uo5VArT18yGOd2+Ky+X+jzuPHnO5QUGdxcpBACbj+QDMDUV6xTTMNUyJTHc5yXjfdtFYM6Y7j4+aoOZl3XCM5N747ZLO0nanxcOiXyD5eVERORTjoLuNqEar48nNXBtE6LBrqzCRjeNEkvi20cF4VRhlcNMt7v1e2UwrWc7pEu0x/dP7lkHStbnuLlKY1vKhZjmDv5t1+gGGoLuSh+Wl0t9Hpduy8LajBw8M7k3okI0dp8PUjLmYrn8yt1nEKJuyFdFBqswZ0x3vPbjCe8fiI3P9v6NyCCVz44nsm3mtyurEJ/sPu32drxwSOQbHgfd+fn5ePTRR/Hjjz+ioKDAbikxg6H1zFkhIiLfq7QJum27gXvKXYALAKEaBe5blWG13Je3HaPF8XaKCcGpwiqHmW5X6/eKId6CKcmcC+knLXFOfUu5ENPcwb8YWIvzuYGG8vJag2m6iUapcHhbT0j5XBDlltbgvlX7rbbZzteWqrK2Yf+tR88h43SJR7eXoqSRn5mRQSq8Oe0iyOUynK/QObwI2VJer0QXCo/Ly++44w5kZGTgmWeewZo1a/DVV19Z/UdERBc2X5eXiwGu6/s02K2v7W2ZsTinu3N9GamjRmpAw/q9WpX1P6XxEVouF+ZnzZ3NdcTV67QpL8SIwZSze5HBFHD6K5iqtOlcDgAhFgG4r0rMpXwuuCJ+Ppw6X9mocTQ2QG4M23Msq//vpev74vIebTGsWxtcPaAdhibF2L3uLJ8/R8cBeOGQyJc8znTv2LEDv/zyCwYMGOCH4RARUWtnm+n2xbJhYoD72Jo/JAfx3pYZi8G72DCpyKK83Hbd43HJ8ejbLgK/nSoGACyfPpDdfptAc2dznRFfp0+u/dMqGItvwnW6m7sKo8pBplshlyFYrUBVrQEVujrENGK6iaXUlAT8e0oy0tYf9vi24ufDZ3vPID5ci/wy9xnzlkA8a/83ogu+PZhrVfHh6etMfL3adm1vytcr0YXC46C7Q4cOdiXlREREIrG8VKOUQ1dnbHSmW5SakoBfTpzHp3vOAAC0Sjlq3JSGelNmLC4Z1jnGFHQXV9ZCEARsOpTncEkho0WTppR2EQy4m0BLLo1NTUlAQbkO//7mEABg/sReuOvyrk36uhCDqflf/YniqqYN/h1lugHTvG4x6PYlMYCPC9cgv0zn0W0FAHllOkwd2A5rM3J8Oi5fiQxSOb2A83hqb6uLgN70sUhNScC45PhGH4eIXPM46H7ttdfw5JNP4u2330bnzp39MCQiImrNxC/VCRFanCqssluCqzEsA153AbclT8qMxfF2rC8vrzMKWLc/B/O+OOhw3WPLbZ7ODyXvWGdzxZylSUsoja2yWDarY3Rws4wjNSUBZ4qq8OKGowBMQfCOJ0b7fSziY7fMdAOmed0F5TqfdjAHgMNnywCYun7nlxV4dYw1GTmIDFahpKrxc6l9XW7+v1sGQi6XOQyIFXKZT3oW+Oo4ROScx0H3TTfdhKqqKiQlJSE4OBgqlXWHxaIirudHRNSa2ZZQe5r1EIPu+Pqg21Gm29v7+Ke4SvoDseCqzNhyLJHBKtTWB86xYRpzSeyiDUddrnss0ukZdDeV1JQEvHlzfzz91QGUWvS6awmlsZaBpa8zu574u6ja/HOlzoA6oxEKeeObmLkiTi+x7F4OWCwb5qPnQ3zfbj9mCrQv79EGh86WSWqs5khjA26gIUDOK61GUWUtzhRX4eNdp+FNgahYrXGpg/nYRNT6eJXpJiKiwJSemeuwhFpqECMIgvlLd2JEEAD7Rmre3ocgCMgprnb6d2dcNY1yNBbA9IU3RK1EVLAaVbXVOFchrWxVV8cVPJrShD5xKDxuwIIM09eZkT3a4IM7hjR7kGIZWNr2OGhKpwqtm4Sdr6hFu8igRh3T3QUzc6ZbY5PplhB0GwVgT3YRCqvqXF6Mc/S+fWPLSUwd1A7v/JwNGewviPmTqwD5ks4xuG+V4/n1goOfxd8BNjIjCiQeB90zZszwxziIiKiZpWfmYvbKDIcl1LNXZkjqyK2rM6Kufo5zfIQpu2zZSK0x91FSpUelRdmuUi6DwSi4/XL9zOTeDr+4bszMw0Of/+HwNgKAHw7nITpEjZwS6YE+y8ubnmVxgValaBFBiuWFJsvXbFM7XWhdGXKuXNeooFvKBbNKB+t0A+6D7k2H8pGWoUDJ7n1Ojy2OwdFnSFFlLd75ORv/N6ILvjlwFnkezu/2lrsAeVK/BCyXO29WBoCNzIguAB4H3YBpLe6vv/4aR44cAQD06dMHV111FRQK/5YsERGRfxiMAtLWH3ZaQi21C7hlVi8uXAy663xyH7bBb6hGabdMmCPPfX8EcrnM6gvs/vMyfLzbccAtSlt/GEltQ9we3xKD7qans3jKfdW0r7EqdA2vy+bKdOsNRvN7Jj5ci7yyGhSUeb+EmtQLZo66lwMNa3U7mtOdnpmLB1c77plgeWwpnyHfHszFf6b2x20f7PXqcboTHaJGUWXDfAYpAbK7ZmVsZEYU+DwOuk+ePIlJkyYhJycHPXv2BAAsWrQIHTp0wPfff4+kpCSfD5KIiPxrb3aRXYm1JaldwCvNX7gViAgy9fwQG5NJvY/dWYUOGweJ87ljQtQorKyFrs6IZdMHYs7nB1DjYi617Rf3TYfyseKE3On+otzSGhRW1Lrdz5JOz/LypqazeMpbTtDd/OXlOcXVMBgFaFVypLQLR15ZDc5V6Lzqp+Au2AWAp9b9iWq90VzS7qh7OWCf6bY+tvU4bI9dVKGT9BmyJ9v3/YXEEvKfHrsCv58u9jhAdtWsjI3MiAKfx0H3Qw89hKSkJOzevRvR0aY5coWFhZg+fToeeughfP/99z4fJBER+ZfU7t7u9iuvz/CFaJQIDzL9EyMGQlLv4/5VGVYdgMUS03/q53MnJ4bjlxPnUa03YHSvOPM62WLTM1uWWfTRveLwfH03ZylqDZ5lrpnpbno1hoaAxxdrwvuCdSO15rkQIwa/naJDEFtfdfLryUIs3XrSaXm4s4Dc3QUzACiq1OORzw+Yf//rvPV88uD6cvODf5dgV1Zho47tnm9ndFuWkKuVcgbIROQxj4Pun376ySrgBoCYmBi89NJLGDZsmE8HR0RETcNVd29P9hMz3WEaJcK0pky3GAhJvQ/bJXfETPWonm0BAL3iw/DLifMATFl0cR1iRwG3SMyAfbLrVP1cT9+UbqoVMtQaGr7gM+huepYxbdkFnukWg+a80mqkH8oDAIRplYgJUQMAvv8z1+424vvr/0Z0wbcHcx0G5N68rlfv/RujerRFakoC0jNz8enuMwCAn0+cx88nzjfq2O4M7doGazNyvO5kbotzrImosTwOujUaDcrLy+22V1RUQK1W+2RQRETUtIZ0iUZChNbpl1SxtNJZF3CRebkgjRJhWutMt7v7cEbcd0d9oG0wCgjVKFChM6C0Wm81v9Kd00XeLTnmjMFo/UjYvbzpWZeX6yEIAmSyFtS9vLZpgm5nnfj3nS7Gsbwyp7cTX8Fv/5xt9zcxIJ8ztrtXY0pbfxhGo6l6xdl8bW+P7YhlF3FxHffGdjJ/4IokPDKuJ+dYE1GjuJ/UZuPKK6/E//3f/2HPnj0QBAGCIGD37t249957cdVVV/ljjERE5GcKuczcSdeW+KX15os74Ls/zmJXVqFdsCmqMAfdCotMd53dfXjz9VVff58f7DyF6vqsdnFlLYqrpAfdnaKDvbhn58Qkd3j9BQau0930LBup6Q1Ci6g2aOp1usUmZ87KtMu9LHEX3+Wf7T2D+HBplSqWcktr8K9vMl3OBReP7auQVuwinpqSgGXTB5pXUfDWsG5tGXATUaN5HHS/8cYbSEpKwtChQ6HVaqHVajFs2DB069YNr7/+uj/GSEREPmIwCtiVVYhvDuTYBc/il9ToEOuqpYhgFSKDVViy5QQeXn0A097djeGLtyI9075UVcx0h1pkumsNRtTUNxgT7yPO5otwZH3TNcmPo37Y6w+ehVD/s6sv7jKYSmVvG9oZ8eEa+HrOZ/soUzDfEgK+C41tPFnWzPO6DUbBapkwf5eXu2py5gsCgLwyndcXD1xVoojHHt4txmKL9+aM7WFVAp6akoAdT4zGp3de4vFnjPiZ4a66h4hICo+D7sjISHzzzTc4duwY1qxZgzVr1uDYsWNYt24dIiIi/DFGIiLygfTMXAxfvBXT3t3tNHhOTUnAQouM9+BOkSit0qOkyvE8a9vAu8KivDxUrYRY5WvZVTo1JQHpD19u/l0uA96cdpFXj2ltRg4AIDJYhYVXOc6i2zZB+tekXm6PG6xWuMy8aZTW/3x2iDatfczy8qanM1ifqbLq5p3XbVtOXunnRmq7/yp024jMF/yZsV+TkVPfaK1xGeXObewrWRRyGYZ1b4OXru8LmcR7cLf2NhGRpzwOukXdu3fHlClTMGXKFHTr1s2XYyIiIh9zVn7qKHgutgiwD+WWOy0NFQAs/PaQVbbcMuiWy2UIVYvzuq2Ddssv8EYB6BEfhoQIz0tMxeNEh6idlpPGhmvMy4UBwIQ+cegb5TqjVlVrcJlzm9I/0fyz5ZiZ6W56NTYxbXN3MLddh9qfc7rTM3Nx/6cZfjt+Y0UFS88uV7pohCiVq2aNzj4fIusreSzFR2itPjOIiBpLUiO1uXPn4rnnnkNISAjmzp3rct9XX33VJwMjIiLfcLfGrric1rjkeCjkMhRW6Mx/r3bzRTivTIelW0/i4fpmSGIpbVj9mrxhWiXKdXV2XaVLbTqUF1bUmhsfeUPszpyakoBxyfHYm12Eh1bvx7lyHf5zfX+MqO98bjAK2JNdhPxqU6h89+VdYDAK+GDnKUn3I5eZLhJ0axtq3iYA2HQoHwBwLM++0Sj5l+1L1NFa3d6sTe0t24ywv8rLxQtp/ior9wWjICAyWIXSKr3fxymlFNzy88HytQCgyV4fRHRhkhR079+/H3q93vwzERG1Hu7WwRWX09qbXYShSTEo9KAbOAAs2XIcPeNDkZqSYF6TOMQi6EYp8MOhPFTXGsxfZm2D7nMVOoxLjscDo5Pw5tYszx4gYDUPXSGXYWhSDAZ2jMSmQ/k4ca4CI3q2tenubPpC/VXGPzC4iQY0Sjl0dUZM6ZeA9X+YKgJeSne81vfWowVIz8xlhqwJ2We6rYNcR129E/y4BJR4/xFBKpRW6+ubuxmgUSp8dh/+nsftK2XVdU02Rqml4OLngy2uvU1E/iQp6N62bZvDn4mIqOUrKJc231Pcr7DCs6AbaMiUWy4Zlp6Zi7/OVwIA3tqehbe2Z5mDHVs/HsnHk2v/sAqMVHJAajPwmFCN3baecWHYdCgfx/PKnWYFCyvdlyKLJeP/lFRLGotl1QD5n87mNWLZSM3ZeRenVfijhFjMdMeFa8wXlyp1vg263V1I85VglRxVjejIL1bSBGsUfpvbLpcBS6exFJyIWjaP53TPmjXL4TrdlZWVmDVrlk8GRUREvuNqnqOj/QorG8rLFRLjRjFTLgbdp85XYPbKDOht0shisCOuuS36eNdpuyDCk+/6MTYd1wHTPHEAOJpX5pOs4J//lEraT3wuqGmIjdTEKQ3inG530yoA0wUSZ8vfeUuc0x0ZpIZWZfqa5esS8y2H83x6PGcaE3CLBPi3mdzSaRdhUj8G3ETUsnkcdH/00Ueorra/2l9dXY2PP/7YJ4MiIiLfGdIl2mWTMtulcSzLyzUq6dm5gvIalNcHF+v/yHUZ7Hxz8Kzk4zois3kwtsucAaZMNwAcPlvmk6xgnQfBmdTqAmo8MZ4TG2SJ5d2eTKvwpQqdKegP1SoRWn8hwJfN1NIzc/G+xB4Es0d2dfjeaG0cNTtLiNBi+fSBmNQv0cmtiIhaDknl5QBQVlYGQRAgCALKy8uh1TZkTgwGAzZs2IDY2Fi/DJKIiLynkMucNilztDSOZXl5td6AOWO647UfT7i9n9gwrTmjZ7vEmCUBDYGR2JjMU4LNbRyVlx/LN1Vl6RuRyZTBFMzll9V4NE6p1QXUeJZB94mCCvNry9NpFb4i3n+oRokQjRLnK2p9lukWs/fuiK/b4d3bYtlPf/nkvhsrOkSN4spajytOnpncG3cM6wKAzc6IqPWSHHRHRkZCJpNBJpOhR48edn+XyWRIS0vz6eCIiMg3xOVyHl59wGpZq3ibhlJ6g9GqyZkgALdf1hn/237SrlRcJH7BH9Il2uPgok2oBgXlOvc7umFbXp6emYsHVzWu8aflBYmXNh7FqcIqAKY1vKtdLCkmpYsy+Y456A43Xegoq3/9ejqtwlfEOd2hWiWC65fMq/CyvNq267pRECRVbQgwvW7PVzT+vdVY4ufDM5OTcf+qDMgASYG3eLs7hnUxB9dsdkZErZXkoHvbtm0QBAGjR4/G2rVrER3d8IVCrVajU6dOSExkiQ8RUUuVmpKAdpFH8dd5U/DYMToY2x4dZZUtKq4vLZfLAKVCjto6Iyp1dYgOUSO/zP4LvGVgCgBFEhqTWeoUE+yToNuyhNbTzs4yABHBKmiVCuSVNQQ0lhckPtt7xhx0X9QhEr9mFToNHqR2USbfEBupJdSXl4vL04nTKvJKaxyeJ8uLRb5kuWxeqEZhtc2Su2XMHHVdjwyStu71rGGdkZqSgF1ZhY15KI1m+fmQmpKAZfKBdo/J3e34XiKiQCA56B45ciQAIDs7Gx06dIBc7vF0cCIiakZGo4B/Shq+7J6v0MH2++z5+tLy6BA15DIZCsp1KK3Wm7PjbULV5n0AIC5Ci4X1AffwxVutOkc7IwOgrl+G6+LO0fjtVLFHj0MGIDZcY3URwDLT7UlnZ/Hhv3RdX4fr9yrkMqRn5lqNcWdWoXl+qW0ZfbvIIHZRbkK6OiMMguksxkcEAWhopGY5rcL2Akljgjp3wbI5011fXm65Tbz90q0n8eHObJRYVJVYLmPmrOt6SbW0i1rjkuMBuL/w4G+2lTSO1skurqzFc99bB+K2tyMiau0kB92iTp06AQCqqqpw5swZ1NZaLy3Tr18/34yMiIh8Kr+8BrV1RijlMhgFAVW1Bpwr1yE2vKG8tqg+0x0TooFREFBQrkNhZa05uNzw0OXIOleBWSt+Q7XeiHduG4SzJdUOAwRHxNAkPkKL04VV6FnfYVwq8fbPXJmMByzKx6Msgm5P5ujafrm3LV91FvyUVukhAHhkbHd0bhOCwgodnv3uCDQqXpBuSpYZ5PgI07x+y3W6xWkVC749ZHWRxtugzlH2OT5cg2lDOqJzmxDEhmnN5e2h2oagWxxnemYunvzqT4c9D/JKa3Dvygw8PKYbPvr1tFdBsm323tWFB3964IpuGNatjcN5147WyZ6QEo9dJwvwwy97MP7ySzC0Wywz3EQUUDwOus+dO4eZM2di48aNDv9uMPhvWQgiIvLe6fry6PZRQTAIAv4uqsapwiqroFtcLiw6RA29wZTdzj5XAcBUch4TqkFsuBb92kdiT3YRjuaVY8nm45K/zIvBzksbjwIAEiODEKRSoFpv/2+Ho2yyZbD0xJo/UFlrQESQCipFQ7ArdY7u9Rcl4uUbBjj9cu9uySkZgNW//Y0dT4zGnzmm5cR0PlhiqSVyl91tLlW1pteNViVHRJDpwotttUVqSgI6x4Qg9fVfAABhWiV2PDHa4/E7XfO7TIclWxoaDWqUptdiqEaJUHVD0J2emYt7HTQzFInHff3Hkx6NS+Qsey9eeLC9WJAQocVV/RPwzs/ZVvffGGLQ/8i4Hh49vwq5DJd0iUbhEQGXtJDXFhGRL3kcdM+ZMwclJSXYs2cPRo0ahXXr1iE/Px/PP/88XnnlFX+MkYiIfOBMkSno7hAdDAD1QXel1ZxWsXN5TKga1fUBzV/nKwEA0SEa85fhnvFh2JNdhE/32K+v7Uy4VonHU3shIkiN4irT/UQEqRAbrjFfEOgUHYy543uYAzvAccdig1GAViVHZa0BwSoFDEbBPDZpJbUCvtp/FuP6xDvNdnqy5JR4gcCySV2gcJTdTWgh5b9iBjlErUS4Vlyn237+tOUyeBW6OgiCeNlEGk/6BIivgZMF5eZMd7muTlLX8caIDFZh0XV9HZ4TR2Xd4nvpoo5RdufX2aoCrgJ1zsMmInLO46B769at+OabbzB48GDI5XJ06tQJ48aNQ3h4OBYtWoTJkyf7Y5xERNRIZ8TANsYUdP9yAjhdWGm1j5jpjglRo1xhCl7+Omfap02oKZOYnpmLbw6Y1tk++Hep5Psvq6nDI58fsNoWEaRCmxC1OehOig3Blf0Srb60Oyr5Tlt/GIX1Tdtyy2owfPFWcxAoltS6yiqKIULa+sMYlxzvMEjwZMmpuHBTabOuLrCqvZxmd0trMHtlBpZNH9isgbeY6Q5WKxBe32RMDKplFou5W55LQQCKq/RoG2a/zJwznvQJEH35ew5uGdIBAJB9rtIna8W7olHKzXO5HXFU1g04DsgHdYrC76eLkVdajaLKWkSHahAf7jpQ5zxsIiLnPA66KysrzetxR0VF4dy5c+jRowf69u2LjAxXX3CIiKixGlPmK2a6O9ZnugFg58lCDO9WaD5OQ6ZbYw5a/qovL48JVTsNwrz1zk9ZOHS2zPz71qPnrAJoW1KDwNSUBDwytrtV2a8ty0y1o2DEkyWnNCpTl+pAynRLKa93ddGiKVTU1me6NUqE1We6DUZTvwIxywwABTad94sqaz0Kur1Zy7uostacYRcrO/wpr0zn9LXsjqOA3NVxXGXOiYjInsdBd8+ePXHs2DF07twZ/fv3x9tvv43OnTtj+fLlSEjg1U0iIn9pTJmvwSjg0FlTVvqPf0qx8+R5AMCBv0sw7d3diA5R4doB7XCioCHANtTXl56tv7/oYLVHS3FJ8f7OU3bbnGVRPQ0CO7cJkTQGZwGVJ0tOiUFVbZ3RLsvaWnlSXu+v9ZPdXWSqrF//OkStQJBKYZ56UFajtw66bZalK6zQAZDexM/btbzrHNVo+5E3Fwe85SxzTkRE9jwOuh9++GHk5uYCABYsWIDU1FR8+umnUKvVWLFiha/HR0REaFyZr22w/t0fuXb7FFXqrQLgM4WViAsPstpHbzT6vUQWcJ5F9TQI9CRT7YgnS06JzbMAU7ZbW5/5lqKlNinzpLzeH6RcZKoyZ7oVkMlkCNMqUVKlR3lNHRIiLMdoHXSfr/Qs8+zt0lux9dl0tUKO+HCt1Trw/uDtxQEiIvIvj4Pu6dOnm38eNGgQTp8+jaNHj6Jjx45o06aNTwdHRESNK/P1thz87Z+zcdulHa22KeWeLYcVGaSSvK6wLUdZVE+DQE8y1c446/xsO39Vo2wIsj0Jultyk7LGXrRoDKkXmRoy3aavM+FaVX3Qbf26K6gPdsVMuCnTLZ3lBRip4sO16JtoivxzSqpR4+f5/gluXstERNR8PF5Q9Nlnn0VVVZX59+DgYAwcOBAhISF49tlnfTo4IiLyLMNryZOOy46s3HPG6veECGnB1QNXdMNnd1+K/9060Mt7bmAZaHsaBIqBEuCoT7XpWZHSaTk1JQE7nhiNz+6+FK/fPACf3X0pdjwx2iooVilkECvKpTZTEwNL23MrBpbpmfYVCU1JvGjh7NmRwT+BnruLTIDpIpM4dxsAgjWmixyh9f//w+F87MoqNE+ROFef6U5qa5pyIPYu8ERqSgL+dWWy5P3/fWWyubnbqcIqh2tz+xK7hhMRtVweB91paWmoqKiw215VVYW0tDSfDIqIiBp4W+brTcdlS4JN1DO4k+sgDADUChkeGtMdQ5NicGnXGLf7u2MZaHsTBIqZ6nibCwaRauDNm/tLziaL81evHtAOQ5Ni7IIbmayhxFzKWt2eBJbNxfKihS1/Lg/lyUUmyyXD0jNzcbK+J8HbP/2Fae/uxvDFW5GemWsOunsnhAMwdek3GAXsyirENwdyzAG6uG1dxj94/5e/sG5/jlXwLnbwF8+1OJfclkouQ1SI2mr9eH+Ry4C3bmneLvJEROSax+XlzhrEHDx4ENHRLGsiIvI1b8t8fT3Xtm24xukcZ1GtQcDI/2wzl0e7298ZR6XfnsyxtmTbaTkmWIlzh3djQp84D0bknkapQI3eKKmDeUtoUiaFeNFi/ld/otgiUxsVosaL16b4JdDz5CJTRX2mO7+sxmU5uri9V3w4vsFZHDpbhuGLt1qdA3GtdUcZ6cggFWYO64zK+vubmBKPrw+cRWWtAe0itcgpMaBzTDBO1S99pzcKmPbubvPa4f60dNpFmNSPATcRUUsm+RJsVFQUoqOjIZPJ0KNHD0RHR5v/i4iIwLhx43DjjTf6c6xERBckb8t8fT3Xtk2Ixmnm2JJlebSr/VMSwyGDfem3uwDa0fHiI7Qum8lZZqov6RINf1ThmjPdEsrLm7tJmSdSUxLw6ISeVttG9WwDXZ3RKgvsiqOssjOeXGQSG6ntzCpyWjUgbtcoZehcv0b9H/+U2l30KKnSOy0BL6nWY8mWE3jvl78AAAM7RaF9lGmcOSWm44gBt6WymjpJj8UbCRFaLJ8+EJP6JfrtPoiIyDckX4J97bXXIAgCZs2ahbS0NERENLQFVavV6Ny5M4YOHeqXQRIRXcjcNXESAExKMWVyLTtfe9tx2ZmY+tLa1JQEjO4Vh0sX/YgiB12gbZu7iZnmrUfycfcnv5v3G9M7Dg+M7ua2SZmtlrpGsEYlBt3uM93N2aTMG+I610q5DHVGAV9lnMVXGWcBuG/85mmzOCmv26hgFfLKanCmqBoAUKFzH9xqlApEBavd7ueKeK3gxe+PwGA7/8KPxMqOR8Z2R+c2IS3mNU9ERNJIDrpnzJgBAOjSpQsuu+wyqFQqvw2KiIisiRneR744iOrahkyqXGYKBN7feQrv7zxlFcx403HZGbVCbrXu8e+nix0G3CLb8miFXIZxfeLrS3FNwVdxZS3GJcd7FUC3xDWCxQ7mUuZ0+6KzelPKr+/+7WjdaVfL1nmy1J3l0mk3X9wRr2057nQ8xVV6PPL5AY8eQ1lNHTYe8k1zuhoJF1akkAGIC9fglRsH4HyFDrFhWhRX1uK57z27EEVERC2bx5ONunTpYl6n25GOHTs6/RsREXkvNSUBn+09g5+Onzdvs42BbIMZMVi/79MMq33jwzWYNqQjiqtq8dGu03ZN02yFaxUwGAVzMOxNeXR6Zq5V1+iPd5/G5iP5ARNMeFJe7uqCiD+blHkrr7Ta6d+cLVvnyVJ3mw/n2WXDI4NVPu/4vW5/jk+P1xjimV14VR8M62a95OqElJZXyUFERN7zOOju3Lmzw0ZqIoPBv+tQEhFdyPJKXa8v7CgAGpccb/77s1f3QffYMOsy9M4xuG+V62z4+Uo9hi/eag6QPS2P9iTj2Vo1BN3SsqDiBZFHv/zDqjzaH1lNyyyysyDO1T5/nbefr2zJUeM3qc3ilm49ide2HLd7bfhjia2yav/NsfaUq/PcEis5iIjIex4H3fv377f6Xa/XY//+/Xj11Vfxwgsv+GxgRERkL9dFxlFkGwCdK9fBKJjm4956SSe7YGtSvwQslw+0yzTasgyQxyXHSy6P9iTj2Zqzeebycg9Kj1NTEvBrViE+3nUaADBrWGc8Pdm3GW4pc6rd7VNY6fpij8iyskFqNcSHO7N90nOgtfnv1P4Y1r2N+x2JiKjV83gByf79+1v9N3jwYNx9993473//izfeeMOjY/3888+YMmUKEhMTIZPJ8PXXX7u9zfbt2zFw4EBoNBp069YNK1as8PQhEBG1SpW6Oo+6IYtBz9n6QD0uXOs0mEtNScCOJ0bj0zsvQWSQ454dlutHAzCv4eyu+7gny2O1ZuZGanrPKr5KqxsyuhFBap8H3LNXZtg9/5Yd5t3ts/5gDip10h6TZQWE1GqIkmrfZ7Rbg/MSL2QQEVHr53HQ7UzPnj3x22+/eXSbyspK9O/fH//73/8k7Z+dnY3JkyfjiiuuwIEDBzBnzhzcdddd2LRpkzdDJiJqVfLKPFs+Sgx68uqDKVfLfAGmkla5XOYyCLIMkKUu39WalsdqDE/Ly0WWDemKfBiIuaswAICF3x7Cwm9d7/Pcd0fM26QuW2cwCjAaBacXcMTbuPp7oGspnemJiMj/PC4vLysrs/pdEATk5uZi4cKF6N69u0fHmjhxIiZOnCh5/+XLl6NLly545ZVXAAC9e/fGjh07sGTJEkyYMMGj+yYiam3yXGSLLdl2vj5bYsp0J7gJugHPA2Qpy3e1tuWxvOVNeTlgE3T7cB6zlAqDvDL3PQIKyk37xISqUVRRa16+SmRb2eCoVN2ZmcM6Y8mWE273aw5alRxymQxVtdKy/OLz8vCYbvjo19NOL161tM70RETkfx4H3ZGRkXaN1ARBQIcOHbB69WqfDcyRXbt2YezYsVbbJkyYgDlz5vj1fomIWgIxiIkJUaOwPlBzFwABDcG6lKDbmwDZXdOn1rY8lrc86V5uqdgi6C52sQybp3xdOdC1TQheuCbF5brqzhrm2YoKVmHRdX0xLjkeq3/722dryfuC+B567aYBGJccj6VbT+LDndlWQXRksClDb9nszfJ56J0Qbu5M7+79SUREgc/joHvbtm1Wv8vlcrRt2xbdunWDUunx4TySl5eHuLg4q21xcXEoKytDdXU1goKC7G6j0+mg0zVcyRcz9Xq9Hnp9y51HJo6tJY+RpOG5DAwt4TzmFFUCAJITwvDLyULIZUCbUI05EwkAUSEqPDslGWN6tjGPNafY1Hk6NkztdvwXtQ9DfLgG+WU6FwGyBhe1D/PouXh6Yk88uPqg04sET0/sCaOhDsYmWADDX+dSZUp0o1on/d8XQRDMF1AA4HyFzifjMhgF5Je67jjuqbahaozp2Qajul+O6R/8hn2nS3DrkA54ZnIvKOQy1OhqsfDbQy6DZ3Fd+esHJmJU9xjsOlmACcmxWLHrjE/H2hjxERo8PbEXxvRsA6OhDveN7Ix7Lu+EfaeLUVCuQ2yYBoM7RQGA3TaFXAa9Xo8xPdvgzZv74/kNR62qCSyPzX8TrLWEz1hqPJ7HwMFzKY3U50cmCO5WZ20aMpkM69atwzXXXON0nx49emDmzJmYP3++eduGDRswefJkVFVVOQy6Fy5ciLS0NLvtq1atQnBwsE/GTkTUFD7/S45f8+UYm2jElrOmrOr9vevwvyMNFzyv72zAiATrj/UlfypwqkKGmT0MGBDj/iP/YKEMHxwXW35YZuNMt53Vw4j+Eo7j6LhfnZKjpLbhmJFqAdd19u54Lc26U3Jsz5VjTKIRV3WSVmKuMwCP7204fxFqAc8OatyVB0fPs2MCIlQAZEBpLeB4xrYAjRzQGWUYlWDEtZ1Nj2vD33Js+keOS2ONmJZk2naiVIalhxWSxhilNkJnlKGqzvb15Zvsb6hSQEUdPD7eNZ0MGJkgwFdJaKMAZJXJUKYHwlVAUrjvjk1ERM2vqqoKt9xyC0pLSxEeHu50P69S08eOHcObb76JI0dMzVV69+6NBx54AL169fJutBLFx8cjPz/falt+fj7Cw8MdBtwAMH/+fMydO9f8e1lZGTp06IDx48e7fGKam16vx+bNmzFu3DioVBduo5lAwHMZGFrCeVz3SQaQfx6jLk7Bnk3HUV5Th9COycCR4+Z9NLGdMCG1t1UGrubQnwB0mHzFZejfPsLt/UwCMPBQvl2WLiFCi6cn9sKEPnHOb+zmuI8bBYfZwabkr3N5ZPMJbM/NRvtOnTFpkrR/D/8prgb2/mL+vdqowMSJ4+2mcUm16VA+Ptx10G2ptqz+f1+4vj8A4MHVzm4jQ6e2ITieX4mE9h0xIbU3FHIZZJl52PT5H6hWR2HSpEsAAOv/yAUO/ylpnMW1jvq4un7MMgBx4WoAMreVGPNTe+Lhz/8AAI/K1kcMGYAr+7Xu9eJbq5bwGUuNx/MYOHgupbHtd+aMx0H32rVrcfPNN2Pw4MEYOnQoAGD37t3o27cvVq9ejeuvv97TQ0o2dOhQbNiwwWrb5s2bzeNwRKPRQKPR2G1XqVSt4gXUWsZJ7vFcBobmPI/55aYy5HbRIWgTqkF5TR0yc8sBmOZVG4wC9p4qwRWv/uKwiVWHmFDJY79yQHtM7NfOZYM0b6gADO/hXdDua74+l0Fq07H0Rkg+bnmtacpARJAKpdV61NYZUSvIEar2/Jq4wSjghY3HJAWZ8TbrdCuVCjy+5k+U1TSUySnlMmiUchzPN43xs9/+wfbj57FgSjKS20UCAE4WVAAyBfadLsZf531bzm5JfNUtvCoFADB7ZYaLfgZ9kJqSALVKKbmhmyghMoSf082M/1YGBp7HwMFz6ZrU58bjf9Uff/xxzJ8/H88++6zV9gULFuDxxx/3KOiuqKjAyZMnzb9nZ2fjwIEDiI6ORseOHTF//nzk5OTg448/BgDce++9WLp0KR5//HHMmjUL/9/enYc3WaV/A/8mIUk3ulFoyiIttBZK2RlKRRmEQouIoo6DCAo4w4xIlUVRcKGA8wq4ICgFZgP8XYyizgiKQMeyKlBBWhBKAWktMEoXuu9bct4/SkLTJm3SZuf7uS692uc5eXLSk5Tezznnvg8dOoTPPvsMe/fuNfdlEBE5PLVG6ILeAE8lrhdWAADyy2rg7yFHNoBzv5QAAEb09sPJ7KLGIMiI1KvFeMCMWby2EqSRvtt1uk3PXq7NXN7D1x21DWrU1GtQXFkHL6X5QXdb2cqbem1Sf13ADTRmof/hahH+eewqfN07oaS6AQ0agYZmmbu1tbs/fHIo5FIJKuvUGP6XZLPqx7dH85sEm2cOazWhm/Y1aTPr55ZW4829F1FcWefSyfyIiMgxmf2vek5ODp5++ukWx2fOnIl33nnHrGudPn0a999/v+577TLwWbNmYfv27cjJycH167eTq4SEhGDv3r1YtGgRNmzYgJ49e+If//gHy4URkUtRa4TBjMlar/znvC5T9v+KGsuB3RsWgJPZRa1ed9XXFxAbqWLWZCtpT/ZybdDt76lASZUCN0prUFhZh17+5uccMSdb+aq9GZg0KEjvvXCtsHGmuqTaeACt3XX9+u50qG+lhLFmwB1/fyhGhwa0WGWhDahTMvPxzXcnMfG+KESHdmvx3m5648hdIWtjhpwZxYmIyDrMDrrHjh2L7777DqGhoXrHjx07hvvuu8/sa7WWx2379u0GH3PmzBmznoeIyFkkpedg6Rfn9UoRGdK8FvRPuW3vKcotq8XGQ5lYEBPWoT6SYe2p060XdFc3Bt3tLRtmTp3z/PJanMou0lvJkHXT+CqJpgTQ5vvTUsICvYyutpBJJYgK8UfhRYEoE7Y+xEUGmTRDTkREZGlmB90PPfQQXnnlFaSmpmLUqFEAGvd0f/7551i5ciW++uorvbZERGSapPQcPHurtq+59pzLNand+wd+QrjKiwGGFdye6W5f0F1cpdA7Zi5tPXRTl5g3nRlvUGt0M92OxJwbCaZouuTckrkKiIiIWmN20P3cc88BADZt2oRNmzYZPAc0lgBTq21QcJWIyAWoNQIr92TY5LlW7snAhAguM7e023u6Tf+3r7iqMcD281DA37Nl0N10X3/zANHQuYQpESbfuGka0P5SXA2NA1Vts+Yea+YqICIiWzM76NZoTL+DT0REpjEnCVZH5ZTWtFhaTB3XoeXlXo3LywGg6FYgnpSe02IpdNCtpdAAWpzzdZdjzuhg/G5Yd/w77UYbfZXqAlq1RmD/+RyT+2xt3GNNRESupl11uomIyLLMSYLljM93J+jQ8nIPBUo8GoPu4so6JKXnYN6OtBaZtnNLa4zOZJdU1+P9A1cgl7UdqMplEnyfVYgfrhZh+4mrBhP2WYOvR2NplaZ7wpsnNuMeayIicjXtCrp/+OEHHD58GPn5+S1mvtetW2eRjhER3UksvXfV0Z7vTtCR7OV+nnL43drTXVBRi5V7MgyWtjJlBXi9urHVpEgVzv6vRG82XCoBNAKoqFVjxj9PmtxPLV/3ToBEgtKqepP6otU0CzkAvWXxw3v7IfVaMfdYExGRyzI76H7rrbfw+uuvIzw8HIGBgZBIbv/D2PRrIiIynTYJVm5pjVnBjLlYj9h6lPJby8vNqNNdfGvGt4unEqW3vr5eVGWRrQb/vZCLD6YNRZfOSiRn5GLr8avt3retXboePy4MyRm5BktvtaZ5FvLmWxu41YGIiFyZ2UH3hg0bsHXrVsyePdsK3SEiujPJpBIkTInAvHZmLzcF98pal7nLy9UacTuRWpOZbkuV49IIIH7nGWx6cij2p5uW3b45Q3WyjZXeag1XVhAR0Z1MavYDpFKMHj3aGn0hIrqjaYMZv1v7XrV83eVYMD4Urz3Q36zrNY+rVT5u2DxzGPfKWom5y8uLKusgbk0V/5Rbjs7KxvvgpRbeX/36l+ntnjnXzlA3v0kTFxmEY6+Mw7/+EAVfd7mRRzfe6AniygoiIrrDmT3TvWjRIiQmJmL9+vVW6A4R0Z0tLjII1XVqLPrsR4R188KqhyN1s4xfnv3VpGs8Hd0bkyKDuFfWxnTLyw3MdDcv71VcWYflX6Xrzs/85yndTRJzErGZoqiy/UF8azPUMqkEo8MCsOaxgboVGk2Xm3NlBRERUSOzg+6XXnoJkydPRt++fREREQG5XP8O9xdffGGxzhER3Ykq6hpnSvt09dTb62rqEt1JkUG6x3GvrO1oZ7rrGjQQQujynBgq/WWII9XJBkyfoTa23JxZyImIiBqZHXS/8MILOHz4MO6//3506dKFydOIiCys7NbyYm83/ZuabSVbY5I0+9IG3UDjbLWbXGa09Jet+XsqUFxZZ3I/JDBvhjouMggTIlR6s/lcWUFERNTI7KD7o48+wn/+8x9MnjzZGv0hIrrjldc0AAA6Nwu6myZba545mkt57a+T9HbQfSyzAGPCuhot/WUr2hsxb0yOwPyPTcs47uchx+pHB5o9Qy2TSriygoiIyACzE6n5+/ujb9++1ugLEZFDUmsETmYXIbVAgpPZRVBbeR1weU3jTHdnt5b3RbVLeVU++kvNmSTNvpLSc3D/e0d03//xo9MYuuobi5T+aq+mN2IeGGT4fdOUr7sci2LCcPr1CXwfERERWZDZM90rVqxAQkICtm3bBg8PD2v0iYjIYejvx5Xh/66cRpCV96qW3Zrp9jaSFZpLeR2LsSXklXWmZTHvKAmAP40JwVc/5rS6p7r5+ybAUwlIgIKKWr6HiIiIrMjsoPuDDz5AVlYWAgMDERwc3CKRWlqa9WrMEhHZkrFgKre0BvN2pFltZrm1mW4tLuV1DGqNsOsS8qY3gF6O69/mjRi+b4iIiGzP7KB76tSpVugGEZFjaS2YEmicXVy5JwMTIlQWnx3U7un2biXoJsdwKrvI5kvInxp1F4b19ofKWz+wZkBNRETkmMz+iy4hIcEa/SAicihtBVMCQE5pDU5lF1k80DGWvZwcT3655QJuU5KcAcCIYH88PKSHxZ6XiIiIrKvd0yipqam4ePEiAGDAgAEYOnSoxTpFRGRvpgZTlgy6tIxlLyfHY2rt9Lb4e8rx/u+HYNa2H2z2nERERGQbZgfd+fn5eOKJJ3DkyBH4+voCAEpKSnD//fdj586d6Nq1q6X7SERkc6YGNtYIgMpu7en2dufyckenrZ3e3iXm2o0Jbz0yEPeGdWUddiIiIhdkdsmw559/HuXl5bhw4QKKiopQVFSE9PR0lJWV4YUXXrBGH4mIbE4bTBnbrS1BYxIrSwdADWoNqm5lveZMt+PT1k5vr6al3ppeq/n7jnXYiYiInJfZQXdSUhI2bdqE/v37645FREQgMTER+/fvt2jniIjsxV4BUEVtg+7r1rKXk+OIiwzClpnD4Oth3k2SNyb3x7FXxullwGcddiIiItdj9l90Go2mRZkwAJDL5dBoNBbpFBGRI9AGQLfrdDdqXv/YksqqG4Nud7kMcpnZ90XJTrQ1sDceysTWYz+jtKbBaFvtMvHZo0MM3rRhHXYiIiLXYvZfdOPGjcOCBQtw48YN3bFff/0VixYtwvjx4y3aOSIie4uLDMJ3L98Pbbzj6y5vMTtpSWUm1OgmxySTSrAgJgxpyydiUczdBtuYukpCW/7r4SE9EN23CwNuIiIiJ2Z20L1x40aUlZUhODgYffv2Rd++fRESEoKysjJ8+OGH1ugjEZFdVdWrobmV2aqmQW3VAOh25nIG3c5KG3xvmTkMQVwmTkREdMcz+6+6Xr16IS0tDQcOHMClS5cAAP3790dMTIzFO0dE5AhKq+p1X9fUa1DboIayk8wqz3U7czmTqDk7LhMnIiIioJ11uiUSCSZMmIAJEyZYuj9ERA6npEnQDTTORiu9rBN0s0a3a9EuEyciIqI7l8nLyw8dOoSIiAiUlZW1OFdaWooBAwbgu+++s2jniIgcQUl1nd735a0kyeqocu7pJiIiInIpJgfd69evx9y5c+Ht7d3inI+PD/785z9j3bp1Fu0cEZEjKG42011WXW+kZcdps5d7c6abiIiIyCWYHHT/+OOPiIuLM3p+4sSJSE1NtUiniIgcSWmV/ky3dt+1NWhnur05001ERETkEkwOuvPy8gzW59bq1KkTbt68aZFOERE5kuZ7urWz0dbAkmFERERErsXkoLtHjx5IT083ev7cuXMICmIJFCJyPSXNlpNbd6b71vJyZi8nIiIicgkmB90PPPAA3njjDdTU1LQ4V11djYSEBDz44IMW7RwRkSMormqeSM36QTdnuomIiIhcg8l/1b3++uv44osvcPfddyM+Ph7h4eEAgEuXLiExMRFqtRqvvfaa1TpKRGQv2jrdcqlAvUZim+XlSs50ExEREbkCk4PuwMBAnDhxAvPmzcOyZcsghADQWLM7NjYWiYmJCAwMtFpHiYjsRbu8vIsSyK3m8nIiIiIiMp1Z6xd79+6Nffv2obi4GJmZmRBCICwsDH5+ftbqHxGR3WmXlwe4CeRWS6xaMox1uomIiIhcS7v+qvPz88NvfvMbS/eFiMgq1BqBU9lFyC+vQbfObhgZ4g+ZVGLy47XLy7soG78vq7Hi8vJq7ukmIiIiciX8q46IXFpSeg5W7slATuntJJBBPm5ImBKBuMi2Ky4IIW4vL3dr3FZjrURqlbUNqFNrAACXc8sR5ONu1s0BIiIiInI8JmcvJyJyNknpOZi3I00v4AaA3NIazNuRhqT0nDavUVHbALWmMdju4tZ4zBqJ1JLSc3D/u0d03//ho9O4d+0hk/pIRERERI6LQTcRuSS1RmDlngwIA+e0x1buydAF1MaU3Fpa7iaXwkfe2NbSidS0Nwfyy2v1jptzc4CIiIiIHBODbiJySaeyi1rMcDclAOSU1uBUdlGr19EG3T7ucrjJGo+1J5GaWiOQklWIL8/+ipSsQl2wb6mbA0RERETkmLinm4hcUn658YDbnHYl1Y2Zy33d5XC/9Ruzsk6NBrUGnWSm3bdsbV+5j7vC5JsD0X27mPR8REREROQ4GHQTkUvq1tnNIu2Kb810+3rI4S67fbyitgG+Hoo2M6Nrl443n6fWLh1/ZnSwSf009SYCERERETkWBt1E5JJGhvgjyMcNuaU1BpduSwCofBqD5NaU3qrR7eMuh0wKeChkqKpTo6y6Ad//XNhqZvS2lo5LAOw6+6tJr8fUmwhERERE5Fi4p5uIXJJMKkHClAiD57Tz0AlTItosyaXd0+3rLgcAdFY23qs0lhk9p7QGz+5Iw4YDP+H7nwvbXDpeVFkPf08FjPVCgsZAvq2bA0RERETkmBh0E5HLiosMwuaZw+Dtpr+op2tnJTbPHGa0Trc26dmutF9w7MpNAEBVXQM0Auh861pbjv5scAZb6/0DV/Dcv9JM6mdUiJ/R2XjAtJsDREREROSYuLyciFxaXGQQTmQV4v9SrumOvff4YNx3d1eD7Q0lPQOAr8/n4ZhCBj/vxvC46Nay89aUmpjlfH96nsHjqiZL1YmIiIjIOTHoJiKXl11Qqff9LyXVBtsZS3qmVVIHlBRUWbh3hi2KCUP8uDDOcBMRERE5OS4vJyKXdyWvAgAwsIcPAOBaYcvAubWkZ7fZJgCWANj5w/9s8lxEREREZF0MuonIpZXX1CO3rHGp+Lh+3QAA14sqW7Q7lV3UatIzW2pam5uIiIiInBuDbiJyWWqNwO4zjSW5fN3liAjyBmB4ptsR62A7Yp+IiIiIyDzc001ELql5QrSS6nq8tvs8AOB6YRWEEJBIbi8Xd8Q62I7YJyIiIiIyj0PMdCcmJiI4OBhubm6IiorCqVOnjLbdvn07JBKJ3n9ubvzDlIhuM1ZDu7CiMeN4eW2Drv621sgQfwT5OM7vEtbmJiIiInINdg+6P/30UyxevBgJCQlIS0vD4MGDERsbi/z8fKOP8fb2Rk5Oju6/a9euGW1LRM5PWzf7y7O/IiWrEGqN8XRnrSVEa3rso5SreteSSSVImBLRRqq01tOsWRJrcxMRERG5BrsvL1+3bh3mzp2LOXPmAAC2bNmCvXv3YuvWrVi6dKnBx0gkEqhUKlt2k4jsxFDd7KBW6lebmhBt/YErAK7A112OOaODET8uDBMiVJg8KAhfn8sx8qjWg2AvZSdU1Da0+dytkUqAjdOHsTY3ERERkYuw60x3XV0dUlNTERMTozsmlUoRExODlJQUo4+rqKhA79690atXLzz88MO4cOGCLbpLRDZmbJl4bmkN5u1IQ1J6y+DY3ORjJdX1eP/AFfRfnoTBK7/RC7h93Drhd8N64KlRvU261u9H9OxwUbGN04figUEMuImIiIhchV1nugsKCqBWqxEYGKh3PDAwEJcuXTL4mPDwcGzduhWDBg1CaWkp3n33Xdxzzz24cOECevbs2aJ9bW0tamtrdd+XlZUBAOrr61FfX9+ivaPQ9s2R+0im4Vi2j1ojsOKrC0aXiUsArNxzAWPDuuiWYas1AnmlLTOTm6KuQYO6Bo3esbKaBvwn7Vc8f39fk64xLjwAw3r54C/7LiG3rLbF+SAfJZbFhiOroBLbU66jtLpe79xrk/phQv+ufK9YGT+TroNj6To4lq6B4+g6OJamMfXnIxFC2G6TYjM3btxAjx49cOLECURHR+uOv/zyyzh69ChOnjzZ5jXq6+vRv39/TJ8+HW+++WaL8ytWrMDKlStbHP/444/h4eHRsRdARFZzpVSCjRmyNts9118NqQQ4Xwyk3pSiosHS+6AFfOQAJEBpHWB4ibmArwJIGNbYF40AssokKKkDKuqBznLARwH09RbQbtPWtimrB7zl+ueIiIiIyPFVVVXhySefRGlpKby9vY22s+tMd0BAAGQyGfLy8vSO5+XlmbxnWy6XY+jQocjMzDR4ftmyZVi8eLHu+7KyMvTq1QsTJ05s9Qdjb/X19UhOTsaECRMgl8vt3R3qAI5l++w5lwNknG+z3fYsBarq1FbsiQSl9UD8b4Ox8Wg2JNBPpya59f+/PDoYsQMCDV6BHAs/k66DY+k6OJaugePoOjiWptGuom6LXYNuhUKB4cOH4+DBg5g6dSoAQKPR4ODBg4iPjzfpGmq1GufPn8cDDzxg8LxSqYRSqWxxXC6XO8UbyFn6SW3jWOpTawROZRchv7wG3To3lsdqmq07yNfTpOtYN+C+rU+3znjmbg325XroLR1XtZLUjRwbP5Oug2PpOjiWroHj6Do4lq0z9Wdj9+zlixcvxqxZszBixAiMHDkS69evR2VlpS6b+dNPP40ePXpg9erVAIBVq1Zh1KhRCA0NRUlJCd555x1cu3YNf/zjH+35MojIDKZkJC+urNUt1XYE3TorMbiLwMszxuDML+VGbxYQERERETVl96B72rRpuHnzJpYvX47c3FwMGTIESUlJuuRq169fh1R6O8l6cXEx5s6di9zcXPj5+WH48OE4ceIEIiIi7PUSiOyqrRlje9L2Lbe0GkWVdfD3UuJaQSXWH7zSoq02I/nmmcMAAPM/PmPDqtjGSdA4mz2itx/+e7Gxnnd03y727hYREREROQm7B90AEB8fb3Q5+ZEjR/S+f//99/H+++/boFdEjs/cGtaGWCtoN9S31mgD7IQv0yGRSK0WcHsoZCYvSdf+FBKmRDjMjQwiIiIici4OEXQTkfm0NaybB6dNZ4zbCrwNBca+7nLMGR2M+HFh7Q40jfXNFHnlde16TlP9/akROH2tGH/9NqvN4Lvpfm2WzCAiIiKi9mDQTeSE1BqBlXsy2qhhnYEJESqjgbOxwLikuh7vH7iCbSeuYs2jA81OENZa3+xJu0x8VN8uGB0WgPhxodh4KBPbjmejpEm9bH9POR4Z0gMxESqHWqpPRERERM6JQTeREzqVXdTqsm0BIKe0BqeyiwzuPzYlMC6pqjc4Y958n7avhwIlVY37tVXebtAIYfKSclsxtExcJpVgQUwY4seFOuyeeCIiIiJyfgy6iZxQfrlpQa22XfN926YGxgLAq7vOY1y/QCg6SU3ap62Q2TdgdeskhUwqQWWTpeOtlfViYjQiIiIisiYG3URO6GpBpUntunV2M7pv21RFlfWIeusARocG4OtzOW22r1PbZ2G5p0KGP43pg/hxYQDA2WsiIiIicggMuomciFojsPFQJt4/0LLkVlPa/cvFlXWY/7HhfdvmKK6qNyngtoXm2ceNJX7j7DUREREROQIG3UROIik9Byu+uoDcslqT2r8xuT/e3Ot4Cc066u9PjYBUKuEsNhERERE5BQbdRE7A3BJcC2Puhp+n0uESmnVE0+zjDLKJiIiIyFkw6CZycO0pwRUc4GFysjVbe+2Bfojo7oOCilpcLahqUbLLEEPZx4mIiIiInAGDbiIH11Z5MEMCPJW4lFtmpR61j3am+pl7++gFzsbqZTfVWvZxIiIiIiJHxqCbyMGZO2Mtl0nw/M4zKKqss1KPzNfaTLWhetkBnkpAAhRU1HLfNhERERE5NQbdRA6uW2c3s9rXq4VDBdyAaTPVrJdNRERERK6IQTeRgxsZ4o8gHzfkltbYLBO5RAIIE57sd8N6ILpvAFKyCpB8MR+lTZaH+3vK8ciQHoiJUHGmmoiIiIjuWAy6iRyYWiNwKrsIkyJV2Hr8qs2ed3Z0b2w7cc3oeT8POVY/OlA3c/3Y8J66vrKUFxERERHRbQy6iZpxlOAxKT0HK/dk6CVRaz4D7e8pR1Fl65m/22PigCBE9enS4vl93eWYMzoY8ePCDO7N5vJwIiIiIiJ9DLqJmjAU6AbZIXO2sbrc2oC7u68b3nt8CHLLarDo07MWe15thnHtjYYJESqHuAFBREREROSsGHQT3WIs0M0trcG8HWnYPHOYTQJvU+pyl1TVY2SIP05lF1nseQ1lGOfsNRERERFRx0jt3QEiR9BaoKs9tnJPBtSali3UGoGUrEJ8efZXpGQVGmxjah9SsgrxfvLlNutyV9WpcSq7SJdkzZy5ZwmAP48JQZCPflZ0lY+bzW4sEBERERHdKTjTTQTgVHZRq4GuAJBTWoPvswoxOixAd9xSy9ENXact+eU1kEklSJgSgXk70iAB2sxu3rRvL8f159JxIiIiIiIrY9BNhMYA1hTzP07Dmscas3YbW46eU1qDZ3ekYdOTQ/HAoO5Gr6VN2JackduuzOTa+t1xkUHYPHNYi6Dd31OOhwd3R08/D/h7KaHy1g+suXSciIiIiMj6GHQT4XYA25aS6nrM25GGxCeHYtXXF1udWZ7/8RksyKvAs2OCoRHAyewiFFY1oFtnNxRX1uHNvebNbDcV6K3EyBB/3fdxkUFMekZERERE5IAYdBMBur3RuaU1bS7RBoAl/zmHylp1q20EgPUHr+Bv3/0MaGSo+v60RfoKACsfGsCSXUREREREToCJ1IjQGLC+MTnCpIBbAG0G3E1V1alR1dDurrXQ1UuBCREqy12QiIiIiIishkE33fHUGoENB67g1V3nrfgsHVvm3fTRNyvqcO/aQ0hKz+lYl4iIiIiIyOoYdNMdLSk9B8P/koz3D/yEkup6e3fHKGO1wxl4ExERERE5Nu7ppjuKNmN4fnkNsm9WYv3BK/buUrsINM5+r9yTgQkRKiZMIyIiIiJyUAy66Y6g1ghsPJSJbcezHXpG2xza2uGnsouYQI2IiIiIyEEx6CaX0XQWW1syCwA2HsrEX7/NQlWd6cnPnImpNcaJiIiIiMj2GHS7EENBpz2WHVujH21dMyk9Byv36Ne99vWQo65B47LBtpapNcaJiIiIiMj2GHS7CENBZ5CPGxKmRCAuMsip+9HWNZPSczBvR1qLZGMlVbZdRq7yVmJEsD++++kmSmssWCPMCAkAlc/tGX0iIiIiInI8zF7uArRBZ9OgFLB9hmtr9MPYNXNKa/DsjjR8ffZXrNyTYVJ9bWtaFBOG40vHY+OTw7Bp5nCrP592jj9hSgSTqBEREREROTAG3U5OrRFGg07tsZV7MqDWWDcstUY/Wrum1vM7z7YIyC3Fz0OOLTOHYcvMYQjyMbyEO8jHDVtmDsOCmLt1wW9BRa1V+tOUyscNm2cOs+kqBiIiIiIiMh+Xlzu5U9lFrQadtspwbY1+tHVN7XUtTQJgwfgwPD8+TBdIT4hQ4VR2EXJLq1FUWQd/LyVU3ob3q3d0j7WvhxyA/vJ4lbcS00feheAAT7vu1yciIiIiIvMw6HZypmautnaGa2v0w15ZuROfHIoHBnXXOyaTSky+WTAyxB9BPm7ILa1p86ZAkI8b3pjcH36eyhZZ1x0hKR4REREREXUMg24nZ+qsqrUzXFujH7bOym2pxHMyqQQJUyIwb0caJDA8G/+H0cGIiVC1Gkyz9jYRERERkfNj0O2ktCW0ckur4e+pQHFlndFZVV93OTRCQK0RVpstbWt2tz2ZtrXXtMaebU+FDH+8LwQjQ7qgoKLW4rPJcZFB2DxzmENklCciIiIiIvth0O2EDJXQak1JdT1m/OOkVQO+prO7xpibaVsmleCNyRF47mPj1zSXr7scc0YHI35cmNWXa8dFBmFChAopmfn45ruTmHhfFKJDu3GZOBERERHRHYRBt5MxVpPaFNrSXdbKeq2d3V2w8yxqGzS6434ecqx+dKDec2pn6vPLaxDgqQQkQH5ZjV6SsuLKOry5N8Ni/VsUE2aTYLspmVSCqBB/FF4UiOK+bCIiIiKiOw6DbidiSgmt1gg0LvNeuScDEyJUVgkAYweo4KWUobZBg15+7vhfcTVG9PZDdZ0a//zuZ/h6KJCSVYDki/kora5v+4IWwCXdRERERERkLwy6nYgpJbTaYs0SYmqNwL7zOSisrIdUAozr1w0fpVxD8sV8JF/Mt+hzmSr+/r5YNCGcM8xERERERGQXDLqdiCVLaFnyWmqNwMZDmdh2PBslt2avNQL4KOWaxZ6jvUaHdmXATUREREREdsOg24lYsoRW02s13V/dVhbvplnTiyrr8EtJNT4//Qsqahss1jdLaE+2dCIiIiIiIktj0O1E2irLZYrmwaihTOjaPdATIlR6yc5+uFqE7Seu6mazHZX2doG52dKJiIiIiIgsjUG3EzGlLJcptMGosUzoOaU1eHZHGjwUMlTVqTv0XNYilTQuYTdExcRpRERERETkIBh0O5nbZbnOoLbBvPnuzm6d8M7vBiEuMgh1DRq8uiu91RlzRw24JQA2Th8KP0+lXsmxgoraNpfHExERERER2RKDbicUFxmE4C4/4XJehUntw7p54Up+BUK6eKC6To2XPjuL/em5qHTQoLo1LP9FRERERETOhEG3E6pr0CDrZiUA4P89EomNhzL19mR7KmR6AfXEiEBcya/AuV/LsOizH23eX0tZFBOG+HFhnMUmIiIiIiKnwaDbCWXmV6BBI+Dt1glPjrwLT/zmLl3Cs6sFVdh6PBvA7aA78UiW/TrbBl93OWbd0xsjQ7ogv6wGxzMLkHwxH6VNkrVxdpuIiIiIiJwVg24HphHAyewiFFY16PYt55fV4MjlmwCA7r7u0IjGBGvRfbsgKT0H6w/81O7M5pbm5yHH/5saCT9Ppa7EmK+HAiVVdfD3UkLl3XL/9SPDeppVwoyIiIiIiMiRMeh2UP+9kIeVaTKUfH/aaJtLueW4d+0hXXmvlXsyHCLg9nWXY87o4HYvBdfeRCAiIiIiInJ2DLod0L5zOYjfadre65zSGszbkYaFMWF6+7ptzd9TjkeG9EBMhIoz00RERERERLdI7d0BAEhMTERwcDDc3NwQFRWFU6dOtdr+888/R79+/eDm5oaBAwdi3759Nuqp9e07dwPxn2jrcJseuG47ftUq/THGx60TfjesB96fNgSfzB2FH16bgDemDEB03y4MuImIiIiIiG6x+0z3p59+isWLF2PLli2IiorC+vXrERsbi8uXL6Nbt24t2p84cQLTp0/H6tWr8eCDD+Ljjz/G1KlTkZaWhsjISDu8AstJSs/Bcx+fMftxAkBJk8RjltY02RlrYRMREREREZnO7kH3unXrMHfuXMyZMwcAsGXLFuzduxdbt27F0qVLW7TfsGED4uLisGTJEgDAm2++ieTkZGzcuBFbtmyxad8tSa0RWLkno0PX8HWXo7S6vl37ug0lPTOW7IyIiIiIiIhMY9egu66uDqmpqVi2bJnumFQqRUxMDFJSUgw+JiUlBYsXL9Y7Fhsbi927dxtsX1tbi9raWt33ZWVlAID6+nrU11tvdthcJ7OLOrwne1b0XfjgUBYkgMmBt697Jzw9qjeeG9unSWDtrddGo26ARt3ysWQa7fvMkd5vZD6Oo+vgWLoOjqXr4Fi6Bo6j6+BYmsbUn49dg+6CggKo1WoEBgbqHQ8MDMSlS5cMPiY3N9dg+9zcXIPtV69ejZUrV7Y4/s0338DDw6OdPbe81AIJAFk7Hy3gqwCCqy5jzt0SfHFVipK62zPTvgqBqb018JIDJXVART3QWQ74KIC+3g2Q1lzGf5MuW+R1kHHJycn27gJZAMfRdXAsXQfH0nVwLF0Dx9F1cCxbV1VVZVI7uy8vt7Zly5bpzYyXlZWhV69emDhxIry9vVt5pG11yS7C/10xXh6sNRJI8JdHByN2QCAeBPCyRuD0tWLkl9eiW2clRvT24/JwO6qvr0dycjImTJgAuVxu7+5QO3EcXQfH0nVwLF0Hx9I1cBxdB8fSNNpV1G2xa9AdEBAAmUyGvLw8veN5eXlQqVQGH6NSqcxqr1QqoVQqWxyXy+UO9QaKDu2GIB835JbWmLUnO8jHDQlTIhAXGaQ7Jgdw792Bxh9EduFo7zlqH46j6+BYug6OpevgWLoGjqPr4Fi2ztSfjV2DboVCgeHDh+PgwYOYOnUqAECj0eDgwYOIj483+Jjo6GgcPHgQCxcu1B1LTk5GdHS0DXpsPTKpBAlTIjBvR5rRPdkLx4eidxdPJjkjIiIiIiJyEnZfXr548WLMmjULI0aMwMiRI7F+/XpUVlbqspk//fTT6NGjB1avXg0AWLBgAX7729/ivffew+TJk7Fz506cPn0af/vb3+z5MiwiLjIIm2cOw8o9GXpJ1QzNZhMREREREZHjs3vQPW3aNNy8eRPLly9Hbm4uhgwZgqSkJF2ytOvXr0Mqlera33PPPfj444/x+uuv49VXX0VYWBh2797t9DW6teIigzAhQoWUzHx8891JTLwvCtGh3TibTURERERE5ITsHnQDQHx8vNHl5EeOHGlx7PHHH8fjjz9u5V7Zj0wqQVSIPwovCkRx+TgREREREZHTkrbdhIiIiIiIiIjag0E3ERERERERkZUw6CYiIiIiIiKyEgbdRERERERERFbCoJuIiIiIiIjIShh0ExEREREREVkJg24iIiIiIiIiK2HQTURERERERGQlDLqJiIiIiIiIrIRBNxEREREREZGVMOgmIiIiIiIispJO9u6ArQkhAABlZWV27knr6uvrUVVVhbKyMsjlcnt3hzqAY+kaOI6ug2PpOjiWroNj6Ro4jq6DY2kabUypjTGNueOC7vLycgBAr1697NwTIiIiIiIicnbl5eXw8fExel4i2grLXYxGo8GNGzfQuXNnSCQSe3fHqLKyMvTq1Qv/+9//4O3tbe/uUAdwLF0Dx9F1cCxdB8fSdXAsXQPH0XVwLE0jhEB5eTm6d+8OqdT4zu07bqZbKpWiZ8+e9u6Gyby9vflGdxEcS9fAcXQdHEvXwbF0HRxL18BxdB0cy7a1NsOtxURqRERERERERFbCoJuIiIiIiIjIShh0OyilUomEhAQolUp7d4U6iGPpGjiOroNj6To4lq6DY+kaOI6ug2NpWXdcIjUiIiIiIiIiW+FMNxEREREREZGVMOgmIiIiIiIishIG3URERERERERWwqDbQSUmJiI4OBhubm6IiorCqVOn7N0lamLFihWQSCR6//Xr1093vqamBvPnz0eXLl3g5eWFxx57DHl5eXrXuH79OiZPngwPDw9069YNS5YsQUNDg61fyh3l22+/xZQpU9C9e3dIJBLs3r1b77wQAsuXL0dQUBDc3d0RExODK1eu6LUpKirCjBkz4O3tDV9fX/zhD39ARUWFXptz587hvvvug5ubG3r16oW3337b2i/tjtPWWM6ePbvFZzQuLk6vDcfS/lavXo3f/OY36Ny5M7p164apU6fi8uXLem0s9fv0yJEjGDZsGJRKJUJDQ7F9+3Zrv7w7iiljOXbs2Bafy2effVavDcfS/jZv3oxBgwbp6jNHR0dj//79uvP8TDqPtsaSn0kbEuRwdu7cKRQKhdi6dau4cOGCmDt3rvD19RV5eXn27hrdkpCQIAYMGCBycnJ0/928eVN3/tlnnxW9evUSBw8eFKdPnxajRo0S99xzj+58Q0ODiIyMFDExMeLMmTNi3759IiAgQCxbtsweL+eOsW/fPvHaa6+JL774QgAQu3bt0ju/Zs0a4ePjI3bv3i1+/PFH8dBDD4mQkBBRXV2taxMXFycGDx4svv/+e/Hdd9+J0NBQMX36dN350tJSERgYKGbMmCHS09PFJ598Itzd3cVf//pXW73MO0JbYzlr1iwRFxen9xktKirSa8OxtL/Y2Fixbds2kZ6eLs6ePSseeOABcdddd4mKigpdG0v8Pv3555+Fh4eHWLx4scjIyBAffvihkMlkIikpyaav15WZMpa//e1vxdy5c/U+l6WlpbrzHEvH8NVXX4m9e/eKn376SVy+fFm8+uqrQi6Xi/T0dCEEP5POpK2x5GfSdhh0O6CRI0eK+fPn675Xq9Wie/fuYvXq1XbsFTWVkJAgBg8ebPBcSUmJkMvl4vPPP9cdu3jxogAgUlJShBCNAYNUKhW5ubm6Nps3bxbe3t6itrbWqn2nRs0DNY1GI1QqlXjnnXd0x0pKSoRSqRSffPKJEEKIjIwMAUD88MMPujb79+8XEolE/Prrr0IIITZt2iT8/Pz0xvGVV14R4eHhVn5Fdy5jQffDDz9s9DEcS8eUn58vAIijR48KISz3+/Tll18WAwYM0HuuadOmidjYWGu/pDtW87EUovEP/AULFhh9DMfScfn5+Yl//OMf/Ey6AO1YCsHPpC1xebmDqaurQ2pqKmJiYnTHpFIpYmJikJKSYseeUXNXrlxB9+7d0adPH8yYMQPXr18HAKSmpqK+vl5vDPv164e77rpLN4YpKSkYOHAgAgMDdW1iY2NRVlaGCxcu2PaFEAAgOzsbubm5euPm4+ODqKgovXHz9fXFiBEjdG1iYmIglUpx8uRJXZsxY8ZAoVDo2sTGxuLy5csoLi620ashoHG5W7du3RAeHo558+ahsLBQd45j6ZhKS0sBAP7+/gAs9/s0JSVF7xraNvx31Xqaj6XWv/71LwQEBCAyMhLLli1DVVWV7hzH0vGo1Wrs3LkTlZWViI6O5mfSiTUfSy1+Jm2jk707QPoKCgqgVqv13twAEBgYiEuXLtmpV9RcVFQUtm/fjvDwcOTk5GDlypW47777kJ6ejtzcXCgUCvj6+uo9JjAwELm5uQCA3Nxcg2OsPUe2p/25GxqXpuPWrVs3vfOdOnWCv7+/XpuQkJAW19Ce8/Pzs0r/SV9cXBweffRRhISEICsrC6+++iomTZqElJQUyGQyjqUD0mg0WLhwIUaPHo3IyEgAsNjvU2NtysrKUF1dDXd3d2u8pDuWobEEgCeffBK9e/dG9+7dce7cObzyyiu4fPkyvvjiCwAcS0dy/vx5REdHo6amBl5eXti1axciIiJw9uxZfiadjLGxBPiZtCUG3UTtMGnSJN3XgwYNQlRUFHr37o3PPvuMv1yIHMATTzyh+3rgwIEYNGgQ+vbtiyNHjmD8+PF27BkZM3/+fKSnp+PYsWP27gp1kLGx/NOf/qT7euDAgQgKCsL48eORlZWFvn372rqb1Irw8HCcPXsWpaWl+Pe//41Zs2bh6NGj9u4WtYOxsYyIiOBn0oa4vNzBBAQEQCaTtcgCmZeXB5VKZadeUVt8fX1x9913IzMzEyqVCnV1dSgpKdFr03QMVSqVwTHWniPb0/7cW/vsqVQq5Ofn651vaGhAUVERx9bB9enTBwEBAcjMzATAsXQ08fHx+Prrr3H48GH07NlTd9xSv0+NtfH29uaNUgszNpaGREVFAYDe55Jj6RgUCgVCQ0MxfPhwrF69GoMHD8aGDRv4mXRCxsbSEH4mrYdBt4NRKBQYPnw4Dh48qDum0Whw8OBBvf0X5FgqKiqQlZWFoKAgDB8+HHK5XG8ML1++jOvXr+vGMDo6GufPn9f7oz85ORne3t66JT9kWyEhIVCpVHrjVlZWhpMnT+qNW0lJCVJTU3VtDh06BI1Go/uHKjo6Gt9++y3q6+t1bZKTkxEeHs7lyHb0yy+/oLCwEEFBQQA4lo5CCIH4+Hjs2rULhw4darGc31K/T6Ojo/WuoW3Df1ctp62xNOTs2bMAoPe55Fg6Jo1Gg9raWn4mXYB2LA3hZ9KK7J3JjVrauXOnUCqVYvv27SIjI0P86U9/Er6+vnqZA8m+XnzxRXHkyBGRnZ0tjh8/LmJiYkRAQIDIz88XQjSW07jrrrvEoUOHxOnTp0V0dLSIjo7WPV5bgmHixIni7NmzIikpSXTt2pUlw6ysvLxcnDlzRpw5c0YAEOvWrRNnzpwR165dE0I0lgzz9fUVX375pTh37px4+OGHDZYMGzp0qDh58qQ4duyYCAsL0yszVVJSIgIDA8VTTz0l0tPTxc6dO4WHhwfLTFlYa2NZXl4uXnrpJZGSkiKys7PFgQMHxLBhw0RYWJioqanRXYNjaX/z5s0TPj4+4siRI3ola6qqqnRtLPH7VFvSZsmSJeLixYsiMTGRJW0srK2xzMzMFKtWrRKnT58W2dnZ4ssvvxR9+vQRY8aM0V2DY+kYli5dKo4ePSqys7PFuXPnxNKlS4VEIhHffPONEIKfSWfS2ljyM2lbDLod1IcffijuuusuoVAoxMiRI8X3339v7y5RE9OmTRNBQUFCoVCIHj16iGnTponMzEzd+erqavHcc88JPz8/4eHhIR555BGRk5Ojd42rV6+KSZMmCXd3dxEQECBefPFFUV9fb+uXckc5fPiwANDiv1mzZgkhGsuGvfHGGyIwMFAolUoxfvx4cfnyZb1rFBYWiunTpwsvLy/h7e0t5syZI8rLy/Xa/Pjjj+Lee+8VSqVS9OjRQ6xZs8ZWL/GO0dpYVlVViYkTJ4quXbsKuVwuevfuLebOndvixiXH0v4MjSEAsW3bNl0bS/0+PXz4sBgyZIhQKBSiT58+es9BHdfWWF6/fl2MGTNG+Pv7C6VSKUJDQ8WSJUv0agILwbF0BM8884zo3bu3UCgUomvXrmL8+PG6gFsIfiadSWtjyc+kbUmEEMJ28+pEREREREREdw7u6SYiIiIiIiKyEgbdRERERERERFbCoJuIiIiIiIjIShh0ExEREREREVkJg24iIiIiIiIiK2HQTURERERERGQlDLqJiIiIiIiIrIRBNxEREREREZGVMOgmIiJyMlevXoVEIsHZs2ft3RWdS5cuYdSoUXBzc8OQIUPs3R0iIiKHwaCbiIjITLNnz4ZEIsGaNWv0ju/evRsSicROvbKvhIQEeHp64vLlyzh48KDBNrNnz8bUqVN1348dOxYLFy60TQeJiIjshEE3ERFRO7i5uWHt2rUoLi62d1cspq6urt2PzcrKwr333ovevXujS5cuFuwVERGRc2PQTURE1A4xMTFQqVRYvXq10TYrVqxosdR6/fr1CA4O1n2vnf196623EBgYCF9fX6xatQoNDQ1YsmQJ/P390bNnT2zbtq3F9S9duoR77rkHbm5uiIyMxNGjR/XOp6enY9KkSfDy8kJgYCCeeuopFBQU6M6PHTsW8fHxWLhwIQICAhAbG2vwdWg0GqxatQo9e/aEUqnEkCFDkJSUpDsvkUiQmpqKVatWQSKRYMWKFa385G6/7qNHj2LDhg2QSCSQSCS4evWqyf1+/vnnsXDhQvj5+SEwMBB///vfUVlZiTlz5qBz584IDQ3F/v37dY8pLi7GjBkz0LVrV7i7uyMsLMzgz5SIiMjSGHQTERG1g0wmw1tvvYUPP/wQv/zyS4eudejQIdy4cQPffvst1q1bh4SEBDz44IPw8/PDyZMn8eyzz+LPf/5zi+dZsmQJXnzxRZw5cwbR0dGYMmUKCgsLAQAlJSUYN24chg4ditOnTyMpKQl5eXn4/e9/r3eNjz76CAqFAsePH8eWLVsM9m/Dhg1477338O677+LcuXOIjY3FQw89hCtXrgAAcnJyMGDAALz44ovIycnBSy+91OZr3rBhA6KjozF37lzk5OQgJycHvXr1MqvfAQEBOHXqFJ5//nnMmzcPjz/+OO655x6kpaVh4sSJeOqpp1BVVQUAeOONN5CRkYH9+/fj4sWL2Lx5MwICAkwbICIiog5g0E1ERNROjzzyCIYMGYKEhIQOXcff3x8ffPABwsPD8cwzzyA8PBxVVVV49dVXERYWhmXLlkGhUODYsWN6j4uPj8djjz2G/v37Y/PmzfDx8cE///lPAMDGjRsxdOhQvPXWW+jXrx+GDh2KrVu34vDhw/jpp5901wgLC8Pbb7+N8PBwhIeHG+zfu+++i1deeQVPPPEEwsPDsXbtWgwZMgTr168HAKhUKnTq1AleXl5QqVTw8vJq8zX7+PhAoVDAw8MDKpUKKpUKMpnM5H4PHjwYr7/+uu7n4+bmhoCAAMydOxdhYWFYvnw5CgsLce7cOQDA9evXMXToUIwYMQLBwcGIiYnBlClTzBonIiKi9mDQTURE1AFr167FRx99hIsXL7b7GgMGDIBUevuf5MDAQAwcOFD3vUwmQ5cuXZCfn6/3uOjoaN3XnTp1wogRI3T9+PHHH3H48GF4eXnp/uvXrx+Axv3XWsOHD2+1b2VlZbhx4wZGjx6td3z06NEdes3GmNrvQYMG6b7W/nya/swCAwMBQPczmzdvHnbu3IkhQ4bg5ZdfxokTJyzedyIiIkM62bsDREREzmzMmDGIjY3FsmXLMHv2bL1zUqkUQgi9Y/X19S2uIZfL9b6XSCQGj2k0GpP7VVFRgSlTpmDt2rUtzgUFBem+9vT0NPmatmBqv9v6mWmzyGt/ZpMmTcK1a9ewb98+JCcnY/z48Zg/fz7effdda7wMIiIiHc50ExERddCaNWuwZ88epKSk6B3v2rUrcnNz9QJvS9bW/v7773VfNzQ0IDU1Ff379wcADBs2DBcuXEBwcDBCQ0P1/jMn0Pb29kb37t1x/PhxvePHjx9HREREh/qvUCigVqv1jlmq34Z07doVs2bNwo4dO7B+/Xr87W9/69D1iIiITMGgm4iIqIMGDhyIGTNm4IMPPtA7PnbsWNy8eRNvv/02srKykJiYqJdRu6MSExOxa9cuXLp0CfPnz0dxcTGeeeYZAMD8+fNRVFSE6dOn44cffkBWVhb++9//Ys6cOS0C3bYsWbIEa9euxaefforLly9j6dKlOHv2LBYsWNCh/gcHB+PkyZO4evUqCgoKoNFoLNrvppYvX44vv/wSmZmZuHDhAr7++mvdDQoiIiJrYtBNRERkAatWrWqx/Lt///7YtGkTEhMTMXjwYJw6dcqkzN6mWrNmDdasWYPBgwfj2LFj+Oqrr3QZubWz02q1GhMnTsTAgQOxcOFC+Pr66u0fN8ULL7yAxYsX48UXX8TAgQORlJSEr776CmFhYR3q/0svvQSZTIaIiAh07doV169ft2i/m1IoFFi2bBkGDRqEMWPGQCaTYefOnR3qPxERkSkkovlmMyIiIiIiIiKyCM50ExEREREREVkJg24iIiIiIiIiK2HQTURERERERGQlDLqJiIiIiIiIrIRBNxEREREREZGVMOgmIiIiIiIishIG3URERERERERWwqCbiIiIiIiIyEoYdBMRERERERFZCYNuIiIiIiIiIith0E1ERERERERkJQy6iYiIiIiIiKzk/wOfTm9Tbz9DcQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# plot the computation time as the number of items increases\n",
        "plt.plot(range(0, pmf_item_vect.shape[0],10), comp_time, marker='o',\n",
        "         label='Computation_time')\n",
        "plt.xlabel('Number of Items')\n",
        "plt.ylabel('Computation Time (seconds)')\n",
        "plt.title('Inner product computation time (seconds) vs. number of items')\n",
        "plt.grid()\n",
        "plt.gcf().set_size_inches(10, 5)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PVHVHI-uoYc_"
      },
      "source": [
        "**Observation #2: Retrieval time scales linearly with the number of latent factors**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49,
          "referenced_widgets": [
            "f3e91bc8622c4f258d42cf4aba26a448",
            "875b29b153cd4b84a9fe32e8c08d4b41",
            "fa4a2182f65b4923bb7cff887c411474",
            "b7b969009a5d4743a8f287273188b652",
            "4de4311550bb4fa888b37101e5c2ea61",
            "240ef7fe301b44009ac95cde724cada4",
            "ae2257b977f2457e8c1b5518d8f514fd",
            "69a8456fa8a44e0d917980d772cd8abb",
            "3f4ba442783e4649b7d3cf636b8f1394",
            "b4821a35d02049d4b70ea5741d438636",
            "c5b6c65a32b1430593fbf60552088f91"
          ]
        },
        "id": "LdcN_VdJoiun",
        "outputId": "c5379c9f-9bc9-459a-cec5-9f7cd97f66eb",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703821952,
          "user_tz": -480,
          "elapsed": 9785,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/100 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "f3e91bc8622c4f258d42cf4aba26a448"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "comp_time = []\n",
        "\n",
        "for d in tqdm.trange(pmf.k, disable=not VERBOSE):\n",
        "  start_time = time.time()\n",
        "  pred = np.matmul(pmf_item_vect[:incr_size, :d], pmf_user_vect[:,:d].T)\n",
        "  end_time = time.time()\n",
        "\n",
        "  # average the computation time\n",
        "  comp_time.append((end_time - start_time) / pmf_user_vect.shape[0])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "id": "KskaILijjngX",
        "outputId": "64083efd-aa5f-447b-8298-76126511d97a",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703822232,
          "user_tz": -480,
          "elapsed": 274,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# plot the computation time as the number of dimension increases\n",
        "plt.plot(range(pmf.k), comp_time, marker='o', label='Computation_time')\n",
        "plt.title('Inner product computation time (seconds) vs. number of features')\n",
        "plt.xlabel('Number of features')\n",
        "plt.ylabel('Computation Time (seconds)')\n",
        "plt.grid()\n",
        "plt.gcf().set_size_inches(10, 5)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bh7V67efp54Q"
      },
      "source": [
        "## 3. Scalable Recommendation Retrieval with Locality Sensitive Hashing\n",
        "From the previous example, we can see that the cost of **exhaustive search** scales linearly to the number of items, i.e., $M$ and number of features, i.e., $d$. For modern real-world systems, the number of items could go up to the scale of millons.  Therefore, it would be fruitful to make the search more efficient."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fdjNO883q3np"
      },
      "source": [
        "### Locality Sensitive Hashing\n",
        "One way to do so is to use Locality Sensitive Hashing (LSH), which is a probabilistic space-partitioning indexing technique. One important element of LSH is the hashing function $h(.)$, which maps a data point into a hash value. This hashing function is usually designed with the *locality-sensitive* property, stated as: *two similar data points are more likely to get the same hash values as compared to two distant data points.*\n",
        "\n",
        "One of the most popular search protocols using LSH is hash table look-up.  In a nutshell, we first derive the hash codes for all items and construct a hash table that links a hash code to items of that code. When a user appears, we hash the user's latent vector into a hash code.  We then look up items of that hash code and compute the top-$K$ based on inner product *only among those items*, thus drastically reducing the number of items we need to consider.  To increase the search space, we can also use multiple hash tables, in which case we look up the multiple hash tables and compute the top-$K$ across the tables."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "anAqQ3Rwi-3-",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703822235,
          "user_tz": -480,
          "elapsed": 2,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "random.seed(SEED)\n",
        "\n",
        "# Implementation of Locality Sensitive Hashing for Maximum Cosine Similarity Search\n",
        "class LSHIndex:\n",
        "\n",
        "  def __init__(self, hash_family, k, L):\n",
        "    self.hash_family = hash_family\n",
        "    self.k = k\n",
        "    self.L = 0\n",
        "    self.hash_tables = []\n",
        "    self.resize(L)\n",
        "\n",
        "  def resize(self, L):\n",
        "    \"\"\" update the number of hash tables to be used \"\"\"\n",
        "    if L < self.L:\n",
        "      self.hash_tables = self.hash_tables[:L]\n",
        "    else:\n",
        "      # initialise a new hash table for each hash function\n",
        "      hash_funcs = [[self.hash_family.create_hash_func() for h in range(self.k)]\n",
        "                    for l in range(self.L, L)]\n",
        "      self.hash_tables.extend([(g, defaultdict(lambda:[])) for g in hash_funcs])\n",
        "\n",
        "  def hash(self, g, p):\n",
        "    return self.hash_family.combine([h.hash(p) for h in g])\n",
        "\n",
        "  def index(self, points):\n",
        "    \"\"\" index the supplied points \"\"\"\n",
        "    self.points = points\n",
        "    for g, table in self.hash_tables:\n",
        "        for ix, p in enumerate(self.points):\n",
        "            table[self.hash(g,p)].append(ix)\n",
        "    # reset stats\n",
        "    self.tot_touched = 0\n",
        "    self.num_queries = 0\n",
        "\n",
        "  def query(self, q, metric, max_results):\n",
        "    \"\"\" find the max_results closest indexed points to q according to the supplied metric \"\"\"\n",
        "    candidates = set()\n",
        "    for g, table in self.hash_tables:\n",
        "        matches = table.get(self.hash(g,q), [])\n",
        "        candidates.update(matches)\n",
        "\n",
        "    # update stats\n",
        "    self.tot_touched += len(candidates)\n",
        "    self.num_queries += 1\n",
        "\n",
        "    # rerank candidates\n",
        "    candidates = [(ix, metric(q, self.points[ix])) for ix in candidates]\n",
        "    candidates.sort(key = itemgetter(1))\n",
        "    return candidates[:max_results]\n",
        "\n",
        "  def get_avg_touched(self):\n",
        "    \"\"\" mean number of candidates inspected per query \"\"\"\n",
        "    return self.tot_touched/self.num_queries\n",
        "\n",
        "\n",
        "#################################################################################################\n",
        "#--------------------------------- Cosine LSH Hash Family --------------------------------------#\n",
        "#################################################################################################\n",
        "class CosineHashFamily:\n",
        "\n",
        "  def __init__(self,d):\n",
        "    self.d = d\n",
        "\n",
        "  def create_hash_func(self):\n",
        "    # each CosineHash is initialised with a random projection vector\n",
        "    return CosineHash(self.rand_vec())\n",
        "\n",
        "  def rand_vec(self):\n",
        "    return [random.gauss(0,1) for i in range(self.d)]\n",
        "\n",
        "  def combine(self, hashes):\n",
        "    \"\"\"combine by treating as a bitvector\"\"\"\n",
        "    return sum(2**i if h > 0 else 0 for i,h in enumerate(hashes))\n",
        "\n",
        "class CosineHash:\n",
        "\n",
        "  def __init__(self, r):\n",
        "    self.r = r\n",
        "\n",
        "  def hash(self, vec):\n",
        "    return self.sgn(dot(vec, self.r))\n",
        "\n",
        "  def sgn(self,x):\n",
        "    return int(x > 0)\n",
        "\n",
        "#--- inner product ---\n",
        "def dot(u,v):\n",
        "\treturn np.dot(u, v)\n",
        "\n",
        "#-- cosine distance ---\n",
        "def cosine_distance(u,v):\n",
        "\treturn 1 - dot(u,v)/(dot(u,u)*dot(v,v))**0.5"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "ZKKYp5aujPUz",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703822265,
          "user_tz": -480,
          "elapsed": 29,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "# helper function to measure precision, recall, and touched values\n",
        "# of using LSH for top-k recommendation retrieval\n",
        "# ------------------------------------------------------------------------\n",
        "def evaluate_LSHTopK(test_data, item_vect, user_vect, lsh_index, sim_metric, topK):\n",
        "\n",
        "  lsh_prec = 0.0\n",
        "  lsh_recall = 0.0\n",
        "\n",
        "  #build index\n",
        "  lsh_index.index(item_vect.tolist())\n",
        "\n",
        "  for id in range(user_vect.shape[0]):\n",
        "    test_item_ids = list(test_data.csr_matrix.getrow(id).nonzero()[1])\n",
        "\n",
        "    if len(test_item_ids) > 0:\n",
        "      # top-k by LSH\n",
        "      lsh_rec_list = list(map(itemgetter(0), lsh_index.query(user_vect[id, :], sim_metric, topK)))\n",
        "      lsh_overlaps = list(set(lsh_rec_list).intersection(test_item_ids))\n",
        "\n",
        "      lsh_prec   += len(lsh_overlaps) * 1.0/topK\n",
        "      lsh_recall += len(lsh_overlaps) * 1.0/len(test_item_ids)\n",
        "\n",
        "  touched = lsh_index.get_avg_touched() * 1.0/item_vect.shape[0]\n",
        "  return lsh_prec/user_vect.shape[0], lsh_recall/user_vect.shape[0], touched"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kG3HZIUVsGaT"
      },
      "source": [
        "### Issue with Using Locality Sensitive Hashing for Recommendation Retrieval\n",
        "\n",
        "Recommendation retrieval, which relies on inner product computation is not directly compatible with Locality Sensitive Hashing, which is designed for nearest neighbor search or maximum cosine similarity search. This might lead to the significant degeneration of recommendation accuracy after indexing [2].\n",
        "\n",
        "In the following, we introduce two approaches to this issue:\n",
        "\n",
        "1.   Vector Augmentation\n",
        "2.   Indexable Representation\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NtVrcg_Ysmj0"
      },
      "source": [
        "### Solution I: Vector Augmentation\n",
        "In this solution, we first apply the vector transformation for both user and item vectors, as introduced in the paper [3].\n",
        "\n",
        "For each item vector $\\mathbf{v}_j$:\n",
        "\\begin{equation}\n",
        "\\mathbf{\\tilde{v}}_j = [\\mathbf{v}_j; \\sqrt{\\phi^2 - ||\\mathbf{v}_j||^2}]  \\hspace{1cm}(\\mathrm{where}\\ \\phi = \\max\\{||\\mathbf{v}_j||\\})\n",
        "\\end{equation}\n",
        "\n",
        "For each user vector $\\mathbf{u}_i$:\n",
        "\\begin{equation}\n",
        "\\mathbf{\\tilde{u}}_i = [\\mathbf{u}_i; 0]\n",
        "\\end{equation}\n",
        "\n",
        "We have the following observation:\n",
        "\n",
        "\\begin{equation}\n",
        "\\frac{\\mathbf{\\tilde{u}}_i^T\\mathbf{\\tilde{v}}_j}{||\\mathbf{\\tilde{u}}_i||\\times ||\\mathbf{\\tilde{v}}_j||} = \\frac{\\mathbf{\\tilde{u}}_i^T\\mathbf{\\tilde{v}}_j}{\\phi ||\\mathbf{\\tilde{u}}_i||}\n",
        "\\end{equation}\n",
        "\n",
        "i.e.,\n",
        "\n",
        "\\begin{equation}\n",
        "\\arg\\max_{1\\leq j\\leq M}{\\mathbf{{u}}_i^T\\mathbf{{v}}_j} = \\arg\\max_{1\\leq j\\leq M}\\frac{\\mathbf{\\tilde{u}}_i^T\\mathbf{\\tilde{v}}_j}{||\\mathbf{\\tilde{u}}_i||\\times ||\\mathbf{\\tilde{v}}_j||}\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "With this vector augmentation, we effectively convert a Maximum Inner Product Search (MIPS) problem to a Maximum Cosine Similarity Search (MCCS), which can be solved with LSH.  Hypothetically, this will make the user and item latent vectors more compatible with LSH."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "duk8--B6stCt",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703822267,
          "user_tz": -480,
          "elapsed": 8,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "#apply vector augmentation\n",
        "M = np.linalg.norm(pmf_item_vect, axis=1) # compute item vector norms\n",
        "max_norm = max(M) # max item norm\n",
        "\n",
        "xbox_item_vect = np.concatenate(\n",
        "  (pmf_item_vect, np.sqrt(max_norm**2 - pow(M, 2)).reshape(pmf_item_vect.shape[0], -1)),\n",
        "  axis=1\n",
        ")\n",
        "xbox_user_vect = np.concatenate(\n",
        "  (pmf_user_vect, np.zeros((pmf_user_vect.shape[0], 1))),\n",
        "  axis=1\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4BhzCTwxjLGN"
      },
      "source": [
        "#### Effectiveness of Vector Augmentation\n",
        "\n",
        "In this experiment, we build LSH index on the output of PMF algorithm and compare the latent vectors before and after vector augmentation for LSH recommendation retrieval.\n",
        "\n",
        "Since the augmented user and item vectors are in $(d+1)-$dimensional space, for comparison purpose we append 0s to the original non-augmented user and item vectors (to make them the same length), i.e.,\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathbf{\\tilde{v}}_j = [\\mathbf{v}_j; 0]\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathbf{\\tilde{u}}_i = [\\mathbf{u}_i; 0]\n",
        "\\end{equation}\n",
        "\n",
        "With this non-augmented \"transformation\", we have no change to the original inner product:\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathbf{\\tilde{u}}_i^T\\mathbf{\\tilde{v}}_j = \\mathbf{{u}}_i^T\\mathbf{{v}}_j\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "mC8TxRaWjQbf",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703822268,
          "user_tz": -480,
          "elapsed": 8,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "padded_user_vect = np.concatenate((pmf_user_vect, np.zeros((pmf_user_vect.shape[0], 1))), axis=1)\n",
        "padded_item_vect = np.concatenate((pmf_item_vect, np.zeros((pmf_item_vect.shape[0], 1))), axis=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U_aWFxs3tFyk"
      },
      "source": [
        "\n",
        "Specifically, we report three evaluation metrics as follows:\n",
        "\n",
        "1. \blsh_prec@10 = $\\text{precision@10 of LSH Indexing}$\n",
        "&nbsp;\n",
        "&nbsp;\n",
        "&nbsp;  \n",
        "&nbsp;\n",
        "2. lsh_rec@10    = $\\text{recall@10 of LSH Indexing}$\n",
        "&nbsp;\n",
        "&nbsp;\n",
        "&nbsp;  \n",
        "&nbsp;\n",
        "3. touched = $\\frac{\\text{Average number of investigated items by LSH}}{\\text{Total number of items}}$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j8XWv-7ntKTQ",
        "outputId": "d94f2377-63f2-49f0-fb38-11f49eb955d2",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744703998903,
          "user_tz": -480,
          "elapsed": 176640,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "#table \t#bit \t ?Augmented \t lsh_prec@10 \t lsh_recall@10 \t touched\n",
            "---------------------------------------------------------------------------------\n",
            "10\t4\tNo\t0.1128\t0.0105\t0.4536\n",
            "10\t4\tYes\t0.1150\t0.0107\t0.6716\n",
            "---------------------------------------------------------------------------------\n",
            "10\t8\tNo\t0.0596\t0.0046\t0.0382\n",
            "10\t8\tYes\t0.0702\t0.0056\t0.0693\n",
            "---------------------------------------------------------------------------------\n",
            "20\t4\tNo\t0.1146\t0.0107\t0.6871\n",
            "20\t4\tYes\t0.1231\t0.0115\t0.8735\n",
            "---------------------------------------------------------------------------------\n",
            "20\t8\tNo\t0.0741\t0.0060\t0.0758\n",
            "20\t8\tYes\t0.0892\t0.0081\t0.1386\n"
          ]
        }
      ],
      "source": [
        "topK = 10 # @param - top-K value\n",
        "b_vals = [4, 8] # @param - number of hash function\n",
        "L_vals = [10, 20] # @param - number of hashtables\n",
        "\n",
        "test_data  = ratio_split.test_set # testing data\n",
        "\n",
        "print('#table \\t#bit \\t ?Augmented \\t lsh_prec@{0} \\t lsh_recall@{0} \\t touched'.format(topK))\n",
        "for nt in L_vals:\n",
        "  for b in b_vals:\n",
        "    #init lsh index:\n",
        "    #------ hash-family: the LSH scheme/family\n",
        "    #------ k          : number of hash functions\n",
        "    #------ L          : number of hash tables\n",
        "    lsh_index = LSHIndex(hash_family = CosineHashFamily(padded_item_vect.shape[1]), k = b, L=nt)\n",
        "\n",
        "    #performance without employing vector augmentation\n",
        "    print('---------------------------------------------------------------------------------')\n",
        "    prec_1, recall_1, touched_1 = evaluate_LSHTopK(\n",
        "      test_data, padded_item_vect, -padded_user_vect[:1000], lsh_index, dot, topK\n",
        "    )\n",
        "    print(\"{}\\t{}\\t{}\\t{:.4f}\\t{:.4f}\\t{:.4f}\".format(nt, b, 'No', prec_1, recall_1, touched_1))\n",
        "\n",
        "    #performance with vector augmentation\n",
        "    prec_2, recall_2, touched_2 = evaluate_LSHTopK(\n",
        "      test_data, xbox_item_vect, -xbox_user_vect[:1000], lsh_index, dot, topK\n",
        "    )\n",
        "    print(\"{}\\t{}\\t{}\\t{:.4f}\\t{:.4f}\\t{:.4f}\".format(nt, b, 'Yes', prec_2, recall_2, touched_2))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mDl-lSEojgAC"
      },
      "source": [
        "We observe from the results above that with vector augmentation, we can achieve higher recommendation accuracy after using Locality Sensitive Hashing.\n",
        "\n",
        "What is the effect of increasing the number of bits, or the number of hash tables? Why?\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fcPi3CaOeFcf"
      },
      "source": [
        "### Solution II: Indexable Representation Learning\n",
        "Another solution is \"Indexable representation\", which refers to recommendation algorithms whose user/item vectors are immediately sublinearly searchable. In this tutorial, we are going to experiment with one such model, namely Indexable Bayesian Personalized Ranking or IBPR [5] for short. IBPR is an extension of the popular framework for implicit feedback: Bayesian Personalized Ranking (BPR) [4].\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xu5vliwGbi0H"
      },
      "source": [
        "#### Bayesian Personalized Ranking - BPR\n",
        "\n",
        "Let us see the performance of BPR with exhaustive search."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 188,
          "referenced_widgets": [
            "09f702c28ebc478782957a7714f8f7a3",
            "00a18051aa2a44b588423643e6cf7c3d",
            "832f2ebfa918429bace695b51fd1869f",
            "72ac73be4df44ccc8dd222b7bb566a8f",
            "b9195d35d52541e4ab6e488b04a8df4a",
            "bfcd8ca0607b4ea6a12ad5724c1d1b3b",
            "6782692bb16540679ddfc8d4a34ff68a",
            "ebaacaadba4842bfb22ad59437a875a4",
            "2596503a4c664eb386f88d70763f0abc",
            "47dfd5a29e384f22af22ab8f438bdb13",
            "67b36f59f55e4a7aa5858a26fe4af469"
          ]
        },
        "id": "Rd7_awdLh9rZ",
        "outputId": "8163ef8d-c9b9-497b-ab62-0b4c3e7fbf60",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744704015920,
          "user_tz": -480,
          "elapsed": 17016,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/100 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "09f702c28ebc478782957a7714f8f7a3"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimization finished!\n",
            "\n",
            "TEST:\n",
            "...\n",
            "    | Precision@10 | Recall@10 | Train (s) | Test (s)\n",
            "--- + ------------ + --------- + --------- + --------\n",
            "BPR |       0.2875 |    0.0598 |   13.2934 |   3.7064\n",
            "\n"
          ]
        }
      ],
      "source": [
        "rec_bpr = BPR(k=20, max_iter=100, learning_rate=0.001, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "cornac.Experiment(\n",
        "  eval_method=ratio_split, models=[rec_bpr], metrics=[rec_10, pre_10],\n",
        ").run()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t5ddSbTG3j7T"
      },
      "source": [
        "We now measure the performance of BPR after LSH indexing."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "urSv8wsriwwj",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744704015922,
          "user_tz": -480,
          "elapsed": 7,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "bpr_user_vect  = rec_bpr.u_factors\n",
        "bpr_item_vect  = rec_bpr.i_factors\n",
        "\n",
        "# apply Xbox transformation\n",
        "M = np.linalg.norm(bpr_item_vect, axis=1) # compute item vector norms\n",
        "max_norm = max(M) # max item norm\n",
        "\n",
        "xbox_bpr_item_vect = np.concatenate(\n",
        "  (bpr_item_vect, np.sqrt(max_norm**2 - pow(M, 2)).reshape(bpr_item_vect.shape[0], -1)),\n",
        "  axis=1\n",
        ")\n",
        "xbox_bpr_user_vect = np.concatenate(\n",
        "  (bpr_user_vect, np.zeros((bpr_user_vect.shape[0], 1))),\n",
        "  axis = 1\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4PUKWLDuobXp",
        "outputId": "376a3b93-0ad9-4b73-c460-a30907c55cab",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744704041632,
          "user_tz": -480,
          "elapsed": 25702,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "#table\t #bit \t model \t lsh_prec@10 \t lsh_recall@10 \t touched\n",
            "------------------------------------------------------------------------------\n",
            "10\t4\tBPR\t0.0431\t0.0029\t0.4836\n",
            "10\t8\tBPR\t0.0333\t0.0020\t0.0459\n",
            "------------------------------------------------------------------------------\n",
            "20\t4\tBPR\t0.0441\t0.0027\t0.7166\n",
            "20\t8\tBPR\t0.0391\t0.0024\t0.0953\n"
          ]
        }
      ],
      "source": [
        "topK = 10 # @param\n",
        "b_vals = [4, 8] # @param\n",
        "L_vals = [10, 20] # @param\n",
        "\n",
        "test_data  = ratio_split.test_set # testing data\n",
        "\n",
        "print('#table\\t #bit \\t model \\t lsh_prec@{0} \\t lsh_recall@{0} \\t touched'.format(topK))\n",
        "for nt in L_vals:\n",
        "  print('------------------------------------------------------------------------------')\n",
        "  for b in b_vals:\n",
        "    # lsh index:\n",
        "    #------ hash-family: the LSH scheme/family\n",
        "    #------ k          : number of hash functions\n",
        "    #------ L          : number of hash tables\n",
        "    lsh_index = LSHIndex(hash_family = CosineHashFamily(xbox_bpr_item_vect.shape[1]), k = b, L = nt)\n",
        "\n",
        "    lsh_bpr_prec, lsh_bpr_recall, touched_bpr = evaluate_LSHTopK(\n",
        "      test_data, xbox_bpr_item_vect, -xbox_bpr_user_vect[:1000, :], lsh_index, dot, topK\n",
        "    )\n",
        "    print(\"{}\\t{}\\t{}\\t{:.4f}\\t{:.4f}\\t{:.4f}\".format(\n",
        "      nt, b, 'BPR', lsh_bpr_prec, lsh_bpr_recall, touched_bpr)\n",
        "    )"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uD9Av1mcbt9q"
      },
      "source": [
        "The results above show that in relative terms, the performance degenerates for both precision and recall.\n",
        "\n",
        "\n",
        "#### Indexable Bayesian Personalized Ranking - IBPR\n",
        "\n",
        "We will now test the effectiveness of indexable model IBPR. In this experiment, we train IBPR with the same data we use for BPR and measure the performance after LSH indexing."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 618,
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          "text": [
            "\n",
            "TEST:\n",
            "...\n",
            "     | Precision@10 | Recall@10 | Train (s) | Test (s)\n",
            "---- + ------------ + --------- + --------- + --------\n",
            "IBPR |       0.2546 |    0.0497 |  548.1109 |   2.8216\n",
            "\n"
          ]
        }
      ],
      "source": [
        "rec_ibpr = IBPR(k=20, max_iter=15, learning_rate=0.001, verbose=VERBOSE)\n",
        "\n",
        "cornac.Experiment(\n",
        "  eval_method=ratio_split, models =[rec_ibpr], metrics=[rec_10, pre_10]\n",
        ").run()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "wX-QuXqfpfO2",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744704592622,
          "user_tz": -480,
          "elapsed": 1,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [],
      "source": [
        "ibpr_user_vect = rec_ibpr.U\n",
        "ibpr_item_vect = rec_ibpr.V"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "udt0kG_zo9Mx",
        "outputId": "32ee11bd-8a54-4fb8-e046-a113e1af226d",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1744704633425,
          "user_tz": -480,
          "elapsed": 40802,
          "user": {
            "displayName": "Jaime Hieu Do",
            "userId": "16382807970500480792"
          }
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "#table\t #bit \t model \t lsh_prec@10 \t lsh_recall@10 \t touched\n",
            "------------------------------------------------------------------------------\n",
            "10\t4\tIBPR\t0.0684\t0.0044\t0.6747\n",
            "10\t8\tIBPR\t0.0230\t0.0014\t0.4269\n",
            "------------------------------------------------------------------------------\n",
            "20\t4\tIBPR\t0.0903\t0.0064\t0.7043\n",
            "20\t8\tIBPR\t0.0339\t0.0022\t0.5172\n"
          ]
        }
      ],
      "source": [
        "topK = 10 # @param\n",
        "b_vals = [4, 8] # @param\n",
        "L_vals = [10, 20] # @param\n",
        "\n",
        "test_data = ratio_split.test_set # testing data\n",
        "\n",
        "print('#table\\t #bit \\t model \\t lsh_prec@{0} \\t lsh_recall@{0} \\t touched'.format(topK))\n",
        "for nt in L_vals:\n",
        "  print('------------------------------------------------------------------------------')\n",
        "  for b in b_vals:\n",
        "    # lsh index:\n",
        "    #------ hash-family: the LSH scheme/family\n",
        "    #------ k          : number of hash functions\n",
        "    #------ L          : number of hash tables\n",
        "    lsh_index = LSHIndex(hash_family = CosineHashFamily(ibpr_item_vect.shape[1]), k = b, L = nt)\n",
        "\n",
        "    lsh_ibpr_prec, lsh_ibpr_recall, touched_ibpr = evaluate_LSHTopK(\n",
        "      test_data, ibpr_item_vect, -ibpr_user_vect[:1000,:], lsh_index, dot, topK\n",
        "    )\n",
        "    print(\"{}\\t{}\\t{}\\t{:.4f}\\t{:.4f}\\t{:.4f}\".format(\n",
        "      nt, b, 'IBPR', lsh_ibpr_prec, lsh_ibpr_recall, touched_ibpr)\n",
        "    )"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "83P1kPKI4WqM"
      },
      "source": [
        "We observe that the performance after LSH of IBPR (without vector augmentation) could be better than that of BPR (with vector augmentation), which may be attributed to having representations more compatible with indexing.  As a result, we could speed up top-$K$ recommendation retrieval, while better preserving the accuracy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b7t7OUvQ1IF1"
      },
      "source": [
        "## References\n",
        "\n",
        "1. Mnih, Andriy, and Russ R. Salakhutdinov. \"Probabilistic matrix factorization.\" Advances in neural information processing systems. 2008.\n",
        "\n",
        "2. Stochastically Robust Personalized Ranking for LSH Recommendation Retrieval, Dung D. Le and Hady W. Lauw\n",
        "AAAI Conference on Artificial Intelligence (AAAI-20)\n",
        "\n",
        "3. Bachrach, Yoram, et al. \"Speeding up the xbox recommender system using a euclidean transformation for inner-product spaces.\" Proceedings of the 8th ACM Conference on Recommender systems. 2014.\n",
        "\n",
        "4. Rendle, Steffen, et al. \"BPR: Bayesian personalized ranking from implicit feedback.\" arXiv preprint arXiv:1205.2618 (2012).\n",
        "\n",
        "5. Le, Dung D., and Hady W. Lauw. \"Indexable Bayesian personalized ranking for efficient top-k recommendation.\" Proceedings of the 2017 ACM on Conference on Information and Knowledge Management. 2017.\n",
        "\n",
        "6.   Cornac - A Comparative Framework for Multimodal Recommender Systems (https://cornac.preferred.ai/)\n"
      ]
    }
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