H_score_Seq.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/XiangxiangXu/NFL/blob/main/H_score_Seq.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# H-score: Exploring Dependence Between Sequential Observations\n",
        "\n",
        "A demo for\n",
        "[![blog](https://img.shields.io/badge/blog-gilearning.github.io-black)](https://gilearning.github.io/)"
      ],
      "metadata": {
        "id": "mcfGopzulQsY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This is a supporting demo for [this post](https://gilearning.github.io/HScore/) on the H-score network. This demo illustrates how we use H-score to explore the dependence between high-dimensional data observations. Here we consider the sequential data, for example, speech/vibration measured by sensors. We will use H-score to learn the dependence between the readings collected by two sensors.\n",
        "\n"
      ],
      "metadata": {
        "id": "kaHan7sinrU-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Set up GPU for Training"
      ],
      "metadata": {
        "id": "_YrltU66qvy1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "if torch.cuda.is_available():\n",
        "    device = torch.device(\"cuda\")\n",
        "    print(f'There are {torch.cuda.device_count()} GPU(s) available.')\n",
        "    print('Device name:', torch.cuda.get_device_name(0))\n",
        "\n",
        "else:\n",
        "    print('No GPU available, using the CPU instead.')\n",
        "    device = torch.device(\"cpu\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gmgvPz-Pm4Aq",
        "outputId": "8d07eccc-733a-4316-9b64-2d9d8323542d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "There are 1 GPU(s) available.\n",
            "Device name: Tesla T4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Generate Sequential Observations\n",
        "\n",
        "Let $\\underline{\\sf x} \\triangleq (\\mathsf{x}_1, \\dots, \\mathsf{x}_{l_x})$ and $\\underline{\\sf y} \\triangleq (\\mathsf{y}_1, \\dots, \\mathsf{y}_{l_y})$ denote the readings from two sensors, with lengths $l_x, l_y$, respectively.\n",
        "\n",
        "Suppose the observation $\\underline{\\sf x}$ is induced by some physical event, denoted by a hidden variable $\\sf u$. Similarly, $\\underline{\\sf y}$ is induced by another event, represented by a hidden variable $\\sf v$. These two hidden variables $\\sf u, v$ can be dependent. Mathematically, this says that $\\underline{\\sf x}$ and $\\underline{\\sf y}$ are dependent through the hidden variables $\\sf u$ and $\\sf v$, and we have the Markov relation $\\underline{\\mathsf{x}}-{\\sf u-v}-\\underline{\\mathsf{y}}$.\n"
      ],
      "metadata": {
        "id": "qAvPh3CdWf7t"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For simplicity, we assume both $\\sf u$ and $\\sf v$ are binary, and the observations are also quantized as binary sequences."
      ],
      "metadata": {
        "id": "TWpUqSxZY4Sz"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xEFvM46zlR-_"
      },
      "outputs": [],
      "source": [
        "u_card = 2  # cardinality for u\n",
        "v_card = 2  # cardinality for v"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_card_sym = 2 # cardinality for each symbol in x sequence\n",
        "y_card_sym = 2 # cardinality for each symbol in y sequence\n",
        "len_x = 40 # l_x\n",
        "len_y = 30 # l_y"
      ],
      "metadata": {
        "id": "QYthZng07rTN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FaObBdQL9FYN"
      },
      "source": [
        "In addition, we assume the $\\underline{\\sf x}$ sequence will have high frequency (switches between 0 and 1 frequently) if $\\sf u = 1$, and will be low-freqency if $\\sf u = 0$. Similarly, $\\underline{\\sf y}$ will be high-frequency if $\\sf v = 1$, and will be low-freqency otherwise."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We use the following first-order Markov chain to simulate the sequences $\\sf x$ and $\\sf y$, where the freqeuncy is tuned by parameter $q \\in [0, 1]$. A large $q$ will lead to a high frequency.\n",
        "\n"
      ],
      "metadata": {
        "id": "n-npP8y564ND"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![markov_seq_wide.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "VBUU0P5pkqPc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We use the following two values of $q$ to generate x and y sequences accoding to values of $\\sf u, v$. For example, if $\\sf u = 1$, $\\sf x$ will be generated by the Markov chain with $q = q_1$.\n"
      ],
      "metadata": {
        "id": "xFnyILx3a59e"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "q0, q1 = (.1, .9)"
      ],
      "metadata": {
        "id": "Mn3oJFAVk7jd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The above generation processes can also be formally written as\n",
        "$$\\mathsf{x}_{i + 1} = \\mathsf{x}_{i} + \\mathsf{z}_{i},\\quad i = 1, \\dots, l_x - 1,$$\n",
        "$$\\mathsf{y}_{i + 1} = \\mathsf{y}_{i} + \\mathsf{z}'_{i}, \\quad i = 1, \\dots, l_y - 1,$$\n",
        "where the plus \"$+$\" is defined as the modulo two sum, and the noise terms $\\mathsf{z}_{i} \\overset{\\text{i.i.d.}}{\\sim} \\mathrm{Bern}(q_{\\sf u})$ and  $\\mathsf{z}'_{i} \\overset{\\text{i.i.d.}}{\\sim} \\mathrm{Bern}(q_{\\sf v})$ are mutually indpendent."
      ],
      "metadata": {
        "id": "bG69JQGjq5Sn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We then set how hidden variables $\\sf u$, $\\sf v$ are dependent, by assigning a value for joint distribution $\\mathtt{p\\_vu}$."
      ],
      "metadata": {
        "id": "Uv107ARecb3u"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "M6wFi9wg9LC2"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "p_vu = np.array([[.1, .2],\n",
        "                 [.4, .3]])\n",
        "\n",
        "# row indices   <-> different values of v\n",
        "# colum indices <-> different values of u\n",
        "\n",
        "# compute the marginal distributions\n",
        "p_v = np.sum(p_vu, axis = 1)\n",
        "p_u = np.sum(p_vu, axis = 0)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Parameters for training."
      ],
      "metadata": {
        "id": "vdjmsmVOcmeB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# number of samples\n",
        "nSamples_train = 50000\n",
        "nSamples_test = 10000\n",
        "nSamples = nSamples_train + nSamples_test\n",
        "\n",
        "\n",
        "## Parameters for Training\n",
        "# batch size\n",
        "batchsize = 128\n",
        "\n",
        "# number of epochs\n",
        "nEpochs = 50"
      ],
      "metadata": {
        "id": "KV7o3B5bl71g"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5tsxu9SY9MVg"
      },
      "source": [
        "We first genearate $(\\sf{u}, \\sf{v})$ joint samples as we did in previous demos. Then we generate $\\underline{\\sf x}, \\underline{\\sf y}$ sequences as the corresponding first-order Markov chains parameterized by $\\sf u, v$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5d1mNyTHlz0j"
      },
      "outputs": [],
      "source": [
        "\"\"\"\n",
        "Generate random discrete samples\n",
        "\"\"\"\n",
        "def GenerateDiscreteSamples(p_xy, nSamples):\n",
        "    '''\n",
        "    generate n samples of (X, Y) pairs, with distribution p_xy\n",
        "    '''\n",
        "    (x_card, y_card) = p_xy.shape\n",
        "    p_xy_vec = p_xy.reshape(-1)\n",
        "    key = np.random.choice(range(x_card*y_card), nSamples, p=p_xy_vec)\n",
        "\n",
        "    X = (key / y_card).astype(int)\n",
        "    Y = (key % y_card)\n",
        "\n",
        "    return([X, Y])\n",
        "\n",
        "\n",
        "[V, U] = GenerateDiscreteSamples(p_vu, nSamples)\n",
        "\n",
        "def GenBinSeq(q, len, n = 1):\n",
        "    # generate n binary sequences with length len\n",
        "    # j-th sequence take the form x[i+1] = x[i] + z[i]\n",
        "    # where z[1]... z[n] are i.i.d., z[j] ~ Bern(q[j])\n",
        "    # Input: q   -- length n list, Bernoulli parameter for each sequence\n",
        "    #        len -- length of seqs\n",
        "    #        n   -- number of seqs\n",
        "    # Output: n by len matrix\n",
        "    seq = (np.random.rand(n, len) < q.reshape(n, 1) * np.ones((1, len))) # all entries are Bern(p)\n",
        "    seq = np.cumsum(seq, axis = 1)  # sum over rows\n",
        "    seq = seq % 2 # module 2\n",
        "    return seq\n",
        "\n",
        "\n",
        "qx_vec = np.ones((1, nSamples)) * (q1 * U + q0 * (1-U))\n",
        "qy_vec = np.ones((1, nSamples)) * (q1 * V + q0 * (1-V))\n",
        "X = GenBinSeq(qx_vec, len_x, nSamples)\n",
        "Y = GenBinSeq(qy_vec, len_y, nSamples)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Define dataset and dataloader."
      ],
      "metadata": {
        "id": "HNCXDYG4cK6-"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YqEJg0eKXBcL"
      },
      "outputs": [],
      "source": [
        "import torch.nn.functional as F\n",
        "Xt = torch.tensor(X)\n",
        "Xt = F.one_hot(Xt, x_card_sym).type(torch.FloatTensor)\n",
        "Yt = torch.tensor(Y)\n",
        "Yt = F.one_hot(Yt, y_card_sym).type(torch.FloatTensor)\n",
        "\n",
        "from torch.utils.data import TensorDataset, DataLoader\n",
        "\n",
        "# dataloder for training\n",
        "ds = TensorDataset(Xt[:nSamples_train], Yt[:nSamples_train])\n",
        "dl = DataLoader(ds, batch_size=batchsize, shuffle = True)\n",
        "\n",
        "# test data\n",
        "X_test = X[nSamples_train:]\n",
        "Y_test = Y[nSamples_train:]\n",
        "\n",
        "# one-hot tensor\n",
        "Xt_test = Xt[nSamples_train:]\n",
        "Yt_test = Yt[nSamples_train:]\n",
        "U_test = U[nSamples_train:]\n",
        "V_test = V[nSamples_train:]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's first take a look at the binary sequences. With each row indicating one sequence pair, let's plot the first 10 pairs of $\\sf x$ and $\\sf y$ sequences."
      ],
      "metadata": {
        "id": "_Er512AnvsW9"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "P2u0IxMpfAYd",
        "outputId": "76931b70-d992-4bed-fc66-6e7e28ffe2ec"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-9-369aa41c4f8a>:5: MatplotlibDeprecationWarning: The 'use_line_collection' parameter of stem() was deprecated in Matplotlib 3.6 and will be removed two minor releases later. If any parameter follows 'use_line_collection', they should be passed as keyword, not positionally.\n",
            "  a0.stem(X[i], use_line_collection = True)\n",
            "<ipython-input-9-369aa41c4f8a>:8: MatplotlibDeprecationWarning: The 'use_line_collection' parameter of stem() was deprecated in Matplotlib 3.6 and will be removed two minor releases later. If any parameter follows 'use_line_collection', they should be passed as keyword, not positionally.\n",
            "  a1.stem(Y[i], use_line_collection = True)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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y5EiDj4mMjFRxcbHr9s0335gKGgCA5kZ9A4Cm87qpeOKJJzR16lRNnjxZvXv31qpVq9S6dWu9+OKLDT7G4XAoNjbWdYuJiTEVNAAAzY36BgBN51VTUV1drby8PI0YMeK/KwgJ0YgRI5Sbm9vg406ePKnu3bsrISFBY8eO1SeffHLB56mqqlJ5ebnbDQAAX7GivlHbAAQzr5qKo0ePqqamps5/YmJiYlRSUlLvY3r16qUXX3xRr7/+uv785z+rtrZWV111lb799tsGnycjI0NRUVGuW0JCgjdhAgDgFSvqG7UNQDDz+dWfUlJSNHHiRPXr10/XXHONtmzZos6dO+vZZ59t8DHz5s1TWVmZ63b48GFfhwkAgFe8rW/UNgDBLMybwZ06dVJoaKhKS0vdlpeWlio2NtajdbRq1Ur9+/fXwYMHGxzjdDrldDq9CQ0AgCazor5R2wAEM6/OVISHh2vgwIHKyspyLautrVVWVpZSUlI8WkdNTY327dunuLg47yIFAMBHqG8AYI5XZyokKS0tTZMmTdKgQYM0ZMgQLV++XKdOndLkyZMlSRMnTlSXLl2UkZEhSVq8eLGGDh2qnj176sSJE1q6dKm++eYbTZkypXm3BAAAE6hvANB0XjcV48eP17///W8tXLhQJSUl6tevnzIzM10fbissLFRIyH9PgBw/flxTp05VSUmJ2rdvr4EDB+qDDz5Q7969m28rAAAwifoGAE3ndVMhSbNmzdKsWbPqvS87O9vt92XLlmnZsmVNeRoAACxFfQOApvH51Z8AAAAABDeaCgAAAACm0FQAAAAAMIWmAgAAAIApNBUAAAAATKGpAAAAAGAKTQUAAAAAU2gqAAAAAJhCUwEAAADAFJoKAAAAAKbQVAAAAAAwhaYCAAAAgCk0FQAAAABMoakAAAAAYApNBQAAAABTaCoAAAAAmEJTAQAAAMAUmgoAAAAAptBUAAAAADCFpgIAAACAKTQVAAAAAEyhqQAAAABgCk0FAAAAAFNoKgAAAACYQlMBAAAAwBSaCgAAAACm0FQAAAAAMIWmAgAAAIApNBUAAAAATKGpAAAAAGAKTQUAAAAAU2gqAAAAAJgS1pQHrVixQkuXLlVJSYmSkpL09NNPa8iQIQ2O37Rpkx588EF9/fXXuuyyy/Too4/qF7/4RZODboqaWkM7C77TkYpKRbeN0JDEDgoNcQT8GKvZbfuDOddonN3miNXz0W7zPxhea3avb3abh3bfnw2x42ssUI8Ndowb/uF1U7Fx40alpaVp1apVSk5O1vLlyzVy5EgdOHBA0dHRdcZ/8MEHmjBhgjIyMnTjjTfqlVde0bhx47Rnzx716dOnWTaiMZn7i/XQG5+quKzStSwuKkLpY3prVJ+4gB1jNbttfzDnGo2z2xyxej7abf4Hw2vN7vXNbvPQ7vuzIXZ8jQXqscGOccN/HIZhGN48IDk5WYMHD9af/vQnSVJtba0SEhJ0zz33aO7cuXXGjx8/XqdOndKbb77pWjZ06FD169dPq1at8ug5y8vLFRUVpbKyMkVGRnoTrjL3F2v6n/fo/I0819M+kzpAkgJuzLkXz+nqH9R74d8lSZ8uHqnW4XX7xOYYE6x59GSMN7n2dBxjzOWxpc9HK7ffk/nfXPF4+0eBmdpQH6vrmzfxB+Kc//H+tMsxxpM8Wv0aa64xxG3930bNvS6r466PmeOqV2cqqqurlZeXp3nz5rmWhYSEaMSIEcrNza33Mbm5uUpLS3NbNnLkSG3bts2rQJuiptbQQ298enYCGoacNdVu9zsk/d+/7JHkUPgPVfWuw45jMrbs1fBLIhUa4lBt9Q9y/mds7enTqv2h7i41O6am1lDGlr222X4751oyn2/GXHhcS5+P13Zra9n2ezL/zeyPqtBwGQ6HHJIeeuNTXdc71m9vY7BzfQvEWvbjuSPZ4xjjyVy1+jUWqMcGO8Zt9d9GvliXL8Z4ee7AFK/OVBQVFalLly764IMPlJKS4lp+//33KycnRx999FGdx4SHh2vdunWaMGGCa9nKlSv10EMPqbS0tN7nqaqqUlXVfydOeXm5EhISvO6acg8d04TnPpQkOX+o0rY3/4/HjwUA+Na4Gx9RVZjT9furU4cq5dKOHj++Oc9UWFHfmlrbqGUAmirhw4/Upp3nx0czx1VbXv0pIyNDUVFRrltCQkKT1nOkorLxQQAAWwj2Y3ZTa1uw5wWA73jz1iezvHqmTp06KTQ0tM5/YEpLSxUbG1vvY2JjY70aL0nz5s1zO6V87r853opuG+H6uSo0XONufMTrddjV2slDlJzYwZLn+qjgO925Zqclz2VHVuYajWvp83HuqMu1JPNzy56vsflvZn9UhYa7/f7jY7bVrKhvTa1tgVrL7Hbs9HSuWv0aay7Ebb85ZweOiy6y7Lm8airCw8M1cOBAZWVlady4cZLOfpAtKytLs2bNqvcxKSkpysrK0uzZs13LduzY4XZ6+XxOp1NOp7PB+z01JLGD4qIiVFJWKcPhcDvNLp19D15MpFOSQ6XllXU+/GPXMbFRERryP10UYtF7j4f8z0Xq0DHqbB4biMluOQrUXKNxLX0+3nHt5Vq9q9iS7fdk/jfX/oiNOntpSH+xor41tbYFYi2z47HTk7lq9WssUI8NdozbjnOupfH67U9paWl67rnntG7dOn322WeaPn26Tp06pcmTJ0uSJk6c6PZBt3vvvVeZmZl6/PHH9fnnn2vRokXavXt3gwfp5hQa4lD6mN6Szk64Hzv3+6KbrtCimwJrTPqY3pZ+mDFY82jHXKNxLX0+hoeFWLb9nsz/5tofdnit2bW+BeKct8P+PJ8nebT6NRaoxwY7xm3HOdfSeN1UjB8/Xn/84x+1cOFC9evXT/n5+crMzFRMTIwkqbCwUMXFxa7xV111lV555RWtXr1aSUlJ2rx5s7Zt22bZd1SM6hOnZ1IHKDbK/bR6bFSE6/JjgTjGanbb/mDONRpntzli9Xy02/wPlteaneub3eZhIOzP+tjxNRaoxwY7xg3/8vp7KvyhOa7wYbdvjgzUb4202/YHc67ROLvNkUD99tlA/Ubt5v6eCqs1JX67zcNAPXba8TUWqMcGO8aNpjNzXG0xTQUAILgEem0I9PgBBB/LvvzOX871PeXl5X6OBABgF+dqQgD8b6xe1DYAdmPmuBoQTUVFRYUkNfn7KgAAwauiokJRUVH+DsNr1DYAdtWU42pAvP2ptrZWRUVFatu2rRyOpr9v7tw1wQ8fPhwwp5oDMWYpMOMOxJilwIw7EGOWiNtKnsRsGIYqKioUHx+vkBBbfpfrBTW1tgXi/pSI22rEba1gidvMcTUgzlSEhISoa9euzba+yMjIgNrhUmDGLAVm3IEYsxSYcQdizBJxW6mxmAPxDMU5ZmtbIO5PibitRtzWCoa4m3pcDbx/7QAAAACwFZoKAAAAAKa0qKbC6XQqPT1dTqfT36F4LBBjlgIz7kCMWQrMuAMxZom4rRSIMVslUHND3NYibmsRd4B8UBsAAACAfbWoMxUAAAAAmh9NBQAAAABTaCoAAAAAmEJTAQAAAMCUFtNUrFixQpdccokiIiKUnJysnTt3+jukC1q0aJEcDofb7fLLL/d3WG7ee+89jRkzRvHx8XI4HNq2bZvb/YZhaOHChYqLi9NFF12kESNG6Msvv/RPsD/SWNx33nlnndyPGjXKP8H+R0ZGhgYPHqy2bdsqOjpa48aN04EDB9zGVFZWaubMmerYsaPatGmjW2+9VaWlpX6K+CxP4r722mvr5HvatGl+ilh65pln1LdvX9cXAaWkpGj79u2u++2YZ6nxuO2W5/osWbJEDodDs2fPdi2za779hVrmG9Qza1HTrGVVXWsRTcXGjRuVlpam9PR07dmzR0lJSRo5cqSOHDni79Au6IorrlBxcbHr9q9//cvfIbk5deqUkpKStGLFinrvf+yxx/TUU09p1apV+uijj3TxxRdr5MiRqqystDhSd43FLUmjRo1yy/2rr75qYYR15eTkaObMmfrwww+1Y8cOff/997r++ut16tQp15j77rtPb7zxhjZt2qScnBwVFRXplltu8WPUnsUtSVOnTnXL92OPPeaniKWuXbtqyZIlysvL0+7du/Xzn/9cY8eO1SeffCLJnnmWGo9bsleez7dr1y49++yz6tu3r9tyu+bbH6hlvkM9sxY1zVqW1TWjBRgyZIgxc+ZM1+81NTVGfHy8kZGR4ceoLiw9Pd1ISkrydxgek2Rs3brV9Xttba0RGxtrLF261LXsxIkThtPpNF599VU/RFi/8+M2DMOYNGmSMXbsWL/E46kjR44YkoycnBzDMM7mtlWrVsamTZtcYz777DNDkpGbm+uvMOs4P27DMIxrrrnGuPfee/0XlAfat29vPP/88wGT53POxW0Y9s5zRUWFcdlllxk7duxwizPQ8u1r1DJrUM+sR02zni/qWtCfqaiurlZeXp5GjBjhWhYSEqIRI0YoNzfXj5E17ssvv1R8fLx69OihO+64Q4WFhf4OyWMFBQUqKSlxy3tUVJSSk5Ntn3dJys7OVnR0tHr16qXp06fr2LFj/g7JTVlZmSSpQ4cOkqS8vDx9//33bvm+/PLL1a1bN1vl+/y4z3n55ZfVqVMn9enTR/PmzdPp06f9EV4dNTU12rBhg06dOqWUlJSAyfP5cZ9j1zzPnDlTN9xwg1tepcCZ11aglvkP9cz3qGnW8WVdC2vuYO3m6NGjqqmpUUxMjNvymJgYff75536KqnHJyclau3atevXqpeLiYj300EO6+uqrtX//frVt29bf4TWqpKREkurN+7n77GrUqFG65ZZblJiYqEOHDmn+/PkaPXq0cnNzFRoa6u/wVFtbq9mzZ+unP/2p+vTpI+lsvsPDw9WuXTu3sXbKd31xS9KvfvUrde/eXfHx8fr444/1wAMP6MCBA9qyZYvfYt23b59SUlJUWVmpNm3aaOvWrerdu7fy8/NtneeG4pbsmWdJ2rBhg/bs2aNdu3bVuS8Q5rVVqGX+Qz3zLWqaNayoa0HfVASq0aNHu37u27evkpOT1b17d7322mv69a9/7cfIgt/tt9/u+vnKK69U3759demllyo7O1vDhw/3Y2RnzZw5U/v377fl+5IvpKG47777btfPV155peLi4jR8+HAdOnRIl156qdVhSpJ69eql/Px8lZWVafPmzZo0aZJycnL8Eos3Goq7d+/etszz4cOHde+992rHjh2KiIjwSwzwLWqZf9m9nknUNKtYUdeC/u1PnTp1UmhoaJ1PsZeWlio2NtZPUXmvXbt2+slPfqKDBw/6OxSPnMttoOddknr06KFOnTrZIvezZs3Sm2++qXfffVddu3Z1LY+NjVV1dbVOnDjhNt4u+W4o7vokJydLkl/zHR4erp49e2rgwIHKyMhQUlKSnnzySdvnuaG462OHPOfl5enIkSMaMGCAwsLCFBYWppycHD311FMKCwtTTEyMrfNtJWqZ/1DPfIeaZh0r6lrQNxXh4eEaOHCgsrKyXMtqa2uVlZXl9l5juzt58qQOHTqkuLg4f4fikcTERMXGxrrlvby8XB999FFA5V2Svv32Wx07dsyvuTcMQ7NmzdLWrVv1zjvvKDEx0e3+gQMHqlWrVm75PnDggAoLC/2a78birk9+fr4k2Wqu19bWqqqqyrZ5bsi5uOtjhzwPHz5c+/btU35+vus2aNAg3XHHHa6fAynfvkQt8x/qWfOjpvmfT+pac36S3K42bNhgOJ1OY+3atcann35q3H333Ua7du2MkpISf4fWoN/97ndGdna2UVBQYLz//vvGiBEjjE6dOhlHjhzxd2guFRUVxt69e429e/cakownnnjC2Lt3r/HNN98YhmEYS5YsMdq1a2e8/vrrxscff2yMHTvWSExMNM6cOWPbuCsqKow5c+YYubm5RkFBgfGPf/zDGDBggHHZZZcZlZWVfot5+vTpRlRUlJGdnW0UFxe7bqdPn3aNmTZtmtGtWzfjnXfeMXbv3m2kpKQYKSkpfovZMBqP++DBg8bixYuN3bt3GwUFBcbrr79u9OjRwxg2bJjfYp47d66Rk5NjFBQUGB9//LExd+5cw+FwGG+//bZhGPbMs2FcOG475rkh5185xa759gdqme9Qz6xFTbOWVXWtRTQVhmEYTz/9tNGtWzcjPDzcGDJkiPHhhx/6O6QLGj9+vBEXF2eEh4cbXbp0McaPH28cPHjQ32G5effddw1JdW6TJk0yDOPsZfgefPBBIyYmxnA6ncbw4cONAwcO+Ddo48Jxnz592rj++uuNzp07G61atTK6d+9uTJ061e9Fu754JRlr1qxxjTlz5owxY8YMo3379kbr1q2Nm2++2SguLvZf0EbjcRcWFhrDhg0zOnToYDidTqNnz57G73//e6OsrMxvMd91111G9+7djfDwcKNz587G8OHDXQdew7Bnng3jwnHbMc8NOb+psGu+/YVa5hvUM2tR06xlVV1zGIZheHduAwAAAAD+K+g/UwEAAADAt2gqAAAAAJhCUwEAAADAFJoKAAAAAKbQVAAAAAAwhaYCAAAAgCk0FQAAAABMoakAAAAAYApNBQAAAABTaCoAAAAAmEJTAQAAAMAUmgoAAAAApvx/ejICBB7dTmYAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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UAAAAALCEpgIAAACAJTQVAAAAACyhqQAAAABgCU0FAAAAAEsa1FQsXLhQZ511luLj45WVlaWNGzfWOfb555+Xy+XyucXHxzc4MAAAoUJ9A4CGCbipeOWVV5STk6Pc3Fxt2bJFGRkZGjhwoPbs2VPnOomJiSopKfHefvjhB0uhAQAINuobADRcwE3FvHnzNGbMGI0ePVrdunXT4sWL1aJFCz333HN1ruNyuZScnOy9JSUlWQoNAECwUd8AoOECaiqOHj2qwsJCDRgw4NcNREVpwIAB2rBhQ53rHThwQJ07d1ZaWpqGDBmiL7744rT7OXLkiCoqKnxuAACEih31jdoGoDELqKnYu3evqqura/wlJikpSaWlpbWu07VrVz333HN67bXX9MILL8jj8ejiiy/Wjz/+WOd+8vLy5Ha7vbe0tLRAYgIAEBA76hu1DUBjFvKrP2VnZ+vGG2/URRddpMsuu0yrVq1Su3bt9PTTT9e5zvTp01VeXu69FRcXhzomAAABCbS+UdsANGYxgQxu27atoqOjVVZW5rO8rKxMycnJfm2jWbNm6tmzp7799ts6x8TFxSkuLi6QaAAANJgd9Y3aBqAxC+iVitjYWGVmZio/P9+7zOPxKD8/X9nZ2X5to7q6Wp9//rlSUlICSwoAQIhQ3wDAmoBeqZCknJwcjRo1Sr1791bfvn01f/58HTx4UKNHj5Yk3XjjjerQoYPy8vIkSbNnz9bvf/97nXPOOdq/f7/mzp2rH374QbfccktwjwQAAAuobwDQcAE3FcOHD9dPP/2kmTNnqrS0VBdddJHWrl3r/XDbrl27FBX16wsgv/zyi8aMGaPS0lKdeeaZyszM1EcffaRu3boF7ygAALCI+gYADRdwUyFJkyZN0qRJk2q9b/369T4/P/bYY3rssccashsAAGxFfQOAhgn51Z8AAAAANG40FQAAAAAsoakAAAAAYAlNBQAAAABLaCoAAAAAWEJTAQAAAMASmgoAAAAAltBUAAAAALCEpgIAAACAJTQVAAAAACyhqQAAAABgCU0FAAAAAEtoKgAAAABYQlMBAAAAwBKaCgAAAACW0FQAAAAAsISmAgAAAIAlNBUAAAAALKGpAAAAAGAJTQUAAAAAS2gqAAAAAFhCUwEAAADAEpoKAAAAAJbQVAAAAACwhKYCAAAAgCU0FQAAAAAsoakAAAAAYAlNBQAAAABLaCoAAAAAWEJTAQAAAMASmgoAAAAAltBUAAAAALAkpiErLVy4UHPnzlVpaakyMjL0xBNPqG/fvnWOX7lype655x59//33Ovfcc/XQQw/pT3/6U4NDN0S1x2hj0c/aU1ml9gnx6pveWtFRLsYEMMaJmZw2xomZ/M0NnE5T+X2MxPp2qmDNcTAfK6dlCub5PFj7Y77J5LR9BSrgpuKVV15RTk6OFi9erKysLM2fP18DBw7Ujh071L59+xrjP/roI40YMUJ5eXm6+uqr9dJLL2no0KHasmWLunfvHpSDqM/a7SW6940vVVJe5V2W4o5X7uBuGtQ9hTF+jHFiJqeNcWImf3MDp9NUfh8jsb6dKlhzHMzHymmZgnk+D9b+mG8yOW1fDRHw25/mzZunMWPGaPTo0erWrZsWL16sFi1a6Lnnnqt1/IIFCzRo0CDdcccd+t3vfqf77rtPvXr10pNPPmk5vD/Wbi/R+Be2+DwAklRaXqXxL2zR2u0ljKlnDPPYeOcIqE9T+n2MtPp2qmDNcTAfK6dlCub5PFj7Y77905gzOW1fDRXQKxVHjx5VYWGhpk+f7l0WFRWlAQMGaMOGDbWus2HDBuXk5PgsGzhwoNasWRN42gBVe4zufeNLGUkyRnHVR33ud0l68P9tkeRS7PEjtW6jqY/JW7VVl3dKUN6qrY7J5LQxkTpHeau2qv9ZiYqOcslz9Lji/nes59AheY7XPDXYOcbu/UXiGDv2V+0xIf29PhIdK+NyySXp3je+1B+7JYftZfxIqW/GmAY/Vv4854O1HSdm8nc7/pzPg7W/YJ6rI3W+T25HsnYuitTf798KRW5jTK3rhILLBLC33bt3q0OHDvroo4+UnZ3tXX7nnXeqoKBAn3zySY11YmNjtXTpUo0YMcK77KmnntK9996rsrKyWvdz5MgRHTny68RVVFQoLS1N5eXlSkxM9DeuNuzcpxH/+FiSFHf8iNa8+Xe/1wUAhNbQqx/QkZg4788vj/m9ss9u4/f6FRUVcrvdAdeG2thR34JR2w7sr1Dx77MCOTQATVjax5+oZSv/z49WzquOvPpTXl6e3G6395aWltag7eyprKp/EADAERr7OTsYta1FbIOurwKgibLznBHQntq2bavo6Ogaf4EpKytTcnJyreskJycHNF6Spk+f7vOS8sm/5gSqfUK8999HomM19OoHAt4GpLsGna85a78OdwxHi9Q5en50X2Wltw53DDjUJ0U/66YlG0O2/SPRsT4///acbTc76lswapureXN13VJYY7m/j1V9z/lgbceJmfzdjr/n82Dtzx+Neb4j8diCva36WNmXq3lzS/sOREBNRWxsrDIzM5Wfn6+hQ4dKkjwej/Lz8zVp0qRa18nOzlZ+fr4mT57sXbZu3Tqfl5dPFRcXp7i4uDrv91ff9NZKccertLxKxuXyeZldOvEetKTEOEkulVVUqbb3gTX1McnueN1w+fl6ZlPJiXl0QCanjYnUOUp2x6vv7zooyiGXooPz9P1dc7Vu47bl9zrZfeLSiOFiR30LRm1zuVxytWhRY7k/j5U/z/lgbceJmfzdjj/n82DtL5jn6kid70g8tmBvqz527suKgN/+lJOTo3/84x9aunSpvvrqK40fP14HDx7U6NGjJUk33nijzwfdbr/9dq1du1aPPvqovv76a82aNUubN2+u8yQdTNFRLuUO7ibpxIT/1smfZ11zgWZdw5i6xuQO7qbYmCjm8TRjInWOcgd3c8y1reFMdp5DnfD7GEn17VT+PFb+zHGwtuPETP5ux5/zebD2F8znRqTOdyQeW7C35aR9WRFwUzF8+HA98sgjmjlzpi666CJt27ZNa9euVVJSkiRp165dKin59bJWF198sV566SU988wzysjI0Kuvvqo1a9bYdg3vQd1TtGhkLyW7fV9WT3bHa9HIXhrUPYUx9YxhHhvvHAH1aUq/j5FW304VrDkO5mPltEzBPJ8Ha3/Mt38acyan7auhArr6U7gE4wofTvsG40gc48RMThvjxExO/vZNRA4n/j4G8+pP4RCq/I35G4f5Ru3gHl+kbaexZ3LCvqycl5pMUwEAaFwivTZEen4AjY+V81JEXJvuZN9TUVER5iQAAKc4WRMi4G9jtaK2AXAaK+fViGgqKisrJanB31cBAGi8Kisr5Xa7wx0jYNQ2AE7VkPNqRLz9yePxaPfu3UpISJDL1fD3jZ28JnhxcXHEvNQciZmlyMwdiZmlyMwdiZklctvJn8zGGFVWVio1NVVRUY78LtfTamhti8THUyK33chtr8aS28p5NSJeqYiKilLHjh2Dtr3ExMSIesClyMwsRWbuSMwsRWbuSMwskdtO9WWOxFcoTrJa2yLx8ZTIbTdy26sx5G7oeTXy/rQDAAAAwFFoKgAAAABY0qSairi4OOXm5iouLi7cUfwWiZmlyMwdiZmlyMwdiZklctspEjPbJVLnhtz2Ire9yB0hH9QGAAAA4FxN6pUKAAAAAMFHUwEAAADAEpoKAAAAAJbQVAAAAACwpMk0FQsXLtRZZ52l+Ph4ZWVlaePGjeGOdFqzZs2Sy+XyuZ1//vnhjuXjgw8+0ODBg5WamiqXy6U1a9b43G+M0cyZM5WSkqLmzZtrwIAB+uabb8IT9jfqy33TTTfVmPtBgwaFJ+z/ysvLU58+fZSQkKD27dtr6NCh2rFjh8+YqqoqTZw4UW3atFHLli01bNgwlZWVhSnxCf7kvvzyy2vM97hx48KUWFq0aJF69Ojh/SKg7OxsvfPOO977nTjPUv25nTbPtZkzZ45cLpcmT57sXebU+Q4XalloUM/sRU2zl111rUk0Fa+88opycnKUm5urLVu2KCMjQwMHDtSePXvCHe20LrjgApWUlHhvH374Ybgj+Th48KAyMjK0cOHCWu9/+OGH9fjjj2vx4sX65JNPdMYZZ2jgwIGqqqqyOamv+nJL0qBBg3zm/uWXX7YxYU0FBQWaOHGiPv74Y61bt07Hjh3TFVdcoYMHD3rHTJkyRW+88YZWrlypgoIC7d69W9ddd10YU/uXW5LGjBnjM98PP/xwmBJLHTt21Jw5c1RYWKjNmzerX79+GjJkiL744gtJzpxnqf7ckrPm+VSbNm3S008/rR49evgsd+p8hwO1LHSoZ/aiptnLtrpmmoC+ffuaiRMnen+urq42qampJi8vL4ypTi83N9dkZGSEO4bfJJnVq1d7f/Z4PCY5OdnMnTvXu2z//v0mLi7OvPzyy2FIWLtTcxtjzKhRo8yQIUPCksdfe/bsMZJMQUGBMebE3DZr1sysXLnSO+arr74yksyGDRvCFbOGU3MbY8xll11mbr/99vCF8sOZZ55pnn322YiZ55NO5jbG2fNcWVlpzj33XLNu3TqfnJE236FGLbMH9cx+1DT7haKuNfpXKo4eParCwkINGDDAuywqKkoDBgzQhg0bwpisft98841SU1PVpUsX3XDDDdq1a1e4I/mtqKhIpaWlPvPudruVlZXl+HmXpPXr16t9+/bq2rWrxo8fr3379oU7ko/y8nJJUuvWrSVJhYWFOnbsmM98n3/++erUqZOj5vvU3Ce9+OKLatu2rbp3767p06fr0KFD4YhXQ3V1tZYvX66DBw8qOzs7Yub51NwnOXWeJ06cqKuuuspnXqXI+b22A7UsfKhnoUdNs08o61pMsMM6zd69e1VdXa2kpCSf5UlJSfr666/DlKp+WVlZev7559W1a1eVlJTo3nvv1R/+8Adt375dCQkJ4Y5Xr9LSUkmqdd5P3udUgwYN0nXXXaf09HTt3LlTM2bM0JVXXqkNGzYoOjo63PHk8Xg0efJkXXLJJerevbukE/MdGxurVq1a+Yx10nzXlluS/vKXv6hz585KTU3VZ599pmnTpmnHjh1atWpV2LJ+/vnnys7OVlVVlVq2bKnVq1erW7du2rZtm6Pnua7ckjPnWZKWL1+uLVu2aNOmTTXui4Tfa7tQy8KHehZa1DR72FHXGn1TEamuvPJK77979OihrKwsde7cWStWrNBf//rXMCZr/K6//nrvvy+88EL16NFDZ599ttavX6/+/fuHMdkJEydO1Pbt2x35vuTTqSv32LFjvf++8MILlZKSov79+2vnzp06++yz7Y4pSeratau2bdum8vJyvfrqqxo1apQKCgrCkiUQdeXu1q2bI+e5uLhYt99+u9atW6f4+PiwZEBoUcvCy+n1TKKm2cWOutbo3/7Utm1bRUdH1/gUe1lZmZKTk8OUKnCtWrXSeeedp2+//TbcUfxycm4jfd4lqUuXLmrbtq0j5n7SpEl688039f7776tjx47e5cnJyTp69Kj279/vM94p811X7tpkZWVJUljnOzY2Vuecc44yMzOVl5enjIwMLViwwPHzXFfu2jhhngsLC7Vnzx716tVLMTExiomJUUFBgR5//HHFxMQoKSnJ0fNtJ2pZ+FDPQoeaZh876lqjbypiY2OVmZmp/Px87zKPx6P8/Hyf9xo73YEDB7Rz506lpKSEO4pf0tPTlZyc7DPvFRUV+uSTTyJq3iXpxx9/1L59+8I698YYTZo0SatXr9Z7772n9PR0n/szMzPVrFkzn/nesWOHdu3aFdb5ri93bbZt2yZJjvpd93g8OnLkiGPnuS4nc9fGCfPcv39/ff7559q2bZv31rt3b91www3ef0fSfIcStSx8qGfBR00Lv5DUtWB+ktypli9fbuLi4szzzz9vvvzySzN27FjTqlUrU1paGu5odfrb3/5m1q9fb4qKisy///1vM2DAANO2bVuzZ8+ecEfzqqysNFu3bjVbt241ksy8efPM1q1bzQ8//GCMMWbOnDmmVatW5rXXXjOfffaZGTJkiElPTzeHDx92bO7KykozdepUs2HDBlNUVGTeffdd06tXL3PuueeaqqqqsGUeP368cbvdZv369aakpMR7O3TokHfMuHHjTKdOncx7771nNm/ebLKzs012dnbYMhtTf+5vv/3WzJ4922zevNkUFRWZ1157zXTp0sVceumlYct81113mYKCAlNUVGQ+++wzc9dddxmXy2X+9a9/GWOcOc/GnD63E+e5LqdeOcWp8x0O1LLQoZ7Zi5pmL7vqWpNoKowx5oknnjCdOnUysbGxpm/fvubjjz8Od6TTGj58uElJSTGxsbGmQ4cOZvjw4ebbb78Ndywf77//vpFU4zZq1ChjzInL8N1zzz0mKSnJxMXFmf79+5sdO3aEN7Q5fe5Dhw6ZK664wrRr1840a9bMdO7c2YwZMybsRbu2vJLMkiVLvGMOHz5sJkyYYM4880zTokULc+2115qSkpLwhTb15961a5e59NJLTevWrU1cXJw555xzzB133GHKy8vDlvnmm282nTt3NrGxsaZdu3amf//+3hOvMc6cZ2NOn9uJ81yXU5sKp853uFDLQoN6Zi9qmr3sqmsuY4wJ7LUNAAAAAPhVo/9MBQAAAIDQoqkAAAAAYAlNBQAAAABLaCoAAAAAWEJTAQAAAMASmgoAAAAAltBUAAAAALCEpgIAAACAJTQVAAAAACyhqQAAAABgCU0FAAAAAEtoKgAAAABY8v8Bbs8Kj+bOPJMAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x180 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from matplotlib import pyplot as plt\n",
        "\n",
        "def plot_i_th_pair(i):\n",
        "    fig, (a0, a1) = plt.subplots(1, 2, figsize=(8, 1.8), gridspec_kw={'width_ratios': [len_x, len_y]})\n",
        "    a0.stem(X[i], use_line_collection = True)\n",
        "    a0.set_title('X[' + str(i) + ']')\n",
        "    a0.set_ylim([-0.1, 1.1])\n",
        "    a1.stem(Y[i], use_line_collection = True)\n",
        "    a1.set_title('Y[' + str(i) + ']')\n",
        "    a1.set_ylim([-0.1, 1.1])\n",
        "    fig.tight_layout()\n",
        "\n",
        "for i in range(10):\n",
        "    plot_i_th_pair(i)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## H-score Network and Trainning\n",
        "\n",
        "Here we use one-dimensional convolutional neural networks to extract the features from sequences. Such networks are commonly used for [sentence classification](https://arxiv.org/abs/1408.5882).\n",
        "\n",
        "The network architecture is defiend in the class $\\mathtt{cnn\\_seq}$."
      ],
      "metadata": {
        "id": "eFQmYdyjJMHP"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mwE7z5wbrFAE"
      },
      "outputs": [],
      "source": [
        "from torch import optim\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "\n",
        "\n",
        "class cnn_seq(nn.Module):\n",
        "    \"\"\"An 1D Convulational Neural Network for Sequence Processing.\"\"\"\n",
        "    # modified from https://colab.research.google.com/drive/1b7aZamr065WPuLpq9C4RU6irB59gbX_K#scrollTo=ejGLw8TKViBY\n",
        "    def __init__(self,\n",
        "                 input_dim,\n",
        "                 embed_dim,\n",
        "                 out_dim,\n",
        "                 filter_size,\n",
        "                 num_filters):\n",
        "        \"\"\"\n",
        "        The constructor for cnn_seq class.\n",
        "\n",
        "        Args:\n",
        "            input_dim (int): Dimension of inputs\n",
        "            embed_dim (int): Dimension of embedings.\n",
        "            out_dim (int): Dimension of output features\n",
        "            filter_size (int): filter size\n",
        "            num_filters (int): number of filters\n",
        "        \"\"\"\n",
        "\n",
        "        super(cnn_seq, self).__init__()\n",
        "        # Embedding layer\n",
        "        self.input_dim = input_dim\n",
        "        self.embed_dim = embed_dim\n",
        "        self.embedding = nn.Linear(input_dim, embed_dim)\n",
        "\n",
        "        # Conv Network\n",
        "        self.conv1d = nn.Conv1d(in_channels=self.embed_dim,\n",
        "                      out_channels=num_filters,\n",
        "                      kernel_size=filter_size)\n",
        "        # Fully-connected layer\n",
        "        self.fc = nn.Linear(num_filters, out_dim)\n",
        "\n",
        "    def forward(self, x_input):\n",
        "        \"\"\"Perform a forward pass through the network.\n",
        "\n",
        "        Args:\n",
        "            x_input (torch.Tensor): input tensor with shape\n",
        "                (batch_size, x_card_sym)\n",
        "\n",
        "        Returns:\n",
        "            f (torch.Tensor): Output features with shape (batch_size, out_dim)\n",
        "        \"\"\"\n",
        "\n",
        "        # Get embeddings from inputs. Output shape: (b, max_len, embed_dim)\n",
        "        x_embed = self.embedding(x_input)\n",
        "\n",
        "        # Permute `x_embed` to match input shape requirement of `nn.Conv1d`.\n",
        "        # Output shape: (b, embed_dim, max_len)\n",
        "        x_reshaped = x_embed.permute(0, 2, 1)\n",
        "\n",
        "        # Apply CNN and Relu. Output shape: (b, num_filters, L_out)\n",
        "        #       L_out is the length of features after convolution\n",
        "        x_conv = F.relu(self.conv1d(x_reshaped))\n",
        "\n",
        "        # Avg pooling. Output shape: (b, num_filters, 1)\n",
        "        x_pool = F.avg_pool1d(x_conv, kernel_size=x_conv.shape[2])\n",
        "\n",
        "        # Concatenate x_pool_list to feed the fully connected layer.\n",
        "        # Output shape: (b, num_filters)\n",
        "        x_fc = x_pool.squeeze(dim=2)\n",
        "\n",
        "        # Compute features. Output shape: (b, out_dim)\n",
        "        f = self.fc(x_fc)\n",
        "\n",
        "        return f\n",
        "\n",
        "class fg_nn(nn.Module): # f_net, g_net\n",
        "    def __init__(self, f_net, g_net):\n",
        "        super().__init__()\n",
        "        self.f_net = f_net\n",
        "        self.g_net = g_net\n",
        "\n",
        "    def forward(self, x, y):\n",
        "        f = self.f_net(x)\n",
        "        g = self.g_net(y)\n",
        "        return f, g\n",
        "\n",
        "    def get_f(self, x):\n",
        "        f = self.f_net(x)\n",
        "        return f\n",
        "\n",
        "    def get_g(self, y):\n",
        "        g = self.g_net(y)\n",
        "        return g\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We set the parameters for the one-dimensional cnn. Note that here we only extract $k = 1$ dimensional feature ($\\mathtt{out\\_dim} = 1$)."
      ],
      "metadata": {
        "id": "vQusqRlIPjzc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "embed_dim = 4\n",
        "filter_size = 4\n",
        "num_filters = 32\n",
        "\n",
        "out_dim = 1 # k = 1\n",
        "\n",
        "f_net = cnn_seq(input_dim = x_card_sym, embed_dim = embed_dim, out_dim = out_dim, filter_size = filter_size, num_filters = num_filters)\n",
        "g_net = cnn_seq(input_dim = y_card_sym, embed_dim = embed_dim, out_dim = out_dim, filter_size = filter_size, num_filters = num_filters)\n",
        "\n",
        "model = fg_nn(f_net, g_net)\n",
        "model.to(device)\n",
        "opt = optim.Adam(model.parameters())"
      ],
      "metadata": {
        "id": "Www-DKxZPfq6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We maximize the H-score to train the neural feature extractors."
      ],
      "metadata": {
        "id": "Ni27ZJwzP1g5"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1cZgm3V9Ad9K",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fdba4673-cfd8-4032-8d6e-7cca07aa41f8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Train:\n",
            "Epoch 0/50\n",
            "Epoch 10/50\n",
            "Epoch 20/50\n",
            "Epoch 30/50\n",
            "Epoch 40/50\n"
          ]
        }
      ],
      "source": [
        "centralize = lambda x: x - torch.mean(x, 0) # zero-mean\n",
        "cov = lambda x: x.T @ x / (x.size()[0]-1.) # covariance\n",
        "\n",
        "def neg_hscore(f, g):\n",
        "    \"\"\"\n",
        "    compute the negative h-score\n",
        "    \"\"\"\n",
        "    f0 = centralize(f)\n",
        "    g0 = centralize(g)\n",
        "    corr = torch.mean(torch.sum(f0*g0, 1))\n",
        "    # to generate zero-mean f, g\n",
        "    cov_f = cov(f)\n",
        "    cov_g = cov(g)\n",
        "    return - corr + torch.trace(cov_f @ cov_g) / 2.\n",
        "\n",
        "# define a function for training\n",
        "def train(model, dataloder, loss_func, optimizer, nEpochs):\n",
        "    for epoch in range(nEpochs):\n",
        "        if epoch % 10 == 0:\n",
        "            print(\"Epoch \" + str(epoch) + '/' + str(nEpochs))\n",
        "        for x, y in dataloder:\n",
        "            f, g = model(x.to(device), y.to(device))\n",
        "            loss = loss_func(f, g)\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "            optimizer.zero_grad()\n",
        "\n",
        "print(\"Train:\")\n",
        "train(model = model, dataloder = dl, loss_func = neg_hscore, optimizer = opt, nEpochs = nEpochs)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Analyizing Dependence Structure From Features\n",
        "\n",
        "First, let's extract features from the test data and take a look at their distributions."
      ],
      "metadata": {
        "id": "LDBY9QVNCmC8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "f_test = f_net(Xt_test.to(device)).cpu().detach().numpy()\n",
        "g_test = g_net(Yt_test.to(device)).cpu().detach().numpy()\n",
        "\n",
        "# whiten\n",
        "from scipy.cluster.vq import whiten\n",
        "f_test = whiten(f_test)\n",
        "g_test = whiten(g_test)"
      ],
      "metadata": {
        "id": "MjGK8NVNjGbL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(f_test, bins = 20)[-1]\n",
        "plt.title(\"Histogram of f\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "dcX1bE6zjIbn",
        "outputId": "ab38ef08-a779-45f1-ddf1-200bf1679c32"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(g_test, bins = 20)[-1]\n",
        "plt.title(\"Histogram of g\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "yZ08ptIcjL1M",
        "outputId": "b1a07f7e-714b-4572-90a8-76b728c55242"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can note that both $f(\\underline{\\sf x})$ and $g(\\underline{\\sf y})$ form two clusters. We may guess that one cluster corresponds to high-frequency sequences, and the other is high-frequency sequences.\n",
        "\n",
        "If this is the case, when we plot the pair $(f(\\underline{\\sf x}), g(\\underline{\\sf y}))$ on a plane, we shall see four clusters, which corresponds to all four combinations of x sequence and y sequence:\n",
        "\n"
      ],
      "metadata": {
        "id": "Uk9Afxt411Iu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure()\n",
        "len_plot = nSamples_test # number of points to plot\n",
        "f_test_plot = f_test[:len_plot]\n",
        "g_test_plot = g_test[:len_plot]\n",
        "plt.scatter(f_test_plot, g_test_plot, alpha = .3)\n",
        "plt.xlabel('f(x)')\n",
        "plt.ylabel('g(y)')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "qGd7C3m5x6RM",
        "outputId": "4f1faee7-e0fe-4036-afbf-90dfc6bb5b12"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'g(y)')"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As expected, the feature pairs are well-clustered on four corners. We further apply k-menas clustering algorithm to get these clusters, and plot the feature pairs in differnt colors."
      ],
      "metadata": {
        "id": "L-UAwKcGwPHQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.cluster.vq import kmeans2\n",
        "f_min = np.min(f_test_plot)\n",
        "f_max = np.max(f_test_plot)\n",
        "g_min = np.min(g_test_plot)\n",
        "g_max = np.max(g_test_plot)\n",
        "centroid_initial = np.array([[f_min, g_max],\n",
        "                             [f_max, g_max],\n",
        "                             [f_min, g_min],\n",
        "                             [f_max, g_min]])\n",
        "centroid, label_kmeans = kmeans2(np.concatenate([f_test_plot, g_test_plot], axis = 1), centroid_initial, minit='matrix')\n",
        "\n",
        "# plot\n",
        "plt.figure()\n",
        "plt.xlabel('f')\n",
        "plt.ylabel('g')\n",
        "plt.scatter(f_test_plot,\n",
        "            g_test_plot,\n",
        "            c = label_kmeans,\n",
        "            alpha = .3)\n",
        "plt.xlabel('f(x)')\n",
        "plt.ylabel('g(y)')"
      ],
      "metadata": {
        "id": "wR0uk1ZPOy1M",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "outputId": "da7d7db8-47a8-40b0-b635-f9cca896b0be"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'g(y)')"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Then we can count the number of points in these clusters and get the proportion of each cluster."
      ],
      "metadata": {
        "id": "WqssuyzNxGDI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "_, counts = np.unique(label_kmeans, return_counts=True)\n",
        "\n",
        "with np.printoptions(precision=2, suppress=True):\n",
        "    print('proportion = \\n', counts.reshape(v_card, u_card)/len_plot)"
      ],
      "metadata": {
        "id": "eWtKfec7wOYe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e78c8020-efc4-48ae-84cd-b24b348b56cb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "proportion = \n",
            " [[0.11 0.2 ]\n",
            " [0.39 0.3 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This should correspond to the dependence between hidden variables $\\sf u$, $\\sf v$, up to the some permutation of rows and columns:"
      ],
      "metadata": {
        "id": "H9EsSPPC0jP1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p_vu"
      ],
      "metadata": {
        "id": "OfC1OtTjydg1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "920a191e-ea76-41a6-a963-abfe47a6670a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.1, 0.2],\n",
              "       [0.4, 0.3]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Of course, we can also directly compare the clustering results with the ture label $\\sf (u, v)$. Let's plot the feature pairs again, but use the true label to color the points. This should give us the same cluster."
      ],
      "metadata": {
        "id": "ty8CUW21_oto"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "label_uv = V_test*2 + U_test\n",
        "plt.figure()\n",
        "#len_plot = len(f_test) # number of points to show\n",
        "plt.xlabel('f(x)')\n",
        "plt.ylabel('g(y)')\n",
        "plt.scatter(f_test,\n",
        "            g_test,\n",
        "            c = label_uv,\n",
        "            alpha = .3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "LV-wzoS5wZj9",
        "outputId": "5865b4cc-5198-4d32-c713-52770c9d55af"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f8e58c4a7d0>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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eIEsEKi9Eku3aGGNIk4zRyRitDVprhBAYbXAD0LFGG4Pj2+SZor87YKe6z/B4xMWXz4EQDI5GTAZTbv7qLuOTMQhBninG/Smv/r2XufzKRQRFb47t2acl3I9i+dwCfs1n+/ouWmlmo5Bwvmd99buXufC1zU88Vq3FJi99/xpv/s177N0+oNauYoxhNpxhew7f+A9e+kgxVlJS8uUkyRQn4xmNikeS5fTGMwaToin4eDRjsVlFaUPgObRMwHAWYz98845iDvpjxmGC79q06wGCws/HkoJxGBMlGUIIPArB4jk2mTZMw5hcFedWrTVJrsnyQtiY+Uk6yyEEslwjMKS5JsnV6doFxai9AEyueXga1UCmPlz3KXjyVz8dH2w+yDLNNE6I05zhLCSMM+pVn6bts3U0xLYspJTkuSLXGoEgzRUGMNpw2J+QKUXVd6lXPKIk+y1W9runFEJfIN79yQ3uv7ONGzhYUpBnObZjkcWgUoXRH/jT/eArQBfj9tl8b1nI4o8zm+9PC8n7/TSm+B5AGs7/WCXkaY4Ucu7HY5iNIuJJQlD1efDODid7PfJMUa1XiKYxvf0evx7NePtvrtNZabJxbY2lc4ssnltASMG0P6PaKCYsomlMOA6LF7aAarvKq3/3ZV77y7d472e3UErhV33q7SrTwYz3fnqT1UsrqCzHdm26q+0nNmhffPk81WaF7Zv7HG/3EEJw8eXzxVo2Fz6H31BJSckXgUmYstc/ZjJLsG1JlORMohQhBIFrY0nJxmKTesWjNw6ZRAl5rphFydyg0CKdC5ZJ9HAKTKMNCIoKjtFgWznOvKqttUFazBuW7aLCkymMBgSIhzUjY1DGPCZizAf+fSiCfhuh81nItGYSJQynIVGcYdsWgWMTZzmZUgghEAKULgQcgC0FtmVhRLHYRsXDkpI4VVS8syU9ztZqSj6SwdGQt390nSRKyeKM4+0eSZigcoXtOhhSdK7RH3FlAJDNe4hOqzHzmxrNvIL0EffVoHODJieNMyxb4ng2k9EUaQsO7h2jtcGruPT2BqRxgpSSNM5IohTLkfi7fWzXIU9z4llMnmu8qsfwaMTJTo8kSlG5JpyEXP3WJY7mX/u9//hbOJ6FlBZCCo62jvm3//d/T3u5SWetgwAaCw2ufusS51/ceKxBe+ncIkvnFt83VHTKP/mSkq8qnmPRrPj86tZtXMui26wgpaTmu+z1R0xmReXGYJBS0qwEHA4muJbFQrNGveLRn0akmWIwKfpqMqXJVDGUYslia0orjRZFBeqheWAhYAxSFL07rm0VVSIg1wZtcjIlUObTyZunJYKgeMvIc8Pu8RiEoep7HA6nREmGMea058i2JHLewwRFH5MUkqrv0KoGRFlOnOV0GmfLzLZ8V/gCkGc5P//fXuPGL27TWmji+i6T/pQkShBza1KlNOZjRNAjPOFmHyeggPm+L/MtrxlLm13GvSnRNGHUnxBUffREMe5PioktSxLUA7yKixDgV32GhyNWLy1jWRaz0Yxbv7zD0fYJ9W4dx7HAlqxcWCJLcn74//wRS+cWmQymVOo+lUaF6WDK9o098lSRpTkrFxYRQjA8GvHaX72JEHD+xSdvm5UCqKSkRIiiAfpkOMWxbHqTEFtKmjWflXadySwmU4reeEauNDsnI476U6qBQ8V3mUUJRoOQhlmckWYKSwqs+daQEAJpDNIqtomSDHzXwbEt4kyhNGj0+2LHGPIP9PboTymCngVCGJQpLphHs5hcKYQoxM/7fUnv70o87FkystgiG4cxlpSstut49tk6H5+t1ZQ8kfvvbHP/nW2q9Urh5ZNmWK6FCUEl+dOpkc4fP0sy0ihh6fwCw+Mxs36R4eX6NsPjMdE0wXJkUeFRGq0U7rwxe9ybcv3nt1jc6NI/HGI5Fle/dbnY4nNt2stN/JrPuz+5yfWf3WI6mFJtVpG2pLPaBm2IZwnLF5eYDibEs4Raq0p3rcPJbp/br91j9fJK6RZdUlLyRLJccXe/R640cZYi5maGB4MJlpAstGqkWU5vFBKnqvAYci2a1QDfdeiNZoRpRjAXN2Gao5WZR1ZIoiSj4jtYlkWuFHGWwzQk/mCvjyhO2Wmu+OCJW0qQBvIzqIVc26LiOXSbAcejokdIzrfzovjJNiSnI/u6iBapV3zWuw3ajcpvFE/yeVIKoTNOlmY8eGeHxkKdcX/Czu0iNwxdvICf5kaxmP/xTochD97exnaL5ucsyRkcDEmTHK/iElR9omlYNNgNQyzb5ninx6Q/ZXAw4Hi7x+7tfYJ6wLf+3stsXtug0gg43jrmF//f1zm4d8R0FHLw4JjFdUWa5Nx7exu05sLLm7zfMvg+7eUmB/ePGRwMP9IVu6Sk5KvBeBazczJk62hIlits26LmO0zChBvbxyy163TqFSZhQphkjKYhozCh7njYrsPRPLur4jl06hVWuw0OBxOa1YA4zchzg+fa2CLFYApRY+aj6ZmiQlEpyZUiTnMUhTdPJXBxLEmuNKnSZNn7IsKdGynyaSv7TwkB+K5Nveqz1GoyCzNmcYotLVzHJsnUE+/nWOI0J61R8fiDr12gVSu2Gn3XoT8OC6+iee/Qs6QUQmeccBwxHc5YvbDEwd1DDu4cE0cJ4SRC6483Ffw8kFJQqQfYnoPRmvZSk5PdPkmqqLVr6FyBMYX51zwHZ3wyZt+RSGGRpRnmYEA0iUijlF//xZvce2sLgNHJmPHxBNuziacRu8MZ02HI6sVlqo2AnRt7RZBsnNNdbT/iJWTZFsaY016gkpKSryZHwyk/e+8B/UmEJQRbJ0OOh1MMhiwrenlSpWhVA5ZaNXZ7I4QULLWqRGlOnGZAYVg4iWJcS3IoBA+OBkgp8D2XzMpJM0WmiuETG4HjSBZrFcazmFFYNF7bUsy92EArcB2bwLGx5tWjWIrCH4iiauK6Fql6srB4VhggTFIsKTkcjEnynIprI6XFLE4+8jq8yCOzyXJF4DqsdhrsnoyZRRnvPjjgzbt7SCHoNCo8t77IuaXWM0umL4XQGUfM66gGQ54phr0R8TRGP4P6qdGGPFWkScb61TXiSUyW59SaVZIwI54l5ElKnijyXKHyHDdwEUIwOByiMo1X8XA8B9uxSeOU3bsHHG4fo1KFsCSWbVGzq0jLQkhJPIvZu3dIZ7mJVprjnROyJOfKKxcecY5OwgTHsfCrH2+0WFJS8uVDa8NgWmzZ/PzmFkmas95t8O7WEWmWc3GlwziMubvX49xSi93emJu7x5xbbNEbzwhcF601O8dDlNLYlkXVF8zinPe2j/BdF8eWeI5NnBS+OZnSSCHwbIkQEgnkuQIhsO3i84VmlWrgM5lFDGcxaZqRphm+65BkOXGmTsfUcwMmPVsi6CFaG7QxnIymJJmiHrgUTtkSPkK4GQNplmOAJM+5vXPCyXiG5xRTec1agNaak/GM4+GUJN34jYJsfxeUQuiMU21VaC02uP6LW7z+w7cJh9GzXhLT+RbXwkaXvVv7SNvCr3nMRjOSMC0qVUIg56XRJEop5vSLFHmVK7I4JRxHGAOZJYqcNGUQUjA+GSNsSaNVYzqcMdwfkM5ijDboSOP5ESe7fdavrCItiTGGk70BqxeXaC83P3H9JSUlXx52T0Zc3z7ieDjleDTjwWGfS6tdcqXpT0K6jSpSCqp+EfUwi1POLbd5+94+r93eJc0Uvucwm/vkLDarCCGo+S5prgmTjOE0REqJJUXR5EPRbyTnU2JSFl5tYZKRZDm2kBgMjm1htCmq1UoRuC65gjTPSXM1nzZ7nzO2K3aKnosaa36+nUTpJzZ2azht24iSnL3+GCHglStr+O7DPk6L1Y5DfxLyzoND1haa1D7BLPfzoBRCZxyVa9I444f/8kec7A2e9XKQtiSJU7be2+bgwXHhXC0FWZKjMoXj2whLksU5lrTJVU6aFH5HjucgLYEQgizNwRIIXUy8WUJgjCbPckyu8WwfI4oqlJDF7V3fJahUyDPFnTe36K62aS01GZ1MaHSqXPjaJvn8diUlJV8ulNacjGbM4vQ0NX0wjfjpuw/IlGKhWSXNFa5tcTSccu+wj2tZp425ji1pVHyOhjOSXOFYFrZl4zpF03KSFp4/3UaFUZgQJcXWmKRohM60BiUwovACAoMyAtcShf+a0cVUmDZoUTx+1XcJ44xZkiGkZBrlGAxCQJ4//daG3xRDYQVQswshlH6GtUtgpV0DiiiT/f6Ei8udR9o827WAraMhB/0JV9ZLIVTyAXZu7vH2j67zl/+Pv2F0PHm6xhEf5tR7yKByTZ4qollCUAvwA3fuaaQhAq/i4vkuru+QJil5Gs63vSRpkqOnMVmaYdkOGo0w4nSSQiLRNqhcMe3P0PMqEQYsWxJUPaJZTBom7NzYw696VBsBWZrz2g/ewnZs1q+scO6FDZplllhJyZeC/jjk9Tu7HAwm5PMqSsVzGExCqoHH+kJRCZZC4Do2C80qRw+mJPajTbiOJRlMQ9I8p+a7uI6D0ppJVIzN50pzMJhiScEkTMgyhWNbgE2SpzxM7lLCFOIHQ5wUokfMxVExTm6Kxw2LykmS5mTq8dyvLxLKGEbhZ88I00BvHOI5Dp5js3M8ZLFRpVZ5X/A8bAFJnlGPZymEzij79w751V++yfhkwmQwQVgCx7PfN0V82sxfwYXf0Psv5yRKcT0H23PI8xg0pFGKZUnSrIj3EIDKcqZphi0lwpIYI04bm4UEISXVZuE0nSUZcZgghERIgdEK27GpNiuFo6qU+DWP9moLt+IxPhlTa1bxaz55mvPez25z/51t1p9bRUpBnmsq9YCF9Q7t5SaOW47Xl5R8UZiEMT997wH9SchSu4bn2Ghj2D4a8u6DI166uFLc0IA/t87IlaZVDdjrj8nznFzDfm/M7skIEMRpzmgW064FTKKU/mRGkipsq8jUqgUuSZaTa02WKJR5/6wnKcbG1UNRZAxG5RhhoY0pUt11Mdk6mIYEnkP+hPDTrxLaGBCG/iQkU4r+cviIEDKmmC5zPtD3+TQphdAZRGvNnTfuo3ON7dpMetPT/LCzhkoV4TRGzx1SDYVYCicxVlScMpTWp8E1udEIXZxVpJTznB1RhKsasD0byynCXh9GiLieQ2elhV/xSJOM1mKD6WDG7q19bMfm4svnHjFMTKKEN/7dO7z1oxs0u7VitD/OaS7WeeH3n+Pqty5z8eVzWNazedGVlJR8eu4fDjgezTi33JpvSRWVn4rv4Hs2R4Mpnm0zDmMmUcxwEnE8nNJuVLAtydFgxixN6Y8iqr5LLfBwHYtxmDCeJYxnhdGfYxcNwXGaF+csA5YlybK8iMGgEEGWJQoDj3mPsKHoofnwGLktIc0U0zjlDPskPhUG45CNxSbKKEaziNE0hg/0RY/DhKrvstx+NvmPpRA6g0z6U3ZvHTAeTHjtL95keDRCn+H95CzOAFOcLCSg53k5SoERj6T3CYB5js7DgFdpC6qNCkIKklnhll2p+0SzIg260gyQloXWhkanTr1bZ+vdbYbHE7652n5EBI17E+69tY1X9+jt9lFpRnuljevaDA5H3H3jAdNBSDxLeOn7157ZuGZJSckno7Vh62hAveKeiqCHOJaF5zjsnAzpT2Y0az6B67DUqXN3/4T3HhxiCcEsTJklCSvtBrYt2TkaIqRASotpHCMlLLXqjMKYwSTiYe1Hm3kvzwfOX5pPduF/SK4NuT6bU2BPG2UMSkOWFwG0g2mIMaaY9ptFhHHGK5fXaD6jqd9SCJ1B7r71gHd+fJ292weMexPUGawEnSKK3p384djnw6UaMKqwov/gbc38exgworCil1YR5lptVTFAa6mBZVmMTsb4FY9Gt44XuDh+MXafhAkgcH3ndDvtISe7fbIkm8eQzFjaXDgNd22vtJiNQhzP5s4b91l/bpX2UjllVlJyVlFak+fFOPuHqVc8bEtwMppyZXWBmu8hBYRxhmfbKGWoBC6+Z2NJQZxlzMYpSZYjpCBOI+JUIQWMwgRbSlzbRukiFT7N8mLYFZDi7E50fREwWtOs+mitiZMcpQzbxyME0KoFfO3aClfWn10QdimEniEPKyIPqxJKKd744bv85b/49+zc2KN/MEBIiTjLL0DDx5Z9DczT7gtnaiHF3FzMFCcYS5BnislghpCC5751iX/w3/xdertDfvK//IKgHjAbhWSZQimNykOyNKe73mb1wiJ5msN8r1kpzeh4TFDz6R8WJmnOB+I2HM9B5UVfUjxLONo6KYVQSckZJc1y9vuTIvV8FnFldYHAf//1bEmJFEWa+fbJkME0ItOaaRhjWRYXVtsErotjCeIs58b2Ma5tcXG1Q38SEac5rm0RJRnDaUyr6tGuVfA9m2mUcDScoo3BtSWeIxlHpVnrb0qiDNe3jmhVPNqNgK9dXOH7L10sDBXrAe4zzoIshdBTxhjD4YNjdm7u0d8fIi3J2pUV1i4vs/XeLv/+//1jpqMZeZaTRhnCEkUfzVOM0visqI+wWIeiqdCYYv22YyOEwHHtwmHaPKwIgeM4tFdaeL7Laz94h2vfucziZpckTGksNIjGIeP+lCQsJtW6Ky02nl+nt9snmkT09gfEs4SD+8fU2xUm/TFB1SeoBY8vyoDtWKRR8jkelZKSkt+U3ZMRb9zZozcJ6Y1m3Dvo0x+HnF9uc26pjZSCNFfcP+gTuDb1iscszjgeTQjjjMB1CdzC/FAAu/0JYZSiPYc4zdHaFFNieWH4l6vCCLEauEV/EO8HTQsg03P7oA+cis/o6fjMcjScMA5jLqy06TYqrHXPzlRvKYSeIsYYrv/8Ftd/fpssVbiujcHw1t+8x5t//S7RNEYgCKo+eaYRUswdpMXHl13OMMYUjdHCKqbE7HkUhtZFUKFlWwgDi+e6NLp1bNfm+k9vcfvXd1naXGQ2mqG1JpolSEuysN4pTkBCEo5Ddm8dEI4i6gs1PN8liRIOHxxjO5KF9e4j7tN5liGlRVD3GZ1M8CpP36+ipKTk4zkeFREZaa5Y7zRoVj2SLGf3ZMzJeEaUZqx1m9zcPiLOcs4ttQozwygjyzSWkCRZzr2DPhhDLfAZhzFgGM5yZnGGawkEglwXp1ZbCHKliJKEKM2J4iIeSAO5MZiHE67zU/EX82z87BAUE2FRmrF1NHzWy3mMUgg9RY62TnjnJzdJZgnT4Yx4FqOVodII6O30MQJqrQqHWydopQrbdltDLjjDXUIfj3n4jwEFmc6LoEEN2oY8s/AClyRKObx3zLQ/JagGpEmGdCzqiw3uvn6PWrNCc6GJUgq/6rN0vsvOzX0mgymtxSbDwxFZmqOyHMuxcPxCZOZpkWyvdbFt1l5uI6QgqPksnXt2e9IlJSVP5t5+n1mcstyuc2vvhJNxSJJmWBaMZimv396j4hWeNF+/uMq9gz6ZUhiKi6vAs0HAcBIihUTKYpw+y/PCIVkqQpi3JRTCJtea0SwhSnK01qcXaibXaGU+2PpY8htgKJy4bSGIk5z3to7401eee9bLOqUUQk+RB9d32b2xR5pkCClIw4RRf0Yyixj3ZlSbAetX1+gfDKjUA7IkJwkTpG1Bpr7Yr8KHu2cfqCnrvPhGQkJvt184liY19CJYtmA2nNLo1lhY7xBPE9IkpdKoUKkH7N06YOfmPkmcIoTEq3j4FQ+lNEHdJ5rEzEYhOzf38Coeli1pdOs0FuqMe1Ne+t7V0nCxpOSMEac5u70x1cDj5s4xx+MZNd/FGAsrkbi2ZDCO6I0jlppV4izj3a2MKM3QWuO7DrlSKGXIlcGxi7F2137oa2ZQ2uBYgornUDE2kzgtJrzmFiAYgzKGh2kaX9Bi/JnDllbhp2Q0Dw76z3o5j1AKoaeEMYZ7b9xnMpjRXGxwvN0jmkZ4FRe/0mQ6CjnaOsH2HHSukb5La7HB0fYJeZw96+V/rkhLYrk2eZKRJTmTwQSdabIo52S3j9GGcByyenmFlQtLjI7HjHoTBkcjokmEJSXP//5ztJaayHlQ69GDI9zAY/XyMuEoxPVdGgt1OsstLn39HOdf2ixH50tKzhhFNUYzjVJOxjNaVZ/9/oTRLMaWEs9xcN2U127v4joWFc8hSlLiNGcWZXieRZprsixDCHBtC0tKqp7LaFb0BDqWLDIOM4Xn2ggB1lzwaKMxmnmuWDEC/0mZWiWfjjTPsS2LXCuG02efmflBSiH0lBBCMDweY4xhfDIinkU0uu+bRy2sdZn2Z8wGMyrNCmmU4ng2zYUGvb0+fIkHFrI4L0JaBcSzmHga4fguXsWludRg3BsjpWBwMOT+O1skYUKWFvlA7nxbbff2Plmas7S5gF/1qbZrGG34T/8v/xFBrZg8EwLqnVrpLF1SckbxXJvavBpkycLleTSNqFc8LCnJdTFKP4kSRjNFPfBoVHwaVdjNR9hSYnmSkzglV5o0L8wRLVkkpWujix5FIM7VqQO0Y0vSXGH03CARTWkB9LtFaYPSOQLwztg5WH7yTc4Of/3Xf80//If/kLW1NYQQ/Kt/9a8+9vY//OEPT8fTP/hxcHDwdBb8AYwxBDWfNEqZDEOC+qPTTK5v41WKsFDblixudE7jey3HRnyhflOfnSzJyFJVhLfmGiFgOpgxG82IxjGO72KAg7tHuIFLUPWK6S/bwnYtVKbYvbnP/t1D4mmEMcUev9YGv+LRXW3TWWmXIqik5BkTJRlbRwPu7vfY643J1PuKw5KSS6tdwiRFKc1wGuO5NpaUKG046E04GRfBq7aUDKYR20dDjgZTcq0ZTiMmYYJtFSfMLFckWUacKXzPxrXnmWCmuDjVc+UjpMC25Gn3gTHvf5R1498ND7siNNBtPGGa9xnyhaoIzWYzvvGNb/Bf/9f/Nf/5f/6ff+r73bhxg0bj/X6QpaWlj7n154MQgqVzC9x98z6Dw5Dg3Pt/CCpXRNOYhY0uraUW9996gFaGcX9COI5QH7B4/9KiobhOE0XZOs1xPYfB4Yh4ljAbR3SWW3O7+6JcXfgTGWbjosyqck2WZvT2Briew3PfuoiUX3IFWVLyBUFrw63dY65vHTEOExCFUWG3UeUbl9dY7RTn6AsrbS6vLfDz97YI04xGxSWMU47Hs6Lfx7JwLYt61ScZTokzRZzl83DTDITAtS1sW2KJQuBEaY4lBbnSSCnwHKsYi1eKTGvypLj4Ot0EK3fDPlfkGbuy/0IJoT//8z/nz//8zz/z/ZaWlmi1Wp/qtkmSkCTv+8uMx+PP/PM+iqvfusydN+4z6c2Y9idFoChgWRaVepXGQp31y8v093tEk6TIunGtua/Fl79Oa+YVMIPBaIPlOKhMFX0DuaZ30EdaFsPjEZVGhUa3waQ3Ic8UQkqkZdC5xvFs8ryY/viw83RJScmz4fbuMb+8uU3Fc9lYbCKlIMsVR8MpP33vAX/4tYssNms4lsXf++ZVToZTru8ckysAg2NbNKsBvfEMW0riJMN1bM4ttdnrj4niFGMM4TzbS4giJiPLcnIDaVaUd7QyZLk+rTIVj142RX/efLCyFj2jlPmP4mzJss+JV155hdXVVf7sz/6MH/3oRx972//+v//vaTabpx+bm5u/s3WsXl7mxe9do73apNausXxhiZXzSyxsdKi2KqxfWeZ4t8fixmKRuxUl6Ex9rGHhlxJRbJWF45A8U1TrFRY2uzi+U4S7CsnapWWaC3W0gaXzC1SbVbQyWI6FH7hU5luPs1H42MPnWc7Jbo+D+0cMj0enxmmfBa01aZySn7EXdEnJWSROc27sHON7Dp1GBSmLt0XHtlhfaDKNEu7s9k5vv9Zt8HdefY61boOKa9Oo+Li2VeQUaoNtSZI8x3Nscq1BQJIr8ixHSoFjSXzXRgqDOQ1qLRqlMQ+DUr/aifBPG9uS2FbRnpKkZ2sA6AtVEfqsrK6u8k//6T/l29/+NkmS8M/+2T/jT/7kT/jZz37Gq6+++sT7/ON//I/5b//b//b08/F4/DsTQ0HV5zt//xVmo5DX/upNZsMZfs2nUq/QnYeHRpOYarNCGqd4NZ9pf3amA1c/F+Z7845rY9lFFpklJXmcoXLNyV6fPM3J0pzWcoMszommU7QuLAb6hyMa3TrTQUhvt3cao2GMYefmHrdfu8fgcITKFW7gsnRugRd+7zlai58ct5FnOTs399l6b4fZKETakvUrq5x7fv2R5veSkpL36Y1nDGcx6x9hWdGuBez3x0RJRuA5SCl45dI6UZLzb391k4PBGKU0C40ageuwczIijDOU0sRpxjRKCZMUDLiOje9aZLnG9z2yLCdOi3wxW0qw5/1B2mBUIYYEDytIT/WwfKXI1cOmdUG98mzCVT+KL7UQunbtGteuXTv9/Pvf/z537tzhf/gf/gf+xb/4F0+8j+d5eN7n5zhca1X5B//N3+XCixu885ObczHk4fgOrcU6555f597b2yRRSjyJyeL0c1vLmUIUH1KK03TnYgTWkElJfxbjBC6Nuk8ySwinESpTpLHAcR38mke9VWVxc4F6p4ZlW2zf3GP31gFXvnkJgO0be/z6375ROFRvdHFcm2gas3tjj9lwxnf/was0Oh8tZvIs5/UfvsO9t7bwfIegHpBnind/fIO9Owd868++QXe1/TSOVknJFwqlCwtn6yN69hzbIkryIuqCYqBBSsH3XzzPYrPK/+8X17m+fYznSMKk2P6aRQlau4AhTDIkAssqxE6WG4QQGG3wHBsjih5CKSW2EEgJSZojJAgN1txpOv2IgGvHEihtSqH0W2Ao7AhcS3BuqfWsl/MIX2oh9CS++93v8rd/+7fPdA1SSr72hy9w9duX6e0NyNIcL3DprLb4yf/yK376b36JUYY8V1+ZfWs5D2MVUgIGYwwCge04pEnRANmoV2gvtRiejPA8hzhK6O0NqTYCLrx8jstfP481D+9TucL1XXZv73P/7S1ypXn7b95F2haLG93TnxvUfFavrLJ7c48H72zz8h+9+JFr3L6xx703H7C4uYAXuKdfby7U2b97xNt/e50//M+++0isR0lJCQSug21ZJFmxnfVhpnFKxXfxPzTVKYTg6sYijcDjX//kHfqTGVGSs9ZtkGuNY1vM4gSjDY4lcRwLbQx5rnEdGwmkuaLiuuRW0WKQZDlpZlDzCy4hip8jpUQq/ZiLv+D9CbLTz3+3h+crhTbgnLEhlq+cEHr99ddZXV191ssAwPVdVi8tP/K1xkKdNMlxKw5fJb8/rQzSlqf9OpYl8as+QcOHSUIWp0z7U4QsQl6dVgXLdZgOZtiezeh4zPbNPZoLDYJ6wHQwAwx333hAnivyJOfeWw9or7QZHg6pNCvU2zWqzQCtDfVOjd1b+1z99mW84PGKoFKKB+9u41W8R0QQFCfRxY0Oxzs9ent9ls4tPo1DVlLyhaHbqLLSqbN7MmJjsfmImWmWKyazhBeeX8L5iIuIlW6DP/zaBf7lD19HSKgGLu16hVmcYEuLat0jyXMcSxImGUobcq2RGJQqxEuz6pPlmixXCBRSCpQpNsaklDiWRW5pUEXP0QerPx/sIyxF0G9O0RpmuH88eNZLeYQvlBCaTqfcvn379PN79+7x+uuv0+l0OHfuHP/4H/9jdnd3+R//x/8RgH/yT/4JFy9e5KWXXiKOY/7ZP/tn/OAHP+Av/uIvntVT+ERcz2Hl4hIP3tkuojW+QmilkbZACgutNXmeE01jwklEluYwjZiOZiAEg6Mxru+QRglxGBPPEuJZwqA1xBjwAodaq4oTeKxdWmbvziHDkzG9gyF7t/dpr7TJ5vEcreUGQggqjQqT/hRv/XEhlMYZ4Sii8hH+F47noLUmnMSf92EqKfnCIaXg5YurTOOEB4cDWrUAx7YIk5RZlHFxtcOl1Y/P/uvUqyy362itublzQmVeZcKE2LZFkucoDSutGsMwZholpLoY25/GCc1agO8WSfOzGESuMVpTbIoVX/dde953lJ9OEkmr2K4vBdBvh5QgKSalj/rTZ72cR/hCCaFf/vKX/Omf/unp5w+bmv+r/+q/4p//83/O/v4+W1tbp99P05T/7r/779jd3aVSqfD1r3+dv/zLv3zkMc4aKlc89+olXN8lnEZEo7NlRf65Yh5a2wvQxf5+ninMvL/AzJOig6qLEJIkTMgzhes5uF5RQat364WL9+GQWrtGe6VFluTs3TlESovuRofJYMroZEye5uSZAgl+xWPcm/DmX7/L7/3H36LaeHTs3rItpC0/coJP62IUxbLPVsm3pOSssNCs8kdfu8S9gz5bRwOiJKPqubx8YZXzyx189+PfjpTWNKo+m4stKp7L3f0+S60ad/d7jKOYwLOZhAmea2NmAs9xyJRCqcKNuj+eYVkW9YqLbVlIKUjSnEkYk+VFhShwbZQQKKXRRqM05KqUQL8tEvBtG20Maa5Izti07RdKCP3Jn/zJx446//N//s8f+fwf/aN/xD/6R//oc17V75Zqo4K0BN/8uy+xf3ef/v7wSz81JqRASIHWGmNAWhZBo4IXuMRhwlwHYdmymCSzLCzXIk+yopdICmyvaF6++PI5Rkdjent9psMZi5tdensDLEvSXm4STRPiMCWNEjavrZNningSY9kWV169xPFOj1u/ussrf/q1R9boeg6rl5a5+cs71Du1x3LKpoMp1WaFTtksXVLykbRqAd+8ss5L55eL8FPbOnWB/iQCz8GzLZI0Z2OxRX8SMYkSlto1MqXxHBvHsjgaTEnznHY1IFWKwLWxLYuT8YxJFFN1Ha5tLuLaxWTZzsmQw8GUNMsRQuB7Nu1agDaGw+GUNFOFGWPZKf0bYwDXsUjnF5Ll1FjJx7J8foFGp87xTp9Ko4Lt2qT5l29yTEgB8yZFx7VxfId4liAE2K6FEJClGWlUPHfLtoqMIKVJkwxXFvb4li0LX4pZjOtaDA9H9A+HSEtSbVYIaj57tw+K/6/77NzcY9Kf4FU8tNForRj1JixsdFk5v0iW5uze2ue5Vy9SbVYfWfO5FzbYv3PA4f1jFjY62I6NMYZJf8q4N+Gl7197rJJUUlLyOO4TGqY/iU69wkqnwdbRgM3FFlc3Fri112MSxniOxV4vRIhiWmy5VaNe9Vls1lhqVUnSnPuHA45GU9r1gD96+RIgOBpOuLjWRWvFzvGIwHNJs5ya7zCcJZyMQ2zL/EZeYyXvY4AwydDa4DkWa90n2yg8K0ohdMaoNqu8+P1r/E//5H+lt9tHfFmvQkSROi8QBPWgqITJKVppHM/B8R2SMEWrYvorqHnMxiEq0+gkm+/XF5WkLM0Iaj6VZoXmYp1au8ph4FFvF6JEm8KArVqvsrDR5eDBCbZrEU8TbMeitdRg89oaXsXD8RzGJ2OiafyYEGovNXn1z77BOz+6wdGDk0KYaU21UeHF713l2neuPPXDWFLyVUEIwcsXVpmECVuHQ5o1n6vrCxwMJjiWxYXlLlIafn1rj/MrbeqBR+DaReSGY7O52CTJcrJccWevR5zlpPMtGmMMge/yf/yTb6K05sfv3GfnZAeMwXNtouRsGQB+EdG6OJa+69CqlRWhkg8QTSNUrvEq7mkg6PkXNqh3a0Uiu2NB/CV8EZqiymNZFo5noY3Gdi38ShXHs8nSHMezkVZtHrdh41c9kjBF5TlpnM7HNwyu51FpBLi+i1aGcy9sMDoZo5Wm0qhQa1QYHo/wqz6OZ1NvV9m4ulZ4BhlDPItpLBT+QXmWI20L+RHl+qXNBTr/+xbHOz3iaYy0LbqrbWqt6hNvX1JS8ruj06jwh1+7yJ29HtvHQ3KlWes0+P6LF7i82uX69hH3D4e0az6O/ejbWzXwcCzBfi9i53jI2kKTZtUnSXN64ymukNzd7/Gt5zZYatWKsfz5rLwUAlW2S/9WdBtVwOC5Dllm6I9DOmekgl4KoWdEb3/A/Xe2Obx3RJ4rgprPuRc2uPDSBq5fjGfX2lWaYZMkTE5NBr8MSFsW3h0AGMJRhLRSbEdSaQbUOzUO7hzRXmyiMUz7s8JLSBchq5btAPmpVb7j21iOzerFJca9CXt3Dmh2G9iOxfF2j0oz4ODBMcdbJ0hbsHpxCce1cQOXwcGAzkqL+txIcXg0pr3cpLn40aVb27FZvbj8kd8vKSn5/GjVAr51dYOXLqyQKYVnW6dbbReWO3TrASejGavd953ip1FCfxxyMo7ItWIUxoieoOq7eI7N+eUO55bbHA4mDGcxf/i1i/zq5i639/okWV6k1Jf8xkgBaZ7jOBZX1xfwXMm9g/6ZEULliMsz4GjrmJ/9b7/m3psPcHyHeqdGlmS8/u/e4ld/+SbRNKbWrCCFpFLzvzxj9BL8uofj2acJ8/NGoaJRGlCpQgqBXyms8RfXu9S7NfI0J4lSDEWfkFZFf5Bf8QiqPnmaE04idK7ZvbnH87//HH/+3/xdzr2wRq1ZpbvWRjqS1mKLzRfWmI1Ctq/vUGtXOf/iJhhDb3+A1porr1zEsr4kx7yk5EuK79rUA++RfqNOo8K3r24SxjkH/SKWYziJuLff4/5hH1sKLix3WO00MECj6vH1S2tc21gicB0C12HraEC7XuG//LNXubjSxrZlMcTxCeuZm+Mj5aMBoyXQqPisdZtsLrQIfJdK4LFzMiTLz0aOZlkResrkWc47P75JMktYf+59Y0e/4lFr19i5vsfSxgIrFxZpdGvs3NpDnjEXzs+MLCa+bMvG8z2UKvw7LNum0a2SpwqDIagFSEuSZ4rLr5zHdh0aC3U6qy2qjQrbN/ZQeU48TZCeQ3OhzsLGApWaTziNmQ5mXPvuc6g858o3LrC40aW11OT533sOKSXj3oT9u4cMDkdUG1XCSYQlJYPDwnuouVDj5T98/pHfS0lJyReLv/Pqc2gDP7v+gBs7x5wMZyBgqVVjpV0n05rFZo0kzQuvoTwnSmSx9WXEad/Q5bUF/os/+Sb/9N/8hP3B+InxGoKi2hF4hadRlKbk2hTGr1/W/s7fACEMC83CVDOMU6ZhgtuwisnBZ704SiH01DnZ7dPbH7B07nHzMMe1qTQrPHhvh4tf26S90i6Slh0LcE8nqJ4Fjm9jtEZrsByJVgaVFmpeSLBdG32a0yNO/XZsz6LRqRHUA+JpAhiai3W0qrN4bpFr376M5zm4FZc8zbEdm1FvwnPzUfalcwu4nsPR1glv//g6lm3x4O0tVK5oLTUxphCXAoHKFdVmQBZn3HnzAW//6Dp5muMGHpvXVrnw0uYjW1pJlHC80ydLMhzPYXGj80RX6ZKSkrNFrjR6HrHxYSsLx7L48+8+z3eubfDDN+7w5t19zi+32VhsMZiEvLd1hJk3QR8MJvzy5g71wMMYzSxO+frFNZIsx7EsOo0Kz59fBmGYzBLyeUir0Rrbsah5Ho2qR5prbEtQr3RI05zj8ZRplGK0IfoI77EvGh+OFrElGA0f9ewkYNsSpYq4pDDJ2O+P8V2HwSTi/HIb94zsdpRC6CmThAkYg/MR5mFB1SeexixudumstnACF5VrVJ4/3EXiWWxXS9vCKLAci+rcXXl4PC48joRA5boIMERgORae7xLPYqS05uaHKQao1AMcz8HzXb7+Ry9w+RsXHvtZ4uYeC+ttKnWf+29vU21VUbkqsscsC8e1yTOFF7i4gQsI4jAhDRPe+dvreFUPISWd1RaVRoV4lvDmX7/LyU6Pb/2Hr1CpF+v3Ao+NsvpTUvKFYTCNeHDYZ/toiNKGRtXj4kqXzcXWY35EC80az60vEqX5achnu16h4ruMwwRjDL3xDEsKFltV0kyhDRwNp/zi+jaXVjvcPxiw3m1wPJjQqFTIVY5SxQi4EIKa7xJlGZ5TPEa94nNj+4hcaWwpifMvz6DLQxFkyyJ+5En2dlIUOWJCCixLYrTBmCL3rVnxmMQJw0lEI/C5tNpFyrOxiVgKoaeM5RT9MVrpJ04mZUmG5dh4FZ/lcwtc/sYFHry7RTwrohuElAhZ3P9pDjHkcY60BUZpZuMQozk1ehQP/5tfMuhcYwc2tmdTaQR4NY8syvAqDp3VNrZr0+jWWb249MSfpXLF9o19+vsD7r1dPPfWQoM8z/ArLkG9wmwac3D/CNd3qTQC8lTRXm5yvNOjvdzi3IsbWPPjG9R8Gt0au7cPaL1xn5f/8IWnddhKSkp+RxwNp/zk3fsMZzHNiodlSY4GU3ZPxlzbXOTVKxuPiSHHLt6MH+K7NpdWOry3dciDwwFZrqjVK8ziFK0Nz28usbrQ4O5BjzBN2esNmUQJjm2hdE7V99C6cEeehjG50lxeW0BgsG2b/ZMRkyhBa4MG0i/RkMsH+ahdP20gUxoLgW1JklyhMWR5zsFgiiWKgN2NhSabZyiBvhRCT5nuWpt6p8roZEJ7ufnI94wxjPsTXvj9q7ieg1/1ufzyOSzHIk8U/YMBGIGwQGWgsqdUGhKFOFGq8P5RH3JH10ZTrVVwvGJ7LJol5GlRsWkuNHA8G+U71Dp1nvvmRRrdOkdbPXr7A8a96SP5XXmac+vXd089foJ6gOPaHO/2qbUqDI7HDA6HVBsV0ihlNo7oHYzwA5fmYoPGQp16t14Iysr721yWbdFcqLN7c4/nXr2EXym3wEpKvihkSvHrWzvM4pTzS63T7bBGxSdKMm5sH7PYrHFxpfPI/RabNVzHIkoyAq/oRllq1xjOIh4cDYjTjCTLMNpwabXDxmILKQSeY3N3v8fJKASKbaFZnBKnGbkyKKUI04zATVhfaCIEHB0PORmH85h6QZ59eapBH+STgg40RYi20hm2JfFth2rgMw5jMLC20OSFc0tYQnI8nHIynqG1oeK7rHYanxi18nlQCqGnTFD1ufLNi7zxw3cxxtBcbGBZRW5Wb69Pe7nF+Rc2AIpIh1/dQRhDGqVFJSlXkBkeRgAKKbBsgdYG27XJ4ux3v3Vm3v9Xa100b3/wh5jCBbq+UMOv+Ez6E2ajkDTJiKYRfqVJpVZj6dwClufQPxgyOBxytH2MVoY8zfGrHn7N53i7RzgJefF712gtvi8U8yzn3Z/cJJpEWK6NZckiCb7isRQ4OL5LpVkhizNcz37kKvD02NcDBgdD4llcCqGSki8Qh/0JvfGMlU79sZ6gwHXI8pzX7+zSqvq0asHpbbqNKhdXOlzfPqbbCKgFHrky7JyMGE1jWlWfbr1KrhR7vTGubbHSaRB4DtvHKb1JhCXB9xw6jYDDgUagsSxBlGW4to1r21zfOWQapQjAkoJMKdIPKQYpCo305awRPY5r21gSmjWfhWYV17ZwnSJSJUwzfnb9AQ8OByS5Ot1N6NQrfPPKOusLzU98/N8lpRB6Blz6+nmEENx54z4Hdw+BwjBw5eIyL37vKo1u4Wlj2Ra3fn2Po/vH1Lu1IhU5TIrmYCOwncKMR6vi/lrpz71/SMyDUbUyRb+SKSztda6LYFIJtWaVNMqod6r83n/8LcJxxHQ45WT7hO3re1QbAX7FQ+U54ShGaU04CVnc7JJnOVpDb69PPIsRQuJXPaqNAMe1OB5Mqbar5GmO5dhUmxWWLyxSqfkcbp0QjkPay01c//FZhDzNsW0L+zPY+6tcsX/viN2be0wGM/yax8Zza6xeWnpiY/WpUCwpKfmdESYZ2lCkzX+A0Sxm+2jIQX/Mje1joiRnc7HJC+eWWWhWkVLwzSvrWJbkweGA3njA7f0THhwM8D2HKxsLRe6VMYyjhNu7J7hOkUDfqgXkeU5mBDXfYzCNaARFYOs0SojmDvf98YwwynAsiTYGx7ZxLEXEoxWhr9oQWeAV2W/rC002F1sEroNtCW7v9ri5fYzjWKy066eVOq0Nh8MJP7+xxX/gXn6qHkOlEHoGSCm5/I0LbFxdpX8wROUav+rRWWkhpSRNMg7uHfL/+r/+K453CkNAgyGaRCRhUjSgKYPRRUMaBlSmnko4qzGFoHiIsMRppWgymDDRgiRMsGzJwkaXeJYUMRTNGjs3D5gOJrCxQDiJ6O0P6K52qNYD0iQrXKOVRkrYvrFHZ7mF7VhopbE9m97BgDTJ6fguXsUjqAckYcLB3UNWLi4X+WUGvIqH9YRphOHhiI2rq1Sbn+4FlqUZb/71e9x7awvLKgTZbBSyd/uQtcvLvPr3vk6lHqCUYv/uETs39xifTHA8h42rq6w/t3ramF1SUvKbY0nxWN7XcBpxffuIJM3xXJt6xadecbl32Gc4jfj+SxfoNqq4js23r26y1mnw7964zWAS06z5TGYp9/b7LLfrLLZqNCo+vfGMrYMhmVYEnk2YZiilybQiTjIsS3A4nBInGZnSRHHK9bQQPIF0UErTD2dF4/WzOFBniDRTpFnOuw8O2Tka0qoHtKoBgecwmEZ87eLKqQgCkFKw2mmwdTjg/uHTNVsshdAzxAu8xxyK4zDhtR+8xTs/usH9d7aod2rYjsXerX1GJxOMKcbsszSfb/8YvIoHgkJ0POWkevOw1msgHqdFI7c2VKs+Ks1572c38Ssek/6U2TgEBNPBDAFE45DjXM/FSZWjB0f09oe4gYfrWUz6E9zAw2jNZGtKNIlxA5fuegcMTIczHNcmDhO23tvGq/q88P1r+FWP3l6f1lITy7bI0pz+3gC/6nHpGxceK61/FA/e2eHO6/dZ2uwWx3hOnil2bx8Q1ANe+ZOXeOtv3+POa/eRliSo+cxGM177q7fYubnHt/7sG6cVvpKSkt+MhWaNiucyCRPqFQ9jYPtoSJzmdBsVjkczNhYKMVMPPLaPhtzYPub7LxXRN1GS8c79A46HM5oVj7Vug6PhlO3jEQ+OhuRas95tkKY5P9/aYmOxxYvnF6n7Hv1JSBQnTOOMKE1JM41lSWwpSZViFqfI+TlFAFGaf2W2vz6O2TyfTQAYwyiMOXSmrC806NQDqvMEhQ9Tr3jsnoz4+qW1x5rfPy9KIXTGuPGL22y/t4tX8ZDSorPcYnA4YNyfFiPkcu5yKgVIieM75JkqAkyf1iiiKLbtEEUlCgOWa9FdbRGFCSrLUJli++b+qQu04zlIKYrG6TxnNooKAyIgiTIc3yWN08JBOk6xbQspBfVOnUo9QCtDmuQYA63FJpWGz3QwY3wyRUhBOI3ZuLrK/+7//PcYnUy4+cs7HNw7wmCQUtJZafP8711hcaP7qZ5ilmY8eHebaiN4RAQB2E6RL7Z/5wC/4nL71/fornXwq+/frr2s2btzwNt/+x6//w+/XW6XlZT8FjSrPpdWO7x1/6D4gjGMZhG1wKE/Dqn5LovzvD8hBJ1Ghb3+mPEsplH12T4estefsNKpM5zFIASLrRpSSo6GE7YOh/RGM45GU3Kl8V2L4TQh8BzU2KCUZhomaGPwPQtLzCvOKSityZVmOvd5K0XQ+wgKyxffdeg2KkyihN2TMSudj44wklKi9ft9sE+DUgidIWbjkN2b+7SWmwwPRwgpydOcg3vHRcioFhijseY9OlD052A0WaKKBp6ngQDLKvyCEqWLfiFLkqYZxhjyTGM7oqhaKYPlWngVl2gao5Sm0giwHIs0Kq4YwmlENCnCZ2udKsPDIWmmcAOXyWA23zLLkVIgbcnwaES1VaW11KK12CSaxezdPuDqty/TWmzSWmyyenGJ3t6ALM3xApfuWvsz9QZFk5jpKKS58OQXbKUR0NsfcOu1e7i+84gIgmK6bnGjy+HWCf2DIQtrnSc+TklJyafj5UuF59fdgz4H/THHo5B2LaAxF0m1ec9elGQMpxEno5B7B31eOLfE1tGAwLOpeC6OVbhHu47NQrNK4Ni8Nd0nzRSOJVlp1jkaTri92yPwHRqBx2gWFY7TUlCXHo5tMU1SbEsi4LHG6JKCYn6uEIuWJQlchzzXHA0nTMOE2hOGVqZRwuZiC+cpxhyVQugMMR3MmI1D1p9bxXZtas2Ak90e0+EMo0FaAiEFQkqYN+XmuSLPFVqZ+Rv9U3hBakAIjCl8jSyr+Nm1VhWtNYODEdbc9DDNMoQlsSwLL3AJR0UemOs5ZHPvjmSWYCimuiaDWfH8RDERZ4wmDmOM1njVgLXLy6RxxuBggBBF34DtWKxeXOKF7z53ukTXd1m99JsHowopkFJ8wC37UYw26FwRjiKWzy8+8TZexUNlitkoLIVQSclviWNZvPrcBpfXFrize4IxRWzDcquOZUmU1mwfDdnrFZWgTGt+cXOLO3snbB0P8Rwb0RA0qgEn4xkLjSpSCHrzLfuq75BrXdiV5IrlTp1ZnLLQqmKA49GMTGmSPCfTxXnXsiT5V60L+jOiDcRpTprnNGsBji3JcsX28ZBr55ZOtxWhEEEA55ef7vmyFELPiDzLOdo64WjrmDTJqber2I6NkMUofFD1ufiNC/z4X/+CbN6Mx3xKS+XFdpTtSFSu0bkB8VAoff7O08IRuL6H7VpYVobSCtezsWyLeBwXDc6ZngsZg1aKLMlAgBs4RaXIFFNmD7fDFje62K5Fb2+AZVvUWtVTIZGnOZWGz2wcFfli6x0uvLRZVKKkIJ4lLJ9ffCS2JIkSDh+ccLJzgso17eUWKxeXqM3L51BU4NIoxfGcR74OUG1WaK+0ONnuE9T8x47BuD+l3ikm+ZR6ssm8MQZjzKmxY0lJyW9Ps+rzypV1JlHCzsno9PW1czzi3kGfqufgOhYXum1safGLm9sc9CdUPIeFVg3PtrGlxcl4hlKao9EEZTS5NlQ8B60UFd/BsSSebaGNYalVY/twQK6KbTDUvMohBVKALcVnEkQfjqv4svLweQoBFc+lVQ2I4oxOvUKzFrB1OKDqu1iWZBanWELw0vkVNsrx+S8/0Szm9X/3Nru39ovYCNfiXpji+g7hOGR8Mqa50ODaty5x9417nOwck5si20sIEFbhLp2l6tQvx/Fs3MAtUt3jz9nISwFognqVNEnRuSHPFJPBlNkonMduFP1DDxuTo2mE5VjF3q9WGKXxah6OFAT1gEorYDYI57fRNLt1/LkAiSYxbsVFKcO4N6Wz0qK11ERrw+BgSK1Z4fnvXjnd+hqdjHntB29xvN0rRvotyb23tmh0a7z8xy9S79S48/p99u8cksQpjmuzfGGRy9+4QGelDRT71BdeOsfxVo/h0YjmYuP0ucxGIdPBlK//8YtMhjMevL1NvV177DBNhzOqjcpjxpklJSW/HVIKXji/zGAasX00pFZx2T0ZYUnJLMmoBx6WKEbm27UKWa6IkpxG4BFnOWBY7zY4GYfkyrDSqfPSuRVu7BzRn0bU59syji2J0pxZHJHOk9KN1ggpsaVAaY02BikFthCFSPoUfBVEEHzAgs7AJEzJ1Zgkz7myvsDf/9ZVDgZTto4KgXl5tcu5pTarncZTj94ohdBTxhjDOz++wfZ7u6xcXML5wPjg6GTM1vVd9u4c4lU8XNchqPk0F1v09/uoXCNtC7/ikueaLCq2lqDYhqk2K0gpPnchJKRAKwjHISopqj22I4mmMVqZeSUElFJIaWHZkqARoFKNylMcvwhYTcKEtUsrLG52qdQDxtUJxhiicUQSp6fVsThKaCw0aC23UGlOrV0tKkeOxfL5RS6/coGVC0VcR5ZmvP7v3uFku8fq5ZXTq0VjDCe7fX76v/4K13OIpgnt5Sa1To0szrj/9g69vQHf/vuvnG5jrV9ZIf2Tl7j+81vs3NhDWhKtNH7N5/nfe44r37zI4HDIwd1Djnd6dFfbp7Eps3HI8HDEi9+/RrVZffKBLCkp+Y1ZatX4g5cu8N7WEe9uHXI4nLLUrLLYqrPSrnNrr4frWlQDlyXqHAzGDGYxgWsTZzmTMKFZ8Vhq1/n21XXWOk1OxjN2e2OyisKxigu3wSTieDRBWiARZNpgoREIcq1QGhyr8BoKk7TsF/oAgsJI0nUsAs/maDClXvH4/ovn6TSqdBpVXjy/fOpH96wohdBTZnQyZu/2Ad31ziMi6CGT3oRoEqGVZpbPmI0jkjDGDTwwReUlDotU44ciSMiiCqQqmqAeEI5D8vTzezHqXBOOQ+RUIiyQc2drcoVlS7KkmBR7WKHR2hShq6bwS6q1amRJhlaKWqfKZDhj3JsS1D1aS03OvbjBwb2jeayHZnGzy8a1VY63Tnjp+1f5u/+nP8Z2bWzHotGtPzKRdbzd43jnhOWLS49sSQkhWNzo8rP/9VdYts2rf/b106sOx7UJ6j77dw658fPbdP6TYspLCMGlr59n+fwCR1snRLME13NY2OjQXCgqRAvrXV75Oy/zzo+vs3fnAAFoU1gaXP3OZa595/Ln9nsoKfmqs9iqsdCs0qr5GG24sNKh4jn0pyFhnNCpFxchti3pNqpsLrboT0LyXNGfhPzBSxdpVHxcxwYBL55fZq83YjRLsKTgeDhlOA3Jco1t2wijeZi3bigu+AAsKedJ6h65ij6VeeJXZXtMG8hyTX8U0qoFXNtYpNt4tIL+LEUQlELoqTPuTUnC5LEx7jxTPHh3G8u2WL6wxJVvXiSaRMxGIaOjEYOjEe2VFsPDMfEsRhuDzvIi+V1pkAKtcuJIkX/OGWRCPrSKL2YCPK8Y4bc8h3q7ymwcoVKF5VpkcUq9W2c2CJG2wK/6dNdatFfaOPOTT2uhwfFuj2qzwuBwRFDxWb2wzMleD2lJmt06h/eOsByL9nKL2Shk5cLiEysto5MJRvPECbEkSolmMUE9eKz0KoSgs9bmeKfH6HhMe7l1+r1qs8rFlz+6qrPx3CoL651CLE3jwkxy/X2xVFJS8vkhRGHE16oFWNbcbX9elX74Oo/TnIrnsLnYYnOpxSRMGM1ivv/SBY4GE35xc5v+pHijfuXyOm/d3+d4OMNog+c6SKkIPIc00zgqJ8kUtiUJPEmWKTp1H8uyECLDc2ziT/ASkqLom/mUO2lfOARFtIZWCmXg6voCV9YXuHZuiVmYMpqHiJ8VSiH0lDk1IPwQ45Mxk/6M5kIDlSv8qocQAiEtzr24ibQsJv3CM6exUCNLFLPRDMuyCVwJRhCOE7I0/dwvM4QUOI5DnmboXKNyDQjUPGaj1qoiLXla2QqqPlppFje6WI7N4kaX7lqXJEzI0ozLr1yg0a3x3LevcPvXd7n167tYtuTlP3oBlWu2b+yBEFx4cZM0zvjVX7xBY6HBN/6DFz/TZFiWZqhc4bqPV+IA/IrHSZKTzP1APgt+xePc8+uf+X4lJSW/Pd1GlZVOnZ2TIRuLLXzHxrEtkixHCkGS5Vxc7pwKo1wpWjWfiudwZX0RbQzXt4/ZOR4W/mWBx8loxkK7xu7xCK1BKY0lwbKcedyHxLYkmSp83LqNCvcOB+RKYUmJY0vSvOjjtCyBmF+0PgykF+LRmlDRc/Q03XM+P2wJjcAlyRSdRpU//70XWZxfuM6iDG3O1rMshdBTptGt4849dT44jfTwzTcJEyzH4uYv7zIdhehcMTgY4Nc8lNIEVQ/bschUzsEdjRAC13dwfYej7R7Ssj73VHpjiqm3U8v7+VaQtCziMAEECxsd6u0a4/6Y9mobpTTVVgWJJBxHdNeKx3jYzCwtydrlZb7+xy8UcRW39jjZPuH26/dZWGtx9dtXaC015z/OcLzd440fvk2lEVBtVrBsCyEEjW4NIYoKm+086kNh2xYqU4+k3X+QNE6xHeuJW5YlJSVnFykFr1xeI0oytg6H1AIH37XZOR5RD1zWuk2W5wMNaa6YhCnfubZRbIkBz59b5vxyh6PhlFwpNhdbLLeLgNdpmCBF/IEcMYkElDFoDcIYojhjICKqrk2cFJNmlhR4jlU0WRuBbQkcyyZMcj5YJxbzjy9TcSjTMIsz2vUKa50GkzBhsVlFaQ0G2rWzFT1UCqGnTGuxwdrlZe69ucXKpWUct/gVSCmJZ/G8nCuptU0REWFJtFK88+MbxGGCe34R13IJexMc10ZliizNEAK0KXK6fmM+tGltuxZ5+qHRcFn4Nur5HzRAnmkqjoXruTS6NWajiEarRpZlqLyKyooKF0YgbEGe66IpehJz/qUNwnFEtVWl3imcXtevrLB+ZYX772wzHRa+Sh/MDhNC0F5u8s5PbtDbG9Jd7+BXXc6/sMHS+UUWN7sc3j9i9dLyafOyMYbpMCyqUpZ4YnNe/2BId61Na+mjXU9LSkrOJu16hT96+SL3DwdsHQ1Y7zTBzM8X9YBpnBKnGXGSc3m1y+W1hUfuH3gO55eLqdHR3JF6vdvk/kGfd7cOydIc22iUKfzcpAZhQT3wqVVcfv/58zRqPv/2V7cYTUJSZUiyDFvKomdISHKlEBIsaYExOBZUfY9Ma+I4/VJUgwAcS3J+uY1tW4yimChJ0caw35+w0Kqy2j1b59hSCD1lhBB87Q+eJ0ty9m4fIKTAdmxGvfGpsKg0fBrzPxRjimgJKAwM0zCh0amj8iKxHSGptSokUYpKFVhyHoQ6L7F+lsuMhzagAlzPodoMGB5PMKe13OI2Hy5rGmOYjUJyPyvMyNKM/tGIznKTzorH6GRCY6FBnuZkiaGx4NHf71Pv1mh064xPJrz8xy8QVB/165kMpli29ViAahKl3Hn9Pof3jommMQsbHca9Kb/4/77OxrU1nv/uc2hl2L19gOPaSEuQhCm1To0/+T/8AVvX99i7c0h3rY1f8UjjlP7BEMe1ee5bl7CeoqNpSUnJ7456xefli6u8eH65GNLIcraOhjw47JNminatwualFuvd5sc6F1f8wq5DSsHXLqxwe69XiBhRmAEmaeFMvdis4EjJQqtGveqz1m1yebXDriOJUkV/FKKMRhlDrhTGgO/Y84kzTc3zWGrVOBlP0comyfLTBuyHl2lfRHHUrPpUPJc4y+hPIg4HU6q+x2KzyrevbuB9Bpf/p8HZWs1XhKAW8J3/6BWOtk44fHBMGmdc+eYFFtba/OTf/JrOB3xnZsMZJzvFKLhWiqMHx0yHM7I4xfU98iyj2qjMU9uL6S0hBIZiUkJrg/6ErTJpiyLR3oBlWViOpL3aorXQLBqfs2J6SwgwT/AOdDwHaQmyVJOECUmYgCi2urprbc6/tEkSJTx4d5fRwRDXd2gv1qm3qoTjiCvfvMiVb1781Mdv79Y+vf0BzaUGtVb1NNQ0z3J2buzR6Nb53n/ybQ7vH3G0fYJSms7cULHRqbN8YYkbv7jN8XaPk7iH7dp0V9tc/fbl0zH8kpKSLy6WlFgSHNvixfPLPL+5xMmoCFm9uXPMe1tHNCoeF1c6nFtqPxbuudKuUw1chtOIjaUWz613ub3XwxiwtcS2LFY7ddq1ClGWkeaKO3snxUSaMiAkjaqD1ppRmNAOXDKlUdrQqvrYUjKOYlzLKjqnEVS9wsQxSjKUMUgh0ejP3SD343goxhxboo1BqU/uYRJAp17hwkqH4+GUNFN0GhW+9+J51heaHxm2+iwphdAzwnEd1q+ssn5l9fRrjW6d268/IM8VJ7s9oJiCcjyb8y9sYDsSKYq8rVHPwa95hOOYo60TtCoalZMonZeDAQSOa5Hkn9BAPbf+tCyBZUvciocfeORpjud7ZDKFOMdIMB8cc5i7WVebFbyKR55mLJ7rIqVFliTYtkW1UTntA7r23SssbXTprraQlkVQ91m9uMzCRueJVZj2UvPUSfthVSiexfT2B9TbVaaD2SNZYLZj01ios3Njl8uvXOD8i5ucf3Hzscftrrb53j/8NsPjMWmUYrs2raVGWQkqKfmScjSc8rP3HhRbXjUfxxIcj6bs9cacjGa8+tzGI2KoVQt48dwyr93eJU5znt9cIkpy0ixnGqd0mxWuri/iuw4/u/6AaZRwfrmNJSWNqkd/GpKkOYuNGo5lUwkcLCGpVz3WOg1Wuw3qgcd7Dw745a1dXNs6daFXpqhkCfNsRRC8/7aR5xppCVxb4rg2YZSeVq4++NYiAcexqAQucZrjuQ5fu7jCd69tcnXjyVFEZ4FSCJ0h6p0aF762ibRk4Sc0LVKSKw2fSiMgmkSsX13FdiT9gyFJOBc9lsQSAmHJuT/P3NAwz8lT3v9LnW97SUuCmUdyCIGUkqDq41Vd/MDDqbiE44g8U0XfjiUJJxHjkwkaffoYQggqNZ9qI8DxHfLUJhyGvPC9q0TTlNHJuOhfkpJKzefi18/z/f/0O586d2vp3AIL610O7x+zcnEJaUmSKCWOEuxcEdR9uqvtR+5TbVY42ekTTaLHtto+iBCC9lLp+FxS8mUnyxWv39lllqScW26d9gbWKz5xmnFj55jFVo2LK4+el57fXCLwHG7vnnCYK+oVl2loWO10qVd80lwV4a/DGe1aQNVzyXJFLfB46fwy9w76hHHGSxeW2VxsEfgOK50GK+06K506jmWx3m0ySzKSLGccJoRxihhOsWWxBYfSZGdgxt4AUkiqFZeFeoVdPSbLNeahUhMC15JYVnGxbiGo+A6X2m3iVLHQfNx5/yxRCqEzRHOhQWuhzi//4o1i+ivPGZ+MGRyOCMcRWZyzdG4Bv+KzeW2deBZz960tmt06s+EMpTWOV2R5gSkS6h+KIAm1Vm1uQlgjS4sML2MMftXj4tfO0Vlpcenr5/BrPq/91dskUUI4jopYi9UWR57N6HjM6nMrZElGb3eAcCym4xAxEeRJhhu4zEYhtuuwuLnAy3/0QjEdJwTH2z1e/8FbfO8ffvtTuS27vssrf/oSv/6rt4p+H88+FWQL610ufu3cYxNgKlOnU2glJSUlh4MJvfGMlU79sQEJ3y22o+4d9Liw3H7k+1IKLq50WG7XeP32HpMo4bVbu+z0DnBtm1rgMppGZEoxmEbc3D3Bd208x6ZVDWjWfDzH4T/89jVevrRKMLft2OuNeOPOHsfDKYfDKdoYXrm8Ti3w0Frz79+8w+7JmIVGlSTPubvXI0oyLKsYx38Y42FJ+LCJtTVfvuNYtGsBg0mE1ppaJcCSECcpkzj/xGP2YfezauBSD9z58bJ5YXOZ4/GUKMkK9+j59l7hreTQrldYbddJlaLbqLB2xpqjP0wphM4QaZwSTWOiWYJlSRoLDSzHZvfWIUcPTmgvN2mvtti/e8DgaEytWaHRrlJtVZmOQvI0R1oS27FQWiOMLkQBAulYeIHDwsYClUaA41oMDkc4joXSBsux53EeTYZHY174/atYtqS32+f+uztMehMWNxaIw5RwHOHYNkJIdJqjhTjtS6rUfI63+6xdWSncn137dBx95eISuzeLRuXnXr30qY5Je7nF9//T73B4/5jjnRPyNEcIcD2XzoeqQVA4d7eXW9Q7Z/sKpKSk5OkQJhlKg/0RW9/VwGU8S8hydTpO/5BMKV67vcvt3R5xmrHYqrG51GQSJkyjFCEE3XqFTOnTx5+GCf1JxGqnwcZCk9Vu41QE3dk74Zc3t8nnvUIV32EWZ7y3dcT5pTbNWoCQkqrvFhX7nMKgcW5XYlsCW1ogIFfF1FnRG6rxHAd3no3muTZSyEIMzSKUykkzQ/7kfOjH+MDcDK5j4bsOrVqFJM0YTEOatS7fuLTGfn9CbzTFtiziNEPKwiupPw358bv3WWrX+c4fbZ7JvqAPUgqhM8TB/WPG/Rnf/fNvcrLbp7fX53j7pOhhWW6ilGJ4MMSyJbPhjOPtE6qtKmmSodKMPMmQtl2k2OcKZYoXiEJjCwuMwKs4JGHMtJdhew4LmwssbXZ56fvPE00jbvziNuEk4pt/+jLSkjQ6dS6+fJ5wHDI4HPGjf/1zdm7uY7ds/IqL67sIKUiiFK0UQaMCAk52ejz36qVibH6OnAes7t05+NRCCCCo+lx4aZMLLxX9PquXVvjVv32D4fF4HrFRNIkPj0ZoZbj0jQtlv09JSQkAlizGXT8qzypXGlvKR6J6HrLfG3N3v0+75rPXG9Gu+wSeS6dR5cFRn63jAd1GBSGL9oSlVg2DIZ8Pl/iujTV/3EmU8Oa9fWzbYqUxj/6wJHutMVGc8evbO9iWpD8OEQK2j4aMZhFSSCqeQ5hkPPTjlcZgCYHv2qRKYUzR7hCnOdpotNZFn5EAow1xlhcN5JaATxlF+TA1vjCCVFhSEPgukzgly3OqvstL55fZ7/kMZzHNWgetNdMw5cK8kpYrzf2DAReWu/ju2ZUbZ3dlX0H27x7ieg71do16u0ZjoU40iemudTi4d8Thg+MigqIRYDkWcZii8qKPJ8+L0cwsSZFSIm0LIcCy5WlCvdaKwf6QPFNIKejUfKJxSDip8Lf/009RSqFyxWwc8+L3rj3SY1NpVKg0Krz4/Wv094fzyowgmkXYjo3r2TQWOqhcgTEkyhDU/cdOLpYtybNPeVnyEZx/cYM8zbn567vs3tpDzqtR9XaVV/7O11i/svJbPX5JScmXh4VmjYrvMo0S6pVH+waNMYxnCd+4vPrY5BjA1tEQa+74nGSKRuX9CzudGxzLYhKlLLaqxElO4Dl48zf8+wd9RAe6jQoAB/0J41nC+eUW2hjGs5jBJGIyi7mz10NpTadRwbYtwjhlGiUALDarVHyXVOWMpzGp0nTqRU/S9vGIcJqdPhdlDEobwjgnsxS2baO0xnddrm0skGvD9e0jslwhhTiNInnSLI0tJY4tyJUmSjLiJCviRhC0akHhyZRmxFlOnOasejYYwcsX1ji31AIBSmt2jkfs98eP9WCdJUohdIZI4xTbfb+SkcVZobBPZkhLsnxhkWa3wcJGl8MHx+Rpzuh4zOBwCNogHQvXKnK/jNZIp7jKMRqkLZFW4ckzGYYIA8Ia4td8JoPZvPkZ4lnC6GTMT/7nX/Kn/8UfPHYFFQ5DLn79HGmUMh3MiMMElSmCWkCl7jM4GGEwLF9YpNZ+vA8oHEes/ZZCRQjBlW9eZPXyMic7PbIkx/Edlja7BGfMsbSkpOTZ0qz6XFrp8Na9AwBqQRFflOWKw+GUTj3gwvKT36SnYVIIm/lp0JxO5EJuDIHnorRmEianIc/GGGZxSpYr1hdap545YZwW1WtjuHfQZ683Js+L/qI8V2RaczIOwRQN3gvNKpMwoRq4VAOPSVjYwvm2jZmbE+YqJ3AdplEyn+IyVFynGHXXBq012hQ2AkIIHFvguTa5Ujh20UKRzhuNPuinW/T9gNbz3DZlGEwjLCvBtiRX1hdo1ysc9ifc3evjuzbdeo3lTp3FRvX0eBU2BpLj4bQUQiWfjuZCg6Otk0e+Fs1iomlCvV1l0p9iuzb9/QFHD46xPQckBJUAL/BIooQ8LaIlkijFElZh2OhZOH4xbi+kwOQ5ylBkg1lF87Scv1A6K5IkTLn9q7ucf2Gdy69cxJgiPT6cREyGIeeurZMmGdEkotIISJOceBKTZzm262DZEiEF7oeiKsa9CbZrs3b5d1OxqTYqVF+s/E4e68PMxiEqU3gVFy/wPvkOJSUlZ5aXL60CgrsHPfqT4WmD70KzxqtX1ml9xAVUNXDpT0MWmzUCz2GWZNSCoro0nkYMpxGtmk9vNMP3HPqTEMuS+K7N+kKT59YL9+pMKeIsI4pTdk9GbB0NaVZ8tGs4GYWcX+0wmkTM0hStDZ5TGC1qrelPormw0ri2jWUJ0lwXE2ZSUAtcZnGG0hopigqOY8tHRI5Smp2TEd16BUlxMSkAx7LIVSGWpASj3/fgLbzjJGIuj2Zxsduw1Kyx2KjSblRAGy6tdVhu1bm6ucQTdh7nqQdn2xayFEJniNVLy9x78wGzUUi1WSGo+uSJAl04N89GIeOTMeE0IRyHqCxH2LLI2ZISK1ekUVFFKkJQi2gLrQyu49BZbjEbhlhOMdmg0hwpJJP+lDwpJgmkLal3i3iMd350gzxTTPrTov9GGxzXZjYOWdpcYNybYjsOru9Ra1aLZj63T7VZKdbam56uLRyFWLbkxe9fY3Gj+2wP9Mdwstfn3lsPOHxwjMo0XsVl89oal75+vqw2lZR8QXEsi1efW+fKWpeT8QylDVXfYbFV+1iH6c3FFvcO+yBgtVPn+vYR+70x+/0Ro1lMminS3MH3HBqBh+faXF5dAGEIXJfFVpUb20fc2eux3x9za/eYMMlo1Sq4jsU0TlFak+WCaZJhCcEszfAdOBlNMQiG0xm1wKfquzQqHoNpVIzqV3KyXOG7NoFnM41SNIZkXl3SSuN7NmABBgFEaVaM5SNIc4UUFN50shBGwoYsL/qbpJQYijw1KYuBGK0NSitOxiF7/TFJluPaNnf2+wgpWG7XsaQgjDM816Ze8ciUotv45CnhZ0kphM4Qixtdrn7nCu/99BbTwYxKM8CvuOzfOUDahUeQtC1sR6JyRZrkWLmYR1FIaq1qIXZGMyaDkCxO0UpT79ZpLtQZHY/BGJY2F+jt95kOZhhjqLVruL4HGKbDGV7FY2GtjTGG3sEAnSlWr6ywuNElnsa8+5Ob6FzT7NZOzQ29wKV/OETlioW1Nn/4n/0etmOxd+cQrTQXXj7HxnOrLJ1beGLD4lngaOuYX/7bNwlHIa2lJo5nE01i3v7b6/T3B3z7779SiqGSki8wjapP42P8xT7M+kKTS8tdbu+f4FlFgOrdvR6pynEsC9uSzKIEz7FY7TaYhQkH/THrCw1ePL/Mze1jbmwf43kWFc9FSsnW8ZBhGGFLQa3iESUZB4MJnmPRbtRIck3gORhjyGKFAVxH0qr5uHaxBgGkmUIIQW8SAhB4duEfpzSubWF7Dr7ngtGEcU6c5biujec4aJ2Ra43BYFsWlhRYUlD1XIZhXOSjYchzVZjmBi7uvHoUpTm3d0/oNqs0qz7LbZdZnPLGnT3COCVTugimlYJa4PG1Cyvl+HzJp0cIwfPfvUKjU+PBuzuMjsesX1tj7/YB4SwGBCpTxNO4GJN3LXRuyNMccNBKo7TGdh26qy3GvQm1dpUXv3+NcBjSWmyxcnERr+Lx0//lV4x7E8JpTJbmOJ6DMVBrVml264x7E6S0+NofLHHx5fOnazTGgBS887c3WNrs0lqsMzgYMR3N8CseL37vGt/6D7/B5rU1hBC88PtXMcY8cSLjLKFyxXs/u0U8jVl/7n23b9d3qbWr7N7e5/4727zwe1ef4SpLSkqeJo5t8e1rm9QqLj98407Rs1Nx6NoBtYpHux6gteFgUHgCNas+GMPvv3AeISS/3DuhVnHZOR4xmEZFgr1lMZkmvH5vn0vLHcIkRQrB+kITS1pUPBtLCDzf5WQY4jo2Sht2jodoDVmeIys+nUaVaZSQZgrLsVGqMLu1hKBR9bEtSZxkGCSWFCS5YjiNwRgyrcAUlbJOI6BRDZhFKXFW+AJZlkAageWI0/H5h2aJ/XHE3YMTbFuwsdhgtdMgSjKubx3Sn0YErsNis0aaK/b7EzzHZud4xLXN0lm65FMipWTj6hprV1ZIopRJf8pgf8jdNx8QTSLSJKXRrWE5Ra9QOI0Q0sF2LVSmsC0Lp2pTa1fwqz5B3adSD0BDd71TNAmmOUHNw7Lt4vNE4XgulZo3T4WPGPenNLo1lj+UvSWEYPPqWhH6Opqx8dwqa5eWaS23WH9uhXPPbzyWFH9WK0AfpLc/oLc3YGH98YY+y7aot+ts39jj8isXH+t9Kikp+fLiuzbPrS9yfesIKQR7vTFrC43TsXiAVq3CJEy4urGA69h0G1Vev7NHrjTXt444HEyoBR5V32Ot2yDTmv5oRpxlrHRqKA1JmgM59YrPeJawfzAgVTlaGXy7qMZIKbFtm0wpVqsN0ixnYjSutBFI4ixHUbyPBK5DnOakmcK2JYFXeL+lmUIbQ5rm5FoxnP7/2fvvIMuzu7D/fp9vujl0ztOTdmZnNgeFlUACJLEW2EaP4XlAhhJWwnI9uGytXTbCFBjKZUGVCYWNHzkUqUBlcJWQfwUYI4lgll2lzWE2TOrp7ul8c/qmc54/zre7p2e6d2dnJ3RPn9dW12zf8L3f2zN97+ee8wldpEJPGxCCXNrDD2NSnoPr6OCnF4S4tkM65eAmCd8Zz+X0/BqObXNxtY4QgvH+ItV2Fz+KGB8oMlzKcnGtxVeffpWj4wMbCeW7jQmEdqn1sRd+x2fi6CiNSpOZl2d1MrLnoqSkPFxGAX7bR8WSKIrpGy0xfGCIsBdy5P48axerzLw0S/9YH343wO/4REFEtpglk08TxzGu55IvZckWM0gpqS01CIOIQn9BB1GXEUIwPDVAMFDgO//fj5DJXVkmv9f4HZ84lhvNHy+Xyadprw+7NYGQYewrvUD38Bnpy1NpdrEu672cSenKrVjqrSbHtqk02py5uMq5pSoZzyGIYqSCIIyIpaKUSxOEMdlUhsFyjqVKg5V6B0sIukFAPuXSBjpxgB/FOpdJKSIliSLB/Gqdjh8kw1xDXT4fSxzbwrUt/DAmjGJiqbfK+go5gjAi5TqIHsk8M4tYKmIpGRsoMVzMsFjVw2nTnkMhm6bV6ZFyHcJYslJrIYSgF0RUWl1c2+L0/ApnFtZQQBDFOMIikpJm10cpRX8pw8xyjXOLaxyd2J2rQiYQ2uVczyHfl+PQPVOsXFhNOjU7eOkU6ZyHl3VZPr+Ck3JIZVLYtu4fNHF0lKkTE5x/YRY35SIjSeSHZIsZBsf7aNVbDIz10W33qK829N5yGCEBN+2QyrgU+nPIWG47riLshdieTSrt7fkgCMDxHIRgy4DXS623NnB2cVMwwzDeXBRLlmst1hp6LFExm2asv0jmDT7guLaN69g4jm5u2Opt7UkUxbovT7sbcGJ6hLTnsFxtMbNcI+269CW5hUopOr5NtdWh2Y3wHIu1RotCJkXKdenPp6k2u7iWQxCHtHq6Ua1v6eDGdR3arS5RHLPaaG88vp6xLch4DuV8moznkvYcpJQEYaQDsCSxWgK1VhfHtkm7NiCYHu7j8PggHT/AtjvYliDl2HT9gI6vRzYFUQQIXRIvLNrdAKkUa40OK402Gc8lm3IRQDbtUUh7NLuBDpDCiGbSF2k3Mq/qu1yulGPk4JDuojxUxO8ElIfLG9d7nkuulKU8UiaTSzF9cpKDd0+RKWRYna9SX2vQN1yittZk6s4J+kfL+F0f1/PIFDL0jffhZTxc18FJu2SyKcojZaoLeptofWTFpaRUNCot7vnOEzju7fFPaGC8n9JgkdpynYHLhsIqpaivNrnznUdNKb1h7GHtXsC3X5tlbqWuq2uFQElFXzHDQ3dMMj6w/SDmXNrDc21eOr9IEMUs15r05TMMl/LYjk210UWiGO0rcGR0gHq7RyQlXpJQvV7FhdDDSHuBTksY7ctT7/i4jk2z69MNIjphTBhFtLsBcRyTcm0ynkMUS8IowA+jZBsNUp6DY1t620zo/kNRrPjA/XeQ8hxemlnildllKs025XwG2xI02116YUjW08+pF+pGkPmMB+jeQ8VcmnTKI4hjhBUQRQrXcShkPLp+hOvaFLJp/CDk4lqdKI5x7BQIoXsdeS6WZVHIpqg0u3iORdrbvSvpt8e72G3uyH0HWZuvMDTRz7kXLtBYa+C4Dr2OTxRGDEwMkEq7FAcLHLxrilQuzSvfeJ2Zl+foHy2THS0zf3qRb/zp0+SKGTL5DNXFGnEcsTZXoTRY5Mj9B7EdG7/t06q1GT44xF3vvZOFM0vIuEJ5uITt2HRbPdYuVhic6OfAnRNX/RyklFQWa1QWqkRhTLaQYfjA4LZbb7eCl3I59tBhnv7qC6zOrVEeKeO4Nr2OT+Wifv7TJydv9WkahnGNYil56rU5zi9VGe8vbMwVk1KxVG3yjVdm+a77PErZNKuNNqv1FlEsSXsOK7U2i5UmtVaXIIrxw5jX5lY5c3GNQjZFIZPmnXce4L33HKK/mOX8YoWU5zDcl+elmSVSSZ82nS6pK7RG+gocGO5nrL/AXz53mgvLdfoLaaRMOjmHEVIpHNshVopyNk0QRVRbXRBgJUNOXcdBEBHFMbFUrDXafOPV87zz+DTf96476fR86u0ulaYe3dHo9ACwbIFCbVSMrW+tdYKIjOcxWMwhVUwQRvT8kEImBcnIjb58hmant5EnlXb0zDSlFGnP3ZitZglBq+szOVjk8NjubZtiAqE9oH+0j4cfvR8vk6Lb7rF8YY2wF5ErZzlwfILySInlC6uk8ylqKw0qL8ywNLPKkfsPcvjeg1i2oLJY59Vvvs7yhVWGpvpBQG25STrnkS1maKw2AEjl0vSP9zE6PcTxh4+iIsmpb7zOmWfPkylkGBjrY+rOCU686w7y5avrDRH0Al54/BVmT80R+NHGkMDiQJG733ucyWPjN/LHd9UOnJhEWBavP3WW5Zll3Tcp5TJ2ZJQT77qD0uDuLgE1DGNnK7U2c6s1xi4JgkD3yBkbKDKzVOXM3ApBLJlZqhJGMcKC5Vqb5VqLuw+OctfBUb792ix+Mrur4wekPJfjk8N88ME7NvrlKHSAlUt7OLaFH8WkHBspFRIQwsaPIlzHpi+fxQ8iyvm0TmaOIj2rDJAKuoFuZIjS0+XXq8NkMnjVtiSxVISx2pgttlBp6r4+5QInpkeoNTusNDv0ggiFQCno+RGe65BN6dWbmeUara5Ps+2TSUtSro0QDjnPpdMLEULo6fOOxYHhPqqtLiv1FkJYuK7u1O0HMYPFHLalv6+0ulgC7j40vtFhezfavWdmbDE4McB3/fB7OPrAIV564hUqCzUc18ZybArlLPd9111M3DFGs9LiW//7GfrH+jdmbq3Or9Hr+Bx98BCN1SbNWpuRA0Pky1lkpOgbKXHo7gNYtoWUil6rx8BEP0995XlqSzXdUyftboyyuOPBQ28pKHj5ydc4/cxZBicGcDwH27YQlkVlocqzf/Ei6VyKwYlb/2lBCMGBOycYOzxMdam+0Vm6PFy6LfKgDGM/q7Y6RJHc8Q05m3Z54tSMzhkaKJD2XOIkn0gAZxbWEAqGSnkmB8vJYNMYx7awbMEzp+d5/71HcB2bQiZFs+vT6vo8cHSCuZU63SDEsy1s22ax0mBhtUljosfXnnudbhAy3Fcgl07RaPd000OVjL1IRmeAohvGG5PhPdve6CCtgFza1cUzQUw+m2Z2uc5v/Z9vEcUxa+0ethAMlfPkewHVdo841n2EFDpnyLYtPNsmm/boK+j2AH4YMTVc1qXzln5/WA8iCxmP0b4xqq0OnV7Isckhzlxco9Ls0Oj4CEtQzqYYGhvgPSent/2Z7xYmENpDLMviwJ0TTB0fp7bSoF3X7dzLI6WNAanrfX4Gxvs2vl+dq2DbFsWBIoX+ApWFCifefRwlJedfmmNpZpl8MUe+P0+2mObIfdMsz67SbflMHBvHsnSFhIwli+eWee6vXuK9H3nnVeXLNNaanH/xAnEYc/qZcwTdANuxGZjoZ2hygOpilZlT87siEFrnei7DU4O3+jQMw7iO1HoEsYNeELFSb3N0fHAjn6UXRvT8iJH+AjOLFYIo5q7pkY2BY3mlWK23KWXTLFabLFabTA2VKeXSOqcnlhSzKY5O6LyhZsdnrdEBAeVCmlIuTb3j4zg28yt1pkf6sG1B2nVxrJh2NyaUChUpYkfhrneARk+eT3sOfhCRdnUDQ73iIwnDmHavRy+MsLCw0K9rloBCNk2YrDj5kW602Oz69OUz1Ns+U8NlDg6Xqba7oPR4jP5ijjjpUzdUylPOZxgp6z/PLVYQAvqLWU4eGGGh2qDjh6RcB9vSyeWmoaJx3Qkh6Bsu0Td8ZWLfRt+eZLSLjGM6zS6prHfFbQfG+ykOFHj1qRSH75/m4F0HGBjvY2lmhdPPnGcyaYq4zrItRg8Nc/H0AovnV5g+8eY5M0sXVnj9mXOgwMt6eCmPOIq58PIc1cUaoweHWbmwQtAL8NJXnqNhGMb1UMjqYatRUmJ+uZV6i5Rrk8tc9jqUTCPVycq6BN66LKBybIteCJVGh8nBEiuNNmnXJuU4XFxrkEt7ZFIuQajHWtwxMUTGc/Ecm4xrM1IusFBpMLtSo9nx8YMIz9Xjk+Jk6v34QIkwimn7UXIeeisMIRCWII4VYRxjoYOPob4CrY7PwmqdyaESrV5Axw8ZKeco59IsVBp4rk293QMFSgkmhorcf2Sc/kKO5VqThbUGF9caZFMOac/j2OQgw+WCHtAdRCxUGowPFJkcLPH6xTXm1upk0y4pT4/8yLk2D94xuaXCbjcygdBtxst4yFjy6rdPUx4sJrPGJELp39xuq0cqmyJb1EnKbsqlNJBn+uQUB++aAuCFvzlFKnnRuJxlW9iuQ3WxelWB0PzrC9RX6hy8e3pLWXq2mKGyWOXi2UWmT0wi5e4eymcYxt422ldguJxnodJgYrCEdcnrW63VxbUs+vJbhzhnPJdcWo+Q0K+Hgkvnh3b8kEzKJZfxkkAj4OunZphZqjK/2kjygBw6fkhfPkM25TJczjM5WKLS7OK6DoPlPI2uTzmf4eWZJXpBhG0lM78Q2LZFxtNT7kMZU87rbta9MKDZCVBKEcU6wLMF5PJpxgaKeoZYUsU1WMrRX8yxVG3S7PSYGi4zXNbdn0/NLjFYzHPPoVFG+gobI0gmBkuM9Rcp5yvcf2ScIIqYXa5xYbmKUtDs9pBSbvQVcmyLfCarJwkIwZGxAQ4M9dFfvDGDsa8nEwjdRprVFs/91UuszK1y8fVFKgs13JSD3/FRUuGlXDr1DhPHxpCxpNPoEoUR2bxOgr7UmzWDvpphwoEfUlmokcnrRo02WztOF/sLLJ5b5vC903jp3VtaaRjG3uc6Ng/dMck3X7nAhaUqmZSLbVl0/RDPsXng6ATnl6r4SdNB0InU4wNFTl1YJo5j3UMnWQ4KQl3ifmi0H8e29IT3lRodP2KonOOug6O8Pr9CPpOi2Q3IZ1JkksTkdi8gn3Ep53RwtFTVqy+6n5CNSvr+CEswkM5h24J82mOqUGKp2tJl70HE/FqDVtfHtixKuQz9+TTCsjb6FnWDiKFyHj+UDJVz5NIetVaHuw6O0l/IEoQx7V7A5FCJOyavbHYolcJzbYb7dPB2fHKYSrPD6/MrdIOAUjG7ETzW2z06fsC9B8e45/DYnpgosM4EQreJKIx47q9eYuHsEscfPkppsMTCmcWkm3RAdblOr91j5NAwrWqLldlVei2fKIq5/3vu3lghAhic6Gfu1Ysopa74xyxjSRTG9I+W3/Sc/I6P7doMTfbTWG3QP9qHuCTpWMaSMIgYnOg3yciGYdxwg6Uc77v3MPOrdeZWakRScXCkn6nhMgPFLH4YM79aZ3KovJEbOVTOU2l2qNTbhFJxYXk9iNLzwSaGSixUmtiWoNUNmRou6eaLlkWl2WG10SGbslmqNsmkXKrNDn2FDEeGBnAdC9fxGOsrcPbiKo5tkctk6QURwxmPYjZDMZei0e4ShJJG26c/qUzz3IhSPkunF5BybQZLOVrdQDc+TJo7urbFgZE+LixVaXcDHEeX26dcB6UUK/UWx6eGUIotAeC6lVqLwWKWkXIeIQT9xSxSKZodn8nB0pYtr0zKZaXe5slTMyAER8YHyO2RdAcTCN0mVmbXWDy/zMjBYVzPYfLYGOXhItWlBn6nx8KZRRCClbk1LEuQyqZJZzxKw0Waq02e/+uXue+77sJ2bMYOj3D2+RlWZlcZmtqcFi+lYmlmhYGxPoan37xVumVbOI7N2JFRsJZZu1jFy7hYtkWY9JwYmR5kPKluMwzDuNHymRTHp4Y5PjV8xXUP3DFJEMXMLFXJpl0c26LTCylm0/zg++6jEwS8eHaBUEqGSjny6RQXVxsMlnTJ+Fqjg5ukAKQ8h+NTw2RXaqzWWjTaeispl/E4PD7ISH9h43H1fLI8fQXF9Egf7V5Ivd3FsS0cy6LZ8ak0uzx8bJJ7Do3T6vmcX6pSaXToCkUsFfVWj4nBIrVOjwvLNfrzGQ6O9jE5VMa2BOcWKixUGgyXc7S7Piu1Fv2FLA/ee4TzSxVOz6+RS+ttviiW1FpdcimPew+Pb2k3cHGtQS+Mtpx/GElmliqs1FosVFpUWl3unBri0Gg/Jw+MbLn/brS7z864atXlOkrqkRygt54KfXkKfXkAMoUMF07Ncvd77sTL6LEY+b4c2UKGXsfnzHPnSeVSDI73k8p63Pv+kzz/1y8z9+pFUlkPpfRYjfJIifu+6+RGldobyRWzDE8PMvPyPMcfPkJlscbaxSpRqOeYRWFMeahAvrT795ANw7j99eUzvO+ew8yt1rmwrHsJjfeXODDSx2hfAcsSvOvOaeZWaqzU29hC9yAaHyjy7ddmcZ2tK9t6YOsgU0NlZperTAyWyGdSnFlYo9Hp6SaFQKcX0Or6nJwe4djUEJawqDY7rNR1Y8cwlhwc6ePew+NkUi7ZtEs5n6He6jK/1qCUTXP3wVEqzY4uza80GekvbHTKHu0r0PVDUp7DeH+BUi7DXQfHmBrSqzrD5TxDpTxnL67R6gXYluCO8SGOjA8wVM5veU7Nbg/P3UxziKXk9fkVFioNitkUw+UshayHJQTPnb2IH0Q8fHxqy5Da3cYEQrcJJeUb5vW0a22CbsjUnRNXbHd1G13OvzTLxdOLjB8dxct4DB8Y5O733qk7SS9UQcDw5CCjh4bfUjfoQ3cfYHlmlepSncGJAYYPDLF4fpnzL16gsdpEhqM88b++xeTxCe548JAZYWEYxi2VTXscmxzi2DY5M6CDpfUcnEuV8xlml2vb3iftObiuw9RQH3dMDpJJuVxYqnKhWQME6ZTLobF+hvryGwFDfzFLfzFLKZdmqdLi5PTolnlonmMzVM6TSekp8yenR8imPZRSnF1Y4+WZJeZW6zqhUwjG+ot86KFjHBjuu+L8XMfm2OQQh8cG6AUhtmXtOHst5TpEkdz4vtrsslxrMVDI4jg2nV5IynEo5zOkPYczC2tMj/QzeskK0m5jAqHbRHGgoAenxhJ7m9LQZqVFoT9/RRBUWahy+lnd3ydbyDB5bJxuq8fF1xdoVlq888MPcMeDh6/5vAYnBnjwQ/fy8pOvsTyzwuK5JRbPr5AvZ7nrvccZOzxKp9HhpSdepV1r8+CH7sXdxTNpDMMwtjMxUOLV2WWand4V5eLr20zjA0VSrsPDx6Y4PjVMvdUFdBB1dmGNZ89cxLEsirk0lhAbc80yaT2uYye6il6/tgshODI+yMRgmeVaizDSuT/D5fybblHpyq83/jA6PlDk1dmVjZyiSkOP7nAcmyjWDR/XK8XWm1IuVBomEDJuvJHpIfrHyizPrDB6aHhLwFNdqpEtZq6Yqi5jyfyZRWSsyBazGwnTmXya9JFR5l+7yNnnZ3jwA/e+rXMbOzTCYDInrVltcfd7Bxg9PLzRN6g4UCCTTzP76kXGj44ydfzqZ5gZhmHsBoOlHCenR3n+7ALNbkApl9YDm9s9BHD/0YktpeSFTGpjawzg5PQoQghOz68yu1xDkDTRHeqjkNHH2k693WNqqEza2/p2nvYcDlwyoPt6GS4XODjax+vzq0mCeYglBF0/pNHxGesv0JfbXDFzHF3htpvt3k27bfzf//t/+Xt/7+8xPq4b/X35y19+0/v81V/9FQ8++CCpVIqjR4/y27/92zf8PG8FL+1x3/tPku/LM/fqRVbm1li7WGH21XlkLHnHow/QN1qm3ehs3KdZbdOqtMkW0sRhvKWEXghBeaTM4tllOs3u2z4/N5lGnC1kOHBy8ormiW7KxXZt5l5feNuPZRiGcbMJIbhrepTvuPsQI315On5IL4iYGCjx3rsPc+c2ydmXcmyLew6N8aGHjvG+ew7znrsO8j0PHOX7332Sk9MjrNY7+OHWgKLa7GAJwaHR/ptWru7YFg8fm+Lug6OEYUyj47NabxNGMdPDZY5ODG7ZlQiiOJlsv3vtqRWhdrvNfffdxyc+8Qn+wT/4B296+3PnzvH93//9fOYzn+H3f//3+drXvsanPvUpxsbGePTRR2/CGd9cgxMDvPcHHmb+9UVe+dZpli+sYrs25aESxcE8k8fGOPvcDKEfUezPE4cR3XaXOI4ZGO+nPFLecjwv7epeQ9cpmve7PtY223brUhmPTuPtB12GYRi3gmUJpkf6mBoq0w1CBLqs/K0EKflM6ortqXsPjxPGMecXq7onm20RRroC7YGjE0wMXjll4Eba2N6bHOLQ6ABPnpphpC/PYGnrIO5mp0fGdRjrNyM2rpsPf/jDfPjDH77q23/hC1/g0KFD/PIv/zIAJ06c4PHHH+dXf/VXdwyEfN/H9/2N7xuNxts76ZsslU3RbnQI/YjycIlUNkWn2eVbf/YsI9ND3PHQYRbPLbNwdolWvYOKFUOTAxy8+8BGxdm6XtvHS7u4lzU7jKOY1fkK3VYPx7XpH+u7qgTqVFZ3ud6J3w3oH7sykc8wDGMvsSxxXXvopD2Hd5+Y5vDYAIuVJmEUkc+kGR8oUt4mcftmiGJJs+vjujaj/QUurtWJYkk5r/Oj6snw2HsOjTOwy7tL76lA6K168skn+eAHP7jlskcffZR//s//+Y73+fznP8/P//zP3+Azu3FmXp7j9DPnGJwcIJ3d/FQRhTELZxbJlXO8///zHhqrTeIo5sXHT9GqdUhdtnQppaK+0uDOd92xpVR+ZW6Nl554hbWLVR3UCEG+lOXwvdMcffAQtr01D+lSw1ODZAuZjcTtSwV+SBRETN4xdp1+EoZhGLcP27IY6y/uitWVervHU6/NslBpEkuJVGqjs3YvyJHxXPoKWY6MD3Bw5OZt212r2zoQWlxcZGRkZMtlIyMjNBoNut0umcyVkfTnPvc5HnvssY3vG40GU1NTN/xcr4cojJh5eVYnO2e3Lq2ur9wsnFnkjgcPMZI0RHQ8h2//+XPMn16kb6SEm3LptXvUluoMTvZz6J4DG8eoLtd56ivP0Wl0GZoaxPUcpFQ015o8/zenQMDxh4/ueH7FgQJHHjjIS0+8it8NKA0WEJZFu9amvtbg0N0HGD30xvvohmEYxq3jhxHfevUCF9cajA0U8ZIinDCKmV9tUMqleM/JQwyUsru6d9ClbutA6FqkUilSqb3Zy6bT7NKstikObF+mmC1mqC7VaNc6FJNSxuGpQd754Qc48+x5Vi6s0gibpNIexx4+wpH7D240ZAS4cGqOZqXFxB2bc2QsS1AaKqKAc8/PcODOCTJvsFR7/B1HSefSnHthhrWFKkoqssUM93znSY7efxBnl3cgNQzD2M8W1hosrDWZHCxtSYp2HZup4RJzK3VaPf8Ny/13m9v6XWd0dJSlpaUtly0tLVEsFrddDdrrLMvCsgRqh0nuG9WXl61SDo73MzDWR6vWJgoiPZ3+spyfoBewcGaR4kBh22XO4kCBi2cWWVuoMXnHzj9by7I4dPcBpo6P01hrohTkStkrVrAMwzCM3Wep2sSyxLb96mzLwrEtFitNDo8N3IKzuza3dSD0yCOP8Kd/+qdbLvvKV77CI488covO6MbKFjP0jZZZna2QyV85AqNZaVLoy1EevrLCYH0kx07iKCaOJOn89gmAliUQye2uhuM69I+axGjDMIy9JJIS29o558e2LGK5c1HMbrQ3NvASrVaLZ599lmeffRbQ5fHPPvssFy5cAHR+z8c+9rGN23/mM5/h7Nmz/Kt/9a945ZVX+M//+T/zh3/4h3z2s5+9Fad/w1mWxcG7DqCUorbS2NKAq9Po0lhrMX3X1FXNCbucl/bIFjN0d+gpFPghwhJkcmZlxzAM43bVX8jih9GODR57QbTrq8Qut6cCoW9/+9s88MADPPDAAwA89thjPPDAA/zsz/4sAAsLCxtBEcChQ4f4kz/5E77yla9w33338cu//Mv89//+32/LHkLrJo6Ocs/7TqBiydyrF5l/fYHZV+Zp1drc+c6j1zwuw3ZsDpyYpNPoEvjhluuUUqzNVxiaHGBgov96PA3DMAzjMlIqekFEeJUr7zfCxECJYi7Nar19xXWrjTaFjLcx7HWvEGqnsM4AdNVYqVSiXq9TLN76ssWr1ay2WL6wSq/dw025DE700zdSfltljIEf8uxfvMD5F2fJFDJkCxnCIKSx1qI0WOCh772PwXETCBmGYVxPYRQzs1Tl7MIa7V6AbVtMDZU5NNp/S/oInV+s8O3X5+j2go3mj62uTybl8eAdE7smP+hq379NIPQm9mogdKMEfsjcqxeZeXmWbrOH5dhMHB3hwIlJSoPm52MYhnE9hVHMt16d5fT8KumUQy7tEcaSertHfz7Du09MM1S++RVaq/U2F5arXFzTTYfH+oscGCkzVNo91WImELpOTCC0vTiOCXohtmPjpcy0eMMwjBvh9flVnnj5PGP9BVKXtBdRSjG/2mCkL89333/0lvXsWQ8hdmPTxKt9/95TOULG7mHbNplc2gRBhmEYN0gsJWcX1sh67pYgCHTgMdyXZ6nWYrnWukVnqM9jNwZBb4UJhAzDMAxjFwrCmFbXJ7fD9HbPsZFS0b2sgMV4a0wgZBiGYRi7kGUJbMvasUpMKoVSas+MstitzE/PMAzDMHahlOswMVSi3u5t27en0e5RyKYYLOVuwdndPm7rztKGYRiGsVd1egFCwfxqndfmV5gYKDHaX6CYS9Pq+NTbPR48Okkuvf3WmXF1TCBkGIZhGLtMrdXl66dmWKq2GC7lmV+r8/rcCq/PrzJcznNsYpAHjk5wYnr4Vp/qnmcCIcMwDMPYRaRUPHN6npV6mwPDZSxLcGi8n3q7R7XRoe2HnJge4cSBkVt9qrcFkyNkGIZhGLvISr3FYqXJSF8eKxlwalsW/YUsRyYGGShmWa62dpz3Zbw1ZkVoD+m2uizPrhF0AxzPYWhygHzZJMkZhmHcTpodnzCOr+gdtK6YTVFpdQiinW9jXD3zE9wjzr80yyvffJ3GWgshBEopcsUMR+4/yLGHj2CZ8knDMIzbwvoq0E6kAgvB3m5juHuYQGgPuHhmkWf/8kVcz2HijjEsSwdCzUqLFx9/BcdzOHr/oVt9moZhGMZ10JfPkPZc2r1g24qwervL8clhPLMadF2YZYRdTkrJ2RdmUErRP9a38UlBCEFxoECmkOHs8xcIesEtPlPDMAzjeijnMxwc6WO51qIXbHaNlkqxXGuRSXkcHO2/hWd4ezHh5C7XqrWpLNR2nOxeGiyweH6Z2nKd4QNDN/nsDMMwjOtNCMG9h8eJYsnMUpUw3kyJKOXS3H9kguFbMHH+dmUCoV1OxhIZS2zX3vZ627FB6XJLwzAM4/aQ9hzefWKaoxODrNZbhJEkn/EY7S+aBorXmQmEdrlsIUO2mKFd6+CNlK64vt3okM6myBYzt+DsDMMwjBvFsgTD5bxZ/bnBTI7QLuelPQ7cOUGz2iS8bMJwHMVULlYZOzpKsb9wi87QMAzDMPYusyK0Bxy+d5r6aoMLp+bx0i7pXJqgF9Jtdhk9NMyd7zx6q0/RMAzDuIGUUtRaXbpBiGPb9BUyuPb2KRPGW2MCoT3AS3s88IF7GT04zIVTc3SaPfJ9OU4+cozxo6NkculbfYqGYRjGDVJtdnjx/CILaw38MMKyLQYKWU4cGOHAcBkhTEeht8MEQnuEl3KZPjnF9Mkp4ijGsi3zj98wDOM2V2/3eOLlGSqNNkPlPJmUSxjFVJodnnz5PFJNc8iU0r8tJkdoD7Id2wRBhmEY+8CZi6us1ltMDpfJpFwAXMdmpK+AbVmcmlkiCKNbfJZ7mwmEDMMwDGMX6gURF5ZrlPMZrG0+/A4Us1RbHVYb7VtwdrcPEwgZhmEYxi4UxjFRLHccrGrbFlJBEMY3+cxuLyYQMgzDMIxdKOXYpFybbhBue30YxVhCkPJMuu/bYQIhwzAMw9iFPNdheqSfeqtHLOUV16/UWwyVcgyVTMPFt8OEkYZhGIaxSx0ZH2C51uTCco2+fIZs2tuoGst6LncfGsWxzZrG22ECIcMwDMPYpXJpj3efmOa1uRVmlmus1ds4ts30cB/HJocY6TNTBd4uEwgZhmEYxi6Wz6R48I5JThwYoReE2JZFIZsybVSuExMIGYZhGMYekEm5G72EjOvHbCwahmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvveVAqFar8Vu/9Vt84hOf4AMf+ACPPPIIf//v/31+7ud+jieeeOJGnOMWv/Ebv8HBgwdJp9O8613v4pvf/OaOt/3t3/5thBBbvtLp9A0/R8MwDMMw9oarDoQuXrzIpz71KcbGxvh3/+7f0e12uf/++/nABz7A5OQkf/mXf8mHPvQhTp48yR/8wR/ckJP9gz/4Ax577DF+7ud+jqeffpr77ruPRx99lOXl5R3vUywWWVhY2PiamZm5IedmGIZhGMbe41ztDR944AF+/Md/nKeeeoqTJ09ue5tut8uXv/xlfu3Xfo3Z2Vn+5b/8l9ftRAF+5Vd+hU9/+tN8/OMfB+ALX/gCf/Inf8Jv/uZv8lM/9VPb3kcIwejo6HU9D8MwDMMwbg9XHQi9/PLLDAwMvOFtMpkMH/3oR/noRz/K2tra2z65SwVBwFNPPcXnPve5jcssy+KDH/wgTz755I73a7VaTE9PI6XkwQcf5N//+3/PXXfdtePtfd/H9/2N7xuNxvV5AoZhGIZh7DpXvTV2aRDUbrff0u2vh9XVVeI4ZmRkZMvlIyMjLC4ubnuf48eP85u/+Zv8r//1v/i93/s9pJS85z3vYW5ubsfH+fznP0+pVNr4mpqauq7PwzAMwzCM3eOaqsZGRkb4xCc+weOPP369z+e6euSRR/jYxz7G/fffz/vf/36+9KUvMTQ0xH/5L/9lx/t87nOfo16vb3zNzs7exDM2DMMwDONmuqZA6Pd+7/eoVCp8z/d8D8eOHeMXf/EXuXjx4vU+ty0GBwexbZulpaUtly8tLV11DpDrujzwwAOcPn16x9ukUimKxeKWL8MwDMMwbk/XFAh95CMf4ctf/jLz8/N85jOf4Ytf/CLT09P83b/7d/nSl75EFEXX+zzxPI+HHnqIr33taxuXSSn52te+xiOPPHJVx4jjmBdeeIGxsbHrfn6GYRiGYew9b6uh4tDQEI899hjPP/88v/Irv8JXv/pVfuiHfojx8XF+9md/lk6nc73OE4DHHnuM//bf/hu/8zu/w6lTp/gn/+Sf0G63N6rIPvaxj21Jpv6FX/gF/vzP/5yzZ8/y9NNP82M/9mPMzMzwqU996rqel2EYhmEYe9NVV41tZ2lpid/5nd/ht3/7t5mZmeGHfuiH+OQnP8nc3By/9Eu/xNe//nX+/M///HqdKz/8wz/MysoKP/uzP8vi4iL3338/f/Znf7aRQH3hwgUsazO2q1arfPrTn2ZxcZG+vj4eeughnnjiiR3L/w3DMAzD2F+EUkq91Tt96Utf4rd+67f4P//n/3Dy5Ek+9alP8WM/9mOUy+WN25w5c4YTJ04QBMH1PN+brtFoUCqVqNfrJl/IMAzDMPaIq33/vqYVoY9//OP8yI/8CH/7t3/LO97xjm1vMz4+zr/5N//mWg5vGIZhGIZxU1zTilCn0yGbzd6I89l1zIqQYRiGYew9V/v+fdXJ0pc2UbyaIOhqmi4ahmEYhmHcSlcdCB09epRf/MVfZGFhYcfbKKX4yle+woc//GF+/dd//bqcoGEYhmEYxo1y1TlCf/VXf8VP//RP82//7b/lvvvu4+GHH2Z8fJx0Ok21WuXll1/mySefxHEcPve5z/GP//E/vpHnbRiGYRiG8ba95RyhCxcu8Id/+Ic8/vjjzMzM0O12GRwc5IEHHuDRRx/lwx/+MLZt36jzvelMjpBhGIZh7D1X+/59TcnS+4kJhAzDMAxj77mh5fOPPfbYtpcLIUin0xw9epQf+IEfoL+//1oObxiGYRiGcVNc04rQd3/3d/P0008TxzHHjx8H4LXXXsO2be68805effVVhBA8/vjje76Ls1kRMgzDMIy957qXz1/qB37gB/jgBz/IxYsXeeqpp3jqqaeYm5vjQx/6EB/96EeZn5/nfe97H5/97Gev+QkYhmEYhmHcaNe0IjQxMcFXvvKVK1Z7XnrpJb73e7+X+fl5nn76ab73e7+X1dXV63ayt4JZETIMwzCMveeGrgjV63WWl5evuHxlZYVGowFAuVze83PGDMMwDMO4vV3z1tgnPvEJ/uiP/oi5uTnm5ub4oz/6Iz75yU/ykY98BIBvfvObHDt27Hqeq2EYhmEYxnV1TVtjrVaLz372s/zu7/4uURQB4DgOP/7jP86v/uqvksvlePbZZwG4//77r+f53nRma8wwDMMw9p6b0keo1Wpx9uxZAA4fPkw+n7/WQ+1aJhAyDMMwjL3nhvYRWpfP57n33nvfziEMwzAMwzBumWvKETIMwzAMw7gdmEDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr5lAiHDMAzDMPYtEwgZhmEYhrFvmUDIMAzDMIx9ywRChmEYhmHsWyYQMgzDMAxj3zKBkGEYhmEY+5YJhAzDMAzD2LdMIGQYhmEYxr615wKh3/iN3+DgwYOk02ne9a538c1vfvMNb/8//+f/5M477ySdTnPPPffwp3/6pzfpTA3DMAzD2O32VCD0B3/wBzz22GP83M/9HE8//TT33Xcfjz76KMvLy9ve/oknnuCjH/0on/zkJ3nmmWf4yEc+wkc+8hFefPHFm3zmhmEYhmHsRkIppW71SVytd73rXbzjHe/gP/2n/wSAlJKpqSn+6T/9p/zUT/3UFbf/4R/+YdrtNn/8x3+8cdm73/1u7r//fr7whS9c1WM2Gg1KpRL1ep1isXh9nohhGIZhGDfU1b5/75kVoSAIeOqpp/jgBz+4cZllWXzwgx/kySef3PY+Tz755JbbAzz66KM73h7A930ajcaWL8MwDMMwbk97JhBaXV0ljmNGRka2XD4yMsLi4uK291lcXHxLtwf4/Oc/T6lU2viampp6+ydvGIZhGMautGcCoZvlc5/7HPV6feNrdnb2Vp+SYRiGYRg3iHOrT+BqDQ4OYts2S0tLWy5fWlpidHR02/uMjo6+pdsDpFIpUqnU2z9hwzAMwzB2vT2zIuR5Hg899BBf+9rXNi6TUvK1r32NRx55ZNv7PPLII1tuD/CVr3xlx9sbhmEYhrG/7JkVIYDHHnuMH//xH+fhhx/mne98J7/2a79Gu93m4x//OAAf+9jHmJiY4POf/zwA/+yf/TPe//7388u//Mt8//d/P//jf/wPvv3tb/Nf/+t/vZVPwzAMwzBuO0pJUB39jcgixN5Ya9lTgdAP//APs7Kyws/+7M+yuLjI/fffz5/92Z9tJERfuHABy9r8wb/nPe/hi1/8Ij/zMz/DT//0T3PHHXfw5S9/mbvvvvtWPYVbIpIxsZK4lo21R/5hbqcWdFjoVqgHXTzLZiRTZiRdwrHsW31qhmEY+5ZSEuJzqPA0yAogwB4E5yjY0wghbvUpvqE91UfoVtjLfYRqQZvz7RVm22vESlJw0xzKD3MgO7jngofTzUVeqF2gFfZI2Q6hlAgBU5kBHho4TNYxeV2GYRg3m1IKFT4H4TOAC6IEKFA1/af7EJZ3axYfrvb9e0+tCBlXb7lX5xurp6mHbYpuFs+yqfgtFro1VgsNHuw/vGeCoYVulacr50hZDgfzQxuXhzLiXHsF27J4ZPDYrv/UYRiGcduRSxC+AKIPYV0abORRsgrh8yh7DGEP3LJTfDN7d5/E2FEkY56tzNCKehzIDtLn5Si4GUaTraTXm4tc6Kze6tO8audbK0RK0p/Kb7nctRxG0kXmOxUqQesWnZ1hGMbbo1QPJSso2WSvbdKoaA4ILguCNGH1geqg4rmbf2JvgVkRug0t9xqsBg1G0+UrVknStotnOZxrLXMwN7Trc4b8OGS5V6fkZra9PuukWPab1IIOA6nCTT47wzCMa6dkBxW9AtFZUD3ABmccnOMIe+c2L7uKqgPbvz4DIFKgmjftdK7F7n4XNK5JJ/ZRSuHusPWVc1I0wx6hjG/ymd0YZkPMMIy9RskOyn8cgqf0BdYAiByEZ1G9v0ZFe6SZr0iBCna+XoXA7s7hNIHQbcgWFgq14xJrpCS2sLB3+WoQgGc5DKYKNMLuttf34gDPsndcMTIMw9iNVHQG4vO6qsrqR4gUwsojnGkgQIXPoVR4q0/zTQl7EpDbnqtSPggL4Yzf/BN7C3b/O6Hxlg2mCuScNM3oyuBBKUUj7DCVG9gTydJCCA7mh7EQ1IPOlusiGbPYrTOe6bsif8gwDGO3UiqE6AyIEkJsk6FiDYNcgXjpyut2G3scnGmIZ1FS52oqpVCyAfEcOIfBGnmTg9xaJkfoNlRwMxzOj/BC7YL+3skghCCUMUu9OiU3x8Hc0JscZfcYz/Rxb98BXqrNUWuvkrZdYhkTKclkrp/7+w/t+lwnwzCMDcrXOUEit+3VQrjJin7v5p7XNRDCA+8RlEhDdAEVrSRX5MC9B+Hdv32wt4vs7rMzrtldpUkEcKa1xIXOKgKBEIJBr8j9/dOUve1/AXcjIQR3FicYSpeY71SoBW08y2E808dYtg/PMv+MDcPYQ4QHwgV84MrXYqXW8ze9G3oaOtgKAYEQ7jUfR1hZROq9KPckyLq+0OpDWKXrcp43mnkHuU05ls29fdMcyg+z6jeJlSRrpxhOF/fEltjlhBAMpgoMmsowwzD2OCE8lH0QwmdQonzlKAq5BlYZ7BuzpaRUDPEFVHQWZBUQKPsAwjn8tvr9CKsPrL7rd6I3iQmE9pBG2GWpV6MbBaRsl+F0kbKbQ6FY9Zv04hBH2Ayk8qRsHd0X3AwFk0hsGIaxqwj3iO6vE8+grBGElUWpSAdBBAj3IYS4/tVWSklU8DRELwI2iAIQQ/Q8KjoH6fci7Inr/ri7mQmE9gClFK81LvJyY55W1MNCIJUiY3sMpgpExKz2WsQqRiAouVnuLE1wOD9sui0bhmHsQsIqQ/o7UcGzEC+gomUQFoh+hPcOsI/cmAeOZyF6CcQgwrp0W64fFc+j/G9DZvCqgjC9teYn36X27PuNCYT2gAudNZ6pnifrpJjODm78Y1vq1fnzhecYSpe4pzxFynaJlaTqt/jW2mkAjhR2d7a+YRjGfiWsfkh9tx5Uqto6b8ga0AnIN4iKzoGyEPY2eaLWqA6U4gVwDu58DKUgnktaACzrC+1hXSFmT+25gMgEQrtcrCSnmwvYwqLvsgTnRthFopBKYiX/8GxhMZgustpr8Ep9nslsPynbpRP5LPZq+HGEa9kMp0sUzZaZYRjGLSWEAHsAuPGzuJSKddBl7VStZqOE0kHZGx0nfAXCb4FSsJ4QHZ1HxRfAfRDcu/ZUMGQCoV2uGfao+m3KXnbL5YGMWPObDKYKdGKfVuTT523+dfal8lzsVDdyh16qzVIPO1hCb6vlnDTHiqOcLE2a0nPDMIx9wQLhgNy+QS0AKrndTlfLCoTPgsgi7P5LDl1Mhqw+B/Yo2IPX66RvOBMI7XIKiUQhLhskEUuJlJK07dKFK7pI28JCopjrVJhpL+NZDgdyg1hCJE0VuzxbncEVDsdLu7vrp2EYxm6nZBviiyjZBGEj7GGwhhFi91TpCiF0tVr8TZQauKJaTck2iLRu6LgDFc2CaiPsw1ce3+pDRWdR8RzCBELG9ZJz0uSdNK2ot1EJBuBaNq7l0Ii6pCyXjL11TzmQETaChW4VpdgykFQIQcnLEqmY081FDuaHthzbMAzDuHoquoAKvgWyhl5NiVHCAfsgeO9EWNk3PsBNJJyDOk8onkXZ4xv9g5RsgVwG9yRY/TsfQNV1sLTjA6STkvy9w+yJ7HKe5XAoP0Qz7OHHm7NcHEuXya/5Lfq8HBlnMxBSSrHca5B30wQyuiK3aF3Zy1ELO1SDN94PNgzDMLan4hWU/6TuFG1PI5xphHNYr6pEr6PCp3ac+3grCKuISL1Hb1/JBVR0XvcTUi1w70Z4D79Jfo8HKtr5ahXphpF7iFkR2gOOFkaph13ONJewhSBjewQyQqI4WhjFFhYVv0XW8QhkTNVvU3Iz3Fmc4Jnq+Y1E6stZCBQKuYt+SQ3DMPYSFZ0DWgj70JbLhUij7HGIZsC5E+zdM9ZI2EOQ/hDIJZBNwAZ7QFexvel9x1HhyygVXtGNWg9elXuuD5EJhPYA13J4uP8wQ6kiz9dmWOhUSdkORwpjHCuMsRo0mGmtUg+6OJbN8eIYhwsj5J00LzfmudBew7NshLDIOSnKbhbbsmhHPhnbI+e8taZdUTKzbMVvEMmYoptlPNNH3n2D5VLDMIzbjO7QPAdi+1ESQmRQalE3SdxFgRCg53/ZE/BWU5jsMT1kNTqXNILUOw5KdkAu6u1Ae2/lnZpAaI9oRT3OtZZpRz7FVBYBzLRXaEZdHh44wrHiOH7SWXp9m2zVb7LWbfJC4wJFJ4NtWVgI+lI5DuVGWPOb3FEco+Rd/f51J/J5au0ss901lAI7GeZadDPc1zfNwfzOSXaGYRi3F4kus3qzUvE3X3VXKkimzQcbCctvZ/7XjSKEC967UcJLhqwmfYREGtw7ko7YZmvMuM4CGfHttbMs9mpMZvuxk0x/qSSL3RrfXj3D+0dObhml0Y58vrV6GseyOF4YY8Vv4AgbW1jMtFZZ7jZ479Bx7i5PXfV5KKV4pnqe8+0Vxi8ZdqqUYs1v8lTlHFknxXB6bwzaMwzDeDuEcFH2IITnt52xpVQAwgaruOMxdHPCs6jgBd3jRwAIsIbAvRfhHLhh53+thJUD7ztQ9kXdgBHAnkTYE3uqf9A6EwjtAYvdGkuXBUEAlrAYy/Qx01llrrPGnaXNfdn5ToVVv8l0fgipJIN+keVejW4cMp4pI7A2ts+u1prfZL6zxkimtGXiuxCCwXSRC+1VLrRXTSBkGMa+IexDqGgGJetbpq0rJSG+qLefrDfo8B+fR/lPAE7SldnWuTZyGeX/LQgHscu2mpQKUeHLEJ0G1dAXxnMo5w5wT5gVIeP6W/ObCMSWIGidSJKnF7u1LYHQQrdK2naxhMASNiOZEiOZElJJBILZToVm2HtL51ELOwRxfEWp/rqim2GhWyOS8Z6ccG8Yxv6jlAJVBdnRzQat/rf2Rm5PgXsfhM+joiqIHBDr7sz2KCL1Dp2Ps+1jRzqgQCAumTQvhAv2hC7LD18Ba+yqV1p09+gVXcUmXLCGrmtgooe2PgXhS3qly5pMrqhD8C2UaoH37l3VP+nNmEBoD1BK8Ua/A+vVX5eSSm4bOFnCohsHrPQaPBefoxV1GUmXGM/2v+nqkELRkwFL3ToSPfS16GY2qtIEulnj5ediGIaxGylZRQXPQTwPyt8Yeop3EuwjVxV8CCHAvRfsYVQ0A3IVcBHOA3qFx8rvfGe5poMWa2z7660BPfdL1UGU3/z5xAv6+chFUHHyfAbAuxvhHE7K+ENAXHv+kVyC6BUd5IlLxjSJfpTIQPS6nlO2hyrHTCC0B/Sl8kR1mcwUuzK4accBx9Jbf5EGUgXmO1c2tar4LV5vLjLfqeAVR1ns1jjfWqHfy/PQwGFGM+XN40Y+ncjHEoKs7THTXOFMcwnXsnEsGxuLcirH4fwweSdNI+pxMDeIa5l/VoZh7G5KNlD+47qJoBhG2LlkS6qC8v8W4Ulwj13VsfS8sDGEvUNAs6MIVPwGQUkMsoaSKyCKV3SC3vJ84iVU729AdZMgxUOpCOQqyn8cFS/oYE9WAIGyJxHOYV1Kf5WUilHByxDXdQ7TZXSVnERFs3uqhN68Y+0BY5kyg6kCC926zu+55FPKSq9BwUkzmd06sG8yO8Dp5iJrfnOjq3QvDpLLGkxk+jhWGCNluyilWOjWeGrtLN81ehexjHm6co75zhoxipTlUgvadOOQAS9PJw4Y9PLESZJ0KOMkf0kwndtdJaKGYRjb0ZPTl8A+uBFg6C2pEd0kMXwRnAOIN+qi/HaJDIg0SrY3ytABlOpCdAHi8zp46WVQ9lmdf7NN8rSUEsIXQNURzpHNwwsHZQ9D8G0IXgDnBNh9QAzRi6joPKQeuaqEbBXNoMJT4H8d1CqoOsoaBmfqspWhFKjO2/ih3HwmENoD0rbHQwOH+dbqGWbaq2RsDyGgEwUU3AwP9h+ifFn36P5Unvv6DvJs9Twz7VXyTorFbo3ZToWJTB+HCiMoFIGM8CyH0UyZmfYKjy+/wqn6HLOdNTK2R8nNkLFTzHZWydgpDuWHaIRdVv0WrmXhCYeZ1goOFh8Yu5vxzJWVE4ZhGLuJUgFE58Aqb7/KYg1AfEEHSs70jTsR0QfOJESnUWoaISwdBIUvQ7wMBGAfT7pAL6H8VeAR3bma9YqzOYhehO7XQKT0/a1R3SARAXElGf2hwC5tJHQrVYboVVT3T1Cp70Q4U1uSvS+lotO6ezaANQhxF7AgPgeqjXJPIkTSj071QLzBduAuZAKhPWI4XeL9oye52KlwsVtFKcXxYpHJ7MAVQdC6I4URSm6G2c4aS706oZQcyPZTdHOcby0TKYklBP1entFMmYrf4uXaHBLFgdwgjrDoxiFnW8sEMqTfy7PiN7mrNEkr6rHmN4mVImO7jGTK3Fncm6WThmHsMyoCFeoVmW0IYelcRxXc0NPQ+UX3oGQD4nMoq6BXgsLXdSKyPQnutF6VsidR8aIus7cn9dZXeArCb4NsJUf0dPAmV0AdBWcK5IJO3JZtCE+h7Em9ahPP622yeBVUA2VPo5yjCO/eLcnVSnV13hEuwh5GiSyoJZ1YLkb01mK8BM6BZGirg3Cuvi3LbmACoT0k76Q5VhznWPHKUspQRnSiADvpHr0ekAymiwymdQ8LP/4Wf7X4Mq1oHseyKbgZCm6a+c4aC90aq706AovRTImU5dCJQtb8Jsu9up5HpqDgZWjHPqOZ8kY+UTVob5uYbRiGsSsJTzcAVF3gytULpSJA6IDhRp+K1Y/yHoHeX0LwtA6CQK+qiAJwScWX6Id4BhVdAKsM4bO6Ss0ZSpK0LZ27I5s6sBKuru6KqyCETroOK3ooqlXQFV9WF5SjA8PgKZRqQ+pdm1uC8aJeUbKTlTFR0veLzyWBpKNL50VKB1zu3W/cLmAXMoHQHhDJmEbYRaIoOOktk+KXe3WeqZxjpr1KKGPKXo4D2QGOFEYZz25uU73WWOBvV17ldGuRoVQBTzi0ox7dKGQkU6QetFjpNThUGMG1bNb8Fq825mlFPrGS9GKf15oXSdkutrB4x8ARSl4WW+hRHQdyA9dtNagT+Sx0qyz36kgFQ+miGeFhGMZ1I4SDco5A8CRK9V1Z3i6X9UgMe/SaH0PJKsSLKOXrbSN7DGGVr7ydkkk/njo4x5Mm1GmwhM4RQqHs6WTlZUH3JiJGWX0g1xDuXfo4YgCil0GVdNm8bELwrF4JQidzY43r1RvVgrAF4qJuHSDOgigCsf6ZhE+j3AcQ7kmdo4S4JI/KQjmHdSAZXwTV1DlB4k5w34Nwj71hUvduZAKhXUwqyWuNi3x77SyznTV8GdHv5rinb5p3DBzmmcp5vrrwPMt+k7yTImN7Gys4C70q7xw4ysH8ME+vneO3z/wl59vL+DLiYrdKzklTTuXI2zbL3QaRirGEhWfZNKMepxtLdOKAPi9HKGO6kY8fhwQq4tnKOaSUTOUHGM/0oVDXLUl6pdfg22tnWAuaG00bz7aWKHs5Huo/vCW4MwzDuFbCPYKKL+oVFqtPr8CoUJe0ixTCve+a+u8oJVHhCzrPR9Z0Do1sgMigvPsg9X6sSxKjdTn6qzqvx/L0lhWx3hpTKYhnkq2uNpBOJru7ED4PKtJbXaqTDFCt62BJeCB9fXx7EGiBtT7+qKa3BuUC4IDIAiHEr6NHhiTT5aMZlP8MpN4FKJSSlwRDNjhTKKuoy+VJg/ceLGd3NX68WiYQ2qWUUjxTOcf/nn+WZtQj76ZIWQ7z3Sov1uf44rnH6UUBPRXS5+WRSuEKG0tYrAVNbEvwQm2WVuTzxXOPc7FbI+ekyQGdOKAd9ehEPgUvgyts+rwcRS/LQKrAS7U5WnGX/uS41aBNKGMk4ChBNw650F6hHQes9Jp8eOx+xq5DknQ76vG1hRdZ6FUZ8PJYtkW/l8MRNou9Gk9VzlJwt44SMQzDuBZCZCD1HahoEKKzOtjA0ZVi7p1vuZuzzvNZ0A0Qw5fB6gfZAFUDhF7R6f4/ehsp8/cRyWqTiuaAGGHpmY/KHoXoNVD5JJenCqyAe1Kvvoh+cA/olZroZQieAaTO2XHv1sGXrAAzQAT2PfrxlU5vIKpDvKLvQwDYye3dZCswSvoP9YE8DT7gjEO8grJSOthSPb0VJ7v6T/sA+H+NjKcR7v0bz2WvMIHQLlUL2/z10ik6ccBUth/HsunEAZGMqQRNVntNUpZL3k0TyZBmpFjoVRFK0FMhL1fmeCZ1nj43RyVsM5Iu0Yp6IHQjxEbYoRF2aQQd+rw8dpIcKBB0Ip9uFNKzQ7pRQCvZlsvYLhknRS8OqUVdBkWRnJNiNFt+0xyhXhzQiyMcy9q2cWM3CvjfF5/lW2unKXoZWmEXhM6LOlIYZTRdZqazynynsqWDtmEYxrUSVhbhPYhyTyT5QnbSr+fqt/mVUknw87wOQqJXdYDAK4CnexGt9wmK1yB6XY/OSD+qmy2qDlvygOzRpNHiEpDXAYxIJQEV4NyBwEXZAxDl9PaZPbzZ4dkaBVlmvUcRIqu3xMJnIT6TbLc19XMlw+bgWKVXxIh0sOO6IEd0LpBzFKJv69wi4ernofTKGc6dkHpQ3zd8CaV8SH3HrhwYuxMTCO1SZ5pLLPl1BlMFIhR+5LPQrVEJ20ilsIVFrCQuNs3Ipxc1CGRMoCI93kJBvd3hPMuU3Rx2SpBzPKpBG6UUoZJ4totSujN1O/LxZcizlXM0ox5KSapBi1rQQaKwEQgEMuwhEBS8HCU3t7FiNJUb3HL+ncgnkDGxksx11phprdCTIa5lM5Yuc7Q4xmDS30gqydOVc7zWuEjBzTCSzCqTSlILOrzWWODu8hRpy2WpVzeBkGEY15UQmR0ryN5UPAPhN5OAYxDEBbBzEJ0BpF5tWR+fYRVBJiXv8SxYJ/T9lL/lXJR7EqKZpON1DcSozuGxJzdHcdgDYJfBf3lrcrLy9X2cAxC3dBm+bCTbay30Ek+MDn5E8thO8n0vOecqhGd1d2jVS1oNZPWqk1wDWiAGk206BcpHWCWdMB2dA+eIfvw9wgRCu9RSt0bVbxNGETGSbhzQDHsEMqQXh8RKd5quRC3iOMaXYVIVAJ5w8SwHS0Az6tGKekil6PdytCOfduyTFi6ObRNKfd84igmlJLIkrmUTK4Uf+kTI5IwUsQzWPzcQdmIydoqSlyGIo43zrgYtTjcWme9WaUc+c51VlNKl/P1JvtHp1hLLvQbvGrqDkXSJVb/JXHeN/lSB1V5z41iWsOjzcqwETVZ6DdK2q/tiGIZh7AI6H+g1wNIjMOS8XuFRSq+WCDcJhPoBN7mdAjxUfBHhnkA4k6joZZTsbGwpCZEF9wTKKuvAw7lT5/rIVZRc0tVk9iDYB8F6Tpf5x0v6pIQD9ri+jlcg+EbSBqAHwka/7a+v4LeTP130ypCNrpZzgEAHeaoDahncd4KVgeA5/SbgjCVbd0u6sswq6ZJ+LFQ8d1VNGncLEwjtQoGMmOtUqAZtshmXlO3SCLs0ww6dOCBtu9hYCAFBFBIhiQFbKRzLIZAhETFp4SDQqzPtyKfitxCAEiCFRMaKSCpiJck6KUZSRV1cIHQCdU+FAPo+bHx+QAChilnoVGlEXdaCJvOdCnOdNV6oXiBSkqlsP93YpxZ0SNkOi90aJS9L3k2Td9PMdSq8WLvA4MhdOgcpjhn0Ciz36htbdKD7bKQtl9Veg4F0gZGkFYBhGMYtpxpJ40Mfgm8mPXzmQQY6SLBHgJbeKrPcZBssowMKJEr1ULhgTUF8FqWKuiwekkTrLjh36eaOcjkJZASoRb2qZBXAPgLO4eSY6HJ6q6hnP1r9+hiynpTirw9CdZKv9TwhBeSS63vJOfYnW2AtEO7GzDRFjE6uXtG3F7bOjbJGwErr4O+SFa69wARCu9Bse5Vu5JO2HJZ7DTzboRH2iJA4Qq/iYOnVH1vYRFKiUMhk+GokJUpGhMTExITJqo6FQKK3nCIVo1A4wibjuCCgKwMsYWMTk7EcWsli0PoI1fW1GE/YSKArQ1LS5Ynl11js1jjbWmapVyNvZ1jpNYiJ6U/lydkpVv0GFzsVjhR0guBQqsBKr8ma30QmQ2X7UjmKbpY1v81AKrclGKqFbY4URpm4bJSIYRjG9aKU0h2co9lk0GkaYU+CPb5DBZmEaFbn0dDVL5YyybEhBmXp4MBO8m9UC5w79KR7qqjuH+utJwWQBEpyfTxFHpwHIX4N4tOAp7fHhK1XnOIlnajsPAgiSqbMb+blKBUDTV3mbq2/iid5UBtB0Pqruki+j/XjWGUdQKkekAU83WAymk2e70JyG18Hgwi96mRlgHDnIbK7lAmEdhmpJE+tnWO516AbBayFLWwsJJJARqQsl0DFZG0Px3L0NpWMkkBIEUiFlfwnhdK/MOh/5jEymVQPCoWFIGW52MImZTlEKmat10AAPbl9R1UBREpHSDERKdth2a8zmM6z1KujFDSjDgt+jVBGTOeGOJAdJO+kWfGbTGYHSNl6lStWMb04TJKnBRaCOwqjvN5YZKXXxBEWQghWeg0O5oZ55+BR00vIMIwbQm9zPQfhi+hVkgyoQG99OdPgvXvLPDAAJUOdgCwreqtKpMEqQWQnK0PngYlke6mnt6wUenWHSH9vDWyW7eMmQURPd4sOnwY5p/sLRTN6ZpjsoD8FD+okaOeQPlZ8HiVySaNIXwdd9iRggZJge0AByOkcIhUCybGw0IGQkzzvUAdz1pBeYVIV8L+lp9qLgp5XpgQQJgGTq8v117cC4wuoeOUtDXS9lUwgtMss9+q8WJ+lErQYTOVJOx71sEM76um8HRliC4u05eJaFinbJZQRYRQjAEfYeJZDrJQOWISNnaz+qI1HUbjYpJKZZd3YR6KQSuLLAHXpB4VLWJdcKNEBl2fpbbrz7VUCGTGS1kuyuThktr3Gcq9OynIYSZfohB1W/RZZ28NOghzXshlMFSi5Gc61VpjM9nN3eYpK0KIedOhEPocLI/yd8fs3OlkbhmFcd/G5pFNzP8IqbFysVAjRWZRII1LvvfI+9JKyc1eXnWOBMwGxl6zkNPX11iC6R09DJ0g7J3Q/Hkiuz6OCpyF6Keni7OocnegccC4Jpta3sYBoBawehN+C3P8XISf0IFnVAyuny+btA9D5f4AFYCrJb0iBSicrS6BXgfrBmgbRTLbWhnRDSRXqpokS/VyEoyvURAnkOYgbOvCyS6CW9Dm7DwISFT4P1vfsibFLJhDaZeY6FdrJNthAukBZQTFMs9xrUPHbSCWxhcASglbk04lDsk4KW1j04hC1vn2mQiIV6X1iSNaI9D9IJ+miGsWRXtFUikDG+kMGNr4KcIS9kRu0bn0VSSSrN/oxA/3/lkXOTiUVbYK07ZK2XaSS1IMOkZI0wy6hjHEsm14UMJwu0okCXurNUQ86zLRXeLVxkeF0kZFMmazjUfIy3F0+wJH83mrZbhjG3qFXg04D7pYgCEAIV+e/RDMo9wTC6t+8Mp4H0mAXk148FvptNQIrBRzW5eyp79Sr89YAhK/onJv1IGj9HGRTV2vFi3rVR9WSgalVdKWXpe+/0QVb6K2x4FuQXkJ4J/TKERFgbxxfOgd1BVtUS7bIZLLl1UYHQcnKjuWDdQS8e3WgFidVa/YIuEeh+9UkKXsFHaQF+rmKDJD0H7IP6Plmqq230NyKrm7b5UwgtItEMk6SijOs+k1QUAs7tKIermWTdTyaYZdI6W2wspdHypism8YVFlW/xZLfoBP38FWcJDfrlSCZhDQOghQOUkCkdHl7FOvgZD2wARBSbAmCgCTTSCGSZOZARix3G2QcFwsQloUvo438nqyTQinFsl9H+TUmMgP0eTmWe3XW/BZrQYvXTv0xQ6kCdxTGeHjgMEvdGhc6a/gy5B0Dd3BveYrhdGlPfKowDGNvUbKTVGK19Bv3RvflrYSVR0UryXbRJYGQEoCtV4BkMUlw9oE0OCV9e3scK/2h5PFaqOi17Uv14+UkCFrRQZCVB6svmSHW1beRSUWYcNBBTEs/RvgEyj2YdH6+ZGCqrAID6EToVZAuOvDx0QGTAPI6WFMRRK8kSdiZZOVqEtw7dD6QM6GTvuMlUAv6/qKgexVZkf5ZxKu6VJ8A4poOINPv2XGq/W5hAqFdRilF0c2RcVzmOms0wi4WIpn3FRApScby8CyHg/khqn6Lbhzg2h7HCuOEKqYWtLGxkiaJOuBZD4QiFLEKQelfATtZMRJqPZlar/qEyC27Y+tB0XqBZcpyiZXEtgShirnQWcWxHBxhUQ/blN0cCkVfKsdCr0rG8kgJl5n2Ct04ZDCdJ1aKmdYqGdtltrPGUXuU46UJjhXHmetUcC2bofRba25mGIbxZpSKUOHLuoOzbOjgJXwd7ApKnLyiM7JSl5eMJJyJpLdOTwcLl84SUxGwujmsFHQOjXDROUib+UZKxbqvUFxFr9SkSJbr2Xz1tYEQXdWVS/4/j65YewmVbgE9lOrqLa3oos4vkjNJ6a+LDqgidBBlAWn9WKqX5A1JEDWIHRCx7oeEpbe/RBbURV39JgvJClgEloSoq5+TaupVIXtQt3OJX0H1Qkh/x9aVtF3GBEK7iGPZ9KfynGuvAFDxm3TjMLlWESuFjYUjLJRStCOfw/lhEIJ22KMZ9XAsh7TtMexmqYUdQhXpLbBLqEv+dIQNStJTEZaKEei8HRsbhSJUMVIpNkMpvX2WtVMEKiKSkkhGSCRhUr3WDnusWg3SToqK3yKWktF8H8JSRKHkYG6ASCnOtpawhUU3DpAq5lx7mZKXIW17DKWLLPVqVIL2RuNFwzCM60EFz+l8IKuk37gFoKoQndfXe/foQakbd1jPndk6Ski4x1H2IR1wEOnbYCX5PFUgC9aADrpEXneNtg9C+AxKlIA4GaS6AMHLOmgBvUKDhQ52Ija7P6O3pkQrCaqSmWLhc9D6/6EIkmTlJBnbvU9Xmm1pfrLeTFGhAyNfb2WJnD6eSOmATij9vP2/gfSj+nxkI/kZhOicKKmDNVVBr0RNAm2Qnh7y6twFchYVPA+p9+/aD7UmENplpvNDPLHyGvWgQ6wkBSeDY1vEUtIIuggLHNsmZbl4lsVEth/XcujGAWtBizCOuCAj/DgkUjFRMiNsJ4GKLukTpDtIR0qRcRxStks78gllREZ4ejUqmT6fsV2CIMK2BEhdwi9ZP5bAwiIlbAKlt92GUgVqYZtq0KIVdXEsm0bYQwArvq6GS9su1aDNWMYjbbu62eNGIGgYhvH2KVnVK0HWAMLa7EumA5pmsooymlRcgVI9vV3l3nPFFo+wyqj0o9D7Ux2AiKT0XUV66rs1DNE5lJzVW0f2kM7jEWUIT+nKLlVHBxEddNDjobeuklUYkYzZ2HglbycrOOsjMpI5Yt2/ATujgy0V60AmfAbing5oCNgMgiw2S+YjoJesGLWTkv9Yb4MppZOl47XNAEnVk/YAzmYF23qApSoQW2CnwJ5GCAclhpMO2VUQu3NVyARCu0y/l6PgpEk7HnEvWYmRCj8ON8rfgzhiJW6w4te52KmRsz0yjocQFo6lK8rqkf6FVOqNwiBt/Z+xlSRBK/TjSaUIZUQgQ3wifZ2UWJYevBqpGEdZuJaFL9fzkAQOAj8OqdPlcH6YngxpRj2k1LlN9bDLUKpI1vaIVEzK8ghkRDvyaQZdxjJ9hDLGRuhxIYZhGNdLvASqtTmqYp09DOq4nhkWPI/y0AGNsMA9jvDu3/Zwwrsb7CwqeDl5w490sCBKOniydfCkZA+CF6D3Dd0IcX3MhhgCO48OgIrogCLU5fMim5S5x8mjOegu0KADmCobJe8iaZIYVfVKDWmdbK1m2Ax+QnTws57k4KKDLoleHUp6Cck4udzW95MVfV9RSh5H6Mo0aygJmOo6+FItHaDZjs5xAoSVS/KrOlvzq3YREwjdQkqpK5YKG2GPvJvhrtIUzUAnyIUywhEWGceDpBN0LHUy9Jrfoqp7K1J0M6Qtj1bUI2enydiKqpJEMrwi8flytrAQCuKktF4qRTPqIoTAEQ5S6QL8kBhbWeQsF5QiUjG9KNxYTbKwQECkFL6MiJUkZblU/Ca2sAjiiJyTIpARnu3Q8nsMeAXybpqL3QrtWHckXfObDKQKDHj56/+DNwxjHwvZHDGxSSDAOYASIklyPqSTmu3hJInaRsm6vq/Ib7x2CyH0bC37IKg6Kl4F/0mw+jf6Dql4Ua8ARaeTlZERfRyrj/VsTexJHfjIpc2cHepsVIwhk3NfP//1VZ1klUd1Ie4CC8nqTSFZbQrYbJ54eeZnmPwZsRksxeigyNq8XnV1ub1cQVeK5XVjSCFA+MmWYlMfX7X04NmejXIOJT9H65Jqt91n957ZbUopxVKvzkx7hVVfNw2cyPYzlR2k5GX1eAmhOy+PZ/sJ45AgaTwYxBGrQQOldFNDyxKEMsQSAgc7KWWHbhziWA6e5Vz1bC6pVLIqZJG2PbqRrh5zsHW5viVwLAeppB7uKiNCqTOH1vOHFLppo4ute5cKi0DqIbD1oItn2QQqIqtSdGVIFpeCk0Ei8eMA13II4ojFbg0F3FmaMCtChmFcX0nFllIyqbIi+b6rt8biKjgHdf5PdFYHNXJJr+hYWb2944zqKfDO1OZhha2vi5dQhJcEQUsQvqS3mIQHYirZglvWqz2iAMSbOUQb4yva6FWiS7ezXHTQAptB0PpqURYdNIWgPIhtdBC08QzRKzzruwSXN4zb7uNycplIJbdPAjKxfpykS7XqAB1QWX0fJXXek1wC6yKkHtGl/7uUCYRuIqUUp+pzvFCfJZZSr4wQ8UzlPOdbK7xz8CgFN0POSVPz26RtBz8KWO41ECh6cUQYx0ngofBwcISNElBwM0RKUg272ELQjnp0lZ5b9marQcAlqdAxnmXTFSCUAKHHcEhAj/Sw8AS0Y39LArU+BtjoVSIA17LpxSGOlAQqRMW6IeRyXKfgppjMjZK1U6z4dSp+e6MXUsnNcmdpggOXTbQ3DMN4O5Rsbr5mySWwx1BEEJ7TXZNlS5eNqwYqeFF3UJYNfR2ASicLJQEqXgDehXCObh5f9ZJVoyD5PoboAnr8Rk9vH8l5UGtsJEGrBrrRYkUHRs50kuy8HuTovkA6CMoDLfRKzXqARHKbJluDnWWuDHbeLPhZXxG6NLna0s0grX69nSeXkgTpBqhMkijdSx7X1/cRMkk8bYJ6FawPbxn/sduYQOgmWurVeaE+S95JU3Q3+0gMeHkudms8XTnHd4/cRdb2+HrjVdZ6LWqBHrSq4hgp1rs7W0RIIiURhCgFK70GCIFUkvCKTtJXLwZ6oY8rbCwEum+0RaQiAiXJOxkcW9KKe9seX4dAenUpVopuHJBxXIpuloKTZs1v0Qy7+FLSiroopXCEQ85J0Y4CHMui38ubSjHDMK4bJVuo8IUkKGknjQtXUNac3raJF5PkY0snM8erydaUD8rXYy+EneTDLOnJ6ypEBc8mIzEUKnxVJ2HHFyE6r8dvWGUdKESrOohQAdBgc1UGdBCT5OOo8xAus1leXwKSIIwim/1/IrY0b1wPWIjYDJK2yw+VbK4yxdtcd/mw1PUtuJ6emabG9CiQ9Xlnai1ZvQqS2yk25pipZGQIjk623sVMIHQTzbRXiKXcEgSB3mMezZSY61R4pTHPudYKzaiHL0M6UY9OpKurNiMP3e9HrY/RSFhKXLZGc23aKgAl8ISDbdmAwhM2DjYpxyGI1veTd6bQozssAX2WbrBY7bWIVEzOSWEJi4V2jRhFJGOEgKydZqFb439e+Dp31af4vskH6PNyrPpN/DjEsxwGUwWzXWYYxlVTqovyn9AT3K1BEINgTYA4A+GryQDRDGDr66UP+Dq3JXw+yW1pJUnLIqnIKuvS9HhGj7UIntejMVSsj6PaED6lc4HkeYhrOs/m8lL4zbNkMwco6diMQFeSCTZXfAI2t8bWJ8dfGgRd2vFtJ5fe7vL5AZefUxIwxU0Qa/q4YhC8d7AxfoOZ5LzTbK4iuTqRGi8Jli68wfnceiYQukmUUqz6TXJOatvr7WSv+hsrpzndXCBluQgEPbU+UHVzQXN9V/vSf766EPLtB0Gw/muqCFSIo2yEEPgyREqfdqS3xC7/LLGdGIVQ0I0DGkGXlOOSd9KEcUQvDqhGPjEKW9jknRTCVqQsBwE8VztPqELGM/3Uwg6xjPFlhCUEU9kBDuaHGU2X3/IQVqnkxpgP+5L8AMMwblPRjH4jtqcvGWvhopxjEJ7WQYs1zMb092hGl56L9bEZEpjQ+T1InYAcvKS3sAB6/1cHTCTNEkVSkh5W0DO+augtLWAjm/JylwYkEt0NOul6q1Loraf1oOdy6wHLGwU1l7o0SFpPwl7fCls/3uW3q0OUrFq5d4JzD/j/Kxkqu16W30uOl9E5UEidMyU7ENevyMnaTUwgdJMIoWdzBRvR/JWCOOSVxjyVoE0r6tGOevpNW9gopQiTf5jbBTzXJwTaPNZ6Gl4vDvEse6OiLOSt9fVxhEMr7BErSZ+bJe+mme9U6UYBvoyxsYgt3S+oQodYKEpOhnbk8zd+k3cOHOWO4ijznSpL3RrVoM2p+hxT2SGmcgPcXZ7iSH7kTRt19eKAC+1VzrWWk+fkcjA/yHRuiOwOwalhGHubUkqv2IjsFbO9kEtJPxypE6Q3qpqCpOw80lthVm6jFBzQjQdVDOFZwILouSTpOQVxGz32Yn37qoEOEJKVoi3BxaWBy+Wv4M3k4pjNqq/tbscll19rMsSlx9jJerCT0YFZ/IoOcESJzVUs2NgeE0m3ajmrr1MLqN5X9bgO++DG67VSwWawKXK3bBSHCYRuoslsP89UzjPg5a944+7FIe2ox0qvQSAjULoc3REWCkVP3dzGgpup0zGRgvXtuLcqUCECi5ybwrUcOlGQjOawsVSMa9kg9MgOBfhRhOc6VKUOBgWCpV6DC51VCk6a/lSeaqCHz0opeapylrTtMpnduSKhE/l8Y+00s+018k6KtO3SkwHfrpzlYrfKuwbueMsrS4Zh7C56DIYuLRcbQU2s35BF6rLbSp0XhEoqnkp6y0cIfVvZ01tmeEk+jNS5RCrps+NM6ARqJfUbuTUE2CDCZAUnAhEkeUdJf5+N/J6Ns3iDZ9Nhc6TGbuCB6EMHieeBul79soZBSl0yD7A+x2zj78JDr5T168o7fwHcDrgnIDqDCk8lydYSyKCcAwj3PsSlgedNYAKhm2gqO8j51goXuzVGM6WNrZleHLLYrZG108TIpCZM92e2LWujlP3WEGRsDz/eeSXrjQQyZjCVI++k6cYB9bCLLyOkksRKEsQhKdvFsfWntV4c0E36HgkBlV6TduyTtT0yth4mWHAzuhzfdgijmNPNJcYzfVg7LLu+2rjIXHuNqWz/Rn5RAejzcsy21zjlzPGOwaPb3tcwjN1NBzUX9MqPrAICZU8hnMPJtPacTvDdItIVTQj9QoOT/AmIZJp8tN4zp6y3w1Qa6OleP8JJVn88dACUTh6bZBUnRic715PHKF/yhr++CnP5VtTl3rwZ7s3TBeXq7UJV0cNfnX5AgeVAnNb/T5B8JUGQKOn8KyuPsCd0V+/wBZRqQXQKSCXJ5o4OpsJTKNmE1PuumPd2I+3ODbvbVMnL8o7Bo5S9LHOdCjPtVWbaq6z5LQ7nR5jI9pFz0gQyohuH9OKAXhQSXbfsn7dOovBljLyKDtXbEejXl0AG1IIuzbBLJGMsBAJBSEwk9bEdy0IqiS9DfBnhYLMcNFjpNfRMtIQjLGJiYiUpe1nWeg3a0eXVDlon8rnQXqXPy12RZG0Li4FUntlOhWbYvabnZxjGraOURAVPo/y/0l2d0cUdRC+gen8B8TzCOQKqh9qyqp6Ml1BN3dkZKykH9/WWmEqhVzJsvUIkLDaHkmZAJVPg7SKQg3j9vusrP84lW21OspK03gdoyzPY4ZmtJyfsFsnzUatAHWQt+Tl1k+vWV9wuzWBNVtNESW8vgg4I5RoEX9dbYfYIQrgIIRBWQQ+ojWdRycy3m2XPBEKVSoUf/dEfpVgsUi6X+eQnP0mr1XrD+3zXd32X/gFf8vWZz3zmJp3x9kbSJb575C7eN3yCB/sP8XD/Yb5n9C4eGbqDkpdjJF0iimMaYWejV8+t1pUB/jX+UgYqoh50WOrWqYUtfBXhy4BuHBAlz053pw5oBj1akc98p8Ka36QZdln1Wyz2qsy0V1nqNZBK6a7UwsGzHSxh6XoLtf0LSifWj7VTknouWanq7BBIGYaxi8VzulpL9CPsSYRVQlj9CPsQ4KOCp1D2MDgH9aqRrCQBUZxs33TBOQzuYd3YUAU6ICIZByGyyQDSI7qTsqNzXLBGAKnzhOSiDsLiFb2ltlHa4qMDgjJ6FEYruXw9QHqjIOjWv+5vtR70rA+BrevnHr6qn7dqs1nRtjm0abMSTq/uCCH0ceJKstW2lW5KWYD4zFWNh7pe9szW2I/+6I+ysLDAV77yFcIw5OMf/zg/8RM/wRe/+MU3vN+nP/1pfuEXfmHj+2z25i237SRlu9s2CxxI5XGFAwJiJRHJ7K9btx709qz/Ojfj3hUtveQlv+gBMWthK1klAhWrpBhUdyj1RJpIRiz3aiglsSyLkVSRnJ1izW+Sc9JvUI0nsIRFpCQOV5bdxyrGFtaO22qGYexeKj6nc3PtbXJKrFGILyDkGqTei7L6ITqTNEe0wTmhmyXS02Xudh7UfHK91ANS5aquCLP79GoFPoQvJqtPWbCEzpWhq9/gN1aFPL1igguWDXK9IeJ6N+b1IGG7lIPd+Hp/adL2+it7nc2+QeszzNbbALiAnbQiaF52rACEu3MFmUjpn+PGANobb08EQqdOneLP/uzP+Na3vsXDDz8MwH/8j/+R7/u+7+M//If/wPj4+I73zWazjI6O3qxTfVvKbo5AhdiWRc5O40u9lBvdxMj4ekrCmi31DOu//pu32ax3sBAU3Qwpy8WzXVpRj64MkBEoUqQsh9nOGseK40zlhvBlRCvyuas8tWNvoZKbZShVYMVvMJa58hNIJWjT7+Xo83LX86kbhnGNlGyhk43TCLFzEYPODapsbrtcRghbv+6oDkKkEd4DKPdOPRVeWCBKKGcSun+UDEvtgVwAkQdrHIiTFyyp78OCXsWQdf1GbQ+DMwnxjP4+XkvygNZXRJR+HNlNtskySXAU6v+3+/XQVRpsNi68tFv0brOe+7QeCK0HMuurROscdLDX07eVVpKjdRgl23prUYidy+lVV6/C3cTwZE98DH7yyScpl8sbQRDABz/4QSzL4hvf+MYb3vf3f//3GRwc5O677+Zzn/scnU7nDW/v+z6NRmPL180iUbjCBgX9qRwDXp6U7V7ltLDdR27T3drCwtGjWTcWT9elLZeck8J1HDK2x+HcEHkng5V0zPZliIUg56RohB1Weg2OF8c4nL9sivSljycsjhbGAN19ez3XSSrFmt8kkjHHimOmSaNh3GIqXkP6f4vq/kny9cdI/6kkMNqOSPJW3qyQY/NVRogMwh7U22fCRqTeA5n/l57xpSId6Fhj+rjC1cnWqfvAntDVZaqqE6dFGujqBEhrVM8gs0eS7R5LX0eQJBgnZedY6O2ypOdOvMpG5+VLh6fuWuvpEZeO9Uhmm218nF2vkJOXfN+BcEEnSstlcB8Ea1Kvtl1Gb1t2Ec6Rm9pzaE+sCC0uLjI8PLzlMsdx6O/vZ3FxcYd7wT/8h/+Q6elpxsfHef755/nX//pf8+qrr/KlL31px/t8/vOf5+d//uev27m/VSnbpeBmyDgejaCDE4dX3SZrL4guWQ+6NB1QAK7j4lguZS9D0c1szFFLWy4HckMU3Awv12fpRAFexuGe8gEO5YffNIiZyg0QqaO8WJtltlPZ+HmWnAwPDxxhOjd0VeeulKIatFkLmiilyDlpRtIlE0QZxtuk4iWU/7iuvLIGk3ydLoRPo+RSUkW0dftLCIGyD0L8dZQavOKNU68+pJLS9u0J4STbZsOg/lAnNVt5XRYev65Xc6Kzeuq67LAxZkPEemyG7IB9hy4Pt9e7Si9DHCeVIutBjpX0Frp0WGmbK0vq94r1wOfSj+nr6/0Wusu0zUbQJ8+Aegd4D4JzF4TPQvCEHkjrTOpVONXUf//OYZ3TdRPd0kDop37qp/ilX/qlN7zNqVOnrvn4P/ETP7Hx//fccw9jY2N84AMf4MyZMxw5cmTb+3zuc5/jscce2/i+0WgwNTW17W2vt5Kbpd/LEcuY5U6NRpSUmt+UR7/5Lg/u/DjAt1yqgZ6jlrE8Aqmrys60FlFKl9ePZfroxgGvNC7iWjYH88PbHv9Sh/LDjGXKLPUaBDLEEw7D6RIZ5+r2oP045LnqeS601+jFIQiwhGAoVeSBvoMMpovX8BMwDENXfj2v83XsQ5s91kQaJYoQn0eFryJSD11xX+Ec1BPi41mUPb4x2FPJlm6Y6J7UgdUbEMIGZwrlHE9WepTe7opmk0TgapJYDXruVyepAlO6ekrOAmW9VWYN6oRpbypZCbL0ceQaegXLTXru+GxtlLjXbNfSZf25xOhVovWcKKl/TuGLuq9SNK8r8Ij0cNloBuwBcI6C+yDCO4kQ2+d83ii3NBD6F//iX/CP/tE/esPbHD58mNHRUZaXl7dcHkURlUrlLeX/vOtd7wLg9OnTOwZCqVSKVOrG/iXUgg4XOxUqQQtbWIxmyoxl+sg4HlPZAdb8Nq24u+3W0u1Kofsp1engxg6BjLGFoBsFOMKm4KWxsUnZDoGMcIVNKCO+vXYWz3IZz16Z/3O5tO0xfRUT7etBh1W/QawkadtjOFXk2doMrzcWGE4XGcno7qeRjFno1fnG2mneN3yCwmUz5AzDuApyVSco21d2iBfC1knO8TmUOokQl81ptAp6RSf4FsiFpNIoKXF370J4D71p13l9oKxOjo5e0V2mVQvIgXwNneui2KwCu3wkRQ9Y0SX08TmgCKpPr26IVJJEXUWP8Miw2aX5dn51v3SAazJ/LJyF4DkQw5D9foT7IMqO9N+9rII9jvAevLq/r+vslgZCQ0NDDA29+bbEI488Qq1W46mnnuKhh/Sngr/4i79ASrkR3FyNZ599FoCxsbFrOt/r4XxrmWerMzTDLmnbRSrJmdYSI+kS7xg4Sj3sEhPvqyDoUo6wyDoeraBLIHUHJRuLSMakHRdFmpfq85xuLXIkN0wj6nG6ucCD/Yc5UZpkNFOiHnSIlCRlO5Td3FX/YkUy5qX6HGeai7QjH0sIFOBaDvWgzcHc0JYVJMeymcj0caG9ymx7jZPlyRv0UzGM25jqgQp2TowWGf1GqXr6/y+/2h6E9IeSkRlNwAJ7EETfFb/7aj3RWehmfxvXq4Yunfef0UGQfThZxUmaLgKbU94vHYux/v16wrACWhD29Jac8JNzCpOvNntzK+ztUEANpJvkYS1AdBZl5XVfIrmqf+b+36DsIXCO3/RgaE/kCJ04cYK/83f+Dp/+9Kf5whe+QBiG/ORP/iQ/8iM/slExNj8/zwc+8AF+93d/l3e+852cOXOGL37xi3zf930fAwMDPP/883z2s5/lfe97H/fee+8teR6rvQZPV84hhGA6N7hRIo+A+U6Vx5dP8cTKqyh1e39W2IktLLqx7irtq5BISWwEPhFRGFMPQYhGEqAozjaWyToeOSfFcq/BXyy+yFCmwHhmAKn0ANexTJk7SxMMpApv+vivNOZ5oXaBPi/HYKqAEIJYSV6ozTLXXmM800fmsnJOSwjyTooLnVVOlCZuyacZw9jThG5cqFS4sbW1hVqfxr7NdeuHEI5OaN4hXU/JCip8CaI59EqFB844yr5TT1DvfUVvh8Xndd5PdJbNlaCIKxOF1126tbU5mAgqejtoYyr8TvffL3ydO4UDRBA8g04mb7NZaj8D3T9GpUNw776pr6V7IhACXf31kz/5k3zgAx/Asix+8Ad/kF//9V/fuD4MQ1599dWNqjDP8/jqV7/Kr/3ar9Fut5mamuIHf/AH+Zmf+Zlb9RSY7azRjnxyToqX63Mb3ZD7U3kiGfNc5RznWsv48laO1Lg1HCzSlosvI1JJ9VgtaGMLmyj2iVAIICUclIJQxUihiKRNKGPStsdCt8qFziqpIY97ywfoxSHn2yvUgg7vGT5Gn7fz/Jp25HO6uUTZzVK8ZIvLFhb9Xp5zrWWWejVK3pV9qGzLJpZxMhbFBEKG8ZZYg0luzSrYW1frlVJ6Zca985rnTylZQfX+Wh/HGgYxqFeXwrPgv5DMzgp1A0VrTJfAqyqbpeJX/UTQb+rblZPvxiaJN9N6NVmoV3/iixCWdH8m1nTOlfL1NmLwtC6fd25Obu762e0J/f39b9g88eDBg8nQPW1qaoq//uu/vhmndlWUUlzsVKmHHWbaqzqv3nGRSs/Cqvht0paDYzn77jODrqkQG18p26UetAlkjGvphpIiCTEiJZFKf28LCyV09+jZ9gopx8PF4UxzkROlCZ1zZQ9wobPG6eYi7xjYfp6YSkrp21Fv2+Gtadslbbus+i0OygjP2vpr04p8DuaGTFNGY19TSl3Tp3ghXHBPovy/RcWLYA0ghItSPZ1Ma5UQzrFrPhcVvqSDoC2J2DmUSEPwJX2d9zAbdawi0p2j4y56VSgZ2/GmgYxE5/9c/gq+37bCthOjw431eWRN9KiObpJHJXSAJJdBgYrOIEwgdHuqhW0udqoMZ4qkraS6AVjzdZ+crgzI2jenk+Zuon81YoK4iwCW/TqRjIlRRMnqmEJhoTtES5TuuK0UndDHsgQXezFDqRJSKWbDNS60VzhaGEMIQZ+XY75T5VihTTcOCZNZZz0ZcKGzSicK6IQ+Fb+VDG/dur7e5+UoORnqQeeKUR6tqIcFV5WEbRi3GyWbqCjZUlIRyh5E2Ad14utb+GAgnMOAQIUvJknPsd4ys8cR3r0I+81zSZXsQDyDis6B8lFWn15pCmfAGroySFNtvQJBshpBkDRLrLG1g7Jgs+z9Tc/iqp/z/nJpkLjeRkDovktCAC0QAzqvSlYhfBWVeu/2W6U3gAmEbhI9YwV6MtwIggACGdGJA4puhkrQouzlSHUdOjJ8g6PdvhTgy2jbBelLGwlIFIGKsLAQShBLnV6esh0aYcDZ5jLjmX6yTtKRurXKVxdeIFAxfhww36kSyoip3BBD6QKNqMtMZxUh4GRpCveS3kCuZTOULiKVYqFbo+RmsIVFM9KjQ06UJhnLlG/0j8YwdhUVr6D8J/SneJHXPXPC13U5u3svuPe+xWDoENiTumePijZ6AF3NMZSso/y/1VsuIquToaMZUC/qLTdru6KapBeOiiF8Hf1GncwCUy22jo1Y7/y8n7e33q71n+e6HDr47OkO3PYIWMWkJcEKSiUx0k1gAqGbRCmFY9kUnTT1sEPRyeiGYICUEl/FZGyPspcj76TpBPszEFp3tZ+rFApLWKRsl07k44uQvJ0iVDHLvQb9qRzPrs1wur3IRLafQ7lhfBnSkyGOsKkGLUYzJY4WRmlHPmebyxSdLIcKm72JenGIZ7s8OnEftrCZa68igQPZAQ7khpjI9pltMWNfUSpMStYryZZT8u/fGkDJBoTP6Zwb58BbOq5IVoHe2rkoVPAMyItgT+u+QABWP0quQvgKWBfAuuOye6ZAhhAvgVXX36teskoEm2/a680DU+hEaxMMXRvF5jZjVm9BInQ+kNUPVlLQImQyi+zmra6ZQOgmEUJQ9nJMZgeohm2WenV8GdIIu6z0mmRsl6KXpRP75J0sy8Hlg+qMy60XrwrQzRdVRCAjRjNl+t0cZ5qLXGg5nGrOUXazlJwMM60Vlv06o5kyw+kiK36DhW6V48Vx7iiO0gy7nGrMk3Fcsk6KduQTSsnRwij3lqdxLJu7y1Mbga1h7EvxYtL7Z+KKFRthFVFRHRWfQ7zFQGidkp0kXyTUK0P2KELskDYg1/QUejG6GQStswaS/kCnUfYhxKX5fXIpWfkJQBXYrGLy2XxlWV8FWs9tga0l9MbVW59V5oI9pf9urH49ngSRJEw3QLk6R2unEsAbwARCN9GB3ADLvTpHU6M8X52hGfbwLJvRTJm1XpOFTo2hVIGUbd5gr5ZEEcmYQIVEUmELQdnNEqiYuW6FrOWStzMczo+SdTwsIbjYq1LzO/R5eQpOmkrQohsH5J00D/Qd5LXmAkoJpIKhdJFDuWEmswMbgY8trLdWTGIYtxulP6jtmMNh5SFeRalIl7Zf7WGVQoWvQPSSztfRj6Jzfbz7tw+sVBPwEdbWik4la0ln6J7eMgueRLl36RWIeB78r+sKMrqbnY43knrXg6H1FQzYLIE33h4bRFEHqKoJcYuNgbMipy93774yqL2BTCB0E01lBznXXObp6nmUUJwsTWAJi24UEMqIFb/Omt+kGfV0MrD51LGj9c9pAr3aZmHR53m4tott2cx3qkilOJQfoRK2ySaNEAWCtOXQkyHNsEvJzdKLQ+IkCdqzHcazfXzPyF2UvRy2sExvIMO4grhk7MR2JJtl429BdBrCbwDZZJvLQqkI5LLOARIO4oqtM0un+lwyzVxFsxCf0StKimSaeRP8x5N5YbVkrtkoxOuvJpfP/coAJWBZP8aWijCzKvTWeWwEmbIFoqy3QVWQ5ISl0W0M+hDu4Zt6Ziax4SbKu2nuKI4hlUQpwVrQYtlv4MuIE6UJDudH8WyHbuybIGgbDhZeMr0+a6XICAdX2BTcNMeLYwylSmRsj+nsIAOpPPf1TXOsNE7G1jPLQA+1TdseUsX04lCP67AcvGS1pxbqlaKyl8OxbBMEGcZ2rEEQKb2FtR3VAPvAW/pUr1SACl8GUnpCfBLUiPXgR/mo8LUtbVL0uQwkQzv1CpKSVYhPo7dgRnQirnscnPfo+V+qqwelOkfBKgEr6CAoDxTQAVAKvQLko9+8U+hBoi6QRSf6mteGq2ejf24JFSWDVZPqMSuZS2aNIFLvQVj9N/XszIrQTeZYNgfzQ5TcLN04xBJQcDNY6K7KNb+DAhwEkQmGNgjAtixsBJGSeLZDKAVShqAEzahHL9ZzydaCJkfyI6Rsh7yTpuzlqPhNBlIFbGHR5+VY81v0Yr0qdLgwgitsqkGbUMYcLYya/B/DeCPWoH4jC0+hxPjGDDClYp07JIoI99BVH04HQc9C9CKIYZRwQZS35h9ZAxAv6O0UsTnkWFh5lHsHBE+jcHXvIRWB1adXfoSty7KjU3rchVJgNYAA4jabuSjykq/1BOkWm7lC4SWXrzdbNK/RV2f9Z5YkTCuZVBV6ukoQmWyLjd30gatgAqGbTqDHMvSnruySOpDK80I0g5LrHYrNL9k6AQglcCwbC4tARoQqxhY2QsBSr07Kcih5LqGMeXjgCM/VZlAoprMDdCOflV6Dgpsma6fIOh5+HJJ1PEIZM9NepeBmeKDvIAdzb96zxDD2MyEEeA/riYjReZTy0cGCAmtQDzu9yk/1Kl5BBd/U1V3RBbCaENu6As09vjloVTi61H2bBoXCvUdvoYWvQfRacjul31ytET3sMzqF3p5ROtl7vWEjOaCbfK3PC0vK6Fmv3k0l3/fYmkxtXJ31nkxpwAc7gxAphD2g58LdYiYQusnKXp6MnaIV9si7W4cMTmT7cW0HSwhQ1kbfnP0aDlnJC41C4WDjWJbe7rcsHCFwccjYLgfzw4ykS2TsFM2wSyf2qQQthlJF5jsVxjJ9HMwP83rjIqcbizSjHsOpAt8xfIJD+RFc28azHEbSpR0nyFeDFvOdCo2gS8p2GcmUGE2XzcqRsW8JkQbvveAc0716iPUWlT2+8wDVyyjZSnoRVfQKk6oDOb2dJZf1RAb3Hr3Fptp66KrIbXMuLnjvQNnTIOeSAMcF6UP0dYgr6CAmWe2xDgChzkkC/f/E6NWhGB3UeWz2vgnZunJ0PeyXD7sWOgAqon+2Ebh36hW7XcIEQjdZ2csynRvkVH0ex7JJ20mHaaXw45BjhTGaYY9G2CGI4n2dKyRROFiAHrKqlGIgVUAiCaX+2Yyl+5nI9JN3UgghaISSqWw/S70aD/UfwbVsTjcXmWmv0I4Cck6K0UyZkUwZX0U4lsWJ4s7DUpVSvNZY4MX6LJ04IG05hEryauMik9kBHh44TNa5+Uu5hrEbiPVGePbItR0gntUBj31Id8+zBvTWGkOb88dkBWWVdXKz94432DrxIX5Fb4uplh6RoeZBdZLqMDuJOzpJovSkvowemw0T10v0g/9/e3ceJFd1H3r8e869t/ee6RnNrn0kEAFkicXIwjYKL8RKmXLBH0kwJg6kcHB4cSokKRySVEKZVBLHoVIVJ1QlFSfgVFLxUgXxq3grP8U8wBYyiwAtGCMhjdaZ0ezd08vdzvvj9Mxo0C40PYzm96lSSeq5fXX6Tuv2b875nd8PO0OksDlDNWbq4Fyq3WOL5d4+tdQ4Vv97B6R+8YKKbc41CYTmwfrCiunlmNBEOEoRxjF5L81HO65CacVPR44QxhGluDbfw50X6qTf09ojqP8UNlQr0pRIExOTc9MEJmR/sZ8mN0019gmISTsJgvIYk01VNrddwWB1gvZUM1cn8uS8FM1eBkdrJoIKu8cP05rM0Z0+/U8nxyqjvDZ2kLSTYFVqZgrXfv9O4GmHD7VdIUnVQlwEEx0FlZnZ7eWuhqBia/yorG19ER4Ep9UWbvTWYeKiDWQAdBNKF+xz/Z12acxbh92ZtA9U3u4co4INYiZsKwciu6VeN9tZo6kif6SY+eCuYJfEptprTP3ZZ6am0BTNTJAUv+txKcBoA8kM0AzuFeC0YYwP0VFMdNzuHNMtKHd5wxOlQQKheZF0PDa1raU338lgZZzQRGTdFO3JPPtLA9SiAJ8IpRZ3ppCDxlGaXCJLSrvU4oDJyOeKXBcnahNMhBV8P6QS1YjimCXJHKuynfhxyPHKGK+P9JF2kkQmZkNhxSnLWE2e7R/WNzl02kDIGMPB0iCxMbQkZk/He9qhI2WX3kb9ydPmfAkhzsGEnLx5WakcxrvW5vBE/YBttaGSH8Y4yzD+bgjfqRdCBFQG464Ed7UNmHQHSucxuhPYX+8hVt8phgc02x5mcQxxn80TmtX6YSoheipHKIWdMUpgd5VVOX2idMzpAx4JhGZ44BTAWwbBXtsTLjpqE6eVBhPbXYOJ61HeuoaOTAKheaKVpjPVTGeqefqxnSMHeHP8KB3JJvbrAeJ48SyMvfu2YrCFC2OgFFTQXhqM3U23Z/wonnYwxuBpjcbBKNsFfsQvUYsDwjjiaGWEPeOHgTNXgc55KYarE8QmPqVNRi0OOVEr0nyGvKGMm+REdYKxQAIhIS6Kbof46KyHlMqA24txltlmrsktNg/J315vl7EE9Cp7sClBsMf2FYuL4NZb4+g8uEvrm5UOgHFsAOT22uW2YD+YIewszhJsgFPGfiQ62ABmKlm6Wh9ZCZtMPRXYTM0Cn+0uLZ3nrXpV6WjANsGNi7avmMqDGcXuGstAXMXUdtiZPqe7YaOTQGgexSamvzJONfYxMbxTHGBJMkd/ZczuiiJeND9PnO5WEpkYRym0sp3iy6GPAiIMLU6Wahww6Ye2W7wy+GHIQHWcQiKDqxz8OORgafCMCdBgvwee9uq79C6CLIkJcdGUuwITvoWJR05dEomH7AyPs8LmEYX76turT/r/rPIYlYJgF1N3EVuA0a8vt3QCgU2eVgnbrkMZ0AmI6onXztJ6BeoAmw+UBerb66l3pwfs8g7M3K3O9H9/ailtsfwYe75cIIRwF8Sd4K0GNTHTsNcUbdI8g5hgpQRCi8HesSP86MRb9JVPEMYRYRxhDNzUvpbD5WHCOEIr0EYTL4pQ6FQRMRqHjOMxUpskJMbTDg6KpGPfuoNBmRhIYHd+lfwyxhi6My2M+WVGakWuzPdQjXxSzuxeRcYYikGVNS1dp83xSWqX9mSeQ+Xh0wZTldC3W/a9zClfE0Kcm3LaMd71ELyCiQ5il5+M/VDUzajEB1E6S1z7KZhodhA0dQ7lYXQWwhM2WIqP2cAmPma34ztL6zNCIYTHwQxAHNo2IOj6jMRUPaFS/c+aUxusvvs+fLZAp94yQpykhF2eLNfbAqydnWSv0jZ4jY7ZpbPkzWdu4XKJSSA0D94Y7ePpQzsohVXak02kEh6HyyMcnBxkoDZOLawx6pcJ4ohoEf9UYYAULpGBoF5eMogNScejFNQoh9WT2iFGmBhcbQPHweo4GTdJGEfk3Qw1E3JN8zLS9VYbkYkZqIxR8DIsz56+joVSilW5Do6URxj3yzQnZgKeII4YqI6zJt9Ja0KWxYS4WDpxFcYpYMKDdulEaXCuRLkrT5olqtmlLbDd7ePheoNUd6ayNEegtg0bhHj1tJ0T9YaseXCuq+cWOTanKB7BLoeFdkaCdL1tSIWZBqFT9YIu5D4sAdDpTdWAioBEfbbuXVQCcGxLFWMaNuEugVCD1aKAbf27KUc+a3KdKKVsbRxl6+X0l0ftfoXIX9RB0BStFCN+cbqyRwz4UQjG5vDMdKBXuNoliEOqUUDWSWKMIe+l6MkWGPPL7Cv205RI14+G1kSO61pXU0iceUanJ93ChpaV7B47zFhpiKTjEpqIyBhWZtvY0LJKdowJ8R4ppwvldJ3lgDwYHxMequf81AMjE9st+CaoB0b1/B4zCapqWzfExiZLx8ds7Rp3vf0Qrv1fUF12pig6UW+8OjXrc/Lsj9yHL52T86vOtNJhQCUamnUggVCD7S/2c6wyyrJ06/QH6Jg/SSmoknWTVAKfiXBSgqC6ifrWVvszngsYIgzl2G5fnUpvdtEoDI7SRMZQjny82KEz3UxPupUliTy1OKA1kSMyhoKX4ZrC8nMmOSuluKp5Ke2pJo6VRxkPyiS0S1e6QHe6gKflv5AQc025SzG1GkRvgmoB56RdnnHJtuYwNXCvB0brwVIedAe4aYiGbS0h3WNnglQ7kAZVA5rASdqdZExgP6CnlramZoQWZ3rCpXXyNUzY74nTYVugTB8yYX93upkpYDn35C7eYMWgSmRiko5LbAzFsMKR8jAxtsXGUKVIIEHQtJP3zfmE9XDHTD/qoKaDxsBEuMohjCPKYY32VDMdyWayTpITtSL7i8dZle0g56UY9ycZ8UtcW1jBmrydoq1GPpNhDa0UzV5m1i6yJck8S5L5S/e6TMx4UCY2hqybPCV/SQhhmXgCE4c2zyeugJMBU+9sbybtbJBuh3A/aA1RaDub66Q9Pq7UY5lRSN5iu9tHP6v3K4tsg9gYbHL01JLYlKmgSLx3MTMJ5k02RyseAnR9+3wAJO330rvughr2vlcSCDVYyk2AMewaO8Th0jClsEoQh7ZejpeiFFbPfZJFyrbtmx0kTjWm9YnAgG/sTcyPQlJhhbRO0F8d48jkEJUo4ER1gqFakaR2mYxqVIcCFFAKq/SVTlCOfTSKJck8a/NdLM8smbX0FcQhg9UJylENR2nakk00nWVX2imvwRgOl4fZX+xnqFYkxpDRCVbm2rmyqWe60rgQC50xMcQnMFN9vVQO5fagzrO1gomGMeFeCI/YgCd82wY4JOz5TLVegyZnq0fHFQiHIR6v70AqM1P4sAY6a4MlU7bHxKNAtv77GDZf6OSlm6l7jcwGXToG0OB02URpY2wApOyWF4jAWYZyVzV0VBIINZhjFPsmBhj0x2b/9zIRZT8409PEBYoxjNVKvDy8j+ZkjnJYZSwoc6I6QUJ7xCYi6XgUEllO+BM0eWkKiSztySYiEzNcKzJYneCDS3pZk7e5C/2VMV4fPchwrTTd8iPjpliT7+Sa5mXn1XfsndIAL4+8gwJaEjkcpSmFVV4f7WPML7OpbS1JCYbEAmeMj/FftcELvp3NIcQEWYz3AZR39Vlz60w0hKk9V2+F0W5nD/T++gxP2v7dVO1SipnqLXYCghewCblT99KpmkCBfW71/9jAyV0LcQDs5dQq0SB5QXMpttW9EzdC8HY9gV3ZWSHdXW/Y23zOs1xKEgg1UH9ljG/2bWfYn5CfMRogIOZweYRj1VG0gc50gY5UE1ppPOVQjnwOlAYZrIzziWU3UosCKmENT7ssSeaZCMrsGTtCd7qFUlDl/w3spRL5LM8sIeG4dvt9WGXX2CEU8IGWlWcdTzmssWfsCMn6+ae0JLLk3BR9kydYmmmdXqoTYqEywR4IdoPuROmZquwmHoXgZdAZu3PrdM81BhPugXgMnFX1DSWmPoMwCKYfwklbgM9M2kRoM9XiYirHB+zHW4xd6jLYAKkKJoJgkjMHQWLOhbtBLwU1DOFRbEf6FeCtR81DN3oJhBroJ0P7eXnkHSIJgxrCAGXjQwQempqxW9610iS0S1K5lMMao7Uizw7sIeelSDt2t0LOTbE808ZkWOG5wTd5dfgAh8tDFBIZhv0iq7MdtCXzNHlpjDG8UxqkN9dJzjtz1+2B6jjjQZkVp9mu72mHtJPg4OQgvbkO2YkmFiwTT9p6PrplVhAEoHQLJipj/J9icFBmHLtLqFAvlujZ3VvhEdDt0/8PFAqju0EN2uTouGh3exHaLfKMM7tVBpxa1Xkq92cU2H7JX7e4EIdh+H+DGrNtVlTaFrv0XyDOfBKd2tLQ0Ugg1CDGGF44sZfJqCZh0DwIiBmvTdKebsLVDoPVCfwooBL6RMowVJuwLTtSLh2JJkphhbcnjjNQHaMWh5TCKp52GKlNMlQrcnRylBuWrGZFto0mL82hySGGahNnDYRqUYCqV8o+nZTjUQ59IhPjNjBRUIhLKh6xgYqz4gwHJMD/EUQHMVMF85QDuguSm2xRPQL74Xgypw3i5bbXWDxut8fHQ9hCfXJXXVhCMG+DaQaVqi+dpmzvsdJXiHUrOrG+YaORQKhBxvxJRvzJ+R7GolaMKoTlCBcHX8XEUYRPhGPqt1GlGK5NkNAObck8e8ePcqA0yLp8N0nt4mpbvdqPQsbDMrvHDtGazJNzkyiliMzZ8wo87YIx9UJhpwZDtTgg72ZwlOxSEQvZmVtQGBPYvKF41DbXnOocbwKIjmBqL0JiI7YCcQ3b8mLqbArjLLUBU1zELmsFzO4LJhaOGCjb5HUc+2e9zLZTqXwPGhgIyR23QSaCCimdwJz0YSmLH40VAaXYZzyuEEQBsbLfA0e5KBTFoEJsDCeqRapRwHC1iCGmM91M0vEIYjvVnnBcsm6KE7UiQ7UJgjhEK03WTZ713+9MNZPz0owF5VPHZmLKoc+qXLssi4mFTTfV2yWUTv1aPGy7yjvL6i0uLKU8O4MUHbe7vZyuegL0u6i0nT1S2fosAszUm5FZoYVlqlZTBNTqZQwGbL5X8AZxVGnoSEQDGAzLM63TPbLsY2I+GGwwk1CObePhuMQmYtQvMVgZ52hlhNdHDzLqT5Jz0yS0SyGRJTSGMLZ5BmnHI4ojRqsl+qsTdKSaaDtHnaGcl2JdUzelsMqJ6kS9v5yhGFQ4PDnM0kwrK7JL5v4CCDGHlC6Au9JunTfvmqUJ+4EI3GWody1IKFXvEB8fR3nXgMpiwkMYU7UJ1KZil07cleA0Y2eMpj7C5IeHhenkgpW1er5QzZY/mG5yO/dkaaxBmrwMK3PtdKdbGCs2LtIVp68NG0YRjnZJaY+0m8Q3Eb4J8U1EWnk2j0dBFNuSjs1emnIiy4hfwok1rtLU4pARf5I1+S42FFae1/b5dU09JLTLzyb66a+OExtD2klwVVMPVxeWS2FFcVlQ3kYbuIRTeUCJ+u6uUXB67IzPaWkwoW23kboF4++yswT49hzOUvBuA1IQHrB1hKY7Dl5oTzAxv6aS1xU2oPXtLKJRtn8cjevhKIFQg7QksizPtnHjkl6OlEeYjGy0O1U5WQq5zw3786LC0w7EhhoRGtBKU0ik8bRLKaiQchK0J/JU45COVBOrMu3U4ojJoMqoP0l3vaVG1k0yFpQZ8ydJapfNbVfyofYrZjVkPet4lGZNvosV2TZG/cnpytKn624vxEKldAaSHwV3NSY6ZGv46OXgrLQ7yow+/SSOqdq6QVAPhjrqzVF9bNXhFpTSxKlftG00qjuwu8Ai7BKZ4czBkNxl319ibAgy1UVy6nsTgdOB0o37Pkkg1CBKKTa0rMSPA96aOMae8aPEJsZVGkdpXDSTkU/l3VPJ4qIpbILy9O1PKVyjSWkX13HJu2mybpJSWCU2MeUowFWKnJuiYgLW5bp5Z3KQw+Uh8p49tjmRRaGohDU+3LaOX+xZP6sVx/nytEtHqrFFw4RoJKUS4Pai3N7px0w8jjHDNiHWmV0vy0SDoPIod9lJ59B2t9i7z+0uwyRuqfcZe8f+jo9dTqkyExilmOkmDzMFFt+9tV40noNNcJ+6QxtsscUWcNqRXmOXqZyb4ua2dSxNt/DV/c+xe/ww5aCGUhqtHFZnOvDjkP2lAZngfY8UkNYeWTdFGEdUogClDK7RuNqhK1Ug4yQITIRG42mXGENHuoWedCs9mRYKXoamRJZd430MVEZxtDO9tf361jXcsfyDFxUECbFYKd0MiQ9iajsw0QHs8ocCikAGlbxpeifZWc+jPEh9FKMMVLdBsM8WYMTH7jhL2W3ZOGAS9cfj+teq9X/TZaa/mGgsF8gyE7Qa7IzfGnDbQOex36/GBEPKmHPs+V3kJiYmaG5uZnx8nKampkt23qmeU6+PHmQyqLEkmefGJb28NtrHF3c9w2h06s4iMSONi6M1WZ1iWW4JyzJLyCRSmCjiSGWE/soY42HZbrk1toaPBgqJLEtSTbQlciilOF4ZYahWYlmmjZ9r7uHKfBcJx5veuTXul+mvjNOeylMKq6S0x1XNS1mb75JWGEJcJBMNYcI+iI/aB3QPyl2Jctov7DwmxkQDdrktOmLzS1Qztm/VoK0irZtBd9st99FbUNter0MERJPAJLYWUcjM7ISHnUmaWp7RzCy5yUfmxZma9XGAZtDp+s6/+uN6GXg99s/u1ajs3Sj13uZqzvfzW2aE5olSihXZtlOqDG9oWcnGttW8MrSfiejya8Dq4kz3j09qz9bmUS5GQVYnCOKYUlylElYJTrrhaEDj4GpFT6qVq5uXkvPSHKuMcufyD/KRjqsA29V9z9hhtg/9jNdHDjEWTBLGEU1uiqTrsTzTRm+uk2rs018ZY0W2nbX5btpTTazNd52ydX08qHBNYRmb269s5GUS4rKmnLZ6K4Ub3tt5lEa53eB2n+czbiVO3Aj+/4OoCLwOsQ+0YWcmXPu7swrCt7DNWFPYekYVZqpX15N7ARs0nZywffIMU/qkvxsWb62jqWXKFlBtdmcYgPLr5RAKdjlMFUAnwLvqPQdBF0ICofeZlkSWD7VdQTGocKA4QDGqEcfRaTuvv5+59eUmjKFqAlw0OTdJ1k3jaYeEdmhKZGlPNbG16wO8XeqnFgV0pgsYYzheHuHNiWPsHTuCb0LSOsGSVJ7eXCfd6QJaKUpB1c4KuTPVnLXSrG9ZybLsEj7SfhUD1XGqUcCSZJ6Mm6QW+ZyoFdFoPtpxFcsybYz6JX4ytI+hWpHWpG2EGsQhJ6oTZN0ka/Nn2uEihFholNdrl+VUPYE7fNk2YlVAcMhu3dYe6M56kJQCEqAStlM6MXZZpwhom9OiQpvobQJssDMJeKC6bWd11WQTxM0Re9z0vfzkBrFnS/Q+HRdIAh31SZUiM4FahUubB5Wsn3sq2DtXInMGaMUGgQrcXvCutrv+TP0H/OiArQel0uDk7HNMDVQKdYY+dHNFAqH3GaUUH22/ihPVCfwopL8yTi2ybRcCExKZeDq/XgFhg4MjW8NV13/+McS2HeKsrztoXO0ChtBENghyUrQl8yQdj9AY0o5HWzLP1u4NfKjtCtY0dfHG6CFO1CaITUwukWFLx8/xc03L0MowUJ0AIOMmqUQ+lcjHUZqeVIHmxKk7rloSOVoSOa5m+TlfU7OXxmB4c+wox8qjxBgcpWlL5llfWEF76tItiQoh5pfSrZDYjPFfBjNkAx5zDEwKvHX1ZbM0uM0QFSA+hg0q6onW2gCt4G21gU20D8jYgIgAuw3cA6cAumCX7EiCdkBda2vlRH0QV+vHJ7FLeVO7qCaZvUxXY3bgoerHZ8FZDslbbFuS6LDdYWdGIRpm9gxWfblPtYPTUa/nNFo/n+bsbUqagUL9XOP29Z0xaNNAux0XJRtgJjaB04udXfMhcRPKW4PxX4LwoH19xtjXrVtt9/kGN16VHKFzmKscoXMZqZV4aXg/L574Ge+UBpmMbH5K2kniaYdiWMFBExvDYHmcsXjyjG9jBeRJgqOpGh8HTUonyblJIiIm/ArVOMBg0CibV1N/o7vaw1WKpE7QmWzGczSBiYnr9XW0VozXKjha0ZzIklAOtTigFgUYpdAo1uW7cbXD0coIgYloSWS5umkZH2xbw7qmnumE4zCOGKoVp4Oc9mQTr4/18U5xgJyX4kR1nDHf5k4VEhnybhqtNP+r61pak++95kQtChiqFQnjiGQ9UDuf2kBCiIXHFmg8honGIT5uk61NAMGboFzwrsHWK9oF0TsQFkGVQa+E9O2Qug2icah9B4KXbUVslQT3GkhsgGC/nUUK99pzO502MCCsV9fuhmgAyIL3AYgO2QayxrO5TCa2S0cR2ABkqgpz/fjULeBdi9Ia8DC6CRUPYcJ+W5U7HgYziU1I9oAkKFPv7VUGf6/dvWciO6Z4kpm8KAMU6jWfCqAzoHrqxx2xM2dxPzZo0/bc5MBdDt6VdnnLuPZ5JEFp0G0o7wpwVqGUwpjY/vvxUD2XKwvOUtS7e8y9B+f7+S2B0DnMVyA0pRzWqEUB5cgnNoacm6TZy/Da6EFeHT1AZ6qZQiLL8fIou0YPMVSdoBqFOFqh0HSnW7imsJQYw9HKKCntsbGwimsKy2hKpCmGFUphlSQenuNSjnwwMFAdo688RC0K6Eo1c0NrL1kvxag/SSmskXUStCSy1OKA45VRdo72UYtDmt0UoYkphVWCOGJtvovrW1cTxJGdPTIxjnLIeanz6qk1UBnj+cGf4mjNkkRuuu5SGEccr4xxRVM3m5aslbYUQoj3xJgQTMkmcfuvT394g4bomJ0Z0q2Q/BjKXT3rnhNHo2DGQWVQug0wGP9FG1ShIDxsZ22UY393Ou0Mks6iUregnC5MPIapPW9ndqKRev0kxy4lqTy4S+1uqsQNKHctSp29pc/pX2NQD440xiQg3gfRCfvvuCshNvXX4YHOoXQThjSK+nKeyqGUSxxHtkBmNAbxQfs1Zy04bSgm7WtWOSCu/3vKlkZo8C5bCYQukfkOhM4kjCN2jR3m7eJx/CjE1ZpqFBCaiI5UM12pAhNBmWJQJTIxnnZYnlnCmnzXeRf/uxD9lTH2lwYYqIwTm5iMm2R1rp3eXOd73l11oDTI66N9FIMKbn0Lu6M0K7Jt3NC6WqoxCyEuKRMexAR77QwNEZACdynKW2+X1s7nHMa35wj32dYg4XEgAN1il46cHlRivS0cOfWceBwT/Mw2po0O25kklbezR95alHvFrOPF2UkgdIm8XwMhsFvwh/0Sg5UxqlFAyknQlS7QkshO/7RSjXxqUUhCu6TduQ0YjDFMRrV62wjPJktfIsWgwvHKGKV6MNSRaqY91SSd2oUQc8KY0C4vEdnlJNVyUTPPJi6DGbdLQcS2pxoJmw9zhvuXMRUwNUw9UQFclH7vy/+LjWyfXwSUUrQl82dt9plyEg2bMVH1qsxzIe+lpQ2FEKJhlHJPqX59UefRGSBzQW1hlUqDSksr2QaRH6eFEEIIsWhJICSEEEKIRUsCISGEEEIsWhIICSGEEGLRkkBICCGEEIuWBEJCCCGEWLQkEBJCCCHEoiWBkBBCCCEWLQmEhBBCCLFoSSAkhBBCiEVLWmycw1QrtomJiXkeiRBCCCHO19Tn9rlaqkogdA7FYhGA5cuXz/NIhBBCCHGhisUizc3NZ/y6dJ8/hziOOXbsGPl8/qI6D8+niYkJli9fzuHDh8/aeVdcOnLNG0+ueePJNW88ueYXzhhDsVikp6cHrc+cCSQzQuegtWbZsmXzPYz3pKmpSf7jNJhc88aTa954cs0bT675hTnbTNAUSZYWQgghxKIlgZAQQgghFi0JhC5jyWSSRx99lGQyOd9DWTTkmjeeXPPGk2veeHLN544kSwshhBBi0ZIZISGEEEIsWhIIn1lEGwAACstJREFUCSGEEGLRkkBICCGEEIuWBEJCCCGEWLQkELrM/MVf/AU333wzmUyGQqFwXs8xxvBnf/ZndHd3k06nue2223j77bfndqCXkZGREe655x6ampooFArcf//9lEqlsz7n53/+51FKzfr1W7/1Ww0a8cLzxBNPsGrVKlKpFJs2beInP/nJWY//5je/yVVXXUUqlWL9+vV85zvfadBILx8Xcs2feuqpU97PqVSqgaNd2J577jk+8YlP0NPTg1KK//qv/zrnc5599lmuv/56kskka9eu5amnnprzcV6uJBC6zPi+z6/8yq/w4IMPnvdzvvSlL/HlL3+Zf/zHf2THjh1ks1m2bt1KtVqdw5FePu655x727NnDD37wA/77v/+b5557jgceeOCcz/vN3/xNjh8/Pv3rS1/6UgNGu/B8/etf5/d///d59NFHefXVV9mwYQNbt25lcHDwtMf/+Mc/5u677+b+++9n586d3Hnnndx5553s3r27wSNfuC70moOteHzy+7mvr6+BI17YJicn2bBhA0888cR5HX/gwAFuv/12br31Vl577TUeeughPvOZz/D9739/jkd6mTLisvTkk0+a5ubmcx4Xx7Hp6uoyf/M3fzP92NjYmEkmk+Y///M/53CEl4e9e/cawLz00kvTj333u981Silz9OjRMz5vy5Yt5nd/93cbMMKF76abbjK//du/Pf33KIpMT0+P+au/+qvTHv+rv/qr5vbbb5/12KZNm8xnP/vZOR3n5eRCr/n53m/EuQHmmWeeOesxn//8580111wz67G77rrLbN26dQ5HdvmSGaFF7sCBA/T393PbbbdNP9bc3MymTZvYvn37PI5sYdi+fTuFQoEbb7xx+rHbbrsNrTU7duw463P/4z/+g7a2Nq699lr+6I/+iHK5PNfDXXB83+eVV16Z9f7UWnPbbbed8f25ffv2WccDbN26Vd7P5+lirjlAqVRi5cqVLF++nDvuuIM9e/Y0YriLkrzHLy1purrI9ff3A9DZ2Tnr8c7OzumviTPr7++no6Nj1mOu69La2nrW6/epT32KlStX0tPTwxtvvMEf/uEf8tZbb/H000/P9ZAXlKGhIaIoOu3786c//elpn9Pf3y/v5/fgYq75unXr+Nd//Vc+8IEPMD4+zuOPP87NN9/Mnj17FnzT6vejM73HJyYmqFQqpNPpeRrZwiQzQgvAI488ckoi4rt/nekGJS7OXF/zBx54gK1bt7J+/Xruuece/u3f/o1nnnmG/fv3X8JXIURjbN68mV//9V9n48aNbNmyhaeffpr29nb+6Z/+ab6HJsQ5yYzQAvAHf/AH3HfffWc9pre396LO3dXVBcDAwADd3d3Tjw8MDLBx48aLOufl4HyveVdX1ykJpGEYMjIyMn1tz8emTZsA2LdvH2vWrLng8V6u2tracByHgYGBWY8PDAyc8fp2dXVd0PFitou55u/meR7XXXcd+/btm4shLnpneo83NTXJbNBFkEBoAWhvb6e9vX1Ozr169Wq6urrYtm3bdOAzMTHBjh07Lmjn2eXmfK/55s2bGRsb45VXXuGGG24A4H/+53+I43g6uDkfr732GsCsYFRAIpHghhtuYNu2bdx5550AxHHMtm3b+NznPnfa52zevJlt27bx0EMPTT/2gx/8gM2bNzdgxAvfxVzzd4uiiF27dvHxj398Dke6eG3evPmUkhDyHn8P5jtbW1xafX19ZufOneYLX/iCyeVyZufOnWbnzp2mWCxOH7Nu3Trz9NNPT//9i1/8oikUCuZb3/qWeeONN8wdd9xhVq9ebSqVyny8hAXnl37pl8x1111nduzYYV544QVzxRVXmLvvvnv660eOHDHr1q0zO3bsMMYYs2/fPvPYY4+Zl19+2Rw4cMB861vfMr29veaWW26Zr5fwvva1r33NJJNJ89RTT5m9e/eaBx54wBQKBdPf32+MMebTn/60eeSRR6aP/9GPfmRc1zWPP/64efPNN82jjz5qPM8zu3btmq+XsOBc6DX/whe+YL7//e+b/fv3m1deecV88pOfNKlUyuzZs2e+XsKCUiwWp+/VgPnbv/1bs3PnTtPX12eMMeaRRx4xn/70p6ePf+edd0wmkzEPP/ywefPNN80TTzxhHMcx3/ve9+brJSxoEghdZu69914DnPLrhz/84fQxgHnyySen/x7HsfnTP/1T09nZaZLJpPmFX/gF89ZbbzV+8AvU8PCwufvuu00ulzNNTU3mN37jN2YFngcOHJj1PTh06JC55ZZbTGtrq0kmk2bt2rXm4YcfNuPj4/P0Ct7//v7v/96sWLHCJBIJc9NNN5kXX3xx+mtbtmwx995776zjv/GNb5grr7zSJBIJc80115hvf/vbDR7xwnch1/yhhx6aPrazs9N8/OMfN6+++uo8jHph+uEPf3ja+/bUNb733nvNli1bTnnOxo0bTSKRML29vbPu6eLCKGOMmZepKCGEEEKIeSa7xoQQQgixaEkgJIQQQohFSwIhIYQQQixaEggJIYQQYtGSQEgIIYQQi5YEQkIIIYRYtCQQEkIIIcSiJYGQEEIIIRYtCYSEEJcdYwwPPPAAra2tKKV47bXXGB4epqOjg4MHD57XOXzfZ9WqVbz88stzO1ghxLySytJCiMvOd7/7Xe644w6effZZent7aWtr4/Of/zzFYpF//ud/Pu/z/MM//APPPPMM27Ztm8PRCiHmk8wICSEuO/v376e7u5ubb76Zrq4ufN/nX/7lX7j//vsv6Dz33HMPL7zwAnv27JmjkQoh5psEQkKIy8p9993H7/zO73Do0CGUUqxatYrvfOc7JJNJPvShD00f99hjj9HT08Pw8PD0Y7fffju33norcRwD0NLSwoc//GG+9rWvNfx1CCEaQwIhIcRl5e/+7u947LHHWLZsGcePH+ell17i+eef54Ybbph13J/8yZ+watUqPvOZzwDwxBNP8OMf/5ivfvWraD1za7zpppt4/vnnG/oahBCN4873AIQQ4lJqbm4mn8/jOA5dXV0A9PX10dPTM+s4x3H493//dzZu3MgjjzzCl7/8Zb7yla+wYsWKWcf19PTQ19fXsPELIRpLAiEhxGWvUqmQSqVOeby3t5fHH3+cz372s9x111186lOfOuWYdDpNuVxuxDCFEPNAlsaEEJe9trY2RkdHT/u15557DsdxOHjwIGEYnvL1kZER2tvb53qIQoh5IoGQEOKyd91117F3795THv/617/O008/zbPPPsuhQ4f48z//81OO2b17N9ddd10jhimEmAcSCAkhLntbt25lz549s2aFjhw5woMPPshf//Vf85GPfIQnn3ySv/zLv+TFF1+c9dznn3+ej33sY40eshCiQSQQEkJc9tavX8/111/PN77xDcBWnr7vvvu46aab+NznPgfYYOnBBx/k137t1yiVSgBs376d8fFxfvmXf3nexi6EmFtSWVoIsSh8+9vf5uGHH2b37t2ztsefzV133cWGDRv44z/+4zkenRBivsiuMSHEonD77bfz9ttvc/ToUZYvX37O433fZ/369fze7/1eA0YnhJgvMiMkhBBCiEVLcoSEEEIIsWhJICSEEEKIRUsCISGEEEIsWhIICSGEEGLRkkBICCGEEIuWBEJCCCGEWLQkEBJCCCHEoiWBkBBCCCEWLQmEhBBCCLFo/X/sUAe4ZFEmzQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ultimate Test: Are the learned featues theoretically optimal?\n",
        "\n",
        "We have already seen that we can obtain the dependence structure by optimizing H-score. Since we only used some common neural archetecture without much tuning, one may ask to which extend the extracted featurs are optimal. Here is the ultimate test: as we know the statistical model behind the sequences, we can compute the the optimal features defined by modal decomposition, or maximal correlation functions. Then we can compare our extracted features with the theoretical ones.\n",
        "\n",
        "With some math, we can obtain the analyitical expression of maximal correlation function, which we then compute using $\\mathtt{max\\_corr\\_seq}$."
      ],
      "metadata": {
        "id": "a3Zr1Qui6gQG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def max_corr_seq(x, c, gamma = 0):\n",
        "    \"\"\"\n",
        "    x: n x len matrix,\n",
        "        n   - number of seqs\n",
        "        len - sequence length\n",
        "    c: scalar\n",
        "\n",
        "    Output:\n",
        "        maximal correlation function\n",
        "    \"\"\"\n",
        "    n, len = x.shape\n",
        "    d_vec = np.sum((x[:, 1:] - x[:, :-1] + 1) % 2, axis = 1, keepdims = True)\n",
        "    return np.tanh(c * ((len-1)/2 - d_vec) + gamma / 2) - np.tanh(gamma/ 2)"
      ],
      "metadata": {
        "id": "MZso0nK37s6m"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "c = np.log(q1/q0)\n",
        "\n",
        "comp_gamma = lambda p: np.log(p[1]/p[0])\n",
        "gamma_X = comp_gamma(p_u)\n",
        "gamma_Y = comp_gamma(p_v)\n",
        "f_opt_test = max_corr_seq(X_test, c, gamma_X)\n",
        "g_opt_test = max_corr_seq(Y_test, c, gamma_Y)"
      ],
      "metadata": {
        "id": "evlFJnbx-lp8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, we can compute the angle (correlation coefficient) between extracted feature and theoretically optimal one."
      ],
      "metadata": {
        "id": "XbZWynLN2nd2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# compute the correlation coefficients between x, y\n",
        "corr = lambda x, y: (np.corrcoef(x.reshape(-1), y.reshape(-1)))[0, 1]\n",
        "\n",
        "corr_f = corr(f_test, f_opt_test)\n",
        "corr_g = corr(g_test, g_opt_test)\n",
        "\n",
        "print('cos(f_learned, f*) =', round(corr_f, 3))\n",
        "print('cos(g_learned, g*) =', round(corr_g, 3))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "35qUseNo-qPA",
        "outputId": "e0d58cb1-c71f-4db5-88f0-bfe0dcc40f0e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cos(f_learned, f*) = 0.995\n",
            "cos(g_learned, g*) = -0.994\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Final Remark on Feature Dimensions\n",
        "Up to this point, we see how to use neural nets to extract dependence modes. Both the data and model are simplified for better demonstration.\n",
        "\n",
        "However, one may be wondering why we (can) use only $k = 1$ dimension features while still obtain meaningful results. Or, would a larger $k$ give us more information about the data? After all, as we illustrated in [the post](https://gilearning.github.io/HScore/), using $k$-dimensional feature will give us the top-$k$ modes of the dependence.\n",
        "\n",
        "The good news is that we can indeed prove the dependence between $\\underline{\\sf{x}}$ and $\\underline{\\sf y}$ has only one mode. Therefore, one-dimensional features can capture all the dependence between them. Even we use more dimensions, we will find the extracted features colinear.\n",
        "\n",
        "In practice, our goal is often to obtain efficient feature representations, and avoid such colinear effects. More generally, if we can extract the dependence modes as ordered in the modal decomposition, we will obtain modes ordered by their importance, which naturally avoids colinear features. To this end, we will introduce a new tool, the nested H-score, in our [next post](https://gilearning.github.io/NestedHScore/). We will also have a demo based on the same sequential dataset, which can be found [here](https://colab.research.google.com/drive/1JtjS1LfWpf0eWx3xWTKYlW1myCTE4vqb#scrollTo=quVfOLn-fR_x)."
      ],
      "metadata": {
        "id": "e1lnpQteLZVw"
      }
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMbMsSqPff/owp5tNqScXbT",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU",
    "gpuClass": "standard"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}