PyTorch Implementation Bayesian Causal Neural Network.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Computing the Conditional Average Treatment Effect (CATE) with Bayesian Neural Networks"
      ],
      "metadata": {
        "id": "9h9_l9faEweK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%%bash\n",
        "pip install torchview\n",
        "pip install git+https://github.com/arose13/ConcreteDropout.git"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UZqeqm2OHukH",
        "outputId": "3311a5b8-27a5-4cef-a1c4-f57b3673b040"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: torchview in /usr/local/lib/python3.10/dist-packages (0.2.6)\n",
            "Collecting git+https://github.com/arose13/ConcreteDropout.git\n",
            "  Cloning https://github.com/arose13/ConcreteDropout.git to /tmp/pip-req-build-fmhx96su\n",
            "  Resolved https://github.com/arose13/ConcreteDropout.git to commit 935f59d68bfae2d760186c0eca313d35cb6a6a82\n",
            "  Preparing metadata (setup.py): started\n",
            "  Preparing metadata (setup.py): finished with status 'done'\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "  Running command git clone --filter=blob:none --quiet https://github.com/arose13/ConcreteDropout.git /tmp/pip-req-build-fmhx96su\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "8F09549GEiMy"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as graph\n",
        "from scipy import stats\n",
        "from scipy.special import expit\n",
        "from sklearn.datasets import make_circles, make_moons\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import accuracy_score\n",
        "from tqdm.auto import tqdm, trange\n",
        "from condrop import ConcreteDropout, concrete_regulariser\n",
        "from torchview import draw_graph\n",
        "from IPython.display import Markdown\n",
        "graph.style.use('fivethirtyeight')\n",
        "graph.rcParams['lines.linewidth'] = 1"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Setup quick fake data\n",
        "n, p = int(1e4), 20\n",
        "treatment_effect = 0.5\n",
        "\n",
        "m = stats.norm().rvs(p)\n",
        "x = stats.norm().rvs((n, p))\n",
        "# treatment_labels = stats.bernoulli(0.2).rvs(n)  # Random assignment (Unconfounded)\n",
        "treatment_labels = expit((x[:, :5] @ m[:5]) + 2*stats.norm().rvs(n)).round()  # Conditional assignment (Confounding)\n",
        "\n",
        "y = x@m + treatment_effect*treatment_labels + stats.norm().rvs(n)\n",
        "\n",
        "print(x.shape, y.shape, treatment_labels.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d0fHNoSiFzmu",
        "outputId": "1d52da51-841f-4740-b3cb-4fca171ec9fb"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(10000, 20) (10000,) (10000,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Naive Estimate\n",
        "sns.histplot(y[treatment_labels.astype(bool)], label='Treatment')\n",
        "sns.histplot(y[~treatment_labels.astype(bool)], label='Control')\n",
        "graph.legend()\n",
        "graph.show()\n",
        "\n",
        "control_mean = y[~treatment_labels.astype(bool)].mean()\n",
        "treatment_mean = y[treatment_labels.astype(bool)].mean()\n",
        "naive_causal_estimate = treatment_mean - control_mean\n",
        "\n",
        "print(f'True Treatment Effect = {treatment_effect}')\n",
        "print(f'Naive Estimate of the Treatment Effect = {naive_causal_estimate:2f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "TsydFGiRF9o-",
        "outputId": "972d8f6f-ce6c-45be-f0b6-77e71c9391a8"
      },
      "execution_count": 4,
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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True Treatment Effect = 0.5\n",
            "Naive Estimate of the Treatment Effect = 3.316012\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "$$CATE = {1 \\over N} \\sum [ f_{treatment}(x) - f_{control}(x) ] $$\n",
        "\n",
        "$$J(\\theta) = {1 \\over N} \\sum [ (f_{t_i}(x_i) - y_i)^2 + \\mathcal{H}_{cross}(g(x_i), t_i) ] $$\n",
        "\n",
        "By optimising $J(\\theta)$ we are sure that we are optimising the CATE directly. This is both the model _must_ learn a covariate set in $Z$ that contains the information for estimating the propensity score. This should be _equivalent_ to adjusting for the propensity score."
      ],
      "metadata": {
        "id": "uPc5PYlhFZhk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Specify the models\n",
        "concrete_dropout_params = {\n",
        "    'weight_regulariser': 1e-8,\n",
        "    'dropout_regulariser': 1e-7,\n",
        "}\n",
        "\n",
        "@concrete_regulariser\n",
        "class LatentModel(nn.Module):\n",
        "    def __init__(self, input_dim, output_dim, hidden_dim=75):\n",
        "        super().__init__()\n",
        "        self.input_dim = input_dim\n",
        "        self.output_dim = output_dim\n",
        "\n",
        "        self.dnn_z = nn.Sequential(\n",
        "            nn.Linear(input_dim, hidden_dim),\n",
        "            nn.GELU(),\n",
        "            nn.BatchNorm1d(hidden_dim),\n",
        "            nn.Linear(hidden_dim, output_dim),\n",
        "            nn.GELU(),\n",
        "            nn.BatchNorm1d(output_dim),\n",
        "\n",
        "        )\n",
        "        self.cd_z = ConcreteDropout(**concrete_dropout_params)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.cd_z(x, self.dnn_z)\n",
        "\n",
        "\n",
        "@concrete_regulariser\n",
        "class PropensityModel(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.propensity = nn.Sequential(\n",
        "            nn.LazyLinear(1),\n",
        "            nn.Sigmoid(),\n",
        "        )\n",
        "        self.cd_g = ConcreteDropout(**concrete_dropout_params)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.cd_g(x, self.propensity)\n",
        "\n",
        "\n",
        "@concrete_regulariser\n",
        "class OutcomeModel(nn.Module):\n",
        "    def __init__(self, hidden_dim=75):\n",
        "        super().__init__()\n",
        "        self.outcome_dnn = nn.Sequential(\n",
        "            nn.LazyLinear(hidden_dim),\n",
        "            nn.GELU(),\n",
        "            nn.LazyLinear(1),\n",
        "        )\n",
        "        self.cd_o = ConcreteDropout(**concrete_dropout_params)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.cd_o(x, self.outcome_dnn)\n",
        "\n",
        "# Contruct the model\n",
        "@concrete_regulariser\n",
        "class CausalModel(nn.Module):\n",
        "    def __init__(self, input_dim):\n",
        "        super().__init__()\n",
        "        self.input_dim = input_dim\n",
        "\n",
        "        # Required modules\n",
        "        self.z_model = LatentModel(input_dim, 1)\n",
        "        self.propensity_model = PropensityModel()\n",
        "        self.q_given_treamtent = OutcomeModel()\n",
        "        self.q_given_control = OutcomeModel()\n",
        "\n",
        "    def forward(self, x):\n",
        "        z = self.z_model(x)\n",
        "        g = self.propensity_model(z)\n",
        "        q_t = self.q_given_treamtent(z)\n",
        "        q_c = self.q_given_control(z)\n",
        "        return g, q_t, q_c, self.regularisation()\n",
        "\n",
        "    def propensity(self, x):\n",
        "        z = self.z_model(x)\n",
        "        g = self.propensity_model(x)\n",
        "        return g\n",
        "\n",
        "    def q(self, x, given):\n",
        "        z = self.z_model(x)\n",
        "        if given.lower() == 't':\n",
        "            return self.q_given_treamtent(x)\n",
        "        elif given.lower() == 'c':\n",
        "            return self.q_given_control(x)\n",
        "\n",
        "    def ite(self, x):\n",
        "        z = self.z_model(x)\n",
        "        return self.q_given_treamtent(z) - self.q_given_control(z)\n",
        "\n",
        "class CausalLoss(nn.modules.loss._Loss):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "\n",
        "    def forward(self, g_hat, is_treatment, qt_hat, qc_hat, y_true, regularization_penalty=0.0):\n",
        "        # Q MSE terms\n",
        "        treatment_mse = (is_treatment) * (qt_hat - y_true)**2\n",
        "        control_mse = (1-is_treatment) * (qc_hat - y_true)**2\n",
        "        q_mse = torch.mean(treatment_mse) + torch.mean(control_mse)\n",
        "\n",
        "        # Binary cross entropy term\n",
        "        g_entropy = F.binary_cross_entropy(g_hat, is_treatment)\n",
        "\n",
        "        return q_mse + g_entropy + regularization_penalty"
      ],
      "metadata": {
        "id": "fjl86_zee-Er"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Contruct the model\n",
        "causal_model = CausalModel(p)\n",
        "optimizer = torch.optim.Adam(causal_model.parameters(), lr=1e-3)\n",
        "loss_func = CausalLoss()\n",
        "\n",
        "# Prep model data\n",
        "x_train, x_test, y_train, y_test, is_treatment_train, is_treatment_test = train_test_split(\n",
        "    x, y, treatment_labels,\n",
        "    test_size=0.2\n",
        ")\n",
        "x_train = torch.from_numpy(x_train).float()\n",
        "y_train = torch.from_numpy(y_train.reshape(-1, 1)).float()\n",
        "x_test = torch.from_numpy(x_test).float()\n",
        "y_test = torch.from_numpy(y_test.reshape(-1, 1)).float()\n",
        "is_treatment_train = torch.from_numpy(is_treatment_train.reshape(-1, 1)).float()\n",
        "is_treatment_test = torch.from_numpy(is_treatment_test.reshape(-1, 1)).float()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DFEv0xncHpvj",
        "outputId": "cad27b70-2cf3-4286-9e77-129684382d44"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/torch/nn/modules/lazy.py:180: UserWarning: Lazy modules are a new feature under heavy development so changes to the API or functionality can happen at any moment.\n",
            "  warnings.warn('Lazy modules are a new feature under heavy development '\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "display(Markdown('## Model Summary'))\n",
        "display(draw_graph(causal_model, input_size=x_train.shape, depth=1).visual_graph)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
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        "outputId": "f73b6601-4d10-4a03-c117-7b959b892c42"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Markdown object>"
            ],
            "text/markdown": "## Model Summary"
          },
          "metadata": {}
        },
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    {
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      "source": [
        "# Training loop\n",
        "n_epochs = int(10e3)\n",
        "hist = []\n",
        "best_epoch = 0\n",
        "best_loss = float('inf')\n",
        "iterator = trange(n_epochs)\n",
        "for epoch in iterator:\n",
        "    # Forward pass\n",
        "    g_hat, qt_hat, qc_hat, model_reg_penalty = causal_model(x_train)\n",
        "    loss_i = loss_func(g_hat, is_treatment_train, qt_hat, qc_hat, y_train, model_reg_penalty)\n",
        "\n",
        "    # Backward pass\n",
        "    optimizer.zero_grad()\n",
        "    loss_i.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    # Evaluate\n",
        "    with torch.inference_mode():\n",
        "        g_hat_test, qt_hat_test, qc_hat_test, _ = causal_model(x_test)\n",
        "        hist.append((\n",
        "            loss_func(\n",
        "                g_hat_test,\n",
        "                is_treatment_test,\n",
        "                qt_hat_test,\n",
        "                qc_hat_test,\n",
        "                y_test\n",
        "            ),\n",
        "            torch.mean(causal_model.ite(x_test))\n",
        "        ))\n",
        "        iterator.set_description(f'i: {epoch:,} | loss: {hist[-1][0].numpy():.8f} | CATE: {hist[-1][1].numpy():.3f}')\n",
        "        if hist[-1][0] < best_loss:\n",
        "            best_loss = hist[-1][0]\n",
        "            best_epoch = epoch\n",
        "        elif (epoch - best_epoch) > 1000:\n",
        "            print(f'Early stopping at epoch {epoch:,}')\n",
        "            break"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 66,
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        },
        "id": "AyMt9_BmOgBQ",
        "outputId": "0bf31255-662d-4747-943f-eea502c0fdbc"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/10000 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
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          "text": [
            "Early stopping at epoch 4,202\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph.plot(np.array([t[0].numpy() for t in hist]), label='Causal Model')\n",
        "# graph.yscale('log')\n",
        "graph.ylabel('Causal Loss')\n",
        "graph.legend()\n",
        "graph.show()\n",
        "\n",
        "graph.plot(np.array([t[1].numpy() for t in hist]), label='Causal Model')\n",
        "graph.axhline(treatment_effect, linestyle='--', color='black', lw=1.5, label='True Treatment Effect')\n",
        "graph.axhline(naive_causal_estimate, linestyle='--', color='red', lw=1.5, label='Naive Treatment Effect')\n",
        "graph.ylabel('CATE')\n",
        "graph.legend()\n",
        "graph.show()"
      ],
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          "base_uri": "https://localhost:8080/",
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      },
      "execution_count": 9,
      "outputs": [
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            ],
            "image/png": 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rV7PACADx8fFWr1Uqlbhz547Zq2OgsAfsypUrpT63fv36GDlyJHbu3AlfX1+ztRCvXr2KJk2aWATGlJQUXLt2rdT72mvEiBFISUmB0Wgs9dU0ALRu3RoAcOTIEYtzN2/exNWrV1GvXj1T+Cse9xgXF2dR/sSJExbfv6ZNm8Lf3x+///57hWesPwwMjS7OV8YxjURE1VVERATeeOMNpKen47nnnrMatDQaDT7//HPTmLni2bsnTpwwG8eYlJSEuXPnWn1OZGQkdDodvvvuO9MxURQxd+5ci1enaWlpOH/+vMU91Go1CgoKzJb+CQsLw9WrV009dsX1nTp1qtNC1NChQ7F27Vps2rSpzFf6ffv2hb+/P9atW2f2+lgURcyZMwd6vR4vvPCC1fKXLl0yHdfpdJg3b57F/WUyGf7xj38gMTERs2bNsvqZz58/X2JP58PG19Muzk8KZHBMIxFRtTVr1ixoNBrExMTgiSeeQOfOnfHII4/Aw8MD169fx4EDB5CRkYFZs2YBAEJCQjBgwABs27YNXbt2RZcuXXD79m3s3r0bXbp0sbqo9iuvvIJ169bh9ddfx4EDB6BSqRAfH4/MzEy0bNnSNAEEAJKTk9G5c2e0bNkSLVq0QGhoKDIyMrBr1y7odDq89tprprLjx4/Hv/71L3Tu3BkDBgyAwWDAL7/8AlEULe7rKL6+vujfv79NZf39/fHZZ59h7Nix6NmzJwYPHozAwEAcOHAAp0+fRmRkJCZNmmQqHxAQgI8++giTJk1C9+7dMWTIEPj7+2P37t3w8vJCSEiIxTNmzpyJM2fOYPny5dizZw86duyIWrVqITk5GefPn8cff/yBvXv3ljiu8mFiaHRxfjIRV/MYGomIqiuJRIIPP/wQzz//PL755hvExcUhLi4ORqMRwcHB6NGjB4YPH46uXbuaromJiUF4eDi2bduGFStWoG7dupg8eTKmTJmCrVu3WjyjefPm2LRpE/7zn/9g69atUCgU6NWrF+bNm4eXX37ZrGx4eDjefvttHDp0CAcPHkRGRgZUKhXatGmDf/7zn+jZs6ep7CuvvAIPDw+sWLECq1evRkBAAHr37o1///vfGD16tLO+ZeUyaNAgBAUF4ZNPPsH27duRn5+P8PBwTJ8+Ha+//rrFjPCXXnoJ/v7+WLRoETZs2AB/f3/06dMH//nPf9CpUyeL+3t6emLTpk1Ys2YNNm7ciO3bt6OgoMC0O84//vEPNG/e/GF93FIJarWaicNFaTQavHskBT+le+LPFyp/0U9yPI1Gg8TERISFhcHLq3Jmf5LzsH0d486dO1WiF8aawokwWsjlcqdMhKHK5Qrt68j/P6rmJySb+XHJHSIiInoIGBpdnJ9URI5ehN7I4EhERETOw9Do4nyLRqVmcwY1ERERORFDo4vzkxWGRa7VSERERM7E0OjiikOjuoChkYiIiJyHodHFFb+e5mQYIiIiciaGRhfnKy0Mi1k69jQSERGR8zA0ujhfaeGvWRzTSERERE7E0OjiZBLAW8rX00RUvYki/wwkepCj/79gaHQD/nKBPY1EVG15eXlBo9FUdjWIqhyNRuPQ3aYYGt2Av4eEYxqJqNpSKBTIyclBfn4+exyJUNjDmJ+fj5ycHCgUCofdV+awO1Gl8fcQ+HqaiKotiUQClUqF3NxcpKWlVXZ1zBiNRlNvT1Xdm5jsV5Xb18vLCyqVyqH1Ymh0A3w9TUTVnUQigZ+fH/z8/Cq7KmY0Gg2ysrIQHBzs0NeEVDVUt/Z1idAYGxuL+Ph4nD59GufPn4dWq8UXX3yB4cOHW5RVKpVl3u+PP/5A3bp1yyzXqlUrJCYmWj0XFRWFnTt3lnmPh8HfQ8Bd9jQSERGRE7lEaJw3bx4SExOhUqkQHBxcYpADgBkzZlg9fvXqVXz33Xdo1qyZTYGxmL+/PyZOnGhxPDw83OZ7OFuAXMD1XPY0EhERkfO4RGhcunQpIiIiEB4ejk8++QRz584tsezMmTOtHp8+fToAYMSIEeV6dkBAQIn3rCr8PATuPU1ERERO5RKhsWvXrhW6XqPR4Pvvv4dcLseLL77omEpVIQEeEk6EISIiIqdyidBYUdu3b4darcbAgQMRGBhYrmu1Wi3WrVuHlJQU+Pn5ITIyEo8//riTamofv6KJMKIoQhCEyq4OERERuaFqERrXrFkDABg1alS5r01NTcXkyZPNjkVGRuKbb75BgwYNbLqHsxad1Wq1AACFYIBeBDJyNVDIGBrdSXEbF/9K7oXt6/7Yxu7NHdq3PLO+3T40Xrt2DYcPH0bdunXRrVu3cl07fPhwdOjQAc2bN4dCocClS5fwxRdfIDY2FgMGDEBcXJxNyzskJyfDYDDY+xHKZMxVA/DCX9eSUMuTr6ndUWpqamVXgZyI7ev+2MbuzVXbVyqVIiIiwubybh8a165dC1EUMXz48HIvcPn222+bfd26dWssX74cQOEyQKtWrcKrr75a5n1CQ0PL9VxbabVapKamIqxWDQD5UNQKQViA2zdptVLcxsHBwZDL5ZVdHXIwtq/7Yxu7t+rWvm6dMIxGIzZs2ACJRFLuWdOlGTNmDGJjY3H8+HGbQqOzF/ys6SMHkA+tIIeXl/v/0FZHcrm8WiwcW12xfd0f29i9VZf2rVp73jjYzz//jKSkJHTr1g1hYWEOu69KpQIA5OXlOeyeFeFTNI4xT89ld4iIiMg53Do0VmQCTGlOnjwJoOos8O0jLQyNuXqOZyQiIiLncNvQmJaWhp9++gmBgYHo06dPieV0Oh0SEhJw9epVs+MJCQlWexITEhIwZ84cAMBzzz3n0Drb615PI0MjEREROYdLjGlcvXo14uPjAQDnz58HUNiLeOTIEQBAhw4dLHoTN2zYAJ1OhxdeeKHUwanJyclo164dwsLCcO7cOdPxzZs3IyYmBh07dkRYWBh8fHxw6dIl7N27FzqdDlOnTkVUVJSjP6pdvItakaGRiIiInMUlQmN8fDw2bNhgduzYsWM4duyY6esHQ+PatWutHrdVp06dkJCQgLNnzyI+Ph55eXlQqVTo1asXxo0bh+7du9t1X2eQCAK8pQJydQyNRERE5BwuERqXLVuGZcuWleua48eP21SuXr16UKvVFsejo6MRHR1drmdWplreEqTmO28tSCIiIqre3HZMY3UT6CVBRgFnTxMREZFzMDS6CYWMr6eJiIjIeRga3YSvhwQ5nAhDRERETsLQ6CZ8PQTk6Ph6moiIiJyDodFNKGQCcvh6moiIiJyEodFN+HgIyOfraSIiInIShkY34SOVcHFvIiIichqGRjfhLWNPIxERETkPQ6Ob8JYJyDcwNBIREZFzMDS6CZ+inkZRZHAkIiIix2NodBPeMgEigALuJEhEREROwNDoJrylAgDwFTURERE5BUOjm/CRFYZGzqAmIiIiZ2BodBPFoTFfz11hiIiIyPEYGt0EexqJiIjImRga3YS3qaeRoZGIiIgcj6HRTZhCIyfCEBERkRMwNLqJ4tfTuTqGRiIiInI8hkY3UbzkDsc0EhERkTMwNLoJb06EISIiIidiaHQTEkGAj0xALkMjEREROQFDoxvxkQnsaSQiIiKnYGh0I4WhkYt7ExERkeMxNLoRBXsaiYiIyEkYGt0IX08TERGRszA0uhGGRiIiInIWhkY34iMTuLg3EREROQVDoxvxkUnY00hEREROwdDoRnw8OHuaiIiInIOh0Y1wcW8iIiJyFoZGN8Ild4iIiMhZGBrdiI9MQD5DIxERETkBQ6Mb4ZI7RERE5CwMjW7ERyZBrl6EKDI4EhERkWMxNLoRf7kAowhOhiEiIiKHY2h0IyrPwuZM13DZHSIiInIshkY3ovAQAIDjGomIiMjhXCI0xsbGYsqUKejatSuCgoKgVCqxbt06q2Xnz58PpVJZ4n/Xr18v17MvXbqEl19+GREREQgJCUFUVBS++eabKjlu0FNaGBo1hqpXNyIiInJtssqugC3mzZuHxMREqFQqBAcHIzExscxrhg0bhvDwcIvjAQEBNj/34sWL6N27NzQaDQYNGoTatWtjz549mDZtGi5evIiFCxeW63M4m3dRaOSyO0RERORoLhEaly5dioiICISHh+OTTz7B3Llzy7zmpZdeQqdOnSr03KlTpyIrKwvff/89evXqBQB49913MXDgQHz11Vd4/vnn0a5duwo9w5G8ZOxpJCIiIudwidfTXbt2tdpr6EyXLl1CXFwcOnXqZAqMACCXy/Huu+8CAFatWvVQ61QWb76eJiIiIidxiZ5Ge8TFxeHUqVOQSCSIiIhA165d4evra/P1R44cAQB0797d4lyHDh2gUChw9OhRh9XXEUw9jXw9TURERA7mtqFx/vz5Zl8HBATgo48+wrBhw2y6/vLlywCAiIgIi3NSqRT16tXDxYsXodfrIZOV/m3UaDQ21rp8tFqt2a+CsTAsZmm00GhcohOZyvBgG5N7Yfu6P7axe3OH9vXy8rK5rNuFxpYtW+Lzzz9HdHQ0QkJCkJqait27d+PDDz/EpEmTEBAQgL59+5Z5n6ysLAAlT5zx8/OD0WhETk4OlEplqfdKTk6GwWAo92exVWpqqun3UnjjVtpdJHronfY8evjub2NyP2xf98c2dm+u2r5SqdRq51hJ3C40PvPMM2Zf16tXD+PHj0fTpk0xaNAgzJs3z6bQ6EihoaFOua9Wq0VqaiqCg4Mhl8sBAF6ydHj7KxEW5u2UZ9LDZa2NyX2wfd0f29i9Vbf2dbvQWJIuXbqgQYMGOH/+PLKysuDv719q+eLzmZmZVs9nZ2dDEASbxkmWp+vXHnK53PQMb5kEBkHm9GfSw3V/G5P7Yfu6P7axe6su7VutBr6pVCoAQH5+fpllGzZsCAC4cuWKxTmDwYDr16+jXr16ZY5nfNi8pALyOXuaiIiIHKzahMbc3FxcvHgRCoXCFB5LExUVBQDYv3+/xbn4+Hjk5uaaylQl3jKBs6eJiIjI4dwqNGZnZ+PSpUsWx/Pz8/HGG28gOzsbgwYNsugdTEhIQEJCgtmxxo0bo2PHjjh8+DD27t1rOq7VavHBBx8AAEaNGuWET1ExiTl6nLzjurO4iIiIqGqqWu9WS7B69WrEx8cDAM6fPw8AWLNmjWktxQ4dOmDUqFHIyMjAE088gcjISDRp0gTBwcG4ffs2Dh48iKSkJDRv3hzvv/++xf2Ld3VRq9VmxxcvXoynnnoKw4cPx+DBgxESEoI9e/bgwoULeOWVV9C+fXsnfmr7aAzAsdsMjURERORYLhEa4+PjsWHDBrNjx44dw7Fjx0xfjxo1CjVq1MC4ceNw6tQp7N27F2q1Gt7e3mjSpAkmTJiAV155Bd7ets8qfuSRR7Bv3z7MmzcPe/bsQV5eHho2bIhFixZh7NixDvt8jvRMPS8kqLncDhERETmWS4TGZcuWYdmyZWWW8/f3x8KFC8t9/wd7GO/XuHHjKrddYGnqKKS4lMnQSERERI7lVmMaCfCRCcjjRBgiIiJyMIZGN+PNJXeIiIjICRga3YyPhwT57GkkIiIiB2NodDM+UgG5ehGiyOBIREREjsPQ6Ga8ZQKMIqA1VnZNiIiIyJ0wNLoZb5kAAHxFTURERA7F0OhmFEWhkTOoiYiIyJEYGt0MexqJiIjIGRga3YxPUWjM1XNQIxERETkOQ6ObYU8jEREROQNDo5vxkhaGRo2hkitCREREboWh0c3cC43saSQiIiLHYWh0MwyNRERE5AwMjW6GoZGIiIicwamhMScnx5m3Jys8pYW/FjA0EhERkQPZHRqvXbuGNWvW4OTJk2bHDQYD5s6di/DwcISHh6N9+/Y4duxYhStKthEEAV5Szp4mIiIix7I7NH799dd44403kJSUZHb8008/xZIlS5CdnQ1RFJGQkIDnn38eiYmJFa4s2cZTKrCnkYiIiBzK7tB49OhReHh4oE+fPqZjRqMRy5Ytg0QiwcKFC3Ho0CEMGjQIOTk5+OKLLxxSYSqbt1RAPkMjEREROZDdofHWrVsICQmBXC43Hfvtt9+QlpaG7t27Y9y4cWjVqhWWLFkCT09PHDhwwBH1JRuwp5GIiIgcze7QmJGRgVq1apkdO3bsGARBQK9evUzHAgICEBERwdfTD5G3TOCYRiIiInIou0OjXC6HWq02O3b8+HEAQPv27c2O+/j4wGDgFiUPi49MQC5DIxERETmQ3aGxQYMGuHr1Km7evAkAyM3NxYEDB+Dn54fWrVublU1NTUVgYGDFako2q+EpgbrAWNnVICIiIjdid2js06cPjEYjhg0bhuXLl2PEiBHIzc1F//79IQiCqdydO3dw8+ZNhIeHO6TCVLYanhLcZWgkIiIiB5LZe+Frr72GrVu34o8//sDMmTMhiiJUKhVmzJhhVm779u0AgOjo6IrVlGymlEtwUa2v7GoQERGRG7E7NPr5+WHfvn1Ys2YN/v77b4SFhWHEiBEWk2Nu3ryJvn37ol+/fhWuLNnGXy4gW8ueRiIiInIcu0MjAPj6+mLixImllnnvvfcq8giyg5+HBNk6ToQhIiIix3Hq3tNUOfw8BGTrjBBFBkciIiJyDLtDY35+Pq5du4b09HSLc/v27cOwYcPQtWtXTJs2DWlpaRWqJJWPr4cEOiNQwFWOiIiIyEHsDo0xMTGIjIzEli1bzI5v27YNzz//PHbv3o0zZ87g22+/Rd++fZGbm1vRupKNavsUNmtiLifDEBERkWPYHRoPHDgAiUSCwYMHmx2fP38+RFHEgAED8OGHH6Jx48a4dOkSvvrqqwpXlmxT00sKAMjW8vU0EREROYbdofHq1auoVasWatasaTr2999/4+LFi2jZsiVWrlyJiRMnYuPGjQCAHTt2VLy2ZBPPolbVcP9pIiIicpAK7T1du3Zts2Px8fEAgAEDBpiONWjQABEREfj777/tfRSVk6e0cHF1rZGhkYiIiBzD7tBoNBqh0WjMjp04cQKCIODJJ580O16jRg3k5+fb+ygqp+LQyJ5GIiIichS7Q2NoaCiuXbuGnJwcAIAoiti/fz88PDzwxBNPmJXNzMxEjRo1KlZTsllxaOTsaSIiInIUu0Njp06doNFoMH36dPz555+YN28ebt26hejoaHh5eZnK5efn4+rVqxavssl5PAvnwUDLnkYiIiJyELt3hJkyZQp+/PFHxMbGIjY2FgAglUoxbdo0s3I///wz9Ho92rVrV7Gaks08JXw9TURERI5ld09jgwYNsGPHDjz99NNo1KgRunXrhs2bN6Njx45m5TZv3gx/f390797d7krGxsZiypQp6Nq1K4KCgqBUKrFu3TqLcjqdDlu3bsU///lPtGvXDnXq1EHdunXRo0cPfPPNNzAYyve+tlWrVlAqlVb/q8p7aUuLQuMFta6Sa0JERETuokJ7T7du3Rrr168vtczKlSsr8ggAwLx585CYmAiVSoXg4GAkJiZaLXf16lWMHj0avr6+6Ny5M/r06YOsrCz89NNPmDZtGvbs2YONGzdCEASbn+3v7291f+3w8HC7P8/DEvNnLj5sp6zsahAREZEbqFBofFiWLl2KiIgIhIeH45NPPsHcuXOtlvP19cWiRYswbNgwKBQK0/F58+ahf//+2L17N7Zu3YpBgwbZ/OyAgADMnDmzoh+BiIiIyKU5JDTqdDqcPHkSf//9N7Kzs+Hn54cmTZrgscceg4eHR4Xv37VrV5vKhYaGYty4cRbHFQoFJk+ejHHjxuHo0aPlCo1ERERE5IDQ+Pnnn+PTTz9Fenq6xTmVSoU333wTkyZNquhjKqw4vEql0nJdp9VqsW7dOqSkpMDPzw+RkZF4/PHHnVFFIiIioiqrQqFx0qRJ2LhxI0RRhFQqRe3atRESEoKUlBTcunULaWlpmDVrFv744w/ExMQ4qs52Wbt2LQCUe0JOamoqJk+ebHYsMjIS33zzDRo0aGDTPR5cBN1RtFqt2a/3e66+HDdyLBdgJ9dSWhuT62P7uj+2sXtzh/a9f5nEstgdGrdt24YNGzZALpfj9ddfx+TJk6FUKk3n1Wo1YmJi8Nlnn2Hjxo3o06cPnnnmGXsfVyErV67E3r170blzZ/Tu3dvm64YPH44OHTqgefPmUCgUuHTpEr744gvExsZiwIABiIuLg5+fX5n3SU5OLvfM7fJITU21OKbPlyNXI5Q4aYhci7U2JvfB9nV/bGP35qrtK5VKERERYXN5u0PjqlWrIAgCYmJi8Oyzz1qcVyqVeOedd9CsWTOMHTsWq1atqpTQ+NNPP2H69OkICwvDihUrynXt22+/bfZ169atsXz5cgCFywCtWrUKr776apn3CQ0NLddzbaXVapGamorg4GDI5XKzczVScyAU6BEWFuSUZ9PDUVobk+tj+7o/trF7q27ta3doPH36NGrXrm01MN5vyJAhmD17Nn7//Xd7H2W3PXv2YPTo0QgKCsL27dsREhLikPuOGTMGsbGxOH78uE2hsTxdv/aQy+UWz/CWa6ATDU5/Nj0c1tqY3Afb1/2xjd1bdWlfuxf3zsnJsTmEhYSEmPaoflh2796NkSNHQqVSYfv27ahfv77D7q1SqQAAeXl5Druno4ki8FemvrKrQURERG7C7tCoUqlw9erVMsfq6fV6XLlyxRS0Hobdu3dj1KhRqFGjBrZv316u9/W2OHnyJICqvcD3svO5AIB8PbcSJCIiooqzOzS2b98earUaixYtKrXcokWLoFar8eSTT9r7qHLZu3cvRo0aBaVSie3bt6Nhw4alltfpdEhISMDVq1fNjickJFjtSUxISMCcOXMAAM8995zD6u1oQd6FTZutM1ZyTYiIiMgd2D2mcfLkydi6dSsWLFiA33//HZMmTULz5s0RGBiItLQ0nD9/Hl988QX27t0LiURisWxNeaxevRrx8fEAgPPnzwMA1qxZgyNHjgAAOnTogFGjRiEhIQEjRoxAQUEBoqOjsWnTJot7hYeHY/jw4aavk5OT0a5dO4SFheHcuXOm45s3b0ZMTAw6duyIsLAw+Pj44NKlS9i7dy90Oh2mTp2KqKgouz+Ts33VuQYG7k5HtlZEkHdl14aIiIhcnd2h8fHHH8f777+P2bNnY8+ePdizZw8AQCKRwGgs7N0SRRGCIOA///kPHnvsMbsrGR8fjw0bNpgdO3bsGI4dO2b6etSoUUhNTUVBQQGAwtBnTVRUlFloLEmnTp2QkJCAs2fPIj4+Hnl5eVCpVOjVqxfGjRtX7vUeHzalJ3saiYiIyHEEtVpdoUFvhw4dwqJFixAXF2c2vlEmkyEqKgrTpk1Dp06dKlxRsqTRaJCYmIiwsDCLWVtXsvSI3JyKrU8FokuoZyXVkCqqtDYm18f2dX9sY/dW3dq3wtsIdu7cGZ07d0ZeXh6uXLmCnJwc+Pr6IiIiAj4+Po6oI9nBUyoAALRGToQhIiKiiqtwaCzm4+ODli1bWj330ksvIScnB9u2bXPU46gMHkVTnHQMjUREROQADguNpTl+/Dju3r37MB5FRTwkhT2NHNJIREREjmD3kjtUtcmKWlbPnkYiIiJyAIZGN+UhsKeRiIiIHIeh0U1xTCMRERE5EkOjm5IWjWn88PesSq4JERERuQOGRjd3K4/vp4mIiKjiGBqJiIiIqEw2L7nz4DZ+5aHVau2+loiIiIgqn82hcdKkSRCKZuSWV/Ee1ERERETkmmwOjXXr1mXwIyIiIqqmbA6N586dc2Y9yAki/KTIN3DJHSIiIqo4ToRxYz3qeKGmJ5uYiIiIKo6Jwo3JpQK0XHGHiIiIHICh0Y15SoECvp4mIiIiB2BodGMeEgE3cgyVXQ0iIiJyAwyNbmxNQi4A4FKmrpJrQkRERK6OodGNJRdtIZij4ytqIiIiqhiGRjcW5F3YvBIur0lEREQVxNDoxpZ1qgEAOJvB19NERERUMQyNbqyNygMAcC2bk2GIiIioYhga3ZiqaGHvcF9pJdeEiIiIXJ1N2wgePXrUIQ+LiopyyH3INoIgwEMCaLlWIxEREVWQTaGxf//+EISKzaYQBAHp6ekVugeVn1zCXWGIiIio4mwKjXXr1q1waKTKIZcCOiN7GomIiKhibAqN586dc3Y9yEnkEoFbCRIREVGFcSKMm/Pg62kiIiJyAIZGNyeXADr2NBIREVEFMTS6uSvZBnz6R05lV4OIiIhcnE1jGkuTnJyMTZs24ezZs8jIyIBOZ333EUEQsG3btoo+joiIiIgqQYVC48qVKzFjxgyzoCiK916FFs+4FkWRs68rSYBcgIavp4mIiKiC7A6N8fHxmDp1Kry9vfHaa69hy5YtuHLlCpYuXYq7d+/i119/xU8//QSZTIZ//etfCAoKcmS9yUaD6ntz72kiIiKqMLtD45dffgkAiImJwcCBA3H06FFcuXIFI0aMMJVJSEjAiy++iP/7v//DoUOHKl5bKrcz6TqcTmdoJCIiooqxeyLMr7/+CqVSiQEDBpRYpkmTJli1ahUSExPx8ccf2/soqoCG/hUetkpERERkf2hMT0832ylGKpUCAPLz883KtWrVCo0bN8ZPP/1UgWqSvbqEegIAjCLHNRIREZH97A6Nfn5+ZpNeAgICAAA3b960KCuXy3Hr1i17H0UV4CUtDPUFhkquCBEREbk0u0NjaGgoUlNTTV83bdoUALB//36zcqmpqbh06RK8vLzsfRRiY2MxZcoUdO3aFUFBQVAqlVi3bl2J5bOysvDOO++gZcuWCAoKQqtWrTB79mzk5JR/vcJ9+/ahb9++qFu3LsLCwtC/f38cPHjQ7s/ysHmaQiN7GomIiMh+dofG9u3bIz093RQc+/fvD1EUMXfuXPzf//0fLly4gAMHDmDYsGHQarWIioqyu5Lz5s3DypUrkZiYiODg4FLL5ubmol+/foiJiUGTJk0wadIkNG7cGEuXLsWAAQOg0Whsfm5sbCyeffZZJCQkYNiwYXjxxRdx8eJFDBo0CFu3brX78zxMnoWjBhgaiYiIqELsDo29e/eG0WjE7t27AQCRkZEYOnQo8vPz8dZbbyEqKgpDhgzB77//DoVCgXfffdfuSi5duhRnz57F5cuX8Y9//KPUsp9++inOnTuHKVOm4IcffsCcOXPwww8/YMqUKfjtt98QExNj0zPVajX+9a9/QaVS4eDBg1i4cCEWLlyIgwcPombNmpg6dSqys7Pt/kwPS/Hraa7VSERERBVhd2js1asXbt68iWHDhpmOxcTE4L333kOjRo3g4eEBf39/9O3bF7t378YjjzxidyW7du2K8PDwMsuJoog1a9bA19cX06dPNzs3ffp0+Pr6YvXq1TY9c8uWLcjMzMT48eNRp04d0/E6derglVdeQXp6Onbs2FG+D1IJ+HqaiIiIHKFCe08rFAp4eHiYvpZKpXjzzTdx4sQJpKam4tq1a1i3bh2aN29e4Yra4vLly7h16xbat28PhUJhUdf27dvj2rVrVifrPOjIkSMAgO7du1uc69GjBwDg6NGjDqi1c3lK2NNIREREFedWi/hdvnwZABAREWH1fEREBPbt24fLly+jbt26Nt2rYcOGFueKjxWXKUt5xlGWh1arNfvVGsGgBwDk5BdAozE6pR7kPLa0Mbkutq/7Yxu7N3do3/JMVHZKaMzLy8O+fftw69YtREZG4vHHH3fGYyxkZWUBuLf8z4P8/f3Nytlyr+Jr7ufn52fzfQAgOTkZBoPz1ry5fxb7gzLyBQDeWH8+HbUacGcYV1VaG5PrY/u6P7axe3PV9pVKpSV2tFljd2jcsWMHvvjiCwwfPtxs68AbN25g8ODBuHr1qunYhAkTMH/+fHsf5fJCQ0Odcl+tVovU1FQEBwdDLpdbLSPmGIBTaqxN8sCiziFOqQc5jy1tTK6L7ev+2Mburbq1r92hccuWLTh+/Dg++ugjs+OzZs3ClStX4Ofnh3r16uHChQtYvnw5unXrht69e1e4wqUp7hXMzMy0er603sOS7pWVlYWaNWuanSueNW3LfYDydf3aQy6Xl/gMH73+odWDnKe0NibXx/Z1f2xj91Zd2tfuiTCnT5+Gn58f2rRpYzqmVqvxv//9DzVq1MCJEydw+PBhxMTEQBRFrFq1yiEVLk3xWMMrV65YPV983No4xZLuZW3cYmnjHauaur6F/y54Msj9/wVEREREzmN3aExLSzNbigYA4uLioNfrMXjwYISEFL4Kff755xEYGIjff/+9YjW1QcOGDVG7dm0cP34cubm5Zudyc3Nx/Phx1KtXr8xJMABMi5E/uMMNULhLzP1lXMGx2647SJeIiIgqn92hMTc3F56enmbHfv31VwiCgE6dOpmOCYKAunXrIi0tzf5a2kgQBIwcORI5OTlYuHCh2bmFCxciJycHo0ePNjuel5eHhIQEJCYmmh0fPHgw/P39sWLFCiQlJZmOJyUl4auvvoJKpUL//v2d92GIiIiIqhC7xzQqlUqzMAXcW9uwffv2ZscNBgO8vb3tfRRWr16N+Ph4AMD58+cBAGvWrDE9r0OHDhg1ahQA4I033sCuXbuwZMkSnD17Fm3atMGZM2ewf/9+REZGYuLEiWb3PnXqFJ555hlERUVh586dZp9v4cKFmDBhArp06YLBgwcDAH788UdkZGTg22+/Nc2irup61PHEvqSCyq4GERERuTC7Q2Pr1q3xyy+/YNu2bRgwYABOnz6NU6dOmV4R3+/atWtl7hldmvj4eGzYsMHs2LFjx3Ds2DHT18WhUaFQYOfOnfjoo4+wfft2HD58GMHBwXj11VcxY8aMcoXXF154ASqVCosXL8b69eshCALatGmD6dOno2vXrnZ/noftUZUcCZn6sgsSERERlcDu0Dhq1Cjs378f48aNwyOPPGKaHFIc3oqdOXMG2dnZ6Natm92VXLZsGZYtW2Zz+YCAAMyfP9+mZX46deoEtVpd4vmePXuiZ8+eNj+7KpJLAS13hCEiIqIKsHtM48CBAzFt2jQYjUacPXsWubm5GDp0KCZNmmRWbuPGjQCALl26VKymZDe5RIDWyNBIRERE9qvQjjCzZs3CpEmTcOXKFYSFhVl9Bf30008jOjoaHTt2rMijqALkUgFa521IQ0RERNVAhbcRrFmzpsXi1/djD2Pl85AAuXr2NBIREZH97H49Ta7jh6v5AICjKZxBTURERPaxu6fx6NGj5b7GlRbDdicFRZNgMrXGSq4JERERuSq7Q2P//v0hCILN5QVBQHp6ur2Powr4pKMSXbbdgbfU9vYiIiIiup/dobFu3bolhsa8vDxTQJTL5RVao5EqLsRbCgDQcNkdIiIispPdofHcuXOlnler1fj666/xySefYNSoUXjrrbfsfRRVkGdRDyPfThMREZG9Kjx7uiRKpRJvvfUWIiIiMG7cODRv3hx9+/Z11uOoFPLCjkbT2EYiIiKi8nL67OkhQ4YgKCgIX3zxhbMfRSXwlBT3NDI0EhERkX0eypI7oaGhZb7OJueRSgRIBHCBbyIiIrKb00Oj0WjElStXYDAwsVQmT4nA19NERERkN6eGRp1Oh3feeQeZmZlo3ry5Mx9FZcg3iPgtTVvZ1SAiIiIXZfdEmMmTJ5d4ThRF3LlzB2fPnsWdO3cgCEKp5enh+P5KPr7iro5ERERkB7tD4/r16yEIAkSx9FeeCoUC7733HgYNGmTvo4iIiIioktkdGmfMmFHiOUEQ4OPjg4YNG6Jz587w9fW19zFEREREVAXYHRrffvttR9aDiIiIiKqwh7LkDlW+kY194Cmt7FoQERGRq2JorCbCfaXw92BzExERkX0cso3gnTt3cO7cOWRkZECn05VYbtiwYY54HNlBLhWg444wREREZKcKhcYbN25g2rRp2L9/f5mzqAGGxsrkIRGgM1Z2LYiIiMhV2R0a09LS8PTTT+PWrVsIDQ1FdnY2cnJy8OSTT+Lu3bu4dOkS9Ho9vL29ERkZ6cg6kx08JGBPIxEREdnN7kFuS5cuxa1bt/Dyyy/jzz//RIsWLQAAu3btQnx8PP7++2+89dZb0Gq1aNSoEXbs2OGwSlP5ySUCtEbY1CNMRERE9CC7exr37t0LuVyO9957z+p5pVKJd999F0FBQZgxYwaeeOIJDB8+3O6KUsUUz4HRi4CHULl1ISIiItdjd0/j9evXER4ejho1apgd1+v1Zl+PGzcOKpUKq1evtvdR5AAeksKkyFfUREREZI8KrcHi7+9v+r1CoQAApKenm5URBAFhYWG4ePFiRR5FFSSXFoZGraGSK0JEREQuye7QWLt2bdy5c8f0dVhYGADgzJkzZuWMRiMSExOh1WrtfRQ5wL3X0+xpJCIiovKzOzQ2bdoUt2/fNq3LGBUVBVEUMX/+fKjValO5+fPnIy0tDU2aNKlwZcl+xa+nMwsYGomIiKj87A6NvXv3RkFBAQ4dOgQAeOaZZxAeHo4zZ86gRYsW6NatG1q2bInFixdDEAS88sorDqs0lV9xB+PEw3crtyJERETkkuyePf3MM89Aq9WiZs2aAABPT0989913GDVqFBISEnD69GkAgIeHB6ZMmYIRI0Y4pMJkHyMKU+OJOxwmQEREROVnd2isWbOmRe9h06ZNcezYMZw6dQrXr1+Ht7c32rVrh8DAwApXlIiIiIgqj0P2nr6fIAh4/PHH8fjjjzv61lQBbVVyAEDTAIc3OREREVUDTBDVRIiPFJ1re6LAwIkwREREVH7lmgjTr18/1KxZE4sXL7ap/OLFi1GzZk0MHjzYrsqRYx26VYDjtzmmkYiIiMrP5tAYFxeHuLg4tG3bFtOmTbPpmmnTpqFt27Y4ePAgTpw4YXclyTGeqedV2VUgIiIiF2VzaNy8eTMEQcCbb75ZrgdMmzYNoiji+++/L3flyLGaKT1Qx0da2dUgIiIiF2RzaDx+/Di8vLzQq1evcj2gZ8+e8PLywvHjx8tdOXutW7cOSqWy1P8GDBhQ5n0OHz5c6j3WrVv3ED6N48glgI47whAREZEdbJ4Ic+PGDYSHh8PLq3yvOD09PVGvXj1cv3693JWzV6tWrTBjxgyr57Zt24YLFy6gR48eNt8vKioK0dHRVp/jSjwkAnRGhkYiIiIqP5tDY35+Pnx9fe16iK+vL/Lz8+261h6tW7dG69atLY5rtVp89dVXkMlkGDZsmM33i46OxsyZMx1ZxUohkwA6Q2XXgoiIiFyRza+nlUol0tPT7XpIeno6AgIC7LrWkXbu3ImMjAw89dRTCAoKquzqPHQeEoGvp4mIiMguNvc01qtXD7/99hvu3LmDWrVq2fyA27dv4/r164iMjLSrgo60evVqAMCoUaPKdd2VK1cQExMDjUaD0NBQdO7cGaGhoc6oolN5SAQUGABRFCEIQmVXh4iIiFyIzaGxU6dO+O233/DNN9/g7bfftvkB33zzDURRROfOne2qoKPcuHEDBw8eRJ06ddCzZ89yXfv999+bzf6WyWQYP3483n//fUilZc9G1mg05a6vLbRardmvZTmYlAcA+PFSFvqGeTqlTuRY5W1jci1sX/fHNnZv7tC+5ZmrYnNoHD16ND7//HMsWbIE0dHRVieGPOjw4cNYsmQJZDJZuXv3HG3dunUwGo0YNmyYTUEPAAIDAzFnzhw89dRTCA8PR15eHk6cOIG5c+ciJiYGgiDggw8+KPM+ycnJMBicN5gwNTXVpnK3sjwBSHEuKQOtoHdafcjxbG1jck1sX/fHNnZvrtq+UqkUERERNpcX1Gq1zYPcZs+ejc8//xxyuRxvvPEGJkyYAJVKZVEuPT0dX375JT777DPodDpMnDjRpnDlLEajEa1bt0ZSUhJ+//131K9fv0L3S01NRVRUFNRqNS5cuFDm63pn9jSmpqYiODgYcrm8zPIvHcjC/ls6zG7rg8mPeDulTuRY5W1jci1sX/fHNnZv7tC+TulpBIC5c+fi6tWr2LlzJxYtWoT//ve/aNasGerXrw+FQoHc3Fxcu3YNFy9ehNFohCiK6Nu3L95///1yfwhHOnDgAG7evIkuXbpUODACQHBwMPr27YvVq1fj5MmT6NOnT6nly7tMUXnJ5XKbnuEpywWggyCVOb1O5Fi2tjG5Jrav+2Mbu7fq0r7lCo0SiQRr167F0qVL8cknn+Du3bv4888/8eeff0IQBIj3zcytUaMGpkyZgtdff93hlS4veyfAlKa4hzUvL89h93S2jsFy/C9RAz8PToIhIiKi8ilXaCz22muvYezYsdi7dy/i4+ORnJyM7Oxs+Pn5ITQ0FB06dEDPnj2hUCgcXd9yy8jIwK5du1CjRg3079/fYfc9efIkACA8PNxh93S2fzRTYPbJLCjlNq+0RERERATAztAIAD4+Phg4cCAGDhzoyPo43MaNG6HVajFmzBh4elqfMZyeno709HSoVCqzMZqnT59G27ZtLcovW7YMhw8fRsOGDavEUkK28pQW9jAWcFcYIiIiKie7Q6OrWLt2LYDSX02vWLECCxYswIwZM8x2fhk5ciQ8PDzw6KOPIjQ0FHl5efj1119x9uxZBAQEYMWKFTbPxK4KZBIBEgHQclcYIiIiKie3Do2nTp3C+fPn8dhjj6FFixblvn7s2LHYt28f4uLikJGRAYlEgrCwMEycOBGvvvoq6tSp44RaO5dRBKbGq/GPZpU/dICIiIhcR7mW3KGqRaPRIDExEWFhYTbP2lJ+mwQAUI9xvcBbHdnTxuQ62L7uj23s3qpb+3JGBBERERGViaGxmjKK7GAmIiIi2zE0VlMaA0MjERER2Y6hsZrS6BkaiYiIyHYMjdWMQla4VmM+l90hIiKicmBorGY29CxcvLyAr6eJiIioHBgaqxmfop7GbJ2xkmtCREREroShsZopDo2vHLxbyTUhIiIiV8LQWM0EehU2eR4nwhAREVE5uPU2gmQpyFuKJgEydKrtWdlVISIiIhfCnsZqKEAucCIMERERlQtDYzUklwrQMjQSERFROTA0VkOeEgEFRoZGIiIish1DYzUklwrQcHFvIiIiKgeGxmrIUwq+niYiIqJyYWishjwlnAhDRERE5cPQWA1JJQLiUrUQRQZHIiIisg1DYzX03eU8AMCRFG0l14SIiIhcBUNjNVT8ZvpOPmfDEBERkW0YGquhou2nIRGEyq0IERERuQyGxmpoaEMfAICOazUSERGRjRgaq6HPopQAAA1nUBMREZGNGBqrIZlEgIB7YxuJiIiIysLQWE2JAKbEqSu7GkREROQiGBqJiIiIqEwMjURERERUJoZGIiIiIioTQyMRERERlYmhkYiIiIjKxNBYTb3W0hdSAcjWGSu7KkREROQCGBqrKb1RhEEEwtbequyqEBERkQtgaKym/lLrK7sKRERE5EIYGqspH5lQ2VUgIiIiF8LQWE15MTQSERFROTA0VlM96nhVdhWIiIjIhTA0VlPDGvlUdhWIiIjIhTA0VmMN/aXoE+aF1DwD1v+dW9nVISIioirMbUNjq1atoFQqrf7Xr1+/ct3ru+++Q/fu3REaGop69erhhRdewOnTp51T8YcoQC7B/xI1GHcwA5OOqCu7OkRERFSFySq7As7k7++PiRMnWhwPDw+3+R6LFi3CvHnzEBYWhjFjxiAnJwc//PADnnrqKWzduhVPPvmkI6v8UP2WpgMAHE7RVnJNiIiIqKpz69AYEBCAmTNn2n395cuX8dFHH6FRo0bYt28fAgICAABjx45Fr1698MYbbyA+Ph4SiXt02BpFERKBs6qJiIjIknukHSdZt24d9Ho9pk2bZgqMANC6dWs8++yz+OuvvxAfH1+JNayYcF+p2ddGsZIqQkRERFWeW4dGrVaLdevWYfHixVixYgVOnjxZruuPHDkCAOjevbvFuR49egAAjh49WvGKVhKVl3nzMzQSERFRSdz69XRqaiomT55sdiwyMhLffPMNGjRoUOb1ly9fhq+vL4KDgy3ONWzY0FSmLBqNxsYal49WqzX7tbwmNvXE+KJxjQCQp9HAKOXr6aqkom1MVRvb1/2xjd2bO7Svl5ft6za7bWgcPnw4OnTogObNm0OhUODSpUv44osvEBsbiwEDBiAuLg5+fn6l3iMrKwu1atWyeq742qysrDLrkpycDIPBUP4PYaPU1FS7rntUAIB76zUmJt6El7TE4lSJ7G1jcg1sX/fHNnZvrtq+UqkUERERNpd329D49ttvm33dunVrLF++HAAQGxuLVatW4dVXX30odQkNDXXKfbVaLVJTUxEcHAy5XG7nXdJNv0vyDEbX2vbeh5zBMW1MVRXb1/2xjd1bdWtftw2NJRkzZgxiY2Nx/PjxMkOjv79/iT2J2dnZpjJlKU/Xrz3kcrndz+hc2xOHbhUAAE5kiHi6AbcXrIoq0sZU9bF93R/b2L1Vl/Z164kw1qhUKgBAXl5emWUbNmyInJwcq93OxWMZi8c2ugOdsbJrQERERFVVtQuNxTOobVngOyoqCgCwf/9+i3P79u0zK+Oq7p/2svSPHOy4ng8A0Og5lZqIiIjuccvQmJCQYLUnMSEhAXPmzAEAPPfcc6bjmZmZSEhIQEpKiln54cOHQyaTYfHixcjMzDQdP3v2LDZv3oymTZuiQ4cOzvkQleQfBzJwJl2LkDXJ+PW2684GIyIiIsdyyzGNmzdvRkxMDDp27IiwsDD4+Pjg0qVL2Lt3L3Q6HaZOnWrWQ7hjxw5MnjwZw4YNw7Jly0zHGzVqhLfffhvz5s1DdHQ0BgwYYNpGEAA+/fRTl98NpmddTxwsGtMIAFojEHu5MHCfzdDiiSA5lN8m4b3H/DG1demzzYmIiMh9uWVo7NSpExISEnD27FnEx8cjLy8PKpUKvXr1wrhx46wu1l2St956C+Hh4Vi2bBn+7//+Dx4eHujQoQPeeecdtG3b1nkf4iF5tYUvZv9qPtkn5s9c0+9ziwY6xl7KY2gkIiKqxgS1Ws3Bay5Ko9EgMTERYWFhFZq1pfw2qcwyMgFIe7mO6etzGTqE+kig4sKOTuWoNqaqie3r/tjG7q26ta9rv1slh0gdVfY6knoR+O5yHsb8kgEA6LT1Np7amebsqhEREVEV4Zavp6l8PG3cOnD8obsAgC5/Fb6+vpSld1qdiIiIqGphTyOV25Q4tcWxLK0R17MZIomIiNwVQyMBAFSe9v8o5OtFhK+7hTabUpGn5wrhRERE7oihkQAARwYF2XXdr7e1iFh/y/T1/b8nIiIi98HQSACA2j5SHBpQq9zX9dp5B/mGexPwNQbg24u5EMWSJ+VvupKHHO5ZSERE5FIYGsnEUWsvvRmvxr6kAqvnUvIMGHfwLmadyLR6noiIiKomhkYyMTiw8++5ven4PU2LE7cLkJJngCiKyNAYoDUWRlO1lsuDEhERuRKGRjKp51e4UPfiDgEOuV+37XfQe2cantp5BzHncxGxIQU5usKwuOVaPhadyS71+hs5evx2h/tfExERVQUMjWSi8pJCPaYOxjbzdeh9r+cY8G7R6+jZv957LT3vt6ySLgEAtP4+Fd133HFoXYiIiMg+DI1k1ZedauDVFr5oo/Jw6H0fHOs44VCGQ+9PREREzsHQSFa92MgH89oFoHhi9GdRSqc8J/ZyvlPuS0RERI7F0EilMhZNXBnZ2AePBTq217HYkRTz3se1f+dC+W2SU55FRERE9mFopFK92MgHACAIAoonV98eFYrYniqHPaP//9LQeettnLqjxa08A149ojY7rzOKaLLxFuJSrC/jU14LTmdhery6zHJERER0D0Mjler1Vn5Qj6kDACjqdIRMAvSu64nZkf4Oe87ZDB167LhjNRj+klSA2/lGLP0jp9RFw201//dsfHUxF1oDl/0hIiKyFUMj2aw4NEoEAYIgYFobP4c/Y+zBuxbHhv6cDgD4X6IGbx3LxJ5EDZTfJiFTa4TBKGLS4bu4nq0v97Mab+SWh0RERLaSVXYFyHV8Hq3E8vO5ZseeCvNCvl7EoVuOeXVclm8u5uKnGxoAwK08AzwlAtZfyoPWKOLrLjXLda9MLjBORERkM/Y0ks3aqOSI6VTD7FhsTxU29Soc3ygRzMv3D/dySj2S8gwAgHeOZ6KgqPvT48GHExERkUMxNFKFyaUCfh0ShJSRofjj+WCMf0QBAHiztR8G1vdCixrmHdpdans65Ln7kwvw5I+3C+sgAYyiiHdOqJGYU/Kr6ilHzV9/H35IPaRERESujqGRHKJxgAfkUgF1fWWooyjcjtDXQ8CqbiocGhBkVnbr04HwcPBP3qqEPCTlGhDzZy5afZ+KoFVJyNEZsTohF0ZRxNC9aTibrsXKhDyz6575Kc2xFSEiInJTHNNIDje5aCeZpsrCdR2l9706zng5FADwx/Mh6LHjDm7mGhz23Fbfp5p+rzUCEw/fxfbrGjQOkGHPzQIYROvbFubojPB1dIolIiJyM/ybkhxOJhHQNdRyPGMdHykkQmGADPaR4vfngq0uGN4kwDH/ltl+vXDCTJ9dhb2JD25hWKzu2ltmS/kYjCJiL+eZjomiiAS1rsznJah1uJpl+WrcKIpc3oeIiFweQyM9NDW8zH/cPCQCvrhvYs2MtoVL+GzurTKtDfnQ6rYyGdOPqQEA6y/lYcKhu1h/qfBV9tZrGrT78TZOp2kBFC42nqU1Ysf1fLOw2e7H23h0873eztUJhTvbzDyeiaDVyQ/vwxARETkBX0/TQ/FNlxp4MthyAkwzpQfef8IfC37PxvQ2fuhU2xNhvpXzY/nVhVxkFhjRsKinc/IRNWp4SvBHRmEv481cA9oGAi//koGdRcv+fNu1BgY38LF6vzUJhcsTxV7Os3qeiIjIlTA00kPxbIT1YAUAr7X0w2stC3sZo0PuBcvrw2tj8ZlsfPZHjtPrV+y7K/lmX7+0L8P0e33RPorFgREAsorWetQbLV8/5+kLjz14qrh3UhDMlwk6m65FLW8pavtI7as8ERGREzE0UpUVIJdAft8kmob+UlzOctzEmfJ6+UAGRiWbh1+DCNRbl2x1ofA/7xaOb8zSFZ5TFxih9JSgWWwKAr0kODoo2Kx852134OchIHFEqJM+ARERkf04ppGqtBFNfNDIX4YfequwuXdgZVcHqx9YsmdqvNoiMCq/TcJNK2tF1l9fuG1har7RFCiLff5HNgAgWyfiiz9zTOMnC+yYQFM85pKIiMiRGBqpSqvvJ8PJZ4PRvY4X6vtZdozLrfwE/7eDEu8+an1f7CdqWc7WdoaW9y3/cz/lt0lmX6sLjBi+Lx2zfr23HNC7JzLRZ1carmfrUe+7DMTdLd//pqN/yUD4Ou6rTUREjsXX0+RSUkaGQieKuHBXh4wCIzrX9oRRLFw2BwAWdwjAP5oV7kjzwe/ZpuvkEmBCc1+8/0SAWXD7LEqJ14+qH+pnKPZggLxfvkHEsduFvY1bUmR4ofW9cweTNZAIAiIDPaCwsr7krqIxl22+T8GqbjXRNlDu2IoTEVG1xNBILsVLJsALAtoFmc/EPj44CJlao8XxYt/3UqFL0dqRkYEe+C1NhxqeAkY1UVRaaCzLhEOFWx7+ki7DK0ey8WxDEWMOZKD4hXWHYDn+17cWgMLX2HIJkF5w77X09RwDlp3PwfLONU3HMjQGKDwk8JRyr24iIiofvp4mt9BU6WERGJ+P8AYArO1eE53v2+96d7/CoKUrmlPzXU/Vw6lkBWxP1OLl+wIjAMSnamEURRhFEcGrk/H5nzlotCHF7LrYy/dmgxcYRERsSMHoXwpnhO+6kY9GG/gam4iIbMPQSG7rqy41oR5TB/3reZstbyMr+m3xod5h93av+fdj/gCAV1v4olXNhzP+sSLy9CJ2FO18s+u+pYDu9/WFHKxOyEVw0QLjPyVqUGAQseB0NtI0RqvLBRW7maNHcq4BWoNYYrnr2Xqs/zu3gp+EiIiqOoZGqnaKA6TkgTe0zWvI8GZrPxwZGIS5j/vDcN9uL8s7F+5c4yUFPm4fAADwkVX+K97/ns3GqKKew/hUrdUybx3LtHgFP/5QBs6kFy5aXrzzDQAs+zMHym+TcDVLj9v5BrT8PhXNv0tB0OpkBK5KRpqmsHtWFEXojCLiUwvQ/6c0TDpy7/65OiOMYumzvjO1pYdVIiKqehgaqdoa/4iv6fefRysRW/SaumVND0glAlZ1uzcWsGvR6+1uoV4Y20yBDsFy7OxT+UsA/fesfQufb712r1fy/kA580QmAODRzanYdi3/wcsw60QmHt+cihork1FrVTL67EpDYk5hkIxPLcD5uzrUWXsLc05mWVybqzPi7eNqaPQi6q27VeJY0kytEb/dsR6AiYio8jA0UrWkHlMH70b6m74e0VhhsX1h4wAPJI2ojb9fDEGglwSD6ntj7uP+kEoE/K9vLTwaKMdbrf0Q21OFDsH3ZijXum+P7SMDg/BUXeuTc6qSv9Q66B7o+XvrWKZFOb0IXMqyXIMSAPrsSkPHLbcBABvv2zqxeM3K1Ql5+PJ8LlYXba+4/XphKJ15XI2G62/hdr4Bx1ILMHJ/BrrvuAO9UURKnuVi7vl66z2UvyRpTPcmIiLHE9RqNd8RuSiNRoPExESEhYXBy8ur7AvIqQ4kazBodzqGN/bBur/zcGRgEFrW9IAoivj8jxzMttL75mq8pQLybVxw/Km6nsjTizicosW+/rVw6FYB5p669z1QyAQkjQw1LT3UJECGhEzLQJo0orZpaaFbeQY8Elu4lNDA+t6mMqIoosbKwjGb6jF1IIoisnUi/K0t5HnfNUdTtYgKllts6Xg/dYERLx/IwLdda6KGp2P/nc3/h90f29i9Vbf2dbuexuTkZMTExGDw4MFo2bIlatWqhSZNmmDkyJE4efKkzfc5fPgwlEplif+tW7fOiZ+CXFHXUC/cHhWKTzsqsa9/LbQsmkgjCAJea+WHuy+Hwvu+pW6a15Dh5ojaZvfIeDkUJ4cE4dUWvqiKbA2MALD7ZgEOpxS+Zu6x445ZYASAXL2IXN29JYKsBUYAuJ1/r0xqUc/jkVsFyNQakak1Ik9vxOar916li6KIry7kInzdLbP7P+jnpAL0/1+axQSiK1l6nL+rM3297HwODiQXWH1dX5rr2XrcsLIzEBGRq3K7dRpXrFiBJUuWoEGDBujWrRsCAwNx+fJl7Ny5Ezt37sTXX3+NIUOG2Hy/qKgoREdHWxxv1aqVI6tNbkJeFAofq2W5oLYgCLjyUm0YRRFr/s7D6CYKeMsEfNmpBm7k6DG0oQ8kgoBGAR54q40fPv/TvvGKrqTO2rKX/Hl0cyq+iFaiRx0vdN1+BwDwd5Ye9UrY9SZTK2J/cgEA4JHYFCzpqET8bS1qeUnQLkgOvRHoWdcLe24WhsXUfPNgGbm5cDcf9Zg6AIAFpwsXic8t4bV4SdpsMr/Pg0RRxM7EArQQgZQ8IwwFejQMKP2PZFEUIQKQlNIzSkTkLG4XGiMjI7Fjxw6LoBcXF4eBAwdi6tSp6NevHzw9bRtnFh0djZkzZzqjqlQNecsEAAL+2fxeT+KLjXwsyinvew268JECbMvwRQ0vKbZdv9cr9mNvFQbvSYevTEBOKYGmuVKGMF8pJrbwxaDd6Y75IA/Z5CNqjCva6QcADhSFQmu0RhHFkSpLJ+IfB+9alHm5iQ9WFu0jbihhpvf7pzLxZut721G+cyITk0rpAT6WWoDVCXmI6VSjtI9icjRVi7FHcjCjoQwfH70LESUHzGJT49X49q+8Mss5k1EUUX/9LXzduabZclVE5P7c7vX0gAEDrPYMduzYEZ06dYJarcb58+croWZE5TPzUT+8H+mDrioDvu/uj9XdVfi5fy3s6hMI9Zg66FbHC+mjQ3H+hZAS7/FWaz8cGhiE2F6BFutOPlPPC+895g+l3DV6rdbYuBZkk40p+F+i9TUrixUHRgCYfiwTym+T8Hua+YztxWdzTNtTFlt05t7WlGfTtdidqMGFolfZrxy6a7Z8UbEEtQ7Kb5Nw8oEZ4TlFr84zdcCDsVVrEKH8Ngk/F/WGZmmNOHG7AN/+de/+qxNy0WXbbaufL18v4sTtkoN1SfRG0WJClGUZIEsr4pNz2aWWIyL343Y9jaXx8Cj8S1Mqldp8zZUrVxATEwONRoPQ0FB07twZoaGhzqoikcmMtv5Fg6zvHXv8gdfeUokAf7mAqy/VhqJo3Ui9KMJHZvnvwRqeEjxRywOjmijw2lE1AuQSTG3th6mt/dBzx22cvKPD/v610H3HHYtrPSTAe4/5Y/avlTeZp8ByIrVDDfwpDVm60gPTvN+yMO+3LPzncX+8V8LEpiMpBYgOufcmo92PhcEuPrUAj9eSIyXPgF4772BQ0USeq/n32urxzam4lKU3rQX63N50qMfUwbiDGdhz814INIpiqdtfTotXY/2lPExqocCH7ZRm5+JTC+DrITH9I+LCXR38PATU9ZUhasttXM3W4/boOvjuch5UXhIM3ZuO5yK8TdtRlmNYKxG5mWozezoxMRGPP/44atSogT///LPM4Hj48GE888wzFsdlMhnGjx+P999/3+bwqdGU3uthL61Wi9TUVAQHB0MutxxDR67PGW2cqTWi6ea72NDVD91qF94zS2tEqkZEY38pQjYUvsJ+s4U3Jj/iDYWscDymKIqovTHD6j2fruOBn5J0Vs9VR0/V8cBuK9+Pmp4CMgrK90fuoHA5ttww76Vs7C/F31mFKXpUI0+0UMowIFyOgyk6HE3V4ZcUHW7mFvZkburujydryfBqfA6igz3w1q+FPbYpw1T45ZYWww5Y9hheG1oT9b8zb+uUYYXrmG6/UYBXjhaOt130hALP1vfExqsFeLlRYVAWAZy4o8djgTJ4PLiC/n1eOZKNwfXkuJ5jxLE7Oqzq7F9iWWebeTIHAXIJ3m5tOVSkolzhz+mr2QZoDCIeUVarfiSHcIX2LUt5Zn1Xi9Co0+kwcOBAxMXF4csvv8SLL75Y5jUXLlzA7t278dRTTyE8PBx5eXk4ceIE5s6di4SEBEyePBkffPCBTc+/cuUKDAYnd5MQOUhqgYA8A9DAp+Q/Gp44UviXa6S/AV+2KoAgAF/fkGH5DfM/NJe20CDIU8TRDCmu50vwZgMtPCVAhzjrfzk3Vhjxd67bjZqpdA19jLicZ/59/U+TAryXYH1sd5DciNta8/K/RudBFIEhp7xwU2PZRmvb5mPBZTnOZRf+Y7qbSo8aHiI0BgEZOgFLWxb2lP6ZLcGtAgEzL5o/O75jHqx0kJvRGABPyb0tQEUR+CNbglb+Jc+Sv19ivoAhp7zxVSsNGiuM8JYW7gxV/PN8LCoPAix3i7JHgRGIjvPBJ801aO1vRI9jPljdNh+P+Jb/r9w3//SESi5iVmMt1DrATwZIHTiqpPjz/xptObyCnEdvBNR6ILASs6ZUKkVERITN5d0+NBqNRkyYMAHff/89Ro8ejU8//bRC90tNTUVUVBTUajUuXLiAWrVqlXkNexrJXlW1jZNyDQj0ksDzvr+5jKKI0KKeyAlNvbD8L42pd+pBGoOI2/lG/JVpwM/JWqy6VBgoTg1QYtO1ArSr5YFWNWTwlhbOWm6y2XIyCz1cx/orsfKSBl9etP7n2a5e/ui71/7hCx89rsBz9T0x9kg2PmmvQKhPYfhMzjNgZ6IWvevI0X67Go+qZKjpKWBfsg6rO/th1KFsrOvih7oKCY6k6jC8oReGHchCpEqGvnXl0BoLX6lHBcmwO0mHlw9n49l6cmy+rsUbzb3RN0yOp3bfW8heJhT2zp67q8egep5QeQpYflGDlxt7wVMKXMk2YvzRbOzoFQBvKfBXlgHNAmTI0YmQCPe2F03OMyByqxp9QmWQGzTYmipDTbmA88/WxJEUHRoHSBHsbZmS8/UiWm+5i41d/fBYYOEQguLe/5RhKoRsSMfYJl744LF7E8N2JRYg3wA8W9++jQTuv39pMrVG6EVAVc71SnP1IvJ0ImpZ+bwPy54kLXqGejh85QGtVou/k1LRuE75/4yeciwHG68WlPl9dzb2NBYxGo2YPHkyNmzYgKFDh+LLL7+ERFLxH9rXX38dq1evxoYNG9CnTx8H1NQ+1W1R0erI1dpY+W0SGvnLcPLZ4HJdt/RcNmafzMKN4bWtLsj9d6YOT/xwG11qe+LEba3V9SIXtA+A1iDiVJoOW67l45VHFPjqwr3JM6+19MXSP9x/GSN3EROtxPdX8vFLKTPli3lJC3shASDIW2K2tmexz6KU+CNDhxUXbN81KCpEjhBvqdk6oMXmPOaPb/7KRWKOAR+0C8C7J8x3UNrUS4Xn9qbj6ToeOJtWgOQCCfw8BPzcvxbaF41zbaaU4djgYOiMIsYdzMD7TxT+DD/+w70JTrv6BKLv/9IAAHdfDkWNlckI8Zbg4ov31ngtXiDf2qz6U3e0eOHndJx7PqRo9QZLxdf/9UIIgovC+rI/c/Dvk5m4PfrePUPXJCNPL5o9Z0+iBl1CPeEpFaAuMMLXQ8CO6xq0qumBml4SCAAG70nD72k6u2b9v370LgK9JHjvscJxvncLjNAaRFM9bbEnUYOhP6djSUclXm6qsDifqzPicpYerVW2hz5RFJGab0Rqdj667MrE6s5+GNCwfEMsmsfeQnKe0fR92Z+kwYLT2djdrxauZOkhAGjgX7WGDFSt2jiQ0WjEpEmTsHHjRjz33HNYtmyZQwIjAKhUhf8qyMtjVz7R/a6+VBulbMJSosktffF8Q58Sd3Ap7nWq7yfF1qdD8em5bPz7ZBa+66lC8xoyeMkEBHrd+0vkzwwdIvxlWPVXLoY08MajgXJMaG4eGv94Phgtvy9cS3FAPS/svqlBqI8UV7Mth5L89mwwFp7JxgYrs6OBwolCD64jHhUix9GUkvfQ7hPmVeYs7+ps0hG1zWU19zWZtcAIoNSJQyUprf3m3LdY/YOBESicxASgaKxv4c91tk40BUYAuKjWQ/ltEv79mD+2XtNg2zUN6ijMw9CsX+/de/yhu6b7FHv/1L3zxeGvmHpMHXx5PgdpGiN+vJqHhEw93mrjB18PCW7k6NG66Oe/WNPYFADAwicDTPvQA4W9n7l6I/KKlvYqnmGfpjFi6M/peK2lL+SSwhUH2qg8cCZdB38PwerEMnWBEQdvFeDL8zn4+Ekl1AVGZGmNaB8sR2KOATU8Jajvdy+arC5a6SA51wBBEEz/Dx4cUAsN/WXw9ZBAaxDxzcVcNA6QYcHpLOztH2S6XhRFDP25sC22X8/H1mv5eLGRD9rVkmNXogZtVB5Yei4bu28W4PRzwQj3lUJnBDylAvRGEXc0Rjy7Ow2fRtXAY7Xu9VSuTsjDG3Fq03NGHcoGDmXj7suhaP5dCmY+6o+OwXL8eVePgfW9kaszmna2upmjR11fmWnVhOKvh+wprOeg3WmmZcUuDQsx+7OtsrllT+P9gXHIkCH46quvyjVjuizPPPMMDh8+jL179+KJJ55w2H3Ly9V6oaj82Mb3HEzWoF2QZ4m9JbZYk5CLYG8pvGQCOtcumrghimbbCP7jQAYG1vdGuK8Ux1K1+Gdzhen8B79lYeF9y+4Uz05OUOsw5kAG/ryrxyvNFPhnc180DJBhWrwa31ws7Nn6tKMSrVUe6Fa0QHnKyFBk5eWjyea7GNPYE6suFaCk1W6uD6+Nl/allxpiKmJTLxX23tRgeTl64ajqC/OVIjHH8h9Bb7T0xacO6HXf/nQgnvkpzebyo5v44FiqFn+VsPtTsR51PDHviQA09JchaHVyqWUD5AIi/GX4Pe3exLOuoZ6o7SOFwShi7hMBeKQoDNtCIROQqxex5SmVxbq2o5r4IMhLimcjvPHJ2Wx8d6V8u0QBQO+6nmYrIRTrUccT+5Isj3cKkWN7n7KHwT0sbhca738lPWjQIHz99deQyUruUE1PT0d6ejpUKpWpBxEATp8+jbZt21qUX7ZsGWbOnImGDRvixIkTDg2j5cVA4f7YxlXTlSw9zqRrMbhB6bNtd17Px/D9GRhc3xvfditcsiZNY4DKUwJBEKDRaHD+aiKa1qsLqdwLeXojanpJsfVaPkb/koGjA4MQ5C1BLW8pjKKImiuT0byGDOfvWv9L9+8XQ2AQgWb3/SX5fIQ3MgqMeDJIjg9+t5wp/Y+mCnzUPgByqYD3T2Vi8dl7YWJEYx+s/ZtvVIgq05nnglHPr2q8GK4atXCgBQsWYMOGDfD19UWjRo2wcOFCizL9+vVD69atARRuO7hgwQLMmDHDbOeXkSNHwsPDA48++ihCQ0ORl5eHX3/9FWfPnkVAQABWrFhRqYGRiCpPhL8METaMNepXzxtXhoWg5n2vlx581eQnK1xv00smwEtWeG5gfW+L8V/Fr8V61fHCoQH+0BuBGcfVWJWQhz39AtEu6N4kiPNDQ5Cab8C0eDU+i6oBb5kAoyjiarYBSk8Bvet6ob2VXtvJLXxRYAAGN/BGjx13MLShD15t6YupcWrEpRb2ci7pqMSUotdyMx/1Q1yKFos6BGD8obum3p6rL9VGg/WFC6Nv6qVCa5UHmmwsDLIN/aW4nGXbahIKmYBHAz3wyiO+GP2L5XJPrWt64GxG6Us9RYfIccRJPbRED0ObTamVugvU/dwuNN64cQMAkJOTg0WLFlktEx4ebgqNJRk7diz27duHuLg4ZGRkQCKRICwsDBMnTsSrr76KOnWqRgMSUdVW04Hjka69VBt+HgKkEgEyCdCrrhdWJeShrsL8j/JQhRShCin2P3NvbJdEEMrc4rCmlxTz2hVOOLj/L6ldfc1fj71zIhN5ehEz2t4b+L+vfy2cTtPhcpYeNTwlUMoFqLUietYt7CH/uH0AWqk80CHYE/GpBVDIBHTedsf0rPY/pOKvTD3UY+qYxuYljbTcSOF/fQNxLFWLuaeyENtLheOpWtT0kuB2vgEeEsEULnvX9cSjgXLMfNTfYqzfxOYKnM3QwWAEvuxcA0/+mIqRTe5NnBpU3xtbrhW+ekwdFYqmG29BrRXxWZQSLzb0KfOV6ZedauCfh0uf8T+qiY9pvB4A1POV4rqVV8m26lLbEwdvlX8XIHIN94+JrExu93q6OuGrS/fHNnZvjmhfjV6EVwXGedrjboEReqOIWt4lB+JbeQbk6oxoFOBRYplfb2shCJY7HR1LLYDOCHSqfa/3tOu223i2gTdea+X34G3MGIwi7mqNFhOjTqVp0UblgTalzJC9qNahwCCijUqOC3d10BlFtFbJUWAQcSNHj8b3fZZvL+biTLoWCZl6xKVq8fuzwdCLImb9moX13WtCKhGQmmdAvqYAuvQk1KlbF2eyCnfiEQH4eUiQrTNierwaBhH4qktN071FUcTJOzo8VssDRhG4oNajvp8UvjIB8ala02zq+219KhBdQj2RrxdRe415qP08WoljqVp81D4AuToR13P0mHsqC0dTtFjWqQYmHr6LoQ290bKGh2mno/92UGJqvNrsPj3reOJnK+Pu7uclBaSCgHBfKb7vpcL+5AJcztRbjKH8sF0A3rlvss2LDb0RXdsT/3cxF1ojMKapD06n6bCmaHhETU8JPotS4lKmHtey9RgS4YN8vYgXiia5/OdxfzRVepi+flCHYDlebqrAhKLJRPOe8Mesoh2u1GPq4JckDQbvsX5teY1q4oPG/jLMfmDXqBBvCVJKmKhVlqrS08jQ6MIYKNwf29i9sX3dnzPaWGsQ4SEp3KmpuBfV2nJVGr2IbJ2x1HAPAIk5etT2kUImKdz5adOVfAxu4I18gwiFTMD1bAP85QJUXlKs+zsX/et5I+CBZ6VpDNAZgdolLIVzKVOHOgqZxZCIv9Q6hPtaHr/fnXwD5FLB4pnWJOcasPBMFv7V1h/qAiPq+UnNtlVt+V0Kprfxw+imCmgNInJ0RtPbgEytEV+ez8H0Nn6QCAJydUZcytIjJc+IXnU9Me+3LIxt5os34+6inq8MCzsocSszDxkpSahdpy5qKLzw6x2taahISp4BtbwkOJxSgEAvKVrWvPePjs1X8rA/uQBLOiohFYCvL+TiX8cz0chfhmODgyArWmH+xO0C/Jamwz+b+5b52R8GhkYXxr9w3B/b2L2xfd2fs9s4T2+EXCKYQgY9XNXt/2G3G9NIRERUXfiUtfcikQPxp42IiIiIysTQSERERERlYmgkIiIiojIxNBIRERFRmRgaiYiIiKhMDI1EREREVCaGRiIiIiIqE0MjEREREZWJoZGIiIiIysTQSERERERlYmgkIiIiojIxNBIRERFRmRgaXZxUKq3sKpCTsY3dG9vX/bGN3Vt1al9BrVaLlV0JIiIiIqra2NNIRERERGViaCQiIiKiMjE0EhEREVGZGBqJiIiIqEwMjURERERUJoZGIiIiIioTQyMRERERlYmh0QX99ttveP755xEeHo7Q0FD07NkTP/74Y2VXq1qLjY3FlClT0LVrVwQFBUGpVGLdunUlls/KysI777yDli1bIigoCK1atcLs2bORk5NjtbzRaMTy5cvRsWNHhISEoGHDhhg7diyuXbtW4jP27duHvn37om7duggLC0P//v1x8ODBin7Uaik5ORkxMTEYPHgwWrZsiVq1aqFJkyYYOXIkTp48afUatrFr0Wg0eOedd9CnTx80a9YMwcHBaNKkCZ566imsXbsWOp3O4hq2sWtbsmQJlEollEolfv31V4vzbF9LXNzbxRw6dAjPPvssvLy8MGTIEPj6+mLbtm1ITEzE+++/j9dee62yq1gttWrVComJiVCpVPDx8UFiYiK++OILDB8+3KJsbm4unn76aZw7dw7du3dH69atcfbsWezfvx+RkZHYtWsXvLy8zK55/fXXsXr1ajzyyCPo3bs3bt26hS1btkChUODnn39Gw4YNzcrHxsZiwoQJCAwMxODBgwEAP/74I9LT07Fy5UoMHDjQed8MNzRnzhwsWbIEDRo0QHR0NAIDA3H58mXs3LkToiji66+/xpAhQ0zl2cauJz09HS1atEBkZCQaNWqEwMBAqNVq7N27F4mJiejevTs2bdoEiaSwr4Vt7NrOnz+Pbt26QSaTITc3F3v37sUTTzxhOs/2tY6h0YXo9Xo88cQTSE5Oxt69e9G6dWsAQGZmJnr06IEbN27g5MmTCA8Pr+SaVj8HDhxAREQEwsPD8cknn2Du3LklhsYPP/wQH3/8MaZMmYI5c+aYjhcHk/feew9Tp041HT906BAGDBiAjh07YsuWLZDL5QCAvXv34vnnn0f37t3xww8/mMqr1Wq0adMGMpkMhw4dQp06dQAASUlJ6Ny5MwDg9OnT8PPzc8a3wi1t27YNNWvWRHR0tNnxuLg4DBw4EAqFAn/99Rc8PT0BsI1dkdFohF6vN33vi+n1egwaNAhHjhxBbGwsnnrqKQBsY1em0+nQs2dPeHh4ICIiAt99951FaGT7WsfX0y7k0KFDuHr1Kp577jlTYASAgIAATJ06FVqtFhs2bKjEGlZfXbt2tSmsi6KINWvWwNfXF9OnTzc7N336dPj6+mL16tVmx4u/fvfdd83+QuvVqxeio6Oxf/9+JCYmmo5v2bIFmZmZGD9+vOkPIgCoU6cOXnnlFaSnp2PHjh12fc7qasCAARaBEQA6duyITp06Qa1W4/z58wDYxq5KIpFYBEYAkMlk6N+/PwDgypUrANjGrm7RokW4ePEiPv/8c6v7RrN9S8bQ6EKOHDkCAOjevbvFuR49egAAjh49+lDrROVz+fJl3Lp1C+3bt4dCoTA7p1Ao0L59e1y7dg03b940HT9y5AgUCgWefPJJi/tZa3f+nDxcHh4eAGD6y4dt7F6MRiP27dsHAGjevDkAtrErO336NBYvXowZM2agWbNmVsuwfUvG0OhCLl++DAAW4yIAIDg4GL6+vqZ/CVPVVNyGERERVs8XHy8ul5ubi5SUFNSrV8/qv4gfLH//7639nBQfu7882S8xMREHDhxASEgIWrRoAYBt7Oq0Wi3mz5+PDz/8ENOnT8eTTz6JvXv3Yvjw4ejSpQsAtrGrKigowMSJE9GqVSu88cYbJZZj+5ZMVtkVINtlZWUBAPz9/a2e9/PzM5Whqqm4fQICAqyeL27b4nJltfmD5cu6pnh8DH9OKk6n02HChAkoKCjAnDlzTH9ZsI1dm1arxYIFC0xfC4KA1157Df/+979Nx9jGrunDDz/E5cuXceDAAavhrhjbt2TsaSQiKiej0YhJkyYhLi4Oo0ePxosvvljZVSIH8fX1hVqtRkZGBv78808sWrQIq1evRv/+/avkX+JkmxMnTmDp0qV46623TMMMqPwYGl2ItX+t3C87O7vEf+lQ1VDcPpmZmVbPP/ivz7La3Nq/Vku7Jjs726I8lY/RaMTkyZPx/fffY+jQofjkk0/MzrON3YNEIkGdOnUwduxYfPrppzh27BgWL14MgG3savR6PSZOnIgWLVrgzTffLLM827dkDI0upLRxDqmpqcjJySlxDAZVDcVtWNLY0+LjxeUUCgVCQkJw/fp1GAyGMsvf/3trPyeljaOhshX3MG7YsAHPPfccli1bZlq3rxjb2P1069YNwL3JC2xj15KTk4PLly/j3LlzqFWrlmlBb6VSaVpxpFevXlAqldixYwfbtxQMjS4kKioKALB//36Lc8Wz+4rLUNXUsGFD1K5dG8ePH0dubq7ZudzcXBw/fhz16tVD3bp1TcejoqKQm5uLY8eOWdyvuN07duxoVh7gz4mjFQfGjRs3YsiQIVi+fLnVcVFsY/eTkpIC4N5Mebaxa/H09MTIkSOt/lcczPr06YORI0ciPDyc7VsKhkYX0qVLF9SvXx+bNm3C2bNnTcczMzPx3//+F3K5nGOrqjhBEDBy5Ejk5ORg4cKFZucWLlyInJwcjB492ux48dcffPABtFqt6fjevXtx5MgRdO/e3WyNyMGDB8Pf3x8rVqxAUlKS6XhSUhK++uorqFQq07pzZJviV9IbN27EoEGDsGLFihIH0rONXdPFixeRl5dncTwvLw/vvvsugMLeKIBt7Gq8vb2xdOlSq/+1a9cOADB16lQsXboUrVu3ZvuWgjvCuBhuI1g1rV69GvHx8QAKt6c6c+YMnnzySTRo0AAA0KFDB4waNQpA4b9Un3rqKfzxxx/o3r072rRpgzNnzpi2p9q5cye8vb3N7v/g9lQpKSn48ccfoVAosHfvXjRq1MisfGnbU3377bcYNGiQk78j7mX+/PlYsGABfH198c9//tNqYOzXr59p0X22seuZP38+YmJi8OSTTyI8PBx+fn5ITk7Gzz//jIyMDHTo0AE//PCDqd3Yxu5h4sSJ2LBhg9VtBNm+lhgaXdCpU6cwf/58nDhxAjqdDs2bN8fkyZPN9r6lh6v4D56SDBs2DMuWLTN9nZmZiY8++gjbt29HamoqgoODMWjQIMyYMcPqtlFGoxErVqzAqlWrcOXKFSgUCnTt2hWzZ882BdMH/fzzz1i8eDHOnj0LQRDQpk0bTJ8+HV27dq3w561uympfABbbRrKNXcvvv/+OlStX4sSJE0hOTkZubi78/f3RokULPPvssxgxYgRkMvNV6tjGrq+k0Aiwfa1haCQiIiKiMnFMIxERERGViaGRiIiIiMrE0EhEREREZWJoJCIiIqIyMTQSERERUZkYGomIiIioTAyNRERERFQmhkYiIiIiKhNDIxERERGViaGRiIiIiMrE0EhEREREZWJoJCIiIqIyMTQSERERUZn+HzYwLSPhk8J5AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "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": [
        "_Stephen Anthony Rose_"
      ],
      "metadata": {
        "id": "o5QUJhbyZAW5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# TODO predictive posterior sampling"
      ],
      "metadata": {
        "id": "Q0PRujpEx_32"
      },
      "execution_count": 10,
      "outputs": []
    }
  ]
}