TF_PINN_Higher_Order_PDEs.ipynb

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  "metadata": {
    "colab": {
      "name": "TF_PINN_Higher_Order_PDEs.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMgHGnBmyI2L5E/P5mDmP3P",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/kochlisGit/Physics-Informed-Neural-Network-PINN-/blob/main/TF_PINN_Higher_Order_PDEs.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this example, I will use **Tensorflow v2** to train a *Physics-Informed Neural Network* (*PINN*) model to solve a second order PDE. Higher-order PDEs are a bit more diffucult than first-order PDEs, because they involve the Hessian Matrix computation. Additionally, the boundary conditions could also be dependent from the derivative of $y$ (also known as *Neumann* BCs), which is of course not known. \n",
        "The equation I will solve is $\\frac{d^2y}{dx^2} = -\\pi^2 sin(\\pi x)$ with $y(0) = 0$ and $\\frac{dy}{dx}(0) = \\pi$ for interval $x \\in [0, 2 \\pi]$ . For evaluation purposes only, we know that the solution of this equation is $y=sin(\\pi x)$."
      ],
      "metadata": {
        "id": "wh1iyUqKzjvw"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "0-Boo3yozAmL"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "num_domain = 1000\n",
        "num_test = 100\n",
        "minval = 0\n",
        "maxval = 2*np.pi\n",
        "\n",
        "def generate_uniform_data(num_domain, minval, maxval):\n",
        "  data_init = tf.random_uniform_initializer(minval=minval, maxval=maxval, seed=0)\n",
        "  return tf.Variable(data_init(shape=[num_domain, 1]), dtype=tf.float32)\n",
        "\n",
        "x_train = generate_uniform_data(num_domain, minval, maxval)\n",
        "x_test = generate_uniform_data(num_test, minval, maxval)\n",
        "x_train.shape, x_test.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8BoKz9nH3YjU",
        "outputId": "674ee9cf-c840-4b0b-c5ef-bd0941ec1676"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(TensorShape([1000, 1]), TensorShape([100, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In order to compute the error of our neural network, we are going to have to compute the derivatives of $\\frac{dy}{dx}$ and $\\frac{d^2y}{dx^2}$. In the previous example, I used the *GradientTape* object to compute Jacobian Matrix of this PDE. In this example, I also need to compute the Hessian Matrix as well.\n",
        "\n",
        "# Jabocian Matrix\n",
        "\n",
        "![Jacobian-matrix-formula.png](data:image/png;base64,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)\n",
        "\n",
        "# Hessian Matrix\n",
        "\n",
        "![hessian-matrix-formula.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "PHDK3U0l4EMX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def jacobian(tape, y, x, i=0, j=0):\n",
        "  if y.shape[1] > 1:\n",
        "    y = y[:, i : i + 1]\n",
        "\n",
        "  grads = tape.gradient(y, x)\n",
        "  return grads[:, j : j + 1]\n",
        "\n",
        "def hessian(tape, y, x, i=0, j=0, component=0):\n",
        "  if y.shape[1] > 1:\n",
        "    y = y[:, i : i + 1]\n",
        "\n",
        "  jacobian_grads = tape.gradient(y, x)[:, i : i + 1]\n",
        "  hessian_grads = tape.gradient(jacobian_grads, x)\n",
        "  return hessian_grads[:, j : j + 1]"
      ],
      "metadata": {
        "id": "mT1XPoYK394Y"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\frac{d^2y}{dx^2} = -\\pi^2 sin(\\pi x) \\Rightarrow \\frac{d^2y}{dx^2} + \\pi^2 sin(\\pi x) = 0$\n",
        "\n",
        "**Domain Loss**: *MSE*($\\frac{d^2y}{dx^2} + \\pi^2 sin(\\pi x)$)\n",
        "\n",
        "**$BC_1$ Loss**: *MSE*($y(0)$)\n",
        "\n",
        "**$BC_2$ Loss**: *MSE*($dy(0) - pi$)\n",
        "\n",
        "Training Loss = Domain Loss + $BC_1$ Loss + $BC_1$ Loss"
      ],
      "metadata": {
        "id": "f69Crtym-cei"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def pde(tape, x, y):\n",
        "  dyy_x = hessian(tape, y, x)\n",
        "  return dyy_x + np.pi**2 * tf.sin(np.pi*x)\n",
        "\n",
        "def dirichlet_bc_0(x):\n",
        "  return 0\n",
        "\n",
        "def neumann_bc_2pi(x):\n",
        "  return np.pi\n",
        "\n",
        "x_0 = tf.Variable([[0]], trainable=True, dtype=tf.float32)"
      ],
      "metadata": {
        "id": "ael3IpC39TDz"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "n_inputs = 1\n",
        "n_outputs = 1\n",
        "hidden_units = [50, 50, 50]\n",
        "activation = 'tanh'\n",
        "\n",
        "model = tf.keras.models.Sequential()\n",
        "model.add(tf.keras.layers.Input((n_inputs,)))\n",
        "\n",
        "for units in hidden_units:\n",
        "  model.add(tf.keras.layers.Dense(units=units, activation=activation))\n",
        "\n",
        "model.add(tf.keras.layers.Dense(units=n_outputs))\n",
        "model.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qYs_693g_2XS",
        "outputId": "f023c7bd-b759-4ede-c673-3ae0485fc732"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_3\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense_12 (Dense)            (None, 50)                100       \n",
            "                                                                 \n",
            " dense_13 (Dense)            (None, 50)                2550      \n",
            "                                                                 \n",
            " dense_14 (Dense)            (None, 50)                2550      \n",
            "                                                                 \n",
            " dense_15 (Dense)            (None, 1)                 51        \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 5,251\n",
            "Trainable params: 5,251\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "epochs = 10000\n",
        "learning_rate = 0.0005\n",
        "\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate=learning_rate)\n",
        "\n",
        "for i in range(epochs + 1):\n",
        "  with tf.GradientTape() as tape_model:\n",
        "    with tf.GradientTape() as neumann_tape:\n",
        "      y_0 = model(x_0, training=True)\n",
        "      dy_0 = neumann_tape.gradient(y_0, x_0)[0][0]\n",
        "      bc2_error = dy_0 - neumann_bc_2pi(x_0)\n",
        "\n",
        "    with tf.GradientTape(persistent=True) as tape_pde:\n",
        "      y = model(x_train, training=True)\n",
        "      y_0 = model(x_0, training=True)[0][0]\n",
        "\n",
        "      domain_error = pde(tape_pde, x_train, y)\n",
        "      bc1_error = y_0 - dirichlet_bc_0(x_0)\n",
        "\n",
        "    domain_mse = mse = tf.math.reduce_mean(tf.math.square(domain_error), axis=0)\n",
        "    bc1_mse =  tf.math.square(bc1_error)\n",
        "    bc2_mse = tf.math.square(bc2_error)\n",
        "    total_mse = domain_mse + bc1_mse + bc2_mse\n",
        "\n",
        "  model_update_gradients = tape_model.gradient(total_mse, model.trainable_variables)\n",
        "  optimizer.apply_gradients(\n",
        "    zip(model_update_gradients, model.trainable_variables)\n",
        "  )\n",
        "\n",
        "  del tape_pde\n",
        "\n",
        "  if i % 1000 == 0:\n",
        "    y_preds = model(x_test)\n",
        "    test_mse = tf.math.reduce_mean(tf.math.square(y_preds - tf.math.sin(np.pi*x_test)), axis=0)\n",
        "    print('Epoch: {}\\tTrain Loss = {},\\tTest Loss = {}'.format(i, total_mse.numpy()[0], test_mse.numpy()[0]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XQ8zWFlC_-Mb",
        "outputId": "ec617a57-f0b4-46d2-e3d3-52bc67ad21f7"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "WARNING:tensorflow:Calling GradientTape.gradient on a persistent tape inside its context is significantly less efficient than calling it outside the context (it causes the gradient ops to be recorded on the tape, leading to increased CPU and memory usage). Only call GradientTape.gradient inside the context if you actually want to trace the gradient in order to compute higher order derivatives.\n",
            "WARNING:tensorflow:Calling GradientTape.gradient on a persistent tape inside its context is significantly less efficient than calling it outside the context (it causes the gradient ops to be recorded on the tape, leading to increased CPU and memory usage). Only call GradientTape.gradient inside the context if you actually want to trace the gradient in order to compute higher order derivatives.\n",
            "Epoch: 0\tTrain Loss = 58.03800582885742,\tTest Loss = 0.8083492517471313\n",
            "Epoch: 1000\tTrain Loss = 2.758319616317749,\tTest Loss = 4.3738555908203125\n",
            "Epoch: 2000\tTrain Loss = 0.006166040897369385,\tTest Loss = 0.22569340467453003\n",
            "Epoch: 3000\tTrain Loss = 0.002479192800819874,\tTest Loss = 0.04237062484025955\n",
            "Epoch: 4000\tTrain Loss = 0.001414923695847392,\tTest Loss = 0.002821091329678893\n",
            "Epoch: 5000\tTrain Loss = 0.0009356021182611585,\tTest Loss = 0.00081308075459674\n",
            "Epoch: 6000\tTrain Loss = 0.0006741658435203135,\tTest Loss = 0.0035664953757077456\n",
            "Epoch: 7000\tTrain Loss = 0.0005045405705459416,\tTest Loss = 0.003558620112016797\n",
            "Epoch: 8000\tTrain Loss = 0.00038028735434636474,\tTest Loss = 0.0020791380666196346\n",
            "Epoch: 9000\tTrain Loss = 0.00029687589267268777,\tTest Loss = 0.0010485361563041806\n",
            "Epoch: 10000\tTrain Loss = 0.00024485262110829353,\tTest Loss = 0.0005908527527935803\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x_test = np.linspace(0, 2*np.pi, 100)\n",
        "y_true = np.sin(np.pi*x_test)\n",
        "y_pred = model(x_test)\n",
        "\n",
        "plt.plot(y_true)\n",
        "plt.plot(y_pred)\n",
        "plt.title('Evaluation')\n",
        "plt.legend(['Real', 'Predicted'])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "TVN6S0N5PqUR",
        "outputId": "6ee3b8a3-8090-4b45-bdf2-aa2626dcd6f5"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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rzz//PNdeey133HEH9fX1BAIB/uqv/oorrriC3bt3841vfAPQSk88+OCDbNu2jZtuuonh4T9ks19//fWEEmF//vOfs3//fvbs2cONN95IZ2cnX//61/nSl77E3r17+d3vfofP5+Md73gHV1xxBVdccQUvvPACAKOjo9x8883s3LmT+++/n3AkBcdM9VGjOfv7H7NXLZC6/52bHqOidiettkoyOn+B1o/HYiMMvvoUbnFQevnmW1bs9GTztNrDGwde0Eod2KxnoXXTfwy7f47DUs8/7ize9DA37Sji3360T/vQ/jwUrVFc7plPwOCpTV/nghRfBrd9YV2H+v1+nnnmGW69Vfv/dvToUU6fPk1lZSUPP/wwWVlZHD58mMXFRd7whjdw8803c+zYMZqammhoaGBoaIj6+nre+973vmZcn8/H+9//fg4ePEhlZSVjY2Pk5ubywQ9+kPT0dD7+8Y8D8O53v5u//Mu/5JprrqG7u5tbbrmZxldf5O8/82muueYaPvWpT/Gzn/2MRx/delFLyxGsk6WW55iVZLZftbW+OUPum7i65xEmhnrILiq99AkW50jtepZXqeeK2s3/3mw2xVjxtWQM/g4ZPIly7w2jhXFO5+8AWPZeTU5a0qaHyUtPpqyylv7BYtxdL8LV/yNcFoaFUBlq0GYE73vf+3jxxRe58sorz5WY/uUvf8nJkyfPrf9PTk7S0tLCwYMHueeee7Db7bjdbm644fxSGocOHeK66647N1Zubu4F7fj1r3/9mpjC1OQkM32NHDz4O370xBMAvPWtbyUnZ+tNHS1HsE6KRl+hLeUydicnb2mcgivega33P2j7/fe4/B1W3Zv1ImMdFC12cbDgQ7zevrWn+Oxdb4bBz+M78XMKLUewbpbbDtIWLOWyuuotj3XrzmJe6K7j7Z0vYF9rZrbOJ/dwE4oRrCYt7Q9xKRHhoYce4pZbbnnNMU8//XTY7AgGgxw6dAiXS4/FTHTB/GREml1Z8+J1MDbUQ3mwh5mSq7c8Vu1lV9FPIY72Z8NgWeIw+OpPAUjb9ZYtj3XFZTtoDJax3Gx9B+smsIzqeZmXgvW8rjpvy8PduKOIl2UH9oVxGGkKg4HR5ZZbbuHf//3fWV5eBqC5uZnZ2Vmuu+46Hn/8cQKBAAMDAzz33HPnnfu6172OgwcP0tHRAcDYmFZwOSMjg+np6XPH3XzzzTz00EPnPh8/+iokpXHdddfx7W9/G4BnnnmG8fHxLf97LEewDjpf1RQmubs2H6QMoWw2erL2Uz57ErHqraybxcZn6AgWceDyK7Y8VklWCqdcl1M4fgyWZsNgXQLQdxRHYJ5jaid7LlDye6N4c1LoTNujfeh6YcvjRZv777+f+vp69u/fz65du/jABz6A3+/nbW97G7W1tdTX1/Oe97yHq68+/+GxoKCAhx9+mLe//e3s2bOHu+/WklNvv/12nnjiiXPB4q985SscOXKE3bt3U19fz9f/89uQlManP/1pDh48yM6dO/nRj34Ulta91tLQOvC3/ZYZSaF69xvCMl6w9GqyJ39OT/NxSrdfHpYx4xr/IiVjh/ll6i3cvgnJ4oVYKr8eZ8sTLLX9jqQdW4v7JASh+EDp1SQ5tv78qJTCW7mDoaZcCjtfQF1x/5bHDBczMzPnbbv++uu5/vrrz3222Wx8/vOf5/Of//x5x371q1+94LjPP//8ufe33XYbt91222v219XVcfLkyddse/xxXWG4MAVjbUhSGnkZGfzyl+GVP4erMc2tSqkmpVSrUuoTF9j/JaXUcf3VrJSaWLEvsGKfKTNMSsYO05q6G6dz8wGylbj3aAGkodPnTxstzme261WSWSJYfk3YxizdcwML4sR3PHY6ZhnJUttBGoOl7KqtCtuYV1blcyiwnUDHC6bMJzAVS7MIcHY0wPxy+FcStuwIlFJ24GvAbUA9cI9S6jVZEyLylyKyV0T2Ag8BP1qxez60T0Tu2Ko94Wakv5NS6WfevfFM1rUoq96Fj2xs3S+Fbcx4ZujMbwEo3vnGsI15RZ2bw7KD5C7LGV8S/xK23lc4FKzndVVbjw+EuLIyh1eC23HMDcFYe9jGjUuWZvDbXPiDiqQtiiUuRDhGvBJoFZF2EVkCvgvceZHj7wG+E4brRoWuV38OQN5lN4VtTGWz0ZW2F8/0MetJaB0Eul6mSwqpr6sJ25ipSQ56sq4gf6ELZreWnh/39GvxgaO2Xez2bqzG1sWoLkjnbLLe2GlFn4hY7JoYUURgeY45knE5bdhtl1YNbfR3GA5H4AF6Vnzu1bedh1KqHKgEfrNis0spdUQpdUgp9cdrXUQp9YB+3BGfzxcGs9dHsP0gk6RRfdnWFUMrWfJcRZGM4utpCeu4cYcIBeMnaE3eSYbLGdahk6teB8BM26Gwjht36PGBQOnrcYbxaVQpRUHFZUyQec4RuFwuRkdHLWewEv8CSJDpQDKpyZcO64oIo6Ojf5CdroNoB4vfBfxARFYucpWLSJ9Sqgr4jVLqlIi0rT5RRB4GHgatZ3F0zAX3xBHaUvey337xdogbpWDnDdD8T/Sc+DUFZXVhHTueCIx3kR0cY7Zwf9jH9uy4Gv9xG6NNvyd99x+Fffx4Yan991r+QG1l2Me+siqPl1q28eaO3+MAvF4vvb29RPNhz/QszsD8GIPiJzNtjKmBS9+2XS4XXq933ZcIhyPoA1amenr1bRfiXcBr0ghFpE//2a6Ueh7YB5znCIxgqKcFjwzR7X1P2Meu3HmAyR+lEex4EfhQ2MePF4bO/BY3kFYTvhhNiF2VJZyVMjJ7rR4RayICfcc4FtzP1WHIH1jNlZW5/DC4ndumDsNkL84s77mMWwudJz7IfOMvuG3qIX7/1zdsqAfEegnHPO8wUKuUqlRKJaHd7M9T/yiltgM5wEsrtuUopZL19/nAGwDTVKHqOapJtAp2vznsYzscDtpTdlE0YdVkvxjTLS8yIy5qd14V9rHTkx10uHZQMHXG6qG7FuMdJC1P0mSvZZc7M+zD7yjJ5LRjl/ahyxJPXJCeV2hJ2kFhhgvPOluzbpQtOwIR8QMPAr8AGoHvicgZpdRnlVIrVUDvAr4rr1382wEcUUqdAJ4DviAipnEEwZ4jTEsKlTsORGT8uZIrKQ32Menrjcj48UDa8KucsdVSmp8ekfHnC/eTInOIL/ayW6NCn/agEijeiyMCahW7TZFRvocFkqD/WNjHj3lmR2CsjRcWq7m8PGfDzZjWS1i+WRF5WkTqRKRaRD6nb/uUiDy54pjPiMgnVp33oohcJiJ79J9bL6MXRrInTtOVXIc9zPGBc+Nvvx6AzmO/ufiBicriDCULbfiy90TsDyCtWgsYj5yNvezWaLDce5QFcZJXGbmaTAeqCmgIlrHc+2rErhGz9B4G4DczFVxevvXicmthlZhYg6XFBSqW25nO3RWxa1TveQPzksRS2+8ido1YZrLtZewEsZWFf1koRM32vUxIGjNt1rLEhVjoPEyDlLOrbP39oTfKVZW5nAxWoQZPaqXBLf5A31EEG6ekkn1lliOIOt2Nr5Ck/DjLIrMsBOBypdCWtI2ssRMRu0YsM9xwEAD3zusido2aogxOUUvK8PnVJhOeYADXyGlOBqvCmj+wmp3uLBqowuGfg9HWiF0nJhk8xUhKOUF7Crs84Y/RhLAcwRqMNWva8pId4akvtBZTOTspW2on4F+O6HViEdX7Cs3iZXtl5Po22G2KoczLKFxoh8XpS5+QSIy04AzM0Zm8jaLM8NR4uhAup/0PM28rTvBaBk/SKOVc5s0i2RGZJWqwHMGaqP5jjJOBu7w2otexe/bhUsv0NVvqodcQDFI0eYrOlF24nJH7AwAQ7wFsCItdloz0Neg35WBJ5Hs2ZJfuZJ4kxHIEf2B2FKb6eHHWw/6yrVd8vRiWI1iD/KkzdLu2oyLcyrBgmxas9DW/EtHrxBpLvlYyZJql4vAnkq0mf5uWo+CzAsavYbH7CDPioqgycnGyEPWleTQEy1nqsQLG5xjUKpGeCpRFNFAMliO4IPMzU5QFupnL3xPxa5XV7GJGUgj0WU9CKxlsehmArKqt9x+4FLuqy2kLluDvtpzxSpa6X+WMVHBZafgTyVZzmSeLk8Eq7EOnrZyOEHq/5oZgeUQDxWA5ggvSdeZF7EpwVUT+JuRwOOhKqiZ74kzErxVLzHYdZUnslG7bF/FrFWQk0+zcTu74SasIYIjAMiljDZwIVnOZJ3KB4hDbizNooBJHwAoYn2PwJOOOAhwZBRGN0YDlCC7IZKv2ZOjdGf6yBhe8XvZOSpfaCVoB43M4h0/TShllBZFdGw0xnbeHzMA4TPZc+uBEYLgRR3CR/tTtW2pUv15cTjtTuZdpH6w4gcbgKZqoZGcEMrpXYzmCC+AYPMYg+RSUbL0F3Hqwe/aRopbobbEkjIBWcXSmicHUWmzrKLkbDlLKtJnHRIcVtAegX/89uCM/IwuRXVrPPMlWwBhgaQ4ZaeaVRa/lCIyiaKaR/tQdUbtewTYtYWqk+eWoXdPMBKYGyJJJFvIiH6QMUVS7n6AoxtstRwCw0HWECUnDU1l/6YPDxC5vLqeD5Sx1WwFjhhtQEuRMoJyd7sgvzVmOYBWT4z68MsBi0e6oXbOsdjez4sJvBYwBGNYVVK6yyMsWQ2wrK6FDipGBU1G7pplZ7jnKqWAlu0ujszQHsMuTxelgJfZhK2AcUgydkQprRmAEPac0CWF65ZVRu6bD4aAzqZqscStgDDDR/ipBUbjrIh+sD5GV4qTTUUXG5NmoXdO0BPykTLTQKOXsjEKgOMSOkkzOUIUjMA8jCd6waeAk8/Z0JpOKKY1A2enVWI5gFTMd2tNo2a7oBIpDTGbvpGypzQoYA2rwJF0UUV1aHNXrTmVto2C5HxYmo3pd0zHWhkOWGE+vI30dHbHChctpZyrHyjAGYPAUrbYqdrizohInsxzBKpwjDfSpIrJyC6N6XZseMO5rteoO5U6dpSe5NqxtEddFsbYcuNib4MtDQ6cBsJVEL0YTIqesXsswHkzg7yAYQIbOcHTRS31J5JeFwHIE55E/28pwSnXUr1tQpwWMfQkeMJb5cQoDg8zmRC9IGSK7Ssti9rUldqmJ+d6TLIudnPKdUb/2Lm8uLUEPi/0J7AhGW1H+eU74y6ISHwDLEbyGhflZvIFeFnKjpxgKUV67m1lJxt+b2FPisTZNMeL0Rj6rezU1VTWMSCYLPYk9K5vvOUmbuKlzR6709Frs8mRxNliGGjJNf6roM6AFihukIiqKIQiTI1BK3aqUalJKtSqlPnGB/fcppXxKqeP66/4V++5VSrXor3vDYc9m6W06il0JSZ7Lon5th9NJp7OGzATPMB5t0Z7GC2qjFygO4c1NpYVyUkYT+ztwjjbSJKVsL8mI+rV3lGTSTCnJiyMwk6AN7IdOEVAOum1eaosi05lvNVt2BEopO/A14DagHrhHKXWhef3jIrJXfz2in5sLfBq4CrgS+LRSKrJFNS7CeIeW0FVQE/lCZxdiKqsOz1InksDNOQL9JxiUHGoqq6J+baUUvrQ6CubbIZCgQfuFSTIWBuh2VFKQnhz1y7ucdiYy9Iq/wwnqkIfP0usoo6o4O2pxsnBc5UqgVUTaRWQJ+C5w5zrPvQX4lYiMicg48Cvg1jDYtCkCA6eYk2Q8ldFfGwWgoJ4M5hjpbzfm+iYgc6KRDkc1aVFUq6xkuXAXSSwT9DUbcn3D0Zdk5nO3R6w96KWwFe96jS2Jhgw30OB3s7MketLdcDgCD7CyQEuvvm0171BKnVRK/UApFeo0st5zUUo9oJQ6opQ64vNFZsqYPtlEj7Mcu8OYm1BGubYuPtiSoNmty/MULXcxmR39GE2IVD2JbbQtMb+D4KCmGEryRC+hcjVebzk+yWR54LRhNhjG4jRqsodTS27qoxQohugFi58CKkRkN9pT/2MbHUBEHhaRAyJyoKCgIOwGSjCIZ7GNyYy6sI+9XjzbLgdgPkGDlVPdp3EQRBUbeBOq2cOiOJnuTExHMN19nAlJw1sWfeVciG3FGTQFS1lKROWQrwmAZimNmmIIwuMI+oCVvQS9+rZziMioiCzqHx8BLl/vudFidKibHKYJFlfXv1EAACAASURBVBq0LATk5OYzQD6OkUbDbDCS4TZNMZVbGb3SEqupLcmmWbzYhhPwaRQIDpzmrJSxPUr69QuxvTiDs1JG8lhz4pWaGNaWw1rEy44ofgfhcASHgVqlVKVSKgl4F/DkygOUUiUrPt4BhO50vwBuVkrl6EHim/VtUWegSVOrpJdHr9rihRh0VZM7m5j12Bf6TrMoTsprjHPGLqed3uQa8qabEq83QTBI2kQzTVJGTWF01CoXojQnlQ5bOY7gAox3GmaHIQw3sqSSUTnlUY2TbdkRiIgfeBDtBt4IfE9EziilPquUukM/7CNKqTNKqRPAR4D79HPHgH9AcyaHgc/q26LObLe2HFO6/fJLHBlZ5rLr8Ph78S8tGGqHETjHztKuvBRkRb62ysWYzd1BRnASpgcMtSPqTHaTFJxjNK024n2iL4bNpljI3a59GEqwmdlwIx2qlNri6AWKIUwxAhF5WkTqRKRaRD6nb/uUiDypv/+kiOwUkT0i8iYRObvi3P8jIjX66z/DYc9mcIw0Mkh+1EtLnGdHyS6cKkB/W+Ktj+bNtjGcUmWYWiVEslvLI5nuPmmoHVFnSJNrBgujn9W9mlTPTgIoZCixJKQy3MjpZTd1UcofCGFlFuvkzbQwaEBpidXkVmlLU6PtiZVhLPPj5AdHWMjeZrQp5FZq6q3RzsQK2i/0nSQoisyy6CdUrqbKXUBnsJjFvgSaEcyNoWYGORv0UlcU3WQ+yxEASwvzeAM9zOUYJ1sMUVq7myWxs9yfQH8AwGiH9vTtLDH+abSqvAyfZOEfSCwd+1z3CbqkkBpvkdGmsK04g7NSigwm0N+BT1soaZZSthVbjiDq9LWewKkCON3GPwm5XCn02L24xhOrLv6ontWdUxH9GkOrKc500aZKSR5vMtqUqGL3NdAkZWwvNk4xFGJ7cSZNwTJcM92wNGu0OdFBVwy1U0pVvrU0FHVG9faERpWWWM1oWg1F821GmxFVlgcamBEXFVXGLw0ppRhNqSJ/vjNxlEP+RTLmeui0l1GS5TLaGnLTkhhwVaGQc0/Kcc/wWeZUGq68UpIc0b01W44A8PdrskVvdfTrr1+I5bwdFMkIs5OjRpsSNZLHmuiwlZFjQH2bC7GYu40UmUcmuo02JTqMtGAjyHx2neHB+hDngtaJEjAebqRNlVJnQA6H5QiA1IlmehylOJxJRpsCgMurLVH1NSVOE++C+XZGUo0P1odIdms3oanuxFBvif7U7SwyPk4WItdTy5wkExxMAEcgggw3cHq5hG1RDhSD5QgAKFjsZCI1+tUu16KoRlMOTXUlhmolMD1MtkyylGv8slCIPD27eTxBlEMzvacJiCKnzDyOYFtJNq3iZmEgATLtZ32o+TGagqVRVwyB5QiYnZ6gRHws59Yabco53KW1TElqwmiofXppiWS3OZbmAKpK3QxILv7BxFAOLfQ30CnFVJfkGW3KObYXZ9AiHtRIAgTt9UBxkwGKIbAcAf16j2Az3YRsdhu9zgoyphKjFHLoqTu/ynjFUIiC9GQ6VCkpE4nxHThHm2kRL7UGlpZYTU1hOq3iJWV+EBamjDYnsgxrS3NdtlLKcqOfWZ/wjmCyS9Ov51cZLx1dyVRGDSVLXQmhWgkMNjAm6VSWVxptyjmUUoymVZM/3wXx3ijIv0TGXDe9jjLyTBKsB63u01S6HjfyxfmswNfItC2T3EIPdlv0g/UJ7wj8Q40sihN3hXnWRgGC+dvIYobx4V6jTYk4qRPNdNnLSXM5jTblNSzn1pHMIhLvhc9GW7ETYC6rxmhLzqdArzkU7xJSXxOt4qXOoByOhHcEKROt9Nk9plEMhUj1ahU4B9viPFgpQtFCO+Np5rsJudzadzAR50H7kGLIbiLFUIgcTzUL4iQwHN+OIOhronG52BDFEFiOgIKFDsbSzKMYClGor5fP9sZ3iv3SWDdpzOPP3260KeeRp9ccmuiK7+Jzs71nCIgiu9R8jqC6KIs2cbPQH8fCidkRbPNjtIrHEMUQJLgjmJuZxC3DLOca15VsLYrdFZpyKM6nxMNtWmmJFI9xPQjWosZbTK/kExiMb/nifP8ZuqWQypJ8o005j9rCBFAO6fGPVnFTZ4BiCBLcEfS36IohExQ6W43NbqPPWUbaVHw3sp/s1mY8BSZSDIXIS0+mw1ZG6mR8K4cco/r6tEFPoxejukBTDqXO9cPijNHmRAbdyfU7y3EbVN4jLI5AKXWrUqpJKdWqlPrEBfZ/VCnVoDevf1YpVb5iX0ApdVx/Pbn63EgyoWeNhpYAzMZkejXFi51GmxFRgsNNjEgmFaWllz7YAMbTqilY6IKA32hTIkNgmczZLrrtZeSlmStOBpCSZGcslOwZr7MCXxMLykV6Qblh5T227AiUUnbga8BtQD1wj1Jq9SP2MeCA3rz+B8A/r9g3LyJ79dcdRBH/YCNL4sBdZb4ZAUAgr45cJpkeGzTalIiROtVKr73U0I5YF8Ofuw0nfmQsTosAjrWfUwyZpcbQauSccih+HUEHHmoMnJGFY0ZwJdAqIu0isgR8F7hz5QEi8pyIzOkfD6E1qTeclIkWeu0enCZTDIVI0VUroaS3uEOEwsUuxtPMkz+wmhRdvTXWFZ9BexnW4h+2QvMF60NkuWtYEgfBofiM1QR9TTT6SwztEx0OR+ABelZ87tW3rcX7gGdWfHYppY4opQ4ppf54rZOUUg/oxx3x+Xxbs1gn36SKoRAFVbsBmO6Oz5uQf2qQDJnBn2Oe8h6rKajQEg0n47T43GzvGa0rWak5Z8UA1UXZtEkJ8/HYKGhxGtt0P61Bt6FZ3VENFiul/gw4APzLis3lInIAeDfwZaXUBUtQisjDInJARA4UFBRs2Zb52WlKgsMsm/gm5C6rZUZcBONUQ+3r0G6uSSXmky2GqPIU0Sv5BIfjc1livv8MPVJAtdvYXt0Xo7Yog1bxoOJxaWhEEyK0iifmZwR9wMpIn1ff9hqUUjcBfwvcISKLoe0i0qf/bAeeB/aFwaZL0td6ApsSkt3mky2GsNtt9DlKSZtqNdqUiDDRpQfrK3YbbMna5KYl0a28pEzG53dgH22mRTzURLlZ+kaoKUynJeglZbYXluYufUIsoTu3Llsp3pzo1xgKEQ5HcBioVUpVKqWSgHcBr1H/KKX2Ad9AcwLDK7bnKKWS9ff5wBuAqMz/QklCuSa+CQFMpFVRuNBptBkRwT90lmlJoazCPH0ILsR4aiV5C3FYcyjgJ3O2k157KQUmqjG0mvRkB6MpFVq3spE4k/L6mvDjwJ5XZUiNoRBbdgQi4gceBH4BNALfE5EzSqnPKqVCKqB/AdKB76+Sie4AjiilTgDPAV8Qkag4Ak0xZMddad4ZAYA/t44Cxpibir9uZckTrXTbvGSmmDNYH2IxpwaXLCKTPZc+OJaY6MIhy8xmmlcxFCIQr8qhkWZ6VAnVxdmGmuEIxyAi8jTw9Kptn1rx/qY1znsRMKTsp2uilX67m4pk8z4JAbjcO6ATBlpOUH35DUabE1byFjo5k3K50WZckqTiHdAHUz1nyMopv/QJMYL4zqIAVWC+zPrVZJRsY7nfjmO4EXO7rI0R9DVx1l9CTYGxS3MJm1mcN9/JWIp5ZYshztW7iTPVisyPkxccYzHbvMH6EDnlWq+K8Tj7Dub6NTlmpte8iqEQ1cXZdEpxfCmH/Iuo8Q5axG1ooBgS1BEsLczjDg6wmG2+iper8VRsi8vqiyMdmiTWUWxe/XqIirIyRiWD5cH4+g5m+xoYlmxKPW6jTbkktUXptIob8cVRjGC0FSVBWoMeag0O1iekI+hvP41dCc4YuAk5nU567V5SJuJLtTKmK4ayy8zTGW4t3Fku2vGSPB5f34EaaaE1aPzT6HqoKdAkpCkz3eBfMtqc8KDHOzqUh4q8NENNSUhHMK5nicbCTQhgLK2KgoUOo80IK4uDWkOgsirz5hCEUEox4qogd74jfjrGiZAx006nzWtYobONkJXqZDi5HJsEYCxOCjGONBNE4c+uIclh7K04IR3Boj7Fd9eYqz3lWixn11AsPhZm46dva9JYM13KTV6mcdrpjbCQXUN6cBpmw5PVbjgzQ7gCM0ynVZpeMRQiEEr+jJfic74mhlQB3qI8oy1JTEfgHG9hgAJS04xpC7dRnMXaU/Nge/yUmsiZ68TnqjDajHVjL9wGwHx/nAQrdT1+IM/8wfoQrhJtKVfiREIqI800BYwtLREiIR1B9mwHwzF0E8ot13IdxuOk8JkszVEQGDJnj9w1yCzVlhFHO+NDObQ4oCmGUtzmVwyFKCvOp1fyWRyIg6B9MICMtNBikhhNwjmCYCCA29/LfKa5s1lX4qm+DL/YWBqKgz8AYKK3ARuCTX/KjgW85TXMiIv5gfiogDnd28C0pFDiNb+EOkRNYQZtQTf+eFDQTfZgCyzSZgLpKCSgIxjqbSVFLaFi6CaUkpJCv62Y5PEWo00JCyN6sbms0tgI1gOU56fRLm6co/EhXwz6mmiTEkNr4G+UmsJ0WsWDa7It9st9jGh/y21BN9UGJ5NBAjoCX7tWYyjDa+7SEqsZcZWTM9dptBlhYb6/kYAoSqpi5ztw2m0MJZeTNRsfipWUyVY6xENZrrGyxY1QlJlMr92LI7AAU71Gm7M19DjHbGY1aclhKfCwJRLOEczpwb6SGnO2p1yL+awaSgJ9BP3LRpuyZeyjLfRShDsvy2hTNsRMRjU5gVFYmDTalK2xOE3Gko+RlArDZYsbQSnFQigJNNYTy0aamVSZ5BeZI5kvdv4XhAnbaDPjZJCTX2y0KRvCXriNJBVgqCv210czZ9sZTCqLGdliiNByYszHanTF0HJO7ATrQziK9CTQGJeQiq+ZlqCb6gJzzMgSzhFkTrcz4Iy9wmEZej2YkVhXrQQDFC33Mpth3s5wa5GuLyeOdsS2ess/pN1Ek2Igs341xSVexiQ95p1xcKSJloCx7SlXknCOoGi5h+kYvAm59aWs+f7YVq3MDbWRhB/JN3/Fy9UUl29nSeznlhdjlaneMyyLnbzS2BFMhAgFjJdiWUI6O4p9fow2MUegGBLMEYz7+slhmmBe7N2EcnLzGSYX+1hsr40O64qhNI/5S0uspqooi04pRsX4ssTy4Fk6pZiqohyjTdkwNYXptAbdOGNZQXeuPaU5pKMQJkeglLpVKdWklGpVSn3iAvuTlVKP6/tfVkpVrNj3SX17k1LqlnDYsxaDrScASPXEThLNSoaSSsmcie2aQzO9ZwAoqIyN8h4rSU1y0OcoI306tr8D50Sr9jRqkpvQRijLTaUTD8lL4zAbo82adEfgSy4nL80cTZm27AiUUnbga8BtQD1wj1Jq9Z32fcC4iNQAXwL+ST+3Hq215U7gVuD/08eLCNP6TaiwMnb06yuZyaimeLknpgufia8Zn2RR6vYYbcqmmEqvIm+5H/yLlz7YjASWyZrrYSiplHQTyBY3itNuYzpDTwaN1ZnZSDNLOEktqDCNYCIcM4IrgVYRaReRJeC7wJ2rjrkTeEx//wPgRqX9Bu4EvisiiyLSAbTq40WEoK+JOUmmyBt7agmAYF4dGcwxPhy7LRNTp9rodZTGlGxxJYHcWuwECY7EaEnqsXbsBJiPofIeq7EV6LGNWO1fPNJMJ26qCs0jnw7HX6MHWHln6tW3XfAYvcfxJJC3znPDRupUO/0OLzZ7xCYdESW0rj7UdsJgSzaJCAWL3Uymxk5Zg9WkuLXvYCxG6z6FCradu5nGINnuSuYkmcBwbM4IAsPNNAdKqC40h3QUYihYrJR6QCl1RCl1xOfbXCngjDv/leVb/yXMlkWPgsrdAMz0xqZqxT81RCYz+HNjp+LlavL1AoBT+jJjrDGt/9/JKI2drO7V1BRl0i4lLMRi28rleWyTXaYKFEN4HEEfULris1ffdsFjlFIOIAsYXee5AIjIwyJyQEQOFBQUbMrQyh372HHFjZs61wyUeCqYlpSYLcM7pCuGkmNQvx6iylNIr+QTjNGn0fn+Bvoll4qSQqNN2TTVBVrbSlssLg2NtqEQ09QYChEOR3AYqFVKVSqlktCCv0+uOuZJ4F79/Z8AvxER0be/S1cVVQK1wCthsCkusdlt9DtKSZtuM9qUTTHZrS2n5FbEnmIoRF56Ml3KQ+pkbH4HtrEWWoMeUz2NbpTqgnRagx5S5vphccZoczaG7ry6bV68OeZpyrRlR6Cv+T8I/AJoBL4nImeUUp9VSt2hH/YokKeUagU+CnxCP/cM8D2gAfg58D9EJLBVm+KZibRKChe6jDZjUywPNTEryZRWxG6gEmA8tZK8he7Yq4ApQuZMBz12L/np5pAtboa0ZAdjKRXah9EYyyfQ21OSV43dZg7FEEBY9GMi8jTw9Kptn1rxfgG4a41zPwd8Lhx2JALLubXkT/2C+alxUjJjKyHINdFKt83LjpTYvQkBLOXUkjz3Y5jsgZwYKlcy1UdycJ6Z9CrTyBY3SyC/DgbRis+59xltzvoZadbbU+YbbclriJlgsYVGcrGWotEfg8qhnPlORlNi6Ma5Bk69+Nx0rAWM9WWJWCzvsZr04jqWxR5z8bLgcBNNgRJqTBQfAMsRxBx5FVoyXGi9PVaQxWkKgz4WYli/HiKnXPsOxmPsOwjVSErzxmZm/Uoqi3PokiIWYqljXDAAoy20BD2my+q2HEGM4anazqI4CAzF0B8AMNat2euIoc5wa1FeVq5VwByMrcJns70NTEoqHk+Z0aZsmVDxOfHF0Hcw0YUtsEireKwZgcXWSE5Kps/uIXkitjJbQ03fM0tj/2nUnZ1COx6SxmPrOwj6mmkVD9WFsdOeci00R+DGNd0F/iWjzVkfejOdNnFTZZI+BCEsRxCDjKZUkDffabQZG2JhoBG/2PBUx2adp5XYbQpfcjk5c7FVfC5tqo12PKaSLW6WvLQk+p1l2CQAYzHSPlSvjTSXVY3Laa7qBpYjiEEWs2soDg7hX5wz2pR14xhtoodiCrNj/2kUYD6rmozgFMyOGG3K+pgfJ90/xmRqpalki5tFKYU/R89Qj5Xic75mxlQ2hYUlRltyHpYjiEEcRduxK2GgPXaClVmzHQwll8e8bDFEqFbPYqw0SBnR9PaxXN5jNckleoZ6jPQvFl8TzQE3tSYLFIPlCGKS7DJteSVmCp/5lyjy9zObGfuKoRAZpdp3MNoZGzLe5UEtWJ9cEnsNgdaivLiAXslncTAGhBMiiO8sLUE3tSaM0ViOIAbxVO8iKIrFGJHOTfc34yCAKoh9/XoId3ktc5IcM61DJ3vOsChO8kvjZ0ZQXaiVmvDHgoJuehDb0jQtYj7pKFiOICbJyMikXxXiHIuN9PrhDu2pOZYrXq6msiCDNnFjH42NZQn/cBPtUkxNkXlq4G+VGr34XPJEu/nLfehxjFYxZ50nyxHEKD5XRcyoVmb7tESm4qo9BlsSPlxOOwNJ5WTNxEbxOddEK23ioTLfXLLFreDJTqHbVoojuACT3Uabc3H0OMZEaiVZKU6DjTkfyxHEKHOZ1ZT4+5CA32hTLoltpIk+ycddmGe0KWFlOrOGnMAILEwabcrFWV4gc6GfEVe56WSLW8FmU8xn6W0rzR4w9p1lRqWRU1R66WMNwHIEMYqtcBvJapnhHpP/AQAZ0+0MOMvjQra4EpWvKYf8QyZXDo22YiPIYhyU91iNI9TbwuQSUhlpojXopsaEgWKwHEHMElKt+NpPGmzJJQgGKF7uYSrUcDyOSNdjHqOd5v4OgsOao7IVx49iKIS72INPMs+posxKcFiTjtYUWY7AIoyU1Gjr7fP95m7XNzfcQTJLcVHxcjUl5TtYFCezJq9COtV9Cr/YyImDYnOrqSlMp0085nYEc2PY53xae0qT1RgKYTmCGCU3N59hcrCZXLUyrM9YUt3xdxOqLs6kTdwok7dMXBxooEuKqHbnGm1K2KkpTKc56MU51gwiRptzYfT/Hy3ipbYoDh2BUipXKfUrpVSL/vO8TilKqb1KqZeUUmeUUieVUnev2PdNpVSHUuq4/tq7FXsSCaUUQ0llZM6Yu87KdJ/2tFxUHbvtKdciNclBn7OMTJMrh5LGmvSbkDmXJbZCeV4arXhx+mdg6oLtzo1H75ngSy4nL82cTZm2OiP4BPCsiNQCz+qfVzMHvEdEdgK3Al9WSmWv2P9XIrJXfx3foj0JxXR6NSXL3eZ9EgJk+Cw+yaLU4zXalIgwnV5N3vIgLM0abcqF8S+SOd/DYFI56clhaUhoKpIcNqYy9CS5YZMG7UeaWSKJtMIK05ZY2aojuBN4TH//GPDHqw8QkWYRadHf9wPDQMEWr2uB1mkqnXnGh8zbwzhtqo0+RylOe3yuQopecygwbNLlodE27ASZz46fjOLV2IpCNYdMGifwNdFBCVVF2Zc+1iC2+tdZJCID+vtBoOhiByulrgSSgJVz6c/pS0ZfUkolX+TcB5RSR5RSR3w+3xbNjg/SdOXQYMsxgy1ZAxGKFruZSIs/xVCIVK+mHBozqXIoOKzdHO1F8acYCuFxe/FJFv5BcwonAkONnA2YM6M4xCUdgVLq10qp0xd43bnyOBERYM01CqVUCfB/gT8XkVA++CeB7cAVQC7w12udLyIPi8gBETlQUGBNKABKarSQymzvKYMtuTCLE32kM0sgjiperqa4YgdLYmem15wFAKe6TxEQRW5Z/JT3WE1tUQZNQS/LAyZUby1MYZ/upSnoNWXV0RCXXDQUkZvW2qeUGlJKlYjIgH6jH17juEzgZ8DfisihFWOHZhOLSqn/BD6+IesTnMJiL6OShTJpu77htlOUAi5P/D6NVhfn0CElJJm0ifriQANjUkSVO76yuldSV5TOS+LldWMHtZpDNhMtQ+r/L5qllD8zsSPY6m/sSeBe/f29wE9WH6CUSgKeAL4lIj9Yta9E/6nQ4gvmfKwyKUop+pPKyZw2Z8vEqR5tppJXsdtgSyJHpstJj6OMdJN+B84xrT2lmZ9Gt0plfhqtlOIIzMNkj9HmvJZhbbmqx1FOSZbLYGPWZquO4AvAm5VSLcBN+meUUgeUUo/ox7wTuA647wIy0f9WSp0CTgH5wD9u0Z6EYzqzBvdyF2LC6ouBobNMSirlZVVGmxJRptKryF0agOV5o015Lf4lsua6GUgqJ8NlvkJn4SLZYWc6Qy+fYbbZ8XAjCyqZlIJK0yqGYB1LQxdDREaBGy+w/Qhwv/7+v4D/WuP8G7ZyfQuQgnrSRn/E6EA7eR5z1ZJJnWii017BnjiULa4kkLcN+1SQoK8Fm9tEs5+xNuwEmMuOv6zu1ThL6qEd7Qm87hajzfkDww20UUq1yct/m2gxzWIzZJRqiVpDrSZTDolQvNDBeLq5nFMkSPVogdjxbnMF7QO6rt4RklfGMd6SEgYkl4DJmtQEhxo4s+xhe7G5k/ksRxDjlNSGlEPmCq8sjPWQziz+vPi/CRVV7mRZ7EybzBFMd58iKIqcsvgr77GauqIMWoIelsykHJodxTbno0m81FmOwCKS5BcUMUwO9hFzrY2GZigp3l0GWxJ5akpy6ZBi1LCJbkLAYn8D3VJIZUmh0aZEnLqidJrFi3O8FYIBo83R0BPcmqWUbSYv72E5ghhHKcVAUiVZ0+aqdzPdrSVYFdXsM9iSyJOdmkSHvYL0SXNlFzvGmmkRj2kLnYWTivw02ijFEViA8U6jzdHQk/kGkiooylwzV9YUWI4gDpjJrMHt70bM8iQEyFAjQ5JNWZzWGFrNZGadVnNocdpoUzQCy2TNdTHgLCczjhVDIZx2G7NZeuKiWZRDww3MqHRyi8pNrRgCyxHEBapwByksMtprnmb2GVMt9DorSHIkyH+xQi1pLmCWMgejbTjwM5cd/8H6EI4SPRYybI6AsQw30ixe6krMvSwEliOIC9LLtHX4oTaTKIeCAYqXOpnMiN/SEqtJL9OC9qMd5vgOgkNavEIVxX+MJkR5cRF9ko/fDMohEWSogQa/x/TxAbAcQVzgqd0PwJxJlEOzQ224WEIK4l8xFKKschvTksJcjzmKz013HccvNrLLEscR1BWlazWH+k3wdzA9gG1xkiYppc5yBBbRIC8vn0HysZukgfdg61EA0ktNlFwVYWqKMmgWL3aTlEJe7DtFm7ip9cRvjaHV1BZl0ChlJE+0gn/JWGP00hLNQcsRWESRweQKsmfNoRya1WsMuRNAMRTC5bTTn1RF7kyLKRoFucYaOStlMbEsES4q8lJpoQKb+I0PGOvJfGNpVeSYtCvZSixHECfMZtXiWe5BAn6jTcHma6RHCvEU5RttSlSZza4jLTgN0wOXPjiSzE+QuTjIoKuGtDgv77ESh93GTI5e6XbQ4OS+4UbGVTbFJR5j7VgnliOIFwrrSVbLDHcZvzSRNd3KQHIFNpu5JXPhxl6ilZpY6DP6JqQtSyzlxW/577VIK6ljgSQYMjZOIMMNNAa9MTMjsxxBnJBdqS3DDLccMdYQ/xIl/l6mM+O/0Nlqcis15dBYu7HKocXeEwCklO4x1A4j2O7OoTFYhr/vhHFGBPyaYihQavrSEiEsRxAnlG/fz7LYWeg18A8AmOhpwEEAW1H817dZTVVZGYOSw5LBqpXprhOMSzql5fFd/vtC1LszaQiWw9Ap42I1oy3YAgucCVZYMwKL6JKelka3zUvKqLEJTcNtxwHILEscxVCIstxUWigjeczgQOXQGc4Gy9hRYu7Sx5FgR4mmHHIsTcFkrzFGDGgS4jNSETPlPbbkCJRSuUqpXymlWvSfOWscF1jRlObJFdsrlVIvK6ValVKP693MLDaJL72Oonljs4sX+k7jFxve2sRzBHabwpdaTf58JxgVtA8GyZxups1WjjcnxRgbDKQww0WfS09kNCpgPHiSJZXEcnYNqUmxEazf6ozgE8CzIlILPKt/vhDzIrJXf92xYvs/AV8SjB1bBgAAGbtJREFUkRpgHHjfFu1JaPz5OymQMWbGBw2zIWnkFJ3KQ2FOpmE2GMlS7nacLMOoQa0rxztICi4wlbUt4YL1IezFOwmijHMEAydoV+VUF2cbc/1NsFVHcCfwmP7+MbS+w+tC71N8AxDqY7yh8y3OJ0Uvc9B/9hXDbCiYaWYwtc70RbYiRZJHmwlNdRsTq5GQWiaBSkusptpTRJcUETTCEYgggyc5ulxKfQzUGAqxVUdQJCIh0fQgULTGcS6l1BGl1CGlVOhmnwdMiEhoDt0LrCm6VUo9oI9xxOfzbdHs+MSz/QoApjqPG3L95clB8mSM+fzEvQkVVe3GLzYmO41RDk13nSAgipyKywy5vhmod2dyJliOv98AZzzRjVqY5Eywgp2e2InRXNIRKKV+rZQ6fYHXnSuPExEB1grTl4vIAeDdwJeVUtUbNVREHhaRAyJyoKCgYKOnJwRFxR6GyMVukIZ64OzLAKSUJk5G8WrqPPm0iOdcwDDaLPSepFOKqfPGfzOatdhRkkljsJykqW5YmIruxQf1QHGwgp3u2FkevWQkQ0RuWmufUmpIKVUiIgNKqRJgeI0x+vSf7Uqp54F9wA+BbKWUQ58VeIG+TfwbLHSUUvQl15A7bUzNockOrcaQW5+ZJCIFGcm8ZK/hTRPHNPlilJfIkkYbaZQyri+OnZtQuKnKT6PFVqF9GDoD5VdH7+IDJwliY9BVhSc7doL1W10aehK4V39/L/CT1QcopXKUUsn6+3zgDUCDPoN4DviTi51vsTFmc3bg8fcQWJqP+rVtQyfpkULKPbGRVh8pprLryQhMwFSUn2sWp8le6GXQVU16ApWWWI3DbmMxT8vyjnrAePAkvXYv1Z6CmIqTbdURfAF4s1KqBbhJ/4xS6oBS6hH9mB3AEaXUCbQb/xdEJCR2/2vgo0qpVrSYwaNbtCfhcXj24FQB+lujHyfInTpLr6sGe4KqVULYvNrS2GL30eheeEj7s1rMTbzSEqsp8lQwTgYyGN0lOhk4ybHlMna6Yyc+AFt0BCIyKiI3ikitiNwkImP69iMicr/+/kURuUxE9ug/H11xfruIXCkiNSJyl4gsbu2fY5FfczkAo62vRvW6wflJSgL9zObsjOp1zUhBzQECohhrja56a6lH+86dpfujel0zUu/O4kygDH9/FB3B7Ahqup9TgfKYig+AlVkcd5TX7GJWkqOumBhq0W9C3r1Rva4Z2VleTIt4CfRFVzk00/4Kw5JNaVnilZZYzY6STE5LJXZfA/ij9Hw5oP3NnZGKxJoRWJiPJKeDLkcl6ePRLXMw1noYgMLaxA0UhyjJctFiryZr/ExU693YB49xIljFLm/sJDJFiu0lmRwP1mALLkcvTqAvQ3XYq6jMT4vONcOE5QjikPHMOjyLrVG9Cf3/7Z15eJXVncc/v5uN7Dtk3xOSkJBAwo4LIFVpldpqp7ad2pYZp7VObTtTa9un29Nl7Mx02tppddxapkOlaFVQsaCIiiiBsAVIIAkQsq8kIQtZ75k/7o1PREIS7hLu+57P89wnec897zm/wwnv9z3nd875WZuO0q5CSEub9spgwyEidIXNI3i0Ey40uqfSgW5C+2qo8s405dESlxLq70NLiH2ast5NJ/I2ldFqmU18XJzH+cm0EBgQNTufYPrpbHTfMQchXRXU+GTg52Pe1SrjscTbpsiG6tzkMLZPS1yMLvCo1SquJCoujTaJhPoDbqlPNZdR5oH+AdBCYEhC0ooBaCx/1y31qeEB4ofP0R2mV6uMMeYw7nCTw3io1vbW65+ip+bGyI8PpXQkDas7RgQXO5GOag6PpGoh0FwbpOUvZVD5cLHGPQ+h8zVHbTEIYs134uhE5CbHUK3i3eYw7jmzn1prNHNTk91SnydQmBjGYWsGlq4a6Gt3bWV2sTmkMj3OUQxaCAxJUEAAp73TCW53z16C1kqb4ERkLHZLfZ5AfJg/lRb3OYx9W45QptKZrx3F71OQGMYRa4btwtWjgtp9WPHihGSQ5SHBaMajhcCgdITlkzRYiRoZcnldw/VH6VH+pGXpPQRj2BzGuQSPnHd9MPu+doIHmqjxm0t0sJ9r6/IgQv196I3MYxQLNLhYCOpKqPFJI2F2NL7envdY9TyLNVPCkrgIf4ZorHK9szK04whV3pkE++uH0Hgk3rbD2OUO4wZb+UNz9B6OS8lOiqGaJJQrRwSjI6iGg5SMZHikfwC0EBiWmNyVALRVvOPSetRgD/FDp+kI1w+hSxlzGHe62GHcX3MAqxJCUotdWo8nsiAxjNKRdJsQWK2uqaTlODLcz7uD6SxIumyQxmseLQQGJSU9h3YV6to3IaCl4j28seKdstSl9XgiucmxVKpErLWuFYKLNfupVnHkpsS5tB5PpDAxnMMqA8tQD3S4KIxrna1/D1qzKE7RQqC5hvDyslAzK5uobtfuqmyv2ANA4vzrXVqPJ5IQ7s9RSw4RnUdcF8NYKfzbyihT6eQleN5qFVeTHRvMCcmyXbjqpaiuhG6faHpnzSEj2jOC1V+KFgID0xe9kMTRegYudLisDu/GA1STQFpCgsvq8FREhM7oRfhZL0Kzi85+6q4nYPg8DQHZhMzycU0dHoyPl4XAuGz6JNB1G8vq9nOELBYmR3hsnGgtBAYmIG0JALXHXeQnsFqJ7z1GfWC+x/4HcDWBmdcB0Fu5xyXlj039qVjzRoWbjMKkCA6PprlmmvRCI3TX8lZ/GkUe6h8ALQSGJiV/JVYl9FS5ZodxT0MFwaqX4Ti9m3Ui5s2dS411Dr1VrhGC/so36VN+hKdrR/FEFCaFcdCaCa0n4GKXcwt/3z+QSZGH+gfAQSEQkQgReU1Equw/P/QvISKrROTIuM/AWAB7EfmjiJwd951eeuJEoqOjqbEk4Nfqmt2tjcd2AxCZo/0DE5EfH8ohsglpOeCSVSvq7NscsGaTn6zjeE9EYWIY74zmIcoKNU4W5LoShsWPU5JKYaLnbuZzdETwELBLKZUJ7LJffwCl1G6lVKFSqhBYDfQDO8dl+dbY90op94fVMjjNwXkk9JW7ZHfrcM0+zqsg5uZq/Z4IX28LLRFFBIx2Q3ulcwvvaSao5wylMo88DzzWwF3Eh/lTGzCPAYs/nH7DuYXXlVDlk0VmbAQBvp574KKjQrAe2Gj/fSPw8Uny3wm8qpTqd7BezRQZiV1IGD101Dk/PkHE+cNU+eYSqJ2UV8QvdQUAA6ed/DZaY/P99MQu98jdrO5CRMhPiuKQ5MHp3c4reLAX1VTG3oE0ipI9d1oIHBeCOUqpsf3zzcCcSfJ/GnjmkrSfiUiZiPxqLMi9xnlEZNuclY1Hdzm13JGeNuJG6rkQpcMiTkZmznxaVRjdJ992arkXK3dzQfkTl63PeJqMouRwdgzkQudZOH/WOYWefQuxDvPGSJ7xhUBEXheR45f5rB+fTymlgAnnH0QkFsgHdoxL/g6QDSwCIrAFs5/o/ntFpFREStva2iYzW2MnK28xbSoM5eQhccMx20PNP325U8s1IguTIzhgzca/qcSp5Y6eeZsSaw5LMyZ7/9KszIhijzXfdnHGSaOCyh0MeQVSap3rsRvJxphUCOxB6fMu89kKtNgf8GMP+tYrFPUp4AWl1PC4spuUjUHgD8CErzZKqceVUsVKqeLoaO0Ymyq+Pl5UBRWT1OVcZ+WFqr0MKy9S569wWplGJdDPm/qQQkKGWqCr1jmFdjcQ1FfLYa88jz3fxp3Miwuhc1YSnd6zneMnUAqqXuOEfxHRoUHEhnp2VDhHp4a2AffYf78H2HqFvHdzybTQOBERbP6F4w7ao7kMw6mrCOMCzZXOO+ogqGkfpyxpxEVHOq1MIyPJtpHT8Nm9zinQvvrlYtxyvL20f2AyLBZheWY0b1vzUWffBuuoYwU2H4OeRl4ZyKcoJcI5Rs4gjv4FPQysFZEq4Cb7NSJSLCJPjmUSkRQgEXjrkvs3icgx4BgQBfzUQXs0lyGp+FYAmg9td0p5o73tJA+UUx+5QodFnCJJOcVcUAF0lTtnWqL/1G46VRAJOdo/MFWuy4jitYFcZKAbGh1cUl1lm+He2juPxameLwQOrXdSSnUAay6TXgr8w7jrGiD+MvlWO1K/ZmqkJKdRJcnMqnOOs7J2/0ukogiYd6tTyjMDi1Kj2GPN48Zzu2xTdBbH3sHU2T2UWHNYlq6nSafKiowofmGdh0KQ029AggOb8Cp30hacS9tAGKvmen4f6DGlCRARGiOWknbxGKODfQ6XN3BiO+0qhILFq5xgnTmIDPLjaNB1BA61Ox4kpbOGwIsNHPXOJzvG86JhzRSJEQGERsZwzjfTsWWkfR1Qf4C31AKyY4JJCA9wnpEzhBYCk+A7dy2+jFBz6DXHChodIeH8uxz3X0xooF7tOx38c9cxpLwYLHvRoXLU6TcBGEpYoc94miYrM6PYOZiLqt8P/eevrpDTuwDFps4cVmXPdqp9M4UWApOQtWgtg8qHC8d3TJ75CnSc2kuw6mUwba2TLDMPNxSk8551HsPl2xza6T145DnOWueQklPkROvMwcqMaF4YWoJYR+DYs1dXSOUOBv0iOTKawhotBBpPIjI8jHKfeUS2OLZqpaV0K8PKi7QltznJMvNQmBDGuz7LCOqrg9byqyukpwXf+r1ssy5nWUaUcw00AcvSIzlFMi2B2XD4T9MvYHQEql/n6KxFhAb4eWxEskvRQmAiOmNXkjRyjr72uqsuI7h+N8e8cshI0tGwpovFIkjOOqxKGD6x7eoKOfECFqwcCVlDuocGQZlJQv19KEgM40VZbVsC2jjN481OvQIDXfy5p4Abs6LxMsjUnBYCExE+/xYAat57/qruH+g4R+LQGVpjrtfLRq+S5QXzOKQyGSi70pabiRk6uoVyazILipbqPrhKrsuI4tGOQpSXHxz+v+ndvO9RBoMS2dafz+oc4+zo1kJgIuYVLuc0Cfif2HxV99fusz28wgs+5kyzTMXStEjetCwmuKsCOmumd3NnDb5NB9k2uozbC/SI7Gq5rSCOLhXE6ajVcGwLDA9M7cbGI1D7HnsjP4lYvLgh0/OXjY6hhcBE+Pp4cSbhDtIGyuk6dxWxjE+9Sr2KpmDBEucbZxJ8vS30p9n2X4yWvzy9m4//FYDq2TeTEhXobNNMQ+acYAoSw3iidwUMdMPJKfZDyWPgG8TvupdRlBxOaIBxTt3VQmAyUtdsYFh5Ubfr8WndN9ReQ/qFfZSF3cQsDz53/VqgeEERFdYkBko3TWv10OCRZym1ZrGsSIeldJRPFSewpSOFoaCEqTmNe1rg2HN0z72Lg82jhlktNIYWApORkZpKqd8SEuu2okaGpnzfub/9GqUg/IavuNA6c3BDVjQb1ToCO8uh8m9Tu6m1Ar+OCl4eXcbH5se61kATcFtBHL7e3uwJuhnOvAn1B698Q+nTYB3m6ZGb8fWy8ImFCW6x011oITAhA/mfIUx1c27f1JzGarCX2NNb2OOzjCWF811snfEJ9POmJ+sT1DOb0d3/NqVRgdr3GKNYaE68lTkhs9xgpbEJmeXDLXkx/KB5JSokHp7/RxjsvXzmoT4ofYrhtLU8flxYXxhHdLCxNlNqITAhRWvupEWFM7B/4+SZgdrdTxOk+hgs+ie9k9VJfHlVNo8Mr8er+ShU7bxy5qajcGgjG0c+wqqiee4x0ATcVZRIw4Af7xb8HM6fgR3f/XCm0WHYcg/0tfNKyN9xcXiUDdelut9YF6OFwISEBPhTFrWOzO73uNhRf+XMVit+B5/gOOlcv3qdeww0AfkJoXRmfJIGoq88KlAKtj9Ir1cov+cubpmnp4WcxfL0SOLD/HmsJhZWPACHNkLFOMex1QovfgWqX2Pko7/i4fIIVmREkh1jvPgPWghMStTKDQhQt/XHV8zXVvYqMcO1nEn/HAF+xlklcS1w35psfju8Hq+mw1D9+uUzHXsW6vbxk4G7+PyqAkOtVJlpLBbhk0UJvFPdTnn2/RAzH7Z+FV76OpQ8Di99zfbvv+aHvOLzEZovDLBhpfFGA6CFwLQUFCzklcBPkFW7hbaDE2xuso7Sv+s/aFVhFK3b4F4DTcCCpHCaU++gkWis2x+E9uoPZhjsQe38PqcsGZSE3Mq916fNjKEG5ovLU4gK8uMbz1Uw+PEnIXY+nHgBXv2WbTXRsvtRK77OU++cJS06kBuzjLVaaAwtBCbFYhEWfPGXnFTJ+L78z4x0N30wg1I0/fk+knsOsytmA/GRoTNjqMG5/6ZcHhj8CkO95+GJVXByu21K4uQrsPF2pLeZhy7+Pd+/LY9ZPl4zba7hCA/05d/vnM+plh5+ecgK97wE366Bb56EL++Fj/yUJ9+poay+my+tSDWsj8whIRCRu0TkhIhYRWTCKA8icouInBKRahF5aFx6qoiU2NP/IiK+jtijmR4J0eE0rP4tftZ+Gv74pQ/MUze/+H1iqzfzjN9drPvCd2bQSmNTnBKBX/pKbun/CednJcDmu+GRAtj8GUZ72/iuuo+wrOWsyTHmm+i1wKq5s/nMkiSe2HOGkjMdIAIhsRCTx6b9tfxsewUfnR/L3YuTZtpUlyHKgeNwRSQHsAL/A/yrPTLZpXm8gEpgLVAPHADuVkqVi8gW4Hml1GYReQw4qpR6dLJ6i4uLVWmpg8E9NO+z5fc/5FOtv6YtMIvRqBwsPn7Mrt7Cy95rWfy1PzE7xLMDc1/rdPYNcf8zhyitbmJTwovM9zrHzuA7+NHpLC4Mwc5vXK93EruYvsER1j2yh5FRxZdWppIfH0pNex/ffr6MVXNn89jnivD19vwJFBE5qJT60Eu7Q0IwrvA3mVgIlgE/UkrdbL8ee718GGgDYpRSI5fmuxJaCJxLd/8Qz//3t0jvOUi6pZF46WCnrCD7vs0kRRtvhcS1yMiolZ9vP8nTe88CtpfSm3LmcN+N6YY56vha50hdF1/ddIiGrovvpy1Pj+TpLywyzLTcRELgjrMC4oHx5x7XA0uASKBLKTUyLv1DcY3HEJF7gXsBkpKMO0SbCUIDfPnig7+hu3+YytYe3mvuZElWLIkRnh+Cz1Pw9rLwg9tyKUgM5XhDN59dkqxHAW6mMDGMvQ+tprVngOMN3bRcGOT2gjjDiMCVmFQIROR1IOYyX31PKXV1Z+leBUqpx4HHwTYicFe9ZiI0wIdFKREsSomYaVNMy/rCeNYXTvg+pHEDs4NnsTrbXLu3JxUCpdRNDtbRACSOu06wp3UAYSLibR8VjKVrNBqNxo24w/txAMi0rxDyBT4NbFM258Ru4E57vnsAt40wNBqNRmPD0eWjd4hIPbAMeEVEdtjT40RkO4D9bf9+YAdQAWxRSp2wF/Ft4JsiUo3NZ/CUI/ZoNBqNZvo4ZdWQu9GrhjQajWb6TLRqyPMXxmo0Go3GIbQQaDQajcnRQqDRaDQmRwuBRqPRmByPdBaLSBtw7ipvjwLanWiOp2DGdpuxzWDOdus2T41kpVT0pYkeKQSOICKll/OaGx0zttuMbQZztlu32TH01JBGo9GYHC0EGo1GY3LMKASPz7QBM4QZ223GNoM5263b7ACm8xFoNBqN5oOYcUSg0Wg0mnFoIdBoNBqTYyohEJFbROSUiFSLyEMzbY8rEJFEEdktIuUickJEHrCnR4jIayJSZf9puPiHIuIlIodF5GX7daqIlNj7+y/2Y9ANhYiEichzInJSRCpEZJnR+1pEvmH/2z4uIs+IyCwj9rWIPC0irSJyfFzaZftWbDxib3+ZiCycTl2mEQIR8QJ+B9wK5AJ3i0juzFrlEkaAf1FK5QJLga/a2/kQsEsplQnssl8bjQewHXU+xi+AXymlMoBOYMOMWOVafgP8TSmVDRRga79h+1pE4oGvAcVKqTzAC1uMEyP29R+BWy5Jm6hvbwUy7Z97gUenU5FphABYDFQrpc4opYaAzcD6GbbJ6SilmpRSh+y/92B7MMRja+tGe7aNwMdnxkLXICIJwEeBJ+3XAqwGnrNnMWKbQ4HrscfxUEoNKaW6MHhfY4us6C8i3kAA0IQB+1op9TZw/pLkifp2PfC/ysY+bNEfY6dal5mEIB6oG3ddb08zLCKSAiwASoA5Sqkm+1fNwJwZMstV/Bp4ELDaryOBLntgJDBmf6cCbcAf7FNiT4pIIAbua6VUA/CfQC02AegGDmL8vh5jor516PlmJiEwFSISBPwV+LpS6sL47+xhQg2zblhEPga0KqUOzrQtbsYbWAg8qpRaAPRxyTSQAfs6HNvbbyoQBwTy4ekTU+DMvjWTEDQAieOuE+xphkNEfLCJwCal1PP25JaxoaL9Z+tM2ecCVgC3i0gNtim/1djmzsPs0wdgzP6uB+qVUiX26+ewCYOR+/om4KxSqk0pNQw8j63/jd7XY0zUtw4938wkBAeATPvqAl9sDqZtM2yT07HPjT8FVCil/mvcV9uAe+y/3wNsdbdtrkIp9R2lVIJSKgVbv76hlPossBu4057NUG0GUEo1A3UiMteetAYox8B9jW1KaKmIBNj/1sfabOi+HsdEfbsN+Lx99dBSoHvcFNLkKKVM8wHWAZXAaeB7M22Pi9q4EttwsQw4Yv+swzZnvguoAl4HImbaVhe1/0bgZfvvacB+oBp4FvCbaftc0N5CoNTe3y8C4Ubva+DHwEngOPAnwM+IfQ08g80PMoxt9Ldhor4FBNuqyNPAMWyrqqZclz5iQqPRaEyOmaaGNBqNRnMZtBBoNBqNydFCoNFoNCZHC4FGo9GYHC0EGo1GY3K0EGg0Go3J0UKg0Wg0Juf/ATtIkBSA1BVhAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}