TensorFlow_Introduction.ipynb

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        "[View in Colaboratory](https://colab.research.google.com/github/pkraison/ex.ai/blob/master/TensorFlow_Introduction.ipynb)"
      ]
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      "source": [
        "#Introducing Tensorflow\n",
        "[Tensorflow](https://www.tensorflow.org/).\n",
        "\n",
        "If you're running this notebook outside the course environment, you'll need to install tensorflow:\n",
        "* `pip install tensorflow` should install cpu-only TF on Linux & Mac OS\n",
        "* If you want GPU support from offset, see [TF install page](https://www.tensorflow.org/install/)"
      ]
    },
    {
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        "id": "KPl-OSINzCbz",
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      "cell_type": "code",
      "source": [
        "import sys"
      ],
      "execution_count": 0,
      "outputs": []
    },
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        },
        "outputId": "0325d797-9014-4fdd-b70c-8cfca8475390"
      },
      "cell_type": "code",
      "source": [
        "! killall tensorboard\n",
        "import os\n",
        "os.system(\"tensorboard --logdir=/tmp/tboard --port=7007 &\");"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/bin/sh: 1: killall: not found\r\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
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        "outputId": "35151af9-b1a2-4be6-bf26-d3f057d7a1d9"
      },
      "cell_type": "code",
      "source": [
        "import tensorflow as tf\n",
        "sess = tf.InteractiveSession()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/tensorflow/python/client/session.py:1714: UserWarning: An interactive session is already active. This can cause out-of-memory errors in some cases. You must explicitly call `InteractiveSession.close()` to release resources held by the other session(s).\n",
            "  warnings.warn('An interactive session is already active. This can '\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "RucwdmvozrCq",
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      "cell_type": "markdown",
      "source": [
        "If you run the notebook locally, you should be able to access TensorBoard on http://127.0.0.1:7007/"
      ]
    },
    {
      "metadata": {
        "id": "d_bl7vO8z3dk",
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      "cell_type": "markdown",
      "source": [
        "let's implement a python function that computes the sum of squares of numbers from 0 to N-1."
      ]
    },
    {
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        "id": "AYCH8ub_ziTU",
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      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "def sum_sin(N):\n",
        "    return np.sum(np.arange(N)**2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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      "cell_type": "code",
      "source": [
        "%%time\n",
        "sum_sin(10**8)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "CPU times: user 524 ms, sys: 1.1 s, total: 1.63 s\n",
            "Wall time: 1.63 s\n"
          ],
          "name": "stdout"
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          "execution_count": 9
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      "source": [
        "now we use TensorFlow for the same computation"
      ]
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      "source": [
        "# An integer parameter\n",
        "N = tf.placeholder('int64', name=\"input_to_your_function\")\n",
        "\n",
        "# A recipe on how to produce the same result\n",
        "result = tf.reduce_sum(tf.range(N)**2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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        },
        "outputId": "4cd53abd-6ba2-4052-b7f8-e563d4368e58"
      },
      "cell_type": "code",
      "source": [
        "%%time\n",
        "result.eval({N: 10**8})"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "CPU times: user 421 ms, sys: 0 ns, total: 421 ms\n",
            "Wall time: 278 ms\n"
          ],
          "name": "stdout"
        },
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      "source": [
        "now we'll write the graph and see the visualization in tensorboard"
      ]
    },
    {
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        "id": "WSuPNX5U0omJ",
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        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "writer = tf.summary.FileWriter(\"/tmp/tboard\", graph=s.graph)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
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      "cell_type": "markdown",
      "source": [
        "# How does it work?\n",
        "1. Define placeholders where you'll send inputs\n",
        "2. Make symbolic graph: a recipe for mathematical transformation of those placeholders\n",
        "3. Compute outputs of your graph with particular values for each placeholder\n",
        "  * `output.eval({placeholder:value})`\n",
        "  * `s.run(output, {placeholder:value})`\n",
        "\n",
        "So far there are two main entities: \"placeholder\" and \"transformation\"\n",
        "* Both can be numbers, vectors, matrices, tensors, etc.\n",
        "* Both can be int32/64, floats, booleans (uint8) of various size.\n",
        "\n",
        "* You can define new transformations as an arbitrary operation on placeholders and other transformations\n",
        " * `tf.reduce_sum(tf.arange(N)**2)` are 3 sequential transformations of placeholder `N`\n",
        " * There's a tensorflow symbolic version for every numpy function\n",
        "   * `a+b, a/b, a**b, ...` behave just like in numpy\n",
        "   * `np.mean` -> `tf.reduce_mean`\n",
        "   * `np.arange` -> `tf.range`\n",
        "   * `np.cumsum` -> `tf.cumsum`\n",
        "   * If if you can't find the op you need, see the [docs](https://www.tensorflow.org/api_docs/python).\n",
        "   \n",
        "`tf.contrib` has many high-level features, may be worth a look."
      ]
    },
    {
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      "source": [
        "with tf.name_scope(\"Placeholders_examples\"):\n",
        "    # Default placeholder that can be arbitrary float32\n",
        "    # scalar, vertor, matrix, etc.\n",
        "    arbitrary_input = tf.placeholder('float32')\n",
        "\n",
        "    # Input vector of arbitrary length\n",
        "    input_vector = tf.placeholder('float32', shape=(None,))\n",
        "\n",
        "    # Input vector that _must_ have 10 elements and integer type\n",
        "    fixed_vector = tf.placeholder('int32', shape=(10,))\n",
        "\n",
        "    # Matrix of arbitrary n_rows and 15 columns\n",
        "    # (e.g. a minibatch your data table)\n",
        "    input_matrix = tf.placeholder('float32', shape=(None, 15))\n",
        "    \n",
        "    # You can generally use None whenever you don't need a specific shape\n",
        "    input1 = tf.placeholder('float64', shape=(None, 100, None))\n",
        "    input2 = tf.placeholder('int32', shape=(None, None, 3, 224, 224))\n",
        "\n",
        "    # elementwise multiplication\n",
        "    double_the_vector = input_vector*2\n",
        "\n",
        "    # elementwise cosine\n",
        "    elementwise_cosine = tf.cos(input_vector)\n",
        "\n",
        "    # difference between squared vector and vector itself plus one\n",
        "    vector_squares = input_vector**2 - input_vector + 1"
      ],
      "execution_count": 0,
      "outputs": []
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      "cell_type": "code",
      "source": [
        "my_vector =  tf.placeholder('float32', shape=(None,), name=\"VECTOR_1\")\n",
        "my_vector2 = tf.placeholder('float32', shape=(None,))\n",
        "my_transformation = my_vector * my_vector2 / (tf.sin(my_vector) + 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "kIaQ_Jk71XWk",
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        },
        "outputId": "81737aa7-4a46-4b29-bf70-aa60c4754687"
      },
      "cell_type": "code",
      "source": [
        "print(my_transformation)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Tensor(\"truediv:0\", shape=(?,), dtype=float32)\n"
          ],
          "name": "stdout"
        }
      ]
    },
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        "outputId": "675ee856-e642-4d76-d6e1-eda90c84d783"
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      "cell_type": "code",
      "source": [
        "dummy = np.arange(5).astype('float32')\n",
        "print(dummy)\n",
        "my_transformation.eval({my_vector:dummy, my_vector2:dummy[::-1]})"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0. 1. 2. 3. 4.]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.       , 1.6291324, 2.0950115, 2.6289961, 0.       ],\n",
              "      dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "metadata": {
        "id": "1nqDRCHR1kLY",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "writer.add_graph(my_transformation.graph)\n",
        "writer.flush()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "BXFZsNRr1tq-",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "TensorBoard allows writing scalars, images, audio, histogram. You can read more on tensorboard usage [here](https://www.tensorflow.org/get_started/graph_viz)."
      ]
    },
    {
      "metadata": {
        "id": "ruLqA7Lj16Yz",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Summary\n",
        "* Tensorflow is based on computation graphs\n",
        "* The graphs consist of placehlders and transformations"
      ]
    },
    {
      "metadata": {
        "id": "5xIRBlky2Ai8",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Mean squared error\n",
        "\n",
        "Your assignment is to implement mean squared error in tensorflow."
      ]
    },
    {
      "metadata": {
        "id": "ptdHYhcS1qkp",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "with tf.name_scope(\"MSE\"):\n",
        "    y_true = tf.placeholder(\"float32\", shape=(None,), name=\"y_true\")\n",
        "    y_predicted = tf.placeholder(\"float32\", shape=(None,), name=\"y_predicted\")\n",
        "    # Your code goes here\n",
        "    # You want to use tf.reduce_mean\n",
        "    # mse = tf.<...>\n",
        "    mse = tf.reduce_mean((y_true-y_predicted)**2)\n",
        "def compute_mse(vector1, vector2):\n",
        "    return mse.eval({y_true: vector1, y_predicted: vector2})"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "avKMdTb61pWo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "writer.add_graph(mse.graph)\n",
        "writer.flush()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "mPNrivug2S0n",
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      "cell_type": "markdown",
      "source": [
        "# Variables\n",
        "\n",
        "The inputs and transformations have no value outside function call. This isn't too comfortable if you want your model to have parameters (e.g. network weights) that are always present, but can change their value over time.\n",
        "\n",
        "Tensorflow solves this with `tf.Variable` objects.\n",
        "* You can assign variable a value at any time in your graph\n",
        "* Unlike placeholders, there's no need to explicitly pass values to variables when `s.run(...)`-ing\n",
        "* You can use variables the same way you use transformations \n",
        " "
      ]
    },
    {
      "metadata": {
        "id": "J-vN3eXd2JOf",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Creating a shared variable\n",
        "shared_vector_1 = tf.Variable(initial_value=np.ones(5),\n",
        "                              name=\"example_variable\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "haPlRdbj2Y_s",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Initialize variable(s) with initial values\n",
        "s.run(tf.global_variables_initializer())\n",
        "\n",
        "# Evaluating shared variable (outside symbolicd graph)\n",
        "print(\"Initial value\", s.run(shared_vector_1))\n",
        "\n",
        "# Within symbolic graph you use them just\n",
        "# as any other inout or transformation, not \"get value\" needed"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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          "height": 34
        },
        "outputId": "341fa2b4-b1dc-44e9-c8d2-ff6a03e17718"
      },
      "cell_type": "code",
      "source": [
        "# Setting a new value\n",
        "s.run(shared_vector_1.assign(np.arange(5)))\n",
        "\n",
        "# Getting that new value\n",
        "print(\"New value\", s.run(shared_vector_1))"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "New value [0. 1. 2. 3. 4.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "lCbPsTRW28om",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# tf.gradients \n",
        "* Tensorflow can compute derivatives and gradients automatically using the computation graph\n",
        "* True to its name it can manage matrix derivatives\n",
        "* Gradients are computed as a product of elementary derivatives via the chain rule:\n",
        "\n",
        "$$ {\\partial f(g(x)) \\over \\partial x} = {\\partial f(g(x)) \\over \\partial g(x)}\\cdot {\\partial g(x) \\over \\partial x} $$\n",
        "\n",
        "It can get you the derivative of any graph as long as it knows how to differentiate elementary operations"
      ]
    },
    {
      "metadata": {
        "id": "Fnj_CwOF2szL",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "my_scalar = tf.placeholder('float32')\n",
        "\n",
        "scalar_squared = my_scalar**2\n",
        "\n",
        "# A derivative of scalar_squared by my_scalar\n",
        "derivative = tf.gradients(scalar_squared, [my_scalar, ])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "kUDnW8KG3D90",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "7c0147fa-4d66-44f4-ae0a-f8212ded100a"
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "x = np.linspace(-3, 3)\n",
        "x_squared, x_squared_der = s.run([scalar_squared, derivative[0]],\n",
        "                                 {my_scalar:x})\n",
        "\n",
        "plt.plot(x, x_squared,label=\"$x^2$\")\n",
        "plt.plot(x, x_squared_der, label=r\"$\\frac{dx^2}{dx}$\")\n",
        "plt.legend();"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/Kn/eqXI0p4ovLhlFfKT1N3iIO9Nh6mRv6SH2lhyk09xFoEcAyxIWMytq2l11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\ngg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f4a24766b00>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "cdRTAsC_3Nqo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "my_vector = tf.placeholder('float32', [None])\n",
        "# Compute the gradient of the next weird function over my_scalar and my_vector\n",
        "# Warning! Trying to understand the meaning of that function may result in permanent brain damage\n",
        "weird_psychotic_function = tf.reduce_mean(\n",
        "    (my_vector+my_scalar)**(1+tf.nn.moments(my_vector,[0])[1]) + \n",
        "    1./ tf.atan(my_scalar))/(my_scalar**2 + 1) + 0.01*tf.sin(\n",
        "    2*my_scalar**1.5)*(tf.reduce_sum(my_vector)* my_scalar**2\n",
        "                      )*tf.exp((my_scalar-4)**2)/(\n",
        "    1+tf.exp((my_scalar-4)**2))*(1.-(tf.exp(-(my_scalar-4)**2)\n",
        "                                    )/(1+tf.exp(-(my_scalar-4)**2)))**2\n",
        "\n",
        "der_by_scalar = tf.gradients(weird_psychotic_function, my_scalar)\n",
        "der_by_vector = tf.gradients(weird_psychotic_function, my_vector)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "n81_jxGt3YOR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "141c7e36-3d92-4c37-d5e8-d0424d469760"
      },
      "cell_type": "code",
      "source": [
        "# Plotting the derivative\n",
        "scalar_space = np.linspace(1, 7, 100)\n",
        "\n",
        "y = [s.run(weird_psychotic_function, {my_scalar:x, my_vector:[1, 2, 3]})\n",
        "     for x in scalar_space]\n",
        "\n",
        "plt.plot(scalar_space, y, label='function')\n",
        "\n",
        "y_der_by_scalar = [s.run(der_by_scalar,\n",
        "                         {my_scalar:x, my_vector:[1, 2, 3]})\n",
        "                   for x in scalar_space]\n",
        "\n",
        "plt.plot(scalar_space, y_der_by_scalar, label='derivative')\n",
        "plt.grid()\n",
        "plt.legend();"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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tsaDWnP5RORiK0D8YYCCWv/f6QwRCYQLBaKXO8ENljEZlaD3AYjJiNUdn8zaL\nCYvZgNVsxGoxYjUbJ1ylE45E8PrDeGNrC/3eAJ7BIP2xWXDfQIDe+P88fupb+4iMcwKOokRbTdgs\npqExGo3R9Y+IDpHYrNofDOELhPH6w4TCYYxFxzBVHcRgi5bORQI2Ip5iTFhxmGzg7GEwrw1jXjf2\neUe4oeoWaotmYbeZMMXWWMIRHY83iMcbpLPXR0NbP42xMtsNW5rZsKUZp83E+UvLWbuyksqSxDf+\ntA4cIxgJjZl6eWVHC398/gCRCPzDVeqYC4fF9ujvSZeve9TGYJecVUl9ay9v7G3jzxsO8NGrFiY0\n1qHql3E6NB5s7uHNfW3MLncPlSqPxJFAp8aLVlTwxBtHeHFbC1e9qwa3Y+zZujfLHRpBgrpII7PJ\nQFGejaKR14lzxmgw4LIbEu7tE9F1PIPBWKD30zcQoG8gSN9AYCiYDviC+AJhfIEQA77gUCopHNYx\nGBQMSjQA2yxGXHYzeaUeBot24zN3oGCg2ryQpQUrWFpaS2mB/aTUSbevh9db3+KZIy/ycPMf+Hj+\nB1jhWHrSGJ02MzMKYd7MfM5dFO2IGApH2N/YzfaDHWzdf3wowM+vyufSs6pYrZaO+wZZ13sEgDn5\ns097LhgK84fnDvDqrqM4bSY+ff0Sls4pHvN+w2fqo1EUhY9etZDm9gFe3tHK/Kp83r10/Pr4RGbq\nkYjOn54/CMAHL18w5qerEz3VR+/UaDYZec+7ZvHnFw7y/JYm1l80b9RrIfu91EGCuhCnMShKNOXi\ntFDNxErRPMEBHj30JG8e3QLAqrLlXD/3akodowfDQlsB1869kll51fx675/4v92/532113Fx9YVj\nfi+T0cDSOcUsnVPMBy6tZcfBDjbubGXv4S4ONfdS6LZy8apK1qyYSf4o+eDRziTd39DNnzYcpLnd\nQ80MF3feuIySgvF7mRTbTszUx2I1G7lj/TK+8eu3+f1zB5hXmc+McXaf9gc8mA2mMbffv7S9hYa2\nfs5fUs78cUonh+fUx3LRypk8+WYDG7Y0c+W5NTjHWMvI9lF2kIGgrqrq3cB5RJevPqdp2uZ0f48z\nkT8coNPbRTASxG6yYTfZcZjsKfW8mCwieoQWzzGa+ptp7G/h2EAbvpAPX9hPMBLCYbLjsrjIs7iY\n6Synyl1Jjbtywm1Ws0HXdTa3beeRg4/jCQ5Q5ZrJreqNSR3gvKxkMV8863bu2/kbHj74d8ocJSwp\nTiw1YTIahlpTt3UP8sKWZl7bfZS/bqznsdcOs3xeMWtWzGTJ7KKTcth1PUdwmZ2U2UuAaF35I6/U\ns+NQtNTvohUz+eBltQkfQhNXPbpNAAAgAElEQVSfqXd5xw7qAGUFdj56pcovH9/HLx7by1c/snrM\nTxb9AQ8us2vUxe1ej5+/bqzHbjUltMU/nvMfr6e61WzkqnNrePClQzy/uYkb1swd9dpsH2UHaQ7q\nqqquBWo1TTtfVdVFwK+B89P5Pc4Euq5zbPA4ezv3s69To9VzbCh/OJzFYGZu/mxqC+exqKiWGnfV\npC8t1HWdxv5mtrTtYGvbDnpPOcPSarRgM1oxGUx0+XpoHTh22j3KHWUsKl7AoqIFLCiYl7WeGok6\nPtjOA9rf2N99EIvBzI3zr+HiqgtTegOudldy+4qP88Mt9/K7fQ/w1XO/QL41ufzWjEIHH7x8ATde\nNJdNe46xcWcr2w92sP1gB2aTgXkz81hQXYDZ7qfb38NM81x+/6zG3iNdtPdEg9KCqnxuvbR21D0Y\no3GZnZgN5nFn6nHnLSln7+EuXt9zjEc31o+6GKnrOp6ghwrn6C0CHnzpEF5/iA9fsWDUTybDJTpT\nB7h4VSVPv9XA81uaueKc6lErj3yx6pepnH65FPgbgKZp76iqWqiqap6maX3jvE4QnXm8eXQLr7e+\nRbv3RNlgia2ISlctxfZCrEYrvpAPb8hH22A7+7sPsr/7II/XP0ONu5K1VRewumzFpAt0ET3Czva9\nPNvw4lCzKIfJznnlZzMnv4YadxUVrnLMhpN/JYOREH3+Ppo9R2nqb6Ghv4lD3fW81PQaLzW9htVo\nYWnxIlaVLWdJsZr0tvZ0CoSDPN/4Ms81vEQoEmJJ8UJuXXADxfbkN9YMV+2u5Ib51/Dwwb/zu30P\ncMfKT2BQkl88tltNXLq6ikvOqqShrZ8397axv6EbrbGH/Y09GIuOYpkPDXUm6o61YrcaWVVbwgXL\nKlhVW5LShEFRFIpthWPm1E/1wcsXcLCll6ffamThrEKWzT09VeWPfZob7VPb/oZu3tjbxqxyN+sS\n3AHqjM3Ux8qpx1kt0dn6Qy/X8fyWZq6/cM6I13mz3HYX0h/Uy4Gtw/7eHntMgvoYWjxHea7hJbYf\n301YD2M2mGJBaiGLi1Tyx+hC1x/wcLCnni3HtrOrYx+/f+dB/lb3FNfOuYLzK87JeXpG13W2Hd/J\nk4c30DZ4HAWFlaXLOK9iNYuKFmAyjP0raDaYKLYXUWwvYkXpEiAa6A/3HmFP5352Ht/D1uM72Xp8\nJ1ajheUlSzh7xkoWFtWOe+90iegRNh/bzuP1z9Lt7yHfksfNC65nZenStH1yWld1AVr3QXZ3vMOG\nhle4YvbFKd9LURRml+cNbcCJtqDuZWP7cd4ZhKuWrWDF5QuYXeFOS5vpIlshxwaP4w35EkpD2K0m\nPnP9Er7z+23872N7+dpHV1NRfHIFT7xFwEhnk3r9If7fsxoK8NEr1YQbhyUzUwe4+KxKnn6rkec3\nN3H52dU4bKf/vp0oaZy6M/VTTe5cQI4d7m3gmSMvsqfzHSCaVriw8jzeVX7WiDW9I3FbXJxVtpyz\nypbT6e1iY8sbbGx5gz9rf+Xl5tdZP/9aFhermfwxRtXY18xDB/9Ofe8RDIqB8yrO5oqadcxwlk3o\nvmaDiQWF81lQOJ8b511Ds6eVbcd3sbVtJ5vbtrO5bTsOk52VpUtZPWMltQVzM/LmFo6E2dmxl2eP\nvEizpxWTwcTlNeu4cvYlac+hKorChxfewnfevpvHDz/LitIlE/53jIu2oC7h6a7jGBUj161cmdZP\nekXDyhorE+z6OLs8j49fvZD/e2IfP3l4F1/7h7NPWpA8sZv05KAe0XX+7/F9tHUNcuW51UmlixxJ\nzNQhukP8ynOreeSVejZsbeK9F5w+W58OJY2tRGfmcTOBo2n+HlPe4d5Gnjz8HO90HQBgbv5srpp9\nCYuL1AnN7IrtRdw4/xouqV7DE/XP8cbRzfxs569YWbqMmxe8lwJres5cHI8nOMBjh57mjaOb0dFZ\nUbqUG+ddM2bFR6oURaHaXUm1u5L3zr2KI31NbG3bwbbjO9l0dDObjm7GaXKwpGQhy0uWsLCodsL/\ngfX6+9ncto1XmjcN5YrPmXEW1829cqguOxNcFie3qDfwf7t/x6N1T/GZ5R9L27394QDNnlZmuavS\nnrobXgGTaFAHOH9pOc0dHp5+s5H7/raHL9yyYuiTQ7yc8dTDN/726mF2HOpg0axCblo3drnhqWxG\nKwbFkPBMHeCSs6p4Zths/dSNTSdy6lM3qD8HfBP4haqqZwGtmqb1j/OaM8aRvkaeOryBvZ37AVhQ\nOJ/3zL6U2sLkfvnGk2/N40OLbmJd9QU8oD3Kjvbd7O86wHXzruKiyvNTyscmIqJHePPoVv5W9yQD\nwUFmOsu5qfa9qEWpHS6QLEVRmJNfw5z8GtbXXktdzxG2Hd/Jro59vH1sG28f24aCQo27ivmFc5ib\nN4sK5wxK7MVjzuS9IS+tnjbqe4+wq2Mvh3sb0dExG8ysqTyfi6suSNuseTwrSpYwL38Ouzv2caD7\nEAsK0/Nv29DXRESPMHeE+vSJSqRWfTTvu2geRzsG2XGog3sf2c1t1y3GaTMPNfPKs5xITW7ef5wn\nNh2htMDG7TcsTTp1pCgKDtPInRpHY7eauOLcGh7dWM9TbzbwvlM6P3pjbxBTNv2iadomVVW3qqq6\nCYgAd6Tz/lNVfW8DTx1+fmhmXlswl2vmXJ72YH6qSlcFnz/rM7zRuplH657ioQOP8dbRrbxfvZFZ\nedVp/V6N/c08dCCaarEYLayffy3rqi7IWU7foBioLZxLbeFcbllwA039Lezq2IvWfYiGvmYa+pt4\nIXatSTFSZC/EYXLgMNkxG0z4wn784QC9/j66/T1D91VQmF8wh+WlS3hX+eqhxbVsURSF99Vey/e3\n/JRHDj7Bl8/557S8SdePUp+eDsVJlDWeyhDrqPizR3ezs66Tb/5mM7ffsJS+oQ6NLgZ9IR577TAv\nbG3GajHyz+9bnvIh8g6TnYFQYumXuMvPrmLjjhaeeauRcxfNOOkgDV/Yj8VgPu2/gz31neQ5LdTM\nSP7UpvGkPaeuadpX0n3PqSiiR9jT8Q4bGjdS13sYiAbz98y5nAUZDubDGRQDF1S+i2Wli/nrwSfY\n3LadH2y5lzWV53PN3MtxmSd2dmR/wMPj9c+yqfVtdHRWli7jptrrKIwdZTYZKIpCTV4VNXlVXMuV\nBMIB6nsbaOpv4ehAG0cH2ujyddPp7Sash4deZ1KMOM0OFhbWUumqoMo9k8VFasbO20zUrLxqzi0/\ni7ePbeOtY9s4v+LsCd/z8Bg7SSeqKMENSKOxW0188ZaV/P31wzz++hG++4etlC45AjbYsreHX+x4\ng77BIGUFdj7+noVUTuDgDYfZQZev+7SukmOxWUx85MqF3PPQTn7z1Dv8x0dXD31KGGlxeO/hLu5+\ncCcra0v47PuWpzzW0ciO0jTzBAZ4+9hWXm19k+OD0Q0bi4oWcOWsS6gtHH2TQqblWdx8bMkHOL/i\nHB448CgbWzbx9rGtXFK9hktq1iRdctUX6OfFxlfZ2LIJfzhAhXMGN9W+l4VFibUkzSWL0cLCotrT\nxqrrOoFIkFAkhNVoyVr1TCreO/cqth/fxeN1z7C6bPmESjkjeoT63gZKbEVjVlqlym1xYTKYUkq/\nxBkMCjesmcv8qnx+89R+OgZ6Mdngpc0dWHCw/qK5XHlu9YSPjnSY7IT0MIFIEGsS/6bL5xVz/pIZ\nvLG3jec3N3PVu2qA6I7S4Z/mej1+/u/xvRgMCte+e/aExjqayftbO4UEwkHe6TrA1rYd7GzfQ0gP\nY1KMnFdxNpdWX5T0GYqZpBbN59/P/QKvtrzBc0de4qkjG3i5+XXOKT+Lc2asZHZezagzlHAkzKGe\nw2xr38VbR7cQjITIs7h579yrWVN5Xs7LJydKURSsRktS/zHnSqGtgIur1/Bcw0tsbHmDy2rWpnyv\nYwPHGQx5WVqyKI0jPMGgGCiyFaQ8Ux9u6ZxifvhP7+burbup64M7rlvN3IoCCt3pyVkP7/+S7O9B\n9CCNLv72aj0ra0soL3LgC/mG9ilEdJ37n9hH32CQWy+Zn/RGrkRJUE+Bruu0ezs42FPPO50H2Nu5\nn0Ak2j613FHGBTPP5dzy1Tn/mD4as8HEJdVreHfFuWxs3sQLTRt5pfl1Xml+nWJbITXuKkrsxRTZ\nCghEgtG8sq8HrfvQUGVAobWAK2ZdzPkVZ0+6jU5nistq1rKx+Q2eb3iZC2eel/KuxZ3te4HoJ8pM\nKbIWcnywA384MOE3TUVRGAwP4DDZWb1gRppGGDW8U2MhyaUQ3Q4LH7p8Af/72F7++3db+PCV8wnp\nYexGGxFd54nXj7D3SDfL5xVzxTnpXdMaToL6OHwhP12+bo4PttPsOUqL5ygNfU30Bk7spyq1F7Oy\ndBmrypZNia36cTaTlStmX8ylNRfxTtcBtrTtZHfHXra37x7x+gJrPmfPWMWK0iUZq/0WiXOaHVxS\ns4anDj/PxuZNKW9I2tm+G6NiZGlxZmbqcHJevcI58UDcH/DgtqQ/VeRMoFPjWM5dNIMBX4gHXjjI\nL57cif0saO8K8aWfvU6PJ0Ch28onrlmU0RhxRgR1Xdfxhf14Q168IR++kB9fOPqnP+zHF/IxGPLh\nDXkZCA7SH/DQH/TQ6+/DExw47X7xDT+1BXNZUDiPGY6yKRPIR2I0GFlasoilJYuI6BH6Ax7avZ10\n+bqxGq3kW93kW/IosOZP6Z9zOrqk+kJeanqNDY2vsKbq/KRr8Du8nTR5WllcrA6lHjIhHtS7fT0T\nDuoRPcJAcJDyDJSRxneVDiRRq36qi1dVsrCmgJ8//RZdQFtHAHMwwprlFQn1YJ+oKR/Uw5EwHb4u\nOrxddHo76fR10+vvozfQT18sKA+GvET0xE6/ibMZreRZ3VS7Kym2FVJiL6bSVUGla2ZGFpMmC4Ni\nIN+aF2saNXI/CzF52E12Lqu5iMfrn+Xlpte5es6lSb1+R/seAFaVLsvE8IYUxaqhun0941w5voHg\nIDr6iC0CJurErtKJneJVUezk49fO50fbYNXcCm676cIJH/aSqCkZ1AeDgzxy6Aka+5o5PthOaFgZ\n2nBOkwOXxUmZowSHyY7d5MBusmIz2bAZh/9pxWGyYzPZcZrtuM0uyROLKWNd1QW82PQqLzRtZG3V\n+Qm3mADYcXw3CgrLShZncIRQaIvuZu7yTzyoJ3OMXbJO9H9JLf0yXCAS3U06q6QoawEdpmhQ7/T1\n8NbRrZiNZipdMyl3llFqL6HYXkiJvYgCaz5ui/u0jn9CTEc2k40rZl3Mo4ee5OkjL/C+2usSel23\nr4fDfY0sKJiX8R71hdYT6ZeJ6ou1a3ZlIqinaaYOJxqDZbNFAEzRoF7tnsmP1n4bs8GUsS3vQkwl\nayvfzcbmTbzSvIk1ledT5igZ9zXxqpeVZZlNvQAUxGbq6QjqnmG7SdPtRE594jP1eIsARxbb7gJM\n2YhoNVokoAsRYzaauWH+NYT1MI/VPZXQa3bEqpziLY0zyWwwkWdxpyf9EiteyMSni/hGIW8aZuq5\n6NAIUzioCyFOtqp0GXPzZ7GjfQ8Hu+vHvLY/4OFQz2Hm5s/KWvfOQlsBPb6epIsWTpWNnPp4R9ol\nIv7GkM0DMkCCuhDThqIorJ8fzaf/9dDjYwbPx+ufQUdnddnKbA2PImsBIT08dMBFqjIZ1M1GM2aD\nKan2u6OJn0+ayVLRkUhQF2IamZNfw9kzVtLY38Lj9c+OeM07XQd4vfVtKl0VXFj5rqyNLd7krds/\nsXYBQwdkZCCnDtFdpaluPhpuMCjpFyFEGtxcez1l9hKea3iJl5tfP+k5X8jHH995GINi4MOLbs5q\n07KhoO7rndB9PAEPRsWYsWDpMNvTM1MPSfpFCJEGLouTO1behtvi4uEDf2f78RNtHx6te4pufw9X\n1Kyjxl2V1XEVWeNBfYIz9YAHt8WVsd3NDpMDb8g34dy/N+RFQcl6g7gpWdIohBhbib2IO1Z8gru3\n3cev9/4R234rET2CL+ynwjmDq+ZclvUxxWfqE62A6Q96KLOPX7KZKofZjo6OL+RLaiPXqbwhHzaT\nLetVehLUhZimqt2VfGb5x3j00FOEIiGMigGH2cH7aq/Lyca84f1fUhUIB/CHAxlp5hXnjHVqHAh6\nJxTUB0NeHFnOp0Mag7qqqh8Dvg3UxR56XtO0/07X/YUQyVtQOJ8vn/PPuR4GAC6zE5PBRNcEgnom\nK1/ihnqqhwaB1A9L94V8lNjTf9j6eNL9dv2ApmlfSvM9hRDTgKIoFFrzTzrzNVm9sRYBeZmcqZvj\nM/XUK2DCkTC+sD/rlS8gC6VCiCwqtBXSH/AQDAdTen2PP1o5k8kNU86h/i+pB3VfONrMK9stAiD9\nM/W1qqo+A5iBL2matj3N9xdCTGFDFTD+3oT605yqJ5a6ifeSyYT46UeeCfR/yVU5I6QY1FVVvQ24\n7ZSH/wx8Q9O0J1VVPR/4HZD5TkFCiCmjcFhf9VSCendspl44yWfqg0NBfYoslGqadj9w/xjPv6Gq\naqmqqkZN00Zudi6EOOMUTbCssdcfPUYyeohLZqQjp+7LUTMvSGNOXVXVf1NV9QOxr5cC7RLQhRDD\nxWfqPSlWwHT7ezEohiwtlKa+q3QwHtSz3PcF0ptT/xPwe1VVPxO77yfSeG8hxDRQGMupp1rW2OPv\nJd+Sl9ENPfGc+kAo9cZjuerQCGkM6pqmNQOpHWcuhDgjnGjqlXxQj+gRev191Lgr0z2sk1iNFkyK\ncUKnH504IGMKp1+EEGI8VqMFp9mR0kzdExwgrIcz3v9dURQcZgcDwdRn6kPplxzM1CWoCyGyqsha\nQLevG13Xk3pdT6y7YybLGeOcZkdaZupTeqFUCCESUWgrJBAJJn0OaHcWNh7FOUwOBkPelDs1emWm\nLoQ4UwyvVU9GbxaDusvsQEcfCs7Jir9OcupCiGmvJNatscPbldTrsjpTHyprTC2vHk+/2CSoCyGm\nu9LYTtJ2b0dSr+vJwm7SuInWqg+GvNiM2e+lDhLUhRBZVhprR9s+2JnU63qysJs07kRP9VRn6r6c\nLJKCBHUhRJYV24pQUFKYqffgNruycq7qUP+XFM8q9Ya8Q33Zs02CuhAiq8xGMwXW/KRy6rqu0+Pr\nzUo5IwzPqSff/yWiR/CF/NiMMlMXQpwhSu3FdPt7CCTYV90b8hKIBCnIQuoFJtbUyx/2o6PjMEtQ\nF0KcIUod0bx6py+x2Xo8n14Q6x2TaRMJ6oPB3NWogwR1IUQOlNpjFTCDieXVs1nOCMODevILpbk8\nIAMkqAshciB+IHO7N7EKmJ5YA7BspV/inRpTWSjNZTMvkKAuhMiB0mSDui+7M3WL0YzZYE5xpi7p\nFyHEGSY+U+9IeKYezalnY+NRnNPsSGnzkQR1IcQZx2aykmdxJ5xTj+8mzc96UE9hoTSHHRphAodk\nqKq6FngI+EdN056IPbYCuA/QgV2apt2ellEKIaadUnsx9b0NhCKhcTcU9fh7sZts2EzWLI0uuqu0\nJXyUcCSM0WBM+HW5bLsLKc7UVVWdB3wReP2Up+4BPqdp2gVAvqqqV09wfEKIaarEXoyOTpeve9xr\ne/y9WcunxzlS3FV6okPj1Eq/HAXWA73xB1RVtQBzNE3bHHvoceCyiQ1PCDFdDZU1jpNX94cDDIa8\nWQ/qqdaqD+a4pDGl9IumaYMAqqoOf7gEGP6WexyoSHlkQohpLb4Babyg3pPlGvW4VIO6L75QmqMd\npeMGdVVVbwNuO+Xhr2ua9uw4L1VSHpUQYtqLlzV2jNOtMd4jJn64RracaOqV7Ew9FtRz1Ptl3KCu\nadr9wP0J3KsdKB7290qgNcVxCSGmuRO16mNXwDT3twBQ5cruB//4BiRPkjN1b8iL1WhJanE1ndJW\n0qhpWhDYr6rqhbGH1gPPpOv+QojpxWF24DQ5xk2/NHmic8MqV2U2hjVkaKaebFAPenOWT4fUq1+u\nUVX1ZeAq4Luqqj4Xe+rzsb+/DtRpmrYhPcMUQkxHJY5iOrxdYx7w3NzfgsNkpyhH6Zdkc+q5PCAD\nUl8ofRJ4coTH9wFrJjooIcSZodReTENfE92+HortRac97w35aPd2sqBwPoqS3WW6oaCeRE5d13W8\nYR8zTGWZGta4ZEepECJn4mWNx0fZWdriOQpAtWtm1sYU5zAlP1P3hwNE9EjOmnmBBHUhRA7NyqsC\noK738IjPN8UXSd3ZD+rO2HF0yeTUc912FySoCyFyaH7BHBQUDnTXjfh8c390kbTGnd1FUgCTwYTV\naElqpn6imZfM1IUQZyC7yU61u5IjfU0EwoHTnm/ytGAxmClzlOZgdOA0O5MK6p6gZ+h1uSJBXQiR\nUwsK5xHWw9T1Hjnp8WAkxNGBNipdFRiU3IQqp8me1EJpXyAa1PMsrkwNaVwS1IUQObWgcB7AaSmY\nowPHiOgRqnKQeolzmp0EwgGCkVBC1/fHgrrb4s7ksMYkQV0IkVPz8mdjUAwcPCWox/Ppuah8iXMk\nuVjaF+gHwC0zdSHEmcpmsjHLXUVDf/NQMyyAplhQz0XlS1w8N55oXr1f0i9CCAG1hfOI6JGT8urN\nnhYMioGZzvKcjcsZK01MPKjLTF0IIU7Lq0f0CM2eo5Q7yjAbzTkbl9sazY3H0yrj6Q8MYDKYsOWo\nQyNIUBdCTALz8mdjVIxDQb3Fc5RAOEB1DhdJAQoseQD0BvoSur4v0I/b7Mp6S4PhUj6jVAgh0sVi\ntDA7r5r63gb+vP8R3jy2FYD5BXNzOq48azSo9/nHn6nruk5/0EOlM7dnA8lMXQgxKSwonIeOzmut\nb5FvyeMD6nrOq1id0zHlx2bqPf7xZ+q+sI9QJJTTfDrITF0IMUlcMPNdHB/sYGnJIlaXrcjZIRPD\n5cVy6omkXybDxiOQoC6EmCQKbQX849IP5XoYJzEbTLjMTnoTmKnHyxldOQ7qkn4RQogx5FvzEgrq\n8QqZvBzuJgUJ6kIIMaZ8Sx6+sA9fyD/mdZ6hFgFTNP2iqupa4CHgHzVNeyL22MuAExiIXfYvmqZt\nnegghRAiV/LjFTCBPmym0btFTumcuqqq84AvAq+P8PTHNU3bM6FRCSHEJJEfS6f0+vvGbAF8Yjfp\n1Ey/HAXWA71pHIsQQkw68Zn6eHn1/qmcftE0bRBAVdWRnv6WqqolwDvA5zVN86Y+PCGEyK2hoD5O\nq4C+gAeDYsCRw6PsIIGgrqrqbcBtpzz8dU3Tnh3h8h8DuzRNq1NV9T7gDuCHEx+mEELkRuIz9X7c\nZmfODvSIGzeoa5p2P3B/IjfTNO3RYX99HLg1xXEJIcSkkJ9g/5e+oIcye0k2hjSmtG0+UlVVAZ4H\nbtI0rQdYB8iCqRBiSsuzuFFQxpyp+8MBAuFAzvPpkOJCqaqq18TKF68Cvquq6nOapunAL4EXVFXd\nCFQDP0vbSIUQIgeMBiMuy9i7Sk8cjpHbyhdIfaH0SeDJER5/EHhwooMSQojJpMCSR5u3A13XR2yr\nOxkOx4iTHaVCCDGOPGsegXAAX3jkXaV9k6ScESSoCyHEuIYWS0dJwQzN1M0S1IUQYtIbr6xxMuXU\nJagLIcQ4TmxAGjmoS/pFCCGmkIJxZ+qTo+8LSFAXQohxjbcBqT/oQUHBZXZkc1gjkqAuhBDjSCSn\n7jQ7JsURfBLUhRBiHG6La8xdpX0Bz6TIp4MEdSGEGJdBMZBncY0Y1IOREN6Qd1Lk00GCuhBCJCTf\nmkdvoA9d10963DNJTjyKk6AuhBAJyLfmDc3Kh+ubRC0CQIK6EEIkJF4B03NKCqbd2wlAgTU/62Ma\niQR1IYRIwIkDqE8+AelQz2EA5uXPzvaQRiRBXQghElBiLwagqb/lpMcP9tRjMZipcVflYlinkaAu\nhBAJWFhUC8C+Tm3osf6Ah2MDbczNnz0patRBgroQQiQkz+Kmxl1FXe8RvCEfAHW9RwCYXzAnhyM7\nWUqHZKiqagJ+BcyL3eNLmqa9pqrqCuA+QCd6APXtaRupEELk2JJilcb+ZrTuQ6wsXcqh7npgcgX1\nVGfqHwEGNE27EPgEcFfs8XuAz2madgGQr6rq1WkYoxBCTApLihcCsK9zPwCHeuoxKUZm59Xkclgn\nSTWo/wH4YuzrdqBYVVULMEfTtM2xxx8HLpvg+IQQYtKYlVeN0+xgb6fGYNBLs+cos/JqMBvNuR7a\nkFTPKA0CwdhfPw/8CSgBuodddhyomNDohBBiEjEoBhYVLWBL2w5ea3kTHZ3awrm5HtZJxg3qqqre\nBtx2ysNf1zTtWVVV7wDOAq4DSk+55vTTWYUQYopbUryQLW07eK7xZWBy5dMhgaCuadr9wP2nPq6q\n6ieIBvMbNE0LqqraDhQPu6QSaE3XQIUQYjJYXKSioOANeTEoBubkzcr1kE6SUk5dVdW5wGeA9Zqm\n+WAoJbNfVdULY5etB55JyyiFEGKScFmczMqrBqDGXYXNZM3xiE6WUk6daDqmGHhKVdX4Y1cQza//\nQlVVA/CWpmkbJj5EIYSYXBYXqxzpa5x0qRcA5dQ2ktnU3t6fu28uhBAp6vH38oD2N26c/x7KHKcu\nJ2Zeaal71DVLCepCCDHFjBXUpU2AEEJMIxLUhRBiGpGgLoQQ04gEdSGEmEYkqAshxDQiQV0IIaYR\nCepCCDGNSFAXQohpJKebj4QQQqSXzNSFEGIakaAuhBDTiAR1IYSYRiSoCyHENCJBXQghphEJ6kII\nMY1IUBdCiGkk1ePsckpV1aXAY8Ddmqbdm+vxTISqqt8H1hD9/+K7mqb9NcdDSomqqg7gt8AMwAZ8\nW9O0J3I6qAlQVdUO7CH6c/w2x8NJiaqq64CHgL2xh3ZrmvbZ3I1oYlRV/RDwb0AI+E9N057M8ZBS\noqrqJ4CPDHvobE3TXOm6/5QL6qqqOoGfAi/keiwTparqxcBSTdPOV1W1GNgOTMmgDlwHbNE07fuq\nqs4CngembFAHvgZ05fPrPJQAAAJ4SURBVHoQafCKpmk35XoQExX77+PrwGrABXwTmJJBXdO0XwG/\nAlBVdS1wSzrvP+WCOuAH3gN8OdcDSYONwNuxr3sAp6qqRk3TwjkcU0o0TXtg2F+rgeZcjWWiVFVd\nCCxmigaNaeoyYIOmaf1AP/CpHI8nXf4T+FA6bzjlgrqmaSEgpKpqrocyYbHgPRD76yeAp6ZiQB9O\nVdVNQBVwba7HMgE/Au4E/iHXA0mDxaqq/h0oAr6padrzuR5QimYDjtjPUgh8Q9O0Kf1pXVXVc4Am\nTdOOpfO+slA6Caiqej3RoH5nrscyUZqmvRt4L/AHVVVHPRx3slJV9aPAG5qmHc71WNLgINE0xfVE\n36B+paqqJbdDSpkCFAPrgY8Bv5mKv1+nuI3oOlRaTbmZ+nSjquqVwH8AV2ma1pvr8aRKVdXVwHFN\n05o0TduhqqoJKAWO53hoyboGmKuq6rVEP3H4VVVt1jRtQ47HlTRN01qAeFqsTlXVY0AlMBXfsNqA\nTbFP6nWqqvYzNX+/hlsHpH3hWoJ6Dqmqmg/8ALhM07Spvih3ETAL+LyqqjOILmZ15HZIydM07db4\n16qqfgM4MhUDOgxVi1RomvZDVVXLiVYmteR4WKl6DvitqqrfI5p+mZK/X3Gqqs4EPJqmBdJ97ykX\n1GMzwh8RzbEFVVW9CVg/RYPirUAJ8OCwNYKPaprWmLshpex/iX68fxWwA3domhbJ8ZjOdH8H/hRL\n71mA2zMRRLJB07QWVVUfBt6MPfTZKf77VUGGPmVIP3UhhJhGZKFUCCGmEQnqQggxjUhQF0KIaUSC\nuhBCTCMS1IUQYhqRoC6EENOIBHUhhJhG/j9OpOATjLiNfwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f4a018b06a0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "YefmYpKn3tJQ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#optimizers\n",
        "\n",
        "While you can perform gradient descent by hand with automatic grads from above, tensorflow also has some optimization methods implemented for you. Recall momentum & rmsprop?"
      ]
    },
    {
      "metadata": {
        "id": "XFvrzJG73c82",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "y_guess = tf.Variable(np.zeros(2, dtype='float32'))\n",
        "y_true = tf.range(1, 3, dtype='float32')\n",
        "loss = tf.reduce_mean((y_guess - y_true + tf.random_normal([2]))**2) \n",
        "#loss = tf.reduce_mean((y_guess - y_true)**2) \n",
        "optimizer = tf.train.MomentumOptimizer(0.01, 0.5).minimize(\n",
        "    loss, var_list=y_guess)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "4uqceKBq3zzG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "outputId": "caf534fb-a8a2-477c-b71f-449778557bbc"
      },
      "cell_type": "code",
      "source": [
        "from matplotlib import animation, rc\n",
        "from IPython.display import HTML\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "y_true_value = s.run(y_true)\n",
        "level_x = np.arange(0, 2, 0.02)\n",
        "level_y = np.arange(0, 3, 0.02)\n",
        "X, Y = np.meshgrid(level_x, level_y)\n",
        "Z = (X - y_true_value[0])**2 + (Y - y_true_value[1])**2\n",
        "ax.set_xlim(-0.02, 2)\n",
        "ax.set_ylim(-0.02, 3)\n",
        "s.run(tf.global_variables_initializer())\n",
        "ax.scatter(*s.run(y_true), c='red')\n",
        "contour = ax.contour(X, Y, Z, 10)\n",
        "ax.clabel(contour, inline=1, fontsize=10)\n",
        "line, = ax.plot([], [], lw=2)\n",
        "\n",
        "def init():\n",
        "    line.set_data([], [])\n",
        "    return (line,)\n",
        "\n",
        "guesses = [s.run(y_guess)]\n",
        "\n",
        "def animate(i):\n",
        "    s.run(optimizer)\n",
        "    guesses.append(s.run(y_guess))\n",
        "    line.set_data(*zip(*guesses))\n",
        "    return (line,)\n",
        "\n",
        "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
        "                               frames=400, interval=20, blit=True)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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eGcDNXDvlF/3hUFj6S0t1NK2Qp72iohQ0Glbqxul0RqXOyAHhyZCuHGHsnp9R\nWFjlCUMh+ppW7jo7ksHApd8fo2kqS0t1TLNK2ayoeBMURWS+yQBtpzMsvWWfd+Wct9hDgQVfunZk\nnZ2y+/MBRiOf/f3RxIVbUVFxOtJQsiwdzwvodIYl99nDpN/+fLJyDlJgwYeD/vx5EH3PC9jbExdr\no2GxuFirgrkVFSdgWTrLy3V0XWM49OYgGwdkRo70259XVs5BCi74otcLQyVZjLj8/nyAMIzY2xuk\nZRhWVioXT0XFQWSphIWFGnEM+/sjBgN31s2aCpoWo2lC7C/ClSMpvOCDKK4WBEL0DWM+RD+Oodsd\n0e+PURQxQavVsqt8/YoKwDQ1lpcb2LaB74fs7Q3mZl1aVRVifxFB2oPoF/aX3pEoUghDcaIMI8b3\n4SJP1HkxGvl4XkirZWPbBoah0e+7c3NxV1S8CYqi0Gxa2LZBHMcMBm7JSyVMoqrCbx/H4PsXK/ZQ\nIsEH6eeaP9EX6WVDajWTRsNkcbGG5wX0+2PCsPyjmYqKs2DbBo2Ghaoq+H6YFiKcF2Yt9lAywQeF\nMIR5FH0QSyV6nk+zaWOaOsvLDUYjn+HQnYMgVUXF0RiGRrNpoesaURTT74/nbB3aOPXZz1LsoXSC\nD0L0FeJY9JaGERMEF5PSdBGEoZg5aJo6zaZFvW5i23pSpmGeboKKy46mqTQaFpYlZEjWnyp/umWe\n4og9lFLwBSKQmy0UEIbZylnzgOcF7O4G1Gom9bpJs2lTq5kMBi6uW/n3K8qLqiqp0CuKgucFDAZu\n6WfMHkZok0y9vOgA7VGcSfDb7faHwG8A/8BxnH904L3HwAYQJi/9tOM4m1Ns47FEUVZOWYh+fK6F\nh2bBaOQxHvvU6ya1msHCQo0wFMu3jceVxV9RHjRNpV43U6EPgpDBwMXzwtM/XDqE90FRiiP2cAbB\nb7fbDeAfAr99wmFfcBynP7VWvQFxLCx9XRfDJkURLp4inNxpIbMVRiMvcfEYtFo29bqZdggVFUVF\n14XQm2Ym9MOhN7cjVUWZnEFbJCP0LHn4LvDjwPNzbstbE8cKvp+tmCV61nnyAwpEQMtld3fAcOih\nqgrNps3KShOgqsRZUShMU9iTy8sNLEssLL6/P2JvbzinYh+jaVEyV0hY9WGoUhSxB1DiM6Z/tNvt\nnwO2j3Hp/GvgbrL/W47jHPulQRDGun4+s0rjOMZ1XVxXzMazbRvTNKvSBRUVFedKFEUMh0PCMERV\nVer1Opo2dZ17ZyGbRtD2Z4HfAnaBfwb8FPDrxx28tzeceL6+3mJrqzeFZmQoioKux4zHY4bD8Tv7\nz86jjdNmfb2F74fpwulhGDHPsjtbAAAgAElEQVQe+4zHfqGyHspyLoveRihWO01Tw7aN1G0TRXEa\neypKG0/iXc6lmDmbuXA8L2Y8Hp7+wTdkfb31zt/xzoLvOM4vy8ftdvvLwHdyguBfBMLFQxohn7fU\nzePodIbouoptG1iWmMRSr5v4fsh47ON5QZXPXzE1dF3FsgwsS0/XeJDXmowrzXdF2MmUyyBQksVL\niqsz7yT47XZ7Efg14Ccdx/GAH2LGYp8hgrmqKlI3DWM+s3gOIhdQ7/ddLEunVhNWl2nqicsroN93\nOYsrzzDERJh5mu1Y8W5ompKKvHTNRlHMaCTmiVyWayUfmC1SFs5pnCVL53PA30f46P12u/1XgH8O\nfMtxnC8lVv3vttvtEfA1CiP4IBdFj6Isi0dVZc6+eH+ecd0A1w1QVSWx+nVMUzuT2FuWjmUZyQUd\n0+uNL6DFFUVE09TkeshEXhgPPuNxcMnqPmW59WWx6vOcKviO4/wH4M+e8P4vAr84xTadA5PWvq7H\nSQ3q+XfzgBDs4dBLM3tOQ1UVdF1jNPLw/ZBGQxSzksN009RpNCw8LyAMIzwvKFScoOLdMQwN09Qn\n3DVyhOi6l9E9GKf6UTarPk9pZ9q+OZPWvqqKYZlwWZTvh3tbziLMpqkThlE681HTFIIgzr2v4XnC\nshPT4nXGYx9NUzAMnSiKL5nVV37kbyfcf1qa2SaDr/L3vlwiL5BrzpbVqs9ziQRfImvrx5fSzXMW\ndF3F88LU9aMoyoRvVte1tJKh74tZkqqqUKuZxDGYpoKuq2lZW2khXhb/bhlQVSW14g1DS38jgCAI\n8bwQzwvS3/dyMum+KdokqrfhEgq+QGby5N08ovcmsWLK+6O+K3HMhNjD5MhAiLtBHIPr+gRBhGXp\nqesIYGmpzmjkp1lD1aSw2aLrKrqeCXz+94gikcLr+2HlngPyyw9K940o2Fj+a/jSCr4gc/PIH9gw\nLpd//zikIIggbyb4ikJS6CrENEX6Zxi6aJqG62YlHhRFdBqNhkW/PyYIonR6fcX5omkiBqPrGoYh\nhD4/+TCKYnw/YDwWFnw18pJMCr2sbjlPBmB19wGy5HIYZkM4Vc379y8XURSlKZmmqR/yx8tp8Z4X\nUKsJ0Y/jOO0UdF0lCMR3KAppLCAILrN74HyQlruuq2iaeJy33uM4Tl1vvh8SBGG1qM4hxCRNWeys\n7H76k6gEf4LMvy97elWN6ff7KEo8Vz39SbhukOTwi+JsYi1hDd8PaTbtdPivaWJGpaoqE24Aw9AI\nwwhd1yZK3qpqKZZQLhyqqqBparpJcQdRp0Yixd3zIoIgJAiiS+6DP40s80aWY5lXoZdUgn8EogJn\nJvwQYhjkXD0wrxcEyIk0frrgiqJkYu26Po2GRRhGKIrCeOwTBCHNpsV4LETfNMWCLXIBaomuny74\nrZZNFEWEYTyxn+fsEFVVUFUVTTu81zT1yFpQ0g0zHHqEoRD3+asn/7bEiPtT7o8mH5C1LItezzvx\n+HmgEvwTkMK/vFyj1xukFr+M2M+zJZBH/L9CTDwvxPeH6QQcKehRFFOvm0SRXLMzxLaN9HOapp4a\nuJUTxI5ug3AZiS3KPY7T9/L7WXYQqqqgKGIT14yCoqiJsB/cju8EoygmCCLC8PAWx6K2ymDgXuB/\nVmwUJUZVxQ8vlkI9+XoLwyyGt7Rk0+vNf5nxmQp+FIXpUKrI6LpOEKjpBaWqpFk9ly2PH0gFPc9g\n4GFZOqqq0OuNALFknW0L/7609i3raEEHcS53dvpp5yD3UhjFhDAVRTm+CmEQhBOzQaX45/fyf4DD\nHYN83mrZE69nRraComTZS0LYJ/dnQXZWQRCkndhlGtVMj8ya1zRxLyqKcNNEkUy8ONrSj2Pl0p3j\nmQr+aNRjf/81ltWgVmuiKMX28cZxFtyVPn6Zxy9u2vmK6L8JcRwfWohFBAg1ajWTMIwYjcQC7Sch\nzuPJfmdhOWebfC7nC5hmlFrYUoTzVvdZOG6kkf9/8x2IEGgpMkePOvKjkop3IatOGUUifiSDrULE\n4+TauJxJFycxU8E3TZs4DnDdAZ43olZrYZq1EtSvz4Rfunk0LbMq5HYZhT9PHJPm5U/3e2UhvKPf\nP8sKYOISU3KPM1ZXm+zsTC7gdtyIoOKikCdeuMlABFhl0DWKlInfUcyol58r330YhgFxHKPrJxse\nb8pMBd8wbK5dW+XZs1eMx32Gw31cd0CttoBhWLNs2hnJfIAisHnY3XOZrf4iIwU8ezxJZYUXgyxx\nIpvtKh4LN2oUxei6eE8Ifubika9lv3Xx78E4jhiP+4zHAzRNp9Vam6oBPPOgraqq1GpNLKvGaNTD\n80b0+7sYhkWt1kLTptvDnQ9KcjFmVr+sk61pl9fXX1HxbsSpWyaOJ2tg5X3zwoWTTaDMu3EywS/2\nfScK0w0Zj/vEcYSiqFhW4/QPviEzF3yJqmo0GktYVp3RqIfvu/i+i2nWqNVaqOr5LIs4fY62+jOX\nT5z4HcWxFRUVpGtQT85uV3JrUyuE4WH3Gwg/vqbFBIFY6S5z/0jXanGJ4xjfHzMa9ZLYlYJtN7Ht\n5rm4tgsj+BJdN2k2V/B9N7X4PW+EZdWx7WaphP+g1a+qIrgkXT4ikFeJf8VlZ7JkeT6HPu+Wydw2\nooNQFOXQ61L8M8u+mAihdxmPe4ShmLl+ERpXOMEHkVVhmjaGYeF5I8bjPq47xHWHWFYD226USPgh\ns/rFhSzFP5/XX4l/xWVFumPgoAtGuG6ElZ8vF6Ekn4tTq19+XtxjkuLdR5nQ9wlDub5EDdtuomnn\nL8eFFHyJoihYVh3TrOF5I0ajHq47wHUHJbT4JSeLP0wGe8vgf6yoeBekkXPYMs+Csnm/vaLEhKGa\nJkjAwbLFxbtfpOtGCL2w6A3DplZrXmicstCCL5kU/iHj8SC1+C+yd5w+R4u/dPsAVbZPxSVAXNPC\nNRPnXssHZaU1H6cWfhlGxHEcJ16KAVE0O6GXlEolhfA3MM166uqRPn7DsBLhN0qQx38Uh8VfzOxl\nIttHun4q679ifpj01x/MrAlD5UC68+TnikgcR0nWzYA4Fg0ugnFaKsGX5C1+MUwapFk9mmZg2w0M\nwy6p8IMUf5GZEKfZPvJmyFv/sgMIw5Ai3wAVl5EY3/eTmegnXZfSwldyAdg4F4iV1vzB7yjetR6G\nQep9kPdjkdzPpRR8iQju1jAMmzD0GY/7+L7LYNBJ8ljrWFa9ECf67cmyfQST1n++hLNhVCOAilly\n2DgZDodo2sFg6tHIWlUyCFsWN2YcxwSBh+sKwxNAUVRsu4lp1gtVFrzUgi9RFCVN5xQ97ADXHSUz\n1vqYpo1lNUrs7skzaf2DEP1aTcfz/Ingb75oWFlunoqykIm6ND7yt5Y0OGzbot/3OH30ma+NwynH\nFoMoivC8Ea47SOs/aZqRuJ2L6WGYC8HPo2k69foitVoL1x0ldXrGeN4YVdVTV1CRet23RwavoF6v\nMxh0AQ6NAIDc9PSsimA1Cqg4G9nylnnr/aDA561yeV3Z9lnLDisUfZIUyDpOPq47xPNG6etlMSrn\nTvAlYkjVwLLqyXBrmMxo6zIadTFNG9Oso+tmoX+gNyPrAOTMxKOG2ZomXofJUUDVCVQctNyPEnfI\n6tpclmsmisLEmh+l2TaqquUMyHK4jedW8CWKomAYFoZh5X60Yc7q1zDNGqZZK2lq52kcjgFANgqQ\nN7MYCWRTE7NO4PLc1JeLzGqvxP1o5CQpzxumvnkQaZWWVU5jcR4V7lhUVcO2m1hWgyDw8Twh/NLX\nr+tGEgSeF5fPUUyOAgQndQLZ+3BSR5D/voriMGmxAycKu3TNXDZxl0iXjUj3HqcplZqmY5rldwdf\nKsGXCKvfxDBM6vUosfZHBIFHEPhAF8OwEvEvQ5nmd+WoTgCOG94f3RGI5wc7g+y9g99dMR0OW+qT\nz4/4xLHCDpfxNxKVKl1Goy6eN04DsLJipWnWpl6XflacSfDb7faHwG8A/8BxnH904L0fAX4BCIEv\nO47z81Nv5TmST9+ULh/PG6V5/QBBMCCOdQzDKvyqXNPlOCsvnhCT0zoDyDqEfr+PpkXJa1WncDyZ\ncE/us/z0breLaR5dIUyeTyHqlbAfRCQvBKlrt9MJkneUxMVro+tW6Vw2p3Gq4Lfb7QbwD4HfPuaQ\nXwL+ArAJ/H/tdvv/dhzno+k18eKQLh/bbibDunFSnz9b/UjEA2wMwy710O7dOEk84gmRyguUokAY\nhknQWBx7kMk1Z/P7fPGsyX2+XcUja2ReO/ICfvi1w8cf+tZYjFTDMJ44R5WoH4901/j+eMKSB2g2\nm4lRV8x0ymlxFgvfBX4c+G8PvtFut+8Du47jbCTPvwz8MHAmwfd9b0JMi4SmGdRqBrbdZHHR4tWr\nHTxvnLP899F1MxF/a04Dvm/DQat98uZZW2uyvd07NEIQe9L9YXfEybVu8ytYZc+POuZ0xuNxOgo5\njaO04ShhPyv5c5d3jx18D2BpqcXWVu/N/sAlQ06KkiIvffLAhNv2ypXFS3EuT1Upx3ECIGi320e9\nfQ3Yyj1/DTw46fuWl+voujDxPvnkE775zQ2Wlpa4desWa2trhbWa79y5AYDniU6q3+8zHo8JAo/R\nCEzTpNFo0Gw2se3ZWAnr660L/5tvw/r6wqnHHFwc/LhNHnvU87fFdd3cKOTNkL97fsH0bEH1s21v\nQhl+84tuYxAEDAYDBoMBw+GQKEnwV1WVZrNFs9mk0Wgc0pqincs4jqeuI9M2S09t3d7eMH2saTWW\nl5fZ29uj0+lgGAbLy+usrKxjGOaUm/b2rK8ftKQMarVlLCtMLAc32Tz29vaSmb9Wmg56ETm6h9tY\nTC6mnQoHM5AOHXHClbq0VKfTGR753sn9yMEvjQ/sp0sZfvOLaGPmqhGjb1lnHrJcecOw0zTK8RjG\n48GFt/MsxHFMv99lZ+c1pmlx48ad9L1pdEjvKvjPEVa+5Gby2plotRa5f/8WGxuv2dl5TaezzevX\nz3n9+jkLC8usrKzTbC4U1qcmLqYGltUgjiN838P3XYLAxffH+P44OU5PxN9MLro3G8WEYUAUReh6\nsWfxFZOjz9dJwq3rOpNL7VUUCRFwDXP3mizdIBCuViuJs2mluGd832Nvb5vd3e00WaTRaE3dyn8n\nwXcc53G73V5ot9t3gWfATwA//abfY9s1bt58j2vXbrG/v8POzhbd7h7d7h6GYbK8vMby8hqmWdwU\nSUVRk9m7dpoBICwOjyBwcV1R4wdA1w103TrTupVyolgcxzQai2iakV4EMuhUlll+FRVvSybwwqjK\n++JVVcMwrGRU/eYG1ayI45heb5+9vS263Q4gdGR5eY2VlSvU6zNYxLzdbn8O+PvAXcBvt9t/Bfjn\nwLccx/kS8NeBX0kO/1XHcT5+28ZomsbKyhWWl9cZjQbs7m6xv7+bWv3N5gLLy2ssLCwX1tcPwmer\naUZSqjkLHElrJAh8oiiiVjt5iCYWftCS+hzqoQtZLvau6wae10VRRBD5PHx/FRUXhbTgxT0jtnxG\njaKoSbKEia4XL2HC973kvj3ZEAvDkKdPPyWOY2y7zsrKOktLK+f6/5wlaPsfgD97wvtfAT4/xTah\nKAr1epN6vcn163fY399lb2+bfr9Lv99FVTUWF5dZWlql0WgVXtzy5R1qNRGIzF/AJ31O181kMlh8\nSPDDMKDZXEbTDBoNjV5PDAVF3SAXiKnVWuh6ceIhFRUHkT54OfExCLwJC17eP7qeCXwR7/l+v8ur\nV5upfi0vr2FZxxtguq5z48Z71Gp1arXpW/NHUayu8QiE1S8Cua47Zm9vm05nh729bfb2tjEMk6Wl\nFRYXV7HtWiEvhIOoqnrmEYrIOAlR1ewil/soChPLX6HRaDAcRqlfs15fSCeSSTfQaNRNYwG23SjN\n0LdifpDWuxB4Ie75ICtkFrwQeLOQAi/dMWEYsLCwjKZpDIf9xEpfZXv7Fdvbr7h5870T276ysn6B\nrS6B4OexLJtr125x9epNBoMenc4O+/t7bG29ZGvrJZZVY3FxhaWlFSzLnnVzp0IUhckkGyHOef+9\nqqqMx32iKKRWExeV74/TQnCapjMc7lOrwXC4n8wXMNKFlCvLv+I8EcXHxARGKfBh6E9Y7yDq1GTi\nbhQ20Jq/954/f0oYhliWzcbGI+7e/YBeb5/bt++jKApLS6s8e/YtRqPBhVnvZ6FUgi9RFIVmc4Fm\nc4EbN96j1+vQ6ezQ6+3z+vUmr19vYtt1FheXWVwsp/jnh4GKohwKzCqKSr2+lPjvRwwGA6LISP3+\nAGHoo6p6alE1m8uAmHAifP+V4FdMB5moEIZBKuxhGNDpTIq7qmrouo2uG2iaWfjMsziO2NnZYjjs\nY1k11tevEYYRvu9z9+4HKIrCw4cfMRz20XWdfr+bpJUb1Go1ut0OtVqjMHG1Ugp+HlVVWVxcYXFR\nrHbV7XbY399N/GlDXr3aTCz/ZRYWlkvj9onjmPG4TxB4gJKKs2x7GAZpUEhVdTQtwnXHiXWk5o7R\nCQIPVdXT781n+BTlQqwoB9IlI8VdbELcD6KqGo1GkyBQEoHXS5dRNhj0GY0GrK9fY3v7JXt7W+i6\nQb3ewHXH2HaNxcVVer19ms1F9vd3WVlZJ45j6vUW+/s7AIW5x0ov+Hk0TU9TODPx36Pf308zfQzD\nYmFhiYWFpUIHfGWgSlHUdL3eIPCSMq01XHeArpvJAi8uhiGGwvlgsO976LpBGPpptT9Rf8Uv3Y1X\ncbHkLXYxD0Q+DjlqIpnIStMn9qqqFmZC02ns7++zublBrVZnYWEpvV+63T1M06JWa7C6epXBoMdw\nKNKr5b22sLDE5uZjbtx4j9evnxNFEaqqEkVhsg5HVJiswrkS/DyT4h/S63Xodjv0eh12dl6xs/MK\nTdNoNhdZWFii2VxE14tzOmSGTt7tIgK4YohsWXVGox6uO0RVVVqtFaJoTL/fwTRrAIShh2038H03\nncMgM4TkMccxHIrlEqVVJreidpAVb04cR4ShsNaF2y+z3A/62SXietAnxL3s10Wvt0+3u02ttsB4\nPKTf73LnjqgQU6836fX2ATFfaDQaAqLj832RXm2aVpJJB4uLy2xtvWBpaYV+v0uj0UJV1cKMpIuj\ncOeIpmksLa2ytLRKFEUMBj263T16PeH+2d/fBcSP22ot0motFdL1I2qtCMtc101ardW0E7AsC0Xx\nMAyLwaCDoihYVj0NiElrRMz+VdG0zOI/iKgPPuQoSy4v/kdtRTtnlxV5XQj3i9znt+DYekOKoqLr\nZiLsWiry8/r7uu6IhYUFWq11fN/j4cNvpO+ZprDQpXtU13XCMEBRxOcsy8a2a9RqDVx3xNWrt+h0\ndnj27DGNRotGQ8y1Kcp5uxSCn0dYw4u0WouJn3xErycs/+Gwz3DY59WrTXTdoNlcoNVaZHGxyDN8\nRScgb17bbmDbjfQCBbHA8mDQwfddFAVqtdapLp3FxfUJ609YfmE6Iea09ogOQE1jCvKx58kc6zcv\nFFaRF/KIwWCQzMKeFHb5/CTExCAh6OK3ko+LlwJ53qysrHP16hJbWz2CIKBeb6b3j2GYaJpGv99l\ncXEFVdUIgoDV1SvppFDDMAjDkGZzAVUVaeSrq1dm/W8dyaUT/DyKoiSTHupcuXKDIPDp97v0evv0\n+/t0Ojt0OjtsbDzCtutpZlCj0SycD/zgTZqfraeqGq3WahpY0zT9xCFmXrThcCZPFrg7aovSDuIo\ner2d3N8RHYGcRZx/LNogX1PS1+alo5DCfdxeVAmN0tekkOet8t4xrnFFUdP0RtnRTo7C1Lk4h9NC\nVTODaXd3i1qtkd4jYlW8Jru7WywurqBpGr7vYlk2a2vX6HS2iWNYXb2aakKRz+1MBd/zXMbj4iwd\nputG6voR1r/w57nugE6nw3g8ZHv7ZdJRNBLxb1GvNwsTlDkJ2Qm8qz9RlI7QT5wCLkUrb3FGUYRl\naQyHbipmIgh4dOdwQgsOlBRWk9c40ClMlijOPiv2k9+XPev1RA2j7H85uHpXVgUzq8Mvl3eUj7N9\nVq45Jh+HeaP/WFFRFA1NyzrHZrPGaBQkz7Vch1lcwZkF+dHucSiKwmgk1riWFSrleVxeXmM47PP4\n8ScEgc/6+rUk/VllZaWYlvxxzFTwHz78mH/xL/6Qq1dvcOfOXW7cuFWYtSOlqNdqDdbXW7x6tc9w\n2EvKO/RS90/+WOmzq9ebp9bRmCUXIQjCylQP3WhHZW0cZ9Uefhwfeixqnb9ph3Eyg0Fnqt8H+Y5I\nurmyUcvB/eRIR753+DdbXS1HBsxFEscxnjdmMOgzGPQYDHooikK7/SdO/Wy/32V19QqihLJcxDym\n2Vzk1q17jEbDC43tidXhpqsjMxX8Wq3O8vIyL14848WLZ2iaxvXrt7h9+z2uXbtZqKwZYVEt0mwu\nAsJqEBdVN0nVEh3A1tYLAGy7TqPRTGsCiSp+leV1FJMupDcnv/BJ3qo+ygKXgejDAcvsebNp0++P\n8y2ceJz9jAdHENnoIRPp+XBBFZUoihiNBun9Nxj0J+YEaJpOo9E6U2rk3t42tm2zt7dDFIUsLCyz\nsLCUim6tVj/X/wWg293n2bMnbGw8ZmVlje/93j891e+fqaLevfuA7/3e7+bhw2c8ffotNjYe8+zZ\nE549e5KK/61bd7h+/WZhLH+JpulpPj+I3ng47CVWhZisMR4P2dl5DZBM1mhSrzeo15vUavXCxQHK\nymG3zbuxtNTC9yvLuWiIUg1eIu5C5Mfj4UTnbRgmzeZKOtq2rLOtPhcEAa3WArpusrCwdGGz8+M4\nptvt8OzZUzY3n7K/L0aXwl20NvW/VwgTemFhkQ8//G6+4zu+i/39PTY2nqTC/+zZE1RV5dq1G9y8\neYfr129hWcXLmtE0jVZriVZLdACZ5SGtj15a418i07lkB2BZtVLEAioqLgLf9xmNBuk2HA4Ozeit\n1erpKLpeb771mhm6rnP9+p3TD5wCcRyzt7fD5uZTnj3boN8Xc15UVU09HDdu3DqXVf8KIfgSUXRI\nFD/78MPvZn+/k5yUJzx//oznz5+hKApra1e4ceMWN27cptks1jqUElVVJ/JwD1on4iIeMh6P2Nvb\nBsT/b9s1bLuRZg/Zdq0aCVTMNfLeGI+HjEZyG6STmSTCel+mVhMj5TKNksMw5PXrlzx/vsHz588Y\nj0VSgKZp3Lx5J/Fk3MIwzteTUSjBzyPEf5mlpWW+4zu+i16vy+bmUzY3N9jaesXW1iv+4A/+AwsL\ni1y/fpPr12+xurpeWAtZURRM08I0LZaWVgFZL2c0YcWI50P2soFAMrmjnnQGYl/FBCrKSBSFjMdj\nxmNh7Ij9MMnWytB1g1ZrKa0VX683CufWPY3RaMjLl5s8f77Jq1cv0tGJaVq89959bt68zdWrNy40\nVllYwT9Iq7XAZz7zIZ/5zIeMxyNevHjG5uYzXr9+geN8hON8hGGYXL16nevXb3Lt2g1s++TyAbMm\nPw8ARF3sKBJF0GQMQI4CXHeX/f3ss6qqYds1LKuGbdtomo/vx4WvPlhxOZDX8cuXA7a29nDdUZL5\n4h461jQtGo2F3Ki2ce6W7nkQRRG7u9u8fPmcly832dvbTd9rNlvcuHGbGzdma5iWRvDz2HaNe/c+\n4N69DwjDgNevXyWZPpup3x9gaWmZq1dvcO3aDdbW1ksx/FNVNdcJCPJD3swqGk2khr54sZF8XsOy\n7EObadqFHf1UlBOxdKeP57m47hjXHSX78ZHCrmkajUYrNVRk3KrIKcynMRwOePXqOS9fvuDVqxfJ\nguoiLfnKlWtcv36L69dv0motzLilglIKfh5N0xOXzs0k4r3Py5ebvHz5nO3t13Q6ezjOH6NpOuvr\nV7l69RpXr15nYWHpjSzhKIrY2nqZFGU733UnD5J3By0sLE+0yfPGjMcjNC1id3cf1x0nI4PBoe8x\nDBPTtLEsK/0+sfC6VeqbruL8kMaG57nJNk4EXjwW8yAm0XU9zZBZXV0iCFQsq4aul79sg+97bG29\n4tWrF7x69TItrAZQrzeSlPIbXLlyvZCjlNILfh5FUVhcXGJxcYl2+zsIAp+trVe8fPmcV69eJh3B\nJiD84leuXOPKlWvcvv3eiRHxMAz55je/zu7uDhCj6zrf9V1/KrXCwzBIJ8tcJKqqJj79OuvrLVot\nkUooJp/krS5xc7ruOJk3cPi7RNllE8OQHYGZrMNrYprm3BbOuuzEsVjMQ4q62Hv4vps+P6rImjBC\nhPEgRpG15Lk94ZMuS3nk4wiCgJ2dLV6/fsnr1y/Z29tJz4em6Vy7dpNr165z9eoNWq2Fwt8jcyX4\nB9F1IxlS3QLE8Ov165e8evWC169fsrHxmI2Nx1y/fvNEwVcUhdXVde7cuUez2eJ3f/d3ePHiGffv\nfxsAH3/8DT755Jusr1/Fsmzu3LnL2trsplyLSpl2kku8NPGeWOdWWmiTmwwYH4WqqhiGKNdsGAaG\nIfbyua6LrXIbFQOxMHiYrBsrBN33xRqy8rHve4cyYfJomo5t13OjQbEJUZ/PWFEQ+OzsbKeJITs7\n22kpDEVRWFlZ48oV4SVYXV0rhZs4z1wL/kHq9QZ37z7g7t0HySLEXXZ3t0+dQaeqKlevXk+f7+/v\ncf/+++nznZ0t/sSf+JOsr1/lxYtnBIGIxr94scnm5lM0TePBgzYLC4vn84+9ASLYK0YFB8l8ssLC\ny6y9bHPd8RHfmqFpWir+uq6nKx1lzwPGYy+txVN1EGdDFlALArmMYEAQ9Nnb6yfrxQapuMvHx5U/\nBrnAjkmj0Uo68Gw0J0Z5ZunE7G1w3THb26/5+OMOGxubExY8KCwvr7C+fpUrV66ytnblXHLjL5JL\nJfh5FEVhYWHxjUTY81w+/vgbLC4uT1jwvV6X9fUrNBpN3n//MwDs7e3y6NHH3Llzj+FwwJMnj/js\nZ78TTdN5+NBhPB5z5TX0Ay8AACAASURBVMo11tbWL9wVdBxSBMRF3TzymCiKEitx0moUVmQmNsd1\nDE+fHvybalpzXey1tEyvLN2rafmKj2r6WlZ2+eSaM7NC1vrJCsllBeOyqqJRbvERsc8eB+nzo5YQ\nPAqxcI6BbdfRdSMdfWWjMTEi07Ty+9PfFDmrdWdnm52dLba3t9JJTyDO3fLyKuvrV1hbu8r6evkF\n/iAzFfznz5/xjW9scf36eywtrcyyKaeytfWKR48+QVVVvv/7fzB9XWYjfPTRHxEEPg8efBtXrlzn\n2bMnXL16g9u37wLwm7/5G3z2s9/JH//xHxAEAbZd46OP/pDv+Z7vTcszlAFVVZNA78lTz+M4SsQ/\nyFmgAZal0u0OUhET74sa+657cg33syA6gaMKk01u4tiDFTQFz5/reF4msLIGT7Y/uhqmEPbJ4m7v\n9r8o6aIblmWnj+UoammpyWgUTIygqlhLxng8Ynd3h91dIfC7uzsTLixdN7h69Tpra1d4//27qGqt\ndLn+b8pMBf+P/ug/8rWv/T4Aa2vrPHjwbbz//rdx8+atQg0nHcdhY2OD9967z7VrNwAhaNLC/Nzn\nvp/V1XWePn3Es2dPaTSajMcjrl+/CYgJGKZpEgQBT59+ix/90Z9Ibk6Vly9flErwz4qiqLnRQsZJ\nQTzptshbu9n+4OpN0cSWr7aZF125slO2wVEreb35/5cVRsuXadb17LEcechRiHwuRi7ZojBixCJe\nk0sGyucnUfaA6DTxPI+9vZ10293dSdeelbRaC6ys3GZ1dZ21tXUWFhbT0XWRzmW/3+Phw0+wLJvP\nfOazU/3umQr+D/zAD/HgwV2+9rU/5MmTR/ze7/0bfu/3/g22bXPv3gPu3/+A+/ffp9E42r1wEfR6\n+3z1q19lYWEZy7IYjYbUavX0QhmPx6ytXUFVVZaXV+l2u2xsPE1SH4XYdTp7LC+vsLX1CtO00HWd\nKIqo1+u8eCGyhoqy5uUsOUud/WkwWV0TMutdsLbWZHu7P9EusYeq+uXsGY9HdDp7dDq77O3tsre3\nw2DQnzjGNC2uX7/J8vIqKytrrK6uvXWdnfMmiiJevNjk4cNPePToU16+fA7AjRu35kvwm80Wn//8\n53n//Q/xfY8nTx7z8OHHPHz4Md/4xh/zjW/8MQDXrl3n3r33uXfvATdv3r7QnPFGo8WP/uiP8umn\nom39fo/V1TVWVta5efM2H330h9y8eZubN+/Q6ewlVpqaDA2FMGxvv2JhYYnd3R1WVkRZBVVV6fW6\nc+cjLAOnVdeUbpOK2RJFEb3ePvv7HTqdPfb39+h09tI6NBLTNLly5RorK6ssL4utXm8UumPu9bp8\n61sP003+T6qqcufOXd5//9t48ODbpv53zyT47Xb7HwDfjxgL/03Hcb6ae+8xsAFIB+xPO46z+aYN\nMQyT998XLp04jtnefs2jR5/y6NGnbGw84eXLF/y7f/c7mKbJnTt3uXv3Affu3WdlZe1cf1hVVVlf\nv4qqZlktMmAJosTz17/+H/n0UwdVVfnMZz5kYWGRf//v/236g7169ZLPfe772d5+xc2b7wEi/avb\n3U9dRMcRRWGh3FsVFdMmjiMGgz77+/t0ux263Q77+x263e6h1cFqtTo3btxKiiwus7S0UnhxB+Fy\n2th4wuPHD3n8+BFbW6/T91qtBdrtb+f+/Q+4e/feuZZmPlXw2+32DwEfOI7z+Xa7/e3A/wl8/sBh\nX3Acp3/402+Hoiisr19lff0q3/d9P4DnuTx58jjpDT/l008/5tNPPwbEyXrvvXvpdhGpjyKNTQR3\nrly5xp//83+R4VBU95P++OXlZX7v9/4Npmmyvn6VpaUl6vVGegFvb28RxzGrq+vp/3wUX/nKb9Pr\nddOMIrEA+wILC4sXuvpORcW7EoYBvV433brdfbrdfXq97qFF1+WMdjmRcnFRFFIsqlvmIGEY8Pz5\nJk+efIsnT77F5uZGOitZ13Xu33+fu3fvc//++6yurl/YfXwWC/+HgX8G4DjON9rt9nK73V5wHKd7\nyuemhmlafPBBmw8+aAOwv9/h8eNHSW/5Lb7+9T/g61//A0DUz3nvvXvcuXOXO3fuXlgNi3q9AWS+\n+A8//B663X0Ggz7Xrl1HUVTu3fuA3//9f0ens0u/3+fu3funxidqtTqDQT+d6ZdH03RarRbN5gJX\nr66hqhbNZotm8+wLP1RUTJMwDBkM+vT7Pfr9Ht/4xpjXr7eTZUEPT/HWNC01ZhYXl5LHSzQazVJd\nv2EY8OLFczY2nqQC7/tZRtC1aze4e/c+d+/e59at2zPLBlJOSx1rt9tfBP6l4zi/kTz/HeCvOY7z\ncfL8MfCvgbvJ/m85jnPslwZBGOv69FwUURTx8uVLPv30Uz755BMePXrEeJzlgK+urnL//n3u37/P\ngwcPWFlZmemFtLOzw9bWFpZlce/evTMHa33fZ29vj06nQ6fTSR/v7++nE73yGIbBwsLCoa3VatFq\ntQpZ56Oi+MRxzHA4pNfr0e12D239/tED/UajwdLSUrotLy+zvLxMs1kuYZf4vs+TJ0949OgRjx49\n4vHjxwcE/hoPHjzggw8+4MGDB9TrU1ke8Z1P1NsEbQ/+0Z8FfgvYRYwEfgr49eM+vLc3OXV/GulQ\nhtHi27/9e/j2b/8eoiji1asXPH36mKdPReXMr371q3z1qyLs0Gy2uHXrdrLowG2uXr12qo98uilb\nJqurIl3zTb9TUWosL9dYXr7OvXvitTiOGY2GaFrA5uYr+v0evZ5YarHT2WdnZ+fI77IsK7fkotzq\nyQpCDWzbPpcJYUVKfzuOMrQRzqedYpWpYbLC1DBZsW1yO6pgGojR6NralXSU2WwucPv2VYJAO9Ki\nHY9hPJ6aJ/idOO1cDgZ9Njc3ePZsg2fPnvLy5fOJ87C+foXbt9/j9u33uHPn7sTIfTAIGQze/Xda\nX3/3xZ7OIvjPgWu55zeAF/KJ4zi/LB+32+0vA9/JCYJ/3ohlwkT1zO/7vh8giiJev36VLAwsVs/6\n5jc/4pvf/AgQlvD16ze5eVOsoHXz5q3UPVMGFEWhXm+wvt7CsibjF3EcJwXT+oe24XDA/v4ee3tH\ndwjZ6lu1tFxzrVZLX7NtOylzW5VdLjqyZIZYeGQ0sQDJaDTKrTI1OrG2jmVZLC4uU683aDSah7aj\nMpvK0nnmiaKQra0tnj/fYHPzGZubGxO17RVF4dq169y6dYdbt97j9u07pdGMswj+/wv8D8D/3m63\n/yTw3HGcHkC73V4Efg34ScdxPOCHmKHYH4VYD/c6165d50/9qe8njmM6nV2ePdtIeuynyWjgcfqZ\nxcWlZAnFm0lGwAez+wfegbxoy+BwHtkhZNbbcMK6G42GJ3YKEtM004VYxPwDWUUxK7YlK3C2WkY1\n5+AdCUNRAG9312dra3eiGJ7ryiqpblqbfjweHwqKHsQ0TRqNbGlNuYSgHP3VavULXZnpopAl1V+8\n+Bbf/OYnPH8uSqvn3TOWZXH//vtJ+vVtbty4WZrg8UFO9eEDtNvt/wn4M0AE/A3ge4B9x3G+1G63\n/ybwXwIj4GvAf32SD39rqzfxXhEsALGC1iabm8+StXM3J3J9VVVlbe0K16+LxVSuX7/B2v/f3pmH\nt1Ve+f8jyZa8SLYkS7blfb9eYmerGwiBsEMhA3QoDNCFTssM05a2zLT8Sh9ogRZKh06nM50OM8y0\nMIVCSXkKhYQ1ISRkhQSy2s71vm+y5X2TLen3x10sOd4SvMhE3+e5z5XuIp179erc877v+X6PLT6o\n/gCLdR8VqeWRkRFVTVOqwDUZLSpOZbqiFzNB0XTR6w1q1tOkAme4nwKnv/BaWIC8gL/+zkI+QBby\nXioM30ldnAkmJjx+AmgTAYJnExMTATpFkj7RuCpi53a753TeCiShvAi5ROZkjywiIkKtlyz14CIX\njewWDP9vfwwODtDe3kpbW6u6njqZbLcrNbNTSE5OIS7OFhR6V3a76RM38nk5/IWEv8Ovq6uho6OJ\n1NQckpKSgybqk6rKu2htbaatrZWurnZaWloCJkel/Px4EhKk3oOkrZ+wbE/+YPhjSQVZJqPMqZGn\nxF3wMDg4HKDEOd2k89liUlRN5ydZMFXWYFIGQRqGkjR0FJkEkNi0BkM4Y2PjM2roKIu/lMOkzEOg\nIJrH4+WTSjkoonaSkqW01uv1xMQY8Xg0fj0pRZveoGrvLPd/arnapc/no6+vl46OdrlYibRMnVSO\niYnB4UgmJycLkykOhyMZgyE4o/cV7/BffPEPvPfeDkAaRikoKCI/v5D8/EIsluARU7PbTbS399LV\n5ZTrVUolzTo7288ovmyxWFXnr6wlzY7F/eMFg8OfD6az078Ih6K4qUS2gRHwhJ/gmr+SZKDKpOJ8\nFQ2eSZ2dhW/r/ho5Est68kEzqfapC+iR+PdUpvZgpipchofrZ+zBrITffClsHB9309XllGtddNDZ\n2Y7T2cHYWGCP02QykZCQpPbUExMd6uRqsNxLj2eCurpaKirKsFgsbNp0qbpvxTv8nh4Xzc01fPjh\nR1RUlDEwMJnan5DgID+/AEEoIC8vf1lrQs7UGDweD93dXWpBFSmaaD9DGthgMGCzxcuyq8ravqAa\nQcHSYOfCctrpr3Dp9QaqXU4eA3Fx0XR3D6kKmpNCaZyhvrmcWAm/+ULa6PF4cLm66erqxOnsVNf+\nE6oKrNY4EhIcJCQkygVLEmf9v52rnZ90Psrr9dLU1MDp0xVyIaVK1X9kZGTxwx8+5G/jsqRlLhgs\nFit5eekUF5fi9XpluWQpg6aqSmTPnl3s2bMLgOTkFHJz88nLyyc3VyAmZvmLAut0OjmST1C3KZNA\nnZ1SpKE0ytZWabbfH5GRkapyX1ycnbg4SeQpJiYmKMYMP23wd9yzJRZFRkZiMHzyYaYQzg3ShHS3\nrFvfRVeXk+5uJz09rjNSQiMjI9UKc8p/cSl07EdHRxgeHsZqjTsrp+/xeGhubqSyUqSysoLq6kqG\nhydT1aVAVxrlkIQNFhbLGuHDbNHzBPX19YhiBaJYTk1NtapfA+BwJJGbK6j6O1Zr3KJFXAsRpUi1\nMbvo6uqkq8uJ09lJd7eT3t6eM4YawsLCsFjiiIuTlP4kUSgrVmvcjNW5VkK0ByvDzpVgI6wMO2fr\nHff19cpSxi5cri5Vu35g4MzjpV6yFBj595QXipE7270cHR0lIkLStxkcHOS3v30Sj8dDZGQUf/3X\nt8yphwWwc+dblJefoqamKoAYarPZEYQC8vMLycvLx2y2zGbjyh7Sgfk32omJCerra6msPE1VVSU1\nNVUBQycWi5Xs7Fyys3PJycldUFXNxfxjTUyMB0QzytLT0x2QGqYgIiICs9mKxWLFYrEQG2vBYrGS\nlZWC260N+pz4leykgg2f1M6RkWGczk4GBvrJzMxWc8l3795JR0cb4eF6rrrqc+c8nOp2j6HVjlNb\n2yTLGffIcsYu+vp6p51TkTTr4wJ6vMrw52IOoSn3cmRkBL1eqgh28OA+Dh7ch9vtZvPmy7nwwk3s\n3bub4eEhrrnmeg4d2k9tbQ1bttw4p4bXL37xGNXVlSQkOMjNzSM3VyAvL19Vz52njSt7SOdsEBYW\npkbzIEUITU0NspBaFdXVlRw58gFHjnwASBFBRkaWrKufQ1ZW9rLOA8yEsLBweXI3MWC7z+dlYGAA\nl6tbjYKk4g4unM4OVTPbH1qt1k9syqzqkyivjUZTSPb3U4qJiQlVw8ZstgSMV4+OjvLee+/gdHaQ\nkpLGhg0XER1t5MMPD+ByuQgPD6etrZWLLrqE1tYWJibGueqq66iuruTYsY9Yt6501vHvjo42mpub\nZIXLXlnyo5eRkeFpj4+OjiYpKUXttUrBSxxWa5xaQ2IpsW/fblpbG+no6GJoaJA777yL+PgEjh37\nmBtvvJns7Fx+/vOfkJ6eSU1NFUVFJQAUF6/h9OlyamtrWLNm3axDO3fccScmk2nZ61qvGIc/FTqd\nThUjuvLKa/H5fHR2dlBTU6UulZWnEcUK9RybzU5mZjaZmdlkZGSSmpq+LA1sPtBotKqoVEZGVsA+\nn89Lf3+/GjX19vYwMjJAZ6eT3l5JWG76z9RgNBr9FDdjMJliMBpNmEySzo5S1DqElYW9e3fR0dGu\nPvQ3bLhIHR44ePB9zGYL11xzPW+88Ro1NVWkpKTS19fHZZddhdls4cUXn6Wry0ltbRXx8QlYrXEU\nFBSxd+97dHU5Z3X4oljBgQPvq+91Oh2xsWaZ8BhPRIRRljKW5IyXI+1RkSeurq4kJyePzMxstTe8\nb9/7lJSs4vrrbyY6Wurl1NXVYLFYMRolOYPMzCzq6mowGk00NtZTWrqB6Oho4uJs1NfXzunwk5NT\nluZC58CKdfhTodFoSEiQZuM3bpRqzg4PD1FfX0tNTTX19bXU1dVw+PAhDh8+BEgRcXJyip+8cgbJ\nyalBRaiaDhrNZCSfni6J6vh3791uN/39fWrEpcjQSnrjfbS3t9La2jzj5xsMEbLzN2I0TlLnFUq9\ntJa0dxa7OlUIc6O310VkZBSf//ytGAwRvPjiszQ21qsOv7+/j4QEB1qtjpwcgd5eF+Xlp0hISETh\nCFitNgYG+hkfH1fTGRW5hL6+XmDmjBRBKMRms/v1JI1BVzrw7bdfp6GhnrS0dHbufJt16z5DaekF\nAGRlSaKK0dHRjI+7CQ/X4/V60Wg0qpx5bm4+1dUiqanpHDiwF5AybJKSkjlx4igws8R5MOFT/W+N\nioqmsLCYwsJiALUXIEkr19HQUEtjo6Sxs2/fHkCKTpKSUkhLk0SQUlPTMZkWfrZ8MaHX67HZpOyf\n6eD1ehkeHpK1yAcYHOyX14FLV5dzzu8yGAwyBT/qDM2dQP0dheGpwePxhIaWFhBms5ULLtjE+Lib\n06fLsdns6kSi2+0mOtqkZrfExsbicklyxdLwgkbebmZ4eIiIiAh10lSr1RIRETGtrLE/lEArWDE0\nNIRer+eOO76C1RrHtm2vUFtbrTr87OxcXnnlT9TWNtDS0sy6daUUFBTKsiPSsFRqahq7d+/kssuu\nZPv2vwDS/RkbG8NsljhDIYcfZPDvBWzYsBGQ5gLa2lpoaKinvr5WVthsoqmpgf37pW6qVqslPj5B\nFktKVddms2VF/MhTodVqVUXD2aCMC08uQ7Lw2jDDw4OqmuLIyDDt7W0zqihOh/DwcJURqrBEFb0d\nZVGKoOv1EgFpkozkT1QKlFuQisMvrNTC2UIifUnEsKmEsamkMoVtPD4eKJ8wPu6WWcpuUlPTueSS\ny2f8PiXyrqmpZs+enWRm5qDVamRbPOj1ejVqDw8Pl2sH62T7pMQAg8FAb6+LuDg7DQ11AIyNjREe\nrg/6RIC5EBUVxTXXXI/P5+ONN7bR1tbCLbfcoe7PzRVYtWoVl1xyBbGxZp5//vdoNBAREUl3dzdZ\nWTnY7fE4nZ1YLHFkZGSxb99uiovXUFFRxsUXX7p8F3eWWFaHf/Dgfg4f3k9+fglr167Hbp8+Il1M\n6HQ62YGncdFFlwBSSmh7exuNjQ00NjbQ3t5MbW0d7e1t6qQwSD2IlJRUVXNDUtxMITIycsmvYzEQ\nFhamDh3NBUmIbUzV21G0dxRFRkl/Zwyfb4K+vgFVcmFkZJje3p4zGMufFIGsV51aa1ghTk2VWvCX\nVggL0zE+rtgzk6SCD5/Pi8cTKKng8XgWnNE714NZGnrwqfnbR44cYs+eXdx8823o9XqioqLo7e0B\nwOv1MT7uJj4+gf7+frq6nNhs8eh0OgYG+ikpWUtVlcjo6IgqT1BcvEb9npUIxe7x8XH6+nqx2+PZ\nuvV57r77HjQaDTExsXzzm9/E5ZKi+eLi1XR1OcnOzuXw4UPk5OQyPDyEIBTgdo9x221fYvv2v3Dw\n4H65znZwjM/PB8vq8A8c2Muf//wn4EUAUlJSWbNmHatXr2X16rUkJ6csSyPT6cJUZbwLL9yE3W6i\ns7Of7u4uNfpvbW2mubmJqiqRysrTAedbLFYcjmSSkpJxOByq4NpCMmuDDZIyZ4ScNjprLvG0Y7pS\ntDsWEOX6R7/SWpJZCJRd8I+gPWpk7fV6mJjwTNG38cpOWnLWPh+qFo4En3otktOeLHYuRczSWnlo\n6HRhhIdrZekDrZ+EwplyCoG9kqnyCZPCcVJPJ1AzZy4Sntfroa2tVS19abcnqPLfWq0Os9mqvleO\nveiiSxHFcsrLT6HX62lrayU3Nx+r1UZBQREvvfQCYWFhJCUlk5KSFpQKpx6Ph64uJ21trbhc3Vx+\n+VWzHh8eHs7tt38ZgMcff4TKytMquen9998nMTEdm81OY2MDiYmJrF9fSl9fD88++zQDA/3ceOPN\naurqrbfeseDzV6OjI5SXl3Hs2MccP36U7OxcvvOdf1rQ71hWh//d736f22+/lV273ufo0Y85ceIY\n27e/yvbtrwJgs9koKVlLSckaSkpWk5OTt2wTqhqNRh0XX7Nmnbp9bGxMVdhsaWmmra2F1tYWystP\nUl5+MuAzTKYYHI4kEhISSUx0qNTvuDjbeT+mrTjDYNAVD5aJxrNBdXUlXq+XdetKaWtrwWqNo7Oz\nHa1Wymbr7Gzn2Wd/i16vp7h4DTqdjtzcfIaGBqmoKCMx0UF+fhEABQVFOBxJqpImLG90Pzw8pMqW\ntLdLImiSllVHgPDehRdeNCMxsa+vF6ezk5SUNCIiIoiNNdPe3qY6fK/Xyx//+Bz9/X3Y7XY2bZJ6\n+xdffCmbNm0+QxRxIZy9y+Xi5MnjnDx5jOPHjyGKFQHXExGx8CMFQUW88ng81NRUq0+448eP4nJN\narFHRERQWLiKVatKKC4uoaioeNZocqFwLg5geHiItjZ/GdY22tpacLm6z+jy63Q6P2p4vJyXH4/d\nLqXHzedhsFKc1EqwcyXYCIF2jowMs2vXOwwPDxMTE8PGjZfQ29uD0WjCYrEyMTHO4OAgkZFRS5oW\nOd97OTw8RGenJEMiiZ91ynWcO6Zl3kZERJCQ4MDhmBRDKyxcNWOadW9vD9u3/4Xo6GgMhgg6OtpZ\nv/6z9Pf3IggFFBbmUF5eTVSUUU3NnKlX88ILz1FefgqtVsu9935/XuSpiQlJFO3UqROUlZ3kxIlj\nNDdPSq3odDry8vIpKVkjj3KsOcO3feqZtj6fj5aWZk6cOMbJk8c5ceI4dXU1AcekpKTKDwEpGyc3\nN2/B88gX0gG43W6ZONWmRi0dHVKB8qGhM7MhtFodcXFx2GwSpVzS3rHJNHMbRqMJjUazIp1UsGIl\n2Agrw07FRqkms4uuLqeqjeN0OuX3nTO0fS02m10WP0tQe8SJiQ5iY81n3etwOjvYt28P0dFG8vOL\nSE1NUz9junspihW8/vo2amuruf32L7Fhw0YaGurZuvV5tmy5kfLyU/T09HDTTTfjcMwsr+D1ernh\nhmsCglej0SgHrqspLl5NUVHxnHN/n3qHPx0GBgYoKzvJqVMnOHXqhKyyOXm+Xq8nJyePgoJCVW45\nPT3jEw2ZLNUfa2hokM7ODjo6pAhHWbq6nPT39017jl6vJy7ORmJiAiaTWWYs+jMYrUHFK1hJTirY\nESx2+nw+hoaG/BjhLlUepL+/l46ODvr6+qadzA4LC5cDmHi5Vyv1bOPjE7DZbEvC8/B6vezcuZ0d\nO94lMzNb1sdx8G//9gssFiuXXnoFTz75a2655TYqK0Xc7jG++tW76Onp4fe//y2CUMDnPrdl1nmO\nRx99CK1WS1FRMatWlZCZmXXW2U/nlbSCApPJxAUXbOSCC6S0SkletJGyspOUlZ2iouIUlZWnKS8/\npZ4TGRlJXp6gKtDl5eWTlpYeVI4QJKJLZqaRzMzsM/aNjY0FREfSWtHe6aat7UypBQUxMbGYzWYs\nFqvKeIyNNctrSX4hOtq44tPvQlh4+JP4+vok2QR/hndPj4ve3h7cbve052u1WiwWK7m5QoA2jrLE\nxpqXtN0dPvwBHR1tXHbZVerQzZEjH1JWVsZdd32Dd955k+3bX+XKK6/G54O1a9eTnp5Bfn4hp06d\nwGQyUVtbDYDZLJVCLSs7OafDf/DBR5bsGmdDcHm8c4BWqyU9PYP09Ayuu+6vAMk5VldXcvp0ORUV\n0nLy5AmOHz+mnmcwRJCTk6PKLeflCWRlZS/KRMlCwGAwqKmf0yE6WkdVVYMsxNYti1RJEVdvbw9t\nba00NjbM+PlarY6YmBhZf0eSdJDkFiYlGEwmkyzFYAwxbFcofD4fo6OjDA7209+vkO766e+fXPsz\ns2fSw1FgMsWQkODAarX6aeJIPUyrNY6cnFQ13XE54fV60Wq1vPbay7hcLtasWac6/NOnK9BqtQhC\nPuDjwIH9vPfeu0RHR6syy2vWrOX111/j0ksvZ9s2KalEo9GQnp6hpmoHWxbTdPhU/msNBgNFRcUU\nFRWr20ZGRqiurkQUKzh9uoKqKpHTp09TVjbZE9BqtaSmppGTkysLteWSlZWDzZa3HJdxVoiKilLr\ncE4Hn8/H8PCQHJEp0VoPfX2T0dvAQD9tbS0BBd1nQkREJEZjoPSCtCiyC8riz8KNxOf79KamLiU8\nngn6+/txOjtlAtywSoQbGhqS15NkucFBSVhtaGhwXpwHabLXQkZGphwAmOXeodmvd2iec74sWLLP\ntFotlZUiLpeL4uISOjuljB2QpNZdrg71dXR0NB0d7bjdY2pt66ysbNraWsnIyFTH4r1eL+Hh4ZhM\nMUGZtjodVpzDV57UAwP9eDyeeWfpREZGqhMkCtxuN3V1NXIufSVVVSI1NVU0NNTz7rs71OOio6PJ\nzMwmOztHVt+UFovFuiJ+ZJCiD8UpKw19OigRoCS7oER7UvQ3ODigSjAoyozNzU1nVZNWoetPFtCO\nwGCIJCJCqceq1GQ1+DFw9TILdzJffbLgediUgudhKqlqueDz+aYtUK4UJQ9k1Y7L/IMxxsbcATWB\nFSLb6OiovEiv3TB64QAAFVlJREFUR0ZGAmpDzAdRUVEYjSZ5ot+oCuYZjSa1Byf16qT3n8YeXGNj\nPWvXrkOnC1erZPl8PmJiYlQJBZMpRpYDiVALsbjdbmJjzXR2dmA2W8jOzmHv3j1cfPFmTpw4xqpV\nJXi93qB5uM2GZf1V33nnTd599y1KStbz2c9eQE5O7qx/VJ/Ph1arZWRkhIcffpDy8jL+53+eITVV\ncmAKvT8pKXle36/X6xGEgoDKMj6fj/b2NmpqqqiurpKF12qoqCjj1KkTAefHxMSSmZkpq3ZKAmwZ\nGZkkJCSumAfBVGg0GiIjpfzr+eij+Hw+3G63GkUODw/5RZnDjIwMy9sk9u3ExBj9/YOMjY3S29tD\ne/vIWUkyzBdTiU/+zNtJpq1WJlLNn2k7Wazc68e0nVpXd+GvR6/Xq5pEZrOFyMgozGYTWm14QE9q\nUtjOSHR0lCp2txKc0WLjnXfe4oknfsXWrS+o2zQaDYmJDgYGBuju7iIuziZXsrKSlpbOwYP7KS3d\ngF6vJy0tnYGBAf7hH+7h5Zdf4k9/egGNRsO99963KPd3MXoNy+rwd+/exTPPPAM8A8D27Tv47Gc3\nzHnev//7L6mrq2Xjxk0BRJ3HHnuEPXveY9WqYnw+H3fddTdXXHE14+Pj807V1Gg0am7vpk2bASkb\noqWlm8bGempra6mtraa+vo76+toz5gZAyhFOTU0nPT1DFmFLJzU1nbS0tE8d21aj0agR+Xzykadm\nlvh8PlmhUYpipcjWzdjYqMq8nVyP+2nNjAdEzQrTdmJiXNWw8XgmAoqZT11L3+/1e61ck/R6sqbt\npAyDwrSVJBvCiIhQCpVrAx4wU7V+9Hq92guRmLThfrpBkxpC/tpCCnNZrzdM61CCJUtnOeDxeOjs\n7FDlT8LDw7jppi/MePzRox/hcCSxe/e7HD36EfX1tfT19XHDDTeRnp7B+Pg4x48f4/LLr6SuroaC\ngiKuueY6mpoa+dnPfkJbWytbttyo+oYvf/lvGR8fJy0tHZ1Od4Zz9vl8/PM/P8rJkyfQ6w08/vgv\nSEx0zHpNbrebl19+iSNHDnPkyIesX/8ZfvnLXy/YPYNldvg//enPueeeb/DWW+9y5MiHlJSsnvV4\njUbDo48+jNFo5KKLLsZujycqapJZV11dxfPP/4miomIOHtxPYqIUof72t0/x7rs7cLvHePDBR9SH\nytk8QZV0T6UAi4KxsTGamhrkB0AdDQ11aiOsqhLP+ByLxUpqqiLCJsk3SOuUoKjTu9TQaDSqswuW\nAjXnsyMNJkxMTNDR0U5LiyRjMrk00tLSHFARLi0tfVaHPzY2RmNjPRMT48TGmsnPL2Tt2vWEhUmB\n4Fe+8hW2b3+Tl1/+E2azhVWrpCInf/M3X6S1VWIu+2t9paSkqqqvH374Ac8//3uqq6v49rf/kSuv\nvJrjx4/S1dXNQw89yt69e3jqqSf5+tf/npSU1BltDAsL44EHfsDAQL88BF3ySW/hmd+x4J94FtDp\ndKxevZqkpCy+9rW/m/VYn8/H669vIywsjHvv/T5PPPEzTCZTAFmhtbWFmJhYtFotF10kaeLv2PEW\nhw4d4Ne/fpK6ulq2bn2B4uIS+vv7eeyxh2lpaaG0tJR77rl3TpGq6WAwGKZ9EHi9Xjo62mlqaqSp\nqYHGxkYaG+tpamri1KkTnDhx7IzPMplMqgCbw+GQ9XiSZC0eBwZDxFnbF0IIwQqfz0dPj4u2tlZa\nW1tpa2uRX7fQ0tJCR0fbtBPMRqOR7OxcUlPT1N5zenrGrN/ln8rd0FDPG29so6amirKyk+TnF3DF\nFVdgtTro7+8jJycPvV6Pz+fDZDLJ2TuwZ8977N27h9bWFqqrK3n44cfYuHETL730IiUlq7n//gf5\n3ve+g9lsZv/+vWRmZpGXJ2C1xvHLX/6cQ4cO8IUv/M2MgaZWq+XXv/4vkpOTKSoqXpRCRCtmZqa/\nv4/f/OZXpKWl83//9zsaGxv4zGdK1f2trS3Exdn41399gqamRu6++1tcffW17N69i5tvvoWkpGQS\nEx3ce++3MBgM3H//97j++r9i3brP8MQTP0MUT7N+feksFpwdtFqt2v377GcvCNg3Pj6uau8o0Utr\nq/S6traG06crpv1MqzVO1uBJVNfSkoBWm4PPF76ocwfKhPlbb73OqVMn+NrX/j5gGKeiopyGhjoy\nMjLJzMzGYDCoQyhzNd6VkuUQwvwxNjZGQ4OLiooaPy2cdpVl3t7ehts9Nu25cXE2CgtXkZSUTHJy\nSkCP2Gw+e5YtTLZfqzWOz33uehISHAEBoxR9SxH4zp1v43Q6ueGGz6vpm88881smJsZ54IGHSUiQ\nZE9qa2vQaGD9+lIcjiRWr17LkSOHiYqKVkUVbTYb6ekZHD360awOH+D66//qrK/rbLBiHH5MTCy/\n+tV/Ull5mm3bXuWDDw6i0WhYtWo18fHxxMXZePLJ/yU/v4DXX9/Gjh1vY7fbGRoaIi0tHQBRPE1u\nbh7V1VWIYgXPPPMHAC699HJ27Hh7QR3+bAgPD1e5A1Ph9XplIpUkwtba2kJ7uyQW1dbWSlWVGEAq\n84dU+MSfsSjJMfgTXWw22zn1FJQJ88pKkTfe2EZERISqsQ6wf/9e3ntvJ2FhYezevYstW25g06bN\n7N27m7/85c90dnZwzTXX853vfAOAXbt2smfPLuLj47nuuhvIzMwKOf0VAq/XS19fXwAJ0Ol0+rHD\nnXR2dqiSzNMhNtZMZmamqoOTmOggOTkZhyMZhyNpUSTGFYKXxCeZvjevtME//OFZBgYG2Lhxk+rw\n161bT39/PwUFherxIyMjqgIqwMaNm3j55Ze44oqreeWVl9TjcnJyOXjwALC8+forxuFrNBpZLqEQ\nvd7AmjXr+PznbyY+Ph6AkyePk58v/RApKSlYrVZ27nyHxESHOlRTVnaSwsJV7N+/l4wMqTSg8tR3\nOp0B75cLWq1WdtR2SkrWnLHf6/XicnWraoHt7ZIOT09PF83NrXR2dnD8+NFZNdmNRiNWqw2bzaYW\nkl6/vpRLLrl0xnMUyeC9e3djMsVQVFQc8B27du0gP7+QW265ja1bX6CyUiQ9PZMDB/Zz8823smnT\nZn7ykx9x6NAhxsc1fPzxYTZvvpzKygr27XufpKTkZal1GoIEj8dDX1+fyp6Vlh5ZIsGlEvq6u7tw\nuVx4PDOn4kZERBAfn0hOTi6pqcmYzTbi4xNISEhQVWKDtWaERqPh2LGP6e3tYcOGC2htbVEDs/Xr\nS7nnnrsJC9Nx+PBhrrtuC9ddt0XlOADk5xdSV1dLUdEqOjqk3H4pZTMMq3X5K2PNy+ELgvAr4AIk\nwfDviqJ42G/flcDPAA/whiiKP10MQ2Hy6SulUiVy4MA+IiOj2LLlBl544TlKSzdw++1fYt8+qeZk\nRkYmVVWVarbFgQP7uOCCjXz00WHWrfsMMEnISElZGUUMFEGpqeUL/ScaJybG6e7uVqMtJQrr6uoK\nkGTwJ1hptdpZHT7AU0/9hvT0TBITHXR3d6kPxoGBATQajZoem56eTlVVFW++uZ20tDRVKmJ8fByv\n18uuXbtIS8vg8suvJD+/gOef/z01NVUUFq5aoLt0/kIh2EnciYEp7NlJFu0k+a5Xrn08vdaNP/R6\nAzabjYKCwgABP0XYT1lLNW1nFiULdtTUVLNx4ybCwsLo6upSt69eLUm1b9iwkdtv/zI/+tH9GAwG\noqOj6ezswO12Y7fbaW5uxm63U1hYxPbtr7Flyw0cOLCPDRsuXPZe7JwOXxCEzUCuKIoXClLC+tPA\nhX6H/Bq4BmgB9giC8GdRFMsXw1jlRl177XWAEpVIBZbvvPNr/OxnP+G55/6P+PgE7r//QdLS0vm7\nv7tTTbc7duwo99xzL++++w6XXnoFAF1dXTQ3N3LrrXcEfMdUlJeX0dvbQ26ugM1mC+qhh7Cw8HnV\nGZ2YGKenpweXq3vOCeuamioArrrqWj788BAjI8NYLBLpbXBwAK/Xq1bG0mp1uN1jcl5zHEajlIqq\npCPW1tayZs16AKxWKwMDA4yOjn6ia16p8Hg8MtFqLIBYpdRTVaqH+TNph4eHGRoaZGJiDJer149J\nK5WinC8PQKvVEhMTozJqLRZJZ2lSJsGq9gCt1rgAR/5phdfr5dVXX+bZZ1/kqaf+Uy1iDlLP+D/+\n47/kWsBw0003U1VVSXHxanbseJtNmy7BYrFSUFDAwMAADz30KE899Z/893//BpPJxO23f3HZ7998\nIvwrgL8AiKJYIQiCRRCEGFEU+wVByAJcoig2AQiC8IZ8/KI4/KnQ6XTqpOHq1WvZuvUVAFyubnX7\nVVddy733fgutVstdd91NVlY2GzZspK6uFoDt218lNtbMmjVrgZkd/tNP/y/PPvs0IIkm5eYK5OTk\n8sADD6vDSisNYWHh8lj/3PYfO3aUgwf3U1Z2iv7+PkZHR7FYrFx22ZVERkYyPDxMRIQ0NzAyMqLW\nTQ0LC1dzyEdHR+Ui2f1qCqpGo2VwcGDGwhUKfve7p3j++d/LeepSRSiDwb/2rVJBKiyAdavUulUW\nqTKVUvZQqWKlZfJn12C3W3A6FSYmajlDn8+Hx+NVc/c9nsnatf71a/2ZtRMT4wH8gclFcvL+qYXn\niqioaIxGIzabnczMLEwmk8qknWTRxhAba1bXsbGxGI2m80Ywb+vWF3j99ddISkrm5z//5YzHHTy4\nn9TUNLZte5X9+/dSWSnS09PDl750JzqdjsOHPyA/v5Dk5BTq6mqJjIzk1ltvp6Ojne985xs0NTVy\n113/oCZs3HffD1VuDyx/csJ8HH4i8JHfe6e8rV9eO/32dQJnSj36wWKJIiwskERit599OuRs8P+8\n++67l/vuu5f29nY1L//rX/8Kt912G3v37iI2NpbHH3+cvLyMWT/zjjtuJSkpnoqKCioqKvj44yMc\nPvwBTz315IwTQEuNhb6P/rj77q/xxS/eysTEBE8//TTDw8Ns3ryRhIRYEhJi6ehoJTHRgt1uoq5O\nJDU1GYdDmjS32aRJsvb2Fmw2G+HhOtLTHXJ3fxSDIZz09MRZ7U9NdZCbmyuTsyRn2ds75FcK8ZM7\nTgUFBQVUVEyfKXW2UHgGkxIReszmWHVbZGSkSrJSGM7KEhUVRXR0NJGRkapGkbJITt1IVFRU0LNo\nF7NdzheNjTW89dYblJaWzmiP3W5Cr4fGxjrCw7WkpCRhs1nZsuUaEhOl3mtfXxc//vEPGB4elvPm\nH8DhsPCDH3yPtrY2kpKSAvg0dnv+klzffHEuk7azPZ7mfHT19AQq5y3VGJ9OF+33PQb++MdXcDqd\n8tCEg87O/hmfvHa7iXXrNrJu3UZ1m9vtpqmpgdFRGB1d/jHKpRsrDcPj0ZKYmMrHH58iPFxk7dr1\nbNiwkRde+BMFBUUcPvwRmzdfjdFo5Kc//TGXXXYtPp8Tn09DXFwc6elZHDtWjtWaxJtv7sRuT8Tn\n089q/9VX38DVV98w435Fv8btdsusW6XWrScgAldq3Ho8XmCyILnyGQBmcxS9vcNqe/Avdq4URVd6\nCf69B39mbXh4GOHh+kV1xiZT8I+PB8sY/p133s3f/u03sNls09qj2FlaejHPPSdxeKqqKtm69QX2\n7j3E22/vorR0AzfddBtZWfmEh+spLCxCo9HIvkNLXFwyY2Ms2vUuxINzzgIogiA8DLSJoviU/L4W\nWC2K4oAgCBnAH0VRvFDe9xDQLYribz6xZSGEEEIIISwo5jOA9w7wBQBBENYBraIoDgCIolgPxAiC\nkCEIQhiwRT4+hBBCCCGEIMO8ShwKgvBz4BLAC3wLWAv0iaL4iiAIlwD/LB/6Z1EU/2WxjA0hhBBC\nCOHcseQ1bUMIIYQQQlgenB85WSGEEEIIIYQcfgghhBDC+YKQww8hhBBCOE8QcvghhBBCCOcJFlUt\n81xE12Y7Z5nsvAx4XLZTBO5Cylh6CSiTDzspiuK3l9HGeqBJthHgi6Iotiz1vZzp+wRBSAae9zs0\nC7gf0AM/BWrk7TtEUXxsMW2U7VkFvAr8aipnJMja5Wx2Bku7nM3GeoKgXc5mZzC1TUEQngAuRvLL\nj4ui+LLfvgVpl4vm8M9FdA2wz3HOctj5P8Bloig2C4LwEnAtMAzsEUVx5ppqS2sjwOdEURw8y3OW\nxEZRFFuAS+XjwoDdwGtI/I6toih+f7HsmsbOaOA/gHdnOCRY2uVcdgZDu5zLRljmdjmXncHSNuUH\n+Cr5vsQBR4GX/Q5ZkHa5mEM6AaJrgEUQhBgAf9E1URS9gCK6NuM5y2GnjPWiKDbLr53A3JW6Fx7n\ncl+W+l7O9/u+isTXGJxm31JgDLgOaJ26I8ja5Yx2ygiGdjmXjdMhGO+lgq+yfG3zfeAW+XUvEC0I\ngg4Wtl0u5pDOuYiu2WY5ZznsRBTFfgBBEBzA1cCPgGKgUBCE1wAr8IgoijuWy0YZ/y1LXewDfjjP\nc5baRpCGHq72e79ZEIS3gHDg+6IoHl0k+wAQRXECmBAEYbrdQdMu57AzKNrlXDbKWO52OV87YRnb\npiiKHmBIfvt1pGEbZShswdrlUk7anovo2nLoiJ7xnYIgxAPbgG+KotgNVAGPADcCdwK/EwRBv4w2\n/hj4J6Su6Srg5nmcs9iY7j5eCJxWnBVwCHhYFMVrgQeBZ5fQvvkgmNrlGQjCdjkVwdgup0WwtE1B\nEG5Ecvj3zHLYObfLxYzwW5GeNgqSgLYZ9iXL29yznLNYmM1O5C7Sm8ADoii+A+q431b5kBpBENqR\nrqFuOWwURVFtjHJNguK5zllqG2VsAXYqb0RRPA2cll8fFATBLgiCzi+yWWoEU7ucFUHSLmdFkLTL\n+WLZ26YgCNcADwDXiqLY57drwdrlYkb45yK6NuM5y2GnjF8izey/pWwQBOGLgiB8X36dCCQgTaYs\nuY2CIMQKgvC2XyS3GTg1j+taMhv9UAocV94IgvD/BEG4XX69CnAuo7MPtnY5F4KhXc6IIGqX88Wy\ntk1BEGKBXwBbRFF0+e9byHa5qFo6wjmIrk09RxTF42d+8tLYCbwN9AAH/Q5/AfijvDYjpW89Iori\nG8tho3wvv4vUhR9Bmt3/tiiKvqW+l7PZKO8/CVwpimKH/D4FeA4p8AgD/lEUxQ8X2cb1SM4yAxhH\ncoivAXXB1C5ns5MgaZfzuJfB0i5ntVM+ZlnbpiAIfw88DFT6bd6FlFq7YO0yJJ4WQgghhHCeIMS0\nDSGEEEI4TxBy+CGEEEII5wlCDj+EEEII4TxByOGHEEIIIZwnCDn8EEIIIYTzBCGHH0IIIYRwniDk\n8EMIIYQQzhP8f0l2zD+kdeugAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f4a00ca00f0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "VlgYoOGs5CX1",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Logistic regression\n",
        "Your assignment is to implement the logistic regression\n",
        "\n",
        "Plan:\n",
        "* Use a shared variable for weights\n",
        "* Use a matrix placeholder for `X`\n",
        " \n",
        "We shall train on a two-class MNIST dataset\n",
        "* please note that target `y` are `{0,1}` and not `{-1,1}` as in some formulae"
      ]
    },
    {
      "metadata": {
        "id": "n30vCCyf4IRF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "d875c8ec-99ee-4550-e1e7-5357cd925c3a"
      },
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_digits\n",
        "mnist = load_digits(2)\n",
        "\n",
        "X, y = mnist.data, mnist.target\n",
        "\n",
        "print(\"y [shape - %s]:\" % (str(y.shape)), y[:10])\n",
        "print(\"X [shape - %s]:\" % (str(X.shape)))"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "y [shape - (360,)]: [0 1 0 1 0 1 0 0 1 1]\n",
            "X [shape - (360, 64)]:\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "S6LqICGJ4qY8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        },
        "outputId": "bc22b9bb-15eb-4921-e914-5d2aecb415c3"
      },
      "cell_type": "code",
      "source": [
        "print('X:\\n',X[:3,:10])\n",
        "print('y:\\n',y[:10])\n",
        "plt.imshow(X[0].reshape([8,8]));"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "X:\n",
            " [[ 0.  0.  5. 13.  9.  1.  0.  0.  0.  0.]\n",
            " [ 0.  0.  0. 12. 13.  5.  0.  0.  0.  0.]\n",
            " [ 0.  0.  1.  9. 15. 11.  0.  0.  0.  0.]]\n",
            "y:\n",
            " [0 1 0 1 0 1 0 0 1 1]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f49ff950908>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "zP91GbDI5XGp",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "It's your turn now!\n",
        "Just a small reminder of the relevant math:\n",
        "\n",
        "$$\n",
        "P(y=1|X) = \\sigma(X \\cdot W + b)\n",
        "$$\n",
        "$$\n",
        "\\text{loss} = -\\log\\left(P\\left(y_\\text{predicted} = 1\\right)\\right)\\cdot y_\\text{true} - \\log\\left(1 - P\\left(y_\\text{predicted} = 1\\right)\\right)\\cdot\\left(1 - y_\\text{true}\\right)\n",
        "$$\n",
        "\n",
        "$\\sigma(x)$ is available via `tf.nn.sigmoid` and matrix multiplication via `tf.matmul`"
      ]
    },
    {
      "metadata": {
        "id": "DporjK6m5OUq",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "X_train, X_test, y_train, y_test = train_test_split(\n",
        "    X, y, random_state=42)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "kPwFHIVR5d5b",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Model parameters - weights and bias\n",
        "# weights = tf.Variable(...) shape should be (X.shape[1], 1)\n",
        "# b = tf.Variable(...)\n",
        "weights = tf.Variable(tf.random_normal(shape=(X.shape[1],1), stddev=0.01, dtype=tf.float32))\n",
        "b = tf.Variable(0.0, dtype=tf.float32)\n",
        "s.run(tf.global_variables_initializer())"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "wWmHBK8w5i4E",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Placeholders for the input data\n",
        "# input_X = tf.placeholder(...)\n",
        "# input_y = tf.placeholder(...)\n",
        "input_X = tf.placeholder(tf.float32, (None, None))\n",
        "input_y = tf.placeholder(tf.float32, (None, ))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "klGQQZo45mYx",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# The model code\n",
        "\n",
        "# Compute a vector of predictions, resulting shape should be [input_X.shape[0],]\n",
        "# This is 1D, if you have extra dimensions, you can  get rid of them with tf.squeeze .\n",
        "# Don't forget the sigmoid.\n",
        "# predicted_y = <predicted probabilities for input_X>\n",
        "predicted_y = tf.squeeze(tf.sigmoid(tf.matmul(input_X, weights) + b))\n",
        "\n",
        "# Loss. Should be a scalar number - average loss over all the objects\n",
        "# tf.reduce_mean is your friend here\n",
        "# loss = <logistic loss (scalar, mean over sample)>\n",
        "loss = - tf.reduce_mean(input_y * tf.log(predicted_y) + (1-input_y) * tf.log(1-predicted_y))\n",
        "\n",
        "# See above for an example. tf.train.*Optimizer\n",
        "# optimizer = <optimizer that minimizes loss>\n",
        "optimizer = tf.train.AdamOptimizer(0.01).minimize(loss)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "6gH8mq095sdI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 608
        },
        "outputId": "912d61b4-c819-4324-ca95-004875396969"
      },
      "cell_type": "code",
      "source": [
        "validation_weights = 1e-3 * np.fromiter(map(lambda x:\n",
        "        s.run(weird_psychotic_function, {my_scalar:x, my_vector:[1, 0.1, 2]}),\n",
        "                                   0.15 * np.arange(1, X.shape[1] + 1)),\n",
        "                                   count=X.shape[1], dtype=np.float32)[:, np.newaxis]\n",
        "# Compute predictions for given weights and bias\n",
        "prediction_validation = s.run(\n",
        "    predicted_y, {\n",
        "    input_X: X,\n",
        "    weights: validation_weights,\n",
        "    b: 1e-1})\n",
        "\n",
        "# Load the reference values for the predictions\n",
        "validation_true_values = np.loadtxt(\"validation_predictons.txt\")\n",
        "\n",
        "assert prediction_validation.shape == (X.shape[0],),\\\n",
        "       \"Predictions must be a 1D array with length equal to the number \" \\\n",
        "       \"of examples in input_X\"\n",
        "assert np.allclose(validation_true_values, prediction_validation)\n",
        "loss_validation = s.run(\n",
        "        loss, {\n",
        "            input_X: X[:100],\n",
        "            input_y: y[-100:],\n",
        "            weights: validation_weights+1.21e-3,\n",
        "            b: -1e-1})\n",
        "assert np.allclose(loss_validation, 0.728689)"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "error",
          "ename": "OSError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mOSError\u001b[0m                                   Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-36-6741195dd4e5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;31m# Load the reference values for the predictions\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m \u001b[0mvalidation_true_values\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloadtxt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"validation_predictons.txt\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mprediction_validation\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m       \u001b[0;34m\"Predictions must be a 1D array with length equal to the number \"\u001b[0m        \u001b[0;34m\"of examples in input_X\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/numpy/lib/npyio.py\u001b[0m in \u001b[0;36mloadtxt\u001b[0;34m(fname, dtype, comments, delimiter, converters, skiprows, usecols, unpack, ndmin, encoding)\u001b[0m\n\u001b[1;32m    915\u001b[0m             \u001b[0mfname\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    916\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0m_is_string_like\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 917\u001b[0;31m             \u001b[0mfh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_datasource\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'rt'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mencoding\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    918\u001b[0m             \u001b[0mfencoding\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'encoding'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'latin1'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    919\u001b[0m             \u001b[0mfh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfh\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/numpy/lib/_datasource.py\u001b[0m in \u001b[0;36mopen\u001b[0;34m(path, mode, destpath, encoding, newline)\u001b[0m\n\u001b[1;32m    258\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    259\u001b[0m     \u001b[0mds\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDataSource\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdestpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 260\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mds\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mencoding\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnewline\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnewline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    261\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    262\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/numpy/lib/_datasource.py\u001b[0m in \u001b[0;36mopen\u001b[0;34m(self, path, mode, encoding, newline)\u001b[0m\n\u001b[1;32m    614\u001b[0m                                       encoding=encoding, newline=newline)\n\u001b[1;32m    615\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 616\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mIOError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"%s not found.\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    617\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    618\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mOSError\u001b[0m: validation_predictons.txt not found."
          ]
        }
      ]
    },
    {
      "metadata": {
        "id": "uYQAofwd5yS1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "3ee200f4-d3fd-4ff3-9c67-5af3372d9cc3"
      },
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import roc_auc_score\n",
        "s.run(tf.global_variables_initializer())\n",
        "for i in range(5):\n",
        "    s.run(optimizer, {input_X: X_train, input_y: y_train})\n",
        "    loss_i = s.run(loss, {input_X: X_train, input_y: y_train})\n",
        "    print(\"loss at iter %i:%.4f\" % (i, loss_i))\n",
        "    print(\"train auc:\", roc_auc_score(y_train, s.run(predicted_y, {input_X:X_train})))\n",
        "    print(\"test auc:\", roc_auc_score(y_test, s.run(predicted_y, {input_X:X_test})))"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "loss at iter 0:0.4690\n",
            "train auc: 0.9936868686868687\n",
            "test auc: 0.9965415019762845\n",
            "loss at iter 1:0.2466\n",
            "train auc: 0.9993412384716732\n",
            "test auc: 1.0\n",
            "loss at iter 2:0.1170\n",
            "train auc: 0.9998353096179183\n",
            "test auc: 1.0\n",
            "loss at iter 3:0.0808\n",
            "train auc: 0.9998902064119456\n",
            "test auc: 1.0\n",
            "loss at iter 4:0.0681\n",
            "train auc: 0.9998902064119456\n",
            "test auc: 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "5I3nmOJb59MS",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "test_weights = 1e-3 * np.fromiter(map(lambda x:\n",
        "    s.run(weird_psychotic_function, {my_scalar:x, my_vector:[1, 2, 3]}),\n",
        "                               0.1 * np.arange(1, X.shape[1] + 1)),\n",
        "                               count=X.shape[1], dtype=np.float32)[:, np.newaxis]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "pnfOML1A6P2Y",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        ""
      ]
    },
    {
      "metadata": {
        "id": "dZ5p3sw36Qkm",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "prediction_test = sess.run(\n",
        "    predicted_y, {\n",
        "    input_X: X,\n",
        "    weights: test_weights,\n",
        "    b: 1e-1})"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "dZT6lFnL6gVQ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "assert prediction_test.shape == (X.shape[0],),\\\n",
        "       \"Predictions must be a 1D array with length equal to the number \" \\\n",
        "       \"of examples in X_test\""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "0OICfouV6haV",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "loss_test = sess.run(\n",
        "    loss, {\n",
        "        input_X: X[:100],\n",
        "        input_y: y[-100:],\n",
        "        weights: test_weights+1.21e-3,\n",
        "        b: -1e-1})\n",
        "# Yes, the X/y indices mistmach is intentional"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "_0c9WXYw6om6",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}