2. Automatic Differentiation.ipynb

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      "source": [
        "# How to learn DL models?\n",
        "\n",
        "> The **backpropagation** algorithm was originally introduced in the 1970s, but its importance wasn't fully appreciated until a famous 1986 paper by David Rumelhart, Geoffrey Hinton, and Ronald Williams.\n",
        "\n",
        "> **Backpropagation** is the key algorithm that makes training deep models computationally tractable. For modern neural networks, it can make training with gradient descent as much as ten million times faster, relative to a naive implementation. That’s the difference between a model taking a week to train and taking 200,000 years. (Christopher Olah, 2016)\n",
        "\n",
        "We have seen that in order to optimize our models we need to compute the derivative of the loss function with respect to all model paramaters. For example, given:\n",
        "\n",
        "$$ L(y, f_{\\mathbf w}(\\mathbf{x})) = \\frac{1}{n} \\sum_i (y_i - f_{\\mathbf w}(\\mathbf{x}_i))^2  $$\n",
        "\n",
        "where ${\\mathbf w} = (w_1, w_2, \\dots, w_m)$, we need to compute:\n",
        "\n",
        "$$\n",
        "\\frac{\\delta L}{\\delta w_i}\n",
        "$$\n",
        "\n",
        "The computation of derivatives in computer models is addressed by four main methods: \n",
        "\n",
        "+ Manually working out derivatives and coding the result (as in the original paper describing backpropagation); \n",
        "\n",
        "![alt text](https://github.com/DataScienceUB/DeepLearningMaster2019/blob/master/images/back.png?raw=1)\n",
        "\n",
        "\n",
        "+ Numerical differentiation (using finite difference approximations); \n",
        "+ Symbolic differentiation (using expression manipulation in software, such as Sympy); \n",
        "+ and Automatic differentiation (AD).\n",
        "\n",
        "## Automatic differentiation\n",
        "\n",
        "**Automatic differentiation** (AD) works by systematically applying the **chain rule** of differential calculus at the elementary operator level.\n",
        "\n",
        "Let $ y = f(g(x)) $ our target function. In its basic form, the chain rule states:\n",
        "\n",
        "$$ \\frac{\\partial f}{\\partial x} = \\frac{\\partial f}{\\partial g} \\frac{\\partial g}{\\partial x} $$\n",
        "\n",
        "or, if there are more than one variable $g_i$ in-between $y$ and $x$ (f.e. if $f$ is a two dimensional function such as $f(g_1(x), g_2(x))$), then:\n",
        "\n",
        "$$ \\frac{\\partial f}{\\partial x} = \\sum_i \\frac{\\partial f}{\\partial g_i} \\frac{\\partial g_i}{\\partial x} $$\n",
        "\n",
        "> See https://www.math.hmc.edu/calculus/tutorials/multichainrule/\n",
        "\n",
        "Now, **let's see how AD allows the accurate evaluation of derivatives at machine precision**, with only a small constant factor of overhead.\n",
        "\n",
        "In its most basic description, AD relies on the fact that all numerical computations\n",
        "are ultimately compositions of a finite set of elementary operations for which derivatives are known."
      ]
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      "source": [
        "For example, let's consider the computation of the derivative of this function, that represents a 1-layer neural network model:\n",
        "\n",
        "$$\n",
        "    f(x) = \\frac{1}{1 + e^{- ({w}^T \\cdot  x + b)}} \n",
        "$$\n",
        "\n",
        "\n",
        "First, let's write how to evaluate $f(x)$ via a sequence of primitive operations:\n",
        "\n",
        "\n",
        "```python\n",
        "x = ?  # This is an arbitrary point\n",
        "f1 = w * x\n",
        "f2 = f1 + b\n",
        "f3 = -f2\n",
        "f4 = 2.718281828459 ** f3\n",
        "f5 = 1.0 + f4\n",
        "f = 1.0/f5\n",
        "```\n",
        "\n",
        "The question mark indicates that $x$ is a value that must be provided. \n",
        "\n",
        "This *program* can compute the value of $f(x)$ and also **populate program variables**. \n",
        "\n",
        "By using this sequence, we can evaluate $\\frac{\\partial f}{\\partial x}$ at any $x$ by using the chain rule. This is called *forward-mode differentiation*. \n",
        "\n",
        "In our case:"
      ]
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      "source": [
        "def f(x,w,b):\n",
        "    f1 = w * x\n",
        "    f2 = f1 + b\n",
        "    f3 = -f2\n",
        "    f4 = 2.718281828459 ** f3\n",
        "    f5 = 1.0 + f4\n",
        "    return 1.0/f5\n",
        "\n",
        "def dfdx_forward(x, w, b):\n",
        "    f1 = w * x\n",
        "    p1 = w                            # p1 = df1/dx\n",
        "    f2 = f1 + b\n",
        "    p2 = p1 * 1.0                     # p2 = p1 * df2/df1 \n",
        "    f3 = -f2\n",
        "    p3 = p2 * -1.0                    # p3 = p2 * df3/df2\n",
        "    f4 = 2.718281828459 ** f3\n",
        "    p4 = p3 * 2.718281828459 ** f3    # p4 = p3 * df4/df3\n",
        "    f5 = 1.0 + f4\n",
        "    p5 = p4 * 1.0                     # p5 = p4 * df5/df4\n",
        "    f6 = 1.0/f5\n",
        "    dfx = p5 * -1.0 / f5 ** 2.0        # df/dx = p5 * df6/df5\n",
        "    return f6, dfx\n",
        "\n",
        "der = (f(3+0.00001, 2, 1) - f(3, 2, 1))/0.00001\n",
        "\n",
        "print(\"Value of the function at (3, 2, 1): \",f(3, 2, 1))\n",
        "print(\"df/dx Derivative (fin diff) at (3, 2, 1): \",der)\n",
        "print(\"df/dx Derivative (aut diff) at (3, 2, 1): \",dfdx_forward(3, 2, 1)[1])"
      ],
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            "Value of the function at (3, 2, 1):  0.9990889488055992\n",
            "df/dx Derivative (fin diff) at (3, 2, 1):  0.0018204242002717306\n",
            "df/dx Derivative (aut diff) at (3, 2, 1):  0.0018204423602438651\n"
          ],
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        }
      ]
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      "source": [
        "It is interesting to note that this *program* can be automatically derived  if we have access to **subroutines implementing the derivatives of primitive functions** (such as $\\exp{(x)}$ or $1/x$) and all intermediate variables are computed in the right order. \n",
        "\n",
        "It is also interesting to note that AD allows the accurate evaluation of derivatives at **machine precision**, with only a small constant factor of overhead.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dY5UTgP3KxBo",
        "colab_type": "text"
      },
      "source": [
        "> **Exercise**: Write an automatic differentiation program to compute $\\partial f/ \\partial w$ and $\\partial f/\\partial b$."
      ]
    },
    {
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        "id": "cnQMZuwjKxBp",
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      "source": [
        "def f(x,w,b):\n",
        "    f1 = w * x\n",
        "    f2 = f1 + b\n",
        "    f3 = -f2\n",
        "    f4 = 2.718281828459 ** f3\n",
        "    f5 = 1.0 + f4\n",
        "    return 1.0/f5\n",
        "\n",
        "# solution code\n",
        "\n",
        "def dfdx_forward_w(x, w, b):\n",
        "    pass\n",
        "\n",
        "def dfdx_forward_b(x, w, b):\n",
        "    pass\n",
        "\n",
        "print(\"df/dw Derivative (aut diff) at (3, 2, 1): \",\n",
        "      dfdx_forward_w(3, 2, 1))\n",
        "print(\"df/db Derivative (aut diff) at (3, 2, 1): \",\n",
        "      dfdx_forward_b(3, 2, 1))\n",
        "\n",
        "# approximate results (just for checking)\n",
        "\n",
        "derw = (f(3, 2+0.00001, 1) - f(3, 2, 1))/0.00001\n",
        "derb = (f(3, 2, 1+0.00001) - f(3, 2, 1))/0.00001\n",
        "\n",
        "print(\"df/dw Derivative (fin diff) at (3, 2, 1): \",derw)\n",
        "print(\"df/db Derivative (fin diff) at (3, 2, 1): \",derb)\n"
      ],
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      "outputs": [
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          "output_type": "stream",
          "text": [
            "df/dw Derivative (aut diff) at (3, 2, 1):  None\n",
            "df/db Derivative (aut diff) at (3, 2, 1):  None\n",
            "df/dw Derivative (fin diff) at (3, 2, 1):  0.0027306226724199685\n",
            "df/db Derivative (fin diff) at (3, 2, 1):  0.0009102166464991511\n"
          ],
          "name": "stdout"
        }
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      "cell_type": "markdown",
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      "source": [
        "Forward differentiation is efficient for functions $f : \\mathbb{R}^n \\rightarrow \\mathbb{R}^m$ with $n << m$ (only $O(n)$ sweeps are necessary).  This is not the case of neural networks!\n",
        "\n",
        "For cases $n >> m$ a different technique is needed. To this end, we will rewrite the chain rule as:\n",
        "\n",
        "$$\n",
        "\\frac{\\partial f}{\\partial x} = \\frac{\\partial g}{\\partial x} \\frac{\\partial f}{\\partial g}\n",
        "$$\n",
        "\n",
        "to propagate derivatives backward from a given output. This is called *reverse-mode differentiation*. Reverse pass starts at the end (i.e. $\\frac{\\partial f}{\\partial f} = 1$) and propagates backward to all dependencies."
      ]
    },
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      "source": [
        "def dfdx_backward(x, w, b):\n",
        "    \n",
        "    import numpy as np\n",
        "    f1 = w * x\n",
        "    f2 = f1 + b\n",
        "    f3 = -f2\n",
        "    f4 = 2.718281828459 ** f3\n",
        "    f5 = 1.0 + f4\n",
        "    f = 1.0/f5\n",
        "    \n",
        "    pf = 1.0                           # pf = df/df\n",
        "    p5 = 1.0 * -1.0 / (f5 * f5)        # p5 = pf * df/df5 \n",
        "    p4 = p5 * 1.0                      # p4 = p5 * df5/df4\n",
        "    p3 = p4 * np.log(2.718281828459) \\\n",
        "          * 2.718281828459 ** f3       # p3 = p4 * df4/df3\n",
        "    p2 = p3 * -1.0                     # p2 = p3 * df3/df2\n",
        "    p1 = p2 * 1.0                      # p1 = p2 * df2/df1\n",
        "    dfx = p1 * w                       # df/dx = p1 * df1/dx \n",
        "    \n",
        "    return f, dfx\n",
        "\n",
        "print(\"df/dx Derivative (aut diff) at (3, 2, 1): \",\n",
        "      dfdx_backward(3, 2, 1)[1])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "df/dx Derivative (aut diff) at (3, 2, 1):  0.0018204423602438348\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bFds_nWeKxBy",
        "colab_type": "text"
      },
      "source": [
        "> **Exercise**:  Write an automatic differentiation program to compute $\\partial f/ \\partial w$ and $\\partial f/\\partial b$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KGz7dXuVKxBz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# solution code\n",
        "\n",
        "def dfdx_backward(x, w, b):\n",
        "    pass"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f0I-yLHWKxB6",
        "colab_type": "text"
      },
      "source": [
        "In practice, reverse-mode differentiation is a two-stage process. In the first stage the original function code is run forward, populating $f_i$ variables. In the second stage, derivatives are calculated by propagating in reverse, from the outputs to the inputs.\n",
        "\n",
        "The most important property of reverse-mode differentiation is that it is **cheaper than forward-mode differentiation for functions with a high number of input variables**. In our case, $f : \\mathbb{R}^n \\rightarrow \\mathbb{R}$, only one application of the reverse mode is sufficient to compute the full gradient of the function $\\nabla f = \\big( \\frac{\\partial y}{\\partial x_1}, \\dots ,\\frac{\\partial y}{\\partial x_n} \\big)$. This is the case of deep learning, where the number of input variables is very high. \n",
        "\n",
        "> As we have seen, AD relies on the fact that all numerical computations\n",
        "are ultimately compositions of a finite set of elementary operations for which derivatives are known. \n",
        "\n",
        "> For this reason, given a library of derivatives of all elementary functions in a deep neural network, we are able of computing the derivatives of the network with respect to all parameters at machine precision and applying stochastic gradient methods to its training. Without this automation process the design and debugging of optimization processes for complex neural networks with millions of parameters would be impossible. "
      ]
    },
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      "cell_type": "markdown",
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      "source": [
        "## Autograd\n",
        "\n",
        "Autograd is a Python module (with only one function) that implements automatic differentiation.\n",
        "\n",
        "Autograd can automatically differentiate Python and Numpy code:\n",
        "\n",
        "+ It can handle most of Python’s features, including loops, if statements, recursion and closures.\n",
        "+ Autograd allows you to compute gradients of many types of data structures (Any nested combination of lists, tuples, arrays, or dicts).\n",
        "+ It can also compute higher-order derivatives.\n",
        "+ Uses reverse-mode differentiation (backpropagation) so it can efficiently take gradients of scalar-valued functions with respect to array-valued or vector-valued arguments.\n",
        "+ You can easily implement your custim gradients (good for speed, numerical stability, non-compliant code, etc)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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        "colab_type": "code",
        "outputId": "7d304015-4651-4150-dbc8-d2b97661a59f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "import autograd.numpy as np\n",
        "from autograd import grad\n",
        "\n",
        "x1 = np.array([2, 2], dtype=float)\n",
        "x2 = np.array([5, 2], dtype=float)\n",
        "\n",
        "def test(x):\n",
        "    if x[0]>3:\n",
        "        return np.log(x[0]) + x[0]*x[1] - np.sin(x[1])\n",
        "    else:\n",
        "        return np.log(x[0]) + x[0]*x[1] + np.sin(x[1])\n",
        "      \n",
        "grad_test = grad(test)\n",
        "\n",
        "print(\"({:.2f},{:.2f})\".format(grad_test(x1)[0],grad_test(x1)[1]))\n",
        "print(\"({:.2f},{:.2f})\".format(grad_test(x2)[0],grad_test(x2)[1]))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(2.50,1.58)\n",
            "(2.20,5.42)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QvIOvBsiKxCC",
        "colab_type": "text"
      },
      "source": [
        "Then, a simple (there is no bias term) logistic regression model for $n$-dimensional data like this\n",
        "\n",
        "$$  f(x) = \\frac{1}{1 + \\exp^{-(\\mathbf{w}^T \\mathbf{x})}} $$\n",
        "\n",
        "can be implemented in this way:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zr2i7IfZKxCD",
        "colab_type": "code",
        "outputId": "d19114ac-82f0-40e3-d7cf-1c029008fcf6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "source": [
        "import autograd.numpy as np\n",
        "from autograd import grad\n",
        "\n",
        "def sigmoid(x):\n",
        "    return 1 / (1 + np.exp(-x))\n",
        "\n",
        "def logistic_predictions(weights, inputs):\n",
        "    return sigmoid(np.dot(inputs, weights))\n",
        "\n",
        "def training_loss(weights, inputs, targets):\n",
        "    preds = logistic_predictions(weights, inputs)\n",
        "    loss = preds * targets + (1 - preds) * (1 - targets)\n",
        "    return -np.sum(np.log(loss))\n",
        "\n",
        "def optimize(inputs, targets, training_loss):\n",
        "    # Optimize weights using gradient descent.\n",
        "    gradient_loss = grad(training_loss)\n",
        "    weights = np.zeros(inputs.shape[1])\n",
        "    print(\"Initial loss:\", training_loss(weights, inputs, targets))\n",
        "    for i in range(100):\n",
        "        weights -= gradient_loss(weights, inputs, targets) * 0.01\n",
        "    print(\"Final loss:\", training_loss(weights, inputs, targets))\n",
        "    return weights\n",
        "\n",
        "# Build a toy dataset with 3d data\n",
        "inputs = np.array([[0.52, 1.12,  0.77],\n",
        "                   [0.88, -1.08, 0.15],\n",
        "                   [0.52, 0.06, -1.30],\n",
        "                   [0.74, -2.49, 1.39]])\n",
        "targets = np.array([True, True, False, True])\n",
        "\n",
        "weights = optimize(inputs, targets, training_loss)\n",
        "print(\"Weights:\", weights)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Initial loss: 2.772588722239781\n",
            "Final loss: 1.0672706757870165\n",
            "Weights: [ 0.48307366 -0.37057217  1.06937395]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HhK50JDuKxCH",
        "colab_type": "text"
      },
      "source": [
        "Any complex function that can be decomposed in a set of elementary functions can be derived in an automatic way, at machine precision, by this algorithm!\n",
        "\n",
        "**We no longer need to code complex derivatives to apply SGD!** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "riYg8Y5fKxCH",
        "colab_type": "text"
      },
      "source": [
        "> **Exercise**:  Make the necessary changes to the code below in order to compute a max-margin solution for a linear separation problem by using SGD. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pnjCRoiRKxCJ",
        "colab_type": "code",
        "outputId": "a071ef02-bf50-47bf-a9b3-eba440295084",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "%reset"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rhjw6j0_KxCQ",
        "colab_type": "code",
        "outputId": "86b4aef0-a8eb-434c-e980-f1d1a30dbd03",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "#Example dataset\n",
        "N_samples_per_class = 100\n",
        "d_dimensions = 2\n",
        "x = np.vstack((np.random.randn(N_samples_per_class, d_dimensions),\n",
        "               np.random.randn(N_samples_per_class, d_dimensions)\n",
        "               +np.array([5,5])))\n",
        "y = np.concatenate([-1.0*np.ones(N_samples_per_class),\n",
        "              1.*np.ones(N_samples_per_class)])\n",
        "\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, ax = plt.subplots(1, 1)\n",
        "fig.set_facecolor('#EAEAF2')\n",
        "idx = y==1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.25)\n",
        "idx = y==-1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.5,color='pink')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fa6afc0ce48>"
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          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
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qA0ChUnNQFXLtZk4mDYk3QewA47JJ1jGqnpRrp01UG2404cbgHDfPWgA2o3/M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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mYy0z5SaKxCU",
        "colab_type": "code",
        "outputId": "240512f0-12f6-4b82-d180-bbba1d6404dd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 243
        }
      },
      "source": [
        "import autograd.numpy as np\n",
        "from autograd import grad\n",
        "\n",
        "def SVM_predictions(w, inputs):\n",
        "    return np.dot(w[0,:-1],inputs.T)+w[0,-1]\n",
        "\n",
        "def SVM_training_loss(weights, inputs, targets):\n",
        "    pred = SVM_predictions(weights, inputs)\n",
        "    return np.sum((targets-pred)**2)/inputs.shape[0]\n",
        "\n",
        "def optimize(inputs, targets, training_loss):\n",
        "    gradient_loss = grad(training_loss)\n",
        "    weights = np.zeros((1,inputs.shape[1]+1))\n",
        "    print(\"Initial loss:\", training_loss(weights, inputs, targets))\n",
        "    for i in range(100000):\n",
        "        weights -= gradient_loss(weights, inputs, targets) * 0.001\n",
        "        if i%10000 == 0:\n",
        "            print(\" Loss:\", training_loss(weights, inputs, targets))\n",
        "    print(\"Final loss:\", training_loss(weights, inputs, targets))\n",
        "    return weights\n",
        "\n",
        "weights = optimize(x, y, SVM_training_loss)\n",
        "print(\"Weights\", weights)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Initial loss: 1.0\n",
            " Loss: 0.9524140689814686\n",
            " Loss: 0.08706236829021527\n",
            " Loss: 0.08706236575690411\n",
            " Loss: 0.0870623657569041\n",
            " Loss: 0.0870623657569041\n",
            " Loss: 0.0870623657569041\n",
            " Loss: 0.0870623657569041\n",
            " Loss: 0.0870623657569041\n",
            " Loss: 0.0870623657569041\n",
            " Loss: 0.0870623657569041\n",
            "Final loss: 0.0870623657569041\n",
            "Weights [[ 0.18082104  0.18867935 -0.92233123]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2u3e4WQNKxCY",
        "colab_type": "code",
        "outputId": "5fb15fad-731a-4ffe-f742-9e357cc8618a",
        "colab": {}
      },
      "source": [
        "delta = 0.1\n",
        "xx = np.arange(-4.0, 10.0, delta)\n",
        "yy = np.arange(-4.0, 10.0, delta)\n",
        "XX, YY = np.meshgrid(xx, yy)\n",
        "Xf = XX.flatten()\n",
        "Yf = YY.flatten()\n",
        "sz=XX.shape\n",
        "test_data = np.concatenate([Xf[:,np.newaxis],Yf[:,np.newaxis]],axis=1)\n",
        "Z = SVM_predictions(weights,test_data)\n",
        "\n",
        "fig, ax = plt.subplots(1, 1)\n",
        "fig.set_facecolor('#EAEAF2')\n",
        "Z = np.reshape(Z,(xx.shape[0],xx.shape[0]))\n",
        "plt.contour(XX,YY,Z,[0])\n",
        "idx = y==1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.25)\n",
        "idx = y==-1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.5,color='pink')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fdc230f2438>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nMFEFUOJ1vjpzEzIJh/hbGVDLpVDJpDDZ7EgyWDGuZ4NS1dmX5jMReXHXivFKg1KLFi3duhhRNhRKOV5+/X/o0r89lr/8NuY8uhR9BnfHqFUvQR+sEzs8wosIwnstJQtnrqdBIZGgZqgWNUM0CMquVCmqYamk8b9FNSPJJFyJjVHBGgXMNidaVA/EtRQjMsxWyKQStK8TUipBFurm7U4n4m8ZYDDbIJNKILvMoV+raqX/hRGFQp2nlYhGMfXx9ok38cHivfjwjc9wKu4sXt0wDJ0fayd2aIQXEITXyTtxI9WEdKMVCpkM5qR0HDh/ByqZBJFBatQL0xS6WCmULtqdTlxLMeaIZr0wdvMvqrP114tJiApUwWB15CyKBqrleebBN47S59wUmlcLzMm0O9QLKdVnTDVa82T+ASoFTDY7jv+Xgg71SneTIIqGZsVUMhRKOV5a+BzePr4UQREBeO2JZVj6wlpkJPvervGVCV8YQ3shIRNO3okTV1JwPTkLVgeP5Cwz/riaDp4HJByHTJMdx6+k4vzt9ALvbxylx600I07+lwKLzQGFVIoMkx0pWRYkZZoLbUay2h24nmpEpsWeZ1H0dpoJHLic38mFhEw0idLlKcVsEqXDhYTMUv3OgjUKXEw0QC2XQi2XguPY5wrTKst9m7+qBAl7JaVBm7pYd+wNvDBvAH7+6AiGNp+IXz8/LnZYlY6kTDO+PnMLbx24hN+vpkHKcaLVZ19LycKlRAMMZjsUUuY//3kzAwazHXIpYLI5oZBKUDtEg58uJBZ4f7LBgpP/JePUf6k48m8yUo0WxNQORrUgDS4kZBbajHTmehoUMg7/JGTiwp1M2J1OcBxw9mYaUrIseWrWzycY0DhKj0dbVUfjKD3OJxhKXdPeOEqPu5kWgAd4nofZ5oDR6kCDCC1V13gREvZKjFwhx+D5z2Dd8TcQEh2M+U8ux5JBq5F+N0Ps0CoFgvVx+a4B4ToFpBLgz1sZsDmcBbpEKyKjTzfZIOE4yKUS3EgzQS2XQi7j4OSB2xkWSMCjbrgW0YFqJGbk3U/3/O10vHf0Gqx2J+6J1iMqQIV/7hhw8r9knLmeht/+vYswnSJPCeatVCP+vJ2B2qFa3FMtAOA5/HkrExxYFl0tSJNnhozD4cQnp67jqzM38cmp63A4nKXewCNcr0L7uiFw8kC62Z7TwKWQSWmImBchYfcDGrRm2fuLC57FL58cxdDmk/DLpzSIrSQE6+NyogGXk7JwK80EJ8/jeooxT5doRXVcBqhkcPJApsWGNKMFN9NMAM9BIQXCtApEBqmhU8qQbrYhIkCZE9vhi0lY/9MlZJpt0CjlsPGAVAIYLXb8c8cAhYyDUi7F+QRDHjsl0WBGs2oB0Cnl0KvkaBKtR8sagZDLJNAopHlsmzSjFf/ezUJaFlugTcvK/t4ly3Z3YFmHeqGoFapBqxpBaF49EHKppNAaf1+wxyorJOx+gkwuw/Nzn8bbJ95EeI0QLHx6BRb/bxXSkgp6sQRDsD7kMgnkUg52J49bqSbcyTDnmZdSXtvL5ad2qA7hWgWSs6zQquTQKqQIVsthcwBquRQ8zxYf04w29GgckeeGY7HzUEg5GK0OZJhsSMy0QqeUIctih9nuRKNIPXRKGe4arDnNSDWCmbgarQ6YbQ7wPA/wwN1MC5pGB+Sxba6nGCHhgFC9ChzHbhQ3Uo34/s8EnLuRhjSj1e2BZe6MTqDxBZ5BVTF+Rr2WtbH2tyX4aNkXeG/hHpw+EI9xbw/FfU93Ejs0n0OwPmoEa/DX7QyYrA4YLTYkZ1lRO1SDvi2iAZRcRugtWOXJXdQI1kAlkwIc2HRIKXAzzYwsix1apRT9WkajSXQgDl9MyrnhBGsVsNgcCFDLYXc4kWm2w2K1IUAtR4vqgQhUK8DzfJ6YgzUK3Ek3QyrhcDHRAB5AlF6J9nVD0KFeKH69lJz7WQ0WSKUcaoVokGa0ItPigN3hhAQsxlNXU1ErRI32dUNw+GKSWw1V5TXXnqCM3S+RyWUYNPsprD+1DOG1wrDomVgsejYWqYmUvbsiWB9mmwMAD4fTCZ7noZDl/WfhyTjd0hCuV6FmiBq1Q9RIN1nA8zzqhGpQM0SHeuE6LH6yBUbd3xBNogMB5J3f3qZmIDLNNlhtTjidToRpldCpFejbIhqBakWhMYfpFDjy711cvWsEeB5wAncNFjSI0OXJqq/czUSayYpMsx3Xko34+3YGwrQK1AnTQq+Ww+pwIEAtg0zClWlBtTBolybPIGH3Y+o2r4W3fluCV5YMxG9fnMDQZhPx80e/skduArVDdagfpkWq0Qa5RII6oVq0rxeKjvVDcypJgIqd+1IrRItWNUPwRJuaaBihh4MHnDzQvm7BGm/XG06tUB363BMJqYSD0eZEjRAV2tUJRqhWVWTMlxKzoJRLoZBz4DhAIWcWy6VENp01XK9C4yg9tEoFOtQLhV4lQ4bZhvMJGcg02cBxHLo3jkCn+uFoEK7D0csp+PtWOi4nGZBusnlkWVXUzdRfIWH3c6QyKZ6b0R8bfl+G6HoRWPy/1Vg4YCVS76SJHZroCIOzAlUytKoRhOggNSQSCWqFaPJkh0L2arY5cOTSXfxxLQWycvqXI9xEhGqRVjWCUCtUgw71Qos8VrjhhOpUaFUzEI+1qo4m0QGoHaqD2WYv0sc+fzsD0YEqNIkKQPPqQWgSFYDoQBXO386tqhIskehADVrWCEKAWg65BEgyWHIsnjSjFb9fS4Pd6USYTplTC5+WnXWXJcumXZo8g4S9ilD7nppY8+tivPLGIBz75ne80mwiDnx4uEpn74JgB2nluGswQyGT5IhVYdmh3cmjda1gdGkQDpVcVi6LeaWZyZ7/WLPNDgBQyaUI1Sqhkkthd+ZuhgEgT5WJ0WoDBy7POTlw4JH7d8LVEglUK9CiehAeaVkdWqUMMokEPM/j4h0DAB4NInSwOJxQyVlFzfUUY5mzbNqlyTNo8bQKIZVJ8dz0J9DpsXuxYsh6vDFoDQ7tOYLx64chJKrooW3+TLhehadjauYZTCVkh61q5mbJZV3MK8skw5IWFovieqoRETpVoTECKDAnxuEEbmeYUC1QDaVMAovdiTSTDa1rBuacs7CNqxUyKdrXDckRXavdgZjaweA4DudusnUcpVSCuwYLIgJUeX6PpaGsvweChL1KUrtpDaw+vAh7Y7/GjnkfYWiziRiz9hX0HNgVHMeVfAI/w50Ru2WpjDl/Ox1fnL4Fp5OHUi6Bxe7A/j8TcqpOhPOXdYxt/qFe8TfSkGl2QKOU5QwME2LMf2OyZWfWf99Oh9nqRKBGjiC1ArVC1HlsH2FGjHCuwqYxBmtyp0oKQ8LuZpoRpFVQli0SZMVUUaRSKZ6Z+jg2/rEcNZtUx9IX1uK1/suQfDtV7NBEoaTNJlwX89KMVpy7kYaDFxJxI9VYqB3jurm0WsEWJK+nmKFVSHE5yZhj43hSr52/vj5Ur4KEYzXnAoIV4mqppBmtiL+ZDr1KjmpBKgA8Lt3JhMVuy7NIK9xwjFYbLiZm4MrdzEItEVc/PEAlR70wHZpWC8LTMTVJ1EWCMvYqTq0m1RF7aCE+Xf0tdsz9EEObTcToNS+j9/P3VcnsvSiEzDU9uwNTwgFSKYfIABV+vZRcQOzY5tJOhGrVuJJsgE4lAwcg3WSHTCbNUy1S1jG2+Z8iaoVocPZGGq4lG8HzPFKyrJBIODzemp1HsFSEztrEDDP+SzYhXKdEhF4FuwM4fiUFlxINSDdZcSPVjIaROtQJ1eVk6oU9TQibfPx0IRGJGRZEBCjRo3EEibqIkLATkEqlGDD5UXR6NAYrXlmPZS+uw8GPj2DCxuEIq142f9TfEOwaNiPFgSC9CrVCNAhUK5BlsRfw2lONVoTolDDbHTBZHdAoZAB4pBltqBOmzWPjFDXGtkGEFncN1iItmvz+d6BagQi9EteSjdBmSRCiUyJcr8TxK6yK53yCAWF6JdKNNsglzA+PClQhUCOH1e7EhTsGZJptiArUQCnjIJVw+DcpCxqFLKcWXvicrvYRBw4pWRY0jAhAqxrMrjmfYECoTkniLhJkxRA51GhUDSt/XoBRsS/h9IF4DG0+Cd/v+KlKV87kJ8vsKNDAVFhJX7BGgXC9EiabA1IJB6vdgSyLAxKOQ80QTY5FUtQYW7VMgi9O3yrWoimsJPBOhgU9Gkfg/iZRaFkjGBqFjHneBjs61gsFeA5XU4y4lMSeFjJMNiRkmGG2OeHgnbDYnbA5nTBYHQhSy6GWS3Et29oRPmd+++jyXQOupZhgczhLNXKBZsGUHyTsRB6kUimenPAINp1ZgXota2PFkPWY3e8NJN1IFjs0URHETCGTQimTwWp34tzNdKSbCp+R0jhKDwknQf1wLaICVEgyWGG2OdG5fkjO0KswnQJpRhtOXEnBf0lZyDRZc8bY2uwOXEs24MyNNMTfTC904mRhJYE1glWIDlLnHHMtxYhAtRw2pxPBWiXa1Q1Bq2oBuJiYhUyzHekmG9KMVtxMM0HGARa7E3qlDHqlDBa7EyqZFAazDUCuX5/f27c7nAhSy/N4+yXVr9MsmPKFhJ0olOoNorHip/kYvfplnDv4F4Y2n4jvth2ostm7IGYNI3Uw2RzgAKhkEvxzJ7PQxhlBdCP0KjSK0uOptjXwSMsoaFXynE0qzicYoJJL0bpmIGwOHn8lZMJic6BWiBr/pZigVsjzbH5htTsKiGX+Rd/a2X64gMHMatX12XZNmtGKi0kGBKplCNHKc7xzrVyChAwLbqSaYDDbEKiWwWh1IM1khTZ7mJjwOfO3++tUcvDgkWmx57xWUv16RQ1Wq6qQx04UiUQiQf/xD6PDI22xcugGrBy6AQf3HMHEzSMRUTNM7PAqFGGhkuNkaF49ENdTjMg02+HkncU2EBXlMbsO8GpWPQhOpIMDqz2/k2GFUi5BRIASHMdBJWcieikxC21rBxUbZ/7yRJlUgjSTDTG1WZ/C9RQjrHYn6ofrwPMcIgPVSEw34UY6m//eMFILJ4CrKSaEaxVINFigV8mgkktySkDze/u1QjQ4+V8KAlRs0Jhwsyiufr2w8lGbw4HT11JLXfZJFIQydqJEqtWPwvIfX8OYtUMQf/g8hjWfhG+3/FClsnfXcscgjQItagShVc0gdKofVibxKdjRGQi9SoaEDDOsdge6NwoDx3Ew2RxsPhfP426WpcSW+vz2TL0wHWqFqCGXsi7RZIMFcpkE0UFq1A3XQq+UQSKRIFijQK+mkejVNAoBajkcDgfMDgeGdK2LgR3q5CkBze/ty7LHMNQL17jdJZp/Fky6yYpTV1OhkEnJmvEClLETbiGRSPDE2L7o8EhbxA7dgFUjNuHgJ79h8paRiKhVcGNlf6OoRp2ydlUWVtFSP1yCZtVY16fZ5kSQRolrKUZkmK2QSSVoX8e9zZ7zPykIFSzClEalTIobqSZUD1SjbpguW+wVuKdaYPZNJnfEb3GjDFwbuvq2iC7VDS7/7/OfO5kAODSM1OVYMwCN6S0rXsvYHQ4HevbsikGDBnjrlIQPEl03Em/GzcP4t4firyMXMLT5JHy9Kc7vs3dvzy4pbsiV8DOZRILm1QLRskYwaoVo0aFeSJljF6Y0tq8TiogAFcJ1CtxIM+K/ZANkMgliagfnDPQqqflKOGdxDV3uxOT6+7TYHGhbKyinYxagMb2e4LWMffPmDWjUqBEyM2nxw9+RSCR4dNSDaNe3DWKHbcSaUZtx6JPfMGnLSETViRA7vHLDG7NLXOu/ZRIOZpsdJpu9wBiD/BlxjWAdLiRk4ujl5DL5z66LlZrsJiWZRIIgrRzPd6yN8wkG3Eo1utV85Sn5Ryh0rBeKYI0CZpszz3E0prfseCVjv3XrJn744XsMGvSiN05HVBKi6kTgzf1z8eqG4Th/7CKGtZiErzZ8D6fTWfKbqyD5S/zyT190FU/XjLhxlL7ABhb7zt3G12duul0D7urpC2sE3RtHoEawBk2iA9GlQSgSDWY4HGwXppY1ghAdqPF6pUpRZY75N9qmMb2e4RVhnzNnBubNWwiJhNZiqxocx6HfiD7Yci4W93RujLVjtmJ6n4W4feWO2KH5HGUt8StQN+6yK4i+AAAgAElEQVR04lqKEZeTjG4vNJa0cUW4XoUawRp0bxyJFtWDcjpNvW2HFPU7uGuw0pheL+KxFbN//z6EhYWhVas2+PXXX4o8bufO7di1awcAIDW1aje7+CORtcOx9Ls52Lf1R2yashPDW07GK28MwmOjH6xyN/yipjVeS2FNQVkWO3QqOWqFaBCgkpe4d2r+0kCh6UgY5pVpsUMukUAmAfq1ql7oOdxZ/C1sRK+37ZDipmTSmF7v4fG/uOPHj+H77/chJqY5hg9/GYcPH8KoUUMLHDd48MuIizuIuLiDCA/3/yqKqgjHcXh4WG9sObcSzbs2wdvjt2FqrwW49W+C2KFVGEVZDedvp+N6igmZZjsCVIqcztWEDFOJwpk/2zaYbciy2JGUaYHN4USgSgYJxwZ4FbfYWVJGXBG7FtGWdxUDl5iY4bVyhl9//QXr16/F++/vKfa4vn174OTJk966LOGD8DyP77YdwMbJ78Jpd2LIkoF4fOxDfp+9H76YO5tcIMtix8XEDEToVLh8NwsahRRKGWsccjh5DOlat8TNOlw3Ajl5NQV/38pEnTA1wnTsfSabA06eR9tawTm7JZWFss6GL835XT9LYfPdiaJp3bot4uIOlngc1bET5QLHcej7Si/c+2BrrB65CesnbMcve49i8jujUL1BtNjhlRtFWQ2JGRa0qhGcU5GSbrZDr5RBp5K6taOSa5VMvTAdrqUYoVHIwPNgEyRtDjSvFuCxH16SHeKp8LuzqQnhOV7N2N2FMvaqBc/ziNt5EOsnbIfdaseQxQPx+LiHIJVKS35zJaO4jL1hRECB11VyCRpH6Ustll+fuYXLdw2wO5w5fr1MIoFKLvEoYy+OorLtJlG6YscLE96DMnbCZ+A4Dg+8eD/a9m6B1SM3Y8OkHTi09zdMeWc0ajQqfjOJykZRi5Q9GkfgfIKhwOs1gnUF9iJ1rR0XMuRrKVlIN9kQoJKhdqgODSK0sDv5AiJb1k5YoORsvLB9X9ONVnxx+hZiaocUGj8hDv5teBI+RVj1UCz6cgam7RiLq3/ewIjWU/BJ7FdwOBwlv7mSUNQipVArnv/1uwZrkSWQQoacmGnGjVQTsiwO3Eyz4E66GecTDGgSpfNaeaA7Y3TzT3UEgLsGC5xOJ01p9DEoYycqFI7j0Gdwd7Tp3QJrRm3Gpik7s7330ajVpPBSvcpGUT51Ya8fvZxcZPmfkCFfvmuARiGDWi6F2eZAcpYV9cKZ/eEt26WwbFx4PXfT6oLlkClZbKeowuIvDeW9aFvVoIydEIWwaiFY+Pl0TN85DtfP38TINlOxZ8WXfpW9u0Nx5X9Chmww26CSsUxZKZMg02L3euNQYdl4/msUVg4pkXAI1+cV9tKWL9KmG96HhJ0QDY7j0Pv5+7D1z1Vo37c1Nk/bhYnd5uLq3zfEDq3CKK52XBB9nUoOs52Jv7DDkbdrv92pLy/MZnq8dTVIOIlHte+06Yb3IWEnRCckKhiv7Z2Kme+/ipsXEzCq7TTsfvNzOOz+n70X1zgkiH6YTgGj1Y5UoxVZVgdCtQqvNw6525yUf6pjUWsHpbFR3HlaIEoHeeyET8BxHHr+ryva9GyOtWO24p2Z7+Pwp0cxZdsY1GlWU+zwypXiPHmh5ttsc+RUxUQGqrzuQXtSX+7pKICKGGVQ1SBhJ3yK4MggzNszGYf2/Ia3xm7F6JhpeOG1Z/DM1Mcglflf3XtJ5Ipm+Y/hEGtWi7c3MSHIiiF8EI7j0P2ZztgSvwodH7sX22Z/gPGdZ+NK/DWxQyPKAW9vYkKQsBM+THBEIOZ9PBlzPpqExKtJGB0zDe8v3gu7zS52aISX8XRHJiIvJOyEz9N9QCdsiY9Fl/7tsWPubozvNAuXz14VO6xiSco04/DFJLc3wiAIb0LCTlQKgsIDMWf3JMz7ZAqSbqRgTLvp2LVwj09m71SXTYgNCTtRqej2ZAdsjY9F16c6Yuf8jzG2w0xcOn1F7LDyQHXZhNiQsBOVjsCwAMz+YALmfzoVKbdTMbb9TOyc/zFsVpvYoQGgumxCfEjYiUpLlyfaY2v8Ktz/XGfsWriHZe9/iJ+90y5BhNiQsBOVmoBQPWbsHI8Fn09D2p10jO0wEzvm7obVIl72XhFbzBFEcZCwE35B58faYUt8LHr8rwveX7wXY9pNxz+n/hUlFqrLJsSGhJ3wGwJC9Jj+7jgs+nIGMlMMGNdxFrbP+VCU7J3qsgkxIWEn/I6O/WKw5Vwsej3fDR8s+RRj7p2OCycuiR0WQVQYJOy+gsEI/HcTOH+FfTUYxY6oUqMP1mHa9rFY/M0sGNKyML7TLLwz831YzVSZQvg/JOy+gMEI3EgAbHZAKWdfbySQuHuB9n3bYGt8LB548X7sfvNzjL53Os4fvyh2WARRrpCw+wJ3UwGpFJDLAI5jX6VS9jrhMdpALSa/MxpLvp0FY4YJr3aejS3T36PsnfBbPBb2mzdvoH//R9C1azt069Yemzev90ZcVQuzFcg/klYmZa8TXqPdQ22w5dxKPDSkJz5e/gVGtp2Gv47+I3ZYBOF1PBZ2mUyGBQsW4/DhE9i370ds27YFFy6c90ZsVQcJB6RmAHfTgLRMwGoD7A5ARQ0t3kYbqMXEzSPxxndzYDFaMLHrHGyashMWU+k2XyYIX8ZjYY+MjELLlq0BADqdHo0aNcbt27c8DqzKYDACFisTcg7sa1oGy9bDgsWOzm+594FW2Hx2JfoO7Y1PYr/CyDZT8eeRC2KHRRBewase+7VrV3Hu3FnExNzrzdP6N3dTAZUSCNQxXx1gXxUyQKcp/fmousZttAEaTNg4HG/GzYPNYsfEbnOxcdIOmI2UvROVG69tjWcwGDBkyAtYtGgp9PqAAj/fuXM7du3aAQBITU321mUrP2Yrq4ThZIAy23rhecDdphqDkd0czFaW8VvtzMJxra6pEVW2m0QVoW2vFth8diW2Tn8Pe1d/g9++PoWp20ajedemYodGEGWCS0zM4D09ic1mw6BBA9CjR2+MGjW2xOP79u2BkydPenrZyourGJstrApGq879uc3OXqtTveTz3EhgGb5MCqSkAw4HEBQAKOSlOxcBADj9UzxWDt2AO/8l4YlxfTFkyUCoNEqxwyIIAEDr1m0RF3ewxOM8tmJ4nseECWPQqFFjt0S9ypO/Zl0hBzKNQJaJZeo2OxNnd/z1/GWSPACJFDC6bOhA1TWlonWP5th8ZgUeHfUAPlv7LUa0moyzh/4SOyyCKBUeC/uxY0exZ89u/PLLIfTo0QU9enTBDz98743Y/JP8YqxRAQFaJugWG3s9v3VSlG+ev0xSJs1dgBWg6ppSo9apMW7dUKw4MB88D0y+/zW8PX4bTFm0AxJROfDYY+/YsRMSEzO8EUvVQPDUXZFK8oqxK652S37fXKXItVoAQK0E0g1M4HmendPhAKLDy/cz+Smt7m+GTWdWYNvMD/D5un049u3vmLx1FFrd30zs0AiiWKjztKJRKfKKuNUGpGeyTJsD88njLwEXruR68UV1pYYFM+G22ZmQSyRM3HWaorN/olSotSqMWTsEsQcXgpNwmNJzPt4auxUmg0ns0AiiSEjYK5r8YmwwAuBYRUxmFvPJ5dLcTN1gLLorVadhwi2X5Qp5ZGjuwinhNVp0a4pNp1fgyVcfwVcb9mN4y8n4/cdzYodFEIVCwl7R5BdjJ888drsD4CTMlpFImMBLpez1/DaNq2+u07CKlyZ12U0jJd0/h4n5QH2+SqPEqFUvIfbQQkjlMkzvsxBrRm2GMZOyd8K3IGEXgzxiHJQr4BKO/ZznWVYukzKhd83wi6ua8ddhYj42/bJ5lybY+MdyPDWxH77Z/APL3n84K0osBFEYJOxio1GxBU+LFTCZAVt2Fq9WMrHXawvaLUX55uU1TEzsbNkHb1gqjRIjV76IVb8sglwpw/QHFmH1yM3IyvCDpyOi0kPCLiYGI7NO1EqWiTp5tpiqlDM7xmxh39+4w46vEcky/aIWQ/MvzAKelzu6ZsuFLe5WBK43LKuNDUpLy2RD00S2mZp1boyNfyzHgMmPYt/WHzCsxSSc3H9G1JgIgoRdTIRMVKtm1kp4MJsbY7EBTicAjmWo7toP+RdmS9PsVFKMPF/04m55I9ywrDYgwwA4nMy24uATawhKtRLDlw/GqsOvQ6VVYeZDryN22EZkpWeJGhdRdSFhF5PCrBOJhAmXycLEqzT2Q2FVMq62TWktFYORZcXpBpapO/mCi7sVYYcINyyhgogDu75OI7ol48o9HRth4+/L8Oy0x/H99gMY1mIyTnz3h9hhEVUQEnYxcbVOLFY2WsDuYJMdrTY2GsDi4o+745frNEwIVQp27N1UJoilXYAUjhcWdB1OwG5n8dns7L/TDRVjhwg3LGf2WCOJBNBrWImoj41MUKgUGLr0eaw5shiaADVmPbwEK4ashyGNsnei4iBhFxNX68RozhZNG/ve6WR/XDeAcMcvL0rAb94p3QKkYMHoNAB4JvA8AEu27y/J/qsj4SrGDtFpWAVRoA4I0udOwvTRkQlN2jfE+pNv4rkZ/RG382cMbT4Rx779XeywiCoCCbuYuFonZisTebmcfS+RMAE1W4v3y/PbK0UJeGYxjU6FIdhECjnz/Xlk19Q7mR0jlQLgK9YOKY81hHJEoVLglSUDsfa3JdAH6zCn3xtY9vI6ZKYaxA6N8HNI2MVGqGlXK5mICoKskDORB1/8cLD82XlqJhM7VwRBL03FjGATZWaxBUs+218HmC3D80CAjsVZUXZISWsIPkrjdg3w9sk38b+Z/fHje79gaPNJOPr1KbHDIvwYEnZfQRBNm43Vs2eZAKeDWQ5N6hZe5lhYfbdCxt7rit3BultLk+2GBbNyywwDy9a57EVLqZQ9TdjtQEYWKzs0mivODnFt7iqu9NPHUCjlGLJ4IN46ugSBYXrMfWwp3nzxLWSkZIodGuGHkLD7Cnoty35tdrZIKMmuPsmpBimEwuq7BfvGaGYCbjTnNkBxXO7uTK7ZbmHVMrrsxUlkL55KOGbJSLncRVQJx+LNNLJGK6JEGsXUx9snluL5uU/jpw9/xbDmk3DkyxNih0X4GSTs3sLT7syw4OwRvHImkko5IJMBalVe/9r1OmYLE27X+m65jP0xmpigG025Ex8lErYg69roVFy1jJNnsaiV2aIuRc4YSpmU/VwuY08DRppV7i5yhRwvLngW6469gaCIQLz2xDIsfWEtMpIpeye8Awm7N/DGLBOdJlvMpdkNONklfRpVrn9d1O5LaZnIqe8W3uvkmfCrVawBqqhKmOLa9VUKdg0nz24IPM/OL5UAIYGsSiVIz4S/PD12sUcalBMN2tTFuuNvYPBrz+Dnj45gaPOJOPzZMbHDIvwAEnZv4K1ZJnptblmfUNLnusBZ1O5LwqIozwO8k/1Mlj1YrKRa+OLmy4QFMxFXK9k5bXb2N0avyTsauDxLDn1sAJi3kSvkeOG1AXj7xFKERAdjwVMrsHjgaqTfpc1riLJDwu4NPBm+5ZqNWqzsPUUtcBZ2HaGaJlCXvam1UEmTXSZptbGsXiC/CBc3X0aoQtGqWeYfEQI0qJW7FuBpyaE7mbgPDgArD+q3qoN1x97A4PnP4PDeoxjafBJ++ZSyd6JskLB7g7IO38qfjUokAPjCFziLu45Q8WLNnjFjtgAOngkwn/292VK4CJdUG56/CiUi1Dslh+5m4uU1sdIHkclleGHeALx94k2E1wjBwqdX4PXnYpGWlC52aEQlw+M9TwkwEbyRwP5bsEDc2Wv05h1Wmshnv09YpJTLmIgWdx2nk73XageC9czzNlvZa5wk16+XcCweg4lZPNHhBUWY49hCK8BuEiUJtU5TOiEXtvgzW9nNKSw4byYO5H69m5r33Pn3dQV8ttvUW9RrWRtrf1uCj5d/iV0LPsbpA/EY9/YwdB/QSezQiEoCZezeoCyNMwYjayYCmI/tdDLLxOEoOhsVrsPzbMGU54EgHcv0U9KBauG5m14L5xQqVxzOwmO4kcDeHxrI7BxnIce5Hl/aRcziMnN3MvFK1m3qLWRyGQbOehIbfl+OyDoReP3ZWCx8ZiVSEyl7J0qGhN1blLZx5m4qayYSRvM6edaclJzObJOiRFOXvXAZEgiEBuVm+FIpWygN1rPjHM7coVk82LXy2x2l8a8Tk5mgJ6awBiqj2b1FzKKuUdKWf66ftxJ2m3qLOs1qYu2RxXhlyUAc/fIkhjabiJ92/wqe58UOjfBhSNhLorxK7cxWtijJO5k3brXmlhUq5MWLZnG+c/XI7MVOJRNyW/ZgMaG+3VW4S/Kvhc8efxG4dI0Jr1zG4jSa2NeiauyF31VR1yjNln+VtNvUW0hlUjw3oz82/L4M1epHYsnA1Vjw9Aqk3kkTOzTCR/GKsB84EIdOndqifftWWLs21hun9A3Ks9ROpWAWSEC2/cGD+eEaFftTXOVHSZUsIYFsKqTQHSoMGbNY8wp3cedx/ew2O+AEE16hjp2T5FbxFPe74lD4NdzZ8s9P69fLSu17amL14dcxdOnzOP7tHxjafBIOfHiYsneiAB4Lu8PhwPTpk/Hhh3tx+PAJfPrpJ7hw4bw3YhOf8iy1c/WOcywTPnccrUxauLAZjCzDT0kHktMKr3YxmplfLswsl8uZwAtiL9gdxfnXrp89R8zBxgkAueMEiqqxF35XHFf0NYrLxP28fr2sSGVSPDvtcZa9N4jCG4PWYP6Ty5F827/KPwnP8FjYf//9JOrWrYc6depCoVCgf/+n8N1333gjNvEpz1I718ya55loumbWJpcSRUHYrtwALl4F0gzMYskyM8/bYs2b7Qpxa1TM6hEWTq22gqWMQtZsMLKKGrsjd3MO4bML1gmQO9nR7mBPHMXV2DudbFCY3cHObTC675FXkfr1slK7aQ2sPrwIw5e9gJPfn8aw5hPxw3uHKHsnAHhB2BMSbqN69Ro530dHV8Pt27cKHLdz53b06dMdffp0R1JSkqeXrRjcqU8vyi5wx0YQMuvwYOarS6RM4A1G9jO1Kq+wCVMfbVZ2nCx70mJWvnOrFOzGYDQzIbbZWFmkQl5QVIUdl+Qy5s1r1ewmYrbkbvKhUbEMXRhMJmxsXauYGnurDUjPZMcJ55XLcjP1kqhC9etlRSqVYsCUx7Dxj+Wo2bQG3hz8FuY9/ibu3koROzRCZCps8XTw4JcRF3cQcXEHER5eQn23r1BSqV1RdkFicumabxRy5rVLs2e88GDvyz8x0Z6dfXOS7L1Hs8VWyLIFNCqWKQv139JsgaxWSA07UHh2rFaxeFPSWY07z7Of6dSsA7VJPdasVNTvStifVKcpW8Zd1qavKkjNxtURe3ABRq58Eb//cBbDmk9C3M6DlL1XYTwW9qioaNy8eSPn+9u3byE6upqnp/UNSiq1K8ouuJXkno3gKl4KOZsPE6RnjUR6bUFhE/6hcpzri0zoXTNZo5n560IFi1zGvi9qAmNR2bHdkSvoEgm7YdStUXhliuvvKsvEzils7We15Z7T3Yy7itavlxWpVIqnJvbDptMrUKd5TSx7aR3mPrYUd28mix0aIQIeC3ubNjG4fPkyrl79D1arFZ99thcPPviwN2LzDYpb4CtKEC02z5tvCvuZ0EkqVNHwfG7Xqmsma7YyERZuEkH6vFMi8yPhgNQMtjG1MNM9y8SeGkKD2DmEmvniMm7B1pFlN0kJC68ZBnbO0mTcVbx+vazUaFQNK39egNGrX8bpA/EY2nwSvt/xE2XvVQyPRwrIZDIsXboczz7bHw6HAwMHvoAmTZp6Izbfp6h2d6U8t+bb9fWimm+EdntJdrPSlRu5C57CeAKplPnUUinbUNqRvXgpTF90zWTzx2WxMmuEB/P7NSqWvQt15iZLblmkHUBaBps1IzQ7CbiTcbtugp1pZKkDz7FraVQlj1nI//shIS81EokE/cc/jPYPt8HKVzZgxZD1OLjnN0zcNALhNUJLPgFR6eESEzMq/Fbet28PnDx5sqIv630Ej10qzTsjJiSQedOFvW40552ZIgiXcC6zNbf5h+dzzxGgZf9ttjBBFxY29RrWlFRYqaBUyq6bkQWABwL12Rl0FrsZWK1sUVXYz5Tn2eYeUgm7CQTq8t6chJtFYXNsBM5fYTc2jsut7hEspSZ1SagrGKfTiS/WfYdtsz6ARCbByJUv4qEhPcHlsfOIykLr1m0RF3ewxOOo89QTirILCpuAKIh9UQuqd1OZ6Ao+uFTKxNXuYJUlZis7j0rJMvd7m7E/jQsRS6GUMsvE7BWHA9Bm17QLfndGFhN1YTYMxwFKZe64AqW89B63wchuPEmp2Zt/gNlAgTpm55CoVzhC9r7pzAo0aFMXscM2YmbfxUi8Vkkq04gyQcLuKUV58PlfN5qLX1A1W5noCouV2TvQAXzeuSru2CFCNYtWnT1LRs5KJa02lkXb7bnXAZi4C12qwrXc6QzNf80bCezGwIHdCDKy2M2FFj1Fp1r9KCz/8TWMfesV/PnreQxrMRnfbvmBvHc/hYS9oiipLlvwxSX5/pcIA8KE9woCXFyNvGu1jrDgyoOJvTCzXXgSF54MhG3vJJx7naH5Ea6pUTHLRy7LzfRp0dMnkEgkeHzMQ9h8diUatauPVSM2YcaDi3DnKmXv/gYJe0VRUl12WHD24ilyRTb/+2323M7U4mrkXW8iaiW7jsXqsoUesqdJ2nNfE1r/BXvJ1ft3Z16L6zWF0s3wYPbEQKLuU0TXjcSb++di/Pph+PvoRQxrMQlfb4qj7N2PIGGvKNzZqahWNFu8FOrG5fLcbe+Qbd8oZLmjeouqkXe9iSizh40J5xSalfLYPWA/06rz7mVamnkt1FBUqZBIJHh05APYfHYlmnZsiDWjNmP6A4tw+8odsUMjvAAJe0VRXF22kBWnZLAql9AgIDgAiAoFmjUAmjfMtUOEunVX8vvu+W8iwijg0ED2VZZdaSOV5gq/TJo7TkAQ79LMa6GGokpJVJ0ILP1+LiZuGoELxy9heMvJ+GrD93AWt+EK4fPQ1ngVSWF12a6liUL9u8NRtC+dv0bdamPncPLs5iB446718YrsZiGlgtWWC5tRc9nNTkpZblbvukWd2cpicqWoxdv811Qp8m7DJ9woMrOYzSST5jY0kVUjKhzH4eFhvXHvg62wcthGrB2zFQf3/IbJW0chul6k2OERZYCEXWyK2/sTYPuiZmZbHwFa5l2nZG+P5nSyQVvg2M+EbDv/2AO7nVXFAKxG3e5glk6ALrvGHXmfAgTxLu1+o0U1FAk3L4cz96Zgs7GbSf54CdGIqBWOpd/Nwb53DmDT5HcxvOVkvLJ0EB4b/SAk+Rf1CZ+G/m95iqebQRRVLZOZxTpQ0w25PnhaBnAnhdWZy2VM8KVS5sG7bpEnjN0V/HGtGtCos5uassscNdnTFjkATkfegWOCeHvLXhFuXjY7u7HIZWySpdVGo3h9DI7j8PDQXtgSH4sW9zXF2+O3YUrP+bj1b4LYoRGlgITdE7yxGURRi46O7C3zBC9cJgWkMpbpGs255YchgbmbcwijA+6ksK3shAFgXPbOTIE6IDiQ+fUaFfP6dRpArWbHFLYRhjfmtQg3L7sjt3ZeqJmnUbw+SUTNMCz+ZhYmbx2Ff0//h+EtJ+PTNd+Q915JICvGE4qzUdwVv7BgdjMA8o4fEP5b4tL6LYiha+17lomJsTBkS8Kx92aZWNZvVDGbRlg0NVsLWiaC/12YN+6NeS2CpSOTZtfQu9TmU+WMz8JxHB4a0hMxD7TCqhGbsGHiDvyy9ygmvzMaNRpGix0eUQyUsXuCtzaDkEiY5ZKczoRPyIqFmnYBZ/ZMF0EINSpmxwj16E4n21nJas8tb7TaSp6uWN6bRQuWjjDt0WZn9o9CTpUzlYDwGqFY/PVMTN0+BlfOXcPI1lPw6epv4HA4Sn4zIQok7J7gae22YOVwHCtFDNTlCnlY9q5KQgZvdwAOO6ttd93bNECbO3ddKs3N8IXWfp4HkD1dUSwRFSwdrZr9boSNPDQqWjitJHAchwdevB9b42PRplcLbJi0A5Pvfw03/im4WxohPiTsnuDp4mJxdeI6DdvUIlDHatcBICgAqOuSUZutrLM0SM92NnJtLpJJcyc1Akz4S5r14skicEkITwUtGgGtm7Da/PJ4OiDKlbDqoVj4xXRM3zkO1/66gRGtp2DPyq8oe/cxyGP3hJJqt0uipDpxnYZNbywMYZJihiHXP7fbcytonE5mxQTqsrtYZSUP8BJq6QsrmySIbDiOQ+/n70ObXi2wZtRmbJ66E7/s/Q1Tto1BrSbFjHQmKgzK2D3FE3+6rFZOYZMUTRZm08iy79U8z7J4iaTkp4jSdJiKTXk/WRBuExodjAWfTcOMXeNx45/bGNlmKj5e/gVl7z4ACbuYlNXKKWqSIs8D99QHWjZiYwmE+TIlZd7eWgQub7xRXkp4FY7j0GtQN2yNj0X7vq2xZfp7mNB1Lq7+faPkNxPlBgm7mJS1TrykSYqlfYqoLAO8KtOTRRUjJCoYr+2dilkfTMCtSwkY1XYadi/9DI78f6+ICoGEXWzKYuV4W4grywCvyvJkUUXhOA49nuuCrfGx6NivLd6Z9QFe7TIb//15XezQqhwk7JUFV2/ZYmVi5i0h9laHaXlTWZ4sqjjBkUGY+/FkzNk9EQlXEjE6Zho+WPIpZe8VCAl7ZSC/tyyRAMj21L0lxKV9chBjEbOyPFkQ4DgO3Z/pjK1/rkKnx9th+5wPMa7TLFyJvyZ2aFUCEvbKQGHesip74+ny6hYtDrEWMSvLkwWRQ1B4IOZ+NAlzP56EpGt3MTpmGt5/fS/sNrvYofk1Hgn7/Plz0LlzDLp374QXXxyI9PQ0b8VFuOKpt+zt7FrMRczyHn9AlAv3Pd0JW/9cha5PdsCOebsxruMs/HvmP760/eMAAAuISURBVLHD8ls8Evbu3Xvg0KFjOHjwN9Sv3wBr1sR6Ky7CFU+85fLIrmkRkygDgWEBmP3hRMz7ZAru3kzBmHYzsGvhHsreywGPhL1Hj16QZTfExMS0w61bN70SFJEPT7zl8siuaRGT8IBuT3bA1vhYdH+mE3bO/xhjO8zEpdNXxA7Lr/Cax/7hh7vQq1cfb52OcMUTb7k8smtaxCQ8JDAsADPfexXzP52KlNupGNt+Jt597SPYrDaxQ/MLSpwV89RTjyEpqeDO5TNnzkPfvo8AAFatWg6pVIann362yPPs3Lkdu3btAACkpiaXMdwqhOuMdEn2Jhg8cnc2ctdbLu32dkXF4HpdT2fkEEQ2XZ5ojxb3NcX6Cdvx3qJPcOSLE5i6fQwatCliRhLhFlxiYgZf8mFFs3v3+3j33W3Yu/craDTu/cPu27cHTp486cll/RvXoVz59zWVSovf7Lq4c7lu5FHS+8v6PoIoI0e+PIE1IzcjLSkD/5vRHwPnPAVF/iF5VZzWrdsiLu5gicd5ZMUcOBCHdetWY9euj9wWdcINXH1xk4VtiSfYJ6X1yMtq41D7PlHBdH6sHbb+uQq9BnXD+4v3Yky76bhw8l+xw6qUeCTsM2ZMgcFgwIABj6NHjy6YMmWCt+Kq2rj64sJ2dxyXu2BZWo+8LCWC7njzNGmR8DL6YB2m7RiLRV/OQGaKAeM7zcK22R/AaiHvvTR4NI/9+PEz3oqDcMXVF5dJ2XZyHPKKfXlXoJTkzdMMd6Ic6dgvBlvjV2HDpB348I3P8NuXJzFl22g0btdA7NAqBdR56ou4Vp2olWxLPEFUK6oCpaTKF7JqiHJGF6TF1G1jsPibWTCkZWF859l4Z+b7sFK/RImQsPsirr44D7YlXqAObs9X93YMhXnz1KREVBDt+7bB1vhYPDC4O3a/+TlGxUzD38cuih2WT0Nb4/kqQlmhr8bgSRklQZQSbaAWk98Zjfue6YxVwzZiQpfZeHrSoxi84Bko1Uqxw/M5KGMnygY1KREi0O7B1thybiUeGtITH6/4EqPaTsNfv10QOyyfg4SdKBs0aZEQCW2gFhM3j8TS7+fAYrJiQte52Dj5XVhMFrFD8xlI2ImyQ5MWCRGJ6dMKm8+uxCPDe2Pvqq8xss1U/HmEsneAhJ0giEqMNkCDVzcMx5tx82Cz2DGx21xsnLQDZmPVzt5J2AmCqPS07dUCm8+uRL8RfbB39TcY0XoKzv3yt9hhiQYJO0EQfoFGr8b49cOw/MfX4HQ4Mfn+17B+wnaYssxih1bhkLATBOFXtO7RHJvPrMBjox/EZ2u/xcjWU3Dm4J9ih1WhkLATBOF3qHVqjH3rFaz4aT54HpjSYz7WjXsHJoNJ7NAqBBJ2giD8llbdm2HTmRV4YlxffLn+ewxvNQWnf4oXO6xyh4SdIAi/Rq1VYcyaIVjx03xIJBym9lqAtWO2+nX2TsJOEESVoOV992DTmZV48tVH8PXG/RjecjL+OHBO7LDKBRJ2giCqDCqNEqNWvYTYQwshlcswrfdCrBm1GcZM/8reSdgJgqhyNO/SBBv/WI6nJvbDN5t/wLAWk3Aqzn/2lyBhJwiiSqLSKDFy5YtYfXgRlGoFZjz4OlYN34isjMq/ExgJO0EQVZp7OjXGht+XYcDkR/HdtgMY1mISTu6v3Nk7CTtBEFUepVqJ4csHY/Wvi6HWqTDzodexcugGZKVniR1amSBhJwiCyKZph4bYcGoZnp32OPbv+AnDWkzG8X1/iB1WqSFhJwiCcEGhUmDo0uex5shiaALUmP3IEqwYsh6GtMqTvZOwEwRBFEKT9g2x/tQyPDejP+J2HcTQ5hNx7JtTYoflFl4R9vXr30JERACSk5O9cTqCIAifQKGU45UlA7H2tyXQB+sw59GlWPbSOmSmGsQOrVg8FvabN2/g559/RI0aNb0RD0EQhM/R+N76ePvkmxg460n8+P4vGNp8En776qTYYRWJx8I+d+5MzJu3CBzHeSMegiAIn0ShlOPl1/+HdcfeQFB4AOY9/iaWDl6LjJRMsUMrgEfCvm/fN4iOjkbz5i28FQ9BEIRP07BtPaw7/gZemDcAP+8+gm82/SB2SAXgEhMz+OIOeOqpx5CUdKfA6zNnzsOaNSvw8cefIyAgEDExzbF//0GEhoYWep6dO7dj164dAIC///4TTZs28zx6kUhOvovQ0DCxwygzFL/4VPbPQPGLw/XrV3H+/H8lHleisBfFX3/9iaeffhRqNduZ/tatm4iKisZ33/2EyMjIYt/bp093xMUdLMtlfQKKX1wqe/xA5f8MFL9vIyvrG++5pxn++utyzvclZewEQRBExUB17ARBEH6GdOrUmfO9caIRI0ZDo9G4fXyrVm28cVnRoPjFpbLHD1T+z0Dx+y5l9tgJgiAI34SsGIIgCD9DdGGvrOMI5s+fg86dY9C9eye8+OJApKeniR2SWxw4EIdOndqifftWWLs2VuxwSsXNmzfQv/8j6Nq1Hbp1a4/Nm9eLHVKZcDgc6NmzKwYNGiB2KKUmPT0NQ4a8gM6dY9Cly704ceKY2CGVio0b16Fbt/a4774OGDHiZZjNZrFDKhdEFfbKPI6ge/ceOHToGA4e/A316zfAmjW+L5IOhwPTp0/Ghx/uxeHDJ/Dpp5/gwoXzYoflNjKZDAsWLMbhwyewb9+P2LZtS6WKX2Dz5g1o1KiR2GGUidmzp6Nnz944cuQUfvrpCBo1aix2SG5z+/YtbN26Cfv3H8ShQ8fgcDjx+ed7xQ6rXBBV2CvzOIIePXpBJmPVojEx7XDr1k2RIyqZ338/ibp166FOnbpQKBTo3/8pfPfdN2KH5TaRkVFo2bI1AECn06NRo8a4ffuWyFGVjlu3buKHH77HoEEvih1KqcnISMfRo0cwaNBgAIBCoUBgYJDIUZUOu90Os9kEu90Ok8mIyMgosUMqF0QTdn8aR/Dhh7vQq1cfscMokYSE26hevUbO99HR1SqdMApcu3YV586dRUzMvWKHUirmzJmBefMWQiIR3QUtNVevXkVoaCjGjx+Fnj27YuLEscjKqjwzyqOjq2H06HFo06YZWrRoCL0+AD169BI7rHKhXP92PfXUY7jvvg4F/uzb9w3WrFmB6dNnl+flPaa4+AVWrVoOqVSGp59+VsRIqxYGgwFDhryARYuWQq8PEDsct9m/fx/CwsIqbZmdw2HH2bNn8NJLr+DAgcPQaDR46y3ftyAF0tJS8d133+LkyXM4e/YfGI1G7NmzW+ywyoUyd566w969Xxb6+l9//Ylr166iR48uANjjae/e3dwaR1CRFBW/wO7d72P//u+wd+9XlcJOioqKxs2bN3K+v337FqKjq4kYUemx2WwYMuR5PPXUM+jX7zGxwykVx48fw/ff78OPP8bBbDbDYMjEqFFDsWHDVrFDc4vo6OqoVq06YmLaAQAeffSJSrUAf+jQz6hVqzbCwtiMmEceeRQnThzDgAHPiRyZ9xHleVAYR3DqVDxOnYpHtWrV8cMPv/iUqJfEgQNxWLduNXbt+qhUjVli0qZNDC5fvoyrV/+D1WrFZ5/txYMPPix2WG7D8zwmTBiDRo0aY9SosWKHU2rmzJmPM2fO49SpeGzevB1du95XaUQdACIjI1GtWnVcunQRABPKRo2aiByV+1SvXgOnTp2A0WgEz/P45ZeDlWrxtzSUa8buz8yYMQVWqxUDBjwOgC2grlixWuSoikcmk2Hp0uV49tn+cDgcGDjwBTRp0lTssNzm2LGj2LNnN5o2bZbztDd79jz07v2gyJFVHZYsWY5Ro4bCarWidu06WLu28pScxsS0Q79+j6N37274f/t2TAMACARBkOLlEBxR4N8EDugI4TKj4KttLl9VrffR5lyvz7rC5ylAmP+meQCOhB0gjLADhBF2gDDCDhBG2AHCCDtAGGEHCLMBc+fUTqww6LwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fdc480e2a58>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xLsrJmrkKxCb",
        "colab_type": "text"
      },
      "source": [
        ">  **Exercise**:  Make the necessary changes to the code below in order to compute a **new sample** that is optimal for the classifier you have learned in the previous exercise. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lRhvJzt6KxCe",
        "colab_type": "code",
        "outputId": "34458470-fd24-4012-9c7b-a2a813ad7880",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "%reset"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ph3NeC4gKxCj",
        "colab_type": "code",
        "outputId": "84dff6b0-159f-4467-a512-077ff210535c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "#Example dataset\n",
        "N_samples_per_class = 100\n",
        "d_dimensions = 2\n",
        "x = np.vstack((np.random.randn(N_samples_per_class, d_dimensions),\n",
        "               np.random.randn(N_samples_per_class, d_dimensions)\n",
        "               +np.array([2,2])))\n",
        "y = np.concatenate([-1.0*np.ones(N_samples_per_class),\n",
        "              1.*np.ones(N_samples_per_class)])\n",
        "\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, ax = plt.subplots(1, 1)\n",
        "fig.set_facecolor('#EAEAF2')\n",
        "idx = y==1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.25)\n",
        "idx = y==-1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.5,color='pink')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f090515a908>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZGqHpdqyOKkv3b4z92SazVph6OfMjzsswTayt5HE0h8k5YTbIhunt3QMS+jmq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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OtwHivGDKxCo",
        "colab_type": "code",
        "outputId": "2908fd9b-f8cf-4537-8d0e-67654db66e2e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 243
        }
      },
      "source": [
        "# solution code\n",
        "\n",
        "\n",
        "import autograd.numpy as np\n",
        "from autograd import grad\n",
        "\n",
        "def SVM_predictions(w, inputs):\n",
        "    return np.dot(w[0,:-1],inputs.T)+w[0,-1]\n",
        "\n",
        "def SVM_training_loss(weights, inputs, targets):\n",
        "    pred = SVM_predictions(weights, inputs)\n",
        "    return np.sum(np.maximum(0,1-targets*pred))/inputs.shape[0]\n",
        "\n",
        "def optimize(inputs, targets, training_loss):\n",
        "    gradient_loss = grad(training_loss)\n",
        "    weights = np.array([[1.15196035, 1.06797815, -2.0131]])\n",
        "    print(\"Initial loss:\", training_loss(weights, inputs, targets))\n",
        "    for i in range(10000):\n",
        "        weights -= gradient_loss(weights, inputs, targets) * 0.01\n",
        "        if i%1000 == 0:\n",
        "            print(\" Loss:\", training_loss(weights, inputs, targets))\n",
        "    print(\"Final loss:\", training_loss(weights, inputs, targets))\n",
        "    return weights\n",
        "\n",
        "weights = optimize(x, y, SVM_training_loss)\n",
        "print(\"Weights\", weights)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Initial loss: 0.11547117164624694\n",
            " Loss: 0.11543851021340351\n",
            " Loss: 0.1044484126850999\n",
            " Loss: 0.10308719202082123\n",
            " Loss: 0.10246507297625403\n",
            " Loss: 0.10184294851743438\n",
            " Loss: 0.10122439265474972\n",
            " Loss: 0.10071013581427715\n",
            " Loss: 0.10032757623245615\n",
            " Loss: 0.10011631048697275\n",
            " Loss: 0.09995075500888156\n",
            "Final loss: 0.09978501637762706\n",
            "Weights [[ 1.31607029  1.58204853 -2.6459    ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rP6p90ElKxCs",
        "colab_type": "code",
        "outputId": "28d0b056-cbc7-41e9-a2ce-7d4c550959e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "delta = 0.1\n",
        "xx = np.arange(-4.0, 6.0, delta)\n",
        "yy = np.arange(-4.0, 6.0, delta)\n",
        "XX, YY = np.meshgrid(xx, yy)\n",
        "Xf = XX.flatten()\n",
        "Yf = YY.flatten()\n",
        "sz=XX.shape\n",
        "test_data = np.concatenate([Xf[:,np.newaxis],Yf[:,np.newaxis]],axis=1)\n",
        "Z = SVM_predictions(weights,test_data)\n",
        "\n",
        "fig, ax = plt.subplots(1, 1)\n",
        "fig.set_facecolor('#EAEAF2')\n",
        "Z = np.reshape(Z,(xx.shape[0],xx.shape[0]))\n",
        "plt.contour(XX,YY,Z,[0])\n",
        "idx = y==1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.25)\n",
        "idx = y==-1\n",
        "plt.scatter(x[idx.ravel(),0],x[idx.ravel(),1],alpha=0.5,color='pink')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f090734b320>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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vmCNmU/M4dwkS7+vAWN56GzbAdVF1DLz87TOYloF3PFHHE7druHPkIwzVgIiJ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\nTRAEsYeQeBMEQewhJN4EQRB7yP8PdeN8UcZUAz4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RkrUqJbDKxCw",
        "colab_type": "text"
      },
      "source": [
        "## Neural Network"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S1-BTXeiKxCx",
        "colab_type": "code",
        "outputId": "34805222-7935-4736-d8fa-230b81fa5744",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "%reset"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jxexqS7fKxC1",
        "colab_type": "code",
        "outputId": "166fb72c-9394-4e9b-928c-ed1b947f1646",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 395
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import sklearn\n",
        "import sklearn.datasets\n",
        "import sklearn.linear_model\n",
        "import matplotlib\n",
        "import autograd.numpy as np\n",
        "from autograd import grad\n",
        "from autograd.misc.flatten import flatten\n",
        "\n",
        "# Display plots inline and change default figure size\n",
        "%matplotlib inline\n",
        "matplotlib.rcParams['figure.figsize'] = (12.0, 6.0)\n",
        "\n",
        "# Generate a dataset and plot it\n",
        "np.random.seed(0)\n",
        "X, y = sklearn.datasets.make_moons(200, noise=0.20)\n",
        "plt.scatter(X[:,0], X[:,1], s=40, c=y, alpha=0.75)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f18f6c994a8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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66SqU53SZRm4A1ixczwv3vElxfglo8AWSuf6fV9JraLdEhyZEo6Kj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BOefWbDv4UpZjnI7NS04y0mUfcxeP4lUErutnS9AIuWpRtUG1lojfPO7v5Y8vHjwHz9fQpmttrM\nbjSz1y3wmCIi0iI83oBXH8XnbPvWGsxy2OAFYL1Q3RhqZn0ICsdhhWPTDq9uvPQbIE6S5lJIpH0M\nyEI8CZM/xYfO2+rPynrfBmQgHkpeXBQhXgddh2gSZQexaAlWODK8KWneLtsccTazq4G5mnF+YPon\n7u5mNl/Pmr3d/VEzewZwjZnd6e73z3GsM4EzAfbaS7+gIiKtyuMN+MhnoXRrqJm0Xrz3LKLCkWmH\nNifLPhOWXRoWRfERyO6HZXZNO6w6m/YvuPpUSHwtC1STWuXlUHkIyrdB18Gbv6r6KD52aWhVRhfk\nDgplGZV7IeqDnrdjPSc3+5sRaUnbTJzd/VXzPWZmfzazXd39MTPbFXhinud4NHn/gJldB7wQmJU4\nu/slwCUQltyu6TsQEZGmcnd86J+g8ocwcWyqV/LIZ/BoScsuJW2Wg64Xpx1Gw1jXy/Hx74SJdT5G\nUugcSi0yS5MWZFW8fD+WJM5efQrf+N6wvw0CMZR+DblnYyt+gM25+qTI4rXQUo0rgNOSj08DfrDl\nDma21JLKfjNbARwC3L3A44qISFoqa6DyYFjRbapLRdKJwce/mWpoi1p2X+g+IZSh4EAlaTM2kCTF\nhO4J02qHffJHof1btCyUeFguGZle23EdR0TqYaGJ84XAq83sPuBVyeeY2Soz+0Kyz3OB1WZ2B3At\ncKG7K3EWEWlX1ccB37yIglfDyoTVdVBejVcfTzW8xcrMsN4zscFPQv6YUNOd2R0ye4efVTwStnW9\ndPMXle8IL3pmPhF4jJf/f3O/AZE2sKB7MO6+DnjlHNtXA2ckH/8GeP5CjiMiIi0ks1uSXCWjmpW1\nQDlJoPP4hrPw/g8S5Q9KO9JFx8wgdwC25ADiycNg9GLw4fCzipZh/R+cueR6tDOwdo5nijqqVZ9I\nvah4SUREtk/2uaEsoPx7iMdCP2Qs3OrP7BXej3wa7/oaNmdP4PbjHuOTP4Txy0Kv4+yzsN7TsRau\nmY4Kr8Lzr4DKfUAess/EbOaNZut+LV76VejCMfWzisfAClj+kOYHLdLitOS2iIhsFzPDBj4CXa8A\n30Ao28hCtHfowmDdQBEqv0871LrxsUth9N+ByTASW30EH/4QcfGWtEPbKrM8ltsfy+07K2kGsNzz\noPfspO3cUHizAjb4UWyq57WIbKIRZxER2W4WDcDAeXjp12A9YPnNNc9TvDOaI3k8DJOXJ5MhM2Gj\n9YVJdeNfhDYvSYm6j8Pzh4cXOtYF2eeom4bIPDTiLCItz+NRvHwvXn0y7VBkGjOD/JFJK7NpSbNP\nEvoBPze12Oqq+hCbSlGms16oPNjSi7/UyqIerOtFYXRaSbPIvPTbISItyz3Gx78CE98j9KSt4LmD\nsP5/mDnBSVJjvafjld+FjhqWCRMELQP953dMfXNYfjoOI+gzRtXLYP1AZp4vFJFOo8RZRFqWT1wB\n49+GaDDU0HoM5ZvxkU9hgx9NOzwBLLMCllyMF6+D8p0Q7YJ1H41ldk87tLqx7B54diWU1yTlGqFd\nG/Ew9L49jLyLyKKgxFlEWpK7w8S3IOpNlg0mWWxjGZRuw6t/wjK7pRqjBBb1Yd2vge7XpB1Kw9jA\nefjwx8Iy1B4BMRSOxbrflHZoItJESpxFpEVVId4A0YqZm81CIh0/FfoJizSBRUth8DOh3jleD5k9\nZ6zAJyKLgxJnEWlJZlk8s0dInq1n8wMeA1XI7JFabLI4mRlk9wH2STkSWQgv341P/AT8Kci9GCsc\nHbrEiNRAXTVEpHX1nA4+AfF4mJjl5TDalz8ai5alHZ2ItJl44kf40PugdC2U74GxL+Eb341X16Ud\nmrQJJc4i0rKiwqHQfy5E/SFh9jL0vAXre1faoYm0JPcYL95EPPxp4uFP48WbcI/TDqsleDwMY5eE\nTijR0vB3JbMcquvwiW+kHZ60CZVqiEhLiwqH4/nDwMfDimZb9tIVESBJmkf+GUq/ZKpFnpeug67D\nof99c64cuKiU7wp3rqLczO3RABSvh76z04lL2soi/y0SkXZgZljUq6RZZGvKt4UE0JZCtCS82bKw\nrXxr2tGlz7KhHfwsMZCb6wGRWZQ4i4iIdAAv3hASw+kjy2Zghhd/nVpcLSP3fCCXrGyZcId4BApH\npxaWtBclziIiIh1hvn/pvpXHFg+zbug/D7wUVrqM14WuPbn9sO43ph2etAnVOIuIiHQAyx+OT/4s\ntGycGnX2GDw8JhDlD8KzX8SL10O8HsvtD12rIF5PPH7ltG0HY6byDZlNibOIiOwQr/wRn/wpVB+D\n3AFY4ZXqh5um3AFQOBaKPw1lu1P1vIVjw2MChGXiref1mz6PizfDyMeBMmD4xBWQfQYMfhKL+lKL\nU1qTEmcREdlu8eRvYPST4FWwHJRuwie+C0v+F5bZOe3w6s7dofpw6O6S3QezQtohzWJmoTNE4YhN\nNc2WPwSy+4fHBAjdRyjfDtWHcRuA0X8B6wIbmNoBKmvx8W9hfe9IN1hpOUqcRUQEAI/H8InvwORV\nQBnyh2M9p85abMa9BKMXgRUgmpZAVtfhY5diA+c2N/AG8+qj+PAnofogoVY4i/eeQdR9fMqRzWZm\nkHs+lnt+2qG0JI+H8aEPQPUP4UUfxVDvnNtv805mocdz8SpQ4ixb0GwBERHBvYIPnw/j32LqljUT\nV+Ib34vHIzN3rtwLlELiPF20BEq/CqOzHcK9jA+dD9WHwJZANBhG2Ef/D166Le3wZDv56CVQWRt+\nlpkVYH1AFSoPhZHmTaKwXWQLSpxFRARKN0N5LUTLwfLh1nVmOVSfxCev2mLn+W77d2D3hvJvobo+\n6YmcfN/WBZbFJy5LNzbZLu6lsDhMtHTaz7IXyIJPAKXNO8dD0HVYGmFKi+uwv3AiIrIjvHwXmG9O\nKKZYF5RXz9yW3S+MNsfjM7fHQ5A/orPqaatPgc0x8mgFqP6p+fHIjvNKUp4xvc91FjK7AXFoTReP\nhNKNzE5Yz1vSilRamBJnERGBLeqYN6tAtNOMLWY5rP+88NhUL9zqesjsgvWe3uhImyu7NxBtcRuf\nZJLgc1IJSXaMRT2QfRb4FqVHUR9k94HCcZDbH3rPwJZ8HsssTyVOaW2aHCgiIlj+MHz8q2FVtana\nZS8DjhWOm71/1wth6X/ixWuh+jhkV2KFQ8MiE50kuzIkyOU1oVyDTJJ4ZbCeN6UdnWwn63tnqFmP\n14P1JKsIxtB3DlHhqLTDkzZgrTqJY9WqVb569ept7ygiInURF2+CkU8B5VCubAa9ZxJ1vybt0FLl\n8Sg+dmnosuAlyD4b6zsLy61MOzTZAV55CB+/LExyze6Odb8hLHoii5qZ3eruq7a5nxJnERGZ4j4B\npd8BVcjtrwVNpnGvAFXM8mmHIiJ1VmvirFINERHZxKwb8i9JO4yWZJZF/zZFFjdNDhQRERERqYES\nZxERERGRGihxFhERERGpgRJnEREREZEaaJaDiIjIdvLK/fjEj6D6COSehxWOxzJPSzssEWkwJc4i\nIiLbIZ78DYx+EoiBLiivwSevhMF/xrL7pBydiDSSSjVERERq5F6Csc+F1RWjZWG55sxy8El89D/S\nDk9EGkyJs4iISK0qf5i5LPkUG4DyHSGxFpGOpcRZRESkVpYFHGatuutgEfq3KtLZ9BsuIiJSq8wz\nIFoBPjpze7wRug5LVhcUkU6lxFlERKRGZob1nw+Wg+p6qK6DeANkdsP6zkg7PBFpML00FhER2Q6W\n2xeWfgkv3gDx41j2WdD1Esy60g5NRBpMibOIiMh2sqgf6z4u7TBEpMlUqiEiIiIiUgMlziIiIiIi\nNVDiLCIiIiJSAyXOIiIiIiI1UOIsIiIiIlIDJc4iIiIiIjVQ4iwiIiIiUgP1cRYREZEF8fJ9+PhX\noLwGomXQfTJWOAYzSzs0kbpS4iwiIiI7zMu/x4fOBWKwvrAE+ej/xquPaBly6Tgq1RAREZEd5mNf\nBhyiJWBZiHogWgqT38fj9WmHJ1JXSpxFRERkx1XuAuufuc0yQASV+1MJSaRRlDiLiIjIjrMBoDRz\nmzuhdKN/rq8QaVtKnEVERGTHdb8O4lHwePM2H4JoV8jul15cIg2gyYEiIiKyw6z7JLz6RyheAx4R\n6p2fhg1+WF01pOMocRYREZEdZpbF+s/Be06FygMQDUL2eZjpprZ0HiXOIiIismCW2Q0yu6UdhkhD\nLejloJm90czWmFlsZqu2st+xZnavma01s/cv5JgiIiIiImlY6H2Uu4DXA9fPt4OZZYDPA8cBK4FT\nzWzlAo8rIiIiItJUCyrVcPd7gG0V/x8MrHX3B5J9vwmcCNy9kGOLiIiIiDRTMyr3dwcenvb5I8k2\nEREREZG2sc0RZzO7Gthljoc+4O4/qGcwZnYmcCbAXnvtVc+nFhERERFZkG0mzu7+qgUe41Fgz2mf\n75Fsm+tYlwCXAKxatcoXeFwRERERkbppRqnGLcC+ZvZ0M+sCTgGuaMJxRURERETqZqHt6E4ys0eA\nlwFXmtnPku27mdmPAdy9ApwN/Ay4B/i2u69ZWNgiIiIiIs210K4alwOXz7H9T8Dx0z7/MfDjhRxL\nRERERCRNWg9TRERERKQGSpxFRERERGpg7q3ZvMLMngQemufhFcBTTQyn0+l81pfOZ/3pnNaXzmd9\n6XzWl85nfel81mZvd99pWzu1bOK8NWa22t1XpR1Hp9D5rC+dz/rTOa0vnc/60vmsL53P+tL5rC+V\naoiIiIiI1ECJs4iIiIhIDdo1cb4k7QA6jM5nfel81p/OaX3pfNaXzmd96XzWl85nHbVljbOIiIiI\nSLO164iziIiIiEhTtUXibGZvNLM1Zhab2bwzQ83sQTO708xuN7PVzYyxnWzH+TzWzO41s7Vm9v5m\nxthOzGyZmV1lZvcl75fOs181uTZvN7Mrmh1nq9vW9WZmeTP7VvL4TWa2T/OjbB81nM/TzezJadfk\nGWnE2S7M7Etm9oSZ3TXP42Zm/5Kc79+Z2YuaHWM7qeF8HmFmQ9Ouzw81O8Z2YmZ7mtm1ZnZ38v/9\n7+bYR9doHbRF4gzcBbweuL6GfY909wPVemWrtnk+zSwDfB44DlgJnGpmK5sTXtt5P/ALd98X+EXy\n+VwmkmvzQHc/oXnhtb4ar7d3ABvc/VnAZ4FPNTfK9rEdv7/fmnZNfqGpQbafS4Fjt/L4ccC+yduZ\nwL81IaZ2dilbP58Av5p2fV7QhJjaWQU4x91XAi8F3j3H77yu0Tpoi8TZ3e9x93vTjqNT1Hg+DwbW\nuvsD7l4Cvgmc2Pjo2tKJwJeTj78MvC7FWNpVLdfb9PN8GfBKM7MmxthO9PtbZ+5+PbB+K7ucCHzF\ngxuBJWa2a3Oiaz81nE/ZDu7+mLvflnw8AtwD7L7FbrpG66AtEuft4MDPzexWMzsz7WDa3O7Aw9M+\nf4TZv4QS7OzujyUfPw7sPM9+BTNbbWY3mpmS65lqud427ePuFWAIWN6U6NpPrb+/b0hu2V5mZns2\nJ7SOpb+Z9fcyM7vDzH5iZs9LO5h2kZSxvRC4aYuHdI3WQTbtAKaY2dXALnM89AF3/0GNT3Oouz9q\nZk8DrjKz3yevahedOp1PSWztfE7/xN3dzOZrVbN3cn0+A7jGzO509/vrHatIjX4IfMPdi2Z2FmE0\n/6iUYxKZchvhb+aomR0PfJ9QYiBbYWZ9wHeB97j7cNrxdKKWSZzd/VV1eI5Hk/dPmNnlhNuVizJx\nrsP5fBSYPgK1R7JtUdra+TSzP5vZru7+WHLb64l5nmPq+nzAzK4jjAgocQ5qud6m9nnEzLLAILCu\nOeG1nW2eT3effu6+AHy6CXF1Mv3NrKPpSZ+7/9jMLjazFe7+VJpxtTIzyxGS5q+5+/fm2EXXaB10\nTKmGmfWaWf/Ux8DRhElwsmNuAfY1s6ebWRdwCqBOEHO7Ajgt+fg0YNaIvpktNbN88vEK4BDg7qZF\n2Ppqud6mn+eTgWtcjejns83zuUVt4wmEmkjZcVcAf5l0LngpMDSthEu2k5ntMjWHwcwOJuQreqE8\nj+RcfRG4x90vmmc3XaN10DIjzltjZicB/wrsBFxpZre7+zFmthvwBXc/nlBXennye5YFvu7uP00t\n6MXPO6wAAAD5SURBVBZWy/l094qZnQ38DMgAX3L3NSmG3couBL5tZu8AHgLeBGCh1d873f0M4LnA\nf5hZTPgHcKG7K3FOzHe9mdkFwGp3v4LwT+GrZraWMKnolPQibm01ns+/NbMTCLPx1wOnpxZwGzCz\nbwBHACvM7BHgfwI5AHf/d+DHwPHAWmAc+Kt0Im0PNZzPk4G/MbMKMAGcohfKW3UI8HbgTjO7Pdl2\nPrAX6BqtJ60cKCIiIiJSg44p1RARERERaSQlziIiIiIiNVDiLCIiIiJSAyXOIiIiIiI1UOIsIiIi\nIlIDJc4iIiIiIjVQ4iwiIiIiUgMlziIiIiIiNfhvxFtkQDf6/KUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aSYNZFVKKxC5",
        "colab_type": "text"
      },
      "source": [
        "Let's now build a 3-layer neural network with one input layer, one hidden layer, and one output layer. The number of nodes in the input layer is determined by the dimensionality of our data, 2. Similarly, the number of nodes in the output layer is determined by the number of classes we have, also 2. \n",
        "\n",
        "Our network makes predictions using forward propagation, which is just a bunch of matrix multiplications and the application of the activation function(s). If $x$ is the 2-dimensional input to our network then we calculate our prediction $\\hat{y}$ (also two-dimensional) as follows:\n",
        "\n",
        "$$ z_1 = x W_1 + b_1 $$\n",
        "$$ a_1 = \\mbox{tanh}(z_1) $$\n",
        "$$ z_2 = a_1 W_2 + b_2$$\n",
        "$$ a_2 = \\mbox{softmax}({z_2})$$\n",
        "\n",
        "$W_1, b_1, W_2, b_2$ are parameters of our network, which we need to learn from our training data. You can think of them as matrices transforming data between layers of the network. Looking at the matrix multiplications above we can figure out the dimensionality of these matrices. If we use 500 nodes for our hidden layer then $W_1 \\in \\mathbb{R}^{2\\times500}$, $b_1 \\in \\mathbb{R}^{500}$, $W_2 \\in \\mathbb{R}^{500\\times2}$, $b_2 \\in \\mathbb{R}^{2}$. \n",
        "\n",
        "A common choice with the softmax output is the **cross-entropy loss**. If we have $N$ training examples and $C$ classes then the loss for our prediction $\\hat{y}$ with respect to the true labels $y$ is given by:\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "L(y,\\hat{y}) = - \\frac{1}{N} \\sum_{n \\in N} \\sum_{i \\in C} y_{n,i} \\log\\hat{y}_{n,i}\n",
        "\\end{aligned}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hSFFByrKKxC6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "num_examples = len(X)     # training set size\n",
        "nn_input_dim = 2          # input layer dimensionality\n",
        "nn_output_dim = 2         # output layer dimensionality\n",
        "\n",
        "# Gradient descent parameters \n",
        "\n",
        "epsilon = 0.01            # learning rate for gradient descent\n",
        "\n",
        "def calculate_loss(model):\n",
        "    W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']\n",
        "    \n",
        "    # Forward propagation to calculate our predictions\n",
        "    \n",
        "    z1 = np.dot(X,W1) + b1\n",
        "    a1 = np.tanh(z1)\n",
        "    z2 = np.dot(a1,W2) + b2\n",
        "    exp_scores = np.exp(z2)\n",
        "    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)\n",
        "    \n",
        "    # Calculating the loss\n",
        "    \n",
        "    corect_logprobs = -np.log(probs[range(num_examples), y])\n",
        "    data_loss = np.sum(corect_logprobs)\n",
        "    \n",
        "    return 1./num_examples * data_loss\n",
        "\n",
        "# output (0 or 1)\n",
        "def predict(model, x):\n",
        "    W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']\n",
        "    \n",
        "    # Forward propagation\n",
        "    \n",
        "    z1 = np.dot(x,W1) + b1\n",
        "    a1 = np.tanh(z1)\n",
        "    z2 = np.dot(a1,W2) + b2\n",
        "    exp_scores = np.exp(z2)\n",
        "    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)\n",
        "    return np.argmax(probs, axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GhXotrEuKxDB",
        "colab_type": "text"
      },
      "source": [
        "This program solves the optimization problem by using AD:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yC5iegM7KxDC",
        "colab_type": "code",
        "outputId": "14edb61a-a3ac-436f-c421-e5030b29bc2c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 757
        }
      },
      "source": [
        "# This function learns parameters for the neural network and returns the model.\n",
        "# - nn_hdim: Number of nodes in the hidden layer\n",
        "# - num_passes: Number of passes through the training data for gradient descent\n",
        "# - print_loss: If True, print the loss every 1000 iterations\n",
        "def build_model(nn_hdim, num_passes=20000, print_loss=False):\n",
        "    \n",
        "    # Initialize the parameters to random values. We need to learn these.\n",
        "    np.random.seed(0)\n",
        "    W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)\n",
        "    b1 = np.zeros((1, nn_hdim))\n",
        "    W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)\n",
        "    b2 = np.zeros((1, nn_output_dim))\n",
        "\n",
        "    # This is what we return at the end\n",
        "    model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}\n",
        "    \n",
        "    # Gradient descent. For each batch...\n",
        "    for i in range(0, num_passes):\n",
        "\n",
        "        # Forward propagation\n",
        "        z1 = np.dot(X,model['W1']) + model['b1']\n",
        "        a1 = np.tanh(z1)\n",
        "        z2 = np.dot(a1,model['W2']) + model['b2']\n",
        "        exp_scores = np.exp(z2)\n",
        "        probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)\n",
        "                \n",
        "        gradient_loss = grad(calculate_loss)\n",
        "        \n",
        "        model_flat, unflatten_m = flatten(model)\n",
        "        grad_flat, unflatten_g = flatten(gradient_loss(model))\n",
        "        model_flat -= grad_flat * 0.05\n",
        "        model = unflatten_m(model_flat)\n",
        "\n",
        "        \n",
        "        # Optionally print the loss.\n",
        "        # This is expensive because it uses the whole dataset, so we don't want to do it too often.\n",
        "        if print_loss and i % 1000 == 0:\n",
        "            print(\"Loss after iteration %i: %f\" %(i, calculate_loss(model)))\n",
        "    \n",
        "    return model\n",
        "\n",
        "def plot_decision_boundary(pred_func):\n",
        "    # Set min and max values and give it some padding\n",
        "    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
        "    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
        "    h = 0.01\n",
        "    # Generate a grid of points with distance h between them\n",
        "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
        "    # Predict the function value for the whole gid\n",
        "    Z = pred_func(np.c_[xx.ravel(), yy.ravel()])\n",
        "    Z = Z.reshape(xx.shape)\n",
        "    # Plot the contour and training examples\n",
        "    plt.contourf(xx, yy, Z, alpha=0.45)\n",
        "    plt.scatter(X[:, 0], X[:, 1], c=y, alpha=0.45)\n",
        "\n",
        "# Build a model with a 3-dimensional hidden layer\n",
        "model = build_model(3, print_loss=True)\n",
        "\n",
        "# Plot the decision boundary\n",
        "plot_decision_boundary(lambda x: predict(model, x))\n",
        "plt.title(\"Decision Boundary for hidden layer size 3\")"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Loss after iteration 0: 0.578567\n",
            "Loss after iteration 1000: 0.288832\n",
            "Loss after iteration 2000: 0.233156\n",
            "Loss after iteration 3000: 0.182124\n",
            "Loss after iteration 4000: 0.147160\n",
            "Loss after iteration 5000: 0.118781\n",
            "Loss after iteration 6000: 0.100822\n",
            "Loss after iteration 7000: 0.089667\n",
            "Loss after iteration 8000: 0.082638\n",
            "Loss after iteration 9000: 0.078198\n",
            "Loss after iteration 10000: 0.075316\n",
            "Loss after iteration 11000: 0.073359\n",
            "Loss after iteration 12000: 0.071963\n",
            "Loss after iteration 13000: 0.070921\n",
            "Loss after iteration 14000: 0.070112\n",
            "Loss after iteration 15000: 0.069465\n",
            "Loss after iteration 16000: 0.068932\n",
            "Loss after iteration 17000: 0.068485\n",
            "Loss after iteration 18000: 0.068102\n",
            "Loss after iteration 19000: 0.067770\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Decision Boundary for hidden layer size 3')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CdnwLiCmlatOWS4gHEKoPUcguLg1WyBbwhwM1C5rnJua48tplSsUi4QYnr/j6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\nTfTzv49/36r7rK+/STg8RibTyPGnNQ3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krmpr8l0fQTbslJbIJLjyzlXG+sfIT+dIN6Rp\nONq4IXWSvzo+wLeiNh+efPel+5St48S9n4MIQrQSRLuUrfMbfUsHjuXOgzuRfdZac/bNs9y5fofs\nRFAJUUrRc+34rg/XLmbw/iDGM6TqAgk5O2JjOzZ9n/XS0N6w56TdFhNNRlfNMC9m4P4AlvNi/sGO\n2KTqk/TfeUbrqVYsa3tK8d/xP+WD0PRk1/B0M7Y/iKgX3zVFHk83vshCL0bZlJzXUJJHSQlRcUSF\n7ZX7gWoEzv8AnFRKHSMImP858K3FOyilWkVkqPLjPwXuVuG8IctY3Nt4kBARxp+NM3Cvn1K+RF1b\nPZ1nj67I9FSb7GSWX/7dL/FdD1WRnxrvn6CmKUNDewOdF7oWHM/EX72PUWuN75mqrKeUL9H3eR8T\nlcxcQ3sDx6/0bKj3ORKP0H5qc4Yh3x28wwfvXKcts3bQb3QNBft1HP8xlsxiVIay1Y3Rh7tqtNh5\n8No3/4TvfP4V/rX1+raeM1Wb4tpvXiM7NovvGdIN6T33ID0zOk00sXRNTtQhOzFHuVQmGt++gdud\nID+dW3EttmwL3zd4ZQ8rXv3A+eN7vfz2P/8xv3o0ND3ZLVyrC8tMoM1M4GoqLiiH8joKGaISq7S6\nhexlXjlwFhFPKfV7wF8S1Cn+QERuK6X+LfCpiPwp8K+UUv8U8IBJ4F+86nlDDg+D9wfp/ayXeCpG\nJB5hon+cqcEpLv/G5Q1Z9W4FEeHhzx6iLUUiE2QQUnVJZsZm6bnas2KqP54OFC9KhdLCjV9EKBfK\nVSmTG99w+0e3KcwVFizNJ4emyM3e4so7V6qexbrxcJj33v8h3U11C9rFa65PZyjpS1Vdw0FhPvsM\n1/n447ptzzxbllXVCke1SWQSTI9MLwkufc9H23pPKfGIBIO+s+OzOBGH+vb6DbW/ZZoyjDweXfL+\nvLKHE7G3NbkRmp7sLqJiFJwvYJtRtMxiSOJbLYja3w+CISupSo+ziPy5iJwSkR4R+Z8q2/5NJWhG\nRP4HETkvIpdE5NdF5F41zhuy/xARpoenePTpQx79/BEzozNr7u+7Pk9vPyVVlyQSj2DZFsnaJL7r\nrVC0qCalfIn8TG5FYB5LRhl9NrZif6UVp984jVfyyU5kyU3nyI5naTjaSGPHqwfOM2Mz5GZzpCoD\noIHld5LCbIGZkbX/hgD52TxTw1MU5jYunaUttaGgOWR9elLniERtrn3zT/j4Xu9uL2dXaTvdjud6\nwdAtQdA8NzlHx9mObWtj2CzGGB789AE3//omT2894dGnD/n5n3/K7Pjsuq9tO9WO0orcTA7f8ynl\nS+Rm8nS/dmyFbGjIPkIM2syhJP/yfZSDZ7VTts/i2Z1h0HxA2TuP9yF7mpEnI/Tf7qc4V6CmuYau\n17q3JCH1+PPHDNwbwInYCIHGbNeFLrouru6GVyqUML5ZYaLixJ0N3cS2yvwNbqW9r7zU0CXTlOHa\nP7nGxMAE5WKZmuYaapprqnKzLBfKFWe+VX5XCUBWw3d9Hv7sAWP940HvqBFaeo7Qc7Xnpa6SNx4O\nU/v+91lVoiFky3x48t0dbdvYq2QaM5z78jn6PusjO5HFciy6Lx+j48z6w6o7xdTgFCNPRsg0vnBd\nLOVL3P/pfV7/J6+v2YedyCS49PYlBu70Mz0yTSwV48S1E7umqR/y6mgzRdS7jZYyogSjaijZ59c0\nOAk5uISBc8i6DPUO8fBnD0ikE6TqU+Rn8tz865tc/seXSdWl1j9AhbnpOZ7ff06mIb1w4wlsa5/R\n3N1MPL3yIhSJRVCruY0VPRo6kq/+5l5CJB6hrrWe6dFpUrXJhbWWCmVOHH/51HM0Ed2wmcNmiGfi\ngFoRyAOr/t3meXb3GWP946QbKrbdIgw9GiJRk3hpz/MnyUneX2cgMGRrLG7b6OM603/0rV13G9wN\n6tsaqGutD3p+beulD3G7xdizUSIxZ8l3LZqIkp3Iks/mSdasfe1J1iQ5/cUz271M4IXpSXg73x6U\nFIl5nwMRjA6SRVrmiLk3KTi/ciiVgw47e+tqFbLnMMbw7NZTkrVJnMqNJJaKYdl60/JKcxNzAEuy\nNfPZ2OwiPeTF2BGb9tNtZCeyeK6HiATtBgpat9k97MTrJ0hmEmQnskH7xVSOzvNHqW+r39bzrka6\nPk1DRwOzY7OUi2XcosvM2Cz1bXVkGlfP/IsIQw+HSNYmXrgGKkUiE2fo4dCqr/nu4B3ee+eHxDeg\nuBGyNXpS5/j2ha8TidrUvv99vju43GT1cKCUwok6ey5ohuC69DLjkt22Ll/O45NT1KTj4YPuNmH5\nY4Fi0KK2C1EplMwFWvUhh47wETVkTbyyh1v2iKWW9vpGYhHmplYPdiFoafA9H8uxFm40L2txgJe3\nPwB0XujCjjgM3BugMFsg01TDsUvHlhh6bAfRRJRLb18mO5XFK7okapPbNoy4HkopTn/xNDXNNYz0\njYAIPdd6OHL8yEtv5IFroFnpGmhpygV3xf43Hg7T8ObjDQ8EhrwaH558lx+NfBK4DY4+5uwn1w5l\n9nknMcYszAisRXN3MyOPRzDGLDzcF2YLJOtSa1Z4dou6WChjtl0oyiilVyoxK4Vi4+6rIQeHMHAO\nWRM7YuNEbLyyt2TivVwoU9+xsmdPRBh8OEj/7X68sks8FefYlWPUtzVQe6QWO2IvUZ4o5UpEYpE1\nXcO01nSc6aD9dHvggraDGSql1Z6xA7Ysi/ZT7RuWldNa09Bez9TI1JLS8lqugXbEoiO58xn1w8q8\n22Dk4V9Qfv8+3/3Lr/Gv2kJlhGqTn83z+PPHTA1NYjk27afaaF9jGLH2SB2dF7rov/NsYVssFefM\nPzq95zLOIduL0bXgPwEWuaCKQQFGbbxVMeTgsPdqZCF7Cq01nRe7yE3nKBfLiBEK2QLGN7SfXhnA\nDT4YpPfTRzgxm3RDGmMMt6/fYWZsBifqcP4r50FU0P4wOYeyNOe/cgHLWX+aXim1J8u6e5nuS8ew\nHTvozZzJB86SqRhHzx5dst+Nh8PcffPnvNEQSqzvBh+efJfuprog+9zyg91ezp7Bcz0mBiYY6Rtm\nbnpuS8coF8rc/OubzI7PkKpPEU1EeHrrKX03+pbsJyJkJ7KMPh1lenSazvOdvP7eFzjzpbNc+LWL\nXP3a1W3Xjg/Ze/iqHk83oZlBSQElObTMUtI9oWrGISXMOIesS2tPK7Zt8+zOM3LTOWqaa+m62EWq\ndunTtjGG/jvPSNYlF1ztIvEIvufz/N5zappqyDRmeP2918lN51AokrXJPe0Utt+Jp+NceecqEwPj\n5GbypOtS1Hc0rHAd/CQ5yftHe/nw5Hu7tNKQ+eyzvvtn9DXf588OefZ5bnqO2393u6IaE2T7Wk+0\n0nOlZ1PXjNGno3hll3RDoMdu2RbpxjQjfSN0nuskmoziez73f3KPieeTQVJRINWQ5tyXz1VFTnK7\n+I7/KR9cvg7sXd3ufY9SlOwLeGYMW0YRLDzditHh3/ywEgbOIRuiqauJpq6mNffxXR+37K3oAXRi\nDrmZ3MLPWus9ZQF80HGizgrDltUIBwL3Bh+dfW9J7/PvjPzmbi9pxxERHvz0PiBkGtML24YeDFJ/\npG5T0m656dwKYxWlFKhAYi6ajDL0aIjxgYkl8nPZiSxPbz7l5K+crNr7qiYf3+vlg29e583u0C1w\n21Ea32rBp2W3VxKyBwjr3iFVw47YxJJR3OLSwbNSvkRNU80urSpkPeaVNEJ2GXFxvF7i5U/4Wp3m\nX565xJdb7x9Kw5RCtkB+Jr9kKFkphRNzGH06uqljpevTeGV/yTZjDAgLxx/uHSaRiS/pX07WJRl9\nMoLxzSu8k+0lErXDoDkkZIcJA+eQqqGU4til4xTmChTniviuH2SahT1lbvCqeGUP3/XX33Gf0HAl\nUNL4Rtfbu72Uw4v4xNzPcfwnBIVARdR/wLn0XOg2+Io0dTURSUSYm5zD93zckkt2PEv7qTYi8cBC\nezV9dIVCAFmppxASEnKICVs1QqpK49FGLv76a/Tf7acwW6ChvZGOsx0kavb/UE1hNk/vZ31MD08B\n0NzdwrFLx3Bi+7/FYb8qaSgpYvv92GYMURFc3YlvNe/2sjaNJZNYzGL0i8qMoYY3mxRjUj50boPx\ndJxETYLiXHEhKywilItlmrs29//rRB1e+2pwTZroH0cEoskYw33DTA5P0X6mnebuJp79sn+hLQQg\nN5On6WjjnrEBX0xoehISsnuE37qQqlPbUktty8vl5fYjXtnj1t/dwvd8UvUpRITRp6MU5gq89tXX\nNi1RNTM2w8C9AfKzeWqbamk/077tutSr8b2WH/DF5vtAz46f+1VRUibm/hwlJUQl0FIk5v2CkpzC\ns1e3cN+raDPHigKgUiCKd9uv8aBuHG39mD7/Oj//+Lf45pn99/+1GZRSnP5HZ/jl3/2S2fEsIICi\n7VQ7da0rH/LccpBFRgWW3suHX2PJGCdfP0nnuU4++8vP8F2PWDqG7/o8+Ml9jl7opKa5hpnRmQXF\nsXg6QfelY9v/ZrfA45NTfDUdD6tEISG7QBg47zPECEO9gwzce45XdKlvr6frQlcok7TNTA5NUsqX\nFzJSSinS9Slmx2bJTmY3pfU8OTjB7R/dxok5OFGHsWejjPWPcfntyzuamf/4Xi9fuvyAj85+fcfO\nuSnExZJpwGBU7QrpJ8sfRktxIUsr2AgOEdOHJ22g9k8lwKg4wmq9tIIQoyd1jp6z5/jjp391aLLP\niUyCzvOdPP5FH27Zo/XEEbovdq9Q1JgYmOD+T+8t9CJbtsWZL52l7shK1YORx8N4rke6PlAEsiwL\n27EZvD/IF77+BfLTOfKzBWLJKDVHavdktnme0PRkbYJq1HMsmcGoJK7Vgai1rdJDQjZCGDjvM57c\nekL/7WckahPEa+JMDk0yMzrD5XeuLJiKhFSf4lwBba3MKisN7ioufC9DROj77DGxdIxILOivtCM2\nuekcA/cGOPXGqaqteT2GMiXSib1587X8CaL+LcBHCaA0Jes0ntX2Yh+ZXqmjqiwwEgTU+yhw9nUj\n4sdRkkVIAYKWLJ6uw6gX7QPf6Hqb3rk7wHX6uM70H33rwLoNPv78MQP3+4klY0TiEUb6RsjP5Ln4\n1YsLAW2pUOL+T+4RSUZwKqowbsnl3id3ef3rX8CJLv0MzI5niSxrrdKWBhHcokvtkTpqVwm4Q/YX\nSgrE3E9R4oKKomUGxwxSsK8EhiYhIa9AOBy4j3CLLs/vPyfdmMaJOGitSdYk8coeo483N2kesjlS\ndekV0/UiAgLxzMYteD3XozhXWAia54kmo8yMTFdlrRth15Q0REDWGawUl6h/CyGCqBqMrsGQIOrf\nQ0l+YTejkiDLHlpEKh0OEfYVyqboXMHXjWjJoiSHa3VQsi++cCur0JM6x7cvfJ1I1Kb2/e/zHf/T\nqizBd33Gno3x9NZTxp6N4Xu7NwBbzBUZfPicTEOGaCKKE3XINKbJTmSZGppa2G96ZBpjzELQDEFP\ns+/7zIzOrDhuqi5JeZnqjzEGFAuDgiH7H8d/isJDdAZRUUSlg2qU97Cq51GSJ+LdIVH+MbHyz7D8\nkeAaF3KgCTPO+4hSvgQEOsiLsaM22cnsbizp0FDbUkumqYbZsRni6XjgoDhX5MiJI5vqTbZsCzti\n47nekj5Mr+SRrNu5MmLDlcfU7GSPpAi230/EPEVJGV/XULZOLhmGm8eSGcCHxcGvshAjWP4Enh38\nvT2rFcc8Q0kBUXEQHy3ZSkl2/1VfRMUp2RcpWZUHNLV2XuPDk+/yo5FP+ODydW78UccrZZ5L+RK3\n/vYWhbkCWiuMb0jUJLn4axd3JaDMz+YBtaItw3I02fHsgimJGAkeYJcjwe+W03L8CIMPhyhkC8RS\nMXzPJzed5+i5oyuy03uV0PRkfSwzjrA0oSEqhiWzIB6otUMfbWZxzFO0yWJ0Bld3YfRS7wElReLu\npyh8DAk0LjHvJiVr2YyFCFpm0FJAVASf2uC7HVq371vCjPM+IpIIbmDGLM18eiWPdF1oKLKdaEtz\n/svn6b50DKUUdtTh1K+c5MS1E5s7jtYcPddJbiq/IGnnFl3KRZeOZTbY283Fhrb1d6oSjv+YqLmP\n4GBUBi0F4t4NlORW2ftlGRu15HeiEhTtqxhiaJlFUaBsdVO29qZhxYZRet2geZ63Wt5EW4ra97/P\njYfDWz7l01tPKeWLZBrSpOpSZBozFGbz9N95tuVjvgqRWGTVgNh4hlj6RXtRTVMNiiDQ98oeuZkc\nuZkcAmSaVs4dxFNxXvvqa6Tq0mQn53BLHsevHKfr4v4YJr3xcJgPLgemJ2+1vLnby9mziIqh8JZt\n9BFs1gt7tJkh7n2KZSYBjWUmiHv/gDZLKxi2/xzEC1qplIWoKEZliJjHQXBeOWfUu0nc/ZSod5NE\n+a+pKf1nEqW/wfEevdgvZF8RZpz3EZFYhPaTbfTfGyBZk8CyLQrZApZj03xs/0lw7TfsiM3Rs0c5\n+ooBbtvJNkSEgTv9eLMe0WSUs186S23zAe29Ew/HPMVQsxAQisRAsjj+AGX79JLdfVUL6KWZITGg\nBN9aqqhgdA3FyBcqLRs66HE+ZHx09j3+48O/oPb97/PdLdp0jz0dJVG7tHKSqE0w+mSUnk0+HFaD\nVF2K2iO1zIxMk6xLopSiOFfEiTo0LHINjKfjdF8+xq2/uUl2MlvR3oCWYy2rZpznj33h1y4gRjZl\n3b1X0JYKTU/WwdWdxLybCE5wTRCDJktZ96z7UBrxexGcoIpFMHSMFIj4fRT1lYX9LJmFVWYslDEo\nSgg2tj+AbcYwKoNtnqEwCApNjoj/FC05Ss6lqr//kO0lDJz3GV2XuokkowzcHaAwV6ShrZ6u17qJ\nJvZfafqworSi40wHbSfb8D0f27F39Aa+0xJ0ijJKBNFBMGyZiaCPFx8lJcrW8aUKGMqhZJ0n5t8G\nY4JgSEFJn0RU6iUn2R9l9u1ivm1j3qb77CfXNtW6oS0dBJqLYgoxgt5FVYkzXzzD488fB06BImSa\naui51rNiPiBVmySSjNKciaO1Jp5J4JVc7v/0PpfefnlQsh+D5pCN4VvNlOQ0EdOHMj6iFGXdjWut\nX1mwzPSSgVwAIYZlppZsMyqJlmlg0b1XDKIUQvAZdcwgRiVRkkOLi1ExgsHfPK4+gm3GcU12RRtI\nyN4mDJz3GVpr2k+1036qfbeXEvKKaEsHE/07yG5I0AlRRFlgXGwZRIkb3FikhFYFYt5NivbVJT1/\nvtVMXmeCcqkIvlX7UikpJWUc/wm2GUbQeLoD1zp66LLPb7W8yVstEHn4F5Tfv7+p7HPryVb67/ST\naQzaG0SE3HSe7te6t3HFa+NEHU69cYqeqz0YWToAuJiRJyMk0vElswaRmEN2YpZCtkA8vfHh3b3M\njYfD1L7/fYKcesh6ePZRPGlDUQyuNxt8uDYqAbjAiwc0hVvZ/gLXasc2z4MZC2KAj2aOsu5ecS5F\nadWeZlEKRREIA+f9RNjjHBJyyLDtHQ4olUVZH8eSicqAjINWLmgLT7eizTRaViogiIrhWW14dvvL\n9VfFJ+Z+hu0PIEQBm4j/iKh/d3vf0x7mw5Pv0t1UF2SfW36wodccPdtJQ1sD2fEs2Yk5spNzNHU2\n0X569x/QLcd6adAMQd/z8oHpAPXSdo39yCfJSSJRm4/OvrfbS9k/KCu4dmyiIlW2jqEl/0KxR1yU\n5ClbS81wRCUp2tcwKoGSLIoyJX0C1zq+sI+r29CSC5IHFZ12RRmjUoBCiawIyEP2PmHGOSTkkFBV\nm17x0JJHVARR62tBe/ZRymaKmD+LwsdXSXxVD8pBCYHu8haWYckEijlkmVW17Y9Qtrpf3tpRDcTF\n8R/jmCEAPN0a3Fz3QNvIfPZZ3/0z+prvr+s2aDkW575ynrmpOUq5ErFUjGTt/jCLaOxsYqx/nGgy\nuuDgWcqXiCajBybbPE98jQeIkOrgWy2U8In4vSjJI0Qo2efwrZYV+xqdoaivVSQ2VypleFYHlkxh\nmTEQ0DKLUUl8VYOWGTzrSGjKsg8JA+eQkENCtWx6ba+fiOmtaCYLnm6mZJ1ZV+LJt9vxGcOolRJ0\nRm0twNFmDoVeqsOhVDCAIwX87QqcRYh5N9FmuhKcK2x/AG1mKDrXNqyKsd18dPa9BbfB742e5ndG\nfnPN/VN1KVJ12/iwsQ00tDfQ1NnEWP8YlqUxRrBsiwtvnQ37mEO2hGe14ekjgAfY63+fX9YWpixK\n9iW0zGDJLNqMYZlcYOikT+JZHdVeesgOEAbOISGHiFe16bXMBFH/fjA8oy1EBNsfQbAp22fWfK2v\n6vCpwTKBBS6Aljk83YhRG7csX4xRiVWtqpVIpe9we9AyHQwRLcp0i8pgyQyWTAfZ9D3C/IOSvvtn\nfPyjM2tmnvcj2tKc+eIZWk+0MjM2QyTm0NDeuGn96fxMnqFHg8xN5cg0Zmg90UostfIzNDs+y+iT\nEbyyR2NnE/Wt9ds+q/Ad/1M+eOc6cLAy6HsapVnc57z14yiMqsVQC1bnqx8vZNcJA+eQkENAtUwT\nbL8/MBeZz7AohSGNbYYoS8/abQpKU3Qu4fhPccwQgqJs9VQG+baWGVywqjbZSslTXgTj2ziprqW4\nqtq0SGD3uxexdUPT0QAAIABJREFUbYtr3/wTPl6nbWM/orSitqWW2patSTrOTsxy629uoVQwlPj8\nwXOG+4a59PalJUOHgw+f0/vzXizHQmvN2NMxGo82cvpXz7ykz/rVufFwmPY3R+huqgu1m0NC9gB7\no54YEhKybXx8r5ffvvbjqpgmKMoIy8qSSgOCYgMWzcrBtU+Qj3yZQuRNPKsNx+8n5v6ciHcPbTbp\ngKlsis5VPKsZLXMoipStLkr2+c0dZ5OYl/R1K1jQf91rfHjyXWrSca5980+qZtN9UHj8+WNsxyJZ\nmyQSj5CuTyFi6L/Tv7CPW3R5/PljkrVJkjVJ4uk46cY04wPjzIysHG6tJnbEoiO5d6oYISGHmTDj\nHBJyCLBtqyqmCb5qwjF9yCI7bCUlhHhF1WLjKCkSc3+OkhKoKFqyOGaQonUJ32pY/wAVRMUo2+cp\nW+d2zMbWqFqMrq1ovgY9wUrm8FVNxcBl8ygpYJlpQOHrum2xDf9G19v0zt1BWz+mz7++7tDgYcD4\nhuz4LKn6pb3dsVSMqaHJhZ/npucQA9YiVRqlFJZtMT0yTV1raIG9LmLQkgVkwXEvJGS/EWacQ0JC\nNoxrBdJw2sygpIAyFRkm+8ymg1bbHwiCbp1BVBRRKYQoEf9B0POwWXYoaJ4/V9F+jbLVhaKIoohr\ndVJ0Lm1pMND2+km4f0/Uu0PUu03c/Xssf2wbFg49qXN8dPa9MPtcQWmFHXXwvaUVE7/sLzGWshyL\n1ezgjRGc6PbkoOa1m99ouLvjboFK8ijJb+27uArazBJ3/56Y+3Pi3g0S7v+HNpPrvzAkZI8RZpxD\nQg4wVZWgA1ARCs41bH8Ei0kMCTyrdUuSSraZWNHWICqKltlKS8ged8OstJ24vJoltZI8UfMAQwp0\nJQMnLlH/l+T1m9smbzeffYbr9HGd6T/61qbcBg8KSimOnj1K741e0vUptKXxPZ9CtsDZN18Eq+m6\nNImaJPmZPImaoO/ZLbkoBY1Hm7ZlbZ8kJ3k/avPhyXe35firoSRP1L2DZhYlwQBuyT7/ajMD4hHz\nfgGo4EEZQMrEvJsUnC9uS3UlJGS7CDPOBxy35FKYK2DMVlRyV8cre4w+Hlmww/Vcr2rHDqkuj09O\nUZOOV/fGqxw8u4OS/RqufWLLOqSioiiWfXbEIChkHz/TKymhzewLA4V1sPyJIKm3uGytHMBgyfS2\nrHGentQ5vn3h60SiNrXvf5/vDt7Z1vPtVdpOttF1oYvCbIG5yTmKuRI9r5+gqfNFQKy04tyb54jX\nJMhOBEYxvms49+Xzq6pvVIsd1W4Wn5j7OZocojIYnUHhEvM+W/p5Fh/LjOF4fVj+8Lqf9eBzXF6q\n+a4iKPGxzMT2vJeDgAiWmSDi3anMgEyt/5qQbWf/3p1C1sR3ffo+72Pk8QgQWND2XDtBQ/vGe0dX\no5QrcfNvb1KcK2I5GuMaYpk4F3/9ItF4mDXYi7yqBN124VqdxNwbCE6gAS0GLbOUre792fsoPhH/\nQaAYIoBSlPVxPLtrt1e2Lh+efJcfjXzCe+/8kD5+eOiyz0orui520X6mHbfoEolHlvQyzxNLxbj8\n9mXys3mMb0hkEtsuRbeTWDKNprBEa11UHG1msGQSX7WAuMTcz7GYBTSIwagYRefqGoOxPkpAlnVT\nBZnn6iV1DhoR/wGO348oBxAcf4CydRzXPr7ua0O2j4PzjQ9ZQu9nvQz3DpGsTSyUH+98coe5yblX\nOu6TXz6hXCiTaUyTrEmSbkxTnCvSf7t//ReH7CgvJOj2Jr6up2SfQ1FGm1kUc7hWJ+4ya9vtRMkc\nlhlFm5lX7uV0/D4cfxBDulKOThD1H2L5o2u+zrcaAsc7WdRjKy5gbXnQcCu81fLmQvb5k+Th7D21\nHZt4Or5q0LyYRCZBqi61rUHzdwfv8N47P9y246+Ot1obN6BQpgSA4z/DklmMqsGoNEbXoHCJ+I9e\nelSjMhXJmUVBshgULNFCD3mBNrM4/gBG1SAqiagURmWImCd7VvLysBBmnA8g5WKZscejpOvTC85Z\nTtShXCwz1DvEyfqTWzquiDD+dIxEbWLJ9mRNgrGno5x4/dV6PUOqx42Hw3zw/nXe7O7Z8aGizRA4\ndLWgKFUyz2uXpZWUsP1+bDOGKAdXd+Drls0PBooh6t/F9oeDHwGjaynaF0FtwfRAfBzzvKIUUFmL\nshBiOKYf32p++UtVgpJ1iqj/AIwBFKI0Jevirth3xyMO773zQ777l/Cv2vbuZ+eg03Dl8Y5rNxuV\nCrLCIi8+xyKALAS4thleMDCaR0gGw6yWv2q1SFSckj4ZfMaxgOBBsWx1bqve+n5Gm0qb1uJrm9Jg\nAutuf4/KXh4GwsD5AOKVPVCssJu1HZtirrjl485LL4mRJbUKYwx6nQxNyM6jLbWng+YFlIWQWH8/\ncYm5N1BSCMrHUiLm/ZKyld906dL2B7H9oaAkXbkxaTNDxO+lbJ/dwpswKHxkmaKGYKGkvO6rPasD\nXzdimWlEKYyqWyL5t5N8o+vthbaN740+5uwn1w5V28ZeYqe1m0UlcXUnEf8pQgRQKEp4Vusid08N\nK9w6hSCl/PIHWM/urEg4jgKCrxsxO1hR2Xe87KFZCWHotruErRoHkGgyiuVYQQC9iFKh/Mpao60n\n28hN55BKWVtEyE/naTvZ9krHDakeH9/rpfb97+/2MqqObUbRkkd0BpSDqOii0uX6wenSYw1gVGJJ\nNkdUKshAywaMXJajHHzSKFn6YKqkgKc3prggKoZnHcHXLbsWNM8z37bx1tHeQz00eBhxrRMUncv4\nug5fZyhaFylZZxe+K67uQC+TqVOSxbNa15ViNDoTKNHYJzG6bmclJPcZnm5AlB3o3FdQUkCI7mgL\nV8hKwsD5AGJZFsev9pCfLZCfzVMulMmOZ4mn47R0t7zSsTvOdtB0tIm5iTmyk3PMTc7R1N1M2+kw\ncN4rDGVK1KTjfHT2vd1eSlXRMl0ZkllE5Ua92Z4/tZAhW7o1yJxtrde5bJ8G3EDbWgpoM1MJho9u\n6Xh7gQ9Pvkt3U12QfW75wW4v51Bw4+Ew32v5AV9qfbA7C1AKXzdSsi9Ssi/hWy1LAmLPasez2tAy\nizazaDODr+soW4fbSKfqqAhF+zKCoCp/Z8GmaF/en8PTB4gw339Aae5qJpaIMfhokFKuxJETrRw5\ndgQn+mo9k5ZtceZLZ8nP5Cnmi8SSMRKZDZTZN4Hv+viejxNzgqGpfYqIkJvKUS6UiKfjxKv8dzps\nCEmQkaXxbqX/crMZWk8fIeL3LikVK3L4uiFQ+NgCRtdQcN7A9ofQ5PCpxbOObK1neg/xVsubvNUC\n+u6f0dd8P3Qb3GY+SU7y/tFePjy5Rx98laZkn6NsdQUVIKJLe/tDqkZwTflVtMwBKnApDf/Ou04Y\nOB9gMk0ZMk2Z9XfcAomaxIIJQLXwfZ+nN58y9GgQESGWjNNzrYe6I/vPytYtu9z7+3vMDE+DVogR\njvQcoedaD1qHhZ6t4FlHcMxTlOQR4oCgJYtntawhg7U6rtWBZSawZAbQCAYhRtne2uDsPKISuPbB\nDCo/Ovsef/z0rwK3wc+/wr+2Xt/tJR1YdlS7eYuISuJvUcP9QCMCmOplhZVe1F/+CoeRIlrmEJyK\nykkYgG+VMHAO2TM8/uwxgw8HF+TzyoUyt6/f5vJvXCZVm9rt5W2KJ794wszINOnGYGJcRBh6NES6\nPsWRntZtO+93/E/54J3rwMGbuBYVo2hfJeI/wJJpRDRl6yiutQVNU+VQdK5iyRTaZDEqhq8bt5xt\nPizMuw1q68f0+df3TPa5lC/hll3iqfWl5Hab+fmQ1appLyToDt7398AjBtvvJ2KegrgYnaFsncTo\n3e9Hdrw+IuZxRTc7mOcoOq9tOuEQEhDeJUL2BG7RZbhvmHRDaiEjG4lHcEsuI73DpK7tH6k73/cZ\neTJCsu5FNkYpRTwdY/DR0LYFzjceDtP+5siel6B7FYxOU9TXKjrH+tWyOkrjq4agPWO7EQ/bjGCZ\nCURF8XTbvpXh6kmdo+fsuT2RffbKHo8+fcR4/ziooJXs+JXjtBx7tVmO7aCUL/Hk1hPGn46htKL1\nRCtHz3ViR17chndDgi6kOjj+EyKmF0MadAItReLeZ+SdLyBqncSPuGgpYlSs6hKUlpkg4vdVssw6\nUNySOaLeXYrO1aqe67AQBs4hewK35KJgRRuDHbHJZ/eX2LsYQYysyCgprTDe9rpk2RELlttYH0R2\nQd94y8w7rcksUrEZts1zStaFNfWd9zrz2We4Th+7k33uvfGI8WdjpBpSKKXwXI8H//UB8VR829rU\ntoLv+tz6u1uUckUStQlEhIF7z8nN5Lnw1oUl++60BF1IFRAPxzzFULMwSCkqhhIvcPuzz7zkdRIY\nJ5mnFUU/has7gypalVopbDMYzIAsGvAUkmiZXpD2DNkcVWm2VEp9TSl1Xyn1SCn136/y+6hS6j9X\nfv9flVLd1ThvyMEhmoqibQvPXRr0lQtlalt2v9S1GWzHpr61nsLs0oC/MFuguXtj0mSb5cbDYWrf\n/z5vNNw9sNnm/YY2U8Tcz0mW/hrHPMGoOKLigckEcaL+/X1vN9yTOse3L3ydmnQ8yD77n+7YucvF\nMmNPxxeCZgi+e3bEYqh3aMfWsREmhyYpzBYCt0GtsSyLTGOaqaFJ5ibnFpQ0vth8f7eXGrIFFGWU\nyAo5PiFSGexbHdsfIGL6EFIVt9EkEfMY2x+o3trEZ0Wop1Sw3i0qCB12XjlwVkpZwL8H3gXOAR8q\npZbfuf8lMCUiJ4D/HfhfXvW8IQcLy7I4dvkYuek8hbkCbsklO5Elkoi+soTebnD88jEsxyI7niU3\nnWN2fJZ0Q4bWbdK7/iQ5SSRqHzgJuv2K5Y8Rd2+gJYuWAlrKOKYf5vWmlYMSF8Wyaop4aDONNtlX\ntgDfSb7R9TZvdvfwweXr9F3837jxcLjq5yjlSuRn8xgTPGz4ZQ9YWdmxbItyvrTKEXaPQraAtlZm\nEJXSFPNFev0cX2p9wLcvfD188N2HCFFEWSDLqn1SWlNzOchSp14E3EpjSOKYZ1VbW+DMWlymu13E\nqERlyDpks1SjVeNXgEci0geglPpPwG8BixXzfwv4Hyv//i/Av1NKKZF9dGcI2XaOHD9CLBHl+YPn\nlHIlOs4epfVkK5H4/pPzimcSXPnaVSafT1KcK5KqS1HbWotlbd/g0n6YxN8S4mGZcSzJYlQKTzfu\nbKuGuNj+CBbTGJJ41pG1y5siRPyHGBUHFUFUBJEyCrBkCl+1VCyNhcB+OMDyR4n6d1H4IGBUkqJz\nEVE7K2OoJA+YQP5vE+XintQ5ei6c4z8+/IvANOUvv1YVy+5yocyDnz1gengKUEQSEU69cYpMY2Zh\nDmKxzGY5X6btdPsrn7eaJGuSGH/p7U5EQIRYKgZzM9h7fKjxQCCClmm0lDAqUT0ZPWVR1seJ+vcR\n4gg2mgKiLDzr5Z9FLeVgDUuw0LJ1h9/leLoZy4xim3FAgwiiLEr2xVBZY4tUI3BuB/oX/TwAvPGy\nfUTEU0rNAA3A+OKdlFK/C/wuQGP9/u39C9k6tUfqqN2H8nOr4UScPTmktJ9QUiLm3gj0YpWFEoOj\nohSdqzvSm7f0/BEsGcUxTynaVzH6ZT20HprigoSU0TVY/gxG7CDDLFJxWmtGVKxynhwx/5cY4oHJ\ni6psc29ScN7YkRuckgJR7zZaZlCiMCpKyT6/aVWAD0++WzXLbhHh7t/fZW4yS6o+aMkoF8vc/tFt\nrr57lROvn+DOJ3coF8pYjkW54JKsTe65711tay3J2iTZyTkSmThihNxMnqbOJv4g/4z3vvlDwpGj\nbUbKxNxfoGV2QQre042U7AtVkY7z7KOIiuKYZ2gp4OpmXKt7zeuUZzVhmcngIbWCIo9nNb7yel4c\nMAiSPZlCm+nAedBqQlS0euc4ZOwpQVkR+Q8i8rqIvJ5J7a++1pCQ3eI7/qcVCauDh+M/DsqKugZR\nKYzOoCgT8ft25Py234+SfOX88cDuG4uIv1YvqoVgL5RtRcXwdCsKFyU+mtnAmc16MTBk+6NBJXVR\nJl1UEiU5tGS3580tRqQSVOQQVVP5O0PM+3yJ5e9GqZZld24mR3Z8llTdiz7mSCyCGMP4s3Hq2xq4\n/BtXaDl2hHR9mp5rPbz21ddw9lj1xbIsLvzaBdpOtlEuuPiez7FLxzj1ximKLXm6m+r48OS7u73M\nA03E70NLFtE1GF2DURlsM1bVfmLfaqbovE4+8mXK9rl1q0Vl6zigUGYWJUWUmQV0ZXsVURpfN+Da\nPXh2Rxg0vyLVeMR9Diz2lO2obFttnwGllA3UABNVOHdIyKGnvW3kwEpY2WZkxc1HSGL7o5Ssc9ue\nibXN2Mrzq3hgnCLu6i0jSlPW3UT9B5X+RRujoqBaKDpnMLphRRZK4a0YLIJ5rd/tV0kJssz5yoNB\ngKgo2hSx/DE8u2NLx12eff6dkd/c1Ou9srfq/7HlWJQqfcyp2hSpa3tf5z0Si3D8ynGOX1kWFPm7\ns55DhRhsf2ipLJxSlX7i53h07c6yVJKC8yuB26jMYnQGz2pdqESF7E2qETj/A3BSKXWMIED+58C3\nlu3zp8C3gZ8AHwB/E/Y3h4RUj4MrYaVZOfktiNIbD5pFCIJPe9OBtigHLUWERQGyGASLtQp2nhXk\nEiLmSZCxJkbRuYRvra6q4ut6HP8pgrxYo3gIapUeyOoTBO6rXJKVRlF+pWMvt+z+s030PidrkigC\nbfTF8wFe2duXjqLL+V7LD/ig+T6w/9/LXkcF364VW2F3lW1ExXDtY7u6hpDN8cqBc6Vn+feAvySY\ndPkDEbmtlPq3wKci8qfA/wn830qpR8AkQXAdEhLyCsxL0H3JUkCVS3t7BFcfJeI/quijqspwzxxl\nq3tDr7f9QRy/D00JQ4yydRzf2rgBjauPEvNuIVR0UEXQMkvZ6ly7L1IpPLsTTzoIUoprB+2+qsez\njmD7w5Ug3QCmklXf/rYDo1IoFCLmReZbBMRUzfnso7PvbTr77EQdui8fo+9GL3bERluaUr5MXWsd\nta37u53v43u9fOnyAz46+/XdXsrBR2k8qxnLH0MWPYgG15KDee0M2T6qMo0gIn8O/Pmybf9m0b+L\nwDerca6QkJCAT5KTvB+1D3RvpGsdRZPDMsMggfaoZwVDN+th+SNEvTsYlcSomsCIxLtNEWvDxiO+\nbqZsncAxj4OhPsCzjmzc5ltpNjRKohQl6xyebsUyYwg2vm7ZMXdBUTHK+jgR/1ElcNcoSni6BV9V\nLxu6PPu8EdOU9lPtJGuTjPQN45U8ui820tjZtK0KNdvNx/d6ufbNP8G2w4HAnaJsnSBm5tAyA6IA\nwdd1uNbRdV8bErKY8FsbErKPObASdPMoi5J9HiXdC5a0opLrvw4qNrOJFxlb5SDEcfwnG3fsUwrX\n7saV9gVljW1T89hJC/BVcO1ufJ3BNsMofDzVjK+bqtNHLh62P4gtw4DmX5x6nT8cuLVhy+7a5lpq\nm/dHhrlcLPPsl88YfTKCUoojPa0cPXd0ibX245NTfDUd5xtdb+/iSg8w86Yfiz67omIUnC9gySTK\nFBGdCB4KV5ktCAlZizBwDgkJ2fOISuJvMGAOXiBoyS9Iwi1sxsGS3OYXoJwga33AMbqesq5yv7wY\not5NbDNZGbQ0xPxb/Hb7Ue4WDdr6MX3+7lh2Vxvf97n9o1+Sm86RrE1WrLUHyE3Pcf6tCyil+I7/\nKR9cvk5dLOxrrjbaTBHxHlY036O41jE83fYigFYWvmraHj0xkYoCjo9RqZ3Vmg/ZUcLAOSRkH/Ld\nwTsVCbrQ+WlVlMLXtWgpILyYUFcU8avUsxuyNsYIA3dzPPtskIiapOdKmvYTGqUUIlFs85wTyS/S\nc/Ycf/z0r7j2zT/he6OnAV5J+3k3mRmZYW4qR6bxRYtNpjHN1PA02cksjybz/PY3f8yvHu3ZnEOg\nGCwzhi2jCBpft+JX+wFnn6PNDHHvBkIUo4PWrKh3ByyDZ29vO4aSPDH3JkpywecbRck6s6l5ipD9\nQxg4h4TsQxquPD6wEnTVomz1EPduVFQwIihKKPxwGGgHEBF++ocj3PvJFMlkDm3g3qclrv43Nl94\nJwJKoYxCSw5fJfhG19v0zt3hzW6Pnw09pfz+/Q21cOw1Ctn8qpV/peAHv+zljd/7W0BtMmgWot5t\nbBlBiAIGxx+ibPXsqhqDkhKO/wTbBO03ru7AXW9odhtxzDME54WUm3IwpImYx3jSXt2WDDFYMoFl\nRkEsbDMCCkTXBMod4hH171BUqR2bUwjZOcLAOSRkn3JwJeiqg9G1FOxrOOYp2mTxdT2u7lrD8S+k\nWow/K/LgZ9M0d8WxlIdtIG0Un/+tx6lrNjWNGkECtZIK88Fkz8lz9M7dAa7Tx3Wm/+hb+yb7HE8n\nkFXUzX5uRnn7n31KzRb6mrVMYZvRoFWo0nIgmEpAuEuav+IRcz8LtL9VEhAifi+aucDKeRfQZm7J\n5wkAZVcs5D1Y/rutIkLUvx1ozBNBSRHbDOHp9mDmsHJeRGOZkTBwPoCEXfEhIfuIGw+H+V7LD/hi\n81rOdSHzGF1DyX6NQuRLlOyLYdC8Q4z3F1AKlFYYlQQsLO2hEMafG5TJYlRmRQ/6PD2pc3z7wteJ\nRO1Xch7caWpbaknVBdbavu/jez69j4bJnHZ5+x8d29IwoGWmg2zp4iFNpRECObXdwDITKHKBYY6y\nKiY/Ndj+KGqX1uTrDIri0o3iYogC1es3tmQS2x/BUIOoROAoioMlYwtuoQE60EcPOXCEGeeQkH1E\nr5/jraO9fHgy1H7dMhJoJKPCy992EU0u/ttauFYHthkFCsRiHr7VTNk6ta5ix3LnQYCJz45t2EBl\np9GW5sJbF3l25xmjj0e4PzXDmW/d59Ibwon0e1s6phAJPrPL/1QigbV7tRAP24xU3DJtXN2GeUkf\ntZY5FNZSQ5FKb6+WAr7aeSdH1+rCNqMoySHEKhb3RYr2+ao6jGozHVw7FrL/UcAC8VCUgv8TEZS4\n+LqxaucN2TuEd46QkJDDgfg4fh+O/xylDL6qoWydCkup20DbqSSRuEVuxiVZ4yBEmJhqJlovZE51\nUbKjGz7WvPbzm3N3GMhN8qT5/pbsu3cKJ+bQc7WHP7w0xQeX726pPWMxvtWEmF6UlBAV/N2U5JB5\nffJqID4x7yaWmQxaP8Rg+8OUrNOrDtYZlUSWe4WLoESWDOPuJKJSFO3XccwTLDOFUQlc+0zVg1fB\nqRgFVTYojaebccwzlBQAQYmPZx3BV2E73UEkDJxDQkIOBVH/HrY/jFEpBI2WHDHvBgXnjd3pEz3A\nxJIWb//LDq5/f4iJgSIiQt2RKF/5nTbsyMaD5sX0pM7Rk2KJgcpPKioc1Q+ihWRinGRyBM+Lks22\n43qJDb1y3tHzA+DN7k2qZ6y2EhWlaF8i6t1Bm1lECUbVUHpJJlXJHJY/CYBvNWxI99ySCSyZWuIS\nKUSJmEd4cmSFtJqvGxE/gTKziEoBgRSbp5t39UHU6DQlvb091r7VBKYXpAyq0jetNGV9DE93oJSH\nrxuCoLmKme6QvUMYOIeE7BO+O3iH9775Q8Kv7eZRUsA2w0FP7UKJNbjx2/4wrt29uws8gDR1xvlv\n//UxZkbKKA01zRFUlQKJj86+t6DC8ff9fQtB9PPBlioocRg62j+lvr4XMRZog5jPefLkK8zlWtZ8\n5XcH7/De+z8kUmVHT6NrKThfRJEHVEUPeyW294yIecj8lJoyD4OssdWx5vEtM7my7UNZqIrFvVnu\nHqlsis6VSgVnBFGasnUM1+ra6lvcN4iKU7IvEfVug5lFIfgqQyly/qX/LyEHi/AOHBKyTyi25EMJ\nui2ipAyolRkgZaPYgiFKyIbQWlHXurUM83osqHCcPbcoiA7MVF4liE6nh6mvf0Q+38h8Pd6yihw9\n+hPu3f86Ikvl1r47eIeGK0H/9XsX72/fd1QphJdnj5XkiZqHGNKgg7l/EZ+o/yDIEK9RVRGigdve\nKn3ULxusExWjbJ+jbO/NfvPtxNf15J0voWUOURZCIswuHyLCwDkkJOTAs2CTLWaJnqsSF8MBdwQU\nQVFGsA7sQORqQfQnTwI5u5+Mnt7UQGEmM4DvR1kcRfp+jEhkklhsmkIhsES/8XCYu2/+fCFY7kjW\n05PavaFdy0wHca5eJJalLDCClhn8NQJnTzcT8e+hzThGxRGJo8jh61qM3vlBv32B0i9VhQk52BzM\nq2hIyAFi/gb9QfN9ILTp3QqiIpR1NxG/FyGBYPH/t3dnMZLd133Hv+f/v7X0Mj0bZ99IDqnR0BqK\nMmVRMgkocRTYMujYJkTDCiD4IYFeYiAB8hADfsmjoIcAMeAXwQmSBymOhdihARkW4MQGg8RxTFEi\nxW04HC6afZ/p6enuqnv//5OHW9PTPQvZM13d1dX9+wAEp6pr6p7pruo693/P/xzzabKNUMWPv/w+\nzGK6RDO9izEDGGXYRxkfGdiQipUwl0R/pk6iH952fm5D4e3ullB7jpjd2Yz5vStX+dOtf83lsj4J\n+9KRozwbjW8cXi0dbgyDhZ0u5n3tnryimY5iOCFfInoCazAbD9EtPrM8oYoMMSXOIqvc8XSDZ3e9\nu4o+oIdTGR8h2yiNfALzLmXcTxX33bHxaa0I+Trt9BpOC7cJ8EwzfYiR6RafGnR4K2L+hsLnphb2\ngp7foWO+7Y1pfm3sOJeabZLXq7cbig7b2lf5Qk4c2brn5rMveeNfP6WwBbcAXt56TXsXt0i6vUZ5\nnkY6QZGvkMJ2km0DSoJP42FkrouHiNyixFlkCBTF2l0hXDFmpLiTFIdjCt1SFfkkTriV/FggM0GR\nT9H1R9bsCcO93J7k3iuhhiYb2M7nONdbvXUSTUbGXuTwIjpUDIpbi078DK30Jvh0796CTjzysT/r\nIp/uDamAYYv+AAAgAElEQVShV6fbJFNQpHN046f7O6paZA1Q4iwisgYFn+aOjV0WsOwYJd7HaWrD\n7F6rxuYdgk/i1FPxfAgSyBS3MR2eJfo1wEi2cZF17Xcv8Bg67r0hJHHdnRjKylHiLLKKqQXdALgT\n/UqvZ26LKjzU3w9hr4h+GctdctiwoEVePyXbQsgfwPzL7V7hVvSmna0+5jMU6TTRr5NsgiruHliP\nbbdWr3RhyFiDZIsf+lGF3TTTcbLd6uFsPkUVdw3VanPIV2hV7/Tq+aEKO+nGx5VAS9/p01hkFVML\nuhXmiVb1BkW+AATAaVqD2eLn+9JdIOQp2tWPe+3xgARV3EknHu57klLF3RT5dG9IxUhvBHGXTvHE\nrc2B7hizvRW6Zl+Pf7/q782Pem3RmoR8mUY+yUzj6UUN8ZAHU8Z9BL9GkS/ivQ2GySYo48FBh7Zo\n5tOMVD/Bac7V8zfSGYxEp1jegSiy/ihxFhHpKfJZinxhwQQ182ma1dvMNn9haU/uTrOq62lz2Dh3\nX5FPU9lDpD5393BrMdt4miKdpMiXSLaRsthHDvUY4JAv91boZjHqlmSdeGhgK3SNdLyOO/RafFkb\n8yma6X0lP8vJCjrFZyn9GsFnyNaqV5+HaLW5SGdwBw8L6/ljvoD5zK12lCJ9oMRZZJX67o4fqAXd\nCivy2Ts+ZN1GCT6J+eySygaMGQJT9YrY3J2Ge5tGPtv3xBnqIRVl8Rgljy2MxW8wUr02t0Ln7sR0\nnpZnOo0n+x7HYhT5EtkWjmt2RinSJTr6pFpeZmTbRGbTJz+2H/rcWzwwc+fzmEGue7UrcZZ+0q8j\nkVXo1WNnefYptaBbeXV5xgLuGM7H9sJdlHt32fUVHjpWpLO3rdAZzgaiXxzYCp1bE6hYuKExke9V\nQuIV4PdeIfeSRvqIRj6DE6jCHsq4b033sB4G9ZWOo3O9xauwh248uKSfS7LNFH5u4evWU++EQEmz\n9NfwXIsREVlmZdiN+Uxv1HDNmKKyhzC/QbN6m2b1FjFfXPCYxXAbIbMR83kjvt0x71CF3f36JyzK\nPVfovF6heyBeEvI1bK4V2v3phgMEbtTTHQE8E7hBGQ/ccZxm9Raj3ZcZK/8X7fLHC7+nAJ5olz+h\nkT7qdQ+JNNN7tKo3Hyg26Y+QpxipfoKR6ysdjNFIJ2imY0t63ipsJ9s4IV8D72I+Q/DrdMNj2hwo\nfacVZxFZl8xnaaQPaKRzuAXKsJcy7KeMByjyCSzXK8TZxnFajJSv4r0P4UY6TRn30i0+fV/H7DSe\noF3+mODX5hafy7jvvrog9EO9Qnf2Lit04YFW6IrqBM38HobjOMm20il+7r6SliruxejSyD+D7GBG\nNzy68KTCnXb1OiFfw20cxwg+Sbv8MTONZ+aOF/0KkclbteRAZiNFvkCZr5PDhtsPLyugyKcAu623\n+AYa+TSlP9q76vAArMFM4+dppFNEP48zRlnsJds4MV/qtRRcnu41sv4ocRZZZb7/znGefvElikJv\nz2XjFe3yVcw7veEPmWZ6n8ANOsURSt9L8CmcBk6L0epvex+89UU6x2mkU1RhNzlMfPyx5h/WRplp\nfJHoVzEvSWEct6V367hfVdhBYaeI+VqvbjvVHTceYHNgzJdppaNk24BbrNv59e7r3M/IZjPK4iCl\n7yd4h2ytO2IJfp2Yry5IiJ0xQq67QlRxV/24PFXXv9jC58cNYxpQ4jwIwafv7B9uATJACSyhs4s1\nKIuHKXkYgKL6iNH8Wn1+6o7bGLONz6reWZZMn8wiq8yZiQ4bN4zwGwe+MuhQ1qyYL9YdBOYSsFCv\nSKbzdOMN3MZINtp77Ll6dTjMq2zrlTWEfPW+Euf670aSbe3Lv+OBWcFs43MU6QyFn8etRRn2zHXc\nuB9FPlWvFN6sUe3VSxf5PF3v3v8qojXI90jejQ5+t1VDC3WJTU8Oo3i+WymN4wymL7RAZVto5csL\nN9l6hVvsz8/FneBXKdJZmul4fSUnFGD1hthW9Sazjc8v/TiyrilxFpF1J/iNOzcjmfUu/c+QFvQN\nLu69L3DAvY+XxBpUxX4q9i/tabwL3OV76QBpSc99u/rqgNf15QsS6Lyg/CLZVpxRLF+f6wEd/DpV\n2FxfOZCByGEzpIqYzpBsE2b1hMZOcXjpmza9olW9TpGvEPwKwacxOlS+B6zAbYzYq8H33kmxyINQ\n4iyyinx3xw94/shRNrfVgm45ZRvDb0/q3DH3O2p8k20i01rQbcK8g1tB9QArtGuKJzJtinyGFLbO\nlVaYd3DafV/ddRulCnto5BO4j+IEgt8g2SZwp1W9AThV2Mls8RSN/H5dw45Rxn104yOqc71fXlGk\nUzTyabzXBaOKuxckuvVmvLoH9L2G1RTpJK30LmAYJY18gjLspdP4XP3aWaJGOkGRr5DDRixP42TM\nS2K+SIo7b0aKeV7xLjaytihxFlklXj12lmJf5LmHD3Jw/IlBh7OmpfAQnuavSGaCT1HFnXd+8Ftk\ntvEU7fINQp4EIFuLTvHUcK84L5H5FO3yNYLPEP06MV0i2RayjWMGs8VTy5KkduOnyDZBkU9hXtGN\nj4HP0q5e75WFGEU6Rxn30I1P0I2995IS5vvnubeKe5lsYxiZVjpK5Fpdv+6ZZnq3l1SDuVOFbb3p\nlLfSC/Ppug6e8XpDYNgCXmHM3NG7+0EV+Qy5t5KcGSdynUyb4FMkzxhlb7iLVptlaZQ4i6wiz2x9\nm4Pjzw86jLWvV+N7q6tGpBsPUsa7ly24jTPTeKYu8cDrkoEhmqzWd+60yzcwMjlsomsThDxJ8MtU\n8WHK4uDyXQ63QBV316ue9Ia5lP+XbBvnkmOnTSOdpgp77r8GXeZEv9pbxb01GCXTqE9MwgFCvkYj\nn6gHp1jdU6XIF8jpA8ri8VvPk66Az1L4td7GzwbJtmLUNcnJtvch2lsnRm7jJB8n+nXMEpYnIcTe\nye46ft9KXyhxFpF1ya1NtzhMtzi8uL9gRh5AB4zVKPgUwW/c2lxpgRw3gRdgzRWtIY35OubgYd6K\n8tzmzcm+J86Wr9Eu3yDmC7iN0Wk8QRX39PUYq4XlKe4o8L/Z75tpGvkkmbFbq/lmZMZppFOU8eBc\nkmo+RZEv4jZK7nVxaeQzpD6tNkPdg72VjpGpT6BS2AVWkBiljAdJcduSJn+K3KTEWfqm7JScOnqK\n8x+cw6Kx6+Audn1qNzFqUtcnudmCbunT6URWguN3ea3W9+WVjcQa93zbeOjv8IuQrzDe+UvMu736\n6ssU3ZNMF1+ibNxfT+9h4GHkHt1JwLk56fH2NCJgJOZPyYw+CQTcQ+9nFclEgk+S2Eg/VHFvb4X8\nYr13FKOybXQan33w/tAid6HEWfoip8ybL7/J1KXrjGwcwd15/ycfcP3yFIefXeSK3jqmFnQyTLKN\n1xsBc4dAh+BXMC9xQj0+eQXVmzfbC7ol1Bs5GyTr7+bNdvka5l3MMoFunaB5xWj5v7kWD0BYWz2C\nk23BGcF8CqfuaGI+RbIJsm2iCjtopBP4vE4lxjRVeGjB5sHALJXtJPrFefm0kZno3wh0i3SKJyl9\ncm6jYl2+o9IM6S8lztIXV89d5fql60w8dOvS28RDBZdOXGTqyhTjm3WJW2TNsMBs8RlGuy9T5Cs4\nBRDw0KCZ3q83X67UZfHe5s1W+RYxT3KzBv1+Jxd+IneiX6hXUz3h1mtT6JHALM30Pt3wc/073mpg\nkdnG52hWx4j5AmCkuKPekGlGFfdT5Eu9SY4F5hXZmnSLxxY8TbIJYnBKHqnHvQPZi17S3McrkmZk\n21iXa4gsEyXO0hc3rt0gxIXXS83qyV2zUzNKnD/Gt9MrfO2XXwbW1mqVrA7mNwg+BRQk29y3Fbhs\n47iNUYZRMMdtBKeN+XWKdJqyeLQvx1kMtzFmm7+A+TR1Gclo/7tomNX/Pi7edlLgOJGYL/b3eKuE\n2widxpPgFfUkkTjvay1mGp+nyBcIfp3MKFXcfke3mTI+QlG9AkBmDKNLYJbZ+KS6ncjQUeIsfTGy\nYYSc7qxtdIfmaGsAEQ2HV4+d5cAvXVQLOuk/d5rpXYp8EnPAIDPaGzu89M17wTs4AY+3b75rEn2S\ncslHWATPFOkkjXwC85Iqbqdcxl7NnXiIRv5ZnURaUff+pkvFpv6ubq9Gdo90wYreqPNd9/yrOUww\nUzxNM33Qm7Y5Rlkc7kv/ZpGVpsRZ+mLzzs2MbBhl6soNxjaO4u7cuHqDTds3smFL/3ZOi8jiRL9A\nI/2MbJvmOk6YT9Gq3ma28fSSnz9bq9dhIS9cxfaSFFbmPV/3EK47O7iNUuRzxHyFmcYXliWRLYvH\n6aT3aeUPeiuwkNjSq/fd3ffjrWbms8R0EaMi3ZzI+DEnLDlsZDY8tYIRiiwPJc7SF7GIHPkHR/jw\n9Q+4cOIiZsaux3ax/8iBumRDRFZUI52pSwrmvf+cMaJfxXx26TXI1qAM+2jmD8i+AYgYM70+y/de\nfewX81ka+dRc+zEAZwMhX6NI56iKvctwUGOm9Q/xzgYCV3EvIBSksIUyLsPxVqmYLtFKr2OeAYPk\nvYEzh1R6cS9e96yO+Spurd4+AHX7GEZKnKVvWmMtDn3p0zz+TMYwLOgX6Me52YLumWjAytWDynrR\nS2rmM8Md5rcKW4oyPorTpJk/wvwGKWylG5dx+Mk85jPUNbfz/o1e1xsHri/bcd1azLS+RPQrmHfI\nNrpg+Mqa54lWehOnhYde4udOI50khW0kU/nFHTzTSm8S0zmMCGTcCmaLp271QpehocRZ+i4Etf9Z\nDLWgk+VUhZ11guOtuaTOfJrMBG592ohqgarYT8X+ekPDCiaPcyvm7oAT/DIxX8N8FsiUcf+d49P7\nxcLqSxA9E/1yr8PFCFXYtizlKsGn6jKVMO/kyAynQcwXVbd8FzFfoMjnyLYRn3svztKq3mKm8cX1\nc9K1RihxFhFZg6qwg+gXKdI58AA4bs3FT0q8Xyv84e82Qhl200gnMb9BzFO4hbmTgpHyR8w0nsFt\nHWxO9op29RrRrwAFeKJpx5lpfA7v+7RL425XLIyMo0WTuyn8HE5rYdmUtQn5GsZ0r0e2DIslJc5m\ntgX4r8DDwIfAb7n7lbs8LgE/7d38mbv/k6UcV2TYqQWdLDsLdOJnKMM+Qp7EQ6seCLKGuj904+O4\nGyPV/wMryLaBFLaANQl5kpjOUxX7Bh3mfTHvEvMl8JIcNi1qZHiRThHzFXLY1HuS+upCqzral42g\n82XbgNtob8hM7/eXJ/BMCjv6eqy1oz5xvZ0baFrs8FnqivPvAf/D3b9lZr/Xu/1v7vK4GXfXdlqR\nnj27z6kFnSw/M7JtupVQrTUWSXE7yfeQ2XDbil4kcGOAwd2/kK/Srl7Deh07qBJV3EY3HsLDvevG\ni3yWfFtduTNC9Gvg3Tv6Ki+JGZ3iCK3qNYJP0ut0SCd+alFJ/npUhV0U6SxOe64DjfmNXunG8u8H\nkP5aauL868A/6P35PwN/w90TZxERkb6rVz3vUjrgVd0ibVh4plW9ARTkMEbIl4l+maI8QyOdpiwO\n0Imfvns/ZYuYV3d8F+rb/V/RzGGcmcYXCX4NI5FtYn2UxDygZFvoxkdp5g8g1z+PbCN0Ci2cDKOl\nJs473P1M789ngXtdp2mb2StABXzL3f/7Eo8rIiIrzTNFPkuRT4E7VdhJFXffezjGSoRkbbphH838\nEdnHgFBvgrTReoPckAg+hXkXDxOYTxHzxbouNtQ1xfWKZUG3+PTc3zG/QZHOYD5LyBdJtgtC7H1t\nihS3L19pjkWybVme515rzCiLR6l8F8GncIpeJxbVhA+jT/xtZ2Z/Bey8y5d+f/4Nd3czu1ePowPu\nfsrMHgX+p5n91N2P3+VY3wS+CfDQlu2fGLzIsLnZgu5LABwccDQi96eZjtLIJ3FGcYxWepfol+gU\nnx1oElDGx3Ebo0gnMCrKuJcqHhiyem6b23YX81Wc4tb31ALZJijyabr+GFhBTBdpp9dxDDxiJJr5\nOCXbMYwUNtGJnxrkP0hu4zZC6ldHGxmYT0yc3f2evbLM7JyZ7XL3M2a2Czh/j+c41fv/+2b2N8Dn\ngDsSZ3f/DvAdgIMHDvWn0ajIKtNsFXz98a8OOgyR+2J+g0Y6TbZNc7XEmUiRL1D5lcG2ZzOjinuo\n4p7BxbBE2cbJNtLrT524uaHMPJPDOFjA3OvuFZ5ppqNk2nX9skHFAUK+1LsKsJ9sC2u+RaQ/lrpE\n8OfA7/T+/DvAS7c/wMw2m9XFT2b2EPAs8NYSjysiIiso+A3mBo54IuZzNPL7NPIZ2t1XCHly0CEO\nNzM6xWdu3iD4DQIdqrC118VilsQG3JoYswSfvWPTn9s4gW69SU9Js8iyWGri/C3gH5vZMeArvduY\n2efN7I96jzkMvGJmrwF/TV3jrMRZ1p1vp1d4+sWXGGkO0+VjkZrTxHvbzWI+W7e4o4XTBDLt6se9\n4SNDxJ2YztIuX6Hd/Tsa1Yfg5cDCyWED041fZLrxi5RxD5Vtwa2N5UmgpFsc6j0y9k5gbr8wW2mM\ns8gyW9KODne/BPyju9z/CvDPe3/+P8CRpRxHZK14eNtmvrzjuUGHIXLfsm0k2wQxXyLmG2RrY17i\nVpDDlnoISTpPVewfdKiL1kjHaOaP5mq2m+k9Yr7AbOPnweJggrJIijuZDlsp8nmCX8UZpYo75/om\nu7WownZiOo/fbMPnCfOSMgxvuYrIMNDkQBER+WRmdBpP0ip/QmFnMQy/2bnCIhAJTA86ykUzn6GZ\nT5CZV7NtTaJfI/plkg24I4c1ejXbd0+EO/EQLc9Ev1C3OLNApzhMDptXNk6RdUaJs4isDe4U+TSN\n9DPMO6T4EN34qAYM9JFbi07jKaJfJzMGYX7ZUUWy4Rm0Eny6Ljy5oxY4EvI10mpvZWcNOo0nMZ/B\nvKwHoAywLaDIeqF3mcgye/XYWTa98D2+BuwdUwu65dJIH9BM75NtFLdRYr7ISL7MTOMLuLUHHd6a\n4daqhzmk93Fv4wSCT5Ns4+pPNudxGpjfHHs8/wvp1ijpIeA2MlTxigw7Jc4iy+x4usGX1IJueXlJ\nI39UT4rr9b51xrE8SZHOUBaPDDjAtaWMj5BtnEY+CV7RiY/3BqEMqC74AWTbQAqbCfkqbuPUfZRn\ncGsM1eAUEVlZSpxFZOgFn607DITbGgX1alYH1ydhjTIjxe31ZLphZcZscYRmepcin8Nwkm2iUxy6\no82brIyQJwl+A7eCZFuG6kRM1g8lziLL6A9Ov8XzL/4leqstr2xt6rFreeEEO++SwoaBxSWrnDXo\nFj9H1w8BPmSTBteQ3kCXRjrdqzsHp81s4yncxgYdncgC+jQXWUazO6bVgm4lWIMy7KeZPyD7BiBi\nTIPFuoRA5OOslk11ninyGYp0EqOiCjuo4v4135s55gs08skFUynNp2lVbzPb+PyAoxNZaKkDUERE\nVoUyPkonHMIoCX6dZJuYLZ7WxikZGs30Hq30FkYCIo30M9rlq+DVoENbVo18Bqe9oMOJ2yjBJ3sj\nyEVWj1Vymi0iskQWqIr9VOyv6501cliGiPlMveo6r6+02wTm14j5IinuHHCEg3D7ZESRwVPiLLIM\n5regAw0kWHFKmmXI3LuvdEH0SRJrN3Euwy7a6QLu7QWlGtk26oqRrDpKnEWWSYjGNw4/P+gwRPrL\nHeMG5plsY+p80Cf1CHPHWXi1xLwis7aH+KSwjdL31psDnXpzoDfINsJo92XAKcMuyviINnDKwClx\nFhGRRTGfoVW+QfRJHAMr6MTDpDi8fY/NO0C+o8Z2pbmNUYVtFPk8mQnqvtLTuDWphrnt32JYoFsc\nprKdFPkcTkHgCo18hmx1V5xGOknM15htPL2wc47IClPiLNJnf3D6LZ5/4S8pCr29ZHjEfIlG+rCe\nAhg2UYaHyfNb+bnTKn9KYJocNvbuK2mnnzIdnhm6tmHmszSrdyj8Eg5kNtAtPk0OEwOLqVM8gac2\nRToNZFLYQrd4fF30lY7pEq30JkaJeZeYL1LGh+euaLhNEP0a0a+QbOtgg5V1TZ/sIstALehkmMR0\nnnb1Om5tnCYxXybmi8wWn59LnoNfJ/r1W0kzgDXwPEuRzg/XdEZ3WuXr9UkAE2BG8Bna1U+YaXxx\ncO3frKBbfIpufIy6r/T6KIMx79BKr+O0e900rgNGkc9QhgO3vg9uWJ5RPzAZKL38RETWM3ea6T2y\njeLWBou91eNAI/9s3gPT3UsZLGB0Vyravgg+SfDr9ajtuQ4WI5iXxHxhwNFRlyKsk6QZIObLmOe5\n+mW3AicCCWNeOzrLeNBmQRksJc4iIutaRWD2jnIAp0XI1+ZuZxuv65o9zXuQY16SwnBdOjfKe58E\neGflA1rvPC1oPFevPI9guVu/3jxjeZLEBMnUpUgGS6UaIn3y6rGzvP3cj3j+yFHUgk6GR4HTqIds\nzJugZ3RJtrAsoxsP0areBgJOxOhShe0k27LyYS9BtrF6QvsdI9rzwlIUWREpbsLSvJ+HGZVtpwj1\nSZr5NFXc0+uqofU+GSwlziJ99Oyud/nG4V8bdBgii2dGNz5Cq3qHzBhYo7fqWlLGAwseWsXdZBun\nyOeALilsrzdqDVky4zZCN+ynmT7EaQGG+SxVeEgrmgPgNk43PkwzfQgE3B3DmSm+QFXsG3R4Igso\ncRYRWeeqsAcKaKQPsTxNtnHK+BQ5bLrjsTlM0B1g54l+KeNBcthII50GElV8hCrsHLqTgLWiLA6S\nwkPEfBEwUti2sKuLyCqhxFmkD9SCToaaGVXcWyfQ5PWxMc2MZNtIYXh7UK81OWxUqYysevqUF+mT\njRtG+I0DXxl0GCIPzgxYB0mziMgD0jUpEREREZFF0IqziIiIlxTpLIVfIluLKuwZ6BRBEVmdlDiL\nLNF3d/yA548cZXNbu/FFhpKXtMsfE30StzbBr1Lk03TiEVLcPujoRGQVUeIssgSvHjtLsS/y3MMH\nOTj+xKDDEZEHUKSzvXHi87qIeEkrvcN02Lo+NkuKyKKoxllERNa1wi/h1lp4pzUwrxaOfBaRdU+J\ns8gD+v47x9n0wvd4ZuvbWm0WGWLZWkC18E53MAcagwhJRFYpJc4iD+jMRIeNG0b4xuHnBx2KiCxB\n3b86gZf1He6YT1KFHXeuRIvIuqbEWURE1rUcJujEIxglIU8SmCTFHXTioUGHJiKrjDYHiojIupfi\ndqbD1l5Nc0MrzSJyV0qcRR6AWtCJrEEWccYHHYWIrGJKnEUekFrQiYiIrC+qcRYRERERWQStOIvc\nh++/c5ynX3yJZ6NxcFzdNERERNYTJc4i96nZKvj6418ddBgiIg8s5ElCvgIUpLgVt/agQxIZCkqc\nRURE1gt3muldGukkYIDjOdCJT5Li1kFHJ7LqqcZZRERknQh+hUY6QbYJcpggh404LVrpTfA06PBE\nVj0lziKL9O30Ck+/+BIjTY3gFZHhVOSLuBVgdutOa2JUBL8+uMBEhoRKNUTuw8PbNvPlHc8NOgwR\nkQfiBAzHb7/fHa2liXwyvUtERETWiRS2g+cFZRnms7i1yabhLyKfRCvOIp/gZgu634rG3rFHBx2O\niMgDy2GCTvwUrXwMsoMZTpNO8SSY1tJEPsmSEmczexH4t8Bh4Avu/so9HvcrwL8HIvBH7v6tpRxX\nZKWpBZ2IrBVVsY/k23o1zYFkm8DioMMSGQpLPb18A3gBePleDzCzCPwh8FXgCeDrZqY5xSIiIgPi\n1iaFbaSwVUmzyH1Y0oqzu78NYPN3597pC8B77v5+77F/DPw68NZSji0iIiIispJWoqBpD3Bi3u2T\nvftEVj21oBMREZGbPnHF2cz+Cth5ly/9vru/1M9gzOybwDcBHtqyvZ9PLfLA1IJOREREYBGJs7t/\nZYnHOAXsm3d7b+++ux3rO8B3AA4eOHR7m0kRERERkYFZiXZ0fw88bmaPUCfMvw380xU4rsgDe/XY\nWTa98D21oBMREZE5S6pxNrPfNLOTwJeAH5jZD3v37zazvwBw9wr4XeCHwNvAn7j7m0sLW2T5hWh8\n4/DzHBxXExgRERFZeleNPwP+7C73nwZ+dd7tvwD+YinHEhEREREZJI0JErmL4+nGoEMQERGRVUaJ\ns8ht/uD0Wzz94ktsGG0POhQRERFZRVZic6DIUJndMa0WdCIiInIHrTiLiIiIiCyCVpxFem62oPsa\nsHfs4KDDERERkVVGibPIPDdb0ImIiIjcTqUaIiIiIiKLoMRZRERERGQRlDiLULeg2/TC9yiKOOhQ\nREREZJVSjbNIz8YNI/zGga8MOgwRERFZpbTiLELdu1lERETk42jFWda1V4+d5e3nfsTXth/lyFa1\noBMREZF704qzrHtFM/Lcwwc5OP7EoEMRERGRVUyJs4iIiIjIIihxlnXvma1vDzoEERERGQJKnGXd\nmt+CTmUaIiIi8km0OVDWNbWgExERkcXSirOIiIiIyCJoxVnWpe/u+AHPHznK5vbmQYciIiIiQ0KJ\ns6xbakEnIiIi90OlGiIiIiIii6DEWdadV4+dHXQIIiIiMoSUOMu68v13jrPphe/x5X3HVaYhIiIi\n90WJs6w7zVbB1x//6qDDEBERkSGjxFnWlTMTnUGHICIiIkNKibOsG99Or/D8L/8luyc2DDoUERER\nGUJKnGVdeXjbZr6847lBhyEiIiJDSImziIiIiMgiKHGWdeHVY2fZs/vcoMMQERGRIabJgbLmff+d\n4zz94kt8uVXw5R3qpiEiIiIPRivOsi6oBZ2IiIgslRJnWfPUgk5ERET6QYmzrGlqQSciIiL9osRZ\n1jy1oBMREZF+UOIsIiIiIrIISpxlTVMLOhEREekXtaOTNenVY2fZ9ML3eDYaX97x/KDDERERkTVA\nibOsWWpBJyIiIv1k7j7oGO7KzC4AHw06DllRDwEXBx2EDDW9hqQf9DqSftDraLgccPdtn/SgVZs4\ny/tlwXUAAAI3SURBVPpjZq+4++cHHYcML72GpB/0OpJ+0OtobdLmQBERERGRRVDiLCIiIiKyCEqc\nZTX5zqADkKGn15D0g15H0g96Ha1BqnEWEREREVkErTiLiIiIiCyCEmdZVczsRTN708yymWk3siya\nmf2KmR01s/fM7PcGHY8MHzP7j2Z23szeGHQsMpzMbJ+Z/bWZvdX7LPuXg45J+kuJs6w2bwAvAC8P\nOhAZHmYWgT8Evgo8AXzdzJ4YbFQyhP4T8CuDDkKGWgX8a3d/Avgi8C/0u2htUeIsq4q7v+3uRwcd\nhwydLwDvufv77t4F/hj49QHHJEPG3V8GLg86Dhle7n7G3V/t/fk68DawZ7BRST8pcRaRtWAPcGLe\n7ZPow0pEBsjMHgY+B/zdYCORfioGHYCsP2b2V8DOu3zp9939pZWOR0REpJ/MbBz4b8C/cvfJQccj\n/aPEWVacu39l0DHImnMK2Dfv9t7efSIiK8rMGtRJ83fd/U8HHY/0l0o1RGQt+HvgcTN7xMyawG8D\nfz7gmERknTEzA/4D8La7/7tBxyP9p8RZVhUz+00zOwl8CfiBmf1w0DHJ6ufuFfC7wA+pN+P8ibu/\nOdioZNiY2X8B/hY4ZGYnzeyfDTomGTrPAt8AfsnMftL771cHHZT0jyYHioiIiIgsglacRUREREQW\nQYmziIiIiMgiKHEWEREREVkEJc4iIiIiIougxFlEREREZBGUOIuIiIiILIISZxERERGRRVDiLCIi\nIiKyCP8fRo/GB2xomK0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ULlIqHJCKxDF",
        "colab_type": "text"
      },
      "source": [
        "Let's now get a sense of how varying the hidden layer size affects the result."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0b9gZLY2KxDG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "plt.figure(figsize=(16, 32))\n",
        "hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]\n",
        "for i, nn_hdim in enumerate(hidden_layer_dimensions):\n",
        "    plt.subplot(5, 2, i+1)\n",
        "    plt.title('Hidden Layer size %d' % nn_hdim)\n",
        "    model = build_model(nn_hdim)\n",
        "    plot_decision_boundary(lambda x: predict(model, x))\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yMLSJEhlKxDK",
        "colab_type": "text"
      },
      "source": [
        "## Deep Learning tricks\n",
        "\n",
        "\n",
        "> A naïve description of the basic setup in deep learning would be: *a many-layers-deep network of linear layers, linear convolutions and occasionally recurrent structures with nonlinear activation functions that is trained by computing the gradient of the training error through reverse mode AD.*.\n",
        "\n",
        "AD is a critical component when developing deep models because the use of SGD is much more easy and robust (f.e. derivative computation is free of bugs!), but in spite of this fact optimization of deep models is not yet an easy task. Gradient-based optimization still suffers from some problems:\n",
        "+ The system can be **poorly conditioned** (changing one parameter requires precise compensatory changes to other parameters to avoid large increases in the optimization criterion). \n",
        "+ Simply calculating the actual gradient is so **slow** in deep learning systems that it is impractical to use the true gradient for purposes of optimization.\n",
        "\n",
        "In order to address each issues, deep learning community has developed some **tricks**. First, **gradient tricks**, namely methods to make the gradient either easier to calculate or to give it more desirable properties. And second, **optimization tricks**, namely new methods related to stochastic optimization.\n",
        "\n",
        "The deep learning community has been developing many methods to make gradient descent work with deep architectures. These methods (related to model architectures and gradient calculation) are  numerous. Here we discuss only a small sample of methods.\n",
        "\n",
        "+ It is not really feasible to calculate the true gradient when there is a large dataset.  Instead a sample is used. Calculating the gradient of the error of just a random sample from the dataset (or sequential windows, assuming the dataset has been randomly shuffled) is much faster.\n",
        "+ In calculating the stochastic gradient, it is tempting to do the minimal amount of computation necessary to obtain an unbiased estimate, which would involve a single sample from the training set. In practice it has proven much better to use a block of contiguous samples, on the order of dozens.  This has two advantages: the first is less noise, and the second is that data-parallelism can be used.\n",
        "+ In a multi-layered structure, one would expect the gradients of quantities at early layers to be nearly zero (assuming the gains at intermediate levels are below unity) or to be enormous (assuming the gains are above unity). The tricks are:\n",
        "    + Rectified linear units instead of sigmoids. Classic multi-layer perceptrons use the sigmoid activation function, but this has a derivative which goes to zero when its input is too strong.  That means that when a unit in the network receives a very strong signal, it becomes difficult to change. Using a rectified linear unit (ReLU) function, overcomes this problem, making the system more plastic even when strong signals are present.\n",
        "    + Gradient clipping. In the domain of deep learning, there are often outliers in the training set: exemplars that are being classified incorrectly, for example, or improper images in a visual classification task, or mislabeled examples, and the like. These can cause a large gradient inside a single mini-batch, which washes out the more appropriate signals. For this reason a technique called gradient clipping is often used, in which components of the gradient exceeding a threshold (in absolute value) are pushed down to that threshold.\n",
        "+ Keeping the error surface well conditioned for gradient optimization has been one of the keys to the current widespread deployment of deep learning.\n",
        "    + Dropout. Imagine a network in which multiple units together represent some important feature, requiring a precise weighting of their values in downstream processing. This would make optimization quite difficult, as it sets up couplings between parameters which must be maintained. A technique to avoid such “unfortunate collusions” is dropout, in which each unit in the network is, on each training pattern pass, randomly “dropped out” with some probability (typically 50%) by holding its value at zero. This encourages detected features to be independently meaningful. (In “production mode” dropout is turned off, and the weights scaled to compensate, to minimize the noise when performance matters.)\n",
        "    + Batch normalization. Batch Normalization is a technique to provide any layer in a neural network with inputs that are zero mean/unit variance. \n",
        "    + Careful initialization. Considering how the variances of activation values and gradients can be maintained between the layers in a network leads to intelligent normalized initialization schemes, which enable substantially faster optimization convergence. \n",
        "+ Early stopping. When fitting a dynamic system to data, as exact a match as possible is desired, so the true optimum is sought. This is not the case in machine learning, where the optimization is of error on a training set, while the primary concern is generally not performance on the training set, but on as-yet-unseen new data. There is often a tradeoff between the two, encountered after optimization has proceeded for a significant amount of time. This is addressed by early stopping, in which an estimate of performance on unseen data is maintained, and optimization is halted early when this estimated generalization performance stops improving, even if performance on the training set is continuing to improve. \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eQIKHvMVKxDL",
        "colab_type": "text"
      },
      "source": [
        "## Playing with neural nets.\n",
        "\n",
        "http://playground.tensorflow.org"
      ]
    }
  ]
}