practical1_SOLUTION.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
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    "id": "JVvNUpj6ZKmM"
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   "source": [
    "# DL Indaba Practical 1\n",
    "# From linear to non-linear models\n",
    "*Developed by Stephan Gouws, Avishkar Bhoopchand & Ulrich Paquet.*\n",
    "\n",
    "**Introduction**\n",
    "\n",
    "In this practical we will develop our intuition of machine learning models, and implement a linear and non-linear model from scratch that can classify a variant of the classic \"swiss roll\" dataset. We will then show how to do the same using the TensorFlow framework.\n",
    "\n",
    "**Learning objectives**:\n",
    "* Understand how the different ML components (data, model parameters, loss functions) work together.\n",
    "* Understand the intuition of gradient-based optimization.\n",
    "* Be able to derive gradients of the softmax loss wrt output dL/dOut, and wrt the model parameters dL/dW.\n",
    "* Understand what is meant by a decision boundary & how it visualizes the models predictions.\n",
    "* Understand the basics of TensorFlow, especially:\n",
    "    * the computation graph abstraction (define-**and**-run vs define-**by**-run),\n",
    "    * how TensorFlow can automatically derive gradients (relate it to the graph abstraction).\n",
    "\n",
    "**What is expected of you:**\n",
    "* Step through the cells and discuss the questions with your lab partner.\n",
    "* Fill in the missing code sections (\"# IMPLEMENT-ME\") by pair-programming with your partner.\n",
    "* Change the values for $w$ and $\\alpha$, try out different regularization strengths, look at and discuss the decision boundaries.\n",
    "* 5min before the end, pair up with someone else and explain the concepts from the Learning Objectives (above) to each other, and ask the tutors if you are stuck.\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "j9-CLiXs36tt"
   },
   "source": [
    "# Building Intuitions: Our First Classifier on Simple Toy Data\n",
    "\n",
    "Run the code in the cell below, and look at the resulting plot. It should produce a simple 2D data set consisting of 2 classes of points, a weight vector in black, and a decision boundary in red. The goal is to obtain a decision boundary that best separates the different classes of points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 514,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 770,
     "status": "ok",
     "timestamp": 1504366737227,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "Kx2JGMPS3_4O",
    "outputId": "cc3fb57c-e77d-4bf9-fd48-6d44890e540f"
   },
   "outputs": [
    {
     "data": {
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WfsaeV+jnpHOa1g31vdkfsmVjJbHojn2TgoEQz9z+QpOuvbNIOFLrPltFI1He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\nsgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46c46b8510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np                 # Numpy is an efficient linear algebra library.\n",
    "import matplotlib.pyplot as plt    # Matplotlib is used to generate plots of data.\n",
    "\n",
    "centre = 1.0\n",
    "points_in_class = 20\n",
    "# Setting a random seed allows us to recreate the same data each time we run the cell.\n",
    "np.random.seed(0)\n",
    "\n",
    "# Generate random points in the \"positive\" class\n",
    "x_pos = np.random.normal(loc=centre, scale=1.0, size=[points_in_class, 2])     \n",
    "# Generate random points in the \"negative\" class\n",
    "x_neg = np.random.normal(loc=-centre, scale=1.0, size=[points_in_class, 2])    \n",
    "# Put these together\n",
    "x = np.concatenate((x_pos, x_neg), axis=0) \n",
    "    \n",
    "# The class (or \"y\") value is +1 or -1 for the two classes\n",
    "y_pos = np.ones(points_in_class)    \n",
    "y_neg = - np.ones(points_in_class)\n",
    "y = np.concatenate((y_pos, y_neg), axis=0)\n",
    "\n",
    "# N is the total data set size\n",
    "N = 2 * points_in_class\n",
    "\n",
    "# Plot the data using Matplotlib\n",
    "fig = plt.figure()    \n",
    "plt.scatter(x[:, 0], x[:, 1], c=y, s=40)\n",
    "plt.axis('equal')\n",
    "\n",
    "# Pick a weight vector. In the exercise below, you are going to change the\n",
    "# values in this weight vector to see how the decision boundary changes.\n",
    "\n",
    "w = [-1.5, 1.6]    # CHANGE ME!! \n",
    "\n",
    "# Add the weight vector to the plot.\n",
    "plt.plot([0, w[0]], [0, w[1]], 'k-')\n",
    "\n",
    "# Plot part of the decision boundary in red. It is orthogonal to the weight vector.\n",
    "t = 2\n",
    "plt.plot([-t * w[1], t * w[1]], [t * w[0], -t * w[0]], 'r-')\n",
    "\n",
    "# Add some labels to the plot and display it\n",
    "plt.xlabel('x0')\n",
    "plt.ylabel('x1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OidhcGh6xtwN"
   },
   "source": [
    "# What do parameters do?\n",
    "\n",
    "* Change the line `w = [0.5, 1.6]` to use different values, and re-run the above code.\n",
    "\n",
    "* How does the decision boundary (the red line) change?\n",
    "\n",
    "* For what values of $x_0$ and $x_1$ is the inner product between $w$ and $x$ positive? negative? zero?\n",
    " * Can you relate this to the decision boundary? \n",
    " * Can you use this to determine the class labels $y$?\n",
    "\n",
    "* By changing $w$, can you manually find a weight vector that does a good job of discriminating between the two classes?\n",
    "    * How did you manually find it? What made you move from one choice to the next?\n",
    "\n",
    "* Now that you've found it manually, chat with your friend next to you.\n",
    "    * How will you find it automatically?\n",
    "    * Can you devise a function, where minimizing it does the same thing as the way you manually searched?\n",
    "    * Pause here and think.\n",
    "        * Which values of $w$ give \"bad solutions\", according to you?\n",
    "        * Which ones give good solutions?\n",
    "\n",
    "* Try to draw the function that you devised on a piece of paper. It should be small when $w$ gives a \"good solution\", and it should be big when $w$ gives a \"bad solution\". Be creative and think of your own function. Show your drawing to your neighbour.\n",
    "\n",
    "DO NOT PROCEED ANY FURTHER UNTIL YOU'VE THOROUGHLY ATTEMPTED ALL THE ABOVE QUESTIONS. (Ask your tutors for help if you're stuck!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "c58IjWnlyMh2"
   },
   "source": [
    "# A loss function of w\n",
    "\n",
    "* Below we will formulate the above as a **loss function**.\n",
    "\n",
    "* Run the code below, and look at the plot of the loss function. Note that it is not in x-space (***data***) any more, but that our axis labels are w[0] and w[1] (***parameters***)!\n",
    "\n",
    "* Are the weights $w$ that you found manually close to the minimum of the loss function?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 524,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 841,
     "status": "ok",
     "timestamp": 1504366743571,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "oFSdDg89xBW4",
    "outputId": "ae131b29-955f-4ff1-bf3c-ae595ed85f45"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cSAqb/CO7jYCaz6rKIITWP7VUbvasCj8YGYAdnwd0M6gNkEPQbCJrUxssNouW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\n8AxgXWF4PbBfaR1V88xos+x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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46a3766610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def compute_loss(w0, w1, x, y, alpha):\n",
    "    # We start with a regularizer.\n",
    "    \n",
    "    # What is its effects on the loss function? Does it change the loss function's\n",
    "    # minimum?\n",
    "    \n",
    "    # Note: In this practical we won't see too much benefit from this as we don't\n",
    "    # have a    separate test set, but it is good practice to include one and will \n",
    "    # become very important soon enough!\n",
    "    \n",
    "    loss = alpha * (w0 * w0 + w1 * w1)\n",
    "    \n",
    "    # Add the data point's contribution to the loss. We do this for every data\n",
    "    # point. (We don't have to do it in a for-loop, but below, you can really see\n",
    "    # what is happening...)\n",
    "    for n in xrange(N):\n",
    "        \n",
    "        # Get the inner product x' * w for data point x.\n",
    "        inner = w0 * x[n, 0] + w1 * x[n, 1]\n",
    "        \n",
    "        # Now look at the plot with a weight vector in our \"data space\".\n",
    "        loss += np.log(1 + np.exp(- y[n] * inner))\n",
    "    \n",
    "    return loss\n",
    "    \n",
    "lim = 5\n",
    "ind = np.linspace(-lim, lim, 50)\n",
    "w0, w1 = np.meshgrid(ind, ind)\n",
    "\n",
    "# You will change the value of alpha (below), to see how the loss function\n",
    "# changes. It has to be alpha >= 0. No negative values (otherwise the loss\n",
    "# function's minimum is at negative infinity)!\n",
    "alpha = 0.1\n",
    "loss = compute_loss(w0, w1, x, y, alpha)\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.contourf(w0, w1, np.exp(-loss), 20, cmap=plt.cm.jet)\n",
    "cbar = plt.colorbar()\n",
    "# We plot exp(-1oss) here, to let the colours show clearly in the plot. This is\n",
    "# incidentally also proportional to the joint distribution\n",
    "# p(y, w | x) = p(y | x, w) p(w), which you'll encounter on Wednesday in the\n",
    "# Indaba, and can safely ignore for now.\n",
    "plt.title('A plot of exp(-loss), as a function of weight vector [w0, w1]; '\n",
    "                    + 'alpha = ' + str(alpha))\n",
    "plt.xlabel('w0')\n",
    "plt.ylabel('w1')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ViYDcDH1cbx3"
   },
   "source": [
    "# Trying different loss functions\n",
    "\n",
    "* As a first exercise, look at the function that computes the loss. There is a for-loop, essentially a sum.\n",
    "    * Can you write down the loss function on a piece of paper? As a mathematical expression...\n",
    "    \n",
    "* On a piece of paper, can you draw\n",
    "                log(1 + exp(- y[n] * inner))\n",
    "    as a function of the inner product, the value of $y$, etc.\n",
    "    * When is it almost zero, and the contribution to the loss is neglible?\n",
    "    * Where does it become almost linear?\n",
    "        \n",
    "        After you've done your drawings, explain to yourself why the function is equivalent to\n",
    "                inner = y[n] * (w0 * x[n, 0] + w1 * x[n, 1])     \n",
    "                loss += np.log(1 + np.exp(- inner))\n",
    "        What is the effect of the class label $y$ on the weight vector. What happens if we multiply a weight vector with -1?\n",
    "\n",
    "* Now change the setting of alpha. Make it bigger, and smaller. What happens to the minimum?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hwxeymnrToNF"
   },
   "source": [
    "# Working with More Complex Data\n",
    "\n",
    "Real-world data is unfortunately not as simple as our toy bimodal Gaussian example above. Real data (e.g. pixels from vision, or speech phonemes, or words of a language) can have very complex, high-dimensional distributions. Before we get our hands dirty with that, we'll move one step up and work with another toy dataset, but this time non-linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 51,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "collapsed": true,
    "executionInfo": {
     "elapsed": 377,
     "status": "ok",
     "timestamp": 1504364165949,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "T0eBZ4aq2IH2",
    "outputId": "e72c0bb3-fc30-4434-9260-5a72ac7968ea"
   },
   "outputs": [],
   "source": [
    "import numpy as np    # Numpy is an efficient linear algebra library.\n",
    "import matplotlib.pyplot as plt    # Matplotlib is used to generate plots of data.\n",
    "\n",
    "def reset_matplotlib():\n",
    "    %matplotlib inline\n",
    "    plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots\n",
    "    plt.rcParams['image.interpolation'] = 'nearest'\n",
    "    plt.rcParams['image.cmap'] = 'gray'\n",
    "\n",
    "reset_matplotlib()\n",
    "# for auto-reloading external modules\n",
    "# (if you're curious, see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython)\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nlzlDave2e8K"
   },
   "source": [
    "Let's generate a dataset with three spirals arranged in a swiss-roll type structure, and where each spiral forms a \"class\" that we want to be able to classify (i.e. the classes are very non-linearly distributed).\n",
    "\n",
    "## Hyperparameters\n",
    "\n",
    "First we define some hyperparameters that will be used by the next few cells. Try changing these values to see how the models work with different data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "O3WJV8EI-4xp"
   },
   "outputs": [],
   "source": [
    "num_classes = 3    # The number of classes (distinct groups) of data (these are our \"y\" values)\n",
    "dimensions = 2    # The number of dimensions of our input or \"X\" values\n",
    "points_per_class = 100    # number of X points to generate for each of the y values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 499,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 712,
     "status": "ok",
     "timestamp": 1504366756191,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "gGuvwWo72eFH",
    "outputId": "f8b67840-35c4-4d17-c1d1-f120e0a34f49"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qhQnkh/bieMcwfy9+TO6+cTjP9xuIuYWvabctev6jmCFeLyagK6V3wfFBYof4\nNSaIO4Isskm9ZARtB+lY8XYUnWbfaq1Ptfv/J5VSv1dKDerOe9u97y7gLoCqqqp4M1mzTt2J5rj7\nLEtx4ljT6WHI935oPnOrRvHy89tpbQ5RdfYYzjxnjCS5FWlUSvyJ5cWYYCaM8/ChjbnRDSP7b94K\nE3zmQgAqem4UJkirwXyuK+ldnr7dmLQ50b+VVswinvk4TzE4RPz5dIfp+0rRugTHr0eCttRLRtC2\nCpislBqPCbhuAG5q/wKl1DCgRmutlVJnYUL+E5jfesL35rqy8gLssPMk5lDIZkB5x3QGU2YMYcqM\nzhnihUiXIsw8ms6r56JDYGAWKsQTxvQo9CRth43JO+Xu4fuE6E+FmF6x3grgPMwaxswpm+vwnkR5\n5xLt6654f1+K7CoXlzv6HLRprUNKqc8Dz2AGuP+std6olPp0ZP+dwHuAzyilQpgr+A1aaw04vrev\nbcomhYUeFi4ex8rlewi2S2Dr8bhYsGg0xSXyhyEy3UxMD0F0KKUIE7BFi2x7iN8b19MSOwcwk9ij\n7y2NnF/+TkS2O4l52HFacVwf5z2DiC3LReQ4yVjYMYq2mrjtKWBEEo4vekqZ2Cm7VFVV6erq6nQ3\nI2kC/hB//PUK1lUfwO1xEQqGmT1vJJ/+6mLHdBtCZK5ozdDO3iL2xqMwN5bulp46iin23fkGUoiZ\nFJ3tQ6wiv9VikvQ6BW0u4HyH7TawGtPzHP27sDA9ZFUkZ6HAIUzt1ejfl8akSJERn55QSq3WWida\nttwtEhFkAK/PzRe+eQG1J5o5eqSBIUNLqBjU99WZB/bWsXL5XsIhm/kLRzNx6qCOKUR6qK62mVee\n38HxmkYmTRvMovPHS1CZd6K5p+owk5xH0DH3U7zP10w6pgbRmDlvU3tw7j04z68JYAJCWSgjslk5\nzn8/CjPv04mFme+2H7MwAMzih9Ekb2XnCEyAVkdbOhSZR50u0tOWox56YB1PPryRcMhGa43H6+LM\ns8fyyS+e06vAbdP6w/z6xy8Rtm1CQRtfgZuiIg+3/ecVDKxIZ81HkTpBzFO9HxM8RVf/TaN7q+Q0\nJj1BC2YItayH538F516IaN4qGa4R2a4eWI/5W7ExwVERZj6bPCBns2T1tGV7gpyctH3LUe78r+X8\n/Lbneebfm2lp6VlNvr27annq4Y0EA2FsW6O1SSFS/cY+1qzc3/UBOgmHbX77i1fw+0OnC8f7W0Oc\nrG/lvj+hQS84AAAgAElEQVS+2ePjiWy1G9NTFu3tit5YttC9Sc8Kk8JgGD0P2CB+mSOVYJ8Q2aQc\nU6d3MiaP4SxMVQYJ2IQhn4QM8/i/NvDoP9afLgq/ffNRnnlsM9//5RWUlnVvpdzyF3cSDDoXeX/p\nue0sWNSzPHc7thwjHIrtkbVtzdpVB7BtjWXJfKLcV4PzggKFmY/T33NcxmPm/HTOAl+ICQa7K5qE\ndB+m17AEmNDDYwjRX9xIr7GIR3raMkhdbTOP/G19h6LwgUCY+roWHvn7+m4fJ+A3yXed+Ft7vgw8\nHLaJN6KqtSbuyUSOSfR77s1nQGOCvcN0r5B1JWYo1oO5dKnItrn0bBHCHkwJoCZMD2E9Zr5dbQ+O\nIYQQqSdBWwZZt/oglsNvJByyWbVib7ePs2DRaHwFsZ2oXp+LReeN63G7Jk0d7FjEHgXTZg7FcsnH\nKD/ESyFg0/NFAC3A65ies22YrO5v0XWB9aHAuZii3osxWd89PThvkI7JS6NszAo5IYTIXHK3zSBm\niNG5x6AniwdmzR3BlOmDO6zs9HpdDBlW2qs6pV6fmw9/aiFen+t0j5vbbVFY6OGDnzqrx8cT2Woi\nbb1cUVZke0/KNWlgHWZoMowJmGzMIoUd3Xh/NLFnb2Z3NBC/V6592gQhhMg8Mqctg8ytGsV9d8ZO\n7Hd7LM6+cHy3j2NZii//x8WseHEXLz+/g3DIZtH547noHZPx9jJFx7kXTWDE6AE889hmjtY0MGXG\nEC67ajoVlTIBPH/4MPnQDmKGEn2YMjY9LULdiHPNUhuTtmAK/ZdzLVGi3+iQqxBCZCZJ+ZFhXnh6\nGw/8uZpQyMa2Nb4CNxWVRdz688spKpbi0yIXJEoiCnAB/TcIoIGVxJbWiubCmtZP5xVC5DNJrpuj\nLl46hSnTB/PSczs4Vd/KnAUjOOvccXi9ksxQ5IpEReaL6N9ZGwqYQ9v8uWg7SmirlSqESC2NWZC0\nD5MsO7qiu6e9+LlPgrYMNGrsQD7wiTPT3Qwh+okHU9PwALFF5ien4PxFwNmYHr9oyo8yZGhUiHTZ\nRcfrwUnMvNfZtNUwFiBBmxAiLSZg8qtFn6yLI9tSVYoqWQW1hRB9E8SU4erc+25jFibJYrf2JGgT\nQqSBwiQQlSSiQuS3U5iHKKc5rk2Y4E0SXURJ0CZETmnGDDXUY+oWjsQMRfbXRS9aQL4eKACGY1aV\nCiFEdyRaYCcrujuToE2InNECVNP2xBrE1Autx0y+T7YApoB8gLan4b2YeomV/XA+IUTuKcHMc+3c\n02ZhHgIlaGtP+hyFyBm7ib3w2UAd3SsT1VM7MBP5o5OHo0lyNyJJaoUQ3aOAMzA9bi5MWGJhFgf1\nPBl8rpOeNiFyRl2c7dHl9MUk9zntGPFTd9Qjq76EEF3zA4doC9oGAEMwqYFEZxK05bCmRj+vPLeD\n7VuPMXxkGRe9YwqDhpSku1mi37gxQ5WdacxFsQaYQfKGLhMl5paeNiFEV5oxUyza50xswKwsl6DN\niQRtWcjvD1H9+j5qjzcxbmIlM88YHqlb2qbm8Cl+8I2nCPjDBAJhXG6LZx/fwhe/dSGz5sqKvdw0\nCjNk6RQwaSCEqURwFuai2FcDMbnOnM4lSTGFEF3ZjrkutWdHtg/F9LyJ9iRoyzJ7d9Xys1ufIxSy\nCQbCeL0uBg0t4ds/fgfFJW2rcO75/Rs0NQaIVikLh2zCIfjDfy3njnveg+WS6Yy5ZwQmKeUx4vd0\naUzt0GRk/59M7FNytIC8XFqEEIlonB/6wMxzq0cWNMWSO3cWsW3Nr378Ik2NAfytIWxb09oa4vDB\nU9z/p1WnXxcMhtm68ShOZWVDwTC7d55IYatF6ijM8GcVJuu/E01s3c3eKsL02o3GDGUMBuZievyE\nEKIriVaGyqpRJxK0ZZHdO47T0hQ7Zykcsln56h5s20RpTsFaG9XFfpH9ijFDC05/3hZmoq8TP2ZY\n4g1MD1oNieetgcnJNhETKM5KcGwhhGhPYR704gVnMsXCiQRtWaS1JYSynD/g4bCNjkRjXq+LSdMG\nO/4tuFyK8ZOkyzn3jcD5z9uFyX3UmR9YhRk6bcFkKd8MrMSkEmntn2YKIfLYZNpWjUJbuo9ZSHji\nTH4qWWTC5EpCIee5SmMnVOBqN0/to59ZRFGRB4/HbLNcCq/Pxc1fOrfD60Su8gIL6Pi0OjCyzePw\n+t2YZLzte9aiQ6l7MMGbDKsLIZLJCywEpmAeJscCi5B0QfHJbOEsUljk5d03ncHDD6wj4DdJVJUC\nj9fFB2/uWFR3xOgB/Ox3V7Ps6W3s2HKMYSPLWHLFNIaNLEtH00VaFAHzaFuUkChY7yogiybNXdzF\ncYQQoidcwLDIl+iKBG1Z5oprZjJi5AAef2gDtceamTB1EFdfP5vR4wbGvLasvJBrbzgjDa0UmaU7\nQVZ3l9bXISu6hBAiPSRoy0JzzxzF3DNlhZ5IphGYIdKukuLKKhYhhEgXGecQQmDSdAwg8SVBkuYK\nIUQ6SU+bEAITrJ2BSc57FFOrVNMxae4k5JIhhBDpI1dgIUSEwvSklWNWcR3AZCUvoK0nTgghRLpI\n0CaEcBBNmiuEECJTyJw2IYQQQogsIEGbEEIIIUQWkOFRIYQQQuSwRkwCcQtT77Qgvc3pAwnahMhb\njcA+oAEoxCw+kMUGQohcoYGtQA1tK+F3YVbCj0xXo/pEgjYh8lI9sI62ZLrNmGoH04Ch6WqUEEIk\n0TFMwNY+abgGdmDqmxamo1F9InPahMhLW4itfmAD2xy2CyFENjqI8/VMA0dS3JbkkKBNiLwTBFrj\n7NNAUwrbIoQQ/SUUZ7tOsC+zyfCoEHlHJdinkWc5IUTmCGLmoR2N/HswMB6TS7IrgzFTPzr3trmA\nymQ1MKUkaBMi77gxVQ/qHPb5gKLUNkcIkceOAruBFsyqznHAsMi+MFAN+GlbSHAEsxJ0IV2HMCOB\nQ0CAjiX5yoCBSWl9qskjtRB5aSrmabM9BcwgcU+cEEIky0FgM6Y3TGMCt63A/sj+GjoGXNA2tHmo\nG8f3AGcCozGLDoqBCcAcsvU6Jz1tQuSlYzhP0D2MeQoVQoj+ZGOGPZ0WRO3G9JLVOuyPvqYWGNON\n83gwJflyoyyf9LQJkXc0sJeOT6/R7Ucwc0iEEKI/+Um8Ur2FxPPWvMltTpaQoE2IvBOk64ulEEL0\nJzexD45RNqaHbATOYYoFjOqndmU2CdqEyEmtkS+ni2JXF8vsnOshhMgmHswKzs7XG4VZKOXFzEGb\ngglVXJEvCzPUmZ/TOJIyp00ptRT4b8xP9G6t9U877X8/8E3Mb6MB+IzWel1k357ItjAQ0lpXJaNN\nQuSnBmATbXnYfJjFBe0vcFZke7xcbbVAaX81UAghIqYB6zEl9RTmYbIImNnuNcOBQZjrksYEep7U\nNjOD9DloU0q5gN8BS4ADwCql1GNa603tXrYbuEBrXaeUuhy4C7NeN+oirfXxvrZFiPzmB97CPP9E\ntQBrgbPoWCS588rR9gLJb5oQQsTwAAswD5tNmICtlNjeNw9SXs9IxvDoWcAOrfUurXUA+BtwdfsX\naK1f01pHk0K9Qb4ORgvRrw7hPOxpY5bWt1eB8zCoCzM0IYQQqVKKyc1WhkzPSCwZQdtI2pKqgOlt\nG5ng9R8Hnmr3bw08r5RarZS6OQntESLHaEwqjtXAKmAPziVYGolfZ6+x07bROOdpKyRbM4ULIUSu\nS2meNqXURZigbXG7zYu11geVUkOA55RSW7TWrzi892bgZoAxY7qTmyUz7Ntdy3OPb6HmSANTpg/h\n0iunUT6wMN3NEhlNA6cwqzxLMckm62gLyJoxqTmq6PgnXILJFN65t01F9rXnwySd3Bl5j4V50h2H\nrE8SQojMlIyg7SDmsT1qFLFjMSil5gB3A5drrU9Et2utD0b+e1Qp9TBmuDUmaNNa34WZC0dVVVW8\npW8ZZeXyPdz9m9cIhWxsW7Nz23GWPbWVW39+OcNHDkh380RGagbW0ZYrzSY2CLMx89cOAmPbbR+B\n6fQOd3q9hXPndwEdJ/wKIYTIZMl4pF4FTFZKjVdKeYEbgMfav0ApNQZ4CPig1npbu+3FSqnS6P8D\nlwEbktCmtAsEwvz5d28QCISxbXPTDQVtWpqD/OXON9PcOpGZNGYhQSsm8AqTODXH0U7bfMBczBCn\nFfkqAM6g4yIEIYQQ2ajPPW1a65BS6vPAM5hJMn/WWm9USn06sv9O4FbMRJnfK6WgLbXHUODhyDY3\n8Fet9dN9bVMm2Ln1mON0Sq1hy8YawmEblyv9w1C7th/n6Uc3cfRII5OmDWbpu6YzaEjnoTSRGrXE\n9pIl4rQCtAyzMDuazqMAmdgrhBC5ISlz2rTWTwJPdtp2Z7v//wTwCYf37cJ0A+Qcy1LoOL0kisy4\nja54aRf3/uENgoEwWpv5d68u28F3bl/KmHED0928PNS5MHIi8YY8oW1BgRBCiFyS/q6eHDVp2mDH\nnjTLgjnzR2CluZctEAhz350rCfhNwAYQDmtaW0Lcd+fKtLYtf3WV0DYa6luYjush/dscIYQQGUWC\ntn7icll89mvn4fW5cLvNj9nnc1NaVsCHPrWwi3f3v13bj6Ms5/6+HduOEwr2ZJhOJEcJMIDYP0sL\nU9VgHDAGM29tJpnRXyuEECJVUpryI9/MmjuCn/72al5+bjtHjzQwefoQzrlwAoWF6S/B4XZbaB1n\n+FYRN6AT/W02sAuTly2Mqb03GZDhapEZ7FCYug27cRV4GTB1NJE5yUKIFJCgrZ9VDi7m3TfNTXcz\nYkyYVInX66a1pWOSVstSnLFgZEYskshPLkyQNhkzv623N8QmTPW4U5jCy2OBwclooIjj5Lb9nNpx\niPJpoymdMCLdzekXex56lddu/iXhYAjCmsIRlVz0j1upnDsp3U0TIi+oeL0tmayqqkpXV1enuxlZ\nb+vGGn75wxewbU0wEMZX4KaoyMOtv7iCisqidDdP9NopTOqQ9tURLMzQ6ljMKtUgZqVpccpbl2sC\nJxtZds2tHHtzC5bXje0PMvzieVz0j1txF/VvqpXG/UfZ/qcnadh1mCHnzmLi+y/FU9I/i1COr9nG\nk+d/iXCzv8N274Birt/zV7wDZNW5EPEopVZHsmb07TgStOW3U/UtLH9xF0drGpg4eTALF4/F65MO\n2Oy2GhO4daYwPXmatlWqlZj5cl31rJ7C1DYNAoMwiyASFZ3PH8+/6zscfHY1diB4epurwMu46y/g\n/L/c0m/nPfhsNS+8+zbscBjbH8RdXICnrJh3vvk7ikcmv1f1pRt/yO4HXwa74z3DXVRA1c9vZvpn\nr47zTiFEsoI2GQPLc2XlhVxx7Uw+8ulFnHfJRAnYsl60BFa8fSHMXDk78nUC2NfFMfdgeu4OA8eB\nbZjA0Kn+aX5pOVrHwec6BmwA4dYAex58mWBjS7+c1w6GeOmGHxJqbsX2m3OHmlppPVrHG5+/o1/O\neXLL/piADSDU3Mqp7Qf65ZxCiI4kaBMiqzUBxzDlr8D0pvXkz9rGoepcO63AXjoOtdpAC6ZkVn5r\nOVKLy+u8sEhZCn9tvAC6b46+thFt2zHbddhm/xNvOO7rq8r5k1Hu2N5Vd0kBFWdMTPr5hBCxpFsl\nA9XXtfDc41vYsrGGykHFvONd05g4RSaRi/aCwNtAAyZQ05g5arMxhd8P0/1EvYl6zI7HOY6NKVo/\nvpvnyE2lE0dgh53T41geN0XDK/vlvHYoQUqefpryMvsbN7D77y8RanduZVl4igsZ/94L++WcQoiO\npKctw9QcPsW3Pv8YTz+2iR1bjvHmij389LvP8eIz27p+s8gjmzHDoDZtw50nga3AREzOt2iviIvE\n88+6Suor4vEUFzLra+/FXeTrsN1dVMDc730Yy9M/z8VDzpmJdhiqRCmGXTQXZSX/0j5g6mgue/qn\nDJg2BsvrwfK6GXLebK58/bf9vuBCCGFIT1uGuf/ualqaA6cflrWGgD/MX/9UzaLzx2dEjjeRbgHM\nCtDON22NGSqdCiwA6jGBnQ+T7mMbpsh851WlidI1VAI7Hc6lMKWDxbzbPoxvYCnrb/8rrUfrKRpR\nydzbPsTUT17Vb+d0+TwMvWAOB59oV73EsvCUFnL2Hf+v3847dPFs3r3pHlqP1WN53bJiVIgUk6At\nw2xYe8hxdMPlsti6oYa5Z45KfaNEhgligi2nITIV2e/GJORtn5R3GqYH7gBtKT8mRP4bTyEmTUj7\neW0WphD9mF5/B7lEKcXML17HzC9ehx0OY7m6t6o21Bpgy+8fZfs9T6PDNhNuvJiZX7oOT2nX6XbW\n/uA+jry4tlNDYOh5sxkwdXRvvo0eKRhc3u/nEELEkqAtw1iWRTjOHBmXW0azBZiAKR4L07PmRAGj\nMXPeFN3/8x+HCf7ap/wYiqT8iNXdgM0OhXn6kq9Su3Yn4RaT92z97X9l1wMv8K7qPyQcbrRDYTb+\n6l8x+dII2xx+fg3NR2opGlbR6+9BCJG5JApIE601O7cd55Xnd7D57SPYkfkpVWePweVyyIKvYNos\nGY4SYIKlMTjXKB3nsD2qHlgJrACWA29iFjNswyxoSGQAMB2YA4xAAra+2ffoCure3nU6YAOTJqRx\nXw3b730m4XsDJxsJd0oxEmX5PDTuPpzUtgohMof0tKVBc1OAX3x/GQf31Z+uVFQ+sJBbfnQZN31s\nAdu3HKXhlB9/awi3x8KyFJ/5ynl4PHKjFFFjAQ8mh1oA07s2Hhge5/VNwDo6zmdrinyBWW06Hhny\nTI39/36dUGNrzPZws5+9D72aMFGtt7wEV4H3dH629uzWAKUT01NCyw6Hqd+4B8vtYsD0sVKTVIh+\nIEFbGtzz+zfYt6uWUKjtBnrsaCN3/Oxlbvv55dz+26t5c8Uetm6ooXJICedfMpGKQVJuSLSngJGY\nYcojmJ4yPyaA8zq8fh+JU4DYmFqlQ0g8/CqSwTOgGCwLHPKpecsTT+63XC5mf/MG1v/ofkLNbYGf\nq9DH2HcvpnDIwATv7h8HnlrJqx/5OaEWP2hNwaABXPj3Wxl81rSUt0WIXCZBW4r5/SHWrNzfIWAD\nsMOa/XvqOFbTyOChJSy+aCKLL0qcsFJrzdEjjQAMGVYiT7Z5pwVTmSCa8kNhgrMzMMOZ7TXQdd42\njcnLJotd+lvxmKGgYwM2d3EBUz95ZZfvn/PNG7EDITb85z9Aa3TYZuIHLmXRbz7fp3bVLH+bHfc9\nS9gfZNx15zPqyoVdztOr37SHF67/foc5do1NrTyz5Otct/2+tASRQvSMBuowScqLMHN4M/N+KkFb\nirW2BON+Flwui8YGP4OHdr2MfvuWo/zxVys4WWfK5AwYWMinv7yYSdMkCW/+2IJZGBClMQHcBuAc\nOn7QCmkbCk0k+Zn0RUdHXlnPW7fe45BFRTHl41cw4jJTnrClphaUcgx6lFLMu/VDzPnmDTQfrqVg\n8AA8xb0vFB/2B3jlIz9j/2OvEW4NgtbsfXg5Q86ewZInbsdyqIQQtfHX/3Ieqg2F2H7vM8z5xg29\nbpcQ/S+AKdPn5/R8JbzAPOIv6kofWYiQYmUDCigpcf4gaFszYnTnHpJYJ4418YvvLeNYTSOBQJhA\nIMyxmkZ+/r3nqT3enRuzyH5hTDLdePs6fw7G0vWfu8KsDBX96a3b7u2wACHKVehl9FWLOLFmOw/P\n/jj/GHcT/xh7I4/Ou5na9Tsdj+XyeSkdN6xPAdv2vzzD/YOuYc/fXyLcEjhdUSHU2MLR1zay8/7n\nE76/ftNedDg22A+3BDi5pau6tkKk2yZMD1t0xCKMGcXYmM5GxSVBW4oppbjp41V4vR2fXL0+F9fc\nOAdfNwq2v/D0VsIhh4tk2OaFp6VyQn7oaqiz8+ejDJOnzY3zyk8LMyzadY4w0Tf1m/Y6btdhm5oV\nG3j64q9Qv3EPtj+I7Q9Su24nT17wZVqO1nV5bK11j+qOHnllPa9/7r8JN8UGkWCK0G+/5+mExxhU\nNRXlUPnBXVRA5fzJ3W6LEKkXxKyqd3IK0/uWWSRoS4OFi8fxhVsuYNzECgoK3AwfVcbHP382V1wz\ns1vv37+3PmZOHEAoaLN/T9cXdpEL3EC8xSkKk0S3s6HAucBcTMWESZi5G4MxqTyk6Hd/CjW3suLm\nX9J63LmH1OV1U7dhD2F/bC1Y2x9k291Pxj128+ETvHD99/iL7x3c672Mpy75KvWbnYPD9tb/7IHY\nfG+dOPWitTfjS9fh8nWq1GIpXIVeJn1wSZdtECJ9QsSfu2aRuC5zesictjSZM38kc+aP7NV7x06o\nYOO6w4SCHS+mbo/F2ImSVDN/TMPMxbBp63mzItvjPY9ZtFVAKMMk2xXJorXmyEtr2fGXZwm1+Bn/\n3gsZdeUi9j70Kiu/+Fv8dQ2OBd2Vy8I7sJTgySZshxxs4dYAJ9ZsdzxnqMXP44s+R/PhWnSkmPuR\nl9bx+Dlf4NoNf6J4ZPx5rg07Dib8flxFPiZ+4NKErykdN4yly/6TFZ/8pRkO1TDozKksvucbUuZK\nZDANnCD+PF6FmQucWSRoy0IXL53Cs//eHBu0uS0ufseUNLVKpF4pcBawH9OVX4QJwpJ5o2zGlL1q\nwPTsjSZ+D5944wt3sOMvzxBqMqk49j/xBpbXg+0PmPliTpSiYt4kLn7we2y64yGOvLwOO9jxCd/y\neRg4a5zj23f//UX8dQ2nAzYAtCbU3MrL7/8JLYdrCQeCjLvuPObcchMFg9rmzVbOn0LDzsOOQ6qW\nz0PFnAlM/sg7uvy+B585jWvW/g+tJ05iuV0SrIkssAez2t5JtCZz5g1GZl6LRJcGVhRxyw8vY+To\nAXg8Fm6PxcgxA/jWjy6jvELmJOWXAmAyMBOz0mkP5kLknDG/Z+qBVcBBTFB4GKjGFKsXnR17cwvb\n7336dMAGJllusL4xfsAGWF4373rzD5SMHcr0z12D5Y19lrY8bqbe7FyA/uhrGx0T9epgmJrlb3Nq\n+wGa9taw+beP8NiCT+Gvbzz9mjnfvglXQaehTQWuAi/n/OFLXP7Sr3D5nPL+OSuoHCABm8gCIcx1\n0qmXTWGup/ESlaeX9LRlqfGTKvnJHe+irrYZBRKs5bU6YD2muz/a5b8PM2+tt937GpNSpPNFzQY2\nE5tSROx+8KWEwVk8RcMrT/9/6fjhLHnidl754E/w1zagtaZw6EAuuP87FI1wXtlbMn44VoEXu9Xh\n3HbbUKwdCNF67CRbfv8oZ3z7/QBUzJ7Akid/ymuf/TUN281Q6YjLFnDuXV/t0K6u1G/Zx75HVwAw\n9prFKSlaL0TvNRP/+qVom0KSeSRoy3IDJVjLcxqzNL19cGVHvrZgcg31RoD4K6dCmCXx+fvZCzW3\nUrtuJ76KsrYAxe5qRW8sd1EBc751Y4dtw86fw7l3f43qb91N4+7DFA6vINjQHPcYkz/yDtb/5P5u\nZdgLtwbY98iK00Fb9Hzv3vBn/PWNuLzuhMXqnVR/+242/fe/sCPDs2t/cB8zv3I9C374sR4dR4jU\n8RJ/Bb4mk2sry/CoEFmtgfgTaU9icg71hiJxWpH87WXb8F8P8sDQ63j28lt4dMGneOSMT9Cw6xDj\nrr8gdqgxAcvrZsaXrmPKJzpWQNj5wDKWXXsrtWu2E6hr5Nhrm1h27a1x86UVDa/kkkd+iLeiFE9Z\nEZ6yIpTHhXI5X969FaWO233lJT0O2I68up7Nv3mYcEsAHQyjg2HCLQE2/eqf1KzY4Pgebdts/PU/\n+dvI67nXexkPz/k4+59c2aPzJrLnoVf517QPc69nCX8beT0bf/MQ2mHxh8hnBZg5wZ2vYxZmlb0E\nbUKIftFfNyMv8RccFJCJq6pSYc9Dr/LWrfcQamoleKqZcLOfuo17ePLCL1O5YAqlk7pYEa5MKoxR\nVyzkhiP/ZMGPPtah/JwdDrPyi7+NScMRbvaz8ku/ww47B+EjLpnPjYf/yaWP/oiLHryNd1Xf6Tg3\nzl1ckLAYfU9t/9NTpt5oJ6GWANv+5JyiZOVX/sDq//gzLZHVrvUb9vDi9d9n7yPL+9yenX99nlc+\neDunth1Ah21aDtey5tt/ovqbd/X52CLXzMJc4yxMkGZhyv9l9mI+CdqEyGpOT4vt9/XliXEGZgZF\n9DIRvbjN6MMxs4/WmsDJRuxgiOpv3kWoc14zWxM82cShZ6sTFkj3VZYx+WOXs+SJ27n03z/GVx7b\n49W4pybuvLhwa4CGXYfjHt/yuBl2wRmMXFJFxewJLPz153AVeHEV+rB8HlyFPiZ/dCmj33l2977x\nbgicbHRMYYLWBE7GVmdpPX6SbXc9HhuUtvhZ9bU7e92OYGMLy2/+Ja984PaYahOh5lY2//aRDgsw\nhDAPpmcC8zFpkqowOSwzt5cNZE6bEFnOAqbTcV6bhQnk4gcQ3VMMLAKOAI2Rfw8Huj8EmO12PrCM\n6q//kdZjJ8FSjjU2AcLBMI17jjDmneew6/7nTf3OTjRw7h+/jLLiPyt7y4pOzw3rzA6F8Q7ofrqV\nqZ+8itFXnc3eh14l7A8y+spFSV8gMPba8zj0/JoOK2bB5HfzDijm+Wu+S+HQgUz91FUMmj+F2rU7\nsHwewg6LJhr2HCHsD/RotSqYoPrZpd/kWPXWuK+xfB7qN+5h6LmzenRskQ9KI1/ZQYK2LFB7vImH\nH1jHW6sO4PW6uGDJZC6/dmZMKSyRrwZhnhIPYlZFlQEjSU6xYw/5moB39z9fZsXH/9MxwIihNQNn\nT2DIuTMhTlAW9gc4/OJaRlwyP+5hCgaXM+TsGdQs39Ah75pyWQxeNMOxeHwiRcMrmf65a3r0np4Y\n/74L2fjrf3Jy6/7TPYRWgQcdCrP7Hy8RbvajLIud9z/PmT+7mWEXzkUHnYNSd6EPy9vzB4Jjb2yi\ndt1OdCB+9no7EKRwmCQeF9lPhkczXH1dC7d+5QmWv7iLhlN+Thxv5t//2sDPb3sOuxer1USuKsbM\nxQzxqg8AACAASURBVJgLTMA5YGvGpALZC2wHVgJvYHK7ZV65lnTa++gKXrrhR90L2ADvgGKGnjcb\nyxV/AQA2NO6OP7wZdcH936Fk7FDcpYVYPg/u0kJKxg7lwvu/3ZNvISVcPi9XLv8Nc2/7MOUzxlI+\ncxyD5ps5QdEhUG3bhJv9rPr6HykcUk7p5JExPyNXoZcpn7yyw/y+7tr995cS/p6U20XF3EmUTRzR\n42MLkWmkpy3DPf3YJlqagx0CtGAgzL7ddWxaf5hZc+VCJLpjJ6ayQTSXW3t7gaOYvG7Se3t89TZe\nfv+PoZuF15XL4oxv33Q64CifMZbjK7fEvk5B+cxxXR6vaHgl795yL4eeW82pbQcomzKKEUsWYLky\n83fjLipgzjduYM43bgDggWHXYTv0eim3i/1PrmTJv3/MM5d9naYDx1GWwg6EGLGkiqrbP9Hjc1d/\n6262/PHf8eujKkX5zHFc8tD3e3xsITKRBG0Zbn31Qcfi8P7WEJvfPiJBm+iGOkzAFi8IsTF5146S\nqVnAU2n9Tx/oUZJcb3kJkz92xel/z//BR1l27a0dJttbXjcDpo9h8KLuLeKwXC5GLT0Llp7V/YZn\nA60pHjWYazfew7GVm2naf4yKuRMZMHlUjw9Vv2Ufm37zr7jzDC2vhzO++8EOAbUQ2U6GRzNcSZnz\nvCSPx6K0rGc5lUS+OkT8gC3KBo5F/j+MKVm1GdgFxJZIyjV2yJR8OvLyOuo37XFeERmhLAt3cQGu\nAi8DZ43nild+jaekLQXKyCVVnP+XWygaOQjL58HyeRhz9bm849lf5EXwMP69FzqmG9GhMKOvXASA\nUoohi2Yw/voLehWwAex7dAXa4YHWnADmfOtGCdhEzpGetgx32VXT2bOjFr+/43CDUoqF541LT6NE\nlunufDU3phJCNaZ2qY1ZhbofU4uvfRklDTRF9heRzcl2Dz5Xzcs3/uj0qs1Qs9+MZcYL3LwuLvjr\nf1AxZwIlY4c6vmTcdecz9t3n0XqsHk9JYY+T1mazed/7MPufWEnr0TpCTa0oy8Iq8FD1009SMLg8\naedJFIyVTRnNvNs+nLRzCdGmAXNNbAXKgVGY9CGpIUFbhluwaDQXLJnEi89uRwHKUmhbc/OXzpUS\nVqKbBmGKvyfqbbOAEZgFCgHa5r1F58BtAs7FzHk7gemFsyP7vJigLnPr9cXTuP8oL1x7G6HmHvQm\nBsPsf+INxnSR70wp1ePVnrnAV1HGNev/h53/+zwHnlpJ4bCK0yk/Ejm5bT+rv/MnDi97C3dJIVM/\ndRWzv/4+XO1WlNau28nG//4XjbuPUD5zrFnQ0Gl01FXoZfJHl/bHtyby3mFgG23X0lOYVfsLSFVZ\nP5WN5T2qqqp0dXV1upuRUsdqGnj7rcN4fS7mnTma4pLURfYi24UxvWetOAduFiatxwTg5TivcWEC\ns4LIsTq/xoXJ6ZZdn8s1t93D2z/7O3ag053fUijL6pB2o71hF83l8mW/TEEL08MOhVGRn0Ei/roG\n9j68nFBjCyMunU/5jHG9Ol/DrkM8Ov9TBBtbTtdwdRX6GLp4Fpc9/TOUUux8YBkrPvlL7NYg2rax\nCkz9SIUiHAiCrXEXFzBg6miueOXXedW7KVIhDCzH+fpYAZyR8N1KqdVa66q+tkJ62rLE4KGlXLw0\nexIAikziwjwJ7gdqMEOZlbRVOxhE21NioiLKezBpQ5wuWhqThHdMshqdEg07DsUGbAC2pmDEQFoO\nnYgpBG/5PAw5JzeTtB6v3sobX7iDY29uwfK4GPee81n0my/gq4jtRd37yHJefv9PzArQsI1SivHv\nu5DFd3+ty2Cvs7U/+F+ToLfdzzrc4ufoaxs5tnIzFWdM5LVP/arD4g67NQBKMejMqVTMmYC/vpGx\n1yxm3HvO79A7J0Ry1BN/Gkgd5hrY/9NEJGgTIi+4gfGRLzAXmHrMxeY4pkiyD/PEeMLh/TZmKCAe\nGzPHLbsMOXcW+x57LSajv+V103KkLiZgA3AVeJn+ueTV78wUJ7fu56mLvnL6Z2EHQux58BVOrNnB\nNevvxnK3pRxpPVbPy+//SUzJqB33PsOO+55l8MLpLPyvzzJ44fRunfvQC285pu0IB4LULN9AqLEF\nZTncELXmxOptXPXaHT0OFIXoma4CstTM65VPeY4JBcOsWbmfF57exp6dTjdfIWxgLfA2JkfbLkyS\n3RpgMibA680FqLt5xMKYXrs3Il+7SVdy30kfXIKnpLBjslelTADhNDSqFJc+8gOKcjC7/vrb/xqT\npNYOhmg6eIwDT67ssH33gy/HP5CtOfb6Jp6+5KuceGt7t87tq3SeD+nyeiioLIufsBjz+GF3M6ee\nEL2XaBHNoAT7kkuCthyyb08dX/z4v/jjr5fz1z9X8+NvP8PPb3uOQMB5Xo7IV/sxvWbRz4XGBHJb\nMAHbQmAsMAAYSPcvE4cix27ATNbdiBkybX9DtYHVmGCxJfK1F1jTrj2p4ykt4qqVv2Pk0jNNYKAU\nvsrSuMlaPSWFNB+pS3ErU+Po6xsdv+9QQwvHV2/rsC1Q1+g8rNz+fS0B1tx6T7fOPfNL1+Eudp6D\nNva68xhy7qz4PWm2zf3l7+KN/3cHoW5WsBCi5yzMvN5obefoNh/mYTd1rRA5wLY1v/zBMhpP+Wlt\nCREMhAn4w2zbdIyHH1j7/9k7z/A4yqsN3zPb1YslWbYl9947xh3b2AZMBwMBEkICCSQfhJpAAoTe\nS4DQO6FX44pt3I17t2VLcpVlWdXqW2fm+zFqq91Vsbr03tfFhTQ75SxoZ5857znPaenwBK2KQL5t\nEvpSqRl9GXUU0Ju6Z9009MkL29E7qrKAQ+iNC+WZtCx0oaZWO67c3Lf5CUmMY9yLt2GODEW2mXHm\n1LQMDJaIkGaKrHkJTvRvX2IMthLcLcZrW+fpIzBYa2k60TSy/UyG8EefG8+n9/UzMVjNGIOsGENt\nmEJtzPjxccxhwRjMJqZ+9iDGIKuvB5ymj8xKfncxq64Skw8ETUk0+kNtInpJSd+y3xtjznPdEKKt\nnZCclIXD7vvk63YrrP65bksUgo5CTZMRqme7Qqhf6Wv1MVkqevPC8bLfswNcv6q5b/Oz6upHceYW\noJY6a95Rlog/b2TzBNXMDL1vPoYg3y8fyWCg5/xpXttiJwwibvIwv/tXxRZXN8sTSZI4942/cdm+\n9xj/yu1Mfu9ersn4hi5V/lt3mzOOyw68z9D7rsEUEexzDsXhIuOXHRQcSqvTNQWCs8OK3mk/CN0m\nqXnHywnR1k4oLnISKCPisIth4IKqRAfYLqE3IlTfNgT9xlR+u6jvTUpDH1R/oJZjy8Whp2z/7cBu\n9Oxf01kTHf12LWd2H67TJaZ8+gCyqX32b3WdNYYxT/0Rg82CKSwIY6gNW+dIZi9/FnOYt0iSJImZ\nPz7GqEdvIrR3F92MuBrGICtD751frxhCe3Wh380X0OPKqX4tO0IS4xj16E0oJf7FtWw0krf7cL2u\nKRC0Jdrn3acD0qd/DJ4AnlI9+wT6khZ0THqiCyEPlUpFBjrj3yAyDJhA5dJmKJCH3rhQHzGVReX0\nhOrHlZv7utGXU11UZuTy0Wei9gOcZf/YgIbbOihOFxtuehaCLEgTB4Gioq7bh+Su9lmSJGLGDSCx\nbAxTVVRVA01DrqFYvq0w6K+X0fd3s8nadABTiI2Y8QMD1pLJJiND7rqKIXddRe6uVJZf+A88xQ6Q\nQHW66f/nefS+YVaTxGmNjaA0Pcdnu6ZpBCfE+DlCIGgfNIpokyRpDvAK+mP0u5qmPV3tdans9QvQ\n10p+p2najrocK6gbEZE2zpvTj9U/p+ByVn7hmC0Grru5wX5+gnaFBRiHns3KRRc/3YCavuxMQNcq\nv0cBBejiSkEXYuVirCavNzu6OKwq+CR0c98I9Jo4J75LrKfKrlda5Trx6DUlZ99qf2r5dlwXjmOT\n2hNJBlUB94Uj0RQNg8dNl+OH6HvyILbwIKZ9+S+vY3OzS/j4rc3s2XEKDRg4JI7f3jqezl3b3mSI\nqphCg+g6q373jOgRfbj6xBdkrd+H80wRsRMGYYtrug7bIffOZ/sD73r5tkkGmeBunYg5Z1CTXVcg\naGkaPBFBkiQDeqvYLOAksBW4VtO0A1X2uQD4K7poGw+8omna+Loc64+OOBGhLmiaxtoVqSz54QCF\nBQ569onmyutHikyboIlQ0bNn+ejNC1HoYiyDwMJNRhdakVTWsJWb+2rAr+iirS5UneQA+sSHVCp9\n5mKAPtQ0pWHdq1/w8To3rgBNhxIaMRFmHnxhHhHRlUuE9lIX9932I0UFjooRpZIEtiAzT79+MeER\nNv8nFDQKmqax9b63OPj6j8gWE6rbQ3i/bsxc8IRP04RA0BpoTRMRxgGpmqYdAZAk6QvgEvQClnIu\nAT7WdIW4SZKkCEmS4oEedThWUEckSWLqrL5MndV87ceCjkz5kmoosA/d7gP0pLlK4A5VW9k/Vacn\nFKJbhNRVsFF2/pPoy70eKgfdl1MuKMehmwinl+0Xg541LCRJMeL2BLau0JDIyndz5x++IzI6iMSe\nkcy6cACn0wtx2N1eM+U1DdwuDyuXHOLya0fU430I6oskSYx77k8M/8d15O0+jK1zFBEDu7d0WAJB\nk9MYoq0rlXdr0O+i4+uwT9c6HguAJEm3ALcAJCa2rVE5AkHbxIGetSofe+WvU9CD7rFWtdlFxXu5\ntComfE0qXehmv2fj01be8Zru53gNXcTtQfeOKxeRJei3HTfZWQpaHXxZNQ3yckrJyyllz/Z0rDaz\nVxlCOW63SvKBLJSysU6yPxd/QaNhiQojfnrjdPN6Sh0c/XI1+UnHiRjUnZ5XTxPzSwWtjjbTiKBp\n2tvA26Avj7ZwOAJBO+cYlTYdACnonm3dqu2XReBZpEHowk+q8vtQfGvQTnP23aFG9MzemQBxqOi1\ncNW36fv2H2ThSIqLGpJtvmdUobQksIlr+ol8br7yf8iyxMhxCdx46zixXNrKKUhOY9GkO1AcLjzF\ndozBVrbd/w4XbvgPxiALx79fj+ry0O2C8YT3T2jpcAUdmMYQbenohSXldCvbVpd9THU4ViAQNCsF\n6IKtugg6jJ4lq2ouG2iAfDkT0TNbJnTR5iz73UalhUhJLecIhIxeYSFxtuaWMy8MYeWSYhSPRgPL\neysoLNCXeBVFY8eWNI6m5vLMfy/BZGpePydB3Vl93RM4cwsp/yPwlDjwlDpZOuteHJln9NFmqsr2\nf75H/1suYtyLtyH5sTkRCJqaxuhR3wr0lSSppyRJZuAaYEG1fRYAN0o65wAFmqZl1PFYQQBUVSM7\ns5jiwvrUAQkEtZFO4KzVqWrbggl8GwlFfy4ML/v3TvRZo9uB9VRWRoTWcI5AGNEbEMo7WrsFOEfN\nX6wRkQYefjaWwcMtTTLvWVU0SoqcbNt4ovFPLmgUSk/lkL//GD6qXdMoOZ6J4nCh2J2oTjeK3UXy\nu4s5uWhTi8QqEDQ406ZpmkeSpL8Ay9DXKd7XNG2/JEl/Knv9TWAxeudoKvqj+U01HdvQmDoCm9cf\n49N3tuJwuFEVjX6DYrn1b5OIiBTLMIKGUtNaYfVlwVj0DFx1kSdT2WigodesleK9DHoEvbOzM/rQ\n+OrnMKDPQD1ZFpOELtK6oWfWqqqsoLJzOaqdoxveZbO+dO5q4t5HYlAUDUmSyc0ZzOP3r6Go0IGi\nNDz95nB4SD2UzYSpPRt8LkHj47G7kA1ynXO9nhIHSW8sIOGiCU0al0Dgj0apadM0bTG6MKu67c0q\nP2vA7XU9VlAzB/Zk8O6rG70KoQ/uy+TJB5bx9OuXiOJnQQOJRu+69CfEOlXbZgBGA0noHaASunga\nQOUyaiG6mKougFT02rm4KucoKnvNVnaOcHTxp5Rdy9/fdjb6sHt/kz8y/b5DfxgMwcBwYmKtPPnq\nPL7/Yg+/rjlCSYkLCb2W7WwwmmRi4trnvNL2QGjPzpjCQ/DUNsKsCq4zRbXvJBA0AW2mEUFQyfdf\n7PHpXFNVjYIzdvbvzmDoyC4tFJmgfdAZPTtV1eRWQp+5F+tnfxv6cHk3uhAz4y2u7DVcqzwzFoQu\n3Mq/OKvWqEkEvlWdxH+mr5zADQM65UuqIcDwiusEh1i4/g9juf4PY/F4VHZuSeP7L3dz+mQRiqJf\ny2w2oChqrdk4j1vliw+3s3blYa69abT4fNYRTVVxF9sxhdgCTmU4WxzZ+TjzigjtFY9sMjLxnbtZ\ndfW/URwuUDWQJWSjAUmW9W1VMFjNJF48sVHjETQXGnrTkh29tCOcutdFONFXC2zo98KWQYi2NkhG\neqHf7R5FJeNkgfhSEDQQIzAGvRkhE/2mFoe+VFnTl2egsVLlxrn+KF/Oz0f32S4pu14s+tiqmm5R\nCvoSa00pMH+2I+XbO6Gb/Iagj+ryf/M2GmXGntudMRMS2b09nVVLkykpcTHmnEQ6xYbw1kvrcblq\ntivRNL2r9D9Preb//jFNfEZrQNM0kl79nl2PfYK7sASDzcLgO69g+L9uQDY0rJnDkZ3P6uueIHP9\nXmSTEdkgM+bZW+j/x4u4cP1/2PvM55zZd4zIIT0Ycs98Nt/xGrk7U1Hs+sOEbDZhjY1gwJ/nNcZb\nFTQrDvS6Wjf6PaHcM3IENY/EU9FXAXKovJ9EAINpCQklRFsbJC4+lKKC6rU7+pdLXHzbHqEjaC2Y\n0KcJ9GmEc4WiP9UW4y2gZHRj3CL0wfDl4ktDtxIpQRePgZ6ES+pw7fJjqws3Cf291f2JWZIkRozp\nxogx3rYntqDpfPXxTk6eOIPHXfMaqsul8OWH24Voq4H9L33Dzoc+xFOq3+NUdyn7nv8KV0EJ41/y\nW2VTJzRNY8mMuyk4lIbmVlCdeu3m5r/9F2unCLpfNolpn3uPKpu94nkO/Oc7Ut5bgupy0+OqqQy9\n/xrM4WK5u+2xD9+a1xL00oqhNRyXgi7Yqn62z6ALuZqOaxra/oTjDsil84dhtng/ccqyREiohaEj\n41soKoEgEBL60mNU2c8y+vNiX/TpBP6yZeVzSvNrOK+Jmv3dJHRLkGFl+xrK/jGXbWucJY7Bw+P5\n9wsX8PCzc7Haan8OPplW3TdOUI7qUdj92CcVgq0cT6mTQ28txFVQfNbnztqwj+JjmWhu76yoUupk\n5yMf+T3GaDUz7L5ruOLQR1x19DPGPnsr1ujws45B0FLY8f+Qp6EbiAfKlCvoPpL+7k951F5+0fiI\nTFsbZOjILvz2lnF89sF2PB4VVVHp3jua2++ZjGyoXYfv2naSBV/tJTurmITukVx27TD6DvBXqyQQ\nNBYmdKHkQV+esFD5zBjoi1hFz8JFBnjdhr706u94GeiPXp8Hul9c+X4hNIW/R5eECOQ61F6FhASe\nhdrRcWTno7j8dy8rDhcb//wyE9+5G1Nw/bvkC5JP+tp6lFF0NKPe5xO0JTzU/Jkvb3Tyd1wgJPQ6\nt+b9PAvR1kaZNKMP50ztRVZGEbZgE5FRQXU6bsWig3z58Y6KRob9+RmkHMziL/dNZfjorrUcLRA0\nFCO+tx0L/p9YZWrPhg1Br1PxUFmnYgVG4l2nIqEv0zYdRqPM9X8cy4dvbPI74gpAliGxZxSF+XbC\nxJQEH8yRodT05Xr8+/UUH8/kwvX/qbe5bU2TDMJ6i+Xq9k1N348mAte0mdDvQ4GmvjT/Z1iItjaM\n0SjTJaHuqXqX08NXn+z0+UJxORU+fmsLz791qXD5FrQA3YED1M1ipDo2YAL6UkV5R1gETeKUWwcm\nTutFRISV159fR0mxrxBVVUhOyuLeP/3AfY/OpFNsCCsXH+LQgSyio4PQgN070vG4VQYPi2f+70bR\nuUvHqVM1Ws30vWk2KR8sqyj+r4rqdHNm7xEy1+2l85Rh9Tp37LmDCe3dhfyk495LpAaZxEsmoqlq\no3epCloLBvT62eqlGDJ6mUag+4WMfn+q7iMpo3tGikYEQROSdjwfOYAoy88rpaTIRUjY2Y0DEgjO\nnhj02rNjVN48y5dT6/IlWj7QvnVwJs9eY0OC26XgBl59ag1Ol4Lb5cHtZ/+dW9NI2neaJ16ZR3RM\ncBNG3LoY9+JtuPJLOPLZSr+vKw432ZuT6i3aJElizornWXvDU6Sv2A5l1i0oKvte/JrMdXuYteRp\nDOaaOgkFbZcE9Cz8MfSGhCB0IRdVh+Mk9G56D/o9KQH9ntX8iMeKDkRwsLnCY8of1ZsbBILmozt6\n3dkQ9KXNc9CzZm2PtStScTprqoXRyc+3Yy91+RVsoJdfuZweFn23r7FDbNUYzCamfvoAkcN7+X/d\nasbWubYvWv9YO4Uz4Y07MZi88xWeYjtZm5NIfmfRWZ1X0FaIAcYCk9F9IevydyShi7SJwKSyY3vS\nUtl8Ido6EJ27hhHTOZTqyTaDUWb46K6YLSLxKmhJjOg30Zrrmlo7dR19pWkB6+K9znVgz+lGiKrt\nMfwfv8EY7FvTKBlkul8+6azPe+ybtWh+xlsopU4OCdEmCEi5yXfL3puEaOtg3PGPaYRH2rDajBiN\nMlarkc7xofz+djFHTyBoDM6d1rNRs9bhHXSecI+rpjLojsuRLSZMYUGYQoOwdApn9rJnz6p7tBzV\n5UYLsOKgBuhcFQhaCyK10sGIiw/lhbcvZ/e2kxWWHwOHdhbzSgWCRmLyjD6sW3mY9LT8gF2kAN17\nRpF2PK/GmaYWi5E5Fw9sgihbP5IkMfrxmxn0f5eTtWE/prAgOk8djmxsmCDudsF4dj/5P5Rqs0Zl\ni4me86c36NwCQVMjRFs7IzuziPwzdromRBAU7N8/xmiUGX1OYjNHJhB0DMxmAw8+NZtf1x7l47e2\n4PYz4spkkhk7MZH8/FLsJe6AY7BmzO3HyHGBrSo6ArbYSLpfdvbLodWJHtGH3tfN4Mjnv+Ap0U18\nDTYzQfHRDLrjika7jkDQFAjR1k4ozLfzn2fWcOxwHkajjMejMuuiAVx9w0hh4yEQNDMmk4EpM/rw\n/ee7ycsp9bOHhNVm4pn/XspXH+1g9c8pqKpW7Ryy6OZuIs596y66zR3PwTcX4C4spfsVk+l/y0WY\nw9pm84ug4yBEWzvh+Ud/Ie34GVRFq3iyX7HoIBGRNmbP65jLKwJBSzN+YneWLzqEx+O7BjpiTDds\nNhOSLPkINgC3W2XbphNcePmQ5gi1QyFJEt0vm9SoGTyBoDkQjQjtgONH8jidXoharWvN5VRY9G3H\nsgsQCFoTF105lIgoG2ZzZR2WxWJk7qUDiYnTh44HBZkI5OkaHCwybQKBoBKRaWsHZGcVIxv8L4EW\nFjj8bhcIBE1PSKiFx1+Zx9oVqezYnEZomIUZc/szcKg+E1VVVNLTCvw2I1gsRmbM7dfMEQsEgtaM\nEG3tgITuEX6XXwBiOjftvEWBQFAzNpuJ2fMG+i1TWLogiX27Tvk9btJ5vRgxtltThycQCNoQYnm0\nHRAXH8agYZ0xmb1b4c1mA1ddP6KFohIIBLXx88KDfm1BLBYjI8cliCYigUDghci0tRP+cu8UPnt/\nG+tXHUFTNYJDLcy/cRTjJvao0/G52SV8+fEOdm89iWyQOWdyD668fiTBIf5tQwQCQcMpKfYdig4g\nSVCYL0obBAKBN0K0tRPMFiO/+/M5XP/HcTgdboKCzXV+Si8scPDw3YsoKXZW1NasWZFK0t7TPP7y\nRRhNYiapQNDY7Np2MqCptaJo9O7XqZkjEvgj69f9bLnnTXK3JWMKC6L/rRcx4qEbxWB5QYsgRFs7\nw2iUMYbUr+NsxeKDOOxur2JoxaOSl1vK1l9PMGFKz0aOUiDo2Pz8UxJff7rT79Ko2WxgxNhudO4a\nVrEt5WAWX360g+NH8ggOsTB73gBmzxuIbBAVLk1J9taDLJ11b8X0BGduIftf+pYze44wc8ETLRyd\noCMiPvEC9u3KwO32bWRwOjwk7fUdVq2qGsVFzoDNDwKBIDBOhzugYJNliXlXDuFPd1X6hyUnZfHs\nwytIScrG5VQ4k1vKd5/v5r3XNzVn2B2S7Q+86zPuSrE7ObVyJ2f2HW2hqAQdGZFpExAZFQQSUM3f\n02iUiYzyHsy8cskhvvtsNw67G9kgMX12P66+cRRGo9D/AkFdOHY4D4NBBnxFm6ZpGIwyudklxJZ1\nfn/xwXYfgedyKmxed4zLrhlGp9iQ5gi7Q5Kz9ZDf7ZIkkb05icghYhVC0LyIb1oBsy4a4GX+WY4s\nS0ye0afi91XLkvniw+0VWTaXU2HV0mTef+3X5gxXIGjT2IJMficgAGgafPf5bh746098/8VuQDfP\n9ofBKHE4OafJ4hSAtVO43+2SQcbWOaqZoxEIhGgTAAMGx3H5tcMxmQxYbUasNhNmi4Fb7pxY8RSv\naRrffbbb94nfpbB5wzHyz9hbInSBoM2R0COS8Aibnt32g8et4nYrLP5+P8kHsrAFBS54Dwu3NlGU\nAoDBd1+FMcj3v7HBZqbr7LEtEJGgoyOWRwUAzL10MJPO683+3RkYjQaGjIjHaqv8snA6PBQHsCcw\nmQxknCwgItLm93WBQFCJJEnc+eA0nnrwZ9xuBYfd43c/l0th9c/JzLxwAIu+3YfLVeWBSdJNe/sP\njmumqDsmA26dx5k9R0n9cCmyxQQaGEOsnL/0GWSj6KoXND9CtAkqCA2zcs5k/zUaZosRs9mIw+72\nec3jUekUG9zU4QkE7YauCRG89N4V7NicxoKv93LyeL7vThqkpxVw45/O4eTxM+zalo4sS0gSWK0m\n7v33zICWIYLGQZJlzn3jToY/+BuyNx3AEh1G3JRhyAYh2AQtg6Rp/msrWjNjxozRtm3b1tJhdDi+\n/WwXS3884LVEajTK9BsUy/2PzmrByASCtsuGVUf46K3NOB2+GTeTSSY41MKDT85GVTQOp+QQHmFl\n0NDOFXYfTqeHjJMFhIZZiY4RD0/NibvYDpqGKTSopUMRNDkakAucAjxADBBPXXNfkiRt1zRtmTjA\nFwAAIABJREFUTEOjEJk2QZ25bP4wigudrFt5GKNJxuNR6T8oltvumdLSoQkEzYaiqCz+fj/LFx2i\ntMRFzz7RzP/tKPr0jzmr842b1J0lP+7ndHqhj/WO262Sn2fn1WfW8NhLF3l5t2maxsJv97Hg673I\nsoziUejZpxN/uX+KXjMnqDPuYjuH3lnEsW/WYAqx0f+Wi+h++eSABuUFKSfZcPPzZG0+AEDU8N5M\nevceoob1bs6wBc1KCpABlH9Gi4CTwBig+YyWRaZNUGeKCh188+kutmw4hqJojBjTld/8Yaz4ghB0\nKP77/Dp2bk3zyjibLQb+/tgsevc7O+HmsLtZ9O0+Fnyzz+/rkgxPv3YJnbtUirZ1K1P5+O0tXnHI\nBoku3cJ5/OWLxNzSOuIuKuWncbdRfCILxa7X7RqDrfS4YgqTP7zfZ3/nmSK+7Xcjzrwivd23DFNo\nEJcnfUBQFzHJov1RAmyjUrCVIwHdgdqtXxor0ya6RwV1wulw88g9i1m38jClJW6cDg/bfj3Bw3cv\nxl7qaunwBIJm4fSpQnZsTvPrm/blhzvO+rxWm4mZFw3AaPJ/S9ZUWPz9fq9tC77e6xOHqmhkZxYL\nK5B6kPTaDxQfz6wQbACeEgdHv1lDzjZfn7aUD5biKXV6CTYAxeUm6fUfmzxeQUuQg4+RKZRty2zW\nSIRoE9SJDauPUFjgQFEqnzQURaOkyMnalYdbMDKBoPk4nJyDbPCfwTp6OLdB5w4LtxJSwwi6zeuP\no1b5/OXllvrdT5Ig+3Rxg2LpSBz5chWKw/fBU3G4OLFgo8/2nK0HvQReOarTTdamA00So6ClqSlr\n3bwZbSHa2hjFRU7+995W7rjpG+78/bd8+dGOZsl07duV4XfsjsulsG/nqSa/vkDQGggLtxJo1TEo\n2Nygc0uSxKyLBgR83e1ScDormxXiyiYmVEdVNbok+DeFFfgSaPC7ZJAxWH3/n4b3T9DtP6rvbzQQ\nMTCx0eMTtAZi8S/OZKBLs0YiRFsbwmHXlyhXLkkm/4ydM3ml/LwwiUfvW+rt4dQEREbZ/NoLSLJE\nRJTonBJ0DAYN64zZ4tu/ZTYbOH/ewAaff/KM3hgCjISzBZmwWCvFwpXXj/SZZGI0yvToHU33XsKt\nv670vXkuBj8GurLBQI+rpvps7/fHC/16tBnMRgb99fImiVHQ0liBXnhLJgMQCnRt1kiEaGtDrPvl\nMAX5dpQqg9o9bpXc7BK2rD/WpNeePruf3/miJqPMjLn9mvTaAkFrwWCQuf/fMwmPsGK1mbBajZhM\nBsZMSGTuxQ0XbeERNsZP7O4jxswWA5fMH+b14DRqfAK/+/N4wiKsmMwGjCaZMRMSuetf5zU4jo5E\nv5svIG7SEIwhunCTDDIGm4URD99IeN9uPvsHd41h1qKnsMVHYQyxYQq1YekUzvSvHya8f0Jzhy9o\nNhKA0WX/jgcGASNpbhklukfbEM89soJ9uzL8vjZuYnduv7dprTd++noP336uz0OUJQlJlvjNzWM5\nb44QbYKOhaqoJO3LpDDfQe/+nSqGuzcGHrfC5x9sZ+2KVDQNTGYDl84fyvnzBvrtCFVVjcJ8O7Zg\nMxY/WUBB7WiqyqkVOzixYAOm0CB6Xz+LyME9aj0mb88RNEUlakRvYbgrqBHh09YBCY/Q62mq62xZ\nhrDwwAXMjcGBPRks+GYfkiShKhqaDEZZ9lmGyc4s5qdv9rJ/dwYhYVbmzBvIOVN6CPsBQbtCNsgM\nHh5f5/01TWPLhuOsWpaMw+5hzIREZszthy3It2bKaDJwwy3juOam0ZSWuAgJtWAwBH6al0WJQoOR\nZJmu54+h6/l1/06VZJnoEX2aMCqBwBexPNqGmD6nHyaz79Oc0Whg6vlNl+1SVY23X96Ay6mgKlrF\nNqfTw7uvVnZXZWYU8q+/LWTdysPkZJVwLDWXD/67iU/f2dpksQkEbYF3/rOR9177laS9mRxNzeWH\nL/fw0F2LKCkO3ERkMhkIj7DVKNgEgdE0jewtB0n/eRvO/Pp102qqysE3F/DtgN/yWcxlrLzsIc7s\nP9Y0gQoE9UDcDdoQfQfEcsnVwzCZDJgtBiwWAyaTzNW/HUVij8gmu+7p9EJKS3xnjgJkZRRRkG8H\n4OtPduJweFDVylSg0+lhzfIUsjOFBYGgY3I0NZetG497jalyuxTO5JayfGFSC0bWfjmz7yhf97yO\npTPvYdXVj/Jll6vY9dgndT5+wy0vsuWeNylMPokzt5ATCzay8Jzbydsj7I06LuWebDuB7cAJ9HFW\nzYtYHm1jXHTFEM6d1ovd204iyRIjxnQjIrJpJxLIsoTm11iw8nWA/bsz0FTf/WRZImnvaWLixFKC\noOOxe/tJ3H66u91ulc0bjnPpNcNbIKq2Q/GJTDJ+2YkpNIhuc8dh9NPpWRXF6WLJeXfjzCnw2r73\nmc8JH5BITz8doVUpOnKKI5+t9PZu0zQ8JQ62/f0dzl/89Fm/F0FbRQMOoJvsljcCFqPPIR1Dc0op\nIdraIFHRQUyf3XzF/3FdQgmPsPlmyyTo1j2C0DD9Jmq2GP1m5CRZwmprvtlsAkFrwmQyYjDos3qr\nk59n5/iRPGHR4QdN09jyt/9y6O2FSAYZSZYBjfO+/TddZo4OeFzaT7+iOn3vQ55SJ3ue+bxW0XZ6\n3V6kALYrmev9jxkTtHcK8RZslP3sBNLRR1k1D2J5VFArkiTx57snY7Xp9gag+1IFBZn44x0TK/ab\ndn5fvzV3mgbDxzSvl41A0FoYNzERyY/HIUBpqYvH/7GUXdtONnNUrZ+jX6wi+b3FKA4XnhIH7qJS\n3EV2Vl72UI01aiVp2Sh+RBtAaXrt470sUaFIkv+vRlOYaPjomFQXbOWoQFazRiJEm6BO9O7XiWff\nuJSLrx7KOZN7cPm1w3nuzcvolhhRsc9FVwyhd79OWKxGZJmyujsj//f3qcKKQNBhiYkL5eobRvqf\nK6rpc0vff+1Xr1pQAex/+Rs8JQ7fFzQ49tXqgMdFj+mHbPJjvyFJdBpd+wpF19ljkfyZ59osDPjz\nxbUeL2iPyAQeV9W8Mkp8kwrqTHiEjYuvGhrwdZPJwN8fm0XygSySk7IICbUwbmJ3gmuYpygQdATO\nm9ufkmInP3y51+/rDruHzIxC4ruK8VPlOLIL/G5XnC4cOf5fA4ibNJSIwT3I233Ya5nUYDMz8tHf\n1Xpdg9nErEVPsnzu31FVFc2jABJdZo5i2H3X1PdtCNoFceiNB9UfrJp/jFWDRJskSVHAl0AP4Bhw\ntaZpZ6rtkwB8jP6uNeBtTdNeKXvtEeCPQHbZ7g9omra4ITEJWhZJkug/OI7+g+NaOhSBoFVQkG/n\n0fuWUFToO2S8HFXTMJvFM3RV4meMJPXDZWiK97KUwWomblLgh0dJkpiz/Dm23PMmhz9ZjuJ0EzWi\nN+e88hc6japbLXDsOYOYf+pr0hZuwpGdT9zEIUQN792g9yNoywRRKXPK/x5lIAJd2jQfDZqIIEnS\ns0CepmlPS5L0dyBS07T7q+0TD8RrmrZDkqRQ9F7ZSzVNO1Am2oo1TXu+PtftqBMRBAJB2+PlJ1ex\ne3t6hcehDxJ0S4zgiVfmNW9grZyioxn8OOpW3EWlULZ0bLCZ6TR2AHNXvVgnw25N09BUVUwrEDQS\nJcBpdOEWDUQSeNnUm8aaiNDQxdhLgI/Kfv4IuLT6DpqmZWiatqPs5yIgieaesCoQCATNjKpq7N6e\nzq6tgQWbyWzAajXidin8/opPufP337DspyTa4njBxia0ZzzztvyX7pdNwhQWjC0+iqH3zuf8pc/U\necKKJElCsAkakWCgN9AXiKKugq0xaWimLV/TtIiynyXgTPnvAfbvAawFhmiaVliWabsJKAC2AXdX\nX171h8i0CQSC1kxhvp0nH/yZvNxSL1PdqhiNMsNGd2XvzlNePm5mi4Hp5/fjupsrH8o9HpV9u05R\nmO+gT/8YuiSI2jeBoC3RbLNHJUlaAXT289KDVX/RNE2TJCmgApQkKQT4FrhT07TCss1vAI+h17o9\nBrwA/D7A8bcAtwAkJibWFrZAIBC0GG+9vIGs00UogZZE0UXbiaN5Psa7LqfCyqWHmHfVEELDrJw4\nmsezD6/A7VbQVL3+bdiortx2z2SMAfzEBAJB+6TWT7ymaTM1TRvi558fgcyymrXy2jW/hiWSJJnQ\nBdv/NE37rsq5MzVNUzRNU4F3gHE1xPG2pmljNE0bExMTU793KRAIBM1ESbGTg/syaxRsZouB+b8d\nRW52qd/XTSYDJ46eQVFUnntkJUWFThx2D06nB7dLYe+OdBZ9J4xe64uroJjSjFyx/CxoszT0MW0B\n8Nuyn38L/Fh9h7Jl0/eAJE3TXqz2WnyVXy8DxF1IUGcURV8y2rz+GGfy/H/5CQTNjb3UjWwIXOvS\nvWckd/9rBtNm98Nk9n8LVhSV8EgbB/acxuXyXV51uRRWLD7UaDG3d0pP5bB01r18HncF3/S+nq97\nXsfJJZtbOiyBoN40tMf8aeArSZJuBo4DVwNIktQFeFfTtAuAicANwF5JknaVHVdu7fGsJEkj0JdH\njwG3NjAeQRvFXuri54UH2bLhOCaTgamz+jBlZh8MBv9fakdScnjhsV/wuFVAw+NROW+2XgdU1yJl\ngaApiIoOwmo14XL6zhsFOJVeyLpfUuk3KJaps/qy+ucUryVSWZaIiw+jW2IEaUcDl/jaS/27/gu8\nUT0KiybdQUlaVoV9SMmJLH656t/MXfUiMWMHtHCEAkHdaZBo0zQtF5jhZ/sp4IKyn9cToMVC07Qb\nGnJ9QfvAbnfz8N2Lycspxe3Wv7zS0/LZvimNux86z0eEuZwenntkJaUlLq/ta5an0r13FJOmCz8l\nQcshG2R+84exvPfqRlz+BsW7FLZuOMGgofFcfeMosjOL2b87A4NBQtMgMjqIu/45HYA+Azqh+JlZ\nCtCrT3STvo/2QtrCX3HkFvj4vSl2F7sf+5SZCx5vocgEgvoj3BwFLc7qpcnk5VYKNtCLsZOTsjiw\n5zSDh8d77b9z60lUxfeLzOn0sOT7A0K0CVqccyb3IDTMwvuv/0pOVonP606nh+WLDjJxei/+9uB0\nMtILOHH0DNGdgundv1PFg0pMXCjnTOnJ5vXHvDJ3ZouB+b8LPDRdUEn+geN4SvwYG2saeXuPNH9A\nAkEDEK1HghZny8bjPh10AE6Hh51bfQdpF+Tb8fgRbQCFBX5mFQoELcDg4fFMmdGHQKv1VTPF8V3D\nGT+pB30GxPhkln9/+wSuun4knWKDsdqMDBrWmQeemE3vfp2aMvx2Q2jvLhiD/Y/SC+/XrZmjEQga\nhsi0CVoci9X/n6EsS1htJp/tvfvFYJBlPHgLN0mCvgNEZ7Gg9TBwWGd++mafVxYZwGCUGT6mbh7j\nsixx/ryBnD9vYFOE2O7pfulEttz5uj58Xq3sGjUGWRj+wG9aMDKBoP6ITJugxTlvTn8sFl/hZjDK\nnDulp8/2Xn2j6dWvEyaTt9O52Wzk8uuGN1mcAkF9yTxViMfjm0W2Wo1cePmQFoio42GwmLlg3StE\nDu2FwWbBGGrDHBHCuW/dReep4n4haFuITJugxRl7biI7t6SxbdMJ3C4FWZaRDRJXXDfcr/O7JEnc\n9a/z+OGL3axenoLT7qHPgBiuvWk03bpHtsA7EAh8cdjdfPTmZvxZgvXsG01EpK35g+qghPXpyqU7\n36boaAbuolLC+nQl5cNl/DjqVhSni57zpzP4jssxh4e0dKgCQY00aIxVSyHGWLVPjqTksGvrSUxm\nA+Mm9iAuPrSlQxIIzgpV1Xj7lfX8uuaY39eNRpn3vhFLcy2Bpqosm3M/WRv3o5TqDQoGq5mgrp24\nZMdbmEKDWjhCQXuk2cZYCQTNRa++nejVVxRXC9o+/3tvK1s3ngj4uvASbDlOrdhB9qYDFYINQHG4\nKD2Vw8G3FzL07qtbMDqBoGZETZtAIBA0IsVFTtb8nFJm/OyLJMOocxKaOSpBOWkLf8VT7Ntlrthd\nHP9mbQtEJBDUHZFpEwiqoGkau7els2Z5Kk6nm3GTenDu1F6YzYbaDxYIgIz0AowmA+4Aos1qNSHL\nEgu/3cuk8/qI2rZmxhQahGQ0oPlpEDGGiv8XgtaNEG0CQRXef30Tm9cfw+nQ5z2mHsxh5eJD/Ovp\nOZj9dLgK2gdZp4v46eu9JO3LJCzcypxLBjH23MSzWsaMig4OmGUDUBWNX9ccxWSS+fGrvdz1z/MY\nOLRzQ8IX1IPe189k/8vfoFQTbcZgKwNunddCUQkEdUMsjwoEZRxOzmHTuqMVgg105/rT6YWs/jkF\ngKJCBzlZxahq22vgEfjn1MkCHvrbItavOkJ2ZjGHk3N49z8b+erjHWd1vuiYYPoMiMFg9L69ShIg\n6X9TAG63isup8Ooza1ACmEULGp+Igd0Z9cTNGKxmZLMRySBjCLLQ8+ppdL98ckuHJxDUiEgdCARl\nbN98wu9kBpdLYe3KVLZtSuPwoWxkWcIWbObGW8cx5pzEFoi0fVFS7GL7phOUlrgYOLQz3XtFNev1\nv/xoBw6H28uaw+n0sHzhIc6fN5DIqPp3E/7lvim88tRqjqXmYjDKuF0eFEUDP1pfUTRSDmYzYHBc\nA96FoD4MufNKul8ykWPfrEVxukm4cDzRI/u2dFgCQa0I0SYQlGGQZSRJwp8NTsbJQlRVq8iwuVx2\n3nppPWGPzKTfwNjmDrXdsHtbOq89twYJCUVRkWWJYaO7cvs9k5EN9V8IKCl2kp5WQGRUEDFxdfPc\nStpz2q+XmsEgkbT3NOdO7VXvOEJCLTz45GxOnyokJ6uYzl3DueeW7/zuKwEet+/DgqBpCe0Zz9B7\n57d0GAJBvRCiTSAoY9zE7iz98QCuatk2o0kXD9WXRF1OhR+/3MO9j8xsthjbEyXFLl57bo3XIHSA\nPTvS+WVpMjMvHFDnc6mqxufvb2PVshSMJhmPR6VX32j+7/5phIT5nztZjsliqFiy9ELyP0atPnTu\nEkbnLmEA9B8cx8H9mT7ZNkVV6Vsm/BVFZd0vh1m9LAW3S2HcpO7MunAAQcHmBsUhqBulp/NIfmcR\neXuOED2yD/1unostrnkzvwJBTYiaNkG7IT+vlJ1b0jicnO03W1YbCT0iOX/eQMwWQ8WQb4vVSFR0\nEIrHf83RqbSChoTcodm++YTfQn+XU2HFkkP1Otfi7/ezenkKbreCvdSN26WQejCHF5/4pdZjp8zo\ng8nkeyuUgCEjutQrjpq48dZx2Gymilo3SQKz2cANfxyHxWJE0zReeXI1/3t3G0dTczl5Ip+fvt7H\nw3cvwl7qqvnkggaTs+0Q3/X/Lbuf+ozj365l9+Of8m3/35K7K7WlQxMIKhCZNkGbR1U1Pn1nC2tW\npGIyGVBVjbBwK/c+MoPwCBulpW4iIm3Icu2dgFfdMJJR4xPYsOowToeHMRMScbtV3nttIw67bzam\nc9ewpnhLHQJ7iTtgAb691F2vcy3+fr9Pxk5RVNKOnSE9LZ+uCREBj730mmEkH8gk7Xg+LqcHs9kI\nEtzxwLRGtXrpmhDBk/+Zx7Kfkkg+kEWn2BDmXDKQ3v1iAEjae5qD+zJxVcn6ud0K+Xl2flmaLGaV\nNiGaprHm+idxF5VWbFMcLhSHi7XXP8ll+95vwegEgkqEaBO0eVYsOsi6Xw7jcasVVgs5zmL+ecdC\nvU7KIGOzmbjmptFMnFZ7fVLvfp3o3a9yMoPHo/LZeyacTgWtyhKp2WLgkquHNf4bqoWCfDsrlxwi\n+UAWsZ1DOW9uf04czWPdysOoisbE6T2ZPKMPJlPr9pYbOKwzsp9MmyxLDB1Z9wyXqqiUFPvPRBkM\nMjlZJTWKNovFyD+fnkPS3tOkHMwmLNzKuIk9CA5p/CXJqE7BXHuT/0k2u7al+12mdbkUtm48IURb\nAziz7yiHP12Ou9hO4rxz6TJrNJJcmV0tPp5JSVq232OLjmRQkp5NcNeY5gpXIAiIEG2CNs+SHw/4\nZFk0jYraNEVRcLsUPnxjE8HBZkaM7Vav8xuNMv98eg6vP7+OtKNnkA0SJpOB6/84lgFDmrfjLyO9\ngEfvW4LbpeB2qxzan8XaFakYDHodF8CJY7qAe/DJ2RhbsXBL7BHJiLHd2LXtZMX/P1nW68gunV93\nMSwbZKI7BZObU+Lzmset0C0xsGArR5IkBg2LZ9Cw+Lq/gUbGajNiMEh6l2k1LFZxq64rmqriyM7H\nFBqEMcjKnme/YNe/P0Z1udEUldSPfyZ2wmBmLXwS2VT231VV9fXwgOcUFj+C1oG4EwjaPEWFztp3\nQq+V+uZ/u+ot2gA6xYbw8LNzycstxWF30zk+9Ky6GxvKx29uwV5aaU9R3hzhqVJz53IqpKcVsGn9\nMSZN793sMdaHP981iVU/p7Bi8SFKi530HxzHBZcNplNs4M7PkmInOzafxO1WGDoynpi4UK64fgQf\nvrHJS7ybzAaGj+lKdExwc7yVBjNhSk8Wf38ARfF+ALFYjEyfLewo6sLhz1ey9a43cBWUoGkaXWaO\nImPlThRHZSbWU+wgc8M+kt9fUmGmG9IzHltsJMXHTvucMzghluBugbNsGat2suuxTylMOUnE4B6M\neOhG4s4d3PhvTiBAiDZBOyChRyRHknPqtG9mRmGDrhUVXX/PrsZCUVSS9mf6taeojtPhYfO61i/a\nZIPMjLn96ZoQwXuvbWTH5pNs35RG915R3Pq3icTFe9cMblp3jPde3YgkS2iqxmcanDe3H9feNBrF\no/L1pzspLXYhGySmzOzDNb8b3ULvrP7Edw3nyutH8M2nu1AVDVVVMZkNjBrfjXETe7R0eK2etIW/\nsuGPL3gNgj+5ZKueRauGUuok+d3FFaJNkiSmfPIPfp5zP6rbg+ryIJuNyGYTkz+6P+BkjMP/W8GG\nW1+suGZpeg6Z6/cy7bN/knjxuU3wLgUdHSHaBG2e+TeO4oVHV/pYdfijrWRdQC+OPnY4j9ISFz37\nRGO1GpHw68/qF7O5bXy8T6UV8MJjK72yZEdScnjs/qU8/9ZlFbYbeTklvPvqRh8D5NXLUhgwOI4p\nM/sweUZvSktcWKwmjMa21xw/5+JBjBybwJYNx3C7FEaM7Uavvp1qP1DA9n++7yXYAL+CreIll3ez\nS9zEIVy69z2SXv+BM3uOEDWiDwNvv4SQRP8lEKpHYdP/veZzTaXUycbbXibhonO86uYEgsagbdzV\nBYIaGDAkjjsfnM7nH2wj7Xg+NpsJ2SBRWuzyykqZLYZ61Uq1JOlp+bz02CoKCx3IsoTHo3LJVUMZ\nMrIL+3aeqnWMlsVqZMrMPs0UbcNY/P1+n1md5TWJm9YfY9osfWlw45qjfmuLnE4PPy9MYtT4BCRJ\nIjikZl+21k5cfCjzrhza0mG0OQpT0uu8r8Fqptc15/lsD+3RmXHP/alO5yg4lIbq9uPvB7jOFFGS\nnkNIgjDeFjQuQrQJ2gWDh8fz+Mvz0DQNSZLIP2Pn9efWcjQlF4NRQtPgsmuHc87kni0daq243QpP\nPfgzRUVOr7Tagm/2cu1NYziWmovD4cblVDAaZVRNQ5YlFI+KpoHFYmDcud0ZNrrxPMaakuNH8/yK\nUKfDw4mjZyp+Lyp0etXuVaW4SPiYdXSCu3aiMNVXuElGA7LRUFHXZrBZCE6IYeBfLm3Q9UxhQWge\n/9l9TdEwBVsbdH6BwB9CtAnaFeW1JxGRNh58cjZ5OSUUFTqJ7xbeqJ5bTYHHo5J6KJukvadxuTw+\n66Aup8Lqn1N49o1LWL/qCClJuuXHtPP7UlToZMuGY6gqjJ2QSO/+nQLW4bQ2uiZEkHY83yeLZrEY\n6ZoQXvH74OGdWbUsGafDO7thNMkMbyMCVdB0DP/n9fx62yt4Sh0V2ySjgdA+XRj92O859M4i3EWl\n9Lx6Gv1uvgBTiA3QpyAc/XIV7oIS4meOJnbCoDp9dkISYokc0pPcHSloVZZhJYNM3KQhWKKEh6Og\n8ZHOxjm+pRkzZoy2bdu2lg5DIGg0dm9P580X16GqoHh0Ow9/hIVbefWjq5o5uqblxNE8Hrt/qU9N\nYlCwmRfevqxihJOqajzxj6UcP3qmoq5NNkgEh5h58pV5hEXYAl7D5VLYsuEYe3ecIjzCytTz+9bo\n3SZoe2iaxt5nv2D3458iGWRUl4foUX2Z/vXDBMVHA5C35zA7HvqQ7E0HsMVFEjd5GCkfLAENFJcb\no81C56nDmPHD48jG2h/yio6dZvHkO3AXluKxOzHazFiiw7lw/SsEdRG1iK0fDcgAjgNOwAb0Ahrf\nk0+SpO2apvk3aazPeYRoEwhaluzMIh746091aqQYNqoLdz80oxmial52b0vn3dc24nR40FSN6Nhg\nbr9nCgk9Ir32c7kUlny/nzUrUnG7FEaN78aEqT1xORW6JkT4bTQpKXbx2P1LyMstxenwIMsSRqPM\n9X8cy9RZwkqjvaAqCqWncjGYjZSczMEaE+7VRJCz7RBLpt2Fx+6kphZsQ5CFMU/9gUF/vbxu13V7\nSFu4iYLkNCIGdafb3PF1EnyC1sAxdMFW9SFZBvoBjevZKERbM4s21aOQuW4P7mI7cRNF6lvQeHz1\n8Q6WLkgKON+0HLPFwANPzKZnn+hmiqx5UVWNU2kF7NyaxpYNx3HYPYwc25ULrxhCuJ8sWnGhk5ee\n+IUTR89gMMp43AojxyVw650TvUyF//feVn5ZkuxTD2cyybz83pW1DpQXtH6S31/CtvvfxlPqRFNV\nEuZNYNI7d2MOr/T7WzzlTjLX763T+cIHJHL5gQ+aKlxBq0AB1uMt2MoxAROp0XG5njSWaBP9yHUg\na9MBvuhyFSsvfYi1NzzFl93ms/upz1o6LEE7ISujKLBgk/TB4gndI7j7oRntVrCBPg3hx6/28NPX\n+zhx9AxZp4tYuSSZf96xkPwzdp/9//PMao6m5uFylQ2Jd6vs3HqSLz7c4bXfprXH/DYBls6EAAAg\nAElEQVQwGAwyu7fXveNQ0Do59u1aNv3fqzhzC1HsTlSnm7SffmX5hQ947Ze9OanO5/SUOGrfSdDG\nKSWwKFOA1tncJERbLbiLSvl5zv04cwpwF5XiLixFcbjY88SnnPhpY0uHJ2gH9B0Ui9niu5xiMukW\nJe9+dR2PvzKPAYObd2RWc7Nh9RG2/nrca/6mx6NSUuJi0Xf7vPbNzizmSEquz8B5t0thzYoUL5Gm\nBlhN0KBW6xRB62fHv3z92VSnm7xdqeTuSq3YZgyuW0ZVMhlIuHhCo8YoaI2YCex6qdFa+zSFaKuF\no1+vQVN8n9I9pU72PfdlC0QkaG9MPq83VqsJWfZ+6pNk2L7pBH//ywI+fHMTudm+szXbKoeTc/jv\nC+t49L4lfPXxDrZuPM57r25E85NwVDwqO7ec9Np2Jrc0oHmuomheHaZjJyRi8DNyTFFUho4SXadt\nnaKjvqOnQO/izD9wvOL3vjdfgMFqrvFcssmIJTKU4Q/8plFjFLRGLEAYvtk2Cb0RoXXWJbZOKdmK\nKD2Vi6e6y3YZJel1G50kENREULCZh5+by8dvbWHvzlMAhEVYKSl2kXYsH4C1y1PZvO44j754ITFx\ngedytgXWrkjlk7e34HYraJru06Z4NGqqry2filBOl4RwH0PecoJDzAQFV+5/+bXD2bUtnZIiJy6X\ngiTpc0kvu3Y4EZGBO04FbYPgbjEUHT7ls11TNcL6dq34fdSjN5G7PZmcrYdQPQqy2YhkMDD4zis4\nuXATrsISEi48hyH3zieoc1RzvgVBizEY2E3lUqmGLuT6t2RQNSJEWy3EjO2PMdiKp9i7pkYyyMRN\nHNJCUQnaMikHs1i7PJWSEhejxycyblJ3OsWGcNe/zkNVVE6fKuShuxd7jWtSFA2H3cX3X+zmljsm\ntmD0DcPpcPPJO1u8OmUDia9yjCaZGXP7eW0LCbUw9fy+rF2R4jX+ymwxcNX1I718tsIibDz16jzW\nLE9l9/Z0wiNszLygP30GNH5bv6D5GfGvG9h428teS6SSyUhY3250GlP55Wu0WZiz8gVythwke3MS\nlk7hmMKDUe1OBtx6EbY4IdQ6HmZgDFAE2IFgoHU/FAvRVgtdZo0mrE8X8pNOoDorZ9UZbBaGP3h9\nC0YmaAkURWXJDwdYvugg9lI3fQfEcPWNo+jeq243/O8+38WSHw7gdulZpn27Mli64AD/fHoOFosR\n2SCTtC/Tb3msqsKeNl44f+hAVtlSZe32JuX0GxjLVD8juX5z8xjCI60s/eEAJcUuojoFceVvRjJx\nei+ffW1BZuZcMog5lwxqSPiCVkifG8/HkZ3Pzn9/jCSB6laInTiEaZ896GOSK0kSMeMHArD8ogf0\nMVRlHm2D77iC0U/9oc2YUgsaCwk9u9Y2HCGEaKsFSZaZu/oltt73Nkf+twLF4SJ20hDGv3Q74f0T\nWjo8QTPz3+fXsWd7ekWmaN+uDFKSlvHPp2eT2LNm4Xb6VCGLvz/glUFzOjxkpBeyfOFBLrpCz9xa\nbb71beVYrGf/kXU5PRQVOgmLsGIytUy9htEo133iPRAZZeO+f8/0+0UqyxIXXzmUi68ciqKofuvW\nBB2DIXdfzYDbL6Uw5STWTuEVZrr+cJfYWTb7ftyF3jWiSa//QNTIPvSaP72pwxUIzhoh2uqAOSyY\niW/+jYlv/q2lQ+lQqKqGvdSNzaZnoFqakyfy2b093Ut0AThdHr7+ZGetprc7Nqf57VZ0uxQ2rDpS\nIdpGjevGh29s8tnPbDYwfXY/n+214fGofP7+NtauSC2zEJGYc8kgLp0/LKA4bCr6DYzFXyJDNkhY\nLUYUVUPxqBhNMiaTgXsDCLbqCMEmMFrNRA2tzLJqmkbx8UwkSSI4Mbbi7+jE9+u9xk6V4ylxsO/5\nr4RoE7RqhGgTtDo0TWPZgiQWfL0Xp8OD0WRg9sUDufTqoS0q3lIPZvsVHGiQcjC7bicJkGXSqrxg\nCzJz+71TeP3ZtSCBx61gMhnpOzCGORcPrHfcH725mU1rj3rVkS35YT+yBJdeM7ze5wuEpmmkHsom\nP89Or76d/E4nMJoM3HbvFP7z9GpUVcPjVrFYjYSEWHjouTlknCzk+NE8ojsFM2Jst0bLCBYXOVm3\nIpXDKTl06RbOtPP7EtXJNz5B+yDr1/2svfFpSk/lAhrBCbFM+eQfxIwdQGlGHorTvweX/XRe8wYq\nENQTIdoErY5F3+/nxy/3VBSYezwqS37Yj6PUzXU3N9hQ+qwJDbMEzEwFh9TuATVqXALffb4bpVo5\nl8lsYFK1OqwRY7rx0rtXsHnDMUqLXfQfEkffATH1rrcpLnKycc0Rn2J/l1NhyQ8HuOjKoQGtM+pD\nZkYRzz2ygqICB5Ik4fEojJvYnT/89VwfoT10ZBee+e+lrP8llezMEvoNjGX8pO6YLUYiIoMYOLRz\ng+Opyun0Qh69fwlul4LLpWA0ySz9MYm7Hjqv3XvfdUSKT2SybPb9Xs1jhcknWTbzXi4/+CEx5wzE\nYDHhcXt/ECVZH/QuELRmhGgTtCo8HpWFX+/z6ggEXWT8siyZy64dhi2oZq+ls8Vhd7NqaTKbNxzH\nZDYw7fy+TJjco0J0DBvd1e8ynNliYPa8AbWev3PXMOZeMpClC5L0rJcGFouB2PhQZl3oe3xImIUZ\ncxvWep6dWYzJZPDboamqGkWFDiKjghp0DVXVePbh5eRml3iNdNz66wk6dw3n4quG+hwTFR3ExVcN\na9B168q7r22ktMRVEZvHreJB5Y3n1/HSe1c0+xKxoGk5+N8FqC63z3bF7eHQ2wsZ8dCNRA3vTe72\nFBRHZcbNYDMz4qEbK37XNI3MdXspOJRGeL9uxE0ZJpoUBC2OEG2CVkVhvt3H5b4co1Em63RxnTs1\n64PD7uaRexaTk11SUbN27HAuOzan8Zf7piBJkl5j9chMnv/3CjxlvmKqqjH23O7M9CO6/HHFb0Yy\nZEQX1pRZfoydkMj4yT2arDEgOibYJ6NQjiRJhIQ2fO5m6sFsigudPjO4XU6F5QsP+hVtzYXd7uZI\nco7f+eB2u5u0Y2ea5O9J0HLk7U5FdXl8tqsOF3m7jyBJErOXPcuOf31AygdL8JQ6iZ04hHEv/JmI\ngd0BsGedYemMeyg+nommqkiyTHBiLHN/eQFbbGRzvyWBoAIh2gStipBQS8DmQrdbITKqacxQVy1N\n9hJsoIuOvTtOkXwgi/5ly2g9+0TzygdXsW/XKYoLnfQdGEtcfGi9rtV/cFzF+WrDYXejadpZZxfD\nwq2MGp/Iji1pXu/NbDEw44J+jSIWC/Lt+C/2g5Ji/8bUzUYNhr2SRI2GvoK2SdSIPmSs2u2TbTNY\nzUSN6A2AMcjKuBf+zLgX/uz3HGtveIqC5DS0Kg88hSknWfObJ5mz/LmmC14gqAXRciVoVZgtRiaf\n1xuT2VtMmEwyw0d3JSyiaUTb5g3HfbpCQe8M3VFthJLRKDNiTDcmnde73oKtrpw+VcgTDyzjtuu/\n5PYbvuKRexZz4ujZFUn/4a8TGDMhEZNJxmozYTIbmDKzL1deP7JRYu3ROzrgwPtu3f1nJRRFZf/u\nDLZuPE5+XmmjxOEPW5A5oBWLyWQgsYfImrQ3Btx2CbLZNx8hm4z0v+WiWo935BRweu0eL8EGoLkV\nMtfvxZGd32ixCgT1RWTaBK2O624eg93uZuvG42X1WAqDR3Rp0kkA1UViObIk+R3m3pQUFzl55J5F\n2Esrl3iOpubyxAM/89RrFxMVXb8aNLPFyJ/+NoniP4wlL7eUmNjgRq0LjIkLYcyERLZvOuHVoWo2\nG7jmd6N89j+amsuLj/1Stq+Gx6MyY25/rr1pdJPUDP3+LxN48h/LcHsUPG4V2SBhNMrccufEVmEl\nI2hcQhJimbP8Odbe+DQlaVn6th6dmfLJP+o0nsqVX4xsNHiZqZcjGw0484uxxkQ0etwCQV2Q2uLy\nwJgxY7Rt27a1dBiCJqYg307mqSI6xYXUW6jUlw2rj/DRm5u9Bo2DLuYefeFCuiSEN+n1y8nPK+Xh\nuxeTf8bu85rRKDP7koFcfYOvEGppFEVl4bf7WL7wICXFLrp1j+Dam0YzaFi8134ul8Kdv/+GkmJv\nywWzxchv/zSOSdN7N0l8Z/JKWbn4EEeSc4jvFsasCwfSuWvbcEAXnB2apumiTZIISYit83GqR+Hz\nzlfgyivyec0cGcK1md8hG1vnMHFB60WSpO2apjXY/kBk2gStlvAIG+FNtBxanQmTe7B90wn27czA\n6fIgSxIGo8yl/9/efcdJVd3/H3+dqVtZylKW3qQKogEVFUGxATYsWPKNJtGoSSwxaiQklmj0Z0xM\nTL6JJsSvJUbRKBpRsSAqKCq9KL0IwtLL9joz5/fHDLi7M8uWmd3ZmX0/H4997Mxt87mHO5fPnnPP\nOVcMb7aEDeCPv/0oYsIGwZ61Wzbsb7ZYGsLpdHDRlOFcNOXoPUJXLN4RsaNJRbmP2a+vabKkrV37\ntJg1B0tiMMaQ0bPhQ7o4XE5G/f5Gvrjlf6vNZ+pM8zLy0RuVsElcKWkTARxOB7fcPZb1a/ayfNEO\nPB4nJ5/em249mq8ZJHd7Hrty82tdbwzkdGu+BLIp5B0qqfX5t4L8smaORiSyAT+YQGrHtiy77zkK\nN+eS2a8rx99/LT0vOCXeoUkrF1XSZoxpD7wM9Aa2AlOstYcibLcVKCQ4S7TvcBVhffcXaQ7GGAYN\n7Ry3AVcP7i856mTqLreDs8+v39AiLVW/Adk4HA6geuJmDPQfmB2foEQi6HH+aHqcPzreYYhUE+1T\nuFOBudbaY4C5ofe1OcNaO6JGm25D9hdJaj37tKOy1jHV4JZfjKNr98Suaet7TDZ9B3QI7x3scXHJ\n1SPiFJWISGKINmm7CHgu9Po54OJm3l8kaWS1TeW0M/qF9VZ1uR38+I7TOG5ktzhFFjvGGH5+z3jO\nnjSQtHQPTpeDgUM6Me2hczT8hojUUyWwHpgPzAO+AiI/C5xsouo9aozJs9a2Db02wKHD72ts9zWQ\nT7Dd5x/W2ukN2b8m9R6VZBXwB3jrtdW8N2stRYXldMrJ5Iprjmfk6F7xDk1EpAUIAIuAMqg2FLsL\nOAlommkOo9VsvUeNMR8AkWZw/lXVN9Zaa4ypLQM8zVqba4zpBMwxxqyz1s5vwP4YY24AbgDo2bNn\nXWGLJCSH08GFlw/jwsuHYa3VXIciItXsA8ohbO6cALAdaJoe6C1FnUmbtfas2tYZY/YYY3KstbuM\nMTnA3lqOkRv6vdcY8zpwIsF6zXrtH9p3OjAdgjVtdcUtkuiUsImI1JRHzY5MQQEg+fsxRvtM2yzg\n2tDra4E3am5gjEk3xmQefg2cQ7ABul77i4iIiAR5gNr+oPU2ZyBxEW3S9ghwtjFmI3BW6D3GmK7G\nmNmhbToDnxpjVhJsiH7bWvvu0fYXERERCZdD5KTNAXRv5liaX1TjtFlrDwDjIyzfCUwMvd4CHNeQ\n/UVERETCpQBDgdV8m7xZoA+Q/D3QNSOCiIi0WDYQoGTnAdxt0vC0SY93ONIiZAOnAQcJJmztAHdc\nI2ouStpERKRF2vTvOSy+4+9UFpViAwG6TziR0/7vLrztMuMdmsSdE+gY7yCaXbTPtImIiMTc9rc+\n57Ob/kTZvjz8peUEyivZMXsh753zC6IZX1QkkSlpExGRFmfZPc/gLymvtixQ4SN/3TfsX7QuTlGJ\nxJeSNhERaRYFm3ey9bVP2L9kfZ21ZQWbcmtdl7dmW6xDE0kIeqZNRESalL+8go+v+i257y7G4XFh\n/QEy++RwzruPkNY1O+I+6T07k782QnJmILN/1yaOWKRlUk2biIg0qSVT/0nue4vxl1VQWVCCr7iM\nvLXb+OCie2rd5/j7rsGZVn2wVONykt6zM51PG9bUIYu0SEraRESkyQT8fjY8NRt/aUW15dYfIG/t\nNvLWfRNxvz5TxvGdh6/DlZGKOzMVp9dNx9FDOO+DP2iKN2m1lLSJiEiTCZRX4i+riLjO4XZRuutA\nrfsOvfVSpnzzEj0uOhXjcrL30y95f8Ld7Pp4RVOFK9KiKWkTEZEm40z1ktY98nNr/rIK2g3ve9T9\nP77iAba9Oh9fcRlYOLRyC3MmTWPPZ6ubIlyRFk1Jm4iINBljDKN+f1PY82nONC8Db7yAlA5Zte57\ncOVm9iz4Kqymzl9aztJpTzVJvCItmXqPxlnJzv2sfPgFtr/1Ba70VAb9+AIG3XQhDpcz3qGJiMRE\nn8vG4vS4WTJ1OgUbc0nJzuLYO6cw9PbLjrrf/iXrMREnB4eDKzY1RagiLZqStjgq2XWA/464gYq8\nIqzPDwR7We2cs5Tx/31QD9uKSNLoeeEp9LzwlAbtk9YtG+OM3CCU0rFtLMISSShqHo2jVY/MoDK/\n+EjCBuAvKWfX3OXsW7g2jpGJiMRf17O+gyszFWr8AetKT2HYL66MU1Qi8aOkLY52vP0FgUpf2HJ/\neQW7Plweh4hERFoOh8vJhLmPkdG7c3DojzbpOFM8DLzxfAZcPzHe4Yk0OzWPxpE7Kz3icofHjbtN\n5HUiIq1J1sAeXLbp3+xftI6y/flkjxpIaqd28Q5LJC5U0xZHQ26ejCs9JcIaS58pY5s9HhGRlsgY\nQ8eTBtNj0slK2KRVU9IWR/2vPYeeF52KM82Lw+PCmebFmeplzHNTdWMSERGRatQ8GkfG4WDsv6dx\ncNVmds5Ziisjld6Xnk5Kdu3jFomIiEjrpKStBWg/vB/th/eLdxgiIiLSgql5VERERCQBqKZNRKQV\nO7BiE+uenEXJrgN0P3cU/a89F3dGarzDEpEIlLS1Er7ScjY++x5bXpyL0+tmwHUT6T1lLA6npssS\naa3W/eNNFt3xJIHySqw/wO4Pl/Pl71/mwsVPasYBkRZISVsr4Cst5+3TbiV//Xb8JeUA7Fu4lq9f\n+ZgzZ/7myHRZgUofW2fOZ+ur83FnpHLMD86jy9jj4hm6iDSRsgP5LLr9iWqTsftKyvHvOsDSXz/N\nqf/4eRyjE5FI9ExbK7Dx2feqJWwAvuIyds5Zyq6PVgDBWRhmj72dBT96jG2vfcKm5+cw5/xpLLzj\niYjH9JdXkL9+O+UHC5rlHEQktnLfW4Jxhde020o/W1+dH4eIRKQuStqSjK+sgrw1Wynbl3dk2dcz\nPqyWsB3ZtriMba8Fb87r//k2B1dtxldcFlxpLb7iMtb//S0Ortx8ZB9rLasefYkXO17CrFE/5qVu\nU5h76X1UFBQ37YmJSMzVmNLzCF9ZBZVFpc0bjIjUSUlbkjicTM3odAlvjr6Zl3teyZwLplGeV4Qj\nxR15J4cDp9cDwKZ/vR8xsQtUVLJ15rd/da+f/hYrH3geX1EpvqJSAuWV7Ji9kLmT722S8xKRptH9\nvFEEKv0R19lKHzOP+R5F2/Y0c1QicjRK2pLExqff+TaZKgwmUzvnLOWD86cx4IcTIk6X5Uxx0/e7\n4+s+uP325coHn8dXUlZtdaC8kn1frCV//fZoT0NEmom3fRtO+vNPcaR4wtZZn5+y/fksuPGPMfms\n8kOF5K3ZGnbvEJGGUdKWJFY88K/wZKrCx4EVm2g7uBfdzh0VTNyMCdawpXkZcuslZJ8wAID+15yD\nM80bdlyHx02vS8cAwdq8kp0HIn6+w+Mif0PzJG0Bn59Dq7eqFkAkSgN/dD6n/d+dGHeEZ9v8AXZ9\nuBxflY4KDVVZXMrHVz3IS10v563RN/Nip0tY+uunsYFANGGLtFrqPZokinP3R1zucDkp2LyTM165\nj93zVrLttU9weN30u3o8HY4/5sh2A66fxJYX5nLoq6+Dz7UZgyvNy4DrJtJhRH8gOGlzWrdsSiJ8\nVqDCR9aAHk1zclVseelDPr/5LwQqfFi/n6xBPTnj5Xtp079bk3+2SDLK7JODK9VLZWVJ5A2iSLDm\nffdhdr6/hEB5JYHySgDWPD4Td2Yqw+++qtHHFWmtlLQliYwenSLWPAUq/bQd1ANjDDnjRpAzbkTE\n/V0pHibOf5ytr87n61c+xpWewoAfTqBLje1H3Ps9Ft3+ZLVaPYfXTadThpA1sGmTtt2frOLT6/6A\nv/TbZ+8OrtzM7DG3cfnWF488nyci9dfhhGNq7ZHQ4TsDcKWFP1pRH8U79rHz/SXVhhQB8JWU8eXv\nXmLYXVdgHGrsEWkIfWOSxPG/uTasedPhddPxxEG0HdK7XsdwuF30vepMxr/2AGOfn0bOGccfGcPt\nsAHXT2LE/dfgzkzDlZGCw+umxwWjGf/aA7E6lVqtfOiFagkbAAFLZXEZ2/67oMk/XyQZOT1uTnvq\nTpxp3iNJlMPjwp2Zxql/v73Rxy3cvBOHN3InqMqi0m97qotIvammLUn0v+ZcKgpKWH7PMwR8fgI+\nPz0vGM2pT90Z088xxjDszisYcstkirfvw5udhbdtRkw/ozYFtTwz5yspo2BjbrPEIJKMel96Om36\nd2P146+Sv2EHnU4ewpDbLiGjZ+dGHzOzf9cjTaI1udukRewcJSJHp6QtiQy5eTKDbryA4h378LbP\nxJPVdMmU0+tp9ufI2h7bh6Jte8Haasvd6Sm0HdKrWWMRaYnKDxbgcAdryRqq/XH9GPPM3TGLJb1b\nR7pPOokdby+s1kTqSvNy3LTvqmlUpBH0rUkyDreLzD45TZqwxcuIX38PZ2r159aM04GnXSY9Lxgd\np6hEoldZXMrav/2Xd8bfwdxL7yP3vcXYGn+cHM2ez1bz2tAf8lLXy3kxezLvnnUnRd/Ev3f16f/6\nJX2uOANnigdXegqujFSGTb2aobdfFu/QRBKSaciNoaUYOXKkXbJkSbzDkDjYPnshn//4T5Tty8cG\nLJ1OHcrp/5pKereO8Q5NpFEqCop566SfUrR975EBrl3pKQz40SRO+uNP6tw/f/12Zo28qdozYsbp\nIKVTOy7b9Dyu1PChfJpbZWEJZfvySOuWrQ5D0ioZY5Zaa0dGexw1j0pM2ECA4tz9eNqkxayWr3jH\nPr7+z8f4Ssrpft4oskcOpMfEk+i+dQYlO/fjSkvB2y4zJp8lEi+r//QqRVt346/y/JevuIz1/3iT\ngT+aRNvBR2/6X/XojLAemtYfoLKwhK2vzKP/Nec0SdwN4c5Ma1STrYhUp6RNorZ5xlwW3f4ElYWl\nWL+frmd/hzHP3k1Kh6xGH3P9U2+z8Na/Yq3F+vx8+ciL9LjoFMY+Pw3jcKhmTZLGlhkfVkvYDgv4\n/Hwz67M6k7YDSzZi/eFjqfmKSjmwYlOLSNpEJDb0TJvUmw0EyH1/CSsfeoGNz7xLZWEJO95dxIIf\nPUbZ3jz8peUEKnzsfH8p746/s0HP5FRVtG0PC2/9K/6yCgLllVh/AF9JOdtnfc6WF+fG+KxE4svh\nCp+NAMAYR63rqmozsHvEcdZcaSlkHdM96vhEpOVQTZvUS2VhCbPH3U7Bxlx8JWW4Ur0svP1vpHXP\nDptoPlDpo3DLTvZ8+iVdxgxv8GdtefmjiNPc+IrLWPvELPr9z9mNPo+GsNaCterlJk2q//fPZfl9\nz4WNQWgchl6XjKlz/2F3XRHsoVlzf7eTvlefGdNYRSS+9L+R1MviX0wnb802fEWlELD4isuoLCgh\nf+03Ebe3AUvemm2N+qzKwhIClb5a1zW1yuJSPvvJ4zyfMYln3ecwa9SP2fPZ6ib/XIkvGwhQsHkn\nxbn7mvVzB988mfbH9cWVkQoEOxE4U72MuP9aMvvk1Ll/x1GDGPPs3XjaZQYHvU5PIbNvDhM++mNS\n9iIXac1U0yb1svnfcyIPlGlM2LhpAMbhoE0jm2a6nzuKNY/PDBsx3eF10/vSumseGqI8r4iyPYdI\n79UZV4oHay3vn3s3+5duOHK+B5Zu4L1z7mLi/MfJPmFATD9fWoYd7y5iwfV/oDyvCAKWrMG9GPfi\nr5p8ajY4PIXcn9n+5ud8M2sB7qwMBvzgPNof16/ex+hz+Vh6XXwqB1dtwZXqIWtwr7DZTEQk8WnI\nD6mXZ91nR3zY2Znqxfr9BCq+rRkzTgeZfXO4ZO2zjWpatNYy9+J72DV3Gb5Q06vD6ya1Y1suWjEd\nb/s2jT+RkMriUhZc/we2/XcBDrcLrOXYu64g58zjmTNhavgUO8bQfeKJnP3mw1F/trQsB1du5q1T\nb6nezG8M3g6ZXL7lRdyhGrBEEfD72f7m52x7/VNc6Skcc+25dDxpcLzDEmnVNOSHNKtOpwxlzydf\nhq+wAU546DpWPvh8sKdnhY/sUQMZ99I9jX4WzBjDmTN/w8an32HdP97EV1xG70tPZ+jPL4tJwgbw\n8ZUPsvODZQTKK4/UqH316MscWL6RgM8fvoO17F+8PiafLS3LqkdfChsyA2vxl1bw9csfMeC6ifEJ\nrBH8FZVHaop9RaXgMGz61/sMve1SvvPQdfEOT0SipKRN6uWkP9/M7NN/hr+0/EiNmys9hWF3X8Ww\nO6Yw5JbJFGzYgaddRkyG43C4nAy84XwG3nB+1MeqqXDrbnbNXR7W3OsrKWPX3OUYtxMiNAWn5nSI\neSwSf4e+/BoC4S0OvuIy8tbW/VxmoNJHwcYduLPS4z4Uzcan32Xf4nXf1hoGLP6SclY/PpO+V51J\nu2P7xDU+EYmOkjaplw4j+nPh4idZ8dvn2btgNWndshl21xX0vPAUAJwed8L8h1C4KRen1x1euwL4\nS8txt03HX1S9edSVnsLwX1zZXCFKM2o3rA/5a7aF9Vh2ZaTQdkjvo+678bn3WHT7EwR8fqzPT/sR\n/Rj38r1k9OjUhBEfJZ5n3gnrzQ3gL6/g61fnJcx3VEQii6r3qDGmvTFmjjFmY+h3uwjbDDTGrKjy\nU2CM+Vlo3f3GmNwq6xKnHaIVyhrYg7HPT+PyLS8w6ZM/H0nYEk2bY7pHHMwUwNMug/PmPkZa9464\nMlNxt0nHmeJm6M8vo8+VZzRzpNIcht99JY4Ud/WFxuBM8dLninG17pf7/hI+/1er6XkAABMmSURB\nVOmfqcgrwldUir+sgv2L1zP79J8R8EdoYm8GFXlFkVcELBWHalknIgkj2pq2qcBca+0jxpipofd3\nV93AWrseGAFgjHECucDrVTb5k7X2D1HGIa3EvsXr2PHOIlwpHnpPGUdm7y4NPkZGr850PesEdn6w\nrFptmystheHTvkuH4f2YsvVF9i1cS/mhIjqeNCiq2R2kZWs/vB/jZ/6GT3/0GOUHC8AfoO2xfRj7\n4q9wp9feCWHFg8+H1WpZf4CKgwXkvrOIHuePburQwzg8td/SI3UkEpHEEm3SdhEwLvT6OeBjaiRt\nNYwHNltrGzeAl7RaNhBg3vce5ps3PsNfVoHD5WT5/c8x6vc3MvinFzf4eGNn/JrPbvwTW2fOD/Ye\nJVjjMvS2S4HgkCWdRg+N6TlIy9Xt3FFM2TaDoq27caZ4SKvH84sFG3MjLveX+2pd19QcHnftKzUC\niEjCizZp62yt3RV6vRvoXMf2VwIzaiy7xRhzDbAEuMNaeyjSjsaYG4AbAHr27Nn4iCUhbXnpI7bP\n+vxIzcbhIUYW3/UPup13Im36dW3Q8dzpqYz99zRG/+1WyvblB5tDUzwxj1sShzGmXoPZHtZ2cE92\n7w2/XTm8LrIGx+ce1e2ckeSt3kagonrzvysjlS6nHxeXmEQkdup8ps0Y84Ex5qsIPxdV3c4GB3yr\nddA3Y4wHuBB4pcriJ4G+BJtPdwGP1ba/tXa6tXaktXZkx46aLLy1Wff3WeFjpxFs8tkyo/HzkXqy\nMmjTv5sSNmmwEfddgzPNW22ZcTlJ7dyebufUfzimrTPnM3PQtTzrPpuXu09hzV9fb/S8vUNuuxRX\nRkq14XYcHjfpPTrS6+JTG3VMEWk56kzarLVnWWuPjfDzBrDHGJMDEPq99yiHmgAss9buqXLsPdZa\nv7U2APwTODG605Fk5Ssqjbg8UOmjsjDyOpGmlDNuBGOevZvULu1wpnpxeNzkjBvBxPmP13uMws0v\nfMD8ax+hYMMOrD9Ayc4DLJn6T5b9+ulGxZTWpT0XLn6SnpNPxZnmxZOVzoDrJzBpwf8eeQxARBJX\ntN/iWcC1wCOh328cZdurqNE0aozJqdK8Ohn4Ksp4JEn1umQM+eu2hw3T4UpPocekk+MUVWIp25/P\n0mlP8fUr8yBg6XnxqYz8f9eT1jU73qElrD6XjaX3JWMo3r4Pd2ZqgwZ/ttay+K5/hHVm8JeUs/pP\nrzLs7ivxtElvcEyZfXI485X7G7yfiLR80U4Y/whwtjFmI3BW6D3GmK7GmNmHNzLGpANnA6/V2P9R\nY8yXxphVwBnA7VHGI0lq8M2TSe3SDof32wetXekpdBl3HJ3HDItjZInBV1LGmyf+hE3PvU9lfjGV\nhSVsmfEhs0b+ODjfpjRI6Z6D7Fu8jrID+RiHg4xenRs8W0f5wQLKDxZGXOfwuMhbo/5aIlJdVDVt\n1toDBHuE1ly+E5hY5X0xENYdy1r7vWg+X1oPb9sMLlw2nTV/nsnWV+bhTPUy6Mbz6f/98zQxdj1s\nmfEhZfvyCFR+O0es9fmpyC9mwz/fZthdV8QxusThKynjk+//ju1vfYHD6yZQXknfq8/klCdvb3Dz\nozsjFeOIfO0GKnykdmkfi5BFJIlEW9Mm0my8bTM4/r5rmfzV01y4+EkGXD8Jh8sZ77ASws4Plkbs\nyOEvLSd3zpI4RNR0KgtLKNm5P2yGg1j49Lrfs/2tL/CXVVCZX4y/rIItMz5i0Z1/b/CxnF4P/f7n\nLJw1OsEYl5MO3xnQqDEIRSS5KWkTaQXSumZjIiW4DkN6t+rPtAV8fra9sYAvH32Jb2Z9RsAXn9H9\nG6r8UCFzL7mXFztewqv9v8fL3abw9X8+itnxy/bn881/F4Q9V+kvLWfDU7PxRZgWrS4nPf5Tupwx\nAkeKG2eqB4fXTdvBvThz5v0xilpEkom6E4m0AgNvOJ91f38Tf40EzJniqTY4cdH2vcwecxsVh4rw\nlZbjSvXgaZfJpE//Qnr3ljvUjrWWd8ffSd6arUfG8Cstq+CTH/4eT9vMBg3BUZviHftweN2Rp0Az\nUL4/H1cDy8iVlkLXs05g14fLwYDD5aRwy072fr6GXhdpiA4RqU41bSKtQNbAHpw6/ec4U72426Th\nykzDmeLhxD/cRPbIgUe2m3f1Q5Tk7qeysATr81NZWEpJ7n7mXf3bOEZft72fraZgU+6RhO0wf0k5\ny+5p3PAZNWX26RJ2/MMcTicpndo2+Ji7561k2T3PECivxF9aga+4DF9xGfOufoiib/bUfQARaVVU\n0ybSSvT77ln0uGA0O99fQsAfoNs5I/G2yzyyvmT3QfYvWR82R6X1B9i3eD2lew6S2rllPhyft2Zb\nrc+w5W/YEZPP8GRlMOD6iWx4+p1qw3S40lM49q4rcB5tCqlarP7La2FDfkCwzDc99x4j7rkmqphF\nJLkoaRNpRTxt0ul92diI6yoLS3C4nAQiNP85nE4qi8pIrWuiujjJ7NcV44zccJDRs1PMPufEP/4E\nV5qXtX97A+sP4PC4GPaLKxn+y6sbdbzSnfsjLg9UVFKcG3mdiLReStpEBIDMvjk4U70Re5m60lPI\n6N1CMzYgZ9xxpHZuT1HJrmo1ha40LyPujV1tlcPlZOQjN3D8Az+g4lAh3g5ZUfVgzhn/HQ6s2ByW\nKLsyUskZOyLacEUkyeiZNpEk0Ni5KqtyOJ2M/uutYfNpOtO8nPzXW3E4W+7wKsbhYMJHj5E9aiDO\nFA/uzDRcGamc8PB19L709Jh/ntPjJrVz+6iHnBly62TcGalQba5QF+ndsul16ZhowxSRJGNicbNv\nbiNHjrRLliTX2FLSOpQfKmT3vJW4Ur10OWNEo56Dqmr3/FUs+vkTHFixCXd6KgN+NJETfnsdrhpj\nfzXomPNWsuLB58lfv52sgT0Yce81dDl9eFRxNqeib/ZQfrCQrEE9oyqH5lK0bQ+L757Ojre/wOFy\n0vfqMznht9dVe95QRBKbMWaptTbqbuxK2kSayVeP/Ydl9zyDwxN8KsEYwxmv3k/X8Sc06nj7Fq7l\nnfF3VHuQ3ZniofPpwzn33d/FJGZpPBsIsOm591nz19epyCui+3mjGP7L77booVNEpGnEKmlT86hI\nM9g5dxnL73suOJJ+QQmVBSVU5Bcz9+J7KNuX16hjLpn2VPhk42UV7Pn0Sw6s2BSLsCUKn/7w93xx\n6/9ycPkmir7ezfp/zuaNETdQtH1vvEMTkQSlpE2kGXz1x1fwlYQ/4G/9ATa98EGjjnlg6YZa1+1f\nvL5Rx5TYOLR6K1+/Mq9apw7r81NRUMyKB/4Vx8hEJJEpaRNpBiXb90Vc7i+roKSRQzukdGoXcbnD\n6SSta4dGHVNiY9fcZRE7h1ifnx2zF8YhIhFJBkraRJpBl3HHYdzhI+y4MlLpfMqxjTrmsLum4EpL\nqb7QGFxpXrqdO6pRx5TYcGem4ahl3Dh3RmozRyMiyUJJm0gzOPbOKbhSPWDMkWUOj4v0Hh3pccHo\nRh1zwPWTGHDDJJxed2hqqlTSu3fkvA8fi3ooColOz4tPxQbCa9qcaV4G3nRhHCISkWSg3qMizSRv\n3Tcs+vkT7PpwOQ63i75XncnIR2/E2zYjquOW7jnIvkXr8HbIotPJgzEO/S3WEmx7YwHzrn4IDATK\nK3GmeOgy7jjGv/YAjgi1riKSvDTkh5I2EWnhyvbns/WVeVTkFdHljBF0PGkwpkptq4i0DrFK2vTn\nnog0Wv767Sy771n2zF+FN7sNQ392Gcf84DwlJiEp2VkM+rGaQ0UkNpS0iUijHFq9lbdG3xwcyiRg\nKd19kIW3/pX9Szdwyt9ui3d4IiJJRw+/iEijLJk6PTgOWZUH7n0lZWx65h0Kt+6OY2QiIslJSZuI\nNMrueasgwjOxxuViz/xVcYhIRCS5KWkTkUapbbwxYwyeKHvEiohIOCVtItIoA286H2eqN2y5cRi6\nnRt1JykREalBSZuINMrwqVfTecwwXOkpODxuXBmpuDPTOOuth3F6PfEOT0Qk6aj3qIg0itPj5tx3\nf8e+RevYu+ArUjpm0XPyabjTNU2TiEhTUNImIlHpeOIgOp44KN5hiIgkPTWPioiIiCQAJW0iIiIi\nCUBJm4iIiEgCUNImIiIikgCUtImIiIgkACVtIiIiIglASZuIiIhIAlDSJiIiIpIAlLSJiIiIJAAl\nbSIiIiIJQEmbiIiISAJQ0iYiIiKSAJS0iYiIiCQAJW0iIiIiCUBJm4iIiEgCUNImIiIikgCUtImI\niIgkACVtIiIiIglASZuIiIhIAogqaTPGXG6MWW2MCRhjRh5lu/OMMeuNMZuMMVOrLG9vjJljjNkY\n+t0umnhEREREklW0NW1fAZcA82vbwBjjBP4GTACGAFcZY4aEVk8F5lprjwHmht6LiIiISA1RJW3W\n2rXW2vV1bHYisMlau8VaWwG8BFwUWncR8Fzo9XPAxdHEIyIiIpKsmuOZtm7A9irvd4SWAXS21u4K\nvd4NdG6GeEREREQSjquuDYwxHwBdIqz6lbX2jVgFYq21xhh7lDhuAG4IvS03xnwVq89OItnA/ngH\n0cKoTCJTuUSmcolM5RJOZRKZyiWygbE4SJ1Jm7X2rCg/IxfoUeV999AygD3GmBxr7S5jTA6w9yhx\nTAemAxhjllhra+340FqpXMKpTCJTuUSmcolM5RJOZRKZyiUyY8ySWBynOZpHFwPHGGP6GGM8wJXA\nrNC6WcC1odfXAjGruRMRERFJJtEO+THZGLMDGA28bYx5L7S8qzFmNoC11gfcDLwHrAX+Y61dHTrE\nI8DZxpiNwFmh9yIiIiJSQ53No0djrX0deD3C8p3AxCrvZwOzI2x3ABjfiI+e3oh9WgOVSziVSWQq\nl8hULpGpXMKpTCJTuUQWk3Ix1tb67L+IiIiItBCaxkpEREQkAbTYpE1TZIWrzzkZYwYaY1ZU+Skw\nxvwstO5+Y0xulXUTwz8l8dT339oYs9UY82Xo3Jc0dP9EU8/rpYcx5iNjzJrQ9+22KuuS5nqp7T5R\nZb0xxvwltH6VMeaE+u6byOpRLt8NlceXxpjPjDHHVVkX8fuUDOpRLuOMMflVvhv31nffRFaPcrmr\nSpl8ZYzxG2Pah9Yl5fVijHnaGLPX1DIMWczvLdbaFvkDDCY4rsnHwMhatnECm4G+gAdYCQwJrXsU\nmBp6PRX4XbzPKQZl0qBzCpXPbqBX6P39wJ3xPo94lQuwFciOtlwT5ac+5wXkACeEXmcCG6p8h5Li\nejnafaLKNhOBdwADnAwsrO++ifpTz3I5BWgXej3hcLmE3kf8PiX6Tz3LZRzwVmP2TdSfhp4bcAHw\nYSu4Xk4HTgC+qmV9TO8tLbamzWqKrEgaek7jgc3W2m1NGlX8RftvnYzXCtTjvKy1u6y1y0KvCwn2\n8O5Wc7sEd7T7xGEXAf+yQV8AbU1w7Mj67Juo6jw3a+1n1tpDobdfEBxnM9lF82/eqq+XGq4CZjRL\nZHFkrZ0PHDzKJjG9t7TYpK2eWtsUWQ09pysJ/9LcEqqifTpZmgGpf7lY4ANjzFITnGGjofsnmgad\nlzGmN3A8sLDK4mS4Xo52n6hrm/rsm6gaem7XEawxOKy271Oiq2+5nBL6brxjjBnawH0TUb3PzRiT\nBpwHzKyyOFmvl7rE9N4S1ZAf0TItZIqsluRoZVL1TV3nZIIDGV8I/LLK4ieBBwl+eR4EHgN+GG3M\nzSFG5XKatTbXGNMJmGOMWRf6K6m++7c4MbxeMgjeYH9mrS0ILU7Y60ViyxhzBsGk7bQqi+v8PiWx\nZUBPa21R6FnP/wLHxDmmluQCYIG1tmoNVGu+XmImrkmbbSFTZLUkRysTY0xDzmkCsMxau6fKsY+8\nNsb8E3grFjE3h1iUi7U2N/R7rzHmdYLV0/NJ0GsFYlMuxhg3wYTtBWvta1WOnbDXSw1Hu0/UtY27\nHvsmqvqUC8aY4cBTwAQbHFsTOOr3KdHVWS5V/rDBWjvbGPOEMSa7PvsmsIacW1grTxJfL3WJ6b0l\n0ZtHW9sUWQ05p7DnCUL/cR82GYjY2yUB1Vkuxph0Y0zm4dfAOXx7/sl4rUD9ysUA/westdb+sca6\nZLlejnafOGwWcE2op9fJQH6oabk++yaqOs/NGNMTeA34nrV2Q5XlR/s+Jbr6lEuX0HcHY8yJBP8v\nPVCffRNYvc7NGJMFjKXK/SbJr5e6xPbe0tw9Ler7Q/A/iR1AObAHeC+0vCswu8p2Ewn2eNtMsFn1\n8PIOwFxgI/AB0D7e5xSDMol4ThHKJJ3gDSSrxv7PA18Cq0IXR068z6m5yoVgD52VoZ/VyX6tNKBc\nTiPY/LkKWBH6mZhs10uk+wRwE3BT6LUB/hZa/yVVeqzXdo9Jhp96lMtTwKEq18aS0PJav0/J8FOP\ncrk5dN4rCXbQOEXXy5Ftvg+8VGO/pL1eCFaO7AIqCeYs1zXlvUUzIoiIiIgkgERvHhURERFpFZS0\niYiIiCQAJW0iIiIiCUBJm4iIiEgCUNImIiIikgCUtImIiIgkACVtIiIiIglASZuIiIhIAvj/Y5M2\nRtKm0EoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46a38425d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Setting a random seed allows us to get the exact same data each time we run \n",
    "# the cell.\n",
    "np.random.seed(0)    \n",
    "\n",
    "def generate_spiral_data(num_classes, dimensions, points_per_class):\n",
    "    \"\"\"Generate `num_classes` spirals with `points_per_class` points per spiral.\"\"\"\n",
    "    \n",
    "    X = np.zeros((points_per_class*num_classes, dimensions), dtype='float32')    # Create an empty matrix to hold our X values\n",
    "    y = np.zeros(points_per_class*num_classes, dtype='uint8')    # Create an empty vector to hold our y values\n",
    "\n",
    "    for y_value in xrange(num_classes):     # Generate data for each class\n",
    "        ix = range(points_per_class*y_value, points_per_class*(y_value+1))    # The indices in X and y where we will save this class of data\n",
    "\n",
    "        radius = np.linspace(0.0, 1, points_per_class)    # Generate evenly spaced numbers in the interval 0 to 1\n",
    "        theta = np.linspace(y_value*4, (y_value+1)*4, points_per_class) + np.random.randn(points_per_class) * 0.2    \n",
    "\n",
    "        X[ix] = np.column_stack([radius*np.sin(theta), radius*np.cos(theta)])     # Convert polar coordinates to standard Euclidian coordinates\n",
    "        y[ix] = y_value\n",
    "    \n",
    "    return X, y\n",
    "    \n",
    "    \n",
    "def plot_data(X, y):\n",
    "    \"\"\"Use Matplotlib to plot X, y data on a figure.\"\"\"\n",
    "    fig = plt.figure()\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)\n",
    "    plt.xlim([-1,1])\n",
    "    plt.ylim([-1,1])\n",
    "    return fig\n",
    "\n",
    "X, y = generate_spiral_data(num_classes, dimensions, points_per_class)\n",
    "fig = plot_data(X, y)\n",
    "\n",
    "# fig.savefig('spiral_raw.png')    # Uncomment this line if you want to save your image to a file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "py9FsXFCaNBl"
   },
   "source": [
    "Let's look quickly at some of the raw values to get a better sense of the datastructure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 265,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 256,
     "status": "ok",
     "timestamp": 1503396527717,
     "user": {
      "displayName": "Avishkar Bhoopchand",
      "photoUrl": "//lh5.googleusercontent.com/-OainnMWSi6A/AAAAAAAAAAI/AAAAAAAAAOQ/eI7Z19q5v7E/s50-c-k-no/photo.jpg",
      "userId": "105781587643595215149"
     },
     "user_tz": -60
    },
    "id": "2dYbunVuaRyg",
    "outputId": "e548f57c-d2f5-4dc8-a43c-5e2d8077e775"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X values: \n",
      "[[ 0.07453433  0.08240335]\n",
      " [-0.02794273 -0.01172508]\n",
      " [ 0.02408017  0.07713684]\n",
      " [-0.33180022 -0.48284459]\n",
      " [ 0.08547524 -0.08594394]\n",
      " [-0.19078229  0.45670244]\n",
      " [-0.67819595  0.66452307]\n",
      " [ 0.11460172 -0.79991317]\n",
      " [-0.31485459  0.23675902]\n",
      " [ 0.41948399 -0.45131844]]\n",
      "\n",
      "Y values: \n",
      "[0 1 0 2 2 1 2 0 1 0]\n"
     ]
    }
   ],
   "source": [
    "idx = np.random.choice(range(y.size), size=10, replace=False)\n",
    "print \"X values: \\n\", X[idx,]\n",
    "print\n",
    "print \"Y values: \\n\", y[idx]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4NPYAO6t2yyL"
   },
   "source": [
    "# Implementing a Classifier from Scratch\n",
    "Before experimenting with libraries like TensorFlow, we start by implementing a *simple linear classifier* and then a *more complex nonlinear classifier* from scratch in Numpy. This allows us to be able to go through all the low-level details of how to make predictions and how to train our models, as these details are very important. \n",
    "\n",
    "Later on, we will then reimplement these two classifiers using TensorFlow, and hopefully we will see that this makes things much easier (especially as the models get more complex!).\n",
    "\n",
    "## Implementing a linear classifier\n",
    "How do we define and train a model that learns to separate the num_classes different classes, based on their coordinates in X space? We start by using a **linear classifier**.\n",
    "\n",
    "A classifer is a function that takes an object's characteristics (or features) as inputs and outputs a prediction of the class (or group) that the object belongs to. It may make a single prediction for each input or it may output some score (for example a probability) for each of the possible classes. A classifier is **linear** when the scores are derived through some [linear combination](https://en.wikipedia.org/wiki/Linear_combination) of the input features. An input feature can, for example, be a projection of the raw data onto some basis functions.\n",
    "\n",
    "\n",
    "\n",
    "The linear classifier we will implement computes the scores for a given input X using the formula $z = Wx + b$ where $W$ is a weight matrix of shape $[d, k]$ where $d$ is the dimensionality of the input and $k$ is the number of possible classes and $b$ is a bias vector of length $k$. \n",
    "\n",
    "By normalising the output score vector, using the so-called [**softmax**](https://en.wikipedia.org/wiki/Softmax_function) function, we can derive a probability distribution: \n",
    "\n",
    "$y'(j) = P(y=j\\ |\\ z) = \\frac{e^{z_j}}{\\sum_{i=1}^k e^{z_i}}$\n",
    "\n",
    "Here j refers to the jth possible class and $z_j$ to the jth element of vector $z$. \n",
    "\n",
    "In this probabilistic form, we can also describe the classifier as a linear **discriminitive** classifier. This means that it directly models the probability distribution of the unobserved class conditioned on (\"given\") the input. In contrast, **generative** models, which we will encounter later in the Indaba, model the generative process of the data. \n",
    "\n",
    "Finally, we need to define a loss function, such that minimising the loss function by gradient descent, results in parameters $W$ and $b$ which make good predictions about the class of each input $X$. For this purpose we use the **cross entropy** loss (also called the negative log likelihood loss). The cross entropy loss compares two probability distributions, the true distribution $y$ and the predicted distribution from our classifier, $y'$ using the formula:\n",
    "\n",
    "$H(y, y') = - \\sum_{j=1}^k y(j)log[y'(j)] $\n",
    "\n",
    "Here the \"probability distribution\" $y$ is the so called \"one-hot\" encoding of the true class of the particular example. \n",
    "Earlier in the practical, you experimented with a loss function that looked like this (in code):\n",
    "\n",
    "```\n",
    "inner = y[n] * (w0 * x[n, 0] + w1 * x[n, 1])     \n",
    "loss += np.log(1 + np.exp(- inner))\n",
    "```\n",
    "        \n",
    "Can you figure out how the cross entropy loss we defined here, combined with the softmax function, compares to this when **k=2**? And if we restrict our y values to be in the set {-1, 1}?\n",
    "\n",
    "\n",
    "Let's implement these in Numpy! \n",
    "\n",
    "(Remember that Numpy is a linear algebra library that works most efficiently with vector and matrix operations, try to define all your formulas in vector and matrix form, rather than using loops!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MwDLKxvedst3"
   },
   "source": [
    "### Define the hyperparameters\n",
    "\n",
    "Model hyperparameters include all choices about a model that are made prior to training. In a sense, these are the \"meta parameters\": parameters chosen by the practitioner and are not set by the optimization algorithm. This includes choices of learning rate, number of examples in a batch, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "_E1ELA7ydv5Q"
   },
   "outputs": [],
   "source": [
    "learning_rate = 1e-0    # \"Step-size\": How far along the gradient do we want to \n",
    "                                            # travel when doing gradient descent?\n",
    "reg_lambda = 1e-3    # Regularization strength.\n",
    "\n",
    "# Define the initial random value of W here so we can re-use it later.\n",
    "# There are various initialization schemes that exist, and we will see later    \n",
    "# how these can have a big influence on model training. For now we will just\n",
    "# initialize our weights with random normal(0, 0.01) values.\n",
    "\n",
    "W_init = 0.01 * np.random.randn(dimensions, num_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "Bl3KVZy3euSF"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "V6Y5ebQLj--W"
   },
   "source": [
    "### Defining helper functions\n",
    "Begin by defining some re-usable helper functions. You may want to look ahead to the `LinearModel` class before implementing these to see how they get used. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
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    "colab_type": "code",
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    "id": "vzxWhYPVj-et"
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   "outputs": [],
   "source": [
    "## IMPLEMENT-ME: All 3 below.\n",
    "\n",
    "def softmax(logits):\n",
    "    \"\"\"Convert un-normalised model scores(logits) into a probability distribution.\n",
    "\n",
    "    Args:\n",
    "        logits: The un-normalised scores assigned by the model.\n",
    "    \"\"\"\n",
    "    exp_logits = np.exp(logits)\n",
    "    # Notice this trick for numerical stability.\n",
    "    #exp_logits -= np.max(exp_logits)\n",
    "    probs = exp_logits / np.sum(exp_logits, axis=1, keepdims=True)    \n",
    "    return probs\n",
    "\n",
    "def cross_entropy(predictions, targets):\n",
    "    \"\"\"Calculate the cross entropy loss given some predictions and target (true) values.\n",
    "\n",
    "    Args:\n",
    "        predictions: The model predictions (of shape [num_examples, num_classes])\n",
    "        targets: The correct labels for the data (of shape [num_examples])\n",
    "    \"\"\"\n",
    "    num_examples = predictions.shape[0]\n",
    "    \n",
    "    # NOTE: xent(pred, trgt) = -sum_i p_trgt[i] * log(pred[i]). But since we\n",
    "    # use one-hot encodings for p_trgt[i], it means all p_trgt[i] are zero\n",
    "    # except for the observed class. We therefore only compute the logs of the\n",
    "    # predictions of the observed classes below. To do that, we use advanced\n",
    "    # indexing X[[0, 1, 2, 3, ..., num_examples], target_ids] which extracts the \n",
    "    # predicted log-prob for the correct target class (target_ids) for each example.\n",
    "    # QUESTION: Can you see why this works? Lookup \"advanced indexing\" if unsure.\n",
    "    correct_logprobs = -np.log(predictions[range(num_examples), targets])\n",
    "    \n",
    "    # NOTE: When dealing with a batch of data, we compute the average cross\n",
    "    # entropy over the batch (i.e. we want the average per-example loss).\n",
    "    # QUESTION: Why do we use the average loss?\n",
    "    crossentropy = np.sum(correct_logprobs) / num_examples\n",
    "    return crossentropy\n",
    "\n",
    "def l2_loss(parameters):\n",
    "    \"\"\"Calculate the L2 regularisation of a list of parameters.\"\"\"\n",
    "    reg = 0.0\n",
    "    for param in parameters:\n",
    "        reg += 0.5 * reg_lambda * np.sum(param * param)\n",
    "    return reg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LksU46NvBjlt"
   },
   "source": [
    "### Defining the linear model\n",
    "Now we define the linear model itself. We put this in a class so that we can think of it as a \"black box\" that takes in our inputs and returns some predictions and a loss value that tells us how good our predictions are. We can also update the model using its update method. Doing it this way gives a clean separation between the model definition and training of the model and will be a useful pattern to use going forward.\n",
    "\n",
    "#### Gradient-based optimization\n",
    "Machine learning models assign a scalar cost/loss/error function $E(\\theta)$ (these terms are largely interchangeable) to *how well the model is doing*, as a function of the model parameters $\\theta$. We want to find a setting of the parameters $\\theta$ that gives us the best model possible on our data. For this we use gradient-based optimization, and particularly stochastic gradient descent (we'll talk more about this in Practical 2). The SGD algorithm\n",
    "computes the gradient $\\frac{\\partial E}{\\partial \\theta}$ on a sample of the data, and then takes a small step/update in the negative direction of the gradient (which minimizes $E$). I.e.\n",
    "\n",
    "$\\theta^{t+1} = \\theta^t - \\eta \\frac{\\partial E}{\\partial \\theta}$\n",
    "\n",
    "Here, $\\eta$ is referred to as the \"learning rate\". There's a lot more to say about this, but this is all we need for now. To implement this, we need to compute the gradients of the loss function wrt the model parameters.\n",
    "\n",
    "#### Deriving the Softmax Gradients\n",
    "\n",
    "Recall the definition of the softmax above, written in terms of the **logits** (unnormalized scores) $z$):\n",
    "\n",
    "$P(y=j\\ |\\ z) = \\frac{e^{z_j}}{\\sum_{i=1}^k e^{z_i}}$\n",
    "\n",
    "Our loss (error function) is the cross-entropy function:\n",
    "\n",
    "$E = - \\sum_k (\\log p_k).y_k$, \n",
    "\n",
    "where $y_k$ is the **\"one-hot\" encoding** of the target class, so the terms of the sum is zero everywhere except for the observed class (i.e. we can ignore the sum and let $k$ be equal to the observed class). The above sum really just \"picks out\" one $\\log p_k$ (compare this to the code for `cross_entropy()` above). We require the gradient of the loss with respect to the logits, i.e.\n",
    "\n",
    "$\\frac{\\partial E}{\\partial z_k} = - \\frac{\\partial}{\\partial z_k} [ \\log p_k ]$\n",
    "\n",
    "By substituting the softmax equation for $p_k$, and expanding the log-quotient into two terms, we get (just the RHS for now)\n",
    "\n",
    "$\\frac{\\partial}{\\partial z_k} (\\log(e^{z_k}) - \\log \\sum_j e^{z_j})$\n",
    "\n",
    "where the first term reduces to 1, and the second is known as the \"log-sum-exp\". This arises frequently in normalized probabilistic models, and we can deal with that as follows:\n",
    "\n",
    "\\begin{aligned}\n",
    " \\frac{\\partial}{\\partial z_k} \\log \\sum_j e^{z_j} &= \n",
    "     \\frac{1}{\\sum_j e^{z_j}} \\left [ \\frac{\\partial}{\\partial z_k} \\sum_j e^{z_j} \\right ] \n",
    "         && \\vartriangleright \\frac{d}{dx} \\log f(x) = \\frac{1}{f(x)} \\frac{d}{dx}f(x)\\\\\n",
    " &= \\frac{e^{z_k}}{\\sum_j e^{z_j}}    \n",
    "         && \\vartriangleright    \\frac{d}{dx} e^{f(x)} = e^{f(x)}    \\frac{d}{dx}f(x) \\\\\n",
    " &= p_k\n",
    "\\end{aligned}\n",
    "\n",
    "Putting it all together we get this elegant expression for the **softmax gradient**:\n",
    "\n",
    "$\\frac{\\partial E}{\\partial z_k} = - [1 - p_k ] = p_k - 1$.\n",
    "\n",
    "#### What does this mean?\n",
    "\n",
    "Look at the derivative. When is it big? When $p_k$ is far from one, and we mis-classified the point. The derivative is big and we have some more work to do! When is the derivative small? It is when $p_k \\approx 1$. In that case, we correctly classified the point, and don't need to sweat and labour any more.\n",
    "\n",
    "\n",
    "**NOTE**: The derivative is for each example, and in the full derivative, many data points play a role. The misclassified ones play a bigger role. So, we typically compute this for a *batch* of examples by computing the **average per-example cross-entropy** over the batch. \n",
    "\n",
    "**QUESTION**: Why do we compute the average loss? Hint: What happens to the loss as batch-size changes without averaging? Also, what happens to the gradients as batch-size changes? How could these be a problem? \n",
    "\n",
    "#### Deriving the Weights Gradients\n",
    "\n",
    "We now have $\\frac{\\partial E}{\\partial z_k}$ (the derivative of the loss with respect to the logit for class $k$). Next we want the gradient on the weights $W$. \n",
    "\n",
    "**QUESTION**: How can we compute $\\frac{\\partial E}{\\partial W}$? **Note**: This is a derivative of a matrix (gradient). \n",
    "\n",
    "To derive this, let's think about the shape of W, and then derive the gradient on each of its elements first. W is a [input_dim, output_dim] matrix. Let $w_{ij}$ by the weight at W[i,j] (connecting input element $i$ to output class $j$). \n",
    "\n",
    "Now let's use the [chain rule](https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-chain-rule/a/chain-rule-review) to derive this:\n",
    "\n",
    "$\\frac{\\partial E}{\\partial w_{ij}} = \\frac{\\partial E}{\\partial z_j} \\frac{\\partial z_j}{\\partial w_{ij}}$\n",
    "\n",
    "This gradient is the product of two terms. Notice that we already computed the first term above! So we just need the second term:\n",
    "\n",
    "To start, notice that $z_j = x^T W_j + b_j = \\sum_i x_i w_{ij} + b_j$ ($W_j$ is the j-th column of matrix W). Use this to answer the following question:\n",
    "\n",
    "**QUESTIONs:**\n",
    "1. Derive $\\frac{\\partial z_j}{\\partial w_{ij}}$.\n",
    "2. Now put this together to get $\\frac{\\partial E}{\\partial w_{ij}}$.\n",
    "3. Do the same for $\\frac{\\partial E}{\\partial b_{j}}$.\n",
    "4. Put these together to arrive at $\\frac{\\partial E}{\\partial W}$ (a matrix) and $\\frac{\\partial E}{\\partial b}$ (a vector) **HINT**: Think about the ingredients: the vector of activations $x$ and the vector of logits $z$. What is the dimension of each? Now think about the dimensions of W. Which linear algebra operator can take two vectors and output a matrix? :)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
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    "id": "QzlF2JiS2d5E"
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   "source": [
    "class LinearModel(object):\n",
    "    def __init__(self):\n",
    "        # Initialize the model parameters.\n",
    "        self.W = np.copy(W_init)\n",
    "        self.b = np.zeros((1, num_classes))\n",
    "    \n",
    "    def predictions(self, X):\n",
    "        \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
    "        # Evaluate class scores/\"logits\": [points_per_class*num_classes x num_classes].\n",
    "        logits = self.get_logits(X)\n",
    "\n",
    "        # Compute the class probabilities.\n",
    "        probs = softmax(logits)\n",
    "        \n",
    "        return probs\n",
    "    \n",
    "    def loss(self, probs, y):\n",
    "        \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
    "        num_examples = probs.shape[0]\n",
    "        data_loss = cross_entropy(probs, y)\n",
    "        regulariser = l2_loss([self.W])\n",
    "        return data_loss + regulariser\n",
    "    \n",
    "    def update(self, probs, X, y):    \n",
    "        \"\"\"Update the model parameters using back-propagation and gradient descent.\"\"\"\n",
    "        # Calculate the gradient of the loss with respect to logits\n",
    "        dlogits = self.derivative_loss_logits(probs, y)    \n",
    "        \n",
    "        # Gradient of the loss wrt W\n",
    "        dW = self.derivative_loss_W(X, dlogits)\n",
    "        \n",
    "        # Gradient of the loss wrt b\n",
    "        db = self.derivative_loss_b(dlogits)\n",
    "        \n",
    "        # Don't forget the gradient on the regularization term.\n",
    "        dW += self.derivative_regularisation()\n",
    "        \n",
    "        # Perform a parameter update.\n",
    "        self.W += -learning_rate * dW\n",
    "        self.b += -learning_rate * db\n",
    "        \n",
    "    \n",
    "    ##### Now we define some helper functions     \n",
    "    ## IMPLEMENT-ME: ...\n",
    "    def get_logits(self, X):\n",
    "        \"\"\"Calculate the un-normalised model scores.\"\"\"\n",
    "        return np.dot(X, self.W) + self.b \n",
    "\n",
    "    def derivative_loss_logits(self, probs, y):\n",
    "        \"\"\"Calculate the derivative of the loss with respect to logits.\"\"\"\n",
    "        num_examples = y.shape[0]\n",
    "        dlogits = probs\n",
    "        dlogits[range(num_examples), y] -= 1\n",
    "        dlogits /= num_examples\n",
    "        return dlogits\n",
    "    \n",
    "    def derivative_loss_W(self, X, dlogits):\n",
    "        \"\"\"Calculate the derivative of the loss wrt W.\"\"\"\n",
    "        return np.dot(X.T, dlogits)\n",
    "    \n",
    "    def derivative_loss_b(self, dlogits):\n",
    "        \"\"\"Calculate the derivative of the loss wrt b.\"\"\"\n",
    "        return np.sum(dlogits, axis=0, keepdims=True)\n",
    "    \n",
    "    def derivative_regularisation(self):\n",
    "        return reg_lambda * self.W     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tc3wrrwVCQNU"
   },
   "source": [
    "### Training the linear model\n",
    "Now that we've defined our \"black box\" linear model. We can train it on our dummy spiral dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "ARwVZj5zEPTv"
   },
   "outputs": [],
   "source": [
    "# Define a function that trains a model for a given number of epochs \n",
    "# (iterations through the data).\n",
    "\n",
    "def train_model(model, epochs, report_every, render_fn=None, render_args={}):\n",
    "    frames = []\n",
    "    for i in xrange(epochs):\n",
    "    \n",
    "        # Get the model predictions for our spiral dataset X.\n",
    "        probs = model.predictions(X)\n",
    "\n",
    "        # Compute the loss\n",
    "        loss = model.loss(probs, y)\n",
    "\n",
    "        # Print the loss value every `report_every` steps.\n",
    "        if i % report_every == 0:\n",
    "            print \"iteration %d: loss %f\" % (i, loss)\n",
    "            if render_fn:\n",
    "                frame = render_fn(**render_args)\n",
    "                frames.append(frame)\n",
    "\n",
    "        # Use back-propagation to update the model parameters:\n",
    "        model.update(probs, X, y)    \n",
    "        \n",
    "    if frames: return frames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 357,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 436,
     "status": "ok",
     "timestamp": 1504361656248,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
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    },
    "id": "OuR6eFwoCXcf",
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 0: loss 1.100447\n",
      "iteration 10: loss 0.918496\n",
      "iteration 20: loss 0.852024\n",
      "iteration 30: loss 0.822591\n",
      "iteration 40: loss 0.807724\n",
      "iteration 50: loss 0.799528\n",
      "iteration 60: loss 0.794729\n",
      "iteration 70: loss 0.791794\n",
      "iteration 80: loss 0.789940\n",
      "iteration 90: loss 0.788739\n",
      "iteration 100: loss 0.787946\n",
      "iteration 110: loss 0.787414\n",
      "iteration 120: loss 0.787053\n",
      "iteration 130: loss 0.786806\n",
      "iteration 140: loss 0.786634\n",
      "iteration 150: loss 0.786515\n",
      "iteration 160: loss 0.786432\n",
      "iteration 170: loss 0.786373\n",
      "iteration 180: loss 0.786332\n",
      "iteration 190: loss 0.786303\n"
     ]
    }
   ],
   "source": [
    "# Create an instance of our LinearModel.\n",
    "linear_model = LinearModel()\n",
    "\n",
    "# Now we train the linear model for 200 epochs.\n",
    "train_model(linear_model, 200, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1gPfOe1E3W5j"
   },
   "source": [
    "### Evaluating the model\n",
    "The training of the model should have converged to a value around 0.786 if you used the default data parameters earlier. (Convergence means that the loss decreases to a point and then stops decreasing). But how do we interpret this? Is our model actually good at making predictions? Let's work out the **accuracy** of the model to see:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "PH-cpnO-Er6F"
   },
   "outputs": [],
   "source": [
    "# Define a function that calcuates and prints the accuracy of a model's predictions\n",
    "def evaluate_model(model):\n",
    "    # Get the probabilites/scores that the model assigns to each class for each X datapoint.\n",
    "    scores = model.get_logits(X)    # The shape of scores is [num_data_points, num_classes]\n",
    "\n",
    "    # The index of the maximum score along the 2nd dimension is the class that the model thinks is most likely (y^) for each datapoint.\n",
    "    predicted_class = np.argmax(scores, axis=1)\n",
    "\n",
    "    # What proportion of the class predictions made by the model (y^) agree with the true class values (y) ?\n",
    "    print 'Accuracy: %.2f' % (np.mean(predicted_class == y))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 54,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 168,
     "status": "ok",
     "timestamp": 1502706247541,
     "user": {
      "displayName": "Ulrich Paquet",
      "photoUrl": "//lh3.googleusercontent.com/-q3A91HQu7t8/AAAAAAAAAAI/AAAAAAAAAAw/O3bjgikw0xQ/s50-c-k-no/photo.jpg",
      "userId": "117228953648657363788"
     },
     "user_tz": -60
    },
    "id": "KC_V-9pn3Zpi",
    "outputId": "f8370335-7a2f-4b66-8cde-8a69440fe0bb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.49\n"
     ]
    }
   ],
   "source": [
    "# Now evaluate the trained linear model\n",
    "evaluate_model(linear_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "z_b6b1GyGmod"
   },
   "source": [
    "This is not a very good result (we are misclassifying around 50% of the data points, and these are data points that we've seen before!), lets visualise the decision boundary to determine what's going on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "i00J82lT3iKt"
   },
   "source": [
    "### Visualizing the linear model's decision boundary\n",
    "\n",
    "Let's visualize the decision boundary of this linear classifier on the swiss roll dataset.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "2qtWT9HYlwZ2"
   },
   "outputs": [],
   "source": [
    "# Define a function that plots the decision boundary of a model\n",
    "def plot_decision_boundary(X, model, render=True):\n",
    "    \"\"\"Overlays the classifier's decision boundary on the dataset [X, y].\n",
    "    \n",
    "    Args:\n",
    "        X: 2-d matrix input data,\n",
    "        model: The model to evaluate\n",
    "    \"\"\"\n",
    "    \n",
    "    step_size = 0.02    # Discretization step-size\n",
    "    \n",
    "    # Get the boundaries of the dataset.\n",
    "    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "    # Generate a grid of points, step_size apart, over the above region.\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, step_size),\n",
    "                                             np.arange(y_min, y_max, step_size))\n",
    "    \n",
    "    # Flatten the data and get the logits of the classifier (the \"scores\") for \n",
    "    #     each point in the generated mesh-grid.\n",
    "    meshgrid_matrix = np.c_[xx.ravel(), yy.ravel()]\n",
    "    Z = model.get_logits(meshgrid_matrix)\n",
    "    \n",
    "    # Get the class predictions for each point.\n",
    "    Z = np.argmax(Z, axis=1)\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    \n",
    "    old_backend = plt.rcParams['backend']    # Save backend.\n",
    "    if not render:\n",
    "        plt.rcParams['backend'] = 'agg'\n",
    "\n",
    "    # Overlay both of these on one figure.\n",
    "    fig = plt.figure()\n",
    "    axes = plt.gca()\n",
    "\n",
    "    axes.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)\n",
    "    axes.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)\n",
    "    \n",
    "    plt.xlim(xx.min(), xx.max())\n",
    "    plt.ylim(yy.min(), yy.max())\n",
    "    \n",
    "    if not render:\n",
    "        # Now we can save it to a numpy array.\n",
    "        fig.tight_layout(pad=0)\n",
    "        fig.canvas.draw()\n",
    "        data = np.fromstring(fig.canvas.tostring_rgb(), dtype=np.uint8, sep='')\n",
    "        data = data.reshape(fig.canvas.get_width_height()[::-1] + (3,))\n",
    "        # Restore old backend\n",
    "        plt.rcParams['backend'] = old_backend\n",
    "        \n",
    "        return data\n",
    "    \n",
    "    #fig.savefig('spiral_linear.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "bgy6T0Gpz5Dn"
   },
   "outputs": [],
   "source": [
    "from matplotlib import animation\n",
    "from IPython.display import display\n",
    "from IPython.display import HTML\n",
    "\n",
    "def display_frames_as_gif(frames):\n",
    "        \"\"\"\n",
    "        Displays a list of frames as a gif.\n",
    "        \"\"\"\n",
    "        plt.figure(figsize=(frames[0].shape[1] / 72.0, frames[0].shape[0] / 72.0), dpi = 72)\n",
    "        patch = plt.imshow(frames[0])\n",
    "        #plt.axis('off')\n",
    "\n",
    "        def animate(i):\n",
    "                patch.set_data(frames[i])\n",
    "\n",
    "        anim = animation.FuncAnimation(plt.gcf(), animate, frames = len(frames), interval=50)\n",
    "        ##display(display_animation(anim, default_mode='loop'))\n",
    "        HTML(anim.to_html5_video())\n",
    "        # METHOD 2\n",
    "        #plt.rcParams['animation.html'] = 'html5'\n",
    "        #anim        \n",
    "        return anim\n",
    "\n",
    "#display_frames_as_gif(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 357,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 362,
     "status": "ok",
     "timestamp": 1504368307657,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "-oAjAAmp3mK-",
    "outputId": "1e173f1b-4e32-4acd-bab7-ece33962448f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 0: loss 1.100447\n",
      "iteration 10: loss 0.918496\n",
      "iteration 20: loss 0.852024\n",
      "iteration 30: loss 0.822591\n",
      "iteration 40: loss 0.807724\n",
      "iteration 50: loss 0.799528\n",
      "iteration 60: loss 0.794729\n",
      "iteration 70: loss 0.791794\n",
      "iteration 80: loss 0.789940\n",
      "iteration 90: loss 0.788739\n",
      "iteration 100: loss 0.787946\n",
      "iteration 110: loss 0.787414\n",
      "iteration 120: loss 0.787053\n",
      "iteration 130: loss 0.786806\n",
      "iteration 140: loss 0.786634\n",
      "iteration 150: loss 0.786515\n",
      "iteration 160: loss 0.786432\n",
      "iteration 170: loss 0.786373\n",
      "iteration 180: loss 0.786332\n",
      "iteration 190: loss 0.786303\n"
     ]
    }
   ],
   "source": [
    "# Plot the decision boundary of our trained linear model on the dataset X\n",
    "# plot_decision_boundary(X, linear_model)\n",
    "\n",
    "# Create an instance of our LinearModel.\n",
    "reset_matplotlib()\n",
    "linear_model = LinearModel()\n",
    "\n",
    "train_model(linear_model, 200, 10)\n",
    "\n",
    "# For rendering animations.\n",
    "#frames = train_model(linear_model, 200, 10, \n",
    "#                                         plot_decision_boundary,\n",
    "#                                        {'X':X, 'model':linear_model, 'render':False})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 494,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 649,
     "status": "ok",
     "timestamp": 1504366521548,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "sbEaMsUM_MRu",
    "outputId": "3ba645c8-c741-4a72-c5ca-6f4499e3c383"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j8ZsTFjpzlfCibGhHueXFVEvKIsuYvnNFoLY1RIVj8NZGmSEn5eFt6ag9zjUk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\nB2vdhb1/Qm+dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46a36d47d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(X, linear_model)\n",
    "\n",
    "#reset_matplot_lib()\n",
    "#anim = display_frames_as_gif(frames)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AjDp48EyGymu"
   },
   "source": [
    "What can you deduce from this decision boundary? Does it help explain why the linear model makes bad predictions? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "69-CauTN3z5a"
   },
   "source": [
    "## Using a nonlinear model\n",
    "\n",
    "The linear model resulted in decision boundaries that were straight lines in 2D space. Using these straight lines, it is impossible to accurately separate our spiral-shaped data. We need a more complex model that can represent more complex (nonlinear) decision boundaries. Intuitively, we want a \"curved\" decision boundary that can adapt to the curved shape of the data. Let's see how converting our model to be a non-linear function of its parameters could resolve this. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0c6TUH9FZjUU"
   },
   "source": [
    "### Define the non-linear model\n",
    "We define this as a class with the same interface as the LinearModel. This way we can reuse exactly the same training and evaluation functions we defined earlier!\n",
    "\n",
    "**Forward pass**\n",
    "\n",
    "So far the logits (scores) were a linear function of the inputs ($\\Delta \\textrm{logits} = W*\\Delta \\textrm{inputs}$; put another way, a small change in inputs leads to a proportionally small change in outputs). We can make the model more powerful by making logits a non-linear function of inputs, e.g. $\\Delta\\textrm{logits} = W_2 * \\sigma(W * \\Delta \\textrm{inputs})$. Here, $\\sigma$ is a nonlinear function (non-linearity / **activation function**). There are many different types, but a popular choice is the **rectified linear unit (ReLU)**:\n",
    "\n",
    "$\\sigma_\\textrm{ReLU}(x) = \\max(0, x)$\n",
    "\n",
    "In code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "Lm4WKUbGZrs2"
   },
   "outputs": [],
   "source": [
    "def relu(value):\n",
    "    \"\"\" ReLU is the \"Rectified Linear Unit activation function\", defined as:\n",
    "                relu(x) = x if x > 0, and 0 if x <= 0\n",
    "    \"\"\"\n",
    "    return np.maximum(0, value)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "C9-uGQloclnO"
   },
   "source": [
    "**QUESTION**: Why does adding this \"non-linearity\" make the model more powerful? **HINT**: Think about the decision boundary of the linear model above, and convince yourself that adding a nonlinearity allows the model more freedom in how it structures its decision boundary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vOZd0ZxxD7Um"
   },
   "source": [
    "**Backward pass: Deriving the gradients** \n",
    "\n",
    "Our model has now changed a little, but notice that $W_2$ (which maps from the hidden layer to logits) is now doing the same thing as $W$ in our linear model, just on a transformed version of the inputs $z_2 = W_2h$, with the hidden layer activations $h = \\sigma_{ReLU}(z_1)$ and $z_1 = Wx + b$. \n",
    "\n",
    "So the good news is that the *mechanics* of computing the gradient wrt $W_2$ will be similar to how we derived $\\frac{\\partial E}{\\partial W}$ for the linear model above, but now we just need to replace 'input activations' $X$ with the 'hidden activations' $h$ (compare `derivative_loss_W2()` below with `derivative_loss_W()` in the linear model above). \n",
    "\n",
    "So all that's left is to compute $\\frac{\\partial E}{\\partial W}$, the gradients on $W$ (the input-to-hidden layer weights; omitting the biases for now). For this, we will again use the chain rule to derive \n",
    "\n",
    "$\\frac{\\partial E}{\\partial W} = \\frac{\\partial E}{\\partial z_2} \\frac{\\partial z_2}{\\partial z_1} \\frac{\\partial z_1}{\\partial W}$\n",
    "\n",
    "Convince yourself that this is again just an application of the [chain rule for derivatives](https://en.wikipedia.org/wiki/Chain_rule), but over a longer chain ($E\\rightarrow z_2 \\rightarrow z_1 \\rightarrow W$)!\n",
    "\n",
    "**NOTE**:\n",
    "* The gradient on input weights W is a product of three terms.\n",
    "* We already know the first term $\\frac{\\partial E}{\\partial z_2}$.\n",
    "\n",
    "**QUESTIONS**:\n",
    "* Compute: $\\frac{\\partial z_2}{\\partial z_1} = \\frac{\\partial W_2 h}{\\partial z_1} = \\frac{\\partial W_2 \\sigma_{ReLU}(z_1)}{\\partial z_1} = \\ldots$. **HINT**: For sigmoidal activations we use the identity $\\frac{d}{dz} \\sigma(z) = \\sigma(z)(1 - \\sigma(z))$. Can you derive this? \n",
    "* Compute: $\\frac{\\partial z_1}{\\partial W}$. \n",
    "\n",
    "**ASIDE: What is happening here**:\n",
    "\n",
    "So far we have been manually deriving the gradients of the loss wrt to all model parameters. Notice that a specific pattern is emerging:\n",
    " \n",
    "* propagate activations forward through the network (\"make a prediction\"), \n",
    "* compute an error delta (\"see how far we're off\") , and \n",
    "* propagate errors backwards to update the weights (\"update the weights to do better next time\").\n",
    " \n",
    "Derivatives of the loss with respect to the inputs of a layer (e.g. $\\frac{\\partial E}{\\partial z}$) are referred to as (error) **delta**s.    For now we just need the gradients calculated above, but we will use this insight in the next practical when we show how this all forms part of a more general algorithm for efficiently computing gradients in deep neural networks (called **(error) back-propagation**).\n",
    "\n",
    "Let's implement this:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "DwXofyX0dio1"
   },
   "outputs": [],
   "source": [
    "learning_rate = 1e-0    # How far along the gradient do we want to travel when doing \n",
    "                                            # gradient descent?\n",
    "reg_lambda = 1e-3    # Regularization strength\n",
    "num_hidden = 100    # Size of hidden layer.\n",
    "\n",
    "non_linear_W_init = 0.01 * np.random.randn(dimensions, num_hidden)\n",
    "non_linear_W2_init = 0.01 * np.random.randn(num_hidden, num_classes)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "1HsSVOuQ37R0"
   },
   "outputs": [],
   "source": [
    "class NonLinearModel(object):\n",
    "    def __init__(self):\n",
    "        # Initialize the model parameters.\n",
    "        self.W = non_linear_W_init\n",
    "        self.b = np.zeros((1, num_hidden))\n",
    "        self.W2 = non_linear_W2_init\n",
    "        self.b2 = np.zeros((1, num_classes))\n",
    "\n",
    "    def predictions(self, X):\n",
    "        \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
    "        # Evaluate class scores/\"logits\": [points_per_class*num_classes x num_classes].\n",
    "        logits = self.get_logits(X)\n",
    "\n",
    "        # Compute the class probabilities.\n",
    "        probs = softmax(logits)\n",
    "        \n",
    "        return probs\n",
    "    \n",
    "    def loss(self, probs, y):\n",
    "        \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
    "        data_loss = cross_entropy(probs, y)\n",
    "        regulariser = l2_loss([self.W, self.W2])\n",
    "        return data_loss + regulariser\n",
    "    \n",
    "    def update(self, probs, X, y):    \n",
    "        \"\"\"Update the model parameters using back-propagation and gradient descent.\"\"\"\n",
    "        hidden_output = self.hidden_layer(X)\n",
    "        \n",
    "        # Calculate the gradient of the loss with respect to logits\n",
    "        dlogits = self.derivative_loss_logits(probs, y)    \n",
    "        \n",
    "        # Backpropagate the gradient to the parameters.\n",
    "        \n",
    "        # We first backprop into parameters W2 and b2.\n",
    "        dW2 = self.derivative_loss_W2(hidden_output, dlogits)\n",
    "        db2 = self.derivative_loss_b2(dlogits)\n",
    "\n",
    "        # Next, backprop into the hidden layer.\n",
    "        dhidden = self.derivative_hidden(hidden_output, dlogits)\n",
    "\n",
    "        # Finally, backprop into W,b.\n",
    "        dW = self.derivative_loss_W(X, dhidden)\n",
    "        db = self.derivative_loss_b(dhidden)\n",
    "\n",
    "        # Add regularization gradient contribution.\n",
    "        dW2 += self.derivative_regularisation_W2()\n",
    "        dW += self.derivative_regularisation_W()\n",
    "\n",
    "        # Perform a parameter update (one step of gradient descent).\n",
    "        self.W += -learning_rate * dW\n",
    "        self.b += -learning_rate * db\n",
    "        self.W2 += -learning_rate * dW2\n",
    "        self.b2 += -learning_rate * db2\n",
    "        \n",
    "\n",
    "    ## DEFINE THE MODEL HELPER FUNCTIONS    \n",
    "    \n",
    "    def hidden_layer(self, X):\n",
    "        \"\"\"Calculate the output of the hidden layer.\"\"\"\n",
    "        return relu(np.dot(X, self.W) + self.b)\n",
    "        \n",
    "    def get_logits(self, X):\n",
    "        \"\"\"Calculate the logits from the input data X.\"\"\"\n",
    "        hidden_output = self.hidden_layer(X)\n",
    "        logits = np.dot(hidden_output, self.W2) + self.b2\n",
    "        return logits\n",
    "    \n",
    "    def derivative_loss_logits(self, logits, y):\n",
    "        \"\"\"Calculate the derivative of the loss with respect to logits.\"\"\"\n",
    "        num_examples = y.shape[0]\n",
    "        dlogits = logits\n",
    "        dlogits[range(num_examples),y] -= 1\n",
    "        dlogits /= num_examples\n",
    "        return dlogits\n",
    "    \n",
    "    def derivative_loss_W2(self, hidden_output, dlogits):\n",
    "        \"\"\"Calculate the derivative of the loss wrt W2.\"\"\"\n",
    "        dW2 = np.dot(hidden_output.T, dlogits)\n",
    "        return dW2\n",
    "    \n",
    "    def derivative_loss_b2(self, dlogits):\n",
    "        \"\"\"Calculate the derivative of the loss wrt b2.\"\"\"\n",
    "        return np.sum(dlogits, axis=0, keepdims=True)\n",
    "        \n",
    "    def derivative_hidden(self, hidden_output, dlogits):\n",
    "        \"\"\"Calculate the derivative of the loss wrt the hidden layer.\"\"\"\n",
    "        # Calculate the gradient as if the hidden layer were a normal linear layer. \n",
    "        dhidden = np.dot(dlogits, self.W2.T)\n",
    "        \n",
    "        # Now take the Relu non-linearity into account\n",
    "        dhidden[hidden_output <= 0] = 0\n",
    "        \n",
    "        return dhidden\n",
    "        \n",
    "    def derivative_loss_W(self, X, dhidden):\n",
    "        \"\"\"Calculate the derivative of the loss wrt W.\"\"\"\n",
    "        return np.dot(X.T, dhidden)\n",
    "    \n",
    "    def derivative_loss_b(self, dhidden):\n",
    "        \"\"\"Calculate the derivative of the loss wrt b.\"\"\"\n",
    "        return np.sum(dhidden, axis=0, keepdims=True)\n",
    "    \n",
    "    def derivative_regularisation_W(self):\n",
    "        \"\"\"Calculate the gradient of the L2 loss wrt W.\"\"\"\n",
    "        return reg_lambda * self.W \n",
    "    \n",
    "    def derivative_regularisation_W2(self):\n",
    "        \"\"\"Calculate the gradient of the L2 loss wrt W2.\"\"\"\n",
    "        return reg_lambda * self.W2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "f8tDrHHRFdcs"
   },
   "source": [
    "### Train the non linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 187,
     "output_extras": [
      {
       "item_id": 10
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 20243,
     "status": "ok",
     "timestamp": 1504366817848,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "ntVMzdM8Fg9u",
    "outputId": "594e6c68-3dde-4c0c-8bfd-4618f96de913"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 0: loss 1.098706\n",
      "iteration 1000: loss 0.310401\n",
      "iteration 2000: loss 0.267694\n",
      "iteration 3000: loss 0.251005\n",
      "iteration 4000: loss 0.248199\n",
      "iteration 5000: loss 0.247441\n",
      "iteration 6000: loss 0.246914\n",
      "iteration 7000: loss 0.246429\n",
      "iteration 8000: loss 0.246247\n",
      "iteration 9000: loss 0.246120\n"
     ]
    }
   ],
   "source": [
    "# Create an instance of our non-linear model.\n",
    "non_linear_model = NonLinearModel()\n",
    "\n",
    "# Train the model for 10000 epochs\n",
    "train_model(non_linear_model, 10000, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 34,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 346,
     "status": "ok",
     "timestamp": 1504366820369,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "eEseRPX_4C6g",
    "outputId": "231970ae-1c5c-4161-9d9e-06877954c02b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.98\n"
     ]
    }
   ],
   "source": [
    "# evaluate training set accuracy of the non-linear model\n",
    "evaluate_model(non_linear_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tmcEejSmIGLc"
   },
   "source": [
    "Much better! Is it possible to get to 100%? What factors about the dataset would influence this?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Fu5JRcMtYOms"
   },
   "source": [
    "### Visualize the nonlinear model's decision boundary\n",
    "Lets see what the decision boundary of the non-linear model looks like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 494,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 709,
     "status": "ok",
     "timestamp": 1504366824830,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "gb3KwDN84P8z",
    "outputId": "8b577ed6-ef41-4360-fd79-fd01f585fd4c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ljU68R+Df73xPohHiyhdRiKDgwlsPGY3ShRQ9BEV3rFa/Gu0lzCzHXh0CBlLx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\nhi8iIiIiBzF8ERERETno/wMirNHbbII7WwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46a34f33d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the decision boundary of the non-linear model on the dataset X\n",
    "plot_decision_boundary(X, non_linear_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RsR2U3klH5SU"
   },
   "source": [
    "# Using TensorFlow\n",
    "\n",
    "The above models worked well, but it was a little tedius to implement the gradients by hand. TensorFlow (TF) is an open source software library for numerical computation using data flow graphs. Nodes in the graph represent mathematical operations, while the graph edges represent the multidimensional data arrays (tensors) communicated between them. Besides offering computational speedups due to efficient backends, one of the big advantages is also that TensorFlow can be used to automatically derive the gradients of any mathematical expressions. It achieve this through a process called \"[automatic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation)\". \n",
    "\n",
    "TF builds a **computational graph** (a DAG structure where nodes represent mathematical operations and data flows on the edges connecting them). The graph chains together all the mathematical operations in order. Given such a graph for a neural network with a loss function, TF can then automatically \"unroll\" it backwards to compute the gradients that we had to compute by hand above! \n",
    "\n",
    "**NOTE**: Chat to your neighbour and the tutors to make sure you understand (at least conceptually) how this graph formalism is different from e.g. Numpy's (imperative) formalism before moving on.\n",
    "\n",
    "**QUESTION**: What are the advantages and disadvantages of such a computational graph approach?\n",
    "\n",
    "Now let's re-implement the above models using TensorFlow and see how it compares."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OGrFDQ1KGmv8"
   },
   "source": [
    "### Create a session\n",
    "\n",
    "TensorFlow makes use of \"[sessions](https://www.tensorflow.org/versions/r0.12/api_docs/python/client/session_management)\" to encapsulate the environment and manage the resources within which graphs are executed. Sessions are also used to run the graph operations you are interested in. There are different ways to create sessions, but for now we will make use of the [interactive session](https://www.tensorflow.org/versions/r0.12/api_docs/python/client/session_management#InteractiveSession), which sets a default environment that will be shared across all code cells, and avoids the need to explicitly pass around a reference to the current session object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "COL_PqgMmx5Y"
   },
   "outputs": [],
   "source": [
    "# First we need to import TensorFlow.\n",
    "import tensorflow as tf\n",
    "\n",
    "tf.reset_default_graph() # Clear the graph between different invocations.\n",
    "sess = tf.InteractiveSession() # Create and register the default Session.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yiseUdITmzT0"
   },
   "source": [
    "### Define hyperparameters\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "MMTIs4bYKgCX"
   },
   "outputs": [],
   "source": [
    "### HYPERPARAMETERS\n",
    "learning_rate = 1e-0\n",
    "reg_lambda = 1e-3\n",
    "training_iterations = 200    # 'epochs'\n",
    "batch_size = X.shape[0]    # The whole dataset; i.e. batch gradient descent.\n",
    "display_step = 10    # How often should we print our results\n",
    "###\n",
    "\n",
    "# Network Parameters\n",
    "num_input = 2 # 2-dimensional input data\n",
    "num_classes = 3 # red, yellow and blue!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4NgyMmZeRtZX"
   },
   "source": [
    "### Graph input placeholders\n",
    "\n",
    "Graphs provide an abstract definition of what computations we want to perform on our data. TensorFlow provides [placeholders](https://www.tensorflow.org/api_docs/python/tf/placeholder) as a means for injecting data into our graph at execution time, through a process called \"feeding\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "9gDraGrsRw-4"
   },
   "outputs": [],
   "source": [
    "# placeholders for the inputs and labels. We will 'feed' these to the graph.\n",
    "# Note that using 'None' for a dimension means that TensorFlow will adapt to\n",
    "# whatever the size is of the input we feed in.\n",
    "x_tf = tf.placeholder(tf.float32, [None, num_input])\n",
    "y_tf = tf.placeholder(tf.int32, [None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "eyfHfdka9NKY"
   },
   "source": [
    "### Define helper functions\n",
    "Let's create some helper functions that we can re-use in the Tensorflow models. We need fewer than before because Tensorflow already provides lots of useful functions out the box! \n",
    "\n",
    "**Note**: TensorFlow has a built-in cross entropy function that is more numerically stable than our implementation, and should be used under normal circumstances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "CRWJAimx9MXm"
   },
   "outputs": [],
   "source": [
    "def cross_entropy_tf(predictions, targets):\n",
    "    \"\"\"Calculate the cross entropy loss given some model predictions and target (true) values.\"\"\"\n",
    "    targets = tf.one_hot(targets, num_classes)\n",
    "    return tf.reduce_mean(-tf.reduce_sum(targets * tf.log(predictions), axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YocWzSZFXMQL"
   },
   "source": [
    "## Linear model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YlhRC4-gWSUU"
   },
   "source": [
    "We construct a linear model with the same architecture as above. Notice how TensorFlow provides out-the-box many of the functions we had to previously define ourselves. There is another major difference between the TensorFlow code and Numpy code that may not be immediately apparant. In TensorFlow, when we call functions like tf.nn.softmax() we are not performing a computation, rather **we are defining an operation in the computation graph that gets run later** (when we feed in real data). \n",
    "\n",
    "**NOTE**:    This is called \"define-**and**-run\", and it is different from e.g. Numpy's \"define-**by**-run\" (imperative) approach. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "UcS63poGGTYr"
   },
   "outputs": [],
   "source": [
    "class TFLinearModel(object):\n",
    "    def __init__(self):\n",
    "        # Initialise the variables\n",
    "        # Tensorflow variables can be updated automatically by optimisers.\n",
    "        self.W = tf.Variable(W_init, dtype=tf.float32)\n",
    "        self.b = tf.Variable(tf.zeros([num_classes]), dtype=tf.float32)\n",
    "\n",
    "    def predictions(self, X):\n",
    "        \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
    "        logits = self.get_logits(X)\n",
    "\n",
    "        # Compute the class probabilities.\n",
    "        probs = tf.nn.softmax(logits)\n",
    "        \n",
    "        return probs\n",
    "    \n",
    "    def loss(self, probs, y):\n",
    "        \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
    "        data_loss = cross_entropy_tf(probs, y)\n",
    "        regulariser = reg_lambda * tf.nn.l2_loss(self.W)\n",
    "        return data_loss + regulariser\n",
    "        \n",
    "    def get_logits(self, X):\n",
    "        # An affine function.\n",
    "        return tf.add(tf.matmul(X, self.W), self.b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tZMShhHyOYAq"
   },
   "source": [
    "![alt text](https://)Remember, up until now we've been defining (constructing) a computation graph. Now we can run this graph multiple times, feeding in our data, in a training loop. The training loop is a bit more complex than before, but by wrapping up our models in classes, we can again benefit from re-using the same training loop on multiple models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "CLlW9MiUHutE"
   },
   "outputs": [],
   "source": [
    "def train_tf_model(tf_model, epochs, report_every):\n",
    "    \n",
    "    # Get the op which, when executed, will initialize the variables.\n",
    "    init = tf.global_variables_initializer()\n",
    "    \n",
    "    # Get the model probabilities\n",
    "    probs = tf_model.predictions(x_tf)\n",
    "    \n",
    "    # Get the model loss\n",
    "    loss = tf_model.loss(probs, y_tf)\n",
    "    \n",
    "    # Create a Gradient Descent optimizer using our own learning rate.\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "    \n",
    "    # Now we create an op that computes the gradient of the loss with respect \n",
    "    # to the model parameters and performs one update to all of the parameters \n",
    "    # in the direction of their gradients.\n",
    "    # NOTE: TensorFlow uses \"automatic differentiation\" to automatically derive \n",
    "    # the gradients of the loss wrt all trainable parameters for us! This is \n",
    "    # a huge saving as models get deeper and loss functions get more complex.\n",
    "    optimizer_step = optimizer.minimize(loss)\n",
    "    \n",
    "    # Actually initialize the variables (run the op).\n",
    "    sess.run(init)\n",
    "\n",
    "    # Training cycle.\n",
    "    for iteration in range(epochs):\n",
    "            avg_cost = 0.\n",
    "            total_batch = int(X.shape[0] / batch_size)\n",
    "\n",
    "            # Loop over all batches.\n",
    "            for i in range(total_batch):\n",
    "\n",
    "                    batch_x = X[i * batch_size : (i + 1) * batch_size, :]\n",
    "                    batch_y = y[i * batch_size : (i + 1) * batch_size]\n",
    "\n",
    "                    # Run optimization op (backprop) and cost op (to get loss value).\n",
    "                    _, c = sess.run([optimizer_step, loss], feed_dict={x_tf: batch_x,\n",
    "                                                                                                                         y_tf: batch_y})\n",
    "                    # Compute average loss.\n",
    "                    avg_cost += c / total_batch\n",
    "\n",
    "            # Display logs per iteration/epoch step.\n",
    "            if iteration % report_every == 0:\n",
    "                    print \"Iteration:\", '%04d' % (iteration + 1), \"cost=\", \\\n",
    "                            \"{:.9f}\".format(avg_cost)\n",
    "\n",
    "    print \"Optimization Finished!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 374,
     "output_extras": [
      {
       "item_id": 2
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 546,
     "status": "ok",
     "timestamp": 1504357778404,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "jQt4FzSbHvKq",
    "outputId": "1332f0e0-74f1-4540-f7a0-60dd6e8e7fff"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 0001 cost= 1.100447059\n",
      "Iteration: 0011 cost= 0.918495715\n",
      "Iteration: 0021 cost= 0.852024496\n",
      "Iteration: 0031 cost= 0.822591126\n",
      "Iteration: 0041 cost= 0.807723522\n",
      "Iteration: 0051 cost= 0.799528003\n",
      "Iteration: 0061 cost= 0.794729173\n",
      "Iteration: 0071 cost= 0.791794062\n",
      "Iteration: 0081 cost= 0.789939761\n",
      "Iteration: 0091 cost= 0.788739026\n",
      "Iteration: 0101 cost= 0.787945986\n",
      "Iteration: 0111 cost= 0.787414253\n",
      "Iteration: 0121 cost= 0.787053227\n",
      "Iteration: 0131 cost= 0.786805689\n",
      "Iteration: 0141 cost= 0.786634445\n",
      "Iteration: 0151 cost= 0.786515296\n",
      "Iteration: 0161 cost= 0.786431968\n",
      "Iteration: 0171 cost= 0.786373317\n",
      "Iteration: 0181 cost= 0.786331892\n",
      "Iteration: 0191 cost= 0.786302507\n",
      "Optimization Finished!\n"
     ]
    }
   ],
   "source": [
    "# Intialize our TensorFlow Linear Model\n",
    "tf_linear_model = TFLinearModel()\n",
    "\n",
    "# Train the model for 200 epochs\n",
    "train_tf_model(tf_linear_model, 200, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ltr_n567HPEj"
   },
   "source": [
    "**NOTE**: Our final cost (0.786) matches the final cost reached in our Numpy implementation above. This is not by accident, but because we used exactly the same initial values for the parameters, the same optimizer with the same update rules on the same data. (The exact value may be different if you changed some of the HyperParameters)\n",
    "\n",
    "Notice how much less code we had to write for the TensorFlow model compared to the Numpy one earlier! TensorFlow is designed for deep learning and provides a number of common functions. In fact, it's possible to define a linear model like this in even fewer lines in TensorFlow, but we wanted to make this example as clear as possible!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1OFoR4Oz8CNF"
   },
   "source": [
    "### Visualizing the linear model's decision boundary\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 494,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 617,
     "status": "ok",
     "timestamp": 1504357803056,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "i38AYE4F8Bal",
    "outputId": "1a6a9477-b88c-44d4-8146-7a14624a2e41"
   },
   "outputs": [
    {
     "data": {
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j8ZsTFjpzlfCibGhHueXFVEvKIsuYvnNFoLY1RIVj8NZGmSEn5eFt6ag9zjUk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\nB2vdhb1/Qm+dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46955d5450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here we wrap the TensorFlow model so that it behaves more like a Numpy model \n",
    "# which the plot_decision_boundary function expects. Don't worry about \n",
    "# the details, it's just so we can visualise the decision boundary!\n",
    "\n",
    "class TFModelWrapper(object):\n",
    "    def __init__(self, model):\n",
    "        self._model = model\n",
    "    \n",
    "    def get_logits(self, x): \n",
    "        return tf.get_default_session().run(self._model.get_logits(x_tf),\n",
    "                                            feed_dict={x_tf : x,\n",
    "                                                       y_tf : np.zeros(x.shape[0])})\n",
    "    \n",
    "wrapper = TFModelWrapper(tf_linear_model)\n",
    "plot_decision_boundary(X, wrapper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GRGbrnuyrNzh"
   },
   "source": [
    "## Using a nonlinear classifier\n",
    "\n",
    "Let's replicate the nonlinear model in TensorFlow. TensorFlow saves us from writing more code as the model becomes more complex. In particular, this is because we don't have to implement the derivatives ourselves!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "LrNH71Jv31RB"
   },
   "outputs": [],
   "source": [
    "class TFNonLinearModel(object):\n",
    "    def __init__(self):\n",
    "        # Initialise the variables\n",
    "        # Tensorflow variables can be updated automatically by optimisers.\n",
    "        self.W = tf.Variable(non_linear_W_init, dtype=tf.float32)\n",
    "        self.b = tf.Variable(tf.zeros([num_hidden]), dtype=tf.float32)\n",
    "        self.W2 = tf.Variable(non_linear_W2_init, dtype=tf.float32)\n",
    "        self.b2 = tf.Variable(tf.zeros([num_classes]), dtype=tf.float32)\n",
    "\n",
    "    def predictions(self, X):\n",
    "        \"\"\"Make predictions of classes (y values) given some inputs (X).\"\"\"\n",
    "        logits = self.get_logits(X)\n",
    "\n",
    "        # Compute the class probabilities.\n",
    "        probs = tf.nn.softmax(logits)\n",
    "        \n",
    "        return probs\n",
    "    \n",
    "    def loss(self, probs, y):\n",
    "        \"\"\"Calculate the loss given model predictions and true targets.\"\"\"\n",
    "        data_loss = cross_entropy_tf(probs, y)\n",
    "        regulariser = reg_lambda * tf.nn.l2_loss(self.W) + reg_lambda * tf.nn.l2_loss(self.W2)\n",
    "        return data_loss + regulariser\n",
    "        \n",
    "    def get_logits(self, X):\n",
    "        hidden_output = self.hidden_layer(X)\n",
    "        logits = tf.add(tf.matmul(hidden_output, self.W2), self.b2)\n",
    "        return logits\n",
    "    \n",
    "    def hidden_layer(self, X):\n",
    "        linear = tf.add(tf.matmul(X, self.W), self.b)\n",
    "        return tf.nn.relu(linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 204,
     "output_extras": [
      {
       "item_id": 10
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 14955,
     "status": "ok",
     "timestamp": 1504357823271,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "RI0a_no65COO",
    "outputId": "0358b279-3689-4b7a-db8c-d440395b364f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 0001 cost= 3.430649281\n",
      "Iteration: 1001 cost= 0.246243224\n",
      "Iteration: 2001 cost= 0.246076643\n",
      "Iteration: 3001 cost= 0.245949924\n",
      "Iteration: 4001 cost= 0.245859504\n",
      "Iteration: 5001 cost= 0.245793104\n",
      "Iteration: 6001 cost= 0.245740667\n",
      "Iteration: 7001 cost= 0.245695874\n",
      "Iteration: 8001 cost= 0.245662034\n",
      "Iteration: 9001 cost= 0.245632291\n",
      "Optimization Finished!\n"
     ]
    }
   ],
   "source": [
    "# Create an instance of the TensorFlow Non Linear model\n",
    "tf_non_linear_model = TFNonLinearModel()\n",
    "\n",
    "# Train it for 10000 epochs\n",
    "train_tf_model(tf_non_linear_model, 10000, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7CKPywnwrUWo"
   },
   "source": [
    "### Visualizing the nonlinear model's decision boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 494,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 636,
     "status": "ok",
     "timestamp": 1504357828658,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "51oCM2Y_hh1b",
    "outputId": "7794e0ca-9ba5-44e5-87ff-849b67ceb03c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9OtD2EmUP0u3JUOvwU2il8CfJwzhWRrIrw74EAIDKnBr2JRy8vWq6lBqNeZxE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\nIiIishHDFxEREZGN/j9KGtxBToHxtgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4694cb20d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wrapper = TFModelWrapper(tf_non_linear_model)\n",
    "plot_decision_boundary(X, wrapper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pY8YwfFVo51Y"
   },
   "source": [
    "This decision boundary should look very similar to the one obtained earlier, which is of course the goal. Congrats!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PLcdu8psoqLY"
   },
   "source": [
    "## EXTRA: The effect of regularization on the decision boundary\n",
    "\n",
    "Change the `l2_lambda` parameter and observe the effect it has on the decision boundary. \n",
    "\n",
    "**QUESTION**: Can you explain why this happens?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "height": 3422,
     "output_extras": [
      {
       "item_id": 60
      },
      {
       "item_id": 61
      },
      {
       "item_id": 62
      },
      {
       "item_id": 63
      },
      {
       "item_id": 64
      },
      {
       "item_id": 65
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 99239,
     "status": "ok",
     "timestamp": 1504367163153,
     "user": {
      "displayName": "Stephan Gouws",
      "photoUrl": "//lh4.googleusercontent.com/-6znVyM1oxdg/AAAAAAAAAAI/AAAAAAAAABI/vEPo2Ce7Rpc/s50-c-k-no/photo.jpg",
      "userId": "102606466886131565871"
     },
     "user_tz": -60
    },
    "id": "t7WyzLseo62d",
    "outputId": "abaf5079-2c03-4156-b964-ead8db35332d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setting reg_lambda to  0.0\n",
      "Iteration: 0001 cost= 3.293793201\n",
      "Iteration: 1001 cost= 0.045659613\n",
      "Iteration: 2001 cost= 0.034318779\n",
      "Iteration: 3001 cost= 0.029046485\n",
      "Iteration: 4001 cost= 0.025907867\n",
      "Iteration: 5001 cost= 0.023753971\n",
      "Iteration: 6001 cost= 0.022159759\n",
      "Iteration: 7001 cost= 0.020927856\n",
      "Iteration: 8001 cost= 0.019980222\n",
      "Iteration: 9001 cost= 0.019212436\n",
      "Optimization Finished!\n",
      "Setting reg_lambda to  0.0001\n",
      "Iteration: 0001 cost= 3.307478905\n",
      "Iteration: 1001 cost= 0.076687112\n",
      "Iteration: 2001 cost= 0.071806177\n",
      "Iteration: 3001 cost= 0.070404142\n",
      "Iteration: 4001 cost= 0.069816492\n",
      "Iteration: 5001 cost= 0.069518209\n",
      "Iteration: 6001 cost= 0.069387846\n",
      "Iteration: 7001 cost= 0.069318637\n",
      "Iteration: 8001 cost= 0.069280162\n",
      "Iteration: 9001 cost= 0.069252878\n",
      "Optimization Finished!\n",
      "Setting reg_lambda to  0.001\n",
      "Iteration: 0001 cost= 3.430649281\n",
      "Iteration: 1001 cost= 0.246243224\n",
      "Iteration: 2001 cost= 0.246076643\n",
      "Iteration: 3001 cost= 0.245949924\n",
      "Iteration: 4001 cost= 0.245859504\n",
      "Iteration: 5001 cost= 0.245793104\n",
      "Iteration: 6001 cost= 0.245740667\n",
      "Iteration: 7001 cost= 0.245695874\n",
      "Iteration: 8001 cost= 0.245662034\n",
      "Iteration: 9001 cost= 0.245632291\n",
      "Optimization Finished!\n",
      "Setting reg_lambda to  0.1\n",
      "Iteration: 0001 cost= 16.979393005\n",
      "Iteration: 1001 cost= 1.086608529\n",
      "Iteration: 2001 cost= 1.086589098\n",
      "Iteration: 3001 cost= 1.086582422\n",
      "Iteration: 4001 cost= 1.086578965\n",
      "Iteration: 5001 cost= 1.086575508\n",
      "Iteration: 6001 cost= 1.086574912\n",
      "Iteration: 7001 cost= 1.086574316\n",
      "Iteration: 8001 cost= 1.086573124\n",
      "Iteration: 9001 cost= 1.086572766\n",
      "Optimization Finished!\n",
      "Setting reg_lambda to  1.0\n",
      "Iteration: 0001 cost= 140.149795532\n",
      "Iteration: 1001 cost= 1.098611832\n",
      "Iteration: 2001 cost= 1.098611832\n",
      "Iteration: 3001 cost= 1.098611832\n",
      "Iteration: 4001 cost= 1.098611832\n",
      "Iteration: 5001 cost= 1.098611832\n",
      "Iteration: 6001 cost= 1.098611832\n",
      "Iteration: 7001 cost= 1.098611832\n",
      "Iteration: 8001 cost= 1.098611832\n",
      "Iteration: 9001 cost= 1.098611832\n",
      "Optimization Finished!\n"
     ]
    },
    {
     "data": {
      "image/png": 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RA4BCdYVJV/tlqaYVs0TMBLlBnoj0fKDiQmJmNTTye8ZSQHNGSoWc4hQxbTXy1TYatRXZ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\nj44DZ/eh06HX14cXr2J9ZVOdmADBvg4c/Y3WrnHbi8ZD1xB6ZDDflgJ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1MnwRERFRSysp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\nLmL4IiIiInIRwxcRERGRi/4/5Qq1qXfHCZUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46a3874550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AKyOSuws4FXjff6N+m1+udAQvAHjzxQmcffmbmP7MPIyg+YY9MD/yM1w9M83w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\nvexRgech2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f46a34ba610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9OtD2EmUP0u3JUOvwU2il8CfJwzhWRrIrw74EAIDKnBr2JRy8vWq6lBqNeZxE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\nIiIishHDFxEREZGN/j9KGtxBToHxtgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f468f1618d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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q0Y+u1pU2MdR+TiVo6zgimSPGHb6stR7w+8CPgeeAO6y1zxhjfs8Y83ulh90E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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f468ef60590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5HlBfz/c/JQkB1MVzvbYKaqraCgPtaYRavDi1/fwyKyKz17WWiBX25UrbalSttUztFTQt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\nIiIiIgcxfBERERE5iOGLiIiIyEH/B4oQEn25WsGHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f468eda7b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### CHANGE ME: \n",
    "### E.g. for reg_lambda = [0., 1e-4, 1e-3, 1e-1, 1.]:\n",
    "\n",
    "for v in [0., 1e-4, 1e-3, 1e-1, 1.]:\n",
    "    print \"Setting reg_lambda to \", v\n",
    "    reg_lambda = v\n",
    "    tf_non_linear_model = TFNonLinearModel()\n",
    "    train_tf_model(tf_non_linear_model, 10000, 1000)\n",
    "    wrapper = TFModelWrapper(tf_non_linear_model)\n",
    "    plot_decision_boundary(X, wrapper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "rAIL8rWa5iuA"
   },
   "source": [
    "# More resources\n",
    "\n",
    "* TensorFlow has a great website where you can play with different toy datasets, different model and training choices, and see how that affects model performance: http://playground.tensorflow.org/\n",
    "* deeplearn.js is a library for doing deep learning directly in the browser: https://pair-code.github.io/deeplearnjs/. Have a look at the \"Model Builder\" section and play around with training a few feedforward models on MNIST.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1v3S6TszbAln"
   },
   "source": [
    "# NB: Before you go (5min)\n",
    "\n",
    "Pair up with someone else and go through the questions in \"Learning Objectives\" at the top. Take turns explaining each of these to each other, and be sure to ask the tutors if you're both unsure!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qiseJLFuzyuM"
   },
   "source": [
    "# Acknowledgements\n",
    "\n",
    "* http://cs.stanford.edu/people/karpathy/cs231nfiles/minimal_net.html \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "B2hocuTT3XvV"
   },
   "source": [
    "# Feedback\n",
    "\n",
    "Please send any bugs and comments to dli-practicals@googlegroups.com."
   ]
  }
 ],
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