{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Debugging bias-variance with learning curves\n",
    "\n",
    "![Curves](notebooks/bias-variance-learning-curves-files/curves2.jpeg?raw=true \"Curves\")\n",
    "\n",
    "In this notebook we build a couple of regression models as an excuse to explore learning and validation curves. These are powerful tools that tell us about the bias and variance in machine learning models.\n",
    "\n",
    "You can find this code in modules [here](https://github.com/arturomp/coursera-machine-learning-in-python/tree/master/mlclass-ex5-004/mlclass-ex5), along with the files used.\n",
    "\n",
    "This code was ported from Octave/Matlab to python and was part of the absolutely excellent [Machine Learning course](http://ml-class.org) by Stanford's [Andrew Ng](http://www.andrewng.org) on Coursera.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first import the appropriate libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Visualization and data\n",
    "\n",
    "We can visualize our data points describing water levels in a dam.\n",
    "\n",
    "Note that we have divided data in training (``X``, ``y``), validation (``Xval``, ``yval``) and testing (``Xtest``, ``ytest``).\n",
    "\n",
    "If you look at the [full code files](https://github.com/arturomp/coursera-machine-learning-in-python/tree/master/mlclass-ex5-004/mlclass-ex5), you can see more comments on many lines' particular functions, for this or any section going forward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uHkVk110N1lKDqjc0vhD4F2Aj8HGKkL0v8BTgXyJiW2a+u+K+PgJMAXeMiB8D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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2c8f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat = scipy.io.loadmat(\"notebooks/bias-variance-learning-curves-files/ex5data1.mat\")\n",
    "\n",
    "X = mat[\"X\"]\n",
    "y = mat[\"y\"]\n",
    "Xval = mat[\"Xval\"]\n",
    "yval = mat[\"yval\"]\n",
    "Xtest = mat[\"Xtest\"]\n",
    "ytest = mat[\"ytest\"]\n",
    "\n",
    "m = X.shape[0]\n",
    "\n",
    "plt.close()\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(X, y, 'rx', markersize=20, mew=3)\n",
    "plt.xlabel('Change in water level (x)', fontsize=15)\n",
    "plt.ylabel('Water flowing out of the dam (y)', fontsize=15)\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we implement linear regression with a regularized cost function and evaluate the cost and gradient values with fixed ``theta`` parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linearRegCostFunction(X, y, theta, lambda_val):\n",
    "    \"\"\"Compute cost and gradient for regularized linear \n",
    "    regression with multiple variables\n",
    "    \"\"\"\n",
    "    m = len(y) \n",
    "    \n",
    "    theta = np.reshape(theta, (-1,y.shape[1]))\n",
    "\n",
    "    J = ( 1./(2*m)) * np.power( (np.dot(X, theta) - y) , 2).sum() + \\\n",
    "                    ( float(lambda_val) / (2*m)) * np.power(theta[1:theta.shape[0]],2).sum()\n",
    "\n",
    "    grad                   = (1./m) * np.dot( X.T, np.dot(X,theta) - y) + ( float(lambda_val) / m )*theta\n",
    "    grad_no_regularization = (1./m) * np.dot( X.T, np.dot(X,theta) - y)\n",
    "    \n",
    "    grad[0] = grad_no_regularization[0]\n",
    "\n",
    "    return J, grad.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost should be about 303.993192, and the gradient around (-15.303016, 598.250744)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at theta = [1, 1]: 303.993192\n",
      "Gradient at theta = [1, 1]:  [-15.303016, 598.250744])\n"
     ]
    }
   ],
   "source": [
    "theta = np.array([[1] , [1]])\n",
    "X_padded = np.column_stack((np.ones((m,1)), X))\n",
    "J, grad = linearRegCostFunction(X_padded, y, theta, 1)\n",
    "print('Cost at theta = [1, 1]: {:f}'.format(J))\n",
    "print('Gradient at theta = [1, 1]:  [{:f}, {:f}])'.format(grad[0], grad[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember that regularization with the ``lambda_val`` regularization term helps prevent overfitting by penalizing the cost ``J``. As the parameters in ``theta`` increase, the penalty increases as well. Smaller parameters results in\n",
    "\n",
    "1. a simpler hypothesis\n",
    "2. a smoother function\n",
    "\n",
    "This makes overfitting more difficult! At the same time, note that if ``lambda_val`` is too large, we force our parameters close to 0 and end up with an an oversimplified, model-assumption trusting, data-ignoring, underfit hypothesis.\n",
    "\n",
    "We now fit a linear regression model with [``trainLinearReg()``](https://github.com/arturomp/coursera-machine-learning-in-python/blob/master/mlclass-ex5-004/mlclass-ex5/trainLinearReg.py):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def trainLinearReg(X, y, lambda_val):\n",
    "    \"\"\"Trains linear regression given a dataset (X, y) and a\n",
    "    regularization parameter lambda_val\"\"\"\n",
    "    \n",
    "    initial_theta = np.zeros((X.shape[1], 1))\n",
    "\n",
    "    # Short hand for cost function to be minimized\n",
    "    def costFunc(theta):\n",
    "        return linearRegCostFunction(X, y, theta, lambda_val)\n",
    "\n",
    "    maxiter = 200\n",
    "    results = minimize(costFunc, x0=initial_theta, \n",
    "                       options={'disp': True, 'maxiter':maxiter}, method=\"L-BFGS-B\", jac=True)\n",
    "\n",
    "    theta = results[\"x\"]\n",
    "\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RJQofBuYBqXxbWuF+AXyswXVJkqQCvOc98I1vjG+fOjVbKURSfSru+BgRzwV2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\nZmZ9zEm2mZmZmVkfc5JtZmZmZtbHnGSbmZmZmfU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111080b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_val = 0\n",
    "theta = trainLinearReg(X_padded, y, lambda_val)\n",
    "\n",
    "plt.close()\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(X, np.dot(np.column_stack((np.ones((m,1)), X)), theta), '-', linewidth=2)\n",
    "plt.plot(X, y, 'rx', markersize=20, mew=3)\n",
    "plt.xlabel('Change in water level (x)', fontsize=15)\n",
    "plt.ylabel('Water flowing out of the dam (y)', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's visually clear that this linear model is a bad fit to the data: the data points don't have a linear pattern. Learning curves will confirm that and make it easy to debug models where the data and fitted models are not as easy to visualize.\n",
    "\n",
    "## Learning curves as bias-variance diagnostics\n",
    "\n",
    "Learning curves plot training and validation error as a function of trainng set size. That is, as we get more data, they show how a model trained on that data fares against the same data points it trained on vs. against the validation set. \n",
    "\n",
    "Learning curves can be extremely useful in diagnosing machine learning models as they allow us to diagnose bias and variance errors.\n",
    "\n",
    "Below we graph the learning curves for the linear regression we've worked with so far:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def learningCurve(X, y, Xval, yval, lambda_val):\n",
    "    \"\"\"Generates the train and validation set errors needed \n",
    "    to plot a learning curve\"\"\"\n",
    "\n",
    "    m = len(X)\n",
    "\n",
    "    error_train = np.zeros((m, 1))\n",
    "    error_val   = np.zeros((m, 1))\n",
    "\n",
    "    for i in xrange(1,m+1):\n",
    "\n",
    "        X_train = X[:i]\n",
    "        y_train = y[:i]\n",
    "\n",
    "        theta = trainLinearReg(X_train, y_train, lambda_val)\n",
    "\n",
    "        # note that for error computation, we set lambda_val=0\n",
    "        error_train[i-1], _ = linearRegCostFunction(X_train, y_train, theta, 0)\n",
    "        error_val[i-1], _   = linearRegCostFunction(Xval   , yval   , theta, 0)\n",
    "                \n",
    "    return error_train, error_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rZ9BiAgAAgLCLy9A9tPNQdWnVRZv3btZHWz7yuxwAAADEuLgM3QmWUHqjHFpM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\nodvMzMzMrMr+H2qY8imI7qZoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f7ff10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Training Examples\tTrain Error\tValidation Error\n",
      "\n",
      "  \t1\t\t0.000000\t205.121096\n",
      "\n",
      "  \t2\t\t0.000000\t110.300366\n",
      "\n",
      "  \t3\t\t3.286595\t45.010231\n",
      "\n",
      "  \t4\t\t2.842678\t48.368911\n",
      "\n",
      "  \t5\t\t13.154049\t35.865165\n",
      "\n",
      "  \t6\t\t19.443963\t33.829962\n",
      "\n",
      "  \t7\t\t20.098522\t31.970986\n",
      "\n",
      "  \t8\t\t18.172859\t30.862446\n",
      "\n",
      "  \t9\t\t22.609405\t31.135998\n",
      "\n",
      "  \t10\t\t23.261462\t28.936207\n",
      "\n",
      "  \t11\t\t24.317250\t29.551432\n",
      "\n",
      "  \t12\t\t22.373906\t29.433818\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lambda_val = 0\n",
    "error_train, error_val = learningCurve(np.column_stack((np.ones((m,1)), X)), \n",
    "                                       y, \n",
    "                                       np.column_stack((np.ones((Xval.shape[0], 1)), Xval)), \n",
    "                                       yval, \n",
    "                                       lambda_val)\n",
    "\n",
    "plt.close()\n",
    "plt.figure(figsize=(12,8))\n",
    "\n",
    "p1, p2 = plt.plot(range(m), error_train, range(m), error_val, linewidth=2)\n",
    "plt.title('Learning curve for linear regression', fontsize=15)\n",
    "legend = plt.legend((p1, p2), ('Train', 'Validation'), numpoints=1, handlelength=0.5, fontsize=15)\n",
    "for label in legend.get_lines():\n",
    "    label.set_linewidth(3)\n",
    "plt.xlabel('Number of training examples', fontsize=15)\n",
    "plt.ylabel('Error', fontsize=15)\n",
    "plt.show()\n",
    "plt.axis([0, 13, 0, 150])\n",
    "\n",
    "print('# Training Examples\\tTrain Error\\tValidation Error\\n')\n",
    "for i in xrange(m):\n",
    "    print('  \\t{:d}\\t\\t{:f}\\t{:f}\\n'.format(i+1, float(error_train[i]), float(error_val[i])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The learning curves, which show the error or cost of the model, get close to each other with more training data. At the same time, note that the error is very high for both of them. These two observations indicate that the model has a high bias - its hypothesis is too simple to fit the data properly, and the algorithm weighs its hypothesis more than the data when making predictions.\n",
    "\n",
    "## More complex regression\n",
    "\n",
    "We need a model with more features to closer fit our data. \n",
    "\n",
    "Polynomial regression allows us to increase the complexity of the model by defining our own features. These new features define a nonlinear relationship between the training data and the output variables - an n-th degree polynomial.\n",
    "\n",
    "In our case, the new features are powers of the original features. e.g. \n",
    "\n",
    "* feature1 = waterLevel\n",
    "* feature2 = waterLevel$^{2}$\n",
    "* feature3 = waterLevel$^{3}$\n",
    "* ...\n",
    "* featureN = waterLevel$^{N}$\n",
    "\n",
    "Because we're using powers, it's important to normalize our features so that the numerical optimization works in an efficient manner (or at all).\n",
    "\n",
    "We obtain polynomial features for the training, test and validation set with the code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polyFeatures(X, p):\n",
    "    \"\"\"Maps X (1D vector) into the p-th power\"\"\"\n",
    "\n",
    "    X_poly = X\n",
    "    if p >= 2:\n",
    "        for k in xrange(1,p):\n",
    "            X_poly = np.column_stack((X_poly, np.power(X,k+1)))\n",
    "            \n",
    "    return X_poly\n",
    "\n",
    "def featureNormalize(X):\n",
    "    \"\"\"Normalizes the features in X\"\"\"\n",
    "    \n",
    "    mu = np.mean(X, axis=0)\n",
    "    X_norm = X - mu\n",
    "\n",
    "    sigma = np.std(X_norm, axis=0)\n",
    "    X_norm = X_norm/sigma\n",
    "\n",
    "    return X_norm, mu, sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normalized Training Example 1:\n",
      "  [ 1.         -0.3782437  -0.78866232  0.19032872 -0.7375913   0.32025197\n",
      " -0.6171516   0.35983501 -0.53109126]  \n"
     ]
    }
   ],
   "source": [
    "p = 8\n",
    "\n",
    "X_poly = polyFeatures(X, p)\n",
    "X_poly, mu, sigma = featureNormalize(X_poly)  \n",
    "X_poly = np.column_stack((np.ones((m,1)), X_poly))\n",
    "\n",
    "X_poly_test = polyFeatures(Xtest, p)\n",
    "X_poly_test = (X_poly_test - mu) / sigma\n",
    "X_poly_test = np.column_stack((np.ones((X_poly_test.shape[0],1)), X_poly_test)) # Add Ones\n",
    "\n",
    "X_poly_val = polyFeatures(Xval, p)\n",
    "X_poly_val = (X_poly_val - mu) / sigma\n",
    "X_poly_val = np.column_stack((np.ones((X_poly_val.shape[0],1)), X_poly_val)) # Add Ones\n",
    "\n",
    "print('Normalized Training Example 1:')\n",
    "print('  {:s}  '.format(X_poly[0, :]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that even with polynomial features, we still perform linear regression optimization on them.\n",
    "\n",
    "## Unregularized polynomial regression\n",
    "\n",
    "Below, we can see the polynomial fit on the data and its learning curves. We set ``lambda_val=0`` to graph unregularized polynomial regression for now.\n",
    "\n",
    "Note that the graph below will vary depending on the numerical optimization function you use in ``trainLinearReg()``. Here, we use [scipy.optimize.minimize](https://docs.scipy.org/doc/scipy-0.19.0/reference/generated/scipy.optimize.minimize.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plotFit(min_x, max_x, mu, sigma, theta, p, left=15, right=25):\n",
    "    \"\"\"Plots a learned polynomial regression fit over an existing figure.\n",
    "    Also works with linear regression.\n",
    "    \"\"\"\n",
    "    x = np.array(np.arange(min_x - left, max_x + right, 0.05))\n",
    "\n",
    "    X_poly = polyFeatures(x, p)\n",
    "    X_poly = (X_poly - mu) / sigma\n",
    "    X_poly = np.column_stack((np.ones((x.shape[0],1)), X_poly))\n",
    "\n",
    "    plt.plot(x, np.dot(X_poly, theta), '-', linewidth=2)\n",
    "    \n",
    "def plotPolyReg(lambda_val=1):\n",
    "    theta = trainLinearReg(X_poly, y, lambda_val)\n",
    "\n",
    "    plt.close()\n",
    "    plt.figure(figsize=(12,8))\n",
    "\n",
    "    plt.plot(X, y, 'rx', markersize=10, mew=3)\n",
    "    plotFit(min(X), max(X), mu, sigma, theta, p, right=15)\n",
    "    plt.xlabel('Change in water level (x)', fontsize=15) \n",
    "    plt.ylabel('Water flowing out of the dam (y)', fontsize=15)\n",
    "    plt.title ('Polynomial Regression Fit (lambda = {:f})'.format(lambda_val), fontsize=15)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dYqOdUMZ0PqX6m/2TkpDtweKjrGxWvd6917nuBb4+yPm/Wt3r11dxP0dJnHfuddxy1bXn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\naGwfM7Orzey9WJeZcxo78fRuJ1H3iyfM7IzoWGvM7Hkz+38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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e947a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotPolyReg(lambda_val=0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model fits the data _very_ well. Too well, perhaps. Without regularization, overfitting is somewhat evident in the graph above in how the values dramatically shoot up or down a short distance from the data (notice the scale of the y axis!).\n",
    "\n",
    "The high variance of the model makes it resemble the data it's trained on too closely, making the model generalize poorly.\n",
    "\n",
    "We can diagnose high variance with learning curves given that the validation error stays high even as we train with more data. Another indication of high variance in the learning curves is that the training error is at or close to 0  given how tightly overfit the model is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plotPolyLearningCurves(lambda_val=1.):\n",
    "\n",
    "    plt.close()\n",
    "    plt.figure(figsize=(12,8))\n",
    "\n",
    "    error_train, error_val = learningCurve(X_poly, y, X_poly_val, yval, lambda_val)\n",
    "    p1, p2 = plt.plot(range(1,m+1), error_train, range(1,m+1), error_val, linewidth=2)\n",
    "\n",
    "    plt.axis([0, 13, 0, 100])\n",
    "    legend = plt.legend((p1, p2), ('Train', 'Validation'), fontsize=15)\n",
    "    for label in legend.get_lines():\n",
    "        label.set_linewidth(3)\n",
    "    plt.title('Polynomial Regression Learning Curve (lambda = {:f})'.format(lambda_val), fontsize=15)\n",
    "    plt.xlabel('Number of training examples', fontsize=15)\n",
    "    plt.ylabel('Error', fontsize=15)\n",
    "    plt.show()\n",
    "\n",
    "    print('Polynomial Regression (lambda = {:f})\\n\\n'.format(lambda_val))\n",
    "    print('# Training Examples\\tTrain Error\\tValidation Error\\n')\n",
    "    for i in xrange(m):\n",
    "        print('  \\t{:d}\\t\\t{:f}\\t{:f}\\n'.format(i+1, float(error_train[i]), float(error_val[i])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XXc+LPiVDaeRa0tUtwJ/Ma/11D7AA+Hfgp85r49SXO/FKKvKIP+qSyCm4oWx/MB4HbjSz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9009d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial Regression (lambda = 0.000000)\n",
      "\n",
      "\n",
      "# Training Examples\tTrain Error\tValidation Error\n",
      "\n",
      "  \t1\t\t0.000000\t161.442168\n",
      "\n",
      "  \t2\t\t0.000000\t160.792306\n",
      "\n",
      "  \t3\t\t0.000000\t67.085334\n",
      "\n",
      "  \t4\t\t0.000000\t67.726856\n",
      "\n",
      "  \t5\t\t0.000000\t6.617001\n",
      "\n",
      "  \t6\t\t0.000000\t10.641948\n",
      "\n",
      "  \t7\t\t0.000000\t27.990140\n",
      "\n",
      "  \t8\t\t0.000000\t22.704612\n",
      "\n",
      "  \t9\t\t0.000258\t32.498514\n",
      "\n",
      "  \t10\t\t0.010818\t96.883940\n",
      "\n",
      "  \t11\t\t0.031219\t50.927977\n",
      "\n",
      "  \t12\t\t0.028890\t53.837921\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plotPolyLearningCurves(lambda_val=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularized polynomial regression\n",
    "\n",
    "We can try different values for ``lambda_val`` and, with the help of learning curves, see the effects of regularization on our model. We start with ``lambda_val=1``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mn+57tW+PY9endF79N/Aw8OVezh+U5Pahar+r6WV0mzY+16WUkrSmfg4+fDTi0T2M1ZCK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\nREREmoiCaxERERGRJqLgWkRERESkifwv+bILBo9XQ6oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111226e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotPolyReg(lambda_val=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the the model beyond our data doesn't have violent changes up our down. We seem to have balanced variance error - the model is no longer oversensitive to each data point - with the bias error - the model's assumption that the data has a polynomial behaviour is not too far off. \n",
    "\n",
    "Learning curves confirm that this regularized model is a decent fit. As we increase the training data size, we see lower error values for both the validation and training data. Both errors are also close to 0 (but not too much)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XKCjxiWQYMQQAgH7Nnz9fa9as0fLly9XW1qbFixf3OJHx+9//vq644gqdd955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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11131c310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial Regression (lambda = 1.000000)\n",
      "\n",
      "\n",
      "# Training Examples\tTrain Error\tValidation Error\n",
      "\n",
      "  \t1\t\t0.000000\t138.846731\n",
      "\n",
      "  \t2\t\t0.042839\t143.502495\n",
      "\n",
      "  \t3\t\t2.515217\t5.749648\n",
      "\n",
      "  \t4\t\t1.285542\t6.890110\n",
      "\n",
      "  \t5\t\t1.028307\t6.900155\n",
      "\n",
      "  \t6\t\t0.794844\t8.581363\n",
      "\n",
      "  \t7\t\t1.409964\t5.842339\n",
      "\n",
      "  \t8\t\t1.316231\t5.575941\n",
      "\n",
      "  \t9\t\t1.458736\t6.300211\n",
      "\n",
      "  \t10\t\t1.353304\t6.033562\n",
      "\n",
      "  \t11\t\t1.228546\t6.089839\n",
      "\n",
      "  \t12\t\t1.958697\t4.263453\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plotPolyLearningCurves(lambda_val=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also can go crazy with the regularization and set ``lambda_val=100``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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f/CJstVW7K1oyNY/zHRFfBg4jh+4EBPAs8F3gpE7paG2fb0mSOsyUKXDssdX7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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11154f990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotPolyReg(lambda_val=100.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model, like our initial (nonpolynomial) linear regression, has high bias - it trusts its assumptions too much and doesn't fit the data closely. As before, we see converging train and validation data errors that are both too high."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PHTrAX3+5HZFSSilPmlyrgHFN4WsICQphZ8xOYs/HJjuftlwrX9e/v02yT560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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3431d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial Regression (lambda = 100.000000)\n",
      "\n",
      "\n",
      "# Training Examples\tTrain Error\tValidation Error\n",
      "\n",
      "  \t1\t\t0.000000\t138.846777\n",
      "\n",
      "  \t2\t\t0.113986\t144.124029\n",
      "\n",
      "  \t3\t\t105.959154\t70.036422\n",
      "\n",
      "  \t4\t\t119.945285\t76.910566\n",
      "\n",
      "  \t5\t\t100.886412\t62.513581\n",
      "\n",
      "  \t6\t\t95.257984\t58.095056\n",
      "\n",
      "  \t7\t\t81.687969\t58.149081\n",
      "\n",
      "  \t8\t\t74.884577\t57.213744\n",
      "\n",
      "  \t9\t\t69.819836\t58.029974\n",
      "\n",
      "  \t10\t\t62.963981\t58.171676\n",
      "\n",
      "  \t11\t\t57.731688\t58.833223\n",
      "\n",
      "  \t12\t\t56.725813\t56.287752\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plotPolyLearningCurves(lambda_val=100.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Picking the regularization term automatically using the validation set\n",
    "\n",
    "Given how much ``lambda_val`` can change the performance of our model, we want to explore a few possible values for it and pick the best one. Doing this automatically (and visually) is even better.\n",
    "\n",
    "We explore the following range of values for ``lambda_val`` {0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10} and graph their training and validation errors. We'll then look to see which value of ``lambda_val`` has the lowest error for both trainig and validation data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def validationCurve(X, y, Xval, yval):\n",
    "    \"\"\"Generate the train and validation errors needed to\n",
    "    plot a validation curve that we can use to select lambda\"\"\"\n",
    "    lambda_vec = np.array([0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10])\n",
    "\n",
    "    error_train = np.zeros((len(lambda_vec), 1))\n",
    "    error_val = np.zeros((len(lambda_vec), 1))\n",
    "\n",
    "    for i in xrange(len(lambda_vec)):\n",
    "\n",
    "        lambda_val = lambda_vec[i]\n",
    "\n",
    "        theta = trainLinearReg(X, y, lambda_val)\n",
    "\n",
    "        # note that for error computation, we set lambda_val = 0 \n",
    "        error_train[i], _ = linearRegCostFunction(X,    y,    theta, 0)\n",
    "        error_val[i], _   = linearRegCostFunction(Xval, yval, theta, 0)\n",
    "         \n",
    "    return lambda_vec, error_train, error_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hPTXi6H891xLhGgAAfyostP3UzzwjFVcfhPy739lQPXCgu7UBga62bSGLJR0v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\nAABihHANAAAAxMj/A3mi2Faj7wYcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed9c2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda\t\tTrain Error\tValidation Error\n",
      "\n",
      " 0.000000\t0.028890\t53.837921\n",
      "\n",
      " 0.001000\t0.107976\t9.350064\n",
      "\n",
      " 0.003000\t0.166720\t15.919731\n",
      "\n",
      " 0.010000\t0.217958\t17.149315\n",
      "\n",
      " 0.030000\t0.275149\t13.216183\n",
      "\n",
      " 0.100000\t0.438656\t7.926826\n",
      "\n",
      " 0.300000\t0.868209\t4.760732\n",
      "\n",
      " 1.000000\t1.958697\t4.263453\n",
      "\n",
      " 3.000000\t4.525101\t3.832184\n",
      "\n",
      " 10.000000\t14.825780\t8.889697\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lambda_vec, error_train, error_val = validationCurve(X_poly, y, X_poly_val, yval)\n",
    "\n",
    "plt.close()\n",
    "plt.figure(figsize=(12,8))\n",
    "p1, p2 = plt.plot(lambda_vec, error_train, lambda_vec, error_val, linewidth=2)\n",
    "legend = plt.legend((p1, p2), ('Train', 'Validation'), fontsize=15)\n",
    "for label in legend.get_lines():\n",
    "    label.set_linewidth(3)\n",
    "plt.xlabel('lambda', fontsize=15)\n",
    "plt.ylabel('Error', fontsize=15)\n",
    "plt.axis([0, 10, 0, 20])\n",
    "plt.show()\n",
    "\n",
    "print('lambda\\t\\tTrain Error\\tValidation Error\\n')\n",
    "for i in xrange(len(lambda_vec)):\n",
    "    print(' {:f}\\t{:f}\\t{:f}\\n'.format(lambda_vec[i], error_train[i][0], error_val[i][0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The lowest validation error happens when ``lambda_val=3``, which is the optimal choice from the range explored.\n",
    "\n",
    "## Evaluating tuned model on test set\n",
    "\n",
    "Now that we have tuned the ``lambda_val`` value with the validation set, we can finally use it to compute the error on the test set. It should be around 3.8599."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set error: 3.572020\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lambda_val = 3\n",
    "theta = trainLinearReg(X_poly, y, lambda_val)\n",
    "\n",
    "error_test = linearRegCostFunction(X_poly_test, ytest, theta, 0)\n",
    "print('Test set error: {:f}\\n'.format(error_test[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even better! \n",
    "\n",
    "## Learning curves with randomly selected examples\n",
    "\n",
    "With such a small learning set, it often helps to plot learning curves with the average of different randomly selected data from your training and validation set.\n",
    "\n",
    "For $i$ examples, we randomply pick $i$ data points from the training set and $i$ data points from the validation set. We learn the regression parameters using the chosen training set, and then evaluate the error of those parameters with the same training set and with the chosen validation set. We repeat this many times (50 in our case) and use the averaged error as the training and validation error for $i$ examples.\n",
    "\n",
    "The graphs below show averaged learning curves with randomly picked examples for ``lambda_val=0.01`` and the previously chosen ``lambda_val=3``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plotLearningCurvesRandomEx(lambda_val=1., times=50):\n",
    "\n",
    "    error_train_rand = np.zeros((m, times))\n",
    "    error_val_rand   = np.zeros((m, times))\n",
    "\n",
    "    for i in xrange(1,m+1):\n",
    "\n",
    "        for k in xrange(times):\n",
    "\n",
    "            # choose i random training examples\n",
    "            rand_sample_train = np.random.permutation(X_poly.shape[0])\n",
    "            rand_sample_train = rand_sample_train[:i]\n",
    "\n",
    "            # choose i random validation examples\n",
    "            rand_sample_val   = np.random.permutation(X_poly_val.shape[0])\n",
    "            rand_sample_val   = rand_sample_val[:i]\n",
    "\n",
    "            # define training and validation sets for this loop\n",
    "            X_poly_train_rand = X_poly[rand_sample_train,:]\n",
    "            y_train_rand      = y[rand_sample_train]\n",
    "            X_poly_val_rand   = X_poly_val[rand_sample_val,:]\n",
    "            yval_rand         = yval[rand_sample_val]           \n",
    "\n",
    "            theta = trainLinearReg(X_poly_train_rand, y_train_rand, lambda_val)\n",
    "\n",
    "            error_train_rand[i-1,k], _ = linearRegCostFunction(X_poly_train_rand, y_train_rand, theta, 0)\n",
    "            error_val_rand[i-1,k], _   = linearRegCostFunction(X_poly_val_rand,   yval_rand,    theta, 0)\n",
    "\n",
    "\n",
    "    error_train = np.mean(error_train_rand, axis=1)\n",
    "    error_val   = np.mean(error_val_rand, axis=1)\n",
    "\n",
    "\n",
    "    plt.close()\n",
    "    plt.figure(figsize=(12,8))\n",
    "    p1, p2 = plt.plot(range(m), error_train, range(m), error_val)\n",
    "    plt.title('Polynomial Regression Learning Curve (lambda = {:f})'.format(lambda_val), fontsize=15)\n",
    "    plt.legend((p1, p2), ('Train', 'Validation'), fontsize=15)\n",
    "    for label in legend.get_lines():\n",
    "        label.set_linewidth(3)\n",
    "    plt.xlabel('Number of training examples', fontsize=15)\n",
    "    plt.ylabel('Error', fontsize=15)\n",
    "    plt.axis([0, 13, 0, 150])\n",
    "    plt.show(block=False)\n",
    "\n",
    "\n",
    "    print('# Training Examples\\tTrain Error\\tValidation Error\\n')\n",
    "    for i in xrange(m):\n",
    "        print('  \\t{:d}\\t\\t{:f}\\t{:f}\\n'.format(i+1, error_train[i], error_val[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VPz/wwAPdsGHDKqzroosucmlpae7dd9+NuK2SkhK3detW17x5c/f000+XT+/f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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11154fb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Training Examples\tTrain Error\tValidation Error\n",
      "\n",
      "  \t1\t\t0.000000\t182.877750\n",
      "\n",
      "  \t2\t\t0.003656\t85.562485\n",
      "\n",
      "  \t3\t\t0.011556\t50.394730\n",
      "\n",
      "  \t4\t\t0.033551\t37.958793\n",
      "\n",
      "  \t5\t\t0.051329\t18.224140\n",
      "\n",
      "  \t6\t\t0.057915\t15.628155\n",
      "\n",
      "  \t7\t\t0.094242\t13.797389\n",
      "\n",
      "  \t8\t\t0.122968\t20.143734\n",
      "\n",
      "  \t9\t\t0.136763\t21.369283\n",
      "\n",
      "  \t10\t\t0.171900\t16.398111\n",
      "\n",
      "  \t11\t\t0.199906\t17.246456\n",
      "\n",
      "  \t12\t\t0.217958\t15.875173\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plotLearningCurvesRandomEx(0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AArFRZb9hLxpuRMVrlatXr64zzzxTL730ku6++25J0osvvqiWLVvq6KOP9tbj\nnO6//36NHTtWK1as0Pbt2yV5CemqVavUokWLUteza9cuzZs3b6+bDc8888y9kutZs2ZpxIgRmjt3\nrjZs2LBnXUuXLi3Ttu3evVtffvmlxowZU2T4Oeeco5tvvlmzZ89W37599wzv2bPnnvdNmzZVkyZN\ntGrVqjKtsyxIrqOQnZmt4TOHBx0GAABIILFIguNp4MCBGjdunGbPnq3OnTtr8uTJuuKKK/aMv/fe\ne3XTTTfplltu0R//+Ec1bNhQH3/8sa666qo9iXZp8vLyVFBQoIyMjCLDMzIyitzQuGLFCp188sk6\n7rjj9NRTT2m//fZTjRo11KtXr6jXFbrO/Pz8Pa3ThQo/FybuhRo2LPqU7Ro1apR5nWVBch2Ftvu2\n1apfV2nrzq2qW6Nu0OEAAACUqlu3bsrIyNDEiRP1008/acuWLRowYMCe8a+88ooGDhyoESNG7Bn2\n5ZdflmkdGRkZSktLU15eXpHheXl5Reqkp0yZop07d2rSpEmqUaOGJK/Ve9OmTWXeroyMDKWnp++1\nzsI66saNG5d5mbHEDY1RqJZWTYc1OUwL1y4MOhQAAICopKWlqX///nrppZc0YcIEtWvXTllZWXvG\nb9u2TTVr1iwyz/PPP1+mdVSvXl3Z2dmaNGlSkeGvvvpqkc/bt29Xenq60tPT9wx74YUXivTuIUXX\nqlytWjV17txZL7/8cpHhL774oqpVq6auXbuWaRtijeQ6SlmZWfQYAgAAksrAgQO1evVqvfHGGxo0\naFCRcT179tSECRP0+OOPa9q0aTrvvPO0cuXKMq/jpptu0ptvvqkrr7xS06dP14033qj33nuvyDQ9\nevTQzp07ddFFF2nGjBl68MEHNXz4cDVo0KDIdIcddpjef/99TZ8+XZ9//rk2btwYcZ2jRo3S9OnT\nddlll2natGn617/+pVGjRmnIkCF7lYtUNpLrKGVn0B0fAABILl27dlWrVq0kqUhJiOQlqP3799fN\nN9+sQYMGqX79+kV69CgU3g2emRUZdvbZZ+uhhx7SG2+8oX79+mnhwoV6+umni8zTqVMnjR07Vh9/\n/LFOP/10vfLKK3rttddUv379ItMNHz5cbdu2Vf/+/XXUUUdp6tSpEdd5yimnaMKECfrkk0/Up08f\nPfroo7rhhhsixh9pe8rz9MhoWSyfnhMkM3Px3Jbp30zXPz/8p3Ivyo3bOgAAQPDMLKZPF0TyKe0c\n8MdHzNDaJKheAAAgAElEQVRpuY5Sdma2FuQt4I8NAAAAxSK5jlJmvUxVS6umnzb/FHQoAAAASFAk\n12XAY9ABAABQEpLrMuCmRgAAAJSE5LoMsjOzNT+P5BoAAACRkVyXAWUhAAAAKAnJdRm0a9pOyzcs\n147dO4IOBQAAAAmoWtABJJNa1WqpdaPW+nrd1+rUrFPQ4QAAgDho2bJlXB8ygsTXsmXLcs9Lcl1G\nWRneY9BJrgEASE0rVqwIOgQkMcpCyoi6awAAABSH5LqM6DEEAAAAxSG5LiNargEAAFAckusyOnCf\nA7Vt1zat3bo26FAAAACQYEiuy8jMlJ2ZrQV5C4IOBQAAAAmG5LocKA0BAABAJCTX5UByDQAAgEhI\nrsuB5BoAAACRkFyXQ8eMjlq0dpF2F+wOOhQAAAAkEJLrcqhXo572r7+/lm9YHnQoAAAASCAk1+VE\naQgAAADCkVyXU1ZGFsk1AAAAiiC5LidargEAABCO5LqcSK4BAAAQjuS6nFo3aq11v63TL9t/CToU\nAAAAJAiS63JKT0tXh4wO+irvq6BDAQAAQIIgua6A7AxKQwAAAPA7kusKoO4aAAAAoUiuKyA7M1vz\n80iuAQAA4CG5roCszCwtWLNABa4g6FAAAACQAEiuK6Bx7cZqUKuBVm5aGXQoAAAASAAk1xVE3TUA\nAAAKkVxXED2GAAAAoBDJdQVlZWZxUyMAAAAkkVxXGGUhAAAAKERyXUGH7nuovv/le/2267egQwEA\nAEDAKj25NrOxZrbGzOaHDPuXmS02sy/N7FUz2ydk3I1mtswf36uy4y1N9fTqOnTfQ7Uwb2HQoQAA\nACBgQbRcj5N0UtiwaZI6OOcOl7RM0o2SZGbtJfWX1E7SKZJGm5lVYqxRoTQEAAAAUgDJtXPuf5I2\nhg1717k9T2KZLam5/76PpInOud3OuRXyEu+jKivWaGVnZmtB3oKgwwAAAEDAErHmerCkKf77AyT9\nEDLuR39YQqHlGgAAAFKCJddmdrOkXc65F4KOpSwKk2vnXNChAAAAIEDVgg6gkJldJKm3pO4hg3+U\ndGDI5+b+sIhGjhy5531OTo5ycnJiGWKxMutmKs3S9POWn7V//f0rZZ0AAACoHLm5ucrNzY1qWgui\ntdXMWkl60zmX5X8+WdJ9kk5wzq0Pma69pOclHS2vHGS6pDYuQtBmFmlwpTnx2RN13bHX6eRDTg4s\nBgAAAMSfmck5F7GTjSC64psgaZaktmb2vZldLOkRSfUkTTezL8xstCQ55xZJeknSInl12EMDzaBL\nQN01AAAAAmm5joegW67//eW/9e637+q5M58LLAYAAADEX0K1XKeqrIwsWq4BAACqOJLrGGnftL2W\nbVimnfk7gw4FAAAAASG5jpHa1WurVcNW+nrd10GHAgAAgICQXMcQNzUCAABUbSTXMZSdQXINAABQ\nlZFcx1B2ZrYW5C0IOgwAAAAEhOQ6higLAQAAqNpIrmOoRYMW2rJzi9b9ti7oUAAAABAAkusYMjOv\nNGQNpSEAAABVEcl1jHFTIwAAQNVFch1j1F0DAABUXSTXMZaVmaX5eSTXAAAAVRHJdYx1zOioRWsX\nKb8gP+hQAAAAUMlIrmNsn5r7KLNuppZvWB50KAAAAKhkJNdxQN01AABA1URyHQck1wAAAFUTyXUc\nZGdmc1MjAABAFURyHQc8SAYAAKBqIrmOg4MbHaw1W9fo1x2/Bh0KAAAAKhHJdRykp6WrQ9MO+irv\nq6BDAQAAQCUiuY4TbmoEAACoekiu44TkGgAAoOohuY4TkmsAAICqh+Q6TrIysjR/zXw554IOBQAA\nAJWE5DpO9q2zr+rXrK+Vv6wMOhQAAABUEpLrOKI0BAAAoGohuY6j7AySawAAgKqE5DqOaLkGAACo\nWkiu44jkGgAAoGohuY6jQ5scqpW/rNS2XduCDgUAAACVgOQ6jmqk11Dbfdtq0dpFQYcCAACASkBy\nHWeUhgAAAFQdJNdxRo8hAAAAVQfJdZxlZ2Zrfh7JNQAAQFVAch1n2ZnZmrd6Ho9BBwAAqAJIruOs\nWb1mkqTVW1YHHAkAAADijeQ6zsyMmxoBAACqCJLrSkByDQAAUDWQXFcCbmoEAACoGkiuKwEt1wAA\nAFUDyXUlaN+0vZauX6qd+TuDDgUAAABxRHJdCepUr6OWDVpqybolQYcCAACAOCK5riTZmdlakLcg\n6DAAAAAQRyTXlYS6awAAgNRHcl1JSK4BAABSH8l1JSG5BgAASH0k15WkZYOW2rxzs9b/tj7oUAAA\nABAnJNeVxMzUMaMjNzUCAACkMJLrSpSdQWkIAABAKiO5rkTUXQMAAKQ2kutKRHINAACQ2io9uTaz\nsWa2xszmhwxrZGbTzGyJmb1jZg1Cxt1oZsvMbLGZ9arseGOpY0ZHLVy7UPkF+UGHAgAAgDgIouV6\nnKSTwobdIOld59yhkmZIulGSzKy9pP6S2kk6RdJoM7NKjDWmGtRqoIy6Gfpm4zdBhwIAAIA4qPTk\n2jn3P0kbwwb3lTTefz9e0hn++z6SJjrndjvnVkhaJumoyogzXigNAQAASF2JUnOd4ZxbI0nOudWS\nMvzhB0j6IWS6H/1hSSs7I1sL1tAdHwAAQCqqFnQAxXDlmWnkyJF73ufk5CgnJydG4cROdma2Jnw1\nIegwAAAAEKXc3Fzl5uZGNa05V648tkLMrKWkN51z2f7nxZJynHNrzKyZpJnOuXZmdoMk55y725/u\nbUkjnHOfRFimC2JbymrJuiXqPaG3vvk/6q4BAACSkZnJORfxPsCgykLMfxWaLOki//2FkiaFDB9g\nZjXM7CBJh0j6tLKCjIdDGh+i1VtWa/OOzUGHAgAAgBgLoiu+CZJmSWprZt+b2cWS7pLU08yWSOrh\nf5ZzbpGklyQtkjRF0tCkaJ4uQXpauto1aaev8r4KOhQAAADEWCBlIfGQLGUhkjR40mAdfcDR+suR\nfwk6FAAAAJRRIpaFVGl0xwcAAJCaSK4DkJ2Zrfl5JNcAAACphuQ6AFkZWZq/Zr6SpYwFAAAA0SG5\nDkDTuk1Vt3pdff/L90GHAgAAgBgiuQ4IddcAAACph+Q6ICTXAAAAqYfkOiDZmdlakLcg6DAAAAAQ\nQyTXAaHlGgAAIPWQXAfksCaH6btN32n77u1BhwIAAIAYIbkOSI30GmrTuI0WrV0UdCgAAACIEZLr\nAGVlZlEaAgAAkEJIrgOUnUHdNQAAQCohuQ4QNzUCAACkFpLrAGVnZmvemnk8Bh0AACBFkFwHaP/6\n+6vAFWjN1jVBhwIAAIAYILkOkJlRGgIAAJBCSK4Dxk2NAAAAqYPkOmC0XAMAAKQOkuuAkVwDAACk\nDpLrgHXI6KCl65dqV/6uoEMBAABABZFcB6xO9To6sMGBWrp+adChAAAAoIJIrhMApSEAAACpgeQ6\nAWRlZJFcAwAApACS6wSQnZmt+Xkk1wAAAMmO5DoBUBYCAACQGkiuE0Crhq20afsmbdi2IehQAAAA\nUAEk1wkgzdKUlZGlBWsWBB0KAAAAKoDkOkFQGgIAAJD8SK4TBMk1AABA8iO5ThD0GAIAAJD8SK4T\nRFZGlhbmLVSBKwg6FAAAAJQTyXWCaFCrgZrUaaJvN34bdCgAAAAoJ5LrBELdNQAAQHIjuU4gJNcA\nAADJjeQ6gWRlZJFcAwAAJDGS6wRCyzUAAEByI7lOIG32baOfNv+kLTu3BB0KAAAAyoHkOoFUS6um\ndk3b6au8r4IOBQAAAOVAcp1gKA0BAABIXiTXCSY7g+QaAAAgWZFcJxhargEAAJIXyXWCKUyunXNB\nhwIAAIAyIrlOME3rNlXt6rX1w68/BB0KAAAAyojkOgFlZ2Zr1g+zgg4DAAAAZURynYCu7nq1bnj3\nBm3esTnoUAAAAFAGliq1vWbmUmVbJOniSRerTrU6euzUx4IOBQAAACHMTM45izSOlusEdX+v+zVp\nySTlrsgNOhQAAABEieQ6QTWq3UhjTh2jSyZfoq07twYdDgAAAKJAWUiCO++189SkThM9ePKDQYcC\nAAAAlVwWQnKd4Nb/tl4dx3TUK39+Rce1OC7ocAAAAKo8aq6T2L519tWjpzyqwZMHa9uubUGHAwAA\ngBIkVHJtZjea2UIzm29mz5tZDTNrZGbTzGyJmb1jZg2CjrOyndX+LHXK7KQRuSOCDgUAAAAlSJjk\n2sxaSrpMUmfnXLakapIGSrpB0rvOuUMlzZB0Y3BRBufR3o/q2XnP6pNVnwQdCgAAAIqRMMm1pF8l\n7ZRU18yqSaot6UdJfSWN96cZL+mMYMILVkbdDD148oMaPHmwduzeEXQ4AAAAiCDq5NrMaprZzWbW\nKR6BOOc2SrpP0vfykupfnHPvSsp0zq3xp1ktKSMe608G53Q4R233bavb3r8t6FAAAAAQQbVoJ3TO\n7TCzmyX9Lx6BmFlrSVdLainpF0kvm9m5ksK7ACm2S5CRI0fueZ+Tk6OcnJyYxxkkM9Po3qPV6fFO\nOqv9WfrDfn8IOiQAAICUl5ubq9zc3KimLVNXfGY2U9Jk59wD5QutxGX3l9TTOXeZ//l8SV0ldZeU\n45xbY2bNJM10zrWLMH9KdsUXybPzntV9H9+nOZfNUY30GkGHAwAAUKXEsiu+v0saamZXmFlrM6tr\nZnVCXxWIc4mkrmZWy8xMUg9JiyRNlnSRP82FkiZVYB0p4fzs89V8n+a688M7gw4FAAAAIcracl0Q\n8jHijM659HIHY3a9vEQ6X9JcSZdKqi/pJUkHSlopqb9zblOEeatMy7Ukrfp1lTo/0VnvXfCesjOz\ngw4HAACgyojZExrN7CKVUPMsSc658SWNj5eqllxL0tgvxmr0Z6M1+5LZqp5ePehwAAAAqgQef56i\nnHM66bmTlNMqRzcdf1PQ4QAAAFQJMU+uzWx/ScdIaixpg6SPnXM/VSjKCqqKybUkrdy0Ukc8eYQ+\nuPgDtW/aPuhwAAAAUl4sy0LSJT0i70mKobXV+ZKelHSlc64g0rzxVlWTa0kaM2eMxs8br48Gf6T0\ntHKXvAMAACAKsewtZJSkwZJuktRK3lMUW/mfB0saWd4gUX5/OfIvql29th6YHfMeEgEAAFAGZW25\n/l7Sw865eyOMu07S/znnWsQwvqhV5ZZrSfp247c66qmjNOuSWWq7b9ugwwEAAEhZsWy5zpA0v5hx\n81WFH00etNaNWmv4n4Zr8KTByi/IDzocAACAKqmsyfVSSQOKGTdA3oNgEJArjrpCkvTYnMcCjgQA\nAKBqKmtZSH9JEyXNkPSKpDXyWqv/LKmbpAHOuZfjEGc0sVXpspBCS9cv1bFjj9Unl36igxsfHHQ4\nAAAAKSemXfGZWS95Nzb+QVJ1SbskfS5phHNuegVjLTeS69/dO+tevbXsLb13wXtKs7JenAAAAEBJ\n4vIQGTNLk9RE0rqgut8Li4fk2pdfkK/jnjlOF3a6UEO6DAk6HAAAgJQSkxsazayWme0wszMkyTlX\n4JzLS4TEGkWlp6Xrmb7P6NaZt2rlppVBhwMAAFBlRJ1cO+e2S8qTtDt+4SBW2jdtr2uPuVaXvXmZ\naNEHAACoHGUtyH1C0v+ZWfV4BIPYuv6467Vh2wY9M/eZoEMBAACoEsraW8i9kgZJcpLek9dbSOgC\nnHPu/8U0wuhjo+Y6gvlr5qvHsz009y9z1Xyf5kGHAwAAkPRidkOjmX1XyiTOOde6LMHFCsl18Ubl\njtKnP32q/w78r8wingcAAACIUlx6C0k0JNfF25m/U12e6qJrj7lWF3S6IOhwAAAAklosewuZZmY5\nMYsMlaJGeg2N6ztO1027Tj9v/jnocAAAAFJWWXsL6SIpPX7hIF7+sN8fdPkRl2vIW0PoPQQAACBO\nytpbyGRJZ8QjEMTfrSfcqmUblunFhS8GHQoAAEBKKusNjYMk3SPpY0lTtHdvIXLOTYllgNGi5jo6\nn/74qfq80Efzh8xXRt2MoMMBAABIOrHsLaS0pzE651wgZSMk19H7+/S/a8WmFXrpzy8FHQoAAEDS\niWVy3bK0aZxzgTxvm+Q6ett2bdPhTxyuO7rfobPanxV0OAAAAEmlQr2FmNkgM2sseYmznzw7ST8W\nfvaH7ZJ0biwDR3zUrl5b4/qO0xVTr9D639YHHQ4AAEDKKLXl2szyJR3jnPvU/5wuaaekLs65L0Km\nO1rSLMpCksfVb1+ttb+t1XNnPhd0KAAAAEmjov1cR5qRx/ylgNu7367Zq2brzSVvBh0KAABASihr\nV3xIIXVr1NXTfZ7WkLeGaOO2jUGHAwAAkPRIrqu4nFY56ntoX10z7ZqgQwEAAEh60SbXkYqZKXBO\nEXf3vFu5K3I1ddnUoEMBAABIatHc0FggaZOk3SGDm0QYVk1SA25oTE7vfvuuBk8arK+GfqV9au4T\ndDgAAAAJq0L9XJvZiLKszDk3qizTxwrJdcVd/ublMpmeOP2JoEMBAABIWDF7iEwiI7muuF+2/6Ks\nMVka13ecerTuEXQ4AAAACamiXfGhimhQq4GeOO0JXfrmpdqyc0vQ4QAAACQdWq6xl4veuEj1atTT\no70fDToUAACAhEPLNcrkgZMe0Otfv64PVn4QdCgAAABJheQae2lUu5HGnDpGl0y+RL/t+i3ocAAA\nAJIGZSEo1rmvnavMupm6/6T7gw4FAAAgYdBbCMpl3W/rlDUmS6/2f1XHHnhs0OEAAAAkBGquUS5N\n6jTRI6c8osGTBmvbrm1BhwMAAJDwSK5RorPbn62szCyNej+QZwMBAAAkFcpCUKq8rXnKHpOtNwe+\nqS4HdAk6HAAAgEBRFoIKyaiboQdOekAXT7pYO3bvCDocAACAhEVyjagM6DhAhzQ+RLd/cHvQoQAA\nACQsykIQtZ83/6xOj3fSO+e9o877dQ46HAAAgEBQFoKY2K/+frqn5z26eNLF2pm/M+hwAAAAEg7J\nNcrkgk4XaP/6++vu/90ddCgAAAAJh7IQlNmqX1ep8xOdNeOCGcrKzAo6HAAAgEpFWQhiqvk+zXVn\njzt18aSLtbtgd9DhAAAAJAySa5TLJZ0vUaPajXTvrHuDDgUAACBhUBaCcluxaYWOfPJIfXjxh2rX\ntF3Q4QAAAFQKykIQF60attJt3W7T4MmDlV+QH3Q4AAAAgUuo5NrMGpjZy2a22MwWmtnRZtbIzKaZ\n2RIze8fMGgQdJ3731yP/qlrVaumhTx4KOhQAAIDAJVRyLekhSVOcc+0kdZL0taQbJL3rnDtU0gxJ\nNwYYH8KkWZqePv1p3fHhHVq2flnQ4QAAAAQqYWquzWwfSXOdcweHDf9a0p+cc2vMrJmkXOfcYRHm\np+Y6QA/NfkivLn5VuRflKs0S7TcbAABA7CRLzfVBktaZ2Tgz+8LMnjSzOpIynXNrJMk5t1pSRqBR\nIqIrj75SBa5Aj336WNChAAAABKZa0AGEqCbpD5KGOec+M7MH5JWEhDdHF9s8PXLkyD3vc3JylJOT\nE/soEVGapWlsn7E67pnjdGrbU9W6UeugQwIAAIiJ3Nxc5ebmRjVtIpWFZEr62DnX2v/8R3nJ9cGS\nckLKQmb6Ndnh81MWkgDu+egeTV0+Ve9d8J7MIl4tAQAASGpJURbil378YGZt/UE9JC2UNFnSRf6w\nCyVNqvzoEK1rjrlGW3dt1ZOfPxl0KAAAAJUuYVquJcnMOkl6WlJ1Sd9KulhSuqSXJB0oaaWk/s65\nTRHmpeU6QSxau0h/+vef9Pnln6tFgxZBhwMAABBTJbVcJ1RyXREk14nljg/v0Psr39fb575NeQgA\nAEgpSVEWgtRy/bHXa91v6zTuy3FBhwIAAFBpaLlG3MxbPU8n/udEffmXL3XAPgcEHQ4AAEBM0HKN\nQHRq1knDugzT+a+fr7yteUGHAwAAEHck14irm4+/WUfsd4Q6ju6oxz97XAWuIOiQAAAA4oayEFSK\nBWsWaMhbQ7SrYJceP/Vxdd6vc9AhAQAAlAu9hSAhFLgCjf9yvG5870b179Bf/+j2DzWo1SDosAAA\nAMqEmmskhDRL08WdL9bCoQu1bdc2tR/dXhO/mih+FAEAgFRByzUCM+uHWRry1hBl1M3QY70fU9t9\n25Y+EwAAQMBouUZCOvbAY/X55Z+r9yG9dezYYzV85nBt27Ut6LAAAADKjeQagaqWVk1XH3O15v11\nnr5e97U6jumoqcumBh0WAABAuVAWgoTy9vK3dcWUK3R4s8P14MkPqvk+zYMOCQAAoAjKQpA0Tj7k\nZC0YskAdmnbQ4Y8frvtm3add+buCDgsAACAqtFwjYS1bv0zDpgzT6i2rNebUMTquxXFBhwQAAEA/\n10hezjm9vOhlXfPONTr5kJN114l3qUmdJkGHBQAAqjDKQpC0zEz9O/TXomGLVK9GPXUY3UFjvxjL\nY9QBAEBCouUaSWXuz3M15K0hSk9L15hTxyg7MzvokAAAQBVDyzVSRuf9OmvWJbN0YacLdeKzJ+ra\nd67V5h2bgw4LAABAEsk1klCapenyIy7XV0O/0vpt69V+dHu9sugVHqMOAAACR1kIkt4HKz/Q0LeG\n6sAGB+rRUx7VwY0PDjokAACQwigLQUo7oeUJmvuXuereqruOfvpo3fb+bdqxe0fQYQEAgCqIlmuk\nlO9/+V5XvX2VFuYt1OhTR+vE1icGHRIAAEgx9HONKue/S/+rK6deqa7Nu+q+Xvdp//r7Bx0SAABI\nEZSFoMo5re1pWjh0oVo3bK1Oj3fSw588rN0Fu4MOCwAApDharpHyFq9drGFThmnT9k0ac+oYHd38\n6KBDAgAASYyyEFR5zjlNWDBB10+/Xn0O7aM7e9ypRrUbBR0WAABIQpSFoMozM52bfa4WDVukdEtX\nu8faafyX4+kbGwAAxBQt16iS5vw4R0PeGqK6NepqdO/R6pDRIeiQAABAkqDlGgjT5YAu+uTST9S/\nfX/ljM/RDe/eoK07twYdFgAASHIk16iy0tPSNeyoYVowZIFW/bpK7Ue316SvJwUdFgAASGKUhQC+\nGd/N0NC3hqrtvm318CkPq1XDVkGHBAAAEhBlIUAUuh/UXfP+Ok9dm3fVkU8eqTs/vFM783cGHRYA\nAEgitFwDEXy38TtdOfVKfbPxG43uPVrdDuoWdEgAACBB0M81UA7OOU1aMklXvX2VTmh5gu7tea8y\n62UGHRYAAAgYZSFAOZiZzjjsDC0culD71dtPHcd01Og5o5VfkB90aAAAIEHRcg1E6au8rzRsyjCt\n/229but2m/od1k9mEX+0AgCAFEZZCBAjzjlNXT5Vt8y4RWam27vdrpMPOZkkGwCAKoTkGoixAleg\n1xe/rltn3qrGtRvr9u63K6dVTtBhAQCASkByDcRJfkG+JiyYoJHvj1TrRq11e7fbdXTzo4MOCwAA\nxBHJNRBnu/J3adyX4/SPD/6hzs066x/d/qFOzToFHRYAAIgDkmugkmzfvV1PfPaE7vroLp3Q8gSN\nyhmlw5ocFnRYAAAghuiKD6gktarV0lVdr9LyK5erc7POOn7c8bp40sX6buN3QYcGAAAqAck1EAd1\na9TVDX+8QcuuXKYW+7TQkU8dqaFvDdVPm38KOjQAABBHJNdAHDWs1VCjuo3SkiuWqG71uuo4uqOu\nfedard26NujQAABAHJBcA5WgSZ0muqfXPVo4dKF25O/QYY8dpltm3KJN2zcFHRoAAIghkmugEu1X\nfz892vtRfXH5F/p5889q80gb/fODf2rLzi1BhwYAAGKA5BoIQMuGLTW271h9NPgjLVy7UIc8fIge\n+PgBbdu1LejQAABABdAVH5AAFqxZoFtn3qrPfvpMt5xwiwZ3Hqwa6TWCDgsAAERAP9dAkpjz4xzd\nOvNWLV2/VCP+NELnZZ+n9LT0oMMCAAAhSK6BJPPByg90y4xbtPa3tRqVM0pntz9baUYVFwAAiYDk\nGkhCzjlN/3a6bp5xs3bl79Lt3W/XqW1OlVnEv2UAAFBJSK6BJOac0+Qlk3XrzFtVt0Zd3d7tdnU/\nqDtJNgAAAUmq5NrM0iR9JmmVc66PmTWS9KKklpJWSOrvnPslwnwk10hpBa5ALy18ScNnDtcB+xyg\nf3b/p4498NigwwIAoMopKblOxCLOqyQtCvl8g6R3nXOHSpoh6cZAogIClmZpGtBxgBYNW6Tzs8/X\noFcHqffzvfXFz18EHRoAAPAlVHJtZs0l9Zb0dMjgvpLG++/HSzqjsuMCEkm1tGoa3HmwllyxRKe2\nOVWnv3C6zn7pbC3MWxh0aAAAVHkJlVxLekDS9ZJC6zsynXNrJMk5t1pSRhCBAYmmZrWaGnbUMC27\ncpm6Nu+q7s921/mvn69vNnwTdGgAAFRZ1YIOoJCZnSppjXPuSzPLKWHSYgurR44cued9Tk6OcnJK\nWgyQGupUr6Prjr1Olx9xuR6a/ZCOfvpondnuTN16wq06sMGBQYcHAEDSy83NVW5ublTTJswNjWZ2\nh6TzJO2WVFtSfUmvSzpSUo5zbo2ZNZM00znXLsL83NAISNqwbYPu+egePfnFkzov6zzddPxNyqyX\nGXRYAACkjKS4odE5d5NzroVzrrWkAZJmOOfOl/SmpIv8yS6UNCmgEIGk0Lh2Y9154p1aNHSRzEzt\nR7fXDe/eoA3bNgQdGgAAKS9hkusS3CWpp5ktkdTD/wygFJn1MvXgyQ/qy798qY3bNqrtI2112/u3\n6dcdvwYdGgAAKSthykIqirIQoGTfbPhGo94fpXe+eUfXHXOdhh01THWq1wk6LAAAkk5SlIUAiK+D\nGx+sZ/s9q5kXztSnP32qQx4+RE9+/qT4UQoAQOzQcg1UUV/8/IUunXypOjfrrDGnjVGN9BpBhwQA\nQFJIqseflxfJNVB2W3Zu0bmvnavNOzbr1f6vqlHtRkGHBABAwqMsBEBE9WrU02v9X1PnZp3VdWxX\nLd+wPOiQAABIaiTXQBWXnpau+066T9d0vUZ/fOaP+nDlh0GHBABA0qIsBMAe076ZpvNeO0/3n3S/\nzmJ39QsAACAASURBVMs+L+hwAABISNRcA4jawryFOu2F03R+9vkalTNKZhH/7wAAoMoiuQZQJmu2\nrNEZL56hVg1baVzfcapVrVbQIQEAkDC4oRFAmWTWy9SMC2bIOafu47srb2te0CEBAJAUSK4BRFS7\nem1NOGuCehzUQ12f7qpFaxcFHRIAAAmPshAApXp23rO6btp1ev7M59Xz4J5BhwMAQKCouQZQYR+s\n/ED9X+6v27rdpsuPuDzocAAACAzJNYCYWLZ+mU574TSd3vZ03X3i3UpPSw86JAAAKh3JNYCY2bBt\ng8566Sw1qNlAz5/5vOrWqBt0SAAAVCp6CwEQM41rN9Y75/3/9u48Pqry/Pv450oyWcgGEYKCirRo\nVeyqFgQRqIp1ty4VWx9rrcVH9GdrixtWQWitIG2fX6v9VVHRX1UqiK3di4i4bxVRQISKiKVAwppA\nFrLM/fxxn5DJMNkwyZlJvu/X67zmnDNnuc6cE7jmnuvc5x/0yenDSQ+fxH/K/xN2SCIiIklDybWI\ntFtmeiYPnfMQFx19ESc8eAJvb3o77JBERESSgspCROQTmb9yPhP/OpGHznmIsz9zdtjhiIiIdLqW\nykIyujoYEeleLhp6EYcWHsr5885n7Y61fG/Y9/TIdBER6bHUci0iHWL9zvWcNfcsRh06il+e/ksy\n0vTdXUREuif1FiIiXaJ8TzkXP3kxURdl3oXzKMwuDDskERGRDqfeQkSkSxRkFfCnS/7EkD5DGPnQ\nSD7a+VHYIYmIiHQpJdci0qEy0jK454x7mHDsBEY8OILXNrwWdkgiIiJdRmUhItJp/rzmz3z76W9z\nz+n3cPExF4cdjoiISIdQzbWIhGbZ5mWcM/ccrjr2KiaPmqyeREREJOUpuRaRUG3ctZFz5p7DMcXH\ncN9Z95GVkRV2SCIiIvtNNzSKSKgG5A/g+cufp2xPGeMeHce2ym1hhyQiItIplFyLSJfIzcxlwdcX\nMGzgMIY/OJw129aEHZKIiEiHU3ItIl0mzdKYeepMbhxxIyfNOYnnP3o+7JBEREQ6lGquRSQUiz5c\nxDcWfIOZp87k8i9cHnY4IiIibaYbGkUkKa3asoqz5p7F+KHjmf6V6aSZfkwTEZHkp+RaRJLWloot\nnPfEeQzMH8gj5z1CTiQn7JBERERapN5CRCRp9cvtx7OXPUtGWgZjHxlLye6SsEMSERHZb0quRSR0\n2RnZPHb+Y3x1yFcZ9sAwVpSuCDskERGR/aKyEBFJKo+9+xjX/+N6fvu133LakNPCDkdERGQfqrkW\nkZTy0scvceG8C5kyegpXH3912OGIiIg0oeRaRFLO2u1rOfPxMzl9yOnMGjeL9LT0sEMSEREBlFyL\nSIraUbWDC+dfSK9IL+ZeMJe8zLywQxIREVFvISKSmvrk9OHv3/w7/XP7M2rOKDaUbwg7JBERkRYp\nuRaRpBZJjzD77NlccswlDH9gOG9tfCvskERERJqlshARSRlPrXqKq/58FbPPns15R54XdjgiItJD\ntVQWktHVwYiI7K/zjzqfQwoO4bwnzmPt9rX84IQfYJbw3zYREZFQqOVaRFLOx2Ufc9bjZzH84OHc\ne8a9RNIjYYckIiI9iHoLEZFuZ9eeXYxfMJ6a+hrmXzSf3tm9ww5JRER6CPUWIiLdTn5WPk+Pf5qj\n+h7FiAdH8OGOD8MOSURERMm1iKSujLQMfnn6L5l4/ERGPjSSp1Y9hX7BEhGRMKksRES6hcXrFjNp\n4STMjGljpnHG4WfoZkcREekUqrkWkR4h6qL84f0/cPtzt5OXmcf0sdM55VOnKMkWEZEOpeRaRHqU\nqIsyb+U8pi6ZSnFuMdPHTmf0YaPDDktERLoJJdci0iPVRet4fPnj3PH8HQzuPZjpY6dzwiEnhB2W\niIikOCXXItKj1dbX8sg7jzD9hekM7TeUaWOncdyA48IOS0REUlRKdMVnZgeb2WIzW2lmy83sumB+\nHzNbaGarzewfZlYYdqwikloi6RGu/NKVrLl2DWcdcRbn/u5czvvdebxb8m7YoYmISDeTNC3XZnYg\ncKBzbpmZ5QFvAecC3wa2OedmmtlNQB/n3M0J1lfLtYi0SVVtFb/552+Y8fIMThp0ElPHTOXofkeH\nHZaIiKSIlCwLMbM/APcEw2jnXEmQgC9xzh2ZYHkl1yLSLhU1Fdz75r3MemUW4z49jimjp3D4AYeH\nHZaIiCS5lCgLiWVmhwFfAF4D+jvnSgCcc5uB4vAiE5HuJDczlxtH3sgH133AkX2PZMRDI7ji6StY\nt2Nd2KGJiEiKygg7gHhBSciTwPecc7vNLL45utnm6alTp+4dHzNmDGPGjOmMEEWkmynIKuBHJ/2I\na46/hp+/+nOOm30cFx19EbeOupVDCg8JOzwREQnZkiVLWLJkSZuWTaqyEDPLAP4M/M0599/BvFXA\nmJiykOecc0clWFdlISLSIbZWbuXul+9m9tLZXPq5S7nlxFs4KP+gsMMSEZEkkUplIQ8B7zUk1oE/\nApcH498Cnu7qoESkZ+nbqy8zTp3BqmtWkZGWwTH/cwyTFk5iS8WWsEMTEZEklzQt12Y2EngBWI4v\n/XDAZOANYB5wCLAe+LpzbmeC9dVyLSKdYuOujdz54p3MXTGXq469ikkjJlGUUxR2WCIiEpKU7C2k\nvZRci0hnW79zPT9+4cf8/v3fc+2Xr+X64ddTmK2u90VEeppUKgsREUlag3oPYvY5s3n9ytdZt3Md\nQ341hDtfvJPdNbvDDk1ERJKEWq5FRPbT+1vfZ9rz03h23bPcMOIGJh4/kV6RXmGHJSIinUxlISIi\nnWhF6QqmLJnCq/9+lZtPvJkJx04gOyM77LBERKSTKLkWEekCb296m9uX3M6yzcu4ddStXPHFK8hM\nzww7LBER6WBKrkVEutDrG17n9iW3s2bbGm476TYu+/xlZKQl3TO7RERkPym5FhEJwUsfv8Rtz93G\nhvINTBk9hUuOuYT0tPSwwxIRkU9IybWISIgWr1vMbc/dxo6qHdwx5g4uOPoC0kydNYmIpCol1yIi\nIXPO8Y+1/+C2526jpr6GO8bcwbmfORezhP82i4hIElNyLSKSJJxz/GnNn7j9udvJSMtg2thpnD7k\ndCXZIiIpRMm1iEiSibooT616iilLplCYVci0sdM4efDJSrJFRFKAkmsRkSRVH63niZVPMHXJVAbk\nD2D62OmMGjQq7LBERKQFSq5FRJJcXbSOR999lGnPT2NI0RCmj53OsIOHhR2WiIgkoORaRCRF1NbX\nMmfZHKa/MJ3hBw/npyf/lCFFQ8IOS0REYrSUXKsvKBGRJBJJjzDh2AmsvnY1Xzzwiwx/YDjf//v3\n2Va5LezQRESkDZRci4gkoV6RXkweNZn3rnmP2vpajrz3SO5++W6q66rDDk1ERFqgshARkRSweutq\nblp0E8s2L+POk+9k/DHj9SAaEZGQqOZaRKSbeGH9C0xaOImoizJr3CzGHDYm7JBERHocJdciIt1I\n1EWZt3Ietzx7C58t/iwzTpnBUf2OCjssEZEeQzc0ioh0I2mWxvhjxvP+Ne8zetBoTnr4JK7+89WU\n7C4JOzQRkR5PybWISIrKysjihyN+yOprV5MTyWHor4fy4xd+TGVtZdihiYj0WEquRURSXFFOET8/\n7ee8fuXrLC9dzhG/OoI5b8+hPlofdmgiIj2Oaq6lUzkHlZXQqxdYwsokEelor214jUkLJ1G+p5xZ\n42Yx7tPjwg5JRKRb0Q2N0mVqa2HZMnj5ZXjlFf+6bZtPrA88EA46qPE10XhxMWRkhH0UIqnPOccf\n3v8DNy26icF9BnP3qXfzuf6fCzssEZFuQcm1dJodO+DVVxuT6X/+EwYPhhEjYORIPwwe7FuvN2+G\nTZsaX2PHG163bYMDDmhbIp6bG/bRiyS/2vpa7nvrPqa/MJ0zDz+T6WOnM7BgYNhhiYikNCXX0iGc\ng7VrfSLdkEyvXw9f/nJjMj18OPTuvf/7qKuDLVtaT8I3bYJIpOXku+H1gAMgTXcXSA9XVl3GXS/d\nxf1L72ficRO5ceSN5Gflhx2WiEhKUnIt+2XPHli6tGkynZnpk+iGZPrznw+njMM5KC9vOfluGN+1\nC/r3bz75bpjXvz9kZXX9sYh0pY/LPuZHi3/EMx8+w5TRU7jyS1eSkaZaLBGR9lByLW2ydWtjnfTL\nL/va6SOOaJpMH3po2FG23549UFLSehJeUgL5+c0n3w3jeXn+C0WiIT1dN25Kali6aSk3PHMDG3dt\nZMYpMzj7iLMxXbwiIm2i5Fr24RysXt2YSL/8sk8yhw9vTKaHDfPJZk8RjcL27a2XpFRW+vKV5ob0\n9OaT7/YMkUjHbKelISsL+vb1N5L26+e/OCi/6jmcc/ztg79xwzM30K9XP2aNm8VxA44LOywRkaSn\n5FqoqvI3GzYk0q++6hPnhpsOR46EoUN9Yij7zzmor285+e6Ioba2Y7ZTVeV/sdiyBUpL/ReMfv0a\nk+3WXnVTafdQF61jzttzmLJkCmMHj+UnX/kJh/U+LOywRESSlpLrHmjz5qYlHsuX++S5IZEeMQIG\nDAg7Skk2FRU+0W5Itlt7TUtrXzKekxP2EUpLdtfsZtYrs/jVG7/iO1/8DpNHTaZ39ie4Q1lEpJtS\nct3NRaOwcmXTZHrHDjjhhMZk+vjj/YNcRDqKc43JeFsS8S1bfKlLe5Jx3WAajo27NjLluSn8cc0f\nmXziZK4+/moy0zPDDktEJGkoue5mKirg9dcbk+nXXvOJSGzf0kceqe7nJLk453tuaSn5jp+Xk+Ov\n7bYk4v36+d5spOOsKF3Bjc/cyJpta7jrlLu44KgLdNOjiAhKrlPehg1Nn3j4/vu+C7yGZHrECJ9g\niHQnDd0ttrVVfOtWfzNmJOKT7MzM/R/viG20ddupkKsu+nARNzxzAzkZOcwaN4sRh4wIOyQRkVAp\nuU4xq1fDM880JtOVlU27wzv2WMjODjtKkeTinL/Rs6bGD6kwXlvre21pLhHPyfHlXDk5jUPsdEvv\ntTbd3v7poy7Ko+8+yq2Lb2XYwGHcdcpdDCka0jknU0QkySm5TgFVVbBgAdx/P3zwAZx5ZmMyffjh\nqdG6JSLt45zvtSVRAr5nD1RX+y/XVVV+iB3/pNNpafuXqGdkV/FG2v9jSc3PGJn/TS4+6Db65/dt\ncf3sbJWpiUj3ouQ6ia1cCbNnw6OP+psOr7rKJ9aRSNiRiUh31dDK/0kS923VpbzZaxof5T3B4I03\nULzuOvZUZCdcfs+expb47Gw/NIwnmtee91tbNiOjYxon6qP1bKvaRmlFKWXVZeRl5lGYXUhBVgEF\nWQV6yqVID6PkOslUVcH8+b6Vet06uOIK+M534LDDwo5MRKR9Vm9dzc3P3szSTUu58yt3cslnLyHN\nmjZTR6ONLfFVVf41djzRvPa839KyzjWffEd6VZKWX4rlleB6lVKfU0pdVgm1maXUREqpSi+l0kqo\noJRKt51eaYUUZhSTH+nNHrebqmg5FfVlVNSVk5WeTUGmT7Z75xRSmF1AYZafLswq3JuI752XYDo3\nkqsbRkVShJLrJLFihW+lfuwx//TDCRN8K3V7ax9FRJLNi+tf5IcLf0i9q2fWqbMYO3hsl8cQdVG2\nVfrW5dKKUkoqSti0q5RNZaVsKi+hpKKULRWlbK0uZVt1CXXROvpE+lOQXkx+Wn9yKaaXKyanvj9Z\ndcVEaorJqCkmvao/VPalpjpjb9LepFW/ylFZW0FltIzqaDlVrgzLLiczv4yMvHIieWWk9SojLacc\nyy7DZZXjMsuIZpRTl1FGXXo5NWll1LOHLMsn2wrolVZIbnohuZEC8iOF5Gf6BLwwu4A+OYUU5RZw\nQF4hffMK6FdQSN+8IKHPLlS3iSJdQMl1iCorG1upP/rIt1B/5zswaFDYkYmIdKyoizJv5TwmPzuZ\nocVDmXnKTI7qd9Qn2mZVbRUlFSV7E+bSilJKdgfTlTHjFaVsq9pGYVYhxbnFFOcW0z+vP8W9iptO\nN4zn9icvM69TWoobym7ik/DWht2VdZRVl1NWXUZ5TTm7anyreEVdGZX1PmmvduXUWBk1aWXUppdT\nn1FGfUY5ZJVBVvDq0kmvLSS9voBIfSGRaAFZrpAsCshJKyQnrcAn7hk+ac+P9KEg0oeCSBG9s4oo\nyCwkOyt9nx5uIpF9e71p6TVVesMR2R9KrkOwfLlPqB9/3D/MZcIEOOMMtVKLSPe3p24P9755Lz99\n6adccNQFTB0zlQPzDgR8Ar69anvTJDmmpTl+vLa+tklS3JAYJxrv26svkfSeecNKfX1Drbtj5+5q\nSsvL2LqrjG0V5WyvKGNnVTk7q8oo21NO+Z4ydteWs6u2jIq6MqrcTirddqptB9W2nVrbRSRaQKS+\nD5G6IjJqi8ioKSKtpoi0PX2w6iKoLoLKIlxlH6KVRdTvKqJ+dxG11Vl7b8ytq/P/57U1EW9r0t7a\nOvszZGU1bkM330pbKLnuIpWVMG+eT6o//rixlfrQQ0MNS0QkFNurtvOTF37Cw+88zMEFB1NaUcrW\nyq0UZBW0mCTHtjLnZ+arDrmL1Ufr2Vm9k+1V29lRvYPtVdv3DjuqgunquOlgiKRH6JPdh6KcIopy\nfEt4YWYfCjKLKIgUUZBRRF56EbnpfehlReSmFZFDEZFoPrW11qSbytjx1l6b6/Yy0bBnT8vvN3SP\n2RlDQxLf1uHgg6GoKOwrQhJRct3J3n3XJ9Rz5/ru8yZMgNNPVyu1iAjAhvINbK3cSv/c/j26dbm7\nc85RWVvZNBmPS86bS9ir6qrond17b1LeMMQm6gmnc/p0aE8t8d1jftKhtUS+tWHyZBg/vsMOTzqQ\nkutOUFEBTzzhk+r//AeuvNL3+nHIIV0WgoiISLdQW1+7N+mObw3fJxmPmd5RtYNekV6NLeXZvclM\nzySSHvGvaY2v+8xLjzQZb2m5/dlGJC2iX126MSXXHeiddxpbqU88sbGVOj2903ctIiIiMaIuyq49\nu/Ym3Durd1JTX0Ntfa1/jdbunY4db/G9aDuXb+a9umgdGWkZnyi5/+6Xvsupnz417I9ZEmgpuVbh\nQhvs3t3YSr1pk2+lfvddXwslIiIi4UiztKCLwkIO631Y2OE04ZyjNlq7X4l6w3iyHZO0jVquW/D2\n2z6hfuIJGDXKPz3xtNPUSi0iIiLSk6nluh1274bf/c4n1SUlvpV6+XIYODDsyEREREQk2anlOrB0\nqU+o582D0aN9LfW4cWqlFhEREZGm1HLdjF27/I2J998PW7f6VuoVK2DAgLAjExEREZFU1CNbrt96\nq7GVeuxY30p96qlqpRYRERGR1qnlGigvb2yl3r4dvvtdeO89OOigsCMTERERke4iLewA2srMvmpm\n75vZGjO7qS3rOAdvvukT6UGDYOFCuPNOWLvWP/VIiXXXWLJkSdghSDN0bpKXzk3y0rlJXjo3yasn\nnZuUSK7NLA24BzgNGApcYmZHNrd8eTn85jdw7LFw8cXwqU/5VuoFC3xXemkpcdTdR0/6g0o1OjfJ\nS+cmeencJC+dm+TVk85NqpSFfBn4l3NuPYCZ/Q44F3g/dqE33vBlHwsWwCmnwIwZcPLJSqZFRERE\npGukSnI9EPh3zPQGfMLdxCWX+BKQVavgwAO7LDYRERERESBFegsxswuA05xzE4LpS4EvO+eui1km\n+Q9ERERERLqFVO8t5D/AoTHTBwfz9mruAEVEREREukqqVCO/CQwxs0FmlgmMB/4YckwiIiIiIk2k\nRMu1c67ezK4FFuK/EDzonFsVclgiIiIiIk2kRM21iIiIiEgqSJWykBbtzwNmpPOZ2cFmttjMVprZ\ncjO7rvW1pCuZWZqZLTUzlVklETMrNLP5ZrYq+PsZFnZM4pnZLcE5edfMHgtKFSUEZvagmZWY2bsx\n8/qY2UIzW21m/zCzwjBj7KmaOTczg3/TlpnZAjMrCDPGzpTyyXV7HzAjXaoO+IFzbihwAnCNzk3S\n+R7wXthByD7+G/irc+4o4POAyuCSgJkNAr4LfNE59zl8aeX4cKPq0ebg/++PdTOwyDn3GWAxcEuX\nRyWQ+NwsBIY6574A/ItufG5SPrkm5gEzzrlaoOEBMxIy59xm59yyYHw3PkEYGG5U0sDMDgbOAB4I\nOxZpFLTmjHLOzQFwztU558pDDku8cqAGyDWzDKAXsDHckHou59xLwI642ecCjwTjjwDndWlQAiQ+\nN865Rc65aDD5Gr7nt26pOyTXiR4wowQuyZjZYcAXgNfDjURi/AK4AdCNF8llMLDVzOYEJTv3m1lO\n2EEJOOd2AD8DPsZ3B7vTObco3KgkTrFzrgR8Aw9QHHI8ktgVwN/CDqKzdIfkWpKcmeUBTwLfC1qw\nJWRmdiZQEvyyYMEgySED+BJwr3PuS0Al/qduCZmZfQq4HhgEDADyzOwb4UYlrVDjQZIxs1uBWufc\n42HH0lm6Q3Ld6gNmJDzBT6dPAr91zj0ddjyy10jgHDP7EJgLjDWz/w05JvE2AP92zv0zmH4Sn2xL\n+I4DXnbObXfO1QNPASNCjkmaKjGz/gBmdiBQGnI8EsPMLseXI3brL6XdIbnWA2aS20PAe865/w47\nEGnknJvsnDvUOfcp/N/MYufcZWHHJRD8pP1vMzsimHUyuuk0WawGhptZtpkZ/tzoZtNwxf/y9kfg\n8mD8W4AadcLT5NyY2VfxpYjnOOf2hBZVF0iJh8i0RA+YSV5mNhL4JrDczN7G/zw32Tn393AjE0l6\n1wGPmVkE+BD4dsjxCOCceyf4hectoB54G7g/3Kh6LjN7HBgDHGBmHwNTgLuA+WZ2BbAe+Hp4EfZc\nzZybyUAm8Iz/bsprzrmJoQXZifQQGRERERGRDtIdykJERERERJKCkmsRERERkQ6i5FpEREREpIMo\nuRYRERER6SBKrkVEREREOoiSaxERERGRDqLkWkQ6jJlNMbOomf0twXvzzWxxF8YyOojl6K7aZ3uY\n2ZFm9qKZ7TazejM7NMEykeAz/VwH73uOmb2xH+s9Z2bzOjKWnsTM1pnZzLDjEJHOlfIPkRGRpDTO\nzI51zr0VchzJ3JH/3UABcBZQCWxKsEwm/uEL64B3O3Df04Cc/VjvaqC2A+MQEel2lFyLSEfbDmwA\nbgXODzmWTmNmWZ/wEb5HAk8755a0tJt2xJPtnKtuy7LOuXVt3W7ceu/vz3oiIj2JykJEpKNFgZ8A\n55rZ0OYWMrOpZrYlwfyomU2MmV5nZneb2U1mttHMdprZz4L3zjGzlWZWZmZPmVlhgl0NNLM/BeUX\n683sqgT7HGVmS8yswsy2mtn9ZpYX8/7lQVzHB6URlcCkFo7tC2b2bLC97Wb2qJkVB+8NMrMo8Cng\nB8F2myuXKce3vj8cLFdvZoc2bMPMvmFmj5jZDuCPwfb/T1Busi3Y92IzOzYuvofN7M0Ex3eMmS0M\nPqtVZva1uPWWxJaFNJzD4HhfDY53qZmdGLdeppn9j5ntCJafaWbfDz6HFgUx/cXMyoNhnpn1j3n/\nHjMrNbO+MfMuCI7nlGD6QDN70MzWmlmlma02s+nmHy/fsE7DZ3qxmT0U7OvfZnZp8P7k4PorNbO7\n4mJs+BxGmNlbZlZlZm+b2cg2HF9r116hmT1gZv8JtrvezO5rbbsiEh4l1yLS4Zxz84F/4Vuvm12M\ntpdtjAeOBy4HZgDXm9mv8SUTk4H/C4wBfhq3ngEPAO8AXwP+AvzazM7Yu4BPgJ4BNgIXAN8DzgAe\niosV4HF8Ens68OdEgQZJ3nNAVhD3tcBoYKGZZeDLP4YDJcBjwfjERNsCvhIcw7RguRNoWj5yNz4B\nvxC4M5g3GHgUuAi4BPgYeMHMDos7Hhc3TRDP08B5+PM318wGJFgudroX8DDwG/wvFXuABWaWHRfn\nZfjz9U3gEOAHCbbXhJl9GngJXx7zTeBbwFCCLxKBG4GdwH3BOsXAr4FfO+cWBcv0BXYAPwROA2bi\nr6VfJtjtXfhr4WvAC/gvNvcCXwjW+QVwo5l9PcHn8Ntg3xcG+/trw5eqZo6vLdfeL4ARwXvjgFtI\n7nInEXHOadCgQUOHDPjkqTQY/xa+PndIMD0fWJxo2bhtRIGJMdPrgDWAxcx7HagBDo2ZNwPYFDM9\nOtjW/8RtfyHwSsz0i8CiuGXGBuseHXMsUeDaNnwGd+FLY3Jj5n05WP/iuOOa2cq2coP1LoubPyiY\n/2Qr6xuQDqwCfhQzfw7wRsx0w/F9K2ZeUXD+JsTMew6YF3cO64HRMfM+H2xrXMx2KoEfxMW2Aqhv\nJf7fBrGnx8wbAtQBp8fMGxHEeinwFP6LQU4L203Hf/GoBDLiPtMHYpbLD66z1Qmuv7kJPofY85sL\nbAPubO6ct/HaWw5c01l/sxo0aOj4QS3XItJZHgX+jW9p+6SWOOdiW+s+AD5yzn0cN69f0Doc6w9x\n008Bx5qXg28Rnm9m6Q0D8DI+WYstp3DAX9sQ6/HAQudcxd4VnXsD+Ag4sbmV9tM+8ZjZUWb2ezPb\njE/4aoEjgqElDt+K6iec2w6UAge3sl6Nc+75mOn3gteG9T6Lb8X/U9x68dOJnAz8HiDm3HwUDMfF\nxPoK8HNgNnA2/ktCVeyGgjKUleZLemrxrfRZQHwvLXtLdJxzu4AtwPMJrr+BCeLde60F5/8Z/Ber\nfbTj2luGbym/2swOT7QtEUkuSq5FpFM45+rxP79fagm6mWunnXHTNc3MM3wJwd4w8AlirFL8zdx9\ngT74Vsxf4xOahqE6WOaQuHVL2hDrQc0sV4Jvxe1ITfYT1OouxCd+1+OT+ePwPY1k77P2vhJ9pq2t\ntyt2wjnX0JtIw3oHBq/x9fX71Nsn0Be4iabnpgZf+hJ/bn6HT5ZXBMn2XmZ2Pb40ZQFwDv4L0DVx\ncTZo67UWv95ut+8NrqX46yGRtl571+K/YNwGrDazNWZ2cTPbFJEkoN5CRKQzPYSvu74pwXvVpFVx\nDgAAA6dJREFUNE2EMbPeHbx/A+JrXovxZQVb8d3ROfzP+olapTfGTbel1nVTgn0C9Af+2Yb12yM+\nnhOAAcBXnHP/aphpiW/07Cqbg9d+NE1Sm61FjrEd/0vDbPbtOWVrw0jQ4jsb/yViqJld6Zx7IGbZ\nC4H5zrnbY9Zp9mbb/ZRn+/YgU0ziLhbBfxatXnvOuTLg+8D3zewYfI35o2b2jlPvLSJJSS3XItJp\nnHM1wM+AK9i3BW8DkG9msfNP64QwvhY3fT7wlvMqgdeAzzjnliYYNu+7uVa9DpxmZrkNM8zseOAw\nfI1te9QEr21pdYbGvqsb1sPMRgT7Dsty/E2O58bNP7sN6z4LDHXOvZ3g3MSWBN0KHB7sYybws7hf\nS3KCGGJd2q6jaJu911rwK8Kp+OthH/tz7TnnVuCT63R8V44ikoTUci0ine0+fI8eI4AlMfP/jm+9\nnmO+a73B+F4/OronhNPN7MfA8/geGU7GlwY0uBFYZGYOeBJf5jAI32vDZOfcB+3c38/xD1tZaGYz\n8DfF/RTfY8lT7dmQc67WzNYBXzezlfjP650WVnkNqAAeMP8kwEPwLaMb2nkMHcY5t93MZgPTzKwO\nf4Pit/GfS2vneirwupn9Bf8ryFZ8LfcpwBzn3Atm9kV8cn2Nc269md2BT9zn4M81+Nrn/zL/VMq1\n+J5HPt2Bhwn+3PzEzPLxrdWTgAiJeyRp0Oq1Z2Yv4stCVuA/rwnAbqDdT9gUka6hlmsR6VTBjWW/\nIK77N+fcNnwr8kB88vANfA8O+2yC/U+4HXAl8KVgH2fgeyL5S0wcLwMn4et7/xffzdskfBd2bamx\nbrpD57biuwWswnfd9yt8Yj/OOVcXF1tbjuuqILZn8AlVQ9d4+6zrnCvFl0D0x99cd12wfnu/IMTG\nuL/rxa57Az7ZnYL/TDYDD+K7EWx+I760ZTj+C8N9+PKJKfhE9oOgn+qHgWcbykCCmu/LgJFm1lBX\nPQ2YC0wP9l8N/Fczcbd2LM2pCPY7Ed8zTgG+R5PYayj+b6At194r+N5c5gNP4Ov2v+qciy9ZEpEk\nYU1vgBYREel8ZrYI38Xe2LBj+aTMbAq+5bwtdeQi0s2pLERERDqVmY0BhgFL8TexXozvz/nCEMMS\nEekUSq5FRKSz7cY/9fFm/M2Z/8L3Rf37UKMSEekEKgsREREREekguqFRRERERKSDKLkWEREREekg\nSq5FRERERDqIkmsRERERkQ6i5FpEREREpIP8f7nBFC+Q5JQXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3372d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Training Examples\tTrain Error\tValidation Error\n",
      "\n",
      "  \t1\t\t0.000000\t180.185330\n",
      "\n",
      "  \t2\t\t6.905803\t83.683827\n",
      "\n",
      "  \t3\t\t10.878026\t57.439726\n",
      "\n",
      "  \t4\t\t9.213417\t46.845166\n",
      "\n",
      "  \t5\t\t8.941584\t37.880179\n",
      "\n",
      "  \t6\t\t7.488739\t23.144008\n",
      "\n",
      "  \t7\t\t7.105995\t14.287260\n",
      "\n",
      "  \t8\t\t6.479766\t4.724394\n",
      "\n",
      "  \t9\t\t5.914499\t6.231427\n",
      "\n",
      "  \t10\t\t5.302415\t5.247132\n",
      "\n",
      "  \t11\t\t4.933575\t4.045779\n",
      "\n",
      "  \t12\t\t4.525101\t3.679319\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plotLearningCurvesRandomEx(3)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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