03-SVM_Fin.ipynb 740 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this lesson we will introduce the the Support Vector Machines (SVM) classifier. We will first explain the concept behind the SVM algorithm and then explain how we can use *kernels* to generate nonlinear boundaries, how we can deal with datasets that have crossover regions and how we can implement multinomial classification.\n",
    "\n",
    "First, import the necessary libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear kernels with hard boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we will create some artificial datasets using the `sklearn` method `make_blobs`. This creates `n` blobs of data, with each point having coordinates `X` and label `y`. For two centres, we have a binary classification problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# used to generate the two-dimensional data sets for classification\n",
    "from sklearn.datasets import make_blobs \n",
    "\n",
    "# X are the features of the datasets, and y are the labels. We aim to classify the points based on these labels\n",
    "# In this case we want two sets of blobs, with 25 points in each and a standard deviation around the centres of 0.6.\n",
    "X, y  = make_blobs(n_samples=50, centers=2, random_state=0, cluster_std=0.6) \n",
    "# plot the features and colour the points based on the labels y\n",
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter'); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume first that the two clusters are clearly separated in feature space. The Support Vector Machine (SVM) classifier then creates decision boundaries between the clusters, rather than assigning a probability to a point being in a particular class as is done for Logistic Regression. For the SVM classifier all data points on either side of the decision boundary are then given a particular label. Consquently, once the training of the model is completed, the classification is simple and rapid. For a binary problem with a linear kernel (kernels will be explained later), the decision boundary will be a hyperplane, or in two-dimensional feature space a line. \n",
    "\n",
    "For our blobs data set three possible decision boundaries are shown below. There will be an infinite number of possible decision boundaries which lie between the two clusters. The binary classification of the point marked by a cross, will then depend on the particular chosen decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, 3.5)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 3.5) # create a linear array from -1 to 3.5\n",
    "# plot the features and colour the points based on the labels y\n",
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter')\n",
    "# plot a red cross at (0.6,2.1) for comparison with the possible deicision boundaries\n",
    "plt.plot([0.6], [2.1], 'x', color='red', markeredgewidth=2, markersize=10)\n",
    "# plot three lines of the form y = m*x+b, where we are looping over the values of m and b in the array\n",
    "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n",
    "    plt.plot(xfit, m*xfit+b, '-k')\n",
    "plt.xlim(-1, 3.5) # set the limits of the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For SVM the optimal decision boundary is chosen as the boundary which has the widest open region (i.e., points on the margins of the region are not included) on either side which does not include any points from the binary training sets. This region is defined by two lines or margins (hyperplanes in higher dimensions) which are parallel and equidistant from the decision boundary. The boundary can therefore be found as the solution of an optimization problem, where the width of the strip is maximized. For the three possible decision boundaries being considered, it can be seen the middle line bounded by the orange region has the largest region. However, this is not necessarily the optimal decision boundary. There are other wider regions which could be defined. The optimal region must be in contact with at least two points in one cluster and one point in the other cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, 3.5)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 3.5) # create a linear array from -1 to 3.5\n",
    "# plot the features and colour the points based on the labels y\n",
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter')\n",
    "# plot three lines of the form y = m*x+b, and plot a strip on either side of these lines of width d\n",
    "# we are now looping over the values of m, b and d in the array\n",
    "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n",
    "    yfit = m*xfit+b\n",
    "    plt.plot(xfit, yfit, '-k')\n",
    "     # fill the regions between the upper and lower limits for y\n",
    "    plt.fill_between(xfit, yfit-d, yfit+d, edgecolor='none', alpha=0.4)\n",
    "plt.xlim(-1, 3.5) # set the limits of the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now use the SVM classifier `SVC` to determine the optimal boundary for our blobs dataset. The process is the same as other `sklearn` classifiers, e.g., Logistic Regression. We instantatiate the model, then fit the data. Here we will not split the data into testing and training sets, though to test the accuracy of the model this would need to be done. The parameters that are passed to `SVC` are to use linear functions (kernels) for the classifier, which will result in linear decision boundaries, and the parameter `C` is set to a very large value, which means that we have *hard* decision regions, i.e., no training points are allowed to fall in the decision regions. We will investigate later the effect of changing these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC # import the SVM classifier from sklearn\n",
    "\n",
    "model = SVC(kernel='linear', C=1.E10) # instantatiate the model with a linear kernel and hard boundaries\n",
    "model.fit(X, y); # fit our blob data to the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a function which will be used to plot the optimal decision strip or region for an SVM classifier (SVC). This is very similar to the plotting function that was defined for Multinomial Logistic Regression.\n",
    "\n",
    "The function uses two properties of the SVC. The first of these is the `decision_function`. This is a function which is 0 on the decision boundary and -1 and 1 on the boundaries of the decision region. Therefore the decision region can be identified by plotting the contours where the `decision_function` is -1, 0 and 1. The second property which identifies the decision region is the `support_vectors`, from which the classifier gets its name. These are the training points which are on the boundary of the decision region. The fitting of the model only depends on these points. Any points that are further away from the decision boundary do not modify the fit, as they do not contribute to the width of the decision strip."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_svc_decision_function(model, ax=None, plot_support=True):\n",
    "    '''Plot the decision function for a two-dimensional SVC'''\n",
    "    if ax is None: # check if the axes are specified, if not get the parameters of the current axes\n",
    "        ax = plt.gca()\n",
    "    xlim = ax.get_xlim() # retrieve the x limits\n",
    "    ylim = ax.get_ylim() # retrieve the y limits\n",
    "    \n",
    "    x = np.linspace(xlim[0], xlim[1], 30) # create a linear array for the x range of the plot\n",
    "    y = np.linspace(ylim[0], ylim[1], 30) # create a linear array for the y range of the plot\n",
    "    X, Y = np.meshgrid(x, y) # create two-dimensional arrays X and Y which have the values of x and y\n",
    "    # ravel converts X and Y to one dimensional arrays and then we put each of them in the columns of\n",
    "    # the vector xy\n",
    "    xy = np.column_stack([X.ravel(), Y.ravel()]) \n",
    "    # calculate the values of model decision function at each point xy and then reshape to have \n",
    "    # the shape of the two-dimensional array X\n",
    "    P = model.decision_function(xy).reshape(X.shape)\n",
    "    # plot the contours corresponding to P=[-1,0,1] in two-dimensional space\n",
    "    # for P=[-1,1] use dashed line, for P=0 use a solid line\n",
    "    ax.contour(X, Y, P, colors='k', levels=[-1, 0, 1], linestyles=['--','-','--'])\n",
    "    \n",
    "    if plot_support: # if plot_support is True plot the support vectors as a circle surrounding the filled points\n",
    "        # s specifies the size of the circle, facecolor='none' specifies to not fill the circle\n",
    "        # and edgecolors='k' specifies to draw a black boundary\n",
    "        ax.scatter(model.support_vectors_[:,0],\n",
    "                   model.support_vectors_[:,1],\n",
    "                   s=300, linewidth=1, facecolor='none', edgecolors='k')\n",
    "    ax.set_xlim(xlim) # set the x limits\n",
    "    ax.set_ylim(ylim) # set the y limits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our blobs data set we now plot the output of the SVC, which is the decision boundary and the support vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter') # scatter plot of the blob data\n",
    "plot_svc_decision_function(model) # overlay the decision boundaries and support vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case the support vectors have the particular values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.44359863, 3.11530945],\n",
       "       [2.33812285, 3.43116792],\n",
       "       [2.06156753, 1.96918596]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.support_vectors_ # print the support vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the sensitivity of the SVC to the number of points used from a data set. If we take 60 and 120 samples from a dataset of 200 samples, we see that the support vectors do not change as we add further points. If we reduced the number of points used the support vectors would change, e.g., compare this example for 30 and 60 points. However, for a sufficient large number of points the near extreme values of the cluster are sampled and these then determine the decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_svm(N=10, ax=None): # set the default values of 10 points and axes are not specified\n",
    "    '''\n",
    "    Define a function which generates a blob data set and classifies the first N points\n",
    "    of this dataset using SVC with a linear kernel and hard boundaries.\n",
    "    Then plots the dataset and overlays the decision boundaries and support vectors.\n",
    "    '''\n",
    "    # generate a blobs dataset with 200 samples\n",
    "    X, y  = make_blobs(n_samples=200, centers=2, random_state=0, cluster_std=0.6)\n",
    "    \n",
    "    X = X[:N] # take the first N features\n",
    "    y = y[:N] # take the first N labels\n",
    "    model = SVC(kernel='linear', C=1.E10) # instantatiate the SVC with linear kernel and hard boundaries\n",
    "    model.fit(X, y) # fit the blobs data using SVC\n",
    "    \n",
    "    if ax is None: # check if the axes are specified, if not get the parameters of the current axes\n",
    "        ax = plt.gca()\n",
    "    ax.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter') # plot the data with labels y\n",
    "    ax.set_xlim(-1, 4) # set the x limits\n",
    "    ax.set_ylim(-1, 6) # set the y limits\n",
    "    plot_svc_decision_function(model, ax) # overlay the decision boundaries and support vectors\n",
    "    \n",
    "fig, ax = plt.subplots(1, 2, figsize=(12, 5)) # generate axes to two subplots in a figure of size (12,5) \n",
    "# zip bundles the two arrays together, loop through the axes and the values of N that we want to plot\n",
    "for axi, N in zip(ax, [60, 120]): \n",
    "    plot_svm(N, axi) # classify and plot the blobs data set for the given value of N\n",
    "    axi.set_title('N = {0}'.format(N)) # add a title which includes the current value of N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we have done so far could have been easily achieved with another linear classifier such as Logistic Regression. The power of the SVM algorithm is that *kernels* allow classification to occur with nonlinear boundaries. Kernels essentially correspond to using a different basis function for the classification, similar to what occured when we used Linear Regression to fit data to a polynomial. For a linear basis functions the kernel has the form\n",
    "\n",
    "$$ \\phi(X,Y) = X^T Y = X_1Y_1+X_2Y_2+\\cdots+X_nY_n, $$\n",
    "\n",
    "where $X$ and $Y$ are two points or vectors in decision space and each has n features. This is also known as the dot product of the two vectors. The kernel must be a scalar and be symmetric, i.e., $\\phi(X,Y) = \\phi(Y,X)$. From this it is apparent that, as for the other regression models and classifiers that have been considered, it is important to make sure the feature data is normalized.\n",
    "\n",
    "Consider the following example using the `sklearn` method `make_circles`, which creates two sets of data which lie approximately on two circles and have different labels on each circle. The scale of the inner and outer circle is determined by the parameter `factor`. If we try to use a linear classifier such as SVC, this is unable to separate the two datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.7/site-packages/sklearn/utils/deprecation.py:143: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# used to generate the two-dimensional data sets for classification\n",
    "from sklearn.datasets.samples_generator import make_circles \n",
    "# make two datasets which are approximately circles, each with 50 points, the ratio of the circles is specified\n",
    "# by factor and the amount of noise is specified by noise\n",
    "X, y  = make_circles(100, factor=0.1, noise=0.1, random_state=0) \n",
    "\n",
    "clf = SVC(kernel='linear') # instantatiate the SVC with linear kernel and the default value of C=1\n",
    "clf.fit(X, y) # fit the circle data using SVC\n",
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter') # plot the data labelled by y\n",
    "plot_svc_decision_function(clf, plot_support=False); # overlay the decision function boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we can add an extra dimension to our data which is a Gaussian function dependent on the distance from the origin in the original plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate a Guassian radial basis function, sum(1) denotes to sum of the second component\n",
    "r = np.exp(-( X**2 ).sum(1)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then plotting the data in three dimensions we can clearly identify a linear decision boundary at approximately r=0.7, which separates the two datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'r')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nzp2AVjOYm5ura3y5k9rJVh3pViLaatS7rFbrspGuTrTRaBSbzVYT0Zbvp5Wk2w7k83mOHTtGPB43dB+aIbDTiaRbD8pJGLT7Z3Z21rDdcTgcRiTcjki3lSmt8v20a5kvSVLJ82e32+nr66Ovr8/4+fz8vGF3VCgUlh1f7hSsCtJNpVLGHH4tRFuMSqSbyWSMiFYn2uJqez1odaGrVUin00YvbaFQYO3atXUNb3QSVFR+LBzlE5bHmBQSeHFyk7KBP1H24FbtuNC+52Y8mDoJ632rurLXxMQE4XCYZDJJX19f0+QVy9Gu9MLFJN1yWK1WgsEgwWAQ0K5BIpEoGV/Wi3ODg4NNaVNrBlYF6X73u98llUrxjne8o+6uA33ZX0y0Vqu1KURbaT+rAdls1mjxstls9Pf3s2vXLo4ePWq0+jQTrYp09wtTfMLyOE+K51BQ2a32cbWyhs9bniDHhfx3lCx3Wp7hTsszODhPHCMqPtnOe7iW96vXIdKcyKhY2UtRFNasWUM+n2dycpKxsTFsNpsRCTdL4/aFRrrlEEURn8+Hz+czJhX1/uxOsqBaFaTr9/uZnJys+6bKZDLMzMywsLDAkSNHmk60xeh00i0UCkQiEcLhMAD9/f3s3r3bmBiSJKljpB1Xwn3Ccd5q/QmzQq7k338lnOJXllPL/m6O89+RCGExy0f4Dz7Cf/Be+WreK1/LANUXCFeCqqo4nU5CoZAhr5jNZks0bq1Wq0HCPp+v5nvdJN3F0Puz3W53Q9tpNjrnSJaB3+9nbm6upt/Ro7iZmRksFgt9fX10dXVxxRVXtOgoNbSLdGtpQ5IkyZBLLBQK9PX1sWPHjorLrVbnXZu17T+1/oJvigeasq1ifMHyFF+3HOBT0it4m7KnKdus9F05nU4GBwcZHBwEtDFafVjj8OHDWK1Wo0+4Gi2DS5V0u7q62rKvdmJVkK7P52N+fn7Fz2WzWWZmZohEIoiiSF9fH7t27TKiuImJiZb3TFoslrpa02qBTowrtSnpvbSZTIZQKMTmzZtX7KXtdOeIU8zxd5ZH+Y54sAlHVBkp8rzH+kvmpBzvV65reHvVEKLD4VhEwnqL3pEjR0qGCyqRcLu6F1ZTpNupWBVnFAgElox0c7mckZesRLTF0HtcW3nTWCwWcrncyh9sAHpbV/mDrKqq8aAmk0kCgQDr16+vaay1lS+keqPoAjIJ8vybOMZfWB8mRX7lX2oQKvAx6yNcVxjienVtY9uq40VfrmWgDwnogjK6/KJOwi+E7oVG0EldDKuCdMvTC7lczohoAfr6+rjssstWtBnROxhaTbqtTi8UD0gUW/vMzs7i8/kYHBxk27ZtdffStgq1km6GAv+f9TH+yfIcWSSS5LEg0K6mMwmVv7P8mjul1zJEN1bqI7Vm9Ona7fZFJDw7O8vMzAzj4+MUCgW6uroMPYNWRYjtjD5N0r2I8Hq9ZLNZ/uEf/oG9e/cCLDvjvxT0pX8tv1Mr2kG6oiiSSCSYn58nFosZjhPl1j6rGSoqf9j1U/ZZplCBBfKoaETYLiioPCieYav9TiwIvEHZwj9Ir8VNbTKFrejTLbfcOXXqFAsLC8RiMY4dO2ZIK+oDG80ir9Ua6XYSOvqMMpkM3/72t/nXf/1Xzpw5QywWW7IAVA3aMbjQStLNZDJGRCtJEkNDQy1TM2sFaiGe71vHeEw8i4RKgYvf7iOj8m/iEY7aZnmicDuWGqLedkk7er1eY1hDt2HXp7eAkhHaejt3WjniXo5mkW4nTaNBh5OuIAhkMhm+9a1v8frXv54PfehDDV28labSmoFmk25xztpisdDf308wGGTdunV0d3c3bT+dAhWVj9kf5Sv2Zy60ddWLSrdKg4HymBDlQeEUr1I3VP077egsKK9V6MM+xdNbs7OzxONxTpw4gaqqJZFwtURabr/eSjSLdDttCrLuM7rjjjv42c9+Rl9fHwcPLq4kq6rKn//5n3PPPffgcrm46667uPLKK2vah9Pp5L3vfS9wYdKrkS+hHZ0FzSDdQqFgyCWqqrqoOJhIJDqq2btZkCSJH6QP8LW+/ciKTE0p1GrfxQINEa+Ewj+Lh3i5vB471a0wOkFlzGq1lujbFpPwyZMnURQFn89nkPBSTg/tTC9A83Kxl0Ske/vtt/Oe97yH2267reLPf/GLXzA+Ps74+DhPPvkk73rXu3jyySfrPtCenh7m5+eNkb960MmRrizLRnEwn8/T29vL9u3bK0YVnT6AUQt0J+DJ8BSpbJpvXTWOZFFxCjZSFFbeAFRPuMtABKyIbFB9HBVmUZZh5n+xjHGP5Ti/L2/jb+Qb8LNy5HexSbcclUh4bm7OUFJbioTbTbqXIuom3Ze97GWcOnVqyZ//+Mc/5rbbbkMQBK677jrm5uaYmpoy+hBrhd7BcCmR7nLW48uh1Zq6rYZuJDk9Pc2R9DR3b5/msXUzqAJkBAkBsCBiRahYOBMRUFGbVlJzKRYEUeR/ytfyYfl63mj9IT8Tx5f8vBWRBDm+Yfkt/2Q5yCekV/J25Yq6uxuagUZTGOU27LIsl5CwLMv4fD5SqVRLRsRbhU5LLUALc7qTk5OGLibA8PAwk5OTdZNutQMSy0F3CWglVopointpdYuYStbjy2G1km4mkyGXy7Fv3z5cLhfWNV4+MnSMuJDBiRUBWKBAAQUBARc2FiggF9GrFQERASc2XqKs5R7xeG0HoYIdC7vUXm5Q1uMLywzYeni9dze+8xHrp6RX8qD9FOkKkbaIQAbJyFJkkPgL60M8qpzh29J/aZp2Q61odv+5xWIpEZPRSTgWizE+Ps7Ro0cNWcVAIND0jqBmdny8YAppld4wjZy43+9ndna2kUNqS6RbCXpkFw6HDRX8gYGBuntp20G6zcpDFms96OaAumTmJ+yPMydkDbUvgB7VQUzIkEXChh03NtIUkFCxIeLGhgc7dxVu5SXqWl5su4tnmF6cYtBvP6H0//ekg/w49XuEevyIosjx+eO43W583gspgo34eSp/B++w/YwnhHNGqsGBSA7F2KROvAVkHhZP84hwhhvU9Q1fs3rQ6uEInYRdLhc7duzAbreXyCpKktRU48lLtV0MWki6w8PDnD171vj/iYkJQ+yjHtSjv1COdpNuKpUiHA4bFuz9/f1NsR5vlzllvaSrKArRaJTp6Wny+XxJT/VTTz1lPEw/tx7HUsaWDix4cZAgh6KqqAJ042CLGuDP5KsZVLu5Vl1jtGzdJb2el9q+TVotUBC0a+JQLfTgYJPq52mmsCKyRxngY5nr2TDjIBKfYnz+ME6n01iWl5/vRvw8WPgjAH4iHuVPrb8gi0S+QvuagEAOmR+IY9wgXxzSbbf2QiXPM52EJyYmDG1b/TO1krBJunXg1ltv5ctf/jJvetObePLJJ/F6vXWnFkBLLzQa6baje0FfQj/11FM4HI6mW7BDe8wpa32IVVVlbm7OSJsEg0E2bNiwrJ2PsMRS3KVasSPyJ4U9eAUn1zLENeqaip/fogbZl38bn7U8wc8s41gReZO8kz+TryZAmViKDViD8fLPZDKMjY0xMzPD5OQkbre7oiPwy5R1KKglaQ7QolwBcGJBBdJClYW/FqCdpFuJDPWxZL/fz8aNG0tI+LnnniOfz5dEwisJ2Vyq02jQAOm++c1v5uGHHyYajTI8PMzHPvYxw9b8ne98J7fccgv33HMPmzZtwuVy8a1vfauhAw0EAoyPL13cqAatGo7I5/OGALi+hN69e3fLJt8sFkuJhXyzUcu47sLCAtPT08RiMbq7uxkYGGDr1q1V3ej/pbCZL9ufprxDtIBCUO3iA/lrsVttK5LJWnr4gnwTX5BvquqYdehjs16vl97eXtLptDFMkEql8Hg8BINBAoEA/1t8ER+3Pk6GCy9tAa2oZj9Puq9WNta0/2aiXaRb7UhzJRJOJBLE43EOHTpELpcriYTLSbhQKJikW46777572Z8LgsBXvvKVeje/CJ2WXijupVUUpUT/Yf/+/S19AFqdXlhp+/rARjgcNjQB6onm/7iwm+/bxogIC9ixIJ5fplsQ+LvcyxBpXwGk2IxSdwROpVLEYjGOHDnC3ozEh9ft5JMjh5i15BCBLqw4sZJHYZ3aw63KlrYcayW0S2WsXhQLjG/YsKHE5eH5558nm83S3d1tkHAzByMuGdJtN/x+f8PdC42SlSzLhi5tLpejt7eXbdu2LXpLt9oRuF053WLofcTT09PIsrxI/LweBOniZ5k38n/tT/Bj6zhpQeIKuZ8P5a/jenm40dOoCks9lLoAdnd3t2ERflkiwWuObeTzrn38e/8EiAKyqHKTPMLn1JtxXsTHqV0qY81CucuDoigkk0ni8ThjY2Mkk0nsdjtdXV1GJNxp5FkvXlCkWw/Ke2mryVW2enihXZGubrs+PT3NwsICvb29bNmyZUVN3lrQr7r5bO5GPpu7ERV1yTzvxYYgCHi9XrxeL3eykc8pecbnp1HiafIzCcal3zJzfpggEAg09DKqB6vdgl0UReP6jo6OcurUKQqFApIkcfjwYdLpdEkk7HK5OkKutB6sKtJtNL1QLYqLQvPz8/j9foaHh6u2Hm816RZLOzYbqqoiSRKnTp0imUzWfO6N4GIQbr3Lzy7Rzm7vOvACo6XDBKdPn0ZRFKOHtV0N+q3+fto5aCDLslEj0FcaeiR85MgRg4T1a+x2u5c8f5N060SzIl3dGaGSALjeSzs7O2tYj1dbFCpGOyLdZm8/m80yPT3NzMwMhUKBYDDItm3bVnX01E6UDxPo2gaxWIx0Os0TTzxhRGl+v7+j869LoZ3RdHlOVxAEenp66OnpMUhYN50cHx9nYWEBj8djXOPlSPhiY9WQrs1mawrR6B0M+s2zsLBAOBwmGo3icrma0ku7WtILejFwenoaQRDo7+9nz549HDt2rCU24Z2KVjycuraB7npy1VVXlYiOi6JodEbUY0R5MdBJWrrFOff169eXkPCxY8dIpVK43W56e3sZHR1tyzFXi1VDujoarUZarVYWFhaYn59nZmYGu91OX18fV111VdNuqE4mXd07bXp6mmw2W9GkUh8WeCGg1eep36/lUou6/c7U1BSHDx/GZrMZJNzT09ORJNzJrhGVSHhhYYFMJtPCo6wPq4Z09fnpekk3n88TiUSYm5sjl8sxODi4am3Ya00v6JY+09PThmjQyMjIknq8rTSn7DS0uqVoqSV5uf1ONps1RmoTiQROp5NAIEAwGKxJl6OV6KRIdyUIgoDH42lq0bdZWDWkC+DxeEgmk3i93qo+L0mS0UsryzJ9fX2EQiEGBgbw+/0tO85WT75VW0hLp9NMT08TjUbxeDwMDAywZcuWFR/gdtiwdwKJtAPVnqvT6WTNmjXGtFw6nTa0bpPJpDEtFwwGL1q+cjWRbjE67V5bVaSrjwIvR7qyLBvW49lsllAoVNLmdOLEibZY9rTSEXi59ELxdJzVamVgYID169fX9LC0siWtUV2HVqCVx1LvubpcLlwuF8PDw8ZSubhopLdPBYNBHA5HW65nO0n3UtbtXVWku1TbmN5PGg6HSaVSBINBRkdHK0YEnaapWw/Kz0kf2pienkaSpGVt6Kvdfqsj3U5Bq4+lGRV/fans8XgWTcvpPaz5fJ7JyUmCwWDL7HRWm2uE/t120gseVhnp+nw+g3RVVWV+fp5wOMzc3Bx+v5+hoaEV+0lXi2XPSlBVlXg8zvT0NKlUilAoxKZNm1YUQK8GrY50Ow2dGOkuh/JpuWw2y/79+8nlchw8eJBcLofX6zUKc83SAFmN0Wcn3m+rjnSfe+45Qzaup6eH/v5+Nm/eXHU0YbVaW17RbCXpplIppqenSafTzMzMsGbNGrxeb1NvrlZGutVuW++yWFhYaGlva7u6F1oNu93Ohg0bDF2D+fl5YrGYoXXr8/kMEm7ECbgdpNtJK6FWYFWQ7smTJ/nud7/LXXfdxZo1a9ixYwd79+6t6wZYjTbs2WzWyNM6nU4GBgaIx+Ns3bq1afsoRqvHjJd7qJLJJFNTU8zOzhqN7tFolPHx8ZIBhGa2VV2M7oVW7qNY4QtKXR90/zO/308wGMTv91ddsGpXy1gzr5kZ6daJ3/72t4yOjvLhD6oTVjIAACAASURBVH+YaDTKjTfeWPe2VktOV5IkQ8lLVVX6+/u54oorjChlOX+6RtHqSLcc+Xye6elpwuEwXV1dDAwMsGnTJkRRxGq1GjrMuVzOiN4SiQRdXV0GCddb0b8UIt2VFMaWm5Y7duwYgiAYRTmfz7fktmRZbplcaTEu5c4FaALp3nvvvfz5n/85sizz9re/nQ996EMlPz9z5gxvfetbmZubQ5ZlPvnJT3LLLbfUtI/f/d3fBeAnP/kJx44da+h4O5l0dXGd6elpMpnMkipmOlr1QLeyT1cndN1dYmpqCkmSFr1UKsHhcBhtVaqqGvq3ekW/p6eHUChUs1PBao90a1UYK3cCLhQKxONxIpEIR44cwWq1GiRcPJm4lIB5s3EpyzpCg6QryzLvfve7uf/++xkeHubqq6/m1ltvZceOHcZn/vZv/5Y/+IM/4F3vehfPP/88t9xyS91RWqdp6i6FWkhXH1zQNR8CgQDr168vcS6ohFa2Xomi2JJrpIvpHDt2jGQy2VDxr5L+bSKRIBaLGXl/fQkdCASWfIgvlUi3EWK32Wz09/fT398PaCuKeDzOuXPnGBsbM6bl0ul0Q27c1eJStuqBBkn3P//zP9m0aRMbNmwA4E1vehM//vGPS0hXEAQSiQQA8/PzF90nrR3dC9U8ZOl0mnA4zMzMDG63u2RJXQ3qsdSpFs2OdHO5HNPT00QiEfL5PMPDw2zfvr3pxT9dGnDDhg1GHjMajXL8+HFEUSxZQhdft9XWvVCOZt8HDoeDwcFBI62TzWaJxWIkEgkOHTqE2+02XmatmJYzSXcZVLJZf/LJJ0s+89GPfpSbbrqJ//f//h8LCws88MADde8vEAg0rDTWjnaupVAoFAiHw4TDYSwWCwMDA1x55ZV13WCtlHdshvZCsei5oigMDAywZ88enn/+eXw+X8uJqDyPWax1MDY2htPpJBgMks/nWxrtNtNKfLl9tLKrwOl0MjQ0RDQaZcOGDVgsFmKxWMm0nE7CzZiWaybpdqKGRUNnVo3N+t13383tt9/O+9//fn7zm9/wR3/0Rxw8eLCui9EMecd253j0CbliZ1zd1qcRtNKcst5Cmt47PT09TSKRWDQN2Mi2G0W51kEmkyEWi5FKpfjtb39r9LUGg8EVTRNrQbWeYo2gXa4Rek63q6sLl8vF2rVrjWm54tx6d3e3QcL1aB+Yke4yqMZm/Rvf+Ab33nsvAC960YvIZrNEo1FDbakWOJ1O8vl8I4fcFui5S912pBq3iVrRyrauWredzWaZmppiZmYGj8fD4ODgkjrEF4t0y9HV1cXw8DCxWMxIj0WjUQ4dOmQ41+rE0YgLxGpMLyyFSn26xdNyurpXse1ONpulp6fHuJbVFDhN0l0GV199NePj45w8eZKhoSH++Z//me9973sln1m3bh2/+tWvuP32240vQa+a1otm3MiteBh0Z9xoNGpU5Ldt29ayYlerOwyWgyzLRCIRpqenAWpKlXQC6RZDJ47u7m7Dr0vva9VdIAKBAKFQaNmWqkq41Em3HOVi48UuwLoVe/GgRqUXmiRJTWtNu+S6F6xWK1/+8pe5+eabkWWZO+64g507d/JXf/VX7N27l1tvvZXPfvazvOMd7+Dzn/88giBw11131X0h9N9r9EbW86HNyIPlcjljcKHYGffAgQMttbi5GJGubmM0NTVFKpVasaWtEjrtIah0L+lFt0AgAGgkUNxSpVfz9SGN5c7pYgxHdNJ+KrkAF9saybJsWO7o03JmpLsCbrnllkV9t3/9139t/PeOHTt47LHHGt2NAZfLRSaTaUhjQG8bq5d0yyUj+/v7F2nz6pNvrbp5WlkQLI90iyUiu7u7Gxo97pT0Qi2wWq0lAuS69u3p06dJJBJGISkYDC4yTGxXpNsuI8xGz6X4hbZp0yZkWWZ2dtaQsdR7uB0OBz6fr+Hnp9Ne8rBKJtKKocs7NoN0a1nC1OqMq7emtWqCp9WRriRJnDt3junpaURRZGBgoGnuGp1EuvWQYrH2bXEh6ciRI2QyGSOHGQwG20K6q81+vRgWi4VQKEQoFAK0gObpp58mmUzy1FNPlZB0ramdTsWqJN25uTmGh4fr3ka1AxLFZpXxeBy/38/atWur6k1sl016M6GqKrOzs5w9e5b5+Xk8Hs8iK59G0YmRRyMoLyTpOcxYLMaBAwdIp9O43W5cLldNOge1YLXbrxfDarVitVrZvHmzUTjXZVv1aTk9H7ycj18nvdjLsSpJd3Z2tqFtrDQgkclkjMEFXQugVrPKVk++NZN09QJgLBbD6/UyMDCAKIqMjIw0ZfvF6MT0QjNfBMU5zI0bN3Ly5EkjHXHs2DHDkLJ8xLYRtIN02/mdFed07XZ7xWm5yclJnn/+eRwOR4m3XPF3qVt8dRpWHek2axS4PB9aKBQMgRlBEIxm/nojk06PdPXznZ6eNkRlRkZGsFgshqpZK9AI6YbDEI0KdHWpjIxAM3im1WSiV/OHhoYAbUgjFosZpKEPaQSDwRVHv5fCpVSsg+W7JMqn5TKZTEl+3eVyGemIZrZoNhOrknQbHZDQo9BqnHHrRaeZU8JiQZ3+/v6KgxqdFo2m0/C974k8+6yIIKioKoRCcMcdMg1kmYD2G1Pa7fYS0tBFe44fP04qlSrJB1d7H7Z6Ig061zWiq6uLoaEhhoaGDBGkeDzOiRMnWLt2bVMHXZqFVUe6gUCgoShMVVVjJPTs2bOGtU+z34qtJl2LxUKhUKjqs7rweSwWw+/3ryioc7F7gMvxve+JHDwosm6din7I8Th89asWPvxhmWq/urk5ePZZgYkJgVBI5YorWv9iWYnUdS80fbormUyWiPZUIz7ejkLaanCNKBZBGh4e7sjUAqxC0vX5fBw9erTm31tYWCAcDhONRrHZbHR1dbFjx46WfTHtiHSXI0bdoDIcDhvR1YYNG6p6ODvBOUJHOAzPPltKuACBAJw5AwcOCFx/feXtTU/DoUMCCwtgs8Gvfy2iquByqRw8KPLgg7Brl4tNmwSefVZg/34BVYU9e1R271ZpRpBUy7Jcs+Hpwe3uYXR0tER8/OTJk+fPO2CIj+vbbZd85GpzjTBJt0moJadbTDw2m81wxk0kEszMzLT0S7FaraTT6ZZtvxLpFqdLcrkc/f397N69u+YezuUIXVHg7FmBfB6GhlRqHa2vlXSjUQFRLCVcHV1dcOpUZdJ9+GGBX/5SxGpVEUV4+GERr1fl5S/XyVQll4N77+3l1CkbiYRIIKBt50c/EvnNb1Te/nal6ih6KVSbvsjn4f77Be69VySZFFi7VuV1rxO45poLoj267q1eybfb7QSDQXK5XFva0tpBus3aT6dq6cIlSLq6ulU4HDZGccuJpx2WPe0qpOnOsMUWN42mS5YixiNHRP7+721EIgKiCBYLvOENBW69Va67qJXPw/i4SDwu4POpbNmiUJxidrs1oq+EXA78/sXHeeoU3HuvyNq1KlYrhMMCXV2gKALPPgvXXqv9jsMBkYgDsJQQt9ercuaMwK9/LfCa1zQWeRU//MePw4MPipw6JeD3q9xwg8qVV2o56q98RWT/fpGBARW/XyWRgC9/2cJb3iIbx1Cue6tLLqbTaZ5++mlDaEYf0mgmGhkmqnU/l/I0GqxC0g0EAotIV+8vLXbG3bx585I3XqcJmdcD3Xxw3759iyxuGkWlCOHcOYGPf9yO06kyPKyRQD4Pd99tx2bL89rXVneuxYQ+NSXwzW/aSCS0TgRZFvB4VN761jx+f+L8i2QeRdnKmTMehoa6jAc/n9c+f+WVi0lx3z4Rl0sjXAA99d3TA5GIQDp9IUKPxWxU6owbHFR54gmRV79arhhlV4N8Hs6dsyDLFk6cEPjOd0Q8HvB6IZkUuOsugaNHtVTGgQMCIyMXInqvF7q6VP7t30Re+tLKeWtdcnFiYoIrr7zSIGFd46RYOa3RibXV5hoBZnqhadBJV4/wpqenicfj+Hy+qizYYfWSbrHFTS6XQxTFFS1umoX77rOgKODzXfg3ux0GBxV+9CMbr3qVTDXPtU66kgR33WVDVVXWrdN+JssS584t8IlPLPCOd4QZHR1k+/bt9PVl+NKXJJ5+OobDISGKXdjtXdx2m5WBgcXf9ewsJflYt1sFBAQBBEEjQ5cLVBUKBYHzw1AlsFq1zymKFtHXit/8RuC++0QmJ4M4nR6ee87C3r0qutaT3Q7d3drnpqe1/y+/be12LTo/dkxYtuindy8U27IXOwKfOXPGEO3R/9QatbYrvWCSbgciFouRzWZ59atfzac//WkGBwdrHlxoh3tEs0hXr2hPTU0xNzdnWNwIgsCJEyfaQrgAzz1nwedb/OA7HBCLwcyMwNBQdUtxVVU5flxkdhbWr9fapubn55EkiZ6ebmR5EJutj0BAKxBt29bN//2/WufB8eMKVmuCoaGTiGKUffvsxhipLqC9fr3K2bMCPT3a/vx+6O2FmRktotYJORKB/v4cVqsDKH1A43HYuFGti3D37RP40Y9EhoZUFCVPPg+SpBX9PB6V7m7tc6KoXb+zZ5uvmFfsCLxp0ybDjDIajXLs2LGanZVXI+l2KqwAgvaNCaqqti4J2SDS6TSvf/3rUVWVbDbLD3/4w7olIpvhjLASGiXdYosbl8vFwMAAW7ZsMR6ubDbb0pxxObq7Vc6dExYVzlQVZBmczpWv58ICnDrlxO22kUxmSSRkzpyZo6uri0AgYPQLp1ICs7OlJOLxwItfrPLiFwuA9/yfLWQyGYNIdHPKoaE+ZLmfVEo0luVXXaXwq1+J5/O4AooCa9eqvPWtZ3n22ctIJjHIMJXSjuEtb6n9+5NleOABLTfrcGjXR1E0chUEOH1a4LLLLlwrUYQ1a7T0gqqWRrv5PIiiyqZNK1/balZ3xWaUtTorr0bS7dhIVxCErwIvAt4AnK53Qyu5AgP8y7/8Cx/96EcRBIHLL798kfbucnC5XHz3u99lcHCQK664whDI6FTUQ7pLWdxUuglb6RxRCTfdJPPFL9rw+Uo7CSIRgZ07FZbzK1RVePRRkfvvtzAz40aSJNLpHJLk4bLL1lZ4wDE6CVZCV1cXa9euNfpc5+fniUajXHXVNPff3wu46erqwuFwcvvtCi96kUI6LeB2qwwOwpNPptizR+Kee+ycPasdq98Pt9+uMDpa+3VKJiGRwEiZqKqK36/9t9OpRdvFyGbhxhu1a6oX0pxObRuxmMAf/mH1fci1oFZnZVmW26Jk9kKJdL+tquqfNrKRalyBx8fH+cQnPsFjjz2G3+8nEonUvB99isdut5PL5ZoqxNJsVEu61VjcLLX9dka6114r8+IXi/zmNxbcbrBaVVIpgZ4elTvuWHpIQ1VVnngiwz/9k4LPl6C3V8Tj8eBy+fn3f7cyPq6wZcuF85ib0yLO4n+rFoIgGLoHmzbBLbdIPPvsPJHIBFZrlN5eC/l8kIGB0HmVOo3st26FbdtkYjGMabd665E6LymKtg1V1VrUtm1T2b//Qv5YkuDcORgZUdm5U2X7dpX771f55S9FIhGtZewtb5G5+urWD3BU46wsCALBYJDe3t6WkqIkSW1LmV0sWFVVfaLRjVTjCvy1r32Nd7/73fjPv/brsevRoYve6CRcD1rppqtvf7kURiaTYXp6uiqLm6W2307StVjgPe8pcP31Mo88YmFhQWDPHonLLpOZnBQ5e1Zg3TqVgQG9syHP9PQ04XCYn/50A2vX9tDbu47Z2VksFgsOB7zkJRIHD4o4ndrSGrSq/R//cYFmKGI6nVauuSYIBIENJdFcOp3G6/WSy+XI5/N0dXXRoKEJoBXodu1SGRuDC85VAtu3q8TjWoR99qxGyC95icprXqMYXRavfa3KLbfIFYt3yaQWJXd1wcDA4qJbM1HJWfnZZ58lnU6XyC1WclZuFJIkNW10t2PTC83YSDWuwPoU2fXXX48sy3z0ox/l1a9+dV370/UXGiFdvZjWLvFnaMziphwX44ayWGDvXoW9exVUFe6/38Kdd164fqoK27bNs2fPMWQ5x8DAADt3XsFPf+qmr089f9wXtrdmDUiSym23SczNaS1dGzcqtCrQKR651SUYo9EoBw4cACix5GmESF7zGoWJCQunT2u5YYtFJJsVuOUWhTe+USGX01INlW49QSglXEmCn/9c4Ne/1qfPtKGUt7xFofj2z+fhmWcEDh4UcLvh2mu19EgzbhOLxYLdbmdoaAifz7fIWVlX+gqFQnWL9uhoRnqhk3RDKqEppFuNK7AkSYyPj/Pwww8zMTHBS1/6Ug4ePIivuAepSuiauo2gHQMS0ByLm4uF5aZ6Dh0Sue8+K2vXKqhqgUQiQSqV4vHH/QwMbOGWWxznt6FFZ7kc56PXC326mYw23FBPKqFR6BKMDoeDa665BlmWF1m0610R5W4QK8Hng3e/W+a55wR+8Ys8IyMq116rsGWL1g1RSxT/05+KPPywwPr1F8g4GhX46lctfPCDMh6PSjJp5X//b8v5LggVWRb4wQ9Efu/3FN7yFqUpxFtcSFvKWfnEiRMkk8mSIY1a7/MXRCGtGRupxhV4eHiY6667DpvNxujoKFu3bmV8fJyrr7665v01Q1O31b266XSaXC7HU0891bDFzcWA3k+71PE+9JCIzZZgenrOkC9ct24d/f0C+/YJ3HxzHotFi7Re/GKZ++6znG/+133utCLcrbcu/R0oioIsyy3XRRUEYdG0VzqdJhqNcvToUSMVEQqFCAaDRs7x7FmtjS0W04h2926V9eu1c3a5tMk3UQxz+eUD2O21V/6TSXj00VLCBS3nfOYM/Pa3Atdfr/DTnw5x7JjA3JzAwoJ2nXp6VL7zHZGdO5sj7LNc94LurDw8PGz0z+vOyrlcbkUjymI0i3Q7+TlrCulW4wr8hje8gbvvvpvbb7/duJn1HHCtaJambrNJV5IkI30giiKiKNadPrjYqDQKrBdYpqamePbZXoaG7Ph8/SWFD61CL5DNaiO8AC96kczEhMDYmEguZ0UQYG5OYPduhauuWhzlyrJs5Kv1Y9CJV1/2N+uhWmop6nK5WLduHevWrTMGDaLRKKdPn0ZVVaLRNRw50kd/vxOvV2RhAe65R+Caa1T27lVLtl/vsUYii9MNOjwejZB/8hML//qvw6iqSDCoGsMrqZTA1BR885sCX/xiZe2KWlAtGWqiPd11Oyu/ULoXGt9IFa7AN998M/fddx87duzAYrHw6U9/2hDyqBXNIN1mDUjoI8hTU1Ok02l6e3sNTd5nnnmm4e1fLBSTbnFRzOVyMTg4yOWX95FICIvyr9msNr5a3Fhit8Ob3yxx6pTA449nEAS4/non69apRpeAoiiGlgRoy3+r1VpSkNQ/oxNw8Z9WonjQAGBursDXv57D6YwyNZUiHnfQ09NDb283Tz/tYPNmrSAIjZGuw7G07sTRo/DUUxbsdpV0WiPnc+cEcjkVmw3m5zVRoh/+0EJPj8A739mY9nC9fbq1OiubkW4NWMkVWBAEPve5z/G5z32u4X0FAgHOnDnT0DYajXTLLW6Gh4cXjSDrbWOtfHO3Sk1JEASi0SgzMzPMzMiEQv3s2nUFTqfGsi9/ucI//qMNj0cxIjFFgelpkVtukRZFZ6IIGzaoOJ1pFEVheNh3Pn2gGlGtIAgG0RYXsvTzu5CaUEs6NxqNgmv9fCxmo7vbwfBwD6qqksvlzk8NTnLuHDzyiMzVV3sIBoMNdcgMDcHAgNb1cJ6zAC0X/utfiwwMgMOhTd9ZrRrxRiICTqeWR1dVLUqemICPfczKZz4jGS+DWtGsTp+VnJWz2SyTk5MVnZVrwQuCdNuJZrlH1FpIW87iphJaLXqzUt61HqTTaaampkgkEszP93DgwA7i8S5EUVvS3nyzxGWXKVx2mcKrXiXx4IOl5753r8xLX7r8OSuKQqFQMI7dYrFgsVhq0p0tJmB9mzoRi6LY0ihYVQVjuS4IAk6nE6fTSW9vLw6HSm/vPMlkmFOnTpFKpTh+/DihUKhmTzRBgLe8ReHv/97CmTNa/3IuB+PjGql6vVr3h9WqDZSIovbi06fgVBV8PpW+Pi0H/OijIq99bf1Fy1Zcy3Jn5UcffRRVVSs6K1frrN3Jso6wikm3GTndavRuq7W4qYR2CZk3GoHorWxTU1OIoni+Fa+Phx7aRHe3lXXrNGJLp+H737ciihI7dijcfLPM3r0KJ04ISJLW6D84WDlHWpw6mJmZMbRg7XZ7Q8ff6ii4EkIhFVUVjAEIHaqqEfKmTT2EQj1s3ryZxx57jO7ubsMTzeVyGe1V1cgvDg/DBz4g88wzmvCN1wsbNmgykdr5gM8nkUxayOe1Y5AkjXR7elQ2btQ+5/GoHDgAr31tw6ffMugv4PXr11d0VpZlGZ/PRygUapmzcjuwKo+6HYW0Wi1uKqEdlj31DkgUF8USiURJLhrgBz/Qro0+wgpaRT4UUnngAQvbt2utSMGgSjC4vAKWLMtG9NHf34/H4yEej/Pcc88BF/pjq1GIWwkrRcHlJFwPfD7YuVPluecE+vu13Gs+r7lcbNmilqiW6SanAwMDxrhtNBo15Bd1ElnOjsfrhVe8QuUVr9DO59gxga98hfMDJSrBoISi2LFYBGRZa8NzuzXS1V+YhQJ1pxbahfKiZrmzsi7a00pn5XZgVZJuJU3dWlGpkNaIxc1S++g0c8riopiidBOJrCUa9eL1qgiCwsiIduOfPu1mzRqZ8lvE44GJCYFU6oJATDn0qLZ4uW+xWAyys9vt+P1+Nm7caDTaT0xMkEgk8Hg8NS8nl0KlKFg/PkVRyOVyhkFpramIF79YxeuF/fs1jQSbTeW667RptOWORx+31SO5ubk5otEoJ0+eNEZt9RfQUvfdpk0qL3mJwiOPiPT0aIWzdetgYkI9T64qmzZpgj6aPCRkMgIvfanC/LwmW6l3llSDdg0brFSsKxftWcpZubhw14lYlaTb3d1NKpVqaBuVHIEbsbiphIvlk6aqGjHGYgJ9fSoDAxca/3M5bVKst3cP3/62i3xeW3qeOSPyn/9p5cYbJV71KhmnUyGfX7xPfXeVVnZ6VAsXloor5WqLG+31Hs9YLMbBgweRJKmp46aCIBiaxJOTk0iSZIy56j+vNhUhihrB7twJ+bxGfLUW98sr+zqJTExMMD8/j8vlMnqDy1MRn/qUzN/9HfzsZyJgwWKBl79c5e1vl/na17RUQyajaVmk0wIjIyr/639ZOHJES4ts3arykY/IvPzlKxNqu3KktXYuLOWsPDExYZJus6E/FPXeDLo8ZCKR4KmnnmqKxU0lXAzSjUYFPvMZG888Y2F2ViWTkdi0Kcn/+T/z7NypnaOiwBe+YMNu14osGlRkWeWhhyxs26awa9cC+/YFFqmHRSIC27bJhibtcq1etaK4x3NkZMRYTuqeYLr8YCgUqnnSKZPJMDk5yczMDIFAgM2bN5d83/UW5EQRmqW7VEwiqqqysLBQkorw+/1GKsLttvLxj8vcdluUo0czXHHFWkPZbMsWiYceEjl0SMDrVfH5VD7xCcv5F6yWBz56VOC222x84xsFfud3lifedvXONroffcy7nZok9WBVkm69b119aR2JRHA4HIiiyNVXX92yXFC7SVeS4C//0saTT8LMjHL+GGw89VQ/f/InffzqVxk8HpWpKYF4XGR4uPTmtFg019wDB0R27MgyM5Pn1Ck7fr82vjo3J9DdDb/zOxKyXJonrdTq1SiKl5PF8oOHDx8ml8vh9/sNZ9xKy9LiqFaWZYaGhhgdHa342YtRkFsOgiDg8XjweDyMnHeCmJ2dJRaLcfz4cURRJBQKYbPBzp0XpCQB+vrgv/037dgVBV73Oiv5fKnrh88H8/Mqf/M3Vl75ysKyqmqmlm5zsSpJFy7kZFeSgSu2uNGNKi+//HKsVquhmNTKYywUlpY9bMb29SJVIpHghz9M8cAD65mddSCKYLMJOJ2aH1g0KvChDzn4+tezZLMAlaMbh0Pz73I4BH7v91JMTzvZv18knxd4xSsK7NqVx+1WUZTaW70aQbn8YLE9+fHjx0ua7EVR5Ny5c0tGtdXur5aCXDsGNPTzgwupiDNnzpBOp0kmkxVXATMzWuGtUqOE262NMp85A5V84nSsRtLtZKzaM/R6vczNzVV0j1jK4sZdS/WgCWh1pKuqKuFwmOPHj6OqHv7lX3aRTDqwWLRmeUWBREKgu1vLOT79tMjMjEBvr0YisnwhDzk7C088YWFszMLQkMLMTID/+l9Vdu+W2LVLNTQQyotiFwvFdjOg5fNOnz7NqVOnkGWZnp4eRkZGzkeDjcmWrVSQa/eEHFxIReh1iWAwaOgd5PN5oytCVQOoauXz150qVlqNr0bSNSPdFkBvGysm3ZUsbtqNVplTxuNxzp07Z0Q3V1xxBQ884KRQsAGCsVQURe2hWlgQ6OrSiDceF9i6VeXaa2Uee0xTCQuHBb79bRu5nEbC586JfPGLgzz0UJ7vfCePw6Et9dsV1daC4lxtMBhk7969dHV1GbKNZ8+eLekK6O7ubkpbWvHfy6UiWl35100pK6UiotEosdhx1qzZxfh4D4FA6YsynYbR0dLURCWsRtLtZKzaM9TlHWuxuClHKya6itFM0l1YWGBqaopYLEYgEGDDhg3E43Hsdjs2m40nnrAwMqJw+LBILneBeAVBi2gVRdNE6OvTyOE1r9GsxZ94wsIPfmA7r5mgeaFZLFp++Le/tfLVr57jj/6IpkSMzYKiKMzMzDA5OYmqqqxZs2ZRa5/e3wmlS/FkMonH4zG6AprRpVIpFZFKpZicnDQmH4s/U3y//cd/CNx5p4XjxwU2bFB517tkbriheqJWFGXR91KeivjUpwq86U0Qjaq4XBkEQSSbtWK3W/jAB6SKnSjFaCfpNvp9dLqWLqxS0tXn3T/5yU9y44038upXv7oqnWJP6QAAIABJREFUi5tytFoboVHSLVYts1gsi/qG5+bmiirtWj72yitlHn/ciiRdGAuVZW0c9KabZGPYwWqF171OZnRU4fvftxEKqSXiNVarFacT/uM/1vPmNx/n0KFDRgtXPSOtzUAmk2FiYoJoNEowGGTr1q1VpYzKuwKSySSxWIxnn33WUL1qRoO9Xj+YmJhAVVWGh4fZtGnTklHwF79o4fOf174rm00TrHniCZH3vlfmfe+r7r7RI93lcN11Nn70I4WPfczK/v1dgMrGjVne9KaT+P0zjI35l53yahfpFgqFmp/hSmhXiqderDrS/f73v8+nPvUpAG6++Wb++3//73XfEHqvbieRrl4U09MHfX19JZNixSgejnjpS2W+8Q0bl12mIggS+/ZZjJytywW/8zsy73vfhcZbPR8pSSJ2u064FzQFtOOHTMbKyMiI0cKl9/sePnwYt9ttLNsbHWRYCuVR7dDQEBs3bqybHHXt356eHkZHRxedkz6mW4sAty7SEolECAQCS74MinPBp0+rfO5zdqxW9byDhKbYJsvwhS9Y+P3flysu+1UVDh0SeOQRrd92/Xob11678rXYswf+/d8l8nltOs3lsiIIm0mnN/DAAwv88Ic5RPEke/ak2LLFa6h+CYLQ1ki3Hfu52Fh1pHvttdfyyCOP8I//+I/kcrmGvqRmyTsut/1qSTefzzM1NUUkEsHtdjM4OMi2bdsqvrHn5+HBB6088EA/IHHTTRa8XpVwWGD/fpH+fpWbb5aIRESyWXjve/O89rXy+VSDXFKB37QJRFEbHy1/9+Ry8JKXXIjSihWiivtIDx48iCzLTYsYQSuMTU5O1hzV1oryc9Lb0sbGxsjn80ZvbLn2q6qqxiRdPp9naGiIa665Ztn7sTi9cN99VmRZwOHQl8Pa3xYL5HICP/+5yLveVVrhkiR4//st/PKXIheaYtbxildI3HknVdkc2e0XbILOnYO/+AsHkYgDiwVkeQ2PPSbzh38YZefO00YqRm9fazVkWW5KCquTo1xoMulWY8MO8IMf/IA3vvGNPPXUU+zdu7emfYyc720JBAKMjY01dLyttuxZiXT1abipqSkKhUJV+ehoVOAv/9JONCoiSTJTU3buvddBKiXg96s4HHDihMjx4yK33irxvvflGR2VkaQLx1E8wOBwwDvfKfGlL2n7tFq1aCqT0Zr+3/GOyi+l8j7SSlGwnjetNgpudlRbKyq1pekFqfHxcex2Oz6fD0mSDEnP0dFRenp6at5XKgWyXDn/KMsqiYSCJEklXSLf+paFe+4R6em5ILSTySg89JCTr31N4U//tPqhAFWFT37SytwcRTq7KrmcyPe+18eXvxxg1y5tQvDo0aOcO3eO6enpkgGNZkelhULBLKTVgmps2AGSySRf+tKXuPbaaxvaX6e6RxRjqep1paJYtZHEP/2TlXhcoKdHYWzMiqoqpNPam71Q0LoULr9cQZJUDh0S8flyyPLyrV7veY92Df7+77UmelnW5vY/+9m8ocWwEqqJgvVccHkkUhzVhkIhtm3b1pTcXqOwWCzGi2N+fp5Tp04ZxTG9AJvNZnG5XDWTxd69Ck7nhbYtHaqqveyuuUYfbrjQG/z1r9twOkuVzQRBpatL4ZvftPCud1Xvh3biBJw4IbBmTen3q78fH3hA5G1vU+ju7qanp4e1a9cSDAZLXkJ6b3SzukKaZUrZaR025Wga6VZjww7wkY98hA9+8IN85jOfaWh/zdDUbXV6oRgrFcWqQS4Hjz1mob9f5fBhEYdDIRrV7MttNu3nsqwyN6cpfyUSAk8/7eTmm5e/EUUR/uzPJN7+domjRzU32U2b6rd4qRQFx2Ixzp07x9jYGG6325iND4fDgOah186othpIksTU1BTnzp3D7XYzMjJivDR0C59YLMapU6dKOgaqIaDrr9eMKp9/XsThUI2iZy4HO3aovOQlaklBSJZVZma01cyF97j23Tscmj9aPl+96WU8LiCKlb9jpxMmJy/8QM/p6i+h0HkZtWw2a5x/IpGgu7vbeElVqkGshBeCawQ0kXSrsWHfv38/Z8+e5XWve13DpBsIBJoiZN5K0lVVFUmSGBsbM4piO3furLvoVCiAogjIsmrYeMuynifUIlSbTevLDYUEVFUgk7EiitWlUFwummJiWA6r1WqYPi4sLHDy5EljlFUf9XU4HB3zsCSTSc6ePUsikTBSPuWtTOUWPrlcznBASKVSJY64ldqgRBHuvjvHBz5g54EHRGw27ft91asUPv3p/KKxXItFoL9fJZnUpgxlWaFQyKMoKrmcQCCgYLHIqGp1E3IDAyqyvDjSBi21tGnThftgqUKa0+lkaGiIoaGhkq6Q5557jkKhYOT4q01FrIYotRloGumuZMOuKArve9/7uOuuu5qyv2alF/KVpLQaRPGQhp6rXaooVgvcbhgeVojHdcFscDolwI4s68IrAqKoWXFbLIJhb64oGJFQu7lNURQikQiTk5MIgsDQ0BA7duxAFEUKhQLxeJzJyUnGxsYMacdQKNSUHtpqIcsy4XCYyclJ7HY7w8PDbN++vervzOFwLGpLi0ajHDhwAFVVSzSDdWLx+eBrX8sTjWqR5Zo1KhUGLA287W15Pv5xK5KUw2oVz18fkWRS4D3vKaCqCpJUnVjP2rWwZ4/KgQMCg4MX7olUSsvr33jjhfxwNd0L5V0huqV9LBYzUhF6lFyrLnWt6JSX91JoGumuZMOeTCY5ePAgN9xwAwDT09Pceuut/OQnP6m5mAbaGHAikWjomKt1j6gGSxXF9u/fj8/na8qNIAjw5jfn+eQnHdhsCvm8iMejADKFgkgopP0dDGoz97t2KQwNqXz0o1Z++EMtX7t2rcr/+B8Sr3+93HLyXVhYYHJyklgsRigUYvv27YtytcXW58X23XoPbbFIdSsepoWFBSYmJojH4/T19bFr1666lsbFKCagDRs2GC8WPb1SLNnodDoJhTRx+JWOccuWOK961eU89JCfTEYgk9EI8vWvl7njDrlEfa8asZ4PfEDmb/7GwtiYeP5eUOnqgr/6K5nzTvRAfX26FoulRPtWT0WcOHGCZDJp2PC0ot2w00lXWGGCo+q1piRJbNmyhV/96lcMDQ1x9dVX873vfY+dO3dW/PwNN9zAZz7zmboIF7Qba8+ePfz617+u6/dBGy6IRCJs2bKl7m2UF8UGBwdLimLPPPMMu3fvbjhXVdzq9fjjVv7hH5yMjYmAgMejkskoRKNgscj09Ehcd12eD35Q4c/+LMCJEwIej953qy1jP/CBAn/8x83v3FAUhRMnZpiaOofbrXUg9Pb21rVs1MkqGo0aAufNmCTTuyQmJiYQBIHh4WFCoVBblrZ6kTEWixGLxSgUCiVqacXEqR8jaEFNb28vgiAwPi7w6KMiqqq19G3ZsvRjqj/fxc+5vg+t0AtHj4qcPavJPu7Zoy6Sqty3bx+7du1qGjkWrwRisRiSJOH3+4lEIlx//fUNdUUoioLdbu+Eft8lmb9pkW41NuzNRPHYZb1vtnpzunpRbGpqCqvVWnEMVUcjU29LadW+8pUiL3uZxKFDAs8+KxIOCzgcWuphYEBgzRoZqzXO3XerHD7swetVASuCYMHlEigU4ItftPEHfyDX5CCwHBYWFvj5z+f49Kd7OX16HYKwnj17VD7+8QL9/fXpm1YTBddi85PNZpmYmDB0GipF3q1GcZFx/fr1RlvazMyMsQwXRZF0Ok0oFKrYn7x5s8rmzdW9MJfTidDFejZvVtiyZelURLOHI8pXApIkMTMzw9TUFE8++WTDqYgXTKR7MXDllVfy4IMP1n1DZDIZxsfH2b1794qfVVWV+fl5pqamjKLY4ODgim//gwcPsmHDhqof7kpWN8V/asHb3mbnyScFXC4ZSZIMDQCr1UouZ+POOwslww+1QlEUIw966JCXD3/4MgoF0Wi+z+e1PPNPf5rl8subeysVCgUjWtQr55UKV6qqEovFOHv2LJmMzBNPbOPf/i1IIiFw/fUy73ufxNatF/c216cQz549awwkSJJU4qHWCiPGSlFwpVTE448/zote9KKWklkmk2FsbIwrr7ySbDZLNBolGo2SSqXo6empuudbURRDK/sio/WR7sVAd3c38/PzdVtzVBPp6kWxcDiMx+NhzZo1NRXFqp1KK7a60X+vUVUv7RAF/v/2vjy8qTJt/z5Zu+/pmhSoUET2HdFB1sHSwuCKKCCKAyLINgOjo/ihIxd+P3U+hxboyCIqI4tKSwUsIggOoFKwLApCsS1ZuiVtumY9y++PwzkkbdqmaZKmkPu6uIA27XmznOd93ue5n/sWCkUQCkU21yFhsVjw229XERcn7LCWgm0dVCaToX///vj73yNAkgI7ypJUCphMwNtvi/H55+5tWIrFYsTHx4MkE2CxAJGR9TAatbh48SIAtubPae5GREQgObk35syJuaUNzL42n38uQl6eCPv2mTu1+bgKiqJQUVEBjUaDgIAAKBQKu/o/56HG1UJFIhG/sbijGdWeZCX3PW84MdjSxQICAiCXyyGXy/kNiWtK2nK+m08JNn9evopuHXQ5pbHOBF1HAbF5UywhIQHDhg1zKdNoy7G3eVbLZaHu0qpNT6dw5ozAjhYkEAhAkhIEBQGzZvWG0Xh7iqytmiln067RaCAQCCCXy9GnTx8IBOyo8cWLLO2JYdgMl6ZvO1F8/73QITWpMyguJrBwoQSXL7OZtcUSgGeeicSaNVpUVipRVVUFiUQChmG1gPfsIVBYyFrF296nJhOwcKEEv/xiatM9wZ0wGAxQq9Worq7mRfUdZXDNPdTMZjOqq6tRUlKCpqYmvhkVHR3t1vFZgiBAkiQ0Gg3Ky8sRHR3NT8d5Sri9NY4uQRAIDw9HeHg47whcU1ODqqoqXLt2DRKJhP/MemNU2R3o1kG3s7QxTtqRQ/Om2D333NPpeX9HAxjNbck95cCQlkbhk0+E+O03AYKC2ABoMLAz/GvXWhEaKkJo6O0pssbGRmi1t7PFmJgYBAcH87bXXFbbXAiGINg/VivQ1MR+zTbIulsyoa4O+OMfpdDrWYEekwmgaQaffCLAzZtS7NjRk6/zck2b3buDYTIxEAoZcCc/NoCwNkSXLhGtcpR//lmA9etF+PFHISQSBo89RmH1aqtdh789MAzDK5DRNM0rkHXkPZdKpUhMTERiYqJdBsixhtxhZd/U1ASVSgW9Xo/ExEQMHz4cYrHY4+4Zzg5G2E4+AmxZgnMPaWxsRM+ePfkBLV9Ftw66XKbbGTAMg7KyMqeaYq6AUwJrzZbcmXq0xQL8/jsbIO65h2lX/5RDQADwyScWZGeLsHevCHo96wK7bJkVkyfbZ98EcdsUskePHigrK4NSqeTrwFFRUQgLC3PIGpBKgREjKHz3nZAPtNzfHJ+Yky90B/7zHxGamggQBAOGYW4FeAKAEKdORaOuznSreXi7aWO1BkAgYF9D9mcYPpAQBFBXRwFo+Z7/978CzJ4thcnE0rOMRgKffCLC118LceKEqU1eLcDWnjUaDSoqKhAeHu6SdZAjNM8AOaYHZ2XfEe0Lru6tVCoBAAqFAn379rULoo5KEdwfd7hnuDqNFhgYyJciuGTGX17wIKKiolwKulxTrKysDEajEVarFQMGDPCIPKFAIIDZbOY/DB3Nag8fFiAzUwyjkQ1e4eHAX/9qxbhxztXZQkOB1atJrF5NtnvE54S3Oc7qsGHDEBgYyI+86nQ6lJSU2HWXuQbhkCEMTpyAzYgqC4JgVa2OHxdg6tTO1wYpisLBgzSMRtZ2vPkNLhIBZ88KkJxsXzaaOJFCcbHo1ppu/wxNM7BaGTDMBRQUUHZaAgCBVaskMJtvK3MB7DSZTkcgK0uMN9907IFn2xhLSkrCiBEjPCrm4ojp0Z6VPUmSKCsrQ1lZGRgmCpcuDcLZs4EIDGRLU5Mm0WiNmedIuL0zRp7uGAHmynO+Dt9fYRvoaKZrNpt5+cTQ0FAkJiaiqakJCoXCrUd7W6pXWFgYiouLUVVVBZlMxtNgnMGJEwKsXy9GRARwa9wdTU3Aa6+JsXGjBUOHdqzr7uhzz01ilZWVQSgU2tVqOTQfeTUajdDpdLh27RrvyltV1QdSqQgUxWa1AJvZBgay48mlpQIArgfdxsZGqNVq6PV6BAUNB0EIHNZgCQIIDm75urz0Eoldu0RobMStYM3WncViAgsXUhg/flgLh4mmphio1QMgFDoOGPv3C+2CLsfmUKvVkEgkUCgUuO+++7yeedmeWjjtC71ej6qqKly/fp0PTJwkZWzsCCxfHozaWva1oyigsFCMQ4dovPeetV2LeWcacu1NyJEk6TFNZl9Dtw66UVFRKC4ubvMxXFOsrKwMJEm2aIqJxWK32IS01hTj6mwWi4XPFJuamuwk8hwFfIYBtm4VISSEDVwcgoNZUZQdO0TIzHTdadg2q21sVOD48ZHQaMQYMIDG009TkMtbD+iBgYFQKBRQKBQ8z1Qm00MkkkIisb/B2NcCSE7ueMDlxofVajW/IfTt2xeLFglx+jRbQ7a9f2mafd3Gj295LYWCwcGDJixcKMXNm7eNO1980YrXXmN3ieYOE5cuNQFgbpWHWN1h2+fFadraOlrIZDK3TLW5EyKRCDExMSAIAgaDARRFITg4GAKBAOXl5diyJRo1NRIkJIj41zM8nEFhoQCHDrGC6h1BW9xg7uvNs2CSJN2il+zrpQWgmwfdtjLdpqYmlJWVoaamBtHR0a26AXO0MVeDrrNNMYlEwjdBbI0Di4qK+LFQmUzGr8NgAG7eJBw2a8LDWbZAR2GrLyASiSCXy/Hjj/3w1lsS3t7n++8F2LZNhA8/tDgMXs3BKU8tWwZ8+qkIFgsDhrmd4ZCkAFFRDCZOpNAGddEOtkEsJiamRfNu0iQaU6ZQOHpUCLOZDbwMw5YANm60oDXDh8GDGfz0kwk3bhBoaABSU5lWm3wEQWDgwBBERgqg0xEQCsE/LzaIELj//lr8/PNvoCjKJZU0lYrAt98KYLUSePBBCvfd536+sG0JITw8HKmpqXYnrepqGkVFYoSFmVBb2wiCICCRSCCRSBAWJkROTseDbnO0VoqwTVAsFoudZGZnruXr6NZBtzl7gSRJVFZWoqKiAmKxGAkJCe3eCK7IO3I3nqu25LYygLbas5w4CstBlEEkkjp0dCBJdmTTFhYLK5oSEtJSNMX2aG6rL6BUEnjrLQmEQntJQIsFWLxYgvPnTXB2YCsuDti2zYwXXpCCooSwWgGplNV63bDhN/z8cyVPco+KimpBcbLt7rcXxAQC4KOPLNi3T4jsbBG0WgJDh9JYuZLEiBHtbxS2ClptQSAA3n7biqVLJbeoZlwtlEFAgBUzZlyH2WyGWCyGyWRCU1OTU/xZhgHefluE7dvFt7JzBiKRCJMm0diyxeKWhmNrLITmMJuFEItFCA1ldx+apmGxWGAwNMFopGG1ilBZqXf4nrkC2yy4eQMvICDAzsSzow05T5rMuhPdPujq9XpcuXIFAPtBi42N7VBTrCOjwM0HGNxhS247FtqzZ0++rqhWl+Dee5tw7lwcEhMFEIvF/AdKrwfmziVvrQnYvl2IrVvFvAD50KE0/ud/TAgMZIn3YrEYSUlJLTrSX3zB+qg1f6lY3itw7JgQ06c7n+X88Y80CguNyM0VQqUSoG9fGn/6E4WgoBQwTC/U19dDq9Xi5s2bEAqFvJCNXq9HZWUlIiMj2+3uK5UEtm8X4fx5AeRytuY4cqTnyPuPPkpBLLZg7VohNBo2UIwYYcL77zMYMGAIgNtuw6WlpXYTVK0Fqv37hdi+XQSRiOHr0gwDHD0qwLvvivD3v7smN2obxBiGQXJyMv+e6/XAjz+yTtFDh9Lo0YPdeGJjGYSEsJocgYFsQhAQEICAgAAYjQTGjGlCY2MjHxi5ZKEztDSKolBeXg61Wo2wsDC77NtZsZ7ujG47BqzRaLBp0ybs3LkTDz/8MN58802XlKhKSkoQEhLCqyE1R2tUL3cNMLSFqioaf/6zEBoNDZHIDIFACJKUIjWVwJYtFEJDgawsEbZsESEkhDU4JEkaNTUUAgMt2L5dg/7941qtL65ZI8aePcIWWTPAljfWrbNi/nz3i+IwDIPKykrcvHkTBoOBL1HExsYiMjKyVRrdiRMCPPOMlN9cAHbDWLbMildfdb8usn1NWYTQ0B6Ii4tAaGjrnzGOGaPT6VBTU8Ofamx1BMaPl6KkhGix2ZEke6r59VeTw2y3qQmorwdkMvvTT/MSgkKhsNu4PvtMiH/+U8zXvAFg6lQK//iHFWIxuwm8/74I0dGs3RPDAA0NgMVCYNs2C+65h/0hi8XCCxBx48pcEHYmybHVvoiPj0dSUlKbZb3WxHpay4JpmoZIJHJLRu4GtPoh6ZZBt7KyEk8++SSefvppZGdn4/vvv3f5d6lUKohEIiQkJNh9nXXKtZ/C8cQAQ3uorwfy84X49lsBGIbEqFE69Ot3ExIJiaCgWMyZk4qAAAKAFRaLBQQhgEQiRkODGEuXknjxxdaD0e7dQrz+urjFzc8wbJNo1y4LxoxxXxZptVp5TnRoaCjkcjnCw8Ptatx6vR5SqZRnenAbhtkMpKYG8uwD27WKREB+vvv0HWzdfWNiYiCXy512Bm4ObopMp9OhqakJ4eHhmDZtCEQix+wLi4XATz8Z7Wr5Oh3w1lti5OezPOjAQGDRIhJz5tRBo7ldQkhMTGwRcH74QYDFiyUIC2P4QE7TrHPE/PkkVq5kqYR79wrx0UcimM3sY2QyBq++SmLYMMfvv60AUXV1dQtLJtv7pK6uDkqlEkajEQqFAnFxcS7dR7bcaqBlFswwjK8ojAHeDrrtGVT+85//xLZt23jXgB07dqBHjx4dvo475B3LyspAURQUCoVDVS9nBxi8DavViq+/rsaaNbGQSkkIhQKIxZJbZQg2K0pNZbBnT+uaB42NwIMPBqCujh2k4BpSRiOrZPXNN+ZOj+5yk1NqtRoNDQ1ITExEQkJCm9mIwWDgBU84B4ILF+RYuTIKjjTnaRp49lkS77/vOpuDYRjo9XqoVCqeShUXF+fW956madTX12PSpAhUVAghFrN1Yi5747L3K1dM/EZoNALTpkmhVBIICmI3HJOJgtFIY9q0Crz1FnhmgiO88IIEFy4QCA+3/7rVyroOnzxp4ilhJhM7Xi2VAikpHbNr4sZzq6urUVtbi4CAAEilUjQ0NCAgIADJyclu05UGWmbBTU1N2L17NzIyMtC7d2+3XKOT8J7gjTMGlUOHDsW5c+cQFBSELVu2YM2aNdi7d6/L1+ysvKPJZIL1Fv/Hk2O57gAnklJWVgaLJRxisQKhoYGgKAokaYXBwGa7ZrMEAQFt75khIcDevWY895wEVVUEz13t35/B9u2dC7gkSfLr5ARMnOWsBgUF3XLj7YEPPhDg2DEBDAYajY00hMLb1C0ONA1UVLi2WFsfNK6uHt48QrkJAoEAERERWL5ciLVrJRCJGDAMqwBH0wxIUognnjDc4gWzt+ahQ0K+QUqSJCwWEgKBEKGhIhw7psBbb5nafJ+KigiHzVB2JJyBTkfw9MCAALjMoODGcyMjI6HRaKDRaEBRrLC60WhEVVUVKIpqs3zUEXDvf0VFBbKzs/H1119j1qxZLuuweBNuD7rOGFROmDCB//eYMWOwa9cul67VGU1drikmFotRWVkJmqYRFxfnMYeCzqKhoQFqtRq1tbWIi4vDwIEDMXx4ALKyBGhoAIKChBCJ2A8zRdFoaqIxdGgRzp7VITo6GjKZzKFhYt++DE6dMuPcOVaXt1cvGv37u25K2djYCJVKhdraWsTHx7cq5tIeCgsJzJgRAJOJzb4pis3OSBKQSmlwhzCCYAccRo7sWO3ZltGRkJDg0AetNVRXA3v2iFBQIEBSEoNnniE7FKyeeYbCuXMkvvpKCItFCEAIqRQYONCC559X4uefq/lGY15eMiwWAgTB2pMHBATw7yFJAgUFQkyb1vpzj49nUFpKtKgRs/5oBD8u3VkYDAYolUro9XokJSVh9OjRPBeeU3vT6XS4ceMGJBIJXwsODg7u8P3GMAwuX76MrKwsXL9+HYsXL8bbb7/dbYYr3B50nTGotMX27duRlpbm8vVCQkL4jnF7cET1ioyMxKhRo6DX66FWq3H16lVERERAJpO1OrjgLXAUOI1GA6lUiqSkpBaykuvXs5Sm2logKIgBSQImkxBjxxJYvDgFBKGATqfjDRPDw8P558ZlHALBbctvV2A7iSUSiaBQKDrtCbd0qQRNTbf1GoRCNuiyAZhVFmM1HRhIJBTuvfdHXLkS3OK5NV8n58bAKaU1Z3Tcfixw9SoBs5nAfffR/BG8sJDAY49JYTYTt4YzGOzcKcLf/mbFsmXONfOEQmDjRisWLCDx9ddCWCzAxIk0xo6lIRDcA4ZJQUVFBUpLS2EwhIAkYxEYKABB3P4scg1+sbjtoDlnDoXXXxcjKMieKaHXE0hLY5uxroIrySiVSpAkaceWsH++Qj7IAuD1cn///XcYDAaEh4fzmsFtlZ1omsbRo0eRlZUFqVSKVatWYeLEiT55Im0Lbg+67RlU2mLXrl04d+4cTp486fL1uAGJtoJue1QvoVDIz61zGqackn9QUBDf1PGWUWJ9fT00Go1T2eIDD9DYvduMbdtEOHdOgPBw4KmnrHjsMerW3LyYn7Linhv3gXfUsOoIbCUKZTIZBgwY4HLDyRZKJYHiYkELfnJQEFvjpCjwQTcmBvjsMxKDBw/nWQPFxcV2+hBCoRAajQaVlZWIiopq1zHi+HEBli+XQK8n+JHhv/3Nij//mcS8eVI0NRGQSDiqHQGaBv7f/xNj/HgKgwY5nzkOHsxg8ODbgZokSajVt1kIAwcOxIsvhuHSJQmEQgo0TaGujkZDgxgUxZbWHjWOAAAgAElEQVSDjh0TYPRoGq19/NPTKRQUEPjqKxFomt0kBALWsPSVV1yrgdM0jYqKCqjVagQFBSElJcWppIeDrV5ucyt7giB4oR7uZGY0GrFnzx7s2LEDQ4YMwcaNG7tkvNpdcHvQbc+gksO3336L9evX4+TJk506FnBBNzk52e7rrmrV2mqYcoMLnNwhQRC82Z67bV5sa6BSqRRyudzpbPHeexm89177N1BzfVZuKOPXX38FRVFtliE40DTNDzEwDOOSRGF74BgKzWWICYKtO4aFMXj/fStiYxmMGUPfyuDs9SEMBgNUKhXOnTsHq9WKiIgI9OnTp93TS2EhgblzpbBab6+BooB//EMMpZKVlWy+9woELK/5449FLjXz2hpkmDCBxujRNM6cEcJkEoHzYiUIIDTUis8+o/HTTyQ+/bQG8fFRLQRfBALgzTdJPPEEhSNHhDAagbFjaYwbR3d4CMNisUCtVqOyshIymczl0pH9+uzfN1v9C64ZX1ZWhlmzZuHw4cOI64iepo/C7ewFZwwqCwsL8fjjjyM/Px99+vRxYdm3sXTpUqSlpWHcuHEAblO9APc3xcxmM7RaLbRaLcxmMx+kOlMH5jr7dXV1iI+PR2JiYpfUpjj7G61W67AMYUujioqKglwud8usvCOYzUCfPoEwGtGCVkVRwCOPkNi61XFw44j3ZWVlvEZESEgIT0mrra3lTy+O+KWzZ0tw9KiwRWClKPYoz0pDtnyvLRZg3DjKaYeM5oMMCoWCN5509Luzs4V44w0JGIbNsCMjGQQFsZuCwUBj9WoVBg8u5XUWXK2XOkJjYyNfnpLL5YiPj/cYo4dhGPz222/YtGkTLly4gPT0dIhEIpw4cQKzZ8/GwoULPXJdD8C7lLHDhw9jxYoVvEHla6+9ZmdQOXnyZFy+fJnnxiYnJyMvL8+VS2Ht2rXo27cv0tPTeV1Pb1C9KIrig1R9fT3CwsIQGxvbaj3RFo6y2qioKJ85LnFHvqqqKmi1Wt6YUKFQQC6Xe4VC969/ifDOO2JeE4JrpgUEAMeOmXDvvfYfTVsLobaI97Zj1zqdroXBZUpKIIxGwiGHlhW9Yf80f6soCnj55faHNNobZGgN+fkCrFwpcaj41dgITJlCY/NmC291rtPpYDAYeI81Zz6XtuDGslUqFQiCQHJyskc/ozRN4+TJk8jMzARFUVixYgXS0tK6Xb3WBnfWcIQtFi9eDLVajb///e/o168fRCKR198obgpJq9WiuroaAQEBfBnC9sbnstr6+nrExcV1WVbbHiwWC8rKylBRUcGPtHJyjlwZorMOBe2BYdjA+/777BmYothO/KZNFtx/P33rMbcDAwCXrNS5DJ+bspo37wHU1oohFtv/Dk6MvX9/Gr/+SkAkIvjAy+pMAD/8YEJiouNbpnkJwdEgQ1toK+g2NAAPP0whK8s++7f1WKupqYFYLObfu6CgIIfvHXec12g0CA8PR3JyssdONAB7evz888+xdetW3HvvvfjLX/6CwYMH+0wC0gncuUH3+vXryM/Px3fffYeSkhI89NBDyMjIsKOseBtcHVir1fJTMkajEUFBQT6X1XLgNo7r18tw5EgQlMoE9OoViCefZOwEYpoHKa7zHB0d7ZEM2GgEfvuN5ZqmprJUNovFwrsxREZGQqFQuCUwMAyDdesobNkSDIZhbmW0xC3pQQKjRtHYudOM2bOluHaN9Z4TCACJhMHOnZYW5pYdKSG0h7o6YPToAIjF9iPA3DDLv/5lwcMPt81A4VgD1dXVLbJgq9UKlUoFnU6H+Ph4yOVyj47TVldXY8eOHfjiiy+QkZGBpUuXIikpyWPX6wLcuUHXFgaDAUePHkVubi4KCgowfPhwZGRkYMKECW5vfLUFbgpLo9Ggrq4OwcHBoCgKZrMZUVFRkMlkbp3O6QxshwOqq6OxevV9aGpiHXMFAkAkIrBmjRUvvdTy2MwwDM+GqK6uhlQq5SUqPaEnW1dXB5VKhaamJn6yzd0ba309MHVqAEpLCZAkA/YWYCCVUti69QZGjQpDREQkLl0S4tdfBYiJYTBhAm03Su1qCaE9/PvfQrz3nhhCIVtmYemBwJAhNPbssTht4wTczoI1Gg10Oh0AQCaToUePHm5xGnYEhmFw48YNbN68GWfPnsWCBQvw3HPPeTST7kLcHUHXFiRJ4syZM8jNzcXx48fRo0cPpKenIy0tzWOZJhfAysvLeVpMZGQkfy2KolBTUwOtVou6ujqEhobyDR1vZ+UNDQ1QqVSor69HfHw8EhISMWlSKEpLCbsjLEuiB3JyzO06VXDju1qtFiRJ8o3GzipScRxgRzblnkBjI/DJJyJ89pkQJhPLZ120yILAwBpeHyIgIICnpHEbTGdLCM7g4EEhNm4UoahIgMhIdjDjpZfIVjWEHYET8lGpVJBKpUhOTkZAQABf5zaZTIiIiEB0dHSHa8GtXe/MmTPIyspCfX09li9fjhkzZvjkeL0bcfcFXVvQNI0rV64gJycHhw8fhlQqxbRp05CRkYEePXp06gZuri3AMRDa4/RyP8fVgSUSSac4s87AVsRcLBZDoVDwG1BhIYFHHw2AQNByGs1kAh57jMK//uU8HYokSb7R2NDQgLCwMH6DceZmsxUyj42NRVJSkk+5MXDNOI7JwjAMxGIxevXq5XIJoSNwxdKeM8nkbNUVCoVDXrUtn1uv1zv0xHP2ejk5OcjOzkbPnj2xatUqjBw50idOeF7A3R10bcEwDDQaDXJzc5GXlwe9Xo8pU6YgIyMDgwYNcroJY7VaUVFR0WpW21EYDAZotVq+WcUd091x1LPt7LcWwPLzBViyROLwRjabgREjaOTkOEeHao7mjUbbDcb2pudqoCqVihcyj42N9ckOtm0JgfMja2hoQH19PUJCQvgg5Qsyg1wGXltby2fgHTlZcTbntlkwN0HmaAOtra3Fxx9/jN27d2PKlClYtmyZS4JW3Rz+oNsa9Ho9Dh8+jNzcXFy7dg0PPvggMjIy8MADDzh0N3Alq+0orFYrn0U1NTXZ1YGdDUC2I68EQbTb2b9+ncCUKQEQiVpmumYz8NxzFN56y3UVL1sYjUZ+g+EGF7iR0oiICMjl8ltuvL6H9koIDMOgoaGBr3MD4AOwp2qljsC9njdv3gRN00hOTm5TjcxZcDKcHCNCIpGAJEkEBQUhNDQUmzdvxsmTJzF//nwsWLDAY+JB3QD+oOsMzGYzjh8/jtzcXJw+fRoDBw5ERkYGhg8fjiNHjmDQoEEICgpCUlJSp7LajoCmab4OXFtbywuux8TEOMxWbIWio6OjIZfLnT4SzpwpwfnzrK6BLR1KIACOHTMjJcW9H4f6+noolUrU1tZCLBaDoii7oQxfsdO2zcBpmu4QC4EzJOX0dF3lzToLToVOrVYjJCQEycnJHt3ADAYD/vOf/2Dbtm1QKpUYO3YsP7DkiycUL8IfdDsKkiSxc+dObNy4EWVlZRg0aBAef/xxpKWlITY2tkvqUlwWxWWJYrGYr5NyOghWq5U/lnf0ptZqgWeekaKoSHDLm42lTW3aZMHUqe4RM29uU25LobN1XaiuruafX/MyhLfgbhaCba2UyxLd9fzMZjPUajWqqqoQGxsLuVzuUQ44SZI4ePAgtmzZgtjYWKxYsQIjR47Ef//7X5w6dQrr1q27W2q3rcEfdDsKhmGwatUqzJw5E3/4wx9QVFSE3NxcfPXVVwCAtLQ0pKeno0+fPl324aqrq0NJSQlqamogFAohk8n4o7mra2IYoKBAgF9/JRAZCUyZQrXqmNsR2GbgMpkMSUlJ7QYabiBDq9XCarXyxH5Py2/alhASEhKQlJTkkdqs7fOzWCy880JHykgNDQ1QKpVobGzkXRk8yQpoaGjAp59+ik8//RTjxo3D8uXLfUU03NfgD7ruAufvlZeXhwMHDqC8vByTJk1Ceno6hg8f7nEaDMeNValUMBqNSEpKQnx8PH8E5rQTIiIieFHprjrmMQyDmpoaqNVqWCwWyOVyl61aOGcCbuza3XS7zpQQ3AGOTsjpQwQHB/O14OY9A4ZhoNVqoVKpIBAI0KNHD4+XuzQaDbKzs/HNN9/gmWeewcKFC31CMPzzzz/HunXrcPXqVZw9exYjRoxw+Lj23Gw8AH/Q9RQaGhqQn5+PAwcO4MKFC7j//vuRnp6Ohx56yK3HO6vVaudwwPmLOdaCZY+xVVVV0Ov1CA4O5o+x3uimN+/sKxSKDkn/tYfmdDuO0iSTyTp8TPfUIENnYOs/ptPpwDAMz5mtr69HeXk5IiIi3DaJ19Y6Ll68iMzMTJSUlGDJkiWYNWuW1yROncHVq1chEAiwaNEivPfeew6DLkVRSE1NtXOz2b17t52xggfgD7regNVqxffff4+cnBx8//33SE1NRXp6OqZOnYqIiAiXfmd9fT1UKhUaGhqQkJDQYcI9dwNzdWBb511310k514i6ujqX1uoqmh/TnVF/81YJwR1oaGjAjRs3UFtby8tzxsbGemyohqIoHDlyBJs2bUJwcDD+8pe/4KGHHvLpxtj48eNbDbo//PAD1q1bhyNHjgAANmzYAAB49dVXPbkk73mk3c0Qi8WYNGkSJk2aBJqmceHCBeTk5GDmzJm3XGDZgYzExMQ2j4JcB5pzjFAoFC6LNhMEwfNIU1JS+Pn7q1ev8nXSzkyNcdQ0lUrFK5F11jWio+AkHBUKBV+G0Gg0uHr1ql0ZQigUtightOYc0dXgmoo3b96ExWJBcnIyLwTDNRtLS29LOcbExHQ66zUYDPjss8/w0UcfYfTo0di8ebPX30tPoKNuNp6GP+h6CAKBAMOGDcOwYcPw1ltvoaSkBAcOHMDChQthNBoxdepUTJ8+Hffeey+fQdj6dsXFxblFJLo5bFX7uakxLpN2ZOXTGmy75dHR0ejfv3+XMAyagzNIjI2N5csQlZWVuH79OqxWK0JCQpCSkoKYmJiuXqpDcOwOlUqFgIAAh0aZERERiIiIQO/evflNtKioCCaTCZGRkfzggrOZaUVFBT788EMcOnQITzzxBL755hvIZDJPPD2XMHnyZFRUVLT4+vr16/GnP/2p3Z/viJuNN+APul4AQRBISUnBypUrsXLlSuh0Ohw8eBDr16/HjRs30KtXL5SWlmL16tUYN24cUlNTvXKUE4lEdjZF3NTY77//jsDAwBY2RbZNPJPJBLlcjlGjRvnsDL3BYEB5eTn0ej0UCgWio6P59d+4cYNnQ/iC+JDVaoVarUZFRQViYmIwaNAgp8aem1vf6PV6aLVaXL9+HYGBgS30ITgwDIMrV64gMzMTV65cweLFi1FQUOBTo9Ycvv322079vLNuNt6Cv6bbhdi6dSs2btyIvn37IjAwEIWFhV2mjGYLW5sirpHDyVNyjTFfnTRyloXAidDrdDpefIiTqPRmbbepqQlKpRJ1dXVISkpCYmKiWzYxhmF4ASKdTscL5wcHB4MkSWRnZ0MgEGDlypWYMmWKT9drnUFbNV1n3Gw8AH8jzRdRUlJiJ2TeFcpobYFrNtXU1PDylM42qryNzrAQuDIEN5TBNRs94YXHXa+mpsZOZ9cdI7ptobGxERs3bsShQ4dw8+ZNjB07FvPnz8fjjz/usWt6Azk5OXj55Zeh1WoRERGBIUOG4MiRIygrK8MLL7yAw4cPA3DsZuNh+INud4MnldHau66tTUvzgODIpqgj6mHuhq2YC2fT09lMlauTcgpinPZFeHh4pzJCzr9No9EgNDQUycnJHqen6XQ6bNu2Dfv378fMmTOxZMkSxMXFobCwEJcvX8b8+fM9ev27GP6g253hSBlt8uTJmD59eoeU0dqCrRuDs8aTzdXDOEt3mUzm0RFUbw4yNNdA5rQvOlKGMJvNUKlU0Gq1iIuLg1wu9yjXlWEYXL9+HZs2bcL58+excOFCPPvss11WrrpL4Q+6dxJqa2tx6NAhHDhwAL/99hseeOABTJ8+3aEyWlvggqZKpYLBYEBSUhISEhJczlib14G5I7q7XGm7epDBVvvCtgzRGl2LE/QxGAy8i64na6c0TePUqVPYuHEjzGYzli9fjvT0dJ9pdNbU1GDWrFkoLS1Fz549sW/fPt563RZCoRADBw4E0DnT2i6GP+hy8OGxQZfAKaMdOHAAp0+fxoABA5CRkYEpU6a0GpBsecAcx9Xd9VlOXUur1cJgMLgkT8nBYDDwtWVfGmTgyhCczmxUVBSio6N5JoJIJEKPHj08zo6wWCz48ssv8eGHH6JPnz5YuXIlhg0b5jP1dg5r1qxBVFQUXnnlFbzzzjvQ6/X43//93xaPCwkJQWNjYxes0K3wB10OPjw22GlQFIWCggLk5ubi6NGjiI2NRUZGBqZNm4bY2FiUlJTAarWipqYGcXFxSEpK8oobMUVR0Ov1qKqqctqmqKu1EDoKs9mMGzduQKvVAgDCw8MRHx/v0dFrvV6PHTt2YN++fUhLS8PLL79sNwTga+jbty9OnDiBhIQElJeXY/z48bh27VqLx93pQfeu4+n269ev3cecPXsWvXv3RkpKCgDgqaeewoEDB3w+6AqFQowZMwZjxozBhg0bcP36dezfvx8ZGRmor69HREQEMjMzvc6ttT2G2+omlJaW8vKNnJll8xJCnz59ulwLoS0YjUYolUrU1NQgMTERqampEIlEvJB5YWEhBAKBXamlsyguLsamTZtw5swZPP/88zhz5ozPir7borKyEgkJCQCAhIQEVFVVOXycyWTCiBEjIBKJ8Morr2DmzJneXKbHcdcFXWfga2ODroAgCPTt2xcFBQUYP348nnzySVy7dg3vvvsuysvLMXHiRF6g3ZsBmCAIhIeHIzw8HL179+ZdJC5dugSj0QgAiI+Px7Bhw3xKWMUW3JCIUqmE1WqFQqFAamqqXRYeFhaGsLAwpKSkwGw2t5ga62iphWEY/Pjjj8jMzERNTQ2WLVuGzMxMnxF659DW9JizUCqVSExMRHFxMSZOnIiBAwfinnvucecyuxS+9Y65CXfa2GBn8MUXX/A39kMPPYSFCxfyymjbtm3D0qVLMWbMGGRkZLhdGa09cEMYXFMqNTUVDMNAp9Ph/PnzfHDqSnlKW9iO6AYFBTkc0XUEqVSKpKQkJCUl8aWWyspKXLt2rV0FOKvViq+++gqbN29GUlIS1qxZg/vvv99nP49tTY/FxcWhvLycLy/ExsY6fBw3LZaSkoLx48ejsLDQH3R9HXfa2GBn4ChYhYaG4oknnsATTzzBK6Pl5ubijTfeQJ8+fZCRkdEpZbT2wFnVazQahIWFtSghJCYmthhp9bY8pS0sFgvUajUqKyshk8mcHtF1hOalFk4B7sKFCyAIgi+x9OzZE7t27cKuXbswceJE7Nq1iy93dVfMmDEDH3/8MV555RV8/PHHDhMgvV6PoKAgSKVS6HQ6nD59GmvWrOmC1XoOd10jjYMPjg12OThltNzcXOTn53dIGc0ZuMpC4IJTVVUVnxVzdWBPiuw0NjZCqVSivr4ecrm8U3Q6Z2A2m3Hs2DGsX78eJSUlGDhwIFavXo20tDSfYGt0FtXV1XjyySehVCqRnJyMzz//HFFRUTh37hyys7Oxbds2nDlzBosWLYJAIABN01ixYgUWLFjQ1Ut3BX72AgcfHhv0KTAMwyuj5eXlwWAw4OGHH0ZGRgb69evXoVqku1kIJpMJWq3WzsanM/KUjtarVCoBsDzR6Ohojx7nGYbB+fPnkZmZCY1Gg6VLl2L69Ok4ffo0Dh48iNdffx3x8fEeu74fHoE/6HoLdyoBnFNGO3DgAIqLizF+/Hikp6djzJgxDps5zUsInhp55eQptVotGhoaEBERwctTdqQOzI3oqtVqj663+TUPHTqEzZs3IyoqCitXrsQf/vAHn6hf+9Fp+IOut3A3EMCNRiOOHj2KnJwcFBQUYNiwYcjIyMDEiRNRXFyMxsZGMAzj9UEGzqZIq9WipqYGQUFBLeQpm8NkMkGlUkGn0/HaDZ5mTTQ2NmLXrl345JNPMHbsWKxYsaJLDU6B9oeBzGYz5s2bh/PnzyM6Ohp79+5Fz549u2ax3QP+oOst3GUEcJAkiVOnTiEzMxPHjx9HfHw85syZgzlz5nhcOastNJenJAiCrwMHBQWhrq4OSqUSRqORd9H1dIZZXl6O7Oxs5Ofn46mnnsKLL76I6Ohoj17TGTgzDLR582ZcunQJ2dnZ2LNnD3JycrB3794uXLXPwz8c4S3cbQRwkUiEK1euQCaT4eTJkxAIBMjNzcXs2bMhkUiQlpaGjIwM9OzZ06sBmCAIhISEICQkBL169YLZbEZVVRUuXboEg8EAqVSK5ORk9O/f36PBlmEYXL58GZmZmSgqKsJLL72Et99+26vUvPbgzDDQgQMHsG7dOgDA448/jqVLl4JhGJ+lrvky/EHXBfgJ4PZ46aWX7P4/YMAAvPbaa9BoNDhw4ABWrlzpEWU0Z8E5KZeXlyMqKgoDBgyAwWCAVquFWq3ukE2Rs6BpGt988w2ysrIQGBiIVatWYcKECT5Zr3VmGMj2MSKRCOHh4aiurvZZ2yNfhj/ougA/Abx9EAQBuVyOJUuWYMmSJaitrcXhw4fxwQcf4OrVq3jwwQddUkbrCAwGA5RKJfR6PU/945p+ISEhvI9aXV0dqqqq8PvvvyMgIIAvQ7hS2zUajdi9ezd27NiB4cOHIysrC/369fPpjNCZYaA7aWCoq+EPum6GnwDuGBEREXj66afx9NNPw2w247vvvkNubi7WrFmDgQMHIiMjA5MnT+60hgDDMNDr9VAqlSBJEsnJyW06/hIEwRs9ArflKS9evAgAfABuTzOhqqoKH374IfLy8vDYY48hPz+/1Q3X1+DMMBD3GM7QtK6uDlFRUd5e6h0BfyPNzbjLCOCdBk3TKCgoQE5ODq+Mlp6ejmnTpiEuLs7pbIqmaVRUVEClUiE4OBjJyckICwvr1No4ecqqqipeupHTTCAIAgzD4OrVq9i0aRMuXbqERYsWYe7cuT7hitwRODMMtGnTJly+fJlvpO3fvx/79u3rwlX7PPzshe6Ou4HSwzke5Obm4uDBg6Bpmm/EtUapslgsUKlUqKqqgkwmg0Kh8EiTytZBYsuWLSgtLYVer0d4eDj++te/Ii0tzSfrtc7C0TDQG2+8gREjRmDGjBkwmUyYO3cuCgsLERUVhT179nT7sWQPwx90uzPuRkoPwzCorKxEXl4e8vLyUFZWZqeMdv78eUilUt4KPj4+3uNqaWazGfv27cPWrVuRkpKCsLAwXLx4EUOGDMHWrVs9em0/uh38Qbc744cffsC6detw5MgRAMCGDRsAAK+++ir/mKlTp2LdunW4//77QZIk4uPjodVq75hmR0NDAw4fPozs7GxcvnwZiYmJWLVqFWbMmOGy+IyzqK6uxvbt2/Hll18iIyMDL7/8sl3NU6/XO5w69OOuRqs3Xvc9D91FcETp0Wg0rT7GltJzpyA0NBQFBQW47777cOLECXzwwQc4f/48xo8fj7lz52Lv3r2ora112/UYhkFRURFWrFiB6dOnIyYmBj/++CM2bNjQosnkzYCbn5+Pvn37onfv3njnnXdafH/nzp2QyWQYMmQIhgwZgm3btnltbX44Bz97oRvAT+lh8e6779o9p4kTJ4KmaVy8eBE5OTmYOXMmwsLCMG3aNEyfPt0lZTSapnH69GlkZWWhoaEBy5cvx5YtW3zC3JGiKCxZssSuzDRjxowWjiazZs1CVlaWV9dWUFCABQsW4OzZs6AoCqNGjcLevXsxYMAAr66jO8AfdLsB/JQeFo4CqEAgwNChQzF06FC8+eabvDLaokWL0NTU5LQymtVqxf79+/Hvf/8bvXr14ptIvrRx+bKNFLcBvP766zAajZgzZ44/4LYCf3mhG2DkyJEoKipCSUkJLBYL9uzZgxkzZtg9huMHA6xbxMSJE30qYHgDBEEgJSUFK1euxPHjx3Ho0CH06tULGzZswAMPPIBXXnkFp06dAkmS/M/U1tbigw8+wIMPPohffvkF+/btw+7duzFy5Eife/2cKTMBwJdffolBgwbh8ccft9usPY033ngDR48exblz5+543nln4M90uwFEIhGysrIwdepUntLTv39/O0rPggULMHfuXPTu3Zun9NztiImJwfz58zF//nxeGW3Pnj1YtWoV+vfvD6vVihs3bmD+/Pk4ffp0p3m9noYzJaTp06dj9uzZkEqlyM7OxrPPPovjx497ZX01NTVobGyE1WqFyWRyiwnnnQg/e8EPO7THB965cydWr16NpKQkAMDSpUvxwgsvdMVSXQZJksjPz0dBQQHWrl3rc+aOrcEZFostKIpCVFQU6urqvLK+GTNm4KmnnkJJSQnKy8u9Xlf2MbR+TGIYpq0/ftxFIEmSSUlJYX7//XfGbDYzgwYNYn799Ve7x3z00UfMkiVLumiFdzesVivTq1cvpri4mH9/fvnlF7vHlJWV8f/ev38/M3r0aK+s7eOPP2YeeeQRhmHYz9GoUaOYY8eOeeXaPopW42r32OLvQKxduxYxMTFYvnw5AOC1115DXFwcli1b1mVr8uVGjR/OlZk2btyIvLw8iEQiREVFYefOnV5Z27x58zBv3jwArCtKc5UyP27DX17oIpSWluLRRx/Fzz//DJqm0adPH5w9e7ZLRa2/+OIL3podAD799FP89NNPdsfEnTt34tVXX4VMJkNqair+7//+z66544cffgDwD0f4Hnr27Ino6GgUFhbim2++wdChQ7vcRcDRBuyoUVNaWopLly5h8uTJePbZZ721PD/8uCPgLy90IV544QXs3LkTFRUVeP7557t6OU7xgW03hj//+c/429/+5rX1+eHHnQB/ptuFeOSRR/gu+tSpU7t6OU7xgcvLy/l/5+XloV+/ft5epk/j+eefR2xsbKuDAQzDYNmyZejduzcGDVW6EkwAAAHnSURBVBqEn3/+2csr9KOr4c90uxASiQQTJkxARESET4yZ+nKjprtg/vz5WLp0Kd9Uao6vv/4aRUVFKCoqwk8//YTFixf7m053G9qiNnifZXF3gaIoZvDgwcz169e7eilexXPPPcfIZDKmf//+Dr9P0zTz8ssvM/fccw8zcOBA5vz5815eYedQUlLS6nNbuHAh89lnn/H/T01NtaN5+XHHoNW46i8vdBGuXLmC3r17Y9KkSejTp09XL8ermD9/PvLz81v9vm02+OGHH2Lx4sVeXJ1n4eworx93LvzlhS7Cfffdh+Li4q5eRpdg3LhxKC0tbfX7Bw4cwLx580AQBMaMGYPa2lre7LO7g7kL1OD8aBv+TNcPn8OdnA06wxDx485Ge8MRfvjhERAE0RPAQYZhWrT5CYI4BGADwzCnbv3/GIA1DMOc9+oiXUQ7zy0dwFIA0wCMBrCRYZhRXl2gH10Kf3nBD1+EGoDtmJscQFkXraVDIAhiN4DxAGIIglAD+B8AYgBgGCYbwGGwAfcGAAOA57pmpX50FfxB1w9fRB6ApQRB7AGbDdYxDFPezs/4BBiGmd3O9xkAS7y0HD98EP6g64fX4c8G/bib4a/p+uGHH354EX72gh9++OGHF+EPun744YcfXsT/B6GHjJCIe9AEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d # import function to enable 3-dimensional plotting in matplotlib\n",
    "\n",
    "ax = plt.subplot(projection='3d') # setup figure for a 3-d plot\n",
    "ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='winter') # 3d scatter of X (2 components) and r, labelled by y\n",
    "ax.view_init(elev=30, azim=40) # set in degrees the elevation and azimuthal angle for plot\n",
    "ax.set_xlabel('x') # x label\n",
    "ax.set_ylabel('y') # y label\n",
    "ax.set_zlabel('r') # z label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to classify this data would be to plot the data in polar coordinates in terms of the radius and angle of each point about a point in feature space. This point needs to be chosen so that the decision boundaries are vertical lines, since they must be periodic. In this case SVC is easily able to delineate the two datasets. In terms of the original variables, these decision boundaries are then circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Angle')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = np.zeros(X.shape) # create an array of zeros with the same shape as X\n",
    "Z[:,0] = np.sqrt((X[:,0]-.01)**2 + X[:,1]**2) # first component is the distance from (.01,0)\n",
    "Z[:,1] = np.arctan2(X[:,0]-.01, X[:,1]) # second component is the angle between X and (.01,0)\n",
    "\n",
    "clf = SVC(kernel='linear',C=1.E10) # instantatiate SVC with linear kernel and hard boundaries\n",
    "clf.fit(Z, y) # fit the Z and y data to the model\n",
    "plt.scatter(Z[:,0], Z[:,1], c=y, s=50, cmap='winter') # scatter plot of Z labelled by y\n",
    "plot_svc_decision_function(clf, plot_support=True); # plot the decision boundaries and support vectors\n",
    "plt.xlabel('Radius') # x label\n",
    "plt.ylabel('Angle') # y label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gaussian or exponential function dependent on the distance from the origin is known as a radial basis function or `rbf`. If we specify the `kernel='rbf'` then radial basis functions are used to transform the data to a new feature space. They are then classified in the new feature space using `SVC`. The actual form of the kernel for radial basis functions used in the SVC is\n",
    "\n",
    "$$ \\phi(X,Y) = \\exp (-{\\rm gamma } (d(X,Y))^2 ), $$\n",
    "\n",
    "where $d(X,Y)$ is the distance between points $X$ and $Y$ in feature space. The accuracy of the classifier is therefore dependent on the parameter `gamma`, which needs to be specified in calling `SVC`. Setting `gamma=auto` sets this to a default value. The optimal value of this hyperparameter should be determined using a cross-validation grid search, such as the `sklearn` function `GridSearchCV`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = SVC(kernel='rbf', C=1.E6, gamma='auto') # instantatiate SVC with rbf kernel and hard boundaries\n",
    "clf.fit(X, y); # fit the X and y data using SVC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plotting the decision function and the support vectors it can be seen that SVC is able to correctly classify the circles dataset. Now the decision boundaries are ellipses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter') # scatter plot of X labelled by y\n",
    "plot_svc_decision_function(clf) # plot the decision boundaries and support vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Radial basis functions are just one type of kernel that can be used by SVC. Other options are polynomials, the sigmoid function (a smooth step function similar to the logistic function), and user defined kernel functions. Each of these functions are dependent of particular hyperparameters for which the optimal parameters must be determined by cross-validation grid search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Soft boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far we have only considered datasets which are clearly dilineated in feature space, and for that we have set the hyperparameter `C` to some large value. However, if the datasets merge in some region we can relax the hardness of the boundaries by using smaller values of `C`. This allows somes data points to lie in the decision region. \n",
    "\n",
    "For example, if we return to the blobs dataset but increase the standard deviation then we have a region of crossover of our datasets. In this case, if we specify a hard boundary we would not be able to separate the two datasets, and the width of the decision boundary would go to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a blobs dataset with a larger standard deviation so that the blobs intersect\n",
    "X, y  = make_blobs(n_samples=100, centers=2, random_state=0, cluster_std=1.)\n",
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter'); # scatterplot of blobs "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the effect of changing `C` for this dataset. For large `C` the width of the decision strip becomes smaller, with only a few points lying in this region. For smaller `C` the margins are softer and the decision strip grows in width, with more points lying in this region."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 5)) # setup two subplots on figures of size (12,5)\n",
    "\n",
    "# zip bundles together the axis indices and values of C, and we loop over these\n",
    "for axi, C in zip(ax, [10.0, 0.1]): \n",
    "    model = SVC(kernel='linear', C=C) # instantatiate SVC with linear kernels and variable softness of boundaries\n",
    "    model.fit(X, y) # fit X and y using SVC\n",
    "    axi.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter') # scatterplot of blobs\n",
    "    plot_svc_decision_function(model, axi) # overlay decision boundaries and support vectors on current axes\n",
    "    axi.set_title('C = {0:.1f}'.format(C)) # add a title which include current value of C to 1 decimal place"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimal value of `C` would again need to be determined by investigating the accuracy for a test set using a cross-validation grid search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multinomial classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To classify multinomial data `SVC` uses the One vs One algorithm, and divides the problem into N(N-1)/2 binary classification problems, where there are N labels. For linear kernels the classifier `LinearSVC` uses the One vs Rest algorithm, which divides the problem into N binary classification problems. \n",
    "\n",
    "First we include the function for plotting multinomial decision boundaries for a two dimensional problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plt_decision_boundaries(skm,X):\n",
    "    \"\"\"\n",
    "    Takes a sklearn model (skm) with two features specified by the (N,2) array X and plots the decision boundaries.\n",
    "    \"\"\"\n",
    "    h = .02  # step size in the mesh\n",
    "    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1 # find the minimum and maximum of the first feature\n",
    "    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1 # find the minimum and maximum of the second feature\n",
    "    # create a rectangular grid which goes from the minimum to maximum values in step-size of h\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),np.arange(y_min, y_max, h)) \n",
    "    # ravel is a numpy method which converts a two-dimensional array of size (n,m) to a vector of length nm\n",
    "    # column_stack is a numpy function which takes two column arrays of length N \n",
    "    # and creates a two-dimensional array of size (N,2)\n",
    "    # now pass the (N,2) array to the model and predict values based on these features, zz will have size (N,1)\n",
    "    zz = skm.predict(np.column_stack([xx.ravel(), yy.ravel()]))  \n",
    "    zz = zz.reshape(xx.shape) # reshape zz so it has the size of the original array xx, i.e., (n,m)\n",
    "    plt.contourf(xx, yy, zz, cmap=plt.cm.Paired) # plot the decision boundaries as filled contours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now investigate using third order polynomial kernels to classify a blobs dataset with three labels. This is specified by setting the parameters `kernel='poly'` and `degree=3` when we instantatiate the classifier. The accuracy of the model will then be dependent on the parameters `gamma`, `coef0`, and `C`, and the optimal values would need to be determined using a cross-validation grid search using `GridSearchCV`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create 3 sets of blobs each labelled by y, each will have 50 points\n",
    "X, y  = make_blobs(n_samples=150, centers=3, random_state=0, cluster_std=.8) \n",
    "\n",
    "# instantatiate SVC with polynomial kernel of degree 3, with parameters gamma and coef0, \n",
    "# the boundary is relatively soft\n",
    "model = SVC(kernel='poly', degree=3, gamma='auto', coef0=2, C=1.) \n",
    "model.fit(X, y) # fit the X and y data using SVC\n",
    "plt_decision_boundaries(model, X) # plot the decision boundaries\n",
    "plt.scatter(X[:,0], X[:,1], c=y, s=50, cmap='winter'); # scatter plot of X labelled by y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Penguins Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Penguins dataset is one of the builtin datasets for `seaborn`. It classifies three species of penguins on islands in the South Atlantic based on four physical characteristics. It can be imported in the same manner as the Iris dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "penguins = sns.load_dataset('penguins')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first need to do some preliminary EDA on the data. If we look at the header it is apparent that there are missing entries, as signified by `NaN`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>species</th>\n",
       "      <th>island</th>\n",
       "      <th>bill_length_mm</th>\n",
       "      <th>bill_depth_mm</th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "      <th>sex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.1</td>\n",
       "      <td>18.7</td>\n",
       "      <td>181.0</td>\n",
       "      <td>3750.0</td>\n",
       "      <td>MALE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.5</td>\n",
       "      <td>17.4</td>\n",
       "      <td>186.0</td>\n",
       "      <td>3800.0</td>\n",
       "      <td>FEMALE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>40.3</td>\n",
       "      <td>18.0</td>\n",
       "      <td>195.0</td>\n",
       "      <td>3250.0</td>\n",
       "      <td>FEMALE</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>36.7</td>\n",
       "      <td>19.3</td>\n",
       "      <td>193.0</td>\n",
       "      <td>3450.0</td>\n",
       "      <td>FEMALE</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  species     island  bill_length_mm  bill_depth_mm  flipper_length_mm  \\\n",
       "0  Adelie  Torgersen            39.1           18.7              181.0   \n",
       "1  Adelie  Torgersen            39.5           17.4              186.0   \n",
       "2  Adelie  Torgersen            40.3           18.0              195.0   \n",
       "3  Adelie  Torgersen             NaN            NaN                NaN   \n",
       "4  Adelie  Torgersen            36.7           19.3              193.0   \n",
       "\n",
       "   body_mass_g     sex  \n",
       "0       3750.0    MALE  \n",
       "1       3800.0  FEMALE  \n",
       "2       3250.0  FEMALE  \n",
       "3          NaN     NaN  \n",
       "4       3450.0  FEMALE  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "penguins.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are not going to use the sex of the penguins or the island that they are found on, however the four other characteristics will be investigated. We can then investigate how many rows having missing entries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>species</th>\n",
       "      <th>island</th>\n",
       "      <th>bill_length_mm</th>\n",
       "      <th>bill_depth_mm</th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "      <th>sex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>34.1</td>\n",
       "      <td>18.1</td>\n",
       "      <td>193.0</td>\n",
       "      <td>3475.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>42.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>190.0</td>\n",
       "      <td>4250.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>37.8</td>\n",
       "      <td>17.1</td>\n",
       "      <td>186.0</td>\n",
       "      <td>3300.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>37.8</td>\n",
       "      <td>17.3</td>\n",
       "      <td>180.0</td>\n",
       "      <td>3700.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>47</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Dream</td>\n",
       "      <td>37.5</td>\n",
       "      <td>18.9</td>\n",
       "      <td>179.0</td>\n",
       "      <td>2975.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>246</td>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>44.5</td>\n",
       "      <td>14.3</td>\n",
       "      <td>216.0</td>\n",
       "      <td>4100.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>286</td>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>46.2</td>\n",
       "      <td>14.4</td>\n",
       "      <td>214.0</td>\n",
       "      <td>4650.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>324</td>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>47.3</td>\n",
       "      <td>13.8</td>\n",
       "      <td>216.0</td>\n",
       "      <td>4725.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>336</td>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>44.5</td>\n",
       "      <td>15.7</td>\n",
       "      <td>217.0</td>\n",
       "      <td>4875.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>339</td>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    species     island  bill_length_mm  bill_depth_mm  flipper_length_mm  \\\n",
       "3    Adelie  Torgersen             NaN            NaN                NaN   \n",
       "8    Adelie  Torgersen            34.1           18.1              193.0   \n",
       "9    Adelie  Torgersen            42.0           20.2              190.0   \n",
       "10   Adelie  Torgersen            37.8           17.1              186.0   \n",
       "11   Adelie  Torgersen            37.8           17.3              180.0   \n",
       "47   Adelie      Dream            37.5           18.9              179.0   \n",
       "246  Gentoo     Biscoe            44.5           14.3              216.0   \n",
       "286  Gentoo     Biscoe            46.2           14.4              214.0   \n",
       "324  Gentoo     Biscoe            47.3           13.8              216.0   \n",
       "336  Gentoo     Biscoe            44.5           15.7              217.0   \n",
       "339  Gentoo     Biscoe             NaN            NaN                NaN   \n",
       "\n",
       "     body_mass_g  sex  \n",
       "3            NaN  NaN  \n",
       "8         3475.0  NaN  \n",
       "9         4250.0  NaN  \n",
       "10        3300.0  NaN  \n",
       "11        3700.0  NaN  \n",
       "47        2975.0  NaN  \n",
       "246       4100.0  NaN  \n",
       "286       4650.0  NaN  \n",
       "324       4725.0  NaN  \n",
       "336       4875.0  NaN  \n",
       "339          NaN  NaN  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = penguins[penguins.isna().any(axis=1)]\n",
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are only two rows with missing entries in the physical characteristics, so we will drop these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(342, 7)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "penguins.dropna(subset=['bill_length_mm','bill_depth_mm','flipper_length_mm','body_mass_g'],\n",
    "                how='any',inplace=True)\n",
    "penguins.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This leaves us with a dataframe of 342 entries. Now we will concentrate on the features of interest.\n",
    "\n",
    "First, we can investigate the species of penguins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Adelie', 'Chinstrap', 'Gentoo'], dtype=object)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "penguins['species'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can look at the descriptive statistics for the numerical values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bill_length_mm</th>\n",
       "      <th>bill_depth_mm</th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>342.000000</td>\n",
       "      <td>342.000000</td>\n",
       "      <td>342.000000</td>\n",
       "      <td>342.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>43.921930</td>\n",
       "      <td>17.151170</td>\n",
       "      <td>200.915205</td>\n",
       "      <td>4201.754386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>5.459584</td>\n",
       "      <td>1.974793</td>\n",
       "      <td>14.061714</td>\n",
       "      <td>801.954536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>32.100000</td>\n",
       "      <td>13.100000</td>\n",
       "      <td>172.000000</td>\n",
       "      <td>2700.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>39.225000</td>\n",
       "      <td>15.600000</td>\n",
       "      <td>190.000000</td>\n",
       "      <td>3550.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>44.450000</td>\n",
       "      <td>17.300000</td>\n",
       "      <td>197.000000</td>\n",
       "      <td>4050.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>48.500000</td>\n",
       "      <td>18.700000</td>\n",
       "      <td>213.000000</td>\n",
       "      <td>4750.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>59.600000</td>\n",
       "      <td>21.500000</td>\n",
       "      <td>231.000000</td>\n",
       "      <td>6300.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       bill_length_mm  bill_depth_mm  flipper_length_mm  body_mass_g\n",
       "count      342.000000     342.000000         342.000000   342.000000\n",
       "mean        43.921930      17.151170         200.915205  4201.754386\n",
       "std          5.459584       1.974793          14.061714   801.954536\n",
       "min         32.100000      13.100000         172.000000  2700.000000\n",
       "25%         39.225000      15.600000         190.000000  3550.000000\n",
       "50%         44.450000      17.300000         197.000000  4050.000000\n",
       "75%         48.500000      18.700000         213.000000  4750.000000\n",
       "max         59.600000      21.500000         231.000000  6300.000000"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "penguins.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to investigate these features is to plot histograms of the features, which shows that the features are clearly not normally distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "penguins[['bill_length_mm','bill_depth_mm','flipper_length_mm','body_mass_g']].hist(alpha=0.5, bins=50,\n",
    "                                                                                   figsize=(10,8));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also create scatter plots of the classifications as a function of the numerical features. In this case we will concentrate on the bill measurements. If you investigate the other features it is apparent that the classifications are much more delineated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 444.125x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(\"bill_depth_mm\",\"bill_length_mm\",hue='species',data=penguins,fit_reg=False) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first will attempt to model the Chinstrap penguin as a function of the bill measurements using SVM with a linear kernel. The first step is to convert the classification to binary columns using one-hot-encoding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>species</th>\n",
       "      <th>island</th>\n",
       "      <th>bill_length_mm</th>\n",
       "      <th>bill_depth_mm</th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "      <th>sex</th>\n",
       "      <th>code</th>\n",
       "      <th>species_Adelie</th>\n",
       "      <th>species_Chinstrap</th>\n",
       "      <th>species_Gentoo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.1</td>\n",
       "      <td>18.7</td>\n",
       "      <td>181.0</td>\n",
       "      <td>3750.0</td>\n",
       "      <td>MALE</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.5</td>\n",
       "      <td>17.4</td>\n",
       "      <td>186.0</td>\n",
       "      <td>3800.0</td>\n",
       "      <td>FEMALE</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>40.3</td>\n",
       "      <td>18.0</td>\n",
       "      <td>195.0</td>\n",
       "      <td>3250.0</td>\n",
       "      <td>FEMALE</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>36.7</td>\n",
       "      <td>19.3</td>\n",
       "      <td>193.0</td>\n",
       "      <td>3450.0</td>\n",
       "      <td>FEMALE</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.3</td>\n",
       "      <td>20.6</td>\n",
       "      <td>190.0</td>\n",
       "      <td>3650.0</td>\n",
       "      <td>MALE</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  species     island  bill_length_mm  bill_depth_mm  flipper_length_mm  \\\n",
       "0  Adelie  Torgersen            39.1           18.7              181.0   \n",
       "1  Adelie  Torgersen            39.5           17.4              186.0   \n",
       "2  Adelie  Torgersen            40.3           18.0              195.0   \n",
       "4  Adelie  Torgersen            36.7           19.3              193.0   \n",
       "5  Adelie  Torgersen            39.3           20.6              190.0   \n",
       "\n",
       "   body_mass_g     sex  code  species_Adelie  species_Chinstrap  \\\n",
       "0       3750.0    MALE     0               1                  0   \n",
       "1       3800.0  FEMALE     0               1                  0   \n",
       "2       3250.0  FEMALE     0               1                  0   \n",
       "4       3450.0  FEMALE     0               1                  0   \n",
       "5       3650.0    MALE     0               1                  0   \n",
       "\n",
       "   species_Gentoo  \n",
       "0               0  \n",
       "1               0  \n",
       "2               0  \n",
       "4               0  \n",
       "5               0  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "penguins['code'] = penguins.species.astype('category').cat.codes \n",
    "categories = penguins.species.unique() # create a vector with the category names,\n",
    "lencat = len(categories) # store the length of the categories vector to use later\n",
    "# one hot encoding, create three new columns which are true for that particular species, and false if not\n",
    "for species in categories: # loop over all the labels in categories\n",
    "    # + concatenates two strings\n",
    "    penguins['species_'+species] = pd.Series(penguins['species']==species).astype(int)\n",
    "    \n",
    "penguins.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we create our feature table and our target variable, and then normalize the feature variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = penguins[['bill_length_mm','bill_depth_mm']]\n",
    "Y = penguins['species_Chinstrap']\n",
    "\n",
    "XX = (X-X.mean())/X.std();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we split these tables into testing and training sets. Note that because of the cost of SVM, we split them into equal sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split # import the splitting method from sklearn\n",
    "\n",
    "X_train,X_test,Y_train,Y_test=train_test_split(XX,Y,train_size=0.5,random_state=0) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now model the species using SVM with a linear kernel and hard boundaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC # import the SVM classifier from sklearn\n",
    "\n",
    "model = SVC(kernel='linear', C=1.E10) # instantatiate the model with a linear kernel and hard boundaries\n",
    "model.fit(X_train, Y_train); # fit our data to the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model can be assessed by plotting the SVC decision function against the training variables. As is apparent, the fit is not particularly great."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train.iloc[:,0], X_train.iloc[:,1], c=Y_train, s=50, cmap='winter') # scatter plot of the data\n",
    "plot_svc_decision_function(model) # overlay the decision boundaries and support vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could investigate the confusion matrix, but here we will just concentrate on the accuracy measurements for the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.895\n",
      "Precision: 0.767\n",
      "Recall: 0.676\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score, precision_score, recall_score # import the score functions \n",
    "\n",
    "y_pred = model.predict(X_test)\n",
    "print(\"Accuracy:\",np.round(accuracy_score(Y_test, y_pred),3)) # calculate and print the accuracy score\n",
    "print(\"Precision:\",np.round(precision_score(Y_test, y_pred),3)) # calculate and print the precision score\n",
    "print(\"Recall:\",np.round(recall_score(Y_test, y_pred),3)) # calculate and print the recall score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows that the model is reasonable, but clearly the boundary is not a linear hyperplane. Therefore, rather than experiment on changing the hardness of the boundaries, it is better to investigate using nonlinear kernels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use SVC with `rbf` and `poly` kernels to try to get a better accuracy for the model. For the polynomial kernel, use degree=3 (the default value). By varying the coefficients and the hardness of the boundaries, you should be able to achieve an accurary of at least 97% for both nonlinear kernels. Include plots of the decision function against the training set for your optimal parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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1628
    "Optimal parameters for polynomial kernel. They don't need to use `GridSearchCV`, rather just show the final parameters they used. Parameters don't have to be exactly as shown, but accuracy for both should be 97%. (3 marks)"
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   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.977\n"
     ]
    },
    {
     "data": {
      "image/png": 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