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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Sebastian Raschka](http://sebastianraschka.com)  \n",
      "\n",
      "- [Open in IPython nbviewer](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/python_howtos/scikit_linear_classificationreate=1)  \n",
      "\n",
      "- [Link to this IPython notebook on Github](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/machine_learning/scikit-learn/scikit_linear_classification.ipynb)  \n",
      "\n",
      "- [Link to the GitHub Repository pattern_classification](https://github.com/rasbt/pattern_classification)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import time\n",
      "import platform\n",
      "print('Last updated: %s' %time.strftime('%d/%m/%Y'))\n",
      "print('Created using Python', platform.python_version())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Last updated: 26/06/2014\n",
        "Created using Python 3.4.1\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<hr>\n",
      "I would be happy to hear your comments and suggestions.  \n",
      "Please feel free to drop me a note via\n",
      "[twitter](https://twitter.com/rasbt), [email](mailto:bluewoodtree@gmail.com), or [google+](https://plus.google.com/+SebastianRaschka).\n",
      "<hr>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "An Introduction to simple linear supervised classification using `scikit-learn`"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this introduction I want to give a brief overview of how Python's `scikit-learn` machine learning library can be used for simple linear classification."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Sections"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [About the dataset](#About-the-dataset)\n",
      "- [Reading in a dataset from a CSV file](#Reading-in-a-dataset-from-a-CSV-file)\n",
      "- [Visualizing the Wine dataset](#Visualizing-the-Wine-dataset)\n",
      "- [Splitting into training and test dataset](#Splitting-into-training-and-test-dataset)\n",
      "- [Feature Scaling](#Feature-Scaling)\n",
      "- [Introduction to Multiple Discriminant Analysis (MDA)](#MDA)\n",
      "- [Classification via LDA](#LDA)\n",
      "- [Stochastic Gradient Descent (SGD) as linear classifier](#SGD)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "About the dataset"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For the following tutorial, we will be working with the free \"Wine\" Dataset that is deposited on the UCI machine learning repository  \n",
      "(http://archive.ics.uci.edu/ml/datasets/Wine).\n",
      "\n",
      "<br>\n",
      "\n",
      "<font size=\"1\">\n",
      "**Reference:**\n",
      "Forina, M. et al, PARVUS - An Extendible Package for Data\n",
      "Exploration, Classification and Correlation. Institute of Pharmaceutical\n",
      "and Food Analysis and Technologies, Via Brigata Salerno, \n",
      "16147 Genoa, Italy.</font>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Wine dataset consists of 3 different classes where each row correspond to a particular wine sample.\n",
      "\n",
      "The class labels (1, 2, 3) are listed in the first column, and the columns 2-14 correspond to the following 13 attributes (features):\n",
      "\n",
      "1) Alcohol  \n",
      "2) Malic acid  \n",
      "3) Ash  \n",
      "4) Alcalinity of ash    \n",
      "5) Magnesium  \n",
      "6) Total phenols  \n",
      "7) Flavanoids  \n",
      "8) Nonflavanoid phenols  \n",
      "9) Proanthocyanins  \n",
      "10) Color intensity  \n",
      "11) Hue  \n",
      "12) OD280/OD315 of diluted wines  \n",
      "13) Proline     \n",
      "\n",
      "An excerpt from the wine_data.csv dataset:\n",
      "    \n",
      "<pre>1,14.23,1.71,2.43,15.6,127,2.8,3.06,.28,2.29,5.64,1.04,3.92,1065\n",
      "1,13.2,1.78,2.14,11.2,100,2.65,2.76,.26,1.28,4.38,1.05,3.4,1050\n",
      "[...]\n",
      "2,12.37,.94,1.36,10.6,88,1.98,.57,.28,.42,1.95,1.05,1.82,520\n",
      "2,12.33,1.1,2.28,16,101,2.05,1.09,.63,.41,3.27,1.25,1.67,680\n",
      "[...]\n",
      "3,12.86,1.35,2.32,18,122,1.51,1.25,.21,.94,4.1,.76,1.29,630\n",
      "3,12.88,2.99,2.4,20,104,1.3,1.22,.24,.83,5.4,.74,1.42,530</pre>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Reading in a dataset from a CSV file"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since it is quite typical to have the input data stored locally, as mentioned above, we will use the [`numpy.loadtxt`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html) function  now to read in the data from the CSV file.  \n",
      "(alternatively [`np.genfromtxt()`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.genfromtxt.html) could be used in similar way, it provides some additional options)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "# reading in all data into a NumPy array\n",
      "all_data = np.loadtxt(open(\"../../data/wine_data.csv\",\"r\"),\n",
      "        delimiter=\",\", \n",
      "        skiprows=0, \n",
      "        dtype=np.float64\n",
      "        )\n",
      "\n",
      "# load class labels from column 1\n",
      "y_wine = all_data[:,0]\n",
      "\n",
      "# conversion of the class labels to integer-type array\n",
      "y_wine = y_wine.astype(np.int64, copy=False)\n",
      "\n",
      "# load the 14 features\n",
      "X_wine = all_data[:,1:]\n",
      "\n",
      "# printing some general information about the data\n",
      "print('\\ntotal number of samples (rows):', X_wine.shape[0])\n",
      "print('total number of features (columns):', X_wine.shape[1])\n",
      "\n",
      "# printing the 1st wine sample\n",
      "float_formatter = lambda x: '{:.2f}'.format(x)\n",
      "np.set_printoptions(formatter={'float_kind':float_formatter})\n",
      "print('\\n1st sample (i.e., 1st row):\\nClass label: {:d}\\n{:}\\n'\n",
      "          .format(int(y_wine[0]), X_wine[0]))\n",
      "\n",
      "# printing the rel.frequency of the class labels\n",
      "print('Class label frequencies')\n",
      "print('Class 1 samples: {:.2%}'.format(list(y_wine).count(1)/y_wine.shape[0]))\n",
      "print('Class 2 samples: {:.2%}'.format(list(y_wine).count(2)/y_wine.shape[0]))\n",
      "print('Class 3 samples: {:.2%}'.format(list(y_wine).count(3)/y_wine.shape[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "total number of samples (rows): 178\n",
        "total number of features (columns): 13\n",
        "\n",
        "1st sample (i.e., 1st row):\n",
        "Class label: 1\n",
        "[14.23 1.71 2.43 15.60 127.00 2.80 3.06 0.28 2.29 5.64 1.04 3.92 1065.00]\n",
        "\n",
        "Class label frequencies\n",
        "Class 1 samples: 33.15%\n",
        "Class 2 samples: 39.89%\n",
        "Class 3 samples: 26.97%\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Visualizing the Wine dataset"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are endless way to visualize datasets for get an initial idea of how the data looks like. The most common ones are probably histograms and scatter plots."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Scatter plots are useful for visualizing features in more than just one dimension, for example to get a feeling for the correlation between particular features.  \n",
      "Unfortunately, we can't plot all 13 features here at once, since the visual cortex of us humans is limited to a maximum of three dimensions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below, we will create an example 2D-Scatter plot from the features \"Alcohol content\" and \"Malic acid content\".  \n",
      "Additionally, we will use the [`scipy.stats.pearsonr`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html) function to calculate a Pearson correlation coefficient between these two features.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "from scipy.stats import pearsonr\n",
      "\n",
      "plt.figure(figsize=(10,8))\n",
      "\n",
      "for label,marker,color in zip(\n",
      "        range(1,4),('x', 'o', '^'),('blue', 'red', 'green')):\n",
      "\n",
      "    # Calculate Pearson correlation coefficient\n",
      "    R = pearsonr(X_wine[:,0][y_wine == label], X_wine[:,1][y_wine == label])\n",
      "    plt.scatter(x=X_wine[:,0][y_wine == label], # x-axis: feat. from col. 1\n",
      "                y=X_wine[:,1][y_wine == label], # y-axis: feat. from col. 2\n",
      "                marker=marker, # data point symbol for the scatter plot\n",
      "                color=color,\n",
      "                alpha=0.7, \n",
      "                label='class {:}, R={:.2f}'.format(label, R[0]) # label for the legend\n",
      "                )\n",
      "    \n",
      "plt.title('Wine Dataset')\n",
      "plt.xlabel('alcohol by volume in percent')\n",
      "plt.ylabel('malic acid in g/l')\n",
      "plt.legend(loc='upper right')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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HmTt3bqnnqioKWiIiUi+1aAHt25973KsXVPQLd08+eW64MCzM3rtVkXOYzWZWrVrFoUOH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\nah7OJ7wrYQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106298160>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we want to pack 3 different features into one scatter plot at once, we can also do the same thing in 3D:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "\n",
      "fig = plt.figure(figsize=(8,8))\n",
      "ax = fig.add_subplot(111, projection='3d')\n",
      "   \n",
      "for label,marker,color in zip(\n",
      "        range(1,4),('x', 'o', '^'),('blue','red','green')):\n",
      "    \n",
      "    ax.scatter(X_wine[:,0][y_wine == label], \n",
      "               X_wine[:,1][y_wine == label], \n",
      "               X_wine[:,2][y_wine == label],  \n",
      "               marker=marker, \n",
      "               color=color, \n",
      "               s=40, \n",
      "               alpha=0.7,\n",
      "               label='class {}'.format(label))\n",
      "\n",
      "ax.set_xlabel('alcohol by volume in percent')\n",
      "ax.set_ylabel('malic acid in g/l')\n",
      "ax.set_zlabel('ash content in g/l')\n",
      "\n",
      "plt.title('Wine dataset')\n",
      "     \n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ls25A/wkwG/etUSazSqHcIpWMkX4zKqA8z6vCWc4m2qksTOaSrXAy5VZGIhFE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\nxYsXlf3P9evXk52dzeLFi2udBWtJn37j4uJwdHTE3d3d2ENplNq2bUtwc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       "text": [
        "<matplotlib.figure.Figure at 0x10753d748>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Splitting into training and test dataset "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is a typical procedure for machine learning and pattern classification tasks to split one dataset into two: a training dataset and a test dataset.  \n",
      "The training dataset is henceforth used to train our algorithms or classifier, and the test dataset is a way to validate the outcome quite objectively before we apply it to \"new, real world data\".\n",
      "\n",
      "Here, we will split the dataset randomly so that 70% of the total dataset will become our training dataset, and 30% will become our test dataset, respectively."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cross_validation import train_test_split\n",
      "from sklearn import preprocessing\n",
      "\n",
      "X_train, X_test, y_train, y_test = train_test_split(X_wine, y_wine,\n",
      "     test_size=0.30, random_state=123)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that since this a random assignment, the original relative frequencies for each class label are not maintained."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('Class label frequencies')\n",
      "        \n",
      "print('\\nTraining Dataset:')    \n",
      "for l in range(1,4):\n",
      "    print('Class {:} samples: {:.2%}'.format(l, list(y_train).count(l)/y_train.shape[0]))\n",
      "    \n",
      "print('\\nTest Dataset:')     \n",
      "for l in range(1,4):\n",
      "    print('Class {:} samples: {:.2%}'.format(l, list(y_test).count(l)/y_test.shape[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Class label frequencies\n",
        "\n",
        "Training Dataset:\n",
        "Class 1 samples: 36.29%\n",
        "Class 2 samples: 42.74%\n",
        "Class 3 samples: 20.97%\n",
        "\n",
        "Test Dataset:\n",
        "Class 1 samples: 25.93%\n",
        "Class 2 samples: 33.33%\n",
        "Class 3 samples: 40.74%\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Feature Scaling"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another popular procedure is to standardize the data prior to fitting the model and other analyses so that the features will have the properties of a standard normal distribution with   \n",
      "\n",
      "$\\mu = 0$ and $\\sigma = 1$\n",
      "\n",
      "where $\\mu$ is the mean (average) and $\\sigma$ is the standard deviation from the mean, so that the standard scores of the samples are calculated as follows:\n",
      "\n",
      "\\begin{equation} z = \\frac{x - \\mu}{\\sigma}\\end{equation} "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "std_scale = preprocessing.StandardScaler().fit(X_train)\n",
      "X_train = std_scale.transform(X_train)\n",
      "X_test = std_scale.transform(X_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, ax = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(10,5))\n",
      "\n",
      "for a,x_dat, y_lab in zip(ax, (X_train, X_test), (y_train, y_test)):\n",
      "\n",
      "    for label,marker,color in zip(\n",
      "        range(1,4),('x', 'o', '^'),('blue','red','green')):\n",
      "\n",
      "        a.scatter(x=x_dat[:,0][y_lab == label], \n",
      "                y=x_dat[:,1][y_lab == label], \n",
      "                marker=marker, \n",
      "                color=color,   \n",
      "                alpha=0.7,   \n",
      "                label='class {}'.format(label)\n",
      "                )\n",
      "\n",
      "    a.legend(loc='upper right')\n",
      "\n",
      "ax[0].set_title('Training Dataset')\n",
      "ax[1].set_title('Test Dataset')\n",
      "f.text(0.5, 0.04, 'malic acid (standardized)', ha='center', va='center')\n",
      "f.text(0.08, 0.5, 'alcohol (standardized)', ha='center', va='center', rotation='vertical')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2FTNizQhS81MdHYpdVVf9JQmZEHb0+fbP2Xt2b5nbLMrCp9s/ZcnhJcSlxZV7\njOOZx7Eoy1WdPykpiUceeYSQkBCCg4MZPnx4mfuNHDmSiIgI/P39ad++PVu3brVui42NpX379vj7\n+xMWFsarr74KaLNqDBw4kODgYAIDA4mOjiYtLa3M47du3RpPT0/rsqurKyEhIVdVJiFE9dh9Zjdf\n/PFFudtXHl3J6mOrmbt/brn7ZBRmkFWUdVXnr2v1lyRkQthJfGY8s/fNZtK2SWX2HdhxegfHzh3D\nx92HqbumlnmMM3lneOrnp9iauLXM7ZdjNpvp2bMnzZo1IyEhgeTkZJ544oky942Ojmb//v1kZWXR\nv39/+vTpg8GgzdU5cuRIRo0aRU5ODidOnKBv374AzJkzh9zcXE6fPk1mZibTpk3Dy8ur3HheeOEF\n6tWrR+vWrRkzZgz/+te/Kl0mIUT1sCgLE7dNZNa+WZzMOnnJ9mJTMVN3TaWRXyOW/rm0zFYypRRv\nrX+LCZsmVPr8dbH+koRMCDuZtnsaXm5eHM08yo7kHaW2WZSFybGT8XD1IMg7iB2nd5TZSjZr7ywy\nizP54o8vKt1KFhsby9mzZ5k4cSJeXl54eHjQoUOHMvcdMGAAgYGB6PV6XnnlFUpKSjhy5AgA7u7u\nHDt2jIyMDLy9vYmOjrauP3fuHMeOHUOn0xEVFYWvb/njOE2ZMoX8/HzWrVvHmDFjiI2NrVR5hBDV\nZ3vSduIz4/Fw8eC7Pd9dsn3l0ZXklOTg5+GHWZnLbCXbn7qfPWf3sDVxK0cyjlTq/HWx/pKETAg7\niM+MZ+OpjdT3ro+HiweTd0wu1Uq2M3kne87uochURGp+KjklOUzbNa3UMc7knWHFkRU0DWhKYk5i\npVvJkpKSaNKkCXr9lS/zSZMmERkZSUBAAIGBgeTk5JCRkQHAjBkzOHr0KK1atSI6OppVq1YBMGjQ\nIO6//3769etHo0aNePPNNzGZTJc9j06no0uXLvTp04eFCxdWqjxCiOpx/gejp5sn9b3r89uJ30q1\nkhnMBqbsnEKhsZCzeWcxmo0sjFtIekG6dR+lFFN2TsHdxR1XF9dy7wKUpy7WXzVuHDIhKstkMVFo\nLMTPw8/RoVh9u+dbckpyrMt7U/YSmxzLrdfcCkCwdzCvdXit1GdC6pXukzBr7ywUCle9K15uXnzx\nxxd0jOiIXlex31GNGzcmMTERs9mMi4tLuftt2bKFiRMn8vvvv9O6dWsAgoKCrAlkixYtWLBgAQBL\nly7lsccy2cw5AAAgAElEQVQeIzMzEy8vL8aOHcvYsWNJSEige/futGzZkqeffvqKsRmNRurXr1+h\ncgghqtcfp/9gf8p+fD18KTGVkFucy/Q90/ngngtPFw5pN4QSc4l1WYcONxc36/L+1P3sPbuXUJ9Q\nFMraStYyuGWFYqiL9ZckZKLWm7t/LutPrOf7R76vcLJib+3D21+SYF2cMDYPak7zoOblfr7EVMJv\nJ35DKUVavtbRNCk3ib8y/iKyQcXmdr311lsJDw9n9OjRvPvuu+j1evbs2XNJs39eXh6urq4EBwdj\nMBj4z3/+Q25urnX7vHnzuP/++2nQoAH+/tpUM3q9ng0bNhAcHExkZCS+vr64ubmVWXGmp6ezfv16\nevXqhaenJ+vWrePHH39k3bp1FSqHEKJ6+Xv488zNz5RaF+EfYX3v7uLOoJsGXfYYK4+uxGgxWlvN\nTBYTq4+trnBCVhfrL0nIRK2WV5LHrH2zyC/JZ1vSNjpGdHR0SAD0ad2nSp/3cPVgeb/lGC1G6zod\nOoK8gip8DL1eT0xMDCNGjCAiIgKdTseAAQPo0KEDOp0OnU4HQLdu3ejWrRvXX3899erVY9SoUURE\nXKh8f/nlF1599VUKCwtp2rQpixYtwsPDg9TUVJ5//nlOnz6Nj48P/fr1Y9CgSytpnU7H1KlTef75\n51FKcf311/P9999zyy23VOEvJISwl9YhrWkd0rpKx3itw2s81/65UusqcxejLtZfNW6k/oqojSML\nC/uYuXcm3+z8Bk83T8J9wln02KJqbSWT76JtyUj9QlQv+T7allON1C9ERZ1vHQv0CsTfw5+TWSfZ\nlrTN0WEJIYQQlSYJmai1fjvxG7nFueQb8sksysRgMTDvwDxHhyWEEEJUmtyyFLVWXkkeSblJpdYF\neAbQ0LdhtcUg30XbkluWQlQv+T7aVlXqMEnIhKgC+S7aliRkQlQv+T7alvQhE0IIIYSoxSQhE0II\nIYRwMBmHTIgqCAwMtI6HI6ouMDDQ0SEI4XSUUuXWU1KH2VZV6jDpQyaEDSXmJNJzQU88XT3R6/Tk\nGfJoF9qOeY/Mk0qvCpzpmnemsoiab/GhxZzIOsHojqMdHUqdVpHrXlrIhLCxfm36YVEW67K/h78k\nY0KIaldgKODrnV9TaChk4I0DucbvGkeHJC5DWsiEEDWeM13zzlQWUbPNOzCPL3Z8gR493a/rzrgu\n4xwdUp0lT1kKIYQQdVCBoYDv9nxHgGcA9b3rs+rYKk7nnnZ0WOIyJCETQgghnEzM0RhS8lLIKsoi\nrSCN7OJs5uyb4+iwxGXILUshRI3nTNe8M5VF1FxHMo5wOP1wqXWN/RvTvmF7B0VUt8lI/UIIp+BM\n17wzlUUIUTHSh0wIIYQQohaQhEwIIYQQwsEkIRNCCFFrKaXILs52dBhCVJkkZEIIIWqtHck7eGzx\nY5KUiVpPEjIhhBC1klKKyTsmk5SbxOJDix0djhBVIgmZEEKIWmlH8g6OZh6laUBT5u6fS05xjqND\nEuKqSUImhBCi1jnfOubh4oG7izsGs4EfDv3g6LCEuGqSkAkhhKh14tLi+DPjT8wWM+cKz2FRFhbF\nLcJkMVV7LDuTd5JRmFFt5zOajdV2LlF9ZGBYIUSN50zXvDOVxZGMZiNHzx1FceFv6enqSfPA5uh0\numqLI68kj+7zu3PvtfdWy+TdmUWZPLXsKb7o9gXXBl5r9/MJ25CBYYUQQjglNxc3Woe0pk1IG+ur\nRVCLak3GAJYcXkKBsYBVx1aRlJNk9/MtPLiQw+mH+W73d3Y/l6hekpAJIYQQVyGvJI+Z+2YS7B2M\nDh0z98606/kyizKZf3A+1wZey/qT6zmRdcKu5xPVSxIyIYQQ4iosObyEAkMBLnoX/D39iTkaY9dW\nsoUHF2K0GPF09USHTlrJnIwkZEIIIcRVOJB2AF8PXwqNhZSYS/B19+Vw+mG7nKvAUMDCuIWYLWbS\nC9KxKAu/xP9Ccm6yXc4nqp906hdC1HjOdM07U1lE9TFbzOxI3lHqCUudTkd0o2g8XT0dGJmoiIpc\n9zUuIUtKSuLJJ58kLS0NnU7HsGHDGDFiRKl9pEITom5xpmvemcoihKiYWpmQpaSkkJKSQrt27cjP\nz+fmm29m2bJltGrVyrqPVGhC1C3OdM07U1lqhUOH4NNPISMDunSBF18EDw9HRyXqmIpc966X25iW\nlsaPP/7I5s2bOXXqFDqdjiZNmnDnnXfSp08fQkJCbBowQFhYGGFhYQD4+PjQqlUrzpw5UyohE0II\nIa4oORmeew4sFvDygvnzobAQxoxxdGRCXKLcFrKhQ4cSHx/PAw88QHR0NOHh4SilOHv2LLGxsaxd\nu5YWLVowffp0uwV36tQpOnfuzKFDh/Dx8bkQtPzCFKJOcaZr3pnKUuPFxMCECfD3j3xMJsjJgW3b\nHBuXqHOq1EI2YsQIbrrppkvWt2rVirvvvpvRo0dz4MCBqkdZjvz8fB577DG++OKLUsnYeePHj7e+\n79KlC126dLFbLEL8U3ZxNu9teo8Jd02gnns9R4fjdDZu3MjGjRsdHYbdSP1VTTw84OL/CRqNWkuZ\nEHZ2NXVYjetDBmA0GunZsycPPPAAL7/88iXb5RemcLRpu6YxcdtE3u3yLgNuHODocJyeM13zzlSW\nGq+oCIYMgaNHQf/3KE/jxkGvXo6NS9Q5VerU37Zt28se2F6tY0opnnrqKerXr8/nn39e7vnrbIUW\nFwczZ2oVzcMPQ9eu8M+pQoqLtf2UgjZt5BehjWUXZ9NjQQ9c9a7o0LGq/yppJbMzZ7rmnakstUJB\ngXbrMjsb2rfXXkJUsyrdsoyJiQFgypQpAAwaNAilFPPnz7dhiJf63//+x7x587jxxhuJiooC4KOP\nPqJbt252PW+tcPQoPPus9t7VFXbu1Jrge/a8sE9ODgwbBqdOactNmsC330JAQLWH60hGs5GdZ3bS\noXEHmx/7h7gfMJgNBHkFkZKfwrK/lkkrmRA1Vb160K+fo6MQ4oqueMuyXbt27Nu3r9S6qKgo9u7d\na9fALqfO/sKcPBlmz4aGDbXl3Fxo3Bjmzbuwz+efa08ShYdry2fPQt++8Prr1R6uI608upJxG8ax\n6LFFXFf/OpsdN7ckl67fd6XYVIybixslphICPQNZO3AtXm7SEmkvznTNO1NZhBAVU+VhL0C7hbh1\n61Y6duwIaC1YUpk4iItL6duTSmnrLpaYCJ4Xjdrs6amtq0OMZiNfx36NwWLg293fMrHrRJse/6mb\nnsJouTBatqerJwq5JoQQQly9KyZkM2fOZMiQIeTk5AAQEBDArFmz7B6YKEOPHrBoEaSkaImY2QxP\nP116n3/9CzZtAn9/bbmoCG6+ufpjdaBf4n8hozCDCP8INp7ayLFzx2zWSubn4cfztzxvk2MJIYQQ\n51X4KcucnByUUgTUgL5IdbrJ/+RJLSkrKtIStFtvLb3dZIIPPoCVK7UWtB49tEEQ3dwcE281M5qN\nPLjwQYpMRdRzr0dGQQZ3NrnT5q1kono50zXvTGURQlSMTaZOSklJ4e233yY5OZm1a9dy+PBhtm/f\nztChQ20abGVIhVYBBQXav/Xq1tN/R88d5ZkVz1BiKrGuq+9dn5/7/oyHq0yXUls50zXvTGURQlSM\nTRKybt26MWTIED744AMOHDiA0WgkKiqKuLg4mwZbGVKhCVG3ONM170xlEUJUTEWue/2VDpKRkUHf\nvn1x+bvzuJubG66uV+x6JkSdlJybzLI/lzk6DCGEELXMFRMyHx8fzp07Z13+448/8D/fYVwIUcqU\nnVN4d9O7JOcmV/qzmUWZTNg0AZPFZIfIhBBC1GRXTMg+/fRTevXqxYkTJ+jQoQODBg3iyy+/rI7Y\nhKhVTmad5LcTv+Gid2H2vtmV/vy8A/OYd2Ae60+st31wQggharQKPWVpMpn466+/UErRsmVL3N3d\nqyO2ckkfDFETvb3+bdadWEeQdxDnCs/xc9+faeTXqEKfzSzKpMeCHuh1egI9A1ny2DI83S90DTCZ\ntMkZ6ipnuuadqSxCiIqxSR+ya6+9lu+++442bdrQtm1b3N3d6XnxVD1CCE5mnWTVsVV4unlSbCqm\nyFhUqVayeQfmYbaYCfIKIrUglaffX8/vv2vbjhyB4cOhpOTyxxBCCFF7XfE3t5ubGxs3biQ2Npap\nU6fi4eFBcnLl+8cI4cwyCjO4KfQmLMoCwDW+12AwGyr02cyiTL7f/z0KRUZhBiWmElKbTGbWnHs4\netSVrVth5EhwcMO0EEIIO7piQubt7c0PP/zAJ598wp133snixYurIy4hKu3YMfDxuTCNZ2ws3Hhj\n6Zmk7OWWRrcwp/ecq/qsyWKid6vepaZjKsypx1m9hZgY6NxZK1tqaul55IUQQjiPK/Yhu3gi8XXr\n1vHiiy+SmZlJenp6tQRYFumDIcry22+wcKE2UUFcHCxYAB99BGFhjo6s8g4fhoED4brrIDkZ6teH\nOXOgBkyU4RDOdM07U1mEEBVjk8nFJ0yYYH1/77338uuvvzJnztW1BAhhT/fdp03vOWyYtjx1au1M\nxgB+/hmmTNGSSy8vaNRI+1cIIYRzKjch+/PPP2nVqhUNGzZkz549pbb16NHD7oEJURalFEm5SUT4\nR5S5/e/xiwHQl/PISnxmPDvP7KRfm352iNA23npLa+275hqtdUyvB53O0VEJIYSwl3JvWT777LN8\n9913dOnSBV0Z/yfYsGGD3YMrjzT51117z+7lpTUvMf+R+TQNaFpq2/r1MG8evP8+HDwIixdrtyxD\nQ0sf46XVL7E1cSur+q+q8LAU1e3IEZg8WSuLry989hlcey08+qijI3MMZ7rmnaksNYHBbGB/yn5u\naXSLfU5gNmu/hsr7hSdEBdhkLsuaSCq0OujgQdT69Txj+JEt7md5vG1/3r/n/VK7HDmidepv9HeO\n9ccfcNNNpW/1HUo7xOBlgwF4+IaHefvOt6upAJVnMFx4stJsBqXq7lhkznTNO1NZaoJlfy7jg60f\nsPTxpeW2nF8VgwE++QRWrNCSsWHDYMgQaaoWV6VKCdnSpUvLbBk775FHHqladFUgFVr1SMpJItQn\nFHcXB4+3sGMHjBjB3np5DLvxFA2UNxktG7O4/8+XtJJdyUurX2L3md0EeAVUevBW4TjOdM07U1kc\nzWA20HNBT87kneGRVo8w4a4JV/5QRU2dCt9+q3VEtVggPV1rcu/a1XbnqKTsbO2H5623astHjoCH\nBzRt6rCQRAVVaWDYmJgYYmJimDFjBkOHDmX+/PnMnz+fZ555hpkzZ9o8WFGzFBoLGbpiKIsP1YBh\nTr75BuXuxleR+bi5euBiMKLLzmH67umVOsyhtENsStiEq4srBYYCCgwFVzXFkRCiZlh9dDVZRVlE\n+Eew9vhaEnMSbXfwrVvBz0/rmOrmpr1iY213/KuQmwtffw2bN2vJ2HvvwUVTTYtartyEbPbs2cya\nNQuDwcDhw4dZunQpS5cu5dChQxgMFRvwUtRey/9aTkp+CtP3TKfAUFAt5/zqK228LYDMTPjPf7S7\nBhQVkeBjIs4rD7MO0t1NKIuZDQkbyCnOqfDxi0xF3BlxJ21D2tImpA2dm3bG283bPoURQtiVwWxg\nyq4p+Hr44qLXnuaZvqdyP9IuKzwcioouLBuNDn9sOyJCS8ImToTXXoOXX4abb3ZoSMKGrtgjJSkp\nibCLvoShoaEkJtrwV4iocQqNhXy7+1tC6oWQU5LDz3/9zMAbB9r9vLfcAhMmaNMEzZoFd931dx+q\n3r1pMvETlh1ohcVkBJMZPp2EW6s2+Hv6V/j47Ru2p33D9vYrgBCi2hw9d5S8kjxKzCVkF2cDEJsc\ni8liwlVvg86Ww4fDvn3aiMwAzZtD375VP24VFRdfeF9Y6Lg4hO1d8Vt77733cv/999O/f3+UUvzw\nww/cd9991RGbcJDlfy0n35hPmE8YOp2O6Xum0/uG3tRzr2fX8956K2Rlab8AO3SAxx//e8Pjj6PT\n6Qhftkzrof/889DeTk9UCSE0GRmwZYv2/o47ICTEsfH8Q5uQNmx/Zrv9ThARAT/8AHv3arcrb7nF\n4YMBxsdr9eO4cdCgAbzzjvagT4cODg1L2EiFnrL86aef2PL3hXnnnXfSu3dvuwd2OdIp1r76/tiX\n45nHcXNxA8BoNvKfe//Dfc3tm4hnZsLbb2tPSqakwNix2kj1QjjTNV8rypKcDIMHaxclaFNEzJql\nJSnCYQoK4ORJaNNGW05I0O4inJ8uTtRcVR72wmQy0aZNG/766y+bB1cVtaJCq8VyS3IpMhaVWhfs\nHWztp2Evb7+tDVPx+OPag5XffgvffCOTagvnuuZrRVk+/BCWLbswiF9qKnTvDuPHOzQsUdqhtEPs\nSN7B01FPOzoUcQVVnjrJ1dWVli1bkpCQQJMmTWwanKi5/Dz88PPwq/bzjh6tDYIK2u3LyEhJxoRw\niMxM7Tbdee7uWn8CUWMopZi4bSL7U/bTtXlXrvG7xtEhiSq6Yh+yzMxMWrduTXR0NPXqaX2IdDod\nK1assHtwom45n4yVtyyEqCZ33QUbNmhPGep0Wu/xu+92dFTiInvO7uFQ+iHcXNyYsWcG47qMc3RI\nooqu2Ids48aNZa7v0qWLHcKpmFrR5C+EsBlnuuZrRVmU0iZTnT1bez9okPaSUeprBKUUQ5YP4Vjm\nMfw9/MkozOCnvj9JK1kNJlMnCSGcgjNd885UFuEYu8/s5sllT+LvoQ37k1WcRZ/IPradqUDYVJVG\n6j9v+/bt3HLLLfj4+ODm5oZer8fPr/r7FwlRntT81Dr3PziLRRuz7dQpbfnkSW3ZYnFoWEKIaqDX\n6Xm45cN0adqFLk270D68PWuOrcFkMTk6NFEFV0zIXnrpJRYsWMB1111HcXExM2bM4IUXXqiO2IST\n2JeyD4uyT6aQWZRJv6X9+F/S/+xy/JpKr9e69Iwdq3X1GTdOW9Zf8YoWQtR2UeFRfHDPB3x4z4e8\nf/f7FBoLKTAWsC5+naNDE1VQoer7uuuuw2w24+LiwpAhQ1i7dq294xJO4kjGEYbFDGN7kn0GcFxw\ncAFn8s4wecdkuyV9NVXHjto8x599pv3bsaOjIxJCVLctCVtIzEkkpF4IX+38SlrJarErJmT16tWj\npKSEm266iTfeeIPPPvuszt0eEldv6q6p5BvymRxr+4QpsyiTBQcX0DSgKSeyTrAtaZtNj1/TnTwJ\nv/6qJWK//nrh9qUQom6wKAtf7vgSLzcvfD18SS1IlVayWuyKCdncuXOxWCx89dVXeHt7c/r0aZYu\nXVodsYla7kjGEbYmbqVZYDPiM+Nt3kq24OACTBYT7i7ueLp51qlWMosFPv8chg2DN9/U/v3sM+lD\nJkRdEpscy9HMoxjMBtIL0jGYDEzfa8MJ1kW1kqcshd2MWjuKP5L/INg7mOzibBr5NmLBowvQ66re\n0clkMdH1+67kleRZJxI2mA3MengWN4beWOXj1wYlJeDhUf6yM3Gma96ZyiLKV2QswsvNvnNfZhdn\ncyD1QKl1vu6+RIVH2fW8ovKqNOxF27ZtL3vgAwcOlLvd3qRCK0dRERw5os02e8MN2r8OkluSS6+F\nvSgwFFjXubu4saDd+zQlQJuksopP6ybnJlNsKrYu63Q6mvg3sfsUT6L6OdM170xlEWU7m3eWp5Y9\nxbe9vqVpQFNHhyNqgCpNnRQTEwPAlClTABg0aBBKKebPn2/DEIXNpKdr963OntXuW0VFwRdfgKen\nQ8Lx8/Djt0G/YbaYtRUWC7oPPsBz6mgtUfTxgalToXnzqz5HI79GNopWCCFsZ87+OcRnxTN993Te\nv+d9R4cjaokr3rJs164d+/btK7UuKiqKvXv32jWwy5FfmGUYM0br2R0aqo2sffYsjBoFAwc6OjLN\nxo3w6qsQFqaNzZCRAS1awPffOzoyUQs40zXvTGURlzqbd5beP/TG39OfrKIsFvdZLK1kwjYDwyql\n2Lp1q3X5f//7n1QmNdHJk/D3XKPodNrEwAkJjo3pYikpWqJ4fqAsf39ITHRsTEIIcZWOZx5n/oFL\n7xjN2T8Hi7Lg7uKODh3Td0sne1ExV0zIZs6cyQsvvECTJk1o0qQJL7zwAjNnzrRbQE8//TShoaGX\n7cMmytCuHeTmakmP2QxGI7Rp4+ioLmjRQkvGjEYtxsxMkP/GQoha6rPtnzFx20RO5562rssuzmb5\nkeUopcgozECh+CX+F1LyUxwYqagtKvyUZU5ODgD+/v52DWjLli34+Pjw5JNPcvDgwTL3kSb/MhQU\naOMf7NihLT/6KLzxRs0aun32bPjmG+19ixbw3/9CgwYODUnUDs50zTtTWeqquLQ4Bi8bjE6no9f1\nvRjbeSwAZouZfSn7Sg3OqtfpiQqPsj4NLuomm0wuXlxczNKlSzl16hQmk8l64LFjx9ou0n84deoU\nvXr1koSsspSCrCyt03xNnW+0oEB7GjQoyC7JYnJuMsuPLOeFW2R6L2fiTNe8M5Wlrnph1QvsPbuX\nQK9AzhWeY2nfpVzjd42jwxI1mE36kD300EOsWLECNzc3fHx88PHxod75vkqiZtHptESnpiZjoPVz\nCw62W8vdt7u/5avYrziYWnYybwt1ZfBZIcSl4tLi2JKwBRe9C3mGPNIL0/k69mtHhyWcwBXbUJOT\nk/nll1+qI5ZKGT9+vPV9ly5d6NKli8NiETVDYk4ia46vwcfdh292fcOUHlNsfo4jGUcY8/sY5vSe\ng7ebt82PLzQbN25k48aNjg7DbqT+qr1KTCXc3exuFIoSUwnHzx3nyLkjdj1ndnE2AZ4Bdj2HsK2r\nqcOueMty2LBhvPTSS9x4Y/WNfi63LMXVGLdhHGuPr6VBvQakFqQy88GZtA217YMDI9eOZPXR1bx7\n17v0b9vfpscW5XOma96ZylLXTd01lWm7puHp5knMEzEEewfb/ByxybG8tf4tljy+RJKyWswmtyy3\nbNnCzTffzPXXX0/btm1p27ZttSZnQlREYk4iy48sR6/Xk12cTaGxkCk7bdtC9mf6n2xL3EZEQATf\n7f6OQmOhTY8vhKg9souz+X7/94T4hGC2mJl3YJ7Nz6GUYvKOySTmJLIwbqHNjy9qliveslyzZk11\nxGH1xBNPsGnTJs6dO0fjxo2ZMGECQ4YMqdYY6iSLRRsXzGiEpk21ccxqkRJTCfc1v69U/64G3rZ9\ngnPq7qm46F3wdvMmJT+FZX8tk1YyIeqoRXGLKDGXEKAPIMAzgEVxixh440CbtpLtPLOTvzL+ollg\nM77f/z1PtHnisq1kOcU51HOvJ0901lIVHvYiLS2N4uIL8wZGRETYLagrkSZ/GzMa4a23YNMmrbN9\ns2YwZQoEBjo6shojPjOeR354BHdXd/ToKTYX08C7AWsHrpXKrxo40zXvTGWpy4YuH8qh9EPWZRe9\nC+/d9R53N7vbJsdXSvHkz09yMvskgV6BpOSn8HTU0zzf/vky97coCwN/GshdTe/i2ZuftUkMwnZs\nMuzFihUrePXVVzlz5gwhISEkJCTQqlUrDh06dLmP2ZVUaDa2eDF8/LE2rZFOB6mp0KMHXNTxuC4w\nmo24uZTdMphvyGd70nYUF753Hi4edGrSCb2uBo315qSc6Zp3prII+zmUdohBPw/Cw8UDnU6HwWzA\nz8OPXwb+UmY9tSVhCyPWjKCeez1WD1iNn0cNftq+DqrS5OLnjRkzhu3bt3Pfffexd+9eNmzYwPcy\n/6BziY/Xxi47PxSFjw8cse9TQzXNiawTjFw7krkPzyXQ60LLoNms/Vl83H24r/l9mM3g4uLAQIUQ\ndULL4JZ83/v7S34EltUib1EWvtzxJb4evhSZivgh7gdpJauFrvjT3s3NjeDgYCwWC2azmbvuuotd\nu3ZVR2yiulx/PZhMWj8ypSA/HyIjHR1Vtfp297ccTj98ScfZ6dNh4ULtz5KeDi+9pDUgCiGEPbnq\nXWkd0po2IW2sr+vqX4dOp7tk362JWzmVfQo/Dz8CPQOZs38OuSW5DohaVMUVW8gCAwPJy8ujU6dO\nDBgwgJCQEHx8fKojNlFdHnoI9uyB337TbllGRsLw4Y6OqtqcyDrB7yd/59rAa5l3YB5PtHnC2krW\nty+MGaMlY3Fx0LMnhIY6OGAhhLjIgoMLMFqMZBZlAlBgKODX+F95LPIxB0cmKuOKfcgKCgrw9PTE\nYrEwf/58cnNzGTBgAPXr16+uGC8hfTCqTilFSn4K4b7h51fA2bNaB/9rrqlT9+VGrxvNxlMbaVCv\nASn5KQxpN6TU1EvHjsErr4C3NyxapOWsono50zXvTGWpbTIKM/Dz8MPdxd3RodhUSn4K2cXZpdY1\n9mtMPXeZVaemsMk4ZBMmTMDFxQU3NzcGDx7MiBEj+OSTT2wWpHCM7ae3029pPzIKM7QVOh00bAhN\nmtSpZOx07ml+jf8Vs8VMekE6ZouZhQcXWscYS0+HTz6BPn20edDP374UQtQuZouZ51Y+x+x9sx0d\nis2F+YRxQ/ANpV6SjNU+V2whi4qKYu/evaXWtW3bttxR9KuD/MKsGouy0H9pf/am7OW5m59j1O2j\nHB0ScWlxuOndaBncslrPW2wqJjY5ttT3yc3FjVsb3YqL3oUZM7SpNx96CLKz4f334fXX5bZldXOm\na96ZylKbrItfx+u/vU4993qs6r8Kf09/R4ck6pAqDXvxzTffMGXKFOLj42nevLl1fV5eHnfccQfz\n58+3bbSVIBVa1WxL2saINSMI9g4mpziHmP72mfKjoswWM4/88Aierp4sfGxhjRpGQqnStyj/uSyq\nhzNd885UltrCbDHz6OJHySrOotBYyLP/epZhNw+r8nFNFhPpBekXun4IUY4q3bLs378/MTExPPjg\ng6xcuZKYmBhiYmLYs2ePQ5MxUTXnH4/2cvPCzcUNszLz/X7HDmOy4eQGzuSd4UTWCbYlbXNoLP/0\nz9OBAPgAACAASURBVORLkjEhap8NJzeQnJuMn4cfQV5BzN0/l5zinCofd+nhpQxePpgiY5ENohR1\nXbkJmb+/P02bNuX9998nNDSUpk2bcvLkSebNm0d2dnZ5HxM13OH0wxzPPI7RbCSjMAOlFMuPLMdg\nNjgkHrPFzOTYyXi7e+Pp5snkHZNLTX8khBBVtfjwYkzKREZhBrklueQb8ll3Yl2VjllkLGLq7qmc\nyT1DzNEYG0Uq6rIr9iFr164du3bt4tSpU3Tv3p2HHnqIQ4cOsXr16uqK8RLS5H/1LMpCYk5iqXXu\nLu409G3okHjO9+toUE+bdzK9IJ3J3SfTMaKjQ+IRNZMzXfPOVJZKKSiAv/7S5smNjNQGo64m5wrP\nkWfIK7UuzCcMT1fPqz7mD3E/MGn7JPw9/FFKsbL/SrzcvKoaqnBSNhmpX6fT4erqyk8//cTw4cMZ\nPnw4UVFRNgtSVC+9Tk/TgKaODsPqyLkjhPpc6CEf6hPK0XNHJSETwpmkpsKzz0JamjYAdbt28OWX\n4Hn1CVFl1PeuT31v2w3VdL51zN/DHy83L1LyUog5GsPjrR+32TlE3XPFhMzd3Z0FCxYwd+5cYmK0\nZlmj0Wj3wETd8GL0i7wY/aKjwxBC2NPnn0NKivZ4slKwezf89BP07+/oyK7KtqRt5BTn4OHiQYGh\nAAsWfjz0oyRkokqumJDNnDmTadOm8fbbb9OsWTNOnjzJoEGDqiM2IYQQziAhAer9PS6WTqfdrkxM\nvPxnKiMnB6ZOhePHoXVrGDZMG8nZTjo37czyfstLrZNxv0RVXbEPWU1UZ/tg1AEGs4HR60bzeofX\n5VFyYeVM17wzlaXCPvkEfvgBwsO1W5apqTBhAvToUfVjG40wZIjWP61ePW0u3ttv126J6mvOEDqi\nbqvSsBc9evTgxx9/pLCw8JJthYWF/PDDD3Tv3r3qUQpxkbXH1xJzJMYpR9MWos568UXo0EFLxNLT\ntVuVDzxgm2PHx2vzm4WFgZ+flvTFxmrnEqIWKbeFLC0tja+++oolS5bg4uJCeHi4Nv9hSgomk4m+\nffvy4osv0qBBg+qOuW7+wqwDDGYDvRb2othUTLGpmGV9l0krmQCc65p3prJUilLarUVXV/Dxsd1x\njx6FgQMhJES7HWqxaElfTIxMqVEB+YZ8vt75Na/c9gpuLm6ODsdpVWmk/oulpKSQkJAAQJMmTQgL\nC7NNhFepzlZoTm7FkRW8t+k9wnzDSM1PpfcNvfm/Tv/n6LBEDeBM17wzlaVGMJu1FridO8HDA0pK\n4L774KOPZCTnCpi7fy7vb36fz+7/jJ7X93R0OE7LZglZTSMVmvMxWUx0n9+d5LxkvFy9MCszKFg7\ncG2pYTFE3eRM17wzlaXGKCqCBQu0W5dt2kDfvtp4Z+Ky8g359JjfA6PFSIBnAMv7LZdWMjuxyThk\nwkGUgoMH4dw5aNECGjd2dER2pZSif9v+FJuKretcdC5SOQghrszLC4YOdXQUtc5Pf/5EoamQMJ8w\nUvJS+CX+F2klcyBpIfv/9s48Pqa7++OfyZ6IJbZYQqO1C4mlVbREUWqrpRvd1NKVp61SlGoeLdqi\nLVV9PB7Lr7UURdGi9rW1Kw2KIkQ2IbIvk5n5/v74dDIJ2cRM7szkvF+vvDJ3MnPvuXdyz5zvWe0R\npYBPP2WfHldXPvfZZ0CnTtrKJQga4Uz3vDOdS1kk25iNd7a8g7EdxtpVk+27JVWfih5LeyDTkAlP\nN0+kZ6ejRrka2DBogyyEbYB4yByV8HAaY9Wrs2w7PR2YPBnYtUvKuAVBEDTk14u/YuvFrfDz8sMn\nXT7RWpwSk2nIRGhgaJ45xj7uPtAb9WKQaUSBHrLmzZsX/CadDqdOnbKZUEXh9CvMPXuAceMAcwWr\nUuxyvXevTZsdCoK94kz3vDOdS1kj25iNviv6It2QjozsDKx6epVDe8mE0uOePGTmMUmCBtSvz+qg\ntDQaYPHxQIMGYowVQGxqLCKTIlHP80F4eVkq6q9eBQICSu5U1Bv18HD1sJ6ggiA4NL9e/BU30m+g\nRvkayMzOxP+O/c+hvWSCfVHgV1VgYGDOj7e3N/7880+Eh4fDx8cHgYGBpShiGaR2bWDGDPbTiY0F\n7r8fmDVLa6nslq8OfoX3tr6HTdvTMHkyG3X/+ScwYQJw7VrJ9pmqT8VTq55C+PVw6worCIJDYjQZ\n8c3hb5CanYqo5ChkGbOw/tx6XE2y4gioIohNjS21YwmlT5E5ZKtWrcLYsWPR6Z+E8pEjR2LGjBl4\n+umnbS5cmeaRR4CdO9lTx9tbOzmUAlavBtasAby8gNdeY8dtO+HSrUvYeXknjCYj0Gotmqa+iEGD\nWAvx8cdA3bol2++PZ37E2RtnMe/IPMzrNc+6QguC4HDodDoMbzU8TyW4TqdDOffSmWF5+vppvPbz\na1g6YKmESZ2UIqssW7Roge3bt6N69eoAgPj4eHTp0kVyyMoKq1ez4rNCBcBgAPR6YMECoEULrSUD\nAIzfPh67Lu9CBa8K0Bv0+Cx4E6Z+RAW5YkXJGoKnZKWg1/Je8HTzRGJGIhY9uQjN/QvOqbQ2BpMB\nAODmIjU3ZpzpnnemcxFKj5GbRuLXi7/i2abPSpjUAbmnWZZmlFJ5xiNVqVJFlElZ4qefgPLladlU\nqsQw6rZtWksFgN6xbRe3oaJXRbjqXHE9KRnv/nctpk4FnnwSOeHLu2XN2TXINGTCy80Lbq5u+Pbo\nt9YXvhA+2fsJZv42s1SPKQiC/XL6+mkcunYI9SvXx9ZLWxGRGKG1SIINKNIg69GjB7p3744lS5Zg\n8eLF6NmzJ56w1lBYwf7x8aFnzIzJVGhxQWka63/F/wU/bz8YTAbojXr4uPihaafTaNGCPSIffhjI\nzCx6P7nJNmbj+5Pfw2Ay4EbaDZiUCb9F/obzN8/b5iRu42rSVWy6sAnr/lqHmJSYUjmmIAj2zbdH\nv4WbixvcXNyg0+nwv2P/01okwQYUGbJUSmHt2rXYv38/dDodHn30UfTv37+05MsXcfnbmN9/B44e\nBapW5YSAMWNolCkF+PkB338P1Lxz6Hf49XB8+fuXmN9nvsOG20zKhGPRx5BlzMrzfOuareHtbvtc\nvsm7JmPL31sAQGZ55sKZ7nlnOhfB9lxLvoaBKwdCp9NBBx1MygQXFxf8MvgXVPaurLV4QjGRWZbC\n3bN6NacC6HQc2tu4MTB2LHDgAJP6e/WiMXb+PLBkCVtz9O4NdO2KNze9he2XtmNOjzno0aCH1mfi\ncFxNuoqnVj2Fqj5VoaCQkJGAn579CTXL32n8ljWc6Z53pnMRbI9SCleSrsCkTDnPubm4oU6FOtDJ\n8HSHwSqd+tesWYPx48cjLi4uZ2c6nQ7JycnWkVKwH5QCvv4aqFwZ8PTkcxcuAImJwMiRltdFRABD\nhwLZ2Rzge+AA/rz1F44kHUGt8rUw98hcdH2ga4FeMqWUKJJ8WHV6FdKy0+CayXFZqfpU/HjmR4xq\nO0pjyYQyh1LAsWPsG1OnDtC6tdYSlVl0Op1UVZYRijTI3n//ffz8889o0qRJacgjaIlSbLORuzRR\np+Nzudm6leOcatfmdkoKvj0wG24tqqG8Z3nEpsZi+8Xt+XrJ9l7Zix/Cf8A3Pb8Ro+w2nmn2DDrU\n6ZDnuToVnXuovGCnfPMN8H//Z9keMQJ49VXt5BGEMkCRSf01atQQY6ys4OIC9OwJxMXR4Lpxgwn8\nLVvmfZ1Ox59/OOudhj3l4pFtzEZsaizSs9Mx7+i8O9yzRpMRX/7+JfZd2YfDUYfvWdzffgNSUvjY\nZAJ27OBvR6VuxbpoV6ddnp+ACgFaiyWUNWJigO++Yw5pjRr8vXAh9YEgCDajQA/ZmjVrAABt2rTB\ns88+i379+sHDg2NkdDodBgwYUDoSCqXL+PHsObZ3L8c1jR4N+PvnfU337kzsj4sD3NxQXWVjatDb\nQKtWOS/xcfe5wwO298peXEu+hgpeFTD38Fw8VPuhe/KSXbgArFzJBrDffQdERgIdOjDVTRCEEpKc\nzMWZ2z9fD25uXIAlJ9M4EwTBJhSY1D9kyJCcL8v8cn4WL15se+kKQJJi7YBLl4ClS5nU/8QTQGho\noS83mox4atVTSMhMQHmP8ohKicKgoEF4v8P7JRZBKdYVrF3LNJdZs7QdaiDYDme65+3+XDIygAED\ngKQk9h68dQuoUoXTOsy5pYIg3BVSZSnYDfuu7MOrP78KXw9f6KDD1aSr0Bv1ODziMOpXrl+ifZpM\nwLx5wK+/ArVqATNnsoet4Hw40z3vEOdy+TIwaRLw999Aw4bAJ58A992ntVSC4LBYpVN/ZGQk+vfv\nj2rVqqFatWoYOHAgrpV0YnMx2bJlCxo3bowGDRrgs88+s+mxhNKhfuX6mNFtBj7q9BHeffhdVPKq\nhGo+1TD/6PwS73P+fIYpV60C2rXj90dGhhWFFoSySr16wLJlwKFDTE8QY0wQbE6RHrKuXbvi+eef\nxwsvvAAAWLZsGZYtW4ZtNhqfYzQa0ahRI2zfvh21a9fGgw8+iBUrVuQpLHCIFaZQIHMOzcHSU0tR\nrVw1XE+7jhUDV5TIS3byJBfv3t4MXx4+DDz0UJ56A8FJcKZ73pnORRCE4mEVD1l8fDxeeeUVuLu7\nw93dHUOGDMH169etJuTtHD58GPXr10dgYCDc3d3x3HPPYf369TY7nlC6JGQkYOmppfBy80KmIRMG\no6HEXrLgYEvOmE4HtG0rxpggCILgmBRpkFWpUgXff/89jEYjDAYDli5diqo2rLSJiopCnTqW3ksB\nAQGIioqy2fGE0iU6JRr1KtVDNZ9qqORZCff73Y+07DStxRIEQRAETSmyMeyiRYswatQojB49GgDQ\nvn17m1ZYFrcNQlhYWM7j0NBQhBZR5VcmSUoCoqOBatXsplw9qHoQVj69UmsxBDtn9+7d2L17t9Zi\n2AzRX4KzYDQCrhwuAqVYbGXeLsuURIfZXZXlwYMHERYWhi1bOGB5+vTpcHFxwbhx43JeIzkYxeDw\nYQ4Fz87mXTJ+PNCvn9ZSCf/w229A3bpAQAA/nl9+Abp0kbYdBeFM97wznYtQtomK4ujjsDDAz4/1\nH0Yj8MorWktmf1glh+yll15CYmJizvatW7cwdOjQe5euANq0aYMLFy4gIiICer0eK1euRN++fW12\nPIfg2jX2/Fq+nM1Yi0KvB95/n8uUqlXZ6HX6dHrLBLsgI4NVodeusQn6jh1UZILgVBw5AvTty47N\n779vGa0hOAW1a/OjnTgRmDMHOHoUGDhQa6kclyJDlqdOnUKlSpVytv38/HD8+HHbCeTmhrlz56J7\n9+4wGo0YNmxY2R7d9PffHOSdmsrthQs5Yy6gkJE6t27xG796dW57erLzdkwMG3YJmtOlC3+/8Qa9\nYosW5R0hKggOz9WrwNtvA+7uXBSaVx2zZmktmWBFnnmG/oJr14C5c/lRCyWjSA+ZUgoJCQk52wkJ\nCTDaeCn/xBNP4Ny5c/j7778xYcIEmx7L7lm4kMO9a9fmT3Iy+wMVhp8fUK4cXwsAmZn8bR4GLmiO\nUuy9CTDnIpcTWhCcg/BwwGDgN7SbG+di7tvHf/7icOMGUy2eeooxMblJ7A6lGKasVw948kng00+B\nXOaCcJcU6SF777330K5dOzzzzDNQSmH16tWYOHFiacgmADSq/pkhCoCKzWxoFYSHB/DFF8C77wLx\n8fSOffQRFaIDkpDAdhZ+fty+epWOPrci/3vtl2XLgNOngRUr2Htz0iROGrCT2gtByJ+0NGDTJhpH\nDz5I9+7EiezQ3LQpMHWqxQvv68tvbKV4A2dk0DgrTuGWXg+8/jpvdl9f4OefuYJZtEgyxu2I6Gjg\n1CkOcqhQgZNSNm4EXn5Za8kck2Il9Z8+fRo7d+6ETqfDY489hqZNm5aGbAVSppJiN2wA/v1vzpRT\nisbY558Djz1W9HvT04HYWEsemYOyaRP18dSpPJ2pU2lfNmigtWQlJyKCH4uXF+3ls2eBJk3oLXNk\nQ9NWONM977Dnkp4ODBnCNAqdzmJs+fgAFSty5VS7NkdnuLrSO/avf7HASKfjz/Tplnh9Yfz1F49V\nrRq3leLics2awtM1hFLHZKIOK2hbIMW57wtU/bnDlDVr1sTgwYNzdpqQkIDKlStbScwyjvkDKmjV\n2KcPFeGyZfwvf/vt4hljABXl/fdbR04N6dmTduhLL3E7LMyxjTEACAzk7xUrGJl56y12KfnwQ2D0\naKf42ARnY+9e4NIlS+pDbCxw4QLw6KPcrlaNiUTx8fTGu7kx03vPHv5zN2sGNGpUvGN5ePCb3fzt\nbu6nkDtaINgFtxtfYoyVnAINslatWhXaE+yyOQFGKBkmE7BgAfDdd3w8aBAwcuSd/806HfDcc/wp\nwwQHW1LnimOsmKMkBW3bC/360QE6dSrd/506iTEm2CnmXFQz3t5M0jc3otLreZPlrk5xcyueR+x2\nAgN5M+zcafG29e9v8ZgJghNid33IioPDuvxzs349v4mrVaMSu36dZeFl3PDKj7NnabC8+y4X5Hv3\nctucU3Y7BgNzst54gzORw8OBtWvpfbJHoywmBnj1VT5ev754K0yleJ7u7tzW6/nYHs/PGjjFPf8P\nDnsuV69y4ajTMdZ+8ybg708Xr/kf7513gOeft87xDAYmJF28CDRuTFe5uF8EB6U4932xDLJbt27h\nwoULyMy1QurYseO9S1hCHFah5eb994EDBwBz6DcxEWjRAvjmG23lskOOHePv1q35e8MGDhEvrEZh\n717gf/+jfbtsGTBuHC+vvXHrFnOiH3qIaTO1azN8WdT3zq5ddB5MmkQHa1gYvW3t2pWK2KWOU9zz\n/+DQ53LqFNtWJCQAoaH06v/xB8OX9erZ500mCHbAPeWQmVmwYAHmzJmDyMhItGzZEgcPHkS7du2w\nc+dOqwlaJvH3ZzsLM1lZlr5hQh7MhpiZ4vQJ7tiRnrFvvwVee81+vyd27qSszz3HIrTp04ErV/jd\nlpuUFOC//6XXz8cHqFKFudUTJ9KR0KABh6sLgk1p0YJ9EHMj/3glIk2fhnIe5TSVIXcqh/mxo6R7\nOCNF+n9nz56Nw4cPIzAwELt27cKJEydQsWLF0pDNuXn5Zbp4YmMZs/LwoJskTQZtW4PwcDogH3+c\nRV9XrmgtUf4MGGCJUnt7M4p9uzEGsK2cjw+rSw8f5riSt98Gzp1jRGfYMInmCIKjcCLmBAauGoik\nzCTNZNi2DfjPf+hhz85m64rNm9mH3DzUZdkyet8NBs3ELFMUqcK9vLzg/c+AvczMTDRu3Bjnzp2z\nuWBOT9WqHIUUFkZvWXo6v42ffVZGHN0jBgMwbx7DlKNGAcOHc9saUaL4eMtjcyX+vXD7yrOglaiL\nCz196enAxx/znD74gP86nToBkyezh+aZM/cmjyAItkUphbmH5+LirYtYeXqlZnJ06MCi2blzgWnT\nmIPapQtrKHr2ZIHswoVMb84dzBFsR5EGWZ06dXDr1i3069cP3bp1Q9++fRFortkX7o0KFegRi41l\nM8Vq1fgN/8UXWkvm0Li5AbNnW8KUHTty9XcvbnelmDj/wQfA1q0sLPvuO+DLL61j6BWHM2eYahgQ\nwPBlxYocUl6tGle2W7awMaMgOA0pKWwI60SRgz9i/8DJuJOoV6kevjv5nWZeMh8f5qBu28YZlGPG\nMFDz3/9yATh1Kv0Gn39OD71ge+6qynL37t1ITk5Gjx494KFhPxiHToq9nVmzgJUr6eoAqHiqVAFW\nr9ZWLmsSFUWlWr060LCh1tLkISODocKittesYSulTp3o1Dx+HGjThqvL0jCCkpOZPz1mDBAUBMyf\nz++q7GyuZM1GWZ06tpdFC5zpnnemc7Epu3czSdJkovtm5kymdTgwSikM3zAcZ2+cRRWfKohLjcPw\nVsPxautXS7zPrCxeHnPKwu06rCCys+kZMxr5tVO/Pr3wK1awICo2lvvctk1GIFuD4tz3d5V1Ehoa\nir59+2pqjDkdzZvzjjAY6GpJSgJatdJaKuuxaxdn0Y0ZA7zwApMW7ITMTBo5a9YwuX7dOibV//wz\nXflxccCbb7Lav2tXzmybOJH5aC4u7NlbWh6pChWAr7+m188cvnz+ea5sASrUQ4dKRxZBsDkJCXRH\ne3nRTePqCowdy5i9A3Pu5jkcjz0OpRRupN+ASZmw4s8V0Bv1Jd7n8uXUDSYTs13eeotr4KLYsQPw\n9GS6w8cfU+dt2QIsXswuIwcPsl7jpZe4+BNsj/Qh0xqTiXfT0qXcbtuWGdvO4CPW6zlVwMuLSzaD\ngb2LVqwAHnig2LuJiWG40dzm4uxZNk/19OT299/T8da2LfX17Nk0WG4fJnHuHFC3rmX1ePIkjZvJ\nkznKqFYt4JlnWAwwbRq/B3btooIKCGC4cP9+KqdNm+jKHzSIhQPWJvf4EZPJMnkm999feolyr1jB\nPmsLFrCq1Nw43Zlwpnvemc7FZoSHAyNG5B3uGh8P/PCDZcyFA6I36hF+PTzP5+/p5olm1ZoV2oi9\nMDIzgSlTuK6Pi+NCrVu3ot9nHn5gHg1qMDDd48QJesvKl+ffDx4EHn5YiobuFav1IbM3nFKhpaXR\nh1yxovPUGN+8CXTvTh96cjItoQoV2GvtLkrld+zgKnDqVK78vvySKzpzNeLff7MeYuhQGkr330+D\n7HYFMn8+V4FhYQzv/foroyCzZzM6kpZG/b94seV7wGRiFWRqKqPKiYn8/fDDVHq//go8/TQrH80N\nySMi6OgMDi7ZZTt1ipWhkyYxp+Prr2lwPvFE3tedP8+m6LVqUbkeP855mD4+JTuuPeNM97wznYvN\nuHGDLmhfXy7o0tMZm/v1V+dYrFqZS5dYdQ0Uv7m0ULpYPWQp2JBy5ThAPD9jTCl2Ol22jC4aaylz\npbjPxx/nz9Klxdt3QgI7coeGcjl2/nz+r6tUiZ1PIyKoUGNiqDnust+atzcNjREj2PahZcu8I+3q\n12c044svuIh+7TXq7lzjWHH9OmcVBwTQC/bTTzTwtm9nSLJTJ4YiL1ygcQbQE/bii8zLCg6mZ+6r\nr+jAXL6cpzN0KL87pkyhERURQY9bSgpXrAsX0hYF+LolS4q+xEFBNAinTKHBGBcHdO585+saNrTk\nduh07NfmjMaYUAapWpU3e2oqb5zMTLqtxRi7g+hoLlBffZUZMObwZVkiIYELaaOR2+HhDL86GmKQ\n2TtKATNmcOL0rFk0hL780jr7/uUXWjHmIb5ffsnnipJn9GjG9by8aIG8/joNr9tJTaUC9fXlneLh\nwbjjzZt3JWaNGgwdJiQAkZHsaF+hguXv6emWsKXBABw5wp/x46nLo6PZAiM83GLAeHrSVX/yJNCr\nF/f7ww80/saM4cSWt97ilIAPP6TxNm0asG8fnZjDhjHx9fJlfiyDBrHqctQoGo6PPMJVqrs7PV2X\nLzP/rEKFoh2gLi5sa7F6NT+OceP4/vfec6piM0EonB49mNC5cCF/azgdxp7Zvx8YPJgOxcmTqXZj\nY7WWqnTx9aWO/PJLRhg+/RSoWVNrqe4eMcjsnZgY4Mcf6VWqXZu/f/iBbpN7ZccOWiC5f3bsKPw9\nSUnA6dOM27m7M1ErPT1/L5mbGy2fVq0Y43v4YSYmuBU5IILExAA7dyLrwFG4u5rg4UEbMCsrb27v\nwoUMU86YwXDkvHlAs2YM8b3yCj1mgwfTE7Z1K1dSLVrwph03js7B6dOp7//7X57a9Ok8zZkz6ehz\ncWE63Asv0Hbt0wd48EHgX/9iSku3bhZDKyaGBp3JRA+bvz+P374952+a7VGTia+7vemiycT8NKUs\nXrh+/fjxmB0ECRkJmLZvGgwm6dgoaExKCj34+/czPcGaVKkCNG1a8OBaAc88AwS2uoBMQya8vLjw\nK2tVkR4eXPj+9hvP/733Sp4yoiVikNk7aWm0BsyZl66u3LaGq6RyZSbem9Hri1Z83t48fnY2t83e\ntfxCCeXKMcHq+nUacrGxVK7NmhUt2/HjfO8HHyDw8zcw7tZ4VCxvQu3arHzPHbIcNsySM1a/Pg2y\nKlXypqm1bMnnzL113nqLBpibG0+pShW+rmlTrqwuXeLfHnzwTtH27+cNf+gQT33hQibYjx7NkOTW\nrfSezZrFEOjy5bxcx44B165RYdy4wfDnoUMWN7uZ8HA+99NPlHXrVhp1n3xiec3SU0ux5I8l2H15\nd9HXUhBsRVwc3cNjx/IGePFF3utCDkpxMWgmK8s662kzKb/vxqvT2+GHQc2BCRNw+lAqfv7Z8vef\nfmK6hbNz/jx1tqsr/Qq361VHQAwye6duXXrF4uNpMF2/ToshIODe9z1kCGNo0dH8qVCBLiXAYjF8\n8AHDBebEJ09PuoUSEphhHxvLBKemTfM/xpgxjPn16MEeE998Q89aUYSF8c6qVg1Jnv6ofX4nlr91\nADNnMoE+d4d8H5+8SazlyvF0Jk6kqEOH8jSaNrUk67u4MFSZWxSlLMbS669zv//6l8X2NGPucH3+\nPA2ljh2Z4rJnDy9h//7c/8WLlvS8I0fYt+zUKV6uV15hMcKHH1qqRc20aMGcEFdXnkeNGjQaT57k\n32+m38SK8BWoVq4avj78NYwmB9Q8gnPw7bfUSdWr82aIiLBUjAsAqKs++IA6ICuLuaGFZYYkJDB9\nztxqYv9+LvryJSICP84chgRkYFHdm0jZsRmB30/B+vXAhg1s6bN5s/XHJKenU5eZuXateK02bEVc\nHCMeEycyl/fWLephc+j27FlL1MGekSpLRyAqimWEFy6wQczkySULkF+8SCMrLo5WxKuvWno5nD8P\n/PEHLYknnmCz2thYWixxcew82qwZXVFt29Ldc+EC7/ROnSwePGvx8MP04Lm6MqQXFwu3jyYBTz6Z\nI05hlUR//knxzeXfGzfy0jVoUPB7lKLN+MQTQO/eVKBffUWv1+025IULdAgA9IAlJrI+4sABeE9d\nygAAIABJREFU5jOMG0fbMyKCMrz3HuWNjual3bWLxuGsWXe25wAYquzdm+8dNsxyrB9+ABaGz8HS\nU0vh7+uP2JRYTO8yHV0f6FrMC+uYONM970znghEj2E/GPN/45k2uOKZO1VauUiAtjSkUZtWXnJw3\ntzU3584xpJaZydSHt98uWH8pRZ1z8iTXscuXFzzjNmX9KvTaMQyebp5IcjXgzbi6GHLOG9c3HMSw\n4cyhWLLEEgGwFhERXEyOHMlMmkmTuPDVKs1PKep789eiXs9WQFu30mm7cCF1cMuW2sgHSNsLITfx\n8Uw2yMykuyUpiZOtJ07kUmfECMYBXV1pAJpMdClFR9P60OnoutHr2fDKPJfIVowcyXievz9lTk5m\n5n6jRjY9bFGd+wGuXD/8kDkKSvHyffwx+/fMmMGor48Pi1AHDOB3U6VKwLvvsrN/bCzfv3Eju2B/\n8YUl4qsUL2/Hjlx1tmlDhdy5My99nYYJ6P59d0AHuLu4I1WfisBKgVj37Dq4uljZKLYjnOmed6Zz\nwaJFXHn4+/Of9/p1/nP366e1ZDZnwQIuxEaPZoV2WBi9MOZ+ibnJymL+aWYmL09RAweUokqOi6P+\nKEjdLl7xPr499A38db7I1BmRpQz45a9W2Dp8J5Yt42uGDAH69r2XM82f3IvSd96xtP2xJ774govf\nN9+8s21QaSNtLwQLx46x/KZqVX77+/vTp20ycRlhMtFqKF+ey77ERL4vNpaBeRcX/t1kohVha6ZM\nAUJCePysLC4RbWyMAXcaX/mNIDl/niutIUMYegwJYU7a1Kms8gkMZAf9Ll1o406caFEG3bpZwpRP\nPUW7M3erCp2OUerPP2dUetIkXvbGjWkAZhuz0bthb/R4oAe61OuCJxs9iQ51OsCoJGwpaMCLL3LV\nER9P79jLL9vm298OefllqtSRI3lPv/56wcbYlCks6pkxg6POjhwpfN8HDnAB1rIlbd6COuVvdrkE\nYzlvxKlUJJkykI5s/NC1F7ZupcH4n/9w4WeLKR65daOvr/X3f6+cPctU5HbtWLHuCJWn4iErK+zc\nyTiaWWNkZdH9s3cvV7hLllj8vfHxdM/UqsVs1ORk/q1KFfrp33qLS46iSElhwpfJxOz4SpXuXu7b\nB7XZKQsXMi/E3JzW3K2kpIpq5Uqm4oSGchXqLL2CS4oz3fPOdC45ZGfzn7S4FdRaYr72Vrip/vqL\n9Qzu7vzSzy9zIzGRumHQIKqxc+eoVgvqpp+QwPDa5Mlc3C1ZQhVsbvyam0xDJrIz0oAD+4HkFKBp\nE3g0aIX0dF1OfVZCAtfZt6ddJCZaVLJ5al9xVXRUFBeaL77IBeSUKWz5Yy+jRvV6GspvvEGjdtMm\ntiyaNk07XSohy+Jw8ybvlowMxomaNLHOfrXA3NXUw4PJB+aB5QDP7+WXmUnu5sYSlLFj2YY+Kopl\ngomJFqU6eTLw++8s+du7l752gBpn5kzmnxXGzZt0H5mXJVWqcKl3D81hlLLcTLkflza3H9u8ffIk\n8PH4NHTP3ojhAxKge/DB/Ms0iyAxkZ6x5GR+FFOnOmZPHWviTEaMM52LQ6HXc5W0cSNd1CNHspK7\nhJinfgwbxvWury8XT9ZIp83MZKACoH7JyrJsWwO9nsbKK6+wSGnFCrb5KW7qX1IScOYMvU8Av3pc\nXO5qIp7NyX0N89subcQgK4obN2jix8XxG9Xdnf5kezHz74ZTp+gzz8riHVylCjuV5v4mT0lhpuON\nGzzH3EMPo6MZwtTrGWszt6a4eJH5IEYjrQM/Px5jx47Cu2Z/+SWTn8weubg4GolTppTo9LZvZyLp\nsGEUZeZMJr0HBZVodyXGaKStOnw4k2zPnaMye/ttYMqEDAz7bRjKXfsLVau7oLwvaFkVkU9jLs92\ndeVHN2YMu+4PGsRJMevW0YnpCM4HW+FMRowznYtD8fXXdDdVr87mf7duUd+3b1+i3a1ZQ/Xavj3V\n5jffcHCJtSsabYV5qki5ctQ9n3xSsiCGUDyKc9+XYRUPesbi4lgmAtA1MXcuDRl74vp1zus5f555\nVOPH5x26C7D8HLB0BIyJocYYOdLymvLl6SUzT6vOTa1aNOhuJzGRS7/cx7t+3dKFvyDi4vL6yL28\n+L4S8vDDdDvPn29prNq4cYl3V2JcXYGePVmWPngww4rvvks938vvNzTzuICMlrVx/gLQrEYG3L/6\nqkiDbMMGrjDNnfiTk5mXptPRhm3TpmwbY4JgFfbsYTWom5slL/bw4RIbZAMHWh57eFAPOBL33cev\nk4MHqfrFGNMe+07MsTXp6Xlzk9zd7W82jV7PfK19+xh23LOHOVy3N8dKT89rALm40GjKTVoa88ja\ntmWrig0bij7+Aw/QvZ+YSPdNfDwN2NsNwttp356etOxsrkbT0jhPqIT4+nI198svVCDjxmlnpLRv\nz9yub74BnnyS3qy33gK6PJIFnYsOPj5Ai+aAu48HP7MiVkW9evHj++gjYMKEOyPnRV1qQRCKQbVq\neScJGAzW7wfhIChFz35MDCvEV65k9yNBW8q2Qfboo3R5JCXxGzEpiTNx7ImrV5lg7+/PspYaNVhj\nfe1a3tf17k0DzOxiUerOrNGZMxn7q16dRtbHH7P3GEDldOoUqzFzG6WVKtFr6OfHfLD69enmLypR\nondv1m0nJTE08MILjMGVEIOBBlDz5gwVFmdIty3YtYuG4Y4d7Cc0bRqNRA8PQNeqJT2BN2/CJSuD\n16tnzyKT3Tw86Mg8eZIf9+DBksQvCFZn9GjqvdhYiy4rA+058iM7m5fgk0/ojZ8yhenCgraU7Rwy\ngInrc+fSIOvblyE9e6rou3aNZeXmTqgmE71U69fnzQ8zmbjM+fFHespef51unNw8/jh/m1vDR0cz\n+emZZ9iS3twYtnp11kznLgowH+Nur41S/LnHa7ppE/t8jRvH5MzJk1mHEBJyT7u9a1JT6cHq3Jk2\n6tWrjNx+8cU/RtTZs+z2Gh9Pg3/UqDtb8d9GcjIrlkJCOOTcx4fhS2v32nVknCnvypnOxaYoxZBi\ndDTja61a3fs+4+K46PT0ZEZ67p4zgmBDJKnfGVCKPbg2bLAYZOaGrnfrRnnhBWZy+vlZJlf/+9/0\nYn3xBQ08nY65Xo89xgnbJSElhYleZq+eFTCPzDSHKbOzizeByRYkJNBuB1gjAdybLJs28XK98ALP\n6/PPWfxVCm3XHAZnuued6VxsyhdfMK4GUF+98QaregTBARGDzJ5JTWXXvnPn+M37+usFN60yN2+9\ndIk5Xd26lczjFB5OpabXc58tWnAS9xdfcAKtuTwoNZWhUbMyLA5KsSnPli2cIeTmxtXnV18V2dV/\n4/mNqO5THW0D2hb6OnvAYGB9RUYGf+rVY4qfiwsv6759tGV1OhazRkQwKb8wbm+LpGVLD3vFKe75\nf3Cmc7EZkZHMmq9ala5ig4EroS1bkNNgSxAcCKmytFeMRoYKT55kvOvECRoz8+fnH6dycWG53d2y\ndSsNrsxMetWGD+fk1VOn6Ll6+GEmMDVvzlCn0chjpaQw96m4mLugLl9u6XPWvDn3N3o0p9sW4EJK\nyUrBZ/s/Q2Xvylj77Fq4udj3v+SuXfwdFkZvVlgYP77WrVnDsH49o8y9enGgcK9eRRtktxtfYowJ\nZZ6UFOoRsz50c+ONkZIiBpngtNhRslQZIjKS3qoaNTiNtkYNTsOOjLTeMY4coUWQlMTV5fz57NFQ\nsybQvTsTodLT2WesUycm3MfHM8eiffvideI3c/Ik21SXK0fDy9WVBmb58kyQSkgo8K2rz6xGliEL\nMakx2HV5lxVO3LZ07Wqp8PT2ZiPF1q35t/LlmST7669suNizJ6swBUG4S+67jzfUjRtc2MXHU0/a\nsENyUmaSzfYtCMVBDDItcHG5s0TQConvedizh/vz9aXlUKEC3f1mtmyhxfDCC6ws7dyZ7p9t24DZ\nswvvMXY78fE8ljlBVqdj/C4lhccuYEWbkpWCxX8shp+3H3zcffD14a9hMBnu4aRtz+3TYW5vvWGO\nBgO0hSUyJQgloFw59lasV48LusaNWXxlo8TRpMwkPL36aRy6ZoOhj4JQTMQg04KAAFb4xMQwmzsm\nhl6pgADrHaNCBUsLeIDxtIoV+Tgujsn85cpZmlyNGcPwZaVKdx8zM8/LUIqPMzOpOE0mZqh7eOT7\nttVnVuNm+k2kZ6fDaDLi4q2L2Hlp512eaClhMDAEvGIFPYL5kJhIp+RzzzGN7tixu0vDEwQhF/ff\nzzSIgwfZ58aa+hGASZlgUlw9rTy9EleSrmDOoTmS3ydohn0n7DgrLi7MuVqxgqG9xo0tk2etxYAB\nnLkTFUUDy8uL3UsBPgdYBnuVL8/Kyps3SxYSuP9+Gngff8xjPfYY8M47LFMvpP2zt5s3uj/QPc9z\nOntMoDIYeD4HD9LIdHXlSKTb4pEVKnDEpzln7JNPLJdaEAT74rP9n6GcRzm8HPwyvjv5He6reB/O\n3zyPw1GHHaLASHA+pMrSmUlIYBgyK4seuMBAPh8TA/TvTwvC05NVlUox+cncMysigrPf4uKYbzZ0\naNGt8Q0G7qtiRefKTD90iJ1b/f15XllZPM/9++2rZ50T40z3vDOdi6MSlRyF/iv7w9XFFU83fRo/\nhP8Af19/3Mq4hfsq3oelA5ba5+JQcFikyrKsU7ly3oFrZqpVA4KD6aFzceEopMWLLcbYjRvs95Oc\nzOfOnGE87v33Cz+em5tzDkRLS+N1MitoDw8mixkMBYZjBUGwX5b8sQQAYDQZ8e2Rb1HBqwJupt+E\ngsKZG2cQfj0czf2bayukUOawK4Ns9erVCAsLw19//YUjR46glTU6Mwt38t13wNGjjK1lZDDnK/ds\nzKNH2YL+xg16zry9OQVg7Fjn8nwVl2bNaJjeusW8u5s3LS1DBEFwKKKSo7D+3HpU8akCZVLINmbj\nq+5fwc/bUnzUsEpDDSUUyip2FW9p3rw51q1bh44dO2otinOzYwfDleakfnd3djQ1Ex3NH7N7NTW1\nbCdD+fuzn1tAAD1jXbpwiKUgCLbl9GlWfp87Z7Vd/hD+A1L0KbiVfguJmYnINGbiTPwZBFUPyvnx\ncJXFllD62JWHrHHjxlqLUDaoXJld/82TAYxGPmfG15fPZWbSI2Yy0YArywQFAT/8oLUUglB2WLAA\n+O9/LSPjxo7l3N2iMBiYYlGxYr5tMvo06oOQGnmH4Nbzq2ctqQWhxNiVQSaUAKWAnTu5iqxYkX3F\n6tQp/D0jRwIjRjC5HwBq1QKeesry98RES18x83Bwvb5shisFQSh9oqNpkFWtytxUvR6YNYtNrc3t\ne/LjzBng3XeZXuDjA3z6KdMLctGwSkMJSQp2SakbZN26dUNsbOwdz0+bNg19+vQp9n7CwsJyHoeG\nhiI0NNQK0jkgGzaw3YSHB1eG27axd0+NGgW/p1EjJvQfPkxl17FjXiVXowZbYdy6xW03NxYCyJBF\noZTYvXs3du/erbUYNkP0VxHcusX2MubKbg8PLhLNnq/80Os5ki4zk2kGqan0qq1fnzcCIAilQEl0\nmF22vejcuTNmzZpVYFK/lI3n4skn2RHf3Fk/KopNXgcPLvk+Dx4EHn/c0nNLr+eA8EPSxVrQBme6\n553pXGxGSgp1W3Y2DbCEBP5ev77gYppr1+jpr1bN8tzNm8B//kP9JQgaUpz73q6S+nMjCquY3O61\n0unufV5PQgLDmJ6e3F/VqvS+2ctnkp3NWaDh4TQWBUFwLsqX56ikihWZWlGjBrcLq2z286MXLSOD\n23o9c2HN00gEwc6xqxyydevW4V//+hdu3LiBXr16oWXLlti8ebPWYtk3zz/P8URZWTRUfH2Bewl/\n6PXA2bP0jrVqZem5ZS+GT1oaJw6cPcvt+vU5866sFx0IgrPRtCnw88/UPcVpMVOuHBAWBnz0EcOV\nJhMwejQXlyXFZJLmz0KpYZchy6IQl38ulKLS+vVXGiXDhllmS94tmZnAG28Ap04Bly9TEQYGcsTS\nuHHA009bVfQSMW8esHChZcRTbCyHR44Zo61cgk1xpnvemc7FLomOBiIj6VW7776S7ePoUeDDD9mL\nMTgYmD49byhUEO4S6dRfFtDpgD59+HOvbN1KY6xmTaB6dc7ZNBg4lLFHj3vfvzW4dIkGojlM6+1N\n47EwDAZWXxmNnBvq7W17OQVB0IZate7NKxYTw+IAd3cWB5w6Bbz3HhtqC4INEYPMmYiLA44cYWVS\nhw7Mw7gbEhP5W6fjLMubN/n400/ZFDUoyOoi3zVBQWzzYTJxOz298ITd9HS2+Th9mtsBAextVKWK\n7WUVBMHxOHcub2/G6tW5oEtPZysNQbARYpA5EhkZQHw8jQlzVaWZS5cYrjQPCg8IAJYsubvZksHB\nzJeIjaXbH6C3zGgEJk5khZMWnDgB7NlDA7NnTyrM7dv5t86dgSFDCn7vihXAyZM8D52OI6G++QaY\nPLlURBcEwcGoVIk6z5w/lplJr7yXl9aSCU6OGGSOwrFjdJtnZtIDNnUq0KmT5e9ff02Dzdx/LDIS\nWLUKePXV4h8jOJhJsRMmUCHVrAncfz8NGfMopdLuQ7Zrl2WoudEI/Pgj8P337C9kMtE4LUymK1eY\nEGx+jY9P0SFOQRDKLi1aMEVjyxbqDZ2OvR4luV+wMWKQOQIZGTTGACaWpqcDH3wAbNxocavHx+dd\nwbm5MeR4t/TqRSPspZe4b1dX4Pp1DtjWoinsvHk0osxVlFFRzHUrbp+1Fi2AX36hMefiQg9iy5a2\nk1cQBMfGxQX497+B3r2pQxs2ZDW3INgYMfkdgfh4trUw54SZRxqZw4oAW10kJ7P1RWYmE9nbty/Z\n8Zo0YVVlUhLz0urW1W6YdlZW3nl0Ot3dteDo3x8YMIDXMC6OUwlGjLC+nIIgOA8uLkDbtkyREGNM\nKCWk7YUjkJbGGW6enjTGMjPp6dmwwVKKbTAAc+YAa9fSgHn9dQ7ivRevVkYGj125snbu+kWLmPNV\noQINMZOJIcu7VZIpKfSSVawo458cEGe6553pXARBKB7Fue/FIHMU9uxhmNI87HvSJIYXnR2TCVi6\nFNi8mU1v33oLCAnRWiqhlHGme96ZzkUQhOIhBpmzkZDAMKW/vzQpFMoUznTPO9O5CIJQPMQg04L9\n+9lA0GgEBg0CunbVWiJBcHjs+p6/S5zpXARBKB5ikJU2R44Ab75pGcqdkQHMmMFeWYIglBi7vedL\ngDOdiyAIxaM4971UWVqTn35iuwk/PzYX9PJikr0gCIIgCEIhiEFmTby8GKo0YzTSWyYIgiAIglAI\nYpBZk+eeY1f4mBiOHwLYYFUQBEEQBKEQJIfM2vz9N2c+GgxA375ssioIwj1h1/f8XeJM5yIIQvGQ\npH5BEJwCZ7rnnelcBEEoHpLULwiCIAiC4ACIQSYIgiAIgqAxYpAJgiAIgiBojBhkgiAIgiAIGiMG\nmSAIgiAIgsaIQSYIgiAIgqAxYpAJgiAIgiBojBhkgiAIgiAIGiMGmSAIgiAIgsaIQSYIgiAIgqAx\nYpAJgiAIgiBojBhkgiAIgiAIGiMGmSAIgiAIgsaIQSYIgiAIgqAxYpAJgiAIgiBojBhkgiAIgiAI\nGiMGmSAIgiAIgsaIQSYIgiAIgqAxYpAJgiAIgiBojBhkgiAIgiAIGiMGmSAIgiAIgsbYlUE2duxY\nNGnSBMHBwRgwYACSkpK0Fume2L17t9YiFAuR0/o4iqyOIqdQ+jjS/4ajyCpyWhdHkbO42JVB9vjj\nj+P06dM4efIkGjZsiOnTp2st0j3hKP8sIqf1cRRZHUVOofRxpP8NR5FV5LQujiJncbErg6xbt25w\ncaFIbdu2xbVr1zSWSBAEQRAEwfbYlUGWm0WLFqFnz55aiyEIgiAIgmBzdEopVZoH7NatG2JjY+94\nftq0aejTpw8AYOrUqTh+/DjWrFmT7z7q16+Pixcv2lROQRDshwceeAB///231mJYBdFfglD2KI4O\nK3WDrCiWLFmCBQsWYMeOHfDy8tJaHEEQBEEQBJvjprUAudmyZQtmzJiBPXv2iDEmCIIgCEKZwa48\nZA0aNIBer0flypUBAO3atcO8efM0lkoQBEEQBMG22JVBJgiCIAiCUBax2yrLwvjwww8RHByMkJAQ\ndOnSBZGRkVqLVCCO0ux29erVaNasGVxdXXH8+HGtxbmDLVu2oHHjxmjQoAE+++wzrcUpkKFDh8Lf\n3x/NmzfXWpRCiYyMROfOndGsWTMEBQVhzpw5WouUL5mZmWjbti1CQkLQtGlTTJgwQWuRrIKj6DDR\nX9ZB9Jd1cVr9pRyQ5OTknMdz5sxRw4YN01Cawtm6dasyGo1KKaXGjRunxo0bp7FE+XP27Fl17tw5\nFRoaqo4dO6a1OHkwGAzqgQceUJcvX1Z6vV4FBwerM2fOaC1Wvuzdu1cdP35cBQUFaS1KocTExKgT\nJ04opZRKSUlRDRs2tNtrmpaWppRSKjs7W7Vt21bt27dPY4nuHUfRYaK/7h3RX9bHWfWXQ3rIypcv\nn/M4NTUVVatW1VCawnGUZreNGzdGw4YNtRYjXw4fPoz69esjMDAQ7u7ueO6557B+/XqtxcqXRx99\nFH5+flqLUSQ1atRASEgIAMDX1xdNmjRBdHS0xlLlj4+PDwBAr9fDaDTm5Jg6Mo6iw0R/3Tuiv6yP\ns+ovhzTIAGDixImoW7cu/u///g/jx4/XWpxiIc1uS0ZUVBTq1KmTsx0QEICoqCgNJXIuIiIicOLE\nCbRt21ZrUfLFZDIhJCQE/v7+6Ny5M5o2baq1SFbB0XSY6K+SIfrLtjiT/rJbg6xbt25o3rz5HT8b\nN24EwOaxV69exZAhQ/Duu+/atawA5fXw8MDgwYPtWk57RKfTaS2C05KamoqnnnoKs2fPhq+vr9bi\n5IuLiwv++OMPXLt2DXv37nWY+XWOosNEf9kW0V+2w9n0l131IcvNtm3bivW6wYMHa75qK0rWJUuW\nYNOmTdixY0cpSZQ/xb2m9kbt2rXzJD1HRkYiICBAQ4mcg+zsbAwcOBAvvPAC+vXrp7U4RVKxYkX0\n6tULR48eRWhoqNbiFImj6DDRX7ZF9JdtcEb9ZbcessK4cOFCzuP169ejZcuWGkpTOOZmt+vXr3eY\nZrfKzjqhtGnTBhcuXEBERAT0ej1WrlyJvn37ai2WQ6OUwrBhw9C0aVO88847WotTIDdu3EBiYiIA\nICMjA9u2bbPr+724OIoOE/1174j+sj5Oq79Ko8rA2gwcOFAFBQWp4OBgNWDAABUXF6e1SAVSv359\nVbduXRUSEqJCQkLUG2+8obVI+bJ27VoVEBCgvLy8lL+/v+rRo4fWIuVh06ZNqmHDhuqBBx5Q06ZN\n01qcAnnuuedUzZo1lYeHhwoICFCLFi3SWqR82bdvn9LpdCo4ODjnf3Pz5s1ai3UHp06dUi1btlTB\nwcGqefPm6vPPP9daJKvgKDpM9Jd1EP1lXZxVf0ljWEEQBEEQBI1xyJClIAiCIAiCMyEGmSAIgiAI\ngsaIQSYIgiAIgqAxYpAJgiAIgiBojBhkgiAIgiAIGiMGmSAIgiAIgsaIQSYIgiAIgqAxYpAJgiAI\ngiBojBhkgiAIgiAIGiMGmSAIgiAIgsaIQSYIgiAIgqAxYpAJgiAIgiBojBhkgiAIgiAIGiMGmSAI\nxWb37t3o06cPAGDjxo347LPPbHKcY8eO4e233873b4GBgUhISMj3b127dkVKSkqB+/3qq6+QkZFh\nFRmLkqU4LFmyBKNGjQIAzJ8/H99//73VZMrKykLHjh1hMpnueZ+CINgeN60FEATBMenTp0+OcWZt\nWrdujdatW+f7N51Ol+/zO3fuRKNGjVC+fPkC9zt79my8+OKL8Pb2toqcBclSECaTCS4u+a+DX3vt\nNWuIlCOTp6cnHn30Ufz0008YMGCAVfYtCILtEA+ZIJQhIiIi0LhxY7zyyito1KgRnn/+eWzduhUd\nOnRAw4YNceTIEQDA4cOH0b59e7Rq1QodOnTA+fPn79hXbu9OXFwc+vfvj5CQEISEhOD333+/4/Vv\nvvkmHnzwQQQFBSEsLCzn+SNHjqBDhw4ICQlB27ZtkZqamscTd/PmTTz++OMICgrCiBEjoJTK99yW\nL1+OJ598EgCQlpaGXr16ISQkBM2bN8eqVavw9ddfIzo6Gp07d0aXLl0AAG+88Ua+MgUGBiIsLAyt\nW7dGixYtcO7cuSJl6d+/P9q0aYOgoCAsWLAg53lfX1+MGTMm57osXrwYjRo1Qtu2bfHbb7/lvC4s\nLAyzZs1CTEwMWrZsmfPj5uaGyMhIxMfH46mnnsJDDz2Ehx56KOe9hcnUt29frFixIt/rJQiCnaEE\nQSgzXL58Wbm5uanw8HBlMplU69at1dChQ5VSSq1fv17169dPKaVUcnKyMhgMSimltm3bpgYOHKiU\nUmrXrl2qd+/eSimlFi9erEaOHKmUUuqZZ55Rs2fPVkopZTQaVVJS0h3HTkhIUEopZTAYVGhoqDp1\n6pTKyspS999/vzp69KhSSqmUlBRlMBjyHGfUqFHq448/Vkop9csvvyidTqdu3rx5x/4bN26c8/yP\nP/6oRowYkfO35ORkpZRSgYGBed57u0x//vlnzuvmzp2rlFJq3rx5avjw4UXKYt5Xenq6CgoKytnW\n6XRq9erVSimloqOjVd26ddWNGzeUXq9XHTp0UKNGjVJKKRUWFqZmzpyZ55zmzp2rnn32WaWUUoMG\nDVL79+9XSil15coV1aRJkyJlyszMVLVq1brjWgmCYH9IyFIQyhj16tVDs2bNAADNmjVD165dAQBB\nQUGIiIgAACQmJuKll17C33//DZ1Oh+zs7EL3uWvXLixduhQA4OLiggoVKtzxmpUrV2LBggUwGAyI\niYnBmTNnAAA1a9bMCU/6+vre8b59+/Zh3bp1AICePXvCz88vXxmio6NRuXJlAECLFi1Btf/VAAAD\nqklEQVQwZswYjB8/Hr1798YjjzyS73vykykoKAgAcsJ8rVq1wtq1a4uUZfbs2fjpp58AAJGRkbhw\n4QIeeughuLq6YuDAgQCAQ4cOoXPnzqhSpQoA4Nlnn83X+wgABw4cwP/+9z8cOHAAALB9+3acPXs2\n5+8pKSlIS0srVCZPT0+YTCZkZmbCy8sr3+MIgmAfiEEmCGUMT0/PnMcuLi7w8PDIeWwwGAAAH374\nIbp06YJ169bhypUrCA0NLXK/qoBQIgBcvnwZs2bNwtGjR1GxYkW88soryMzMLHYOVmH7zo8GDRrg\nxIkT+OWXXzBp0iR06dIFH374YbFkMmO+Tq6urjnXpSBZdu/ejR07duDgwYPw8vJC586dc/bl5eWV\nc546nS7P+ws6r5iYGAwfPhwbN26Ej49PzmsPHTqU83nlprDro5S661w3QRBKH8khEwThDpKTk1Gr\nVi0AwOLFi4t8fZcuXfDtt98CAIxGI5KTk+/YX7ly5VChQgXExcVh8+bN0Ol0aNSoEWJiYnD06FEA\n9PoYjcY87+3YsSOWL18OANi8eTNu3bqVrwy1atXKqXiMiYmBl5cXnn/+eYwZMwYnTpwAAJQvXz5H\ntvxkKoqCZElOToafnx+8vLzw119/4eDBg/m+/6GHHsKePXuQkJCA7OxsrF69OsdYMhtVBoMBTz/9\nND7//HPUr18/572PP/445syZk7N98uTJIq9PVlYWXF1d8xjhgiDYJ2KQCUIZ43ZvSe5t8+P3338f\nEyZMQKtWrWA0GvN9jU6ny3k8e/Zs7Nq1Cy1atECbNm3yhNYAIDg4GC1btkTjxo3x/PPP54QQ3d3d\nsXLlSowaNQohISHo3r17jufMvO+PPvoIe/fuRVBQENatW4f77rsv3/N65JFHcooS/vzzT7Rt2xYt\nW7bElClTMGnSJADAq6++ih49eqBLly4FypTf9SpKlh49esBgMKBp06aYMGEC2rVrl+/1rVmzJsLC\nwtCuXTs88sgjOaHj3Mf57bffcOzYMUyePDknsT82NhZz5szB0aNHERwcjGbNmmH+/PlFXp8TJ07k\nkUUQBPtFp+42FiAIgmCH7N69GytXrszx1AnABx98gAcffBD9+/fXWhRBEIpAPGSCIDgFoaGhuHDh\nQqGNYcsSWVlZ2L9/P/r166e1KIIgFAPxkAmCIAiCIGiMeMgEQRAEQRA0RgwyQRAEQRAEjRGDTBAE\nQRAEQWPEIBMEQRAEQdAYMcgEQRAEQRA05v8BtYjSBsR6FHsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107af1080>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id=\"PCA\"></a>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id='MDA'></a>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Linear Transformation & Classification: Multiple Discriminant Analysis (MDA)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The main purposes of a Multiple Discriminant Analysis is to analyze the data to identify patterns to project it onto a subspace that yields a better separation of the classes. Also, the dimensionality of the dataset shall be reduced with minimal loss of information.\n",
      "\n",
      "**The approach is very similar to a Principal Component Analysis (PCA), but in addition to finding the component axes that maximize the variance of our data, we are additionally interested in the axes that maximize the separation of our classes (e.g., in a supervised pattern classification problem)**\n",
      "\n",
      "Here, our desired outcome of the multiple discriminant analysis is to project a feature space (our dataset consisting of n d-dimensional samples) onto a smaller subspace that represents our data \"well\" and has a good class separation. A possible application would be a pattern classification task, where we want to reduce the computational costs and the error of parameter estimation by reducing the number of dimensions of our feature space by extracting a subspace that describes our data \"best\"."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Principal Component Analysis (PCA) Vs. Multiple Discriminant Analysis (MDA)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Both Multiple Discriminant Analysis (MDA) and Principal Component Analysis (PCA) are linear transformation methods and closely related to each other. In PCA, we are interested to find the directions (components) that maximize the variance in our dataset, where in MDA, we are additionally interested to find the directions that maximize the separation (or discrimination) between different classes (for example, in pattern classification problems where our dataset consists of multiple classes. In contrast two PCA, which ignores the class labels).\n",
      "\n",
      "**In other words, via PCA, we are projecting the entire set of data (without class labels) onto a different subspace, and in MDA, we are trying to determine a suitable subspace to distinguish between patterns that belong to different classes. Or, roughly speaking in PCA we are trying to find the axes with maximum variances where the data is most spread (within a class, since PCA treats the whole data set as one class), and in MDA we are additionally maximizing the spread between classes.**\n",
      "\n",
      "In typical pattern recognition problems, a PCA is often followed by an MDA."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![](https://raw.githubusercontent.com/rasbt/pattern_classification/master/Images/mda_overview.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you are interested, you can find more information about the MDA in my IPython notebook   \n",
      "[Stepping through a Multiple Discriminant Analysis - using Python's NumPy and matplotlib](http://nbviewer.ipython.org/github/rasbt/pattern_classification/blob/master/dimensionality_reduction/projection/linear_discriminant_analysis.ipynb?create=1)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Like we did in the PCA section above, we will use a `scikit-learn` funcion, [`sklearn.lda.LDA`](http://scikit-learn.org/stable/modules/generated/sklearn.lda.LDA.html) in order to transform our training data onto 2 dimensional subspace, where MDA is basically the more generalized form of an LDA (Linear Discriminant Analysis):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.lda import LDA\n",
      "sklearn_lda = LDA(n_components=2)\n",
      "sklearn_transf = sklearn_lda.fit_transform(X_train, y_train)\n",
      "\n",
      "plt.figure(figsize=(10,8))\n",
      "\n",
      "for label,marker,color in zip(\n",
      "        range(1,4),('x', 'o', '^'),('blue', 'red', 'green')):\n",
      "\n",
      "\n",
      "    plt.scatter(x=sklearn_transf[:,0][y_train == label],\n",
      "                y=sklearn_transf[:,1][y_train == label], \n",
      "                marker=marker, \n",
      "                color=color,\n",
      "                alpha=0.7, \n",
      "                label='class {}'.format(label)\n",
      "                )\n",
      "\n",
      "plt.xlabel('vector 1')\n",
      "plt.ylabel('vector 2')\n",
      "\n",
      "plt.legend()\n",
      "plt.title('Most significant singular vectors after linear transformation via LDA')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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u15gtaERERERmhgkaERERkZlhgkZERERkZpigEREREZkZJmhEREREZoYJGhER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\nNCIiIiKF+X/RNt9EvCI3jgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107c35b38>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Classification via LDA"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The LDA that we've just used in the section above can also be used as a simple linear classifier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# fit model\n",
      "lda_clf = LDA()\n",
      "lda_clf.fit(X_train, y_train)\n",
      "LDA(n_components=None, priors=None)\n",
      "\n",
      "# prediction\n",
      "print('1st sample from test dataset classified as:', lda_clf.predict(X_test[0,:]))\n",
      "print('actual class label:', y_test[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1st sample from test dataset classified as: [3]\n",
        "actual class label: 3\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another handy subpackage of sklearn is `metrics`. The [`metrics.accuracy_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html), for example, is quite useful to evaluate how many samples can be classified correctly:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import metrics\n",
      "pred_train = lda_clf.predict(X_train)\n",
      "\n",
      "print('Prediction accuracy for the training dataset')\n",
      "print('{:.2%}'.format(metrics.accuracy_score(y_train, pred_train)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Prediction accuracy for the training dataset\n",
        "100.00%\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To verify that over model was not overfitted to the training dataset, let us evaluate the classifier's accuracy on the test dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pred_test = lda_clf.predict(X_test)\n",
      "\n",
      "print('Prediction accuracy for the test dataset')\n",
      "print('{:.2%}'.format(metrics.accuracy_score(y_test, pred_test)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Prediction accuracy for the test dataset\n",
        "98.15%\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Confusion Matrix**  \n",
      "As we can see above, there was a very low misclassification rate when we'd apply the classifier on the test data set. A confusion matrix can tell us in more detail which particular classes could not classified correctly.\n",
      "\n",
      "<table cellspacing=\"0\" border=\"0\">\n",
      "\t<colgroup width=\"60\"></colgroup>\n",
      "\t<colgroup span=\"4\" width=\"82\"></colgroup>\n",
      "\t<tr>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" colspan=2 rowspan=2 height=\"44\" align=\"center\" bgcolor=\"#FFFFFF\"><b><font face=\"Helvetica\" size=4><br></font></b></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" colspan=3 align=\"center\" bgcolor=\"#FFFFFF\"><b><font face=\"Helvetica\" size=4>predicted class</font></b></td>\n",
      "\t\t</tr>\n",
      "\t<tr>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 1</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 2</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 3</font></td>\n",
      "\t</tr>\n",
      "\t<tr>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" rowspan=3 height=\"116\" align=\"center\" bgcolor=\"#F6F6F6\"><b><font face=\"Helvetica\" size=4>actual class</font></b></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 1</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#99FFCC\"><font face=\"Helvetica\" size=4>True positives</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
      "\t</tr>\n",
      "\t<tr>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 2</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#FFFFFF\"><font face=\"Helvetica\" size=4><br></font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#99FFCC\"><font face=\"Helvetica\" size=4>True positives</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#FFFFFF\"><font face=\"Helvetica\" size=4><br></font></td>\n",
      "\t</tr>\n",
      "\t<tr>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#EEEEEE\"><font face=\"Helvetica\" size=4>class 3</font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#F6F6F6\"><font face=\"Helvetica\" size=4><br></font></td>\n",
      "\t\t<td style=\"border-top: 1px solid #c1c1c1; border-bottom: 1px solid #c1c1c1; border-left: 1px solid #c1c1c1; border-right: 1px solid #c1c1c1\" align=\"left\" bgcolor=\"#99FFCC\"><font face=\"Helvetica\" size=4>True positives</font></td>\n",
      "\t</tr>\n",
      "</table>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('Confusion Matrix of the LDA-classifier')\n",
      "print(metrics.confusion_matrix(y_test, lda_clf.predict(X_test)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Confusion Matrix of the LDA-classifier\n",
        "[[14  0  0]\n",
        " [ 1 17  0]\n",
        " [ 0  0 22]]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we can see, one sample from class 2 was incorrectly labeled as class 1, from the perspective of class 1, this would be 1 \"False Negative\" or a \"False Postive\" from the perspective of class 2, respectively"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a id='SGD'></a>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Stochastic Gradient Descent (SGD) as linear classifier"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[[back to top]](#Sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let us now compare the classification accuracy of the LDA classifier with a simple classification (we also use the probably not ideal default settings here) via stochastic gradient descent, an algorithm that minimizes a linear objective function.  \n",
      "More information about the `sklearn.linear_model.SGDClassifier` can be found [here](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDClassifier.html)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.linear_model import SGDClassifier\n",
      "\n",
      "sgd_clf = SGDClassifier()\n",
      "sgd_clf.fit(X_train, y_train)\n",
      "\n",
      "pred_train = sgd_clf.predict(X_train)\n",
      "pred_test = sgd_clf.predict(X_test)\n",
      "\n",
      "print('\\nPrediction accuracy for the training dataset')\n",
      "print('{:.2%}\\n'.format(metrics.accuracy_score(y_train, pred_train)))\n",
      "\n",
      "print('Prediction accuracy for the test dataset')\n",
      "print('{:.2%}\\n'.format(metrics.accuracy_score(y_test, pred_test)))\n",
      "\n",
      "print('Confusion Matrix of the SGD-classifier')\n",
      "print(metrics.confusion_matrix(y_test, sgd_clf.predict(X_test)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Prediction accuracy for the training dataset\n",
        "99.19%\n",
        "\n",
        "Prediction accuracy for the test dataset\n",
        "100.00%\n",
        "\n",
        "Confusion Matrix of the SGD-classifier\n",
        "[[14  0  0]\n",
        " [ 0 18  0]\n",
        " [ 0  0 22]]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Quite impressively, we achieved a 100% prediction accuracy on the test dataset without any additional efforts of tweaking any parameters and settings."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}