Hyper Parameter Optimization of Clustering Algorithms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyper Parameter Optimization of Clustering Algorithms\n",
    "Written by Dr. Hanan Shteingart, All rights reserved\n",
    "## Q. How do you know how to set parameters such as linkage, metrics etc for an unsupervised clustering algorithms? \n",
    "## A. You can estimate clustering quality using intrinsic metrics such as silhouette score!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get some DATA!\n",
    "As usual, we will use the Iris dataset as an example...\n",
    "![Iris](http://dataaspirant.com/wp-content/uploads/2017/01/irises.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np # impoty numpy\n",
    "import pandas as pd # import pandas package, this is for describing a dataset etc.\n",
    "#this is just for making plot inline in the notebook:\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets # import datasets package\n",
    "iris = datasets.load_iris() # get iris data into iris variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parse the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris Plants Database\n",
      "====================\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20  0.76     0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "This is a copy of UCI ML iris datasets.\n",
      "http://archive.ics.uci.edu/ml/datasets/Iris\n",
      "\n",
      "The famous Iris database, first used by Sir R.A Fisher\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      "References\n",
      "----------\n",
      "   - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n",
      "\n",
      "                0           1           2           3\n",
      "count  150.000000  150.000000  150.000000  150.000000\n",
      "mean     5.843333    3.054000    3.758667    1.198667\n",
      "std      0.828066    0.433594    1.764420    0.763161\n",
      "min      4.300000    2.000000    1.000000    0.100000\n",
      "25%      5.100000    2.800000    1.600000    0.300000\n",
      "50%      5.800000    3.000000    4.350000    1.300000\n",
      "75%      6.400000    3.300000    5.100000    1.800000\n",
      "max      7.900000    4.400000    6.900000    2.500000\n"
     ]
    }
   ],
   "source": [
    "# define a feature matrix\n",
    "feature_matrix = iris['data'] # get the feature matrix\n",
    "# define the labels. NOTE: we will regard these as unknowns!\n",
    "labels = iris['target'] # get the label\n",
    "n_labels = len(np.unique(labels)) # how many unique labels?\n",
    "n_clusters = n_labels # set the clustering number to the correct one\n",
    "# describe the data\n",
    "print(iris['DESCR'])\n",
    "print(pd.DataFrame(feature_matrix).describe())\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalize the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import scale\n",
    "feature_matrix = scale(feature_matrix, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Build a simple clustering model\n",
    "[Quick refresher on How Agglomerative Clustering works](https://youtu.be/XJ3194AmH40?t=269)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster.hierarchical import AgglomerativeClustering # import the Agglomerative Clustering algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model = AgglomerativeClustering(linkage = \"ward\", n_clusters=n_clusters, affinity='euclidean') # initiate the model\n",
    "y_hat=model.fit_predict(feature_matrix) # fit the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How well did we do?\n",
    "## If we know the true underlying labels, it's easy! Use Supervised Metrics, e.g. V-Score\n",
    "\n",
    "A well know metric is the **v-score** metric scroe. \n",
    "* This score is identical to normalized mutual information score.\n",
    "* The V-measure is the harmonic mean between *homogeneity* and *completeness*:\n",
    "\n",
    "$v = \\dfrac{2 \\times(homogeneity \\times completeness}{homogeneity + completeness}$\n",
    "\n",
    "* Homogeneity - Clusters contain only data points which are members of a single class.\n",
    "* Completness - Data points that are members of a given class are elements of the same cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v_measure_score = 0.560637716465\n",
      "v_measure_score with perfect clusters = 1.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import v_measure_score\n",
    "# Homogenity: each cluster contains only members of a single class\n",
    "print('v_measure_score = %s' % v_measure_score(labels_true=labels, labels_pred=y_hat))\n",
    "print('v_measure_score with perfect clusters = %s' % v_measure_score(labels_true=labels, labels_pred=labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What if we don't know the real labels?... more realistic scenario\n",
    "\n",
    "We can use [Silhouette coefficients][1]. \n",
    "\n",
    "* It's a number between -1 and 1. \n",
    "* ~1 - sample is far away from the neighboring clusters. [GOOD]\n",
    "* ~0 - the sample is on or very close to the decision boundary between two neighboring clusters [BAD]\n",
    "* ~-1 - the sample might have been assigned to the wrong cluster. [UGLY]\n",
    "\n",
    "Formally:\n",
    "\n",
    "* Assume the data have been clustered via any technique, such as k-means, into $k$ clusters. \n",
    "* For each datum $i$, let $a(i)$ be the **average dissimilarity** of $i$ with all other data within the same cluster. We can interpre $a(i)$ as how well $i$ is assigned to its cluster (the smaller the value, the better the assignment). \n",
    "* We then define the average dissimilarity of point $i$ to a cluster $c$ as the average of the distance from $i$ to all points in $c$.\n",
    "* Let $b(i)$ be the lowest average dissimilarity of $i$ to any other cluster, of which $i$ is **NOT** a member. The cluster with this lowest average dissimilarity is said to be the **\"neighbouring cluster\"** of $i$ because it is the next best fit cluster for point $i$. \n",
    "* We now define a silhouette: $s(i) = \\frac{b(i) - a(i)}{\\max\\{a(i),b(i)\\}}$\n",
    "\n",
    "[1]: https://en.wikipedia.org/wiki/Silhouette_(clustering)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score = 0.445539563992\n",
      "perfect score = 0.379753292616\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "print('score = %s' % silhouette_score(feature_matrix, y_hat, metric='euclidean'))\n",
    "print('perfect score = %s' % silhouette_score(feature_matrix, labels, metric='euclidean'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Helper function to compute both scores and print it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# calc performance\n",
    "def calc_metric(x, labels_true, labels_pred):\n",
    "    return {'v_measure_score': v_measure_score(labels_true, labels_pred), \n",
    "            'silhoette': silhouette_score(x, labels_pred, metric='euclidean')}\n",
    "def print_dict(d):\n",
    "    for k, v in d.items():\n",
    "        print('%s = %s' % (k,v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true labels:\n",
      "============\n",
      "v_measure_score = 1.0\n",
      "silhoette = 0.379753292616\n",
      "predicted labels:\n",
      "=================\n",
      "v_measure_score = 0.675470185344\n",
      "silhoette = 0.445539563992\n"
     ]
    }
   ],
   "source": [
    "print('true labels:')\n",
    "print('============')\n",
    "print_dict(calc_metric(feature_matrix, labels, labels))\n",
    "print('predicted labels:')\n",
    "print('=================')\n",
    "print_dict(calc_metric(feature_matrix, labels, y_hat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How does intrinsic metric change when data is shuffled?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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mapVPqgqe7fSOckuXYR96yRZEQzZAEAgI6t99LJDj9LtjwpeeTs5PGLkpkf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\neZtudGmbunCMab3bW/Oo08Xzx6dmMzUr7LY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe1468535c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.utils import shuffle\n",
    "\n",
    "shuffle_size_list = np.linspace(0,1,20) # define a shuffle size range\n",
    "metric = [] # an empty list to contain the results\n",
    "n = len(labels) # data set size\n",
    "index = np.arange(n) # index 0:n-1 in an array to be used for shuffeling\n",
    "for shuffle_size in shuffle_size_list: # for every shuffle size\n",
    "    size = int(np.round(shuffle_size * n))\n",
    "    shuffle_indices = np.random.choice(index, size=size ,replace=False)\n",
    "    y_hat = labels.copy() # copy by value to protect original array\n",
    "    y_hat[shuffle_indices] = shuffle(y_hat[shuffle_indices]) # create a shuffled version\n",
    "    metric.append(calc_metric(feature_matrix, labels, y_hat)) # keep the result\n",
    "\n",
    "# convert to a pandas's DataFrame\n",
    "metric_df = pd.DataFrame(metric)\n",
    "# plot\n",
    "metric_df.index = shuffle_size_list\n",
    "metric_df.index.name = 'shuffle fraction'\n",
    "plt.figure(figsize=(10,5), dpi=300)\n",
    "metric_df.plot(legend=True, ax = plt.gca());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interim Conclusion \n",
    "Intrinsic measurement such as silhouette can be a proxy for clustering performance even if we do **NOT** know the true underlying true labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyper Parameter Clustering Optimization Using Intrinsic Metric\n",
    "So, if we can measure performance, we can optimize meta-parameters of the clustering. \n",
    "Let's take as an example the problem of decising on the linkage method.\n",
    "\n",
    "Reminder:\n",
    "![type of linkages](https://i.ytimg.com/vi/vg1w5ZUF5lA/maxresdefault.jpg)\n",
    "[source of image](https://i.ytimg.com/vi/vg1w5ZUF5lA/maxresdefault.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loop around parameters and decide which is best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ground truth:\n",
      "v_measure_score = 1.0\n",
      "silhoette = 0.379753292616\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hanan/anaconda3/lib/python3.6/site-packages/pandas/tools/plotting.py:2470: UserWarning: To output multiple subplots, the figure containing the passed axes is being cleared\n",
      "  plot_obj.generate()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>silhoette</th>\n",
       "      <th>v_measure_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ward</th>\n",
       "      <td>0.445540</td>\n",
       "      <td>0.675470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>complete</th>\n",
       "      <td>0.448791</td>\n",
       "      <td>0.653048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>average</th>\n",
       "      <td>0.479451</td>\n",
       "      <td>0.713099</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          silhoette  v_measure_score\n",
       "ward       0.445540         0.675470\n",
       "complete   0.448791         0.653048\n",
       "average    0.479451         0.713099"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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FqtsCJEmS1E3NCEYfL9NGi4xqx//STjtjgPHAk8DVEVGfV9uwfkJEzADIzEmt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\nhxzSpWDXnfd3zDHHMH36dM4991x23XVX9tprL7b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Zz7Y47l6KwVO3UoTfEcD7gK8BxwOL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\nUqiq5i4ZegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe14a6f7358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LINKAGES = [\"ward\", \"complete\", \"average\"]\n",
    "print('ground truth:')\n",
    "print_dict(calc_metric(feature_matrix, labels, labels))\n",
    "metric = []\n",
    "for linkage in LINKAGES:\n",
    "    model = AgglomerativeClustering(linkage =linkage, n_clusters=n_clusters, affinity='euclidean')\n",
    "    y_hat = model.fit_predict(feature_matrix)\n",
    "    metric.append(calc_metric(feature_matrix, labels, y_hat))\n",
    "df = pd.DataFrame(metric, index=LINKAGES)\n",
    "plt.figure(figsize=(5,5), dpi=150)\n",
    "ax1, ax2 = df.plot(kind='bar', subplots=True,ax = plt.gca(), sharex=True)\n",
    "ax1.set_ylim(0.4,0.5)\n",
    "ax2.set_ylim(0.6, 0.8)\n",
    "df\n",
    "# life is tough. Sometimes it doen't work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hanan/anaconda3/lib/python3.6/site-packages/pandas/tools/plotting.py:2470: UserWarning: To output multiple subplots, the figure containing the passed axes is being cleared\n",
      "  plot_obj.generate()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.text.Text at 0x7fe144ce27f0>,\n",
       " <matplotlib.text.Text at 0x7fe144cb2550>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IiIiIiJ+44n7o95y3fHSHayOKU4eci0lERESqLSXsyuiWfCPqVv18lF9STjsY\njYiIiIhUup6PwDX51oc8shWmDoK0lKLvERERESkDbTpRRl2a1aZ1/Uh2HE4DYM7avfyhX1uHoxIR\nERGRSnXV466NKBJedJUPJbuSdqMWQIQ2IhMRAXjiiSc4cuRIia6dPHly5QYjHqNHjy7RdfXq1Svz\nJhhScZSwKyNjDLd0b8bfv9gCwOzEvfz+mjYEBBiHIxMRERGRStX7z66k3Tfu/8z8ugmm3Qwj50N4\nbWdjExHxAbNnz2b37t0lulYJu6ozZcqUEl3XokULJex8gKbElsPNl8SRl5/bdzydVTs1HUJERESk\n2jMGrv4LXPmIt+7AevhoCGScdC4uEREfsWvXLqy1JXpJ1Snpn8muXbucDlVQwq5cGsaE0bttfU95\n9pq9DkYjIiIiIlXGGOj3LFzxgLduXyJ8PAzOpDoXl4iIiFQLStiV07BuzTzvF/14gNSMLAejERER\nEZEqYwz0fwEuvcdbt+d7+NdwyExzLi4RERHxe0rYldO1HRpQOyIYgIysXBZtOuBwRCIi1Ysx3rVB\nc3JyHIxExCs3N9fzPv/vqNRAxsB/vwxdR3nrdq+E6bdBVrpzcYmIiIhfU8KunEKDAhnUuYmnPEvT\nYkVEKpQxhtDQUABOntTaUOIb0tJco6dCQkKUsBMICICbXocud3jrdn4NM26HrAzn4hKRMsv/d3v+\nL2lEpPrzlS9mtUtsBRjWrRlTvnPtgLNm9zF2HkmjZb1Ih6MSEak+6tSpw8GDBzl06BDZ2dlER0cT\nGhqqRIlUudzcXNLS0vj1118BiI6Odjgi8RkBATDwDcjNho2fuOp2LIWZd8LwjyAo1Nn4RKRUjDGE\nhISQmZlJWloatWrVcjokEakivvLFrBJ2FaBTXAztGkWz5aBrgeHZiXv4Y/92DkclIlJ91KpVi4yM\nDI4fP87Ro0c5evSo0yGJEBYWRmxsrNNhiC8JCIRBb0JOFiR96qrbtgRm3QW3ToHAYGfjE5FSiY6O\nJiUlxfMlTWRkJAEBmqQmUl352hezSthVAGMMw7o15W+fbwbg07X7eKzfRQQGaOSHiEhFCAgIoFGj\nRkRGRpKamkpaWprWsxPHhISEEB0dTWxsLIGBgU6HI74mMAiGTILcLNi80FX30+cwewwM+9B1XkT8\nQmxsLGlpaWRkZLB//36nwxGRKuQLX8yqx1BBBl8Sx9+/2EJ2ruXAiQxWbj/Cf7Wt73RYIiLVhjGG\nmJgYYmIBlWgIAAAgAElEQVRiALDWYq11OCqpaYwxmootxQsMhqEfwMyRsPULV93mBTD3Xhjyrmsk\nnoj4vMDAQJo3b05KSgqpqalkZmY6HZKIVDJf+mJWCbsKUi8qlD4XNeA/m11DJ2cn7lXCTkSkEilx\nIiI+LSjENQ12xh2w/UtX3Y9zICAYBr+ppJ2InwgMDKRBgwY0aNBAXxaKVHO+9v8LJewq0C3dm3oS\ndv9OOsiJ9CxqhWutEhEREZEaKSjUteHE9Nvg52Wuuo0zXNNiB7zh2qhCRPyGr/1nXkSqN/USKlDf\nixpQNzIEgDPZuXy2UesciIiIiNRowWFw27/ggqu8des+gs8fA43UERERkSIoYVeBQoICGNwlzlOe\ntWavg9GIiIiIiE8IiYDbP4HmV3rrEj+EL/6kpJ2IiIgUSgm7CjasW1PP+/V7jrP9UKqD0YiIiIiI\nTwiJhDtmQtPLvHWrJ8G/n1LSTkRERM6hhF0F69Akho5NYjzlWYkaZSciIiIiQGg0jJgNTbp661ZN\nhP88o6SdiIiIFKCEXSW4Jd8ou0/X7iM7J9fBaERERETEZ4TVgjs/hcadvXUrx8OyF5yLSURERHyO\nEnaVYGCXOIIDXbsHHU49wzfbjjgckYiIiIj4jPA6cOc8aNjJW/f1S7D8JediEhEREZ+ihF0lqBsZ\nwrXtG3rKsxL3OBiNiIiIiPiciLowcj7Ub++tW/Y8fPOqczGJiIiIz1DCrpLk33ziP8mHOJaW6WA0\nIiIiIuJzIuvBqAVQr6237qtx8O0E52ISERERn6CEXSXp3bY+9aJCAcjMyWXBhv0ORyQiIiIiPieq\nAYxcAHVbeeuWPAXfv+NcTCIiIuI4JewqSVBgAEO6xnnKs7VbrIiIiIgUJqYxjFoItVt46774E/zw\nvnMxiYiIiKOUsKtE+afFbtp3gi0HTzoYjYiIiIj4rFpNYfRnUKuZt+7zx2DtVOdiEhEREccoYVeJ\n2jaMpnPTWp7y7DUaZSciIiIiRajd3DXSLsY7S4MFj8D66c7FJCIiIo5Qwq6SDevu/ZZ03vp9ZOXk\nOhiNiIiIiPi0ui1dSbuoRu4KC/MfgI2zHA1LREREqpYSdpVsYHwTQoJcP+YjpzJZtuWQwxGJiIiI\niE+Lbe1K2kXWd5VtLsy9D5LmOhuXiIiIVBkl7CpZrYhgruvQ0FPW5hMiIiIiUqz6bV1Ju4hYV9nm\nwJx7YPNnzsYlIiIiVUIJuypwS75psUu3HOLIqTMORiMiIiIifqFBexg5H8LruMq52TBrNPy02NGw\nREREpPIpYVcFel1Yj0YxYQBk51rmr9/vcEQiIiIi4hcaXQx3zoMw90ZmuVkw807Y/h9n4xIREZFK\npYRdFQgMMAzp6t3ta9aaPVhrHYxIRERERPxGky5w51wIjXGVczJhxh3wc4KjYYmIiEjlUcKuigzr\n1tTzfsvBVJL2n3QwGhEREZGSM8aEG2OeNcZsNcZkGGP2G2M+MMbEFX+35xmjjTG2BK+R+e4JMcYM\nNsa8b4xZb4w5ZoxJN8ZsNsa8YoypXzmf2AfFdYMRcyAkylXOzoB/3Qa7Vjgbl4iIiFQKJeyqSKv6\nUXRrUcdT1uYTIiIi4g+MMWHAUuCvQBQwH9gD3AWsM8a0KuGjtgNTinjNy3dd/gzUfwFzgTFALXcc\nXwL1gMeBjcaYi8r0wfxRs8vgjlkQHOEqZ6fDx7fC7u+cjUtEREQqnBJ2VSj/KLt56/dxJjvHwWhE\nRERESuQvwBXAd0Bba+1wa+3luBJm9YEPSvIQa+0Ka+3owl7AEvdlK621P+e7LReYCVxurW1prR1q\nrR0IXAj8G2gEfFgRH9JvtLgSbv8EglzrI5OVBh/fAnt+cDYuERERqVBK2FWhG+MbExbs+pEfP53F\n0s2HHI5IREREpGjGmBDgIXfxQWvtqbxz1tpXgY1Ab2NMt3I2NcJ9nJa/0lq71J0gXH1W/Qlco+4A\nehhjWpSzff/S8r/gN9MhMNRVzkyFj4bAvrXOxiUiIiIVRgm7KhQTFsz1HRt5ypoWKyIiIj6uJ66p\nqDustesKOT/bfRxQ1gaMMS2BK4FMXKPpSsRaux847C42KWv7fqv11XDbxxAY4iqfOQnTBsOBDc7G\nJSIiIhVCCbsqdkv3Zp73CVsPcyg1w8FoRERERM6rs/tY1NCtvPr4crSRN7ruc2vtsZLeZIypDeQt\nEHywHO37rzb94NapEBDkKmecgKmD4dckZ+MSERGRclPCror1aBVLXO1wAHJyLXPX7nM4IhEREZEi\nNXcfi5oWkFdfnimphU6HLYEHgSBgk7V2Zzna928X/TcM+xBMoKucfhSmDIRDW5yNS0RERMpFCbsq\nFhBgGNo1zlOenbgXa62DEYmIiIgUKcp9PF3E+TT3MbosDzfGXAa0BY4Cn5fivktwbYYB8OdStplU\n2AtoXZrn+JQOA2Hou2DcXfvTR2DKADiyzdm4REREpMyUsHPA0Hy7xW47dIoNe084GI2IiIiIY/JG\n18201maW5AZjTEPgUyAMeN1a+0VlBedXOg2FwW8DxlVOO+RK2qXscDQsERERKZsKS9gZY8KNMc8a\nY7YaYzKMMfuNMR8YY+KKv7vAc3YZY+x5Xu0KuWdyMff8rqI+Z0VoERvJZS3resqzE/c4GI2IiIhI\nkfJ2hY0o4nyk+5ha2gcbY4KA4e5iiabDGmOigUXABcAs4PHStmut7VjYC/D/zFbn4TBoorecesA1\nPfbYLsdCEhERkbIJqoiHGGPCgKXAFcABYD6ujtRdwE3GmCustT+X8rFTiqg/33C0f1P4osM/lbLt\nSndLt6as3nkUgAXr9/OXGzsQFhzocFQiIiIiBfziPjYt4nxe/e4yPPs6oAHws7X22+Iudvc3FwBd\ngSXACGttbhnard4uuQNys2Dh713lk3tdI+1GL4Lazc5/r4iIiPiMCknY4VpD5ArgO+A6a+0pAGPM\nY8D/AR8AfUrzQGvt6DLE8XdrbUIZ7qtyN1zcmGcWJHE6M4eTGdl8mfwrAzo3cTosERERkfw2uI9d\nizifV7+xDM/Omw77UXEXukfjfYKrP/ktMKSkU2hrpG6jIScLFj3hKh//BabcBHd9ATHqb4qIiPiD\nck+JNcaEAA+5iw/mJesArLWv4urA9TbGdCtvW9VJZGgQN1zc2FOelVjU5msiIiIijlmJa3ZDa2NM\nl0LOD3MfF5bmocaYKGCQu3jehJ0xxgAfAgOB9cCN1tq0890jwGW/hf4vesvHdrlG2qUWNhlFRERE\nfE1FrGHXE6gF7LDWrivk/Gz3cUAFtFWtDMu3+cSKbYc5eCLDwWhERERECnKPYpvgLk40xuStWZc3\nkyIeWG6tTcxX/5AxZosx5kWKNgTXunirrLXFbWX6Oq7ReFtwzeQ4XoaPUjP1eAD6Pestp2x3rWl3\n6pBzMYmIiEiJVMSU2M7u49oizufVx5fmocaYPwKtgTNAEjDXWnu4mNuGGGOGAoHATmChtXZLadqt\nSpddUJfmdSP45ehpci3MWbuXB/te6HRYIiIiIvn9DbgWuBLYZoz5BmgBXA4cBsacdX094CKgMUXL\nmw573s0mjDGDgEfcxT3Ay64Bd+f4uy/3+RzV8/eu6bFLn3OVj/wEUwfBqM8gMtbZ2ERERKRIFTHC\nrrn7WNSczrz6FqV87kvAfbg6ae8Au4wxZ3cIz/Ywrum597vvTzbGTHSve+JzAgIMQ7t6R9nNSdyL\ntdbBiEREREQKstZmAH2B54DTwGBc/brJQNfSbixmjGkMXA1k4VqX7nzq5HvfDxhVxKtRaWKocf7r\nCej9pLd8KBmmDYLTR52LSURERM6rIhJ2Ue7j6SLO560xEl3C5y3ANU2iBa6pEp2AV4FQ4D33N61n\nWwf8DmjrvqcV8CBwHHgAeLmEbQNgjEkq7IVrxF+FGtotjrwvin8+ksbaX45VdBMiIiIi5WKtTbfW\nPm2tvdBaG2qtbWytvctae84XttbasdZaU9QGYtbaA9baIGttiLU2pZh2J7ufVdwroWI+aTXW50m4\n6nFv+eAmmHYzpGuGsYiIiC+qiIRdhbLWPmKtnWut/cXdOUyy1j6Oa9ScAf5RyD3jrbXvWGu3ue/Z\naa19E7gKyAQeMsb45D72TetEcGVr73SEWWu0+YSIiIiIVDBj4Oq/wpUPe+sOrIePhkLGSefiEhER\nkUJVRMIub1fYiCLO5y1OnFrOdt4HDgEXGWMuKMkN1tokXCP2goBrStqQtbZjYS9gR+nDLl7+zSc+\n23iA9MycymhGRERERGoyY6Dfc3D5/d66fWvg41vgzKmi7xMREZEqVxEJu1/cx6ZFnM+r312eRqy1\nuXgTZudbxPhseTuPleaeKnV9x8ZEhbqW2Tt1JpvFSQccjkhEREREqiVj4PoXofvd3ro9q+Bft0Jm\nWtH3iYiISJWqiITdBvexaxHn8+o3VkBbeQsPl6Y3UZZ7qlR4SCA3xXvzibMTNS1WRERERCqJMXDD\nK9B1pLdu90qYfhtkpTsXl4iIiHhURMJuJXACaG2M6VLI+WHu48LyNGKM6QhchGtziy0lvCcUuNFd\nXFue9ivbLd29AxS/3ZHC3mNF7eEhIiIiIlJOAQFw03jocoe3bufXMON2yMpwLi4REREBKiBhZ63N\nBCa4ixONMXlr1mGMeQyIB5ZbaxPz1T9kjNlijHkx/7OMMTcYY64+uw1jTDwwC9emE++528w7184Y\nc6c7OZf/nvrADKAZrlGAK8v5UStV1+Z1aFXP9aOzFj5du8/hiERERESkWgsIgIFvwMW3eut2LIWZ\nIyH7jHNxiYiISIXtEvs34HvgSmCbMeYTY8wq4P+Aw8CYs66vh2u03Nnryl0GfGWM2WWMmW+MmW6M\n+R5IBNoDCcCTZ93TCJgKHDDGLDHGfGyMWYZrvbvBwF7gVmutraDPWimMMQzNt/nE7MS95Ob6dMgi\nIiIi4u8CAmHwW9DxZm/dtn/DrLsgJ8u5uERERGq4CknYWWszgL7Ac7imrA4GWgCTga7W2p9L+Kh/\nAx8AJ4GeuKbTXgisAH4LXGutPXthja3A68BPwMXALUB3XJtNjAPirbVby/rZqtKQrnEEGNf7X46e\n5oddR50NSERERESqv8AgGPIutLvJW/fT5zDnbsjJdi4uERGRGiyooh7kTqQ97X4Vd+1YYGwh9d8B\n35Wy3f3AH0pzj69qXCucXm3q8/XWwwDMStzL5a1iHY5KRERERKq9wGAY9qFrOuzWL1x1yfMh4D4Y\nMsk1Ek9ERESqTEVNiZUKMizftNhFmw6QdkbfaoqIiIhIFQgKgVunwIXXeut+nA3zHoDcHOfiEhER\nqYGUsPMx13VoSEyYa+Dj6cwcFm064HBEIiIiIlJjBIXC8I+gVR9v3cYZsPARyM11KioREZEaRwk7\nHxMWHMjALk085VmJex2MRkRERERqnOBwuG06XHCVt27dR/D5Y+Db+7iJiIhUG0rY+aBh3Zp53q/e\neZTdKWkORiMiIiIiNU5IBPxmBjTv4a1L/BC++JOSdiIiIlVACTsf1LlpLdo0iPKU52iUnYiIiIhU\ntdAouGMWNL3MW7d6Evz7KSXtREREKpkSdj7IGFNg84k5a/eRm6tOkYiIiIhUsdBoGDEbmlzirVs1\nEf4zVkk7ERGRSqSEnY+6+ZI4AgMMAPuOp/PdzykORyQiIiIiNVJYLbhzLjSK99atfN010i4rw7m4\nREREqjEl7HxUg5gweret7ynP1rRYEREREXFKeB0YOR8adPTWrZoIb/eEnV87F5eIiEg1pYSdD7sl\n37TYL348wMmMLAejEREREZEaLaIujFoA9dt761K2w5QBMPd3kHbEudhERESqGSXsfNjV7RtQOyIY\ngIysXBZtPOBwRCIiIiJSo0XWg3u+hMvvB5PvvxIbpsOE7rB2KuTmOhefiIhINaGEnQ8LDQpkcJc4\nT3mWpsWKiIiIiNNCo+G//w6/XQqNO3vr04/Bgodh8o1waItz8YmIiFQDStj5uPy7xSbuPsaOw6cc\njEZERERExK3JJXDPUrj+7xAS5a3/5Vt4uxd89RxkpTsXn4iIiB9Tws7HdWwSQ7tG0Z7yHI2yExER\nERFfERgEV9wPD66Gdjd563Oz4JtX4M0esGOpc/GJiIj4KSXsfJwxhlu6N/OUP127j5xc62BEIiIi\nIiJnqRUHt30Mv5kBtbx9V47thGk3w5x74NQh5+ITERHxM0rY+YHBXZoQFGAAOHgygxXbtQOXiIiI\niPigi/4bHlgFPR4CE+it3zTLtSnFmg+1KYWIiEgJKGHnB2KjQrm6XQNPedaaPQ5GIyIiIiJyHqFR\n0P95uDcB4rp56zNOwGePwofXw69JTkUnIiLiF5Sw8xP5N59YkvwrJ05nORiNiIiIiEgxGsfD3V/C\nDa9AaIy3fs/38M5/wZfPQOZp5+ITERHxYUrY+Ym+7RoQGxkCQGZ2Lgs27nc4IhERERGRYgQEwmW/\ndW1K0WGwtz43G1a+Dm9eDtu+dC4+ERERH6WEnZ8IDgxg8CVxnvJs7RYrIiIiIv4ipjHcOgVunwW1\nm3vrj/8CHw+DWaMh9aBj4YmIiPgaJez8SP5psRv2HGfbr6kORiMiIiIiUkptr4MHvoeej0JAkLc+\naS5MuBRWvwu5Oc7FJyIi4iOUsPMj7RvH0CnOu/6HRtmJiIiIiN8JiYB+4+C+r6HpZd76Mydh0RPw\nfj84sNG5+ERERHyAEnZ+5pZuzTzvP123j+ycXAejEREREREpo4YdYcy/4abXILSWt35fIkzqA/9+\nCs6cciw8ERERJylh52cGdm5CSKDrj+1w6hmWbz3scEQiIiIiImUUEADdx8BDP0CnYd56mwPfTYA3\nr4CfvnAuPhEREYcoYedn6kSGcG2HBp6ypsWKiIiIiN+LbgjD3ocRn0KdC7z1J/bA9NvgkxFwcr9j\n4YmIiFQ1Jez8UP5psf/Z/CtH0zIdjEZEREREpIJceA08sAquegICgr31mxfChMtg1dvalEJERGoE\nJez80FVt6tEgOhSArBzLgvX7HI5IRERERKSCBIfDNX+F362A5j289ZmpsPjP8N41sH+9c/GJiIhU\nASXs/FBQYAA3d43zlGdpWqyIiIiIVDcN2sHoRTDwDQir7a3fvw7e7QuL/wfOpDoXn4iISCVSws5P\n3dKtqed90v6TJO8/6WA0IiIiIiKVICAAuo6Eh9ZA/G3eepsLq96EiZfD5s+ci09ERKSSKGHnpy5s\nEE2XZt5vGrX5hIiIiIhUW1H1Ycg7MHI+1G3trT+5Dz65A6b/Bo7vcS4+ERGRCqaEnR8blm+U3bz1\n+8jMznUwGhERERGRStaqD9z/LfT+MwSGeOt/WuQabfftBMjJdio6ERGRCqOEnR8b0LkJIUGuP8Kj\naZks++mQwxGJiIiIiFSy4DDo+7/wu5XQope3PisNljwF7/aBfYmOhSciIlIRlLDzY7XCg+nfsZGn\nrGmxIiIiIlJj1G8Loz+DwW9BeF1v/cFN8O41sOiPkHHCufhERETKQQk7P5d/84llWw5x5NQZB6MR\nEREREalCxkCX212bUnQZke+EhdWTYMJlkDQPrHUsRBERkbJQws7P9bywHo1rhQGQnWuZt26fwxGJ\niIiIiFSxyFgYPBFGfQaxbbz1pw7CrFHwr1vh2G7n4hMRESklJez8XGCAYUjXOE951pq9WH2DKCIi\nIiI1Ucur4P6V0PcpCAz11m9b4tqUYsXrkJPlXHwiIiIlpIRdNTCsWzPP+59+TeXHfScdjEZERERE\nxEFBodD7T/DAd9Cyt7c+Ox3+8wy80xv2rHYuPhERkRJQwq4aaFkvku4t6njKsxP3OBiNiIiIiIgP\niG0NI+fDkHchop63/lASvH8dfPYHSD/uXHwiIiLnoYRdNXFLd+/mE/M37OdMdo6D0YiIiIiI+ABj\nIP5WeOgH6Doq3wkLaz6ACZfCptnalEJERHyOEnbVxA0XNyYs2PXHefx0Fl9tPuRwRCIiIiIiPiKi\nLgz8J9y1GOq389anHYI5d8NHQ+Doz87FJyIichYl7KqJ6LBgbujU2FOetUbTYkVERERECmjRA+77\nBq55GoLCvPU7lsKbPeDrVyA707n4RERE3JSwq0aGdfNOi12+9TCHTmY4GI2IiIiIiA8KCoGrHndt\nStH6Gm99dgYsfQ7euQp2f+dcfCIiIihhV61c0SqWuNrhAORa+HTdPocjEhERERHxUXVbwYg5MPR9\niGzgrT+8BT68HhY8DKePOhefiIjUaErYVSMBAYah+UbZzU7ci9UCuiIiIiIihTMGLh7m2pSi+xjA\neM+tneralGLDJ9qUQkREqpwSdtXMsK7ehN32Q6dYv0db1YuIiIiInFd4bbjpNbj7S2jYyVt/+gjM\nvRemDoKUHc7FJyIiNY4SdtVM89gILm9Z11OelbjXwWhERERERPxIs0vh3gTo9ywEhXvrdy53bUqx\n/CXIPuNUdCIiUoMoYVcN3dK9mef9wg37ycjKcTAaERERERE/EhgMPX8PD34Pba7z1uecgWXPw1s9\nYdcK5+ITEZEaQQm7auiGixsRGRIIQGpGNv9OOuhwRCIiIiIifqZOC7h9JtwyBaIaeetTtsHkG2He\nA5CW4lx8IiJSrSlhVw1FhARxw8WNPeXZmhYrIiIiIlJ6xkDHwfDQarjsXgpsSrH+Y5jQHdb/S5tS\niIhIhVPCrprKPy12xfYj7D+e7mA0IiIiIiJ+LKwW3PAy3PMVNLrYW59+FObdD1MGwOGtzsUnIiLV\njhJ21dSlF9ShRWwE4PrCb+66fQ5HJCIiIv7KGBNujHnWGLPVGJNhjNlvjPnAGBNXimeMNsbYErxG\nFnJvoDHmD8aYTcaYdGPMYWPMTGNM+4r9pCLFaNoNfpsA/V+A4Ehv/a5v4O2esOwFyMpwLDwREak+\nlLCrpowxDOva1FOetWYPVkP1RUREpJSMMWHAUuCvQBQwH9gD3AWsM8a0KuGjtgNTinjNy3ddgdX8\njTEBwCzgVaAp8DmQBAwD1hhjLivTBxMpq8Ag6PGga1OKi27w1udkwvJ/wFtXws8JjoUnIiLVgxJ2\n1diQbk0x7mU2dqWcJnH3MWcDEhEREX/0F+AK4DugrbV2uLX2cuBxoD7wQUkeYq1dYa0dXdgLWOK+\nbKW19uezbh0D3AxsA9pZa4dZa/sAtwARwMfGmKByfkaR0qvdDH4zHYZ/DNFNvPVHd8DUQfDpvXDq\nsHPxiYiIX1PCrhqLqx1Oz9b1POVZa7T5hIiIiJScMSYEeMhdfNBaeyrvnLX2VWAj0NsY062cTY1w\nH6cVcu4x9/FP1tpf87U/B1gAXAgMKmf7ImXX/ibXphRXPAAm33+vNn7i2pRi7VTIzXUuPhER8UtK\n2FVzw7p5p8V+vukApzOzHYxGRERE/ExPoBaww1q7rpDzs93HAWVtwBjTErgSyARmFnKuPZCOayps\nhbcvUiFCo+H6F+G3y6BxF299xnFY8DBMuQkyTjoXn4iI+B0l7Kq5/h0bER3qmiVy6kw2i3886HBE\nIiIi4kc6u49rizifVx9fjjbyRtd9bq09e/2OvPZ/tNZmVVL7IhWnSRf47VL475cgJNpbv3slfDXO\nubhERMTvKGFXzYWHBHJT58aesqbFioiISCk0dx+L6kDk1bcoRxvnmw5bFe2LVKyAQLj8Ptc02fyb\nUmycCZmnnYtLRET8ihJ2NcCwbs0877/7OYU9R9VREBERkRKJch+L6jykuY/RRZw/L/cOr22BoxQ+\n5bXC2zfGJBX2AlqX9BkiJRLTBIa8CyHuX+MzJyF5vrMxiYiI31DCrgbo2rw2repHespz1mqUnYiI\niPiEvNF1M621mY5GIlIZQqOg01BveV1hA0lFRETOpYRdDWCMKbD5xJy1e8nNtQ5GJCIiIn4ib1fY\niCLO530jmFraBxtjgoDh7mJRWYwKb99a27GwF7CjpM8QKZWuI73vd6+EI9udi0VERPyGEnY1xJBL\nmhJgXO/3HE3n+51HnQ1IRERE/MEv7mPTIs7n1e8uw7OvAxoAP1trv3WgfZGqEdcN6rf3ljXKTkRE\nSkAJuxqiUa0wrmpT31OenahpsSIiIlKsDe5j1yLO59VvLMOz86bDflSC9jsZY4IruH2RqmFMwVF2\nG6ZDTrZz8YiIiF9Qwq4GuaW798vpRZsOcOqMOgoiIiJyXiuBE0BrY0yXQs4Pcx8XluahxpgoYJC7\nWGTCzlq7E9gMhAM3VlT7IlUufjgEuHPOp36FbUucjUdERHyeEnY1yLXtGxITFgRAelYOizYdcDgi\nERER8WXujSAmuIsTjTGeXayMMY8B8cBya21ivvqHjDFbjDEvnufRQ3CtS7fKWrutmDBedR9fMsY0\nyNfOEGAgsB3Q1pvi2yJjoV2+nLOmxYqISDGUsKtBwoIDGdQlzlOevUbTYkVERKRYfwO+B64Ethlj\nPjHGrPp/9u48yo66zv//892dfSeEQEgCIStrSAIKgsoObigiyKCioDOCwuggzvY7OuNXHZ3RIcqI\n2+igghsSRBQ3dpBNMQmENQlZCCEBEkJC9q3fvz/u7b7X2A3dSaeru+/zcc49Ve+qW5969Rlwmnd/\nqj7A5cAK4IM7fH8YMAkY8QpjNj4O25quxVXADcAE4MmIuC4i7gBmABuB92Wmjw2o85t2XmV/3u9h\n7XPFZZEkdXo27GpM9Wqxf1q8isUr1xeYRpIkdXaZuQk4AfgcsAE4A9gf+D4wLTMXtmW8iBgBnAhs\nBa5txf0bgLOBy4BlwNuAw4DrgSMz849tub9UmLEnwODRpf3cDg/9uNg8kqROzYZdjZk8ajAT9x7Q\nVF8/y1l2kiTplWXmxsz8t8wcn5m9M3NEZl6QmX/1i0RmfiYzIzPPb2Gs5ZnZIzN7ZeaLrbz/9syc\nnpmHZmbfzByWmWdn5uO7+KNJHaeuHqa8t1LP/iFkFpdHktSp2bCrMRHxF7Psrp+5lO0N/qIgSZIk\n7TVIrKAAACAASURBVHZT3wtEaX/VAnj6vkLjSJI6Lxt2NeiMqSOpryv9orBszSbuX9CqP25LkiRJ\n2hVD9oNxJ1TqWVcXl0WS1KnZsKtBwwf24YRJezXV1818psA0kiRJUg2ZWrX4xOM3wqY1xWWRJHVa\nNuxqVPVjsb979Dle3rS1wDSSJElSjTjwrdB3aGl/20Z4ZEaxeSRJnZINuxp14oF7s0e/ngBs3tbA\nTQ8vLziRJEmSVAN69IbJ51RqH4uVJDXDhl2N6tWjjndMGdlUz/CxWEmSJKljTKt6LHb5Q/DcI8Vl\nkSR1SjbsatjZR1Yei521ZDVPvbCuwDSSJElSjdj7EBh5RKWedU1xWSRJnZINuxp2yL6DOWjEoKb6\n+llLC0wjSZIk1ZDqxSfmXAtbNxWXRZLU6diwq3FnVy0+8fNZS9nekAWmkSRJkmrEoe+Cnv1K+5tW\nw5M3FZtHktSp2LCrce+Ysi896gKA51/ezN3zVxScSJIkSaoBfQbBIe+s1C4+IUmqYsOuxu05oDcn\nHTS8qZ4x08diJUmSpA5R/VjsorvgpcWFRZEkdS427MRZR4xu2r/lsedZvWFLgWkkSZKkGrHf0bDn\nhEo9+4fFZZEkdSo27MTxk/Zi2IBeAGzZ3sCvHl5WcCJJkiSpBkTAtKpZdg/9GBq2F5dHktRp2LAT\nPevreOfUkU31dT4WK0mSJHWMw8+Fuh6l/ZefhQW3F5tHktQp2LAT8JePxc5Zuoa5z60tMI0kSZJU\nIwYMh4lvqtQuPiFJwoadyibtM5DJowY31TNmPlNgGkmSJKmGVC8+Mfc3sG5FcVkkSZ1CuzXsIqJv\nRHw2IuZFxKaIWBYRV0XEyFe/+i/GWRwR+QqfA1u4rj4iLo2IRyJiY0SsiIifRcRB7fMTdn9nHTGq\naf+G2cvYur2hwDSSJElSjRh/MgwcUdpv2AZzflpsHklS4dqlYRcRfYDbgU8DA4AbgWeAC4DZETF2\nJ4b9QQufNc3cvw64DpgOjAJ+DTwGnAX8OSJeuxP3rzlvP3xfetWX/pFYuW4zd831L3uSJEnSblff\nA6a8p1LPugYyi8sjSSpce82w+xRwNHA/MDEzz8nMo4DLgL2Aq9o6YGae38JneTNf/yDwTmA+cGBm\nnpWZxwNnA/2AH0VEj5370WrHkH69OOXgvZvqGS4+IUmSJHWMqe+r7K+cC0sfLC6LJKlwu9ywi4he\nwCXl8uLMXNd4LjOnA3OA4yLiiF291yv4RHn7T5n5fNX9rwd+CYwH3rEb799tnHVk5bHY2558nlXr\ntxSYRpIkSaoRQ8fCmDdU6lk/KC6LJKlw7THD7lhgMLAgM2c3c35GeXt6O9zrr0TEAcBBwEZKj8J2\n6P27mzeMH8bwgb0B2Lo9+cXsZwtOJEmSJNWIae+v7D96A2xeW1wWSVKh2qNhd3h5O6uF843HJ7dl\n0Ij4x4j4VkRcEREfjoi9XuX+j2bm1va6f63qUV/HmdMqs+x8LFaSJEnqIAedDr0Hl/a3rofHbig2\njySpMO3RsNuvvG2ps9N4fP82jvsl4ELgY8C3gcUR8cEOvH/Nql4t9vHlL/PYsr9a50OSJElSe+vZ\nFyafXalnXV1cFklSodqjYTegvN3Qwvn15e3AVo73S+BMSg22fsChlFZ/7Q18NyJ2fBdde9+fiHis\nuQ8wrrVjdGXjhw9g6n5Dmmpn2UmSJEkdpPqx2KUPwgtPFpdFklSY9loltt1k5scy84bMXJKZGzPz\nscy8DPgIEMB/FRyxJpx9xOim/RsfWsaWbQ0FppEkSZJqxIjDYZ+qt/nMvqa4LJKkwrRHw65xVdh+\nLZzvX97u6htT/w94AZgUEWN25/0z85DmPsCCNmbust52+Ah69yj947Fq/RZuf/KFghNJkiRJNaJ6\nlt3DP4FtW4rLIkkqRHs07JaUt6NaON94/OlduUlmNlBpmI3o6PvXmkF9evKmQ/dpqmfMfKbANJIk\nSVINOewsqO9d2t/wIsz9TbF5JEkdrj0adg+Xt9NaON94fE473GuP8nZ91bHG+x8aET138/1rSvXi\nE3fMXcGKtZsLTCNJkiTViL57wMFVr+72sVhJqjnt0bC7F1gDjIuIKc2cP6u8/dWu3CQiDgEmUVpc\nounNq5m5CHgC6Au8dXfdvxYdM24Y+w7uA8D2huQXs58tOJEkSZJUI6adV9l/6jZY40JwklRLdrlh\nl5lbgCvL5dcjovGdcUTEJ4DJwF2ZObPq+CUR8WREfLF6rIh4S0ScuOM9ImIycB2lRSe+W75ntenl\n7ZciYnjVdWcCbweeAm7c2Z+xVtXXBWdOq8yymzFzKZlZYCJJkiSpRuz/ethjTLlIeOjHRaaRJHWw\n9lol9vPAH4FjgPkRcW1EPABcDqwAPrjD94dRmi03YofjrwVui4jFEXFjRPwkIv4IzAQOAu4E/qWZ\n+18F3ABMAJ6MiOsi4g5gBrAReF9mbmuHn7PmVD8WO/f5tTzy7JoC00iSJEk1oq4OplbNspt9DTQ0\nFJdHktSh2qVhl5mbgBOAz1F6ZPUMYH/g+8C0zFzYyqF+T6n59jJwLKXHWccD9wB/B5ycmRubuX8D\ncDZwGbAMeBtwGHA9cGRm/nFnf7ZaN2ZYf14zZo+m+ro/OxVfkiRJ6hBT3gNR/k+21Utg0V3F5pEk\ndZj2mmFHZm7MzH/LzPGZ2TszR2TmBZn5Vx2ezPxMZkZmnr/D8fsz80OZOTkzh2Vmz8zcMzNPyMzv\nZub2V7j/9sycnpmHZmbf8vVnZ+bj7fUz1qqzjxjdtP/Lh5exaWuL/2eQJEmS1F4G7QvjT6nULj4h\nSTWj3Rp26r7eMnkEfXvWA7Bm41ZufeL5ghNJkiRJNaJ68YknfgUbVhWXRZLUYWzY6VUN6N2DNx+2\nT1M9Y6aPxUqSJEkdYuKboP9epf3tW2DOz4rNI0nqEDbs1CrVj8XePW8Fz63ZVGAaSZIkqUbU94TD\nz63Us6+BzOLySJI6hA07tcpRBwxl1B59AWhIuGH2swUnkiRJkmpE9Wqxzz8Ky2YXl0WS1CFs2KlV\n6uqCs44Y1VRfN/MZ0r/sSZIkSbvfXhNhv9dV6llXF5dFktQhbNip1d41rdKwW7hiPbOfWV1gGkmS\nJKmGVM+ye/R62LKhuCySpN3Ohp1abfTQfrxu7J5N9XV/dvEJSZIkqUMccgb0Glja3/wyPH5jsXkk\nSbuVDTu1SfVjsTc9vIxNW7cXmEaSJEmqEb36w6FnVurZ1xSXRZK029mwU5u8+bB96N+rHoC1m7fx\n+8eeKziRJEmSVCOmfaCy//S9sPKp4rJIknYrG3Zqk369evDWySOaah+LlSRJkjrIyGkw/OBK7Sw7\nSeq2bNipzc4+cnTT/r0LVvLs6o0FppEkSZJqRMRfLj7x8E9g+9bi8kiSdhsbdmqzI/ffgzF79gMg\nE34+01l2kiRJUoeYfA7U9Sztr3se5t9cbB5J0m5hw05tFhF/sfjEjFlLycwCE0mSJEk1ov+ecNDb\nKvUsH4uVpO7Ihp12ypnTRhFR2n/6xQ08uPilYgNJkiRJtaL6sdj5N8NaF4KTpO7Ghp12yr5D+vL6\n8cOa6hkznykwjSRJklRDxp4Ag8vvlc7t8NCPi80jSWp3Nuy006ofi/31nOVs2LKtwDSSJElSjair\ng6nvq9Szrym9XFqS1G3YsNNOO+2QfRjYpwcA67ds57ePOBVfkiRJ6hBT3guU31GzaiE8fW+hcSRJ\n7cuGnXZan571nH74vk31dT4WK0mSJHWMIaNh3AmV2sUnJKlbsWGnXVL9WOwDC1ex5MUNBaaRJEmS\nakj14hOP/wI2ri4uiySpXdmw0y6ZOnoI4/bq31RfP2tpgWkkSZKkGnLgW6Hv0NL+tk3w6Ixi80iS\n2o0NO+2SiOCsI0Y31TNmLqWhwRfeSpIkSbtdj95w+N9Uah+LlaRuw4addtmZ00ZSV37f7bOrN/LA\noheLDSRJkiTViurHYpc/BMvnFJdFktRubNhpl+09qA/HTdyrqZ7xZx+LlSRJkjrE3gfDyCMr9Wxn\n2UlSd2DDTu2i+rHY3zy6nLWbthaYRpIkSaoh06pm2c35GWzdVFwWSVK7sGGndnHywcMZ3LcnAJu2\nNvCbR5YXnEiSJEmqEYecCT37lfY3rYYnbyo2jyRpl9mwU7vo3aOed0zZt6meMdPHYiVJ6i4iom9E\nfDYi5kXEpohYFhFXRcTInRxvTER8KyIWlcd7ISLuiYhPtvD9iRHxvYh4OiK2RMTaiHgwIi6NiF67\n9tNJ3UCfQXDIOyv1rKuLyyJJahc27NRuzq56LPbBxS+xaOX6AtNIkqT2EBF9gNuBTwMDgBuBZ4AL\ngNkRMbaN470ZeAz4MPAicAPwEDAOuKiZ7x8DzAbOB9YDvwDuAw4BpgM3R0SPnfjRpO5l2vsr+4vu\nglWLissiSdplNuzUbg4dOYhJew9sqq93lp0kSd3Bp4CjgfuBiZl5TmYeBVwG7AVc1dqBIuJA4OeU\nGm+vz8wjM/PczDwVGAn8TTOXXQn0A/41Mw/OzHdn5mnAeGAhcBxwXjPXSbVl9FGw54RK/dCPissi\nSdplNuzUbiKCs48c1VRfP2sp2xuywESSJGlXlB83vaRcXpyZ6xrPZeZ0YA5wXEQc0cohpwN9gPMz\n877qE5nZkJl/3uH+A4CpwAbgSzt8fxmlZh7Aa1p5f6n7ivjLxSdm/wgatheXR5K0S2zYqV29Y8pI\n6usCgOVrNnHvUysLTiRJknbBscBgYEFmzm7m/Izy9vRXGygiRgOnAQsz8zetvP9WoKEV33uxleNJ\n3dvh50Jd+QnxtcvgqduKzSNJ2mk27NSu9hrYmxMmDW+qXXxCkqQu7fDydlYL5xuPT27FWMdT+t3z\nvojoERHvjogrIuLKiLgoIvbY8YLM3AzcTemR2H+qPhcR+wIXU2rqXdOK+0vd34DhMPFNlXq2i09I\nUldlw07t7qwjKo/F/u7R51i2emOBaSRJ0i7Yr7xt6S9wjcf3b8VYB5e364A/ANcCH6PUdPsm8FRE\nnNDMdRdRWuTiixHxeET8LCJ+BzwFBPDWzJzXivtLtaF68Ym5v4V1K4rLIknaaTbs1O5OPHA4+wzq\nA8CW7Q1cecdTBSeSJEk7aUB5u6GF841Lwg9s4Xy1xhl0fwscCLwHGApMAn5Y3r8hIkZWX5SZc4HX\nU5rNdxBwNqVHa/sAd1BacbbVIuKx5j6UVqmVur5xJ8HAEaX9hm0w56fF5pEk7RQbdmp3vXrUccmJ\n45vqnz34DEtebOn3fEmSVCMaf+/sAVyYmT/JzJcyc15mngc8SOl9eR+tvigiTgQeBnoCJwKDgAOA\n/wAuAO6NiL066GeQOr/6HjDlvZV61tWQLgQnSV2NDTvtFu8+cjSj9ugLwLaG5Irb5hecSJIk7YTG\nVWH7tXC+f3m7tg1jrQOua+b898rb4xoPRMTQ8nd7Am/OzDsyc21mLs7MTwNfB8YAn2zF/QHIzEOa\n+wALWjuG1OlNfV9lf+U8eOZPxWWRJO0UG3baLXr1qOPjJ01oqm+YvZSnXlj3CldIkqROaEl5O6qF\n843Hn27FWI3fWZLZ7HSfxeXt8Kpjb6X0qOwDmflsM9c0Nv7e2Ir7S7Vj6AEw5g2V2sUnJKnLsWGn\n3eadU0cydljpD+8NCV+91fdBS5LUxTxc3k5r4Xzj8TmtGGt2eftXq8GWDS1vq//C19gQXNPCNY3H\nWxpTql3Vi088egNsbs1EWElSZ2HDTrtNj/o6Pn5yZZbdTXOW88TylwtMJEmS2uheSk2xcRExpZnz\nZ5W3v2rFWPcBLwL7RMSkZs43Pgo7u+rYc+Xt1Iiob+aa15S3i1txf6m2HHQ69Blc2t+6Hh79ebF5\nJEltYsNOu9Xpk/dl0t6VheO+couz7CRJ6ioycwtwZbn8ekQ0vrOOiPgEMBm4KzNnVh2/JCKejIgv\n7jDWNmA6EOWxBlVdczJwPpDAt6su+x2wmdIiE5+LiLqqayYBny2XM3bxR5W6n5594bB3V+rZ1xSX\nRZLUZjbstFvV1QWXnjKxqb758eeZs3R1gYkkSVIbfR74I3AMMD8iro2IB4DLgRXAB3f4/jBgEjCi\nmbG+DNwKnATMi4hfRMQ9lBpzPYFPZWbT2/EzczmlBSUS+Nfy/WdExB2UHtfdF/gN8P12+lml7mXa\neZX9pQ/CC08Ul0WS1CY27LTbnXbI3hw6sumP6Fx+s7PsJEnqKjJzE3AC8DlgA3AGsD+lJtm0zFzY\nhrG2Am8B/hlYCZwGHAbcBZyemV9o5porgROBX1BarfYdlN6dNxu4GHh7efaepB2NOLz0aTTLWXaS\n1FXYsNNuFxFcdmrlVTV3zVvBg4tXFZhIkiS1RWZuzMx/y8zxmdk7M0dk5gWZubSZ734mMyMzz29h\nrK2Z+aXMPDQz+2bm4Mw8KTNveoX735mZ7yzft2f5mtdl5jcyc3s7/qhS9zO1apbdnJ/Cti3FZZEk\ntZoNO3WI4yfuxbT9hjTV//37uWRmgYkkSZKkGnDY2dCjT2l/w4sw9zfF5pEktYoNO3WIiOCTVbPs\n/rhoFfcteLHARJIkSVIN6DsEDnp7pXbxCUnqEmzYqcMcM34Yrxu7Z1N9+c3OspMkSZJ2u2nvr+w/\ndRusfqa4LJKkVrFhpw512amVFWNnLVnNnXNXFJhGkiRJqgFjXg97HFAuEh76caFxJEmvzoadOtSR\nY4Zy/KS9mur/dpadJEmStHtFwNT3VeqHfggNDcXlkSS9Kht26nCXnVJ5l91jy17m9489V2AaSZIk\nqQZMeQ9E+T//Vi+BRXcVm0eS9Ips2KnDHTZqMKcdsndTPf2WeWxvcJadJEmStNsM2hcmnFqpZ11d\nXBZJ0quyYadCXHrKRCJK+/OeX8dNc5YVG0iSJEnq7qaeV9l/8ibYsKq4LJKkV2TDToU4cJ9BvG3y\nvk31V2+dz7btvkdDkiRJ2m0mngb9h5f2t2+BOT8rNo8kqUU27FSYfzh5AnXlWXaLVq7n57OfLTaQ\nJEmS1J3V94Qp51bqWVeDC8BJUqdkw06FGbfXAM6cNqqpvuLW+WzZ5iw7SZIkabepfiz2hcdg2azi\nskiSWmTDToX6+EkT6FGeZvfs6o1c++dnCk4kSZIkdWPDJsB+r6vUs64pLoskqUU27FSo0UP7cc5r\nRjfVV94+n01btxeYSJIkSermqmfZPXo9bFlfXBZJUrNs2Klwl5w4nl49Sv8oPv/yZn74wNMFJ5Ik\nSZK6sUPOgF4DS/ubX4bHbyw2jyTpr9iwU+FGDO7Le4/ar6n+1l0LWL95W4GJJEmSpG6sV3847F2V\n2sdiJanTsWGnTuEjx4+jb896AFau28IP7l9caB5JkiSpW5v6/sr+kvtg5VPFZZEk/RUbduoUhg/s\nwweOGdNUf/uuhby8aWtxgSRJkqTubOQ0GH5IpZ59dXFZJEl/xYadOo0L3ziWAb17ALBm41b+7w+L\nCk4kSZIkdVMRMK1q8YmHfgLb/YO5JHUWNuzUaezRvxcfev0BTfX/3bOIl9ZvKTCRJEmS1I1NPgfq\ne5X2178A828uNo8kqYkNO3UqH3rDAQzu2xOAdZu38e27FxacSJIkSeqm+g2FA99aqV18QpI6DRt2\n6lQG9enJh984tqn+wX2LWbF2c4GJJEmSpG5sWtXiE/N/Dy8vLy6LJKmJDTt1OucfM4Y9+5em5m/c\nup1v3rmg4ESSJElSN3XA8TB4v9J+NsDDPy40jiSpxIadOp3+vXvwkePHNdU//OPTLF+zscBEkiRJ\nUjdVVwdT31upZ/8QMovLI0kCbNipk3rf0fuz96DeAGzZ1sCVtz9VcCJJkiSpm5ryXiBK+6sWwtP3\nFhpHkmTDTp1Un571XHLihKb62gef4ZlVGwpMJEmSJHVTQ0bDuBMr9ayri8siSQJs2KkTO+fI0Ywc\n0heAbQ3JFbfNLziRJEmS1E1NO6+y//iNsHF1cVkkSTbs1Hn16lHHx0+qzLL7+aylLFyxrsBEkiRJ\nUjc16S3Qd2hpf9smeHRGsXkkqcbZsFOndua0kYzZsx8ADQlfvdVZdpIkSVK769EbDj+3UvtYrCQV\nyoadOrUe9XVcesrEpvpXc5bx5HMvF5hIkiRJ6qaqH4td/jAsn1NcFkmqcTbs1Om9bfK+TNx7AFBa\nYf4rt8wrOJEkSZLUDQ0/CEYeWalnX1NcFkmqcTbs1OnV1wWfqJpl9/vHnueRpWsKTCRJkiR1U9Wz\n7OZcC1s3FpdFkmqYDTt1Cacdsg+H7Duoqb78lrkFppEkSZK6qUPfBT37l/Y3rYEnbio2jyTVKBt2\n6hIigstOrcyyu3PuCmY+varARJIkSVI31HsgHPLOSj3bxSckqQg27NRlnDBpOFP3G9JUX36z77KT\nJEmS2l31Y7GL7oZVi4rLIkk1yoaduoyI4JOnTmqq71vwIvc9tbLARJIkSVI3NPooGFZ5uoWHflRc\nFkmqUTbs1KUcM25Pjh47tKm+/JZ5ZGaBiSRJkqRuJgKmVs2ym/0jaNheXB5JqkE27NSllN5lV5ll\nN/Ppl7hz3ooCE0mSJEnd0OHnQl2P0v7aZfDUbcXmkaQaY8NOXc5rxgzljRP3aqqn3+wsO0mSJKld\nDdgLJr6pUrv4hCR1KBt26pIuO6XyTo1Hnl3DzY8/X2AaSZIkqRua9oHK/tzfwroXissiSTXGhp26\npMNHD+GUg/duqqffPI+GBmfZSZIkSe1m/EkwcN/SfsM2ePinxeaRpBrSbg27iOgbEZ+NiHkRsSki\nlkXEVRExchfHnRARGyMiI+LWFr7z/fL5lj4X7UoGdU6fqJplN/f5tdz0yPIC00iSJEndTF09THlP\npZ59DfgqGknqEO3SsIuIPsDtwKeBAcCNwDPABcDsiBi7C8P/L9C7ld/9PfCDZj5zd+H+6qQOGjGI\nt00e0VR/9ZZ5bNveUGAiSZIkqZuZ+r7K/sp58MyfissiSTWkvWbYfQo4GrgfmJiZ52TmUcBlwF7A\nVTszaER8CDge+E4rL/nPzDy/mc8dO3N/dX7/cPJE6qK0v3Dlem6Y/WyxgSRJkqTuZOgBcMAbK/Us\nF5+QpI6wyw27iOgFXFIuL87MdY3nMnM6MAc4LiKOaOO4ewNfBm4BfrKrOdU9jR8+gDOmVp66vuK2\n+WzZ5iw7SZIkqd1MfX9l/7EbYPPa4rJIUo1ojxl2xwKDgQWZObuZ8zPK29PbOO4VQF/go7uQTTXg\n4ydNoEd5mt3SlzZy3cxnCk4kSZIkdSMHvQ36DC7tb10Pj/682DySVAPao2F3eHk7q4Xzjccnt3bA\niHgLcA7whcx8qg1ZzoyIr0XENyLiHyPiwDZcqy5q/z37c/aRo5vqr932FJu2bi8wkSRJktSN9OwL\nk8+p1D4WK0m7XXs07PYrb5e2cL7x+P6tGSwi+gPfoLRQxH+1McvfU3o89yPAl4DHI+LrEdGjjeOo\ni/n7E8fTq770j/NzL2/ix39cUnAiSZIkqRuZel5l/9k/wwtPFJdFkmpAezTsBpS3G1o4v768HdjK\n8T5Pqbl3UWZuaeU1s4GLgIlAP2AscDGwmtIjtV9u5TgARMRjzX2AcW0ZRx1n3yF9ec9R+zXV37jz\nKTZs2VZgIkmSJKkbGTEZRhxeqWddU1wWSaoB7bVKbLuIiCOBjwFXZ+adrb0uM6/IzG9n5vzM3JiZ\nizLzG8AbgC3AJREx+lWGURf30RPG0adn6R/pleu28IP7ni44kSRJktSNVM+ym/NT2La5uCyS1M21\nR8OucVXYfi2c71/evuJSQuXHVr9DaVbcJ9shF5n5GPBLoAdwUhuuO6S5D7CgPXJp9xg+sA8fOGZM\nU/3tuxewdtPW4gJJkiRJ3clhZ0OPPqX9DS/C3N8Um0eSurH2aNg1vixsVAvnG4+/2nSnUcAUSjPi\nrouIOxs/wFfL3zmi6lhrzS9vR7ThGnVRF75xHP171QOwesNWrrpncbGBJEmSpO6i7xA4+B2V2sdi\nJWm3aY+G3cPl7bQWzjcen9PK8fYBjtvh0/iyhCFVx1prj/J2/St+S93C0P69+NDrD2iqv/uHhaze\n0NpXIUqSJEl6RdWPxS64HVY/U1wWSerG2qNhdy+wBhgXEVOaOX9WefurVxokMxdnZjT3AU4of+22\nqmOvKiJ6A28tl7Nac426vg+9YSyD+pQWBl67eRv/e/fCghNJkiRJ3cSY18PQseUi4aEfFxpHkrqr\nXW7YlVdyvbJcfj0iGt9ZR0R8ApgM3JWZM6uOXxIRT0bEF3f1/hFxYEScV27OVR/fC/gpMJrSLMB7\nd/Ve6hoG9+3JhcdVFvT93r2LWbnOF+JKkiRJuywCpr6vUs/+ITQ0FJdHkrqp9lol9vPAH4FjgPkR\ncW1EPABcDqwAPrjD94cBk2if98rtA1wNLI+ImyPiRxFxB6UFIs4AlgLvzsxsh3upizj/mDEM7d8L\ngI1bt/PNO10vRJIkSWoXh78HovyfkmuWwKI7C40jSd1RuzTsMnMTpcdWPwdsoNQo2x/4PjAtM3fn\nM4nzKC1KMRc4DDgbOJLSYhP/D5icmfN24/3VCfXv3YOPHl+ZZXfNA0/z3JpNBSaSJEmSuolBI2DC\nqZXaxSckqd211ww7MnNjZv5bZo7PzN6ZOSIzL8jMpc189zPld9Gd38qx7yx//+Rmzi3LzEsz83Xl\ne/bKzIGZeUT5Pi+1w4+nLuh9R+/P8IGlJ6W3bGvg63c8VXAiSZIkqZuY9v7K/pM3wYZVxWWRpG6o\n3Rp2UmfTp2c9l5w4vqn+6YNLeGbVhgITSZIkSd3EhFOh//DS/vYtMOfaYvNIUjdjw07d2jmvGc3I\nIX0B2Lo9+drt8wtOJElS1xMRfSPisxExLyI2RcSyiLgqIkbu5HhjIuJbEbGoPN4LEXFPRHzyFa4Z\nEBH/HhFzImJdRKyOiIcj4sqIGLDzP52knVLfE6acW6lnXQO+NlyS2o0NO3VrvXvU87GTKrPsdyyS\ndAAAIABJREFUrp/1LAtXrCswkSRJXUtE9AFuBz4NDABuBJ4BLgBmR8TYNo73ZuAx4MPAi8ANwEPA\nOOCiFq45AJgDfAboD/wWuBvoA1wMDGnjjyWpPUw9r7L/wmOwbFZxWSSpm7Fhp27vzGmjGLNnPwC2\nNyRX3OYsO0mS2uBTwNHA/cDEzDwnM48CLgP2Aq5q7UARcSDwc2A98PrMPDIzz83MU4GRwN80c01v\nSg26/YCLMnNcZp6dmW/PzEmUFh3z5VlSEYZNgP2OqdSzri4uiyR1Mzbs1O31rK/jH06e2FT/8uFl\nzH1ubYGJJEnqGiKiF3BJubw4M5umqWfmdEqz3o6LiCNaOeR0SrPizs/M+6pPZGZDZv65mWs+DkwC\npmfmt3c8mZmPZqYvqZWKMq1qlt0j18OW9cVlkaRuxIadasLph+/LhOGl19tkwldvnVdwIkmSuoRj\ngcHAgsyc3cz5GeXt6a82UESMBk4DFmbmb9qQ4e/K26+14RpJHeXgd0CvgaX9LWvh8RuLzSNJ3YQN\nO9WE+rrg0lMqs+x+++hzPPrsmgITSZLUJRxe3rb0YqrG45NbMdbxlH73vC8iekTEuyPiivKiERdF\nxB47XlBu8o0HlmbmMxFxbET8V3nBin+OiPE7XiOpg/XqD4edValnXVNcFknqRmzYqWa86ZB9OHjE\noKZ6+i3OspMk6VXsV94ubeF84/H9WzHWweXtOuAPwLXAxygtGvFN4KmIOKGFa5ZFxNeBe4B/Ai4E\n/hN4IiIua8W9Je1O1Y/FLrkPVvrOaEnaVTbsVDPq6oLLTq3Msrv9yReY+fRLBSaSJKnTG1DetvSO\nuMaXVQ1sxViNM+j+FjgQeA8wlNL76X5Y3r8hIkY2c800SivIfgYYDYwA/rl87r8j4q2tuD8AEfFY\ncx9Kq9RK2hn7ToPhh1Tq2c6yk6RdZcNONeXEA4czZfSQpnr6LXMLTCNJUk1p/L2zB3BhZv4kM1/K\nzHmZeR7wIKX35X20hWu+nZn/LzOXZuZzmfkl4Cvl8/9fR/wAkloQ8Zez7B76CWzfWlweSeoGbNip\npkQEnzx1UlN971Mvcv+CFwtMJElSp9a4Kmy/Fs73L29bs/z6uqrtdc2c/155e1wz11Sfb+6aoyKi\nTysykJmHNPcBFrTmekktmHwO1Pcq7a9/Aeb9vtg8ktTF2bBTzTl2/J689oChTfX0W+aSmQUmkiSp\n01pS3o5q4Xzj8adbMVbjd5Zk8/+Pd3F5O7yZa6rPN3dNPaVHaiUVpd9QOPBtldrHYiVpl9iwU82J\nCC6rWjH2wcUvcff8lQUmkiSp03q4vJ3WwvnG43NaMdbs8vavVoMta2y4Vc+qexLY9ArXVTfp1jVz\nXlJHqn4sdv7N8PLy4rJIUhdnw0416aixe/KGCcOa6stvdpadJEnNuBdYA4yLiCnNnD+rvP1VK8a6\nD3gR2CciJjVzvvFR2MbGHpm5GWh8ru74V7hmYWa+3IoMknanA46HweXFpbMBHv5xoXEkqSuzYaea\ndVnVu+zmLF3DLY8/X2AaSZI6n8zcAlxZLr8eEY3vrCMiPgFMBu7KzJlVxy+JiCcj4os7jLUNmA5E\neaxBVdecDJwPJPDtHWJ8qbz9dERMrLrmAOBz5fJbO/1DSmo/dXUw9X2VetY10NBQXB5J6sJs2Klm\nTRk9hJMP2rupnn7LPBoanGUnSdIOPg/8ETgGmB8R10bEA8DlwArggzt8fxgwCRjRzFhfBm4FTgLm\nRcQvIuIe4HdAT+BTmfmn6gsy8z7gs5Telzc7Im6OiN9Selx3LPBbSo1ASZ3BlPdQ6ssDLy2Cp+8t\nNI4kdVU27FTTPlH1Lrsnn1vLrx/xPRuSJFXLzE3ACZRms20AzgD2B74PTMvMhW0YayvwFuCfgZXA\nacBhwF3A6Zn5hRau+3fgXcBM4GhKj8IuAC4F3p6Z23fmZ5O0GwwZDeNOrNQuPiFJO8WGnWrawfsO\n4q2HVSYAfOXWeWzb7rR9SZKqZebGzPy3zByfmb0zc0RmXpCZS5v57mcyMzLz/BbG2pqZX8rMQzOz\nb2YOzsyTMvOmV8nw88x8Y2YOysx+mTk1M79aftRWUmcy7f2V/cdvhI2ri8siSV2UDTvVvEtPmUBd\nedb+whXrufGhZcUGkiRJkrqySW+BfnuW9rdtgkeuKzaPJHVBNuxU88YPH8gZU0Y21V+9bR5bnWUn\nSZIk7ZwevWDy31RqH4uVpDazYScBHz95AvXlaXbPrNrIdX/+qyd8JEmSJLXWtPMq+8sfLn0kSa1m\nw04C9t+zP+8+clRT/bXb57Npq++vliRJknbK8INg1Gsq9Sxn2UlSW9iwk8ouOXECvepL/0osX7OJ\nn/xpScGJJEmSpC5satUsu0d+Bls3FpdFkroYG3ZS2cghfTn3taOb6q/fsYCNW5xlJ0mSJO2UQ8+E\nnv1L+5vWwBOvuBi0JKmKDTupysUnjKd3j9K/FivXbebq+xcXmkeSJEnqsnoPhEPfWalnX11cFknq\nYmzYSVWGD+rDB44Z01R/664FrN20tbhAkiRJUlc29f2V/UV3w6qFxWWRpC7Ehp20gwvfOJb+veoB\neGnDVr537+JiA0mSJEld1ejXwrCJlXr2j4rLIkldiA07aQd7DujNB19/QFP9nbsXsnrDlgITSZIk\nSV1UxF8uPvHQj2H7tuLySFIXYcNOasbfvmEsg/r0AGDt5m185w9O3ZckSZJ2yuHnQl3pd2vWLoMF\ntxWbR5K6ABt2UjMG9+3Jh984tqn+3r2LeXHd5gITSZIkSV3UgL1g0psr9SwXn5CkV2PDTmrB+cce\nwB79egKwYct2vnXXgoITSZIkSV1U9eIT834H614oLoskdQE27KQWDOjdg48cP66pvvr+p3n+5U0F\nJpIkSZK6qPEnwcB9S/sN2+DhnxabR5I6ORt20is47+gx7DWwNwCbtzXw9TueKjiRJEmS1AXV1cPU\n91bqWVdDZnF5JKmTs2EnvYK+veq55ITxTfVP/rSEpS9tKDCRJEmS1EVNqWrYvTgfnvljcVkkqZOz\nYSe9ir957Wj2HdwHgK3bk6/d5iw7SZIkqc2GHgAHvLFSz7qmuCyS1MnZsJNeRe8e9XzspAlN9YxZ\nS1m8cn2BiSRJkqQuatoHKvuP/Rw2vVxcFknqxGzYSa3wriNGsd/QfgBsb0iuuG1+wYkkSZKkLujA\nt0GfIaX9rRtKTTtJ0l+xYSe1Qs/6Ov7h5Mosu1889Czzn19bYCJJkiSpC+rZBya/u1L7WKwkNcuG\nndRK75gyknF79QdKC1p95dZ5BSeSJEmSuqCp51X2n/0zPP94cVkkqZOyYSe1Un1d8IlTJjXVv3nk\nOR59dk2BiSRJkqQuaMRkGDGlUs92lp0k7ciGndQGbz50Hw4aMaip/sotzrKTJEmS2mxa1Sy7h38K\n2zYXl0WSOiEbdlIb1NUFl50ysam+7ckXmL3kpQITSZIkSV3QoWdBjz6l/Y2rYO5vis0jSZ2MDTup\njU46aDiHjx7SVE93lp0kSZLUNn2HwMFnVGoXn5Ckv2DDTmqjiL+cZfeH+St5YOGLBSaSJEmSuqDq\nx2IX3A6rlxSXRZI6GRt20k54w4RhvHbM0KZ6+s3zyMwCE0mSJEldzP7HwtCx5SLhoR8XGkeSOhMb\ndtJOiAguO7Uyy+5Pi1fxh/krC0wkSZIkdTERMPV9lXr2j6Chobg8ktSJ2LCTdtJRY/fkDROGNdWX\n3zzXWXaSJElSWxz+Hoj60v6aJbDozkLjSFJnYcNO2gWfqHqX3cNL13DbEy8UmEaSJEnqYgaNgAmn\nVupZVxeXRZI6ERt20i6Yut8enHTg8Kb68lvm0dDgLDtJkiSp1aoXn3jy17BhVXFZJKmTsGEn7aJL\nq2bZPbH8ZX776HMFppEkSZK6mAmnwoC9S/vbt8Cca4vNI0mdgA07aRcdOnIwbzlsn6Z6+i1z2e4s\nO0mSJKl16nvC4edW6pnfh+3bCosjSZ2BDTupHVx68kQiSvsLVqznxoeeLTaQJEmS1JVMrXosdsWT\ncMfni8siSZ2ADTupHUzYeyBnTBnZVH/11vls3e6S9JIkSVKrDBv/l7Ps7vkKPPmb4vJIUsFs2Ent\n5OMnTaC+rjTNbsmqDVw/c2nBiSRJkqQu5C3/DcMmVeobLoJVi4rLI0kFsmEntZMxw/pz1rRRTfX/\n3Dafzdu2F5hIkiRJ6kJ6D4BzroGe/Uv15jXws/fD1k3F5pKkAtiwk9rR3580np71pVl2y9Zs4qd/\neqbgRJIkSVIXstckeMfXKvVzc+C3/1hcHkkqiA07qR2N2qMf5752v6b6yjueYuMWZ9lJkiRJrXbo\nu+C1F1bqWVfD7B8Vl0eSCmDDTmpnF58wnt49Sv9qrVi7mWseWFxsIEmSJKmrOfXzMOo1lfrXn4Dn\nHi0ujyR1MBt2Ujvbe1Af3v+6/Zvqb965gHWbtxWYSJIkSepievSCs78PfYeW6m2b4GfnwaY1hcaS\npI5iw07aDS46bhz9etUD8NKGrXz/Xle3kiRJktpk8Ch413eB0juiWbUQbrwYMguNJUkdwYadtBvs\nOaA3Fxw7pqn+9t0LWbNha3GBJEmSpK5o/Elw/L9U6id+BfdfWVweSeogNuyk3eTDbxjHwD49AFi7\naRvfvWdhwYkkSZKkLuiN/wTjTqrUt/w7PH1fcXkkqQPYsJN2k8H9evJ3bxjbVF91zyJeXLe5wESS\nJElSF1RXB2d+BwaNKtW5Ha67ANa9UGwuSdqNbNhJu9EFx45hj349AVi/ZTvfvttZdpIkSVKb9d8T\n3v0DqCv9bs2652DGB2G7i7tJ6p5s2Em70cA+PbnouHFN9Q/uW8wLL28qMJEkSZLURY06Ek77QqVe\n/Ae44z+KyyNJu5ENO2k3e//rxjBsQG8ANm9r4Bt3Lig4kSRJktRFvfbv4NB3Vep7psPc3xaXR5J2\nExt20m7Wt1c9F59QmWX34z8u4dnVGwtMJEmSJHVREXD6/8CwSZVjN1wIqxYVl0mSdgMbdlIHOPe1\n+zFicB8Atmxv4Mrb5xecSJIkSeqieg+Ac66Bnv1L9aY1cN0HYKuvnpHUfdiwkzpAn571/P2JE5rq\nn/15KYtXri8wkSRJktSF7TUJ3v4/lXr5w/C7fy4ujyS1Mxt2Ugc5+8hR7De0HwDbG5L/uc1ZdpIk\nSdJOO+wseM3fVeqZ34eHflJYHElqTzbspA7Ss76Oj59UmWV3w0PP8tQLawtMJEmSJHVxp/0HjDyi\nUt90KTz/WHF5JKmd2LCTOtAZU0cybq/SuzYy4Su3OstOkiRJ2mk9esPZP4C+Q0v1to1w7Xml99pJ\nUhdmw07qQPV1waWnTGyqfz1nOY8ve7nARJIkSVIXN2Q0vOs7QJTqVQvgxotLfyGXpC7Khp3Uwd5y\n6AgO3GdgUz39lnkFppEkSZK6gfEnw3FVi0488St44BvF5ZGkXWTDTupgdXXBJ6pm2d36xPM89Mzq\nAhNJkiRJ3cBx/wTjTqzUt/wbLHmguDyStAts2EkFOOXgvZk8anBTffnNcwtMI0mSJHUDdfVw5ndh\n0MhS3bANrjsf1q0oNJYk7QwbdlIBIoLLTp3UVP9h/kr+tGhVgYkkSWpZRPSNiM9GxLyI2BQRyyLi\nqogYuZPjjYmIb0XEovJ4L0TEPRHxyVZc2ysiHo+IjIhtO3N/Sd1Y/z1Li1DU9SzVa5fD9R+Ehu3F\n5pKkNrJhJxXkjROG8ZoxezTV/33zXNIX40qSOpmI6APcDnwaGADcCDwDXADMjoixbRzvzcBjwIeB\nF4EbgIeAccBFrRji/wMObMs9JdWY0a+B0/6jUi+6G+74j5a/L0mdkA07qSA7zrL706JV/OC+xcUF\nkiSpeZ8CjgbuByZm5jmZeRRwGbAXcFVrB4qIA4GfA+uB12fmkZl5bmaeCowE/uZVrj8I+FfgOzv1\nk0iqHa/9MBz6rkr9h8th3u+LyyNJbWTDTirQ0WP35NjxezbVn/nV4/z7jY+ybXtDgakkSSqJiF7A\nJeXy4sxc13guM6cDc4DjIuKIVg45HegDnJ+Z91WfyMyGzPzzK2QJ4H+B1cC/tP6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3KTooWEwsD3oVp9J/bmwsQbIXW3u3lJUFPBTkTKtbrVIxl1fTdCPU5L+p0HMhn+yQJy8rwuZyYi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\nOK2q3thfhcORZC/gc8DGtLxwB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3p+koOBdwJXAAfMNm9J55xu+brVLlKSJK1LzHlLxJwn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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe14508d978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CLUSTER_SIZE = np.arange(2,10)\n",
    "metric = []\n",
    "for n_clusters in CLUSTER_SIZE:\n",
    "    model = AgglomerativeClustering(linkage ='average', n_clusters=n_clusters)\n",
    "    y_hat = model.fit_predict(feature_matrix)\n",
    "    current_metric = calc_metric(feature_matrix, labels, y_hat)\n",
    "    metric.append(current_metric)\n",
    "\n",
    "df = pd.DataFrame(metric, index=CLUSTER_SIZE)\n",
    "fig = plt.figure(figsize=(10,5), dpi = 150)\n",
    "ax = df.plot(subplots=True, layout=(1,2), ax=plt.gca());\n",
    "[a.set_xlabel('cluster size') for a in ax.ravel()]\n",
    "#[a.set_ylim(0,1)for a in ax.ravel()]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "* We learned about extrinsic (supervised) and intrisinc (unsupervised) clustering metrics.\n",
    "* We showed how silohette score can help in optimizing for hyper-parameter optimization in clustering problems.\n",
    "* We showed that for selecting the number of clusters, the method failed. There are other methods such as in the refernecs below which are more accureate (e.g. elbow method for explained variance, gap-statistics etc.). \n",
    "* Note that in a [toy examples](http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html#sphx-glr-auto-examples-cluster-plot-kmeans-silhouette-analysis-py) it actually works very well...\n",
    "* In R there is a special package ([fviz_nbclust](https://rdrr.io/cran/factoextra/)) for comparing 40 (!!!) different methods of # of clusters. Here is what it gets for the Iris example above:\n",
    "![](http://www.sthda.com/sthda/RDoc/figure/clustering/determining-the-number-of-clusters-nbclust-ggplot2-1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# References\n",
    "\n",
    "1. [Sklearn Clustering Metrics](http://scikit-learn.org/stable/modules/classes.html#clustering-metrics)\n",
    "1. [Determining the optimal number of clusters: 3 must known methods - Unsupervised Machine Learning](http://www.sthda.com/english/wiki/determining-the-optimal-number-of-clusters-3-must-known-methods-unsupervised-machine-learning)\n",
    "2. [Choosing the right linkage method for hierarchical clustering](https://stats.stackexchange.com/questions/195446/choosing-the-right-linkage-method-for-hierarchical-clustering)\n",
    "3. [How to select a clustering method? How to validate a cluster solution (to warrant the method choice)?](https://stats.stackexchange.com/questions/195456/how-to-select-a-clustering-method-how-to-validate-a-cluster-solution-to-warran/195481#195481)\n",
    "4. [Calinski-Harabaz Index](http://scikit-learn.org/stable/modules/clustering.html#calinski-harabaz-index)\n",
    "5. [Sillohette][1]\n",
    "\n",
    "[1]: https://en.wikipedia.org/wiki/Silhouette_(clustering)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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