Mini_Project_Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Customer Segmentation using Clustering\n",
    "***\n",
    "This mini-project is based on [this blog post](http://blog.yhat.com/posts/customer-segmentation-using-python.html) by yhat. Please feel free to refer to the post for additional information, and solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import sklearn\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "\n",
    "# Setup Seaborn\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "The dataset contains information on marketing newsletters/e-mail campaigns (e-mail offers sent to customers) and transaction level data from customers. The transactional data shows which offer customers responded to, and what the customer ended up buying. The data is presented as an Excel workbook containing two worksheets. Each worksheet contains a different dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>offer_id</th>\n",
       "      <th>campaign</th>\n",
       "      <th>varietal</th>\n",
       "      <th>min_qty</th>\n",
       "      <th>discount</th>\n",
       "      <th>origin</th>\n",
       "      <th>past_peak</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>January</td>\n",
       "      <td>Malbec</td>\n",
       "      <td>72</td>\n",
       "      <td>56</td>\n",
       "      <td>France</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>January</td>\n",
       "      <td>Pinot Noir</td>\n",
       "      <td>72</td>\n",
       "      <td>17</td>\n",
       "      <td>France</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>February</td>\n",
       "      <td>Espumante</td>\n",
       "      <td>144</td>\n",
       "      <td>32</td>\n",
       "      <td>Oregon</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>February</td>\n",
       "      <td>Champagne</td>\n",
       "      <td>72</td>\n",
       "      <td>48</td>\n",
       "      <td>France</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>February</td>\n",
       "      <td>Cabernet Sauvignon</td>\n",
       "      <td>144</td>\n",
       "      <td>44</td>\n",
       "      <td>New Zealand</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   offer_id  campaign            varietal  min_qty  discount       origin  \\\n",
       "0         1   January              Malbec       72        56       France   \n",
       "1         2   January          Pinot Noir       72        17       France   \n",
       "2         3  February           Espumante      144        32       Oregon   \n",
       "3         4  February           Champagne       72        48       France   \n",
       "4         5  February  Cabernet Sauvignon      144        44  New Zealand   \n",
       "\n",
       "   past_peak  \n",
       "0      False  \n",
       "1      False  \n",
       "2       True  \n",
       "3       True  \n",
       "4       True  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_offers = pd.read_excel(\"./WineKMC.xlsx\", sheetname=0)\n",
    "df_offers.columns = [\"offer_id\", \"campaign\", \"varietal\", \"min_qty\", \"discount\", \"origin\", \"past_peak\"]\n",
    "df_offers.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the first dataset contains information about each offer such as the month it is in effect and several attributes about the wine that the offer refers to: the variety, minimum quantity, discount, country of origin and whether or not it is past peak. The second dataset in the second worksheet contains transactional data -- which offer each customer responded to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>customer_name</th>\n",
       "      <th>offer_id</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Smith</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Smith</td>\n",
       "      <td>24</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Johnson</td>\n",
       "      <td>17</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Johnson</td>\n",
       "      <td>24</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Johnson</td>\n",
       "      <td>26</td>\n",
       "      <td>1</td>\n",
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      ],
      "text/plain": [
       "  customer_name  offer_id  n\n",
       "0         Smith         2  1\n",
       "1         Smith        24  1\n",
       "2       Johnson        17  1\n",
       "3       Johnson        24  1\n",
       "4       Johnson        26  1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "df_transactions = pd.read_excel(\"./WineKMC.xlsx\", sheetname=1)\n",
    "df_transactions.columns = [\"customer_name\", \"offer_id\"]\n",
    "df_transactions['n'] = 1\n",
    "df_transactions.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data wrangling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're trying to learn more about how our customers behave, so we can use their behavior (whether or not they purchased something based on an offer) as a way to group similar minded customers together. We can then study those groups to look for patterns and trends which can help us formulate future offers.\n",
    "\n",
    "The first thing we need is a way to compare customers. To do this, we're going to create a matrix that contains each customer and a 0/1 indicator for whether or not they responded to a given offer. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Checkup Exercise Set I</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Create a data frame where each row has the following columns (Use the pandas [`merge`](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.merge.html) and [`pivot_table`](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.pivot_table.html) functions for this purpose):\n",
    "<ul>\n",
    "<li> customer_name\n",
    "<li> One column for each offer, with a 1 if the customer responded to the offer\n",
    "</ul>\n",
    "<p>Make sure you also deal with any weird values such as `NaN`. Read the documentation to develop your solution.</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
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       "      <th>Anderson</th>\n",
       "      <td>0</td>\n",
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       "      <th>Bailey</th>\n",
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       "      <th>Barnes</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>Bennett</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>Brooks</th>\n",
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       "      <th>Brown</th>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>Butler</th>\n",
       "      <td>1</td>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>Campbell</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Carter</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Clark</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Collins</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cook</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cooper</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cox</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cruz</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Davis</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diaz</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Edwards</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Evans</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fisher</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Flores</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Foster</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Garcia</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gomez</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gonzalez</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gray</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Reed</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Reyes</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Richardson</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rivera</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Roberts</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Robinson</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rodriguez</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rogers</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ross</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Russell</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sanchez</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sanders</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Scott</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Smith</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Stewart</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sullivan</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Taylor</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Thomas</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Thompson</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Torres</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Turner</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Walker</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ward</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Watson</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>White</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Williams</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wilson</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wood</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wright</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Young</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               n                            ...                              \n",
       "offer_id      1  2  3  4  5  6  7  8  9  10 ... 23 24 25 26 27 28 29 30 31 32\n",
       "customer_name                               ...                              \n",
       "Adams          0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Allen          0  0  0  0  0  0  0  0  1  0 ...  0  0  0  0  1  0  0  0  0  0\n",
       "Anderson       0  0  0  0  0  0  0  0  0  0 ...  0  1  0  1  0  0  0  0  0  0\n",
       "Bailey         0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  0  1  0  0\n",
       "Baker          0  0  0  0  0  0  1  0  0  1 ...  0  0  0  0  0  0  0  0  1  0\n",
       "Barnes         0  0  0  0  0  0  0  0  0  1 ...  0  0  0  0  0  0  0  0  1  0\n",
       "Bell           0  1  0  0  0  0  0  0  0  0 ...  0  1  0  1  0  0  0  0  0  0\n",
       "Bennett        0  0  0  0  0  0  0  1  0  0 ...  0  0  0  0  0  0  1  0  0  0\n",
       "Brooks         0  0  1  0  0  0  0  1  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Brown          0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Butler         1  0  0  1  0  0  0  0  0  0 ...  0  0  0  0  0  1  0  1  0  0\n",
       "Campbell       0  1  0  0  0  0  0  0  0  0 ...  0  1  0  1  0  0  0  0  0  0\n",
       "Carter         0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Clark          0  0  0  1  0  0  0  0  0  0 ...  0  0  0  0  0  1  0  0  1  0\n",
       "Collins        0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  1  0  0\n",
       "Cook           0  0  0  0  0  0  0  0  0  0 ...  0  1  0  1  0  0  0  0  0  0\n",
       "Cooper         0  0  0  1  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  0  1\n",
       "Cox            0  1  0  0  0  0  0  0  0  0 ...  0  1  0  1  0  0  0  0  0  0\n",
       "Cruz           0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Davis          0  0  0  0  0  0  0  0  0  0 ...  0  0  1  0  0  0  0  0  0  0\n",
       "Diaz           0  0  0  0  0  0  1  1  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Edwards        0  0  0  0  0  0  0  1  0  0 ...  0  0  0  0  1  0  0  0  0  0\n",
       "Evans          0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  1  0  0  0  0  0\n",
       "Fisher         1  1  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  1  0  1  1  0\n",
       "Flores         0  0  0  0  0  0  0  0  0  0 ...  0  1  0  0  0  0  0  0  0  0\n",
       "Foster         1  0  0  0  0  0  0  0  1  0 ...  1  0  0  0  0  0  0  0  0  0\n",
       "Garcia         0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Gomez          0  0  0  0  0  0  0  0  0  0 ...  0  0  1  0  0  0  0  0  0  1\n",
       "Gonzalez       0  0  0  0  0  0  0  0  1  0 ...  0  0  0  0  0  0  0  0  1  0\n",
       "Gray           0  0  0  0  0  0  0  0  0  0 ...  0  0  0  1  0  0  0  0  0  0\n",
       "...           .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. ..\n",
       "Reed           0  0  0  0  1  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Reyes          0  0  0  0  0  0  0  0  1  0 ...  1  0  0  0  0  0  0  0  0  0\n",
       "Richardson     0  0  1  0  0  1  0  0  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Rivera         0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Roberts        0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  1  0\n",
       "Robinson       0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  1  0  0  0\n",
       "Rodriguez      0  1  0  0  0  0  0  0  0  0 ...  0  0  0  1  0  0  0  0  0  0\n",
       "Rogers         0  0  1  0  0  0  1  1  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Ross           0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Russell        0  0  0  0  0  0  0  0  0  0 ...  0  0  0  1  0  0  0  0  0  0\n",
       "Sanchez        0  0  0  1  1  0  0  0  0  0 ...  0  0  0  1  0  0  0  0  0  0\n",
       "Sanders        1  0  0  1  1  1  0  0  1  0 ...  0  0  1  1  0  0  0  0  0  0\n",
       "Scott          0  0  0  0  0  1  0  0  0  0 ...  1  0  0  0  0  0  0  0  0  0\n",
       "Smith          0  1  0  0  0  0  0  0  0  0 ...  0  1  0  0  0  0  0  0  0  0\n",
       "Stewart        0  0  0  0  0  0  0  1  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Sullivan       0  0  0  0  0  0  0  1  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Taylor         0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  1  1  0  0\n",
       "Thomas         1  0  0  1  0  0  0  0  1  0 ...  0  0  0  1  0  0  0  0  0  0\n",
       "Thompson       0  0  0  0  0  0  0  0  1  0 ...  0  0  1  0  0  0  0  1  0  0\n",
       "Torres         0  0  0  0  0  0  0  1  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Turner         0  0  0  1  0  1  0  0  0  0 ...  0  0  0  0  1  0  0  0  1  0\n",
       "Walker         0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  1  0  0  0\n",
       "Ward           0  0  0  1  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  0  0\n",
       "Watson         0  0  0  0  0  0  1  0  0  0 ...  0  0  0  0  0  0  1  0  0  0\n",
       "White          0  0  0  0  0  0  0  0  0  0 ...  0  0  1  0  0  0  0  1  0  0\n",
       "Williams       0  0  0  0  0  0  0  0  0  0 ...  0  0  0  0  0  0  0  0  1  0\n",
       "Wilson         0  0  0  0  0  0  0  1  0  0 ...  0  0  0  0  0  0  0  1  0  0\n",
       "Wood           1  0  0  0  0  0  0  0  0  1 ...  0  0  0  0  0  0  0  0  1  0\n",
       "Wright         0  0  0  1  0  1  0  0  0  0 ...  0  0  0  0  1  0  0  0  0  0\n",
       "Young          0  0  0  0  0  1  0  0  1  0 ...  0  0  0  0  0  0  0  0  1  1\n",
       "\n",
       "[100 rows x 32 columns]"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Merge the dataframes\n",
    "cust_compare = df_transactions.merge(df_offers, on = 'offer_id')\n",
    "\n",
    "#Drop unnecessary columns\n",
    "cust_compare = cust_compare.drop(['campaign', 'varietal', 'min_qty', 'discount', 'origin', 'past_peak'], axis = 1)\n",
    "\n",
    "#Create pivot table\n",
    "table = pd.pivot_table(cust_compare,  index = 'customer_name', columns = 'offer_id', aggfunc=np.sum, fill_value = 0)\n",
    "table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check if any values are left null\n",
    "table.isnull().values.any()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Means Clustering\n",
    "\n",
    "Recall that in K-Means Clustering we want to *maximize* the distance between centroids and *minimize* the distance between data points and the respective centroid for the cluster they are in. True evaluation for unsupervised learning would require labeled data; however, we can use a variety of intuitive metrics to try to pick the number of clusters K. We will introduce two methods: the Elbow method, the Silhouette method and the gap statistic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing K: The Elbow Sum-of-Squares Method\n",
    "\n",
    "The first method looks at the sum-of-squares error in each cluster against $K$. We compute the distance from each data point to the center of the cluster (centroid) to which the data point was assigned. \n",
    "\n",
    "$$SS = \\sum_k \\sum_{x_i \\in C_k} \\sum_{x_j \\in C_k} \\left( x_i - x_j \\right)^2 = \\sum_k \\sum_{x_i \\in C_k} \\left( x_i - \\mu_k \\right)^2$$\n",
    "\n",
    "where $x_i$ is a point, $C_k$ represents cluster $k$ and $\\mu_k$ is the centroid for cluster $k$. We can plot SS vs. $K$ and choose the *elbow point* in the plot as the best value for $K$. The elbow point is the point at which the plot starts descending much more slowly. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Checkup Exercise Set II</h3>\n",
    "\n",
    "<p><b>Exercise:</b></p> \n",
    "<ul>\n",
    "<li> What values of $SS$ do you believe represent better clusterings? Why?\n",
    "<li> Create a numpy matrix `x_cols` with only the columns representing the offers (i.e. the 0/1 colums) \n",
    "<li> Write code that applies the [`KMeans`](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) clustering method from scikit-learn to this matrix. \n",
    "<li> Construct a plot showing $SS$ for each $K$ and pick $K$ using this plot. For simplicity, test $2 \\le K \\le 10$.\n",
    "<li> Make a bar chart showing the number of points in each cluster for k-means under the best $K$.\n",
    "<li> What challenges did you experience using the Elbow method to pick $K$?\n",
    "</ul>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VqU3z5s0jNjb2vre0/Tvvvfceffv25erVq/Z5Hh4e9lvNOjs74+XlRcOGDdmxYwfHjh2z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\nEEIIIYRoN0kohBBCCCGEEO32f7+t5IiwUgv1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a0936c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Smaller values of SS will represent better clusterings because the points are more tightly centered around the centroid\n",
    "\n",
    "offers = table.columns.get_level_values('offer_id')\n",
    "x_cols = np.matrix(offers)\n",
    "SS = []\n",
    "from sklearn.cluster import KMeans\n",
    "for K in range(2, 11):\n",
    "    kmeans = KMeans(n_clusters = K).fit(table) #Using all default values from method\n",
    "    SS.append(kmeans.inertia_)\n",
    "    \n",
    "plt.plot(range(2,11), SS);\n",
    "plt.xlabel('Number of clusters');\n",
    "plt.ylabel('Sum of squares');\n",
    "plt.title('Sum of squares for various K');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QhZUCgDVen3/M6hJwD97v72N1CQDgVpaGhTspVKiQIiIi5OPjY5/Q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\nu/4PmhE4BO1cZusAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a18c2f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Choosing K=5\n",
    "kmeans_5 = KMeans(n_clusters = 5).fit_predict(table)\n",
    "points = list(kmeans_5)\n",
    "d = {x:points.count(x) for x in points}\n",
    "heights = list(d.values())\n",
    "plt.bar(range(5),heights);\n",
    "plt.xlabel('Clusters');\n",
    "plt.ylabel('Number of points');\n",
    "plt.title('Number of points in each cluster');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above does not appear to have much of an elbow and it appeared as if the sum of squares decreased somewhat linearly with K."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing K: The Silhouette Method\n",
    "\n",
    "There exists another method that measures how well each datapoint $x_i$ \"fits\" its assigned cluster *and also* how poorly it fits into other clusters. This is a different way of looking at the same objective. Denote $a_{x_i}$ as the *average* distance from $x_i$ to all other points within its own cluster $k$. The lower the value, the better. On the other hand $b_{x_i}$ is the minimum average distance from $x_i$ to points in a different cluster, minimized over clusters. That is, compute separately for each cluster the average distance from $x_i$ to the points within that cluster, and then take the minimum. The silhouette $s(x_i)$ is defined as\n",
    "\n",
    "$$s(x_i) = \\frac{b_{x_i} - a_{x_i}}{\\max{\\left( a_{x_i}, b_{x_i}\\right)}}$$\n",
    "\n",
    "The silhouette score is computed on *every datapoint in every cluster*. The silhouette score ranges from -1 (a poor clustering) to +1 (a very dense clustering) with 0 denoting the situation where clusters overlap. Some criteria for the silhouette coefficient is provided in the table below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "\n",
    "| Range       | Interpretation                                |\n",
    "|-------------|-----------------------------------------------|\n",
    "| 0.71 - 1.0  | A strong structure has been found.            |\n",
    "| 0.51 - 0.7  | A reasonable structure has been found.        |\n",
    "| 0.26 - 0.5  | The structure is weak and could be artificial.|\n",
    "| < 0.25      | No substantial structure has been found.      |\n",
    "\n",
    "</pre>\n",
    "Source: http://www.stat.berkeley.edu/~spector/s133/Clus.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fortunately, scikit-learn provides a function to compute this for us (phew!) called [`sklearn.metrics.silhouette_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html). Take a look at [this article](http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html) on picking $K$ in scikit-learn, as it will help you in the next exercise set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Checkup Exercise Set III</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Using the documentation for the `silhouette_score` function above, construct a series of silhouette plots like the ones in the article linked above.</p>\n",
    "\n",
    "<p><b>Exercise:</b> Compute the average silhouette score for each $K$ and plot it. What $K$ does the plot suggest we should choose? Does it differ from what we found using the Elbow method?</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 2 The average silhouette score is: 0.0917487150875\n"
     ]
    },
    {
     "data": {
      "image/png": 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KFSpw8uRJVqxYwe7du1mzZk2mr9ldvXqV/v37U7x4cQYMGEDBggU5dOgQixYt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\nFRERyR7DioiIZI9hRUREsvd/NuWS1Yjz7ioAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a0968c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 3 The average silhouette score is: 0.116278652401\n"
     ]
    },
    {
     "data": {
      "image/png": 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arTbd/M+cOcPLL7/Mw4cP6dSpE+XLl+fIkSMsWrSI7du3s3z58hzfszt//jy9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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a0d3a208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 4 The average silhouette score is: 0.125476564367\n"
     ]
    },
    {
     "data": {
      "image/png": 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duzddu3bNlP09uf0go+vHLCjCwNXVVWnUqFGq/V1dXZWzZ88ausXFxSnNmjVT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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1c324e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 5 The average silhouette score is: 0.13323551628\n"
     ]
    },
    {
     "data": {
      "image/png": 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ff7BmzZoM37O7cuUKvXv3pmDBgvTp0wdHR0cOHjzI/PnzuXz5MnPmzElz/Fmz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\n8pMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a16ae0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 6 The average silhouette score is: 0.121163203588\n"
     ]
    },
    {
     "data": {
      "image/png": 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nTp1i+fLl/Prrr6xZsybDbXbXr1+nb9++FClShH79+mFvb8/hw4eZP38+165d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\naO1kj7Am7ght7AJrOe/RR9VX5bA6ePBglZYLCws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374+ePXuiTZs2ei/iILI0DCsiA40f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\nGsaNG4fvv/9et63vv/8ekZGR0Gq1mDt3LsaNG4ezZ88iPDwcd+/e1Z0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1910c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 7 The average silhouette score is: 0.141895833698\n"
     ]
    },
    {
     "data": {
      "image/png": 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BAQF88MEHqKrKmjVrGDt2LE+ePOGdd96hY8eOObK9p7YdZHf5WARVmHh7e6sN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\n/JzuYw0DLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1d7b390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 8 The average silhouette score is: 0.118524006572\n"
     ]
    },
    {
     "data": {
      "image/png": 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9evDixQu6du1K+fLlOXv2LMuWLWP//v2sWbMm0212N2/epF+/fhQrVoz+/fvj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\ngQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1d50128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 9 The average silhouette score is: 0.133825979477\n"
     ]
    },
    {
     "data": {
      "image/png": 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Vq1aMHDkSa2trrly5Qv/+/QGwtbXN8brlt+emZvXnn3+yaNEiqlevzltvvUXr1q1p3bo1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\nkewxrIiISPb+H4iBndrZjm52AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1c570b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K = 10 The average silhouette score is: 0.126621265233\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bvb19lvPr0KEDixYtYsOGDfj5+Zm7K4rC999/j5eXFzVr1gRg+PDh/Prrr7zy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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a10aaa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make silhouette plots\n",
    "from sklearn.metrics import silhouette_score, silhouette_samples\n",
    "import matplotlib.cm as cm\n",
    "\n",
    "for K in range(2, 11):\n",
    "    fig, ax1 = plt.subplots(1,1)\n",
    "    fig.set_size_inches(7,7)\n",
    "    ax1.set_xlim([-0.5,0.5])\n",
    "    ax1.set_ylim([0,len(table) + (K + 1) * 10])\n",
    "    \n",
    "    clusterer = KMeans(n_clusters = K)\n",
    "    cluster_labels = clusterer.fit_predict(table)\n",
    "    \n",
    "    silhouette_avg = silhouette_score(table, cluster_labels)\n",
    "    print('For K =', K, 'The average silhouette score is:', silhouette_avg)\n",
    "    \n",
    "    sample_silhouette_values = silhouette_samples(table, cluster_labels)\n",
    "    \n",
    "    y_lower = 10\n",
    "    for i in range(K):\n",
    "        ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i]\n",
    "        ith_cluster_silhouette_values.sort()\n",
    "        \n",
    "        size_cluster_i = ith_cluster_silhouette_values.shape[0]\n",
    "        y_upper = y_lower + size_cluster_i\n",
    "        \n",
    "        color = cm.spectral(float(i) / K)\n",
    "        ax1.fill_betweenx(np.arange(y_lower, y_upper), 0, ith_cluster_silhouette_values, facecolor = color, edgecolor = color, alpha = 0.7)\n",
    "        ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))\n",
    "        y_lower = y_upper + 10\n",
    "    \n",
    "    ax1.set_title('The silhouette plot for various clusters')\n",
    "    ax1.set_xlabel('Silhouette coefficients')\n",
    "    ax1.set_ylabel('Cluster label')\n",
    "    \n",
    "    ax1.axvline(x = silhouette_avg, color = 'r', linestyle = '--')\n",
    "    ax1.set_yticks([])\n",
    "    \n",
    "    plt.suptitle(('Silhouette analysis for K-means clustering with K = %d' %K), fontsize = 14, fontweight = 'bold')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9GuXp1KQqzXwr4eig2adERMRcpiUYhmEA5Nov+X5XuJ0+fTouLi489dRT9x3b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1039320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot average silhouette score for range of K's\n",
    "score = []\n",
    "for K in range(2,11):\n",
    "    clusterer = KMeans(n_clusters = K, random_state = 10)\n",
    "    cluster_labels = clusterer.fit_predict(table)\n",
    "    score.append(silhouette_score(table, cluster_labels))\n",
    "    \n",
    "plt.plot(range(2,11), score);\n",
    "plt.xlabel('K');\n",
    "plt.ylabel('Average silhouette score');\n",
    "plt.title('Avg silhouette score for range of Ks');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No K included on this graph is above 0.25, the cutoff to even consider a structure in this data. However, we do have a peak at K = 5 so we can consider that to be the best K of this range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing $K$: The Gap Statistic\n",
    "\n",
    "There is one last method worth covering for picking $K$, the so-called Gap statistic. The computation for the gap statistic builds on the sum-of-squares established in the Elbow method discussion, and compares it to the sum-of-squares of a \"null distribution,\" that is, a random set of points with no clustering. The estimate for the optimal number of clusters $K$ is the value for which $\\log{SS}$ falls the farthest below that of the reference distribution:\n",
    "\n",
    "$$G_k = E_n^*\\{\\log SS_k\\} - \\log SS_k$$\n",
    "\n",
    "In other words a good clustering yields a much larger difference between the reference distribution and the clustered data. The reference distribution is a Monte Carlo (randomization) procedure that constructs $B$ random distributions of points within the bounding box (limits) of the original data and then applies K-means to this synthetic distribution of data points.. $E_n^*\\{\\log SS_k\\}$ is just the average $SS_k$ over all $B$ replicates. We then compute the standard deviation $\\sigma_{SS}$ of the values of $SS_k$ computed from the $B$ replicates of the reference distribution and compute\n",
    "\n",
    "$$s_k = \\sqrt{1+1/B}\\sigma_{SS}$$\n",
    "\n",
    "Finally, we choose $K=k$ such that $G_k \\geq G_{k+1} - s_{k+1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aside: Choosing $K$ when we Have Labels\n",
    "\n",
    "Unsupervised learning expects that we do not have the labels. In some situations, we may wish to cluster data that is labeled. Computing the optimal number of clusters is much easier if we have access to labels. There are several methods available. We will not go into the math or details since it is rare to have access to the labels, but we provide the names and references of these measures.\n",
    "\n",
    "* Adjusted Rand Index\n",
    "* Mutual Information\n",
    "* V-Measure\n",
    "* Fowlkes–Mallows index\n",
    "\n",
    "See [this article](http://scikit-learn.org/stable/modules/clustering.html) for more information about these metrics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing Clusters using PCA\n",
    "\n",
    "How do we visualize clusters? If we only had two features, we could likely plot the data as is. But we have 100 data points each containing 32 features (dimensions). Principal Component Analysis (PCA) will help us reduce the dimensionality of our data from 32 to something lower. For a visualization on the coordinate plane, we will use 2 dimensions. In this exercise, we're going to use it to transform our multi-dimensional dataset into a 2 dimensional dataset.\n",
    "\n",
    "This is only one use of PCA for dimension reduction. We can also use PCA when we want to perform regression but we have a set of highly correlated variables. PCA untangles these correlations into a smaller number of features/predictors all of which are orthogonal (not correlated). PCA is also used to reduce a large set of variables into a much smaller one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Checkup Exercise Set IV</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Use PCA to plot your clusters:</p>\n",
    "\n",
    "<ul>\n",
    "<li> Use scikit-learn's [`PCA`](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) function to reduce the dimensionality of your clustering data to 2 components\n",
    "<li> Create a data frame with the following fields:\n",
    "  <ul>\n",
    "  <li> customer name\n",
    "  <li> cluster id the customer belongs to\n",
    "  <li> the two PCA components (label them `x` and `y`)\n",
    "  </ul>\n",
    "<li> Plot a scatterplot of the `x` vs `y` columns\n",
    "<li> Color-code points differently based on cluster ID\n",
    "<li> How do the clusters look? \n",
    "<li> Based on what you see, what seems to be the best value for $K$? Moreover, which method of choosing $K$ seems to have produced the optimal result visually?\n",
    "</ul>\n",
    "\n",
    "<p><b>Exercise:</b> Now look at both the original raw data about the offers and transactions and look at the fitted clusters. Tell a story about the clusters in context of the original data. For example, do the clusters correspond to wine variants or something else interesting?</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we've done is we've taken those columns of 0/1 indicator variables, and we've transformed them into a 2-D dataset. We took one column and arbitrarily called it `x` and then called the other `y`. Now we can throw each point into a scatterplot. We color coded each point based on it's cluster so it's easier to see them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wFUBzXuOkEhGRO2Gokkc5VnDM5vGjBUcdXBIickcMVfIoEQERdTpORFQXDFXy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\nIiIiiXCoEhERSYRDlYiISCL/Bo39m+1ovz3mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a0969e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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u3kElIiJXwlAlt1JqyK1h+1E7l4SIXBFDldyKtyysXtuJiOqDoUpuxV+uggda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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1405f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Vci/lWiA7GvgjA4AOyE9FO1kocn1WOLtmROQBOPxL7uXmqnuBCgDQwVd/DAHa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\noUpERCSRfwOmKz/oj/W89QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a14cf7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XESkrhar4HVungdQPvirftvqmq7B1GuimEomIr1Coit+pFVyDE3eM44HWYbSp\nXZ8HWodxYrAGKYlI5Wn0r/ilWsE1WNj1TncXQ0R8jFqqIiIiBlGoioiIGETdv+Kz7DnZxB3+nsSf\nj/P7zCDu+V1rdxdJRHycQlV8kj0nm/4bF5N45hhZOAgCVl04TmL79pgCg9xdPBHxUer+FZ8099D3\nrkAFyAa2p58l7vD37i2YiPg0har4pKSzx12B6pQNJP583D0FEhG/oFAVn2Rp3JJgAvJtC/ptu4hI\nVVGoik+yhkZgadLKFaxBQFTtRlhDI9xbMBHxaRqoJD7JFBhEwq1DC43+1SAlEalKClXxWabAIGLa\nRBLTJpK9e/e6uzgi4gfU/SsiImIQhaqIiIhBFKoiIiIGUaiKiIgYRKEqIiJiEIWqiIiIQRSqIiIi\nBlGoioiIGEShKiIiYhCFqoiIiEEUqiIiIgZRqIqIiBhEoSoiImIQhaqIiIhBFKoiIiIGUaiKiIgY\nRKEqIiJikGB3F0DEE53PvMjtG5ew58JZbqjXiC9uHUL9GiHuLpaIeDi1VEUKOJ95kUYr3uabX0+R\nlm3nm19P0WjF25zPvOjuoomIh/OqUF23bh2RkZGl7rd//35GjBhBZGQkvXv3xmaz4XA4qqGE4gv6\nb1xMNvnfL9k4uH3jEjeVSES8hdd0/27fvp0JEyaUut/Zs2exWq20bduW6dOns3v3bqZPn05QUBCj\nR4+uhpKKt9t74Zcit++5cLaaSyIi3sbjQzUzM5P58+fz1ltvUatWLex2e4n7L1q0iKysLGbPnk1I\nSAi9evUiMzMTm83G8OHDMZlM1VRy8VY31GvEN7+eKnK7iEhJPL77d+PGjdhsNp5++mkefPDBUvdP\nSkqie/fuhIRcGVTSr18/zp07x65du6qyqOIjvrh1CEEE5NsWRABf3DrETSUSEW/h8S3V8PBw1q1b\nR7169Xj77bdL3f/w4cN07do137ZrrrnGdVtUVFS5y7B3795y38eTXbyYO+DG1+pVkvLWOTFsAA8f\n3MKBzDSuq1GH99p058SBw5yoykJWAb3W/sEf6wyeWW+PD9Wrr766XPunpaVRu3btfNucv6elpRlW\nLvFt9YJqsLhtL3cXQ0S8jMeHqpECAyvW2x0WFmZwSdzLeVTna/UqiT/WGfyz3qqz/3Bnvbdt21bk\ndo8/p1pederUIT09Pd825+916tRxR5FERMRP+FyohoaGcuzYsXzbjh49CkCbNm3cUSQREfETPheq\n3bp1IynTnaHaAAAgAElEQVQpiYyMDNe2tWvX0qBBA9q3b+/GkomIiK/z+lBNTU1lx44drt+HDRuG\n3W4nJiaG9evXM3v2bGw2GzExMdSoUcONJRUREV/n9aE6a9Yshg4d6vq9adOmxMXFkZWVxfjx41my\nZAlPPvmkZlMSEZEq51Wjfx9//HEef/zxfNumTZvGtGnT8m0LDw/no48+qs6iiYiIeH9LVURExFN4\nVUtVxBtpbVYR/6GWqkgV0tqsIv5FoSpShbQ2q4h/UaiKVCGtzSriXxSqIlWouDVYtTariG9SqIpU\nIa3NKuJfFKoiVah+jRDO3vU4XRo2o06QiS4Nm3H2rsc1+lfER+mSGpEqVr9GCF/3G+HuYohINVBL\nVURExCAKVREREYOo+1fEAPacbOIOf0/iz8exNG6JNTQCU2CQu4slItVMoSpSSfacbPpvXEzimWNk\n4SD+yB7iU/eScOtQBauIn1H3r0glzT30vStQAbJwkHjmGHGHv3dzyUSkuilURSop6exxV6A6ZeEg\n8efjbiqRiLiLQlWkkiyNWxJcYIKHYAKwNG7pphKJiLsoVEUKsOdkYzuYzIhvPsN2MBl7TnaJ+1tD\nI7A0aeUK1mAC6NGkFdbQiOooroh4EA1UEsmjIoOOTIFBJNw6VKN/RUShKpJXSYOOYtpEFns/U2AQ\nMW0iS9xHRHyfun9F8tCgIxGpDIWqSB4adCQilaFQFclDg45EpDJ0TlUkDw06EpHKUKiKFKBBRyJS\nUer+FRERMYhCVURExCAKVREREYMoVEVERAyiUBURETGIQlVERMQgClURERGDKFRFREQMolAVEREx\niEJVRETEIApVERERgyhURUREDKJQFRERMYhCVURExCAKVREREYNoPVWRCrDnZGshcxEpRKEqUk72\nnGz6b1xM4pljZOEg/sge4lP3knDrUAWriJ9T969IOc099L0rUAGycJB45hhxh78HckPXdjCZEd98\nhu1gMvacbHcWV0SqkVqqIuWUdPa4K1CdsnCQ+PNxrKERasWK+DG1VEXKydK4JcEE5NsWTACWxi1L\nbcWKiG9TqIqUkzU0AkuTVq5gDSaAHk1aYQ2NKLEVKyK+T92/IuVkCgwi4dahRY7+tTRuSfyRPfmC\n1dmKFRHfp1AVqQBTYBAxbSKJaROZb7s1NIL41L2uLuC8rVgR8X0KVREDldSKFRHfp1AVMVhxrVgR\n8X0aqCQiImIQrwjVJUuWcPvttxMREcHQoUNJTk4ucf+xY8diNpsL/aSnp1dTiUVExB95fPfvsmXL\nmDJlCrGxsYSHh/PBBx8wevRoVqxYwTXXXFPkffbt28fw4cOJjo7Otz0kJKQ6iiwiIn7Ko0PV4XDw\n9ttvM2TIEB577DEAbrnlFgYOHMj8+fOZNGlSoftcuHCBkydP0rNnTzp27FjdRRYRET/m0d2/R44c\n4fjx49x2222ubSaTid69e7Np06Yi75OSkgKA2WyuljKKiIg4eXRL9fDhwwBce+21+bZfc801pKam\nkp2dTVBQ/ksVUlJSqFGjBtOnT+fLL7/k0qVL9OrVi8mTJ9OkSZMKlWPv3r0Vup+nunjxIuB79SqJ\nP9YZ/LPeqrP/8MR6e3RLNS0tDYDatWvn2167dm1ycnJcf9C8UlJSyMzMpHbt2syYMYMpU6awY8cO\nRowYQWZmZrWU29/ZHTksPnuYZ49uZ/HZw9gdOe4ukohItfDolqrDkTvVW0BAQJG3F7V95MiRREdH\n061bNwBuvvlmrrvuOoYMGcKqVav44x//WO5yhIWFlfs+nsx5VFcV9Sq41uiq88fZkPWr21dpqco6\nezJ/rLfq7D/cWe9t27YVud2jW6p169YFKHQpTHp6OkFBQYVasADXXXedK1CdOnToQL169VznW6Xq\naJUWEfFnHh2qznOpR48ezbf96NGjhIaGFnmflStX8u233+bb5nA4yMzMpGHDhlVSTrlCq7SIiD/z\n6FANDQ2lefPmrF271rXNbrezYcMGunfvXuR9PvzwQ6ZOnUpOzpXzeF999RWXLl2ic+fOVV5mf1fS\nWqMiIr7Oo0M1ICCAhx9+mI8++og333yTr776inHjxvHrr78ycuRIAFJTU9mxY4frPo888gj79u1j\nwoQJJCYmsmjRIp5++mkGDBhAVFSUm2riP0paa1RExNd59EAlgAceeIDLly+zYMEC5s2bR1hYGO+/\n/75rNqVZs2axbNky1/nSnj17Mnv2bGbOnElsbCx16tTh3nvv5YknnnBnNfyGVmkREX/m8aEKMGrU\nKEaNGlXkbdOmTWPatGn5tvXp04c+ffpUR9GkCFqlRUT8lUd3/4qIiHgThaqIiIhBFKoiIiIGUaiK\niIgYRKEqIiJiEIWqiIiIQRSqIiIiBlGoioiIGEShKiIiYhCFqoiIiEEUqiIiIgZRqIqIiBhEoSoi\nImIQhaqIiIhBvGLpNxGPkmOHlDg4lQjNLGC2QqDJ3aUSEQ+gUBUpjxw7rOyfG6iOLPgxPvcnOkHB\nKiLq/hUpl5S5VwIVcv89lZjbchURv6dQFSmPU0lXAtXJGawi4vcUqiLl0cwCAQXOmgQE524XEb+n\nUBUpD7M1f7AGBEOzHrnbRcTvaaCSSEmKGukbnaDRvyJSJIWqSHFKGukbFpP7IyKSh7p/RYqjkb4i\nUk4KVZHiaKSviJSTQlWkOBrpKyLlpFAVKY5G+opIOWmgkkhxAk0a6Ssi5aJQFSlJoEkjfUWkzNT9\nKyJ+y263Y7PZGDFiBDabDbvd7u4iiZdTS1XEk2mZuSpjt9vp378/iYmJZGVlER8fT3x8PAkJCZhM\n+htLxailKuKpnJNPbI6FHxbk/ruyf+52qbS5c+e6AhUgKyuLxMRE4uJ0HbJUnEJVxFP50OQTntjN\nmpSU5ApUJ2ewilSUQlXEU/nI5BPObtbY2FgWLFhAbGws/fv3d3uwWiwWgoPznwELDg7GYtF1yFJx\nClURT+Ujk094ajer1WrNF6zBwcH06NEDq1XXIUvFlTlU33nnHY4ePVqVZRGRvHxk8glP7WY1mUwk\nJCQwc+ZMhg8fzsyZM/niiy80SEkqpcyjf2fMmMFbb73FjTfeSHR0NH/4wx9o1qxZVZZNxPc5R/ee\n3AQ4gABo3vPKKF8fmHzCYrEQHx+fL1g9pZvVZDIRExNDTIyuQxZjlDlUN2/ezJo1a1i9ejWvv/46\nr732Gh06dGDw4MEMGDCAxo0bV2U5RXxPwaXlnH788MoScz4w+YTVaiU+Pt7VBaxuVvFlZe7+bdCg\nAUOHDiUuLo5NmzYxefJkatSowcsvv0yvXr0YMWIEH3/8MefPn6/K8kp55Nhhrw3Wj8j9V5dieJaC\no3tdsr1nlG8Z3mPqZhV/UqHJH373u99x//33c//993Ps2DFef/11Vq9ezTfffMM///lP+vTpw6hR\no+jYsaPR5ZWyKmmBbfEMRY3udXKO8vXkFmpJ77ECXdS+3M1qt9uJi4sjMTERi8WC1WrVAYMfq1Co\nnj59mi+++II1a9awY8cOsrOziYyMZPDgwQB88skn3H///UycOJGHHnrI0AJLGZV4jWNPtxZNftPM\nkhtCRQWrN4zyLek95skHAwbylFmZ7HY7S5cu5dChQwp2NytzqJ46dYrVq1ezZs0adu7cSU5ODu3b\nt+eJJ54gOjqaFi1auPa97777+POf/8yMGTMUqu5S0jWOzRSqVa60AUiQ+/8/xhfRBRzkHaN8S3qP\n+UmolnS5UHW1yu12O2PGjGH79u1kZ2drukU3K3Oo9u7dG4Brr72WRx99lOjoaNq0aVPkvkFBQbRq\n1YpLly4ZUkipgKJaQd7Q+vEFZR2AlHd0b0nh66l88D2WkZFBTEwMW7ZsoXv37kyfPp0nn3zS9bvN\nZqNWrVqu/Uu6XKi6QnXu3LmuQM37/NUZ7HJFmUPVarUyePBgbrzxxjLt//rrr1OjRo0KF0wqqWAr\nKO81jik/urt0vq0sA5CcLTlvHt1b0nvMC2VkZNCiRQvXYMuDBw+yaNEi1+0HDx5k8eLFnDx50nW1\ngydcLpSUlOQKVKfqDna5osyjf5955pkyByqgQHU3Zyuox0xoOzz33+gvPL/14wvKMgDJF5TyHnPO\n9zt21P2csoWSM7cOLOsKmZ55hcDDDz9c6tULWVlZtGjRgoyMDMAzZmWyWCwEBQXl2+Yp1wH7Iy39\n5su8uRXkzbx9AFJ5FPMecw7g2fntRn56zUGwAwKywPHTNzjm/Y7sB05jqu1Z17Zv3bq1TPvZ7XZi\nYmJYuHCh63Ihd47+tVqtzJkzx9UFXN5g1+hlYylURYzm7QOQDOAcwLPpKQfBQRAQkLs9IABw5JAy\n/feYn/6l2r+8SwqQ7t27c/DgwTI9zpYtW6qymOViMpmYM2dOhUb/esroZV+iUBUxmrcPQDKAcwDP\nDc2vBKpTQAC0rpNW7QNpSgsQm83GZ599VqYJbLp3716mx6wuJpOJoUOHEhYWVq77ecLoZV+jVWpE\njJJ3dqGUuNwAve0DuG1h7r9hMX4RqHBlWbXdJ8DhyH+bwwG7T1DtE+qXtlpOrVq1OHHiBA888ABt\n2rThgQce4MiRI4XCsX79+thstjI9pqfz1MUOvJlCVcQIzstoNsfCDwty/13ZP/+0fd42bWQlyusc\nwDNoRgBZ2VeC1eGArGwYNCOg2gfSlCVAatWqxcKFCzlw4AALFy6kdevWnDt3Ll/QnjhxwnVZjbeH\nktaUNZ5CVcQIJc5gRdlC15NUsrzOATyvvPkOsd8MYceJGly4CFsPQtMJAXTs0qvaJ9SvaIAUDNq8\n16l6eyh5wuhlX+MVobpkyRJuv/12IiIiGDp0KMnJySXuv3//fkaMGEFkZCS9e/fGZrPhKNgHJWKk\nkmYXgtJD19MYUF7nfL+2eYu5aVIaH4W8yzunhvPKm++4ZUL9qggQbw8lLXZgPI8fqLRs2TKmTJlC\nbGws4eHhfPDBB4wePZoVK1ZwzTXXFNr/7NmzWK1W2rZty/Tp09m9ezfTp08nKCiI0aNHu6EG4hdK\nm13I26b0K628zmkYy7jOqydMqF8Vl794wiU1leUJr40v8ehQdTgcvP322wwZMoTHHnsMgFtuuYWB\nAwcyf/58Jk2aVOg+ixYtIisri9mzZxMSEkKvXr3IzMzEZrMxfPhwr3qzixdp+yDsfB0u/EjuaN8C\nl89425R+JZW3HKvTeJqqCBBvCCVdi1p9PLr798iRIxw/fpzbbrvNtc1kMtG7d282bdpU5H2SkpLo\n3r07ISEhrm39+vXj3Llz7Nq1q8rLLH4oxw6fD4L/HcJ1+Uy96+APK/NPnt/MkhtM4PlT+pVUXm/r\nyvZzzst+YmNjWbBgAWPHjuWmm25yzQpVneWw2WyMGDECm82G3e6h4wkqyaNbqocPHwZyJ/HP65pr\nriE1NZXs7OxC03MdPnyYrl27FtrfeVtUVFS5y7F3795y38eTXbx4EfC9epWkzHXOsVP/9FJqXUgm\no14k56++p9TWV4OTi2l2cjMBOOdfdeC4cICTG1/lfPOhV3Zs8x/q1y7w2FU8D3OlXutiyts8ZRUN\niugaPpeykpMesKxgVb2/ncurJScnExkZyT333OMxrb2S6rx48WI2b97smh/Y4XCwf/9+brjhBj79\n9NNK16Esf5eCK+ksWrSIOXPmMGfOnEo9vyd+l3l0qKalpQFQu3btfNtr165NTk4OFy9epE6dOoXu\nU9T+eR9PpEg5dlrvGkOtC9sJIJv6P62k/k+rSA2fU2KwhlxIzhOouQLIptaF5PyhGmjifPOh+bd5\nsmLKm1E3gvo//ZcArgz+cxBERr3I6i5htSkYCp9++inz5s3jk08+yTca2BMlJycXmnAfIDU1laVL\nlzJ0aMXfjwX/LitXrmTVqlWFwnLp0qX5VtLJzs7mu+++4+OPP2bYsGEVfn5P5NGh6hyxG1BwSpbf\nFLe9OIGBFevtLu8sJZ7OeVTna/UqSZnqvPdd+F8y/BaQAWRT+3/JhAVuLWUwUTScWVXo/GMDczQN\n3Pw3Nvy1zrHDDxuB/KPpA5pZaNH7eVp4wDnVqnh/v/vuu4XC6ciRI9x///3s3r3b7S3WkuocHR3N\nf//730JXQDgcDg4dOkRYWFiFz7kW/LtkZ2eTnJzM1q1b851jPnToUKFgdzgcvPfee7zwwgsV/vu5\n87ts27ZtRW736HOqdevWBSA9PT3f9vT0dIKCggq1SAHq1KlT5P7O20SKVdplMcXxtvOllZEyF04n\nFdgYCNcN9fhBSpVR1CQPAD/++KPHz57kvBqioKCgICwWS6FzrrGxsfTv379M5zzLOvmFxWIpshF0\n5swZj//7lZdHh6rzXOrRo0fzbT969CihoaFF3ic0NJRjx44V2h8odlF1ESB/MLoEQtOuRe5+ZRc/\nWmavyGXtcuCnr91SnOpSXCg4HA6Pnz3JZDKRnJxM27ZtXXUICgqiZ8+eWK3WSk21WNbJL6xWK02b\nNi10/5ycHI//+5WXR4dqaGgozZs3Z+3ata5tdrudDRs2uCa0Lqhbt24kJSXlG9m2du1aGjRoQPv2\n7au8zOLFzFa4+pYCG3PgwEelzyTkXAKtz3zfnuO3qAMPT740yCCltfY8Xa1atdi9ezfvvPMOw4cP\nZ9asWa5JHioz1WJZJ78wmUy88MILhU7BedPsU2Xl0aEaEBDAww8/zEcffcSbb77JV199xbhx4/j1\n118ZOXIkkHuyfceOHa77DBs2zLXe4fr165k9ezY2m42YmBgtnC4lCzTldmNSoEVyeosuF3Hyp67u\nPEpr7XkD5/W08+fPJyYmxnUeszJTLZZnRqaHH36Ynj17eu3sU2Xl0QOVAB544AEuX77MggULmDdv\nHmFhYbz//vuuy2RmzZrFsmXLSElJAaBp06bExcUxdepUxo8fT+PGjXnyySc1m5KUzU9fU3AQjkfP\nfFTd8i5rV8bZlHyFs7Xna5MoWK1W4uPjXV3A5Q27sk5+4QuzT5VFgEOT4pZo27ZtdOrUyd3FMJRG\n/5a0oy138viCMwn1mOmVoarX2j9Uts7eOuOSu0f/FpUNHt9SFalWZmvulHvOGYP8pHtT/Js3TLXo\nLRSqInn5cfemiFSeQlWkIOdIXi/s7hUR9/Lo0b8iIiLeRC3V6lLO9SdFRMT7KFSrgxevPykiUl28\ndRRyXur+rQ5af9JYOfbcS1/Wj8j9t7TZjjyQHTs2bIxgBDZs2PG+OogYqTJzEJflsatrLVeFanWo\n6ETtUpiz1b85Fn5YkPvvyv5eFax27PSnP7HEsoAFxBJLf/p7dbD6ywLU3sBbX4vKzEFckqoM66Io\nVKuDn86XWiV8oNU/l7kkkkgWv315kEUiicThPXXIq7q/tKR43vxaVGYO4pJUVVgXR6FaHfx0vtQq\n4QOt/iSSXIHq5AxWb1TdX1pSPG9+Lco6B3HelvjixYtLPWCoqrAujkK1OvjT0mBVzQda/RYsBBcY\nIxhMMBa8pw55VfeXlhTPm1+Lsqx4U7Al/tJLLzFmzJgSg7UyCwZUhEK1uvjL0mBVzQda/Vas+YI1\nmGB60AMr3lOHvKr7S0uK582vRVlWvCnYEs/Ozmb79u0ltsTLujydURSq4l18oNVvwkQCCcxkJsMZ\nzkxm8gVfYMJ76pBXdX9pSfG8/bUobnk6p6Ja4tnZ2SW2xMuzPJ0RdJ2qeB83TyNox04ccSSSiAUL\nVqzlDkQTJmJ++8/b+cuSXt7A118Li8VCfHx8vmAty0Lx1blggJZ+K4WWfvMNRtXZeTmMc/Su81xo\nAgke2dLUa+0f/KXOznOqzi7goKAgoqKiSExMrPYDBy39JlKaMkwlWdLlML7Q6hTxZAVb4r///e+5\n5557PKolrlAVgTJPJVnS5TAKVZGql7cr19lC9yQaqCQCZZ5UwtcuhxERYylUfYUPzIfrVmWcVMLX\nLocREWOp+9cXaBWcymtmyf2b5Q3WIiaVcF4OU9nRvyLim9RS9QU+MB+u25VjUgnn5TDzmU8MMVUe\nqFrRRsR7qKXqC0rqunTTtZxexzmphIctJF/wEp743/7z1Et4RPydWqq+wAfmw/UI1TiVZFlbn762\noo2Ir1Oo+gIfmA/XaxgwIKw866n62oo2Ir5OoeoLfGA+XK9g0ALp5Wl96hIeEe+iUPUVWgWn6hk0\nIKw8rU9dwiPiXRSqImVl0ALp5Wl9+tqKNkXJu+i0zWYrddFpEU+m0b8iZVXGa1lLY8VKPPH5JuUv\nqfXpSyvaFFRwgvT4+Hji4+NJSEjwqPlcRcpKLVWRsjJoQJg/tD7LquCi01lZWSQmJpa46LSIJ1NL\nVaSsDLyW1Zdbn+VR1KLTzmCtjrUvRYymlqpIeWhAmKEsFgvBwQXOLwcHl7rotIinUqhK5Wgif6kE\nq9WaL1iDg4Pp0aMHVqtGN4t3UvevVJw3T+RfhgXJpeoVXHTaYrFgtVo1SEm8lkJVKq6k6zY9ec7h\nog4Gdr4BTbtA856FAtZudxAXd4HExMtYLFdhtdbDZApwYwV8S95Fp0W8nbp/peIMum6z2hV1MHBh\nP/y4sNAsSXa7g/79TxIbe5YFC9KIjT1L//4nsdsdbqyAiHgqhapUnLdO5F/UwYBTgVmS5s69QGLi\nJZwDVLOyIDHxEnFxF6qpsCLiTRSqUnHeOpF/UQcDeeVpbSclXabAFR+/BevlKiygiHgrhapUnLdO\n5F/wYKCgPK1ti+UqClzxQXBw7nYRkYI0UEkqx3ndpicPTALsdli6NJBDh37KHWw04gtMB+fByU3w\n09dw4SCQXai1bbXWIz4+3dUFHBwMPXrUxGqt59b6iIhnUqiKz7BjJ444EknEggUrVkyYsNsdjBlj\nYvv2ALKz04iPTyM+viYJCQ9jCosp8fIakymAhITmGv0rImWiUBWf4Fz42zlJffxv/yWQwNy5Gb8F\nam4Q5h1sFBNTv9TWtskUQExMfXTFh4iURudUxSeUtPB3UtJlV6A6abCRiFQFhap4NTt2bNh4lVeL\nXfjbYrmKoKD815VqsJGIVAWFqngtZ5dvLLEc5GCh250Lf1ut9YiKcriCVYONRKSq6JyqeK2CXb55\n5V3422QKYM4c+2+jfxtqsJGIVBmFqnitJJKKDNQ2tOEZnnGN/gUwmWDo0BzCwppWdzFFxI+o+1e8\nlgULwQWOC4MJ5hmeIYYYV6CKiFQXhap4LSvWfMGat8vXb2g9WxGPou5f8VomTCSQUOSED37Bm9ez\nFfFRClXxaiZMxPz2n98xaD3b4maiEpHy8/ju3/379zNixAgiIyPp3bs3NpsNh6PktSzXrFmD2Wwu\n9LNw4cJqKrVINTBgPdu8lyUtYAGxxNKf/thRN7JIRXh0S/Xs2bNYrVbatm3L9OnT2b17N9OnTyco\nKIjRo0cXe799+/Zx7bXX8uqrr+bb3qpVq6ousnggO3YW119Mcq1koon2nZZYM0tud2/eYC3nerYl\nzUTll61/kUry6FBdtGgRWVlZzJ49m5CQEHr16kVmZiY2m43hw4djMhX9xZiSksKNN95Ix44dq7nE\n4mmcLbHNzTeTHZDNKla55gT2+mA1W3ND1dkFXIH1bIu6LMkZrApVkfLz6O7fpKQkunfvTkhIiGtb\nv379OHfuHLt27Sr2fikpKZjN5uooong4Z0ssOyAbyN8S83oGrGdb3GVJFsre2hWRKzy6pXr48GG6\ndu2ab9s111zjui0qKqrQfdLS0jh+/Dh79uxhwIABHDt2jDZt2vC3v/2NXr16Vagce/furdD9PNXF\nixcB36tXUVY1X0VWg8ItsZXnVtLzZE83lcpoPaHZb3VJ+THfLaW91t3oRmTrSLbX2k52QDZBjiAi\nMyLpltqNvXjn+8Of3t9O/lhn8Mx6uy1U7XY7qampxd7euHFj0tLSqF27dr7tzt/T0tKKvN/+/ftx\nOBwcO3aMZ599lqCgIOLj4xk7dixxcXF069bNuEpIyXLs1D+9lFoXksmoF8n5q++p9ks9IjMiWVl/\npaulCriCw9vZsbO0/lKSayUTmRHJPefvKXeXtgkTc1LnVPpxRCSX20L19OnTDBo0qNjbn3vuuRLv\nHxhYdM/19ddfj81mo1OnTtSpUwcAi8XCXXfdxezZsysUqmFhYeW+jydzHtVVab0KXEPZ4MwqWqRv\nqPZrKJ/neTawgc2O3HOqwQTTI6AHz7d4HlML7w2OguvHrmqwig0tNhQ6V1zW1zqCiNz/aQC0qKpS\nV49qeX97GH+sM7i33tu2bStyu9tCtVWrVqSkpJS4zzvvvEN6enq+bc7fnYFZUL169Qp18wYFBXHL\nLbewYsWKSpRYysWgaygryzlBxNSTU3NH/zbwjdG/GrUr4pk8eqBSaGgox44dy7ft6NGjALRp06bI\n++zZs4ePP/640PZLly7RsGFD4wspRTPgGkqjmDAx9PxQpp2c5jNzApc0aldE3MejQ7Vbt24kJSWR\nkZHh2rZ27VoaNGhA+/bti7zP3r17mTRpEnv27HFtu3TpEhs3bqRLly5VXmb5TTNL7iUeeZXzGkop\nnkbtingmjw7VYcOGYbfbiYmJYf369cyePRubzUZMTAw1atQAcgcs7dixg19++QWAgQMHEhoayhNP\nPMGqVatYt24do0aNIiMjg0cffdSd1fEvZmv+YK3ANZRSPC0mIOKZPDpUmzZtSlxcHFlZWYwfP54l\nS5bw5JNP5ptNaffu3QwdOpQNGzYAuaOD582bR3h4OC+99BJPPfUUISEhLFy4kObNm7upJn7IgGso\npXjOc8UzmclwhjOTmXzBFz7RtS3izTz6OlWA8PBwPvroo2Jv79q1a6EBT82bN+ff//53VRdNShNo\nyh2UVI0Dk3xOjj13cNepxNyWv9nqOjDx68UERDyUx4eqiN/S0m4iXseju39F/I0dOzZsjGAEG1Os\nOIq7LElEPJJaqiIeouCEDn1PBXBrwWUOncGqLnURj6SWqoiHKDihw+ZmDuwBBXbSZUkiHk2hKlLV\nco8WstgAABIVSURBVOyw1wbrR+T+m1P0AuAFJ3SIM8PmZpAV8Fuy6rIkEY+n7l+RqlSOwUYWLMQT\nf2XqwUAYFB3EmpT7uPVUUKHRvyLiedRSFb9mtzuw2c4zYsRP2Gznsdsdpd+pPEqaA7mAoiZ06BbY\nk+5hcdBnfu55VAWqiEdTS1X8lt3uoH//kyQmXiIrC+Lj04iPTychoTkmU8GTmRVU0hzIBQYbOSd0\niCOORBKxYPGJyf9F/IlaquK35s694ApUgKwsSEy8RFzcBeOepJxzIDsndJjPfJ+Z/F/EnyhUxeNV\nVRdtUtJlV6A65QbrZUMeH9AcyCJ+Rt2/4tGqsovWYrmK+Pi0fMEaHJy73TDOOZCLmWpQRHyLWqri\n0aqyi9ZqrYfFUpPg3w4tg4OhR4+aWK31Kv3Y+TjnQNZgIxGfp1AVj1aVXbQmUwAJCc2ZObMRw4fX\nYebMRnzxhYGDlETE7yhUxaNZLFe5WpJO5emidc6l+2zzZ1lcfzF28k+8YDIFEBNTn/nzmxITU1+B\nKiKVonOq4tGs1nrEx6e7uoDL00Wbby7dBlmsrL+SDWwggQSNqhWRKqGWqni0ynTRFpxLNzsgm0QS\niUOrvIhI1VBLVTyes4s2ppwLsxScSxcgiywSSdTC3iJSJdRSFZ+Vd8o/p2CCsaBVXkSkaihUxWcV\nnEs3yBFEG9qwiU3YsBUatCQiUlkKVfFZzrl0ZzKTO87dQavMVhzgAAtZSCyx9Ke/glVEDKVQFZ/m\nnEs36mIUx2ocI5ts4Mq5VQ1aEhEjKVTFLySHJJMdkJ1vmzNY3c15Le0IRqhbWsTLKVTFL0RmRBLk\nCMq3zRMGLTmvpY0llgUsULe0iJdTqIpfuOf8PURlROVbALwHPbDi3tViCl5Lq25pEe+mUBW/YMLE\nnNQ5zGQmwxnOTGbyBV+4fWalkq6lFRHvo8kfxG84By150sQPFizEE58vWD2hW1pEKkYtVRE3Kngt\nrad0S7tTVS1KL1Id1FIVcSPntbRxxJFIIhYsWLG6vVvaXapyUXqR6qCWqoibObul5zOfGGL8NlCh\nahelF6kOClUR8RhVuSi9SHVQqIqIx6jsovQi7qZQFRGPYbXWw2Kp6QrW8ixKL+IJNFBJRDyGc1H6\nuLgLJCZexmK5Cqu1ngYpiddQqIqIR6noovQinkDdvyIiIgZRqIqIiBhEoSoiImIQhaqIiIhBFKri\nFprfVUR8kUb/SrXT/K4i4qvUUpVqp/ldRcRXKVSl2ml+VxHxVQpVqXaa31VEfJVCVaqd5ncVEV+l\ngUpS7TS/q4j4KoWquIXmdxURX6TuXxEREYMoVEVERAyiUBURETGIQlVERMQgXhOqaWlp9OnTh9Wr\nV5e6b2ZmJv/617+wWCxERkYyfvx4Tp8+XQ2lFBERf+YVoZqWlsa4ceM4ceJEmfafMmUKK1as4Kmn\nnuLll19m3759xMTEkJ2dXcUlFRERf+bxl9R88803TJkyhbNnz5Zp/9TUVJYvX84bb7zBoEGDAGjf\nvj0DBw5k3bp13H777VVZXBER8WMe31KNjY2lXbt2zJkzp0z7b926FYDevXu7toWGhtK2bVs2bdpU\nFUUUEREBvKClumjRItq1a8exY8fKtP+hQ4do3LgxtWrVyre9VatWHD58uEJl2Lt3b4Xu56kuXrwI\n+F69SuKPdQb/rLfq7D88sd5uC1W73U5qamqxtzdu3Jj69evTrl27cj1ueno6tWvXLrS9du3anDp1\nqtzlFHGy22Hp0kCSkwOIjHRwzz05mEzuLpWIeBK3herp06dd5zyL8txzzzFy5MhyP67D4SAgoOg5\nZIvbXpqwsLAK3c9TOY/qfK1eJalsnQsurL5qFWzYUNPjF1bXa+0f/LHO4N56b9u2rcjtbgvVVq1a\nkZKSYvjj1qlTh/T09ELb09PTqVu3ruHPJ/6hpIXVY2Lqu7dwIuIxPH6gUnmFhoby888/c+nSpXzb\njx07xu9//3s3lcr72bFjw8YIRmDDhh27u4tUrbSwuoiUhc+Favfu3cnOzubLL790bTt8+DA//PAD\n3bt3d2PJvJcdO/3pTyyxLGABscTSn/5+FaxaWF1EysLrQzUtLY0dO3bwyy+/ANC6dWsGDhzI5MmT\nWbJkCatXryYmJgaz2Uy/fv3cXFrvNJe5JJJIFrlNtSyySCSROOLcXLLqo4XVRaQsvD5Ud+/ezdCh\nQ9mwYYNr28svv8ygQYN4/fXXmTRpEu3bt8dmsxEUFOS+gnqxJJJcgerkDFZ/4VxYfebMRgwfXoeZ\nMxvxxReePUhJRKqfx1+n6lTcwKauXbsW2l6rVi1efPFFXnzxxeoqnk+zYCGe+HzBGkwwFixuLFX1\n08LqIlIar2+pStWzYsWCheDfjsGCCaYHPbBidXPJREQ8i9e0VMV9TJhIIIE44kgkEQsWrFgxoZkP\nRETyUqhKmZgwEfPbfyIiUjR1/4qIiBhEoSoiImIQhaqIiIhBFKoiIiIGUaiKiIgYRKEqIiJiEIWq\niIiIQRSq4vfLuomIGEWTP/g557JuzlVo4n/7L4EEzZgkIlJOaqn6OS3rJiJiHIWqn9OybiIixlGo\n+rm8q884+eOybiIiRlCo+jkt6yYi8v/bu9fYJss+juO/2YcF2GTOzIhxZIVBh0EYy9xg7gVjMR42\niSQm7o3htMRMCURMdKKLkHhCE7UY43SREJmHRIIMEw5LYHGgEzWChzgtHnbqCItikLRsdmHX88Jn\nfTLXHdpdW+/i95PwgqvXvf3/9x/4tXdvOnu4Uelfjh/rhkH96ufPATBBhCr4sW7gLnDAEi7/AuAu\ncMASQhUAd4EDlhCqALgLHLCEUAXAXeCAJdyoBIC7wAFLCFUAkrgLHLCBy78AAFhCqAIAYAmhCgCA\nJYQqAACWEKoAAFhCqAIAYAmhCgCAJYQqAACWEKoAAFhCqAIAYAmhCgCAJYQqAACWEKoAAFhCqAIA\nYAmhCgCAJUnGGBPvIpzsq6++incJAAAHys/PH7ZGqAIAYAmXfwEAsIRQBQDAEkIVAABLCFUAACwh\nVAEAsIRQBQDAEkIVAABLCFUAACwhVAEAsIRQ/RcJBAJauXKljhw5MubeUCik5557TsXFxcrLy9Pm\nzZvV09MzBVXacebMGa1du1Z5eXkqKSlRXV2dxvrwsMbGRuXk5Az79c4770xR1dH74IMPdPvtt2vJ\nkiWqqKjQ6dOnR90fy3lxmmh7rqqqijjXYDA4RRXbdezYMeXl5Y2570qY9aDx9uyEWf9nyr4T4ioQ\nCOihhx7S2bNnx7V/27ZtampqUnV1tWbOnKmXX35ZDzzwgD788EO5XK5JrnZizp8/r/Xr12vBggXy\ner36/vvv5fV65XK5VFlZOeJxP/74o7KysvTiiy8OWc/MzJzskmOyf/9+bdu2TRs3btTixYtVX1+v\nyspKHThwQHPmzBm2P9bz4iTR9iz9Pdc1a9aovLx8yPqMGTOmomSrTp06pUcffXTMfVfCrAeNt2fJ\nIbM2uOJ9/vnn5s477zQFBQXG4/GYw4cPj7q/o6PDLFy40Bw8eDC81tbWZnJyckxjY+NklzthO3fu\nNIWFhebSpUvhtVdeecUUFhaaUCg04nEPPvigefjhh6eixAkbGBgwK1euNE899VR4LRQKmdLSUvP0\n009HPCbW8+IUsfT8559/Go/HY5qbm6eqzEnx119/mbq6OrNo0SJTUFBgli5dOur+RJ+1MdH37JRZ\nc/n3X2Djxo3yeDx66623xrX/5MmTkqSSkpLwmtvt1oIFC3TixInJKNGqlpYWFRUVDXl2etttt+nC\nhQv67rvvRjzO5/MpJydnKkqcsI6ODnV3d6u0tDS8Nm3aNJWUlIw4o1jPi1PE0rPP55OkhJnrSI4f\nP666ujo99thjuv/++8fcn+izlqLv2SmzJlT/Bd59913t3LlT11577bj2t7W1KSMjQzNnzhyynpmZ\nqfb29kmo0K729nZlZWUNWRu8NDhS/YFAQN3d3WptbdUdd9yhRYsWadWqVWpubp7scmMy2EekPjs7\nO3X58uWIx0R7Xpwklp59Pp+Sk5Pl9Xq1bNky5ebmavPmzfrtt9+momRrFi9erGPHjmnNmjVKSkoa\nc3+iz1qKvmenzJr3VBNYf3+/Ojs7R3w8IyNDaWlp8ng8UX3dYDColJSUYespKSk6d+5c1HXaNJ6e\nA4HAsPoHfx8IBCIed+bMGRlj5Pf79fjjj8vlcum9995TVVWVdu/ereXLl9trwoLBPiL1OTAwoN7e\nXqWmpg47Jtrz4iSx9Ozz+RQKhZSSkqLXXntNXV1d8nq9Wrt2rRoaGpScnDxl9U/E9ddfH9X+RJ+1\nFH3PTpk1oZrAenp6VFZWNuLjW7du1bp166L+usaYEZ8ZjucZ42QaT8+jueqqyBdn5s+fr7q6OuXn\n54f/YS4uLtY999yj2tpax4Wq+d9dnLbmNNJ5cZJYel63bp3Ky8vD8ysoKFB2drbuu+8+HTp0SKtX\nr568gh0qEWYdC6fMmlBNYJmZmeH3EWxKTU2NeAt6MBjU1Vdfbf37RWM8Pb/xxhvD6h/8/T9fyQya\nNWuWVqxYMWTN5XLp1ltv1YEDByZQ8eQYnEMwGFRGRkZ4PRgMyuVyRbzSEGmuY50XJ4ml5+zsbGVn\nZw9Zy83N1axZsybl745TJPqsY+GUWV+ZT1kwIW63W7///rv6+vqGrPv9fs2dOzdOVY2f2+2W3+8f\nstbV1SVJmjdvXsRjWltbtXfv3mHrfX19Sk9Pt1/kBA2+XzbY16Curi653e6Ix8RyXpwklp4PHjyo\nL7/8csiaMUahUMiRc7Ul0WcdC6fMmlDFMEVFRbp8+bKamprCa+3t7frpp59UVFQUx8rGZ/ny5Wpp\nadGlS5fCa0ePHtU111yjhQsXRjzmhx9+UE1NjVpbW8NrfX19On78uAoLCye95mi53W7dcMMNOnr0\naHitv79fH3/88YgziuW8OEksPb///vt69tlnNTAwEF5rbm5WX1+fbrnllkmvOV4SfdaxcMqsXdu3\nb98+Zd8NcXXx4kXt2bNHd911l+bPnx9eDwQCam1tVXJysmbMmKG0tDT9/PPPevvtt5Wenq6uri49\n8cQTmj17trZu3er492TmzZun+vp6ffbZZ0pPT9eRI0dUW1urTZs2qaCgQNLwnrOystTY2KjDhw8r\nIyNDnZ2d2r59u3p6evTSSy/F/bL3PyUlJWnatGl6/fXX1d/fr1AopOeff16//vqrXnjhBaWlpamz\ns1NtbW2aPXu2pPGdFyeLpefrrrtOu3fvVnt7u1JTU3XixAk988wzKikp0YYNG+LcUWy++OILnT59\nWlVVVeG1K23W/zSenh0z63j+J1lMra6urogf/nDy5Enj8XjMvn37wmvBYNDU1NSYgoICk5+fbzZt\n2mTOnTs31SXH7NtvvzUVFRXm5ptvNiUlJebNN98c8nikns+ePWu2bNliioqKTG5urtmwYYPx+XxT\nXXpUdu3aZVasWGGWLFliKioqzKlTp8KPVVdXG4/HM2T/WOclEUTbc1NTk7n33ntNbm6uKS4uNjt2\n7DC9vb1TXbY1r7766rAPQrhSZz1ovD07YdZJxiToh0ECAOAwzr6OBwBAAiFUAQCwhFAFAMASQhUA\nAEsIVQAALCFUAQCwhFAFAMASQhUAAEsIVQAALCFUAQCwhFAFEFFTU5NycnL05JNPDllfv369li5d\nqo6OjjhVBjgXoQogotLSUpWVlWnfvn365ptvJEl79+5VS0uLHnnkkfDPNwXwf3ygPoARnT9/XmVl\nZbrxxhtVW1ur8vJy3XTTTdqzZ4+SkpLiXR7gOIQqgFE1NDSourpamZmZ+uOPP/TRRx9pzpw58S4L\ncCQu/wIY1erVq1VYWCi/36+qqioCFRgFoQpgVBcuXNAvv/wi6e+blwYGBuJcEeBchCqAUe3YsUMX\nL17Uli1b9PXXX6u+vj7eJQGORagCGNGnn36q/fv3q7KyUlVVVSouLpbX61V3d3e8SwMciRuVAETU\n29uru+++W8YYHTp0SNOnT1dbW5tWrVqlZcuWadeuXfEuEXAcXqkCiMjr9crv96umpkbTp0+XJM2d\nO1eVlZX65JNP1NDQEOcKAefhlSoAAJbwShUAAEsIVQAALCFUAQCwhFAFAMASQhUAAEsIVQAALCFU\nAQCwhFAFAMASQhUAAEsIVQAALPkvCIDbLgbB47kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a0a46a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sxifUQPfv348ff/wRTZs2Re/evZGZmYnvvvsOVqsVMTExlZbJlfBcC99DVakcPPTQQ2LT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\ngEkIVQAATEKoAgBgkv8DGjt1YZaogrYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a19f12e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BfkokD2zq6mIQkZfhpTkREZFMGKpEREQyYfMveS3BLCLh+B2kXyrE3xRKDLuP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\nBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1b02d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WHw9QiUSkqlGoStjYfPC83+2bitguIlJWClUJG70ur16m7SIiZaVQlbCRMKwJ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\nVAEAMAmhCgCASQhVAABM8v9iZ8HiRy3O+gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a17b2b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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b9JEQkbJTT1WqnYc27PIGqsdpu5OEDbsCVJGIVBUKVal2Nhw/XWj7+ou0i4iU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a16aaef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FRET8RKEqtVJeXh633347HTt25PbbbycvLy/QJYlIGAippd9E/CEvL482bdqQ\nnZ0NwN69e/n44485fPgwDRo0CHB1IhLK1FKVWufOO+/0BapXdnY2drs9QBWJSLhQqEqts3HjxjK3\nb9iwoYYrEZFwo1CVWic+Pr5K20VEKkuhKrVOSkoKUVFRxbZFRUWRkpISoIpEJFwoVKXWadCgAYcP\nH2bUqFF06NCBUaNGaZCSiPiFRv9KrdSgQQMWLlwY6DJEJMyopSoiIuInClURERE/UfevhCWn00lq\naioOhwOr1Uq/fv0wm82BLktEwpxCVcKO0+kkMTERh8OBy+UiLS2NuLg43njjjUCXJiJhTt2/Enbm\nzp3rC1QAl8vF5s2bWbJkSYArE5Fwp1CVsJORkeELVC+3282WLVsCVJGI1BYKVQk7VqsVk6n4kQ2j\n0UhcXFyAKhKR2kKhKmHHZrMVC1aTyUSPHj246aabAlyZiIQ7DVSSsGM2m0lPT9foXxGpcQpVCUtm\nsxm73e5bzm3Xrl0BrkhEagN1/4qIiPiJQlVERMRPFKoiIiJ+olAVERHxE4WqiIiInyhURURE/ESh\nKiIi4icKVRERET9RqIqIiPiJQlVERMRPFKoiIiJ+olAVERHxE4WqiIiInyhURURE/EShKiIi4icK\nVRERET9RqIqUITs7m759+9K4cWP69u1LdnZ2oEsSkRBgCnQBIsEmOzubZs2a4Xa7Afjqq69o1qwZ\nx48fJyoqKsDViUgwU0tVpITExERfoHq53W6uuuqqAFUkIqEipEJ11apVxMXFnfVyu3fvZvTo0cTF\nxTFw4EBSUlLweDw1UKGEg127dpW5fefOnTVciYiEmpAJ1c2bN/PQQw+d9XLHjx/HZrNhMBiYMWMG\nw4cPZ8aMGcydO7cGqpRw0KVLlyptFxHxCvpjqvn5+cyfP5+XX36ZBg0a4HQ6K7z8okWLcLlczJkz\nh/r16zNgwADy8/NJSUkhOTkZs9lcQ5VLqFqxYkWxY6oARqORFStWBLAqEQkFQd9SXbt2LSkpKUye\nPJnbb7/9rJfPyMggPj6e+vXr+7ZdeeWVnDhxgu3bt1dnqRImoqKiOH78OH369KFRo0b06dNHg5RE\npFKCvqUaExPDqlWriIyM5JVXXjnr5ffv30/fvn2Lbbvooot8f+vRo0eVayjvGFuoOnXqFBB++1WR\nc9nnefPm+f7/8OHDHD582N9lVTs917VDbdxnCM79DvpQbdWqVZUun5OTQ8OGDYtt8/6ek5Pjt7pE\nRERKCvq+EShxAAAgAElEQVRQ9aeIiHPr7e7cubOfKwks77e6cNuvitTGfYbaud/a59ojkPu9adOm\nMrcH/THVqmrUqBG5ubnFtnl/b9SoUSBKEhGRWiLsQrV9+/YcPHiw2LYDBw4A0KFDh0CUJCIitUTY\nhWq/fv3IyMggLy/Pt23lypU0adKETp06BbAyEREJdyEfqllZWWzdutX3+2233YbT6cRut7N69Wrm\nzJlDSkoKdrudOnXqBLBSEREJdyEfqrNnz2bEiBG+31u2bElqaioul4v77ruPd999lwceeIBx48YF\nsEoREakNQmr077333su9995bbNv06dOZPn16sW0xMTG88847NVmaiIhI6LdURYKd1mYVqT1CqqUq\nEmq0NqtI7aKWqkg10tqsIrWLQlWkGmltVpHaRaEqUo20NqtI7aJQFalGK1aswGg0FtumtVlFwpdC\nVaQaaW1WkdpFo39FqllUVBRffvlloMsQkRqglqqIiIifKFRFRET8RKEqIiLiJwpVET9wOp2kpKQw\nevRoUlJScDqdgS5JRAJAA5VEzpPT6SQxMRGHw4HL5SItLY20tDTS09Mxm82BLk9EapBaqiLnae7c\nub5ABXC5XDgcDlJTUwNcmYjUNIWqyHnKyMjwBaqXN1hFpHZRqIqcJ6vVislU/EiKyWTCarUGqCIR\nCRSFqkgJVR10ZLPZigWryWQiISEBm81WE+WKSBDRQCWRIs5l0JHZbCY9PZ3U1FQcDgdWqxWbzaZB\nSiK1kFqqIkWc66Ajs9mM3W5n/vz52O12BapILaVQFSlCg45E5HwoVEWK0KAjETkfClWRIjToSETO\nhwYqiRShQUcicj4UqiIleAcd2e32QJciIiFG3b8iIiJ+olAVERHxE4WqiIiInyhURURE/EShKiIi\n4icKVRERET9RqIqIiPiJQlVERMRPFKoiIiJ+olAVERHxE4WqiIiInyhURURE/EShKiIi4icKVRER\nET9RqIqIiPiJQlXkHDidTlJSUhg9ejQpKSk4nc5AlyQiQUCLlItUkdPpJDExEYfDgcvlIi0tjbS0\nNNLT0zGbzYEuT0QCSC1VkSqaO3euL1ABXC4XDoeD1NRUQK1YkdpMoSpSRRkZGb5A9fIGq7cVO2nS\nJBYsWMCkSZNITExUsIrUEgpVkSqyWq2YTMWPnJhMJqxW61lbsSIS3hSqIlVks9mKBavJZCIhIQGb\nzVZhK1ZEwp9CVaSKzGYz6enpzJo1i+TkZGbNmsWKFSswm80VtmJFJPxp9K/IOTCbzdjtdux2e7Ht\nNpuNtLQ0Xxdw0VasiIQ/haqIH3lbsampqTgcDqxWKzabTafaiNQSClURPyuvFSsi4U/HVEVERPwk\nJEL13Xff5aqrriI2NpYRI0awZcuWCi8/YcIELBZLqZ/c3NwaqlhERGqjoO/+/eCDD3j88ceZNGkS\nMTExvPXWW4wbN46lS5dy0UUXlXmdb7/9luTkZJKSkoptr1+/fk2ULCIitVRQh6rH4+GVV15h+PDh\n3HPPPQBcccUVXH311cyfP5+pU6eWus7Jkyc5cuQI/fv3p3v37jVdsoiI1GJB3f37ww8/cOjQIQYP\nHuzbZjabGThwIOvWrSvzOpmZmQBYLJYaqVFERMQrqFuq+/fvB6Bdu3bFtl900UVkZWXhdrsxGo3F\n/paZmUmdOnWYMWMGn3/+OadPn2bAgAFMmzaNFi1anFMdu3btOqfrBatTp04B4bdfFamN+wy1c7+1\nz7VHMO53ULdUc3JyAGjYsGGx7Q0bNqSgoMD3gBaVmZlJfn4+DRs2ZObMmTz++ONs3bqV0aNHk5+f\nXyN1i4hI7RTULVWPxwOAwWAo8+9lbR8zZgxJSUn069cPgN69e9OxY0eGDx/OJ598wg033FDlOjp3\n7lzl6wQz77e66tovp9MZdJMfVPc+B6vauN/a59ojkPu9adOmMrcHdag2btwYgNzcXJo3b+7bnpub\ni9FoLNWCBejYsSMdO3Ystq1bt25ERkb6jrdK9dEC3iJSmwV196/3WOqBAweKbT9w4ADt27cv8zrL\nli3j3//+d7FtHo+H/Px8mjZtWi11yu+09JmI1GZBHart27cnOjqalStX+rY5nU7WrFlDfHx8mdd5\n++23efrppykoKPBt++KLLzh9+jS9evWq9pprOy19JiK1WVCHqsFg4M477+Sdd97hpZde4osvvmDi\nxIn8+uuvjBkzBoCsrCy2bt3qu85dd93Ft99+y0MPPYTD4WDRokVMnjyZoUOH0qNHjwDtSe2hpc9E\npDYL6lAFGDVqFJMnT2bp0qXcd999/Pe//+XNN9/0zaY0e/ZsRowY4bt8//79mTNnDj/88AOTJk1i\nzpw53HzzzTz33HOB2oVapaIFvEVEwl1QD1TyGjt2LGPHji3zb9OnT2f69OnFtg0aNIhBgwbVRGlS\ngpY+E5HaLCRCVUKLlj4Tkdoq6Lt/RUREQoVCVURExE8UqiIiIn6iUBUREfEThaqIiIifKFRFRET8\nRKEqIiLiJwpVERERP1GoioiI+IlCVURExE8UqiIiIn6iUBUREfEThaqIiIifKFRFqsjpdJKSksLo\n0aNJSUnB6XQGuiQRCRJa+k2kCpxOJ4mJiTgcDlwuF2lpaaSlpZGenq41Y0VELVWRqpg7d64vUAFc\nLhcOh4PU1NQAVyYiwUChKlIFGRkZvkD18gariIhCVaQKrFYrJlPxoyYmkwmr1RqgikQkmChURarA\nZrMVC1aTyURCQgI2my3AlYlIMNBAJZEqMJvNpKenk5qaisPhwGq1YrPZNEhJRACFqkiFnE4Pqakn\ncTjOYLXWxWaLxGw2Y7fbsdvtgS5PRIKMQlWkHE6nh8TEIzgcp3G5IC0th7S0XNLTozGbDYEuT0SC\nkI6pipRj7tyTvkAFcLnA4ThNaurJwBYmIkFLoSpSjoyMM5Q4e+a3YD0TmIJEJOgpVEXKYbXWpcTZ\nM5hMhdtFRMqiUBUph80WidVazxesJhMkJNTDZosMbGEiErQ0UEmkHGazgfT06DJG/2qQkoiUTaEq\nUgGz2YDdHoXOnglPbqebb1IzOeQ4yoXW1sTaLBjNxkCXJSFMoSoSxMo+T1YtZX9wO928k7iMg46j\neFwedqTtYWfaHkamJylY5ZzpmKpIkPKeJztp0nEWLMhh0qTjJCYewen0BLq0sPDN3ExfoAJ4XB4O\nOo7yTWpmgCuTUKZQFQlS4XSerNvpZkvKTj4e/TlbUnbidroDXRKHMn4PVC+Py8Mhx9EAVSThQKEq\nEqTC5TxZbzfriknr+c+C71gxaT3vJC4LeLBeaG2NwVS8K91gMnChtXWAKpJwoFAVCVLhcp5ssHaz\nxtostC0SrAaTgbYJhYOVRM5VpUP11Vdf5cCBA9VZi4gUES7nyQZrN6vRbGRkehJXzUrg8uRLuWpW\nAiNXaJCSnJ9Kj/6dOXMmL7/8Ml27diUpKYk//elPtG6tbhKR8+Ed3btu3Wk8HjAYoH//er5RvuFw\nnuyF1tbsSNtTLFiDpZvVaDYSZ+9CnL1LoEuRMFHpUF2/fj3Lly/ns88+4/nnn+df//oX3bp1Y9iw\nYQwdOpTmzZtXZ50iYafkKjheb7+dW2w1nFA/TzbWZmFn2h5fF7C6WSWcVbr7t0mTJowYMYLU1FTW\nrVvHtGnTqFOnDs888wwDBgxg9OjRvPfee2RnZ1dnvVIFTqeHlJRsRo/+kZSUbJ2KEWRKju71crtD\na5SvEycppDCa0aSQghNnsb+rm1Vqk3Oa/OGCCy7g1ltv5dZbb+XgwYM8//zzfPbZZ3z11Vc8+eST\nDBo0iLFjx9K9e3d/1yuVVNFaoBIcyhrd6+Ud5RvsLVQnThJJxIEDFy7SfvsvnXTMmH2XC+duVs3K\nJEWdU6geO3aMFStWsHz5crZu3Yrb7SYuLo5hw4YB8P7773PrrbcyZcoU7rjjDr8WLJVT0TmO/fsH\ntjYpZLXWJS0tp8xgDZVRvnOZ6wtUABcuHDhIJRU7Qf6NwA+CZVamAmcBWUuO8f2+Iwr2AKt0qB49\nepTPPvuM5cuXs23bNgoKCujUqRP3338/SUlJtGnTxnfZkSNH8uc//5mZM2cqVAOkonMcFarVz1ng\nJPVwKutOrMODBwMG+jfpj62NDXNEYQvOZoskLS23VBew0Rg6o3wzyPAFqpc3WGtDqFZ0ulBNtcrd\nTjcZ47dzfHM2uNF0iwFW6VAdOHAgAO3atePuu+8mKSmJDh06lHlZo9FI27ZtOX36tF+KlKorqxUU\nKq2fUOcscJK4JRHHCUexwHn72NukHUsjPS4dc4S52Oje8kb/BjsrVtJIK7afJkxYsQawqnOXRx52\n7GxgA/HE82reDHLsD3BmwwbqxsfTMiWFiAYNfJev6HShmgrVb+Zm+gLVe/81Hezyu0qHqs1mY9iw\nYXTt2rVSl3/++eepU6fOORcm56dkK6joOY579hwOdHlhbe7huaUCFcCNG8cJB6mHU7G3LWzF/T66\nNyoQpZ43GzbSSPN1AZswkUACNmyBLq3K8sijDW3IpnCw5eG8vTzYZhGRv429dO7dS/a7H9Lu8CHq\nNS98voLhdKFDGUd9gepV08Euv6v06N+HH3640oEKKFADzNsKmjWrGcnJjZg1qxkrVkSHROsn1GVk\nl+4S9XLhwpHtqOGKqo8ZM+mkM4tZJJPMLGaxghWYMf8+3++tH5HZPpa9jRqR1bcv7iA9Q+BO7vQF\nKsBTd0LjIqUaAKMzlw3RV5OfVzjCORhmZbrQ2hpK9PIGy3nAtZGWfgtj4XCOYyiyRllJO5pWZrCa\nMGGNCs2u0fKYMWP/7T8v7wCeI2v3cb3nrxgowAPkf/UVe5tcQM4MB7ETewfVMb+NbCz2e9zGwiAt\nygBc4NrDZ/a1XLdwiO90oUCO/o21Wfj6jW98XcBVDXaNXvYvhaqIn9na2Eg7llaqC9iIkYQmCdja\nhF7XaFV5B/AM9LyEgQJfOBX+W0D+AyN554P/rfHBNBUFSDzx7GWv77Kb4+HivcWD1QP8zB84tOGY\nb1uBuYB/29fjsDuwYuVyLsVYsulYjYxmI1e8EUPWkmO491GlYAyW0cvhRKEq4mfmCDPpcelnHf0b\nzrwDeKI4WmZrL4qjARklW1GApJDCx3zs6wKelgJD/h80PllYswdwUp9N3EGn+FZA5c/TrW4R5gja\nj4imc+fOVbpeMIxeDjdapUbET4rOYJX6Rh62Vnfy1uVvsfDyhbx1+VvY29prRaDC78uqZdOakvN4\neaBwew1Pqn+21XIa0IDDHGYUo+hAB25uMIp23x/mgKkfOTTnB3rz/3gWc1Qjrk75I1DxebqhIFgX\nOwhlClURP/DOYDVp0nEWLMhh0qTjJCYeKTY1ZKhNG3k+9XoH8Kwz/AUPEb5g9QAeIljLAwEZJXu2\nAGlAAxaykO/5noUs5ILm0Viz1/LDqHfY3eEBOo3qwqTDt1OnQeGXo4rO0w0FWlPW/xSqIn5Q0QxW\nULnQDSbnW693AM+QVxPJHPkBrnaX44qox3Ha8SEvUGBqEJBRsucSIHUamLlu4RDu/v42rls4xBeo\nUHierqnEUbRQOk83GEYvh5uQCNV3332Xq666itjYWEaMGMGWLVsqvPzu3bsZPXo0cXFxDBw4kJSU\nFDye4PzwkvBQ0QxWcPbQDTb+qNc73++wt6+j0/7tXHI6hzqvfULn5NiATKpfHQFiw1YsWEPtPF0t\nduB/QR+qH3zwAY8//jjXXXcdr7zyCo0bN2bcuHHlLph+/PhxbDYbBoOBGTNmMHz4cGbMmMHcuXNr\nuHKpTazWur7FxL2KzmB1ttANNmer91y6hn0hO38wcfYuNf7BXR0BUtF5uqEi0M9LuAnq0b8ej4dX\nXnmF4cOHc8899wBwxRVXcPXVVzN//nymTp1a6jqLFi3C5XIxZ84c6tevz4ABA8jPzyclJYXk5GTM\n5tB5sUvouH10fZ7f9X/sqbsRz/aeGFfdQkJ8Y9/8vaE2bWRF9Va0AlKwTy5SHavllHWebrDxOJ2c\nTE3ltMNBPauVSJsNgz4Lq0VQt1R/+OEHDh06xODBg33bzGYzAwcOZN26dWVeJyMjg/j4eOrXr+/b\nduWVV3LixAm2b99e7TVL7eMscHLNf65i37DH8CR+gOH+J+j4f+NY9llzX8jYbJFYrfV8rdmi00YG\no4rqDbWu7NrO43RyODGRnydNImfBAn6eNInDiYl4nM6zX1mqLKhDdf/+/UDhJP5FXXTRRWRlZeF2\nu8u8TlmXL3p7IuU5l27NknP9eowu9tb/koU/zfNdJtSmjayo3lDryvYXj9NJdkoKx0aPJjslJWRC\n6eTcuZx2OCj6LejUuvWceP1Nv9y+bzrK0Z+zJWUnbmfpz2UI3cevqoK6+zcnJweAhg0bFtvesGFD\nCgoKOHXqFI0aNSp1nbIuX/T2qmrXrl3ndL1gderUKSD89qsildlnpxPGjzezebMBt9vAokX/5Y03\nfuKNN5xU1FP2ya+flHlaxbKsZfT/b/F19vr3x7f0Xk0sbHC+z3VZ9Xa42M2thg+J82xmEz15n1vw\nGE384Q+/smvXcb/UfT6q5fXtdGIaPx7D5s0Y3G7++9Yivp/yvxy7+0Uu/vOFRJgD2z6paJ+Nn3yC\nscS3IEOBmx1/S6NpQv/zqr3AWVBs2bn/LPqOr9/4hiveiCl+u9X0+AXjZ1lQt1S9I3YNhrK/zZe3\nvTwREUG9uxJgS5ZE+AIVwO02sHmzgSVLKn7dxNWJKzUtnREjcXXiqq3WgHE6GfnpWB73/J2b+IAn\neIL5jKZ39zPcdFNBoKurNhFLlvgCAcDgcdP4+C5OPj2fjPHbKXAG77574uLwGIq/PguI4NAvF5G1\n5PfpFp04WRy1mEeiH2Fx1GKcnL0lmbXkaLFl53DD8c3ZxW4XQvvxq6qgbqk2btwYgNzcXJo3b+7b\nnpubi9FoLNUiBWjUqBG5ubnFtnl/L9mqrayqTv0V7Lzf6sJtvypSmX3et+9H3O7ivRlut4F9+5rS\nuXPLcq/3WMFjrNmyxtcFbMJEQpMEHot7LOAzKPn7uc5+7TV+3rYFfmuZm3HRO2ITy8au44LYu/xy\nH+erOl7fx/btI6fE4aYICmju2cv+LSfJ32ggzh6491NF++x57DG2v/oh9Y9tJ4ICCojgZy5hv8dK\n132F1yk53eInTT5hTZs1Z51u8ft9R0otO4cb3PuK11Jdj18gP8s2bdpU5vagbrp5j42WPH3mwIED\ntG/fvszrtG/fnoMHD5a6PFDuouoiUPZpMRER0LdvxSN0vXP9zrLMIrl1MrMss1gRtyLggVodTmdk\nUPKAakSBC+eXGQGqqGbUs1op+eIoDKcOQT+tn8Fsxv34fDYbbmU//djMSNZyP5hMvokvznW6xcpO\nqBHKj19VBXWotm/fnujoaFauXOnb5nQ6WbNmDfHx8WVep1+/fmRkZJCXl+fbtnLlSpo0aUKnTp2q\nvWYJXTZbJFdcUTxACwrgnXdyzjpgyRxhxt7Wzvyu88N6jt+yPhwxmQq3h7FIm416ViueiMJuVF9r\nD2tITOsXO/5yXH8cztcmG/v4I5hMxSa+ONfpFis7oUaoP35VYXziiSeeCHQR5TEYDJjNZmbPno3T\n6SQ/P59nnnmGvXv38uyzzxIVFUVWVhb79u2jdevCJ6VDhw689dZbbNiwgaZNm/LZZ58xZ84c7r33\nXnr37l3lGo4cOUKbNm38vWsB9fPPPwPQokWLAFdScyqzz0ajgVOnCvj001PFth8+7KZNGyM9e9ar\n1hqrg7+f67qxsZxaswbXoUOF3zhMJuolJND8xRcxGINj0oDqeH0bjEYajxpFRKtoftiUx7d5V7CN\nP/vCaciL8UQYA9dGOds+Rxgj6DrqEhq1aUj9C+oSN6ELQ16M90308BM/8RmfUcDvxzZNmJjABHrS\ns9z7PdvtelXX4xfIz7LyssHgCYH5++bOncuCBQv49ddf6dy5Mw8//DBxcYWDQB555BE++OADMjMz\nfZffvn07Tz/9NDt27KB58+bceuut2M9xpe5NmzbRs2f5L6pQpGOq5Rs9+kcWLCg9Sjw5uRHz55d/\nXDVYVcdzHewTCVT36zsYF/U+330ueUzVO91idcwO5c/HL9DHVMvKhpAI1UBSqIaHyu5zSko2kyYd\nLzWT0KxZzbDbo6qzxGqh57p28Mc+O3GSSioOChdbt2EL+ukWgzFUg3r0r0hNs9kiSUvL9c0YFOwz\nH4n4SyhMtxgKFKoiRXhnEkpNPYnDcQartS42W2TQznwkIsFFoSpSgtlswG6P4hwPw4tILRbUp9SI\niIiEEoVqDTmXidpFRCS0qPu3BoTy+pMiIjUlGE9XqiqFag2oaP3JUDxNQ0TE39xON+8kLuOg4yge\nl4cdaXvYmbaHkelJ5x2sNRnW6v6tAbV1/cnqEg5d6U63h5Sd2Yz+/EdSdmbjdIfePhRV2TU1pfqF\n6nPxzdxMX6ACeFweDjqO8k1q5lmuWTFvWK+YtJ7/LPiOFZPW807ismp7XNRSrQFWa13S0nJKTShg\ntVY8UbuUFg5d6U63h8RlR3AcPY3LA2l7ckjbk0t6UjRmY2jsQ1HV2cKQqgnl5+JQxu+B6uWdbD/O\n3uWcb7eisD6f2y2PWqo1wGaLxGqt55uHXBMKnLuKutJDxdzMk75ABXB5wHH0NKmZobMPRVVXC0Oq\nLpSfi8queOPESQopjGZ0pdZ9rSisq4NCtQZ4JxSYNasZycmNmDWrGStWhE7LKpiEQ1d6xtEzlHiP\n/xasobMPRdX0h5aUL5Sfi8qseOOdo3gSk1jAAp6KforxF4+vMFgrG9b+olCtId4JBebPb4ndHqVA\nPUdlrXkaal3p1tZ1KfEex2Qo3B6KavpDS8oXys+F0WxkZHoSV81K4PLkS7lqVgIjVxTvti657qvb\n4GZzg80Vrvta2eXp/EWhKiElHLrSbZZIrK3r+YLVZICE1vWwWUJnH4qq6Q8tKV+oPxdGs5E4exeG\nzR9MnL1LqePAZa376ja4K1z3tTJh7U8aqCQhJRjm5nW6PaRmnsRx9AzW1nWxWSKrNMDIbDSQnhR9\nXrcRTLwfWqF+fmE4CPfnwoqVNNKKBavRY8RqsFZ4PW9YV8fApJK09NtZaOm38OCvfS45crew27Ze\n0I7c1XNdO9SWfS657qvRY6RHXg8cDR01vkydln4T8YOKRu7au2giD5HqZMZMOum+dV//cOQP3JR9\nE+bOwbPuq46pivzGWeAk5WAKo3eMJuVgCs6C0iMKw23krkio8a77Op/5jMgeEXQLqaulKkJhoCZu\nScRxorBbKe1oGmnH0kiPS8cc8fub1tq6Lml7cooFayiP3BUR/1JLVQSYe3iuL1ABXLhwnHCQerj4\nUP1wG7krIv6lUA0XBU7YlQKrRxf+W0bXpZQvI7v0UH0XLhzZxYfqe0fuzkpoRvKljZiV0IwVQTpI\nSURqnrp/w0GBE5YlwlEHeFywJ63wJykdIoLreEOwskZZSTtafKi+CRPWqNJD9c1GA/YuUdTA6Hyg\ncL7jQJ5CJCKVp5ZqOMic+3ugQuG/Rx2QWf4sI1KcrY0NaxMrpt++Z5owkdAkAVsbW0Dr8i4gMGnS\ncRYsyGHSpOMkJh4JyZV5RGoDhWo4OJrxe6B6eYNVKsUcYSY9Lp1Zllkkt05mlmUWK+JWFBuk5E+V\nXfotHBYQEKlN1P0bDlpbC7t7iwarwVS4XSrNHGHG3taOva29/AsVOAt7AI46Ch9fi63KXexVWfqt\nogUE7BWUKSKBoZZqOLDYCj/gDb99RzKYoHVC4XbxH++x6/WT4LsFhf8uS6zyoLCqLP0WDgsIiNQm\nCtVwEGEuHJSUMAsuTS78N2mFBin5m5+OXVdlAolwWEBApDZR92+4iDBDZ3vhj1SPio5dV+Fxr8oE\nEsGwgEB1c+L0TTtnxYoNW9DNkiNSWQpVkcry07FrmyWStD25xSblr2gCCe9avOF4DLXkBOlpv/2X\nTrqCVUKSun9FKstPx641gcTvSi467cKFA0eFi06LBDO1VEUqy3vs+jxH/0LNTyARrMpadNobrHbC\nsGkuYU8tVZGq8B67HjS/8F8NBjsvVn6fcMPLhAkrOh1MQpNCVc6P5hyW82DDVixYTZhIIAEbOh1M\nQpO6f+XchfKcw36YxEHOX8lFpzX6V0KdQlXOXUXnbQbzqT1lfRnY9gK07APR/RWwNcy76LSOoUo4\nUPevnLtQnXO4rC8DJ3fDnoVlz5KkLm4RqSSFqpy7oqeXeIXCnMNlfRnwKjlLkp+mJhSR2kGhKucu\nVOccLuvLQFFFW9taVk9EqkChKucuVOccLvlloKSire1Q7eIWkYDQQCU5PyEz57CT+vWXkJuzD5PJ\nSp1rPsGweyEcWQc/fgkn9wLu0q1tLasnIlWgUJWw5/E4uaDJeOrU2Ywz340zP418UxqNOqVj6Gyv\n+PQai60wVL1dwKHSxS0iAaFQlbDhdHtIzTyJ4+gZrK3rYrNEYjYayD8zlzp1NmMwuH+7pAu3y0H+\nmVTq1rNX3Nr249SEIhL+FKoSFpxuD4nLjvhWfknbk0PanlzSk6JxuTKKBKqXC5fLQd3KnBsZMl3c\nIhJoGqgkYWFu5klfoIJ30e/TpGaexGSy4vEYS1zDhMmk46Ii4l8KVQlZTqeHlJRsRo/+kXnr/lts\n0W/wBusZ6tS1kZ/fo0iwmjCaEqhTV8dFRcS/1P0rIcnp9JCYeASH4zQuFxj2AyOAIg1SkwGsreti\nMJj55cQb1K+/hBbNfxv9W9eGwaDjoiLiXwpVCUlz5570BSqAZz3QCyIugwIKAzWhdT1slsjfrmHm\n1KkRNGzUOUAVi0htoFCVkJSRccYXqEBhks6APn+tw2V/qlNs9K+ISE3RMVUJSVZrXUwlvhKaIsB2\naWPmD26JvUtU7QhUTfYvElQUqhKSbLZIrNZ6vmA1mSAhoR42W2TFVwwnmuxfJOio+1dCktlsID09\nmseXTB8AABmJSURBVNTUkzgcZ7Ba62KzRWI214LWqZef1rMtb9IMEam6oG+p7t69m9GjRxMXF8fA\ngQNJSUnB4/FUeJ3ly5djsVhK/SxcuLCGqpaaYDYbsNujmD+/JXZ7VO0KVPDLZP/eSTMmrT/Ogu9y\nmLT+OInLjuB0V/weE5GyBXVL9fjx49hsNi699FJmzJjBjh07mDFjBkajkXHjxpV7vW+//ZZ27drx\n3HPPFdvetm3b6i5ZgpDT7WHxkQi2ZBtI8mSHT0vMD5P9VzRphr1LlJ8LFgl/QR2qixYtwuVyMWfO\nHOrXr8+AAQPIz88nJSWF5ORkzOayzzPMzMyka9eudO/evYYrlmDjbYmtP2LCjYFPfjrum74w5IPV\nD5P9Zxw9U+6kGfYufq5XpBYI6u7fjIwM4uPjqV+/vm/blVdeyYkTJ9i+fXu518vMzMRisdREiRLk\nvC0xN4UBWrQlFvL8sJ6ttXVdTCW+W3gnzRCRqgvqUN2/fz/t2rUrtu2iiy7y/a0sOTk5HDp0iJ07\ndzJ06FC6du3KtddeyxdffFHd5UoQqqglFha8k/0Pml/4bxVXz7FZIrG2rucL1tKTZohIVQSs+9fp\ndJKVlVXu35s3b05OTg4NGzYstt37e05OTpnX2717Nx6Ph4MHD/LII49gNBpJS0tjwoQJpKam0q9f\nvyrXumvXripfJ5idOnUKqP79cnqcLMlbwpb8LcTVieOmBjdhruGpAf9ABEZMvpYqgBEPf+BXdu06\nXqO1BEJlnuv/7QhLGhUec46L8nBTqzPs2Z1dUyX6XU29voNJbdxnCM79DlioHjt2jGuuuabcvz/6\n6KMVXj8iouxG9iWXXEJKSgo9e/akUaNGAFitVq6//nrmzJlzTqEqVef0OBl/fDyb8zfjxs2yU8v4\n5NQnvNHsjRoN1ptaFfDJjx42Z4MbA0Y89Igq4KZWBTVWQ3VxFsCSY0XDsADzOfQ9mSNgRHQBI6L9\nX6NIbROwUG3bti2ZmZkVXubVV18lNze32Dbv797ALCkyMpIBAwYU22Y0GrniiitYunTpOdXauXN4\nzRfr/VZXnfv12sHX2HJkC24K1zF142ZL/hY2Rm7E3rZm1yV1dPLw9Be7C0f/WlqFxejfkuvHfvIT\nrMmpV2oAVk0818FG+1x7BHK/N23aVOb2oD6m2r59ew4ePFhs24EDBwDo0KFDmdfZuXMn7733Xqnt\np0+fpmnTpv4vUsqUkZ2Bi+LnULpw4ciu/DmU/mI2GhgRXcD0Tu6wmb6wolNhRCRwgjpU+/XrR0ZG\nBnl5eb5tK1eupEmTJnTq1KnM6+zatYupU6eyc+dO37bTp0+zdu1a+vTpU+01SyFrlBVTiY4QEyas\nUVoY3B/CfgCWSIgK6lC97bbbcDqd2O12Vq9ezZw5c0hJScFut1OnTh2gcMDS1q1b+eWXXwC4+uqr\nad++Pffffz+ffPIJq1atYuzYseTl5XH33XcHcndqFVsbG9YmvwerCRMJTRKwtdHC4P6gU2FEglNQ\nh2rLli1JTU3F5XJx33338e677/LAAw8Um01px44djBgxgjVr1gCFo4PnzZtHTEwMTz31FA8++CD1\n69dn4cKFREdrJEZNMUeYSY9LZ5ZlFsmtk5llmcWKuBWYq3jKh5RNp8KIBKegnlEJICYmhnfeeafc\nv/ft27fUgKfo6GhefPHF6i5NzsIcYcbe1l7jA5NqA7PRQHpStCbCFwkyQR+qIrVagbNw1ZmjjsI5\nfS023wQPZqMBe5coTScoEkQUqiJBpOgybAktIxi39xYijv02t++etMKfpPQqz5wkIjVDoSoSJEqe\ne9pgTxpjcBDB+a2XKiI1J6gHKonUJiXPPe3n2YyZ81svVURqlkJVJEiUPPfUQU+cnhKdSVVcL1VE\napZCVaSaOQvcpOzdwuivPiZl7xacBe4yL1fy3NNUbiHD0BO39yjNOayXKiI1S8dURaqRs8BN4trF\nOH46iAsPaT/sJC1rF+l/HIE5wljssjZLJGl7cn/vAjaY+cf/b+/+g6Mq7z2Of5bdTUISEmHiGCRK\n+LUBKWCKAdNlroERS4NOnXam/NMBInfSVEamttNSKi3O0IrtVBs7bakZJCPU9N46KnRuEC6S4YdJ\nqR2hpUM0gE1IAk0qeIHukmR/5Nw/1iyG/GA3nOyezb5fM4zDs+fsfp991M+ec57nnLv+W/tn7pf+\n1TBg9i8A6yFUkdyGWbJihp3Np8KBKkkBGar/uF3VLadUPr2w37ZDrT112L8hzf2GaTUBGD2EKpJX\nr1+qXR4K1FFastJw+UI4UPsEZKj+0oUBoSqx9hRIdFxTheUZhl893VXyetaop7tKhuE3542bdt4I\nVKn/khWTuHOmyKH+dzlyyCZ3zhTTPgOAdRCqsDTD8Mvz7+Xqur5eft8udV1fL8+/l5sTrB0NNwI1\n/IHmLlkpy58v95154WB1yKYld+apLH++aZ8BwDo4/QtL8/XsVDBQL4XXawYUDNTL11Ot1LTbvAFC\nrjt0uvezwWrykhXnOLsO/scqVbecUv2lC3LnTFFZ/vwBk5QAjA0cqcLSAoEG6eYbICigQMCEo8mC\nslCA2kZ3yYpznF3l0wv16qJHVT69kEAFxjCOVGFpDodbfl+N+gerQw5HZEeT/t6gqltOqbatUYXp\nk/RMr+tGqI1zhiYljeLsXwDJhVCFpaWklsnnq/nMKWCH7I4lSkm99dHkzWtEa6+26/DR/+u/RnSc\nM3QfXe6lC8AEnP6FpdlsTmVOOKjx6b+WM2W1xqf/WpkT/lc2262PJm9eIxqUwmtEAWA0EKqwPJvN\nqdS0cmVkvqrUtPKIAlUafo0oAIwGQhVjFmtEAcQaoYox6+Y1onZJ09Nzdax5sqoar8ofNIZ/AwCI\nEhOVMGZ9do3o/5xr1Kn/u1MfXZiuM8Z1/ddH11VzzquDKyfLabfd+s0AIAIcqWJM61sj+nn7A2q/\nMkNBI/SvfMCQ6ju6Vd10Lc4VAhhLCFUkhZPXbAredH01FKw9carohkiftwrA+jj9i6RQmG2o9l9G\nv2B12EIPBo+naJ63CsD6OFJFUvjKXb36fLYhx6eZ6rBJS3LTVFaQFde6hnveKoDEw5EqkoJznLRj\nnl/HbXf3ewB4vCcpRfu8VQDWRqgiaTjHSeVzrPUAcHfOFNWcb+wXrKylBRIXp3+BOOJ5q8DYwpEq\nEEc8b3UQvX6eHISERagCcda3lpZrqAoFau3yUKAagdBD5M/VhB7RR7AiAXD6F4B1NO28EahS6J8d\n9aEjVyABEKoArKOj4Uag9ukLViABEKoArCPXLdluuiplc4TagQRAqAKwjoKy/sFqc0i5S0LtQAJg\nohIA6xjnDE1KYvYvEhShCsBaxjmlOeWhP0CC4fQvAAAmIVQBADAJoQoAgEkIVcSFYfjV010lr2eN\nerqrZBj+eJcEALeNiUqIOcPwy/Pv5QoG6iUF5PfVyOerUeaEg7LZmOUJIHFxpIqY8/XsDAdqSEDB\nQL18PdyKDkBiI1QRc4FAg24EarhVgQC3ogOQ2AhVxJzD4dbAKw+OT9sBIHERqoi5lNQy2fsFq0N2\nxxKlpHIrOgCJjYlKiDmbzanMCQfl66lWIFAvh8OtlNQyJikBSHiEKuLCZnMqNa1cqeJWdADGDk7/\nAgBgEkIVAACTEKoAAJiEUAUAwCSEKgAAJkmYUPV4PFq6dKn2799/y219Pp+ee+45ud1uFRYWasOG\nDers7IxBlQCAZJYQoerxePTkk0/q4sWLEW2/ZcsW7d27V9/5zne0bds2ffjhhyovL1cwGBzlSgEA\nyczy61Tfe+89bdmyRZcvX45o+9bWVu3Zs0cvvPCCSktLJUmzZ8/WihUrdOjQIT3yyCOjWS4AIIlZ\n/kh1/fr1crlc2rFjR0TbHz9+XJJUUlISbsvPz9esWbN07Nix0SgRAABJCXCk+tprr8nlcqm9vT2i\n7Zubm5WTk6P09PR+7Xl5eWppaRlRDR988MGI9rOqrq4uSWOvX8Mxp89+jR//plKcJ+XzF6qr6yuS\nrH1rRcY6OSRjnyVr9jtuoer3+9Xa2jrk6zk5OcrOzpbL5Yrqfb1erzIyMga0Z2RkqKOjI+o6gRC/\nJt3xn0pJOSGbLajxabUan7pPn1zZIasHK4DYiVuodnZ2hq95DmbTpk1au3Zt1O9rGIZsNtugrw3V\nfitz5swZ0X5W1ferbqz1azi32+ee7pfVdf2kpNBkN5stqNTUk5o+7bhS06x7/2LGOjkkY5+l+Pb7\n/fffH7Q9bqGal5enpqYm0983MzNTXq93QLvX69WECRNM/7xk4Q8aqm66pvqOHrlzU1VWkCWnfWQ/\nUhLRcA9W56EAAPpYfqJStPLz83Xp0iV1d3f3a29vb9e0adPiVFVi8wcNLa/9p9a/e1m7znq0/t3L\nWl77T/mDRrxLixkerA4gEmMuVIuLixUMBlVXVxdua2lp0dmzZ1VcXBzHyhLXzqZrqu/oVuDTDA0Y\nUn1Ht6qbrsW3sBjiweoAImH52b+34vF4dO7cOd17772aNGmS7r33Xq1YsUI//OEP5fF4lJWVpRdf\nfFEFBQV6+OGH411uQmro6AkHap9QsPao/L741BRrPFgdQCQS/kj19OnTWrVqlQ4fPhxu27Ztm0pL\nS/Xzn/9cmzdv1uzZs1VVVSW73R6/QhOYOzdVjpsunzpsofZk0vdg9YzMV5WaVk6gAhggYY5Uh5rY\ntHjx4gHt6enp2rp1q7Zu3Rqr8sa0soIs1Zzzhk8BO2zSktw0lRVkxbs0ALCUhAlVxI/TbtPBlZOT\nevYvAESCUEVEnHabyu/LTpprqAAwEgl/TRUAAKsgVAEAMAmhCgCASQhVAABMQqgCAGASQhUAAJMQ\nqgAAmIRQhfy9flW1V2nN6TWqaq+Sv9cf75IAICFx84ck5+/1a/nJ5aq/Uq+AAqrpqFFNZ40OFh6U\ncxz3tgWAaHCkmuR2XtwZDlRJCiig+iv1qr5YHefKACDxEKpJruFqQzhQ+wQUUP3V+jhVBACJi1BN\ncu5stxw3XQVwyCF3tjtOFQFA4iJUk1zZ3WVy33EjWB1yaMkdS1R2d1mcKwOAxMNEpSTnHOfUwcKD\nqr5Yrfqr9XJnu1V2dxmTlJKQP2jweD/gNhGqkHOcU+V55SrPK493KYgTf9DQ8tp/hh9EX3POo5pz\nXh1cOZlgBaLA6V8A2tl0LRyokhQwpPqOblU3XYtvYUCCIVQBqKGjJxyofULB2hOfgoAERagCkDs3\nVY6bzvI6bKF2AJEjVAGorCBL7ty0cLA6bNKS3DSVFWTFtzAgwTBRCYCcdpsOrpzM7F/gNhGqACSF\ngrX8vmyV3xfvSoDExelfAABMQqgCAGASQhUAAJMQqgAAmIRQBQDAJIQqAAAmIVQBADAJoQoAgEkI\nVQAATEKoAgBgEkIVAACTEKoAAJiEUAUAwCSEKgAAJiFUAQAwic0wDCPeRVjZ+++/H+8SAAAWtHDh\nwgFthCoAACbh9C8AACYhVAEAMAmhCgCASQhVAABMQqgCAGASQhUAAJMQqgAAmIRQBQDAJIQqAAAm\nIVSTiMfj0dKlS7V///5bbuvz+fTcc8/J7XarsLBQGzZsUGdnZwyqNMeZM2e0Zs0aFRYWqqSkRFVV\nVbrVzcMOHDiggoKCAX9+97vfxajq6P3hD3/QI488ovnz52vVqlU6efLksNuP5Huxomj7XVFRMejY\ner3eGFVsnkOHDqmwsPCW242VsZYi77MVxtkRs09CXHk8Hj355JO6ePFiRNtv2bJFdXV12rhxo9LT\n0/Xiiy+qvLxcb775pux2+yhXe3suX76ssrIyzZo1S5WVlTp9+rQqKytlt9u1bt26Iff78MMPNXXq\nVP3sZz/r156XlzfaJY/IW2+9pS1btmj9+vWaN2+edu/erXXr1mnv3r265557Bmw/0u/FaqLttxQa\n29WrV2vlypX92sePHx+Lkk1z4sQJffe7373ldmNlrKXI+yxZZJwNjHl//vOfjRUrVhhFRUWGy+Uy\n3n777WG3P3/+vDF79myjtrY23Nbc3GwUFBQYBw4cGO1yb9tLL71kLFq0yLh+/Xq47Re/+IWxaNEi\nw+fzDbnfN7/5TeNb3/pWLEq8bb29vcbSpUuNH/3oR+E2n89nLFu2zNi6deug+4z0e7GSkfT76tWr\nhsvlMo4cORKrMk3X09NjVFVVGXPnzjWKioqM+++/f9jtx8JYR9tnq4wzp3+TwPr16+VyubRjx46I\ntj9+/LgkqaSkJNyWn5+vWbNm6dixY6NRoqkaGhpUXFzc79fpww8/rCtXrujvf//7kPs1NTWpoKAg\nFiXetvPnz+vChQtatmxZuM3pdKqkpGTIMRrp92IlI+l3U1OTJCXM2A7m6NGjqqqq0ve+9z19/etf\nv+X2Y2Gso+2zVcaZUE0Cr732ml566SVNmjQpou2bm5uVk5Oj9PT0fu15eXlqaWkZhQrN1dLSoqlT\np/Zr6zstOFT9Ho9HFy5cUGNjo774xS9q7ty5euyxx3TkyJHRLndE+voxWD9bW1sVDAYH3Sfa78Vq\nRtLvpqYmpaSkqLKyUosXL9aCBQu0YcMGffzxx7Eo2RTz5s3ToUOHtHr1atlstltuPxbGOto+W2Wc\nuaaawPx+v1pbW4d8PScnR9nZ2XK5XFG9r9frVUZGxoD2jIwMdXR0RF2nmSLps8fjGVB/3989Hs+g\n+505c0aGYai9vV3f//73ZbfbVVNTo4qKClVXV+vBBx80rxMm6OvHYP3s7e1VV1eXMjMzB+wT7fdi\nNSPpd1NTk3w+nzIyMvSrX/1KbW1tqqys1Jo1a7Rnzx6lpKTErP6Ruuuuu6LafiyMdbR9tso4E6oJ\nrLOzU6WlpUO+vmnTJq1duzbq9zUMY8hfhpH8YhxNkfR5OOPGDX5yZubMmaqqqtLChQvD/1N2u936\n8pe/rO3bt1suVI1PZ3GaNU5DfS9WM5J+r127VitXrgyPYVFRkWbMmKGvfe1r2rdvnx5//PHRK9iC\nEmWso2WVcSZUE1heXl74OoKZMjMzB52C7vV6NWHCBNM/LxqR9Pm3v/3tgPr7/n7zUUyfrKwsPfTQ\nQ/3a7Ha7vvCFL2jv3r23UfHo6BsHr9ernJyccLvX65Xdbh/0TMNg43qr78VqRtLvGTNmaMaMGf3a\nFixYoKysrFH578cKxsJYR8sq4zw2f7LgtuTn5+vSpUvq7u7u197e3q5p06bFqarI5efnq729vV9b\nW1ubJGn69OmD7tPY2KjXX399QHt3d7cmTpxofpG3qe96WV+/+rS1tSk/P3/QfUbyvVjNSPpdW1ur\nv/zlL/3aDMOQz+ez5NiaYSyMdbSsMs6EKgYoLi5WMBhUXV1duK2lpUVnz55VcXFxHCuLzIMPPqiG\nhgZdv3493PbOO+/ojjvu0OzZswfd54MPPtDmzZvV2NgYbuvu7tbRo0e1aNGiUa85Wvn5+Zo8ebLe\neeedcJvf79fhw4eHHKORfC9WM5J+//73v9dPfvIT9fb2htuOHDmi7u5uPfDAA6NeczyMhbGOllXG\n2f7ss88+G7NPQ1xdu3ZNu3bt0pe+9CXNnDkz3O7xeNTY2KiUlBSNHz9e2dnZOnfunF599VVNnDhR\nbW1t+sEPfqDc3Fxt2rTJ8tdkpk+frt27d+tPf/qTJk6cqP3792v79u166qmnVFRUJGlgn6dOnaoD\nBw7o7bffVk5OjlpbW/Xss8+qs7NTL7zwQtxPe9/MZrPJ6XTqN7/5jfx+v3w+n7Zt26Z//OMf+ulP\nf6rs7Gy1traqublZubm5kiL7XqxuJP2+8847VV1drZaWFmVmZurYsWP68Y9/rJKSEj3xxBNx7lH0\n3nvvPZ08eVIVFRXhtrE41p8VSZ8tM87xXCSL2Gpraxv05g/Hjx83XC6X8cYbb4TbvF6vsXnzZqOo\nqMhYuHCh8dRTTxkdHR2xLnnETp06Zaxatcr43Oc+Z5SUlBgvv/xyv9cH6/PFixeNp59+2iguLjYW\nLFhgPPHEE0ZTU1OsS4/KK6+8Yjz00EPG/PnzjVWrVhknTpwIv7Zx40bD5XL12/5W30uiiLbfdXV1\nxle/+lVjwYIFhtvtNp5//nmjq6sr1mWb4pe//OWAGyGM5bE2jMj7bIVxthlGgt4MEgAAi7H2eTwA\nABIIoQoAgEkIVQAATEKoAgBgEkIVAACTEKoAAJiEUAUAwCSEKgAAJiFUAQAwCaEKAIBJCFUAg6qr\nq1NBQYGeeeaZfu1lZWW6//77df78+ThVBlgXoQpgUMuWLVNpaaneeOMN/e1vf5Mkvf7662poaNC3\nv/3t8LNNAdzADfUBDOny5csqLS3VlClTtH37dq1cuVJz5szRrl27ZLPZ4l0eYDmEKoBh7dmzRxs3\nblReXp4++eQT/fGPf9Q999wT77IAS+L0L4BhPf7441q0aJHa29tVUVFBoALDIFQBDOvKlSv66KOP\nJIUmL/X29sa5IsC6CFUAw3r++ed17do1Pf300/rrX/+q3bt3x7skwLIIVQBDqq+v11tvvaV169ap\noqJCbrdblZWVunDhQrxLAyyJiUoABtXV1aVHH31UhmFo3759SktLU3Nzsx577DEtXrxYr7zySrxL\nBCyHI1UAg6qsrFR7e7s2b96stLQ0SdK0adO0bt06vfvuu9qzZ0+cKwSshyNVAABMwpEqAAAmIVQB\nADAJoQoAgEkIVQAATEKoAgBgEkIVAACTEKoAAJiEUAUAwCSEKgAAJiFUAQAwyf8DbJrWyJL5jJ0A\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a170ac88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your turn\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components = 2)\n",
    "x = pca.fit_transform(table)[:,0]\n",
    "y = pca.fit_transform(table)[:,1]\n",
    "for K in range(2,11):\n",
    "    fig, ax1 = plt.subplots(1,1)\n",
    "    fig.set_size_inches(7,7)\n",
    "    kmeans = KMeans(n_clusters = K, random_state = 10).fit_predict(table)\n",
    "    df = pd.DataFrame({'customer_name': table.index, 'cluster_id':kmeans, 'x':x, 'y':y})\n",
    "    for i in range(K):\n",
    "        color = cm.spectral(float(i) / K)\n",
    "        clustered_data = df[df.cluster_id == i]\n",
    "        ax1.scatter(clustered_data.x, clustered_data.y, color = color, marker = '.')\n",
    "    ax1.set_xlabel('x')\n",
    "    ax1.set_ylabel('y')\n",
    "    plt.suptitle(('Silhouette analysis for K-means clustering with K = %d' %K), fontsize = 14, fontweight = 'bold')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visually, it looks like K=4 might be best."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    customer_name  offer_id  n   campaign            varietal  min_qty  discount        origin  past_peak  cluster_id\n",
      "56         Thomas        26  1    October          Pinot Noir      144        83     Australia      False           0\n",
      "57         Thomas        14  1       June              Merlot       72        64         Chile      False           0\n",
      "206         Clark        11  1        May           Champagne       72        85        France      False           0\n",
      "282      Thompson        16  1       June              Merlot       72        88    California      False           0\n",
      "283       Collins        30  1   December              Malbec        6        54        France      False           0\n",
      "284       Collins        11  1        May           Champagne       72        85        France      False           0\n",
      "227         Kelly        31  1   December           Champagne       72        89        France      False           0\n",
      "194        Butler        28  1   November  Cabernet Sauvignon       12        56        France       True           0\n",
      "58         Thomas         1  1    January              Malbec       72        56        France      False           0\n",
      "195        Butler         1  1    January              Malbec       72        56        France      False           0\n",
      "223        Parker        16  1       June              Merlot       72        88    California      False           0\n",
      "222        Parker        11  1        May           Champagne       72        85        France      False           0\n",
      "221        Parker        29  1   November        Pinot Grigio        6        87        France      False           0\n",
      "220        Parker        31  1   December           Champagne       72        89        France      False           0\n",
      "196        Butler         4  1   February           Champagne       72        48        France       True           0\n",
      "192        Butler        22  1     August           Champagne       72        63        France      False           0\n",
      "80        Sanders        20  1     August  Cabernet Sauvignon       72        82         Italy      False           0\n",
      "224        Parker        20  1     August  Cabernet Sauvignon       72        82         Italy      False           0\n",
      "228         Kelly         6  1      March            Prosecco      144        86         Chile      False           0\n",
      "59         Thomas         4  1   February           Champagne       72        48        France       True           0\n",
      "61         Thomas        11  1        May           Champagne       72        85        France      False           0\n",
      "77        Sanders         9  1      April          Chardonnay      144        57         Chile      False           0\n",
      "76        Sanders         4  1   February           Champagne       72        48        France       True           0\n",
      "75        Sanders         1  1    January              Malbec       72        56        France      False           0\n",
      "74        Sanders        25  1    October  Cabernet Sauvignon       72        59        Oregon       True           0\n",
      "73        Sanders         6  1      March            Prosecco      144        86         Chile      False           0\n",
      "72        Sanders        26  1    October          Pinot Noir      144        83     Australia      False           0\n",
      "279      Thompson        30  1   December              Malbec        6        54        France      False           0\n",
      "60         Thomas         9  1      April          Chardonnay      144        57         Chile      False           0\n",
      "280      Thompson        25  1    October  Cabernet Sauvignon       72        59        Oregon       True           0\n",
      "68        Sanchez        20  1     August  Cabernet Sauvignon       72        82         Italy      False           0\n",
      "67        Sanchez         5  1   February  Cabernet Sauvignon      144        44   New Zealand       True           0\n",
      "66        Sanchez         4  1   February           Champagne       72        48        France       True           0\n",
      "65        Sanchez        15  1       June  Cabernet Sauvignon      144        19         Italy      False           0\n",
      "64        Sanchez        14  1       June              Merlot       72        64         Chile      False           0\n",
      "63        Sanchez        22  1     August           Champagne       72        63        France      False           0\n",
      "62        Sanchez        26  1    October          Pinot Noir      144        83     Australia      False           0\n",
      "281      Thompson         9  1      April          Chardonnay      144        57         Chile      False           0\n",
      "229         Kelly        32  1   December  Cabernet Sauvignon       72        45       Germany       True           0\n",
      "230         Kelly        20  1     August  Cabernet Sauvignon       72        82         Italy      False           0\n",
      "193        Butler        30  1   December              Malbec        6        54        France      False           0\n",
      "314         Gomez        20  1     August  Cabernet Sauvignon       72        82         Italy      False           0\n",
      "315        Cooper         4  1   February           Champagne       72        48        France       True           0\n",
      "316        Cooper        16  1       June              Merlot       72        88    California      False           0\n",
      "317        Cooper        32  1   December  Cabernet Sauvignon       72        45       Germany       True           0\n",
      "318        Cooper        20  1     August  Cabernet Sauvignon       72        82         Italy      False           0\n",
      "11        Jackson        11  1        May           Champagne       72        85        France      False           0\n",
      "10        Jackson         1  1    January              Malbec       72        56        France      False           0\n",
      "313         Gomez        32  1   December  Cabernet Sauvignon       72        45       Germany       True           0\n",
      "9         Jackson        15  1       June  Cabernet Sauvignon      144        19         Italy      False           0\n",
      "7         Jackson         2  1    January          Pinot Noir       72        17        France      False           0\n",
      "6          Martin        11  1        May           Champagne       72        85        France      False           0\n",
      "5          Martin        28  1   November  Cabernet Sauvignon       12        56        France       True           0\n",
      "4          Martin         2  1    January          Pinot Noir       72        17        France      False           0\n",
      "203         Clark        31  1   December           Champagne       72        89        France      False           0\n",
      "204         Clark        28  1   November  Cabernet Sauvignon       12        56        France       True           0\n",
      "205         Clark         4  1   February           Champagne       72        48        France       True           0\n",
      "8         Jackson        22  1     August           Champagne       72        63        France      False           0\n",
      "312         Gomez        11  1        May           Champagne       72        85        France      False           0\n",
      "311         Gomez        25  1    October  Cabernet Sauvignon       72        59        Oregon       True           0\n",
      "158         Young        32  1   December  Cabernet Sauvignon       72        45       Germany       True           0\n",
      "37         Fisher        11  1        May           Champagne       72        85        France      False           0\n",
      "36         Fisher         1  1    January              Malbec       72        56        France      False           0\n",
      "35         Fisher        28  1   November  Cabernet Sauvignon       12        56        France       True           0\n",
      "34         Fisher        30  1   December              Malbec        6        54        France      False           0\n",
      "33         Fisher        31  1   December           Champagne       72        89        France      False           0\n",
      "32         Fisher        22  1     August           Champagne       72        63        France      False           0\n",
      "31         Fisher         2  1    January          Pinot Noir       72        17        France      False           0\n",
      "153         Young        22  1     August           Champagne       72        63        France      False           0\n",
      "301         Lopez        15  1       June  Cabernet Sauvignon      144        19         Italy      False           0\n",
      "302         Lopez         9  1      April          Chardonnay      144        57         Chile      False           0\n",
      "303         Lopez        11  1        May           Champagne       72        85        France      False           0\n",
      "304         Lopez        16  1       June              Merlot       72        88    California      False           0\n",
      "305         Lopez        27  1    October           Champagne       72        88   New Zealand      False           0\n",
      "154         Young        31  1   December           Champagne       72        89        France      False           0\n",
      "155         Young         6  1      March            Prosecco      144        86         Chile      False           0\n",
      "156         Young        15  1       June  Cabernet Sauvignon      144        19         Italy      False           0\n",
      "157         Young         9  1      April          Chardonnay      144        57         Chile      False           0\n",
      "78        Sanders        11  1        May           Champagne       72        85        France      False           0\n",
      "79        Sanders         5  1   February  Cabernet Sauvignon      144        44   New Zealand       True           0\n",
      "197        Barnes        22  1     August           Champagne       72        63        France      False           1\n",
      "199        Barnes        10  1      April            Prosecco       72        52    California      False           1\n",
      "200        Barnes        21  1     August           Champagne       12        50    California      False           1\n",
      "201      Gonzalez        31  1   December           Champagne       72        89        France      False           1\n",
      "202      Gonzalez         9  1      April          Chardonnay      144        57         Chile      False           1\n",
      "198        Barnes        31  1   December           Champagne       72        89        France      False           1\n",
      "191       Morales        19  1       July           Champagne       12        66       Germany      False           1\n",
      "161        Rogers        22  1     August           Champagne       72        63        France      False           1\n",
      "189       Morales         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "166        Rogers        21  1     August           Champagne       12        50    California      False           1\n",
      "167        Howard        22  1     August           Champagne       72        63        France      False           1\n",
      "168        Howard        12  1        May            Prosecco       72        83     Australia      False           1\n",
      "169        Howard        11  1        May           Champagne       72        85        France      False           1\n",
      "170    Richardson        22  1     August           Champagne       72        63        France      False           1\n",
      "171    Richardson         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "172    Richardson         3  1   February           Espumante      144        32        Oregon       True           1\n",
      "173        Brooks        22  1     August           Champagne       72        63        France      False           1\n",
      "174        Brooks         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "175        Brooks        11  1        May           Champagne       72        85        France      False           1\n",
      "176        Brooks         3  1   February           Espumante      144        32        Oregon       True           1\n",
      "177         Price        22  1     August           Champagne       72        63        France      False           1\n",
      "178         Price        31  1   December           Champagne       72        89        France      False           1\n",
      "179         Price        30  1   December              Malbec        6        54        France      False           1\n",
      "180         Price         1  1    January              Malbec       72        56        France      False           1\n",
      "181        Foster        22  1     August           Champagne       72        63        France      False           1\n",
      "182        Foster        14  1       June              Merlot       72        64         Chile      False           1\n",
      "183        Foster        23  1  September          Chardonnay      144        39  South Africa      False           1\n",
      "184        Foster         1  1    January              Malbec       72        56        France      False           1\n",
      "185        Foster         9  1      April          Chardonnay      144        57         Chile      False           1\n",
      "186       Morales        22  1     August           Champagne       72        63        France      False           1\n",
      "187       Morales        31  1   December           Champagne       72        89        France      False           1\n",
      "188       Morales         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "190       Morales         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "207         Baker        31  1   December           Champagne       72        89        France      False           1\n",
      "265          Long         3  1   February           Espumante      144        32        Oregon       True           1\n",
      "209         Baker        10  1      April            Prosecco       72        52    California      False           1\n",
      "288       Edwards        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "289         Ortiz         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "290        Wright         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "291        Wright         4  1   February           Champagne       72        48        France       True           1\n",
      "292        Wright        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "293        Wright        21  1     August           Champagne       12        50    California      False           1\n",
      "294         Scott         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "295         Scott        14  1       June              Merlot       72        64         Chile      False           1\n",
      "296         Scott        23  1  September          Chardonnay      144        39  South Africa      False           1\n",
      "297        Garcia        14  1       June              Merlot       72        64         Chile      False           1\n",
      "298        Garcia        15  1       June  Cabernet Sauvignon      144        19         Italy      False           1\n",
      "299          Reed        14  1       June              Merlot       72        64         Chile      False           1\n",
      "300          Reed         5  1   February  Cabernet Sauvignon      144        44   New Zealand       True           1\n",
      "306         Reyes        23  1  September          Chardonnay      144        39  South Africa      False           1\n",
      "307         Reyes         9  1      April          Chardonnay      144        57         Chile      False           1\n",
      "308      Martinez        12  1        May            Prosecco       72        83     Australia      False           1\n",
      "309      Martinez        25  1    October  Cabernet Sauvignon       72        59        Oregon       True           1\n",
      "310      Martinez        28  1   November  Cabernet Sauvignon       12        56        France       True           1\n",
      "319          Ward         4  1   February           Champagne       72        48        France       True           1\n",
      "320         Allen         9  1      April          Chardonnay      144        57         Chile      False           1\n",
      "321         Allen        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "287       Edwards         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "208         Baker         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "286        Torres         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "165        Rogers        19  1       July           Champagne       12        66       Germany      False           1\n",
      "210         Baker        19  1       July           Champagne       12        66       Germany      False           1\n",
      "211        Nelson        31  1   December           Champagne       72        89        France      False           1\n",
      "212        Nelson         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "213        Nelson         4  1   February           Champagne       72        48        France       True           1\n",
      "214        Nelson         3  1   February           Espumante      144        32        Oregon       True           1\n",
      "215       Roberts        31  1   December           Champagne       72        89        France      False           1\n",
      "216        Turner        31  1   December           Champagne       72        89        France      False           1\n",
      "217        Turner         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "218        Turner         4  1   February           Champagne       72        48        France       True           1\n",
      "219        Turner        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "225        Nguyen        31  1   December           Champagne       72        89        France      False           1\n",
      "226        Nguyen        19  1       July           Champagne       12        66       Germany      False           1\n",
      "231          Wood        31  1   December           Champagne       72        89        France      False           1\n",
      "232          Wood        10  1      April            Prosecco       72        52    California      False           1\n",
      "233          Wood        14  1       June              Merlot       72        64         Chile      False           1\n",
      "234          Wood         1  1    January              Malbec       72        56        France      False           1\n",
      "243         Green         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "248        Murphy         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "249        Murphy        12  1        May            Prosecco       72        83     Australia      False           1\n",
      "263          Long         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "264          Long        10  1      April            Prosecco       72        52    California      False           1\n",
      "285         Jones         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "164        Rogers         3  1   February           Espumante      144        32        Oregon       True           1\n",
      "323        Powell         5  1   February  Cabernet Sauvignon      144        44   New Zealand       True           1\n",
      "162        Rogers         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "133         Davis        22  1     August           Champagne       72        63        France      False           1\n",
      "132        Miller        23  1  September          Chardonnay      144        39  South Africa      False           1\n",
      "131        Miller        15  1       June  Cabernet Sauvignon      144        19         Italy      False           1\n",
      "130        Miller        14  1       June              Merlot       72        64         Chile      False           1\n",
      "129        Miller        10  1      April            Prosecco       72        52    California      False           1\n",
      "128        Miller         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "127        Miller        31  1   December           Champagne       72        89        France      False           1\n",
      "126        Miller        22  1     August           Champagne       72        63        France      False           1\n",
      "121     Gutierrez        10  1      April            Prosecco       72        52    California      False           1\n",
      "120     Gutierrez         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "118     Gutierrez        18  1       July           Espumante        6        50        Oregon      False           1\n",
      "114          Ross        21  1     August           Champagne       12        50    California      False           1\n",
      "113          Ross        18  1       July           Espumante        6        50        Oregon      False           1\n",
      "82       Williams        18  1       July           Espumante        6        50        Oregon      False           1\n",
      "83       Williams        22  1     August           Champagne       72        63        France      False           1\n",
      "84       Williams        31  1   December           Champagne       72        89        France      False           1\n",
      "163        Rogers         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "134         Davis        12  1        May            Prosecco       72        83     Australia      False           1\n",
      "135         Davis        25  1    October  Cabernet Sauvignon       72        59        Oregon       True           1\n",
      "119     Gutierrez         8  1      March           Espumante        6        45  South Africa      False           1\n",
      "137         White        30  1   December              Malbec        6        54        France      False           1\n",
      "159         Evans        22  1     August           Champagne       72        63        France      False           1\n",
      "152          Hall        11  1        May           Champagne       72        85        France      False           1\n",
      "136         White        22  1     August           Champagne       72        63        France      False           1\n",
      "151          Hall        22  1     August           Champagne       72        63        France      False           1\n",
      "150        Harris        19  1       July           Champagne       12        66       Germany      False           1\n",
      "160         Evans        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "148        Harris         4  1   February           Champagne       72        48        France       True           1\n",
      "147        Harris         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "322       Ramirez         9  1      April          Chardonnay      144        57         Chile      False           1\n",
      "149        Harris        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "141           Lee         6  1      March            Prosecco      144        86         Chile      False           1\n",
      "146        Harris         7  1      March            Prosecco        6        40     Australia       True           1\n",
      "145        Harris        22  1     August           Champagne       72        63        France      False           1\n",
      "144           Lee         3  1   February           Espumante      144        32        Oregon       True           1\n",
      "138         White        14  1       June              Merlot       72        64         Chile      False           1\n",
      "139         White        25  1    October  Cabernet Sauvignon       72        59        Oregon       True           1\n",
      "143           Lee        27  1    October           Champagne       72        88   New Zealand      False           1\n",
      "142           Lee         4  1   February           Champagne       72        48        France       True           1\n",
      "140           Lee        22  1     August           Champagne       72        63        France      False           1\n",
      "256        Watson         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "255          Diaz         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "254          Diaz        30  1   December              Malbec        6        54        France      False           2\n",
      "253          Diaz        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "252          Diaz         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "86         Taylor         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "250        Bailey         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "242      Robinson        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "85         Taylor        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "247        Carter        13  1        May              Merlot        6        43         Chile      False           2\n",
      "257        Watson        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "246        Carter        30  1   December              Malbec        6        54        France      False           2\n",
      "245        Carter        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "251        Bailey        30  1   December              Malbec        6        54        France      False           2\n",
      "258        Hughes         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "268       Stewart        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "260        Hughes        30  1   December              Malbec        6        54        France      False           2\n",
      "278        Wilson         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "277        Wilson        30  1   December              Malbec        6        54        France      False           2\n",
      "276          Cruz        30  1   December              Malbec        6        54        France      False           2\n",
      "275          Cruz        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "241      Robinson         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "274       Bennett         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "273       Bennett        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "272        Morgan         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "271        Morgan        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "270       Stewart         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "269       Stewart        30  1   December              Malbec        6        54        France      False           2\n",
      "267     Hernandez        28  1   November  Cabernet Sauvignon       12        56        France       True           2\n",
      "266     Hernandez        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "262        Hughes        13  1        May              Merlot        6        43         Chile      False           2\n",
      "261        Hughes         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "259        Hughes        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "240         Lewis         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "244        Carter         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "238         Lewis         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "104        Rivera        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "105        Rivera         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "106         James        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "107         James         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "108         James        30  1   December              Malbec        6        54        France      False           2\n",
      "109         James         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "110         James        13  1        May              Merlot        6        43         Chile      False           2\n",
      "103          Hill        13  1        May              Merlot        6        43         Chile      False           2\n",
      "112         Myers        30  1   December              Malbec        6        54        France      False           2\n",
      "116      Sullivan         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "117      Sullivan        13  1        May              Merlot        6        43         Chile      False           2\n",
      "122         Perry        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "123         Perry        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "124         Perry        30  1   December              Malbec        6        54        France      False           2\n",
      "125         Perry         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "239         Lewis        30  1   December              Malbec        6        54        France      False           2\n",
      "115      Sullivan        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "102          Hill         8  1      March           Espumante        6        45  South Africa      False           2\n",
      "111         Myers        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "100          Hill        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "237         Brown        30  1   December              Malbec        6        54        France      False           2\n",
      "101          Hill        30  1   December              Malbec        6        54        France      False           2\n",
      "236         Brown        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "235         Brown         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "87         Taylor        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "88         Taylor        30  1   December              Malbec        6        54        France      False           2\n",
      "90         Walker        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "91          Perez        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "92          Perez        30  1   December              Malbec        6        54        France      False           2\n",
      "89         Walker        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "93           King        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "94           King         7  1      March            Prosecco        6        40     Australia       True           2\n",
      "95           King        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "96           King        13  1        May              Merlot        6        43         Chile      False           2\n",
      "97          Adams        18  1       July           Espumante        6        50        Oregon      False           2\n",
      "98          Adams        29  1   November        Pinot Grigio        6        87        France      False           2\n",
      "99          Adams        30  1   December              Malbec        6        54        France      False           2\n",
      "20       Peterson        23  1  September          Chardonnay      144        39  South Africa      False           3\n",
      "27            Cox         2  1    January          Pinot Noir       72        17        France      False           3\n",
      "25           Bell        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "24           Bell        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "23           Bell         2  1    January          Pinot Noir       72        17        France      False           3\n",
      "22       Peterson        27  1    October           Champagne       72        88   New Zealand      False           3\n",
      "21       Peterson         1  1    January              Malbec       72        56        France      False           3\n",
      "26           Bell        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "19       Peterson        10  1      April            Prosecco       72        52    California      False           3\n",
      "3       Rodriguez        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "17       Peterson         2  1    January          Pinot Noir       72        17        France      False           3\n",
      "16       Mitchell         1  1    January              Malbec       72        56        France      False           3\n",
      "15       Mitchell         2  1    January          Pinot Noir       72        17        France      False           3\n",
      "14       Campbell        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "13       Campbell        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "12       Campbell         2  1    January          Pinot Noir       72        17        France      False           3\n",
      "2       Rodriguez         2  1    January          Pinot Noir       72        17        France      False           3\n",
      "28            Cox        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "1           Smith        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "18       Peterson        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "29            Cox        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "55        Jenkins        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "38        Johnson        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "81        Russell        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "71           Gray        16  1       June              Merlot       72        88    California      False           3\n",
      "70           Gray        12  1        May            Prosecco       72        83     Australia      False           3\n",
      "69           Gray        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "54        Jenkins        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "53           Cook        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "52           Cook        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "51         Morris        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "50         Morris        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "30            Cox        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "49         Morris        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "47         Flores        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "46       Phillips        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "45       Phillips        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "44          Moore        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "43          Moore        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "42       Anderson        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "41       Anderson        24  1  September          Pinot Noir        6        34         Italy      False           3\n",
      "40        Johnson        26  1    October          Pinot Noir      144        83     Australia      False           3\n",
      "39        Johnson        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "48         Flores        17  1       July          Pinot Noir       12        47       Germany      False           3\n",
      "0           Smith         2  1    January          Pinot Noir       72        17        France      False           3\n"
     ]
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters = 4, random_state = 10).fit_predict(table)\n",
    "new_df = pd.DataFrame({'customer_name': table.index, 'cluster_id':kmeans})\n",
    "raw_data = df_transactions.merge(df_offers, on = 'offer_id')\n",
    "total_df = raw_data.merge(new_df, on = 'customer_name')\n",
    "total_df = total_df.sort_values(by = 'cluster_id')\n",
    "print(total_df.to_string())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cluster 3 seems to be entirely pinot noir, cluster 0 often cabernet sauvignon, cluster 1 is often a champange, prosecco or espumante (all sparkling wines).  Cluster 2 has a wide variety of wines but all minimum quantity of 6.  The variety within cluster 0 would seem to indicate that further clustering is warranted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Exercise Set V</h3>\n",
    "\n",
    "<p>As we saw earlier, PCA has a lot of other uses. Since we wanted to visualize our data in 2 dimensions, restricted the number of dimensions to 2 in PCA. But what is the true optimal number of dimensions?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Using a new PCA object shown in the next cell, plot the `explained_variance_` field and look for the elbow point, the point where the curve's rate of descent seems to slow sharply. This value is one possible value for the optimal number of dimensions. What is it?</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NCREREclGDh48SI0aNVL1+Y+Ojmbjxo0ULlw4Q4/GFhExk7pjiYiIZCNVq1bF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\nS35+Pu+//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SVbqa5du/amvn9JSQmrVq0yPy4qKmLJkiXm9SReXl6EhoaybNkycnJyzP0u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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a12aa550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your turn\n",
    "# Initialize a new PCA model with a default number of components.\n",
    "import sklearn.decomposition\n",
    "variance = []\n",
    "#as explained_variance is given as an array for n-components, find the mean for each # of dimensions\n",
    "for dim in range(2, 11):\n",
    "    pca = sklearn.decomposition.PCA(n_components = dim)\n",
    "    pca.fit(table)\n",
    "    variance.append(pca.explained_variance_.mean()) \n",
    "plt.plot(range(2,11), variance);\n",
    "plt.xlabel('Number of dimensions');\n",
    "plt.ylabel('Explained variance');\n",
    "plt.title('Explained variance across range of dimensions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, a clear elbow does not present itself.  If pressed, 5 dimensions would be chosen from this graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other Clustering Algorithms\n",
    "\n",
    "k-means is only one of a ton of clustering algorithms. Below is a brief description of several clustering algorithms, and the table provides references to the other clustering algorithms in scikit-learn. \n",
    "\n",
    "* **Affinity Propagation** does not require the number of clusters $K$ to be known in advance! AP uses a \"message passing\" paradigm to cluster points based on their similarity. \n",
    "\n",
    "* **Spectral Clustering** uses the eigenvalues of a similarity matrix to reduce the dimensionality of the data before clustering in a lower dimensional space. This is tangentially similar to what we did to visualize k-means clusters using PCA. The number of clusters must be known a priori.\n",
    "\n",
    "* **Ward's Method** applies to hierarchical clustering. Hierarchical clustering algorithms take a set of data and successively divide the observations into more and more clusters at each layer of the hierarchy. Ward's method is used to determine when two clusters in the hierarchy should be combined into one. It is basically an extension of hierarchical clustering. Hierarchical clustering is *divisive*, that is, all observations are part of the same cluster at first, and at each successive iteration, the clusters are made smaller and smaller. With hierarchical clustering, a hierarchy is constructed, and there is not really the concept of \"number of clusters.\" The number of clusters simply determines how low or how high in the hierarchy we reference and can be determined empirically or by looking at the [dendogram](https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.cluster.hierarchy.dendrogram.html).\n",
    "\n",
    "* **Agglomerative Clustering** is similar to hierarchical clustering but but is not divisive, it is *agglomerative*. That is, every observation is placed into its own cluster and at each iteration or level or the hierarchy, observations are merged into fewer and fewer clusters until convergence. Similar to hierarchical clustering, the constructed hierarchy contains all possible numbers of clusters and it is up to the analyst to pick the number by reviewing statistics or the dendogram.\n",
    "\n",
    "* **DBSCAN** is based on point density rather than distance. It groups together points with many nearby neighbors. DBSCAN is one of the most cited algorithms in the literature. It does not require knowing the number of clusters a priori, but does require specifying the neighborhood size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering Algorithms in Scikit-learn\n",
    "<table border=\"1\">\n",
    "<colgroup>\n",
    "<col width=\"15%\" />\n",
    "<col width=\"16%\" />\n",
    "<col width=\"20%\" />\n",
    "<col width=\"27%\" />\n",
    "<col width=\"22%\" />\n",
    "</colgroup>\n",
    "<thead valign=\"bottom\">\n",
    "<tr><th>Method name</th>\n",
    "<th>Parameters</th>\n",
    "<th>Scalability</th>\n",
    "<th>Use Case</th>\n",
    "<th>Geometry (metric used)</th>\n",
    "</tr>\n",
    "</thead>\n",
    "<tbody valign=\"top\">\n",
    "<tr><td>K-Means</span></a></td>\n",
    "<td>number of clusters</td>\n",
    "<td>Very large<span class=\"pre\">n_samples</span>, medium <span class=\"pre\">n_clusters</span> with\n",
    "MiniBatch code</td>\n",
    "<td>General-purpose, even cluster size, flat geometry, not too many clusters</td>\n",
    "<td>Distances between points</td>\n",
    "</tr>\n",
    "<tr><td>Affinity propagation</td>\n",
    "<td>damping, sample preference</td>\n",
    "<td>Not scalable with n_samples</td>\n",
    "<td>Many clusters, uneven cluster size, non-flat geometry</td>\n",
    "<td>Graph distance (e.g. nearest-neighbor graph)</td>\n",
    "</tr>\n",
    "<tr><td>Mean-shift</td>\n",
    "<td>bandwidth</td>\n",
    "<td>Not scalable with <span class=\"pre\">n_samples</span></td>\n",
    "<td>Many clusters, uneven cluster size, non-flat geometry</td>\n",
    "<td>Distances between points</td>\n",
    "</tr>\n",
    "<tr><td>Spectral clustering</td>\n",
    "<td>number of clusters</td>\n",
    "<td>Medium <span class=\"pre\">n_samples</span>, small <span class=\"pre\">n_clusters</span></td>\n",
    "<td>Few clusters, even cluster size, non-flat geometry</td>\n",
    "<td>Graph distance (e.g. nearest-neighbor graph)</td>\n",
    "</tr>\n",
    "<tr><td>Ward hierarchical clustering</td>\n",
    "<td>number of clusters</td>\n",
    "<td>Large <span class=\"pre\">n_samples</span> and <span class=\"pre\">n_clusters</span></td>\n",
    "<td>Many clusters, possibly connectivity constraints</td>\n",
    "<td>Distances between points</td>\n",
    "</tr>\n",
    "<tr><td>Agglomerative clustering</td>\n",
    "<td>number of clusters, linkage type, distance</td>\n",
    "<td>Large <span class=\"pre\">n_samples</span> and <span class=\"pre\">n_clusters</span></td>\n",
    "<td>Many clusters, possibly connectivity constraints, non Euclidean\n",
    "distances</td>\n",
    "<td>Any pairwise distance</td>\n",
    "</tr>\n",
    "<tr><td>DBSCAN</td>\n",
    "<td>neighborhood size</td>\n",
    "<td>Very large <span class=\"pre\">n_samples</span>, medium <span class=\"pre\">n_clusters</span></td>\n",
    "<td>Non-flat geometry, uneven cluster sizes</td>\n",
    "<td>Distances between nearest points</td>\n",
    "</tr>\n",
    "<tr><td>Gaussian mixtures</td>\n",
    "<td>many</td>\n",
    "<td>Not scalable</td>\n",
    "<td>Flat geometry, good for density estimation</td>\n",
    "<td>Mahalanobis distances to  centers</td>\n",
    "</tr>\n",
    "<tr><td>Birch</td>\n",
    "<td>branching factor, threshold, optional global clusterer.</td>\n",
    "<td>Large <span class=\"pre\">n_clusters</span> and <span class=\"pre\">n_samples</span></td>\n",
    "<td>Large dataset, outlier removal, data reduction.</td>\n",
    "<td>Euclidean distance between points</td>\n",
    "</tr>\n",
    "</tbody>\n",
    "</table>\n",
    "Source: http://scikit-learn.org/stable/modules/clustering.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Exercise Set VI</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Try clustering using the following algorithms. </p>\n",
    "<ol>\n",
    "<li>Affinity propagation\n",
    "<li>Spectral clustering\n",
    "<li>Agglomerative clustering\n",
    "<li>DBSCAN\n",
    "</ol>\n",
    "<p>How do their results compare? Which performs the best? Tell a story why you think it performs the best.</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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B2rdvn137xcTE6Pnnn9eGDRtSze3Zs0edOnVSjRo11KxZM3355Zdmlw0AAAAg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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e4a1ae97b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AffinityPropagation, SpectralClustering, AgglomerativeClustering, DBSCAN\n",
    "\n",
    "# Affinity propagation\n",
    "cluster_labels = AffinityPropagation().fit_predict(table)\n",
    "ap_score = silhouette_score(table, cluster_labels)\n",
    "\n",
    "fig, ax1 = plt.subplots(1,1)\n",
    "plot1 = ax1.axhline(y=ap_score, color=\"r\", label = 'Affinity propagation')\n",
    "\n",
    "#Spectral clustering\n",
    "sc_score = []\n",
    "for K in range(2,11):\n",
    "    clustering = SpectralClustering().fit_predict(table)\n",
    "    sc_score.append(silhouette_score(table, clustering))\n",
    "plot2 = ax1.plot(range(2,11), sc_score, color = 'b', label = 'Spectral clustering')\n",
    "\n",
    "#Agglomerative clustering\n",
    "ac_score = []\n",
    "for K in range(2,11):\n",
    "    clustering = AgglomerativeClustering().fit_predict(table)\n",
    "    ac_score.append(silhouette_score(table, clustering))\n",
    "plot3 = ax1.plot(range(2,11), ac_score, color = 'g', label = 'Agglomerative clustering')\n",
    "\n",
    "ax1.set_xlabel('K');\n",
    "ax1.set_ylabel('Silhouette score')\n",
    "ax1.set_title('Silhouette score for various K');\n",
    "ax1.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,\n",
       "       -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,\n",
       "       -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,\n",
       "       -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,\n",
       "       -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,\n",
       "       -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], dtype=int64)"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster_labels = DBSCAN().fit_predict(table)\n",
    "cluster_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the average silhouette scores, affinity propagation may perform the best out of the 4, however the score is still to low to surmise any structure.  Additionally, affinity propagation split the dataset into 13 clusters, which may be too many for practical purposes. The DBSCAN clustering gave all -1's as the cluster labels, indicating that the data is too noisy for this method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}