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": {},
   "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",
    "# 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": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Program Files\\Anaconda3\\lib\\site-packages\\pandas\\util\\_decorators.py:118: FutureWarning: The `sheetname` keyword is deprecated, use `sheet_name` instead\n",
      "  return func(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_offers = pd.read_excel(\"./WineKMC.xlsx\", sheetname=0)\n",
    "\n",
    "df_offers.columns = [\"offer_id\", \"campaign\", \"varietal\", \"min_qty\", \"discount\", \"origin\", \"past_peak\"]\n",
    "\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": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Program Files\\Anaconda3\\lib\\site-packages\\pandas\\util\\_decorators.py:118: FutureWarning: The `sheetname` keyword is deprecated, use `sheet_name` instead\n",
      "  return func(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\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>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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Smith</td>\n",
       "      <td>24</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Johnson</td>\n",
       "      <td>26</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "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": 26,
     "metadata": {},
     "output_type": "execute_result"
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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": 36,
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NaN count:  0\n"
     ]
    },
    {
     "data": {
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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>customer_name</th>\n",
       "      <th>offer_num_1</th>\n",
       "      <th>offer_num_2</th>\n",
       "      <th>offer_num_3</th>\n",
       "      <th>offer_num_4</th>\n",
       "      <th>offer_num_5</th>\n",
       "      <th>offer_num_6</th>\n",
       "      <th>offer_num_7</th>\n",
       "      <th>offer_num_8</th>\n",
       "      <th>offer_num_9</th>\n",
       "      <th>...</th>\n",
       "      <th>offer_num_23</th>\n",
       "      <th>offer_num_24</th>\n",
       "      <th>offer_num_25</th>\n",
       "      <th>offer_num_26</th>\n",
       "      <th>offer_num_27</th>\n",
       "      <th>offer_num_28</th>\n",
       "      <th>offer_num_29</th>\n",
       "      <th>offer_num_30</th>\n",
       "      <th>offer_num_31</th>\n",
       "      <th>offer_num_32</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Adams</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>1</th>\n",
       "      <td>Allen</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>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>2</th>\n",
       "      <td>Anderson</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>3</th>\n",
       "      <td>Bailey</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>4</th>\n",
       "      <td>Baker</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>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 33 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "  customer_name  offer_num_1  offer_num_2  offer_num_3  offer_num_4  \\\n",
       "0         Adams            0            0            0            0   \n",
       "1         Allen            0            0            0            0   \n",
       "2      Anderson            0            0            0            0   \n",
       "3        Bailey            0            0            0            0   \n",
       "4         Baker            0            0            0            0   \n",
       "\n",
       "   offer_num_5  offer_num_6  offer_num_7  offer_num_8  offer_num_9  \\\n",
       "0            0            0            0            0            0   \n",
       "1            0            0            0            0            1   \n",
       "2            0            0            0            0            0   \n",
       "3            0            0            1            0            0   \n",
       "4            0            0            1            0            0   \n",
       "\n",
       "       ...       offer_num_23  offer_num_24  offer_num_25  offer_num_26  \\\n",
       "0      ...                  0             0             0             0   \n",
       "1      ...                  0             0             0             0   \n",
       "2      ...                  0             1             0             1   \n",
       "3      ...                  0             0             0             0   \n",
       "4      ...                  0             0             0             0   \n",
       "\n",
       "   offer_num_27  offer_num_28  offer_num_29  offer_num_30  offer_num_31  \\\n",
       "0             0             0             1             1             0   \n",
       "1             1             0             0             0             0   \n",
       "2             0             0             0             0             0   \n",
       "3             0             0             0             1             0   \n",
       "4             0             0             0             0             1   \n",
       "\n",
       "   offer_num_32  \n",
       "0             0  \n",
       "1             0  \n",
       "2             0  \n",
       "3             0  \n",
       "4             0  \n",
       "\n",
       "[5 rows x 33 columns]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#your turn\n",
    "df = pd.merge(df_offers, df_transactions, on='offer_id', how='outer')\n",
    "df\n",
    "df = pd.pivot_table(df,columns='offer_id', index='customer_name', values='n', fill_value=0)\n",
    "df\n",
    "df.columns = ['offer_num_' + str(c) for c in df.columns]\n",
    "df\n",
    "df.reset_index(inplace=True)\n",
    "df\n",
    "print(\"NaN count: \", df.isnull().sum().sum())\n",
    "\n",
    "df.head()\n"
   ]
  },
  {
   "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": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beaa0307f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+/vjjDyxatKjWMG8oXbt2xYMHD7B//36l8zPl5eWIiIiAnp4ePDw81FpDffHwVAMLDQ1V/A906NAhuLq6QiaT4erVq0hOTkZRUREWLVqE4cOHK17j4eGBc+fOYdasWZg+fbri06VMJlP65O3t7Y2vv/4as2fPxtSpU9GpUyfk5OTg888/R8eOHTFq1CgAQMuWLdGkSRNkZGQgKSkJQ4YMQceOHXHhwgXcuHEDgwcPRps2beqch6+vL3JycvDFF1/gwoULGDt2LDp16oQ7d+7g0KFDuHHjBlxcXPDee+8pXrNq1Sp4eXlhxowZmDp1Krp164ZffvkFycnJ6NSpkyIw6zPn+qht3nWJjIzE77//DhsbG2RkZOC7776Di4sL3NzcAADm5uYICAhAZGQkJkyYgHHjxsHY2BgpKSk4f/48Jk+eDDs7O5XqBVTbzs/q3Lkz+vbti5MnT2Lp0qXo378/fv31VyQnJyv2lADA0NAQ/v7+CAsLg7e3N9zd3WFkZITTp08jMzMTPj4+eO211wBA8f74/PPPcfv2bYwbNw7+/v44duwY1q9frzgE++9//xtffPEFgD8vNVb1cFRNFi9ejMzMTAQHByM9PR29evXCtWvXsGfPHrRo0QKrVq1qsLGe5ufnhxMnTuDcuXP4+OOP6zwc96IMDQ3x0UcfYeHChZg0aRKmTp0KQ0NDpKSk4NKlSwgICICNjY3axleJdi/eejU9efJE7N27V3h6eoohQ4YIa2tr4eTkJIKCgsS5c+eqLV9ZWSkSEhLEyJEjhbW1tRgxYoTYunWr+P7776tdhnjlyhURFBQkhg4dKqytrcXQoUPFypUrlS5HFUKI+Ph4MWDAAGFjYyP2798vhPjPJYxnz56VPJdTp06JgIAA4eLiImxsbETfvn2Fl5eXOHDggKisrKy2/PXr18WSJUuEk5OTYi6hoaEiPz9fpTnXdRmtl5eXsLKyeu68a1L12gsXLggPDw9hY2Mj3nrrLRETEyPKysqqLX/48GExdepUYW9vL+zt7YWHh4f44osvREVFhWKZqktuDxw4UPdGrUF9tnNNtxG5e/euWLx4sXB0dBS2trbC09NTnDt3TsydO7fapc379u0TEydOFP369RO2trZi/PjxIjExUWkuBQUFws/PT/Tu3Vv069dPFBcXK9r/53/+R7i6ugpra2sxePBgMWfOnGqXgdf0u6lLbbctuX//vli9erV48803hbW1tXjzzTfFBx98UO0WKvUdr7bbiFS5ceOGcHBwEHK5XBw7dkzyelV14sQJ4enpKezs7ISdnZ2YNGmSOHTokNrHVYWeEDr81UMiNfH29sb58+fxv//7v9ouheilwnMaREQkGUODiIgkY2gQEZFkPKdBRESScU+DiIgke6W/p3H+/Hltl0BE9FLq27dvje2vdGgAtU9cF1y5cgUAYGVlpeVKNK8xzx1o3PPn3HV/7nV94ObhKSIikoyhQUREkjE0iIhIMoYGERFJxtAgIiLJGBpERCQZQ4OIiCRjaBARkWQMDSIikuyV/0Y4qaZbSIqGRrqm9hGyQ8eofQyixoJ7GkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyjYdGaWkpNm7cCGdnZ9jb28PHxweXL19W9AshEB0djeHDh8POzg4zZ85EVlaWpsskIqIaaDw01q9fj507d8Lf3x+bN29Gs2bN4OPjg5s3bwIAtmzZgujoaMyaNQvh4eEoKCiAr68vCgoKNF0qERE9Q6OhUVBQgL179yIoKAjTp0/HkCFDEBERgfLychw8eBCFhYWIj49HYGAgfHx8MGLECMTHx6OoqAj79u3TZKlERFQDjYZGs2bNkJSUhAkTJijaDAwMoKenh9LSUly8eBHFxcUYMWKEol8mk8HR0RGnTp3SZKlERFQDjYaGgYEBevXqBZlMhsrKSuTk5GDFihXQ09PDuHHjkJ2dDQDo3Lmz0uvMzMwUfUREpD0G2ho4KioKkZGRAID58+eje/fuSE1NhZGREYyMjJSWNTY2RmFhoUrjXLly5YVrVZeSkhIAul3jq0AXt29j/t1z7i/33LUWGq6urnB0dERGRgaioqJQVlaG1157DXp6ejUuX1s7ERFpjtZCo2fPngAAR0dHFBUVIT4+HsHBwSgtLUVZWRkMDQ0VyxYVFcHU1FSlcaysrBqkXnWo+rShmzVe03YBDUYXt69u/+7Vi3PX/bmfP3++1j6NntO4f/8+9u/fX+1Qk5WVFUpLSyGTySCEQG5urlJ/bm4uzM3NNVkqERHVQKOh8fjxY6xYsQLff/+9Uvvp06fRunVruLq6omnTpjh69Kii79GjR8jMzMSgQYM0WSoREdVAo4enevToATc3N2zYsAFlZWXo3Lkzjhw5goMHD2LdunUwMTGBl5cXIiIioK+vj27duiEmJgYmJiaYNGmSJkslIqIaaPycxoYNG7B582bExcXh3r17sLCwQEREBEaNGgUAWLRoEfT19ZGQkIDi4mI4ODggNDRU5XMaRETUcDQeGs2aNcOSJUuwZMmSGvsNDAwQHByM4OBgDVdGRETPw7vcEhGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJDOQuuDy5csxd+5cdOnSpVrf1atXERYWhpiYmAYtTpu6haRocLRral17dugYta6fiBqPOkPj3//+NwBACIGvvvoKbm5uMDY2rrbcjz/+iDNnzqinQiIi0hl1hsaiRYuQmZkJANDT08PcuXNrXdbe3r5hKyMiIp1TZ2isWrUK3377LYQQ2LJlCyZMmICOHTsqLaOvrw+ZTAY3Nze1FkpERNpXZ2j06NEDgYGBAIBbt25hzpw5NZ7TICKixkHyifD169ersw4iInoJSA6NoqIihIWFITU1FUVFRaisrFTq19PTw9///vfnrqeiogKJiYlISkrC7du30bFjR0yfPh2enp7Q09ODEAIxMTH48ssv8fDhQ/Tp0wcrV65Ejx496j87IiJqUPXa09i3bx/69euHTp06QV9fta94REVFIS4uDvPmzYO9vT3OnTuHdevWoaSkBP7+/tiyZQvi4uIQHByMTp06ITo6Gr6+vjh8+DBMTU1VGpOIiBqG5NA4evQo5s6diwULFqg8WGVlJbZt2wY/Pz/FlViDBg1CXl4eEhISMG3aNMTHxyMwMBA+Pj4AgH79+sHZ2Rn79u3DzJkzVR6biIhenOTdhT/++AOOjo4vNFhBQQE8PDwwcuRIpXZzc3Pk5eXh7NmzKC4uxogRIxR9MpkMjo6OOHXq1AuNTUREL05yaNjY2OCXX355ocFkMhlWrVqFXr16KbUfP34c7du3x927dwEAnTt3Vuo3MzNDdnb2C41NREQvTvLhqaVLlyIwMBBt2rRBv3790Lx582rLtG7dut4F7N27F2fOnMHKlStRWFgIIyMjGBkZKS1jbGyMwsLCeq8bAK5cuaLS614ljX0b6OL8S0pKAOhmberGub/cc5ccGn5+figpKcGKFStqXaa+G+Lrr7/Ghx9+CDc3N3h5eSE2NhZ6eno1LltbOxERaY7k0PDx8WnQP9zbt29HaGgoXFxcEBYWBj09PZiamqK0tBRlZWUwNDRULFtUVKTylVNWVlYqVqjemwhqkmrboLHPX72qPmDpYm3qxrnr/tzPnz9fa5/k0AgKCmqQYgAgPDwcsbGx8PDwwNq1a2Fg8GcZXbt2hRACubm5MDc3Vyz/7L+JiEg7JIfGrVu3nrvMs/elqsmOHTsQGxsLHx8frFixQmnvxcHBAU2bNsXRo0fh7+8PAHj06BEyMzMVtzMhIiLtkRwaLi4uzz089bxzGvfu3UNYWBjkcjnGjBmDixcvKvXb2NjAy8sLERER0NfXR7du3RATEwMTExNMmjRJaqlERKQmkkNj0aJF1dqKioqQkZGBnJwcvP/++89dx48//ojS0lL861//wpQpU6r1p6enY9GiRdDX10dCQgKKi4vh4OCA0NBQfhuciEgHSA6N2bNn19q3cOFCnD9/Hu7u7nWuY8KECZgwYcJzxwoODkZwcLDU0oiISEMa5BnhEyZMwLffftsQqyIiIh3WIKGRl5en+NIKERG9uiQfnjp8+HC1tsrKSty6dQvbtm2Dg4NDgxZGRES6p14nwqued/EsMzMzhISENGhhRESkeySHRmJiYrU2PT09mJiYoGfPnrzNBxFRIyA5NF70tuhERPTykxwaAHD37l1ERkbizJkzKCgoQMuWLTFw4EDMnTsXHTp0UFeNRESkIySHxp07d/Duu+8iPz8f9vb2eOONN3D37l3s378faWlpSE5ORrt27dRZKxERaZnk0Ni4cSMA4MCBA7CwsFC0X716FTNnzsSmTZuwdu3ahq+QiIh0huTvaZw6dQoBAQFKgQEAFhYWmDt3Lk6ePNngxRERkW6RHBolJSUwMzOrsc/MzAz5+fkNVhQREekmyYenunbtivT0dAwdOrRaX3p6uqTbohO9DLqFpGhwNPU+7Co7dIxa1/+q0dzvXv0POVPX717ynsakSZOQmJiIuLg43L9/HwBw//59xMXFYefOnRg/frxaCiQiIt0heU9j6tSpSE9PR3h4ODZu3Kj4drgQAs7OznXeBZeIiF4NkkOjSZMm2Lx5M86cOYP09HTk5+ejRYsWGDRoEJycnNRZIxER6YjnhkZlZSX27t2L1q1bw9XVFU5OTnByckJ5eTneeecdtG/fnqFBRNRI1HlOQwiBJUuWYPXq1Th9+rRS3/3795Gfn4+//e1vWL58uVqLJCIi3VBnaBw6dAgpKSlYsGABVqxYodTXoUMH/PDDDwgICMCBAweQmpqq1kKJiEj76gyNpKQkjB8/HnPmzIGhoWH1F+vrIzAwEM7Ozti1a5faiiQiIt1QZ2hcu3YNrq6uz13JmDFjkJWV1WBFERGRbqozNEpKStC8efPnrqRVq1YoKipqsKKIiEg31Rka7du3x7Vrz//m4rVr19CmTZsGK4qIiHRTnaExdOhQ7NmzB6WlpbUuU1paij179qBPnz4NXhwREemWOkPDy8sLt27dwrx583Dnzp1q/bdu3UJAQAB+//13eHp6qq1IIiLSDXV+ua9Lly6K72G4urrCysoKXbp0QXl5OXJycvDPf/4T+vr6WLlyJWxtbTVVMxERaclzvxE+ZswYdO/eHbGxsfjhhx/wj3/8AwBgamoKd3d3/Nd//Rd69uyp9kKJiEj7JN17ysrKCp9++ikA4OHDh2jSpAlef/11tRZGRES6R/INC6u0bNlSHXUQEdFLQPLzNIiIiBgaREQkGUODiIgkY2gQEZFkDA0iIpKMoUFERJIxNIiISDKGBhERScbQICIiyRgaREQkGUODiIgkY2gQEZFkDA0iIpKMoUFERJIxNIiISDKGBhERScbQICIiyRgaREQkmVZDIy0tDQ4ODkptQghER0dj+PDhsLOzw8yZM5GVlaWlComI6GlaC42ff/4ZS5Ysqda+ZcsWREdHY9asWQgPD0dBQQF8fX1RUFCghSqJiOhpGg+N0tJSbN26FT4+PjAwMFDqKywsRHx8PAIDA+Hj44MRI0YgPj4eRUVF2Ldvn6ZLJSKiZ2g8NE6ePIm4uDgsXboUXl5eSn0XL15EcXExRowYoWiTyWRwdHTEqVOnNF0qERE9Q+Oh0bt3b6SlpcHHxwd6enpKfdnZ2QCAzp07K7WbmZkp+oiISHsMnr9Iw2rXrl2tfYWFhTAyMoKRkZFSu7GxMQoLC1Xk/WTyAAANHklEQVQa78qVKyq97lXS2LdBY56/Ls69pKQEgG7W9ipR1/bVqUtuhRDV9j6q1NZORESao/E9jbqYmpqitLQUZWVlMDQ0VLQXFRXB1NRUpXVaWVmpWM01FV+ne1TbBo15/o157upX9QlYF2vj7/5P58+fr7VPp/Y0unbtCiEEcnNzldpzc3Nhbm6upaqIiKiKToWGg4MDmjZtiqNHjyraHj16hMzMTAwaNEiLlREREaBjh6eMjY3h5eWFiIgI6Ovro1u3boiJiYGJiQkmTZqk7fKIiBo9nQoNAFi0aBH09fWRkJCA4uJiODg4IDQ0VOVzGkRE1HC0GhpBQUEICgpSajMwMEBwcDCCg4O1VBVR49YtJEVDI6n3pHN26Bi1rr+x0qlzGkREpNsYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgyhgYREUnG0CAiIskYGkREJBlDg4iIJGNoEBGRZAwNIiKSjKFBRESSMTSIiEgynQ2NpKQkjBw5Era2tpgyZQouXLig7ZKIiBo9nQyNAwcO4MMPP8S4ceMQGRkJU1NT+Pn5IScnR9ulERE1ajoXGkIIbNq0CZMnT0ZgYCCGDRuG6OhotGzZEjt27NB2eUREjZrOhcb169dx8+ZNuLi4KNoMDQ0xfPhwnDp1SouVERGRzoVGdnY2AKBr165K7Z07d8aNGzdQUVGhhaqIiAgADLRdwLMKCwsBAMbGxkrtxsbGqKysRElJCUxMTCSv78qVKw1a38uosW+Dxjx/zr3xUtf8dS40hBAAAD09PUntz1NcXKxSHfsntVfpdbpIlW3QmOffmOcOvDrzb8xzB1T/2/c8OhcapqamAICioiK0adNG0V5cXAx9fX00b95c8rr69u3b4PURETVmOndOo+pcxrOX1+bk5MDc3LzeexpERNRwdC40unXrhg4dOuDo0aOKtrKyMpw4cQKDBg3SYmVERKRzh6f09PTg7++PNWvWQCaToU+fPti1axcePnwIX19fbZdHRNSo6YmqM8w6JiEhAYmJiXj48CGsrKywbNkyODg4aLssIqJGTWdDg4iIdI/OndMgIiLdxdAgIiLJGBpERCQZQ4OIiCRjaGgJHzIFpKWlNbor4ioqKrBt2zaMHj0a9vb2cHd3x65du9AYrkcpLS3Fxo0b4ezsDHt7e/j4+ODy5cvaLkvjSktLMXr0aISEhGi7FJUwNLSAD5kCfv75ZyxZskTbZWhcVFQUwsPDMW7cOERHR2P06NFYt24dPvvsM22Xpnbr16/Hzp074e/vj82bN6NZs2bw8fHBzZs3tV2aRm3evBnXrl3TdhmqE6RRlZWVwtnZWaxatUrRVlpaKlxcXMSaNWu0WJlmPHnyRMTFxQlra2vRv39/YW9vr+2SNKaiokI4ODiIjRs3KrWvXr1aDBw4UEtVacbjx4+FtbW1SEhIULSVlJQIW1tbsWXLFi1WplmXL18W9vb2YsCAAWLZsmXaLkcl3NPQsMb+kKmTJ08iLi4OS5cuhZeXl7bL0aiCggJ4eHhg5MiRSu3m5ubIy8tT211JdUGzZs2QlJSECRMmKNoMDAygp6eH0tJSLVamOeXl5VixYgX8/PzQrl07bZejMoaGhjX2h0z17t0baWlp8PHxaXQ3n5TJZFi1ahV69eql1H78+HG0b9++XndwftkYGBigV69ekMlkqKysRE5ODlasWAE9PT2MGzdO2+VpxNatW1FWVobZs2dru5QXonP3nnrVNfRDpl42L/MnLHXYu3cvzpw5g5UrV2q7FI2JiopCZGQkAGD+/Pno3r27litSv6ysLMTExGD79u0wMjLSdjkvhKGhYaKBHzJFL6+vv/4aH374Idzc3BrVoTpXV1c4OjoiIyMDUVFRKCsrw8KFC7VdltpUVlbi/fffx7vvvvtKXC3I0NCwhnzIFL28tm/fjtDQULi4uCAsLKxRfVjo2bMnAMDR0RFFRUWIj49HQEAADA0NtVyZeuzcuRO3bt1CbGwsysvLFe1CCJSXl8PA4OX6M8xzGhrGh0xReHg41q9fj/Hjx2PTpk0v/eEKKe7fv4/9+/crDs9WsbKyQmlpKfLz87VUmfodPXoUd+/ehaOjI6ytrWFtbY1//vOfOHDgAKytrZGbm6vtEuvl5Yq4V8DTD5kaMmQIgP88ZGr48OHaLY7UbseOHYiNjYWPj4/iRHBj8PjxY6xYsQIAMHHiREX76dOn0bp1a7Ru3VpbpandRx99hKKiIqW24OBgmJubIyAgAG3bttVSZaphaGgYHzLVeN27dw9hYWGQy+UYM2YMLl68qNRvY2Pz0h2qkKpHjx5wc3PDhg0bUFZWhs6dO+PIkSM4ePAg1q1bB339V/egR00n+l977TW0aNECvXv31kJFL+bVfIfqOE9PTzx58gSJiYnYvn07rKysEB8fj86dO2u7NFKjH3/8EaWlpfjXv/6FKVOmVOtPT09Hq1attFCZZmzYsAGbN29GXFwc7t27BwsLC0RERGDUqFHaLo3qgQ9hIiIiyV7dfUIiImpwDA0iIpKMoUFERJIxNIiISDKGBhERScbQINJxvMCRdAlDg6gW169fx7p16zBq1CjY29tj0KBB8PT0xMGDB1FZWQkAyM3NhaWlJeLi4hp8/Lt372L+/Pm4dOlSg6+bSFUMDaIapKSkYPz48Th16hSmTZuGyMhIrF69Gh07dsTSpUuxZMkSpZvPqcPp06fx/fffc0+DdAq/EU70jCtXriAkJAT9+/dHdHQ0mjZtquhzc3ND9+7d8emnn6Jfv34YOnSoFisl0jzuaRA9IzY2FhUVFVizZo1SYFTx8/PD1KlTa7zJXm2Hq1JSUmBpaYmMjAwAf56niIqKwqhRo2Bra4sBAwYgKCgIWVlZAIDIyEgsX74cADBlyhR4e3sr1nX27Fl4e3vDwcEBDg4OmD17Nn799Vel8SwtLbFx40b4+fnBzs4OPj4+L7ZRiP4f9zSInnHixAlYWVmhU6dONfYbGRnho48+AgCVb2v92WefYcuWLZg/fz5sbW1x7949REREYNasWUhNTcXEiRNRXl6OmJgY/Pd//zfs7e0BAGlpaQgKCkK/fv2wYcMGPHnyBAkJCZg6dSq+/PJLyOVyxRjx8fGYPHkyfH19FedgiF4UQ4PoKXl5eSgpKUGXLl3UOk5GRgbMzMwwe/Zsxe3RzczMcPz4cRQUFKBjx46KZ69YWlrC0tISQgisXbsWFhYWSEhIUNwR18XFBaNGjUJYWJjSHk6HDh2wcuXKV/oOsqR5fDcRPaVJkyYAgIqKCrWOM3ToUGRnZ8PDwwObN2/G+fPnYWdnh+Dg4FqfLZGdnY2bN29ixIgRAIDy8nKUl5ejadOmGD58ONLT01FWVqZY/i9/+QsDgxoc9zSIniKTyWBqalrtyYrPunXrFt544w2Vx5kxYwZkMhn279+PmJgYREZGokWLFpg8eTIWLlyoCK+n5eXlAQCioqIQFRVV43rz8vLQrl07AFB6nDBRQ2FoED1j2LBhSElJQW5uLszMzKr1V1RUYMqUKZDJZIiJiVHqqzrU9OyeyrOPOQUADw8PeHh4oKSkBOfOncPevXsRFxeH9u3bw9PTs9ryMpkMAODv7w83N7caa2/ZsqW0SRKpiPuuRM/w9/dHkyZN8OGHH+LJkyfV+qOjo3Hv3j1Mnjy5Wp+JiQkA4Pbt20rtVVdNVZkxYwYCAgIAAM2aNcPQoUOxZs0aAP85uf7soaXu3bujXbt2uHr1Knr37q30s2fPHiQmJsLQ0FDFWRNJwz0Nomf07NkTK1euxJo1azBx4kRMnToV3bt3R15eHg4fPoy0tDR4eHjA29sbN2/eVHqtTCZD//79ceDAAcjlcpibmyM1NbVaaAwePBiffPIJVq9eDRcXF5SVlWH37t0wMDDA6NGjFesCgNTUVBgaGsLa2hohISFYtGgR5s+fj7Fjx8LIyAjJycn47rvvsHTp0kbzzHHSHoYGUQ2mTZuGXr16YdeuXdi2bRsePHgAExMTdO/eHREREXBzc6v1D/SGDRuwbt06fPLJJ9DX18fw4cMRFham9Az42bNno1mzZkhKSsLBgwcB/PmM8Pj4eNja2gIABg4ciDfffBOJiYk4efIkDh06BHd3d8VhsaVLlwL4cw9kw4YN8PDwUO9GIQIf90pERPXAcxpERCQZQ4OIiCRjaBARkWQMDSIikoyhQUREkjE0iIhIMoYGERFJxtAgIiLJGBpERCTZ/wHVlJKxMUN5hQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2bea8b357f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn\n",
    "x_cols = np.matrix(df.drop('customer_name', axis=1))\n",
    "x_cols\n",
    "\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "SS = []\n",
    "\n",
    "for k in range(2, 11):\n",
    "    kmeans_cluster = KMeans(n_clusters = k, random_state=42).fit(x_cols)\n",
    "    SS.append(kmeans_cluster.inertia_)\n",
    "SS\n",
    "plt.plot(range(2,11), SS)\n",
    "plt.xlabel(\"Number of clusters\")\n",
    "plt.ylabel(\"Sum of squares error\")\n",
    "plt.show();\n",
    "\n",
    "\n",
    "kmeans_cluster = KMeans(n_clusters = 5, random_state=42).fit(x_cols)\n",
    "\n",
    "counts = [0 for i in range(5)]\n",
    "for i in range(5):\n",
    "     for label in kmeans_cluster.labels_:\n",
    "            if label == i:\n",
    "                counts[i] += 1\n",
    "\n",
    "plt.bar(range(5), counts)\n",
    "plt.xlabel(\"Cluster\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.title(\"Cust. Count per Cluster for K = 5\")\n",
    "plt.show();"
   ]
  },
  {
   "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": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Automatically created module for IPython interactive environment\n",
      "For n_clusters = 2 The average silhouette_score is : 0.09365573283492713\n",
      "For n_clusters = 3 The average silhouette_score is : 0.11889942863638556\n",
      "For n_clusters = 4 The average silhouette_score is : 0.12347053919571699\n",
      "For n_clusters = 5 The average silhouette_score is : 0.14092516241984757\n",
      "For n_clusters = 6 The average silhouette_score is : 0.1371798939109807\n",
      "For n_clusters = 7 The average silhouette_score is : 0.1161092456616906\n",
      "For n_clusters = 8 The average silhouette_score is : 0.11339573832632867\n",
      "For n_clusters = 9 The average silhouette_score is : 0.12505960527779877\n",
      "For n_clusters = 10 The average silhouette_score is : 0.11928332134753233\n"
     ]
    }
   ],
   "source": [
    "# Your turn.\n",
    "from __future__ import print_function\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_samples, silhouette_score\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "import numpy as np\n",
    "print(__doc__)\n",
    "\n",
    "range_n_clusters = [i for i in range(2,11)]\n",
    "\n",
    "# for n_clusters in range_n_clusters:\n",
    "#     # Create a subplot with 1 row and 2 columns\n",
    "#     fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "#     fig.set_size_inches(18, 7)\n",
    "\n",
    "#     # The 1st subplot is the silhouette plot\n",
    "#     # The silhouette coefficient can range from -1, 1 but in this example all\n",
    "#     # lie within [-0.1, 1]\n",
    "    \n",
    "#     ax1.set_xlim([-0.1, 1])\n",
    "    \n",
    "#     # The (n_clusters+1)*10 is for inserting blank space between silhouette\n",
    "#     # plots of individual clusters, to demarcate them clearly.\n",
    "    \n",
    "#     ax1.set_ylim([0, len(x_cols) + (n_clusters + 1) * 10])\n",
    "\n",
    "    # Initialize the clusterer with n_clusters value and a random generator\n",
    "    # seed of 10 for reproducibility.\n",
    "    \n",
    "for n_clusters in range_n_clusters:\n",
    "    \n",
    "    clusterer = KMeans(n_clusters=n_clusters, random_state=10)\n",
    "    cluster_labels = clusterer.fit_predict(x_cols)\n",
    "\n",
    "    # The silhouette_score gives the average value for all the samples.\n",
    "    # This gives a perspective into the density and separation of the formed\n",
    "    # clusters\n",
    "    \n",
    "    silhouette_avg = silhouette_score(x_cols, cluster_labels)\n",
    "    print(\"For n_clusters =\", n_clusters,\n",
    "          \"The average silhouette_score is :\", silhouette_avg)\n",
    "    \n",
    "\n",
    "\n",
    "#     # Compute the silhouette scores for each sample\n",
    "#     sample_silhouette_values = silhouette_samples(x_cols, cluster_labels)\n",
    "\n",
    "#     y_lower = 10\n",
    "#     for i in range(n_clusters):\n",
    "#         # Aggregate the silhouette scores for samples belonging to\n",
    "#         # cluster i, and sort them\n",
    "#         ith_cluster_silhouette_values = \\\n",
    "#             sample_silhouette_values[cluster_labels == i]\n",
    "\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.tab20c(float(i) / n_clusters)\n",
    "#         ax1.fill_betweenx(np.arange(y_lower, y_upper),\n",
    "#                           0, ith_cluster_silhouette_values,\n",
    "#                           facecolor=color, edgecolor=color, alpha=0.7)\n",
    "\n",
    "#         # Label the silhouette plots with their cluster numbers at the middle\n",
    "#         ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))\n",
    "\n",
    "#         # Compute the new y_lower for next plot\n",
    "#         y_lower = y_upper + 10  # 10 for the 0 samples\n",
    "\n",
    "#     ax1.set_title(\"The silhouette plot for the various clusters.\")\n",
    "#     ax1.set_xlabel(\"The silhouette coefficient values\")\n",
    "#     ax1.set_ylabel(\"Cluster label\")\n",
    "\n",
    "#     # The vertical line for average silhouette score of all the values\n",
    "#     ax1.axvline(x=silhouette_avg, color=\"red\", linestyle=\"--\")\n",
    "\n",
    "#     ax1.set_yticks([])  # Clear the yaxis labels / ticks\n",
    "#     ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])\n",
    "\n",
    "#     # 2nd Plot showing the actual clusters formed\n",
    "#     colors = cm.tab20c(cluster_labels.astype(float) / n_clusters)\n",
    "#     #ax2.scatter(x_cols[:, 0], x_cols[:, 1], marker='.', s=30, lw=0, alpha=0.7, c=colors)\n",
    "\n",
    "#     # Labeling the clusters\n",
    "#     centers = clusterer.cluster_centers_\n",
    "#     # Draw white circles at cluster centers\n",
    "#     ax2.scatter(centers[:, 0], centers[:, 1], marker='o',\n",
    "#                 c=\"white\", alpha=1, s=200, edgecolor='k')\n",
    "\n",
    "#     for i, c in enumerate(centers):\n",
    "#         ax2.scatter(c[0], c[1], marker='$%d$' % i, alpha=1,\n",
    "#                     s=50, edgecolor='k')\n",
    "\n",
    "#     ax2.set_title(\"The visualization of the clustered data.\")\n",
    "#     ax2.set_xlabel(\"Feature space for the 1st feature\")\n",
    "#     ax2.set_ylabel(\"Feature space for the 2nd feature\")\n",
    "\n",
    "#     plt.suptitle((\"Silhouette analysis for KMeans clustering on sample data \"\n",
    "#                   \"with n_clusters = %d\" % n_clusters),\n",
    "#                  fontsize=14, fontweight='bold')\n",
    "\n",
    "#     plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beac1af6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "\n",
    "scores = []\n",
    "\n",
    "#print(kmeans_cluster.labels_.reshape(-1,1))\n",
    "for k in range(2,11):\n",
    "    clusters = KMeans(n_clusters = k, random_state = 10).fit(x_cols)\n",
    "    \n",
    "    score = silhouette_score(x_cols, clusters.labels_)\n",
    "    scores.append(score)\n",
    "    \n",
    "plt.scatter(range(2,11), scores)\n",
    "plt.xlabel(\"Number of clusters\")\n",
    "plt.ylabel(\"Silhouette score\");"
   ]
  },
  {
   "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": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beac1af208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your turn\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = pd.DataFrame(PCA(n_components=2).fit_transform(x_cols))\n",
    "pca.columns = ['x','y']\n",
    "pca['cluster'] = pd.Series(KMeans(n_clusters=5).fit(x_cols).labels_)\n",
    "pca['name'] = df.customer_name\n",
    "sns.lmplot('x','y', data = pca, hue = 'cluster', fit_reg=False, size = 8, scatter_kws={'alpha':.6})\n",
    "plt.title('Clusters in PCA-derived 2d Space')\n",
    "plt.show()"
   ]
  },
  {
   "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": "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": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.4096489  0.30753551 0.2022926  0.16703717 0.15015248 0.1434373\n",
      " 0.13818887 0.12192294 0.11636172 0.10804271 0.09937813 0.09495961\n",
      " 0.08690352 0.07256738 0.0660996  0.06245473 0.05634388 0.05327395\n",
      " 0.04728801 0.04393911 0.03900424 0.03625783 0.03455714 0.03235091\n",
      " 0.02940632 0.02618221 0.02308167 0.02142632 0.018814   0.0165252\n",
      " 0.01426187 0.0077789 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beab3e0390>"
      ]
     },
     "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",
    "pca = sklearn.decomposition.PCA()\n",
    "pca.fit(x_cols)\n",
    "\n",
    "# Do the rest on your own :)\n",
    "\n",
    "print(pca.explained_variance_)\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(range(1, len(pca.explained_variance_) + 1), pca.explained_variance_)\n",
    "\n",
    "plt.xlabel(\"Component number\")\n",
    "plt.ylabel(\"Explained variance\")\n",
    "plt.xticks(np.arange(16))\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rate of descent slows sharply after 5.\n"
   ]
  },
  {
   "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": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0JTPHi3IAAEAzIYQAiFtTskbqrJ4DVHcQMTS2ZyYNCwEAaGEIIQDi2v2jLtEN3zxb3dp30FdhxFC39h10wzfP1h9GXRzL8gAAQBPQMR1A3JuSNVJTskbqYKBcu8oOqWdSJ/aAAADQghFCALQYnRMSCR8AALQCLMcCAAAA4ClCCAAAAABPEUIAAAAAeIoQAiBm3JAjtzQoN+TEuhQAAOAhNqYD8Jyz/bDs1btkry+RHEcyTVmDUmWN7CkzvWOsywMAAFFGCAHgKXvtbgVfL5Rc96uLjiM7b5/sdfvln9BP1oi0mNUHAACij+VYADzjbD9cM4BU5boKvl4op+iwp3UBAABvEUIAeMZevavuAFLBdcPjAABAq0UIAeAJN+SE94BEwM4vYbM6AACtGCEEgDeO2eFN6JFwHClgR7ceAECbcfjwYU2bNk3Z2dm67LLLJEn33nuvRowYodNOO02vvfaaBg0apF27IpuJnzt3rs4777zKv3/88cf66KOPolL7191+++3Kzc1tlq8VCoW0aNGiZvlajUUIAeCNdpZkRvgjxzSlBCu69QAA2oxXX31VK1eu1LPPPquHH35YmzZt0qJFi3TbbbdpyZIlOvfcc/XOO++oR48eEX29q6++Wn//+98r/z516lRt2bIlWuVHzeuvv6577703JvcmhADwhOEzZQ1MjWisNShVho8fTwCA5nHo0CF1795dQ4cOVVpamg4fDh+AcuaZZ+ob3/iGEhIS1L17d5kRvlmWnJysLl26VP7dbWi/Y5yKZd38lgcQsRNtLmjl9JQMo/5BhiFrZM8mfX0AQNu1bt06/eQnP9Fpp52mU045Reeff77++c9/6vbbb9cDDzygHTt2aNCgQXr55Zd1+eWXS5LOPfdc3X777Vq5cmW15Vjjx4/XE088oWuuuUbDhg3Tueeeq0ceeaTyXlWXY40fP16BQEC//OUv9aMf/Ui//e1vdeGFF1arbfPmzRo0aJA2btwY0fdSXFysm266STk5OTr99NN1ww03aO/evTXGfb3u2q4tX75c3//+9zV06FCNHj1av//97xUIBLRy5UrddNNNklT5XCTp/fff12WXXabs7Gydd955euihhxQMBiVJ27dv16BBgzR//nyNGjVKF1xwQeXHGosQAqBBzvbDCi4u0LE/rtaxuR/p2B9XK7ikoNFH6ZrpHeWf0K/uIGIY8k/sT8NCAECjlJWV6eqrr1bv3r314osvasmSJRo+fLh+9atfadasWbr22mvVs2dPvfPOO/rOd76jBQsWSJJeeOEF/epXv6r1a86ZM0fjx4/X4sWL9d3vflcPPfRQrfs+XnzxRSUkJOiOO+7Q3LlzdfHFF6ugoEDr1q2rHLNkyRINGzZMmZmZDX4vwWBQP/7xj1VUVKTHHntMTz31lHbv3q2f//znjX4u+/fv1w033KAf/OAH+r//+z/dd999+uc//6knnnhCI0aM0N133y1Jlc9l06ZNmjFjhiZMmKB//etfuuuuu/Tqq6/qvvvuq/Z1//Wvf+nZZ5/VH/7wB/n9/kbXJdGsEEADmru5oDUiTUaPpHDH9Hw6pgMATlx5eblyc3M1depUtW/fXpJ0zTXX6OWXX9aePXuUnJwsy7LUvXt3SVLnzp0lSV26dFHHjrX/3hk3bpwmT54sSbrhhhv07LPPau3atTrttNOqjatYltWxY0elpKQoJSVFAwcO1CuvvKLBgwfLdV298sor+slPfhLR9/Lee+9pw4YNeuONN5SRkSFJuueee7R48eJGzzrs2rVLwWBQvXv3Vnp6utLT0/WXv/xFHTt2VEJCQuX3XvFcHnvsMY0bN07Tp0+XJPXt21d33nmnZsyYoRtvvLHy61555ZURBar6EEIA1CnS5oJGj6RGhQczvaPM9I7yhY6fgpVgsQcEANBkXbt21Q9/+EO99NJLys/PV2FhofLy8iSFT4Bqiv79+1f7e4cOHSIOARdffLEWLVqkm2++WWvWrNGePXv0ne98J6LPLSgoUJcuXSoDiCRlZmbqF7/4ReTFHzdkyBBNmjRJM2bMUK9evTR69GhNmjRJ2dnZtY5fv3698vPzNWLEiMprruvKcRwVFhYqJSVFktSnT59G1/J1hBAAdWpMc8GmzGAYPlMifAAATlBxcbEuu+wy9ezZU2PHjtXYsWPVvXv3yuN4m6K2ZUaRbuT+3ve+pwceeECrV6/Wv/71L40bN67yBXxDEhISZDS0f/K42sZVDV2GYWjOnDkqKCjQf/7zH73zzjuaPn26pkyZojvvvLPG59q2rYsuuqhyJqSqtLS0yn0p7dq1i6i++vDbH0CtaC4IAGgp/v3vf6usrEx//etf9bOf/UznnHNOrRu5o+XrYaBbt24aM2aMXn/9dS1fvlwXX3xxxF9rwIAB2r9/v3bs2FF5LT8/X9/61re0e/fuamMrgtKRI0cqr1U9KvjTTz/Vvffeq6ysLM2YMUNPPfWUrr/++spN6F+vOzMzUxs3blTfvn0r/+zatUsPPPBAkzeg14UQAqB2NBcEALQQqampKi0t1dKlS1VUVKQ33nijctN1IBCI+v2TkpK0YcMG7du3r/LaJZdcohdeeEGu62rMmDERf61vf/vbOvnkk3Xrrbfqiy++UF5enu6++24NHjxYaWnV92BmZWUpKSlJjz76qLZu3aoVK1boySefrPx4p06d9Ne//lUPPvigtm7dqi+//FL//e9/NWzYsMq6Jemzzz5TaWmppk+frk8++USzZ8/Wpk2b9MEHH+iXv/ylAoFAnXtnmooQAqB2NBcEALQQ559/vq666ir9/ve/14UXXqi5c+fq5z//uXr16qXPP/886vefNm2annvuOU2bNq3y2rhx49S+fXt997vflc8X+Q4I0zQ1b948paam6sorr1Rubq7S09P1pz/9qcbYDh066A9/+IM+//xzfec739FDDz2k2267rfLj/fr109y5c7VixQp973vfU25urjIyMnT//fdLkkaOHKnTTz9dP/zhD/X8889r8ODBevTRR7V69Wp9//vf1y9+8QuNHj26cnxzMtyW2l0lij766KMaJx/gxFRsDhsyZEiMK2mbmvr8g4sLZK/b1+A4a0hX+b+f1aTa2gL+/ccWzz+2eP6xw7OPrf379+uss87Siy++qMGDB8e6nLjDxnQAdbJyesrO31//5nSaCwIAUKmkpEQffvihFi9erOHDhxNA6kAIAVCniuaCdR7TS3NBAACqCQQCuuOOO5SWlqaHH3642seuvfZarVy5ss7PtSxLq1evjnaJcYEQAqBeNBcEACByaWlptXZWl6S7775bR48erfNzIz2atzUghABoEM0FAQA4cV8/3aotI4QAiBjNBQEAQHPg1QQAAAAATxFCAAAAAHiKEAIAAADAU4QQAAAAAJ4ihAAAAADwFCEEAAAAaCI3ZMstLZcbsmNWw/PPP68JEyZo6NChmjx5stauXRuzWiLFEb0AAABAIzk7imWvyZOzYWtlI18zq6+sEUNk9u7uWR2LFy/WXXfdpZkzZyo7O1tPP/20pk2bpiVLligjI8OzOhqLmRAAAACgEexP1yv496Vy1heGA4gkOY6c/M0K/v3/ZH+63pM6XNfVQw89pMsvv1zXXXedxo4dq/nz5ys1NVWLFi3ypIamIoQAAAAAEXJ2FCu0/APJdWsf4LoKLf9Azo49Ua9ly5YtKioq0vjx4yuv+f1+nX322Xr77bejfv8TQQgBAAAAImSvyas7gFRwXdlr86JeS2FhoSSpb9++1a5nZGRo69atsu3Y7VNpCCEEAAAAiIAbssN7QCLgFGyJ+mb1I0eOSJKSk5OrXU9OTpbjOCovL4/q/U8EIQQAAACIxLHAV3tAGuI4UiAY1XLc4zMyhmFEdD2eEEIAAACASLRLkMwIXz6bppTgj2o5HTt2lCSVlpZWu15WVibTNJWUlBTV+58IQggAAAAQAcNnyTypT0Rjzay+MnxWVOup2Auybdu2ate3bdum/v37MxMCAAAAtAbWqSdLDb24NwxZI4ZEvZZ+/fqpV69eeuONNyqvBYNBvfXWWzrjjDOifv8TQbNCAAAAIEJm7+7ynTOq7mN6DUO+c0Z50rDQMAxNnz5dv/vd79S5c2edeuqpeuaZZ1RSUqLc3Nyo3/9EEEIAAACARrCGDpTRLVX22jw5BVti2jF9ypQpOnbsmJ566iktXLhQQ4YM0eOPPx7X3dIlQggAAADQaGbv7jJ7dw8fwxsISgn+qO8BqcvVV1+tq6++Oib3bipCCAAAANBEhs+SYhQ+WjI2pgMAAADwFCEEAAAAgKcIIQAAAAA8RQgBAAAA4ClCCICoc0OO3NKg3JAT61IAAEAc4HQsAFHjbD8se/Uu2etLKs9QtwalyhrZU2Z6x1iXBwAAYoQQAiAq7LW7FXy9sHo3WceRnbdP9rr98k/oJ2tEWszqAwAAscNyLADNztl+uGYAqcp1FXy9UE7R4ZofYukWAACtHjMhAJqdvXpX3QGkguvKXr2rclkWS7cAAGg7mAkB0KzckBMOEhGw80vC49fuVuDZL2Wv2xcOIFLl0q3AM1/KXrs7ihUDANB0bigop+yg3FAw1qVo+fLlGjFiRKzLiAgzIQCa1zH7qyDREMeRU3gwoqVbRo8kZkQAAHHD3lWgwGdLFdq8WnJsybTk65+jhKETZaVleV7PmjVrdMstt3h+36ZiJgRA82pnSWaEP1pMU/aneyJeugUAQDwIfPmmypb8TqGNK8MBRJIcW6GNH6hs8e8U+PJN72oJBPTYY49p6tSp8vlazvwCIQRAszJ8pqyBqRGNNbNS5Gw4ENHYiqVbAADEkr2rQMfeXii5dfxOch0de3uh7N0FntSzYsUKLViwQLfeequuvPJKT+7ZHAghAJqdldNTMoz6BxmGrOzujVq6pYB94sUBAHACAp8trTuAVHAdBT5d5kk92dnZWr58uaZOnSqjod+9cYQQAqDZmekd5Z/Qr+4gYhjyT+wvs1/nRi3dUoLVbDUCANBYbigY3gMSgdDmVZ5sVk9LS1OnTp2ifp/m1nIWjgFoUawRaTJ6JIWP3c2v+9hda2Bq+FSshr7eoFQZPt43AQDEjhso+2oPSEMcW26wXIbPH92iWihCCICoMdM7ykzvKF/o+FKqBKtGkLByesrO31//5nTDkDWyZ5SrBQCgfkZCkmRakQUR05LhT4x+US0UbysCiDrDZ8pI8tc6kxHx0i2O5wUAxJjh88vXf2REY339c5gFqQczIQBiLtKlWwAAxFrC0EkKbVpV/+Z0w1TC0IneFdUCEUIAxIVIlm4BABBrVlqW2o3JrfuYXsNUuzG5MWlY2JIQQgDEFcNnSoQPAEAcSzh5vKyuGQp8ukyhzaviomN6S0MIAQAAABrJSstS4nlZckPB8ClY/sSY7wGZNWuWZs2aFdMaIkUIAQAAAJrI8PljHj5aItY8AAAAAPAUIQQAAACApwghAAAAADxFCAEAAADgKUIIAAAAAE/FbQh5/vnnNWHCBA0dOlSTJ0/W2rVr6x1/zTXXaNCgQTX+lJaWelQxAAAAgEjE5RG9ixcv1l133aWZM2cqOztbTz/9tKZNm6YlS5YoIyOj1s/Jz8/X1KlTdcEFF1S7npiY6EXJAAAAACIUdyHEdV099NBDuvzyy3XddddJkr797W9r0qRJWrRoke68884an3Po0CHt3LlTY8aM0fDhw70uGQAAAEAjxN1yrC1btqioqEjjx4+vvOb3+3X22Wfr7bffrvVz8vPzJUmDBg3ypEYAAAAATRd3MyGFhYWSpL59+1a7npGRoa1bt8q2bVmWVe1j+fn5SkhI0IMPPqg333xTR48e1dixY/XrX/9a3bt3b1IdeXl5Tfo81K68vFxSnD5X25UZdOX4DckyYl1NVMT1828DeP6xxfOPLZ5/7LTGZz9kyJBYl1CDYwdlB8tk+ZNkWt53TrdtW0899ZSef/557dy5U71799YVV1yhKVOmyDDi93VN3IWQI0eOSJKSk5OrXU9OTpbjOCovL1eHDh2qfSw/P1+BQEDJycl6+OGHtW3bNj344IO66qqrtHjxYiUkJHhWP1oO/96AkteXK3H7Mcl1JcNQ+TfaqXRgkoLdvP8hAgAAWo5DKCo2AAAgAElEQVTSvQXaW7BUh4pWy3VsGaalzuk56jpwopK7ZnlWx7x587RgwQL97Gc/0/Dhw7V69Wrde++9Ki8v1/Tp0z2ro7HiLoS4ritJNZJbXdclKTc3VxdccIFGjRolScrJyVFmZqYuv/xyvfbaa7rooosaXUc8Ju2WrOJdmHh5rvba3Qq+Vyi5ktq1q7zefo+Uurdc/glpskakxay+5hZvz7+t4fnHFs8/tnj+scOzj559G99U0ZqFkutUXnMdWwe2faAD2z9U+qm56po5vu4v0Ewcx9GTTz6padOm6ac//akk6YwzztD+/fv1xBNPxHUIibs9IR07dpSkGkfrlpWVyTRNJSUl1ficzMzMygBSYdiwYerUqVPlfhGggrP9sIKvF4ZnP2rjugq+Xiin6LCndQEAgPhXuregRgCpxnVUtGahSvcVRL2Ww4cP66KLLtKECROqXe/fv7/279+vsrKyqNfQVHEXQir2gmzbtq3a9W3btql///61zoS8+uqrWrVqVbVrrusqEAgoNTU1esWiRbJX76o7gFRw3fA4AACAKvYWLK07gFRwHe1bvyzqtXTu3Fm/+c1vdPLJJ1e7/p///Ec9e/as9c37eBF3IaRfv37q1auX3njjjcprwWBQb731ls4444xaP+e5557TPffcI8f56h/Ef//7Xx09elQjR46Mes1oOdyQI3t9SURj7fwSuaEGfsgAAIA2w7GDOlS0OqKxB4tWybGDUa6ophdeeEHvvfeefvKTn3h+78aIuz0hhmFo+vTp+t3vfqfOnTvr1FNP1TPPPKOSkhLl5uZKkrZu3ar9+/dX9gS55pprNH36dN1yyy265JJLVFhYqDlz5mjixIk69dRTY/jdIO4csyUnwmDhOFLAlnxxl9UBAEAM2MEyuY4d0VjXseUEyz09MeuVV17RXXfdpYkTJ+rKK6/07L5NEXchRJKmTJmiY8eO6amnntLChQs1ZMgQPf7445Xd0ufNm6d//OMflfs9xowZo/nz5+uRRx7RzJkz1aFDB1166aW64YYbYvltIB61syTTjCyImKaUYDU8DgAAtAmWP0mGaUUURAzTkulP9KCqsIULF2r27NkaP3687r///rg+nleK0xAiSVdffbWuvvrqWj82e/ZszZ49u9q1cePGady4cV6UhhbM8JmyBqbKXrevwbHWoFQZzIIAAIDjTMuvTukjdXDbygbHdk7P8WwW5I9//KP+/Oc/66KLLtI999wjny9uX+JX4hUW2hwrp6fU0LsDhiFrZE9vCgIAAC1Gt4GTJKOBl9CGqa4DJ3pSz6JFi/TnP/9ZU6dO1ezZs1tEAJHieCYEiBYzvaP8E/rVfUyvYcg/sb/M9I6e1wYAAOJbctcspZ+aW/cxvYap9NNyPWlYWFxcrPvvv18DBw7UBRdcoE8++aTax0855ZS4DSXxWRUQZdaINBk9kmSv3iU7vyS8R8Q0ZQ1KlTWyJwEEAADUqWvmeLVPydC+9ct0sGhVzDqmv/POOwoEAlq/fr0mT55c4+Pvv/++unTp4kktjUUIQZtlpneUmd5RvtDxU7ASLPaAAACAiCR3zVLyGVly7GD4FCx/oqcnYUnSJZdcoksuucTTezYXQgjaPMNncgwvAABoEtPyex4+WgNeeQEAAADwFCEEAAAAgKcIIQAAAAA8RQgBAAAA4ClCCAAAAABPEUIAAAAAeIoQAgAAAMBThBAAAAAAniKEAAAAAPAUIQQAAABoItsO6tixg7LtYEzuHwgE9Kc//Unjxo3T8OHDNXXqVH3xxRcxqaUxfLEuAAAAAGhpDuxfry2bl6l45yo5ri3TsNSjV476DpiklNQsz+r43//9Xy1ZskQ333yz+vTpo6efflpTp07VK6+8ovT0dM/qaCxmQgAAAIBG2LZluT5873fateMDOa4tSXJcW7t2fKAP3/2ttm1Z7kkdhw8f1gsvvKBZs2bpiiuu0OjRozVnzhyFQiEtWbLEkxqaipkQAAAAIEIH9q9X3mcL5bpOrR93XUd5ny1Ux059oj4jkpiYqOeff77ajIfP55NhGAoEAlG994liJgQAAACI0JbNy+oMIBVc19GWTUujXovP59PJJ5+szp07y3Ecbdu2TXfccYcMw9D3vve9qN//RDATAgAAAETAtoMq3rkqorHFO1fJtoOyLH+UqwqbN2+e5s6dK0m6/vrrNWDAAE/u21SEEAAAACACoVBZ5R6QhjiuLTtU7lkIOffcc3X66adr5cqVmjdvnoLBoG688UZP7t0UhBAAAAAgAj5fkkzDiiiImIYly5foQVVhgwcPliSdfvrpKi0t1eOPP66ZM2fK7/cmBDUWe0IAAACACFiWXz165UQ0tkevnKjPguzZs0cvvfSSjhw5Uu36kCFDFAgEdODAgaje/0QQQgAAAIAI9R0wSYZR/0towzDVd8CkqNdy6NAh3XHHHVq2bFm16++++666du2qrl27Rr2GpmI5FgAAABChlNQsDcnOrfOYXsMwdXL2jz1pWJiZmamJEyfqvvvuUzAYVEZGhl5//XUtWbJE9957r0wzfucbCCEAAABAI2T0PUcdO/XRlk1LY94x/b777tPDDz+sBQsWqLi4WCeddJLmzJmjSZOiPxNzIgghAAAAQCOlpGYp5bQs2XYwfAqWL9Gzk7CqSkxM1C233KJbbrnF83ufCEIIAAAA0ESW5Y9J+Gjp4nehGIAWzw05ckuDckP1d5YFAABtCzMhAJqds/2w7NW7ZK8vkRxHMk1Zg1JljewpM71jrMsDAAAxRggB0KzstbsVfL1Qct2vLjqO7Lx9stftl39CP1kj0mJWHwAAiD2WYwFoNs72wzUDSFWuq+DrhXKKDntaFwAAiC+EEADNxl69q+4AUsF1w+MAAECbRQgB0CzckBPeAxIBO7+EzeoAALRhhBAAzeOYHd6EHgnHkQJ2dOsBAABxixACoHm0syQzwh8ppiklWNGtBwAAxC1CCIBmYfhMWQNTIxprDUqV4ePHDwAAbRWvAgA0Gyunp2QY9Q8yDFkje3pTEAAAUWbbQZUfOyjbDsa0jkAgoPPPP1+33357TOuIFH1CAJwQN+SE94O0s2Smd5R/Qr+6j+k1DPkn9qdhIQCgxdt9YL0+37pMW4pXyXFtmYalfj1y9M0+k5SWkuV5PQ8//LA2bdqkYcOGeX7vpiCEAGiS+rqiJ1x5cvhj+XRMBwC0Pnnbl+u9dQvlul8dyOK4tjbt/kCbiz/Utwfnasg3zvGsni+//FJPP/20UlMjWxYdDwghABotkq7o/u9nyRc6fgpWgsUeEABAq7D7wPoaAaQq13X03rqF6tKhjyczIqFQSHfccYemTZumf//731G/X3PhVQGARmlMV3TDZ8pI8hNAAACtxudbl9UZQCq4rqMvti71pJ7HHntMwWBQM2bM8OR+zYWZEACN0piu6Cy9AgC0JrYd1JbiVRGNLSxeJdsOyrL8Uatn48aNevTRR7Vw4UIlJCRE7T7RwNuTACJGV3QAQFsWCJXJcSNrtuu4tgJ2edRqcRxHv/rVr/Q///M/GjFiRNTuEy3MhACIXFO6orMUCwDQSiT4kmQaVkRBxDQsJViJUavl6aef1o4dO/TnP/9ZoVCo8rrrugqFQvL54vtlfnxXByC+VHRFjySI0BUdANDKWJZffXvkaPPuDxoc269HTlSXYr3xxhvavXu3Tj/99GrX161bp8WLF2v58uX6xje+EbX7nyhCCICIVXRFt9fta3AsXdEBAK3RKX0mqbD4w3o3pxuGqW/2mRTVOu6++26VlpZWu3bzzTerf//+mjlzpnr06BHV+58oQgiARrFyesrO31//5nS6ogMAWqm0lCx9e3Buncf0GoapMwf/OOrH8w4YMKDGtfbt2yslJUXZ2dlRvXdzIIQAaBS6ogMA2roh3zhHXTr00Rdbl6owTjqmtzSEEACNZo1Ik9Ejia7oAIA2Ky0lS2kpWbLtoAJ2uRKsxKjuAYnEkiVLYnr/xiCEAGgSM72jzPSOdEVHm+KGbOlYQGqXIMPHwQsAwpvVE2McPloiQgiAE2L4zFZxDK9ju7IDkpUgmZYR63IQZ5wdxbLX5MnZsLVy5s/M6itrxBCZvbvHujwAaHEIIQDatCO7He35LKQDhbZcRzJMKaW/pR6n+JSc1vLDFU6c/el6hZZ/UH0PlOPIyd8sZ32hfOeMkjV0YOwKBIAWiBACoM3amxfStneC1V5buo5UstHWgU22Mkb71W0IPybbMmdHcc0AUpXrKrT8AxndUpkRAYBG4G0+AG3Skd1OjQBSletK294JqnR3hB3i0SrZa/LqP45aklxX9to8bwoCgFaCEAKgTdrzWSiS15Yq/jzkTUGIO27IDu8BiYBTsCW8aR0AEBFCCIA2x7FdHSiM7AXjgc22HLuBtNKGuSFbbml563wBfiwQ3oQeCceRAsHo1gMArQiLnQG0OXYgvPcjEq4THm8mRremlqZNnBbVLkEyzciCiGlKCRzRCQCRIoQAaHOshPApWJEEEcMMj8dX2sppUYbPknlSHznrCxsca2b1pW8IADQCy7EAtDmmZSilX2QvGFP6W/QNqSLS06KcHXu8LSxKrFNPlowG/v83DFkjhnhTEAC0EoQQAG1Sj2xfJK8t1eMUJoyramunRZm9u8t3zqi6g4hhyHfOqNazBA1AowWdoA4GDivoxGZfWElJiQYNGlTjz/XXXx+TeiLFb1cArY5tuwoEw0v0rTpmMZLTTGWM9td5TK9hSBmj/TQsrKIpp0W1hiVK1tCBMrqlyl6bJ6dgS+vdAwOgUQoOFWpp0Qqt3vuZbNeWZVjK6TZUE9PHKKtTP8/qWLdunSTp8ccfV4cOHSqvp6SkeFZDUxBCALQau/c5+nxDSIVFthxXMg2pX7qlb/Z31aPDURkJSTJ8X20e7jbEp8Qupoo/D+nAZjqmN6gpp0W1ghAihWdEzN7dw6eAHU+4rSFgAWiaN3e+r4UbXpJTZXOh7dr6YM9afbj3E+WedKnG9zrDk1ry8/PVrVs3jR492pP7NRdCCIBWIW9TSO+uDarqpIYdOKoNXx7ShrVHlKOlyjI/la9/jhKGTpSVliUpPCPSPy1Bju3KDoQ3obMHpA6cFhUOHoQPoE0rOFRYI4BU5biOFm54SRnJvTyZEcnPz9egQYOifp/mFtHbfE899ZQOHToU7VoAoEl273NqBBC3/JCcAzvlHiuVK0OrNFF7nTSFNn6gssW/U+DLN6t9DdMy5E80CCD1qDgtKhKcFgWgtVpatKLOAFLBcR0tK3rbk3ry8/NVXl6uH/zgB8rOztZZZ52lxx57TG5D+/diLKIQMnv2bJ111lm67bbb9NFHH0W7JrRAtu2q/Kgrm6ZuiIHPN4SqB5DgUTlH9lUb48rUOp1+/C+Ojr29UPbuAu+KjGO2HdSxYwdl2w1vquS0KABtWdAJavXezyIau2rvp1HfrO44jjZu3KjNmzdr8uTJeuyxx3TBBRfoj3/8ox555JGo3vtERbQc680339SLL76ol19+Wa+88ooGDBigyZMn6/vf/746d+4c7RoRx+pag3/KST6ldWU9PaLPtl0VFlXv1u2W1z5zu02DZMuSJVtyHQU+XabE87K8KDMuHdi/Xls2L1PxzlVyXFumYalHrxz1HTBJKam1P5eK06LqPKaX06KahRuyw3tw2iUwowTEkbLQUdmu3fBAhfeIlIeOyR/Fpamu6+rRRx9V79691bdvX0nSqFGjVFZWpr/85S+aPn262rVrF7X7n4iIQkjPnj113XXXaebMmVqxYoVeeOEF/eEPf9ADDzygiRMnavLkyTrttNOiXSviTG1r8B1X2rTd1ubtts4c4deQAWw7QnQFguF/d5VcV+6x0lrHOrIUVDtZKpMkhTavkhsKVtus3lZs27JceZ8tlFtlSYHj2tq14wPt3vmhhmTnKqPvObV+LqdFRU+b6EQPtGBJvvayDCuiIGIZlhJ90Q0AlmXpjDNqboAfM2aM/va3v2nLli0aODA+m8c26hWiYRgaO3asxo4dq6KiIt1555165ZVX9M9//lNZWVn66U9/qvPPPz9atSKO1LYGvypX0rtrg+rS2WRGBFGV4A/PwFUGkXrW6Zqy5dexry44ttxgeZsLIQf2r68RQKpyXUd5ny1Ux0596p0R4bSo5tWqO9HbjtzScmZ20OL5Tb9GdsvWyj0fNzg2p9tQ+c3o/n7ZvXu33nrrLZ133nnq0qVL5fVjx8K/61JTU6N6/xPRqBDiuq5WrFihl156SW+99ZYcx9GkSZN07rnnavny5brppptUUFAQ981RcOK+vga/Nu7xcWldE7woCW2UZRnql25p0/bj70oZdYfeDOWHl2JVMC0Z/sQoVxh/tmxeVmcAqeC6jrZsWqqU0+pfrsZpUc0j0k70RrfUFjUj4uwoVuqHeWq/c68CCauZ2UGrMCn9LK3a+2m9m9NNw9TE9DFRryUQCOg3v/mNysvLlZubW3l92bJl6tevn7p3j9//ziIKIVu3btVLL72kxYsXq7i4WL169dLPfvYzXXbZZeratask6cILL5Tf79fTTz9NCGnlaluDX5fCIpvN6miSioaDPtOVbKPeo3NPOcmnzdvtcDA2DBntkmssyTLkaLA+rHbN1z+nzc2C2HZQxTtXRTS2eOcq2XZQltW2nlEsNKYTfUt58V4xs5NYXv7VxdYys4M2LatTP+WedGmdx/Sahqncky715HjejIwMXXjhhZozZ44Mw1BmZqaWLl2q119/vXVsTJ8wYYJM09RZZ52l3/72tzrrrLNk1HI6Sp8+fapNBaF1qrEGvx6OKwVC0a0HrUvFYQc7NoTU4YCrpFKpnd9QUqLUPctXaxPBtK6mzhzhr1wiaCR2qhZCDDk6XUvVTTu++iTDVMLQiR59V/EjFCqTE+GmSse1ZYfKCSENcI4GpMOlUsdkme0bP/PbGjvRt9aZHaDC+F5nKCO5l5YVva1Vez+Nacf0e+65R/PmzdOiRYu0Z88eZWZmau7cuTrnnNr39cWLiELItddeq8mTJ6tXr171jrvmmmt03XXXNUthiF811uDXwzSkBPamI0IVhx0kH3TVY68r4/i/sUDAVSAghb4M6cAmWxmj/eo2pPo/rCEDfOrS2Tx+Wlt7qUNX6cgeZWidBuvDGgGk3ZjcyoaFbYnPlyTTsCIKIqZhyfK1veVqkQp9sk72W6vk7twbfrFtGDJ6dZd1do58w8KNw8pCAe07ekxd27dTkq+OgNIKO9G3xpkd4OuyOvVTVqd+CjpBlYeOKdHXLup7QGrTvn173XTTTbrppps8v/eJiOjl4Y033hjRF/P7ebesLaixBr8e/dItWTR/QwQqDjtIOOqqS5UAUtWRMleWJW17J6jELmatMyJpXRPCS7lC7WXtPyT7810Kbd4tOZJMq0bH9LbGsvzq0StHu3Z80ODYHr1ymAWpQ/Cfb8l+d231F9quK3dHsULPvaY3Czfp750MbTx0UK5cGTJ0UucUXZE1WOPT+1b/Yq2sE31rnNkB6uM3/VE9hre14j1qNEm1Nfh1MI6PAyJRcdhBxwO1B5AK5cckv08q/jyk/mm1v7NsWYYSLUm9sqReWXJDwfApWP7ENrcHpDZ9B0zS7p0f1rs53TBM9R0wycOqWo7QJ+tqBpAq5n8jWYsDe+Ue8Mkww2/COHK1/sB+3b36fX2xf59mZZ9aOb6iE72zvrDBe7eITvStcGYHQPPj7FQ0ScUa/LrmOAxJo0/1czwvIlJ52IET3gNSn0DQlSvpwGZbToSHHhg+v8zETgSQ41JSszQkO1dGHSeJGYapk7N/XOvxvFW7qx8MHNWXJft0MHA02iXHFfutVXUGkLdS22lxWmL4DRrbluPYsu1jskNHZdvHFAod1d8LPtMLH/+r2ue1qk70FTM7kWgBMzsAooO3qdFk1dfg0zEdTVdx2IHpqN5ZEEmSG3795zqSHZBMtiw0SUbfc9SxUx9t2bQ0oo7pVburrwhl6H2nv46ovXT8rYhu7RN1RdZgXZF1cgy+G+84RwPhPSB1+HuvpMoZYle2nFo2z7muq78WrFNWaIOGjwwvd25Nnehb3cwOgKgghOCEVF+DH96Ezh4QNFblYQem5BoNBBEj/IaxYUoWLWhOSEpqllJOy5JtB8OnYPkSa90DUrW7+l9DpyrfTavyUVeSob1Hy/XQZ2u1dm+x/nDG2V59C947XFrnLEiZKW1OCv9adQ1XTj3/kPeYXfXFuoXq2j27sjN9a+pEb516cvh7qG9zejPN7LghO7wEjEaIQItCCEGzqFyDDzRB1cMOypJdJR+pe2yC35AhKaW/VWffEDSOZfnr3IBetbv6O3a/rwWQ8Lv6klt5bPvbO7fr8U9WaNqws6Jddmx0TA6n4FpeXJf4TFXshHDVQDNIGSpz22vd509XhhCp9XSirzazU5tmmNlxdhTLXpMX3gTfggMb0FaxXgZAXDjlJJ8MSYdSDLn1ZIvEduHXgD1O4T0UL1Ttrv6+0/+rD7gVAeT4X6v87+c2rte2Lcs9q7G5Vd338nVm+wQZvbrV+nmpIafyl2p9/4YlyZCrJJXrYEmBgoGyGh8PmY4O+YIKmRFu8I5D1tCB8k8+X+Xf6C73+AZ9mabMQf3ln3z+CTUqtD9dr+Dfl4aXfFVsgj/eCDH49/+T/en6E/8GAEQVv8UBxIWqDQf3d1Otx/R2SDaU4DeUMdpf43heNL+q3dXLbOv4HpAwt56z8Y6ovT76+Gl17NSn1s3t8arqvpf69shYZ5+u0HOv1ZgNSXKk/mUhbUxq+Fdrd2efEhSS60rHjpXIn5AkSSo4VKilRSu0eu9nMW1+1lzM3t1VkjNEsh0NHpDZLDM7NEIEWgdCCIC4YNuu+vW2lNLR0JebbO3YGFKHksg6piM6qnZXL1FS5XW3oSZ0kkrcdtqyaalSTmsZIaTqvpcKjmtr144PtHvnhxqSnVu5bMo3bJDcrTtrPab3BzvLdG9mp3rvZUgaGVgb/t+GoXbtUiVJb+58Xws3vCSnSg22a+uDPWv14d5PlHvSpRrf64zm+Ha9Z5kykto3PC4CNEIEWgdCCICY2r3PqfWEtXPOa6fUTqZ8hivZhqwEsQfEY1W7q6eq5pKh+qSoXMU7V8m2g3Hf8LDqvpfauK6jvM8WVpvZ8X/3bBl9eh3vmL6nsmP62Ymdta5LT71wsKjWsGZIGh78VAOdzZKkzqlZ8ickqeBQYY0AUpXjOlq44SVlJPdqkTMizYVGiEDrQQgBEDN5m0J6d22w2sIex5U2bbe1ebutM0f4NWRAzR9TQcdWWSikJJ9PfpMXGBVs263Yy9wsp9RV7a6eZNnq4ByttiSrLh10VElWOFTaofK4DyFV973UxXWdGjM7vmGD5Bs2SM7RgFRaJiUnyWyfoBsk9f74X/prwTrtMbse75fuqruzTyMDaysDiAxDg0/5kSRpadGKOgNIBcd1tKzo7TYdQmiEiHgU/p0UUJIvIWa/k95//3398Y9/VH5+vrp27aqLL75YM2fOlGXF779/QgiAmNi9z6kRQKpyJb27Nqgunc3KnjMFB0v0+rZCfbRnt2zXlWUYGtm9pyZk9NVJnVM9qz3e1DWb1Bz9eqp2Vz/T3KRlTu19QIwqjfbONDdJkkzDkuWL70YuVfe9NKSumR2zfYLUvvp50ZcNv1BZoQ36Yt1ClbntlaRyJSj01QDDUNbgy5XR9xwFnaBW7/0sohpW7f1UQScovxnfwS5qKhohRhJEaISIKCs4WKxl29fpo71bZbuOLMPUyO59NDF9iE7q7N1SwI8++kjTp0/XhRdeqJtuuklffPGF5syZI9M0dd1113lWR2MRQgDExOcbQvVsbQ5zj49L65qg/xRt1VPrv5RTZYmL7bpaWbxTq/bs0tSBJ2tcep+o1hyPmjqbFKmK7up5ny3Ut60tKnS7Kt/tUe1+hr4KIIOM3fq2tUWS1KNXTtzPglTd99IQx7UbNbMzfOSN6to9W+s+f1oHSwqOr9gy1Dk1S4NP+VHlHpOy0FHZEdZgu7bKQ8fkb6MvrmmEiHjx5o71WrR+ZbVDOmzX0criQn1YvEVXDfyWxvdu+glwjfHAAw/ozDPP1OzZsyVJZ5xxhg4cOKCVK1cSQgCgKtt2VVgU2YuuwiJb6/aX1AggVTmuq6fWf6mMDh3b1IxIU2aTmqJqd/Urd67SikBPvedkqtRICp+XrPASrDPNTZUBxDBM9R0wqcn39ErVfS8NacrMTkbfc8KzHYEyHTtWonbtUitPwqqQ5Gsvy7AiCiKWYSnR165RNbQ2XjZCBGpTcLC4RgCpypWrRetXqk9yatRnRPbv3681a9bokUceqXb95ptvjup9mwMhBIDnAsHwu/WRcFzp31u31hlAvhrn6vVtW9pUCGnsbNKJqNpdfWyoXDt3vK+1nz6nEredUlSuJOurF9CGYerk7B+3iON5q+57aciJzOz4E5JqhI/Kj5l+jeyWrZV7Pm7w6+R0G9p2l2IdV60RYm0/F5qhESJQn2Xb19V7TLkUDiLLivKiHkLy8/Pluq6SkpJ07bXX6t1331WHDh10xRVXaObMmTLN+D1NkhACwHMJ/vC+hUiCiGG4Wrt/V0Rfd/WeXQo6dpvYrN7Y2STbdptts7pl+dW3/0R1ThmgLZuWHu+roTr7asS7qvte6hLtmZ1J6Wdp1d5P692cbhqmJqaPiVoNLYk1dKCMbqmy1+aFZ0XomA6PBB1bH+2N7IS21Xu2Rv13UklJiSTp1ltv1YUXXqjc3FytWrVK8+fPV7t27TRjxoyo3ftEEUIAeM6yDPVLt7Rpa0imIzmmwqmkFr17SvbRyE7DsV1X5aGQ/AmtP4Q0djYpEJISqzwW2w4qECpTgi+pye/uV50dsUPlsnyJcb8HpDZV973UFkS8mNnJ6tRPuSddWucxvaZhKvekS9v2yVYwHX8AACAASURBVFhfY/buLrN3d7khWxXHwrEHBNFWFgrIbuAkuwq266g8FIzq76RgMChJGj16tG677TZJ0qhRo1RSUqL58+dr2rRpcXtCFiEEgOeO7HaUVuwqtDncFd01pLJkV4dSDAXafxVGDEnDBvr14meG7Aga5FmGoURf2/ix1pjZJNOQEo4/lt0H1uvzrcu0pfirruD9euTom30mKS2laS+yK2ZHWrKq+14a6pgeLeN7naGM5F5aVvS2Vu39tFV0TPeC4bM4hhee+f/s3Xt8VPWdP/7X51xmMrlfIIGGIQESJGBYuaQC2q+ICmx1V7/frb1Yi6hbH+3+iuu26Nq1F922uz62ttW6LZSuil3dR3XtRfvQB4qg4g0JFxUIQrjkQoSEWwJJJjPnfM7n98eQkJCZzOQyl0xez8eDPzjzSc6HIZlz3ufzfr8/6YYLutCiCkR0ocFjxPazMSMjAwDwuc/1XSVdtGgRnn32WTQ1NWHy5ORs2jI2rtZElDRO7rPR+I4FpYAsj0B7ZzAQyWgH0jsUTo8D2nOC/ZaunGuieJyBeeOLsK0lckrW/PETxkQqFtBrNelo5JSs0mIdui6w7+gmvPdJ/13BDzdvxZGWbVg0YyUqJl0Ty2kntWRY2SnPLkV5diksx4LP9sNjuMdkDYgjLUirE7qZDm2UB7iUWkxNx7xxk7HtRF3EsfPHT475Nak7wOheEelm28GW4L3bpyebpK1Wef7557F06VLMnj0bX/rSl7Br164Bxx84cAC33XYb5syZg8WLF2PdunUhd6slosRpb3Z6AhAASHML5GQJuFwCEIBQQMFJhak5Gv5msRszpgSfkyzzlkKL8EGqCYGl3pJY/xOSyqVlBiJdXsT5cc2tB/oFIL0p5eC9T9ajubV2xOc52ui6CZc7O6GrO6ZmItuVOeYCkI6Ttah//3Hs/dPfY99L/x/2/PFOHHnnZ2hv2ZfoqRH1WD6pok9r8lAEBJYVx75DW1lZGYqKirBhw4Y+x9966y0UFhaiuLg45nMYqqQMQv785z/jhz/8If72b/8Wjz/+OLKysnDnnXeisbEx5PhTp07h9ttvhxACjz76KL74xS/i0UcfxZNPPhnnmROlLikt+PxtkNKKPDiME7vtfs1sTEMgO0OgIFdDfq6GglwNU4Xo01K2LCcPK6bPDBuIaELgtumzxlRnLAAoKtBwxRwz7KWwezWpqEDDnobodgXf27BhwDFEsXLq0GYceuNHaGv8ADLQiUBHC3ynD6Fl7x+x909fx/5XVqPj1OgMkpUtoTp8wfoVGvXKcsbjtumXhw1EBARWTr88LhsWapqGb3/729i8eTN++MMf4v3338fPfvYz/OlPf2J3rMFSSuGXv/wlvvjFL/ZssLJo0SIsX74cTz/9NL73ve/1+5pnn30Wtm1jzZo18Hg8uOqqqxAIBLBu3TqsWLECpjm2niQRjaSRqiFwpEJrXfgLsEDPlhNoPSLhSAWtVzenq4snw5uZhdca67H9xHHumH5exVQD+TnagDumS2mhviW6XcHrWkLvCk4jx3IkOm0b6YYxZtIHI+k4WYumnesB5cD2n4PVefKiEQqtje/D19YA72e/gYJpS+I+x6GkiDmftkDu3AfnYAPgOFBCQJsyCfq8mdC9E2I8Y4qlJZ+ZjskZeXi1aR+2n0jsjuk33XQTDMPAb37zG/zxj3/ExIkT8dBDD+FLX/pS3OYwFEkXhNTX16OpqQlLllz4gDFNE4sXL8bbb78d8mvee+89LFy4EB7PhU2krr32WqxZswa7d+/G3LlzYz5volQ0kjUEMgBE2VAEygmO1y7aF64sJw9lOXmwHAmfbcPDmzgAwRWRogIXpFQI2MEi9N7teAO9dgWXSsCCARM2dNE/ZdVREgHpg4dByIirbTuD1xrrsONEM4Poi5ys3QAoB47tDxGAXGD7WtG0cz3Scr3IKIhPG+iOk7U4WbsBZ5u2QzkSQtORU1yFgunLBpyD/PhAz14mKmABvi7Ab8E5fhLO1o8gL5kCY9kVbCc8ipXljEdZzvjz1yQLHsNM2DXphhtuwA033JCQcw9V0gUhdXV1AICSkr653V6vFw0NDZBS9ms1VldXh8svv7zf+O7XhhKE7NvH/NOR5PP5APB9TZShvP+tvgbsaPotMMCGTJt2rUHbCRs5aZE7bygJdPmLBvp2Fwig9lAdRIrEF4n++XccG8d9aTjsFKNZjYcDAQ0KE8QJlGqNyBNne8YKaDhcWw9NS7rLw5Al+v0HgO1nz+DlU819fvyVUniz/iC2NBzG9QUTMD87NQORSO+/cmy0H3w7GIT4T0M54Z9WOP52SL0D+99/Fp5psX/KG2iphr/+L7j4g8tX+yaO174Fd8nfwFVY1e/rzFNnMf7tjwCloPkt6D5/3wFKwdl3CF1Hj+HMvEvQOWViTOafDD/7I62iIvZ1FoNlavqYaA0/0pIuUay9vR3AhZZj3TIyMuA4Ts8v1MVfE2p87+9HRIPT2PYeIkcMCg2t70f1/YQOmIVdUY01C7tSJgBJBjvbz6FaLcIxVQjnfA6zA4FPVSHel3PR4HymZ+z4zFkpFYAkg8auzj4BiOMEYAVOw9/1Kfxdx+HzfYo/H9uHg62HEzrPRFGyK7j8qRSUHekzQgFwYJ+pgXLsfq/ayka77ISt+r82WLK9IWQA0nsu/vq/QLb3r1fNPNQEKAVhy/4BSC9aVwC5Hx2Eefps2DFEqSrprjTdHa0ubikW7ngkQy3IScZIezTrfgrD9zUxBvv+S2nh/aYjSEtLizi2XR7G9OllUdUQdOQ7OPCSv19xem9CANMX5yKj6DPhB40yifz5r207g83H65GZno/WjmMhx9SoGRhnWigwOnDVnK8Oeb+QZJXoz5/Ne3bBff53KRA4i4D/FIC+1ydH+bGleQcu+0wavCWp1SY50vvvSAt7D2TAkQF0dQkgQtehtLR0CCEwfVoJjLRsAEDt2TpsaNqC7ad2j9j+KvXvvw4nzR1xXLZ9AJMrlvb8XdkSgVe3A2lpUG3nLhS7haBJB6bLjZJWP8wrRv7nM9E/+0QDSbqVkKysLABAR0dHn+OdnZ3QNA3p6en9viYzM7Pf+O6/Z2ZmxmimRKmrdw1BJN01BNHIKNLgvdIMe00WAvBeaSKjKOk+mkat1xrr4CgFQ09DZlpByDEKAofsz+CKGbenXACSaJYjseNEMwBA2l3o8p0KO/awysfuj59G65nR2QFqqDTdRHbxfAgR+fdeNzMghIDQdGhmsGhs87H38aOP/hMfnPgQsqf2SWLriV340Uf/ic3Holut7c2RFs42bY9qbFtTNZzeXQP9gWARulKAP0I3QaWCqVm19eycRWNO0l3pu2tBLm7H29jYiClTpoRcCSktLcXRo0f7jQeAqVOnxmimRKnLZaRDC5EPpZSC48g+e/BoQodL9/QbG864CgPT/9aNvGk6uu85hAbkTdMx/W/dGFeRdAu0o1bvG2AASHNlIzdjItxm3/RVt5mBzrTZmPaZq+I9xZTXaduQ539fAoGBU24caAgogfrDY69N8rjpywGhQ3dlDDiue+Ujp7gKmm6i9mwd1h/8A5wwXS8c5WD9wT+g9mzdoOYjrU4oJ7qgQDkSjtXrQYzbBWhaT4AxICGCfxwHCAy9/TnRaJR0V/vS0lJMnDgRr7/+Oq688koAwV0g33zzTSxevDjk1yxYsADPPfccOjs7e1ZKXn/9deTm5mLGjBnxmjpRytB1EyWFVTjSvBUAIG0//IE22FYHlApeMw0zA25XDqYWXzXodq4ZRRqmFLngSAUZAHQX+rTjpZHR+wa4m6GnIcuThqw0BQcONGg96SI+22Zx5QhLNwzoQkA6DiyrY8CxGhyYkGg5NvbaJGcUlKN47ko0blsLGQj9PpnpBdCMNEBoKJi+DACwoWlL2ACkm6McvNr09qDSsnQzHULTowpEeq/KAIAwdGhlkyH3Hwn+bg0UiLhdwewzTQNcY+f/mwhIwpUQIQS+/vWv4/e//z1+8Ytf4K233sI//MM/4MyZM1i5ciUAoKGhAR9++GHP19xyyy2wLAt33XUX3njjDaxZswbr1q3DXXfdBZfLlaB/CdHodunk5RBCQyBwDh0dn8IKdPRcS5UCrEAHOjqOYZw59I4+mi5gegQDkBjpvgEOSYjgatf513Uh4DGS7rnUqGdqOuaNL4JC5P7UU8QpGELBURLSji7FMZUUTFuC8qU/Qe7kRehdF6KbGXBnTYThzgaEhuJ5K5FRUA7LsbD95O6ovnf1yY9hOdGvNHSniEWje1WmN33uTAhNA9wDBxYiPVgrpJWXQBh8AEBjS9IFIQDw1a9+Fffddx9efPFF3H333Th37hyeeOKJnra7v/71r/tswFJYWIinnnoKtm3j7rvvxvPPP4977rkHd955Z6L+CUSjXlFuOf5q0jJ0+U6FfJAnAEw08nH80KtjLod9tOi+AY7G/PETuOdKjCzzloZMb+xNQGG2FmwcoAkduhF9imMqySgoxyV//VPM/L+/RdHM/wdP/lS4MguhuzKQ612AaUu+j4KpwX3EOu2unhqQSKSS8Nnhu1SFEkwRi3Cb1GtVpjftM+NhXLMASA///yiyMwHTAISAPoeF4zT2JO1jrzvuuAN33HFHyNcefvhhPPzww32OVVZW4ve//308pkY0ZpgdZzDFnIBT8izOyg4oBIOPbD0DBXo20rU0KOWg/vAG5M5jQXMyWuYtxfYTzXAGSAnRhMBSb0nY12l4ynLycNsls7B2VwsCIVKyBBQ+px1CkTgHACicWDWmUrFCySqsQFZhBRxpwbF80ExPv9WGdCMNutCjCkR0ocNjRO501Vt3ilj3Tu799FqVCXnO2dMhxuXBfvVdOPuPoCeX1e0KroCcD0CMaxZww0Iak5I2CCGixJLSQsuxaqRraUjX0uAYF2oItItSfMZiDvtoUZaThxXTZ+J3B2pCBiKaELht+qwxv2N3rF1dPBm5zmX4nx0v4rDKP/+b5GCKOIXZ2rGeAEQIDSVTlyd4tslD081+wUc3UzMxf1wlPjjxYcjXe6saNxumNvjPp4JpS5CW68WpA6+iral6UDumA8EVEdftN0E2HoezowZOXVOwCF3ToJWXQJ9TwQCExiwGIUQUkn1Rm15NCGgInVLSncPOICQ5XV08Gd7MLLzWWI/tJ45DKgVdCMwfPwFLvSUMQOJkjvevMM45id0fP42AEjAhYYgLgaEQGmZW3o7cPK4qRmt58f9B9cmPByxO14SGZcWfG/I5MgrKkbGwfMBVmUh07wTo3gnBNrwBC3CZrAFJIZYj0WnbSDeMuKe1fvDBB1ixYkXY1zdv3ozi4uI4zih6DEKIKCTjfJveaPYLGcs57KNFWU4eynLyYDkSPtuGJwEXSwK8JdcgK3sy6g9vQMuxajhKQhM6CidWoWTqcgYgg1SeXYqVZX8Xtk2vJjSsLPu7IW9Y2Od7DbAqEy1h6ACDj5RR23YGrzXWYceJ5oQ93Jk1axaee+65Psf8fj/uvvtuzJo1CxMnTozLPIaCQQgRhaTrJgonVuH4p1sjjmUO++hhajrb8CZYbl45cueVQ0oruIJoePj7MwxLJi6EN2MiXm16G9UnPx6xHdOJBvJGU0O/NFepFD5oOYbqE8exYvpMXF08OebzyMzMxGWXXdbn2E9+8hMIIfDII49A05KyBxUABiFENICSqcvRfGwb1ACpDsxhJxoaXTcZfIyQ8uxSlGeXwnIs+Gw/PIZ7SDUgRNGobTsTts4OAByl8LsDNfBmZsU93fXgwYN49tln8YMf/AD5+flxPfdgJW94REQJl5tXjorKlRBh2lQyh52Ikompmch2ZTIAoZh6rbFuwI6DQDAQea2xPk4zuuAXv/gFSktL8cUvfjHu5x4sroQQ0YCYw05ERBRkORI7TjRHNXb7ieOwHBm3+rvGxkZs3rwZ//qv/5rUaVjdGIQQUUTMYSciIgI6bRsywipIN6kUfLYdtzq8//3f/0V2djZuvPHGuJxvuBiEEFHUmMNORERjWbphQBciqkBEFwIeI3632q+//jquvfZauFyuuJ1zOJJ/rYaIiIiIKAmYmo5544uiGjt//IS4pWJ9+umnOHToEJYuXRqX840EBiFJSEoFX5eClNEt9xERERFRfCzzlkITYsAxmhBY6i2J04yAjz/+GAAwe/bsuJ1zuJiOlUSaTznYc9BGXZOEowBNAKXFOi4tM1BUwHiRiIiIKNHKcvKwYvrMsG16NSFw2/RZcW3PW1tbi7y8POTlxbcl8HAwCEkS+w7beHeXhd4/yo4CDh+VOHJU4oo5Jiqm8r+LiIhorHCkBWl1QjfTh71bO42sq4snw5uZhdca67H9xPGE7Zje7dSpU8jOzo7rOYeLd7VJoPmU0y8A6U0BeHeXhfwcjSsiREREKa7jZC1O1m7A2abtUI6E0HTkFFehYPoyZBTEvy06g6HQynLyUJaTB8uR8Nk2PIYRtxqQiz344IMJOe9wMAhJAnsO2mEDkG7q/LiigtHR8YCGT0qFgAW4TEDXB849JUDZCuhSQJqAMPh+EdHodOrQZjTtXA8op+eYciRaG7ei9eg2FM9diYJpS+Iyl2QLhpKVqelxa8ObShiEJJiUCnVNMqqxdU0SUirekKY41gYNjtNgw97qh9xnARKADugzTRgL3NC8/IgbDCkt2HYnDCOdrZgp5vh0vb+Ok7X9ApA+lIOmneuRluuNeRCQTMEQpSZeoRMsYAVrP6LhKCBgAx4G2ymLtUGDY1f7Yb3sA3pfryUgd1uQey2Y13tgVLkTNr/RovX0AdQfeRUtx6rhKAlN6CicWIWSqcuRm8ennTSy+HQ9vJO1G8IHIN2Ug1MHXkXGwti9V8kUDFHq4t1MgrnM4JPuaAIRTQAu/o+lLNYGDY7TYPcPQPoMAKyXfdAm6FwRGUBj/Sbs270eqtfNhqMkjn+6Fc3HtqGiciW8JdckcIaUSvh0PTxHWjjbtD2qsW1N1XCkFbMVpGQJhii18U4mwXRdoLQ4uqWN0mKdqVgpbDC1QQTYW/3hA5BuzvlxFFLr6QP9ApDelHKwb/d6tJ6pjfPMKBVF+3S949TY/HmTVieUE116tnIkHMsX8jXLsdAWOAfLsYY0j6EEQ0RDwceDSeDSMgNHjsoBb0DF+XGUmlgbNDjKVsEakCjIGgvKVixWD6H+yKthA5BuSjmoP7wBufP4tJOGh0/XB6ab6RCaHlUgIjQdmunpc6z2bB02NG3B9pO7IZWELnRMEZ/BoszLUIGKqOcxlGCINT00FLyrTQJFBRqumGOGTcURAK6cazIFJ4WxNmiQulSwCD0aEoBfAQxC+pDSQsux6qjGthyrhpQWi9VpyJRjJ02qUbLSdBPZxfPR1vhBxLE5xVV93p/Nx97H+oN/gNMryJNKYo+vFns7D8I4loYlExdGNY/hBkNE0eJdbZKomGrgbxa7MXWSDu38vZImgKmTdPzNYjdmTGG8mMq6a4OiwdogAGkCiDYI0wG4GYBczLY74ajoIjlHSUg7dOoHUTSU7BqRVKNUN276ckBEuDUTGgqmL+v5a+3Zun4BSG8KCusP/gG1Z+uimkN3MBSNi4MhosEY67cySaWoQENRgSu4P4QdvNEcyyk3Y0l3bdDho5Ev0qwNAoQhoFeYkHsip2TpM02mYoVgGOnQhB5VIKIJHbrBp500dEJP49P1KGQUlKN47srwtTNCQ/G8lX06Um1o2hI2AOnmKAevNr2N8uzSqOYxbvpytB2tHjh97qJgiGiwuBKShHRdwOMWY/5Gc6y5tMxApP9x1gZdYCx0R/4E0wBjAVv0hqLrJgonVkU1tnBiFVOxaFiEZvDpepQKpi3BtCXfR653AcT53beFpiPXuwDTlnwfBVMvdA+zHAvbT+6O6vtWn/w46mL17mAo7KpMiGCIaLB4N0OUJFgbNDia14B5vSd8m14NMG/wsD3vAEqmLkfzsW0DFqcLoaFk6vI4zopSFZ+uRy+joBwZC8vhSCtY+G16QgZmnXYXZJRplVJJ+Gw/TFd0AV7BtCVIy/Xi1IFX0dZUzT1dBmA5DjptiXRDh6nF/xotpcSTTz6J559/HidPnkRZWRm+/e1vY+HC6OqAEoVXZ6IkUjHVQH6OllI7pitbBQvJ08SIp0UZVW5oE/Tgjuk13DF9sHLzylFRuTJsm14hNMysvJ0bFtKIGEqq0Vin6eaAq0LpRhp0oUcViOhCh8cY3MpwtMHQWFXbeg4bG5uxo+U0pFLQhcD8wnxcN3kCynIy4zaPJ554Ao8++ijuvvtuzJ49G3/4wx/w9a9/Hc8//zxmzpwZt3kMFq/QREkmVWqDnAY7GBzsi21woHkNuLxGMNjxK8A98sFOKvOWXIOs7MmoP7yBO6ZTzPHp+sgyNRPzx1XigxMfRhxbNW42TG1oAUSkYGgseuNoC/77kzo4vXIXpFL4oPkUqptP42szSnH1pMK4zOVPf/oTbrjhBnzjG98AAFx++eXYsWMHXnjhBfzgBz+IyxyGgkEIUZLSdTFq2/Da1f7+aVISkLstyL0WzOs9MKpGtlZDGIJteIcoN68cufPKIaUFafugGx7WgFDM8On6yFpe/H9QffLjAYvTNaFhWfHn4jir1Fbbeq5fANKbA4X//qQO3qz0uKyIBAIBZGZeOI+u68jKykJbW1vMzz0coy+3g4iSmtNgh6/TAAAHsF72wWnkzu/JRtdNuNzZDEAoLjTdhJGWzQBkmMqzS7Gy7O+ghSkiFxBYWfZ3UXfGosg2NjaHDUC6OVDY2HA8LvP56le/ihdffBHvv/8+zp07h6effhq1tbX4/Oc/H5fzDxVXQogoIkcqyACguwAtQmqYvdUfPgDp+YbBcS7WbBARDduSiQvhzZiIV5veRvXJj3t2TL80vRyLMi+LeqNCisxyHOxoOR3V2O0tp2E5TsyL1b/yla9g69atWLlyZc+xe+65B9dcc01MzztcvAMgorDamx2c2G2jtU5COcFujblTdBReaiCjqP+HqrJVsAYkCrLGgrIV6zeIiEZAeXYpyrNLYTkWfLYfHsONg/sPJnpaKafTlpBq4FWQblIp+GwJ0xW7IEQphTvvvBOHDh3CD3/4Q0ybNg3vvfcefvWrXyE7Oxtf/epXY3bu4WIQQkQhndxno/EdC70/a5UDnDkk0XpYwnuliXEVF32EdKlgEXo0JIKF5AxCiIhGjKmZUbfhpcFLN3ToQkQViOhCwGPEtrhzx44d2LFjBx599FH89V//NYBgYbqUEj/96U9x0003ISMjI6ZzGCrWhBBRP+3NTr8ApDelgMZ3LHQ0X5R3lSaAaD9vdQBuBiBERDR6mJqGeYX5UY2dX5gf81Ss48eDdSeXXXZZn+Pz5s2Dz+dDU1NTTM8/HAxCiKifE7vtsAFIN6WAlj19i8uFIaBXRPcETp9pMhWLiIhGnaWTJ0DDwNcvDQLXTZ4Q87mUlpYCAHbu3Nnn+EcffQTDMDBhQuznMFRMx6KoDaY4mUYvRyq01kWXU9V6RMKRqs/Pg7HQHdw4cKDidA0wFoxsi14iIqJ4KMvJxNdmlIZt06tBYEVFaVza81566aVYvHgxHnroIbS2tmLatGnYtm0b/uu//gsrVqxAdnZ2zOcwVAxCKKLBFifT6CYDoTczDkU5wfGa58IxzWvAvN4Tvk2vBpg3eLibORERjVpXTyqENysdGxuOY3uCd0x/7LHH8Oijj2Lt2rVoa2tDSUkJHnjgAXz5y1+O2xyGgncBNKAhFSfTqKa7goFmNIGI0ILjL2ZUuaFN0IM7ptfEdsd0IiKiRCjLyURZZRksx4HPlvAYesxrQEJJS0vD/fffj/vvvz/u5x4O3glQWNEWJ3vyNa6IpBBNF8gt1XHmcOSUrNwpetjUPM1rwOU1oGwV7ILlFqOiBkTZKtjlK210zJeIiBLL1LSYtuFNVQxCKKzBFCdPKQrxOJxGrcJKA61H5ID//0IAhZdG/ggRhhgVbXidBju4crOPKzdERESxxrCNQhpKcTKljowiDd4rTYgwsYMQgPdKM2VWwOxqP/xPtkPusS7scyIBuduC/4l22NX+hM6PiIgo1fDxHoU03OJkGv3GVRjw5Gto2WMHV0WSvCnBUNOonAY7fBE9ADiA9bIP2gSdKyJEREQjhFdUCmkkipNp9Mso0jClyJXU7ZmHm0Zlb/UP3E4YAJzgOBeDECIiohHBKyqFNFLFyZQaNF0MeqVL2RZUoBPClQ5hRLeB4WDZ1f7+qxjn06jkXgvm9R4YVeH3I1G2CgYvUZA1FpStWKxOREQ0AhiEUFgjWZxMY4c8XovA7g2wj2wHHAloOowpVXDNXga9qHzEzjMiaVRd6kINSCQSwS5fDEKIiIiGLbmSuimpjLXiZBq+QM1mdL74I9iHPggGIADgSNiHtqLzzz9CoGbziJ1rMGlUYaUJQI/yhDoANwMQIiKikcBH2DSg0VacTIkjj9fC//b68IVEyoH/7fXQC7zDXhEZqTQqYQjoFWawK1YE+kyTqVhEREQjhEEIRTQaipMp8QK7N0TuZKAcBD5+FZ7rhpmWNYJpVMZCd3BX94GmrgHGgvC1JRQdy5HotG2kGwZMLdolKCIiSkUMQihqQylOprFB2VawBiQK9pFqKNsaXrF6dxpVNIFIhDQqzWvAvN4Tvr5EA8wbPGzPOwy1bWfwWmMddpxohlQKuhCYP34ClnpLUJaTl+jpERENiyUVfLYDj6HBTMBD2o6ODvzsZz/Dhg0b4PP5MHfuXNx7772YMWNG3OcyGLyqEtGwqUDnhRqQSBwJZfmGFYSMdBqVUeWGNkEPtvqt4Y7pI+mNpgb87kANnF4dLqRS+KDlGKpPHMeK6TNxdfHkBM6QiGhoDp7xY2P9Oexs8fU8YJlX5MF1JVmYlhu/1fO7774bO3fuxLe+9S1ccskl+MtftyQ9XQAAIABJREFU/oJbbrkFL7zwAqZOnRq3eQwWr6xENGzClQ5oenSBiKZDmMNfUhvpNCrNa8DlNYKbHvoV4B7cpofUX23bmX4BSG+OUvjdgRp4M7O4IkJEo8qbje14puZ03w7xSmHb8U5sP96JW2fmY7E3M+bz2LNnD9555x089NBD+PKXvwwAuPLKK1FfX4/HHnsMjz32WMznMFSsKiaiYROGCWPK/KjGGlOqRmTfkO40qrCfYkNMoxKGgMjQGICMgNca68IGIN0cpfBaY32cZkRENHwHz/j7BSC9OQCeqTmNQ60DdGccIXV1dQCCgUdvc+bMwTvvvBPz8w8HgxAiGhGu2cuDrdMGIjS4Zi8bsXMaVW6478yEXmleaLWrA3qlCfedmTDms5g8USxHYseJ5qjGbj9xHFa06XxERAm2sf5cNB3isbH+XMznMmHCBADAsWPH+hxvampCe3s7WltbYz6HoWI6FhGNCL2oHO7PrQzfpldocH9u5YhuWAgwjSpZddo2ZIRVkG5SKfhsG6aLHbOIKLlZUmFniy+qsTuafbCkimmx+uzZs1FaWoqHHnoI//7v/46SkhK88soreOuttwAAPp8Pubm5MTv/cHAlhIhGjGvmEqTf9H0Y0xYEa0SA4I7p0xYg/abvwzVzSczOzTSq5JJuGNDD7XR6EV0IeAw+EyOi5OezncE9YJGR1kyGx+Vy4T//8z+haRq+8IUvoKqqCn/+85/x93//9wCAtLS0mJ5/OPipT0QjSi8qh+e6cijbCnbBMj0jUgNCo4up6Zg3vgjbWo5HHDt//ATuG0JEo4LH0KALEVUgogsBjx775/3l5eV46aWXcOzYMdi2Da/X2xOYZGVlxfz8Q8WVEEp5Ulrw+dsgZXQ7bNPIEIYJzZPNAGQMW+YthRZhNUQTAku9JXGaERHR8Ji6wNzC6Do8zivyxHzfEJ/Phz//+c9obm7GxIkT4fV6AQD79+9HeXk5jCReZWYQQimrufUANn38OJ5+4048u+Uf8PQbd2Lzx4+jubU20VMjGhPKcvKwYvrMsIGIJgRumz6L7XmJaFRZWpoV8QZaA3BdSexXIQzDwIMPPohXXnml51hjYyPeeustXH311TE//3Akb3hENAz7jm7Ce5+sh+pVIO0oicPNW3GkZRsWzViJiknXJHCGyUVKCwG7Ey4jHbrOlQsaOVcXT4Y3MwuvNdZj+4nj3DGdiEa9ablu3DozP2ybXg3A12bmx2XDQtM08YUvfAFr165Ffn4+MjMz8cgjjyA/Px8rV66M+fmHg0EIpZzm1gP9ApDelHLw3ifrkZ85GUW5I9upabRpbj2APQ2vor6lGo6S0ISO0sIqzJq8HOOyShmY0Igoy8lDWU4eLEfCZ9vwGAZrQIhoVFvszYQ3y8TG+nPY0ZzYHdNXr14NIQR++tOfwu/3Y8GCBbjvvvuQl5fcD3kYhFDK2dPwatgApJtSDvY2bBjTQUi41aL9n76Fj+r+ApfhgdvM7BOYDPR+cTWFIjE1nW14iShlTMt1Y1quG5YMdsHy6FrMa0BCSUtLwwMPPIAHHngg7uceDgYhlFKktFDfUh3V2LqWakhpjckb5nCrRV2Bc2jvOgkA8Fvt0DQDpp42YBrbQKspYznIIyKiscHUBUydD1gGi0EIpZSA3QlHRbfzsqMkAtIHzxgMQkKtFlnS3xOAdPMFzsL0BHuMh0pjY+0NERERDQW7Y1FKcRnp0ER0TyM0ocOlR9dmL5WEWy3yBdr6HQtYHVC9eqF3p7EB0dfesBsZERERXYxBCKUUXTdRUlgV1djSwqoxmYoVarVIKYWA1RFy/MVBRnca22Bqb4iIiIh6YxBCKefSycshxMA/2kJomDV5eZxmlFxCrRYNFExc/F46SsIXODvo2hsiIiKibgxCKOUU5ZZj0YyVYQMRITRcMeP2MVs0HWq1KNx75TIzIC7aaC4YwKhB194QERERdWNhOqWkiknXID9zMvY2bEAduzb1sBwHnbbEJZOWoa5lW88KiBACLjOjX0qWx5Xd73uUFlbB48qBJvSoApGxWntDRERE4TEIoZRVlFuOotzy4P4V0geX7hmTNSAA0NhlYWtrJ+o/3d6zoVJp+m1IO/ci8rTTAACPK6dPEJKZVgBTT+vzfbrT2LpXU440b4147rFae0NEREThMR2LUp6um/C4ssfsjfAbR1vwVNMZ1LT7Ic93upJK4VBnFj7GzehMvw6a0GHqbmR5CuE2M5GTMRFpF62CXJzGxtobIiIiGiquhBCNYspWQJcC0gSE0X+X1trWc/jvT+rQq8tuH7ruxoe+mbh/7o3wZgbTpk6eq4sqja279iZcm96xXntDRERE4TEIIRqFnAYb9lY/5D4LkAB0QJ9pwljghua98Gu9sbEZDsJEIN3fCwqbmk7hm5VlAAaXxsbaGyIiGuukVAhYgMsEdL3/A8F42rRpE1avXo1du3b1HFNKYe3atXjuuedw5swZzJ07F9/73vcwbdq0BM6UQQjRqGNX+2G97AN6Lz5IQO62IPdaMK/3wKhyw3Ic7Gg5HdX33N5yGpbjwNQupFfpuhnVbvKsvSEiorGo+ZSDPQdt1DVJOArQBFBarOPSMgNFBfGveNi5cyfuvffefsd/9atfYd26dVi9ejWKi4uxZs0arFy5Eq+88gqysrLiPs9urAkhGkWcBrt/ANJnAGC97IPTaKPTlj01IJFIpeCzo2u5G85Yr70hIqKxY99hG39504/DR4MBCAA4Cjh8VOIvb/qx77Adt7kEAgH89re/xYoVK2AYfdcX2tvb8cQTT+Bb3/oWVqxYgWuuuQZPPPEEOjo68MILL8RtjqEwCCEaReyt/vABSDcnOC7d0KGL6JaFdSHgMfTIA4mIiMa45lMO3t1lhU12VgDe3WWh+VSkC/bI2LJlC9atW4f77rsPt956a5/XPvroI3R2duKaa67pOZaTk4PPfvazePvtt+Myv3AYhBCNEk6XA7kngLBV5r3IGguGIzCvMD+q7z2/ML9PKhYRERGFtuegHaHaMhiI7DkYn9WQyspKbNq0CStWrOi3wXBdXR0AwOv19jk+adKkntcShTUhREmuuwjd3hOA+lQCAhBpAsjQIFxhVjokAL/C0skTsL154LoQDQLXTZ4w8hMnIiJKMVIq1DVFl75c1yQhpYp5sXpRUVHY19rb2+FyueByufocz8jIQHt7e0znFQkffRIlMbvaD/+T7ZB7LPQ8dlGA8imokxKqM8xSrw7ALVCWk4mvzShFuKwsDQIrKkpRlpMZi+kTERGllICFnhqQSBwFBOJXGhKSUqrf6ki3cMfjhSshREnq4iJ0IQSURwC+C59+qtUBDNFvRUSfafbsG3L1pEJYJ47jg9ZO1DmiZ8f0+YX5uG7yBAYgREREUXKZwS5Y0QQimgBcCb7TzsrKQiAQgGVZMM0LjWM6OjoS2hkLYBBClLRCFaGLDA3Kd9EycIcDuHoVlWuAscDdZ4g3zYR3Qg7KLrkEPlvCY+isASEiIhokXRcoLdZx+GjklKzSYj3h+4aUlJRAKYWjR49iypQpPccv/nsi8C6EKAkpWwU3IryIcAmInL6/tqpLXShW1wDzBk+fDQt7MzUN2S6TAQgREdEQXVpmIFJoIc6PS7Q5c+bA7Xbj9ddf7znW1taGbdu2YeHChQmcGVdCiJJTlwoWl4cgMjTAFFAdTjA1SwEQgF7Zf8d0IiIiGllFBRqumGOGbdMrAFw510zIhoUXy8jIwK233orHHnsMmqahtLQUa9euRWZmJm6++eaEzo13K0TJKE0Ei8vDBSIuAeHSoXIVIAD3v+RAS0v8h91Yo2wLKtAJ4UqHMLhJIxHRWFEx1UB+jpZUO6aH8+1vfxuapuHJJ59EZ2cn5syZg4cffpg1IUTUnzAE9Aoz2BVroHFCQK80GYDEmTxei8DuDbCPbAccCWg6jClVcM1eBr2oPNHTIyKiOCgq0FBU4IKUCgE7WISe6BqQVatWYdWqVX2OGYaB1atXY/Xq1QmaVWgMQoiSlLHQDVljDbxDeogidIqtQM1m+N9eD6he/zGOhH1oK+zD2+D+3Eq4Zi5J2PyIiCi+dF3Ao0ceR33x8SlRktK8BszrPeF/SyMUodPIk8dr+wcgvSkH/rfXQzbXxnVeREREow2DEKIkZlS54b4zE3qlGawRAQA9WITuvjMTxnyugsRTYPeG8AFIN+Ug8PGrI35uKS34/W2QcuAUPSIiotGAj1CJkpzmNeDyGlC2AvwKcIuejQgpfpRtBWtAomAfqYayrREpVm89fQD1R15Fy7FqOEpCEzoKJ1ahZOpy5Oax/oSIiEYnBiFEo4QwBMDgI2FUoDNYhB4NR0JZvmEHIY31m7Bv93qoXqsvjpI4/ulWNB/bhorKlfCWXDOscxARESUC07GIUpyyFTSfCNvul6IjXOmAFmXloaZDmJ5hna/19IF+AUhvSjnYt3s9Ws+w/oSIiEYfroQQpSinwYa91Q+5z8L4jhxAAwLzOrih4RAJw4QxZT7sQx9EHGtMqRr2Kkj9kVfDBiDdlHJQf3gDcucxLYuIiEYXroQQpSC72g//k+3BfUa6V0AcQO624H+iHXa1P6HzG61cs5cDIsLHptDgmr1sWOeR0kLLseqoxrYcq2axOhERjToMQohSjNNgw3rZF35/EQewXvbBabTjOq9UoBeVw/25leEDEaHB/bmVw96w0LY74ajo8uccJSFt37DOR0REFG9JGYQcOHAAt912G+bMmYPFixdj3bp1UEoN+DUbNmzAJZdc0u/PM888E6dZEyUHe6t/4A0OAcA5P44GzTVzCdJv+j6MaQsu1IhoOoxpC5B+0/dHZKNCw0iHJqKrP9GEDt0YXv0JERFRvCVdYvipU6dw++23o7y8HI8++ij27t2LRx99FLqu48477wz7dfv370dJSQn+4z/+o8/xSZMmxXrKRElD2QpyX3SpObLGgrIV2/0OgV5UDs915VC2FeyCZXpGpB1vz/fXTRROrMLxT7dGHFs4sQq6PnLnJiKiwXGkggwAugvQ9MReUzdt2oTVq1dj165dIV9/8skn8eKLL+LFF1+M88z6S7og5Nlnn4Vt21izZg08Hg+uuuoqBAIBrFu3DitWrIBphr7Y7t+/H7NmzcJll10W5xkTJZEuFX0XLIngviMMQoZMGOaIBh+9lUxdjuZj2wYsThdCQ8nU5TE5PxERDay92cGJ3TZa6ySUE8zUzZ2io/BSAxlF8U822rlzJ+69996wr2/YsAE/+9nPUFZWFsdZhZd06VjvvfceFi5cCI/nQnrBtddei9bWVuzevTvs1+3fvx+XXHJJPKZIKUxKBV+XgpQDp/8lrTRxYWf1SHQAbgYgQ2E5Em0BP6xo9w0Zgty8clRUroQIU38ihIaZlbdzw0IiogQ4uc9G7Ut+nDkcDEAAQDnAmUMSB17y4+S++NVdBgIB/Pa3v8WKFStgGP3XF9rb2/Hwww/jnnvuQUZGRtzmFUnSrYTU1dXh8ssv73PM6/X2vDZ37tx+X9PR0YGmpibU1NRg2bJlOHr0KKZOnYrVq1fjqquuGtI89u3bN6Svo9B8vmDhbLK+r63tJhpb0tHSmgalACGAwtwuTC7sRE7m6Oo8lFOYgbQjfZ/OKyf4CenrulDA3DXFQlvtsbjObbRr7OrE1rNnsK/jHBwEn+LMzMjC5dn58KaFr8sY+s//ZzBu4q1oPfU+2tv2QsGBgIbMnFnILViIc50Tk/Z3Kpkk++dPquP7nzip+N5XVFQkegpob3bQ+I6FcOXKSgGN71jw5GtxWRHZsmUL1q1bh/vuuw+tra146qmn+rz+3HPP4eWXX8bPf/5zbN68GbW1ybG/VFyDEMuy0NDQEPb1cePGob29vV+U1v339vb2kF+3f/9+KKVw9OhR3H///dB1Hf/zP/+Db3zjG3jqqaewYMGCkftHUMo5esKDTxqzgV4fJkoBzWfS0Nyahhnes5g0fvR0H+qc2YW0OrPPv6cfERxH0dt+9gxePtXc5211AOzpOIe9HedwfUER5mfnjfh5PemT4UmfDKfYhuP4oWluaFrSPT8iIhozTuy2wwYg3ZQCWvbYmFLkivl8KisrsWnTJmRnZ+Pxxx/v9/p1112HW2+9FW63G5s3b475fKIV1ytZc3MzPv/5z4d9/bvf/e6AX69poaPJsrIyrFu3DvPmzUNmZiYA4IorrsCNN96INWvWDCkISYZIO5V0P4VJtve1+ZSDd2v8SEsLP6b+hAezZ7lRVJB02YuhVQB2ur9Pm97uFRBPmgfQAPMGD/LnT0zgJEeX2rYz2Hy8Hu4BflA2d57FwhkVKMvpH4gk68//WMH3P7H4/icO3/uR50iF1rroUnFbj0g4UsW8WL2oqGjA1ydPnhzT8w9VXIOQSZMmYf/+/QOOWbt2LTo6Ovoc6/57d4Bxsezs7H5pV7quY9GiRUlR/U/Ja89Be8AFAyC4oLDnoI2igtg/zRgpRpUb2gQ9uGN6zfl0Mg3QK03umD4ErzXWwYnw2MtRCq811ocMQoiIKDXIADBAv5A+lBMcr7GLekhJdydSWlqKo0eP9jnW2NgIAJg6dWrIr6mpqcHevXtx88039zne1dWFvDzeEFBoUirUNUX3NKOuSUJKBT3BrfcGQ/MacHkNKFuh/uPjUC6F/Eu5+jFYliOx40RzVGO3nzgOy5EwtWi7AxAR0Wiiu4JdsKIJRIQWHE+hJV1+yYIFC/Dee++hs7Oz59jrr7+O3NxczJgxI+TX7Nu3D9/73vdQU1PTc6yrqwtbtmzBZz/72ZjPmUangAU4UTbBchQQGKUbjAtDQHlU9F2zqI9O24aMlPx7nlQKPnuU/qAQEVFEmi6QWxrdBTV3ip7wfUOSWdIFIbfccgssy8Jdd92FN954A2vWrMG6detw1113weUKhpPt7e348MMPcfr0aQDA8uXLUVpain/8x3/EK6+8gk2bNuGOO+5AZ2cnvvnNbybyn0NJzGUCWpSfDZoAXEm3bkjxkG4Y0EV0Pyi6EPCEaI9IRESpo7DSQKTLghBA4aW8Hgwk6YKQwsJCPPXUU7BtG3fffTeef/553HPPPX12S9+7dy++9KUv4c033wQQ7J61fv16VFZW4sc//jG+853vwOPx4JlnnsHEiUw/odB0XaC0OLqnGaXF+qhKxaKRY2o65o0fuOiv2/zxE5iKRUSU4jKKNHivNMMGIkIA3ivNhGxYOJokZYhWWVmJ3//+92Ffv/zyy/sVuE+cOBE///nPYz01SjGXlhk4clRG6maLS8uS8leF4mSZtxTbTzQPWJyuCYGl3pI4zoqIiBJlXIUBT76Glj02Wo8kx47pow3vrGhMKyrQcMUcE+/uskIGIgLAlXPN0dOel2KiLCcPK6bPxO8O1IQMRDQhcNv0WeyMRUQ0hmQUaZhS5IIjFWQgWISe6BqQVatWYdWqVWFff+SRR+I4m4ExCKExr2KqgfwcDXsO2qhrknBUsAaktFjHpWUGAxACAFxdPBnezCy81liP7SeOQyoFXQjMHz8BS70lDECIiMYoTRdswzsEDEKIEFwRKSpwQUqFgB0sQmcNyNgipYWA3QmXkQ5dN0OOKcvJQ1lOHixHwmfb8BgGa0CIiIiGgEEIUS+6LuDhPeWY0tx6AHsaXkV9SzUcJaEJHaWFVZg1eTmKcstDfo2p6TBd/EEhIiIaKgYhRDSmKFsBXQpIE/jk+Ga898l6qF67TjlK4nDzVhxp2YZFM1aiYtI1CZwtERFRamIQQkRjgtNgw97qh9xnARKwVBfas1qQXVqEtrxj/cYr5eC9T9YjP3Ny2BURIiIiGhpW3BJRyrOr/fA/2Q65JxiAAICvqw1Fn16Cy9//CiY1zA75dUo52NuwIY4zJSIiGhsYhBBRSnMabFgv+4ALGVdQUAjYnef/IjBzz7XIORN6Y9O6lmpIacVhpkRERGMHgxAiSmn2Vn+fAAQIrnCo3vt9KIGSunkhv95REgHpi+EMiYiIxh4GIUSUspStgjUgFxFCgxB9WzAXHS+HJvt3vNKEDpfOBvBEREQjiUEIEY0allQ465ewZKj97UPoUj01IL0JCLiM9L7HHA267eo3trSwKuy+IURERDQ07I5FREnv4Bk/Ntafw84WX89O5fOKPLiuJAvTct3hvzBNADpCBiIeVw4CdmdPWpbSHEgj0GeMEBpmTV4+gv8SIiJKNb1bvwsjsRsdb9q0CatXr8auXbt6jnV1dWHNmjV45ZVXcPLkSZSUlOCuu+7C5z//+QTOlEEIESW5Nxvb8UzN6T5lHVIpbDveie3HO3HrzHws9maG/FphCOgVZrAr1kVMPQ0ZaQXo6DoFpRSaJ9TC0S9EK0JouGLG7WzPS0REIV3c+h06oM80YSxwQ/PG/xZ7586duPfee/sdf/DBB/H666/jnnvuwdSpU7F582b80z/9EwAkNBBhEEJESevgGX+/AKQ3B8AzNafhzTLDrogYC92QNVa/4nQA8JjZMDQXfFYbGqd8CABR7ZhORERjm13t79d5ERKQuy3IvRbM6z0wqgZYqR9BgUAATz/9NB577DGkp6fDsi48eDt9+jT+9Kc/4cc//jFuvvlmAMCiRYvQ0NCAJ598kkEIESUPy3HQaUukGzpMLbFlYxvrz4UNQLo558eFC0I0rwHzek//i8V5ppmG9P+bh5vm/BgB6YNL97AGhIiIwgrV+r3vAMB62Qdtgh6XFZEtW7Zg3bp1uO+++9Da2oqnnnqq57WOjg58+ctfxpVXXtnna6ZMmYKPP/445nMbCIMQIgIA1Laew8bGZuxoOd1TdzG/MB/XTZ6AspzQ6U6xZEmFnS3Rtcbd0eyDJRVMPXQurlHlhjZBDy6b14RfNvcw+CAioghCtX7vxwmOc8UhCKmsrMSmTZuQnZ2Nxx9/vM9rXq8XDz30UJ9jUkps2bIFU6dOjfncBsIghIjwxtEW/PcndXBwoeuUVAofNJ9CdfNpfG1GKa6eVBjXOflsB1JF1wVLKgWfdGDq/VvsdtO8BlxeI1hA6FeAO/EFhERENLqEa/0eiqyxoGwV82tNUVHRoMb/8pe/xOHDh7FmzZoYzSg6bNFLlGDKVlDtTvDmOAFqW8/1C0B6c6Dw35/U4WBbe1zn5TE06CK6D25dCHj06D7OhCEgMjQGIERENHhhWr+HJBF86JVE1q1bh7Vr1+KOO+7AkiVLEjoXroQQJUiydNXY2NgcNgDp5kBhY8NxlFWWxWlWgKkLzC30oLq5M+LYeUWesKlYREREI2aA1u/96ADcyXFtUkrh4Ycfxvr163HLLbfgvvvuS/SUGIQQJUKydNWwHAc7Wk5HNXZ7y2lYjhPXYvWlpVnY0dw5YOqtBuC6kqx4TYmIiMawgVq/X0yfaSbFqrvjOPjnf/5nvPTSS/jGN77R05430ZiORRRn0XbVcBrtmM+l05aDq7uwo12DHhnTct24dWZ+2A8qDcDXZuYPvGEhERHRCDIWuiPfQWuAsSA5rk0PP/wwXnrpJdx///1JE4AAXAkhirtk6qqRbujQhYgqENGFgMcIX/gdK4u9mfBmmdhYfw47mge5YzoREdEIi9T6HRpg3uBJyIaFF9u7dy9+97vf4YorrsCcOXPw4Ycf9rymaRpmz56dsLkl/t0hGkOSrauGqWmYV5iPbc2nIo6dX5ifsH1DpuW6MS3XDUsGu2B5dI01IERElDDRtn5PtM2bN0MphXfffRfvvvtun9fS09Oxa9euBM2MQQhRfA2lq0aM80mXTp6A7c2nByxO1yBw3eQJMZ1HNExdDNiGl4iIKF6SsfX7qlWrsGrVqrB/TyasCSGKp+6uGtGIU1eNspxMfG1GKTSEPpcGgRUVpQnZsJCIiCjZsfX70HAlhCiO4t1Vw5IKPtuB7QDGAI8crp5UCG9WOjY2HMf2JNkxnYiIiFIXgxCiODMWuoP5oxH6zg6nq8bBM35srD+HnS3BQm6rS8eMTIUvT/SHLeQuy8lEWWUZLMeBz5bwGHrCakCIiIgotfEOgyjOurtqDNR3djhdNd5sbMfD25pR3dzZ0/VKKmDvOYF//6AZbzYOvPO5qWnIdpkMQIiIiChmuBJClACx6qpx8Iwfz9ScHmgLEjxTcxreLJOtbYmIiChhGIQQJUgsumpsrD8XzRYk2Fh/jkEIERERJQyDEKIEE4YYkTa8llTY2eKLauyOZh8sqbjXBhERESUEk76JUoTPdqLa+RwApApu+kdERESUCAxCiFKEx9Cgi+hWNnQh4NH5609ERESJwbsQohRh6gJzCz0Rx+kSWJjtgRHdogkRERHRiGMQQpRClpZmhf2lLm7T8Te7TNyz0Y3/9xcNXT9pQ+B/O+A02nGdIxERUSpRtgPVYUHZiU9z3rRpE+bMmdPn2Llz5/Dggw/iyiuvxJw5c/DNb34TDQ0NCZrhBSxMJ0oh03LduHVmfr82vXOaTPz1AQ90IVCQZsCta4AE5G4Lcq8F83oPjCp2yyIiIoqWc/Qc5PbjkAfOAI4DaBr0S/Kgz58ArTgr7vPZuXMn7r333n7Hv/Od76CmpgarV69GXl4efv3rX+NrX/saXn75ZWRmZsZ9nt0YhBClmMXeTHizTGysP4cdzT4UnQY+f8ADjwbkp5vBAKQ3B7Be9kGboA95fxIiIqKxRO5qhvVaHdC7IYzjQO47BfnJaZhLS6HPKYrLXAKBAJ5++mk89thjSE9Ph2VZPa8dPHgQb731Fh5//HEsXboUAFBWVoYlS5Zg06ZNuPHGG+Myx1B4x0GUgqblujEt1w1LKnQ93wHLfQ4A+gcg3RzA3uqHi0EIERHRgJyj5/oHIL0pBeu1OojC9LisiGzZsgXr1q3Dfffdh9bWVjz11FM9r3m9Xjz//POYMWNGzzHTNAEEg5dEYk0IUQozFGAciK7mQ9ZYwY0TU4glFc76JSyZWv8uIiJKHLl4MUqRAAAZSElEQVT9ePgApJtSwXFxUFlZiU2bNmHFihUQF3XJdLvd+Ku/+iu43W7Yto2DBw/iX/7lXzBu3Dhce+21cZlfOHzsSZTKuhQgoxwrEdy5fQQ2Tky0g2f82Fh/DjtbfJBKQRcC84o8uK4kizvFExHRkCnbCdaAREHuPwPDdiCM2D7zLyqKLu3r+9//Pv74xz9C0zT827/9G/Ly8mI6r0gYhBClsjQB6FGO1QG4R38A8mZje7/CfKkUth3vxPbjnbh1Zj4WexNXiEdERKOYXwaL0KPhOEBAAjEOQqL1la98BTfeeCNef/113H///bBtGzfffHPC5sMghCiFCUNArzCB7b6IY/WZJsQoXwU5eMbfLwDpzQHwTM1peLNMrogQEdHguXVA06ILRDQNcEX7JDD2Zs+eDQBYsGABmpub8Zvf/CahQUhyhGZEFDPGQjcQKbbQAGPB6L8p31h/LmwA0s05P46IiGiwhKFBnx5dGpN+SV7MU7EiaWxsxAsvvAB1UQ1LRUUFmpubEzSrIAYhRClO8xo4u7AzfCCiAeYNnlHfnteSCjtbIq/4AMCOZh+L1YmIaEj0qgmAiPB0Twjo8yfEZ0IDOHLkCB544AF88MEHPceUUnjvvfcwffr0BM6M6VhEY4LvkgDsPInJLdmQNVawCF0PpmAZC9yjPgABAJ/tQEbqVnKeVAo+6cDUk2eZnIiIRgetOAvm0tLwbXqFgLlsSkI2LLzYokWLcNlll+G73/0u7rnnHuTl5eGFF17Azp078dvf/jahcxv9dx5EFBWrUMJ1VUawDa9fAW4x6mtAevMYGnQhogpEdCHgCbdnChERUQT6nCKIwvTgjun7k2PH9FAMw8DatWvx85//HI888gja2towa9YsPPnkk1iwYEFi55bQsxNR3AlDpEQb3ouZusDcQg+qmzsjjp1X5IGpp957QERE8aMVZ0ErzoJhn++C5dITXgOyatUqrFq1qs+xvLw8/OhHP0rQjMLjo0AiShlLS7MifqhpAK4rSY4nVBQkpQW/vw1SWomeChHRoAlDg0g3Ex6AjDZcCSGilDEt141bZ+aHbdOrAfjazHy2500SracPoP7Iq2g5Vg1HSWhCR+HEKpRMXY7cvPJET4+IiGKIQQgRpZTF3kx4s0xsrD+HHc3cMT1ZNdZvwr7d66HUhXDRURLHP92K5mPbUFG5Et6SaxI4QyIiiiUGIUSUcqblujEt1w1LBrtgeXSNNSBJpPX0gX4BSG9KOdi3ez2ysidzRYSIKEUxeY2IUpapC2S7dAYgSab+yKthA5BuSjmoP7whTjMiIqJ4YxBCRERxI6WFlmPVUY1tOVbNYnUiohTFIISIiOLGtjvhKBnVWEdJSNsX4xkREVEiMAghIqK4MYx0aCK6neo1oUM3PDGeERERJQKDECIiihtdN1E4sSqqsYUTq6DrZoxnREREicAghIiI4qpk6nIIMfDlRwgNJVOXx2lGREQUbwxCiIgornLzylFRuTJsICKEhpmVt7M9LxFRCuM+IUREFHfekmuQlT0Z9Yc3cMd0IqIxiEEIERElRG5eOXLnlUNKC9L2QTc8rAEhIhojGIQQEVFC6brJ4IOIaIxhTQgREREREcUVgxAiIiIiIoorBiFERERERBRXDEKIiIiIiCiuGIQQEREREVFcMQghGgbLcdAWsGA5TqKnQkRERP9/e/ceHNVZ/3H8s7ekuUAMk9LoLwmhhCUUKSIkJeIMSaelCF46OsroVMB2prbFMjpWKw4aZmiDOhapt2qs07FYdeqoMA4tbQELOEjLpaOV0BQqYRP4JdwsdnPb2/P7A7O/huyS3TT77KXv1wx/8OxzNl+e85A5n3POcw6yBo/oBcbg+Jtv6YXOHh0+e1FhY+RyODR/8iTdWlWumpLidJcHAACQ0QghQJL+0nVWW17rUEQm2hY2Ri/1XNDBnov6fG21miomp7FCAACAzMbtWEASjr/51ogA8nYRGW15rUMnLvktVwYAAJA9CCFAEl7o7IkbQIZEZPSCr9tSRQAAANmHEAIkKBiJ6PDZiwn1PXT2IovVAQAA4iCEAAnqC4UVNle/CjIkbIz6Q+EUVwQAAJCdCCFAggrdLrkcjoT6uhwOFbhdKa4IAAAgOxFCgAR5nE7Nmzwpob7zJ0+Sx8l/LwAAgFg4SgKSsLiqXE5d/WqIUw7dWlVuqSIAAIDsQwgBklBTUqzP11bHDSJOObRiZjUvLAQAALgKXlYIJKmpYrIqJxTqBV+3DvHGdAAAgKQRQoAxqCkpVs3sGgUjEfWHwipwu1gDAgAAkCBCCPAOeJxOefIIHwAAAMng6AkAAACAVYQQAAAAAFYRQgAAAABYRQgBAAAAYBUhBAAAAIBVhBAAAAAAVhFCAAAAAFhFCAEAAABgFSEEAAAAgFWEEAAAAABWEUIAAAAAWJXRIcTv96upqUk7duwYtW8gEFBLS4sWLlyouXPnas2aNerp6bFQJQAAAIBkZGwI8fv9uu+++3TmzJmE+jc3N2vbtm366le/qo0bN+q1117T3XffrXA4nOJKAQAAACTDne4CYnn55ZfV3NysCxcuJNTf5/Np69ateuSRR7R06VJJUm1trZYsWaJdu3Zp8eLFqSwXAAAAQBIy8krI6tWr5fV69fjjjyfU/8CBA5KkxsbGaFt1dbWmT5+uffv2paJEAHEEIxFdCgQVjETSXQoAAMhQGXkl5KmnnpLX61VXV1dC/U+ePKmysjIVFhYOa6+oqFBHR0cKKgRwpeNvvqUXOnt0+OxFhY2Ry+HQ/MmTdGtVuWpKitNdHgAAyCBWQ0gwGJTP54v7eVlZmUpKSuT1epP63t7eXhUVFY1oLyoqUnd3d9J1StKxY8fGtB1i6+/vl8S4pkuqx//QpX49c/4tGTO8fU/Hae09dVpLyyZofklBSn52NmD+pxfjn16Mf/rk4tjPnDkz3SVgnFgNIT09PdE1G7GsXbtWq1atSvp7jTFyOBwJtwMYP50DwZgBZIgx0jPn39J1+W5VXuOxWxwAAMhIVkNIRUWF2tvbx/17i4uL1dvbO6K9r69PEyZMGNN3krTH19BZGMY1PVI5/n959YTyr+kftd8b7kItnlkz7j8/GzD/04vxTy/GP30Ye2SyjFyYnqzq6mqdP39eAwMDw9q7uro0derUNFUFW0zIyPgjMqE4p+KRMsFIRIfPXkyo76GzF1msDgAAJGXowvRkNTQ0KBwOa/fu3dHbvTo6OnT8+HF96UtfSnN1SJWIL6TQgUGFjwWlsCSX5LrBI/eCfDkrc2JqZ7y+UFjhePdhXSFsjPpDYXnycuLcBwAAeAey8kjN7/frxIkTqqqq0qRJk1RVVaUlS5boW9/6lvx+vyZOnKhNmzZpxowZuuWWW9JdLlIgdHBQwe390ttPrIel8KtBhY8G5VlWIHddftrqe7codLvkcjgSCiIuh0MFbpeFqgAAQKbLylOSR48e1fLly/Xiiy9G2zZu3KilS5fq+9//vtatW6fa2lq1trbK5eKgJ9dEfKGRAWRYBym4vV+RzpDVut6NPE6n5k2elFDf+ZMnyePMyl85AABgnGX0lZB4C9lvuummEe2FhYXasGGDNmzYYKs8pEnowGD8ADIkcrlfHrdlpdziqnId6rmoiOJfDXHKoVuryi1WBQAAMhmnJZFVTMhcXgOSgHBbkMXqFtSUFOvztdVyKvbjsJ1yaMXMal5YCAAAojhNjOwyYC4vQk9EWNKgkdy8KybVmiomq3JCoV7wdesQb0wHAACjIIQgu1zjkFxKLIi4JOUTQGypKSlWzewaBSMR9YfCKnC7WAMCAABi4ggBWcXhdsg1M7G3brtu8MjBVRDrPE6nJuZ5CCAAACAujhKQddwN+aPPXKfkXsAjegEAADIRIQRZx1nplmdZQfzZ65Q8Hy3ghYUAAAAZiqM0ZCV3Xb6c5a7Lb0xv443pAAAA2YQjNWQtZ6VbeZXuy4/hHTRSvoM1IAAAAFmAEIKs53A7eAwvAABAFmFNCAAAAACrCCEAAAAArCKEAAAAALCKEAIAAADAKkIIAAAAAKsIIQAAAACsIoQAAAAAsIoQAgAAAMAqQggAAAAAqwghAAAAAKwihAAAAACwihCCjGBCRsYfkQmZdJcCAACAFHOnuwC8u0V8IYUODCp8LCiFJbkk1w0euRfky1nJ9AQAAMhFHOUhbUIHBxXc3i9F3tYYlsKvBhU+GpRnWYHcdflpqw8AAACpwe1YSIuILzQygAzrIAW39yvSGbJaFwAAAFKPEIK0CB0YjB9AhkT+2w8AAAA5hRAC60zIXF4DkoBwW5DF6gAAADmGEAL7BszlReiJCEsaJIQAAADkEkII7LvGIbkS7OuSlO9IZTUAAACwjBAC6xxuh1wzPQn1dd3gkcNNCAEAAMglhBCkhbshf/TZ55TcC3hELwAAQK4hhCAtnJVueZYVxJ+BTsnz0QJeWAhcIRgJ61JgUMFIogurAADIPBzhIW3cdflylrsuvzG9jTemA1dz/NK/9Xxnhw6f61HYGLkcDs2/tlyLK6eopqQ03eUBAJAUjvKQVs5Kt/Iq3ZcfwztopHwHa0CAK/zltE9Pvt6miPn/J8WFjdFLZ/9XB891a4X3BjX9T1UaKwQAIDncjoWM4HA75ChyEkCAKxy/9O8RAeTtIsboydfbdOLSvy1XBgDA2BFCACCDPd/ZETeADIkYo+c7T1mqCACAd44QAgAZKhgJ6/C5noT6HjrXzWJ1AEDWIIQAQIbqC4UUHuUqyJCwMeoPhVJcEQAA44MQAgAZqtDtlsuR2Dopl8OhAjfPGgEAZAdCCABkKI/TpXnXXpdQ3/nXlsvjdKW4IgAAxgchBAAy2G2V1XKOcjXE6XBoceUUSxUBAPDOEUIAIIPVlJRqhfeGuEHE6XBopXcWLywEAGQVbiAGgAzX9D9VqiyeoOc7T+nQuW7emA4AyHqEEADIAjUlpaopKVUwElZ/KKQCt5s1IACArEUIAYAs4nG65MkjfAAAshtrQgAAAABYRQgBAAAAYBUhBAAAAIBVhBAAAAAAVhFCAAAAAFhFCAEAAABgFSEEAAAAgFWEEAAAAABWEUIAAAAAWEUIAQAAAGAVIQQAAACAVYQQAAAAAFYRQgAAAABYRQgBAAAAYBUhBAAAAIBVhBAAAAAAVhFCAAAAAFhFCAEAAABgFSEEAAAAgFWEEAAAAABWEUIAAAAAWEUIAQAAAGAVIQQAAACAVYQQAAAAAFYRQgAAAABYRQgBAAAAYJXDGGPSXUSmOXz4cLpLAAAAQAzz5s1LdwkYB4QQAAAAAFZxOxYAAAAAqwghAAAAAKwihAAAAACwihACAAAAwCpCCAAAAACrCCEAAAAArCKEAAAAALCKEAIAAADAKkIIAAAAAKsIIQAAAACsIoQgpfx+v5qamrRjx45R+wYCAbW0tGjhwoWaO3eu1qxZo56eHgtV5p7XX39dK1eu1Ny5c9XY2KjW1lYZY666zY4dOzRjxowRf379619bqjp7Pf3001q8eLFuvPFGLV++XK+88spV+49l/yC+ZMf/i1/8Ysy53tvba6ni3LRr1y7NnTt31H7M/9RIdPyZ/8gU7nQXgNzl9/t133336cyZMwn1b25u1u7du/Xggw+qsLBQmzZt0t13360//vGPcrlcKa42d1y4cEFf+MIXNH36dG3evFlHjx7V5s2b5XK5dNddd8Xdrr29XVOmTNH3vve9Ye0VFRWpLjmrbd26Vc3NzVq9erVmz56tLVu26K677tK2bdtUWVk5ov9Y9w9iS3b8pctzfcWKFVq2bNmw9oKCAhsl56QjR47oa1/72qj9mP+pkej4S8x/ZBADpMBLL71klixZYurq6ozX6zXPPvvsVfufOnXK1NbWmu3bt0fbTp48aWbMmGGee+65VJebUx599FFTX19v+vr6om0/+MEPTH19vQkEAnG3u/fee82Xv/xlGyXmjEgkYpqamsy3v/3taFsgEDA333yz2bBhQ8xtxrp/MNJYxv/SpUvG6/WaPXv22Cozpw0ODprW1lYza9YsU1dXZz7wgQ9ctT/zf3wlO/7Mf2QSbsdCSqxevVper1ePP/54Qv0PHDggSWpsbIy2VVdXa/r06dq3b18qSsxZ+/fvV0NDw7CzWrfccovefPNNvfrqq3G3a29v14wZM2yUmDNOnTql06dP6+abb462eTweNTY2xp23Y90/GGks49/e3i5JzPVxsnfvXrW2turrX/+67rjjjlH7M//HV7Ljz/xHJiGEICWeeuopPfroo5o0aVJC/U+ePKmysjIVFhYOa6+oqFBHR0cKKsxdHR0dmjJlyrC2odtS4o1lb2+vTp8+rba2Nt12222aNWuWPvaxj2nPnj2pLjerDY1nrPH2+XwKh8Mxt0l2/yC2sYx/e3u78vLytHnzZt10002aM2eO1qxZo3PnztkoOefMnj1bu3bt0ooVK+RwOEbtz/wfX8mOP/MfmYQ1IUhKMBiUz+eL+3lZWZlKSkrk9XqT+t7e3l4VFRWNaC8qKlJ3d3fSdeaqRMbf7/ePGMuhv/v9/pjbtbe3yxijrq4ufeMb35DL5dJvfvMb3XPPPXriiSe0YMGC8ftH5JCh8Yw13pFIRP39/SouLh6xTbL7B7GNZfzb29sVCARUVFSkH//4x+rs7NTmzZu1cuVKbd26VXl5edbqzwXXXXddUv2Z/+Mr2fFn/iOTEEKQlJ6eHi1dujTu52vXrtWqVauS/l5jTMyzOPHa360SGf+rcTpjX/ysqalRa2ur5s2bFz1oW7hwoT7xiU/oscceI4TEYf77RJ8r52i89tHE2z+IbSzjv2rVKi1btiw6p+vq6jRt2jR95jOf0TPPPKPbb789xVUjHuZ/6jH/kUkIIUhKRUVF9J7S8VRcXBzz8YB9fX2aMGHCuP+8bJXI+P/sZz8bMZZDf7/yrPCQiRMnatGiRcPaXC6XPvShD2nbtm3voOLcNjQ3e3t7VVZWFm3v6+uT0+kccXuhFHuuj7Z/ENtYxn/atGmaNm3asLY5c+Zo4sSJKfndhuGY/+nF/Ecm4bQDMkJ1dbXOnz+vgYGBYe1dXV2aOnVqmqrKTtXV1erq6hrW1tnZKUm6/vrrY27T1tam3//+9yPaBwYGVFpaOv5F5oihe9uHxndIZ2enpk6dGvNM/Fj2D2Iby/hv375dBw8eHNZmjFEgEGCuW8D8Ty/mPzIJIQQZoaGhQeFwWLt37462dXR06Pjx42poaEhjZdlnwYIF2r9/v/r6+qJtO3fu1Hve8x7V1tbG3ObYsWNat26d2traom0DAwPau3ev6uvrU15ztqqurtZ73/te7dy5M9oWDAb14osvxp23Y9k/iG0s4//b3/5WDz/8sCKRSLRtz549GhgY0Pz581Ne87sd8z+9mP/IJK7169evT3cRyF3/+c9/9OSTT+ojH/mIampqou1+v19tbW3Ky8tTQUGBSkpKdOLECf3qV79SaWmpOjs79c1vflPl5eVau3Yt9won4frrr9eWLVv0t7/9TaWlpdqxY4cee+wx3X///aqrq5M0cvynTJmi5557Ts8++6zKysrk8/m0fv169fT06JFHHuGWuDgcDoc8Ho9++tOfKhgMKhAIaOPGjfrXv/6l7373uyopKZHP59PJkydVXl4uKbH9g8SMZfyvvfZaPfHEE+ro6FBxcbH27dunhx56SI2NjbrzzjvT/C/Kbi+//LJeeeUV3XPPPdE25r89iYw/8x8ZJW1vKMG7QmdnZ8yXFR44cMB4vV7zhz/8IdrW29tr1q1bZ+rq6sy8efPM/fffb7q7u22XnBP+8Y9/mOXLl5v3v//9prGx0fz85z8f9nms8T9z5oz5yle+YhoaGsycOXPMnXfeadrb222XnpV++ctfmkWLFpkbb7zRLF++3Bw5ciT62YMPPmi8Xu+w/qPtHyQn2fHfvXu3+dSnPmXmzJljFi5caL7zne+Y/v5+22XnnB/+8IcjXpbH/Lcn0fFn/iNTOIz572NEAAAAAMAC7nEBAAAAYBUhBAAAAIBVhBAAAAAAVhFCAAAAAFhFCAEAAABgFSEEAAAAgFWEEAAAAABWEUIAAAAAWEUIAQAAAGAVIQQAcshf//pX1dbW6oEHHoi2hcNhffazn1V9fb3OnDmTxuoAALiMEAIAOeTDH/6wVq5cqT//+c/auXOnJOknP/mJjhw5opaWFr3vfe9Lc4UAAEgOY4xJdxEAgPETCAT06U9/WhcuXNDDDz+se++9V5/73Oe0bt26dJcGAIAkQggA5KQ33nhDn/zkJxUIBDRz5kz97ne/U15eXrrLAgBAErdjAUBOmjZtmj74wQ8qEolo0aJFBBAAQEYhhABADvrTn/6k/fv3a9asWfrFL36hf/7zn+kuCQCAKG7HAoAc4/P5dPvtt6u+vl6bNm3Sxz/+cblcLm3dulUFBQXpLg8AAK6EAEAuCYVCeuCBB+TxePTQQw+psLBQLS0tOnXqlFpaWtJdHgAAkgghAJBTfvSjH+nvf/+7mpubVVZWJkmqr6/XHXfcoaeffjr62F4AANKJ27EAAAAAWMWVEAAAAABWEUIAAAAAWEUIAQAAAGAVIQQAAACAVYQQAAAAAFYRQgAAAABYRQgBAAAAYBUhBAAAAIBV/wf+2L4pkbbY3QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beac789390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your turn\n",
    "from sklearn.cluster import AffinityPropagation, AgglomerativeClustering, DBSCAN, SpectralClustering\n",
    "pca = pd.DataFrame(PCA(n_components=2).fit_transform(x_cols))\n",
    "pca.columns = ['x','y']\n",
    "\n",
    "\n",
    "# Affinity propagation\n",
    "pca['affinity_cluster']=AffinityPropagation().fit(x_cols).labels_\n",
    "sns.lmplot(x='x', y='y', hue='affinity_cluster', data=pca, fit_reg=False, size=10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beaa056198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# spectral clustering\n",
    "pca['spectral_cluster']=SpectralClustering(n_clusters=3).fit(x_cols).labels_\n",
    "sns.lmplot(x='x', y='y', hue='spectral_cluster', data=pca, fit_reg=False, size=10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beaa001208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Agglomerative clustering\n",
    "pca['agg_cluster']=AgglomerativeClustering(n_clusters=3).fit(x_cols).labels_\n",
    "sns.lmplot(x='x', y='y', hue='agg_cluster', data=pca, fit_reg=False, size=10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2beaa08d2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# DBSCAN\n",
    "pca['db_cluster']=DBSCAN(min_samples=4, eps = 1.3).fit(x_cols).labels_\n",
    "sns.lmplot(x='x', y='y', hue='db_cluster', data=pca, fit_reg=False, size=10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CONCLUSION:\n",
    "\n",
    "Affinity propagation performed really bad and looked the worst out of the four different clustering techniques performed.\n",
    "\n",
    "Agglomerative,spectral and DBSCAN did quite well as can be seen from the plots above. However Agglomerative clustering was\n",
    "\n",
    "the winner of the four.\n",
    "\n",
    "The reason agglomerative performed well with our dataset is because the data doesn't have a strong structure. Since\n",
    "\n",
    "Agglomerative Clustering looks at pairwise distances with all points in isolation before merging together, it allowed the model \n",
    "\n",
    "to not  fall victim to the same problems that hindered the distance minimization algorithms."
   ]
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}