clv-bq-notebook.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This document walks through how to do Customer Lifetime Value (CLV) analysis\n",
      "using [BigQuery Export for Google Analytics](https://support.google.com/analytics/answer/3437618?hl=en). "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Intro"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to follow this guide and execute all of the code using your own data, you need the following:\n",
      "\n",
      "  1. Access to [BigQuery Export for Google Analytics](https://support.google.com/analytics/answer/3437618) \n",
      "  2. Ecommerce or another conversion activity being tracked\n",
      "  3. Data for at least a few months\n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Outline"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This article will use BigQuery Export to calculate Customer Lifetime Value and\n",
      "some related metrics by completing the following steps:\n",
      "\n",
      "  1. Query BigQuery to extract the data needed\n",
      "  2. Import this data into R \n",
      "  3. Use the data to build a model that forecasts CLV and related metrics for each customer:\n",
      "     * Customer Lifetime Value\n",
      "     * Expected transactions\n",
      "     * Expected spend per transaction\n",
      "     * The probability that a given customer is still active\n",
      "  4. Import the CLV calculations back into BigQuery\n",
      "  5. Analyze the CLV calculations using BigQuery\n",
      "\n",
      "This article will outline each of these steps."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "CLV"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Customer Lifetime Value is is the dollar amount of money that an individual\n",
      "customer will spend with a given business in the future. It is often used to:\n",
      "\n",
      "  * Value segments or all of your customer base \n",
      "  * Decide how much to spend acquiring new customers in a given segment\n",
      "  * Decide how much to spend retaining certain customers \n",
      "  * Rank customers\n",
      "  * Measure success of marketing action based upon baseline CLV forecast\n",
      "\n",
      "Additionally, the probability that a customer is active is used to:\n",
      "\n",
      "  * Determine size of active customer base\n",
      "  * Identify customers who are on the brink of becoming inactive and take action\n",
      "\n",
      "Taken together, a strong model of user behavior serves as the foundation for\n",
      "many marketing activities and measurement.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Talk about the model\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Big Query"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, you need to extract the data from BigQuery. The following `gcp.bigquery` import makes the BigQuery functionality available to this notebook. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import gcp\n",
      "import gcp.bigquery as bq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 213
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As long as you are using Ecommerce tracking or Goals, all of the data needed to\n",
      "calculate CLV is available via BigQuery Export. \n",
      "\n",
      "This query extracts the date, number of transactions, and transaction revenue\n",
      "for all transactions among first time visitors in a given date range (i.e. a cohort).\n",
      "\n",
      "The query below is customized as follows. Modify to suit your business. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ga_view_id = 33324909\n",
      "visitor_id = 'fullVisitorId'\n",
      "conversion = 'totals.transaction'\n",
      "conversion_revenue = 'totals.transactionRevenue'\n",
      "start_date = '2014-01-01'\n",
      "end_date = '2014-07-01'\n",
      "cohort_end_date = '2014-03-01'\n",
      "sampling_rate = '1/100'\n",
      "join_each_used = '' # if needed set this to 'EACH' rename to use_join_each"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 215
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that all of the input values needed have been specified, run the query below to view the raw data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bq_sql event_log_query\n",
      "SELECT\n",
      "  *\n",
      "FROM\n",
      "  (\n",
      "  SELECT\n",
      "    date,\n",
      "    fullVisitorId,\n",
      "    totals.transactionRevenue,\n",
      "    totals.transactions,\n",
      "  FROM\n",
      "    TABLE_DATE_RANGE([941929509095:$ga_view_id.ga_sessions_],\n",
      "      TIMESTAMP('2014-01-01'),\n",
      "      TIMESTAMP('2014-07-01'))\n",
      "  WHERE\n",
      "    totals.transactions IS NOT NULL\n",
      "    ) a\n",
      "JOIN\n",
      "  EACH\n",
      "  (\n",
      "  SELECT\n",
      "    fullVisitorId\n",
      "  FROM\n",
      "    TABLE_DATE_RANGE([941929509095:$ga_view_id.ga_sessions_],\n",
      "      TIMESTAMP('2014-01-01'),\n",
      "      TIMESTAMP('2014-02-28'))\n",
      "  WHERE\n",
      "    totals.newVisits IS NOT NULL\n",
      "    AND RAND() < 1/50\n",
      "  GROUP BY\n",
      "    1\n",
      "    ) b\n",
      "ON\n",
      "  a.fullVisitorId=b.fullVisitorId\n",
      "ORDER BY\n",
      "  date"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 508
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "event_log_data = event_log_query.results()\n",
      "event_log_data.to_dataframe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>a_date</th>\n",
        "      <th>a_fullVisitorId</th>\n",
        "      <th>a_totals_transactionRevenue</th>\n",
        "      <th>a_totals_transactions</th>\n",
        "      <th>b_fullVisitorId</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 3042168694840230537</td>\n",
        "      <td> 1195000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 3042168694840230537</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 8924832537990093347</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  15</td>\n",
        "      <td> 8924832537990093347</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td>  714043219200733579</td>\n",
        "      <td>   18000000</td>\n",
        "      <td>   2</td>\n",
        "      <td>  714043219200733579</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7505732264870046495</td>\n",
        "      <td>  400000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 7505732264870046495</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4341147125057584911</td>\n",
        "      <td>  250000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4341147125057584911</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7505732264870046495</td>\n",
        "      <td>   72000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 7505732264870046495</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7429785058254482749</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  15</td>\n",
        "      <td> 7429785058254482749</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 3561198007749992729</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>  20</td>\n",
        "      <td> 3561198007749992729</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7016217589259128618</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   6</td>\n",
        "      <td> 7016217589259128618</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2262217666272156871</td>\n",
        "      <td>   25000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 2262217666272156871</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 6947327825661948935</td>\n",
        "      <td>   20000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 6947327825661948935</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 6947327825661948935</td>\n",
        "      <td>   20000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 6947327825661948935</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 8924832537990093347</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 8924832537990093347</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 6892690052040949435</td>\n",
        "      <td>   27000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 6892690052040949435</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4977336737705331512</td>\n",
        "      <td>   79000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4977336737705331512</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>15   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 8629966025049461252</td>\n",
        "      <td>   79000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 8629966025049461252</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>16   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 3150652052544444442</td>\n",
        "      <td>  120000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 3150652052544444442</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>17   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4897175115911168432</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4897175115911168432</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>18   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 3685076954899575005</td>\n",
        "      <td>    5000000</td>\n",
        "      <td> 107</td>\n",
        "      <td> 3685076954899575005</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>19   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4376618435321541163</td>\n",
        "      <td>  249000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4376618435321541163</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>20   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4514326133487179449</td>\n",
        "      <td>   24000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4514326133487179449</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>21   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2144514474072365663</td>\n",
        "      <td>   40000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 2144514474072365663</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>22   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td>  766621036312791959</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   1</td>\n",
        "      <td>  766621036312791959</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>23   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2199974562131850050</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 2199974562131850050</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7976895889547718123</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 7976895889547718123</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>25   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2092914539409733232</td>\n",
        "      <td>  250000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 2092914539409733232</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>26   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7170660653265594962</td>\n",
        "      <td>   25000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 7170660653265594962</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>27   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 5126766325036917003</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>   5</td>\n",
        "      <td> 5126766325036917003</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>28   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2773339944389961006</td>\n",
        "      <td>   56000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 2773339944389961006</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>29   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7482947746832596218</td>\n",
        "      <td>  390000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 7482947746832596218</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24487</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 2931214485401641773</td>\n",
        "      <td>    2000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 2931214485401641773</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24488</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 3698684910213821827</td>\n",
        "      <td>   14000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 3698684910213821827</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24489</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 3661600234166346291</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 3661600234166346291</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24490</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8167756183118293254</td>\n",
        "      <td>   39000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 8167756183118293254</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24491</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 3128131279833581086</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 3128131279833581086</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24492</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 9069272459954552209</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 9069272459954552209</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24493</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 9051252731393454059</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 9051252731393454059</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24494</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 7301844085659509164</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 7301844085659509164</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24495</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8856959814056816291</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 8856959814056816291</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24496</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 4665622116041834681</td>\n",
        "      <td>   54000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4665622116041834681</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24497</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 6674530379404665831</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   9</td>\n",
        "      <td> 6674530379404665831</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24498</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 4408350843413681256</td>\n",
        "      <td>    9000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4408350843413681256</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24499</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 4014827084845085021</td>\n",
        "      <td>  199000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4014827084845085021</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24500</th>\n",
        "      <td> 20140701</td>\n",
        "      <td>  929954424922763869</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>   1</td>\n",
        "      <td>  929954424922763869</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24501</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8856959814056816291</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 8856959814056816291</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24502</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8721307618519797706</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 8721307618519797706</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24503</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 3684664994522942421</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 3684664994522942421</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24504</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 3607584749758573775</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  14</td>\n",
        "      <td> 3607584749758573775</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24505</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 2571023315178796003</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  10</td>\n",
        "      <td> 2571023315178796003</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24506</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 4408350843413681256</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4408350843413681256</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24507</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 3725349158135323469</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>  26</td>\n",
        "      <td> 3725349158135323469</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24508</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8966875255592639394</td>\n",
        "      <td>  225000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 8966875255592639394</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24509</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8966875255592639394</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 8966875255592639394</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24510</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 7868897463709962929</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 7868897463709962929</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24511</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 6886057651876777002</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 6886057651876777002</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24512</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 2577388826088375619</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 2577388826088375619</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24513</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 4357957691482259718</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   1</td>\n",
        "      <td> 4357957691482259718</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24514</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 2608462682541938071</td>\n",
        "      <td>  150000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 2608462682541938071</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24515</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 2825125245549307673</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>   2</td>\n",
        "      <td> 2825125245549307673</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24516</th>\n",
        "      <td> 20140701</td>\n",
        "      <td> 8933072218000202445</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>   4</td>\n",
        "      <td> 8933072218000202445</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>24517 rows \u00d7 5 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 509,
       "text": [
        "         a_date      a_fullVisitorId  a_totals_transactionRevenue  \\\n",
        "0      20140101  3042168694840230537                   1195000000   \n",
        "1      20140101  8924832537990093347                      5000000   \n",
        "2      20140101   714043219200733579                     18000000   \n",
        "3      20140101  7505732264870046495                    400000000   \n",
        "4      20140101  4341147125057584911                    250000000   \n",
        "5      20140101  7505732264870046495                     72000000   \n",
        "6      20140101  7429785058254482749                      1000000   \n",
        "7      20140101  3561198007749992729                     10000000   \n",
        "8      20140101  7016217589259128618                      1000000   \n",
        "9      20140101  2262217666272156871                     25000000   \n",
        "10     20140101  6947327825661948935                     20000000   \n",
        "11     20140101  6947327825661948935                     20000000   \n",
        "12     20140101  8924832537990093347                      1000000   \n",
        "13     20140101  6892690052040949435                     27000000   \n",
        "14     20140101  4977336737705331512                     79000000   \n",
        "15     20140101  8629966025049461252                     79000000   \n",
        "16     20140101  3150652052544444442                    120000000   \n",
        "17     20140101  4897175115911168432                      5000000   \n",
        "18     20140101  3685076954899575005                      5000000   \n",
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        "22     20140101   766621036312791959                      1000000   \n",
        "23     20140101  2199974562131850050                      5000000   \n",
        "24     20140101  7976895889547718123                      1000000   \n",
        "25     20140101  2092914539409733232                    250000000   \n",
        "26     20140101  7170660653265594962                     25000000   \n",
        "27     20140101  5126766325036917003                      5000000   \n",
        "28     20140101  2773339944389961006                     56000000   \n",
        "29     20140101  7482947746832596218                    390000000   \n",
        "...         ...                  ...                          ...   \n",
        "24487  20140701  2931214485401641773                      2000000   \n",
        "24488  20140701  3698684910213821827                     14000000   \n",
        "24489  20140701  3661600234166346291                     15000000   \n",
        "24490  20140701  8167756183118293254                     39000000   \n",
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        "24493  20140701  9051252731393454059                     10000000   \n",
        "24494  20140701  7301844085659509164                      5000000   \n",
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        "24497  20140701  6674530379404665831                      1000000   \n",
        "24498  20140701  4408350843413681256                      9000000   \n",
        "24499  20140701  4014827084845085021                    199000000   \n",
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        "24501  20140701  8856959814056816291                     15000000   \n",
        "24502  20140701  8721307618519797706                     15000000   \n",
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        "24508  20140701  8966875255592639394                    225000000   \n",
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        "24516  20140701  8933072218000202445                     15000000   \n",
        "\n",
        "       a_totals_transactions      b_fullVisitorId  \n",
        "0                          1  3042168694840230537  \n",
        "1                         15  8924832537990093347  \n",
        "2                          2   714043219200733579  \n",
        "3                          1  7505732264870046495  \n",
        "4                          1  4341147125057584911  \n",
        "5                          1  7505732264870046495  \n",
        "6                         15  7429785058254482749  \n",
        "7                         20  3561198007749992729  \n",
        "8                          6  7016217589259128618  \n",
        "9                          2  2262217666272156871  \n",
        "10                         1  6947327825661948935  \n",
        "11                         1  6947327825661948935  \n",
        "12                         1  8924832537990093347  \n",
        "13                         1  6892690052040949435  \n",
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        "15                         1  8629966025049461252  \n",
        "16                         1  3150652052544444442  \n",
        "17                         1  4897175115911168432  \n",
        "18                       107  3685076954899575005  \n",
        "19                         1  4376618435321541163  \n",
        "20                         1  4514326133487179449  \n",
        "21                         1  2144514474072365663  \n",
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        "23                         1  2199974562131850050  \n",
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        "25                         1  2092914539409733232  \n",
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        "27                         5  5126766325036917003  \n",
        "28                         1  2773339944389961006  \n",
        "29                         1  7482947746832596218  \n",
        "...                      ...                  ...  \n",
        "24487                      1  2931214485401641773  \n",
        "24488                      1  3698684910213821827  \n",
        "24489                      2  3661600234166346291  \n",
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        "24501                      1  8856959814056816291  \n",
        "24502                      1  8721307618519797706  \n",
        "24503                      2  3684664994522942421  \n",
        "24504                     14  3607584749758573775  \n",
        "24505                     10  2571023315178796003  \n",
        "24506                      1  4408350843413681256  \n",
        "24507                     26  3725349158135323469  \n",
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        "24509                      1  8966875255592639394  \n",
        "24510                      1  7868897463709962929  \n",
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        "24514                      2  2608462682541938071  \n",
        "24515                      2  2825125245549307673  \n",
        "24516                      4  8933072218000202445  \n",
        "\n",
        "[24517 rows x 5 columns]"
       ]
      }
     ],
     "prompt_number": 509
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Building the Model in R"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that the data needed for the model is loaded into the notebook, R is used to build a model of customer behavior. This model will then be used to calculate CLV and related metrics. The [BTYD R package](http://cran.r-project.org/package=BTYD) will be used to run the Pareto/NBD Buy 'Til You Die (BTYD) model first\n",
      "introduced by [Schmittlein, Morrison, and Colombo](http://www.jstor.org/discover/10.2307/2631608?uid=3739584&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=21105176808473) and later popularized by [Fader, Hardie, and Lee](http://brucehardie.com/papers/bgnbd_2004-04-20.pdf). TODO: add overview of Pareto/NBD"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "R Setup"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you do not already have R and rpy2 installed, do so now:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bash\n",
      "apt-get update\n",
      "apt-get install r-base-dev -y\n",
      "apt-get install python-rpy2 -y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Hit http://security.debian.org jessie/updates InRelease\n",
        "Get:1 http://ftp.us.debian.org testing InRelease [191 kB]\n",
        "Hit http://security.debian.org jessie/updates/main amd64 Packages\n",
        "Get:2 http://http.debian.net jessie InRelease [191 kB]\n",
        "Get:3 http://ftp.us.debian.org testing/main Sources [9270 kB]\n",
        "Get:4 http://http.debian.net jessie-updates InRelease [117 kB]\n",
        "Get:5 http://http.debian.net jessie/main amd64 Packages [9088 kB]\n",
        "Get:6 http://http.debian.net jessie-updates/main amd64 Packages [20 B]\n",
        "Fetched 18.9 MB in 4s (4194 kB/s)\n",
        "Reading package lists...\n",
        "Reading package lists...\n",
        "Building dependency tree...\n",
        "Reading state information...\n",
        "r-base-dev is already the newest version.\n",
        "0 upgraded, 0 newly installed, 0 to remove and 174 not upgraded.\n",
        "Reading package lists...\n",
        "Building dependency tree...\n",
        "Reading state information...\n",
        "python-rpy2 is already the newest version.\n",
        "0 upgraded, 0 newly installed, 0 to remove and 174 not upgraded.\n"
       ]
      }
     ],
     "prompt_number": 184
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now load rpy2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rpy2.ipython"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The rpy2.ipython extension is already loaded. To reload it, use:\n",
        "  %reload_ext rpy2.ipython\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Install the [BTYD R Package](http://cran.r-project.org/web/packages/BTYD/index.html)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "install.packages('BTYD', repos='http://cran.us.r-project.org', dependencies=TRUE)\n",
      "library(BTYD)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Installing package into '/usr/local/lib/R/site-library'\n",
        "(as 'lib' is unspecified)\n",
        "trying URL 'http://cran.us.r-project.org/src/contrib/BTYD_2.4.tar.gz'\n",
        "Content type 'application/x-gzip' length 692236 bytes (676 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 676 Kb\n",
        "\n",
        "\n",
        "The downloaded source packages are in\n",
        "\t'/tmp/RtmpB5Zkxy/downloaded_packages'\n",
        "Loading required package: hypergeo\n"
       ]
      }
     ],
     "prompt_number": 146
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Run the Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to run the BTYD models, import the data from BigQuery into R."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas\n",
      "df = pandas.DataFrame(event_log_data)\n",
      "#dataframe = com.convert_to_r_dataframe(df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 510
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%Rpush df"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 511
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The code below prepares the data for the Pareto/NBD, runs the model, and then prints out the parameter estimates."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i start_date,end_date,cohort_end_date\n",
      "\n",
      "numCusts <- length(df)\n",
      "date <- rep(NA, numCusts)\n",
      "cust <- rep(NA, numCusts)\n",
      "sales <- rep(NA, numCusts)\n",
      "for(i in 1:numCusts) {\n",
      "    date[i] <- df[[i]][1][[1]]\n",
      "    cust[i] <- df[[i]][2][[1]]\n",
      "    sales[i] <- df[[i]][3][[1]]\n",
      "}\n",
      "elog <- data.frame(cust = cust, date = date, sales = sales)\n",
      "elog$sales <- elog$sales / 10^6\n",
      "\n",
      "# format dates\n",
      "elog$date <- as.Date(elog$date, \"%Y%m%d\")\n",
      "\n",
      "# set key dates\n",
      "end.of.cal.period <- as.Date(end_date)\n",
      "T.end <- max(elog$date)\n",
      "T.star <- as.numeric(T.end - end.of.cal.period)\n",
      "T.tot <- as.numeric(max(elog$date) - min(elog$date))\n",
      "\n",
      "dataset <- dc.ElogToCbsCbt(elog, per=\"day\", \n",
      "  T.cal=end.of.cal.period, cohort.birth.per=as.Date(cohort_end_date))\n",
      "\n",
      "# estimate model\n",
      "cal.cbs <- dataset[[\"cal\"]][[\"cbs\"]]\n",
      "params <- pnbd.EstimateParameters(cal.cbs)\n",
      "\n",
      "print(params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Started making CBS and CBT from the ELOG...\n",
        "...Completed Freq CBT\n",
        "Finished filtering out customers not in the birth period.\n",
        "No dissipation requested.\n",
        "Started merging same-date transactions...\n",
        "... Finished merging same-date transactions.\n",
        "Started Creating Repeat Purchases\n",
        "Finished Creating Repeat Purchases\n",
        "Started Building CBS and CBT for calibration period...\n",
        "Started Building CBT...\n",
        "...Completed Freq CBT\n",
        "Started Building CBT...\n",
        "...Completed Freq CBT\n",
        "Started making calibration period CBS...\n",
        "Finished building CBS.\n",
        "Finished building CBS and CBT for calibration period.\n",
        "...Finished Making All CBS and CBT\n",
        "[1] 0.3674061 4.8437347 0.9404154 6.9846649\n"
       ]
      }
     ],
     "prompt_number": 512
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Analyze the Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have estimated the parameters of the Pareto/NBD, we can use it to make projections. For example, the code below prints the expected number of transactions for a new customer in one year."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R print(pnbd.Expectation(params, t=365))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 2.376353\n"
       ]
      }
     ],
     "prompt_number": 513
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Model fit can also be assessed. The graph below is a histogram of repeat transactions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# histogram\n",
      "pnbd.PlotFrequencyInCalibration(params, cal.cbs, 7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]\n",
        "[1,] 4264.000 761.0000 327.0000 212.0000 125.0000 98.00000 86.00000 405.0000\n",
        "[2,] 4270.503 767.4463 339.5965 195.1645 127.8474 90.68475 67.87222 418.8852\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oqKio7777zvr2kUK8a3XjNCFOR0YS0IDMEhMTFy5cOGTIECHEU089lZCQoGxPSEiIi4sb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\nAJIioAFAUgQ0AEjq/wGOFlZrFJlXewAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 514
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following two graphs show incremental and cumulative transactions, respectively, for both the data and as fit by the model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# inc tracking\n",
      "T.cal <- cal.cbs[,3]\n",
      "actual.inc.tracking.data <- cbind(dataset[['cal']][['cbt']], \n",
      "  dataset[['holdout']][['cbt']])\n",
      "actual.inc.tracking.data <- apply(actual.inc.tracking.data, 2, sum)\n",
      "inc.tracking <- pnbd.PlotTrackingInc(params, T.cal, T.tot, \n",
      "  actual.inc.tracking.data, xlab=\"Day\", title=\"Tracking Daily Transactions\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Z6ha00+v1PosWQVWVQqEoLy+3P1QUaARpBCjQjqPZc9DEB81KcXTo0KFbt26W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\nWcqNrlq1KiYmZvny5RERER4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afZIQXf8Ir10cCHes2uzgvtPOZDJRFAVxcaBUgoVO0Xh5\nebGytK6Bt7f3iRMnWBYOAPD19R07diyrMTw8fNasWcytih944IGzZWWweTPcvJmcnNytWzfWGnpo\nGYFOSUnhchmCOAAU6CbBmiRkRdB5eXkBAQEwciR89ZWdTlatWtW9e3eHjNehkMWEkZGRHK+fP3/+\nKsZCns6dOyfdvg2bN8OMGbeuXn3ggQe8vLwaJ9DcUxwGg6GgoECn03EcM+KS8NTFgamMhmI2mwUC\nAck4M0uGkpLQ6enp3fz8QCQCejGhNZRKpUuu3vT29u7Vqxf3l0YqtdKHEolEq9VCx46wenXK9evd\nu3dnraEHzgJtMpm8vLy4TBJqNBqz2ZyXl8dxzIhLgi4Ol4JISUVFBanFAfcL2pl37x7bhn8v+/j4\nWM4QNoiakHnQoNv5+cHBwV5eXmVlZcwLOAq02Wz28PDQarX1XkmmdlGgEZ6AAt0MkBSHyWSio0WV\nSlVZUNBh796il15y7ticSHR09LL7m5c3jm7duiUnJ5MfdtQ773SsqKAjaKPR6ObmxlGguUOWgDLt\nfUgbhL8uDqQRWJZeUyqVkUeO/NmpU2DXrs4aldNxd3f38/NrSg9EoNesWdOrVy+YP3/ojz9q7y84\nVKvVUqmUrkpaUVExc+bMpo+Z1L3DCLqNgy4Ol8KyeLFKpfojMnK3XB4aGuqsUbkA3bp1W7RoUWFh\n4X//+18ICbkza9bgb78lp4hACwQCEl9nZWVdvHix6XfUaDQdOnTACBrhCSjQzUCtQFdXw5IlsG6d\nUqnMVquLS0td0uDsMPr06XPw4MGVK1eSkq3mIUN+GD6cnCICTV+Zl5eXmZnZ9DsSgcYIuo3DUxcH\n0jikUmlBQYGXTAbPPgthYTBvHr3hE9IUxGLxwIED6UOVSpVDJvpu366qqpLJZPSp3NxcW/Y4kq0G\nAIFAYDQa7d9RrVZ37NgRy+22cdDF4VJIJJLc3NweZjNMmgSzZgEAyWPa2UgFaQS1Lo6333Y/epT5\n9ubl5ZGtDyyfRe9oY7kQ0erF7du3r9kjEUGcDQp04zGbzaRKiVQqzc3NLQkPh/srmAUCQUZGBiag\nm5fahSrffuu/bVskwxOdl5fXp08fq9vP08kQT0/PeteqqNVqmUxmMpmac9xIawNdHK4AvaW3SCR6\nOD+fVbZNLBbz5G/sMnh4eNQkMRSKi+++2yUrCwAEAoHJZMrNze3bt6/VNLRGo+Eu0PTFSFsGXRyu\nAKmUBACQl/e82cwqBq1SqTCCbjmKJZJr48bB/bUqeXl5ffv2bZYIWiKRyGSyevcUB6x7h7Q8KNCN\nh9QaBQA4c+aSRMKKoJVKJQp0y0HL7rwbNzRZWRUVFV26dLEaQRPNBQC5XF7vam8SQfv7+3Nx2j32\n2GONGjvCd9DF4QrQKQ44d+6SpydLoL29vcOsbXCFNAu0QCd07ix/+WWp0di+fXurEXRDUxwSiSQg\nIICL065ZjH0ID0EXB9+prq6u95raFMeSJbdVKpZAb9mypXazK6SZoEtq0AKdGRGR/fLL76SktGvX\nrrCw0PIpDU1xcI+g0S6NtDQo0NZ5/PHH6/341aY4VCoPixQHLlFpCWgjBy27MpksOSho8+DBFEVZ\nLcdIpziaN4I2GAxVVVVcCjAhrQ50cfCdjIyMjRs32r+mJsVx8SKcOyexEGikJVAqlcQKzRTo1NRU\n78BAABhWVGSyWB/UiElCLhE06YrjJgBI6wJdHHzH19f3999/tx8fabVaDw8P2L0bKEoqlbrkvoJ8\ngxTaBguBJtuEu/v6Vo8dC3WXmdBXcp8kDAwMRIFG+AAKtHUEAsEzzzyzZ88eO9fodDqZQAAnT0Lf\nvn379mXtOY20BAqFgo6gSeJCJpPduXPH398fAIr69El75RV48klgCLHVSUKz2fz8889b9k9SHH5+\nfvWmOIjHDp12Lgm6OHgN+fC/8sor27ZtY526cOEC/Vin04Xn5cGCBSASffzxx8zSEEgLYTXFQQt0\n+/btk/394bvvQCymn2I1B11SUnL69GnL/km3dJxuB4ygXRh0cfCa0tJSlUrl5eUlFouZCxZSUlKG\nDRtWUFBADnU6Xf4DD8CUKU4aZluE3jeWKdBpaWkkxREcHJyVlQUdOoC7O9y9C9evg40IOj8/Pycn\nx3JJN5lXoCjKZDLZ3wGusrJSJBKhQCMtCgq0FUpKSkhC2c/PLz8/nzSaTKbXXntt+PDhGRkZpEWY\nkVHj4kAchVUXh1arpSPoWm+yVAqvvQbHjlmdJMzPzzcYDHbyGJGRkbdv37YzksrKSu47hSOtC3Rx\n8JrS+3WcmQK9cePGoUOHjh49ukagb9zot2lTjQ8acRR0iqNmhhaAZJbqRNAEPz/45Rf44ouuV69a\npjjy8/OlUqmdlSYDBw48f/68nZFUuNpclwAAIABJREFUVVX5+/ujQLsk6OLgNVYj6N27d7/zzjuh\noaEZGRlgMsFrr52aOBEF2sHQKQ4AIKUEZTKZQqEgEhwYGHj37t3aq+VyOHDgtqcniaBray0B5Ofn\n9+7d2+rKQ0K9Al1ZWRkQEICThEiLggJtBasRtNlsFolEoaGh9+7dg4MHYfjwHG9vTHE4GG9vb9Zy\nQZlMRsJnABAKhUKhsM7+kGJxmkgklUph925gRLv5+fkPPvignQi6R48eiYmJdkZSWVmJEbSrgi4O\nXlNSUkIE2t/fn6Qp6dLPYWFh6enp8OSTsHRp7VJvxFEEBgZmZGTo9Xq6hSnQANCvXz/W5oQ1OWiF\nAh5/PLS62mAwAEB+fr6t8qQEoVAoEolYewEzqaysDAwMrNdYjbRG0MXBa0pLS0mKw9fXl3g2iouL\nvb29AcDHZPK4P0lYu9QbcSCPPPLIqVOn6ENvb+85c+bQh/379//nn3+Y19fY7MaOhW3bFqWkFJ47\nBwD5+flRUVFWd2ChiYqKSkhIsHW2qqrKz88PUxxIi4ICbQVmBE1SHNnZ2cHBwQBAzZolu7+vXW01\nO8SBPPfccz/99BN9KBaLJ02aRB8OGjTo3LlzzOurq6tFIhEAQMeOu15+OU0gAIDi4uKePXuy9h6s\nrq4WCoV2umJCctCY4nBJ0MXBaywj6JycnICAAEhLA6EwzceHzDWhQDuFPn362Als6zjtLPBv3z47\nNxeqqz+4dk1UWMiqWUgvaSFYBuNMSA4aI2iXBF0cvIYWaHd3d1KOIycnJzAwEH78EWJiQkJCiARg\nDtopUBQ1aNAgO+88PXNgSY18C4U7Q0JgwoT+xcXMs6z9rmwVmCZgBI04ABRoK5SVlbFK02VnZwcF\nBcGiRTB6dEhICLFCYw7aWTzzzDN2dg4cMGAAc0U+E2KUNhgMaT4+EBcXrVaXMIoi0ft/0ygUivLy\ncqtdoQ/ahUEXB68xGo1ubm7ksUAgMJvNNRE0AADUWKExxeE8oqOj165da+usHQtzcHBwZmZmQUGB\nr68vKBS/jxuXWVAAGg3cugWM1Yk0vXr1unbtmtWu1Gq1UqmkjdWIK4EujlaDSqUqLi6uTE/vtnAh\nGAzAEGhMcTgLiqLat29v62z//v3//PPPUaNGDR06lOVlJrO++fn5vr6+QK881OthzhxYtkxbWcmK\noHv37m3rg0o7LxGk5UCBrgc/P7+yixff+eMP4bvvgkgEADVrVRirjRFeIZfLT506dezYse3bt7/2\n2mvMUwKBwGQy5efn+/n5AZ2S9vKCo0fB27vj3LlSC4G2MyGJuCr8cXEI67+kjcHMbwCAn5+f5Ouv\nP+zc+bsRI0hLSEjIvXv30tLSKioq5HK5k4aJ1E94ePiRI0dYITBFUXl5eUSgg4OD//zzTwAAgQBe\ney2+QwfJ1avMizt16pSSkuLAISO8AF0c/IU1Q+jn53f6+efvMWo9e3h4VFVVzZgxY+PGjfgjl+e4\nu7sPGDCA2eLr65uYmEiq39GGHEKlwSCRSCAvDwYPhvPnAYB8VdvZQRj/AyAtCgo0G9pjR/Dz87t5\n8yZrB1itVvvII4906dLF4aNDmkpwcHBCQgLJQQcFBTGNdDU2O39/2LcP1q6FWbPAaOzUqZPVuqNE\nmknlaIcNHnEM6OLgL3QpO8KIdesSEhKCgoKY17z//vuLFy92+NCQZiA4OPjy5cskxSGRSMrKyujF\nJrU2u4AA2LEDZs0CirI6T6jRaOhip8wtHRDXoG25OMxmc2xsbHR0tEqlEgqFKpUqOjo6NjbW/o4V\nzoJe5w0AkJUl9vC4fPkyS6CfeOIJMWNTJaQVERISUlBQQFIcAPDiiy9u3bqVPGbb7Pr0AYGgT48e\nvZYuhbNnmZ1UVlZ6enoCgKenJ9ZLQloORwj04sWLN2zYsHTp0lu3bmk0mlu3bi1dunTDhg1Llixx\nwN0bSp0Ux7591NNP3717l1kvDWnVBAUFSSQSIq8A8MILL+zcuZPECpYLVQCg+4MPfhYWBuvXw9Sp\ncL8UdVVVFelBJpPham/Xgz8uDkcI9KZNm/bs2TNu3DhfX1+RSOTr6ztu3Lg9e/Zs2rTJAXdvKHQx\naACAsDDZlCkURbEiaKT10r59e5LfIHh6eg4aNOj3338Hi1ocBIVCkVpdDTt3wptvwv3ffJWVlWQn\nF+YuLYjLgC4OAAD+pDg2b95MT/XUyUGPHy9Qqdq1a0cvI0RaO0FBQayv27lz527YsAEsanHQuLm5\nGY1G6NcPyDf3nDnSHTsUFvscIkiz4wiBjomJmTBhQlxcXGFhocFgKCwsjIuLmzBhwsyZMx1w93pJ\nSUmZP3/+4cOHyWFtBF1dDSUlAODn54cRtMsgFosPHTrEbImIiCgqKgIbKQ4ACAoKqlM5es0aY1HR\nnB9+gNOnMcXhkrQtF8eqVatiYmKWL18eERHh4eERERGxfPnymTNnfvrppw64e72sX7/+66+//vrr\nr8lhbQ760CH47jsAeOGFF9q1a+fEESLNC9l7gQlZfGRZi4NAL+6vQSxOevzxX+bMgc6dPT09tYWF\ngE4714I/Lg5HrCSkKGr27NmzZ89u0LMuXLhw8uRJVmN8fLxCoWi+oUFpaenFixe//PLLI0eOXL16\ntVevXrUujkuXYMQIAFi4cGEz3hHhIVFRUZcvX7Yj0Onp6UOGDKFbKioqRD4+4Ofn6emp+Ptv2LgR\nXn8dnn0WBOhbRZoT/v5/Cg4O7muBv79/85a/2Lp168svvwwA8+bN++qrr4Bps0tIgKioZrwXwluI\n2dlWiiMsLKxOBF3XZpfUtSscPAhJSfDKKw4aLtLCtC0XB43RaFywYIFKpQoICJg/f779Uo3BwcEj\nLQgJCanZvqiZOHjw4JQpUwBgyJAhJSUlo0aN0mq1NZ/SmBhgrFhBXJiePXteu3bNlkCzVoQDw2bn\n6elZVVUFSiV8+CF88w0AQEUFfPcdtHwZ0tdffz2XUcwaaUbalouDrlewfv36ixcvXrlyJT4+PjEx\n8ZNPPnHA3e1gNBoFAgH9q3b37t3Hjh2rzas88YTTRoY4loCAgNzcXFvlCWu2cmfAjKDZLg6JBMrK\nYMQIWLUKWnINS1JSEmv/csT1cGgEHRsbu2bNmtDQ0Pbt269du3bHjh2OvLslaWlpHTp0sH4uPx/y\n8x07HMSZyOVyW2sCLU8xF6qwBVoohNdegz//hA4doO6WWs1LSUkJTyayXI+25eKgSU1N7dGjB3kc\nGRlpZ3NPx5CcnNy1a1fr57ZvB9sbhiKuR/fu3bn/h6x/oYpQCM89B2FhAACrV8PkyXDiBDSr8V+n\n09na7QVpIvxxcThUoD08POgSFikpKZ07d3bk3S25fv36Aw88YP3cpUs4Q9imePDBB+3sj8PanNBe\nisOShQth5Uo4eBDeeKOZBgsA4OPjU8edjbgiDhJoiqIoiiopKaFbVq5c+d577znm7rZITk62LtC3\nbkFpKQQHO3xEiNPo3bu31RlCAssK3TCBBoCICPjiC/jySwCAkhJYsAAuX27KaKurq4VCoVQqxVp6\nLUHbcnGYGdCNu3btmjhxogPuboeMjIzQ0FArJ8LCYO9ehw8HcSadO3e2s6CfrGShD6uqqkiKozEr\nCVUqmDQJPv8chgz53xtvNK7gQVlZmVKp7N69+/Xr1xvxdMQ+bcvFwU/MZrPJZBJYriyoqgJ3d7C2\nYAFxYYRCoeXCKBpWBE1v6F5TpqOhPPQQfP89xMV9tHNnbm4unD4N586RMxzlnrj17expywQXo7de\n2q5AZ2VlWdkZetcuWLPGGcNBeA29U3AzklNVda+gIC0tDQID4YcfoH9/WLnyySefLCsrq/e5xcXF\nKpWqV69eXAR6zpw5x48fb44htxXaqIuDVyQlJXXr1q1OU3k5rF8PCxY4aUQIf2FF0MyoudFFGa9c\nuRIeHp6WlgYREfDll3D6NIwcWVBQkJGRAYcOAWPCxpKSkhJvb+9u3bolJyezTu3du5dlCkxJSdnL\nLWV39OhRnHiENuvi4AlkD9Dk5GS2QK9aBUuWYHIDsYRZ0O7vv/9mbkcZEhJy586dRvR55cqVJ598\nMi0trebY3R0GDiwuLs7IyIDCQpg8GSZNolMfLEiKQywWGwwG1jfEN998wxqPm5vb5cuXueydGBcX\nh4tfeEVbFOg+ffrExsZaiaDfeQcef9xJg0J4jZubW3V1dV5eHgCsW7fu9ddfp089++yz+/bta0Sf\nV65cefrpp2sFGgAAioqKMjIyYPp0OHIE1qwBUkYxJwd++gkYhg2S4gCA8PDwu3fvMnvIyMgoKCig\nD0msPWjQoHM2tJ5JWVmZ01cn8IG25eLgFYWFhWFhYVeuXPnxxx8jIyPrnMPKG4htli1b9vrrr2dn\nZxcUFPTq1YtuHzNmzG+//daIDrOysgYNGsRcRK7RaEQiUW2yOzAQOnUCAJBKISUFRo+GiRMhPR3u\nyy7cL/PE7JYl0CkpKZ06deL4LVJeXs7c5rzNgi4Op3H+/PkhQ4asW7fu0qVLdTZ+fftt5w0KaQU8\n8sgjSqXyueee+9e//sVsl0ql3t7eDQ08SWEmsVis1+vpxuLi4t69e7Mq5wEAeHnBkiVw+jR89hmJ\nqQMvXuz855+Qk8MS6PLy8srKysLCQrrl9u3bkZGRgwYNOn/+fL2jKi8vxwiaV7Q5gb5w4cLAgQMB\noGPHjrWtN29CTo7TxoS0ElavXu3v7z9+/HhW+9NPP71///4GdZWYmEjKHohEIoPBQBqLiop69Ohh\nb5ouPBxkMgC46u4u9fCAmJhHVqy4yhDojIyMbt26WUbQAoGgR48eiYmJ9kel0Why8IOALg4n8s8/\n//Tr14/d+u238NJLzhgO0prw8vLau3evm5sbq/3xxx8/cOCAnVm4o0ePbt68effu3XTLlStXevfu\nDXUNfMXFxb6+vlyM1elarXDuXDh0SHTyZAGJl+fOhbffrvr11/5RUZYCDQD9+/e/dOmS/W7d3NyY\nEX2bBV0czsFsNldVVcnlcvYJNzcYOdIZI0JcAYVCMX78+GeeecaWhfnf//63SqX67LPPtFotaaEF\nukOHDvQ8YXFxsY+PD5fFL2VlZV5eXuSxl5dXeXk5rFsHU6cK//prZlFRTYojMxMAMjMzid+f46oW\nhFe0LYG+efOm9QpNy5aBRViEINyZP3/+3LlzH3/8cTpfwUQkEk2cOLFv3770lCBtImIKdFFRkbe3\nd3BwcL1mZOYi2JrlKgIB9OmzLypKv2hRUVERGAywaBE89NAbt24Jrl4FgO7du9eb4gCLslBtE3Rx\nOAc6AV2H6mpnjAVxNUaNGjV+/HhLs0RFRQX50VazLAUAAAwGA9kbiBVBe3t7s/eorQ9maJyRkdGh\nQwej0QgiEXz/fdHBg6c6dwaxGAAkeXmTbt6EEydAo8nOzrb8IiEFmNq3b4/zhOjicA7nz5+3ItBv\nvgm3bjljOIirMWPGjNjYWFZjTk4OKcNEa3F5eTm997FliiMkJKTRAk3fi3D7zh1B//5ASjaGht6L\njKw4eBAef/zzKVPOnDkDGg0zOqmoqFAoFMHBwei04w9tS6CtF4BOSACWIRpBGoW3t3fHjh1Zi/Fy\ncnKCgoKAocXE+kbOBgYG0gkNkuKoN4LW6XRMh2inTp1u375NHhuNRjc3N4FAQGYs6RlCAACBwH3k\nyFOjRlX8/POWy5eTk5Ph9Gl49FEYOxY++QTU6rKyMoVCgRE0oIvDKZB6p+wp+OJiUKnAsqYdgjSK\nefPmrVu3jtmSnZ3NiqCZukmLKTBSHPYLM9GrVOgeKIoyGo1EnQHA29ub1F5nfhMAQO/eva9evXr4\n8OFnn302OTkZRo2CP/+E3bvJ3hTl5eVjMzIePn7c/a+/oL4CeFqttjFl/FoJ6OJwAqxffzXodMBY\ntosgTaRHjx63b99m1seg/+P5+voSA1xKSgpTN+mq/6WlpSqVqt4ImhTiYLb079//1KlT9I3atWtH\nbsSaFSfJkH379r377rs3b96saVUoYNw4kErLyspuDRggHDrUKzERZs2qORsfD3WXkhO++OKLxi1w\nRxpEGxJo1qeihsBAePRRZwwHcVlCQkKYNgxmZECE+/bt27WZB4DIyEiSoyDbzBMfhcFg+O9//0vb\n8rZv367T6chjuhAHzaxZs7766it6Awr6myArKyuYsTFQUFDQnTt38vLyunbtSvdMU15eLvHxUT33\n3MaAAPj++5rWO3fg/ffh4YdhzpyaFqOR9HzLdWdu0MXhBFifihqsRQcI0hQ6deqUkpJCH2ZnZ5Mc\nNAAolcqysrL09PQwsp9s3espiiItRqNx3Lhxv//++86dOwGguLh4zpw5Z8+eJWdZKQ4A6Nixo8lk\nOnXqFJEVX1/fwsJCYsWj+yTI5fLRo0cDgJeXV2lpKfMUmbpkb+L13HPw3Xdw6hR8/XVNy8svw8MP\nP3PokOzEiUa/RTwHXRxOwEoEfeUKrFzppOEgLgtLoPPy8vz9/cljkoamk8UEOoKmefLJJ1evXr1z\n586tW7cCQGxs7LPPPnviviBapjgAYO7cuatWrSIRNElxpKWlhYeHsy574YUXJk+eDACWtaTJJCHr\n+uXLl//+++91mr79Fk6d+sbP7xqpOl1dDWPGwMyZsGkThjvNThsSaCsR9HffwfPPO2k4iMvCElza\n8gwA4eHhCQkJ9CJAAhF0tVotvV+L/O233+7Tp49SqezVq9eJEyf27Nmzdu1aOoK2THEAwPDhw4OD\ng0lgTlIcViqeA0yfPp1UobEU6PLycjIwd3d3Op2SmJh46tQpy9eYLpGkeHgAAAiFEBcHCxaApyeQ\nV11cDHPmwMaNcOECaDTc3jMAgMzMzFWrVq1atcrpGy2ii8MJ5Ofn+/n51R4bjXDmDDzyiPNGhLgm\nrAiaSYcOHY4ePcr6JUdqOhOPHev6efPmTZ8+fdy4cUql0s3NjSQfLFMcAEBR1G+//UYUmaQ4rAo0\njVWBJhE00wqdlZX1zz//sJ5rNpspivLy8qpZ2i4QwP+3d+9xMWb/A8A/00xKuk8pJX5y29bXbdmE\nSGpTrrvJSknZ7WJ3s7GEsLKum7Bui8h9c0kWZYUiYV0WbVhJUrqgMukibDU1vz+OfUwzzTT3eUyf\n9x/PazrzzJkz85z5dObM5zmPnR34+r5bL8HUFGbOBENDOHoUSHAvKoKVK+GPPyA/H0SvWJKWlsbh\ncLS1tRMSEkTtoxqYxaFqpEs1KdLSgj17MMEOKZyZmRm14Cd1/W+iS5cuqampAt/kWCwWl8slZ6kI\nVGVnZ+fh4TFjxgwAcHR0JIPZZqc4AMDa2pqc/02mOGQI0GQE3alTJ+qUdC0trdevXwtctKW8vJzN\nZgvPzPDXDj4+EB0Nbm4AAJaW8OmncP8+LFsG168DAOTmwrZtcPUq8K1eUlZWNnz4cHd395KSElHN\nbm1aS3ji/6HmHQYDPvpITc1BGo7BYJDsZoHkzi5durx48UI4m8jAwODJkyfC42IAiImJITWMHDmS\nXHe8tLS02QBNISPovLy8JmvqNiW85gY1B927d++7d+8CQElJiYWFRY8ePQQSNsiLor4o5Ofn86+f\n1wxtbXBzg3nzYM8eGDIEAMDMDExNISkJpk0DMqFx926HS5f+r7q6g4kJuXKNGmEWh6oJ/kLY2Aj7\n96uvOUjDdezYkcwSCIwMDAwMzMzMhLOJunXr9tdffzUboCn29vbXrl1buHAhi8XiT54Tpqur+/bt\n28bGRuGVUfnp6em94buMFjXFQZ07Tn62sbe3F1jsn7yobt26kQC9cuXKvXv3inmiZhgbw+TJsHo1\nnDwJvXoBAJiZccvKOp87ZxIUxCJrUl+/DjExkJ4O4qO/EmAWh6oJ/kKYlfXuqxZCSkAFL+HTo5yc\nnEiuBb/u3bvfuHFDeIqDX5s2bWxsbMzNzX/77TfxkRcAOByO4FdGIR9//PG9e/eoP8laHABga2tL\nLjtLznh0cHAQCNDUCDo3N5fL5f7999/p6enin6tlVlZHTE2ZW7fCqVOl5ER2GxswMoKzZyEwEMhg\n//Rp2LQJLlxoPekirSVAC46gr16FwYPV1xyk4aj1MYQDdEJCgnB47dat282bN8WPoAHg4MGDs2fP\nlqQB+vr6YiagCXd398TEROpPLpdLGsZgMJhMZn19PTlT/OOPPxZIqyAvipzxeOnSpVGjRr169arZ\ndValUlNTwz9fD9bW4O0Nq1bByZNA8v8GDgRra/jzT1izBkieyc6dEBEBsbFw5Yqczy7QEsziUKlH\njx717Nnz/d937sDQoeprDtJw1LxtMz9+iNi/urpa/AhaKubm5s2sC9aUi4vLxYsXm73Lzs4uOzs7\nJyenR48eTCZTV1eXfzLk2bNn1tbW5MICR48e9fLycnBwuK64r6Tv80MEtG8PEyfCjz/C1q2gowMA\n8OWXMGEC6OkBlWry00/g7Q0REXDokMwNwCwOVeNwOE16/6+/gujfTxCSU9euXR8/fgyiVoAR0qlT\nJ21t7RZH0JLr0KFDLzK3KxqTyezRoweVy8Gf5tSnT5+7d+9Sp9gMGDCAnNNIPH/+3NLSEgCMjY1v\n3LjRv39/JycnUbFeBhYWFmVlZRLtamQEDg7g4wPUF4vISNi0CSZMAOrCSeHh4OAAbm4QGfmupLgY\nxF6UoLKykkzyqF1rCdCCOXYIKRObzS4tLc3LyysoKCCxTDwWi9WlSxcFBuidO3e2OIIGAE9PT2rN\nI/5cuj59+mRmZlJ/Ll68+PLly/Pnzycr2HE4HDMzMwDo3r378OHDGQzGsGHDmj2fBQDq6ury8vLy\n8vLEX+2Qf41sCwsL8Zl2PB7vrZhTYNq3BwcHGDv23Z/R0XD9Ohw5AsHB70oOHAAvLxg4EMLC3pX8\n8QekpUFODvz7LwAcOXKEOvlTvVpFgCaXinj/9/XrcP68+pqDWoUvvvgiKirKycmJf+1mMX788Udj\nY2Nlt0qAm5sbOZO7rq5Oh0waAABA7969U1NTqX8tbdu23bdvn5aW1v79+4HvrIJJkyaFhIQAgIGB\nAZfLbTZo7tixIzQ0dNasWQKrsArgP4/M0tJSfIBOSUkJCgqS6pWCiQlQqS8REXDuHNy6BRs3vitp\naIArV2DdOoiKamhoOHPmjLSXaVcSVsu7fPiof/jvnDjx/r8rQsoRHh4u1f5Tp05VUkvE0NHR6dCh\nw5MnT/T19fkX4mjXrt2bN28E0gHDwsKCg4MDAgKo76MODg7UvY6Ojn5+fmw2OzQ0tHfv3lR5Tk7O\nqlWrbGxsAgIC5syZI6olZWVl1KDVwsJCfCr0kydPkpKSJJw+ksj48TB+PLl58vffR48eTZ2dr16t\nYgQteJL3rVvwySfqaw5CNOLm5nb27FnhlZL69u0rEKAtLS3fvn1bUFDQ7GkyCxYsWLNmjaura1xc\nHH85SQVhs9lVVVViMj2kGkEXFRXNmDFj+/btLb46GezYscPX1xezOFRHMEB37gz/rUqDUCtHTlCk\nzvOmfPnll/wDZGLMmDGxsbHN5qXo6enZ2tqOHz9eIJ2jpqZGX18fAOzt7f/66y9RzSgrKzM3Nye3\nLS0txY+gCwsLQ0JCzp8/Ty3qpCjPnz/X19fX09PDLA7VEQzQu3apry0I0Qu5wpbwCNrLy+sjobUQ\nPD09Y2NjxUws6OjotG3blkqS41/Jz8XF5YLoJaT5P6Qt/kj49OlTGxubSZMmHT16VMxuMuBwOAqb\nNlGEVhGgS0tLmwRohBCfPn36XL58WWAE3axOnTp16dJFfGb3iBEjyJohAJCfn9+lSxdy28nJ6dKl\nS6Iexb9qtqGh4Suy2LQIJO4PGzYsIyOjxTZLhSxEhWtxqNSLFy/eB+ivvgLNvdglQjJwcnJKSkoS\nXq2/WV9//bX4BL4RI0ZQZ37zX7VWT0+vsbFRVHrcixcvqCkOaJrzJ4BaY8TU1PTly5eStFlylZWV\nxsbGuBaHSr3/9tTQAI8eQUvrGCDUqjg7O9++fVvCAB0YGCg8N81vwIABt27dIrcFLis+dOhQUbMc\nAgGawWBQMbqyspJ/fe2SkhKS/2dqalpeXi5JmyVHArRi65RHKwvQd+9Cnz7qbg5C9GJhYWFnZydh\ngG4Ri8UyMTGhrl/OnwoSFBS0evXqpKQk4UcJnKxgampaUVFBbm/YsCGSOgkQgLo2roGBgfiZEBmQ\nKQ5ci0Ol3v9CXVMDEyaouzkI0c6ECRMU+OPYZ599dvbsWRAaQdvY2Jw5cyYuLm7JkiUNYmcaqd8J\na2trU1NTi4uLqYSNwsJCMkHMP8pWFDKCxrU4VOr9URw27N0lHhBCfFauXNlHcV8ufX199+3bB0IX\nlAEAfX39Q4cOmZqajh07NiUlJTU1lcPhNDQ0NDnXly8VOj4+3svLy83NLSUlhdxFjaBBCUs4iLpa\njbq0igD9Hper7hYgpPlMTU27du169erVZs/HYzAYs2bNWrp0aUZGxpUrV3x9fV+8eCGwkh91MuGe\nPXumT5/Ov2ZIUVERuTYuKGEQTUbQ9Mni0PxTvd+8efPuf/g//8C+fRAdre4WIaT5Zs6cGRgYKGZF\nvUGDBg0aNAgAFixYEBUVJZAI27Fjx/Dw8JiYmL59+xoZGRkZGT18+JDMU/OPoMmFuyRJEJRQRUUF\nrbI4ND9Av0+CPn0aHB3V3RyEWoVevXrp6+sLX9xL2NKlS/v37z9lyhT+wrFjx45tumAOWdHU1dWV\nP9GCJHIoMEDzL6pHB5o/xfE+hSMtDUaOVHdzEGotVq1aNXr06BZ309XVjYuLc3d3F7+bn5/fhg0b\nBAoVngrN4/G0tLTok8Wh+SPo9wHa1/f9Gt4IISX79NNPJdzzEwkWL7Ozsxs4cOCmTZv4f3Vks9kK\nT4UGOl1RRfMD9PvTCNWxnCNCSFEWLFgwaNCgIUOGUCXKOJmQVlrNFEd+vrobghCSi66u7rZt29z4\nMmUVG6Dr6+tJth9mcajOux8oXW7dAAARiElEQVQJ/f0hLQ1P8kbog8Y/fAYANpudnZ2tqMorKytJ\nEjR9sjhaxQi6AwCw2RidEdIwbDZbgSNoui3EAa0kQJvfv4/5GwhpHsVOcVCnEWIWh+rU1dWxHB2B\nTrmNCCGFUGyArqysJCnVmMWhIlVVVW3atIH/lgxHCGkSfX39mpoaRdVGzUHTh4ZPcSQmJk4ZPhya\nXiQNIYSEUVMc9Mni0PAAffz48Yn19VBcrO6GIITojizEAZjFoRqvXr16+fKl0Z074Oys7rYghJSC\nwWA0NjYqpCqc4lCp5OTksR4eUFUFTVcyRAhpDGNjY+oi4nKi0uzok8WhyQH6xIkTEzw94exZdTcE\nIaQsUiVyiP9FkQrQ9Mni0OQA7e7u3r17d9DRUXdDEELKInmA3rFjR79+/agrjguj5qDpQ5MD9LQp\nU+Dnn9XdCoSQEkl4be9nz54dOHDg8uXL69at8/PzCwkJSUhIIHe9evXqyJEjAFBbW6urqwt0yuLQ\n6DzotDSorlZ3IxBCSiTh2d5hYWHR0dEdOnQ4ceLEkydPeDxeQECAl5cXACQmJoaFhfFfHwCzOFTi\nxAm8hjdCmq3FKY66urrvvvvOzs7OwcEBALS0tGxtbbt27WpnZ3fv3j0A+P333wMDA3/77TcVtVga\nGh2gmUyQeMlwhNCHiM1mnzp1Kioq6s8//xS+9+XLl6NHjx44cOCyZcsE7vL09Dx27Njr168rKysX\nLVpELkNOYBaHSmzeDFoa/QIRavWGDBkSHh7+ySefhIeHC09G//DDD+Hh4dOnTxd+4MiRI8+fP5+c\nnOzu7m5gYGBvb6+vr0/uok8Wh0bPQSOENJ2Ojo6LiwsAaGlpzZkzZ+/evdRd586dYzKZo0aNavaB\nbdq06dy5c3R09MGDBwEgNDQ0Li5OJU2WAg4wEUKawMXFhclkJiUlkT9fvny5dOlS8b/1eXp61tbW\ndu3aFQC6desWGRlJyjGLAyGEFGz9+vVTpkwpKCgYPnx4SEhIdHS0+FO3x4wZY2trK1yOWRwIIaRg\nRkZGSUlJRUVF33//fXx8vKOjo/j9dXR0+vXrp5q2yUYVAZrH48XGxjo6OpqYmLBYLBMTE0dHx9jY\nWB6Pp4JnRwi1HkwmMyoq6uLFi/LMUdAni0MVUxwREREpKSkrVqwYOHCgsbFxZWXlrVu3Fi9e/Pjx\n49WrV6ugAQghJLnWlcURExOTkZHR5b/Lmpibm3t4eHz00UcDBgwQE6CPHTu2fft2gcJHjx717NlT\niW1FCCHaUOePhOKnOCZOnDhx4kSBwvj4eA6Ho8xGIYRaO/pkcahiDjooKMjLyys5OZnD4dTX13M4\nnOTkZC8vr+DgYBU8O0IISYU+WRyqGEFHRUXFxMQsX778/v37NTU1+vr6vXr1Cg4OxgCNEEJiqCJA\nMxiMGTNmzJgxQwXPhRBCcqqpqdm0adPChQvV3RDMg0YIoabok8WBARohhGgKAzRCCDXRurI4EELo\nA0KfLA4M0AghRFMYoBFCqAn6rMWBARohhJrALA6EEEItYHxYa36eO3cuNDTU0NBQkp0fPHgAAPX1\n9dra2mrZslgsLpcrsG1oaGAymXJutbS0GhsbqS2Px2MwGDJsm33fZKuKwWDwN6mxsVH+l8lkMoXf\nQC6Xq64DSrdta+tgyuhmzXYwFovV2Nj4v//9T5I4U11dffHiRSsrK0l2lhpPc40YMUIhW2dn58bG\nRldX1/r6ejc3t9raWg8Pjzdv3owZM6ampmb8+PFVVVWff/55RUXFxIkTORzOpEmTysrKvL29nz9/\n7uPj8/TpUz8/v8LCwoCAgPz8/K+++urx48dBQUE5OTkhISHZ2dnffvvt/fv3Q0ND7927FxYWlpmZ\nOXv27IyMjLlz5968eXPevHk3btyIiIi4evXqokWLrly5smTJkvT09MjIyLS0tGXLlqWmpq5YseLc\nuXOrV69OTk5es2bNqVOn1q5dm5iY+Msvvxw/fnzjxo3Hjh3bsmVLfHz81q1bDx8+HBMTExcXt3Pn\nzgMHDuzevXvv3r179+7dvXv3gQMHdu7cGRcXFxMTc/jw4a1bt8bHx2/ZsuXYsWMbN248fvz4L7/8\nkpiYuHbt2lOnTq1ZsyY5OXn16tXnzp1bsWJFamrqsmXL0tLSIiMj09PTlyxZcuXKlUWLFl29ejUi\nIuLGjRvz5s27efPm3LlzMzIyZs+enZmZGRYWdu/evdDQ0Pv373/77bfZ2dkhISE5OTlBQUGPHz/+\n6quv8vPzAwICCgsL/fz8nj596uPj8/z5c29v77KyskmTJnE4nIkTJ1ZUVHz++edVVVXjx4+vqakZ\nM2bMmzdvPDw8amtr3dzc6uvrXV1dGxsbnZ2dFdglFLslHczFxYXL5ZIO5u7u/vbtW9LBxo0bV11d\nTTqYp6dneXk56WCTJ08uKSkhHWzq1KlFRUX+/v5PnjyZPn16Xl5eYGDgo0ePgoODHz58+M0332Rl\nZZEO9v3339+5c4d0sDlz5ty6dYt0sAULFly7do10sB9//PHSpUukg/3000/nz58nHWzVqlVnzpyJ\nior6448/oqOjk5KS1q9ff+LEiQ0bNvz++++bN28+evQo6WDbt28/ePAg6WC7du3at28f6WD79++P\njY0lHezQoUPbtm0jHSwhIWHTpk2kg508eXLdunWkg50+ffrnn38+e/bsypUrU1JSli9ffuHChaVL\nl5IOdvny5cWLF5MOdv369fnz55MOdvv27R9++IF0sLt3786cOZN0sAcPHsyYMYN0sNzc3K+//pp0\nsIKCgmnTphUXF/v6+j579mzKlCmlpaVffvmlMoOTpHCKAyGEaAoDNEII0RQGaIQQoikM0AghRFMY\noBFCiKbUeckrZdPW1lbIlsVikS2DwWAymWSrpaVFthLif4hCtopC0pUAgLwuRVH4S5b2faYOFnX4\nFNglFLtttoNR3UwqCnzPFYvH431wHUxZgUkq6k4jUaJ///33Q982NjbW1taK3zY0NNTV1Ynacrlc\nsq2vrxe1pYjZjapKzNO12NTGxka1v6W4VWwHo7qZ+P7TYgejulmLT9diB1NgN1O7D+xEFYQQaj3o\nMYxHCCEkBAM0QgjRFAZohBCiKQzQCCFEUxigEUKIpjBAI4QQTWGARgghmtLMAM34jwIfe/r0aScn\nJ11dXSsrq4CAgNLSUsnrPHPmjIuLS9u2ba2srAIDA8vLywWeizAyMpKhwU5OTvytVchrF6hBVLmE\n7ty5M2rUKH19fWtr6927d5PCyspKf39/Npttbm6+dOlSqSrMy8sbN26ciYmJiYnJuHHj8vLySLk8\nx0hUe+Q8RqLeNGV0M2nrVMbHhCLQLeU53GKeq9mupZCPFU1oZoAmJ+Eo9rFr166dNWtWSUnJw4cP\nbW1tfXx8JK9z/fr1c+fOffHiRWZmJovF8vf3538uIiEhITg4WNrW7tu3j8vlStJ+CfE3SZLyFuXk\n5IwbN27atGlFRUXXrl1LTU0l5bNnz66rq8vKyvrnn38ePHiwZ88eyeucOnVq37598/Pz8/Pze/fu\nPXXqVFIuzzES1R45j5God0wZ3UzaOpXxMSGEu6U8h1vUc4nqWvJ/rGhEirMOPzTyvDrxj3316pWe\nnp5sNVdXVxsaGgqX29vbFxcXS1XVy5cvO3XqlJ2dLdxa2V67qEfJ805OmTJly5YtwuVsNru0tJTc\nLikpcXR0lLxOPT296upqcruqqqrZYyHtMZKkPTIcI0K2N1a2biZtnQr/mDTbLeU53KKeS1TX4ifz\nIaMJzRxBK9Xr16+3bNni7Ows28MvXLjQt29fgcLExMRevXpZW1tLVVVERMTMmTN79uwpW0uaZW5u\n3q5du969e2/atKmhoaHF8hZduHChtLTUysqKzWb7+/tXVlZSd1FfWhkMxj///CN5naNHj167dm1V\nVVVlZWV0dPTo0aMFdpDtGIlvj2zHSGZydjOV1SlMVLeU+XCLIqZrESo+ZEqh7v8QSiTPqxP1WPKm\ntW/f/tGjRzJUm5GR0bFjx7///lug3N7ePisrS6qqrl+/PmTIkIaGhmZbK89r//fff2/evDl06NBZ\ns2ZJUi4ek8mcOnVqaWlpaWmpt7d3QEAAKffz8/P19SXlPj4+LBZL8jqLi4s7d+5MjkXnzp2fPn3K\nf69sx6jF9shwjPibJG25zN1M2joV+zER1S3lOdyinktU16LIc8hoAgO01I+tqqqKjIwcNmyYtHWm\npaV17NgxPT1doPz06dPjxo2TtrbBgwc/ePCA3FZsgCYKCgqMjY0lLxfF0NCwrKyM3C4tLTUzMyO3\ny8vLfXx8TExMLCwsVq5caWlpKXmdrq6uERERFRUVFRUVERERrq6uAjvIcIzEt0e2Y0SRNkDz5Ohm\n0tap2I+JqG4pz+EW9VyiuhYh5yGjCQzQsjy2qqqqXbt2UlV4+PBhKyurGzduCN81ePDgK1euSNc+\n0b87UfdKW6GAoqIiCwsLyctFcXR05J98FPgUEb/++quPj4/kdbZt27bFOWgZjpGY9sh2jCgyBGie\nrC9B2joV+zGR5Du6tIdb1HOJ71pyHjKawAAt6WP9/PyysrLq6uoKCwtDQ0PHjBkjeW3r1q3r1KlT\ns9+2UlJShgwZInM7CUWNoL29ve/du1dbW5uVleXq6jpz5kzx5ZLYtWsX9d3W29t7+vTppNzX17eo\nqKiiouLQoUM2NjbZ2dmS1zl48ODFixeTEfTChQuHDh1KyuU5RmLaI/8xkjxAy/MSZKtTeeMY/nvl\nOdyinktU1+Ip6GNFB5oZoOWZZxf12Pj4+D59+rRp08bGxiYkJKS8vFzmOgHg1atX5K7hw4efOHFC\nqhY2W3+L7ZcEeY06Ojpdu3ZdtGjR27dvxZdLaMmSJWZmZiYmJn5+fhUVFaRw165dVlZWenp6n332\nWUZGhlQV5uTkuLu7GxkZGRkZeXh45Obm8rdTtmMkpj3yHCNRh0MF3azFOpXxMRHYh7otz+EW81zN\ndi2egj5WdIAL9iOEEE1hmh1CCNEUBmiEEKIpDNAIIURTGKARQoimMEAjhBBNYYBGCCGawgCNEEI0\nhQEaIYRoCgM0QgjRFAZohBCiKQzQCCFEUxigEUKIpjBAI4QQTWGARgghmsIAjRBCNIUBGiGEaAoD\nNEII0RQGaIQQoikM0AghRFMYoJHGYjAYDAZDW1vb2tp68uTJmZmZ6m4RQtLBAI00GY/He/PmTXp6\ner9+/ZydnW/fvq3uFiEkBQzQSMNpa2t369YtIiJi/vz5y5cvJ4U5OTleXl5sNtvIyMjT05PD4VRU\nVJibm3M4HLJDfX19+/bty8rK1NdwhDBAo1Zj0qRJf/75J3X7u+++Ky4uLiwstLa2joiIMDEx8fb2\n3rFjB9khLS3N3t6+ffv26msvQsDg8XjqbgNCSsFgNOneb9++NTQ0rK+vF9iturq6V69eRUVFeXl5\nzs7Oubm52tra33zzjZOTk7e3t2qbjFATOIJGrcWzZ89MTEzI7Vu3brm4uJiamjIYDCMjo+fPnwOA\nra2tvb19QkICj8dLS0ubMGGCWtuLEAZo1GrEx8c7OjqS297e3v7+/rm5uVwut7y8vKGhgZTPnTt3\n48aN165dGzx4cNu2bdXXWIQAAFjqbgBCysXlcgsKCuLj49euXZuamkoKX79+bWho2K5du4KCgnnz\n5lE7Dxo0SFtbe+HChUuWLFFTexF6D0fQSJMxGAxdXd1hw4ZlZmampaX179+flO/atWvBggUGBgbO\nzs5OTk78D5k7d+7jx49HjBihhuYi1BT+SIhQE9u3b8/Pz4+KilJ3QxDCAI0Qn6qqKnt7+wsXLlhb\nW6u7LQjhHDRC/2EwGFpaWps3b8bojGgCR9AIIURT+CMhQgjRFAZohBCiKQzQCCFEUxigEUKIpjBA\nI4QQTWGARgghmsIAjRBCNIUBGiGEaAoDNEII0RQGaIQQoikM0AghRFMYoBFCiKYwQCOEEE1hgEYI\nIZrCAI0QQjT1/3ASxXGr/VAsAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 515
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# cum tracking\n",
      "cum.tracking <- pnbd.PlotTrackingCum(params, T.cal, T.tot,\n",
      "  cumsum(actual.inc.tracking.data), xlab=\"Day\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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05Aiys6RhdRXHggULiIhfBF0M48VQ63z48MHU1HTChAnjxo2rzvNbtaKQEJKW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\n"
      }
     ],
     "prompt_number": 516
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In addition to forecasting how many times a new customer will purchase in the next year, you can use the model to forecast how many times each existing customer will purchase in the next year, conditional on their past behavior. You can also compute the probability that they are still alive or active (p_Alive). Both the expected transactions and probability of being alive for each customer are computed below, conditional on their observed behavior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "x <- cal.cbs[, \"x\"]\n",
      "t.x <- cal.cbs[, \"t.x\"]\n",
      "T.cal <- cal.cbs[, \"T.cal\"]\n",
      "conditional_expected_transactions <- pnbd.ConditionalExpectedTransactions(params, T.star = 365,\n",
      "x, t.x, T.cal)\n",
      "p_Alive <- pnbd.PAlive(params, x, t.x, T.cal)\n",
      "output <- data.frame(visitorId=dataset$cust.data$cust, conditional_expected_transactions=conditional_expected_transactions, p_Alive=p_Alive)\n",
      "head(output)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "            visitorId conditional_expected_transactions     p_Alive\n",
        "1 4267659195240979286                       0.002074432 0.001214972\n",
        "2 5643813381699005286                       0.008010164 0.015121718\n",
        "3 8445352417811622261                       2.323994918 0.805524617\n",
        "4 7934359074614033866                       0.008010164 0.015121718\n",
        "5 2134408454679554310                       4.019851821 0.767084713\n",
        "6 4741996826496431299                       0.008010164 0.015121718\n"
       ]
      }
     ],
     "prompt_number": 483
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is one final step before importing this table back into BigQuery - forecasting how much each customer will spend per transaction. The Gamma / Gamma model to forecast average spend per customer is run below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "#cal.cbt <- dc.CreateSpendCBT(elog, is.avg.spend = FALSE)\n",
      "cal.cbt <- dc.ElogToCbsCbt(elog, per=\"day\", T.cal=end.of.cal.period, cohort.birth.per=as.Date(cohort_end_date), statistic=\"total.spend\")\n",
      "cal.cbt <- cal.cbt$cal$cbt\n",
      "calculateAvgSpend <- function(cbt.row) {\n",
      "    purchaseCols = which(cbt.row != 0)\n",
      "    sum(cbt.row[purchaseCols]) / length(purchaseCols)\n",
      "}\n",
      "\n",
      "m.x <- apply(cal.cbt, 1, calculateAvgSpend)\n",
      "m.x[which(is.na(m.x))] <- 0\n",
      "spendParams <- spend.EstimateParameters(m.x, cal.cbs[,1])\n",
      "print(spendParams)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Started making CBS and CBT from the ELOG...\n",
        "...Completed Freq CBT\n",
        "Finished filtering out customers not in the birth period.\n",
        "No dissipation requested.\n",
        "Started merging same-date transactions...\n",
        "... Finished merging same-date transactions.\n",
        "Started Creating Repeat Purchases\n",
        "Finished Creating Repeat Purchases\n",
        "Started Building CBS and CBT for calibration period...\n",
        "Started Building CBT...\n",
        "...Completed Spend CBT\n",
        "Started Building CBT...\n",
        "...Completed Spend CBT\n",
        "Started making calibration period CBS...\n",
        "Finished building CBS.\n",
        "Finished building CBS and CBT for calibration period.\n",
        "...Finished Making All CBS and CBT\n",
        "[1]  0.5498189  1.3636491 56.6677359\n"
       ]
      }
     ],
     "prompt_number": 491
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "spend.plot.average.transaction.value <- function(params, m.x.vector, x.vector, \n",
      "    xlab = \"Average Transaction Value\", ylab = \"Marginal Distribution of Average Transaction Value\", \n",
      "    title = \"Actual vs. Expected Average Transaction Value Across Customers\") {\n",
      "    \n",
      "    if (any(m.x.vector < 0) || !is.numeric(m.x.vector)) \n",
      "        stop(\"m.x must be numeric and may not contain negative numbers.\")\n",
      "    if (any(x.vector < 0) || !is.numeric(x.vector)) \n",
      "        stop(\"x must be numeric and may not contain negative numbers.\")\n",
      "    \n",
      "    if (any(x.vector == 0) || any(m.x.vector == 0)) {\n",
      "        warning(\"Customers with 0 transactions or 0 average spend in spend.plot.average.transaction.value have been removed before plotting.\")\n",
      "    }\n",
      "    \n",
      "    if (length(m.x.vector) != length(x.vector)) {\n",
      "        stop(\"m.x.vector and x.vector must be the same length.\")\n",
      "    }\n",
      "    \n",
      "    # remove any customers with zero repeat transactions\n",
      "    ave.spending <- m.x.vector[which(x.vector > 0)]\n",
      "    tot.transactions <- x.vector[which(x.vector > 0)]\n",
      "    \n",
      "    f.m.x <- spend.marginal.likelihood(params, ave.spending, tot.transactions)\n",
      "    plot(ave.spending, y = f.m.x, pch = 16, type = \"n\", xlab = xlab, ylab = ylab, \n",
      "        main = title)\n",
      "    lines(density(ave.spending, bw = \"nrd\", adjust = 0.6), col = 1, lty = 1)\n",
      "    lines(smooth.spline(ave.spending, y = f.m.x, w = tot.transactions, df = 15), \n",
      "        col = 2, lty = 2)\n",
      "    legend(\"topright\", legend = c(\"Actual\", \"Model\"), col = 1:2, lty = 1:2, lwd = 1)\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 497
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R \n",
      "spend.plot.average.transaction.value(spendParams, m.x, cal.cbs[,1], title = \"Actual vs. Expected Avg Transaction Value Across Customers\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qAQA6Nyw3CgCgpxgS9N27d318fExMTDgy1GmDoqj4+HgfHx+hUMjj8YRCoY+P\nT3x8POPIGgAAaAwJWiQSjR8/XiwWUzLUaSMsLCw2NjY8PDwzM7O2tjYzMzM8PDw2Nnb9+vXqVAsA\n0LkxzEHfunXr3LlzJiYmmmojLi7uxo0bzs7O9FNra2tfX18PDw8vLy9cqwIA0BqGEbSNjU1paSkL\nbWOKAwBAAYYR9Lp160JCQmJjY21tbTXShkgk8vf3j4qKGjZsmIWFRWVl5fXr1yMiIoKCghR86scf\nf/zmm2/kCm/dukVfiAgA0OlxWg5jGQ8JqjPapSgqLi7uwIEDaWlpz549MzU19fT0nD9/flBQkILD\nj/X19dXV1XKF4eHhZWVlP/zwQ7uDAQDQoMDAwLCwMC0tms8wgtb4zAOHwwkODg4ODlbpU0ZGRtLL\nDqWMjY1xB1sA6CJwHjQAgJ5iSNBisVgkEjk4OPB4PI2cBw0AAO3AkKCDgoJMTEzS09ObmprKysqm\nTp26a9cujTeMvA8AoBjDHPT58+fz8vLMzMwIIZaWllu3bh03btyyZcs02zDOsQMAUIxhBM3lcumj\nc5aWlpWVlfb29gUFBawHBgDQ1TEk6DFjxiQnJxNCBg0adPLkyaSkJDXPIMFaHAAA7cAwxbFp06aA\ngIDU1NTo6OjZs2fX1NQkJCSo00ZYWNjZs2ejoqKGDh1qaWlZUVGRkpISERGRnZ2NS70BAFrDkKDd\n3d1TU1MJIcOHD8/Ozla/DazFAQDQDgxTHAYGLJ0cjSkOAAAFGHKxnZ1dUVGRBtug1+JISkoSi8UN\nDQ1isTgpKcnf31/xWhwAAF0cQ4IODQ1dvnz5o0ePNDXCjY6OFolEkZGRrq6ufD7f1dU1MjIyKCjo\n008/1Uj9AACd0nNz0BwOh6KoNWvWEEKOHTsm+5I6ybp9a3EAAHRxbCyWBAAA7YDFkgAA9JT8CLq1\n9TEwrAYAYJl8gkYiBgDQE5jiAADQU0jQAAB66rkEjfkNAAD9gRE0AICeQoIGANBTSNAAAHoKCRoA\nQE8xJOjq6urQ0FAnJycul0sImTVr1smTJ1kPDACgq2NI0MuXLy8tLb127VpzczMhJDw8fMOGDawH\nBgDQ1TEslnTixIns7GyhUEhf9u3u7n7//n3WAwMA6OoYRtBmZmZVVVXk73U5srOzpXerAgAA1jAk\n6EWLFolEovv373M4nNzc3BUrVixfvpz9yAvQK2YAACAASURBVAAAujiGBB0RETFhwgQ/Pz8jIyNf\nX98pU6YsWbKE/cgAALo4hjloLpcbGhoaGhrKfjQAACClm/OgW1t1GgAApBgSNKcFIyMjFxeX9957\nr7a2th1ttKxQWqhu+AAAnRdDgo6Ojp4wYUJaWlptbW1aWtr48eM3bNiQmJh469atkJCQdrTx6quv\njhgx4v79+9TfCCHSBwAAwIghQcfExHz11Vf9+/fn8/n9+/f/+uuvv/zyy4EDB+7bty8xMbEdbfzy\nyy8ikWjcuHExMTH0xS8AANAmhgTd0NDAWGJqatruMe+CBQtu3bqVmZn5yiuv3Lt3r32VAAB0KQwJ\nOiAgIDAw8N69exKJ5N69e4GBgTNmzCCEfPzxxxEREe1uSSgUxsXFff7554sWLWp/vAAAXQbDaXY7\nduyIioqaOHFiYWGhnZ3dnDlz6Ly8Y8cO9dt76aWXrl69qn49AACdHkOC5vP5UVFRUVFR7EcDAABS\nbJwHTVFUfHy8j4+PUCjk8XhCodDHxyc+Ph5ncQAAKMCQoMVisUgkcnBw4PF4smcut1tYWFhsbGx4\neHhmZmZtbW1mZmZ4eHhsbOz69evVqRYAoHNjmOIICgpycHBIT083NzcvKysLDAx8/fXX1WkjLi7u\nxo0b0iXxrK2tfX19PTw8vLy8Nm/erE7NAACdGEOCPn/+fF5enpmZGSHE0tJy69at48aNW7Zsmcbb\nxhQHAIACDFMcXC7XyMiIEGJpaVlZWWlvb19QUKBOGyKRyN/fPykpSSwWNzQ0iMXipKQkf3//oKAg\nBZ9qaGgob0EikSCtA0AXwTCCHjNmTHJy8ujRowcNGnTy5Elzc3NXV1d12oiOjo6Li4uMjExLS3v2\n7Jmpqamnp2dQUJDiBH3q1KlDhw7JFd66datPnz7qBAMA0FFwWg5IMzMzAwICUlNT//jjj9mzZ9fU\n1CQkJEyYMEEn8ckJCQkpKir6/vvvdR0IAAAhhAQGBoaFhak5im0Nwwja3d09NTWVEDJ8+PDs7Gxt\ntAoAAG1imIM2MNDNItEAACCLIRfb2dkVFRVpu2GsBw0AoBhDgg4NDV2+fPmjR4+0er4E1oMGAFCM\nYQ56zZo1hJBjx47JFiKZAgCwjGEETTFRpw2sxQEA0A4MI2iNCwsLO3v2bFRU1NChQy0tLSsqKlJS\nUiIiIrKzs3GpNwBAaxhG0NXV1aGhoU5OTlwulxAya9askydPqtNGXFzckSNHfH19ra2tDQ0N6bU4\njhw5EhcXp061AACdG0OCXr58eWlp6bVr1+j7B4aHh2/YsEEbbWOKAwBAAYYEfeLEiR07dtjY2NCn\nwbm7u9+/f1+dNtq3FgcAQBfHMAdtZmZWVVUlFArpBJ2dnS1dKbR92rcWBwBAF8eQoBctWiQSib74\n4gsOh5Obm7tixYrly5er0waHwwkODg4ODlanEgCAroZhiiMiImLChAl+fn5GRka+vr5TpkxZsmQJ\n+5EBAHRxDCPotLS00NDQ0NBQ9qMBAAAphhH01KlThw4dGhsbW1FRwX5AAABAY0jQWVlZmzdvvnjx\noqOj49y5c8+fP4/z4QAA2MeQoDkczrhx4w4fPpyVlTVo0KClS5e6uLiwHxkAQBfXxtLPWBEUAEBX\nmBdLOnfu3MyZM93c3G7cuPHll1/m5OSwHxkAQBfHkKDd3NzWrVs3atSoR48ebdu27c6dO4MHD2Y/\nMgCALo4hQR8/fvzq1avW1tZvv/22vb393bt3d+zYwX5kAABdnHyC/v333//973/b2dnt2bNn1qxZ\njY2N+/btGzVqlE6CAwDoyp67UMXd3Z3L5c6bNy81NdXe3p4Q8s477+goMACAro75NDv24wAAADnP\nJejMzMx9+/bl5ua++OKL48eP//bbb3UVFgAAyI+gR4wYERcXV1hYGBgYeOjQIS6Xu2DBgkuXLuki\nNgCALo35QhVjY+MZM2acOnWqoKBg4MCBq1atYjksAABo40pCGxubNWvWpKamshMNAABItZGgAQBA\nV5CgAQD0FBI0AICe+idBS09/1vh50MXFxa+//nq3bt3eeuutrKysV1991dTU9K233nry5IlmGwIA\n6Ez+SdC9e/f+/ffftbE2//vvvz9q1KjHjx97e3uPHDlyzJgxhYWFzs7O4eHhGm8LAKDT+CdB79ix\nY+7cuTwejxDCaUGdNs6ePRsSEmJqarpq1aqSkpI1a9aYm5uvXbv21KlT6oYPANB5/ZOgp0+fnpOT\n09TURAihWlCnjYqKipqaGkKIqakpIcTc3JwQYmNjU1JSolbsAACdGvOC/ZptY/jw4cnJyXKVZ2dn\n9+vXT7MNAQB0JgwJuq6ubsOGDW5ubgKBwM3N7cMPP5RIJOq08cEHH+zcuVOucPPmzREREepU27YV\nK7RbPwCANjEk6LVr1169ejUxMbG8vDwxMfHy5cvr1q1Tp40333zz/PnzcoUHDhwICAhQp9q23b2r\n3foBALSJIUEfPnx4//79AwYM4PP5AwYMOHDgwPfff89+ZJqhhZNSAADYwcaFKhRFxcfH+/j4CIVC\nHo8nFAp9fHzi4+O1cUrfc4YNI42N2m0CAEBrGBL0jBkzFi5cmJ6eXldXl56evnDhwlmzZqnTRlhY\nWGxsbHh4eGZmZm1tbWZmZnh4eGxs7Pr169Wptm1bthBDQ+02AQCgNbyWRVu2bImKipo0aVJhYaGd\nnd3cuXPVvKIkLi7uxo0bzs7O9FNra2tfX18PDw8vL6/NmzerUzMAQCfGkKD5fH5UVFRUVJS229b6\nFEdMDHnrLYKT+QCgY2JI0BonEon8/f2joqKGDRtmYWFRWVl5/fr1iIiIoKAgBZ/6448/Ll68KFeY\nkpJCX+eilOpqUlCABA0AHRQbCTo6OjouLi4yMjItLe3Zs2empqaenp5BQUGKE7SNjY2Xl5dc4R9/\n/EFf66gUc3NSVdW+mAEAdI6NBM3hcIKDg4ODg1X6lKOjo6Ojo1zhqVOnioqKlK2ib19ibKxSowAA\n+oONBK0zEyfqOgIAgPbDgv0AAHqKIUHfvXvXx8fHxMREU8uNMtJStc/JyCBbtmi3CQAArWFI0CKR\naPz48WKxWFPLjTLSUrVybZCHD7XbBACA1jDMQd+6devcuXMmJibsR6NhFhakslLXQQAAtBPDCNrG\nxqa0tFSDbehsLY7u3YmTk3abAADQGoYEvW7dupCQkOLiYk21obO1OAQC8skn2m0CAEBrGKY4li5d\nSghJTEyULVRntIu1OAAA2oH5lleavSdha7Q+xUEIWbhQ600AAGgHG+dB02txJCUlicXihoYGsVic\nlJTk7++v+FJvzcjN1XoTAADawcY9CaOjo0UiUWRkpKurK5/Pd3V1jYyMDAoK+vTTT9WpVikcDm6q\nAgAdFMMc9Nq1a9PS0hITE93c3LKyslauXLlu3brt27e3u432rcWhGcOHk4YGYmSkg6YBANTT2e9J\nGB2N7AwAHRTW4gAA0FNs3JNQl774gvz5p66DAABoD4YEvWXLlpdeemnSpElCoXDSpEne3t7R0dHs\nR6YZjY0kP1/XQQAAtIcu70nIBqGQVFToOggAgPbo7HPQrq5E+XsYAgDok+dG0BwOh6IoxmWa2bjq\nTxteeUXXEQAAtNNzCZrOwh01FwMAdC6dfYrjyROyZo2ugwAAaA+GBN1yikPr96bSHmNjcv++roMA\nAGiPtkfQGRkZlpaWLISiFd26kepqXQcBANAe8gcJWz7o0aPHhg0b2I5Lg159VdcRAAC0B8NBQvpc\nDh3FowUff6zrCAAA2oN5wX724wAAADnMBwlbYj8yjVm5kjx9qusgAABUxnCpt+wIuri4+N133/X1\n9WUxJE2rqSGPHxMzM13HAQCgmjbO4rC1td2+fTsbtz7Rnu7dyZMnug4CAEBlbZ9m17Nnz5KSEhZC\n0Zbhwwmfr+sgAABUxjDFIaumpiYmJmbQoEHaaPvZs2empqbaqPk5/v5abwIAQAvaOEhoZWV15syZ\nPXv2qNNGWVnZW2+9ZWFhMWrUqFu3bknLzTAvDADQOubT7KRqa2uvXLkyYMAAddpYu3ato6Njfn5+\nSEjIpEmTrly5ok5tKrt5k3zyCastAgBoQhtTHBpx+vTp27dvm5mZ+fn5OTo6Tpky5fjx415eXiw0\nTQghxsa4qQoAdEQMI2iJRPLhhx+6ubkJBAI3N7ePPvqovr5enTYqKipMTEzox4MHDz5w4MDkyZPv\n3bunTp0qwFkcANAxMSTokJCQ5OTkH3/8sby8/MSJE1euXFmj3oqd3t7ely9flj597bXXYmJi3njj\nDXXqVEGPHsTTk6W2AAA0hyFBf//991999VX//v35fL6np2dCQsJ3332nThtr1679/PPPZUtmzZq1\ncuVKdepUAY9HNm5kqS0AAM1hSNCGhoZyJTyeWlPVb7zxxpkzZ+QK16xZg0U/AAAUYEjQoaGhixYt\nSk9Pr6urS09PX7BgQWhoKPuRaRJOhQaADuifobHcikieMvO2586dW7t2bbvboChq3759CQkJaWlp\nT58+NTMz8/T0XLBgweLFi7W9DNPly5eHDh0qqK0l1dWkWzettgUAoFn/jKAphdRpIywsLDY2Njw8\nPDMzs7a2NjMzMzw8PDY2dv369WrH34Yvvvji5s2bpEcPIhZruy0AAM1i4zzouLi4GzduODs700+t\nra19fX09PDy8vLw2b96s1aYfP36clpY2YuRIwuVqtSEAAI2Tv+UVRVGM0w7aOKDHwkHCkpKSe/fu\nkZgYbTcEAKBxDLe80njeFIlE/v7+UVFRw4YNs7CwqKysvH79ekRERFBQkIJPHT16dPfu3XKFmZmZ\nffv2Vb7pbt26ZWRktCdoAABdY5jiMDAwaG5u1mAb0dHRcXFxkZGRaWlp9Ap2np6eQUFBihP09OnT\np0+fLlcYEhJSVFSkZLsNDQ1CobC6upokJZGCAhIY2M4vAACgCwwJ2s7OrqioqFevXppqg8PhBAcH\nBwcHa6pCJZWUlPTs2bOgoIAIBFiOAwA6HObzoJcvX/7o0aOOfiHJ48ePe/bsSQihrKxwFgcAdDgM\nI2h65Y1jx47JFnbEZE2PoM3MzKq7dzcdOFDX4QAAqKaNm8ZqD32uiFbbKi8v7969u4WFRXlzs6nC\n+W4AAD3U9j0JtUT961/aVFtba2JiIhQKKyoqtNoQAIA2MN/yqs2SDqG2tlYgEFhaWlZUVJBp03Qd\nDgCAatoeQWdkZFhaWqrTBkVR8fHxPj4+QqGQx+MJhUIfH5/4+HgWRtACgcDCwqKiooKUlWm1LQAA\njZO/krDlgx49emzYsEGdNsLCws6ePRsVFTV06FB6PJuSkhIREZGdna3VS71ra2v5fP5fI+hu3UhN\nDfn7xi4AAPqP4UpC+oJvDbahq7U4pFMcRUVFZNIkotGrbwAAtI35rt7stM3OFMdfI+glS4ipqVab\nAwDQLIYEvXfv3sDAQELI6dOne/Xq1bt374sXL6rTBr0WR1JSklgsbmhoEIvFSUlJ/v7+ii/1Vl9d\nXd0/CbqpiXTAU7kBoCtjOA/6k08++fXXXwkhq1evjo+Pb2pqCg0NvXHjRrvbaN9aHOqjR9A8Hq+y\nspIcPEi6dSMBAVptEQBAgxgS9OPHj21sbPLy8p48efLmm2/W19fPnDlTnTZ0tRZHTU2NQCDo1q1b\nRUUFMTUlxcUsBwAAoA6GBN2vX7///ve/+fn5r7zyCofDyc7OdnJyYj0wDaCnOIyNjSsrK4m1Nblz\nR9cRAQCogCFBb9myZcGCBTweLzExkRASGRn54Ycfsh6YBkinOOrr64mbGyko0HVEAAAqYEjQ48eP\nLywslD797rvvWIxHkxobG3k8HqFP6+7dm8yZo+uIAABUoLO1ONj01/l8jY26DgQAQAXPJWj6AkIO\nEx2Fp1FTpug6AgAAFbBxT0KdEwgEdXV1/GfPdB0IAIAKusQUx1/rJXWO/wMAoMuQT9ApKSlTpkyx\ntrY2NDS0sbGZNm3arVu3dBKZBllaWlZWVpJp00hTk65jAQBQ1nMJ+saNG2PHjvX29k5OTq6qqrp6\n9eqwYcNef/3127dv6yo+jbCwsKisrCQrVxIuV9exAAAo67k56M2bN69bt+6DDz6gn7q6uoaFhRFC\nNm3a9P333+sgOjU0NjZy/07Hf01xNDYSHsNphQAA+um5EfSVK1dmzJgh946AgIDLly+zGJJm0JcR\n0o//uutVbCz56SfdRgUAoLznEnRpaamjo6PcOxwdHUtKSlgMSTPq6ur4fD79uEePHqWlpcTcnBQV\n6TYqAADlPZegm5qaeC0mAQwNDRs74CUeEonE2NiYftyjRw+xWEysrUlpqW6jAgBQnnw67iTXpLRI\n0GVlZeSFF7AkNAB0IAwXqnQOslMcVlZWZWVlxMGBODjoNioAAOV12gtVGKY4CCHV1bqMCQBAFV0i\nQRsbG0skEkII8fPTZUwAAKroEgmaSOfW6+t1FhAAgIo6bYKuq6uTTdB/4XBwnBAAOgpdJmitnjEi\nN4Lm8/m1tbVk7lzS3Ky9RgEANOifBM24DHTHXQ9aIpFIz+IghPTu3bugoICIRFiOAwA6in8SNKWQ\nOm3oJOnLjaD/StASCe6rAgAdBUtTHBpP+m2Sm4P+K0EfOECOHtVquwAAmsKQoMVisUgkcnBw4PF4\nnWaKw97evqCggFhbYzkOAOgoGBJ0UFCQiYlJenp6U1NTWVnZ1KlTd+3apU4brQ2WtTqIZp7isLVF\nggaAjoJhfeTz58/n5eWZmZkRQiwtLbdu3Tpu3Lhly5axHptamBN0v35k+HAdRgUAoDyGETSXyzUy\nMiJ/3ynqr8kBNVAUFR8f7+PjIxQKeTyeUCj08fGJj49ncwRtZWVVWlpKhEIyfbr2GgUA0CCGEfSY\nMWOSk5NHjx49aNCgkydPmpubu7q6qtNGWFjY2bNno6Kihg4damlpWVFRkZKSEhERkZ2dvXnzZnVq\nVkB2sSRCCIfD+evvQXU16dZNS40CAGgQQ4LetGlTQEBAampqdHT07Nmza2pqEhIS1GkjLi7uxo0b\nzs7O9FNra2tfX18PDw8vLy/tJWi5ETQhxMTEpKamxsTPj5w9q6VGAQA0iCFBu7u7p6amEkKGDx+e\nnZ2tvbbZnOIghDg5OeXl5XnweKSmhpiYaK9pAACNYOMmqiKRyN/fPyoqatiwYfQNtq9fvx4REREU\nFKTgU3l5edeuXZMrfPDggaGhoTKNtkzQjo6ODx8+9LC3J4WFxM1N1W8BAMAyhgR99+7d4ODgGzdu\n1NbWSgvVGe1GR0fHxcVFRkampaU9e/bM1NTU09MzKChIcYIuLi7OycmRK6ysrDQ3N1emUbk5aPJ3\ngiYzZxIzM1W/AgAA+xgStEgk8vX1PXPmjImG5gE4HE5wcHBwcLBKnxo+fPjwFqfEFRcXFyl3IrNE\nIqHPRZFycnI6efIkUTEMAABdYUjQt27dOnfunKays67IXUlICHFxccnJySFNTaSiglhZ6SowAAAl\nMZwHbWNjU9rx737dcoqjZ8+eJSUlJCuLbNigq6gAAJTHkKDXrVsXEhJSXFys1Ya1vcRHY2Mjj/fc\n/wd/nQptb08ePtReuwAAmsIwxbF06VJCSGJiomyhxk+J08kdxE1MTGo4HJOaGvabBgBQFcMImv2l\nQVnz14kcISG6DgQAoG1srAetk7U4GLm6uj548IBMmcJyuwAA7cAwS8s4NaxOMtXJWhyM+vbtm5mZ\nSUpLiYkJVuQAAD33XIKms7DGB7Y6WYuDUd++fU+dOkVOnCACAZk7l82mAQBUpcu7erM/xfHXqdCu\nrkSba4wAAGgEQ4JueXdXIyMjFxeX9957T/bib+XRa3EkJSWJxeKGhgaxWJyUlOTv76/4Um91tJb6\njY2NJRIJ6duXPHigpaYBADSFIUFHR0dPmDAhLS2ttrY2LS1t/PjxGzZsSExMvHXrVki7zn+Ijo4W\niUSRkZGurq58Pt/V1TUyMjIoKOjTTz9VO35mLVdKkrK2ti4xNCQzZmipaQAATWE4DzomJubmzZt2\ndnaEkP79+3/99ddDhgzZsGHDvn37Xnrppd27d6vaRvvW4lBHXV2dQCBgfGnYsGEpf/755qRJrAUD\nANA+DCPohoYGxhJTU9OOckJ0bW2tggR9/fp1kp1N2jVdAwDAGoYEHRAQEBgYeO/ePYlEcu/evcDA\nwBkzZhBCPv7444iICNYjbA/FCfrKlSvkP/8hFy+yHBUAgEoYEvSOHTuGDBkyceJES0vLiRMnenl5\nbd++nS5fsWIF6xG2R21trdxKSVLm5uY2Njb5lpbk7l2WowIAUAnDHDSfz4+KioqKimI/Gk1RMIIm\nhKxevTryww/jLCzYDAkAQFUMI2gDA12eHK0RihP00KFDqd69b40ezWZIAACqYsjFdnZ2St61RG8p\nOIuDtnbt2o9On2YtHgCAdmBI0KGhocuXL3/06FFHOWejJcUjaEKIm5ubaXl5VXo6ayEBAKiKIUGv\nWbPm2LFjTk5OBgYG0osJ2Y9MHW0maEKIX79++R99xE48AADt0DnXg1ZwFodU/8BA6upVduIBAGiH\nDn88kJEyI2iPoUPrnz0j9fXshAQAoCqGBC0Wi0UikYODA4/H68RTHBwO58uXXiopL2cnJAAAVTEk\n6KCgIBMTk/T09KamprKysqlTp+7atYv9yNTR8pbejPqOHv17cjIL8QAAtANDgj5//vzHH39sZmZG\nCLG0tNy6dWtMTAzrgamlurq6mxI3THn11Vebdu0iHW2GHQC6CIYEzeVyjYyMCCGWlpaVlZX29vYF\nBQWsB6aWyspKCyUuFBw6dChJTyfXr7MQEgCAqhgS9JgxY5KTkwkhgwYNOnnyZFJSkqurK+uBqaWq\nqsrc3LzNtxkaGl51dpbEx7MQEgCAqhjW4ti0aVNAQEBqamp0dPTs2bNramoSEhJYD0wtFRUVlpaW\nyryz7zvv/C8hwU3bAQEAqI4hQbu7u6emphJChg8fnt0x79337NkzU1NTZd45efLk+UePntF2QAAA\nquuc50E3NzcrueRTr1693N3dD+zejUOFAKBvnstiLW8X20HPg1bJ1q1bOUeOJAwZUlFRoetYAAD+\n8VyCPn369OjRo4ODgzMyMjR4qTdFUfHx8T4+PkKhkMfjCYVCHx+f+Ph47V1BrtJfFIFA8M7p09Oa\nmlZOm9bhLmoHgE7suQTt6+t74cKFt956a968eb6+vj///LNGElZYWFhsbGx4eHhmZmZtbW1mZmZ4\neHhsbOz69evVr7yl9sRsZGS+Z8+64uKDBw9qISIAgPZgmKidOHHiH3/8sXTp0vXr13t6eqrfRlxc\n3JEjR3x9fa2trQ0NDa2trX19fY8cORIXF6d+5S1VV1creYTwOS+/7Hz27O7du6uqqp4+fZqUlITR\nNADoFsNZHISQ5uZmiUTS3Nys1dlnLWVAJa9Sacmkd+8PP/xw9ahR9wQCDw+PM2fObNu2TePhAQAo\nSX4E3dTUdPDgwYEDBx48eHDr1q1paWnqtyESifz9/ZOSksRicUNDg1gsTkpK8vf3DwoKUr/yltqd\noAkhEyZM2Dl69C+enl/FxhYVFV3HRYYAoDvPjaD37t0bFxf32muvnTx50tnZWVNtREdHx8XFRUZG\npqWl0Wcoe3p6BgUFaSlBl5eXK3mVCiPTzz8n33xDxo/ftnPnrJUrExMThUKhBsMDAFDScwmazph/\n/vlny9WR1JmO4HA4wcHBwcHB7a5BJbm5uY6OjmpV8fbbZNy4XpaW//rXv6aPH7903Tp/f38NRQcA\noKznpjgY76XS4e6okpWV5eam9sXbNjbE2Hj06NE/DRzouXbtzpEjq8vKNBEdAICy2LiSkOXzoDWT\noP9mtG/f/125MtbFZduQITNmzJjy1lvLp049evRoQUFBbGyst7f3yJEjO9x62QDQITCfxaFZYWFh\nZ8+ejYqKGjp0qKWlZUVFRUpKSkRERHZ29ubNmzXeXH5+vr29vSZrtLPrf/Cge2Pj06dPBTU1DStW\nVL73XiFF9Zo169KlS4Y83orly7dv37569WpCSHNzc3p6uru7O71kKwBAu7GRoOPi4m7cuCE96kif\nB+3h4eHl5aXxBN3Y2NjU1KTkQhwqocf+RCjkHztmRoj948fDuFxibEzu3dt171768eM5u3eXLV0a\n9uOP7mZm3dPTJy9cONzX93/m5r9du9bc3Dx8+HAXFxdpYPX19YWFhX369NFGqKp69uzZb7/9NmTI\nEGtra13HAgD/YCNBt0YbUxxHjx719fXVeLUMbGz+euDhwbl40aOpad+XXxaVliYkJNgbGtZ99935\nb789uWvXr+7uTtOnW+TmNrz/fkZ1dTOHE9e3730LC/fq6tkFBTdra21sbLihoZSHR96lS7xLlwQC\nQd++fV1WrjSwt6cePy75z38KqqsJh1Pl4UHMzd1797arqvqr3YEDiaEhaWiQZGU9ePAgLy+v0d7+\nxcGDHR0cSGUl/Zb6bt0ePnxYVVVlZmbWs2fP6urq+vp6MzMz2UR89uzZ9evXv/nmm5s2bZo7d65I\nJNLSye/Pnj1raGjg8/lt3i4SAGgcFg4Arl279vz581FRUcOGDbOwsKisrLx+/XpERMTYsWOjo6Nb\n+9TRo0d3794tV/jgwYN+/fr9/PPPrX3q4MGDkyZNUuc0O5Y0NRGxmHr27OZvv/10/341IZ62toPL\nyyUSyc2bN//75Ekxl2tbVzeLw+nRo4eBgUFm//7FFhZPfv/d6/ZtiqK4XO75Xr0emZm5PXs2pbCw\nh7l5d2Pj30eNSnr82CIryz87m8vlcjicIy4u9QMHekok486da2hoIIQcHzYshcPpXVgYkpnJ4XCa\nm5uPv/HGu3v2CHNzqbVrHz58+OTJk31ubg8sLPpVVS3KyqKD3efmlmlu3vfp05CMDLpkm4fHA3Nz\nu4KClcXFzc3Nzc3NX7u7ZwuFsp/a+4RGNAAACyVJREFU6+KSaW7uWFa2NiuLEMLlcr8YMCC3e3e7\n4uJ3c3L+eo+b200OZ1BDw+LsbAMDAw6HE9unT6qh4XAOR6512ZrjXV2vNTW9UFe3oqiosbHR0NCw\n5XtkSyiKamxs/MrDI9vcvO/Tp2vu3ZN+i0wzM7eqqlVpaVwulxDyWd++ud27t/ymLUvcqqrokubm\n5p2enplmZu7PnrX8VOCDB3/F3LfvAzMzxSWKvwX7JbsdHVMNDQc1NCzKyuJyuQYGBvoWoZZKGhsb\n9zg753TvTg8pQkJC3nzzTdKKwMDAsLAwLd3VhI0ETVFUXFzcgQMHZM+Dnj9/flBQkKqDtcOHD4vF\n4qVLl2opVAAAlWg1QbMxxcHyedAAAJ2D7o9QAQAAIyRoAAA9pbME3elv1AIAoCadnWbXsS4fBwBg\nH6Y4AAD0VCdciwMAoHPohGtxAAB0Dp1tLQ4AgE5Dl3PQmOIAAFCAjQTN8j0JAQA6hw62FseZM2eW\nL19ubm6uzJsz/l65BtrU0NBgaGio6yg6hqamJg6How/rxOo/iqLMzMwcHBx0HYgWVVVVXbp0yc7O\nThuVs5GgdWX06NEXL17UdRQdw9y5c7du3aqlnayT2bFjR58+faZOnarrQDqA5OTkEydO4FBTu2EU\nAACgp5CgAQD0FBI0AICeQoIGANBTSNAAAHqqMydonDemPAMDA5w3piQul0vfwBDaRN/JUNdRdGCd\n+TQ7iURibGys6yg6BvSV8hoaGgwMDJCjlUFRVENDg5GRka4D6ag6c4IGAOjQ8N8HAICeQoIGANBT\nSNAAAHoKCRoAQE8hQQMA6CkkaAAAPYUEDQCgpzpngqYoat26dUKhsHv37mFhYTjXmxDCeZ60vLW+\n6mp92LJnaKr2T1fot9b6CvuY5lGd0e7du4cMGZKTk5OTkzNkyJC9e/fqOiLda21bt9ZXXbMPW/aS\nqv3TdfqtZV9hH9O4zpmgvb29T58+TT8+ffr0yJEjdRuPPmjtx9NaX3XNPmzZS6r2T9fpN+UTNPqq\n3TpngjY3Ny8tLaUfl5SUWFpa6jYefUAI6dGjh4mJyYABA3bs2NHY2EiXt9ZXXbMPW6YYVfun6/Qb\nY4LGPqZZnXMtDi6XW1dXR69m19DQIBAIGhsbdR2UXpBIJHfu3Fm9evWwYcO2bdtGWu+rrtmHHI78\nL0LV/uk6/dayr2jYxzSocx4kNDU1rayspB9XVFSYmZnpNh79YWxsPHTo0EOHDiUkJNAlrfUV+pCm\nav+g37CPaVDnTNCenp7Xr1+nH6ekpHh6euo2Hn1jYGAgXVy0tb5CH9JU7R/0Gw37mGboeIpFO2Jj\nY3F0WM6sWbPu3LkjkUjS09PHjh27YsUKury1vuqafdjyF6Fq/3SdfmvZV9jHNK5zJujm5ub333/f\n0tLS0tJy3bp1zc3Nuo5I9w4fPjxw4EBjY2NXV9fw8PDa2lq6vLW+6mp92NrARdX+6Qr91lpfYR/T\nuM55kBAAoBPonHPQAACdABI0AICeQoIGANBTSNAAAHoKCRoAQE8hQQMA6CkkaAAAPYUEDQCgp5Cg\nAQD0FBI0AICeQoIGANBTSNAAAHoKCRoAQE8hQQMA6CkkaAAAPYUEDQCgp5CgAQD0FBI0AICeQoIG\n6JA4HI6uQwCtQ4KGf7i7u7u7u+s6CgYcJjoPScFTVe3Zs2fmzJkty2fMmLFnzx51aoYODQka/nL1\n6lUul8vlcn///XddxyJPepNjucf6Q8145s2bd/ny5YcPH8oWPnz48MqVK/PmzVMrMujIkKDhL/v3\n758/f/68efP279+fmprq6uoqTToURbm6ut6+fbu5uTkqKsrZ2bl79+6LFi2qrq6m38DhcLZt2+bg\n4GBgYEAIyczM9Pf3t7KysrCwmDZtmlgspt8mkUiWLFliZWVla2u7ZcsW6aiztWoVULJFDoeze/du\nJycngUDg7e199+5duvz8+fNDhgwRCAROTk7x8fF0YWuVNDY2bty40dHRUSgUxsTEkL/Hy7IDeekD\niUSyevVqW1tbW1vb1atXSyQSxZHQ+Hx+cHDwjh07ZAu3b98eHBycl5fHGJVsVzA+bUevgt6hACiq\nrq7Oysrqf//73//+9z8rK6u6urohQ4acO3eOfvXs2bNeXl4URcXExLz++us5OTlPnjx5++2316xZ\nQ7+BEDJlypSCggL66cCBAy9cuFBTU1NRUbF8+fLAwEC6PCIiwtfXt6CgoKCgYPz48dLdr7VqW5J+\nRMkWCSF+fn65ubnPnj376KOPRo4cSZf36tXryJEjdXV1jx49Wrx4seJKoqKiXnvttaysrCdPnqxe\nvVouErmnGzZsGDt2LN2To0eP3rhxo+JIpEpLS21sbCoqKuin5eXlPXv2LC0tVfDVFEeifK+C3kKC\nBoqiqB9++GHcuHH047Fjxx4+fHjXrl0zZsygSwICAr788kuKojw8PO7du0cXFhcXOzo60o8JIQ8f\nPmSsubKy0t7enn7s4uKSkZFBP05LS5OmktaqbUk2KynTIiGkqKiIflxdXS0QCOjHDg4OO3fuzMvL\na60h2Urc3Nzu3LnTWiRyT11cXNLS0ujHd+7cof8RURCJrCVLlmzZsoV+HB0dvWTJEsVfTXEkyvcq\n6C0kaKAoinrzzTe/+eYb+vHBgwcnTpxYXl5ubm5eWlpaUlJibm5eXl5OUZRAIKDnqemJBQMDA/oj\nhJDm5mZpbdevXx8zZoxQKKT/S+NyuXQ5n8+vq6ujH9fW1kpTSWvVtiSblZRpsbXk9eeff/r5+VlZ\nWfXt2/f06dNthl1bW9taJHJPZd9cW1vL5/MVv1/WgwcPHB0dGxoa6uvr+/Tp8+DBA2W+Wms1K9+r\noLeQoIEqLi7m8XiyE188Hq+4uHj27Nlbt27dsmXLnDlz6Hf269cvNze3ZQ1yOcLV1XX//v1lZWWN\njY1lZWWyo0vGEXRr1SpoSMkWFafF5ubm//73v7a2toor6du3b8sRNIfDYaxZwQhaQSRSU6dO/eab\nbw4ePDh16lQlvxqfz6+urqYfFxUVtaNXQW/hICGQb7/9du7cubK7xbx58w4dOrRo0aK9e/fGx8cv\nWrSIfueSJUtEIlFGRkZ9ff2dO3dmzZrFWGF1dbW5uXm3bt0ePXoUFBQkLZ89e/aaNWsKCwsLCwvX\nrFkjLVeyWgVaa7E1s2fPTk9Pb2hoIITQA0wFlSxYsGDFihU5OTnl5eUhISF0YY8ePTIyMhhrXrVq\nVX5+fn5+/qpVq2bPnq3SF3nvvfdiYmJiYmLee+89Jb+al5fXZ599Vl1dnZub++6770rL1e9V0D1d\n/WUA/TFw4MCLFy/Klly6dOnFF19sbm52cnJycnKSTiY0NTXt3LnTw8PD2Nj4hRdeSExMpMvldqRT\np07169fP0NCwT58+O3fulL5aW1sbFBQkFAp79uz58ccfGxoaKq62JdLK0Li1Fkkr49bvvvuuX79+\nfD5/8ODBFy5cUFxJfX39+vXr7e3thULh559/ThfGxMRYWlq2bKi2tnbFihU2NjY2NjYrVqyQTne0\nFklL3t7e3t7eyn+1O3fuvPzyy3w+39HR8d///re0XPleBb3FofTsfFLoIm7fvu3n55eTk6PrQAD0\nF6Y4gFUhISHFxcWPHj1as2aNn5+frsMB0Gu8tt8CoDlOTk7Dhg2rr6+fMmVKVFSUrsMB0GuY4gAA\n0FOY4gAA0FNI0AAAegoJGgBATyFBAwDoKSRoAAA9hQQNAKCnkKABAPQUEjQAgJ5CggYA0FNI0AAA\negoJGgBATyFBAwDoKSRoAAA9hQQNAKCnkKABAPTU/wNXgSEcidDNcAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 499
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "expected_spend <- spend.expected.value(spendParams, m.x, cal.cbs[,1])\n",
      "output$expected_spend <- expected_spend\n",
      "output$clv <- output$expected_spend * output$conditional_expected_transactions\n",
      "head(output)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "            visitorId conditional_expected_transactions     p_Alive\n",
        "1 4267659195240979286                       0.002074432 0.001214972\n",
        "2 5643813381699005286                       0.008010164 0.015121718\n",
        "3 8445352417811622261                       2.323994918 0.805524617\n",
        "4 7934359074614033866                       0.008010164 0.015121718\n",
        "5 2134408454679554310                       4.019851821 0.767084713\n",
        "6 4741996826496431299                       0.008010164 0.015121718\n",
        "  expected_spend         clv\n",
        "1      648.04925   1.3443341\n",
        "2       85.67872   0.6863006\n",
        "3      134.01518 311.4505989\n",
        "4       85.67872   0.6863006\n",
        "5       20.95246  84.2257676\n",
        "6       85.67872   0.6863006\n"
       ]
      }
     ],
     "prompt_number": 506
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "head(cal.cbs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "     [,1] [,2] [,3]\n",
        "[1,]    1    1  181\n",
        "[2,]    0    0  181\n",
        "[3,]    2  147  181\n",
        "[4,]    0    0  181\n",
        "[5,]    4  147  181\n",
        "[6,]    0    0  181\n"
       ]
      }
     ],
     "prompt_number": 507
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Analyzing the data in BigQuery"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Import CLV table into BigQuery and run some queries and do analysis"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 467
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}