Unsupervised Learning with R
2022-05-27
1. Defining the Question
Research Question
Kira Plastinina is a Russian brand that is sold through a defunct chain of retail stores in Russia, Ukraine, Kazakhstan, Belarus, China, Philippines, and Armenia. The brand’s Sales and Marketing team would like to understand their customer’s behavior from data that they have collected over the past year. More specifically, they would like to learn the characteristics of customer groups.
Websites earn revenue when visitors engage with their ads, commonly by generating impressions, engagements, or clicks.
a.) Specifying the question
Perform clustering stating insights drawn from the analysis and visualizations for customer habits in amid to understand customer behaviour/groups.
Upon implementation, provide comparisons between the approaches of K-Means clustering vs Hierarchical clustering highlighting the strengths and limitations of each approach in the context of the analysis.
b.) The metric for success
Performing univariate, bivariate and multivariate analysis on the cleaned dataset then clustering to determine habits of customer groups.
c.) Understanding the context
The dataset provided contains various information regarding the kind of visitor of the ecommerce site. The class label determines whether the user’s attributes generated revenue for the site or not.
d.) Experimental design taken
- Reading the data
- Checking the data - data understanding
- Data cleaning - checking for outliers and anomalies, missing values and duplicates.
- Performing EDA(univariate, bivariate and multivariate analysis) on the dataset.
- Implementing the solution - Modelling(KMeans and Hierarchical Clustering)
- Challenge the solution
- Follow up Questions
- Conclusion.
- Recommendations.
e.) Data appropriateness to answer the given question.
We aim to determine various customer groups that visit the ecommerce site. This information will be used for strategic marketing which will involve targetting customer groups accordingly based on their preference.
2. Loading the dataset
# load Tibble library
library(tibble)
# load the dataset as dataframe
df <- read.csv('http://bit.ly/EcommerceCustomersDataset')
# convert dataframe to tibble and set options to show all columns
df <- as_tibble(df)
#check data structure of our dataset
class(df)## [1] "tbl_df" "tbl" "data.frame"3. Checking the data
# preview the first 6 rows of the dataset
head(df)# preview the last 6 rows of the dataset
tail(df)The dataset consists of 10 numerical and 8 categorical attributes. The ‘Revenue’ attribute can be used as the class label.
“Administrative”, “Administrative Duration”, “Informational”, “Informational Duration”, “Product Related” and “Product Related Duration” represents the number of different types of pages visited by the visitor in that session and total time spent in each of these page categories. The values of these features are derived from the URL information of the pages visited by the user and updated in real-time when a user takes an action, e.g. moving from one page to another.
The “Bounce Rate”, “Exit Rate” and “Page Value” features represent the metrics measured by “Google Analytics” for each page in the e-commerce site.
The value of the “Bounce Rate” feature for a web page refers to the percentage of visitors who enter the site from that page and then leave (“bounce”) without triggering any other requests to the analytics server during that session.
The value of the “Exit Rate” feature for a specific web page is calculated as for all pageviews to the page, the percentage that was the last in the session.
The “Page Value” feature represents the average value for a web page that a user visited before completing an e-commerce transaction.
The “Special Day” feature indicates the closeness of the site visiting time to a specific special day (e.g. Mother’s Day, Valentine’s Day) in which the sessions are more likely to be finalized with the transaction. The value of this attribute is determined by considering the dynamics of e-commerce such as the duration between the order date and delivery date. For example, for Valentine’s day, this value takes a non-zero value between February 2 and February 12, zero before and after this date unless it is close to another special day, and its maximum value of 1 on February 8.
The dataset also includes the operating system, browser, region, traffic type, visitor type as returning or new visitor, a Boolean value indicating whether the date of the visit is weekend, and month of the year.
# get number of records
nrow(df); ncol(df)## [1] 12330## [1] 18The dataset contains 12330 visitor records and 18 variables.
# check datatypes of each column using class
sapply(df, class)## Administrative Administrative_Duration Informational
## "integer" "numeric" "integer"
## Informational_Duration ProductRelated ProductRelated_Duration
## "numeric" "integer" "numeric"
## BounceRates ExitRates PageValues
## "numeric" "numeric" "numeric"
## SpecialDay Month OperatingSystems
## "numeric" "character" "integer"
## Browser Region TrafficType
## "integer" "integer" "integer"
## VisitorType Weekend Revenue
## "character" "logical" "logical"# convert logical values to integer then to factor
logical.to.factor <- function(column){
as.factor(as.integer(column))
}
# logical columns
df$Revenue <- logical.to.factor(df$Revenue)
df$Weekend <- logical.to.factor(df$Weekend)
df$SpecialDay <- logical.to.factor(df$SpecialDay)
head(df)# Convert other categorical columns to factors
# columns to factor datatype function
to.factor <- function(column){
as.factor(column)
}
# call function on columns
df$Month <- to.factor(df$Month)
df$Region <- to.factor(df$Region)
df$VisitorType <- to.factor(df$VisitorType)
df$OperatingSystems <- to.factor(df$OperatingSystems)
df$Browser <- to.factor(df$Browser)
df$TrafficType <- to.factor(df$TrafficType)
# preview dataset to ascertain change
head(df)# inspect variable classes
str(df)## tibble [12,330 × 18] (S3: tbl_df/tbl/data.frame)
## $ Administrative : int [1:12330] 0 0 0 0 0 0 0 1 0 0 ...
## $ Administrative_Duration: num [1:12330] 0 0 -1 0 0 0 -1 -1 0 0 ...
## $ Informational : int [1:12330] 0 0 0 0 0 0 0 0 0 0 ...
## $ Informational_Duration : num [1:12330] 0 0 -1 0 0 0 -1 -1 0 0 ...
## $ ProductRelated : int [1:12330] 1 2 1 2 10 19 1 1 2 3 ...
## $ ProductRelated_Duration: num [1:12330] 0 64 -1 2.67 627.5 ...
## $ BounceRates : num [1:12330] 0.2 0 0.2 0.05 0.02 ...
## $ ExitRates : num [1:12330] 0.2 0.1 0.2 0.14 0.05 ...
## $ PageValues : num [1:12330] 0 0 0 0 0 0 0 0 0 0 ...
## $ SpecialDay : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ Month : Factor w/ 10 levels "Aug","Dec","Feb",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ OperatingSystems : Factor w/ 8 levels "1","2","3","4",..: 1 2 4 3 3 2 2 1 2 2 ...
## $ Browser : Factor w/ 13 levels "1","2","3","4",..: 1 2 1 2 3 2 4 2 2 4 ...
## $ Region : Factor w/ 9 levels "1","2","3","4",..: 1 1 9 2 1 1 3 1 2 1 ...
## $ TrafficType : Factor w/ 20 levels "1","2","3","4",..: 1 2 3 4 4 3 3 5 3 2 ...
## $ VisitorType : Factor w/ 3 levels "New_Visitor",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ Weekend : Factor w/ 2 levels "0","1": 1 1 1 1 2 1 1 2 1 1 ...
## $ Revenue : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...4. Data Cleaning
a.) Validation
The dataset provided by the client has some attributes collected by Google Analytics hence valid.
b.) Outliers
# check for outliers
# select only numerical variables
library("dplyr")##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniondata_num <- select_if(df, is.numeric)
head(data_num)# import ggplot2 package for visualization
library(ggplot2)
# vectorize column names
columns <- c(names(data_num))
# plot boxplot
boxplots <- function(column_name){
column <- c(data_num[,column_name])
boxplot(column, width=1,height=1, main=paste("Boxplot for", columns[x]))
}
# create 9 subplots
par(mfrow=c(3,3),mar=c(0.5,2,1.5,0.5))
for (x in 1:length(columns)){
boxplots(x)
}
All numerical columns contain outliers. We shall investigate the validity of these outliers when checking range of values and interquatile range.
# check anomalies
# -1 durationb.) Missing values
# import Amelia and Rcpp libraries
library(Amelia,Rcpp)## Loading required package: Rcpp## ##
## ## Amelia II: Multiple Imputation
## ## (Version 1.8.0, built: 2021-05-26)
## ## Copyright (C) 2005-2022 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ###checking missing data visualization
missmap(df)## Warning: Unknown or uninitialised column: `arguments`.
## Unknown or uninitialised column: `arguments`.## Warning: Unknown or uninitialised column: `imputations`.
There are very few missing values in our dataframe as seen by the thin lines across some columns.
# checking columns with missing values
colSums(is.na(df))## Administrative Administrative_Duration Informational
## 14 14 14
## Informational_Duration ProductRelated ProductRelated_Duration
## 14 14 14
## BounceRates ExitRates PageValues
## 14 14 0
## SpecialDay Month OperatingSystems
## 0 0 0
## Browser Region TrafficType
## 0 0 0
## VisitorType Weekend Revenue
## 0 0 0The first 8 columns each contain 14 missing values.
# checking percentage of missing values for each column
percent <- 14/nrow(df) * 100
print(percent)## [1] 0.1135442Each column with missing values contains 0.11% missing values.
# check if missing values are on same rows
# check for rows with missing values in 8 columns
missing <- df[rowSums(is.na(df)) == 8, ]
print(missing)## # A tibble: 14 × 18
## Administrative Administrative_… Informational Informational_D… ProductRelated
## <int> <dbl> <int> <dbl> <int>
## 1 NA NA NA NA NA
## 2 NA NA NA NA NA
## 3 NA NA NA NA NA
## 4 NA NA NA NA NA
## 5 NA NA NA NA NA
## 6 NA NA NA NA NA
## 7 NA NA NA NA NA
## 8 NA NA NA NA NA
## 9 NA NA NA NA NA
## 10 NA NA NA NA NA
## 11 NA NA NA NA NA
## 12 NA NA NA NA NA
## 13 NA NA NA NA NA
## 14 NA NA NA NA NA
## # … with 13 more variables: ProductRelated_Duration <dbl>, BounceRates <dbl>,
## # ExitRates <dbl>, PageValues <dbl>, SpecialDay <fct>, Month <fct>,
## # OperatingSystems <fct>, Browser <fct>, Region <fct>, TrafficType <fct>,
## # VisitorType <fct>, Weekend <fct>, Revenue <fct># drop these rows
df <- df[complete.cases(df[ , 1:7]),]
# check missing values
colSums(is.na(df))## Administrative Administrative_Duration Informational
## 0 0 0
## Informational_Duration ProductRelated ProductRelated_Duration
## 0 0 0
## BounceRates ExitRates PageValues
## 0 0 0
## SpecialDay Month OperatingSystems
## 0 0 0
## Browser Region TrafficType
## 0 0 0
## VisitorType Weekend Revenue
## 0 0 0# check number of remaining records
nrow(df)## [1] 12316c.) Duplicate values
# check for duplicates
anyDuplicated(df)## [1] 70There are 70 duplicated values in our dataset.
# drop duplicate values
df <- df %>% distinct()
# check if duplicates are removed
anyDuplicated(df)## [1] 0# rename columns for uniformity
names(df) <- c("administrative", "administrative_duration", "informational", "informational_duration", "product_related", "product_related_duration", "bounce_rates", "exit_rates", "page_values", "special_day", "month", "operating_systems", "browser", "region", "traffic_type", "visitor_type","weekend","revenue")
# rename data_ num columns
names(data_num) <- c("administrative", "administrative_duration", "informational", "informational_duration", "product_related", "product_related_duration", "bounce_rates", "exit_rates", "page_values")
# preview change
print("df Column names:")## [1] "df Column names:"names(df)## [1] "administrative" "administrative_duration"
## [3] "informational" "informational_duration"
## [5] "product_related" "product_related_duration"
## [7] "bounce_rates" "exit_rates"
## [9] "page_values" "special_day"
## [11] "month" "operating_systems"
## [13] "browser" "region"
## [15] "traffic_type" "visitor_type"
## [17] "weekend" "revenue"print("Numerical data Column names:")## [1] "Numerical data Column names:"names(data_num)## [1] "administrative" "administrative_duration"
## [3] "informational" "informational_duration"
## [5] "product_related" "product_related_duration"
## [7] "bounce_rates" "exit_rates"
## [9] "page_values"5. Univariate Analysis
# check univariate summary of our dataset.
summary(df)## administrative administrative_duration informational
## Min. : 0.000 Min. : -1.00 Min. : 0.0000
## 1st Qu.: 0.000 1st Qu.: 0.00 1st Qu.: 0.0000
## Median : 1.000 Median : 9.50 Median : 0.0000
## Mean : 2.344 Mean : 81.82 Mean : 0.5097
## 3rd Qu.: 4.000 3rd Qu.: 95.00 3rd Qu.: 0.0000
## Max. :27.000 Max. :3398.75 Max. :24.0000
##
## informational_duration product_related product_related_duration
## Min. : -1.0 Min. : 0.00 Min. : -1.0
## 1st Qu.: 0.0 1st Qu.: 8.00 1st Qu.: 195.4
## Median : 0.0 Median : 18.00 Median : 612.0
## Mean : 34.9 Mean : 32.11 Mean : 1209.6
## 3rd Qu.: 0.0 3rd Qu.: 38.00 3rd Qu.: 1481.0
## Max. :2549.4 Max. :705.00 Max. :63973.5
##
## bounce_rates exit_rates page_values special_day
## Min. :0.000000 Min. :0.00000 Min. : 0.000 0:12024
## 1st Qu.:0.000000 1st Qu.:0.01420 1st Qu.: 0.000 1: 154
## Median :0.002884 Median :0.02500 Median : 0.000
## Mean :0.020137 Mean :0.04122 Mean : 5.963
## 3rd Qu.:0.016445 3rd Qu.:0.04815 3rd Qu.: 0.000
## Max. :0.200000 Max. :0.20000 Max. :361.764
##
## month operating_systems browser region traffic_type
## May :3311 2 :6528 2 :7866 1 :4697 2 :3906
## Nov :2983 1 :2540 1 :2418 3 :2376 1 :2380
## Mar :1853 3 :2525 4 : 729 4 :1167 3 :2006
## Dec :1706 4 : 478 5 : 466 2 :1127 4 :1066
## Oct : 549 8 : 75 6 : 174 6 : 800 13 : 724
## Sep : 448 6 : 19 10 : 163 7 : 758 10 : 450
## (Other):1328 (Other): 13 (Other): 362 (Other):1253 (Other):1646
## visitor_type weekend revenue
## New_Visitor : 1693 0:9323 0:10270
## Other : 81 1:2855 1: 1908
## Returning_Visitor:10404
##
##
##
## # let's define a function that will print results for numeric columns
library(dplyr)
printing <- function(func){
print(paste("Administrative: ", func(df$administrative)))
print(paste("Administrative Duration: ", func(df$administrative_duration)))
print(paste("Informational: ", func(df$informational)))
print(paste("Informational Duration: ", func(df$informational_duration)))
print(paste("Product Related: ", func(df$product_related)))
print(paste("Product Related Duration: ", func(df$product_related_duration)))
print(paste("Bounce Rates: ", func(df$bounce_rates)))
print(paste("Exit Rates: ", func(df$exit_rates)))
print(paste("Page Values: ", func(df$page_values)))
}# use above function to print range
paste("The range of each column is as shown below:-")## [1] "The range of each column is as shown below:-"printing(range)## [1] "Administrative: 0" "Administrative: 27"
## [1] "Administrative Duration: -1" "Administrative Duration: 3398.75"
## [1] "Informational: 0" "Informational: 24"
## [1] "Informational Duration: -1" "Informational Duration: 2549.375"
## [1] "Product Related: 0" "Product Related: 705"
## [1] "Product Related Duration: -1"
## [2] "Product Related Duration: 63973.52223"
## [1] "Bounce Rates: 0" "Bounce Rates: 0.2"
## [1] "Exit Rates: 0" "Exit Rates: 0.2"
## [1] "Page Values: 0" "Page Values: 361.7637419"# checking values with -1 in duration
nrow(df[df$informational_duration==-1,])## [1] 33nrow(df[df$administrative_duration==-1,])## [1] 33nrow(df[df$product_related_duration==-1,])## [1] 33No deeper meaning to these page duration values has been provided. However, there are 33 records for each with this value hence may be meaningful. We shall assume that the client has meaning for this.
paste("The interquartile range of each column is shown beow:-")## [1] "The interquartile range of each column is shown beow:-"# use IQR function
printing(IQR)## [1] "Administrative: 4"
## [1] "Administrative Duration: 95"
## [1] "Informational: 0"
## [1] "Informational Duration: 0"
## [1] "Product Related: 30"
## [1] "Product Related Duration: 1285.560416475"
## [1] "Bounce Rates: 0.016445496"
## [1] "Exit Rates: 0.033947146"
## [1] "Page Values: 0"The interquatile range explains the range where the bulk of the values lie.
# function for mode for all columns
getmode <- function(v) {
uniqv <- unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}
paste("The mode of the columns is as shown below:-")## [1] "The mode of the columns is as shown below:-"printing(getmode)## [1] "Administrative: 0"
## [1] "Administrative Duration: 0"
## [1] "Informational: 0"
## [1] "Informational Duration: 0"
## [1] "Product Related: 1"
## [1] "Product Related Duration: 0"
## [1] "Bounce Rates: 0"
## [1] "Exit Rates: 0.2"
## [1] "Page Values: 0"# add the rest of the columns whose mode can be obtained
print(paste("Special Day: ", getmode(df$special_day)))## [1] "Special Day: 0"print(paste("Month: ", getmode(df$month)))## [1] "Month: May"print(paste("Operating System: ", getmode(df$operating_systems)))## [1] "Operating System: 2"print(paste("Traffic Type: ", getmode(df$traffic_type)))## [1] "Traffic Type: 2"print(paste("Revenue: ", getmode(df$revenue)))## [1] "Revenue: 0"print(paste("Region: ", getmode(df$region)))## [1] "Region: 1"print(paste("Browser: ", getmode(df$browser)))## [1] "Browser: 2"print(paste("Visitor Type: ", getmode(df$visitor_type)))## [1] "Visitor Type: Returning_Visitor"print(paste("Weekend: ", getmode(df$weekend)))## [1] "Weekend: 0"The mode of the columns as shown above represents the column values that are most repeated for each column.
print("The variance of numerical columns is as shown below:-")## [1] "The variance of numerical columns is as shown below:-"printing(var)## [1] "Administrative: 11.1042437184501"
## [1] "Administrative Duration: 31559.0760330231"
## [1] "Informational: 1.6300695267064"
## [1] "Informational Duration: 20042.919630442"
## [1] "Product Related: 1991.02554977087"
## [1] "Product Related Duration: 3689959.56472567"
## [1] "Bounce Rates: 0.00200924754719707"
## [1] "Exit Rates: 0.00209908697730803"
## [1] "Page Values: 348.652316251833"The variance explains the measure of spread of the data points within the data set.
print("The standard deviation of the numerical columns is as shown below:-")## [1] "The standard deviation of the numerical columns is as shown below:-"printing(sd)## [1] "Administrative: 3.33230306521632"
## [1] "Administrative Duration: 177.648743404008"
## [1] "Informational: 1.27674176194969"
## [1] "Informational Duration: 141.57301872335"
## [1] "Product Related: 44.6209093337515"
## [1] "Product Related Duration: 1920.92674631951"
## [1] "Bounce Rates: 0.04482463103247"
## [1] "Exit Rates: 0.045815793972254"
## [1] "Page Values: 18.6722338313292"The standard deviation measures the distribution of data points around the mean.
# skewness
# import moments package
library(moments)
printing(skewness)## [1] "Administrative: 1.9440216948556"
## [1] "Administrative Duration: 5.58624533275611"
## [1] "Informational: 4.00969334679153"
## [1] "Informational Duration: 7.53087854131104"
## [1] "Product Related: 4.33076548095007"
## [1] "Product Related Duration: 7.24975534421644"
## [1] "Bounce Rates: 3.19191830119169"
## [1] "Exit Rates: 2.24724552267589"
## [1] "Page Values: 6.34327331222869"All the columns are positively/right skewed meaning that majority of the data values are less than the mean.
# kurtosis
printing(kurtosis)## [1] "Administrative: 7.62610879933741"
## [1] "Administrative Duration: 53.0234107601945"
## [1] "Informational: 29.5966828223451"
## [1] "Informational Duration: 78.332613783527"
## [1] "Product Related: 34.0255780804155"
## [1] "Product Related Duration: 139.509095334058"
## [1] "Bounce Rates: 12.5654697488922"
## [1] "Exit Rates: 7.73547425097368"
## [1] "Page Values: 67.8331995029106"The kurtosis coefficient of all values is greater than 3 hence all columns are leptokurtic(thin and long)
# filter data to only those that have revenue
data <- df %>% filter(revenue == 1)
data# filter data to only those that do not have revenue
data_ <- df %>% filter(revenue == 0)
data_# Pie chart function
# import plotrix for 3D plot
library(plotrix)
piechart <- function(column, title){
# define labels and values
slices <- c(tabulate(column))
lbls <- c(levels(column))
# convert values to percentage
pct <- round(slices/sum(slices)*100)
# add percentages to labels
lbls <- paste(lbls,":", pct)
# ad % to labels
lbls <- paste(lbls,"%",sep="")
# plot pie chart in 3D
pie3D(slices,labels=lbls, col=rainbow(length(lbls)),
explode=0.1, radius=1, start=110, main=title)
}# Revenue representation
piechart(df$revenue, "Pie Chart for Revenue representation")
Our dataset is imbalanced since only 16% of customers generated revenue for the site.
# Weekend representation
piechart(df$weekend, "Pie Chart for Weekend representation")
Most visitors visited the e-commerce site during the weekday than weekends.
# Visitor type representation
piechart(df$visitor_type, "Visitor Type representation")
Majority of visitors are returning visitors and only few visitors belong
to an other group.
# Special day representation
piechart(df$special_day, "Pie Chart for Special Day representation")
Visitors who visited the site were more on normal days than days that were near holidays or special celebrations. This may be due to the fact that special days are less compared to normal days.
# histograms function
histogram <- function(column,title, xlab){
hist(column, main= title, xlab=xlab, ylab = "Frequency", col = "lightgreen")
} # Administrative Duration representation
histogram(df$administrative_duration, "Histogram for Time spent on Administrative pages", "Admin Duration")
# administrative Duration representation and Revenue
par(mfrow=c(1,2))
histogram(data$administrative_duration, "Admin Duration(with Rev)", "Admin Duration")
histogram(data_$administrative_duration, "Admin Duration(without Rev)", "Admin Duration")
More revenue was generated from customers who spent less time in administrative pages.
# Informational Duration representation
histogram(df$informational_duration, "Histogram for Time spent on Informational pages", "Informational pages Duration")
# Informational Duration representation and Revenue
par(mfrow=c(1,2))
histogram(data$informational_duration, "Info Duration(with Rev)", "Info Duration")
histogram(data_$informational_duration, "Info Duration(without Rev)", "Info Duration")
Customers that generated revenue for the e-commerce site also spent less time in informational pages.
# Product Related Duration representation
histogram(df$product_related_duration, "Histogram for Time spent on product related pages", "Product Related Duration")
# Product Related Pages Duration representation and Revenue
par(mfrow=c(1,2))
histogram(data$product_related_duration, "Prod. Related Duration(with Rev)", "Prod. Related Duration")
histogram(data_$product_related_duration, "Prod. Related(without Rev)", "Prod. Related Duration")
Most people who visit product related pages spend less time on the page and are more likely to contribute to the site’s revenue.
# Bounce rate representation
histogram(df$bounce_rates, "Bounce Rate Representation", "Bounce Rate")
There is low chance of a visitor visiting the site and leaving without triggering any other requests(Bounce rate for most customers is 0.05 and below).
# Exit rate representation
histogram(df$exit_rates, "Exit rate Histogram", "Exit rate")
The exit rate for pages in this site is generally low.
# Page values representation
histogram(df$page_values, "Page values Histogram", "Page values")
# barplot function
bar <- function(column, title, xlab){
# create frequency table
freq <- table(column)
# sort frequency table
sorted_freq <- (freq[order(freq,decreasing=TRUE)])
# adjust margins of frequency table
par(mar=c(5,5,5,5))
# plot bar graph for first 20 values with the highest count
barplot(sorted_freq[1:20], main=title, ylab="Frequency" ,las=2, col="lightblue")
title(xlab = xlab, line=10)
}# Month representation
bar(df$month, "Barplot for Month representation", "Month")
Most people visited the eCommerce site in May, November and March respectively.
# Operating Systems representation
bar(df$operating_systems, "Operating Systems Type representation", "Operating Systems")
Most of the visitors use type 2 operating system.
# Region representation
bar(df$region, "Barplot for Region representation", "Region")
Most people who visited the site were from region 1.
# Browser representation
bar(df$browser, "Browser representation", "Browser")
Most visitors who visited the site used browser type 2.
# Traffic type representation
bar(df$traffic_type, "Traffic Type representation", "Traffic Type")
Most visitors are part of traffic type 2. Traffic is the number of visits and visitors accessing a site at a time.
6. Bivariate analysis
a.) Numerical - Numerical
# check covariance in numerical variables with covariance matrix
cov(data_num, use="complete.obs")## administrative administrative_duration informational
## administrative 11.04069336 353.459826 1.590858944
## administrative_duration 353.45982649 31279.612416 68.015825905
## informational 1.59085894 68.015826 1.614681693
## informational_duration 119.67596098 5926.705121 110.762027207
## product_related 63.69014669 2272.992111 21.149213940
## product_related_duration 2376.76409600 120275.480302 942.499952306
## bounce_rates -0.03595945 -1.234436 -0.007142583
## exit_rates -0.05098419 -1.764732 -0.010084391
## page_values 6.09713438 221.661591 1.145855832
## informational_duration product_related
## administrative 119.6759610 63.6901467
## administrative_duration 5926.7051209 2272.9921112
## informational 110.7620272 21.1492139
## informational_duration 19831.8156453 1754.0893636
## product_related 1754.0893636 1979.3902863
## product_related_duration 93629.4573503 73321.0730543
## bounce_rates -0.5051863 -0.4405367
## exit_rates -0.7189559 -0.6309006
## page_values 80.5459932 46.3414868
## product_related_duration bounce_rates exit_rates
## administrative 2376.76410 -0.035959450 -0.050984188
## administrative_duration 120275.48030 -1.234436283 -1.764732353
## informational 942.49995 -0.007142583 -0.010084391
## informational_duration 93629.45735 -0.505186348 -0.718955880
## product_related 73321.07305 -0.440536664 -0.630900569
## product_related_duration 3664822.11031 -17.096094015 -23.377628092
## bounce_rates -17.09609 0.002345187 0.002146610
## exit_rates -23.37763 0.002146610 0.002354899
## page_values 1871.52913 -0.107382203 -0.157225332
## page_values
## administrative 6.0971344
## administrative_duration 221.6615910
## informational 1.1458558
## informational_duration 80.5459932
## product_related 46.3414868
## product_related_duration 1871.5291268
## bounce_rates -0.1073822
## exit_rates -0.1572253
## page_values 345.1393266Covariance is the measure of how two random variables vary together. A high negative covariance indicates negative correlation while a high positive covariance indicates positive correlation. A value close to zero indicates weak covariance.
We can say the following, for example, have positive covariance indicating positive correlation:- * Administrative page count and Administrative Duration * Informational page count and Informational Duration * Product Related page count and Product Related Duration * Product Related Duration and page values
The following have negative covariance indicating negative correlation:- * Product Related Duration and Bounce Rate * Product Related Duration and Exit Rates
In order to measure the strength of this relationship, we shall use a correlation matrix.
# correlation matrix
# import ggcorrplot package
library(ggcorrplot)
corr <- round(cor(data_num, use='complete.obs'),1)
ggcorrplot(corr, lab=TRUE, title='Correlation Heatmap', colors=c('#E799A3','#43302E','#E799A3'))
The correlation matrix tries to explain the covariance between variables.
A strong positive correlation exists between:- * product_related and product_related_duration * exit_rates and bounce_rates * informational and informational_duration * administrative and administrative_duration
All other variables are weakly correlated.
# scatterplot function
scatter <- function(column1, column2, x_label, y_label, title){
# Change point shapes and color by the levels of revenue
ggplot(df, aes(x=column1, y=column2, shape=revenue, color=revenue)) +
geom_point() + labs(title=title) + xlab(x_label) + ylab(y_label)
}# plot product related page count against product related duration
scatter(df$product_related, df$product_related_duration, 'product_related', 'product_related_duration', 'Product related page count against product related duration')
Here we note that customers who spent a highly abnormal amount of time in product related pages mostly do not generate revenue. These are seen as outliers. This observation may be due to the fact that they are unable to find what they are looking for hence end up surfing through various product pages in vain.
# plot informational against informational_duration
scatter(df$informational, df$informational_duration, 'informational page count', 'informational_duration', 'informational page count against informational_duration')
A similar trend as in product related pages is seen. Most visitors who spend a higher amount of time on informational pages most likely do not contribute to the site’s revenue.
# plot administrative against administrative_duration
scatter(df$administrative, df$administrative_duration, 'administrative page count', 'administrative_duration', 'administrative page count against administrative_duration')
As noted from previous pages, visitors who visit several administrative pages and/or spend an unusual amount of time on the site do not contribute to the revenue.
# plot exit_rates against bounce_rates
scatter(df$exit_rates, df$bounce_rates, 'exit rates', 'bounce rates', 'Exit Rates against Bounce Rates')
Visitors with high exit rates and bounce rates usually do not generate revenue for the ecommerce site.
b.) Categorical - categorical
# create funtion to plot stacked barchart
stacked <- function(column1, column2, title, value1, value2, legend){
# vectorize the two columns to plot
attribute1 <- c(column1)
attribute2 <- c(column2)
# create dataframe of the two columns
data <- data.frame(attribute1, attribute2)
# plot stacked bargraph
ggplot(data=data) + geom_bar(aes(fill=attribute2, x=attribute1)) + ggtitle(title) + xlab(value1) + ylab(value2) + theme(plot.title = element_text(hjust=0.5)) + labs(fill=legend) + theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1), plot.title = element_text(hjust=0.5))
}# Month against Revenue
stacked(df$month, df$revenue, "Month against Revenue", "Month", "Revenue",
"Revenue")
Most people who actually purchased products visited the site in November despite May recording the highest number of visitors. This is a fact that could be investigated further.
# Traffic Type against Revenue
stacked(df$traffic_type, df$revenue, "Traffic Type against Revenue", "Traffic Type", "Renenue","Revenue")
Most visitors who use traffic type 2 may have the site’s efficiency and userbility advantage thus profiting the site as well.
# Browser against Revenue
stacked(df$browser, df$revenue, "Browser against Revenue", "Browser", "Renenue","Revenue")
Browser type 2 is also used by most visitors and hence generates more revenue for the site.
# Operating Systems against Revenue
stacked(df$operating_systems, df$revenue, "Operating Systems against Revenue", "Operating Systems Type", "Renenue","Revenue")
Most visitors use type 2 operating system hence generate more income for
the site.
# Region against Revenue
# create contingency table
revenue <- df$revenue
region <- df$region
reg <- table(revenue,region)
reg## region
## revenue 1 2 3 4 5 6 7 8 9
## 0 3926 939 2027 992 265 688 639 375 419
## 1 771 188 349 175 52 112 119 56 86# plot mosaicplot for revenue against region
mosaicplot(reg, xlab="Revenue", ylab="Region", main="Revenue against Region", color="#68a3b3")
Region 1 has the highest number of visitors who visited the site and hence the highest generated revenue. This region may be more familiar with the site than other regions hence the significant difference in number of visitors.
# Visitor type against Region
# create contingency table
visitor <- df$visitor_type
region <- df$region
reg <- table(visitor,region)
reg## region
## visitor 1 2 3 4 5 6 7 8 9
## New_Visitor 656 149 312 139 50 121 100 74 92
## Other 8 5 8 5 0 1 2 1 51
## Returning_Visitor 4033 973 2056 1023 267 678 656 356 362# plot mosaicplot for revenue against region
mosaicplot(reg, xlab="Visitor Type", ylab="Region", main="Visitor Type against Region", color="#68a3b3")
Region 1 has the highest number of new and returning visitors followed by region 3.
The ecommerce site seems to be most popular in region 1. Further investigations can be carried out to determine what factors have contributed to this. This knowledge can help boost popularity of the site in regions 5 and 8.
C.) Categorical to numerical
# Barplot function
barc <- function(column1,column2, xlabel, ylabel, title){
ggplot(data=df, aes(x=column1, y=column2)) + stat_summary(fun='median') + geom_bar(stat="identity",fill="steelblue") + xlab(xlabel) +ylab(ylabel) + ggtitle(title) + theme(plot.title = element_text(hjust=0.5))
} # Region vs Bounce Rates
barc(df$region, df$bounce_rates, 'Region', 'Bounce Rates', 'Region vs Bounce Rates')## Warning: Removed 9 rows containing missing values (geom_segment).
Number of bounce rates per region is parallel to number of visitors in that region.
# Region vs Exit Rates
barc(df$region, df$exit_rates, 'Region', 'Exit Rates', 'Region vs Exit Rates')## Warning: Removed 9 rows containing missing values (geom_segment).
Exit rates are generally higher than bounce rates.
# Revenue vs Bounce Rates
barc(df$revenue, df$bounce_rates, 'Revenue', 'Bounce Rates', 'Revenue vs Bounce Rates')## Warning: Removed 2 rows containing missing values (geom_segment).
High bounce rates results to no profit for the site.
# Revenue vs Exit Rates
barc(df$revenue, df$exit_rates, 'Revenue', 'Exit Rates', 'Revenue vs Exit Rates')## Warning: Removed 2 rows containing missing values (geom_segment).
Similarly, high exit rates resulted in no revenue for the site.
# Revenue vs Page values
barc(df$revenue, df$page_values, 'Revenue', 'Page Values', 'Revenue vs Page Values')## Warning: Removed 2 rows containing missing values (geom_segment).
7. Modelling
We shall build a kmeans clustering and heirachical clusterng model to determine customer groups’ behaviour.
Feature Engineering
unique(df$month)## [1] Feb Mar May Oct June Jul Aug Nov Sep Dec
## Levels: Aug Dec Feb Jul June Mar May Nov Oct Sep# Replace June with its abbreviation Jun
df$month <- as.character(df$month)
df$month[df$month == "June"] <- "Jun"
df$month <- as.factor(df$month)
levels(df$month)## [1] "Aug" "Dec" "Feb" "Jul" "Jun" "Mar" "May" "Nov" "Oct" "Sep"# convert month to numeric
months <- c(df$month)
df$month <- c(match(months,month.abb))
df$month <- as.numeric(df$month)
# convert visitor type to numeric
df$visitor_type <- as.numeric(df$visitor_type)
# convert all other factors to numeric
fact.to.int <- function(column)(
as.integer(as.character(column))
)
df$revenue <- fact.to.int(df$revenue)
df$region <- fact.to.int(df$region)
df$traffic_type <- fact.to.int(df$traffic_type)
df$browser <- fact.to.int(df$browser)
df$operating_systems <- fact.to.int(df$operating_systems)
df$special_day <- fact.to.int(df$special_day)
df$weekend <- fact.to.int(df$weekend)
# preview dataset
head(df)# split variables into dependent and independent variables
# independent variables matrix
customer.attribute <- select(df,-revenue)
# dependent variable matrix
customer.group <- as.factor(df$revenue)# since our data is skewed, we shall normalize the data.
normal <- function(x) (
return( ((x - min(x)) /(max(x)-min(x))) )
)
normal(1:17)## [1] 0.0000 0.0625 0.1250 0.1875 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625
## [11] 0.6250 0.6875 0.7500 0.8125 0.8750 0.9375 1.0000data.scaled <- as.data.frame(lapply(customer.attribute, normal))
head(data.scaled)I.) KMeans Clustering
set.seed(123) # ensure randomness remains the same
# perform kmeans clustering
kmeans_model <- kmeans(customer.attribute, centers = 2,
iter.max = 10,
nstart = 25)
kmeans_model## K-means clustering with 2 clusters of sizes 11249, 929
##
## Cluster means:
## administrative administrative_duration informational informational_duration
## 1 2.072540 71.38779 0.4064361 25.67287
## 2 5.631862 208.18005 1.7599569 146.59477
## product_related product_related_duration bounce_rates exit_rates page_values
## 1 23.55578 805.3365 0.021261505 0.04291342 5.845940
## 2 135.71259 6104.5881 0.006522122 0.02076017 7.377369
## special_day month operating_systems browser region traffic_type
## 1 0.01262334 7.558005 2.123389 2.358432 3.176371 4.112366
## 2 0.01291712 9.101184 2.142088 2.369214 2.906351 3.599569
## visitor_type weekend
## 1 2.695084 0.2345097
## 2 2.960172 0.2335845
##
## Clustering vector:
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [37] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [73] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [109] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [181] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [217] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [253] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [289] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [325] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [361] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [397] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [433] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [469] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [505] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [541] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [577] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1
## [613] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [649] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [685] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [721] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [757] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [793] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [829] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [865] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [901] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [937] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [973] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1009] 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1045] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1081] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1117] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1153] 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [1189] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1225] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1261] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1297] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [1477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2
## [1513] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1549] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1585] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1621] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [1693] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [1729] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1765] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [1801] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [1837] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1873] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [1909] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [1945] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1981] 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1
## [2017] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1
## [2053] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [2089] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2125] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2
## [2161] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [2197] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2233] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2269] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2305] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [2341] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [2377] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [2413] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2449] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [2485] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [2521] 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2557] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [2593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2773] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2809] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [2845] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1
## [2881] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2917] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2953] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2989] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [3025] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [3061] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
## [3097] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3133] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [3169] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [3205] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [3241] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [3277] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3313] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3349] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [3385] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3421] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1
## [3457] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [3493] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2
## [3529] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [3565] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3601] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [3637] 1 1 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [3673] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3709] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3745] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3781] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3817] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [3853] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [3889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [3925] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1
## [3961] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3997] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [4033] 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4069] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4105] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [4141] 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [4177] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4213] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [4249] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [4285] 1 1 2 1 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1
## [4321] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4357] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4393] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1
## [4429] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [4465] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4501] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1
## [4537] 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [4573] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [4609] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4645] 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4681] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4717] 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4753] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4789] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4825] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1
## [4861] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4897] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [4933] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4969] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5005] 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5041] 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5077] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5113] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5221] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5257] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5293] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5329] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1
## [5365] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [5401] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5437] 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [5473] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [5509] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5545] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1
## [5581] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5617] 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1
## [5653] 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [5689] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [5725] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5761] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5797] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5833] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [5869] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [5905] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [5941] 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [5977] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6013] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6049] 1 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [6085] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [6121] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6157] 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1
## [6193] 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1
## [6229] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6265] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1
## [6301] 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1
## [6337] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1
## [6373] 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1
## [6409] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1
## [6445] 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [6481] 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [6517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6553] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [6589] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1
## [6625] 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1
## [6661] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [6697] 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1
## [6733] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [6769] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6805] 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1
## [6841] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6877] 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6913] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6949] 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
## [6985] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [7021] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7057] 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [7093] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [7129] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7165] 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [7201] 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7237] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [7273] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
## [7309] 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7345] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7381] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [7417] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7453] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7489] 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7525] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7561] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7597] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7633] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
## [7669] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1
## [7705] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7741] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7777] 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [7813] 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [7849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
## [7885] 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [7921] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2
## [7957] 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7993] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1
## [8029] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [8065] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [8101] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
## [8137] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 2 2 2 1 2 1 1 2 1 1 1
## [8173] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8209] 1 1 1 1 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 1
## [8245] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [8281] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8317] 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1
## [8353] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [8389] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1
## [8425] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [8461] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 1 2 2 1 1 1 2
## [8497] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8533] 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1
## [8569] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [8605] 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8641] 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1
## [8677] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 2 1 1
## [8713] 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8749] 1 1 1 1 1 1 1 2 1 2 1 1 2 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8785] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1
## [8821] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2
## [8857] 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1
## [8893] 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2
## [8929] 2 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [8965] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [9001] 1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [9037] 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1
## [9073] 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1
## [9109] 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 2 2 1 1 1 2 1 2 1 1 1 1 1
## [9145] 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [9181] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9217] 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [9253] 1 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 1
## [9289] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9325] 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1
## [9361] 1 1 1 1 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9397] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1 1 2 1 1 2 1 1
## [9433] 1 1 1 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [9469] 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9505] 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9541] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1
## [9577] 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9613] 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9649] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1
## [9685] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [9721] 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 2
## [9757] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1
## [9793] 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [9829] 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1
## [9865] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [9901] 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [9937] 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1
## [9973] 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10009] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 2
## [10045] 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 2 2 1 1 2 2
## [10081] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [10117] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [10153] 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [10189] 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1 1 2 2 1
## [10225] 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1
## [10261] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [10297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1
## [10333] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
## [10369] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10405] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10441] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10477] 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 1
## [10513] 1 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
## [10549] 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [10585] 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10621] 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2
## [10657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 2
## [10693] 1 1 2 1 1 1 1 1 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10729] 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1
## [10765] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 1 1
## [10801] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10837] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [10873] 1 1 2 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10909] 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 1 1 1 1
## [10945] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 2 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1
## [10981] 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [11017] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [11053] 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1
## [11089] 1 2 2 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1
## [11125] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
## [11161] 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [11197] 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11233] 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
## [11269] 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [11305] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
## [11341] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2
## [11377] 1 2 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1
## [11413] 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 1
## [11449] 1 1 1 2 1 1 1 1 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11485] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [11521] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1
## [11557] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [11593] 2 2 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11629] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
## [11665] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1
## [11701] 1 1 1 2 2 2 2 2 2 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [11737] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 2 1
## [11773] 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [11809] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 2 1 2 1 1 2 1
## [11845] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1
## [11881] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11917] 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1
## [11953] 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1
## [11989] 1 1 2 1 2 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 1
## [12025] 1 1 1 1 2 2 1 1 1 1 1 1 2 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [12061] 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1
## [12097] 1 1 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1
## [12133] 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 1 1 1 1 1 1 1
## [12169] 1 1 1 1 1 1 1 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 7731497443 13721089926
## (between_SS / total_SS = 52.9 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"The kmeans model predicted that 11249 are in the first cluster and 929 in the second cluster.
# visualize output
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBafviz_cluster(kmeans_model, data = customer.attribute)
We need to determine the optimal value of k.
a.) Elbow method
# Determining Optimal clusters (k) Using Elbow method
fviz_nbclust(x = customer.attribute ,FUNcluster = kmeans, method = 'wss' )
Optimal k value according to elbow method is either 2 or 3.
# perform kmeans clustering with k=3
kmeans_model_elbow <- kmeans(customer.attribute, centers = 3,
iter.max = 10,
nstart = 25)
kmeans_model_elbow## K-means clustering with 3 clusters of sizes 10009, 205, 1964
##
## Cluster means:
## administrative administrative_duration informational informational_duration
## 1 1.848636 62.97512 0.3328005 20.28687
## 2 7.439024 295.64171 2.7707317 269.29600
## 3 4.337067 155.55803 1.1751527 84.88988
## product_related product_related_duration bounce_rates exit_rates page_values
## 1 18.91118 587.0995 0.022978738 0.04549968 5.598237
## 2 236.98537 10922.7713 0.005918204 0.01970622 4.543675
## 3 78.00000 3368.0985 0.007139664 0.02167676 7.968604
## special_day month operating_systems browser region traffic_type
## 1 0.013088221 7.466380 2.122090 2.369867 3.179938 4.153362
## 2 0.009756098 9.429268 2.146341 2.312195 2.570732 3.639024
## 3 0.010692464 8.559572 2.136456 2.310081 3.093686 3.710285
## visitor_type weekend
## 1 2.672495 0.2373864
## 2 2.985366 0.2439024
## 3 2.905295 0.2184318
##
## Clustering vector:
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [37] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
## [73] 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 3
## [109] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [181] 1 3 1 3 1 3 1 1 1 3 3 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [217] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 3 1 1 1 1 1 1
## [253] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1
## [289] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1
## [325] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 3 1 1
## [361] 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [397] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [433] 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1
## [469] 3 3 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1 1 1 1 1 1 2 1 1
## [505] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [541] 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [577] 3 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 1 1 1 1
## [613] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [649] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [685] 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [721] 1 3 3 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
## [757] 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2 1 1 1 1 1 1
## [793] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1
## [829] 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [865] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 3
## [901] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1
## [937] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [973] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1
## [1009] 1 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3
## [1045] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1081] 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1117] 1 3 1 2 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1153] 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [1189] 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1225] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1
## [1261] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1 1 1
## [1297] 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1333] 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [1369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1405] 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
## [1441] 3 3 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1
## [1477] 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 3 1 1 1 3 1 2
## [1513] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1549] 1 1 1 1 3 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [1585] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1
## [1621] 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [1657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3
## [1693] 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 3 1 1
## [1729] 1 1 1 3 1 1 1 1 1 1 3 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1765] 1 1 1 1 1 1 3 1 3 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [1801] 3 1 1 1 2 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 1 1 1
## [1837] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1873] 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1
## [1909] 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 1 1
## [1945] 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1981] 1 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1
## [2017] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 1 3 1 1 1 3 1 3 3 1
## [2053] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1 1 1 1 1 3 1 1 1 1
## [2089] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1
## [2125] 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 3 3 3 1 3 3 1 1 1 1 1 1 3 1 1 3 1 3
## [2161] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 3 1 3 3 1 1 1 1 1 1 1 1 3 3 3 1
## [2197] 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1
## [2233] 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2269] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2305] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 3 3 1 1 1 1 1 1 3 3 1 1 1 1
## [2341] 1 1 1 1 1 1 3 1 1 3 1 1 3 2 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
## [2377] 1 1 1 1 1 1 1 1 3 1 1 1 1 3 3 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1
## [2413] 1 1 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1
## [2449] 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [2485] 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1
## [2521] 1 1 1 1 1 1 2 1 1 1 3 3 1 1 1 2 3 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 3 1 1
## [2557] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 2 1 3 1 1 3 1 1 1 1 1 1
## [2593] 1 1 1 1 1 1 3 3 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2629] 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 3 1 1 1
## [2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2701] 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [2737] 1 1 1 1 1 1 3 1 1 3 1 1 1 3 1 3 1 3 3 3 2 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [2773] 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [2809] 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [2845] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 3 3 1 1 1 1 2 1 3 1 1 1 3 1 1 1
## [2881] 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1
## [2917] 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2953] 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1
## [2989] 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 3 3
## [3025] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 3 1
## [3061] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 3
## [3097] 1 3 1 1 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 3 1 3 1
## [3133] 3 3 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 3 1 1
## [3169] 1 1 1 3 1 3 1 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1
## [3205] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1
## [3241] 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 3 3 1
## [3277] 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1
## [3313] 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 3 3 1 1 1 1 1 1 1 1
## [3349] 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1
## [3385] 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3421] 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 1 3 1 1 3 1 3 1 1 1
## [3457] 1 1 1 3 1 3 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [3493] 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3
## [3529] 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1
## [3565] 3 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3601] 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [3637] 1 1 1 1 1 3 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1
## [3673] 3 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
## [3709] 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 3 3 1 2 1 1 1 1 3 3 1 1 1 1 1 1 1 1
## [3745] 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [3781] 1 1 3 3 3 1 1 3 1 1 1 3 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 1 1 1 1 1 3
## [3817] 3 3 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 3 3 1 1
## [3853] 1 3 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1
## [3889] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1
## [3925] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 3 3 1 1 1 1 1 1 1 1 1
## [3961] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 3 3 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [3997] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 1 1
## [4033] 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4069] 3 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 3 1 1 1
## [4105] 1 1 1 1 1 3 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 1 1 1
## [4141] 1 1 2 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 3 1 1 1 3 1 2 1 1 1 1 1 1 3
## [4177] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 3 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1
## [4213] 3 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [4249] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1
## [4285] 1 1 3 1 3 1 1 3 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 3 1 1 1 1 1
## [4321] 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1
## [4357] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4393] 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 3 1 3 1 1 1
## [4429] 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 1 3 1 1 1 1 1
## [4465] 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 3 1 1 1 1 1 1 3 1
## [4501] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1
## [4537] 2 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 3
## [4573] 3 1 1 3 1 1 1 1 1 2 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [4609] 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
## [4645] 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4681] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4717] 1 1 1 1 1 3 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4753] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1
## [4789] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1
## [4825] 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 3 3 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 3 1 1 1
## [4861] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 3 1 3 3 1 1 1 3
## [4897] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [4933] 1 3 1 1 1 1 1 1 3 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3
## [4969] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
## [5005] 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [5041] 1 1 1 3 1 1 1 1 3 1 2 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [5077] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5113] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
## [5149] 1 1 1 3 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
## [5185] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [5221] 1 1 3 3 1 1 1 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5257] 3 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [5293] 1 1 1 3 1 3 1 1 3 3 1 1 1 1 3 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5329] 1 1 3 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 3 1 1 1
## [5365] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1
## [5401] 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5437] 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 3 1 3 1
## [5473] 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 3 1 1 1
## [5509] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 3 2 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1
## [5545] 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1 1 1 1 3 1 3 1 1
## [5581] 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5617] 1 3 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1 3 1 1
## [5653] 1 1 1 1 1 1 1 1 3 1 1 3 1 1 3 3 1 1 1 3 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1
## [5689] 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 3 1 1 1 3 3
## [5725] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1
## [5761] 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 3 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1
## [5797] 1 1 1 1 1 3 1 2 3 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 3 1 1
## [5833] 3 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2 1 1 3 1 1 1 3 1 1
## [5869] 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 3 1
## [5905] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 3
## [5941] 3 1 1 1 1 1 3 1 3 1 3 1 1 2 1 1 3 1 1 3 1 3 1 1 1 3 1 1 1 3 1 1 1 2 1 1
## [5977] 3 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6013] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
## [6049] 3 3 1 1 2 1 1 1 3 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1
## [6085] 1 1 3 1 1 1 1 1 1 1 1 3 1 3 1 3 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1
## [6121] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6157] 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 3
## [6193] 1 3 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1 1 1 3 1 1 1 2 3 2 1 1 1
## [6229] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1
## [6265] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1
## [6301] 1 1 1 1 1 1 1 1 3 2 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1
## [6337] 1 1 1 3 1 3 1 3 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 3 2 1 3 3 1 1 1 1 1 1 1
## [6373] 1 1 1 2 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 3 1 1 1 1 1 1 1 3 1
## [6409] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 2 1 1 1 3 1 1
## [6445] 3 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 3
## [6481] 1 1 1 3 1 1 1 1 3 3 2 1 1 1 3 1 3 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1
## [6517] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [6553] 1 1 1 1 1 1 1 1 1 2 1 1 3 1 1 3 1 1 1 2 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1
## [6589] 1 1 1 1 3 1 1 3 1 3 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 3 1 3 1 1 1 2 3 3 1
## [6625] 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 3 3 1 1 3 3 1 1 1 1 2 1 1 1 3 1 1 1 2 1 1
## [6661] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 2 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## [6697] 1 1 1 3 1 1 1 1 1 1 3 2 1 1 1 3 1 1 1 1 1 1 3 1 1 3 1 3 1 1 1 1 1 1 1 1
## [6733] 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [6769] 1 1 3 1 3 1 1 1 1 1 3 1 3 1 1 1 1 3 1 3 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1
## [6805] 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 1 1 2 1 1 1 1 3 1 3 1 1 1 3 1
## [6841] 1 1 3 1 1 3 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1
## [6877] 1 1 2 1 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [6913] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [6949] 1 3 3 1 1 1 3 1 1 1 1 3 1 3 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1
## [6985] 3 1 1 1 1 3 1 1 1 1 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1
## [7021] 1 1 1 1 1 1 3 1 1 1 1 3 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3
## [7057] 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 3
## [7093] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 3 1 1
## [7129] 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1
## [7165] 1 1 3 1 1 1 1 3 1 1 1 2 1 2 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3
## [7201] 3 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1
## [7237] 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 3
## [7273] 3 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 3 1 1 1
## [7309] 1 3 3 1 3 1 1 1 3 2 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1
## [7345] 1 1 1 1 1 3 1 1 3 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1
## [7381] 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1
## [7417] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 3 1 1 1
## [7453] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7489] 3 1 1 3 1 1 1 1 3 1 3 1 1 3 1 1 1 3 1 3 3 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1
## [7525] 1 1 1 3 3 1 1 3 1 1 3 3 1 3 3 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7561] 1 1 1 2 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7597] 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1
## [7633] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 3 3 1 1 1 1 1 3 1 3 1 3 1 3 1
## [7669] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1
## [7705] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
## [7741] 3 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7777] 1 3 1 1 1 1 1 3 2 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 2 1 1
## [7813] 1 1 3 1 1 1 1 1 3 3 3 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1
## [7849] 3 1 1 1 1 1 1 3 1 1 1 1 3 1 1 3 3 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 3
## [7885] 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 3 3 1 1 3 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1
## [7921] 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 2
## [7957] 1 1 1 1 3 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 2 2 3 1 1 3 1 1 1 1 1 1 1 1 1
## [7993] 1 1 1 1 1 1 1 1 3 3 1 3 1 1 1 1 1 2 1 1 1 1 1 3 1 1 1 3 3 3 3 1 1 1 3 1
## [8029] 1 3 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1
## [8065] 1 3 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 3 1 3 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1
## [8101] 1 1 1 1 1 1 1 3 1 1 1 1 3 1 2 1 1 1 3 1 1 1 2 1 1 3 1 1 1 1 1 1 3 1 1 1
## [8137] 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 3 3 1 1 1 3 1 1 3 2 3 1 3 1 1 3 1 1 1
## [8173] 1 1 1 3 1 3 1 1 1 1 3 1 1 3 1 3 1 1 1 1 2 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## [8209] 1 1 3 1 1 1 3 1 3 1 1 3 1 3 1 1 1 3 1 3 3 1 1 1 3 3 1 1 1 1 1 2 1 1 3 1
## [8245] 1 1 1 3 1 1 1 1 1 1 1 3 1 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 1
## [8281] 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 2 1 3 3 1 1 1 1 1 3 1 1 1 1 1 1 1
## [8317] 1 3 1 3 1 1 2 1 1 3 1 1 1 3 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 3 1 1 1 3 3 1
## [8353] 1 1 1 1 3 1 1 1 1 3 1 3 1 3 1 1 1 2 3 3 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1
## [8389] 3 1 1 1 1 1 1 3 1 1 3 1 1 1 1 3 1 3 1 3 3 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1
## [8425] 1 1 1 1 3 3 1 2 1 1 1 3 1 1 3 1 2 1 3 3 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1
## [8461] 1 3 1 3 1 3 1 1 3 1 1 1 1 1 1 1 3 3 1 3 1 1 1 3 1 2 1 1 1 1 3 3 1 1 1 3
## [8497] 1 1 1 1 1 2 1 1 1 1 3 1 3 1 3 1 3 2 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8533] 1 1 1 1 1 1 2 1 1 3 1 3 1 1 1 3 1 1 1 1 1 3 1 1 3 1 1 1 3 1 1 1 3 3 1 1
## [8569] 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 3 1 3 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1
## [8605] 1 1 3 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 3
## [8641] 1 3 1 1 1 1 3 3 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 2 3 1 3 1 1 1 3 3
## [8677] 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 3 1 1 1 1 1 1 3 3 1 1
## [8713] 1 2 3 1 3 3 1 3 1 1 1 1 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 1 1
## [8749] 1 1 1 1 3 3 1 2 1 3 1 1 2 2 3 1 1 1 2 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [8785] 1 1 1 3 1 3 3 3 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 3
## [8821] 1 1 1 1 1 1 1 1 1 3 2 1 1 1 3 3 3 1 3 1 1 1 1 1 3 1 1 1 3 1 1 1 3 1 1 2
## [8857] 1 1 3 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 3 2 1 1 1
## [8893] 1 1 3 1 1 1 3 1 1 3 3 1 1 3 1 3 1 1 1 3 1 1 3 1 1 3 2 1 1 1 1 1 3 1 3 3
## [8929] 3 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 3 1 3 1 3 1 1 3 3 1 3 1 1 1 1 3 3 1 3
## [8965] 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 3 1 3 1 3 1 1 3 1 3 1 1 1 3 1
## [9001] 1 1 1 1 1 2 1 1 3 1 1 3 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1
## [9037] 1 1 1 2 1 3 3 3 1 1 3 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 1
## [9073] 1 1 1 1 1 1 2 3 1 1 1 1 1 3 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 3
## [9109] 1 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 3 1 1 3 1 1 2 3 1 3 1 3 1 3 1 1 1 1 1
## [9145] 3 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1
## [9181] 3 2 1 3 1 1 1 1 1 1 1 1 1 3 1 3 1 1 3 3 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 3
## [9217] 3 3 3 1 1 1 3 1 1 3 1 1 3 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 3 1 3 1
## [9253] 1 2 3 1 1 3 1 1 3 1 1 1 3 3 1 1 3 3 1 3 3 1 1 1 3 1 1 1 3 1 2 1 3 1 1 1
## [9289] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 3
## [9325] 1 1 1 1 3 1 3 1 1 1 3 1 1 3 1 3 3 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 3 3 1
## [9361] 1 1 1 3 1 2 2 1 3 3 1 1 3 1 1 1 1 1 1 3 1 1 3 1 3 1 3 1 1 1 3 1 1 1 1 1
## [9397] 1 3 1 1 1 1 1 3 1 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 2 1 3 1 1 1 3 1 1 3 1 1
## [9433] 1 1 1 1 1 1 3 3 3 1 1 3 3 3 1 1 1 1 1 3 1 1 1 2 1 1 1 1 3 1 3 1 1 1 1 1
## [9469] 1 1 1 3 3 3 1 1 3 1 1 3 1 3 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [9505] 1 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1
## [9541] 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 3 1 1 1 1 1 1
## [9577] 1 1 1 1 1 1 2 3 1 1 1 2 1 1 3 1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1
## [9613] 1 3 3 3 1 1 1 3 1 1 1 3 1 3 1 1 1 1 1 1 3 1 1 3 3 1 1 1 3 3 1 1 3 1 1 1
## [9649] 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 3 1 1 3 3 1 1 1 1 1 1 3 3 1 3 1 1 3 3
## [9685] 3 1 1 1 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 2 1 1 1 1 3 1
## [9721] 1 2 3 1 1 1 1 1 1 1 1 2 1 3 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 3 1 3 3
## [9757] 3 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 2 1 1 3 1 1 1 1 1 1 3 2 1 1 1 1
## [9793] 2 3 1 1 3 1 1 1 1 1 1 1 2 1 1 3 1 3 1 1 1 3 1 3 1 1 1 3 1 1 1 1 1 3 1 1
## [9829] 1 1 3 1 3 3 1 1 1 3 1 3 1 3 1 3 1 2 1 3 1 1 2 1 1 1 1 3 3 1 1 3 1 1 1 3
## [9865] 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [9901] 1 1 1 1 1 3 1 1 3 1 3 1 1 1 1 1 3 1 3 1 2 1 1 3 1 1 1 1 1 1 3 1 3 1 1 1
## [9937] 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1 3 3 1 3 1 1 1 1 3 1 3 1 3 1 1 1 1 1 1
## [9973] 1 1 1 1 3 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1
## [10009] 3 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 3 2 1 3 1 3 3 1 1 1 2 1 3
## [10045] 3 3 1 1 3 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2 1 1 3 3 1 3 3 3
## [10081] 1 3 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 2 1 3 3 3 1
## [10117] 2 3 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 2 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [10153] 1 1 1 3 1 1 1 3 1 1 1 1 1 2 3 2 3 3 1 1 2 2 3 3 1 1 1 1 1 1 3 1 3 1 1 1
## [10189] 3 2 1 1 3 1 1 3 1 1 3 1 3 1 1 1 1 1 3 1 1 1 3 3 1 1 1 1 1 1 3 1 1 2 3 1
## [10225] 1 1 1 1 3 1 1 3 1 3 3 1 1 3 3 1 1 1 1 3 1 1 1 1 1 3 1 1 3 1 2 1 1 1 1 1
## [10261] 1 1 1 1 1 1 1 1 3 1 1 1 2 3 1 1 3 3 1 3 3 1 3 3 1 3 1 1 1 1 1 2 1 1 1 3
## [10297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 1 3 1 1 1 3 1 1 1 3 1
## [10333] 1 3 3 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 2 1 1 1 1 1 3 3 1 1 3 1 1 1 1 1
## [10369] 1 1 2 1 1 1 1 1 3 1 1 1 1 3 3 1 3 1 3 3 3 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1
## [10405] 1 1 1 1 1 3 1 3 1 3 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
## [10441] 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 3 1
## [10477] 2 1 1 1 3 3 1 1 1 1 3 1 1 3 3 3 1 3 1 3 1 1 1 1 1 1 1 1 3 1 1 3 1 3 3 1
## [10513] 3 3 1 1 1 1 1 1 1 1 1 3 3 1 1 3 1 1 1 1 3 3 1 1 1 2 1 1 1 3 1 2 1 1 1 3
## [10549] 1 1 1 3 3 1 3 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1
## [10585] 3 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10621] 3 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 1 1 1 1 3
## [10657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 3 1 1 3 1 1 1 3 2
## [10693] 1 1 3 1 1 1 1 3 3 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1
## [10729] 3 3 1 1 1 1 1 2 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1 3 3 1 1 3
## [10765] 1 1 1 1 1 1 1 1 1 1 3 1 3 1 2 1 1 1 3 1 1 3 3 1 1 1 3 1 1 3 1 1 2 1 1 3
## [10801] 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1
## [10837] 1 1 3 2 1 1 1 1 3 1 1 1 1 3 1 1 3 3 3 3 1 3 1 1 3 1 1 1 3 1 1 3 1 1 1 1
## [10873] 1 1 3 1 1 3 3 1 1 3 1 1 1 1 1 1 1 3 1 3 1 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1
## [10909] 1 1 1 1 1 1 1 1 3 1 3 3 2 1 3 1 1 1 3 1 1 2 1 1 1 3 1 3 3 1 1 1 3 1 3 1
## [10945] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 2 1 1 2 1 1 1 3 3 3 3 1 1 1 1 3 1 3 1 1
## [10981] 3 1 1 1 3 1 1 1 3 1 1 1 3 1 2 3 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1
## [11017] 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 3 3 1 3 1 1 1
## [11053] 1 3 1 1 3 3 1 1 1 1 1 3 2 3 1 3 1 3 3 1 1 1 1 1 1 3 3 3 1 3 3 1 1 1 1 1
## [11089] 1 3 2 1 1 1 1 3 3 1 3 1 3 3 1 1 1 3 1 3 1 3 1 1 3 3 1 3 1 1 3 3 3 2 1 1
## [11125] 1 1 1 1 1 3 1 1 1 3 1 1 1 3 1 3 3 3 3 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 2 1
## [11161] 1 1 1 3 3 1 3 1 1 1 1 1 1 1 3 3 1 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3
## [11197] 3 1 3 1 1 1 1 1 1 3 1 3 1 3 3 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 3 1
## [11233] 1 1 3 1 1 1 2 1 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 2 1 1 1 1
## [11269] 3 3 3 1 1 1 1 1 1 3 1 3 1 1 3 1 1 3 1 1 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1
## [11305] 3 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 3 2
## [11341] 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 3 2 2
## [11377] 1 3 1 3 3 3 1 1 1 1 3 3 1 1 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 1 3 1 1 3 2 3
## [11413] 1 1 1 3 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 3 1 2 2 1 1 1 1 1 1 1 1 1 3 3 1
## [11449] 1 1 3 2 1 1 3 1 2 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
## [11485] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 3 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
## [11521] 1 1 3 3 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 1 3 1 1
## [11557] 1 1 1 3 1 3 1 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1
## [11593] 2 2 3 3 1 1 1 1 3 1 1 1 1 1 3 1 1 3 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1
## [11629] 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 2 1 1 1 1
## [11665] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 1 3 3 3 3 3 3 3 1 1 1 1 1 3 1 3 1 1 1 3 1
## [11701] 1 1 1 2 3 3 3 3 3 1 3 3 1 1 3 1 3 1 1 2 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1
## [11737] 1 1 1 1 1 2 1 3 1 1 1 1 3 1 1 1 1 1 3 1 1 3 3 1 2 1 1 1 3 3 1 3 1 3 2 1
## [11773] 1 3 1 2 1 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1
## [11809] 1 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 3 3 1 1 2 1 2 1 3 3 1
## [11845] 1 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 1
## [11881] 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [11917] 3 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1 1 1
## [11953] 1 3 1 1 1 3 1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 2 1 1 1 1 3 1 2 1 1 1 1 1 1 1
## [11989] 1 1 3 1 2 1 3 1 3 1 1 3 1 3 1 3 1 1 1 1 1 1 1 3 1 3 1 1 3 1 3 1 3 3 3 1
## [12025] 1 1 1 1 2 2 1 1 1 1 1 1 3 1 3 3 1 1 1 3 3 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1
## [12061] 1 1 3 1 3 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 3 3 1 1
## [12097] 1 1 3 1 1 1 1 3 1 1 3 1 3 3 3 1 1 3 3 1 1 1 3 1 3 1 1 3 1 1 3 1 3 1 2 1
## [12133] 3 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 2 3 1 1 1 1 1 1
## [12169] 1 1 1 1 1 1 1 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 3074496977 6794542425 3294704760
## (between_SS / total_SS = 71.1 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"The 3 clusters have the following size respectively: 1964, 207, 10007
# visualize output
fviz_cluster(kmeans_model_elbow, data = customer.attribute)
b.) Silhouette method
# Determining Optimal clusters (k) Using Average Silhouette Method
fviz_nbclust(x = customer.attribute, FUNcluster = kmeans, method = 'silhouette' )
Silhouette method chose 2 as the optimal value for k.
c.) Gap Statistic method
# compute gap statistic
# import cluster package
library(cluster)
set.seed(123)
gap_statistic <- clusGap(x = customer.attribute, FUN = kmeans, K.max = 15, nstart = 25, B = 50, iter.max=1000)## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
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## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
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## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
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## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)
## Warning: Quick-TRANSfer stage steps exceeded maximum (= 608900)# Print the result
print(gap_statistic, method = "firstmax")## Clustering Gap statistic ["clusGap"] from call:
## clusGap(x = customer.attribute, FUNcluster = kmeans, K.max = 15, B = 50, nstart = 25, iter.max = 1000)
## B=50 simulated reference sets, k = 1..15; spaceH0="scaledPCA"
## --> Number of clusters (method 'firstmax'): 1
## logW E.logW gap SE.sim
## [1,] 15.35733 17.99820 2.640876 0.004617610
## [2,] 14.99368 17.32466 2.330984 0.003602062
## [3,] 14.73270 16.94389 2.211191 0.004549928
## [4,] 14.54029 16.68674 2.146451 0.003947392
## [5,] 14.40428 16.49480 2.090515 0.003792278
## [6,] 14.25115 16.34830 2.097148 0.003992810
## [7,] 14.12070 16.23042 2.109722 0.002977658
## [8,] 14.10652 16.13491 2.028390 0.002595882
## [9,] 13.97845 16.05535 2.076893 0.002822510
## [10,] 13.87980 15.98808 2.108280 0.002560380
## [11,] 13.80040 15.93117 2.130772 0.002168585
## [12,] 13.75113 15.88215 2.131015 0.002980513
## [13,] 13.72384 15.83968 2.115834 0.002478171
## [14,] 13.64804 15.80275 2.154711 0.002426903
## [15,] 13.60727 15.77012 2.162845 0.002294835# plot the result to determine the optimal k value.
fviz_gap_stat(gap_statistic)
Gap statistic chose 1 as the optimal value for k.
# perform kmeans clustering with k=1
kmeans_model_gap <- kmeans(customer.attribute, centers = 1,
iter.max = 10,
nstart = 25)
kmeans_model_gap## K-means clustering with 1 clusters of sizes 12178
##
## Cluster means:
## administrative administrative_duration informational informational_duration
## 1 2.344063 81.823 0.5096896 34.89741
## product_related product_related_duration bounce_rates exit_rates page_values
## 1 32.11168 1209.59 0.02013711 0.04122346 5.962765
## special_day month operating_systems browser region traffic_type
## 1 0.01264575 7.675727 2.124815 2.359254 3.155773 4.073247
## visitor_type weekend
## 1 2.715306 0.2344392
##
## Clustering vector:
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [37] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [73] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [109] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [181] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [217] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [253] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [289] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [325] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [361] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [397] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [433] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [469] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [505] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [541] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [577] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [613] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [649] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [685] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [721] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [757] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [793] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [829] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [865] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [901] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [937] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [973] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1009] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1045] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1081] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1117] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1153] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1189] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1225] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1261] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1513] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1549] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1585] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1621] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1693] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1729] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1765] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1801] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1837] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1873] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1909] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1945] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1981] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2017] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2053] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2089] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2125] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2161] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2197] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2233] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2269] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2305] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2341] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2377] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2413] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2449] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2485] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2521] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2557] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2773] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2809] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2845] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2881] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2917] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2953] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2989] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3025] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3061] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3097] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3133] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3169] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3205] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3241] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3277] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3313] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3349] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3385] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3421] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3457] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3493] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3529] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3565] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3601] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3637] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3673] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3709] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3745] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3781] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3817] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3853] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3925] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3961] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3997] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4033] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4069] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4105] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4141] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4177] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4213] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4249] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4285] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4321] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4357] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4393] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4429] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4465] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4501] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4537] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4573] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4609] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4645] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4681] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4717] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4753] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4789] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4825] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4861] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4897] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4933] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4969] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5005] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5041] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5077] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5113] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5257] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5293] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5329] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5365] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5401] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5437] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5473] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5509] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5545] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5581] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5617] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5653] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5689] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5725] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5761] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5797] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5833] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5869] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5905] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5941] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [5977] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6013] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6049] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6085] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6121] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6157] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6193] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6229] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6265] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6301] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6337] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6373] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6409] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6553] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6589] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6625] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6661] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6697] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6733] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6769] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6805] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6841] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6877] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6913] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6949] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [6985] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7021] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7057] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7093] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7129] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7165] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7201] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7237] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7273] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7309] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7345] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7381] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7417] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7453] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7489] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7525] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7561] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7597] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7633] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7669] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7705] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7813] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7885] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7921] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7957] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [7993] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8029] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8065] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8101] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8137] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8173] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8209] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8245] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8281] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8317] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8353] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8389] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8425] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8461] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8497] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8533] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8569] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8605] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8641] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8677] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8713] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8749] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8785] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8821] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8857] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8893] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8929] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [8965] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9001] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9073] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9109] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9181] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9217] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9253] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9289] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9325] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9361] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9397] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9433] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9469] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9505] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9541] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9577] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9613] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9649] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9685] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9721] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9757] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9793] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9829] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9865] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9901] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9937] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [9973] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10009] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10045] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10081] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10117] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10153] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10189] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10225] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10261] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10513] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10549] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10585] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10621] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10657] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10693] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10729] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10765] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10801] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10837] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10873] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10909] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10945] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [10981] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11017] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11053] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11089] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11125] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11161] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11197] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11233] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11269] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11305] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11341] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11377] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11413] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11449] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11485] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11521] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11557] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11773] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11809] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11845] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11881] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11917] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11953] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [11989] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12025] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12061] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12097] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12133] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12169] 1 1 1 1 1 1 1 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 45590100682
## (between_SS / total_SS = -0.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"# visualize output
fviz_cluster(kmeans_model_gap, data = customer.attribute)
This would mean that all customers are in a single group hence not beneficial.
- The 2-cluster plot(chosen by two methods) shows a better representation of customer groups despite the fact that they appear very close to each other. A disadvantage however of kmeans algorithm is the inability to validate results since there is no target value hence results are less accurate and trustworthy.
ii.) Heirarchical clustering
#compute distance matrix
d <- dist(customer.attribute, method = "euclidean")
#perform hierarchical clustering using Ward's method
clust<- hclust(d, method = "ward.D2")
#clust <- agnes(customer.attribute, method = "ward")# plot dendogram
plot(clust, cex = 0.6, hang = -1)
The hierarchical clustering model determines 2 parent clusters before splitting further into several clusters.
The heirachical clustering does not require specification of k hence easier to implement. It is however a cumbesome method for huge datasets due to high space and time complexity.
Despite its limitations, heirarchical clustering would be prefered for this model rather than using flat kmeans clusters. Heirarchical clusters are able to provide more in depth information as to how the clusters were created.
Next step would be to determine optimal methods of pruning the tree for better results.
Conclusion
Both
8. Challenging the solution
We are able to determine three overlapping customer groups. We may require more data in order to make these clusters distinct.
9. Follow up Questions
Do we have the right data?
We had the right data to determine customer groups
Do we have the right question?
The research question was given by the client hence the right question was already provided.
9. Conclusion
According to our analysis, gender contributes the least to who clicks on the ad or not. This is seen from the small change in percentage from the whole dataset to those who clicked on the ad. However, the rest of the attributes to some extent have an impact to this effect. Geographical location, Internet accessibility, Age and Date determine who clicks the ad.
10. Recommendations
From our findings, we are able to deduce the following in an attempt to determine a customer groups:
i.) Time spent on a page does not contribute to revenue since visitors who spent more time in pages did not contribute to revenue. ii.) The ecommerce site is most popular in region 1 and least popular in region 5. Further investigations should be done to determine why this is so. iii.) Most revenue is collected in the month of November. Further investigations can be done to determine why. iv.) Most users prefer using type 2 operating systems and browsers