R Notebook
This first chunk simply examines whether zip codes with a TT customer are different than a zip code without a TT customer.
library(pacman)
p_load(dplyr, tidyr, readr, tigris, acs, magrittr, foreign, ggplot2, ggthemes, tidyverse, rgdal, VIM, cluster )
##clear workspace
remove(list = ls())
##read in TT data
tt_data_raw <- read_csv("C:/Users/kevin.haynes/Documents/TT/raw/TT data/data_joined_and_cleaned 2.20.csv")## Warning: Missing column names filled in: 'X1' [1]## Parsed with column specification:
## cols(
## .default = col_character(),
## X1 = col_integer(),
## id = col_integer(),
## confirmed_at = col_datetime(format = ""),
## owners_created_at = col_datetime(format = ""),
## listing_created_at = col_datetime(format = ""),
## listing_transunion_id = col_integer(),
## listing_syndication_expires_on = col_datetime(format = ""),
## listing_partial = col_integer(),
## listing_description_length = col_double(),
## listing_available_date = col_date(format = ""),
## listings_count = col_integer(),
## listing_rent_amount = col_double(),
## rental_requests_count = col_integer(),
## photos_count = col_integer(),
## rental_request_created_at = col_datetime(format = ""),
## payments_count = col_integer(),
## properties = col_double(),
## free_email = col_integer(),
## hours_until_listing = col_double(),
## owners_created_at_hour = col_integer()
## # ... with 10 more columns
## )## See spec(...) for full column specifications.## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)## Warning: 11 parsing failures.
## row # A tibble: 5 x 5 col row col expected actual file expected <int> <chr> <chr> <chr> <chr> actual 1 1554 listing_avai~ "date li~ 20171-0~ 'C:/Users/kevin.haynes/Documents~ file 2 16725 listing_avai~ "date li~ 12016-0~ 'C:/Users/kevin.haynes/Documents~ row 3 27500 listing_avai~ "date li~ 12017-1~ 'C:/Users/kevin.haynes/Documents~ col 4 29300 listing_avai~ "date li~ 20171-0~ 'C:/Users/kevin.haynes/Documents~ expected 5 34803 listing_avai~ "date li~ 20175-0~ 'C:/Users/kevin.haynes/Documents~
## ... ................. ... .......................................................................... ........ .......................................................................... ...... .......................................................................... .... .......................................................................... ... .......................................................................... ... .......................................................................... ........ ..........................................................................
## See problems(...) for more details. ##prep TT data for analysis
tt_data <- tt_data_raw %>%
rename(GEOID=listing_zip) %>%
#for now omit any records with no zip
drop_na(GEOID) %>%
#keep just customers
filter(customer==1) %>%
select(GEOID, listing_created_at, listing_available_date, listings_count,
listing_rent_amount, payments_count, properties, whale, customer, process_marketing,
process_screen_tenant, process_receive_application, `Original Source`, `Original Source Drill-Down 1`, `Original Source Drill-Down 2`)
##aggregate TT data by zip code
tt_data_zip_agg <- tt_data %>%
#omit any records with no zip
drop_na(GEOID) %>%
group_by(GEOID) %>%
summarise(payments_total=sum(payments_count, na.rm=TRUE),
payments_mean=mean(payments_count, na.rm=TRUE),
customers_total=sum(customer, na.rm=TRUE),
listing_amount_mean=mean(listing_rent_amount, na.rm=TRUE))
##read in acs and zillow data
acs_zillow_data <- read_csv("C:/Users/kevin.haynes/Documents/TT/raw/acs_zillow_data.csv")## Warning: Missing column names filled in: 'X1' [1]## Parsed with column specification:
## cols(
## .default = col_character(),
## X1 = col_integer(),
## median_age_all_2017 = col_double(),
## median_income_2017 = col_double(),
## total_bach_perc = col_double(),
## total_population_2017 = col_integer(),
## undergrad_enrollment_2017 = col_integer(),
## college_enrollment_perc_2017 = col_double(),
## monthly_housing_costs_2017 = col_integer(),
## owner_occupied = col_integer(),
## renter_occupied = col_integer(),
## owner_perc = col_double(),
## renter_perc = col_double()
## )
## See spec(...) for full column specifications. #merge tt with acs and zillow data at the individual record level
tt_acs_zillow_data <- left_join(tt_data, acs_zillow_data, by="GEOID")
#change char to numeric
tt_acs_zillow_data$rental_costs_2018_dec <- as.numeric(as.character(tt_acs_zillow_data$rental_costs_2018_dec))
tt_acs_zillow_data$HVI_2018_12 <- as.numeric(as.character(tt_acs_zillow_data$HVI_2018_12))
##merge tt aggregated at the zip level with acs and zillow data (using acs and zillow data as base file)
acs_zillow_tt_agg_by_zip <- left_join(acs_zillow_data, tt_data_zip_agg, by="GEOID")
#flag any zip with at least one customer
acs_zillow_tt_agg_by_zip <- acs_zillow_tt_agg_by_zip %>%
mutate(customer_present=ifelse(customers_total>0, 1, 0))
#change NAs to 0
acs_zillow_tt_agg_by_zip$customer_present[is.na(acs_zillow_tt_agg_by_zip$customer_present)] <- 0
#change chars to numeric where needed
acs_zillow_tt_agg_by_zip$rental_costs_2018_dec <- as.numeric(as.character(acs_zillow_tt_agg_by_zip$rental_costs_2018_dec))
acs_zillow_tt_agg_by_zip$HVI_2018_12 <- as.numeric(as.character(acs_zillow_tt_agg_by_zip$HVI_2018_12))
#run quick numbers on zips
zip_stats <- acs_zillow_tt_agg_by_zip %>%
group_by(customer_present) %>%
mutate(record=1) %>%
summarise(age_mean=mean(median_age_all_2017, na.rm=TRUE),
income_mean=mean(median_income_2017, na.rm=TRUE),
college_enroll_total=mean(undergrad_enrollment_2017, na.rm=TRUE),
bach_perc_mean=mean(total_bach_perc, na.rm=TRUE),
college_enroll=mean(college_enrollment_perc_2017, na.rm=TRUE),
monthly_housing_costs_mean=mean(monthly_housing_costs_2017, na.rm=TRUE),
owner_occupied_perc_mean=mean(owner_perc, na.rm=TRUE),
renter_occupied_perc_mean=mean(renter_perc, na.rm=TRUE),
owner_occupied_total_mean=mean(owner_occupied, na.rm=TRUE),
renter_occupied_total_mean=mean(renter_occupied, na.rm=TRUE),
rental_costs_2018_mean=mean(rental_costs_2018_dec, na.rm=TRUE),
HVI_2018_mean=mean(HVI_2018_12, na.rm=TRUE),
records_n=sum(record))
zip_statsAnd the next table examines whether they’re a diference between zips with multiple TT customers, zips with just one TT customer, and zips with none.
zip_stats_mult_customers <- acs_zillow_tt_agg_by_zip %>%
mutate(multiple_customers=ifelse(customers_total>1, 1, 0)) %>%
group_by(multiple_customers) %>%
mutate(record=1) %>%
summarise(age_mean=mean(median_age_all_2017, na.rm=TRUE),
income_mean=mean(median_income_2017, na.rm=TRUE),
college_enroll_total=mean(undergrad_enrollment_2017, na.rm=TRUE),
bach_perc_mean=mean(total_bach_perc, na.rm=TRUE),
college_enroll=mean(college_enrollment_perc_2017, na.rm=TRUE),
monthly_housing_costs_mean=mean(monthly_housing_costs_2017, na.rm=TRUE),
owner_occupied_perc_mean=mean(owner_perc, na.rm=TRUE),
renter_occupied_perc_mean=mean(renter_perc, na.rm=TRUE),
owner_occupied_total_mean=mean(owner_occupied, na.rm=TRUE),
renter_occupied_total_mean=mean(renter_occupied, na.rm=TRUE),
rental_costs_2018_mean=mean(rental_costs_2018_dec, na.rm=TRUE),
HVI_2018_mean=mean(HVI_2018_12, na.rm=TRUE),
records_n=sum(record))
zip_stats_mult_customersNow start looking to form clusters. First examine each metric for outliers to see if they need to be mitigated or removed.
Definitely some skewed data on income and total population but that’s probably okay - it’s how zips occur naturally. also some issue here with scaling as some numbers are total counts and others are percentages. for the most part, let’s go with total counts since we’re just looking for absolutes. also suspect that while there may technically be outliers in this data (such as a manhattan zip code vs cincinnati), it’s not as if there’s only one zip code with incomes or housing costs as high as manhattan;in fact there are likely several, or more than enough for them to form their own cluster.
########################################################
###identify zip clusters - first start with just TT zips
#bring in acs and zillow data to tt zip data
tt_zip_agg_with_acs_zillow <- left_join(tt_data_zip_agg, acs_zillow_data, by="GEOID")
#select only acs numerical data that's not in percentages (dropping zillow as too many zips have missing data) and remove id column
tt_for_clusters <- tt_zip_agg_with_acs_zillow %>%
select(median_age_all_2017, median_income_2017, total_population_2017,
undergrad_enrollment_2017, monthly_housing_costs_2017, owner_occupied, renter_occupied) %>%
#drop NAs (just this one does it)
drop_na(median_income_2017)
#check for outliers
boxplot(tt_for_clusters)
Take the same data, scale it, then plot the elbow curve to identify how many clusters should be formed. Plot suggests either 5 or 6.
#scale the values to maintain uniformity
tt_for_clusters_scaled <- scale(tt_for_clusters[,1:7])
#calculate variance and store at the first index in new object called wss
wss <- (nrow(tt_for_clusters_scaled)-1)*sum(apply(tt_for_clusters_scaled, 2, var))
## iterate through wss array 15 times and sum up all the variance in every iteration and store it in wss array
for(i in 2:15)wss[i]<- sum(fit=kmeans(tt_for_clusters_scaled,centers=i,15)$withinss)
#plot each iteration to display the elbow graph
plot(1:15,wss,type="b",main="15 clusters",xlab="no. of cluster",ylab="with clsuter sum of squares")
Run the clusters and produce output to examine them.
#set the seed to run the clusters
set.seed(5000)
#create clusters - select only zips with no missing data
tt_clusters <- kmeans(na.omit(tt_for_clusters_scaled), 6)
#examine cluster centroids
tt_clusters_nums <- tt_clusters$centers
#check summary of kmeans objects
tt_clusters## K-means clustering with 6 clusters of sizes 1374, 471, 815, 1566, 1129, 1926
##
## Cluster means:
## median_age_all_2017 median_income_2017 total_population_2017
## 1 1.25327457 -0.1623728 -0.9607210
## 2 -1.15861243 -0.6126977 1.7161439
## 3 -0.07069054 0.5472371 1.3973302
## 4 -0.53959827 -0.5920365 -0.6717039
## 5 0.24306006 1.5578979 -0.2518889
## 6 -0.28457109 -0.3977440 0.3682106
## undergrad_enrollment_2017 monthly_housing_costs_2017 owner_occupied
## 1 -0.6621347 -0.4878192 -0.75533074
## 2 2.3402755 0.0429709 0.44366275
## 3 0.6243962 0.5318404 1.73873412
## 4 -0.4054391 -0.5552237 -0.75388807
## 5 -0.2557610 1.5241831 -0.06374507
## 6 0.1154165 -0.3295681 0.34493659
## renter_occupied
## 1 -0.8317963
## 2 2.2877774
## 3 0.4798990
## 4 -0.4092866
## 5 -0.3980597
## 6 0.3969779
##
## Clustering vector:
## [1] 6 3 2 4 6 1 1 1 6 1 4 3 4 5 4 6 4 4 6 1 1 1 1 1 1 6 1 4 5 6 1 4 1 1
## [35] 1 5 1 4 4 1 5 4 1 1 4 4 5 4 1 6 4 6 6 1 1 5 6 5 5 5 5 3 6 5 3 5 5 5
## [69] 6 4 4 6 4 3 5 4 6 6 1 5 4 2 5 5 1 3 1 1 1 1 1 3 3 1 5 5 5 5 5 1 5 5
## [103] 5 5 5 5 5 2 6 4 2 6 6 6 6 5 3 6 5 4 2 6 2 2 5 5 6 2 6 6 3 3 3 5 5 5
## [137] 5 5 1 5 2 2 1 1 5 5 5 3 6 5 5 5 5 5 5 5 5 5 1 5 1 1 1 1 1 1 3 6 6 4
## [171] 4 1 6 4 6 4 6 5 5 3 5 6 1 1 6 1 1 6 6 4 1 1 1 6 1 6 1 6 6 6 4 6 2 6
## [205] 4 4 4 1 6 5 1 6 1 5 5 5 1 6 5 4 6 6 6 6 5 1 1 1 1 4 1 1 1 6 1 1 6 1
## [239] 1 1 1 6 1 1 1 6 2 1 5 1 1 1 1 4 1 1 1 6 1 1 4 1 1 1 1 5 1 4 4 6 6 1
## [273] 4 1 1 1 6 1 1 6 4 1 1 1 1 1 1 1 1 1 1 6 1 1 1 1 4 5 1 4 5 1 1 1 1 1
## [307] 4 4 3 1 1 5 6 5 1 6 4 6 6 5 3 5 1 5 1 4 2 5 4 6 4 6 4 4 5 5 4 1 1 1
## [341] 1 1 1 6 6 1 6 1 1 1 4 1 1 4 5 5 1 5 6 6 2 3 5 1 1 5 1 3 3 3 2 6 6 6
## [375] 4 2 4 1 6 4 3 4 4 4 5 3 1 4 6 6 4 1 5 6 5 1 6 5 5 5 5 5 6 5 5 2 5 5
## [409] 2 3 6 5 5 5 6 6 5 5 3 6 4 3 4 6 6 5 5 5 2 3 5 2 6 4 4 6 5 1 4 5 3 5
## [443] 2 1 2 5 4 6 2 2 6 6 4 6 2 4 4 4 6 4 4 4 4 5 6 2 2 6 5 5 5 5 3 6 4 4
## [477] 5 5 4 4 6 5 5 5 5 6 5 5 4 5 4 5 5 5 6 1 5 3 1 4 1 6 5 5 5 3 5 5 5 6
## [511] 5 5 5 5 3 5 5 5 5 1 6 4 6 4 4 1 1 5 1 5 1 3 3 5 4 5 4 6 5 4 3 3 5 1
## [545] 1 1 5 4 3 1 4 4 4 4 4 6 1 5 1 4 3 6 1 4 1 6 6 5 1 6 6 1 1 5 1 5 3 1
## [579] 5 3 5 1 5 4 6 4 2 1 4 4 5 5 2 5 6 3 1 1 5 1 3 1 1 1 4 5 5 3 5 5 5 3
## [613] 5 4 5 5 4 1 5 5 2 5 6 4 3 5 1 4 1 2 3 2 5 5 5 5 2 3 5 2 2 2 6 2 2 2
## [647] 6 5 5 2 3 4 6 3 3 5 5 4 3 3 2 2 2 2 3 2 2 2 2 4 2 2 5 5 1 5 5 6 5 6
## [681] 5 5 2 4 6 5 5 5 5 5 5 1 3 6 1 5 1 4 5 5 5 6 6 2 3 2 2 2 2 2 2 2 2 2
## [715] 2 2 3 2 5 2 5 2 2 2 2 5 2 3 2 2 2 2 2 5 3 6 2 6 6 2 6 3 2 6 5 2 3 3
## [749] 5 6 6 5 6 5 2 2 5 5 3 5 5 3 5 5 5 5 5 5 5 3 5 2 4 4 5 3 5 5 5 5 5 5
## [783] 5 5 5 5 3 5 5 5 5 5 5 5 5 1 5 6 5 5 6 1 1 4 1 3 1 4 4 1 1 2 4 4 4 6
## [817] 4 4 6 4 4 1 4 6 1 1 1 4 1 1 1 3 6 5 3 1 4 1 1 3 1 1 1 6 1 6 1 4 4 1
## [851] 4 4 4 4 4 4 4 2 1 4 1 1 1 6 6 6 4 1 1 1 6 1 1 1 1 1 6 3 1 1 1 3 4 4
## [885] 4 4 4 4 4 4 6 6 4 4 3 4 6 3 6 6 6 4 4 1 1 1 1 1 1 1 3 4 6 1 4 6 4 6
## [919] 1 4 6 6 1 2 6 6 1 4 1 6 1 1 6 1 1 1 5 1 1 1 1 3 1 1 4 1 1 4 1 4 4 4
## [953] 4 6 4 1 6 4 6 2 6 6 4 6 5 4 4 6 1 4 4 4 1 6 3 1 1 3 4 1 1 5 6 1 1 3
## [987] 1 3 6 1 1 2 1 1 1 1 1 5 1 4 5 6 1 1 1 1 1 1 4 4 4 6 6 4 2 1 6 6 1 6
## [1021] 4 4 1 6 6 3 6 6 1 4 4 6 6 6 4 6 6 4 1 6 1 3 1 1 1 6 6 6 4 6 4 4 3 6
## [1055] 2 6 1 4 1 1 6 1 4 1 6 6 6 5 1 6 1 6 1 1 1 6 6 3 1 4 1 1 6 1 1 4 1 1
## [1089] 1 1 1 1 4 1 4 1 1 1 1 1 6 6 1 1 1 1 5 5 5 5 6 1 3 3 5 5 4 6 6 3 4 4
## [1123] 6 4 1 4 1 3 6 1 4 4 5 3 1 5 5 4 1 4 6 5 4 6 2 4 3 6 6 6 2 2 4 4 2 4
## [1157] 4 4 6 4 6 2 6 4 6 6 6 4 6 6 6 6 4 2 6 6 6 6 3 3 6 6 6 4 6 1 3 3 5 1
## [1191] 5 5 4 3 3 6 3 5 5 3 5 5 3 5 3 6 5 1 1 1 1 1 6 4 4 1 6 5 1 1 4 3 3 4
## [1225] 5 3 2 6 5 4 6 5 6 1 3 5 6 6 4 4 4 1 1 1 1 1 1 6 6 2 2 5 5 5 5 5 3 6
## [1259] 3 1 5 5 4 2 2 5 6 5 5 5 6 3 5 5 5 5 3 5 5 5 5 5 5 5 5 5 3 5 1 5 5 5
## [1293] 5 5 5 5 5 4 4 4 5 6 1 5 5 3 5 6 4 4 5 5 5 5 5 5 5 4 2 6 3 6 6 6 6 5
## [1327] 5 6 3 3 4 6 6 6 6 5 5 5 3 5 3 5 5 5 5 5 3 5 3 5 5 5 3 3 5 3 3 6 6 5
## [1361] 5 3 5 5 6 5 4 5 3 3 3 5 5 6 3 1 5 5 3 1 5 5 3 3 5 5 6 6 5 5 3 4 4 5
## [1395] 4 6 3 3 6 4 6 1 6 6 6 2 6 6 3 4 3 6 4 6 3 6 6 4 3 3 6 6 6 5 5 5 6 1
## [1429] 1 1 1 1 5 1 1 3 3 6 5 1 3 6 5 5 5 3 1 6 2 4 1 1 3 5 5 5 3 5 5 5 5 5
## [1463] 5 5 5 5 5 5 5 5 5 5 5 4 5 5 3 3 3 5 5 5 3 5 5 5 5 5 5 5 5 3 6 5 5 5
## [1497] 4 5 5 5 6 5 5 3 5 1 1 5 1 1 3 5 4 6 6 1 1 6 4 1 4 1 4 2 1 1 1 6 2 1
## [1531] 1 1 1 4 1 6 4 1 5 3 1 1 1 3 3 1 5 3 3 2 4 4 2 6 6 5 6 6 6 5 6 5 4 4
## [1565] 1 1 3 6 3 6 4 4 1 3 5 1 3 3 6 3 3 3 2 3 4 6 4 6 4 2 4 4 6 6 4 6 6 6
## [1599] 4 6 1 1 4 4 2 6 5 6 4 6 4 4 6 4 1 6 3 6 5 1 4 6 4 1 4 4 6 1 4 4 6 6
## [1633] 1 2 1 1 6 1 1 6 4 6 2 1 4 1 1 1 1 1 1 1 4 1 4 4 1 4 4 1 1 1 4 4 4 4
## [1667] 1 1 4 4 1 6 1 6 1 2 6 1 1 1 1 1 4 6 6 6 6 6 6 1 4 4 6 4 4 3 3 6 1 4
## [1701] 6 1 1 6 4 4 6 6 2 2 4 3 6 4 3 4 6 3 2 3 5 3 6 4 4 3 5 3 6 6 4 5 5 6
## [1735] 4 6 6 1 4 4 4 3 4 4 4 4 3 6 2 2 5 6 2 6 3 5 3 3 4 4 3 6 2 2 3 4 1 6
## [1769] 1 2 2 6 6 6 1 1 4 6 1 3 3 5 1 4 5 1 6 6 6 3 6 6 4 6 6 5 3 3 6 3 4 1
## [1803] 6 6 1 3 4 5 4 4 6 5 6 6 3 6 6 3 3 4 3 3 2 3 5 6 3 5 4 6 6 1 6 6 4 2
## [1837] 4 4 4 1 4 1 6 4 1 6 4 1 6 1 4 4 1 4 2 6 3 6 6 1 1 1 1 6 4 1 1 4 1 1
## [1871] 1 4 6 2 6 6 4 1 6 1 3 6 1 2 1 6 6 1 3 6 1 6 1 1 1 1 1 6 1 1 1 1 1 1
## [1905] 1 4 1 1 6 6 1 6 1 4 1 5 1 4 4 4 3 1 3 4 6 4 6 4 2 6 6 4 6 6 6 3 3 6
## [1939] 1 4 4 6 4 4 6 1 4 4 6 6 6 4 3 6 4 4 1 6 3 1 5 1 6 6 3 5 3 3 4 6 4 6
## [1973] 4 6 1 1 1 6 6 1 1 6 4 6 6 6 6 6 6 6 4 4 6 6 4 6 6 6 4 4 1 1 6 4 6 3
## [2007] 6 4 4 5 5 6 6 6 3 3 6 6 3 1 6 4 4 4 4 1 6 1 1 1 1 3 5 6 5 4 4 6 3 5
## [2041] 3 3 3 6 6 6 6 6 4 6 3 3 3 3 3 3 6 3 3 3 3 3 2 4 3 3 6 2 6 2 6 3 6 6
## [2075] 2 6 2 3 3 6 4 3 3 6 6 4 4 6 3 6 6 3 4 1 2 1 3 3 6 6 4 4 6 3 3 6 1 3
## [2109] 6 6 4 6 6 3 3 4 3 6 4 5 4 4 3 4 4 4 6 6 4 4 5 4 4 6 6 6 6 2 6 6 4 2
## [2143] 3 6 5 3 6 2 4 5 6 6 6 6 2 6 4 4 4 1 4 2 3 4 1 1 4 3 3 1 6 6 4 1 4 4
## [2177] 1 4 2 2 4 1 1 1 4 4 1 6 1 4 6 4 6 1 6 3 6 6 4 4 6 3 6 4 6 4 4 4 2 4
## [2211] 3 6 6 4 6 4 4 4 4 4 4 6 4 6 5 4 1 4 6 6 6 4 5 4 2 4 4 4 1 6 4 4 6 6
## [2245] 4 1 4 6 4 4 4 5 4 4 6 2 6 5 4 1 1 4 4 1 6 3 6 1 5 5 6 1 5 1 4 4 6 1
## [2279] 6 1 1 1 3 3 3 1 3 1 4 6 6 6 6 3 6 6 4 3 6 1 3 3 6 3 3 6 4 2 6 6 3 4
## [2313] 6 2 2 4 6 6 4 4 5 6 1 4 6 6 4 4 1 4 1 4 1 1 4 6 6 6 6 2 6 1 1 4 6 5
## [2347] 6 4 1 5 6 3 4 6 6 6 1 4 6 6 2 2 4 4 1 1 1 6 6 6 3 3 1 6 6 6 3 4 1 6
## [2381] 3 1 6 1 4 2 5 3 6 1 1 5 6 6 2 4 4 1 4 6 6 2 6 6 2 6 6 2 6 3 2 5 3 4
## [2415] 5 6 5 3 2 6 1 6 6 6 1 4 1 1 1 6 1 3 1 3 1 1 1 1 1 4 6 2 6 6 2 6 3 6
## [2449] 3 3 3 2 3 5 6 6 2 1 6 1 1 1 1 6 6 6 1 3 3 3 1 5 6 3 5 2 2 6 5 5 6 6
## [2483] 6 4 6 6 6 2 6 6 6 4 5 3 3 3 2 6 3 4 6 6 4 6 3 3 3 6 5 4 3 4 3 3 4 1
## [2517] 1 6 2 3 2 6 1 3 3 3 5 5 5 5 5 6 6 6 4 6 4 6 6 1 6 3 3 3 6 6 6 3 5 1
## [2551] 3 6 3 6 6 4 6 1 1 3 6 6 3 3 1 5 5 1 1 1 5 5 6 2 4 4 4 1 1 5 5 5 1 4
## [2585] 6 4 5 1 3 5 6 6 5 5 4 6 4 6 6 4 6 6 6 6 6 4 2 6 6 6 5 5 4 4 4 3 1 6
## [2619] 1 1 6 1 1 1 1 6 4 6 1 4 6 1 4 1 1 1 6 1 1 1 1 1 1 6 1 1 6 6 6 3 4 1
## [2653] 3 4 6 6 4 1 6 1 1 6 6 4 4 1 1 6 4 1 6 1 6 1 1 1 1 1 6 6 4 4 4 4 1 1
## [2687] 6 1 4 1 1 1 6 1 5 5 1 3 4 5 5 6 6 6 6 1 5 5 6 1 1 1 1 6 1 1 4 1 1 1
## [2721] 1 1 4 1 1 1 1 1 1 1 1 1 4 6 6 4 4 1 1 1 1 1 1 6 6 5 6 1 6 1 3 1 6 1
## [2755] 6 1 1 1 1 6 3 1 1 1 6 6 6 4 1 4 6 6 6 4 1 6 1 5 3 1 1 4 1 6 3 1 4 1
## [2789] 6 5 1 3 4 1 6 4 4 5 1 4 4 4 4 6 1 6 6 4 4 4 4 6 1 6 1 6 6 4 3 4 4 3
## [2823] 4 6 2 4 4 6 6 1 6 1 5 1 4 3 4 6 1 4 6 6 6 4 4 1 4 5 6 4 1 4 6 4 4 6
## [2857] 3 6 4 6 4 1 1 6 6 1 1 1 1 4 4 6 6 4 4 4 3 4 2 4 4 4 2 4 1 3 1 2 2 3
## [2891] 1 6 4 3 3 5 6 3 6 6 1 4 6 3 3 3 2 5 6 4 4 6 4 3 6 6 5 4 4 5 6 6 4 6
## [2925] 4 2 6 6 5 4 6 4 3 6 1 6 6 6 6 4 4 4 4 4 4 6 4 3 6 6 4 1 6 1 6 1 1 1
## [2959] 1 1 1 6 6 1 6 1 6 6 1 4 1 6 4 4 4 4 6 6 6 6 5 6 4 6 4 5 4 6 3 6 4 6
## [2993] 1 4 6 4 4 4 6 2 4 4 6 6 6 4 6 4 6 6 4 6 5 4 4 3 1 1 4 3 1 1 1 6 6 1
## [3027] 1 6 3 2 6 4 4 4 6 6 3 6 6 1 4 4 6 4 6 6 4 4 2 6 1 4 6 4 3 4 4 4 4 6
## [3061] 4 1 4 4 4 4 4 6 5 6 4 6 4 4 6 4 4 4 4 4 6 4 6 4 6 6 6 6 6 6 3 3 4 4
## [3095] 6 1 1 6 6 6 6 2 6 6 5 6 6 4 4 6 4 6 6 1 4 4 4 1 1 6 6 1 1 6 6 1 6 4
## [3129] 1 3 6 6 3 6 3 5 3 1 5 6 6 5 3 6 3 4 3 6 6 3 3 1 3 2 6 4 6 4 4 6 6 4
## [3163] 4 6 6 4 6 6 4 6 4 6 2 3 4 6 6 4 6 1 4 1 1 1 6 4 4 4 4 6 6 6 6 1 1 4
## [3197] 4 4 1 1 1 4 5 1 3 6 6 4 4 4 3 1 6 6 4 4 6 6 2 6 4 6 4 1 6 4 6 6 6 4
## [3231] 6 6 6 3 6 6 4 1 1 4 6 6 1 1 6 3 6 6 1 5 2 1 6 1 6 4 4 4 4 4 6 6 4 1
## [3265] 1 1 1 4 1 4 4 1 1 6 4 1 1 6 4 6 4 6 1 1 1 1 4 6 6 3 3 6 4 6 5 3 6 1
## [3299] 5 3 6 4 6 4 4 4 4 4 4 4 4 6 4 4 6 4 2 4 4 1 4 4 6 6 6 4 6 6 6 1 5 6
## [3333] 4 1 1 2 6 1 6 6 6 4 4 4 4 4 6 1 6 3 4 6 1 4 6 4 4 4 1 4 2 6 1 4 6 4
## [3367] 3 1 1 4 3 5 3 3 4 1 1 6 4 5 4 5 1 4 6 6 6 4 6 6 6 1 6 1 6 6 6 4 4 6
## [3401] 6 6 4 6 6 2 6 6 5 6 4 6 6 6 4 4 6 3 4 1 4 4 1 4 4 4 6 4 6 6 6 3 1 4
## [3435] 4 4 6 6 6 6 1 6 1 1 1 4 4 6 4 4 4 4 1 4 1 6 4 4 4 6 5 1 1 1 1 1 1 1
## [3469] 6 6 4 6 6 4 6 6 6 1 6 2 6 2 1 1 4 1 1 6 1 4 1 4 4 4 6 2 6 1 5 4 4 6
## [3503] 1 4 4 4 6 1 4 3 6 3 1 6 6 6 4 6 6 1 6 4 5 6 6 6 1 5 1 3 2 6 6 1 4 6
## [3537] 4 2 5 6 4 6 6 3 6 4 5 1 6 3 6 4 6 6 3 1 6 6 2 6 4 4 4 6 4 6 4 4 6 6
## [3571] 6 4 6 4 6 6 4 1 6 6 5 6 6 4 3 5 6 6 1 5 4 6 1 5 1 6 6 4 4 1 1 1 4 1
## [3605] 5 6 1 6 1 3 6 1 6 6 6 1 1 4 1 6 6 1 6 1 1 4 2 1 4 4 4 2 6 6 6 4 4 2
## [3639] 4 6 6 1 1 1 4 1 6 1 1 4 4 4 1 5 1 4 4 4 1 6 1 4 1 6 6 6 4 6 1 1 6 1
## [3673] 1 6 6 6 6 6 6 6 6 1 6 6 1 1 1 1 1 1 1 6 1 1 4 2 6 4 4 4 5 1 4 4 6 6
## [3707] 4 6 4 4 4 6 6 6 1 1 6 1 1 1 4 4 4 6 4 1 6 6 1 1 6 4 1 1 4 4 6 6 6 4
## [3741] 1 4 6 1 6 6 1 4 4 6 6 5 1 1 1 1 1 6 1 6 4 1 4 4 6 1 4 1 6 1 1 6 1 4
## [3775] 1 1 1 6 6 6 6 6 4 6 6 4 2 6 6 6 2 6 5 6 6 6 6 6 4 4 1 6 4 1 4 1 4 1
## [3809] 1 6 1 1 1 1 2 6 4 4 4 6 1 1 4 4 4 4 4 1 6 6 4 1 1 6 6 6 6 1 6 1 4 1
## [3843] 1 1 2 6 4 4 1 6 2 4 1 6 6 1 5 1 6 3 6 5 1 3 4 6 4 1 3 1 4 4 2 6 2 4
## [3877] 4 6 3 3 3 6 6 6 4 6 5 3 6 4 4 3 3 1 4 4 5 4 5 6 4 1 3 5 3 1 6 5 5 5
## [3911] 4 4 1 4 3 5 4 5 3 5 4 6 4 6 6 6 4 5 4 4 2 6 6 6 4 6 6 6 5 6 6 6 6 1
## [3945] 6 6 6 1 5 1 4 6 5 6 5 1 4 1 1 1 4 1 1 4 4 6 4 3 6 6 6 2 1 1 1 1 4 1
## [3979] 4 6 6 1 4 1 4 1 1 1 1 4 4 4 6 4 1 4 6 4 6 6 2 6 4 1 4 1 1 4 1 4 4 1
## [4013] 1 1 4 1 1 1 4 1 1 1 1 6 3 6 1 1 4 4 6 6 1 1 4 1 1 4 1 6 6 1 4 1 6 4
## [4047] 2 4 6 1 4 1 1 1 4 1 1 2 4 4 1 4 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3 6
## [4081] 6 4 3 3 5 3 1 4 3 3 3 1 1 5 3 5 5 6 5 5 3 3 4 3 3 4 3 6 6 6 4 2 3 6
## [4115] 5 6 6 6 5 3 4 3 6 2 1 6 6 5 3 4 6 5 1 5 3 6 5 1 3 4 1 4 4 4 4 6 4 5
## [4149] 4 6 5 4 5 4 6 5 3 5 4 3 5 4 2 6 6 5 3 4 6 5 3 4 1 4 5 5 6 4 1 4 6 4
## [4183] 6 3 6 5 3 5 1 3 4 3 5 1 4 5 4 5 4 1 3 4 1 4 5 5 6 2 3 5 4 6 5 6 1 6
## [4217] 5 6 4 6 3 3 1 5 5 3 5 5 3 5 5 5 5 2 2 2 5 6 2 2 2 2 2 2 2 2 6 2 2 6
## [4251] 2 2 3 2 3 6 2 3 6 2 3 2 2 2 5 3 6 6 1 2 2 2 6 5 5 6 2 6 2 5 1 6 1 4
## [4285] 2 4 6 6 1 4 1 1 1 1 1 6 4 1 4 4 6 6 6 4 6 1 4 4 4 1 6 1 1 4 6 4 6 6
## [4319] 6 6 1 2 2 6 1 4 1 1 4 6 1 6 1 4 4 4 6 6 4 4 4 1 4 1 4 6 1 6 1 1 1 6
## [4353] 6 6 1 4 1 4 6 1 6 3 4 3 3 6 5 4 4 1 4 1 4 1 1 4 4 4 5 4 6 6 4 6 4 6
## [4387] 4 6 6 4 6 3 3 5 1 3 6 4 6 4 6 4 6 4 3 3 1 1 3 3 3 4 4 3 1 4 1 1 4 1
## [4421] 1 4 6 4 4 4 6 1 1 4 6 4 1 4 6 4 4 4 4 4 6 4 4 6 6 4 4 4 4 4 4 6 6 6
## [4455] 6 5 1 4 1 6 4 4 1 1 1 1 6 6 2 6 3 4 1 6 4 1 6 1 1 4 6 1 4 1 1 6 2 6
## [4489] 4 2 4 1 4 4 2 4 6 3 3 1 4 4 4 4 4 4 4 4 4 4 4 5 5 4 1 6 5 4 6 5 4 5
## [4523] 4 4 4 1 4 4 6 6 4 4 1 4 6 4 5 6 4 4 6 4 4 4 4 6 4 4 5 4 1 6 4 4 1 6
## [4557] 4 4 4 4 6 6 4 5 4 4 5 6 5 5 6 4 6 6 4 4 6 4 6 4 1 1 4 6 4 6 6 4 6 6
## [4591] 4 3 3 1 4 6 1 6 2 6 1 6 6 5 4 4 4 4 6 6 1 6 4 4 6 4 1 1 5 5 6 6 4 6
## [4625] 1 6 2 6 4 4 4 6 6 4 4 6 6 6 4 4 4 6 1 3 3 1 4 4 1 6 6 4 6 6 6 3 6 6
## [4659] 3 4 2 4 4 4 6 6 4 4 4 4 4 4 1 6 1 6 4 1 4 4 6 6 2 4 6 4 1 6 1 6 4 4
## [4693] 4 2 6 6 1 1 4 1 6 6 3 1 4 6 6 6 4 4 1 4 4 5 3 5 3 4 6 2 2 4 1 3 6 6
## [4727] 4 6 4 1 4 6 4 4 6 4 4 6 3 6 3 5 4 4 6 4 6 1 4 6 6 6 4 6 3 3 1 4 4 1
## [4761] 4 4 4 1 3 6 6 4 4 6 4 4 4 4 1 4 4 4 6 4 6 6 4 1 4 6 1 1 4 1 1 1 4 4
## [4795] 1 1 1 4 4 3 6 3 5 6 5 3 1 1 5 3 3 3 3 5 3 3 5 3 6 6 3 3 3 3 4 6 6 2
## [4829] 6 1 2 3 3 3 3 6 1 3 5 5 5 6 3 3 3 4 1 4 3 4 4 6 2 6 1 4 5 4 2 4 6 6
## [4863] 2 6 6 6 6 5 6 2 6 6 6 4 4 6 4 2 5 4 6 4 6 4 4 5 1 4 4 4 4 1 6 6 4 4
## [4897] 4 4 4 1 6 6 4 4 4 4 1 1 4 4 4 1 6 1 1 4 5 5 4 4 2 4 6 6 5 3 6 3 4 4
## [4931] 6 6 1 1 3 5 6 1 3 6 4 1 4 5 4 4 6 6 6 6 6 4 6 4 6 4 4 5 1 6 6 3 4 4
## [4965] 3 6 4 3 6 4 4 4 3 5 5 4 3 5 5 1 5 4 4 4 4 4 6 4 6 6 1 4 2 6 6 2 4 4
## [4999] 4 4 1 4 6 2 4 4 6 4 6 6 4 4 2 6 5 3 6 4 6 6 6 5 4 6 4 4 4 6 2 4 6 2
## [5033] 6 6 6 6 4 6 6 6 5 6 4 5 3 1 6 2 6 6 2 4 5 2 2 2 6 6 3 2 6 3 5 2 6 4
## [5067] 4 6 1 6 4 6 3 2 5 3 6 6 3 3 5 3 5 5 3 5 3 3 3 4 3 3 4 3 3 3 1 3 4 6
## [5101] 6 3 6 6 6 6 3 5 6 6 4 3 4 4 4 6 4 6 3 4 4 3 6 3 5 4 6 4 4 6 4 4 1 4
## [5135] 4 6 6 4 4 6 2 2 6 6 1 6 5 6 3 4 1 5 6 3 1 6 6 6 4 3 6 4 6 6 6 6 4 4
## [5169] 6 4 6 4 2 6 6 6 6 2 4 6 3 3 3 3 3 3 3 5 4 4 6 6 2 6 6 2 4 3 6 2 6 6
## [5203] 6 3 6 2 6 1 6 4 3 4 1 6 6 1 6 3 3 4 1 1 4 3 3 3 2 1 3 5 4 2 2 4 4 6
## [5237] 4 6 6 5 5 5 5 5 5 2 6 2 5 5 3 3 4 4 2 4 4 6 2 6 1 4 4 4 6 6 4 4 1 4
## [5271] 4 4 1 4 4 6 6 6 4 4 6 6 3 4 4 6 6 6 5 4 4 6 6 2 2 3 6 4 2 3 4 6 3 5
## [5305] 5 6 6 6 3 6 3 3 6 5 3 6 6 6 5 4 6 6 1 5 1 5 5 4 5 5 6 6 5 5 3 5 3 3
## [5339] 3 5 5 5 4 3 5 5 6 6 6 6 6 5 3 6 4 6 4 4 4 3 6 6 6 4 4 6 6 6 3 6 6 3
## [5373] 6 4 4 6 5 6 5 4 6 5 6 5 2 6 5 5 3 4 1 5 4 1 5 1 1 1 1 1 4 4 5 1 1 4
## [5407] 1 6 5 3 1 1 4 5 4 2 6 3 2 5 5 1 1 6 3 1 5 4 5 6 5 4 4 4 2 3 4 1 4 4
## [5441] 6 1 1 5 1 4 4 1 4 6 6 5 6 6 6 4 6 6 3 5 3 5 5 5 5 5 5 6 4 6 6 6 4 4
## [5475] 1 6 1 4 1 4 6 1 1 1 6 6 1 1 4 4 1 1 4 5 5 5 5 5 1 5 4 4 4 4 4 4 4 4
## [5509] 1 1 6 4 4 5 4 3 4 1 6 4 4 1 2 4 6 6 4 1 1 4 4 6 3 4 6 4 6 6 6 4 6 6
## [5543] 2 3 6 1 1 6 6 1 1 6 1 1 3 4 3 3 4 3 4 4 4 5 6 3 4 4 6 5 4 6 2 5 6 3
## [5577] 4 3 4 3 5 6 5 5 5 3 3 4 5 4 4 6 4 6 6 6 5 6 4 6 6 6 6 6 3 6 4 4 4 4
## [5611] 6 6 3 6 6 4 4 6 2 2 4 6 6 4 4 4 4 5 1 6 4 6 4 4 4 2 6 1 4 6 6 6 6 6
## [5645] 6 3 6 6 6 5 6 4 3 2 4 2 6 4 3 6 6 3 5 5 6 5 5 5 3 1 6 4 6 6 4 6 3 6
## [5679] 4 1 2 6 6 2 6 6 3 3 6 5 6 6 2 6 6 3 1 5 1 6 3 5 6 1 5 3 1 2 2 2 3 3
## [5713] 3 5 5 2 6 4 3 6 3 5 3 6 6 4 4 2 3 1 3 3 5 3 3 1 5 1 6 1 4 1 1 1 1 6
## [5747] 1 5 4 6 2 6 3 6 6 6 4 1 6 1 2 6 1 6 6 6 5 1 1 1 6 4 1 2 6 4 1 1 1 6
## [5781] 1 1 1 1 6 4 4 6 1 4 4 3 6 6 6 6 6 3 6 4 3 3 3 5 3 3 4 4 1 6 1 4 2 6
## [5815] 6 1 4 4 6 6 4 6 6 4 6 6 6 6 1 6 3 6 5 3 6 6 6 6 2 6 4 6 2 1 2 6 2 3
## [5849] 4 2 6 2 6 3 6 3 6 3 1 5 6 5 6 5 6 3 3 6 6 4 4 6 6 1 4 1 1 1 6 6 3 1
## [5883] 1 1 1 6 6 6 6 1 4 5 6 4 5 2 2 2 2 2 2 2 6 2 6 2 2 2 2 2 6 2 2 2 2 2
## [5917] 6 6 2 2 5 6 5 4 6 2 6 2 3 2 6 5 5 2 6 4 6 2 5 6 2 5 5 2 5 5 6 6 4 5
## [5951] 5 5 6 6 5 6 6 2 5 2 6 2 5 5 4 5 5 5 2 5 5 5 5 6 6 4 4 1 5 5 5 5 6 1
## [5985] 3 5 5 6 4 5 6 6 3 6 5 3 3 3 2 2 3 6 3 2 6 5 5 5 4 2 2 5 5 5 5 2 3 5
## [6019] 2 5 2 2 6 6 5 2 4 3 5 5 5 6 5 1 6 6 5 5 5 5 6 5 4 4 6 6 5 5 5 5 6 3
## [6053] 3 5 3 5 5 6 6 6 5 2 2 6 3 2 3 5 5 5 6 5 5 5 3 5 5 3 5 5 5 5 5 6 2 5
## [6087] 2 2 6 5 5 5 4 5 5 5 2 5 5 2 6 6 3 2 2 3 3 3 4 5 2 4 2 5 5 5 5 2 3 3
## [6121] 5 6 6 6 2 6 2 3 2 6 6 3 5 6 6 5 2 5 3 5 5 2 6 5 5 2 2 3 5 4 5 5 6 6
## [6155] 1 3 5 1 5 5 5 5 5 3 2 2 3 2 3 3 3 5 5 3 6 3 3 2 3 3 5 3 3 5 3 5 1 6
## [6189] 3 5 2 2 6 2 2 6 5 2 6 2 2 3 2 6 3 5 5 5 2 5 5 2 5 3 3 5 5 6 2 3 6 1
## [6223] 6 3 4 3 6 6 6 4 4 1 3 6 1 1 1 4 4 4 6 6 6 1 1 4 2 1 2 3 6 1 5 3 3 1
## [6257] 4 1 1 4 4 4 6 2 4 3 6 6 4 3 2 4 2 6 4 2 2 6 3 2 3 6 5 1 6 6 6 1 6 2
## [6291] 3 3 1 3 3 6 3 4 3 4 1 5 1 3 3 5 5 5 5 5 5 5 2 5 5 3 5 5 3 2 5 3 1 3
## [6325] 2 3 5 5 4 3 5 5 5 5 5 3 5 2 3 3 3 5 2 2 2 3 6 2 3 5 2 6 2 2 5 5 5 2
## [6359] 6 3 5 3 6 6 4 5 5 5 5 3 5 5 3 3 3 5 3 6 3 5 3 5 5 1 5 2 5 6 4 6 3 3
## [6393] 6 5 5 5 5 5 2 4 6 1 2 6 2 4 4 2 6 4 6 6 4 6 6 3 2 2 2 3 3 3 5 6 1 2
## [6427] 5 6 1 4 3 1 5 4 3 6 3 6 1 1 5 4 4 1 1 6 2 3 4 4 2 3 6 1 6 4 6 1 4 3
## [6461] 6 5 4 4 4 6 6 6 1 6 6 2 6 3 2 4 2 2 4 5 5 5 5 6 5 6 5 5 3 3 5 5 5 5
## [6495] 5 5 5 5 5 5 5 5 5 5 5 5 5 3 5 5 3 6 6 5 5 4 2 2 3 5 5 3 5 5 3 3 5 6
## [6529] 5 5 2 6 3 5 5 5 5 5 5 5 5 3 5 5 5 5 3 3 5 5 6 3 5 1 5 5 5 2 5 3 3 5
## [6563] 2 5 2 5 3 5 5 3 5 5 3 5 5 3 6 5 3 2 5 5 4 3 6 5 5 5 5 5 3 5 6 6 3 5
## [6597] 5 5 2 6 6 3 6 6 6 6 5 5 4 5 5 6 5 5 2 5 5 5 5 4 4 6 5 6 2 3 5 5 2 5
## [6631] 4 5 5 5 5 5 5 5 5 5 3 5 5 5 3 3 5 5 3 3 5 5 3 5 2 3 5 5 5 2 5 3 2 5
## [6665] 2 5 5 5 5 3 3 5 3 5 3 5 5 5 5 5 5 5 5 5 5 4 4 6 6 2 2 3 6 5 6 1 5 4
## [6699] 6 1 1 6 5 4 4 1 5 6 6 6 4 6 6 6 4 3 6 4 4 6 4 5 4 4 1 3 5 6 6 4 4 5
## [6733] 6 3 3 5 6 5 1 1 4 1 1 1 1 5 1 1 1 1 1 5 3 1 5 4 1 6 3 6 2 5 4 6 3 1
## [6767] 3 3 1 1 3 1 6 5 6 1 6 3 5 5 6 6 1 3 3 4 6 6 1 5 3 3 3 5 5 4 4 4 4 6
## [6801] 5 6 6 6 2 4 2 6 3 5 1 3 4 6 6 5 6 4 6 3 5 4 2 2 1 1 1 1 1 4 4 6 1 1
## [6835] 6 4 6 6 6 6 6 4 4 1 1 1 6 1 1 4 1 4 6 5 5 3 5 1 5 3 5 1 6 5 1 6 3 5
## [6869] 1 5 1 5 4 1 4 1 1 5 3 1 5 6 3 6 1 6 3 2 2 5 3 5 6 6 2 3 6 1 4 4 4 6
## [6903] 4 5 5 3 4 4 4 4 6 1 6 4 3 6 1 1 4 6 1 3 3 4 6 1 6 1 5 4 4 1 6 6 3 4
## [6937] 4 6 5 6 6 1 4 6 4 3 6 1 6 3 6 4 3 6 4 6 6 5 6 6 2 6 6 6 6 6 4 6 6 2
## [6971] 6 1 4 6 1 1 1 4 1 2 2 6 3 1 1 6 1 1 6 6 1 6 6 6 6 1 6 6 1 1 1 1 4 6
## [7005] 1 3 3 1 1 1 1 6 1 1 4 1 4 4 5 6 6 5 5 5 5 5 1 5 3 5 5 5 1 3 3 5 5 5
## [7039] 6 6 6 5 3 6 6 5 5 3 4 5 3 5 5 6 4 3 5 5 5 5 5 6 3 4 6 3 2 6 5 4 5 5
## [7073] 5 3 5 5 6 5 5 2 6 6 3 5 6 6 4 3 1 6 5 6 6 6 5 6 6 6 5 3 1 3 2 6 6 1
## [7107] 1 1 4 6 1 1 1 1 5 4 3 6 6 6 5 6 1 6 6 1 5 4 6 6 1 5 1 1 5 5 4 5 1 1
## [7141] 5 1 1 1 6 5 1 1 6 4 3 5 1 1 1 3 1 4 3 1 4 4 6 4 6 1 4 4 4 5 6 6 4 6
## [7175] 6 6 6 6 6 1 6 6 5 4 4 4 4 1 1 1 1 1 6 1 4 6 5 1 4 1 1 5 4 6 6 4 4 6
## [7209] 1 1 3 6 6 5 5 6 6 1 4 1 6 4 4 4 1 1 6 1 2 4 4 4 4 1 4 1 1 1 1 1 2 4
## [7243] 4 1 4 6 6 6 3 4 6 4 6 3 1 4 6 4 6 4 5 4 3 3 6 5 5 4 5 5 5 5 4 6 3 1
## [7277] 4 5 4 5 4
##
## Within cluster sum of squares by cluster:
## [1] 3126.198 4804.953 2803.426 2647.803 4317.247 3908.090
## (between_SS / total_SS = 57.6 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault" #get size of clusters
tt_clusters$size## [1] 1374 471 815 1566 1129 1926 ## checking withinss i.e. the intra cluster bond strength factor for each cluster
tt_clusters$withinss## [1] 3126.198 4804.953 2803.426 2647.803 4317.247 3908.090 ##run a cluster plot
clusplot(tt_for_clusters_scaled, tt_clusters$cluster, color=TRUE, shade=TRUE, labels=2, lines=0 )