Ego Network Analyis of Laser Institute

1 PURPOSE

1a. Motivation and Focus

Ego networks are valuable to understand the relationships that individuals create with their peers. Social networks, like Twitter, are very interesting to see who each individual are interacting with and building onto their communities. Moreover, online relationships can be described with an ego network to understand resource sharing, collaboration,and diffusion of information.

Companies may be particularly interested in how information is being shared from the “friends” on their site. In this case study we will investigate:

1. What can an ego network tell us about followers of the Laser Institute?

1b. Load Libraries

Let’s first load our libraries to read in packages that we will use to answer our questions. Additionally, let’s set colors to use throughout and write a function to save in our Global Environment to use later with ggplot in the MODEL Section.

library(lubridate)
library(readr)
library(readxl)
library(writexl)
library(tidyr)
library(rtweet)
library(tidytext)
library(textdata)
library(ggplot2)
library(tidyverse)
library(tidygraph)

#for visualizations
library(ggplot2)
library(scales)
library(wordcloud2)
library(gridExtra) 
library(knitr) 
library(kableExtra) 
library(formattable) 
library(yarrr)  
library(radarchart) 
library(igraph) 
library(ggraph) 
library(graphlayouts)

2 Wrangle

2a. Connecting to API and pulling initial data

After loading the libraries, we connect to the Twitter Resting API using a previously saved function named get_token(). The codes are not viewable but used to connect directly to Twitter’s Resting API.

We have several steps to gather to create a data set for the **Ego-Network.*

STEP 1

1a. Look up Laser Institute users 1b. Pull Laser followers and retry on rate limit. 1c. Combine the data into a detail_folower data set

Since Twitter changes and restrictions on the dates and amount of tweet followers you can pull, we will write the data files throughout the case to save and read in a later code chunk.

#connect to Twitter API
get_token()
# gather Laser Instutite data
laser_user <- lookup_users("LASER_Institute")

# get Laser Institute followers and its account details
laser_folower <- get_followers("LASER_Institute",
                               n= laser_user$followers_count,
                               retryonratelimit = T)
detail_folower <- lookup_users(laser_folower$user_id)

detail_folower <- data.frame(lapply(detail_folower,as.character),
                             stringsAsFactors = F)

write_xlsx(laser_folower, "data/laser_folower.xlsx")
write_xlsx(detail_folower, "data/detail.folower.xlsx")

WOW! A wooping 75000 followers!

We need to read in the file detail.folower.xlsx and then inspect it. We can see that

# read in previously saved detail_folower data frame
detail_folower <- read_excel("data/detail.folower.xlsx")

#inspect data
detail_folower %>%
  head()%>%
  kbl(caption = "RLaser Institute ") %>%
  kable_styling(bootstrap_options = c("striped", "hover"))

RLaser Institute

user_id	status_id	created_at	screen_name	text	source	display_text_width	reply_to_status_id	reply_to_user_id	reply_to_screen_name	is_quote	is_retweet	favorite_count	retweet_count	quote_count	reply_count	hashtags	symbols	urls_url	urls_t.co	urls_expanded_url	media_url	media_t.co	media_expanded_url	media_type	ext_media_url	ext_media_t.co	ext_media_expanded_url	ext_media_type	mentions_user_id	mentions_screen_name	lang	quoted_status_id	quoted_text	quoted_created_at	quoted_source	quoted_favorite_count	quoted_retweet_count	quoted_user_id	quoted_screen_name	quoted_name	quoted_followers_count	quoted_friends_count	quoted_statuses_count	quoted_location	quoted_description	quoted_verified	retweet_status_id	retweet_text	retweet_created_at	retweet_source	retweet_favorite_count	retweet_retweet_count	retweet_user_id	retweet_screen_name	retweet_name	retweet_followers_count	retweet_friends_count	retweet_statuses_count	retweet_location	retweet_description	retweet_verified	place_url	place_name	place_full_name	place_type	country	country_code	geo_coords	coords_coords	bbox_coords	status_url	name	location	description	url	protected	followers_count	friends_count	listed_count	statuses_count	favourites_count	account_created_at	verified	profile_url	profile_expanded_url	account_lang	profile_banner_url	profile_background_url	profile_image_url
933175355128668161	1521252017485848576	2022-05-02 22:15:19	KuhlmannShelbi	@rebekah_freed https://t.co/q4dsaKwirm	Twitter for iPhone	NA	1521220433902718981	3436476670	rebekah_freed	FALSE	FALSE	2	0	NA	NA	NA	NA	NA	NA	NA	http://pbs.twimg.com/tweet_video_thumb/FRySpPhWQAIw85M.jpg	https://t.co/q4dsaKwirm	https://twitter.com/KuhlmannShelbi/status/1521252017485848576/photo/1	photo	http://pbs.twimg.com/tweet_video_thumb/FRySpPhWQAIw85M.jpg	https://t.co/q4dsaKwirm	https://twitter.com/KuhlmannShelbi/status/1521252017485848576/photo/1	NA	3436476670	rebekah_freed	und	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(NA, NA)	c(NA, NA)	c(NA, NA, NA, NA, NA, NA, NA, NA)	https://twitter.com/NA/status/1521252017485848576	Shelbi Kuhlmann	Raleigh, NC	Postdoctoral Researcher in Learning Sciences at UNC Chapel Hill. Researching how to help students learn meaningfully and persist in STEM. She/Her	NA	FALSE	429	578	2	469	7128	2017-11-22 03:28:36	FALSE	NA	NA	NA	https://pbs.twimg.com/profile_banners/933175355128668161/1511322245	NA	http://pbs.twimg.com/profile_images/1300544955811794944/WzFF0hzy_normal.jpg
1027337792257503233	1519304992854667264	2022-04-27 13:18:32	STEAM__ON	So excited for this “Novice to RMarkdown” series with @RLadiesRTP. Come join us, https://t.co/YqJG3x5avL… https://t.co/JXc0V9ENgE	Twitter Web App	NA	NA	NA	NA	FALSE	FALSE	6	4	NA	NA	NA	NA	c(“meetup.com/rladies-rtp/ev…”, “twitter.com/i/web/status/1…”)	c(“https://t.co/YqJG3x5avL”, “https://t.co/JXc0V9ENgE”)	c(“https://www.meetup.com/rladies-rtp/events/285489059/”, “https://twitter.com/i/web/status/1519304992854667264”)	NA	NA	NA	NA	NA	NA	NA	NA	747584164245864448	RLadiesRTP	en	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(NA, NA)	c(NA, NA)	c(NA, NA, NA, NA, NA, NA, NA, NA)	https://twitter.com/NA/status/1519304992854667264	★·.·´¯·.·★🅹🅴🅰🅽🅽🅴 🅼🅲🅲🅻🆄🆁🅴★·.·¯´·.·★	Garner, NC	Doctoral Student TELS👩‍🔬 Learning Analytics🔬LifeLongLearner 🕵️Designer 🎨 Maker 🛠️ Tech-i 🌺Horticulturist 📲 Design Thinker💡STEAM 🐺Wolfpack	NA	FALSE	218	402	3	445	1806	2018-08-08 23:36:31	FALSE	NA	NA	NA	https://pbs.twimg.com/profile_banners/1027337792257503233/1572787953	NA	http://pbs.twimg.com/profile_images/1409991470837374977/FUcoAEfs_normal.jpg
1431308746366455809	1503626581264138242	2022-03-15 06:58:07	thuynguyen_ed	@BichTNTran @DartmouthInst @JonathanLWai @ua_edreform @uacoehp Congratulations!	Twitter for iPhone	NA	1500866045157982213	754675597	bichtntran	FALSE	FALSE	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(“754675597”, “2243909509”, “260462570”, “3248083454”, “2361771324”)	c(“bichtntran”, “DartmouthInst”, “JonathanLWai”, “ua_edreform”, “uacoehp”)	en	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(NA, NA)	c(NA, NA)	c(NA, NA, NA, NA, NA, NA, NA, NA)	https://twitter.com/NA/status/1503626581264138242	thuy nguyen (rachel)	San Francisco Bay Area	k-12 and higher ed research analyst • from 🇻🇳	https://t.co/VR2q82MmJf	FALSE	35	119	0	13	80	2021-08-27 17:33:01	FALSE	https://t.co/VR2q82MmJf	http://linkedin.com/in/rachelthuyng	NA	https://pbs.twimg.com/profile_banners/1431308746366455809/1630088450	NA	http://pbs.twimg.com/profile_images/1432231095035064325/QWpI6SLx_normal.jpg
414070938	1520979951058620416	2022-05-02 04:14:13	francisojo_	Today is dedicated to @theplatformng, excited to listen to @LekeAlder & @olakunlesoriyan as they both share perspec… https://t.co/EUOy6eqQQD	Twitter for iPhone	NA	NA	NA	NA	FALSE	FALSE	2	1	NA	NA	NA	NA	twitter.com/i/web/status/1…	https://t.co/EUOy6eqQQD	https://twitter.com/i/web/status/1520979951058620416	NA	NA	NA	NA	NA	NA	NA	NA	c(“180933127”, “142341247”, “209620101”)	c(“theplatformng”, “LekeAlder”, “olakunlesoriyan”)	en	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(NA, NA)	c(NA, NA)	c(NA, NA, NA, NA, NA, NA, NA, NA)	https://twitter.com/NA/status/1520979951058620416	Francis Ojo	Lagos, Nigeria	EdTech | Learning | Product | Advisor	https://t.co/7bnxji50N4	FALSE	460	1349	11	1059	140	2011-11-16 15:58:56	FALSE	https://t.co/7bnxji50N4	http://www.francisojo.com	NA	https://pbs.twimg.com/profile_banners/414070938/1576591246	http://abs.twimg.com/images/themes/theme1/bg.png	http://pbs.twimg.com/profile_images/1348224812578123778/pOCxMpkg_normal.jpg
1210038044	1463643532623761413	2021-11-24 22:59:46	L4NDON_B	Honored to share my story for the premier podcast episode with @uwpdc. Hear a bit of my journey into… https://t.co/zuTirMmz4n	Twitter Web App	NA	NA	NA	NA	FALSE	FALSE	1	0	NA	NA	NA	NA	twitter.com/i/web/status/1…	https://t.co/zuTirMmz4n	https://twitter.com/i/web/status/1463643532623761413	NA	NA	NA	NA	NA	NA	NA	NA	1217903920678428677	uwpdc	en	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(NA, NA)	c(NA, NA)	c(NA, NA, NA, NA, NA, NA, NA, NA)	https://twitter.com/NA/status/1463643532623761413	Landon B	NA	Turning educational data into meaningful stories.	NA	FALSE	6	68	0	2	0	2013-02-22 23:11:23	FALSE	NA	NA	NA	https://pbs.twimg.com/profile_banners/1210038044/1637172708	http://abs.twimg.com/images/themes/theme1/bg.png	http://pbs.twimg.com/profile_images/1461030773209841667/44reWfSl_normal.jpg
1457866469656592384	NA	NA	DoreenMushi13	NA	NA	NA	NA	NA	NA	FALSE	FALSE	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	c(NA, NA)	c(NA, NA)	c(NA, NA, NA, NA, NA, NA, NA, NA)	NA	Doreen Mushi	NA	NA	NA	FALSE	0	17	0	0	0	2021-11-09 00:24:25	FALSE	NA	NA	NA	NA	NA	http://pbs.twimg.com/profile_images/1457866634253664261/jM13WWoo_normal.jpg

Laser_Institute Twitter account has 143 followers (on 15 April 22). We need to gather all of their followers and following Followers_count> 100 and < 6000,following_count> 75,favorites_count` > 10. To know they are active we will include that they have tweeted within the last 2 months.

active_fol <- detail_folower %>% select(user_id,
                                        screen_name,
                                        created_at,
                                        followers_count,
                                        friends_count,favourites_count) %>%
  mutate(created_at = ymd_hms(created_at),
         followers_count = as.numeric(followers_count),
         friends_count = as.numeric(friends_count),
         favourites_count = as.numeric(favourites_count)) %>%
  filter((followers_count > 100 & followers_count < 6000), 
         friends_count > 75, favourites_count > 10, 
         created_at > "2022-2-15") %>%
  arrange(-followers_count)



# top 10 active followers on LASER
active_fol %>%
  head(n=10)%>%
  kbl(caption = "Top Laser Institute active followers") %>%
  kable_styling(bootstrap_options = c("striped", "hover"))

Top Laser Institute active followers

user_id	screen_name	created_at	followers_count	friends_count	favourites_count
24298665	tjscience	2022-04-29 16:57:37	4451	2441	9687
23216407	edtechdev	2022-05-03 17:40:06	4379	4911	15532
1279411194	GaleSinatra	2022-05-03 16:57:04	3506	2567	26185
2393099288	drncgarrett	2022-05-03 23:54:07	2960	2402	17068
16088783	caroyce	2022-04-30 18:50:20	2544	2505	7145
29460806	DukeLearning	2022-05-03 19:00:54	2392	307	622
765730657796435970	carlton_fong	2022-05-02 22:09:04	2359	1560	21406
971880841939996672	DrTeyaR	2022-05-01 18:27:36	2128	2324	9748
45256556	robmoore3	2022-05-04 00:30:27	1727	740	731
27845032	bod0ng	2022-04-27 23:52:02	1717	1287	5635

write_xlsx(active_fol, "data/active_fol.xlsx")

Now we have 101 users that considered as active users. Next, we will gather all of their followers. Let’s create a loop to gather all of the active_fol followers by using an adapted script by @JoeChristianP. This loop reduces the chance of crashing during retrieval and minimizes the number by retrieving half of the followers if they have more than 1500 followers, and 75% followers if they have less than 1500. @JoeChristianP suggests I order the loop to sleep every 5 gathered accounts to avoid “rate limit exceeded.”

I tried doing it at 3 minutes but received the ratelimit exceeded so I switched back to sleeping for 5 minutes. This takes some time so we will not include in knitted document.

STEP 2

2a. Set a function to limit rate exceeding limit 2b. Create an empty data frame to fill when pulling data 2c. Look up Laser Institute active followers.

#create a function to retrieve 50% of followers if > 1500 followers otherwise retrieve retrieve 75%
flt_n <- function(x){
  if(x > 1500){
    x*0.5
  }else{x*0.75}
}

# Create empty list and name it after their screen name
foler <- vector(mode = 'list', length = length(active_fol$screen_name))
names(foler) <- active_fol$screen_name
# 
for (i in seq_along(active_fol$screen_name)) {
  message("Getting followers for user #", i, "/130")
  foler[[i]] <- get_followers(active_fol$screen_name[i], 
                                  n = round(flt_n(active_fol$followers_count[i])), 
                                retryonratelimit = TRUE)
  
  if(i %% 5 == 0){
    message("sleep for 5 minutes")
    Sys.sleep(5*60)
    } 
}

STEP 3

3a. Subset rows and columns of followers 3b. Bind the list to data frame 3c. Convert the username to user_id by left_join from active_fol data, and build clean data frame without NA

# convert list to dataframe
folerx <- bind_rows(foler, .id = "screen_name")
active_fol_x <- active_fol %>% 
  select(user_id,
         screen_name)

# left join to convert screen_name into its user id
foler_join <- left_join(folerx, active_fol_x, 
                        by="screen_name")

# subset to new dataframe with new column name and delete NA
laser_follower <- foler_join %>% 
  select(user_id.x,user_id.y) %>%
  setNames(c("follower",
             "active_user")) %>% 
  na.omit()


laser_followertable <- laser_follower %>%
  head()%>%
  kbl(caption = "Laser Institute ") %>%
  kable_styling(bootstrap_options = c("striped", "hover"))

###write another script to retrieve friends folowers build a loop function to gather the following. in rtweet package, following is also called as friend. Store the data to dataframe. get_friends() function gives 2 columns as their output; friend list and the query then row bind them.

friend <- data.frame()
for (i in seq_along(active_fol$screen_name)) {
  message("Getting followers for user #", i, "/161")
  kk <- get_friends(active_fol$screen_name[i],
                        n = round(flt_n(active_fol$friends_count[i])),
                        retryonratelimit = TRUE)
  
  friend <- rbind(friend,kk)
  
  if(i %% 5 == 0){
    message("sleep for 5 minutes")
    Sys.sleep(5*60)
    } 
}

write_xlsx(friend, "data/friend.xlsx")

Join active followers and friends

friend1 <- read_xlsx(friend, "data/friend.xlsx")

all_friend <- friend1 %>% 
  setNames(c("screen_name","user_id"))
all_friendx <- left_join(all_friend, 
                         active_fol_x, by="screen_name")
laser_friend1 <- all_friendx %>% 
  select(user_id.x,screen_name) %>%
  setNames(c("following","active_user"))

laser_friend1
write_xlsx(laser_friend1, "data/laser_friend1.xlsx")

read_xlsx(laser_friend1, "data/laser_friend1.xlsx")
# collect unique user_id in laser_friend df
laser_friend1 %>% 
  filter(!active_user %in% laser_follower$active_user)

# collect unique user_id in laser_friend1df
un_active <- unique(laser_friend1$active_user) %>%
  data.frame(stringsAsFactors = FALSE) %>%
  setNames("active_user")

# create empty dataframe
laser_mutual <- data.frame()

# loop function to filter the df by selected unique user, then find user that presence in both laser _friend$following and laser_follower$follower column set column name, and store it to algo_mutual df

for (i in seq_along(un_active$active_user)){
  aa <- laser_friend1 %>% 
    filter(active_user == un_active$active_user[i])
  
  bb <- aa %>% 
    filter(aa$following %in% laser_follower$follower) %>%
    setNames(c("mutual","active_user"))
  
  laser_mutual <- rbind(laser_mutual,bb)
}

laser_mutual
write_xlsx(laser_mutual, "data/laser_mutual.xlsx")

un_active <- un_active %>% 
  mutate(mutual = rep("LASER_Institute"))

# swap column order
un_active <- un_active[,c(2,1)]

# rbind to laser_mutual df
laser_mutual <- rbind(laser_mutual,un_active)
laser_mutual

2b. Create Network

we will use the tbl_graph() function from the {tidygraph} package to convert our graph. - First, we will use active users as the actors or vertices and save it as nodes. - Then we will use the mutual friends as the ties or edges. - Finally we will combine that into a graph object. Create a directed and undirected network.

# create nodes data
nodes3 <- data.frame(V = unique(c(laser_mutual$mutual,laser_mutual$active_user)),
                    stringsAsFactors = FALSE)

# create edges data
edges3 <- laser_mutual%>%
  setNames(c("from", "to"))

#create table graph
laser_network_ego <- graph_from_data_frame(d = edges3, vertices = nodes3, directed = F) %>%
  as_tbl_graph()

direct_network <- tbl_graph(edges = edges3,
                          nodes = nodes3,
                          directed = TRUE)

3 Explore

3a. Components

When we look at components we see we have one weak and one strong. But let’s print them so you can see. We will use out directed graph again.

autograph(direct_network)

components(direct_network, mode = c("weak"))

## $membership
##     [1] 1 1 1 1 1 1 1 1 1 1 1 1 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
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##  [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
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##  [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
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##  [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
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##  [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
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## [17497] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 
## $csize
## [1] 17518
## 
## $no
## [1] 1

components(direct_network, mode = c("strong"))

## $membership
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##  [1657] 15761 15760 15759 15758 15757 15756 15755 15754 15753 15752 15751 15750
##  [1669] 15749 15748 15747 15746 15745 15744 15743 15742 15741 15740 15739 15738
##  [1681] 15737 15736 15735 15734 15733 15732 15731 15730 15729 15728 15727 15726
##  [1693] 15725 15724 15723 15722 15721 15720 15719 15718 15717 15716 15715 15714
##  [1705] 15713 15712 15711 15710 15709 15708 15707 15706 15705 15704 15703 15702
##  [1717] 15701 15700 15699 15698 15697 15696 15695 15694 15693 15692 15691 15690
##  [1729] 15689 15688 15687 15686 15685 15684 15683 15682 15681 15680 15679 15678
##  [1741] 15677 15676 15675 15674 15673 15672 15671 15670 15669 15668 15667 15666
##  [1753] 15665 15664 15663 15662 15661 15660 15659 15658 15657 15656 15655 15654
##  [1765] 15653 15652 15651 15650 15649 15648 15647 15646 15645 15644 15643 15642
##  [1777] 15641 15640 15639 15638 15637 15636 15635 15634 15633 15632 15631 15630
##  [1789] 15629 15628 15627 15626 15625 15624 15623 15622 15621 15620 15619 15618
##  [1801] 15617 15616 15615 15614 15613 15612 15611 15610 15609 15608 15607 15606
##  [1813] 15605 15604 15603 15602 15601 15600 15599 15598 15597 15596 15595 15594
##  [1825] 15593 15592 15591 15590 15589 15588 15587 15586 15585 15584 15583 15582
##  [1837] 15581 15580 15579 15578 15577 15576 15575 15574 15573 15572 15571 15570
##  [1849] 15569 15568 15567 15566 15565 15564 15563 15562 15561 15560 15559 15558
##  [1861] 15557 15556 15555 15554 15553 15552 15551 15550 15549 15548 15547 15546
##  [1873] 15545 15544 15543 15542 15541 15540 15539 15538 15537 15536 15535 15534
##  [1885] 15533 15532 15531 15530 15529 15528 15527 15526 15525 15524 15523 15522
##  [1897] 15521 15520 15519 15518 15517 15516 15515 15514 15513 15512 15511 15510
##  [1909] 15509 15508 15507 15506 15505 15504 15503 15502 15501 15500 15499 15498
##  [1921] 15497 15496 15495 15494 15493 15492 15491 15490 15489 15488 15487 15486
##  [1933] 15485 15484 15483 15482 15481 15480 15479 15478 15477 15476 15475 15474
##  [1945] 15473 15472 15471 15470 15469 15468 15467 15466 15465 15464 15463 15462
##  [1957] 15461 15460 15459 15458 15457 15456 15455 15454 15453 15452 15451 15450
##  [1969] 15449 15448 15447 15446 15445 15444 15443 15442 15441 15440 15439 15438
##  [1981] 15437 15436 15435 15434 15433 15432 15431 15430 15429 15428 15427 15426
##  [1993] 15425 15424 15423 15422 15421 15420 15419 15418 15417 15416 15415 15414
##  [2005] 15413 15412 15411 15410 15409 15408 15407 15406 15405 15404 15403 15402
##  [2017] 15401 15400 15399 15398 15397 15396 15395 15394 15393 15392 15391 15390
##  [2029] 15389 15388 15387 15386 15385 15384 15383 15382 15381 15380 15379 15378
##  [2041] 15377 15376 15375 15374 15373 15372 15371 15370 15369 15368 15367 15366
##  [2053] 15365 15364 15363 15362 15361 15360 15359 15358 15357 15356 15355 15354
##  [2065] 15353 15352 15351 15350 15349 15348 15347 15346 15345 15344 15343 15342
##  [2077] 15341 15340 15339 15338 15337 15336 15335 15334 15333 15332 15331 15330
##  [2089] 15329 15328 15327 15326 15325 15324 15323 15322 15321 15320 15319 15318
##  [2101] 15317 15316 15315 15314 15313 15312 15311 15310 15309 15308 15307 15306
##  [2113] 15305 15304 15303 15302 15301 15300 15299 15298 15297 15296 15295 15294
##  [2125] 15293 15292 15291 15290 15289 15288 15287 15286 15285 15284 15283 15282
##  [2137] 15281 15280 15279 15278 15277 15276 15275 15274 15273 15272 15271 15270
##  [2149] 15269 15268 15267 15266 15265 15264 15263 15262 15261 15260 15259 15258
##  [2161] 15257 15256 15255 15254 15253 15252 15251 15250 15249 15248 15247 15246
##  [2173] 15245 15244 15243 15242 15241 15240 15239 15238 15237 15236 15235 15234
##  [2185] 15233 15232 15231 15230 15229 15228 15227 15226 15225 15224 15223 15222
##  [2197] 15221 15220 15219 15218 15217 15216 15215 15214 15213 15212 15211 15210
##  [2209] 15209 15208 15207 15206 15205 15204 15203 15202 15201 15200 15199 15198
##  [2221] 15197 15196 15195 15194 15193 15192 15191 15190 15189 15188 15187 15186
##  [2233] 15185 15184 15183 15182 15181 15180 15179 15178 15177 15176 15175 15174
##  [2245] 15173 15172 15171 15170 15169 15168 15167 15166 15165 15164 15163 15162
##  [2257] 15161 15160 15159 15158 15157 15156 15155 15154 15153 15152 15151 15150
##  [2269] 15149 15148 15147 15146 15145 15144 15143 15142 15141 15140 15139 15138
##  [2281] 15137 15136 15135 15134 15133 15132 15131 15130 15129 15128 15127 15126
##  [2293] 15125 15124 15123 15122 15121 15120 15119 15118 15117 15116 15115 15114
##  [2305] 15113 15112 15111 15110 15109 15108 15107 15106 15105 15104 15103 15102
##  [2317] 15101 15100 15099 15098 15097 15096 15095 15094 15093 15092 15091 15090
##  [2329] 15089 15088 15087 15086 15085 15084 15083 15082 15081 15080 15079 15078
##  [2341] 15077 15076 15075 15074 15073 15072 15071 15070 15069 15068 15067 15066
##  [2353] 15065 15064 15063 15062 15061 15060 15059 15058 15057 15056 15055 15054
##  [2365] 15053 15052 15051 15050 15049 15048 15047 15046 15045 15044 15043 15042
##  [2377] 15041 15040 15039 15038 15037 15036 15035 15034 15033 15032 15031 15030
##  [2389] 15029 15028 15027 15026 15025 15024 15023 15022 15021 15020 15019 15018
##  [2401] 15017 15016 15015 15014 15013 15012 15011 15010 15009 15008 15007 15006
##  [2413] 15005 15004 15003 15002 15001 15000 14999 14998 14997 14996 14995 14994
##  [2425] 14993 14992 14991 14990 14989 14988 14987 14986 14985 14984 14983 14982
##  [2437] 14981 14980 14979 14978 14977 14976 14975 14974 14973 14972 14971 14970
##  [2449] 14969 14968 14967 14966 14965 14964 14963 14962 14961 14960 14959 14958
##  [2461] 14957 14956 14955 14954 14953 14952 14951 14950 14949 14948 14947 14946
##  [2473] 14945 14944 14943 14942 14941 14940 14939 14938 14937 14936 14935 14934
##  [2485] 14933 14932 14931 14930 14929 14928 14927 14926 14925 14924 14923 14922
##  [2497] 14921 14920 14919 14918 14917 14916 14915 14914 14913 14912 14911 14910
##  [2509] 14909 14908 14907 14906 14905 14904 14903 14902 14901 14900 14899 14898
##  [2521] 14897 14896 14895 14894 14893 14892 14891 14890 14889 14888 14887 14886
##  [2533] 14885 14884 14883 14882 14881 14880 14879 14878 14877 14876 14875 14874
##  [2545] 14873 14872 14871 14870 14869 14868 14867 14866 14865 14864 14863 14862
##  [2557] 14861 14860 14859 14858 14857 14856 14855 14854 14853 14852 14851 14850
##  [2569] 14849 14848 14847 14846 14845 14844 14843 14842 14841 14840 14839 14838
##  [2581] 14837 14836 14835 14834 14833 14832 14831 14830 14829 14828 14827 14826
##  [2593] 14825 14824 14823 14822 14821 14820 14819 14818 14817 14816 14815 14814
##  [2605] 14813 14812 14811 14810 14809 14808 14807 14806 14805 14804 14803 14802
##  [2617] 14801 14800 14799 14798 14797 14796 14795 14794 14793 14792 14791 14790
##  [2629] 14789 14788 14787 14786 14785 14784 14783 14782 14781 14780 14779 14778
##  [2641] 14777 14776 14775 14774 14773 14772 14771 14770 14769 14768 14767 14766
##  [2653] 14765 14764 14763 14762 14761 14760 14759 14758 14757 14756 14755 14754
##  [2665] 14753 14752 14751 14750 14749 14748 14747 14746 14745 14744 14743 14742
##  [2677] 14741 14740 14739 14738 14737 14736 14735 14734 14733 14732 14731 14730
##  [2689] 14729 14728 14727 14726 14725 14724 14723 14722 14721 14720 14719 14718
##  [2701] 14717 14716 14715 14714 14713 14712 14711 14710 14709 14708 14707 14706
##  [2713] 14705 14704 14703 14702 14701 14700 14699 14698 14697 14696 14695 14694
##  [2725] 14693 14692 14691 14690 14689 14688 14687 14686 14685 14684 14683 14682
##  [2737] 14681 14680 14679 14678 14677 14676 14675 14674 14673 14672 14671 14670
##  [2749] 14669 14668 14667 14666 14665 14664 14663 14662 14661 14660 14659 14658
##  [2761] 14657 14656 14655 14654 14653 14652 14651 14650 14649 14648 14647 14646
##  [2773] 14645 14644 14643 14642 14641 14640 14639 14638 14637 14636 14635 14634
##  [2785] 14633 14632 14631 14630 14629 14628 14627 14626 14625 14624 14623 14622
##  [2797] 14621 14620 14619 14618 14617 14616 14615 14614 14613 14612 14611 14610
##  [2809] 14609 14608 14607 14606 14605 14604 14603 14602 14601 14600 14599 14598
##  [2821] 14597 14596 14595 14594 14593 14592 14591 14590 14589 14588 14587 14586
##  [2833] 14585 14584 14583 14582 14581 14580 14579 14578 14577 14576 14575 14574
##  [2845] 14573 14572 14571 14570 14569 14568 14567 14566 14565 14564 14563 14562
##  [2857] 14561 14560 14559 14558 14557 14556 14555 14554 14553 14552 14551 14550
##  [2869] 14549 14548 14547 14546 14545 14544 14543 14542 14541 14540 14539 14538
##  [2881] 14537 14536 14535 14534 14533 14532 14531 14530 14529 14528 14527 14526
##  [2893] 14525 14524 14523 14522 14521 14520 14519 14518 14517 14516 14515 14514
##  [2905] 14513 14512 14511 14510 14509 14508 14507 14506 14505 14504 14503 14502
##  [2917] 14501 14500 14499 14498 14497 14496 14495 14494 14493 14492 14491 14490
##  [2929] 14489 14488 14487 14486 14485 14484 14483 14482 14481 14480 14479 14478
##  [2941] 14477 14476 14475 14474 14473 14472 14471 14470 14469 14468 14467 14466
##  [2953] 14465 14464 14463 14462 14461 14460 14459 14458 14457 14456 14455 14454
##  [2965] 14453 14452 14451 14450 14449 14448 14447 14446 14445 14444 14443 14442
##  [2977] 14441 14440 14439 14438 14437 14436 14435 14434 14433 14432 14431 14430
##  [2989] 14429 14428 14427 14426 14425 14424 14423 14422 14421 14420 14419 14418
##  [3001] 14417 14416 14415 14414 14413 14412 14411 14410 14409 14408 14407 14406
##  [3013] 14405 14404 14403 14402 14401 14400 14399 14398 14397 14396 14395 14394
##  [3025] 14393 14392 14391 14390 14389 14388 14387 14386 14385 14384 14383 14382
##  [3037] 14381 14380 14379 14378 14377 14376 14375 14374 14373 14372 14371 14370
##  [3049] 14369 14368 14367 14366 14365 14364 14363 14362 14361 14360 14359 14358
##  [3061] 14357 14356 14355 14354 14353 14352 14351 14350 14349 14348 14347 14346
##  [3073] 14345 14344 14343 14342 14341 14340 14339 14338 14337 14336 14335 14334
##  [3085] 14333 14332 14331 14330 14329 14328 14327 14326 14325 14324 14323 14322
##  [3097] 14321 14320 14319 14318 14317 14316 14315 14314 14313 14312 14311 14310
##  [3109] 14309 14308 14307 14306 14305 14304 14303 14302 14301 14300 14299 14298
##  [3121] 14297 14296 14295 14294 14293 14292 14291 14290 14289 14288 14287 14286
##  [3133] 14285 14284 14283 14282 14281 14280 14279 14278 14277 14276 14275 14274
##  [3145] 14273 14272 14271 14270 14269 14268 14267 14266 14265 14264 14263 14262
##  [3157] 14261 14260 14259 14258 14257 14256 14255 14254 14253 14252 14251 14250
##  [3169] 14249 14248 14247 14246 14245 14244 14243 14242 14241 14240 14239 14238
##  [3181] 14237 14236 14235 14234 14233 14232 14231 14230 14229 14228 14227 14226
##  [3193] 14225 14224 14223 14222 14221 14220 14219 14218 14217 14216 14215 14214
##  [3205] 14213 14212 14211 14210 14209 14208 14207 14206 14205 14204 14203 14202
##  [3217] 14201 14200 14199 14198 14197 14196 14195 14194 14193 14192 14191 14190
##  [3229] 14189 14188 14187 14186 14185 14184 14183 14182 14181 14180 14179 14178
##  [3241] 14177 14176 14175 14174 14173 14172 14171 14170 14169 14168 14167 14166
##  [3253] 14165 14164 14163 14162 14161 14160 14159 14158 14157 14156 14155 14154
##  [3265] 14153 14152 14151 14150 14149 14148 14147 14146 14145 14144 14143 14142
##  [3277] 14141 14140 14139 14138 14137 14136 14135 14134 14133 14132 14131 14130
##  [3289] 14129 14128 14127 14126 14125 14124 14123 14122 14121 14120 14119 14118
##  [3301] 14117 14116 14115 14114 14113 14112 14111 14110 14109 14108 14107 14106
##  [3313] 14105 14104 14103 14102 14101 14100 14099 14098 14097 14096 14095 14094
##  [3325] 14093 14092 14091 14090 14089 14088 14087 14086 14085 14084 14083 14082
##  [3337] 14081 14080 14079 14078 14077 14076 14075 14074 14073 14072 14071 14070
##  [3349] 14069 14068 14067 14066 14065 14064 14063 14062 14061 14060 14059 14058
##  [3361] 14057 14056 14055 14054 14053 14052 14051 14050 14049 14048 14047 14046
##  [3373] 14045 14044 14043 14042 14041 14040 14039 14038 14037 14036 14035 14034
##  [3385] 14033 14032 14031 14030 14029 14028 14027 14026 14025 14024 14023 14022
##  [3397] 14021 14020 14019 14018 14017 14016 14015 14014 14013 14012 14011 14010
##  [3409] 14009 14008 14007 14006 14005 14004 14003 14002 14001 14000 13999 13998
##  [3421] 13997 13996 13995 13994 13993 13992 13991 13990 13989 13988 13987 13986
##  [3433] 13985 13984 13983 13982 13981 13980 13979 13978 13977 13976 13975 13974
##  [3445] 13973 13972 13971 13970 13969 13968 13967 13966 13965 13964 13963 13962
##  [3457] 13961 13960 13959 13958 13957 13956 13955 13954 13953 13952 13951 13950
##  [3469] 13949 13948 13947 13946 13945 13944 13943 13942 13941 13940 13939 13938
##  [3481] 13937 13936 13935 13934 13933 13932 13931 13930 13929 13928 13927 13926
##  [3493] 13925 13924 13923 13922 13921 13920 13919 13918 13917 13916 13915 13914
##  [3505] 13913 13912 13911 13910 13909 13908 13907 13906 13905 13904 13903 13902
##  [3517] 13901 13900 13899 13898 13897 13896 13895 13894 13893 13892 13891 13890
##  [3529] 13889 13888 13887 13886 13885 13884 13883 13882 13881 13880 13879 13878
##  [3541] 13877 13876 13875 13874 13873 13872 13871 13870 13869 13868 13867 13866
##  [3553] 13865 13864 13863 13862 13861 13860 13859 13858 13857 13856 13855 13854
##  [3565] 13853 13852 13851 13850 13849 13848 13847 13846 13845 13844 13843 13842
##  [3577] 13841 13840 13839 13838 13837 13836 13835 13834 13833 13832 13831 13830
##  [3589] 13829 13828 13827 13826 13825 13824 13823 13822 13821 13820 13819 13818
##  [3601] 13817 13816 13815 13814 13813 13812 13811 13810 13809 13808 13807 13806
##  [3613] 13805 13804 13803 13802 13801 13800 13799 13798 13797 13796 13795 13794
##  [3625] 13793 13792 13791 13790 13789 13788 13787 13786 13785 13784 13783 13782
##  [3637] 13781 13780 13779 13778 13777 13776 13775 13774 13773 13772 13771 13770
##  [3649] 13769 13768 13767 13766 13765 13764 13763 13762 13761 13760 13759 13758
##  [3661] 13757 13756 13755 13754 13753 13752 13751 13750 13749 13748 13747 13746
##  [3673] 13745 13744 13743 13742 13741 13740 13739 13738 13737 13736 13735 13734
##  [3685] 13733 13732 13731 13730 13729 13728 13727 13726 13725 13724 13723 13722
##  [3697] 13721 13720 13719 13718 13717 13716 13715 13714 13713 13712 13711 13710
##  [3709] 13709 13708 13707 13706 13705 13704 13703 13702 13701 13700 13699 13698
##  [3721] 13697 13696 13695 13694 13693 13692 13691 13690 13689 13688 13687 13686
##  [3733] 13685 13684 13683 13682 13681 13680 13679 13678 13677 13676 13675 13674
##  [3745] 13673 13672 13671 13670 13669 13668 13667 13666 13665 13664 13663 13662
##  [3757] 13661 13660 13659 13658 13657 13656 13655 13654 13653 13652 13651 13650
##  [3769] 13649 13648 13647 13646 13645 13644 13643 13642 13641 13640 13639 13638
##  [3781] 13637 13636 13635 13634 13633 13632 13631 13630 13629 13628 13627 13626
##  [3793] 13625 13624 13623 13622 13621 13620 13619 13618 13617 13616 13615 13614
##  [3805] 13613 13612 13611 13610 13609 13608 13607 13606 13605 13604 13603 13602
##  [3817] 13601 13600 13599 13598 13597 13596 13595 13594 13593 13592 13591 13590
##  [3829] 13589 13588 13587 13586 13585 13584 13583 13582 13581 13580 13579 13578
##  [3841] 13577 13576 13575 13574 13573 13572 13571 13570 13569 13568 13567 13566
##  [3853] 13565 13564 13563 13562 13561 13560 13559 13558 13557 13556 13555 13554
##  [3865] 13553 13552 13551 13550 13549 13548 13547 13546 13545 13544 13543 13542
##  [3877] 13541 13540 13539 13538 13537 13536 13535 13534 13533 13532 13531 13530
##  [3889] 13529 13528 13527 13526 13525 13524 13523 13522 13521 13520 13519 13518
##  [3901] 13517 13516 13515 13514 13513 13512 13511 13510 13509 13508 13507 13506
##  [3913] 13505 13504 13503 13502 13501 13500 13499 13498 13497 13496 13495 13494
##  [3925] 13493 13492 13491 13490 13489 13488 13487 13486 13485 13484 13483 13482
##  [3937] 13481 13480 13479 13478 13477 13476 13475 13474 13473 13472 13471 13470
##  [3949] 13469 13468 13467 13466 13465 13464 13463 13462 13461 13460 13459 13458
##  [3961] 13457 13456 13455 13454 13453 13452 13451 13450 13449 13448 13447 13446
##  [3973] 13445 13444 13443 13442 13441 13440 13439 13438 13437 13436 13435 13434
##  [3985] 13433 13432 13431 13430 13429 13428 13427 13426 13425 13424 13423 13422
##  [3997] 13421 13420 13419 13418 13417 13416 13415 13414 13413 13412 13411 13410
##  [4009] 13409 13408 13407 13406 13405 13404 13403 13402 13401 13400 13399 13398
##  [4021] 13397 13396 13395 13394 13393 13392 13391 13390 13389 13388 13387 13386
##  [4033] 13385 13384 13383 13382 13381 13380 13379 13378 13377 13376 13375 13374
##  [4045] 13373 13372 13371 13370 13369 13368 13367 13366 13365 13364 13363 13362
##  [4057] 13361 13360 13359 13358 13357 13356 13355 13354 13353 13352 13351 13350
##  [4069] 13349 13348 13347 13346 13345 13344 13343 13342 13341 13340 13339 13338
##  [4081] 13337 13336 13335 13334 13333 13332 13331 13330 13329 13328 13327 13326
##  [4093] 13325 13324 13323 13322 13321 13320 13319 13318 13317 13316 13315 13314
##  [4105] 13313 13312 13311 13310 13309 13308 13307 13306 13305 13304 13303 13302
##  [4117] 13301 13300 13299 13298 13297 13296 13295 13294 13293 13292 13291 13290
##  [4129] 13289 13288 13287 13286 13285 13284 13283 13282 13281 13280 13279 13278
##  [4141] 13277 13276 13275 13274 13273 13272 13271 13270 13269 13268 13267 13266
##  [4153] 13265 13264 13263 13262 13261 13260 13259 13258 13257 13256 13255 13254
##  [4165] 13253 13252 13251 13250 13249 13248 13247 13246 13245 13244 13243 13242
##  [4177] 13241 13240 13239 13238 13237 13236 13235 13234 13233 13232 13231 13230
##  [4189] 13229 13228 13227 13226 13225 13224 13223 13222 13221 13220 13219 13218
##  [4201] 13217 13216 13215 13214 13213 13212 13211 13210 13209 13208 13207 13206
##  [4213] 13205 13204 13203 13202 13201 13200 13199 13198 13197 13196 13195 13194
##  [4225] 13193 13192 13191 13190 13189 13188 13187 13186 13185 13184 13183 13182
##  [4237] 13181 13180 13179 13178 13177 13176 13175 13174 13173 13172 13171 13170
##  [4249] 13169 13168 13167 13166 13165 13164 13163 13162 13161 13160 13159 13158
##  [4261] 13157 13156 13155 13154 13153 13152 13151 13150 13149 13148 13147 13146
##  [4273] 13145 13144 13143 13142 13141 13140 13139 13138 13137 13136 13135 13134
##  [4285] 13133 13132 13131 13130 13129 13128 13127 13126 13125 13124 13123 13122
##  [4297] 13121 13120 13119 13118 13117 13116 13115 13114 13113 13112 13111 13110
##  [4309] 13109 13108 13107 13106 13105 13104 13103 13102 13101 13100 13099 13098
##  [4321] 13097 13096 13095 13094 13093 13092 13091 13090 13089 13088 13087 13086
##  [4333] 13085 13084 13083 13082 13081 13080 13079 13078 13077 13076 13075 13074
##  [4345] 13073 13072 13071 13070 13069 13068 13067 13066 13065 13064 13063 13062
##  [4357] 13061 13060 13059 13058 13057 13056 13055 13054 13053 13052 13051 13050
##  [4369] 13049 13048 13047 13046 13045 13044 13043 13042 13041 13040 13039 13038
##  [4381] 13037 13036 13035 13034 13033 13032 13031 13030 13029 13028 13027 13026
##  [4393] 13025 13024 13023 13022 13021 13020 13019 13018 13017 13016 13015 13014
##  [4405] 13013 13012 13011 13010 13009 13008 13007 13006 13005 13004 13003 13002
##  [4417] 13001 13000 12999 12998 12997 12996 12995 12994 12993 12992 12991 12990
##  [4429] 12989 12988 12987 12986 12985 12984 12983 12982 12981 12980 12979 12978
##  [4441] 12977 12976 12975 12974 12973 12972 12971 12970 12969 12968 12967 12966
##  [4453] 12965 12964 12963 12962 12961 12960 12959 12958 12957 12956 12955 12954
##  [4465] 12953 12952 12951 12950 12949 12948 12947 12946 12945 12944 12943 12942
##  [4477] 12941 12940 12939 12938 12937 12936 12935 12934 12933 12932 12931 12930
##  [4489] 12929 12928 12927 12926 12925 12924 12923 12922 12921 12920 12919 12918
##  [4501] 12917 12916 12915 12914 12913 12912 12911 12910 12909 12908 12907 12906
##  [4513] 12905 12904 12903 12902 12901 12900 12899 12898 12897 12896 12895 12894
##  [4525] 12893 12892 12891 12890 12889 12888 12887 12886 12885 12884 12883 12882
##  [4537] 12881 12880 12879 12878 12877 12876 12875 12874 12873 12872 12871 12870
##  [4549] 12869 12868 12867 12866 12865 12864 12863 12862 12861 12860 12859 12858
##  [4561] 12857 12856 12855 12854 12853 12852 12851 12850 12849 12848 12847 12846
##  [4573] 12845 12844 12843 12842 12841 12840 12839 12838 12837 12836 12835 12834
##  [4585] 12833 12832 12831 12830 12829 12828 12827 12826 12825 12824 12823 12822
##  [4597] 12821 12820 12819 12818 12817 12816 12815 12814 12813 12812 12811 12810
##  [4609] 12809 12808 12807 12806 12805 12804 12803 12802 12801 12800 12799 12798
##  [4621] 12797 12796 12795 12794 12793 12792 12791 12790 12789 12788 12787 12786
##  [4633] 12785 12784 12783 12782 12781 12780 12779 12778 12777 12776 12775 12774
##  [4645] 12773 12772 12771 12770 12769 12768 12767 12766 12765 12764 12763 12762
##  [4657] 12761 12760 12759 12758 12757 12756 12755 12754 12753 12752 12751 12750
##  [4669] 12749 12748 12747 12746 12745 12744 12743 12742 12741 12740 12739 12738
##  [4681] 12737 12736 12735 12734 12733 12732 12731 12730 12729 12728 12727 12726
##  [4693] 12725 12724 12723 12722 12721 12720 12719 12718 12717 12716 12715 12714
##  [4705] 12713 12712 12711 12710 12709 12708 12707 12706 12705 12704 12703 12702
##  [4717] 12701 12700 12699 12698 12697 12696 12695 12694 12693 12692 12691 12690
##  [4729] 12689 12688 12687 12686 12685 12684 12683 12682 12681 12680 12679 12678
##  [4741] 12677 12676 12675 12674 12673 12672 12671 12670 12669 12668 12667 12666
##  [4753] 12665 12664 12663 12662 12661 12660 12659 12658 12657 12656 12655 12654
##  [4765] 12653 12652 12651 12650 12649 12648 12647 12646 12645 12644 12643 12642
##  [4777] 12641 12640 12639 12638 12637 12636 12635 12634 12633 12632 12631 12630
##  [4789] 12629 12628 12627 12626 12625 12624 12623 12622 12621 12620 12619 12618
##  [4801] 12617 12616 12615 12614 12613 12612 12611 12610 12609 12608 12607 12606
##  [4813] 12605 12604 12603 12602 12601 12600 12599 12598 12597 12596 12595 12594
##  [4825] 12593 12592 12591 12590 12589 12588 12587 12586 12585 12584 12583 12582
##  [4837] 12581 12580 12579 12578 12577 12576 12575 12574 12573 12572 12571 12570
##  [4849] 12569 12568 12567 12566 12565 12564 12563 12562 12561 12560 12559 12558
##  [4861] 12557 12556 12555 12554 12553 12552 12551 12550 12549 12548 12547 12546
##  [4873] 12545 12544 12543 12542 12541 12540 12539 12538 12537 12536 12535 12534
##  [4885] 12533 12532 12531 12530 12529 12528 12527 12526 12525 12524 12523 12522
##  [4897] 12521 12520 12519 12518 12517 12516 12515 12514 12513 12512 12511 12510
##  [4909] 12509 12508 12507 12506 12505 12504 12503 12502 12501 12500 12499 12498
##  [4921] 12497 12496 12495 12494 12493 12492 12491 12490 12489 12488 12487 12486
##  [4933] 12485 12484 12483 12482 12481 12480 12479 12478 12477 12476 12475 12474
##  [4945] 12473 12472 12471 12470 12469 12468 12467 12466 12465 12464 12463 12462
##  [4957] 12461 12460 12459 12458 12457 12456 12455 12454 12453 12452 12451 12450
##  [4969] 12449 12448 12447 12446 12445 12444 12443 12442 12441 12440 12439 12438
##  [4981] 12437 12436 12435 12434 12433 12432 12431 12430 12429 12428 12427 12426
##  [4993] 12425 12424 12423 12422 12421 12420 12419 12418 12417 12416 12415 12414
##  [5005] 12413 12412 12411 12410 12409 12408 12407 12406 12405 12404 12403 12402
##  [5017] 12401 12400 12399 12398 12397 12396 12395 12394 12393 12392 12391 12390
##  [5029] 12389 12388 12387 12386 12385 12384 12383 12382 12381 12380 12379 12378
##  [5041] 12377 12376 12375 12374 12373 12372 12371 12370 12369 12368 12367 12366
##  [5053] 12365 12364 12363 12362 12361 12360 12359 12358 12357 12356 12355 12354
##  [5065] 12353 12352 12351 12350 12349 12348 12347 12346 12345 12344 12343 12342
##  [5077] 12341 12340 12339 12338 12337 12336 12335 12334 12333 12332 12331 12330
##  [5089] 12329 12328 12327 12326 12325 12324 12323 12322 12321 12320 12319 12318
##  [5101] 12317 12316 12315 12314 12313 12312 12311 12310 12309 12308 12307 12306
##  [5113] 12305 12304 12303 12302 12301 12300 12299 12298 12297 12296 12295 12294
##  [5125] 12293 12292 12291 12290 12289 12288 12287 12286 12285 12284 12283 12282
##  [5137] 12281 12280 12279 12278 12277 12276 12275 12274 12273 12272 12271 12270
##  [5149] 12269 12268 12267 12266 12265 12264 12263 12262 12261 12260 12259 12258
##  [5161] 12257 12256 12255 12254 12253 12252 12251 12250 12249 12248 12247 12246
##  [5173] 12245 12244 12243 12242 12241 12240 12239 12238 12237 12236 12235 12234
##  [5185] 12233 12232 12231 12230 12229 12228 12227 12226 12225 12224 12223 12222
##  [5197] 12221 12220 12219 12218 12217 12216 12215 12214 12213 12212 12211 12210
##  [5209] 12209 12208 12207 12206 12205 12204 12203 12202 12201 12200 12199 12198
##  [5221] 12197 12196 12195 12194 12193 12192 12191 12190 12189 12188 12187 12186
##  [5233] 12185 12184 12183 12182 12181 12180 12179 12178 12177 12176 12175 12174
##  [5245] 12173 12172 12171 12170 12169 12168 12167 12166 12165 12164 12163 12162
##  [5257] 12161 12160 12159 12158 12157 12156 12155 12154 12153 12152 12151 12150
##  [5269] 12149 12148 12147 12146 12145 12144 12143 12142 12141 12140 12139 12138
##  [5281] 12137 12136 12135 12134 12133 12132 12131 12130 12129 12128 12127 12126
##  [5293] 12125 12124 12123 12122 12121 12120 12119 12118 12117 12116 12115 12114
##  [5305] 12113 12112 12111 12110 12109 12108 12107 12106 12105 12104 12103 12102
##  [5317] 12101 12100 12099 12098 12097 12096 12095 12094 12093 12092 12091 12090
##  [5329] 12089 12088 12087 12086 12085 12084 12083 12082 12081 12080 12079 12078
##  [5341] 12077 12076 12075 12074 12073 12072 12071 12070 12069 12068 12067 12066
##  [5353] 12065 12064 12063 12062 12061 12060 12059 12058 12057 12056 12055 12054
##  [5365] 12053 12052 12051 12050 12049 12048 12047 12046 12045 12044 12043 12042
##  [5377] 12041 12040 12039 12038 12037 12036 12035 12034 12033 12032 12031 12030
##  [5389] 12029 12028 12027 12026 12025 12024 12023 12022 12021 12020 12019 12018
##  [5401] 12017 12016 12015 12014 12013 12012 12011 12010 12009 12008 12007 12006
##  [5413] 12005 12004 12003 12002 12001 12000 11999 11998 11997 11996 11995 11994
##  [5425] 11993 11992 11991 11990 11989 11988 11987 11986 11985 11984 11983 11982
##  [5437] 11981 11980 11979 11978 11977 11976 11975 11974 11973 11972 11971 11970
##  [5449] 11969 11968 11967 11966 11965 11964 11963 11962 11961 11960 11959 11958
##  [5461] 11957 11956 11955 11954 11953 11952 11951 11950 11949 11948 11947 11946
##  [5473] 11945 11944 11943 11942 11941 11940 11939 11938 11937 11936 11935 11934
##  [5485] 11933 11932 11931 11930 11929 11928 11927 11926 11925 11924 11923 11922
##  [5497] 11921 11920 11919 11918 11917 11916 11915 11914 11913 11912 11911 11910
##  [5509] 11909 11908 11907 11906 11905 11904 11903 11902 11901 11900 11899 11898
##  [5521] 11897 11896 11895 11894 11893 11892 11891 11890 11889 11888 11887 11886
##  [5533] 11885 11884 11883 11882 11881 11880 11879 11878 11877 11876 11875 11874
##  [5545] 11873 11872 11871 11870 11869 11868 11867 11866 11865 11864 11863 11862
##  [5557] 11861 11860 11859 11858 11857 11856 11855 11854 11853 11852 11851 11850
##  [5569] 11849 11848 11847 11846 11845 11844 11843 11842 11841 11840 11839 11838
##  [5581] 11837 11836 11835 11834 11833 11832 11831 11830 11829 11828 11827 11826
##  [5593] 11825 11824 11823 11822 11821 11820 11819 11818 11817 11816 11815 11814
##  [5605] 11813 11812 11811 11810 11809 11808 11807 11806 11805 11804 11803 11802
##  [5617] 11801 11800 11799 11798 11797 11796 11795 11794 11793 11792 11791 11790
##  [5629] 11789 11788 11787 11786 11785 11784 11783 11782 11781 11780 11779 11778
##  [5641] 11777 11776 11775 11774 11773 11772 11771 11770 11769 11768 11767 11766
##  [5653] 11765 11764 11763 11762 11761 11760 11759 11758 11757 11756 11755 11754
##  [5665] 11753 11752 11751 11750 11749 11748 11747 11746 11745 11744 11743 11742
##  [5677] 11741 11740 11739 11738 11737 11736 11735 11734 11733 11732 11731 11730
##  [5689] 11729 11728 11727 11726 11725 11724 11723 11722 11721 11720 11719 11718
##  [5701] 11717 11716 11715 11714 11713 11712 11711 11710 11709 11708 11707 11706
##  [5713] 11705 11704 11703 11702 11701 11700 11699 11698 11697 11696 11695 11694
##  [5725] 11693 11692 11691 11690 11689 11688 11687 11686 11685 11684 11683 11682
##  [5737] 11681 11680 11679 11678 11677 11676 11675 11674 11673 11672 11671 11670
##  [5749] 11669 11668 11667 11666 11665 11664 11663 11662 11661 11660 11659 11658
##  [5761] 11657 11656 11655 11654 11653 11652 11651 11650 11649 11648 11647 11646
##  [5773] 11645 11644 11643 11642 11641 11640 11639 11638 11637 11636 11635 11634
##  [5785] 11633 11632 11631 11630 11629 11628 11627 11626 11625 11624 11623 11622
##  [5797] 11621 11620 11619 11618 11617 11616 11615 11614 11613 11612 11611 11610
##  [5809] 11609 11608 11607 11606 11605 11604 11603 11602 11601 11600 11599 11598
##  [5821] 11597 11596 11595 11594 11593 11592 11591 11590 11589 11588 11587 11586
##  [5833] 11585 11584 11583 11582 11581 11580 11579 11578 11577 11576 11575 11574
##  [5845] 11573 11572 11571 11570 11569 11568 11567 11566 11565 11564 11563 11562
##  [5857] 11561 11560 11559 11558 11557 11556 11555 11554 11553 11552 11551 11550
##  [5869] 11549 11548 11547 11546 11545 11544 11543 11542 11541 11540 11539 11538
##  [5881] 11537 11536 11535 11534 11533 11532 11531 11530 11529 11528 11527 11526
##  [5893] 11525 11524 11523 11522 11521 11520 11519 11518 11517 11516 11515 11514
##  [5905] 11513 11512 11511 11510 11509 11508 11507 11506 11505 11504 11503 11502
##  [5917] 11501 11500 11499 11498 11497 11496 11495 11494 11493 11492 11491 11490
##  [5929] 11489 11488 11487 11486 11485 11484 11483 11482 11481 11480 11479 11478
##  [5941] 11477 11476 11475 11474 11473 11472 11471 11470 11469 11468 11467 11466
##  [5953] 11465 11464 11463 11462 11461 11460 11459 11458 11457 11456 11455 11454
##  [5965] 11453 11452 11451 11450 11449 11448 11447 11446 11445 11444 11443 11442
##  [5977] 11441 11440 11439 11438 11437 11436 11435 11434 11433 11432 11431 11430
##  [5989] 11429 11428 11427 11426 11425 11424 11423 11422 11421 11420 11419 11418
##  [6001] 11417 11416 11415 11414 11413 11412 11411 11410 11409 11408 11407 11406
##  [6013] 11405 11404 11403 11402 11401 11400 11399 11398 11397 11396 11395 11394
##  [6025] 11393 11392 11391 11390 11389 11388 11387 11386 11385 11384 11383 11382
##  [6037] 11381 11380 11379 11378 11377 11376 11375 11374 11373 11372 11371 11370
##  [6049] 11369 11368 11367 11366 11365 11364 11363 11362 11361 11360 11359 11358
##  [6061] 11357 11356 11355 11354 11353 11352 11351 11350 11349 11348 11347 11346
##  [6073] 11345 11344 11343 11342 11341 11340 11339 11338 11337 11336 11335 11334
##  [6085] 11333 11332 11331 11330 11329 11328 11327 11326 11325 11324 11323 11322
##  [6097] 11321 11320 11319 11318 11317 11316 11315 11314 11313 11312 11311 11310
##  [6109] 11309 11308 11307 11306 11305 11304 11303 11302 11301 11300 11299 11298
##  [6121] 11297 11296 11295 11294 11293 11292 11291 11290 11289 11288 11287 11286
##  [6133] 11285 11284 11283 11282 11281 11280 11279 11278 11277 11276 11275 11274
##  [6145] 11273 11272 11271 11270 11269 11268 11267 11266 11265 11264 11263 11262
##  [6157] 11261 11260 11259 11258 11257 11256 11255 11254 11253 11252 11251 11250
##  [6169] 11249 11248 11247 11246 11245 11244 11243 11242 11241 11240 11239 11238
##  [6181] 11237 11236 11235 11234 11233 11232 11231 11230 11229 11228 11227 11226
##  [6193] 11225 11224 11223 11222 11221 11220 11219 11218 11217 11216 11215 11214
##  [6205] 11213 11212 11211 11210 11209 11208 11207 11206 11205 11204 11203 11202
##  [6217] 11201 11200 11199 11198 11197 11196 11195 11194 11193 11192 11191 11190
##  [6229] 11189 11188 11187 11186 11185 11184 11183 11182 11181 11180 11179 11178
##  [6241] 11177 11176 11175 11174 11173 11172 11171 11170 11169 11168 11167 11166
##  [6253] 11165 11164 11163 11162 11161 11160 11159 11158 11157 11156 11155 11154
##  [6265] 11153 11152 11151 11150 11149 11148 11147 11146 11145 11144 11143 11142
##  [6277] 11141 11140 11139 11138 11137 11136 11135 11134 11133 11132 11131 11130
##  [6289] 11129 11128 11127 11126 11125 11124 11123 11122 11121 11120 11119 11118
##  [6301] 11117 11116 11115 11114 11113 11112 11111 11110 11109 11108 11107 11106
##  [6313] 11105 11104 11103 11102 11101 11100 11099 11098 11097 11096 11095 11094
##  [6325] 11093 11092 11091 11090 11089 11088 11087 11086 11085 11084 11083 11082
##  [6337] 11081 11080 11079 11078 11077 11076 11075 11074 11073 11072 11071 11070
##  [6349] 11069 11068 11067 11066 11065 11064 11063 11062 11061 11060 11059 11058
##  [6361] 11057 11056 11055 11054 11053 11052 11051 11050 11049 11048 11047 11046
##  [6373] 11045 11044 11043 11042 11041 11040 11039 11038 11037 11036 11035 11034
##  [6385] 11033 11032 11031 11030 11029 11028 11027 11026 11025 11024 11023 11022
##  [6397] 11021 11020 11019 11018 11017 11016 11015 11014 11013 11012 11011 11010
##  [6409] 11009 11008 11007 11006 11005 11004 11003 11002 11001 11000 10999 10998
##  [6421] 10997 10996 10995 10994 10993 10992 10991 10990 10989 10988 10987 10986
##  [6433] 10985 10984 10983 10982 10981 10980 10979 10978 10977 10976 10975 10974
##  [6445] 10973 10972 10971 10970 10969 10968 10967 10966 10965 10964 10963 10962
##  [6457] 10961 10960 10959 10958 10957 10956 10955 10954 10953 10952 10951 10950
##  [6469] 10949 10948 10947 10946 10945 10944 10943 10942 10941 10940 10939 10938
##  [6481] 10937 10936 10935 10934 10933 10932 10931 10930 10929 10928 10927 10926
##  [6493] 10925 10924 10923 10922 10921 10920 10919 10918 10917 10916 10915 10914
##  [6505] 10913 10912 10911 10910 10909 10908 10907 10906 10905 10904 10903 10902
##  [6517] 10901 10900 10899 10898 10897 10896 10895 10894 10893 10892 10891 10890
##  [6529] 10889 10888 10887 10886 10885 10884 10883 10882 10881 10880 10879 10878
##  [6541] 10877 10876 10875 10874 10873 10872 10871 10870 10869 10868 10867 10866
##  [6553] 10865 10864 10863 10862 10861 10860 10859 10858 10857 10856 10855 10854
##  [6565] 10853 10852 10851 10850 10849 10848 10847 10846 10845 10844 10843 10842
##  [6577] 10841 10840 10839 10838 10837 10836 10835 10834 10833 10832 10831 10830
##  [6589] 10829 10828 10827 10826 10825 10824 10823 10822 10821 10820 10819 10818
##  [6601] 10817 10816 10815 10814 10813 10812 10811 10810 10809 10808 10807 10806
##  [6613] 10805 10804 10803 10802 10801 10800 10799 10798 10797 10796 10795 10794
##  [6625] 10793 10792 10791 10790 10789 10788 10787 10786 10785 10784 10783 10782
##  [6637] 10781 10780 10779 10778 10777 10776 10775 10774 10773 10772 10771 10770
##  [6649] 10769 10768 10767 10766 10765 10764 10763 10762 10761 10760 10759 10758
##  [6661] 10757 10756 10755 10754 10753 10752 10751 10750 10749 10748 10747 10746
##  [6673] 10745 10744 10743 10742 10741 10740 10739 10738 10737 10736 10735 10734
##  [6685] 10733 10732 10731 10730 10729 10728 10727 10726 10725 10724 10723 10722
##  [6697] 10721 10720 10719 10718 10717 10716 10715 10714 10713 10712 10711 10710
##  [6709] 10709 10708 10707 10706 10705 10704 10703 10702 10701 10700 10699 10698
##  [6721] 10697 10696 10695 10694 10693 10692 10691 10690 10689 10688 10687 10686
##  [6733] 10685 10684 10683 10682 10681 10680 10679 10678 10677 10676 10675 10674
##  [6745] 10673 10672 10671 10670 10669 10668 10667 10666 10665 10664 10663 10662
##  [6757] 10661 10660 10659 10658 10657 10656 10655 10654 10653 10652 10651 10650
##  [6769] 10649 10648 10647 10646 10645 10644 10643 10642 10641 10640 10639 10638
##  [6781] 10637 10636 10635 10634 10633 10632 10631 10630 10629 10628 10627 10626
##  [6793] 10625 10624 10623 10622 10621 10620 10619 10618 10617 10616 10615 10614
##  [6805] 10613 10612 10611 10610 10609 10608 10607 10606 10605 10604 10603 10602
##  [6817] 10601 10600 10599 10598 10597 10596 10595 10594 10593 10592 10591 10590
##  [6829] 10589 10588 10587 10586 10585 10584 10583 10582 10581 10580 10579 10578
##  [6841] 10577 10576 10575 10574 10573 10572 10571 10570 10569 10568 10567 10566
##  [6853] 10565 10564 10563 10562 10561 10560 10559 10558 10557 10556 10555 10554
##  [6865] 10553 10552 10551 10550 10549 10548 10547 10546 10545 10544 10543 10542
##  [6877] 10541 10540 10539 10538 10537 10536 10535 10534 10533 10532 10531 10530
##  [6889] 10529 10528 10527 10526 10525 10524 10523 10522 10521 10520 10519 10518
##  [6901] 10517 10516 10515 10514 10513 10512 10511 10510 10509 10508 10507 10506
##  [6913] 10505 10504 10503 10502 10501 10500 10499 10498 10497 10496 10495 10494
##  [6925] 10493 10492 10491 10490 10489 10488 10487 10486 10485 10484 10483 10482
##  [6937] 10481 10480 10479 10478 10477 10476 10475 10474 10473 10472 10471 10470
##  [6949] 10469 10468 10467 10466 10465 10464 10463 10462 10461 10460 10459 10458
##  [6961] 10457 10456 10455 10454 10453 10452 10451 10450 10449 10448 10447 10446
##  [6973] 10445 10444 10443 10442 10441 10440 10439 10438 10437 10436 10435 10434
##  [6985] 10433 10432 10431 10430 10429 10428 10427 10426 10425 10424 10423 10422
##  [6997] 10421 10420 10419 10418 10417 10416 10415 10414 10413 10412 10411 10410
##  [7009] 10409 10408 10407 10406 10405 10404 10403 10402 10401 10400 10399 10398
##  [7021] 10397 10396 10395 10394 10393 10392 10391 10390 10389 10388 10387 10386
##  [7033] 10385 10384 10383 10382 10381 10380 10379 10378 10377 10376 10375 10374
##  [7045] 10373 10372 10371 10370 10369 10368 10367 10366 10365 10364 10363 10362
##  [7057] 10361 10360 10359 10358 10357 10356 10355 10354 10353 10352 10351 10350
##  [7069] 10349 10348 10347 10346 10345 10344 10343 10342 10341 10340 10339 10338
##  [7081] 10337 10336 10335 10334 10333 10332 10331 10330 10329 10328 10327 10326
##  [7093] 10325 10324 10323 10322 10321 10320 10319 10318 10317 10316 10315 10314
##  [7105] 10313 10312 10311 10310 10309 10308 10307 10306 10305 10304 10303 10302
##  [7117] 10301 10300 10299 10298 10297 10296 10295 10294 10293 10292 10291 10290
##  [7129] 10289 10288 10287 10286 10285 10284 10283 10282 10281 10280 10279 10278
##  [7141] 10277 10276 10275 10274 10273 10272 10271 10270 10269 10268 10267 10266
##  [7153] 10265 10264 10263 10262 10261 10260 10259 10258 10257 10256 10255 10254
##  [7165] 10253 10252 10251 10250 10249 10248 10247 10246 10245 10244 10243 10242
##  [7177] 10241 10240 10239 10238 10237 10236 10235 10234 10233 10232 10231 10230
##  [7189] 10229 10228 10227 10226 10225 10224 10223 10222 10221 10220 10219 10218
##  [7201] 10217 10216 10215 10214 10213 10212 10211 10210 10209 10208 10207 10206
##  [7213] 10205 10204 10203 10202 10201 10200 10199 10198 10197 10196 10195 10194
##  [7225] 10193 10192 10191 10190 10189 10188 10187 10186 10185 10184 10183 10182
##  [7237] 10181 10180 10179 10178 10177 10176 10175 10174 10173 10172 10171 10170
##  [7249] 10169 10168 10167 10166 10165 10164 10163 10162 10161 10160 10159 10158
##  [7261] 10157 10156 10155 10154 10153 10152 10151 10150 10149 10148 10147 10146
##  [7273] 10145 10144 10143 10142 10141 10140 10139 10138 10137 10136 10135 10134
##  [7285] 10133 10132 10131 10130 10129 10128 10127 10126 10125 10124 10123 10122
##  [7297] 10121 10120 10119 10118 10117 10116 10115 10114 10113 10112 10111 10110
##  [7309] 10109 10108 10107 10106 10105 10104 10103 10102 10101 10100 10099 10098
##  [7321] 10097 10096 10095 10094 10093 10092 10091 10090 10089 10088 10087 10086
##  [7333] 10085 10084 10083 10082 10081 10080 10079 10078 10077 10076 10075 10074
##  [7345] 10073 10072 10071 10070 10069 10068 10067 10066 10065 10064 10063 10062
##  [7357] 10061 10060 10059 10058 10057 10056 10055 10054 10053 10052 10051 10050
##  [7369] 10049 10048 10047 10046 10045 10044 10043 10042 10041 10040 10039 10038
##  [7381] 10037 10036 10035 10034 10033 10032 10031 10030 10029 10028 10027 10026
##  [7393] 10025 10024 10023 10022 10021 10020 10019 10018 10017 10016 10015 10014
##  [7405] 10013 10012 10011 10010 10009 10008 10007 10006 10005 10004 10003 10002
##  [7417] 10001 10000  9999  9998  9997  9996  9995  9994  9993  9992  9991  9990
##  [7429]  9989  9988  9987  9986  9985  9984  9983  9982  9981  9980  9979  9978
##  [7441]  9977  9976  9975  9974  9973  9972  9971  9970  9969  9968  9967  9966
##  [7453]  9965  9964  9963  9962  9961  9960  9959  9958  9957  9956  9955  9954
##  [7465]  9953  9952  9951  9950  9949  9948  9947  9946  9945  9944  9943  9942
##  [7477]  9941  9940  9939  9938  9937  9936  9935  9934  9933  9932  9931  9930
##  [7489]  9929  9928  9927  9926  9925  9924  9923  9922  9921  9920  9919  9918
##  [7501]  9917  9916  9915  9914  9913  9912  9911  9910  9909  9908  9907  9906
##  [7513]  9905  9904  9903  9902  9901  9900  9899  9898  9897  9896  9895  9894
##  [7525]  9893  9892  9891  9890  9889  9888  9887  9886  9885  9884  9883  9882
##  [7537]  9881  9880  9879  9878  9877  9876  9875  9874  9873  9872  9871  9870
##  [7549]  9869  9868  9867  9866  9865  9864  9863  9862  9861  9860  9859  9858
##  [7561]  9857  9856  9855  9854  9853  9852  9851  9850  9849  9848  9847  9846
##  [7573]  9845  9844  9843  9842  9841  9840  9839  9838  9837  9836  9835  9834
##  [7585]  9833  9832  9831  9830  9829  9828  9827  9826  9825  9824  9823  9822
##  [7597]  9821  9820  9819  9818  9817  9816  9815  9814  9813  9812  9811  9810
##  [7609]  9809  9808  9807  9806  9805  9804  9803  9802  9801  9800  9799  9798
##  [7621]  9797  9796  9795  9794  9793  9792  9791  9790  9789  9788  9787  9786
##  [7633]  9785  9784  9783  9782  9781  9780  9779  9778  9777  9776  9775  9774
##  [7645]  9773  9772  9771  9770  9769  9768  9767  9766  9765  9764  9763  9762
##  [7657]  9761  9760  9759  9758  9757  9756  9755  9754  9753  9752  9751  9750
##  [7669]  9749  9748  9747  9746  9745  9744  9743  9742  9741  9740  9739  9738
##  [7681]  9737  9736  9735  9734  9733  9732  9731  9730  9729  9728  9727  9726
##  [7693]  9725  9724  9723  9722  9721  9720  9719  9718  9717  9716  9715  9714
##  [7705]  9713  9712  9711  9710  9709  9708  9707  9706  9705  9704  9703  9702
##  [7717]  9701  9700  9699  9698  9697  9696  9695  9694  9693  9692  9691  9690
##  [7729]  9689  9688  9687  9686  9685  9684  9683  9682  9681  9680  9679  9678
##  [7741]  9677  9676  9675  9674  9673  9672  9671  9670  9669  9668  9667  9666
##  [7753]  9665  9664  9663  9662  9661  9660  9659  9658  9657  9656  9655  9654
##  [7765]  9653  9652  9651  9650  9649  9648  9647  9646  9645  9644  9643  9642
##  [7777]  9641  9640  9639  9638  9637  9636  9635  9634  9633  9632  9631  9630
##  [7789]  9629  9628  9627  9626  9625  9624  9623  9622  9621  9620  9619  9618
##  [7801]  9617  9616  9615  9614  9613  9612  9611  9610  9609  9608  9607  9606
##  [7813]  9605  9604  9603  9602  9601  9600  9599  9598  9597  9596  9595  9594
##  [7825]  9593  9592  9591  9590  9589  9588  9587  9586  9585  9584  9583  9582
##  [7837]  9581  9580  9579  9578  9577  9576  9575  9574  9573  9572  9571  9570
##  [7849]  9569  9568  9567  9566  9565  9564  9563  9562  9561  9560  9559  9558
##  [7861]  9557  9556  9555  9554  9553  9552  9551  9550  9549  9548  9547  9546
##  [7873]  9545  9544  9543  9542  9541  9540  9539  9538  9537  9536  9535  9534
##  [7885]  9533  9532  9531  9530  9529  9528  9527  9526  9525  9524  9523  9522
##  [7897]  9521  9520  9519  9518  9517  9516  9515  9514  9513  9512  9511  9510
##  [7909]  9509  9508  9507  9506  9505  9504  9503  9502  9501  9500  9499  9498
##  [7921]  9497  9496  9495  9494  9493  9492  9491  9490  9489  9488  9487  9486
##  [7933]  9485  9484  9483  9482  9481  9480  9479  9478  9477  9476  9475  9474
##  [7945]  9473  9472  9471  9470  9469  9468  9467  9466  9465  9464  9463  9462
##  [7957]  9461  9460  9459  9458  9457  9456  9455  9454  9453  9452  9451  9450
##  [7969]  9449  9448  9447  9446  9445  9444  9443  9442  9441  9440  9439  9438
##  [7981]  9437  9436  9435  9434  9433  9432  9431  9430  9429  9428  9427  9426
##  [7993]  9425  9424  9423  9422  9421  9420  9419  9418  9417  9416  9415  9414
##  [8005]  9413  9412  9411  9410  9409  9408  9407  9406  9405  9404  9403  9402
##  [8017]  9401  9400  9399  9398  9397  9396  9395  9394  9393  9392  9391  9390
##  [8029]  9389  9388  9387  9386  9385  9384  9383  9382  9381  9380  9379  9378
##  [8041]  9377  9376  9375  9374  9373  9372  9371  9370  9369  9368  9367  9366
##  [8053]  9365  9364  9363  9362  9361  9360  9359  9358  9357  9356  9355  9354
##  [8065]  9353  9352  9351  9350  9349  9348  9347  9346  9345  9344  9343  9342
##  [8077]  9341  9340  9339  9338  9337  9336  9335  9334  9333  9332  9331  9330
##  [8089]  9329  9328  9327  9326  9325  9324  9323  9322  9321  9320  9319  9318
##  [8101]  9317  9316  9315  9314  9313  9312  9311  9310  9309  9308  9307  9306
##  [8113]  9305  9304  9303  9302  9301  9300  9299  9298  9297  9296  9295  9294
##  [8125]  9293  9292  9291  9290  9289  9288  9287  9286  9285  9284  9283  9282
##  [8137]  9281  9280  9279  9278  9277  9276  9275  9274  9273  9272  9271  9270
##  [8149]  9269  9268  9267  9266  9265  9264  9263  9262  9261  9260  9259  9258
##  [8161]  9257  9256  9255  9254  9253  9252  9251  9250  9249  9248  9247  9246
##  [8173]  9245  9244  9243  9242  9241  9240  9239  9238  9237  9236  9235  9234
##  [8185]  9233  9232  9231  9230  9229  9228  9227  9226  9225  9224  9223  9222
##  [8197]  9221  9220  9219  9218  9217  9216  9215  9214  9213  9212  9211  9210
##  [8209]  9209  9208  9207  9206  9205  9204  9203  9202  9201  9200  9199  9198
##  [8221]  9197  9196  9195  9194  9193  9192  9191  9190  9189  9188  9187  9186
##  [8233]  9185  9184  9183  9182  9181  9180  9179  9178  9177  9176  9175  9174
##  [8245]  9173  9172  9171  9170  9169  9168  9167  9166  9165  9164  9163  9162
##  [8257]  9161  9160  9159  9158  9157  9156  9155  9154  9153  9152  9151  9150
##  [8269]  9149  9148  9147  9146  9145  9144  9143  9142  9141  9140  9139  9138
##  [8281]  9137  9136  9135  9134  9133  9132  9131  9130  9129  9128  9127  9126
##  [8293]  9125  9124  9123  9122  9121  9120  9119  9118  9117  9116  9115  9114
##  [8305]  9113  9112  9111  9110  9109  9108  9107  9106  9105  9104  9103  9102
##  [8317]  9101  9100  9099  9098  9097  9096  9095  9094  9093  9092  9091  9090
##  [8329]  9089  9088  9087  9086  9085  9084  9083  9082  9081  9080  9079  9078
##  [8341]  9077  9076  9075  9074  9073  9072  9071  9070  9069  9068  9067  9066
##  [8353]  9065  9064  9063  9062  9061  9060  9059  9058  9057  9056  9055  9054
##  [8365]  9053  9052  9051  9050  9049  9048  9047  9046  9045  9044  9043  9042
##  [8377]  9041  9040  9039  9038  9037  9036  9035  9034  9033  9032  9031  9030
##  [8389]  9029  9028  9027  9026  9025  9024  9023  9022  9021  9020  9019  9018
##  [8401]  9017  9016  9015  9014  9013  9012  9011  9010  9009  9008  9007  9006
##  [8413]  9005  9004  9003  9002  9001  9000  8999  8998  8997  8996  8995  8994
##  [8425]  8993  8992  8991  8990  8989  8988  8987  8986  8985  8984  8983  8982
##  [8437]  8981  8980  8979  8978  8977  8976  8975  8974  8973  8972  8971  8970
##  [8449]  8969  8968  8967  8966  8965  8964  8963  8962  8961  8960  8959  8958
##  [8461]  8957  8956  8955  8954  8953  8952  8951  8950  8949  8948  8947  8946
##  [8473]  8945  8944  8943  8942  8941  8940  8939  8938  8937  8936  8935  8934
##  [8485]  8933  8932  8931  8930  8929  8928  8927  8926  8925  8924  8923  8922
##  [8497]  8921  8920  8919  8918  8917  8916  8915  8914  8913  8912  8911  8910
##  [8509]  8909  8908  8907  8906  8905  8904  8903  8902  8901  8900  8899  8898
##  [8521]  8897  8896  8895  8894  8893  8892  8891  8890  8889  8888  8887  8886
##  [8533]  8885  8884  8883  8882  8881  8880  8879  8878  8877  8876  8875  8874
##  [8545]  8873  8872  8871  8870  8869  8868  8867  8866  8865  8864  8863  8862
##  [8557]  8861  8860  8859  8858  8857  8856  8855  8854  8853  8852  8851  8850
##  [8569]  8849  8848  8847  8846  8845  8844  8843  8842  8841  8840  8839  8838
##  [8581]  8837  8836  8835  8834  8833  8832  8831  8830  8829  8828  8827  8826
##  [8593]  8825  8824  8823  8822  8821  8820  8819  8818  8817  8816  8815  8814
##  [8605]  8813  8812  8811  8810  8809  8808  8807  8806  8805  8804  8803  8802
##  [8617]  8801  8800  8799  8798  8797  8796  8795  8794  8793  8792  8791  8790
##  [8629]  8789  8788  8787  8786  8785  8784  8783  8782  8781  8780  8779  8778
##  [8641]  8777  8776  8775  8774  8773  8772  8771  8770  8769  8768  8767  8766
##  [8653]  8765  8764  8763  8762  8761  8760  8759  8758  8757  8756  8755  8754
##  [8665]  8753  8752  8751  8750  8749  8748  8747  8746  8745  8744  8743  8742
##  [8677]  8741  8740  8739  8738  8737  8736  8735  8734  8733  8732  8731  8730
##  [8689]  8729  8728  8727  8726  8725  8724  8723  8722  8721  8720  8719  8718
##  [8701]  8717  8716  8715  8714  8713  8712  8711  8710  8709  8708  8707  8706
##  [8713]  8705  8704  8703  8702  8701  8700  8699  8698  8697  8696  8695  8694
##  [8725]  8693  8692  8691  8690  8689  8688  8687  8686  8685  8684  8683  8682
##  [8737]  8681  8680  8679  8678  8677  8676  8675  8674  8673  8672  8671  8670
##  [8749]  8669  8668  8667  8666  8665  8664  8663  8662  8661  8660  8659  8658
##  [8761]  8657  8656  8655  8654  8653  8652  8651  8650  8649  8648  8647  8646
##  [8773]  8645  8644  8643  8642  8641  8640  8639  8638  8637  8636  8635  8634
##  [8785]  8633  8632  8631  8630  8629  8628  8627  8626  8625  8624  8623  8622
##  [8797]  8621  8620  8619  8618  8617  8616  8615  8614  8613  8612  8611  8610
##  [8809]  8609  8608  8607  8606  8605  8604  8603  8602  8601  8600  8599  8598
##  [8821]  8597  8596  8595  8594  8593  8592  8591  8590  8589  8588  8587  8586
##  [8833]  8585  8584  8583  8582  8581  8580  8579  8578  8577  8576  8575  8574
##  [8845]  8573  8572  8571  8570  8569  8568  8567  8566  8565  8564  8563  8562
##  [8857]  8561  8560  8559  8558  8557  8556  8555  8554  8553  8552  8551  8550
##  [8869]  8549  8548  8547  8546  8545  8544  8543  8542  8541  8540  8539  8538
##  [8881]  8537  8536  8535  8534  8533  8532  8531  8530  8529  8528  8527  8526
##  [8893]  8525  8524  8523  8522  8521  8520  8519  8518  8517  8516  8515  8514
##  [8905]  8513  8512  8511  8510  8509  8508  8507  8506  8505  8504  8503  8502
##  [8917]  8501  8500  8499  8498  8497  8496  8495  8494  8493  8492  8491  8490
##  [8929]  8489  8488  8487  8486  8485  8484  8483  8482  8481  8480  8479  8478
##  [8941]  8477  8476  8475  8474  8473  8472  8471  8470  8469  8468  8467  8466
##  [8953]  8465  8464  8463  8462  8461  8460  8459  8458  8457  8456  8455  8454
##  [8965]  8453  8452  8451  8450  8449  8448  8447  8446  8445  8444  8443  8442
##  [8977]  8441  8440  8439  8438  8437  8436  8435  8434  8433  8432  8431  8430
##  [8989]  8429  8428  8427  8426  8425  8424  8423  8422  8421  8420  8419  8418
##  [9001]  8417  8416  8415  8414  8413  8412  8411  8410  8409  8408  8407  8406
##  [9013]  8405  8404  8403  8402  8401  8400  8399  8398  8397  8396  8395  8394
##  [9025]  8393  8392  8391  8390  8389  8388  8387  8386  8385  8384  8383  8382
##  [9037]  8381  8380  8379  8378  8377  8376  8375  8374  8373  8372  8371  8370
##  [9049]  8369  8368  8367  8366  8365  8364  8363  8362  8361  8360  8359  8358
##  [9061]  8357  8356  8355  8354  8353  8352  8351  8350  8349  8348  8347  8346
##  [9073]  8345  8344  8343  8342  8341  8340  8339  8338  8337  8336  8335  8334
##  [9085]  8333  8332  8331  8330  8329  8328  8327  8326  8325  8324  8323  8322
##  [9097]  8321  8320  8319  8318  8317  8316  8315  8314  8313  8312  8311  8310
##  [9109]  8309  8308  8307  8306  8305  8304  8303  8302  8301  8300  8299  8298
##  [9121]  8297  8296  8295  8294  8293  8292  8291  8290  8289  8288  8287  8286
##  [9133]  8285  8284  8283  8282  8281  8280  8279  8278  8277  8276  8275  8274
##  [9145]  8273  8272  8271  8270  8269  8268  8267  8266  8265  8264  8263  8262
##  [9157]  8261  8260  8259  8258  8257  8256  8255  8254  8253  8252  8251  8250
##  [9169]  8249  8248  8247  8246  8245  8244  8243  8242  8241  8240  8239  8238
##  [9181]  8237  8236  8235  8234  8233  8232  8231  8230  8229  8228  8227  8226
##  [9193]  8225  8224  8223  8222  8221  8220  8219  8218  8217  8216  8215  8214
##  [9205]  8213  8212  8211  8210  8209  8208  8207  8206  8205  8204  8203  8202
##  [9217]  8201  8200  8199  8198  8197  8196  8195  8194  8193  8192  8191  8190
##  [9229]  8189  8188  8187  8186  8185  8184  8183  8182  8181  8180  8179  8178
##  [9241]  8177  8176  8175  8174  8173  8172  8171  8170  8169  8168  8167  8166
##  [9253]  8165  8164  8163  8162  8161  8160  8159  8158  8157  8156  8155  8154
##  [9265]  8153  8152  8151  8150  8149  8148  8147  8146  8145  8144  8143  8142
##  [9277]  8141  8140  8139  8138  8137  8136  8135  8134  8133  8132  8131  8130
##  [9289]  8129  8128  8127  8126  8125  8124  8123  8122  8121  8120  8119  8118
##  [9301]  8117  8116  8115  8114  8113  8112  8111  8110  8109  8108  8107  8106
##  [9313]  8105  8104  8103  8102  8101  8100  8099  8098  8097  8096  8095  8094
##  [9325]  8093  8092  8091  8090  8089  8088  8087  8086  8085  8084  8083  8082
##  [9337]  8081  8080  8079  8078  8077  8076  8075  8074  8073  8072  8071  8070
##  [9349]  8069  8068  8067  8066  8065  8064  8063  8062  8061  8060  8059  8058
##  [9361]  8057  8056  8055  8054  8053  8052  8051  8050  8049  8048  8047  8046
##  [9373]  8045  8044  8043  8042  8041  8040  8039  8038  8037  8036  8035  8034
##  [9385]  8033  8032  8031  8030  8029  8028  8027  8026  8025  8024  8023  8022
##  [9397]  8021  8020  8019  8018  8017  8016  8015  8014  8013  8012  8011  8010
##  [9409]  8009  8008  8007  8006  8005  8004  8003  8002  8001  8000  7999  7998
##  [9421]  7997  7996  7995  7994  7993  7992  7991  7990  7989  7988  7987  7986
##  [9433]  7985  7984  7983  7982  7981  7980  7979  7978  7977  7976  7975  7974
##  [9445]  7973  7972  7971  7970  7969  7968  7967  7966  7965  7964  7963  7962
##  [9457]  7961  7960  7959  7958  7957  7956  7955  7954  7953  7952  7951  7950
##  [9469]  7949  7948  7947  7946  7945  7944  7943  7942  7941  7940  7939  7938
##  [9481]  7937  7936  7935  7934  7933  7932  7931  7930  7929  7928  7927  7926
##  [9493]  7925  7924  7923  7922  7921  7920  7919  7918  7917  7916  7915  7914
##  [9505]  7913  7912  7911  7910  7909  7908  7907  7906  7905  7904  7903  7902
##  [9517]  7901  7900  7899  7898  7897  7896  7895  7894  7893  7892  7891  7890
##  [9529]  7889  7888  7887  7886  7885  7884  7883  7882  7881  7880  7879  7878
##  [9541]  7877  7876  7875  7874  7873  7872  7871  7870  7869  7868  7867  7866
##  [9553]  7865  7864  7863  7862  7861  7860  7859  7858  7857  7856  7855  7854
##  [9565]  7853  7852  7851  7850  7849  7848  7847  7846  7845  7844  7843  7842
##  [9577]  7841  7840  7839  7838  7837  7836  7835  7834  7833  7832  7831  7830
##  [9589]  7829  7828  7827  7826  7825  7824  7823  7822  7821  7820  7819  7818
##  [9601]  7817  7816  7815  7814  7813  7812  7811  7810  7809  7808  7807  7806
##  [9613]  7805  7804  7803  7802  7801  7800  7799  7798  7797  7796  7795  7794
##  [9625]  7793  7792  7791  7790  7789  7788  7787  7786  7785  7784  7783  7782
##  [9637]  7781  7780  7779  7778  7777  7776  7775  7774  7773  7772  7771  7770
##  [9649]  7769  7768  7767  7766  7765  7764  7763  7762  7761  7760  7759  7758
##  [9661]  7757  7756  7755  7754  7753  7752  7751  7750  7749  7748  7747  7746
##  [9673]  7745  7744  7743  7742  7741  7740  7739  7738  7737  7736  7735  7734
##  [9685]  7733  7732  7731  7730  7729  7728  7727  7726  7725  7724  7723  7722
##  [9697]  7721  7720  7719  7718  7717  7716  7715  7714  7713  7712  7711  7710
##  [9709]  7709  7708  7707  7706  7705  7704  7703  7702  7701  7700  7699  7698
##  [9721]  7697  7696  7695  7694  7693  7692  7691  7690  7689  7688  7687  7686
##  [9733]  7685  7684  7683  7682  7681  7680  7679  7678  7677  7676  7675  7674
##  [9745]  7673  7672  7671  7670  7669  7668  7667  7666  7665  7664  7663  7662
##  [9757]  7661  7660  7659  7658  7657  7656  7655  7654  7653  7652  7651  7650
##  [9769]  7649  7648  7647  7646  7645  7644  7643  7642  7641  7640  7639  7638
##  [9781]  7637  7636  7635  7634  7633  7632  7631  7630  7629  7628  7627  7626
##  [9793]  7625  7624  7623  7622  7621  7620  7619  7618  7617  7616  7615  7614
##  [9805]  7613  7612  7611  7610  7609  7608  7607  7606  7605  7604  7603  7602
##  [9817]  7601  7600  7599  7598  7597  7596  7595  7594  7593  7592  7591  7590
##  [9829]  7589  7588  7587  7586  7585  7584  7583  7582  7581  7580  7579  7578
##  [9841]  7577  7576  7575  7574  7573  7572  7571  7570  7569  7568  7567  7566
##  [9853]  7565  7564  7563  7562  7561  7560  7559  7558  7557  7556  7555  7554
##  [9865]  7553  7552  7551  7550  7549  7548  7547  7546  7545  7544  7543  7542
##  [9877]  7541  7540  7539  7538  7537  7536  7535  7534  7533  7532  7531  7530
##  [9889]  7529  7528  7527  7526  7525  7524  7523  7522  7521  7520  7519  7518
##  [9901]  7517  7516  7515  7514  7513  7512  7511  7510  7509  7508  7507  7506
##  [9913]  7505  7504  7503  7502  7501  7500  7499  7498  7497  7496  7495  7494
##  [9925]  7493  7492  7491  7490  7489  7488  7487  7486  7485  7484  7483  7482
##  [9937]  7481  7480  7479  7478  7477  7476  7475  7474  7473  7472  7471  7470
##  [9949]  7469  7468  7467  7466  7465  7464  7463  7462  7461  7460  7459  7458
##  [9961]  7457  7456  7455  7454  7453  7452  7451  7450  7449  7448  7447  7446
##  [9973]  7445  7444  7443  7442  7441  7440  7439  7438  7437  7436  7435  7434
##  [9985]  7433  7432  7431  7430  7429  7428  7427  7426  7425  7424  7423  7422
##  [9997]  7421  7420  7419  7418  7417  7416  7415  7414  7413  7412  7411  7410
## [10009]  7409  7408  7407  7406  7405  7404  7403  7402  7401  7400  7399  7398
## [10021]  7397  7396  7395  7394  7393  7392  7391  7390  7389  7388  7387  7386
## [10033]  7385  7384  7383  7382  7381  7380  7379  7378  7377  7376  7375  7374
## [10045]  7373  7372  7371  7370  7369  7368  7367  7366  7365  7364  7363  7362
## [10057]  7361  7360  7359  7358  7357  7356  7355  7354  7353  7352  7351  7350
## [10069]  7349  7348  7347  7346  7345  7344  7343  7342  7341  7340  7339  7338
## [10081]  7337  7336  7335  7334  7333  7332  7331  7330  7329  7328  7327  7326
## [10093]  7325  7324  7323  7322  7321  7320  7319  7318  7317  7316  7315  7314
## [10105]  7313  7312  7311  7310  7309  7308  7307  7306  7305  7304  7303  7302
## [10117]  7301  7300  7299  7298  7297  7296  7295  7294  7293  7292  7291  7290
## [10129]  7289  7288  7287  7286  7285  7284  7283  7282  7281  7280  7279  7278
## [10141]  7277  7276  7275  7274  7273  7272  7271  7270  7269  7268  7267  7266
## [10153]  7265  7264  7263  7262  7261  7260  7259  7258  7257  7256  7255  7254
## [10165]  7253  7252  7251  7250  7249  7248  7247  7246  7245  7244  7243  7242
## [10177]  7241  7240  7239  7238  7237  7236  7235  7234  7233  7232  7231  7230
## [10189]  7229  7228  7227  7226  7225  7224  7223  7222  7221  7220  7219  7218
## [10201]  7217  7216  7215  7214  7213  7212  7211  7210  7209  7208  7207  7206
## [10213]  7205  7204  7203  7202  7201  7200  7199  7198  7197  7196  7195  7194
## [10225]  7193  7192  7191  7190  7189  7188  7187  7186  7185  7184  7183  7182
## [10237]  7181  7180  7179  7178  7177  7176  7175  7174  7173  7172  7171  7170
## [10249]  7169  7168  7167  7166  7165  7164  7163  7162  7161  7160  7159  7158
## [10261]  7157  7156  7155  7154  7153  7152  7151  7150  7149  7148  7147  7146
## [10273]  7145  7144  7143  7142  7141  7140  7139  7138  7137  7136  7135  7134
## [10285]  7133  7132  7131  7130  7129  7128  7127  7126  7125  7124  7123  7122
## [10297]  7121  7120  7119  7118  7117  7116  7115  7114  7113  7112  7111  7110
## [10309]  7109  7108  7107  7106  7105  7104  7103  7102  7101  7100  7099  7098
## [10321]  7097  7096  7095  7094  7093  7092  7091  7090  7089  7088  7087  7086
## [10333]  7085  7084  7083  7082  7081  7080  7079  7078  7077  7076  7075  7074
## [10345]  7073  7072  7071  7070  7069  7068  7067  7066  7065  7064  7063  7062
## [10357]  7061  7060  7059  7058  7057  7056  7055  7054  7053  7052  7051  7050
## [10369]  7049  7048  7047  7046  7045  7044  7043  7042  7041  7040  7039  7038
## [10381]  7037  7036  7035  7034  7033  7032  7031  7030  7029  7028  7027  7026
## [10393]  7025  7024  7023  7022  7021  7020  7019  7018  7017  7016  7015  7014
## [10405]  7013  7012  7011  7010  7009  7008  7007  7006  7005  7004  7003  7002
## [10417]  7001  7000  6999  6998  6997  6996  6995  6994  6993  6992  6991  6990
## [10429]  6989  6988  6987  6986  6985  6984  6983  6982  6981  6980  6979  6978
## [10441]  6977  6976  6975  6974  6973  6972  6971  6970  6969  6968  6967  6966
## [10453]  6965  6964  6963  6962  6961  6960  6959  6958  6957  6956  6955  6954
## [10465]  6953  6952  6951  6950  6949  6948  6947  6946  6945  6944  6943  6942
## [10477]  6941  6940  6939  6938  6937  6936  6935  6934  6933  6932  6931  6930
## [10489]  6929  6928  6927  6926  6925  6924  6923  6922  6921  6920  6919  6918
## [10501]  6917  6916  6915  6914  6913  6912  6911  6910  6909  6908  6907  6906
## [10513]  6905  6904  6903  6902  6901  6900  6899  6898  6897  6896  6895  6894
## [10525]  6893  6892  6891  6890  6889  6888  6887  6886  6885  6884  6883  6882
## [10537]  6881  6880  6879  6878  6877  6876  6875  6874  6873  6872  6871  6870
## [10549]  6869  6868  6867  6866  6865  6864  6863  6862  6861  6860  6859  6858
## [10561]  6857  6856  6855  6854  6853  6852  6851  6850  6849  6848  6847  6846
## [10573]  6845  6844  6843  6842  6841  6840  6839  6838  6837  6836  6835  6834
## [10585]  6833  6832  6831  6830  6829  6828  6827  6826  6825  6824  6823  6822
## [10597]  6821  6820  6819  6818  6817  6816  6815  6814  6813  6812  6811  6810
## [10609]  6809  6808  6807  6806  6805  6804  6803  6802  6801  6800  6799  6798
## [10621]  6797  6796  6795  6794  6793  6792  6791  6790  6789  6788  6787  6786
## [10633]  6785  6784  6783  6782  6781  6780  6779  6778  6777  6776  6775  6774
## [10645]  6773  6772  6771  6770  6769  6768  6767  6766  6765  6764  6763  6762
## [10657]  6761  6760  6759  6758  6757  6756  6755  6754  6753  6752  6751  6750
## [10669]  6749  6748  6747  6746  6745  6744  6743  6742  6741  6740  6739  6738
## [10681]  6737  6736  6735  6734  6733  6732  6731  6730  6729  6728  6727  6726
## [10693]  6725  6724  6723  6722  6721  6720  6719  6718  6717  6716  6715  6714
## [10705]  6713  6712  6711  6710  6709  6708  6707  6706  6705  6704  6703  6702
## [10717]  6701  6700  6699  6698  6697  6696  6695  6694  6693  6692  6691  6690
## [10729]  6689  6688  6687  6686  6685  6684  6683  6682  6681  6680  6679  6678
## [10741]  6677  6676  6675  6674  6673  6672  6671  6670  6669  6668  6667  6666
## [10753]  6665  6664  6663  6662  6661  6660  6659  6658  6657  6656  6655  6654
## [10765]  6653  6652  6651  6650  6649  6648  6647  6646  6645  6644  6643  6642
## [10777]  6641  6640  6639  6638  6637  6636  6635  6634  6633  6632  6631  6630
## [10789]  6629  6628  6627  6626  6625  6624  6623  6622  6621  6620  6619  6618
## [10801]  6617  6616  6615  6614  6613  6612  6611  6610  6609  6608  6607  6606
## [10813]  6605  6604  6603  6602  6601  6600  6599  6598  6597  6596  6595  6594
## [10825]  6593  6592  6591  6590  6589  6588  6587  6586  6585  6584  6583  6582
## [10837]  6581  6580  6579  6578  6577  6576  6575  6574  6573  6572  6571  6570
## [10849]  6569  6568  6567  6566  6565  6564  6563  6562  6561  6560  6559  6558
## [10861]  6557  6556  6555  6554  6553  6552  6551  6550  6549  6548  6547  6546
## [10873]  6545  6544  6543  6542  6541  6540  6539  6538  6537  6536  6535  6534
## [10885]  6533  6532  6531  6530  6529  6528  6527  6526  6525  6524  6523  6522
## [10897]  6521  6520  6519  6518  6517  6516  6515  6514  6513  6512  6511  6510
## [10909]  6509  6508  6507  6506  6505  6504  6503  6502  6501  6500  6499  6498
## [10921]  6497  6496  6495  6494  6493  6492  6491  6490  6489  6488  6487  6486
## [10933]  6485  6484  6483  6482  6481  6480  6479  6478  6477  6476  6475  6474
## [10945]  6473  6472  6471  6470  6469  6468  6467  6466  6465  6464  6463  6462
## [10957]  6461  6460  6459  6458  6457  6456  6455  6454  6453  6452  6451  6450
## [10969]  6449  6448  6447  6446  6445  6444  6443  6442  6441  6440  6439  6438
## [10981]  6437  6436  6435  6434  6433  6432  6431  6430  6429  6428  6427  6426
## [10993]  6425  6424  6423  6422  6421  6420  6419  6418  6417  6416  6415  6414
## [11005]  6413  6412  6411  6410  6409  6408  6407  6406  6405  6404  6403  6402
## [11017]  6401  6400  6399  6398  6397  6396  6395  6394  6393  6392  6391  6390
## [11029]  6389  6388  6387  6386  6385  6384  6383  6382  6381  6380  6379  6378
## [11041]  6377  6376  6375  6374  6373  6372  6371  6370  6369  6368  6367  6366
## [11053]  6365  6364  6363  6362  6361  6360  6359  6358  6357  6356  6355  6354
## [11065]  6353  6352  6351  6350  6349  6348  6347  6346  6345  6344  6343  6342
## [11077]  6341  6340  6339  6338  6337  6336  6335  6334  6333  6332  6331  6330
## [11089]  6329  6328  6327  6326  6325  6324  6323  6322  6321  6320  6319  6318
## [11101]  6317  6316  6315  6314  6313  6312  6311  6310  6309  6308  6307  6306
## [11113]  6305  6304  6303  6302  6301  6300  6299  6298  6297  6296  6295  6294
## [11125]  6293  6292  6291  6290  6289  6288  6287  6286  6285  6284  6283  6282
## [11137]  6281  6280  6279  6278  6277  6276  6275  6274  6273  6272  6271  6270
## [11149]  6269  6268  6267  6266  6265  6264  6263  6262  6261  6260  6259  6258
## [11161]  6257  6256  6255  6254  6253  6252  6251  6250  6249  6248  6247  6246
## [11173]  6245  6244  6243  6242  6241  6240  6239  6238  6237  6236  6235  6234
## [11185]  6233  6232  6231  6230  6229  6228  6227  6226  6225  6224  6223  6222
## [11197]  6221  6220  6219  6218  6217  6216  6215  6214  6213  6212  6211  6210
## [11209]  6209  6208  6207  6206  6205  6204  6203  6202  6201  6200  6199  6198
## [11221]  6197  6196  6195  6194  6193  6192  6191  6190  6189  6188  6187  6186
## [11233]  6185  6184  6183  6182  6181  6180  6179  6178  6177  6176  6175  6174
## [11245]  6173  6172  6171  6170  6169  6168  6167  6166  6165  6164  6163  6162
## [11257]  6161  6160  6159  6158  6157  6156  6155  6154  6153  6152  6151  6150
## [11269]  6149  6148  6147  6146  6145  6144  6143  6142  6141  6140  6139  6138
## [11281]  6137  6136  6135  6134  6133  6132  6131  6130  6129  6128  6127  6126
## [11293]  6125  6124  6123  6122  6121  6120  6119  6118  6117  6116  6115  6114
## [11305]  6113  6112  6111  6110  6109  6108  6107  6106  6105  6104  6103  6102
## [11317]  6101  6100  6099  6098  6097  6096  6095  6094  6093  6092  6091  6090
## [11329]  6089  6088  6087  6086  6085  6084  6083  6082  6081  6080  6079  6078
## [11341]  6077  6076  6075  6074  6073  6072  6071  6070  6069  6068  6067  6066
## [11353]  6065  6064  6063  6062  6061  6060  6059  6058  6057  6056  6055  6054
## [11365]  6053  6052  6051  6050  6049  6048  6047  6046  6045  6044  6043  6042
## [11377]  6041  6040  6039  6038  6037  6036  6035  6034  6033  6032  6031  6030
## [11389]  6029  6028  6027  6026  6025  6024  6023  6022  6021  6020  6019  6018
## [11401]  6017  6016  6015  6014  6013  6012  6011  6010  6009  6008  6007  6006
## [11413]  6005  6004  6003  6002  6001  6000  5999  5998  5997  5996  5995  5994
## [11425]  5993  5992  5991  5990  5989  5988  5987  5986  5985  5984  5983  5982
## [11437]  5981  5980  5979  5978  5977  5976  5975  5974  5973  5972  5971  5970
## [11449]  5969  5968  5967  5966  5965  5964  5963  5962  5961  5960  5959  5958
## [11461]  5957  5956  5955  5954  5953  5952  5951  5950  5949  5948  5947  5946
## [11473]  5945  5944  5943  5942  5941  5940  5939  5938  5937  5936  5935  5934
## [11485]  5933  5932  5931  5930  5929  5928  5927  5926  5925  5924  5923  5922
## [11497]  5921  5920  5919  5918  5917  5916  5915  5914  5913  5912  5911  5910
## [11509]  5909  5908  5907  5906  5905  5904  5903  5902  5901  5900  5899  5898
## [11521]  5897  5896  5895  5894  5893  5892  5891  5890  5889  5888  5887  5886
## [11533]  5885  5884  5883  5882  5881  5880  5879  5878  5877  5876  5875  5874
## [11545]  5873  5872  5871  5870  5869  5868  5867  5866  5865  5864  5863  5862
## [11557]  5861  5860  5859  5858  5857  5856  5855  5854  5853  5852  5851  5850
## [11569]  5849  5848  5847  5846  5845  5844  5843  5842  5841  5840  5839  5838
## [11581]  5837  5836  5835  5834  5833  5832  5831  5830  5829  5828  5827  5826
## [11593]  5825  5824  5823  5822  5821  5820  5819  5818  5817  5816  5815  5814
## [11605]  5813  5812  5811  5810  5809  5808  5807  5806  5805  5804  5803  5802
## [11617]  5801  5800  5799  5798  5797  5796  5795  5794  5793  5792  5791  5790
## [11629]  5789  5788  5787  5786  5785  5784  5783  5782  5781  5780  5779  5778
## [11641]  5777  5776  5775  5774  5773  5772  5771  5770  5769  5768  5767  5766
## [11653]  5765  5764  5763  5762  5761  5760  5759  5758  5757  5756  5755  5754
## [11665]  5753  5752  5751  5750  5749  5748  5747  5746  5745  5744  5743  5742
## [11677]  5741  5740  5739  5738  5737  5736  5735  5734  5733  5732  5731  5730
## [11689]  5729  5728  5727  5726  5725  5724  5723  5722  5721  5720  5719  5718
## [11701]  5717  5716  5715  5714  5713  5712  5711  5710  5709  5708  5707  5706
## [11713]  5705  5704  5703  5702  5701  5700  5699  5698  5697  5696  5695  5694
## [11725]  5693  5692  5691  5690  5689  5688  5687  5686  5685  5684  5683  5682
## [11737]  5681  5680  5679  5678  5677  5676  5675  5674  5673  5672  5671  5670
## [11749]  5669  5668  5667  5666  5665  5664  5663  5662  5661  5660  5659  5658
## [11761]  5657  5656  5655  5654  5653  5652  5651  5650  5649  5648  5647  5646
## [11773]  5645  5644  5643  5642  5641  5640  5639  5638  5637  5636  5635  5634
## [11785]  5633  5632  5631  5630  5629  5628  5627  5626  5625  5624  5623  5622
## [11797]  5621  5620  5619  5618  5617  5616  5615  5614  5613  5612  5611  5610
## [11809]  5609  5608  5607  5606  5605  5604  5603  5602  5601  5600  5599  5598
## [11821]  5597  5596  5595  5594  5593  5592  5591  5590  5589  5588  5587  5586
## [11833]  5585  5584  5583  5582  5581  5580  5579  5578  5577  5576  5575  5574
## [11845]  5573  5572  5571  5570  5569  5568  5567  5566  5565  5564  5563  5562
## [11857]  5561  5560  5559  5558  5557  5556  5555  5554  5553  5552  5551  5550
## [11869]  5549  5548  5547  5546  5545  5544  5543  5542  5541  5540  5539  5538
## [11881]  5537  5536  5535  5534  5533  5532  5531  5530  5529  5528  5527  5526
## [11893]  5525  5524  5523  5522  5521  5520  5519  5518  5517  5516  5515  5514
## [11905]  5513  5512  5511  5510  5509  5508  5507  5506  5505  5504  5503  5502
## [11917]  5501  5500  5499  5498  5497  5496  5495  5494  5493  5492  5491  5490
## [11929]  5489  5488  5487  5486  5485  5484  5483  5482  5481  5480  5479  5478
## [11941]  5477  5476  5475  5474  5473  5472  5471  5470  5469  5468  5467  5466
## [11953]  5465  5464  5463  5462  5461  5460  5459  5458  5457  5456  5455  5454
## [11965]  5453  5452  5451  5450  5449  5448  5447  5446  5445  5444  5443  5442
## [11977]  5441  5440  5439  5438  5437  5436  5435  5434  5433  5432  5431  5430
## [11989]  5429  5428  5427  5426  5425  5424  5423  5422  5421  5420  5419  5418
## [12001]  5417  5416  5415  5414  5413  5412  5411  5410  5409  5408  5407  5406
## [12013]  5405  5404  5403  5402  5401  5400  5399  5398  5397  5396  5395  5394
## [12025]  5393  5392  5391  5390  5389  5388  5387  5386  5385  5384  5383  5382
## [12037]  5381  5380  5379  5378  5377  5376  5375  5374  5373  5372  5371  5370
## [12049]  5369  5368  5367  5366  5365  5364  5363  5362  5361  5360  5359  5358
## [12061]  5357  5356  5355  5354  5353  5352  5351  5350  5349  5348  5347  5346
## [12073]  5345  5344  5343  5342  5341  5340  5339  5338  5337  5336  5335  5334
## [12085]  5333  5332  5331  5330  5329  5328  5327  5326  5325  5324  5323  5322
## [12097]  5321  5320  5319  5318  5317  5316  5315  5314  5313  5312  5311  5310
## [12109]  5309  5308  5307  5306  5305  5304  5303  5302  5301  5300  5299  5298
## [12121]  5297  5296  5295  5294  5293  5292  5291  5290  5289  5288  5287  5286
## [12133]  5285  5284  5283  5282  5281  5280  5279  5278  5277  5276  5275  5274
## [12145]  5273  5272  5271  5270  5269  5268  5267  5266  5265  5264  5263  5262
## [12157]  5261  5260  5259  5258  5257  5256  5255  5254  5253  5252  5251  5250
## [12169]  5249  5248  5247  5246  5245  5244  5243  5242  5241  5240  5239  5238
## [12181]  5237  5236  5235  5234  5233  5232  5231  5230  5229  5228  5227  5226
## [12193]  5225  5224  5223  5222  5221  5220  5219  5218  5217  5216  5215  5214
## [12205]  5213  5212  5211  5210  5209  5208  5207  5206  5205  5204  5203  5202
## [12217]  5201  5200  5199  5198  5197  5196  5195  5194  5193  5192  5191  5190
## [12229]  5189  5188  5187  5186  5185  5184  5183  5182  5181  5180  5179  5178
## [12241]  5177  5176  5175  5174  5173  5172  5171  5170  5169  5168  5167  5166
## [12253]  5165  5164  5163  5162  5161  5160  5159  5158  5157  5156  5155  5154
## [12265]  5153  5152  5151  5150  5149  5148  5147  5146  5145  5144  5143  5142
## [12277]  5141  5140  5139  5138  5137  5136  5135  5134  5133  5132  5131  5130
## [12289]  5129  5128  5127  5126  5125  5124  5123  5122  5121  5120  5119  5118
## [12301]  5117  5116  5115  5114  5113  5112  5111  5110  5109  5108  5107  5106
## [12313]  5105  5104  5103  5102  5101  5100  5099  5098  5097  5096  5095  5094
## [12325]  5093  5092  5091  5090  5089  5088  5087  5086  5085  5084  5083  5082
## [12337]  5081  5080  5079  5078  5077  5076  5075  5074  5073  5072  5071  5070
## [12349]  5069  5068  5067  5066  5065  5064  5063  5062  5061  5060  5059  5058
## [12361]  5057  5056  5055  5054  5053  5052  5051  5050  5049  5048  5047  5046
## [12373]  5045  5044  5043  5042  5041  5040  5039  5038  5037  5036  5035  5034
## [12385]  5033  5032  5031  5030  5029  5028  5027  5026  5025  5024  5023  5022
## [12397]  5021  5020  5019  5018  5017  5016  5015  5014  5013  5012  5011  5010
## [12409]  5009  5008  5007  5006  5005  5004  5003  5002  5001  5000  4999  4998
## [12421]  4997  4996  4995  4994  4993  4992  4991  4990  4989  4988  4987  4986
## [12433]  4985  4984  4983  4982  4981  4980  4979  4978  4977  4976  4975  4974
## [12445]  4973  4972  4971  4970  4969  4968  4967  4966  4965  4964  4963  4962
## [12457]  4961  4960  4959  4958  4957  4956  4955  4954  4953  4952  4951  4950
## [12469]  4949  4948  4947  4946  4945  4944  4943  4942  4941  4940  4939  4938
## [12481]  4937  4936  4935  4934  4933  4932  4931  4930  4929  4928  4927  4926
## [12493]  4925  4924  4923  4922  4921  4920  4919  4918  4917  4916  4915  4914
## [12505]  4913  4912  4911  4910  4909  4908  4907  4906  4905  4904  4903  4902
## [12517]  4901  4900  4899  4898  4897  4896  4895  4894  4893  4892  4891  4890
## [12529]  4889  4888  4887  4886  4885  4884  4883  4882  4881  4880  4879  4878
## [12541]  4877  4876  4875  4874  4873  4872  4871  4870  4869  4868  4867  4866
## [12553]  4865  4864  4863  4862  4861  4860  4859  4858  4857  4856  4855  4854
## [12565]  4853  4852  4851  4850  4849  4848  4847  4846  4845  4844  4843  4842
## [12577]  4841  4840  4839  4838  4837  4836  4835  4834  4833  4832  4831  4830
## [12589]  4829  4828  4827  4826  4825  4824  4823  4822  4821  4820  4819  4818
## [12601]  4817  4816  4815  4814  4813  4812  4811  4810  4809  4808  4807  4806
## [12613]  4805  4804  4803  4802  4801  4800  4799  4798  4797  4796  4795  4794
## [12625]  4793  4792  4791  4790  4789  4788  4787  4786  4785  4784  4783  4782
## [12637]  4781  4780  4779  4778  4777  4776  4775  4774  4773  4772  4771  4770
## [12649]  4769  4768  4767  4766  4765  4764  4763  4762  4761  4760  4759  4758
## [12661]  4757  4756  4755  4754  4753  4752  4751  4750  4749  4748  4747  4746
## [12673]  4745  4744  4743  4742  4741  4740  4739  4738  4737  4736  4735  4734
## [12685]  4733  4732  4731  4730  4729  4728  4727  4726  4725  4724  4723  4722
## [12697]  4721  4720  4719  4718  4717  4716  4715  4714  4713  4712  4711  4710
## [12709]  4709  4708  4707  4706  4705  4704  4703  4702  4701  4700  4699  4698
## [12721]  4697  4696  4695  4694  4693  4692  4691  4690  4689  4688  4687  4686
## [12733]  4685  4684  4683  4682  4681  4680  4679  4678  4677  4676  4675  4674
## [12745]  4673  4672  4671  4670  4669  4668  4667  4666  4665  4664  4663  4662
## [12757]  4661  4660  4659  4658  4657  4656  4655  4654  4653  4652  4651  4650
## [12769]  4649  4648  4647  4646  4645  4644  4643  4642  4641  4640  4639  4638
## [12781]  4637  4636  4635  4634  4633  4632  4631  4630  4629  4628  4627  4626
## [12793]  4625  4624  4623  4622  4621  4620  4619  4618  4617  4616  4615  4614
## [12805]  4613  4612  4611  4610  4609  4608  4607  4606  4605  4604  4603  4602
## [12817]  4601  4600  4599  4598  4597  4596  4595  4594  4593  4592  4591  4590
## [12829]  4589  4588  4587  4586  4585  4584  4583  4582  4581  4580  4579  4578
## [12841]  4577  4576  4575  4574  4573  4572  4571  4570  4569  4568  4567  4566
## [12853]  4565  4564  4563  4562  4561  4560  4559  4558  4557  4556  4555  4554
## [12865]  4553  4552  4551  4550  4549  4548  4547  4546  4545  4544  4543  4542
## [12877]  4541  4540  4539  4538  4537  4536  4535  4534  4533  4532  4531  4530
## [12889]  4529  4528  4527  4526  4525  4524  4523  4522  4521  4520  4519  4518
## [12901]  4517  4516  4515  4514  4513  4512  4511  4510  4509  4508  4507  4506
## [12913]  4505  4504  4503  4502  4501  4500  4499  4498  4497  4496  4495  4494
## [12925]  4493  4492  4491  4490  4489  4488  4487  4486  4485  4484  4483  4482
## [12937]  4481  4480  4479  4478  4477  4476  4475  4474  4473  4472  4471  4470
## [12949]  4469  4468  4467  4466  4465  4464  4463  4462  4461  4460  4459  4458
## [12961]  4457  4456  4455  4454  4453  4452  4451  4450  4449  4448  4447  4446
## [12973]  4445  4444  4443  4442  4441  4440  4439  4438  4437  4436  4435  4434
## [12985]  4433  4432  4431  4430  4429  4428  4427  4426  4425  4424  4423  4422
## [12997]  4421  4420  4419  4418  4417  4416  4415  4414  4413  4412  4411  4410
## [13009]  4409  4408  4407  4406  4405  4404  4403  4402  4401  4400  4399  4398
## [13021]  4397  4396  4395  4394  4393  4392  4391  4390  4389  4388  4387  4386
## [13033]  4385  4384  4383  4382  4381  4380  4379  4378  4377  4376  4375  4374
## [13045]  4373  4372  4371  4370  4369  4368  4367  4366  4365  4364  4363  4362
## [13057]  4361  4360  4359  4358  4357  4356  4355  4354  4353  4352  4351  4350
## [13069]  4349  4348  4347  4346  4345  4344  4343  4342  4341  4340  4339  4338
## [13081]  4337  4336  4335  4334  4333  4332  4331  4330  4329  4328  4327  4326
## [13093]  4325  4324  4323  4322  4321  4320  4319  4318  4317  4316  4315  4314
## [13105]  4313  4312  4311  4310  4309  4308  4307  4306  4305  4304  4303  4302
## [13117]  4301  4300  4299  4298  4297  4296  4295  4294  4293  4292  4291  4290
## [13129]  4289  4288  4287  4286  4285  4284  4283  4282  4281  4280  4279  4278
## [13141]  4277  4276  4275  4274  4273  4272  4271  4270  4269  4268  4267  4266
## [13153]  4265  4264  4263  4262  4261  4260  4259  4258  4257  4256  4255  4254
## [13165]  4253  4252  4251  4250  4249  4248  4247  4246  4245  4244  4243  4242
## [13177]  4241  4240  4239  4238  4237  4236  4235  4234  4233  4232  4231  4230
## [13189]  4229  4228  4227  4226  4225  4224  4223  4222  4221  4220  4219  4218
## [13201]  4217  4216  4215  4214  4213  4212  4211  4210  4209  4208  4207  4206
## [13213]  4205  4204  4203  4202  4201  4200  4199  4198  4197  4196  4195  4194
## [13225]  4193  4192  4191  4190  4189  4188  4187  4186  4185  4184  4183  4182
## [13237]  4181  4180  4179  4178  4177  4176  4175  4174  4173  4172  4171  4170
## [13249]  4169  4168  4167  4166  4165  4164  4163  4162  4161  4160  4159  4158
## [13261]  4157  4156  4155  4154  4153  4152  4151  4150  4149  4148  4147  4146
## [13273]  4145  4144  4143  4142  4141  4140  4139  4138  4137  4136  4135  4134
## [13285]  4133  4132  4131  4130  4129  4128  4127  4126  4125  4124  4123  4122
## [13297]  4121  4120  4119  4118  4117  4116  4115  4114  4113  4112  4111  4110
## [13309]  4109  4108  4107  4106  4105  4104  4103  4102  4101  4100  4099  4098
## [13321]  4097  4096  4095  4094  4093  4092  4091  4090  4089  4088  4087  4086
## [13333]  4085  4084  4083  4082  4081  4080  4079  4078  4077  4076  4075  4074
## [13345]  4073  4072  4071  4070  4069  4068  4067  4066  4065  4064  4063  4062
## [13357]  4061  4060  4059  4058  4057  4056  4055  4054  4053  4052  4051  4050
## [13369]  4049  4048  4047  4046  4045  4044  4043  4042  4041  4040  4039  4038
## [13381]  4037  4036  4035  4034  4033  4032  4031  4030  4029  4028  4027  4026
## [13393]  4025  4024  4023  4022  4021  4020  4019  4018  4017  4016  4015  4014
## [13405]  4013  4012  4011  4010  4009  4008  4007  4006  4005  4004  4003  4002
## [13417]  4001  4000  3999  3998  3997  3996  3995  3994  3993  3992  3991  3990
## [13429]  3989  3988  3987  3986  3985  3984  3983  3982  3981  3980  3979  3978
## [13441]  3977  3976  3975  3974  3973  3972  3971  3970  3969  3968  3967  3966
## [13453]  3965  3964  3963  3962  3961  3960  3959  3958  3957  3956  3955  3954
## [13465]  3953  3952  3951  3950  3949  3948  3947  3946  3945  3944  3943  3942
## [13477]  3941  3940  3939  3938  3937  3936  3935  3934  3933  3932  3931  3930
## [13489]  3929  3928  3927  3926  3925  3924  3923  3922  3921  3920  3919  3918
## [13501]  3917  3916  3915  3914  3913  3912  3911  3910  3909  3908  3907  3906
## [13513]  3905  3904  3903  3902  3901  3900  3899  3898  3897  3896  3895  3894
## [13525]  3893  3892  3891  3890  3889  3888  3887  3886  3885  3884  3883  3882
## [13537]  3881  3880  3879  3878  3877  3876  3875  3874  3873  3872  3871  3870
## [13549]  3869  3868  3867  3866  3865  3864  3863  3862  3861  3860  3859  3858
## [13561]  3857  3856  3855  3854  3853  3852  3851  3850  3849  3848  3847  3846
## [13573]  3845  3844  3843  3842  3841  3840  3839  3838  3837  3836  3835  3834
## [13585]  3833  3832  3831  3830  3829  3828  3827  3826  3825  3824  3823  3822
## [13597]  3821  3820  3819  3818  3817  3816  3815  3814  3813  3812  3811  3810
## [13609]  3809  3808  3807  3806  3805  3804  3803  3802  3801  3800  3799  3798
## [13621]  3797  3796  3795  3794  3793  3792  3791  3790  3789  3788  3787  3786
## [13633]  3785  3784  3783  3782  3781  3780  3779  3778  3777  3776  3775  3774
## [13645]  3773  3772  3771  3770  3769  3768  3767  3766  3765  3764  3763  3762
## [13657]  3761  3760  3759  3758  3757  3756  3755  3754  3753  3752  3751  3750
## [13669]  3749  3748  3747  3746  3745  3744  3743  3742  3741  3740  3739  3738
## [13681]  3737  3736  3735  3734  3733  3732  3731  3730  3729  3728  3727  3726
## [13693]  3725  3724  3723  3722  3721  3720  3719  3718  3717  3716  3715  3714
## [13705]  3713  3712  3711  3710  3709  3708  3707  3706  3705  3704  3703  3702
## [13717]  3701  3700  3699  3698  3697  3696  3695  3694  3693  3692  3691  3690
## [13729]  3689  3688  3687  3686  3685  3684  3683  3682  3681  3680  3679  3678
## [13741]  3677  3676  3675  3674  3673  3672  3671  3670  3669  3668  3667  3666
## [13753]  3665  3664  3663  3662  3661  3660  3659  3658  3657  3656  3655  3654
## [13765]  3653  3652  3651  3650  3649  3648  3647  3646  3645  3644  3643  3642
## [13777]  3641  3640  3639  3638  3637  3636  3635  3634  3633  3632  3631  3630
## [13789]  3629  3628  3627  3626  3625  3624  3623  3622  3621  3620  3619  3618
## [13801]  3617  3616  3615  3614  3613  3612  3611  3610  3609  3608  3607  3606
## [13813]  3605  3604  3603  3602  3601  3600  3599  3598  3597  3596  3595  3594
## [13825]  3593  3592  3591  3590  3589  3588  3587  3586  3585  3584  3583  3582
## [13837]  3581  3580  3579  3578  3577  3576  3575  3574  3573  3572  3571  3570
## [13849]  3569  3568  3567  3566  3565  3564  3563  3562  3561  3560  3559  3558
## [13861]  3557  3556  3555  3554  3553  3552  3551  3550  3549  3548  3547  3546
## [13873]  3545  3544  3543  3542  3541  3540  3539  3538  3537  3536  3535  3534
## [13885]  3533  3532  3531  3530  3529  3528  3527  3526  3525  3524  3523  3522
## [13897]  3521  3520  3519  3518  3517  3516  3515  3514  3513  3512  3511  3510
## [13909]  3509  3508  3507  3506  3505  3504  3503  3502  3501  3500  3499  3498
## [13921]  3497  3496  3495  3494  3493  3492  3491  3490  3489  3488  3487  3486
## [13933]  3485  3484  3483  3482  3481  3480  3479  3478  3477  3476  3475  3474
## [13945]  3473  3472  3471  3470  3469  3468  3467  3466  3465  3464  3463  3462
## [13957]  3461  3460  3459  3458  3457  3456  3455  3454  3453  3452  3451  3450
## [13969]  3449  3448  3447  3446  3445  3444  3443  3442  3441  3440  3439  3438
## [13981]  3437  3436  3435  3434  3433  3432  3431  3430  3429  3428  3427  3426
## [13993]  3425  3424  3423  3422  3421  3420  3419  3418  3417  3416  3415  3414
## [14005]  3413  3412  3411  3410  3409  3408  3407  3406  3405  3404  3403  3402
## [14017]  3401  3400  3399  3398  3397  3396  3395  3394  3393  3392  3391  3390
## [14029]  3389  3388  3387  3386  3385  3384  3383  3382  3381  3380  3379  3378
## [14041]  3377  3376  3375  3374  3373  3372  3371  3370  3369  3368  3367  3366
## [14053]  3365  3364  3363  3362  3361  3360  3359  3358  3357  3356  3355  3354
## [14065]  3353  3352  3351  3350  3349  3348  3347  3346  3345  3344  3343  3342
## [14077]  3341  3340  3339  3338  3337  3336  3335  3334  3333  3332  3331  3330
## [14089]  3329  3328  3327  3326  3325  3324  3323  3322  3321  3320  3319  3318
## [14101]  3317  3316  3315  3314  3313  3312  3311  3310  3309  3308  3307  3306
## [14113]  3305  3304  3303  3302  3301  3300  3299  3298  3297  3296  3295  3294
## [14125]  3293  3292  3291  3290  3289  3288  3287  3286  3285  3284  3283  3282
## [14137]  3281  3280  3279  3278  3277  3276  3275  3274  3273  3272  3271  3270
## [14149]  3269  3268  3267  3266  3265  3264  3263  3262  3261  3260  3259  3258
## [14161]  3257  3256  3255  3254  3253  3252  3251  3250  3249  3248  3247  3246
## [14173]  3245  3244  3243  3242  3241  3240  3239  3238  3237  3236  3235  3234
## [14185]  3233  3232  3231  3230  3229  3228  3227  3226  3225  3224  3223  3222
## [14197]  3221  3220  3219  3218  3217  3216  3215  3214  3213  3212  3211  3210
## [14209]  3209  3208  3207  3206  3205  3204  3203  3202  3201  3200  3199  3198
## [14221]  3197  3196  3195  3194  3193  3192  3191  3190  3189  3188  3187  3186
## [14233]  3185  3184  3183  3182  3181  3180  3179  3178  3177  3176  3175  3174
## [14245]  3173  3172  3171  3170  3169  3168  3167  3166  3165  3164  3163  3162
## [14257]  3161  3160  3159  3158  3157  3156  3155  3154  3153  3152  3151  3150
## [14269]  3149  3148  3147  3146  3145  3144  3143  3142  3141  3140  3139  3138
## [14281]  3137  3136  3135  3134  3133  3132  3131  3130  3129  3128  3127  3126
## [14293]  3125  3124  3123  3122  3121  3120  3119  3118  3117  3116  3115  3114
## [14305]  3113  3112  3111  3110  3109  3108  3107  3106  3105  3104  3103  3102
## [14317]  3101  3100  3099  3098  3097  3096  3095  3094  3093  3092  3091  3090
## [14329]  3089  3088  3087  3086  3085  3084  3083  3082  3081  3080  3079  3078
## [14341]  3077  3076  3075  3074  3073  3072  3071  3070  3069  3068  3067  3066
## [14353]  3065  3064  3063  3062  3061  3060  3059  3058  3057  3056  3055  3054
## [14365]  3053  3052  3051  3050  3049  3048  3047  3046  3045  3044  3043  3042
## [14377]  3041  3040  3039  3038  3037  3036  3035  3034  3033  3032  3031  3030
## [14389]  3029  3028  3027  3026  3025  3024  3023  3022  3021  3020  3019  3018
## [14401]  3017  3016  3015  3014  3013  3012  3011  3010  3009  3008  3007  3006
## [14413]  3005  3004  3003  3002  3001  3000  2999  2998  2997  2996  2995  2994
## [14425]  2993  2992  2991  2990  2989  2988  2987  2986  2985  2984  2983  2982
## [14437]  2981  2980  2979  2978  2977  2976  2975  2974  2973  2972  2971  2970
## [14449]  2969  2968  2967  2966  2965  2964  2963  2962  2961  2960  2959  2958
## [14461]  2957  2956  2955  2954  2953  2952  2951  2950  2949  2948  2947  2946
## [14473]  2945  2944  2943  2942  2941  2940  2939  2938  2937  2936  2935  2934
## [14485]  2933  2932  2931  2930  2929  2928  2927  2926  2925  2924  2923  2922
## [14497]  2921  2920  2919  2918  2917  2916  2915  2914  2913  2912  2911  2910
## [14509]  2909  2908  2907  2906  2905  2904  2903  2902  2901  2900  2899  2898
## [14521]  2897  2896  2895  2894  2893  2892  2891  2890  2889  2888  2887  2886
## [14533]  2885  2884  2883  2882  2881  2880  2879  2878  2877  2876  2875  2874
## [14545]  2873  2872  2871  2870  2869  2868  2867  2866  2865  2864  2863  2862
## [14557]  2861  2860  2859  2858  2857  2856  2855  2854  2853  2852  2851  2850
## [14569]  2849  2848  2847  2846  2845  2844  2843  2842  2841  2840  2839  2838
## [14581]  2837  2836  2835  2834  2833  2832  2831  2830  2829  2828  2827  2826
## [14593]  2825  2824  2823  2822  2821  2820  2819  2818  2817  2816  2815  2814
## [14605]  2813  2812  2811  2810  2809  2808  2807  2806  2805  2804  2803  2802
## [14617]  2801  2800  2799  2798  2797  2796  2795  2794  2793  2792  2791  2790
## [14629]  2789  2788  2787  2786  2785  2784  2783  2782  2781  2780  2779  2778
## [14641]  2777  2776  2775  2774  2773  2772  2771  2770  2769  2768  2767  2766
## [14653]  2765  2764  2763  2762  2761  2760  2759  2758  2757  2756  2755  2754
## [14665]  2753  2752  2751  2750  2749  2748  2747  2746  2745  2744  2743  2742
## [14677]  2741  2740  2739  2738  2737  2736  2735  2734  2733  2732  2731  2730
## [14689]  2729  2728  2727  2726  2725  2724  2723  2722  2721  2720  2719  2718
## [14701]  2717  2716  2715  2714  2713  2712  2711  2710  2709  2708  2707  2706
## [14713]  2705  2704  2703  2702  2701  2700  2699  2698  2697  2696  2695  2694
## [14725]  2693  2692  2691  2690  2689  2688  2687  2686  2685  2684  2683  2682
## [14737]  2681  2680  2679  2678  2677  2676  2675  2674  2673  2672  2671  2670
## [14749]  2669  2668  2667  2666  2665  2664  2663  2662  2661  2660  2659  2658
## [14761]  2657  2656  2655  2654  2653  2652  2651  2650  2649  2648  2647  2646
## [14773]  2645  2644  2643  2642  2641  2640  2639  2638  2637  2636  2635  2634
## [14785]  2633  2632  2631  2630  2629  2628  2627  2626  2625  2624  2623  2622
## [14797]  2621  2620  2619  2618  2617  2616  2615  2614  2613  2612  2611  2610
## [14809]  2609  2608  2607  2606  2605  2604  2603  2602  2601  2600  2599  2598
## [14821]  2597  2596  2595  2594  2593  2592  2591  2590  2589  2588  2587  2586
## [14833]  2585  2584  2583  2582  2581  2580  2579  2578  2577  2576  2575  2574
## [14845]  2573  2572  2571  2570  2569  2568  2567  2566  2565  2564  2563  2562
## [14857]  2561  2560  2559  2558  2557  2556  2555  2554  2553  2552  2551  2550
## [14869]  2549  2548  2547  2546  2545  2544  2543  2542  2541  2540  2539  2538
## [14881]  2537  2536  2535  2534  2533  2532  2531  2530  2529  2528  2527  2526
## [14893]  2525  2524  2523  2522  2521  2520  2519  2518  2517  2516  2515  2514
## [14905]  2513  2512  2511  2510  2509  2508  2507  2506  2505  2504  2503  2502
## [14917]  2501  2500  2499  2498  2497  2496  2495  2494  2493  2492  2491  2490
## [14929]  2489  2488  2487  2486  2485  2484  2483  2482  2481  2480  2479  2478
## [14941]  2477  2476  2475  2474  2473  2472  2471  2470  2469  2468  2467  2466
## [14953]  2465  2464  2463  2462  2461  2460  2459  2458  2457  2456  2455  2454
## [14965]  2453  2452  2451  2450  2449  2448  2447  2446  2445  2444  2443  2442
## [14977]  2441  2440  2439  2438  2437  2436  2435  2434  2433  2432  2431  2430
## [14989]  2429  2428  2427  2426  2425  2424  2423  2422  2421  2420  2419  2418
## [15001]  2417  2416  2415  2414  2413  2412  2411  2410  2409  2408  2407  2406
## [15013]  2405  2404  2403  2402  2401  2400  2399  2398  2397  2396  2395  2394
## [15025]  2393  2392  2391  2390  2389  2388  2387  2386  2385  2384  2383  2382
## [15037]  2381  2380  2379  2378  2377  2376  2375  2374  2373  2372  2371  2370
## [15049]  2369  2368  2367  2366  2365  2364  2363  2362  2361  2360  2359  2358
## [15061]  2357  2356  2355  2354  2353  2352  2351  2350  2349  2348  2347  2346
## [15073]  2345  2344  2343  2342  2341  2340  2339  2338  2337  2336  2335  2334
## [15085]  2333  2332  2331  2330  2329  2328  2327  2326  2325  2324  2323  2322
## [15097]  2321  2320  2319  2318  2317  2316  2315  2314  2313  2312  2311  2310
## [15109]  2309  2308  2307  2306  2305  2304  2303  2302  2301  2300  2299  2298
## [15121]  2297  2296  2295  2294  2293  2292  2291  2290  2289  2288  2287  2286
## [15133]  2285  2284  2283  2282  2281  2280  2279  2278  2277  2276  2275  2274
## [15145]  2273  2272  2271  2270  2269  2268  2267  2266  2265  2264  2263  2262
## [15157]  2261  2260  2259  2258  2257  2256  2255  2254  2253  2252  2251  2250
## [15169]  2249  2248  2247  2246  2245  2244  2243  2242  2241  2240  2239  2238
## [15181]  2237  2236  2235  2234  2233  2232  2231  2230  2229  2228  2227  2226
## [15193]  2225  2224  2223  2222  2221  2220  2219  2218  2217  2216  2215  2214
## [15205]  2213  2212  2211  2210  2209  2208  2207  2206  2205  2204  2203  2202
## [15217]  2201  2200  2199  2198  2197  2196  2195  2194  2193  2192  2191  2190
## [15229]  2189  2188  2187  2186  2185  2184  2183  2182  2181  2180  2179  2178
## [15241]  2177  2176  2175  2174  2173  2172  2171  2170  2169  2168  2167  2166
## [15253]  2165  2164  2163  2162  2161  2160  2159  2158  2157  2156  2155  2154
## [15265]  2153  2152  2151  2150  2149  2148  2147  2146  2145  2144  2143  2142
## [15277]  2141  2140  2139  2138  2137  2136  2135  2134  2133  2132  2131  2130
## [15289]  2129  2128  2127  2126  2125  2124  2123  2122  2121  2120  2119  2118
## [15301]  2117  2116  2115  2114  2113  2112  2111  2110  2109  2108  2107  2106
## [15313]  2105  2104  2103  2102  2101  2100  2099  2098  2097  2096  2095  2094
## [15325]  2093  2092  2091  2090  2089  2088  2087  2086  2085  2084  2083  2082
## [15337]  2081  2080  2079  2078  2077  2076  2075  2074  2073  2072  2071  2070
## [15349]  2069  2068  2067  2066  2065  2064  2063  2062  2061  2060  2059  2058
## [15361]  2057  2056  2055  2054  2053  2052  2051  2050  2049  2048  2047  2046
## [15373]  2045  2044  2043  2042  2041  2040  2039  2038  2037  2036  2035  2034
## [15385]  2033  2032  2031  2030  2029  2028  2027  2026  2025  2024  2023  2022
## [15397]  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010
## [15409]  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998
## [15421]  1997  1996  1995  1994  1993  1992  1991  1990  1989  1988  1987  1986
## [15433]  1985  1984  1983  1982  1981  1980  1979  1978  1977  1976  1975  1974
## [15445]  1973  1972  1971  1970  1969  1968  1967  1966  1965  1964  1963  1962
## [15457]  1961  1960  1959  1958  1957  1956  1955  1954  1953  1952  1951  1950
## [15469]  1949  1948  1947  1946  1945  1944  1943  1942  1941  1940  1939  1938
## [15481]  1937  1936  1935  1934  1933  1932  1931  1930  1929  1928  1927  1926
## [15493]  1925  1924  1923  1922  1921  1920  1919  1918  1917  1916  1915  1914
## [15505]  1913  1912  1911  1910  1909  1908  1907  1906  1905  1904  1903  1902
## [15517]  1901  1900  1899  1898  1897  1896  1895  1894  1893  1892  1891  1890
## [15529]  1889  1888  1887  1886  1885  1884  1883  1882  1881  1880  1879  1878
## [15541]  1877  1876  1875  1874  1873  1872  1871  1870  1869  1868  1867  1866
## [15553]  1865  1864  1863  1862  1861  1860  1859  1858  1857  1856  1855  1854
## [15565]  1853  1852  1851  1850  1849  1848  1847  1846  1845  1844  1843  1842
## [15577]  1841  1840  1839  1838  1837  1836  1835  1834  1833  1832  1831  1830
## [15589]  1829  1828  1827  1826  1825  1824  1823  1822  1821  1820  1819  1818
## [15601]  1817  1816  1815  1814  1813  1812  1811  1810  1809  1808  1807  1806
## [15613]  1805  1804  1803  1802  1801  1800  1799  1798  1797  1796  1795  1794
## [15625]  1793  1792  1791  1790  1789  1788  1787  1786  1785  1784  1783  1782
## [15637]  1781  1780  1779  1778  1777  1776  1775  1774  1773  1772  1771  1770
## [15649]  1769  1768  1767  1766  1765  1764  1763  1762  1761  1760  1759  1758
## [15661]  1757  1756  1755  1754  1753  1752  1751  1750  1749  1748  1747  1746
## [15673]  1745  1744  1743  1742  1741  1740  1739  1738  1737  1736  1735  1734
## [15685]  1733  1732  1731  1730  1729  1728  1727  1726  1725  1724  1723  1722
## [15697]  1721  1720  1719  1718  1717  1716  1715  1714  1713  1712  1711  1710
## [15709]  1709  1708  1707  1706  1705  1704  1703  1702  1701  1700  1699  1698
## [15721]  1697  1696  1695  1694  1693  1692  1691  1690  1689  1688  1687  1686
## [15733]  1685  1684  1683  1682  1681  1680  1679  1678  1677  1676  1675  1674
## [15745]  1673  1672  1671  1670  1669  1668  1667  1666  1665  1664  1663  1662
## [15757]  1661  1660  1659  1658  1657  1656  1655  1654  1653  1652  1651  1650
## [15769]  1649  1648  1647  1646  1645  1644  1643  1642  1641  1640  1639  1638
## [15781]  1637  1636  1635  1634  1633  1632  1631  1630  1629  1628  1627  1626
## [15793]  1625  1624  1623  1622  1621  1620  1619  1618  1617  1616  1615  1614
## [15805]  1613  1612  1611  1610  1609  1608  1607  1606  1605  1604  1603  1602
## [15817]  1601  1600  1599  1598  1597  1596  1595  1594  1593  1592  1591  1590
## [15829]  1589  1588  1587  1586  1585  1584  1583  1582  1581  1580  1579  1578
## [15841]  1577  1576  1575  1574  1573  1572  1571  1570  1569  1568  1567  1566
## [15853]  1565  1564  1563  1562  1561  1560  1559  1558  1557  1556  1555  1554
## [15865]  1553  1552  1551  1550  1549  1548  1547  1546  1545  1544  1543  1542
## [15877]  1541  1540  1539  1538  1537  1536  1535  1534  1533  1532  1531  1530
## [15889]  1529  1528  1527  1526  1525  1524  1523  1522  1521  1520  1519  1518
## [15901]  1517  1516  1515  1514  1513  1512  1511  1510  1509  1508  1507  1506
## [15913]  1505  1504  1503  1502  1501  1500  1499  1498  1497  1496  1495  1494
## [15925]  1493  1492  1491  1490  1489  1488  1487  1486  1485  1484  1483  1482
## [15937]  1481  1480  1479  1478  1477  1476  1475  1474  1473  1472  1471  1470
## [15949]  1469  1468  1467  1466  1465  1464  1463  1462  1461  1460  1459  1458
## [15961]  1457  1456  1455  1454  1453  1452  1451  1450  1449  1448  1447  1446
## [15973]  1445  1444  1443  1442  1441  1440  1439  1438  1437  1436  1435  1434
## [15985]  1433  1432  1431  1430  1429  1428  1427  1426  1425  1424  1423  1422
## [15997]  1421  1420  1419  1418  1417  1416  1415  1414  1413  1412  1411  1410
## [16009]  1409  1408  1407  1406  1405  1404  1403  1402  1401  1400  1399  1398
## [16021]  1397  1396  1395  1394  1393  1392  1391  1390  1389  1388  1387  1386
## [16033]  1385  1384  1383  1382  1381  1380  1379  1378  1377  1376  1375  1374
## [16045]  1373  1372  1371  1370  1369  1368  1367  1366  1365  1364  1363  1362
## [16057]  1361  1360  1359  1358  1357  1356  1355  1354  1353  1352  1351  1350
## [16069]  1349  1348  1347  1346  1345  1344  1343  1342  1341  1340  1339  1338
## [16081]  1337  1336  1335  1334  1333  1332  1331  1330  1329  1328  1327  1326
## [16093]  1325  1324  1323  1322  1321  1320  1319  1318  1317  1316  1315  1314
## [16105]  1313  1312  1311  1310  1309  1308  1307  1306  1305  1304  1303  1302
## [16117]  1301  1300  1299  1298  1297  1296  1295  1294  1293  1292  1291  1290
## [16129]  1289  1288  1287  1286  1285  1284  1283  1282  1281  1280  1279  1278
## [16141]  1277  1276  1275  1274  1273  1272  1271  1270  1269  1268  1267  1266
## [16153]  1265  1264  1263  1262  1261  1260  1259  1258  1257  1256  1255  1254
## [16165]  1253  1252  1251  1250  1249  1248  1247  1246  1245  1244  1243  1242
## [16177]  1241  1240  1239  1238  1237  1236  1235  1234  1233  1232  1231  1230
## [16189]  1229  1228  1227  1226  1225  1224  1223  1222  1221  1220  1219  1218
## [16201]  1217  1216  1215  1214  1213  1212  1211  1210  1209  1208  1207  1206
## [16213]  1205  1204  1203  1202  1201  1200  1199  1198  1197  1196  1195  1194
## [16225]  1193  1192  1191  1190  1189  1188  1187  1186  1185  1184  1183  1182
## [16237]  1181  1180  1179  1178  1177  1176  1175  1174  1173  1172  1171  1170
## [16249]  1169  1168  1167  1166  1165  1164  1163  1162  1161  1160  1159  1158
## [16261]  1157  1156  1155  1154  1153  1152  1151  1150  1149  1148  1147  1146
## [16273]  1145  1144  1143  1142  1141  1140  1139  1138  1137  1136  1135  1134
## [16285]  1133  1132  1131  1130  1129  1128  1127  1126  1125  1124  1123  1122
## [16297]  1121  1120  1119  1118  1117  1116  1115  1114  1113  1112  1111  1110
## [16309]  1109  1108  1107  1106  1105  1104  1103  1102  1101  1100  1099  1098
## [16321]  1097  1096  1095  1094  1093  1092  1091  1090  1089  1088  1087  1086
## [16333]  1085  1084  1083  1082  1081  1080  1079  1078  1077  1076  1075  1074
## [16345]  1073  1072  1071  1070  1069  1068  1067  1066  1065  1064  1063  1062
## [16357]  1061  1060  1059  1058  1057  1056  1055  1054  1053  1052  1051  1050
## [16369]  1049  1048  1047  1046  1045  1044  1043  1042  1041  1040  1039  1038
## [16381]  1037  1036  1035  1034  1033  1032  1031  1030  1029  1028  1027  1026
## [16393]  1025  1024  1023  1022  1021  1020  1019  1018  1017  1016  1015  1014
## [16405]  1013  1012  1011  1010  1009  1008  1007  1006  1005  1004  1003  1002
## [16417]  1001  1000   999   998   997   996   995   994   993   992   991   990
## [16429]   989   988   987   986   985   984   983   982   981   980   979   978
## [16441]   977   976   975   974   973   972   971   970   969   968   967   966
## [16453]   965   964   963   962   961   960   959   958   957   956   955   954
## [16465]   953   952   951   950   949   948   947   946   945   944   943   942
## [16477]   941   940   939   938   937   936   935   934   933   932   931   930
## [16489]   929   928   927   926   925   924   923   922   921   920   919   918
## [16501]   917   916   915   914   913   912   911   910   909   908   907   906
## [16513]   905   904   903   902   901   900   899   898   897   896   895   894
## [16525]   893   892   891   890   889   888   887   886   885   884   883   882
## [16537]   881   880   879   878   877   876   875   874   873   872   871   870
## [16549]   869   868   867   866   865   864   863   862   861   860   859   858
## [16561]   857   856   855   854   853   852   851   850   849   848   847   846
## [16573]   845   844   843   842   841   840   839   838   837   836   835   834
## [16585]   833   832   831   830   829   828   827   826   825   824   823   822
## [16597]   821   820   819   818   817   816   815   814   813   812   811   810
## [16609]   809   808   807   806   805   804   803   802   801   800   799   798
## [16621]   797   796   795   794   793   792   791   790   789   788   787   786
## [16633]   785   784   783   782   781   780   779   778   777   776   775   774
## [16645]   773   772   771   770   769   768   767   766   765   764   763   762
## [16657]   761   760   759   758   757   756   755   754   753   752   751   750
## [16669]   749   748   747   746   745   744   743   742   741   740   739   738
## [16681]   737   736   735   734   733   732   731   730   729   728   727   726
## [16693]   725   724   723   722   721   720   719   718   717   716   715   714
## [16705]   713   712   711   710   709   708   707   706   705   704   703   702
## [16717]   701   700   699   698   697   696   695   694   693   692   691   690
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## 
## $csize
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##  [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
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##  [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
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##  [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
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##  [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
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##  [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
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##  [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
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##  [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
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## [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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12205] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12241] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12277] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12313] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12349] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12385] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12421] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12457] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12493] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12529] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12565] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12601] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12637] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12673] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12709] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12745] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12781] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12817] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12853] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12925] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12961] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [12997] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13033] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13069] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13105] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13141] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13177] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13213] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13249] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13285] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13321] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13357] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13393] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13429] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13465] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13501] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13537] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13573] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13609] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13645] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13681] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13717] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13753] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13789] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13825] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13861] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13897] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13933] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [13969] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14005] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14041] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14077] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14113] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14257] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14293] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14329] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14365] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14401] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14437] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14473] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14509] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14545] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14581] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14617] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14653] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14689] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14725] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14761] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14797] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14833] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14869] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14905] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14941] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [14977] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15013] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15049] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15085] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15121] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15157] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15193] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15229] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15265] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15301] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15337] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15373] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15409] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15553] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15589] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15625] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15661] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15697] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15733] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15769] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15805] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15841] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15877] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15913] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15949] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [15985] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16021] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16057] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16093] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16129] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16165] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16201] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16237] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16273] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16309] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16345] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16381] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16417] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16453] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16489] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16525] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16561] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16597] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16633] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16669] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16705] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16813] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16885] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16921] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16957] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [16993] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17029] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17065] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17101] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17137] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17173] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17209] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17245] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17281] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17317] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17353] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17389] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17425] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17461] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [17497] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 
## $no
## [1] 17518

laser_net_dir1 <- direct_network |>
  activate(nodes) |>
  mutate(strong_component = group_components(type = "strong"))
laser_net_dir1

## # A tbl_graph: 17518 nodes and 32157 edges
## #
## # A directed acyclic simple graph with 1 component
## #
## # Node Data: 17,518 × 2 (active)
##   V          strong_component
##   <chr>                 <int>
## 1 427940768             17517
## 2 403419745             17506
## 3 4352612794            17505
## 4 422743098             17500
## 5 3161354381            17499
## 6 34733487              17498
## # … with 17,512 more rows
## #
## # Edge Data: 32,157 × 2
##    from    to
##   <int> <int>
## 1     1 17418
## 2     2 17418
## 3     3 17418
## # … with 32,154 more rows

laser_net_dir1 |>
  as_tibble() |>
  group_by(strong_component) |>
  summarise(count = n()) |>
  arrange(desc(count))

## # A tibble: 17,518 × 2
##    strong_component count
##               <int> <int>
##  1                1     1
##  2                2     1
##  3                3     1
##  4                4     1
##  5                5     1
##  6                6     1
##  7                7     1
##  8                8     1
##  9                9     1
## 10               10     1
## # … with 17,508 more rows

3b. Measure betweenness centrality

We will use centrality_degree() for calculating degree, in-degree, and out-degree for all actors in a network.

direct_network <- direct_network |>
  activate(nodes) |>
  mutate(in_degree = centrality_degree(mode = "in"),
         out_degree = centrality_degree(mode = "out"))
  
direct_network |> 
  as_tibble()

## # A tibble: 17,518 × 3
##    V                   in_degree out_degree
##    <chr>                   <dbl>      <dbl>
##  1 427940768                   0          1
##  2 403419745                   0         11
##  3 4352612794                  0          1
##  4 422743098                   0          8
##  5 3161354381                  0          3
##  6 34733487                    0          3
##  7 859809032739205121          0         15
##  8 1058355281812439040         0          4
##  9 1293184903215898631         0          6
## 10 1007434757167345665         0          2
## # … with 17,508 more rows

We can also look at the distribution of the centrality deree.

direct_network |>
  as_tibble() |>
  ggplot() +
  geom_histogram(aes(x = out_degree,), bins = 30)

4 Model

4a.

Mutate the and recalculate centrality, closeness, betweeness and eigen.

set.seed(713)
laser_network_ego2 <- laser_network_ego %>% 
  activate(nodes) %>% 
  mutate(community = as.factor(group_louvain())) %>%
  mutate(degree_c = centrality_degree()) %>%
  mutate(betweenness_c = centrality_betweenness(directed = F,normalized = T)) %>%
  mutate(closeness_c = centrality_closeness(normalized = T)) %>%
  mutate(eigen = centrality_eigen(directed = F))

Let’s look at the top six followers.

laser_keyego <- data.frame(
  laser_network_ego2 %>% arrange(-degree_c) %>% select(name) %>% slice(1:6),
  laser_network_ego2 %>% arrange(-betweenness_c) %>% select(name) %>% slice(1:6),
  laser_network_ego2 %>% arrange(-closeness_c) %>% select(name) %>% slice(1:6),
  laser_network_ego2 %>% arrange(-eigen) %>% select(name) %>% slice(1:6)
) %>% 
  setNames(c("degree","betweenness","closeness","eigen"))
laser_keyego[-1,]

##           degree         betweenness           closeness          eigen
## 2        caroyce 1391035578381127691 1391035578381127691        DrTeyaR
## 3 AimeeHollander           edtechdev           edtechdev   juliahuprich
## 4   juliahuprich             caroyce             caroyce   carlton_fong
## 5        DrTeyaR      AimeeHollander      AimeeHollander        czpuede
## 6     Tina_Cheuk          Tina_Cheuk        juliahuprich PaulineMuljana

4b. Model Centrality

Before we can visualize centrality we need to create a new graph with our un-directed network. Since the network is large we will reduce it with degree centrality over 20, betweeness centrality over .01 and Eigen over .15

library(ggrepel)

set.seed(334)

options(ggrepel.max.overlaps = Inf)
network_viz3 <- laser_network_ego2%>%
  filter(community %in% 1:3) %>%
  dplyr::mutate(node_size = ifelse(degree_c >= 20,degree_c,0)) %>%
  dplyr::mutate(node_label = ifelse(betweenness_c >= 0.003,name,NA)) %>%
  filter(eigen>.15)


network_viz3

## # A tbl_graph: 93 nodes and 665 edges
## #
## # An undirected simple graph with 1 component
## #
## # Node Data: 93 × 8 (active)
##   name   community degree_c betweenness_c closeness_c eigen node_size node_label
##   <chr>  <fct>        <dbl>         <dbl>       <dbl> <dbl>     <dbl> <chr>     
## 1 85980… 1               15       0.00139       0.294 0.162         0 <NA>      
## 2 97188… 2               30       0.00296       0.304 0.243        30 <NA>      
## 3 11530… 1               36       0.00460       0.319 0.336        36 115303528…
## 4 76573… 2               28       0.00313       0.307 0.232        28 765730657…
## 5 30791… 1               23       0.00469       0.309 0.194        23 3079182816
## 6 71158… 2               21       0.00168       0.298 0.187        21 <NA>      
## # … with 87 more rows
## #
## # Edge Data: 665 × 2
##    from    to
##   <int> <int>
## 1     1    56
## 2     2    56
## 3     3    56
## # … with 662 more rows

Now, let’s visualize the the centrality index that calculates the centrality of an actor based not only on their connections, but also based on the centrality of that actor’s connections. Looking at the individuals with a higher centrality degree so that our graph is readable

library(ggraph)
set.seed(334)
ggraph(network_viz3, layout = "lgl") +
  geom_edge_link0(aes(edge_alpha = betweenness), edge_color = "grey66", alpha = 0.2) +
  scale_edge_width_continuous(range = c(0.2, 10)) +
  geom_node_point(aes(size = node_size, color = eigen)) +
  scale_color_gradient(low = "lightblue", high = "red") +
  theme_void()

4c. Top three communities

Finally, let’s visualize the top three communities that the individuals are in and see if there is any overlap. We will scale the nodes by degree centrality, and color it by community. We should see Laser Institute in the middle acting as a bridge to connect the clusters. We do see the individuals with the highest centrality and the nodes behind nodes behind them are their mutual friends who don’t follow Laser Institute account .

set.seed(334)

options(ggrepel.max.overlaps = Inf)
plot_ego <- laser_network_ego2 %>%
  filter(community %in% 1:3) %>%
  top_n(1000,degree_c) %>%
  mutate(node_size = ifelse(degree_c >= 25,degree_c,0)) %>%
  mutate(node_label = ifelse(betweenness_c >= 0.03,name,""))%>%
  ggraph(layout = "stress") +
  geom_edge_fan(alpha = 0.05) +
  geom_node_point(aes(color = as.factor(community),size = node_size)) +
  geom_node_label(aes(label = node_label),repel = T,
                 show.legend = F, family = "serif", label.size = .05,
                 segment.colour="slateblue", fill = "#ffffff66") +
  geom_node_text(aes(filter = betweenness_c >= 0.03, label = name), family = "serif") +
  coord_fixed() +
  theme_graph() + theme(legend.position = "none") +
  labs(title = "Laser Institute Mutual Communities",
       subtitle = "Top 3 Community")
plot_ego

5 Communicate

For this analysis we looked at the Laser Institute Twitter account to understand what the ego network looks like for that account.

Actors in the network were categorized into distinct mutually exclusive groups using the core-periphery and regular equivalence functions. The top two actors have the highest betweeness and closeness. They are both followers of Laser Institute.

In the centrality graph, we need to understand that a person with few connections could have a very high eigenvector centrality if those few connections were to very well-connected others. That connection to some vertices has more benefits than connecting to others. Moreover, the eigenvector shows the individual’s importance as more vertices than other nodes connect them. The second visualization should show Laser Institute acting as a bridge to the clusters in the center. Not showing that it has a high closeness would warrant a closer look. If Laser Institute wants to get information out, they should get it out to the top individuals with the most increased closeness and high eigenvector. When looking at the visualization, we can see that the community most valuable to Laser Institute to spread information and news widely and fast would be the red community.

A case study like this would be valuable for organizations looking to increase awareness about new products, events, or other important business that would increase exposure. This study would be most beneficial for social media accounts like Instagram, Twitter, and Facebook.

References: Christian, J. (2020, June, 1). Social Network Analysis in R part 1: Ego Network [BLOG] Medium. https://medium.com/analytics-vidhya/social-network-analysis-in-r-part-1-ego-network-ab6b0d23ebc8 Kellogg, S. (2022, Feb.21). Unit 3: Components, Cliques, & Key Actors. [Assignment] https://rpubs.com/jmmcclu3/869088 McNulty, K. (2022). Handbook of Graphs and Networks in People Analytics: With Examples in R and Python. CRC Press. Schoch,D.(2022).Network Visualizations in R using ggraph and graphlayouts. David Schoch https://mr.schochastics.net/material/netvizr/