1. Association Rules on Cosmetics data

Data Set name : Cosmetics.xlsx Step 1: Download the data on cosmetics purchases (Cosmetics.xls) from below link website http://dataminingbook.com/.

Step 2: Using XLMiner, apply association rules to these data.

Step 3: Order the rules based on Lift Ratio, highest to lowest.

1.1. Association Rules Execution through XLMiner

Steps to follow in XLMiner

Step 1:

Select XLminer -> Associate -> Association Rules

Step 2:

In Association Rules box select the worksheet where the cosmetics data present and check the box “Data in binary matrix foramt” in Input Data Foramt. In parameters box by default the “Minimum support” will be 20% of the total transctions. Here the total number of trasnctions are 1000 and hence the minimum support is 200. Minimum Confidence should be given in input. Here the input value is 40%. Generally the acceptable confidence level is more than 50%.

Step 3:

The below are the input details.

Step 4:

List of Rules in Sorted order of Lift Ratio.

Steps to follow in R

#Specify the libraries required
library("xlsx")
library("Matrix")
library("arules")
#library("arulesViz")

#Set working directory 
setwd("J:\\ISB Business Analytics\\Data Mining\\Data Mining Assignment 2")

#Read the data
mydata<-read.xlsx("Cosmetics.xls", sheetName = "Sheet1")
#first records of data 
head(mydata)
##   Trans.. Bag Blush Nail.Polish Brushes Concealer Eyebrow.Pencils Bronzer
## 1       1   0     1           1       1         1               0       1
## 2       2   0     0           1       0         1               0       1
## 3       3   0     1           0       0         1               1       1
## 4       4   0     0           1       1         1               0       1
## 5       5   0     1           0       0         1               0       1
## 6       6   0     0           0       0         1               0       0
##   Lip.liner Mascara Eye.shadow Foundation Lip.Gloss Lipstick Eyeliner
## 1         1       1          0          0         0        0        1
## 2         1       0          0          1         1        0        0
## 3         1       1          1          1         1        1        0
## 4         0       0          0          1         0        0        1
## 5         1       1          1          0         1        1        0
## 6         0       0          0          0         0        0        1
#trailer records of data
tail(mydata)
##      Trans.. Bag Blush Nail.Polish Brushes Concealer Eyebrow.Pencils
## 995      995   0     1           0       0         0               0
## 996      996   0     0           0       0         0               0
## 997      997   0     0           0       0         0               0
## 998      998   0     1           1       1         1               0
## 999      999   1     1           0       0         1               0
## 1000    1000   0     0           0       0         1               0
##      Bronzer Lip.liner Mascara Eye.shadow Foundation Lip.Gloss Lipstick
## 995        0         0       1          1          1         1        0
## 996        0         0       0          0          0         0        0
## 997        0         0       0          0          1         1        0
## 998        0         1       0          0          1         0        1
## 999        0         0       1          1          0         0        1
## 1000       1         1       0          1          0         0        0
##      Eyeliner
## 995         0
## 996         0
## 997         0
## 998         1
## 999         1
## 1000        1
#Number of rows in the data set
nrow(mydata)
## [1] 1000
#Number of columns in the data set
ncol(mydata)
## [1] 15
#Summary
summary(mydata)
##     Trans..            Bag            Blush        Nail.Polish  
##  Min.   :   1.0   Min.   :0.000   Min.   :0.000   Min.   :0.00  
##  1st Qu.: 250.8   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.00  
##  Median : 500.5   Median :0.000   Median :0.000   Median :0.00  
##  Mean   : 500.5   Mean   :0.054   Mean   :0.363   Mean   :0.28  
##  3rd Qu.: 750.2   3rd Qu.:0.000   3rd Qu.:1.000   3rd Qu.:1.00  
##  Max.   :1000.0   Max.   :1.000   Max.   :1.000   Max.   :1.00  
##     Brushes        Concealer     Eyebrow.Pencils    Bronzer     
##  Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.000  
##  1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000  
##  Median :0.000   Median :0.000   Median :0.000   Median :0.000  
##  Mean   :0.149   Mean   :0.442   Mean   :0.042   Mean   :0.279  
##  3rd Qu.:0.000   3rd Qu.:1.000   3rd Qu.:0.000   3rd Qu.:1.000  
##  Max.   :1.000   Max.   :1.000   Max.   :1.000   Max.   :1.000  
##    Lip.liner        Mascara        Eye.shadow      Foundation   
##  Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.000  
##  1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000  
##  Median :0.000   Median :0.000   Median :0.000   Median :1.000  
##  Mean   :0.234   Mean   :0.357   Mean   :0.381   Mean   :0.536  
##  3rd Qu.:0.000   3rd Qu.:1.000   3rd Qu.:1.000   3rd Qu.:1.000  
##  Max.   :1.000   Max.   :1.000   Max.   :1.000   Max.   :1.000  
##    Lip.Gloss       Lipstick        Eyeliner    
##  Min.   :0.00   Min.   :0.000   Min.   :0.000  
##  1st Qu.:0.00   1st Qu.:0.000   1st Qu.:0.000  
##  Median :0.00   Median :0.000   Median :0.000  
##  Mean   :0.49   Mean   :0.322   Mean   :0.457  
##  3rd Qu.:1.00   3rd Qu.:1.000   3rd Qu.:1.000  
##  Max.   :1.00   Max.   :1.000   Max.   :1.000
# Apriori application
# Support will indicate the percentage of transctions, Here it's 20% and confidence is 40% 
rules = apriori(as.matrix(mydata[,2:15]), parameter=list(support=0.1, confidence=0.80,minlen=2))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport support minlen maxlen
##         0.8    0.1    1 none FALSE            TRUE     0.1      2     10
##  target   ext
##   rules FALSE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 100 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[14 item(s), 1000 transaction(s)] done [0.00s].
## sorting and recoding items ... [12 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [26 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
rules
## set of 26 rules
# Output of Apriori with first 15 rules 
rules15 <- inspect(head(sort(rules, by="lift"),15))
##    lhs                                rhs           support confidence
## 1  {Brushes}                       => {Nail.Polish} 0.149   1.0000000 
## 23 {Blush,Concealer,Eye.shadow}    => {Mascara}     0.119   0.9596774 
## 15 {Blush,Eye.shadow}              => {Mascara}     0.169   0.9285714 
## 10 {Nail.Polish,Eye.shadow}        => {Mascara}     0.119   0.9083969 
## 20 {Concealer,Eye.shadow}          => {Mascara}     0.179   0.8905473 
## 12 {Bronzer,Eye.shadow}            => {Mascara}     0.124   0.8794326 
## 25 {Concealer,Eye.shadow,Eyeliner} => {Mascara}     0.114   0.8769231 
## 14 {Blush,Mascara}                 => {Eye.shadow}  0.169   0.9184783 
## 8  {Eye.shadow,Lipstick}           => {Mascara}     0.110   0.8527132 
## 7  {Mascara,Lipstick}              => {Eye.shadow}  0.110   0.9090909 
## 22 {Blush,Concealer,Mascara}       => {Eye.shadow}  0.119   0.9083969 
## 11 {Bronzer,Mascara}               => {Eye.shadow}  0.124   0.9051095 
## 2  {Mascara}                       => {Eye.shadow}  0.321   0.8991597 
## 3  {Eye.shadow}                    => {Mascara}     0.321   0.8425197 
## 9  {Nail.Polish,Mascara}           => {Eye.shadow}  0.119   0.8880597 
##    lift    
## 1  3.571429
## 23 2.688172
## 15 2.601040
## 10 2.544529
## 20 2.494530
## 12 2.463397
## 25 2.456367
## 14 2.410704
## 8  2.388552
## 7  2.386065
## 22 2.384244
## 11 2.375615
## 2  2.359999
## 3  2.359999
## 9  2.330865

a) Please include (copy-paste) the XLMiner (or whichever software that you are using) output ??? first fifteen rules along with header and input details ??? in your submission.

In the above section all the oupt details are included.

b) For the first row, explain the “Support(a)”, “Support(c)”, and “Support (aUc)” output and how it is calculated.

The first row of the rules output.

inspect(head(sort(rules, by="lift"),1))
##   lhs          rhs           support confidence lift    
## 1 {Brushes} => {Nail.Polish} 0.149   1          3.571429

Each product count which is support of the respective product.

colSums(mydata[,-1])
##             Bag           Blush     Nail.Polish         Brushes 
##              54             363             280             149 
##       Concealer Eyebrow.Pencils         Bronzer       Lip.liner 
##             442              42             279             234 
##         Mascara      Eye.shadow      Foundation       Lip.Gloss 
##             357             381             536             490 
##        Lipstick        Eyeliner 
##             322             457

Union count which is support of both the products together if the sum is 2.

BrushesNail.Polish <- mydata$Brushes + mydata$Nail.Polish

as.data.frame(table(BrushesNail.Polish))
##   BrushesNail.Polish Freq
## 1                  0  720
## 2                  1  131
## 3                  2  149

Calculation and Explanation :

Support(Brushes/Antecedent) = (Total Number of transactions for Brushes / Total Number of transactions)100 = (149/1000)100 = 0.149*100 = 14.9%

Support(Nail.Polish/Consequent) = (Total Number of transactions for Nail.Polish / Total Number of transactions)100 = (280/1000)100 = 0.280*100 = 28.0%

Support(Brushes U Nail.Polish / Antecedent U Consequent)
= (Total number of transactions both Brushes and Nail.Polish together / Total Number of transactions)100 = (149/1000)100 = 14.9%

From above, 14.9% of transactions involve purchase of Brushes, 28.0% of transactions involve purchase of Nail.Polish and 14.9% of transactions involve both Mascara and Eye.shadow purchases.                      

c) For the first row, explain the “Conf. %” output and how it is calculated.

For first row of the rules output the confidence % is 1 = 100%

Confidence(Brushes, Nail.Polish) = P(Nail.Polish/Brushes) = P(Brushes & Nail.Polish) / P(Brushes) = 0.149 / 0.149 = 1 = 100 %

  Out of 149 customers who purchase Brushes, 149 bought Nail.Polish. It can be infered that if a customer buys
  Brushes then there is 100 % chance that the same customer buys Nail.Polish also.

d) For the first row, explain the “Lift Ratio” and how it is calculated.

For first row of the rules output the Lift ratio is 3.571429.

The lift ratio is given by:

Lift Ratio = Confidence / Benchmark Confidence

Benchmark Confidence is given by assuming the independence between Antecedent and Consequent.

Benchmark COnfidence = P(Nail.Polish/Brushes) = P(Brushes & Nail.Polish) / P(Brushes) = P(Brushes)*P(Nail.Polish) / P(Brushes) = P(Nail.Polish) = Number of purchases of Nail.Polish / Total Number of Purchases = 280/1000 = 0.28

Lift Ratio = 1/0.28 = 3.5714

  The lift ratio is greater than 1, Hence pruschase of Brushes have increased probability to buy  Nail.Polish along with Brushes.
  

e) Reviewing the first fifteen rules, comment on their redundancy (read as, has same item set). How many unique rules did you find from the first 15 rules ?

The 15 rules are as given below.

# first 15 rules
rules15
##                                lhs              rhs support confidence
## 1                        {Brushes} => {Nail.Polish}   0.149  1.0000000
## 23    {Blush,Concealer,Eye.shadow} =>     {Mascara}   0.119  0.9596774
## 15              {Blush,Eye.shadow} =>     {Mascara}   0.169  0.9285714
## 10        {Nail.Polish,Eye.shadow} =>     {Mascara}   0.119  0.9083969
## 20          {Concealer,Eye.shadow} =>     {Mascara}   0.179  0.8905473
## 12            {Bronzer,Eye.shadow} =>     {Mascara}   0.124  0.8794326
## 25 {Concealer,Eye.shadow,Eyeliner} =>     {Mascara}   0.114  0.8769231
## 14                 {Blush,Mascara} =>  {Eye.shadow}   0.169  0.9184783
## 8            {Eye.shadow,Lipstick} =>     {Mascara}   0.110  0.8527132
## 7               {Mascara,Lipstick} =>  {Eye.shadow}   0.110  0.9090909
## 22       {Blush,Concealer,Mascara} =>  {Eye.shadow}   0.119  0.9083969
## 11               {Bronzer,Mascara} =>  {Eye.shadow}   0.124  0.9051095
## 2                        {Mascara} =>  {Eye.shadow}   0.321  0.8991597
## 3                     {Eye.shadow} =>     {Mascara}   0.321  0.8425197
## 9            {Nail.Polish,Mascara} =>  {Eye.shadow}   0.119  0.8880597
##        lift
## 1  3.571429
## 23 2.688172
## 15 2.601040
## 10 2.544529
## 20 2.494530
## 12 2.463397
## 25 2.456367
## 14 2.410704
## 8  2.388552
## 7  2.386065
## 22 2.384244
## 11 2.375615
## 2  2.359999
## 3  2.359999
## 9  2.330865
The Unique rules from first 15 rules are 3.
Total 6 rules are redudantant in first 15 rules. 
Out of 6 redudant rules, thes rules have approximately same lift ratio.      

(f) Interpret the first three distinct (i.e., excluding the redundant - consisting same item set) rules in the output in words.

# first 3 rules excluding redudant rules
rules.sorted    <- sort(rules, by="lift")
subset.matrix   <- is.subset(rules.sorted, rules.sorted)
subset.matrix[lower.tri(subset.matrix, diag=T)] <- NA
redundant      <- colSums(subset.matrix, na.rm=T) >= 1
rules.pruned   <- rules.sorted[!redundant]
inspect(rules.pruned)
##    lhs                             rhs           support confidence
## 1  {Brushes}                    => {Nail.Polish} 0.149   1.0000000 
## 23 {Blush,Concealer,Eye.shadow} => {Mascara}     0.119   0.9596774 
## 15 {Blush,Eye.shadow}           => {Mascara}     0.169   0.9285714 
## 10 {Nail.Polish,Eye.shadow}     => {Mascara}     0.119   0.9083969 
## 20 {Concealer,Eye.shadow}       => {Mascara}     0.179   0.8905473 
## 12 {Bronzer,Eye.shadow}         => {Mascara}     0.124   0.8794326 
## 8  {Eye.shadow,Lipstick}        => {Mascara}     0.110   0.8527132 
## 2  {Mascara}                    => {Eye.shadow}  0.321   0.8991597 
## 6  {Lip.liner,Eyeliner}         => {Concealer}   0.120   0.9230769 
## 5  {Blush,Lip.liner}            => {Concealer}   0.108   0.8709677 
## 13 {Bronzer,Eyeliner}           => {Concealer}   0.119   0.8150685 
## 4  {Bronzer,Lip.liner}          => {Concealer}   0.103   0.8046875 
##    lift    
## 1  3.571429
## 23 2.688172
## 15 2.601040
## 10 2.544529
## 20 2.494530
## 12 2.463397
## 8  2.388552
## 2  2.359999
## 6  2.088409
## 5  1.970515
## 13 1.844046
## 4  1.820560
#inspect(head(rules.sorted[!redundant]),3))
The first 3 rules are as below. 

{Brushes}                    => {Nail.Polish}
{Blush,Concealer,Eye.shadow} => {Mascara} 
{Blush,Eye.shadow}           => {Mascara} 

The first rule (Brushes,Nail.Polish) is having lift ratio very high(3.571429) and confidence of 100%. The support is 149 which means out of 1000 transctions for 149 transactions both Brushes and Nail.Polish are happening.

The second rule ({Blush,Concealer,Eye.shadow},{Mascara}) 

The third rule ({Blush,Eye.shadow} ,{Mascara}) 

From the first three it can inferred that customers buying Concealer and Eye Shadow can opt for multiple items to go along with it whereas Nail Polish has one item as a consequent. The Lift ratio is above 3 for all the three transactions making it most likely item to be picked up in combination (strong association).

g) Based on the distinct rules that you identified in Part (f), suggest some action that’ll benefit the business owner.

Seeing the above three rules the variety of products that can be sold with Concealer & Eye Shadow are more. The store manager can strategically place the Mascara and Blush on one side of the Concealer  and on the other side can place the Eyeliner along with Eye Shadow making each item easily accessible and reachable for the customer. 

2. Airlines Network

2.1 Step 1:

Download (1) airports.dat, (2) airlines.dat, and (3) routes.dat from http://openflights.org/data.html Refer to the data descriptions provided on the site itself.

#Airlines Network using Edge List
library("igraph")
## 
## Attaching package: 'igraph'
## The following object is masked from 'package:arules':
## 
##     union
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union
setwd("J:\\ISB Business Analytics\\Data Mining\\Data Mining Assignment 2\\New folder")

#Load airports.csv data
airports <- read.csv("airports.csv",header=FALSE)
colnames(airports) <- c("Airport ID","Name","City","Country","IATA_FAA","ICAO","Latitude","Longitude","Altitude","Timezone","DST","Tz database timezone")

head(airports)
##   Airport ID                       Name         City          Country
## 1          1                     Goroka       Goroka Papua New Guinea
## 2          2                     Madang       Madang Papua New Guinea
## 3          3                Mount Hagen  Mount Hagen Papua New Guinea
## 4          4                     Nadzab       Nadzab Papua New Guinea
## 5          5 Port Moresby Jacksons Intl Port Moresby Papua New Guinea
## 6          6                 Wewak Intl        Wewak Papua New Guinea
##   IATA_FAA ICAO  Latitude Longitude Altitude Timezone DST
## 1      GKA AYGA -6.081689  145.3919     5282       10   U
## 2      MAG AYMD -5.207083  145.7887       20       10   U
## 3      HGU AYMH -5.826789  144.2959     5388       10   U
## 4      LAE AYNZ -6.569828  146.7262      239       10   U
## 5      POM AYPY -9.443383  147.2200      146       10   U
## 6      WWK AYWK -3.583828  143.6692       19       10   U
##   Tz database timezone
## 1 Pacific/Port_Moresby
## 2 Pacific/Port_Moresby
## 3 Pacific/Port_Moresby
## 4 Pacific/Port_Moresby
## 5 Pacific/Port_Moresby
## 6 Pacific/Port_Moresby
tail(airports)
##      Airport ID                              Name            City
## 8102       9536    Pender Harbour Water Aerodrome  Pender Harbour
## 8103       9537   Mansons Landing Water Aerodrome Mansons Landing
## 8104       9538              Port McNeill Airport    Port McNeill
## 8105       9539      Sullivan Bay Water Aerodrome    Sullivan Bay
## 8106       9540              Deer Harbor Seaplane     Deer Harbor
## 8107       9541 San Diego Old Town Transit Center       San Diego
##            Country IATA_FAA ICAO Latitude Longitude Altitude Timezone DST
## 8102        Canada      YPT  \\N 49.61667 -124.0167        0       -8   A
## 8103        Canada      YMU  \\N 50.06667 -124.9833        0       -8   A
## 8104        Canada      YMP  \\N 50.57556 -127.0286      225       -8   A
## 8105        Canada      YTG  \\N 50.88333 -126.8333        0       -8   A
## 8106 United States      DHB  \\N 48.61840 -123.0060        0       -8   A
## 8107 United States      OLT  \\N 32.75520 -117.1995        0       -8   A
##      Tz database timezone
## 8102    America/Vancouver
## 8103    America/Vancouver
## 8104    America/Vancouver
## 8105    America/Vancouver
## 8106  America/Los_Angeles
## 8107  America/Los_Angeles
#Load routes.csv
setwd("J:\\ISB Business Analytics\\Data Mining\\Data Mining Assignment 2\\New folder")
airline_routes <- read.csv("routes.csv",header=FALSE) ## source: http://openflights.org/data.html
colnames(airline_routes) <- c("Airline", "Airline ID", "Source Airport","Source Airport ID","Destination Airport","Destination Airport ID","Codeshare","Stops","Equipment")

head(airline_routes)
##   Airline Airline ID Source Airport Source Airport ID Destination Airport
## 1      2B        410            AER              2965                 KZN
## 2      2B        410            ASF              2966                 KZN
## 3      2B        410            ASF              2966                 MRV
## 4      2B        410            CEK              2968                 KZN
## 5      2B        410            CEK              2968                 OVB
## 6      2B        410            DME              4029                 KZN
##   Destination Airport ID Codeshare Stops Equipment
## 1                   2990               0       CR2
## 2                   2990               0       CR2
## 3                   2962               0       CR2
## 4                   2990               0       CR2
## 5                   4078               0       CR2
## 6                   2990               0       CR2
tail(airline_routes)
##       Airline Airline ID Source Airport Source Airport ID
## 67658      ZL       4178            WIN              6337
## 67659      ZL       4178            WYA              6334
## 67660      ZM      19016            DME              4029
## 67661      ZM      19016            FRU              2912
## 67662      ZM      19016            FRU              2912
## 67663      ZM      19016            OSS              2913
##       Destination Airport Destination Airport ID Codeshare Stops Equipment
## 67658                 TSV                   3330               0       SF3
## 67659                 ADL                   3341               0       SF3
## 67660                 FRU                   2912               0       734
## 67661                 DME                   4029               0       734
## 67662                 OSS                   2913               0       734
## 67663                 FRU                   2912               0       734

2.2 Step 2: Create a directed network graph of airline routes using routes.dat

#Create a graph from an edge list matrix
AirlineNW <- graph_from_edgelist(as.matrix(airline_routes[,c(3,5)]),directed=TRUE)
plot(AirlineNW)

2.3 Step 3: Create community based clusters.

AAA <- leading.eigenvector.community(AirlineNW)
#membership(AAA)
plot(AAA,AirlineNW)

2.4 Step 4: Communicty

(a) What would you call a community in a social-media network?

A community in social-media is broadly known as a group of people having same interests or having particular characteristics.

Some examples for social media communities, Facebook(social media), Linkedin(Professional networks), blogs and etc.

The communities are formed based on their social interests, technical interests, geographical interests, professional interests and etc.

Social interests are referring to the examples like following an NGO community(say NGO: MAke A Difference), Animals related communities, travel lover communities, music communities, sports communities and etc.

Technical interests are referring to the examples like Analytics enthusiastics community, Open Source tools community, particular tool or languange communities and etc.

Geographical interests are referring to the examples like same college, same village/town/state/country and etc.

Professional intereset are referring to the examples like same company and etc.

(b) Extend the definition of community (as you suggested above in Part a) to the community of airports.

Airports can be broadly categorized into below communities.

  1. Domestic or International Airports
  2. Commerical or Non-Commercial Airports
  3. Civil or Non Civil Airports
  4. Primary or secondary Airports

(c) How many distinct airports are there in the dataset? How many communities of airports got identified? List the number of airports in each cluster/community in a table.

Distinct Airports

length(unique(AAA$names))
## [1] 3425

Number of community Airports

max(AAA$membership)
## [1] 25

List the number of airports in each cluster/community in a table

comm <- membership(AAA)

# table of communities and their counts
table(comm)
## comm
##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18 
## 137   2   4   2   4   2   4  10 635 340 776 334 274   1   6   1   2  21 
##  19  20  21  22  23  24  25 
## 198 656   1   1   1   1  12

2.5 Step 5: Compute the centralities (in-degree, out-degree, in-closeness, eigenvector,betweenness) of each airport. Now, run k-Means clustering to group the airports based on centralities alone. Take k as the number of communities you obtained in Part c, above.

In-Degree

indegree <- degree(AirlineNW,mode="in")
max(indegree)
## [1] 911
head(indegree)
## AER KZN ASF MRV CEK OVB 
##  26  28   8  22  20  90

Out-Degree

outdegree <- degree(AirlineNW,mode="out")
max(outdegree)
## [1] 915
head(outdegree)
## AER KZN ASF MRV CEK OVB 
##  26  28   8  22  20  87

In-Closeness

closeness_in <- closeness(AirlineNW, mode="in",normalized = TRUE)
max(closeness_in)
## [1] 0.01835305
head(closeness_in)
##        AER        KZN        ASF        MRV        CEK        OVB 
## 0.01801138 0.01801868 0.01796951 0.01805165 0.01797724 0.01813761

Eigenvector

indegree <- degree(AirlineNW,mode="in")
max(indegree)
## [1] 911
head(indegree)
## AER KZN ASF MRV CEK OVB 
##  26  28   8  22  20  90

Eigenvector

pg_rank <- page_rank(AirlineNW,damping = 0)
pg_rank$vector
##          AER          KZN          ASF          MRV          CEK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OVB          DME          NBC          TGK          UUA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EGO          KGD          GYD          LED          SVX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NJC          NUX          BTK          IKT          HTA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KCK          ODO          UKX          ULK          YKS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MJZ          AYP          LIM          CUZ          PEM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HUU          IQT          PCL          TPP          ABJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BOY          OUA          ACC          BKO          DKR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          COO          LFW          NIM          BOG          GYE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UIO          CLO          SCY          OCC          BDS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZRH          BOD          BRS          GVA          LPA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LCA          RMF          TFS          AJR          LYC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ARN          GEV          HAD          JKG          KRF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KSD          MHQ          OER          POR          TRF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VBY          VHM          VXO          HMV          KOK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TKU          OSL          ADQ          AOS          KKB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KLN          KOZ          OLH          KZB          SYB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KYK          ORI          KPR          BSO          MNL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BXU          CBO          CGY          CRM          DGT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DWC          GES          KLO          LGP          MPH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OZC          PPS          RXS          SUG          TUG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZAM          AUX          PMW          BRA          BSB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SSA          OPS          RAO          CAC          GRU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CGB          GYN          CGR          DOU          GIG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UBA          UDI          VDC          PLU          SJP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BRL          ORD          STL          DEC          JBR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CGA          HYL          KTN          KTB          MTM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LOS          ROB          BCN          BJL          FNA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CKY          OXB          DLA          LGW          AKV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YIK          YPX          XGR          YVP          YGL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YGW          YUL          YPH          YSK          YUD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YUY          YZG          YKG          YPJ          YQC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YKL          YQB          YWK          YZV          YTQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YWB          JIB          DXB          JED          MGQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NBO          BKK          SIN          DRW          HAK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HGH          HKG          HKT          KIX          TPE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KUL          PEN          PER          PNH          REP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RGN          SGN          SWA          ACH          EBA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DRS          DUS          FDH          MUC          HAM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OLB          TXL          ZAD          FMM          NAP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GRZ          SZG          ATL          LWB          MCN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MEI          MSL          PIB          TUP          BIM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FLL          ELH          PBI          EYW          RSW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TPA          FPO          GGT          GHB          MCO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MHH          TCB          GLH          GNV          JAX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PNS          TLH          AMS          NDR          TNG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CMN          BGY          BLQ          BRU          CGN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CUF          LYS          MPL          SAW          TLS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TSF          FEZ          PMI          AUA          LSP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MAR          BON          CUR          BHK          FEG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KSQ          NMA          NVI          SKD          TIV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ANU          PTP          CAY          FDF          SDQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DOM          SXM          SLU          SBH          SFG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BHY          XIY          CAN          CKG          CTU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SPN          CGO          CGQ          HRB          KMG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          URC          NKG          TNA          TSN          CSX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CZX          DLC          DYG          INC          KHN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LHW          LJG          LXA          NGB          NNG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PEK          PVG          PZI          SYD          SYX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SZX          TSA          TYN          WUH          WUX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          XNN          YIH          ZHA          FOC          SHE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WNZ          XMN          DCY          DSN          HDG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HET          HFE          ICN          JHG          JIQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JZH          KOW          KWE          LUM          LZY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MEL          SJW          TAO          WXN          XIC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          XUZ          YTY          ZUH          DAT          DNH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GXH          NZH          KWL          JGN          JJN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KHG          MIG          LYI          NTG          ZHY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YVR          YBP          TVS          UYN          LAS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LAX          CAI          TLV          MCG          NIB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TCT          TLJ          EYK          VKO          NCU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TJM          UFA          NYM          OVS          UCT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DAC          BZL          CCU          CGP          MCT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CXB          JSR          KTM          SPD          ZYL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RJH          YGZ          YRB          DFW          EZE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JFK          MIA          PUJ          YEG          YXY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YLW          YOW          YZF          YYC          ACA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MEX          TLC          AGU          CEN          CJS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CME          CPE          CTM          CUL          CUN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MTY          CUU          CZM          GDL          SAT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SJD          SNA          TIJ          GUA          HAV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HMO          HUX          LAP          MID          MTT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MZT          OAX          PQM          PVR          REX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SJO          TAM          TGZ          TRC          VER 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VSA          ZCL          ZIH          ZLO          DEL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HEA          KBL          ISB          MZR          AYT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BSL          HRG          PRN          SKP          AGP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          STR          ALG          AOI          ATH          HAJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BEG          BGO          BHX          BIA          BIO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BRE          BRI          BUD          CAG          CDG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CFU          CLY          CTA          DBV          DUB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EDI          FAO          FCO          HDF          HER 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IBZ          JMK          JTR          KGS          KLU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KVA          LEJ          LHR          LIS          MAN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MXP          NCE          PMO          PRG          PSA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PUY          RAK          RHO          RJK          RLG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SJJ          SKG          SPU          STN          SUF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TUN          VCE          VIE          VRN          WAW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          XRY          ZAG          CWL          DTM          KTW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MAD          NQY          NUE          POZ          TRN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WRO          FKB          FRA          HEL          KRK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LIN          AKP          FAI          BTT          CXF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CEM          IRC          CIK          FYU          MLY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RMP          SVS          TAL          WBQ          MNT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AKI          TLT          ATT          KUK          BET 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EEK          GNU          KPN          KWN          KWT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MLL          NME          WNA          WTL          CYF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PTU          KKH          KWK          KKI          NUP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PQS          OOK          TNK          PKA          WWT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BOC          DRK          FON          XQP          GLF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PJM          LIR          SYQ          TNO          MGA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NOB          TMU          PMZ          TTQ          KMS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EDL          LOK          JUB          KIS          LAU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MYD          MBA          ZNZ          BCD          CEB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DVO          BKI          BWN          CGM          CRK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DPL          IAO          ILO          PAG          PUS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TAC          USU          CGK          MFM          CYZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DPS          HAN          LAO          NGO          NRT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SJI          TAG          VRC          WNP          NEV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ARH          CSH          MMK          NNM          SVO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          USK          SCW          TOS          ANF          IQQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CCP          SCL          AEP          MVD          PDP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ASU          CWB          POA          YBK          YCS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YXN          YCB          YCO          YYH          YRT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YCY          YFB          YIO          YEK          YYQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YEV          YVQ          YGT          YTE          YUX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YXP          YHK          YUT          YZS          YTH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YVM          YWG          BZE          FRS          SAP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TGU          RTB          CPT          PBZ          ELL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JNB          MGH          AMD          BLR          BOM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GOI          HYD          JAI          MAA          PNQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BBI          VTZ          BDQ          COK          GAU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LKO          NAG          TRV          CJB          IDR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IXC          IXJ          PAT          SXR          DIB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IMF          IXA          IXB          IXR          RPR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VNS          ETH          SDV          SXF          TBS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CPH          SGD          YHI          YPC          YSY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YUB          ZFM          KRR          PYJ          KJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AKY          SNW          HEH          MDL          KAW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MGZ          NYU          THL          TVY          RTW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EVN          RIX          CJJ          CJU          GMP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FUK          GUM          GWT          YAB          YLC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YFS          YHY          HND          KKJ          ABL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OTZ          SHG          ANC          AIN          ATK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BRW          ANI          CDV          ENA          HOM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KSM          UNK          VDZ          CHU          HCR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KLG          RSH          SHX          ANV          KGX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AUK          EMK          SXP          HPB          VAK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BKC          DRG          NUI          PIZ          BTI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SCC          CKD          RDV          SLQ          ELI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KKA          OME          KOT          GAL          RBY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HSL          KAL          NUL          GAM          SVA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GLV          WMO          SCM          KYU          IAN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ORV          SKK          WBB          MOU          KTS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TLA          WAA          KVL          TOG          MYU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OBU          SHH          PHO          WLK          WTK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SRV          SMK          CCS          LRM          VLN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BRM          CLT          KIN          MDE          PBM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          POS          PAP          DYU          ALA          LBD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FRU          IKA          IST          SGC          SHJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACU          PAC          BFQ          JQE          CHX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DAV          GHE          MPP          OGM          OTD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SIC          PUE          PVE          PYC          SAX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CZJ          AKX          CSY          ESL          GRV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IJK          MCX          PES          PEZ          SKX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ULV          VKT          VOZ          KUF          ROV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VOG          IAR          KRO          KVX          MQF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          URJ          CNX          AKK          LUR          TNC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BAV          TCZ          DIG          DLU          SYM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YIC          SHA          QBC          YAA          YBL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YQQ          ZEL          YKT          YXC          YPW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YWL          YYJ          YZT          YZZ          ZMT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ADA          ADB          BJV          DIY          DLM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ECN          ERZ          EZS          GNY          GZP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GZT          MLX          ODS          TZX          MDQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PRA          ROS          SFN          BHI          REL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BRC          CRD          EQS          COR          MDZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NQN          RGL          RGA          USH          YFJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YLE          YRA          YSG          AKF          BEN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AMM          TIP          MRA          HBE          SFA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TOB          AET          HUS          ARC          VEE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KBC          LMA          CGD          LYA          HIA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HSG          IBR          KHH          ZYI          TAK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NDJ          AZO          CHA          CID          CRW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CVG          EVV          FWA          GSO          GSP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LAN          LEX          MBS          MSP          ROA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SYR          TYS          XNA          DTW          MSY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GFK          TVF          LGA          MDT          MEM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACK          BOS          EWB          HYA          MVY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ALB          MSS          OGS          AUG          AXA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SJU          BHB          BIL          GDV          GGW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HVR          OLF          SDY          LEB          PVC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RKD          RUT          SLK          CGI          CPX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EIS          STT          HPN          IRK          MAZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MWA          OWB          STX          VIJ          VQS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TBN          UIN          YDQ          YYE          YOJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YOP          YXJ          YKA          YXS          YLL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YQZ          YXT          YYD          BCV          CUK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SPR          SQS          TZA          DGA          PLJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CZH          PND          GDT          PLS          SLX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACR          LCR          SVI          ADZ          PVA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          APO          EOH          AUC          BUN          CZU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FLA          IPI          MVP          PCR          PDA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PSO          PUU          RVE          SJE          TME 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UIB          VGZ          VVC          BSC          GPI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NQU          LET          LPD          TCD          LMC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LQM          KIV          BVA          KBP          OTP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BLA          PMV          PTY          PZO          BNS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MRD          VLV          AJL          AUH          ATQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CCJ          DMM          KWI          BAH          BHJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BHO          BHU          IXE          CMB          DIU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DOH          IXU          JDH          RAJ          RUH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UDR          EWR          YYZ          IXS          IXZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DED          GOP          IXL          PBD          RJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IXM          TRZ          JSH          JKH          KLX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SMI          AOK          KSJ          AXD          CHQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EFL          IEV          IOA          JIK          JKL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JNX          JSI          JSY          JTY          KIT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LRS          LXS          MJT          MLO          MRS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NTE          PAS          PHL          SKU          SOF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TIA          ZTH          OPO          KZS          BYC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SRZ          TJA          CBB          TDD          CIJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GYA          LPB          POI          ORU          RIB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AGF          DCM          ORY          AJA          BVE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PIS          CFE          SXB          AUR          BES 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LIL          BIQ          CFR          ETZ          FLR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FSC          GOT          LAI          LDE          LRH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LRT          MLH          PUF          RNS          PGF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RDZ          UIP          EBB          KSE          PAF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BUS          KUT          ABE          ABI          ABQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PHX          ABZ          ACT          ADL          BNE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AEX          AGS          DCA          AKL          PPT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ALO          AMA          AQP          ART          ASP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IAD          LHE          AUS          AVL          AVP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BDA          BDL          PIT          BFL          BGI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BGM          BGR          BHD          BHM          BJX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BMI          BNA          CBR          CNS          TSV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BOI          BUF          PDX          RIC          ROC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SAN          SEA          BPT          BRO          BTR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BTV          BUR          BWI          CAE          CAK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CHC          CHO          CHS          CLE          CLL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CMH          DAB          DAY          DEN          DSM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EWN          FAY          FLO          GCM          GPT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HHH          HSV          HTS          IAH          ILM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IND          JAN          LIT          LYH          MBJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MCI          MGM          MHT          MKE          MLB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MOB          MYR          NAS          OAJ          OMA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ORF          PGV          PHF          PVD          PWM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RDU          SAV          SBY          SDF          SFO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLC          SMF          SRQ          TRI          UVF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VPS          CMI          CNF          COS          COU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CRP          CTS          CWA          DBQ          ISP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YHZ          DRO          ELP          FAR          FAT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FSD          FSM          GCK          GGG          GJT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GRI          GRK          GRR          HNL          HOU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ICT          JLN          LAW          LBB          LCH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LFT          LRD          MAF          MFE          MHK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MLI          MLM          MLU          MSN          OGG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OKC          ONT          PBC          PIA          PSP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          QRO          RAP          RNO          ROW          SAF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SAL          SGF          SHV          SJC          SJT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLP          SPI          SPS          TUL          TUS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TXK          TYR          ELM          ERI          EUG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FLG          FNT          GEG          GIB          GLA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GND          GRB          OAK          HVN          IPT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ITH          ITM          LCY          JNU          JUL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KOA          LGK          LIH          MFR          MMH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MRY          NAN          RDM          STS          LBA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LGB          LUX          NCL          RTM          SVG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VVI          LSE          MAO          POP          REC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SKB          STI          MQT          RST          SUX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TOL          TVC          YKF          SCE          SWF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SBA          SBP          YUM          PMC          PUQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACE          FUE          ALC          FMO          PAD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MAH          NBE          DJE          FNC          GCI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JER          PDL          PVK          SPC          VRA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GDN          LNZ          INN          LEI          MLA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SCN          SVQ          VLC          VOL          GNM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LAZ          ADD          AZS          BJM          KGL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LAD          CCC          VNO          YMM          YQR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YXE          FIH          HOG          YYT          YXU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SNU          TRD          YAM          YBC          YYY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YBG          YCD          YCG          YDF          YYR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YQU          YFC          YGK          YGP          YGR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YQM          YQX          YQY          YSJ          YYG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YPR          YQF          YQG          YQL          YQT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YSB          YTS          YTZ          YVO          ZBF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZSA          YYF          YZP          YXH          YYB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YZR          AAX          POJ          AFL          AJU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MCZ          VCP          AQA          ARU          ATM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BEL          STM          MAB          BAZ          CKS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FOR          IMP          MCP          BPS          SDU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BVB          BVH          BYO          CAW          CCM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CFB          JPR          LDB          MGF          OAL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PVH          ROO          CGH          CMG          CIZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CLV          CPV          IPN          IZA          MOC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLZ          VIX          PNZ          CXJ          IGU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ERN          TFF          FEN          NAT          FLN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JPA          PHB          THE          IOS          NVT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GVR          IRZ          ITB          JDO          JOI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JTC          MII          LEC          TUR          PIN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TBT          MEA          OLC          PAV          PET 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PFB          SJK          RIA          XAP          PPB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RBR          RVD          SJL          TMT          RMQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HUN          KNH          MXZ          MZG          OKA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YNZ          TTT          ABV          PHC          ABY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LGG          HRE          JRO          ANR          ATW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BQK          CSG          DAL          DHN          ECP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GTR          MDW          SBN          VLD          SOU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BEY          BGF          NSI          EBU          KBV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LPQ          BLL          BZV          EXT          GOA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LBV          LJU          MRU          NKC          PNR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RBA          TNR          VGO          DAR          SSG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DOL          DZA          HAH          EGC          ENH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LUN          IVL          KTT          LIG          LLW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LVI          RUN          ZSE          NBS          TLN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ROR          AAE          ORN          AZR          BJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BLJ          BSK          CZL          DJG          EBH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ELU          GHA          HME          HRM          INZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MUW          MZW          OGX          QSF          TEE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TGR          TID          TLM          BMW          CBH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CFK          TMR          ELG          IAM          AGR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HJR          AGX          GWL          IXD          JGA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DMU          SHL          DHM          JLR          KNU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KUU          LUH          STV          TIR          VGA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MLE          AOR          BDO          JHB          KBR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KCH          MYY          SDK          TWU          BPN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BTJ          BTU          DMK          HDY          SBW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JOG          LBU          LOP          PDG          PKU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PLM          SOC          SRG          SUB          TGG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UPG          URT          VTE          CLQ          CVM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DGO          TAP          LMM          MXL          JAL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LZC          MAM          NLD          PAZ          PDS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PXM          SLW          TPQ          AFA          CPC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CTC          FMA          FTE          IGR          IRJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JUJ          LUQ          PSS          RES          RHD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RSA          SDE          SLA          TUC          UAQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VDM          ADK          AKN          ALW          CDB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DLG          SDP          SNP          STG          BLI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LWS          PBG          PQI          BZN          YAK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EAT          FCA          GTF          HLN          PSG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SIT          WRG          LTO          PUW          MSO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PSC          YKM          AGA          EUN          VIL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AHU          RAI          OUD          GLN          OZZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TFN          TTU          ESU          TTA          AXM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BAQ          BGA          CTG          CUC          EJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EYP          IBE          MTR          MZL          NVA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PEI          PPN          RCH          SMR          VUP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TCO          TML          BMA          MMX          UME 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JOE          JYV          KAJ          KAO          KEF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KEM          KUO          MSQ          NRK          OUL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RVN          SVL          TAY          TLL          TMP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VAA          AAL          PNA          AES          AHO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HUY          KRS          MME          NWI          KHI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KRT          SEZ          BAY          IAS          BZO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CIY          CLJ          REG          TGD          TRS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LCG          PSR          OMR          SUJ          TSR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TAS          TGM          ASB          TSE          ASV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WIL          HGA          WJR          KTL          LKG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MRE          UKA          BQN          ORH          PSE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ABD          MHD          THR          AWZ          IFN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KIH          SRY          SYZ          AZD          BND 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GSM          KSH          RAS          TBZ          ZAH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AAR          TAB          DUR          PLZ          GRX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IOM          VFA          WDH          PFO          SPB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SSB          SDJ          UKB          YGJ          KOJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ISG          MMY          NGS          KOI          LSI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EMA          INV          BEB          SYY          NOC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WAT          BRR          CAL          CFN          DND 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DSA          WIC          ILY          TRE          LPL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GTE          MZV          MIR          HJJ          LLF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TEN          YNT          HEK          OHE          JGD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JMU          JXA          BMV          VII          CXR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DAD          HPH          PQC          EBJ          KSU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EVE          BBK          GBE          MUB          FRW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AKJ          HKD          KMQ          OKJ          TXN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PLQ          BKY          KND          KOO          BNB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MDK          BNC          BUX          GOM          IRP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FBM          KGA          MJM          FKI          TSH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GMA          FMI          LJA          CYO          SCU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GEO          BSG          AKU          BPX          DAX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GYS          HYN          JDZ          LZO          WUS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YCU          CHG          CIF          CIH          KRL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YIN          YIW          DDG          HIJ          DQA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FNJ          FUG          HLD          HLH          HMI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HSN          HTN          YNJ          JGS          JIU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JNZ          JUZ          LZH          MDG          MWX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NDG          RLK          TAE          TGO          ULN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WUA          XFN          XIL          PEU          AVN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          POM          BUA          RAB          DAU          LAE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UNG          GKA          HGU          MAG          GUR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LSA          MIS          PNP          MXH          TBG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TIZ          WWK          HKN          KVG          MAS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LNV          TFI          BUL          FSZ          TNN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KMI          TOY          CMW          GAO          KHV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          USM          VVO          AAT          ACX          AOG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AQG          AVA          BFJ          BSD          HZH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JNG          JUH          LLB          LYG          NAO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NNY          KIJ          LDS          KCA          LNJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WNH          ZAT          KRY          NLT          OSS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TCG          ENY          CEE          VUS          KVK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NLA          OOL          AGH          KLR          RNB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SDL          THN          GSE          BFV          CEI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CJM          UTH          KOP          LOE          MAQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NNT          NST          PHS          PRH          ROI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SNO          TST          UBP          UNN          ABR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          APN          BIS          BJI          BRD          INL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BTM          BTS          CDC          CIU          CNY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          COD          CPR          DIK          DLH          ESC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PLN          EKO          GCC          RKS          HIB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IDA          IMT          RHI          ISN          JAC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KSC          LNK          MOT          PIH          SGU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TWF          VEL          CSK          ZIG          CAB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SZA          CBT          VPE          LUO          MEG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MSZ          NOV          SDD          SPP          SVP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TMS          VHC          SCO          CIT          DMB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DZN          KGF          KOV          KSN          PLX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PPK          UKK          GUW          KZO          URA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SZI          RNN          MOL          SRP          RYG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ALF          KRN          LLA          BDU          BOJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BOO          KRP          HAU          KKN          LYR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MJV          SZZ          POG          COQ          MXV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ULG          ULO          KQT          TJU          REN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ORK          SNN          BLK          BOH          KIR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SCQ          SEN          BGW          BKQ          LRE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ROK          BSR          GOV          EBL          MED 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PEW          SAH          SKT          WLG          ZQN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DOK          ELQ          TIF          TUU          YNB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACZ          ADU          AFZ          PGU          BDH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BJB          BUZ          BXR          DEF          LFM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LRR          ZBR          GBT          GCH          HDM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IIL          ISU          KDH          KER          KHY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NSH          RZR          OMH          PFQ          SDG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YES          ESM          CUE          ETR          GPS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LOH          LTX          LGQ          MEC          TNW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TUA          XMS          MLW          AMH          ASO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AXU          BJR          DIR          ENU          GDQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GMB          JIJ          JIM          MPM          MQX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SZE          LLI          BLZ          GDE          SHC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HRI          PXO          NYK          UAS          SSY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LMP          LUG          PNL          TPS          AIA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CDR          ALS          FMN          TTN          ATY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PIR          BKG          CYS          WRL          DDC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LBL          ILG          SOW          HON          IGM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PGA          UST          VAR          KKC          NAW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ESB          SFB          APW          CXI          FUN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SUV          HIR          VLI          ICI          KDV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LBS          LKB          RTA          SVU          TBU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TRW          TVU          VBV          HRL          SHP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AAY          ADE          AHB          GXF          RIY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AXK          TAI          HOD          SCT          CRL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EIN          HHN          LTN          NRN          PIK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SDR          ZAZ          CIA          NYO          VST 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GRO          PMF          KUN          MST          WMI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VLL          LBC          LPP          BZG          LDY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          REU          CCF          BZR          BRQ          RZE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PEG          FNI          DLE          DNR          TUF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GPA          GRQ          SFT          PDV          LUZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          XCR          OSI          OSR          FKS          OIT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SZB          BTH          IPH          KTE          KUA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HAS          HRK          MUX          NJF          PZU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLL          CZS          PGD          PIE          AZA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OGD          PVU          RFD          STC          BLV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CKB          HGR          IAG          SCK          SMX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LCK          YNG          PSM          AEB          DOY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WUZ          ATZ          HMB          HOF          AMQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BDJ          BEJ          BIK          DJJ          BKS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BMU          MDC          TRK          TKG          DJB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MLG          PGK          PKY          PLW          PNK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TJQ          TNJ          TTE          MKQ          MKW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TIM          KOE          LBJ          TMC          ENE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GTO          KDI          SOQ          KUH          MYJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AGM          IOQ          KUS          KUZ          SGG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TQI          AOQ          JUV          CNP          OBY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SFJ          GOH          JAV          JFR          JHS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JSU          UAK          IKE          SAE          UMD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IOT          JUU          IUI          TQA          JEG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JQA          JJU          JNN          JNS          LLU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          QFG          QJH          QUW          XEQ          QFX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          JUK          KGQ          KHQ          NAQ          NSQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UPK          SRK          THU          NIQ          QOQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          QFN          QUV          SVR          KSO          KZI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACI          BPL          ERL          IQN          JIC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YZY          AKB          DUT          KCG          KLL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PIP          WSN          KFP          KVC          NLG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IKO          KQA          EGX          IGG          KCL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KCQ          KPV          UGB          PTH          AIT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AIU          RAR          MGS          MOI          MUK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CJC          LSC          ARI          BBA          ZAL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZCO          CPO          RUA          ITO          LNY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MKK          PPG          MMB          OBO          BLD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GCW          PRI          LCX          YNY          OST 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BLE          ORB          OSD          WEF          SID 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YGH          ZFN          YWJ          AZN          UGC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TMJ          BVV          UUS          DEE          EKS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OHH          KLW          BHV          UET          LYP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MLN          OVD          EAS          LEN          RGS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLM          ILD          RJL          ATD          BNY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RNL          CHY          GZO          EGM          RBV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VAO          FRE          MUA          IRA          JJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KGE          NNB          RNA          RUS          SCZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OMO          SSH          SXK          PKN          OKL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WMX          DOB          LUV          KTG          ABA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BQS          OMS          ISC          GDX          KYZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UUD          LEQ          SLY          KHD          XBJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AAN          ASM          HFA          KVD          YSM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YPY          EGN          ELF          UYL          AGN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TKE          ELV          GST          HNH          HNS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SGY          PEC          RDN          LXR          BNX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CXH          YWH          YIE          BFN          HLA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GRJ          AOJ          NKM          MMJ          GAJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HNA          KCZ          KMJ          AGT          RIG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ASJ          AXT          IZO          MSJ          SHM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TKS          UBJ          DUD          AVV          AYQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HBA          HTI          LST          MKY          NTL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PPP          BNK          MCY          FKQ          NBX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KBU          NTX          BUW          BXB          MOF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WGP          KNG          KAZ          LUW          MNA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NAH          MJU          PSJ          PUM          BBO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BSA          GLK          YAG          YQK          YFO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YQD          YHD          YRL          YXL          YYU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CAP          XSC          EDA          HYG          KCC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WWP          KPB          PPV          NKI          AHN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MKL          IPL          ELD          HOT          HRO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLN          OTH          PDT          KOS          HGN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PYY          PBH          PWQ          HIN          KUV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KWJ          RSU          USN          WJU          KPO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LPI          NAY          FUO          ILI          APL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          POL          MWZ          CYB          LYB          LCE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OUZ          NDB          CIX          CJA          IPC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PIU          TBP          TCQ          TRU          MHC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MPN          ZOS          OLL          ANG          BVC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BFS          GOJ          LWO          SBZ          OGL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SVD          EOI          NDY          NRL          PPW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SOY          WRY          GHT          LAQ          LTD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          QUB          SRX          CNM          LAM          LNS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VCT          OLA          VDB          ASW          BFI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CLM          ESD          DHB          RCE          WSX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FRD          FBS          LKE          LPS          ORX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BVS          MEU          MTE          OZH          UDJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ANM          TMM          WMN          DIE          NOS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SVB          MJN          FTU          TLE          MOQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SMS          WMR          KAN          BBN          MUR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KUD          LDU          LWY          BKM          MKM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TGC          LBP          LGL          LKH          LMN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ODN          DIL          RRG          ELS          YGX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BYN          LTI          HVD          DLZ          ULZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ABS          KGT          GOQ          NGQ          NYT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZQZ          YUS          JHM          HNM          MUE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ORZ          INB          SVK          JBQ          AUY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TAH          AWD          FTA          SON          CCV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LNB          NUS          ULB          DLY          IPA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EAE          LNE          LOD          LPM          MTV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SLH          TOH          ZGU          MWF          NOU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SWJ          PBJ          SSR          WLH          TGH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VLS          SHB          WKJ          FUJ          TSJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HAC          IWJ          IWK          MBE          NTQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          OIM          ONJ          SYO          TTJ          IKI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CFC          JCB          GPB          ERM          GEL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SRA          URG          ACY          LBE          SKZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GMZ          VDE          UEO          AEY          RKV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EGS          IFJ          BHE          GIS          HLZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KAT          KKE          NPE          NPL          NSN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PMR          PPQ          ROT          TRG          TUO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WAG          WHK          WRE          ALH          CNJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NLK          BQB          HKK          IVC          DCN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EPR          GET          IUE          KGI          KNX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LEA          PBO          RVT          PQQ          TIU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WSZ          NYI          TKD          SRE          KLV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PEE          INU          MAJ          DNK          BWK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PMY          CIP          KAA          MFU          SLI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MNS          LUK          MMU          MBL          GJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UII          YHU          YVB          YGV          YAY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YBX          YCL          YDP          YNP          YHO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YMN          YJT          YSO          ZUM          VAN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ASR          HTY          MQM          VAS          KYA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BAL          DNZ          EDO          ERC          KCM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MSR          MZH          NAV          LPT          TDX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          THS          UTP          CKH          CYX          IKS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MQJ          NER          SUK          FSP          RYK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CJL          DBA          DEA          DSK          PZH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GIL          GWD          TUK          KDU          MJD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PJG          ATC          LGI          RCY          RSD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SML          TBI          CYP          JOL          MBT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          IFO          ARK          BKZ          MBI          MYW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CMU          VAI          MDU          WBM          GAN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DRV          HAQ          FVM          KDM          GKK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KDO          CKX          TKJ          HKB          ABM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AUU          CUQ          BEU          BQL          BVI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RMA          TWB          ISA          BUC          DMD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ONG          WNR          CMA          SGO          XTG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          EDR          IRG          KWM          NTN          WEI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CTL          ULP          YPN          YIF          ZGS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YNA          SXI          GOU          MVR          NGE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ABX          OLP          PLO          ARM          BCI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BDB          BME          KTA          EMD          GLT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HVB          LDH          MOV          PHE          ZBL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CFS          HID          DBO          DPO          MQL 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MRZ          ZNE          TMW          WGA          STD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VIG          ZVK          HOE          PKZ          LXG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ODY          XKH          OSW          DYR          NGK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RMI          PWE          MUN          FAE          AZI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FJR          XSB          ZDY          AQJ          OSM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HOR          PIX          SMA          TER          CDJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CMP          GRP          MQH          BSS          OIA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RDC          STZ          SXO          SXX          AAQ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BAX          KEJ          NOZ          NSK          OGZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RGK          SIP          STW          TOF          PKC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BEW          BUQ          HDS          KIM          MQP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UTN          WVB          MSU          MTS          PHW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PTG          PZB          RCB          TET          UTT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VNX          FUT          WLS          HBX          IXG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MYQ          TCR          PUG          BWT          KNS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FLS          MEB          PTJ          CVU          FLW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          GRW          SJZ          AGB          ERF          KSF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CEG          ONQ          XFW          GDZ          ABT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AJF          AQI          BHH          EAM          GIZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          DWD          EJH          RAE          SHW          URY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WAE          ULH          RAH          TUI          ERS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MPA          NDU          OND          LUD          OMD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BRN          HMA          DIJ          PGX          LEH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VDA          TEB          ADF          AJI          AOE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BGG          CKZ          CND          IGD          KCO 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KSY          TEQ          ISE          KFS          KZR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NAJ          NOP          MCV          MNG          ELC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MGT          VXC          UEL          INH          VPY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VXE          TOE          BMY          GEA          KOC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ILP          KNQ          LIF          MEE          TGJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TOU          UVE          GBB          LLK          LWN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ACV          CEC          AOO          JST          ASE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BFD          JHW          BKW          SHD          CIC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MGW          CLD          DUJ          FKL          PKB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CMX          EGE          GUC          HDN          LAR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MTJ          PUB          EAU          FOE          ROP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TKK          YAP          HOB          KSA          KWA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PNI          LMT          MKG          MOD          PAH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RDD          LPY          MSW          GAE          GAF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BTC          GIU          KCT          DIW          TRR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PED          AXP          CRI          IGA          MYG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NYA          UTS          TBW          URS          BJZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CAJ          CBS          CUM          CZE          LFR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          PYH          SOM          SVZ          PBL          SNV 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VLY          GLO          CCK          XCH          DLI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HUI          UIH          CAH          PXU          DIN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TBB          VCA          VCL          VDH          THD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          VCS          VKG          MMO          SFL          SNE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          AHE          XMH          AUQ          NHV          UAH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          UAP          AXR          KKR          BOB          HUH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MAU          MOZ          RFP          RGI          TIH 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FAV          GMR          HOI          MKP          KHZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KXU          MVT          RKA          RMT          RUR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RVV          TKX          TUB          TKP          EVG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          HFS          KID          MXX          TYF          PJA 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MHG          URE          VIN          ABB          BNI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          CBQ          GMO          IBA          ILR          QOW 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          QRW          SKO          YOL          JOS          KAD 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          QUO          ANS          ATA          JAU          TGI 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ARW          CRA          DEB          TZL          KET 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          KYP          MYT          PBU          KME          HFT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          LKL          SOJ          VDS          ANX          BNN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          FDE          FRO          HOV          SKE          SOG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BJF          BVG          MEH          VAW          MQN 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SSJ          LKN          MJF          NVK          RET 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SKN          SVJ          HAA          HVG          OSY 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RVK          RRS          SDN          YHR          ZTB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZLT          YRG          ZKG          EUX          SAB 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YBR          YHM          YXX          KEW          KIF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WNN          MSA          XBE          ZPB          ZRJ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SUR          YAX          YTL          XKS          YAC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YER          YFH          YLH          YOG          YHP 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YNO          YWP          YPL          YPM          YVZ 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          ZSJ          KHS          ZQW          EXI          KAE 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          APF          UPN          IAA          TGP          THX 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MRX          NOJ          KGP          TQL          YAT 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YPO          ZKE          YFA          YMO          YKU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          YKQ          YMT          YNS          ZEM          YNC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MCM          GCN          BDP          BHR          BIR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BWA          DHI          JKR          KEP          PKR 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          TMI          KWF          UKS          RBQ          UYU 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          BFF          CEZ          EAR          LBF          MCK 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          RIW          SHR          MCE          PRC          VIS 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          SVC          BHQ          CED          CPD          KGC 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          MGB          WYA          BHS          PKE          GFF 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          NRA          GFN          TRO          JCK          RCM 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708 
##          WIN          LSY          MIM          MYA          OAG 
## 0.0002919708 0.0002919708 0.0002919708 0.0002919708 0.0002919708
max(pg_rank$vector)
## [1] 0.0002919708

K-means Clustering

setwd("J:\\ISB Business Analytics\\Data Mining\\Data Mining Assignment 2\\New folder")
airports <- read.csv("airports.csv",header=FALSE) ## source: http://openflights.org/data.html
colnames(airports) <- c("Airport ID","Name","City","Country","IATA_FAA","ICAO","Latitude","Longitude","Altitude","Timezone","DST","Tz database timezone")

setwd("J:\\ISB Business Analytics\\Data Mining\\Data Mining Assignment 2\\New folder")
airline_routes <- read.csv("routes.csv",header=FALSE) ## source: http://openflights.org/data.html
colnames(airline_routes) <- c("Airline", "Airline ID", "Source Airport","Source Airport ID","Destination Airport","Destination Airport ID","Codeshare","Stops","Equipment")

AirlineNW <- graph.edgelist(as.matrix(airline_routes[,c(3,5)]),directed=TRUE)

indegree <- degree(AirlineNW,mode="in")
outdegree <- degree(AirlineNW,mode="out")
closeness_in <- closeness(AirlineNW, mode="in",normalized = TRUE)
btwn <- betweenness(AirlineNW,normalized = TRUE)

centralities <- cbind(indegree,outdegree,closeness_in,btwn)

normalized_data <- scale(centralities)

fit <- kmeans(normalized_data, 25) # 3 cluster solution

fit
## K-means clustering with 25 clusters of sizes 45, 37, 174, 65, 4, 24, 19, 90, 130, 6, 7, 71, 262, 613, 12, 16, 15, 304, 24, 47, 16, 853, 451, 35, 105
## 
## Cluster means:
##        indegree    outdegree closeness_in        btwn
## 1   1.610094794  1.604411269   0.25682340  0.15462538
## 2  -0.081085594 -0.074873498   0.10435259  0.90616276
## 3  -0.002746344 -0.002095973   0.20397013 -0.16472135
## 4  -0.230587459 -0.231054792   0.07605877  0.15923278
## 5   3.422859504  3.416968811   0.30672890 11.83519441
## 6   3.634645689  3.636192054   0.30740644  2.79456249
## 7   3.673844026  3.658652274   0.27085042  0.46318611
## 8   0.566220743  0.561709587   0.23498032  0.01836778
## 9   0.256779264  0.256913464   0.21551515 -0.10504238
## 10  2.996161137  3.015969710   0.29707059  6.13113479
## 11 10.419506978 10.457746234   0.35480173 13.05595374
## 12  1.043822935  1.046509669   0.24374267 -0.04930877
## 13 -0.148542471 -0.150001979   0.18946962 -0.18627853
## 14 -0.331953027 -0.332114805   0.05198930 -0.19030391
## 15  0.339065080  0.352524324   0.18147851  3.03487911
## 16  5.480155201  5.497639240   0.30162704  1.58010972
## 17  6.651700112  6.612791213   0.33189773  6.70668220
## 18 -0.328088141 -0.327461914  -0.06904242 -0.16820804
## 19  0.507087331  0.506994794   0.21810750  1.33870402
## 20 -0.344197693 -0.340418322  -8.41655715 -0.16394425
## 21  1.707860299  1.690878325   0.27904673  1.93935852
## 22 -0.328978086 -0.328653374   0.14389456 -0.19543601
## 23 -0.251096506 -0.251453175   0.15689835 -0.18557445
## 24  2.367836069  2.376600161   0.25967009  0.18923492
## 25 -0.340883568 -0.339583629  -0.28149669 -0.14705002
## 
## Clustering vector:
## AER KZN ASF MRV CEK OVB DME NBC TGK UUA EGO KGD GYD LED SVX NJC NUX BTK 
##   3   9  23   3   3  12  17  23  22  22  13  13  12   7   1  13   3  22 
## IKT HTA KCK ODO UKX ULK YKS MJZ AYP LIM CUZ PEM HUU IQT PCL TPP ABJ BOY 
##   8  13  14  14  14  23   8  23  22  21  13  22  22  23  23  23   8  14 
## OUA ACC BKO DKR COO LFW NIM BOG GYE UIO CLO SCY OCC BDS ZRH BOD BRS GVA 
##   9   8   9  12   9   3   3  10   9  19   9  14  14   3   7  12   1  24 
## LPA LCA RMF TFS AJR LYC ARN GEV HAD JKG KRF KSD MHQ OER POR TRF VBY VHM 
##  24   1  23  24  14  23   6  23  23  22  22  22  22  22  22   9  23  23 
## VXO HMV KOK TKU OSL ADQ AOS KKB KLN KOZ OLH KZB SYB KYK ORI KPR BSO MNL 
##  23  14  22  23   6   2  14  14  14  18  18  14  14  14  18  14  22   6 
## BXU CBO CGY CRM DGT DWC GES KLO LGP MPH OZC PPS RXS SUG TUG ZAM AUX PMW 
##  22  22  23  22  22   8  23   3  22  22  22  23  22  22  22  23  14  23 
## BRA BSB SSA OPS RAO CAC GRU CGB GYN CGR DOU GIG UBA UDI VDC PLU SJP BRL 
##  23  21   8  14   3  22   5   9   3   3  22  21  22  13  23   4  23  22 
## ORD STL DEC JBR CGA HYL KTN KTB MTM LOS ROB BCN BJL FNA CKY OXB DLA LGW 
##  11   1  22  22  14  14  19  14  14  19   3  16  13   3   3  23   8  16 
## AKV YIK YPX XGR YVP YGL YGW YUL YPH YSK YUD YUY YZG YKG YPJ YQC YKL YQB 
##  18  25   4  14   2   4   4  10  14  14  14  23  25   4  14  18  23   2 
## YWK YZV YTQ YWB JIB DXB JED MGQ NBO BKK SIN DRW HAK HGH HKG HKT KIX TPE 
##   3   2  14  25   3   5   6  13  21  17  17   8   1   7  17  12  24  16 
## KUL PEN PER PNH REP RGN SGN SWA ACH EBA DRS DUS FDH MUC HAM OLB TXL ZAD 
##   6   9  21   9   9  19  21   9  22  23   3  16  13  16  24   8   7   3 
## FMM NAP GRZ SZG ATL LWB MCN MEI MSL PIB TUP BIM FLL ELH PBI EYW RSW TPA 
##   3  12   3   9  11  22  22  22  22  22  22  22   7  23   8   3  12  24 
## FPO GGT GHB MCO MHH TCB GLH GNV JAX PNS TLH AMS NDR TNG CMN BGY BLQ BRU 
##  13  13  23   7  13  22  14  13   8   3  13  17   3   3  21  12  12  16 
## CGN CUF LYS MPL SAW TLS TSF FEZ PMI AUA LSP MAR BON CUR BHK FEG KSQ NMA 
##  24  23  24   3  24  12   9   3  16   8  22  13  13   9  23  23  23  13 
## NVI SKD TIV ANU PTP CAY FDF SDQ DOM SXM SLU SBH SFG BHY XIY CAN CKG CTU 
##  23  23  13   9   9  23   3   8   3   8  13  13  14   3  16  16   7  16 
## SPN CGO CGQ HRB KMG URC NKG TNA TSN CSX CZX DLC DYG INC KHN LHW LJG LXA 
##  13  24  12  24  16  24  24  24  24   7   9  24   3  12  12  12  12   9 
## NGB NNG PEK PVG PZI SYD SYX SZX TSA TYN WUH WUX XNN YIH ZHA FOC SHE WNZ 
##  12   1  11  17  22  10   1   7   9   1   7   8   8   3   3  24  24  12 
## XMN DCY DSN HDG HET HFE ICN JHG JIQ JZH KOW KWE LUM LZY MEL SJW TAO WXN 
##   7  22   3  23  12  12  17   3  23   3  13  24  23  23  21  12   7  13 
## XIC XUZ YTY ZUH DAT DNH GXH NZH KWL JGN JJN KHG MIG LYI NTG ZHY YVR YBP 
##  23   3   3   8  13  23  14  13   1  23   8  13   3   3   3  22   6  13 
## TVS UYN LAS LAX CAI TLV MCG NIB TCT TLJ EYK VKO NCU TJM UFA NYM OVS UCT 
##  23  13   6  11  24  24   4  18  18  25  22  21  22   3   3  23  23  22 
## DAC BZL CCU CGP MCT CXB JSR KTM SPD ZYL RJH YGZ YRB DFW EZE JFK MIA PUJ 
##  12  22   1   3   1  22  22  19  22  23  18  25  25  17  12  17  17  12 
## YEG YXY YLW YOW YZF YYC ACA MEX TLC AGU CEN CJS CME CPE CTM CUL CUN MTY 
##  19  23  13  19  15  21  23   6  13  13  23  13  22  22  22   3  24  12 
## CUU CZM GDL SAT SJD SNA TIJ GUA HAV HMO HUX LAP MID MTT MZT OAX PQM PVR 
##   3   3   1  12   8   9   9   9   8   3  22  13  13  22  13  23  22   8 
## REX SJO TAM TGZ TRC VER VSA ZCL ZIH ZLO DEL HEA KBL ISB MZR AYT BSL HRG 
##  23  15  23  23  13   3  13  23  13  23   6  23   9   8  22  24   1   9 
## PRN SKP AGP STR ALG AOI ATH HAJ BEG BGO BHX BIA BIO BRE BRI BUD CAG CDG 
##   3   3   7  24  21  13   6  12  12  12  24   9  12   8   8   1   8  11 
## CFU CLY CTA DBV DUB EDI FAO FCO HDF HER IBZ JMK JTR KGS KLU KVA LEJ LHR 
##   8   3   1   8   7   1   1  16  23   1   1  13  13   8  23  23   9  11 
## LIS MAN MXP NCE PMO PRG PSA PUY RAK RHO RJK RLG SJJ SKG SPU STN SUF TUN 
##   6  16   7  24  12  24  12  13  12  12  23  23   3  12   8  24   3   1 
## VCE VIE VRN WAW XRY ZAG CWL DTM KTW MAD NQY NUE POZ TRN WRO FKB FRA HEL 
##   1  16   9   1   3   8   9   9   9  17  23   8   3   9   9   3  11  21 
## KRK LIN AKP FAI BTT CXF CEM IRC CIK FYU MLY RMP SVS TAL WBQ MNT AKI TLT 
##   8   8  14  15  14  18  14  18  14   4  14  14  14  14  14  18  25  18 
## ATT KUK BET EEK GNU KPN KWN KWT MLL NME WNA WTL CYF PTU KKH KWK KKI NUP 
##  18  18  15  18  18  18  18  18  18  18  18  18  18  25  18  18  25  25 
## PQS OOK TNK PKA WWT BOC DRK FON XQP GLF PJM LIR SYQ TNO MGA NOB TMU PMZ 
##  18  18  25  25  25   2  22  22  23  22  22   3  14  22  13  22  22  22 
## TTQ KMS EDL LOK JUB KIS LAU MYD MBA ZNZ BCD CEB DVO BKI BWN CGM CRK DPL 
##  22  22  22  22  13  22  18  23  13  13  23   8  13   8   3  14  13  22 
## IAO ILO PAG PUS TAC USU CGK MFM CYZ DPS HAN LAO NGO NRT SJI TAG VRC WNP 
##  14  13  22  12  23  22   6  12  22   1   1  22  12  17  22  22  22  22 
## NEV ARH CSH MMK NNM SVO USK SCW TOS ANF IQQ CCP SCL AEP MVD PDP ASU CWB 
##  23   4  14  23  14   6  14  23   2  13  13  23  15  15   3  14   3   8 
## POA YBK YCS YXN YCB YCO YYH YRT YCY YFB YIO YEK YYQ YEV YVQ YGT YTE YUX 
##  19  18  18  18  18  18  14   2  18   2  25  18  23   4   2  18  18  18 
## YXP YHK YUT YZS YTH YVM YWG BZE FRS SAP TGU RTB CPT PBZ ELL JNB MGH AMD 
##  18  14  18  18  23  25  15  19  22   3   3  13   8  14  22  10  22   9 
## BLR BOM GOI HYD JAI MAA PNQ BBI VTZ BDQ COK GAU LKO NAG TRV CJB IDR IXC 
##   1   6   9  12   3   1   9  23   3  23   8   9   3  13   8   3   3  23 
## IXJ PAT SXR DIB IMF IXA IXB IXR RPR VNS ETH SDV SXF TBS CPH SGD YHI YPC 
##  13  13  13  23  23  23   3  13  13  13   4  14  12   9  10  22  18  25 
## YSY YUB ZFM KRR PYJ KJA AKY SNW HEH MDL KAW MGZ NYU THL TVY RTW EVN RIX 
##  25  25  25   8  23   8  14  14  23   3  25  18  23  14   4  23   8   1 
## CJJ CJU GMP FUK GUM GWT YAB YLC YFS YHY HND KKJ ABL OTZ SHG ANC AIN ATK 
##  13   8   9  12   9  23   4  18  14  22   6  22  18   2  18   5  18  18 
## BRW ANI CDV ENA HOM KSM UNK VDZ CHU HCR KLG RSH SHX ANV KGX AUK EMK SXP 
##   4   2  14  14  14   4   4  14  18  18  18  18  18  25  25  25  18  18 
## HPB VAK BKC DRG NUI PIZ BTI SCC CKD RDV SLQ ELI KKA OME KOT GAL RBY HSL 
##  18  18  18  18  18  18  18   4  25  25  25  18  18   2  18   4  14  18 
## KAL NUL GAM SVA GLV WMO SCM KYU IAN ORV SKK WBB MOU KTS TLA WAA KVL TOG 
##  18  18  18  18  18  18  25  25  18  18  18  18  18  18  18  18  18  25 
## MYU OBU SHH PHO WLK WTK SRV SMK CCS LRM VLN BRM CLT KIN MDE PBM POS PAP 
##  25  25  18  18  18  18  25  18  21  13  13  23  16   9   3  13   9   3 
## DYU ALA LBD FRU IKA IST SGC SHJ ACU PAC BFQ JQE CHX DAV GHE MPP OGM OTD 
##   8  12   9   8   8  17  13   1  25   2  25  25  25   2  25  25  25  25 
## SIC PUE PVE PYC SAX CZJ AKX CSY ESL GRV IJK MCX PES PEZ SKX ULV VKT VOZ 
##  25  25  18  25  25  18  23  22  22  22  22  22  22  22  22  22  22  23 
## KUF ROV VOG IAR KRO KVX MQF URJ CNX AKK LUR TNC BAV TCZ DIG DLU SYM YIC 
##   9   9  13  22  22  22  22  22   8  18  25  18   9  23  23  23  14  23 
## SHA QBC YAA YBL YQQ ZEL YKT YXC YPW YWL YYJ YZT YZZ ZMT ADA ADB BJV DIY 
##   7  22  14  23  23  18  18  22  22  23  13  22  22  22   3  12   9  23 
## DLM ECN ERZ EZS GNY GZP GZT MLX ODS TZX MDQ PRA ROS SFN BHI REL BRC CRD 
##   8  13  23  23  23  23  13  22   3  13  14  14  23  14  14  23  23  14 
## EQS COR MDZ NQN RGL RGA USH YFJ YLE YRA YSG AKF BEN AMM TIP MRA HBE SFA 
##  14  13  13  14  14  14  23  14  14  14  14  22   3   1   8  13   9  13 
## TOB AET HUS ARC VEE KBC LMA CGD LYA HIA HSG IBR KHH ZYI TAK NDJ AZO CHA 
##  23  14  18  25  18  14  14  23  13  13  22  23  12  13  23  13  23   3 
## CID CRW CVG EVV FWA GSO GSP LAN LEX MBS MSP ROA SYR TYS XNA DTW MSY GFK 
##   3  13  12  13   3   3   9  23   3  23   6  13   3   9   3   7   1  23 
## TVF LGA MDT MEM ACK BOS EWB HYA MVY ALB MSS OGS AUG AXA SJU BHB BIL GDV 
##  14  24   3   8  23   6  14  22  22   9  14  14  22  23   1  22   4  14 
## GGW HVR OLF SDY LEB PVC RKD RUT SLK CGI CPX EIS STT HPN IRK MAZ MWA OWB 
##  14  14  14  14  22  22  22  22  22  22  22  13   9   3  22  22  22  22 
## STX VIJ VQS TBN UIN YDQ YYE YOJ YOP YXJ YKA YXS YLL YQZ YXT YYD BCV CUK 
##  23  22  23  22  22  22  14  22  22  23  23  13  22  22  23  22  23  23 
## SPR SQS TZA DGA PLJ CZH PND GDT PLS SLX ACR LCR SVI ADZ PVA APO EOH AUC 
##   4  14  23  23   4  18  18  14   9  18  18  18  22  13  14  22   4  22 
## BUN CZU FLA IPI MVP PCR PDA PSO PUU RVE SJE TME UIB VGZ VVC BSC GPI NQU 
##  22  22  22  22  22  22  22  22  22  22  22  22  23  22  23  18  14  18 
## LET LPD TCD LMC LQM KIV BVA KBP OTP BLA PMV PTY PZO BNS MRD VLV AJL AUH 
##   4  18  18  18  18   9   8   1   1  13   3   1   4  22  22  22  23   6 
## ATQ CCJ DMM KWI BAH BHJ BHO BHU IXE CMB DIU DOH IXU JDH RAJ RUH UDR EWR 
##  13   9  12   1  12  22  23  22  13   1  22   6  23  23  22  24  23   6 
## YYZ IXS IXZ DED GOP IXL PBD RJA IXM TRZ JSH JKH KLX SMI AOK KSJ AXD CHQ 
##  17  23  13  23  22  23  18  14  23  23  23  23  13  13  23  14  22   8 
## EFL IEV IOA JIK JKL JNX JSI JSY JTY KIT LRS LXS MJT MLO MRS NTE PAS PHL 
##  23   3  22  22  23  22  22  22  22  22  23  23  13  22  24  12  22  16 
## SKU SOF TIA ZTH OPO KZS BYC SRZ TJA CBB TDD CIJ GYA LPB POI ORU RIB AGF 
##  22  12   9   3   1  14  18  14  23   4   4  14  18   2  14  18  18  22 
## DCM ORY AJA BVE PIS CFE SXB AUR BES LIL BIQ CFR ETZ FLR FSC GOT LAI LDE 
##  22   6   9  23  23  13   9  22   3   9  13  22  23   8  13   8  22  23 
## LRH LRT MLH PUF RNS PGF RDZ UIP EBB KSE PAF BUS KUT ABE ABI ABQ PHX ABZ 
##  13  22  13  23  13  23  22  22   9  14  14  23  23  13  22   8   7   8 
## ACT ADL BNE AEX AGS DCA AKL PPT ALO AMA AQP ART ASP IAD LHE AUS AVL AVP 
##  22  19  10  23  23   7  21  15  22  13  13  22  13   6   8  12  13  13 
## BDA BDL PIT BFL BGI BGM BGR BHD BHM BJX BMI BNA CBR CNS TSV BOI BUF PDX 
##  13   8  12  23   3  22  23   3   9  13  13  12  13  19   3   3   9   1 
## RIC ROC SAN SEA BPT BRO BTR BTV BUR BWI CAE CAK CHC CHO CHS CLE CLL CMH 
##   9   9   1   5  22  22  23  13   3  24   3   3   9  13   9  12  22  12 
## DAB DAY DEN DSM EWN FAY FLO GCM GPT HHH HSV HTS IAH ILM IND JAN LIT LYH 
##  23   9  17   9  23  23  22   9  13  22   3  23   6  13  12   3   9  22 
## MBJ MCI MGM MHT MKE MLB MOB MYR NAS OAJ OMA ORF PGV PHF PVD PWM RDU SAV 
##   8  12  23   3  12  23  13   9  19  23   9   9  22  13   9  13  12   3 
## SBY SDF SFO SLC SMF SRQ TRI UVF VPS CMI CNF COS COU CRP CTS CWA DBQ ISP 
##  22   9   6  24   8  13  23   3  13  22   8  13  22  23  12  23  22   3 
## YHZ DRO ELP FAR FAT FSD FSM GCK GGG GJT GRI GRK GRR HNL HOU ICT JLN LAW 
##   8  23   3  13   3  13  23  22  22  23  22  23   9  21  12   3  22  22 
## LBB LCH LFT LRD MAF MFE MHK MLI MLM MLU MSN OGG OKC ONT PBC PIA PSP QRO 
##  13  22  23  22  23  23  22  13  13  23   3   8   9   3  23  13   3  23 
## RAP RNO ROW SAF SAL SGF SHV SJC SJT SLP SPI SPS TUL TUS TXK TYR ELM ERI 
##  23   9  22  23   8  13  23   8  22  23  22  22   9   9  22  22  23  22 
## EUG FLG FNT GEG GIB GLA GND GRB OAK HVN IPT ITH ITM LCY JNU JUL KOA LGK 
##  13  22  13  13  23   1  13  23   8  22  22  22   9  12   2  23   3   3 
## LIH MFR MMH MRY NAN RDM STS LBA LGB LUX NCL RTM SVG VVI LSE MAO POP REC 
##   3  13  22  13  19  23  23  12   3  12  12   9   8   4  22  19  13   9 
## SKB STI MQT RST SUX TOL TVC YKF SCE SWF SBA SBP YUM PMC PUQ ACE FUE ALC 
##  13  13  22  22  22  23  23  22  23  23  23  22  22  13  23   1   1  24 
## FMO PAD MAH NBE DJE FNC GCI JER PDL PVK SPC VRA GDN LNZ INN LEI MLA SCN 
##  13  13   9   8   9   8   3   9   3  13  23  13   8  13  23   3   1  23 
## SVQ VLC VOL GNM LAZ ADD AZS BJM KGL LAD CCC VNO YMM YQR YXE FIH HOG YYT 
##  12  12  23  18  14  21  23  13   9  19  23   8  13   3  13  19  13   2 
## YXU SNU TRD YAM YBC YYY YBG YCD YCG YDF YYR YQU YFC YGK YGP YGR YQM YQX 
##  23  13   8  22  23  23  22  22  22  23   2  22  22  22  14  14  13  22 
## YQY YSJ YYG YPR YQF YQG YQL YQT YSB YTS YTZ YVO ZBF ZSA YYF YZP YXH YYB 
##  22  22  22  22  22  22  22  15  23   4  13   4  22  22  22  22  22  22 
## YZR AAX POJ AFL AJU MCZ VCP AQA ARU ATM BEL STM MAB BAZ CKS FOR IMP MCP 
##  22  14  14  14  13  13  19  14  22  14   2   4   4  14  14   9  23  14 
## BPS SDU BVB BVH BYO CAW CCM CFB JPR LDB MGF OAL PVH ROO CGH CMG CIZ CLV 
##  13   9  14  14  14  14  14  14  14  13  13  14  23  14   8  14  14  14 
## CPV IPN IZA MOC SLZ VIX PNZ CXJ IGU ERN TFF FEN NAT FLN JPA PHB THE IOS 
##  14  22  14  14  13   3  23  14  13  18   4  14   3   3  13  14  13  23 
## NVT GVR IRZ ITB JDO JOI JTC MII LEC TUR PIN TBT MEA OLC PAV PET PFB SJK 
##  23  14  18  18  23  23  14  14  14  18  14  14  14  18  14  14  23  14 
## RIA XAP PPB RBR RVD SJL TMT RMQ HUN KNH MXZ MZG OKA YNZ TTT ABV PHC ABY 
##  14  14  14  23  14  18  18   9  14  14  23  14   8   3  14   2  23  22 
## LGG HRE JRO ANR ATW BQK CSG DAL DHN ECP GTR MDW SBN VLD SOU BEY BGF NSI 
##  23   9   2  14  13  22  22   9  22  23  22  24  13  22   9  12  22   3 
## EBU KBV LPQ BLL BZV EXT GOA LBV LJU MRU NKC PNR RBA TNR VGO DAR SSG DOL 
##  23   3  13   8   3   3   3   3   9   8  13   3  13   2  13   9  13  14 
## DZA HAH EGC ENH LUN IVL KTT LIG LLW LVI RUN ZSE NBS TLN ROR AAE ORN AZR 
##  13  13  13  22   9  22  18  13  13  23   3  22  23  22  13  13   9  23 
## BJA BLJ BSK CZL DJG EBH ELU GHA HME HRM INZ MUW MZW OGX QSF TEE TGR TID 
##  23  22  22   3  22  22  22  22  23  22  22  22  22  23  23  22  22  22 
## TLM BMW CBH CFK TMR ELG IAM AGR HJR AGX GWL IXD JGA DMU SHL DHM JLR KNU 
##  23  18  14  22  18  18  14  22  18  14  22  22  22  14  14  22  22  22 
## KUU LUH STV TIR VGA MLE AOR BDO JHB KBR KCH MYY SDK TWU BPN BTJ BTU DMK 
##  22  22  22  14  22   8  23   3   3  13   9   2  23  23   9  23  23  19 
## HDY SBW JOG LBU LOP PDG PKU PLM SOC SRG SUB TGG UPG URT VTE CLQ CVM DGO 
##  23  23   9  22   3  23   3  13  23   3  12  23  19  22   9  22  22  23 
## TAP LMM MXL JAL LZC MAM NLD PAZ PDS PXM SLW TPQ AFA CPC CTC FMA FTE IGR 
##  22  23  22  22  22  22  22  23  22  22  22  22  14  14  14  14  22  22 
## IRJ JUJ LUQ PSS RES RHD RSA SDE SLA TUC UAQ VDM ADK AKN ALW CDB DLG SDP 
##  14  14  14  14  14  14  14  14  14  14  14  14  14   2  22   4  14  14 
## SNP STG BLI LWS PBG PQI BZN YAK EAT FCA GTF HLN PSG SIT WRG LTO PUW MSO 
##  14  14  13  22  23  22  23  14  22  23  23  23  14  14  14  22  22  23 
## PSC YKM AGA EUN VIL AHU RAI OUD GLN OZZ TFN TTU ESU TTA AXM BAQ BGA CTG 
##  23  22   9  22  22  18   3  13  22  22   9  22  22  14  22  13  23  13 
## CUC EJA EYP IBE MTR MZL NVA PEI PPN RCH SMR VUP TCO TML BMA MMX UME JOE 
##  22  22  22  22  22  22  22  23  22  22  22  22  14  22   9   3  23  22 
## JYV KAJ KAO KEF KEM KUO MSQ NRK OUL RVN SVL TAY TLL TMP VAA AAL PNA AES 
##  22  22  22  19  22  22   8  22  22  22  22  22   9  13  23   3  22  13 
## AHO HUY KRS MME NWI KHI KRT SEZ BAY IAS BZO CIY CLJ REG TGD TRS LCG PSR 
##   9  23  13  22  13   8   8  13  22  13  22  23   3  23   3  13  13  23 
## OMR SUJ TSR TAS TGM ASB TSE ASV WIL HGA WJR KTL LKG MRE UKA BQN ORH PSE 
##  22  22  13  12  22  13   8  18   2  23  23  18  18  18  18  22  22  22 
## ABD MHD THR AWZ IFN KIH SRY SYZ AZD BND GSM KSH RAS TBZ ZAH AAR TAB DUR 
##  23  19  19   3   3   3  23   8  23   3  23  23  13  13  13  23  23   3 
## PLZ GRX IOM VFA WDH PFO SPB SSB SDJ UKB YGJ KOJ ISG MMY NGS KOI LSI EMA 
##  23  13  13  23   3   9  20  20   9  13  23   3  13  23   3   2  23   1 
## INV BEB SYY NOC WAT BRR CAL CFN DND DSA WIC ILY TRE LPL GTE MZV MIR HJJ 
##  13  22  23  13  22  22  22  22  14  23  22  22  22   8  14  23  13  22 
## LLF TEN YNT HEK OHE JGD JMU JXA BMV VII CXR DAD HPH PQC EBJ KSU EVE BBK 
##  14  23   8  14  14  14  13  23  23  23  23   9  22  23  22  23  23  22 
## GBE MUB FRW AKJ HKD KMQ OKJ TXN PLQ BKY KND KOO BNB MDK BNC BUX GOM IRP 
##  23  23  22  23  13   3  13   3  22  18   4  18  14  14  25  25   4  25 
## FBM KGA MJM FKI TSH GMA FMI LJA CYO SCU GEO BSG AKU BPX DAX GYS HYN JDZ 
##  13  14  14   4  14  18  18  20  22  23  23  14  23  22  13  23  13   3 
## LZO WUS YCU CHG CIF CIH KRL YIN YIW DDG HIJ DQA FNJ FUG HLD HLH HMI HSN 
##  13  13   9  22  13   3  13  22   3  23   3  23  23  13   3  23  13  13 
## HTN YNJ JGS JIU JNZ JUZ LZH MDG MWX NDG RLK TAE TGO ULN WUA XFN XIL PEU 
##  23  13  13  23  23  23  13  13  23  23  23  23  13   2  23  13  23  14 
## AVN POM BUA RAB DAU LAE UNG GKA HGU MAG GUR LSA MIS PNP MXH TBG TIZ WWK 
##  14  15  14  13  14  13  14  14  13  23   4  18  18  14  14  14  14  23 
## HKN KVG MAS LNV TFI BUL FSZ TNN KMI TOY CMW GAO KHV USM VVO AAT ACX AOG 
##  23  14  14  14  14  14  13  22  13  13  22  22   9   3   3  14  23  22 
## AQG AVA BFJ BSD HZH JNG JUH LLB LYG NAO NNY KIJ LDS KCA LNJ WNH ZAT KRY 
##  23  22  23  14  22  13  23  22   3  23  23   3  14  14  14  14  22  14 
## NLT OSS TCG ENY CEE VUS KVK NLA OOL AGH KLR RNB SDL THN GSE BFV CEI CJM 
##  14   9  14  23  23  14  22  13   9  22  22  22  23  14   3  14  13  14 
## UTH KOP LOE MAQ NNT NST PHS PRH ROI SNO TST UBP UNN ABR APN BIS BJI BRD 
##  23  14  14  14  14  14  14  14  14  14  14  22  14  22  22  23  22  22 
## INL BTM BTS CDC CIU CNY COD CPR DIK DLH ESC PLN EKO GCC RKS HIB IDA IMT 
##  22  22   3  22  22  22  22  22  22  22  22  22  22  22  22  22  22  22 
## RHI ISN JAC KSC LNK MOT PIH SGU TWF VEL CSK ZIG CAB SZA CBT VPE LUO MEG 
##  22  22  22  23  22  23  22  22  22  22  18  22  22  22  22  23  22  22 
## MSZ NOV SDD SPP SVP TMS VHC SCO CIT DMB DZN KGF KOV KSN PLX PPK UKK GUW 
##  22  22  22  22  22  22  22   3  13  22  22  23  22  22  22  22  23  13 
## KZO URA SZI RNN MOL SRP RYG ALF KRN LLA BDU BOJ BOO KRP HAU KKN LYR MJV 
##  22  22  14  22  23  22   9   4  22  23  22  13   4  22  13  23  22   3 
## SZZ POG COQ MXV ULG ULO KQT TJU REN ORK SNN BLK BOH KIR SCQ SEN BGW BKQ 
##  23  14  14  14  14  14  23  23  23   9   9  23   3  23   9  13  13  22 
## LRE ROK BSR GOV EBL MED PEW SAH SKT WLG ZQN DOK ELQ TIF TUU YNB ACZ ADU 
##  22  23  23  14   9   8   9   9  13   9  23  13  13  13  13  13  14  14 
## AFZ PGU BDH BJB BUZ BXR DEF LFM LRR ZBR GBT GCH HDM IIL ISU KDH KER KHY 
##  14  14  22  14  23  14  14  22  23  23  23  14  14  14  13  23  14  14 
## NSH RZR OMH PFQ SDG YES ESM CUE ETR GPS LOH LTX LGQ MEC TNW TUA XMS MLW 
##  14  14  22  14  14  14  22  22  14  14  14  14  14  14  18  22  14  22 
## AMH ASO AXU BJR DIR ENU GDQ GMB JIJ JIM MPM MQX SZE LLI BLZ GDE SHC HRI 
##  22  22  22  22  22  22  22  22  22  22   3  22  22  18  23  18  18  23 
## PXO NYK UAS SSY LMP LUG PNL TPS AIA CDR ALS FMN TTN ATY PIR BKG CYS WRL 
##  22  18  18  22  22  22  22   9  22  18  23  23  13  22  23  22  23  14 
## DDC LBL ILG SOW HON IGM PGA UST VAR KKC NAW ESB SFB APW CXI FUN SUV HIR 
##  23  23  23  23  14  22  23  14  13  22  14   8   8  23  22  14   4  19 
## VLI ICI KDV LBS LKB RTA SVU TBU TRW TVU VBV HRL SHP AAY ADE AHB GXF RIY 
##  19  14  14  14  14  14  14  23  14  14  14  23  23  14   3  13  23  13 
## AXK TAI HOD SCT CRL EIN HHN LTN NRN PIK SDR ZAZ CIA NYO VST GRO PMF KUN 
##  14  23  23  14  12  12   8   1   9   3   3  23   8   9  22   8  14   3 
## MST WMI VLL LBC LPP BZG LDY REU CCF BZR BRQ RZE PEG FNI DLE DNR TUF GPA 
##  13   3  22  22  14  22  23   3  13  23  14  13  23  22  22  22  23  22 
## GRQ SFT PDV LUZ XCR OSI OSR FKS OIT SZB BTH IPH KTE KUA HAS HRK MUX NJF 
##  23  22  14  23  22  22  22  14  13   9   9  22  14  23  23  13  13  13 
## PZU SLL CZS PGD PIE AZA OGD PVU RFD STC BLV CKB HGR IAG SCK SMX LCK YNG 
##  23  23  18   3   9   9  14  22  23  22  14  14  22  23  22  22  14  22 
## PSM AEB DOY WUZ ATZ HMB HOF AMQ BDJ BEJ BIK DJJ BKS BMU MDC TRK TKG DJB 
##  14  22  23  14  23  23  22   4  13  14  14   4  23  14   4  23  23  23 
## MLG PGK PKY PLW PNK TJQ TNJ TTE MKQ MKW TIM KOE LBJ TMC ENE GTO KDI SOQ 
##  22  23  22  23  23  22  22  23  18  14  14  13  14  14  18  14  22   4 
## KUH MYJ AGM IOQ KUS KUZ SGG TQI AOQ JUV CNP OBY SFJ GOH JAV JFR JHS JSU 
##  23  13   4  25   2  25  25  25  25   2  18  25  15   2  15  18  14  14 
## UAK IKE SAE UMD IOT JUU IUI TQA JEG JQA JJU JNN JNS LLU QFG QJH QUW XEQ 
##   2  25  25   4  25  25  25  25  14   2   2  25  18  25  25  25  25  25 
## QFX JUK KGQ KHQ NAQ NSQ UPK SRK THU NIQ QOQ QFN QUV SVR KSO KZI ACI BPL 
##  18  25  25  25  25  25  25  25  25  25  25  25  25  25  22  22  14  14 
## ERL IQN JIC YZY AKB DUT KCG KLL PIP WSN KFP KVC NLG IKO KQA EGX IGG KCL 
##  22  23  23  14  20  20  18  18  18  18  18  18  18  20  20  25  25  25 
## KCQ KPV UGB PTH AIT AIU RAR MGS MOI MUK CJC LSC ARI BBA ZAL ZCO CPO RUA 
##  25  25  25  25  14  14   4  14  14  14  23  23  23  22  18  22  22  14 
## ITO LNY MKK PPG MMB OBO BLD GCW PRI LCX YNY OST BLE ORB OSD WEF SID YGH 
##  22  22  22  22  23  22  20  20  14  14  22  22  14  14  22  23   3  18 
## ZFN YWJ AZN UGC TMJ BVV UUS DEE EKS OHH KLW BHV UET LYP MLN OVD EAS LEN 
##  18  18  22  23  22  14   4  14  14  14  14  23  13  22  23   3  22  22 
## RGS SLM ILD RJL ATD BNY RNL CHY GZO EGM RBV VAO FRE MUA IRA JJA KGE NNB 
##  22  22  22  22  18  18  18  18  18  18  18  18  18  18  18  18  18  18 
## RNA RUS SCZ OMO SSH SXK PKN OKL WMX DOB LUV KTG ABA BQS OMS ISC GDX KYZ 
##  18  18  18  14   9  18  23  18  18  25  18  18  22  23   3  14  23  14 
## UUD LEQ SLY KHD XBJ AAN ASM HFA KVD YSM YPY EGN ELF UYL AGN TKE ELV GST 
##  13  18  23  14  14  14  23  14  23  22  14  14  14  14  14  18  18  14 
## HNH HNS SGY PEC RDN LXR BNX CXH YWH YIE BFN HLA GRJ AOJ NKM MMJ GAJ HNA 
##  14  14  14  14  22  13  22  20  20  14  22  14  23  23  14  22  22  22 
## KCZ KMJ AGT RIG ASJ AXT IZO MSJ SHM TKS UBJ DUD AVV AYQ HBA HTI LST MKY 
##  22  13  22  18  22  23  22  22  22  22  22  23  22  22  23  23   4  23 
## NTL PPP BNK MCY FKQ NBX KBU NTX BUW BXB MOF WGP KNG KAZ LUW MNA NAH MJU 
##  23  22  23  23  18  18  14  18  14  18  14  14  25  14  14  14  14  14 
## PSJ PUM BBO BSA GLK YAG YQK YFO YQD YHD YRL YXL YYU CAP XSC EDA HYG KCC 
##  14  14  23  14  22  14  14  14  14  18   2   2  14  14  14  18  14  18 
## WWP KPB PPV NKI AHN MKL IPL ELD HOT HRO SLN OTH PDT KOS HGN PYY PBH PWQ 
##  18  14  18  25  14  14  22  14  14  22  14  22  22  14  14  14  23  22 
## HIN KUV KWJ RSU USN WJU KPO LPI NAY FUO ILI APL POL MWZ CYB LYB LCE OUZ 
##  14  14  14  14  14  14  14  22  12  14  14  23  23  23  22  14   4  22 
## NDB CIX CJA IPC PIU TBP TCQ TRU MHC MPN ZOS OLL ANG BVC BFS GOJ LWO SBZ 
##  22  22  22  22  22  22  22  22  18  18  22  14  14  13   9   3   3  23 
## OGL SVD EOI NDY NRL PPW SOY WRY GHT LAQ LTD QUB SRX CNM LAM LNS VCT OLA 
##  14  14  18  18  18  18  18  18  14  22  14  14  22  14  14  22  22  22 
## VDB ASW BFI CLM ESD DHB RCE WSX FRD FBS LKE LPS ORX BVS MEU MTE OZH UDJ 
##  22  23  20  20  20  20  20  20  20  20  20  20  14  22  14  14  22  14 
## ANM TMM WMN DIE NOS SVB MJN FTU TLE MOQ SMS WMR KAN BBN MUR KUD LDU LWY 
##  14  23  14  23  14  14  14  14  14  14  14  18  23  14  14  14  14  14 
## BKM MKM TGC LBP LGL LKH LMN ODN DIL RRG ELS YGX BYN LTI HVD DLZ ULZ ABS 
##  18  14  14  18  14  14  14  14  22  22  23  14  14  18  14  22  14  14 
## KGT GOQ NGQ NYT ZQZ YUS JHM HNM MUE ORZ INB SVK JBQ AUY TAH AWD FTA SON 
##  22  14  14  22  14  14  22  14  14  18  18  18  14  18   4  18  18   2 
## CCV LNB NUS ULB DLY IPA EAE LNE LOD LPM MTV SLH TOH ZGU MWF NOU SWJ PBJ 
##  14  14  14  18  14  14  14  14  18  14  18  18  18  18  18  13  14  14 
## SSR WLH TGH VLS SHB WKJ FUJ TSJ HAC IWJ IWK MBE NTQ OIM ONJ SYO TTJ IKI 
##  18  18  14  14  22  22  22  22  22  22  22  22  22  22  22  22  22  14 
## CFC JCB GPB ERM GEL SRA URG ACY LBE SKZ GMZ VDE UEO AEY RKV EGS IFJ BHE 
##  14  14  14  14  18  14  18  13  22  23  14  22  14  18   4  18  18  22 
## GIS HLZ KAT KKE NPE NPL NSN PMR PPQ ROT TRG TUO WAG WHK WRE ALH CNJ NLK 
##  22  22  22  22  22  22  22  23  22  22  22  22  22  22  22  14  23  22 
## BQB HKK IVC DCN EPR GET IUE KGI KNX LEA PBO RVT PQQ TIU WSZ NYI TKD SRE 
##  14  14  14  14  14  14  20  23  23  14  14  14  23  14  14  22  22  23 
## KLV PEE INU MAJ DNK BWK PMY CIP KAA MFU SLI MNS LUK MMU MBL GJA UII YHU 
##  23  23  22   4  13  14  14  14  14  14  14  14  22  22  14  18  14  14 
## YVB YGV YAY YBX YCL YDP YNP YHO YMN YJT YSO ZUM VAN ASR HTY MQM VAS KYA 
##  14  14  14  18  22  18  25  25  25  14  18  14  23  23  13  23  22  22 
## BAL DNZ EDO ERC KCM MSR MZH NAV LPT TDX THS UTP CKH CYX IKS MQJ NER SUK 
##  22  22  22  22  22  22  22  22  22  22  22  22  14  14  14  14  23  14 
## FSP RYK CJL DBA DEA DSK PZH GIL GWD TUK KDU MJD PJG ATC LGI RCY RSD SML 
##  22  22  22  18  22  14  14  22  22  23  22  22  22  22  22  22  22  22 
## TBI CYP JOL MBT IFO ARK BKZ MBI MYW CMU VAI MDU WBM GAN DRV HAQ FVM KDM 
##  22  22  18  22  22  14  18  14  14  14  14  14  14  22  22  14  22  22 
## GKK KDO CKX TKJ HKB ABM AUU CUQ BEU BQL BVI RMA TWB ISA BUC DMD ONG WNR 
##  22  22  20  20  14  14  14  14  18  18  25  22   4   2  18  18  18  18 
## CMA SGO XTG EDR IRG KWM NTN WEI CTL ULP YPN YIF ZGS YNA SXI GOU MVR NGE 
##  18   4  25  14  14  14  14  14   4  18  14  18   4   4  14  14  14  14 
## ABX OLP PLO ARM BCI BDB BME KTA EMD GLT HVB LDH MOV PHE ZBL CFS HID DBO 
##  22  14  14  22  22  22  13  23  22  22  22  22  22  23  22  22  14  22 
## DPO MQL MRZ ZNE TMW WGA STD VIG ZVK HOE PKZ LXG ODY XKH OSW DYR NGK RMI 
##  22  23  22  14  22  22  22  22  22  14  23  14  14  14  22  22  14  22 
## PWE MUN FAE AZI FJR XSB ZDY AQJ OSM HOR PIX SMA TER CDJ CMP GRP MQH BSS 
##  22  22  22   4  14  22  14  22  22  23  22  22  13  14  14  20  20  14 
## OIA RDC STZ SXO SXX AAQ BAX KEJ NOZ NSK OGZ RGK SIP STW TOF PKC BEW BUQ 
##  18  14  20  20  20  22  22  22  22  13  22  22  23  22  23  23  23  22 
## HDS KIM MQP UTN WVB MSU MTS PHW PTG PZB RCB TET UTT VNX FUT WLS HBX IXG 
##  22  22  22  22  22  22  22  22  22  22  22  23  22  22  18  14  22  22 
## MYQ TCR PUG BWT KNS FLS MEB PTJ CVU FLW GRW SJZ AGB ERF KSF CEG ONQ XFW 
##  22  22  14  22  22  18  20  20  14  14  14  14  22  23  22  22  22  22 
## GDZ ABT AJF AQI BHH EAM GIZ DWD EJH RAE SHW URY WAE ULH RAH TUI ERS MPA 
##  22  22  22  22  22  22  23  22  22  22  22  22  22  22  22  22  20  20 
## NDU OND LUD OMD BRN HMA DIJ PGX LEH VDA TEB ADF AJI AOE BGG CKZ CND IGD 
##  20  20  14  18  13  23  22  22  22  20  14  22  22  22  22  14  22  22 
## KCO KSY TEQ ISE KFS KZR NAJ NOP MCV MNG ELC MGT VXC UEL INH VPY VXE TOE 
##  14  22  14  22  22  22  22  22  14   4  18  18  14  14  22  14  23  22 
## BMY GEA KOC ILP KNQ LIF MEE TGJ TOU UVE GBB LLK LWN ACV CEC AOO JST ASE 
##  20  20  20  20  20  20  20  20  20  20  22  22  22  22  22  22  22  22 
## BFD JHW BKW SHD CIC MGW CLD DUJ FKL PKB CMX EGE GUC HDN LAR MTJ PUB EAU 
##  22  22  22  22  22  22  22  22  22  14  22  22  22  22  22  22  22  22 
## FOE ROP TKK YAP HOB KSA KWA PNI LMT MKG MOD PAH RDD LPY MSW GAE GAF BTC 
##  22  14  14  14  22  18  18  18  22  22  22  22  22  22  20  22  22  18 
## GIU KCT DIW TRR PED AXP CRI IGA MYG NYA UTS TBW URS BJZ CAJ CBS CUM CZE 
##   4  22  18  18  22  22  22  22  22  22  14  22  22  22  18  22  22  22 
## LFR PYH SOM SVZ PBL SNV VLY GLO CCK XCH DLI HUI UIH CAH PXU DIN TBB VCA 
##  22  22  22  22  14  18  14  14  18  14  23  22  22  22  22  22  22  22 
## VCL VDH THD VCS VKG MMO SFL SNE AHE XMH AUQ NHV UAH UAP AXR KKR BOB HUH 
##  22  22  22  22  22  14  14  14  14  14  14  14  18  18  14  18  23  14 
## MAU MOZ RFP RGI TIH FAV GMR HOI MKP KHZ KXU MVT RKA RMT RUR RVV TKX TUB 
##  14  14  14  23  14  14  18  14  18  18  25  14  14  14  14  14  14  14 
## TKP EVG HFS KID MXX TYF PJA MHG URE VIN ABB BNI CBQ GMO IBA ILR QOW QRW 
##  18  22  22  22  22  14  14  22  14  22  22  22  22  14  14  14  22  22 
## SKO YOL JOS KAD QUO ANS ATA JAU TGI ARW CRA DEB TZL KET KYP MYT PBU KME 
##  14  14  22  22  22  22  22  22  22  14  22  22  14  18  14  14  18  14 
## HFT LKL SOJ VDS ANX BNN FDE FRO HOV SKE SOG BJF BVG MEH VAW MQN SSJ LKN 
##   4  14  14  23  14  23  22  23  22  14  22  18  18  18  18  14  23  18 
## MJF NVK RET SKN SVJ HAA HVG OSY RVK RRS SDN YHR ZTB ZLT YRG ZKG EUX SAB 
##  14  18  18  14  18  14  18  14  14  22  22  18  25  25  18  18  22  22 
## YBR YHM YXX KEW KIF WNN MSA XBE ZPB ZRJ SUR YAX YTL XKS YAC YER YFH YLH 
##  22  22  22  25  18  18  18  18  18  18  25  18  18  18  18  18   4  18 
## YOG YHP YNO YWP YPL YPM YVZ ZSJ KHS ZQW EXI KAE APF UPN IAA TGP THX MRX 
##  18  25  25  14  18  18  18  18  22  23  14  14  22  22  14  14  14  14 
## NOJ KGP TQL YAT YPO ZKE YFA YMO YKU YKQ YMT YNS ZEM YNC MCM GCN BDP BHR 
##  23  22  14  25  25  25   4   4  18  18   4  14  18  18  22  14  14  14 
## BIR BWA DHI JKR KEP PKR TMI KWF UKS RBQ UYU BFF CEZ EAR LBF MCK RIW SHR 
##  14  14  14  14  14  14  14  14  22  14  14  22  22  22  22  22  22  22 
## MCE PRC VIS SVC BHQ CED CPD KGC MGB WYA BHS PKE GFF NRA GFN TRO JCK RCM 
##  22  22  22  22  22  14  14  14  22  14  22  22  22  22  14  22  18  18 
## WIN LSY MIM MYA OAG 
##  14  22  22  22  22 
## 
## Within cluster sum of squares by cluster:
##  [1]   8.0436976   5.6999398   2.0068893   2.7816807  49.4401768
##  [6]  26.6731883  14.8075891   7.8556135   4.5286978   8.5245708
## [11] 167.8981048   6.0945424   1.3037050   1.7156726   8.8787815
## [16]  22.9882700  58.5233522   1.7169417   6.7776807   0.3868652
## [21]   8.7060835   1.5636750   1.7056406   9.5042685   1.5921893
##  (between_SS / total_SS =  96.9 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"    
## [5] "tot.withinss" "betweenss"    "size"         "iter"        
## [9] "ifault"      
## Warning: did *not* converge in specified number of iterations
centralities<- data.frame(centralities, fit$cluster) # append cluster membership
head(centralities)
##     indegree outdegree closeness_in         btwn fit.cluster
## AER       26        26   0.01801138 2.057750e-05           3
## KZN       28        28   0.01801868 2.211094e-05           9
## ASF        8         8   0.01796951 3.970297e-07          23
## MRV       22        22   0.01805165 2.315226e-05           3
## CEK       20        20   0.01797724 2.473746e-06           3
## OVB       90        87   0.01813761 1.385724e-03          12
aggregate(centralities, by=list(fit$cluster), FUN=mean) 
##    Group.1   indegree  outdegree closeness_in         btwn fit.cluster
## 1        1 105.600000 105.444444 0.0181196358 1.589851e-03           1
## 2        2  15.432432  15.756757 0.0178062465 4.977908e-03           2
## 3        3  19.609195  19.643678 0.0180110009 1.501828e-04           3
## 4        4   7.461538   7.415385 0.0177480913 1.610622e-03           4
## 5        5 202.250000 202.250000 0.0182222118 5.424781e-02           5
## 6        6 213.541667 213.958333 0.0182236044 1.349113e-02           6
## 7        7 215.631579 215.157895 0.0181484670 2.980895e-03           7
## 8        8  49.944444  49.755556 0.0180747394 9.755793e-04           8
## 9        9  33.446154  33.476923 0.0180347306 4.192256e-04           9
## 10      10 179.500000 180.833333 0.0182023601 2.853296e-02          10
## 11      11 575.285714 578.285714 0.0183210210 5.975120e-02          11
## 12      12  75.408451  75.647887 0.0180927496 6.704821e-04          12
## 13      13  11.835878  11.744275 0.0179811965 5.299944e-05          13
## 14      14   2.057096   2.017945 0.0176986187 3.485233e-05          14
## 15      15  37.833333  38.583333 0.0179647715 1.457452e-02          15
## 16      16 311.937500 313.375000 0.0182117254 8.016174e-03          16
## 17      17 374.400000 372.933333 0.0182739440 3.112762e-02          17
## 18      18   2.263158   2.266447 0.0174498495 1.344642e-04          18
## 19      19  46.791667  46.833333 0.0180400589 6.927876e-03          19
## 20      20   1.404255   1.574468 0.0002923251 1.536861e-04          20
## 21      21 110.812500 110.062500 0.0181653137 9.635728e-03          21
## 22      22   2.215709   2.202814 0.0178875213 1.171597e-05          22
## 23      23   6.368071   6.325942 0.0179142493 5.617353e-05          23
## 24      24 146.000000 146.685714 0.0181254869 1.745877e-03          24
## 25      25   1.580952   1.619048 0.0170131699 2.298481e-04          25

(d) Do you observe the groups obtained in Step 4 to be similar to or different from what you obtained in Step 5? Why?

From the above it can be inferred that K-Mean Clustering is more efficient as it groups the Airports with higher Modularity. With Clauset-Newman-Moore Algorithm having low modularity reduces its  strength to bring out the optimized solution. K-mean provide us with that, With K-mean airports are spread across different grops efficiently.  

2.6 Step 6: Carefully observe the centralities of the airports in the dataset

(e) Identify a few (3-4) airports that you already know of to some extent in terms of their characteristics. Explain how centralities of those airports relative to that of the other airports in the network are in line with the characteristics you alreadyknow of about those airports.

The above results show that main airports are Delhi, Bangalore, Mumbai, Hyderabad as they have high closeness and betweeness centrality which is quiet apt as these are the metropolitan cities of India and have majority of corporate hubs. On the other hand if the Airport in Leh, depending on the Leh topography it is opened only for couple of months in the entire year making the  usage of the airport here almost nil.

(f) If your organization is planning on launching a new flight service on a couple of new routes, what will that be (based on the information you have in THIS dataset)? Explain your answer. What other information will help you being more comfortable you’re your decision.

It's advisable to introduce the new flight between two airports which are not having direct flights i.e., not having direct edge but connected using some other nodes, the metric is that the airports which are having more between centrality.