Unstandardized LPA

#import data 
library(readr)
data <- read_csv("~/Desktop/Lab/FirstGen Professional/FGP Exploratory Study/FGP Exploratory Study Analyses/data.csv")

## New names:
## Rows: 211 Columns: 30
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (7): recruitment, year, occupation, duration, Q19, Q22, Q23 dbl (23): ...1, ID,
## age, gender, sexuality, born, ethnicity, income, fam_inc...
## ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
## Specify the column types or set `show_col_types = FALSE` to quiet this message.
## • `` -> `...1`

library(dplyr)

## 
## Attaching package: 'dplyr'
## 
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## 
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

fgp_data <- data %>% filter(fgp == '1')

d <- data.frame(fgp_data$sap_stand, fgp_data$sap_dis, fgp_data$anxiety, fgp_data$depression, fgp_data$wswb, fgp_data$wellbeing, fgp_data$age, fgp_data$sexuality, fgp_data$gender, fgp_data$income, fgp_data$fam_income, fgp_data$ethnicity, fgp_data$edu, fgp_data$religion, fgp_data$year)

d <- rename(d, standards = fgp_data.sap_stand, discrepancy = fgp_data.sap_dis, anxiety = fgp_data.anxiety, depression = fgp_data.depression, swfw = fgp_data.wswb, wellbeing = fgp_data.wellbeing, age = fgp_data.age, sexuality = fgp_data.sexuality, 
gender = fgp_data.gender, income = fgp_data.income, fam_income = fgp_data.fam_income, ethnicity = fgp_data.ethnicity, edu = fgp_data.edu, religion = fgp_data.religion, year = fgp_data.year)

write.csv(d, file = "fgp_lpa_data.csv", row.names = FALSE)

Using kmeans

#make a dataframe of just standards and discrepancies
cluster_data <- data.frame(d$standards, d$discrepancy)
cluster_data <- rename(cluster_data,standards = d.standards, discrepancy = d.discrepancy )
# remove missing data
cluster_data <- na.omit(cluster_data)

library(factoextra)

## Loading required package: ggplot2

## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

#calculate distance metrics between oberservations
distance <- dist(cluster_data)
distance

##             1         2         3         4         5         6         7
## 2   10.630146                                                            
## 3   14.422205  4.123106                                                  
## 4   14.866069  4.472136  3.605551                                        
## 5    3.605551  7.071068 10.816654 11.401754                              
## 6   12.727922  2.236068  3.162278  2.236068  9.219544                    
## 7   15.620499  5.000000  2.000000  2.236068 12.041595  3.162278          
## 8   12.041595  2.000000  4.123106  2.828427  8.602325  1.000000  4.123106
## 9    9.219544  1.414214  5.385165  5.830952  5.656854  3.605551  6.403124
## 10   1.000000  9.899495 13.601471 14.212670  2.828427 12.041595 14.866069
## 11   2.236068  8.485281 12.206556 12.806248  1.414214 10.630146 13.453624
## 12  10.000000  1.000000  4.472136  5.385165  6.403124  3.162278  5.656854
## 13   6.403124  4.242641  8.062258  8.602325  2.828427  6.403124  9.219544
## 14  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 15   2.236068  8.485281 12.206556 12.806248  1.414214 10.630146 13.453624
## 16  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 17   1.000000  9.899495 13.601471 14.212670  2.828427 12.041595 14.866069
## 18  10.816654  1.414214  3.605551  5.099020  7.211103  3.000000  5.000000
## 19   7.810250  2.828427  6.708204  7.211103  4.242641  5.000000  7.810250
## 20  10.630146  1.414214  5.000000  4.242641  7.211103  2.236068  5.385165
## 21   1.000000  9.899495 13.601471 14.212670  2.828427 12.041595 14.866069
## 22  15.620499  5.000000  2.000000  2.236068 12.041595  3.162278  0.000000
## 23   9.219544  1.414214  5.385165  5.830952  5.656854  3.605551  6.403124
## 24  10.000000  1.000000  4.472136  5.385165  6.403124  3.162278  5.656854
## 25   5.830952  5.000000  8.602325  9.433981  2.236068  7.211103  9.899495
## 26   8.602325  2.236068  5.830952  6.708204  5.000000  4.472136  7.071068
## 27   2.236068 12.727922 16.401219 17.029386  5.656854 14.866069 17.691806
## 28   2.236068 12.727922 16.401219 17.029386  5.656854 14.866069 17.691806
## 29   4.123106  7.211103 10.630146 11.661904  1.414214  9.433981 12.041595
## 30   1.414214 10.630146 14.212670 15.000000  3.605551 12.806248 15.556349
## 31   3.162278  7.810250 11.401754 12.206556  1.000000 10.000000 12.727922
## 32   9.219544  1.414214  5.385165  5.830952  5.656854  3.605551  6.403124
## 33   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 34   2.236068 10.000000 13.453624 14.422205  3.162278 12.206556 14.866069
## 35   1.414214 12.041595 15.811388 16.278821  5.000000 14.142136 17.029386
## 36  12.727922  2.236068  3.162278  2.236068  9.219544  0.000000  3.162278
## 37   7.810250  2.828427  6.708204  7.211103  4.242641  5.000000  7.810250
## 38   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 39   6.403124  4.242641  8.062258  8.602325  2.828427  6.403124  9.219544
## 40  17.691806  7.071068  4.123106  3.162278 14.142136  5.000000  2.236068
## 41  14.866069  4.242641  2.236068  1.414214 11.313708  2.236068  1.000000
## 42   4.242641  6.403124 10.295630 10.630146  1.000000  8.485281 11.401754
## 43  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 44  10.630146  0.000000  4.123106  4.472136  7.071068  2.236068  5.000000
## 45  12.727922  2.236068  3.162278  2.236068  9.219544  0.000000  3.162278
## 46   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 47  10.630146  0.000000  4.123106  4.472136  7.071068  2.236068  5.000000
## 48  11.313708  1.000000  4.000000  3.605551  7.810250  1.414214  4.472136
## 49   4.000000  8.062258 11.313708 12.529964  2.236068 10.295630 12.806248
## 50  17.029386  6.403124  3.162278  3.000000 13.453624  4.472136  1.414214
## 51   5.000000  5.656854  9.433981 10.000000  1.414214  7.810250 10.630146
## 52   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 53  14.866069  4.242641  2.236068  1.414214 11.313708  2.236068  1.000000
## 54  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 55   2.236068 12.727922 16.401219 17.029386  5.656854 14.866069 17.691806
## 56   5.000000  5.656854  9.433981 10.000000  1.414214  7.810250 10.630146
## 57  17.691806  7.071068  4.123106  3.162278 14.142136  5.000000  2.236068
## 58   8.485281  2.236068  6.324555  6.403124  5.000000  4.242641  7.211103
## 59  13.038405  3.000000  1.414214  4.123106  9.433981  2.828427  3.162278
## 60   8.944272  3.000000  5.656854  7.280110  5.385165  5.099020  7.211103
## 61  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 62   2.236068 12.727922 16.401219 17.029386  5.656854 14.866069 17.691806
## 63   5.830952  5.000000  8.602325  9.433981  2.236068  7.211103  9.899495
## 64  15.620499  5.000000  2.000000  2.236068 12.041595  3.162278  0.000000
## 65   1.414214 12.041595 15.811388 16.278821  5.000000 14.142136 17.029386
## 66   2.236068  8.602325 12.529964 12.727922  2.000000 10.630146 13.601471
## 67   2.236068 10.000000 13.453624 14.422205  3.162278 12.206556 14.866069
## 68   1.414214 12.041595 15.811388 16.278821  5.000000 14.142136 17.029386
## 69   1.414214  9.219544 13.038405 13.453624  2.236068 11.313708 14.212670
## 70   5.000000  5.656854  9.433981 10.000000  1.414214  7.810250 10.630146
## 71   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 72   3.000000  8.602325 12.041595 13.038405  2.000000 10.816654 13.453624
## 73   5.830952  5.000000  8.602325  9.433981  2.236068  7.211103  9.899495
## 74  12.806248  2.236068  2.000000  3.000000  9.219544  1.414214  2.828427
## 75   1.414214  9.219544 13.038405 13.453624  2.236068 11.313708 14.212670
## 76   5.000000  5.656854  9.433981 10.000000  1.414214  7.810250 10.630146
## 77  10.630146  1.414214  5.000000  4.242641  7.211103  2.236068  5.385165
## 78   3.162278  7.810250 11.401754 12.206556  1.000000 10.000000 12.727922
## 79   6.403124  4.242641  8.062258  8.602325  2.828427  6.403124  9.219544
## 80  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 81  18.439089  7.810250  4.472136  4.123106 14.866069  5.830952  2.828427
## 82   8.602325  3.000000  7.071068  6.403124  5.385165  4.472136  7.615773
## 83   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 84   9.219544  1.414214  5.385165  5.830952  5.656854  3.605551  6.403124
## 85   6.403124  4.242641  8.062258  8.602325  2.828427  6.403124  9.219544
## 86  12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 87  15.556349  5.000000  3.162278  1.000000 12.041595  2.828427  1.414214
## 88   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 89   2.236068 12.727922 16.401219 17.029386  5.656854 14.866069 17.691806
## 90   4.472136  6.403124 10.000000 10.816654  1.000000  8.602325 11.313708
## 91  16.278821  5.656854  3.000000  2.000000 12.727922  3.605551  1.000000
## 92   3.162278  9.848858 13.928388 13.601471  4.123106 11.661904 14.764823
## 93   2.236068  8.485281 12.206556 12.806248  1.414214 10.630146 13.453624
## 94  13.453624  2.828427  2.236068  2.000000  9.899495  1.000000  2.236068
## 95   1.414214  9.219544 13.038405 13.453624  2.236068 11.313708 14.212670
## 96  10.630146  0.000000  4.123106  4.472136  7.071068  2.236068  5.000000
## 97   9.899495  1.000000  5.099020  5.000000  6.403124  2.828427  5.830952
## 98   3.605551  7.071068 10.816654 11.401754  0.000000  9.219544 12.041595
## 99   9.219544  1.414214  5.385165  5.830952  5.656854  3.605551  6.403124
## 100  6.403124  4.242641  8.062258  8.602325  2.828427  6.403124  9.219544
## 101  3.000000  8.602325 12.041595 13.038405  2.000000 10.816654 13.453624
## 102 18.439089  7.810250  4.472136  4.123106 14.866069  5.830952  2.828427
## 103 10.630146  0.000000  4.123106  4.472136  7.071068  2.236068  5.000000
## 104  6.403124  4.242641  8.062258  8.602325  2.828427  6.403124  9.219544
## 105 12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 106  2.236068 12.727922 16.401219 17.029386  5.656854 14.866069 17.691806
## 107 12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 108  5.385165  5.830952  9.219544 10.295630  2.000000  8.062258 10.630146
## 109 12.041595  1.414214  3.000000  3.162278  8.485281  1.000000  3.605551
## 110 16.401219  5.830952  2.236068  3.162278 12.806248  4.123106  1.000000
## 111 14.866069  4.242641  2.236068  1.414214 11.313708  2.236068  1.000000
## 112 16.278821  5.656854  3.000000  2.000000 12.727922  3.605551  1.000000
## 113 14.866069  4.242641  2.236068  1.414214 11.313708  2.236068  1.000000
## 114 12.806248  2.236068  2.000000  3.000000  9.219544  1.414214  2.828427
## 115  1.000000 11.313708 15.000000 15.620499  4.242641 13.453624 16.278821
## 116 11.661904  2.236068  2.828427  5.000000  8.062258  3.162278  4.472136
## 117 14.866069  4.242641  2.236068  1.414214 11.313708  2.236068  1.000000
## 118  7.810250  2.828427  6.708204  7.211103  4.242641  5.000000  7.810250
## 119 20.518285  9.899495  6.708204  5.830952 16.970563  7.810250  5.000000
## 120  9.219544  1.414214  5.385165  5.830952  5.656854  3.605551  6.403124
## 121 13.892444  5.099020  6.403124  3.162278 10.770330  3.605551  5.385165
##             8         9        10        11        12        13        14
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9    3.162278                                                            
## 10  11.401754  8.485281                                                  
## 11  10.000000  7.071068  1.414214                                        
## 12   3.000000  1.000000  9.219544  7.810250                              
## 13   5.830952  2.828427  5.656854  4.242641  3.605551                    
## 14   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854          
## 15  10.000000  7.071068  1.414214  0.000000  7.810250  4.242641  9.899495
## 16   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 17  11.401754  8.485281  0.000000  1.414214  9.219544  5.656854 11.313708
## 18   3.162278  2.000000 10.000000  8.602325  1.000000  4.472136  2.000000
## 19   4.472136  1.414214  7.071068  5.656854  2.236068  1.414214  4.242641
## 20   1.414214  2.000000 10.000000  8.602325  2.236068  4.472136  2.000000
## 21  11.401754  8.485281  0.000000  1.414214  9.219544  5.656854 11.313708
## 22   4.123106  6.403124 14.866069 13.453624  5.656854  9.219544  3.605551
## 23   3.162278  0.000000  8.485281  7.071068  1.000000  2.828427  2.828427
## 24   3.000000  1.000000  9.219544  7.810250  0.000000  3.605551  2.236068
## 25   6.708204  3.605551  5.000000  3.605551  4.242641  1.000000  6.403124
## 26   4.123106  1.000000  7.810250  6.403124  1.414214  2.236068  3.605551
## 27  14.212670 11.313708  2.828427  4.242641 12.041595  8.485281 14.142136
## 28  14.212670 11.313708  2.828427  4.242641 12.041595  8.485281 14.142136
## 29   8.944272  5.830952  3.162278  2.000000  6.403124  3.162278  8.602325
## 30  12.206556  9.219544  1.000000  2.236068  9.899495  6.403124 12.041595
## 31   9.433981  6.403124  2.236068  1.000000  7.071068  3.605551  9.219544
## 32   3.162278  0.000000  8.485281  7.071068  1.000000  2.828427  2.828427
## 33   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 34  11.661904  8.602325  1.414214  2.000000  9.219544  5.830952 11.401754
## 35  13.453624 10.630146  2.236068  3.605551 11.401754  7.810250 13.453624
## 36   1.000000  3.605551 12.041595 10.630146  3.162278  6.403124  1.000000
## 37   4.472136  1.414214  7.071068  5.656854  2.236068  1.414214  4.242641
## 38   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 39   5.830952  2.828427  5.656854  4.242641  3.605551  0.000000  5.656854
## 40   5.830952  8.485281 16.970563 15.556349  7.810250 11.313708  5.656854
## 41   3.162278  5.656854 14.142136 12.727922  5.000000  8.485281  2.828427
## 42   7.810250  5.000000  3.605551  2.236068  5.830952  2.236068  7.810250
## 43   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 44   2.000000  1.414214  9.899495  8.485281  1.000000  4.242641  1.414214
## 45   1.000000  3.605551 12.041595 10.630146  3.162278  6.403124  1.000000
## 46   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 47   2.000000  1.414214  9.899495  8.485281  1.000000  4.242641  1.414214
## 48   1.000000  2.236068 10.630146  9.219544  2.000000  5.000000  1.000000
## 49   9.848858  6.708204  3.000000  2.236068  7.211103  4.123106  9.433981
## 50   5.385165  7.810250 16.278821 14.866069  7.071068 10.630146  5.000000
## 51   7.211103  4.242641  4.242641  2.828427  5.000000  1.414214  7.071068
## 52   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 53   3.162278  5.656854 14.142136 12.727922  5.000000  8.485281  2.828427
## 54   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 55  14.212670 11.313708  2.828427  4.242641 12.041595  8.485281 14.142136
## 56   7.211103  4.242641  4.242641  2.828427  5.000000  1.414214  7.071068
## 57   5.830952  8.485281 16.970563 15.556349  7.810250 11.313708  5.656854
## 58   3.605551  1.000000  7.810250  6.403124  2.000000  2.236068  3.605551
## 59   3.605551  4.123106 12.206556 10.816654  3.162278  6.708204  2.236068
## 60   5.000000  2.236068  8.062258  6.708204  2.000000  3.000000  4.123106
## 61   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 62  14.212670 11.313708  2.828427  4.242641 12.041595  8.485281 14.142136
## 63   6.708204  3.605551  5.000000  3.605551  4.242641  1.000000  6.403124
## 64   4.123106  6.403124 14.866069 13.453624  5.656854  9.219544  3.605551
## 65  13.453624 10.630146  2.236068  3.605551 11.401754  7.810250 13.453624
## 66   9.899495  7.211103  2.000000  1.414214  8.062258  4.472136 10.000000
## 67  11.661904  8.602325  1.414214  2.000000  9.219544  5.830952 11.401754
## 68  13.453624 10.630146  2.236068  3.605551 11.401754  7.810250 13.453624
## 69  10.630146  7.810250  1.000000  1.000000  8.602325  5.000000 10.630146
## 70   7.211103  4.242641  4.242641  2.828427  5.000000  1.414214  7.071068
## 71   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 72  10.295630  7.211103  2.000000  1.414214  7.810250  4.472136 10.000000
## 73   6.708204  3.605551  5.000000  3.605551  4.242641  1.000000  6.403124
## 74   2.236068  3.605551 12.041595 10.630146  2.828427  6.403124  1.000000
## 75  10.630146  7.810250  1.000000  1.000000  8.602325  5.000000 10.630146
## 76   7.211103  4.242641  4.242641  2.828427  5.000000  1.414214  7.071068
## 77   1.414214  2.000000 10.000000  8.602325  2.236068  4.472136  2.000000
## 78   9.433981  6.403124  2.236068  1.000000  7.071068  3.605551  9.219544
## 79   5.830952  2.828427  5.656854  4.242641  3.605551  0.000000  5.656854
## 80   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 81   6.708204  9.219544 17.691806 16.278821  8.485281 12.041595  6.403124
## 82   3.605551  2.236068  8.062258  6.708204  3.162278  3.000000  4.123106
## 83   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 84   3.162278  0.000000  8.485281  7.071068  1.000000  2.828427  2.828427
## 85   5.830952  2.828427  5.656854  4.242641  3.605551  0.000000  5.656854
## 86   1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 87   3.605551  6.403124 14.866069 13.453624  5.830952  9.219544  3.605551
## 88   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 89  14.212670 11.313708  2.828427  4.242641 12.041595  8.485281 14.142136
## 90   8.062258  5.000000  3.605551  2.236068  5.656854  2.236068  7.810250
## 91   4.472136  7.071068 15.556349 14.142136  6.403124  9.899495  4.242641
## 92  10.816654  8.544004  3.605551  3.605551  9.486833  6.082763 11.180340
## 93  10.000000  7.071068  1.414214  0.000000  7.810250  4.242641  9.899495
## 94   2.000000  4.242641 12.727922 11.313708  3.605551  7.071068  1.414214
## 95  10.630146  7.810250  1.000000  1.000000  8.602325  5.000000 10.630146
## 96   2.000000  1.414214  9.899495  8.485281  1.000000  4.242641  1.414214
## 97   2.236068  1.000000  9.219544  7.810250  1.414214  3.605551  2.236068
## 98   8.602325  5.656854  2.828427  1.414214  6.403124  2.828427  8.485281
## 99   3.162278  0.000000  8.485281  7.071068  1.000000  2.828427  2.828427
## 100  5.830952  2.828427  5.656854  4.242641  3.605551  0.000000  5.656854
## 101 10.295630  7.211103  2.000000  1.414214  7.810250  4.472136 10.000000
## 102  6.708204  9.219544 17.691806 16.278821  8.485281 12.041595  6.403124
## 103  2.000000  1.414214  9.899495  8.485281  1.000000  4.242641  1.414214
## 104  5.830952  2.828427  5.656854  4.242641  3.605551  0.000000  5.656854
## 105  1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 106 14.212670 11.313708  2.828427  4.242641 12.041595  8.485281 14.142136
## 107  1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 108  7.615773  4.472136  4.472136  3.162278  5.000000  2.000000  7.211103
## 109  1.414214  2.828427 11.313708  9.899495  2.236068  5.656854  0.000000
## 110  5.099020  7.211103 15.620499 14.212670  6.403124 10.000000  4.472136
## 111  3.162278  5.656854 14.142136 12.727922  5.000000  8.485281  2.828427
## 112  4.472136  7.071068 15.556349 14.142136  6.403124  9.899495  4.242641
## 113  3.162278  5.656854 14.142136 12.727922  5.000000  8.485281  2.828427
## 114  2.236068  3.605551 12.041595 10.630146  2.828427  6.403124  1.000000
## 115 12.806248  9.899495  1.414214  2.828427 10.630146  7.071068 12.727922
## 116  3.605551  3.000000 10.816654  9.433981  2.000000  5.385165  2.236068
## 117  3.162278  5.656854 14.142136 12.727922  5.000000  8.485281  2.828427
## 118  4.472136  1.414214  7.071068  5.656854  2.236068  1.414214  4.242641
## 119  8.602325 11.313708 19.798990 18.384776 10.630146 14.142136  8.485281
## 120  3.162278  0.000000  8.485281  7.071068  1.000000  2.828427  2.828427
## 121  3.162278  6.000000 13.416408 12.083046  6.082763  8.246211  4.472136
##            15        16        17        18        19        20        21
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16   9.899495                                                            
## 17   1.414214 11.313708                                                  
## 18   8.602325  2.000000 10.000000                                        
## 19   5.656854  4.242641  7.071068  3.162278                              
## 20   8.602325  2.000000 10.000000  2.828427  3.162278                    
## 21   1.414214 11.313708  0.000000 10.000000  7.071068 10.000000          
## 22  13.453624  3.605551 14.866069  5.000000  7.810250  5.385165 14.866069
## 23   7.071068  2.828427  8.485281  2.000000  1.414214  2.000000  8.485281
## 24   7.810250  2.236068  9.219544  1.000000  2.236068  2.236068  9.219544
## 25   3.605551  6.403124  5.000000  5.000000  2.236068  5.385165  5.000000
## 26   6.403124  3.605551  7.810250  2.236068  1.000000  3.000000  7.810250
## 27   4.242641 14.142136  2.828427 12.806248  9.899495 12.806248  2.828427
## 28   4.242641 14.142136  2.828427 12.806248  9.899495 12.806248  2.828427
## 29   2.000000  8.602325  3.162278  7.071068  4.472136  7.615773  3.162278
## 30   2.236068 12.041595  1.000000 10.630146  7.810250 10.816654  1.000000
## 31   1.000000  9.219544  2.236068  7.810250  5.000000  8.062258  2.236068
## 32   7.071068  2.828427  8.485281  2.000000  1.414214  2.000000  8.485281
## 33   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 34   2.000000 11.401754  1.414214  9.899495  7.211103 10.295630  1.414214
## 35   3.605551 13.453624  2.236068 12.206556  9.219544 12.041595  2.236068
## 36  10.630146  1.000000 12.041595  3.000000  5.000000  2.236068 12.041595
## 37   5.656854  4.242641  7.071068  3.162278  0.000000  3.162278  7.071068
## 38   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 39   4.242641  5.656854  5.656854  4.472136  1.414214  4.472136  5.656854
## 40  15.556349  5.656854 16.970563  7.211103  9.899495  7.211103 16.970563
## 41  12.727922  2.828427 14.142136  4.472136  7.071068  4.472136 14.142136
## 42   2.236068  7.810250  3.605551  6.708204  3.605551  6.403124  3.605551
## 43   9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 44   8.485281  1.414214  9.899495  1.414214  2.828427  1.414214  9.899495
## 45  10.630146  1.000000 12.041595  3.000000  5.000000  2.236068 12.041595
## 46   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 47   8.485281  1.414214  9.899495  1.414214  2.828427  1.414214  9.899495
## 48   9.219544  1.000000 10.630146  2.236068  3.605551  1.000000 10.630146
## 49   2.236068  9.433981  3.000000  7.810250  5.385165  8.544004  3.000000
## 50  14.866069  5.000000 16.278821  6.403124  9.219544  6.708204 16.278821
## 51   2.828427  7.071068  4.242641  5.830952  2.828427  5.830952  4.242641
## 52   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 53  12.727922  2.828427 14.142136  4.472136  7.071068  4.472136 14.142136
## 54   9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 55   4.242641 14.142136  2.828427 12.806248  9.899495 12.806248  2.828427
## 56   2.828427  7.071068  4.242641  5.830952  2.828427  5.830952  4.242641
## 57  15.556349  5.656854 16.970563  7.211103  9.899495  7.211103 16.970563
## 58   6.403124  3.605551  7.810250  3.000000  1.000000  2.236068  7.810250
## 59  10.816654  2.236068 12.206556  2.236068  5.385165  4.123106 12.206556
## 60   6.708204  4.123106  8.062258  2.236068  2.236068  4.123106  8.062258
## 61   9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 62   4.242641 14.142136  2.828427 12.806248  9.899495 12.806248  2.828427
## 63   3.605551  6.403124  5.000000  5.000000  2.236068  5.385165  5.000000
## 64  13.453624  3.605551 14.866069  5.000000  7.810250  5.385165 14.866069
## 65   3.605551 13.453624  2.236068 12.206556  9.219544 12.041595  2.236068
## 66   1.414214 10.000000  2.000000  8.944272  5.830952  8.485281  2.000000
## 67   2.000000 11.401754  1.414214  9.899495  7.211103 10.295630  1.414214
## 68   3.605551 13.453624  2.236068 12.206556  9.219544 12.041595  2.236068
## 69   1.000000 10.630146  1.000000  9.433981  6.403124  9.219544  1.000000
## 70   2.828427  7.071068  4.242641  5.830952  2.828427  5.830952  4.242641
## 71   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 72   1.414214 10.000000  2.000000  8.485281  5.830952  8.944272  2.000000
## 73   3.605551  6.403124  5.000000  5.000000  2.236068  5.385165  5.000000
## 74  10.630146  1.000000 12.041595  2.236068  5.000000  3.000000 12.041595
## 75   1.000000 10.630146  1.000000  9.433981  6.403124  9.219544  1.000000
## 76   2.828427  7.071068  4.242641  5.830952  2.828427  5.830952  4.242641
## 77   8.602325  2.000000 10.000000  2.828427  3.162278  0.000000 10.000000
## 78   1.000000  9.219544  2.236068  7.810250  5.000000  8.062258  2.236068
## 79   4.242641  5.656854  5.656854  4.472136  1.414214  4.472136  5.656854
## 80   9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 81  16.278821  6.403124 17.691806  7.810250 10.630146  8.062258 17.691806
## 82   6.708204  4.123106  8.062258  4.123106  2.236068  2.236068  8.062258
## 83   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 84   7.071068  2.828427  8.485281  2.000000  1.414214  2.000000  8.485281
## 85   4.242641  5.656854  5.656854  4.472136  1.414214  4.472136  5.656854
## 86   9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 87  13.453624  3.605551 14.866069  5.385165  7.810250  5.000000 14.866069
## 88   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 89   4.242641 14.142136  2.828427 12.806248  9.899495 12.806248  2.828427
## 90   2.236068  7.810250  3.605551  6.403124  3.605551  6.708204  3.605551
## 91  14.142136  4.242641 15.556349  5.830952  8.485281  5.830952 15.556349
## 92   3.605551 11.180340  3.605551 10.440307  7.280110  9.433981  3.605551
## 93   0.000000  9.899495  1.414214  8.602325  5.656854  8.602325  1.414214
## 94  11.313708  1.414214 12.727922  3.162278  5.656854  3.162278 12.727922
## 95   1.000000 10.630146  1.000000  9.433981  6.403124  9.219544  1.000000
## 96   8.485281  1.414214  9.899495  1.414214  2.828427  1.414214  9.899495
## 97   7.810250  2.236068  9.219544  2.236068  2.236068  1.000000  9.219544
## 98   1.414214  8.485281  2.828427  7.211103  4.242641  7.211103  2.828427
## 99   7.071068  2.828427  8.485281  2.000000  1.414214  2.000000  8.485281
## 100  4.242641  5.656854  5.656854  4.472136  1.414214  4.472136  5.656854
## 101  1.414214 10.000000  2.000000  8.485281  5.830952  8.944272  2.000000
## 102 16.278821  6.403124 17.691806  7.810250 10.630146  8.062258 17.691806
## 103  8.485281  1.414214  9.899495  1.414214  2.828427  1.414214  9.899495
## 104  4.242641  5.656854  5.656854  4.472136  1.414214  4.472136  5.656854
## 105  9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 106  4.242641 14.142136  2.828427 12.806248  9.899495 12.806248  2.828427
## 107  9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 108  3.162278  7.211103  4.472136  5.656854  3.162278  6.324555  4.472136
## 109  9.899495  0.000000 11.313708  2.000000  4.242641  2.000000 11.313708
## 110 14.212670  4.472136 15.620499  5.656854  8.602325  6.324555 15.620499
## 111 12.727922  2.828427 14.142136  4.472136  7.071068  4.472136 14.142136
## 112 14.142136  4.242641 15.556349  5.830952  8.485281  5.830952 15.556349
## 113 12.727922  2.828427 14.142136  4.472136  7.071068  4.472136 14.142136
## 114 10.630146  1.000000 12.041595  2.236068  5.000000  3.000000 12.041595
## 115  2.828427 12.727922  1.414214 11.401754  8.485281 11.401754  1.414214
## 116  9.433981  2.236068 10.816654  1.000000  4.123106  3.605551 10.816654
## 117 12.727922  2.828427 14.142136  4.472136  7.071068  4.472136 14.142136
## 118  5.656854  4.242641  7.071068  3.162278  0.000000  3.162278  7.071068
## 119 18.384776  8.485281 19.798990 10.000000 12.727922 10.000000 19.798990
## 120  7.071068  2.828427  8.485281  2.000000  1.414214  2.000000  8.485281
## 121 12.083046  4.472136 13.416408  6.324555  7.071068  4.000000 13.416408
##            22        23        24        25        26        27        28
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23   6.403124                                                            
## 24   5.656854  1.000000                                                  
## 25   9.899495  3.605551  4.242641                                        
## 26   7.071068  1.000000  1.414214  2.828427                              
## 27  17.691806 11.313708 12.041595  7.810250 10.630146                    
## 28  17.691806 11.313708 12.041595  7.810250 10.630146  0.000000          
## 29  12.041595  5.830952  6.403124  2.236068  5.000000  5.830952  5.830952
## 30  15.556349  9.219544  9.899495  5.656854  8.485281  2.236068  2.236068
## 31  12.727922  6.403124  7.071068  2.828427  5.656854  5.000000  5.000000
## 32   6.403124  0.000000  1.000000  3.605551  1.000000 11.313708 11.313708
## 33  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 34  14.866069  8.602325  9.219544  5.000000  7.810250  3.162278  3.162278
## 35  17.029386 10.630146 11.401754  7.211103 10.000000  1.000000  1.000000
## 36   3.162278  3.605551  3.162278  7.211103  4.472136 14.866069 14.866069
## 37   7.810250  1.414214  2.236068  2.236068  1.000000  9.899495  9.899495
## 38  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 39   9.219544  2.828427  3.605551  1.000000  2.236068  8.485281  8.485281
## 40   2.236068  8.485281  7.810250 12.041595  9.219544 19.798990 19.798990
## 41   1.000000  5.656854  5.000000  9.219544  6.403124 16.970563 16.970563
## 42  11.401754  5.000000  5.830952  2.000000  4.472136  6.403124  6.403124
## 43   3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 44   5.000000  1.414214  1.000000  5.000000  2.236068 12.727922 12.727922
## 45   3.162278  3.605551  3.162278  7.211103  4.472136 14.866069 14.866069
## 46  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 47   5.000000  1.414214  1.000000  5.000000  2.236068 12.727922 12.727922
## 48   4.472136  2.236068  2.000000  5.830952  3.162278 13.453624 13.453624
## 49  12.806248  6.708204  7.211103  3.162278  5.830952  5.385165  5.385165
## 50   1.414214  7.810250  7.071068 11.313708  8.485281 19.104973 19.104973
## 51  10.630146  4.242641  5.000000  1.000000  3.605551  7.071068  7.071068
## 52  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 53   1.000000  5.656854  5.000000  9.219544  6.403124 16.970563 16.970563
## 54   3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 55  17.691806 11.313708 12.041595  7.810250 10.630146  0.000000  0.000000
## 56  10.630146  4.242641  5.000000  1.000000  3.605551  7.071068  7.071068
## 57   2.236068  8.485281  7.810250 12.041595  9.219544 19.798990 19.798990
## 58   7.211103  1.000000  2.000000  3.162278  1.414214 10.630146 10.630146
## 59   3.162278  4.123106  3.162278  7.211103  4.472136 15.000000 15.000000
## 60   7.211103  2.236068  2.000000  3.162278  1.414214 10.816654 10.816654
## 61   3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 62  17.691806 11.313708 12.041595  7.810250 10.630146  0.000000  0.000000
## 63   9.899495  3.605551  4.242641  0.000000  2.828427  7.810250  7.810250
## 64   0.000000  6.403124  5.656854  9.899495  7.071068 17.691806 17.691806
## 65  17.029386 10.630146 11.401754  7.211103 10.000000  1.000000  1.000000
## 66  13.601471  7.211103  8.062258  4.123106  6.708204  4.472136  4.472136
## 67  14.866069  8.602325  9.219544  5.000000  7.810250  3.162278  3.162278
## 68  17.029386 10.630146 11.401754  7.211103 10.000000  1.000000  1.000000
## 69  14.212670  7.810250  8.602325  4.472136  7.211103  3.605551  3.605551
## 70  10.630146  4.242641  5.000000  1.000000  3.605551  7.071068  7.071068
## 71  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 72  13.453624  7.211103  7.810250  3.605551  6.403124  4.472136  4.472136
## 73   9.899495  3.605551  4.242641  0.000000  2.828427  7.810250  7.810250
## 74   2.828427  3.605551  2.828427  7.071068  4.242641 14.866069 14.866069
## 75  14.212670  7.810250  8.602325  4.472136  7.211103  3.605551  3.605551
## 76  10.630146  4.242641  5.000000  1.000000  3.605551  7.071068  7.071068
## 77   5.385165  2.000000  2.236068  5.385165  3.000000 12.806248 12.806248
## 78  12.727922  6.403124  7.071068  2.828427  5.656854  5.000000  5.000000
## 79   9.219544  2.828427  3.605551  1.000000  2.236068  8.485281  8.485281
## 80   3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 81   2.828427  9.219544  8.485281 12.727922  9.899495 20.518285 20.518285
## 82   7.615773  2.236068  3.162278  4.000000  2.828427 10.816654 10.816654
## 83  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 84   6.403124  0.000000  1.000000  3.605551  1.000000 11.313708 11.313708
## 85   9.219544  2.828427  3.605551  1.000000  2.236068  8.485281  8.485281
## 86   3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 87   1.414214  6.403124  5.830952 10.000000  7.211103 17.691806 17.691806
## 88  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 89  17.691806 11.313708 12.041595  7.810250 10.630146  0.000000  0.000000
## 90  11.313708  5.000000  5.656854  1.414214  4.242641  6.403124  6.403124
## 91   1.000000  7.071068  6.403124 10.630146  7.810250 18.384776 18.384776
## 92  14.764823  8.544004  9.486833  6.000000  8.246211  5.000000  5.000000
## 93  13.453624  7.071068  7.810250  3.605551  6.403124  4.242641  4.242641
## 94   2.236068  4.242641  3.605551  7.810250  5.000000 15.556349 15.556349
## 95  14.212670  7.810250  8.602325  4.472136  7.211103  3.605551  3.605551
## 96   5.000000  1.414214  1.000000  5.000000  2.236068 12.727922 12.727922
## 97   5.830952  1.000000  1.414214  4.472136  2.000000 12.041595 12.041595
## 98  12.041595  5.656854  6.403124  2.236068  5.000000  5.656854  5.656854
## 99   6.403124  0.000000  1.000000  3.605551  1.000000 11.313708 11.313708
## 100  9.219544  2.828427  3.605551  1.000000  2.236068  8.485281  8.485281
## 101 13.453624  7.211103  7.810250  3.605551  6.403124  4.472136  4.472136
## 102  2.828427  9.219544  8.485281 12.727922  9.899495 20.518285 20.518285
## 103  5.000000  1.414214  1.000000  5.000000  2.236068 12.727922 12.727922
## 104  9.219544  2.828427  3.605551  1.000000  2.236068  8.485281  8.485281
## 105  3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 106 17.691806 11.313708 12.041595  7.810250 10.630146  0.000000  0.000000
## 107  3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 108 10.630146  4.472136  5.000000  1.000000  3.605551  7.211103  7.211103
## 109  3.605551  2.828427  2.236068  6.403124  3.605551 14.142136 14.142136
## 110  1.000000  7.211103  6.403124 10.630146  7.810250 18.439089 18.439089
## 111  1.000000  5.656854  5.000000  9.219544  6.403124 16.970563 16.970563
## 112  1.000000  7.071068  6.403124 10.630146  7.810250 18.384776 18.384776
## 113  1.000000  5.656854  5.000000  9.219544  6.403124 16.970563 16.970563
## 114  2.828427  3.605551  2.828427  7.071068  4.242641 14.866069 14.866069
## 115 16.278821  9.899495 10.630146  6.403124  9.219544  1.414214  1.414214
## 116  4.472136  3.000000  2.000000  5.830952  3.162278 13.601471 13.601471
## 117  1.000000  5.656854  5.000000  9.219544  6.403124 16.970563 16.970563
## 118  7.810250  1.414214  2.236068  2.236068  1.000000  9.899495  9.899495
## 119  5.000000 11.313708 10.630146 14.866069 12.041595 22.627417 22.627417
## 120  6.403124  0.000000  1.000000  3.605551  1.000000 11.313708 11.313708
## 121  5.385165  6.000000  6.082763  9.219544  7.000000 16.124515 16.124515
##            29        30        31        32        33        34        35
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30   3.605551                                                            
## 31   1.000000  2.828427                                                  
## 32   5.830952  9.219544  6.403124                                        
## 33   1.414214  3.605551  1.000000  5.656854                              
## 34   2.828427  1.000000  2.236068  8.602325  3.162278                    
## 35   5.385165  2.000000  4.472136 10.630146  5.000000  3.000000          
## 36   9.433981 12.806248 10.000000  3.605551  9.219544 12.206556 14.142136
## 37   4.472136  7.810250  5.000000  1.414214  4.242641  7.211103  9.219544
## 38   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 39   3.162278  6.403124  3.605551  2.828427  2.828427  5.830952  7.810250
## 40  14.212670 17.691806 14.866069  8.485281 14.142136 17.029386 19.104973
## 41  11.401754 14.866069 12.041595  5.656854 11.313708 14.212670 16.278821
## 42   2.236068  4.472136  2.000000  5.000000  1.000000  4.123106  5.656854
## 43   8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 44   7.211103 10.630146  7.810250  1.414214  7.071068 10.000000 12.041595
## 45   9.433981 12.806248 10.000000  3.605551  9.219544 12.206556 14.142136
## 46   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 47   7.211103 10.630146  7.810250  1.414214  7.071068 10.000000 12.041595
## 48   8.062258 11.401754  8.602325  2.236068  7.810250 10.816654 12.727922
## 49   1.000000  3.162278  1.414214  6.708204  2.236068  2.236068  5.099020
## 50  13.453624 16.970563 14.142136  7.810250 13.453624 16.278821 18.439089
## 51   2.000000  5.000000  2.236068  4.242641  1.414214  4.472136  6.403124
## 52   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 53  11.401754 14.866069 12.041595  5.656854 11.313708 14.212670 16.278821
## 54   8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 55   5.830952  2.236068  5.000000 11.313708  5.656854  3.162278  1.000000
## 56   2.000000  5.000000  2.236068  4.242641  1.414214  4.472136  6.403124
## 57  14.212670 17.691806 14.866069  8.485281 14.142136 17.029386 19.104973
## 58   5.385165  8.602325  5.830952  1.000000  5.000000  8.062258  9.899495
## 59   9.219544 12.806248 10.000000  4.123106  9.433981 12.041595 14.422205
## 60   5.000000  8.602325  5.830952  2.236068  5.385165  7.810250 10.295630
## 61   8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 62   5.830952  2.236068  5.000000 11.313708  5.656854  3.162278  1.000000
## 63   2.236068  5.656854  2.828427  3.605551  2.236068  5.000000  7.211103
## 64  12.041595 15.556349 12.727922  6.403124 12.041595 14.866069 17.029386
## 65   5.385165  2.000000  4.472136 10.630146  5.000000  3.000000  0.000000
## 66   3.162278  3.000000  2.236068  7.211103  2.000000  3.162278  3.605551
## 67   2.828427  1.000000  2.236068  8.602325  3.162278  0.000000  3.000000
## 68   5.385165  2.000000  4.472136 10.630146  5.000000  3.000000  0.000000
## 69   3.000000  2.000000  2.000000  7.810250  2.236068  2.236068  2.828427
## 70   2.000000  5.000000  2.236068  4.242641  1.414214  4.472136  6.403124
## 71   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 72   1.414214  2.236068  1.000000  7.211103  2.000000  1.414214  4.123106
## 73   2.236068  5.656854  2.828427  3.605551  2.236068  5.000000  7.211103
## 74   9.219544 12.727922  9.899495  3.605551  9.219544 12.041595 14.212670
## 75   3.000000  2.000000  2.000000  7.810250  2.236068  2.236068  2.828427
## 76   2.000000  5.000000  2.236068  4.242641  1.414214  4.472136  6.403124
## 77   7.615773 10.816654  8.062258  2.000000  7.211103 10.295630 12.041595
## 78   1.000000  2.828427  0.000000  6.403124  1.000000  2.236068  4.472136
## 79   3.162278  6.403124  3.605551  2.828427  2.828427  5.830952  7.810250
## 80   8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 81  14.866069 18.384776 15.556349  9.219544 14.866069 17.691806 19.849433
## 82   6.082763  8.944272  6.324555  2.236068  5.385165  8.544004 10.000000
## 83   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 84   5.830952  9.219544  6.403124  0.000000  5.656854  8.602325 10.630146
## 85   3.162278  6.403124  3.605551  2.828427  2.828427  5.830952  7.810250
## 86   8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 87  12.206556 15.620499 12.806248  6.403124 12.041595 15.000000 16.970563
## 88   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 89   5.830952  2.236068  5.000000 11.313708  5.656854  3.162278  1.000000
## 90   1.000000  4.242641  1.414214  5.000000  1.000000  3.605551  5.830952
## 91  12.806248 16.278821 13.453624  7.071068 12.727922 15.620499 17.691806
## 92   5.385165  4.472136  4.472136  8.544004  4.123106  5.000000  4.000000
## 93   2.000000  2.236068  1.000000  7.071068  1.414214  2.000000  3.605551
## 94  10.000000 13.453624 10.630146  4.242641  9.899495 12.806248 14.866069
## 95   3.000000  2.000000  2.000000  7.810250  2.236068  2.236068  2.828427
## 96   7.211103 10.630146  7.810250  1.414214  7.071068 10.000000 12.041595
## 97   6.708204 10.000000  7.211103  1.000000  6.403124  9.433981 11.313708
## 98   1.414214  3.605551  1.000000  5.656854  0.000000  3.162278  5.000000
## 99   5.830952  9.219544  6.403124  0.000000  5.656854  8.602325 10.630146
## 100  3.162278  6.403124  3.605551  2.828427  2.828427  5.830952  7.810250
## 101  1.414214  2.236068  1.000000  7.211103  2.000000  1.414214  4.123106
## 102 14.866069 18.384776 15.556349  9.219544 14.866069 17.691806 19.849433
## 103  7.211103 10.630146  7.810250  1.414214  7.071068 10.000000 12.041595
## 104  3.162278  6.403124  3.605551  2.828427  2.828427  5.830952  7.810250
## 105  8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 106  5.830952  2.236068  5.000000 11.313708  5.656854  3.162278  1.000000
## 107  8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 108  1.414214  5.000000  2.236068  4.472136  2.000000  4.242641  6.708204
## 109  8.602325 12.041595  9.219544  2.828427  8.485281 11.401754 13.453624
## 110 12.727922 16.278821 13.453624  7.211103 12.806248 15.556349 17.804494
## 111 11.401754 14.866069 12.041595  5.656854 11.313708 14.212670 16.278821
## 112 12.806248 16.278821 13.453624  7.071068 12.727922 15.620499 17.691806
## 113 11.401754 14.866069 12.041595  5.656854 11.313708 14.212670 16.278821
## 114  9.219544 12.727922  9.899495  3.605551  9.219544 12.041595 14.212670
## 115  4.472136  1.000000  3.605551  9.899495  4.242641  2.000000  1.000000
## 116  7.810250 11.401754  8.602325  3.000000  8.062258 10.630146 13.038405
## 117 11.401754 14.866069 12.041595  5.656854 11.313708 14.212670 16.278821
## 118  4.472136  7.810250  5.000000  1.414214  4.242641  7.211103  9.219544
## 119 17.029386 20.518285 17.691806 11.313708 16.970563 19.849433 21.931712
## 120  5.830952  9.219544  6.403124  0.000000  5.656854  8.602325 10.630146
## 121 11.401754 14.317821 11.704700  6.000000 10.770330 13.928388 15.264338
##            36        37        38        39        40        41        42
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37   5.000000                                                            
## 38   9.219544  4.242641                                                  
## 39   6.403124  1.414214  2.828427                                        
## 40   5.000000  9.899495 14.142136 11.313708                              
## 41   2.236068  7.071068 11.313708  8.485281  2.828427                    
## 42   8.485281  3.605551  1.000000  2.236068 13.453624 10.630146          
## 43   1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 44   2.236068  2.828427  7.071068  4.242641  7.071068  4.242641  6.403124
## 45   0.000000  5.000000  9.219544  6.403124  5.000000  2.236068  8.485281
## 46   9.219544  4.242641  0.000000  2.828427 14.142136 11.313708  1.000000
## 47   2.236068  2.828427  7.071068  4.242641  7.071068  4.242641  6.403124
## 48   1.414214  3.605551  7.810250  5.000000  6.403124  3.605551  7.071068
## 49  10.295630  5.385165  2.236068  4.123106 15.000000 12.206556  3.162278
## 50   4.472136  9.219544 13.453624 10.630146  1.000000  2.236068 12.806248
## 51   7.810250  2.828427  1.414214  1.414214 12.727922  9.899495  1.000000
## 52   9.219544  4.242641  0.000000  2.828427 14.142136 11.313708  1.000000
## 53   2.236068  7.071068 11.313708  8.485281  2.828427  0.000000 10.630146
## 54   1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 55  14.866069  9.899495  5.656854  8.485281 19.798990 16.970563  6.403124
## 56   7.810250  2.828427  1.414214  1.414214 12.727922  9.899495  1.000000
## 57   5.000000  9.899495 14.142136 11.313708  0.000000  2.828427 13.453624
## 58   4.242641  1.000000  5.000000  2.236068  9.219544  6.403124  4.242641
## 59   2.828427  5.385165  9.433981  6.708204  5.385165  3.000000  8.944272
## 60   5.099020  2.236068  5.385165  3.000000  9.433981  6.708204  5.099020
## 61   1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 62  14.866069  9.899495  5.656854  8.485281 19.798990 16.970563  6.403124
## 63   7.211103  2.236068  2.236068  1.000000 12.041595  9.219544  2.000000
## 64   3.162278  7.810250 12.041595  9.219544  2.236068  1.000000 11.401754
## 65  14.142136  9.219544  5.000000  7.810250 19.104973 16.278821  5.656854
## 66  10.630146  5.830952  2.000000  4.472136 15.620499 12.806248  2.236068
## 67  12.206556  7.211103  3.162278  5.830952 17.029386 14.212670  4.123106
## 68  14.142136  9.219544  5.000000  7.810250 19.104973 16.278821  5.656854
## 69  11.313708  6.403124  2.236068  5.000000 16.278821 13.453624  2.828427
## 70   7.810250  2.828427  1.414214  1.414214 12.727922  9.899495  1.000000
## 71   9.219544  4.242641  0.000000  2.828427 14.142136 11.313708  1.000000
## 72  10.816654  5.830952  2.000000  4.472136 15.620499 12.806248  3.000000
## 73   7.211103  2.236068  2.236068  1.000000 12.041595  9.219544  2.000000
## 74   1.414214  5.000000  9.219544  6.403124  5.000000  2.236068  8.602325
## 75  11.313708  6.403124  2.236068  5.000000 16.278821 13.453624  2.828427
## 76   7.810250  2.828427  1.414214  1.414214 12.727922  9.899495  1.000000
## 77   2.236068  3.162278  7.211103  4.472136  7.211103  4.472136  6.403124
## 78  10.000000  5.000000  1.000000  3.605551 14.866069 12.041595  2.000000
## 79   6.403124  1.414214  2.828427  0.000000 11.313708  8.485281  2.236068
## 80   1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 81   5.830952 10.630146 14.866069 12.041595  1.000000  3.605551 14.212670
## 82   4.472136  2.236068  5.385165  3.000000  9.433981  6.708204  4.472136
## 83   9.219544  4.242641  0.000000  2.828427 14.142136 11.313708  1.000000
## 84   3.605551  1.414214  5.656854  2.828427  8.485281  5.656854  5.000000
## 85   6.403124  1.414214  2.828427  0.000000 11.313708  8.485281  2.236068
## 86   1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 87   2.828427  7.810250 12.041595  9.219544  2.236068  1.000000 11.313708
## 88   9.219544  4.242641  0.000000  2.828427 14.142136 11.313708  1.000000
## 89  14.866069  9.899495  5.656854  8.485281 19.798990 16.970563  6.403124
## 90   8.602325  3.605551  1.000000  2.236068 13.453624 10.630146  1.414214
## 91   3.605551  8.485281 12.727922  9.899495  1.414214  1.414214 12.041595
## 92  11.661904  7.280110  4.123106  6.082763 16.643317 13.892444  4.000000
## 93  10.630146  5.656854  1.414214  4.242641 15.556349 12.727922  2.236068
## 94   1.000000  5.656854  9.899495  7.071068  4.242641  1.414214  9.219544
## 95  11.313708  6.403124  2.236068  5.000000 16.278821 13.453624  2.828427
## 96   2.236068  2.828427  7.071068  4.242641  7.071068  4.242641  6.403124
## 97   2.828427  2.236068  6.403124  3.605551  7.810250  5.000000  5.656854
## 98   9.219544  4.242641  0.000000  2.828427 14.142136 11.313708  1.000000
## 99   3.605551  1.414214  5.656854  2.828427  8.485281  5.656854  5.000000
## 100  6.403124  1.414214  2.828427  0.000000 11.313708  8.485281  2.236068
## 101 10.816654  5.830952  2.000000  4.472136 15.620499 12.806248  3.000000
## 102  5.830952 10.630146 14.866069 12.041595  1.000000  3.605551 14.212670
## 103  2.236068  2.828427  7.071068  4.242641  7.071068  4.242641  6.403124
## 104  6.403124  1.414214  2.828427  0.000000 11.313708  8.485281  2.236068
## 105  1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 106 14.866069  9.899495  5.656854  8.485281 19.798990 16.970563  6.403124
## 107  1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 108  8.062258  3.162278  2.000000  2.000000 12.806248 10.000000  2.236068
## 109  1.000000  4.242641  8.485281  5.656854  5.656854  2.828427  7.810250
## 110  4.123106  8.602325 12.806248 10.000000  2.000000  2.000000 12.206556
## 111  2.236068  7.071068 11.313708  8.485281  2.828427  0.000000 10.630146
## 112  3.605551  8.485281 12.727922  9.899495  1.414214  1.414214 12.041595
## 113  2.236068  7.071068 11.313708  8.485281  2.828427  0.000000 10.630146
## 114  1.414214  5.000000  9.219544  6.403124  5.000000  2.236068  8.602325
## 115 13.453624  8.485281  4.242641  7.071068 18.384776 15.556349  5.000000
## 116  3.162278  4.123106  8.062258  5.385165  6.708204  4.123106  7.615773
## 117  2.236068  7.071068 11.313708  8.485281  2.828427  0.000000 10.630146
## 118  5.000000  0.000000  4.242641  1.414214  9.899495  7.071068  3.605551
## 119  7.810250 12.727922 16.970563 14.142136  2.828427  5.656854 16.278821
## 120  3.605551  1.414214  5.656854  2.828427  8.485281  5.656854  5.000000
## 121  3.605551  7.071068 10.770330  8.246211  6.000000  4.472136  9.848858
##            43        44        45        46        47        48        49
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44   1.414214                                                            
## 45   1.000000  2.236068                                                  
## 46   8.485281  7.071068  9.219544                                        
## 47   1.414214  0.000000  2.236068  7.071068                              
## 48   1.000000  1.000000  1.414214  7.810250  1.000000                    
## 49   9.433981  8.062258 10.295630  2.236068  8.062258  8.944272          
## 50   5.000000  6.403124  4.472136 13.453624  6.403124  5.830952 14.212670
## 51   7.071068  5.656854  7.810250  1.414214  5.656854  6.403124  3.000000
## 52   8.485281  7.071068  9.219544  0.000000  7.071068  7.810250  2.236068
## 53   2.828427  4.242641  2.236068 11.313708  4.242641  3.605551 12.206556
## 54   0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 55  14.142136 12.727922 14.866069  5.656854 12.727922 13.453624  5.385165
## 56   7.071068  5.656854  7.810250  1.414214  5.656854  6.403124  3.000000
## 57   5.656854  7.071068  5.000000 14.142136  7.071068  6.403124 15.000000
## 58   3.605551  2.236068  4.242641  5.000000  2.236068  2.828427  6.324555
## 59   2.236068  3.000000  2.828427  9.433981  3.000000  3.162278  9.899495
## 60   4.123106  3.000000  5.099020  5.385165  3.000000  4.000000  5.656854
## 61   0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 62  14.142136 12.727922 14.866069  5.656854 12.727922 13.453624  5.385165
## 63   6.403124  5.000000  7.211103  2.236068  5.000000  5.830952  3.162278
## 64   3.605551  5.000000  3.162278 12.041595  5.000000  4.472136 12.806248
## 65  13.453624 12.041595 14.142136  5.000000 12.041595 12.727922  5.099020
## 66  10.000000  8.602325 10.630146  2.000000  8.602325  9.219544  3.605551
## 67  11.401754 10.000000 12.206556  3.162278 10.000000 10.816654  2.236068
## 68  13.453624 12.041595 14.142136  5.000000 12.041595 12.727922  5.099020
## 69  10.630146  9.219544 11.313708  2.236068  9.219544  9.899495  3.162278
## 70   7.071068  5.656854  7.810250  1.414214  5.656854  6.403124  3.000000
## 71   8.485281  7.071068  9.219544  0.000000  7.071068  7.810250  2.236068
## 72  10.000000  8.602325 10.816654  2.000000  8.602325  9.433981  1.000000
## 73   6.403124  5.000000  7.211103  2.236068  5.000000  5.830952  3.162278
## 74   1.000000  2.236068  1.414214  9.219544  2.236068  2.000000 10.000000
## 75  10.630146  9.219544 11.313708  2.236068  9.219544  9.899495  3.162278
## 76   7.071068  5.656854  7.810250  1.414214  5.656854  6.403124  3.000000
## 77   2.000000  1.414214  2.236068  7.211103  1.414214  1.000000  8.544004
## 78   9.219544  7.810250 10.000000  1.000000  7.810250  8.602325  1.414214
## 79   5.656854  4.242641  6.403124  2.828427  4.242641  5.000000  4.123106
## 80   0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 81   6.403124  7.810250  5.830952 14.866069  7.810250  7.211103 15.620499
## 82   4.123106  3.000000  4.472136  5.385165  3.000000  3.162278  7.071068
## 83   8.485281  7.071068  9.219544  0.000000  7.071068  7.810250  2.236068
## 84   2.828427  1.414214  3.605551  5.656854  1.414214  2.236068  6.708204
## 85   5.656854  4.242641  6.403124  2.828427  4.242641  5.000000  4.123106
## 86   0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 87   3.605551  5.000000  2.828427 12.041595  5.000000  4.242641 13.038405
## 88   8.485281  7.071068  9.219544  0.000000  7.071068  7.810250  2.236068
## 89  14.142136 12.727922 14.866069  5.656854 12.727922 13.453624  5.385165
## 90   7.810250  6.403124  8.602325  1.000000  6.403124  7.211103  2.000000
## 91   4.242641  5.656854  3.605551 12.727922  5.656854  5.000000 13.601471
## 92  11.180340  9.848858 11.661904  4.123106  9.848858 10.295630  5.830952
## 93   9.899495  8.485281 10.630146  1.414214  8.485281  9.219544  2.236068
## 94   1.414214  2.828427  1.000000  9.899495  2.828427  2.236068 10.816654
## 95  10.630146  9.219544 11.313708  2.236068  9.219544  9.899495  3.162278
## 96   1.414214  0.000000  2.236068  7.071068  0.000000  1.000000  8.062258
## 97   2.236068  1.000000  2.828427  6.403124  1.000000  1.414214  7.615773
## 98   8.485281  7.071068  9.219544  0.000000  7.071068  7.810250  2.236068
## 99   2.828427  1.414214  3.605551  5.656854  1.414214  2.236068  6.708204
## 100  5.656854  4.242641  6.403124  2.828427  4.242641  5.000000  4.123106
## 101 10.000000  8.602325 10.816654  2.000000  8.602325  9.433981  1.000000
## 102  6.403124  7.810250  5.830952 14.866069  7.810250  7.211103 15.620499
## 103  1.414214  0.000000  2.236068  7.071068  0.000000  1.000000  8.062258
## 104  5.656854  4.242641  6.403124  2.828427  4.242641  5.000000  4.123106
## 105  0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 106 14.142136 12.727922 14.866069  5.656854 12.727922 13.453624  5.385165
## 107  0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 108  7.211103  5.830952  8.062258  2.000000  5.830952  6.708204  2.236068
## 109  0.000000  1.414214  1.000000  8.485281  1.414214  1.000000  9.433981
## 110  4.472136  5.830952  4.123106 12.806248  5.830952  5.385165 13.453624
## 111  2.828427  4.242641  2.236068 11.313708  4.242641  3.605551 12.206556
## 112  4.242641  5.656854  3.605551 12.727922  5.656854  5.000000 13.601471
## 113  2.828427  4.242641  2.236068 11.313708  4.242641  3.605551 12.206556
## 114  1.000000  2.236068  1.414214  9.219544  2.236068  2.000000 10.000000
## 115 12.727922 11.313708 13.453624  4.242641 11.313708 12.041595  4.123106
## 116  2.236068  2.236068  3.162278  8.062258  2.236068  2.828427  8.485281
## 117  2.828427  4.242641  2.236068 11.313708  4.242641  3.605551 12.206556
## 118  4.242641  2.828427  5.000000  4.242641  2.828427  3.605551  5.385165
## 119  8.485281  9.899495  7.810250 16.970563  9.899495  9.219544 17.804494
## 120  2.828427  1.414214  3.605551  5.656854  1.414214  2.236068  6.708204
## 121  4.472136  5.099020  3.605551 10.770330  5.099020  4.123106 12.369317
##            50        51        52        53        54        55        56
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51  12.041595                                                            
## 52  13.453624  1.414214                                                  
## 53   2.236068  9.899495 11.313708                                        
## 54   5.000000  7.071068  8.485281  2.828427                              
## 55  19.104973  7.071068  5.656854 16.970563 14.142136                    
## 56  12.041595  0.000000  1.414214  9.899495  7.071068  7.071068          
## 57   1.000000 12.727922 14.142136  2.828427  5.656854 19.798990 12.727922
## 58   8.602325  3.605551  5.000000  6.403124  3.605551 10.630146  3.605551
## 59   4.472136  8.062258  9.433981  3.000000  2.236068 15.000000  8.062258
## 60   8.602325  4.123106  5.385165  6.708204  4.123106 10.816654  4.123106
## 61   5.000000  7.071068  8.485281  2.828427  0.000000 14.142136  7.071068
## 62  19.104973  7.071068  5.656854 16.970563 14.142136  0.000000  7.071068
## 63  11.313708  1.000000  2.236068  9.219544  6.403124  7.810250  1.000000
## 64   1.414214 10.630146 12.041595  1.000000  3.605551 17.691806 10.630146
## 65  18.439089  6.403124  5.000000 16.278821 13.453624  1.000000  6.403124
## 66  15.000000  3.162278  2.000000 12.806248 10.000000  4.472136  3.162278
## 67  16.278821  4.472136  3.162278 14.212670 11.401754  3.162278  4.472136
## 68  18.439089  6.403124  5.000000 16.278821 13.453624  1.000000  6.403124
## 69  15.620499  3.605551  2.236068 13.453624 10.630146  3.605551  3.605551
## 70  12.041595  0.000000  1.414214  9.899495  7.071068  7.071068  0.000000
## 71  13.453624  1.414214  0.000000 11.313708  8.485281  5.656854  1.414214
## 72  14.866069  3.162278  2.000000 12.806248 10.000000  4.472136  3.162278
## 73  11.313708  1.000000  2.236068  9.219544  6.403124  7.810250  1.000000
## 74   4.242641  7.810250  9.219544  2.236068  1.000000 14.866069  7.810250
## 75  15.620499  3.605551  2.236068 13.453624 10.630146  3.605551  3.605551
## 76  12.041595  0.000000  1.414214  9.899495  7.071068  7.071068  0.000000
## 77   6.708204  5.830952  7.211103  4.472136  2.000000 12.806248  5.830952
## 78  14.142136  2.236068  1.000000 12.041595  9.219544  5.000000  2.236068
## 79  10.630146  1.414214  2.828427  8.485281  5.656854  8.485281  1.414214
## 80   5.000000  7.071068  8.485281  2.828427  0.000000 14.142136  7.071068
## 81   1.414214 13.453624 14.866069  3.605551  6.403124 20.518285 13.453624
## 82   8.944272  4.123106  5.385165  6.708204  4.123106 10.816654  4.123106
## 83  13.453624  1.414214  0.000000 11.313708  8.485281  5.656854  1.414214
## 84   7.810250  4.242641  5.656854  5.656854  2.828427 11.313708  4.242641
## 85  10.630146  1.414214  2.828427  8.485281  5.656854  8.485281  1.414214
## 86   5.000000  7.071068  8.485281  2.828427  0.000000 14.142136  7.071068
## 87   2.000000 10.630146 12.041595  1.000000  3.605551 17.691806 10.630146
## 88  13.453624  1.414214  0.000000 11.313708  8.485281  5.656854  1.414214
## 89  19.104973  7.071068  5.656854 16.970563 14.142136  0.000000  7.071068
## 90  12.727922  1.000000  1.000000 10.630146  7.810250  6.403124  1.000000
## 91   1.000000 11.313708 12.727922  1.414214  4.242641 18.384776 11.313708
## 92  16.124515  5.000000  4.123106 13.892444 11.180340  5.000000  5.000000
## 93  14.866069  2.828427  1.414214 12.727922  9.899495  4.242641  2.828427
## 94   3.605551  8.485281  9.899495  1.414214  1.414214 15.556349  8.485281
## 95  15.620499  3.605551  2.236068 13.453624 10.630146  3.605551  3.605551
## 96   6.403124  5.656854  7.071068  4.242641  1.414214 12.727922  5.656854
## 97   7.211103  5.000000  6.403124  5.000000  2.236068 12.041595  5.000000
## 98  13.453624  1.414214  0.000000 11.313708  8.485281  5.656854  1.414214
## 99   7.810250  4.242641  5.656854  5.656854  2.828427 11.313708  4.242641
## 100 10.630146  1.414214  2.828427  8.485281  5.656854  8.485281  1.414214
## 101 14.866069  3.162278  2.000000 12.806248 10.000000  4.472136  3.162278
## 102  1.414214 13.453624 14.866069  3.605551  6.403124 20.518285 13.453624
## 103  6.403124  5.656854  7.071068  4.242641  1.414214 12.727922  5.656854
## 104 10.630146  1.414214  2.828427  8.485281  5.656854  8.485281  1.414214
## 105  5.000000  7.071068  8.485281  2.828427  0.000000 14.142136  7.071068
## 106 19.104973  7.071068  5.656854 16.970563 14.142136  0.000000  7.071068
## 107  5.000000  7.071068  8.485281  2.828427  0.000000 14.142136  7.071068
## 108 12.041595  1.414214  2.000000 10.000000  7.211103  7.211103  1.414214
## 109  5.000000  7.071068  8.485281  2.828427  0.000000 14.142136  7.071068
## 110  1.000000 11.401754 12.806248  2.000000  4.472136 18.439089 11.401754
## 111  2.236068  9.899495 11.313708  0.000000  2.828427 16.970563  9.899495
## 112  1.000000 11.313708 12.727922  1.414214  4.242641 18.384776 11.313708
## 113  2.236068  9.899495 11.313708  0.000000  2.828427 16.970563  9.899495
## 114  4.242641  7.810250  9.219544  2.236068  1.000000 14.866069  7.810250
## 115 17.691806  5.656854  4.242641 15.556349 12.727922  1.414214  5.656854
## 116  5.830952  6.708204  8.062258  4.123106  2.236068 13.601471  6.708204
## 117  2.236068  9.899495 11.313708  0.000000  2.828427 16.970563  9.899495
## 118  9.219544  2.828427  4.242641  7.071068  4.242641  9.899495  2.828427
## 119  3.605551 15.556349 16.970563  5.656854  8.485281 22.627417 15.556349
## 120  7.810250  4.242641  5.656854  5.656854  2.828427 11.313708  4.242641
## 121  6.082763  9.486833 10.770330  4.472136  4.472136 16.124515  9.486833
##            57        58        59        60        61        62        63
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58   9.219544                                                            
## 59   5.385165  5.099020                                                  
## 60   9.433981  2.828427  4.242641                                        
## 61   5.656854  3.605551  2.236068  4.123106                              
## 62  19.798990 10.630146 15.000000 10.816654 14.142136                    
## 63  12.041595  3.162278  7.211103  3.162278  6.403124  7.810250          
## 64   2.236068  7.211103  3.162278  7.211103  3.605551 17.691806  9.899495
## 65  19.104973  9.899495 14.422205 10.295630 13.453624  1.000000  7.211103
## 66  15.620499  6.403124 11.180340  7.280110 10.000000  4.472136  4.123106
## 67  17.029386  8.062258 12.041595  7.810250 11.401754  3.162278  5.000000
## 68  19.104973  9.899495 14.422205 10.295630 13.453624  1.000000  7.211103
## 69  16.278821  7.071068 11.661904  7.615773 10.630146  3.605551  4.472136
## 70  12.727922  3.605551  8.062258  4.123106  7.071068  7.071068  1.000000
## 71  14.142136  5.000000  9.433981  5.385165  8.485281  5.656854  2.236068
## 72  15.620499  6.708204 10.630146  6.403124 10.000000  4.472136  3.605551
## 73  12.041595  3.162278  7.211103  3.162278  6.403124  7.810250  0.000000
## 74   5.000000  4.472136  1.414214  4.472136  1.000000 14.866069  7.071068
## 75  16.278821  7.071068 11.661904  7.615773 10.630146  3.605551  4.472136
## 76  12.727922  3.605551  8.062258  4.123106  7.071068  7.071068  1.000000
## 77   7.211103  2.236068  4.123106  4.123106  2.000000 12.806248  5.385165
## 78  14.866069  5.830952 10.000000  5.830952  9.219544  5.000000  2.828427
## 79  11.313708  2.236068  6.708204  3.000000  5.656854  8.485281  1.000000
## 80   5.656854  3.605551  2.236068  4.123106  0.000000 14.142136  6.403124
## 81   1.000000 10.000000  5.830952 10.000000  6.403124 20.518285 12.727922
## 82   9.433981  1.414214  6.000000  4.242641  4.123106 10.816654  4.000000
## 83  14.142136  5.000000  9.433981  5.385165  8.485281  5.656854  2.236068
## 84   8.485281  1.000000  4.123106  2.236068  2.828427 11.313708  3.605551
## 85  11.313708  2.236068  6.708204  3.000000  5.656854  8.485281  1.000000
## 86   5.656854  3.605551  2.236068  4.123106  0.000000 14.142136  6.403124
## 87   2.236068  7.071068  4.000000  7.615773  3.605551 17.691806 10.000000
## 88  14.142136  5.000000  9.433981  5.385165  8.485281  5.656854  2.236068
## 89  19.798990 10.630146 15.000000 10.816654 14.142136  0.000000  7.810250
## 90  13.453624  4.472136  8.602325  4.472136  7.810250  6.403124  1.414214
## 91   1.414214  7.810250  4.123106  8.062258  4.242641 18.384776 10.630146
## 92  16.643317  7.615773 12.649111  9.055385 11.180340  5.000000  6.000000
## 93  15.556349  6.403124 10.816654  6.708204  9.899495  4.242641  3.605551
## 94   4.242641  5.000000  2.236068  5.385165  1.414214 15.556349  7.810250
## 95  16.278821  7.071068 11.661904  7.615773 10.630146  3.605551  4.472136
## 96   7.071068  2.236068  3.000000  3.000000  1.414214 12.727922  5.000000
## 97   7.810250  1.414214  4.000000  3.162278  2.236068 12.041595  4.472136
## 98  14.142136  5.000000  9.433981  5.385165  8.485281  5.656854  2.236068
## 99   8.485281  1.000000  4.123106  2.236068  2.828427 11.313708  3.605551
## 100 11.313708  2.236068  6.708204  3.000000  5.656854  8.485281  1.000000
## 101 15.620499  6.708204 10.630146  6.403124 10.000000  4.472136  3.605551
## 102  1.000000 10.000000  5.830952 10.000000  6.403124 20.518285 12.727922
## 103  7.071068  2.236068  3.000000  3.000000  1.414214 12.727922  5.000000
## 104 11.313708  2.236068  6.708204  3.000000  5.656854  8.485281  1.000000
## 105  5.656854  3.605551  2.236068  4.123106  0.000000 14.142136  6.403124
## 106 19.798990 10.630146 15.000000 10.816654 14.142136  0.000000  7.810250
## 107  5.656854  3.605551  2.236068  4.123106  0.000000 14.142136  6.403124
## 108 12.806248  4.123106  7.810250  3.605551  7.211103  7.211103  1.000000
## 109  5.656854  3.605551  2.236068  4.123106  0.000000 14.142136  6.403124
## 110  2.000000  8.062258  3.605551  7.810250  4.472136 18.439089 10.630146
## 111  2.828427  6.403124  3.000000  6.708204  2.828427 16.970563  9.219544
## 112  1.414214  7.810250  4.123106  8.062258  4.242641 18.384776 10.630146
## 113  2.828427  6.403124  3.000000  6.708204  2.828427 16.970563  9.219544
## 114  5.000000  4.472136  1.414214  4.472136  1.000000 14.866069  7.071068
## 115 18.384776  9.219544 13.601471  9.433981 12.727922  1.414214  6.403124
## 116  6.708204  4.000000  1.414214  2.828427  2.236068 13.601471  5.830952
## 117  2.828427  6.403124  3.000000  6.708204  2.828427 16.970563  9.219544
## 118  9.899495  1.000000  5.385165  2.236068  4.242641  9.899495  2.236068
## 119  2.828427 12.041595  8.062258 12.206556  8.485281 22.627417 14.866069
## 120  8.485281  1.000000  4.123106  2.236068  2.828427 11.313708  3.605551
## 121  6.000000  6.082763  6.403124  8.062258  4.472136 16.124515  9.219544
##            64        65        66        67        68        69        70
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65  17.029386                                                            
## 66  13.601471  3.605551                                                  
## 67  14.866069  3.000000  3.162278                                        
## 68  17.029386  0.000000  3.605551  3.000000                              
## 69  14.212670  2.828427  1.000000  2.236068  2.828427                    
## 70  10.630146  6.403124  3.162278  4.472136  6.403124  3.605551          
## 71  12.041595  5.000000  2.000000  3.162278  5.000000  2.236068  1.414214
## 72  13.453624  4.123106  2.828427  1.414214  4.123106  2.236068  3.162278
## 73   9.899495  7.211103  4.123106  5.000000  7.211103  4.472136  1.000000
## 74   2.828427 14.212670 10.816654 12.041595 14.212670 11.401754  7.810250
## 75  14.212670  2.828427  1.000000  2.236068  2.828427  0.000000  3.605551
## 76  10.630146  6.403124  3.162278  4.472136  6.403124  3.605551  0.000000
## 77   5.385165 12.041595  8.485281 10.295630 12.041595  9.219544  5.830952
## 78  12.727922  4.472136  2.236068  2.236068  4.472136  2.000000  2.236068
## 79   9.219544  7.810250  4.472136  5.830952  7.810250  5.000000  1.414214
## 80   3.605551 13.453624 10.000000 11.401754 13.453624 10.630146  7.071068
## 81   2.828427 19.849433 16.401219 17.691806 19.849433 17.029386 13.453624
## 82   7.615773 10.000000  6.403124  8.544004 10.000000  7.211103  4.123106
## 83  12.041595  5.000000  2.000000  3.162278  5.000000  2.236068  1.414214
## 84   6.403124 10.630146  7.211103  8.602325 10.630146  7.810250  4.242641
## 85   9.219544  7.810250  4.472136  5.830952  7.810250  5.000000  1.414214
## 86   3.605551 13.453624 10.000000 11.401754 13.453624 10.630146  7.071068
## 87   1.414214 16.970563 13.453624 15.000000 16.970563 14.142136 10.630146
## 88  12.041595  5.000000  2.000000  3.162278  5.000000  2.236068  1.414214
## 89  17.691806  1.000000  4.472136  3.162278  1.000000  3.605551  7.071068
## 90  11.313708  5.830952  3.000000  3.605551  5.830952  3.162278  1.000000
## 91   1.000000 17.691806 14.212670 15.620499 17.691806 14.866069 11.313708
## 92  14.764823  4.000000  2.236068  5.000000  4.000000  2.828427  5.000000
## 93  13.453624  3.605551  1.414214  2.000000  3.605551  1.000000  2.828427
## 94   2.236068 14.866069 11.401754 12.806248 14.866069 12.041595  8.485281
## 95  14.212670  2.828427  1.000000  2.236068  2.828427  0.000000  3.605551
## 96   5.000000 12.041595  8.602325 10.000000 12.041595  9.219544  5.656854
## 97   5.830952 11.313708  7.810250  9.433981 11.313708  8.485281  5.000000
## 98  12.041595  5.000000  2.000000  3.162278  5.000000  2.236068  1.414214
## 99   6.403124 10.630146  7.211103  8.602325 10.630146  7.810250  4.242641
## 100  9.219544  7.810250  4.472136  5.830952  7.810250  5.000000  1.414214
## 101 13.453624  4.123106  2.828427  1.414214  4.123106  2.236068  3.162278
## 102  2.828427 19.849433 16.401219 17.691806 19.849433 17.029386 13.453624
## 103  5.000000 12.041595  8.602325 10.000000 12.041595  9.219544  5.656854
## 104  9.219544  7.810250  4.472136  5.830952  7.810250  5.000000  1.414214
## 105  3.605551 13.453624 10.000000 11.401754 13.453624 10.630146  7.071068
## 106 17.691806  1.000000  4.472136  3.162278  1.000000  3.605551  7.071068
## 107  3.605551 13.453624 10.000000 11.401754 13.453624 10.630146  7.071068
## 108 10.630146  6.708204  4.000000  4.242641  6.708204  4.123106  1.414214
## 109  3.605551 13.453624 10.000000 11.401754 13.453624 10.630146  7.071068
## 110  1.000000 17.804494 14.422205 15.556349 17.804494 15.000000 11.401754
## 111  1.000000 16.278821 12.806248 14.212670 16.278821 13.453624  9.899495
## 112  1.000000 17.691806 14.212670 15.620499 17.691806 14.866069 11.313708
## 113  1.000000 16.278821 12.806248 14.212670 16.278821 13.453624  9.899495
## 114  2.828427 14.212670 10.816654 12.041595 14.212670 11.401754  7.810250
## 115 16.278821  1.000000  3.162278  2.000000  1.000000  2.236068  5.656854
## 116  4.472136 13.038405  9.848858 10.630146 13.038405 10.295630  6.708204
## 117  1.000000 16.278821 12.806248 14.212670 16.278821 13.453624  9.899495
## 118  7.810250  9.219544  5.830952  7.211103  9.219544  6.403124  2.828427
## 119  5.000000 21.931712 18.439089 19.849433 21.931712 19.104973 15.556349
## 120  6.403124 10.630146  7.211103  8.602325 10.630146  7.810250  4.242641
## 121  5.385165 15.264338 11.661904 13.928388 15.264338 12.529964  9.486833
##            71        72        73        74        75        76        77
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65                                                                       
## 66                                                                       
## 67                                                                       
## 68                                                                       
## 69                                                                       
## 70                                                                       
## 71                                                                       
## 72   2.000000                                                            
## 73   2.236068  3.605551                                                  
## 74   9.219544 10.630146  7.071068                                        
## 75   2.236068  2.236068  4.472136 11.401754                              
## 76   1.414214  3.162278  1.000000  7.810250  3.605551                    
## 77   7.211103  8.944272  5.385165  3.000000  9.219544  5.830952          
## 78   1.000000  1.000000  2.828427  9.899495  2.000000  2.236068  8.062258
## 79   2.828427  4.472136  1.000000  6.403124  5.000000  1.414214  4.472136
## 80   8.485281 10.000000  6.403124  1.000000 10.630146  7.071068  2.000000
## 81  14.866069 16.278821 12.727922  5.656854 17.029386 13.453624  8.062258
## 82   5.385165  7.280110  4.000000  5.099020  7.211103  4.123106  2.236068
## 83   0.000000  2.000000  2.236068  9.219544  2.236068  1.414214  7.211103
## 84   5.656854  7.211103  3.605551  3.605551  7.810250  4.242641  2.000000
## 85   2.828427  4.472136  1.000000  6.403124  5.000000  1.414214  4.472136
## 86   8.485281 10.000000  6.403124  1.000000 10.630146  7.071068  2.000000
## 87  12.041595 13.601471 10.000000  3.162278 14.142136 10.630146  5.000000
## 88   0.000000  2.000000  2.236068  9.219544  2.236068  1.414214  7.211103
## 89   5.656854  4.472136  7.810250 14.866069  3.605551  7.071068 12.806248
## 90   1.000000  2.236068  1.414214  8.485281  3.162278  1.000000  6.708204
## 91  12.727922 14.212670 10.630146  3.605551 14.866069 11.313708  5.830952
## 92   4.123106  5.000000  6.000000 12.083046  2.828427  5.000000  9.433981
## 93   1.414214  1.414214  3.605551 10.630146  1.000000  2.828427  8.602325
## 94   9.899495 11.401754  7.810250  1.000000 12.041595  8.485281  3.162278
## 95   2.236068  2.236068  4.472136 11.401754  0.000000  3.605551  9.219544
## 96   7.071068  8.602325  5.000000  2.236068  9.219544  5.656854  1.414214
## 97   6.403124  8.062258  4.472136  3.162278  8.485281  5.000000  1.000000
## 98   0.000000  2.000000  2.236068  9.219544  2.236068  1.414214  7.211103
## 99   5.656854  7.211103  3.605551  3.605551  7.810250  4.242641  2.000000
## 100  2.828427  4.472136  1.000000  6.403124  5.000000  1.414214  4.472136
## 101  2.000000  0.000000  3.605551 10.630146  2.236068  3.162278  8.944272
## 102 14.866069 16.278821 12.727922  5.656854 17.029386 13.453624  8.062258
## 103  7.071068  8.602325  5.000000  2.236068  9.219544  5.656854  1.414214
## 104  2.828427  4.472136  1.000000  6.403124  5.000000  1.414214  4.472136
## 105  8.485281 10.000000  6.403124  1.000000 10.630146  7.071068  2.000000
## 106  5.656854  4.472136  7.810250 14.866069  3.605551  7.071068 12.806248
## 107  8.485281 10.000000  6.403124  1.000000 10.630146  7.071068  2.000000
## 108  2.000000  2.828427  1.000000  7.810250  4.123106  1.414214  6.324555
## 109  8.485281 10.000000  6.403124  1.000000 10.630146  7.071068  2.000000
## 110 12.806248 14.142136 10.630146  3.605551 15.000000 11.401754  6.324555
## 111 11.313708 12.806248  9.219544  2.236068 13.453624  9.899495  4.472136
## 112 12.727922 14.212670 10.630146  3.605551 14.866069 11.313708  5.830952
## 113 11.313708 12.806248  9.219544  2.236068 13.453624  9.899495  4.472136
## 114  9.219544 10.630146  7.071068  0.000000 11.401754  7.810250  3.000000
## 115  4.242641  3.162278  6.403124 13.453624  2.236068  5.656854 11.401754
## 116  8.062258  9.219544  5.830952  2.000000 10.295630  6.708204  3.605551
## 117 11.313708 12.806248  9.219544  2.236068 13.453624  9.899495  4.472136
## 118  4.242641  5.830952  2.236068  5.000000  6.403124  2.828427  3.162278
## 119 16.970563 18.439089 14.866069  7.810250 19.104973 15.556349 10.000000
## 120  5.656854  7.211103  3.605551  3.605551  7.810250  4.242641  2.000000
## 121 10.770330 12.649111  9.219544  5.000000 12.529964  9.486833  4.000000
##            78        79        80        81        82        83        84
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65                                                                       
## 66                                                                       
## 67                                                                       
## 68                                                                       
## 69                                                                       
## 70                                                                       
## 71                                                                       
## 72                                                                       
## 73                                                                       
## 74                                                                       
## 75                                                                       
## 76                                                                       
## 77                                                                       
## 78                                                                       
## 79   3.605551                                                            
## 80   9.219544  5.656854                                                  
## 81  15.556349 12.041595  6.403124                                        
## 82   6.324555  3.000000  4.123106 10.295630                              
## 83   1.000000  2.828427  8.485281 14.866069  5.385165                    
## 84   6.403124  2.828427  2.828427  9.219544  2.236068  5.656854          
## 85   3.605551  0.000000  5.656854 12.041595  3.000000  2.828427  2.828427
## 86   9.219544  5.656854  0.000000  6.403124  4.123106  8.485281  2.828427
## 87  12.806248  9.219544  3.605551  3.162278  7.211103 12.041595  6.403124
## 88   1.000000  2.828427  8.485281 14.866069  5.385165  0.000000  5.656854
## 89   5.000000  8.485281 14.142136 20.518285 10.816654  5.656854 11.313708
## 90   1.414214  2.236068  7.810250 14.142136  5.099020  1.000000  5.000000
## 91  13.453624  9.899495  4.242641  2.236068  8.062258 12.727922  7.071068
## 92   4.472136  6.082763 11.180340 17.492856  7.211103  4.123106  8.544004
## 93   1.000000  4.242641  9.899495 16.278821  6.708204  1.414214  7.071068
## 94  10.630146  7.071068  1.414214  5.000000  5.385165  9.899495  4.242641
## 95   2.000000  5.000000 10.630146 17.029386  7.211103  2.236068  7.810250
## 96   7.810250  4.242641  1.414214  7.810250  3.000000  7.071068  1.414214
## 97   7.211103  3.605551  2.236068  8.602325  2.000000  6.403124  1.000000
## 98   1.000000  2.828427  8.485281 14.866069  5.385165  0.000000  5.656854
## 99   6.403124  2.828427  2.828427  9.219544  2.236068  5.656854  0.000000
## 100  3.605551  0.000000  5.656854 12.041595  3.000000  2.828427  2.828427
## 101  1.000000  4.472136 10.000000 16.278821  7.280110  2.000000  7.211103
## 102 15.556349 12.041595  6.403124  0.000000 10.295630 14.866069  9.219544
## 103  7.810250  4.242641  1.414214  7.810250  3.000000  7.071068  1.414214
## 104  3.605551  0.000000  5.656854 12.041595  3.000000  2.828427  2.828427
## 105  9.219544  5.656854  0.000000  6.403124  4.123106  8.485281  2.828427
## 106  5.000000  8.485281 14.142136 20.518285 10.816654  5.656854 11.313708
## 107  9.219544  5.656854  0.000000  6.403124  4.123106  8.485281  2.828427
## 108  2.236068  2.000000  7.211103 13.453624  5.000000  2.000000  4.472136
## 109  9.219544  5.656854  0.000000  6.403124  4.123106  8.485281  2.828427
## 110 13.453624 10.000000  4.472136  2.236068  8.544004 12.806248  7.211103
## 111 12.041595  8.485281  2.828427  3.605551  6.708204 11.313708  5.656854
## 112 13.453624  9.899495  4.242641  2.236068  8.062258 12.727922  7.071068
## 113 12.041595  8.485281  2.828427  3.605551  6.708204 11.313708  5.656854
## 114  9.899495  6.403124  1.000000  5.656854  5.099020  9.219544  3.605551
## 115  3.605551  7.071068 12.727922 19.104973  9.433981  4.242641  9.899495
## 116  8.602325  5.385165  2.236068  7.211103  5.099020  8.062258  3.000000
## 117 12.041595  8.485281  2.828427  3.605551  6.708204 11.313708  5.656854
## 118  5.000000  1.414214  4.242641 10.630146  2.236068  4.242641  1.414214
## 119 17.691806 14.142136  8.485281  2.236068 12.206556 16.970563 11.313708
## 120  6.403124  2.828427  2.828427  9.219544  2.236068  5.656854  0.000000
## 121 11.704700  8.246211  4.472136  7.000000  5.385165 10.770330  6.000000
##            85        86        87        88        89        90        91
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65                                                                       
## 66                                                                       
## 67                                                                       
## 68                                                                       
## 69                                                                       
## 70                                                                       
## 71                                                                       
## 72                                                                       
## 73                                                                       
## 74                                                                       
## 75                                                                       
## 76                                                                       
## 77                                                                       
## 78                                                                       
## 79                                                                       
## 80                                                                       
## 81                                                                       
## 82                                                                       
## 83                                                                       
## 84                                                                       
## 85                                                                       
## 86   5.656854                                                            
## 87   9.219544  3.605551                                                  
## 88   2.828427  8.485281 12.041595                                        
## 89   8.485281 14.142136 17.691806  5.656854                              
## 90   2.236068  7.810250 11.401754  1.000000  6.403124                    
## 91   9.899495  4.242641  1.000000 12.727922 18.384776 12.041595          
## 92   6.082763 11.180340 14.422205  4.123106  5.000000  5.099020 15.264338
## 93   4.242641  9.899495 13.453624  1.414214  4.242641  2.236068 14.142136
## 94   7.071068  1.414214  2.236068  9.899495 15.556349  9.219544  2.828427
## 95   5.000000 10.630146 14.142136  2.236068  3.605551  3.162278 14.866069
## 96   4.242641  1.414214  5.000000  7.071068 12.727922  6.403124  5.656854
## 97   3.605551  2.236068  5.656854  6.403124 12.041595  5.830952  6.403124
## 98   2.828427  8.485281 12.041595  0.000000  5.656854  1.000000 12.727922
## 99   2.828427  2.828427  6.403124  5.656854 11.313708  5.000000  7.071068
## 100  0.000000  5.656854  9.219544  2.828427  8.485281  2.236068  9.899495
## 101  4.472136 10.000000 13.601471  2.000000  4.472136  2.236068 14.212670
## 102 12.041595  6.403124  3.162278 14.866069 20.518285 14.142136  2.236068
## 103  4.242641  1.414214  5.000000  7.071068 12.727922  6.403124  5.656854
## 104  0.000000  5.656854  9.219544  2.828427  8.485281  2.236068  9.899495
## 105  5.656854  0.000000  3.605551  8.485281 14.142136  7.810250  4.242641
## 106  8.485281 14.142136 17.691806  5.656854  0.000000  6.403124 18.384776
## 107  5.656854  0.000000  3.605551  8.485281 14.142136  7.810250  4.242641
## 108  2.000000  7.211103 10.816654  2.000000  7.211103  1.000000 11.401754
## 109  5.656854  0.000000  3.605551  8.485281 14.142136  7.810250  4.242641
## 110 10.000000  4.472136  2.236068 12.806248 18.439089 12.041595  1.414214
## 111  8.485281  2.828427  1.000000 11.313708 16.970563 10.630146  1.414214
## 112  9.899495  4.242641  1.000000 12.727922 18.384776 12.041595  0.000000
## 113  8.485281  2.828427  1.000000 11.313708 16.970563 10.630146  1.414214
## 114  6.403124  1.000000  3.162278  9.219544 14.866069  8.485281  3.605551
## 115  7.071068 12.727922 16.278821  4.242641  1.414214  5.000000 16.970563
## 116  5.385165  2.236068  5.099020  8.062258 13.601471  7.211103  5.385165
## 117  8.485281  2.828427  1.000000 11.313708 16.970563 10.630146  1.414214
## 118  1.414214  4.242641  7.810250  4.242641  9.899495  3.605551  8.485281
## 119 14.142136  8.485281  5.000000 16.970563 22.627417 16.278821  4.242641
## 120  2.828427  2.828427  6.403124  5.656854 11.313708  5.000000  7.071068
## 121  8.246211  4.472136  4.123106 10.770330 16.124515 10.440307  5.099020
##            92        93        94        95        96        97        98
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65                                                                       
## 66                                                                       
## 67                                                                       
## 68                                                                       
## 69                                                                       
## 70                                                                       
## 71                                                                       
## 72                                                                       
## 73                                                                       
## 74                                                                       
## 75                                                                       
## 76                                                                       
## 77                                                                       
## 78                                                                       
## 79                                                                       
## 80                                                                       
## 81                                                                       
## 82                                                                       
## 83                                                                       
## 84                                                                       
## 85                                                                       
## 86                                                                       
## 87                                                                       
## 88                                                                       
## 89                                                                       
## 90                                                                       
## 91                                                                       
## 92                                                                       
## 93   3.605551                                                            
## 94  12.529964 11.313708                                                  
## 95   2.828427  1.000000 12.041595                                        
## 96   9.848858  8.485281  2.828427  9.219544                              
## 97   8.944272  7.810250  3.605551  8.485281  1.000000                    
## 98   4.123106  1.414214  9.899495  2.236068  7.071068  6.403124          
## 99   8.544004  7.071068  4.242641  7.810250  1.414214  1.000000  5.656854
## 100  6.082763  4.242641  7.071068  5.000000  4.242641  3.605551  2.828427
## 101  5.000000  1.414214 11.401754  2.236068  8.602325  8.062258  2.000000
## 102 17.492856 16.278821  5.000000 17.029386  7.810250  8.602325 14.866069
## 103  9.848858  8.485281  2.828427  9.219544  0.000000  1.000000  7.071068
## 104  6.082763  4.242641  7.071068  5.000000  4.242641  3.605551  2.828427
## 105 11.180340  9.899495  1.414214 10.630146  1.414214  2.236068  8.485281
## 106  5.000000  4.242641 15.556349  3.605551 12.727922 12.041595  5.656854
## 107 11.180340  9.899495  1.414214 10.630146  1.414214  2.236068  8.485281
## 108  6.082763  3.162278  8.602325  4.123106  5.830952  5.385165  2.000000
## 109 11.180340  9.899495  1.414214 10.630146  1.414214  2.236068  8.485281
## 110 15.652476 14.212670  3.162278 15.000000  5.830952  6.708204 12.806248
## 111 13.892444 12.727922  1.414214 13.453624  4.242641  5.000000 11.313708
## 112 15.264338 14.142136  2.828427 14.866069  5.656854  6.403124 12.727922
## 113 13.892444 12.727922  1.414214 13.453624  4.242641  5.000000 11.313708
## 114 12.083046 10.630146  1.000000 11.401754  2.236068  3.162278  9.219544
## 115  4.123106  2.828427 14.142136  2.236068 11.313708 10.630146  4.242641
## 116 11.401754  9.433981  3.000000 10.295630  2.236068  3.162278  8.062258
## 117 13.892444 12.727922  1.414214 13.453624  4.242641  5.000000 11.313708
## 118  7.280110  5.656854  5.656854  6.403124  2.828427  2.236068  4.242641
## 119 19.416488 18.384776  7.071068 19.104973  9.899495 10.630146 16.970563
## 120  8.544004  7.071068  4.242641  7.810250  1.414214  1.000000  5.656854
## 121 12.041595 12.083046  4.242641 12.529964  5.099020  5.000000 10.770330
##            99       100       101       102       103       104       105
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65                                                                       
## 66                                                                       
## 67                                                                       
## 68                                                                       
## 69                                                                       
## 70                                                                       
## 71                                                                       
## 72                                                                       
## 73                                                                       
## 74                                                                       
## 75                                                                       
## 76                                                                       
## 77                                                                       
## 78                                                                       
## 79                                                                       
## 80                                                                       
## 81                                                                       
## 82                                                                       
## 83                                                                       
## 84                                                                       
## 85                                                                       
## 86                                                                       
## 87                                                                       
## 88                                                                       
## 89                                                                       
## 90                                                                       
## 91                                                                       
## 92                                                                       
## 93                                                                       
## 94                                                                       
## 95                                                                       
## 96                                                                       
## 97                                                                       
## 98                                                                       
## 99                                                                       
## 100  2.828427                                                            
## 101  7.211103  4.472136                                                  
## 102  9.219544 12.041595 16.278821                                        
## 103  1.414214  4.242641  8.602325  7.810250                              
## 104  2.828427  0.000000  4.472136 12.041595  4.242641                    
## 105  2.828427  5.656854 10.000000  6.403124  1.414214  5.656854          
## 106 11.313708  8.485281  4.472136 20.518285 12.727922  8.485281 14.142136
## 107  2.828427  5.656854 10.000000  6.403124  1.414214  5.656854  0.000000
## 108  4.472136  2.000000  2.828427 13.453624  5.830952  2.000000  7.211103
## 109  2.828427  5.656854 10.000000  6.403124  1.414214  5.656854  0.000000
## 110  7.211103 10.000000 14.142136  2.236068  5.830952 10.000000  4.472136
## 111  5.656854  8.485281 12.806248  3.605551  4.242641  8.485281  2.828427
## 112  7.071068  9.899495 14.212670  2.236068  5.656854  9.899495  4.242641
## 113  5.656854  8.485281 12.806248  3.605551  4.242641  8.485281  2.828427
## 114  3.605551  6.403124 10.630146  5.656854  2.236068  6.403124  1.000000
## 115  9.899495  7.071068  3.162278 19.104973 11.313708  7.071068 12.727922
## 116  3.000000  5.385165  9.219544  7.211103  2.236068  5.385165  2.236068
## 117  5.656854  8.485281 12.806248  3.605551  4.242641  8.485281  2.828427
## 118  1.414214  1.414214  5.830952 10.630146  2.828427  1.414214  4.242641
## 119 11.313708 14.142136 18.439089  2.236068  9.899495 14.142136  8.485281
## 120  0.000000  2.828427  7.211103  9.219544  1.414214  2.828427  2.828427
## 121  6.000000  8.246211 12.649111  7.000000  5.099020  8.246211  4.472136
##           106       107       108       109       110       111       112
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
## 26                                                                       
## 27                                                                       
## 28                                                                       
## 29                                                                       
## 30                                                                       
## 31                                                                       
## 32                                                                       
## 33                                                                       
## 34                                                                       
## 35                                                                       
## 36                                                                       
## 37                                                                       
## 38                                                                       
## 39                                                                       
## 40                                                                       
## 41                                                                       
## 42                                                                       
## 43                                                                       
## 44                                                                       
## 45                                                                       
## 46                                                                       
## 47                                                                       
## 48                                                                       
## 49                                                                       
## 50                                                                       
## 51                                                                       
## 52                                                                       
## 53                                                                       
## 54                                                                       
## 55                                                                       
## 56                                                                       
## 57                                                                       
## 58                                                                       
## 59                                                                       
## 60                                                                       
## 61                                                                       
## 62                                                                       
## 63                                                                       
## 64                                                                       
## 65                                                                       
## 66                                                                       
## 67                                                                       
## 68                                                                       
## 69                                                                       
## 70                                                                       
## 71                                                                       
## 72                                                                       
## 73                                                                       
## 74                                                                       
## 75                                                                       
## 76                                                                       
## 77                                                                       
## 78                                                                       
## 79                                                                       
## 80                                                                       
## 81                                                                       
## 82                                                                       
## 83                                                                       
## 84                                                                       
## 85                                                                       
## 86                                                                       
## 87                                                                       
## 88                                                                       
## 89                                                                       
## 90                                                                       
## 91                                                                       
## 92                                                                       
## 93                                                                       
## 94                                                                       
## 95                                                                       
## 96                                                                       
## 97                                                                       
## 98                                                                       
## 99                                                                       
## 100                                                                      
## 101                                                                      
## 102                                                                      
## 103                                                                      
## 104                                                                      
## 105                                                                      
## 106                                                                      
## 107 14.142136                                                            
## 108  7.211103  7.211103                                                  
## 109 14.142136  0.000000  7.211103                                        
## 110 18.439089  4.472136 11.313708  4.472136                              
## 111 16.970563  2.828427 10.000000  2.828427  2.000000                    
## 112 18.384776  4.242641 11.401754  4.242641  1.414214  1.414214          
## 113 16.970563  2.828427 10.000000  2.828427  2.000000  0.000000  1.414214
## 114 14.866069  1.000000  7.810250  1.000000  3.605551  2.236068  3.605551
## 115  1.414214 12.727922  5.830952 12.727922 17.029386 15.556349 16.970563
## 116 13.601471  2.236068  6.403124  2.236068  5.000000  4.123106  5.385165
## 117 16.970563  2.828427 10.000000  2.828427  2.000000  0.000000  1.414214
## 118  9.899495  4.242641  3.162278  4.242641  8.602325  7.071068  8.485281
## 119 22.627417  8.485281 15.620499  8.485281  4.472136  5.656854  4.242641
## 120 11.313708  2.828427  4.472136  2.828427  7.211103  5.656854  7.071068
## 121 16.124515  4.472136 10.198039  4.472136  6.324555  4.472136  5.099020
##           113       114       115       116       117       118       119
## 2                                                                        
## 3                                                                        
## 4                                                                        
## 5                                                                        
## 6                                                                        
## 7                                                                        
## 8                                                                        
## 9                                                                        
## 10                                                                       
## 11                                                                       
## 12                                                                       
## 13                                                                       
## 14                                                                       
## 15                                                                       
## 16                                                                       
## 17                                                                       
## 18                                                                       
## 19                                                                       
## 20                                                                       
## 21                                                                       
## 22                                                                       
## 23                                                                       
## 24                                                                       
## 25                                                                       
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## 114  2.236068                                                            
## 115 15.556349 13.453624                                                  
## 116  4.123106  2.000000 12.206556                                        
## 117  0.000000  2.236068 15.556349  4.123106                              
## 118  7.071068  5.000000  8.485281  4.123106  7.071068                    
## 119  5.656854  7.810250 21.213203  9.433981  5.656854 12.727922          
## 120  5.656854  3.605551  9.899495  3.000000  5.656854  1.414214 11.313708
## 121  4.472136  5.000000 14.764823  6.708204  4.472136  7.071068  8.246211
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#calculate how many clusters I need
fviz_nbclust(cluster_data, kmeans, method = "wss") + #within sums squares = type of measure identifying what needs to/doesn't need to be merged
  labs(title = "Figure 1.", subtitle = "Optimal Number of Clusters - Elbow method") 

    #when looking at the elbow plot, you're trying to determine the however # of clusters that we need to use (aka the optimal number)
    #when looking at degree, you want to look at diminishing returns
      #so when slopes are getting closer to zero,is how many clusters you should look at

#choose number of clusters
k <- 4

# Run the cluster analysis
cluster <- kmeans(cluster_data, k)
cluster

## K-means clustering with 4 clusters of sizes 25, 45, 31, 20
## 
## Cluster means:
##   standards discrepancy
## 1  26.32000    26.68000
## 2  18.82222    18.93333
## 3  23.64516    23.12903
## 4  15.25000    14.85000
## 
## Clustering vector:
##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
##   1   2   4   4   3   2   4   2   2   1   1   2   3   2   1   2   1   2   2   2 
##  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
##   1   4   2   2   3   2   1   1   3   1   3   2   3   1   1   2   2   3   3   4 
##  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60 
##   4   3   2   2   2   3   2   2   3   4   3   3   4   2   1   3   4   2   2   2 
##  61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80 
##   2   1   3   4   1   1   1   1   1   3   3   3   3   2   1   3   2   3   3   2 
##  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100 
##   4   2   3   2   3   2   4   3   1   3   4   1   1   2   1   2   2   3   2   3 
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 
##   3   4   2   3   2   1   2   3   2   4   4   4   4   2   1   2   4   2   4   2 
## 121 
##   2 
## 
## Within cluster sum of squares by cluster:
## [1]  82.88000 169.37778  66.58065  60.30000
##  (between_SS / total_SS =  90.7 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

#visualize the clustering alogrithim results
library(factoextra)
fviz_cluster(cluster, data = cluster_data, geom = "point", stand = FALSE, 
             ellipse.type = "t", palette = "jco", ggtheme = theme_minimal()) +
  labs(title = "Figure 2.", subtitle = "Cluster Plot")

#OR 

plot(cluster_data, col = cluster$cluster)

# count
table(cluster$cluster)

## 
##  1  2  3  4 
## 25 45 31 20

library(dplyr)
library(psych)

## 
## Attaching package: 'psych'

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

# Assign cluster labels to each row in the original data frame
cluster_assignments <- cbind(cluster_data, cluster = cluster$cluster)
cluster_assignments <- cluster_assignments %>% mutate(ID = row_number())

#make a dataframe of just outcome variables
outcome_data <- data.frame(d$anxiety, d$depression, d$swfw, d$wellbeing)
outcome_data <- rename(outcome_data, anxiety = d.anxiety, depression = d.depression, swfw = d.swfw, wellbeing = d.wellbeing)

outcome_data <- outcome_data %>% mutate(ID = row_number())

# Join the cluster assignments with the outcomes_data data frame by participant_id
df_merged <- left_join(cluster_assignments, outcome_data, by = "ID")

options(scipen = 999)

# Conduct ANOVAs for each outcome variable, comparing the means of each cluster
anova_result_anxiety <- aov(anxiety ~ cluster, data = df_merged)
anova_result_depression <- aov(depression ~ cluster, data = df_merged)
anova_result_standards <- aov(standards ~ cluster, data = df_merged)
anova_result_discrepancy <- aov(discrepancy ~ cluster, data = df_merged)

summary(anova_result_anxiety)

##              Df Sum Sq Mean Sq F value  Pr(>F)   
## cluster       1   5.63   5.630   10.87 0.00129 **
## Residuals   118  61.11   0.518                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingness

summary(anova_result_depression)

##              Df Sum Sq Mean Sq F value  Pr(>F)   
## cluster       1    4.5   4.503   10.87 0.00129 **
## Residuals   119   49.3   0.414                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(anova_result_standards)

##              Df Sum Sq Mean Sq F value           Pr(>F)    
## cluster       1  669.9   669.9   59.31 0.00000000000442 ***
## Residuals   119 1344.1    11.3                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(anova_result_discrepancy)

##              Df Sum Sq Mean Sq F value             Pr(>F)    
## cluster       1  858.4   858.4   85.05 0.0000000000000013 ***
## Residuals   119 1201.0    10.1                               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Conduct Bonferroni-corrected pairwise comparisons between the clusters for each outcome variable
pairwise_anxiety <- pairwise.t.test(df_merged$anxiety, df_merged$cluster, p.adj = "bonferroni")
pairwise_depression <- pairwise.t.test(df_merged$depression, df_merged$cluster, p.adj = "bonferroni")
pairwise_standards <- pairwise.t.test(df_merged$standards, df_merged$cluster, p.adj = "bonferroni")
pairwise_discrepancy <- pairwise.t.test(df_merged$discrepancy, df_merged$cluster, p.adj = "bonferroni")

print(pairwise_anxiety)

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  df_merged$anxiety and df_merged$cluster 
## 
##   1        2       3      
## 2 0.00025  -       -      
## 3 0.48747  0.08568 -      
## 4 0.000024 0.89504 0.00587
## 
## P value adjustment method: bonferroni

print(pairwise_depression)

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  df_merged$depression and df_merged$cluster 
## 
##   1        2      3     
## 2 0.0045   -      -     
## 3 0.8530   0.2895 -     
## 4 0.000065 0.3426 0.0051
## 
## P value adjustment method: bonferroni

print(pairwise_standards)

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  df_merged$standards and df_merged$cluster 
## 
##   1                    2                    3                   
## 2 < 0.0000000000000002 -                    -                   
## 3 0.00000000018149413  < 0.0000000000000002 -                   
## 4 < 0.0000000000000002 0.00000000000000037  < 0.0000000000000002
## 
## P value adjustment method: bonferroni

print(pairwise_discrepancy)

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  df_merged$discrepancy and df_merged$cluster 
## 
##   1                   2                   3                  
## 2 <0.0000000000000002 -                   -                  
## 3 <0.0000000000000002 <0.0000000000000002 -                  
## 4 <0.0000000000000002 <0.0000000000000002 <0.0000000000000002
## 
## P value adjustment method: bonferroni

# plot a box plot 
anxiety_boxplot <- boxplot(anxiety ~ cluster, data = df_merged, 
        main = "Anxiety by Cluster", 
        xlab = "Cluster", ylab = "Anxiety")

depression_boxplot <- boxplot(depression ~ cluster, data = df_merged, 
        main = "Depression by Cluster", 
        xlab = "Cluster", ylab = "Depression")

standards_boxplot <- boxplot(standards ~ cluster, data = df_merged, 
        main = "Standards by Cluster", 
        xlab = "Cluster", ylab = "Standards")

discrepancy_boxplot <- boxplot(discrepancy ~ cluster, data = df_merged, 
        main = "Discrepancy by Cluster", 
        xlab = "Cluster", ylab = "Discrepancy")

demo_data <- data.frame(fgp_data$age, fgp_data$sexuality, fgp_data$gender, fgp_data$income, fgp_data$fam_income, fgp_data$ethnicity, fgp_data$edu, fgp_data$religion, cluster_assignments$cluster)

demo_data <- rename(demo_data, age = fgp_data.age, sexuality = fgp_data.sexuality, 
gender = fgp_data.gender, income = fgp_data.income, fam_income = fgp_data.fam_income, ethnicity = fgp_data.ethnicity, 
edu = fgp_data.edu, religion = fgp_data.religion, cluster = cluster_assignments.cluster)

library(dplyr)

# Count occurrences of each value within each cluster
cluster_demographics <- demo_data %>%
  group_by(cluster) %>%
  summarize(cluster_size = n(),
            cisgender_female = sum(gender == 1, na.rm = TRUE),
            cisgender_male = sum(gender == 2, na.rm = TRUE),
            gender_fluid_nonconforming = sum(gender == 5, na.rm = TRUE),
            asexual = sum(sexuality == 1, na.rm = TRUE),
            bisexual = sum(sexuality == 2, na.rm = TRUE),
            gay = sum(sexuality == 3, na.rm = TRUE),
            lesbian = sum(sexuality == 4, na.rm = TRUE),
            heterosexual = sum (sexuality == 5, na.rm = TRUE),
            queer = sum(sexuality == 7, na.rm = TRUE),
            latine = sum (ethnicity == 1, na.rm = TRUE),
            black = sum (ethnicity == 2, na.rm = TRUE),
            asian = sum (ethnicity == 3, na.rm = TRUE),
            middle_eastern = sum (ethnicity == 4, na.rm = TRUE),
            native_american = sum (ethnicity == 5, na.rm = TRUE),
            white = sum (ethnicity == 6, na.rm = TRUE),
            multiracial = sum (ethnicity == 7, na.rm = TRUE),
            level1 = sum (income == 1, na.rm = TRUE),
            level2 = sum (income == 2, na.rm = TRUE),
            level3 = sum (income == 3, na.rm = TRUE),
            level4 = sum (income == 4, na.rm = TRUE),
            level5 = sum (income == 5, na.rm = TRUE),
            level6 = sum (income == 6, na.rm = TRUE),
            level7 = sum (income == 7, na.rm = TRUE),
            level8 = sum (income == 8, na.rm = TRUE),
            level9 = sum (income == 9, na.rm = TRUE),
            level10 = sum (income == 10, na.rm = TRUE),
            level1 = sum (fam_income == 1, na.rm = TRUE),
            level2 = sum (fam_income == 2, na.rm = TRUE),
            level3 = sum (fam_income == 3, na.rm = TRUE),
            level4 = sum (fam_income == 4, na.rm = TRUE),
            level5 = sum (fam_income == 5, na.rm = TRUE),
            level6 = sum (fam_income == 6, na.rm = TRUE),
            level7 = sum (fam_income == 7, na.rm = TRUE),
            level8 = sum (fam_income == 8, na.rm = TRUE),
            level9 = sum (fam_income == 9, na.rm = TRUE),
            level10 = sum (fam_income == 10, na.rm = TRUE),
            agnostic = sum(religion == 1, na.rm = TRUE),
            atheist = sum(religion == 2, na.rm = TRUE),
            buddhist = sum(religion == 3, na.rm = TRUE),
            catholic = sum(religion == 4, na.rm = TRUE),
            christian = sum(religion == 5, na.rm = TRUE),
            hindu = sum(religion == 6, na.rm = TRUE),
            jewish = sum(religion == 7, na.rm = TRUE),
            muslim = sum(religion == 8, na.rm = TRUE),
            unitarian = sum(religion == 9, na.rm = TRUE),
            spiritual = sum(religion == 10, na.rm = TRUE),
            religious = sum(religion == 11, na.rm = TRUE),
            multiple = sum(religion == 12, na.rm = TRUE),
            secular = sum(religion == 13, na.rm = TRUE),
            prefer = sum(religion == 14, na.rm = TRUE),
            associates = sum(edu == 1, na.rm = TRUE),
            bachelors = sum(edu == 2, na.rm = TRUE),
            masters = sum(edu == 3, na.rm = TRUE),
            doctorate = sum(edu == 4, na.rm = TRUE),
            professional = sum(edu == 5, na.rm = TRUE),
            prefer = sum(edu == 6, na.rm = TRUE))
# View the results
print(cluster_demographics)

## # A tibble: 4 × 47
##   cluster cluster_size cisgender_female cisgender_male gender_fluid_non… asexual
##     <int>        <int>            <int>          <int>             <int>   <int>
## 1       1           25               12             13                 0       1
## 2       2           45               17             28                 0       1
## 3       3           31               13             18                 0       0
## 4       4           20                9             10                 1       0
## # … with 41 more variables: bisexual <int>, gay <int>, lesbian <int>,
## #   heterosexual <int>, queer <int>, latine <int>, black <int>, asian <int>,
## #   middle_eastern <int>, native_american <int>, white <int>,
## #   multiracial <int>, level1 <int>, level2 <int>, level3 <int>, level4 <int>,
## #   level5 <int>, level6 <int>, level7 <int>, level8 <int>, level9 <int>,
## #   level10 <int>, agnostic <int>, atheist <int>, buddhist <int>,
## #   catholic <int>, christian <int>, hindu <int>, jewish <int>, muslim <int>, …

cluster_age <- demo_data %>%
  group_by(cluster) %>%
  summarize(mean_age = mean(age, na.rm = TRUE))


# View the results
print(cluster_age)

## # A tibble: 4 × 2
##   cluster mean_age
##     <int>    <dbl>
## 1       1     31.0
## 2       2     33.9
## 3       3     32.2
## 4       4     36.6