Veri simülasyonu

Öğrenme Günlüğü

Bu hafta derste yapılan simülasyon ve paralel işlem kodlarını tekrar etmeye çalıştım. Kodların her aşamasını daha iyi anlamak için AI desteğinden yararlandım. Özellikle veri üretimi, parametre kestirimi, hata hesaplamaları ve paralel işlem yapısının nasıl çalıştığını adım adım incelememe çalıştım.Ayrıca önceki hafta işlediğimiz MTK dersi konuları da bu hafta yaptığımız MTK ödevini yapmamda çok etkili oldu, bunun için de teşekkür etmek istedim.

Veri Üretme

Ortalaması 100, standart sapması 20 olan normal dağılımlı 100 gözlem üretme Not: rnorm() fonksiyonu ile veri üretildiğinde, ortalaması tam olarak 100 olan değerler elde edilmez; sonuçlar genellikle 100’e yakın olur. Bunun nedeni, fonksiyonun ortalaması 100 ve standart sapması 20 olan teorik bir normal dağılımdan rastgele örnekler üretmesidir. Örneklem büyüklüğü arttıkça elde edilen ortalama ve standart sapma değerleri teorik değerlere daha fazla yaklaşır

set.seed(41)
x <- rnorm(100,100,20)
mean(x)

## [1] 103.8063

sd(x)

## [1] 20.56458

KÜçük ve Büyük Veri KArşılaştırma

n_k <- 10
b_k <- 50

tekrar <- 1000
kucuk_orn <- numeric(tekrar)
buyuk_orn <- numeric(tekrar)

for(i in 1:tekrar){
  kucuk_orn[i] <- mean(rnorm(n=n_k, mean=35, sd=15))
  buyuk_orn[i] <- mean(rnorm(n=b_k, mean=35, sd=15))
}

hist(kucuk_orn)

hist(buyuk_orn)

Burada küçük ve büyük örneklemlerden elde edilen ortalamaların dağılımları karşılaştırılmdı. örneklem büyüklüğü daha kararlı ve güvenilir sonuçlar elde edilir (Merkezi Limit Teoremi)

3 Parametreli Lojistik Model (3PL) için madde ve birey parametreleri üretme

set.seed(41)
madde <- 8

maddepar <- cbind(
  rnorm( madde, mean = 0 , sd =0.75),
  rnorm( madde, mean = 0.30 , sd =0.50),
  rnorm( madde, mean = 0.16, sd =0.05)
  )

## yetenek par

set.seed(41)
birey <- 1000
yetenek <- rnorm( birey, 0,1)
yetenek[1:10]

##  [1] -0.7943683  0.1972575  1.0017043  1.2888254  0.9057534  0.4936675
##  [7]  0.5992858 -1.5796070  1.0006207  2.1880077

3 Parametreli Lojistik Model (3PL) için madde ve birey parametreleri üretildi. İlk bölümde 8 madde için madde parametreleri oluşturuldu. rnorm() fonksiyonu kullanılarak maddelerin ayırt edicilik, güçlük ve şans parametreleri normal dağılımdan rastgele üretilmiş ve maddepar adlı matriste birleştirildi.

İkinci bölümde ise 1000 birey için yetenek (yetenek) değerleri üretildi. Bu yetenek değerleri ortalaması 0 ve standart sapması 1 olan normal dağılımdan çekildi.

3 Parametreli Lojistik Model (3PL) ile Veri Simülasyonu

library(psych)

## Warning: package 'psych' was built under R version 4.5.3

library(irtoys)

## Warning: package 'irtoys' was built under R version 4.5.3

## Zorunlu paket yükleniyor: sm

## Warning: package 'sm' was built under R version 4.5.3

## Package 'sm', version 2.2-6.0: type help(sm) for summary information

## Zorunlu paket yükleniyor: ltm

## Warning: package 'ltm' was built under R version 4.5.3

## Zorunlu paket yükleniyor: MASS

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:sm':
## 
##     muscle

## Zorunlu paket yükleniyor: msm

## Warning: package 'msm' was built under R version 4.5.3

## Zorunlu paket yükleniyor: polycor

## Warning: package 'polycor' was built under R version 4.5.3

## 
## Attaching package: 'polycor'

## The following object is masked from 'package:psych':
## 
##     polyserial

## 
## Attaching package: 'ltm'

## The following object is masked from 'package:psych':
## 
##     factor.scores

## 
## Attaching package: 'irtoys'

## The following object is masked from 'package:psych':
## 
##     sim

library(mirt)

## Warning: package 'mirt' was built under R version 4.5.3

## Zorunlu paket yükleniyor: stats4

## Zorunlu paket yükleniyor: lattice

## 
## Attaching package: 'mirt'

## The following object is masked from 'package:ltm':
## 
##     Science

# irtoys paketindeki sim() fonksiyonu ile 3PL modele göre veri üretme

# irtoys paketindeki sim() fonksiyonu ile 3PL modele göre veri üretilir
# ip = madde parametreleri, x = bireylerin yetenek düzeyleridir
veri <- irtoys::sim(ip = maddepar, x = yetenek)

# Üretilen veri setinin ilk 6 satırı görüntülenir
head(veri)

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,]    0    1    1    0    0    0    1    1
## [2,]    1    0    1    1    1    1    0    0
## [3,]    1    1    1    1    0    1    0    1
## [4,]    1    1    0    1    0    1    1    0
## [5,]    0    1    0    1    1    1    1    1
## [6,]    1    0    1    0    0    1    0    0

# Veri setindeki maddelere madde_1, madde_2, ... şeklinde isim verilir
colnames(veri) <- paste0("madde_", 1:madde)

# Sütun isimleri düzenlendikten sonra veri setinin ilk 6 satırı tekrar görüntülenir
head(veri)

##      madde_1 madde_2 madde_3 madde_4 madde_5 madde_6 madde_7 madde_8
## [1,]       0       1       1       0       0       0       1       1
## [2,]       1       0       1       1       1       1       0       0
## [3,]       1       1       1       1       0       1       0       1
## [4,]       1       1       0       1       0       1       1       0
## [5,]       0       1       0       1       1       1       1       1
## [6,]       1       0       1       0       0       1       0       0

# Aşağıdaki kod, sim() fonksiyonunun arka planda yaptığı işlemi göstermektedir

# Madde parametreleri ip nesnesine atanır
ip <- maddepar

# Bireylerin yetenek değerleri x nesnesine atanır
x <- yetenek

# Madde tepki fonksiyonundan her birey-madde için doğru yanıtlama olasılıkları hesaplanır
i <- irf(ip = ip, x = x)

# Hesaplanan olasılıkların ilk satırları görüntülenir
head(i)

## $x
##    [1] -0.7943683371  0.1972575391  1.0017043217  1.2888253933  0.9057534131
##    [6]  0.4936674707  0.5992857964 -1.5796070072  1.0006206611  2.1880076813
##   [11] -1.2093243663 -0.5873119374  1.0561205840 -0.3165849251 -0.0545410382
##   [16]  0.3297513055  0.6630950965  0.8783281516  0.2028742692  2.2744024710
##   [21] -0.8992970378  2.1394902977 -1.1659509915 -0.0471303980  0.4158762627
##   [26]  1.7200804886 -0.7843606885 -1.3039296474 -0.4520358962 -1.7739919174
##   [31] -0.0501536127 -1.0374966974  0.6222005426  0.1271929680 -1.7408762330
##   [36] -0.5732123366  0.9119497830  1.2343650239  0.6612353661 -0.8610522673
##   [41] -0.5330392645  0.3207890885 -0.0044843610  1.5981956415  1.3274498010
##   [46] -0.1191853218  0.0815543310 -0.0198322879 -0.8252251515  0.7016745739
##   [51] -0.1960757883 -0.1578275442  0.2235278995  0.3049519720  1.3689034938
##   [56] -1.3885221874 -1.6444363571  1.4261473589  0.0966294522  0.3122675994
##   [61]  0.8818241877  0.8989142610  1.5030842292  0.5051171071 -0.3409508939
##   [66]  1.3732091360  0.8188045818  1.4257418554  2.1957613588 -0.8957317631
##   [71] -1.6901690214 -0.4674173645 -0.3599244767  0.7461725482  0.1687014789
##   [76]  1.6501830755  0.0334761784 -1.0324903347 -0.6324367667  0.5781459060
##   [81]  1.8417429224 -0.0580244925 -0.2570523573 -2.1666761404  0.1098698432
##   [86]  1.3147025151 -0.8927359522 -1.0436829676 -0.5419373647 -0.3307311076
##   [91]  1.6720183622 -1.0526666498  0.0808250825  0.7032265012  1.5114293387
##   [96]  0.0007684692  1.4314714820 -1.1116999603  0.5684251853  1.3377335810
##  [101]  0.0728266174  1.1957098837 -2.1116319848  0.6713904563 -0.1862067771
##  [106] -0.1915767402  0.7867440159  0.5623474758 -0.0191025851 -0.2603593162
##  [111] -0.1620156495 -2.0898603722  0.4493790711 -0.6970796964  0.7818080414
##  [116] -0.2648105694  0.0203910869  0.4014797752  1.9670246875  0.9540720284
##  [121]  0.1047482570 -1.0487528849  0.8892201596 -0.5555417844  0.3448860647
##  [126]  0.5572786756  0.1388569768 -0.0972605939  0.5675639425  0.0520882099
##  [131] -1.4570958536  0.8728978717 -0.1777534992 -0.3446559461  0.3827202146
##  [136] -1.6018670460  1.2143653589  0.5878769598 -0.5942114672 -0.9426570122
##  [141]  1.2617963164  0.2671627947  1.3102189823 -0.8622288742  0.7138615823
##  [146]  0.0929176508 -0.8308830773  0.7807843771 -0.0184277345 -0.3734615564
##  [151]  0.6946223901 -1.2637178490  0.3782203232 -0.5337647519 -0.8124478601
##  [156] -1.4793362949 -0.2509673475  0.2025754181 -0.1760727919 -0.8119837758
##  [161] -0.1171815225  1.2742668529 -1.1959400657 -0.8706028843  0.4342770471
##  [166] -0.4259590527  0.3220432745  0.2265057661 -1.1556220442 -0.3207033096
##  [171] -1.0715591685 -0.9972490059  0.8638246889  0.2409908302 -0.5912144229
##  [176] -1.8270152329 -0.3394150049  1.6107131240 -0.6640609761 -0.5654703484
##  [181] -0.2959334024  0.0763755458 -0.1709701952  0.7698079789  1.4484128915
##  [186] -1.8509602953  0.7684454298  1.3895106695 -1.5770350765  0.0423986754
##  [191]  3.3257131388 -0.5218399043  0.6724964993 -0.7688995474  0.0831912929
##  [196]  1.5326904572 -0.2053479603  0.9202723500 -0.8008416843  0.4460956869
##  [201] -0.7508653045 -0.5664612902  0.6997741077 -0.6372901069 -0.2729578554
##  [206]  2.2046235644  0.7251548731  1.0999496865 -0.9479549940  0.7174260940
##  [211] -1.5923131523  0.2893996051 -1.0540199292 -1.2698211033 -0.2171511668
##  [216] -0.4171594630 -1.6639701578  0.9769753188 -0.2697414979  0.5845977850
##  [221]  2.1070313140 -0.5200849160  1.2000225931  0.6419340644  1.3527168783
##  [226] -1.0607330030 -0.7451255335 -0.9358858448 -0.8430447822 -0.4362811025
##  [231]  0.4726484951  1.0888264400  0.1668940468 -1.5910011751  1.0904637450
##  [236] -0.3568814999  1.2203470226  1.0667420612  0.3579293656 -1.1613750369
##  [241]  0.8029577308  0.1980174514 -0.0724087388  0.1787147930  1.0385972801
##  [246]  1.4898656355 -0.1158394211 -1.4176947348 -0.9525835430 -1.7383254254
##  [251] -0.8901771184 -0.3575894254 -0.8056999814 -1.1850134133  1.1891711242
##  [256]  2.4375924911 -0.6507113623 -1.2616107321  2.2731949059  0.2368291907
##  [261] -2.2146475311  0.0924848175  0.1206470459 -0.9476883464 -0.6791356220
##  [266] -0.5926883884 -0.0695348367 -0.4065058807 -0.6513919976 -0.6178214472
##  [271] -0.1036103722 -2.4776689546  1.4309006964  0.3812457507  1.5968830193
##  [276]  0.1285815490 -0.5045461068  0.7497278657 -1.6001842549 -0.3032943136
##  [281]  0.1095354642  0.3825328207 -0.0770386495 -0.4637049540  1.1559806032
##  [286] -0.5110495846  0.5086128851  1.4234781218 -2.2412505479 -0.2482560988
##  [291] -1.5342054049 -1.0011950435  1.0041461084 -0.1272086156  2.6391134503
##  [296]  0.0947183387  0.5569487139  1.2535496515  0.2848162951 -1.3341250668
##  [301]  1.1087749777  1.5010384108 -0.7319724997 -0.2904926420 -1.2377852788
##  [306] -1.7414808862  0.9983224642 -2.1809988592 -0.0362456191 -0.5224137483
##  [311] -1.0237394280 -0.6345043450  0.8310493304  1.0720861871  0.2719903196
##  [316]  0.3039359205 -1.5780620770  1.3731237941 -0.3053540799 -0.8190102303
##  [321]  0.0429283530 -0.2792513603 -2.0053778717 -0.8405423962 -1.5829427314
##  [326] -2.3271742059 -0.4524593683  0.6927352455  1.6539478946 -0.0544116920
##  [331] -1.1020878966  1.5869138898  0.3505165700  0.7582912690  0.3727748484
##  [336]  0.3977541035 -0.6467834838  0.4667840010 -0.3758954434  0.2413869932
##  [341]  0.2912326220 -0.0138854019  0.2150897324 -2.0673994007  1.0240870319
##  [346] -1.2199076114 -0.2990046398 -0.7685511392 -0.9217321927  0.2446118539
##  [351]  0.6047321215 -0.2580335614  1.3660464769  1.4062963534  0.8631395439
##  [356]  0.1306922970  0.1281420088 -0.2608530752 -0.7602391768  1.2422214381
##  [361]  2.9734156637  0.2375710561 -0.4780131870  0.1586532828  0.6015687211
##  [366]  0.9202420399  1.1323662751 -0.0537099453  0.3239796328 -0.8394760792
##  [371] -1.4324513279 -0.0379574201  0.1631425253 -1.1056708899 -0.3905356480
##  [376] -0.7728170834 -1.3482739421  1.0287741069  1.1587542206  1.7453867139
##  [381]  2.3833870143 -1.1129710858  1.1331737592  1.0213762781  1.7829657835
##  [386] -1.8060548800  1.7401290469  0.9924639341 -0.1641633108 -0.8932438835
##  [391] -0.9683970499 -0.3477245286  1.2297996959  0.1983288155 -1.8282991417
##  [396]  0.7003529337  0.6337153712  0.0981615572  0.6717222519 -0.3022182350
##  [401] -0.4146978154 -0.3503991940  0.3240540926  0.1341382216  0.8308673021
##  [406] -0.7343330114 -1.0884542951  0.5901482550  0.0388983290  1.0822931684
##  [411]  1.3970680037 -0.2306042517 -0.5673191192 -0.0447896923 -0.8007726197
##  [416]  0.8953756856  0.9641421446  0.6328460319 -0.4516871532 -1.6322248101
##  [421] -0.2875981967  0.5203126281 -0.1191834781  0.1994915163  1.7612547870
##  [426] -0.4225860971  0.6618908285 -1.1833616474  0.2279252242 -1.0289949320
##  [431] -0.8998626246  0.5764044614  0.7581249094 -0.1649482262  0.6440576729
##  [436]  0.1694136898 -0.9995414228 -0.4596238333  0.9904282472  0.7163112830
##  [441]  0.5862873028 -2.3061671970 -2.0046901199 -0.2399030525  0.3021327052
##  [446] -0.6308843414  0.1299078732 -1.8119018338  0.5052910597 -1.6469413642
##  [451]  0.3009753071 -0.4246957483  1.2758092684 -0.3353432183  1.1226585204
##  [456] -1.1457605103 -0.5947543187  0.7772366639 -0.3987511119  0.1446689654
##  [461]  0.4484053482 -0.1862583210 -0.0889768822 -0.8154624714  0.6231016473
##  [466] -0.5203317454 -0.6773540975  0.6608907229 -0.2550504173  2.6417952587
##  [471] -0.0292493858 -0.3097261094  1.4551544923 -0.3475432801 -0.5751007307
##  [476] -1.4781956372  0.4202029902 -0.3814962579 -1.1021979045 -0.1617309944
##  [481]  0.1738899225  0.6070296301  1.1495102282 -0.6271024534 -1.7156249618
##  [486]  0.3936878830  0.3075111893  1.6866422485 -0.3965578389  0.0154881935
##  [491] -1.0058731215 -0.9830864245  0.5743768356 -0.2662440963 -0.4698083436
##  [496]  0.2248012505 -1.2488277358 -0.2360643824 -1.0558952400  2.6202197987
##  [501] -0.0882117002 -0.1006252792  1.2657040909 -0.0228846249 -0.2490832845
##  [506]  0.0237865936  1.2536055757  0.1316889412 -0.0111142845 -1.0921739620
##  [511]  1.2986970980  0.8946337155  0.9022912230 -1.1413648777  0.2749367435
##  [516]  0.7363523288 -0.5363179200  0.4881003509  1.2325621566 -0.3879936142
##  [521] -0.2611059656  0.2220539836 -0.9231822938 -0.1158880894 -0.5237467995
##  [526] -0.3936985865  1.9303780120 -0.9644533714 -0.3546791020  0.9393755437
##  [531] -0.2514741065  2.5085204100 -0.3314577791 -0.2421350199 -0.1539190482
##  [536] -1.6768497641  1.6900406045 -1.7343872665 -0.7324209779  1.8076666683
##  [541] -1.2553856376 -0.7243621698 -0.0331227932  0.7595822528 -0.1228256333
##  [546] -0.9524608524 -1.3573368712  1.2300125138  0.8249949652 -1.2085197088
##  [551]  0.8210357132  0.7387963588 -0.7520413416 -0.2149605719  0.2995117104
##  [556] -0.3164075461 -1.0478584352  0.3233705020  0.3576183942  1.1344700582
##  [561]  0.1055340536  1.7073854468  0.1271889073 -1.3946111947 -1.3208308953
##  [566]  0.0720923526  0.2166881738  0.7143845119 -0.4349925660  0.8719167768
##  [571] -0.5867197605 -0.0873678052 -0.5352062893  1.5097682040 -0.0143801082
##  [576] -0.0448810825  0.7567069910  0.1447661942  0.6712343944  1.0824656394
##  [581]  1.1618720380  1.0449652027  0.4155646850  0.7581951735 -0.0825598743
##  [586]  0.0603525195  0.2341363190  0.2393889399  0.1389536749  0.9544875143
##  [591] -0.5346871320 -0.4550318369  1.3841653394 -0.6864908143 -1.0517055278
##  [596] -2.3110141794 -0.8878986002 -2.0316366817  1.5977947338  2.0034784241
##  [601]  0.0269782152  2.6276046851 -0.9957792125  0.3932140099  0.0951815310
##  [606] -0.9164226808  1.4422581680 -1.0952443124 -1.2030621235 -1.1483873659
##  [611] -1.3616961862  0.1243731348 -0.5040704254  1.2221627299  1.7357934726
##  [616]  0.5392764469  0.1604054828  0.2302369951  0.1518643662 -1.7274093755
##  [621] -0.7246297573 -0.9439894291  2.8612455736  0.5877490061  1.1164188120
##  [626]  1.6044347229  0.3268642215 -1.5534526232  0.7075679492 -1.2392502524
##  [631] -1.3368995173  0.2540377708 -0.2415122504  0.2904252572 -0.4515019531
##  [636]  0.6016677613 -2.1633831801 -0.6986787712  0.5071717142 -0.8796491670
##  [641]  0.6805785075 -1.0985837492  0.0750607893 -1.5763748700  0.2793270462
##  [646] -0.4205139535  0.3956638866  0.3363078352  0.1324648127 -0.9455440811
##  [651] -1.1692449009  0.3849853451  0.9790908835 -1.1862453504 -1.6827502311
##  [656]  0.2062712998 -0.8018831074  0.0812719608  1.4763789063 -0.1490461453
##  [661]  0.7888540413 -0.1048242303  0.5422398924  0.7758194120 -0.2727346685
##  [666]  0.5747714641  0.9118768332  1.6742885478  0.4206304122  1.2042435609
##  [671]  1.0409536540 -0.8471738288  0.2895584160  0.3902372700  1.4812770147
##  [676]  0.1604852909  0.6257421500 -1.5142195296  0.8949140039  0.8524960451
##  [681]  0.0076548391  0.7850420730 -2.1070459761 -1.0664051020 -0.6505673208
##  [686]  0.9198929541 -0.7766448194  0.0936720239  0.5176597878  0.7166128415
##  [691]  0.3253241843 -0.9446404376  0.3893824144  1.3002330415  0.1892226971
##  [696]  0.0912306585  0.0406910313 -0.1606671633 -0.5595206466 -0.6681588728
##  [701]  0.8016321637  1.1102204261  1.2786559993 -0.2160928150 -1.1224578504
##  [706] -0.7701912191 -0.8922310068  0.2010367905 -0.6061844797  1.6940504878
##  [711]  0.2769775189  1.0603442728  0.2268929907  0.5548140930 -1.1256159150
##  [716] -0.4022082460  0.5165211341 -0.5310122496 -1.0761139740 -3.2588834671
##  [721] -0.5469660983  0.9705887326  1.8649483429  0.1063304895 -0.0415721469
##  [726] -0.1834397913  0.9113161040  0.3832196567 -1.1876225729  0.7491122747
##  [731] -1.1800620530 -0.6698823517  0.3702727903  1.1514697889 -0.9193554644
##  [736]  0.1630671205 -0.0374767613 -0.2074361333 -1.1185052234  0.7827072720
##  [741]  0.4032309397  1.0165823950  0.6509808237 -0.4033942821 -0.0931569323
##  [746] -1.7129634350 -1.1101868346  0.1828684602  0.1311155125  1.4454072700
##  [751] -0.8457786597  1.2526557234 -0.6487439491 -0.3888959609 -2.0605362023
##  [756] -0.6020553959 -1.7341186006  0.4960929455 -0.5902545920 -1.0663827754
##  [761] -0.0390771658 -1.0436621175  1.3305884583  0.6573345407 -0.5509478604
##  [766]  0.6811589326 -2.0025199164  0.6365943181 -1.5077075565  0.3807683977
##  [771]  1.1256763494 -1.3805174024 -0.4908485663  1.1832143271  0.8132426959
##  [776]  1.3701034755 -0.3176859473  1.2256155739  0.3666348055 -2.3256772219
##  [781] -1.2658445769 -1.6624955025  0.2631966856  2.7511952868 -1.4626720785
##  [786]  1.0045025421  0.0738946074 -0.9453199506  0.0927709515 -0.4255060829
##  [791]  0.8528046061 -1.3804388307  0.6460161977  0.4567533275  0.2517950705
##  [796] -0.0371645529  1.1106099661  0.4426911911 -0.7206825875  0.7490080279
##  [801]  1.3672934779 -0.9064190504  1.0800374052  1.0702859661 -1.9334371209
##  [806]  0.4589963395  1.2208668969 -0.5082568499  1.1166380804 -0.1704584668
##  [811]  0.1599568321 -0.5628954580  0.8371384958  0.4260184422 -1.0139026194
##  [816] -0.0347001269 -1.1937776119  1.0189045662  0.4407795470 -0.9574550950
##  [821] -0.1475631249 -0.5353772813 -0.0460149216 -0.3963580091  0.1622826680
##  [826] -0.8314715020  0.4207158296 -0.2828369729 -0.5973911338 -0.4913941969
##  [831]  0.2875582669  0.0109309024 -0.2366679492  0.5220522340 -1.3060404816
##  [836]  1.9044069412 -0.7937373413 -0.8858396093  0.2742841113  1.2176592012
##  [841] -2.6040044842  0.8733445489 -1.4957319539  0.2869907903 -1.1199067327
##  [846] -0.0207056812  0.1922588026  0.6816275862 -0.0064894258 -1.2525625533
##  [851]  0.9273183619 -0.9592804374 -0.6653986418  0.9439845040  0.2231164529
##  [856]  0.9419838982  0.3718687477 -0.0526475362  0.2119965183 -2.8567256629
##  [861] -0.0517677259 -0.2831369559 -1.3829513825  1.1745196805  1.2397777466
##  [866]  0.5996155973  1.8180552596  0.0734619158  0.4536043617  0.0046076174
##  [871] -0.7591548423  2.4315896210  0.6455051693  0.0826064911 -1.7425483383
##  [876] -0.1783334681 -0.4351791885  1.4805208639 -0.6647495431  0.0264039339
##  [881] -0.5303202739 -0.3530383720 -1.8180913412  0.9105305218 -0.6989158374
##  [886]  0.4138807237 -0.3251691316 -1.7248914638  0.1780243093 -0.8557697994
##  [891] -0.7356656004 -0.9104223412 -0.3454935348 -1.2108201687 -0.6973028806
##  [896]  0.1131511353  0.7047984373  0.5853718910 -2.4342463611 -0.0168926517
##  [901] -0.8087389804 -0.9401052176 -1.9933693599 -1.9189411977 -0.2179530034
##  [906]  0.0999148268  0.5113104515  0.4386665501 -1.8332848127 -1.6442016802
##  [911] -1.1043827663  0.5997634605 -1.5727759921 -0.0472654114  1.5553842115
##  [916]  0.5561109157  1.4776341932  0.3163586286 -1.2829360276 -2.2269516074
##  [921]  1.0409745445  1.1343301630  0.4055581216  0.2471073542 -1.2986653847
##  [926]  1.4885475557 -0.6205217469  0.2767704341  0.0409351814 -0.0098741808
##  [931] -1.0284301210  0.1221835970  0.3330752699 -0.2546413142  0.2670042359
##  [936]  1.3381457141 -0.5456764113  0.6192183708  0.1491498074 -1.6411758093
##  [941] -0.1318376923  1.2178456822 -0.4813797941 -1.1303140422 -0.8055579481
##  [946]  1.1571185414  1.1862701586 -0.3871604098 -0.2259925902  0.3309488980
##  [951] -0.1287723996  0.0298699559 -0.2401645223  0.0366348762  0.0018273119
##  [956] -1.7721096059  2.0223351746  0.7676418466 -2.8930102140  1.0588117793
##  [961]  1.3820449295 -1.0496349125 -0.1708415564 -1.3889557307 -0.9678364923
##  [966] -0.5316930066  1.2849655324  1.3048702207  0.8663651949  0.0452553311
##  [971]  0.9523453193 -0.3972608332  0.3972250794  0.1486975848 -0.4206595136
##  [976]  0.1492080518  1.1331927950  0.6902719825  0.0120319459 -0.2719657816
##  [981] -0.3117271509  2.2675173334 -1.0737678153  0.9731092826  0.3217170660
##  [986] -0.1739101567 -1.1041108333 -0.7458694356 -0.9486939177  0.7681204291
##  [991]  0.5089808548 -0.8136008664  1.1521990653  1.1509370281 -0.4664162350
##  [996]  0.0754462317 -1.0531126581  0.2245914393 -0.4199706340 -0.8567978808
## 
## $f
##              [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
##    [1,] 0.7749947 0.5380812 0.5095941 0.5029471 0.3356915 0.5706020 0.4451587
##    [2,] 0.6682795 0.5668132 0.6623887 0.6702723 0.4641372 0.6372562 0.5432340
##    [3,] 0.5724039 0.5904107 0.7737769 0.7992191 0.5835847 0.6913506 0.6237813
##    [4,] 0.5382811 0.5988614 0.8074882 0.8369551 0.6262072 0.7101708 0.6516678
##    [5,] 0.5839099 0.5875885 0.7617225 0.7854700 0.5691916 0.6849854 0.6143199
##    [6,] 0.6333260 0.5754880 0.7059016 0.7208425 0.5074758 0.6573343 0.5731340
##    [7,] 0.6207066 0.5785856 0.7207878 0.7381684 0.5232035 0.6644603 0.5837542
##    [8,] 0.8426722 0.5157891 0.4002722 0.4026738 0.2593459 0.5204937 0.3739802
##    [9,] 0.5725337 0.5903788 0.7736429 0.7990669 0.5834224 0.6912790 0.6236748
##   [10,] 0.4387029 0.6253098 0.8894375 0.9213869 0.7485128 0.7660490 0.7330602
##   [11,] 0.8128464 0.5262401 0.4492565 0.4450761 0.2923495 0.5436835 0.4065522
##   [12,] 0.7544442 0.5440349 0.5411819 0.5354361 0.3597998 0.5843209 0.4651053
##   [13,] 0.5658948 0.5920117 0.7804412 0.8067700 0.5917249 0.6949450 0.6291183
##   [14,] 0.7260573 0.5518591 0.5832136 0.5806389 0.3936600 0.6024662 0.4917123
##   [15,] 0.6971445 0.5594701 0.6239422 0.6261773 0.4287051 0.6201775 0.5178766
##   [16,] 0.6527592 0.5706872 0.6821233 0.6931632 0.4833325 0.6462410 0.5566066
##   [17,] 0.6130580 0.5804584 0.7295985 0.7484046 0.5327505 0.6687544 0.5901532
##   [18,] 0.5872033 0.5867821 0.7582074 0.7814411 0.5650717 0.6831600 0.6116046
##   [19,] 0.6676256 0.5669773 0.6632334 0.6712495 0.4649441 0.6376373 0.5438007
##   [20,] 0.4300001 0.6278439 0.8955109 0.9270527 0.7589430 0.7711144 0.7402877
##   [21,] 0.7849966 0.5350751 0.4939014 0.4873407 0.3240969 0.5637159 0.4352109
##   [22,] 0.4436683 0.6238859 0.8858975 0.9180382 0.7425376 0.7631785 0.7289508
##   [23,] 0.8091063 0.5274717 0.4553244 0.4506259 0.2965641 0.5464551 0.4104905
##   [24,] 0.6963088 0.5596858 0.6250868 0.6274769 0.4297252 0.6206797 0.5186206
##   [25,] 0.6425758 0.5732086 0.6947129 0.7078125 0.4959710 0.6520739 0.5652952
##   [26,] 0.4887295 0.6115573 0.8512126 0.8836294 0.6876245 0.7376339 0.6920012
##   [27,] 0.7740260 0.5383683 0.5111033 0.5044674 0.3368195 0.5712612 0.4461134
##   [28,] 0.8208256 0.5235589 0.4362477 0.4333934 0.2834125 0.5376762 0.3980479
##   [29,] 0.7404639 0.5479392 0.5621251 0.5577011 0.3764006 0.5933628 0.4783349
##   [30,] 0.8568239 0.5103512 0.3767899 0.3839363 0.2440979 0.5086941 0.3576926
##   [31,] 0.6966498 0.5595978 0.6246200 0.6269467 0.4293088 0.6204748 0.5183171
##   [32,] 0.7977299 0.5311278 0.4736503 0.4677649 0.3094793 0.5547245 0.4222934
##   [33,] 0.6179616 0.5792581 0.7239682 0.7418656 0.5266287 0.6660034 0.5860539
##   [34,] 0.6764022 0.5647673 0.6517979 0.6580461 0.4541282 0.6325024 0.5361663
##   [35,] 0.8544855 0.5112751 0.3806749 0.3869624 0.2465977 0.5106846 0.3604257
##   [36,] 0.7530069 0.5444413 0.5433562 0.5377220 0.3614994 0.5852606 0.4664774
##   [37,] 0.5831661 0.5877707 0.7625124 0.7863743 0.5701221 0.6853975 0.6149328
##   [38,] 0.5447037 0.5972581 0.8013726 0.8302024 0.6181974 0.7066300 0.6464336
##   [39,] 0.6132811 0.5804038 0.7293438 0.7481089 0.5324718 0.6686293 0.5899670
##   [40,] 0.7813841 0.5361699 0.4995921 0.4929572 0.3282737 0.5662201 0.4388233
##   [41,] 0.7488860 0.5456000 0.5495633 0.5442812 0.3663815 0.5879418 0.4703959
##   [42,] 0.6538150 0.5704249 0.6808018 0.6916270 0.4820241 0.6456336 0.5557021
##   [43,] 0.6914821 0.5609277 0.6316613 0.6349596 0.4356242 0.6235704 0.5229059
##   [44,] 0.5024574 0.6079699 0.8397010 0.8716502 0.6706935 0.7299839 0.6808199
##   [45,] 0.5337441 0.5999986 0.8117451 0.8416272 0.6318604 0.7126730 0.6553628
##   [46,] 0.7043947 0.5575893 0.6139342 0.6148555 0.4198708 0.6157992 0.5113940
##   [47,] 0.6816576 0.5634357 0.6448500 0.6500543 0.4476674 0.6294060 0.5315662
##   [48,] 0.6932226 0.5604806 0.6292977 0.6322661 0.4334957 0.6225299 0.5213631
##   [49,] 0.7779655 0.5371964 0.5049538 0.4982938 0.3322377 0.5685720 0.4422214
##   [50,] 0.6084275 0.5815912 0.7348552 0.7545012 0.5385344 0.6713459 0.5940145
##   [51,] 0.7129213 0.5553550 0.6019871 0.6014465 0.4095194 0.6105982 0.5037052
##   [52,] 0.7086934 0.5564661 0.6079348 0.6081068 0.4146468 0.6131844 0.5075267
##   [53,] 0.6652180 0.5675808 0.6663337 0.6748384 0.4679166 0.6390384 0.5458851
##   [54,] 0.6556786 0.5699616 0.6784616 0.6889076 0.4797153 0.6445601 0.5541036
##   [55,] 0.5288928 0.6012192 0.8162394 0.8465333 0.6379001 0.7153499 0.6593118
##   [56,] 0.8277519 0.5211678 0.4248923 0.4234411 0.2757167 0.5323510 0.3905470
##   [57,] 0.8475064 0.5139717 0.3922605 0.3961614 0.2541055 0.5165279 0.3684831
##   [58,] 0.5222269 0.6029046 0.8223184 0.8531237 0.6461891 0.7190313 0.6647358
##   [59,] 0.6799249 0.5638754 0.6471490 0.6526959 0.4497962 0.6304287 0.5330853
##   [60,] 0.6548181 0.5701756 0.6795434 0.6901645 0.4807813 0.6450560 0.5548420
##   [61,] 0.5867834 0.5868849 0.7586572 0.7819571 0.5655970 0.6833928 0.6119510
##   [62,] 0.5847311 0.5873874 0.7608488 0.7844693 0.5681643 0.6845304 0.6136432
##   [63,] 0.5133342 0.6051699 0.8302563 0.8616451 0.6572275 0.7239505 0.6719700
##   [64,] 0.6319610 0.5758237 0.7075327 0.7227421 0.5091754 0.6581077 0.5742867
##   [65,] 0.7286777 0.5511532 0.5794161 0.5764727 0.3905099 0.6008254 0.4892972
##   [66,] 0.5283901 0.6013459 0.8167017 0.8470364 0.6385257 0.7156274 0.6597210
##   [67,] 0.5943549 0.5850324 0.7504743 0.7725508 0.5561265 0.6791897 0.6056960
##   [68,] 0.5222740 0.6028927 0.8222759 0.8530778 0.6461307 0.7190053 0.6646975
##   [69,] 0.4379145 0.6255373 0.8899945 0.9219108 0.7494599 0.7665061 0.7337135
##   [70,] 0.7846615 0.5351771 0.4944304 0.4878607 0.3244839 0.5639491 0.4355470
##   [71,] 0.8508475 0.5126919 0.3867164 0.3917269 0.2505026 0.5137485 0.3646442
##   [72,] 0.7420746 0.5474947 0.5597359 0.5551340 0.3744803 0.5923319 0.4768236
##   [73,] 0.7307096 0.5506037 0.5764597 0.5732398 0.3880705 0.5995486 0.4874191
##   [74,] 0.6030828 0.5828982 0.7408503 0.7614419 0.5452136 0.6743303 0.5984602
##   [75,] 0.6715977 0.5659791 0.6580840 0.6652969 0.4600451 0.6353188 0.5403527
##   [76,] 0.4965716 0.6095002 0.8446920 0.8768742 0.6779621 0.7332584 0.6856116
##   [77,] 0.6871614 0.5620338 0.6374936 0.6416217 0.4409150 0.6261447 0.5267247
##   [78,] 0.7972775 0.5312705 0.4743747 0.4684538 0.3099958 0.5550486 0.4227575
##   [79,] 0.7590123 0.5427350 0.5342405 0.5281795 0.3544093 0.5813176 0.4607251
##   [80,] 0.6232370 0.5779654 0.7178377 0.7347373 0.5200473 0.6630357 0.5816311
##   [81,] 0.4752897 0.6151365 0.8620486 0.8946681 0.7041187 0.7451727 0.7029717
##   [82,] 0.6975370 0.5593687 0.6234040 0.6255665 0.4282261 0.6199415 0.5175269
##   [83,] 0.7196039 0.5535851 0.5924917 0.5908797 0.4014375 0.6064801 0.4976273
##   [84,] 0.8823349 0.4994773 0.3344488 0.3529209 0.2173736 0.4857474 0.3266453
##   [85,] 0.6784004 0.5642618 0.6491650 0.6550146 0.4516702 0.6313271 0.5344198
##   [86,] 0.5352397 0.5996233 0.8103476 0.8400960 0.6299974 0.7118480 0.6541450
##   [87,] 0.7843796 0.5352628 0.4948752 0.4882983 0.3248094 0.5641451 0.4358295
##   [88,] 0.7982880 0.5309514 0.4727562 0.4669158 0.3088425 0.5543243 0.4217204
##   [89,] 0.7498020 0.5453433 0.5481870 0.5428226 0.3652951 0.5873475 0.4695268
##   [90,] 0.7275801 0.5514492 0.5810088 0.5782182 0.3918287 0.6015134 0.4903097
##   [91,] 0.4941128 0.6101428 0.8467523 0.8790174 0.6809944 0.7346286 0.6876143
##   [92,] 0.7990966 0.5306954 0.4714597 0.4656869 0.3079203 0.5537434 0.4208890
##   [93,] 0.6817413 0.5634144 0.6447387 0.6499265 0.4475646 0.6293565 0.5314927
##   [94,] 0.6082412 0.5816368 0.7350655 0.7547449 0.5387672 0.6714501 0.5941697
##   [95,] 0.5123745 0.6054156 0.8311012 0.8625463 0.6584173 0.7244820 0.6727507
##   [96,] 0.6908856 0.5610807 0.6324695 0.6358815 0.4363541 0.6239266 0.5234341
##   [97,] 0.5216090 0.6030614 0.8228763 0.8537258 0.6469569 0.7193728 0.6652386
##   [98,] 0.8043561 0.5290142 0.4630012 0.4577371 0.3019396 0.5499367 0.4154504
##   [99,] 0.6243999 0.5776802 0.7164762 0.7331532 0.5185972 0.6623803 0.5806544
##  [100,] 0.5325388 0.6003014 0.8128672 0.8428548 0.6333615 0.7133379 0.6563441
##  [101,] 0.6826592 0.5631811 0.6435173 0.6485243 0.4464375 0.6288139 0.5306870
##  [102,] 0.5492788 0.5961201 0.7969518 0.8252930 0.6124871 0.7041082 0.6427017
##  [103,] 0.8790005 0.5009921 0.3399662 0.3567542 0.2208067 0.4888881 0.3308426
##  [104,] 0.6120627 0.5807020 0.7307334 0.7497215 0.5339935 0.6693119 0.5909840
##  [105,] 0.7118330 0.5556416 0.6035225 0.6031629 0.4108382 0.6112653 0.5046906
##  [106,] 0.7124254 0.5554856 0.6026871 0.6022288 0.4101203 0.6109023 0.5041544
##  [107,] 0.5982077 0.5840902 0.7462512 0.7676817 0.5513085 0.6770466 0.6025054
##  [108,] 0.6251267 0.5775019 0.7156233 0.7321607 0.5176910 0.6619705 0.5800435
##  [109,] 0.6931400 0.5605019 0.6294102 0.6323942 0.4335967 0.6225794 0.5214364
##  [110,] 0.7199643 0.5534892 0.5919764 0.5903088 0.4010025 0.6062570 0.4972982
##  [111,] 0.7091576 0.5563444 0.6072840 0.6073765 0.4140832 0.6129011 0.5071079
##  [112,] 0.8776603 0.5015922 0.3421862 0.3583145 0.2221919 0.4901374 0.3325169
##  [113,] 0.6385975 0.5741901 0.6995538 0.7134497 0.5009164 0.6543405 0.5686726
##  [114,] 0.7654705 0.5408752 0.5243476 0.5179492 0.3468187 0.5770279 0.4544815
##  [115,] 0.5988009 0.5839452 0.7455975 0.7669272 0.5505668 0.6767164 0.6020137
##  [116,] 0.7204490 0.5533601 0.5912828 0.5895406 0.4004175 0.6059566 0.4968553
##  [117,] 0.6886533 0.5616525 0.6354854 0.6393254 0.4390871 0.6252572 0.5254079
##  [118,] 0.6442825 0.5727869 0.6926228 0.7053790 0.4938506 0.6510994 0.5638434
##  [119,] 0.4617530 0.6188200 0.8725372 0.9051121 0.7206379 0.7528283 0.7140582
##  [120,] 0.5781120 0.5890095 0.7678406 0.7924620 0.5764446 0.6881950 0.6190922
##  [121,] 0.6789904 0.5641123 0.6483855 0.6541179 0.4509448 0.6309796 0.5339036
##  [122,] 0.7987446 0.5308069 0.4720242 0.4662216 0.3083217 0.5539964 0.4212511
##  [123,] 0.5858952 0.5871024 0.7596071 0.7830463 0.5667081 0.6838853 0.6126836
##  [124,] 0.7511989 0.5449509 0.5460843 0.5405988 0.3636396 0.5864393 0.4681994
##  [125,] 0.6509746 0.5711301 0.6843502 0.6957526 0.4855451 0.6472666 0.5581339
##  [126,] 0.6257327 0.5773533 0.7149110 0.7313318 0.5169355 0.6616286 0.5795340
##  [127,] 0.6750544 0.5651078 0.6535676 0.6600855 0.4557870 0.6332938 0.5373425
##  [128,] 0.7019438 0.5582270 0.6173329 0.6186917 0.4228539 0.6172837 0.5135909
##  [129,] 0.6245029 0.5776550 0.7163554 0.7330126 0.5184688 0.6623222 0.5805678
##  [130,] 0.6850348 0.5625764 0.6403456 0.6448873 0.4435223 0.6274071 0.5285983
##  [131,] 0.8332219 0.5192339 0.4158885 0.4157160 0.2696814 0.5280677 0.3845405
##  [132,] 0.5878555 0.5866225 0.7575078 0.7806383 0.5642558 0.6827983 0.6110664
##  [133,] 0.7108994 0.5558871 0.6048373 0.6046343 0.4119701 0.6118368 0.5055350
##  [134,] 0.7290751 0.5510459 0.5788388 0.5758406 0.3900326 0.6005760 0.4889303
##  [135,] 0.6465039 0.5722376 0.6898903 0.7021984 0.4910922 0.6498293 0.5619512
##  [136,] 0.8443451 0.5151646 0.3975012 0.4004075 0.2575288 0.5191286 0.3720855
##  [137,] 0.5470692 0.5966693 0.7990936 0.8276744 0.6152454 0.7053261 0.6445044
##  [138,] 0.6220725 0.5782509 0.7191976 0.7363191 0.5214997 0.6636915 0.5826086
##  [139,] 0.7551458 0.5438361 0.5401189 0.5343207 0.3589708 0.5838612 0.4644344
##  [140,] 0.7890461 0.5338351 0.4874929 0.4810758 0.3194303 0.5608849 0.4311347
##  [141,] 0.5414651 0.5980656 0.8044695 0.8336278 0.6222373 0.7084153 0.6490735
##  [142,] 0.6601150 0.5688564 0.6728525 0.6823952 0.4742242 0.6419980 0.5502893
##  [143,] 0.5357662 0.5994913 0.8098543 0.8395549 0.6293414 0.7115577 0.6537163
##  [144,] 0.7814958 0.5361362 0.4994165 0.4927832 0.3281443 0.5661430 0.4387119
##  [145,] 0.6069640 0.5819491 0.7365045 0.7564120 0.5403630 0.6721638 0.5952330
##  [146,] 0.6803518 0.5637672 0.6465833 0.6520456 0.4492715 0.6301769 0.5327112
##  [147,] 0.7785076 0.5370342 0.5041052 0.4974463 0.3316084 0.5682002 0.4416838
##  [148,] 0.5989239 0.5839151 0.7454618 0.7667706 0.5504130 0.6766479 0.6019117
##  [149,] 0.6930635 0.5605215 0.6295142 0.6325126 0.4336902 0.6226251 0.5215042
##  [150,] 0.7321546 0.5502118 0.5743510 0.5709395 0.3863374 0.5986382 0.4860806
##  [151,] 0.6092742 0.5813841 0.7338984 0.7533921 0.5374766 0.6708725 0.5933092
##  [152,] 0.8174641 0.5246976 0.4417383 0.4382880 0.2871684 0.5402231 0.4016480
##  [153,] 0.6470363 0.5721059 0.6892334 0.7014339 0.4904312 0.6495246 0.5614973
##  [154,] 0.7489608 0.5455790 0.5494511 0.5441621 0.3662928 0.5878933 0.4703250
##  [155,] 0.7767383 0.5375627 0.5068728 0.5002144 0.3336634 0.5694121 0.4434365
##  [156,] 0.8349682 0.5186076 0.4130082 0.4132763 0.2677627 0.5266852 0.3826070
##  [157,] 0.7189403 0.5537617 0.5934398 0.5919310 0.4022388 0.6068908 0.4982329
##  [158,] 0.6676604 0.5669686 0.6631885 0.6711975 0.4649011 0.6376170 0.5437706
##  [159,] 0.7107136 0.5559360 0.6050986 0.6049270 0.4121955 0.6119505 0.5057029
##  [160,] 0.7766937 0.5375760 0.5069426 0.5002843 0.3337153 0.5694426 0.4434807
##  [161,] 0.7041710 0.5576476 0.6142450 0.6152059 0.4201428 0.6159349 0.5115947
##  [162,] 0.5399952 0.5984328 0.8058663 0.8351688 0.6240703 0.7092257 0.6502714
##  [163,] 0.8116978 0.5266200 0.4511222 0.4467757 0.2936422 0.5445376 0.4077649
##  [164,] 0.7822898 0.5358964 0.4981678 0.4915468 0.3272253 0.5655942 0.4379197
##  [165,] 0.6403919 0.5737476 0.6973758 0.7109132 0.4986853 0.6533189 0.5671504
##  [166,] 0.7377212 0.5486930 0.5661792 0.5620721 0.3796749 0.5951118 0.4809008
##  [167,] 0.6536673 0.5704616 0.6809868 0.6918421 0.4822071 0.6457186 0.5558287
##  [168,] 0.6648704 0.5676679 0.6667800 0.6753553 0.4683459 0.6392404 0.5461857
##  [169,] 0.8082081 0.5277652 0.4567786 0.4519653 0.2975786 0.5471167 0.4114320
##  [170,] 0.7265011 0.5517398 0.5825717 0.5799336 0.3931262 0.6021887 0.4913038
##  [171,] 0.8007900 0.5301571 0.4687412 0.4631189 0.3059914 0.5525231 0.4191439
##  [172,] 0.7940739 0.5322759 0.4794943 0.4733470 0.3136593 0.5573334 0.4260327
##  [173,] 0.5889455 0.5863557 0.7563362 0.7792931 0.5628924 0.6821937 0.6101668
##  [174,] 0.6631783 0.5680912 0.6689478 0.6778670 0.4704366 0.6402229 0.5476476
##  [175,] 0.7548412 0.5439225 0.5405806 0.5348050 0.3593307 0.5840609 0.4647258
##  [176,] 0.8605064 0.5088741 0.3706700 0.3792296 0.2401775 0.5055242 0.3533528
##  [177,] 0.7285129 0.5511977 0.5796555 0.5767349 0.3907079 0.6009288 0.4894493
##  [178,] 0.5010362 0.6083384 0.8409137 0.8729237 0.6724498 0.7307738 0.6819767
##  [179,] 0.7621845 0.5418248 0.5293927 0.5231497 0.3506764 0.5792172 0.4576660
##  [180,] 0.7522157 0.5446645 0.5445510 0.5389808 0.3624357 0.5857769 0.4672316
##  [181,] 0.7238268 0.5524576 0.5864323 0.5841819 0.3963451 0.6038578 0.4937619
##  [182,] 0.6822521 0.5632846 0.6440594 0.6491465 0.4469374 0.6290546 0.5310445
##  [183,] 0.7101492 0.5560842 0.6058920 0.6058158 0.4128800 0.6122955 0.5062128
##  [184,] 0.6002429 0.5835926 0.7440043 0.7650875 0.5487638 0.6759133 0.6008178
##  [185,] 0.5196452 0.6035602 0.8246431 0.8556294 0.6493962 0.7204584 0.6668361
##  [186,] 0.8621447 0.5082079 0.3679470 0.3771594 0.2384399 0.5040997 0.3514077
##  [187,] 0.6004066 0.5835525 0.7438231 0.7648781 0.5485591 0.6758221 0.6006819
##  [188,] 0.5264886 0.6018259 0.8184448 0.8489304 0.6408911 0.7166772 0.6612684
##  [189,] 0.8424781 0.5158613 0.4005937 0.4029376 0.2595571 0.5206516 0.3741996
##  [190,] 0.6861426 0.5622939 0.6388615 0.6431873 0.4421638 0.6267498 0.5276228
##  [191,] 0.3397942 0.6584511 0.9490680 0.9717879 0.8629210 0.8275531 0.8183072
##  [192,] 0.7477305 0.5459232 0.5512967 0.5461215 0.3677528 0.5886901 0.4714905
##  [193,] 0.6119300 0.5807344 0.7308845 0.7498969 0.5341592 0.6693862 0.5910948
##  [194,] 0.7725244 0.5388120 0.5134390 0.5068266 0.3385697 0.5722806 0.4475904
##  [195,] 0.6814696 0.5634834 0.6450998 0.6503412 0.4478983 0.6295170 0.5317311
##  [196,] 0.5099340 0.6060415 0.8332398 0.8648220 0.6614415 0.7258343 0.6747361
##  [197,] 0.7139421 0.5550857 0.6005441 0.5998353 0.4082831 0.6099716 0.5027798
##  [198,] 0.5821671 0.5880155 0.7635710 0.7875853 0.5713718 0.6859507 0.6157555
##  [199,] 0.7756200 0.5378956 0.5086190 0.5019666 0.3349639 0.5701758 0.4445417
##  [200,] 0.6389878 0.5740939 0.6990809 0.7128989 0.5004311 0.6541184 0.5683416
##  [201,] 0.7707653 0.5393298 0.5161692 0.5095945 0.3406226 0.5734707 0.4493161
##  [202,] 0.7523170 0.5446360 0.5443980 0.5388195 0.3623158 0.5857108 0.4671350
##  [203,] 0.6086557 0.5815354 0.7345975 0.7542025 0.5382493 0.6712184 0.5938245
##  [204,] 0.7595007 0.5425953 0.5334955 0.5274045 0.3538340 0.5809951 0.4602550
##  [205,] 0.7213351 0.5531238 0.5900132 0.5881357 0.3993484 0.6054070 0.4960450
##  [206,] 0.4370152 0.6257973 0.8906283 0.9225058 0.7505398 0.7670279 0.7344592
##  [207,] 0.6056077 0.5822808 0.7380278 0.7581760 0.5420580 0.6729214 0.5963615
##  [208,] 0.5606636 0.5933015 0.7857167 0.8127185 0.5982647 0.6978312 0.6334005
##  [209,] 0.7895375 0.5336837 0.4867132 0.4803179 0.3188652 0.5605396 0.4306381
##  [210,] 0.6065360 0.5820538 0.7369858 0.7569694 0.5408979 0.6724030 0.5955893
##  [211,] 0.8436287 0.5154326 0.3986880 0.4013763 0.2583064 0.5197140 0.3728978
##  [212,] 0.6575063 0.5695067 0.6761573 0.6862312 0.4774523 0.6435058 0.5525339
##  [213,] 0.7992182 0.5306568 0.4712646 0.4655022 0.3077817 0.5536559 0.4207639
##  [214,] 0.8179771 0.5245247 0.4409012 0.4375383 0.2865943 0.5398359 0.4011002
##  [215,] 0.7152391 0.5547430 0.5987067 0.5977865 0.4067131 0.6091742 0.5016024
##  [216,] 0.7367924 0.5489475 0.5675481 0.5635523 0.3807851 0.5957024 0.4817677
##  [217,] 0.8489404 0.5134248 0.3898815 0.3942512 0.2525572 0.5153388 0.3668394
##  [218,] 0.5753663 0.5896832 0.7707068 0.7957281 0.5798793 0.6897134 0.6213489
##  [219,] 0.7209854 0.5532171 0.5905144 0.5886901 0.3997702 0.6056240 0.4963649
##  [220,] 0.6224650 0.5781547 0.7187397 0.7357865 0.5210102 0.6634706 0.5822792
##  [221,] 0.4470209 0.6229330 0.8834763 0.9157290 0.7384938 0.7612478 0.7261817
##  [222,] 0.7475492 0.5459738 0.5515685 0.5464104 0.3679681 0.5888074 0.4716622
##  [223,] 0.5487678 0.5962471 0.7974483 0.8258455 0.6131252 0.7043899 0.6431187
##  [224,] 0.6155961 0.5798372 0.7266925 0.7450306 0.5295814 0.6673313 0.5880328
##  [225,] 0.5307848 0.6007426 0.8144936 0.8446309 0.6355453 0.7143057 0.6577719
##  [226,] 0.7998208 0.5304655 0.4702977 0.4645877 0.3070950 0.5532221 0.4201434
##  [227,] 0.7702037 0.5394946 0.5170395 0.5104791 0.3412786 0.5738498 0.4498660
##  [228,] 0.7884170 0.5340287 0.4884905 0.4820468 0.3201542 0.5613264 0.4317699
##  [229,] 0.7796700 0.5366857 0.5022834 0.4956305 0.3302599 0.5674015 0.4405296
##  [230,] 0.7388087 0.5483946 0.5645740 0.5603391 0.3783760 0.5944193 0.4798846
##  [231,] 0.6358295 0.5748719 0.7028964 0.7173427 0.5043598 0.6559138 0.5710171
##  [232,] 0.5619901 0.5929742 0.7843857 0.8112203 0.5966066 0.6970995 0.6323152
##  [233,] 0.6718074 0.5659264 0.6578110 0.6649816 0.4597867 0.6351962 0.5401704
##  [234,] 0.8435302 0.5154694 0.3988512 0.4015098 0.2584135 0.5197945 0.3730094
##  [235,] 0.5617948 0.5930223 0.7845819 0.8114413 0.5968507 0.6972072 0.6324750
##  [236,] 0.7303842 0.5506919 0.5769338 0.5737576 0.3884609 0.5997533 0.4877202
##  [237,] 0.5463613 0.5968454 0.7997771 0.8284332 0.6161289 0.7057163 0.6450818
##  [238,] 0.5646261 0.5923243 0.7817273 0.8082226 0.5933113 0.6956452 0.6301575
##  [239,] 0.6494348 0.5715118 0.6862645 0.6979793 0.4874549 0.6481502 0.5594501
##  [240,] 0.8087088 0.5276017 0.4559682 0.4512184 0.2970130 0.5467481 0.4109074
##  [241,] 0.5962592 0.5845667 0.7483920 0.7701510 0.5537449 0.6781308 0.6041196
##  [242,] 0.6681910 0.5668354 0.6625030 0.6704046 0.4642463 0.6373078 0.5433106
##  [243,] 0.6991556 0.5589500 0.6211801 0.6230449 0.4262516 0.6189669 0.5160833
##  [244,] 0.6704353 0.5662716 0.6595954 0.6670429 0.4614781 0.6359982 0.5413630
##  [245,] 0.5679893 0.5914961 0.7783089 0.8043583 0.5891059 0.6937888 0.6274021
##  [246,] 0.5148563 0.6047807 0.8289114 0.8602084 0.6553398 0.7231077 0.6707318
##  [247,] 0.7040212 0.5576866 0.6144531 0.6154407 0.4203251 0.6160257 0.5117292
##  [248,] 0.8300948 0.5203446 0.4210394 0.4201172 0.2731270 0.5305251 0.3879835
##  [249,] 0.7899662 0.5335515 0.4860326 0.4796571 0.3183723 0.5602380 0.4302045
##  [250,] 0.8543042 0.5113464 0.3809762 0.3871983 0.2467919 0.5108383 0.3606369
##  [251,] 0.7841386 0.5353361 0.4952552 0.4886724 0.3250878 0.5643125 0.4360709
##  [252,] 0.7304599 0.5506714 0.5768235 0.5736371 0.3883700 0.5997057 0.4876501
##  [253,] 0.7760885 0.5377562 0.5078877 0.5012322 0.3344189 0.5698560 0.4440789
##  [254,] 0.8107564 0.5269302 0.4526498 0.4481718 0.2947027 0.5452357 0.4087566
##  [255,] 0.5500540 0.5959276 0.7961974 0.8244530 0.6115193 0.7036809 0.6420691
##  [256,] 0.4140648 0.6326245 0.9062045 0.9367711 0.7778894 0.7805162 0.7536174
##  [257,] 0.7608484 0.5422090 0.5314373 0.5252672 0.3522477 0.5801034 0.4589562
##  [258,] 0.8172867 0.5247574 0.4420276 0.4385474 0.2873669 0.5403568 0.4018372
##  [259,] 0.4301204 0.6278085 0.8954280 0.9269760 0.7587991 0.7710440 0.7401875
##  [260,] 0.6636647 0.5679696 0.6683254 0.6771458 0.4698355 0.6399407 0.5472276
##  [261,] 0.8851784 0.4981596 0.3297513 0.3497077 0.2144611 0.4830312 0.3230293
##  [262,] 0.6804016 0.5637545 0.6465173 0.6519698 0.4492104 0.6301475 0.5326676
##  [263,] 0.6771577 0.5645763 0.6508036 0.6569009 0.4531986 0.6320583 0.5355063
##  [264,] 0.7895128 0.5336913 0.4867524 0.4803560 0.3188936 0.5605570 0.4306631
##  [265,] 0.7636880 0.5413912 0.5270872 0.5207688 0.3489101 0.5782172 0.4562109
##  [266,] 0.7549910 0.5438800 0.5403535 0.5345667 0.3591536 0.5839627 0.4645825
##  [267,] 0.6988325 0.5590337 0.6216246 0.6235486 0.4266457 0.6191616 0.5163717
##  [268,] 0.7356655 0.5492556 0.5692059 0.5653477 0.3821328 0.5964177 0.4828180
##  [269,] 0.7609166 0.5421894 0.5313330 0.5251590 0.3521674 0.5800582 0.4588904
##  [270,] 0.7575381 0.5431559 0.5364857 0.5305197 0.3561470 0.5822896 0.4621419
##  [271,] 0.7026545 0.5580423 0.6163490 0.6175802 0.4219885 0.6168537 0.5129545
##  [272,] 0.8997633 0.4909793 0.3058117 0.3340662 0.1997501 0.4684944 0.3039066
##  [273,] 0.5216752 0.6030446 0.8228166 0.8536614 0.6468746 0.7193362 0.6651847
##  [274,] 0.6466784 0.5721944 0.6896752 0.7019479 0.4908756 0.6497295 0.5618025
##  [275,] 0.5026065 0.6079313 0.8395734 0.8715160 0.6705091 0.7299010 0.6806985
##  [276,] 0.6762418 0.5648078 0.6520087 0.6582889 0.4543255 0.6325967 0.5363063
##  [277,] 0.7459406 0.5464224 0.5539757 0.5489731 0.3698792 0.5898465 0.4731828
##  [278,] 0.6026557 0.5830026 0.7413261 0.7619921 0.5457476 0.6745686 0.5988150
##  [279,] 0.8442191 0.5152118 0.3977100 0.4005778 0.2576656 0.5192317 0.3722285
##  [280,] 0.7246228 0.5522443 0.5852851 0.5829178 0.3953864 0.6033617 0.4930310
##  [281,] 0.6784389 0.5642520 0.6491141 0.6549561 0.4516228 0.6313044 0.5343861
##  [282,] 0.6465261 0.5722321 0.6898630 0.7021665 0.4910646 0.6498166 0.5619323
##  [283,] 0.6996759 0.5588153 0.6204638 0.6222336 0.4256173 0.6186533 0.5156188
##  [284,] 0.7416863 0.5476020 0.5603124 0.5557528 0.3749430 0.5925807 0.4771882
##  [285,] 0.5539940 0.5949506 0.7923393 0.8201470 0.6065987 0.7015089 0.6388523
##  [286,] 0.7466145 0.5462346 0.5529679 0.5478994 0.3690783 0.5894115 0.4725461
##  [287,] 0.6315441 0.5759262 0.7080300 0.7233211 0.5096946 0.6583439 0.5746386
##  [288,] 0.5225368 0.6028260 0.8220383 0.8528212 0.6458040 0.7188601 0.6644837
##  [289,] 0.8867304 0.4974300 0.3271907 0.3479758 0.2128773 0.4815334 0.3210410
##  [290,] 0.7186444 0.5538403 0.5938622 0.5923996 0.4025962 0.6070738 0.4985029
##  [291,] 0.8392181 0.5170642 0.4059878 0.4073942 0.2631098 0.5232886 0.3778678
##  [292,] 0.7944343 0.5321633 0.4789193 0.4727953 0.3132466 0.5570772 0.4256653
##  [293,] 0.5721115 0.5904825 0.7740786 0.7995618 0.5839504 0.6915122 0.6240213
##  [294,] 0.7052894 0.5573561 0.6126895 0.6134529 0.4187825 0.6152561 0.5105906
##  [295,] 0.3953350 0.6385156 0.9180815 0.9471480 0.7998801 0.7918148 0.7694779
##  [296,] 0.6801447 0.5638197 0.6468578 0.6523611 0.4495260 0.6302991 0.5328927
##  [297,] 0.6257722 0.5773436 0.7148646 0.7312778 0.5168863 0.6616063 0.5795008
##  [298,] 0.5424380 0.5978229 0.8035420 0.8326031 0.6210239 0.7078790 0.6482806
##  [299,] 0.6580444 0.5693726 0.6754771 0.6854415 0.4767862 0.6431950 0.5520712
##  [300,] 0.8233206 0.5227047 0.4321636 0.4297873 0.2806336 0.5357702 0.3953590
##  [301,] 0.5596117 0.5935612 0.7867689 0.8139018 0.5995795 0.6984114 0.6342609
##  [302,] 0.5135696 0.6051096 0.8300486 0.8614235 0.6569356 0.7238201 0.6717785
##  [303,] 0.7689137 0.5398724 0.5190360 0.5125124 0.3427866 0.5747190 0.4511274
##  [304,] 0.7232377 0.5526154 0.5872803 0.5851171 0.3970547 0.6042246 0.4943023
##  [305,] 0.8152727 0.5254327 0.4453098 0.4415003 0.2896241 0.5418707 0.4039812
##  [306,] 0.8545285 0.5112583 0.3806036 0.3869066 0.2465517 0.5106482 0.3603756
##  [307,] 0.5728089 0.5903112 0.7733585 0.7987439 0.5830782 0.6911269 0.6234489
##  [308,] 0.8831899 0.4990836 0.3330355 0.3519492 0.2164964 0.4849344 0.3255616
##  [309,] 0.6950797 0.5600027 0.6267669 0.6293863 0.4312262 0.6214174 0.5197139
##  [310,] 0.7477898 0.5459066 0.5512079 0.5460271 0.3676824 0.5886518 0.4714344
##  [311,] 0.7964851 0.5315201 0.4756427 0.4696617 0.3109009 0.5556153 0.4235694
##  [312,] 0.7592205 0.5426755 0.5339231 0.5278492 0.3541642 0.5811802 0.4605248
##  [313,] 0.5928834 0.5853923 0.7520766 0.7743957 0.5579668 0.6800074 0.6069131
##  [314,] 0.5639879 0.5924815 0.7823725 0.8089508 0.5941091 0.6959973 0.6306800
##  [315,] 0.6595491 0.5689975 0.6735709 0.6832289 0.4749242 0.6423253 0.5507766
##  [316,] 0.6557981 0.5699319 0.6783112 0.6887329 0.4795674 0.6444913 0.5540011
##  [317,] 0.8425556 0.5158325 0.4004652 0.4028322 0.2594727 0.5205885 0.3741120
##  [318,] 0.5284000 0.6013434 0.8166926 0.8470265 0.6385133 0.7156219 0.6597129
##  [319,] 0.7248454 0.5521846 0.5849640 0.5825644 0.3951185 0.6032228 0.4928266
##  [320,] 0.7773691 0.5373746 0.5058868 0.4992269 0.3329304 0.5689805 0.4428122
##  [321,] 0.6860821 0.5623094 0.6389427 0.6432803 0.4422380 0.6267858 0.5276761
##  [322,] 0.7220187 0.5529413 0.5890323 0.5870514 0.3985241 0.6049825 0.4954193
##  [323,] 0.8723442 0.5039251 0.3510027 0.3646117 0.2277156 0.4950222 0.3390892
##  [324,] 0.7794311 0.5367574 0.5026580 0.4960035 0.3305369 0.5675658 0.4407669
##  [325,] 0.8429238 0.5156955 0.3998556 0.4023321 0.2590724 0.5202889 0.3736958
##  [326,] 0.8916237 0.4950785 0.3191358 0.3426190 0.2079120 0.4767375 0.3147020
##  [327,] 0.7405083 0.5479269 0.5620593 0.5576303 0.3763476 0.5933344 0.4782932
##  [328,] 0.6095008 0.5813287 0.7336420 0.7530949 0.5371935 0.6707458 0.5931204
##  [329,] 0.4961471 0.6096110 0.8450487 0.8772459 0.6784858 0.7334948 0.6859573
##  [330,] 0.6971299 0.5594738 0.6239622 0.6261999 0.4287229 0.6201863 0.5178896
##  [331,] 0.8035061 0.5292878 0.4643711 0.4590166 0.3029040 0.5505553 0.4163330
##  [332,] 0.5037404 0.6076378 0.8386019 0.8704938 0.6691073 0.7292711 0.6797757
##  [333,] 0.6503101 0.5712949 0.6851771 0.6967144 0.4863692 0.6476481 0.5587021
##  [334,] 0.6016267 0.5832542 0.7424701 0.7633147 0.5470338 0.6751422 0.5996693
##  [335,] 0.6476804 0.5719464 0.6884378 0.7005079 0.4896319 0.6491558 0.5609479
##  [336,] 0.6447239 0.5726778 0.6920809 0.7047482 0.4933024 0.6508472 0.5634677
##  [337,] 0.7604544 0.5423220 0.5320394 0.5258918 0.3527113 0.5803643 0.4593362
##  [338,] 0.6365275 0.5747001 0.7020556 0.7163633 0.5034914 0.6555174 0.5704263
##  [339,] 0.7324140 0.5501414 0.5739719 0.5705265 0.3860264 0.5984746 0.4858400
##  [340,] 0.6631320 0.5681028 0.6690070 0.6779357 0.4704938 0.6402498 0.5476876
##  [341,] 0.6572910 0.5695603 0.6764292 0.6865470 0.4777188 0.6436301 0.5527189
##  [342,] 0.6925487 0.5606538 0.6302139 0.6333097 0.4343197 0.6229331 0.5219608
##  [343,] 0.6662023 0.5673342 0.6650682 0.6733730 0.4667011 0.6384660 0.5450335
##  [344,] 0.8762649 0.5022117 0.3444988 0.3599507 0.2236372 0.4914304 0.3342526
##  [345,] 0.5697248 0.5910692 0.7765333 0.8023470 0.5869355 0.6928305 0.6259792
##  [346,] 0.8137512 0.5259398 0.4477857 0.4437403 0.2913324 0.5430088 0.4055949
##  [347,] 0.7241591 0.5523686 0.5859537 0.5836543 0.3959449 0.6036508 0.4934569
##  [348,] 0.7724905 0.5388220 0.5134917 0.5068800 0.3386092 0.5723035 0.4476237
##  [349,] 0.7870980 0.5344334 0.4905796 0.4840853 0.3216732 0.5622500 0.4330992
##  [350,] 0.6627550 0.5681971 0.6694890 0.6784943 0.4709598 0.6404686 0.5480131
##  [351,] 0.6200544 0.5787454 0.7215453 0.7390493 0.5240173 0.6648271 0.5843009
##  [352,] 0.7197109 0.5535567 0.5923388 0.5907103 0.4013084 0.6064139 0.4975296
##  [353,] 0.5292266 0.6011350 0.8159321 0.8461988 0.6374848 0.7151657 0.6590402
##  [354,] 0.5245340 0.6023201 0.8202271 0.8508625 0.6433217 0.7177567 0.6628588
##  [355,] 0.5890278 0.5863356 0.7562476 0.7791914 0.5627895 0.6821480 0.6100989
##  [356,] 0.6759980 0.5648694 0.6523291 0.6586581 0.4546255 0.6327399 0.5365191
##  [357,] 0.6762926 0.5647950 0.6519420 0.6582120 0.4542630 0.6325668 0.5362620
##  [358,] 0.7200180 0.5534749 0.5918995 0.5902235 0.4009376 0.6062237 0.4972490
##  [359,] 0.7716807 0.5390606 0.5147493 0.5081537 0.3395540 0.5728519 0.4484187
##  [360,] 0.5437754 0.5974893 0.8022630 0.8311884 0.6193555 0.7071417 0.6471904
##  [361,] 0.3666757 0.6482516 0.9348469 0.9609575 0.8328571 0.8097620 0.7942733
##  [362,] 0.6635780 0.5679913 0.6684364 0.6772744 0.4699426 0.6399910 0.5473025
##  [363,] 0.7431811 0.5471886 0.5580909 0.5533706 0.3731623 0.5916222 0.4757835
##  [364,] 0.6727628 0.5656857 0.6565653 0.6635435 0.4586093 0.6346370 0.5393391
##  [365,] 0.6204332 0.5786526 0.7211054 0.7385378 0.5235446 0.6646140 0.5839834
##  [366,] 0.5821707 0.5880146 0.7635671 0.7875809 0.5713673 0.6859487 0.6157525
##  [367,] 0.5568023 0.5942556 0.7895649 0.8170405 0.6030903 0.6999606 0.6365578
##  [368,] 0.6970508 0.5594942 0.6240706 0.6263230 0.4288194 0.6202338 0.5179600
##  [369,] 0.6534392 0.5705183 0.6812725 0.6921741 0.4824897 0.6458499 0.5560241
##  [370,] 0.7793293 0.5367880 0.5028176 0.4961625 0.3306550 0.5676358 0.4408681
##  [371,] 0.8312710 0.5199285 0.4191031 0.4184571 0.2718296 0.5296036 0.3866914
##  [372,] 0.6952731 0.5599528 0.6265028 0.6290859 0.4309900 0.6213013 0.5195419
##  [373,] 0.6722424 0.5658168 0.6572441 0.6643270 0.4592505 0.6349416 0.5397920
##  [374,] 0.8038233 0.5291858 0.4638601 0.4585390 0.3025441 0.5503246 0.4160039
##  [375,] 0.7339716 0.5497177 0.5716920 0.5680460 0.3841602 0.5974906 0.4843939
##  [376,] 0.7729055 0.5386996 0.5128467 0.5062277 0.3381253 0.5720222 0.4472159
##  [377,] 0.8244810 0.5223047 0.4302615 0.4281180 0.2793437 0.5348791 0.3941034
##  [378,] 0.5691641 0.5912071 0.7771078 0.8029981 0.5876367 0.6931401 0.6264390
##  [379,] 0.5536644 0.5950323 0.7926636 0.8205095 0.6070104 0.7016906 0.6391214
##  [380,] 0.4859114 0.6123019 0.8535200 0.8860001 0.6910901 0.7392102 0.6942991
##  [381,] 0.4192833 0.6310375 0.9027628 0.9336805 0.7717074 0.7774178 0.7492373
##  [382,] 0.8044683 0.5289781 0.4628202 0.4575684 0.3018123 0.5498550 0.4153338
##  [383,] 0.5567062 0.5942793 0.7896602 0.8171473 0.6032104 0.7000136 0.6366363
##  [384,] 0.5700492 0.5909894 0.7762006 0.8019698 0.5865298 0.6926514 0.6257132
##  [385,] 0.4817481 0.6134076 0.8568945 0.8894477 0.6962034 0.7415430 0.6976961
##  [386,] 0.8590597 0.5094577 0.3730744 0.3810700 0.2417152 0.5067747 0.3550629
##  [387,] 0.4864959 0.6121472 0.8530430 0.8855108 0.6903716 0.7388830 0.6938224
##  [388,] 0.5735105 0.5901388 0.7726327 0.7979190 0.5822006 0.6907391 0.6228729
##  [389,] 0.7093956 0.5562820 0.6069502 0.6070020 0.4137944 0.6127558 0.5068932
##  [390,] 0.7844274 0.5352483 0.4947997 0.4882241 0.3247542 0.5641118 0.4357816
##  [391,] 0.7914265 0.5330997 0.4837116 0.4774093 0.3166948 0.5592085 0.4287249
##  [392,] 0.7294040 0.5509570 0.5783606 0.5753174 0.3896376 0.6003695 0.4886265
##  [393,] 0.5452434 0.5971237 0.8008539 0.8296276 0.6175240 0.7063326 0.6459935
##  [394,] 0.6681548 0.5668445 0.6625499 0.6704587 0.4642911 0.6373289 0.5433421
##  [395,] 0.8605946 0.5088383 0.3705233 0.3791178 0.2400838 0.5054477 0.3532482
##  [396,] 0.6085862 0.5815524 0.7346760 0.7542935 0.5383361 0.6712572 0.5938824
##  [397,] 0.6165815 0.5795960 0.7255595 0.7437146 0.5283513 0.6667784 0.5872088
##  [398,] 0.6797486 0.5639201 0.6473824 0.6529643 0.4500128 0.6305327 0.5332397
##  [399,] 0.6120229 0.5807117 0.7307787 0.7497741 0.5340432 0.6693342 0.5910172
##  [400,] 0.7245065 0.5522755 0.5854528 0.5831025 0.3955264 0.6034342 0.4931379
##  [401,] 0.7365322 0.5490187 0.5679311 0.5639668 0.3810962 0.5958677 0.4820104
##  [402,] 0.7296905 0.5508796 0.5779438 0.5748616 0.3892936 0.6001895 0.4883617
##  [403,] 0.6534305 0.5705205 0.6812834 0.6921869 0.4825006 0.6458549 0.5560316
##  [404,] 0.6755999 0.5649700 0.6528520 0.6592606 0.4551155 0.6329737 0.5368666
##  [405,] 0.5929053 0.5853869 0.7520528 0.7743683 0.5579394 0.6799952 0.6068950
##  [406,] 0.7691455 0.5398046 0.5186775 0.5121468 0.3425155 0.5745629 0.4509009
##  [407,] 0.8022963 0.5296759 0.4663192 0.4608414 0.3042783 0.5514334 0.4175869
##  [408,] 0.6218006 0.5783175 0.7195145 0.7366877 0.5218388 0.6638446 0.5828367
##  [409,] 0.6865424 0.5621919 0.6383250 0.6425732 0.4416736 0.6265124 0.5272704
##  [410,] 0.5627696 0.5927819 0.7836014 0.8103366 0.5956322 0.6966695 0.6316773
##  [411,] 0.5256081 0.6020484 0.8192488 0.8498026 0.6419861 0.7171634 0.6619848
##  [412,] 0.7167142 0.5543526 0.5966118 0.5954544 0.4049288 0.6082655 0.5002612
##  [413,] 0.7524047 0.5446112 0.5442656 0.5386800 0.3622119 0.5856536 0.4670514
##  [414,] 0.6960447 0.5597539 0.6254483 0.6278875 0.4300477 0.6208383 0.5188557
##  [415,] 0.7756133 0.5378975 0.5086294 0.5019770 0.3349717 0.5701803 0.4445483
##  [416,] 0.5851560 0.5872834 0.7603960 0.7839505 0.5676328 0.6842950 0.6132930
##  [417,] 0.5769045 0.5893057 0.7691035 0.7939019 0.5779551 0.6888629 0.6200849
##  [418,] 0.6166857 0.5795705 0.7254395 0.7435752 0.5282213 0.6667199 0.5871216
##  [419,] 0.7404273 0.5479492 0.5621793 0.5577594 0.3764442 0.5933861 0.4783691
##  [420,] 0.8466046 0.5143137 0.3937560 0.3973677 0.2550806 0.5172726 0.3695137
##  [421,] 0.7229241 0.5526993 0.5877315 0.5856148 0.3974327 0.6044197 0.4945898
##  [422,] 0.6301482 0.5762692 0.7096912 0.7252554 0.5114331 0.6591339 0.5758161
##  [423,] 0.7043944 0.5575894 0.6139345 0.6148558 0.4198710 0.6157993 0.5113942
##  [424,] 0.6680195 0.5668785 0.6627248 0.6706611 0.4644581 0.6374078 0.5434594
##  [425,] 0.4841502 0.6127688 0.8549525 0.8874664 0.6932541 0.7401964 0.6957358
##  [426,] 0.7373654 0.5487906 0.5667039 0.5626392 0.3801001 0.5953382 0.4812330
##  [427,] 0.6132025 0.5804231 0.7294336 0.7482131 0.5325700 0.6686734 0.5900326
##  [428,] 0.8106138 0.5269771 0.4528811 0.4483835 0.2948634 0.5453413 0.4089067
##  [429,] 0.6647047 0.5677093 0.6669926 0.6756016 0.4685506 0.6393367 0.5463289
##  [430,] 0.7969612 0.5313702 0.4748809 0.4689357 0.3103570 0.5552749 0.4230817
##  [431,] 0.7850498 0.5350589 0.4938175 0.4872583 0.3240356 0.5636789 0.4351576
##  [432,] 0.6234454 0.5779143 0.7175941 0.7344538 0.5197874 0.6629183 0.5814561
##  [433,] 0.6016467 0.5832493 0.7424479 0.7632891 0.5470088 0.6751311 0.5996527
##  [434,] 0.7094825 0.5562592 0.6068282 0.6068652 0.4136889 0.6127027 0.5068148
##  [435,] 0.6153415 0.5798996 0.7269848 0.7453701 0.5298993 0.6674742 0.5882457
##  [436,] 0.6715151 0.5659999 0.6581915 0.6654211 0.4601469 0.6353671 0.5404246
##  [437,] 0.7942833 0.5322105 0.4791602 0.4730264 0.3134195 0.5571846 0.4258192
##  [438,] 0.7412592 0.5477199 0.5609463 0.5564336 0.3754522 0.5928542 0.4775891
##  [439,] 0.5737544 0.5900789 0.7723802 0.7976318 0.5818955 0.6906044 0.6226727
##  [440,] 0.6066698 0.5820211 0.7368353 0.7567951 0.5407306 0.6723282 0.5954778
##  [441,] 0.6222628 0.5782042 0.7189757 0.7360610 0.5212624 0.6635844 0.5824489
##  [442,] 0.8904441 0.4956527 0.3210749 0.3438958 0.2091050 0.4779041 0.3162400
##  [443,] 0.8723002 0.5039442 0.3510758 0.3646646 0.2277615 0.4950622 0.3391432
##  [444,] 0.7177318 0.5540827 0.5951634 0.5938444 0.4036988 0.6076377 0.4993347
##  [445,] 0.6560101 0.5698791 0.6780443 0.6884229 0.4793048 0.6443690 0.5538191
##  [446,] 0.7588560 0.5427797 0.5344788 0.5284276 0.3545935 0.5814208 0.4608755
##  [447,] 0.6760886 0.5648465 0.6522101 0.6585209 0.4545140 0.6326866 0.5364400
##  [448,] 0.8594644 0.5092948 0.3724017 0.3805539 0.2412847 0.5064255 0.3545852
##  [449,] 0.6319403 0.5758288 0.7075575 0.7227709 0.5092012 0.6581195 0.5743042
##  [450,] 0.8476909 0.5139015 0.3919545 0.3959151 0.2539062 0.5163752 0.3682720
##  [451,] 0.6561462 0.5698453 0.6778729 0.6882238 0.4791363 0.6442906 0.5537023
##  [452,] 0.7375880 0.5487296 0.5663757 0.5622844 0.3798341 0.5951966 0.4810252
##  [453,] 0.5398135 0.5984782 0.8060386 0.8353587 0.6242968 0.7093259 0.6504194
##  [454,] 0.7280757 0.5513156 0.5802900 0.5774301 0.3912331 0.6012029 0.4898527
##  [455,] 0.5579579 0.5939698 0.7884173 0.8157532 0.6016463 0.6993234 0.6356132
##  [456,] 0.8073478 0.5280455 0.4581703 0.4532505 0.2985511 0.5477490 0.4123321
##  [457,] 0.7552010 0.5438204 0.5400353 0.5342330 0.3589056 0.5838251 0.4643817
##  [458,] 0.5993502 0.5838108 0.7449913 0.7662273 0.5498799 0.6764105 0.6015582
##  [459,] 0.7348437 0.5494800 0.5704130 0.5666570 0.3831162 0.5969386 0.4835830
##  [460,] 0.6743822 0.5652774 0.6544485 0.6611012 0.4566147 0.6336882 0.5379286
##  [461,] 0.6387133 0.5741615 0.6994136 0.7132864 0.5007725 0.6542746 0.5685744
##  [462,] 0.7118387 0.5556401 0.6035145 0.6031539 0.4108313 0.6112618 0.5046854
##  [463,] 0.7010156 0.5584680 0.6186159 0.6201422 0.4239845 0.6178446 0.5144214
##  [464,] 0.7770282 0.5374763 0.5064197 0.4997604 0.3333265 0.5692138 0.4431496
##  [465,] 0.6178536 0.5792845 0.7240929 0.7420105 0.5267635 0.6660640 0.5861442
##  [466,] 0.7475747 0.5459667 0.5515302 0.5463698 0.3679378 0.5887909 0.4716380
##  [467,] 0.7635107 0.5414424 0.5273594 0.5210496 0.3491184 0.5783353 0.4563827
##  [468,] 0.6133225 0.5803937 0.7292965 0.7480541 0.5324202 0.6686062 0.5899324
##  [469,] 0.7193857 0.5536432 0.5928036 0.5912255 0.4017010 0.6066152 0.4978265
##  [470,] 0.3950930 0.6385939 0.9182301 0.9472749 0.8001621 0.7919628 0.7696844
##  [471,] 0.6942887 0.5602064 0.6278461 0.6306137 0.4321927 0.6218916 0.5204167
##  [472,] 0.7253175 0.5520579 0.5842826 0.5818144 0.3945502 0.6029282 0.4923927
##  [473,] 0.5188648 0.6037587 0.8253425 0.8563817 0.6503653 0.7208899 0.6674710
##  [474,] 0.7293845 0.5509623 0.5783888 0.5753483 0.3896609 0.6003817 0.4886444
##  [475,] 0.7531997 0.5443869 0.5430648 0.5374153 0.3612714 0.5851347 0.4662936
##  [476,] 0.8348789 0.5186397 0.4131555 0.4134006 0.2678606 0.5267560 0.3827059
##  [477,] 0.6420625 0.5733353 0.6953400 0.7085426 0.4966088 0.6523667 0.5657315
##  [478,] 0.7330104 0.5499793 0.5730996 0.5695768 0.3853116 0.5980981 0.4852866
##  [479,] 0.8035159 0.5292847 0.4643554 0.4590019 0.3028930 0.5505482 0.4163229
##  [480,] 0.7091261 0.5563526 0.6073282 0.6074261 0.4141215 0.6129203 0.5071364
##  [481,] 0.6709956 0.5661307 0.6588674 0.6662018 0.4607873 0.6356708 0.5408762
##  [482,] 0.6197792 0.5788128 0.7218646 0.7394204 0.5243606 0.6649819 0.5845315
##  [483,] 0.5547631 0.5947602 0.7915816 0.8192993 0.6056380 0.7010850 0.6382240
##  [484,] 0.7584749 0.5428886 0.5350596 0.5290325 0.3550427 0.5816723 0.4612420
##  [485,] 0.8526826 0.5119804 0.3836695 0.3893152 0.2485305 0.5122080 0.3625214
##  [486,] 0.6452056 0.5725588 0.6914890 0.7040592 0.4927043 0.6505719 0.5630575
##  [487,] 0.6553776 0.5700365 0.6788402 0.6893474 0.4800881 0.6447336 0.5543620
##  [488,] 0.4924706 0.6105732 0.8481203 0.8804359 0.6830183 0.7355446 0.6889522
##  [489,] 0.7346110 0.5495434 0.5707544 0.5670276 0.3833947 0.5970859 0.4837995
##  [490,] 0.6892116 0.5615096 0.6347324 0.6384649 0.4384033 0.6249247 0.5249146
##  [491,] 0.7948609 0.5320298 0.4782382 0.4721425 0.3127582 0.5567737 0.4252299
##  [492,] 0.7927772 0.5326802 0.4815616 0.4753348 0.3151452 0.5582533 0.4273530
##  [493,] 0.6236880 0.5778548 0.7173102 0.7341235 0.5194849 0.6627816 0.5812524
##  [494,] 0.7206050 0.5533185 0.5910594 0.5892933 0.4002293 0.6058599 0.4967127
##  [495,] 0.7423245 0.5474256 0.5593646 0.5547357 0.3741825 0.5921718 0.4765888
##  [496,] 0.6650694 0.5676180 0.6665246 0.6750594 0.4681002 0.6391248 0.5460136
##  [497,] 0.8162081 0.5251196 0.4437861 0.4401272 0.2885752 0.5411686 0.4029866
##  [498,] 0.7173119 0.5541941 0.5957614 0.5945088 0.4042063 0.6078968 0.4997171
##  [499,] 0.7993867 0.5306033 0.4709944 0.4652465 0.3075897 0.5535347 0.4205905
##  [500,] 0.3970453 0.6379639 0.9170275 0.9462460 0.7978854 0.7907705 0.7680197
##  [501,] 0.7009298 0.5584902 0.6187344 0.6202762 0.4240890 0.6178965 0.5144982
##  [502,] 0.7023205 0.5581291 0.6168116 0.6181027 0.4223952 0.6170558 0.5132537
##  [503,] 0.5410043 0.5981807 0.8049079 0.8341117 0.6228119 0.7086694 0.6494490
##  [504,] 0.6935683 0.5603917 0.6288273 0.6317305 0.4330731 0.6223230 0.5210563
##  [505,] 0.7187347 0.5538163 0.5937333 0.5922566 0.4024872 0.6070180 0.4984205
##  [506,] 0.6882664 0.5617514 0.6360068 0.6399213 0.4395610 0.6254875 0.5257496
##  [507,] 0.5424314 0.5978245 0.8035483 0.8326101 0.6210321 0.7078826 0.6482860
##  [508,] 0.6758829 0.5648985 0.6524804 0.6588323 0.4547672 0.6328075 0.5366196
##  [509,] 0.6922345 0.5607346 0.6306406 0.6337960 0.4347040 0.6231209 0.5222393
##  [510,] 0.8026269 0.5295700 0.4657871 0.4603424 0.3039026 0.5511938 0.4172446
##  [511,] 0.5371200 0.5991521 0.8085825 0.8381584 0.6276543 0.7108111 0.6526136
##  [512,] 0.5852451 0.5872615 0.7603010 0.7838416 0.5675214 0.6842456 0.6132195
##  [513,] 0.5843256 0.5874867 0.7612804 0.7849637 0.5686716 0.6847551 0.6139774
##  [514,] 0.8069635 0.5281705 0.4587917 0.4538254 0.2989859 0.5480309 0.4127337
##  [515,] 0.6592036 0.5690837 0.6740092 0.6837375 0.4753517 0.6425251 0.5510740
##  [516,] 0.6042626 0.5826097 0.7395336 0.7599188 0.5437390 0.6736722 0.5974799
##  [517,] 0.7492238 0.5455054 0.5490561 0.5437434 0.3659808 0.5877228 0.4700756
##  [518,] 0.6339893 0.5753248 0.7051069 0.7199171 0.5066500 0.6569581 0.5725734
##  [519,] 0.5449168 0.5972050 0.8011679 0.8299756 0.6179315 0.7065126 0.6462598
##  [520,] 0.7337015 0.5497913 0.5720878 0.5684762 0.3844837 0.5976614 0.4846449
##  [521,] 0.7200456 0.5534676 0.5918601 0.5901799 0.4009043 0.6062066 0.4972239
##  [522,] 0.6653900 0.5675378 0.6661128 0.6745825 0.4677042 0.6389384 0.5457364
##  [523,] 0.7872334 0.5343919 0.4903654 0.4838760 0.3215172 0.5621553 0.4329629
##  [524,] 0.7040266 0.5576852 0.6144456 0.6154321 0.4203185 0.6160224 0.5117243
##  [525,] 0.7479275 0.5458681 0.5510015 0.5458078 0.3675190 0.5885627 0.4713041
##  [526,] 0.7343075 0.5496262 0.5711995 0.5675110 0.3837580 0.5972780 0.4840817
##  [527,] 0.4656793 0.6177428 0.8695385 0.9021516 0.7158570 0.7506006 0.7108380
##  [528,] 0.7910630 0.5332123 0.4842898 0.4779685 0.3171122 0.5594652 0.4290936
##  [529,] 0.7301486 0.5507556 0.5772770 0.5741326 0.3887437 0.5999015 0.4879381
##  [530,] 0.5798748 0.5885773 0.7659899 0.7903498 0.5742395 0.6872197 0.6176423
##  [531,] 0.7189956 0.5537470 0.5933608 0.5918434 0.4021720 0.6068566 0.4981825
##  [532,] 0.4073508 0.6346996 0.9105471 0.9406183 0.7858087 0.7845329 0.7592765
##  [533,] 0.7276583 0.5514282 0.5808955 0.5780940 0.3917348 0.6014645 0.4902377
##  [534,] 0.7179758 0.5540179 0.5948158 0.5934582 0.4034040 0.6074870 0.4991124
##  [535,] 0.7082598 0.5565796 0.6085421 0.6087886 0.4151732 0.6134488 0.5079176
##  [536,] 0.8498803 0.5130644 0.3883218 0.3930049 0.2515440 0.5145564 0.3657589
##  [537,] 0.4920895 0.6106733 0.8484368 0.8807637 0.6834878 0.7357573 0.6892627
##  [538,] 0.8540239 0.5114563 0.3814418 0.3875633 0.2470921 0.5110756 0.3609633
##  [539,] 0.7689577 0.5398595 0.5189679 0.5124429 0.3427351 0.5746893 0.4510843
##  [540,] 0.4790259 0.6141342 0.8590789 0.8916670 0.6995422 0.7430713 0.6999188
##  [541,] 0.8167620 0.5249338 0.4428832 0.4393154 0.2879545 0.5407520 0.4023967
##  [542,] 0.7681653 0.5400910 0.5201927 0.5136929 0.3436621 0.5752222 0.4518579
##  [543,] 0.6947267 0.5600936 0.6272487 0.6299341 0.4316575 0.6216290 0.5200276
##  [544,] 0.6014716 0.5832921 0.7426424 0.7635138 0.5472277 0.6752287 0.5997981
##  [545,] 0.7048008 0.5574835 0.6133695 0.6142190 0.4193768 0.6155528 0.5110294
##  [546,] 0.7899548 0.5335550 0.4860507 0.4796746 0.3183854 0.5602460 0.4302160
##  [547,] 0.8252214 0.5220486 0.4290471 0.4270557 0.2785215 0.5343089 0.3933006
##  [548,] 0.5452182 0.5971299 0.8008781 0.8296545 0.6175554 0.7063464 0.6460140
##  [549,] 0.5936110 0.5852143 0.7512851 0.7734845 0.5570569 0.6796031 0.6063114
##  [550,] 0.8127775 0.5262629 0.4493685 0.4451779 0.2924270 0.5437348 0.4066250
##  [551,] 0.5940867 0.5850980 0.7507667 0.7728876 0.5564618 0.6793387 0.6059178
##  [552,] 0.6039690 0.5826815 0.7398616 0.7602983 0.5441060 0.6738360 0.5977239
##  [553,] 0.7708803 0.5392960 0.5159910 0.5094135 0.3404884 0.5733931 0.4492035
##  [554,] 0.7149986 0.5548066 0.5990478 0.5981666 0.4070041 0.6093222 0.5018208
##  [555,] 0.6563182 0.5698024 0.6776562 0.6879720 0.4789232 0.6441913 0.5535545
##  [556,] 0.7260382 0.5518642 0.5832412 0.5806693 0.3936830 0.6024781 0.4917299
##  [557,] 0.7986641 0.5308324 0.4721533 0.4663440 0.3084135 0.5540542 0.4213339
##  [558,] 0.6535110 0.5705005 0.6811826 0.6920697 0.4824008 0.6458086 0.5559626
##  [559,] 0.6494715 0.5715027 0.6862189 0.6979263 0.4874094 0.6481292 0.5594187
##  [560,] 0.5565519 0.5943175 0.7898131 0.8173187 0.6034031 0.7000987 0.6367624
##  [561,] 0.6788999 0.5641352 0.6485051 0.6542555 0.4510561 0.6310329 0.5339828
##  [562,] 0.4901475 0.6111837 0.8500444 0.8824252 0.6858793 0.7368415 0.6908453
##  [563,] 0.6764026 0.5647672 0.6517973 0.6580453 0.4541276 0.6325022 0.5361659
##  [564,] 0.8282428 0.5209959 0.4240854 0.4227427 0.2751735 0.5319694 0.3900109
##  [565,] 0.8222252 0.5230807 0.4339575 0.4313676 0.2818527 0.5366087 0.3965413
##  [566,] 0.6827435 0.5631597 0.6434051 0.6483956 0.4463341 0.6287641 0.5306130
##  [567,] 0.6660159 0.5673810 0.6653081 0.6736507 0.4669313 0.6385744 0.5451948
##  [568,] 0.6069012 0.5819645 0.7365751 0.7564938 0.5404414 0.6721989 0.5952853
##  [569,] 0.7386731 0.5484318 0.5647744 0.5605553 0.3785380 0.5945057 0.4800114
##  [570,] 0.5879734 0.5865936 0.7573813 0.7804930 0.5641084 0.6827329 0.6109692
##  [571,] 0.7543839 0.5440520 0.5412732 0.5355319 0.3598711 0.5843603 0.4651629
##  [572,] 0.7008352 0.5585148 0.6188650 0.6204240 0.4242044 0.6179536 0.5145828
##  [573,] 0.7491093 0.5455375 0.5492281 0.5439257 0.3661166 0.5877970 0.4701842
##  [574,] 0.5125655 0.6053667 0.8309333 0.8623673 0.6581806 0.7243762 0.6725954
##  [575,] 0.6926048 0.5606394 0.6301377 0.6332229 0.4342511 0.6228995 0.5219111
##  [576,] 0.6960550 0.5597513 0.6254341 0.6278714 0.4300351 0.6208321 0.5188465
##  [577,] 0.6018171 0.5832077 0.7422587 0.7630703 0.5467958 0.6750361 0.5995113
##  [578,] 0.6743709 0.5652803 0.6544632 0.6611182 0.4566286 0.6336948 0.5379384
##  [579,] 0.6120814 0.5806974 0.7307120 0.7496968 0.5339701 0.6693014 0.5909684
##  [580,] 0.5627490 0.5927870 0.7836222 0.8103600 0.5956579 0.6966808 0.6316941
##  [581,] 0.5532940 0.5951240 0.7930277 0.8209165 0.6074731 0.7018948 0.6394240
##  [582,] 0.5672280 0.5916835 0.7790853 0.8052369 0.5900579 0.6942091 0.6280261
##  [583,] 0.6426127 0.5731995 0.6946678 0.7077599 0.4959251 0.6520528 0.5652638
##  [584,] 0.6016383 0.5832514 0.7424573 0.7632999 0.5470193 0.6751358 0.5996598
##  [585,] 0.7002958 0.5586547 0.6196093 0.6212662 0.4248617 0.6182793 0.5150650
##  [586,] 0.6840889 0.5628174 0.6416104 0.6463369 0.4446827 0.6279677 0.5294305
##  [587,] 0.6639794 0.5678909 0.6679225 0.6766789 0.4694467 0.6397580 0.5469558
##  [588,] 0.6633656 0.5680444 0.6687083 0.6775895 0.4702051 0.6401143 0.5474860
##  [589,] 0.6750432 0.5651106 0.6535823 0.6601024 0.4558008 0.6333004 0.5373522
##  [590,] 0.5780622 0.5890217 0.7678928 0.7925215 0.5765070 0.6882226 0.6191332
##  [591,] 0.7490558 0.5455524 0.5493084 0.5440108 0.3661801 0.5878317 0.4702349
##  [592,] 0.7407781 0.5478526 0.5616596 0.5572004 0.3760259 0.5931619 0.4780404
##  [593,] 0.5271117 0.6016685 0.8178745 0.8483113 0.6401160 0.7163331 0.6607613
##  [594,] 0.7644196 0.5411797 0.5259636 0.5196112 0.3480514 0.5777296 0.4555017
##  [595,] 0.7990102 0.5307228 0.4715983 0.4658181 0.3080188 0.5538055 0.4209779
##  [596,] 0.8907172 0.4955202 0.3206257 0.3435994 0.2088285 0.4776346 0.3158845
##  [597,] 0.7839239 0.5354013 0.4955938 0.4890059 0.3253358 0.5644616 0.4362859
##  [598,] 0.8740163 0.5031992 0.3482279 0.3626125 0.2259731 0.4934976 0.3370336
##  [599,] 0.5025029 0.6079581 0.8396620 0.8716092 0.6706372 0.7299586 0.6807828
##  [600,] 0.4578757 0.6198913 0.8754639 0.9079812 0.7253503 0.7550346 0.7172424
##  [601,] 0.6879026 0.5618444 0.6364967 0.6404814 0.4400067 0.6257040 0.5260707
##  [602,] 0.3963756 0.6381796 0.9174409 0.9466002 0.7986667 0.7911791 0.7685903
##  [603,] 0.7939396 0.5323179 0.4797086 0.4735527 0.3138131 0.5574288 0.4261696
##  [604,] 0.6452617 0.5725449 0.6914200 0.7039789 0.4926346 0.6505398 0.5630097
##  [605,] 0.6800915 0.5638332 0.6469283 0.6524423 0.4495915 0.6303305 0.5329394
##  [606,] 0.7866019 0.5345852 0.4913646 0.4848531 0.3222450 0.5625967 0.4335985
##  [607,] 0.5203582 0.6033790 0.8240027 0.8549400 0.6485107 0.7200642 0.6662561
##  [608,] 0.8028995 0.5294826 0.4653482 0.4599311 0.3035929 0.5509960 0.4169621
##  [609,] 0.8123096 0.5264178 0.4501287 0.4458698 0.2929534 0.5440830 0.4071193
##  [610,] 0.8075772 0.5279708 0.4577993 0.4529076 0.2982917 0.5475805 0.4120922
##  [611,] 0.8255768 0.5219254 0.4284641 0.4265466 0.2781271 0.5340349 0.3929149
##  [612,] 0.6767277 0.5646850 0.6513697 0.6575528 0.4537276 0.6323111 0.5358820
##  [613,] 0.7458913 0.5464361 0.5540494 0.5490517 0.3699379 0.5898783 0.4732294
##  [614,] 0.5461465 0.5968988 0.7999842 0.8286631 0.6163970 0.7058347 0.6452570
##  [615,] 0.4869783 0.6120196 0.8526487 0.8851060 0.6897785 0.7386131 0.6934290
##  [616,] 0.6278840 0.5768253 0.7123746 0.7283795 0.5142542 0.6604140 0.5777239
##  [617,] 0.6725597 0.5657369 0.6568303 0.6638494 0.4588595 0.6347559 0.5395159
##  [618,] 0.6644348 0.5677769 0.6673388 0.6760026 0.4688840 0.6394935 0.5465622
##  [619,] 0.6735493 0.5654875 0.6555381 0.6623582 0.4576405 0.6341764 0.5386543
##  [620,] 0.8535261 0.5116512 0.3822685 0.3882123 0.2476256 0.5114965 0.3615421
##  [621,] 0.7681916 0.5400834 0.5201520 0.5136514 0.3436313 0.5752045 0.4518322
##  [622,] 0.7891697 0.5337971 0.4872968 0.4808850 0.3192881 0.5607981 0.4310098
##  [623,] 0.3759511 0.6449905 0.9296044 0.9567525 0.8222808 0.8038535 0.7861677
##  [624,] 0.6220878 0.5782471 0.7191797 0.7362983 0.5214806 0.6636829 0.5825957
##  [625,] 0.5587010 0.5937862 0.7876775 0.8149226 0.6007176 0.6989136 0.6350057
##  [626,] 0.5017487 0.6081536 0.8403063 0.8722862 0.6715693 0.7303777 0.6813967
##  [627,] 0.6530994 0.5706027 0.6816978 0.6926685 0.4829109 0.6460454 0.5563152
##  [628,] 0.8406893 0.5165234 0.4035543 0.4053769 0.2615046 0.5221020 0.3762160
##  [629,] 0.6077198 0.5817643 0.7356534 0.7554261 0.5394186 0.6717415 0.5946038
##  [630,] 0.8153970 0.5253912 0.4451074 0.4413177 0.2894847 0.5417775 0.4038492
##  [631,] 0.8235485 0.5226263 0.4317900 0.4294589 0.2803800 0.5355954 0.3951126
##  [632,] 0.6616522 0.5684726 0.6708963 0.6801261 0.4723231 0.6411079 0.5489645
##  [633,] 0.7179077 0.5540360 0.5949128 0.5935659 0.4034862 0.6075290 0.4991745
##  [634,] 0.6573858 0.5695367 0.6763095 0.6864079 0.4776014 0.6435753 0.5526374
##  [635,] 0.7404079 0.5479546 0.5622081 0.5577903 0.3764674 0.5933986 0.4783874
##  [636,] 0.6204214 0.5786555 0.7211192 0.7385538 0.5235594 0.6646207 0.5839933
##  [637,] 0.8821376 0.4995678 0.3347750 0.3531458 0.2175763 0.4859346 0.3268950
##  [638,] 0.7656289 0.5408292 0.5241037 0.5176987 0.3466329 0.5769220 0.4543276
##  [639,] 0.6317160 0.5758839 0.7078250 0.7230824 0.5094805 0.6582465 0.5744935
##  [640,] 0.7831455 0.5356374 0.4968206 0.4902157 0.3262356 0.5650016 0.4370648
##  [641,] 0.6109600 0.5809717 0.7319874 0.7511763 0.5353707 0.6699293 0.5919039
##  [642,] 0.8031957 0.5293875 0.4648713 0.4594845 0.3032566 0.5507809 0.4166551
##  [643,] 0.6824029 0.5632463 0.6438586 0.6489160 0.4467521 0.6289655 0.5309120
##  [644,] 0.8424282 0.5158798 0.4006762 0.4030054 0.2596113 0.5206922 0.3742560
##  [645,] 0.6586886 0.5692121 0.6746618 0.6844950 0.4759890 0.6428228 0.5515172
##  [646,] 0.7371467 0.5488505 0.5670262 0.5629877 0.3803616 0.5954772 0.4814372
##  [647,] 0.6449715 0.5726166 0.6917767 0.7043941 0.4929949 0.6507057 0.5632568
##  [648,] 0.6519864 0.5708790 0.6830887 0.6942857 0.4842906 0.6466853 0.5572683
##  [649,] 0.6757933 0.5649212 0.6525981 0.6589680 0.4548775 0.6328601 0.5366979
##  [650,] 0.7893139 0.5337526 0.4870680 0.4806626 0.3191222 0.5606967 0.4308640
##  [651,] 0.8093922 0.5273781 0.4548614 0.4502001 0.2962414 0.5462443 0.4101906
##  [652,] 0.6462359 0.5723039 0.6902208 0.7025830 0.4914249 0.6499827 0.5621797
##  [653,] 0.5751127 0.5897454 0.7709705 0.7960282 0.5801964 0.6898536 0.6215571
##  [654,] 0.8108627 0.5268952 0.4524774 0.4480140 0.2945829 0.5451569 0.4086447
##  [655,] 0.8503094 0.5128993 0.3876097 0.3924374 0.2510819 0.5141983 0.3652647
##  [656,] 0.6672300 0.5670766 0.6637440 0.6718403 0.4654324 0.6378678 0.5441436
##  [657,] 0.7757205 0.5378657 0.5084622 0.5018091 0.3348470 0.5701072 0.4444425
##  [658,] 0.6816900 0.5634274 0.6448069 0.6500048 0.4476276 0.6293868 0.5315378
##  [659,] 0.5164119 0.6043836 0.8275312 0.8587309 0.6534100 0.7222468 0.6694664
##  [660,] 0.7077189 0.5567213 0.6092991 0.6096388 0.4158301 0.6137784 0.5084050
##  [661,] 0.5979541 0.5841522 0.7465304 0.7680039 0.5516255 0.6771878 0.6027155
##  [662,] 0.7027903 0.5580070 0.6161609 0.6173678 0.4218232 0.6167715 0.5128328
##  [663,] 0.6275300 0.5769122 0.7127928 0.7288664 0.5146954 0.6606140 0.5780219
##  [664,] 0.5995205 0.5837692 0.7448031 0.7660100 0.5496670 0.6763157 0.6014169
##  [665,] 0.7213108 0.5531303 0.5900479 0.5881741 0.3993777 0.6054221 0.4960672
##  [666,] 0.6236408 0.5778664 0.7173654 0.7341878 0.5195438 0.6628082 0.5812921
##  [667,] 0.5831748 0.5877686 0.7625032 0.7863636 0.5701112 0.6853926 0.6149255
##  [668,] 0.4938576 0.6102097 0.8469653 0.8792385 0.6813090 0.7347709 0.6878221
##  [669,] 0.6420118 0.5733478 0.6954019 0.7086147 0.4966718 0.6523956 0.5657746
##  [670,] 0.5482677 0.5963713 0.7979334 0.8263851 0.6137494 0.7046655 0.6435267
##  [671,] 0.5677075 0.5915654 0.7785964 0.8046837 0.5894582 0.6939443 0.6276330
##  [672,] 0.7800637 0.5365674 0.5016657 0.4950159 0.3298034 0.5671305 0.4401380
##  [673,] 0.6574876 0.5695113 0.6761809 0.6862586 0.4774754 0.6435166 0.5525499
##  [674,] 0.6456142 0.5724577 0.6909864 0.7034741 0.4921969 0.6503383 0.5627095
##  [675,] 0.5158466 0.6045278 0.8280334 0.8592689 0.6541113 0.7225596 0.6699262
##  [676,] 0.6725505 0.5657392 0.6568424 0.6638633 0.4588709 0.6347613 0.5395239
##  [677,] 0.6175372 0.5793620 0.7244581 0.7424349 0.5271585 0.6662418 0.5864091
##  [678,] 0.8376797 0.5176261 0.4085308 0.4095142 0.2647913 0.5245234 0.3795889
##  [679,] 0.5852114 0.5872698 0.7603369 0.7838828 0.5675635 0.6842642 0.6132473
##  [680,] 0.5903065 0.5860227 0.7548687 0.7776071 0.5611900 0.6814384 0.6090429
##  [681,] 0.6901029 0.5612813 0.6335285 0.6370901 0.4373121 0.6243935 0.5241267
##  [682,] 0.5984122 0.5840402 0.7460260 0.7674217 0.5510527 0.6769328 0.6023358
##  [683,] 0.8787192 0.5011185 0.3404321 0.3570808 0.2210972 0.4891509 0.3311946
##  [684,] 0.8003290 0.5303039 0.4694817 0.4638173 0.3065162 0.5528558 0.4196195
##  [685,] 0.7608340 0.5422131 0.5314593 0.5252900 0.3522647 0.5801130 0.4589702
##  [686,] 0.5822126 0.5880043 0.7635228 0.7875302 0.5713149 0.6859255 0.6157180
##  [687,] 0.7732774 0.5385897 0.5122683 0.5056432 0.3376918 0.5717698 0.4468502
##  [688,] 0.6802651 0.5637892 0.6466983 0.6521778 0.4493781 0.6302281 0.5327872
##  [689,] 0.6304648 0.5761914 0.7093149 0.7248173 0.5110388 0.6589548 0.5755491
##  [690,] 0.6066336 0.5820299 0.7368760 0.7568423 0.5407759 0.6723484 0.5955080
##  [691,] 0.6532808 0.5705576 0.6814707 0.6924046 0.4826860 0.6459410 0.5561598
##  [692,] 0.7892301 0.5337785 0.4872010 0.4807918 0.3192186 0.5607556 0.4309488
##  [693,] 0.6457154 0.5724327 0.6908618 0.7033291 0.4920712 0.6502804 0.5626233
##  [694,] 0.5369395 0.5991973 0.8087524 0.8383451 0.6278794 0.7109106 0.6527607
##  [695,] 0.6692142 0.5665785 0.6611792 0.6688736 0.4629841 0.6367111 0.5424232
##  [696,] 0.6805458 0.5637179 0.6463261 0.6517501 0.4490332 0.6300625 0.5325412
##  [697,] 0.6863377 0.5622441 0.6385998 0.6428877 0.4419246 0.6266340 0.5274509
##  [698,] 0.7090082 0.5563836 0.6074935 0.6076116 0.4142646 0.6129923 0.5072428
##  [699,] 0.7516067 0.5448361 0.5454697 0.5399499 0.3631567 0.5861739 0.4678114
##  [700,] 0.7625938 0.5417069 0.5287656 0.5225014 0.3501954 0.5789452 0.4572702
##  [701,] 0.5964185 0.5845277 0.7482173 0.7699497 0.5535457 0.6780422 0.6039877
##  [702,] 0.5594394 0.5936038 0.7869409 0.8140951 0.5997948 0.6985064 0.6344018
##  [703,] 0.5394782 0.5985620 0.8063562 0.8357088 0.6247149 0.7095108 0.6506926
##  [704,] 0.7151229 0.5547738 0.5988715 0.5979701 0.4068537 0.6092457 0.5017079
##  [705,] 0.8053044 0.5287082 0.4614714 0.4563121 0.3008644 0.5492450 0.4144639
##  [706,] 0.7726501 0.5387750 0.5132437 0.5066291 0.3384231 0.5721954 0.4474669
##  [707,] 0.7843320 0.5352773 0.4949502 0.4883721 0.3248643 0.5641781 0.4358771
##  [708,] 0.6678396 0.5669236 0.6629572 0.6709299 0.4646801 0.6375126 0.5436153
##  [709,] 0.7563606 0.5434911 0.5382756 0.5323900 0.3575363 0.5830640 0.4632713
##  [710,] 0.4916400 0.6107913 0.8488096 0.8811495 0.6840414 0.7360081 0.6896289
##  [711,] 0.6589642 0.5691434 0.6743126 0.6840896 0.4756479 0.6426635 0.5512800
##  [712,] 0.5653902 0.5921360 0.7809532 0.8073485 0.5923559 0.6952235 0.6295317
##  [713,] 0.6648252 0.5676792 0.6668380 0.6754224 0.4684017 0.6392667 0.5462247
##  [714,] 0.6260274 0.5772810 0.7145644 0.7309284 0.5165682 0.6614623 0.5792863
##  [715,] 0.8055822 0.5286183 0.4610230 0.4558952 0.3005497 0.5490421 0.4141746
##  [716,] 0.7352102 0.5493800 0.5698748 0.5660731 0.3826775 0.5967064 0.4832419
##  [717,] 0.6306007 0.5761580 0.7091533 0.7246292 0.5108696 0.6588779 0.5754345
##  [718,] 0.7486771 0.5456585 0.5498770 0.5446139 0.3666293 0.5880772 0.4705939
##  [719,] 0.8011969 0.5300273 0.4680874 0.4625032 0.3055284 0.5522292 0.4187238
##  [720,] 0.9340142 0.4701247 0.2514847 0.3033861 0.1669093 0.4290713 0.2541968
##  [721,] 0.7503189 0.5451982 0.5474095 0.5419997 0.3646824 0.5870117 0.4690360
##  [722,] 0.5761317 0.5894953 0.7699098 0.7948205 0.5789218 0.6892902 0.6207200
##  [723,] 0.4727584 0.6158190 0.8640422 0.8966721 0.7072154 0.7465991 0.7050417
##  [724,] 0.6788082 0.5641585 0.6486264 0.6543949 0.4511688 0.6310869 0.5340630
##  [725,] 0.6956814 0.5598476 0.6259449 0.6284518 0.4304913 0.6210564 0.5191788
##  [726,] 0.7115275 0.5557220 0.6039529 0.6036444 0.4112085 0.6114524 0.5049670
##  [727,] 0.5832421 0.5877521 0.7624317 0.7862819 0.5700270 0.6853553 0.6148701
##  [728,] 0.6464448 0.5722522 0.6899632 0.7022832 0.4911655 0.6498631 0.5620016
##  [729,] 0.8109815 0.5268561 0.4522847 0.4478377 0.2944490 0.5450689 0.4085197
##  [730,] 0.6027296 0.5829845 0.7412437 0.7618969 0.5456551 0.6745273 0.5987536
##  [731,] 0.8103288 0.5270708 0.4533433 0.4488070 0.2951848 0.5455522 0.4092066
##  [732,] 0.7627658 0.5416574 0.5285019 0.5222289 0.3499933 0.5788309 0.4571038
##  [733,] 0.6479762 0.5718732 0.6880719 0.7000822 0.4892647 0.6489863 0.5606955
##  [734,] 0.5545301 0.5948179 0.7918112 0.8195563 0.6059290 0.7012134 0.6384143
##  [735,] 0.7868760 0.5345013 0.4909309 0.4844288 0.3219290 0.5624052 0.4333227
##  [736,] 0.6722512 0.5658146 0.6572327 0.6643139 0.4592397 0.6349365 0.5397843
##  [737,] 0.6952188 0.5599668 0.6265770 0.6291703 0.4310563 0.6213339 0.5195902
##  [738,] 0.7141717 0.5550251 0.6002191 0.5994727 0.4080050 0.6098305 0.5025714
##  [739,] 0.8049564 0.5288206 0.4620330 0.4568348 0.3012589 0.5494991 0.4148262
##  [740,] 0.5986928 0.5839716 0.7457167 0.7670648 0.5507019 0.6767766 0.6021033
##  [741,] 0.6440750 0.5728382 0.6928773 0.7056753 0.4941084 0.6512180 0.5640200
##  [742,] 0.5706228 0.5908484 0.7756115 0.8013017 0.5858124 0.6923345 0.6252427
##  [743,] 0.6145112 0.5801028 0.7279368 0.7464756 0.5309359 0.6679398 0.5889395
##  [744,] 0.7353359 0.5493457 0.5696902 0.5658728 0.3825271 0.5966267 0.4831249
##  [745,] 0.7014841 0.5583464 0.6179686 0.6194102 0.4234137 0.6175616 0.5140023
##  [746,] 0.8524915 0.5120547 0.3839868 0.3895654 0.2487356 0.5123688 0.3627428
##  [747,] 0.8042225 0.5290573 0.4632166 0.4579382 0.3020911 0.5500341 0.4155893
##  [748,] 0.6699528 0.5663929 0.6602217 0.6677667 0.4620731 0.6362800 0.5417821
##  [749,] 0.6759491 0.5648818 0.6523933 0.6587321 0.4546857 0.6327686 0.5365618
##  [750,] 0.5199934 0.6034717 0.8243306 0.8552931 0.6489638 0.7202659 0.6665529
##  [751,] 0.7799307 0.5366074 0.5018744 0.4952235 0.3299576 0.5672221 0.4402703
##  [752,] 0.5425435 0.5977965 0.8034413 0.8324918 0.6208923 0.7078209 0.6481946
##  [753,] 0.7606511 0.5422656 0.5317388 0.5255799 0.3524798 0.5802341 0.4591465
##  [754,] 0.7337974 0.5497651 0.5719473 0.5683235 0.3843689 0.5976007 0.4845558
##  [755,] 0.8758360 0.5024011 0.3452100 0.3604562 0.2240822 0.4918263 0.3347846
##  [756,] 0.7559421 0.5436101 0.5389111 0.5330551 0.3580304 0.5833389 0.4636723
##  [757,] 0.8540047 0.5114638 0.3814736 0.3875882 0.2471127 0.5110918 0.3609855
##  [758,] 0.6330369 0.5755591 0.7062474 0.7212453 0.5078357 0.6574981 0.5733782
##  [759,] 0.7547436 0.5439501 0.5407285 0.5349601 0.3594460 0.5841248 0.4648191
##  [760,] 0.8003270 0.5303045 0.4694850 0.4638203 0.3065185 0.5528573 0.4196216
##  [761,] 0.6953996 0.5599202 0.6263300 0.6288895 0.4308354 0.6212255 0.5194294
##  [762,] 0.7982861 0.5309520 0.4727592 0.4669186 0.3088446 0.5543256 0.4217223
##  [763,] 0.5333761 0.6000910 0.8120881 0.8420026 0.6323188 0.7128760 0.6556624
##  [764,] 0.6137491 0.5802893 0.7288090 0.7474882 0.5318875 0.6683671 0.5895762
##  [765,] 0.7507277 0.5450834 0.5467941 0.5413489 0.3641979 0.5867459 0.4686475
##  [766,] 0.6108904 0.5809888 0.7320666 0.7512681 0.5354577 0.6699683 0.5919620
##  [767,] 0.8721611 0.5040042 0.3513066 0.3648316 0.2279066 0.4951885 0.3393137
##  [768,] 0.6162363 0.5796805 0.7259567 0.7441759 0.5287822 0.6669721 0.5874974
##  [769,] 0.8371761 0.5178092 0.4093629 0.4102106 0.2653425 0.5249264 0.3801509
##  [770,] 0.6467349 0.5721805 0.6896055 0.7018668 0.4908054 0.6496971 0.5617543
##  [771,] 0.5575986 0.5940587 0.7887745 0.8161540 0.6020953 0.6995216 0.6359069
##  [772,] 0.8271049 0.5213938 0.4259552 0.4243628 0.2764331 0.5328530 0.3912525
##  [773,] 0.7445180 0.5468179 0.5560995 0.5512400 0.3715710 0.5907629 0.4745248
##  [774,] 0.5507605 0.5957523 0.7955086 0.8236854 0.6106371 0.7032914 0.6414925
##  [775,] 0.5950232 0.5848689 0.7497446 0.7717101 0.5552906 0.6788182 0.6051429
##  [776,] 0.5287527 0.6012545 0.8163683 0.8466736 0.6380745 0.7154272 0.6594259
##  [777,] 0.7261760 0.5518272 0.5830419 0.5804503 0.3935172 0.6023920 0.4916031
##  [778,] 0.5457381 0.5970005 0.8003777 0.8290997 0.6169066 0.7060598 0.6455901
##  [779,] 0.6484062 0.5717667 0.6875396 0.6994629 0.4887311 0.6487399 0.5603285
##  [780,] 0.8915400 0.4951194 0.3192734 0.3427093 0.2079965 0.4768205 0.3148113
##  [781,] 0.8176430 0.5246374 0.4414464 0.4380265 0.2869682 0.5400881 0.4014570
##  [782,] 0.8488325 0.5134661 0.3900605 0.3943946 0.2526736 0.5154285 0.3669633
##  [783,] 0.6605797 0.5687404 0.6722618 0.6817099 0.4736494 0.6417290 0.5498890
##  [784,] 0.3853867 0.6417853 0.9240918 0.9522177 0.8114251 0.7979447 0.7780044
##  [785,] 0.8336610 0.5190768 0.4151645 0.4151013 0.2691985 0.5277208 0.3840550
##  [786,] 0.5720688 0.5904930 0.7741226 0.7996118 0.5840038 0.6915358 0.6240563
##  [787,] 0.6825367 0.5632123 0.6436804 0.6487116 0.4465879 0.6288863 0.5307945
##  [788,] 0.7892932 0.5337590 0.4871009 0.4806946 0.3191461 0.5607113 0.4308851
##  [789,] 0.6803687 0.5637629 0.6465609 0.6520199 0.4492508 0.6301670 0.5326964
##  [790,] 0.7376735 0.5487061 0.5662497 0.5621482 0.3797320 0.5951422 0.4809454
##  [791,] 0.5902694 0.5860318 0.7549088 0.7776532 0.5612364 0.6814590 0.6090735
##  [792,] 0.8270986 0.5213960 0.4259657 0.4243719 0.2764401 0.5328579 0.3912594
##  [793,] 0.6151066 0.5799571 0.7272543 0.7456831 0.5301925 0.6676059 0.5884420
##  [794,] 0.6377207 0.5744061 0.7006149 0.7146855 0.5020069 0.6548392 0.5694157
##  [795,] 0.6619147 0.5684071 0.6705616 0.6797380 0.4719986 0.6409557 0.5487382
##  [796,] 0.6951835 0.5599759 0.6266251 0.6292250 0.4310994 0.6213551 0.5196216
##  [797,] 0.5593930 0.5936152 0.7869872 0.8141472 0.5998528 0.6985320 0.6344398
##  [798,] 0.6393923 0.5739941 0.6985901 0.7123274 0.4999280 0.6538881 0.5679985
##  [799,] 0.7678029 0.5401968 0.5207523 0.5142648 0.3440862 0.5754655 0.4522114
##  [800,] 0.6027421 0.5829815 0.7412298 0.7618808 0.5456395 0.6745203 0.5987432
##  [801,] 0.5290809 0.6011718 0.8160662 0.8463448 0.6376661 0.7152461 0.6591588
##  [802,] 0.7856651 0.5348713 0.4928455 0.4863041 0.3233254 0.5632503 0.4345400
##  [803,] 0.5630388 0.5927155 0.7833302 0.8100309 0.5952956 0.6965209 0.6314569
##  [804,] 0.5642029 0.5924285 0.7821553 0.8087057 0.5938404 0.6958787 0.6305040
##  [805,] 0.8676707 0.5059175 0.3587638 0.3702869 0.2326093 0.4992277 0.3447795
##  [806,] 0.6374540 0.5744719 0.7009373 0.7150610 0.5023388 0.6549908 0.5696417
##  [807,] 0.5462998 0.5968607 0.7998364 0.8284991 0.6162056 0.7057502 0.6451320
##  [808,] 0.7463252 0.5463152 0.5534007 0.5483603 0.3694221 0.5895983 0.4728195
##  [809,] 0.5586749 0.5937927 0.7877035 0.8149518 0.6007503 0.6989280 0.6350270
##  [810,] 0.7100926 0.5560991 0.6059716 0.6059049 0.4129487 0.6123301 0.5062640
##  [811,] 0.6726117 0.5657238 0.6567624 0.6637711 0.4587954 0.6347255 0.5394706
##  [812,] 0.7519522 0.5447388 0.5449485 0.5394000 0.3627476 0.5859487 0.4674825
##  [813,] 0.5921517 0.5855713 0.7528712 0.7753101 0.5588820 0.6804138 0.6075181
##  [814,] 0.6413724 0.5735057 0.6961819 0.7095229 0.4974665 0.6527602 0.5663178
##  [815,] 0.7955919 0.5318007 0.4770706 0.4710252 0.3119220 0.5562529 0.4244832
##  [816,] 0.6949050 0.5600477 0.6270054 0.6296574 0.4314396 0.6215221 0.5198691
##  [817,] 0.8115117 0.5266813 0.4514242 0.4470514 0.2938517 0.5446757 0.4079610
##  [818,] 0.5703449 0.5909167 0.7758970 0.8016255 0.5861599 0.6924880 0.6254707
##  [819,] 0.6396195 0.5739381 0.6983144 0.7120063 0.4996456 0.6537588 0.5678058
##  [820,] 0.7904168 0.5334123 0.4853169 0.4789631 0.3178545 0.5599208 0.4297484
##  [821,] 0.7075542 0.5567644 0.6095294 0.6098977 0.4160302 0.6138788 0.5085534
##  [822,] 0.7491269 0.5455325 0.5492016 0.5438976 0.3660957 0.5877856 0.4701675
##  [823,] 0.6961829 0.5597182 0.6252591 0.6276726 0.4298789 0.6207553 0.5187327
##  [824,] 0.7345898 0.5495492 0.5707855 0.5670614 0.3834201 0.5970994 0.4838192
##  [825,] 0.6723421 0.5657917 0.6571141 0.6641770 0.4591277 0.6348833 0.5397052
##  [826,] 0.7785639 0.5370174 0.5040169 0.4973583 0.3315431 0.5681615 0.4416280
##  [827,] 0.6420016 0.5733503 0.6954142 0.7086291 0.4966844 0.6524014 0.5657832
##  [828,] 0.7224078 0.5528373 0.5884735 0.5864341 0.3980550 0.6047407 0.4950629
##  [829,] 0.7554688 0.5437445 0.5396292 0.5338073 0.3585893 0.5836495 0.4641254
##  [830,] 0.7445747 0.5468021 0.5560148 0.5511495 0.3715035 0.5907264 0.4744713
##  [831,] 0.6577225 0.5694528 0.6758841 0.6859140 0.4771847 0.6433809 0.5523480
##  [832,] 0.6897303 0.5613768 0.6340321 0.6376651 0.4377683 0.6246157 0.5244562
##  [833,] 0.7173779 0.5541766 0.5956674 0.5944043 0.4041264 0.6078561 0.4996570
##  [834,] 0.6299406 0.5763202 0.7099378 0.7255426 0.5116918 0.6592514 0.5759911
##  [835,] 0.8210008 0.5234992 0.4359611 0.4331394 0.2832171 0.5375428 0.3978595
##  [836,] 0.4684788 0.6169793 0.8673788 0.9000066 0.7124429 0.7490159 0.7085444
##  [837,] 0.7749337 0.5380993 0.5096892 0.5030428 0.3357625 0.5706436 0.4452189
##  [838,] 0.7837298 0.5354602 0.4958998 0.4893074 0.3255602 0.5645963 0.4364802
##  [839,] 0.6592801 0.5690646 0.6739121 0.6836248 0.4752570 0.6424809 0.5510081
##  [840,] 0.5466794 0.5967662 0.7994701 0.8280925 0.6157320 0.7055410 0.6448224
##  [841,] 0.9061859 0.4875577 0.2953811 0.3276441 0.1933999 0.4617320 0.2951484
##  [842,] 0.5878019 0.5866356 0.7575654 0.7807044 0.5643229 0.6828280 0.6111107
##  [843,] 0.8362468 0.5181461 0.4108976 0.4114983 0.2663603 0.5256681 0.3811862
##  [844,] 0.6577891 0.5694362 0.6757999 0.6858162 0.4771022 0.6433425 0.5522907
##  [845,] 0.8050798 0.5287807 0.4618338 0.4566494 0.3011190 0.5494090 0.4146977
##  [846,] 0.6933216 0.5604552 0.6291631 0.6321129 0.4333747 0.6224707 0.5212753
##  [847,] 0.6688611 0.5666672 0.6616364 0.6694022 0.4634197 0.6369171 0.5427295
##  [848,] 0.6108341 0.5810025 0.7321304 0.7513422 0.5355280 0.6699997 0.5920089
##  [849,] 0.6917097 0.5608693 0.6313527 0.6346077 0.4353458 0.6234345 0.5227043
##  [850,] 0.8165237 0.5250138 0.4432717 0.4396645 0.2882215 0.5409313 0.4026506
##  [851,] 0.5813215 0.5882227 0.7644649 0.7886075 0.5724297 0.6864189 0.6164517
##  [852,] 0.7905854 0.5333601 0.4850489 0.4787034 0.3176607 0.5598019 0.4295775
##  [853,] 0.7623182 0.5417864 0.5291879 0.5229379 0.3505194 0.5791284 0.4575368
##  [854,] 0.5793219 0.5887128 0.7665713 0.7910136 0.5749311 0.6875256 0.6180972
##  [855,] 0.6652660 0.5675688 0.6662721 0.6747670 0.4678573 0.6390105 0.5458436
##  [856,] 0.5795619 0.5886540 0.7663190 0.7907256 0.5746309 0.6873928 0.6178997
##  [857,] 0.6477875 0.5719199 0.6883053 0.7003538 0.4894989 0.6490944 0.5608565
##  [858,] 0.6969311 0.5595252 0.6242348 0.6265093 0.4289656 0.6203058 0.5180667
##  [859,] 0.6665628 0.5672439 0.6646039 0.6728355 0.4662559 0.6382562 0.5447213
##  [860,] 0.9179658 0.4807685 0.2764996 0.3166476 0.1819730 0.4486467 0.2784643
##  [861,] 0.6968319 0.5595508 0.6243707 0.6266636 0.4290867 0.6203654 0.5181550
##  [862,] 0.7224403 0.5528286 0.5884268 0.5863825 0.3980157 0.6047205 0.4950331
##  [863,] 0.8273018 0.5213251 0.4256317 0.4240821 0.2762150 0.5327003 0.3910379
##  [864,] 0.5517922 0.5954963 0.7945003 0.8225609 0.6093488 0.7027227 0.6406502
##  [865,] 0.5440641 0.5974174 0.8019863 0.8308822 0.6189954 0.7069826 0.6469550
##  [866,] 0.6206671 0.5785953 0.7208337 0.7382218 0.5232528 0.6644825 0.5837873
##  [867,] 0.4778845 0.6144398 0.8599896 0.8925893 0.7009411 0.7437128 0.7008512
##  [868,] 0.6825864 0.5631997 0.6436143 0.6486357 0.4465269 0.6288570 0.5307510
##  [869,] 0.6380952 0.5743139 0.7001620 0.7141580 0.5015412 0.6546262 0.5690984
##  [870,] 0.6904493 0.5611926 0.6330600 0.6365553 0.4368881 0.6241869 0.5238202
##  [871,] 0.7715749 0.5390918 0.5149135 0.5083201 0.3396774 0.5729235 0.4485225
##  [872,] 0.4146390 0.6324488 0.9058287 0.9364354 0.7772103 0.7801743 0.7531347
##  [873,] 0.6151679 0.5799421 0.7271840 0.7456014 0.5301160 0.6675716 0.5883907
##  [874,] 0.6815368 0.5634664 0.6450106 0.6502388 0.4478158 0.6294774 0.5316722
##  [875,] 0.8546043 0.5112285 0.3804776 0.3868080 0.2464705 0.5105839 0.3602873
##  [876,] 0.7109635 0.5558703 0.6047471 0.6045333 0.4118924 0.6117976 0.5054771
##  [877,] 0.7386927 0.5484264 0.5647453 0.5605240 0.3785145 0.5944932 0.4799930
##  [878,] 0.5159339 0.6045056 0.8279560 0.8591859 0.6540031 0.7225113 0.6698552
##  [879,] 0.7622533 0.5418050 0.5292873 0.5230407 0.3505956 0.5791715 0.4575994
##  [880,] 0.6879681 0.5618277 0.6364085 0.6403806 0.4399265 0.6256650 0.5260129
##  [881,] 0.7486058 0.5456784 0.5499841 0.5447275 0.3667140 0.5881234 0.4706615
##  [882,] 0.7299730 0.5508031 0.5775326 0.5744120 0.3889544 0.6000119 0.4881005
##  [883,] 0.8598919 0.5091225 0.3716913 0.3800099 0.2408303 0.5060562 0.3540800
##  [884,] 0.5833364 0.5877290 0.7623317 0.7861673 0.5699090 0.6853031 0.6147924
##  [885,] 0.7656524 0.5408224 0.5240676 0.5176616 0.3466054 0.5769063 0.4543047
##  [886,] 0.6428124 0.5731501 0.6944236 0.7074756 0.4956769 0.6519388 0.5650940
##  [887,] 0.7269819 0.5516104 0.5818756 0.5791693 0.3925480 0.6018880 0.4908610
##  [888,] 0.8533462 0.5117215 0.3825674 0.3884472 0.2478185 0.5116484 0.3617511
##  [889,] 0.6705155 0.5662514 0.6594912 0.6669225 0.4613792 0.6359513 0.5412933
##  [890,] 0.7808821 0.5363212 0.5003808 0.4937395 0.3288550 0.5665666 0.4393235
##  [891,] 0.7692763 0.5397663 0.5184751 0.5119406 0.3423625 0.5744748 0.4507730
##  [892,] 0.7860403 0.5347568 0.4922526 0.4857228 0.3228926 0.5629887 0.4341631
##  [893,] 0.7291649 0.5510216 0.5787082 0.5756978 0.3899247 0.6005196 0.4888474
##  [894,] 0.8129745 0.5261976 0.4490484 0.4448868 0.2922055 0.5435881 0.4064168
##  [895,] 0.7654926 0.5408688 0.5243135 0.5179142 0.3467928 0.5770132 0.4544600
##  [896,] 0.6780222 0.5643575 0.6496641 0.6555890 0.4521352 0.6315497 0.5347506
##  [897,] 0.6080524 0.5816830 0.7352785 0.7549917 0.5390031 0.6715556 0.5943269
##  [898,] 0.6223723 0.5781774 0.7188478 0.7359123 0.5211257 0.6635227 0.5823570
##  [899,] 0.8974701 0.4921595 0.3095547 0.3364297 0.2020369 0.4708521 0.3069811
##  [900,] 0.6928896 0.5605663 0.6297507 0.6327820 0.4339029 0.6227292 0.5216585
##  [901,] 0.7763813 0.5376691 0.5074305 0.5007735 0.3340785 0.5696561 0.4437895
##  [902,] 0.7888091 0.5339081 0.4878688 0.4814414 0.3197029 0.5610513 0.4313740
##  [903,] 0.8715735 0.5042573 0.3522820 0.3655387 0.2285202 0.4957213 0.3400331
##  [904,] 0.8667125 0.5063195 0.3603558 0.3714661 0.2336169 0.5000801 0.3459364
##  [905,] 0.7153271 0.5547198 0.5985819 0.5976474 0.4066066 0.6091200 0.5015224
##  [906,] 0.6795469 0.5639713 0.6476495 0.6532714 0.4502608 0.6306516 0.5334164
##  [907,] 0.6312223 0.5760052 0.7084134 0.7237675 0.5100953 0.6585260 0.5749101
##  [908,] 0.6398705 0.5738762 0.6980095 0.7116513 0.4993335 0.6536159 0.5675929
##  [909,] 0.8609368 0.5086996 0.3699545 0.3786843 0.2397206 0.5051508 0.3528426
##  [910,] 0.8474891 0.5139782 0.3922892 0.3961845 0.2541242 0.5165422 0.3685029
##  [911,] 0.8037093 0.5292225 0.4640438 0.4587106 0.3026734 0.5504075 0.4161222
##  [912,] 0.6206494 0.5785996 0.7208543 0.7382457 0.5232749 0.6644924 0.5838021
##  [913,] 0.8421561 0.5159808 0.4011266 0.4033755 0.2599072 0.5209133 0.3745632
##  [914,] 0.6963240 0.5596818 0.6250660 0.6274532 0.4297066 0.6206705 0.5186071
##  [915,] 0.5073364 0.6067096 0.8355000 0.8672187 0.6646581 0.7272748 0.6768495
##  [916,] 0.6258723 0.5773190 0.7147468 0.7311407 0.5167615 0.6615498 0.5794166
##  [917,] 0.5162670 0.6044206 0.8276600 0.8588689 0.6535898 0.7223270 0.6695843
##  [918,] 0.6543366 0.5702953 0.6801477 0.6908669 0.4813778 0.6453333 0.5552549
##  [919,] 0.8190762 0.5241533 0.4391069 0.4359356 0.2853655 0.5390046 0.3999247
##  [920,] 0.8858984 0.4978221 0.3285631 0.3489023 0.2137258 0.4823377 0.3221082
##  [921,] 0.5677050 0.5915660 0.7785990 0.8046866 0.5894613 0.6939457 0.6276351
##  [922,] 0.5565686 0.5943134 0.7897966 0.8173002 0.6033823 0.7000895 0.6367488
##  [923,] 0.6437992 0.5729064 0.6932155 0.7060690 0.4944510 0.6513755 0.5642547
##  [924,] 0.6624631 0.5682700 0.6698617 0.6789265 0.4713206 0.6406378 0.5482650
##  [925,] 0.8203881 0.5237079 0.4369631 0.4340282 0.2839006 0.5380091 0.3985179
##  [926,] 0.5150083 0.6047419 0.8287769 0.8600646 0.6551514 0.7230236 0.6706082
##  [927,] 0.7578109 0.5430781 0.5360707 0.5300866 0.3558254 0.5821100 0.4618800
##  [928,] 0.6589885 0.5691373 0.6742818 0.6840539 0.4756178 0.6426495 0.5512591
##  [929,] 0.6863098 0.5622513 0.6386372 0.6429306 0.4419588 0.6266506 0.5274755
##  [930,] 0.6920938 0.5607707 0.6308316 0.6340137 0.4348760 0.6232050 0.5223640
##  [931,] 0.7969101 0.5313863 0.4749627 0.4690137 0.3104154 0.5553115 0.4231341
##  [932,] 0.6769804 0.5646211 0.6510371 0.6571697 0.4534167 0.6321625 0.5356612
##  [933,] 0.6523675 0.5707844 0.6826129 0.6937324 0.4838181 0.6464663 0.5569420
##  [934,] 0.7193411 0.5536551 0.5928674 0.5912962 0.4017549 0.6066428 0.4978672
##  [935,] 0.6601336 0.5688517 0.6728288 0.6823678 0.4742012 0.6419872 0.5502733
##  [936,] 0.5324905 0.6003135 0.8129121 0.8429038 0.6334216 0.7133646 0.6563834
##  [937,] 0.7501864 0.5452354 0.5476089 0.5422107 0.3648394 0.5870978 0.4691619
##  [938,] 0.6183190 0.5791705 0.7235553 0.7413858 0.5261827 0.6658026 0.5857547
##  [939,] 0.6738636 0.5654082 0.6551272 0.6618840 0.4572533 0.6339922 0.5383805
##  [940,] 0.8472660 0.5140630 0.3926592 0.3964825 0.2543653 0.5167266 0.3687581
##  [941,] 0.7058051 0.5572215 0.6119711 0.6126439 0.4181555 0.6149428 0.5101271
##  [942,] 0.5466573 0.5967717 0.7994914 0.8281162 0.6157595 0.7055532 0.6448404
##  [943,] 0.7435321 0.5470913 0.5575685 0.5528111 0.3727443 0.5913968 0.4754533
##  [944,] 0.8059950 0.5284847 0.4603565 0.4552761 0.3000821 0.5487403 0.4137444
##  [945,] 0.7760748 0.5377603 0.5079091 0.5012537 0.3344348 0.5698654 0.4440924
##  [946,] 0.5538588 0.5949841 0.7924724 0.8202958 0.6067677 0.7015835 0.6389627
##  [947,] 0.5503980 0.5958422 0.7958622 0.8240795 0.6110897 0.7034912 0.6417883
##  [948,] 0.7336129 0.5498154 0.5722175 0.5686173 0.3845898 0.5977174 0.4847272
##  [949,] 0.7162090 0.5544864 0.5973300 0.5962534 0.4055398 0.6085770 0.5007209
##  [950,] 0.6526181 0.5707222 0.6822997 0.6933683 0.4835075 0.6463222 0.5567275
##  [951,] 0.7054637 0.5573106 0.6124468 0.6131796 0.4185707 0.6151503 0.5104340
##  [952,] 0.6875728 0.5619287 0.6369404 0.6409889 0.4404108 0.6259001 0.5263617
##  [953,] 0.7177604 0.5540751 0.5951227 0.5937991 0.4036643 0.6076200 0.4993087
##  [954,] 0.6868009 0.5621259 0.6379780 0.6421760 0.4413568 0.6263589 0.5270426
##  [955,] 0.6907653 0.5611116 0.6326324 0.6360673 0.4365014 0.6239984 0.5235406
##  [956,] 0.8566918 0.5104037 0.3770095 0.3841065 0.2442389 0.5088070 0.3578474
##  [957,] 0.4558814 0.6204453 0.8769559 0.9094360 0.7277707 0.7561721 0.7188820
##  [958,] 0.6005032 0.5835289 0.7437162 0.7647546 0.5484384 0.6757683 0.6006018
##  [959,] 0.9195452 0.4798000 0.2739975 0.3152527 0.1804637 0.4468172 0.2761603
##  [960,] 0.5655733 0.5920909 0.7807675 0.8071387 0.5921270 0.6951224 0.6293817
##  [961,] 0.5273590 0.6016061 0.8176480 0.8480652 0.6398084 0.7161966 0.6605601
##  [962,] 0.7988239 0.5307818 0.4718970 0.4661010 0.3082312 0.5539393 0.4211695
##  [963,] 0.7101350 0.5560879 0.6059120 0.6058382 0.4128973 0.6123042 0.5062257
##  [964,] 0.8277869 0.5211556 0.4248348 0.4233913 0.2756780 0.5323238 0.3905088
##  [965,] 0.7913749 0.5331157 0.4837938 0.4774887 0.3167541 0.5592450 0.4287773
##  [966,] 0.7487473 0.5456388 0.5497716 0.5445021 0.3665461 0.5880317 0.4705274
##  [967,] 0.5387354 0.5987478 0.8070591 0.8364828 0.6256410 0.7099204 0.6512978
##  [968,] 0.5363945 0.5993338 0.8092646 0.8389077 0.6285585 0.7112112 0.6532045
##  [969,] 0.5886403 0.5864304 0.7566646 0.7796703 0.5632742 0.6823630 0.6104188
##  [970,] 0.6858162 0.5623772 0.6392992 0.6436885 0.4425641 0.6269436 0.5279104
##  [971,] 0.5783191 0.5889587 0.7676236 0.7922145 0.5761856 0.6880805 0.6189219
##  [972,] 0.7346856 0.5495231 0.5706449 0.5669088 0.3833054 0.5970387 0.4837301
##  [973,] 0.6447866 0.5726623 0.6920039 0.7046585 0.4932246 0.6508114 0.5634143
##  [974,] 0.6739159 0.5653950 0.6550587 0.6618050 0.4571889 0.6339615 0.5383349
##  [975,] 0.7371620 0.5488463 0.5670036 0.5629632 0.3803432 0.5954675 0.4814228
##  [976,] 0.6738568 0.5654099 0.6551360 0.6618942 0.4572616 0.6339962 0.5383864
##  [977,] 0.5567039 0.5942799 0.7896624 0.8171499 0.6032132 0.7000149 0.6366382
##  [978,] 0.6097965 0.5812564 0.7333072 0.7527067 0.5368241 0.6705804 0.5928739
##  [979,] 0.6896050 0.5614089 0.6342013 0.6378583 0.4379217 0.6246904 0.5245670
##  [980,] 0.7212273 0.5531526 0.5901678 0.5883067 0.3994785 0.6054739 0.4961437
##  [981,] 0.7255334 0.5519999 0.5839707 0.5814713 0.3942903 0.6027934 0.4921942
##  [982,] 0.4306870 0.6276420 0.8950375 0.9266148 0.7581217 0.7707129 0.7397160
##  [983,] 0.8009874 0.5300941 0.4684240 0.4628202 0.3057668 0.5523806 0.4189401
##  [984,] 0.5758296 0.5895695 0.7702246 0.7951790 0.5792997 0.6894572 0.6209682
##  [985,] 0.6537057 0.5704521 0.6809387 0.6917862 0.4821595 0.6456965 0.5557957
##  [986,] 0.7104744 0.5559988 0.6054349 0.6053036 0.4124855 0.6120967 0.5059190
##  [987,] 0.8036852 0.5292302 0.4640826 0.4587468 0.3027008 0.5504250 0.4161472
##  [988,] 0.7702766 0.5394732 0.5169267 0.5103643 0.3411935 0.5738007 0.4497947
##  [989,] 0.7896059 0.5336626 0.4866045 0.4802123 0.3187864 0.5604915 0.4305689
##  [990,] 0.6004457 0.5835430 0.7437798 0.7648281 0.5485103 0.6758004 0.6006495
##  [991,] 0.6315002 0.5759369 0.7080823 0.7233820 0.5097492 0.6583687 0.5746756
##  [992,] 0.7768492 0.5375297 0.5066995 0.5000407 0.3335345 0.5693363 0.4433268
##  [993,] 0.5544434 0.5948393 0.7918967 0.8196519 0.6060373 0.7012612 0.6384851
##  [994,] 0.5545934 0.5948022 0.7917488 0.8194865 0.6058499 0.7011785 0.6383626
##  [995,] 0.7419699 0.5475236 0.5598913 0.5553008 0.3746050 0.5923990 0.4769219
##  [996,] 0.6823587 0.5632575 0.6439174 0.6489836 0.4468064 0.6289916 0.5309509
##  [997,] 0.7991367 0.5306826 0.4713954 0.4656260 0.3078746 0.5537145 0.4208478
##  [998,] 0.6650939 0.5676119 0.6664931 0.6750230 0.4680699 0.6391106 0.5459924
##  [999,] 0.7370893 0.5488662 0.5671107 0.5630791 0.3804301 0.5955137 0.4814907
## [1000,] 0.7809799 0.5362917 0.5002273 0.4935871 0.3287418 0.5664991 0.4392261
##              [,8]
##    [1,] 0.8453039
##    [2,] 0.6450350
##    [3,] 0.4492294
##    [4,] 0.3881618
##    [5,] 0.4712631
##    [6,] 0.5716393
##    [7,] 0.5453590
##    [8,] 0.9313461
##    [9,] 0.4494742
##   [10,] 0.2544504
##   [11,] 0.8981142
##   [12,] 0.8119009
##   [13,] 0.4370635
##   [14,] 0.7609582
##   [15,] 0.7044689
##   [16,] 0.6124616
##   [17,] 0.5295948
##   [18,] 0.4776852
##   [19,] 0.6436676
##   [20,] 0.2460203
##   [21,] 0.8603899
##   [22,] 0.2594853
##   [23,] 0.8934217
##   [24,] 0.7027824
##   [25,] 0.5910430
##   [26,] 0.3129448
##   [27,] 0.8438011
##   [28,] 0.9077336
##   [29,] 0.7874555
##   [30,] 0.9445381
##   [31,] 0.7034710
##   [32,] 0.8784316
##   [33,] 0.5396846
##   [34,] 0.6619630
##   [35,] 0.9424705
##   [36,] 0.8094493
##   [37,] 0.4698194
##   [38,] 0.3991208
##   [39,] 0.5300525
##   [40,] 0.8550325
##   [41,] 0.8023406
##   [42,] 0.6146823
##   [43,] 0.6929938
##   [44,] 0.3320741
##   [45,] 0.3805801
##   [46,] 0.7189885
##   [47,] 0.6728447
##   [48,] 0.6965327
##   [49,] 0.8498672
##   [50,] 0.5201281
##   [51,] 0.7357809
##   [52,] 0.7274952
##   [53,] 0.6386277
##   [54,] 0.6186015
##   [55,] 0.3726227
##   [56,] 0.9156510
##   [57,] 0.9360361
##   [58,] 0.3619456
##   [59,] 0.6692641
##   [60,] 0.6167919
##   [61,] 0.4768636
##   [62,] 0.4728597
##   [63,] 0.3481731
##   [64,] 0.5687840
##   [65,] 0.7658693
##   [66,] 0.3718070
##   [67,] 0.4917928
##   [68,] 0.3620200
##   [69,] 0.2536661
##   [70,] 0.8598973
##   [71,] 0.9391659
##   [72,] 0.7903382
##   [73,] 0.7696503
##   [74,] 0.5092845
##   [75,] 0.6519642
##   [76,] 0.3237091
##   [77,] 0.6841668
##   [78,] 0.8778134
##   [79,] 0.8195955
##   [80,] 0.5506047
##   [81,] 0.2955107
##   [82,] 0.7052602
##   [83,] 0.7487014
##   [84,] 0.9642954
##   [85,] 0.6661079
##   [86,] 0.3830645
##   [87,] 0.8594822
##   [88,] 0.8791920
##   [89,] 0.8039308
##   [90,] 0.7638170
##   [91,] 0.3202872
##   [92,] 0.8802892
##   [93,] 0.6730176
##   [94,] 0.5197485
##   [95,] 0.3467195
##   [96,] 0.6917785
##   [97,] 0.3609711
##   [98,] 0.8872935
##   [99,] 0.5530199
##  [100,] 0.3785885
##  [101,] 0.6749113
##  [102,] 0.4070856
##  [103,] 0.9619980
##  [104,] 0.5275547
##  [105,] 0.7336560
##  [106,] 0.7348133
##  [107,] 0.4994791
##  [108,] 0.5545309
##  [109,] 0.6963648
##  [110,] 0.7493916
##  [111,] 0.7284090
##  [112,] 0.9610510
##  [113,] 0.5826878
##  [114,] 0.8302149
##  [115,] 0.5006676
##  [116,] 0.7503190
##  [117,] 0.6872211
##  [118,] 0.5946307
##  [119,] 0.2792394
##  [120,] 0.4600792
##  [121,] 0.6673300
##  [122,] 0.8798122
##  [123,] 0.4751284
##  [124,] 0.8063449
##  [125,] 0.6087072
##  [126,] 0.5557915
##  [127,] 0.6591626
##  [128,] 0.7141036
##  [129,] 0.5532340
##  [130,] 0.6798020
##  [131,] 0.9216201
##  [132,] 0.4789628
##  [133,] 0.7318287
##  [134,] 0.7666107
##  [135,] 0.5993022
##  [136,] 0.9329908
##  [137,] 0.4032227
##  [138,] 0.5481888
##  [139,] 0.8130924
##  [140,] 0.8662706
##  [141,] 0.3935620
##  [142,] 0.6279240
##  [143,] 0.3839426
##  [144,] 0.8551997
##  [145,] 0.5171498
##  [146,] 0.6701470
##  [147,] 0.8506924
##  [148,] 0.5009142
##  [149,] 0.6962096
##  [150,] 0.7723246
##  [151,] 0.5218544
##  [152,] 0.9037461
##  [153,] 0.6004221
##  [154,] 0.8024706
##  [155,] 0.8479906
##  [156,] 0.9234731
##  [157,] 0.7474284
##  [158,] 0.6437404
##  [159,] 0.7314646
##  [160,] 0.8479221
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##  [782,] 0.9372893
##  [783,] 0.6288998
##  [784,] 0.2102629
##  [785,] 0.9220885
##  [786,] 0.4485977
##  [787,] 0.6746587
##  [788,] 0.8666252
##  [789,] 0.6701819
##  [790,] 0.7824220
##  [791,] 0.4837072
##  [792,] 0.9149213
##  [793,] 0.5338023
##  [794,] 0.5808481
##  [795,] 0.6317019
##  [796,] 0.7005075
##  [797,] 0.4251428
##  [798,] 0.5843561
##  [799,] 0.8339739
##  [800,] 0.5085965
##  [801,] 0.3729283
##  [802,] 0.8613699
##  [803,] 0.4317980
##  [804,] 0.4339386
##  [805,] 0.9535583
##  [806,] 0.5802885
##  [807,] 0.4018848
##  [808,] 0.7978645
##  [809,] 0.4238408
##  [810,] 0.7302464
##  [811,] 0.6540781
##  [812,] 0.8076411
##  [813,] 0.4874240
##  [814,] 0.5885144
##  [815,] 0.8754949
##  [816,] 0.6999438
##  [817,] 0.8964531
##  [818,] 0.4453567
##  [819,] 0.5848330
##  [820,] 0.8682311
##  [821,] 0.7252486
##  [822,] 0.8027593
##  [823,] 0.7025282
##  [824,] 0.7768030
##  [825,] 0.6535163
##  [826,] 0.8507780
##  [827,] 0.5898365
##  [828,] 0.7540543
##  [829,] 0.8136397
##  [830,] 0.7947795
##  [831,] 0.6228980
##  [832,] 0.6894217
##  [833,] 0.7444225
##  [834,] 0.5645624
##  [835,] 0.9079388
##  [836,] 0.2871631
##  [837,] 0.8452095
##  [838,] 0.8585231
##  [839,] 0.6261707
##  [840,] 0.4025443
##  [841,] 0.9783618
##  [842,] 0.4788576
##  [843,] 0.9248139
##  [844,] 0.6230380
##  [845,] 0.8882393
##  [846,] 0.6967335
##  [847,] 0.6462507
##  [848,] 0.5250404
##  [849,] 0.6934571
##  [850,] 0.9026136
##  [851,] 0.4662504
##  [852,] 0.8684713
##  [853,] 0.8250698
##  [854,] 0.4623998
##  [855,] 0.6387283
##  [856,] 0.4628609
##  [857,] 0.6020022
##  [858,] 0.7040384
##  [859,] 0.6414439
##  [860,] 0.9838531
##  [861,] 0.7038383
##  [862,] 0.7541162
##  [863,] 0.9151487
##  [864,] 0.4115157
##  [865,] 0.3980178
##  [866,] 0.5452772
##  [867,] 0.2987771
##  [868,] 0.6747610
##  [869,] 0.5816337
##  [870,] 0.6908891
##  [871,] 0.8399659
##  [872,] 0.2323357
##  [873,] 0.5339284
##  [874,] 0.6725953
##  [875,] 0.9425766
##  [876,] 0.7319543
##  [877,] 0.7842662
##  [878,] 0.3521430
##  [879,] 0.8249632
##  [880,] 0.6858191
##  [881,] 0.8018528
##  [882,] 0.7682825
##  [883,] 0.9471843
##  [884,] 0.4701498
##  [885,] 0.8305096
##  [886,] 0.5915404
##  [887,] 0.7626955
##  [888,] 0.9414471
##  [889,] 0.6497063
##  [890,] 0.8542799
##  [891,] 0.8363274
##  [892,] 0.8619183
##  [893,] 0.7667780
##  [894,] 0.8982728
##  [895,] 0.8302507
##  [896,] 0.6653241
##  [897,] 0.5193641
##  [898,] 0.5488106
##  [899,] 0.9736921
##  [900,] 0.6958562
##  [901,] 0.8474424
##  [902,] 0.8659302
##  [903,] 0.9565773
##  [904,] 0.9527989
##  [905,] 0.7404580
##  [906,] 0.6684819
##  [907,] 0.5672398
##  [908,] 0.5853600
##  [909,] 0.9480684
##  [910,] 0.9360197
##  [911,] 0.8864445
##  [912,] 0.5452405
##  [913,] 0.9308340
##  [914,] 0.7028132
##  [915,] 0.3391933
##  [916,] 0.5560819
##  [917,] 0.3526551
##  [918,] 0.6157794
##  [919,] 0.9056702
##  [920,] 0.9666587
##  [921,] 0.4404242
##  [922,] 0.4200393
##  [923,] 0.5936145
##  [924,] 0.6328525
##  [925,] 0.9072199
##  [926,] 0.3507242
##  [927,] 0.8175863
##  [928,] 0.6255581
##  [929,] 0.6824203
##  [930,] 0.6942386
##  [931,] 0.8773100
##  [932,] 0.6631633
##  [933,] 0.6116375
##  [934,] 0.7481974
##  [935,] 0.6279631
##  [936,] 0.3785090
##  [937,] 0.8045964
##  [938,] 0.5404223
##  [939,] 0.6566852
##  [940,] 0.9358075
##  [941,] 0.7217884
##  [942,] 0.4025060
##  [943,] 0.7929323
##  [944,] 0.8894290
##  [945,] 0.8469710
##  [946,] 0.4151869
##  [947,] 0.4090536
##  [948,] 0.7750108
##  [949,] 0.7421653
##  [950,] 0.6121647
##  [951,] 0.7211114
##  [952,] 0.6850097
##  [953,] 0.7451593
##  [954,] 0.6834277
##  [955,] 0.6915333
##  [956,] 0.9444225
##  [957,] 0.2725794
##  [958,] 0.5040854
##  [959,] 0.9845200
##  [960,] 0.4364684
##  [961,] 0.3701395
##  [962,] 0.8799199
##  [963,] 0.7303296
##  [964,] 0.9156900
##  [965,] 0.8695924
##  [966,] 0.8020992
##  [967,] 0.3889282
##  [968,] 0.3849929
##  [969,] 0.4805024
##  [970,] 0.6814071
##  [971,] 0.4604759
##  [972,] 0.7769784
##  [973,] 0.5956906
##  [974,] 0.6567942
##  [975,] 0.7814941
##  [976,] 0.6566712
##  [977,] 0.4202828
##  [978,] 0.5229203
##  [979,] 0.6891660
##  [980,] 0.7518056
##  [981,] 0.7599717
##  [982,] 0.2466676
##  [983,] 0.8828336
##  [984,] 0.4557213
##  [985,] 0.6144524
##  [986,] 0.7309957
##  [987,] 0.8864128
##  [988,] 0.8379156
##  [989,] 0.8670733
##  [990,] 0.5039697
##  [991,] 0.5678206
##  [992,] 0.8481607
##  [993,] 0.4162302
##  [994,] 0.4164982
##  [995,] 0.7901514
##  [996,] 0.6742915
##  [997,] 0.8803435
##  [998,] 0.6383677
##  [999,] 0.7813620
## [1000,] 0.8544266

# Olasılık matrisinin boyutları alınır
# Satırlar bireyleri, sütunlar maddeleri temsil eder
d <- dim(i)

# Olasılık matrisiyle aynı boyutta rastgele değerler üretilir
# Bu değerler 0 ile 1 arasında uniform dağılımdan gelir
u <- runif(d[1] * d[2])

# Üretilen rastgele değerler, olasılık matrisiyle aynı boyuta getirilir
dim(u) <- d

# Eğer doğru yanıtlama olasılığı rastgele değerden büyükse yanıt 1,
# değilse 0 olarak kodlanır
head(ifelse(i > u, 1, 0))

## logical(0)

Bu kodda irtoys paketinin sim() fonksiyonu kullanılarak 3PL modele göre madde yanıt verisi üretildi. Daha önce oluşturulan madde parametreleri (maddepar) ve birey yetenek değerleri (yetenek) kullanılarak her bireyin maddelere verdiği 0-1 biçimindeki yanıtlar simüle edildi.

Madde tepki fonksiyonları hesaplandı, rastgele olasılık değerleriyle karşılaştırılarak bireylerin doğru (1) veya yanlış (0) yanıtları oluşturuldıu.

3 Parametreli Lojistik Model (3PL) ile Fonksiyon Kullanarak Veri Üretimi

# 3 Parametreli Lojistik Model (3PL) ile Fonksiyon Kullanarak Veri Üretimi

veri_uretimi <- function(maddesay, bireysay, seed){

  set.seed(seed)

  # Madde parametreleri üretilir
  maddepar <- cbind(
    rnorm(maddesay, mean = 1.13, sd = 0.25) * 1.702,
    rnorm(maddesay, mean = 0.30, sd = 0.50) * 1.702,
    rnorm(maddesay, mean = 0.16, sd = 0.05)
  )

  # Yetenek parametreleri üretilir
  yetenek <- rnorm(bireysay, 0, 1)

  # 3PL modele göre cevap verisi üretilir
  cevaplar <- irtoys::sim(ip = maddepar, x = yetenek)

  # Maddelere isim verilir
  colnames(cevaplar) <- paste0("madde_", 1:maddesay)

  # Çıktılar liste halinde kaydedilir
  veri <- list(
    maddepar = maddepar,
    yetenek = yetenek,
    seed = seed,
    cevaplar = cevaplar
  )

  return(veri)
}

# Fonksiyon çalıştırılır
veri_1 <- veri_uretimi(
  maddesay = 8,
  bireysay = 1000,
  seed = 41
)

# Üretilen cevap verileri görüntülenir
veri_1$cevaplar

##         madde_1 madde_2 madde_3 madde_4 madde_5 madde_6 madde_7 madde_8
##    [1,]       0       1       1       1       0       1       1       0
##    [2,]       1       0       1       1       1       1       1       0
##    [3,]       0       0       1       0       0       0       1       0
##    [4,]       1       0       1       0       0       1       0       0
##    [5,]       0       0       1       1       0       0       1       0
##    [6,]       0       0       0       0       0       0       0       0
##    [7,]       0       0       1       0       1       1       1       1
##    [8,]       0       0       0       1       0       1       0       0
##    [9,]       1       0       1       1       0       0       1       0
##   [10,]       1       0       0       1       0       1       0       1
##   [11,]       0       0       0       0       1       0       0       0
##   [12,]       1       0       0       0       0       0       0       0
##   [13,]       0       1       1       1       0       1       0       1
##   [14,]       1       0       1       1       1       1       1       1
##   [15,]       0       0       1       1       0       1       1       0
##   [16,]       0       0       1       0       0       1       0       0
##   [17,]       0       0       0       0       0       0       0       0
##   [18,]       1       0       1       1       0       1       1       0
##   [19,]       1       0       1       1       0       1       0       1
##   [20,]       1       0       1       1       0       1       1       1
##   [21,]       1       0       1       1       1       1       1       0
##   [22,]       0       0       0       0       0       1       0       0
##   [23,]       1       0       1       0       0       1       0       0
##   [24,]       1       0       1       1       0       1       1       0
##   [25,]       0       0       1       1       0       1       0       0
##   [26,]       0       0       1       0       0       1       1       1
##   [27,]       0       0       1       1       0       0       0       0
##   [28,]       0       0       1       1       0       0       1       0
##   [29,]       0       0       1       0       0       1       0       1
##   [30,]       0       0       1       1       0       1       1       0
##   [31,]       1       1       1       1       0       1       1       1
##   [32,]       1       1       1       0       0       1       0       0
##   [33,]       0       0       0       0       0       0       0       0
##   [34,]       0       0       1       1       1       1       1       0
##   [35,]       0       0       1       1       0       1       1       1
##   [36,]       0       0       1       1       0       0       0       1
##   [37,]       0       1       1       1       0       1       1       1
##   [38,]       0       1       1       1       0       1       0       1
##   [39,]       0       0       1       1       1       1       1       0
##   [40,]       0       0       1       1       0       1       0       1
##   [41,]       1       0       1       1       1       1       0       1
##   [42,]       1       0       1       1       0       1       1       0
##   [43,]       1       0       1       0       1       1       0       1
##   [44,]       1       0       1       1       0       1       1       1
##   [45,]       1       1       1       1       1       1       1       1
##   [46,]       1       1       1       1       1       1       0       1
##   [47,]       0       0       0       0       0       0       0       0
##   [48,]       0       0       0       0       0       0       0       1
##   [49,]       0       1       1       1       0       0       0       1
##   [50,]       1       0       1       1       1       1       1       0
##   [51,]       0       1       1       0       0       1       1       1
##   [52,]       1       1       1       1       1       1       1       1
##   [53,]       1       1       1       0       0       0       0       0
##   [54,]       1       0       0       0       0       0       0       0
##   [55,]       1       0       1       0       0       0       0       0
##   [56,]       0       0       1       1       0       0       0       0
##   [57,]       1       0       1       1       1       1       1       0
##   [58,]       0       1       1       0       0       0       1       0
##   [59,]       1       0       1       1       0       0       0       1
##   [60,]       0       1       1       0       0       0       0       1
##   [61,]       1       0       1       1       1       1       0       0
##   [62,]       0       0       1       1       0       1       1       1
##   [63,]       1       0       0       0       0       0       0       0
##   [64,]       0       1       0       0       0       0       0       1
##   [65,]       1       1       0       1       1       0       1       0
##   [66,]       0       0       1       1       0       0       0       1
##   [67,]       0       0       1       1       1       1       1       1
##   [68,]       0       0       0       0       0       0       0       0
##   [69,]       1       0       1       1       0       1       0       1
##   [70,]       0       0       1       1       0       1       1       1
##   [71,]       1       0       1       1       0       1       1       1
##   [72,]       1       0       1       1       0       1       0       0
##   [73,]       1       1       1       1       1       1       0       0
##   [74,]       0       0       0       0       0       1       0       0
##   [75,]       1       0       1       1       0       1       1       0
##   [76,]       1       0       1       1       1       0       1       1
##   [77,]       0       0       1       1       0       1       0       0
##   [78,]       0       1       1       1       0       1       1       1
##   [79,]       1       0       0       0       0       1       0       1
##   [80,]       0       1       0       1       0       1       1       1
##   [81,]       0       0       1       1       0       1       0       0
##   [82,]       1       1       1       0       0       1       1       0
##   [83,]       0       0       1       1       1       1       1       0
##   [84,]       0       1       1       1       0       1       1       1
##   [85,]       0       1       1       1       0       1       1       1
##   [86,]       0       0       0       0       0       0       0       0
##   [87,]       1       0       1       0       0       0       1       0
##   [88,]       0       0       0       1       0       0       0       1
##   [89,]       1       0       1       1       0       1       0       1
##   [90,]       0       0       0       0       0       1       1       0
##   [91,]       0       0       1       1       1       1       1       1
##   [92,]       0       0       1       0       0       0       1       0
##   [93,]       0       1       0       1       1       1       0       0
##   [94,]       0       0       1       1       0       1       1       1
##   [95,]       0       0       1       1       0       1       1       1
##   [96,]       1       0       1       1       0       1       1       0
##   [97,]       0       0       1       1       1       0       0       1
##   [98,]       1       0       0       0       0       1       0       0
##   [99,]       0       0       1       1       0       1       0       0
##  [100,]       1       0       0       0       0       1       0       1
##  [101,]       1       0       1       1       0       1       1       1
##  [102,]       0       0       1       1       0       1       0       0
##  [103,]       1       0       1       1       0       0       1       0
##  [104,]       0       0       1       1       0       1       0       1
##  [105,]       0       0       1       1       0       1       1       0
##  [106,]       0       0       1       0       0       0       1       0
##  [107,]       1       0       1       0       0       0       0       0
##  [108,]       1       0       1       1       0       1       1       0
##  [109,]       1       0       1       0       0       1       1       0
##  [110,]       1       0       1       1       0       1       1       1
##  [111,]       1       0       0       1       0       1       1       1
##  [112,]       0       0       0       0       0       1       0       0
##  [113,]       1       0       1       1       1       1       1       0
##  [114,]       0       0       1       1       0       0       1       1
##  [115,]       1       0       1       0       0       0       0       0
##  [116,]       0       0       0       0       1       0       0       1
##  [117,]       1       0       1       1       1       1       1       1
##  [118,]       1       1       0       1       1       0       1       0
##  [119,]       1       0       1       1       0       1       0       0
##  [120,]       0       0       0       1       0       0       0       0
##  [121,]       0       1       1       1       0       1       0       0
##  [122,]       0       0       1       0       0       0       0       0
##  [123,]       0       0       0       1       0       1       0       1
##  [124,]       0       0       1       1       0       1       1       1
##  [125,]       0       0       0       1       0       0       0       0
##  [126,]       1       0       1       1       0       0       0       0
##  [127,]       0       0       1       1       0       1       1       0
##  [128,]       1       0       0       0       0       0       0       0
##  [129,]       0       1       1       0       1       1       0       0
##  [130,]       0       0       1       1       0       1       0       0
##  [131,]       0       0       0       1       0       0       0       0
##  [132,]       0       0       0       0       0       0       1       0
##  [133,]       1       0       1       1       0       1       0       0
##  [134,]       0       1       1       0       0       0       0       1
##  [135,]       1       0       1       0       0       1       0       1
##  [136,]       1       1       1       0       0       0       0       0
##  [137,]       1       0       1       1       0       0       0       0
##  [138,]       1       0       1       1       0       1       1       1
##  [139,]       1       0       1       1       0       0       0       0
##  [140,]       0       0       0       1       0       1       0       0
##  [141,]       0       0       1       1       0       1       0       1
##  [142,]       1       1       0       0       0       0       0       0
##  [143,]       1       0       1       0       0       0       0       0
##  [144,]       1       1       1       1       0       0       1       0
##  [145,]       0       1       1       0       0       1       0       0
##  [146,]       0       1       0       1       0       1       0       0
##  [147,]       0       0       0       0       0       0       0       0
##  [148,]       0       0       0       1       0       1       0       0
##  [149,]       0       0       1       1       0       1       0       0
##  [150,]       0       0       1       0       0       0       1       0
##  [151,]       1       0       0       0       0       0       0       0
##  [152,]       0       0       1       0       0       1       0       0
##  [153,]       0       0       1       0       0       1       0       1
##  [154,]       1       0       1       1       1       1       1       0
##  [155,]       1       0       1       0       0       0       0       0
##  [156,]       0       0       1       1       0       0       1       1
##  [157,]       0       1       1       1       0       0       0       1
##  [158,]       0       0       1       1       0       1       0       0
##  [159,]       0       0       1       1       0       0       1       0
##  [160,]       0       0       1       1       1       1       1       0
##  [161,]       1       0       1       1       0       1       1       1
##  [162,]       0       0       1       0       0       0       1       0
##  [163,]       0       1       1       1       1       1       1       1
##  [164,]       0       1       1       1       1       1       1       1
##  [165,]       0       0       1       0       0       0       0       0
##  [166,]       0       0       1       0       0       1       0       0
##  [167,]       1       1       1       1       1       1       1       1
##  [168,]       1       0       0       0       0       1       0       1
##  [169,]       1       0       1       1       1       1       1       0
##  [170,]       0       0       0       1       0       1       0       0
##  [171,]       1       0       1       1       1       0       0       0
##  [172,]       1       0       1       1       1       1       1       1
##  [173,]       0       0       1       0       0       0       1       0
##  [174,]       0       0       1       1       1       1       0       0
##  [175,]       0       0       0       0       0       1       0       0
##  [176,]       1       1       1       1       0       0       0       1
##  [177,]       0       1       1       0       0       1       0       1
##  [178,]       0       0       0       0       0       0       1       0
##  [179,]       0       0       1       1       1       1       1       0
##  [180,]       0       0       1       0       0       0       1       0
##  [181,]       0       0       1       0       0       0       0       1
##  [182,]       1       0       1       1       1       1       1       0
##  [183,]       0       0       1       1       0       1       1       1
##  [184,]       0       0       1       1       0       0       1       1
##  [185,]       1       0       0       1       0       1       0       0
##  [186,]       1       0       1       1       0       0       1       0
##  [187,]       0       0       1       1       0       0       0       0
##  [188,]       1       1       1       0       0       0       0       1
##  [189,]       0       0       0       0       0       1       0       0
##  [190,]       0       0       0       1       0       1       0       1
##  [191,]       1       0       1       0       0       1       0       0
##  [192,]       0       0       1       0       0       1       0       0
##  [193,]       0       0       0       0       0       0       0       0
##  [194,]       0       0       1       1       0       1       0       0
##  [195,]       0       0       1       1       0       0       0       0
##  [196,]       0       0       1       1       0       1       0       1
##  [197,]       1       0       1       1       1       1       1       0
##  [198,]       1       0       1       1       0       0       1       0
##  [199,]       0       1       1       1       1       1       1       1
##  [200,]       0       0       1       1       0       1       1       1
##  [201,]       0       0       1       1       1       1       1       0
##  [202,]       1       0       0       0       0       0       0       0
##  [203,]       1       0       1       0       0       0       0       1
##  [204,]       0       0       0       1       0       1       0       0
##  [205,]       0       0       0       1       0       1       0       0
##  [206,]       0       0       0       0       0       0       0       0
##  [207,]       0       1       1       1       0       1       1       1
##  [208,]       1       0       1       1       0       1       0       0
##  [209,]       0       0       1       0       1       1       1       0
##  [210,]       0       0       0       0       0       0       0       0
##  [211,]       0       0       1       1       1       0       1       1
##  [212,]       0       0       1       0       0       1       0       1
##  [213,]       1       0       1       1       1       1       1       1
##  [214,]       1       0       1       1       1       1       0       1
##  [215,]       0       1       1       0       0       1       0       1
##  [216,]       0       0       0       0       0       0       0       0
##  [217,]       1       0       1       0       1       1       1       1
##  [218,]       0       0       1       1       0       0       0       1
##  [219,]       0       0       1       1       0       1       1       0
##  [220,]       1       1       1       1       0       0       0       1
##  [221,]       1       0       1       1       1       1       1       0
##  [222,]       0       0       1       1       1       1       1       1
##  [223,]       1       0       1       1       0       0       0       1
##  [224,]       0       1       0       0       0       0       0       1
##  [225,]       0       0       0       0       0       1       0       1
##  [226,]       0       0       0       0       0       0       0       0
##  [227,]       0       1       1       0       0       0       0       0
##  [228,]       0       0       1       0       0       1       0       0
##  [229,]       1       0       0       0       0       0       1       1
##  [230,]       0       0       0       0       0       0       0       0
##  [231,]       0       0       1       1       1       1       1       1
##  [232,]       1       0       1       1       1       1       1       1
##  [233,]       0       0       1       1       0       0       0       1
##  [234,]       0       0       0       0       0       0       0       0
##  [235,]       1       0       1       1       1       1       1       1
##  [236,]       1       0       1       1       0       0       1       1
##  [237,]       0       0       0       0       1       1       0       0
##  [238,]       0       0       1       0       0       1       0       0
##  [239,]       0       0       1       1       1       1       1       1
##  [240,]       1       0       0       0       0       0       0       1
##  [241,]       0       0       1       1       0       0       0       0
##  [242,]       0       0       1       1       0       0       1       0
##  [243,]       1       0       1       0       0       0       1       0
##  [244,]       0       0       1       1       0       0       0       0
##  [245,]       0       1       0       1       1       0       1       0
##  [246,]       0       0       1       1       0       1       0       0
##  [247,]       0       1       1       1       0       1       0       0
##  [248,]       0       0       0       0       0       0       0       0
##  [249,]       1       1       1       1       1       1       0       1
##  [250,]       0       0       1       1       0       1       0       0
##  [251,]       1       0       1       1       0       1       1       1
##  [252,]       0       1       1       1       0       0       1       0
##  [253,]       0       1       1       1       0       0       1       1
##  [254,]       0       0       1       1       1       1       0       1
##  [255,]       0       0       0       0       0       1       0       0
##  [256,]       1       1       0       0       0       1       0       0
##  [257,]       0       0       1       1       0       1       0       0
##  [258,]       0       0       1       0       0       1       0       1
##  [259,]       0       0       0       1       0       0       1       1
##  [260,]       1       1       1       1       0       1       0       0
##  [261,]       0       1       1       1       1       1       1       0
##  [262,]       0       0       0       1       0       1       1       1
##  [263,]       0       0       1       1       0       1       1       1
##  [264,]       0       1       1       1       0       1       1       1
##  [265,]       0       0       0       0       0       1       0       0
##  [266,]       1       1       0       0       0       1       0       0
##  [267,]       0       0       0       0       0       1       0       1
##  [268,]       1       0       1       0       0       0       0       1
##  [269,]       0       0       1       1       1       1       1       1
##  [270,]       1       1       0       0       1       1       1       1
##  [271,]       1       1       1       1       1       1       1       1
##  [272,]       1       0       0       0       0       1       1       0
##  [273,]       1       0       1       0       0       1       1       1
##  [274,]       0       0       1       1       0       1       0       0
##  [275,]       0       0       1       1       0       1       1       0
##  [276,]       0       0       1       0       0       1       0       0
##  [277,]       0       0       1       1       0       1       0       1
##  [278,]       0       0       1       0       1       1       1       0
##  [279,]       0       0       0       1       0       1       0       1
##  [280,]       1       1       0       0       0       1       0       0
##  [281,]       0       0       0       1       0       0       0       1
##  [282,]       1       0       0       1       0       0       1       0
##  [283,]       1       0       1       1       0       1       0       0
##  [284,]       0       0       0       1       1       0       0       0
##  [285,]       1       0       0       1       0       1       0       1
##  [286,]       0       0       1       1       0       1       0       0
##  [287,]       1       0       0       1       0       0       0       0
##  [288,]       0       0       0       0       0       1       0       0
##  [289,]       1       1       1       0       0       1       0       1
##  [290,]       1       0       1       1       1       1       1       0
##  [291,]       0       0       1       0       0       0       1       0
##  [292,]       1       0       0       1       0       1       0       1
##  [293,]       0       0       0       0       0       0       0       0
##  [294,]       1       0       1       1       0       1       1       1
##  [295,]       0       0       0       0       0       0       0       1
##  [296,]       0       0       1       0       1       1       0       0
##  [297,]       1       0       0       1       1       0       0       1
##  [298,]       1       0       1       0       1       1       0       0
##  [299,]       0       0       0       0       0       1       0       0
##  [300,]       0       1       1       0       1       0       0       0
##  [301,]       0       1       0       0       0       0       0       0
##  [302,]       0       0       0       0       0       0       1       0
##  [303,]       1       0       1       1       1       0       0       0
##  [304,]       0       1       1       1       0       1       1       0
##  [305,]       1       0       1       1       1       1       1       1
##  [306,]       0       0       0       0       0       1       1       1
##  [307,]       0       0       0       0       0       0       0       0
##  [308,]       0       0       1       1       0       1       1       1
##  [309,]       0       0       1       1       0       1       1       1
##  [310,]       1       0       1       1       0       1       1       1
##  [311,]       1       0       1       1       0       0       0       0
##  [312,]       1       0       1       1       0       1       0       0
##  [313,]       0       0       0       0       0       1       0       1
##  [314,]       0       0       1       1       0       1       0       0
##  [315,]       0       0       0       1       0       1       1       0
##  [316,]       0       0       1       0       1       1       1       0
##  [317,]       1       0       1       0       0       1       1       0
##  [318,]       0       0       1       0       0       0       1       1
##  [319,]       0       0       0       0       1       0       0       1
##  [320,]       0       0       0       0       0       0       0       0
##  [321,]       0       0       1       1       0       1       1       0
##  [322,]       0       0       0       0       0       1       1       1
##  [323,]       0       1       1       1       0       0       0       0
##  [324,]       0       0       1       0       0       1       0       0
##  [325,]       0       0       0       0       0       1       0       0
##  [326,]       0       0       1       1       1       1       0       0
##  [327,]       1       1       1       1       0       1       1       0
##  [328,]       0       0       1       0       0       0       1       1
##  [329,]       0       0       1       1       0       1       1       1
##  [330,]       1       0       1       1       0       1       1       1
##  [331,]       0       1       1       1       0       1       1       0
##  [332,]       1       0       1       1       0       1       0       0
##  [333,]       1       0       1       1       0       0       1       1
##  [334,]       0       0       0       1       0       1       0       0
##  [335,]       1       0       1       1       0       0       0       0
##  [336,]       1       1       1       1       0       1       1       1
##  [337,]       1       1       1       1       1       1       1       1
##  [338,]       0       1       1       1       0       0       1       1
##  [339,]       0       0       0       0       0       0       0       0
##  [340,]       0       0       1       1       0       1       0       1
##  [341,]       1       0       1       1       0       0       0       0
##  [342,]       0       1       1       1       1       1       0       1
##  [343,]       1       0       1       1       0       1       1       1
##  [344,]       1       0       0       1       1       1       0       0
##  [345,]       0       0       0       1       0       0       0       0
##  [346,]       1       1       0       0       1       0       0       0
##  [347,]       1       0       0       0       0       0       0       0
##  [348,]       1       0       1       1       1       0       1       0
##  [349,]       0       0       1       1       0       1       0       1
##  [350,]       1       0       1       0       0       1       0       1
##  [351,]       0       0       1       1       0       1       1       1
##  [352,]       0       0       1       1       1       0       0       1
##  [353,]       0       0       1       0       0       0       0       0
##  [354,]       1       0       1       1       1       1       1       1
##  [355,]       0       0       1       1       0       1       1       0
##  [356,]       1       1       1       1       0       1       1       0
##  [357,]       0       0       1       1       1       1       1       0
##  [358,]       0       0       0       0       0       0       0       0
##  [359,]       1       0       1       0       1       0       1       1
##  [360,]       0       0       1       1       0       1       0       0
##  [361,]       1       1       1       1       1       1       0       0
##  [362,]       1       0       0       0       0       0       0       0
##  [363,]       1       0       1       1       1       1       1       0
##  [364,]       1       1       1       1       1       1       0       1
##  [365,]       0       0       1       0       0       1       0       1
##  [366,]       0       0       1       0       0       1       0       0
##  [367,]       0       1       0       0       0       1       0       1
##  [368,]       0       0       1       0       0       1       1       0
##  [369,]       0       1       1       1       0       1       0       1
##  [370,]       0       0       1       0       0       1       0       0
##  [371,]       0       0       0       0       1       1       0       0
##  [372,]       0       0       1       1       1       1       1       1
##  [373,]       1       0       1       1       0       1       1       0
##  [374,]       0       0       1       1       0       1       1       0
##  [375,]       0       1       1       1       0       1       1       1
##  [376,]       0       0       1       1       1       1       0       0
##  [377,]       0       0       1       1       0       0       0       1
##  [378,]       0       0       0       0       0       1       0       0
##  [379,]       0       0       1       0       1       0       0       0
##  [380,]       1       0       1       1       0       1       0       0
##  [381,]       1       0       1       1       0       0       1       1
##  [382,]       0       0       0       0       0       0       0       0
##  [383,]       0       0       1       0       0       1       0       0
##  [384,]       0       0       1       1       1       1       1       1
##  [385,]       1       0       0       1       0       0       1       0
##  [386,]       1       0       1       1       0       1       1       0
##  [387,]       1       0       1       1       1       1       1       0
##  [388,]       0       1       1       1       0       1       0       1
##  [389,]       0       0       0       0       0       1       0       0
##  [390,]       0       0       1       1       0       0       1       1
##  [391,]       1       0       0       0       0       1       1       1
##  [392,]       1       1       1       0       0       1       1       0
##  [393,]       0       0       1       1       1       1       0       1
##  [394,]       0       0       1       1       0       1       0       0
##  [395,]       0       0       0       1       0       1       0       0
##  [396,]       0       0       0       1       0       0       0       0
##  [397,]       0       1       1       1       0       0       0       0
##  [398,]       0       0       1       1       0       1       1       1
##  [399,]       0       0       0       1       0       1       0       1
##  [400,]       0       0       1       1       0       1       0       1
##  [401,]       1       1       1       1       1       1       1       0
##  [402,]       0       1       0       0       0       0       1       0
##  [403,]       1       1       1       1       0       1       1       1
##  [404,]       0       0       1       0       0       1       0       0
##  [405,]       0       0       0       1       0       0       1       0
##  [406,]       0       0       1       0       0       1       0       0
##  [407,]       0       0       0       0       0       0       0       0
##  [408,]       0       0       1       1       1       1       1       0
##  [409,]       0       1       1       1       0       1       1       1
##  [410,]       0       1       0       1       0       0       0       0
##  [411,]       0       1       1       0       0       1       1       0
##  [412,]       0       1       1       0       0       0       0       1
##  [413,]       0       1       0       0       0       0       0       0
##  [414,]       0       0       1       0       0       0       0       0
##  [415,]       0       0       1       1       1       1       1       0
##  [416,]       0       0       1       1       0       1       1       0
##  [417,]       0       0       1       1       0       1       1       1
##  [418,]       0       0       0       0       0       0       0       0
##  [419,]       0       0       0       0       0       0       1       0
##  [420,]       0       1       1       1       0       0       0       0
##  [421,]       0       0       1       1       0       1       0       0
##  [422,]       0       0       0       0       0       0       1       0
##  [423,]       0       0       1       1       0       0       0       0
##  [424,]       0       0       0       1       0       0       0       0
##  [425,]       0       1       1       1       0       1       1       1
##  [426,]       0       0       0       1       0       1       1       0
##  [427,]       0       0       1       1       0       1       1       1
##  [428,]       0       0       1       0       0       1       0       1
##  [429,]       0       1       1       1       1       1       0       1
##  [430,]       0       0       1       0       0       0       0       1
##  [431,]       1       1       1       1       1       1       1       1
##  [432,]       0       0       1       1       0       0       0       0
##  [433,]       0       1       0       0       0       0       1       0
##  [434,]       0       1       1       1       0       0       1       0
##  [435,]       0       0       0       0       0       1       0       1
##  [436,]       1       0       1       1       0       0       1       0
##  [437,]       0       0       0       1       0       1       0       0
##  [438,]       0       0       0       1       0       1       0       1
##  [439,]       1       0       1       0       0       1       0       0
##  [440,]       1       1       1       0       0       1       0       1
##  [441,]       1       0       1       1       0       1       0       0
##  [442,]       0       1       1       0       0       0       1       0
##  [443,]       1       1       1       1       0       1       0       0
##  [444,]       0       0       1       1       1       0       1       1
##  [445,]       0       1       1       1       0       1       1       0
##  [446,]       1       0       1       1       1       1       1       1
##  [447,]       1       1       1       0       0       1       1       1
##  [448,]       1       0       0       0       0       1       1       0
##  [449,]       1       0       1       1       0       1       0       1
##  [450,]       0       0       1       0       0       0       0       0
##  [451,]       0       0       1       1       1       1       0       0
##  [452,]       1       0       1       0       0       1       0       0
##  [453,]       0       1       0       1       0       1       0       1
##  [454,]       0       0       1       0       0       1       0       0
##  [455,]       0       0       0       0       0       0       1       0
##  [456,]       0       0       1       1       0       1       1       1
##  [457,]       0       0       1       1       0       1       0       1
##  [458,]       0       0       1       1       0       1       1       1
##  [459,]       0       0       0       1       0       1       0       1
##  [460,]       1       1       0       1       0       0       0       0
##  [461,]       0       1       1       0       1       0       0       0
##  [462,]       0       0       1       1       1       0       0       1
##  [463,]       0       0       1       1       0       1       0       1
##  [464,]       1       1       1       1       1       1       1       1
##  [465,]       0       0       0       0       0       0       0       0
##  [466,]       0       0       1       0       0       0       0       1
##  [467,]       0       0       0       0       0       0       0       0
##  [468,]       0       0       1       0       0       1       0       0
##  [469,]       0       0       1       1       1       0       0       0
##  [470,]       0       1       1       0       0       0       0       0
##  [471,]       0       0       0       0       0       1       0       0
##  [472,]       0       0       1       1       0       1       1       1
##  [473,]       1       0       0       0       1       0       0       0
##  [474,]       1       0       0       1       0       1       0       0
##  [475,]       0       0       1       0       0       1       0       0
##  [476,]       1       1       1       1       1       1       1       1
##  [477,]       1       0       1       1       1       0       1       0
##  [478,]       1       1       0       0       0       1       1       1
##  [479,]       1       1       1       1       1       0       0       0
##  [480,]       0       0       1       1       0       0       0       1
##  [481,]       0       0       0       0       0       0       0       0
##  [482,]       0       0       1       1       0       0       0       1
##  [483,]       0       1       1       0       1       1       1       1
##  [484,]       0       0       1       0       0       1       0       0
##  [485,]       0       0       1       1       0       1       0       0
##  [486,]       0       0       0       0       0       1       0       1
##  [487,]       0       0       1       1       1       1       1       1
##  [488,]       0       0       1       1       1       1       1       0
##  [489,]       1       1       1       1       0       1       1       0
##  [490,]       0       0       1       0       0       0       0       0
##  [491,]       0       0       1       1       1       1       0       0
##  [492,]       1       1       1       1       0       0       1       0
##  [493,]       0       0       1       0       0       0       0       0
##  [494,]       0       0       1       1       0       1       0       1
##  [495,]       0       0       1       1       0       1       1       1
##  [496,]       0       0       1       0       0       0       0       0
##  [497,]       0       1       1       1       0       0       0       1
##  [498,]       0       0       1       1       0       1       0       0
##  [499,]       0       0       1       0       0       0       0       0
##  [500,]       0       0       0       1       0       0       1       0
##  [501,]       0       0       1       1       0       0       0       0
##  [502,]       0       0       1       0       0       0       0       0
##  [503,]       0       0       1       1       1       1       1       1
##  [504,]       0       0       0       1       1       1       1       0
##  [505,]       0       0       1       1       0       0       0       0
##  [506,]       1       0       1       1       0       0       0       0
##  [507,]       0       1       1       1       1       0       0       0
##  [508,]       1       1       1       1       1       1       1       1
##  [509,]       0       0       1       1       0       1       0       0
##  [510,]       1       0       0       1       1       0       0       0
##  [511,]       0       0       1       0       0       1       1       1
##  [512,]       0       0       0       0       1       0       1       0
##  [513,]       1       0       1       0       1       1       1       1
##  [514,]       0       0       0       1       0       0       0       0
##  [515,]       0       1       0       0       0       0       1       0
##  [516,]       1       1       1       1       0       1       1       1
##  [517,]       0       1       0       0       0       1       0       1
##  [518,]       0       1       1       0       0       1       0       0
##  [519,]       0       0       1       1       0       1       1       0
##  [520,]       1       0       1       1       0       1       1       0
##  [521,]       1       1       1       0       0       1       1       0
##  [522,]       0       1       0       0       0       0       1       0
##  [523,]       1       0       1       0       0       1       0       0
##  [524,]       0       0       1       1       1       1       1       1
##  [525,]       1       0       1       1       1       1       1       0
##  [526,]       0       0       1       0       0       0       0       0
##  [527,]       0       0       1       1       0       1       1       1
##  [528,]       0       1       1       1       0       0       0       1
##  [529,]       1       1       0       0       0       1       0       0
##  [530,]       0       0       1       1       0       1       0       1
##  [531,]       0       1       1       1       0       0       0       1
##  [532,]       1       0       1       1       0       0       0       0
##  [533,]       1       0       0       0       0       0       0       1
##  [534,]       1       0       1       1       0       0       1       1
##  [535,]       1       0       1       1       0       1       0       0
##  [536,]       1       0       1       1       0       1       0       1
##  [537,]       0       1       1       1       0       0       0       1
##  [538,]       1       0       1       1       0       1       1       1
##  [539,]       0       0       1       1       0       0       1       0
##  [540,]       0       0       0       1       0       0       0       0
##  [541,]       1       1       0       0       0       0       0       0
##  [542,]       0       0       1       0       1       0       1       0
##  [543,]       0       0       1       1       0       1       1       0
##  [544,]       0       0       1       1       0       1       0       0
##  [545,]       0       0       1       0       0       1       1       1
##  [546,]       0       0       1       0       1       1       0       1
##  [547,]       0       0       1       0       0       1       1       0
##  [548,]       0       0       1       1       0       1       0       0
##  [549,]       1       0       0       0       0       0       1       1
##  [550,]       1       0       1       1       0       1       1       1
##  [551,]       0       0       0       1       0       0       0       0
##  [552,]       0       0       1       0       0       0       0       0
##  [553,]       0       1       1       1       0       0       1       0
##  [554,]       0       0       1       1       0       1       0       1
##  [555,]       0       1       1       1       0       1       1       0
##  [556,]       1       0       1       1       0       1       1       1
##  [557,]       1       0       1       1       1       0       1       0
##  [558,]       1       1       1       1       1       1       1       1
##  [559,]       1       0       1       1       0       1       0       1
##  [560,]       0       0       1       1       0       1       0       0
##  [561,]       0       0       1       0       1       1       0       1
##  [562,]       0       0       1       0       0       0       0       0
##  [563,]       1       0       1       0       0       1       0       0
##  [564,]       0       1       1       1       0       1       1       0
##  [565,]       0       0       1       1       0       1       0       0
##  [566,]       1       0       1       1       0       1       0       1
##  [567,]       0       0       1       0       0       1       1       0
##  [568,]       1       1       1       0       0       1       0       1
##  [569,]       0       0       1       1       0       1       1       0
##  [570,]       0       0       1       0       1       1       0       0
##  [571,]       0       0       0       0       0       1       0       0
##  [572,]       0       0       1       0       0       0       0       1
##  [573,]       0       0       1       1       0       0       0       0
##  [574,]       0       1       0       0       0       0       0       0
##  [575,]       1       1       1       1       1       1       1       1
##  [576,]       1       0       1       1       0       1       1       1
##  [577,]       0       0       1       1       0       0       0       0
##  [578,]       1       1       1       1       1       1       1       1
##  [579,]       0       0       1       1       0       0       0       0
##  [580,]       1       0       1       1       1       1       1       0
##  [581,]       0       0       1       1       0       1       0       0
##  [582,]       0       0       0       1       0       0       0       0
##  [583,]       1       0       1       1       1       1       1       0
##  [584,]       0       0       0       0       0       0       0       0
##  [585,]       0       0       0       0       1       1       0       0
##  [586,]       0       1       1       0       0       0       1       0
##  [587,]       0       1       1       1       0       0       0       1
##  [588,]       0       0       0       0       0       1       0       0
##  [589,]       0       0       0       1       0       0       0       0
##  [590,]       1       1       1       1       1       1       0       1
##  [591,]       0       1       1       1       0       1       1       1
##  [592,]       1       0       1       1       0       1       1       0
##  [593,]       0       0       0       0       0       1       0       1
##  [594,]       1       0       1       1       0       1       0       0
##  [595,]       0       0       1       0       0       1       0       0
##  [596,]       0       0       1       0       0       0       0       0
##  [597,]       0       0       1       1       0       1       0       0
##  [598,]       1       0       0       1       0       1       1       0
##  [599,]       1       1       1       1       1       1       1       1
##  [600,]       1       0       1       1       0       0       1       1
##  [601,]       1       0       1       1       0       1       1       1
##  [602,]       1       0       1       1       0       1       1       1
##  [603,]       0       0       1       1       0       1       0       0
##  [604,]       0       0       0       1       0       1       0       0
##  [605,]       1       0       1       1       0       0       1       1
##  [606,]       0       0       1       0       0       0       0       0
##  [607,]       0       0       0       0       0       0       0       0
##  [608,]       0       0       1       1       0       0       1       0
##  [609,]       1       0       1       1       1       0       0       0
##  [610,]       0       0       1       0       0       1       0       1
##  [611,]       1       0       1       1       0       1       1       0
##  [612,]       0       1       0       0       0       1       0       1
##  [613,]       0       0       0       0       0       0       0       1
##  [614,]       0       0       0       1       0       0       0       0
##  [615,]       0       0       1       1       1       0       0       1
##  [616,]       0       0       1       0       1       1       0       1
##  [617,]       1       0       1       1       1       1       0       0
##  [618,]       0       0       0       0       0       0       0       0
##  [619,]       0       0       1       0       0       0       1       0
##  [620,]       0       0       1       0       0       1       0       0
##  [621,]       0       0       1       0       0       1       0       0
##  [622,]       0       0       1       0       0       0       0       1
##  [623,]       0       1       1       1       0       1       0       1
##  [624,]       0       1       1       1       1       1       1       0
##  [625,]       0       1       0       1       0       1       0       0
##  [626,]       0       0       1       0       0       0       0       1
##  [627,]       0       0       0       0       0       0       0       0
##  [628,]       0       0       1       1       1       1       0       0
##  [629,]       0       0       1       1       0       0       1       0
##  [630,]       1       0       0       0       0       0       0       0
##  [631,]       1       0       0       0       0       0       0       0
##  [632,]       1       0       1       1       1       0       0       1
##  [633,]       1       1       1       1       0       0       0       1
##  [634,]       0       0       1       0       0       1       0       0
##  [635,]       0       1       1       1       1       1       1       0
##  [636,]       1       1       1       0       0       1       1       0
##  [637,]       0       0       1       1       1       1       1       0
##  [638,]       0       0       0       1       1       0       0       0
##  [639,]       0       0       1       1       1       1       1       1
##  [640,]       0       1       1       1       0       1       0       0
##  [641,]       1       0       1       1       0       1       0       1
##  [642,]       0       1       1       0       1       1       0       0
##  [643,]       0       1       1       0       1       1       1       0
##  [644,]       0       1       1       1       1       1       1       1
##  [645,]       0       1       1       1       1       1       1       1
##  [646,]       0       0       1       1       1       1       1       0
##  [647,]       1       0       1       1       1       1       1       1
##  [648,]       0       1       0       0       0       0       0       0
##  [649,]       0       0       1       1       1       0       0       0
##  [650,]       1       0       1       1       1       0       1       1
##  [651,]       1       0       1       1       1       1       1       1
##  [652,]       0       0       1       0       0       1       0       0
##  [653,]       1       0       1       1       0       1       1       0
##  [654,]       0       0       0       1       0       0       0       0
##  [655,]       1       0       1       1       0       1       1       1
##  [656,]       1       0       1       1       1       0       0       0
##  [657,]       0       0       1       1       0       1       1       1
##  [658,]       1       1       1       1       0       1       0       1
##  [659,]       1       1       0       0       0       0       0       0
##  [660,]       1       0       1       0       0       0       0       0
##  [661,]       0       0       1       0       0       1       0       0
##  [662,]       0       0       1       1       0       1       1       1
##  [663,]       0       0       0       1       0       0       1       0
##  [664,]       0       1       1       0       0       1       1       0
##  [665,]       0       1       1       1       0       0       0       1
##  [666,]       0       0       1       1       0       0       1       0
##  [667,]       0       0       1       1       0       1       1       0
##  [668,]       0       0       1       0       0       0       1       0
##  [669,]       1       1       1       1       0       0       0       0
##  [670,]       0       1       1       1       0       1       1       1
##  [671,]       0       1       1       1       1       1       1       1
##  [672,]       0       0       1       1       0       1       0       0
##  [673,]       0       0       0       0       1       0       0       0
##  [674,]       0       0       1       0       0       1       1       0
##  [675,]       1       1       1       0       0       1       0       0
##  [676,]       0       0       0       0       0       0       1       1
##  [677,]       1       0       1       1       1       1       1       0
##  [678,]       0       0       1       1       0       1       1       0
##  [679,]       1       0       1       1       1       1       1       1
##  [680,]       1       0       1       0       0       1       1       0
##  [681,]       0       1       0       0       0       0       0       0
##  [682,]       0       0       1       1       0       0       0       0
##  [683,]       0       0       0       0       0       0       0       1
##  [684,]       0       0       1       1       1       1       1       1
##  [685,]       0       0       1       0       0       1       0       0
##  [686,]       1       0       1       1       1       1       1       0
##  [687,]       1       0       1       0       0       1       1       0
##  [688,]       1       0       1       1       0       1       1       0
##  [689,]       0       0       1       0       1       1       0       1
##  [690,]       0       0       1       1       0       1       1       0
##  [691,]       0       1       0       0       0       0       0       0
##  [692,]       0       0       1       1       0       1       0       1
##  [693,]       0       0       1       1       0       0       0       1
##  [694,]       0       0       1       0       0       0       0       0
##  [695,]       0       1       0       1       0       0       0       0
##  [696,]       0       0       1       1       0       0       0       0
##  [697,]       0       0       1       1       0       1       0       0
##  [698,]       0       1       1       1       0       1       0       1
##  [699,]       0       0       1       1       1       1       1       0
##  [700,]       0       0       1       1       0       1       1       0
##  [701,]       0       0       1       1       0       0       0       1
##  [702,]       1       0       1       0       0       1       0       0
##  [703,]       1       1       1       1       0       1       0       0
##  [704,]       0       0       1       1       0       1       1       1
##  [705,]       0       0       1       1       0       1       0       0
##  [706,]       0       1       1       1       1       1       1       0
##  [707,]       1       0       0       0       0       0       0       0
##  [708,]       0       1       1       0       0       0       0       1
##  [709,]       0       0       1       1       0       1       0       1
##  [710,]       0       1       1       1       0       0       1       1
##  [711,]       0       1       0       0       1       0       1       1
##  [712,]       0       0       1       1       0       0       1       1
##  [713,]       0       0       0       1       0       1       0       0
##  [714,]       0       0       1       1       0       1       0       0
##  [715,]       0       1       0       0       0       0       0       0
##  [716,]       0       0       1       1       1       0       1       1
##  [717,]       0       0       1       1       0       1       1       1
##  [718,]       1       1       1       1       1       1       1       1
##  [719,]       0       0       1       1       1       1       0       0
##  [720,]       0       0       0       0       1       0       1       0
##  [721,]       0       1       1       1       0       0       0       1
##  [722,]       0       0       0       0       0       0       0       0
##  [723,]       0       1       1       0       0       0       0       0
##  [724,]       1       0       1       1       0       0       0       1
##  [725,]       0       0       1       1       0       0       0       1
##  [726,]       1       1       1       1       0       0       1       0
##  [727,]       0       0       0       0       0       0       0       0
##  [728,]       0       0       1       1       1       0       1       1
##  [729,]       0       1       1       1       0       0       1       0
##  [730,]       0       0       0       1       0       1       0       1
##  [731,]       0       1       1       0       0       0       0       0
##  [732,]       0       0       1       0       0       0       0       0
##  [733,]       0       0       0       0       0       0       1       0
##  [734,]       1       0       1       1       0       0       0       0
##  [735,]       0       1       1       0       0       1       0       0
##  [736,]       1       0       1       1       0       0       0       0
##  [737,]       0       0       1       1       0       1       0       0
##  [738,]       1       1       1       1       0       0       0       0
##  [739,]       0       0       1       1       0       1       1       1
##  [740,]       0       0       1       1       1       1       1       0
##  [741,]       0       0       1       0       0       0       1       1
##  [742,]       1       0       0       1       0       1       1       1
##  [743,]       0       0       1       0       0       1       0       0
##  [744,]       1       1       1       1       0       1       0       0
##  [745,]       0       0       1       0       0       1       1       1
##  [746,]       0       0       1       1       0       1       1       1
##  [747,]       0       1       1       1       0       1       1       1
##  [748,]       0       0       0       0       0       0       0       0
##  [749,]       0       0       1       0       0       0       0       1
##  [750,]       1       1       1       0       0       1       1       0
##  [751,]       1       0       1       1       1       0       1       1
##  [752,]       0       0       1       1       1       1       1       1
##  [753,]       1       1       0       1       0       0       1       0
##  [754,]       1       1       1       1       0       0       1       1
##  [755,]       1       1       1       1       0       1       1       1
##  [756,]       0       1       0       0       0       0       0       0
##  [757,]       0       1       0       0       0       0       0       0
##  [758,]       0       0       0       1       0       0       1       0
##  [759,]       0       0       1       1       1       1       0       1
##  [760,]       1       0       1       1       1       1       1       1
##  [761,]       0       1       1       1       0       0       0       0
##  [762,]       1       0       1       1       0       1       1       1
##  [763,]       0       0       1       0       0       1       0       1
##  [764,]       0       0       0       0       0       1       0       0
##  [765,]       1       1       1       0       1       1       0       0
##  [766,]       0       0       1       1       0       1       0       1
##  [767,]       0       0       1       1       0       1       1       0
##  [768,]       0       1       0       0       0       1       0       0
##  [769,]       1       0       1       1       0       0       1       0
##  [770,]       0       0       1       0       0       1       0       0
##  [771,]       1       0       0       0       0       0       0       0
##  [772,]       0       0       1       0       0       0       1       1
##  [773,]       1       1       1       1       0       1       1       0
##  [774,]       1       0       1       1       0       1       1       0
##  [775,]       0       0       0       0       1       0       0       0
##  [776,]       1       0       0       0       0       0       0       1
##  [777,]       0       0       1       1       1       1       1       0
##  [778,]       0       0       1       0       0       0       0       1
##  [779,]       1       1       1       0       1       1       0       1
##  [780,]       0       0       1       1       0       1       1       1
##  [781,]       0       1       0       0       0       1       0       0
##  [782,]       1       1       1       1       0       0       1       0
##  [783,]       0       0       1       0       1       1       1       0
##  [784,]       1       0       1       0       0       0       0       1
##  [785,]       1       0       1       1       1       0       1       1
##  [786,]       0       0       0       0       0       0       1       1
##  [787,]       0       0       1       1       0       1       0       0
##  [788,]       1       0       1       1       0       0       0       0
##  [789,]       1       0       1       1       0       0       0       1
##  [790,]       1       1       1       0       0       0       0       0
##  [791,]       1       0       0       0       0       0       0       0
##  [792,]       0       0       1       1       0       0       0       0
##  [793,]       1       0       1       0       0       0       0       0
##  [794,]       1       1       1       1       0       1       1       1
##  [795,]       1       0       1       0       0       1       0       1
##  [796,]       0       0       1       0       0       0       0       1
##  [797,]       0       0       1       0       0       0       0       0
##  [798,]       1       0       1       0       0       0       0       0
##  [799,]       1       0       1       0       0       1       1       0
##  [800,]       0       1       1       1       0       1       0       0
##  [801,]       0       0       1       1       0       1       0       0
##  [802,]       0       0       1       0       1       0       0       0
##  [803,]       1       0       1       1       1       1       1       0
##  [804,]       1       1       1       0       0       1       0       0
##  [805,]       1       1       1       1       0       0       0       0
##  [806,]       0       0       0       1       0       0       1       0
##  [807,]       0       0       1       0       0       0       1       1
##  [808,]       0       0       1       0       0       1       1       1
##  [809,]       0       0       0       0       0       0       1       0
##  [810,]       1       0       1       1       1       1       1       1
##  [811,]       0       0       1       1       1       0       0       1
##  [812,]       1       0       1       1       1       1       1       1
##  [813,]       1       1       1       1       0       0       0       1
##  [814,]       0       0       0       0       0       0       0       0
##  [815,]       0       0       1       1       0       1       1       0
##  [816,]       0       0       1       0       0       1       1       1
##  [817,]       0       0       1       0       0       1       0       1
##  [818,]       0       0       1       1       0       1       0       1
##  [819,]       0       0       0       0       0       1       0       1
##  [820,]       0       0       1       1       0       1       0       0
##  [821,]       0       0       0       0       0       0       0       0
##  [822,]       0       1       1       1       0       1       0       0
##  [823,]       1       0       1       1       0       1       0       1
##  [824,]       0       0       1       1       1       1       1       1
##  [825,]       0       0       1       0       0       0       1       0
##  [826,]       0       1       0       0       0       1       1       0
##  [827,]       1       0       1       1       1       1       0       1
##  [828,]       0       1       1       0       1       1       0       1
##  [829,]       0       1       0       1       0       0       0       1
##  [830,]       0       0       1       1       1       1       1       1
##  [831,]       0       0       1       0       0       1       0       0
##  [832,]       1       0       1       1       0       1       0       1
##  [833,]       0       0       1       1       0       1       0       0
##  [834,]       0       0       1       1       0       0       0       1
##  [835,]       0       0       1       1       1       0       1       1
##  [836,]       0       1       0       0       0       1       1       0
##  [837,]       0       0       1       0       1       0       0       0
##  [838,]       0       0       0       0       0       0       1       1
##  [839,]       0       0       0       1       0       0       0       0
##  [840,]       0       1       1       1       0       1       1       1
##  [841,]       1       1       1       0       0       1       0       1
##  [842,]       1       0       1       1       0       0       1       0
##  [843,]       1       0       1       1       0       1       1       1
##  [844,]       0       0       1       1       0       1       1       0
##  [845,]       1       0       0       1       1       0       1       1
##  [846,]       0       0       1       0       0       0       1       0
##  [847,]       0       0       0       0       0       0       0       1
##  [848,]       1       1       1       1       1       1       1       1
##  [849,]       1       0       1       0       1       1       1       1
##  [850,]       0       0       1       1       0       0       1       0
##  [851,]       0       0       0       0       0       1       1       0
##  [852,]       0       0       1       0       0       0       0       1
##  [853,]       0       1       1       0       1       0       1       0
##  [854,]       0       0       1       1       1       1       1       1
##  [855,]       1       1       1       0       0       0       0       0
##  [856,]       0       0       0       0       0       0       1       0
##  [857,]       0       1       1       1       1       1       1       1
##  [858,]       0       1       0       0       0       0       0       0
##  [859,]       0       0       0       0       0       0       0       0
##  [860,]       0       0       1       1       0       1       1       1
##  [861,]       0       0       0       0       0       1       1       0
##  [862,]       0       0       1       1       0       0       1       1
##  [863,]       0       0       0       1       0       0       0       0
##  [864,]       0       0       0       0       0       1       0       0
##  [865,]       1       0       1       1       0       1       1       1
##  [866,]       1       0       1       0       0       0       1       0
##  [867,]       0       0       1       0       0       1       1       0
##  [868,]       1       0       0       1       0       1       0       0
##  [869,]       1       1       1       0       0       1       1       0
##  [870,]       0       1       0       0       1       0       0       0
##  [871,]       0       0       1       0       0       0       0       0
##  [872,]       0       1       1       1       0       1       1       0
##  [873,]       0       0       1       1       0       1       1       1
##  [874,]       0       0       1       1       0       0       1       1
##  [875,]       0       0       0       0       0       0       0       0
##  [876,]       0       0       1       0       0       0       0       1
##  [877,]       0       0       1       0       0       1       0       0
##  [878,]       0       0       1       1       0       0       0       0
##  [879,]       0       1       1       0       0       0       0       0
##  [880,]       0       1       1       1       0       0       0       0
##  [881,]       1       0       1       1       0       0       1       0
##  [882,]       0       0       1       1       0       1       1       1
##  [883,]       0       1       1       0       0       1       1       0
##  [884,]       0       0       1       1       0       0       0       1
##  [885,]       1       0       0       0       0       0       0       0
##  [886,]       0       1       0       0       0       0       0       0
##  [887,]       0       0       0       0       1       0       0       1
##  [888,]       0       0       1       1       0       1       0       0
##  [889,]       0       0       0       0       0       0       0       0
##  [890,]       0       0       1       1       0       1       1       0
##  [891,]       1       0       1       1       0       1       1       1
##  [892,]       0       0       1       1       0       0       1       0
##  [893,]       0       1       1       1       0       1       1       1
##  [894,]       1       1       1       1       1       1       0       1
##  [895,]       0       0       0       0       0       1       0       0
##  [896,]       0       0       0       0       1       0       0       0
##  [897,]       1       0       1       1       0       1       1       0
##  [898,]       1       0       1       1       0       1       1       0
##  [899,]       0       0       1       0       0       1       1       0
##  [900,]       0       1       1       1       0       0       0       0
##  [901,]       0       0       0       0       0       0       0       1
##  [902,]       1       0       1       1       1       1       1       0
##  [903,]       0       0       0       0       0       0       1       0
##  [904,]       0       0       1       1       0       0       1       0
##  [905,]       0       0       1       1       0       0       0       0
##  [906,]       1       0       1       0       0       1       0       1
##  [907,]       0       0       0       0       0       0       0       0
##  [908,]       1       0       1       1       0       1       0       1
##  [909,]       1       0       0       1       0       0       1       1
##  [910,]       0       0       1       0       0       1       0       0
##  [911,]       1       0       1       1       0       1       0       0
##  [912,]       1       1       1       1       1       1       1       1
##  [913,]       0       0       1       1       0       0       1       0
##  [914,]       1       0       1       1       0       1       1       1
##  [915,]       0       0       1       0       1       0       0       1
##  [916,]       1       0       0       0       0       1       0       0
##  [917,]       1       0       1       0       0       1       1       0
##  [918,]       0       0       1       1       0       1       1       1
##  [919,]       0       1       1       1       0       0       0       0
##  [920,]       0       0       1       0       0       0       0       0
##  [921,]       1       0       1       0       0       1       0       0
##  [922,]       1       1       1       1       0       1       1       1
##  [923,]       1       0       1       1       1       0       1       1
##  [924,]       1       1       0       1       0       0       0       1
##  [925,]       0       0       0       1       0       0       1       1
##  [926,]       0       0       0       1       0       0       0       0
##  [927,]       0       0       1       1       0       0       0       1
##  [928,]       0       0       1       0       0       1       0       0
##  [929,]       0       0       1       0       0       0       0       0
##  [930,]       0       1       1       1       0       1       1       1
##  [931,]       0       0       1       1       0       1       0       0
##  [932,]       0       0       0       1       0       1       0       0
##  [933,]       1       0       1       1       1       1       1       1
##  [934,]       0       0       1       1       1       1       1       1
##  [935,]       0       1       0       0       0       0       0       1
##  [936,]       0       0       1       1       0       1       1       1
##  [937,]       0       0       1       1       0       1       1       1
##  [938,]       0       0       0       0       0       0       0       0
##  [939,]       1       0       1       1       0       0       0       1
##  [940,]       0       0       0       0       0       0       1       0
##  [941,]       0       0       0       1       0       1       0       0
##  [942,]       1       1       1       0       0       0       1       1
##  [943,]       1       0       1       1       0       1       1       1
##  [944,]       1       0       1       1       0       1       1       0
##  [945,]       0       0       1       0       0       0       1       0
##  [946,]       0       0       1       1       0       0       0       0
##  [947,]       1       1       1       1       0       0       1       0
##  [948,]       0       0       0       0       0       0       0       1
##  [949,]       1       0       1       1       1       1       0       1
##  [950,]       0       0       1       0       0       1       0       1
##  [951,]       0       0       1       1       0       1       0       0
##  [952,]       0       1       1       1       0       1       0       0
##  [953,]       1       0       1       1       0       1       1       1
##  [954,]       0       0       1       1       1       0       0       1
##  [955,]       1       0       1       0       0       0       1       0
##  [956,]       0       0       1       0       0       1       0       1
##  [957,]       1       0       0       0       0       1       1       0
##  [958,]       1       1       1       1       1       1       1       1
##  [959,]       1       1       0       0       0       0       0       0
##  [960,]       1       1       1       1       1       1       0       0
##  [961,]       0       0       1       1       0       0       0       1
##  [962,]       0       0       1       0       0       0       0       1
##  [963,]       0       0       1       0       0       0       0       0
##  [964,]       0       0       0       1       0       1       0       0
##  [965,]       1       0       0       0       0       0       0       1
##  [966,]       0       0       1       1       0       1       1       0
##  [967,]       1       0       1       1       0       1       1       0
##  [968,]       0       0       0       1       1       1       0       0
##  [969,]       1       0       1       1       1       1       1       0
##  [970,]       0       0       1       1       0       1       1       1
##  [971,]       0       1       1       0       0       1       0       0
##  [972,]       0       1       1       1       0       0       0       0
##  [973,]       0       0       1       0       0       0       0       0
##  [974,]       0       0       1       1       0       1       0       1
##  [975,]       0       0       1       0       1       0       0       0
##  [976,]       0       0       0       1       1       0       1       0
##  [977,]       1       1       1       1       1       1       1       1
##  [978,]       1       0       0       0       0       0       0       0
##  [979,]       0       0       1       1       0       0       1       1
##  [980,]       0       1       0       1       0       0       0       0
##  [981,]       0       0       1       1       0       0       0       0
##  [982,]       0       0       1       0       0       1       0       0
##  [983,]       0       0       1       0       0       1       0       0
##  [984,]       1       0       1       0       0       0       1       1
##  [985,]       0       0       0       0       0       1       0       0
##  [986,]       0       0       1       1       1       0       0       1
##  [987,]       0       0       1       0       0       1       0       1
##  [988,]       0       0       1       1       0       1       1       1
##  [989,]       0       1       1       1       0       0       0       0
##  [990,]       1       0       0       0       0       0       0       0
##  [991,]       0       1       1       1       0       0       1       0
##  [992,]       0       0       0       1       0       1       1       0
##  [993,]       0       0       1       1       0       1       1       0
##  [994,]       1       1       1       0       0       1       1       0
##  [995,]       0       0       0       0       0       0       0       0
##  [996,]       1       0       0       0       0       0       0       1
##  [997,]       1       0       1       1       0       0       1       0
##  [998,]       0       0       0       0       0       1       0       0
##  [999,]       0       0       1       0       0       0       0       0
## [1000,]       0       0       1       1       1       0       1       0

MTK Modellerinde Madde Parametrelerinin Kestirimi

# kestirilen_par isimli fonksiyon tanımlama
# Fonksiyon; cevap verisini ve kullanılacak model türünü girdi olarak alır
kestirilen_par <- function(veri, par = 3){

  # Eğer par = 3 ise 3 Parametreli Lojistik Model (3PL) kurulur
  if(par == 3){

    # mirt paketi ile 3PL modeli kestirilir
    model <- mirt::mirt(
      veri,              # cevap verisi
      1,                 # tek boyutlu model
      itemtype = "3PL",  # 3PL modeli
      verbose = FALSE    # işlem çıktıları ekrana yazdırılmaz
    )

  # Eğer par = 2 ise 2 Parametreli Lojistik Model (2PL) kurulur
  } else if(par == 2){

    # mirt paketi ile 2PL modeli kestirilir
    model <- mirt::mirt(
      veri,
      1,
      itemtype = "2PL",  # 2PL modeli
      verbose = FALSE
    )

  # Diğer durumlarda Rasch (1PL) modeli kurulur
  } else {

    # mirt paketi ile Rasch modeli kestirilir
    model <- mirt::mirt(
      veri,
      1,
      itemtype = "Rasch", # 1PL / Rasch modeli
      verbose = FALSE
    )
  }

  # Kurulan modelden madde parametreleri elde edilir
  kestirim <- mirt::coef(
    model,
    simplify = TRUE, # çıktının sadeleştirilmesi
    IRTpars = TRUE   # parametrelerin IRT formatında verilmesi
  )$item[,1:3]       # ilk 3 parametre seçilir

  # Kestirilen parametreler ekrana yazdırılır
  kestirim
}

# Fonksiyon çalıştırılır
# veri_1 veri setindeki cevaplar kullanılarak parametreler kestirilir
kestirilen_par(veri_1$cevaplar)

## Warning: EM cycles terminated after 500 iterations.

##                 a          b          g
## madde_1 1.0796644  1.5974754 0.18260293
## madde_2 6.8647109  2.2571636 0.22561071
## madde_3 2.1986742 -0.7893405 0.01344374
## madde_4 1.8407876 -0.2041265 0.09446084
## madde_5 1.8772233  1.4455007 0.08694212
## madde_6 1.2045632 -0.1166581 0.11809074
## madde_7 2.8002459  0.6244751 0.18957322
## madde_8 0.8671392  0.7360819 0.05246430

# Simülasyonda kullanılan gerçek madde parametreleri görüntülenir
veri_1$maddepar

##          [,1]        [,2]      [,3]
## [1,] 1.585256  1.36212818 0.1931548
## [2,] 2.007193  2.37259454 0.2039164
## [3,] 2.349485 -0.51853504 0.1701437
## [4,] 2.471655  0.01079754 0.2737201
## [5,] 2.308658  1.40935862 0.1150351
## [6,] 2.133316  0.24118623 0.2669745
## [7,] 2.178256  0.46418558 0.1017025
## [8,] 1.251137  0.79121836 0.1576435

Parametre Kestirim Hatalarının Hesaplanması

# RMSE^2 = Bias^2 + SE^2 ilişkisine dayalı hata hesaplama fonksiyonu

# hata isimli fonksiyon tanımlanır
# Fonksiyon; kestirilen parametreleri ve gerçek parametreleri girdi olarak alır
hata <- function(kestirilen, gercek){

  # Sonuçların saklanacağı veri çerçevesi oluşturulur
  result <- data.frame(
    
    # Parametre isimleri tanımlanır
    parametreler = c("a", "b", "c"),

    # RMSE hesaplanır
    # Kestirilen ve gerçek değerler arasındaki farkların karelerinin ortalamasının karekökü alınır
    rmse = sapply(1:3, function(i)
      sqrt(mean((kestirilen[,i] - gercek[,i])^2))
    ),

    # Bias (yanlılık) hesaplanır
    # Kestirilen ve gerçek değerler arasındaki ortalama fark bulunur
    bias = sapply(1:3, function(i)
      mean(kestirilen[,i] - gercek[,i])
    ),

    # Standart hata (SE) hesaplanır
    # Kestirilen parametrelerin standart sapması alınır
    se = sapply(1:3, function(i)
      sd(kestirilen[,i])
    )
  )

  # Hesaplanan sonuçlar döndürülür
  result
}

# Fonksiyon çalıştırılır
# Kestirilen parametreler ile gerçek parametreler karşılaştırılır
hata(
  kestirilen_par(veri_1$cevaplar),
  veri_1$maddepar
)

## Warning: EM cycles terminated after 500 iterations.

##   parametreler      rmse        bias         se
## 1            a 1.7977376  0.30600650 1.93520557
## 2            b 0.2080661 -0.07279530 1.03476724
## 3            c 0.1112488 -0.06488775 0.07326657

3PL Modeline Göre Otomatik Veri Üretimi

# 3PL Modeline Göre Otomatik Veri Üretimi

# veri_uretimi isimli fonksiyon tanımlanır
# Fonksiyon; madde sayısı, birey sayısı ve isteğe bağlı seed değeri alır
veri_uretimi <- function(maddesay, bireysay, seed = NULL){

  # Eğer kullanıcı seed girerse o değer kullanılır
  if(!is.null(seed)){
    
    # Rastgele sayı üretimi için seed atanır
    set.seed(seed)

  } else {

    # Eğer seed girilmezse rastgele bir seed üretilir
    seed <- sample.int(10000,1)

    # Üretilen seed kullanılır
    set.seed(seed)
  }

  # Kullanılan seed değeri ekrana yazdırılır
  cat("atanan seed", seed, "\n")

  
  # Madde parametreleri üretilir
  print("madde parametreleri üretildi")

  # Ayırt edicilik, güçlük ve şans parametreleri oluşturulur
  maddepar <- cbind(

    # Ayırt edicilik parametreleri log-normal dağılımdan üretilir
    rlnorm(maddesay, meanlog = 0 , sdlog = 0.5)*1.702,

    # Güçlük parametreleri normal dağılımdan üretilir
    rnorm(maddesay, mean = 0.30 , sd =0.50)*1.702,

    # Şans parametreleri normal dağılımdan üretilir
    rnorm(maddesay, mean = 0.16, sd =0.05)
  )


  # Bireylerin yetenek parametreleri üretilir
  # Ortalama 0 ve standart sapma 1 olan normal dağılımdan çekilir
  yetenek <- rnorm(bireysay,0,1)

  # Yetenek üretiminin tamamlandığı bilgisi ekrana yazdırılır
  print("yetenek parametreleri üretildi")


  # irtoys paketinin sim() fonksiyonu ile
  # 3PL modele uygun cevap verileri üretilir
  cevaplar <- irtoys::sim(maddepar, yetenek)

  # Maddelere isim verilir
  colnames(cevaplar) <- paste0("madde",1:maddesay)

  # Veri birleştirme işlemi hakkında bilgi yazdırılır
  print("bileşenler birleştiriliyor")


  # Tüm çıktılar liste halinde birleştirilir
  veri <- list(
    maddepar = maddepar,
    yetenek = yetenek,
    seed = seed,
    cevaplar = cevaplar
  )

  # Oluşturulan veri çıktısı döndürülür
  return(veri)
}

Bu kodda, 3PL modele göre otomatik veri üretimi yapan bir fonksiyon yazıldı. Fonksiyon; madde sayısı, birey sayısı ve isteğe bağlı olarak seed değerini girdi olarak alır.

Fonksiyonun Çalıştırılması

veri_1 <- veri_uretimi(
  maddesay = 8,
  bireysay = 1000,
  seed = 41
)

## atanan seed 41 
## [1] "madde parametreleri üretildi"
## [1] "yetenek parametreleri üretildi"
## [1] "bileşenler birleştiriliyor"

head(veri_1$cevaplar)

##      madde1 madde2 madde3 madde4 madde5 madde6 madde7 madde8
## [1,]      0      1      1      1      0      1      1      0
## [2,]      1      0      1      1      1      1      1      0
## [3,]      0      0      1      0      0      0      1      0
## [4,]      1      0      1      0      0      1      0      0
## [5,]      0      0      1      1      0      0      1      0
## [6,]      0      0      0      0      0      0      0      1

Paralel İşlem Kullanımı

Paralel işlem kullanılarak hesaplamaların aynı anda birden fazla işlemci çekirdeğinde çalıştırılması

library(doParallel)

## Warning: package 'doParallel' was built under R version 4.5.3

## Zorunlu paket yükleniyor: foreach

## Warning: package 'foreach' was built under R version 4.5.3

## Zorunlu paket yükleniyor: iterators

## Warning: package 'iterators' was built under R version 4.5.3

## Zorunlu paket yükleniyor: parallel

# Bilgisayardaki işlemci çekirdeği sayısı görüntülenir
detectCores()

## [1] 4

# 4 çekirdek kullanılarak işlem kümesi oluşturulur
# Genellikle tüm çekirdekler yerine n-2 kadar çekirdek kullanılması önerilir
cl <- makeCluster(4)

# Oluşturulan küme paralel işlem için aktif hale getirilir
registerDoParallel(cl)

# foreach döngüsü paralel şekilde çalıştırılır
# 1’den 4’e kadar sayıların karekökü hesaplanır
foreach(i = 1:4) %dopar% sqrt(i)

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 1.414214
## 
## [[3]]
## [1] 1.732051
## 
## [[4]]
## [1] 2

# İki değişkenli paralel işlem örneği
# i ve j değerlerinin çarpımının karekökü hesaplanır
foreach(i = 1:4, j = 1:4) %dopar% {
  
  sqrt(i * j)

}

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 2
## 
## [[3]]
## [1] 3
## 
## [[4]]
## [1] 4

# İşlem tamamlandıktan sonra küme kapatılır
# Kullanılan çekirdekler serbest bırakılır
stopCluster(cl)

Simülasyon, Parametre Kestirimi ve Hata Hesaplaması

# 12 çekirdekli işlem kümesi oluşturulur
cl <- makeCluster(12)

# Paralel işlem sistemi aktif hale getirilir
registerDoParallel(cl)

# Simülasyon tekrar sayısı belirlenir
tekrar = 100L

# Madde sayısı belirlenir
maddesay = 10

# Birey sayısı belirlenir
bireysay = 1000


# Paralel simülasyon işlemi başlatılır
simulasyon <- foreach(
  
  # Döngü 1’den tekrar sayısına kadar çalışır
  i = 1:tekrar,

  # Kullanılacak paketler belirtilir
  .packages = c("mirt","irtoys","doParallel"),

  # Her tekrarın sonucu satır bazında birleştirilir
  .combine = rbind

) %dopar% {

  # 1. adım:
  # 3PL modele göre veri üretilir
  adim1 <- veri_uretimi(
    maddesay = maddesay,
    bireysay = bireysay
  )

  # 2. adım:
  # Üretilen cevap verileri üzerinden parametre kestirimi yapılır
  adim2 <- kestirilen_par(adim1$cevaplar)

  # 3. adım:
  # Kestirilen parametreler ile gerçek parametreler karşılaştırılır
  hata(adim2, adim1$maddepar)
}

simulasyon

##     parametreler        rmse          bias          se
## 1              a  0.55287313  0.0153206084  0.51997617
## 2              b  0.14198528  0.0072847711  0.71496916
## 3              c  0.07171081  0.0029678972  0.12172797
## 4              a  0.84914346  0.4561420865  1.40322922
## 5              b  0.10418378  0.0795577538  0.90263412
## 6              c  0.05211197  0.0011382216  0.10118130
## 7              a  1.23168927 -0.4861526652  0.63332166
## 8              b  0.15543904  0.0497835037  0.87374369
## 9              c  0.05247382 -0.0191646736  0.08382205
## 10             a  1.11965086  0.2762797329  1.37153982
## 11             b  0.27353165  0.0779764693  0.57798064
## 12             c  0.08720537  0.0141446017  0.10631503
## 13             a  0.60984121  0.2743169311  1.04546231
## 14             b  0.40565127  0.1879663432  0.71177581
## 15             c  0.12751580  0.0392339708  0.12289570
## 16             a  0.56649220  0.1528373554  1.43298846
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## 19             a  2.69139724  0.6024994887  3.89059166
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## 21             c  0.08129606 -0.0043686199  0.09836788
## 22             a  0.36987565 -0.1494724558  0.67387705
## 23             b  0.15070090 -0.0553095140  1.11690436
## 24             c  0.08166042 -0.0577750763  0.03507392
## 25             a  1.86273733  0.6561247877  2.63666543
## 26             b  0.14467504 -0.0303317964  0.66426870
## 27             c  0.06872709 -0.0134859830  0.07567168
## 28             a  0.51484095 -0.1811168560  1.10969096
## 29             b  0.22417579  0.0459942803  0.70959171
## 30             c  0.06877741 -0.0141645099  0.09317076
## 31             a  1.04646179  0.3668537181  0.99738884
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## 39             c  0.19483742  0.0120433007  0.21086417
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## 41             b  0.33477215  0.1024622109  0.78148985
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## 43             a  1.05576861  0.2483720674  1.50813896
## 44             b  0.39661803 -0.0704035992  1.10472821
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## 56             b  0.75284527  0.4444883054  1.43888357
## 57             c  0.14554038  0.0563234423  0.17806726
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## 264            c  0.08103361 -0.0263474367  0.07867524
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## 266            b  0.21614738 -0.0511402309  0.59727517
## 267            c  0.06563178 -0.0028896916  0.07583396
## 268            a  0.54261497  0.2516260904  1.12941483
## 269            b  0.21232380  0.0103709940  1.06237589
## 270            c  0.08583122 -0.0157153209  0.08695383
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## 272            b  0.21255388  0.0795872620  0.67257730
## 273            c  0.11205909  0.0313258343  0.12352553
## 274            a  0.36780557 -0.0860586378  1.21594894
## 275            b  0.54397938 -0.2730519654  0.68966685
## 276            c  0.09375081 -0.0460019482  0.10762758
## 277            a  0.51372011 -0.0303077023  0.65119272
## 278            b  0.38153540 -0.0092224068  0.73008865
## 279            c  0.13518622 -0.0129551746  0.14659868
## 280            a  1.03951295  0.3304873982  1.35333785
## 281            b  0.12296216  0.0303970472  0.79150724
## 282            c  0.06951698  0.0160325931  0.10875079
## 283            a  0.36329500 -0.0517926449  0.69470021
## 284            b  0.20951491 -0.0112256234  1.03610315
## 285            c  0.08076186 -0.0213241337  0.10317500
## 286            a  1.34360511  0.6455021962  2.02675718
## 287            b  0.28575066  0.1423285775  0.64591167
## 288            c  0.06022354  0.0339129360  0.08849159
## 289            a  1.80782865  0.5614359345  2.32248552
## 290            b  0.16361184 -0.0213428556  0.82208495
## 291            c  0.05441786 -0.0217058504  0.08791366
## 292            a  2.12935598  0.3887131096  2.97812464
## 293            b  0.23595081 -0.1378496669  0.81593934
## 294            c  0.09901677 -0.0628194723  0.10466530
## 295            a  0.62443001 -0.0849473832  0.89873072
## 296            b  0.34065211  0.0980513925  1.25065623
## 297            c  0.08394276  0.0183234203  0.10651330
## 298            a  3.41345064  1.7294479418  4.36246491
## 299            b  0.24037437  0.0120318313  0.66549314
## 300            c  0.12673046  0.0417873546  0.11811005

Simülasyon sonuçlarının özetlenmesi

library(tidyverse)

## Warning: package 'ggplot2' was built under R version 4.5.3

## Warning: package 'dplyr' was built under R version 4.5.3

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.2.0     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.2
## ✔ ggplot2   4.0.2     ✔ tibble    3.3.0
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.1.0     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ ggplot2::%+%()      masks psych::%+%()
## ✖ purrr::accumulate() masks foreach::accumulate()
## ✖ ggplot2::alpha()    masks psych::alpha()
## ✖ dplyr::filter()     masks stats::filter()
## ✖ dplyr::lag()        masks stats::lag()
## ✖ dplyr::select()     masks MASS::select()
## ✖ purrr::when()       masks foreach::when()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

# Simülasyon sonuçları düzenlenir ve özetlenir
simulasyon_v1 <- simulasyon %>%
  
  # Sonuçlar parametre türlerine göre gruplanır
  group_by(parametreler) %>%
  
  # Her parametre için ortalama RMSE, Bias ve SE hesaplanır
  summarise(
    rmse = round(mean(rmse), 2),
    bias = round(mean(bias), 2),
    se = round(mean(se), 2)
  ) %>%
  
  # Simülasyon koşulları veri setine eklenir
  mutate(
    maddesay = maddesay,
    bireysay = bireysay
  ) %>%
  
  # Sonuç veri çerçevesine dönüştürülür
  as.data.frame()

# Oluşturulan özet tablo görüntülenir
simulasyon_v1

##   parametreler rmse bias   se maddesay bireysay
## 1            a 0.87 0.19 1.28       10     1000
## 2            b 0.54 0.09 1.09       10     1000
## 3            c 0.10 0.00 0.11       10     1000