analyse de survie : fonction en escalier, "NA" pour certaines modalités d'un facteur

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frederic danjon
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Enregistré le : 18 Sep 2024, 10:31

analyse de survie : fonction en escalier, "NA" pour certaines modalités d'un facteur

Messagepar frederic danjon » 27 Sep 2024, 12:56

Bonjour,

j’ai des données de survie d’arbres dans un dispositif factoriel complet [intensité de labour (soilPrepN 4 niveaux) x type de conteneur (cont 3 niveaux) x bloc (3 blocs)], mais nous avons échantillonné périodiquement des arbres pour des mesures de biomasse, ces arbres et leurs voisins disparaissent alors de l’échantillon (données tronquées), j’ai pour cela utilisé de l’analyse de survie.

Mais les risques ne sont pas proportionnels dans le temps, il y a plus de mortalité les deux premières années pour 2 conteneurs sur 3. Du coup j’ai utilisé une fonction en escalier (step functions) en utilisant survsplit, et j’arrive pas à comprendre le tableau des résultats pour la covariable conteneur : au lieu de ne faire apparaître que cont2 et cont3 (cont1 étant la « base line ») il fait apparaître aussi cont1, mais tout ce qui correspond à « cont3 » est NA :
cont3:strata(tgroup)1 NA NA 0.0000 NA NA
Et je comprends pas pourquoi la covariable “cont” est présentée comme cela : cont:strata(tgroup) et la covariable “soilPrepN” dans l’autre sens :
strata(tgroup):soilPrepN

merci
F Danjon

# Extrait du dataframe :
dfmat[1:50,c("tree","cont","soilPrepN","blocN","time10","status")]
tree cont soilPrepN blocN time10 status
8203 8203 1 2 1 2 0
8205 8205 1 2 1 2 0
8210 8210 1 2 1 3 0
8212 8212 1 2 1 3 0
8217 8217 1 2 1 4 0
8219 8219 1 2 1 4 0
8223 8223 1 2 1 1 1
8224 8224 1 2 1 6 0
8225 8225 1 2 1 6 0
8228 8228 1 2 1 10 0
8229 8229 1 2 1 1 1
8230 8230 1 2 1 10 0
8130 8130 2 2 1 10 0
8129 8129 2 2 1 10 0
8128 8128 2 2 1 10 0
8125 8125 2 2 1 1 1
8124 8124 2 2 1 6 0
8123 8123 2 2 1 6 0
8119 8119 2 2 1 4 0
8117 8117 2 2 1 4 0
8113 8113 2 2 1 3 0
8111 8111 2 2 1 3 0
8109 8109 2 2 1 3 0
8105 8105 2 2 1 2 0
8103 8103 2 2 1 2 0
8023 8023 1 2 1 6 0
8028 8028 1 2 1 10 0
8030 8030 1 2 1 10 0
7525 7525 1 1 1 2 1
7523 7523 1 1 1 6 0
7403 7403 2 1 1 2 0
7405 7405 2 1 1 2 0
7410 7410 2 1 1 1 1
7411 7411 2 1 1 3 0
7412 7412 2 1 1 1 1
7413 7413 2 1 1 3 0
7417 7417 2 1 1 4 0
7419 7419 2 1 1 4 0
7423 7423 2 1 1 2 1
7425 7425 2 1 1 6 0
7428 7428 2 1 1 10 0
7429 7429 2 1 1 10 0
7430 7430 2 1 1 1 1
7330 7330 1 1 1 10 0
7328 7328 1 1 1 10 0
7325 7325 1 1 1 6 0
7323 7323 1 1 1 6 0
7319 7319 1 1 1 4 0
7317 7317 1 1 1 4 0
7312 7312 1 1 1 3 0

dim(dfmat)
[1] 972 16

# analyse survie Cox =====
> fit1 <- coxph(Surv(time10, status) ~ cont + soilPrepN + blocN, dfmat, x = TRUE, y = TRUE, model = T); summary(fit1);

Call:
coxph(formula = Surv(time10, status) ~ cont + soilPrepN + blocN,
data = dfmat, model = T, x = TRUE, y = TRUE)

n= 972, number of events= 161

coef exp(coef) se(coef) z Pr(>|z|)
cont2 -0.12621 0.88143 0.16592 -0.761 0.44684
cont3 -1.86349 0.15513 0.28388 -6.564 5.23e-11 ***
soilPrepN2 0.09237 1.09677 0.31663 0.292 0.77050
soilPrepN3 0.46436 1.59100 0.29517 1.573 0.11568
soilPrepN4 1.93833 6.94714 0.25304 7.660 1.86e-14 ***
blocN2 -0.49901 0.60713 0.19206 -2.598 0.00937 **
blocN3 -0.37360 0.68825 0.18938 -1.973 0.04852 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef) exp(-coef) lower .95 upper .95
cont2 0.8814 1.1345 0.63673 1.2202
cont3 0.1551 6.4462 0.08893 0.2706
soilPrepN2 1.0968 0.9118 0.58965 2.0400
soilPrepN3 1.5910 0.6285 0.89211 2.8374
soilPrepN4 6.9471 0.1439 4.23078 11.4075
blocN2 0.6071 1.6471 0.41668 0.8846
blocN3 0.6883 1.4530 0.47484 0.9976

Concordance= 0.8 (se = 0.018 )
Likelihood ratio test= 177.6 on 7 df, p=<2e-16
Wald test = 157.5 on 7 df, p=<2e-16
Score (logrank) test = 190.9 on 7 df, p=<2e-16


# test des risques proportionnels :
cox.zph(fit1)

chisq df p
cont 11.95 2 0.0025
soilPrepN 13.46 3 0.0037
blocN 6.41 2 0.0406
GLOBAL 34.09 7 1.7e-05

cox.zph(fit1, terms=F)
chisq df p
cont2 2.26 1 0.13294
cont3 11.76 1 0.00060
soilPrepN2 11.61 1 0.00066
soilPrepN3 1.26 1 0.26114
soilPrepN4 4.14 1 0.04181
blocN2 4.55 1 0.03298
blocN3 0.12 1 0.72957
GLOBAL 34.09 7 1.7e-05

# Donc les risques ne sont pas proportionnels pour les covariables “cont” et “soilPrepN”

# Preparation dataframe pour fonction en escalier ===========
dfmat2 <- survSplit(Surv(time10, status == 1) ~ ., data= dfmat, cut=c(2), episode= "tgroup", id="id");
dfmat2 <- transform(dfmat2, tgroup = factor(tgroup)); dfmat2[,"tstart"]


# Cox, fonction en escalier ===========
fitS3 <- coxph(Surv(tstart, time10, status) ~ cont:strata(tgroup) + soilPrepN:strata(tgroup) + blocN, dfmat2, model = T); summary(fitS3);

Call:
coxph(formula = Surv(tstart, time10, status) ~ cont:strata(tgroup) +
soilPrepN:strata(tgroup) + blocN, data = dfmat2, model = T)

n= 1588, number of events= 161

coef exp(coef) se(coef) z Pr(>|z|)
blocN2 -0.4959 0.6090 0.1921 -2.581 0.00985 **
blocN3 -0.3670 0.6928 0.1895 -1.936 0.05281 .
cont1:strata(tgroup)1 3.0207 20.5051 0.5144 5.873 4.29e-09 ***
cont2:strata(tgroup)1 2.8508 17.3009 0.5169 5.515 3.49e-08 ***
cont3:strata(tgroup)1 NA NA 0.0000 NA NA
cont1:strata(tgroup)2 -0.2191 0.8032 0.5158 -0.425 0.67099
cont2:strata(tgroup)2 0.2471 1.2804 0.4304 0.574 0.56584
cont3:strata(tgroup)2 NA NA 0.0000 NA NA
strata(tgroup)1:soilPrepN2 -0.2695 0.7637 0.4206 -0.641 0.52164
strata(tgroup)2:soilPrepN2 0.6120 1.8440 0.5076 1.205 0.22801
strata(tgroup)1:soilPrepN3 0.7261 2.0671 0.3397 2.138 0.03255 *
strata(tgroup)2:soilPrepN3 -0.6508 0.5216 0.7072 -0.920 0.35745
strata(tgroup)1:soilPrepN4 2.1665 8.7274 0.2987 7.253 4.07e-13 ***
strata(tgroup)2:soilPrepN4 0.7693 2.1583 0.5445 1.413 0.15770
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef) exp(-coef) lower .95 upper .95
blocN2 0.6090 1.64197 0.4179 0.8875
blocN3 0.6928 1.44344 0.4778 1.0045
cont1:strata(tgroup)1 20.5051 0.04877 7.4822 56.1943
cont2:strata(tgroup)1 17.3009 0.05780 6.2815 47.6513
cont3:strata(tgroup)1 NA NA NA NA
cont1:strata(tgroup)2 0.8032 1.24498 0.2923 2.2076
cont2:strata(tgroup)2 1.2804 0.78103 0.5508 2.9765
cont3:strata(tgroup)2 NA NA NA NA
strata(tgroup)1:soilPrepN2 0.7637 1.30937 0.3349 1.7417
strata(tgroup)2:soilPrepN2 1.8440 0.54229 0.6818 4.9873
strata(tgroup)1:soilPrepN3 2.0671 0.48378 1.0622 4.0225
strata(tgroup)2:soilPrepN3 0.5216 1.91711 0.1304 2.0862
strata(tgroup)1:soilPrepN4 8.7274 0.11458 4.8600 15.6720
strata(tgroup)2:soilPrepN4 2.1583 0.46332 0.7424 6.2750

Concordance= 0.82 (se = 0.017 )
Likelihood ratio test= 218.3 on 12 df, p=<2e-16
Wald test = 155 on 12 df, p=<2e-16
Score (logrank) test = 217.7 on 12 df, p=<2e-16


# test des risques proportionnels :
zphS3 <- cox.zph(fitS3); zphS3; cox.zph(fitS3, terms=F); fitS3$means;
chisq df p
blocN 7.76 2 0.021
cont:strata(tgroup) 7.35 4 0.118
strata(tgroup):soilPrepN 8.56 6 0.200
GLOBAL 22.41 12 0.033
chisq df p
blocN2 5.47258 1 0.0193
blocN3 0.18618 1 0.6661
cont1:strata(tgroup)1 3.23367 1 0.0721
cont2:strata(tgroup)1 2.44825 1 0.1177
cont1:strata(tgroup)2 0.62469 1 0.4293
cont2:strata(tgroup)2 1.87022 1 0.1714
strata(tgroup)1:soilPrepN2 0.03869 1 0.8441
strata(tgroup)2:soilPrepN2 6.80830 1 0.0091
strata(tgroup)1:soilPrepN3 0.00104 1 0.9742
strata(tgroup)2:soilPrepN3 0.09536 1 0.7575
strata(tgroup)1:soilPrepN4 0.00766 1 0.9303
strata(tgroup)2:soilPrepN4 1.39078 1 0.2383
GLOBAL 22.40814 12 0.0332


# Graphique
ND <- data.frame(status= rep(0,12), cont = factor(rep(c(1, 2, 3), each=4)), soilPrepN = factor(rep(c(1, 2, 3, 4), 3)), blocN = as.factor(1), id = rep(1,12)); ND; ND[,"soilPrep"]; # status necessary, but ignored
NDS <- cbind(tgroup = factor(c(rep(1,nrow(ND)),rep(2,nrow(ND)))), rbind(ND, ND)); NDS; NDS[,"soilPrepN"];

plot(survfit(fitS3, data = dfmat2, newdata=NDS), col = colSoilPrep[NDS[,"soilPrepN"]], lty = ltyCont[NDS[,"cont"]], ylim = c(0.37,1)); legend("bottomright", nameSoilPreps, fill = colSoilPrep[4:1]); legend(8,0.7, nameConts, lty = Lty)

jean lobry
Messages : 746
Enregistré le : 17 Jan 2008, 20:00
Contact :

Re: analyse de survie : fonction en escalier, "NA" pour certaines modalités d'un facteur

Messagepar jean lobry » 28 Sep 2024, 18:05

Bonjour Frédéric,

cela va être difficile de t'aider si tu ne nous donnes pas un code reproductible.

Bien amicalement,

Jean Lobry

frederic danjon
Messages : 2
Enregistré le : 18 Sep 2024, 10:31

Re: analyse de survie : fonction en escalier, "NA" pour certaines modalités d'un facteur

Messagepar frederic danjon » 11 Déc 2024, 09:37

Bonjour,
je m'excuse, j'étais parti sur d'autres dossiers. j'espère vous fournir un code reproductible : la question et les résultats restent les mêmes (voir mon premier envoi), à part : survSplit(Surv(time10, status == 1) ~ ., data= dfmat, cut=c(2), episode= "tgroup", id="id") où j'ai enlevé le status == 1 pour le remplacer par status.

voilà mon environnement ========================================================
sessionInfo()
R version 4.4.2 (2024-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Linux Mint 20.2

Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale:
[1] LC_CTYPE=fr_FR.UTF-8 LC_NUMERIC=C LC_TIME=fr_FR.UTF-8 LC_COLLATE=fr_FR.UTF-8 LC_MONETARY=fr_FR.UTF-8 LC_MESSAGES=fr_FR.UTF-8 LC_PAPER=fr_FR.UTF-8
[8] LC_NAME=C LC_ADDRESS=C LC_TELEPHONE=C LC_MEASUREMENT=fr_FR.UTF-8 LC_IDENTIFICATION=C

time zone: Europe/Paris
tzcode source: system (glibc)

attached base packages:
[1] stats graphics grDevices utils datasets methods base

other attached packages:
[1] survival_3.7-0

loaded via a namespace (and not attached):
[1] compiler_4.4.2 Matrix_1.7-1 tools_4.4.2 splines_4.4.2 grid_4.4.2 lattice_0.22-5
==============================================================================

Le code utilisé : ===================================================================
colnames(dfmat) <- c("Id","tree","cont","soilPrepN","blocN","time10","status"); head(dfmat);
detach(dfmat)
detach(dfmat2)
dfmat <- data.frame(dfmat,row.names="Id", check.rows = TRUE, check.names = TRUE); attach(dfmat); head(dfmat)
dfmat$cont <- factor(cont); dfmat$soilPrepN <- factor(soilPrepN); dfmat$blocN <- factor(blocN);
library(survival)

# 3 SIMPLE COX ANALYSIS ######################
fit1 <- coxph(Surv(time10, status) ~ cont + soilPrepN + blocN, dfmat, x = TRUE, y = TRUE, model = T); print(fit1, digits = 2); summary(fit1); cox.zph(fit1); cox.zph(fit1, terms=F); #; tbl_regression(fit1) #, method = "efron" fit1 <- coxph(Surv(time, status) ~ ph.ecog + wt.loss + strata(sex) + poly(age,3), lung); levels(strata(cont))

# paramètres graphiques ############################
ltyCont <- 1:3; Lty <- 1:3;
colSoilPrep <- c("black","orange","red","green"); colBloc <- c("red","blue","green"); colCont <- c("red","green","black"); XLAB <- "Age (years)"; CEXlegend <- 1; textWidth <- 1.5; experiment <- "AAAK"; legendCont <- c("container", "turf plug", "seeded"); legendSoilPrep <- c("no plough", "33%", "66%","full plough"); legendBloc <- c("bloc 1", "bloc 2", "bloc 3");
nameConts <- c("multi","plug","seeded"); nameSoilPreps <- c("noPlough","narrowPlough","largePlough","fullPlough"); nameBlocs <- c("bloc 1", "bloc 2","bloc 3");

# 3 STEP FUNCTIONS ###################### ========== survival model with several variables violating proportional hazard assumption
dfmat2 <- survSplit(Surv(time10, status) ~ ., data= dfmat, cut=c(2), episode= "tgroup", id="id"); dfmat2[,"tgroup"]; head(dfmat2);
dfmat2 <- transform(dfmat2, tgroup = factor(tgroup)); dfmat2[,"tstart"]
detach(dfmat)
detach(dfmat2)
attach(dfmat2)

fitS2 <- coxph(Surv(tstart, time10, status) ~ cont:strata(tgroup) + soilPrepN:strata(tgroup) + blocN, dfmat2, model = T); summary(fitS2); zphS2 <- cox.zph(fitS2); zphS2; cox.zph(fitS2, terms=F); fitS2$means;
plot(survfit(fitS2, data = dfmat2, newdata=NDS), col = colSoilPrep[NDS[,"soilPrepN"]], lty = ltyCont[NDS[,"cont"]], ylim = c(0.37,1)); legend("bottomright", nameSoilPreps, fill = colSoilPrep[4:1]); legend(8,0.7, nameConts, lty = Lty)

merci
et je colle la matrice d'entrée ci dessous.
merci
bien cordialement
frederic

========== matrice d'entrée ===================
dfmat <- rbind(c(1,8203,1,2,1,2,0),c(2,8205,1,2,1,2,0),c(3,8210,1,2,1,3,0),c(4,8212,1,2,1,3,0),c(5,8217,1,2,1,4,0),c(6,8219,1,2,1,4,0),c(7,8223,1,2,1,1,1),c(8,8224,1,2,1,6,0),c(9,8225,1,2,1,6,0),c(10,8228,1,2,1,10,0),c(11,8229,1,2,1,1,1),c(12,8230,1,2,1,10,0)
,c(13,8130,2,2,1,10,0),c(14,8129,2,2,1,10,0),c(15,8128,2,2,1,10,0),c(16,8125,2,2,1,1,1),c(17,8124,2,2,1,6,0),c(18,8123,2,2,1,6,0),c(19,8119,2,2,1,4,0),c(20,8117,2,2,1,4,0),c(21,8113,2,2,1,3,0),c(22,8111,2,2,1,3,0),c(23,8109,2,2,1,3,0),c(24,8105,2,2,1,2,0),
c(25,8103,2,2,1,2,0),c(26,8023,1,2,1,6,0),c(27,8028,1,2,1,10,0),c(28,8030,1,2,1,10,0),c(29,7525,1,1,1,2,1),c(30,7523,1,1,1,6,0),c(31,7403,2,1,1,2,0),c(32,7405,2,1,1,2,0),c(33,7410,2,1,1,1,1),c(34,7411,2,1,1,3,0),c(35,7412,2,1,1,1,1),c(36,7413,2,1,1,3,0),
c(37,7417,2,1,1,4,0),c(38,7419,2,1,1,4,0),c(39,7423,2,1,1,2,1),c(40,7425,2,1,1,6,0),c(41,7428,2,1,1,10,0),c(42,7429,2,1,1,10,0),c(43,7430,2,1,1,1,1),c(44,7330,1,1,1,10,0),c(45,7328,1,1,1,10,0),c(46,7325,1,1,1,6,0),c(47,7323,1,1,1,6,0),c(48,7319,1,1,1,4,0),
c(49,7317,1,1,1,4,0),c(50,7312,1,1,1,3,0),c(51,7310,1,1,1,3,0),c(52,7305,1,1,1,2,0),c(53,7303,1,1,1,2,0),c(54,7223,2,1,1,6,0),c(55,7224,2,1,1,6,0),c(56,7228,2,1,1,10,0),c(57,7230,2,1,1,10,0),c(58,6913,1,3,1,3,0),c(59,6904,1,3,1,2,0),c(60,6802,2,3,1,2,0),
c(61,6829,2,3,1,10,0),c(62,6730,1,3,1,10,0),c(63,6728,1,3,1,10,0),c(64,6725,1,3,1,6,0),c(65,6723,1,3,1,6,0),c(66,6605,3,3,1,0.01,1),c(67,6610,3,3,1,0.01,1),c(68,6616,3,3,1,3,0),c(69,6624,2,3,1,6,0),c(70,6625,2,3,1,6,0),c(71,6628,2,3,1,10,0),c(72,6630,2,3,1,2,1),
c(73,6230,1,4,1,10,0),c(74,6229,1,4,1,1,1),c(75,6228,1,4,1,1,1),c(76,6225,1,4,1,2,1),c(77,6224,1,4,1,1,1),c(78,6223,1,4,1,1,1),c(79,6210,3,4,1,2,0),c(80,6123,2,4,1,6,0),c(81,6125,2,4,1,6,0),c(82,6128,2,4,1,5,1),c(83,6129,2,4,1,1,1),c(84,6130,2,4,1,1,1),
c(85,6033,3,4,1,10,0),c(86,6030,1,4,1,1,1),c(87,6029,1,4,1,1,1),c(88,6028,1,4,1,2,1),c(89,6025,1,4,1,1,1),c(90,6024,1,4,1,5,1),c(91,6023,1,4,1,3,1),c(92,6020,2,4,1,1,1),c(93,6019,2,4,1,1,1),c(94,6018,2,4,1,1,1),c(95,6017,2,4,1,4,0),c(96,6016,2,4,1,4,0),
c(97,6013,2,4,1,3,0),c(98,6012,2,4,1,1,1),c(99,6010,2,4,1,1,1),c(100,6009,2,4,1,3,0),c(101,6006,2,4,1,1,1),c(102,6005,2,4,1,1,1),c(103,6004,2,4,1,1,1),c(104,6003,2,4,1,1,1),c(105,6002,2,4,1,1,1),c(106,5902,1,4,1,1,1),c(107,5903,1,4,1,1,1),c(108,5904,1,4,1,2,0),
c(109,5905,1,4,1,2,0),c(110,5906,1,4,1,1,1),c(111,5910,1,4,1,1,1),c(112,5911,1,4,1,1,1),c(113,5913,1,4,1,3,0),c(114,5916,1,4,1,4,0),c(115,5917,1,4,1,1,1),c(116,5918,1,4,1,2,1),c(117,5919,1,4,1,1,1),c(118,5923,2,4,1,6,0),c(119,5924,2,4,1,6,0),c(120,5925,2,4,1,1,1),
c(121,5928,2,4,1,10,0),c(122,5930,2,4,1,10,0),c(123,5430,1,4,2,2,1),c(124,5429,1,4,2,2,1),c(125,5428,1,4,2,1,1),c(126,5425,1,4,2,6,0),c(127,5423,1,4,2,2,1),c(128,5420,1,4,2,2,1),c(129,5418,1,4,2,2,1),c(130,5416,1,4,2,4,0),c(131,5413,1,4,2,1,1),c(132,5412,1,4,2,2,1),
c(133,5410,1,4,2,2,1),c(134,5406,1,4,2,2,0),c(135,5404,1,4,2,2,0),c(136,5402,1,4,2,2,0),c(137,5302,2,4,2,2,0),c(138,5304,2,4,2,2,0),c(139,5305,2,4,2,1,1),c(140,5309,2,4,2,2,1),c(141,5310,2,4,2,3,0),c(142,5312,2,4,2,1,1),c(143,5316,2,4,2,1,1),c(144,5317,2,4,2,4,0),
c(145,5319,2,4,2,4,0),c(146,5323,2,4,2,1,1),c(147,5324,2,4,2,6,0),c(148,5325,2,4,2,2,1),c(149,5328,2,4,2,1,1),c(150,5329,2,4,2,10,0),c(151,5330,2,4,2,1,1),c(152,5229,1,4,2,10,0),c(153,5228,1,4,2,10,0),c(154,5225,1,4,2,5,0),c(155,5224,1,4,2,5,0),c(156,5223,1,4,2,5,1),
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c(587,6124,2,4,1,2,1),c(588,6133,3,4,1,10,0),c(589,6134,3,4,1,10,0),c(590,6137,3,4,1,6,0),c(591,6138,3,4,1,6,0),c(592,6038,3,4,1,6,0),c(593,6037,3,4,1,6,0),c(594,6034,3,4,1,10,0),c(595,6011,2,4,1,2,1),c(596,5912,1,4,1,3,0),c(597,5920,1,4,1,2,1),c(598,5929,2,4,1,2,1),
c(599,5933,3,4,1,10,0),c(600,5934,3,4,1,10,0),c(601,5937,3,4,1,6,0),c(602,5938,3,4,1,6,0),c(603,5438,3,4,2,6,0),c(604,5437,3,4,2,6,0),c(605,5434,3,4,2,10,0),c(606,5433,3,4,2,10,0),c(607,5424,1,4,2,6,0),c(608,5419,1,4,2,2,1),c(609,5417,1,4,2,2,1),c(610,5411,1,4,2,3,0),
c(611,5409,1,4,2,3,0),c(612,5405,1,4,2,2,0),c(613,5403,1,4,2,2,0),c(614,5303,2,4,2,2,0),c(615,5306,2,4,2,2,0),c(616,5311,2,4,2,3,0),c(617,5313,2,4,2,2,1),c(618,5318,2,4,2,2,1),c(619,5320,2,4,2,4,0),c(620,5333,3,4,2,10,0),c(621,5334,3,4,2,10,0),c(622,5337,3,4,2,5,1),
c(623,5338,3,4,2,6,0),c(624,5238,3,4,2,6,0),c(625,5237,3,4,2,4,1),c(626,5234,3,4,2,10,0),c(627,5233,3,4,2,10,0),c(628,5230,1,4,2,2,1),c(629,5102,3,4,2,1,0),c(630,5104,3,4,2,1,0),c(631,5105,3,4,2,1,0),c(632,5106,3,4,2,1,0),c(633,5109,3,4,2,2,0),c(634,5110,3,4,2,2,0),
c(635,5111,3,4,2,2,0),c(636,5112,3,4,2,2,0),c(637,5113,3,4,2,2,0),c(638,5116,3,4,2,4,0),c(639,5117,3,4,2,4,0),c(640,5118,3,4,2,4,0),c(641,5119,3,4,2,4,0),c(642,5120,3,4,2,4,0),c(643,5124,2,4,2,6,0),c(644,5128,2,4,2,2,1),c(645,4820,3,2,2,4,0),c(646,4819,3,2,2,4,0),
c(647,4818,3,2,2,4,0),c(648,4817,3,2,2,4,0),c(649,4816,3,2,2,3,0),c(650,4813,3,2,2,2,0),c(651,4812,3,2,2,2,0),c(652,4811,3,2,2,2,0),c(653,4810,3,2,2,2,0),c(654,4809,3,2,2,2,0),c(655,4806,3,2,2,1,0),c(656,4805,3,2,2,1,0),c(657,4804,3,2,2,1,0),c(658,4803,3,2,2,1,0),
c(659,4802,3,2,2,1,0),c(660,4724,1,2,2,6,0),c(661,4729,1,2,2,10,0),c(662,4733,3,2,2,10,0),c(663,4734,3,2,2,10,0),c(664,4737,3,2,2,6,0),c(665,4738,3,2,2,6,0),c(666,4638,3,2,2,6,0),c(667,4637,3,2,2,6,0),c(668,4634,3,2,2,10,0),c(669,4633,3,2,2,10,0),c(670,4629,2,2,2,10,0),
c(671,4624,2,2,2,6,0),c(672,4620,2,2,2,4,0),c(673,4618,2,2,2,4,0),c(674,4616,2,2,2,4,0),c(675,4613,2,2,2,3,0),c(676,4611,2,2,2,3,0),c(677,4609,2,2,2,3,0),c(678,4606,2,2,2,2,0),c(679,4604,2,2,2,2,0),c(680,4602,2,2,2,2,0),c(681,4502,1,2,2,2,0),c(682,4504,1,2,2,2,0),
c(683,4506,1,2,2,2,0),c(684,4509,1,2,2,3,0),c(685,4511,1,2,2,3,0),c(686,4513,1,2,2,3,0),c(687,4516,1,2,2,4,0),c(688,4518,1,2,2,4,0),c(689,4520,1,2,2,4,0),c(690,4529,1,2,2,10,0),c(691,4533,3,2,2,10,0),c(692,4534,3,2,2,10,0),c(693,4537,3,2,2,6,0),c(694,4538,3,2,2,6,0),
c(695,4429,2,2,2,2,1),c(696,4424,2,2,2,10,1),c(697,4102,1,1,2,2,0),c(698,4104,1,1,2,2,0),c(699,4106,1,1,2,2,0),c(700,4111,1,1,2,3,0),c(701,4113,1,1,2,3,0),c(702,4116,1,1,2,4,0),c(703,4118,1,1,2,4,0),c(704,4120,1,1,2,4,0),c(705,4129,1,1,2,10,0),c(706,4038,3,1,2,6,0),
c(707,4037,3,1,2,6,0),c(708,4034,3,1,2,10,0),c(709,4033,3,1,2,10,0),c(710,4029,2,1,2,10,0),c(711,4024,2,1,2,3,1),c(712,4020,2,1,2,4,0),c(713,4018,2,1,2,4,0),c(714,4016,2,1,2,4,0),c(715,4013,2,1,2,3,0),c(716,4011,2,1,2,3,0),c(717,4009,2,1,2,3,0),c(718,4006,2,1,2,2,0),
c(719,4004,2,1,2,2,0),c(720,4002,2,1,2,2,0),c(721,3924,1,1,2,6,0),c(722,3929,1,1,2,10,0),c(723,3933,3,1,2,10,0),c(724,3934,3,1,2,10,0),c(725,3937,3,1,2,3,0),c(726,3938,3,1,2,6,0),c(727,3838,3,1,2,6,0),c(728,3837,3,1,2,4,1),c(729,3834,3,1,2,10,0),c(730,3833,3,1,2,10,0),
c(731,3829,2,1,2,10,0),c(732,3824,2,1,2,6,0),c(733,3820,3,1,2,4,0),c(734,3819,3,1,2,4,0),c(735,3818,3,1,2,4,0),c(736,3817,3,1,2,3,0),c(737,3816,3,1,2,3,0),c(738,3813,3,1,2,2,0),c(739,3812,3,1,2,2,0),c(740,3811,3,1,2,2,0),c(741,3810,3,1,2,2,0),c(742,3809,3,1,2,2,0),
c(743,3806,3,1,2,1,0),c(744,3805,3,1,2,1,0),c(745,3804,3,1,2,1,0),c(746,3803,3,1,2,1,0),c(747,3802,3,1,2,1,0),c(748,3402,3,3,2,1,0),c(749,3403,3,3,2,1,0),c(750,3404,3,3,2,1,0),c(751,3405,3,3,2,1,0),c(752,3406,3,3,2,1,0),c(753,3409,3,3,2,2,0),c(754,3410,3,3,2,2,0),
c(755,3411,3,3,2,2,0),c(756,3412,3,3,2,2,0),c(757,3413,3,3,2,2,0),c(758,3416,3,3,2,3,0),c(759,3417,3,3,2,3,0),c(760,3418,3,3,2,4,0),c(761,3419,3,3,2,4,0),c(762,3420,3,3,2,4,0),c(763,3338,3,3,2,6,0),c(764,3337,3,3,2,6,0),c(765,3334,3,3,2,10,0),c(766,3333,3,3,2,10,0),
c(767,3324,2,3,2,3,1),c(768,3202,2,3,2,2,0),c(769,3204,2,3,2,2,0),c(770,3206,2,3,2,2,0),c(771,3209,2,3,2,3,0),c(772,3211,2,3,2,3,0),c(773,3213,2,3,2,3,0),c(774,3216,2,3,2,4,0),c(775,3218,2,3,2,4,0),c(776,3220,2,3,2,4,0),c(777,3224,1,3,2,6,0),c(778,3233,3,3,2,10,0),
c(779,3234,3,3,2,10,0),c(780,3237,3,3,2,6,0),c(781,3238,3,3,2,6,0),c(782,3138,3,3,2,6,0),c(783,3137,3,3,2,6,0),c(784,3134,3,3,2,10,0),c(785,3133,3,3,2,10,0),c(786,3129,2,3,2,10,0),c(787,3124,2,3,2,6,0),c(788,3120,1,3,2,4,0),c(789,3118,1,3,2,4,0),c(790,3116,1,3,2,4,0),
c(791,3113,1,3,2,3,0),c(792,3111,1,3,2,3,0),c(793,3109,1,3,2,3,0),c(794,3106,1,3,2,2,0),c(795,3104,1,3,2,2,0),c(796,3102,1,3,2,2,0),c(797,2602,1,3,3,2,0),c(798,2604,1,3,3,2,0),c(799,2606,1,3,3,2,0),c(800,2609,1,3,3,2,1),c(801,2611,1,3,3,3,0),c(802,2613,1,3,3,3,0),
c(803,2616,1,3,3,4,0),c(804,2618,1,3,3,4,0),c(805,2620,1,3,3,4,0),c(806,2623,1,3,3,2,1),c(807,2633,3,3,3,10,0),c(808,2634,3,3,3,10,0),c(809,2637,3,3,3,6,0),c(810,2638,3,3,3,6,0),c(811,2538,3,3,3,6,0),c(812,2537,3,3,3,6,0),c(813,2534,3,3,3,10,0),c(814,2533,3,3,3,10,0),
c(815,2529,2,3,3,10,0),c(816,2520,2,3,3,4,0),c(817,2518,2,3,3,2,1),c(818,2516,2,3,3,4,0),c(819,2513,2,3,3,3,0),c(820,2511,2,3,3,3,0),c(821,2509,2,3,3,3,0),c(822,2506,2,3,3,2,0),c(823,2504,2,3,3,2,0),c(824,2502,2,3,3,2,0),c(825,2424,1,3,3,6,0),c(826,2428,1,3,3,2,1),
c(827,2433,3,3,3,10,0),c(828,2434,3,3,3,10,0),c(829,2437,3,3,3,6,0),c(830,2438,3,3,3,6,0),c(831,2330,2,3,3,2,1),c(832,2002,3,4,3,1,0),c(833,2003,3,4,3,1,0),c(834,2004,3,4,3,1,0),c(835,2005,3,4,3,1,0),c(836,2006,3,4,3,1,0),c(837,2009,3,4,3,2,0),c(838,2010,3,4,3,2,0),
c(839,2011,3,4,3,2,0),c(840,2012,3,4,3,2,0),c(841,2013,3,4,3,2,0),c(842,2016,3,4,3,3,0),c(843,2017,3,4,3,4,0),c(844,2018,3,4,3,4,0),c(845,2019,3,4,3,4,0),c(846,2020,3,4,3,4,0),c(847,1938,3,4,3,6,0),c(848,1937,3,4,3,6,0),c(849,1934,3,4,3,3,1),c(850,1933,3,4,3,10,0),
c(851,1924,1,4,3,2,1),c(852,1803,2,4,3,2,0),c(853,1806,2,4,3,2,0),c(854,1818,2,4,3,4,0),c(855,1833,3,4,3,10,0),c(856,1834,3,4,3,2,1),c(857,1837,3,4,3,6,0),c(858,1838,3,4,3,4,1),c(859,1738,3,4,3,6,0),c(860,1737,3,4,3,6,0),c(861,1734,3,4,3,10,0),c(862,1733,3,4,3,10,0),
c(863,1717,1,4,3,2,1),c(864,1712,1,4,3,2,1),c(865,1710,1,4,3,3,0),c(866,1709,1,4,3,3,0),c(867,1706,1,4,3,2,0),c(868,1704,1,4,3,2,0),c(869,1702,1,4,3,2,0),c(870,1629,2,4,3,2,1),c(871,1329,1,2,3,3,1),c(872,1324,1,2,3,6,0),c(873,1320,1,2,3,4,0),c(874,1318,1,2,3,4,0),
c(875,1316,1,2,3,4,0),c(876,1313,1,2,3,3,0),c(877,1311,1,2,3,3,0),c(878,1309,1,2,3,3,0),c(879,1306,1,2,3,2,0),c(880,1304,1,2,3,2,0),c(881,1302,1,2,3,2,0),c(882,1202,2,2,3,2,0),c(883,1204,2,2,3,2,0),c(884,1206,2,2,3,2,0),c(885,1209,2,2,3,3,0),c(886,1213,2,2,3,3,0),
c(887,1216,2,2,3,4,0),c(888,1218,2,2,3,4,0),c(889,1220,2,2,3,4,0),c(890,1224,2,2,3,6,0),c(891,1229,2,2,3,10,0),c(892,1233,3,2,3,10,0),c(893,1234,3,2,3,10,0),c(894,1237,3,2,3,6,0),c(895,1238,3,2,3,6,0),c(896,1138,3,2,3,6,0),c(897,1137,3,2,3,6,0),c(898,1134,3,2,3,10,0),
c(899,1133,3,2,3,8,1),c(900,1129,1,2,3,10,0),c(901,1124,1,2,3,6,0),c(902,1002,3,2,3,1,0),c(903,1003,3,2,3,1,0),c(904,1004,3,2,3,1,0),c(905,1005,3,2,3,1,0),c(906,1006,3,2,3,1,0),c(907,1009,3,2,3,2,0),c(908,1010,3,2,3,2,0),c(909,1011,3,2,3,2,0),c(910,1012,3,2,3,2,0),
c(911,1013,3,2,3,2,0),c(912,1016,3,2,3,3,0),c(913,1017,3,2,3,3,0),c(914,1018,3,2,3,4,0),c(915,1019,3,2,3,4,0),c(916,1020,3,2,3,4,0),c(917,1024,2,2,3,6,0),c(918,1029,2,2,3,2,1),c(919,1033,3,2,3,10,0),c(920,1034,3,2,3,8,1),c(921,1037,3,2,3,6,0),c(922,1038,3,2,3,4,1),
c(923,629,1,1,3,10,0),c(924,624,1,1,3,6,0),c(925,620,3,1,3,4,0),c(926,619,3,1,3,4,0),c(927,618,3,1,3,4,0),c(928,617,3,1,3,3,0),c(929,616,3,1,3,3,0),c(930,613,3,1,3,2,0),c(931,612,3,1,3,2,0),c(932,611,3,1,3,2,0),c(933,610,3,1,3,2,0),c(934,609,3,1,3,2,0),
c(935,606,3,1,3,1,0),c(936,605,3,1,3,1,0),c(937,604,3,1,3,1,0),c(938,603,3,1,3,1,0),c(939,602,3,1,3,1,0),c(940,524,2,1,3,6,0),c(941,529,2,1,3,10,0),c(942,533,3,1,3,10,0),c(943,534,3,1,3,10,0),c(944,537,3,1,3,6,0),c(945,538,3,1,3,6,0),c(946,438,3,1,3,6,0),
c(947,437,3,1,3,6,0),c(948,434,3,1,3,10,0),c(949,433,3,1,3,10,0),c(950,429,1,1,3,10,0),c(951,424,1,1,3,6,0),c(952,420,2,1,3,4,0),c(953,418,2,1,3,4,0),c(954,416,2,1,3,4,0),c(955,412,2,1,3,3,0),c(956,410,2,1,3,3,0),c(957,409,2,1,3,3,0),c(958,404,2,1,3,2,0),
c(959,402,2,1,3,2,0),c(960,306,1,1,3,2,0),c(961,309,1,1,3,3,0),c(962,311,1,1,3,3,0),c(963,313,1,1,3,3,0),c(964,316,1,1,3,4,0),c(965,318,1,1,3,4,0),c(966,320,1,1,3,4,0),c(967,324,2,1,3,6,0),c(968,329,2,1,3,10,0),c(969,333,3,1,3,10,0),c(970,334,3,1,3,10,0),
c(971,337,3,1,3,3,1),c(972,338,3,1,3,4,1))


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